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local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns visual paper paper examples small feature work cells step step process process problems random random random architecture show section fixed fixed rule vectors vectors vectors vectors general theory theory theory theory term term term term result result result result result result research independent independent independent independent log defined estimate estimate estimate estimate terms terms terms terms terms terms terms low low low frequency maximum maximum range learn learn learn learn learn learn position sample sample sample abstract find analog properties references ieee introduction complex hand hand circuit circuit statistical generated generated generated variance search difference complexity complexity complexity variable variable assume assume assume assume lower lower lower lower lower lower lower lower lower rules measure learned part part theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound binary binary binary expected expected expected expected expected make fact fact fact length length finite total total respect sum sum times elements means global global knowledge vol relative samples samples represented desired define define define objects perform connected connected connected institute institute words version synapses synapses synapses internal final graph computing computing equivalent environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment directly directly view limit bit bit bit bit conference upper upper upper statistics statistics statistics basic entropy entropy entropy entropy entropy entropy entropy entropy entropy selected depends biological measured measured technical arbitrary denote denote assumption assumption assumption corresponds corresponds corresponds corresponds complete proof proof proof circuits circuits amount implemented assumed assumed synapse synapse generate supported main main main end ability ability smaller needed technology projection mechanism mechanism mechanism uniform uniform uniform uniform uniform principle bits bits bits bits bits bits bits normalized idea idea ensemble ensemble ensemble pixels subset approximately trans diagonal diagonal diagonal diagonal diagonal diagonal entire grant expression expression concept occur runs starting place depend designed designed designed asymptotic learns suggest strong mechanisms physics drawn california start start introduce scene connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity program force suppose appears relation pro edges produces written ways generating describes label recall coordinates coordinates easy interaction extraction versus boolean boolean choosing independently depending evaluate evaluate restricted roughly strings prove prove prove prove variations holds capable essentially essentially kind interested symmetry contribution contribution hold hold notation involved write denker carried powerful american access mead environments environments environments environments environments environments ideas office gates gates statistically hill plausible predicts opposite automata illustrate aspect aspect obvious formal formal switching switching switching contributions defines handle tive arise consequence scientific acknowledgement gradually simulate quantitative compares ity occurrence collective pasadena sophisticated conclude eventually lim lim lim lim specifies wesley picture picture benefit addison restriction restriction restrict air definitions substituting substituting infor appendix appendix appendix vertices infinity infinity accumulated speaking abu abu abu abu mostafa mostafa mostafa mostafa ber july axe restrictions restrictions convenience reports big num expand afosr relate tune replacement sees sees loaded loaded imple val distinguishing randomness accommodate mcgraw ready aip huge supposed ues ceedings imposes disorder undirected putting extremes vat exposition equiv informal discussing yaser nand nand distinguishable taneously fork vironment limn limn limn limn throwing mally excludes menting spon kohavi firs rtl 
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networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number number number number number number number system system system system system error error error error error state state state state state state results results results results results results units units units units units units units units information information information problem problem problem problem problem problem problem hidden performance performance performance performance based based based based based based space space space space space space space weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer case case case case order shown shown shown shown shown shown shown shown systems systems systems systems values values values values probability probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point single single single single processing processing control control control large local local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test test test test patterns patterns patterns matrix optimal inputs inputs form form shows shows shows shows shows shows shows shows shows signal signal signal signal signal signal algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian visual paper paper small small small small small small small size feature feature net net net work work work task methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step step features classification process process process level level level level level level level level current current trained problems problems random random random high high high high high high high high high memory memory memory similar similar representation architecture show show show show section fixed fixed rule rule rule rule rule rule general real real real approximation average average average average average average states states states theory theory gradient gradient gradient obtained term term note note note note experiments experiments result university university threshold threshold computation computation computation solution solution solution solution research research research research defined constant constant table table table table table table table standard computer connections connections synaptic synaptic synaptic synaptic synaptic synaptic science science left presented presented phase phase phase phase phase phase activation activation activation activation activation activation activation activation activation low low low low low nodes frequency temporal temporal machine machine machine machine maximum range range press press press learn position position components components components basis basis outputs outputs outputs outputs outputs continuous continuous abstract applied applied applied back find find computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important important important important important adaptive adaptive adaptive adaptive adaptive adaptive propagation introduction complex circuit circuit circuit behavior statistical statistical effect effect dynamic dynamic parallel parallel parallel parallel recurrent recurrent recurrent search search search search search search search search search search search search change change difference variable spatial lower rules rules rules rules measure prior representations chosen chosen part part part previous previous type type type type multiple good good binary binary binary long long long conditions conditions conditions distributed chip chip chip chip chip chip chip chip make make make make techniques techniques techniques techniques techniques techniques techniques techniques techniques region region proposed correlation correlation correlation correlation correct correct correct correct correct minimum minimum simulation simulation sum sum sum sum sum performed eq called elements elements elements regions means means means means means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor optimization potential natural feedback feedback global global global global global global global study study study obtain negative vol artificial specific specific specific specific specific samples true true true compared desired desired desired desired provide provide provide define rates proc goal related related connected connected connected connected distributions distributions distributions distributions gain gain gain gain gain gain gain gain gain gain gain gain gain gain brain brain equal power approaches approaches mit voltage voltage voltage voltage voltage voltage comparison comparison larger contrast connection connection connection support dependent dependent source modeling proceedings proceedings proceedings proceedings proceedings report institute department department implementation implementation implementation implementation implementation implementation implementation implementation version synapses technique technique consists internal individual represents difficult difficult final final final final layers addition addition addition addition considered cambridge cambridge cambridge computing computing computing domain equivalent directly directly hinton hinton hinton hinton hinton view view design design design design design design limit limit stage stage stage stage stage bit conference conference conference conference conference efficient requires requires choice significant free speed increase increase channel channel coding weighted randomly developed levels criterion area area area types lines finally processes processes selected simply simply biological biological biological biological biological associative measured technical increases increases describe describe describe close inverse inverse stable surface surface surface surface surface circuits finding amount short effective implemented implemented implemented implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse role square vlsi vlsi vlsi vlsi vlsi pixel cluster cluster cluster cluster cluster cluster future easily rumelhart rumelhart rumelhart rumelhart development sensory smaller hopfield reduced fully technology technology technology technology technology technology block block block block block transfer transfer transfer interesting ratio york york york structures trials trials uniform uniform squared representing making inhibition stored bottom supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised magnitude decay decay decay decay decay decay decay produced run run run run run added added improve improve recent recent recent correlations correlations correlations correlations pair robust reported moving include include subject machines side sejnowski cognitive cognitive highly compare compare previously previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised teacher teacher works works tuning solve correspond differential differential achieve trans trans trans trans diagonal address address address definition evaluation evaluation evaluation evaluation organization storage storage storage storage studied studied studied suggests extended digital digital digital trial locally locally deterministic deterministic deterministic column column column pass demonstrate runs runs runs runs runs runs strength strength conclusion place greater greater hebbian reduce valued valued competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive reward sigmoid measures designed sutton performs weak temperature temperature temperature temperature propose mechanisms presence presence physics physics physics physics cycle sigmoidal solid proportional variety variety variety variety averaged averaged averaged connectivity connectivity minima minima minima annealing annealing annealing annealing question question boltzmann boltzmann boltzmann boltzmann boltzmann explicit appears pro winner winner winner winner winner generating stability stability stability tuned physical physical physical physical physical interaction integrated integrated adding quality competition decreases decreases family formation dependence stages correlated communication variation controlled controlled controlled controlled fraction forms forms forms forms updates sign sign diagram diagram diagram diagram diagram reasonable barto barto normalization initially avoid avoid includes activations activations activations activations usa dominance bell bell assignment determines illustrated illustrated coupled variations absolute discussions characterized major suitable modification divided effectively mcclelland wij wij wij wij identify computations situation characteristic summary summary compact procedures procedures procedures showing anderson conductance conductance conductance conductance conductance conductance issue symmetry symmetry oscillations follow timing sci device device device device hold quantity sampled usual play generalize absence cmos cmos cmos cmos cmos correspondence denker denker denker ill leading leading maximization received principles principles principles consisted software employed employed employed schedule schedule schedule schedule powerful american american american wiley xor xor xor xor essential exponentially mead put put strengths strengths preliminary preliminary mass hall scalar scalar scalar reducing reducing ideas rest detectors plasticity transistor transistor working proper tanh tanh statistically cognition fundamental phases phases phases matched matched naturally closest plausible plausible plausible man man aspect quantities explored logic logic hebb hebb store store switching switching switching attempts electronic electronic electronic electronic electronic electronic electronic electronic electronic electronic electronic electronic electronic electronic electronic defines averages charge charge charge charge charge charge years devices mentioned histogram advanced advanced asynchronous directed critic critic guaranteed phenomena phenomena phenomena phenomena phenomena phenomena phenomena adjacent adjacent floating floating diffusion answer answer correction correction worse worse comparisons stanford stanford implementing berkeley berkeley sys sys sys widely style division transistors transistors controls controls cut separately universal acad grossberg grossberg bandwidth bandwidth incomplete researchers fourth improvements percent double collected substantially pathways led fed fed fed effort cohen slower resistive sharp biologically operate characterize differs branch synchrony synchrony collective collective adjust adjust gave semi electric inherent chose chose chose sophisticated decreased implements eventually progress credit cumulative globally uncorrelated proportion bipolar bipolar amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier summing summing controlling discovery interconnected arranged communications communications saturation saturation saturation saturation adds adds chance stronger adjusting satisfying proceeds logarithmic mos mos resistance resistance abilities viewpoint keeping hope hope operates hint integrator integrator integrator capacitor arrays presentations presentations presentations presentations natl alspector alspector connect decide moved regard washington widrow widrow percepttons counting counter counter arrangement multiplied winning winning advance foundations neuromorphic neuromorphic layout layout record refers verification properly valuable papers speeds hart lett propagate avoiding adopted explorations robert counts ccd ccd divide temperatures rms multiplying multiplying zipser unified unable microstructure ter ter minus minus minus minus solves ent graded graded leaming creates creates emergent diverse diverse ease amherst discovering molecular adjustment adjustment adjustment summarizes increment increment modifying subthreshold resistor magnitudes geoffrey guidance compatible compatible picked books flip flip flip flip guided 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error error error error error error error error error error state state state state state state state state state state state state state state results results results results results problem problem problem problem models models weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer case case case case case case vector vector vector vector vector vector vector vector vector vector order order shown shown parameters parameters noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition recognition recognition recognition method method method method method method approach approach pattern pattern pattern pattern point point point single single single single single processing processing processing control large large large local local neuron neuron neuron patterns analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs form form shows algorithms gaussian paper paper examples examples examples examples small small small small work work work work task fig fig fig fig fig fig fig step process process structure problems response similar show equation equation equation section fixed fixed fixed fixed fixed fixed rule rule rule rule vectors vectors vectors general general general general general general general general general parameter states gradient obtained obtained obtained obtained obtained obtained note note note note dimensional dimensional dimensional result university threshold solution solution solution solution solution solution research research research independent initial initial initial initial constant constant constant constant connections connections connections connections connections connections science prediction direction direction presented presented motion press outputs outputs outputs outputs outputs outputs outputs outputs outputs sample abstract applied applied applied applied back back back computational computational computational computational computational computational properties references component component stochastic stochastic stochastic positive positive important important important propagation propagation introduction hand hand hand behavior behavior effect variance variance parallel recurrent recurrent recurrent change change assume representations part center previous theorem theorem theorem theorem theorem cases required required required required good good conditions distributed expected equations fact fact fact fact proposed proposed proposed minimum classes ing tasks tasks regression respect respect sum sum performed performed performed elements elements elements elements elements means dimension feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback global obtain obtain obtain obtain obtain obtain negative vol vol proc proc proc connected connected connected connected connected connected connected mit mit steps steps larger update update update descent descent descent proceedings report institute institute department implementation consists consists internal represents final final exp scheme scheme ai considered considered considered cambridge experiment environment hinton solutions solutions design design design design san san give condition condition condition condition condition weighted developed types finally finally finally finally backpropagation backpropagation backpropagation backpropagation iteration iteration iteration constraint constraint constraint constraint constraint simply simply achieved feedforward feedforward feedforward feedforward feedforward feedforward feedforward group group group group group group group group group group group group group group group group group group group group group group group group group group group group denote close complete complete stable surface proof proof short implemented implemented supported eds face square square hypothesis makes rumelhart rumelhart objective pairs hopfield hopfield hopfield hopfield fully fully fully technology special leads iterations iterations max max attention minimize minimize produced added added denotes denotes improve takes element element element element element period subject sense recently engineering match differential rl rl diagonal diagonal chain chain symmetric bounded grant expression expression expression expression scaling occur matrices matrices matrices matrices matrices feed move move move move column column conclusion row operator sigmoid asymptotic propose propose physics california variety decrease decrease manner manner groups groups groups groups groups groups groups groups groups groups groups minima minima configuration force solving winner electrical unique unique unique unique unique unique adding equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium independently dependence densities similarly allowed performing performing performing purpose add sufficiently norm avoid usa perceptrons inter determines prove phys discussions characterized suitable successful reached refer refer refer conf conf quickly cun interested sci sci write write write reach attempt extend diego diego american layered requirements updating updating updating updating updating updating put relations steady steady periodic existence existence giving tech project behavioral int int ideal ideal scaled office possibly possibly necessarily rev recognizer singular singular logic chaotic years inequality inequality inequality inequality developing developing asynchronous derivation derivation derivation implementing satisfied widely strictly scientific acknowledgement separately acad beginning beginning begin author annual annual addressed explained argument applies transient completion ity requirement exhibits prevent collective adjust asymmetric asymmetric asymmetric shaped owl june june june differentiable indices indices unity interconnected interconnected interconnected interconnected proceed air tools satisfying satisfying loops loops abilities abilities obtaining generalizes natl substituting governed ensures respective appendix equals sides sides moved matter partitioned lett explorations acknowledge escape sequentially multiplying abu appeared microstructure mostafa ter graded basin opposed axe nition feeding restrictions obtains obtains acceptable management werbos pdp intra intra intra afosr ultimately ultimately pos paris stuck increments differentiating differentiating differentiating differentiating pineda gratefully satisfactory hoc puts inequalities harvard possess devised dissertation 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networks networks networks networks networks algorithm output output output output output output output output output output number number number number number system system system system system system system system system error state results results units units units information problem problem problem problem problem problem models models models models models models models models models models performance based weights weights weights linear linear linear case vector vector vector vector order order shown shown shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems probability probability parameters parameters parameters parameters parameters noise noise noise functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons unit unit recognition recognition method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image processing processing processing processing processing processing processing processing processing control control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test test test test test test test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis matrix matrix optimal inputs form form shows signal signal signal signal signal paper paper paper examples examples size net work task methods fig fig fig fig fig fig fig fig fig fig fig step step step features classification classification classification classification classification process problems problems problems problems memory memory response response response similar similar show show equation equation section section section section section section rule rule rule rule rule rule rule rule rule rule rule generalization generalization generalization generalization speech speech speech speech speech real theory gradient obtained note note experiments activity result result result result university threshold threshold threshold solution solution solution solution independent log sequence sequence sequence target constant constant constant table table table standard connections node node node node science presented presented present present activation activation frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal maximum maximum maximum range range press learn learn position nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous abstract applied applied applied applied applied back find analog analog analog analog analog references ieee procedure adaptive adaptive adaptive propagation propagation introduction introduction hand behavior statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance parallel parallel parallel recurrent tion tion tion tion tion change spatial spatial spatial rules rules rules rules rules rules rules rules rules signals signals representations higher part part center center previous previous cases required good distributed distributed expected make proposed proposed correlation correlation correlation correlation correlation length length length correct observed observed scale finite minimum resulting resulting resulting resulting ing ing tasks simulation simulation times elements elements elements elements elements elements elements mapping potential feedback applications applications filter filter filter filter filter filter filter filter obtain original original vol vol vol vol vol vol vol artificial artificial artificial artificial artificial artificial samples samples application desired perform related connected discrete discrete discrete mit mit descent nets nets nets modeling proceedings proceedings proceedings institute institute department technique technique internal scheme scheme scheme addition ai ai ai ai cambridge cambridge computing domain domain equivalent equivalent equivalent hinton solutions solutions design design transition san stage stage stage stage stage stage bit detection conference conference efficient requires requires choice world vision condition derived developed developed developed robot provided backpropagation biological biological biological biological associative associative associative discussion discussion describe denote tested tested inverse inverse inverse inverse inverse inverse inverse inverse circuits finding adaptation adaptation adaptation adaptation adaptation journal end end future future easily rumelhart noisy noisy noisy noisy noisy noisy simulated simulated simulated pairs pairs hopfield hopfield combination transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer significantly york york york york york york operation operation operation operation operation operation operation operation operation operation operation leads numbers iterations filters filters filters filters filters filters making inhibition inhibition inhibition stored international international early early run added added denotes denotes robust element lateral lateral lateral lateral practical practical practical moving subject subject array cognitive engineering engineering sufficient previously works converge positions positions generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized williams organization organization improvement storage sensitive constructed constructed expression concept occur digital digital spikes alternative alternative correctly correctly conclusion critical critical critical hebbian hebbian hebbian hebbian operator operator operator competitive numerical performs faster practice propose strong physics drawn sigmoidal sigmoidal regularization regularization regularization labeled start exist scene program acoustic relation relation construct winner winner laboratory label mathematical explicitly linearly linearly electrical unique adding frequencies frequencies frequencies frequencies applying minimization springer springer competition competition national expressed expressed expressed expressed review phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme stages stages interpretation variation transform transform transform transform transform transform transform operations labels organizing showed static static static static static static understanding digits digits past past sign sign sign sign diagram calculation calculation calculation additive delays classical intervals false false false remains filtering calculate eeg norm kohonen kohonen koch existing existing existing includes kernels usa sciences memories recognize recognize recognize variations straightforward importance society society delta delta delta delta delta delta delta delta delta included schemes vowel composed verlag verlag repeated procedures prob moore showing classify duration generalize minimizes minimizes minimizes eigenvalue ill ill ill ill thresholds principles principles illustrates software diego american layered wiley wiley wiley wiley replaced replaced recursive recursive recursive issues hall hall helpful fourier fourier fourier fourier fashion ideas ideal ideal stream func statistically statistically fundamental fundamental notion notion matched matched matched matched neu created created prototype prototype prototype prototype prototype prototype prototype aspect portion formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal formal assumes perceptton nervous hebb academic switching amari detected submitted stop band convolution convolution convolution convolution analytical cascade multiplication multiplication multiplication nonlinearity preprocessing operators sgn recognized recognized recognized grossberg calculations bandwidth bandwidth annual conjugate flexible pseudo pseudo pseudo pseudo pseudo pseudo lms lms lack poorly posed posed schematic calculating berlin synthesis limiting gen gen popular tank tank phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes acoustics logical logical yuille conditioning conditioning lim traces diagnosis multidimensional classifying classifying uncorrelated uncorrelated uncorrelated bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar investigation conditioned addresses tem connecting theories proceed ments replacing replacing check bands bands transforms operates reasoning affected selects prentice prentice mance perfor pat pat pat buffer washington washington washington lengths lengths widrow widrow nonlinearities april record clean clean clean clean clean clean late arrows arrows park extensively formant formant formant formant formant designing implicitly hart generalizing generalizing interestingly thresholding stone johnson dividing robert lem associations ence converted converted rigorous leaming leaming formulate bank bank bank bank bank forced spatio spatio spatio spatio spatio pointed pointed convenience connec chapter chapter chapter realize translated care duda convert careful books flip flip interactive relates academy covered memoryless memoryless electronics suffer siam likewise cubic lippman radio examination coordination mcculloch pitts continued marks marks marks terns terns cliffs cliffs lated calculates sensorimotor seattle acoustical equa englewood englewood interpolating interpolating optics cooperation cooperation convention convention transpose america watrous watrous assp fol zeros magazine ings lar doubling neglected prominent hoff responded responded responded atlas atlas voiced tern refine wiener spario spario spario spario biophysics activa activa bio reviews synthesize synthesize aliasing pursued schematically ele multiplications neurodynamics leaky convolving ninth formants calculus rosenblatt engineers lowing missed missed missed missed thirty poral pronunciation pronunciation functionals bandwidths bandwidths 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networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number number number number number number number number number number number number number number number number number number number number number number number number number system system system system system system system system error state state state state state state state state state results results results results results results results units units units units units units units units units units units units units units units information information problem problem problem problem problem problem problem problem problem problem problem models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based space space space space weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer case case case case case case case case case case case case case case vector order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown systems systems systems systems systems systems systems systems systems systems systems values probability parameters parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons unit unit unit unit unit distribution distribution approach approach approach approach pattern point point point point point point point image single single single single single single single single processing processing processing neuron neuron neuron neuron analysis analysis analysis class class class class class class class class class matrix matrix matrix matrix optimal optimal inputs inputs inputs inputs inputs inputs inputs form form algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian examples examples examples examples small small small small small size size size size size size size size size size size size size work work task methods cells points points points points points points points points points points points points points points field classification process process process level level structure structure structure structure structure structure structure structure problems problems problems problems problems problems problems problems problems problems problems problems problems random random random random random random random random random random random random high high memory memory memory memory memory memory memory similar architecture architecture show show show equation section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule rule rule rule rule rule rule vectors vectors vectors vectors vectors general general general general general parameter real average states states states states states states states theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained note note note result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables computation computation computation computation independent found found found sequence dynamics dynamics dynamics dynamics constant constant constant constant estimate computer computer terms terms synaptic node science direction present present phase phase phase low low nodes sets sets maximum range range range press learn nonlinear continuous abstract applied applied back back find computational computational computational computational computational computational computational computational computational computational computational computational analog analog analog properties properties references references references ieee ieee ieee ieee positive positive important important important important important propagation propagation introduction complex complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit generated parallel parallel parallel parallel cost cost cost cost search tion energy energy complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity lower lower lower lower lower lower rules rules measure learned chosen chosen higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher previous previous theorem theorem theorem theorem bound bound bound cases cases type type type required required required required multiple cortex binary binary binary binary long represent distributed distributed expected expected fact fact fact fact region region correlation length observed observed forward classes classes classes classes classes classes classes tasks total total total human computed computed computed computed computed computed computed computed respect multi multi sum sum performed times times elements elements elements elements elements elements elements elements factor factor made natural natural natural natural natural feedback global applications applications applications applications applications knowledge knowledge vol vol vol vol vol vol vol vol vol vol vol vol vol vol vol vol artificial artificial relative define define compute compute compute compute compute compute compute compute compute compute proc proc proc proc proc proc proc perform related related constraints constraints constraints constraints constraints discrete equal equal approaches mit contrast selection report institute institute department synapses represents connectionist connectionist connectionist responses difficult difficult difficult difficult exp bias layers layers addition addition addition graph graph maps considered considered computing computing computing domain equivalent additional additional view view view design design transition san top capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine efficient upper upper upper upper choice choice free free basic increase give con con developed bounds bounds bounds bounds bounds bounds entropy path product product finally finally finally evidence nature nature nature biological biological biological biological associative associative associative associative associative associative associative associative discussion discussion discussion technical technical feedforward feedforward describe arbitrary denote limited close inverse corresponds complete complete complete complete stable stable stable stable stable stable proof proof proof circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits finding amount nearest common effective implemented implemented implemented implemented implemented theoretical require require main eds end vlsi vlsi instance instance instance instance instance future easily easily degree degree degree degree degree degree degree degree rumelhart including smaller hopfield hopfield dynamical functional functional coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients technology programming programming programming interesting interesting ratio projection york york edge edge increasing special special special structures structures mode leads principal pre pre stored stored stored stored bottom depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial attention choose added recent takes reported strategy include quadratic quadratic sense sense sense sense sense sense subset recently engineering sufficient sufficient highly varying previously module tions yields yields correspond rl trans trans trans trans trans trans diagonal diagonal diagonal definition definition symmetric symmetric symmetric symmetric symmetric symmetric gate gate gate gate gate storage storage storage storage storage storage storage storage constructed constructed exists exists exists exists suggests extended extended extended wide wide wide feed width width hardware demonstrate demonstrate demonstrate demonstrate demonstrate conclusion starting minimal minimal minimal row row row trajectories conclusions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions clear exponential exponential exponential exponential exponential exponential exponential faster asymptotic asymptotic asymptotic weak temperature temperature taking taking strong integration physics drawn demonstrated demonstrated california california california turn turn turn turn variety variety exist exist exist exist connectivity program program program configuration question question question appears relation monte construct construct carlo transitions dept implement infinite physical physical physical physical electrical easy spectral spectral spectral spectral scales scales interaction interaction interaction interaction interaction interaction interaction interaction boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean yield choosing family family family independently focus review depending depending communication solved open open open operations fraction fraction evolution evolution evolution evolution evolution static understanding approximated completely constants processor earlier slow delays classical classical classical purpose string construction query koch dendritic degrees precision thesis thesis thesis priori usa strings inter retinal instances memories memories memories memories extension prove discuss activated activated activated specifically absolute phys phys phys discussions structural regular determining straightforward aspects aspects aspects identified importance suitable suitable suitable maximal maximal maximal maximal computationally poggio presentation literature literature efficiently computations computations computations computations computations computations computations comparing situation essentially essentially essentially fine traditional refer soc soc conf conf strongly strongly prob interested interpreted symmetry physiological follow sci comp comp involved usual usual highest processors processors software oriented situations law diego powerful powerful american layered layered layered layered wiley requirements circuitry mead mead relations involving limitations limitations limitations limitations limitations issues issues issues dual dual discriminant behaviour behaviour helpful existence existence giving school tech parity parity parity authors structured structured structured structured structured structured structured structured gates gates gates gates gates gates gates gates hierarchy understand analogous neu examined examined math naturally plausible generalisation generalisation opposite rev ensure subsets versions obvious formal formal noted assumes assumes freedom precise logic logic logic logic logic logic logic logic logic logic store simplest contributions synthetic devices devices spin spin spin spin spin spin spin spin spin spin rows rows rows band band band asynchronous ground analytic analytical glass glass glass glass glass correction london london reasons reasons ganglion considerable turns perspective satisfied broad broad broad choices worst hyperplane products products products mathematics potentially acad calculations lowest lowest bandwidth outer outer outer argument requiring questions substantially pseudo amounts embedded capability readily orders orders adjustable incorporated polynomials synthesis reaches extensions extensions extensions collective chen logical logical attraction attraction attraction attraction attraction progress june proposition proposition proposition wesley wesley univ arithmetic instantaneous contribute acquisition acquisition proofs physiology addison addison investigation restrict restrict restrict acm acm acm acm arguments resources hyperplanes concerned homogeneous homogeneous homogeneous connecting connecting flexibility theories interconnected caltech arranged generality communications anatomical logarithmic odd interconnection familiar familiar familiar programmable abilities occurring bands bands monotonically exceeds exceeds exceeds enhanced natl meaningful separating programs programs iteratively overview vertices infinity counting counting interconnections interconnections interconnections cerebral jolla kearns specificity park hypercube hypercube lett alternatively baldi baldi baldi baldi executed learnable learnable skills lem abu geometrical mostafa outperform sig covering validity opposed opposed emergent axe axe axe axe axe axe propagating pointed theorems conjecture monotonicity ease tradeoff tradeoff amherst solely hundred molecular valiant valiant valiant valiant valiant algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic clas clas argue iff favor deep deep interacting learnability march relate concentrate wise wise surrounding fir projecting harder conversely constructs constructs cation indexed tively minor preprint programmed programmed programmed programmed milliseconds port computa article article status strict shallow shallow shallow shallow shallow shallow shallow shallow shallow shallow shallow shallow shallow shallow shallow shallow architectural capacities capacities capacities mcculloch laws remarks interior traveling pitts unbounded satisfactory justification jointly firstly tanaka termination mirror routines morphology december spins spins spins identically formulae rons venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh anatomy emerges separates fox hamiltonian hamiltonian hamiltonian cardinality poly poly systematically restricting judd salesman appl comm evolutionary amenable longest evolves absent sis relaxed thing computable computable computable computable computable elec elec aip aip faced unusual raised cyclic ically shortly inform inform prescribed prescribed mutation proceeding formulas bidirectional sented terminology noticed repeating spent appli elegant rela plexity plexity phil phil deeper deeper lifetime macro gross psaltis psaltis psaltis formulations edwards seeking permuted philadelphia separability depths depths volumes organisms organisms henceforth sults torre ire contiguous functionals explores brains pierre neighbour concurrent concurrent flips polyhedral densely kronecker logn pitt glasses glasses glasses glasses readers generalised generalised generalised generalised ising ising ising asynchronously stant occuring posner posner asserts otto pennsylvania mceliece mceliece private informal subdivided inexpensive trigonometric standards straints governs siftcation fax ric quired discourse regulated regulated interac hear wells wells akin tuples tuples unreasonable aug polyno lends ingredient exponentials tradeoffs muroga muroga invested quoted mezard jpl borne instructive mial realised characterised characterised complements assertion assertion munications vanishingly stoc stoc stoc neous cision favour interscience halting sical leaxning leaxning santosh taneous complemented rodemich nology orthogonally pretation lutions gree instan conjectures quote yao computability 
#@Baldi_P,Venkatesh_S,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data function function function function figure figure time set set set set set set set set set set set set set networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output number number number number number number number number number system system error error error error error error error error units information information information information information information problem problem problem hidden hidden hidden performance performance performance based based based weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer case case case case case case vector vector vector vector vector vector order order shown systems values values values values values values values values values probability probability probability probability parameters parameters parameters parameters parameters weight functions neurons neurons recognition approach pattern pattern pattern pattern point processing large large large large local local neuron patterns analysis analysis matrix optimal inputs inputs inputs form form algorithms algorithms examples examples examples examples examples examples examples small small size net net net net net net net work classification classification classification classification classification problems problems problems problems representation equation equation equation equation fixed rule vectors vectors vectors vectors vectors general general general generalization generalization parameter real real theory theory gradient gradient gradient gradient obtained term note experiments experiments university university variables variables computation solution research log log log log log log log log defined defined target target target target target standard standard terms connections connections synaptic node node node node node node science prediction prediction direction direction direction presented presented presented presented present present present present activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency press learn learn basis outputs outputs abstract applied applied applied back back back back back back back back back back back back back find likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component ieee important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation context context complex complex generated parallel parallel tion tion tion tion energy energy assume measure representations learned chosen chosen part part part center cases cases cases cases required required good good represent represent bayesian expected make make fact fact fact fact probabilities probabilities probabilities probabilities forward forward minimum ing tasks regression performed performed called called called mapping mapping mapping mapping mapping means made made natural natural natural applications applications applications knowledge vol specific represented true compared compute compute compute compute proc determined goal connected connected distributions distributions distributions brain equal mit mit mit larger larger connection connection connection nets proceedings report institute institute department internal internal layers layers layers layers cambridge cambridge computing equivalent hinton curve view design san conference conference efficient efficient free world world world give con randomly criterion entropy entropy backpropagation backpropagation backpropagation backpropagation backpropagation simply simply discussion covariance normal normal feedforward feedforward feedforward feedforward limited corresponds predictions effective assumed generate generate supported supported theoretical main eds ability future rumelhart rumelhart noisy including including probabilistic probabilistic probabilistic fully interesting numbers international experts supervised supervised supervised supervised expert expert expert minimize choose choose predict perceptron neuronal denotes denotes discussed improve correlations correlations takes takes practical include sejnowski sejnowski recently interest varying varying varying solve yields correspond converge converge address address generalized bounded bounded williams grant grant constructed studied studied studied occur occur alternative locally generally hardware flow flow conclusion place accurate bayes learns constrained suggest propose propose taking taking mechanisms physics physics physics physics california minimizing targets targets manner scene minima base question question question pro construct solving laboratory implement involves easy slightly text consisting adding applying john yield variation past partial calculation normalization fitting fitting closed remains intermediate intermediate intermediate advantages priori perceptrons inter sciences extension maximize specifically tests reason reason importance delta included mcclelland wij wij wij literature literature computations tend essentially conf cun success anderson anderson interpreted dis issue vary vary generalize principles subsequent subsequent subsequent diego american wiley experience difficulty put put put tech behavioral reliable decisions maximizing workshop func neu hill plausible logistic freedom expressions logic finds attempts integrate years devices formula defining defining phenomena fairly baum baum baum starts perspective straight tive constructing immediately arise acknowledgement describing medical medical medical preceding nsf nsf researchers varies capability simulate frequently calculating gen phonemes pasadena adjust logical implements patients differentiable diagnosis diagnosis diagnosis diagnosis diagnosis lab sort sort lecun rational occurred tools replacing loops moment interpret viewpoint serves hope intuitively generalizes eqn eqn corre patient washington widrow widrow accounts arrangement darpa surprisingly record matter sons santa valuable hart alternatively generalizing escape informa ple numerous rigorous achieving super obstacles tween acceptable massively eric constrain ary exam duda management werbos continues relating books paris disease disease sonar sonar nasa round spite advantageous satisfactory satisfactory rosenberg jet conceptual conceptual hoc hoc harvard harvard appealing val propulsion ory sity permanent absent mcgraw bottleneck bottleneck bottleneck aip tained adequately parker ized hoff putative ues ceedings custom snow phy enforced def advice bird neurodynamics puted rosenblatt clarify thirty tributed lacking ire widespread owij frank univer economics numerator imperfect sponds matters vised stance snowbird questionable analogies deriva symptoms gorman iit barbara tropy spartan propaga wescon diagnose wilczek wilczek wid diagnosed diagnosed bottlenecks ently illness pretation nator ately holt inher fabricate cognitiva rected cony 
#@Baum_E,Wilczek_F,
#t1
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set networks networks networks number number system system system results results results results results results results units information information problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models weights layer order shown shown shown shown shown shown shown systems systems systems systems values values parameters parameters noise noise neurons unit unit distribution approach approach approach approach approach point point point point single single single single single processing processing large large local local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns patterns analysis class optimal inputs form form form algorithms simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper small small small small feature feature feature feature net net work work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points points points points points field field field field field field field field field features features features process level cell cell cell cell cell cell cell cell cell structure structure problems random high high high response similar similar similar similar similar architecture architecture architecture architecture show show show line line line general general parameter real real real average average average average average obtained experiments dimensional dimensional result research research independent defined found constant table table estimate computer computer computer computer computer computer computer distance distance distance distance distance distance connections connections connections connections synaptic science science science prediction direction direction direction map map map map map map map map map map map map map map map map map map map map map map map map map map present low low low low machine sets basis continuous abstract applied applied applied density density density density density properties properties references positive positive positive important important introduction effect generated generated parallel parallel parallel parallel parallel parallel tion tion tion tion tion tion tion tion change change change change change change change change spatial assume lower rules rules measure measure measure measure measure measure chosen chosen chosen higher higher higher center center required cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long long long represent distributed distributed expected fact fact fact fact region region region region region region region proposed proposed proposed proposed proposed correlation correlation observed observed observed observed scale scale simulations simulations simulations simulations resulting simulation simulation simulation computed computed respect respect called called times times elements elements elements regions regions regions regions regions mapping made natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation 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receptive receptive provide rates rates rates rates rates rates rates rates proc proc proc proc proc proc location location location determined experimental experimental experimental related related related constraints constraints constraints constraints constraints constraints constraints constraints constraints discrete discrete discrete cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain equal larger larger fields fields dependent report institute department department version version consists individual individual individual individual represents connectionist final exp layers layers layers layers layers sequences maps maps maps considered considered considered considered hinton additional solutions curves design stimuli effects bit bit upper upper upper upper upper approximate vision vision vision vision vision increase give give produce produce produce developed developed levels area area types types types lines path path path nature nature nature sampling constraint constraint constraint constraint constraint constraint constraint constraint constraint discussion fast corresponds stable stable surface surface surface surface surface surface surface amount amount short implemented generate generate generate require eds degree development development noisy fit fit fit simulated simulated simulated simulated simulated typically underlying reduced account unknown significantly edge increasing increasing mechanism consistent uniform uniform principle numbers making window window window depth early minimize minimize produced description description light architectures population discussed recent property property property property pair typical typical reported lateral lateral lateral include sense sejnowski array array array array array array array array array array array recently recently interest highly highly unsupervised volume works tuning tuning tions tions smooth smooth smooth correspond correspond studies studies definition definition locations organization organization organization organization organization organization sensitive sensitive sensitive sensitive sensitive entire increased horizontal horizontal horizontal horizontal horizontal horizontal occur occur suggests derivative derivative rotation rotation rotation rotation rotation rotation locally generally generally column column column column runs hebbian neighbor measures measures measures measures accurate retina clear suggest propose taking taking mechanisms mechanisms physics cycle characteristics variety variety exist selective relationship relationship introduce manner manner appears pro pro van edges produces index index index index index index index index index index index index primary primary primary tuned distinct changing changing changing changing changing changing changing modeled implement physical transformations slightly angle angle scales consisting develop influence detailed restricted organizing organizing organizing ocular ocular ocular ocular ocular ocular ocular showed centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers approximated sizes completely similarly suggested suggested sign earlier calculation measurements spaces neighborhood neighborhood purpose remains intermediate distances distances distances distances distances assigned dendritic degrees degrees degrees recorded figures combinations usa usa dominance dominance dominance dominance dominance dominance maximize holds neighbors neighbors characterized characterized major major regular regular regular regular identified identified closely uniformly differ effectively tend tend orthogonal orthogonal orthogonal refer soc soc conf graphs contained issue satisfy satisfy satisfy comp comp comp comp comp comp bar bar sampled vary vary michael absence realistic realistic realistic realistic providing highest neurosci neurosci neurosci moves mixing preferred preferred preferred preferred preferred preferred preferred satisfies neighboring neighboring oriented bars remain selectivity american layered wiley collection exhibit circuitry circuitry rapidly rapidly rapidly put relations hall examine respond respond fashion biol biol int scaled referred referred topographic fundamental notion notion analogous smallest circles measurement plausible plausible plausible predicts predicts perfect eyes versions noted noted separated mixed attempts attempts attempts years brown great preference developing orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations smoothness smoothness smoothness smoothness track track track track track track track track track analyzed phenomena slope slope slope slope slope slope slope slope slope slope slope slope slope slope slope adjacent reasons comparisons comparisons comparisons considerable straight tive sys sys satisfied broad located located monkey afferent commonly angles angles acad acad members res res localized lowest patches arises recording recording recording linsker linsker addressed addressed geometric reflects reflects dark axes axes generic embedded embedded embedded quantitative quantitative quantitative lattice lattice lattice posed recordings recordings frequently dots dots requirement measuring qualitatively qualitatively gave gave gave inherent inherent physiol physiol specifies june distortion phenomenon phenomenon discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities physiology tation tation drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift perfectly rotated rotated rotated concerned controlling discovery eliminate turned eliminated cellular anatomical stronger proceeds striate striate striate striate striate imposed imposed hyper occurring operates fail implications implications imply illumination arrays arrays arrays arrays arrays arrays carry natl natl published published published published published published published published prentice ranging irregular irregular irregular irregular irregular irregular encountered encountered displayed topological topological topological topological topological topological topological topological topological topological evident monkeys monkeys monkeys originally originally originally arrangement deg layout layout ballard ballard ballard roy roy roy horizon reverse reverse designing discovered ignore interestingly unchanged yielded numerous piece wiesel wiesel wiesel wiesel wiesel wiesel wiesel wiesel wiesel wiesel wiesel wiesel wiesel wiesel ram alternating alternating responds pointed smoothly connec medium regularity preferences preferences preferences spaced flat classic constitutes hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel hubel possibilities sinusoidal electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode reflected acting pub rectangular rectangular rectangular rectangular rectangular rectangular rectangular perpendicular insights alternate alternate tems tems distribu maintained discontinuity discontinuity permits permits relate iso iso iso iso relating maximally wise singularities singularities singularities singularities singularities singularities singularities singularities singularities singularities macaque macaque macaque lond lond lond lond lond records records alternatives figs afferents investigations ation programmed exhibited slopes slopes slopes slopes slopes slopes tissue tissue article rose vice architectural reversal reversal versa discontinuous accordance attributed thousand hundreds neighborhoods neighborhoods neighborhoods virtually spacing spacing spacing spacing spacing diffuse finer stripes stripes stripes stripes stripes broadly essen fre cally rare rare horizontally horizontally horizontally distinguishing conflicting striking proposes intracortical intracortical intracortical neurol neurol neurol neurol neurol neurol kirkpatrick deals baxter tended tracks tracks tracks tracks tracks tracks tracks tracks william reproduced vertically confined confined confined presently tations elec elec elec deformation wong wong bauer bauer bauer bauer bauer bear derives brought zones zones zones zones zones zones zones zones zones zones zones zones newsome daniel dow dow dow dow dow dow hypercolumn tivity hood rotate rotate rotate rotate rotate progresses resemble cats altering simula stryker spots clockwise hirsch quency impor traditionally posi tant postulated blob bruce silverman workers machinery army spontaneously stripe stripe stripe stripe stripe stripe stripe foveal radially encounter functioning snyder mitchison mitchison constantly singularity singularity singularity singularity communicating grain insure slabs slabs slabs permitted regularly susceptible braitenberg braitenberg braitenberg braitenberg braitenberg braitenberg braitenberg braitenberg wheel wheel relied elongated cyber cyber cyber sensitivities ocularity ocularity ocularity giant depict hexagonal maunsell orienta orienta orienta orienta orienta orienta vecchi selectivities selectivities publications manage counterclockwise scattering scattering insures notable scientists reversals reversals reversals reversals reversals reversals reversals reversals reversals reversals opposing opposing swindale swindale swindale retinotopy enlarged orien orien orien heterogeneity heterogeneity heterogeneity heterogeneity transposed react distributing pare violates concentric steadily organiza tangential tangential ellipses sram tionally tally declines buffalo buffalo asymmetries hypercolumns organi informally microelectrode slab lished appreciable signifies signifies paral lel organizations tradi whitteridge pictured pictured biologists larity behar narrowly atten textbooks workings levay nonspecific advancing advancing tighten abnormally presume coincidental appreciably 
#@Baxter_W,Dow_B,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function figure figure figure figure figure figure figure time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output number number number number system error error error error error error error error error error state state state state state results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information problem problem problem problem problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear case case case case case case case case case case systems systems values values values probability probability parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern processing large large large local local local local local local neuron test patterns patterns analysis analysis optimal optimal optimal form shows shows shows signal algorithms algorithms algorithms algorithms algorithms simple simple paper examples examples examples examples examples examples examples examples examples examples examples examples small small small small size net net net net net work task methods methods fig fig fig fig fig fig step level structure structure structure problems problems problems problems problems random random random random random random high similar architecture rule rule rule rule rule rule rule rule rule rule rule rule rule general general generalization parameter parameter average average average gradient gradient gradient gradient gradient gradient gradient obtained term term term threshold threshold threshold threshold solution solution research independent defined defined defined found sequence dynamics dynamics initial initial initial initial initial initial initial initial initial initial constant constant constant terms presented presented present present activation activation activation activation machine machine press press learn learn learn learn nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied find find find properties references stochastic stochastic ieee procedure procedure procedure procedure procedure procedure introduction complex behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior effect effect effect parallel tion tion tion change change energy energy difference variable assume measure chosen chosen chosen chosen higher center cases cases cases cases cases cases cases cases cases type type type good long conditions represent represent represent tree distributed distributed expected fact proposed proposed proposed correct observed observed errors minimum minimum ing total respect eq eq eq eq eq called times times times times means factor factor factor optimization made made global study study study negative original vol artificial compared desired desired rates rates perform perform perform determined determined related connected discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal equal approaches mit comparison comparison larger connection connection update descent descent descent descent descent descent institute implementation version version version consists consists consists consists consists individual represents layers scheme scheme addition addition sequences considered considered considered considered cambridge equivalent directly hinton curve curves curves curves curves curves curves curves curves curves curves san effects detection conference full full full full requires choice choice significant speed increase give produce randomly types finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature depends depends simply simply biological feedforward feedforward arbitrary arbitrary group fast corresponds surface surface surface amount main main adaptation rumelhart rumelhart pairs smaller smaller smaller interesting significantly significantly significantly significantly empirical empirical leads leads squared details direct magnitude decay decay minimize minimize minimize perceptron perceptron improved improved improve takes typical apply introduced strategy strategy observations observations calculated works works works tions tions tions solve converge chain symmetric symmetric symmetric symmetric observation generalized generalized generalized generalized generalized generalized williams organization improvement sensitive sensitive increased lead lead lead lead lead lead lead derivative deterministic deterministic deterministic deterministic deterministic deterministic generally generally demonstrate critical conclusions depend depend sigmoid faster faster learns propose propose physics solid proportional exist decrease averaged minima minima minima attractor attractor attractor boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann produces ways factors factors generating remaining remaining cycles dependence viewed influence variation detailed open open open open restricted restricted updated fraction evolution allowed allowed past sign smoothing smoothing slow slow slow remains valid figures discuss specifically reason reason extra uniformly differ differ delta delta delta delta delta delta included mcclelland wij wij wij presentation presentation presentation detect schemes refer refer refer repeated procedures procedures strongly cun cun symmetry symmetry symmetry symmetry oscillations oscillations strategies strategies thresholds automatically deal minimized remain american layered xor xor xor xor xor xor xor xor xor create investigate exhibit exhibit varied replaced replaced association association association association association preliminary investigated complicated complicated cognition hill circles circles circles circles circles circles circles circles gradients gradients configurations analyze opposite extremely perfect perfect perfect perfect changed changed changed changed changed changed changed adjusted prototype quantities versions versions versions versions obvious formal observe observe expressions extent years brown analyzed guaranteed slope slope analytical analytical adapted adapted sys widely involve beginning qualitative considerably considerably applies applies empirically understood introducing treated exhibits berlin summarized ture cal occurrence prevent prevent modify appropriately climbing clamped clamped saturation convenient adjusting analyzing presentations presentations presentations presentations presentations presentations presentations mance connect respective respective perfor pat bad percepttons foundations matter refers refers eqs eqs broken subsequently valuable explorations accumulated accumulated accumulated accumulated accumulated accumulated divide equivalently emerge forced restrictions connec connec exception argue attempted translated exclusive tems landscape differentiation represen suffer suffer investigations investigations dramatic prevents mann remark served bienenstock preserves satisfactory attributed converging mirror suppress pronounced pronounced ning ning ning practically exposed striking partly huberman huberman triangles triangles triangles triangles ref interpretations carries successively tations prescribed supposed awij awij tern replaces trapped trapped ted discrepancy activa proce suitably suitably dependences dependences mention restart switzerland yann prohibitively symmetries symmetries ting counterparts solu oooo wji behaved earning fogelman conveniently geometrically contin contin awi awi uous uous itive ger disordered consis dure cated prac adaption preferably inevitably drastic drastic tum randomization randomization randomization tection relaxes correspon discrepancies barriers reduc weigh steeper tically wik antisymmetric existent une tative chapters ding lear lear lear papeft interconnec microstruc tabula rasa 
#@Bernasconi_J,
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#*model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input data data data function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time set output output output output output output output output number system state state state state results results results results results units information information information information information information information information information information information information information information information information information information information based linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case order order order shown shown shown systems probability parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method approach point point point single single single single single single single single single single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate test patterns patterns analysis inputs inputs inputs inputs inputs inputs signal signal simple simple simple paper paper paper paper small size size net net cells cells cells cells cells step step points field process level level current current current current current current current current current current current current current current current current current current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure high response response response response response response response response response response response response response response response response response response response response response architecture show line line line line line general parameter real approximation approximation approximation approximation obtained note note note experiments activity activity result result result threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables computation computation computation research research research independent target target target target initial initial constant constant constant constant constant table table table computer computer synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left left presented present phase phase phase activation activation activation activation activation activation low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal range range range range range press abstract applied back computational computational computational properties properties properties properties properties properties references due due due due due important important important important important important important propagation propagation propagation action action action action action action action action action action complex complex complex hand circuit behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect dynamic generated tion tion tion change variable assume lower lower part center center bound cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type type type spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long long conditions conditions conditions tree tree tree fact fact fact region region region region proposed length length observed simulations simulations simulations simulations simulations simulations simulations simulations resulting ing ing ing total simulation simulation simulation called called times times elements elements factor potential potential potential potential potential potential potential potential potential potential potential feedback feedback feedback study negative relative relative specific specific series rates active experimental constraints connected motor cortical cortical cortical brain brain approaches approaches approaches mit mit voltage voltage voltage voltage voltage voltage voltage voltage steps steps steps train train dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent nets institute institute institute synapses synapses synapses individual individual individual responses responses final delay delay addition considered considered considered considered cambridge equivalent equivalent curve curve view curves limit trajectory stage stimuli determine requires basic pages con channel channel channel channel channel channel channel coding levels levels lines finally finally processes evidence evidence nature nature depends biological biological biological biological biological biological normal normal normal technical fast limited close assumption assumption corresponds stable short short short short short effective assumed assumed assumed shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape generate generate role role role role role role role role role theoretical theoretical main journal journal journal end end degree including including including including including typically typically smaller underlying reduced functional functional functional functional functional functional technology technology technology mechanism mechanism mechanism mechanism consistent pre pre pre pre pre pre pre direct making inhibition inhibition inhibition magnitude sources sources description description description description neuronal neuronal neuronal neuronal neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane population population population population population discussed discussed takes reported reported apply period period trees sufficient varying varying previously approximately volume tions tions address channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels entire increased intensity intensity intensity extended wide wide wide wide spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes width width width loop setting demonstrate demonstrate flow flow strength strength strength place minimal depend depend depend central designed clear faster constrained suggest suggest suggest suggest suggest mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms physics largest characteristics characteristics demonstrated solid proportional proportional turn assuming variety variety variety variety ica selective selective relationship relationship relationship force question areas relation relation pro longer ways ways ways ways factors factors generating generating changing changing changing sensitivity explicitly electrical electrical electrical electrical electrical electrical interaction interaction interaction develop develop springer shift blocks potentials potentials independently expressed formation depending operations modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation static completely suggested constants past spectrum key partial partial slow dashed classical classical classical sec sec sec sec sec sec sec reduces event event purpose remains sufficiently koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic degrees fire figures includes includes thesis priori currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents sciences determines activated activated activated activated specifically phys gating aspects identified encoded encoded encoded poggio poggio identify literature computations post post projections comparing situation reached characteristic characteristic verlag quickly allowing allowing allowing contribution contribution contribution physiological physiological timing categories list play play providing delayed operating rat intrinsic intrinsic modelling modelling modelling trains trains trains trains stimulation american investigate investigate rapidly put relations steady steady steady steady dotted dotted preliminary postsynaptic reducing fashion project terminal terminal possibility muscle relationships relationships referred referred complicated complicated complicated affect understand act act act measurement transmission transmission transmission transmission transmission transmission onset onset onset onset portion portion portion assumes assumes freedom shapes nervous message pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal isolated massachusetts massachusetts massachusetts mentioned burst burst slowly distinguish convolution defining growing phenomena phenomena waveform lies reasons lin division operators afferent ion potentially potentially axon axon axon axon axon axon axon axon axon hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal describing axons axons localized localized qualitative integrating integrating populations limits applies reflect reflect transient transient experimentally red marked passed slower slower rep rep rep rep rep release release operate berlin limiting limiting limiting branch branch branch branch branch modulated modulated modulated qualitatively qualitatively conductances conductances logical semi electric kinds fiber neuro begins eventually eventually extreme extreme extreme contribute secondary ear notes forming oxford driving narrow branches branches branches homogeneous purely purely receptors turned plays saturation saturation saturation chemical determination occurring fail roles roles roles roles roles roles roles roles roles roles roles roles roles fires fires reset reset dendrites dendrites dendrites intended intended injection consequences consequences den sim somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma reproduce reproduce tic entries hippocampus modelled modelled modelled axonal axonal axonal axonal thin thin bursts bursts contraction contraction master rich calcium ignore tures discharge cholinergic cholinergic cholinergic cholinergic cholinergic listed shorter graded graded graded graded validity removal opposed encodes diverse diverse propagating terminals connec causing classic classic descriptions possibilities possibilities examining demon reflected var clas mismatch cns summarizes preserved shifting subthreshold exclusive biophysical biophysical thick thick grouped blocking blocking blocking blocking blocking blocking blocking blocking realizable activate activate expand oct met mediated fir distal distal distal conversely selectively weaker weaker afferents afferents intracellular intracellular intracellular likewise fea thousands milliseconds milliseconds prevents tract tract tract tin wider wider helps tonic tonic tonic tonic served lecture versa lation transduction cable cable cable cable cable cable cable agents agents hundreds hundreds inhibited inhibited supply transmitter transmitter char harvard affecting integrates physiologically physiologically wavelength impedance contrasts progressively chan raises degenerate cur ignores quantitatively quantitatively destination vivo establishing presently presently terminates thresh shaping lar transmit transmit blocked blocked excessive putative putative putative putative putative health hyperpolarization hyperpolarization acetylcholine hip depolarization tivity linearities ina ina ina ina ina ina ina ina ina ina ina jack modulate modulate repetitive repetitive repetitive repetitive repetitive repetitive repetitive repetitive repetitive repetitive rises simula activates activates biophysics broadcast eta electrotonic electrotonic electrotonic electrotonic excitable excitable modulating modulating modulating modulating madison traditionally lasting proximal tant nuclear pri parentheses released membranes inhibits torre latch concurrent clamp kinetics originating inactivation inactivation millisecond ulation closing graham graham subsystems neurotransmitter rail opening repertoire depolarized volt looked collateral lumped lumped leftward plications adams collaterals slowing synap outward outward sponses portant decade muscular pus disabled simi opened elicit endogenous strate axo ered depolarizing depolarizing depolarizing clarendon nels inhibiting inhibiting eleven eleven neuromodulatory evoke evoke descrip descrip logically excita sumptions cease ida sistent resetting preparations ach synaptically acteristics influx influx reduc leonard island modulators messenger rectifier steeper conceivably storm storm neurotransmitters cessation cessation cessation sical interrelated ious ents physio modu modu protocols ited subfields lating speculative speculative netics pyra ynaptic stereotyped stereotyped hampered sult regenerative cluding midal buildup affer stereotypical daughter lular eliciting 
#@Borg-Graham_L,
#t1
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#*network learning learning learning learning learning learning learning learning learning neural neural neural neural neural data data data data function time time time set set set set set networks networks networks networks algorithm algorithm algorithm algorithm algorithm number number number number number number number number system error error error results results results results results results results results results results results results results information information information information information information information information problem problem problem problem problem problem problem based based based case case case case case case case case case case case case case case case vector vector order values values values probability probability probability probability probability probability probability noise noise noise noise noise noise noise noise noise weight functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method method method method method method method method method method method method approach approach approach approach pattern pattern pattern single single single single single single single single single single single processing large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate test analysis class class class class class class class class class optimal optimal inputs form shows shows shows signal signal signal signal signal algorithms algorithms simple gaussian paper paper small small small small feature feature feature feature work work work task task methods methods fig fig fig fig fig fig fig fig fig fig fig cells step step features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level level cell cell random response similar similar similar similar section fixed rule rule general general general general general general real real real real real real real real average obtained obtained obtained term note note note note threshold threshold threshold threshold threshold threshold threshold independent defined defined found found sequence estimate estimate estimate estimate standard distance present frequency temporal temporal sets maximum range range range learn position position basis continuous sample abstract applied applied applied density density density density properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component due due due ieee ieee ieee ieee positive positive important important important decision introduction action action action action hand estimation statistical generated generated variance assume rules signals signals signals signals signals signals learned chosen chosen part previous previous previous previous cases cases cases firing firing firing firing firing firing firing firing firing firing type good good spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long represent represent represent make make fact techniques techniques techniques techniques proposed proposed proposed length correct correct scale minimum minimum classes classes classes classes classes classes total human human respect multi multi multi multi sum sum performed performed performed performed eq eq eq means factor factor factor dimension natural study study knowledge knowledge knowledge obtain obtain obtain negative negative original artificial relative samples samples samples samples samples represented represented application cross compute compute rates rates rates rates rates proc related brain brain voltage voltage voltage accuracy accuracy accuracy accuracy accuracy institute institute words implementation individual individual individual represents exp exp scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme considered equivalent experiment experiment experiment experiment experiment experiment curve curve curve curve curve curve curve curve additional estimates estimates stage stage stage stage stage stage detection detection detection detection detection significant free estimated estimated clustering clustering levels actual finally finally simply describe group denote tested corresponds common common effective implemented assumed assumed shape shape shape shape shape shape supported role require easily makes objective smaller smaller reduced account functional technology technology ratio uniform leads window window normalized attention produced choose added added description recent advantage pair pair separate typical typical typical typical typical apply strategy period period engineering compare compare compare previously unsupervised rl trans trans trans definition separation separation interval interval interval interval interval interval interval organization amplitude expression occur extended deviation spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes correctly white occurs pass conclusion operator depend depend central designed peak peak peak peak peak peak peak peak peak peak peak peak propose taking hard physics largest characteristics california solid solid solid solid variety movements iii iii iii groups scene program question estimating estimating describes dept implement category simultaneously simultaneously simultaneously linearly electrical electrical remaining consisting applying events events events events events events events events events implies versus potentials potentials potentials potentials john choosing extracted formation dependence depending overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap densities evaluate understanding understanding approximated approximated approximated activities activities completely constants dashed dashed dashed dashed event event event event event event purpose purpose add foundation classified classified recorded recorded recorded recorded recorded template template inter inter plotted specifically candidate candidate variations variations simplicity reason identified identified importance spiking identify detect detect detect detect schemes schemes schemes comparing situation tend composed refer refer refer notice notice notice notice heuristic interested classify classify classify duration duration duration comp sampled sampled sampled vary write realistic minimizes ill thresholds neurosci overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping illustrates preferred deal rat rat rat receive situations presents presents employed american wiley investigate integral fashion project biol referred reliable reliable fundamental neu smallest possibly possibly created portion portion portion portion observe detector expressions shapes shapes shapes shapes shapes shapes shapes shapes shapes nervous detected detected detected detected detected detected detected detected attempts percentage percentage advanced pairwise band distinguish derivation waveform waveform waveform waveform waveform waveform adjacent adjacent adjacent biology worse handle considerable spatially inside turns producing preprocessing filtered division potentially acknowledgement beginning beginning beginning res recording recording recording recording recording recording recording recording recording recording recording recording recording researchers researchers summation considerably considerably percent fed recordings recordings recordings recordings recordings recordings detecting detecting detecting frequently incorrect templates rely occurrence occurrence occurrence occurrence gave representative classifying classifying classifying classifying classifying classifying temporally temporally narrow concerned neurophysiol caltech plays dealing bower difficulties occurred occurred cerebellum cerebellum cerebellum height occurring obtaining ral effectiveness exceeds published overlaps overlaps overlaps overlaps periods appendix appendix appendix studying encountered encountered equals chooses multiplied multiplied stimulated eng eng eng omitted record record record matter waveforms waveforms waveforms waveforms waveforms waveforms passing observer hart alternatively ignore consecutive fired fired abu approx ence mostafa forced medium classifications acceptable amplitudes solely classifies evoked electrode electrode electrode electrode electrode electrode reject reject reject reject duda interact interact mammalian distant disadvantage considers considers electrodes fir integrals integrals option option option covered sam happen ation ignoring coming coming utilizing differently fortunately resolve thermal impractical assistance confirm aid abeles partly partly tells convention quantitatively sliding complement frequent experienced schmidt artificially devoted decades cope sponsored constituent firings instant instant instant obeys joseph observes observes miss bio bio bio inserting extracellular extracellular inte relying relying mention ply goldstein sought intervening clin aware henceforth med med med resolving sume owing identifiable stant identities identities intend intervention amir nonoverlapping roberts roberts atiya yaser gte orban summations summations discharges tackled erm devising subjectively discrepancies electroenceph encounters microelectrode falsely falsely instants bme bme bme ofx idle idle disregarded wrongly wrongly aix isodata drown tackling extracellularly neurobiologists 
#@Atiya_A,Bower_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data function function time time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm output output output number number number number system system system error error error state results results information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance performance performance performance based based based linear linear layer layer case case case case case case case case case order order order shown shown shown values values values noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach point point single single single single single single single single single single single single single single single single processing processing processing large large large large local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test analysis analysis matrix optimal optimal inputs form form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple paper paper paper paper small small small size size size net net work work work work work work work work task task methods methods methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step step step step step step field field field classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level level level level level level level current current current cell problems problems high similar similar equation equation line line line line rule general real real real real real real real real real real real real real real real real real average term term term term note note note activity activity activity result threshold threshold computation solution solution solution solution solution solution research research found found found found dynamics initial initial constant estimate computer computer terms connections connections synaptic synaptic science map present present present low low nodes temporal sets sets sets sets motion range components nonlinear sample sample sample sample sample abstract applied applied applied find find find find analog analog analog analog analog analog analog references component due due due due ieee ieee ieee procedure procedure procedure important context introduction action action action action action action complex complex hand circuit generated generated variance parallel tion energy energy energy difference complexity classifier lower signals signals signals signals signals signals signals signals signals signals signals signals chosen previous cases cases cases cases cases firing type type type type type type type type type type multiple multiple multiple multiple cortex cortex spike spike chip chip chip chip chip make make make fact techniques techniques proposed correlation correlation correlation correlation correct correct correct correct correct errors errors errors scale simulations simulations simulations minimum minimum minimum minimum minimum resulting ing total respect multi multi multi multi multi performed eq eq eq called elements elements means optimization potential made made natural applications study obtain relative specific samples samples compared application application cross cross cross cross provide provide define proc proc perform perform active determined experimental related brain brain brain brain brain brain equal equal approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches voltage voltage voltage voltage steps accuracy accuracy comparison larger larger larger contrast contrast connection support dependent nets report institute institute implementation implementation implementation synapses synapses technique consists advances represents represents difficult exp delay delay delay delay scheme scheme scheme scheme addition addition addition ai considered computing experiment view view design design design design design design design design stage detection determine efficient full full full full full full full full full full full requires requires give produce produce condition channel channel channel channel channel derived weighted developed developed developed developed levels levels levels criterion actual actual actual actual actual sampling sampling sampling sampling sampling simply technical describe describe describe describe denote fast close corresponds complete stable surface circuits common implemented shape generate supported require require square square vlsi vlsi vlsi ability easily development development fit fit objective objective objective smaller smaller hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield combination combination combination combination reduced functional functional technology technology technology technology technology testing testing significantly ratio ratio matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching principal principal numbers numbers iterations pre window inhibition stored combined minimize minimize choose run light light neuronal neuronal neuronal neuronal improved improved discussed recent recent recent correlations correlations correlations correlations correlations resolution robust robust robust moving include period recently engineering sufficient compare compare compare compare compare previously calculated works works works works tions match match correspond trans trans diagonal locations modified modified modified modified modified modified modified modified modified modified modified modified modified channels channels channels channels channels organization increased grant amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude constructed constructed constructed constructed constructed expression occur occur suggests digital spikes spikes spikes spikes spikes spikes spikes spikes correctly hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware place reduce conclusions sigmoid accurate designed designed designed clear peak peak peak peak peak peak peak performs suggest suggest propose presence presence presence presence presence physics characteristics characteristics demonstrated demonstrated california movements movements iii groups connectivity minima minima minima minima configuration acknowledgements construct construct generating distinct implement implement explicitly simultaneously simultaneously simultaneously simultaneously simultaneously simultaneously electrical involves slightly spectral develop develop mutual events events events events events potentials potentials potentials potentials potentials john review correlated overlap overlap overlap overlap overlap evaluate operations restricted activities activities discrimination discrimination diagram earlier delays delays delays delays reduces event event remains initially distances calculate msec msec foundation foundation classified classified classified classified degrees degrees degrees avoid expect recorded recorded recorded recorded recorded recorded recorded recorded recorded building template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template silicon silicon silicon silicon combinations combinations combinations combinations usa formulation recognize recognize specifically absolute absolute simplicity identified identified identify detect detect detect build build build build post tend essentially characteristic summary traditional soc quickly procedures procedures contained prob allowing interested contribution classify classify classify classify classify sin criteria criteria criteria criteria criteria strategies timing timing sci device duration built involved sampled vary simplified absence realistic wave wave wave delayed cmos reach neurosci neurosci overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping extract deal software rat minimized origin carried american perturbation requirements circuitry varied put involving detail detail limitations accurately preliminary periodic rise successive project biol possibility referred comparable comparable proper understand understand neu neu closest man implementations implementations implementations aspect quantities quantities quantities quantities versions noted assumes precise nervous switching consist detected simplest serial isolated isolated isolated animal years years devices site site site developing costs distinguish distinguish derivation waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform biology floating worse worse reasons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons sys preprocessing constructing division division laboratories recognized separately acad calculations calculations res recording recording recording recording recording recording recording recording recording auto explained reflects apparent considerably considerably considerably considerably considerably evaluating pseudo fed simulate readily documents effort recordings recordings recordings recordings detecting detecting passed reliability compares schematic templates templates templates templates templates templates templates templates templates templates templates templates templates templates templates calculating calculating limiting occurrence tank tank tank pasadena sophisticated specifies progress traces traces classifying classifying classifying cybern feasible sort sv formally temporally temporally ratios ratios animals concerned concerned bin bin bin reconstructed tem turned reaching fails khz bower bower ranges difficulties cerebellum cerebellum programmable mark analyzing natl continue service performances performances excellent mance heavy heavy james studying encountered encountered perfor perfor pat buffer buffer buffer regard evident dif similarities express reveals bins bins record record record probe probe waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms passing storing relies projects designing designing vari acknowledge severe outlined lem verify discharge crossing neurophysiology ple largely visually sig sig creates ties nelson expanding trigger trigger aij amplitudes simulating electrode electrode electrode electrode electrode arising iff biophysical efforts simplifying individually electrodes electrodes electrodes electrodes pos records records records records records cation figs sam confusion confusion meet investigations knowing programmed modifiable modifiable modifiable modifiable rnn rnn demonstrating moderate acquire acquire resolve resolve discretized decided decided decided monitor impractical quantify quantify synthesized synthesized assistance terns ongoing ongoing hop hop hop loaded utilizes abeles abeles abeles interpreting fill powers accomplish converter concern identically identically rons rons tip tip concerns subtracting devised devised judged judged dedicated placement raises digitized digitized neurobiological neurobiological implying smc goodness schmidt schmidt schmidt ings sweep nih wong ically ically adequately syst dij discriminating costly elaborate elaborate bodies tightly demanding demanding joseph formulations formulations multiplications multiplications goldstein goldstein goldstein tiny tiny tiny sible mike ross implementable ously electrically digitally digitally ponent aware exclude brains trouble originating equipment classifi triggers saving implementa complication serially turner standards adams absolutely badly secs additions additions additions additions assure assure discriminated discriminated compressing technically technically nonoverlapping nonoverlapping gle crossed roberts nals arose prin ported unacceptable documented documented cas plates dii discharges cyb oscilloscope oscilloscope oscilloscope msecs stringent stringent overlapped overlapped whitaker unavoidable sepa automate monitors buffering packed bination ably occurence microseconds lowed simultane perimental ferential gerstein erage automat nificantly volves jective rnin rately iis ological hardest abst physi accomplishing jtn multiplica ifj experimenter experimenter nomenclature specif drown microelectrodes teresting physiologists fabricate neurobiologists duplicating cipal lapping 
#@Banik_J,Bower_J,Wong_Y,
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function function function function figure figure time time time time time time time time time time time set set set set set set training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output output number number number number number number number system system system system system state state state state state state state state state state state results results results results results results information information information information information information information information information information information information models based weights weights weights weights weights case case case case case case vector vector vector order order order order order order shown shown shown systems systems probability weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit distribution distribution approach approach pattern pattern pattern pattern pattern pattern point single single single single processing processing processing local local local local neuron neuron rate test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis inputs inputs form form form form shows signal signal signal signal signal simple simple simple paper paper paper paper size work fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step field field field features features features classification current current current current current current current current current trained trained trained trained trained trained trained trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure random random random random random random random random random random memory response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar similar similar similar similar similar similar representation representation representation show rule rule rule rule rule vectors general general general parameter approximation average obtained obtained obtained experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result result threshold threshold computation research research independent independent independent independent defined found found found found target dynamics dynamics dynamics initial computer computer computer computer computer distance distance distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science left left left left left left left left left left presented presented presented presented presented presented presented presented map map present activation frequency frequency frequency temporal temporal range position components components basis basis outputs continuous abstract applied computational convergence convergence density properties properties properties properties properties references component due due due due due positive important important important propagation context context introduction action action action action action behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect generated generated generated generated generated tion tion tion tion tion tion tion change change change change change complexity spatial spatial spatial spatial spatial spatial spatial lower rules measure measure measure signals representations representations representations representations representations representations representations representations representations representations learned learned learned higher cases cases cases cases firing firing type type type type type type type type type type type type type type type type type required multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike spike spike long long conditions conditions conditions conditions represent distributed distributed distributed distributed distributed make make make make fact fact proposed length length length length simulations simulations simulations simulations simulations simulations minimum resulting ing total simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation times means factor potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential made made made feedback feedback feedback feedback study study knowledge original original original relative specific specific specific specific specific represented compared compared compared compared compared compared compared provide provide provide proc location location location active experimental related constraints distributions distributions cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical power comparison comparison connection connection connection support dependent dependent dependent modeling modeling modeling institute institute version synapses synapses synapses synapses represents responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses final exp delay addition computing directly directly additional additional additional additional stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects upper full full full full full significant approximate approximate basic increase increase con con con channel channel channel channel randomly randomly randomly developed developed velocity velocity types types types types lines product actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual provided selected evidence evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply biological discussion discussion technical feedforward feedforward feedforward feedforward describe group limited assumption corresponds excitatory excitatory excitatory excitatory excitatory excitatory surface surface surface finding amount amount amount amount amount common common common common implemented assumed generate generate generate supported role role role require main ability ability ability ability instance degree degree makes development development sensory objective objective simulated simulated simulated simulated simulated simulated simulated simulated simulated simulated simulated simulated simulated pairs pairs underlying underlying functional functional functional fully technology block edge special consistent structures structures structures structures trials trials principle principle details numbers pre pre inhibition inhibition inhibition stored stored stored stored normalized depth depth magnitude combined combined description neuronal neuronal neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane population population correlations correlations correlations property property property separate element lateral introduced include include include period period period period period period subject subject hierarchical subset subset array array interest sufficient highly highly highly varying compare previously previously previously approximately approximately tions tions differential differential trans sparse sparse sparse locations observation observation channels channels channels organization organization storage storage storage storage storage increased increased grant grant amplitude amplitude constructed studied scaling occur occur suggests suggests trial trial trial trial trial trial trial trial trial trial trial trial trial wide occurs demonstrate runs half half strength strength strength minimal assumptions segment segment segment segment segment segment segment segment segment segment segment segment conclusions interactions interactions measures peak learns suggest taking mechanisms mechanisms mechanisms integration presence presence presence presence presence presence physics characteristics characteristics characteristics characteristics demonstrated demonstrated demonstrated demonstrated demonstrated demonstrated california proportional turn turn variety connectivity program acknowledgements explicit appears construct factors primary primary primary generating generating describes mathematical distinct distinct distinct distinct segments modeled modeled modeled recall recall recall sensitivity explicitly simultaneously involves involves remaining slightly text scales interaction develop equilibrium equilibrium equilibrium equilibrium potentials potentials potentials potentials potentials potentials potentials reconstruction reconstruction reconstruction reconstruction overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap influence variation variation detailed evaluate showed showed modulation modulation modulation converges constants allowed discrimination diagram diagram key partial calculation delays reduces intervals roughly roughly generation generation initially msec msec msec msec msec foundation eeg eeg eeg eeg dendritic recorded recorded recorded recorded box figures priori usa currents retrieval weighting determines activated activated activated activated activated absolute partially partially partially successfully major major middle middle closely capable capable capable differ encoded modification modification modification modification modification modification modification modification driven included presentation oscillatory oscillatory oscillatory projections situation essentially receives receives characteristic characteristic characteristic characteristic refer refer soc soc soc repeated repeated procedures procedures induced induced induced contained contained allowing showing showing interested interested interested conductance conductance conductance conductance conductance conductance dis dis oscillations physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological follow sci duration duration duration duration comp comp comp comp involved simplified play dot absence absence paradigm hypotheses neurosci neurosci consisted overlapping overlapping overlapping overlapping overlapping overlapping rat rat intrinsic intrinsic intrinsic intrinsic intrinsic explore explore explore stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation carried american requirements investigate steady detail detail association association association association association accurately issues preliminary preliminary periodic postsynaptic fashion fashion project behavioral biol proper proper pathway pathway presynaptic presynaptic topographic fundamental removed neu circles plausible olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory expressions 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incorporated ity schematic maintain robinson price price exhibits modulated modulated modulated modulated modulated reaches extracting incoming pasadena fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber decreased neuro returns findings simultaneous merging cor lot lot lot lot lot lot lot lot lot naive phenomenon classifying lab primarily modify modify extensive temporally refractory animals animals animals velocities velocities approximates neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol jth odor odor odor odor odor receptors receptors receptors arranged establish bower bower bower bower bower bower anatomical anatomical anatomical significance significance minutes chemical resistance resistance resistance resistance resistance nearby nearby neurobiology roles roles settings implications preparation wilson wilson wilson wilson degradation degradation degradation degradation degradation natl infor interference interference representational james appendix appendix studying studying studying induce pat pat bulb bulb bulb bulb bulb bulb bulb bulb bulb somatic interconnections reproduce dif tic tic exposure multiplied diameter hippocampus axonal axonal cerebral bursts stimulated suggesting record cpu waveforms merge projects projects subsequently convergent explorations yale arcs largely corporation constitute ent shunting latency latency ties presenting emerge spatio pointed additionally aij solely resting rhythm associate evoked evoked evoked demon representa representa representa capacitance capacitance capacitance conduction conduction ibm distant activate activate degraded degraded degraded degraded degraded neurophysiological intra crosses mediated mediated paired differentiation scope scope increasingly records records cation tied oscillating apparently intracellular intracellular intracellular mimic investigations knowing knowing modifiable modifiable refined tract tract reciprocal examination differentiating correlate demonstrating drives bility continued assistance correspondences terns terns inhibit inhibit reflecting mining mining caudal dom connects replicated rons cally excited physiologically mori believed sparsely sparsely emerges progressively neurol neurol push stevens stevens arrives colleagues neurobiological destination destination vivo tance attenuation attenuation leakage establishing multimodal lewis permanent senses ionic ings nih approached modulatory modulatory modulatory modulatory modulatory modulatory assessed episode pitiform undergo tan tory sented sented behaving behaving behaving ference ular pull continuing continuing activating rostral rostral extracellular extracellular extracellular extracellular extracellular inte saved saved schneider sparsity damped awake awake stim uniformity leaky reproduces dissimilar dissimilar dissimilar dissimilar dissimilar untrained untrained compartments deduce structuring clin clin tributed synapfic accelerator testable compartmental compartmental retains med abs abs abs piriform piriform piriform piriform piriform piriform piriform piriform piriform piriform piriform piriform reproducing originating haberly haberly haberly haberly haberly haberly haberly haberly haberly haberly haberly reproduction expressing delivered depolarized partic qualities qualities equipped reinforced reinforced strated triggers rect dave theta instructed sole peri weakened joshua conical conical conical conical conical conical axial axial strengthened associa neur neur neur synap eet assure tex knowl conduc interfere mecha bundle recalling lly hyperpolarizing elicit lan contrasted differentially comple resistant pattems modulator divergent entorhinal pertaining wished aining aining aining integrators activ organiza ulus intemeurons intemeurons intemeurons mately stimu stimu neuroanatomical instructive carded microsystems lus lus electroenceph electroenceph adrian pharmacological coincident nism cult duplicates occurence matthew popula exci andj andj modifi mbytes transmembrane shunt protocols psychophysiology microcomputer pyra caveats ceils ceils characteris tatory ductance diffi modifica ynaptic mimicked forbes shock shock congruence mentary midal gration lax dal sists bracketed nln pyrami mml 
#@Bower_J,Wilson_M,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data function function function time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks output output output number number number number number number number number number number number number number number number number number number number number number number number number number number system error error error error error error error error error error error error error error error results results results results units units units units units units units units units units units units units units units units units units units units units units units units units models models models models models models hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance space space space space space space space space weights weights weights weights weights weights weights linear layer layer layer case order order order order order order order order order order shown shown shown systems values values values values values values parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern point point point single single single single control control control control control control control control large rate rate rate rate test test patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix form shows shows shows shows shows shows shows shows shows shows shows shows shows shows shows shows simple simple simple simple small small small small size size size size size size size size size size fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step step step step step step points field features level level level level level level level level level level level level level current current current current current current current current structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure random high high memory memory memory memory memory memory memory memory memory similar representation representation representation representation representation representation architecture show show equation equation section section line real average states obtained obtained term term dimensional dimensional result threshold computation computation computation computation computation computation computation computation computation independent independent defined defined defined defined defined defined dynamics dynamics table table table computer synaptic presented presented presented presented activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation frequency temporal temporal machine machine machine machine machine machine machine machine machine sets sets sets maximum range range learn learn learn learn components nonlinear nonlinear abstract abstract applied back back back back back computational computational convergence convergence references references references important propagation propagation propagation propagation propagation introduction introduction hand dynamic dynamic parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel cost change energy energy difference difference complexity complexity complexity complexity complexity complexity variable representations chosen chosen higher higher higher higher part previous type type type type type type type type type type type required required required required required required required required required multiple multiple good long represent represent represent represent tree tree tree distributed distributed equations errors forward forward forward forward forward forward forward forward scale simulations simulations simulations simulations simulations simulations simulations total total simulation simulation simulation computed computed computed sum sum sum sum sum sum sum sum sum sum sum performed performed times times times elements mapping mapping made global global global vol samples represented represented represented true compared desired desired cross provide provide provide provide define define compute compute compute proc perform active active determined goal connected connected connected approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches steps steps steps steps comparison comparison comparison comparison comparison larger larger larger connection connection connection connection update update update update update update update update update update update update update update update update update update update update update update update update update update update update update support dependent dependent dependent selection selection selection selection selection report report institute implementation implementation implementation implementation implementation implementation implementation synapses code code code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel exp addition addition addition graph graph graph ai ai ai ai ai ai considered cambridge computing limit top determine efficient requires requires requires requires speed speed speed speed speed speed basic basic increase increase produce produce channel weighted weighted weighted weighted weighted weighted weighted weighted weighted levels types product product provided provided provided selected selected selected selected selected selected iteration simply measured technical technical increases arbitrary tested inverse stable amount common implemented implemented implemented implemented supported require require require adaptation adaptation adaptation simulated simulated simulated simulated hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield functional transfer transfer transfer transfer transfer transfer transfer transfer programming programming edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge mechanism consistent structures structures structures structures structures structures uniform uniform operation operation operation operation operation operation operation operation representing numbers numbers numbers direct stored stored stored stored stored stored stored magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude minimize run run run run run run run added added resolution pair movement apply apply moving include include include include machines machines machines hierarchical hierarchical hierarchical hierarchical subset subset subset array array array array array compare conventional correspond address address address address address address address locations locations locations symmetric symmetric grid grid grid grid constructed suggests digital wide alternative loop loop loop white white column column column column column setting hardware hardware row hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian reduce segment segment segment segment conclusions numerical exponential temperature suggest suggest physics reduction reduction reduction cycle cycle cycle turn variety user exist movements averaged identification identification program program configuration reference reference explicit construct edges edges edges edges edges edges edges edges generating plot laboratory segments metric simultaneously linearly linearly physical physical physical physical physical remaining unique unique unique applying versus boolean boolean decreases expressed communication communication communication communication squares viewed interpretation influence solved transform operations operations operations operations operations operations operations operations updated updated updated updated updated updated updated centers forms forms forms sizes sizes sizes sizes sizes sizes sizes translation updates allowed processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor performing roughly roughly add construction degrees kernels activations activations weighting assignment assignment memories memories plotted plotted black simplicity columns columns columns columns columns columns selecting modification modification modification wij wij wij wij wij wij wij spiking computations computations plots essentially fine composed composed composed allowing link link link link link interpreted interpreted issue content content categories list list list list list list list list list list list list list list list list list list list list list list list list list list involved involved usual backward backward backward backward backward backward backward backward providing processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors american requirements requirements requirements requirements updating updating relations relations replaced mass reducing fashion fashion links links links links mappings mappings mappings mappings relationships relationships comparable proper complicated fundamental momentum momentum matched removed removed act act act act act act act act act act act act act act act act act circles integer integer integer traffic implementations implementations implementations subsets obvious message message serial serial serial serial serial serial serial serial serial spin brown rows growth defining floating floating floating glass multiplication multiplication multiplication multiplication handle nonlinearity nonlinearity spatially processed processed processed processed processed implementing immediately products products controls controls acad computers geometry meaning exemplars exemplars researchers summation summation summation virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite limits limits limits applies effort compares maintain requirement execution execution execution execution execution stack stack spread differs instruction incoming incoming incoming incoming ordered collective sums sums sums sums sums sums sums segmented segmented segmented segmented segmented segmented segmented segmented segmented simultaneous arithmetic realized don addresses addresses addresses addresses interconnected interconnected exemplar exemplar consideration ranges ranges abilities efficacy receiver receiver arrays arrays continue lyapunov lyapunov passive overlaps reset reset reset enhance scan scan scan scan scan scan treatment treatment treatment april april offer arrows storing hypercube hypercube messages messages speeds speeds instructions instructions receiving executed executed sequentially sequentially multiply largely corporation emergent copy copy copy copy copy copy sigma simd forcing acting translated care gained magnitudes thermodynamic dominated picked overhead overhead overhead parallelism parallelism parallelism host host host host host host paris paris deleted deleted deleted constructs attached attached attached attached figs figs descending descending interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect scanning scanning scanning scanning scanning scanning scanning utilizing cube cube 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#@Brown_N,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural function function function function function function function function function function function time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system state state state state state state state state state state state state results results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem case case case case vector vector order order shown shown systems systems systems weight weight neurons method approach point single single local local local local local local local local local local local local local local neuron neuron neuron analysis analysis matrix matrix form paper paper paper small small size size size size size size size size net work current problems problems problems problems problems problems problems problems problems problems problems problems random random memory similar similar show fixed fixed fixed rule general approximation approximation average states states theory theory theory theory note note note note result result result university threshold threshold threshold computation solution solution solution solution solution solution research defined defined node node node node node node nodes nodes maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum basis abstract find find computational convergence convergence properties properties references ieee important important important circuit circuit behavior behavior parallel parallel search search search change energy energy energy energy energy energy energy energy energy energy complexity complexity complexity complexity complexity assume chosen higher theorem cases type type required good good good long represent represent represent fact fact fact fact techniques minimum minimum classes computed computed performed called called called optimization optimization optimization optimization potential dimension global global global global global global global applications applications study vol vol vol specific represented desired desired define define proc perform perform determined related discrete equal power power support proceedings institute department implementation final final graph graph graph graph graph graph considered computing computing equivalent equivalent directly solutions solutions solutions solutions solutions solutions solutions design san conference approximate approximate approximate approximate approximate approximate approximate approximate approximate speed speed weighted path path selected iteration iteration associative arbitrary fast limited corresponds corresponds corresponds corresponds complete complete complete complete complete complete stable stable stable stable stable proof proof proof proof proof finding finding finding finding finding finding finding finding implemented main main main main main journal instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance needed needed hopfield hopfield reduced reduced fully edge edge mode mode mode mode mode mode operation operation operation operation bits bits bits international polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial idea description description description description denotes denotes denotes exact exact exact exact property property property takes takes takes practical quadratic subset engineering interest conventional works solve correspond correspond correspond converge definition definition definition definition definition definition definition background evaluation symmetric observation generalized bounded bounded bounded bounded interval interval exists exists exists exists suggests deterministic performs exponential hard hard hard hard hard hard hard hard hard hard hard hard physics reduction start exist exist min program force question question denoted denoted denoted suppose suppose suppose appears relation construct optical solving solving solving solving solving solving solving laboratory physical electrical develop quality implies implies implies implies lemma lemma lemma lemma restricted suggested converges converges converges key performing performing false distances usa instances recognize recognize holds maximal wij modes modes presentation build efficiently computations refer follow sci device hold comp denker maximization maximization operating operating operating operating operating diego american investigate put hall existence existence existence existence tech biol office decisions proved understand necessarily necessarily changed algo mapped logic generates generates serial serial serial serial optimum optimum optimum devices devices great guaranteed guaranteed guaranteed defining stanford stanford worst sgn sgn cut cut scientific acknowledgement acad computers freeman formulated rep maxima maxima operate operate operate summarized gen proven tank june proposition proposition proposition proposition proposition proposition proposition proposition proofs proofs cybern restriction nat air intelligent check check check abilities definitions guide combinatorial combinatorial combinatorial combinatorial prentice corollary corre decide originally claim reader reader matter johnson abu mostafa solves solves solves solves goodman goodman emergent uniquely imagine iff iff ibm rithms setup setup setup setup attached attached attached attached electronics siam gratefully remarks algorithmic traveling traveling tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp optima believed ters hamiltonian edited deals deals deals optics complement complement salesman salesman company amenable locality aip cuts statements bruck bruck bruck col completeness joseph undirected nondeterministic nondeterministic acknowledged proving icnn propositions propositions propositions cities concluding sponds theme hamiltonjan hamiltonjan hamiltonjan nonincreasing intractability nondecreasing motivations garey sitions timization lective chap chapters erates propo believes algorith 
#@Bruck_J,Goodman_J,
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#*network network network network network network network network network network network network network network network network network learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number system error error error error error error error results results units units problem models models hidden hidden hidden hidden performance performance performance performance performance performance performance based based based space weights weights weights weights linear linear linear layer layer layer layer layer layer layer layer layer layer layer order order order shown shown shown shown shown shown systems systems values values values noise weight weight weight weight neurons neurons neurons neurons recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach pattern pattern pattern pattern pattern pattern pattern point point single single single single single single single processing processing processing large neuron neuron neuron rate test test patterns patterns patterns patterns analysis analysis class class class class class class class matrix matrix optimal inputs inputs form form form shows shows shows shows shows shows shows shows signal simple simple simple simple simple simple simple paper examples small size feature net net work points points points classification classification classification process level trained trained trained trained trained trained trained trained trained trained structure problems problems problems problems random high high response response similar similar representation representation representation representation representation representation representation show show speech speech speech speech speech speech speech speech speech speech speech speech speech approximation average average theory gradient note note note note note experiments experiments experiments activity dimensional university threshold threshold research table table table standard computer connections connections node science science prediction prediction left left left left map map map activation low nodes frequency frequency frequency frequency frequency frequency frequency sets press press learn learn sample sample sample sample sample abstract applied find references due ieee ieee ieee ieee ieee propagation introduction action effect dynamic dynamic dynamic dynamic dynamic parallel parallel parallel tion tion tion energy energy energy energy energy energy energy difference variable classifier measure measure measure representations representations representations representations representations representations word word word word word word word word word learned learned learned chosen chosen part cases cases required good distributed distributed techniques region proposed length length errors resulting classes classes classes classes classes classes tasks tasks total computed computed multi multi performed called times optimization made feedback applications study study obtain obtain negative vol vol vol artificial artificial artificial artificial artificial artificial relative relative specific samples perform perform perform determined experimental related constraints connected connected connected connected power mit mit accuracy accuracy accuracy accuracy accuracy accuracy comparison larger train descent nets nets nets nets nets nets proceedings report report institute institute words words words words words words words words words technique technique technique consists consists consists internal connectionist connectionist responses responses difficult difficult difficult difficult difficult difficult difficult difficult layers scheme cambridge experiment directly directly hinton additional additional solutions san san san detection conference conference conference conference classifiers classifiers full choice approximate produce produce produce produce weighted finally sampling measured normal technical fast corresponds stable short nearest nearest common common implemented eds end degree makes rumelhart rumelhart fit needed jordan programming programming programming testing york consistent trials trials matching language pre pre window window international international attention attention produced produced perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron improved improved improved pair separate typical sense sense sejnowski array array cognitive engineering sufficient highly conventional conventional conventional conventional conventional axis axis solve solve speaker speaker speaker trans diagonal background grid grid williams increased increased increased half half reduce conclusions neighbor neighbor measures accurate performs practice weak weak learns sound sound sound sound sound strong strong hard hard presence physics averaged targets reference digit pro index electrical easy easy slightly slightly text spectral spectral spectral spectral spectral scales applying springer blocks versus national focus focus correlated variation variation variation variation variation transform evaluated frames frames frames frames frames sizes digits digits digits discrimination spectrum spectrum spectrum spectrum spectrum spectrum spectrum earlier reasonable spaces recorded recorded building template template template coordinate perceptrons perceptrons perceptrons perceptrons bell contour contour inter recognize plotted automatic maximize tests successfully simplicity determining capable capable included mcclelland situation plots plots plots plots plots plots plots plots ten ten ten characteristic notice notice notice notice notice verlag contained classify timing timing duration gray providing highest highest consisted preferred diego diego american layered layered layered layered layered layered exhibit difficulty hanson lippmann mass fourier fourier examine successive detectors ideal ideal working complicated scores cognition contours neu hill coefficient onset man perfect recognizer recognizer portion logistic detector perceptton perceptton submitted serial isolated isolated indicating smoothness capabilities comparisons perspective purposes choices sounds sounds beginning beginning beginning ridge ridge english read cybernetics alignment alignment alignment alignment alignment alignment alignment alignment geometric double double syllable spoken spoken spoken conducted peaks peaks peaks detecting employ employ outliers templates templates templates passes vocabulary vocabulary vocabulary vocabulary vocabulary synthesis incoming prevent hamming hamming decreased age windows focused eventually utterances utterances utterances utterances utterances june june june consistently representative representative spectra spectra spectra spectra spectra aligned aligned aligned aligned sensing tem connecting communications khz alpha handwriting utterance utterance utterance vowels equals male male pat tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens smoothed smoothed smoothed smoothed reader jolla late formant formant formant fold ics rms rms rms rms rms discriminate crossing crossing anns discount employs superimposed flat causal unseen publication token token concentrate distinguished sam crossings confusion confusion syllables durbin october spite ucsd triggered rabiner rabiner acoust recogni twenty twenty twenty twenty decided autocorrelation ping rosenberg terns hopkins clarity lists recursion burr burr burr burr rons distinguishing fft fft fft fft fft fft fft fft huang slices characterizes johns minsky assp nettalk feb feb focusing focusing tenth stabilization voiced spec discriminating configured accuracies upward accu illustrating evaluates warp endpoint permuted lpc lpc lpc lpc lpc lpc lpc lpc lpc lpc lpc lpc lpc lpc lpc lpc formants resampled earning voicing voicing aver mere endpoints endpoints papert valley gramming exceeding exceeding primed discriminability warped referring atlanta bet aloud vocabularies vocabularies vocabularies vocabularies discriminants morristown plates pled terrain zeroes jhu eecs tral disjunctive windowed marginally discriminator mutations conceivably recomputed disambiguate aided rately atten alphabetic alphabetic aligns aligns 
#@Burr_D,
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#*network network model model model model model model model model model neural neural neural neural input input input input input input input function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time networks networks output output number number number system system state results results results information information information information information information information information information information information information information information linear case order order order order shown shown neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution method method pattern pattern pattern pattern pattern single single single single single single single single single single single single single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing large rate rate test test test test test test test test test test test patterns patterns patterns analysis analysis shows signal signal signal simple simple paper paper small small small size methods cells points points process process level level level level current current current cell cell cell high high response response response response response response similar similar similar similar show section section section section section section section fixed fixed fixed fixed general average average average states states theory theory note experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables research log log defined defined defined found found sequence initial constant constant constant constant constant computer terms terms synaptic left presented presented presented present phase phase low low low low low low low low low low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal maximum press press outputs outputs abstract back back back density analog properties important important propagation introduction action action action circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect change variable lower lower measure measure higher higher previous previous firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing required multiple multiple long long conditions represent represent tree tree tree tree expected expected equations region region length length observed observed resulting simulation human performed performed performed times regions potential potential potential potential potential applications study study study study knowledge filter filter filter filter filter filter compared desired rates rates determined experimental experimental experimental constraints constraints constraints motor voltage voltage voltage voltage voltage comparison train train dependent dependent source report institute department represents represents represents represents delay delay delay addition addition curve view stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects determine determine determine upper upper upper upper significant basic basic basic increase increase increase increase coding weighted levels levels actual nature depends depends depends depends constraint constraint measured measured measured measured measured measured normal increases increases increases assumption assumption complete circuits short common common generate generate role eds degree degree including simulated smaller smaller needed coefficients block block transfer interesting york york increasing increasing consistent filters filters making bottom description population population discussed discussed recent separate separate element typical typical typical typical typical similarity reported lateral period period period period period period period period period period period trees trees trees trees engineering varying studies differential differential achieve locations interval entire entire increased increased increased amplitude studied studied occur occur suggests suggests suggests suggests deviation wide wide wide predicted occurs occurs half strength strength strength strength starting starting place conclusions designed designed designed designed peak taking mechanisms mechanisms cycle proportional proportional proportional min decrease decrease iii iii manner manner connectivity connectivity connectivity connectivity connectivity connectivity reference longer primary changing changing modeled linearly electrical electrical electrical electrical electrical electrical electrical electrical slightly scales frequencies frequencies frequencies frequencies applying applying applying potentials cycles cycles cycles decreases choosing dependence dependence dependence dependence dependence depending correlated controlled fraction fraction fraction modulation forms understanding suggested past past past past past past past diagram diagram diagram sec construction recorded fire fire figures variations variations variations characterized characterized characterized columns driven oscillatory situation success success return physiological physiological physiological follow timing duration involved vary vary simplified play paradigm leading cat neurosci attempt subsequent subsequent subsequent subsequent deal deal deal deal deal presents presents presents explore remain stimulation stimulation american varied varied periodic existence existence reducing examine respond fashion ideas rest rest rest terminal analytically possibility muscle comparable comparable complicated understand presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic 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chamber interfering bigger safety safety safety safety safety safety safety safety safety safety safety safety safety conducting conducting wurtz modulates modulates contracts pump nonoverlapping elicit nodal persist endogenous vth vth vth bibliography contracting resets raven synaptically interspersed filterbank iol intermittent intermittent intermittent intermittent microelectrode microelectrode regulates conduct cessation innervating rnin contractions delaying evokes mic frogs nerves nerves elicits liss daughter dependen 
#@Carley_L,
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#*learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input input input input figure figure figure figure figure figure figure figure figure figure figure set set networks output output output output output output output output output output output number number number number number number number system error results results results results results information models models models models models models models models models models models models based based weights weights weights weights weights weights weights weights weights weights linear case vector vector order order shown shown shown shown shown systems values values values values values values values values values parameters parameters neurons neurons neurons neurons point single processing neuron neuron neuron rate rate rate rate rate rate rate rate rate test test test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows shows shows signal paper paper paper paper paper paper paper paper methods fig fig structure memory show show show equation equation equation section line line line general parameter parameter parameter obtained obtained obtained obtained term term term term term note result university university research research defined found found found found initial initial constant constant constant constant constant constant constant constant computer computer computer synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science presented presented press position position position position position position outputs outputs outputs abstract applied applied applied find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references due due due ieee ieee positive adaptive adaptive adaptive adaptive adaptive introduction hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus tion change assume measure chosen chosen chosen chosen previous bound conditions conditions conditions conditions expected expected equations equations techniques techniques region proposed proposed proposed scale simulations resulting simulation simulation simulation simulation simulation simulation sum called means factor factor factor natural vol relative specific cross location location location active active approaches mit comparison larger update dependent proceedings institute institute words words internal difficult considered computing environment curve view trajectory trajectory trajectory stimuli stimuli conference conference conference approximate speed condition condition condition condition condition derived weighted weighted developed bounds actual depends describe describe arbitrary denote transformation transformation transformation transformation fast fast assumption complete predictions assumed theoretical theoretical theoretical theoretical theoretical adaptation adaptation adaptation adaptation adaptation adaptation adaptation easily objective simulated ratio ratio operation operation language iterations iterations iterations iterations stored magnitude magnitude magnitude magnitude polynomial choose predict neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal denotes recent recent recent recent recent recent recent recent introduced include side quadratic quadratic quadratic recently recently recently engineering engineering engineering compare calculated yields converge converge converge achieve achieve address bounded bounded bounded expression suggests suggests extended extended deviation occurs trajectories trajectories numerical designed clear sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton faster faster asymptotic presence physics physics sigmoidal sigmoidal exist introduce relation primary primary plot mathematical mathematical electrical electrical electrical spectral versus versus john john john yield expressed review static static static static suggested constants constants allowed past past earlier earlier reasonable barto barto barto barto barto barto barto barto barto barto barto barto barto barto barto barto classical classical classical classical purpose remains euclidean precision eigenvalues recognize determines specifically simplicity simplicity extra svm literature plots plots tend summary traditional procedures showing contribution duration vary realistic nips eigenvalue correspondence american american collection exponentially varied put replaced replaced examine history school school school school plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity analytically scaled authors eigenvectors proved proved affect understand neu trace trace trace trace trace trace trace trace adapt analyze analyze extremely illustrate ensure adjusted hebb hebb hebb hebb analyzed slope slope slope analytical straight straight precisely radius varies readily readily readily readily lack psychological expectations conditioning conditioning conditioning conditioning deviations deviations lim converged converged converged converged summed tation conditioned conditioned conditioned conditioned unity unity unity discover proceed simplify simplify logarithmic logarithmic logarithmic grow serves published ranging dominant similarities young eigenvector papers ignore outlined verify verify verify neurophysiology ber ber decomposed recurrence ibm neurophysiological carefully carefully interactive relates denver inverting rewrite rewrite reciprocal november november spite insufficient confirm determinant recursion attained scenarios transpose reality gence format format energies decades col analyse repetitive altering checked superscript klopf klopf klopf conver postulated sought earliest completes tonal doctoral realizing logs divergent eecs cont cease aca fortran boyd mber mda tput demic 
#@Cheung_J,Omidvar_M,
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#*network network network network network network network network network network network model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data function function figure figure figure figure figure figure figure figure figure figure figure set set set networks algorithm algorithm algorithm output output output output output output output output number number number number number number number number number number number number number number number number system system system error error error error error error error error error error error error error error error error error error error error results results results results results results results units units units information information problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space space space space space space space space space space space space space space space space weights weights weights linear linear linear layer layer layer layer layer case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown shown shown probability probability probability noise weight weight neurons neurons neurons neurons distribution recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method method method method method approach approach approach pattern pattern pattern point point single control control large large large large large large large large neuron neuron neuron rate rate rate rate rate rate rate rate rate analysis analysis class class class class class class class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal paper paper paper paper small small small feature feature feature feature feature feature feature feature feature feature feature feature feature net net work methods methods fig fig fig fig field classification classification classification classification classification classification classification classification classification classification classification classification structure structure structure structure structure problems problems random random random high high memory memory memory memory memory memory memory memory memory memory memory response similar similar representation representation architecture show show show show show show equation equation equation equation section section fixed fixed vectors vectors vectors vectors vectors vectors vectors vectors general general real real average theory theory theory theory theory theory theory obtained term note note note note dimensional result result threshold threshold variables independent independent log defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant estimate terms terms terms terms distance distance distance distance distance distance distance distance distance distance distance presented map present present present machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets sets maximum maximum maximum maximum maximum maximum range press components components components basis abstract find find find find analog analog analog references component component component ieee positive positive decision introduction circuit circuit dynamic generated generated generated generated generated generated generated variance variance complexity complexity complexity assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower lower rules representations representations word higher part previous previous bound bound bound bound bound cases cases cases cases type type good binary binary binary distributed distributed distributed distributed make make techniques techniques techniques region region proposed proposed proposed correlation correlation correlation length length length length length length length length length correct correct correct correct correct errors errors errors errors errors errors errors errors errors errors errors minimum minimum minimum minimum classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes simulation simulation simulation simulation simulation simulation simulation simulation sum sum called times mapping mapping mapping means made feedback filter obtain obtain negative original original vol vol vol vol vol represented cross define proc proc power approaches approaches larger larger connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection institute institute loss technique technique consists internal internal internal internal code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code scheme scheme scheme graph maps maps solutions design design stage capacity upper choice give give produce condition coding coding coding coding coding coding derived randomly randomly randomly randomly product product product product product product product product product product provided provided associative associative associative associative achieved normal describe describe describe denote transformation transformation fast limited limited limited limited limited inverse inverse inverse inverse inverse inverse corresponds complete finding nearest nearest nearest nearest implemented assumed generate generate theoretical theoretical require require main main square pixel pixel pixel pixel pixel easily easily easily degree noisy noisy noisy noisy noisy noisy noisy noisy objective simulated pairs hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield technology block significantly significantly ratio character character character character mechanism matching principle operation operation call numbers filters stored stored stored stored stored stored bits bits bits bits polynomial idea idea attention added denotes denotes advantage property property property pair element typical similarity practical period machines machines array recently compare approximately approximately axis axis rl definition increased constructed exists horizontal expression occur trial trial matrices matrices matrices predicted correctly loop column column conclusion conclusion greater greater operator depend performs asymptotic propose propose hard hard hard hard hard hard physics largest largest california california turn assuming assuming exist exist iii characters program denoted suppose suppose suppose suppose appears relation construct produces produces produces index index index index index index index winner winner describes vertical recall recall explicitly slightly slightly applying springer shift implies implies versus versus stages correlated communication viewed codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes transform transform transform transform labels showed forms approximated earlier calculate calculate calculate construction kohonen classified classified classified classified expect building thesis usa usa memories memories specifically reason columns extra efficiency uniformly uniformly uniformly suitable maximal maximal maximal maximal maximal maximal maximal maximal identify build comparing score essentially orthogonal orthogonal orthogonal composed traditional notice notice verlag decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding success success success success classify classify classify classify classify classify satisfy satisfy providing computes ill automatically received received satisfies deal american transformed transformed transformed difficulty lippmann lippmann periodic fewer scores matched matched closest possibly necessarily necessarily integer analyze singular der mapped store store store generates generates finds established percentage great rows failure correction correction correction correction worse satisfied organized constructing sgn sgn sgn commonly products acad depicted auto recognizing radius radius radius radius radius radius exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars outer outer outer outer outer outer outer outer outer outer outer summation summation applies items pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo passed formulated berlin pasadena hamming hamming hamming hamming hamming hamming decoder decoder decoder decoder decoder decoder decoder decoder attraction attraction attraction attraction attraction attraction expectations tolerance representative corrupted guarantee summing nat nat concerned concerned unity eliminate nonzero exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar outcome proceed caltech generality adds dealing satisfying primitive transforms operates shifts synchronous exceeds exceeds substituting composition reliably reliably reliably reliably recovered recovered negligible negligible dependency lengths infinity infinity belongs belongs belongs express reveals arrive park correcting correcting correcting correcting reverse reverse papers thresholding trading discriminate multiplying abu abu land mostafa mostafa outperform shorter shorter misclassification solves graded equivalently goodman dec formulate conjecture conjecture seek reports tight algebraic iff iff disadvantage exceed differentiating develops picking picking stores sees sees vii transforming confirm identically mistakes venkatesh codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword codeword floor demands comparator cyclic decoded registers decode decode decode degrades degrades moderately comprehensive collecting whilst checks simulates codewords codewords codewords codewords codewords codewords codewords codewords codewords codewords codewords codewords tran tran superiority bernoulli iterates heidelberg confirms seeking picks picks rationale devise circumvent orthogonality orthogonality orthogonality orthogonality blank poorer multiples blend mceliece mceliece mceliece rodney stabilizes flipping flipping decorrelating pseudoinverse pseudoinverse pseudoinverse pseudoinverse pseudoinverse pseudoinverse pseudoinverse hadamard hadamard hadamard hadamard hadamard hadamard hadamard hetero remembered shortening correlating correlating obtainable eee preferably preferably apriori sifier chernoff halfway fixes conjectured equidistant limiter decodes decodes jacques entail scl scl 
#@Chiueh_T,Goodman_R,
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#*network network model model model neural neural neural neural input input input input input input input input input input input input data data data function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure set set set set set set output output output output output number number number number number number number number number number number number number number number number number number number number results results results results information information information information information problem models performance space linear linear linear layer layer layer case case vector vector vector vector shown shown shown shown shown shown shown shown shown shown values values values values values values probability parameters parameters parameters parameters parameters parameters weight functions approach approach approach point large large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate analysis matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal inputs shows signal simple simple paper paper small size size net work random random random random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory representation representation representation representation representation representation representation representation representation section section fixed fixed fixed vectors vectors general general general general theory theory theory result university threshold variables variables research independent independent independent log defined defined defined defined sequence sequence sequence sequence constant constant constant constant constant standard computer computer distance distance distance distance node science science left presented map maximum maximum maximum components components outputs abstract references component component due ieee ieee important behavior behavior parallel search difference lower lower lower lower signals signals signals word word word center previous theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound type required binary binary binary binary conditions distributed fact fact fact length length length length length length correct correct correct correct correct errors errors errors errors errors errors errors errors errors errors total total total total human called called times dimension dimension study specific true provide provide provide define define compute compute rates location location related equal equal equal equal comparison comparison institute institute institute words words words words words words words words words version internal internal internal internal internal difficult exp sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences considered curve top stage bit bit bit bit bit bit bit bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity upper upper upper upper upper upper upper upper upper upper upper increase increase increase produce randomly bounds entropy entropy entropy entropy provided provided provided finally selected depends simply simply associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative achieved achieved achieved achieved increases increases increases increases limited limited close close inverse assumption assumption assumption proof assumed assumed supported easily easily probabilistic pairs pairs pairs pairs pairs hopfield hopfield hopfield hopfield hopfield hopfield hopfield functional unknown york increasing consistent structures operation operation language details stored stored stored stored stored stored stored stored bits bits bits bits bits bottom magnitude polynomial polynomial polynomial light advantage pair robust identical sense sense array array dimensions dimensions sufficient achieve sparse address address address address address address address address address address address address address address address address address address address definition definition definition locations locations locations locations locations locations locations locations locations locations bounded gate grant exists exists exists expression correctly deterministic column conclusion row row row greater greater greater exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential practice asymptotic physics physics largest largest largest drawn proportional proportional proportional turn assuming explicit explicit explicit derive written primary distinct distinct distinct recall explicitly coordinates linearly decreases national family dependence depending interpretation fraction fraction fraction fraction fraction fraction fraction fraction approximations reduces fitting false remains sufficiently sufficiently sufficiently foundation transactions transactions box coordinate coordinate formulation formulation formulation memories memories situation essentially graphs graphs interested lie contribution quantity usual usual usual generalize denker ill thresholds american american access access access access access essential difficulty exponentially exponentially fewer tech tech relationships proved affect notion notion circles adjusted expressions ith ith ith ith ith ith ith ith store store submitted submitted asymptotically asymptotically asymptotically asymptotically advanced slowly formula growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth fairly multiplication turns stanford stanford stanford stanford arc easier strictly style arise universal universal universal universal radius radius radius radius radius radius radius radius radius radius radius radius radius meaning nsf robustness reflects dots rep rep incoming hamming hamming hamming hamming coherent attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction begins extreme cor shifted accomplished fix fix fix arguments addresses addresses addresses addresses addresses addresses addresses addresses impossible grows grows grows grows grows adds overcome grow grow grow moment hope operates intuitively optimally optimally optimally combinatorial generalizes composition reliably reliably reliably falls surprising regarded regarded realization sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere correcting statement propagate thresholding unchanged unified specification specification fellowship equivalently encodes dec failed propagating corrected ease ibm march kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva 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probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters unit unit unit unit distribution approach approach pattern pattern large large large large large large large large local local local patterns patterns patterns analysis matrix inputs inputs inputs inputs form shows signal simple simple simple simple simple simple size size feature fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step process process cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random random random random random high high high memory memory response response response response response similar similar similar similar similar similar show show line rule rule general general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter average average average average average average average states term term note activity activity activity activity activity activity activity activity activity activity activity activity activity activity university threshold threshold threshold threshold threshold defined initial initial initial initial initial initial initial constant computer distance distance synaptic synaptic synaptic left left left phase phase phase phase phase phase phase phase phase phase phase phase phase frequency frequency sets maximum sample abstract properties references stochastic positive positive important propagation propagation introduction complex complex complex complex behavior behavior behavior behavior behavior stimulus statistical effect energy variable rules rules rules rules rules rules rules rules rules prior higher higher part cases cases cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type cortex cortex good long long long long long conditions conditions expected expected expected markov region length length probabilities probabilities finite finite finite finite finite finite finite simulations simulations simulations simulations resulting total simulation respect times times times potential feedback negative negative relative represented represented rates rates active active determined related related related distributions discrete cortical cortical steps comparison comparison institute represents responses responses difficult addition experiment curves transition transition transition transition transition transition transition transition transition stimuli effects conference upper speed speed speed speed basic increase increase give channel conditional levels lines actual selected inhibitory inhibitory inhibitory inhibitory depends describe describe describe denote excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable amount amount amount amount short role theoretical end end development development simulated smaller interesting ratio mode leads call window inhibition inhibition inhibition inhibition inhibition run run run run denotes membrane takes typical typical period period subject array array array array array array array array array array highly compare compare approximately diagonal interval storage amplitude lead studied setting pass demonstrate runs runs conclusion conclusion starting critical critical critical critical critical critical critical critical critical critical critical place greater depend faster faster faster temperature mechanisms mechanisms integration integration physics solid exist exist exist exist decrease iii iii manner configuration configuration areas suppose suppose suppose suppose suppose appears relation edges longer transitions transitions transitions transitions transitions transitions distinct category linearly infinite infinite infinite infinite infinite infinite infinite involves text unique scales consisting consisting equilibrium equilibrium independently independently dependence depending depending squares influence influence influence influence detailed constants key key key dashed dashed classical neighborhood neighborhood neighborhood neighborhood neighborhood intervals initially sufficiently fire fire fire fire fire fire fire fire discuss phys phys neighbors neighbors neighbors simplicity suitable maximal encoded tend tend refer soc soc kind prob symmetry play realistic quantization reach thresholds neurosci neurosci received received received illustrates subsequent operating receive receive receive cowan simpler stimulation stimulation stimulation stimulation stimulation american wiley wiley access experience steady steady steady preliminary successive biol plasticity authors decisions complicated analogous analogous necessarily configurations automata rev aspect quantities impulse impulse assumes message pyramidal answer answer answer briefly reasons ring acknowledgement hippocampal qualitative qualitative preceding preceding mechanics transient transient cohen share sharp limiting display display display drift appropriately refractory refractory proceed rigid reaching reaching reaching arranged spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous cellular cellular bower satisfying analogy proceeds odd settings modifications exceeds arrays arrays arrays carry wilson wilson filled fires fires fires fires fires equals induce conjunction bad consequences hippocampus stimulated ends epsp speeds integers fired fired truncated constitute alternating alternating markovian die die die die die die die die die conjecture ease classic examining auxiliary rectangular intuition alternate elementary relate ultimately ultimately flip exceed records sketch harder barrier figs intracellular bring bring parametrized travel 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#@Chover_J,
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weights weights weights weights layer layer layer case case order order order shown shown shown systems systems systems values values values noise noise weight functions functions functions functions neurons neurons neurons neurons neurons approach approach approach approach pattern pattern pattern point point image image image single single single processing processing processing processing processing processing processing processing processing processing processing control large large large large large local local neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate patterns patterns inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows shows shows shows signal signal signal signal signal signal simple simple simple small small size size size feature feature feature work work work work fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step field features features features current current current current current current current current current current current current current current current current structure high high high memory memory memory memory memory memory memory memory memory memory memory memory response response response similar similar similar similar architecture architecture show equation line real real real real average states states term term term note note note note activity activity activity dimensional dimensional result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold research research dynamics constant estimate estimate computer terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node science science science science present low low low low low low low low low low low low low low low low low nodes frequency frequency frequency temporal temporal temporal maximum range range range range range range range range press press press basis basis basis basis nonlinear nonlinear outputs outputs outputs outputs outputs outputs continuous abstract applied applied applied applied back analog properties references due ieee ieee positive important important important propagation propagation introduction action action action action circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior effect effect dynamic parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel tion tion change complexity complexity complexity spatial lower lower signals part part firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing multiple multiple good spike long long long equations equations chip chip chip chip region region region region proposed observed observed observed observed forward forward scale scale scale scale resulting resulting simulation human times times times elements elements elements elements elements elements elements elements elements means means means factor potential potential potential potential potential potential potential natural obtain vol artificial artificial artificial artificial artificial compared provide provide rates proc proc perform perform active active determined related related related related brain brain brain brain brain brain brain brain equal power power power power power power power power power power power power power power power approaches approaches mit voltage voltage voltage voltage voltage voltage voltage voltage voltage comparison connection modeling institute internal represents represents bias bias bias addition addition addition cambridge computing equivalent equivalent equivalent equivalent equivalent experiment environment directly hinton additional view transition transition stage stage stage vision vision basic basic increase produce produce channel channel channel coding coding coding coding coding levels levels area processes nature inhibitory inhibitory inhibitory biological biological achieved achieved measured discussion discussion discussion increases increases group excitatory excitatory excitatory circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits short supported role role require require main vlsi ability easily easily rumelhart development typically smaller smaller hopfield hopfield hopfield hopfield hopfield reduced technology technology technology technology technology transfer transfer transfer interesting interesting interesting ratio character character character character york york york mode call filters filters pre pre inhibition inhibition stored stored stored stored stored added neuronal architectures architectures architectures discussed recent advantage element element element typical typical typical lateral lateral lateral lateral include period subject sense sejnowski sejnowski sejnowski array array recently dimensions highly conventional works achieve achieve rl rl storage storage storage storage increased grant amplitude amplitude constructed parts parts intensity intensity concept studied scaling occur digital digital wide spikes alternative locally hybrid generally hardware hardware hardware hardware hardware flow strength strength central integration integration integration integration presence physics physics physics physics physics physics external reduction characteristics characteristics demonstrated solid pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse plane plane connectivity connectivity connectivity connectivity acknowledgements pro pro construct produces longer optical optical optical optical optical optical optical optical optical optical generating generating laboratory label modeled linearly linearly linearly electrical electrical unique consisting interaction integrated integrated adding adding potentials potentials letters letters letters dependence depending correlated codes similarly discrimination processor processor processor processor slow additive generation generation generation visible advantages coupling coupling coupling coupling coupling coupling silicon silicon silicon silicon currents currents currents currents discuss coupled phys phys phys major differ modification mcclelland literature excitation excitation quickly contained showing anderson conductance conductance conductance conductance conductance conductance conductance dis sci device device device device device device device play realistic thresholds chips chips chips chips chips processors principles principles load load trains employed employed employed simpler remain stimulation american requirements requirements requirements requirements exhibit experience circuitry mead limitations rise links terminal terminal terminal biol int int int possibility transistor transistor transistor referred comparable analogous math 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operate switch pittsburgh pittsburgh cal tank tank tank suited substantial physiol summed extreme contribute gap picture cybern sensing sensing accomplished temporally refractory refractory count eliminate extending spontaneous spontaneous spontaneous khz fan fan fan interconnection interconnection resistance resistance height contract biased biased resulted viewpoint occurring bands receiver receiver receiver receiver capacitor arrays arrays arrays planar planar planar days natl date elimination passive published periods negligible negligible regard injection injection injection injection injection injection injection injection schwartz schwartz schwartz sim lawrence interconnections yang similarities waves waves arrive sustained proximity erlbaum impact considerations considerations lett ignore tures switches temperatures constitute shepard sig graded graded graded planes focal focal opposed benefits transmitted terminals terminals adopt utilize utilize drain drain avoided 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#@Coon_D,Perera_A,
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class optimal inputs inputs simple paper small small net work work work work task fig points points points points points points points points points points field field field field field field field field field process structure random random high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar architecture architecture architecture show equation equation equation equation section section fixed fixed fixed fixed fixed fixed fixed vectors vectors general general parameter real states theory theory theory theory gradient note note note note note note dimensional result university defined defined initial constant terms terms terms terms distance distance distance distance connections synaptic science science direction presented presented present low motion range range range range position components components nonlinear nonlinear nonlinear outputs continuous continuous continuous continuous continuous abstract computational convergence convergence convergence convergence density density density density density density properties properties properties properties properties references references component component component ieee positive positive positive procedure procedure procedure procedure procedure circuit behavior change energy energy energy difference complexity assume assume assume measure chosen part part center bound type long long equations equations errors errors finite finite finite finite minimum resulting resulting tasks total sum elements elements means potential potential potential potential potential potential potential potential potential potential made made natural natural global negative original vol vol artificial artificial desired desired desired desired desired define define objects proc proc location location perform discrete discrete discrete discrete discrete discrete discrete equal mit comparison fields fields update descent descent institute implementation implementation implementation implementation version version version individual joint layers delay delay delay addition ai ai ai cambridge equivalent equivalent additional design design trajectory capacity capacity capacity capacity capacity capacity speed speed increase give bounds product provided provided provided finally iteration nature nature associative associative associative associative associative normal arbitrary arbitrary denote denote fast limited limited limited complete stable surface surface proof proof proof short short effective implemented require main main instance easily typically hopfield hopfield hopfield hopfield dynamical dynamical block projection operation operation details details stored normalized choose choose description property property property element movement movement include include quadratic sense sense interest trans trans locations bounded organization storage storage storage storage invariant suggests boundary starting minimal trajectories neighbor clear propose physics characteristics radial start minima minima minima minima minima minima minima force force acknowledgements suppose appears construct construct sequential describes laboratory laboratory distinct distinct metric explicitly coordinates physical physical electrical involves involves unique adding adding springer shift potentials yield independently stationary stationary stationary interpretation detailed operations updated updated suggested converges sign sign sign diagram add boundaries closed intermediate intermediate intermediate calculate construction euclidean kohonen expect coordinate coordinate memories memories memories memories memories memories memories memories domains holds phys phys discussions simplicity reason importance uniformly included composed composed refer refer induced induced induced interpreted lie lie content sci relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation satisfies satisfies decreasing oriented simpler unlike unlike unlike carried american essential requirements requirements exhibit difficulty updating varied issues behaviour behaviour rise applicable comparable surfaces closest closest closest extremely rev rev changed separated separated shapes initialized extent simplest submitted submitted submitted explain brown directed analyzed guaranteed guaranteed guaranteed defining reasons inside inside inside inside turns turns turns stanford stanford sites strictly desirable ion ion ion ion ion acad radius continuously ity ity requirement requirement switch berlin synthesis collective enables replace hamming conclude conclude attraction attraction attraction attraction implements proofs saddle cooper cooper nat rotations rigid overcome held abilities exploit intuitively carry natl spurious spurious guarantees expanded regard heart sphere sphere advance surprisingly creating reader reader arrive probe properly inf inf characterization rigorous minus 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systems weight weight functions functions functions functions functions functions unit unit unit unit recognition pattern pattern pattern point single processing processing large large large large large patterns patterns patterns patterns inputs inputs form form shows signal paper examples examples small small small size work methods step process process process similar architecture architecture architecture architecture architecture architecture show equation equation general general general general general general generalization generalization real real average note computation log log log found dynamics initial initial table estimate estimate estimate estimate connections connections connections science present present present range range press learn outputs continuous abstract applied back properties properties references references ieee important propagation context complex hand statistical dynamic dynamic assume previous type required required required required required required required expected make fact proposed proposed observed total sum times means factor factor applications original active connected discrete discrete larger connection connection connection proceedings proceedings proceedings proceedings institute version consists code difficult addition directly directly additional bit conference significant significant approximate basic con weighted entropy entropy entropy entropy entropy actual actual simply simply simply complete complete complete amount amount amount implemented implemented implemented require easily including typically smaller smaller smaller needed needed needed needed hopfield reduced fully technology testing call call numbers making bits bits bits bits bits bits bits bits bits depth magnitude idea discussed exact exact ensemble ensemble ensemble ensemble ensemble ensemble takes typical apply identical engineering compare trans definition definition definition definition expression lead correctly white occurs half conclusion critical place valued depend numerical physics assuming exist configuration question suppose suppose suppose relation derive derive ways estimating describes confidence implement implement remaining remaining remaining easy unique implies versus boolean boolean john john john communication restricted fraction completely completely calculation remains calculate precision precision precision expect building bell recognize determines automatic simplicity efficiency importance importance maximal score score classify satisfy comp usual simplified generalize denker denker denker denker principles situations powerful powerful american create create requirements exhibit ideas combine reliable reliable comparable cover cover possibly possibly versions formal explored expressions capabilities capabilities baum baum considerable commonly laboratories involve lowest argument argument items understood item item item solla adjustable continuously reliability calculating calculating howard measuring richard richard sophisticated june realized contribute consistently cooper forming bin bin impossible nonzero generality generality adjusting proceeds replica viewpoint viewpoint settings settings settings meaningful meaningful regard schwartz consequences searching jackel originally lawrence bins bins bins bins bins bins bins arrive agree abu abu geometrical numerous logarithm pointed generalizations imagine valiant valiant winnow eric adjustment crossover thermodynamic concentrate emphasized siam truth drops durbin differently ble consuming agrees designs water jersey ave reflecting polarity venkatesh venkatesh holmdel suffice thing ben ben elec monotone wires formulas daniel objectives eta psaltis psaltis ver ities nections prohibitively prohibitively disagree permuted ordinate ordinate throw throw temporary ana devise abscissa abscissa expects comput exceptions private replicas replicas bucket badly leon genera arose xve memorize memorize flipped sara unavailable wittner wittner 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#@Denker_J,Wittner_B,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning model model model model model model model model model model model model model model neural neural neural neural input input data function function function function function function figure figure figure time time time time time time time time time time time time set networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm number number number number number number number number number number number system system system system system system system system system system system state state state state state state state state state state state state state state state state results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem models models models models performance performance performance performance based based based space space space space space space space space space space space weights linear case order order shown systems systems systems systems values values values values values values probability parameters noise noise noise noise noise weight neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution approach pattern single single single single processing large large large large large local local local local local local local local local local analysis optimal shows shows signal algorithms simple simple paper paper size size size size size size size net net net net net work task methods methods points points field field field field field field field field field field field field field field field field field field current problems problems problems problems problems problems problems problems random random random random high high high high high similar similar similar architecture architecture architecture show show show show show show equation equation equation equation equation equation rule rule rule rule rule rule images parameter real approximation approximation approximation approximation approximation average average average average average average average average average average average average average average average average states states states states states states states states states states states states states states states states states states states states theory gradient gradient gradient gradient gradient gradient gradient gradient term term term term term term term term experiments result result university variables variables computation solution solution solution solution solution solution solution solution solution research research research independent independent independent defined found found initial initial initial constant constant table table computer computer distance distance connections science direction direction direction direction direction direction presented low low low low low low machine machine machine machine machine machine machine machine machine machine machine motion range range components components components continuous continuous continuous abstract find find find find find find find find computational computational computational computational convergence convergence convergence properties references component stochastic stochastic stochastic due ieee ieee positive important important decision decision decision introduction hand circuit circuit behavior behavior behavior effect effect effect effect parallel parallel search search search search search search search search search 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application perform perform perform determined determined constraints constraints constraints constraints constraints constraints constraints constraints connected connected distributions gain gain gain gain gain discrete discrete discrete discrete equal approaches mit larger contrast connection update descent descent descent descent nets nets nets nets nets nets nets nets nets nets morgan proceedings report institute department implementation technique consists consists individual connectionist connectionist final scheme addition addition graph ai cambridge domain experiment hinton additional solutions solutions solutions solutions design limit effects determine efficient requires choice approximate free speed speed speed give give con weighted weighted randomly types lines lines actual evidence evidence inhibitory inhibitory depends sampling sampling constraint constraint constraint constraint constraint simply biological increases close inverse inverse corresponds corresponds complete excitatory stable circuits finding finding implemented shape supported ability ability ability ability easily degree makes noisy kaufmann probabilistic pairs smaller smaller hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield reduced transfer programming programming ratio trials trials empirical principal representing representing direct direct making inhibition depth magnitude idea run run run light improved advantage advantage property pair ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble takes takes takes takes reported reported reported reported practical introduced identical identical identical identical machines machines machines machines machines machines machines machines machines machines machines machines machines sejnowski sufficient highly varying conventional conventional conventional calculated works tuning axis axis tions converge differential locations locations symmetric modified sensitive entire increased grant derivative derivative derivative move move move move deterministic deterministic deterministic generally generally generally column column column demonstrate half conclusion starting starting place minimal row row row row valued depend interactions differences numerical designed clear exponential faster faster faster temperature temperature temperature temperature temperature temperature temperature temperature suggest taking physics intelligence minimizing user exist decrease decrease decrease minima minima minima minima minima minima minima minima minima minima minima minima minima minima program force acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann produces solving laboratory explicitly coordinates infinite infinite infinite infinite physical involves consisting equilibrium equilibrium equilibrium equilibrium equilibrium quality select decreases decreases decreases choosing national depending communication communication viewed updated completely similarly constants calculation calculation slow spaces combining add valid valid valid valid valid valid valid valid valid valid valid valid intermediate initially distances calculate assigned advantages transactions david existing thesis sciences determines automatic prove holds neighbors neighbors reason columns columns determining determining divided wij wij wij tend quickly repeated allowing allowing heuristic heuristic heuristic link link anderson anderson lie satisfy gibbs list vary relaxation absence highest leading reach automatically moves moves illustrates neighboring decreasing minimized minimized remain remain command american poor essential requirements exhibit updating rise giving tech links links links links links investigated decisions comparable proper understand cognition analogous equally thought thought thought noted separated mapped art ith phd optimum brown advanced rows stop guaranteed guaranteed guaranteed guaranteed explanation easier easier strictly division laboratories consequence potentially beginning gradually gradually lowest lowest cybernetics nsf mellon summation percent carnegie tional tional simulate peter continuously rep reliability calculating gains measuring reaches monotonic monotonic monotonic proven tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank tank collective collective geman geman eventually simultaneous wesley extreme extreme trade gap gap gap gap addison writing guarantee guarantee fix approximates jth impossible naval flexibility smolensky proceed reaching air adds adds numerically convenient convenient stronger satisfying proceeds city city city city imposed resistance contract contract abilities resulted serves mark reasoning monotonically monotonically monotonically intuitively responsible combinatorial heuristics repeat heavy irregular paul negligible vertices infinity infinity infinity infinity searching searching searching chooses peterson peterson april offer shortest shortest shortest vertex theoretically probe probe probe probe probe informative informative steepest steepest hypercube projects designing lett receiving explorations onr escape escape escape escape escape temperatures temperatures largely microstructure fellowship emergent july adopt adopt regularity acceptable ease ease ease tradeoff personal personal tendency affects affects visited pami graduate interacting compatible books academy harder refinement places indication programmed refined intensive september aaai behaves topography topography picking tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour satisfaction satisfaction restoration sees sees interior lation august corners traveling traveling traveling traveling traveling stochastically subjective hop hop hop hop hop hop hop hop hop hop hop hop tsp imple dominates suffices loosely identically agency agency emerges inefficient explanations arpa salesman salesman salesman salesman salesman binomial binomial edition bradford approached defense ensuring monitored monitored proceeding deciding deciding col sponsored moderately ted ted spent upward settles settles deeper putting imposing constituents constituents constituents rigorously jumps jumps wright wright decides adopting mented steepness steepness behaved divides tebelskis tours tours tours tours tours tours tours tours tours tours poorer cities cities cities cities cities cities comers comers subscripts depict discriminability designer designer scripts probing probing probing probing marroquin turner turner joe nicely eet mcc wrap patterson stochasticity relearning chines eventual returning conven probes probes probes probes spends wasteful chances tending barriers deepest deepest escaping waste afb uphill uphill dod probed probed probed probed tln tln transac speeded debugging debugging sigrnoidal superposed encountering invariably wijsj aeronautical aeronautical erik isj avionics lunch 
#@Derthick_M,Tebelskis_J,
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural data function function function function figure figure figure time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks number number number number number number number number number number number number number number number number number system error error state state state state state state state state results units information information information information information information information information problem problem problem problem problem problem hidden space linear linear linear linear linear layer case case case case case vector vector vector vector vector vector vector vector vector vector vector order order order order order order order order order order order order order order order order order order order order shown shown shown shown systems systems values values values probability neurons neurons neurons neurons neurons neurons neurons neurons neurons pattern point processing large large large local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form shows shows algorithms simple paper paper paper paper size methods fig fig step points points points points points points field features trained structure problems problems high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory show show show section section fixed fixed fixed fixed fixed fixed rule rule rule rule vectors vectors vectors vectors vectors general generalization generalization average states states states states states states states states states states states obtained dimensional computation computation solution solution solution solution solution solution solution independent independent defined defined sequence sequence dynamics dynamics dynamics dynamics dynamics initial initial initial computer terms terms distance distance connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left presented presented present present present temporal temporal temporal temporal sets sets maximum components components components sample abstract back properties properties references references references procedure procedure procedure important decision propagation introduction introduction complex parallel recurrent recurrent recurrent recurrent energy complexity complexity rules rules rules rules rules chosen chosen higher previous type required multiple multiple binary long expected make proposed proposed proposed errors forward forward simulations simulations simulations simulations tasks total computed computed computed multi multi performed performed performed performed times potential potential potential potential potential potential potential potential dimension dimension dimension dimension made natural natural feedback applications knowledge represented compared desired provide define compute proc perform determined related connected equal steps larger proceedings proceedings institute synapses consists consists consists layers addition addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences considered computing computing additional solutions solutions solutions curves curves design design design design san bit conference capacity capacity capacity capacity capacity determine efficient full requires choice basic increase increase increase condition condition randomly randomly lines lines provided provided finally finally finally nature biological associative associative associative associative associative associative increases increases increases increases arbitrary limited corresponds stable stable stable stable amount nearest require eds eds ability instance easily hopfield hopfield hopfield account dynamical dynamical dynamical coefficients coefficients coefficients coefficients coefficients fully interesting projection projection projection increasing mode operation leads leads details making stored stored stored stored stored stored stored stored stored stored stored exact introduced period subset subset sufficient sufficient previously conventional solve yields yields organization improvement storage storage storage storage storage storage storage storage storage storage storage storage storage storage exists expression lead occur matrices alternative feed feed deterministic occurs column column conclusion interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions numerical designed propose propose presence physics min iii averaged introduce introduce denoted attractor suppose relation relation relation relation optical transitions transitions transitions transitions recall recall recall recall recall linearly linearly linearly interaction springer springer quality implies letters decreases family correlated codes detailed lee lee static static understanding allowed reduces purpose iterative valid figures usa usa formulation retrieval retrieval retrieval retrieval retrieval retrieval subspace memories extension plotted phys phys phys phys tests tests columns columns columns columns straightforward straightforward suitable suitable identity orthogonal reached reached repeated repeated allowing symmetry classify sci sci write giles denker reach reach illustrates subsequent operating satisfies presents origin remain carried diego american requirements exhibit exhibit relations limitations limitations limitations behaviour biol parity analytically structured proper rev rev rev illustrate perfect perfect implementations rank prototype prototype prototype prototype prototype prototype quantities bifurcation der initialized store store store consist extent submitted mentioned separable growth derivation derivation guaranteed capabilities briefly handle processed purposes sgn products involve acad arises computers addressed improvements limits items led span prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes berlin reaches reaches extensions hamming attraction attraction extreme cybern perfectly discover convenient convenient overcome synchronous exceeds enhanced presentations presentations natl spurious meaningful published published performances sompolinsky governed governed von widrow infinity candidates storing storing storing storing park subsequently papers lett lett lett lett lett lett baldi severe unable unable unable basically guyon guyon guyon guyon guyon guyon forced pieces pieces pieces regularity acceptable opper malsburg flat basins basins avoided avoided stands publication publication exclusive deep evolve elementary distant picked landscape paris paris conversely cij cij cij cij cij cij cij cij cij spanned france france preprint investigations dramatic bienenstock virtually hoc keeler venkatesh ref ref ref ref ref lying optics retrieved degenerate autoassociative autoassociative autoassociative autoassociative autoassociative autoassociative pin pin devoted hoff gardner noticed linearities derivations derivations preventing psaltis saved des nadal nadal nadal europhys europhys europhys initializing fogelman circumvent cog succession icnn maxwell maxwell proportionally 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methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points features level level cell cell cell cell cell cell cell cell cell high high high high high high memory memory similar similar similar architecture equation fixed line rule parameter average average average obtained obtained experiments activity activity activity activity dimensional result university computation found found found dynamics initial table table estimate standard standard standard standard standard standard standard standard standard standard computer synaptic synaptic synaptic synaptic present present present present present phase phase low low frequency sets maximum maximum maximum maximum maximum maximum maximum range range range range range press press position position nonlinear nonlinear nonlinear abstract applied applied properties properties likelihood references due positive positive procedure procedure important important important introduction action stimulus generated change difference difference difference difference difference difference difference difference difference difference difference spatial spatial classifier classifier signals signals higher cases firing firing type type type type type type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike distributed equations equations equations region proposed correlation correct forward forward forward forward classes total regression regression multi multi multi sum sum called elements elements regions means means means made made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback study study study study study study filter negative negative negative negative vol artificial specific true series series series provide proc proc proc proc location experimental related related connected distributions gain gain gain gain gain gain gain gain gain gain gain cortical cortical cortical cortical cortical brain brain equal power power mit voltage voltage comparison comparison contrast dependent nets nets proceedings report institute technique exp layers delay considered environment curve curve curve curve curve curve curve view curves top stage determine significant significant significant significant significant significant significant statistics estimated increase produce channel channel derived conditional conditional levels types product selected evidence evidence inhibitory inhibitory inhibitory inhibitory inhibitory depends measured discussion group group group group group group group group group group group tested close excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory surface surface shape theoretical main main end degree makes underlying hopfield hopfield hopfield hopfield mechanism mechanism structures structures structures operation representing representing representing direct window inhibition inhibition stored normalized normalized normalized normalized normalized normalized normalized depth idea population discussed discussed pair takes reported reported lateral apply period side side side array interest interest previously previously approximately calculated correspond studies studies background background channels amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude exists studied studied studied occur occur occur digital deviation deviation deviation deviation deviation deviation deviation deviation deviation deviation wide spikes spikes derivative derivative derivative derivative derivative locally loop loop loop loop loop loop occurs pass strength greater greater assumptions sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid physics cycle sigmoidal sigmoidal california pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse turn turn assuming exist exist exist relationship relationship relationship manner groups groups groups groups groups groups groups groups derive derive written describes label changing changing student coordinates electrical electrical remaining interaction interaction interaction mutual mutual events versus versus potentials potentials focus expressed expressed earlier earlier earlier measurements intervals generation filtering filtering eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg topology coupling recorded recorded recorded recorded existing thesis usa currents activated regular aspects identified efficiency suitable maximal maximal maximal maximal maximal maximal effectively oscillatory attractors detect detect score characteristic kind repeated procedures classify sci gray gray built comp wave wave wave wave wave wave wave neurosci overlapping rat rat rat modelling stimulation carried carried american layered steady mass existence scalar investigated biol biol scores statistically examined transmission rev rank olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory nervous nervous academic pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal generates motivated motivated animal animal animal burst burst burst derivation variances analyzed phenomena slope slope slope slope slope slope slope slope slope nonlinearity drive berkeley filtered filtered desirable pulses pulses pulses pulses mathematics acad grossberg grossberg grossberg beginning axons res res recording recording recording recording recording geometry geometry cybernetics cybernetics populations freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman substantially embedded recordings slower maxima price rely occurrence asymmetric physiol begins median median baird baird traces traces traces traces lot lot phenomenon room college animals animals animals animals animals labelled labelled labelled count count neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol fits khz bower bower analogy alpha chemical loops obtaining implications wilson nonparametric natl ranging dendrites respective enhance bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb counting similarities similarities similarities waves waves waves express bursts bursts bursts smoothed smoothed record verification passing passing extensively extensively extensively receiving thresholding dividing counts fitted fitted fitted fitted yielded sine session obtains ideally amplitudes amplitudes chapter affects sinusoidal electrode electrode electrode mutually mutually verified verified home packets interneuron file generators compatible electrodes electrodes electrodes electrodes electrodes ultimately relates relates paris siam investigations slopes tract tract examination correlate shallow coming sigmoids sigmoids sigmoids sessions rats rats rats stimulating bursting twenty justification agrees inhibit routines medicine anatomy anatomy conversion conversion conversion conversion tip physiologically sided impedance impedance impedance neurol neurol neurol odors digitized convention permanent senses materials lags lags terminates reviewed aip aip aip granule granule granule granule granule granule granule granule files files prominent shortly inform physica limb limb firings eeckman eeckman apical plotting excite attentive ample entered week awake awake awake awake des concurrently displaced displaced scratch clin corresponded corresponded abstr disk shepherd shepherd shepherd monosynaptic monosynaptic laterally confident functioning feel concurrent concurrent frank haberly haberly haberly haberly pad steep mammals rabbit neurophys micron 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based space space space linear linear linear linear linear linear layer layer layer layer layer case case case case case case case case order order shown shown shown shown systems systems systems systems systems parameters parameters parameters functions functions unit distribution distribution distribution recognition approach approach approach pattern point point single single single processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control local local local local local local local local local local local neuron neuron neuron neuron neuron rate test optimal optimal optimal optimal inputs inputs shows shows shows shows simple simple simple simple simple paper paper paper paper work work work work work work task methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig 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direction presented phase low range press learn basis basis abstract find find references due procedure procedure important important important introduction action action action action action action action action action complex complex complex complex complex hand stimulus dynamic dynamic parallel parallel parallel parallel search tion tion change change energy difference lower lower lower lower lower lower lower lower signals learned learned chosen higher higher higher higher higher higher higher higher part part cases cases type type required required required cortex cortex good good good long long long long long conditions conditions conditions conditions distributed equations make make techniques region proposed simulations simulations ing ing ing tasks tasks tasks tasks tasks tasks total simulation simulation simulation simulation human human human human human respect performed called elements elements elements elements elements elements elements elements elements elements means means means means optimization dimension orientation global applications study vol vol vol application application application application series rates rates perform perform active active experimental goal goal goal goal goal goal goal connected connected motor motor motor motor motor cortical cortical cortical cortical brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain approaches mit steps steps steps comparison comparison larger connection connection nets proceedings report institute implementation implementation implementation implementation consists individual advances responses responses difficult difficult difficult layers layers layers scheme considered considered considered cambridge environment environment environment environment environment directly solutions design stage stimuli stimuli stimuli effects conference upper upper upper upper upper upper full requires requires requires world basic basic basic 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reduced account account unknown testing testing structures structures structures structures structures structures structures structures structures principle representing representing details details details call numbers pre pre direct making stored bottom bottom bottom idea idea minimize run run run run description description perceptron perceptron neuronal neuronal neuronal neuronal neuronal discussed discussed discussed discussed property property separate takes takes takes element element element element element element similarity introduced strategy strategy strategy strategy subject machines hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical sense sense sense sense engineering highly highly compare conventional subjects works module module module axis tions differential trans evaluation organization organization organization organization organization storage storage storage storage storage exists exists parts parts lead concept concept concept concept studied studied extended spikes locally locally move move loop loop loop half half starting starting reduce reduce differences clear faster sound physics physics physics drawn movements iii iii iii iii iii iii iii iii question question question question question acknowledgements reference reference explicit appears sequential generating laboratory vertical mathematical mathematical mathematical explicitly explicitly averaging physical electrical unique predictive predictive predictive predictive predictive predictive predictive predictive minimization springer springer quality formation formation formation influence detailed detailed detailed detailed controlled organizing organizing organizing evolution evolution measurements measurements measurements sec sec sec sec sec roughly roughly penalty closed sufficiently kohonen kohonen advantages coupling avoid building building building building existing figures thesis coordinate usa formulation weighting memories memories memories memories extension illustrated characterized structural planning planning columns columns aspects extra divided driven driven included included build build build efficiently schemes projections situation situation situation situation situation situation reached reached reached reached reached composed verlag verlag verlag verlag kind interpreted interpreted oscillations criteria strategies strategies device hold built built built built built localization simplified reach reach overlapping overlapping software load modelling modelling modelling situations situations situations presents remain american transformed requirements requirements put detail detail association behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour helpful ideas mappings investigated biol biol possibility possibility authors authors working complicated hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy fundamental fundamental math changed changed thought der der formal assumes nervous nervous store store pyramidal consist generates amari amari amari amari extent motivated finds plant plant defines devices mentioned mentioned indicating ment ment theoretic agreement biology biology analytical handle handle starts reasons reasons reasons reasons ring ring organized located located nucleus nucleus nucleus cut cut cut separately describing beginning implicit lowest cybernetics cybernetics recognizing meaning addressed fluctuations mechanics questions questions questions understood understood pure led pseudo pseudo pseudo generic capability simulate effort effort posed frequently variant psychological psychological commands commands span span controllers controllers controllers controllers controllers controllers controllers controllers controllers berlin berlin aim reaches proven qualitatively germany germany germany germany germany logical kinds findings specifies specifies univ picture picture identifying arguments animals proceed inspired inspired inspired extending ments chance chemical intelligent loops loops loops loops loops responsible responsible optimally adequate adequate symposium degradation selects selects filled meaningful meaningful meaningful meaningful evaluations excellent cerebellar cerebellar cerebellar edelman studying cmac cmac cmac assembly cerebral cerebral cerebral layout environmental horizon horizon considerations considerations border characterization generalizing generalizing tures executed empty empty mind microstructure sch outline kinematics accept achieving job abstraction stem chapter chapter chapter chapter chapter chapter chapter chapter chapter hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies tor simulating simulating simulating suppressed guess realize leg acting care goals goals goals goals goals elementary elementary disadvantage met projecting complementary meta manipulator refinement discusses assemblies assemblies assemblies tively supports investigations investigations investigations investigations ation tissue tissue tissue tissue struc mini mini answers answers answers coordination coordination coordination coordination coordination coordination coordination coordination coordination syn mcculloch mcculloch opti remarks handling ate pitts pitts institut satisfactory vii assistance assistance trainable heavily heavily water ers ers ers ers ers ers ers hundreds albus albus albus albus albus albus albus suffices suppress char horizontally disturbances practically sen partly assessment assessment assessment sparsely automation repetition intact cooperation cooperation cooperation cooperation cooperation cooperation cooperation consumption denmark quick articulation articulation meant meant shaping doubling maryland sur unnecessary addi instant instant instant jack cations appli substructures substructures substructures substructures substructures yon yon walking rela topics columnar columnar organisation proce huber suitably subtasks subtasks fukushima fukushima puter ele excluding switzerland untrained damaged structuring thinking thinking calculus rosenblatt rosenblatt motivates biophys fulfilled environ bull standing comprise necessity historical behavioural behavioural wanted mary legs wishes multivariable multivariable multivariable behav expects expects superfluous possi groupings occuring hierarchically intervention intervention intervention reactions reactions complication abstractions ams ams ams ams ams ams zation checking congress requested para ric coordinated lengthy cornell till till als subunits frg frg living living memorization memorization byte crosstalk jumping mountcastle mountcastle mountcastle mountcastle mountcastle atom packages asme eventual perceiving restore jobs descrip stretching stretching cylindrical coordi coordi mized analy shaw shaw situ situ ool indications indications indications mentally printing imitation creatures creatures creatures 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net work task points points field field field field field field field field field field field field field field features features features process process problems high memory response response response response representation representation representation vectors general general general generalization parameter real theory theory theory theory gradient gradient gradient gradient gradient gradient gradient obtained term note note note experiments experiments experiments dimensional computation defined found target target target standard computer computer terms terms terms terms distance distance distance connections left direction direction direction direction direction presented present present present low sets maximum press position basis basis basis abstract applied back analog properties references ieee ieee positive positive procedure procedure procedure important important adaptive decision decision decision decision decision decision decision context introduction action action action complex circuit behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical parallel parallel parallel cost cost cost cost cost cost cost change energy representations representations representations representations representations representations part center center cases cases type type type required good conditions conditions represent represent distributed expected expected equations make techniques techniques observed simulations resulting resulting resulting classes simulation simulation human respect sum performed elements mapping means optimization optimization potential potential potential potential potential global applications applications applications applications applications applications applications applications applications applications knowledge negative negative original vol vol vol artificial relative relative relative specific specific specific represented represented application series provide provide compute compute active determined goal goal related approaches mit fields fields fields fields fields fields fields fields update update update modeling modeling modeling modeling modeling modeling modeling report report institute implementation implementation implementation version technique individual responses responses responses responses responses responses addition maps considered considered equivalent environment environment environment environment additional view design design design design design trajectory stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects effects effects effects efficient efficient full speed basic basic produce coding clustering clustering clustering clustering clustering developed criterion area lines path path path path path path path provided provided provided provided finally processes processes processes processes selected nature simply biological associative associative describe denote inverse surface common effective effective adaptation square ability instance cluster future future future development development development development including objective objective objective objective objective objective simulated typically combination combination technology block interesting projection york york special principle operation squared representing making making making normalized bottom bottom depth idea idea idea produced produced light architectures advantage advantage include include subject identical machines cognitive engineering engineering engineering interest interest sufficient highly varying previously previously unsupervised observations axis smooth modified observation interval lead invariant invariant occur occur derivative predicted predicted operator interactions interactions interactions interactions differences designed constrained constrained suggest taking taking presence physics physics physics external characteristics drawn sigmoidal proportional proportional intelligence turn variety variety exist plane manner force force force force force force base attractor acknowledgements areas index index optical laboratory laboratory changing changing changing changing modeled modeled modeled modeled physical text interaction interaction interaction interaction interaction interaction interaction minimization minimization minimization john yield yield viewed detailed detailed transform operations evolution evolution modulation understanding similarly suggested updates past past sign barto barto performing performing combining boundaries tracking distances filtering assigned transactions building building combinations combinations coordinate formulation formulation formulation color instances sciences automatic automatic prove activated variations discussions planning planning planning planning reason determining straightforward aspects aspects aspects extra closely importance importance uniformly modification paths paths paths driven driven attractors attractors attractors attractors literature computations invariance situation situation tend interpreted follow follow follow follow strategies built simplified dot providing providing reach automatically processors processors intrinsic situations situations situations law law american american wiley experience updating varied varied integral game divergence divergence mass mass mass mass scalar scalar scalar scalar scalar scalar scalar scalar fourier respond history ideas rest behavioral behavioral behavioral mappings mappings investigated possibility relationships workshop cognition momentum analogous analogous analogous concepts editor adapt psychology eyes implementations thought explored explain electronic chaotic synthetic synthetic charge languages site advanced advanced sensors analyzed defining unstable capabilities caused briefly inside purposes ring ring sites sites sites sites forces forces forces forces forces forces forces forces forces laboratories scientific projected projected implicit mechanics mechanics virtual composite evaluating evaluating applies red completion formulated dots dots dots dots psychological operate operate exhibits synthesis resource green green electric phenomenon newton indices lagrange ratios appropriately appropriately dynamically dynamically flexibility outcome robotics eliminated rational air air air air air allocation satisfying simplify analogy chemical imposed intelligent resistance grow methodology affected guide preparation intuitive published utilized utilized utilized utilized utilized ranging programs encountered induce overview consequences consequences enable modelled insight environmental environmental environmental arrows arrows steepest observer sons exploiting implicitly valuable discovered alternatively generalizing fly fly fly fly mechanical trading outlined fusion dramatically grating leaving outline rigorous annals aircraft aircraft transmitted reaction reaction obstacles magnetic magnetic year blue acceleration acceleration laplacian clustered scenario scenario scenario visualization acting acting acting publication modifying deep evolve thick parallelism academy integrals nonetheless sheet sheet superposition superposition sam sam sam sam sam inversely particle particle particle exchange book flight flight flight flight flight exhibited exhibited bring molecules differing supporting completed coordination utilizing circumstances lecture heading laws laws simplification traveling traveling house hypothesized attempting drawing devised meeting automation automation obey scenarios scenarios approaching amenable presently presently experienced experienced ready profit addressing tags carrying watanabe watanabe files manual enabling unexpected unexpected zone particles particles frog frog frog frog frog frog progresses cars assessing altering primal primal aims attracted metal hirsch suitably conceptually enabled lens lens wright atoms atoms emulate seeking exhibiting seemingly seemingly organisms organisms organisms organisms organisms associating plants suppresses positioned utilization utilization utilization exposition masses masses masses birds visualized visualized organism euler braitenberg braitenberg confused granularity opening render earth reinforced reinforced arbib arbib safety mission mission mission mission mission mission vehicles sole entails entails depict reactions reactions reactions reactions emotions fluid fluid traversing charges charges merges merges collisions attainable cheng patterson elliptical conservation pursuing danger innate mahalanobis atom react finely friction triggering triggering triggering triggering aerospace collapsed repulsive passively passively ensuing ensuing abound frontiers imitation contingency rome lucas refines nonadaptive lectures portrayed portrayed portrayed photons photons supercomputers revising recalculated chapters intelligently electrostatic entail frogs multiprocessor desirability bloomington avionics 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#@Fernandez_M,
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#*network model model neural input input input input input input input data data figure time time time time time time time time time time set number number number number number number number number number system system results information information problem linear linear case case case case order order order order order order order order order order order order order shown values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability noise noise noise noise noise noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution approach single single single processing processing large large large neuron neuron rate rate rate rate rate rate rate analysis inputs form form form simple simple gaussian small small small small size size net net net net work fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells features process process process process level cell cell cell cell cell cell cell cell cell cell cell cell structure similar similar similar real note activity activity activity activity activity university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold independent computer connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left left left left left left left direction range components basis abstract computational computational references positive propagation propagation introduction action action circuit effect effect effect effect effect effect effect dynamic generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel recurrent recurrent difference difference difference higher higher higher part part cases cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type multiple cortex cortex spike spike spike spike spike long expected make fact fact fact fact techniques proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation probabilities probabilities forward simulation computed computed computed computed sum sum sum sum sum sum eq eq means means potential potential potential potential potential potential potential feedback feedback feedback feedback feedback feedback feedback feedback relative relative relative specific true cross cross cross cross cross cross cross cross cross cross active determined related connected connected connected connected brain larger contrast connection connection connection connection connection connection connection connection connection connection connection nets institute department individual individual individual represents represents difficult addition addition considered equivalent equivalent directly additional additional additional additional additional trajectory trajectory trajectory trajectory top top top top top top top effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects requires significant increase increase increase increase produce produce produce produce produce produce produce produce produce produce produce produce produce produce produce derived derived randomly conditional levels levels area area area area area types path product provided evidence inhibitory inhibitory inhibitory constraint measured measured normal feedforward feedforward feedforward increases increases limited close inverse excitatory excitatory excitatory excitatory excitatory circuits circuits common common common common common common common common common shape shape shape shape shape synapse supported require fit simulated typically typically smaller underlying underlying underlying underlying underlying underlying underlying underlying underlying combination coefficients edge empirical empirical representing representing direct bottom bottom bottom bottom bottom bottom bottom bottom magnitude magnitude decay produced produced produced produced produced produced produced produced produced produced produced produced produced produced membrane membrane membrane membrane membrane membrane discussed correlations pair pair pair typical typical typical typical identical calculated calculated calculated smooth match match background interval interval interval increased increased increased amplitude amplitude amplitude amplitude amplitude amplitude studied spikes spikes spikes spikes spikes derivative derivative derivative derivative derivative predicted feed loop loop loop loop loop loop loop occurs strength strength strength strength strength greater reduce trajectories trajectories trajectories trajectories conclusions central interactions interactions interactions measures peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak mechanisms presence reduction proportional proportional proportional proportional proportional proportional proportional proportional proportional decrease relationship acknowledgements reference relation relation relation relation relation relation relation relation relation relation derive produces produces sequential sequential sequential mathematical changing simultaneously simultaneously linearly linearly linearly involves formed formed formed formed implies implies potentials potentials potentials potentials potentials decreases depending correlated transform modulation modulation similarly similarly diagram reasonable dashed additive additive intervals add add remains remains valid msec msec sufficiently sufficiently sufficiently recorded fire fire fire combinations combinations combinations coordinate plotted illustrated illustrated illustrated illustrated illustrated specifically phys discussions middle middle middle capable paths paths paths paths essentially soc soc moore link link link link link link link link showing symmetry symmetry timing timing duration duration delayed delayed cat cat cat neurosci neurosci neurosci illustrates subsequent subsequent trains origin origin origin origin remain american circuitry rapidly involving optimized integral integral preliminary postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic rise rise matches successive links links links links links links links links links links links links links investigated analytically analytically reliable coefficient predicts predicts rev changed ensure impulse noted noted noted shapes nervous pyramidal baseline baseline baseline baseline baseline baseline baseline simplest contributions serial serial serial serial serial serial serial serial serial serial histogram histogram advanced advanced advanced convolution convolution convolution convolution convolution convolution analyzed interneurons interneurons interneurons interneurons comparisons comparisons broad bishop afferent consequence res recording author fluctuations summation fourth reflects considerably pathways pathways pathways pathways empirically empirically empirically understood peaks peaks peaks peaks peaks orders recordings calculating aim modulated kinds kinds fiber physiol physiol physiol physiol aligned aligned physiology proportion neurophysiol interconnected adds chance chance chance height loops loops loops loops loops loops occurring occurring effectiveness exceeds fires fires falls equals washington consequences consequences advance cerebral reveals sustained sustained epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp reverse grants convergent convergent counts ics crossing crossing crossing crossing largely indirect latency latency validity hundred hundred causal spinal spinal preserved conduction conduction interneuron interacting inverted inverted efforts mediated mediated wise confirmed confirmed crossings crossings intracellular intracellular algebra algebra interspike interspike interspike reciprocal wider shallow resembles triggered triggered triggered triggered triggered triggered triggered triggered correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram moderate stimulating ase influenced hundreds arrow neocortical neocortical sensorimotor seattle cord cord slices meth raises colleagues arriving quantitatively approaching falling falling compensated closure nih cia aic motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons cope correlational correlational correlational correlational correlational correlational correlational correlational correlational correlational correlational correlational correlational completeness firings firings firings firings firings firings resemble biophysics upward broader broader extracellular mediate convolving convolving convolving intervening intervening psp latencies latencies biophys biophys epsps epsps epsps epsps missed monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic monosynaptic ending correspondingly concurrent rising motoneuron motoneuron motoneuron motoneuron motoneuron motoneuron motoneuron susceptible unitary unitary unitary triggers mediating mediating cited ipsp ipsp eps eps eps eps convolutions linkage linkage divergent garrett shortening confirming distributes intercept correlograms correlograms correlograms correlograms correlograms referenced referenced ata fro trough trough trough trough bic gustafsson gustafsson broadening reverberating reverberating secure abst abst dispersed perkel advancing collaborative 
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probability noise noise noise weight weight functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons point point point point processing local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron class class class class class class class class matrix inputs inputs form shows signal work step points points points points level structure problems random random random random memory memory response similar similar similar show show show show section section section section section section section rule rule rule rule rule vectors vectors generalization generalization generalization generalization generalization real states states states states states theory obtained term term term term term note dimensional dimensional result result result result result threshold threshold threshold threshold threshold variables variables variables variables variables computation solution solution independent log log log log log defined found sequence estimate connections presented presented presented present object range components outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous abstract computational computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties references component component component ieee ieee important important important introduction action action action action parallel change change change change difference assume lower rules rules rules rules signals chosen part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound binary binary conditions distributed fact fact fact correct minimum resulting resulting resulting classes classes classes classes ing multi multi multi sum sum sum sum sum eq called called called regions regions regions factor optimization optimization made natural natural global obtain original original original original original original vol vol vol desired desired desired define define define define define define proc proc perform connected equal equal equal equal voltage connection connection update institute institute technique consists exp exp scheme domain limit conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity upper upper full choice give give condition weighted randomly randomly developed developed developed developed levels product associative associative discussion discussion denote fast corresponds corresponds corresponds stable stable stable stable stable proof proof proof proof proof proof proof proof proof ability objective underlying hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield combination technology increasing increasing increasing special numbers max stored bits bits attention added property property property property property property property property property property property introduced introduced identical engineering engineering sufficient sufficient observations tions tions tions solve yields yields yields differential trans diagonal diagonal diagonal diagonal definition definition definition symmetric symmetric modified observation generalized bounded bounded bounded bounded greater greater asymptotic asymptotic asymptotic taking taking taking physics assuming decrease decrease introduce introduce introduce manner manner base question denoted suppose suppose relation transitions transitions physical electrical develop adding independently communication viewed lemma evolution partition allowed convex combining event event add construction usa usa memories prove prove prove holds middle divided divided wij wij wij allowing interpreted content sci sci hold quantity michael quantization quantization quantization quantization quantization remain american exhibit updating updating relations relations relations relations relations relations relations relations relations rise examine investigated investigated proved proved affect changed der obvious mapped established piecewise inequality pairwise analyzed guaranteed answer lies tool strictly strictly choices sgn sgn sgn immediately hyperplane products products products acad acad outer outer outer outer argument argument argument flexible simulate requirement collective collective collective sums focused eventually proposition synchronization nat nat hyperplanes hyperplanes impossible proceed occurred keeping keeping analyzing observing moments substituting corollary introduces introduces appendix appendix israel israel israel passing abu mostafa graded ties emergent preserving preserving restrictions restrictions aij aij recurrence recurrence tight quantized levin impose denoting picked concentrate noting pos signs completed info remarks remarks unbounded vii vii equa autoregressive gence brackets brackets brackets addressable mle technion replaces richer richer richer rela rela coincides examines sible decides conver conserving divides completes completes completes compose bigger useless asynchronously inn private lhe axi axi axi haifa xixj asymp wixi fleisher fleisher distinguishable distinguishable guaranteeing exten itseft sively fie wijxj wijxj atl totic featuring jacques boundedness boundedness thres 
#@Fleisher_M,
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systems weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution pattern pattern pattern pattern pattern point point point single single processing processing processing control control control control control large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test patterns patterns patterns analysis analysis analysis class matrix form form form shows shows signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple simple gaussian gaussian gaussian small small small small size size task cells cells points points process process process process process current random random random random random memory memory memory memory memory memory memory memory equation line rule general general real states term term term term experiments experiments activity activity activity dimensional dimensional dimensional result result result threshold threshold computation computation independent defined defined defined defined found found sequence sequence standard computer computer computer computer connections connections connections connections direction present present present activation activation activation activation activation nodes nodes frequency machine machine motion components outputs outputs outputs abstract abstract references due important propagation introduction complex complex complex complex complex behavior change change change change variable variable variable variable chosen part type type type type required required required required multiple long length length length length observed observed observed forward forward forward simulations tasks tasks total total total total simulation simulation human multi sum performed mapping made applications applications original artificial specific desired series series objects location perform perform goal related connected connected connected connected connected connected motor motor brain brain power steps connection connection connection connection connection connection connection connection update dependent source selection institute implementation implementation technique consists code individual joint joint joint joint joint joint joint joint joint joint joint joint joint final layers addition view view bit full speed speed con con randomly robot robot robot robot robot robot robot area controller types types types types types types types path path path path path path product product finally backpropagation biological biological associative associative describe describe limited limited close complete actions actions actions amount amount short short short nearest nearest common implemented implemented implemented implemented implemented shape shape shape ability ability future development including simulated simulated typically typically typically fully fully programming edge edge mechanism consistent making window expert run description discussed directions separate takes takes array varying calculated studies definition background grid grid grid grid grid grid grid grid arm arm arm arm arm constructed studied studied occur extended extended extended feed move move move flow flow flow strength strength strength place place place place hebbian neighbor interactions interactions designed encoding strong physics external cycle cycle cycle cycle cycle cycle cycle cycle cycle sigmoidal sigmoidal variety user user user user connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity program program program program program program construct construct produces written stability implement implement easy integrated adding formed implies cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles viewed viewed open open controlled centered centered centered forms activities activities updates updates slow delays delays reduces closed closed initially sufficiently topology topology fire includes inter memories memories memories extension neighbors grammar grammar grammar straightforward sensor sensor capable capable capable capable paths paths oscillatory computations tend receives quickly repeated success success content timing built list list list list involved vary michael binding moves command powerful american layered create create put humans strengths strengths strengths graphical fashion investigated investigated fundamental analyze opposite changed changed thought seconds seconds mentioned percentage sensors sensors sensors track majority capabilities independence tool tool tool tool tool pulses begin researchers requiring virtual apparent collected lattice completion passed incorporated execution execution operate limiting limiting ordered plan plan plan plan begins begins tile summed interface interface interface interface interface acts circular purely theories dealing dealing keeping removing implications guide arrays clock date started started studying lengths lengths multiplied indicator indicator indicator ends stopped thresholding fired pressure usage numerous numerous numerous numerous ram july connec acceptable junction workstation interact mammalian graphics graphics execute activate interacting interacting interacting interacting march careful ltm things experi completed completed stops stores traveling utilizes aid lists flows engine executing grids joints destination inde randomness accommodate motors motors cyclic cyclic cyclic cyclic addressable texas texas stm stm experimented unexpected tivity lisp lisp lisp cons altering 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systems systems parameters functions functions neurons neurons neurons unit unit unit recognition recognition recognition recognition recognition recognition recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point processing local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns small small size size size net net net net net net net net net net net net net net net work methods cells cells cells cells cells cells cells step step step step step points field classification process process level level level level current cell cell cell structure problems memory memory memory response response response response response similar similar similar similar show fixed rule speech real real approximation approximation states states activity activity activity activity activity activity activity activity activity activity result result university university university computation research found found dynamics dynamics dynamics computer computer computer connections connections synaptic synaptic presented presented presented presented presented presented presented presented presented presented present phase temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine sets range range learn nonlinear continuous continuous abstract properties references hand behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus dynamic dynamic dynamic dynamic recurrent recurrent tion energy difference spatial spatial spatial spatial rules word word word higher previous previous firing firing firing multiple long long long long equations equations make fact minimum resulting resulting tasks simulation times times means made feedback feedback study obtain obtain artificial specific specific application series proc proc perform perform perform active active constraints connected discrete discrete cortical brain brain brain brain dependent dependent dependent dependent dependent nets selection selection proceedings proceedings proceedings report institute words individual represents connectionist connectionist layers layers delay delay sequences sequences estimates limit limit limit limit limit limit limit limit limit limit limit limit limit limit stimuli stimuli stimuli stimuli conference conference conference capacity basic increase con developed developed types finally biological associative discussion describe describe group fast stable short implemented generate role require instance instance instance instance easily rumelhart simulated typically typically smaller hopfield hopfield account account jordan jordan transfer interesting significantly significantly significantly mechanism consistent consistent structures structures call international supervised neuronal population population population population population population discussed discussed typical typical typical include include period period period identical cognitive recently relevant engineering interest subjects works works works tions tions correspond studies achieve achieve locations symmetric modified modified generalized channels organization storage sensitive increased exists lead scaling occur feed hebbian hebbian depend differences numerical performs performs performs suggest mechanisms physics external cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle characteristics start exist connectivity minima question attractor explicit suppose appears longer sequential sequential sequential sequential sequential distinct distinct dept recall recall recall consisting develop cycles cycles independently independently formation phoneme phoneme detailed similarly updates allowed past partial reasonable performing delays delays classical event generation msec msec msec string string existing fire usa usa usa strings sciences sciences recognize recognize specifically variations phys successfully selecting aspects capable capable capable importance society effectively delta mcclelland modes modes presentation oscillatory oscillatory attractors reached characteristic quickly physiological sci sci duration duration duration vary generalize realistic delayed principles attempt subsequent decreasing remain american create create exhibit exhibit exhibit exhibit exhibit varied association preliminary periodic periodic periodic periodic reducing respond fashion fashion biol possibility reliable encode func attributes transmission rev created olfactory olfactory formal noted observe explored years mentioned distinguish convolution multiplication spatially spatially spatially organized organized acad acad localized lowest annual recognizing recognizing meaning researchers researchers researchers questions questions apparent apparent populations 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units units units units units units units units units problem problem problem problem problem problem problem performance performance performance performance performance performance performance space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer case case case case case case case case case case case case case vector vector vector order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown shown systems systems systems systems systems values values parameters parameters noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit recognition method method method approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern single single processing processing patterns patterns patterns analysis class class class form form form form form form form form signal signal signal signal signal signal signal simple simple simple simple visual paper paper paper examples small small small size size net net net net net net work methods field field field field field field features level trained structure structure problems problems problems response response similar similar similar similar similar similar architecture architecture architecture architecture architecture show equation fixed fixed fixed rule rule general average theory obtained term term term note note note note dimensional dimensional dimensional dimensional dimensional dimensional threshold threshold threshold variables variables variables solution solution solution research research independent independent independent independent independent independent defined defined defined defined computer terms terms terms connections connections temporal machine object object object maximum range range press press learn learn position position position position position basis outputs continuous continuous abstract applied back back back back find find computational references ieee ieee procedure propagation propagation propagation propagation context introduction hand behavior effect parallel change change change change change energy energy difference complexity complexity variable variable assume assume rules rules representations learned higher higher higher higher higher higher higher higher higher higher higher higher higher part cases type type required required conditions distributed equations equations make make techniques techniques techniques techniques scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale simulations simulations resulting simulation simulation simulation simulation simulation simulation simulation respect multi multi multi eq eq eq eq eq eq eq called regions regions means factor factor factor dimension made made made made orientation study knowledge obtain obtain vol vol artificial specific specific specific application application desired receptive define define objects proc proc perform perform perform related constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected connected connected discrete discrete discrete discrete equal equal approaches approaches approaches mit mit connection train train dependent dependent selection report institute implementation implementation implementation implementation implementation implementation internal individual joint represents final layers layers layers addition addition considered cambridge cambridge equivalent equivalent hinton hinton hinton additional view solutions solutions design design design limit limit limit san stage detection detection detection requires requires requires significant vision condition condition developed nature depends depends depends constraint constraint constraint constraint constraint constraint constraint simply biological achieved discussion discussion increases describe describe arbitrary arbitrary arbitrary group group transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation limited amount common require eds square pixel easily makes rumelhart rumelhart rumelhart development auditory needed reduced reduced account functional functional functional fully fully fully interesting interesting increasing increasing special special special leads making early choose perceptron architectures discussed discussed advantage advantage advantage pair robust moving moving include identical machines side pixels interest interest highly conventional conventional solve studies studies rl rl rl rl rl rl rl rl rl rl rl rl rl background positions modified generalized generalized williams williams sensitive entire entire constructed constructed constructed invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant rotation rotation rotation rotation rotation boundary boundary strength reduce operator differences differences sigmoid sigmoid sigmoid numerical clear performs faster encoding encoding encoding encoding integration integration physics demonstrated demonstrated intelligence manner manner manner force force force question question derive derive construct index factors laboratory mathematical coordinates coordinates coordinates coordinates infinite physical transformations transformations transformations transformations transformations easy unique unique consisting consisting consisting shift shift implies implies letters letters yield stages viewed evaluated lee lee lee translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation allowed allowed normalization reduces reduces combining purpose advantages classified combinations combinations combinations priori coordinate perceptrons formulation formulation discuss discuss simplicity reason selecting encoded encoded computationally included mcclelland build build build invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance conf conf conf contained classify device duration categories built built satisfy satisfy satisfy satisfy generalize giles giles giles giles subsequent operating satisfies deal deal extend extend camera camera employed simpler origin origin diego american layered layered transformed requirements requirements requirements requirements exhibit difficulty humans strengths integral mass hall periodic fourier fourier respond respond investigated office proper complicated encode encode encode math man illustrate adjusted aspect obvious freedom freedom brown great great trivial crucial distinguish distinguish distinguish track answer expensive worse reasons implementing purposes satisfied easier preprocessing constructing incorporate scientific recognized begin arises cybernetics cybernetics sun addressed robustness argument requiring geometric geometric geometric geometric geometric percent limits limits limits limits limits limits freeman readily effort orders orders slower formulated requirement requirement switch occurrence chen chen inherent inherent inherent june 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note note note note activity activity activity activity activity result university university university university university variables variables solution research research research research research research research independent independent log defined defined defined defined defined found found dynamics constant estimate estimate distance map map map activation activation activation activation activation activation frequency maximum maximum maximum press press press press nonlinear continuous continuous sample sample abstract back back back back back back density density density likelihood likelihood references stochastic procedure procedure important propagation propagation propagation propagation propagation propagation introduction introduction hand estimation estimation estimation estimation statistical statistical statistical parallel parallel parallel search tion tion tion tion tion energy energy energy energy energy energy energy energy rules measure part part distributed distributed distributed markov make proposed probabilities minimum minimum respect respect respect called called elements elements elements elements elements elements elements elements made made natural global global applications applications obtain relative represented represented represented true define distributions discrete equal mit mit mit mit connection connection connection connection connection connection connection connection connection connection connection descent descent proceedings institute department department version version connectionist connectionist connectionist connectionist connectionist final exp exp addition maps framework framework cambridge cambridge cambridge computing computing computing equivalent equivalent equivalent equivalent environment environment environment hinton design design detection statistics free basic con con derived derived developed levels levels levels levels provided provided associative associative associative associative covariance group group group inverse assumption assumption assumption assumption proof finding amount assumed assumed supported supported eds eds journal hypothesis degree rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart development probabilistic probabilistic hopfield hopfield hopfield hopfield dynamical numbers direct making minimize architectures discussed property property introduced introduced trees inference subset subset engineering sufficient highly observations observations observations tions yields evaluation modified williams constructed exists exists occur suggests hybrid white white occurs strength row hebbian operator valued designed designed designed exponential exponential physics drawn drawn demonstrated california turn acknowledgements pro pro pro van derive written optical estimating mathematical mathematical explicitly explicitly physical involves involves slightly belief unique expectation national stationary squares viewed viewed influence influence variation transform modulation suggested earlier additive additive normalization sufficiently assigned foundation foundation david david priori usa usa retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval inter inter assignment sciences activated activated specifically discussions characterized tests suitable mcclelland mcclelland mcclelland mcclelland presentation computations identity traditional anderson anderson interpreted interpreted issue gibbs minimizes minimizes correspondence computes principles neighboring neighboring minimized minimized minimized american wiley strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths integral mass helpful scalar office office statistically cognition cognition cognition psychology psychology psychology store multivariate multivariate multivariate asymptotically brown indicating crucial derivation independence multiplication briefly stanford stanford stanford forces immediately probable probable probable probable probable probable probable author author author mellon mellon addressed summation evaluating evaluating tional posed ity summarized pittsburgh pittsburgh pittsburgh characterize incoming cal cal occurrence richard comments specifies specifies irrelevant irrelevant cooper sv arguments member null unity naval naval smolensky smolensky smolensky kullback kullback murphy contract viewpoint harmony analyses analyses decide widrow searching searching multiplied environmental environmental environmental environmental environmental environmental environmental partitioned grants characterization explorations explorations explorations assigns andrew ics posteriori informa unified unified ple microstructure logarithm rigorous annals leibler leibler deriving restrictions convenience generalizations reject distri cessing pdp pdp pdp distribu activate academy importantly sam sam grateful memo tract unpublished manuscript manuscript 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#@Golden_R,
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models models models models models performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case order shown shown shown shown systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters functions functions functions functions neurons neurons neurons neurons neurons unit unit distribution distribution recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point single single single single single single single single processing processing processing processing control control large large large large large large local local local local local local local local neuron rate rate rate rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows shows shows shows shows shows signal signal signal signal signal simple simple simple visual visual paper small size size size feature net net work work work work work task task task task task methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step step step step features features process process process process level current current current trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure problems problems problems problems high high high high high high high high memory memory memory memory memory response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar similar similar similar similar similar similar similar similar similar similar similar similar similar representation architecture architecture architecture architecture fixed fixed fixed fixed fixed line rule rule rule rule rule rule rule rule rule rule rule rule vectors general generalization real real real real theory obtained obtained term term term term term term term term note note experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold solution solution research research research research found sequence sequence initial initial initial initial initial initial constant constant constant computer computer terms distance distance distance connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science science left direction direction presented presented presented presented presented presented presented presented presented presented present activation activation activation activation activation activation activation activation low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal object object sets sets sets sets range range range press press press press press press learn components components components basis nonlinear outputs outputs outputs abstract applied back computational computational computational computational computational convergence density density analog properties properties properties properties properties properties properties properties properties references component due due due positive important adaptive propagation introduction introduction complex complex hand hand circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical dynamic parallel parallel cost cost recurrent recurrent recurrent change change change change change difference difference difference difference difference difference difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume assume lower lower lower lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure measure measure measure measure signals signals signals signals signals prior learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen chosen chosen higher part part part part center center cases cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type type type type required required required multiple multiple multiple multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike long long long long long long long long long long long long long long long long long long long conditions conditions conditions conditions represent distributed distributed expected expected expected fact fact correlation correlation correlation length probabilities probabilities observed simulations simulations resulting resulting resulting classes ing ing ing ing tasks simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation respect respect multi sum sum sum performed performed times times elements mapping means means means optimization potential potential potential potential natural feedback feedback feedback feedback feedback feedback feedback feedback feedback global global study study filter negative original original vol artificial relative specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific samples represented represented compared compared desired series provide objects objects objects objects location perform active active active active active active active active active active active active active active active active active active active active active active active active active active active active experimental experimental goal goal posterior connected gain cortical cortical cortical cortical cortical cortical brain brain brain brain brain brain brain brain brain brain equal equal approaches mit mit mit mit voltage voltage voltage voltage voltage steps accuracy comparison contrast contrast contrast connection dependent dependent dependent source nets modeling selection institute institute institute loss synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses technique internal individual individual individual individual responses responses responses responses responses responses responses responses responses responses responses responses responses layers delay scheme scheme scheme scheme addition sequences sequences framework cambridge cambridge cambridge cambridge experiment environment environment environment directly hinton additional additional additional view solutions solutions design top stimuli stimuli stimuli stimuli stimuli effects effects detection determine determine requires world world world increase increase increase increase increase give give give give give give give give give give give give give give give give con produce produce produce produce produce coding coding derived derived derived derived derived derived weighted weighted randomly randomly randomly randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering developed developed levels levels levels levels levels area types types types types types lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines path product product actual finally finally processes selected selected selected selected selected selected evidence backpropagation nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends depends depends sampling sampling sampling sampling sampling constraint simply simply biological biological biological biological biological biological achieved measured normal feedforward feedforward feedforward feedforward feedforward feedforward feedforward increases increases increases increases group group group denote denote tested tested tested close corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable stable stable stable stable stable circuits circuits amount amount amount amount amount amount short short short short short short short short short short common common common common assumed assumed assumed synapse synapse synapse synapse synapse generate generate generate generate supported supported theoretical theoretical theoretical require eds eds end vlsi ability hypothesis instance cluster cluster cluster cluster cluster cluster future degree degree degree rumelhart rumelhart rumelhart noisy noisy sensory sensory sensory sensory sensory simulated simulated simulated simulated simulated simulated simulated probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically pairs pairs smaller smaller underlying underlying combination combination combination combination combination combination combination reduced functional functional block interesting interesting interesting interesting testing testing significantly projection york york increasing increasing mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism structures structures structures structures structures structures structures structures structures trials trials trials trials trials uniform empirical empirical empirical mode mode principle operation operation operation language principal call numbers numbers pre pre pre pre pre pre direct making window window inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition normalized normalized bottom bottom early early early early idea idea produced produced produced description perceptron neuronal denotes architectures architectures architectures population population discussed discussed discussed discussed discussed discussed recent pair robust separate takes typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity lateral lateral lateral lateral lateral lateral moving moving period period period subject subject subject identical hierarchical sense sense array relevant relevant interest interest dimensions dimensions sufficient sufficient sufficient highly varying varying varying compare previously previously previously previously previously previously approximately approximately approximately approximately approximately subjects subjects calculated tions tions tions solve smooth yields yields correspond correspond studies studies studies differential sparse sparse background background background background positions modified generalized generalized channels interval interval williams organization organization sensitive increased grant amplitude constructed constructed constructed constructed parts parts expression expression expression expression studied occur occur occur wide hybrid hybrid clusters clusters clusters clusters occurs occurs occurs occurs occurs setting pass pass flow flow flow flow flow flow flow strength strength strength critical place greater assumptions hebbian conclusions conclusions interactions differences differences differences measures accurate retina numerical clear clear clear performs practice suggest suggest encoding encoding encoding encoding strong strong strong mechanisms mechanisms physics reduction characteristics characteristics characteristics characteristics characteristics california pulse pulse pulse pulse pulse pulse turn turn turn turn turn assuming assuming assuming min min decrease groups groups connectivity connectivity connectivity connectivity program question question question question question question acknowledgements areas areas areas suppose appears appears pro longer longer longer longer winner winner ways ways ways ways ways primary primary sequential describes distinct distinct distinct distinct distinct distinct distinct distinct distinct distinct distinct distinct distinct distinct distinct changing changing changing recall metric metric category category category category category category category category category category category category category category category category category category category category explicitly simultaneously linearly electrical electrical involves involves involves involves remaining text unique unique unique unique consisting consisting consisting develop develop adding adding events events events events formed potentials potentials potentials select select competition john decreases decreases decreases decreases yield choosing choosing national independently expressed dependence review depending communication overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap viewed viewed influence influence influence influence influence influence influence variation variation detailed open open open open operations controlled restricted showed lee lee forms forms static understanding understanding sizes similarly similarly suggested suggested discrimination discrimination processor past diagram earlier calculation measurements normalization sec sec sec intervals intervals event roughly boundaries boundaries remains initially calculate msec msec msec msec sufficiently sufficiently sufficiently foundation eeg views dendritic building building existing existing existing fire fire fire fire fire fire fire fire fire fire fire fire fire fire combinations currents currents currents currents currents currents currents currents memories determines activated activated activated activated activated candidate discussions tests tests structural major straightforward middle capable differ differ differ differ computationally effectively effectively effectively effectively driven driven driven delta delta delta mcclelland spiking literature literature literature post projections comparing situation tend tend tend tend tend tend reached reached receives receives composed summary refer quickly repeated strongly strongly strongly strongly strongly strongly strongly strongly strongly strongly strongly induced induced induced induced induced induced induced contained prob allowing success interpreted conductance conductance issue issue return sin physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological cue cue cue cue cue cue cue cue cue cue cue cue device duration duration duration categories categories categories categories categories categories categories categories categories categories categories cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues receptor receptor comp comp comp comp comp comp bar involved vary vary absence absence paradigm 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rise rise rise rise rise rise rise rise rise rise rise rise rise rise rise rise fewer reducing reducing successive successive successive successive successive respond respond respond fashion fashion fashion giving history history rest rest behavioral behavioral behavioral incremental plasticity ideal possibility possibility proved encode encode func hierarchy presynaptic fundamental removed examined induction induction induction hill patch patch patch patch patch patch patch patch patch patch naturally naturally transmission possibly necessarily onset onset onset predicts extremely extremely psychology equally thought thought thought prototype aspect versions versions olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory formal noted panel panel panel logistic expressions expressions logic hebb hebb hebb switching fibers fibers fibers fibers fibers fibers pyramidal consist generates detected extent contributions electronic defines seconds animal animal animal massachusetts percentage burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst indicating great advanced slowly formula asynchronous directed directed directed theoretic theoretic theoretic theoretic distinguish coded adjacent adjacent biology biology analytical answer expensive glass interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons reasons drive rapid rapid rapid rapid tive tive purposes purposes sys shared shared shared ring widely strictly precisely constructing incorporate nucleus arise arise arise afferent afferent pulses pulses pulses pulses pulses pulses pulses pulses probable axon 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odor odor odor odor odor odor odor odor tem naval eliminate nonzero enhancement enhancement proceed arranged arranged arranged lost lost lost climbing eliminated inspired anatomical anatomical anatomical anatomical convenient stronger stronger stronger occurred overcome overcome overcome stated chemical chemical chemical familiar efficacy occurring occurring occurring mark neurobiology neurobiology observing fail fail splitting splitting implications imply affected responsible adequate arrays enhanced carry combinatorial selects selects days hours motivation exploring exploring reliably analyses overlaps overlaps overlaps weakly introduces periods connect loo dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites iteratively respective encountered paul surprising pat intended enhance enhance enhance widrow widrow dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite consequences sim sphere bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb dif similarities similarities similarities enable enable multiplied hippocampus hippocampus hippocampus waves membership membership membership infer axonal axonal axonal bursts bursts bursts bursts bursts bursts bursts bursts bursts bursts bursts stimulated reveals ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp arrive arrive locked locked record refers late rich specificity properly contact contact contact contact contact contact contact contact contact epsp epsp epsp epsp epsp epsp epsp variants grants receiving receiving convergent severe divide skills dense fired fired fired linked cholinergic appeared constitute incorporates fellowship graded graded super asked transmitted encodes emergent emergent preserving spatio adopt utilize trigger causing causing blue blue blue amplitudes amplitudes spaced hundred tendency constitutes resting resting resting experiences rhythm rhythm rhythm rhythm rhythm evoked evoked evoked stands pairing adjustment adjustment representa arising peripheral modifying shifting biophysical biophysical biophysical alternate alternate alternate alternate alternate interneuron interneuron interneuron interneuron grouped grouped management gener dominated dominated dominated dominated ization ization activate activate degraded degraded potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation proba expand maximally electrodes differentiation surrounding gluck synchronized synchronized synchronized synchronized parallelism lond noting noting increasingly increasingly complementary distal rhythmic pos records categorization categorization categorization categorization conversely selectively worth nonetheless nonetheless nonetheless distinguished apparently apparently apparently preserve preserve preserve afferents afferents afferents responding intracellular grateful minor induces behave exhibited things prevents prevents radio tract tract tract tract tract travel differing computa differentiating microscopic inactive inactive answers unpublished architectural architectural rats rats electron rarely stimulating bursting bursting algorithmic lation bility send settling converging losing calibration mahowald aid termination dominates developmental adult loosely loosely loosely reflecting transmitter transmitter caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal caudal suppress drawing char calculates affecting injected anatomy anatomy anatomy anatomy anatomy incorporation concerns episodes physiologically practically practically month exclusively possess subtracting anterior anterior anterior sparsely intracortical emerges neurol neurol neurol neurol judged labelling labelling huang slices normalize normalize measurable successively comprising comprising comprising comprising raises intact intact arrives contacts contacts contacts contacts contacts contacts contacts contacts contacts odors odors odors odors odors odors odors odors odors odors odors odors odors odors odors odors odors convention nontrivial neurobiological enhances totally randomness randomness randomness senses senses colors absent binomial experienced encodings encodings encodings encodings encodings irvine restrictive essence electrophysiological feldman feldman priming cess enter thresh categorical categorical appro appro unusual lar sparseness granule indicators prominent episode tenth adequately parker parker pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform ized ated recalled hoff hoff actively greatest silent subtle hyperpolarization hyperpolarization tory probabil enabling unexpected bidirectional spec freely tern depolarization depolarization depolarization depolarization depolarization tivity yellow initiated plastic resemble drug operated cars levy schema notions activates prolonged fractional rhythms cient lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch lynch terminate graphically putting activating activating rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral rostral thalamus assoc dealt ogy enhancing enhancing enhancing advice ther respects rom devel decrement scribed patterned patterned patterned patterned patterned patterned neurodynamics sible lasting lasting lasting lasting lasting lasting proximal quiescent postulated untrained notably begun ously rosenblatt rosenblatt engineers perspectives clamping epsps epsps epsps epsps epsps epsps epsps epsps participate participate previ vitro cent elicited listing contiguous piriform piriform ending utilization succession succession flips taught originating originating originating simu rising haberly haberly haberly haberly haberly haberly laminar laminar anatomically anatomically anatomically sponse acuity acuity critically rabbit depolarized contributed economics unfamiliar categorized particu partic accompanying discriminations discriminations sivilotti sivilotti spheres occuring occuring ist cate collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral collateral theta theta theta theta theta theta theta theta theta theta sit arrived accompanied ipsp ipsp ipsp ipsp ipsp superficial predominantly predominantly berry chemistry arrangements adaline nasal flowing granger granger granger granger granger postulate neur collaterals collaterals collaterals collaterals collaterals collaterals collaterals collaterals collaterals biochemical gary disparate tex subsection pected pus heaviside commissural commissural commissural subjected alternates cycling gle markedly borrowed bringing hyperpolarizing hyperpolarizing hyperpolarizing hyperpolarized recruited recruited recruited innervate innervate reciprocally reciprocally mln raising raising opposing reversing raining differentially differentially tractability tered initiate initiate terminating alters western heterogeneity heterogeneity heterogeneity heterogeneity depolarizing depolarizing intense intense insightful weaken subpopulations entorhinal entorhinal entorhinal innervation spartan oliver behaviorally weakening weakening cup cup cup cup cup cup acta packard gaining requisite instructive fractions directionality dentate engaged engaged engaged benefited tending worlds synaptically acteristics fork michel anesthetized hewlett ulations henry deteriorate underlies acquiring participating participating technol chronic chronic chronic extrinsic extrinsic topo creased erroneously confronted halting abilistic breadth lasts homogeneity probabihty probabihty innervating fic shunt associational encod jos quantal quantal alepolarizing ormation conveying caveats chemically quant perceptions losleben stereotyped ght commonalities biochemistry undergone undergone fies ately looms partitionings retrospect ordinarily abraham metaphors elucidating broadened pharmacology 
#@Ambros-Ingerson_J,Granger_R,Henry_H,Lynch_G,
#t1
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function figure figure figure figure figure figure time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error error error error error error results results results units information information information information information information information information information information information information information problem problem problem models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space space space weights weights weights linear case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order order order order shown systems systems values values values values values probability probability probability probability probability probability probability probability probability probability noise noise noise noise noise unit distribution distribution distribution distribution distribution approach approach point point point single single single single single single single single single single single single single single single single single single processing processing processing large large large large large large large large local local local local rate rate rate rate rate rate rate analysis analysis class class class class inputs inputs inputs inputs inputs simple simple simple paper paper paper paper paper paper paper small small small size size size size size size size size size size size size size size size size size size size size size size feature feature feature net work work task step field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field classification classification process process process process process process level current current structure structure structure structure problems random random random random random random random random high high memory response similar similar representation representation representation representation representation show equation equation section section section fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general real real real real average average average average theory theory theory theory theory theory obtained dimensional dimensional dimensional result result result university computation research research research independent independent independent independent log defined defined defined defined standard standard computer computer computer computer computer terms terms terms terms distance distance distance distance distance distance distance connections connections connections connections connections connections connections connections node node node node node node node node node science science science science presented presented presented presented map map map map present nodes nodes nodes nodes sets maximum maximum maximum maximum maximum maximum range range range range range press position components outputs outputs continuous abstract convergence density references due due due due due positive positive positive positive positive decision introduction action complex complex behavior parallel parallel parallel parallel cost cost cost cost cost cost cost cost cost cost cost cost tion tion change difference complexity variable variable assume assume assume assume classifier measure measure measure measure measure measure measure prior representations representations representations representations word word word word word word word learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen chosen chosen higher higher higher higher part part center center previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem required required required multiple multiple multiple multiple multiple binary distributed distributed distributed distributed distributed distributed distributed distributed expected equations make techniques techniques region length length length length length correct correct probabilities probabilities errors errors errors errors scale scale simulations minimum ing ing total total total total total total total total simulation simulation simulation multi performed called elements elements elements elements mapping mapping mapping mapping means factor potential made global global knowledge original original vol relative relative specific represented desired receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive define define define proc perform active determined determined determined goal related related constraints constraints gain gain discrete discrete cortical brain equal approaches approaches approaches approaches approaches approaches approaches mit larger connection connection connection connection connection fields fields fields fields fields support dependent dependent proceedings report report report report institute institute words words words words department department loss loss implementation implementation implementation implementation implementation implementation version synapses technique technique consists consists consists internal code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code individual individual individual individual individual individual represents connectionist connectionist connectionist difficult exp addition graph graph considered considered considered considered cambridge equivalent equivalent equivalent equivalent equivalent environment directly directly directly hinton additional additional estimates transition effects effects effects bit bit bit bit bit bit bit bit bit capacity capacity capacity efficient efficient requires significant approximate increase increase increase channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel coding derived derived derived derived derived randomly randomly developed levels bounds bounds bounds bounds bounds area area area area area area area area area area area area area area area area lines selected selected evidence depends associative associative associative associative associative technical technical technical increases increases increases increases increases increases increases increases increases increases increases increases increases increases increases arbitrary transformation assumption corresponds surface surface surface proof proof nearest nearest nearest nearest nearest nearest effective assumed assumed assumed assumed assumed assumed assumed assumed supported theoretical main face vlsi vlsi ability easily easily degree degree degree degree makes noisy noisy noisy probabilistic smaller smaller smaller smaller smaller smaller smaller smaller smaller needed combination technology technology block block block block block significantly ratio york increasing increasing increasing increasing increasing increasing increasing increasing increasing increasing special special structures structures uniform uniform mode principle operation operation numbers max making bits bits bits international added added added added architectures architectures architectures architectures discussed improve correlations advantage robust ensemble ensemble element element element element element practical apply introduced strategy moving subset subset subset subset subset cognitive relevant engineering engineering highly highly compare approximately works module tions yields diagonal sparse definition definition definition definition definition definition definition definition symmetric observation grid bounded bounded bounded increased expression expression concept extended wide alternative width occurs occurs occurs occurs generally place assumptions reduce conclusions neighbor neighbor neighbor competitive differences sigmoid moody faster constrained encoding presence presence physics physics proportional exist min plane decrease relationship groups connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity program force question pro derive written factors distinct distinct dept dept modeled implement infinite slightly adding adding applying extraction john decreases independently independently communication communication communication communication communication communication communication communication communication communication communication overlap overlap overlap codes codes codes codes codes codes codes codes codes codes codes codes restricted restricted organizing showed showed lee approximated sizes past earlier reasonable event roughly purpose remains assigned advantages dendritic existing includes silicon silicon silicon silicon silicon silicon silicon priori inter inter inter inter assignment holds neighbors characterized major compression compression compression compression compression compression 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indicating theoretic costs costs costs costs costs costs costs distinguish distinguish analyzed improves improves adjacent analytic analytic majority majority answer expensive tractable baum baum lies london comparisons tive tive sections sites easier widely strictly broad mation ion ion ion ion ion ion ion ion scientific pitch localized auto cybernetics recognizing nsf mellon researchers summation explained requiring carnegie limits limits limits limits cmu offset amounts poorly share incorrect exhibits pittsburgh spread monotonic chen inherent decoder decoder decoder decoder decoder decreased decreased redundancy redundancy redundancy redundancy returns returns returns returns lim trade redundant redundant redundant arguments encoder encoder encoder encoder encoder naval grows grows grows grows air adds ments overcome analogy mos fan fan fan fan interconnection interconnection interconnection stated contract contract keeping analyzing definitions definitions receiver receiver receiver receiver effectiveness effectiveness preparation planar selects continue infor analyses introduces connect sion decide realization belongs belongs belongs uni tic ensembles modelled cerebral cerebral ballard ballard reader roy sons santa onr severe verify corporation constitute ter incorporates vec vec covering job restrictions restrictions theorems theorems par medium classic tor letting imagine massively assess remainder representa cns cns cns cns cns cns cns cns cns cns cns cns cns cns cns cns cns attempted rectangular trends trends favor community mathematically graduate graduate ization distant intra intra intra proba relate simplifying relates importantly memoryless portions interconnect interconnect interconnect interconnect interconnect interconnect interconnect rochester likewise union programmed ignoring oregon oregon oregon cube cube covers sees sees january august unbounded unbounded ping send jointly tors transmitter identically cally tribution dissertation marr marr dedicated neocortex correctness tended approaching hough encodings computable locality locality locality locality locality locality ically devoted supposed decode decode decode degrades ted derivations ton disadvantages metal metal metal metal metal metal metal metal metal metal ness ver ver aliasing aliasing rom ele decides billion emulate utilization utilization han wishes brings maxwell maxwell geometrically categorize ticular recep recep tain equi tha bilities indexes subdivided debate debate gallager gallager gallager hen hen hin dan gle conjunctive effec effec effec effec lly neurm ume ume sender sender sender hammerstrom hammerstrom hammerstrom mountcastle symp optimistic barbara transmits semiconductor differen overlapped beaverton beaverton agreed unavoidable tii tii tii reduc wilczek ime oral inpu bsc bsc cii pacity subvector ere pie ited ami ami emulating compres diminishing diminishing diminishing physi subvectors wrote participates jected tightest noi correc diminish 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#@Hammerstrom_D,
#t1
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#*network network network network network learning learning learning learning learning learning learning learning model model model model neural input input input input input input input input input data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set networks networks training training training training training training algorithm output output output output output output output number number number number number number number error error error error error error error error error error error error error error error error results results results units units units units units units units units information problem problem problem problem problem problem problem problem problem problem problem models models models models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance based space space space space space space space space space weights weights weights linear linear layer layer layer layer case case case case case case case case case case case case case case case shown shown shown shown shown shown shown shown shown shown shown values values values values values values values values values values probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight functions unit unit unit unit unit unit recognition recognition recognition recognition recognition pattern pattern pattern point point single single single large large large large large large large local rate rate rate class optimal optimal optimal shows signal signal signal simple simple gaussian gaussian gaussian gaussian paper paper small small small small small size size size feature feature feature feature feature feature feature feature feature feature points points points points points problems problems problems problems problems problems random random high high similar representation show show equation equation fixed rule rule vectors vectors vectors general general general general generalization speech speech approximation gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term note note experiments dimensional result solution solution solution research independent log defined found found found target target target target standard standard standard standard standard standard terms present present activation activation activation activation low sets maximum maximum maximum maximum maximum range range press learn nonlinear abstract back back back back back back back back back back back back back find computational convergence convergence convergence convergence properties properties properties likelihood likelihood references due due procedure procedure important decision decision decision decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction introduction complex complex complex complex estimation estimation estimation effect effect effect generated change measure measure signals representations center type expected expected expected equations equations make fact fact region proposed errors errors scale simulations minimum minimum minimum classes classes simulation computed computed respect called times regions regions regions regions mapping potential made knowledge negative specific define determined connected distributions distributions distributions distributions distributions equal power power power power power power mit larger larger larger larger larger larger connection connection update update update descent descent modeling modeling modeling report implementation internal represents represents represents connectionist connectionist connectionist connectionist final addition domain domain domain domain hinton hinton curve solutions curves stimuli stimuli effects statistics vision give give derived derived conditional conditional clustering criterion criterion area types lines finally finally nature nature nature simply technical feedforward increases describe arbitrary arbitrary transformation close surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface finding common implemented implemented implemented shape shape shape shape shape shape shape shape shape shape shape shape role main end ability cluster easily easily rumelhart rumelhart objective simulated typically smaller underlying needed needed reduced reduced coefficients block block block transfer transfer transfer transfer significantly increasing increasing increasing special uniform representing representing iterations bits idea produced added improve recent advantage pair robust robust robust separate typical typical sense sense dimensions varying compare previously teacher teacher teacher smooth differential separation separation interval williams williams increased expression studied deviation deviation width clusters clusters clusters white white white generally generally generally generally runs runs runs strength conclusion starting reduce reduce reduce peak peak asymptotic largest reduction reduction reduction reduction minimizing exist plane plane targets targets minima identification base digit digit derive changing metric metric metric metric metric metric metric sensitivity sensitivity linearly linearly involves involves involves boolean family family expressed communication communication squares squares squares estimator influence solved solved variation approximated approximated sizes sizes completely suggested suggested digits digits partition partition discrimination partial smoothing normalization roughly boundaries boundaries boundaries boundaries david activations bell weighting uncertainty discuss variations domains absolute major compression aspects tend tend tend tend tend ten ten capture summary compact compact compact notice procedures procedures procedures stopping stopping vary decreasing decreasing bars simpler simpler layered xor xor xor updating varied involving estimators hanson hanson issues examine investigated decisions surfaces surfaces smallest naturally created changed changed changed noted logistic explored explored isolated inequality separable derivation fairly slope capabilities considerable processed turns purposes arc closer producing ran desirable sgn products cut arises geometry geometry exemplars requiring considerably prop spoken spoken spoken slower outliers partitioning partitioning inherent deviations deviations wesley distortion distortion primarily primarily addison summing resources eliminated communications proceeds fan city city city hyper grow moment implications enhanced generalizes substituting meaningful recovered recovered recovered recovered recovered percepttons consequences laplace recovery creating informative generalizing metrics metrics metrics dramatically constitute piece basically planes planes personal personal token relating wise wise categorization meet normalizing unpublished manuscript stephen distortions jersey err smo burr burr pronounced replicated triangle placement placement minsky minsky distorted presently approached approached cuts cuts outlier mesh mesh mesh mesh recovering tails violate cepstral pull illustrating sought seeking rationale euclidian euclidian euclidian euclidian euclidian euclidian bellcore papert looked looked restored replications traced compressing minkowski minkowski minkowski minkowski minkowski minkowski minkowski minkowski minkowski minkowski minkowski morristown recommended violates speculate supremum ensuing compactness olution paperr dlog psychologically jos papeft lyi lyi 
#@Burr_D,Hanson_S,
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning input input input input input input input input input input input input input input input input input input input data function function function function function time time time time time time time time time time time set set set networks networks networks networks training output output output output output output output output output output output output output output output system system system system system system error error error error error error error error error error error error error error error error error error error error state state state state state state state state units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown shown shown shown shown systems systems systems values values weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method image image image image image image image single test analysis analysis analysis analysis analysis optimal inputs shows shows shows shows simple simple simple simple simple paper small small small small small work work methods fig fig fig fig fig fig fig fig fig fig fig fig level level level current random random high high high high high high similar similar similar representation representation architecture architecture architecture show fixed line line line rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images general general general general average average average average average average average states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term term term term term term activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result university university university university threshold threshold threshold research research research research initial initial constant computer computer connections connections connections connections connections connections connections connections connections synaptic science science science science science science left direction direction direction direction direction range learn learn learn components outputs abstract applied applied applied back back back back back back back back back back back back back back references positive positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction effect effect effect parallel change change change change change change difference difference difference difference difference difference difference difference difference difference difference assume assume lower lower representations representations representations learned learned learned learned higher higher higher higher part cases cases cases cases required good good good conditions conditions conditions conditions conditions conditions conditions conditions conditions represent distributed expected make fact length length observed forward forward simulations simulations simulations simulations simulations simulations simulations simulations simulations ing total total total simulation regression regression regression regression regression regression regression regression regression regression regression sum sum performed eq eq eq eq eq eq eq eq eq eq eq eq called means means means factor negative negative negative negative original original original artificial represented compared desired desired series series proc proc perform perform perform determined related related constraints connected gain equal comparison larger connection connection connection connection connection connection update descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent report report institute institute institute consists internal code connectionist final layers layers addition computing hinton hinton hinton hinton view san top top top top stage stage effects requires requires requires approximate approximate approximate speed increase give produce produce produce condition randomly product product provided provided provided nature constraint biological measured technical technical describe group group group group group group group group group tested close close assumption assumption assumption assumption amount amount amount amount amount amount assumed generate supported role role rumelhart simulated account unknown unknown interesting interesting special special empirical principle squared squared squared squared squared squared squared squared direct making bottom bottom bottom bottom bottom supervised magnitude magnitude magnitude magnitude magnitude minimize run description description improve improve property separate apply moving moving identical identical sejnowski cognitive cognitive cognitive engineering sufficient teacher teacher approximately approximately approximately works works works works module module module module smooth smooth symmetric modified observation observation bounded bounded bounded bounded williams williams williams grant derivative move move move loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop occurs generally setting hardware hardware pass pass pass pass pass pass pass pass pass pass pass pass flow conclusion assumptions reduce measures modules modules accurate designed clear performs performs performs faster learns constrained strong hard hard hard physics california proportional proportional proportional proportional proportional intelligence start movements introduce introduce introduce derivatives derivatives derivatives derivatives derivatives derivatives manner groups groups groups attractor suppose appears construct produces longer mathematical mathematical changing changing changing implement implement implement implement linearly easy easy slightly slightly slightly scales develop applying national reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction stages codes codes codes codes codes restricted fraction converges updates diagram diagram diagram partial purpose closed closed closed remains intermediate initially visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible sufficiently sufficiently expect extension extension discussions compression extra capable capable uniformly society mcclelland wij wij wij wij post tend tend tend composed kind procedures showing showing symmetry symmetry symmetry symmetry symmetry lie follow hold hold satisfy involved modular backward backward thresholds received moves presents simpler diego american american investigate experience rapidly association issues biases helpful giving relationships office comparable encode hierarchy presynaptic psychology psychology equally changed changed changed changed obvious formal logistic logistic logistic precise precise mapped advanced slowly directed directed crucial agreement agreement lies lies correction implementing closer closer easier strictly immediately toronto toronto mellon alignment alignment argument argument carnegie applies double double elman passed passed passed passed requirement passes passes passes measuring pittsburgh anti aim monotonic monotonic incoming serve kinds calls picture picture picture aligned aligned aligned aligned aligned forming modify linearity linearity linearity linearity linearity linearity approximates approximates jth purely reconstructed reconstructed reconstructed reconstructed reconstructed encoder encoder encoder encoder encoder encoder discover naval smolensky smolensky arranged arranged eliminated overcome proceeds loops loops grow contract affected cottrell substituting analyses started ensures james equals moved colorado insight ballard ballard canada passing steepest steepest steepest steepest steepest steepest steepest steepest steepest agree agree implicitly zipser specification solves solves leaming leaming leaming creates creates propagating tendency tendency reconstruct modifying magnitudes geoffrey geoffrey geoffrey boulder relating exceed harder harder happen slopes behaves behaves coming differently council reversed focuses flows ackley seattle seattle raises symmetrical symmetrical symmetrical symmetrical sending establishing ensuring prescribed prescribed prescribed prescribed backwards violated violated experimented analyse goodhill linearities aims whilst enforced adjustments mike neurally oooo oooo wji wji wji wji wji wji wji canadian canadian fellow standpoint unrealistic informal informal informal galland galland departments departments criticism criticism criticism verbal franzini completing wid wik wkj wkj prescribes aligns dispense pictorial eyi 
#@Hinton_G,McClelland_J,
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#*network network network network network network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function figure figure figure time time time time set set set set set set set algorithm output output output output output output number system system system system state state state state state state state results results information information information information information models models performance based based based space case shown shown systems systems systems systems systems systems functions neurons neurons pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern processing control control control control control control control control control control control control control control control control control control control control control control control control control control large local local neuron test patterns patterns patterns matrix matrix inputs inputs inputs inputs inputs inputs form shows shows shows shows shows shows shows signal visual paper paper paper paper small small feature work work fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells features features features features process level level level level level level level level trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure problems problems problems high high high high high high response similar section section section general theory note activity activity activity activity activity activity result university threshold independent target initial constant synaptic presented presented present present present present low low low low frequency frequency frequency frequency frequency frequency temporal object motion range press press press basis outputs outputs outputs outputs outputs continuous continuous abstract back back back properties properties likelihood references due positive positive positive positive important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction circuit behavior behavior behavior behavior stimulus effect dynamic parallel parallel parallel parallel parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change lower signals signals signals signals signals prior higher higher previous previous previous previous previous previous previous firing firing firing type cortex cortex cortex cortex long conditions represent represent tree expected expected length observed observed observed forward total simulation human human called called called called called called elements elements elements means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement potential feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback global applications negative negative negative negative negative negative negative negative vol specific desired desired provide provide provide rates rates rates rates active active determined experimental experimental goal motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor cortical brain brain brain brain brain brain power larger larger contrast source institute synapses consists internal individual individual individual individual individual joint joint joint represents difficult considered considered equivalent environment environment directly additional additional view transition transition limit stage stage stage stage stimuli requires world basic increase give produce produce produce produce produce produce velocity velocity velocity velocity velocity controller controller types path actual actual processes evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply associative achieved achieved feedforward feedforward feedforward feedforward feedforward close corresponds corresponds circuits circuits circuits circuits circuits circuits common assumed assumed shape role main main main hypothesis degree degree sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory fit auditory combination reduced mechanism mechanism operation call inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition magnitude magnitude produced produced produced produced produced produced produced sources neuronal discussed movement movement movement movement movement movement movement movement lateral lateral apply strategy strategy strategy strategy array array array array array array array array array array array recently highly highly highly conventional approximately subjects tions studies studies trans positions positions observation observation gate sensitive amplitude intensity occur occur occur wide alternative alternative feed loop loop loop loop loop loop loop loop loop loop column flow critical reward reward central interactions propose strong mechanisms mechanisms mechanisms integration physics external external external external reduction demonstrated proportional turn turn movements movements movements movements movements movements manner manner manner manner manner connectivity appears appears primary laboratory transitions transitions transitions transitions transitions transitions transitions category explicitly electrical unique unique mutual mutual mutual mutual mutual events events events events review stages stages influence influence detailed detailed evaluate evaluate evaluate evolution centers similarly suggested past diagram diagram barto barto sec sec event purpose purpose generation generation generation intermediate dendritic fire includes includes bell bell inter assignment illustrated illustrated discuss specifically coupled neighbors successfully major major capable capable capable capable importance society detect projections projections projections receives receives receives summary summary kind induced success success interested physiological strategies timing duration duration duration duration categories involved usual play absence providing illustrates illustrates illustrates subsequent load intrinsic intrinsic intrinsic intrinsic receive receive modelling body body body body body body explore stimulation stimulation command command command command command command parametric parametric american american production circuitry circuitry circuitry relations strengths mass rise rise respond ideas ideas ideas ideas school tech project project project detectors biol plasticity muscle muscle muscle muscle muscle authors pathway pathway pathway pathway func notion analogous analogous math trace trace trace trace trace concepts plausible man rev illustrate thought impulse portion portion fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers generates explain explain explain explain explain explain motivated years burst burst burst burst burst burst developing developing developing fairly waveform failure capabilities interneurons starts london considerable considerable considerable processed tive closer closer sites sites strictly forces forces forces division located nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus monkey pool consequence angles axons axons res medical pathways pathways pathways pathways red red red effort marked recordings adjustable adjustable adjustable adjustable adjustable frequently rep commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands maintain operate aim branch modulated gen cal serve serve serve serve suited fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber shaped physiol physiol returns findings focused focused conditioning traces credit summed summed summed cybern physiology physiology generator generator generator generator generator interface extensive member vestibular acts branches controlling controlling controlling controlling neurophysiol receptors receptors receptors arrival robotics arranged climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing spontaneous spontaneous fits anatomical fan fan stated cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum loops loops efficacy serves neurobiology affected affected responsible muscles muscles muscles motivation inferior weakly cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar dendrites james studying regard lengths lengths lengths consequences somatic assembly branching arrangement enable specialized cerebral cerebral bursts bursts sustained sustained sustained sustained sustained waveforms waveforms extends messages messages propagate convergent influences mechanical outlined outlined discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge reflex reflex outline outline outline constitute constitute transmitted transmitted emergent presenting trigger trigger trigger trigger trigger trigger amherst chapter tendency tendency tendency constitutes constitutes chicago spinal spinal spinal spinal spinal spinal adjustment pub peripheral interact interact generators generators generators generators generators generators generators generators generators generators generators generators generators generators generators generators permits neurophysiological mediated argued projecting distal nuclei nuclei nuclei nuclei selectively emphasized diversity finger descending descending book bring tract tract tract tract tract elemental elemental elemental elemental elemental elemental elemental elemental elemental elemental elemental utilizing utilizing utilizing locomotion advantageous advantageous remarkable bursting send heavily ongoing designs spring spring impulses hypothesized hypothesized albus king diffuse diffuse puts somatosensory tors purkinje illinois sensorimotor sensorimotor sensorimotor sensorimotor anatomy cord cord cord cord cord exposed marr loads alan deals colleagues coins accounting resultant resultant bumps handbook meant reviewed shaping unusual transmit transmit granule granule translates ous derives slack houk houk houk houk houk houk houk houk blocked occurrences limb limb limb limb limb limb limb limb unexpected unexpected explaining plenum damping bodies repetitive repetitive repetitive repetitive repetitive tal schema schema schema schema schema schema schema schema schema prime contributing fractional continuing broader adjustments adjustments ito modulating treats posi schematically courses patterned patterned patterned patterned patterned patterned mediate mediate mediate terminated gibson mossy mossy mossy mossy mossy mossy mossy mossy mossy desire participate fruitful serving outlines ant preset preset preset converting brooks reticular reticular stretch continu olivary olivary olivary recep highlights shoulder routed conducting sole sole mediating probing presumed presumed elbow theme trigonometric collaterals collaterals collaterals originate abrupt alterations alterations stiffness sic minimally intriguing paragraph innervate initiate instrumental strained regulate acquires bethesda sect servo irl irl irl irl irl irl irl transmits transmits divergent annu grounds triggering atypical raven oper centrally proposing promote organiza northwestern relay neuroanatomical neurobiol premotor gielen precede precede microelectrode microelectrode biosci lished wrist paragraphs paragraphs cle innervating modelers postulates abundant punishment domi initiates responsiveness communicates succinctly stood liss affirmative collaborative mus 
#@Houk_J,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set set set set networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output number number number system system system system system system system system system system system system system system system system system system system system system system state state state state state performance performance space weights linear layer case case vector vector vector vector vector order order order order order order shown shown shown shown shown shown systems systems systems noise weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method pattern pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single control control control large large neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns inputs form form form form form shows shows shows shows shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal simple paper paper paper small small size size fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step process process process level level problems high high high high high high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response similar architecture architecture architecture architecture architecture show show show show show equation section section section section fixed fixed fixed line line vectors vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images images images images images images images real real theory theory term term term term note experiments experiments experiments experiments activity dimensional dimensional dimensional threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation research research research research research sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant computer computer computer computer connections science presented phase phase phase phase phase phase phase low low low low low frequency sets range range position position position position position position nonlinear nonlinear nonlinear continuous abstract applied back back back back back analog properties references component ieee positive adaptive introduction complex hand behavior behavior behavior effect effect search search change change spatial spatial spatial assume signals part center required required good good long long long long markov make make make fact fact fact correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length correct correct correct correct correct correct classes total respect times times times times elements elements elements elements dimension feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications obtain negative original original original application application desired desired desired cross cross cross provide provide proc experimental experimental goal gain gain gain gain gain gain gain gain gain discrete brain fields proceedings institute institute department loss loss version individual connectionist considered computing computing computing computing experiment experiment experiment experiment design design san effects conference capacity capacity full speed increase give give give lines lines path path path provided finally iteration iteration iteration iteration simply simply simply associative associative associative associative associative associative associative achieved achieved describe describe describe describe fast limited limited close close corresponds corresponds corresponds corresponds corresponds complete complete complete complete stable stable stable stable stable stable implemented implemented implemented implemented implemented implemented implemented assumed supported require main main face face face face face pixel pixel pixel pixel pixel pixel ability instance easily degree development development combination technology testing testing uniform making window window stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored international international international depth depth depth depth depth depth depth produced choose light light light light light light light light perceptron perceptron perceptron perceptron perceptron perceptron perceptron architectures resolution resolution exact advantage separate takes machines side pixels pixels sense array array array array array engineering dimensions sufficient sufficient varying previously volume yields match match match correspond achieve achieve trans channels channels channels channels entire amplitude intensity intensity intensity intensity intensity intensity rotation correctly correctly correctly loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop occurs occurs generally hardware pass pass pass pass pass demonstrate demonstrate demonstrate half strength conclusion reduce interactions designed peak peak peak peak peak peak peak taking strong strong hard mechanisms mechanisms physics external external external external external external external external cycle cycle cycle characteristics california solid proportional proportional proportional proportional turn variety plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane force acknowledgements reference reference appears appears pro construct construct longer index optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical changing changing modeled recall recall recall recall implement implement implement implement implement sensitivity simultaneously physical electrical involves involves spectral integrated adding formed formed formed shift shift shift shift shift shift shift yield yield yield yield yield focus focus formation depending depending correlated correlated overlap overlap variation transform transform controlled lee lee modulation modulation modulation modulation modulation modulation forms forms static discrimination discrimination spectrum diagram key key partial partial partial partial slow dashed dashed combining combining purpose purpose closed closed closed closed classified classified david coupling avoid recorded recorded recorded recorded recognize phys determining selecting efficiency suitable suitable paths paths paths paths paths presentation invariance invariance characteristic characteristic characteristic quickly allowing video video link anderson split classify classify oscillations device device device device device device device device device device device device device sampled write wave reach reach principles moves operating extend camera diego american american transformed create requirements put put limitations hall fourier fourier fourier fourier fourier fourier respond giving authors office office phases matched matched removed created implementations adjusted adjusted adjusted front fisher detector detector detector detector detector detector perceptton perceptton store store detected extent contributions electronic electronic seconds seconds isolated charge charge charge devices devices advanced band band guaranteed improves analytical capabilities independence spatially spatially implementing arc sites constructing controls pool cut cut cut cut cut ion scientific scientific involve opt opt opt opt opt read read read lowest arises arises computers computers computers computers computers recording recording recording recording recording recording demonstrates demonstrates auto auto conjugate reflect capability capability capability fed readily continuously continuously sharp schematic maintain passes gains gains pasadena gave sophisticated tolerance focused eventually traces june distortion instantaneous trade trade phenomenon picture shifted shifted person linearity pick rotated rotated rotated rotated rotated reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed interconnected interconnected arranged air imaging alpha interconnection interconnection attractive imposed grow grow shifts shifts imply spot exceeds arrays eqn eqn eqn interference induce displayed moved topological washington interconnections interconnections interconnections interconnections interconnections interconnections nonlinearities nonlinearities nonlinearities nonlinearities arrangement exposure exposure exposure diameter diameter eng eng record record record properly projects lett material thresholding thresholding ccd ccd discriminate abu mostafa planes planes focal focal die propagating medium corrected superimposed superimposed superimposed superimposed superimposed superimposed classifies associate reconstruct reconstruct evolve grouped compensate disadvantage hughes hughes thresholded thresholded march march march met mediated plate books ultimately win superposition inversely inversely placing modifiable modifiable atr circumstances beam beam beam beam beam beam beam reversed ate saturated saturated monitor monitor monitor impractical assistance spacing reversible mirror mirror mirror mirror pictures incorrectly stay concerns exposed exposed subtracting agency meeting laser laser grids optics optics optics optics screen evolving spie spie amplified appl appl appl cascaded cutoff fidelity materials materials comprised enter compromise broadband broadband aperture defense fixing promise addressable inform recalled recalled recalled mounted wagner wagner wagner holographic holographic holographic holographic holographic hole coincides bright bright hong won won entered psaltis psaltis psaltis psaltis psaltis psaltis psaltis psaltis incident schematically neurodynamics lens lens lens quarter rosenblatt army prism lose stays completes interconnectivity crystals crystals crystals crystals crystals recognizable recognizable correlator correlator awi designer regeneration prog tolerate latched latched latched latched latched transport transfers interfere supplying recalling isolate separations separations tape connors film amplify ken quan geometries plates modulator liquid liquid liquid hsu spartan laid topical demonstrations electronically brady brady sustain redistribution optically optically deteriorate inch modulators yariv crt optoelectronic optoelectronic rockwell rockwell imaged imaged imaged trapping beams beams rudimentary superposed sits readout exposing exposing thinner 
#@Brady_D,Hsu_K,Psaltis_D,
#t1
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#*network network network network network network network network network network learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data data data data data data data data function function function time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number error error error error error error error error error error error error error error state state results results results results results results results results problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case case case shown shown shown shown shown shown shown shown shown systems systems values values probability probability probability probability weight weight weight weight weight weight weight weight weight weight functions functions distribution recognition recognition recognition recognition recognition approach approach pattern pattern pattern point image single processing large large large rate rate rate rate test test test analysis analysis analysis class class class class class class class class class class class class class class inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form form form form form form form form form form form form form form form form form shows shows shows shows simple simple gaussian gaussian gaussian paper paper paper examples examples small small feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net net net net net net net net work work work work methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig points points points points points features classification classification classification classification trained trained trained trained trained trained trained trained trained trained trained trained trained structure problems problems problems problems problems random random random random random high high high high high similar similar similar similar similar similar similar similar similar similar similar representation architecture architecture show equation section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed general general speech speech speech speech speech theory obtained obtained obtained term term variables solution solution research defined table table estimate estimate terms terms connections node node node node node node node node node node node node node node node node node node node node node node left left left left presented presented presented presented presented presented presented map map map map map map map map map map map map map map map map map map map map map map low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum position outputs outputs outputs outputs continuous continuous continuous continuous sample sample abstract applied back back back back back back back back back back back back back back back back back back back back back back back convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density density density density density likelihood likelihood likelihood likelihood likelihood references ieee ieee ieee ieee ieee ieee ieee decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation context introduction introduction complex complex complex complex complex complex complex complex complex complex complex complex complex hand hand behavior generated generated parallel tion tion change difference difference classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier signals representations representations previous previous previous previous cases cases cases cases cases cases required required required required required required required required required required multiple good good good good good long long long represent represent represent markov techniques region region region region region region region region region region region region region region correlation correct errors finite simulations simulations simulations simulations simulations simulations resulting classes classes classes classes classes ing total simulation multi multi multi multi multi multi multi multi multi multi performed performed eq eq called called times times times regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions feedback policy obtain vol vol specific samples samples desired desired desired desired desired cross provide provide provide provide provide provide rates rates rates perform determined connected gain discrete brain equal mit comparison larger connection connection connection train train train train train descent nets nets nets proceedings proceedings institute department consists represents difficult difficult difficult final final layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers addition addition maps considered framework framework computing domain domain domain curve curve curve curve limit top top top top stage conference conference conference conference determine determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper upper upper significant significant randomly clustering developed developed area area types types types types lines lines lines lines lines lines provided provided provided provided provided provided provided selected selected depends simply associative arbitrary arbitrary arbitrary arbitrary arbitrary tested tested tested tested proof proof proof amount nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest implemented generate eds end typically needed fully testing testing york york head trials trials trials trials trials trials trials trials trials trials uniform details numbers numbers numbers stored international international international international bottom supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised combined combined combined combined run perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron architectures architectures improved improve recent robust robust separate separate separate separate reported include include machines machines recently conventional conventional unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised tions smooth converge definition modified observation grid grid grid grid grid grid grid grid organization improvement improvement entire studied suggests alternative alternative alternative generally pass demonstrate demonstrate demonstrate demonstrate demonstrate runs half place reduce reduce conclusions neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor valued valued valued valued interactions interactions designed faster faster faster faster asymptotic suggest suggest hard hard mechanisms physics drawn sigmoidal demonstrated demonstrated solid proportional labeled plane averaged scene force areas areas areas areas digit monte monte monte construct construct construct carlo carlo carlo laboratory implement implement implement implement sensitivity linearly involves involves remaining slightly slightly formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed boolean boolean select select select john expressed squares restricted labels labels organizing organizing forms forms understanding completely sign diagram slow dashed dashed dashed convex convex convex convex convex convex convex convex convex boundaries boundaries boundaries boundaries boundaries calculate assigned kohonen kohonen kohonen classified views transactions usa perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons illustrated selecting symbols comparing vowel vowel vowel vowel vowel vowel vowel ten ten ten ten traditional traditional traditional traditional procedures procedures split issue generative generative quantity automatically attempt illustrates extend situations situations situations explore simpler remain american wiley poor rapidly rapidly steady steady lippmann lippmann lippmann lippmann ml ml fewer fewer fewer tech rest authors cover momentum removed hill hill hill man extremely illustrate created created recognizer adjusted adjusted adjusted noted explored separated separated perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton shapes initialized mentioned percentage percentage percentage percentage histogram histogram histogram advanced separable majority capabilities capabilities worse comparisons rapid filtered hyperplane hyperplane computers cybernetics meaning exemplars exemplars geometric varies percent prop reflect freeman substantially led led flexible tional spoken capability fed slower limiting limiting fall occurrence occurrence adjust richard june june june proofs cooper forming forming forming guarantee summing hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes circular eliminate royal outcome robotics children eliminated air unlabeled unlabeled unlabeled belong disjoint disjoint disjoint disjoint disjoint disjoint disjoint disjoint disjoint disjoint disjoint knn knn knn constructive filled filled vowels vowels vowels mance separating falls sion cmac perfor washington percepttons percepttons percepttons percepttons percepttons percepttons percepttons percepttons histograms counting nonlinearities nonlinearities nonlinearities peterson peterson entries tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens april mem bins arrows arrows extensively hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube formant formant formant sons projects hart influences divide radar unchanged appeared ence gold shorter covering break july failed failed smoothly comparative comparative connec demon alter adapting clas shaded shaded shaded shaded summarizes duda thick interact carefully books books covered discusses book minor page ation slopes gauss gauss vice november covers versa august trainable albus albus puts hid burr agency offsets offsets offsets offsets offsets huang huang ooo classi attained placement william triangular assp mcgraw mcgraw mcgraw voice magazine defense fixing greatest excessive sponsored hood lincoln simula men goldstein phonological strongest untrained lay lay lay tially supervision separability separability proving pronunciation barney brains ions ions eval crafted jacobi strated interna illustrative alternately nique ist confer native government heard establishment deci crossed nilsson lexington insightful spartan spartan integrators intersects hod bined fro propa excessively excessively ceptron women ooooo singleton sifiers trainin trainin trainin inversions uated heed substan tiers 
#@Huang_W,Lippmann_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input function function function function function function function function time time time time time time time time set set output output output output output output output output output number number state state state state results results problem problem problem problem problem problem problem models based based based linear linear linear linear linear case vector vector shown shown shown shown values values parameters parameters functions functions functions neurons neurons neurons neurons neurons neurons method method approach approach approach approach point point processing large large local neuron neuron neuron neuron analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal simple simple simple simple simple simple paper net net net work methods fig fig fig fig fig fig features process memory similar architecture equation equation equation equation equation equation line general states gradient result result result computation computation computation solution solution solution solution independent found dynamics initial initial initial initial initial constant computer terms science nonlinear abstract computational computational computational convergence convergence analog analog analog analog analog analog analog references due due ieee ieee important introduction complex complex circuit circuit circuit behavior effect effect dynamic parallel parallel parallel energy energy energy energy energy energy energy energy complexity required required multiple good distributed correct simulations minimum minimum tasks multi eq eq eq eq eq called times elements elements regions means factor optimization optimization optimization potential potential global represented application provide define define proc proc proc determined experimental experimental voltage voltage voltage voltage accuracy connection descent dependent institute institute loss bias bias bias scheme considered considered directly solutions solutions design speed speed con condition levels nature depends biological associative limited inverse inverse inverse inverse inverse complete stable implemented implemented implemented implemented assumed shape shape square easily simulated needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield unknown coefficients coefficients coefficients jordan jordan technology exact advantage takes takes practical apply introduced sense highly highly highly compare solve solve converge symmetric constructed concept concept concept matrices matrices matrices hybrid column hardware hardware hardware hardware row reduce conclusions sigmoid sigmoid sigmoid numerical designed designed designed designed designed integration physics characteristics demonstrated relationship construct optical optical solving solving solving solving coordinates simultaneously simultaneously unique unique decreases solved lee decomposition decomposition converges constants calculation calculation calculation calculation calculation calculation calculate construction coupling coupling coupling coupling box contour variations efficiently identity characteristic characteristic composed interpreted sci sci device device processors processors processors processors processors processors american wiley rapidly rapidly rapidly rapidly steady steady applicable biol tanh affect configurations configurations singular singular singular singular noted ith ith electronic electronic optimum optimum optimum optimum advanced multiplication nonlinearity nonlinearity sys located located mation inversion inversion inversion inversion inversion inversion inversion inversion inversion acad acad opt opt definite robustness tional capability capability capability readily operate gains tank tank tank collective collective inherent simultaneous simultaneous simultaneous simultaneous converged realized cybern jth jth interconnected interconnected interconnected multiplier multiplier interconnection integrator modifications natl natl infor elimination elimination realization counting nonlinearities young steepest designing lett executed slight goodman goodman evolve tij tij tij mimic rewrite compu computa gauss differently externally traveling tial vii vii converter salesman triangular triangular appl essence ini accu uniformity controllable controllable nakano spontaneously steepness steepness dev unimportant 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#@Jang_J,Lee_S,Shin_S,
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#*model model neural neural neural neural neural input input input data data data data function function time time time time set networks networks system system system system system system system system system system system system system system system system error results results information information information information information information information information information information information information information information information information information information problem models models based based based space space space order systems systems systems probability neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit approach pattern single processing processing control control control control large large large large large large large large large large test test patterns patterns analysis analysis analysis analysis class optimal inputs inputs inputs inputs form signal simple small small small small small net task task task methods methods methods methods methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells process level level level level cell cell structure random response response response response representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture line general general general gradient gradient obtained obtained obtained activity activity activity activity activity activity activity activity activity activity solution solution solution research research defined target target target target target target target target target target target target connections connections connections science science left direction direction presented presented map map map present present present phase phase temporal temporal machine sets range press components outputs continuous continuous continuous sample abstract find computational computational computational references component important important important introduction complex complex behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus generated generated parallel search search search search search search search search search search search search search search search search search search search search search difference learned learned part type type conditions distributed techniques techniques region region region region region region region region region region region region region region region region proposed correct observed errors forward resulting tasks computed performed performed regions regions regions means made made feedback orientation study study study study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge filter filter artificial specific specific represented represented represented application receptive receptive receptive receptive receptive receptive provide compute determined experimental experimental experimental goal goal goal goal goal goal goal goal goal related related constraints connected motor motor motor motor brain brain brain brain brain brain connection fields fields fields dependent source source institute words consists responses responses addition addition considered environment environment environment environment environment environment directly solutions design stimuli stimuli upper requires significant increase channel randomly developed developed levels criterion processes processes processes selected evidence nature nature nature biological biological biological discussion group corresponds complete surface surface circuits amount short assumed generate supported role require end end easily easily degree makes development sensory sensory sensory sensory fit underlying needed combination functional functional interesting interesting increasing increasing increasing head head mechanism mechanism mechanism mechanism consistent structures empirical direct direct making stored frame minimize neuronal neuronal neuronal exact separate separate separate movement movement movement movement lateral lateral lateral introduced strategy strategy strategy strategy moving moving moving period period machines side side side sense subset array relevant highly highly highly varying previously observations observations approximately axis differential achieve mixtures organization organization sensitive grant exists intensity intensity intensity intensity intensity lead lead studied occur trial wide move move generally generally half flow critical critical reduce depend central differences differences differences clear clear suggest suggest suggest suggest propose hard mechanisms physics reduction cycle cycle turn turn exist movements selective selective selective iii iii iii iii manner connectivity identification solving primary transitions distinct dept coordinates involves unique integrated integrated agent agent select select expressed formation formation formation formation formation formation formation formation formation formation formation formation stationary squares influence controlled restricted evolution centers centers modulation modulation forms suggested translation converges tracking tracking tracking tracking tracking tracking tracking tracking tracking classified classified coordinate coordinate coordinate coordinate determines variations partially structural efficiency importance effectively successful successful identify detect projections projections projections projections situation excitation heuristic heuristic success showing showing physiological strategies duration comp comp comp comp comp comp involved involved involved involved play absence ill ill ill processors attempt illustrates illustrates operating extract extract intrinsic receive body body employed stimulation stimulation stimulation american essential rapidly rapidly rapidly rapidly rapidly put humans accurately biases existence project project project project behavioral behavioral behavioral behavioral muscle pathway pathway pathway topographic fundamental fundamental phases hill act naturally opposite opposite facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial subsets portion portion portion portion portion mapped nerve nervous fibers fibers fibers mixed extent extent established integrate animal animal animal animal animal animal indicating site site site site site great advanced directed directed directed directed directed directed directed directed track track track navigation adjacent failure failure biology glass glass glass briefly reasons processed processed turns straight sections sites sites directional directional broad nucleus nucleus nucleus nucleus immediately involve involve gradually gradually axons res res res computers recording behaviors behaviors populations pathways pathways pathways understood recordings recordings recordings recordings continuously continuously continuously continuously continuously frequently dots schematic schematic incoming physiol physiol physiol eventually univ phenomenon acquisition acquisition secondary primarily accomplished accomplished accomplished extensive extensive pick animals animals animals animals branches labelled labelled controlling food food food food food food food food food food food food food food food food receptors suppression suppression extending spontaneous cellular anatomical anatomical anatomical anatomical significance chemical cerebellum intelligent intelligent intelligent intelligent intelligent efficacy resulted exploit carry combinatorial days filled filled muscles muscles muscles muscles analyses utilized utilized lip injection injection injection injection injection injection injection colorado offers enable diameter fish fish fish fish fish fish fish fish fish fish axonal ahead ahead contraction refers refers probe concentration concentration concentration concentration concentration concentration considerations considerations projects adopted influences speaking reflex ure indirect sch constitute hair inferred responds feeding pointed sigma seek causing arg spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal adapting adapting visualization peripheral peripheral peripheral alternate lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe interacting crosses electrodes ultimately projecting interactive interactive nuclei cation amino amino amino finger finger finger denver locking responding descending descending turning turning electronics pools exhibited exhibited helps tonic species species locomotion locomotion tail acquire acquire swimming swimming swimming swimming swimming attributed vii converging ongoing water water ave hypothesized east locate utilizes diffuse caudal caudal caudal caudal caudal caudal caudal caudal suppress injected medicine anatomy tip cord cord cord cord cord cord cord cord cord cord proposal proposal possess anterior impedance neurol neurol neurol tactile symmetrical symmetrical strokes tracks acid acid acid approaching approaching approaching comm fin fin fin fin fin fin fin fin adapts est electrophysiological electrophysiological electrophysiological terminates terminates handbook acids acids acids brainstem brainstem subsystem subsystem subsystem nih artificially clues scattered ipsilateral ipsilateral motoneurons motoneurons objectives elaborate bodies bodies appli survival survival rostral rostral touch localize manipulations ele ascending ascending ascending mediate proximal postulated postulated damaged ninth seeking heat concentrations wired bull pattem ies brains reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular reticular rising highlight behav steep organism lock subsystems crystals stein owing tri dictated liver liver electro superficial validate marcel dekker nasal transport jaw originate reflexive asymmetrical asymmetrical commissural phasic phasic locus pulled ala llll ingredients ingredients longitudinal ingredient newell prey prey loci resets electrophysiology pipelined pipelined pipelined pipelined tracing bilateral bilateral neuroanatomical neuroanatomical directionality directionality thrust thrust neurobiol premotor lobes oral oral oral oral oral oral injections injections organizational lamb moroneurons moroneurons delineated restructuring mediates tonically tonically adoption amine jill transverse musculature musculature disproportionately disproportionately upto upto encyclopedia transduced bait underscores lil substance 
#@Kanwal_J,
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data function function function function function function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number number number number number number number number number number number number number number number number number number system system system system system system system system system system system system system system system system system system system error error error error error error error state state state state results results results units units units units units units units units units units units units information information information information information information information information information information information information information information information information information information information information problem problem models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden performance space space space weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case vector vector vector vector vector vector vector order order order order order order order order order order order order order shown shown shown shown shown systems systems systems values values values values probability probability probability probability probability probability probability probability probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method method method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point single processing large large large large large large large large large local neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple simple simple simple gaussian small small small size size size net net net net net net work work work work work work cells step step step step step step points points field field field process structure structure structure problems problems problems random random random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar similar similar representation architecture architecture show show show show show equation equation equation equation equation equation equation section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general speech speech speech speech real approximation approximation average average average average average states states states states states theory theory term term term term term term term term term term term term term term term term note note note note activity result result result university university university threshold threshold threshold independent independent independent independent independent independent log found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics initial constant constant constant constant constant constant constant constant constant constant constant constant constant terms terms terms terms terms terms terms terms terms terms terms distance distance distance distance distance connections connections connections connections connections connections connections connections connections connections synaptic left direction presented presented presented presented presented presented presented presented presented present temporal temporal maximum maximum maximum range range range press press learn learn learn outputs outputs outputs abstract back back back find convergence convergence convergence convergence convergence density density properties references due ieee ieee ieee positive important context context context introduction behavior behavior statistical effect variance variance variance variance variance variance variance variance variance variance variance search tion tion change energy energy difference difference difference difference variable assume assume assume measure word word chosen chosen chosen chosen chosen chosen chosen chosen higher higher higher bound bound type type type type type binary binary long distributed distributed distributed distributed distributed distributed distributed expected expected expected expected make fact proposed proposed proposed proposed length length length length length length length length correct correct errors finite resulting resulting ing ing ing ing ing total total total total total total sum sum performed eq eq eq eq eq called called times times times elements elements elements elements elements factor made made feedback feedback applications knowledge knowledge filter obtain original original original represented compared compared compared compared desired cross define define rates rates rates proc proc proc determined determined discrete discrete equal equal steps steps comparison comparison comparison connection connection connection connection connection dependent dependent dependent proceedings report institute words words department department consists represents represents represents represents represents represents final delay delay delay delay delay addition addition graph sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences ai ai maps considered considered computing view limit limit san san bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity efficient upper upper requires choice approximate approximate approximate approximate statistics increase give give give channel derived derived randomly randomly randomly randomly randomly randomly randomly randomly developed developed developed product product product product product product product product product product product product product selected selected selected nature simply biological biological biological associative associative associative associative associative associative discussion technical increases increases denote fast fast limited limited limited limited close close close assumption assumption assumption assumption supported role square end easily easily easily rumelhart including pairs hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield account dynamical coefficients interesting ratio ratio ratio york york increasing structures representing iterations making stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored bits bits bits bits bits bits bits bits bits bits bits bits magnitude magnitude idea attention added neuronal denotes discussed discussed discussed recent exact exact exact advantage takes element element typical similarity identical hierarchical hierarchical cognitive relevant varying compare compare approximately approximately works axis axis axis tions smooth smooth yields yields match match converge achieve achieve rl rl rl trans trans trans sparse sparse address address address address address address address address address definition definition definition locations locations symmetric modified modified generalized generalized generalized organization organization storage storage storage storage storage entire entire entire increased increased expression expression expression expression concept suggests correctly correctly loop occurs setting setting setting demonstrate half place row row greater assumptions assumptions assumptions hebbian competitive competitive competitive interactions interactions numerical moody strong mechanisms mechanisms physics physics physics largest characteristics demonstrated california proportional proportional assuming assuming assuming assuming assuming start start decrease relationship introduce configuration denoted acknowledgements suppose suppose suppose suppose suppose suppose suppose suppose appears relation pro construct construct written solving ways sequential sequential vertical mathematical changing recall recall recall missing explicitly explicitly explicitly linearly physical easy easy slightly slightly scales interaction interaction interaction interaction springer formed implies expectation select select select select select select select competition john john john letters letters letters focus focus expressed review review correlated correlated correlated correlated correlated correlated correlated correlated correlated overlap overlap overlap overlap overlap overlap viewed viewed viewed evaluate updated updated fraction fraction fraction showed approximations approximations approximations lee lee converges allowed past past past past sign sign sign sign calculation calculation delays delays delays delays reduces add iterative generation valid valid valid calculate string kohonen david precision precision box thesis activations priori priori usa formulation formulation formulation formulation formulation strings strings retrieval retrieval retrieval retrieval retrieval bell weighting memories memories coupled black holds holds phys phys phys discussions simplicity straightforward middle middle efficiency efficiency efficiency uniformly uniformly uniformly differ modification modification modification modification divided divided effectively included presentation successful successful build reached receives summary conf verlag anderson anderson split dis dis issue content follow sci sci sci sci hold built built write write write write giles delayed delayed delayed denker ill overlapping overlapping presents carried diego diego american wiley wiley production essential circuitry circuitry updating updating updating put put put detail strengths association limitations limitations limitations history history tech rest investigated investigated investigated applicable biol muscle proper analogous analogous matched math math closest concepts reading reading reading man extremely rev rev rev rev illustrate created thought adjusted hebb hebb store store store store store store store store store store store store store store store detected submitted explain years devices spin mentioned rows rows rows rows formula formula formula asynchronous asynchronous asynchronous derivation phenomena coded diffusion independence glass baum baum lies tool stanford stanford stanford sys closer widely constructing products mathematics acad acad grossberg grossberg grossberg calculations optimize read read read read read read cybernetics cybernetics radius radius radius radius radius radius radius sun addressed outer outer outer outer outer outer outer outer outer outer outer outer outer substantially fed lattice incorrect variant psychological price price berlin incoming tank tank qualitatively collective chen adjust adjust song hamming hamming hamming hamming hamming hamming hamming hamming hamming comments attraction attraction attraction attraction attraction contextual notes writing modify modify investigation investigation summing fix ratios arguments recover recover recover recover nat dynamically dynamically tensor tensor tensor tensor addresses addresses jones proceed numerically numerically numerically numerically ments ranges adjusting overcome cerebellum check moment contract keeping synchronous synchronous synchronous modifications continue sompolinsky sompolinsky sompolinsky separating recovered ranging governed james decide pat lengths den sphere entries darpa recog cerebral spatiotemporal spatiotemporal storing storing storing storing storing storing storing relies agree lett lett fold baldi stone fly divide divide dense sequentially abu abu unified numerous mostafa mostafa incorporates vec sig sig basin basin reaction axe willshaw willshaw willshaw propagating pointed pointed pointed connec basins basins basins basins basins examining scenario remainder remainder constrain gained shannon shannon shannon distribu distribu continues playing simplifying books kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva investigating ambiguous nasa nasa son minor minor minor preprint preprint mimic investigations nal nal coming coming walk syn mcculloch mcculloch info gratefully ble pitts pitts hat hop aid attempting dominates hid tors played keeler keeler keeler keeler keeler keeler calculates venkatesh venkatesh dissertation sparsely sparsely accumulate kirkpatrick edited ham zipset transpose tance tance autoassociative autoassociative autoassociative fair binomial fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity differentiate bradford iterating aip dent trend indepen indepen cyclic neglected addressable denominator denominator denominator syst recalled recalled recalled recalled recalled recalled physica proceeding proceeding formulas formulas formulas formulas ming tern winners winners 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gradient gradient gradient gradient gradient gradient gradient obtained term term term term term term term term term term term term note dimensional threshold variables solution solution solution solution solution solution research research sequence sequence initial initial initial initial constant constant estimate estimate estimate standard terms terms terms terms connections connections node node node node node node node left left map map present present low low nodes nodes nodes nodes temporal temporal motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum range components components basis nonlinear outputs sample sample abstract find find computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog likelihood references component component component component ieee introduction introduction introduction complex circuit circuit circuit circuit circuit circuit circuit estimation behavior effect effect parallel parallel cost cost cost cost tion change change energy energy energy energy energy energy energy difference variable variable spatial spatial spatial spatial spatial assume assume assume assume lower lower lower lower measure measure part part part multiple binary binary represent distributed bayesian equations equations equations equations equations chip markov make fact fact fact proposed correct correct errors finite minimum resulting resulting resulting ing tasks computed respect eq eq eq eq eq elements elements potential made natural global applications study study knowledge knowledge obtain negative original original artificial relative specific application define compute objects objects objects proc proc location location location location determined constraints discrete discrete power power mit mit voltage voltage voltage voltage voltage voltage voltage voltage contrast connection update update descent source institute institute institute implementation implementation version technique code individual final final final final bias sequences ai cambridge computing computing equivalent equivalent equivalent directly curve additional additional additional solutions solutions estimates estimates design top top detection conference upper upper requires world world vision vision vision vision vision estimated give give con developed criterion velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines provided processes processes processes processes processes processes processes processes processes processes processes processes nature depends constraint constraint constraint constraint constraint simply biological biological biological biological achieved measured discussion describe assumption assumption assumption corresponds surface surface circuits circuits circuits circuits effective implemented supported supported require require square vlsi vlsi vlsi vlsi vlsi pixel pixel pixel instance instance easily degree development noisy noisy noisy simulated unknown technology technology technology technology technology interesting edge edge edge edge edge mechanism special uniform principle leads leads leads details details iterations iterations stored bottom bottom depth depth depth depth depth early early early early magnitude idea choose run improved discussed improve recent advantage robust movement apply introduced strategy strategy moving moving moving moving moving include identical machines pixels quadratic quadratic quadratic sense interest dimensions approximately tions tions smooth smooth smooth smooth smooth correspond correspond converge converge achieve trans sparse background background chain locations locations locations locations grid grid grid grid entire grant constructed exists exists horizontal horizontal horizontal parts intensity intensity intensity intensity expression expression lead occur extended digital digital digital digital digital digital wide move hybrid hybrid hybrid deterministic occurs boundary boundary boundary setting setting setting hardware flow flow flow flow flow flow flow flow flow flow flow flow flow flow operator depend retina retina retina suggest presence presence presence physics cycle cycle demonstrated california california solid minimizing minimizing minimizing exist exist movements scene configuration configuration areas appears derive edges edges edges optical optical optical optical optical optical optical optical optical optical optical optical solving solving laboratory laboratory vertical vertical vertical segments confidence implement physical unique consisting consisting develop integrated applying minimization formed potentials cycles cycles family formation formation depending stationary stationary stationary squares squares squares squares squares squares overlap overlap solved variation open controlled controlled updated updated approximations evolution completely completely completely converges constants smoothing measurements measurements convex add boundaries boundaries boundaries interpolation remains foundation advantages koch koch koch koch includes silicon priori usa formulation color currents inter coupled neighbors closely effectively poggio poggio poggio poggio successful identify detect detect computations schemes tend soc compact strongly strongly video conductance conductance dis follow follow criteria sci hold hold involved sampled vary absence absence minimizes cmos cmos cmos cmos cmos ill ill processors neighboring neighboring neighboring acknowledgments camera camera law minimized minimized carried powerful american mead mead mead rapidly replaced rise rise giving ideal ideal variational contours measurement gradients gradients gradients naturally plausible reading configurations extremely illustrate voltages voltages voltages voltages eyes implementations portion mapped mixed synthetic synthetic isolated site great great piecewise piecewise ground smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness slope slope adjacent adjacent expensive inside inside stanford implementing implementing purposes incorporate located transistors transistors controls projected acad read computers computers recording demonstrates geometry nsf addressed requiring reflect amounts lattice lattice lattice lattice orders posed posed posed share completion formulated formulated formulated resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive continuously rely measuring gen qualitatively qualitatively prevent prevent pasadena pasadena geman geman geman geman geman geman conductances conductances conductances implements yuille 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work work work methods fig fig fig fig fig cells cells field cell cell structure structure structure structure random random random random random high high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar similar show show show show show equation equation equation equation equation equation equation equation section section section section section section section section section section section section fixed rule rule vectors vectors vectors vectors vectors general speech speech parameter parameter parameter parameter parameter parameter parameter real approximation average average average average states states states states states theory theory theory theory theory obtained term term note note note note activity university variables independent independent independent independent log log defined defined defined defined defined defined defined defined defined defined defined defined defined found found found found initial initial initial initial initial initial constant constant constant constant standard computer terms terms terms distance synaptic synaptic synaptic synaptic synaptic synaptic present phase phase phase phase phase phase activation activation activation activation activation activation activation activation activation activation low low low sets maximum maximum maximum maximum maximum maximum maximum maximum press learn learn learn learn learn learn learn position components components basis nonlinear continuous abstract find find computational computational computational computational analog properties properties references due due ieee ieee ieee important important adaptive adaptive adaptive introduction complex complex behavior behavior behavior effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic tion tion tion tion tion tion tion change change change energy energy energy energy energy difference complexity complexity complexity complexity complexity assume assume assume rules measure measure measure measure measure learned learned learned learned learned chosen chosen chosen chosen previous bound cases type type type binary long conditions conditions conditions conditions represent represent distributed distributed equations proposed probabilities scale scale scale scale finite finite simulations simulations simulations simulations minimum minimum minimum ing tasks simulation performed performed performed called called times elements means factor factor factor factor factor applications applications applications vol vol vol vol vol specific specific desired desired desired define define define define define define rates proc perform perform determined determined related related discrete discrete equal equal larger larger larger larger update update update update update update nets proceedings proceedings institute institute department implementation implementation version version consists difficult difficult difficult scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme addition addition considered considered considered considered equivalent equivalent equivalent directly curves conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine approximate statistics statistics statistics con con condition derived randomly randomly developed robot levels criterion criterion criterion criterion criterion bounds controller finally finally selected nature depends associative associative associative associative associative associative associative associative associative associative associative associative associative measured normal transformation limited assumption corresponds complete short theoretical end hypothesis easily easily including simulated smaller needed hopfield hopfield hopfield hopfield hopfield technology interesting increasing increasing increasing mechanism structures trials trials operation operation operation operation operation call call call numbers max pre stored stored stored stored stored stored stored stored early decay discussed discussed discussed discussed discussed discussed discussed improve directions property separate takes takes introduced introduced introduced introduced introduced introduced introduced introduced introduced introduced introduced introduced moving include period period period period identical recently recently recently recently recently engineering varying varying varying varying varying compare compare conventional conventional works works works tions rl rl rl rl trans trans trans address modified modified generalized generalized bounded storage storage increased increased increased exists intensity intensity intensity intensity concept invariant invariant invariant occur occur occur predicted predicted occurs occurs occurs setting setting strength place place place assumptions assumptions hebbian hebbian hebbian valued valued valued depend depend measures measures measures measures measures measures measures measures measures measures measures accurate asymptotic learns learns mechanisms physics largest largest cycle characteristics california labeled labeled assuming assuming selective selective min min relationship introduce manner pro monte monte carlo carlo longer longer solving ways plot describes describes mathematical dept changing changing changing recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall physical electrical involves slightly consisting events versus choosing independently focus expressed stationary viewed evaluated evaluated evaluate evaluate operations operations operations updated updated updated updated updated updated static static static static static static static updates updates updates allowed key earlier calculation event calculate sufficiently assigned advantages classified classified classified avoid avoid existing usa retrieval retrieval weighting weighting memories memories memories memories memories memories memories memories discuss phys successfully successfully determining aspects closely closely modification divided effectively schemes schemes reached reached reached reached receives characteristic composed summary refer quickly quickly repeated repeated interested dis content manifold criteria sci quantity write simplified simplified eigenvalue highest reach principles deal decreasing simpler american collection exhibit exhibit exhibit exhibit exhibit updating updating steady steady steady steady steady steady steady steady steady steady steady steady steady steady periodic examine giving giving ideas incremental incremental plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity analytically analytically analytically referred referred referred referred complicated func phases removed attributes coefficient coefficient adapt integer analyze analyze analyze rev adjusted quantities quantities quantities quantities quantities formal algo observe nervous defines spin ment developing trivial analyzed analyzed defining defining phenomena phenomena phenomena phenomena explanation analytical capabilities capabilities capabilities capabilities capabilities independence glass briefly starts starts starts snr snr snr snr snr snr tive closer incorporate worst worst worst worst involve acad grossberg grossberg describing gradually begin read qualitative greatly evaluating evaluating evaluating understood conducted 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recovered recovered recovered introduces belongs interconnections interconnections interconnections interconnections interconnections similarities recovery recovery recovery specialized eng repeatedly late probe probe probe probe summarize generalizing tures stopped informa informa abu ence leaving mostafa opposed emergent presenting conjecture conjecture tradeoff basins letting letting letting var var verified intuition formance continues mathematically mathematically disadvantage relate noting exceed pos selectively cation ltm memoryless memoryless memoryless memoryless discusses discusses discusses discusses exhibited holding behaves develops tonic emphasis mcculloch mcculloch mcculloch mcculloch palmer achievable achievable nonnegative nonnegative excess pitts pitts pitts pitts jointly hop adaptively adaptively focuses focuses focuses keeler identically identically venkatesh venkatesh ning separates architec anthony cardinality retrieved governing governing quantitatively 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systems systems systems systems systems values values values values values values values values values values values values values values values values values values values values values values values values values values parameters parameters noise functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition method method method method method method method method method method method method method approach pattern pattern pattern pattern pattern point point point point point point point point point single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing large large local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns analysis analysis class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form form form form form form form form form signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms simple simple gaussian paper paper paper examples examples examples examples small net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net work work work work work work work work work methods methods methods methods methods methods methods methods methods fig step step points points points points points process process process process current trained trained structure problems problems problems problems problems random random high high high high high similar similar similar similar similar 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constant constant constant standard standard standard computer terms prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented map map present present phase phase phase phase phase low low frequency sets maximum maximum range range range range range range range press press learn learn learn learn position position basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs continuous continuous continuous abstract back find references stochastic due due ieee positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important decision decision decision decision decision introduction complex behavior behavior behavior effect dynamic dynamic dynamic dynamic dynamic generated parallel parallel parallel parallel cost lower representations representations representations learned learned chosen chosen chosen chosen chosen chosen chosen higher higher higher previous theorem theorem bound bound cases type type type required good good binary binary represent represent distributed equations equations make make make make fact fact fact fact techniques region correlation correlation correct correct observed observed observed observed observed observed scale scale scale scale finite minimum minimum minimum resulting classes tasks tasks tasks simulation computed sum sum sum sum sum sum sum sum sum sum performed performed performed performed called called called called times times times times times times regions regions regions regions mapping mapping means factor factor potential potential dimension dimension dimension dimension made natural orientation orientation global global applications applications applications applications applications obtain obtain obtain obtain obtain negative original vol specific specific specific represented represented represented true series series series series series series series series series series series series series series provide provide provide provide perform perform perform perform perform perform perform perform determined determined determined goal goal goal related related related connected connected discrete discrete discrete discrete approaches steps steps steps steps steps steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger larger contrast train nets nets nets nets nets nets nets nets nets nets institute version difficult final final final final layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers delay delay delay delay considered considered considered framework framework framework framework framework cambridge computing computing equivalent curve curve additional view view view curves curves limit bit bit bit bit bit determine efficient efficient efficient upper upper full full requires significant significant approximate approximate approximate statistics statistics speed increase increase produce condition condition weighted area lines lines finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration nature nature nature nature nature depends achieved technical feedforward feedforward feedforward feedforward describe arbitrary arbitrary arbitrary group close corresponds surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface predictions predictions common common common effective effective implemented implemented assumed theoretical theoretical square square ability ability ability ability ability future future future future future future future future easily rumelhart typically typically typically pairs pairs smaller underlying needed needed dynamical dynamical dynamical functional functional functional functional functional functional interesting interesting significantly significantly increasing increasing special special operation operation numbers numbers numbers numbers pre pre window window bits magnitude magnitude magnitude polynomial polynomial polynomial minimize produced choose choose choose choose choose run added added predict predict predict predict predict predict predict predict predict predict predict predict predict predict predict predict architectures discussed discussed exact pair robust separate separate separate takes takes takes takes element element typical include period subject identical sense sense sejnowski sejnowski interest interest interest dimensions sufficient sufficient sufficient previously previously conventional conventional conventional conventional conventional conventional conventional conventional works tions tions solve smooth yields yields yields yields correspond differential differential differential differential differential achieve achieve achieve address definition definition positions chain generalized increased increased increased amplitude studied scaling scaling occur occur extended deviation deviation predicted predicted predicted alternative width deterministic deterministic deterministic deterministic occurs occurs occurs generally pass demonstrate demonstrate half conclusion conclusion conclusion critical place place minimal conclusions conclusions valued valued valued valued valued valued valued valued valued editors central central tangent sigmoid accurate accurate accurate accurate accurate accurate numerical numerical numerical numerical learns taking hard physics physics physics drawn sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal turn start exist plane decrease decrease iii manner manner manner manner connectivity connectivity connectivity connectivity minima minima configuration question attractor attractor attractor areas reference relation relation relation pro pro construct construct construct construct produces index index index index plot plot laboratory changing recall recall implement sensitivity multilayer explicitly infinite infinite infinite infinite infinite infinite physical easy slightly text consisting adding adding adding adding predictive predictive minimization minimization springer implies extraction boolean boolean cycles select select yield choosing choosing national dependence review depending viewed codes operations controlled controlled controlled labels lee lee lee evolution evolution forms approximated approximated similarly constants past past past past past sign partial reasonable reasonable reasonable reasonable reasonable slow performing delays expansion roughly add add add add iterative iterative interpolation interpolation interpolation interpolation intermediate string symbol symbol symbol symbol symbol symbol symbol symbol symbol construction construction advantages advantages precision expect template strings bell plotted plotted plotted plotted plotted prove discuss discuss phys phys phys phys phys discussions discussions tests successfully reason determining straightforward selecting closely capable suitable differ differ encoded divided symbols symbols symbols symbols mcclelland successful efficiently genetic situation situation situation tend tend compact kind repeated showing interpreted dis dis issue contribution contribution sampled usual wave wave delayed computes denker denker denker attempt attempt attempt attempt approximating acknowledgments deal modelling extend extend situations trains trains explore american poor xor xor xor collection collection collection essential investigate rapidly 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#@Farber_R,Lapedes_A,
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fig fig cells cells cells cells cells cells cells cells cells cells cell cell cell high high high high response response response response response response response response response response response show equation equation equation equation general average average average gradient activity activity activity dimensional result research research research defined defined found found found dynamics dynamics constant constant synaptic synaptic presented phase phase frequency motion motion range range press abstract properties properties properties properties properties properties properties references due propagation context introduction action complex behavior behavior stimulus stimulus parallel change lower measure measure signals higher part center center center previous firing multiple multiple multiple multiple represent distributed distributed distributed distributed distributed distributed distributed proposed proposed correlation observed observed sum vol vol represented represented application application rates proc location location location location location experimental posterior posterior gain gain gain gain gain gain gain gain gain gain gain power mit steps institute synapses synapses synapses individual individual individual individual individual individual individual individual individual individual represents responses responses responses responses responses scheme cambridge hinton view view view top stimuli determine increase weighted weighted weighted weighted area velocity velocity processes processes increases describe group group excitatory effective assumed supported require require eds degree degree rumelhart rumelhart smaller hopfield account coefficients transfer transfer transfer transfer ratio projection increasing head head head head head magnitude idea description description description description description population movement movement lateral lateral varying varying varying evaluation organization organization organization organization organization organization organization organization organization organization organization entire horizontal horizontal parts parts parts parts parts concept concept invariant spikes spikes spikes spikes rotation rotation strength strength trajectories conclusions central central central central differences differences sigmoid peak physics characteristics characteristics characteristics characteristics relationship iii groups areas areas appears appears primary primary primary primary primary primary primary primary primary plot laboratory tuned modeled sensitivity sensitivity sensitivity remaining versus versus potentials national review reconstruction depending overlap overlap variation variation variation detailed restricted ocular ocular ocular lee centers sizes sizes constants discrimination diagram intervals generation remains valid foundation foundation degrees degrees degrees includes major reason regular regular capable included mcclelland mcclelland post projections projections plots tend tend tend tend tend characteristic characteristic soc contribution physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological sci receptor receptor vary correspondence thresholds neurosci overlapping overlapping deal deal origin remain stimulation american exhibit accurately project muscle office variability cognition coefficient coefficient plausible nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nervous nervous nervous ith fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers consist simplest explain serial attempts seconds averages great great ganglion ganglion ganglion ganglion ganglion processed sections 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spontaneous systematic smith anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical los efficacy efficacy serves hope roles roles natl published irregular irregular surprising topological topological schwartz schwartz assembly assembly offers diameter diameter diameter diameter diameter diameter diameter foundations thin thin thin thin thin thin thin thin subsequently grants grants explorations mechanical microstructure constitute shading hair hair hair hair hair hair hair hair hair hair shorter formulate medium medium regularity regularity acceleration sinusoidal spinal peripheral preserved preserved segregation thick thick thick thick thick thick thick thick pdp mathematically neurophysiological depicts nuclei nuclei nuclei nuclei nuclei nuclei nuclei nuclei nuclei nuclei nuclei nuclei nuclei nuclei assemblies preserve afferents afferents afferents afferents afferents afferents afferents afferents tij tij milliseconds interspike travel travel simplification transduction vestibulo vestibulo vestibulo vestibulo hearing conceptual kth anatomy continuum continuum anterior anterior anterior anterior goldberg periphery periphery periphery periphery quick handbook health unnecessary saturate developments amer frog fractional sensed activating traditionally angeles opportunity postulated canal canal canal canal canal canal ant neck visualize organ emerging unitary electro microns microns microns predominantly postulate pertinent topographically topographically multilayered multilayered canals canals diameters diameters diameters diameters bundle maintenance posture innervate innervate innervate innervate innervate phasic ucla surgery semicircular semicircular semicircular bethesda sect latest arch innervation innervation innervation organs institutes wjk wjk sac intern variabilities innervating innervating ceils ceils reflexes reflexes lau clifford diffused intracellularly thinner 
#@Honrubia_V,Lau_C,
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#*model neural neural neural neural neural input data data data data data function figure figure figure figure figure figure figure time time time time time time time time time time time time time set number number number number number system state state state state state state state state state state state state state results results units units information information information information information information information information information information information information information information information information information information information information information information information information information information information performance based linear order shown systems systems values values values values values noise functions distribution distribution distribution method pattern processing processing processing local analysis analysis analysis class class class optimal shows shows visual visual visual visual visual visual examples examples task fig step step step points field field field field field field field field field field field field field field field field features memory response response similar similar similar show real states states states states states states states states states states states states states states states states states states states states states obtained obtained obtained note note activity activity activity activity activity activity activity activity activity activity result university defined found found sequence sequence constant distance science science left left left left left left left left left left presented presented map map map map map map map map map map map map map map map map map map map present present phase activation activation frequency temporal temporal temporal range press components components abstract references component positive positive procedure important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive hand stimulus stimulus stimulus stimulus stimulus effect effect variance parallel difference difference difference difference complexity spatial spatial spatial spatial spatial lower center cases type type conditions expected proposed forward scale classes classes classes classes classes classes classes classes total total human human human human computed sum called times times elements elements elements means potential potential potential potential potential potential global negative negative samples application series series series series series series series series series series series series series series active determined related related related related related related related posterior posterior constraints distributions brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain power power power power power steps steps steps fields fields support dependent dependent morgan institute department represents responses sequences maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps san stimuli stimuli stimuli effects effects classifiers upper requires requires requires choice choice significant free vision basic basic channel randomly levels types lines lines processes selected nature depends associative measured measured normal normal normal normal fast limited close close stable stable stable stable stable stable stable common effective supported eds eds hypothesis including typically typically typically smaller reduced account functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional unknown york york head head head segmentation mode mode mode leads pre pre pre window stored attention attention attention attention attention attention attention added separate include subject subject array subjects subjects subjects subjects subjects subjects works locations locations locations locations locations locations locations locations locations locations symmetric organization increased increased concept concept studied studied wide white white strength minimal minimal row row row greater segment segment differences differences differences differences differences mechanisms mechanisms mechanisms physics cycle characteristics characteristics characteristics demonstrated demonstrated selective manner identification identification configuration configuration configuration configuration acoustic areas reference construct produces perception perception perception ways sequential describes transitions dept changing segments segments linearly spectral spectral frequencies frequencies frequencies springer springer blocks blocks blocks potentials potentials potentials potentials cycles national extracted extracted depending stages stages viewed viewed viewed showed showed showed showed discrimination slow epochs epochs measurements classical sec event event event event closed closed closed remains intermediate msec msec msec msec msec msec foundation foundation eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg recorded recorded figures contour determines illustrated automatic automatic activated major maximal maximal maximal maximal maximal modes modes modes presentation tend quickly quickly induced induced induced running content content strategies strategies strategies strategies strategies duration duration duration relaxation relaxation automatically illustrates deal american access access investigate varied relations dotted periodic periodic successive successive behavioral mse biol biol int possibility relationships referred reliable examined possibly possibly configurations configurations illustrate voltages eyes eyes eyes adjusted shapes academic seconds established advanced ment ment ment ment ment ment ment spatially spatially spatially filtered consequence involve res reflects populations populations reflect dark flexible slower treated treated continuously incoming occurrence occurrence electric electric electric electric electric electric electric electric electric electric electric electric electric display display physiol synchronization univ extreme extreme extreme picture lab spectra spectra cybern ear ear ear sleep sleep sleep japan tation resources homogeneous neurophysiol neurophysiol neurophysiol neurophysiol addresses arrival arrival rigid spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous ments ments ments ments ments ments ments significance occurred alpha alpha alpha operates imply imply presentations presentations analyses utilized financial viewing similarities multiplied treatment treatment francisco offer record vertex draw material influences accumulated ure associations microstructure minus minus basically reaction reaction reaction reaction reaction reaction nition nition magnetic ical causal electrode electrode electrode electrode electrode reflected reflected conservative remote adjustment adjustment file permits crosses iso electrodes electrodes electrodes wise landscape landscape fir covered covered covered sta exhibited nal supporting triggered triggered circumstances reversal discontinuous discontinuous scalp scalp scalp scalp scalp agents hypothesized interpolated adaptively micro mirror developmental adult inclusion polarity polarity polarity anterior triangle chan chan chan chan chan intact reality reality reality est concatenated lar contents contents prominent adequately durations durations durations dipole suzuki atlas landscapes landscapes landscapes landscapes drug drug drug drug searched searched meaningless yon attentive gross gross gross mentation mentation extrema extrema offered traditionally traditionally switzerland atoms terminated heidelberg acknowledged consciousness consciousness consciousness consciousness paid paid dissimilarity ative clin clin clin rationale nent analysed walter med pal pal pal alertness mined unimportant opens handicapped visualizing electro electro muller diseases millions manifest manifest manifest emotions lesser conscious swiss constrains adults adults persist momentary momentary momentary momentary momentary momentary momentary momentary momentary momentary momentary momentary momentary momentary momentary momentary strate strate aps resorting ain ain corp confi confi confi confi confi confi effected voluntary grass brandeis brandeis emulates wien electroenceph electroenceph electroenceph electroenceph sac neurobiol neurobiol processin processin processin processin processin processin processin processin electromagnetic distinctly hospital connectivities involvement ely descriptors nificantly learnin uration uration uration fellowships adequacy nificant isopotential infancy informations manifests ibaraki hum metabolism hts abstracting 
#@Brandeis_D,Horst_A,Lehmann_D,Ozaki_H,Pal_I,
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#*network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks output output output number number number number system system system system system system system system system system state state state state state state state state state state state state state state results results results results results results results results results results results units units units units units units units units units units units units units units units units units units information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models performance performance performance performance based based based based based based based based based based based based based based space space space weights linear linear linear linear case case case case case case case case case case vector vector vector vector vector vector order order order order order order order order order order order shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values values values values parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method approach approach approach point point point point point point point single large local local local local local rate patterns analysis matrix matrix matrix matrix matrix matrix optimal inputs inputs inputs form shows shows shows simple simple paper paper paper paper small size net work work work work task methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods fig fig fig fig fig fig fig fig fig step points points points points points points points field field field process current problems problems problems problems problems problems problems problems problems high high response similar similar similar similar similar representation representation show show show show equation equation equation equation vectors vectors general general real real real approximation average states states states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term term term note note note note note note note activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result threshold threshold variables variables variables variables variables computation computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research research research research found found found target target target target target target target target target target target target target target dynamics initial initial initial initial initial initial initial initial initial initial constant constant constant constant table table table table table table table table estimate estimate standard computer computer computer computer computer terms terms terms connections connections connections science science left left left presented presented map low low frequency motion range range press press press press press components components components components components basis nonlinear nonlinear outputs outputs continuous sample sample sample sample sample abstract applied find find find find computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational convergence convergence convergence convergence analog analog analog analog references references component component component stochastic ieee ieee ieee ieee ieee positive important important important important introduction introduction action circuit circuit circuit behavior cost cost cost cost cost cost cost search search search search search search search search search search search tion tion tion tion tion tion tion change energy complexity complexity complexity variable variable variable lower lower measure measure measure measure measure chosen chosen chosen chosen chosen chosen part center cases cases cases required required required required required required required required required required required cortex binary binary binary binary long long conditions conditions conditions conditions conditions conditions represent equations equations equations equations equations equations equations make techniques techniques techniques techniques length length length correct correct observed observed observed observed observed observed observed observed forward simulations simulations simulations simulations simulations simulations simulations simulations simulations minimum minimum minimum minimum minimum ing ing simulation human human respect respect respect respect multi multi multi multi multi sum sum sum sum eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq times times times times times times times times elements regions mapping mapping mapping mapping mapping mapping mapping mapping mapping factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization potential potential potential potential potential potential made made global study study study study obtain artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial relative relative relative specific samples represented compared compared compared application application rates proc proc proc proc proc proc location location location location determined determined gain discrete brain brain brain brain steps comparison comparison comparison comparison comparison connection fields fields fields fields support descent dependent source morgan morgan institute institute institute words version version internal bias scheme scheme addition graph graph graph graph considered cambridge computing computing computing computing computing experiment experiment additional additional view view solutions solutions solutions solutions solutions solutions solutions estimates estimates estimates transition transition transition transition transition transition transition trajectory trajectory trajectory trajectory bit bit bit upper full requires requires significant significant significant free world world give give con condition condition derived derived derived derived derived derived derived weighted weighted randomly criterion velocity path path path path path path path path path path path path provided finally inhibitory depends depends simply simply simply achieved measured measured measured measured discussion increases describe describe tested assumption corresponds corresponds corresponds complete stable stable stable surface surface surface surface surface surface surface predictions circuits circuits circuits finding finding finding finding short common effective implemented implemented assumed assumed assumed generate supported role theoretical require require ability ability ability cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster easily makes simulated typically smaller underlying underlying underlying underlying underlying needed needed needed needed needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield combination reduced reduced dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical coefficients coefficients coefficients coefficients technology technology significantly increasing head head consistent consistent consistent principle principle principle principle principle principle principle squared representing representing representing numbers pre bits depth depth depth depth depth depth depth magnitude magnitude magnitude magnitude magnitude magnitude magnitude idea attention combined run added sources sources sources denotes denotes denotes denotes denotes denotes directions directions recent recent advantage property takes element element element element element similarity movement reported reported reported reported reported reported reported reported apply introduced introduced period identical identical side quadratic quadratic quadratic quadratic quadratic quadratic sense sense sense sense subset recently relevant interest interest interest interest sufficient sufficient sufficient compare compare compare calculated calculated calculated calculated calculated works tions tions tions tions solve correspond correspond correspond studies studies converge differential differential differential differential differential trans trans trans trans trans trans diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal definition locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations symmetric observation generalized generalized interval constructed constructed constructed exists horizontal horizontal lead studied deviation derivative derivative derivative derivative correctly hybrid width boundary setting hardware hardware hardware hardware hardware half half half half half half conclusion starting starting starting critical row row row trajectories trajectories operator operator operator operator operator operator operator operator operator operator differences differences differences measures measures numerical numerical numerical numerical numerical clear clear faster faster faster faster faster faster faster suggest suggest suggest suggest suggest suggest suggest physics largest california variety exist exist decrease relationship relationship relationship derivatives derivatives derivatives derivatives manner minima annealing question acknowledgements explicit suppose suppose relation derive derive derive construct written longer longer longer index solving ways estimating describes describes describes describes transitions transitions transitions transitions transitions transitions transitions vertical vertical mathematical explicitly transformations text text angle angle angle angle angle angle develop integrated minimization minimization springer potentials potentials potentials potentials potentials john choosing independently dependence squares transform restricted showed forms forms static understanding suggested sign reasonable reasonable slow dashed measurements measurements measurements measurements measurements measurements measurements measurements spaces spaces neighborhood purpose closed valid valid calculate assigned construction construction koch degrees avoid expect coordinate formulation determines specifically major reason selecting efficiency efficiency efficiency capable capable capable uniformly paths paths driven included identify identify identify efficiently computations genetic genetic comparing comparing comparing situation situation situation tend composed refer verlag prob success interested classify oscillations follow timing sci hold hold satisfy notation notation michael simplified simplified observable denker denker denker leading reach reach received received principles principles illustrates illustrates subsequent neighboring deal decreasing situations american collection exhibit circuitry strengths strengths strengths replaced integral integral mass biases existence existence rise rise scalar scalar scalar scalar scalar examine giving giving history ideas mappings investigated possibility possibility possibility relationships relationships referred referred referred comparable complicated complicated tanh func func func func understand analogous hill hill hill hill smallest measurement plausible necessarily opposite illustrate illustrate singular olfactory der noted noted observe explored mapped nervous academic initialized art extent extent arbitrarily phd electronic electronic years devices devices devices percentage great advanced inequality developing agreement derivation analyzed analyzed defining explanation analytical analytical analytical analytical analytical analytical analytical analytical multiplication baum drive perspective perspective implementing purposes sys closer widely constructing operators immediately involve angles angles acad grossberg calculations beginning definite definite definite res medical medical medical preceding mellon researchers researchers conjugate integrating requiring improvements improvements considerably freeman freeman offset tional tional simulate experimentally experimentally cohen orders orders passed continuously incorrect compares schematic operate summarized summarized monotonic monotonic monotonic monotonic monotonic cal occurrence occurrence tank tank tank serve sums semi semi semi electric electric electric electric electric electric electric electric conclude decreased deviations baird differentiable differentiable differentiable differentiable displays displays irrelevant irrelevant initialization consistently person ordinary ordinary ordinary ordinary benefit proofs indices identifying sort restriction amplifier optimizing concerned unity nonzero climbing climbing platt imaging imaging imaging imaging imaging imaging imaging tools replacing stated multiplicative moment moment moment moment moment moment moment balance occurring transforms analyzing definitions monotonically monotonically imply integrator integrator intuitively adequate adequate corner corner constructive natl moments moments moments moments moments moments moments moments moments moments substituting exploring mance james appendix appendix widths perfor lengths lengths searching sphere sphere sphere interconnections spherical spherical spherical spherical multiplied iterated iterated iterated cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral thin matter refers proximity route hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube eqs eqs eqs eqs eqs std std pen cam convergent lem ple shading shading shading shading shading ter equivalently goodman ties benefits cooperative job revealed axe axe axe axe distinction theorems theorems theorems theorems comparative monotonicity acceptable ical guess guess guess avoided avoided reflected ary visited shaded summarizes summarizes exam exam resistor evolve evolve diag diag tems ization searches searches met kanerva differentiation noting integrals employing covered emphasized emphasized emphasized superposition figs figs electronics nasa nasa son supports amplifiers amplifiers lapedes lapedes nal bill travel travel compu computa computa mea bridge remarks simplification simplification scalp scalp scalp scalp settling settling settling settling settling settling settling settling settling settling settling settling settling settling settling settling settling settling ferent locate aid imple exper suffices mining keeler accomplish stay formulae concerns optima optima devised devised dissertation dissertation settle comprising sij optics governing degenerate neurobiological iti fol creation subscript deter deter vicinity comer comer comer comer comer comer comer comer comer comer comer comer comer comer comprised aip aip aip aip aip scattered dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole dipole began facilitates simula unifying putational putational putational farber farber direc settles settles plausibility plausibility bio superscript accu complications dealt dealt extrema extrema extrema extrema extrema extrema extrema extrema formulations puter constituents superiority holmes bifurcations notably ames terry terry perspectives solu solu clus lowing volumes mented poten optimiza optimiza explores dev circumvent tational gra euler klein leong leong bears multiples contributed concluding conducting comers comers comers comers comparatively settled settled simplifications zation prog traversing traversing hin obser extremum extremum extremum extremum extremum extremum extremum extremum extremum concentrating dient recipes contradiction teukolsky teukolsky brody brody brody als favored flannery flannery wit varia criticism tered print consid consid numer opportunities vetterling loci loci semiconductor semiconductor ineffective advan sistent traverse phi caption unambiguously harrison reside ine electromagnetic electromagnetic electromagnetic assertion deeply optim mine vations guckenheimer guckenheimer converse ncc moffett exci texts sigrnoid excludes hinder erate reviewing tage ships answering verifies rately imag acldey tatory partials qua atten contend instantiate mulated invasive advancing contradict denser homogeneously affirmative sequent ale 
#@Leong_H,
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output number number number number number number system system system state state state state state state state state state state state state state state state state state state state state state state state results results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem models based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case case case case case case case vector order order order order shown shown shown shown shown shown shown systems systems values values values values values values values values values values values values values values values values values values values values probability probability probability probability probability probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise distribution distribution distribution method approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point single processing processing processing processing processing processing processing large large large large large large large local local local local local local local local local rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis optimal optimal inputs inputs inputs inputs form form form form form form form shows shows signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple visual paper paper examples small small small small small small small small small size size size size size size size feature feature feature feature feature work fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells step step step step points points points points points points features features features features features features features process process process process process process process process process process process process process process process process process level level level cell cell cell cell cell cell cell cell cell cell cell cell structure structure problems problems high high memory response response similar similar similar similar similar similar similar representation representation representation show show show section section section section section section section section section section fixed fixed fixed line line line rule rule rule rule rule general general general general general general real approximation average average average states states states states states states states states states states states states states states states states states states states theory theory gradient obtained obtained obtained obtained term term term term note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result variables solution solution solution solution solution solution research independent log log log log log defined defined defined defined defined defined defined defined defined found found found found target target initial estimate estimate computer computer terms terms distance distance distance distance distance distance distance distance distance connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic science left left direction presented map map map map map present present present present present present present low low low low low frequency frequency temporal temporal maximum maximum maximum maximum maximum maximum maximum maximum range range range range press press press position position position position position position position position position position position position position position position nonlinear continuous abstract applied applied applied applied applied find computational density properties properties properties properties properties properties properties properties properties properties properties properties properties properties likelihood references component due positive important important important important introduction complex complex hand hand estimation behavior behavior statistical statistical statistical effect generated variance variance variance variance variance variance variance variance cost search change change difference spatial spatial spatial spatial assume assume assume lower lower lower rules signals signals signals chosen chosen higher part center center center center center center center center center center center center center center center center center center center center previous previous previous previous previous previous previous previous previous previous previous previous cases cases cases cases cases type type type type type type type type required multiple binary long conditions conditions conditions conditions conditions represent represent distributed make make make fact region region region region region region region proposed proposed proposed proposed length length length length length length length probabilities observed scale minimum minimum minimum minimum minimum minimum resulting resulting classes total total total simulation sum elements regions regions regions regions regions regions regions regions regions regions regions regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping means means means optimization optimization optimization optimization optimization optimization dimension made made natural feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global relative relative relative specific specific specific represented represented represented compared compared compared compared compared receptive provide provide provide proc proc proc active determined goal related constraints constraints constraints constraints constraints constraints connected connected distributions gain discrete discrete discrete brain equal equal equal equal equal equal equal power power steps steps steps contrast connection connection connection connection connection fields descent source source selection institute words loss implementation implementation consists consists consists consists consists consists joint final layers layers layers layers layers delay delay maps maps maps maps maps maps maps maps maps maps maps maps maps considered cambridge domain domain domain domain domain domain domain domain equivalent solutions top stage stage stage stage determine determine upper upper choice choice choice significant significant statistics statistics give give produce produce produce produce weighted clustering criterion criterion area area area area area area area types lines lines lines entropy entropy processes nature depends depends biological biological biological associative measured discussion discussion discussion feedforward feedforward feedforward describe arbitrary denote denote denote transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation limited corresponds corresponds corresponds corresponds corresponds corresponds surface surface surface amount amount amount amount short implemented assumed shape shape generate generate generate role main main square square makes development development development development development development including smaller needed reduced reduced reduced account fully character edge structures matching uniform uniform uniform principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle operation operation operation operation leads leads leads principal details call call call call making making bottom minimize description light light discussed discussed discussed discussed discussed directions directions directions directions correlations correlations property property property property ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble typical typical similarity lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral apply apply introduced introduced include include subject subject subject subject identical identical sense sense sense sense sense array array recently relevant relevant relevant relevant interest interest dimensions dimensions dimensions dimensions dimensions approximately approximately pca pca definition background background positions positions positions symmetric interval interval interval interval organization organization organization organization constructed horizontal horizontal horizontal horizontal horizontal horizontal lead lead lead studied suggests suggests suggests suggests suggests move width width deterministic deterministic occurs boundary boundary generally generally setting flow strength greater greater greater greater reduce neighbor neighbor valued interactions interactions interactions interactions differences performs mechanisms presence presence physics largest largest drawn demonstrated proportional proportional labeled labeled labeled labeled turn turn minimizing selective selective relationship relationship iii iii iii iii connectivity acoustic denoted areas areas areas areas reference reference suppose suppose suppose suppose suppose suppose suppose appears relation relation relation relation derive produces written written longer solving describes label stability vertical mathematical segments recall metric metric implement implement explicitly coordinates coordinates coordinates coordinates coordinates coordinates coordinates simultaneously dimensionality dimensionality involves transformations transformations transformations text angle unique interaction interaction interaction develop develop applying springer extraction decreases choosing choosing formation depending depending stationary viewed detailed detailed detailed densities labels organizing organizing organizing organizing evolution centered centered centered forms understanding understanding understanding understanding activities activities activities similarly suggested suggested suggested allowed processor sign diagram key earlier earlier earlier delays spaces spaces neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood intervals purpose generation remains intermediate sufficiently euclidean kohonen kohonen kohonen kohonen kohonen kohonen topology degrees perceptual perceptual perceptual perceptual perceptual perceptual priori coordinate coordinate coordinate coordinate coordinate usa usa formulation formulation formulation bell determines extension discuss discuss activated domains neighbors neighbors neighbors simplicity columns columns straightforward identified capable uniformly uniformly suitable differ differ differ differ encoded encoded encoded modification modification modification modification divided situation tend tend tend tend tend tend receives summary soc verlag induced induced induced induced induced lie content follow sci sci device device satisfy quantity quantity bar bar bar bar bar bar bar bar bar bar bar bar bar simplified simplified relaxation realistic maximization processors received attempt moves illustrates illustrates oriented situations minimized minimized unlike selectivity selectivity selectivity selectivity selectivity selectivity carried american layered layered layered layered wiley wiley transformed production production involving strengths strengths replaced dotted dotted dotted periodic existence rise respond fashion giving tech mappings mappings biol possibility possibility relationships relationships maximizing comparable comparable complicated complicated pathway affect encode statistically topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic attributes attributes attributes attributes smallest math naturally closest closest plausible possibly changed changed thought versions der der portion portion noted mapped mapped mapped mapped hebb hebb hebb hebb hebb hebb hebb message message message message message message message message message message message message message message message message message message consist generates extent extent extent extent explain motivated synthetic synthetic devices developing theoretic theoretic theoretic theoretic distinguish orientations analyzed defining slope lies london processed processed implementing sections sections sections satisfied satisfied satisfied closer closer organized organized arise separately angles acad describing pitch optimize localized localized linsker linsker linsker linsker demonstrates qualitative qualitative qualitative radius radius fluctuations argument geometric geometric geometric geometric geometric geometric geometric geometric geometric geometric greatly behaviors applies fuzzy fuzzy substantially empirically axes share frequently dots biologically biologically biologically maxima exhibits partitioning partitioning partitioning maximizes qualitatively achieves gave sums logp hamming chose sophisticated decreased tolerance tolerance implements tile calls univ sharing irrelevant realized realized trade globally contribute ear accomplished labeling restriction interconnected lost lost oja oja chance satisfying simplify proceeds interconnection stated stated nearby transforms analyzing analyzing roles disjoint intuitive intuitive selects natl natl moments eqn eqn eqn motivation tone equals induce surprising von von sides sides regard regard lengths lengths consequences consequences thomas treatment ensembles emergence emergence emergence emergence thin insight roy draw messages messages messages messages statement border border border border border border border border border border border ignore assigns infomax 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distortions accordance traveling jointly neighborhoods bold reversible dominates clarity interaural interaural cylinder cylinder cast sharply sharply sharply devised progressively preservation preservation preservation preservation preservation preservation lying lying restricting raises adjusts distorted salesman vertically absent encodings encodings positional nominal enforces convey syst watson dissipation ears ears favors imposes schuster sensed ansatz ansatz heights deeper conveyed conveyed conveyed complications dealt imposing helix helix helix helix helix postulated confirms displaced displaced occupied conveys ordinate disk disk disk disk disk disk disk disk rendered comprise responsive bearing functioning exclude signaling signaling mature mature abscissa standpoint narrower ralph organize copenhagen elongated elongated elongated unoriented resemblance resemblance warped heuristically heuristically restricts shed establishment multilayered multilayered deterministically favored beneath yorktown sharpening sharpening alters quiet quiet quiet dimensionalities cylindrical ili gaining rhs eqns tending mil deeply sharpen expose enclosed interscience slab slab cotterill definiteness fuller thermodynamics thermodynamics partitionings tea 
#@Linsker_R,
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#*network network network network model model model model neural neural neural neural neural input input input data data data data data data data data data data data data data data data function function figure time set set networks networks networks output output output output output output output output output output number number number number number number number number number system state state state state state state state state state state state state state state state state state state state results results results results information problem problem problem based space linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown shown shown shown shown shown shown systems systems neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit recognition method pattern image single single single single processing processing large neuron matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form shows small net net net net net net net net net net net net work fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells process cell structure structure structure random random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response similar similar architecture architecture architecture architecture show vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors average average average average average states states states states states states states theory obtained obtained obtained obtained dimensional dimensional dimensional result university threshold research research found found found standard standard computer terms connections connections connections present phase phase machine press press press components basis basis basis basis basis basis basis basis nonlinear nonlinear abstract back back back back back back back back back back back back back back back back find computational analog analog properties references component component component stochastic due due due due ieee ieee adaptive adaptive adaptive adaptive introduction action action action action action effect parallel cost tion tion chosen chosen chosen part part bound bound cases cases required required required good good good good good good fact proposed correlation forward forward forward forward resulting resulting total sum performed called called called called times times elements elements means factor factor dimension dimension dimension dimension feedback feedback feedback feedback applications applications compared compared compared application application proc discrete discrete discrete discrete discrete comparison contrast connection connection connection connection connection connection connection selection report report institute implementation code final layers layers layers layers layers delay considered considered equivalent equivalent equivalent equivalent san conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity upper upper full requires choice speed vision basic produce condition coding coding coding coding product product selected simply simply simply associative associative associative associative associative associative associative associative associative associative associative achieved achieved discussion normal normal increases denote transformation transformation transformation transformation transformation transformation fast complete stable stable stable nearest nearest common effective effective implemented implemented supported require require square square smaller smaller hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield combination combination technology block york special operation operation operation operation operation operation operation call numbers iterations iterations stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored international denotes improved improved discussed improve improve directions advantage robust takes introduced cognitive interest dimensions previously previously calculated calculated calculated tions trans trans modified gate gate gate gate storage storage storage storage storage sensitive expression deviation deviation column column half half half half half half half half flow place row performs taking taking taking taking mechanisms physics reduction proportional selective selective selective relationship manner manner question appears relation monte carlo written optical optical optical optical optical optical optical optical winner winner winner winner winner winner winner winner winner laboratory label label label label label label label label pruning pruning recall recall recall recall recall recall recall recall recall sensitivity sensitivity simultaneously physical blocks versus select choosing choosing choosing choosing influence codes transform transform transform transform transform transform transform updated updated labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels organizing margin calculation initially initially norm norm norm euclidean kohonen kohonen kohonen usa memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories plotted activated variations included modes computations identity orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal composed contained allowing anderson anderson anderson content device device hold notation simplified providing principles operating command diego american put replaced limitations limitations mass ml ml ml ml ml ml scalar scalar scalar fourier fourier giving investigated investigated fault fault fault fault fault fault combine proper workshop affect affect closest configurations configurations perfect perfect front front front front front front front front front front front front front front front front front noted freedom explored academic art art art message extent simplest simplest percentage percentage percentage percentage advanced rows rows rows trivial coded coded coded coded coded coded independence reasons considerable straight tive arise mation products products acad grossberg grossberg opt opt opt opt calculations depicted auto annual nsf outer mechanics robustness conjugate conjugate understood lack cohen passed remove occurrence serve collective coherent boston tolerance tolerance tolerance damage june trade ordinary ordinary accomplished accomplished writing writing bipolar bipolar bipolar oxford investigation concerned unity proceeds replacing contract contract abilities transforms synchronous synchronous synchronous synchronous selects natl spurious spurious spurious spurious started regard dominant dominant dominant dominant dominant arrangement arrangement winning neuromorphic partitioned partitioned projects lett lett lett thresholding thresholding thresholding thresholding thresholding thresholding thresholding thresholding thresholding thresholding reflex graded emergent pointed connec connec acceptable lit avoided avoided massively rain reflected alter stroke stroke stroke stroke stroke stroke stroke stroke stroke alternate graphics thresholded thresholded thresholded thresholded thresholded oct march deleted option figs placing prevents subspaces challenge stores stores loaded loaded orthonormal orthonormal orthonormal orthonormal orthonormal orthonormal orthonormal agency settle partly accumulate optics arpa arpa implied autoassociative autoassociative autoassociative autoassociative autoassociative autoassociative autoassociative autoassociative autoassociative sending reflection reflection appl smc icl icl accounting tations enter defense wong pointer cuts cuts addressable carpenter inappropriate ira bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional deleting deleting holographic entering srm srm srm srm srm srm 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units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information problem problem models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values probability probability probability weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution method method method method method method method method single processing processing processing processing control control control control control control large large large neuron neuron rate analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form form form form form form form form form form form shows shows shows shows signal signal signal algorithms algorithms algorithms simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple paper paper paper paper paper paper paper examples size net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net work work work work work work work work task task methods methods step step current current current current trained trained trained trained cell structure high memory memory memory memory memory memory memory memory memory similar equation equation section section section section section section section section section section section section section section fixed fixed fixed fixed rule rule rule rule rule rule general general general general general general general general general general general speech speech speech real real real real real real states states states states gradient note result result university university university university threshold threshold threshold threshold threshold threshold threshold variables computation solution research independent sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant estimate estimate estimate estimate estimate computer computer connections connections connections connections connections science science science science prediction prediction prediction prediction prediction prediction prediction presented presented present phase activation activation activation activation activation activation activation activation machine machine machine machine machine machine machine machine machine machine machine machine machine machine press press learn learn learn learn learn learn learn learn position basis outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract abstract back back back back back back back back find computational computational computational computational computational computational properties references positive procedure procedure important important important propagation propagation propagation propagation context context context context context context context context context context context context context context introduction action action action action action action action action action complex complex complex circuit behavior effect effect generated parallel parallel parallel parallel parallel parallel parallel recurrent recurrent tion change change difference difference difference assume assume rules rules rules signals signals representations learned learned learned learned learned part part previous previous previous previous previous previous firing firing type required required required required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple binary binary binary binary long long long represent represent represent represent distributed distributed distributed distributed distributed distributed fact length length length length length length length length length length length length probabilities probabilities errors errors forward forward finite finite finite finite finite finite finite simulations tasks tasks simulation simulation simulation simulation multi sum sum sum performed called times elements elements elements means made made made made natural natural feedback feedback global knowledge original original vol vol vol artificial artificial artificial represented represented application desired desired desired desired desired desired proc proc proc perform active active active goal constraints connected connected connected connected connected connected gain motor motor discrete brain brain power power power power power power mit steps steps steps connection connection connection connection descent dependent nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets modeling report report institute department implementation version version version technique internal internal internal connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist responses difficult layers layers layers delay delay delay delay delay delay sequences sequences sequences sequences sequences sequences ai ai ai ai ai ai framework framework equivalent equivalent equivalent equivalent equivalent equivalent equivalent environment environment directly directly directly directly hinton hinton hinton hinton hinton additional view estimates design transition limit san stage conference conference determine approximate world world world vision basic give produce derived weighted weighted weighted conditional conditional conditional conditional conditional robot robot robot robot levels area controller controller controller controller controller controller types product product actual actual actual provided provided processes selected selected nature nature depends depends biological biological achieved complete actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions predictions predictions common common implemented implemented implemented implemented implemented implemented implemented implemented assumed supported ability ability ability ability ability ability future future easily degree rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart sensory simulated simulated simulated simulated simulated probabilistic probabilistic probabilistic typically typically pairs needed combination combination combination combination functional character character character character character character character character character character character character character character character mechanism database database language representing representing representing details numbers direct direct inhibition stored international expert attention combined combined choose choose light light predict predict predict predict predict discussed discussed discussed recent recent recent recent recent pair takes element element typical typical introduced include machines machines machines machines machines sejnowski sejnowski cognitive cognitive recently relevant engineering engineering interest highly previously studies studies studies address channels channels gate gate gate gate williams organization increased extended digital predicted deterministic occurs hardware hardware conclusion place depend interactions performs learns suggest suggest strong physics external external external external external characteristics demonstrated intelligence intelligence intelligence turn assuming variety manner characters characters characters characters characters characters characters characters characters groups connectivity connectivity annealing annealing acknowledgements areas areas areas boltzmann boltzmann boltzmann boltzmann suppose longer winner winner winner ways ways ways ways sequential sequential sequential sequential sequential sequential laboratory dept dept implement implement implement physical electrical involves involves interaction mutual events events events events events formed formed cycles cycles cycles john letters detailed operations controlled updated updated similarly similarly suggested past past past diagram earlier earlier performing performing delays delays reduces combining combining event purpose add iterative iterative initially assigned advantages topology topology avoid avoid expect template template includes includes thesis combinations combinations combinations combinations activations activations activations assignment sciences sciences determines illustrated activated candidate simplicity regular determining extra society effectively effectively delta symbols mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland wij wij wij wij wij wij wij wij successful identity excitation excitation excitation excitation excitation refer soc conf conf kind kind kind interested dis contribution timing hold vary simplified simplified simplified simplified simplified simplified simplified simplified simplified simplified simplified simplified simplified paradigm backward backward providing delayed delayed delayed delayed delayed delayed thresholds thresholds predictor predictor predictor predictor predictor predictor predictor principles moves illustrates illustrates illustrates deal decreasing decreasing receive modelling presents presents presents body body carried diego american layered production production production production production production production production production production production production production production production production production production production production production production production production production production production production production production production production production production requirements investigate association association association limitations game behaviour respond fashion fashion giving giving giving giving history ideas int int int int int possibility referred symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic act math possibly editor man man man predicts predicts predicts automata changed implementations implementations thought adjusted quantities obvious hebb academic speakers arbitrarily explain phd electronic established years languages distinguish expensive independence briefly briefly briefly briefly briefly london drive implementing satisfied commonly potentially universal gradually cybernetics explained explained requiring requiring requiring reflects varies fed fed fed simulate simulate simulate simulate lack lack lack item employ templates controllers gen gen occurrence extensions suited adjust enables enables kinds sophisticated progress june credit differentiable univ forming restriction extensive nat unity unity connecting connecting connecting royal smolensky turned turned lost lost dealing difficulties adjusting held replacing automaton automaton automaton automaton abilities abilities keeping responsible exceeds exceeds phrase presentations motivation repeat repeat predictors predictors predictors predictors iteratively sides buffer buffer buffer widrow propagated counter chooses tic tic tic enable ballard ballard ballard reader augmented augmented properly canada canada passing passing extends designing explains explains fahlman avoiding fired pressure pressure appeared unable unable presenting propagating seek lit chapter chapter chapter chapter classic simulating simulating avoided massively massively auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary rain rain adjustment avoids manipulation manipulation robots robots goals pdp activate playing playing met simplifying parallelism relates relates paradigms distinguished distinguished discusses discusses discusses denver retained port october simplifies externally council unbounded unbounded hoc opponent kth eral connects calculates fre ackley partly partly dedicated dedicated dedicated specialization edited deals colleagues falling falling thing essence feldman feldman feldman computable comprised fixing promise promise hoff indi awij probabil enabling enabling enabling predetermined predetermined predetermined predetermined retaining repeating discrepancy notions subnets competence sensed turing turing turing turing turing turing turing turing turing turing turing turing adjustments ample reviews ities internally patterned comprises comprises challenges remember bruce seeking thinking suggestion neti neti neti volumes volumes tributed earning latch latch latch latch succession clamp ism blank regularly chaining chaining trivially synchronously hoped buffers buffers encouraged quence disappears reactions simplifications simplifications heard latched latched latched latched latched latched latched latched indefinitely indefinitely interacts exemplified manifested investigates paragraph nilsson tape cated relearning relearning evidenced chines remembered remembered accessing manifestation manifestation quently professor latches latches oval tac tac tac preconditions delaying evokes produc equivalents las remembering formalisms executable 
#@MacDonald_B,
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#*network network network network network network learning learning model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure figure figure time time time time time time time networks networks networks networks networks training algorithm algorithm output output output output output output output output output output output output output output number number number number number number number number number system error state units problem hidden based based based case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown values values values values values weight functions functions neurons distribution recognition recognition recognition recognition recognition method approach pattern pattern pattern pattern single single single processing processing processing processing processing processing processing control large local local local rate rate class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs algorithms simple simple simple simple paper small small small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work fig fig cells features features features features features features features features features classification classification classification current current current current current current current current current current cell cell cell structure problems problems high high high high high high high memory memory memory memory memory similar similar representation architecture fixed fixed fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general speech real gradient obtained note experiments dimensional result threshold computation computation computation computation computation research found found found found constant computer computer computer computer computer computer distance distance distance distance distance distance distance connections connections connections connections connections connections connections connections connections connections connections node node node presented present present low low low nodes nodes frequency frequency range press outputs outputs outputs abstract applied applied find find computational computational analog analog analog analog analog analog analog analog analog analog analog references ieee ieee positive important important important important adaptive introduction complex complex hand circuit circuit circuit circuit effect dynamic generated generated parallel parallel parallel parallel parallel parallel difference difference difference difference complexity complexity complexity classifier classifier classifier lower rules word word word word word chosen previous type type required required required required long long represent represent distributed distributed distributed distributed distributed distributed distributed distributed distributed expected expected expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make region scale minimum minimum resulting total total sum sum sum sum performed performed performed performed times elements elements elements elements elements means factor made made made made made made made feedback feedback feedback feedback global applications applications applications applications applications applications negative represented represented represented true compared compared compared compared compared application application series series rates proc perform perform perform perform perform perform perform determined connected connected connected connected gain brain brain brain power power power approaches approaches approaches mit voltage voltage voltage voltage comparison comparison comparison larger connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection update descent proceedings institute words words implementation implementation implementation synapses kernel advances connectionist connectionist connectionist scheme graph sequences sequences equivalent equivalent design design design design design design design design design stage stage stage stage bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit conference conference determine efficient full full speed speed speed speed speed vision give give produce area area area types lines lines lines path product product product product nature inhibitory inhibitory simply simply biological biological associative associative associative achieved achieved increases increases tested tested fast fast limited limited close close complete excitatory circuits circuits circuits circuits circuits circuits short common implemented require eds end end end end vlsi future simulated smaller needed hopfield hopfield reduced fully fully fully technology technology interesting testing character edge special operation operation operation operation details max inhibition stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored bits bits bits bits bits international depth depth magnitude magnitude magnitude decay idea minimize architectures architectures discussed element element element typical typical movement movement strategy strategy identical array interest highly highly highly previously conventional conventional conventional conventional conventional conventional conventional conventional calculated calculated volume match match match match match match match match match match trans chain gate improvement storage storage storage storage horizontal digital digital digital digital digital digital digital wide wide wide matrices matrices hybrid pass strength strength strength strength strength conclusion row greater designed designed designed designed designed designed designed clear performs performs temperature hard hard hard hard integration physics largest largest external external external reduction cycle cycle cycle solid proportional proportional turn turn turn assuming variety minimizing start areas written optical vertical slightly mutual frequencies frequencies springer formed shift shift shift extraction extraction extraction extraction extraction extraction john depending communication communication influence operations operations operations updated static sizes allowed processor processor processor processor processor processor processor processor processor processor processor processor processor diagram diagram reasonable calculation calculation calculation calculation calculation calculation calculation delays sec sec sec purpose remains remains distances distances distances string advantages precision expect silicon silicon silicon strings strings currents currents bell memories memories memories recognize recognize discuss variations characterized reason reason efficiency closely closely paths paths paths paths modes essentially compact compact verlag quickly allowing conductance conductance lie sci device list list list list list list list list list list list list dot dot dot dot cmos cmos cmos cmos cmos cmos denker denker denker chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips processors processors processors processors processors processors illustrates deal extend american layered production experience put put strengths strengths strengths strengths optimized matches matches matches matches fashion tech rest ideal transistor transistor authors referred gates stream stream stream variability smallest closest changed voltages voltages voltages voltages implementations implementations ensure adjusted prototype noted logic store store extent contributions serial electronic charge charge charge years devices advanced costs costs expensive correction reasons stanford ring ring incorporate transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors products products products products products products separately acad calculations calculations read read lowest computers computers computers computers requiring led offset capability capability simulate simulate orders orders completion adjustable passed passed passed compares schematic schematic schematic schematic schematic schematic schematic calculating passes operate howard howard gains instruction instruction instruction instruction maximizes ordered enables enables enables hamming hamming hamming hamming kinds sophisticated summed summed summed summed arithmetic person room fabricated fabricated fabricated fabricated fabricated amplifier amplifier amplifier summing summing summing summing summing summing optimizing member nat flexibility interconnected wrong dealing minutes tools mos interconnection programmable programmable programmable programmable programmable programmable operates wire wire wire clock clock clock clock regard intended schwartz schwartz jackel jackel arrangement arrangement enable april omitted layout matter cpu speeds instructions switches switches acknowledge lag latency latency latency ram ram ram ram pieces malsburg hundred streams adjustment mutually acting shifting resistor resistor resistor mhz mhz mhz execute labs hubbard inverted thresholded switched names tied attached register register register register register sized sized resistors resistors amplifiers amplifiers amplifiers amplifiers amplifiers amplifiers programmed programmed programmed coming electron electron gratefully stores beam consuming consuming thousand designs designs designs designs designs designs designs loaded loaded loaded capacitors capacitors capacitors capacitors capacitors powers graf graf graf graf fabrication fabrication calculates calculates polarity engine holmdel exclusively deals arrives leakage accommodate ready comparator comparator comparator tags contents addressable addressable physica registers registers registers wires wires wires wires wires huge daniel deleting custom custom resemble operated months inserted inserted decoders metal adjustments putting inserting vdd tailored tailored tag tag tag tag tag tag tag tag reminiscent billion billion billion heidelberg vast cooling cooling wired wired wired impressive unix accelerator boards lose stuart closing wafer multiplies throughput throughput throughput numerals pipeline pipeline pipeline pipeline pipeline pipeline pipeline pipeline pipeline millions serially serially ams amorphous distribute distribute hans tiling irrespective grandmother eckmiller slowest vss pipelined pipelined pipelined dram tum duty interfaced transferring cascading accumulator accumulator technological inserts digest speculative idle losleben pads ick everyday mainstream fabricate microelectronic inflexible 
#@Denker_J,Graf_H,Mackie_S,Schwartz_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural input input data function function function time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks number number number number number number number number number number system system system system system state state state state state results results results results units based based space space space space space space space space linear linear linear case case case case vector vector order shown shown shown shown shown systems systems values values probability probability neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons pattern point point point point point point point point point image large large large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs form form shows shows shows shows shows shows shows algorithms simple examples examples small small size size size size size size size size size size size size size size size size net work fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step points points points points points points points points points points points points features features level structure structure structure structure random random random random random random random random random random random random high high high memory memory memory memory memory memory memory memory memory memory memory memory memory response similar similar representation show show show show show show section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule rule rule rule rule rule general real states theory theory theory theory theory note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result university threshold variables computation log defined defined defined dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial constant terms distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections map present present sets sets maximum range components nonlinear nonlinear nonlinear outputs continuous continuous continuous abstract applied find find find find find find find find convergence convergence analog analog analog analog analog analog analog references references component due ieee ieee positive positive positive positive positive important important important important important important important propagation introduction introduction circuit circuit behavior behavior effect parallel change change difference variable assume measure signals chosen part cases long long conditions conditions conditions conditions conditions conditions conditions expected expected expected expected expected expected chip make region scale scale finite resulting total eq eq eq eq eq eq called called times elements elements elements factor factor made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback global study negative negative negative negative negative negative negative negative negative compared compared desired desired cross define proc proc proc location location location perform eye determined related related connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected gain gain gain gain discrete discrete equal equal voltage larger larger larger larger larger contrast contrast connection connection connection connection connection connection fields support nets nets institute department implementation implementation technique consists delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay graph graph graph graph graph graph graph maps cambridge computing curves design design trajectory effects capacity capacity capacity capacity full requires speed condition condition condition condition condition randomly randomly types lines lines lines lines lines path path product product product product actual provided biological associative associative associative associative associative associative associative measured increases increases increases increases describe tested fast fast close close stable stable stable stable circuits amount shape shape supported main vlsi vlsi easily easily makes smaller hopfield hopfield hopfield hopfield reduced dynamical dynamical fully fully fully fully fully fully fully block block interesting ratio ratio ratio ratio ratio ratio increasing special mode mode mode mode leads representing representing numbers numbers numbers stored stored attention combined produced run run run added light discussed improve recent recent typical similarity period period period recently relevant interest interest dimensions volume smooth smooth converge trans symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric observation generalized organization storage storage storage storage storage sensitive constructed constructed lead lead lead lead lead lead studied suggests suggests suggests digital matrices matrices matrices loop loop loop loop loop loop loop loop loop loop generally hardware hardware flow flow critical critical critical critical greater assumptions reduce reduce valued depend editors sigmoid sigmoid numerical designed performs faster suggest encoding presence physics physics physics reduction reduction demonstrated solid plane decrease introduce configuration configuration configuration configuration configuration configuration configuration configuration attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor acknowledgements van edges edges edges edges edges edges edges edges longer longer winner ways plot ann stability stability stability stability metric text adding springer springer formed decreases decreases dependence communication open showed sign diagram diagram dashed measurements measurements roughly roughly visible string construction coupling expect expect building includes retrieval bell sciences memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories plotted activated coupled coupled black phys phys phys phys discussions regular determining identified differ divided included modes modes modes oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors efficiently orthogonal orthogonal reached characteristic characteristic summary notice conf conf verlag graphs strongly allowing oscillations oscillations oscillations oscillations sci sci sci device device built built surround providing delayed delayed delayed cmos denker denker leading illustrates load load intrinsic american wiley investigate circuitry circuitry circuitry rapidly strengths limitations oscillator oscillator oscillator oscillator hall fewer fewer reducing reducing giving investigated investigated ideal possibility comparable complicated oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation affect understand removed math math math measurement measurement measurement measurement measurement coefficient closest configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations rev rev equally equally voltages voltages voltages voltages aspect der der obvious noted observe detector shapes shapes shapes shapes shapes shapes hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb switching switching extent simplest electronic electronic electronic electronic electronic charge charge spin spin spin spin spin spin indicating developing guaranteed defining unstable unstable biology biology glass glass ring ring ring ring ring ring ring ring ring producing producing division leaves laboratories probable acad acad acad grossberg qualitative greatly limits applies understood axes cohen adjustable dots requirement switch mod collective hamming hamming decreased attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction unbiased unbiased unbiased progress instantaneous picture notes forming forming guarantee restrict arguments recover nat nat controlling eliminate interconnected eliminated saturation saturation interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection stated loops loops loops loops loops contract keeping operates observing carry spurious spurious spurious spurious reliably prentice slice slice slice slice slice slice slice irregular irregular irregular irregular irregular vertices vertices vertices vertices vertices schwartz interconnections interconnections treatment emergence young suggesting sustained sustained sustained sustained sustained sustained sustained sustained sustained storing concentration concentration concentration concentration lett propagate switches switches dividing accumulated ccd ccd ccd clique clique clique clique clique clique clique clique clique clique basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin basin break magnetic ideally affects basins basins basins basins basins basins basins basins basins basins basins basins basins basins basins basins basins basins basins basins basins basins discovering unseen pub rectangular capacitance mackey resistor generators maximally maximally confirmed scope scope scope rough breaks reveal reveal tij tij tij tij inverting inverting inverting inverting inverting inverting inverting inverting inverting inverting inverting inverting inverting interconnect amplifiers amplifiers amplifiers amplifiers programmed programmed vanishes dramatic infinitely lecture beam scanned scanned corners saturated quadrant oscillate oscillate keeler harvard hemmen evenly huberman sparsely triangles triangles triangles triangles triangles triangles marcus triangle triangle triangle triangle bond bond slices slices slices slices ref ref ref ref lying sym loads positives screen symmetrical prone prone appl inset inset smc cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques binomial periodically periodically cutoff comparator signed signed reviewed acknowledges aip oscillates oscillates westervelt westervelt westervelt stabilize inst physica physica physica resemble rij stabilizing disorder disorder disorder pull settles settles retrieve plotting plotting undirected hirsch hirsch examines capacitive holmes bifurcations heidelberg heidelberg controllable controllable distinctive concentrations concentrations clipped clipped clipped clipped amit stabilized behaved quadrants densely opens opens disconnected glasses glasses glasses inverses charging rin disappears focussed liapunov gutfreund charged photographs ingredient documented negatives dangerous dangerous nmos guides tii tii diluted diluted diluted instantaneously raster raster guckenheimer fic diodes hatched compromised scholar 
#@Marcus_C,Westervelt_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data function function function function figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number error state state state state state state state state state state state state state state results results results information problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based space space space space space linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown shown shown shown shown shown systems systems values values parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method method approach approach pattern pattern image image single single single single single single processing large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate patterns patterns analysis analysis class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs form form form form form form form signal signal signal signal simple simple paper paper net net net fig fig fig step step step step step step classification process level level level trained trained trained trained trained trained problems memory memory memory memory response response representation architecture architecture architecture show equation equation equation section section section section section section section vectors vectors vectors vectors vectors images general generalization generalization generalization generalization generalization generalization generalization parameter states states states states states states states states states states states states states states states states theory theory theory note note note note dimensional dimensional dimensional result result result result result result result university computation computation solution solution solution solution independent dynamics dynamics dynamics dynamics constant constant constant standard node node node science science science presented nodes machine sets sets sets sets maximum press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous abstract applied applied back back computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic ieee ieee ieee ieee ieee ieee ieee ieee ieee procedure important important important decision propagation propagation introduction introduction hand hand circuit circuit stimulus statistical effect effect generated parallel change change energy energy energy energy energy difference difference complexity assume lower lower representations learned chosen chosen higher part part previous previous bound cases cases cases type type type type conditions distributed bayesian techniques techniques techniques region proposed length errors scale finite minimum resulting resulting ing computed respect sum sum sum sum sum sum called elements elements elements elements optimization optimization optimization made made applications applications study vol vol vol vol vol vol vol vol vol vol vol vol vol vol specific application application desired desired desired define define define define proc proc perform perform perform perform determined connected distributions gain discrete equal equal equal equal equal equal mit accuracy contrast contrast nets nets nets proceedings report institute words loss implementation technique technique final exp exp layers layers layers layers addition considered considered cambridge cambridge computing environment directly additional additional additional additional design san effects capacity capacity capacity capacity capacity capacity capacity capacity determine classifiers classifiers full full full full full full full full full choice choice choice choice speed speed increase increase increase condition coding weighted criterion lines iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration nature constraint constraint constraint simply associative associative associative achieved arbitrary arbitrary arbitrary denote denote denote assumption surface amount role require require require easily easily easily easily rumelhart rumelhart rumelhart auditory simulated simulated needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield combination combination unknown programming programming projection projection projection projection projection projection york increasing special special uniform empirical mode operation operation operation operation operation operation operation stored stored international international magnitude combined choose added perceptron perceptron denotes denotes architectures architectures architectures improved discussed discussed discussed improve improve improve improve improve takes element element element reported practical include include include identical identical machines machines sense sense sense sense cognitive dimensions dimensions sufficient previously conventional solve converge converge converge converge trans trans trans trans trans trans diagonal address address interval improvement storage exists occur extended matrices generally generally generally generally generally column column column column column pass demonstrate row reduce operator operator operator sigmoid sigmoid sigmoid numerical numerical exponential exponential exponential exponential exponential exponential weak strong strong strong physics reduction characteristics sigmoidal proportional intelligence variety plane manner manner manner annealing annealing denoted boltzmann reference reference pro written written written optical plot plot plot recall recall metric coordinates coordinates simultaneously linearly infinite physical remaining remaining remaining remaining remaining unique spectral spectral spectral spectral spectral spectral adding adding springer formed formed versus decreases choosing expressed stationary interpretation interpretation evaluated operations operations restricted updated showed centers similarly converges converges partition partition partition partition partition partition allowed discrimination sign sign sign slow slow slow dashed performing performing convex convex convex convex convex convex reduces reduces roughly iterative iterative remains sufficiently sufficiently assigned foundation advantages expect building box usa formulation eigenvalues eigenvalues eigenvalues eigenvalues subspace subspace subspace sciences memories determines illustrated illustrated prove prove specifically specifically specifically columns columns aspects uniformly projections projections projections plots tend orthogonal orthogonal orthogonal refer conf conf verlag procedures procedures strongly showing return contribution running content criteria criteria criteria notation notation notation notation notation write write simplified relaxation relaxation relaxation relaxation relaxation relaxation relaxation generalize backward eigenvalue eigenvalue reach operating extend explore explore remain unlike diego american layered layered layered layered layered layered layered layered layered layered layered layered layered layered layered xor xor xor xor xor xor xor xor xor xor steady steady steady steady steady steady steady steady lippmann behaviour scalar examine respond respond biol analytically possibility decisions proper proper proper proper eigenvectors oscillation attributes analyze illustrate illustrate rank rank rank rank rank rank rank rank rank rank rank portion portion noted freedom explored art submitted submitted established established established great rows rows rows rows rows cos asynchronous asynchronous asynchronous analyzed analyzed failure biology floating floating floating floating floating floating multiplication nonlinearity nonlinearity nonlinearity perspective purposes strictly operators immediately acad opt opt opt attribute geometry radius radius radius radius radius radius addressed addressed understood understood generic poorly formulated operate partitioning proven tank collective suited geman logical conclude display decreased decreased displays globally initialization lab proofs proofs notes bipolar bipolar restriction conditioned nat controlling homogeneous homogeneous homogeneous homogeneous unity generality clamped clamped clamped clamped clamped clamped clamped clamped clamped clamped clamped imaging imaging abilities viewpoint operates imply affected effectiveness synchronous synchronous synchronous synchronous synchronous synchronous synchronous corner generalizes generalizes generalizes falls james iteratively dominant washington enhance percepttons infinity nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities claim multiplied recog eng arrive augmented augmented augmented canada partitioned partitioned projects inf inf ignore cam thresholding thresholding robert divide abu geometrical geometrical geometrical mostafa outline equivalently equivalently alternating alternating alternating alternating emergent uniquely responds adopt ease generalizations acceleration illustration illustration remainder remainder alter cns shaded publication exclusive exclusive insights diag alternate pami impose elementary books wise wise projecting projecting projecting projecting cosine flip interactive exceed deleted library library library library library library library library library library library library library library memoryless interconnect interconnect interconnect interconnect interconnect interconnect likewise resembles restoration restoration restoration corners marks marks marks marks marks trainable hilbert coin converter affecting affecting medicine ackley seattle tuple kirkpatrick optics optics minsky establishing establishing establishing assp appl appl appl relaxed relaxed magazine magazine bradford shaping indirectly addressable atlas atlas explaining saturate configured configured configured repeating nov superscript cir tll tll tll lens lens lens clamping clamping clamping clamping clamping med med ies augment orthogonality geometrically geometrically visualize pad visualized visualized lira bypass dictated synchronously cyber asynchronously alternately interconnects interconnects interconnects interconnects interconnects interconnects interconnects interconnects mceliece apr nicely exponentiation doubled assure lastly depart les alteration stimulate cas laid cylindrical cylindrical intersects intersects referenced 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training training training training training training training training algorithm algorithm output output output output output output output output number number number number number number number system system system system system system system system system system system system system state state state state state state state state state state state state state state state state units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information problem problem problem problem problem problem models models based based based based based based space space space space space space space space space space space space space space space space weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear layer layer layer case case order order order order shown shown shown systems systems systems systems systems systems systems systems values parameters parameters noise weight weight weight weight functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern point point image image image image image image image image image image image image image image image image image image image single single single single single single single single single single single single processing processing processing processing processing processing processing control control control control control large large large local neuron patterns patterns patterns patterns class optimal inputs inputs inputs form form form form shows shows algorithms algorithms algorithms algorithms simple simple simple simple simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual examples examples small small small small small size feature feature feature feature feature feature feature work work work work work work work work work task task task task task task task fig fig fig step step step step step step step points points points field field field field field field field field field field field field field features features features process process level level level current current current current current current structure structure problems problems problems random memory response similar similar similar representation representation representation representation representation representation representation representation representation architecture architecture section line rule rule rule images general general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech real real approximation average average states states states states states states states theory note note activity activity activity activity activity activity activity dimensional dimensional result result university university variables solution research research research found found sequence target target target target target dynamics initial standard computer computer terms terms terms distance distance distance distance distance connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic science science direction direction direction direction direction direction presented presented presented presented presented map present activation activation activation activation activation machine machine machine machine object object object object object motion maximum range range range press learn learn learn learn learn learn learn learn learn learn learn position position position position position position components outputs outputs outputs continuous continuous continuous continuous sample sample abstract back back properties references due ieee ieee procedure propagation propagation context context action complex complex complex complex complex complex complex hand hand hand hand hand hand hand behavior behavior behavior behavior behavior behavior stimulus effect effect effect effect generated parallel parallel parallel parallel parallel search search search search tion change complexity complexity complexity variable assume assume lower rules representations representations representations representations learned learned learned learned learned learned learned learned learned learned learned chosen chosen chosen chosen center center center center previous previous type type type type multiple long represent distributed equations equations equations region region region correct forward forward forward resulting resulting resulting ing ing tasks tasks total human computed computed multi sum called regions regions regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means reinforcement reinforcement reinforcement dimension dimension made natural global global global global global knowledge knowledge vol vol vol vol artificial artificial specific specific specific specific specific specific specific specific specific specific specific specific represented represented represented represented represented represented desired desired desired cross series series receptive receptive receptive receptive receptive receptive receptive receptive receptive provide provide provide provide compute objects objects objects rates proc proc proc location location location perform active active active active active active active active active active determined goal goal goal goal goal goal goal related motor motor motor motor motor motor motor motor motor equal approaches approaches mit steps steps steps steps steps comparison contrast fields fields fields fields support support train train morgan report institute implementation technique consists consists consists internal internal internal internal internal internal internal joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist responses difficult difficult difficult final final final final final layers scheme scheme scheme scheme scheme scheme scheme scheme scheme sequences sequences considered cambridge cambridge cambridge computing domain domain environment environment environment environment directly directly directly directly hinton hinton hinton hinton hinton hinton additional view view design trajectory trajectory trajectory trajectory trajectory san top top stimuli bit conference upper full full full requires requires requires choice free speed vision vision vision vision basic con produce coding coding coding coding weighted weighted weighted weighted clustering developed developed robot robot robot robot robot criterion path actual actual processes nature nature depends simply simply simply simply biological biological biological biological associative associative discussion arbitrary arbitrary limited close inverse inverse inverse inverse assumption assumption complete actions actions actions actions actions actions actions actions actions actions short common implemented implemented assumed shape generate generate generate require eds eds eds eds eds eds square ability ability instance instance instance instance instance instance instance future future degree degree degree degree rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart development development development development development sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory simulated simulated simulated typically pairs pairs pairs needed needed needed fully programming interesting interesting interesting interesting increasing mechanism mechanism structures structures principle operation language representing representing details direct bottom supervised supervised supervised early frame decay combined produced choose run predict predict predict population population population population population population population population population population population population population population population discussed directions directions directions recent advantage advantage property pair separate typical moving moving sense subset sejnowski sejnowski array cognitive cognitive cognitive cognitive relevant relevant relevant relevant relevant relevant relevant relevant sufficient sufficient highly highly highly highly highly highly highly unsupervised unsupervised unsupervised unsupervised teacher teacher teacher teacher teacher teacher approximately approximately tions solve achieve achieve trans background positions positions positions grid grid grid grid organization entire entire entire increased arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm constructed exists concept studied scaling suggests locally move move move clusters clusters white white white white white white white white white generally generally runs strength critical reduce trajectories trajectories depend competitive reward interactions interactions designed designed clear sutton sutton sutton exponential practice weak learns learns learns learns learns learns learns encoding encoding taking taking presence presence presence physics physics sigmoidal demonstrated intelligence intelligence turn turn turn variety selective plane relationship relationship relationship relationship minima identification configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration force acknowledgements explicit explicit explicit explicit appears relation produces optical solving ways laboratory ann tuned tuned tuned tuned distinct dept multilayer explicitly explicitly coordinates coordinates simultaneously simultaneously physical physical involves involves transformations transformations remaining easy angle angle angle angle angle angle angle unique mutual applying springer formed agent agent agent boolean boolean boolean boolean competition focus review review overlap overlap overlap detailed detailed evaluate operations operations centers centers centered centered completely suggested suggested allowed barto barto barto spaces penalty intermediate intermediate intermediate initially sufficiently kohonen advantages advantages fire fire exploration perceptual perceptual priori color recognize recognize recognize recognize recognize determines illustrated discuss activated activated activated activated activated activated activated activated activated activated activated activated activated specifically domains domains domains domains domains partially planning planning planning planning reason identified capable capable encoded modification modification modification modification driven driven driven driven mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland presentation build schemes traditional traditional traditional soc compact notice conf verlag kind kind kind procedures strongly strongly strongly allowing heuristic heuristic video anderson dis issue sci categories vary play absence reach automatically attempt moves overlapping overlapping overlapping neighboring neighboring neighboring software tesauro tesauro camera camera camera camera camera camera camera camera camera camera situations body explore stimulation command command command american american experience difficulty rapidly rapidly put environments hall fewer fewer reducing fashion fashion history history school school tech behavioral behavioral mappings mappings mappings mappings mappings mappings mappings mappings mappings biol int int parity ideal relationships relationships relationships referred stream workshop workshop encode encode cognition cognition cognition cognition act act coarse coarse coarse coarse coarse coarse trace trace trace trace trace trace trace trace possibly necessarily configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations man man extremely thought thought mapped expressions nervous simplest utility submitted developing directed critic critic critic crucial crucial coded coded coded coded coded coded coded nonlinearity inside drive perspective perspective purposes purposes sys organized organized style desirable afferent commonly laboratories mathematics scientific angles angles angles angles angles acad grossberg linsker author geometry cybernetics radius radius radius addressed fourth fourth geometric questions varies greatly populations populations populations populations populations cmu amounts generic readily autonomous autonomous effort detecting variant rewards operate berlin differs incoming incoming chen suited hamming logical logical kinds sophisticated focused focused begins traces june extreme extreme irrelevant irrelevant representative representative acquisition newton cybern cybern sort writing writing tation concerned concerned mobile repre repre encoder discover eliminate interconnected interconnected robotics robotics robotics robotics proceed reaching extending air kaufman murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy convenient imaging imaging simplify automaton multiplicative multiplicative intelligent intelligent intelligent intelligent intelligent hyper hyper moment moment los efficacy nearby nearby wire spot spot spot guide child child heuristics heuristics natl passive prentice excellent contexts bartlett falls becker representational representational representational irregular paul moved moved conjunction conjunction conjunction mental mental mental mental mental intended intended mel mel interconnections arrangement enable francisco suggesting record repeatedly repeatedly rich ends observer reverse reverse subsequently omohundro omohundro hart discovered discovered cam cam explorations explorations explorations explorations thresholding executed dense mind multiplying associations street summer visually visually visually visually visually visually visually visually kinematics kinematics kinematics deriving covering obstacles obstacles responds incrementally pointed smoothly sigma sigma sigma opper ease ease tradeoff tradeoff classic affects realize illustration continuity continuity continuity continuity backgammon mutually manipulation rectangular rectangular rectangular home publication grouped activate activate mitchell compatible thresholded thresholded retinotopic maximally argued depicts depicts depicts depicts acquired ultimately ultimately topic mask manipulator manipulator alternatives paradigms denver afferents happen happen modality stuck stuck places places modifiable modifiable modifiable refined exploratory exploratory inactive challenge architectural laws bridge bridge expense stephen january discontinuous discontinuous discontinuous sake justification impractical attributed attributed rosenberg send send send jersey attempting supply finer hour illinois illinois kinematic kinematic kinematic kinematic concrete tip tip unreliable tuple progressively progressively substitute dedicated push interpolating outgoing outgoing joints joints joints joints joints joints joints joints joints sending implying smc robotic robotic confined connectionism physically ready south differentiate bradford bradford bradford bradford computable iterating semantics enforces raised decoded translate penalizes backwards backwards backwards recalled physica greatest inappropriate talk tory noticed rotate ted ted ted extrapolation spent searched spots spots spots spots spots decompositions plausibility ohio dead invert sixth plans apparatus apparatus relying mal reminiscent internally internally internally internally projective projective wright wright signalling comprises thumb sought billion billion controllable blob workers scratch wired rendered blur blur encounter positioned constantly percepts insure plex quences altogether calling repertoire repertoire repertoire shoulder shoulder shoulder discriminations reinforced recognizable official discarding champaign intervention conjunctions shifter elbow elbow elbow autonomously consequent imitate imitate experimen infants grasp wasted dur insures insures conjunctive conjunctive conjunctive conjunctive exemplified articulators lly patterson situated education acquires tradeoffs subpopulations subpopulations inevitable scientist subpopulation coarsely coarsely coarsely coarsely michalski behaviorally behaviorally behaviorally typ collapsed perturb orderly inp leaning ouput mentally mentally mentally mentally passively conse continous escaping imitation acquiring imitating realism afb altos needing oral cussed predicates forwards forwards forwards popula vided ified throwing immunity wrist wrist wrist disjunction envision envision envision carbonell carbonell rumel affairs affairs mand acldey subserve backtracking grab grab specifics handful unprocessed unprocessed aeronautical adhere conti endeavor unfor avionics vols tunately 
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results results results results results results results results results results results results information information models models performance based case vector vector vector order order order order systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values parameters parameters functions neurons neurons neurons neurons neurons neurons method method method method method approach approach pattern point point point point point point point point single single single processing processing control large large large large large large large local local local test test test test test test patterns analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs inputs inputs inputs inputs form form form form signal algorithms paper paper paper paper paper paper paper work work methods methods methods points points points points points points points points field field field process structure structure structure structure structure structure structure problems high high high high memory memory similar show show equation equation general general general real real theory theory theory theory theory obtained obtained obtained note note note dimensional dimensional dimensional dimensional result result result result result result result result result result university computation solution solution solution solution solution solution defined defined defined defined defined defined defined defined found dynamics initial constant estimate estimate estimate estimate estimate estimate computer terms terms terms terms terms terms terms terms terms terms terms distance science science presented present present present present present present present present present present present present present sets press press press position position position continuous continuous continuous sample abstract applied applied find computational computational properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties references due ieee ieee positive positive positive positive important adaptive adaptive introduction complex complex complex behavior behavior dynamic parallel parallel assume assume assume assume assume assume assume assume measure theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem type type type type type type long conditions conditions conditions conditions conditions conditions conditions conditions distributed equations equations equations make make make make techniques scale scale scale scale scale scale scale ing sum called potential global applications study obtain obtain obtain obtain negative negative negative negative negative negative relative specific specific specific represented true true true true desired desired desired desired desired desired define proc determined constraints power comparison comparison comparison comparison comparison comparison connection proceedings institute institute department loss technique individual individual individual individual addition addition ai ai ai ai ai ai ai ai ai ai ai ai considered considered computing domain domain domain domain domain domain domain domain domain domain equivalent hinton additional view view view view view solutions solutions solutions solutions estimates estimates estimates estimates estimates estimates estimates design design trajectory trajectory trajectory trajectory trajectory trajectory conference determine determine free free free free free free free free give condition condition condition derived weighted bounds bounds bounds bounds bounds bounds bounds bounds types lines provided provided provided finally nature nature biological associative associative denote denote assumption stable stable stable stable stable stable stable stable stable stable stable proof proof proof proof proof proof proof proof proof circuits assumed supported supported require require vlsi hypothesis hypothesis hypothesis makes makes makes makes makes including hopfield hopfield hopfield hopfield hopfield dynamical dynamical dynamical dynamical dynamical dynamical increasing special consistent structures structures principal principal principal making making making attention choose choose choose choose choose denotes denotes denotes denotes denotes denotes denotes discussed recent advantage apply apply apply include hierarchical subset engineering interest interest interest interest previously conventional tions yields differential differential achieve trans trans diagonal diagonal diagonal diagonal address address positions locations symmetric symmetric generalized organization grant grant exists derivative matrices setting demonstrate place assumptions assumptions editors designed clear exponential exponential exponential asymptotic asymptotic weak weak physics physics largest external external external external assuming start exist exist min min min min iii introduce manner manner manner estimating estimating stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability distinct explicitly electrical easy consisting interaction develop develop develop equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium 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naturally possibly editor changed implementations subsets singular academic academic extent extent submitted isolated isolated years asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically advanced advanced inequality defining unstable unstable unstable unstable unstable unstable nonlinearity nonlinearity considerable satisfied satisfied satisfied satisfied satisfied satisfied satisfied satisfied satisfied satisfied easier strictly located leaves arise arise consequence inversion acad grossberg definite definite definite definite definite definite qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative nsf questions reflects reflect cohen formulated continuously frequently frequently frequently synthesis perturbations perturbations perturbations perturbations perturbations perturbations perturbations popular tank suited enables hamming inherent conclude attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction attraction differentiable lot representative ordinary writing guarantee amplifier flexibility interconnected interconnected interconnected interconnected interconnected interconnected interconnected arranged establish establish establish systematic air convenient difficulties difficulties difficulties tools analogy proceeds interconnection interconnection interconnection interconnection interconnection stated resistance viewpoint viewpoint viewpoint viewpoint analyzing shifts north modifications modifications natl lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov encountered holland interconnections interconnections interconnections interconnections interconnections candidates nonlinearities viewing treatment express insight reader matter onr empty constitute ter basin ties axe adopt theorems utilize utilize aij aij aij aij aij aij aij aij aij aij aij chapter chapter chapter constitutes basins auxiliary capacitance publication concentrate emphasize proach investigating emphasized anal tij tij sta things mini mini mini remarks remarks survey survey ble instability instability instability instability instability instability instability hop hop hop inverter accomplish condi devised devised ref ref ref ref ref ref ref ref sij sij sij ory maxi arriving arriving experienced counterpart subsystem subsystem subsystem carpenter syst dij dij dij equilibria ysis amsterdam rij assessing attracted manipulations ecs counterparts ixl aii aii aii aii aii aii aii aii aii circumvent circumvent circumvent ponents oij disconnected iix ixi subsystems subsystems subsystems subsystems subsystems subsystems subsystems subsystems subsystems sector sume concluding concluding equi equi equi equi equi equi invoked lend cri cri cri cri entails snowbird nicely gle mad philosophy emd ven dii sts 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processing processing processing processing processing large large large large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test test test test test test test test test test test test test test test matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs form form shows shows shows simple paper size size feature work fig fig fig cells cells step step step process process level current current current current current current current current current current current current cell random high high high high high high high high high high memory memory memory memory memory response response architecture architecture architecture show fixed line vectors states obtained obtained obtained threshold threshold threshold threshold solution research found dynamics constant constant constant constant constant distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic low range range range range range outputs outputs outputs sample abstract applied computational convergence convergence convergence convergence convergence density density density density analog analog analog analog analog analog analog analog properties references due due ieee important important mixture introduction effect dynamic parallel parallel parallel difference difference difference prior type required required required required multiple binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary long long long long long long long long long long long conditions represent chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip fact region region region length length observed observed observed observed observed forward scale scale scale simulations multi multi multi multi multi performed times times times times elements elements elements elements elements elements elements elements elements elements elements optimization potential potential potential potential dimension dimension feedback feedback feedback feedback feedback feedback feedback obtain obtain obtain obtain samples represented application application application application desired desired desired series series series series provide provide proc proc proc proc proc proc proc connected connected connected gain discrete discrete power power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage steps larger larger larger connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection source source source source source source selection institute institute institute implementation implementation implementation synapses synapses synapses synapses synapses synapses consists consists consists joint difficult difficult difficult final bias scheme scheme addition computing directly additional additional curves curves design design design design design top top bit determine full choice significant speed speed speed speed basic basic basic channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel weighted developed levels levels area area area area lines lines lines lines product provided provided finally selected inhibitory inhibitory inhibitory depends depends simply associative associative associative associative associative associative associative measured measured measured normal normal normal describe describe tested tested tested close complete complete excitatory excitatory stable surface surface circuits circuits nearest common shape synapse synapse require main vlsi vlsi easily degree development including smaller smaller needed hopfield hopfield reduced functional technology technology technology technology technology technology block block block programming significantly york edge increasing special structures uniform mode operation operation operation operation operation window stored stored stored stored bits bits bottom magnitude run run run sources discussed advantage element element element typical typical include array array array array array array array array array array interest interest dimensions highly highly varying conventional conventional conventional approximately approximately approximately approximately smooth address gate gate gate gate gate gate gate improvement storage lead extended wide matrices alternative feed width width generally hardware hardware hardware hardware hardware runs place row greater greater greater reduce reduce conclusions valued designed designed designed weak weak weak weak weak temperature temperature temperature physics physics reduction characteristics characteristics characteristics characteristics characteristics demonstrated california california targets program configuration configuration configuration configuration configuration annealing acknowledgements appears factors laboratory laboratory stability stability stability stability recall recall simultaneously electrical electrical consisting blocks blocks john yield national depending depending variation variation open evaluate controlled similarly past diagram diagram expansion initially initially advantages precision building building building silicon silicon currents currents memories discuss candidate variations successfully major driven fine conf conf conf sin content content cue sci sci sci device device satisfy vary simplified relaxation providing cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos denker chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips operating operating operating operating software american production access requirements requirements requirements investigate difficulty mead strengths strengths tech investigated fault transistor transistor transistor transistor transistor transistor authors office reliable proper proper matched examined coefficient reading voltages voltages voltages ensure ensure ensure initialized electronic electronic electronic electronic electronic years devices spin developing ground ground ground ground agreement growing coded capabilities glass tool processed transistors acad acad localized computers addressed outer virtual considerably percent percent percent percent percent percent percent limits substantially consistency consistency consistency consistency consistency readily orders resistive resistive resistive resistive resistive resistive resistive resistive requirement requirement operate howard switch switch exhibits exhibits incorporating incorporating incorporating serve serve serve collective pasadena substantial hamming electric windows traces traces traces realized realized room room feasible primarily fabricated fabricated fabricated fabricated fabricated fabricated fabricated fabricated investigation amplifier amplifier acm acts nat nat controlling controlling controlling purely connecting grey grey grey grey arranged air air saturation saturation mos held attractive programmable programmable programmable programmable programmable 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function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm output output output number number number number number system system system system error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results information information information information information information problem problem problem problem models models models performance based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights shown shown shown shown shown shown systems systems systems systems systems systems values values values noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method method method method method approach approach pattern pattern single single single single processing processing processing processing processing processing processing control control control control large large large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate test patterns patterns patterns patterns matrix optimal inputs inputs inputs form form shows shows shows shows signal signal simple simple simple simple visual paper examples small small small small small small small size size size size net net net work work work work work methods fig field field features level level level level problems random high high high high high memory memory memory memory memory memory memory memory memory memory memory memory response similar similar representation representation architecture architecture architecture architecture architecture architecture architecture architecture section section fixed rule general parameter real real real approximation states states states states states states states obtained term term term note experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity dimensional dimensional university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation research research dynamics initial standard terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node science present phase phase activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation low low low frequency machine sets maximum maximum maximum maximum range range range range range range range learn learn learn learn outputs abstract back back computational computational computational computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties references ieee ieee ieee ieee ieee ieee positive propagation introduction complex complex circuit circuit circuit circuit circuit circuit statistical effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic parallel parallel parallel parallel parallel tion tion tion tion tion change change complexity complexity assume signals signals prior representations word word learned learned chosen part type required required good good binary binary long long represent represent represent represent distributed distributed distributed distributed distributed chip techniques techniques techniques techniques techniques proposed length forward simulations ing ing ing ing total total total total total total total simulation simulation simulation multi times times elements elements potential potential natural natural natural natural feedback feedback knowledge negative vol vol vol vol vol artificial represented represented compared desired series rates proc proc proc determined determined related related constraints constraints approaches approaches voltage accuracy larger larger larger larger larger update update update update update support nets nets proceedings institute words department implementation implementation implementation implementation implementation implementation synapses synapses synapses synapses synapses synapses synapses technique technique technique technique internal individual represents represents represents represents connectionist final final delay delay scheme addition addition computing computing hinton view solutions design design design design design design design design transition limit limit limit san effects bit bit bit bit bit bit bit bit 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hopfield reduced reduced technology technology technology block interesting interesting increasing mechanism mechanism structures operation operation language details stored stored stored stored bits bits bits bits early decay decay added added added added architectures discussed discussed advantage property robust separate movement reported reported reported introduced strategy moving moving moving moving moving moving period identical identical array array array array array array array array array array array array array array array array array array array array array recently engineering engineering engineering interest sufficient varying conventional approximately calculated volume works axis tions smooth smooth smooth achieve achieve williams storage increased horizontal horizontal concept concept studied suggests extended extended digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital spikes spikes feed hybrid hybrid hybrid loop loop loop loop occurs column column column column column column hardware hardware hardware hardware hardware runs row greater greater greater conclusions operator operator operator operator operator operator operator sigmoid faster faster constrained temperature temperature temperature temperature temperature hard hard integration integration presence physics largest cycle cycle sigmoidal sigmoidal sigmoidal solid solid proportional pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse groups denoted denoted acknowledgements pro primary recall recall recall recall recall recall recall recall recall recall recall recall simultaneously electrical involves easy slightly belief integrated integrated integrated adding shift shift shift shift shift quality blocks cycles cycles letters yield family communication communication squares operations operations controlled restricted showed forms forms static static activities 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point large large large local local local local local local local local local local local local local local local patterns patterns patterns patterns patterns patterns analysis analysis class class class matrix inputs form signal signal signal signal simple simple gaussian gaussian gaussian examples small net net methods cells cells cells cells cells points points field field process cell cell cell cell structure problems problems random random random random random random high memory memory memory memory memory similar similar similar similar section fixed fixed fixed fixed rule rule vectors vectors vectors vectors images general general general generalization real real real real states theory obtained term term term term note note variables variables variables variables variables variables variables variables variables computation solution independent defined found found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics 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produces produces written written written longer winner describes transitions label stability stability stability stability stability stability stability stability stability stability vertical vertical recall recall implement implement multilayer multilayer explicitly physical electrical easy equilibrium equilibrium equilibrium equilibrium formed implies competition decreases choosing national national national formation stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages overlap viewed viewed codes codes codes codes codes restricted fraction showed evolution evolution evolution evolution decomposition constants constants constants allowed additive reduces reduces intervals intervals add valid intermediate calculate symbol foundation precision avoid priori usa usa inter sciences memories memories memories memories plotted illustrated prove prove prove maximize candidate absolute absolute successfully major extra 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fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule rule vectors vectors vectors general general general generalization generalization generalization generalization parameter real approximation approximation approximation states states states theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained term term note note experiments experiments result result result result university university variables computation solution solution solution solution defined found found sequence sequence target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial constant constant computer computer terms terms distance connections connections connections presented presented presented presented presented presented phase phase activation activation machine sets press press learn learn learn components components components basis nonlinear nonlinear nonlinear continuous abstract applied applied find computational computational computational computational analog properties properties properties references component stochastic ieee ieee important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation introduction introduction hand hand statistical parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change energy difference difference difference lower rules signals chosen chosen chosen chosen higher higher higher higher higher higher higher higher higher higher higher higher higher previous previous previous previous previous previous type required required required required multiple multiple multiple 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report institute words implementation implementation version technique internal represents difficult difficult final bias computing environment environment hinton additional solutions solutions solutions trajectory san conference conference efficient requires requires requires requires requires requires choice choice choice choice condition condition derived randomly randomly randomly randomly product product product product actual provided provided finally finally finally finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation depends depends depends depends simply simply associative associative discussion discussion discussion feedforward feedforward arbitrary arbitrary arbitrary transformation stable stable stable stable stable stable stable common implemented assumed assumed assumed role role main end vlsi 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symmetric modified observation williams entire exists exists lead studied studied studied studied occur occur suggests suggests extended derivative derivative locally locally deterministic deterministic generally generally column hardware starting row trajectories depend depend depend sigmoid numerical numerical clear performs practice practice learns constrained constrained constrained temperature suggest physics physics external external demonstrated demonstrated california proportional proportional labeled assuming minimizing exist averaged targets introduce introduce derivatives derivatives derivatives identification annealing denoted denoted denoted attractor attractor boltzmann explicit explicit suppose suppose suppose appears derive derive derive construct index optical solving ways factors laboratory label label stability stability stability stability stability stability mathematical recall simultaneously physical unique unique unique applying implies john expressed expressed expressed stationary interpretation detailed detailed operations operations operations operations operations operations operations lee lee lee lee forms forms static approximated completely converges converges converges updates updates updates updates key partial partial slow performing purpose calculate calculate visible visible visible visible visible construction advantages topology david david degrees usa usa eigenvalues eigenvalues memories memories memories memories illustrated prove coupled coupled phys discussions major straightforward straightforward closely suitable suitable divided driven mcclelland wij presentation attractors attractors attractors literature essentially essentially receives neuroscience sin oscillations content content content content content content sci sci satisfy generalize paradigm paradigm backward minimizes giles denker leading thresholds consisted illustrates minimized diego american transformed transformed essential requirements exhibit exhibit exhibit rapidly rapidly steady steady steady steady association preliminary preliminary behaviour behaviour behaviour behaviour behaviour applicable office complicated complicated oscillation encode momentum analogous gradients necessarily necessarily man rev illustrate adjusted quantities formal noted logistic freedom precise logic academic amari amari amari amari amari amari amari simplest arbitrarily submitted motivated attempts attempts electronic isolated asymptotically slowly trivial trivial crucial derivation guaranteed stress stress stress stanford implementing purposes sections formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism strictly precisely constructing choices immediately commonly commonly cut inversion involve universal acad acad calculations implicit members definite author annual cybernetics sun outer outer outer outer outer integrating argument populations orders employ employ biologically 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university variables variables variables computation solution solution solution solution solution solution found initial constant estimate estimate standard terms terms terms distance connections science presented presented present present frequency machine machine range press press press press press press position position position nonlinear outputs outputs continuous continuous abstract applied applied back find find find find find computational convergence convergence convergence convergence convergence convergence analog analog analog analog analog analog analog analog analog analog properties properties properties properties references component ieee ieee positive positive positive positive positive positive positive positive positive positive propagation introduction circuit behavior parallel tion change change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference variable variable variable signals theorem theorem theorem multiple multiple multiple multiple multiple multiple good good binary binary conditions distributed distributed expected equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations make techniques region region region region length length correct correct observed finite minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum ing total total total total respect sum performed called elements elements optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization potential potential made global global global applications original specific represented compared compared provide compute proc location perform perform constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected mit descent descent descent descent descent descent institute institute institute words version technique internal internal code difficult difficult difficult final addition addition addition addition addition cambridge cambridge computing directly hinton curve curve curve additional solutions solutions solutions solutions solutions solutions solutions estimates design limit requires requires choice choice speed speed basic basic basic basic basic basic basic increase con channel developed bounds types path path path path path finally nature constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint biological associative increases increases describe close corresponds complete stable finding finding finding finding finding finding finding nearest nearest nearest nearest effective implemented supported square end vlsi vlsi makes makes rumelhart rumelhart noisy simulated needed needed needed hopfield hopfield hopfield hopfield dynamical technology programming programming programming programming programming programming ratio special operation direct making making inhibition inhibition inhibition bits idea minimize minimize minimize minimize minimize minimize minimize choose added added improve robust separate practical apply apply apply include subject subject subject subject subject subject quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic subset subset subset recently previously approximately approximately works tions solve solve solve solve solve solve smooth smooth yields yields studies converge converge converge converge differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential trans trans positions symmetric modified modified modified bounded bounded bounded williams sensitive increased increased exists exists extended digital digital digital wide derivative derivative derivative derivative matrices matrices matrices alternative locally locally locally locally locally move column setting hardware strength strength strength strength strength strength strength critical critical critical row conclusions numerical numerical numerical practice constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained physics physics physics physics external california minimizing start exist exist plane plane plane plane plane groups groups minima minima minima minima minima minima minima annealing force force force force force force attractor construct longer perception solving solving solving stability changing changing recall sensitivity coordinates dimensionality dimensionality easy scales scales consisting mutual mutual mutual adding adding equilibrium applying minimization minimization minimization minimization minimization minimization springer john yield yield expressed stationary stationary stationary stationary solved variation open restricted decomposition converges converges converges converges converges sign sign reasonable performing performing classical classical convex convex convex combining fitting fitting fitting roughly penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty closed remains remains remains valid advantages degrees building existing bell subspace subspace subspace subspace subspace subspace subspace subspace extension extension prove prove discuss absolute columns extra extra extra extra extra differ modification attractors invariance tend summary traditional notice notice conf verlag quickly quickly strongly decoding decoding decoding decoding decoding decoding decoding heuristic issue lie oscillations oscillations oscillations oscillations oscillations oscillations criteria hold satisfy simplified minimizes denker illustrates satisfies satisfies acknowledgments decreasing presents origin unlike american american wiley poor create mead involving strengths strengths strengths strengths strengths strengths replaced mass scalar scalar rest applicable decisions decisions decisions oscillation analogous surfaces contours smallest act closest closest reading man opposite spline spline illustrate freedom nerve academic simplest arbitrarily finds finds rows piecewise piecewise piecewise inequality inequality inequality inequality band band band guaranteed fairly improves answer answer independence lies starts starts stanford stanford lin lin sys easier precisely forces forces forces forces forces desirable laboratories consequence inversion grossberg describing opt circle implicit gradually gradually optimize definite definite definite definite definite res cybernetics cybernetics raw explained prop applies empirically capability cohen splines splines treated incorrect anti reaches reaches popular cal tank tank extensions pasadena decoder decreased begins eventually eventually eventually wesley globally globally pose newton physiology saddle addison lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange investigation restrict summing perfectly ordering ordering turned multipliers multipliers multipliers multipliers multipliers multipliers multipliers 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#@Barr_A,Platt_J,
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#*network network network network network network learning learning learning model neural input input input input input input input input input input input input input input input input input input input input input input input data data data data data time time set set set set set set set set set set training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output number number system system system system system system system error results results results results results units units information problem problem problem problem hidden hidden performance performance space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case vector vector vector vector vector vector vector order shown shown shown systems values values weight unit method pattern pattern point point image image image image image image image image image image image image image image image image image image image image single processing large large test analysis analysis class matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form form shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple visual visual visual visual visual visual visual visual paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small net net work work methods methods methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step step step step step step field field field features trained trained structure problems problems problems problems problems random random random random random random random random random random random similar similar similar similar similar show show show equation equation fixed line line line vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images real approximation approximation approximation approximation average average average average average gradient gradient gradient gradient gradient gradient obtained obtained obtained note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result result result result result computation computation computation computation computation solution solution solution log log log log found constant constant constant constant constant estimate standard standard standard standard computer computer science science prediction left left left present phase low low machine machine object sets maximum range range press learn components components components outputs outputs abstract find find computational computational density properties properties properties references due due positive procedure context action complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical effect effect change change difference spatial assume assume lower signals learned chosen part part part part part center center center previous cases cases type good good long long represent bayesian expected make make techniques techniques techniques techniques techniques proposed correlation correct correct correct correct simulations minimum resulting human regression computed computed computed computed sum eq eq eq regions natural natural natural natural global applications filter filter filter filter filter filter filter filter filter filter filter negative negative negative artificial artificial artificial artificial relative represented true true compared application desired desired desired desired desired receptive receptive receptive receptive define compute compute compute compute objects proc location location perform goal goal related constraints constraints constraints constraints constraints constraints constraints constraints connected cortical brain equal contrast contrast contrast contrast contrast connection connection fields train descent descent descent proceedings institute institute department technique technique technique technique technique technique technique technique technique individual represents represents difficult difficult scheme scheme scheme addition maps cambridge cambridge cambridge cambridge computing computing computing domain equivalent experiment hinton additional solutions solutions top effects requires requires approximate world world world world world world world world world world world vision vision vision vision vision vision vision estimated estimated estimated estimated estimated estimated estimated produce channel channel channel derived derived derived weighted developed area lines lines product actual backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature nature nature simply biological biological tested transformation transformation inverse inverse inverse assumption assumption assumption assumption stable surface surface surface surface surface surface effective shape shape shape generate require require eds eds square square square pixel pixel pixel pixel rumelhart pairs pairs pairs smaller underlying underlying underlying reduced fully technology significantly york york york york edge edge increasing consistent uniform uniform uniform numbers filters direct international bottom depth early early early magnitude run light light light light neuronal discussed improve recent separate takes takes takes element typical apply period identical pixels pixels pixels pixels pixels pixels pixels pixels sense sense cognitive recently sufficient varying varying compare compare approximately approximately tions solve smooth smooth yields converge converge address background background background background background background observation bounded channels channels channels williams entire entire amplitude amplitude amplitude constructed horizontal intensity invariant invariant invariant invariant invariant invariant invariant invariant occur wide matrices column column column demonstrate runs half half starting critical row row assumptions reduce operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator 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#@Hurlbert_A,Poggio_T,
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#*network learning learning learning learning learning learning learning model input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance based space weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case case vector vector vector order order order order shown shown systems systems systems values values values values values values values values noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions unit unit unit unit unit unit distribution recognition recognition recognition method method method approach approach approach pattern pattern pattern pattern point image image single single single single single single processing processing processing processing processing processing control control local rate rate rate test patterns class class class matrix matrix matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs form form form form form form form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal paper paper examples small small size net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net work work task task process process current current current current trained trained trained trained trained trained structure structure structure problems problems problems problems random random memory memory memory memory response response similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture equation equation section section section section fixed line general general general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real real approximation states theory theory gradient gradient term note note result result university university university university university university university solution solution solution solution solution solution research research independent independent independent independent defined defined defined defined defined found found found sequence target target target target constant constant table table computer computer terms node science science science direction direction presented present present activation activation activation activation activation machine machine sets range range range range press press learn learn learn learn outputs outputs outputs outputs outputs outputs continuous continuous sample sample abstract applied applied applied applied back back back back back back back back back back back back computational computational computational computational computational computational computational computational references component procedure important adaptive adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation context context context context context context context context context context context context context introduction complex effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic 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finite finite finite finite finite finite minimum resulting resulting tasks total total times times mapping means factor made feedback filter filter filter original original original original original vol samples samples samples represented represented represented true true compared compared compared application application application application desired desired desired desired desired series define define define define define define compute compute compute rates rates perform determined connected connected discrete power power power mit accuracy comparison comparison comparison comparison comparison larger larger update support train train train train train descent descent descent dependent dependent nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets proceedings report report report report report report institute institute institute department department department department loss implementation implementation implementation version version technique technique technique technique internal internal internal internal internal code code code connectionist connectionist connectionist bias delay delay delay scheme scheme considered cambridge cambridge cambridge cambridge cambridge cambridge computing environment hinton hinton hinton san san san conference capacity determine efficient full requires requires world world coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding developed developed developed levels levels levels levels area actual actual actual iteration iteration iteration constraint simply biological biological associative achieved achieved achieved achieved achieved measured measured measured technical technical technical increases increases arbitrary arbitrary group denote transformation transformation transformation transformation transformation assumption finding finding amount amount common implemented implemented implemented implemented implemented implemented supported require ability degree degree rumelhart rumelhart rumelhart development simulated reduced jordan technology programming testing significantly ratio ratio ratio ratio ratio ratio increasing increasing principle operation operation operation language language squared squared squared stored bits combined combined combined run predict architectures architectures architectures architectures architectures architectures architectures improved recent pair element introduced strategy period period machines machines machines cognitive cognitive relevant engineering engineering engineering engineering engineering sufficient varying previously previously conventional conventional calculated calculated calculated works speaker differential achieve rl channels williams williams williams improvement improvement improvement improvement storage storage storage storage storage storage increased increased grant extended derivative matrices matrices predicted alternative locally pass pass pass pass pass pass pass pass demonstrate half conclusion minimal greater greater reduce reduce editors editors constrained constrained encoding encoding physics largest external external california california california pulse variety introduce manner minima minima boltzmann boltzmann explicit explicit appears relation written longer sequential laboratory linearly linearly infinite infinite infinite infinite involves involves remaining scales adding quality quality yield yield dependence dependence codes variation restricted restricted restricted restricted restricted updated updated modulation forms static static static static static static static static static static static static static static static static static static static static static static static static static static static similarly discrimination processor past past past past past past past past past partial measurements expansion combining valid intermediate calculate calculate calculate construction advantages advantages recorded thesis activations activations activations activations formulation determines extension coupled variations simplicity compression compression compression compression uniformly suitable suitable divided driven mcclelland presentation computations schemes schemes schemes mackay identity decoding decoding allowing link link phonetic duration duration duration quantity backward backward backward computes thresholds thresholds thresholds thresholds thresholds thresholds processors processors jacobs deal deal load load load situations situations presents diego diego diego american layered essential requirements requirements requirements investigate difficulty difficulty updating replaced recursive hall behaviour behaviour reducing giving giving links links authors cognition waibel transmission transmission integer generalisation illustrate changed front impulse impulse versions explored mapped store store store utility submitted serial serial attempts defines seconds established established established optimum optimum optimum optimum defining waveform waveform coded coded coded coded coded coded coded coded failure answer considerable straight sections shared strictly forces incorporate incorporate immediately commonly preceding preceding summation summation substantially elman fed simulate marked passed remove incorporated formulated robinson robinson robinson robinson requirement requirement requirement requirement span span span calculating passes operate rely monotonic achieves enables decoder decoder redundancy summed summed summed cor contextual feasible writing assign forming oxford restriction dynamically encoder encoder unity unity impossible flexibility rational consideration khz overcome analogy stated receiver receiver receiver receiver affected cottrell substituting substituting prentice introduces male buffer buffer buffer buffer propagated propagated propagated propagated interconnections arrangement recog foundations creating storing steepest considerations reverse propagate alternatively explorations divide ics ics ics mind street compressed munro transmitted transmitted formulate dyna dyna feeding feeding copy england edinburgh reconstruct alter concentrated approxi denoting thresholded thresholded books responding normalised normalised port september rabiner gratefully copies expense expense council recogni attributed european jersey cliffs hid hid inclusion transmitter transmitter transmitter recursion recursion believed englewood chan chan plateau zipset zipset watrous iid iid halves acknowledges format format decoded decoded energies enabling ted jack lid lid virtue plausibility plausibility plausibility fallside fallside fallside fallside whilst phil deeper frozen extremes extremes wait cued cued nation froin froin neti neti neti feeds poorer proportionally instantiations instantiations awi proportionality 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#@Fallside_F,Robinson_A,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural input input input input input input input input input function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models performance performance performance performance based based based based based based based space space space space space space space space space weights weights weights weights weights order shown shown shown shown systems systems systems values values values values values values values values values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight method method method approach approach approach approach approach pattern point point control control control control control control large large rate rate rate rate rate patterns class class class class class inputs inputs inputs inputs shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms gaussian paper paper paper small small work work work work work work work task task task methods methods methods step points points process level current current current current current current problems problems problems problems high high similar similar similar similar representation show show show show show show show fixed fixed line line line rule rule rule rule rule rule rule general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real approximation average average average average states states states states states states states states states states states states states states states states states states states states states states states states states states states states states theory gradient obtained term term term term experiments experiments experiments activity activity dimensional result university university solution solution research research found found sequence sequence sequence dynamics dynamics dynamics dynamics dynamics initial constant constant constant constant constant constant constant constant constant constant computer prediction prediction prediction prediction left left left left left left direction direction presented presented presented activation low temporal temporal temporal temporal temporal machine machine range range range range press press press learn learn learn learn learn learn position basis basis basis basis nonlinear nonlinear nonlinear nonlinear outputs outputs abstract applied applied find find convergence likelihood likelihood likelihood references references stochastic stochastic stochastic due due due ieee ieee ieee positive positive positive procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision action action action action action action action action action action action action action action action action action action action action behavior effect dynamic variance variance search search search search search search search search search search search search change change change change change change change difference assume rules rules rules rules learned learned chosen chosen higher part part part part part previous previous previous previous previous previous previous previous previous previous previous previous long long long long distributed expected expected expected expected expected equations equations equations techniques region proposed proposed probabilities observed simulations simulations simulations simulations simulations resulting resulting resulting classes tasks simulation simulation simulation sum sum sum sum called called elements elements elements elements regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made made made made made made made made made feedback feedback applications applications study knowledge knowledge knowledge negative negative compared compared provide provide rates proc proc proc active active active active active active active active active active determined goal goal goal goal goal related discrete discrete approaches steps steps steps steps steps steps steps steps steps steps steps comparison larger contrast contrast dependent institute technique technique technique consists internal individual connectionist connectionist responses difficult final final final delay considered considered considered computing experiment experiment experiment experiment experiment environment environment environment environment directly solutions transition transition transition transition limit limit effects detection detection detection determine requires basic basic basic increase increase increase produce produce condition weighted weighted randomly developed bounds velocity velocity velocity controller controller controller controller controller controller controller controller controller controller controller controller path path product evidence evidence evidence associative achieved achieved discussion normal increases describe describe tested limited assumption stable stable stable actions actions actions actions actions actions actions actions actions predictions amount short short short short short short short short short short assumed assumed assumed assumed assumed require eds adaptation future future future future easily easily degree degree simulated simulated underlying dynamical coefficients significantly trials trials trials trials trials trials trials trials trials trials empirical empirical making early early decay idea attention minimize choose run run run added added predict improved improved improved improved discussed discussed discussed improve improve recent element element element element element moving moving period period identical sufficient varying previously previously previously unsupervised unsupervised solve yields converge differential achieve trans trans address positions bounded improvement arm arm lead concept studied occur occur occur occur trial trial trial trial trial trial trial trial predicted predicted deterministic deterministic deterministic occurs occurs occurs generally runs runs runs strength strength strength conclusion assumptions assumptions reduce valued depend reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward differences differences differences differences differences differences numerical designed designed designed sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton faster learns learns mechanisms physics cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle california california california proportional proportional intelligence exist decrease decrease iii averaged averaged averaged manner groups program program program configuration force areas areas appears edges produces longer longer index describes describes describes mathematical changing metric remaining easy angle unique consisting develop applying predictive predictive boolean cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles decreases choosing choosing stationary overlap overlap viewed influence influence influence influence updated centered forms allowed allowed past diagram earlier earlier reasonable barto barto barto barto barto barto barto barto barto barto barto barto barto barto classical reduces reduces boundaries penalty penalty degrees avoid avoid exploration exploration priori priori priori priori priori assignment assignment assignment assignment assignment sciences determines determines determines extension extension extension extension activated activated absolute characterized simplicity reason modification driven driven driven driven driven successful successful genetic ten ten composed conf conf decoding decoding heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic success success success success anderson anderson anderson anderson anderson anderson anderson anderson interpreted superior return oscillations oscillations oscillations oscillations built paradigm paradigm providing delayed highest highest consisted consisted overlapping operating deal software situations unlike american investigate experience exponentially exponentially updating environments environments detail detail strengths game giving tech tech tech tech applicable int int combine referred decisions decisions decisions decisions decisions comparable oscillation affect fundamental coefficient trace possibly extremely automata automata aspect noted assumes assumes mapped academic academic motivated attempts optimum cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart formula formula formula formula formula directed directed directed costs critic critic track track track analyzed unstable failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure caused caused producing choices choices ran immediately immediately members optimize optimize res preceding applies empirically consistency dark car effort effort completion incorporated passes partitioning measuring differs fall resource substantial substantial decoder decoder chose decreased returns conditioning june credit credit credit credit credit credit credit yielding instantaneous pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole don assign equivalence modify angular velocities controlling discover eliminated inspired fails air smith smith smith consideration ranges ranges ranges ranges ranges ranges ranges ranges ranges ranges ranges ranges ranges adjusting occurred occurred occurred occurred automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton grow los balance balance balance balance balance balance balance balance keeping hope observing definitions responsible responsible responsible heuristics heuristics heuristics exploring heavy falls falls ensures james decide decide holland holland lengths widrow widrow widrow searching chooses enable multiplied multiplied repeatedly repeatedly cpu environmental environmental environmental environmental environmental extends pendulum jump jump balancing balancing balancing balanced balanced executed assigns consecutive boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes associations leaving specification shepard shorter shorter shorter shorter shorter session failed conjecture comparative quasi quasi causing amherst reports stem classic recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence recurrence edinburgh avoided continuity visited visited visited visited visited visited shaded mutually acting penalized penalized penalized modifying ibm exclusive alternate goals decays labs playing playing degraded interacting inverted march efforts altered harder eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility attached inversely permit increments aaai inactive reinforce reinforce reinforce payoff slot ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase converging converging stochastically stochastically stochastically adaptively visit usefulness usefulness returned returned seattle devised judged push swing governing exploits exploits decaying decaying interpolate weather minsky coins coins appl smc smc upright permanent demands rectangles ranged enter correlates enters nonstationary decoded decoded decoded jan allowable allowable began diverge diverge investigator triple ace ace ace ace ace ace ace ace ace ace ace ace ace ace ace virtue synthesize modifies traversed traversed darker angeles lasting klopf anticipate terminated inertia inertia sato bruce seeking participate rosen samuel absorbing absorbing rationale anandan ire exclude explores dev ending recur succession permitted fell multiplies reinforced invoked michie michie michie michie michie michie michie cheaper adaline neuronlike neuronlike lesser bucket bucket traversing utgoff utgoff lighter outward accumulates visiting nonoverlapping nonoverlapping impulsive rewarded rewarded rewarded rewarded rewarded rewarded rewarded rewarded investigates investigates balls balls gte gte alteration alteration dale neurological eventual eventual preclude brigade brigade juggling oliver returning gathering gathering sooner sooner armed armed goodwin travels checkers thrown attaining recency traverse conserve clever traverses traverses revisited reinforcing reinforcing reinforcing reinforcing abe reinforces reinforces connell connell connell rept rept rept rept lasted demanded handed rewarding boyd jacques awj timer desirability desirability unexplored augments circumstance 
#@Goodwin_J,Rosen_B,Vidal_J,
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#*network network network model neural neural neural data function function function figure figure time time time time set set set set set set set set set set number number number number number number number number number number number number number number system system system system system error error error state state results results results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem problem models models models models models models models models based based based based based space space space space space case case case case order order order systems systems systems systems systems systems values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters noise weight neurons unit unit unit unit unit unit unit unit unit unit unit unit unit method method method method approach approach approach approach approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point single single single single processing processing processing processing large large large large patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis optimal optimal form form form form form simple simple paper small small small size size size size size size size size size size size size size size size size size size size size size size size size feature feature feature work task methods methods methods points field field features features features features features level cell structure structure structure structure structure structure random random random random random random random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar representation representation representation representation representation representation representation representation representation architecture show show equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed general general general general generalization parameter parameter parameter parameter approximation approximation theory theory theory obtained term term term term note experiments activity dimensional result result university university university university university threshold threshold threshold solution solution solution solution solution solution research independent independent independent log defined defined defined defined found target initial constant table table table estimate standard computer computer computer terms terms distance distance connections connections science science science science science science science science presented present present present present present low low machine sets maximum maximum maximum maximum range press continuous abstract find find find find computational density properties properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic procedure context introduction behavior behavior effect variance parallel parallel cost cost search search tion assume assume assume representations representations representations representations representations previous previous previous bound bound bound bound bound bound bound bound bound cases cases cases type type required required good good good binary binary binary binary binary binary binary binary binary binary binary binary binary binary long long distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed expected expected expected equations proposed probabilities scale scale finite resulting computed multi eq called called mapping factor made obtain obtain obtain relative relative represented represented represented represented represented represented represented represented represented represented true compared desired desired desired desired receptive receptive receptive receptive receptive receptive receptive provide define define define compute active active active active active active determined determined experimental goal cortical brain brain equal approaches approaches mit accuracy comparison comparison larger fields fields fields fields source proceedings proceedings proceedings report report report institute department department department department implementation implementation version consists internal code code code code code connectionist connectionist connectionist connectionist connectionist connectionist scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme maps considered considered cambridge computing equivalent hinton hinton hinton hinton hinton hinton solutions solutions estimates limit limit conference conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine efficient efficient efficient efficient upper upper upper upper upper upper upper significant free estimated estimated increase give give con produce produce coding coding coding coding coding coding coding derived derived derived derived randomly randomly developed criterion criterion bounds types types actual finally selected nature nature depends constraint constraint constraint simply achieved measured measured measured measured measured discussion technical technical technical arbitrary arbitrary denote denote denote tested assumption corresponds complete complete complete finding short short common implemented generate supported supported role role theoretical require eds degree rumelhart rumelhart typically needed functional functional interesting special structures representing details call numbers max max making stored stored stored stored stored stored stored stored stored stored stored stored stored bits bits bits bits depth minimize produced produced choose resolution exact exact robust typical similarity similarity similarity introduced strategy subject identical trees sense inference inference subset subset subset subset subset cognitive cognitive dimensions previously approximately volume tions yields sparse sparse definition modified modified generalized generalized bounded bounded bounded bounded bounded bounded interval interval entire increased constructed constructed constructed expression expression expression concept concept concept concept concept studied scaling scaling trial deviation wide alternative touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky half half greater reduce reduce valued central numerical numerical numerical numerical exponential exponential exponential exponential exponential encoding encoding strong hard mechanisms physics largest largest largest largest largest proportional assuming relationship relationship relationship averaged groups program program boltzmann reference reference derive construct construct construct produces solving estimating tuned tuned mathematical mathematical mathematical mathematical recall implement missing explicitly simultaneously simultaneously easy easy consisting formed implies john john choosing national national extracted family family expressed overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap viewed codes codes codes codes codes codes fraction understanding understanding sizes sizes earlier reasonable reasonable measurements roughly closed symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol assigned foundation foundation foundation david expect subspace sciences memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories determines determines major major major major simplicity reason reason columns letter efficiency closely capable importance society computationally symbols 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complicated cognition fundamental fundamental examined coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse measurement naturally concepts concepts analyze analyze analyze adjusted subsets subsets subsets subsets subsets subsets subsets subsets front portion noted art art store store arbitrarily sentences optimum mentioned asymptotically great rows pairwise formula formula formula agreement analyzed analyzed analyzed guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed phenomena improves coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded analytical analytical analytical expensive independence lies handle organized strictly strictly strictly constructing mathematics involve optimize optimize definite author annual qualitative meaning mellon mellon mellon summation apparent evaluating carnegie carnegie carnegie limits empirically understood cmu cmu introducing share variant pittsburgh pittsburgh pittsburgh maximizes maximizes suited hamming hamming conclude comments decreased tolerance eventually semantic semantic multidimensional sharing sharing phenomenon phenomenon appearance optimality assign forming formally guarantee investigation restrict restrict ratios arguments approximates repre repre naval receptors receptors turned turned turned establish multiplier consideration minutes ranges adjusting adjusting simplify simplify replacing stated multiplicative attractive check los contract analyzing definitions belong disjoint imply north capacitor exceeds alphabet alphabet substituting reliably meaningful overlaps studying surprising surprising holland searching belongs scan dif emergence emergence reveals ballard ballard cpu ends storing storing storing storing storing storing correcting impact partitioned partitioned partitioned partitioned designing subsequently grants alternatively intersection intersection intersection johnson johnson dividing empty approx linked maintaining appeared slight microstructure rigorous fellowship deriving recursively ties encodes emerge emerge amherst constitutes stands algebraic representa manipulation arising summarizes exclusive geoffrey pdp pdp graduate disadvantage emphasize depicts exceed emphasized paradigms turning happen rochester rochester places union union subspaces answers mea resembles capacities capacities appearing slot slot slot slot marks quantify agrees slots slots slots slots slots developmental distinguishing coincide manipulated obey dedicated deals parti evolving complement accommodate connectionism sis feldman contents bear sentation eighth emerged emerged formulas constituent lisp localist localist localist sentations joseph joseph fractional entities entities ohio enforced ness weakness shortcut recursire undesirable angeles puter imposing burden ronald divides unstructured tebelskis ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost ghost plex contin render weaknesses ist triples pennsylvania visibility visibility simplifications resemblance uous eet ijcai unwanted representable attainable attainable entity entity rosenfeld stacks viability wei atomic fills sured coarsely victor analy guaranteeing guaranteeing deemed deemed imations alon informally tioned symbolics permissible ork rosenreid born fie straightforwardly inspecting produc ezplorations participates participates conclusive ferences subsumes subsumes mathematica abandon 
#@Rosenfeld_R,Touretzky_D,
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#*network network network network network network network network network network model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set algorithm algorithm output output output output output output output output output output number number number number number system system system system system system system system system system system system system system system system system system system state state state state results results results results results results results results results results results results results units units units units information information information information information information performance performance performance performance performance performance performance based based based space space space weights linear layer case case case case case case case vector order order order order order order shown shown shown shown shown shown shown shown shown shown systems systems values values values values values values values values parameters parameters noise noise weight weight neurons neurons unit distribution approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point image image image image image image image image image image image image image image image image image image image image image image image processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing large large large local neuron neuron neuron neuron neuron rate rate patterns patterns optimal optimal form form form form shows shows shows shows shows shows signal signal algorithms algorithms visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper examples examples small size work fig fig fig fig fig fig fig fig fig fig fig step step step step step field field field field field field field features process process process process level level level level level level level level structure structure high high high high high high response response response response response response response response similar representation representation representation representation representation representation representation representation representation show show show show show equation equation equation equation equation section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line line line line line images general general speech average gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained obtained term note note note note experiments experiments experiments experiments activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional result result result result result result research research independent independent independent independent independent independent independent defined defined defined found found found found found initial constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant computer computer computer terms left direction direction direction direction direction direction direction presented presented presented present present low frequency frequency temporal object object object object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range range range range range range range range range range range range range range range range range range press position position position position position position position position outputs outputs outputs outputs outputs outputs continuous abstract back back references due ieee ieee ieee ieee ieee ieee ieee procedure procedure procedure procedure procedure procedure procedure procedure important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive action complex complex hand hand circuit estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect generated difference difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower lower lower lower lower measure measure signals higher higher part part part part part previous firing firing good good long long represent represent represent expected make fact techniques techniques region region proposed correlation correct observed observed observed errors errors simulations simulations simulations minimum minimum classes simulation simulation simulation simulation simulation simulation simulation simulation performed eq eq eq called times times elements elements elements elements elements elements elements regions means means means factor factor factor factor factor factor factor factor factor factor factor factor optimization made made study filter filter filter filter filter filter filter filter obtain original original original original original original original original original vol vol vol vol artificial artificial artificial artificial artificial artificial artificial artificial artificial relative relative specific represented compared application receptive receptive receptive receptive receptive receptive objects objects objects objects objects rates proc proc proc proc eye eye determined determined experimental experimental experimental experimental experimental related related discrete discrete brain equal equal equal equal power larger larger larger larger contrast contrast dependent institute words words department implementation implementation implementation version version technique technique consists consists individual represents responses responses responses responses responses final scheme scheme scheme scheme scheme scheme scheme scheme equivalent environment curve curve curve view limit top stage stage stage stimuli bit bit detection detection upper upper upper upper vision estimated estimated estimated estimated estimated estimated basic increase increase increase increase increase increase increase increase increase increase increase increase increase produce produce produce produce channel derived derived derived derived derived derived developed developed criterion velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines lines lines lines lines lines lines lines lines lines lines lines product product actual finally finally depends sampling achieved measured measured close close inverse corresponds complete circuits amount nearest implemented implemented supported adaptation adaptation adaptation adaptation adaptation adaptation square square square square square square square square square square square ability easily including fit fit fit fit typically smaller needed reduced account programming ratio york york increasing increasing mechanism mechanism mechanism mechanism mechanism mechanism mechanism operation leads details filters filters filters filters filters filters filters filters filters filters filters filters filters filters bottom depth depth depth expert magnitude magnitude magnitude magnitude magnitude frame decay decay decay combined produced added description description description description improved discussed discussed recent resolution advantage advantage property element movement movement movement movement movement movement movement movement movement movement movement movement movement introduced introduced moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving include period period period period identical identical identical machines pixels pixels pixels array array array array array previously previously observations tuning tuning tuning tuning tuning tuning axis axis axis smooth smooth smooth yields differential differential differential differential differential differential differential trans trans trans trans channels channels interval organization improvement improvement improvement sensitive sensitive sensitive entire entire increased horizontal horizontal intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity studied invariant digital digital wide wide wide spikes matrices locally locally move white occurs generally column setting setting setting demonstrate half conclusion conclusion starting minimal conclusions depend central central differences clear clear clear clear peak peak exponential exponential hard physics physics drawn drawn drawn drawn drawn drawn demonstrated demonstrated demonstrated demonstrated demonstrated solid solid proportional pulse start selective min min min relationship relationship relationship relationship averaged averaged averaged introduce manner base question acknowledgements areas areas van van van van van van van produces optical optical optical estimating laboratory tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned vertical mathematical distinct physical easy consisting consisting consisting frequencies springer quality quality potentials decreases dependence review squares squares squares squares influence variation detailed detailed operations modulation modulation modulation modulation forms forms completely suggested constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants sign dashed dashed dashed dashed dashed additive reduces roughly roughly purpose remains remains distances filtering filtering filtering filtering filtering filtering filtering filtering filtering construction foundation classified recorded priori coordinate coordinate coordinate retinal discuss neighbors discussions suitable driven delta poggio poggio post situation situation fine soc soc notice verlag strongly contribution content device device device device device device receptor receptor receptor receptor comp involved wave wave wave wave wave wave wave wave wave wave wave wave wave highest highest principles principles attempt moves overlapping overlapping overlapping preferred preferred neighboring decreasing modelling modelling situations remain remain remain remain remain stimulation selectivity american collection essential circuitry circuitry circuitry steady detail optimized optimized integral accurately behaviour behaviour existence scalar scalar scalar respond behavioral applicable biol biol biol biol possibility authors referred referred comparable proper proper encode smallest smallest smallest measurement gradients adapt integer man extremely extremely rev rev front front impulse impulse precise mapped academic extent extent extent extent extent optimum optimum animal animal mentioned agreement convolution guaranteed defining adapted caused worse reasons ganglion ganglion spatially spatially spatially spatially spatially processed turns rapid straight straight straight purposes purposes organized precisely directional incorporate incorporate worst consequence opt opt res depicted preceding apparent apparent varies understood pure amounts spoken experimentally experimentally experimentally quantitative introducing recordings incorporated slower formulated sharp sharp operate berlin summarized spread serve qualitatively acoustics conclude physiol findings realized phenomenon phenomenon phenomenon picture picture cybern cybern cybern cybern cybern restriction angular velocities velocities velocities velocities velocities velocities velocities velocities velocities velocities velocities velocities velocities velocities null flexibility theories outcome arranged inspired spontaneous spontaneous systematic fits fits adds murphy imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging height keeping optic optic optimally optimally degradation degradation degradation degradation degradation degradation degradation degradation introduces periods realization realization enhance demonstration demonstration histograms scan claim artifacts modelled modelled thin stimulated reveals reveals reader reader matter extensively agree insect considerations designing harris harris displacement displacement fly fly fly fly fly fly fly outlined outlined fitted fitted grating grating grating grating grating grating largely latency revealed evoked eric thick thick thick elementary degraded degraded degraded wise wise ullman ullman lond intensities intensities reveal tune tune reciprocal reciprocal differing mini differentiating differentiating differentiating differentiating differentiating tail tail remarks restoration restoration influenced assistance settling settling settling dropped pronounced integrates horizontally horizontally exclusively wavelength wavelength wavelength wavelength partly contrasts operational operational marr marr constancy constancy inspection inspection smc physically electrophysiological neglected steveninck steveninck steveninck steveninck steveninck adequately adequately ruyter ruyter ruyter ruyter ruyter syst ganglia supposed supposed atlas enabling insert gradual gradual degrade repeating biophysics eta blurred blurred blurred blurred blurred blurred directionally columnar scans hypothetical netherlands netherlands heidelberg silverman silverman biophys wired depths hypothesize organisms blur blur blur blur blur blur blur blur blur blur blur blur blur blur blur blur mosaic suppresses psth psth psth psth psth blurring reichardt reichardt reichardt reichardt kronecker underlie visualized regularly smear blowfly blowfly blowfly compound anatomically resolving equipped equipped restored franco unrelated pilot realizing subdivided outward doubt paragraph delivers situated cas rounding smeared rob sight permitting traverse clever lamina sondhi sondhi weighed erroneously cla mxm automat contr manifests eld tunes 
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layer layer layer layer layer layer layer vector order shown shown systems systems systems systems systems systems systems values values probability probability probability probability probability probability probability probability probability probability probability probability probability functions neurons neurons unit distribution distribution distribution recognition method method method method method method method method method method method approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point image single single large large local local test test patterns patterns patterns patterns patterns patterns analysis class class class class class class matrix matrix matrix form form shows simple simple simple examples small small size feature feature feature feature feature feature feature work work work work work cells cells cells cells points points points points points points field features features features features features classification classification classification current current current cell cell cell cell structure problems problems problems problems high high high high high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response similar similar similar architecture architecture equation equation equation fixed fixed fixed general general generalization parameter real real states note activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional result university threshold threshold variables computation research independent defined defined defined defined found found initial initial constant constant constant computer distance connections connections connections science presented map low low low low low low low low low frequency object sets sets sets sets sets sets sets press continuous abstract applied computational computational computational computational convergence density density density density density density density density density density density properties properties properties references ieee positive procedure important decision introduction complex complex effect recurrent recurrent recurrent change energy energy energy energy energy energy energy energy energy complexity chosen chosen center previous firing firing firing multiple multiple multiple multiple long conditions conditions distributed distributed distributed fact region region correlation correlation scale scale classes classes classes classes classes total simulation respect called called regions regions regions regions regions regions regions regions regions regions regions regions potential potential potential potential potential potential potential feedback global applications applications study study study negative application application application application application application define define rates proc proc proc proc proc location related related distributions distributions distributions distributions distributions distributions distributions distributions distributions accuracy larger contrast proceedings report institute consists internal difficult addition addition addition addition computing environment environment environment environment environment environment environment directly additional transition limit capacity capacity capacity requires choice significant significant significant significant approximate world vision give randomly clustering area types finally nature associative discussion discussion technical feedforward feedforward feedforward feedforward feedforward feedforward describe describe describe arbitrary limited limited limited amount assumed generate theoretical eds square square square future degree development development development development hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield dynamical dynamical dynamical technology york york mechanism empirical language stored stored stored depth depth early combined produced run architectures architectures improved recent recent property property introduced recently interest dimensions smooth studies trans locations locations locations locations organization storage storage storage storage storage storage storage storage storage storage storage storage storage risk risk risk risk risk risk risk risk risk risk risk risk risk risk increased studied occur occur occur suggests correctly flow flow modules clear clear hard presence physics proportional proportional proportional proportional introduce manner manner connectivity connectivity connectivity minima minima minima identification program explicit generating describes distinct distinct modeled recall sensitivity category explicitly explicitly linearly linearly physical physical dimensionality dimensionality equilibrium equilibrium equilibrium equilibrium events events springer potentials competition review review overlap viewed restricted showed completely allowed classical event boundaries boundaries construction kohonen kohonen figures usa usa usa subspace subspace memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories extension discuss variations domains phys reason identify receives composed conf prob prob prob prob anderson content content sci sci sci satisfy quantity quantity relaxation relaxation relaxation relaxation computes consisted satisfies modelling employed carried american detail replaced limitations accurately scalar detectors biol int referred referred proper surfaces circles circles circles circles math closest rev illustrate implementations portion portion separated academic generates contributions submitted serial defines defines charge charge charge animal brown site site site site site advanced separable separable separable separable separable separable separable separable separable separable separable separable separable separable separable separable separable separable separable guaranteed defining slope improves caused caused london rapid implementing sites sites sites sites located acad acad acad describing describing circle radius meaning virtual autonomous employ incorrect compares berlin serve collective collective collective collective inherent attraction attraction focused focused focused focused focused acquisition acquisition acquisition cybern sort cooper cooper cooper cooper cooper cooper investigation dynamically labelled jth intelligent abilities disjoint symposium degradation natl natl natl published published surprising conjunction originally april graded basin emergent july lit reports flat flat basins basins basins basins robots douglas landscape landscape landscape landscape landscape depicts acquired interactive topic importantly covered subspaces unpublished architectural handled covers palmer acquire discontinuous christopher settling dissertation assessment assessment assessment ooo placement degenerate spie charles memorized addressable addressable unrestricted unrestricted unrestricted unrestricted unrestricted recalled zones zones shares stabilizing broadcast respects burden heidelberg reilly reilly reilly reilly reilly reilly reilly workers depths depths rce providence providence incremented isomorphic comput dembo dembo leon scofield scofield scofield scofield liapunov liapunov liapunov opened charges unwanted degeneracy wells wells wells wells wells wells acquires aro intense richmond collins plateaus relaxes constituting xil island occurence biosci proliferation rhode framed electrostatic feinstein economical 
#@Cooper_L,Elbaurn_C,Reilly_D,Scofield_C,
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pattern pattern pattern pattern point point point point single single single single single single single single single single single single large large large local local neuron neuron test test test test patterns analysis analysis analysis analysis analysis matrix matrix matrix form form signal signal signal simple simple simple visual visual visual visual visual visual visual visual visual paper size size work work work methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points points points field field field field field field field field field field field field field field field field field field field field field current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell problems memory memory memory memory memory response response response response response similar similar architecture show show equation fixed fixed fixed fixed fixed fixed rule general general general generalization parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average average average average average states states states states theory theory theory theory theory theory theory theory term note note note note note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result university computation research research independent found initial constant constant constant constant constant constant constant terms terms terms distance distance synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science prediction left left left presented present maximum abstract applied back find find find density density density properties properties properties references component stochastic due positive complex behavior effect effect effect effect effect recurrent change change energy energy energy energy energy difference complexity spatial spatial spatial assume assume assume assume assume measure measure measure measure signals signals signals signals signals signals center previous type type required required cortex cortex cortex cortex cortex cortex cortex cortex cortex conditions conditions represent equations proposed scale scale classes total computed sum sum performed regions mapping factor factor factor potential made feedback feedback feedback feedback orientation orientation orientation global obtain negative original artificial artificial artificial compared application application application application application define proc proc proc location location eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye related cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain connection dependent dependent institute department loss implementation synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists individual individual responses addition addition considered computing experiment experiment environment environment limit stage capacity significant significant significant types types finally finally finally nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory constraint discussion normal transformation limited assumption assumption assumption excitatory excitatory stable surface surface effective effective effective effective synapse synapse supported require square development development development hopfield hopfield hopfield hopfield hopfield ratio consistent consistent leads leads inhibition inhibition stored stored early magnitude idea produced light light denotes denotes population discussed recent advantage lateral practical practical introduced period period period recently sufficient sufficient previously generalized organization storage storage storage storage exists exists studied studied occur suggests suggests extended white occurs strength critical critical hebbian hebbian depend asymptotic asymptotic suggest physics physics reduction assuming selective selective selective selective selective averaged averaged averaged introduce manner manner connectivity connectivity connectivity connectivity connectivity minima minima minima identification explicit primary estimating describes describes stability tuned physical integrated equilibrium equilibrium equilibrium shift shift shift agent focus focus dependence dependence interpretation detailed detailed detailed detailed detailed open open restricted ocular ocular ocular evolution slow reduces closed closed closed closed closed closed closed sufficiently usa usa usa dominance dominance dominance memories memories memories memories memories memories activated partially discussions simplicity simplicity modification modification modification modification driven reached reached receives anderson neuroscience content content physiological sci sci quantity write write relaxation relaxation relaxation neurosci satisfies receive situations employed employed remain remain stimulation selectivity selectivity selectivity selectivity selectivity american collection rapidly rapidly detail strengths replaced replaced replaced replaced ml helpful scalar respond applicable plasticity plasticity plasticity ideal ideal scaled office office lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn circles circles mapped mapped nervous ith ith fibers pyramidal contributions charge charge animal brown site site great slowly slowly agreement analyzed unstable fairly caused caused interneurons drive formalism formalism formalism sites sites sites afferent afferent afferent afferent afferent acad acad acad describing describing describing res res localized recording qualitative virtual varies pathways dark amounts fed quantitative orders anti singer singer proportion primarily cooper cooper cooper cooper cooper cooper modify modify modify modify modify arguments circular jth naval binocular binocular striate chemical nearby imply natl natl natl published published dendrites arrive environmental environmental extensively erlbaum captures munro munro munro transmitted employs expanding preferences preferences preferences transparent monocular monocular monocular monocular monocular blocking intra intra expand importantly reveal intracellular particle modifiable modifiable modifiable modifiable modifiable modifiable modifiable modifiable modifiable modifiable modifiable retained dramatic unpublished spite architectural palmer simplification bienenstock bienenstock christopher sake settling hop adult fabrication bcm sharply exclusively dissertation intracortical intracortical arriving arriving confined experienced bear facts addressable addressable unrestricted mid cats unaffected levy gij broadcast assoc traversed patterned cortico cortico cortico cortico cortico cortico cortico army responsive responsive surrounded unimportant providence providence dembo elongated embody contracts leon scofield scofield scofield scofield charges charges unwanted lij lij lij lij lij lij deprivation deprivation deprivation deprivation deprivation deprivation discussing discussing contrasted resistant richmond relaxes iol traversal island island proliferation postnatal reared rhode rhode geniculo deprived deprived deprived electrostatic feinstein 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units units information information information information information information information information problem problem problem models hidden hidden hidden hidden hidden based based based based based based based based space weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer case case vector vector vector order order order order systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values values values parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions unit unit recognition recognition method method method method approach approach approach approach approach pattern pattern pattern pattern point image image image image image single single single processing processing processing processing processing processing processing processing processing processing control control control control control control control control control control control control control control control control control large large patterns patterns optimal optimal inputs inputs inputs inputs inputs inputs form form form form shows shows signal signal signal visual paper small small net net net work work work work work work task methods methods methods field process process process current trained trained trained trained trained trained trained trained trained trained structure structure structure problems random random random random memory response response response response similar architecture architecture architecture equation equation equation section section line line line line line rule rule rule rule rule rule vectors images general general parameter parameter real real real term term activity threshold threshold research research defined defined found found found target initial initial initial initial constant constant constant constant constant computer computer terms distance distance distance distance distance distance distance distance connections connections left direction presented presented presented machine machine sets range range range press press learn position position position outputs continuous continuous continuous abstract back find find computational computational convergence references component component procedure procedure procedure important important important adaptive adaptive decision decision decision decision decision decision decision decision propagation introduction complex hand hand hand hand hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior effect effect effect generated parallel parallel search search tion tion tion change change change change change change change change change change difference difference difference rules rules rules rules rules rules representations learned part part center bound type type multiple good binary binary binary binary long equations equations make fact techniques techniques techniques techniques techniques techniques length length correct errors errors errors minimum minimum ing ing ing tasks tasks tasks total simulation simulation simulation simulation human human human human human human human human human human human human human human human respect multi multi multi sum times times times times elements elements elements elements factor factor factor factor made made natural orientation orientation applications original vol vol artificial artificial artificial artificial relative relative relative relative compared compared application application application desired desired desired desired desired desired desired desired desired desired series rates active goal goal goal goal goal goal goal goal brain equal power approaches mit steps larger train train train train train report report institute words technique consists internal responses responses difficult difficult difficult difficult final bias layers layers layers layers scheme scheme addition ai cambridge domain equivalent environment environment directly directly hinton curves determine determine efficient efficient significant free world world speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed vision con con con derived weighted weighted developed developed developed robot robot robot robot robot robot robot robot robot robot robot robot robot area types types actual provided constraint simply associative associative achieved discussion increases describe describe complete complete stable actions actions short common effective effective generate role require eds adaptation adaptation adaptation ability ability ability ability future rumelhart rumelhart rumelhart development development including simulated simulated smaller needed needed fully block block block block block block block block block block block transfer transfer programming york database mode mode mode call direct direct direct direct direct making making making making making making bottom expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert magnitude magnitude magnitude magnitude magnitude magnitude magnitude produced produced produced run architectures improved advantage takes takes element element element element element element element element element typical lateral lateral machines quadratic inference cognitive relevant varying varying conventional teacher teacher calculated calculated works works works tions tions solve smooth studies converge rl background background separation symmetric observation generalized channels williams entire constructed constructed studied scaling scaling scaling digital wide wide wide derivative predicted predicted alternative alternative move pass demonstrate demonstrate flow flow tangent tangent differences sigmoid sigmoid designed clear sutton sutton performs practice learns propose physics cycle solid solid variety user start manner configuration configuration base ways ways stability stability changing changing segments multilayer easy angle angle angle scales adding agent agent blocks blocks blocks correlated correlated squares influence influence influence solved variation controlled controlled controlled restricted restricted organizing constants key calculation barto barto intermediate initially initially distances calculate sufficiently assigned construction views degrees formulation inter inter assignment assignment batch recognize automatic automatic automatic automatic discuss specifically sensor sensor aspects suitable suitable modification divided delta mcclelland presentation presentation presentation situation ten fine receives receives receives receives receives composed capture summary road road road road road road road refer quickly quickly repeated heuristic success interested interpreted interpreted interpreted dis superior return ill leading cat processors received consisted consisted operating operating extract extract extract situations trains trains trains remain command command command command command command american varied put put involving involving humans humans humans humans detail detail detail strengths replaced integral issues issues respond fashion fashion fashion giving behavioral investigated applicable analytically scaled decisions decisions comparable complicated tanh proved proved proved understand understand cognition momentum momentum momentum removed traffic traffic traffic traffic traffic traffic configurations man man man predicts extremely adjusted front formal algo perceptton academic switching consist utility defines slowly slowly slowly slowly developing sensors track track track unstable slope adjacent adjacent adjacent capabilities caused caused handle processed processed turns drive drive drive drive rapid perspective straight easier organized preprocessing preprocessing day day day day constructing constructing constructing broad controls controls consequence consequence cut cut cut separately grossberg grossberg grossberg grossberg describing gradually auto cybernetics qualitative summation improvements composite limits reflect dark tional readily autonomous autonomous autonomous autonomous car car car car car car car car effort orders passed continuously reliability compares compares commands commands commands commands commands commands commands commands commands commands maintain maintain maintain release ture limiting differs instruction curvature curvature curvature adjust gave simulator boston sophisticated sophisticated age attraction attraction progress picture shifted formally tation restrict driving driving driving acts concerned controlling circular impossible interconnected interconnected turned minutes minutes ranges occurred proceeds proceeds proceeds logarithmic logarithmic logarithmic interconnection interconnection interconnection interconnection attractive hyper vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle moment abilities abilities abilities keeping nearby removing methodology methodology methodology methodology responsible arrays weakly heavy combines ranging ranging governed sion displayed bad evident consequences facilitate ahead ahead ahead ahead ahead master master master master master refers refers augmented environmental properly ends arrows arrows passing park broken broken speeds instructions influences automated limitation skills mind resonance resonance audio maintaining compressed converted microstructure lane lane lane lane lane lane lane lane lane lane lane lane lane presenting formulate formulate emerge employs employs responds smoothly acceptable classic workstation massively conservative conservative conservative adjustment adjustment adjustment tight illustration param param avoids arising acting increment increment translated concentrated robots magnitudes magnitudes magnitudes rithms compensate graphics graphics maintained maintained permits convert carefully efforts efforts rectangle concentrate books differentiation overhead parallelism employing employing constructs tied attached retained nal steering steering steering steering steering steering steering steering eters corrections worked suggestions emphasis emphasis restoration ate ate hyperbolic instability instability accordance thousand spring hat shot focuses dropped stay incorporation sen equa progressively manually manually manually manually manually swing systematically systematically restricting scenarios intact governing governing tended tended tended tended totally curved safe safe rel rel rel rel presently teaching teaching teaching teaching teaching adapts adapts remained bradford vicinity addressing correlates indirectly cyclic ous carpenter carpenter capturing manual manual discovers undergo ini responded responded experimented addi landmark began spanning developments dist dist dist facilitates resemble cats cars cars cars cars cars cars assessing predic approxima terminate adjustments dard aimed treats ess posi damped decides quarter occupied occupied supervision positively aggressive aggressive standing feeds associating circumvent driver driver driver ions interconnectivity interconnectivity taught taught taught originating originating originating ans ans ans ans ans ans ans ans ans ans ans ans ans ans ans spans teach teach fell behav continu eter handicapped weaknesses accelerate reinforced unitary unitary vehicles vehicles correla wild instructed steer noticeable weakened grained pertinent autonomously imitate imitate fax unspecified relaxing sor deci interfaces negatively cluttered strained vastly backgrounds labor regu coarsely returning promote ior 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#@Macy_S,Shepanski_J,
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order order order shown shown shown shown values functions neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution recognition approach approach approach pattern pattern pattern pattern point image image image image image single processing processing neuron neuron test analysis analysis analysis optimal inputs signal simple simple simple simple simple simple simple simple visual visual visual visual visual visual visual visual visual small small size work work work work task task methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points points points points points points points points field field field field field field field field field field field field field field field process level current current trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems random response similar similar similar similar similar similar representation representation representation representation architecture architecture architecture architecture equation vectors vectors vectors images real real obtained term experiments experiments activity activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university solution defined defined found found found connections connections prediction presented presented map map map map map present present present present activation activation activation temporal temporal machine machine machine object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range range learn position position position position position basis abstract back properties references component important propagation introduction hand hand circuit stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect generated generated parallel parallel parallel parallel parallel tion tion difference difference variable spatial spatial spatial spatial spatial spatial lower signals learned chosen higher part center center center type required required cortex cortex cortex cortex good represent tree distributed make make proposed correct forward ing ing ing human human human human human computed computed respect called regions regions means made made global global obtain obtain artificial represented receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive objects proc location location location perform perform perform connected connected cortical cortical cortical cortical cortical cortical cortical cortical brain brain fields fields fields fields fields fields fields support descent report report report institute institute institute individual individual final layers layers layers graph maps maps maps maps maps maps domain view view solutions san stage stimuli stimuli stimuli stimuli stimuli determine determine determine efficient upper world world speed speed speed speed vision increase give derived randomly randomly randomly developed area area area area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines actual provided provided iteration iteration nature inhibitory inhibitory biological biological biological discussion describe group corresponds corresponds corresponds corresponds excitatory excitatory surface surface shape supported role main square ability hypothesis hypothesis instance reduced functional functional functional fully fully interesting interesting projection york york consistent structures structures iterations direct inhibition early idea predict architectures separate typical moving identical trees sense sejnowski sejnowski cognitive relevant relevant varying subjects subjects subjects subjects axis axis axis axis solve solve solve correspond correspond correspond studies studies studies studies studies address locations organization sensitive horizontal horizontal horizontal horizontal horizontal horizontal horizontal parts wide wide correctly correctly correctly move width flow conclusion central designed suggest encoding strong mechanisms presence physics demonstrated exist averaged areas areas suppose appears relation pro van perception laboratory laboratory ann vertical vertical modeled sensitivity linearly gaussians john viewed solved fraction fraction fraction fraction fraction evolution centered understanding understanding suggested suggested performing sec sec roughly interpolation intermediate initially combinations contour retinal plotted plotted plotted plotted prove reason middle middle middle middle middle middle middle middle middle middle middle extra extra closely maximal computationally detect soc soc allowing superior content physiological physiological physiological bar bar involved involved involved involved involved involved involved involved sampled localization realistic surround neurosci neurosci neurosci moves extract extract diego american circuitry dotted mass examine relationships structured structured structured structured structured structured structured structured structured structured comparable understand understand understand contours examined hill circles man man man man man man man man man predicts rev equally changed thought adjusted portion observe mapped shapes consist attempts directed distinguish distinguish improves adjacent biology immediately monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey projected res patches patches patches qualitative radius radius apparent quantitative psychophysical psychophysical psychophysical psychophysical effort posed detecting dots rep ture extracting extracting extracting extracting display display display display begins summed displays displays hints person fix velocities velocities branches neurophysiol neurophysiol impossible primate primate primate primate striate striate striate moment bands bands obtaining obtaining obtaining obtaining analyzing neurobiology salk salk preparation analyses corre studying von moved moved belongs similarities deg layout jolla refers properly steepest observer speeds material helmholtz helmholtz wiesel ties lesions reports hubel breaking discovering imagine demon electrode lesion thick thresholded retinotopic retinotopic retinotopic retinotopic retinotopic careful careful macaque lond lond mimic rotating rotating rotating round psychophysics psychophysics struc insufficient rosenberg rosenberg suffers mst mst mst mst mst mst mst opponent tanaka hopkins cylinder cylinder cylinder cylinder cylinder cylinder cylinder cylinder cylinder cylinder cylinder cylinder essen sparsely extracts optics screen screen symmetrical inspection acid andersen andersen andersen meant percept rotational rotational sur repetitions saito survival yon primates gross activating avenue resentation ogy posi postulated convolving symmetries puted corresponded abstr thirty standing explores surrounded unstructured unstructured unstructured unstructured unstructured unstructured unstructured unstructured unstructured unstructured unstructured underlie ralph hoped sponds siegel siegel siegel siegel maunsell rotates publications desimone lastly allman woods woods radii radii education comple orthographic rhesus supercomputer organiza abbreviated century stimu albright albright lus stereoscopic recombination signaled cortices mimicking caveat jected phs erro roedial termine strates mentary hikosaka gular 
#@Siegel_R,
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probability weight weight weight weight neurons neurons neurons neurons method method method method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single control control control control control local local local neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix matrix matrix matrix inputs inputs inputs form signal simple simple small small small size fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells classification level level level level trained trained trained trained trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure random response similar fixed fixed line line line line rule rule generalization generalization real states activity activity activity activity activity activity activity result university university threshold threshold solution research independent independent sequence initial initial initial initial constant connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left direction direction direction direction direction presented presented presented presented phase sets sets sets sets sets sets sets range outputs abstract applied back back back references stochastic due due positive procedure procedure propagation propagation introduction complex statistical effect cost recurrent change change complexity complexity lower lower rules measure signals signals signals signals signals signals signals signals representations higher higher higher higher previous previous previous previous previous cases firing firing firing firing firing type forward forward simulations simulations total total simulation simulation multi multi multi sum elements elements elements elements elements factor factor feedback feedback orientation orientation orientation orientation orientation orientation orientation true desired series provide provide provide provide active active active active active connected connected connected connected approaches larger larger connection connection connection report institute words synapses technique internal internal internal individual individual individual individual individual represents represents layers layers layers layers layers layers layers layers layers layers layers layers directly hinton curve design design upper full requires requires requires increase give weighted developed developed levels levels levels levels lines lines lines lines lines lines lines lines provided provided nature nature inhibitory inhibitory inhibitory simply describe group complete excitatory excitatory stable nearest nearest assumed synapse synapse synapse synapse synapse synapse role end degree rumelhart rumelhart simulated smaller combination fully significantly york increasing increasing mechanism mechanism mechanism mechanism principle principle numbers inhibition inhibition inhibition inhibition inhibition inhibition magnitude run property pair element lateral lateral lateral lateral lateral lateral lateral lateral subject side side hierarchical hierarchical hierarchical hierarchical hierarchical subset subset interest previously unsupervised unsupervised address positions modified modified organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization sensitive entire horizontal horizontal horizontal horizontal horizontal horizontal horizontal concept concept extended feed locally locally generally column strength conclusion place place row greater hebbian hebbian neighbor competitive competitive competitive competitive central suggest mechanisms integration physics cycle turn manner manner manner connectivity explicit explicit suppose sequential sequential sequential vertical vertical vertical vertical vertical vertical vertical involves consisting mutual integrated integrated integrated integrated cycles cycles letters viewed viewed variation controlled organizing understanding completely allowed sign sign neighborhood neighborhood neighborhood neighborhood intermediate initially fire fire fire figures determines extension variations variations simplicity middle modification modification modification wij wij wij wij presentation tend orthogonal composed composed composed capture capture capture capture capture excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation repeated repeated link link link link link link link link showing sci usual surround providing providing received attempt consisted consisted consisted subsequent operating american layered layered collection requirements difficulty difficulty successive successive successive successive successive successive successive links biol hierarchy hierarchy hierarchy hierarchy fundamental notion concepts opposite opposite opposite implementations subsets subsets obvious separated indicating directed adjacent ring organized organized afferent afferent afferent afferent afferent afferent controls implicit implicit medical lowest pathways schematic schematic schematic switch mod mod instruction plan specifies specifies calls instantaneous realized naive contribute consistently cybern college generator formally extensive appropriately conditioned circular connecting saturation fan attractive determination modifications exceeds exceeds clock 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#@Noetzel_A,Silverman_R,
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networks networks networks output output output output output output output output output number number system system system state results results results results units units information information information information information problem models based weights weights weights linear layer case case case case case order order systems systems systems systems systems values values values values parameters weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit distribution pattern pattern point single single single single single processing processing processing processing processing processing control control local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis class class class class class class class class inputs inputs inputs inputs inputs inputs inputs shows shows simple simple simple simple simple simple small small methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step field field field classification level level level current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure random random random random random random random random random random random memory response response response response response response response response response response response response response response response similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show fixed fixed fixed fixed fixed fixed fixed general general general general general note experiments activity activity activity activity activity activity activity result result result result result university university computation research research defined defined defined found found found found found target initial constant constant constant computer computer computer terms terms connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science direction presented presented presented presented present present present present temporal temporal temporal temporal temporal temporal temporal temporal temporal sets motion press press press press press press press press nonlinear nonlinear nonlinear nonlinear nonlinear outputs sample sample abstract applied find find computational computational computational computational computational computational computational computational computational computational properties properties properties properties properties properties references important important important important important action action action action action action action action action action complex complex complex complex complex hand circuit stimulus effect dynamic dynamic dynamic generated search spatial spatial spatial spatial spatial measure center firing firing cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike spike represent represent tree tree distributed distributed make make fact fact fact fact fact fact fact fact fact region region finite simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations resulting classes classes classes ing total total total simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation respect respect respect respect respect sum performed times times times times times times times times times times times times times times times times times times elements elements regions means factor potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential made made natural study study study study knowledge original vol artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial relative relative relative relative relative specific represented true true application provide provide provide define perform determined experimental experimental connected connected connected motor cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain brain brain brain brain equal equal mit mit mit fields fields support modeling modeling selection proceedings proceedings institute department synapses synapses synapses synapses synapses synapses individual individual represents represents responses responses responses responses delay delay delay addition graph considered framework cambridge cambridge cambridge experiment experiment experiment environment design design design stimuli effects conference determine significant basic give produce produce produce produce randomly randomly randomly developed developed developed levels levels levels levels levels velocity velocity types path path path path product actual actual actual actual provided finally selected nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends depends constraint simply biological biological biological biological biological biological biological biological measured measured normal arbitrary arbitrary limited complete excitatory excitatory excitatory excitatory excitatory excitatory predictions predictions predictions predictions circuits common effective implemented implemented synapse synapse synapse role role role role role theoretical theoretical eds eds eds eds face journal end ability future easily makes makes development development development sensory simulated simulated simulated pairs underlying combination combination functional ratio york york york mechanism structures trials trials empirical empirical empirical principle leads representing inhibition inhibition inhibition inhibition inhibition inhibition produced produced produced produced produced neuronal architectures architectures membrane membrane membrane membrane property property property property property property property robust robust robust robust robust robust robust takes takes takes reported lateral lateral lateral moving moving period identical identical machines sense cognitive relevant interest interest highly varying varying module module module module module module module module module module module module module module module module module module module locations interval organization organization entire entire amplitude amplitude amplitude amplitude amplitude amplitude constructed studied wide wide wide occurs occurs generally flow strength strength greater greater interactions interactions interactions interactions interactions interactions interactions sigmoid modules modules modules designed strong strong hard integration integration integration integration integration integration presence physics turn variety variety variety variety variety variety exist exist connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity program force explicit explicit van van factors plot label stability stability distinct distinct distinct distinct distinct distinct modeled modeled implement missing sensitivity explicitly easy easy mutual versus versus potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials john national dependence detailed detailed detailed detailed organizing forms completely earlier reasonable classical roughly remains msec msec msec msec msec msec msec msec msec msec msec koch koch dendritic dendritic dendritic existing combinations usa currents plotted specifically candidate absolute characterized structural middle importance importance importance society society poggio poggio poggio poggio oscillatory build computations schemes post post plots plots fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine receives composed excitation strongly neuroscience conductance conductance physiological physiological follow timing timing duration built built involved vary localization simplified play absence modular realistic providing providing delayed correspondence highest processors received neighboring neighboring neighboring rat rat rat receive explore remain selectivity american american varied detail strengths strengths strengths strengths existence postsynaptic postsynaptic postsynaptic postsynaptic rise fewer respond fashion fashion project ideal analytically structured structured structured structured pathway pathway analogous transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission possibly traffic opposite extremely thought aspect der der separated mapped pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal contributions motivated synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic established burst burst brown slowly asynchronous ground ground trivial crucial growing adjacent capabilities capabilities capabilities capabilities capabilities lies nonlinearity nonlinearity london spatially perspective purposes closer directional broad located immediately immediately ion ion ion axon scientific involve qualitative addressed fluctuations robustness robustness robustness robustness robustness robustness robustness fourth varies collected pathways pathways pathways led amounts capability capability capability capability capability experimentally quantitative detecting qualitatively qualitatively singer conductances findings findings specifies simultaneous contribute contribute benefit benefit sort sort primarily primarily arguments refractory driving jones jones jones connecting nonzero enhancement theories theories theories theories theories royal arrival arrival arranged suppression suppression suppression suppression suppression inspired spontaneous saturation consideration anatomical convenient primate determination determination viewpoint keeping intuitive edelman mouse mouse displayed intended interconnections soma nonlinearities nonlinearities foundations cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral reveals matter verification specificity specificity impact exploiting designing alternatively receiving dense dramatically street neurophysiology shunting shunting shunting shunting inferred randomized randomized emergent emerge revealed failed spatio spatio spatio distinction distinction distinction quasi medium amplitudes resting resting resting resting resting resting resting resting resting resting resting illustration summarizes conduction conduction neurophysiological neurophysiological neurophysiological mediated emphasize academy distal records rough weaker nonetheless paradigms paradigms paradigms reveal reveal reveal intracellular macroscopic behave bring milliseconds els els travel travel microscopic elemental spite spite spite spite spite emphasis reversal traveling oscillate conceptual hopkins somatosensory somatosensory somatosensory somatosensory played suppress connects connects anatomy possess meeting meeting meeting intracortical judged manually petsche neocortex neocortex neocortex neocortex neocortex neocortex neocortex neocortex neocortex arrives contacts johns arriving evolving suffice suffice communicate spirit randomness randomness randomness randomness randomness amenable lewis lewis remained ready comprised baltimore emerged proceeding decades replicate medial saturate predetermined modularity plenum plenum replicates spario marker notions biophysics judge generations gross gross gross gross gross synthesize synthesize synthesize tailored def enabled pyramids pyramids pyramids pyramids pyramids pyramids pyramids alexander psp psp vast thinking cortico 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#@Donoghue_J,Singer_A,
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turn turn exist introduce program question question acknowledgements suppose suppose suppose suppose relation produces perception mathematical mathematical mathematical segments segments segments implement simultaneously simultaneously simultaneously simultaneously simultaneously linearly linearly linearly linearly linearly infinite infinite infinite involves transformations remaining easy consisting develop develop extraction letters letters letters national extracted extracted review communication viewed viewed operations approximations decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition forms soft soft static activities activities activities activities completely completely completely past spaces spaces reduces combining combining purpose add closed generation generation generation string string string string symbol construction construction construction 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#@Smolensky_P,
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networks networks networks networks networks networks networks networks networks networks networks networks output output output output number number number number number number system system system system state state state state state state state state state state state state state state state state state state results results results results results results results results results results units information information models models models models models models models models performance based space space space space space space space linear layer layer case case case case case vector order order order shown shown shown shown shown systems systems systems systems systems values values values probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters functions functions functions functions neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern point point image image image image image image processing processing control large large local local patterns analysis class matrix matrix matrix inputs inputs inputs inputs inputs inputs inputs form form form form form form form simple simple simple simple simple simple paper paper paper examples examples examples small small size size feature net net net net net net net work work work fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step field field field field features features process process process process level level level cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure random random random random random random random random random random random random random random random high response representation representation representation section section section section section section section images general general general general general general general parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation average average average states states states theory theory theory obtained obtained obtained obtained obtained experiments experiments activity activity dimensional university university threshold threshold variables variables computation computation computation computation solution solution solution solution solution solution solution solution independent independent independent defined defined defined initial computer computer terms terms terms terms connections connections connections connections connections connections connections connections connections connections connections connections connections node node node node node node node node node node node node node node node node node node node node science science science left left present present present low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal maximum press components basis outputs outputs continuous continuous abstract applied computational properties properties properties properties references stochastic stochastic due due ieee ieee ieee procedure procedure important context introduction introduction hand statistical tion tion tion tion complexity spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume assume assume assume lower rules rules measure measure measure signals chosen center previous previous previous previous previous theorem cases cases cases firing firing firing firing firing firing firing firing type 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related connected connected connected distributions distributions discrete brain brain equal equal comparison connection connection fields fields fields fields nets nets nets nets nets nets nets nets nets nets modeling modeling modeling modeling institute department internal individual individual individual individual individual individual joint represents represents represents represents delay delay delay considered considered considered considered considered considered considered computing computing computing equivalent directly solutions san upper upper choice world world vision estimated basic give con condition condition weighted randomly clustering developed developed levels types types types types product product product provided provided processes processes selected depends depends constraint biological biological technical arbitrary denote stable stable circuits nearest implemented implemented assumed assumed generate supported role theoretical main square square square end easily makes simulated probabilistic hopfield dynamical unknown technology interesting mechanism mechanism principle principle operation operation operation operation operation operation operation operation representing numbers idea idea run run description discussed discussed discussed resolution exact property property takes takes moving moving period period period machines pixels sense array relevant relevant engineering interest varying works axis tions yields yields match correspond studies studies achieve trans grid grid grid grid grid grid grid grid grid grid grid grid interval interval organization organization organization organization organization organization organization organization organization organization increased constructed horizontal horizontal horizontal intensity studied studied studied studied alternative generally hardware flow conclusion critical assumptions assumptions assumptions assumptions assumptions neighbor neighbor neighbor measures modules accurate numerical numerical numerical designed clear performs exponential physics largest external external external external external external external external external cycle characteristics assuming min pro pro pro edges optical generating stability changing changing segments confidence infinite infinite interaction develop develop events boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean national expressed expressed expressed expressed formation depending depending depending squares viewed viewed viewed variation open open open organizing evolution understanding understanding approximated completely delays delays normalization normalization sec sec event false closed topology topology topology figures includes includes sciences illustrated neighbors characterized texture texture determining uniformly uniformly uniformly presentation computations genetic genetic receives receives characteristic composed composed composed excitation excitation excitation excitation excitation refer notice conf interested interested interpreted dis dis follow comp quantity involved realistic providing received principles principles attempt attempt attempt attempt attempt moves moves routing routing routing routing receive situations explore stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation carried diego american investigate investigate investigate exhibit exponentially mead put steady steady steady steady steady lippmann graphical graphical hall behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour periodic existence examine fashion ideas mappings possibility structured structured proper affect affect func phases phases phases phases examined smallest math math traffic automata automata equally quantities formal formal formal assumes logic nervous nervous mixed established years asynchronous asynchronous distinguish phenomena biology biology analytical analytical analytical majority tractable straight sys satisfied division ran immediately immediately ion describing begin res res computers preceding reflects tional fed leave autonomous poisson poisson aim aim cal cal tank marginal logical logical eventually june june phenomenon labeling acm concerned concerned circular repre grey interconnected interconnected receptors arrival arrival arrival arrival proceed arranged plays lost lost systematic fits ments ments interconnection interconnection interconnection balance roles imply corner presentations service service service service service service service service respective intended schwartz belongs interconnections surprisingly eng arrive arrive extensively tures receiving receiving adopted adopted adopted dividing informa abu ence leaving leaving mostafa ter incorporates equivalently deriving ber ties reaction reaction reaction markovian markovian markovian markovian tween constitutes descriptions possibilities gene brightness visited visited visited arising queue rectangular distri genes pami pami num elementary elementary interacting proba oct proach sta fea elsevier nal experi served served mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch ergodic corners fractal pitts pitts pitts pitts pitts pitts jain concern concern concern dom identically identically affecting visit tribution compo station concerns concerns concerns concerns sharply functionally arriving arriving arriving assp comm counterpart server server appro lar modern tained tained inform rem syst amer rij rij spent spent expresses expresses biophysics aims checked nents suitably suitably psaltis theo parame wait visits ele des waiting sing structuring occupied calculus bull bull mag fogelman accord textured originating originating ration reproduction queueing queueing queueing queueing queueing queueing queueing queueing queueing queueing queueing queueing queueing queueing queueing queueing del del routed arrivals kauffman validate validate 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#*network network network network model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data function function function function function figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm output output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system system system system system error error error state state state state results results units units units units units units units units units units information information problem problem problem problem problem problem problem problem problem hidden hidden performance performance performance performance performance performance performance performance based space weights weights weights weights weights weights weights weights weights weights weights layer layer case case case case case shown shown systems systems systems systems systems values values values values values values values values values values values values values values values values values parameters parameters weight weight functions unit unit unit unit unit unit unit recognition recognition recognition recognition approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class optimal optimal inputs inputs inputs inputs inputs inputs form shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple gaussian paper paper small size size size feature feature feature feature feature work work work work work task methods fig fig fig fig fig fig fig fig step step step step step step step step step step points field features features features classification process process process level current current current current trained trained trained trained trained trained trained trained trained trained problems problems problems problems problems problems memory response response response similar similar representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture fixed fixed fixed general general speech speech speech speech speech speech parameter theory obtained obtained obtained obtained note note note experiments experiments experiments result result result university threshold computation computation solution solution solution research independent independent independent independent sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial standard standard terms terms terms node node node node node node node node node node node node left direction presented presented presented map present activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine motion motion motion motion motion motion motion motion motion motion maximum maximum maximum maximum range range range press nonlinear outputs outputs outputs outputs outputs outputs continuous abstract back back back properties references important important important important adaptive decision propagation propagation propagation context context context context context context context context context context context introduction dynamic generated generated parallel parallel parallel parallel recurrent search change change energy difference difference variable spatial spatial spatial signals signals representations representations word word word word word word word word word word learned chosen chosen chosen chosen chosen higher higher part part part center previous cases type spike spike conditions represent represent represent represent represent distributed distributed distributed equations equations make make make fact proposed length length length scale finite resulting tasks computed computed computed computed computed computed computed computed computed computed computed computed computed computed computed computed computed computed respect sum sum sum performed eq eq eq eq times times mapping mapping mapping means factor factor dimension dimension applications filter filter filter filter original original vol vol vol samples samples compared application desired desired desired desired compute compute rates proc proc proc proc proc related related connected discrete brain equal approaches mit steps steps steps steps steps steps larger contrast contrast contrast contrast train train train nets report report institute words words words words words department consists consists represents connectionist difficult layers delay addition sequences sequences ai considered cambridge computing computing domain equivalent equivalent experiment experiment experiment directly hinton curve curve additional additional additional additional additional additional additional additional solutions curves limit effects detection detection detection detection detection determine requires choice choice significant give give produce produce derived velocity velocity velocity provided finally evidence evidence nature depends sampling sampling sampling sampling sampling sampling sampling sampling sampling simply simply achieved discussion tested tested transformation limited close complete stable amount amount generate supported require require require ability ability ability degree degree makes rumelhart typically hopfield hopfield hopfield dynamical dynamical dynamical dynamical jordan transfer transfer transfer significantly mechanism mechanism leads leads representing iterations iterations iterations filters pre direct making window window window window window normalized decay decay decay decay decay decay decay idea recent recent property takes typical apply moving moving include include identical identical identical sense sejnowski sejnowski recently relevant interest dimensions compare previously conventional conventional axis axis speaker speaker converge converge address address channels entire entire increased amplitude amplitude amplitude invariant scaling scaling scaling suggests suggests digital wide derivative derivative alternative correctly correctly correctly correctly width demonstrate half starting place depend performs exponential faster faster practice learns propose propose taking physics physics solid pulse pulse pulse decrease introduce manner acoustic acoustic question attractor acknowledgements suppose suppose suppose relation produces longer factors generating generating ann ann distinct distinct distinct changing changing category infinite infinite unique scales scales adding equilibrium equilibrium equilibrium predictive implies yield choosing dependence depending squares viewed interpretation influence fraction fraction static static static static similarly discrimination discrimination past past partial earlier dashed delays purpose intermediate intermediate initially initially construction advantages advantages instances recognize recognize illustrated discuss specifically specifically variations variations holds phys phys partially discussions differ encoded mcclelland presentation presentation presentation presentation presentation presentation presentation presentation identify identify detect detect essentially receives characteristic characteristic characteristic characteristic characteristic soc soc conf conf conf allowing link interested interpreted issue issue issue lie follow sci sci sci sci sampled sampled sampled sampled relaxation relaxation generalize generalize absence providing providing delayed delayed delayed computes denker received attempt attempt extend american difficulty rapidly rapidly rapidly varied relations involving involving issues issues issues issues preliminary preliminary successive respond respond respond history ideas ideas links links links detectors detectors detectors possibility comparable variability variability naturally adapt integer rev rev illustrate changed thought impulse impulse impulse store store arbitrarily mentioned mentioned slowly processed processed processed rapid stanford stanford stanford precisely desirable recognized recognized recognized acad acad grossberg members read demonstrates recognizing preceding preceding argument requiring elman amounts lack completion employ slower frequently frequently frequently schematic differs reaches tank tank serve serve serve serve extensions sums inherent windows windows utterances univ univ extreme contextual aligned redundant feasible appearance modify modify summing fix refractory refractory velocities velocities velocities nat nat signature signature addresses impossible difficulties difficulties height los contract contract interpret serves utterance utterance north excellent reset loo respective holland lawrence lawrence darpa multiplied creating record verification verification passing erlbaum erlbaum eqs eqs eqs captures statement lett alternatively onr mind discriminate discriminate unified gold encouraging propagating smoothly retraining retraining acceptable possibilities hillsdale hillsdale illustration distant crosses kanerva fir tied drawback emphasized portions portions preserve suffer packet grateful preprint lapedes modifiable milliseconds ward completed removes handled continued rosenberg hopkins replicated replicated 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probability probability probability probability probability unit unit unit unit unit unit method method method pattern pattern pattern pattern pattern pattern pattern pattern processing processing large large large large local rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns optimal optimal algorithms simple paper size size net net net net work task fig fig features features features classification classification classification classification classification classification classification classification process process process current trained trained structure structure structure structure problems problems problems high high high high high high high high memory similar architecture equation equation equation section general gradient gradient note dimensional result result result university variables variables variables found dynamics initial computer terms terms terms terms connections connections connections node node node node node node node node node node node node node node node node node node node nodes nodes machine machine maximum press press learn learn learn nonlinear abstract back back analog analog references stochastic due procedure important important important important important decision decision decision decision decision decision propagation introduction complex hand hand generated parallel parallel parallel parallel difference assume classifier measure measure measure representations learned learned learned chosen chosen higher previous cases binary binary binary represent tree tree tree tree tree tree tree tree tree expected proposed errors errors errors scale scale total human multi multi multi multi multi optimization made made vol vol vol artificial specific represented represented true true true true true desired perform determined power power mit mit accuracy connection connection connection connection update update train descent nets proceedings proceedings institute institute department represents represents difficult final exp layers scheme scheme scheme scheme scheme scheme scheme scheme ai considered cambridge additional choice choice free speed derived randomly randomly entropy entropy entropy entropy entropy entropy actual processes tested limited close supported main adaptation ability ability ability ability including fit needed call call call max bottom attention attention choose added perceptron perceptron practical introduced strategy trees cognitive conventional calculated solve solve studies interval grant constructed scaling greater valued numerical learns propose propose propose taking physics physics physics demonstrated california assuming decrease groups pro construct construct construct construct construct solving sequential sequential sequential sequential ann category category category category category category category category category category category simultaneously applying formed formed implies john john extracted extracted focus communication operations showed lee lee lee lee lee lee similarly partition purpose add visible advantages classified classified classified classified classified classified classified classified classified classified classified expect maximize specifically partially simplicity efficiency importance importance importance importance mcclelland ten summary kind repeated heuristic split split split classify classify classify categories categories quantity generalize giles giles giles denker denker automatically subsequent extract extract extract intrinsic american layered layered layered layered layered mappings affect attributes attributes attributes attributes attributes attributes attributes illustrate friedman perceptton great advanced formula fairly answer implementing organized leaves acknowledgement optimize attribute attribute attribute sun sun sun summation pure pure conducted calculating branch branch branch branch branch branch branch branch resource extensions chen chen chen chen logp logp logp leaf leaf college resources branches branches branches branches branches branches branches repre flexibility reaching allocation breiman stated reasoning splitting splitting splitting affected optimally combinatorial substituting started encountered encountered pat searching facilitate facilitate ranking ranking ranking park propagate stone fly sequentially sequentially logarithm basically equivalently forced axe classifications classifications seek seek associate param avoids exclusive interact interact shannon allocated afosr individually constructs quinlan drawback eters demand satisfactory terns focuses accomplish proposal totally minsky communicate zeros aip aip allocating maryland ira sentations judge judge terminate terminate terminate terminated terminated belmont wji accord maxwell maxwell 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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural input input data data data data data function time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number number number number system system system system error error error error error error error units information information information problem problem problem problem problem problem problem performance based based space case case case case case case order shown systems systems systems values values values values parameters parameters parameters parameters weight unit unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method pattern point point point point point point image image image image image image image image image image image image image image image single processing processing large local rate rate rate rate rate rate rate analysis class form shows shows shows shows shows simple visual visual paper paper examples small small size feature work task task task fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step step step step step step points points points points points points process process current trained trained structure structure structure structure structure structure structure structure structure random memory memory memory response similar similar similar architecture architecture equation section section line line line rule rule rule rule rule images images images images images images images images parameter parameter parameter obtained obtained result university computation computation solution solution research defined defined sequence sequence sequence sequence initial initial estimate distance node science left left direction low nodes nodes nodes nodes nodes nodes frequency frequency frequency machine machine machine machine machine machine machine motion motion motion motion motion position position position position position position position position position position position position position position position continuous sample sample sample sample sample sample abstract back back find find find find find computational references ieee ieee ieee ieee ieee ieee positive introduction complex hand circuit estimation estimation estimation estimation estimation estimation estimation cost cost cost cost search search search tion tion change change assume classifier rules measure measure measure measure measure measure representations word word part part center cases type type type type type type type type type type type type type good binary binary binary long tree tree tree tree tree tree distributed distributed distributed make proposed proposed proposed proposed proposed proposed proposed length correct correct correct correct observed observed observed observed observed finite finite finite finite ing ing ing human performed elements elements mapping means means dimension dimension dimension made natural global global global applications applications knowledge knowledge filter obtain negative artificial relative relative relative samples samples samples samples samples samples samples samples samples samples samples application application define define define define define define define define define define define define define define compute determined experimental experimental experimental related connected discrete equal approaches source report institute words words words loss implementation version synapses technique advances difficult framework computing computing equivalent experiment experiment experiment experiment environment environment directly directly design design limit trajectory top top stage stage stage capacity efficient upper free free speed speed speed vision vision increase increase increase give produce produce randomly randomly robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels levels levels levels criterion criterion criterion area area area area area types product actual finally processes selected nature depends associative associative associative associative associative associative associative associative associative associative associative discussion increases increases increases increases arbitrary denote denote fast corresponds assumed assumed assumed role face square end hypothesis future future pairs hopfield combination combination reduced reduced unknown unknown block head head structures structures structures structures trials trials trials matching database database database database database database database mode principle operation call numbers window window window window window window window window window window bottom bottom expert frame improved improve improve exact property takes element typical typical movement movement movement movement reported practical practical moving subject subject subject machines machines machines sense sense subset recently recently sufficient teacher subjects solve match achieve trans gate gate interval organization organization organization organization organization organization improvement exists exists expression wide alternative alternative move width width width loop white white white boundary boundary boundary boundary boundary boundary hardware hardware pass runs half half conclusion starting operator operator operator operator operator operator operator operator operator operator faster practice learns learns suggest physics demonstrated turn exist decrease iii characters characters characters identification identification identification identification identification identification identification configuration base suppose suppose suppose suppose appears relation relation produces written written factors estimating vertical recall category infinite infinite infinite remaining easy angle interaction develop minimization implies letters letters letters letters letters decreases depending depending stationary correlated operations organizing showed approximations forms understanding similarly suggested converges converges past past past sec intervals roughly purpose purpose purpose purpose generation remains calculate symbol assigned construction construction euclidean euclidean precision recorded building handwritten handwritten handwritten includes discuss candidate black black black black black black black partially discussions major major compression compression compression letter letter letter letter letter letter letter letter suitable maximal divided identify build situation essentially orthogonal composed composed compact compact compact notice conf conf conf quickly kind procedures strongly heuristic heuristic video notation sampled write play dot dot dot dot computes computes computes moves subsequent camera camera camera camera camera camera camera camera american collection put put recursive recursive recursive recursive periodic rest project project mappings mappings terminal int int int int possibility authors authors root root proper proper proper proper cover cover math closest trace reading reading reading reading recognizer recognizer recognizer recognizer aspect front assumes logic detected simplest defines defines established percentage stop slowly developing formula navigation navigation adjacent answer considerable inside processed processed turns tive sections style style style filtered precisely precisely constructing constructing constructing located desirable desirable controls laboratories probable ion english english english res computers incomplete recognizing recognizing recognizing summation summation reflects fuzzy reflect cmu consistency experimentally autonomous autonomous autonomous autonomous autonomous employ incorrect incorrect differs branch fall tank prevent display returns wang converged converged initialization room ordinary ordinary identifying writing japan investigation angular databases databases databases databases databases mobile mobile mobile mobile mobile mobile grows robotics robotics robotics robotics robotics establish establish establish consideration proceeds imposed height height vehicle vehicle mark observing observing observing observing roles hint north effectiveness obstacle obstacle obstacle obstacle obstacle repeat published document document document reset reset reset mouse mouse mouse respective equals negligible negligible regard regard regard regard regard regard stereo stereo belongs counter counter candidates candidates candidates elastic elastic bases bases advance deg deg deg deg deg record route route route route route designing designing implicitly implicitly instructions stopped avoiding avoiding avoiding integers balanced ball empty speaking boxes crossing land slight ber ber obstacles obstacles uniquely axe axe axe propagating par acceptable tendency associate rain stands realize shifting ibm exclusive robots pami wall num gas elementary distant denoting met rejected landscape landscape surrounding topic cartesian anal places places round failures answers scanning scanning scanning suggestions satisfaction satisfaction recogni demand continued identifies builds calibration suffices hull reflecting drawing rare horizontally substitute substitute automation automation automation automation meth establishing ods vicinity addressing ings routes appro pointer mach artificially recalled recalled suzuki excessive dist repeating rises pes observes observes collision collision scans checks 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#@Arimoto_S,Suzuki_H,
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neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution distribution distribution local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs form form simple paper paper small net net net net fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig field field current structure problems problems high equation equation equation equation equation section general parameter parameter states states states states states states term term term term term term term term term term term term term term term term term result result university computation solution solution solution solution solution solution solution solution solution solution solution research research defined defined computer computer terms terms terms connections connections connections synaptic synaptic science presented map map low frequency frequency frequency range outputs outputs outputs outputs outputs abstract find find find find find computational computational convergence analog analog analog properties references ieee positive introduction effect effect generated generated cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search search search tion energy energy energy energy energy energy energy energy energy energy energy energy assume assume lower required good good represent represent techniques proposed minimum minimum minimum minimum minimum minimum minimum minimum resulting resulting resulting ing total total total simulation simulation simulation simulation simulation simulation sum sum sum eq eq eq eq eq optimization optimization made made made global negative represented provide provide provide compute compute proc location location constraints constraints constraints constraints connected connected connected connected connected connected connected gain equal equal equal equal comparison connection connection connection connection connection connection connection institute department synapses technique individual individual represents final curve solutions solutions solutions solutions solutions solutions solutions capacity capacity capacity capacity capacity capacity capacity capacity capacity determine upper upper upper upper choice choice basic con con derived weighted randomly developed area types inhibitory inhibitory constraint constraint constraint normal normal normal corresponds corresponds complete excitatory excitatory stable stable finding implemented assumed assumed assumed synapse supported square square hypothesis hypothesis hypothesis simulated simulated simulated needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield interesting mode details added typical include array array array array array array array array array recently previously tions solve correspond correspond correspond correspond correspond correspond converge trans diagonal diagonal symmetric symmetric constructed wide column column column column column column column column column column column runs strength strength conclusion row row row row row row row greater reduce sigmoid suggest presence physics external external external external variety relationship minima minima produces written modeled modeled modeled implement remaining consisting expressed communication communication squares evaluate operations combining assigned assigned assigned assigned assigned assigned construction combinations formulation currents currents currents assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment illustrated illustrated illustrated successfully effectively delta summary soc notice notice prob prob prob prob link conductance symmetry sci sci sci satisfy satisfy quantity simplified providing providing minimizes processors illustrates presents presents employed command american poor access access collection put strengths hall links func removed neu neu neu circles necessarily algo mapped mapped histogram site site site site site site site site site site site site site site rows rows rows ment ment costs costs costs costs tive sys sys sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites choices located arise acad res lowest arises arises summation conducted resistive schematic maintain summarized resource resource tank tank conductances specifies cumulative globally feasible assign assign assign assign assign amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier rithm tem turned turned allocation allocation ments ments combinatorial heuristics natl prentice entry equals equals decide guarantees arrangement tic entries entries entries enable refers influences influences assigning assigning assigning lem lem lem consecutive exhaustive exhaustive exhaustive exhaustive suboptimal tween restrictions additionally assignments assignments assignments assignments assignments assignments assignments assignments hundred hundred tor gene realize algebraic shaded shaded favor favor favor favor resistor resistor resistor inverted inverted met exceed cij enforce tij tij tij tij inverting amplifiers amplifiers amplifiers page lems capacities opti externally characterizing impractical vii vii hop jersey cliffs tors inclusion ron supplied connects rons rons englewood ally ray amenable zeros zeros feldman twelve enforces enforces defense slack slack slack slack slack slack slack col rij operated bio mal cir army solu associating xij xij xij vij backbone backbone cyber iij iij subscripts edward synap assures cas ifi ifi oper permitting accommodated illus 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#@Page_E,Tagliarini_G,
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#*network learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural data data function function function function function function function function figure figure figure figure figure figure figure time time time time time set set set set networks networks networks output output output output output output number number number number number number number system system system system system system system system system system system system system system state results results results results results results results results results units units units units information information information information information problem problem problem problem models models models performance performance performance performance performance performance linear layer case case case order order shown shown shown shown shown systems values values values values values parameters parameters parameters parameters parameters weight functions functions functions functions functions neurons recognition method method pattern pattern point point single single single single single single single single single single single single processing processing processing processing processing control control control control large large local neuron neuron neuron neuron neuron neuron patterns analysis inputs shows shows signal signal signal signal signal signal signal signal signal signal signal signal simple simple simple visual paper size net task task task methods fig fig fig fig fig fig fig fig fig fig cells cells step process process level structure structure problems high high response similar representation representation representation architecture architecture section section section line line line line line line general speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter real average average obtained obtained term experiments experiments experiments experiments university university university threshold threshold threshold threshold threshold threshold computation computation solution research independent log defined found found found found initial initial constant table table computer science science presented presented present present temporal temporal temporal temporal temporal temporal temporal press press components abstract abstract computational analog analog analog properties properties references ieee important adaptive context introduction circuit behavior behavior stimulus effect generated variance parallel parallel parallel tion tion tion tion tion tion change change energy energy variable measure signals signals signals signals signals signals signals signals signals word chosen part type required multiple multiple multiple multiple multiple spike long conditions conditions make make fact fact correct correct correct correct observed forward ing ing human computed multi performed performed performed elements regions mapping potential made natural natural natural natural natural natural natural natural natural natural natural natural natural feedback feedback feedback study study filter filter vol vol vol vol vol vol vol vol vol vol vol vol vol vol vol vol vol vol artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial specific specific true cross series provide provide define proc perform perform eye eye eye determined experimental goal related constraints connected connected gain gain gain power power comparison comparison connection train dependent dependent selection institute words words words department department loss implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation technique internal internal internal internal code code individual difficult final scheme scheme considered framework computing computing domain experiment environment design design stage effects determine full speed con produce condition channel channel channel channel channel channel channel channel channel channel channel coding coding coding coding coding coding randomly developed area types types path actual provided processes processes evidence evidence evidence achieved feedforward feedforward feedforward increases transformation fast fast limited limited limited close corresponds corresponds finding amount amount amount amount amount implemented implemented implemented eds face journal journal journal end ability future easily easily easily easily easily easily development sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory fit auditory auditory auditory auditory auditory auditory auditory needed needed reduced account fully technology block block transfer transfer transfer transfer significantly significantly increasing structures trials trials operation operation details max max idea idea produced predict population population population improve pair takes element element reported reported reported lateral lateral lateral relevant engineering engineering sufficient subjects subjects subjects subjects works tuning tuning tions tions correspond correspond correspond studies studies studies trans evaluation evaluation evaluation modified modified channels channels channels channels channels improvement risk entire parts parts concept suggests suggests alternative feed move move loop white setting hardware conclusion critical place central central differences differences differences differences measures constrained sound sound sound hard integration physics external external external external cycle characteristics characteristics characteristics drawn variety user user user user start min introduce groups program program acoustic acoustic appears perception perception perception perception perception laboratory ann ann ann ann changing simultaneously physical electrical electrical electrical remaining remaining easy integrated adding potentials extracted review phoneme communication codes operations operations operations controlled controlled controlled controlled organizing modulation modulation modulation modulation understanding suggested allowed discrimination discrimination discrimination processor processor processor processor spectrum spectrum spectrum diagram diagram partial tracking msec msec msec msec msec construction advantages advantages advantages transactions transactions coupling coupling coupling coupling coupling coupling coupling existing inter sciences recognize discuss variations variations black black tests successfully compression compression compression compression compression selecting society society society modification modification modification computationally effectively effectively build efficiently schemes fine reached strongly allowing showing interested sin device device device device device device hold built receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor paradigm paradigm paradigm highest highest highest highest highest thresholds software software decreasing receive presents presents stimulation stimulation stimulation stimulation stimulation carried parametric parametric american american american create requirements circuitry varied put association oscillator oscillator matches school school investigated ideal ideal reliable decisions gates func cover understand transmission possibly possibly man psychology changed portion portion freedom nervous nervous nervous academic detected extent electronic sentences optimum devices devices percentage percentage great sensors phenomena phenomena fairly majority answer answer caused london comparisons comparisons inside processed processed processed implementing tive sections filtered incorporate pitch pitch medical medical lowest depicted summation summation summation requiring fourth improvements cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear flexible flexible flexible amounts tional spoken spoken fed experimentally psychophysical psychophysical recordings recordings incorporated psychological vocabulary modulated modulated instruction incoming cal incorporating phone richard replace replace chose neuro physiol damage damage damage patients patients patients patients patients patients patients patients patients patients wang progress sentence cochlea cochlea cochlea cochlea cochlea cochlea summed summed lot naive representative modify extensive animals member tem receptors receptors receptors receptors receptors receptors receptors receptors receptors children saturation consideration khz ments chance chance tools monotonically north integrator integrator integrator integrator modifications enhanced carry wilson composition reliably elimination performances mance mance mance reset patient patient patient studying induce induce perfor perfor perfor holland expanded conjunction enhance neuromorphic neuromorphic neuromorphic late contact route route inductive inductive inductive speeds tures fitted fitted ure compressed annals annals annals annals hair hair tables encouraging magnetic abstraction quasi sigma sigma seek individuals simd simd tor electrode alter peripheral peripheral increment alternate permits expand picked picked altered altered individually electrodes drawback portions alternatives alternatives discusses discusses west intracellular minor elsevier modifiable permit amplification amplification nal nal psychophysics psychophysics psychophysics psychophysics struc computa november scanning scanning scanning clinical clinical clinical clinical covers externally externally externally sorting sorting sorting sorting sorting designs hearing hearing hearing subjective house house house house micro finer tors concern russell periodicity exposed sen ventral operational attained carries stevens ultimate intact bandpass totally presently presently carrying microphone microphone microphone microphone ated indi wires talk fore opinion replicate sorted dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion amsterdam kong kong nice severely preprocessed tenorio sends scans adjustments men couple couple compress biomedical ogy ogy ogy ogy offered rectification rectification rectification cir mediate counterparts myers myers implementable implementable corresponded poral associating multichannel multichannel multichannel multichannel multichannel multichannel widespread meyer wanted simu gerald bypass bypass coil coil coil coil coil graham recep recep healthy neurocomputer recon robbins bennett recognizable electro implementa native purdue purdue opera neurocomputing neurocomputing incor wolf button gle hans portable portable portable surgery ingredients alters stimulate stimulate testbed alterna manipulate lib bulletin neces acta organs organs tackle inhibi evans sary cuits indications recoding indiana indiana ception lafayette rectifier rectifier bme conceived suffering porated struct comprehension norton multiprocessor trolled compressive investigative clinically tradition thres limita compromising 
#@Tenorio_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data function function function function function function function figure figure figure figure time time time time time time time set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number system error error error state results results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space weights weights weights weights weights weights weights layer layer layer layer layer layer case case case case order order order order order shown shown shown systems systems systems systems systems systems parameters noise noise noise noise weight weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution recognition method method approach approach approach approach approach pattern point point point point point point point point point point point point point point point point single single single processing large large large large large large large large local test test test patterns patterns patterns patterns analysis analysis analysis class inputs inputs inputs form form form shows signal signal signal signal algorithms algorithms algorithms simple simple simple paper examples examples examples examples examples examples examples examples examples examples small small small small size size size size size feature feature feature feature net net work work work work methods fig fig fig fig fig fig fig fig points points points points features features features features features features features features features features features features features features features features features features features features features features features features process level level level level level level level level level level level level current current current current current trained trained trained trained trained trained trained trained structure structure structure structure problems problems problems problems problems random random random random high high high high similar representation representation representation representation representation representation representation representation representation section fixed rule general general general general general general generalization generalization generalization generalization generalization real real real average theory obtained experiments activity activity dimensional dimensional result result result result result university university computation computation computation solution research research research research research independent defined defined defined defined defined defined found found found found found initial initial initial initial initial initial table table table standard standard computer computer computer computer terms terms connections science science science presented presented present present present present present temporal temporal machine machine object range press press learn learn position position position position position position position position position position position position position position position position position position position components basis basis basis continuous sample sample abstract applied applied applied back back back back find find find find computational references due due due due due due due positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important important important important important important important important important propagation propagation context complex complex complex hand hand hand hand hand hand hand behavior effect effect generated parallel parallel parallel parallel search search change change complexity complexity spatial rules representations representations learned learned learned learned learned learned chosen higher part part center center center center center cases cases type type required required required required good good good good good good good long long represent represent represent tree distributed expected expected make make make make make make fact fact techniques techniques techniques techniques techniques techniques techniques techniques correct errors errors errors forward forward scale scale scale resulting resulting classes ing tasks total total human human human human human human human human human human human human human human human computed computed computed computed computed computed computed computed computed computed respect elements means means factor potential potential made made made made made made made made made global applications applications study study study study study study study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge obtain negative negative original original vol artificial artificial relative relative relative specific represented represented true application application desired desired desired receptive provide define location location location location location location perform goal discrete approaches approaches mit mit mit larger contrast contrast connection connection fields train train train source selection morgan proceedings proceedings report report report report institute institute internal code individual individual connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult difficult difficult difficult difficult difficult difficult final final final final final bias layers layers layers layers scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme addition sequences ai ai cambridge cambridge domain experiment experiment experiment experiment experiment directly hinton hinton additional view design design design design design transition transition transition limit top top effects conference conference efficient efficient full requires choice significant significant significant statistics statistics world estimated basic increase give con con produce produce produce produce produce coding coding coding coding coding coding coding coding coding coding coding coding coding developed levels levels types types types lines actual actual actual provided provided provided finally selected evidence evidence evidence nature inhibitory simply simply simply simply simply achieved achieved measured discussion discussion normal normal normal technical technical describe describe describe close corresponds corresponds excitatory excitatory actions amount common generate generate supported supported role eds eds square ability ability ability future future makes makes makes makes rumelhart development development including including objective probabilistic underlying needed needed needed account programming interesting testing testing significantly mechanism mechanism special database leads principal representing representing representing representing numbers numbers pre pre pre pre pre pre pre pre pre pre pre direct making making making making making inhibition bottom experts experts supervised supervised supervised supervised expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert magnitude idea idea produced produced produced produced produced produced produced choose added added added sources sources sources sources description description predict improved discussed discussed exact exact advantage takes takes element element typical typical practical practical introduced side sense sense sejnowski cognitive recently relevant engineering sufficient sufficient sufficient highly highly varying conventional conventional conventional conventional unsupervised unsupervised teacher teacher teacher teacher teacher teacher teacher teacher teacher tuning tuning tuning tions match match match match match match match studies achieve achieve achieve evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation positions positions positions positions positions positions positions positions positions positions positions positions positions positions positions locations interval williams lead concept concept concept studied scaling scaling occur trial alternative feed feed move move move move move move move move move move move move move move move move move move move move move move deterministic white white white white white white white white white white white occurs occurs generally generally demonstrate half half critical minimal row greater reduce valued valued differences measures measures measures measures accurate numerical designed designed clear clear sutton practice practice learns learns encoding encoding encoding encoding encoding encoding encoding strong strong hard presence physics intelligence intelligence assuming variety start decrease decrease decrease iii connectivity minima program program program program program program program program program configuration base base base base base base base base base acknowledgements explicit explicit appears appears appears produces longer ways laboratory dept changing sensitivity multilayer explicitly explicitly remaining develop quality quality quality cycles select national national squares squares squares viewed detailed detailed detailed evaluated evaluated evaluate restricted fraction fraction evolution margin completely processor diagram diagram diagram diagram key reasonable reasonable reduces reduces combining purpose purpose purpose generation remains remains intermediate intermediate intermediate intermediate sufficiently sufficiently assigned foundation avoid expect expect existing perceptrons illustrated domains domains black black black black absolute tests major columns identified closely capable capable importance importance uniformly suitable suitable society encoded encoded encoded included mcclelland computations schemes schemes score score score score score essentially characteristic excitation excitation summary summary traditional notice kind repeated procedures procedures procedures procedures cun prob success success showing interpreted superior superior superior superior issue issue criteria strategies strategies strategies timing hold categories categories quantity bar bar involved usual play play play play play play play play play play play play play play play play play play play play play play play play play generalize generalize paradigm paradigm providing providing board board board board board board board board board board board board board board board board board highest highest received principles principles principles principles moves moves moves moves moves moves moves moves moves moves moves moves moves moves moves moves moves moves moves moves moves moves illustrates operating deal deal deal deal tesauro tesauro tesauro receive receive situations situations bars powerful american poor essential investigate put put humans humans humans humans humans humans humans humans humans detail detail strengths strengths limitations game game game game game game game game game game game game issues issues issues giving giving tech tech fault combine structured scores scores scores scores scores encode encode encode encode encode understand cognition notion notion removed examined act naturally concepts concepts concepts concepts concepts illustrate obvious obvious separated logic improving mixed established years percentage great great great advanced advanced advanced advanced advanced advanced advanced rows rows rows ground defining fairly adjacent failure tractable benchmark lies reasons comparisons considerable purposes ran worst worst worst worst leaves leaves potentially potentially involve beginning res lowest annual qualitative qualitative qualitative nsf sun sun sun raw raw raw raw raw raw raw raw raw apparent apparent improvements greatly percent double substantially led embedded readily lack quantitative quantitative peter effort effort operate characterize characterize differs fall incorporating qualitatively qualitatively suited substantial substantial substantial asymmetric simulator kinds kinds kinds chose sophisticated sophisticated sophisticated sophisticated comments display display progress univ univ hints ordinary feasible sort primarily primarily writing mistake discovery eliminate turned turned turned turned reaching lost eliminated eliminated inspired kaufman dealing chance difficulties held intelligent intelligent intelligent intelligent hit los los occurring scoring removing reasoning implications modifications continue games games games games games games games games games games games games games games games games games games games games games date exploring lip mance mance bartlett programs studying studying surprising perfor perfor holland topological bad bad bad bad enhance consequences consequences consequences mel counting lawrence branching dif exposure claim claim winning young insight ahead clean extensively hypercube erlbaum reverse valuable grants discovered summarize instructions adopted automated automated automated automated explorations severe accumulated drop slight microstructure outperform piece achieving equivalently leaming leaming leaming leaming leaming leaming leaming leaming leaming leaming super removal opposed encodes presenting legal legal 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ref ref interpretations interpretations systematically isolation tended johns quantitatively frequent minsky minsky approaching amenable nettalk scott gammon baltimore memorized alamos promise parker indi massive ini subtle subtle stan urbana urbana urbana entering tal biophysics columnar sixth won won won won won won men men men men men men men men men men men men men men men plans reviews couple substituted substituted impor impor conceptually complications dard posi ply illustrating package tant tant sought ninth rolls rolls rolls tially picks complexities samuel scored scored continuation pattem confident necessity dev presidential teach perf perf tain papert papert economics crafted crafted crafted resort exceptions unrelated champaign champaign champaign champaign native told vised revealing revealing roll roll roll roll roll standards incor traced comment comment manage accumulates prefers prefers unary unary survive causality hans graphic cated prin gte programmer defect 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similar architecture architecture architecture architecture fixed fixed fixed line line general general general general real average average average theory note activity activity result university threshold computation computation computation computation computation computation computation computation computation computation research research research research research found sequence target constant constant standard standard standard computer computer computer computer computer computer terms terms distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections science science science science direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented presented presented presented presented presented presented presented presented map map map map phase machine machine machine machine machine machine machine machine machine machine machine machine machine press press position abstract computational computational computational computational computational due ieee ieee ieee ieee ieee ieee important important propagation introduction introduction introduction complex complex behavior behavior parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel cost search tion tion tion change complexity complexity assume assume rules rules rules word chosen chosen chosen chosen chosen part center center center bound type type required required multiple multiple multiple good conditions represent represent represent distributed chip fact proposed length correct correct simulations simulations ing ing simulation simulation sum performed called called times times times times elements elements elements elements elements elements elements elements elements means means means factor dimension dimension natural natural natural natural natural natural natural applications applications applications applications study knowledge original vol vol vol vol vol vol vol vol vol vol artificial relative relative relative specific represented proc proc proc perform perform active active active determined related connected connected connected connected connected connected connected connected connected brain approaches mit steps steps steps steps steps larger connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection source source source source nets nets nets nets nets proceedings report institute institute implementation implementation implementation implementation implementation implementation implementation technique code code represents difficult difficult difficult final scheme scheme scheme scheme scheme addition graph graph graph graph graph graph graph graph graph graph graph maps considered considered cambridge cambridge computing computing additional additional design limit limit limit limit limit limit limit limit bit bit bit bit bit bit bit bit bit conference conference efficient efficient full requires requires choice free free free free free free free free free free basic basic basic basic basic con con bounds area area controller path path path path path path path path path path path path path path path path path path path path path path path path path path path path path product product provided processes constraint simply biological biological associative achieved achieved arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary group tested finding amount amount implemented implemented assumed assumed synapse supported supported require end end end end end end end end ability ability ability instance instance instance cluster easily easily degree degree makes including fit simulated simulated needed needed hopfield fully technology technology significantly edge edge edge edge consistent consistent structures structures structures operation operation operation representing numbers numbers pre pre pre making stored bits bits bits idea produced produced run added added added added added added added architectures architectures architectures architectures architectures architectures architectures architectures architectures improve directions directions directions directions robust separate separate takes takes takes element movement introduced introduced introduced strategy machines machines machines machines trees trees array array array array array array array array array recently engineering interest sufficient sufficient sufficient sufficient highly highly previously previously tions achieve trans trans trans trans sparse address address address definition locations generalized generalized generalized generalized grid grid grid grid bounded organization storage entire entire constructed constructed constructed constructed constructed constructed exists exists parts invariant invariant occur occur occur suggests trial trial trial trial trial wide wide locally move move loop occurs occurs boundary setting setting hardware hardware hardware hardware hardware hardware hardware pass pass starting starting place minimal assumptions assumptions assumptions conclusions neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor competitive designed suggest physics characteristics proportional proportional proportional proportional proportional assuming variety variety variety start start start start start start start start start start start exist manner groups groups areas suppose suppose suppose appears appears pro pro pro construct edges edges edges edges edges longer ways sequential sequential laboratory label label label label label mathematical dept changing implement implement explicitly simultaneously physical physical involves involves slightly slightly unique unique adding adding adding adding springer formed boolean boolean cycles cycles choosing national national formation formation formation formation communication communication communication communication communication communication variation operations restricted lee lee forms completely processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor key key performing performing add assigned assigned assigned assigned assigned kohonen advantages advantages topology topology topology topology topology topology transactions dendritic recorded recorded existing existing fire box box box box box box inter inter memories memories extension extension maximize maximize activated activated variations holds neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors characterized tests major simplicity regular determining extra extra encoded paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths build build build efficiently schemes essentially essentially reached receives receives verlag quickly quickly quickly graphs graphs graphs graphs moore moore link dis sci device hold built built built write write paradigm paradigm realistic processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors received received attempt moves satisfies neighboring neighboring software software software software software software routing routing routing routing routing routing routing routing routing oriented origin american layered requirements requirements requirements requirements requirements requirements requirements requirements requirements requirements requirements difficulty relations limitations lippmann mass existence examine examine successive successive successive ideas relationships stream workshop workshop fundamental examined naturally concepts integer extremely perfect changed changed logic nervous store message message message message message message message message message message message message message message message message message message message message consist serial serial serial synthetic established established devices mentioned mentioned mentioned brown indicating indicating great great slowly developing asynchronous directed directed directed crucial guaranteed guaranteed fairly analytic floating expensive lies tool starts starts starts starts starts starts implementing implementing implementing arc arc arc arc arc arc arc arc arc arc arc closer constructing directional desirable desirable desirable pool scientific members read computers computers computers author virtual offset embedded embedded embedded embedded embedded embedded conducted simulate simulate lack leave marked passed passed passed slower requirement requirement passes berlin branch instruction instruction instruction instruction instruction suited simulator simulator logical logical logical inherent univ arithmetic realized don labeling labeling labeling forming forming forming forming forming restriction restrict acm acts acts perfectly dynamically dynamically dynamically concerned concerned addresses eliminate connecting flexibility proceed arranged establish adds allocation convenient interconnection interconnection interconnection interconnection interconnection stated abilities abilities serves mark operates wire north north effectiveness synchronous spot natl embedding irregular irregular irregular topological intended realization vertices vertices facilitate branching similarities diameter diameter diameter diameter recovery april april april permutation permutation permutation ahead shortest shortest arrive arrive vertex vertex vertex vertex vertex vertex ends passing passing passing hypercube messages messages messages messages messages messages exploiting discovered propagate propagate alternatively instructions instructions tures integers stone outlined outlined dense consecutive arcs arcs arcs arcs largely numerous indirect listed annals piece validity opposed emergent dec dec july legal propagating adopt restrictions restrictions restrictions par par connec connec solely simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simulating examining massively massively massively massively massively stands realize tight publication goals execute execute activate activate allocated allocated overhead parallelism deleted cation apparently west west west west west turning nasa nasa nasa nasa nasa exchange exchange placing likewise admissible flight thousands thousands thousands thousands port failures completed coming coming coming coming coming stops handled topologies topologies topologies topologies topologies cube cube mcculloch mcculloch simplification survey survey sorting sorting consuming slot slot slot slot slot pitts pitts send send send send send invertible thousand slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots slots maze hundreds hundreds doesn east east east east east east east east east east east east east cornput cornput suffices harvard conflicting exclusively dissertation sparsely architec placement tells arriving contrary destination destination destination destination destination comm gence south south south south south thing thing locality enter addressing addressing elec feb promise tens tens maryland mesh mesh indi col spec sented costly objectives deleting instant applica biophysics attracted transferred plexity permutations sends checks checks won won avenue forthcoming traversed tran scheduled prohibitively thompson occupied occupied 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#@Tomboulian_S,
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single single single single single processing processing processing processing processing processing large large rate rate analysis class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs shows shows signal signal signal signal algorithms paper paper examples small work field field field features process random high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar show show show section section section section section section section section section line vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general general general general general general general general general theory theory theory obtained obtained term term result result result result result threshold threshold threshold threshold threshold threshold threshold threshold computation research research research research independent defined defined defined defined defined defined defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence table table table table table table table table table table table table table computer computer computer computer terms terms distance distance synaptic synaptic node node node node node node science science presented presented presented presented presented present phase nodes nodes nodes maximum maximum maximum press basis basis basis nonlinear abstract applied back computational computational convergence convergence convergence convergence properties properties properties properties properties properties properties properties properties properties properties properties properties references ieee ieee ieee ieee ieee important important adaptive context context introduction hand hand statistical tion signals signals signals signals signals signals signals signals signals representations chosen chosen chosen chosen chosen previous multiple multiple multiple binary binary binary binary binary binary conditions represent represent expected expected equations chip fact correlation correlation correlation length length length length length length errors errors simulations simulations minimum minimum resulting resulting resulting resulting total simulation simulation simulation simulation respect sum sum sum sum sum sum performed performed elements elements elements elements elements elements elements elements elements elements mapping mapping mapping factor optimization optimization dimension feedback global applications applications applications applications applications filter filter filter filter obtain obtain negative negative specific specific specific represented compared application desired cross cross cross define define proc perform perform active active determined connected equal equal equal equal equal equal approaches support nets nets institute loss implementation implementation implementation implementation version version code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code represents represents final final final delay scheme addition addition addition addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences maps domain equivalent equivalent equivalent directly hinton additional design stage bit bit bit bit bit bit bit bit bit bit detection detection conference capacity capacity capacity capacity capacity capacity efficient full choice choice significant basic give give con produce produce channel channel coding coding randomly developed path product finally selected nature nature depends depends associative associative associative associative associative associative associative associative associative associative associative associative discussion technical arbitrary tested close close close corresponds corresponds corresponds stable stable circuits common implemented generate theoretical end pixel instance easily easily development including simulated simulated simulated simulated pairs hopfield hopfield hopfield hopfield hopfield hopfield combination combination functional functional transfer interesting york operation operation making stored stored bits international international minimize light discussed discussed discussed discussed discussed advantage property pair pair pair takes element element element element element element element typical practical machines pixels pixels pixels pixels sejnowski interest interest tions yields yields correspond correspond correspond correspond converge differential trans trans trans diagonal diagonal sparse sparse sparse sparse sparse sparse sparse sparse positions symmetric symmetric generalized generalized generalized storage sensitive intensity expression studied studied studied occur suggests extended wide wide matrices correctly correctly correctly generally setting setting pass pass pass pass pass pass pass pass pass pass demonstrate row reduce conclusions conclusions designed designed designed designed clear hard presence physics physics cycle cycle cycle demonstrated labeled labeled variety variety variety variety user relationship iii iii connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity configuration annealing annealing base boltzmann pro produces written written optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical generating distinct distinct distinct distinct recall implement implement missing missing physical integrated shift shift shift cycles yield family family family family family family family family family family family family family expressed review communication communication communication overlap overlap codes codes codes codes codes codes codes codes codes codes codes codes codes evaluate forms understanding understanding completely allowed processor diagram diagram diagram reasonable purpose purpose filtering filtering filtering filtering filtering sufficiently includes usa bell inter memories recognize recognize discuss specifically specifically specifically specifically specifically discussions importance encoded comparing orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal refer repeated contained oscillations content follow sci sci write write simplified simplified absence principles principles presents body american access access access accurately issues behaviour behaviour ideas project possibility possibility possibility gates gates symbolic encode func fundamental fundamental fundamental neu smallest closest transmission transmission transmission concepts concepts editor necessarily necessarily equally implementations academic switching fibers arbitrarily arbitrarily electronic synthetic established devices devices directed growing coded multiplication multiplication sys constructing division division division products products products products acknowledgement recognized acad grossberg opt calculations implicit auto auto recognizing outer outer outer outer outer explained composite prop prop applies reflect items pseudo fed item passed compares schematic schematic schematic limiting collective hamming hamming logical logical logical decoder decoder comments fiber fiber fiber cor shifted shifted shifted shifted shifted shifted shifted shifted bipolar recover nat dynamically null null null null encoder tem communications communications communications communications communications communications communications multiplier accepted analogy interconnection attractive abilities star star shifts shifts receiver modifications preparation symposium alspector passive expanded intended intended realization realization recovery recovery neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic mem mem mem belonging draw passing correcting correcting thresholding thresholding multiply multiply multiply street users ent ber ber ber ber ber ber emergent responds pointed medium options transparent avoids publication shifting shifting mathematically distant thresholded thresholded simplifying projecting projecting projecting pos mask 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problems problems problems similar general general real average average states activity activity activity dimensional result result university threshold threshold threshold research research found found dynamics dynamics initial initial constant constant synaptic synaptic synaptic synaptic node node node node presented present present phase phase phase phase phase phase phase phase activation activation activation activation nodes nodes nodes nodes frequency frequency frequency frequency maximum range range press continuous continuous continuous abstract find analog properties properties references stochastic positive important introduction action action action action behavior behavior behavior behavior dynamic dynamic dynamic parallel parallel energy energy energy energy energy energy energy energy energy energy difference difference complexity complexity signals higher part firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type type multiple multiple binary spike spike spike spike spike spike spike spike represent represent represent distributed distributed distributed equations make make fact region region proposed observed simulations resulting respect multi called called elements elements potential potential potential potential dimension natural natural natural natural global global global global filter negative original artificial artificial rates rates proc experimental related constraints constraints discrete brain mit steps nets report institute implementation version internal internal individual individual individual individual represents exp delay delay delay sequences considered considered cambridge computing directly hinton view limit trajectory significant produce produce condition weighted levels entropy path path processes nature inhibitory depends constraint constraint simply achieved measured increases increases arbitrary limited limited assumption corresponds excitatory amount short common effective assumed assumed assumed shape supported rumelhart rumelhart simulated typically hopfield hopfield account functional ratio ratio ratio mechanism mechanism special empirical representing pre pre pre inhibition inhibition inhibition inhibition description description perceptron neuronal neuronal neuronal membrane membrane membrane membrane exact pair takes period side array recently engineering correspond studies converge differential differential interval interval interval interval interval williams increased amplitude concept scaling occur digital wide spikes spikes locally occurs occurs occurs critical critical minimal minimal minimal assumptions interactions sigmoid constrained propose hard integration physics cycle cycle cycle demonstrated demonstrated demonstrated california assuming relationship relationship relationship iii iii annealing attractor areas derive longer generating transitions transitions stability stability stability stability linearly electrical interaction interaction interaction interaction interaction integrated equilibrium equilibrium equilibrium equilibrium events minimization minimization potentials potentials cycles john john depending communication communication communication showed modulation earlier intervals event event intermediate advantages coupling fire fire fire fire formulation inter illustrated phys major aspects capable capable importance modes oscillatory oscillatory attractors efficiently post post tend reached excitation excitation traditional procedures moore timing timing timing sci built satisfy simplified relaxation relaxation relaxation relaxation absence absence paradigm delayed delayed ill received received neighboring routing routing receive presents presents presents explore simpler schedule schedule american transformed perturbation perturbation perturbation perturbation exhibit oscillators oscillators oscillators oscillators oscillator oscillator oscillator oscillator oscillator oscillator biol biol biol biol structured oscillation oscillation oscillation cover presynaptic cognition integer voltages impulse precise precise consist extent simplest established mentioned burst advanced crucial agreement unstable coded rapid immediately pulses pulses consequence ion potentially involve universal acad lowest considerably limits passed slower gains gains limiting reaches reaches fall fall occurrence ordered suited adjust shaped physiol begins summed synchronization synchronization synchronization synchronization synchronization synchronization contribute cybern appearance ratios ratios nat branches ordering ordering interconnected outcome arrival arrival establish rational rational fits ranges iiii los los los periods infinity infinity scheduling advance recovery foundations axonal arrive master master locked sustained passing passing messages variants subsequently propagate explorations acknowledge fired fired neurophysiology microstructure constitute transmitted cooperative dec pointed pointed classic constitutes letting quantized mutually subthreshold maintained neurophysiological interactive intensities locking locking locking locking nasa applicability nil dramatic wider hodgkin hodgkin continually develops accumulation satisfaction satisfaction fractal fractal traveling traveling huxley huxley inhibit tsp carrier concern contrasts contrasts accumulate markers cardinality salesman salesman accounting feasibility enters merit zones zones shares firings firings firings firings firings depolarization depolarization instant biophysics sends plausibility excite fukushima fukushima pursued angeles angeles angeles rigorously synchronize sequencing sequencing scheduled machinery rosenblatt spontaneously freitas ramp released rationale membranes invertebrate widespread accumulating regularly regularly isomorphic today quantum inverses organize cyber electro arrivals arrivals cited kohn kohn kohn refractoriness refractoriness joining bullock abrupt breakdown living living ucla ucla collapse slave synchronizing devil shortening appreciated richly fitzhugh fitzhugh abruptly influx reception aero instants instants staircase staircase delaying cooperating jacques disturbed unilateral impinging impinging excit 
#@Haggerty_J,Vidal_J,
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linear linear linear linear linear case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown systems systems probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach pattern point point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single processing processing large large large large large test matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form shows shows shows shows signal simple gaussian gaussian visual paper paper paper paper small small small size size size size size work task task step step points points points features classification classification classification process process process level cell structure structure structure problems high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response response response response response response response response response response response response similar representation representation representation representation representation representation representation representation show equation section section section section line line vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images images images real real real approximation average gradient experiments experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result result result result university solution solution solution research research research research independent independent log log log log log log log log log log log log log log log log log log defined found found estimate estimate estimate estimate estimate computer computer computer computer computer computer science presented presented presented map present phase phase phase phase phase phase phase phase phase frequency object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object sets range press press position components components components basis sample abstract applied back computational properties properties references component component due due due ieee important decision context introduction introduction complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex hand behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect variance variance variance variance variance parallel parallel search tion tion tion change change change change change change energy difference difference difference difference spatial spatial assume assume classifier measure measure representations representations chosen chosen chosen chosen part part center center center center center center center center center type long conditions distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed equations make fact techniques region region proposed length errors scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale finite finite simulations resulting resulting resulting resulting resulting classes classes ing ing computed respect respect sum performed times elements elements elements elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means means means means means factor made made feedback feedback orientation orientation orientation orientation applications filter filter filter original original original vol vol artificial relative relative samples samples samples samples samples samples samples samples true cross objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc proc proc perform active determined determined goal goal goal goal connected discrete mit mit larger contrast dependent dependent source institute department version version consists consists internal internal kernel kernel difficult scheme addition considered domain domain environment curve curve curve curve view estimates stage effects bit detection conference efficient significant world vision vision vision vision vision vision vision vision vision estimated estimated con con produce produce produce produce derived weighted randomly randomly developed developed robot levels area area area lines actual nature sampling sampling sampling constraint simply biological associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative measured discussion describe describe arbitrary group group transformation limited inverse inverse corresponds corresponds corresponds stable finding amount amount amount shape shape generate require main main eds square pixel pixel ability ability future future rumelhart noisy noisy noisy pairs smaller needed hopfield hopfield functional functional unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown block block block interesting testing significantly significantly significantly ratio ratio ratio projection projection york edge edge uniform database database database database operation operation numbers making stored bottom bottom bottom magnitude magnitude magnitude magnitude magnitude magnitude frame frame frame frame frame combined added denotes denotes improved improved improve resolution resolution exact robust element element introduced strategy moving pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels sense engineering dimensions highly highly previously previously approximately axis tions solve solve solve yields achieve trans background generalized organization organization improvement entire increased exists parts parts parts invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant suggests extended derivative rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation width width width loop setting demonstrate flow critical reduce central interactions interactions differences sigmoid exponential propose presence presence physics characteristics drawn solid proportional intelligence radial radial radial radial variety minimizing exist exist plane plane plane plane manner manner question areas van van derive construct construct construct edges edges edges written perception solving solving ways ways factors describes describes vertical mathematical distinct changing changing changing recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall missing sensitivity coordinates coordinates infinite physical electrical involves transformations transformations transformations slightly unique unique develop gaussians springer shift quality quality implies yield dependence review reconstruction reconstruction reconstruction squares viewed viewed viewed transform transform transform transform transform transform transform transform transform transform controlled lee centered centered completely translation translation translation translation translation translation allowed allowed diagram diagram diagram key key key tracking distances filtering filtering filtering visible construction kohonen classified views views views degrees degrees box box usa memories memories recognize discuss discuss specifically black holds characterized characterized structural major sensor sensor compression selecting aspects suitable mcclelland build projections situation essentially identity characteristic characteristic characteristic notice verlag video moore moore anderson anderson anderson anderson split dis dis classify criteria gray involved involved sampled sampled sampled paradigm highest processors deal camera camera presents american wiley create requirements requirements put detail association association mass fourier fourier fourier fourier fourier fourier fourier fourier examine matches behavioral biol fault ideal ideal ideal ideal ideal relationships scaled scaled scaled scaled variability variability variability variability func removed removed removed closest necessarily analyze rev changed der portion portion portion formal assumes assumes mapped mapped mapped mapped mapped mapped mapped mapped mapped mapped mapped mapped mapped hebb arbitrarily histogram histogram histogram histogram formula ground derivation unstable caused processed processed perspective snr snr snr snr snr tive sections filtered filtered leaves desirable consequence consequence ion projected projected acad implicit geometric geometric percent percent percent percent freeman freeman amounts amounts simulate variant variant variant variant price operate operate anti anti characterize characterize spread gen extracting collective age tolerance begins tile summed displays pyramid pyramid corrupted contextual equivalence tation extensive angular rotated rotated rotated rotated circular reconstructed reconstructed reconstructed jones rotations grey interconnected extending ments abilities obtaining transforms transforms shifts implications illumination guide carry filled filled natl excellent mance combines sion encountered encountered perfor expanded topological topological evident belongs captured originally multiplied artifacts recog recog april occlusion occlusion occlusion occlusion occlusion occlusion occlusion creating gaze clean rich correcting projects captures valuable characterization characterization assigning mechanical outlined dense associations associations associations associations associations associations truncated slight ple outline vec vec benefits emergent isotropic nition restrictions spaced tor letting laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian reflected reconstruct reconstruct transparent quantized rectangular exam robots pami interact interact grouped pdp faults lobe mathematically dominated uncertain emphasize fixation surrounding spreading represen cartesian translations translations accounted inversely exhibited bring bring dramatic things ward experi examination simplifies challenge demonstrating covers moderate moderate scanned distortions ping transforming imple powers concern eliminates eliminates affecting inherently horizontally equa marr marr vote carries carries carries dog recognizes recognizes digitized enhances spie spie autoassociative distorted presently experienced experienced feasibility occluded occluded categorical twelve twelve subsystem subsystem subsystem pin memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized memorized doom ically translate recalled recalled recalled recalled recalled recalled recalled recalled recalled recalled recalled recalled brought tan indexing indexing simon simon polar tern stems linearities preprocessed preprocessed tolerant blurred blurred graphically modifies ver aliasing aliasing aliasing convolving convolving paid displaced distinctive tot ages asso poral stays polyhedral george clue tilted aver fulfill emphasizing dam simplistic psychol bilities penrose penrose associa neur reflections concludes associ bet memorization sidered smart crosstalk ject koenderink resistant resistant harry burt interplay distributing distributing ating stretching stretching analyzes rounded ciated minnesota nized minneapolis older bessel bessel sharpens wechsler obscure ritz capa keys keys automat menting digitizing trix rlt ota confounded projec gion scl 
#@Wechsler_H,Zimmerman_G,
#t1
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural input input input input input input input input input input input input input input input input input input input input data function function function function function function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number system system system system state state results results results results results results results results results units information information information information information information information information information information information information information information information models models models models models models models models models models models models hidden hidden performance based based based based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer case case case case case case case case vector order order order shown shown shown shown systems systems systems systems systems systems values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability weight weight weight functions functions functions functions functions functions neurons neurons distribution distribution distribution approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single single single single single processing processing processing processing large large large large neuron test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows shows shows signal signal signal signal signal signal signal simple simple simple simple simple simple simple simple simple simple simple simple simple paper paper paper examples examples small small net net net net net net net net net net net net net net net net net net net work work work work work work task task methods methods fig fig fig fig fig fig fig fig fig fig fig fig step process process process process level current current current trained trained trained trained trained trained trained random random random random random random random random random high high high high high memory memory memory memory response similar similar similar similar section fixed line general general general general general general general general general generalization parameter real real real real average average average average average average average average average average states states theory theory theory theory term term note note note note note note note note note experiments experiments result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables research independent independent independent defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant constant table table table table table table table table standard standard computer computer computer terms connections left left direction direction direction direction presented presented presented presented map present present present present present present present present present present present low sets sets maximum maximum range press learn learn learn learn learn learn learn learn learn learn learn outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied applied applied applied applied applied find find find analog properties properties properties properties properties properties references references stochastic stochastic stochastic stochastic ieee ieee positive positive positive positive positive positive positive positive positive positive positive positive positive important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision context context context introduction action hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior effect effect generated variance parallel recurrent change change change change change difference difference complexity complexity complexity complexity rules rules rules rules signals signals signals signals signals learned learned learned learned learned chosen chosen chosen chosen chosen part part part part part part part part previous cases type type type type type multiple multiple multiple multiple multiple multiple multiple long represent distributed distributed make make make make make make fact correct correct correct correct correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities simulations total total simulation simulation simulation simulation simulation human respect multi eq times times times times times times elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements mapping means means means means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement potential potential potential made made made feedback feedback applications study study knowledge knowledge obtain obtain negative negative negative negative negative negative negative negative negative negative negative negative negative relative specific specific desired desired desired desired desired desired desired desired desired series provide provide provide provide provide define determined experimental experimental goal related connected gain motor discrete equal equal equal equal equal equal equal equal equal mit comparison comparison larger connection train train train train train train train source source nets nets nets nets nets nets nets nets nets nets nets selection proceedings institute institute loss loss consists consists internal internal internal individual responses responses responses difficult final layers layers layers layers layers layers scheme scheme ai ai cambridge computing equivalent equivalent environment environment environment environment environment environment environment environment environment environment environment directly directly hinton top stage stage effects conference efficient efficient choice significant significant significant approximate approximate approximate give give give give produce produce produce produce produce produce produce produce produce produce produce produce produce produce produce channel channel channel channel channel developed developed developed levels criterion criterion criterion criterion criterion criterion criterion criterion criterion area types types types types types types path finally finally processes selected selected selected selected nature depends biological biological associative associative associative associative normal normal normal normal increases arbitrary arbitrary arbitrary arbitrary tested tested close close close close assumption complete proof short common effective generate supported role main ability hypothesis hypothesis hypothesis future easily makes makes makes makes makes rumelhart rumelhart sensory including simulated needed needed combination combination combination combination reduced reduced account unknown programming significantly significantly significantly york york increasing mechanism mechanism special consistent consistent trials trials trials trials matching representing details details call call numbers numbers numbers max max max max making making making bottom bottom combined combined minimize produced produced produced choose run predict improved recent exact exact exact advantage property property property property separate takes takes element element element element element practical practical apply strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy include period machines machines sense sense sense sense subset subset subset subset subset subset subset subset recently sufficient previously approximately approximately match correspond background separation symmetric symmetric channels gate gate gate gate gate gate gate gate williams entire entire grant constructed constructed constructed constructed constructed constructed parts parts parts parts parts parts parts parts lead studied occur occur trial trial trial trial trial trial wide rotation correctly move move move move hybrid deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic generally generally generally half half half half half half starting critical row greater greater valued valued depend depend depend competitive differences differences differences designed sutton faster practice learns suggest physics physics external cycle cycle cycle cycle cycle cycle cycle cycle cycle proportional intelligence variety variety start start start start exist min min min min relationship configuration configuration suppose suppose suppose appears derive produces produces produces produces longer ways primary sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential describes vertical changing changing explicitly easy slightly consisting adding events agent cycles cycles select select select select select select select select select select select decreases national family family focus depending depending fraction showed centered centered completely completely similarly past past past past past reasonable reasonable barto barto barto barto barto barto barto event roughly remains initially initially sufficiently string string transactions transactions building existing figures combinations formulation bell sciences recognize recognize recognize recognize recognize determines extension discuss maximize maximize holds holds selecting selecting selecting selecting capable effectively paths driven mcclelland literature situation situation situation situation situation tend tend tend receives quickly repeated strongly heuristic anderson interested running running running content physiological follow follow strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing notation quantity involved play play play play play play play play paradigm providing providing providing minimizes observable correspondence denker reach received received received received received received received received attempt consisted subsequent receive receive situations situations situations situations presents trains simpler remain american american layered layered layered wiley xor xor xor xor xor xor xor xor rapidly put put put optimized accurately game game game game game game game game game game game game game game game dotted existence fewer giving ideas ideas ideas behavioral incremental applicable comparable gates gates gates complicated complicated analogous adapt adapt adapt adapt adapt adapt adapt adapt adapt adapt adapt adapt necessarily necessarily integer man man opposite opposite opposite opposite automata automata automata automata automata automata automata equally recognizer changed changed changed ensure subsets subsets front assumes assumes logic logic logic logic logic logic logic logic logic logic nervous nervous nervous nervous switching switching switching consist simplest contributions optimum optimum animal animal animal animal animal animal animal animal animal years years mentioned asymptotically slowly theoretic theoretic improves adapted starts starts reasons reasons reasons reasons rapid rapid purposes purposes satisfied closer organized producing producing producing producing producing producing producing producing producing producing laboratories consequence consequence recognized separately describing author author cybernetics cybernetics recognizing recognizing preceding apparent behaviors amounts amounts capability experimentally readily readily adjustable operate operate operate stack stack switch synthesis summarized prevent prevent prevent gave richard logical logical logical logical logical logical conclude focused lot ordinary ordinary ordinary proportion appropriately appropriately appropriately appropriately appropriately appropriately appropriately appropriately appropriately appropriately member nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat nat approximates null unity grows arranged plays plays plays plays plays plays plays plays plays plays plays plays adds wrong chance significance significance significance accepted overcome analogy proceeds intelligent moment abilities resulted keeping keeping neurobiology operates operates monotonically guide intuitive selects selects selects selects selects selects selects selects motivation repeat ensures studying studying regard demonstration demonstration demonstration belongs facilitate winning infer arrive canada variants subsequently subsequently characterization session covering exhaustive suboptimal suboptimal suboptimal distinction acceptable chapter tendency letting letting realize realize realize conservative exclusive alternate alternate compensate compensate compensate compensate impose continues playing playing playing playing playing playing playing playing playing playing rectangle emphasize individually player player player player player player player player player player player player player player win win win termed covered emphasized nonetheless discusses figs responding supports meet meet likewise stuck stuck stuck stuck stuck stuck stuck stuck stuck stuck places knowing behave things things increments increments recognizers recognizers worked vice walk demonstrating sessions sessions sessions sessions sessions sessions sessions versa remarks council influenced hundreds ave ave wins wins focuses focuses opponent opponent opponent loosely identically calculates distinguishing possess partly partly partly inferring ref ref ref ref ref ref ref ref arrives governing governing governing governing transducers complement adjusts smc smc confined adapts adapts players aip artificially deciding deciding subtle subnetwork subnetwork tails tails tails tails freely aggregate aggregate comprehensive mai intrinsically omit omit hysteresis nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic repeats substituted ontario opportunity opportunity accepts ago postulated postulated postulated remember proving anandan ire constantly fell incremented incremented incremented supplies embodied embodied heads heads heads heads heads heads chiang contributed concluding temporarily illustrative embody loses told lacks focussed focussed establishment supplying wealth separations walks transmitting muroga incapable incapable gathering profound ineffective motivations judging deliberately deliberately conceived assert awl nonadaptive nonadaptive nonadaptive interscience reinforces wlx minority chief chief aggregates conventions cooperativity understandable ects refs coworkers 
#@Windecker_R,
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#*network network network network network network network network network network network learning learning input input input input input input input input function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error results units units units units units units units units problem hidden hidden hidden hidden hidden hidden performance based based weights weights weights weights weights weights linear linear linear linear layer case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order weight weight weight functions functions unit unit unit unit unit unit pattern point point point point single single single processing local local analysis analysis class inputs inputs form form form form shows signal signal algorithms simple examples work work task task task methods points field classification classification classification classification classification classification classification classification trained show equation equation equation equation equation section section section fixed line line rule rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors generalization gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient dimensional dimensional solution research target target target target initial estimate estimate estimate distance distance connections connections science direction direction presented presented presented present sets range range press position position nonlinear outputs outputs continuous abstract properties properties properties properties references component component due due due positive positive positive positive positive important behavior variance parallel change assume assume lower lower rules rules previous previous type multiple multiple good good conditions represent represent equations equations make make fact fact fact region region region region region region region region region correct forward finite finite finite simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum tasks tasks tasks tasks multi called times elements means means made made natural global global global global relative represented desired provide define define perform perform mit train train descent descent descent descent descent descent descent descent descent descent descent proceedings report institute loss difficult layers layers considered transition top bit significant speed produce entropy entropy path path path provided group denote denote denote denote assumption surface proof proof finding easily makes rumelhart rumelhart rumelhart including probabilistic pairs pairs pairs hopfield technology interesting call call call call magnitude frame frame frame frame frame idea attention attention choose run light property property property property robust introduced sense sense sense works axis axis converge diagonal definition symmetric symmetric symmetric observation generalized bounded bounded exists exists exists horizontal correctly feed move move white starting greater greater greater greater greater depend differences numerical weak suggest suggest suggest physics solid assuming assuming min plane plane iii iii iii targets targets targets derivatives scene explicit suppose suppose construct construct longer ways changing category category category category formed formed formed formed formed formed formed formed formed formed john john expressed interpretation centered frames frames frames margin margin margin completely suggested key combining remains construction construction classified david coordinate formulation formulation formulation bell prove discuss discuss specifically specifically successfully reason aspects delta delta delta delta delta delta delta delta delta delta mcclelland mcclelland mcclelland situation traditional kind kind contained interested dis contribution contribution contribution classify classify running strategies categories categories categories satisfy michael denker moves operating origin origin origin american layered wiley dotted dotted ideas rest authors tanh switching regime regime regime arbitrarily arbitrarily arbitrarily finds mentioned separable separable separable separable separable guaranteed guaranteed failure failure baum baum lies lies lies lin implementing satisfied satisfied closer choices choices choices located ran leaves laboratories circle beginning begin begin varies varies peter solla solla remove popular tank adjust richard replace begins lim proposition differentiable differentiable lot representative guarantee guarantee guarantee guarantee guarantee restrict rotated concerned impossible arranged generality extending communications wrong convenient adjusting proceeds odd odd held hope obtaining fail fail fail meaningful meaningful james moved percepttons facilitate counter counter counter counter tic tic reader arrows arrows arrows sons border hart hart summarize empty empty empty empty empty empty verify shading shading misclassification presenting guess eric constrain visualization shaded shaded shaded shaded shaded perpendicular care levin levin duda duda pdp discontinuity discontinuity regimes increasingly increasingly misclassified misclassified investigations margins helps bution interior interior saturated inconsistent quadrant quadrant quadrant quadrant quadrant jersey ave holmdel push ray ray ray ray minsky minsky teaching thing ben enter enter compromise compromise enters enters enters vanishing meaningless sition illustrating suggestion desire separability separability consensus consensus tributed ending widespread frank critically papert tly private traced traced traced reformulated draft contradiction bringing suspect discussing marvin remedy assures defects ied obtainable sara intersects ifs fleisher fleisher wittner pushing contradicts ction bowl bowl representatives wilczek wilczek vanishingly pla cept cry papeft propo 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#@Denker_J,Wittner_B,
#t1
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#*network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model model neural neural neural neural neural neural data function function function function function function function function function function figure figure figure figure figure time time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks output output output output output output output output number number number number system system system system system system system state units information information problem models models based based linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case order order shown shown systems systems systems systems systems systems systems values values values values values values functions functions functions functions functions functions functions functions functions method method approach approach approach point point point point point image single single processing processing control control control large local local neuron analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class form form form form form form form shows shows signal signal signal signal algorithms simple simple visual paper paper work work methods fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cell cell cell cell cell cell cell cell cell cell cell cell high memory response response response response similar similar show show show section section fixed line line line line line real real real real real real real real real real real real real real real real real real real real real real real real approximation states theory theory theory theory term term term term note note note note note result result result result result result result solution solution solution research research research research research defined found initial initial initial initial computer terms terms terms terms terms distance science left present present frequency frequency frequency frequency frequency motion maximum range range press press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous abstract applied back analog analog analog analog references ieee positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive important important complex complex complex complex complex complex complex complex complex complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior effect dynamic variable assume rules previous theorem theorem theorem theorem theorem theorem theorem theorem theorem type type required binary conditions conditions conditions conditions equations equations chip chip chip chip fact minimum resulting classes sum sum eq elements elements elements elements elements elements elements means made natural natural natural natural feedback feedback feedback feedback feedback original original original original original vol vol artificial application series active active active active active active goal goal connected connected equal power mit mit voltage larger contrast connection proceedings proceedings report institute institute department loss implementation implementation version version version individual individual individual difficult bias cambridge cambridge computing domain domain directly curves design design design design design design design design design design conference conference full condition condition condition condition condition criterion criterion criterion criterion criterion associative achieved discussion feedforward feedforward feedforward increases describe arbitrary arbitrary denote limited assumption stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable proof proof proof proof circuits common common common vlsi vlsi vlsi vlsi easily easily pairs pairs combination combination unknown coefficients technology ratio york york edge segmentation special empirical principle principle language numbers making inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition early idea idea light population robust robust takes element typical reported lateral lateral lateral lateral lateral lateral lateral lateral practical practical practical identical sense sense sense sense array relevant engineering highly observations axis axis axis axis trans grid grid grid grid grid grid grid grid grid grid grid sensitive exists horizontal intensity intensity occur occur suggests feed locally locally locally boundary half half half half half half half half half half half half greater accurate retina retina retina retina designed practice practice practice practice practice presence physics turn turn plane plane plane plane plane plane plane plane plane plane plane plane plane plane iii iii iii suppose appears edges plot plot plot laboratory stability stability stability mathematical sensitivity simultaneously simultaneously physical physical electrical electrical angle angle angle consisting consisting frequencies equilibrium equilibrium equilibrium equilibrium springer springer implies yield extracted communication lemma lemma lemma lemma processor diagram diagram diagram measurements classical convex convex reduces closed closed closed closed closed closed closed closed closed closed closed closed sufficiently kohonen kohonen koch topology topology topology transactions currents currents currents inter sciences extension automatic neighbors neighbors neighbors characterized characterized simplicity straightforward straightforward capable importance divided paths driven build build computations summary compact verlag repeated link anderson return lie lie oscillations oscillations oscillations oscillations criteria satisfy satisfy satisfy involved write simplified absence cmos chips chips subsequent satisfies satisfies neighboring modelling extend origin origin origin american american collection exhibit circuitry mead mead mead mead mead mead mead preliminary graphical hall tech terminal terminal terminal terminal ideal office oscillation affect hill necessarily necessarily necessarily created created voltages voltages obvious simplest contributions arbitrarily submitted electronic established massachusetts massachusetts advanced advanced advanced unstable unstable analytic explanation lies lies lies lies lies lies lies lies drive stanford straight straight satisfied satisfied strictly strictly strictly division transistors ion scientific acknowledgement involve calculations begin definite read arises computers conjugate apparent applies understood pure amounts experimentally readily effort resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive continuously polynomials synthesis synthesis measuring branch cal achieves conclude wesley realized naive addison fabricated guarantee amplifier driving acts acts perfectly branches branches harmonic harmonic naval nonzero enhancement interconnected interconnected multipliers spontaneous rational khz convenient convenient stronger simplify mos mos interconnection loops contract contract affected intuitively capacitor capacitor capacitor arrays passive passive passive passive passive passive passive passive prentice prentice guarantees guarantees sides realization realization realization photoreceptor demonstration captured arrangement darpa insight omitted layout reader refers sustained passing passing passing relies projects projects influences dividing assigns verify verify resonance neurophysiology ple outline outline rigorous terminals medium personal reports reports perpendicular resistor deep elementary distant crosses careful transconductance transconductance transconductance deleted weaker nonetheless resistors resistors resistors resistors resistors resistors amplifiers amplifiers amplifiers amplifiers vanishes supporting circumstances drives august instability instability instability instability instability quadrant quadrant quadrant quadrant quadrant influenced inhibit cliffs cliffs oscillate mahowald mahowald establishes capacitors capacitors capacitors capacitors capacitors capacitors capacitors capacitors powers inherently agency agency impedance impedance impedance impedance englewood englewood progressively measurable grids vanish vertebrate arpa linearized linearized enhances suffice physically mcgraw poles poles poles poles poles poles oscillates modern defense indirectly jan col rotate carver carver carver carver imposes demanding imaginary imaginary synthesize spence incident incident def def def def def def damped damped rigorously internally enabled parasitic parasitic parasitic parasitic parasitic communicating enormous visualize luo renders sivilotti ist resistances resistances asserts realizes gin badly capacitances capacitances capacitances counterclockwise wyatt unwanted modulus arose absorbed absorbed reads ingredients impedances impedances impedances impedances impedances impedances impedances polysilicon ain positivity ita instrument professor amp usable ils interconnecting marginally dod lightly vidyasagar outset nyquist nyquist nyquist nyquist afford losleben sho igh hopeless 
#@Standley_D,Wyatt_J,
#t1
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural input input input data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output number number number number number number number number number number number number number number number number number number number number system error state state state state results results results results results results results results results results units units units units units units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance based based based space weights linear linear linear linear linear layer layer layer layer layer layer case case order order order order order shown shown shown shown shown shown shown shown systems systems systems probability probability probability probability probability probability probability probability parameters functions functions functions unit unit unit unit unit distribution distribution distribution recognition recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point large large test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis optimal inputs inputs shows shows shows simple paper paper paper small size size size net net net net work work work task task task task task classification classification classification classification process trained trained trained trained structure structure problems problems problems random random high memory response response response response response response response response response response response response response response response similar representation architecture architecture architecture line line line rule rule rule vectors vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real average average average states theory obtained obtained obtained obtained experiments activity activity dimensional dimensional result result result university university threshold solution solution solution solution solution solution solution research independent defined defined defined defined found found found found found found initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial estimate estimate terms distance distance distance distance node node science science left presented presented phase phase activation nodes object learn learn learn learn learn basis basis nonlinear abstract applied back find find find find find find computational computational computational properties references due ieee ieee procedure procedure procedure procedure important important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction behavior behavior statistical statistical statistical statistical statistical statistical effect tion tion tion complexity complexity rules rules rules rules rules rules rules rules learned learned learned part cases type good good binary binary binary conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions represent tree expected equations fact fact correct correct correct forward forward forward forward minimum minimum minimum ing ing tasks tasks tasks human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human computed multi sum performed performed called called times times potential potential potential potential potential dimension natural natural natural applications study study study obtain obtain artificial artificial specific specific specific specific represented represented compared compared desired desired desired desired provide provide define compute objects objects objects objects objects objects objects proc perform perform perform perform determined determined determined experimental experimental experimental goal constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected equal equal approaches larger larger larger descent modeling modeling modeling modeling modeling modeling modeling modeling report report department implementation version technique technique technique technique technique technique consists individual individual individual individual individual individual individual represents represents represents connectionist responses responses responses responses responses responses responses responses responses responses responses responses final final final final final graph graph sequences maps considered considered experiment experiment experiment experiment curve additional additional additional additional solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions curves san stimuli stimuli conference conference determine determine determine upper significant basic increase con con con con weighted randomly randomly randomly clustering clustering clustering clustering developed developed criterion criterion criterion criterion criterion criterion criterion bounds bounds area types types types actual finally processes selected selected sampling constraint biological achieved discussion normal technical increases increases increases describe describe group tested limited limited limited assumption assumption assumption complete stable stable stable stable stable surface surface finding finding finding finding finding finding finding common common common generate supported role theoretical theoretical main journal cluster cluster rumelhart simulated probabilistic account fully programming programming testing consistent consistent consistent consistent trials trials empirical language leads representing details call call call international minimize description light light predict improved discussed ensemble typical typical similarity reported include subject subject subject subject subject subject subject identical quadratic hierarchical subset cognitive dimensions dimensions dimensions dimensions dimensions sufficient previously subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects works tions tions tions tions solve solve achieve definition grant exists expression lead studied studied alternative correctly correctly correctly correctly feed feed feed feed feed deterministic deterministic deterministic clusters clusters half half conclusion starting critical critical minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal row valued valued depend differences differences differences differences clear external demonstrated solid labeled assuming variety minimizing minimizing minimizing exist identification configuration configuration question acknowledgements suppose pro van edges edges solving solving mathematical dept modeled metric category category category remaining remaining develop adding boolean choosing national focus correlated overlap viewed detailed detailed showed forms approximated dashed dashed reduces reduces neighborhood neighborhood valid foundation classified transactions combinations activations activations instances assignment candidate black discussions simplicity simplicity capable society differ differ encoded identify identify comparing reached reached reached graphs moore moore moore moore moore classify strategies strategies strategies strategies hold categories categories categories categories generalize generalize providing nips nips received consisted bars bars explore diego powerful layered xor xor xor xor xor xor xor xor xor xor xor xor perturbation perturbation difficulty rapidly rapidly relations involving humans humans humans humans humans humans humans humans detail detail dual preliminary discriminant reducing examine examine examine examine respond respond tech parity parity parity parity func func cover cover cognition phases examined examined examined closest man analyze analyze psychology psychology psychology equally equally recognizer submitted explain motivated finds electronic directed defining slope adapted briefly baum baum worse considerable rapid stanford stanford stanford stanford tive shared shared widely broad ran desirable involve medical medical lowest computers annual cybernetics researchers fourth questions apparent behaviors considerably profile profile profile profile profile profile profile profile profile profile profile profile dark lack effort introducing haussler haussler incorrect incorrect incorrect incorrect characterize characterize characterize differs gen gen maximizes monotonic hamming conclude conclude comments eventually june june diagnosis hints hints hints proportion proportion assign acm approximates eliminate bower chance imposed imposed imposed imposed imposed mark mark analyzing effectiveness analyses analyses conjunction dif grants discovered assigning learnable consecutive abu abu abu ure appeared mostafa mostafa mostafa asked failed convenience profiles profiles profiles profiles profiles profiles profiles profiles profiles profiles profiles profiles preferences generalizations generalizations generalizations generalizations generalizations generalizations generalizations generalizations generalizations ical assignments examining valiant valiant reflected clas favor exclusive exclusive goals gluck gluck gluck gluck gluck gluck gluck scope investigating investigating categorization categorization categorization categorization categorization categorization categorization categorization categorization categorization categorization categorization categorization categorization diversity responding responding turning nasa behave gordon learners differently differently differently lowe reversed reversed reversed reversed reversed reversed lation august continued sake prefer ferent cally cally condi characterizes judd judd predictable sity comm constraining computable steve tenth generaliza responded responded terminate impor ities undesirable imposing enabled dnf dnf dnf patterned eralization tant unlimited adap designated designated designated biasing ames solu solu comprise behaved seventh simu concluded concluded univer categorize categorized categorized categorized categorized indicative nique ist cate serially straints straints straints experimen jects jects sel assure draft aaa symptoms symptoms disjunctive tally bob nectivity individ ncc olution slo specifi bas apl bns determinants 
#@Gluck_M,Henkle_V,Pavel_M,
#t2
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm 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layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case vector vector vector vector vector vector vector vector vector order order shown shown shown shown shown values values values parameters noise weight weight functions functions functions unit unit unit unit unit unit unit unit distribution distribution recognition recognition pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image single single single single single single single large local neuron rate rate rate analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual examples examples examples examples examples examples feature task task methods methods methods cells cells cells points field field features features process level trained trained trained trained trained trained trained structure problems problems random random random random random high response response response response similar similar similar architecture show show fixed rule rule images images images images images general general parameter parameter approximation approximation average average average theory obtained note note note note note activity activity activity activity activity activity dimensional result solution research research research research research research log defined found found sequence constant estimate synaptic node science science left left left left left presented presented presented presented presented present present present low low frequency frequency press learn components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs sample abstract applied applied back back find find convergence properties references component due ieee ieee positive important important adaptive propagation introduction introduction estimation estimation behavior behavior behavior behavior effect generated variance variance variance variance variance change difference difference spatial assume assume lower measure representations learned learned learned learned chosen part part part center cases cases type cortex cortex cortex good long long represent represent represent make fact region region proposed proposed proposed correlation correlation correlation correlation correlation correlation correlation errors scale simulations minimum total total computed sum sum sum performed performed called elements elements elements mapping orientation applications knowledge knowledge knowledge obtain obtain negative negative negative original original original original artificial artificial artificial samples represented represented represented compared receptive receptive receptive receptive receptive receptive receptive receptive define compute proc proc proc location perform determined determined goal related related related related related mit mit mit larger fields fields fields fields fields fields update support train train nets report report department technique represents connectionist difficult difficult layers layers layers layers ai ai cambridge computing equivalent equivalent equivalent experiment hinton hinton hinton design san top bit bit detection conference conference efficient requires choice choice significant significant approximate basic pages pages pages give con produce produce produce produce coding coding coding coding criterion types types types types types types types types actual provided provided backpropagation backpropagation nature constraint biological feedforward feedforward feedforward describe describe limited stable predictions circuits common implemented shape generate supported square square pixel pixel pixel pixel pixel pixel ability ability ability makes rumelhart rumelhart development pairs pairs pairs combination combination block block interesting edge special principle principle principle principle principle principle principle principle principle principal principal squared squared squared squared squared squared iterations iterations window window bits bits bits bits bottom supervised depth idea minimize minimize choose choose choose recent property property pair similarity pixels pixels pixels cognitive compare previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised volume solve pca studies converge converge converge diagonal diagonal background generalized generalized generalized generalized generalized generalized generalized grid williams organization sensitive sensitive sensitive increased grant grant occur white setting pass half half half half conclusion row row greater hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian operator central central sigmoid sutton practice suggest propose proportional intelligence intelligence intelligence exist min decrease relationship averaged averaged program appears appears edges edges describes laboratory laboratory laboratory ann ann vertical multilayer linearly infinite interaction blocks blocks blocks john decreases yield national national review review reconstruction correlated squares detailed transform centered decomposition decomposition decomposition approximated converges allowed partial performing expansion false remains foundation foundation foundation expect perceptual usa perceptrons eigenvalues subspace sciences maximize maximize maximize maximal maximal poggio presentation detect detect literature identity orthogonal ten procedures heuristic interested neuroscience sin sci write dot dot dot dot surround nips minimizes computes denker thresholds cat principles consisted disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity decreasing oriented minimized selectivity diego steady steady association lippmann lippmann successive respond tech investigated scaled office maximizing maximizing maximizing maximizing eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors encode notion contours singular singular precise shapes switching utility submitted mentioned advanced rows rows rows rows rows variances variances variances coded coded coded nowlan nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity easier organized filtered division division desirable monkey scientific acknowledgement acad medical linsker linsker linsker linsker linsker linsker linsker auto author cybernetics qualitative argument people profile cmu lms remove measuring maximizes proven proven proven ordered ordered boston comments comments physiol converged converged converged summed cor uncorrelated uncorrelated uncorrelated uncorrelated uncorrelated uncorrelated uncorrelated cooper optimality optimality optimality optimality optimality optimality optimality optimality optimality optimality optimality investigation linearity member purely encoder encoder discover naval nonzero arranged lost binocular oja oja primate contract operates sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger bourlard bourlard intuitively intuitive natl widrow widrow stereo stereo stereo stereo nonlinearities nonlinearities nonlinearities entries multiplied multiplied express record rich specificity eigenvector projects summarize onr onr rms maintaining maintaining maintaining ple pointing fellowship planes aircraft munro encodes encouraging encouraging propagating pointed seek reconstruct reconstruct reconstruct quantized quantized quantized modifying graduate hughes pos rectified mask mask mask mask mask tract ward manuscript scanning scanning suggestions sigmoids bienenstock bienenstock interior tom puts svd svd possess agency meeting substitute sloan convolved convolved convolved convolved implied triangular vertically assp magazine steve defense hoff hoff talk sponsored imum tivity stereograms stereograms stereograms stereograms rectification rectification rectification rectification rectification rectification sible army ponent ire formalized karhunen karhunen masks masks masks masks masks masks masks masks masks 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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input input input input input input input input input data data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set set set set set set set set set set networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output number number number system system system system system system system system system error error error error error error error error error error error state state state state units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information problem problem problem problem problem problem problem problem problem problem problem hidden performance based based based space space space space space space space space space space space space space space weights weights weights weights weights linear linear layer case case case vector vector vector vector vector vector vector vector vector order order shown values values values values values values parameters parameters weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit approach approach approach point image single single processing control control control control control control local rate inputs inputs inputs inputs inputs inputs shows shows shows shows shows shows shows shows signal signal paper paper small small small small work work work work work task task task step step step step step points points points process process process process process process current current current current current current current current current current current current current current current current current trained trained trained trained trained problems problems problems problems random random random random random random random high high response response representation representation representation architecture show section section section section section section line rule vectors general general general parameter parameter parameter real real real average average average average average average states gradient gradient obtained term note university university computation computation computation solution solution research research defined defined defined defined defined found found target target target target target target target dynamics dynamics constant constant standard terms terms distance distance connections connections science science left presented presented map map map map map map present activation activation low machine sets maximum maximum range range learn position position position position position position outputs outputs outputs outputs outputs outputs outputs continuous abstract back back back back back back find computational convergence convergence references component due positive positive positive positive positive positive propagation propagation propagation context introduction action action hand hand behavior behavior behavior behavior behavior behavior behavior behavior stimulus effect dynamic generated generated parallel search search search search search search search search search search search search search search search tion change difference variable signals representations learned learned part previous previous previous previous previous cases good long represent represent distributed region correct correct observed errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors forward forward forward forward forward forward forward forward forward simulations minimum minimum resulting resulting resulting resulting resulting resulting resulting ing ing respect sum regions mapping mapping mapping mapping mapping mapping means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement feedback feedback feedback feedback orientation orientation applications knowledge negative negative negative negative negative negative negative negative negative negative specific specific represented compared desired desired desired provide compute compute compute objects location perform perform perform perform eye goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal related constraints gain motor motor equal steps accuracy comparison connection train descent descent dependent report institute implementation version technique internal internal joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint connectionist difficult final addition graph graph maps environment environment environment environment environment hinton hinton san stimuli effects determine determine determine requires requires significant world world world speed produce produce produce produce produce produce produce produce produce channel robot robot robot robot robot robot robot robot robot robot robot robot robot robot actual actual finally selected selected selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration iteration nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory constraint simply biological associative associative associative associative associative associative associative associative associative associative achieved achieved achieved achieved achieved achieved achieved achieved discussion discussion technical technical technical arbitrary arbitrary group denote denote limited limited limited limited close close inverse inverse inverse complete actions short generate generate generate generate end end future future future future rumelhart rumelhart rumelhart simulated simulated pairs needed needed reduced unknown jordan jordan edge head mechanism mechanism uniform uniform leads call iterations max max max max max max inhibition supervised early early decay idea combined choose run run discussed pair typical reported strategy moving include identical side sense cognitive cognitive relevant relevant relevant relevant relevant dimensions previously teacher teacher teacher teacher teacher tions solve definition positions positions positions positions positions positions positions locations locations locations generalized channels williams williams improvement arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm occur suggests predicted locally move occurs strength strength strength strength strength strength strength strength strength place reduce conclusions valued accurate asymptotic learns learns learns physics largest largest drawn demonstrated california california variety min min min averaged targets targets minima configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration question attractor attractor suppose suppose produces longer longer coordinates simultaneously linearly infinite easy slightly angle angle angle angle angle consisting integrated integrated shift quality competition decreases expressed depending communication communication influence influence open open similarly converges key reduces distances euclidean david avoid recorded perceptual perceptual activations activations formulation bell bell bell planning determining delta successful successful successful attractors situation situation situation essentially essentially traditional kind kind success success showing oscillations oscillations backward minimizes reach reach reach moves moves illustrates illustrates illustrates illustrates satisfies body explore origin diego create create rapidly rapidly relations strengths strengths strengths hanson hanson preliminary rise fashion ideas rest rest oscillation notion gradients gradients configurations configurations configurations configurations configurations configurations configurations psychology changed thought aspect front front explored initialized store serial slowly trivial defining failure failure lin easier producing strictly leaves arise angles angles angles angles angles angles angles angles angles angles angles angles beginning gradually arises recording recording demonstrates cybernetics radius questions greatly prop applies pure embedded posed posed posed share incorporated spread serve kinds display display display display display specifies multidimensional displays displays pole pose don don don don don don don don don don don don don don don don don don don don don don don don don don don don don mistake extensive extensive controlling discover grows grows reaching communications communications communications fails ments stronger ranges satisfying logarithmic familiar familiar hit observing monotonically planar selects selects performances interference equals equals displayed expanded expanded evident propagated propagated propagated spherical spherical spherical spherical initialize winning creating reveals record record jolla discovered discovered discovered discovered propagate propagate avoiding balanced limitation ics usage largely vec kinematics kinematics kinematics kinematics kinematics kinematics legal die causing personal personal personal superimposed big tor experiences possibilities rain peripheral summarizes goals goals goals goals goals goals depicts scope scope win constructs cartesian worth drawback apparently suffer exploratory failures failures failures answers answers answers unpublished emphasis tail laws characterizing ble reversed ping vis vis vis vis arrow arrow suffices tors burr burr integrates cally ackley ackley ackley ackley ackley ackley tip tip possess dissertation push joints joints joints joints joints cur approaching approaching suffice feldman feldman positioning twelve twelve twelve translate deciding rent limb subnetwork subnetwork subnetwork subnetwork subnetwork repetitions routine subnetworks subnetworks subnetworks rein occasionally miyata miyata miyata activa inability inability touch touch touch touch albeit darker posi grown pushed seeking translating translating supervision supervision environ temporary overshoot highlight closing successes standpoint possi cheap doctoral succeeded cited backpropagated manifest reachable logarithmically reuse governs imal stabilizes supplying supplying shadow commun shrinks shrinks downhill morristown morristown pursue forget grounds radians xls loc coordi scarce ata biggest exit usable reverses indications declines backpropagate backpropagate memorandum memorandum sti sti iol sophistication petitive nates orienting modi modi criticized attrac clip handed watching acldey acldey cry gles remembering remembering sixty matics matics limbs hills territory kine kine lvi pects anchor fori 
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time time time time time time time time time time time time set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number number number number system system system system system system system system system system system system system error error error error error error error error error error error error state state results results results results results units units units units information information information problem problem problem problem problem problem problem problem problem problem problem problem models models models performance performance based based space space space space space space space space space space space space space space space space space weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case case vector order order order shown shown shown shown systems systems systems systems systems systems systems systems values values values values values values values values values values values values values probability parameters noise noise noise noise noise weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution method method method method method method method approach approach approach approach approach approach point point point point point point point point point image image single single single processing processing processing processing processing processing processing processing processing processing control control control control control control large large large large large local local local local local local local local local rate rate rate test test analysis analysis class class class class matrix optimal optimal inputs shows signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple visual paper paper paper examples examples small size size net net methods methods methods methods methods methods methods methods fig cells points points points points points points classification classification classification process process process level level level level level level level level level level level level level level level level level level level level level level trained trained trained trained trained trained structure structure problems problems problems problems random random high memory memory response response response response response response response response similar similar representation architecture show equation equation equation equation equation section fixed line line line line line line line line line line general general general general general general generalization generalization generalization parameter parameter parameter real real real real real real real real real real real real real real real real real real real approximation approximation approximation approximation average average average gradient gradient gradient gradient obtained note note note note note note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional computation computation computation research independent defined defined defined defined defined found found found sequence sequence sequence initial constant table table table table table table table table table table table table table table table table estimate standard standard standard standard standard standard computer distance science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented presented presented present nodes nodes nodes nodes nodes machine sets maximum learn learn learn learn learn learn learn basis basis nonlinear nonlinear continuous continuous continuous continuous abstract applied applied applied applied applied applied applied back back back back back back back back back back back back back back back back convergence convergence references due ieee ieee ieee procedure procedure procedure procedure important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex complex behavior behavior behavior effect effect parallel cost search tion tion tion difference signals representations representations learned learned chosen chosen previous previous previous cases cases cases required required required required multiple good good good binary tree distributed equations fact techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques correct errors scale scale resulting classes classes classes ing ing total total total regression computed multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi sum sum sum sum sum sum elements regions regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping optimization dimension dimension dimension dimension made global applications applications applications knowledge knowledge filter filter samples represented application application application application application application application application desired desired desired series series series series series receptive perform perform eye determined connected brain equal power approaches approaches approaches approaches accuracy comparison comparison contrast contrast fields support support support support descent descent descent nets modeling morgan proceedings proceedings report report report internal code represents connectionist difficult final layers layers layers layers delay delay considered computing domain equivalent directly hinton curve curve curve curve estimates limit stage conference conference efficient requires approximate approximate statistics speed speed speed speed vision increase con coding developed levels levels levels levels criterion controller lines actual actual actual finally nature nature depends sampling sampling sampling achieved measured discussion technical technical technical increases arbitrary fast fast fast fast fast fast fast fast fast limited limited limited close inverse complete complete complete surface surface surface surface predictions finding common implemented require require face journal journal end ability ability ability ability ability future future future easily easily easily easily fit kaufmann simulated typically typically typically typically underlying needed reduced unknown fully interesting testing significantly significantly projection special special structures structures uniform database mode mode principle operation squared details details pre stored stored international normalized normalized normalized normalized normalized bottom supervised supervised magnitude magnitude polynomial minimize minimize minimize minimize choose run description description description predict predict predict predict perceptron perceptron architectures discussed improve recent correlations resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution exact separate ensemble takes typical typical include include quadratic quadratic hierarchical hierarchical trees trees sejnowski sejnowski sejnowski recently engineering dimensions dimensions dimensions highly varying varying conventional conventional module module tions yields yields correspond differential trans trans trans sparse sparse evaluation symmetric modified storage storage storage entire increased increased grant grant horizontal lead studied studied studied scaling deviation wide wide wide predicted predicted alternative locally locally locally locally touretzky generally column pass runs runs runs row greater reduce segment neighbor valued valued valued depend editors designed moody moody moody moody moody moody faster faster faster learns reduction sigmoidal demonstrated solid solid radial radial variety variety variety start minima identification configuration attractor acknowledgements reference explicit explicit explicit suppose suppose index solving factors primary laboratory laboratory tuned tuned tuned metric metric multilayer multilayer linearly physical dimensionality involves remaining easy text scales scales scales consisting predictive predictive minimization boolean boolean cycles john john letters yield national national review phoneme communication squares overlap detailed evaluated updated lee approximated sizes completely completely past past past spectrum partial earlier slow dashed classical spaces spaces spaces fitting fitting fitting fitting fitting fitting neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood intervals purpose boundaries boundaries interpolation interpolation interpolation interpolation interpolation interpolation initially assigned euclidean precision precision box priori priori priori formulation subspace subspace domains domains domains domains domains characterized characterized successfully regular sensor efficiency capable modification computationally computationally computationally included modes presentation presentation presentation presentation literature build efficiently efficiently situation tend miller miller miller ten fine fine fine fine fine fine fine characteristic capture traditional compact notice quickly graphs kind success dis lie running running physiological follow notation vary vary generalize generalize generalize absence observable thresholds overlapping illustrates subsequent neighboring deal software law body simpler unlike unlike unlike parametric access difficulty rapidly rapidly rapidly varied varied kalman kalman detail detail detail detail strengths replaced replaced limitations periodic helpful reducing successive respond respond school mappings mappings mappings mappings combine relationships relationships comparable complicated oscillation hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy surfaces coarse closest adapt adapt necessarily predicting predicting predicts spline spline extremely extremely extremely extremely extremely implementations implementations friedman formal formal noted assumes generates simplest contributions chaotic chaotic chaotic chaotic chaotic chaotic mentioned great publishers growing adjacent majority expensive glass glass glass glass caused benchmark lies london reasons comparisons rapid purposes purposes sys satisfied organized organized precisely immediately immediately projected universal universal universal circle english localized localized annual meaning meaning sun sun sun sun exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars conjugate integrating virtual virtual virtual virtual fuzzy fuzzy substantially amounts peter peter lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice orders orders adjustable splines splines formulated formulated continuously continuously continuously gen cal proven suited suited suited sums hamming comments comments begins converged converged converged multidimensional multidimensional multidimensional yielding instantaneous pyramid pyramid trade don picture discontinuities college accomplished accomplished accomplished accomplished gabor purely flexibility flexibility exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar robotics robotics robotics lost eliminated inspired inspired communications communications allocation consideration chance minutes minutes minutes darken darken darken overcome held determination moment los los los los resulted nearby monotonically imply excellent excellent excellent contexts cerebellar cerebellar introduces sion cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac guarantees intended intended intended vertices captured captured thomas offers offer repeatedly vertex proximity exploiting omohundro stone acknowledge fly limitation onr divide dense sequentially fitted rms mind yale approx summer piece piece achieving graded graded graded tables formulate isotropic encouraging chaos chaos personal hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies constitutes constitutes descriptions laplacian illustration rectangular rectangular mackey mackey mackey mackey mackey preserved community robots distribu graphics afosr books adelson adelson wise wise lookup lookup lookup lookup lookup lookup lookup lookup lookup lookup lookup lookup manipulator grateful lapedes lapedes lapedes lapedes lapedes dramatic drops drops intensive exploited corrections corrections corrections simplifies spite expansions chris gratefully fractal tom rosenberg multiresolution losing neighborhoods focuses lated spacing albus albus albus imple termination finer cast burr burr equa resolutions emerges automation alan resolved resolved robotic robotic dimen nettalk creation articulation articulation corn alamos alamos alamos alamos cyclic cyclic allocating capturing discovers sur costly hood applica retaining wiener haven intrinsically farber farber tenorio collision collision collision collision collision imation respects formulations schematically schematically eralization ninth classifica manipulators manipulators workers terry army gmdh gmdh mary univer olshen mexico mexico weaknesses qualities cate saving pervised disappears wadsworth queen coarser rameter strange purdue edward edward ficient disparate quired wasted insures casdagli casdagli collisions collisions fined byte farmer farmer farmer farmer farmer hashing hashing hashing hashing hashing 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set set set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number system system error error error error error error error error error error error error error error error error results results results results results results results results results results units units units units units units information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models hidden hidden hidden hidden performance performance performance performance performance based based based based based based based based based space space weights weights linear linear layer layer layer case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order shown shown values values values values values values values values values parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions unit unit unit recognition recognition recognition recognition method method method method method method method method method method method approach pattern point single single single single single single single processing large large large large large large local local local local local local rate rate rate rate test test test test test test analysis class class matrix inputs inputs algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper examples examples small small small small size net work work task task methods methods methods methods step step step step step features current problems problems problems problems problems problems problems problems problems problems problems problems problems random memory similar similar representation architecture architecture architecture show fixed fixed fixed fixed line line line line line rule vectors vectors vectors vectors vectors vectors vectors parameter parameter parameter parameter parameter real real real real approximation average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term experiments experiments dimensional university threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation solution solution solution solution solution research independent log log defined defined defined defined found found found found found target target target target initial constant constant table table table table table table standard standard terms terms terms terms distance node node node node science direction direction direction direction direction direction direction direction direction direction nodes machine machine machine machine machine sets sets sets sets press press learn position components nonlinear nonlinear outputs outputs abstract applied applied back back back back back back back back back back back back back back back back back back back back back back find find find find computational computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties references component procedure procedure important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex hand hand hand hand hand estimation behavior effect generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel cost cost cost cost cost cost cost search search search search search search change complexity rules measure measure measure measure measure representations representations chosen chosen chosen higher previous cases type required multiple good represent represent distributed expected make fact fact techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques region proposed length forward scale finite finite minimum minimum resulting ing tasks total total sum sum sum performed times times times times times times regions regions means means factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization orientation global applications study negative negative vol relative relative relative specific compared compared desired cross cross series define define define define define perform determined determined determined experimental experimental experimental goal mit mit larger connection connection connection connection connection connection descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent morgan morgan proceedings proceedings proceedings report department implementation implementation technique technique internal joint connectionist connectionist connectionist layers addition addition addition framework framework cambridge cambridge hinton hinton hinton hinton curve curve additional additional additional additional additional limit limit san san bit bit determine determine efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient upper full requires requires requires requires requires requires choice free world world estimated pages pages pages pages pages increase increase increase condition randomly randomly developed criterion criterion criterion criterion criterion bounds product finally backpropagation iteration iteration iteration iteration nature nature nature measured technical feedforward feedforward feedforward describe fast limited stable surface surface surface surface surface finding finding finding common effective effective implemented supported require require pixel pixel pixel ability instance easily easily easily easily makes makes rumelhart rumelhart rumelhart noisy noisy fit kaufmann kaufmann objective underlying needed needed needed needed needed combination combination reduced reduced programming programming programming interesting testing significantly significantly ratio character character character special trials trials trials trials trials trials trials trials empirical squared iterations iterations iterations iterations max max window window window normalized normalized decay decay decay decay attention advantage robust typical practical pixels sense cognitive recently sufficient sufficient compare solve match converge converge evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation williams storage storage storage storage storage storage entire grant trial wide derivative move column setting pass demonstrate half starting minimal minimal reduce reduce conclusions valued valued valued numerical 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describing computers meaning mellon researchers researchers conjugate conjugate conjugate conjugate conjugate requiring reflects carnegie summarized pittsburgh proven proven proven suited inherent age deviations progress converged wesley naive naive naive addison guarantee guarantee guarantee investigation rithm rithm approximates approximates count count encoder encoder encoder numerically interconnection exploit prentice becker becker becker mouse entry guarantees bad bad bad bad bad bad evident infinity infinity sim offers foundations refers steepest steepest steepest steepest steepest steepest steepest steepest steepest steepest steepest steepest erlbaum fahlman fahlman fahlman summer summer ple microstructure recursively incrementally incrementally acceptable lit classic massively geoffrey wall wall dominated considers parallelism parallelism speedup emphasized setup electronics memo sweeps travel characterizing jersey cliffs suffers termination concern eral supplied inherently 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activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine machine machine machine maximum maximum press learn components components outputs sample abstract applied back back analog properties properties references stochastic positive procedure procedure procedure procedure procedure propagation context introduction behavior behavior behavior behavior behavior behavior behavior effect generated recurrent search complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier 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called elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement optimization optimization potential made made made original original artificial application series provide compute compute compute active active active active active active active active related connected connected connected connected connected equal equal mit steps larger larger fields support source source source technique technique technique internal joint responses final final final final final bias maps maps considered framework cambridge domain equivalent environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment directly additional additional additional view solutions top bit bit bit bit bit bit conference conference determine determine determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers world give produce produce produce condition derived weighted weighted developed area types finally finally finally finally processes biological discussion feedforward describe group transformation transformation transformation transformation transformation transformation transformation transformation proof proof proof proof proof amount implemented assumed require character character mechanism mechanism matching matching matching matching matching operation operation bits bits bits international international magnitude magnitude produced produced choose choose choose run added added added description description description description predict population population population population population population discussed discussed improve element practical introduced include include side subset subset recently works match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match modified williams occur occur occur suggests feed generally pass half strength strength strength strength strength strength strength strength strength strength strength strength strength strength strength strength strength strength strength strength conclusion conclusion place greater conclusions operator operator operator operator operator sigmoid clear sutton suggest mechanisms mechanisms mechanisms external external cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle demonstrated intelligence turn turn assuming assuming relationship relationship introduce characters characters question question appears appears construct construct written written ways ways ways distinct implement implement transformations transformations interaction applying john john choosing choosing stages viewed viewed viewed open evolution forms suggested translation translation translation measurements add add add add tracking david david david recorded strings weighting weighting prove activated domains black discussions discussions characterized aspects differ successful post post post post post post post post post post post post post post post post post post post post post post post post post genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic composed composed composed composed procedures procedures procedures procedures link link link link link link link link link link link link quantity list list list list list list list list list list list list list write michael correspondence computes leading leading leading thresholds thresholds attempt receive receive employed employed employed carried carried production create create create strengths strengths issues matches matches matches matches matches matches respond respond fashion links links links links links links links links links links links links links links links links links links referred referred referred referred affect affect analogous matched matched matched matched matched matched matched matched matched matched neu induction hill extremely obvious portion formal formal noted initialized message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message submitted explanation explanation handle processed processed sections precisely operators operators commonly laboratories potentially members members members members preceding researchers researchers researchers passed employ employ remove treated passes operate incoming incoming incorporating extensions extensions richard richard replace boston conclude comments comments comments comments wesley displays don classifying sort sort sort sort proportion proportion proportion addison generator equivalence modify modify modify optimizing member count count count eliminate children children children children children climbing eliminated inspired consideration analyzing operates operates operates ral guide modifications modifications modifications modifications preparation carry carry carry alphabet alphabet child child wilson exploring paul holland holland holland expanded intended counting lawrence lawrence lawrence reader reader reader reader record rich environmental environmental environmental environmental environmental environmental environmental environmental environmental environmental environmental environmental environmental environmental environmental inductive messages messages messages messages messages messages messages messages messages messages messages messages messages messages messages messages reverse reverse davis davis davis davis davis davis davis davis papers papers parents parents parents parents parents parents parents parents divide boxes verify linked street leaving corporation benefits preserving preserving axe conjecture individuals care modifying modifying community evolve gained crossover crossover crossover altered employing paradigms attached turning indication port inactive gorithm strict technologies architectural handled handled handled excess january stochastically stochastically stochastically stochastically stochastically maze accomplish lists ron affecting conversion conversion subtracting goldberg goldberg deals inspection sending accommodate periodically raised raised pointer translate translate mutation mutation mutation winners ted altering intrinsically sends entities complications traditionally traditionally strongest strongest subtract paid translating exceeded exciting sorts sorts sorts latch reproduction reproduction reproduction reproduction reproduction reproduction supplies closing isomorphic isomorphic isomorphic isomorphic vation acti concluding organize invoked complication simplifications traversing latched latched concludes negation cycling markedly alterations alterations quotient favoring favoring belew belew belew belew refinements refinements ternary bbn bbn varieties benefited rig intemal craig superset companion companion stewart searchers reweighted mes import import weakest formalisms formalisms appropriateness sty 
#@Davis_L,
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#*network network network network network network network network network network network network network network network network learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time set set set set set set networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number number number number number number number number number number number system system system system system system system system system system system system system system system system system system error error error error error state state state state state state state state state state state state state state results results results results results information information problem problem problem problem problem problem problem models models performance performance performance performance performance performance performance based based based based based based based based space space space weights weights weights weights weights weights weights linear linear case order order shown shown systems systems probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions functions functions neurons neurons neurons method method method method approach approach approach approach approach processing processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis optimal optimal optimal optimal optimal form shows shows shows shows signal signal algorithms algorithms algorithms algorithms simple paper examples small work work work work work work work task step step step points points points process process process current current trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure random random similar similar equation section section section section rule rule rule rule images general general parameter parameter parameter real average theory obtained term term term term dimensional dimensional result university university variables computation log log log log defined sequence initial estimate estimate estimate estimate standard terms connections connections connections connections node node node node node node node node node node node node node node node node prediction prediction left presented low low nodes nodes nodes nodes nodes nodes maximum range components components components nonlinear nonlinear nonlinear nonlinear continuous sample sample abstract applied applied applied back find computational density likelihood references component stochastic stochastic stochastic stochastic due ieee important propagation introduction complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior behavior statistical generated generated generated generated search search search search search search search energy energy energy complexity complexity complexity complexity complexity variable variable variable variable classifier lower measure measure measure chosen part bound bound cases type multiple multiple conditions represent tree distributed bayesian equations fact techniques proposed proposed length length correct correct observed minimum minimum minimum resulting resulting total total regression respect called called called called called times elements mapping mapping optimization potential potential dimension made feedback global applications study knowledge filter obtain negative original original original original vol samples represented true true compared compared compared application application application desired desired desired series series series series series series series series series series compute compute proc discrete equal equal approaches accuracy accuracy accuracy comparison comparison comparison modeling modeling modeling selection selection version version version version represents final final final final final domain estimates stage efficient upper choice approximate approximate approximate estimated estimated estimated estimated basic basic basic give produce developed criterion criterion criterion criterion criterion criterion criterion criterion criterion types actual finally selected iteration nature discussion arbitrary arbitrary tested surface generate generate generate eds square square square future future easily degree including simulated simulated simulated simulated pairs pairs smaller smaller unknown coefficients fully transfer transfer transfer transfer transfer testing testing projection consistent consistent structures structures mode principle representing making normalized normalized supervised polynomial polynomial polynomial polynomial combined produced run run description description description description description description discussed directions separate strategy quadratic quadratic hierarchical hierarchical sense engineering engineering engineering dimensions dimensions dimensions dimensions dimensions dimensions compare previously observations observations observations observations observations volume differential differential definition evaluation evaluation modified modified modified modified modified modified observation generalized entire constructed constructed expression concept concept extended deviation wide predicted setting conclusion minimal minimal minimal greater neighbor accurate accurate performs performs moody moody temperature temperature temperature temperature drawn minimizing decrease iii iii iii iii manner connectivity connectivity identification identification identification identification identification identification identification identification identification configuration annealing annealing annealing annealing attractor construct construct index index index index index generating generating generating describes describes describes describes describes recall category electrical electrical formed quality implies versus estimator estimator estimator viewed viewed organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing lee lee lee lee lee forms allowed partial epochs epochs epochs epochs epochs sec sec sec sec sec sec sec sec sec penalty assigned construction construction construction construction construction advantages topology formulation assignment candidate partially characterized major simplicity simplicity modification computationally mackay mackay ten reached notice heuristic heuristic heuristic heuristic heuristic heuristic criteria gibbs relaxation consisted presents presents simpler schedule create create collection ml school school terminal terminal ideal root surfaces coefficient configurations equally prototype prototype front front front academic generates simplest simplest arbitrarily explain chaotic chaotic chaotic chaotic chaotic optimum stop trivial analyzed glass glass tool tool purposes organized organized incorporate ran pool universal demonstrates demonstrates requiring varies reflect flexible variant requirement operate fall parent parent parent parent geman geman simulator trade corrupted optimality linearity resources children accepted accepted interconnection interconnection primitive loops definitions guide guide child child child continue repeat repeat introduces conjunction dominant interconnections chooses initialize shortest shortest draw variants inf parents unable listed accept accept accept achieving recursively recursively creates terminals terminals terminals terminals terminals generalizations mdl mdl mdl mdl mdl mdl mdl mdl mdl mdl mdl mdl mdl mdl mdl mdl hundred adjustment favor pami pami searches guided constructs constructs pools ation lapedes lapedes lapedes lapedes lapedes restoration dim fractal rissanen rissanen rissanen rissanen rissanen usefulness autoregressive interpolate adjusts spirit accommodate demands sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn tim shares substructures farber farber farber farber farber tenorio tenorio tenorio tenorio tenorio tenorio kolmogorov kolmogorov accepting disadvantages optimizes rmse rmse mal acceptance opportunity tentative named cooling gmdh roots discard dam simplistic hierarchically hierarchically strange purdue purdue purdue purdue extrapolate fernando multilayered iee subsection subsection hypersurface hypersurface hypersurface hypersurface hypersurface hypersurface xlx xlx wei overlapped overlapped overlapped lafayette lafayette aixi automatica accesses lwl provisions 
#@Lee_W,Tenorio_M,
#t2
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural input input input input input data function function function function function function function function set set set set set set set set set networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number error error error error error error error error error results results units units units units units units units units units problem problem problem problem hidden hidden hidden hidden space weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer layer case case case case case values functions unit unit point point point point point point point point point point image large large large large large local local local local local local local local local local local local rate rate rate patterns analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal form form form form form form form form shows shows algorithms algorithms algorithms algorithms simple simple simple examples examples size size feature feature work work step step points points points points points points points points points points points features process problems random similar similar architecture equation equation fixed fixed fixed general gradient gradient gradient obtained experiments result result university defined found computer terms terms terms connections synaptic science direction map map map phase phase sets position abstract applied back back back find properties references references component component component propagation context complex behavior behavior tion tion variable variable assume assume assume assume lower chosen part type required multiple equations fact fact fact fact fact forward simulations minimum minimum minimum minimum minimum minimum simulation regression regression regression computed respect respect respect optimization natural global global global global vol vol relative true define define define compute rates related constraints constraints constraints constraints connected connection connection descent descent descent report institute words technique advances difficult layers layers layers layers layers layers layers layers layers layers addition addition ai ai ai curve additional additional view san effects full full full full full full requires con product product iteration iteration iteration depends constraint associative covariance describe denote denote denote tested fast proof assumed assumed generate supported main main square square noisy reduced coefficients coefficients technology projection projection projection principal principal principal principal principal idea description denotes directions practical side cognitive relevant teacher correspond converge converge converge achieve rl symmetric interval williams williams organization grant suggests matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices feed setting setting conclusion starting critical critical critical critical critical critical minimal greater hebbian depend constrained presence largest external reduction california california turn minimizing minimizing exist min connectivity connectivity connectivity minima minima minima minima minima question pro index index index index index index ways ways laboratory distinct remaining remaining easy easy unique unique unique unique unique formed yield stages stages squares updated centered calculation convex convex convex convex convex convex convex convex convex purpose remains includes perceptual eigenvalues eigenvalues eigenvalues subspace subspace characterized columns compression aspects presentation oscillatory projections identity orthogonal orthogonal orthogonal reached reached notice notice notice induced strategies satisfy notation vary usual usual absence absence eigenvalue eigenvalue satisfies satisfies diego layered investigate exhibit rapidly relations detail detail association issues existence examine examine examine fashion investigated proper eigenvectors eigenvectors eigenvectors eigenvectors func understand momentum smallest gradients gradients necessarily implementations rank rank rank rank rank rank rank rank rank expressions submitted defines optimum slope multiplication correction strictly strictly precisely hyperplane arise products linsker linsker auto auto nsf understood readily detecting ordered pasadena adjust cor ordinary ordinary saddle saddle saddle saddle saddle saddle saddle saddle saddle equivalence formally restriction fix discovery satisfying satisfying contract cottrell cottrell encountered demonstration entries emergence proximity extends eigenvector eigenvector eigenvector propagate intersection baldi baldi avoiding adopted adopted onr escape escape ics zipser constitute incorporates equivalently munro forced conjecture aij aij aij decomposed avoided publication iff iff iff modifying chauvin chauvin deep deep deep alternate impose learnt landscape exceed hornik conversely spanned spanned spanned worth responding admissible subspaces vice rewritten versa externally algorithmic jet invertible invertible invertible invertible spacing orthonormal compo propulsion transpose autoassociative bottleneck lar facts prescribed spa landscapes landscapes landscapes landscapes landscapes landscapes noticed nice iterates ily analyzer nent encounter positioned pierre amples particu gramming decomposing heuristically bet unreasonable attains attains ima terrain pression motivations collapsed propaga plication anymore pace dms trices multiplicity sharkey alp 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#@Baldi_P,
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural input input input input input input input input input input input input input input input input input input input input input input input data function function function function figure figure time time time time time time set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number system system system error error error error error error state state state state state results results results results units units units units units units units units units units units units units units information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case order order order order shown systems systems systems values values values values values values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method method pattern pattern pattern pattern pattern pattern pattern pattern point point point point single single single single large large large large large local local local local local local rate rate patterns patterns patterns patterns patterns patterns patterns analysis inputs inputs inputs inputs inputs form algorithms simple small small small small small size size size size feature feature net work work work work task task methods fig fig cells step field field classification classification process process process process process current current current current current current current cell cell problems problems problems random random random high memory memory response response response response similar representation representation representation architecture architecture architecture architecture section section fixed fixed rule rule rule rule rule general generalization parameter parameter parameter average average states states states states states gradient obtained obtained obtained note experiments result threshold threshold threshold variables variables solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution independent independent defined found found found found found found found found found found target target target target target target target initial initial initial initial constant table table table table table table table table table table table table table table table table table table table table table table computer science direction presented presented presented presented presented presented presented presented presented presented present present present range press learn learn outputs outputs outputs outputs outputs outputs continuous continuous continuous abstract back back back back back back find find find find find find find find convergence references due procedure procedure procedure procedure propagation propagation propagation propagation propagation introduction action hand behavior behavior effect generated generated parallel cost cost cost search search search tion rules measure measure representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations chosen chosen bound cases cases cases type required required required multiple multiple multiple multiple multiple binary binary binary long correct correct correct correct correct correct correct correct correct correct correct errors forward finite minimum resulting total total total simulation eq eq eq called times times elements elements elements means optimization made study obtain artificial desired desired desired desired proc perform determined determined determined determined related connected equal mit steps steps connection connection train train descent source source source source source source report institute department loss implementation version version version version version version version version consists internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal bias bias layers maps maps cambridge hinton hinton view view solutions limit limit limit stage stage stage stage stage determine determine upper requires requires choice choice choice choice choice choice choice choice choice free world basic basic produce condition randomly randomly criterion actual provided nature biological achieved achieved discussion discussion describe arbitrary arbitrary tested limited inverse assumption complete implemented implemented generate generate generate generate require require main makes rumelhart needed needed needed needed needed hopfield account interesting testing york york details pre stored bits bits bits bits bits attention combined combined produced produced run added added architectures architectures discussed directions directions exact ensemble ensemble takes takes typical typical similarity reported apply introduced introduced include subset recently sufficient varying compare teacher works works solve solve solve solve solve yields yields converge converge converge symmetric modified modified modified modified interval williams organization entire entire increased exists exists exists exists studied studied studied deviation feed feed feed column column setting hardware demonstrate runs starting starting place row row row row hebbian hebbian reduce valued valued sigmoid clear clear performs performs taking external cycle demonstrated turn turn turn minimizing minimizing start iii introduce introduce manner manner manner minima program force appears appears produces produces distinct changing multilayer category linearly involves slightly applying minimization minimization formed formed blocks versus cycles cycles cycles yield yield choosing focus stages viewed solved solved fraction sign sign sign reasonable calculate calculate sufficiently assigned views existing perceptrons assignment subspace subspace determines plotted reason maximal modification modification wij wij wij wij wij wij wij presentation computations composed kind induced cun cun prob success symmetry symmetry symmetry symmetry symmetry symmetry symmetry absence denker denker denker thresholds thresholds thresholds thresholds thresholds thresholds thresholds principles deal tesauro tesauro tesauro tesauro situations presents wiley wiley experience updating varied association optimized preliminary fashion tech applicable parity parity parity parity parity parity parity parity scaled proper proper fundamental plausible plausible integer integer integer integer integer integer created changed changed noted precise perceptton perceptton perceptton perceptton logic finds mentioned percentage site site rows stop developing separable fairly fairly failure nowlan briefly briefly correction comparisons sites easier constructing choices choices potentially separately explained varies cmu solla biologically biologically calculating howard measuring limiting extensions enables replace chose median median median median credit realized feasible accomplished guarantee modify modify tation tation pick optimizing partitions repre unity unity impossible connecting generality extending fails wrong wrong wrong wrong dealing accepted check check keeping fail loo entry widrow widrow percepttons percepttons schwartz searching belongs jackel enable israel offer ends draw broken integers insensitive lem sequentially sequentially constitute constitute session tables tables tables tables exhaustive exhaustive presenting presenting revealed guess guess guess imagine attempted increment increment modifying modifying execute searches flip flip flip represen represen electronics sweeps sweeps sweeps sweeps sweeps sweeps sweeps sweeps sweeps sweeps stuck indication parametrized round treating treating tin tin completed walk picking meir meir meir meir meir meir supplied appealing executing couplings corrective minsky minsky reflection lewis lewis restrictive sweep sweep tra vanishing occurrences insert inserted tal sentations accepting entities conceptually incident treats grossman grossman grossman grossman grossman grossman winter winter neurodynamics iterates rosenblatt rosenblatt rosenblatt plp serving contiguous flips domany domany domany domany domany domany predicate predicate predicate predicate bears rejecting chir chir plaut plaut arrived didn lea flipping flipping eytan unidirectional implausible contiguity clumps clumps clumps clumps ima iin spartan weizmann complez illl ili logically wasteful wittner adjacency ques rehovot inpu abort sour sour technological paperr paperr caught imax outpu worry blame tually preassigned isting 
#@Domany_E,Grossman_T,Meir_R,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input input input input input input data function function function function function function function function function function function function function function function function function function time time set set set set set set set set networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number number number number number number number number number error error error error error results results results results results results results units units units units units units units units units information information information problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer case case case case vector order shown systems systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method approach pattern pattern pattern pattern point point processing large large large large test test test test test test analysis analysis class class class class class class class class class class class class class inputs inputs inputs inputs inputs inputs form shows shows shows shows shows algorithms algorithms algorithms algorithms paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small size size size size size size size size size size size size size net net net net net net net net net net net net net net net net net net net work work work points points points points points points points classification process level structure structure problems problems random random random random random random random random random random random random random random random high high high similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show show section section fixed fixed fixed fixed fixed fixed fixed fixed rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech parameter parameter real real theory theory theory theory theory obtained obtained obtained obtained obtained term term note result result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation computation computation computation computation computation computation computation computation computation computation research independent log log log defined defined defined defined sequence sequence sequence sequence target initial constant constant computer terms terms node node node node node node node node node node node node node node node node science science present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine sets maximum maximum press press learn learn position sample sample sample sample sample sample sample abstract back back find find find computational convergence convergence density properties references component stochastic stochastic ieee ieee ieee propagation propagation introduction complex complex estimation statistical generated parallel parallel complexity assume assume assume assume assume assume assume lower lower lower lower lower lower lower lower learned chosen chosen chosen chosen chosen chosen chosen chosen chosen chosen part part center theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound cases multiple conditions conditions conditions represent expected expected expected expected expected fact fact fact fact proposed probabilities probabilities resulting classes classes classes total total regression computed computed computed respect performed called called called called times times mapping factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made natural natural applications applications study study obtain obtain vol artificial artificial relative relative represented represented represented define define define define proc proc goal related related connected connected connected distributions distributions distributions distributions distributions discrete equal approaches approaches mit mit accuracy accuracy larger support train source source source nets nets nets nets nets nets nets nets nets nets nets nets nets institute department version consists individual connectionist bias layers graph graph graph graph graph graph graph ai ai framework domain directly hinton san capacity capacity upper upper upper upper upper full choice choice choice choice choice choice choice choice choice free world increase increase give give give produce randomly randomly randomly developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds types types entropy actual actual finally processes backpropagation normal feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward describe arbitrary arbitrary arbitrary arbitrary denote denote denote denote inverse inverse assumption proof proof proof proof proof finding common theoretical theoretical end ability ability future future future future future future future future future easily easily rumelhart including underlying underlying underlying underlying underlying needed needed needed needed needed needed hopfield reduced coefficients fully fully fully technology technology technology interesting significantly york york edge edge edge edge special special consistent consistent consistent consistent uniform uniform database database empirical details making expert polynomial minimize minimize produced predict architectures architectures discussed recent exact pair pair takes apply apply introduced sejnowski sejnowski sejnowski interest interest sufficient varying approximately approximately approximately trans trans address address address grant exists exists exists exists deviation correctly correctly correctly correctly correctly correctly correctly correctly correctly occurs setting setting pass half half conclusion conclusion minimal greater greater greater greater assumptions valued valued valued valued sigmoid measures measures practice practice learns learns suggest taking physics largest largest drawn drawn drawn drawn drawn drawn drawn drawn drawn drawn california california intelligence labeled assuming assuming assuming assuming minimizing exist plane plane manner manner scene base base question question question question denoted acknowledgements appears derive construct edges edges edges edges edges edges edges edges edges produces produces ways ways ways factors generating laboratory distinct confidence confidence confidence multilayer linearly remaining slightly text frequencies frequencies applying applying events springer springer extraction boolean boolean boolean choosing choosing national independently independently dependence communication learner lemma open open restricted fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction forms suggested suggested partition constants earlier reasonable reasonable spaces spaces remains valid valid valid valid valid valid valid valid valid valid construction construction construction classified classified david degrees priori subspace determines vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik automatic automatic discuss specifically holds determining closely capable uniformly differ identify receives receives conf verlag verlag quickly kind procedures induced induced induced induced induced induced induced prob prob prob prob anderson dis issue classify classify classify classify classify classify hold hold comp play generalize generalize generalize computes denker ill attempt attempt load load load tesauro simpler remain diego exhibit experience exponentially exponentially exponentially exponentially helpful existence fewer fewer fewer fewer fewer giving tech tech rest int cover cover notion removed attributes math math predicting predicts subsets subsets obvious noted freedom explored expressions improving defines years inequality inequality directed agreement capabilities briefly baum baum baum baum baum baum baum baum starts considerable implementing closer protein worst arise read recognizing pure share solla haussler haussler haussler haussler haussler haussler haussler haussler haussler haussler haussler rep rep span howard ture incoming incoming incoming incoming ordered ordered comments implements irrelevant cor realized gap secondary secondary princeton princeton acm acm arguments appropriately establish stronger analogy logarithmic logarithmic hope hope hope removing fail definitions disjoint disjoint implications generalizes contexts slice slice slice corollary corollary corollary corollary corollary corollary corollary corollary corollary corollary corollary sion appendix conjunction widrow widrow widrow percepttons schwartz jackel counting spherical chooses advance treatment deg warmuth warmuth kearns proteins hypercube hypercube inductive santa santa santa santa hart intersection thresholding onr learnable divide geometrical ple largely logarithm logarithm logarithm chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis diverse axe conjecture conjecture lit lit lit personal classifies certainty certainty guess guess valiant valiant valiant valiant valiant eric backgammon backgammon verified verified shifting exam duda pami realizable playing learnability oct sketch sketch conversely conversely deleted spanned confusion nasa supports ignoring subspaces dichotomies dichotomies dichotomies dichotomies rnn suggestions gratefully dim dim dim january crude crude rosenberg jet families loaded loaded loaded doesn aid inequalities ron formulae val tribution dichotomy dichotomy dichotomy dichotomy ples architec cardinality cardinality cardinality outgoing littlestone littlestone occam shattered shattered shattered shattered approaching approaching approaching approaching approaching approaching rivest era comm protocol crl crl cruz cruz cruz cruz gence signed aip dent appro defense indepen acyclic shortly rem dence talk completeness sponsored stems plexity accu blumer blumer dependences ucsc ucsc thumb lay desire biophys perspectives fruitful bull ana associating dev dev dev logn razor closing cov cov amples permission vcdim administration revised sharper specialize ehrenfeucht ehrenfeucht ehrenfeucht adaline rectly zation quantifying hen hin hin hin phoneroes overestimate draft pollard visiting eli aeronautics initiative composing aloud devroye racy consid sink sink ern ern shatter confi counteract knew disjunctive sauer sauer wittner chances unavoidable selections wlog wlog attacked concomitant abound slicing slicing nick priate rum rum rum inl elect wid wid wid organi intelli strategic madaline disagrees reals whe innovative innovative reprint nem ley bitrary atio acknowl 
#@Baum_E,Haussler_D,
#t2
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#*network network network model model neural neural neural neural neural neural neural neural function function figure figure figure figure figure figure set set set networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number system system system system system system system state state state state state state results results results information problem problem problem problem problem problem problem problem problem performance performance performance performance based based based linear linear case case case case case case vector vector shown shown shown shown shown shown systems systems systems systems systems systems values values values values values values probability noise noise weight weight weight functions point point point point point point point image image image single single processing processing processing large large local local analysis analysis optimal optimal optimal form shows shows shows shows signal simple simple simple paper paper small net work work step step step step points field field field field field field field field field field field field field field field field field field field field field field field field field field field process process level structure problems problems problems problems problems random random high high high memory similar fixed fixed fixed fixed fixed fixed images general parameter approximation approximation approximation average average average average average average average average average average average average theory theory gradient term experiments experiments result university threshold variables computation computation solution solution solution solution solution solution solution solution solution solution log found found found found found found found found found sequence dynamics dynamics initial initial initial initial constant table table computer computer terms node node node node node node node science presented presented present present low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency motion range components nonlinear continuous abstract computational computational convergence references stochastic stochastic stochastic stochastic stochastic due due ieee procedure procedure procedure decision context complex behavior behavior behavior behavior effect effect effect effect parallel parallel parallel tion change energy energy energy difference difference lower part center previous previous required required required required conditions equations equations equations equations equations equations equations markov markov markov markov markov make fact fact techniques observed observed minimum minimum ing total computed performed times times means means optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization made global global study original represented compared compared application application cross compute compute perform perform perform determined determined determined experimental goal goal discrete discrete comparison update support descent report department implementation version technique consists advances final final exp exp exp exp exp addition graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph equivalent equivalent solutions solutions solutions solutions solutions limit determine requires speed basic increase con derived weighted weighted randomly clustering product provided depends simply biological achieved achieved achieved achieved arbitrary arbitrary corresponds complete circuits amount effective supported cluster cluster cluster including objective simulated simulated simulated simulated simulated simulated simulated simulated simulated probabilistic underlying needed needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield combination reduced technology transfer edge edge edge edge mechanism special trials operation operation leads leads iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations magnitude magnitude frame combined added discussed movement introduced array sufficient sufficient observations calculated tuning correspond differential trans chain chain chain chain entire concept concept studied occur deviation deviation move white occurs occurs setting starting critical critical critical critical assumptions conclusions faster faster faster faster temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature taking presence physics physics sigmoidal proportional assuming minimizing decrease decrease decrease decrease relationship relationship iii iii iii iii manner minima annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing force force force force force boltzmann van van van van van edges edges edges solving laboratory transitions dept dept dept dept dept changing involves easy interaction interaction equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium applying applying quality versus select decreases operations updated evolution updates processor processor past slow performing performing add iterative calculate advantages david degrees degrees formulation formulation formulation formulation sciences discuss coupled partially partially successfully selecting aspects closely uniformly divided situation tend miller miller miller miller miller essentially graphs graphs prob anderson anderson anderson anderson symmetry hold involved relaxation relaxation relaxation relaxation relaxation relaxation relaxation providing minimizes correspondence highest reach reach moves moves moves neighboring decreasing decreasing employed poor poor rapidly environments replaced replaced replaced optimized existence fewer fewer tech rest investigated analytically analytically office office referred comparable tanh tanh affect affect analogous examined examined math coefficient integer analyze opposite equally equally freedom freedom freedom initialized improving submitted submitted finds finds averages averages averages averages averages averages averages averages averages averages averages averages established optimum optimum optimum spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin slowly derivation derivation unstable adjacent adjacent analytic analytic analytic glass caused caused starts shared forces choices worst ridge ridge depicted cybernetics apparent empirically generic experimentally experimentally experimentally effort effort effort orders orders formulated compares gains gains partitioning partitioning characterize tank tank decreased attraction begins begins begins traces wesley wesley wesley naive lab equivalence formally martin drift bin bin bin tem communications simplify attractive attractive attractive imposed familiar balance contract mark north combinatorial combinatorial natl repeat programs iteratively respective negligible den den den den den thomas schedules peterson peterson initialize iterated iterated eng bins bins bins bins bins extends hypercube assigning temperatures temperatures temperatures ure ure break verified arising compensate annealed interacting interacting met maximally speedup zip holding mann resembles lems palmer palmer opti restoration restoration thermal agrees agrees insufficient solvable conceptual spins spins spins spins spins spins affecting concerns kirkpatrick hamiltonian iterating contents saturate began mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa mfa particles replaces objectives diverge relax altering mization attracted sat settles ece ece ece ece ece phil lowered lowered lowered kirk cooling cooling mag optimiza snyder snyder snyder icnn idealized endpoints trivially ising ising ising nected bout bout bout bout bout predominantly vecchi vecchi amorphous revealing nical freeze freeze combi mcc mcc portant disordered oak oak evidenced possessing gelatt hamiltonjan hamiltonjan hamiltonjan hamiltonjan speedups speedups thouless thouless patrick eration attains factoring distributing freezing effected balances completing carolina repulsive repulsive severity relaxes abruptly div escaping raleigh raleigh raleigh raleigh raleigh physicists quenched crt uphill perature bisection ements zed recast multiprocessor prescribes approzimation laxation laxation reinhold sequent 
#@Bilbro_G,Mann_R,Miller_T,Snyder_W,VandenBout_D,White_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural input input input input input input input input input input input input input input data data data data data data data data function figure figure time set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output number number number number number number system system system system system system system results results results results results units units units units units units units units units problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based based weights weights weights weights layer layer layer layer case case case case order order order shown shown systems systems systems systems systems weight weight functions functions unit unit unit recognition method approach approach approach approach approach approach approach approach approach approach pattern pattern single single single single processing large large large large local rate test test test test test form signal signal signal paper paper examples examples examples examples examples examples small size size net net net net net net net net net work work work task points features features level level level level current current current trained trained trained trained problems problems problems random random high high high similar architecture architecture show section rule real real real real real real real real states obtained obtained obtained obtained result research research defined found initial table table table table standard standard terms terms terms left left presented presented presented low frequency sets sets press press press learn learn position position position position position position position position position basis abstract applied applied back back back find properties properties references component due due procedure procedure important important important important important propagation propagation introduction introduction action complex hand behavior behavior parallel tion tion tion change learned learned learned chosen higher higher center center previous previous previous previous previous type type required required required required good good long represent represent make make make make fact proposed proposed correct forward scale ing ing ing ing tasks tasks tasks human human human human human human human human human human human human computed respect called called called means factor potential potential natural natural applications study policy knowledge knowledge knowledge knowledge artificial relative relative relative relative relative specific specific application application application cross proc perform perform constraints approaches mit mit comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison larger contrast train train train train train nets nets nets nets nets words words consists consists consists code individual individual individual individual individual individual connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult difficult difficult final final final final final final final layers layers layers scheme scheme scheme scheme addition addition ai cambridge domain domain domain domain design transition top full requires choice choice choice choice choice choice choice choice statistics world world world speed estimated increase give con produce produce produce produce coding coding coding coding coding coding developed levels levels levels actual actual selected selected simply simply achieved measured technical technical describe tested close complete main end future future noisy typically pairs smaller needed needed reduced reduced interesting significantly significantly edge consistent consistent consistent mode principle principal numbers numbers numbers experts experts experts supervised supervised expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert decay produced choose choose run added description discussed improve improve advantage takes practical introduced subject sense sejnowski array recently engineering interest interest varying compare compare previously previously teacher teacher teacher works tions match match correspond achieve evaluation evaluation evaluation evaluation positions positions positions positions positions positions positions positions positions positions positions separation improvement improvement studied trial alternative alternative alternative alternative alternative alternative alternative alternative alternative alternative feed move move move move move move move occurs generally half half half half strength conclusion greater reduce conclusions accurate numerical numerical numerical learns learns constrained groups connectivity base base base areas relation relation pro produces solving transitions sensitivity category category category category category linearly remaining easy develop select select select select select select choosing depending solved fraction fraction fraction understanding understanding key slow construction advantages recorded exploration box usa perceptrons coupled domains domains domains domains domains domains absolute absolute absolute absolute major determining closely capable suitable divided mcclelland schemes schemes schemes comparing score score score score score score score score score score score situation tend ten fine refer procedures contained dis issue issue symmetry symmetry symmetry lie sin categories list play play play play play play paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm board board board board board board board board board highest attempt moves moves moves moves preferred preferred preferred deal intrinsic intrinsic tesauro tesauro tesauro tesauro tesauro tesauro tesauro simpler simpler simpler create create experience difficulty involving involving humans limitations limitations game game game game game game examine biol scores scores scores scores encode understand understand understand fundamental naturally concepts extremely extremely thought rank rank rank rank obvious separated extent percentage great separable separable guaranteed guaranteed fairly improves tool worse reasons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons considerable considerable tive tive tive arc easier easier easier forces choices worst worst inversion involve recording author author raw raw explained requiring greatly consistency consistency consistency slower rely summarized measuring ture serve qualitatively substantial substantial substantial substantial simulator simulator logical sophisticated conclude eventually univ consistently benefit secondary guarantee guarantee guarantee guarantee ordering concerned concerned discover overcome satisfying stated resulted scoring scoring scoring scoring ral selects games games games games games games infor elimination ensures respective surprising surprising perfor sides regard bad bad bad counting thomas offers winning treatment specialized record record record snn matter repeatedly proteins papers default default default default limitation informa ure solves ent tables legal preferences preferences preferences preferences preferences preferences solely big backgammon backgammon backgammon backgammon backgammon backgammon publication ibm tems playing playing rejected unconstrained disease importantly importantly worth option emphasized alternatives alternatives alternatives alternatives alternatives alternatives alternatives alternatives alternatives alternatives alternatives alternatives alternatives enforce mea cube remarkable ble consuming agrees ping opponent opponent opponent err hid played concern concern illinois medicine distinguishing gram striking ally judged judged isolation proves minsky comm fin teaching creation est gammon raised bear ensuring watson ated indi huge spec tit tit ard gallant preferable judge rela miss dead invert enforced won sition sition entered posi tant vast ting thinking agation ative tot nation nation engineers previ seemingly henceforth constantly widespread teach perf perf perf mon gerald amples foreign economics crafted tha tha tha bout hoped havior realizes und orderings para knowl gle als sic consis ode tives tives qian yorktown dig vastly vastly alterna alterna alterna alterna tackled cid sured judgement parison rst tral logically chances severity netw netw netw netw netw netw engaged engaged decent nance nance evalu eff uninteresting sitions sitions sitions ined titis ial oval paperr formidable thinks unexplained 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#@Tesauro_G,
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set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number system error error error error error error error error error error error error error error error results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer case case case case shown shown systems systems systems values values values values values values parameters parameters parameters parameters parameters weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method approach approach approach pattern pattern pattern pattern point processing processing large large large large large local local local local rate rate rate patterns patterns patterns patterns patterns analysis optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs shows simple simple simple simple simple paper paper examples examples examples small small net net net net net net net net net net work work work work work work work work work work task task task task task task task step features features features features features process process process trained random random random random random random similar similar similar architecture architecture architecture show fixed rule rule rule rule rule rule rule vectors vectors vectors general generalization generalization generalization generalization generalization approximation approximation approximation average average gradient term note experiments activity activity activity activity result university university computation solution solution solution solution solution solution solution solution solution found target target target target target initial initial initial constant table table table table table table table table estimate standard standard standard standard standard standard standard standard standard standard standard standard computer computer computer terms terms terms terms terms terms terms terms terms connections connections connections connections connections connections connections science science science science presented presented map map present machine sets sets range learn learn learn basis basis basis abstract applied back back back back back back back back back find references procedure procedure procedure procedure procedure procedure procedure procedure important important propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex behavior behavior behavior behavior behavior behavior behavior stimulus generated generated parallel parallel cost cost tion lower lower rules rules rules rules rules rules measure measure measure measure measure measure learned learned chosen higher cases cases cases cases required required required required required required required good binary binary binary binary binary long long expected fact techniques techniques proposed correlation errors simulations simulations simulations simulations minimum minimum minimum ing ing tasks total simulation simulation simulation simulation human computed computed computed respect multi performed performed eq times mapping mapping means means potential made feedback applications study knowledge knowledge knowledge negative relative true application compute compute compute rates perform experimental related constraints constraints steps contrast connection connection connection connection train train train train train train train train descent source source morgan morgan report report institute department department version version technique technique technique technique technique internal individual individual individual individual individual individual advances advances represents connectionist final bias layers computing computing computing hinton hinton additional additional additional solutions san san effects bit bit bit bit bit bit determine determine determine determine determine approximate statistics statistics free speed basic increase con derived weighted developed criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion path actual actual simply measured measured technical feedforward describe describe tested tested tested fast close close complete stable common assumed assumed supported supported role require cluster makes rumelhart kaufmann kaufmann pairs smaller underlying needed needed reduced account coefficients significantly significantly increasing special details details max making making decay idea idea attention run run run improved improve correlations correlations separate takes element element reported reported reported identical quadratic quadratic hierarchical sense sejnowski sejnowski cognitive cognitive relevant relevant relevant relevant relevant relevant relevant interest sufficient highly conventional conventional conventional approximately tions solve yields organization improvement improvement grant grant grant lead studied derivative derivative derivative correctly correctly correctly correctly white white pass runs runs runs runs half flow strength strength conclusion critical critical minimal minimal minimal minimal minimal row row conclusions measures accurate practice learns learns constrained mateo mateo labeled labeled labeled assuming averaged introduce minima minima question acknowledgements explicit suppose appears pro construct construct construct index estimating metric metric metric metric metric metric metric metric category simultaneously averaging involves involves remaining easy text adding versus independently focus correlated communication communication influence influence open open open understanding understanding understanding understanding activities activities activities margin margin suggested updates allowed discrimination discrimination epochs epochs epochs epochs epochs epochs epochs epochs epochs epochs epochs epochs purpose remains initially initially construction foundation foundation david avoid avoid expect weighting mozer mozer mozer mozer mozer mozer mozer mozer mozer mozer candidate holds partially characterized successfully reason reason determining determining straightforward extra closely identify ten ten reached summary quickly quickly procedures strongly cun cun success success dis cue cue satisfy notation usual usual michael michael simplified play reach reach reach reach reach automatically automatically subsequent load load situations trains trains trains simpler poor essential experience difficulty exponentially rapidly put detail strengths replaced hanson hanson hanson fewer tech rest reliable comparable func cover understand phases removed removed removed smallest coefficient coefficient coefficient extremely changed thought adjusted obvious assumes improving improving mentioned stop trivial crucial distinguish failure failure failure failure failure failure adapted caused handle handle comparisons inside rapid constructing ran ran arise mation cut gradually gradually english qualitative qualitative nsf addressed researchers considerably reflect profile led relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance amounts leave car car car car car car car remove slower incorrect operate reaches reaches gen serve serve substantial logical logical attentional median median median median median median irrelevant pose picture secondary redundant redundant recover discover discover impossible eliminate smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky lost fails saturation consideration difficulties adjusting simplify balance resulted serves analyzing operates responsible presentations motivation repeat james iteratively paul paul negligible surprising pat colorado colorado accounts accounts den advance matter informative impact inductive designing grants discovered characterization drop unable sig basically basically removal removal removal presenting failed failed failed responds convenience par connec exception exception exception exception exception exception exception exception exception obtains additionally acceptable preferences ease generalizations personal personal assignments big big avoided avoided demon reflected eric attempted equality chauvin chauvin magnitudes geoffrey approxi continues boulder boulder eliminating eliminating eliminating iri nonetheless west west west west esti happen stuck stuck behave signs failures failures rewritten fat fat functionality functionality regularities excess handling twenty prefer rosenberg rosenberg mcdonnell terns east east east east east hid inclusion incorrectly dom assessment assessment assessment assessment proposes proposes triangle triangle judged pratt pratt pratt goldberg squashing scenarios outgoing outgoing arrives decaying sloan sloan constraining constraining thing compromise counted counted skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton experimented fore ming unnecessary began progresses assessing ton ece cancel conveyed dealt mal mention conversations yann yann retrained puted puted mate pri tially concise sky asso trimming trimming trimming trimming trimming trimming trimming trimming wji brains notational mary salience salience wishes enormous plex tain strated nique dave succeeded cri saving geoff trim trim trim trim trim trim trim skeletonization skeletonization skeletonization skeletonization skeletonization skeletonization skeletonization skeletonization skeletonization skeletonization skeletonization skeletonization skeletonization attend replications replications identi cedure twofold dominating memorize oot flipped distributing michalski michalski sooner ordinal speeding speeding ciated cer elaborated innervated discriminates pur contingent fifteen weightings reduc pronounce grossly founda cdr decline ned impression terion fluctuates erally underestimates disrupt qua moid obscured 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#@Mozer_M,Smolensky_P,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output number number number number system error error error state state state state state state state state state state state state state state state results results results results units units units units units units units units units units units units units units units units units units units units units units units information problem problem problem hidden hidden hidden hidden hidden hidden hidden based based space space space space weights weights weights weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters functions unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution method method approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single processing processing control control large large large patterns patterns patterns class class class class class class class class class class class class matrix matrix matrix matrix matrix inputs inputs form shows algorithms gaussian gaussian paper paper paper examples size net net work work task fig fig fig classification classification classification classification classification classification classification classification classification trained structure structure problems problems random random random random high high high high high high response similar architecture show rule rule rule rule vectors vectors vectors vectors vectors vectors vectors general generalization parameter parameter parameter real average average states states states states states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained term term term note dimensional result university university threshold variables computation computation computation computation research research research independent independent found found estimate computer computer terms terms connections science left left presented presented presented map map present phase activation activation low low low machine machine machine learn components components components components components nonlinear nonlinear outputs outputs outputs abstract back find computational convergence convergence density references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due positive procedure decision decision decision decision decision decision decision decision decision propagation propagation propagation propagation propagation introduction complex hand estimation behavior behavior statistical effect effect generated parallel cost search search change change energy energy energy energy energy energy energy energy energy energy energy complexity complexity complexity complexity complexity complexity assume classifier classifier classifier classifier classifier classifier classifier lower lower lower measure representations chosen chosen chosen center type required required required required required required binary binary binary binary binary binary binary binary conditions conditions distributed bayesian markov markov make make length length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed errors errors forward forward forward forward forward forward forward finite finite resulting classes classes ing ing total simulation simulation computed computed computed multi sum sum sum sum sum sum sum performed eq called called called called called regions regions mapping mapping mapping mapping means factor optimization made made feedback applications applications obtain obtain negative negative original original relative specific represented true true true compared compared compared compared compared compared desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired provide define define compute compute proc determined connected connected connected distributions gain gain gain gain gain gain approaches approaches steps accuracy comparison contrast connection connection connection connection connection connection update update descent source source report words loss loss internal final final exp bias bias bias scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme considered equivalent equivalent equivalent equivalent directly directly hinton hinton hinton hinton curve estimates transition transition transition limit determine determine determine efficient full full statistics statistics speed estimated give randomly randomly conditional conditional types lines lines product actual actual actual provided finally backpropagation backpropagation iteration nature nature constraint measured discussion technical increases describe denote denote denote denote tested finding amount implemented assumed assumed supported role role role eds journal easily rumelhart rumelhart objective simulated simulated underlying hopfield hopfield reduced fully block block block significantly increasing mechanism uniform principle principle operation details call call call call max making making making making inhibition minimize sources sources sources sources sources sources sources perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes exact property similarity lateral period machines machines sejnowski recently engineering dimensions varying tions match match correspond achieve diagonal diagonal diagonal diagonal diagonal evaluation evaluation evaluation chain symmetric symmetric modified observation williams increased increased increased expression expression expression concept matrices feed feed feed feed feed feed feed feed locally deterministic deterministic deterministic deterministic deterministic deterministic deterministic boundary boundary boundary generally column column column setting place greater valued valued competitive differences differences accurate performs exponential practice temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature suggest suggest propose taking hard hard hard hard cycle california california solid manner connectivity connectivity minima program annealing annealing annealing annealing denoted denoted denoted denoted denoted denoted denoted denoted denoted denoted denoted boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann explicit explicit suppose suppose pro pro monte carlo written written written longer winner winner winner winner estimating describes changing changing changing metric multilayer explicitly explicitly electrical involves remaining remaining remaining remaining equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium applying applying minimization minimization formed implies versus versus versus competition competition competition competition competition competition competition competition competition competition competition competition expressed expressed expressed overlap evaluated operations restricted restricted soft soft soft soft soft soft soft soft soft soft soft similarly similarly suggested partition partition partition partition partition partition allowed diagram diagram partial earlier slow dashed normalization intermediate sufficiently sufficiently foundation avoid figures figures priori usa bell illustrated specifically specifically major simplicity simplicity straightforward selecting computationally computationally computationally computationally computationally efficiently computations schemes score score essentially identity composed composed dis lie categories notation quantity simplified simplified play absence computes ill leading reach rat receive receive minimized origin unlike schedule layered layered create exponentially put strengths replaced recursive mass examine fashion fashion fashion links links applicable analytically decisions decisions decisions decisions decisions decisions scores scores scores scores phases notion gradients reading created perfect perfect quantities algo logistic logistic logistic logistic perceptton perceptton perceptton perceptton submitted defines pairwise formula separable defining fairly fairly slope slope expensive nonlinearity nonlinearity starts purposes purposes widely desirable controls probable probable probable scientific acad gradually depicted depicted meaning outer conjugate conjugate conjugate evaluating cmu capability capability red share marked slower ity ity schematic measuring substantial substantial expectations proposition proposition proposition proposition proposition wesley distortion distortion distortion instantaneous instantaneous trade ordinary benefit feasible feasible feasible feasible feasible feasible feasible feasible feasible accomplished addison equivalence restriction restriction rithm conditioned unity unity unity grows interconnected plays generality generality clamped clamped clamped multipliers communications attractive attractive resulted serves obtaining observing affected natl governed sion sion iteratively decide pat pat regarded percepttons interconnections interconnections offers steepest eqs partitioned partitioned santa explains propagate posteriori ure vec graded propagating pointed restrictions classifications classifications classifications decomposed decomposed tor avoided impose proba proba books scope win harder termed drawback drawback rewrite supporting wider completed ergodic satisfaction expense argmax consuming consuming bility thermal thermal thermal thermal thermal thermal allen attributed attributed terns terns virtually micro december supplied ackley ackley conversion conversion practically accumulate kirkpatrick kirkpatrick beneficial sym functionally functionally restricting restricting nontrivial sian fol absent deter gaus comprised mul indi 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#@Gersho_A,Yair_E,
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#*network network network network network network learning learning neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time set networks networks training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output output output output output output number number number system error error error error error error error error error error error error error error error results results results results results results results results results information information problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance based weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown shown shown systems systems values values probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions distribution distribution distribution distribution approach point single single single single single processing processing processing processing processing processing processing processing processing processing processing large rate rate rate rate rate rate rate rate rate optimal optimal optimal inputs form form form form form form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples small small net net net net net net net net work work work work task task task task task task fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step step classification process level level level level current trained trained trained trained trained trained trained trained structure problems problems random random random high high high high high high similar similar similar similar similar section fixed fixed speech speech approximation approximation approximation theory theory theory term term note experiments experiments experiments experiments experiments experiments experiments experiments result university threshold threshold threshold research defined found initial initial standard standard standard computer node science presented presented presented presented presented present present phase low low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency range range range range press position components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous sample abstract back back back back back back back back back back back back back back back convergence density references ieee ieee procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex complex complex complex complex parallel search tion measure signals learned higher center previous previous theorem required required required required required required required required required required required good long distributed region correct minimum minimum minimum resulting ing tasks multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi sum performed performed times times times times regions regions applications study study study policy filter filter filter filter filter filter obtain relative samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples desired desired desired desired desired desired desired provide provide provide provide rates determined gain equal equal mit connection nets modeling institute institute department technique internal connectionist difficult layers layers cambridge hinton curve curve curve curve curve curves design san top detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection determine determine determine determine classifiers requires requires approximate free world speed estimated pages pages pages increase produce condition channel developed levels levels levels levels product provided provided provided provided provided finally selected selected depends measured discussion increases tested close corresponds proof proof proof common effective require end rumelhart rumelhart objective objective typically pairs reduced reduced ratio ratio ratio ratio ratio ratio ratio ratio york york edge trials trials trials trials trials numbers filters filters international bottom produced added description perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron improved improved robust reported identical recently recently sufficient highly varying volume volume smooth smooth studies channels williams improvement sensitive amplitude amplitude horizontal studied deviation deviation deviation wide wide deterministic deterministic deterministic deterministic deterministic occurs demonstrate demonstrate demonstrate half greater editors accurate designed peak performs suggest physics physics reduction sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal demonstrated demonstrated demonstrated pulse pulse pulse pulse pulse pulse pulse variety plane force pro pro construct longer laboratory mathematical mathematical slightly integrated adding adding formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed versus select expressed forms forms approximated approximated approximated approximated approximated completely processor additive additive additive additive additive additive additive additive roughly roughly roughly roughly roughly roughly roughly purpose purpose filtering filtering filtering filtering filtering views transactions perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons inter inter inter inter plotted plotted plotted plotted variations selecting society included mcclelland essentially summary traditional anderson anderson sin duration duration vary illustrates explore explore explore diego american american american difficulty rapidly rapidly rapidly varied lippmann lippmann lippmann lippmann lippmann fewer fewer fewer fewer fewer links mappings mappings mappings mappings authors func momentum matched matched matched matched matched matched matched neu math editor editor editor extremely extremely illustrate equally front front impulse impulse detector detector detector explored optimum optimum advanced ment slowly slowly fairly waveform waveform adapted caused nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity comparisons rapid purposes widely preprocessing preprocessing preprocessing preprocessing preprocessing pulses pulses pulses demonstrates robustness improvements improvements greatly reflect double lms recordings passed dots sharp sharp ity poisson reaches proven acoustics acoustics richard substantial tile tile instantaneous discontinuities corrupted corrupted corrupted ear forming forming ratios ratios ratios ratios ratios arrival arrival arrival arrival communications air ranges promising analogy removing ral disjoint disjoint receiver receiver intuitive presentations constructive prentice ranging paul widrow percepttons nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities multiplied april april foundations projects propagate rms rms discriminate discriminate dramatically sig removal ties chapter flat demon laplacian realize arising cessing careful echo represen memoryless memoryless ation thousands lapedes lapedes nal dramatic drops exploratory october resembles palmer decided impulses impulses hilbert hilbert telephone adaptively adaptively adaptively fre agency huang receivers receivers resultant tations defense ated noiseless percep percep developments sponsored ceedings linearities hole hole hole rises rises lincoln farber quency 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#@Beckman_P,Lippmann_R,
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#*network network network network network network network learning model model neural neural neural neural input input input input input input input input input input input input input input input data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure time time time time time time set set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output number number number number number number number number number number number system system system system system system system system system system system system system system error error error error error error error error error error error error error error error error state state state state state state state results results problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden performance performance space weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer case case case vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown systems systems systems systems values parameters parameters parameters noise noise weight weight weight weight weight weight weight functions unit distribution distribution recognition recognition recognition recognition recognition approach processing large large large large local class class matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs form form shows shows shows shows algorithms algorithms algorithms simple gaussian gaussian paper paper paper paper examples examples examples examples examples small small small small net net net net net net net net work fig fig fig fig points current trained problems problems problems problems problems problems random show show show equation section fixed rule vectors vectors vectors speech speech speech speech average average average average average gradient obtained obtained obtained obtained term note note dimensional dimensional dimensional dimensional threshold threshold threshold threshold variables solution solution solution research research independent defined defined found found found initial initial initial initial initial initial initial constant constant constant estimate estimate estimate estimate estimate terms node node node node node prediction presented presented nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets sets press press components components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs abstract applied applied applied back back back back back back back back back back back back back find find find convergence convergence convergence convergence convergence convergence properties properties references component ieee ieee positive decision decision decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation context introduction complex complex complex complex complex estimation estimation dynamic dynamic dynamic dynamic dynamic parallel assume assume representations chosen higher center cases cases required required conditions conditions conditions conditions conditions represent represent distributed region region region forward forward scale finite classes total total respect regions regions regions regions regions regions regions regions regions mapping means factor dimension dimension applications knowledge knowledge knowledge filter filter filter filter filter filter obtain vol vol vol artificial artificial desired desired desired desired desired series series define compute connected gain gain discrete equal equal equal approaches mit mit update train train dependent nets nets nets nets proceedings report consists internal final layers layers layers layers delay sequences considered considered hinton hinton solutions solutions solutions solutions solutions solutions estimates estimates san conference approximate basic produce randomly conditional conditional conditional conditional conditional iteration iteration covariance covariance covariance describe describe denote complete implemented eds rumelhart rumelhart rumelhart including typically smaller smaller needed needed consistent structures squared numbers iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations international produced added recent element typical typical typical typical sense sense array interest dimensions compare compare previously works axis smooth converge trans modified observation observation observation observation generalized williams increased constructed constructed extended extended extended extended extended extended extended extended extended feed feed white strength conclusions tangent clear faster reduction reduction labeled labeled labeled assuming averaged averaged averaged derivatives identification identification identification mathematical multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer explicitly dependence dependence phoneme estimator viewed viewed solved evaluate fraction showed approximated converges converges converges converges converges converges updates updates partial filtering sufficiently figures figures perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons bell bell plotted automatic uniformly computationally computationally delta delta literature identity reached reached reached refer moore moore moore anderson anderson anderson stopping stopping criteria criteria absence thresholds consisted origin unlike diego layered poor xor xor xor xor xor xor kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman recursive hall fewer fewer fewer examine examine examine mappings relationships root workshop cognition momentum examined waibel waibel configurations adjusted versions versions taylor perceptton ith ith ith optimum slowly capabilities briefly handle nonlinearity nonlinearity sections satisfied widely located inversion fourth applies reflect axes backprop backprop backprop backprop limiting popular june june converged converged forming forming arguments jth jth unity connecting arranged communications communications consideration logarithmic held grow meaningful prentice lang percepttons propagated nonlinearities foundations eng implicitly explorations rms rms rms rms unable microstructure outline constitute randomized failed adopt obtains attempted attempted denoting expand kanerva scope termed sweeps sweeps sweeps thousands thousands atr october simplifies hyperbolic house termination fill loosely kth kth kth kth recursion recursion cast convention convention filling subscript sweep sweep sweep tens derivations shikano fallside fallside surrounded notational 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#@Singhal_S,Wu_L,
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number number number number number number number number number system system system system system system system error error error error error error error error error state state state state results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer 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signal signal signal simple simple simple simple simple simple gaussian small small small size task task task task methods step step points points field field classification process process trained random random random similar architecture show rule rule vectors vectors vectors vectors vectors vectors vectors real real real real approximation approximation gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient experiments experiments result university university variables computation computation computation solution research research research research independent independent independent independent independent found initial table estimate estimate estimate estimate estimate estimate standard computer distance distance connections node science science direction direction presented present present present sets learn components components components outputs abstract applied applied back back back back back back back back convergence convergence convergence analog references stochastic stochastic ieee positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure propagation propagation propagation propagation propagation propagation propagation propagation propagation complex hand estimation estimation estimation estimation effect effect variance cost cost cost cost cost cost cost cost cost cost cost search change change change change difference measure measure measure measure measure measure chosen center previous required required required required required required good binary conditions expected fact fact techniques correct errors forward forward forward forward forward forward forward forward forward finite simulations simulations simulations minimum resulting resulting ing ing total total total total total total total simulation simulation simulation respect performed performed performed times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made made global applications obtain obtain obtain negative relative samples represented true compared desired desired desired desired desired desired receptive receptive receptive receptive compute compute compute compute compute rates rates rates determined determined determined determined determined connected connected connected connected equal equal equal accuracy contrast fields fields update update train proceedings report institute department implementation implementation technique internal code joint connectionist difficult final layers layers layers layers layers layers layers layers considered directly directly directly hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton curve curve curve curve additional curves estimates estimates estimates estimates estimates estimates top effects effects effects determine efficient efficient efficient efficient efficient requires requires approximate world estimated estimated con produce robot robot robot actual actual actual actual actual finally iteration nature depends simply technical tested fast amount implemented generate require require require main main main main square end makes makes rumelhart rumelhart simulated simulated typically needed needed needed reduced unknown unknown unknown unknown fully technology interesting significantly significantly ratio character special special special special special special special squared squared details numbers iterations iterations iterations iterations iterations iterations bottom magnitude minimize run run added predict architectures improved improve directions advantage property takes typical apply pixels pixels array array varying approximately calculated solve solve solve solve smooth achieve diagonal address williams williams arm arm arm arm arm arm arm arm arm deviation derivative derivative derivative matrices predicted correctly correctly feed locally move hybrid hybrid hybrid touretzky width loop loop loop loop loop loop white boundary generally setting hardware hardware hardware pass pass demonstrate runs place assumptions reduce editors sigmoid sigmoid measures modules accurate learns constrained hard largest assuming minimizing decrease averaged derivatives derivatives derivatives derivatives relation digit digit digit digit derive optical optical solving estimating estimating implement implement multilayer coordinates coordinates simultaneously simultaneously averaging averaging linearly linearly linearly linearly easy scales minimization minimization national independently correlated correlated correlated squares variation variation variation variation detailed evaluate evaluate controlled centers centers activities activities activities completely digits converges updates reasonable reasonable calculation calculation barto barto performing iterative sufficiently foundation euclidean euclidean advantages classified transactions degrees degrees degrees avoid avoid avoid handwritten handwritten thesis bell assignment determines black regular efficiency closely capable encoded encoded modification divided wij computations essentially composed summary kind procedures procedures procedures procedures induced induced induced induced induced induced contained contained cun cun cun cun cun cun cun cun cun cun allowing allowing link sin involved computes leading received receive employed explore unlike layered perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation relations biases fewer fewer fewer reducing reducing successive school possibility comparable affect statistically measurement coefficient gradients gradients gradients gradients man changed implementations freedom initialized improving advanced ment slowly slowly cos separable track analytical analytical caused easier laboratories inversion inversion inversion inversion inversion acknowledgement separately angles angles angles angles toronto toronto attribute author cybernetics recognizing radius preceding preceding preceding exemplars considerably pure offset pseudo lms lms lms lms lms continuously passes passes passes passes passes perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations incoming incoming cal ordered suited simultaneous converged credit credit extreme consistently room ordinary newton uncorrelated college appropriately angular linearity linearity linearity repre impossible lecun odd fan los obtaining effectiveness modifications modifications preparation corner repeat started reset becker becker irregular iteratively iteratively induce induce overview injection injection lengths initialize matter repeatedly ends canada grants propagate avoiding convergent summer propagating perturbed perturbed perturbed perturbed quasi spaced spaced spaced param geoffrey geoffrey oct relate singularities relates paris rough associates emphasized funded esti sweeps eters correlate reinforce council quadrant king eliminates injected horizontally holmdel successively inefficient inefficient exploits vertically inde amenable resultant resultant resultant positioning elec sweep backwards deciding shares correlational dist linearities pendent vergence sentations ontario ontario perturbing perturbing perturbing yann mate oooo anandan anandan retains canadian owij allocate fellow unrealistic doctoral kauffman trigonometric ware galland galland galland galland galland galland galland degeneracy orient oxi oxi oxi oxi oxi oxi gan facilitated inaccuracies mor advan perturb perturb perturb engineer crawfords altos jnowski ooooooo tages inefficiency apprentissage sped 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#@Galland_C,Hinton_G,LeCun_Y,
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recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point single single processing large large rate rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis form shows signal signal signal algorithms algorithms simple paper paper paper small small size net net net net net net net net work work task task points points points points points points points points points points points points points points points points points points points points points points points points points points points points current current problems problems problems random random random memory memory memory memory memory similar architecture show show equation equation equation equation equation equation equation equation equation equation equation section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule vectors generalization generalization approximation approximation average average states gradient gradient note note note note result university university computation computation solution defined defined defined found found found found found target target target target target target target dynamics initial initial initial initial constant constant constant table table table standard standard computer computer distance distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections science science left left presented presented presented presented presented presented presented presented presented presented presented map present activation activation activation activation activation activation activation activation sets sets sets maximum maximum maximum range learn learn learn learn learn learn nonlinear abstract back back back back back back back convergence convergence convergence convergence convergence properties properties references ieee ieee important important decision propagation propagation propagation propagation propagation introduction introduction complex hand behavior behavior behavior effect effect effect recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion energy energy energy energy complexity variable variable assume signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals learned learned chosen higher part center center center center previous previous cases cases required conditions represent make make fact fact fact correct correct correct observed errors forward forward forward forward forward forward forward forward forward forward forward forward forward simulations simulations simulations simulations resulting resulting total total simulation computed computed computed computed computed sum called means potential feedback feedback feedback feedback applications applications study study study original true desired desired provide define rates perform perform perform determined goal constraints constraints connected connected connected connected connected connected connected equal equal steps comparison larger connection update update descent nets nets proceedings proceedings report report institute internal internal difficult difficult difficult layers graph ai ai ai computing computing experiment experiment experiment experiment experiment experiment experiment hinton curve curve curve solutions curves curves curves curves curves curves trajectory trajectory trajectory trajectory trajectory san top top conference determine speed speed speed speed increase condition lines path finally finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration iteration nature depends simply associative associative associative associative associative measured measured discussion discussion technical technical feedforward feedforward increases increases arbitrary arbitrary limited close close close inverse inverse inverse assumption assumption complete stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable actions assumed generate require main main main vlsi ability ability easily makes makes makes makes makes rumelhart rumelhart rumelhart smaller smaller smaller needed dynamical fully fully fully fully fully fully jordan jordan jordan technology interesting interesting interesting interesting interesting testing significantly projection york york special trials numbers iterations iterations iterations iterations iterations iterations iterations iterations making making international bottom bottom bottom supervised idea minimize choose description discussed advantage advantage property property property takes introduced moving identical recently interest interest highly varying previously previously volume volume volume volume module module module module module module module module module module module solve yields correspond converge converge converge address definition evaluation symmetric modified williams risk increased increased exists lead studied derivative correctly correctly feed feed feed feed feed feed feed feed feed feed feed occurs conclusion starting starting trajectories trajectories trajectories differences modules modules modules faster faster practice learns learns learns mechanisms california solid solid turn start exist targets introduce question question construct stability stability stability distinct dept changing missing missing sensitivity remaining slightly slightly unique implies depending viewed viewed interpretation variation evaluated evaluate evaluate operations updated updated similarly partial reasonable reasonable slow dashed dashed epochs epochs epochs epochs epochs epochs epochs epochs classical iterative initially distances visible visible visible sufficiently sufficiently advantages advantages advantages advantages topology topology degrees avoid activations activations eigenvalues eigenvalues memories memories memories plotted illustrated structural reason reason reason differ computationally effectively delta presentation presentation presentation successful build build build situation situation allowing success dis issue lie running oscillations content content content content content content content content physiological follow vary michael absence absence absence absence eigenvalue eigenvalue eigenvalue eigenvalue reach thresholds principles moves receive minimized diego create updating rapidly put limitations limitations dotted examine examine successive successive successive fashion school rest affect surfaces removed neu gradients concepts plausible illustrate ensure adjusted assumes assumes assumes logistic freedom perceptton epoch consist chaotic chaotic chaotic isolated massachusetts years great slowly cos formula asynchronous directed guaranteed unstable unstable unstable unstable unstable unstable fairly fairly improves answer expensive lies tool tool starts turns formalism arc arc organized precisely choices desirable simard simard simard simard simard simard simard projected arises depicted auto auto auto auto auto annual incomplete incomplete geometric varies limits axes simulate introducing introducing introducing completion incorrect incorrect incorrect incorrect incorrect rep execution anti incoming richard enables june synchronization representative corrupted corrupted corrupted restriction optimizing dynamically dynamically eliminate clamped clamped clamped clamped fails systematic systematic overcome odd exploit removing fail ral belong belong spurious spurious loo induce surprising guarantees searching propagated propagated competing reproduce multiplied specialized april 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#@Ballard_D,Oftaway_M,Simard_P,
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inputs inputs shows shows shows shows shows signal simple simple simple simple simple paper paper paper paper paper examples examples examples examples examples size size size size size size size size feature net net net net work work task step points features process process process level level level level current current trained trained trained trained problems problems random random random random random random random random random random random random representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show show section fixed fixed fixed fixed fixed fixed fixed line general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real real real approximation average average average average average obtained note note result result university university threshold computation solution research research research research log log log log defined found initial constant constant constant estimate computer computer science science left present present low press press learn learn learn learn learn learn learn learn learn learn learn abstract abstract applied back back back find find find find convergence properties properties properties references ieee ieee positive positive positive positive positive positive procedure procedure propagation propagation propagation introduction complex complex complex behavior parallel parallel change change change difference rules learned learned chosen chosen chosen chosen higher higher center center center center theorem bound cases type type required required required required required required required good good represent distributed expected expected expected expected make fact forward forward simulations simulations simulations simulations simulations ing tasks respect respect multi factor made made made natural applications applications study study study study study study study study study obtain obtain negative negative negative negative negative negative specific represented true desired provide gain mit mit steps larger train proceedings report report department version code difficult final bias bias addition graph graph graph cambridge cambridge domain domain domain domain curves design limit san top effects effects conference choice significant world world world basic basic increase increase give con randomly finally finally biological achieved achieved measured discussion technical technical increases denote tested tested limited close close surface surface finding finding amount common supported theoretical theoretical require makes rumelhart rumelhart rumelhart development objective smaller needed combination interesting significantly significantly york consistent empirical empirical details bottom supervised magnitude minimize choose choose perceptron improved improved improved recent exact exact property typical reported practical practical introduced include machines sense sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sufficient sufficient sufficient sufficient sufficient volume works works works tions studies studies studies achieve trans definition sensitive increased grant lead studied scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling occur suggests wide feed feed setting half half half conclusion conclusion starting greater assumptions editors sigmoid numerical numerical performs exponential faster learns proportional proportional variety variety exist decrease decrease decrease relationship relationship relationship relationship acknowledgements derive solving factors factors factors plot plot plot multilayer category linearly linearly linearly text consisting consisting applying events boolean boolean boolean cycles cycles select decreases decreases decreases decreases choosing choosing national national depending influence detailed fraction showed understanding understanding understanding understanding converges key event event event event remains remains calculate foundation classified box thesis perceptrons instances instances instances instances instances instances partially discussions reason reason reason selecting selecting selecting middle aspects extra importance computationally effectively mcclelland mcclelland mcclelland literature comparing characteristic composed notice contained heuristic showing return return comp notation play consisted tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro situations situations diego layered wiley difficulty exponentially exponentially issues issues issues mass mass helpful examine examine examine respond int relationships relationships relationships affect cover cover cover cognition fundamental notion closest plausible plausible equally perfect perfect perfect perfect perfect perfect changed changed changed changed changed thought quantities precise explored perceptton logic nervous initialized improving simplest simplest motivated averages years mentioned indicating indicating formula separable growth guaranteed guaranteed fairly fairly slope slope failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure analytic majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority expensive caused considerable straight formalism ran hyperplane commonly english author exemplars geometric questions applies substantially substantially treated compares measuring spread gen extracting popular incoming simulator unbiased guarantee tation resources perfectly perfectly perfectly perfectly perfectly perfectly turned clamped clamped systematic dealing odd abilities obtaining obtaining methodology monotonically intuitively intuitive generalizes heuristics substituting contexts separating separating percepttons uni originally facilitate barron foundations insight insight surprisingly theoretically correcting jump border border border border border border border border border border border border border border border border border border border border border border border border summarize summarize material explorations unchanged unchanged slight microstructure ahmad ahmad ahmad ahmad ber encouraging par generalizations generalizations generalizations constrain backgammon argue exponent exponent exponent care ibm alternate num carefully careful maximally represen portions misclassified misclassified 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algorithm algorithm algorithm output output output output output output output output number number number number number error error error error error error error error error error error error error error error error results results results units units units units units information information information information information information problem problem problem problem problem problem models models hidden hidden hidden performance based based based based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer case case case vector vector vector order order order order shown shown shown shown shown shown shown shown shown shown systems systems systems systems values values values values values values values parameters parameters parameters parameters parameters parameters parameters weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit recognition method method method method pattern pattern pattern pattern point point image single single processing processing processing processing processing processing processing processing processing large large large local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate patterns analysis optimal form form form shows shows signal signal signal algorithms simple simple simple simple paper paper paper paper paper paper paper small small net net net work work work work methods classification process level current current trained problems problems problems problems problems problems random high high response similar similar architecture architecture equation equation section section line rule rule rule rule rule rule rule rule general generalization parameter parameter real approximation theory gradient gradient gradient gradient term term term note variables variables research found target target initial initial standard standard standard standard standard standard terms terms terms terms connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science presented present phase phase phase phase activation activation activation activation activation activation activation activation low low sets range range press learn learn learn sample abstract applied applied back back back back back back back computational computational computational convergence convergence convergence convergence properties references component adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation propagation introduction hand hand generated parallel parallel recurrent recurrent tion change variable rules prior prior prior prior higher previous previous previous previous previous cases type type type type type required required represent represent represent represent represent distributed proposed proposed observed observed forward forward forward forward simulations simulations minimum resulting resulting ing ing simulation simulation computed respect respect respect respect sum sum sum performed performed means optimization optimization optimization optimization optimization optimization optimization made made made global global applications applications knowledge knowledge knowledge knowledge knowledge obtain negative artificial artificial relative compared application desired provide compute rates active determined connected comparison comparison comparison connection connection update update update update descent descent descent dependent source source source nets proceedings proceedings proceedings institute institute implementation synapses represents responses final final final scheme scheme scheme considered cambridge domain equivalent curve curve additional additional view view transition efficient requires significant significant significant significant significant statistics statistics speed randomly lines lines product selected selected selected selected evidence backpropagation iteration iteration iteration iteration iteration iteration inhibitory biological achieved increases transformation excitatory finding common synapse synapse synapse synapse synapse synapse supported role role role require require square square easily degree development simulated typically smaller hopfield functional fully fully technology technology significantly york york principle operation squared squared squared numbers numbers iterations iterations iterations iterations iterations supervised supervised supervised supervised supervised magnitude magnitude minimize neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal improved takes element element introduced identical works evaluation chain chain sensitive sensitive exists parts expression expression concept occur suggests extended deviation deviation deviation deviation derivative derivative derivative derivative feed feed feed feed pass pass strength conclusions sigmoid sigmoid sigmoid temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature reduction reduction reduction sigmoidal california california solid solid proportional decrease decrease decrease relationship connectivity minima minima minima annealing acknowledgements areas explicit explicit appears construct written longer primary primary sequential laboratory mathematical mathematical modeled recall recall implement physical involves involves scales scales consisting develop versus cycles cycles national national expressed formation detailed evaluate static key partial dashed dashed reduces advantages precision figures figures figures usa inter extension extension plotted plotted plotted plotted prove specifically specifically characterized characterized major determining computationally mcclelland computations reached characteristic characteristic characteristic capture capture contained contained prob allowing allowing showing lie device quantity involved paradigm backward backward processors xor xor xor xor xor xor updating updating updating strengths strengths optimized optimized recursive issues dotted preliminary fewer reducing fashion fashion fashion incremental investigated applicable parity presynaptic extremely extremely algo logistic freedom observe expressions expressions logic logic logic logic simplest contributions advanced pairwise pairwise agreement derivation tractable benchmark benchmark lies lies considerable implementing implementing formalism strictly strictly broad commonly products consequence involve begin begin optimize optimize definite summation requiring reflect led tional orders marked completion completion passed treated frequently sharp passes ture fall popular collective pasadena adjust realized secondary summing rithm narrow dynamically purely tem plays extending extending fan interconnection interconnection interconnection determination abilities wire wire substituting substituting passive passive published started ranging regarded regard captured propagated offers tic tic treatment neuromorphic neuromorphic offer arrows arrows steepest projects summarize lem temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures leaving drop drop numerous outperform sig deriving 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#@Tawel_R,
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hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear layer case case case case case case case case case order order order order order shown shown shown shown shown shown values values probability parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit distribution recognition recognition recognition recognition recognition method method method method approach approach approach point single single control large large large local rate rate rate rate rate rate test analysis analysis analysis matrix matrix form shows shows simple simple simple simple simple simple paper paper small small small small small size feature feature feature feature feature work work task methods methods methods methods methods methods methods step structure problems problems problems problems random similar similar similar similar similar similar representation representation representation representation show show show equation equation equation line rule rule rule general general general general generalization generalization generalization generalization speech speech speech speech speech speech parameter parameter average average average gradient gradient gradient gradient gradient gradient term term term term term term term term term note note dimensional dimensional university university variables variables variables variables solution solution solution solution research defined defined found constant table table standard standard standard standard standard standard standard terms terms terms terms terms connections science science science left range nonlinear nonlinear nonlinear sample abstract applied applied back back back back back back back back back back back back convergence convergence convergence properties references important important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction introduction introduction complex complex hand estimation behavior behavior behavior statistical statistical effect effect effect variance variance variance variance search search search search change difference difference complexity complexity variable variable spatial lower lower measure representations representations chosen chosen part center type required required multiple conditions conditions expected expected expected make fact techniques proposed proposed correlation correlation errors minimum ing tasks regression regression regression regression regression regression regression regression sum called elements optimization made negative relative samples samples samples samples compared compared desired provide define related constraints approaches steps steps accuracy larger descent descent descent descent dependent dependent technique consists internal connectionist connectionist difficult exp bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias layers graph framework domain environment directly hinton hinton design top top effects effects bit bit bit choice significant basic increase increase increase increase give produce derived weighted types provided finally nature nature nature increases arbitrary arbitrary arbitrary group group group tested surface surface require ability hypothesis rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart development objective simulated simulated typically smaller underlying combination reduced functional functional coefficients transfer transfer transfer transfer transfer testing significantly significantly projection special special uniform uniform leads bottom supervised supervised magnitude decay decay decay decay decay decay decay decay decay decay decay decay idea minimize minimize improved population discussed discussed improve improve robust robust typical typical typical reported introduced moving include quadratic quadratic subset cognitive cognitive recently varying compare previously solve solve speaker converge differential differential achieve rl rl diagonal diagonal diagonal definition separation separation separation williams williams improvement improvement lead lead concept concept suggests derivative derivative derivative derivative generally generally pass runs runs runs runs runs runs runs starting starting starting minimal minimal minimal minimal minimal minimal minimal minimal minimal greater reduce reduce conclusions exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential constrained strong drawn turn assuming minimizing minimizing plane decrease decrease decrease decrease decrease decrease introduce introduce groups minima annealing annealing acknowledgements explicit appears construct construct solving solving laboratory segments category category category involves involves involves adding adding adding extraction select john choosing correlated communication squares squares estimator estimator estimator estimator estimator estimator influence digits digits digits digits updates past past penalty penalty construction construction construction construction construction avoid exploration includes includes bell determines plotted discuss discussions tests simplicity simplicity determining determining effectively delta comparing comparing comparing comparing comparing comparing tend tend tend reached notice notice graphs kind allowing showing criteria categories categories categories usual usual usual board automatically attempt overlapping decreasing minimized explore explore explore xor exponentially updating updating relations estimators hanson hanson hanson hanson optimized optimized biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases examine ideas parity parity parity parity parity parity combine referred understand notion matched removed naturally singular singular obvious ith ith multivariate improving simplest established costs slope capabilities benchmark worse nonlinearity comparisons producing strictly desirable desirable sgn sgn immediately cut potentially potentially projected involve ridge members begin lowest geometry geometry exemplars exemplars requiring collected collected spoken spoken introducing introducing monotonic monotonic kinds kinds unbiased unbiased unbiased unbiased differentiable lab sort guarantee princeton princeton princeton princeton arguments resources member dynamically eliminate communications systematic consideration biased biased biased biased biased removing affected effectiveness intuitive motivation exploring exploring published induce histograms accounts uni counting counting counting counting tokens theoretically theoretically informative impact accumulated street usage usage achieving basically causing causing blue blue blue ease generalizations personal examining constrain verified rectangular exponent exclusive magnitudes impose token disadvantage concentrate individually cole confirmed nonetheless nonetheless apparently sweeps sweeps stephen hyperbolic hyperbolic hyperbolic hyperbolic hyperbolic hyperbolic hyperbolic hyperbolic hyperbolic hyperbolic hyperbolic jersey jersey jersey hoc supplied burr concerns kirkpatrick kirkpatrick pratt pratt pratt pratt pratt inefficient tended tended tended decaying decaying comer cuts cuts cuts cuts derives derives replication replication mesh mesh mesh mesh unnecessary gradual retaining preprocessed 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#@Hanson_S,Pratt_L,
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#*network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function figure figure figure time time time time time time time time time time set set set set set set set set networks networks networks algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output number error results results results information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models space space weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer case case case case case case case case vector vector vector vector order shown shown shown shown systems systems systems systems systems systems systems systems values values values values values values values values values values values values values values probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight functions functions neurons unit distribution distribution distribution method pattern point single single single single single processing processing processing processing processing processing processing control control large large large large local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs form form shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small methods fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points field field features features process process process process process process process level level cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell problems problems random random random response response response show section section section section line line line vectors general general parameter parameter parameter parameter real average average average states theory theory theory theory gradient gradient obtained obtained obtained term term term term term note note note activity dimensional dimensional result variables variables computation computation solution solution solution solution solution solution solution solution research independent independent independent log defined initial constant constant estimate computer terms terms terms terms terms distance connections connections connections connections connections presented presented present present phase phase phase phase temporal temporal temporal temporal maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum range range range range press position components components components components nonlinear continuous abstract applied applied applied applied applied find computational density properties properties properties references component context introduction complex complex behavior behavior statistical effect effect effect effect effect dynamic variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance cost change difference variable spatial lower measure measure signals chosen chosen higher center center center center center center previous previous previous previous bound cases cases cases cases cases cases cases firing required multiple multiple multiple long conditions conditions conditions conditions conditions conditions conditions conditions distributed make make make fact region region proposed correlation length scale resulting resulting resulting total total called called times times times times times times elements mapping mapping mapping mapping mapping means factor factor factor optimization optimization optimization made made natural feedback global applications applications filter negative relative relative relative relative application series receptive receptive receptive receptive provide define define compute determined determined related constraints constraints constraints constraints constraints gain gain gain discrete discrete equal power power steps steps steps larger contrast contrast connection fields fields final exp exp exp exp exp exp exp exp delay considered computing equivalent environment directly curve curve curve curve curve curve curve additional additional additional additional solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions design limit limit stage effects effects capacity capacity choice choice choice free increase increase increase increase produce condition channel channel channel channel derived derived randomly conditional criterion lines lines lines lines entropy entropy actual provided provided selected selected inhibitory inhibitory inhibitory inhibitory inhibitory constraint constraint constraint constraint constraint constraint biological biological biological biological biological biological covariance covariance covariance covariance technical increases increases arbitrary arbitrary arbitrary arbitrary arbitrary limited corresponds excitatory excitatory excitatory short short common generate role end future easily noisy smaller combination combination account transfer transfer character increasing uniform principle principle principle principle principle principle principle principle principle principle principle operation operation leads details max filters filters filters pre depth description denotes discussed discussed discussed discussed discussed discussed recent property ensemble ensemble ensemble ensemble practical apply include include include subject subject identical identical identical identical array array previously approximately solve yields yields yields achieve definition modified generalized bounded bounded interval interval organization sensitive sensitive increased increased increased expression expression studied studied occur extended derivative derivative locally move boundary boundary column setting setting pass starting central central central differences differences sigmoid numerical peak peak peak peak constrained constrained constrained constrained suggest encoding taking physics largest drawn solid solid solid solid turn turn iii averaged manner denoted suppose suppose derive longer solving ways mathematical mathematical recall implement explicitly explicitly simultaneously text text develop mutual mutual versus john decreases yield choosing choosing independently reconstruction reconstruction reconstruction reconstruction correlated correlated correlated correlated correlated correlated correlated communication communication overlap viewed viewed solved transform transform activities activities completely allowed allowed allowed allowed allowed allowed past past spectrum diagram earlier earlier earlier calculation additive additive reduces intervals add intermediate intermediate intermediate expect box includes perceptual eigenvalues eigenvalues eigenvalues eigenvalues discuss maximize maximize maximize maximize maximize maximize maximize variations variations characterized characterized determining straightforward aspects uniformly uniformly computationally literature situation plots tend characteristic capture summary anderson interested interested issue lie contribution oscillations oscillations hold satisfy notation quantity quantity localization realistic realistic realistic surround surround surround surround surround minimizes minimizes attempt extract deal deal situations simpler layered wiley difficulty rapidly replaced limitations dotted dotted dotted dotted hall periodic periodic scalar fourier fourier mappings mappings mappings reliable maximizing comparable affect encode understand phases phases phases naturally transmission transmission plausible integer analyze analyze predicting illustrate noted expressions expressions multivariate simplest contributions arbitrarily arbitrarily arbitrarily explain motivated motivated defines synthetic theoretic analyzed defining adjacent analytical spatially spatially spatially sections satisfied consequence localized localized linsker linsker linsker linsker linsker linsker linsker linsker linsker requiring requiring evaluating applies substantially led passed remove treated biologically biologically biologically biologically biologically biologically maxima maximizes resource redundancy tolerance progress univ distortion distortion distortion distortion distortion corrupted uncorrelated lagrange fix temporally temporally temporally reconstructed unity addresses nonzero multiplier numerically convenient convenient occurred occurred analogy analogy nearby nearby nearby eqn eqn eqn eqn eqn eqn eqn eqn eqn eqn eqn motivation motivation prentice ambiguity ambiguity ambiguity ambiguity negligible sides ascent ascent facilitate competing arrangement multiplied ensembles insight smoothed smoothed smoothed smoothed extends sons pdf pdf pdf displacement displacement limitation infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax unchanged multiplying yielded shorter equivalently equivalently maximized uniquely uniquely seek tradeoff spaced spaced remote remote constrain favor modifying ibm shannon shannon shannon shannon shannon impose impose impose impose march simplifying increasingly increasingly complementary indexed weaker weaker nonetheless diversity denver figs exhibited det prevents rewrite simplifies infinitely shallow resembles replacement regularities nonnegative marks water water water water water jointly jointly cliffs spacing identically illinois affecting pronounced pronounced periodicity periodicity englewood preservation preservation preservation preservation preservation preservation preservation deals deals constancy transpose filling filling goodness goodness demands restrictive locality enters inst prescribed convey convey watson amer favors favors urbana assessing lid ansatz ansatz heights nov superscript imposing hypothetical berger berger ago ago nth nth ordinate penalizing brings ralph unrelated normalizes arrangements gallager gallager discriminated favoring favoring favoring favored rewriting contrasted yorktown instructive mil mil unnecessarily fixes chap complicate weaver resolves sii shallower shallower confounded lil attenuate noisier 
#@Linsker_R,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input input data data data data data function function function function figure figure time time time time time time time time time time time time time time time time time time time time time time time set networks networks networks networks networks networks training algorithm algorithm algorithm output output output output output output output output output output output output output number number number number system system system error error results results information information information information information information information information information information information information information information information information information models models models models models models models models models models models models models models models models models models models models models models models models based based based space weights weights weights weights weights weights weights layer order order order order order shown shown systems systems systems systems systems systems systems systems systems systems systems values weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions neurons neurons neurons method approach point point point single single processing processing processing large large neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate analysis class class optimal inputs shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple visual small small small net net net net net net net work methods methods methods methods methods classification process level level level level level current current current current cell cell problems memory memory memory memory show show show show show equation equation equation line line line line rule rule rule rule rule rule general general generalization real real real real real real average theory theory theory theory theory theory theory theory theory theory note note activity activity activity university university threshold threshold threshold threshold research research research defined defined defined defined found constant constant constant constant estimate computer terms terms terms terms terms terms terms terms terms connections connections synaptic synaptic synaptic synaptic node node science science prediction prediction prediction presented presented present activation activation activation activation activation activation activation activation activation activation activation activation low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine range range range press press press press press press press press press press press press press press press learn continuous continuous abstract abstract applied back computational computational computational computational analog analog analog analog properties properties properties properties properties references component due positive positive positive positive positive important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision propagation introduction action action circuit circuit behavior behavior behavior stimulus stimulus effect effect generated generated parallel tion tion tion tion change change change change difference difference difference difference variable lower lower rules measure measure signals signals representations part previous bound firing firing firing firing firing firing type cortex good represent distributed equations equations make fact proposed proposed proposed proposed proposed proposed proposed proposed observed errors errors minimum ing ing simulation simulation human human regression multi multi sum sum called reinforcement reinforcement potential negative original vol vol relative relative true application series series series series series compute rates rates determined determined experimental related constraints constraints constraints discrete discrete discrete brain mit voltage voltage accuracy comparison contrast update modeling proceedings proceedings proceedings institute institute department version version version synapses synapses synapses consists consists internal individual represents connectionist connectionist connectionist connectionist connectionist responses difficult delay addition graph graph cambridge cambridge cambridge cambridge computing computing computing computing computing computing experiment directly hinton hinton san top stimuli effects conference conference conference determine determine basic basic basic increase con con con con produce coding coding coding coding coding coding coding coding coding coding weighted weighted weighted levels levels levels levels levels levels levels levels levels levels lines path actual provided nature nature inhibitory inhibitory inhibitory inhibitory inhibitory depends simply biological biological biological biological biological biological biological biological associative associative associative associative discussion increases increases describe describe close complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable stable stable predictions predictions circuits amount effective effective synapse synapse synapse synapse synapse synapse synapse synapse supported eds eds eds eds eds eds eds face adaptation journal journal ability ability easily degree rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart fit simulated underlying underlying jordan york york york york increasing mechanism structures trials trials trials trials operation language representing representing details direct window magnitude magnitude magnitude decay decay idea idea produced added predict neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal improved improve recent exact advantage separate introduced cognitive recently engineering engineering engineering highly calculated calculated calculated calculated calculated volume tions differential differential differential differential differential differential interval interval interval williams williams organization grant occur occur occur trial wide wide wide derivative derivative derivative derivative derivative derivative occurs generally generally strength conclusion conclusion critical assumptions assumptions assumptions assumptions hebbian hebbian hebbian hebbian hebbian hebbian hebbian valued valued depend depend depend differences differences differences differences differences differences sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton encoding mechanisms presence physics cycle characteristics characteristics demonstrated california solid solid pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse decrease derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives construct produces longer solving ways ways ways factors mathematical dept category electrical interaction develop develop integrated frequencies frequencies frequencies frequencies predictive expectation expectation review review correlated communication variation evaluate evaluate evaluate evaluate constants key earlier earlier calculation calculation barto barto barto barto barto barto barto barto dashed dashed classical classical classical classical classical classical classical classical classical classical classical classical classical classical sufficiently advantages david fire inter determines variations black simplicity reason society modification mcclelland successful computations computations reached summary graphs procedures contained neuroscience neuroscience neuroscience neuroscience sci absence realistic realistic delayed correspondence denker received received subsequent acknowledgments decreasing oriented trains trains remain diego american wiley exponentially involving involving integral accurately dotted mass hall postsynaptic postsynaptic postsynaptic postsynaptic successive ideas behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral incremental possibility relationships office reliable proper encode presynaptic presynaptic presynaptic presynaptic cognition analogous neu hill hill coarse transmission transmission transmission transmission necessarily predicting predicts psychology psychology psychology psychology illustrate thought adjusted aspect obvious formal formal noted panel hebb hebb hebb academic art switching utility motivated motivated electronic established animal animal animal animal years residual vor developing formula unstable unstable phenomena phenomena fairly coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded coded analytic capabilities capabilities baum comparisons stanford stanford stanford closer easier easier easier precisely precisely pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses involve involve calculations begin read annual annual addressed researchers summation integrating apparent varies varies evaluating reflect empirically empirically relevance offset pseudo simulate car formulated formulated formulated formulated formulated continuously biologically reliability psychological psychological operate summarized extensions richard richard logical tolerance conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning specifies gap acquisition acquisition acquisition cooper cooper tation extensive temporally conditioned conditioned count tem tem naval grows theories theories adds adds bower bower bower bower occurred tools attractive efficacy efficacy efficacy efficacy efficacy efficacy hope nearby mark mark neurobiology receiver receiver receiver receiver implications implications implications implications effectiveness motivation motivation motivation reliably cerebellar governed equals equals evident evident widrow widrow consequences facilitate lawrence lawrence lawrence lawrence lawrence reproduce bases similarities enable enable foundations creating record draw draw extends erlbaum erlbaum erlbaum erlbaum impact sons papers avoiding explorations speaking fired fired informa yielded ple specification specification microstructure constitute incorporates ties transmitted transmitted abstraction abstraction england hillsdale hillsdale hillsdale hillsdale hillsdale molecular auxiliary eric alter insights werbos werbos faults interacting altered gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck noting conversely represen associates associates associates associates associates isi isi reveal electronics ation places els radio supporting examination examination spite moderate drives appearing algorithmic justified loosely harvard calculates fre condi condi seattle unreliable dissertation equa proposes proposes marr offsets mcnaughton mcnaughton outgoing volts convention convention neurobiological sity leakage leakage leakage drastically communicate longest longest elec aip modern transmit transmit transmit bear bear bear facts parker parker parker parker parker parker parker parker parker parker parker parker hoff hoff subtle subtle tory wagner wagner wagner wagner preferable preferable expresses simula activa plausibility lynch lynch bio quency impor formulations decrement klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf klopf tant thompson thompson thompson thompson thompson thompson thompson thompson thompson thompson thompson thompson engineers electrically impressive synapfic synapfic poral poral poten panels earning pared analogously univer nectionist nadel nadel ences economics govern volt accelerate doctoral accelerated efficacies occuring lend awi awi awi awi granger granger indebted incor unconditional sudden reformulation reformulation reformulation reformulation emitted reformulated reformulated plete intriguing tives differencing axi axi crosstalk crosstalk alters western deriva stably puting transmits transmits harry parison extinction extinction extinction extinction eee century hawkins inhibi css propaga rescorla rescorla rescorla rescorla ouput bart 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output output output output output output output number number number number number number number number number number number number number number number system error error error error error error error error error error error results results results results results results results results results results results results results results results units units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based weights weights weights weights weights layer layer layer layer layer layer layer layer vector order order order shown shown shown shown shown shown systems values values values probability probability unit unit unit unit unit distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach pattern pattern pattern point control control large local rate rate test matrix matrix matrix matrix inputs inputs inputs shows shows shows shows shows shows signal signal signal algorithms gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper size size work work task task task task classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process trained trained trained trained trained trained structure structure structure structure problems random response response similar similar representation representation representation line vectors vectors vectors vectors vectors vectors vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech average average average average gradient obtained experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional research research independent independent independent independent independent found found table table table table standard computer distance distance distance connections connections connections connections connections connections connections connections connections connections connections connections connections science temporal sets sets sets range outputs continuous continuous continuous continuous continuous continuous abstract applied back back back back back back back back back back find computational references due due important important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation context context context context context context context hand hand dynamic tion tion tion tion tion energy difference assume assume representations chosen higher center center center conditions conditions represent expected make techniques techniques techniques techniques techniques techniques techniques techniques techniques region region region region correct observed resulting resulting resulting tasks tasks tasks total human human human computed multi multi multi multi performed performed performed performed times elements elements regions made made made applications study study study study study knowledge knowledge knowledge knowledge knowledge knowledge obtain obtain artificial artificial artificial artificial specific represented true provide provide provide proc proc proc perform distributions distributions distributions gain gain discrete equal approaches approaches steps steps accuracy accuracy accuracy comparison comparison comparison connection connection connection connection train train train train descent nets report institute words consists consists internal internal internal layers layers layers layers layers layers layers layers layers sequences framework cambridge experiment experiment experiment experiment environment environment additional additional additional design transition efficient classifiers classifiers full full statistics speed basic con con derived weighted weighted randomly randomly randomly randomly provided finally finally covariance covariance covariance covariance increases increases describe describe group tested assumption corresponds corresponds corresponds amount nearest nearest effective effective square square square square square cluster cluster makes objective auditory auditory auditory auditory auditory auditory simulated smaller smaller underlying account unknown technology testing mechanism database database database database language leads call iterations international international early frame run sources sources sources sources sources sources sources sources improved improved correlations correlations correlations takes takes introduced strategy strategy strategy dimensions sufficient compare compare compare speaker speaker speaker speaker speaker speaker speaker speaker achieve achieve diagonal diagonal diagonal locations parts parts parts suggests deviation wide neighbor neighbor depend sigmoid sigmoid sigmoid numerical numerical designed performs weak suggest integration integration integration integration characteristics characteristics characteristics characteristics characteristics proportional turn iii iii iii iii iii iii annealing acoustic acoustic factors factors factors laboratory ann ann vertical metric metric metric metric explicitly text spectral spectral spectral spectral formed decreases yield extracted extracted extracted focus depending phoneme phoneme overlap influence restricted organizing understanding past spectrum earlier earlier slow add add add add initially initially initially euclidean avoid perceptrons inter weighting sciences sciences recognize recognize determines discuss discuss specifically variations major simplicity straightforward aspects differ differ divided comparing vowel vowel vowel vowel vowel vowel vowel vowel vowel orthogonal ten capture summary traditional traditional traditional traditional repeated heuristic heuristic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic duration duration duration providing ill subsequent extend bars explore powerful american american american poor investigate issues issues examine mse mse root comparable symbolic symbolic variability workshop affect affect understand examined examined examined examined examined circles perfect implementations rank fisher initialized initialized initialized initialized initialized speakers speakers speakers speakers speakers speakers detected improving attempts attempts sentences sentences sentences isolated isolated integrate massachusetts agreement improves improves improves improves comparisons comparisons comparisons comparisons worst desirable mation potentially angles angles angles angles english english recognizing recognizing fourth percent amounts spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken conducted incorporated formulated formulated continuously continuously compares compares compares compares operate measuring extracting fall synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony phonemes phonemes achieves substantial extreme initialization initialization initialization initialization initialization initialization consistently gap spectra contextual contextual contextual primarily investigation investigation restriction fix fix databases proceed saturation saturation knn knn knn knn knn knn corpus corpus intuitive vowels vowels vowels vowels vowels vowels vowels vowels vowels vowels vowels vowels vowels vowels vowels infor contexts contexts contexts contexts male male enhance enhance dif darpa darpa enable tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens recog rich extensively relies agree formant material accumulated linguistic metrics metrics informa ple ent ent nition encouraging icassp icassp female female big stands peripheral concentrated exam distri formance insights insights guidance crosses crosses increasingly cation drops exploited status bution utilizing utilizing utilizing 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#@Leung_H,Zue_V,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data figure figure figure time time time time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training output output output output output output output output number number number error results results results results results results results results results results results results units units units units units units units units units units units units units units units units units units units units units units information information information problem problem problem problem models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems parameters unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach single processing processing processing processing large large large large large large large large large large large large large large large large large rate rate rate rate rate test test test test test test test analysis class class class class class class class class class class class class class class class optimal optimal shows shows shows signal signal signal algorithms paper paper paper small small small small small small small small small size size size size net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net work task task task task task task task task task task task task task task methods methods fig fig fig fig fig fig fig fig fig fig fig features features features features features features features features features features features features features classification process level level trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure structure structure structure structure problems random high high high high similar similar similar similar similar architecture architecture architecture architecture architecture architecture show show show show section section section fixed general general generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average obtained obtained note note experiments experiments experiments experiments experiments experiments dimensional result university university university threshold computation research research found found found initial table table table table connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections left left left presented presented presented presented activation activation range press learn abstract applied back back back back back computational convergence references component component component due ieee ieee ieee procedure important decision decision propagation propagation propagation propagation propagation propagation introduction complex complex hand dynamic parallel parallel search complexity complexity complexity lower lower representations word learned higher higher higher higher previous previous previous previous previous required required required good good good good good distributed expected markov make make fact techniques techniques techniques techniques techniques proposed proposed correct correct correct correct correct observed observed scale scale scale scale resulting resulting resulting resulting resulting classes classes classes classes classes classes classes classes classes classes tasks tasks tasks tasks tasks tasks tasks tasks tasks total total computed performed performed performed performed performed times study samples compared compared application application perform perform perform perform experimental goal mit steps accuracy larger larger larger larger larger larger larger larger larger larger larger larger train train train train nets nets nets nets nets nets nets nets nets nets nets nets nets morgan proceedings proceedings proceedings proceedings report report words words loss version internal individual individual connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult layers layers layers layers layers delay delay delay delay delay addition addition addition considered cambridge experiment experiment experiment experiment experiment hinton hinton hinton hinton additional additional additional additional additional additional additional additional additional view solutions design design design design design design design design design design conference conference efficient full full full free free free free free free free speed pages pages pages increase increase developed actual finally finally finally selected iteration iteration nature inhibitory sampling constraint simply simply achieved achieved achieved achieved achieved achieved achieved achieved achieved measured discussion technical technical fast fast limited proof finding amount amount common common effective ability rumelhart rumelhart rumelhart rumelhart including kaufmann smaller smaller smaller smaller needed needed hopfield combination combination combination combination combination combination combination combination unknown coefficients testing testing testing testing testing testing testing structures database database database database database database database database database empirical operation call iterations max making making window international frame combined combined combined combined run run light architectures improved property separate separate separate practical practical apply apply strategy moving identical sejnowski recently recently recently interest sufficient previously previously previously approximately approximately tuning tuning tuning tuning tuning tuning tuning tuning speaker achieve achieve achieve achieve evaluation evaluation positions williams entire increased increased increased increased constructed constructed constructed constructed lead scaling scaling scaling scaling scaling scaling extended extended alternative correctly correctly touretzky boundary pass demonstrate half conclusion critical row editors clear faster suggest sound largest demonstrated assuming start selective selective identification acoustic acoustic question question question construct construct ways distinct missing missing missing multilayer slightly develop develop develop adding applying shift national extracted extracted extracted phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme detailed detailed evaluated evaluated evaluate fraction frames allowed discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination processor partial partial reasonable slow add msec msec msec construction construction construction construction construction construction construction transactions precision recorded existing thesis inter sciences activated activated black partially major major simplicity middle aspects aspects capable capable society effectively mcclelland successful tdnn tdnn tdnn tdnn tdnn tdnn tdnn invariance score score fine fine fine fine fine reached quickly allowing success phonetic phonetic phonetic phonetic phonetic phonetic phonetic split superior superior strategies strategies categories modular modular modular modular modular modular modular modular modular modular modular modular modular delayed highest leading leading leading attempt attempt subsequent extend extend explore explore explore remain poor put fashion fashion school incremental incremental incremental incremental incremental incremental combine combine proper complicated scores cognition notion surfaces examined waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel coarse coarse coarse coarse naturally concepts editor configurations extremely assumes explored explored explored initialized phd established rows stop stop stop stop distinguish capabilities worse handle handle reasons perspective purposes shared day day constructing laboratories laboratories recognizing mellon mellon explained requiring requiring fourth improvements carnegie carnegie limits cmu amounts amounts spoken spoken effort completion completion compares vocabulary pittsburgh fall incoming incorporating tank tank tank phonemes phonemes extensions achieves achieves acoustics acoustics acoustics substantial findings eventually utterances utterances progress june yielding naive shifted contextual identifying japan japan resources discover interconnected interconnected extending extending khz overcome grow resulted hope exceeds degradation degradation days days vowels connect respective respective respective entry decide male lang mel uni competing similarities tokens tokens tokens tokens tokens april april omitted ahead arrive merge merge exploiting exploiting consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant fahlman fahlman fahlman explorations boxes discriminate yielded yielded summer slight microstructure break july revealed incrementally incrementally incrementally incrementally incrementally distinction retraining retraining chapter breaking massively avoids summarizes summarizes token token token token token token searches expand march careful individually individually academy portions portions atr atr october october stops stops stops stops stops stops stops stops stops stops stops stops satisfaction tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns impractical hoc interpreting interpreting clarity phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic alex japanese japanese japanese japanese proportions distinguishing acoustical believed meeting emerges consonants consonants consonants consonants consonants consonants consonants raises isolation isolation digitized fastest watrous watrous spirit connectionism translates capturing excessive excessive huge modest voiced voiced voiced voiced voiced voiced voiced voiced voiced voiced began modularity modularity modularity cons cons preprocessed collecting subnets subnets subnets exploitation shikano shikano shikano shikano frozen frozen frozen frozen favorably adjustments adjustments inability fight subtasks subtasks aimed aimed aimed aimed undesirable copied copied retrained retrained retrained distinctive distinctive distinctive distinctive distinguishes subclass wanted hanazawa hanazawa contributed permission categorized encouraged pennsylvania matters native arrangements haffner haffner haffner shed pertinent freeze phoneroes concentrating subclasses subclasses tackled methodologies insensitivity unvoiced unvoiced unvoiced reprinted aining filterbank monolithic monolithic monolithic glue glue glue glue glue glue glue glue retrain retrain retrain retrain ang nasals nasals telephony telephony featural supplement discriminatory discriminatory simulators supercomputers encompass copyright sawai fricatives righ stead judicious osaka lye tabulation abandon underneath 
#@Waibel_A,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data data data data data function figure figure figure time time time time time time time time time time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training algorithm output output output output output number number number number system system system system system system system system system error error error error error error error error state results results results results results results results units units units units units units units units units units units information information information problem models hidden hidden hidden hidden hidden hidden hidden based based based based based based linear linear layer layer layer layer layer layer case vector order order systems systems probability probability parameters noise noise noise weight unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach pattern pattern pattern single single single processing processing processing processing processing control control local rate rate rate test test test test test test patterns patterns patterns analysis analysis analysis analysis matrix inputs form shows signal signal signal signal signal signal signal algorithms simple simple paper paper small small task task task task task task fig cells features features features features features features features classification process level level current trained cell cell cell cell cell structure structure high high high response response response similar similar similar similar representation representation representation representation representation architecture architecture architecture architecture show section line rule rule generalization generalization generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech gradient obtained obtained term experiments experiments experiments experiments university solution research research defined defined defined defined defined found sequence computer connections connections synaptic science direction present phase phase low low nodes nodes frequency frequency frequency frequency frequency frequency frequency temporal machine machine sets maximum press press learn components nonlinear nonlinear outputs outputs outputs outputs continuous abstract applied applied applied applied back find computational computational convergence convergence properties properties properties references due due ieee ieee ieee procedure procedure important adaptive propagation propagation context introduction complex complex estimation behavior stimulus generated variance parallel parallel energy energy variable variable variable variable variable variable word word part cases cases cases cases firing firing multiple multiple good good conditions represent represent represent distributed techniques region proposed proposed proposed correct correct correct observed observed errors errors classes classes classes classes classes classes tasks tasks human human human human human human multi multi multi multi multi multi multi multi multi performed called called called called optimization knowledge knowledge knowledge knowledge knowledge knowledge knowledge filter filter filter vol vol vol artificial artificial specific specific samples samples samples represented represented application rates rates proc perform perform perform experimental experimental related connected connected connected connected gain power mit mit mit larger train proceedings proceedings proceedings proceedings proceedings report words words loss internal individual joint joint represents represents responses responses difficult layers scheme addition ai considered considered cambridge domain experiment experiment experiment experiment experiment experiment experiment hinton san top top stage stage effects conference conference conference con produce channel coding coding coding coding coding coding coding coding coding coding coding derived lines lines lines selected evidence technical group group group transformation limited limited limited short implemented synapse synapse adaptation adaptation journal journal journal journal journal journal journal end end end end rumelhart fit objective auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory simulated probabilistic pairs pairs smaller coefficients block block block testing testing head head head segmentation segmentation database database database representing filters filters pre window international depth early combined description membrane membrane membrane recent resolution resolution resolution resolution resolution advantage property property property property property property property property property property pair reported reported reported apply strategy strategy strategy recently relevant varying module module speaker speaker speaker speaker speaker speaker definition observation channels williams increased studied critical critical place reduce segment segment segment modules modules modules modules modules modules accurate designed designed designed peak peak peak peak peak peak performs encoding mechanisms intelligence intelligence intelligence intelligence acoustic base digit digit digit perception perception transitions tuned distinct dept segments modeled sensitivity linearly transformations spectral spectral spectral spectral spectral spectral spectral integrated events blocks blocks extraction letters letters letters extracted phoneme phoneme phoneme phoneme phoneme stages stages evolution frames frames digits digits allowed allowed spectrum sign performing classical normalization normalization combining combining event event event interpolation interpolation transactions transactions exploration includes batch recognize illustrated illustrated automatic automatic automatic automatic automatic specifically domains domains characterized characterized structural middle aspects letter letter letter letter capable society society society society society society driven driven driven driven driven symbols presentation build build invariance situation situation situation situation situation situation vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel miller ten ten ten ten fine capture phonetic phonetic phonetic phonetic phonetic phonetic classify classify classify classify physiological strategies strategies strategies duration duration sampled highest hypotheses hypotheses cat automatically automatically consisted preferred preferred extract deal modelling minimized simpler simpler carried diego layered layered layered layered layered layered layered layered layered put relations steady preliminary preliminary behaviour pathway cognition waibel waibel waibel onset opposite recognizer front front front detector detector detector nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve switching fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers speakers speakers speakers speakers speakers speakers speakers speakers detected detected improving improving attempts attempts established years stop stop slowly band band band band band separable analyzed analyzed analyzed cascade handle rapid preprocessing filtered directional broad broad bengio bengio bengio bengio bengio bengio bengio bengio sounds sounds sounds describing pitch pitch english preceding preceding preceding preceding populations syllable collected transient transient simulate effort peaks release execution execution execution synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony plan gave fiber fiber windows implements implements utterances phenomenon shifted spectra spectra pac ear ear ear ear ear ear ear labeling refractory controlling eliminate khz promising balance occurring utterance optimally alphabet alphabet selects heuristics vowels vowels vowels vowels reliably published excellent combines encountered paul decide male male male male intended thomas candidates candidates nonlinearities specialized young young ends canada extensively consonant consonant generalizing material executed executed dividing discharge discharge discharge discharge microstructure hair hair hair hair bank bank bank icassp icassp instantiation acceleration acceleration female female female female acting rectangular peripheral peripheral deep deep deep deep pami pami execute execute refinement denver locking confusion syllables tune tract aaai january august august accordance decided hearing attempting flows acoustical acoustical acoustical acoustical acoustical acoustical mori mori mori mori mori mori mori mori mori mori mori mori mori mori resolutions consonants fft fft fft clark tokyo periphery bat vocal enhances america america america america america america watanabe prominent tenth montreal bee gradual modularity pes pes pes gross italy sought fur lpc formants formants formants basilar basilar taps canadian yoshua extractor neurotransmitter generalised vibration 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#@Bengio_Y,Cardin_R,Cosi_P,De-Mori_R,
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figure figure figure figure figure time set set set networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number system system system system system system system system system system system system system system system system system error error error error error results results results units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based space layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case shown shown shown shown shown shown shown shown systems values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight unit unit unit unit unit unit unit unit distribution method method method method method method method method method method method method method method method method method method method method method method method method method pattern pattern pattern pattern pattern pattern processing neuron neuron rate test inputs shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal paper small size methods fig fig fig fig fig fig points points points features trained trained trained random random high memory similar show equation section fixed fixed line line line line line rule rule rule general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter obtained experiments experiments experiments experiments result threshold research log log log defined sequence sequence sequence sequence sequence sequence sequence target target target target target target target constant constant constant constant table table science presented activation activation frequency range range press learn learn learn learn learn learn learn learn learn outputs outputs outputs outputs outputs outputs outputs outputs abstract back back back back back back convergence convergence analog analog analog analog analog references positive important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex behavior behavior behavior parallel parallel change change change lower rules rules rules rules rules word previous multiple distributed make make proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed length length errors errors sum performed means natural natural natural natural natural study obtain obtain obtain vol represented represented define define experimental equal equal equal power power power power power power power mit accuracy source source source source source source source institute words consists consists consists difficult final final final final final final final exp layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers delay domain experiment experiment experiment experiment directly curve curve curve curve curves curves curves stage stage stage stage stage stage upper produce produce produce produce produce produce developed area area actual actual actual iteration iteration sampling simply normal arbitrary arbitrary arbitrary group limited stable stable circuits finding square square square makes makes makes rumelhart combination combination unknown coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients block ratio ratio ratio mechanism mechanism window international normalized early frame frame frame frame frame produced separate element element element apply period subject sejnowski sufficient teacher teacher solve smooth smooth smooth converge converge generalized wide conclusion sound propose propose propose hard solid targets targets targets targets targets introduce characters explicitly easy easy text consisting extraction extraction extracted extracted extracted phoneme stages stages stages stages stages stages constants constants diagram delays purpose string string string string string symbol symbol symbol symbol symbol symbol assigned assigned assigned assigned assigned weighting weighting weighting weighting weighting automatic automatic selecting symbols symbols symbols symbols symbols symbols symbols mcclelland composed strategies wave wave automatically acknowledgments powerful production production production production production production production production production production production production production production production production production production production production production production production production production production production production production put accurately accurately accurately dotted ml examine tech mse mse mse mse mse authors complicated removed examined singular singular singular noted noted logistic optimum great advanced derivation improves sections widely producing producing producing producing describing pitch pitch pitch pitch english behaviors behaviors items rep synthesis synthesis synthesis spread spread spread spread spread spread extracting phonemes phonemes sentence converged converged converged summed japan khz difficulties removing utterance waves waves waves waves waves agree converted converted converted sig cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative pdp particle tract tract wider decided decided synthesized synthesized synthesized rosenberg tanaka tanaka tanaka tanaka tanaka phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic phonemic japanese japanese sij vocal vocal sis 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#@Komura_M,Tanaka_A,
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networks networks networks training training training training training training training training training training training algorithm algorithm output output number number system system system system system system system system system system system state state state state state state results results results results results units units units information information information information information information information information information information information information information information information information information information information information information information information information problem models models models models models models models hidden performance based space space space weights weights layer case order order shown shown shown shown shown systems systems systems systems systems systems systems parameters parameters parameters parameters weight weight functions functions functions unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach single processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control control control rate rate rate rate rate rate rate rate rate rate rate test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form shows signal signal signal signal signal visual visual visual visual visual paper size size net work methods methods methods methods methods cells cells step field field field classification classification classification classification level current trained trained trained trained cell structure problems problems high memory memory similar representation representation architecture architecture equation equation equation equation section fixed fixed fixed fixed line line line general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter real states experiments experiments experiments dimensional university university university computation solution research found found found constant constant constant constant computer computer computer connections connections connections connections connections connections connections connections node node node node node node node node node node node node node node node node node node node node node node node node node node node node node science science science direction direction direction direction direction direction presented presented presented present present activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal sets motion motion motion motion motion motion motion maximum maximum range range range range learn learn learn abstract applied back computational references ieee adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation context introduction complex estimation behavior behavior behavior statistical statistical dynamic dynamic parallel recurrent recurrent recurrent recurrent tion tion tion tion difference complexity spatial spatial spatial spatial spatial spatial spatial representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations part part center center center center center center center previous previous firing firing firing firing firing type type type type type type good good binary long long represent represent represent tree distributed distributed expected markov techniques region length length length length correct correct errors errors resulting ing ing ing ing computed respect sum performed performed performed times means natural natural feedback knowledge specific represented series receptive receptive receptive provide provide compute rates rates rates rates rates proc location perform determined constraints connected connected connected motor brain steps steps steps steps larger larger connection connection connection connection connection connection connection connection connection fields update update train nets report consists individual represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist final final delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay sequences sequences sequences sequences ai experiment experiment experiment environment hinton transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition limit san san top stage stimuli effects effects detection conference determine vision increase con weighted weighted weighted types types lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines simply achieved achieved achieved discussion tested tested tested fast limited limited limited limited complete complete amount amount common generate require end end rumelhart rumelhart sensory including including auditory hopfield hopfield functional jordan jordan block testing testing testing edge increasing increasing segmentation mechanism special leads representing details filters filters inhibition inhibition inhibition inhibition stored stored bottom supervised decay decay decay decay decay decay description architectures discussed directions directions directions resolution exact separate takes include subject array sufficient varying axis axis tions tions yields trans gate storage entire constructed horizontal parts occur suggests hybrid hybrid occurs column column runs runs flow flow flow strength strength place place place row row conclusions interactions sigmoid sigmoid accurate retina designed designed designed designed designed sutton sutton peak faster faster faster faster faster learns cycle cycle pulse pulse pulse turn exist averaged averaged introduce acoustic acoustic acoustic areas explicit explicit explicit explicit pro pro pro pro edges perception solving sequential sequential describes transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions tuned vertical dept dept sensitivity sensitivity sensitivity sensitivity sensitivity explicitly infinite slightly slightly spectral interaction interaction frequencies events events events events events events cycles cycles cycles cycles select select john review phoneme interpretation variation variation updated updated lee centers updates past past past earlier earlier barto barto slow slow delays classical classical combining event roughly add false false intermediate assigned koch koch topology dendritic dendritic dendritic existing fire fire perceptual thesis activations retinal determines activated activated variations absolute holds gating middle letter extra efficiency maximal computationally divided mcclelland mcclelland poggio presentation presentation presentation successful identify computations situation vowel vowel vowel vowel vowel identity ten fine composed capture soc soc soc conf quickly strongly allowing allowing anderson anderson classify timing duration categories cues absence absence delayed computes consisted overlapping illustrates preferred preferred preferred preferred preferred acknowledgments deal trains trains selectivity selectivity diego diego parametric parametric parametric parametric parametric powerful exponentially steady steady steady steady rise reducing respond respond respond respond respond giving ideas tech rest detectors detectors detectors detectors detectors detectors detectors detectors int combine working analogous analogous analogous measurement measurement naturally transmission transmission transmission transmission trace trace onset opposite created perfect implementations algo precise precise detector detector detector detector detector detector detector detector detector detector detector detector detector separated nervous nervous store store store store consist motivated serial synthetic synthetic isolated averages integrate ment stop stop ground sensors sensors expensive briefly briefly tool starts ganglion considerable spatially tive incorporate incorporate incorporate controls potentially beginning implicit implicit implicit implicit members author author preceding raw raw researchers behaviors prop limits limits syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable relevance peter incorporated slower slower slower treated continuously psychological span passes branch branch branch branch branch branch branch branch branch branch branch branch reaches popular cal resource tank tank serve prevent acoustics adjust segmented conditioning conditioning conditioning traces traces synchronization merging consistently pose cooper temporally temporally rithm driving acts branches branches purely repre tem lost eliminated saturation chains adjusting occurred simplify primitive interpret serves canonical adequate corpus vowels fires excellent slice slice slice slice slice slice slice slice slice slice combines pat lang buffer buffer buffer widrow spatiotemporal spatiotemporal spatiotemporal spatiotemporal mem ends formant formant formant formant formant formant formant formant formant formant formant formant formant formant formant formant formant formant considerations consonant consonant consonant consonant characterization robert ics sequentially fired converted incorporates incorporates shunting ber preserving forced propagating classifies classifies warping associate associate associate associate adjustment representa mutually unseen queue peripheral preserved preserved exclusive decays activate regulation neurophysiological eliminating relate paired retain spreading spreading interactive interactive interactive distal distal distal distal distal distal represen cation eligibility eligibility eligibility eligibility preserve preserve descending alarm syllables syllables syllables syllables syllables syllables syllables modality elsevier thousands thousands port port port port manuscript coming ucsd drives accumulation ble 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#@Smythe_E,
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hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based based based based space space weights weights weights weights weights weights layer layer layer layer layer layer layer layer shown shown systems systems systems systems systems systems systems systems systems values values values values values values probability probability probability probability probability parameters weight weight weight weight unit unit unit unit unit unit distribution distribution recognition recognition method method approach approach approach pattern pattern pattern pattern pattern pattern single processing processing processing processing processing large large neuron rate rate test test test test patterns patterns analysis class class class class class class class inputs signal signal signal signal algorithms simple simple simple simple visual small small small small small size net work work work work work task task task methods step process process level level level current current trained trained structure problems random response response response representation representation representation architecture rule rule rule rule rule rule images generalization speech speech parameter real average average theory theory activity activity activity result university university university university university university university threshold threshold solution research research research standard computer computer computer computer computer computer connections science science science science science science prediction prediction prediction prediction prediction presented presented activation activation activation activation activation activation activation low low frequency sets range learn learn continuous continuous abstract back back back back back back likelihood references procedure procedure propagation propagation propagation propagation propagation propagation introduction introduction complex complex behavior parallel parallel parallel parallel parallel difference lower rules rules rules rules rules rules measure measure representations representations representations representations representations representations higher higher part previous cases type type required good good good binary conditions distributed distributed distributed distributed make make techniques correct correct classes classes classes classes total total simulation simulation simulation human human human human human human human human multi sum sum performed performed called called called called called called called called elements potential natural study study study knowledge knowledge knowledge knowledge knowledge knowledge knowledge artificial artificial relative relative compared application provide provide proc perform perform determined related constraints cortical brain brain approaches approaches approaches approaches connection update support report report technique internal internal internal internal internal code code code individual individual joint connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult difficult final bias bias layers layers layers addition graph ai cambridge domain domain domain domain environment environment environment directly directly hinton hinton hinton curve curve curve san san top detection detection detection determine upper requires requires significant statistics vision give give coding weighted developed developed developed developed area area area actual provided processes processes processes nature nature nature simply biological technical technical technical group group tested tested tested tested limited limited complete surface amount amount amount square square ability instance easily degree degree makes rumelhart development noisy noisy sensory probabilistic pairs needed needed combination reduced reduced reduced reduced fully technology technology transfer mechanism matching database database mode squared experts expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert decay decay description architectures recent apply period period sejnowski sejnowski sejnowski sejnowski cognitive cognitive cognitive recently engineering engineering engineering engineering sufficient varying varying volume works works works works works correspond converge converge background evaluation modified modified entire constructed constructed constructed constructed invariant occur suggests derivative pass segment conclusions conclusions depend interactions measures measures practice learns learns largest largest cycle demonstrated california california intelligence intelligence user relationship program acknowledgements areas areas construct construct longer ways factors laboratory laboratory dept implement implement implement physical electrical involves unique events formed versus competition updated evolution soft translation allowed allowed past partial earlier earlier reasonable false false false initially calculate symbol david david david degrees existing activations activations activations determines successfully middle mcclelland presentation successful detect build essentially ten characteristic capture traditional traditional traditional conf quickly quickly quickly success success interested oscillations categories categories categories categories involved vary automatically automatically attempt attempt operating remain diego diego production experience strengths strengths reducing examine project project project possibility authors working symbolic symbolic symbolic symbolic proved proved affect momentum momentum surfaces man predicts psychology psychology psychology thought logic ith ith epoch epoch detected attempts years years languages languages mentioned advanced growth growth growth analyzed slope explanation expensive expensive tool tool implementing day day read lowest incomplete sun requiring questions freeman led elman elman fed simulate simulate compares measuring measuring occurrence occurrence curvature richard simulator simulator simulator eventually june calls lot consistently redundant sort sort sort writing forming formally modify oxford jth jth eliminate interconnected smolensky generality clamped dealing imaging minutes minutes promising hit resulted hope hope analyzing reasoning reasoning reasoning reasoning reasoning reasoning reasoning reasoning methodology methodology receiver spot spot spot spot hours hours paul pat intended intended forecasting forecasting forecasting forecasting forecasting colorado colorado colorado colorado colorado originally offer offer matter draw davis davis valuable default acknowledge ics unchanged zipser zipser roc roc drop microstructure microstructure corporation job presenting incrementally smoothly year year affects affects possibilities workstation discovering certainty guess imagine massively shaded care insights insights geoffrey pdp pdp boulder boulder boulder boulder terrence terrence careful books interactive exceed covered paradigms paradigms denver alarm milliseconds status rarely consuming handling inconsistent allen rosenberg rosenberg assistance spring attempting hopkins supplied exposed alarms alarms interpretations zipset johns complement lewis lewis lewis nettalk magazine bradford stabilize raised inaccurate supposed cope unnecessary hits hits explaining developments publishing lisp damping lund stand tracked plausibility fight theo theo theo theo theo theo theo theo theo theo theo theo theo advice week netherlands mediate named claimed engineers scored sorts wji encouragement explosion expressing equipment today informal debate gary sel sel departments intriguing forecast aloud newell 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#@Bradshaw_G,Ceci_L,Fozzard_R,
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number system state state state results results results units units units units units units information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models hidden performance performance performance performance performance based based based based based based based based based based based space space space weights weights weights linear linear layer layer layer layer layer layer layer layer layer case vector order order order order order order order shown shown shown systems systems systems systems systems systems systems systems values values values values values values values probability probability probability probability probability probability weight weight weight weight weight functions neurons neurons unit unit distribution distribution distribution distribution recognition approach approach approach approach approach approach approach approach approach approach approach approach pattern image single large large large large large local local rate rate rate test test test test test test matrix optimal optimal optimal inputs inputs inputs form form form form form shows shows shows simple paper paper paper examples examples small small small small small small small size feature feature net net net work work work task methods methods methods field features features features classification classification classification classification classification classification level current current trained problems problems problems random high high high high high high high high high high high high high high high high high representation representation representation representation representation representation representation representation architecture show section fixed line rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors general general general general parameter real real real real approximation approximation average average average average average average theory theory theory theory theory theory theory theory term term note note threshold threshold variables solution solution research research research independent independent independent log log log log log log log log log log log log log defined defined defined defined target initial initial initial table table table table table standard standard terms terms terms terms connections node node node node science left presented map present activation activation activation activation activation activation activation activation low low low low low low low low low low low low low low low low low low low nodes nodes nodes nodes nodes nodes nodes nodes sets maximum maximum maximum range learn basis basis basis continuous sample sample sample sample sample sample abstract back find find computational properties properties likelihood references component stochastic stochastic due ieee ieee ieee positive important decision decision introduction hand hand hand statistical statistical statistical generated parallel parallel cost recurrent search change change change change change change difference variable variable variable assume assume lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure measure measure measure measure measure measure measure measure learned learned learned chosen higher higher part previous type type type type type type required required multiple multiple multiple good good binary binary binary binary binary conditions conditions represent distributed distributed bayesian make fact techniques region probabilities ing tasks total total total respect multi sum sum called made feedback applications applications knowledge knowledge knowledge knowledge obtain negative negative vol vol vol artificial specific samples samples samples samples samples true true true true compared compared application desired cross cross define define compute perform perform perform perform perform perform determined experimental goal goal goal connected distributions discrete discrete discrete approaches connection connection support support dependent modeling institute department loss consists individual individual joint represents connectionist connectionist connectionist connectionist connectionist difficult difficult bias bias layers layers scheme addition graph graph ai ai ai ai considered domain domain environment directly hinton transition top top conference determine classifiers statistics free world estimated con produce derived weighted randomly developed developed bounds entropy entropy entropy entropy path actual finally processes selected evidence evidence evidence evidence backpropagation backpropagation nature nature nature nature depends simply simply simply simply discussion describe describe arbitrary transformation close inverse inverse assumption finding amount common implemented generate supported supported supported theoretical theoretical theoretical theoretical theoretical require face adaptation hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance instance fit probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic pairs underlying unknown technology testing testing testing ratio york special special structures uniform database database database direct bits bits bits bits international international expert expert expert expert expert expert expert idea produced run architectures exact exact exact exact robust robust robust takes typical typical typical typical typical typical practical introduced side side inference inference inference inference inference inference inference inference inference inference inference inference inference inference sejnowski cognitive recently recently recently engineering interest varying compare observations calculated calculated works yields correspond definition definition storage risk risk risk risk risk grant grant occur locally hybrid column pass strength critical assumptions conclusions valued sigmoid sigmoid sigmoid accurate bayes bayes bayes bayes numerical numerical clear performs practice constrained temperature propose presence sigmoidal california turn user user user manner manner manner program question reference explicit explicit derive produces describes laboratory confidence metric metric implement electrical transformations slightly unique mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual agent expectation boolean cycles john john national expressed communication estimator interpretation interpretation evaluate updated understanding converges allowed discrimination key key earlier performing performing performing classical event assigned assigned advantages topology transactions box perceptual priori priori priori priori priori formulation bell uncertainty uncertainty uncertainty uncertainty discuss variations domains domains domains black tests simplicity columns determining aspects suitable computationally literature literature schemes schemes schemes situation miller miller miller miller miller ten ten refer kind link link interpreted interpreted interpreted return return return classify content content content content criteria hold vary write relaxation relaxation observable predictor automatically automatically principles principles principles extract acknowledgments software load load decreasing decreasing receive modelling carried american wiley requirements updating put association game mass behaviour ideas links links combine decisions symbolic attributes attributes attributes attributes attributes attributes induction induction induction naturally possibly necessarily reading perfect rank der portion portion academic submitted submitted motivated devices percentage advanced preference preference ment directed directed directed theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic growth growth growth growth growth growth distinguish publishers explanation independence tractable lies london drive sys formalism directional laboratories describing implicit begin attribute attribute attribute attribute attribute attribute attribute read arises auto incomplete incomplete qualitative nsf raw raw raw researchers considerably limits reflect items understood lack quantitative autonomous incorporated maintain requirement requirement resource serve collective pasadena pasadena geman geman logp simulator conclude wesley instantaneous instantaneous phenomenon pose intractable addison japan acm ratios perfectly databases databases repre proceed caltech caltech generality clamped clamped clamped clamped extending rational kullback kullback smith consideration ments significance alpha contract interpret reasoning reasoning symposium motivation infor published financial respective equals sides bases infer infer eng omitted probe informative inductive considerations interestingly balanced balanced balanced automated dividing limitation trading posteriori posteriori posteriori fired fired mind metrics ure ure ence corporation misclassification kluwer deriving deriving goodman goodman goodman goodman goodman goodman goodman exhaustive encouraging adopt year year year par tendency chicago beta beta clas constrain quantized quantized unseen unseen publication publication iff iff distri distri tems gener file playing uncertain uncertain searches smyth smyth smyth smyth smyth smyth smyth smyth investigating pearl conversely tied setup truth 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#@Goodman_R,Miller_J,Smyth_P,
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small small size net net net net net work task step step points points points classification process process process process process process process random memory memory memory memory memory representation line line rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images general generalization states states states states states states states states states states obtained university computation research research research defined defined target dynamics initial table table distance science science left present phase learn basis abstract applied applied references due ieee adaptive adaptive adaptive adaptive context circuit parallel cost tion classifier rules rules rules measure measure measure measure type distributed techniques proposed simulation computed regions regions regions dimension dimension dimension dimension global applications study knowledge obtain vol represented compared compared cross proc selection report institute institute implementation technique code code code scheme scheme scheme scheme scheme scheme computing additional additional design limit conference full basic coding coding clustering clustering developed developed developed levels levels selected selected iteration depends biological associative normal corresponds corresponds nearest nearest nearest generate vlsi pixel pixel pixel pixel ability typically typically hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield unknown technology ratio ratio projection projection projection iterations iterations iterations stored bits bits bits bits international idea choose choose light light discussed resolution typical pixels pixels pixels cognitive cognitive dimensions previously correspond generalized generalized generalized organization organization organization organization organization organization storage storage alternative deterministic hardware conclusion place minimal minimal minimal designed physics min attractor attractor attractor attractor explicit explicit pro derive index generating plot plot ann stability develop springer blocks versus select squares overlap overlap overlap overlap codes codes open controlled organizing organizing organizing organizing organizing organizing organizing organizing evolution centers centers key classical classical iterative iterative iterative generation visible euclidean euclidean kohonen kohonen priori usa usa phys phys phys phys phys phys phys regular compression compression compression compression compression compression compression compression extra extra capable uniformly divided attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors computations orthogonal induced induced induced induced induced induced induced induced induced induced induced induced induced induced induced issue sci sci sci gray gray notation notation notation notation list list denker extend referred referred induction induction induction math math transmission configurations configurations rev rev der assumes detected detected spin spin spin spin mentioned defining coded coded coded coded glass glass glass glass located laboratories acad acad grossberg grossberg implicit implicit implicit optimize optimize optimize apparent marked solla prototypes prototypes prototypes prototypes prototypes prototypes howard berlin differs aim resource resource tank attraction attraction coherence june initialization optimality member nat ordering ordering flexibility grey inspired promising krogh cottrell hertz hertz hertz natl published sompolinsky codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook jackel jackel initialize arrows designing lett lett lett dense dense sch guyon suboptimal suboptimal acceptable continuity hubbard met france preserve induces induces behave port bienenstock adaptively devised luminance quantizer kirkpatrick kirkpatrick diamond zipset frequent assp magazine appro baltimore prescribed prescribed prescribed prescribed prescribed prescribed prescribed ized mesh cortes jerusalem metastable metastable metastable metastable metastable metastable metastable sherrington disorder phy substituted avenue tics parisi named named named associating dreyfus recon cedex illustrative personnaz personnaz personnaz apr amir gravity gravity shed gert sel sel finland relaxing stabilizes gutfreund gutfreund diamonds commun virasoro virasoro prescription prescription prescription zard neighbout mezard mezard mezard bernard laboratoire physicists organi aiming algorit television attractions changeux proto proto jean biologists dehaene eindhoven racah nit prescribe prescribe publ 
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#*network network network network network network learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time set set networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number system system system system system system system system system system system error error error error error error error error error error error error error error error error error error error error error error error results results results information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem hidden performance performance performance performance performance performance performance performance performance performance performance performance performance based based space space weights linear linear layer layer layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector order shown shown systems systems systems systems systems systems systems systems values values probability probability probability probability probability noise noise noise noise noise noise noise noise unit recognition method method method method method pattern single single single large large large large large rate rate rate rate rate rate rate analysis analysis analysis analysis analysis class matrix signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples examples examples small net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net methods classification classification process process trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure structure structure problems problems random random random high high similar similar similar representation representation section fixed fixed fixed vectors general speech average average average average average theory theory obtained dimensional result result university solution solution research independent independent log defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence estimate estimate estimate standard standard computer computer node left presented present phase phase phase low low frequency maximum range press press outputs continuous abstract applied applied back back back back back back find computational computational computational computational likelihood likelihood references references due ieee ieee ieee ieee ieee ieee ieee procedure decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision propagation propagation propagation propagation propagation propagation propagation introduction complex variance variance variance parallel parallel tion energy energy difference difference complexity complexity complexity variable assume assume signals signals signals signals signals signals 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relative relative relative relative relative samples represented compared compared compared compared application application application application application application desired desired desired desired cross cross rates rates active active active active gain gain gain equal equal equal power mit accuracy train nets nets nets nets department loss implementation version technique technique technique technique consists internal internal code code code code code code code code code code code difficult bias layers layers delay scheme scheme scheme sequences sequences considered considered considered considered considered considered considered considered domain domain domain environment environment directly hinton curves estimates san effects effects bit bit bit bit bit bit bit bit detection detection detection detection detection detection detection detection conference efficient classifiers classifiers requires requires approximate statistics statistics statistics statistics statistics 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conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional works tions solve correspond studies studies trans trans trans trans trans trans address modified observation observation channels channels channels channels channels channels interval interval interval interval interval interval williams storage storage sensitive amplitude intensity intensity digital alternative feed white occurs boundary boundary boundary boundary boundary setting setting strength strength reduce conclusions depend editors central sigmoid accurate accurate numerical clear asymptotic hard presence presence reduction characteristics drawn proportional pulse assuming user user user user user user user user user user user user user user user user user user user user user user user user user user introduce introduce configuration configuration base denoted pro monte monte monte monte monte carlo carlo carlo carlo carlo written written longer generating electrical easy slightly angle angle scales shift versus versus versus versus versus potentials potentials focus review viewed influence evaluate understanding understanding spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum reasonable additive additive additive delays reduces boundaries sufficiently symbol symbol symbol symbol symbol symbol assigned assigned perceptrons perceptrons formulation plotted plotted illustrated structural simplicity reason efficiency efficiency efficiency efficiency closely closely closely importance importance importance importance importance importance importance importance mcclelland successful comparing situation orthogonal decoding prob prob prob interested issue classify strategies duration duration providing maximization maximization maximization received received received received received attempt illustrates operating software situations situations carried diego layered layered poor poor poor poor poor poor poor poor poor access access access access access access access access access access access access access access access access access access exponentially issues issues issues lippmann lippmann lippmann project detectors detectors parity analytically referred referred referred decisions decisions structured proved proved understand cognition fundamental matched matched matched matched matched matched matched matched matched matched matched neu configurations configurations extremely extremely illustrate illustrate illustrate equally ensure ensure front observe detector perceptton generates motivated optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum cos cos cos band developing asynchronous track track defining waveform benchmark nonlinearity comparisons snr snr snr snr snr snr tive sections filtered division division 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problem problem problem models models models models models hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based layer layer layer layer case case case case case case case case vector vector vector vector vector vector vector vector vector vector shown shown shown systems systems systems systems systems systems systems systems systems noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons distribution distribution recognition recognition pattern optimal optimal form form form shows shows signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian paper feature net net net net net net net net work methods methods methods methods fig features classification classification classification classification classification classification classification classification process process process level level level trained trained trained structure structure random memory similar architecture architecture show show section section vectors average obtained obtained experiments experiments dimensional result university university research defined target target target computer distance presented presented presented presented present present phase phase phase phase phase phase phase phase phase frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency object object maximum maximum maximum maximum range learn position components components components components components components components components components sample abstract properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component ieee ieee ieee procedure decision decision introduction introduction complex complex complex statistical statistical variance variance change change variable classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier measure signals signals signals chosen good conditions region proposed length observed minimum total simulation simulation respect multi multi multi elements means dimension applications study study study knowledge knowledge em vol vol specific samples samples samples represented true compared compared compared desired desired cross cross objects objects perform equal comparison comparison comparison nets nets nets nets nets selection proceedings department consists represents final layers layers layers computing domain domain experiment experiment experiment experiment experiment environment design design effects conference classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full requires free free basic selected associative measured measured measured increases tested tested close actions nearest nearest nearest nearest nearest nearest nearest nearest assumed require square square square noisy noisy noisy noisy noisy typically typically underlying unknown testing ratio increasing database operation max max max max max pre magnitude magnitude description perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron architectures improved discussed discussed sense engineering varying varying compare approximately correspond correspond studies trans evaluation observation observation observation observation observation observation observation organization sensitive sensitive lead alternative white white white conclusions neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor valued depend competitive competitive accurate performs performs performs labeled identification identification identification winner primary laboratory ann modeled modeled modeled modeled modeled implement sensitivity multilayer electrical consisting frequencies frequencies frequencies frequencies springer decreases national evaluated showed additive additive additive additive additive measurements measurements measurements measurements measurements measurements measurements measurements measurements roughly kohonen kohonen topology topology figures automatic characterized identify reached traditional compact repeated superior contribution quantization received received operating lippmann investigated investigated reliable root root measurement measurement coefficient perceptton art improving improving submitted electronic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic band band theoretic theoretic snr snr snr snr snr snr snr snr snr snr sys exemplars capability capability introducing berlin measuring characterize chen coherent coherent coherent coherent coherent coherent coherent coherent sophisticated conclude focused trade optimality investigation lvq establish ments attractive receiver mance loo loo loo loo perfor sim candidates april april insensitive insensitive radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar ple ter vec outperform aircraft aircraft aircraft aircraft aircraft aircraft aircraft july superimposed tor mhz mhz formance magnitudes magnitudes tems maintained investigating superposition tively commercial commercial commercial mea appearing survey tial ongoing meth ods assp feasibility resultant magazine objectives rela ohio ohio ohio quadrature quadrature quadrature quadrature quadrature quadrature quadrature availability traditionally evaluates impressive poten feel feel pared ponents vation resonant iden bor itive obser 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point point image image image image image image single single single single processing processing processing processing processing processing processing processing processing control large local local local local local local local local local local local local local local local local local local local local local local local local local local local rate rate patterns class inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual examples examples examples small small small feature feature feature cells points points points points points field field field features features features features features features features features features features features process process level level level level level level level cell problems high memory memory response similar architecture architecture architecture show equation equation section line line line real real theory term term activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional result university university research log sequence dynamics dynamics dynamics dynamics initial initial initial initial initial computer computer computer computer computer connections connections connections connections left direction map map map map phase activation activation low temporal temporal temporal machine machine object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum maximum maximum maximum maximum maximum maximum range range range press press press position outputs outputs abstract applied applied applied back back back back find computational computational analog analog analog analog analog analog analog properties references ieee ieee positive positive adaptive adaptive introduction stimulus stimulus stimulus stimulus generated parallel parallel recurrent difference spatial spatial lower lower lower lower lower representations representations representations part center center center center center center center center center cases multiple multiple multiple multiple multiple multiple cortex long long long long distributed make forward scale scale scale scale scale scale simulations minimum tasks tasks tasks human human multi times regions mapping factor feedback feedback feedback feedback feedback orientation policy knowledge negative negative artificial relative represented receptive receptive receptive receptive receptive receptive receptive provide provide provide location active eye eye eye eye eye determined determined determined connected gain cortical brain mit mit larger larger larger contrast contrast contrast contrast fields fields fields fields fields fields fields support consists consists consists individual individual joint final layers layers cambridge computing computing additional curves curves trajectory top top stimuli stimuli stimuli stimuli stimuli bit detection detection conference conference upper upper upper upper upper vision vision vision vision vision vision vision vision vision vision vision vision vision vision vision give coding coding developed developed levels levels path path path path path iteration iteration iteration nature inhibitory sampling biological biological biological achieved measured feedforward increases group group group group transformation assumption corresponds complete complete stable stable stable stable stable surface surface short short short implemented shape shape shape generate role role role main journal square square end end ability cluster cluster cluster sensory including typically combination dynamical dynamical functional functional york york edge edge increasing increasing representing call iterations iterations iterations inhibition international bottom bottom depth early early early early early early early early decay decay decay decay decay robust takes takes takes lateral introduced moving side side pixels pixels pixels hierarchical recently varying varying solve smooth smooth correspond correspond studies studies studies differential achieve achieve achieve achieve locations separation separation separation modified interval organization organization organization horizontal invariant invariant invariant extended wide rotation clusters clusters clusters clusters clusters occurs occurs boundary boundary pass demonstrate place place place place place place competitive retina retina suggest intelligence intelligence intelligence variety variety variety start movements plane decrease scene scene connectivity configuration configuration force force force areas areas areas edges longer perception perception perception primary primary plot plot laboratory laboratory laboratory ann modeled modeled category simultaneously physical involves angle scales scales scales scales scales scales scales scales scales scales adding gaussians formed formed shift shift extraction extraction extraction extracted expressed stationary stages interpretation influence codes transform evolution activities activities activities activities key partial classical convex generation filtering views coupling building perceptual perceptual perceptual perceptual perceptual perceptual contour illustrated illustrated automatic coupled coupled characterized determining aspects importance importance divided paths paths literature computations invariance invariance invariance excitation kind allowing allowing allowing video interpreted split cues cues cues sampled michael play play surround surround surround surround surround surround surround surround surround surround surround correspondence leading overlapping illustrates deal oriented law remain transformed create biases successive fashion authors gates pathway pathway workshop hierarchy analogous surfaces surfaces measurement onset predicts psychology illustrate illustrate art art generates detected detected simplest grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping isolated years convolution track phenomena diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion capabilities drive drive rapid forces located located desirable immediately mathematics grossberg grossberg grossberg grossberg sun fourth apparent apparent apparent apparent apparent reflect transient fed fed fed fed psychophysical detecting completion passed maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima compares psychological summarized summarized measuring spread spread serve serve serve curvature curvature curvature curvature curvature curvature boston boston expectations begins begins attentional attentional eventually eventually eventually extreme arithmetic instantaneous gap gap don representative discontinuities primarily accomplished accomplished saccadic saccadic appropriately linearity connecting enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement robotics proceed suppression proceeds proceeds proceeds logarithmic striate attractive attractive attractive interpret serves enhanced corner motivation passive passive passive passive schwartz schwartz schwartz centroid centroid centroid tokens tokens tokens tokens tokens tokens emergence neuromorphic reveals late saccades sustained motions motions motions motions merge merge merge merge merge acknowledge robert resonance crossing outline shunting shunting shunting shunting gaps gaps emerge emerge spatio spatio feeding profiles arbor causing causing perceived superimposed superimposed hundred suppressed workstation realize shifting shifting shifting insights grouped distant distant reflectance fixation spreading spreading spreading multiscale relates regimes regimes complementary rectified superposition slopes diagrams utilizing tail stores algorithmic allen influenced junctions utilizes diffuse realizations harvard engine anatomy anatomy anatomy anatomy emerges interpretations optics inspection filling periodically periodically remained irvine deformation deformation modulatory percept percept percept percept carpenter carpenter allowable allowable polar lights plenum progresses progresses progresses modulate spario 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#*network network network network network network network network network network network network network learning model model model neural neural input input input input input input data data data data function function figure figure set algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output system results results results information information information problem problem based space case systems values values values values values parameters noise noise noise noise recognition method method approach approach approach approach pattern point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single processing processing processing local local local local local analysis class inputs signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple visual visual visual examples examples small feature net net work methods step step step step step points field level problems problems random similar similar similar similar show equation fixed images images images images images images images images images general real real real average average average gradient obtained obtained obtained note note threshold computation computation solution research research research research research research defined initial initial initial constant constant constant constant constant constant constant constant constant constant constant constant standard computer science science science map map present machine machine machine object object object range press components components components nonlinear abstract find find find references component component component stochastic due ieee introduction action generated parallel parallel change change change energy spatial spatial spatial assume higher part center center center center center cases type type good conditions bayesian markov fact techniques region region resulting human respect sum times regions regions regions regions regions regions regions regions regions regions regions regions means factor factor factor factor potential applications knowledge filter original artificial artificial artificial artificial true define objects goal goal goal distributions discrete discrete brain brain mit mit mit mit connection support descent source source source morgan proceedings report institute institute institute institute institute department department department technique consists scheme scheme scheme scheme scheme ai ai ai cambridge cambridge cambridge cambridge computing san stage detection full approximate world vision vision vision estimated give produce channel channel derived criterion provided iteration iteration depends depends constraint constraint simply simply simply biological biological biological describe limited close inverse assumption assumption assumption surface surface surface surface surface surface surface surface surface surface surface finding finding finding amount effective effective assumed supported require require require require journal pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel noisy noisy noisy including kaufmann probabilistic hopfield reduced technology technology technology technology edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation uniform uniform uniform uniform uniform uniform uniform operation operation representing numbers iterations iterations filters magnitude magnitude choose light light improved discussed separate separate separate takes side side side pixels pixels pixels pixels quadratic cognitive cognitive cognitive sufficient solve solve smooth yields yields correspond correspond achieve background background channels channels grant parts occur derivative alternative white white white white boundary boundary pass half half assumptions conclusions operator operator operator central central central differences differences differences performs mateo propose strong strong strong strong strong physics characteristics intelligence intelligence intelligence intelligence intelligence intelligence regularization iii averaged averaged averaged scene scene scene scene acknowledgements edges edges edges edges edges edges edges edges edges edges edges edges edges edges perception optical winner factors describes laboratory laboratory laboratory laboratory label label label label vertical vertical vertical distinct implement explicitly explicitly coordinates coordinates coordinates averaging averaging averaging averaging averaging averaging averaging averaging averaging remaining spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral scales interaction interaction minimization john national reconstruction labels labels labels labels labels lee lee understanding completely allowed discrimination performing sec neighborhood iterative iterative iterative boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries remains visible foundation transactions david avoid thesis thesis color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color inter sciences sciences discuss black black black black absolute neighbors sensor society differ modification paths poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio identify comparing strongly anderson lie contribution cue sci gibbs relaxation surround thresholds processors disparity neighboring body body remain powerful american essential experience difficulty replaced mass rise office workshop analogous surfaces surfaces contours contours gradients editor detector explored phd phd finds synthetic synthetic massachusetts massachusetts massachusetts asymptotically advanced piecewise piecewise piecewise piecewise piecewise crucial distinguish sensors smoothness smoothness adjacent diffusion ring ring ring ring filtered filtered division directional scientific involve computers geometry geometry recognizing integrating requiring reflect dark fed red psychophysical introducing marked marked marked incorporated biologically requirement requirement requirement requirement requirement rely spread spread geman geman geman geman enables sums semi sharing contribute don discontinuities discontinuities discontinuities discontinuities discontinuities college college interface formally tation naval eliminate eliminate grey grey grey grey analogy contract contract serves serves obtaining mark mark mark mark belong illumination illumination illumination illumination illumination continue composition slice slice slice enhance accounts stereo stereo sphere sphere sphere yang reproduce viewing viewing recog specialized april smoothed bins bins clean agree projects splits border cam material material material material material material onr andrew andrew multiplying land ence largely corporation corporation shading rubin rubin aircraft aircraft ties break cooperative cooperative cooperative preserving nition encouraging tween ideally brightness brightness brightness brightness shaded rectangular pami goals goals continues graphics discontinuity reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance hughes hughes thresholded conversely geiger memo mimic loading loading behave psychophysics bridge restoration discontinuous justified attributed mrf mrf blake blake fill fill fill routines steven eliminates distinguishing unreliable unreliable agency wavelength wavelength meeting lightness marr marr luminance luminance luminance luminance luminance exploits sloan constancy constancy constancy constancy america reflection reflection reflection reflection reflection reflection reflection neutral colors colors colors colors colors filling filling materials materials iterating defense segmenting dij shares replicate spec spec jose lights replaces replaces sponsored relax enforcing hij ular contributing weinshall undesirable dana nation army disappear textured stuart highlight highlights nato sensitivities sensitivities sensitivities cate accompanied lumped illusion illusion annulus annulus annulus annulus marroquin marroquin spreads cial hue hue hue hue hue hue hue hue hue hue hue hue hue gions originate ond insures crossed quotient richards richards tomaso tomaso tomaso tomaso tomaso biilthoff inhomogeneous irrespective localised annu fills mas zisserman zisserman dation alt whitaker whitaker whitaker guides cie illusions artifi bipartite lus foun gradi phe regularize specular 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#@Hurlbert_A,Poggio_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output number system system system system system units units units units units units units units units units units units units units units units units units units information information information information information information problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance based based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer vector order order order order shown shown systems systems systems systems systems parameters noise noise noise weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition approach approach pattern pattern point point image image image image image image image image image image image image image image image image image single single single processing processing processing processing processing processing processing processing control large local test test test test analysis signal paper examples examples small feature net net work work work task task task task task task task field field field features features level level level level level level level level current current current current current current trained trained trained trained trained trained trained structure problems random high high high similar similar similar representation representation representation representation representation representation representation representation representation representation representation architecture architecture fixed fixed fixed fixed fixed images images images images images images images images images images images images images general speech speech parameter real real real real real real real real real activity activity dimensional result result university university research research research research independent initial constant computer computer computer computer computer computer computer connections connections connections connections connections connections connections science science science science left left left left left direction direction direction direction direction direction direction direction direction direction direction presented presented map activation activation activation activation activation activation activation activation activation activation activation activation low machine sets range range range range range range range range range range range range range range range range range range range range range range range position position abstract back back back back back references ieee ieee ieee important important important important important adaptive propagation propagation propagation propagation propagation introduction hand hand parallel change representations representations representations representations part center center center center center previous previous previous previous type type conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions represent expected expected expected markov make fact techniques techniques techniques techniques region correct correct correct correct correct correct correct ing simulation simulation human human performed performed performed performed made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation global knowledge filter filter filter vol vol vol artificial artificial artificial artificial artificial relative relative relative specific represented application application application desired desired proc proc location location perform perform perform perform determined connected connected accuracy contrast contrast support support source proceedings proceedings proceedings proceedings report report department implementation version technique consists consists internal individual represents connectionist difficult difficult difficult difficult final bias bias scheme addition cambridge cambridge computing computing hinton additional additional view san san san san conference conference conference conference determine determine determine choice significant significant free world world speed speed speed speed vision vision vision vision vision vision increase increase give con con condition developed developed developed developed developed developed developed robot levels levels levels levels area area area area area area path path path actual provided provided finally processes nature inhibitory depends achieved achieved discussion normal technical group group group group group tested tested limited excitatory excitatory finding finding supported supported role hypothesis development development sensory sensory simulated simulated simulated simulated simulated simulated simulated simulated simulated simulated fully fully jordan jordan jordan jordan interesting interesting interesting testing testing testing testing character york york edge edge edge head structures language representing filters filters making international international international supervised early magnitude sources light architectures directions directions directions resolution advantage robust takes takes typical typical typical practical include include include identical sense recently sufficient highly varying approximately tuning tions correspond trans positions modified grant intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity wide wide wide correctly touretzky touretzky width width width width half conclusion conclusions operator central central accurate accurate retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina designed designed asymptotic characteristics characteristics drawn california proportional proportional intelligence turn turn turn turn turn turn turn variety variety variety variety variety groups groups groups scene scene scene connectivity acknowledgements explicit digit digit pro van produces perception primary distinct involves slightly slightly consisting consisting consisting develop develop develop adding adding versus choosing national formation review depending phoneme stages interpretation interpretation interpretation interpretation lee centered centered forms diagram diagram diagram key partial reasonable epochs boundaries remains filtering sufficiently foundation david degrees degrees avoid expect handwritten handwritten handwritten figures figures priori color color retinal determines illustrated specifically specifically specifically specifically specifically specifically domains characterized tests tests tests planning planning planning planning middle extra capable divided divided effectively successful successful detect situation ten receives receives traditional traditional traditional traditional road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road 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navigation navigation navigation navigation navigation navigation navigation navigation navigation answer comparisons drive straight implementing implementing widely widely style located located located commonly laboratories involve members begin computers depicted annual annual mellon mellon mellon mellon sun sun exemplars exemplars exemplars exemplars improvements varies evaluating carnegie carnegie carnegie carnegie substantially elman elman elman elman cmu cmu cmu cmu cmu cmu cmu cmu cmu conducted conducted conducted autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous poorly schematic schematic schematic pittsburgh differs fall extensions extensions extensions extensions prevent curvature curvature curvature curvature curvature curvature curvature curvature acoustics simulator eventually contribute lab primarily generator generator generator mistake extensive extensive driving driving driving driving driving driving driving driving recover mobile mobile naval naval eliminate flexibility flexibility reaching dealing dealing significance promising difficulties difficulties difficulties vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle contract contract serves hope hope salient salient degradation obstacle obstacle date exploring exploring widths widths displayed pat lang evident uni jackel jackel jackel facilitate facilitate darpa enable suggesting ahead ahead proximity impact projects fly fly outlined dramatically dramatically land land land land land land land land slight slight ter guyon creates creates obstacles obstacles obstacles obstacles obstacles copy blue blue ease amherst solely solely possibilities reflected brightness henderson cessing gained robots hubbard pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau depicts projecting projecting projecting relates pos intensities importantly million finger tively supports supports avoidance bring dramatic travel travel travel travel travel travel travel travel travel travel wider correlate develops develops diagrams circumstances circumstances drives lighting lighting excess inhibit inhibited aid hull graf hour excited agency laser laser laser laser successively periphery periphery arpa cur spie spie weather coins alto robotic robotic accommodate fol adapts zeros charles defense inaccurate discovers dean monitored monitored simon palo tern stems months joseph joseph collecting rela shikano reviews rom darker darker darker darker thorpe thorpe thorpe thorpe thorpe versity retinas retinas warp warp warp warp warp warp warp roads roads roads roads roads roads roads roads roads roads army lowing tums cen snapshots snapshots snapshots 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#*network network network network network network network network network network network network network network model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data function function function figure figure time time time time time time time set set set set networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error state results results information information information information information information problem problem problem problem models performance performance performance performance performance performance based based based based based based space space weights layer vector order order order order systems systems systems systems systems systems systems systems systems values parameters noise noise noise noise noise noise noise noise weight neurons neurons neurons neurons recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point image image image image image image single single single single processing processing processing processing processing control control control control large large neuron neuron neuron rate rate rate patterns patterns patterns class signal signal algorithms simple gaussian paper paper small size size net task task task task field field field field field field field field field field field process process current current current trained problems problems problems problems problems high high high high memory memory memory memory memory memory memory memory response representation representation representation representation architecture architecture architecture architecture architecture architecture architecture section images real real real real experiments activity activity dimensional result computation research independent defined sequence sequence sequence dynamics initial constant table standard standard computer computer computer computer computer terms terms distance distance distance distance distance distance distance distance distance science science left direction presented map map map map low sets sets maximum range range press position position position position position position continuous sample sample sample sample abstract abstract computational computational properties properties properties references due due due important propagation introduction complex complex complex stimulus stimulus statistical effect dynamic dynamic parallel parallel parallel search tion change lower representations higher type required required multiple long conditions distributed distributed expected expected chip make correlation observed forward scale scale minimum minimum tasks tasks total simulation simulation simulation simulation human respect performed performed times times regions means factor optimization orientation orientation orientation applications applications knowledge knowledge vol vol artificial artificial relative relative relative samples receptive provide provide provide rates perform perform perform perform eye constraints constraints gain discrete brain power power mit accuracy accuracy comparison source words loss implementation implementation implementation implementation synapses consists internal code represents scheme addition addition considered cambridge equivalent equivalent directly hinton view view view view view view view view solutions solutions design san san san san san capacity determine determine determine determine full requires requires requires requires requires speed speed speed increase derived derived weighted randomly criterion velocity actual provided sampling biological associative achieved normal limited limited limited limited limited complete complete complete amount synapse synapse generate generate require require require eds face journal end vlsi vlsi vlsi pixel pixel degree development development fit simulated simulated simulated pairs needed needed combination technology technology technology technology transfer increasing mechanism matching database database database representing iterations pre stored stored stored stored stored stored bits bits normalized normalized bottom expert magnitude magnitude magnitude magnitude run architectures improved improve correlations resolution resolution pair pair pair pair pair pair pair pair pair pair pair element typical introduced introduced introduced pixels sejnowski highly highly compare conventional conventional conventional approximately approximately approximately approximately module axis axis axis axis axis axis axis axis match studies sparse address address address storage entire entire entire intensity intensity intensity intensity invariant digital matrices feed width hardware hardware hardware hardware half conclusions central central measures measures measures modules designed clear performs performs faster characteristics california intelligence identification identification identification identification areas monte van carlo optical primary laboratory laboratory laboratory laboratory confidence coordinates coordinates slightly slightly angle develop integrated versus yield correlated transform updated centered reasonable calculation smoothing measurements measurements classical event event initially distances distances degrees precision precision precision precision precision precision precision precision template includes priori priori priori coordinate bell prove prove coupled absolute absolute absolute major major planning reason reason determining sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor aspects identified extra capable importance importance included identify identify projections invariance invariance invariance essentially ten characteristic characteristic heuristic success success success running running device list involved sampled realistic providing board board board board board board board board board board highest highest cat consisted operating operating extract acknowledgments software software software oriented parametric perturbation requirements requirements circuitry involving involving involving optimized limitations limitations limitations limitations issues respond fashion fault scaled scaled workshop analogous neu possibly implementations prototype prototype portion portion portion portion detector mapped art store detected serial serial serial serial serial serial serial serial serial serial serial seconds devices advanced costs ground ground trivial sensors sensors navigation failure failure failure comparisons considerable inside rapid rapid perspective arc preprocessing preprocessing preprocessing preprocessing desirable arise scientific calculations radius radius sun sun sun sun sun sun sun geometric percent transient autonomous passed incorporated treated incorrect reliability reliability passes operate spread aim collective simulator simulator inherent decreased redundancy eventually acquisition acquisition aligned identifying intractable martin martin martin martin fix angular count lost systematic systematic consideration imaging minutes minutes attractive determination determination determination determination determination determination determination determination determination determination star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star star methodology methodology guide guide guide guide guide guide guide guide guide guide motivation motivation motivation document introduces governed governed conjunction searching sphere scan interconnections similarities enable recovery smoothed locked tracker tracker tracker tracker tracker tracker tracker tracker environmental properly horizon valuable speeds discovered automated acknowledge severe severe yale outperforms compressed compressed drop incorporates pointing ram ram dec year decomposed big brightness magnitudes execute guidance acquired ultimately retain intensities discusses electronics nasa interconnect interconnect thousands technologies technologies technologies technologies correlate dim achievable uniqueness thermal identifies jet jet jet heavily ongoing virtually dropped dropped dropped harvard inherently integrates anatomy core emerges operational discarded propulsion propulsion propulsion propulsion inefficient demands remained bottleneck barhen correlates format format subsystem neglected promise inform backwards rotational satellite satellite satellite satellite satellite recovering sorted thc rotate relax occasionally accuracies tolerant retrieve preprocessor preprocessor preprocessor preprocessor preprocessor bright bright proce enabled conversations concurrently volatile translational sky sky sky sky sky sky sky sky disappear thirty stars stars stars stars stars stars stars stars stars stars stars stars mature seventh equipment attitude attitude attitude attitude attitude attitude 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#@Alvelda_P,SanMartin_A,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data function figure figure figure figure figure figure figure figure figure time time set set set networks networks networks networks training training training algorithm algorithm output output output number number number number system system system system system system system system error error error error error state state results results results results results results units information information information information information information problem problem hidden performance performance performance performance performance performance based based based space weights weights linear layer order order order order shown shown systems systems systems systems probability noise noise noise noise noise unit recognition recognition recognition recognition recognition recognition recognition recognition recognition method pattern pattern pattern pattern pattern pattern point point image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single processing processing processing processing processing processing processing large large large rate rate rate rate rate test test patterns analysis analysis matrix form form form shows shows shows algorithms algorithms simple simple simple visual paper paper examples examples examples examples examples examples small small small small size size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net net net work task task task task task task task task task task task methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step step features features features features features features features features features features classification classification classification classification classification process process process level level level trained trained high high memory memory similar similar similar representation representation architecture show line line line line vectors vectors images images images images images images images images images images images general real real theory obtained obtained obtained activity activity activity result threshold computation computation found found found found standard computer computer terms terms science left left left present activation low low low machine object range range press press position outputs outputs outputs outputs abstract applied applied applied find find find find analog analog analog references ieee ieee ieee ieee ieee ieee important important important adaptive adaptive adaptive adaptive decision decision complex complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand circuit parallel parallel parallel parallel parallel parallel parallel cost search tion change variable assume classifier higher part center center previous previous cases required cortex good good good good binary long represent bayesian expected expected chip chip chip chip chip make make make techniques techniques techniques techniques techniques techniques techniques proposed correct errors scale ing tasks human human human multi performed performed performed performed performed performed performed called elements elements means factor factor factor potential obtain artificial specific compared application application receptive provide provide proc proc proc location location location location location perform active active active active active active active determined experimental mit steps steps larger contrast fields source source proceedings implementation implementation version consists code code code code code code code code individual kernel kernel difficult layers scheme maps maps maps maps maps maps maps considered considered framework environment additional estimates design design san san top top stage stage bit bit bit determine classifiers classifiers upper requires requires requires significant world speed vision vision basic increase give con coding derived clustering clustering developed levels lines lines actual actual provided provided provided provided iteration depends simply biological associative increases tested transformation transformation amount nearest nearest nearest nearest common common theoretical require require require main main main end end end vlsi vlsi pixel pixel pixel pixel pixel pixel easily noisy including fit objective objective objective typically smaller needed needed combination functional testing significantly ratio character character character character character character character york edge edge segmentation special matching database database operation operation details details call iterations pre direct making stored expert early idea combined combined combined combined combined minimize minimize sources light discussed resolution advantage advantage advantage separate separate element element typical typical reported practical apply introduced include identical machines pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels inference relevant engineering engineering interest interest highly highly highly varying compare compare compare approximately approximately approximately approximately yields studies studies studies trans address sensitive horizontal horizontal horizontal horizontal horizontal horizontal horizontal parts scaling scaling scaling scaling occur occur digital wide wide rotation rotation width boundary hardware hardware hardware starting place place place greater assumptions conclusions conclusions accurate designed designed designed clear practice taking hard cycle solid intelligence turn variety iii characters characters characters groups scene connectivity connectivity connectivity configuration acknowledgements digit digit digit digit digit edges written written written written written written written written written perception ways describes vertical vertical vertical vertical vertical changing segments confidence confidence confidence category involves involves involves remaining slightly consisting interaction develop integrated blocks extraction extraction extraction extraction john john expressed stages stages stages codes codes codes variation variation operations centered margin completely similarly similarly translation digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits processor reasonable calculation classical classical classical classical classical classical normalization purpose purpose purpose boundaries intermediate calculate sufficiently construction advantages classified transactions transactions degrees degrees precision precision precision precision precision template template template template template template template template template template template template template template template template template template template template template template template template kernels coordinate coordinate bell recognize recognize automatic automatic maximize variations variations black black holds neighbors neighbors neighbors neighbors neighbors discussions closely differ divided divided identify detect detect detect computations schemes schemes post comparing essentially fine capture compact compact conf conf conf repeated allowing split return classify classify gray list write dot realistic quantization cmos cmos denker denker denker denker denker denker denker denker cat chips received deal situations simpler unlike carried diego diego powerful layered layered layered layered wiley wiley create create collection collection humans strengths preliminary preliminary preliminary dataset dataset reducing ideas tech rest project project detectors detectors applicable int int office office decisions working phases analogous removed removed removed coarse coarse man extremely extremely created recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer aspect shapes art art utility arbitrarily motivated motivated motivated motivated motivated serial isolated percentage great great great advanced crucial convolution convolution convolution convolution convolution comparisons considerable rapid stanford easier easier widely preprocessing laboratories separately res res computers computers cybernetics recognizing outer raw raw questions improvements people greatly pure flexible lms passed remove remove remove remove remove formulated dots biologically compares templates templates templates templates templates templates templates templates templates templates templates requirement requirement requirement howard ture extracting suited suited achieves gave gave logical conclude shaped windows windows windows wang wang baird baird baird cor contribute contribute consistently don acquisition acquisition lab room benefit physiology sort writing databases rotated rotated impossible printed printed grey communications binocular systematic fits wrong convenient promising occurred mail mail mail loops loops loops loops loops check check moment moment mark removing knn knn knn knn knn effectiveness salient exceeds corner heuristics moments motivation service service service meaningful meaningful published published mouse sides jackel jackel thin matter matter clean repeatedly ends ends passing storing broken sons sons valuable hart hart pen acknowledge speaking mind resonance appeared compressed arcs unable misclassification accept wiesel wiesel guyon convolutional convolutional opposed formulate rejection preserving forced responds pieces distinction smoothly tradeoff hubel hubel breaking imagine massively massively reject remainder clas henderson preserved care ibm duda duda stroke stroke stroke stroke stroke pami thick thick thick thick blocking graphics parzen parzen parzen activate hubbard hubbard token writer rectangle rectangle careful rejected surrounding parallelism interactive topic deleted deleted importantly zip zip zip zip zip zip zip zip zip zip misclassified misclassified enforce enforce responding intl happen fea investigations indication applicability exploratory psychophysics recognizers recognizers demonstrating handled drives styles fortunately recogni font marks marks marks assistance nested jersey envelope envelope broadly graf graf graf graf graf spins outperformed char eliminates holmdel practically practically sided mori thickness detects substitution recognizes strokes strokes 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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data function function figure figure figure figure figure figure figure figure figure figure time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm algorithm output output number number number number number number number number number number number error error error results results results results units units units units units problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based space weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector vector vector vector vector order order shown unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method pattern pattern pattern pattern pattern pattern pattern pattern single processing large large large large large large local rate rate rate rate rate rate test patterns patterns patterns patterns analysis analysis analysis matrix matrix matrix form shows visual small small small small feature feature feature feature feature feature feature feature feature feature feature net task task task methods methods methods methods methods methods methods methods methods methods fig fig step field process level current trained trained trained trained trained structure structure problems high similar similar similar similar similar similar representation equation equation equation equation vectors vectors real average average average average average theory result result result threshold research found constant estimate left left left left left left left left left direction presented press learn learn learn learn learn learn learn sample sample sample abstract applied applied back computational density density references component component due ieee procedure important propagation propagation introduction complex hand hand hand parallel difference difference difference difference lower learned chosen higher higher required required good distributed make make make make fact fact proposed correlation correlation correlation correlation length correct observed observed forward forward scale scale scale scale tasks total simulation human sum called means made natural global obtain vol samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples compared rates rates rates rates rates connected connected equal mit accuracy accuracy accuracy connection fields support words words implementation individual difficult difficult difficult difficult layers addition computing computing experiment experiment experiment experiment experiment environment environment environment environment environment significant world speed increase types provided backpropagation backpropagation iteration 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#@Mori_Y,Yokosawa_K,
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information information hidden hidden hidden hidden hidden hidden hidden performance performance performance based weights weights weights weights weights weights weights weights linear linear linear layer layer layer layer layer layer case order shown shown shown systems systems systems systems systems values values values values probability probability probability weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons unit unit distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach pattern pattern image image image image image image image image image single single single single single single single single single processing processing processing processing control large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix inputs inputs inputs inputs inputs form signal simple visual visual paper paper small net net net work work task task task task task features classification classification classification classification classification classification classification trained trained trained trained trained trained structure structure structure similar similar similar show equation line line line line images images real approximation theory theory term note university university university university threshold threshold threshold threshold threshold threshold threshold research target target initial computer computer science science science left presented presented presented presented presented presented presented present present present low temporal motion press position basis sample sample sample sample sample sample sample sample sample sample sample abstract references due ieee ieee ieee ieee ieee positive positive important important important important adaptive propagation introduction hand statistical effect dynamic dynamic dynamic dynamic dynamic generated parallel parallel parallel parallel cost cost change variable lower learned cases cases type type good good good binary binary binary binary distributed chip techniques region forward tasks total simulation simulation performed performed regions regions regions means study obtain negative negative vol vol vol vol artificial true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true application application application desired perform active eye experimental connected connected connected mit update train nets proceedings proceedings proceedings report words department consists internal individual individual individual individual final bias framework hinton curve curve effects detection detection conference conference conference conference upper requires requires significant world speed speed con produce produce velocity types actual finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation technical technical feedforward group tested tested close amount short effective shape require require pixel pixel pixel pixel pixel instance rumelhart rumelhart rumelhart fit objective fully fully fully transfer transfer significantly character character character special special details iterations international international normalized normalized experts produced produced run run run run run run run run run added improve improve separate reported include include pixels pixels pixels pixels pixels sejnowski sejnowski sejnowski sejnowski sejnowski array cognitive varying previously calculated tions studies trans separation separation separation williams entire correctly feed white white white white generally conclusion place greater sigmoid clear exponential practice learns taking characteristics labeled labeled targets characters characters identification program question appears digit produces written written written written written index plot plot plot plot plot dept dept dept category electrical electrical electrical electrical remaining remaining text text angle letters extracted overlap overlap codes centered centered static static static static static static allowed discrimination processor calculation false false false false false false false false false false false false false false assigned classified transactions transactions transactions transactions transactions handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten box figures figures instances sciences plotted plotted automatic black black black partially selecting importance society divided divided included included included included included mcclelland presentation successful detect detect post plots online identity ten characteristic content simplified denker leading chips received consisted overlapping operating software software software decreasing camera camera employed employed collection collection updating project project applicable possibility office workshop scores cognition momentum momentum examined examined math trace reading man extremely extremely equally perfect perfect perfect adjusted aspect noted simplest electronic devices devices fairly improves majority stanford stanford stanford stanford stanford stanford lin style style style day desirable laboratories laboratories pool pool involve read depicted author author annual cybernetics people people people people people greatly collected amounts documents documents detecting ture proven sophisticated attraction credit cumulative cumulative cumulative initialization picture picture picture person person lab lab lab benefit writing writing writing writing investigation linearity signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature concerned jth eliminate lost lost eliminated handwriting handwriting handwriting handwriting handwriting spot corner selects falls expanded lengths demonstration demonstration widrow jackel jackel jackel scheduling scheduling lawrence foundations eng eng eng record verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification erlbaum broken tures tures tures receiving avoiding automated automated automated ccd linguistic radar radar radar pressure pressure roc roc roc roc roc roc piece piece goodman goodman goodman goodman goodman goodman legal rejection rejection rejection rejection rejection rejection rejection bank axe feeding year copy blue personal individuals individuals individuals hillsdale massively representa verified verified henderson ibm signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures hubbard proba thresholded oct efforts eliminating writer writer writer writer writer wise wise depicts depicts names employing option zip associates sonar sonar sized likewise dsp nil info info info scanned bility impractical rosenberg rosenberg rosenberg rosenberg jersey spacing hopkins graf devised devised substitute edited capital tokyo strokes johns losses daily implying assp nettalk nettalk nettalk edition ranged fication comprised gathered jan capturing eighth sep 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#*learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural input data data function figure figure figure figure time time time set training training training training training training algorithm algorithm output output number number system system system state state state state state units units units units units units units units units units units units information information problem problem problem problem problem performance performance performance based based based based based based space space space space space space space linear vector vector vector order systems systems systems systems systems systems parameters weight functions neurons unit unit approach approach approach approach approach approach approach approach approach approach pattern pattern image image image image image image image image image image image image image single single single processing processing control control control control control control control control control control control control large local neuron neuron neuron analysis shows shows shows shows algorithms algorithms simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual examples small small size feature feature work work work fig fig fig fig fig fig fig fig fig fig fig fig step step step field field field field field field field field field field field field field process level level current current trained structure structure structure structure problems problems problems random random similar similar representation representation representation representation architecture architecture architecture architecture architecture architecture show section images general general general real real real approximation average note note dimensional university university university threshold computation research research sequence target target target target target target target target dynamics dynamics initial table standard standard computer distance connections synaptic synaptic synaptic synaptic synaptic science left left direction direction direction direction map present activation activation low machine machine machine motion motion motion motion motion motion motion motion press press learn position basis nonlinear continuous sample abstract find computational properties references due ieee procedure introduction action action complex complex complex complex hand hand hand hand hand hand hand hand hand hand hand behavior behavior effect dynamic dynamic dynamic generated generated generated parallel parallel parallel search search search search search search search tion tion change complexity assume lower lower representations representations learned learned learned learned learned learned part center center center previous previous cortex represent equations equations resulting ing ing ing human multi multi multi called mapping mapping mapping mapping mapping mapping mapping mapping made global applications knowledge vol represented represented desired desired desired cross series receptive receptive goal motor motor motor motor motor motor motor motor motor motor cortical cortical brain brain approaches approaches mit steps steps steps fields support train source report report report institute institute institute consists consists consists internal internal joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult final scheme scheme addition ai maps considered cambridge environment environment environment directly additional view view design trajectory stage detection efficient upper upper full full significant approximate world vision vision vision vision vision channel coding weighted robot robot robot robot robot robot robot robot velocity controller controller path depends simply biological associative discussion discussion normal technical describe arbitrary arbitrary inverse inverse inverse inverse inverse inverse inverse finding implemented shape generate supported eds degree makes sensory sensory sensory sensory sensory sensory sensory including including including typically typically reduced reduced reduced functional programming projection york york structures trials trials operation operation principal direct direct direct direct direct direct direct direct direct direct making magnitude frame frame frame frame produced description membrane population population population population population population population population population population discussed takes typical typical movement reported practical moving period hierarchical trees trees cognitive recently relevant relevant engineering highly highly highly 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mathematical distinct implement implement coordinates coordinates simultaneously physical physical physical physical angle angle angle angle angle angle angle consisting national extracted review detailed detailed evaluated evaluated evaluated operations operations operations fraction frames frames static static static static classical spaces sec purpose initially advantages perceptual activated simplicity planning planning planning planning planning planning aspects aspects modification computationally paths paths driven driven driven driven computations schemes post post post essentially online kind kind repeated induced allowing allowing allowing heuristic video video link link running running physiological criteria built quantization quantization reach reach principles principles moves moves moves moves moves overlapping illustrates illustrates subsequent subsequent deal software camera camera camera camera camera camera camera camera remain carried carried american difficulty humans detail fewer giving project mappings mappings referred complicated phases removed coarse measurement naturally trace configurations extremely psychology psychology thought freedom mapped art consist improving utility animal great great ment ment directed coded coded expensive briefly sections closer organized style mathematics scientific angles demonstrates geometry nsf sun virtual virtual fourth fourth questions evaluating evaluating populations populations populations populations populations populations populations populations populations substantially relevance marked commands reaches plan specifies progress progress consistently representative ordinary physiology feasible primarily appropriately labelled concerned repre interconnected interconnected robotics robotics robotics robotics reaching reaching reaching reaching reaching reaching reaching reaching reaching reaching reaching inspired inspired inspired inspired murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy convenient imaging minutes accepted primate resulted keeping nearby north spot guide guide carry hours heuristics obstacle obstacle bartlett cerebellar falls representational representational sion paul cmac mental mental mental mental mental mental mental mental mental mental mental dominant heart mel mel mel mel mel arrangement cerebral layout suggesting suggesting reader repeatedly rich arrows proximity broken jump omohundro tures avoiding explorations explorations explorations explorations explorations treat fired street ple specification workspace workspace workspace workspace visually visually visually visually visually visually visually kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics fellowship super encodes legal obstacles obstacles obstacles obstacles failed responds pieces pointed sigma sigma sigma sigma sigma perceived constitutes affects massively massively var tight representa quantized acting rectangular exam graphics activate guidance thresholded thresholded individually rejected depicts parallelism guided guided guided guided guided guided guided lookup relates speedup manipulator emphasized nonetheless setup setup superposition sweeps modality stuck stuck places places struc september emphasis rarely replacement stephen algorithmic ate heavily evolved albus albus imple imple puts illinois illinois illinois kinematic kinematic kinematic kinematic kinematic concrete episodes sen core automation detects dedicated push interpolating carries deals systematically joints joints joints vertebrate merzenich triangular robotic physically planner translates substrate devoted brought massive limb limb limb sented freely urbana urbana comprehensive rotate spots spots spots spots primates primates collision collision collision collision plausibility phy phy phy phy teachers dealt def treats mentation mentation albeit pursued comprises billion pushed controllable manipulators manipulators pri workers neurally neurally beckman beckman distinguishes conveniently encouragement mary grain originating analogously prevented fell mammals blobs blobs shoulder recognizable champaign lozano manageable elbow heuristically lengthy visiting augmenting living posture posture terminating cluttered jacobjan opportunities asme subpopulations subpopulations subpopulation sory coarsely coarsely raven behaviorally stressed requisite kaas interests synaptically attacked mentally mentally trap appropri ingly wrist thirdly wander ious encod guesses overt combinatorially supercomputing matic flag backtracking psychobiology abc unprocessed projec kine flailing sheer layouts 
#@Mel_B,
#t2
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time set set set set set networks networks networks training training training training training training training training training training training output output output output output output output output output output number system system error error error error error error error error error state state state state state results units units units units units units units units units units units information models models models hidden hidden hidden performance performance based based based space space space space weights weights weights weights weights weights weights weights weights linear layer layer vector vector order shown shown shown shown shown systems values values values values noise weight weight weight weight weight weight unit unit unit unit unit unit approach approach point point point single single processing processing control control control control control control control control control control control local neuron rate test test test test analysis shows shows shows shows signal paper paper examples small size size size size size size size size size size size net work fig random random random high high high response response response architecture architecture architecture show show equation line line line line line line generalization generalization generalization real real theory theory theory experiments experiments university university university threshold research research research independent target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant table table standard standard computer terms connections connections connections science science prediction left left frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal maximum range range range range press learn learn learn position position position position position position position position position nonlinear continuous sample sample abstract applied applied applied references references component ieee ieee ieee positive important adaptive propagation introduction introduction dynamic dynamic dynamic dynamic dynamic generated generated generated parallel measure measure part part part type required distributed expected make fact correct errors errors simulations resulting resulting resulting total computed feedback study study negative negative specific samples samples samples represented application desired desired desired desired desired active determined connected connected motor mit steps steps accuracy accuracy accuracy larger larger larger contrast connection train report report department consists internal joint joint joint joint joint joint represents difficult bias delay addition cambridge cambridge computing equivalent hinton hinton hinton estimates trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory top top effects effects effects effects effects capacity capacity upper speed give derived randomly developed robot robot robot robot robot robot robot area velocity velocity velocity velocity velocity velocity controller controller controller lines backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation sampling sampling achieved measured measured measured measured measured measured measured technical technical feedforward feedforward feedforward limited inverse inverse inverse corresponds common theoretical journal square square ability ability rumelhart including fit pairs needed combination unknown block transfer testing empirical details details numbers filters filters filters direct direct direct direct direct direct direct direct window window window window window window window window window window window window window window window window window window window window window bottom magnitude run predict improved pair movement introduced hierarchical subset subset compare conventional conventional conventional conventional works tions smooth correspond correspond correspond positions positions williams sensitive entire entire entire arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm horizontal parts scaling deviation deviation predicted predicted predicted predicted touretzky loop white strength conclusion place place place trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories sigmoid accurate accurate performs faster faster practice suggest propose largest largest external cycle drawn proportional iii identification acknowledgements primary generating generating plot laboratory ann ann ann ann physical physical physical physical physical physical physical physical remaining remaining interaction john national national family family family family family lee centered sizes sizes translation diagram diagram diagram epochs intervals add filtering filtering msec sufficiently foundation foundation building box figures figures includes thesis formulation black simplicity sensor extra capable divided driven detect literature ten fine fine fine kind interpreted interpreted sin generalize generalize generalize thresholds principles moves modelling remain parametric difficulty recursive mass fashion school links links rest ideal scaled office root root cognition extremely portion logistic shapes epoch improving extent phd seconds rows floating caused nonlinearity drive drive drive drive drive drive drive drive forces division lowest author mellon mellon mellon argument carnegie carnegie carnegie cmu cmu cmu cmu cmu cmu cmu parameterized effort atkeson atkeson marked pittsburgh popular incoming semi chose comments shaped windows windows windows windows windows windows yielding displays newton temporally linearity pick pick nat naval robotics robotics saturation difficulties odd odd odd odd los contract interpret kawato kawato hope mark neurobiology reasoning corpus hertz document april express omitted locked refers draw pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter grants explorations robert treat microstructure torque torque torque torque torque torque torque torque torque torque torque torque torque torque torque torque torque torque feeding conjecture weiss weiss tradeoff decomposed acceleration acceleration acceleration acceleration acceleration acceleration acceleration avoided representa favor compensate maintained books relates manipulator superposition lapedes drives august const const assistance confirm bold bold bold bold conceptual fill december compensation disturbances automation interpolating goldberg goldberg goldberg goldberg goldberg alan outgoing bat joints joints joints magazine bradford addressing gathered alamos translates uno suzuki zone sponsored decompose dead sixth traversed mason multiplications claimed manipulators blob blob experimentation arms arms arms arms comprise ponents prevented fellow euler braun blobs blobs blobs blobs dam permission shoulder shoulder shoulder dave elbow elbow invaluable app eet torques torques torques torques barak eleven cancels memorize friction friction friction voluntary linearize ries photograph rum dat reserved ick aset geared trajecto 
#@Goldberg_K,Pearlmutter_B,
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functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution point processing processing processing control control control control control large local neuron rate rate patterns patterns shows shows simple simple gaussian visual visual visual visual visual visual visual visual visual visual paper paper examples small feature net work work work fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells step field level current cell cell cell cell cell cell cell cell cell cell cell structure problems problems high response response response response similar representation representation architecture architecture architecture architecture architecture show show equation equation equation section section section section rule real real real real average average average average average note experiments experiments activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional university threshold computation research research found target target dynamics dynamics standard standard standard standard standard standard standard computer connections connections synaptic synaptic direction direction direction direction direction presented map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map present present present present present phase phase phase phase phase phase phase activation activation frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency maximum maximum range position position position position position position position position position position position position position position abstract applied properties properties references due adaptive introduction complex stimulus stimulus stimulus stimulus effect effect tion tion tion change difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference spatial spatial spatial spatial spatial lower representations representations higher part part part center center firing firing firing required multiple multiple multiple multiple multiple multiple spike long represent represent represent represent represent represent represent expected make make fact region region simulations ing simulation simulation simulation multi sum called called times regions regions regions regions regions mapping factor potential potential potential orientation orientation orientation orientation applications study artificial artificial represented represented represented represented true true true true true objects location location perform active active active active determined experimental experimental posterior posterior motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor brain brain brain voltage voltage support source source source source source source source source modeling department version version internal represents represents delay delay delay delay delay delay delay delay delay delay delay delay delay delay addition addition maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps experiment environment view stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects upper con derived derived weighted randomly evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological biological group complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory finding amount amount common common common common common common supported face noisy sensory sensory sensory sensory sensory sensory sensory sensory fit auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory simulated simulated dynamical functional interesting york increasing increasing head head head head head head head head head head head head mechanism structures structures structures structures representing representing representing representing representing representing representing representing representing representing call max inhibition inhibition inhibition inhibition inhibition inhibition international combined produced sources sources sources sources sources sources neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal architectures membrane discussed recent property pair separate takes lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral period period side quadratic recently relevant relevant compare compare tuning tuning tions tions correspond address positions positions positions positions positions positions locations locations organization sensitive constructed exists parts parts parts intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity occur occur occur suggests wide spikes spikes spikes derivative move width conclusion editors central differences retina suggest sound presence presence external sigmoidal proportional turn decrease targets targets acoustic acoustic pro construct produces produces ann tuned vertical changing explicitly simultaneously simultaneously averaging averaging averaging averaging averaging easy frequencies frequencies frequencies frequencies equilibrium decreases independently communication communication squares squares centered centered activities similarly earlier earlier reasonable delays combining add false construction construction construction construction construction construction david david degrees degrees degrees degrees degrees degrees fire fire fire fire inter inter inter inter inter inter inter inter plotted discuss discuss discuss black black reason reason aspects differ literature efficiently post projections projections essentially fine receives receives soc soc quickly kind interested neuroscience conductance superior physiological timing cues cues cues cues comp comp quantity bar vary vary usual localization realistic realistic wave computes automatically neurosci neurosci neurosci neurosci neurosci received attempt acknowledgments receive receive receive receive cowan bars stimulation stimulation stimulation stimulation stimulation wiley exponentially steady strengths oscillator oscillator oscillator fewer fashion project project behavioral muscle muscle neu naturally transmission plausible integer onset man opposite extremely rev voltages voltages thought quantities quantities mapped mapped nervous nervous nervous explain years mentioned great great fairly fairly fairly fairly fairly biology interneurons spatially drive sys sys closer organized producing broad broad nucleus nucleus nucleus nucleus potentially sounds grossberg grossberg researchers requiring apparent varies limits pure pure experimentally experimentally continuously biologically ity mod differs monotonic conductances conductances conductances kinds owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl eventually cochlea picture spectra princeton princeton princeton pick pick driving narrow harmonic harmonic tem tem eliminate lost eliminated affected north optic optic optic optic optic fires motivation inferior inferior started tone holland overview overview moved moved mental peterson peterson peterson peterson peterson april thin stimulated stimulated stimulated mem suggesting refers refers refers colliculus colliculus ends agree projects projects projects explains intersection intersection receiving ence shading minus solves equivalently stem stem affects suppressed streams illustration barn barn barn barn barn barn barn barn barn barn barn barn barn barn barn barn capacitance preserved increment trends rectangle rectangle electrodes electrodes constructs constructs associates register apparently figs sized inversely knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen suffer suffer tones ation tune milliseconds tissue experi picking tension drives info stimulating stimulating twenty tial marks inhibit jersey jersey locate locate focuses tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum clarity pearson pearson pearson pearson pearson suppress suppress suppress eral eral incorrectly neocortical affecting essen fre horizontally horizontally settle equa konishi konishi konishi konishi konishi konishi konishi konishi konishi konishi core core obey obey grids arrives arriving tance leakage approaching iid iid iid vertically vertically dimen quick thresh merged promise ears wagner wagner firings imum tectal nice neigh elevation elevation elevation elevation stand lid lid lid lid predic excite men reviews spence spence spence spence spence quency conceptually mention posi damped damped damped accessible accessible begun neurology neurology workers picks itd itd itd itd itd itd itd itd itd itd abstr abstr membranes testable inhibits suppresses ending shell shell shell shell shell shell shell shell shell shell azimuth azimuth azimuth azimuth azimuth azimuth azimuth azimuth aver ghost ghost ghost ghost ghost ghost binaural binaural binaural critically duce looked handles neurophys quantifies sev private private antagonist strip strip strip resemblance lat imitate quadratically quadratically brane conduc 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#@Gelfand_J,Pearson_J,Peterson_R,Spence_C,Sullivan_W,
#t2
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#*network network learning model model model model model model model model model model model model model model model neural neural neural input input input input input input input function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time set number system system system system results results results results results results results results results results results results information problem models models models models models models models models models models models models based weights weights weights linear linear linear linear linear linear layer layer layer layer case case case case case case shown shown shown shown shown shown shown values parameters parameters weight weight functions functions functions functions functions functions unit distribution pattern pattern pattern pattern pattern point single single single single 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constant constant computer terms distance distance distance distance distance connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic prediction left left left presented map map phase activation activation sets maximum range press nonlinear nonlinear continuous abstract find computational properties references ieee positive positive positive positive positive positive positive important introduction complex complex hand behavior statistical effect effect effect effect tion tion change change change change change difference variable variable assume assume lower center previous cases firing firing firing cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long conditions conditions represent equations equations equations equations equations correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation scale scale simulations simulations simulations simulations simulations simulations resulting total total simulation simulation simulation simulation computed computed respect sum performed times mapping made orientation study negative negative negative relative relative specific compared compared compared series receptive receptive receptive receptive receptive receptive receptive receptive rates rates proc proc location location active active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined experimental constraints constraints constraints constraints constraints constraints constraints gain cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain equal mit comparison larger larger fields fields fields fields dependent dependent dependent dependent dependent dependent modeling synapses synapses synapses synapses synapses synapses synapses synapses synapses individual individual individual represents responses responses final final exp exp layers layers addition ai maps framework framework curve limit limit limit limit limit limit san top top effects effects effects effects bit determine significant world basic basic basic increase increase increase give con con condition derived randomly developed developed developed iteration iteration inhibitory inhibitory depends depends constraint biological biological biological biological biological biological biological normal close corresponds corresponds complete complete complete excitatory excitatory excitatory excitatory excitatory excitatory stable short nearest nearest common effective effective implemented assumed assumed synapse synapse supported supported eds eds square square square development development development development development development development development development development development including including typically smaller fully fully projection uniform mode mode mode mode mode mode mode mode mode mode mode principle leads leads representing representing representing representing numbers iterations iterations pre normalized bottom decay added population recent correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations robust typical lateral period period identical side sufficient varying previously unsupervised volume volume tions tions solve yields yields yields correspond studies achieve trans locations symmetric grid grid grid grid grid grid grid grid grid organization organization organization organization amplitude expression expression expression expression lead studied studied studied studied occur occur extended wide predicted locally width white boundary column column column column column column column column column strength strength strength strength strength strength strength strength conclusion critical critical critical greater operator depend interactions interactions differences differences measures accurate peak peak peak peak peak peak weak constrained mechanisms presence presence presence largest proportional variety variety decrease decrease decrease introduce connectivity acknowledgements relation construct written longer index factors factors factors factors stability stability mathematical distinct dept dept dept coordinates coordinates interaction interaction interaction interaction interaction interaction interaction interaction interaction develop adding adding independently formation formation formation formation formation formation formation formation formation dependence review review depending correlated influence influence influence influence codes solved variation variation transform transform transform open ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular centered decomposition understanding activities constants allowed spectrum spectrum spectrum sign sign closed closed initially initially initially calculate assigned foundation foundation fire fire fire perceptual coordinate coordinate usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance illustrated illustrated black black neighbors neighbors columns columns columns columns columns columns columns columns selecting middle modification modification modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes post tend miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller essentially identity identity characteristic characteristic characteristic soc soc neuroscience sci michael absence eigenvalue eigenvalue principles overlapping neighboring load modelling origin remain remain selectivity diego perturbation perturbation create exponentially involving detail strengths hanson accurately periodic periodic periodic fourier fourier fourier fourier giving plasticity plasticity analytically analytically analytically relationships oscillation oscillation oscillation oscillation oscillation oscillation func func statistically patch analyze predicts opposite opposite opposite opposite opposite changed eyes eyes eyes eyes eyes eyes eyes eyes eyes separated separated hebb hebb hebb regime submitted rows rows ment developing developing crucial growth growth growth growth growth growth growth growth growth growth growth growth agreement convolution analyzed growing growing growing growing growing unstable unstable unstable biology analytic analytical analytical analytical analytical analytical diffusion briefly starts drive stanford organized broad broad choices monkey afferent mathematics acad calculations patches patches patches patches patches patches linsker linsker linsker linsker radius radius radius radius radius nsf questions varies varies varies populations release release perturbations anti anti anti anti characterize limiting limiting limiting spread maximizes cal lim cor cor contribute phenomenon physiology physiology optimality interface extensive perfectly neurophysiol purely purely purely purely grows rotations grey grey binocular binocular binocular striate grow grow grow grow transforms sanger sanger selects selects selects weakly ranging ranging corre widths negligible dominant enhance enhance uni lawrence interconnections nonlinearities nonlinearities tic diameter diameter diameter diameter diameter diameter young suggesting erlbaum subsequently hart grants characterization ure appeared largely largely largely incorporates incorporates fellowship wiesel wiesel wiesel wiesel wiesel alternating exception arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor hubel hubel hubel hubel hubel suppressed suppressed hillsdale forcing forcing alter monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular publication equality equality segregation segregation segregation segregation segregation segregation mammalian mammalian dominated dominated intra gluck lond associates sheet afferents afferents reveal reveal eigen prevents examination wider species arbors arbors arbors arbors arbors rfs rfs hat hat inhibited oscillate developmental developmental stripes stripes stripes broadly suppress connects inherently continuum sharply exclusively exclusively exclusively exclusively exclusively subtracting subtracting subtracting wavelength wavelength wavelength wavelength wavelength wavelength wavelength wavelength wavelength wavelength wavelength wavelength wavelength wavelength peaked intracortical emerges measurable grids grids fastest fastest fastest fastest fastest reality confined confined bradford closure robustly carrying tical rem rem eigenfunctions eigenfunctions eigenfunctions eigenfunctions eigenfunctions eigenfunctions eigenfunctions indi spec refine refine repeating stryker stryker stryker stryker stryker stryker stryker stryker stryker stryker stryker stryker stryker putational joseph predic broader broader broader phil coincides dominate corr corr corr corr reproduces cortico serving conserving lose lations mon nectionist conserved synchronously synchronously restored asynchronously ucsf ucsf ucsf keller keller keller keller keller keller keller keller keller mexican mexican reflections bor eigenfunction eigenfunction eigenfunction deprivation strengthening swindale swindale swindale trophic trophic trophic acter supercomputer undertaken innervation kenneth bilateral innervated innervated vidual radically nction ceptive circularly nance conserve conserve conserve segregate neurosc innervating innervating mazimum telling ticity domi rumel mso larity levay levay dimensionm mathemati unilateral acteristic anticorrelated arborization pioneering predoctoral 
#@Keller_J,Miller_K,Stryker_M,
#t2
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information information information models models based based case order order shown shown shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems parameters functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns patterns class class inputs inputs form shows simple small small small small small small small small small small small small small small work work work work work methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells level level level current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell response similar similar similar show show line line line general real real real real real real note note note experiments activity activity activity university research found found found found initial constant constant computer connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic phase phase phase phase phase frequency temporal sets motion press press press press press press learn basis outputs abstract applied analog analog analog analog analog analog properties properties references component positive important important action action action complex complex complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior tion higher part part firing firing firing type type type required multiple spike conditions represent chip chip make techniques length length observed scale minimum ing simulation simulation simulation simulation elements elements potential feedback feedback feedback feedback feedback study negative specific rates active active determined connected gain motor motor motor motor motor mit connection connection connection support train source source source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling institute synapses synapses synapses synapses synapses synapses synapses synapses synapses consists internal internal internal individual bias delay delay delay delay delay delay delay delay delay delay delay addition addition addition cambridge computing stimuli determine basic basic basic produce produce levels types finally processes nature inhibitory inhibitory inhibitory depends biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological normal describe tested fast fast excitatory excitatory excitatory excitatory excitatory circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits common implemented synapse synapse synapse synapse generate generate role role eds square vlsi vlsi vlsi vlsi vlsi vlsi vlsi makes makes development sensory including including smaller underlying account technology technology technology technology block interesting interesting interesting york york mechanism mechanism consistent principle representing details numbers numbers numbers making inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition magnitude magnitude attention produced neuronal neuronal neuronal membrane membrane discussed property property property property pair pair element element element element element typical movement period period identical engineering interest channels organization organization increased constructed studied studied studied digital feed hardware demonstrate runs strength conclusions central central central central central central central central central differences retina retina designed taking hard mechanisms mechanisms mechanisms mechanisms mechanisms integration external external cycle cycle demonstrated california pulse pulse pulse exist selective relationship iii introduce produces produces longer longer ways primary generating generating ann modeled modeled explicitly physical involves interaction formed formed potentials potentials potentials john focus influence detailed detailed understanding understanding constants constants constants diagram diagram slow slow slow delays delays delays delays delays delays sec intervals purpose msec foundation koch building building fire fire fire fire fire fire fire fire fire box figures figures currents illustrated activated coupled structural structural identified closely included oscillatory oscillatory oscillatory build miller miller miller miller receives composed excitation excitation compact kind allowing conductance oscillations duration bar michael simplified simplified play play absence delayed delayed delayed cmos principles attempt attempt acknowledgments intrinsic body essential essential exhibit mead mead mead mead mead mead mead mead put detail detail detail detail integral behaviour ideas investigated transistor relationships relationships office understand act transmission trace reading rev thought generates electronic isolated animal animal years burst burst burst burst great stop fairly biology capabilities ganglion ganglion ganglion ganglion ganglion drive producing transistors transistors transistors transistors immediately controls controls controls pulses pulses pulses potentially potentially begin begin demonstrates nsf researchers greatly prop peter peter peter effort orders recordings incorporated schematic schematic release release exhibits rely differs aim gen qualitatively pasadena enables inherent chose display physiol physiol begins begins eventually simultaneous wesley don addison generator generator generator fabricated fabricated amplifier animals animals animals neurophysiol neurophysiol naval cellular bower bower bower bower bower bower bower chemical hope exploit integrator responsible wilson wilson hours fires date reset james studying reproduce darpa axonal bursts bursts matter contact extensively relies relies alternatively receiving acknowledge numerous alternating alternating medium medium rhythm molecular capacitance insights mammalian mammalian mammalian gener gener generators generators generators generators generators eliminating guided rhythmic rhythmic rhythmic oscillating oscillating oscillating oscillating oscillating oscillating dorsal dorsal accounted intracellular ation flight flight flight flight flight reciprocal reciprocal reciprocal reciprocal resembles functionality externally bursting bursting bursting bursting cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg allen allen allen allen swimming swimming swimming swimming impulses inhibit oscillate evolved pearson pearson pearson fabrication fabrication supplied integrates ventral ventral tended colleagues vertebrate reproduced marder marder mosis ready ionic ionic ionic stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric selverston selverston selverston selverston selverston selverston devoted indi tory enabling sponsored plenum plenum facilitates initiated carver carver configured configured nice repeats wait enabled segev exhibiting electrically released released released inhibits inhibits invertebrate invertebrate invertebrate invertebrate inactivation 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#@Bower_J,Mead_C,Ryckebusch_S,
#t2
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#*network network learning neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data function figure figure figure figure time time networks networks results information information information information based based shown shown shown shown shown shown shown shown neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons pattern pattern pattern single single single single single control control control control control control control control control control control neuron neuron neuron test test test test test patterns patterns optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form algorithms visual visual visual visual visual visual visual feature net net methods fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells field field field field current current current current current current current current current cell cell cell cell structure high high high high high memory memory memory memory memory memory show show theory term term term term term term term term term term term term term term term term term term term note experiments experiments experiments experiments experiments activity activity activity activity activity activity activity university threshold solution research research independent independent found found found constant standard standard synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science present present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation activation activation activation activation low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal press press abstract applied applied applied applied find computational properties properties properties references due important context introduction action action action action action stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical effect effect tion tion change change change change spatial lower prior higher previous firing firing firing firing required cortex cortex cortex cortex spike spike spike long long long long long long long long long long long long long long long long long long long long long long long long long long long conditions conditions conditions tree make techniques observed ing ing total elements potential potential potential potential potential made made orientation original specific specific specific specific application application application series receptive receptive compute proc proc proc active active active related constraints cortical cortical brain brain brain brain brain brain contrast train train train dependent modeling modeling modeling institute department synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses responses responses responses responses responses responses responses layers layers addition experiment experiment san stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli determine efficient upper requires significant increase increase increase con con produce produce condition area path evidence evidence nature nature nature nature nature inhibitory associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative measured covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance increases tested assumption excitatory excitatory predictions finding finding synapse synapse supported eds ability ability hypothesis hypothesis development typically smaller combination reduced account block significantly significantly york mechanism consistent leads pre pre pre pre pre pre pre pre combined produced produced produced produced produced produced produced membrane membrane population population population population population population pair separate separate separate separate typical reported reported lateral lateral identical side side side trees sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive sufficient sufficient sufficient previously previously tions studies studies studies address address interval interval organization organization storage storage storage increased amplitude amplitude amplitude amplitude amplitude amplitude amplitude suggests predicted occurs strength strength strength strength strength strength strength strength strength strength strength hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian conclusions depend interactions weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong strong mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms reduction reduction reduction reduction demonstrated selective min min min decrease manner areas appears produces produces produces laboratory involves involves interaction events springer blocks blocks potentials potentials potentials potentials potentials potentials decreases national formation review depending depending correlated correlated correlated correlated open showed showed understanding past key msec msec foundation kohonen kohonen kohonen dendritic dendritic dendritic dendritic recorded building box usa usa usa usa usa illustrated illustrated activated activated activated activated coupled coupled coupled coupled discussions middle middle capable identify post post post post post post post post post post miller miller miller miller excitation verlag contained showing neuroscience neuroscience sci sci sci duration receptor bar involved cat neurosci neurosci subsequent rat intrinsic tesauro tesauro tesauro trains trains trains unlike stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation selectivity diego requirements experience relations strengths strengths strengths strengths strengths strengths strengths strengths postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic giving biol plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity ideal office pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic neu induction induction induction induction induction induction induction induction induction induction circles circles math transmission transmission explored store pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal baseline seconds seconds burst burst burst burst brown brown brown brown site site site biology glass tive sites sites nucleus pulses pulses consequence hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal involve acad acad acad axons res res read recording recording pathways led led marked marked recordings recordings recordings release release release anti anti anti anti anti singer richard physiol physiol conditioning conditioning traces traces simultaneous simultaneous simultaneous univ college analogue cooper interface bipolar oxford nat neurophysiol naval enhancement receptors receptors cellular cellular cellular cellular binocular resistance hyper balance resulted resulted neurobiology wire salk modifications preparation enhanced enhanced enhanced days filled filled filled natl natl weakly slice slice slice slice dendrites induce induce pat dominant injection injection demonstration den somatic somatic tic tic diameter hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus bursts bursts bursts bursts bursts bursts bursts bursts stimulated stimulated stimulated stimulated stimulated stimulated ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp record repeatedly specificity storing storing storing storing storing storing storing concentration harris harris lett grants balanced yielded depression depression depression depression depression depression depression depression depression depression depression depression depression depression depression munro terminals trigger ical reports superimposed superimposed superimposed evoked evoked evoked evoked evoked evoked evoked evoked evoked rain rain rain rain rain rain rain rain rain pairing pairing pairing pairing pairing illustration alter thick potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation interacting terrence paired paired altered altered electrodes electrodes lond lond lond lond lond lond rhythmic conversely conversely amino amino paradigms paradigms afferents tively intracellular intracellular intracellular intracellular intracellular intracellular intracellular geniculate exhibited exhibited inactive inactive inactive correlate correlate coming persistent persistent stimulating stimulating stimulating bursting bienenstock bienenstock bienenstock bienenstock reversed terns converging converging confirm inhibited supply hopkins morris determinant injected medicine condi tip nmda nmda huang slices slices stevens arrives johns acid iti south acids charles baltimore granule ically tim tim silent hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization col hip depolarization applica repetitive searched levy levy levy levy levy levy altering stryker stryker apical biophysics prolonged lynch lynch lynch lynch lynch activating extracellular extracellular extracellular extracellular extracellular assoc assoc iiiii iiiii iiiii iiiii ogy lowered stim stim stim stim stim stim thorpe patterned lasting lasting lasting lasting lasting lasting lasting lasting lasting nonlinearly heidelberg neurology ously positively vitro vitro asso synapfic synapfic theor symmetrically symmetrically elicited elicited elicited elicited elicited pal neurotransmitter rabbit chamber stant collateral collateral collateral prepared accompanied cited antagonist weakened associa associa para para departments commissural commissural eli alterations alterations hyperpolarizing hyperpolarizing hyperpolarized hyperpolarized elicit negatively negatively terminating aps dale depolarizing contiguity trast neces died subse sary dentate ciative pharmacological chronic campus gustafsson gustafsson kelso kelso kelso kelso parallels exci simultane parkway unaltered lasted rosci etal alepolarizing alepolarizing quent drs glutamate glutamate tate stu shock bly microelectrodes abraham eliciting pyrami 
#@Sejnowski_T,Stanton_P,
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#*model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input input input input function function figure time time time time time time set output output output output output output output output output output output output number number system system system system system system system system state state state results information information information information information information information information information information information models performance based space space space linear linear linear linear linear linear linear linear linear linear case case vector vector order order shown parameters noise noise noise functions neurons unit recognition pattern pattern pattern pattern pattern point point point point point point point single single processing processing processing processing control control large local local local local rate patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows shows signal simple small small small net work fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step field field level level level level level cell cell cell cell cell cell cell cell cell cell structure structure structure random high response response similar show show show show equation equation equation equation equation equation equation equation equation equation section fixed real real approximation approximation states states states states states gradient term activity activity activity activity activity activity dimensional result result result solution solution solution research independent target dynamics dynamics dynamics dynamics initial constant computer computer connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic left phase phase phase phase phase low low frequency frequency frequency frequency frequency frequency frequency frequency frequency motion range range press press position components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous abstract properties references component ieee important decision decision decision decision mixture introduction action complex complex stimulus effect effect effect generated parallel search tion tion change change spatial spatial spatial spatial classifier lower higher higher higher higher higher higher higher part center firing cortex cortex cortex cortex cortex cortex cortex cortex expected equations equations make make make make observed observed observed observed simulations simulations simulations simulation simulation simulation simulation simulation simulation elements means means means optimization made original relative samples represented cross cross define define determined determined determined connected connected gain gain gain cortical cortical brain brain brain brain brain comparison source modeling modeling modeling modeling modeling modeling institute version internal internal responses responses final exp framework computing curve view effects upper world increase give produce condition condition inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends biological achieved measured measured discussion increases increases describe arbitrary group group group group excitatory excitatory excitatory excitatory excitatory excitatory stable stable stable surface surface short assumed synapse supported adaptation adaptation adaptation makes makes makes sensory sensory simulated pairs pairs hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield reduced technology york york increasing mechanism matching uniform mode mode mode mode mode mode mode mode mode mode leads representing representing details details details early added sources neuronal population discussed property pair typical include sense engineering engineering sufficient approximately calculated volume achieve achieve trans diagonal background background background background locations symmetric symmetric generalized generalized organization organization sensitive amplitude amplitude amplitude amplitude amplitude exists studied occur suggests deviation matrices matrices locally occurs starting depend central central central central central central differences differences sigmoid peak weak weak suggest physics external cycle california pulse acknowledgements suppose suppose derive longer index describes ann stability mathematical mathematical changing sensitivity sensitivity sensitivity sensitivity interaction equilibrium equilibrium shift shift potentials cycles cycles cycles cycles yield choosing formation depending variation detailed transform showed centers centers centers centers centers centers centers approximated activities activities activities constants discrimination discrimination sign slow slow slow event closed eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg coupling coupling coupling coupling expect template includes usa bell inter inter sciences determines candidate coupled coupled coupled coupled coupled coupled coupled discussions successfully major simplicity simplicity letter letter extra differ effectively driven included modes modes modes modes modes oscillatory oscillatory oscillatory oscillatory oscillatory computations situation reached characteristic capture quickly interpreted stopping return oscillations oscillations oscillations receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor simplified play absence absence wave wave wave wave wave wave wave wave wave wave eigenvalue neurosci principles intrinsic intrinsic simpler origin selectivity essential exhibit put relations oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators strengths strengths replaced mass oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator postsynaptic rise rise scalar scalar examine respond behavioral biol biol biol ideal possibility possibility eigenvectors oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation pathway understand presynaptic phases phases rev rev rev thought thought thought thought olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory bifurcation obvious nervous academic baseline baseline baseline extent regime submitted animal animal indicating slowly directed distinguish agreement growing growing growing unstable phenomena coded biology adapted satisfied satisfied ring ring division division division located laboratories pulses pulses mathematics circle res geometry cybernetics cybernetics cybernetics recognizing fluctuations behaviors applies freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman freeman pathways relevance capability simulate marked slower rep ity anti modulated modulated modulated modulated fall fall pasadena coherent coherent neuro physiol conditioning deviations baird baird distortion physiology oxford appropriately driving narrow controlling neurophysiol jth odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor impossible enhancement enhancement enhancement receptors communications spiral bower chemical grow contract roles responsible preparation enhanced carry motivation motivation motivation induce induce induce decide pat pat dominant enhance enhance enhance enhance consequences bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb bulb interconnections hippocampus hippocampus bursts insight locked locked locked papers receiving influences vari acknowledge onr informa spirals sig emerge responds connec chaos amplitudes amplitudes amplitudes classifies tor sinusoidal sinusoidal arising acting shifting conduction interact compensate deconvolution eliminating confirmed surrounding rhythmic rhythmic mask selectively selectively superposition nal nal molecules behaves vice versa simplification influenced terns terns oscillate oscillate suppress suppress suppress suppress suppress anatomy anatomy physiologically physiologically physiologically emerges neocortex neocortex raises odors odors odors odors odors odors odors vertebrate fastest sity scott scott locality terminates terminates oscillates raised granule granule granule granule granule granule granule granule granule granule granule granule granule granule granule granule granule granule granule granule physica emerged dissipation tory tory noticed damping orbit orbit orbit simulates dominate schneider schneider schneider schneider schneider schneider damped damped damped damped damped damped damped bifurcations strongest quarter concentrations unclear clin shepherd shepherd shepherd shepherd shepherd shepherd shepherd shepherd shepherd exclude brains aii masses emphasizes univer mammals rabbit rabbit rabbit equi discriminations cyber unitary sensitivities indicative mediating private linearization chemistry structurally postulate linkage manifested stimulations reversing ambient cou oscilla pled adiabatic cancels electrophysiology originates amplifies varieties contamination coherently expo sumed reception ception aids resent cancelling cancelling lamina astronomy zhaoping organizations librium psychophysiology chief negligibly netics eld coworkers plies abil biomed 
#@Hopfield_J,Li_Z,
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#*network network network network network network network learning learning learning model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time set set networks training training training output output output number number system system system system system system system system system system system system system system system system system system system system error state state state state results results results results results results results information information information information information information information information problem problem problem problem problem problem problem problem models models models performance performance performance based based based based space space linear linear linear linear linear case case case case case order shown shown shown systems systems systems systems systems systems parameters parameters noise noise noise functions neurons approach approach approach pattern pattern pattern pattern pattern pattern pattern point point point point image image image single single single single control control control control control control control control control control control control control control control control control control control control control control control control control control test test patterns analysis analysis analysis analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs shows signal signal signal signal signal simple simple simple simple simple simple simple simple gaussian gaussian gaussian visual visual visual visual visual visual visual visual paper paper examples small feature feature work work task task task task fig fig fig current current trained problems problems problems random high high high high response response response response response similar show show section images general general general general real real real real real theory theory theory theory theory theory theory theory theory theory obtained term experiments experiments experiments activity result result solution solution research research found target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant table estimate computer science prediction prediction prediction prediction prediction prediction prediction left left direction direction presented presented present phase phase phase phase phase phase phase activation frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency machine sets motion motion maximum range range range press press press position position components basis basis outputs continuous continuous continuous abstract applied analog analog references component component stochastic stochastic important important important important adaptive context context context context context context introduction complex hand estimation estimation estimation estimation estimation estimation estimation behavior behavior stimulus statistical effect effect dynamic dynamic dynamic dynamic generated generated tion change change spatial measure signals higher higher previous cases cases type required required multiple multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex conditions conditions conditions conditions represent represent distributed expected expected make make fact techniques proposed correct correct observed ing ing ing simulation human computed called factor optimization made natural natural natural feedback orientation knowledge filter filter filter filter filter filter filter filter filter filter filter application desired series provide provide objects proc perform eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye experimental experimental experimental related related gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain motor motor motor motor motor motor motor brain brain brain brain brain brain equal power power power approaches mit larger dependent dependent dependent dependent dependent modeling modeling modeling modeling institute technique internal difficult difficult difficult difficult considered considered framework framework framework view view view view trajectory effects determine requires requires significant world world world world basic basic basic basic give give produce produce produce produce produce randomly developed area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity actual actual actual evidence evidence nature simply measured normal feedforward tested limited stable predictions short effective assumed generate supported role role role role role role role role role theoretical require eds eds adaptation hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis makes noisy noisy noisy noisy noisy sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory simulated underlying account account dynamical dynamical dynamical dynamical technology transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer significantly head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head mechanism matching principle principal filters filters filters direct making stored idea combined combined minimize added sources sources description light light light light light predict predict predict predict improved discussed discussed movement movement movement movement movement movement practical strategy moving include identical sense array relevant varying varying varying varying approximately subjects volume volume works solve trans channels channels organization storage storage storage storage sensitive amplitude amplitude horizontal horizontal parts occur occur occur occur occur suggests wide rotation rotation white white generally demonstrate demonstrate conclusion greater interactions interactions interactions accurate retina retina performs suggest propose mechanisms presence external characteristics demonstrated california turn variety variety movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements selective selective selective plane force question explicit appears appears relation perception factors primary estimating plot plot laboratory ann tuned vertical mathematical mathematical distinct changing modeled modeled implement explicitly coordinates physical involves involves transformations frequencies frequencies frequencies frequencies predictive springer formed shift shift quality quality implies expectation review communication estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator viewed influence detailed controlled ocular ocular ocular ocular ocular ocular ocular modulation static understanding completely completely similarly similarly allowed processor past spectrum spectrum spectrum spectrum spectrum spectrum key slow performing measurements measurements measurements measurements measurements delays delays delays delays classical classical classical classical expansion tracking tracking tracking tracking tracking tracking filtering filtering filtering msec foundation existing exploration figures coordinate retinal extension extension major reason straightforward sensor sensor sensor aspects aspects identified extra driven driven oscillatory computations mackay mackay comparing situation situation situation plots plots plots plots plots receives verlag kind kind induced induced heuristic interpreted interpreted neuroscience contribution running running running oscillations oscillations sci device cues cues involved involved involved michael simplified absence providing neurosci neurosci moves acknowledgments rat modelling modelling situations body explore explore explore selectivity poor circuitry circuitry rapidly rapidly kalman kalman kalman kalman kalman kalman kalman kalman kalman estimators accurately accurately oscillator hall existence rise rise reducing ideas rest biol muscle muscle referred oscillation pathway understand analogous analogous surfaces measurement naturally naturally possibly analyze predicting opposite extremely rev facial changed eyes eyes eyes thought thought aspect taylor nervous nervous nervous nervous multivariate amari amari amari simplest explain animal animal animal animal animal ment slowly vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor band band fairly improves biology caused london drive rapid rapid rapid rapid rapid widely forces division monkey monkey monkey monkey monkey controls probable recognized acad begin optimize optimize optimize localized arises nsf requiring behaviors dark dark simulate experimentally experimentally poorly cohen peaks peaks continuously compares maintain maintain robinson robinson robinson robinson switch switch prevent pasadena adjust adjust electric electric boston sophisticated conclude implements implements deviations cor phenomenon acquisition acquisition acquisition acquisition acquisition acquisition acquisition spectra spectra ear accomplished generator generator generator tation angular narrow narrow vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular tensor tensor controlling controlling neurophysiol unity unity unity unity plays murphy murphy bower bower bower bower bower bower bower ments ments significance primate cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum abilities mark analyzing analyzing operates responsible wilson muscles hours continue exploring repeat analyses weakly cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar heavy heavy james studying pat regarded demonstration claim advance fish young young eng eng waveforms relies relies pendulum pendulum pendulum pendulum projects davis davis davis davis valuable discovered characterization assigns fusion fusion fusion skills ics resonance reflex reflex reflex reflex reflex reflex reflex reflex reflex reflex neurophysiology pointing transmitted torque nelson nelson nelson nelson nelson distinction ical stem stem acceleration sinusoidal sinusoidal sinusoidal sinusoidal examining argue favor modifying conduction compensate compensate chapman mammalian elementary distant inverted inverted inverted inverted march march relating concentrate monitoring paradigms finger tively reveal mimic behave modifiable tune nal compu differing treating exploratory experi coordination stops emphasis opti characterizing vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo monitor quantify lated albus dominates played fre proposal compensation conflicting unreliable sen contrasts marr detects tactile tactile tactile tactile ref functionally modalities modalities ory implied reality lisberger lisberger lisberger lisberger brainstem brainstem nih stabilize memorized counted carpenter carpenter carpenter substrate actively rotational excessive excessive stabilization lights rotate degrade instant modulate wiener wiener entering discrepancy ular joseph prolonged prolonged walking walking walking primates optimizes slip slip quency ito ito ito ito ito ito ito apparatus relying mal ply damped accessible ago conflict ously wolfe wolfe stabilized tums hypothesize theor testable testable dynam dynam neck neck neck neck neck neck neck continu anatomically periments compensatory compensatory compensatory compensatory compensatory compensatory compensatory compensatory compensatory acuity acuity resonant proprioceptive neurophys estima arbib arbib arbib mission rect stant gation cri peri sug prog eet assure sor technically markedly impulsive alert alert inertial posture suspect comple miles miles miles accelerations rhesus rhesus undertaken raven optican optican speculate acta acta valleys oscil monitors thrust neurobiol hemispheres hemispheres compelling oral gest sto founded wearing wearing investi contractions anism musculature bns sheds phenom restoring abandoned opinions drown imprecise accommodates attenuates 
#@Bower_J,Nelson_M,Paulin_M,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time networks training training output output output output output output output number system system system system state state state state results results results models performance performance based linear linear linear order order order order order order order order order order order order shown shown shown shown systems systems systems systems parameters parameters noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition method approach approach point single single processing control control control control control control control control control control control control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate optimal optimal optimal inputs inputs inputs inputs inputs form form shows shows signal algorithms visual visual visual visual paper size size net work work work fig fig cells cells cells cells cells cells features features process level level level level level level level current current trained trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random random random random high memory memory response response response response response response response response response response response response response response response response similar similar show show fixed average term term note note note note note note note experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity result result result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold research research research research initial initial initial constant constant computer computer computer computer computer computer computer computer computer computer terms connections connections connections left left presented present present low frequency frequency frequency frequency frequency frequency temporal maximum maximum maximum maximum press press press components abstract back back convergence convergence properties properties properties properties references component component positive introduction complex circuit circuit circuit behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect effect effect effect effect effect effect effect parallel parallel tion tion tion tion change energy difference difference difference measure signals signals signals higher higher part firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type required required long conditions distributed fact fact observed observed observed observed observed observed observed observed observed forward scale minimum minimum minimum resulting resulting resulting simulation simulation simulation performed elements elements means potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential natural study negative vol specific specific specific specific compared compared desired active active active active active active active determined determined determined experimental experimental goal brain brain brain approaches approaches mit voltage voltage voltage voltage dependent dependent dependent dependent dependent dependent dependent source source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling institute synapses synapses synapses synapses internal internal internal individual individual represents responses exp exp addition addition cambridge cambridge equivalent environment additional top top stimuli stimuli stimuli stimuli stimuli effects effects effects determine determine significant basic basic basic basic basic basic increase increase con produce randomly developed developed levels area area area area velocity lines product processes evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply biological biological biological biological biological biological biological biological biological biological associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative discussion normal normal increases group close close close excitatory excitatory excitatory surface circuits amount amount common implemented synapse synapse synapse synapse synapse synapse supported role theoretical main eds ability degree rumelhart development sensory simulated simulated pairs smaller smaller needed reduced functional transfer testing significantly mechanism mechanism mechanism mechanism mechanism mechanism call making inhibition bottom magnitude magnitude magnitude magnitude magnitude magnitude magnitude decay added added light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane discussed property moving include 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interaction interaction applying potentials decreases focus focus depending influence variation variation open open open showed showed modulation modulation modulation modulation modulation modulation modulation understanding completely allowed past partial reasonable performing measurements classical classical sec intervals remains intermediate intermediate initially dendritic expect expect recorded fire fire fire fire box figures figures figures figures currents currents currents inter instances specifically variations discussions capable capable importance maximal mcclelland presentation presentation post post post post post post post post reached reached refer repeated strongly strongly strongly induced allowing neuroscience dis contribution physiological physiological duration receptor quantity quantity usual usual usual play paradigm providing hypotheses reach received moves subsequent subsequent receive employed remain stimulation stimulation stimulation stimulation american essential essential requirements circuitry exponentially exponentially exponentially exponentially exponentially rapidly rapidly rapidly rapidly varied steady steady association integral integral integral integral integral preliminary rise rise rise reducing respond fashion history behavioral biol authors proper stream stream oscillation understand presynaptic presynaptic presynaptic presynaptic presynaptic fundamental notion analogous analogous removed removed circles measurement trace trace plausible predicts obvious mapped nervous baseline generates electronic isolated isolated isolated optimum charge charge charge charge charge charge integrate animal animal animal animal developing ground ground distinguish london london ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion turns perspective tive sections immediately controls controls controls controls pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses consequence ion ion ion axon scientific beginning definite recording cybernetics virtual varies composite substantially pathways pathways pathways capability peter effort effort effort effort share incorporated incorporated incorporated biologically maintain maintain exhibits exhibits aim modulated modulated modulated modulated modulated incoming incoming ordered prevent inherent decreased returns returns conditioning conditioning conditioning begins begins traces traces displays instantaneous realized naive consistently gap acquisition primarily primarily summing temporally temporally conditioned animals recover vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular signature neurophysiol receptors lost spontaneous cellular cellular cellular cellular cellular ments stronger stronger chemical resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance hyper hyper contract efficacy resulted occurring occurring neurobiology illumination optic optic optic optic optic capacitor capacitor exceeds exceeds enhanced enhanced wilson fires fires fires falls falls falls falls introduces negligible photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor interconnections interconnections thomas competing tic exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure emergence express express reveals environmental contact contact contact summarize adopted insensitive insensitive acknowledge onr fired discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge discharge zipser 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electrophysiological electrophysiological electrophysiological nih tained dence hyperpolarization hyperpolarization hyperpolarization hyperpolarization replicate predetermined daniel depolarization depolarization depolarization operated rises rises rises rises rises rises rises rises altering altering vergence ton biophysics prolonged settles settles eta recovers recovers recovers recovers excite excite bio repeats assoc incident undergoes retention retention retention reproduces untrained untrained kim tially engineers engineers epsps ell fruitful overshoot overshoot overshoot overshoot overshoot overshoot released poten necessity sual turbulence turbulence turbulence turbulence turbulence turbulence turbulence turbulence turbulence associating michigan shell fatigue fatigue fatigue fatigue fatigue fatigue fatigue fatigue fatigue fatigue brings camp weeks quantum quantum quantum quantum quantum quantum quantum quantum quantum quantum quantum owing depolarized depolarized depen foot foot foot temporarily rect indicative charging charging charging charging invoked electro resistances sole loses strip sse barnes collaboration lhe publications incor associa consequent photo overcomes pump interfere exemplified maintenance bringing hyperpolarized hyperpolarized chart bethesda prespecified depolarizing vital precedes precedes resides assisted returning proposing tude eling organs persists referenced agreed exposures inhibi closes closes cie cie cie cie cie cie cie cie cease cease elevated facilitating nicholas nicholas disciplines pavlovian pavlovian tioned blackwell ringing exc lasts cessation cessation cessation strips communities plementation releasing demanded porated mediates mediates emulating emulating commitment exponen elucidate discharging ind nput transduced microelectrodes investiga publ elucidated neurophysiologists blvd 
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#*model model data data function function function figure figure figure figure figure figure figure time time set set set set set set set number number system system system system system system system system system system system system system system state results information information information problem problem models based based space linear linear linear linear case case order order order order shown systems systems values values parameters parameters distribution method method method approach approach pattern pattern point point point point point point point point single processing control control large large large local rate test analysis analysis shows shows shows algorithms simple paper paper paper small small small feature work work methods methods methods methods fig fig fig fig fig fig fig fig cells points points field field field field field field field field field field field field field field field process process current current current current current current current 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difference difference spatial spatial spatial measure measure measure measure measure signals representations chosen chosen higher firing long represent distributed expected equations equations equations equations fact techniques region length observed errors forward finite finite finite finite finite finite finite finite finite finite finite finite finite simulations simulations resulting resulting resulting resulting ing ing ing ing ing simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation respect respect multi sum elements elements elements elements elements factor factor potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential made made made made global global global study study study negative relative relative relative relative relative receptive compute compute objects objects objects objects objects objects objects objects objects objects objects location location location location location active active active experimental experimental experimental experimental experimental experimental goal goal distributions motor motor equal voltage steps accuracy accuracy larger larger fields fields fields fields fields fields fields fields fields fields fields fields fields source source source source source source source source source source source source source source source source source implementation consists internal internal internal individual difficult difficult exp sequences domain domain domain domain equivalent environment environment environment environment environment environment environment environment environment directly directly directly solutions bit determine full requires choice significant world increase con con channel coding randomly developed area lines lines lines lines finally selected sampling measured measured measured measured measured measured technical arbitrary arbitrary close close inverse corresponds corresponds surface surface surface surface amount assumed shape require eds end future degree sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory including objective simulated typically smaller unknown fully testing york head head structures uniform direct direct direct direct making making depth magnitude minimize run sources sources light predict directions resolution exact element element element element element element element element element element element element element element strategy period subject side sense array array array array engineering interest dimensions dimensions compare approximately subjects tions solve match studies studies studies differential achieve positions positions modified grid grid grid grid sensitive amplitude amplitude amplitude constructed expression wide generally depend interactions accurate designed clear clear clear peak peak peak peak weak taking physics largest external variety variety minimizing movements movements movements min relationship relationship groups configuration base reference pro construct produces describes describes changing confidence simultaneously infinite physical electrical electrical electrical electrical electrical involves develop minimization quality potentials potentials potentials potentials potentials extracted family expressed reconstruction correlated influence solved solved densities controlled evolution centered centered decomposition static discrimination discrimination discrimination processor processor sign reasonable performing measurements measurements measurements measurements measurements intervals iterative iterative interpolation interpolation remains valid initially msec advantages advantages recorded recorded recorded existing exploration exploration exploration exploration box box box box determines prove uncertainty regular straightforward aspects differ modification detect schemes fine characteristic procedures interested interested conductance dis sin content timing timing receptor involved sampled sampled sampled vary relaxation absence providing received attempt deal rat extend presents body body body body body body body body body body body body body body wiley varied accurately preliminary hall behaviour respond giving behavioral biol analytically stream complicated understand surfaces surfaces surfaces measurement measurement measurement measurement measurement measurement measurement analyze extremely extremely equally voltages eyes aspect freedom nervous nervous detected extent simplest contributions electronic seconds animal animal animal animal animal animal animal animal great ment developing sensors waveform waveform waveform waveform adjacent biology analytic analytic analytic answer glass glass reasons considerable straight tive sites constructing ran probable consequence consequence res recording recording recording fluctuations conjugate conjugate questions behaviors understood simulate simulate readily readily quantitative quantitative effort posed detecting detecting rely poisson poisson perturbations perturbations perturbations differs tank tank tank tank tank tank qualitatively pasadena substantial substantial simulator simulator electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric chose attentional pose bipolar animals animals animals animals animals animals animals member controlling null null purely reconstructed reconstructed food receptors caltech eliminated khz bower bower bower bower ments adjusting stated nearby mark wire wire wire arrays prentice 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indication exhibited tune drops exploratory exploratory mea cavity bution species rats rats tail tail tail tail monitor christopher quantify thousand water jersey skin skin skin skin skin skin skin skin skin skin calibration calibration calibration aid somatosensory converter eral tip sen equa impedance impedance impedance impedance impedance impedance impedance impedance detects governing digitized inspection reproduced reproduced tube amplified inset dimen filling positioning positioning positioning ance elec elec elec elec tim ears actively dipole mounted tails developments asymmetry stabilizing simula quantified activa minute sition sition conceptually saved puter ele lips reproduces sought gibson gibson challenges seeking poten explores simu visualize visualize lations organ organ organ organ organ organ organ organ organ discriminations conducting conducting conducting conducting resembling rocks sev arrangements straints shed gin walls quantifying heiligenberg heiligenberg 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#@Assad_C,Bower_J,Nelson_M,Rasnow_B,
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#*model model model model model model model model model model model model input input function function function function function function function function function function function figure set set output number number system system system system system results information problem problem linear linear linear linear layer case case case order order order order order order order order systems weight weight functions neurons point point point point single single processing large large analysis analysis analysis simple gaussian visual small work step points level response response response response response response response response representation representation representation representation representation representation representation representation representation show general general general general real note note note result result result university defined defined terms synaptic synaptic presented range range abstract references important introduction stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus tion variable chosen chosen higher higher higher higher higher higher long conditions distributed region proposed proposed finite finite ing ing regions dimension original original represented determined connected discrete discrete approaches larger dependent technique code individual scheme scheme scheme scheme scheme ai ai maps maps curves stage stimuli stimuli stimuli stimuli effects effects effects provided finally finally sampling sampling group group group group group group group limited proof effective shape supported instance sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory smaller underlying reduced coefficients edge edge edge increasing mechanism leads leads direct polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial population discussed resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution identical sense sense array array array array array array array array array array array recently works tuning tuning tuning achieve separation separation generalized generalized sensitive entire entire entire grant intensity concept studied extended extended extended width width width boundary boundary strength conclusion conclusion conclusion central numerical mechanisms integration external demonstrated demonstrated california california proportional proportional selective configuration question reference suppose index index ways ways tuned tuned tuned mathematical sensitivity linearly infinite infinite unique unique implies john yield yield decomposition completely suggested constants partial reduces purpose boundaries sufficiently degrees precision inter inter inter inter inter inter weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting determines determines extension characterized identified uniformly encoded schemes schemes schemes schemes schemes schemes miller miller miller miller miller miller miller miller receives excitation kind kind receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor comp sampled neurosci overlapping jacobs jacobs jacobs jacobs acknowledgments situations periodic reducing fourier investigated biol parity proved proved proved proved proved encode cover neu naturally plausible rank extent extent contributions explain smoothness phenomena explanation interneurons interneurons interneurons berkeley sys directional incorporate located mathematics mathematics res tional treated treated biologically ity polynomials polynomials polynomials polynomials wind ordered serve extensions electric age shaped physiol specifies contribute cybern appropriately appropriately angular circular tem enhancement enhancement enhancement enhancement enhancement receptors receptors receptors receptors receptors receptors receptors receptors receptors arranged eliminated cellular satisfying odd odd stated nearby nearby neurobiology preparation enhanced enhanced zhang zhang zhang zhang zhang enhance enhance enhance infinity infinity offers arrangement fish surprisingly baldi baldi baldi baldi uniquely uniquely employs poses adopt decomposed demon reconstruct argue interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron eliminating represen covers resolve vis spacing spacing spacing spacing broadly broadly broadly ron continuum continuum sen sen laser deals tells receivers nih vanishing monotone eigenfunctions eigenfunctions degrade ted severely direc adopting inactivation acuity strated exceeding exceeding exceeding exceeding arrangements 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#@Miller_J,Zhang_J,
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#*learning neural neural neural neural input data function function function function function function function function function function figure figure figure figure time time time time set set set system system system results results results results problem based based space space space layer layer layer layer layer layer layer layer case case case case case case case case order order order shown shown values values parameters parameters parameters parameters neurons neurons neurons neurons pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point control large large large local neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis gaussian visual visual visual visual visual visual paper examples small small small small small fig fig fig fig fig fig fig fig fig cells step step process process process structure random similar similar show show equation equation line line line images parameter parameter parameter parameter parameter approximation average average theory theory theory theory theory theory theory theory theory theory theory obtained term term term term term term term activity variables solution research found target target constant computer computer computer computer terms terms distance connections connections connections connections connections connections connections synaptic synaptic left left left left map map map present phase phase frequency frequency press press press position position position basis nonlinear abstract find find find find density density references component stochastic stochastic due due hand hand behavior behavior variance difference variable variable spatial spatial spatial chosen center center firing firing firing cortex cortex cortex cortex cortex cortex spike long long long conditions conditions conditions conditions represent equations equations equations equations region region region region region region region proposed proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed observed observed scale simulations simulations simulations simulations simulations simulations simulations total respect eq eq regions regions regions means potential potential orientation specific specific specific specific compared application define define proc eye eye eye determined determined determined determined experimental experimental experimental experimental experimental related cortical cortical cortical cortical cortical cortical cortical cortical equal equal contrast connection connection dependent dependent dependent report synapses synapses synapses synapses synapses synapses synapses maps maps maps maps maps solutions transition limit upper choice world condition condition condition condition area evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory discussion discussion normal normal normal normal normal normal normal describe transformation close close close close corresponds corresponds excitatory excitatory excitatory excitatory short short short effective theoretical main main sensory auditory smaller smaller smaller reduced account ratio ratio structures structures uniform uniform uniform uniform details call predict neuronal membrane membrane membrane membrane membrane membrane discussed property ensemble takes similarity lateral lateral apply period period period side side axis correspond differential rl rl rl rl trans definition positions positions symmetric observation organization organization organization organization organization organization organization amplitude amplitude horizontal suggests wide width column column column column column column half strength strength strength strength strength critical reduce practice temperature strong presence exist plane averaged averaged averaged averaged denoted monte monte van carlo carlo factors primary primary primary primary primary describes describes ann ann mathematical electrical electrical electrical electrical electrical electrical interaction interaction interaction frequencies equilibrium equilibrium equilibrium formed shift potentials potentials potentials competition competition decreases focus expressed formation formation formation formation formation dependence open controlled organizing ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular approximations modulation activities activities activities activities activities activities activities diagram diagram diagram reasonable calculate expect expect dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance retinal illustrated discuss coupled absolute phys discussions successfully simplicity columns importance modification effectively identify situation situation soc soc induced induced induced anderson anderson classify physiological physiological comp simplified relaxation relaxation hypotheses hypotheses hypotheses cat neurosci neurosci neurosci neurosci subsequent receive stimulation stimulation stimulation carried wiley essential essential involving existence postsynaptic postsynaptic fourier project presynaptic presynaptic fundamental predicts predicts predicts rev rev rev eyes singular observe nerve nerve nerve fibers extent submitted explain explain explain animal animal animal animal animal animal animal animal spin spin spin spin spin spin agreement phenomena ganglion straight straight monkey afferent mathematics axon incomplete qualitative qualitative meaning meaning fluctuations explained explained reflects pathways pathways experimentally lattice lattice lattice sharp schematic mod singer singer asymmetric neuro begins japan fix animals animals branches spontaneous spontaneous binocular binocular consideration cerebellum cerebellum grow grow grow viewpoint bands optic excellent falls dominant dominant monkeys monkeys bases diameter specialized stimulated stimulated ends eqs sons balanced balanced neurophysiology corporation visually wiesel wiesel wiesel wiesel wiesel wiesel terminals terminals terminals adopt hubel hubel hubel hubel hubel hubel hubel molecular stands monocular monocular monocular monocular monocular monocular monocular monocular monocular trends segregation segregation mathematically retinotopic argued confirmed projecting projecting projecting projecting scope synchronized synchronized lond lond rough sketch knudsen knudsen applicability modifiable modifiable modifiable modifiable correlate nec vii tanaka tanaka tanaka tanaka tanaka tanaka tanaka tanaka tanaka tanaka hopkins somatosensory developmental contralateral contralateral contralateral contralateral contralateral contralateral stripes neglect physiologically physiologically sharply striking hamiltonian symmetrical johns merzenich contrary reproduced confined potts potts potts proceeding ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral firings firings firings firings firings firings depolarization cats cats cats survival stryker stryker stand stand sends phil oil abnormal ito ito ess blob blob blob blob occupied electrically stripe stripe stripe stripe stripe stripe stripe stripe stripe elicited elicited frank frank ising segregated synchronously imbalance imbalance originate tex deprivation deprivation deprivation deprivation deprivation deprivation deprivation deprivation deprivation deprivation deprivation inh collapse collapse hamiltonjan lattices trophic adiabatic raven ses ses ses kaas kaas fictitious paragraphs cortices colour reared reared reared reared thermodynamics thermodynamics deprived levay nonspecific nerves 
#@Tanaka_S,
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input function function function time time time set set set networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm system system system system system system system system results results units units information problem models models hidden performance based space space space weights weights linear linear linear linear linear linear linear case case vector vector vector vector vector vector vector vector vector vector vector order order order order order order order order order shown systems recognition recognition method approach approach approach approach approach approach approach 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general general parameter real real real states theory theory theory theory theory theory theory theory theory theory theory gradient gradient gradient term term term note activity activity activity result result research independent independent independent found found found dynamics dynamics initial standard standard standard terms terms terms terms terms terms terms connections present phase phase phase phase phase phase phase phase phase phase phase phase nodes frequency frequency temporal temporal press components components components basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract back convergence convergence analog analog references component component component component due ieee ieee procedure decision introduction complex complex complex complex complex complex behavior stimulus dynamic dynamic dynamic generated recurrent recurrent recurrent tion tion difference spatial spatial spatial spatial learned chosen chosen chosen chosen chosen higher higher higher higher higher previous theorem theorem theorem theorem theorem type multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex expected equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations make make make observed observed scale simulations resulting elements factor factor dimension made orientation global global relative relative relative relative relative specific specific desired desired desired provide rates rates proc proc location determined cortical brain equal equal equal power support modeling selection department responses ai equivalent experiment view solutions design san capacity determine full choice choice free give con con con con con con condition condition condition types lines product product product product provided finally finally inhibitory inhibitory biological biological biological associative measured normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal describe describe arbitrary transformation transformation transformation transformation transformation transformation inverse stable stable stable proof proof proof nearest implemented assumed synapse supported square ability easily degree pairs underlying hopfield hopfield coefficients coefficients coefficients coefficients coefficients programming programming programming programming programming programming programming programming programming programming projection projection projection projection projection projection projection uniform uniform uniform uniform mode mode operation operation details numbers making stored stored stored stored stored stored stored stored stored choose choose predict predict neuronal architectures architectures discussed discussed discussed correlations correlations correlations exact pair pair introduced introduced identical 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blocks blocks blocks blocks cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles choosing transform controlled restricted organizing approximations static static static static static static completely similarly additive additive performing expansion expansion reduces reduces reduces reduces reduces neighborhood neighborhood roughly add construction eeg eeg degrees coupling coupling coupling coupling thesis combinations coordinate coordinate coordinate eigenvalues eigenvalues eigenvalues subspace simplicity columns columns columns columns columns determining delta modes modes modes oscillatory attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors orthogonal conf conf kind kind kind kind kind repeated showing neuroscience symmetry sin sin sin sin sin sin sin oscillations physiological hold hold write usual usual usual wave wave wave wave origin diego transformed transformed detail periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic fourier fashion behavioral incremental incremental incremental int int analytically root proper eigenvectors eigenvectors eigenvectors complicated phases phases act possibly thought ensure prototype olfactory olfactory olfactory olfactory bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation freedom separated expressions hebb hebb store store mixed submitted explain established established cos cos cos cos cos cos cos formula unstable lies lin tive berkeley satisfied precisely forces leaves monkey arise geometry geometry cybernetics outer outer outer outer conjugate conjugate conjugate summation requiring fourth fourth varies freeman freeman freeman freeman freeman axes axes axes axes axes axes red car orders introducing biologically variant ity synthesis mod cal extensions singer singer kinds attraction attraction conditioning baird baird baird baird baird baird baird baird baird baird baird baird baird june ordinary proofs indices secondary modify conditioned recover hyperplanes tensor tem impossible grey grey proceed clamped inspired stated determination interpret canonical canonical substituting substituting sion guarantees washington bulb bulb bulb bulb bulb tic entries entries entries entries permutation storing eigenvector reverse reflex truncated sine sine sine sig basin break july employs aij aij amplitudes amplitudes amplitudes amplitudes amplitudes constitutes basins basins rain transparent verified evolve pij pij pij pij pij pij pij pij diag jij jij jij afosr projecting proach employing cartesian cartesian cartesian cartesian cartesian cation locking locking tij tij tij tij tij tij tij grateful mimic programmed programmed eigen bill rnn gorithm strict syn interior traveling traveling tial assistance orthonormal orthonormal morris equa equa couplings couplings core emerges neocortex hopf hopf compartment tended linearized suffice inde sis sweep dent unusual indepen tory ming polar polar polar polar tivity spario spario spario entering biophysics biophysics hirsch imaginary imaginary corr des bifurcations claimed differed ponent standing standing poral walter poten behaved ies ponents idealized oij equivariant periments ore ore ore ore ore ore ore ore equi story correla compactly havior proj inspiration inspiration inspiration cot pnas invaluable synap hen ficient ond itive liapunov als summations ambient rhesus assures xls oll oll oll oll oll oll oll oll eling expres ass ass ass ass ass ass ass instructive excita rota mathe inns aji coef coef unused factory ois parsed oss oss ignorance drs rearranging nega ficients ficients jli commutative commutative tes ctive rai bracketed tro 
#@Baird_B,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input data figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set set set set set set networks networks networks networks networks training training training training training training training training output output output output output output output number system system system system system system system system error results results results units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem models space space weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case order order shown shown shown shown values values values values values probability parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit distribution recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point single single single single single single single single single single single processing processing processing processing control large large large large local local local local local local local local local local local local local local neuron neuron neuron rate rate test patterns patterns patterns patterns patterns analysis inputs inputs simple simple simple simple simple simple gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small small small size size task methods fig fig fig fig fig fig cells cells cells points points field field field field field field field field features features process level trained trained trained trained trained trained cell structure problems random random random random random random random random response response response similar similar similar similar similar architecture architecture architecture architecture show show rule rule rule rule parameter parameter parameter real real real term experiments activity result university solution solution solution solution solution solution solution solution solution found target connections connections connections connections connections connections synaptic synaptic synaptic synaptic science direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented presented map present present present present present present activation low object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum maximum maximum maximum maximum maximum range learn learn learn learn components outputs continuous sample abstract references component component component component component component component component component component component component component component positive positive important important important context introduction complex complex complex complex hand stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect generated generated generated parallel change difference difference rules rules signals chosen chosen higher higher higher multiple multiple multiple cortex cortex cortex long conditions conditions conditions conditions conditions conditions represent fact correlation scale minimum minimum minimum minimum minimum minimum human human respect sum sum times times regions made made orientation orientation orientation orientation orientation orientation orientation negative negative relative relative relative relative true true compared series receptive receptive receptive receptive objects objects objects objects objects objects objects proc proc location location location location location location location connected distributions gain cortical cortical cortical cortical cortical cortical cortical comparison larger contrast contrast contrast fields fields fields update train dependent dependent modeling modeling consists represents connectionist responses difficult final layers layers layers layers layers addition ai equivalent curve curve curves curves curves curves curves curves curves curves curves curves estimates estimates transition transition san stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects full full requires requires significant significant speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed basic produce condition condition condition condition condition weighted weighted randomly randomly randomly randomly randomly randomly randomly randomly area area area area area area area area area area area area area area velocity velocity product evidence evidence inhibitory biological discussion normal feedforward feedforward feedforward feedforward arbitrary excitatory excitatory excitatory excitatory common effective shape generate supported require main eds ability future degree makes development development development typically smaller smaller needed interesting projection projection projection projection edge segmentation structures structures structures structures structures leads representing numbers pre pre pre pre direct making making inhibition inhibition inhibition inhibition inhibition supervised supervised supervised decay run run run run run run directions directions directions directions directions directions directions directions correlations correlations typical typical movement movement lateral practical moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving side side subset cognitive interest dimensions varying varying previously unsupervised unsupervised approximately tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning axis axis solve solve solve solve diagonal background organization sensitive grant constructed constructed constructed exists horizontal parts suggests extended trial rotation rotation rotation rotation rotation rotation rotation rotation locally white generally half flow starting retina clear peak peak peak peak peak faster weak learns suggest mechanisms drawn drawn drawn california variety movements selective selective selective selective selective selective acknowledgements areas areas areas areas areas explicit perception optical primary primary generating transitions ann tuned tuned tuned tuned tuned tuned tuned tuned tuned modeled sensitivity multilayer linearly angle consisting interaction develop develop springer springer formed review stages stages stages correlated squares overlap open open fraction fraction fraction showed showed showed showed showed centered centered understanding translation translation earlier earlier classical boundaries boundaries boundaries intermediate visible views views views views degrees degrees avoid recorded fire box box box perceptual combinations combinations contour contour contour contour contour contour subspace subspace subspace recognize recognize illustrated black discussions characterized characterized characterized successfully texture texture texture reason determining determining determining capable importance presentation presentation schemes post post post projections situation orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal receives excitation soc conf verlag verlag showing physiological sci sci cues cues bar bar absence realistic realistic realistic realistic surround surround surround providing neurosci principles consisted consisted overlapping subsequent oriented oriented oriented oriented oriented oriented simpler selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity diego layered experience experience experience experience experience circuitry divergence respond respond respond project project project behavioral detectors detectors mappings applicable scaled scaled structured topographic topographic contours contours contours contours contours contours contours contours contours examined gradients eyes aspect obvious portion portion hebb hebb hebb hebb hebb detected detected extent serial great developing inside processed nucleus angles acad res linsker linsker linsker linsker linsker summation varies pathways dark flexible offset lack poorly peaks peaks peaks peaks peaks detecting detecting detecting employ dots dots dots sharp sharp biologically biologically biologically prevent conductances substantial simulator kinds comments decreased shaped displays displays uncorrelated indices secondary aligned aligned physiology proportion proportion proportion martin velocities velocities velocities nat circular interconnected rigid rigid primate primate primate primate primate held alpha alpha height balance abilities operates responsible corpus arrays filled filled hours falls connect monkeys monkeys parietal parietal viewing emergence emergence specialized surprisingly jolla saccades horn horn motions motions projects davis speeds speeds speeds speeds speeds speeds avoiding boxes grating grating grating grating grating grating grating appeared indirect shading propagating profiles solely flat illustration ary rectangular rectangular perpendicular perpendicular perpendicular perpendicular perpendicular perpendicular perpendicular interact interact life retinotopic cosine selectively million breaks interconnect rochester rotating geniculate things resp resp appearing saturated crude transparency mst adult cylinder cylinder horizontally horizontally horizontally continuum peaked neurobiological totally suffice vertically vertically comprised saturating nih aperture aperture aperture aperture aperture aperture aperture aperture aperture aperture aperture aperture gratings gratings gratings percept awij tails newsome saturate movshon movshon movshon cats tightly months months months months collecting primates primates shear ample thalamus apparatus shortcut dilation dilation dilation dilation dilation dilation patterned ascending nonlinearly collect translational acknowledged displaced displaced exhibiting clipped clipped clipped abstr cog mature mature mature mature sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno elongated brute occupy resembling resembling unambiguous siegel siegel worthwhile millions millions infant occluding topographically wrap wrap intell minimally minimally hyvarinen cooperate backgrounds libraries divergent divergent divergent shaw trough magnocellular stations stations stations plaid plaid plaid plaid plaid plaid customary satisfactorily parems lined modelers retinotopically artif granted granted sharpened subfields reared fare areal sinusoidally cropped twin unnatural physiologists arielson upside seelen 
#@Sereno_M,
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#*network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input data data function function figure figure figure figure figure figure figure figure time set set set networks networks networks output output output results results results information models models based based based case case case shown shown systems noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions unit unit unit distribution distribution distribution distribution point point point point point single single processing processing large large large local neuron neuron rate inputs simple gaussian visual paper paper paper paper paper paper paper examples examples small small small size work work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points points field field field field field field field field field field field field field field field field field field process cell cell cell cell high high high high high high high high high response similar show show show show equation equation equation equation equation equation equation section general general parameter parameter parameter parameter parameter parameter parameter approximation average average average experiments threshold threshold computation computation research defined defined sequence constant constant standard standard distance distance distance distance synaptic science direction direction direction direction direction direction direction direction direction direction direction phase phase phase activation low low frequency temporal temporal temporal motion motion motion motion motion motion motion motion motion motion range press press press position position nonlinear nonlinear abstract computational properties properties properties references due due due positive introduction introduction complex hand stimulus stimulus stimulus stimulus stimulus effect tion tion spatial spatial assume assume assume assume center center center center multiple multiple multiple multiple spike conditions conditions conditions conditions tree tree tree tree tree tree distributed equations make proposed length length length length observed simulations total computed performed times elements regions regions regions regions means means factor potential potential potential relative relative relative specific represented series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive define proc perform experimental related related distributions distributions gain gain gain gain discrete brain mit voltage voltage voltage voltage larger contrast contrast contrast contrast contrast fields fields modeling institute words loss version version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses responses responses responses responses responses responses responses final maps framework cambridge curve stimuli stimuli full speed speed speed speed speed speed speed speed basic basic basic increase increase increase condition criterion criterion provided finally finally finally finally finally evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological increases increases close excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory amount amount assumed assumed synapse synapse synapse synapse synapse synapse generate generate supported supported theoretical main eds square degree account ratio increasing mechanism mechanism mechanism consistent mode leads leads pre inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition added light membrane directions directions directions recent recent recent advantage robust robust robust robust robust robust robust robust moving moving quadratic trees cognitive relevant highly axis tions tions trans address positions positions improvement grant grant invariant invariant occur deviation deviation wide occurs boundary boundary pass flow strength conclusion critical critical conclusions depend tangent interactions retina retina retina practice propose propose mechanisms integration integration reduction characteristics assuming selective selective selective selective selective selective selective selective selective selective selective derivatives areas produces index label tuned mathematical dept sensitivity sensitivity coordinates coordinates linearly frequencies frequencies shift decreases decreases national national independently overlap overlap overlap modulation suggested constants discrimination slow additive reduces sufficiently foundation foundation foundation koch koch koch koch koch koch koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic figures usa currents retinal retinal retinal retinal retinal retinal retinal retinal retinal illustrated illustrated discussions gamma computationally computationally computationally poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio computations computations computations computations computations invariance invariance plots plots plots fine fine fine fine fine excitation excitation excitation excitation excitation soc soc strongly conductance conductance conductance contribution follow sci sci built comp quantity dot absence wave delayed computes neurosci neurosci illustrates preferred preferred preferred preferred preferred preferred preferred acknowledgments deal deal deal presents origin origin selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity essential put strengths integral integral helpful postsynaptic postsynaptic respond respond biol office understand understand presynaptic presynaptic presynaptic analyze opposite voltages voltages voltages ensure quantities assumes academic submitted submitted explain electronic isolated site advanced band developing convolution phenomena adjacent ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion closer sites sites sites division directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional arise calculations calculations calculations calculations res robustness robustness robustness apparent apparent apparent apparent transient transient poorly formulated biologically mod suited conductances conductances asymmetric asymmetric conclude physiol findings lim univ irrelevant temporally narrow branches controlling null null null null null null null null naval generality extending dealing anatomical anatomical anatomical anatomical resistance resistance shifts dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites respective negligible accounts accounts dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite somatic somatic soma soma soma soma soma soma soma tic spatiotemporal spatiotemporal sustained sustained sustained motions motions motions motions motions motions motions davis speeds grants inf alternatively discriminate linked linked piece shunting shunting shunting shunting shunting shunting pieces feeding resting resting resting sinusoidal sinusoidal sinusoidal stands publication publication favor favor biophysical biophysical gener activate efforts mediated argued scope distal distal rectified barlow barlow barlow barlow barlow accounted applicability els dramatic computa worked spite reversal reversal ate hyperbolic cable justified vis virtually capacitors neglect sharply sen subtracted progressively progressively progressively neurol separates separates deals sloan sloan inset confined electrophysiological locality enters devoted birmingham birmingham health hyperpolarization saturate activates activates activates activates battery battery direc directionally directionally directionally directionally directionally directionally directionally directionally directionally directionally borders grzywacz grzywacz grzywacz grzywacz 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#@Arethor_F,Grzywacz_N,
#t2
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#*network network network network network network network network network network network network network network model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data function figure figure figure figure figure figure time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output number number number system system system system system system system system system system system system system system system system system system system system system units information information information information information models models models models models models performance based based based based based case order systems systems systems systems systems parameters parameters functions functions functions functions neurons neurons neurons neurons neurons neurons neurons unit unit distribution approach approach approach pattern pattern pattern single single single processing processing processing processing processing control control control control control control control control control large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron inputs form shows shows simple simple examples methods methods methods methods fig fig fig fig fig fig fig fig fig fig cells step step features features features process level level level current current current current cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure structure high memory memory similar similar similar representation representation general general computation research research research research defined defined estimate computer computer computer computer computer connections connections connections connections connections synaptic synaptic synaptic maximum range range press press press press press press press press press press components components components components components outputs sample sample abstract abstract applied computational computational computational computational computational computational computational computational computational properties references introduction introduction complex complex hand hand circuit behavior parallel parallel parallel parallel cost variable part cortex cortex cortex cortex represent tree tree distributed distributed make make techniques scale simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations classes simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation multi performed called called elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements means potential made study specific specific specific specific application provide provide provide proc perform perform active active active motor brain mit mit mit mit voltage support support support support modeling modeling modeling modeling modeling modeling modeling morgan institute institute implementation implementation version synapses synapses synapses consists consists consists consists consists code code code code code code code advances represents connectionist delay addition graph graph sequences cambridge cambridge cambridge cambridge additional additional design design design san full significant basic basic basic increase increase channel conditional developed developed developed developed levels levels area types types types types types lines actual simply biological biological biological describe describe group amount amount common implemented implemented implemented implemented synapse synapse synapse synapse synapse synapse generate supported eds easily rumelhart rumelhart development development development kaufmann objective simulated typically hopfield hopfield hopfield functional functional functional functional technology block york york structures language language language language language language making run description neuronal neuronal neuronal neuronal neuronal membrane membrane separate element element element include include hierarchical hierarchical recently engineering interest interest highly approximately calculated volume module module channels channels channels channels organization organization storage entire entire entire constructed touretzky hardware demonstrate runs minimal assumptions editors editors editors central central central central modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules numerical numerical designed designed mateo integration physics california california user user user user user user groups program base base base base construct construct construct written ways modeled explicitly physical involves involves transformations text interaction interaction interaction interaction develop john stages communication detailed detailed operations organizing lee lee evolution understanding sizes key performing delays purpose add construction foundation koch koch koch koch koch dendritic dendritic dendritic building figures includes usa retrieval instances recognize specifically specifically structural selecting efficiency capable capable modification divided mcclelland ten excitation soc soc soc allowing link link link anderson anderson anderson anderson interested neuroscience issue content physiological sci device built built list modular realistic cmos highest neurosci neurosci neurosci attempt acknowledgments software rat receive oriented extend body body body body body body body body body body explore command command american create create create create create access access access requirements mead varied detail graphical graphical graphical graphical graphical graphical graphical graphical respond links links links links links links links referred referred structured complicated hierarchy editor created olfactory olfactory olfactory olfactory olfactory olfactory portion panel observe nerve nervous academic consist utility contributions electronic electronic years developing publishers track growing biology independence briefly tool implementing organized constructing constructing constructing constructing division incorporate nucleus axon axon axon axon axon acad calculations calculations axons computers computers recording nsf sun sun sun sun sun flexible quantitative effort share 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#@Bhalla_U,Bower_J,Uhley_J,Wilson_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data function function function function function figure figure figure figure figure figure time time time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output number number number error state results results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden space space space space space weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer case case shown shown values functions functions functions functions functions functions functions functions method pattern pattern point point point point point point point point point point single single processing large large large class class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small size work points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points features problems problems problems problems problems similar show show show show show vectors approximation approximation theory theory theory term note note dimensional dimensional dimensional dimensional dimensional result result result result result result university threshold threshold threshold threshold threshold threshold solution solution solution solution research research computer computer computer computer terms node node node node node node node node node node node node node node node node node node node node node node node node node node science science science left present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets sets sets press press press position outputs outputs outputs outputs abstract back back back back computational references due positive positive positive positive positive positive decision propagation propagation propagation propagation introduction introduction parallel parallel search complexity complexity center theorem theorem required required required binary distributed make make techniques correct correct finite minimum classes classes classes multi negative negative negative negative original original specific desired desired compute compute compute location perform perform related connected connected connected equal power mit mit mit mit mit connection support support train train proceedings proceedings report consists difficult difficult difficult addition ai ai considered cambridge cambridge computing additional view design san san bit bit conference full approximate pages pages con produce produce types technical increases arbitrary corresponds complete complete complete complete complete complete complete complete complete complete complete complete complete complete complete complete complete complete complete complete proof proof proof proof proof proof finding finding finding common supported ability instance instance instance instance instance rumelhart including typically pairs pairs needed fully programming significantly york york edge consistent call call bits international polynomial polynomial produced run perceptron recent separate separate separate separate separate interest dimensions dimensions dimensions dimensions approximately approximately volume tions solve yields positions locations locations bounded grant grant constructed exists suggests suggests extended wide correctly correctly setting runs place assumptions reduce conclusions neighbor editors editors sigmoid sigmoid practice practice practice encoding encoding hard hard hard hard hard hard hard hard hard hard reduction reduction reduction california labeled labeled labeled labeled labeled variety exist exist exist exist exist exist exist exist exist plane plane plane plane plane question question question question question suppose pro edges produces produces dept multilayer linearly easy consisting develop adding implies implies implies boolean boolean boolean boolean depending viewed solved solved open open open restricted restricted similarly similarly partition partition constants allowed add add remains euclidean classified david thesis coordinate usa usa instances instances batch reason regular regular regular extra closely importance differ mcclelland receives notice notice contained contained showing showing anderson classify michael computes thresholds thresholds intrinsic extend extend extend extend origin origin origin origin origin origin origin origin diego powerful xor xor create create create create collection essential requirements put put put mass mass mass incremental incremental possibility proved func cover naturally possibly necessarily equally perfect thought thought subsets algo separated separated separated separated separated ith consist arbitrarily phd ment slowly slowly distinguish handle handle turns style style style forces worst worst products arises computers geometry annual nsf nsf geometric freeman understood amounts leave poorly poorly incoming proven inherent june lab lab proofs hyperplanes grows inspired inspired difficulties difficulties siemens interconnection stated splitting splitting splitting splitting splitting splitting settings disjoint guide irregular james james decide vertices percepttons claim francisco foundations omitted omitted kearns kearns kearns hypercube hypercube johnson johnson johnson escape divide corporation fellowship planes planes planes planes planes planes planes planes planes planes forced amherst possibilities valiant valiant alter ibm rithms graduate learnability expand considers noting worth breaks compu sigmoids sigmoids demonstrating utilizing cube cube stephen stephen sees august traveling quadrant quadrant quadrant quadrant quadrant quadrant blum blum blum blum formulae sided separates separates separates separates sym judd judd judd judd judd judd judd judd judd degenerate totally minsky salesman rivest rivest rivest confined zeros signed monotone ming completeness completeness completeness completeness completeness completeness completeness intrinsically intrinsically intrinsically putational dnf separability ronald quadrants quadrants quadrants polyhedral tational pitt pitt amples possi papert render prepared bilities neurocomputing edward restricts marvin intractability rosenfeld aro ternary expressive mas duces sistent confine confine daal foun garey garey garey leonard sachusetts thirds leslie almaden existent dations promises surge 
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#*learning learning learning learning model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input data data figure figure time time time time time time time time set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output number number number number number number system error state state state state state state state state state state state state state state results results units units units units units units units information information information information information information information information information information information information information information problem models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden based based based based space space space space linear linear layer layer case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown shown shown systems values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach pattern pattern point single processing processing processing control control large local local local local local local local local local local local local local local test class class class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs form form form signal signal signal signal signal paper size net task methods methods step field field field field features classification classification classification classification classification classification classification process current current current current current current current current current current trained trained trained trained trained trained structure problems problems problems problems memory similar similar representation architecture architecture architecture equation section section fixed rule vectors vectors vectors vectors vectors vectors vectors vectors vectors general generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter parameter parameter parameter states states states states states states states states states states obtained obtained obtained obtained obtained obtained term term note result university solution research independent independent defined defined defined defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target target constant constant estimate estimate standard standard computer terms terms science left map phase phase phase machine maximum maximum press learn components basis outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous abstract back back back find likelihood references stochastic stochastic ieee ieee ieee important important decision decision decision propagation context context context context context context context introduction introduction complex hand hand estimation statistical statistical dynamic dynamic dynamic dynamic dynamic generated parallel parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference difference assume lower rules measure signals representations word higher previous previous previous previous previous previous previous previous bound cases cases binary binary binary represent represent distributed distributed markov markov markov markov markov markov markov markov markov markov markov markov markov markov make fact fact proposed proposed length correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed forward finite finite minimum resulting classes classes classes computed respect respect respect sum performed performed called times times times mapping factor factor factor factor optimization made feedback feedback feedback feedback knowledge knowledge em obtain vol vol vol vol vol relative relative represented represented compared proc proc goal related related constraints connected connected connected distributions discrete discrete equal equal power power mit steps comparison dependent dependent dependent nets modeling proceedings proceedings report report report report institute version consists internal represents represents represents represents represents represents represents connectionist connectionist difficult difficult difficult final final layers delay delay sequences sequences sequences considered considered considered considered considered computing equivalent experiment directly hinton hinton hinton hinton additional solutions estimates estimates design transition transition transition san stage stage conference capacity choice choice significant estimated estimated estimated estimated increase con produce weighted conditional developed criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion entropy entropy entropy path path provided finally selected evidence nature nature depends simply technical technical feedforward arbitrary group denote denote denote tested tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm finding short implemented assumed assumed generate generate require main main square end ability instance instance easily easily easily easily makes rumelhart rumelhart rumelhart rumelhart probabilistic reduced account account account account account account account account jordan jordan jordan mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp programming programming programming programming interesting interesting character character york mode language language leads leads representing max max max max window window window window window window international supervised produced produced perceptron denotes denotes denotes architectures advantage property separate separate takes takes machines side sejnowski sejnowski recently calculated yields speaker speaker correspond trans williams storage sensitive sensitive expression expression occur suggests extended derivative derivative derivative alternative width width generally runs conclusion operator depend depend bayes bayes bayes clear exponential weak weak taking taking taking presence labeled targets groups groups acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic reference explicit explicit pro written written written longer index index index index factors sequential sequential sequential sequential sequential sequential sequential sequential laboratory modeled multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer linearly text mutual events minimization minimization formed implies implies versus versus versus independently independently independently expressed dependence depending depending phoneme phoneme phoneme viewed interpretation centered centered frames frames approximated approximated discrimination discrimination processor partial partial partial partial performing classical classical classical classical purpose remains remains remains valid initially norm euclidean advantages classified classified classified classified topology topology topology topology topology topology topology topology topology exploration thesis priori priori priori usa perceptrons perceptrons perceptrons formulation formulation formulation strings strings strings bell subspace illustrated automatic automatic automatic specifically holds successfully regular extra extra extra extra capable suitable effectively paths mcclelland successful comparing reached reached reached kind kind kind procedures decoding decoding phonetic lie contribution contribution follow criteria criteria comp comp simplified simplified simplified backward providing hypotheses maximization maximization maximization maximization maximization maximization maximization decreasing minimized remain diego layered layered essential requirements exponentially estimators replaced association association optimized lippmann lippmann discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant successive tech links links links links links links int decisions decisions root maximizing variability proved proved proved proved proved statistically statistically cognition waibel waibel waibel closest changed prototype prototype prototype prototype prototype prototype prototype prototype front noted observe perceptton perceptton contributions contributions serial isolated brown brown brown brown separable tool handle handle inside berkeley arc widely widely widely producing precisely incorporate incorporate immediately probable probable probable recognized english preceding preceding preceding preceding preceding preceding mellon summation apparent carnegie limits limits elman cmu lms fed fed solla solla requirement vocabulary rely phonemes viterbi viterbi viterbi viterbi viterbi viterbi viterbi phenomenon indices contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual labeling modify restriction repre flexibility flexibility reaching extending extending convenient promising promising tools replacing replacing familiar utterance utterance belong bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard enhanced lang evident percepttons percepttons percepttons percepttons captured counting recog recog foundations belonging draw consecutive consecutive mind converted microstructure achieving maximized uniquely nition nition tween welch icassp icassp connec classifications classifications arg ideally warping recurrence recurrence associate clas quantized quantized quantized mutually mutually levin exclusive exclusive labs permits denoting considers surrounding cation drawback drawback memoryless stuck permit worked manuscript ucsd ucsd rewritten rewritten rewritten factorized rosenberg rosenberg interpolated puts inherently bilinear interpolating cardinality tokyo restricting rameters contrary watrous watrous watrous assp assp nettalk crl magazine neglected mul denominator ated excessive mle mle mle mle discriminating discriminating predetermined lexical wellekens wellekens wellekens wellekens wellekens wellekens wellekens wellekens wellekens wellekens wellekens ted predefined sentations collecting dtw shikano phonological phonological mmi supervision nation mercer vin 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space weights weights weights case case case case case case case case case case case case vector vector order order order order order order order order order shown systems systems systems values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise functions functions neurons neurons neurons neurons neurons neurons unit distribution recognition approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point processing control control local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix matrix matrix matrix matrix matrix inputs inputs algorithms simple simple paper paper paper examples net work step step step step points points points classification classification process process process level level problems problems random random random random memory memory memory memory memory memory memory architecture show equation equation equation equation equation equation equation equation equation equation equation equation equation section fixed fixed fixed fixed fixed fixed rule rule rule rule rule rule rule rule rule rule rule vectors images general parameter real real real real states states states states obtained obtained obtained note activity university university threshold threshold threshold threshold threshold computation found found sequence dynamics dynamics initial initial initial constant constant constant estimate computer terms terms terms distance distance distance distance distance distance synaptic science science direction presented present present phase phase phase machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets maximum press basis nonlinear abstract find find computational convergence convergence convergence convergence convergence convergence convergence properties references references stochastic stochastic stochastic due due due ieee ieee ieee procedure decision decision decision decision decision decision decision context introduction circuit estimation behavior statistical dynamic parallel energy energy energy energy energy energy energy assume assume assume lower lower lower lower lower lower rules rules rules signals prior learned chosen chosen bound bound bound bound bound cases good binary binary binary binary binary binary binary binary binary conditions conditions represent distributed bayesian equations markov fact techniques proposed proposed proposed proposed length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities errors finite finite minimum minimum minimum minimum minimum minimum minimum resulting tasks respect multi multi performed called called called called called times times elements elements elements elements means means reinforcement optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization global global global global global global global global applications applications study obtain obtain obtain vol vol vol vol vol vol vol vol artificial application provide provide define define proc perform perform determined determined determined related related connected connected connected connected connected distributions mit steps steps comparison comparison larger update nets selection selection proceedings proceedings technique code represents scheme scheme scheme sequences cambridge computing environment environment hinton hinton hinton additional solutions design transition san conference upper upper upper upper upper upper choice free increase coding coding bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds provided iteration nature biological associative associative associative associative achieved describe arbitrary fast close assumption circuits finding amount short common assumed supported main end ability rumelhart rumelhart noisy noisy noisy objective objective simulated simulated simulated simulated simulated probabilistic probabilistic probabilistic needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield fully fully fully fully interesting interesting ratio york york york increasing mechanism structures operation operation representing numbers iterations max pre making making stored stored stored stored stored stored stored stored stored stored stored stored stored bits bits supervised magnitude polynomial polynomial polynomial polynomial choose architectures exact advantage element apply introduced period machines sejnowski sejnowski sejnowski cognitive unsupervised teacher calculated volume match match correspond studies studies studies studies converge rl trans trans definition positions organization grant studied matrices matrices locally locally locally locally deterministic generally conclusion editors designed exponential exponential temperature temperature temperature temperature propose mechanisms external sigmoidal selective iii iii introduce minima minima minima minima minima annealing annealing annealing annealing annealing acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann van dept dept recall physical electrical electrical involves develop minimization choosing family independently independently influence influence influence influence influence influence influence influence detailed organizing evolution evolution similarly suggested calculation purpose purpose distances calculate calculate calculate calculate calculate calculate transactions avoid usa retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval assignment assignment assignment determines phys characterized mcclelland mcclelland wij wij wij wij attractors attractors attractors schemes schemes schemes refer conf procedures induced allowing allowing interpreted symmetry contribution content content content content content content sci notation gibbs relaxation denker processors principles principles principles principles satisfies decreasing law diego american american wiley wiley production production production production updating updating environments association association association association association association association association association association association divergence divergence divergence int int decisions phases smallest editor integer created equally shapes hebb ith ith ith ith amari amari utility utility mentioned asynchronous asynchronous theoretic distinguish capabilities correction considerable worst worst worst worst worst worst sgn recognized recognized acad grossberg grossberg res computers cybernetics nsf items autonomous effort treated howard howard pittsburgh maximizes popular occurrence tank tank tank tank collective geman geman geman geman geman geman hamming hamming hamming decoder decoder decoder attraction attraction attraction attraction attraction eventually progress summed extreme distortion gap gap gap guarantee guarantee princeton nat bin bin bin bin bin bin bin encoder nonzero nonzero proceed climbing wrong wrong accepted replacing determination determination abilities exploit combinatorial spurious spurious spurious spurious spurious spurious spurious spurious utilized periods guarantees sphere sphere sphere sphere sphere sphere competing foundations eng eng contraction contraction shortest correcting exploiting receiving escape escape escape escape escape temperatures appeared numerous leaming creates creates emergent employs rao seek tradeoff associate associate conservative concentrated iri drawback anal suffer modal restoration reversed accordance stochastically families evolved affecting ackley ackley devised assessment assessment assessment tuple tuple tuple tuple kirkpatrick kirkpatrick retrieved arrives distorted multimodal multimodal shaping stabilize mach inst addressable addressable addressable addressable addressable addressable stabilization stabilization stabilization stabilization stabilization predetermined predetermined predetermined predetermined phillips instant instant instant attracted decoders observes fight codewords extrema undesirable undesirable accepts decides 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output output output number number number error error error error error error error error error error error error error units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space space space space weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case order shown values values values values values values weight weight weight weight functions functions unit unit unit unit unit unit unit unit distribution pattern pattern point point point point single processing local local local local local local local local rate rate patterns patterns patterns patterns patterns patterns optimal optimal optimal optimal optimal optimal optimal optimal form shows shows signal signal simple paper paper examples size size size net net net work task task task task task step level current structure problems problems high high high similar similar architecture architecture equation equation rule general generalization speech speech parameter theory gradient gradient gradient gradient gradient term term term term term term term term term term term university university university solution solution solution solution solution solution solution solution solution solution solution research independent log defined found found found initial constant table table estimate standard standard standard standard standard standard standard standard terms terms science left presented presented present present activation activation activation activation activation activation activation activation activation activation low low low low range range range range range press abstract back back back back back back back back back back back back back back back back back back back find find find find find find convergence analog properties references positive procedure propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation behavior behavior behavior parallel cost cost cost cost cost cost tion change change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy complexity chosen higher part previous cases cases type binary binary binary distributed expected make simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum resulting ing ing tasks tasks tasks tasks total total total total respect respect respect sum sum sum sum called means em vol relative desired desired compute compute compute determined constraints constraints constraints constraints equal equal equal mit contrast connection descent descent descent report institute department implementation internal represents layers layers layers layers considered considered considered considered considered cambridge hinton hinton curve curve curve solutions curves design design trajectory trajectory san upper speed increase con weighted actual actual actual constraint constraint constraint constraint simply simply simply simply tested tested tested tested tested tested tested tested tested corresponds complete complete stable short shape theoretical eds makes makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart reduced reduced reduced transfer significantly consistent principle principle principle principle principle principle squared squared squared early early early decay minimize minimize minimize added architectures architectures improved robust typical typical practical subset cognitive previously tions tions solve solve solve solve solve solve yields yields speaker chain williams williams sensitive entire derivative derivative derivative derivative derivative runs conclusion starting starting starting minimal minimal minimal minimal minimal minimal minimal minimal reduce trajectories depend sigmoid sigmoid faster taking variety decrease minima minima minima force attractor attractor appears written written describes label label changing implement implement remaining easy easy frequencies minimization minimization minimization minimization boolean boolean boolean cycles cycles cycles decreases independently independently communication interpretation solved variation centered frames sizes sizes sign sign fitting penalty avoid exploration combinations activations activations activations activations activations activations activations activations activations activations activations activations determines extension automatic variations discussions tests middle middle importance maximal delta delta delta delta delta delta delta mcclelland tend ten reached repeated success phonetic phonetic phonetic symmetry symmetry classify categories built notation quantity write write write reach automatically decreasing presents presents minimized minimized minimized minimized diego xor xor helpful parity parity parity parity parity func func cognition act integer onset psychology equally algo algo algo algo logistic logistic precise precise logic simplest finds finds finds finds growing adapted 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#*network network network network network network network network network network network network learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data function function function function function function function function function function function function function figure figure figure time time time time time set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm output output output output number number number number number number number system system system system system system system system system error state state state state state state state state state state state state state results results units units units units information information information information information problem problem problem problem problem problem problem problem problem problem problem problem models models models models hidden hidden hidden hidden hidden based based based based based based based space space space space space space space space weights linear linear linear layer layer case vector order order order order shown systems systems systems systems systems systems systems systems systems systems systems systems systems values values weight functions functions unit unit recognition recognition method approach pattern pattern pattern pattern pattern pattern pattern pattern point point single single single single single processing processing processing processing processing processing control large large local local local local local test test patterns patterns patterns patterns patterns patterns patterns analysis analysis matrix inputs inputs form form form form signal simple simple simple simple simple simple simple simple simple simple simple visual paper paper small size size size size size feature feature feature feature feature feature feature work work work work work work work task methods step step points points points points points points features process process process level level level level level level level level current trained trained trained trained trained trained structure structure structure structure structure structure problems problems problems random high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response similar similar similar similar similar representation representation representation representation representation representation representation representation architecture architecture show show equation fixed fixed fixed fixed fixed fixed fixed fixed fixed line line rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images generalization generalization speech real states states states states states states states states theory theory theory term note experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university threshold solution research research research research research research defined found found found target initial initial table table standard computer computer computer terms science science science science science science science science science science science prediction prediction left left map map phase phase phase activation activation activation activation low low low frequency machine machine machine machine machine machine sets sets sets sets press position basis basis basis basis basis basis nonlinear outputs outputs continuous abstract applied back back back back back computational computational analog analog analog analog references propagation propagation propagation propagation propagation context context context context context introduction introduction introduction complex complex complex complex complex hand hand hand behavior dynamic parallel parallel parallel cost cost recurrent recurrent recurrent energy energy energy complexity variable variable variable variable assume rules rules rules rules representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations learned chosen higher part part part part center theorem cases type type type type type type type required multiple good good binary binary binary binary binary binary binary binary binary long long long conditions represent represent represent represent represent represent represent represent tree tree tree tree tree tree tree tree distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed make fact fact fact techniques proposed forward scale scale scale scale scale scale finite finite finite finite finite finite finite finite minimum resulting resulting classes ing ing tasks tasks tasks human human human performed called called elements elements regions mapping mapping mapping factor factor dimension made made natural natural natural natural natural natural natural global study knowledge original original original vol artificial artificial artificial artificial artificial relative represented represented compared application application application define define compute objects objects location perform perform perform perform experimental related related related related related constraints connected discrete mit mit steps accuracy larger larger connection fields fields fields fields train nets nets modeling proceedings proceedings proceedings proceedings proceedings proceedings proceedings report report report institute institute words words department version internal code represents connectionist connectionist connectionist connectionist difficult layers layers sequences sequences ai ai ai ai ai ai ai ai ai ai ai ai ai ai considered considered considered framework cambridge cambridge computing computing computing computing domain domain domain experiment experiment experiment experiment environment environment directly directly hinton hinton hinton hinton curve curve curve curve curve additional estimates limit limit limit limit limit limit san san bit bit bit bit bit bit conference conference conference conference conference conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity requires free free free free free vision vision give con con con con con con con developed developed developed robot area area types actual evidence constraint simply biological associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative normal feedforward feedforward describe arbitrary group fast close inverse inverse complete surface surface finding amount short generate generate require require require require main eds eds eds journal journal square end ability hypothesis instance easily easily rumelhart rumelhart rumelhart development development sensory simulated pairs smaller smaller underlying underlying hopfield hopfield hopfield reduced reduced dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical functional unknown jordan technology interesting testing structures structures structures structures structures structures structures structures structures structures structures structures structures matching uniform empirical language language language language language language language language language language language language language leads leads representing numbers numbers pre window window stored stored stored bits bits bottom bottom bottom early idea idea idea idea idea idea choose description description predict architectures architectures discussed discussed discussed recent recent resolution property property element similarity similarity similarity similarity similarity similarity similarity reported reported apply strategy moving moving machines machines trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees sense sense inference inference inference inference inference inference inference inference subset sejnowski cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive recently recently interest sufficient volume volume works tions smooth correspond studies background positions chain symmetric bounded williams storage sensitive entire constructed parts parts parts lead lead lead lead lead concept concept occur suggests alternative feed width width width width width width width width width deterministic boundary boundary generally hardware demonstrate flow conclusion critical critical exponential constrained temperature temperature sound encoding hard hard hard mechanisms physics largest reduction reduction cycle sigmoidal intelligence intelligence intelligence intelligence intelligence intelligence intelligence labeled labeled plane characters minima minima minima minima minima annealing question question attractor attractor attractor attractor areas boltzmann boltzmann explicit appears produces produces longer perception ways sequential plot laboratory laboratory laboratory laboratory transitions transitions transitions dept missing category simultaneously simultaneously infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite physical physical physical electrical electrical dimensionality involves transformations remaining easy easy text unique scales develop develop mutual integrated minimization formed versus versus versus cycles cycles john john john letters letters national national national dependence review reconstruction squares solved operations evolution forms forms understanding understanding completely spectrum earlier reasonable performing classical classical closed initially sufficiently symbol symbol symbol symbol construction construction construction euclidean classified faces building figures perceptual thesis usa retrieval instances sciences sciences memories recognize automatic grammar grammar structural successfully successfully major planning planning planning reason reason regular regular compression compression compression compression compression middle aspects closely society society society society encoded encoded symbols symbols symbols symbols mcclelland mcclelland successful attractors build build build efficiently comparing comparing composed refer kind induced success link showing anderson split return return content content content follow generative strategies categories built quantity involved usual modular modular highest highest binding binding automatically deal deal intrinsic unlike unlike unlike unlike diego diego parametric parametric requirements involving humans humans association accurately accurately recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive dual fashion history ideas tech project mappings terminal terminal terminal terminal terminal terminal terminal terminal fault combine combine combine decisions structured structured working working working symbolic symbolic symbolic symbolic symbolic symbolic symbolic encode cover cognition cognition cognition fundamental notion notion notion surfaces induction induction induction act naturally concepts man automata automata automata automata automata automata automata automata psychology psychology changed thought thought prototype bifurcation formal formal formal precise shapes store detected regime explain attempts chaotic chaotic chaotic chaotic chaotic chaotic chaotic defines defines synthetic sentences sentences sentences sentences sentences devices languages languages great ment developing costs distinguish track analytical floating cascade lies handle reasons perspective sys style style precisely leaves leaves immediately mathematics potentially potentially inversion recognized involve describing members arises auto auto auto auto auto auto auto auto auto auto auto geometry annual annual annual cybernetics recognizing recognizing recognizing meaning addressed questions people behaviors freeman elman elman tional tional lack posed splines variant psychological prototypes prototypes rely limiting cal cal collective logical kinds kinds kinds neuro shaped tolerance tolerance returns wang simultaneous sentence semantic yielding gap don picture picture picture room newton benefit ear sort accomplished accomplished accomplished generator formally tation member member recover perfectly count reconstructed reconstructed discover impossible theories robotics extending cellular cellular smith smith wrong dealing chains occurred analogy analogy analogy odd automaton automaton familiar height height loops los los abilities viewpoint keeping keeping occurring implications implications implications implications implications implications implications guide adequate phrase phrase phrase grammars games reliably repeat started separating representational representational representational representational induce induce surprising pat pat pat mental mental mental mental bad counting originally lawrence viewing similarities iterated iterated iterated recog april ballard ballard pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack late storing parse relies hypercube erlbaum erlbaum inductive inductive inductive inductive vari displacement ball ball ball metrics yale associations associations associations compressed unable microstructure recursively recursively break job job emergent emergent emerge axe axe willshaw willshaw distinction distinction terminals terminals terminals retraining regularity regularity chaos chaos chaos chaos chaos chaos chaos chaos seek hierarchies hillsdale hillsdale imagine clustered chess remainder deep evolve tems pdp pdp graphics file distant token token inverted efforts considers considers landscape landscape landscape depicts noting academy academy unconstrained rough sketch harder represen represen associates distinguished distinguished sized sized sized electronics electronics lapedes lapedes lippman things infinitely infinitely pineda pineda challenge worked correlate develops ucsd sigmoids handled syn bridge survey ble handling compositional compositional fractal fractal fractal fractal fractal fractal fractal fractal tial invertible terns phrases phrases ers generafive conceptual pictures pictures flows illinois ackley ackley seattle seattle seattle compo distinguishing proposal devised devised huberman huberman manually push ooo functionally stevens trol ultimate retrieved retrieved weather syntactic syntactic noun company assp cascaded cascaded evolves rel connectionism connectionism connectionism connectionism filling filling filling encodings gence resultant tations essence zeros feldman magazine priming enter semantics pointer pointer contents contents contents bear alamos surprise tenth tenth tenth addressable physica servan dyer dyer montreal montreal bidirectional rolling addi sorted lexical lexical decode decode constituent urbana landscapes landscapes noticed haven meaningless meaningless notions farber farber farber accepting walking fractional fractional pointers pointers pointers pointers pointers turing dead sixth relying recursire recursire recursire offered albeit extremes angeles hypothetical hypothetical accessible ninth ninth consciousness challenges remember parser heat heat machinery machinery machinery engineers engineers meanings meanings meanings impressive corresponded tums fruitful environ pattem pattem pattem pattem pattem pattem facilitation oooo linguistics inadequate devise inferences inferences inferences inferences inferences inferences inferences inferences inferences historical recur workstations trouble meyer meyer syntax mary mary birds propositions implication implication implication implication implication implication nectionist compose compose flowers braitenberg braitenberg calling mexico render recon recon subtrees subtrees struction struction vehicles occupy nique recognizable saund saund strange strange strange strange landauer landauer door door door roll gestalt doubled disparate itive opened intriguing scientists ucla ucla straint midpoint fodor fodor prince prince modem columbus sive pattems pattems pattems angluin angluin devil underly interplay dangerous lancaster surveys unification unification hillis hillis serf knew demonstrations songs folk century compositionality numeric varieties oth incurs associator associator engines devising devising prohibitive pinker pinker intemal pylyshyn pylyshyn intimately chomsky chomsky hogg hogg universality universality recurslye recurslye panems implicated slate leam thinks thinks thinks thinks sitting wolfram wolfram atmospheric ofthe attacks pervasive staircase love chair emer comprehension father combinatorially las las fusing speeded adequacy adequacy adequacy sequen adjective fractals fractals hague interleaving hills nize mathemati noticing padded subsumes boring excel provid bracketed coincidental 
#@Pollack_J,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input input input input function function function figure figure figure figure figure figure figure figure time time time set set set set set set networks training training training training training training training output output output number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system results units units units units units units units units units information information problem models performance based weights weights weights weights weights weights vector vector order order order systems values values values values weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method single single processing processing processing processing processing processing processing matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form simple simple paper examples examples examples examples small size size work work methods current current current current trained trained problems problems similar similar representation representation representation representation architecture section section fixed fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general general general speech real average university university university solution research research research research research research found found found sequence sequence standard computer computer computer node node node node node node node node science science science science science science left left left left left left presented presented presented presented present present nodes nodes nodes nodes frequency range range press learn learn learn learn learn learn learn learn learn outputs abstract back find computational computational computational computational computational properties references component due due ieee context context context context context context context context introduction introduction complex hand effect generated parallel parallel parallel parallel parallel parallel parallel change difference lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure word word word word word learned learned higher part part part part previous previous previous type represent represent represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed length length length length length correct called called called means natural natural natural knowledge knowledge knowledge negative represented represented represented represented desired determined goal approaches mit train nets report institute words words words department department implementation implementation implementation consists represents connectionist connectionist connectionist connectionist connectionist final scheme scheme scheme scheme addition ai computing view limit san top conference determine determine determine determine requires free free free free free free free free path finally simply normal technical limited complete complete complete complete complete complete complete complete complete assumed supported require ability future easily easily rumelhart rumelhart combination fully edge edge special special consistent consistent consistent language language language language language language language language language language language language language language language language language language language language language language language language language language language language language representing call numbers bottom bottom added denotes denotes denotes architectures improved improve recent takes takes apply apply apply identical trees trees trees trees subset subset cognitive cognitive cognitive previously teacher teacher teacher approximately volume tuning tuning tuning tuning tuning correspond modified generalized constructed exists matrices column column column column column row row conclusions reward learns constrained taking largest largest largest labeled labeled labeled labeled labeled labeled minimizing introduce construct generating label label label stability distinct simultaneously simultaneously slightly slightly consisting consisting adding adding national depending interpretation restricted labels understanding completely suggested allowed partial partial partial combining symbol foundation box discuss grammar grammar grammar columns columns columns columns columns columns determining determining capable capable capable society presentation successful build schemes schemes essentially essentially traditional strongly binding binding attempt employed collection collection collection involving lippmann lippmann fashion fashion applicable ideal ideal combine office structured root cognition coefficient possibly portion portion portion portion improving attempts attempts attempts sentences sentences sentences sentences sentences sentences sentences integrate integrate languages languages mentioned brown brown advanced rows adjacent handle handle processed closer strictly leaves immediately immediately english english toronto annual embedded capability frequently frequently incorrect incorrect incorrect incorrect popular sentence sentence sentence sentence sentence sentence sentence sentence leaf leaf consistently shifted corrupted modify naval eliminate plays lost clamped dealing imposed height contract serves phrase grammars fires continue embedding utilized entry entry entry entry entry entry entry 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kth suppress incorrectly supplied agency preservation correctness arpa totally totally noun noun noun noun noun noun noun noun noun noun noun noun noun noun noun assp positional feldman feldman magazine stabilize defense verb verb verb verb verb verb verb verb modest adv adv moderately rij tightly fanty fanty ninth parser parser parser parser parser parser parser rightmost differed snapshots snapshots snapshots providence blank blank xij fifty waltz waltz manageable snapshot snapshot snapshot chunks contracts easiest aining stating managed bart clearer parses parses inserts prep attachment corrupt microstructures 
#@Santos_E,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model neural neural neural neural neural input input input input input input function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks output number units units information problem models models models models models models models models based based weights case shown shown systems systems functions neurons neurons neurons pattern pattern pattern pattern pattern point point single single processing processing processing local local local local local local local local local local local patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis inputs inputs form form shows shows shows simple simple simple simple simple simple paper paper small small small feature work work work task process process level level level level level level level current current current current current structure structure structure structure structure structure structure structure structure structure structure structure structure problems high similar similar similar similar similar representation representation representation architecture show theory university university university computation research research research independent defined found dynamics computer computer computer computer connections connections connections connections synaptic synaptic node node node node node node node node node node node node node node node node node node node node node science science science science science presented presented presented phase phase activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency object object object object object object object object object object object object object object object object maximum range press press basis abstract back computational computational computational computational computational computational likelihood likelihood likelihood references important important decision propagation propagation propagation context context context context action complex complex complex complex dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated parallel parallel parallel parallel parallel tion tion tion tion complexity representations word word word word word word learned higher part part center previous previous previous previous previous previous bound bound bound required required long long represent represent represent distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed make fact fact resulting ing ing ing ing tasks tasks tasks multi called called elements elements elements means means reinforcement potential made made made made natural natural natural natural natural natural natural feedback knowledge knowledge knowledge knowledge knowledge vol vol artificial artificial artificial represented represented represented represented represented location location location location location location location location location perform perform perform active goal goal goal goal goal goal goal goal goal goal goal related related related constraints brain approaches mit mit connection modeling modeling selection selection proceedings proceedings report department department department joint represents represents represents represents represents represents connectionist connectionist connectionist connectionist responses difficult final final scheme cambridge cambridge domain hinton hinton additional view top top top effects detection detection detection requires con con produce weighted weighted weighted area area area types path path path path path path actual finally selected selected selected selected selected selected evidence evidence evidence evidence evidence evidence evidence evidence inhibitory simply simply simply simply technical arbitrary excitatory excitatory stable stable stable stable surface actions actions actions amount amount amount amount amount generate generate supported role role role role role role role role role role role role role role role role role role role role role role role role role role role role role eds ability ability ability ability future future easily rumelhart including needed needed needed needed transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer mechanism structures language language language language language language language language representing representing representing representing representing representing details max pre pre international bottom depth depth frame frame frame frame decay attention description neuronal directions separate element introduced sense sense sense inference inference inference inference inference cognitive interest highly highly highly highly highly highly volume volume chain organization concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept touretzky touretzky occurs hardware pass conclusion critical greater greater segment segment central central interactions differences performs strong mechanisms california california solid solid intelligence intelligence intelligence exist exist plane plane plane plane plane groups groups connectivity program areas areas reference pro primary sequential describes laboratory distinct simultaneously unique unique blocks john john john john john john john john john john john john john john john interpretation interpretation interpretation interpretation interpretation interpretation interpretation detailed frames frames frames frames frames understanding understanding understanding understanding understanding understanding similarly dashed roughly boundaries boundaries initially initially initially foundation avoid avoid avoid avoid building building existing thesis activations activations activations activations activations activations activations activations instances determines activated activated activated activated activated candidate candidate candidate candidate candidate candidate candidate black black black structural reason selecting differ modification paths paths paths paths paths paths paths paths symbols mcclelland mcclelland mcclelland identify literature build reached receives receives receives capture capture repeated strongly success moore showing showing neuroscience oscillations built built built built involved michael simplified nips binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding maximization automatically received principles illustrates software receive remain unlike create mead put put put relations dotted oscillator matches matches rest possibility possibility relationships relationships symbolic symbolic understand understand understand understand cognition circles concepts concepts concepts concepts concepts concepts plausible plausible plausible created portion logic synthetic sentences sentences crucial multiplication handle handle handle handle handle handle handle handle starts inside inside inside inside inside inside inside inside inside inside inside inside inside inside inside inside inside inside implementing sys shared closer producing producing probable actor actor actor actor actor actor actor actor actor circle circle cybernetics meaning summation summation requiring virtual virtual virtual virtual virtual people pathways pathways pathways pathways embedded embedded lack lack passes spread spread spread spread spread spread spread spread spread plan plan plan plan plan plan plan logical implements eventually sentence sentence sentence sentence sentence semantic semantic semantic semantic identifying identifying identifying identifying identifying identifying dynamically dynamically dynamically signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature reaching generality bower los los los los contract resulted roles roles roles roles cottrell cottrell phrase phrase phrase continue motivation introduces connect respective overview realization propagated propagated interconnections modelled infer reader pollack pollack master locked clean clean grants propagate propagate propagate receiving thresholding assigning discharge usage parsing ple ent ber uniquely uniquely uniquely uniquely uniquely tween propagating instantiation spaced tor massively alter shaded shaded cessing goals num tems signatures signatures signatures signatures signatures signatures generators distant hughes emphasize spreading spreading spreading spreading spreading spreading interactive names ambiguous ambiguous win importantly portions denver locking rochester exhibited completed coming coming coming utilizing builds bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings adaptively aid conceptual conceptual conceptual conceptual conceptual conceptual conceptual conceptual conceptual conceptual arrow king moss thickness thickness discarded discarded interpretations reality quick rectangles planner planner planner planner planner planner planner thing feldman feldman ings semantics ated dyer dyer dyer dyer dyer dyer dyer lange lange lange lange lange lange lange ference ference lisp localist localist localist localist localist localist localist localist localist localist localist schema schema broadcast broadcast continuing settles activa plausibility bio inability forthcoming pursued angeles angeles angeles angeles constituents decides concurrently bind pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot pot meanings neurally neurally standing ant necessity inferences inferences inferences ryckebusch ryckebusch clue mart cleaning regularly vation instantiations waltz waltz acti unrelated disambiguation disambiguation cre spreads spreads kohn heard instantiated bullock ficient opaque genera pol ume accomplishes alteration possessing resorting suf vious ita neces serf pacemaker pacemaker sary cpgs cpgs pacemakers pacemakers pacemakers fion dod sea tivation conceivably disambiguate ofleee comprehension backtracking perkel hav por controversial ovals stereotypical broadcasts identifica 
#@Dyer_M,Lange_T,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model model model model neural input input input figure set set set set set networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm output output output output output output system system system system system system results units units units units units information problem models models models models models models models hidden hidden hidden weights weights weights weights weights weights weights weights weights weights weights weights layer case case vector vector shown shown shown shown systems systems weight weight weight weight weight weight weight weight weight unit unit recognition recognition approach approach pattern processing processing processing processing local local patterns patterns patterns matrix shows signal algorithms simple simple simple simple simple simple paper paper paper net net net work work work work work work features level current trained structure problems high similar representation show show speech real theory theory result result university university university computation research research found found table table table table table table table table table computer computer computer node node node node node node science science science science science presented presented activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes press position basis abstract back references propagation propagation introduction complex complex complex complex hand hand parallel parallel tion tion energy difference representations word word word word word word word word learned learned learned learned learned learned learned learned learned part center type represent distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed fact techniques techniques proposed ing ing ing ing ing tasks human performed performed natural natural em represented provide provide provide provide objects perform perform active gain approaches approaches approaches mit nets modeling institute words department technique technique technique technique internal individual connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist addition addition graph top bit bit bit choice significant world world vision con derived types actual provided provided provided simply limited complete stable require eds rumelhart account account account mechanism structures mode mode language language language representing representing call inhibition inhibition produced run run improved discussed exact property element typical lateral sense sense cognitive cognitive works works studies symmetric grant extended occurs occurs demonstrate demonstrate demonstrate demonstrate strength strength strength strength designed mechanisms integration demonstrated turn relationship relationship connectivity areas pro derive produces solving primary dept dept text develop events agent agent john john john john john john john focus viewed influence forms forms understanding similarly generation remains building coupled reason reason society divided paths included mcclelland orthogonal induced link showing dis built realistic realistic providing providing extend create create put humans replaced issues ml examine examine int int office structured structured structured structured structured structured structured structured structured structured structured structured proper understand cognition fundamental act act act act act act thought formal art motivated phd sentences years advanced ment ment crucial distinguish capabilities handle sys sys day ran ion ion ion ion ion ion ion beginning read read lowest demonstrates author author meaning items backprop share anti spread spread spread spread spread ordered plan specifies sentence sentence sharing college contextual temporally purely purely naval turned intelligent resulted reasoning cottrell started connect connect connect connect james pat pat tic claim multiplied ballard ballard pollack pollack passing passing passing passing passing park explains explains ball ball ball ball ball linked land ties connec assignments tor examining examining examining argue attempted distri tems activate argued spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading ambiguous associates portions accounted dictionary son ation permit permit things struc examination remarks slot tial slots hat hat loosely flows cally dissertation dissertation markers rel senses encodings encodings feldman feldman tra derives syst maryland maryland ini ming explaining explaining explaining explaining lexical tern tern dist dist marker marker transferred plexity activa activa fight fight fight fight fight ago named positively throw throw throw throw throw throw hypothesize linguistics pronunciation behaved behaved pal cog cog cog ions simu mart waltz acti concluding story doctoral tab disambiguation lhe spreads spreads spreads cot cot cot associa sept para gary gary sel lea bet depart tionist funding intersections wit wit wit duplicate rit ern bielefeld vide subsymbolic rst abstracted cont ifs eat shastri pur yer tection semantically semantically bob bob bob determin ive ive ining figtire rea propel propel propel propel propel propel tured roach paral ere atl comprehension posit import apl rained thai hem outpu buted imp ide doc osi nol fect feat 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#@Hendler_J,
#t2
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#*network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input function figure figure figure figure figure time time time time time time time time set output output output output number system system system system state state state results information linear linear linear linear case order order order systems systems systems values values probability parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach pattern pattern large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate inputs inputs signal signal gaussian gaussian gaussian small small small small size feature work work fig fig fig fig fig fig fig fig fig fig fig step step process level structure high high memory memory memory equation section section real states theory obtained obtained term term experiments activity activity activity activity activity activity activity activity activity university threshold threshold threshold threshold threshold threshold threshold threshold threshold research research independent independent dynamics dynamics dynamics initial initial constant standard standard standard computer presented phase phase phase phase phase low frequency frequency frequency frequency maximum range range range range range press abstract find references component component important behavior variable assume lower lower signals signals chosen chosen chosen higher part part center good spike spike long long conditions fact region proposed observed observed scale total simulation simulation simulation sum sum sum elements elements elements means means potential potential potential potential potential potential potential potential applications obtain negative specific compared compared compared provide define active determined connected connected discrete brain brain brain equal equal equal steps loss loss internal internal internal internal internal delay scheme considered environment upper full basic increase increase randomly lines inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends biological achieved increases increases close corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory short short nearest nearest generate square end easily development functional functional interesting interesting interesting increasing structures mode mode decay decay attention attention produced choose choose added membrane membrane membrane membrane membrane membrane membrane membrane period period period period period period period period period period period period period period period period period period varying compare approximately volume volume correspond background chain chain chain chain interval sensitive increased amplitude amplitude parts intensity intensity intensity intensity studied deviation deviation deviation wide wide wide spikes correctly column flow conclusion critical critical critical greater greater central external reduction min plane longer stability stability stability stability stability changing changing linearly electrical remaining slightly develop frequencies potentials decreases decreases decreases dependence dependence interpretation interpretation variation variation controlled controlled modulation modulation constants earlier add closed calculate expect fire fire fire sciences activated activated absolute neighbors neighbors regular middle modes modes oscillatory build situation receives excitation excitation excitation sin oscillations oscillations oscillations oscillations oscillations sci device duration usual relaxation wave ill thresholds thresholds receive trains trains stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation essential exhibit exponentially exponentially oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator behaviour periodic periodic referred working oscillation oscillation oscillation oscillation oscillation oscillation coefficient coefficient changed adjusted impulse impulse nervous generates arbitrarily slowly slowly unstable phenomena starts sites located consequence cut acad beginning gradually summation considerably percent percent percent simulate lattice lattice introducing sharp exhibits exhibits exhibits reaches displays phenomenon generator generator appropriately appropriately refractory cellular integrator adequate fires fires fires falls periods periods interconnections interconnections interconnections modelled bursts master considerations fired resonance resonance unified unified unified unified unified unified ter sine transmitted transmitted big resting tor possibilities associate arising distant distant distant regulation academy iri elsevier elsevier dramatic interspike coming coming discontinuous impulses impulses hundreds station sharply functionally decaying decaying periodically counterpart comparator transmit metastable metastable sends lifetime lifetime lifetime damped comprises justify neighbours neighbouring owing ergodicity imitate regulated regulated regulated llll ast ast ast ast stimulate urn restore russian inhibi pacemaker tio constituted consecutively consecutively ussr ussr ussr stoch moscow unusually submodules submodules submodules submodules rla itl enumerate 
#@Borisyuk_G,Borisyuk_R,Chulaevsky_V,Kirillov_A,Kovalenko_Y,Kryukov_V,Makarenko_V,
#t2
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output number number number system system system system system system system system system system state state results results results results units problem models models models models based linear linear linear linear case case case case case case case case case shown shown shown shown shown shown systems systems systems systems systems systems systems systems values values noise functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons unit pattern pattern pattern point point point point point point point point single single single control large large large large large large large large large large large large large large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix form form form form form form shows shows shows simple paper examples examples small small small small small small small small small size size size size size size size fig fig fig fig fig fig fig points points points points points points points points points points problems problems random random random random memory response response response similar similar show show show show show show show show show equation equation equation equation section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule vectors general general general parameter real real real real real real real real real real real states theory term note experiments result result result university computation computation computation solution solution research research independent defined defined defined defined found found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial constant terms distance connections connections connections connections connections connections connections connections connections connections connections connections connections science prediction left direction direction presented map map present present present present low low low low motion maximum maximum maximum range range components basis continuous continuous continuous abstract applied back find find find find find find find computational analog analog analog analog analog analog properties properties references ieee ieee ieee ieee positive positive important important important introduction complex complex complex circuit circuit circuit circuit behavior behavior behavior dynamic dynamic parallel parallel parallel parallel parallel change assume part part previous previous previous cases type type required multiple long long long conditions conditions distributed equations equations equations equations equations region region region region region region region region region region region region finite simulations minimum minimum minimum performed eq eq eq regions regions natural feedback feedback feedback global global applications study study study knowledge negative negative negative negative negative negative negative negative negative negative negative vol artificial compared desired cross provide define define proc proc proc proc proc proc eye experimental experimental related connected connected connected gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain discrete discrete discrete voltage larger larger larger connection connection connection connection connection connection update update support dependent source institute department version delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay addition sequences sequences considered cambridge equivalent design design limit limit limit limit limit limit limit limit effects effects upper give give produce produce produce produce produce produce produce produce produce produce condition condition condition condition derived criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion product product finally evidence iteration inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends depends simply biological biological biological biological associative achieved increases assumption corresponds excitatory stable stable stable stable stable effective assumed assumed supported supported supported supported supported theoretical theoretical degree makes pairs smaller hopfield hopfield dynamical fully fully transfer transfer transfer transfer interesting ratio york york york york york increasing mode mode mode mode language max max max max max max max inhibition stored normalized magnitude produced description improved discussed recent recent correlations pair pair lateral include period identical identical recently axis axis axis axis axis yields yields studies converge converge differential differential differential differential trans trans symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric observation interval interval organization storage increased increased increased constructed exists parts lead lead lead studied occur occur occur suggests suggests suggests wide predicted predicted alternative deterministic occurs generally pass half half half half half strength conclusion conclusion critical critical critical critical critical critical critical critical critical critical critical depend central central numerical numerical numerical clear exponential taking presence presence physics physics sigmoidal sigmoidal sigmoidal proportional labeled radial assuming exist exist exist min min min min min min plane plane plane plane plane plane plane iii configuration configuration configuration attractor attractor attractor attractor attractor attractor attractor acknowledgements explicit van produces produces produces written index sequential generating describes describes stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability stability mathematical recall recall recall infinite infinite infinite infinite text angle unique unique adding springer springer decreases yield yield squares variation detailed open showed evolution understanding understanding approximated suggested sign diagram delays delays delays delays delays delays delays delays normalization reduces roughly topology building coordinate usa usa bell eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues sciences memories illustrated illustrated prove discuss specifically coupled phys phys phys phys phys phys phys phys phys reason closely modes modes modes modes modes oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory attractors attractors attractors attractors characteristic characteristic characteristic characteristic characteristic characteristic characteristic notice notice conf conf verlag induced induced allowing conductance lie oscillations sci sci device satisfy satisfy relaxation relaxation relaxation relaxation relaxation absence delayed delayed eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue principles satisfies neighboring rat intrinsic intrinsic origin origin origin origin origin origin origin origin origin origin origin origin origin origin origin origin remain powerful american wiley wiley strengths association accurately periodic periodic scalar respond giving investigated biol int scaled eigenvectors tanh tanh tanh oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation understand understand smallest circles math possibly configurations analyze analyze predicts rev rev rev rev rev created created voltages voltages thought bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation der obvious assumes hebb hebb hebb hebb amari amari amari mixed extent motivated electronic electronic electronic electronic electronic electronic electronic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic massachusetts indicating cos cos derivation unstable unstable unstable fairly slope analytical glass glass glass nonlinearity nonlinearity nonlinearity nonlinearity reasons considerable satisfied ring ring ring ring ring ring ring ring widely division desirable sgn laboratories acad acad grossberg grossberg argument requiring varies greatly understood experimentally experimentally cohen cohen cohen cohen resistive frequently gains characterize limiting qualitatively prevent collective asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric coherent coherent coherent coherent coherent coherent coherent coherent coherent attraction attraction realized ordinary uncorrelated notes nat nat purely purely nonzero nonzero inspired numerically numerically numerically odd odd odd odd interconnection interconnection stated familiar contract viewpoint analyzing analyzing exceeds exceeds sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky excellent periods loo studying induce induce induce surprising interconnections iterated iterated young sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained agree eigenvector eigenvector eigenvector border lett lett lett lett ignore crossing appeared constitute shorter basin basin creates creates magnetic conjecture chaos chaos chaos chaos chaos chaos chaos chaos constitutes affects rain realize conservative mutually mackey mackey mackey exponent exponent exponent evolve alternate generators generators jij jij jij jij jij crosses challenging regimes rhythmic rhythmic anal denver inversely siam amplifiers applicability vanishes topologies capacities lecture info sees instability instability justified agrees harvard hemmen usefulness marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus clark clark hopf hopf hopf degenerate linearized linearized prone appl smc smc constraining physically restrictive acknowledges westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt doubling monotone syst physica tan tan tan asymmetry imaginary imaginary imaginary kanter kanter kanter exponents undergoes controllable diverges theor theor symmetrically symmetrically expands repertoire rings rings rings modulo resistances loses loses door jii jii jii fii prog capacitances dropping ond insures insures gutfreund gutfreund gutfreund gutfreund crit disordered crab persist commun rit mech arch overly mezard mezard closes kleinfeld kleinfeld kleinfeld instantaneously complements uninteresting coexist coleman coleman coleman antisymmetric shinomoto shinomoto treatments sii scholar intentional 
#@Marcus_C,Westervelt_R,
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#*network network network learning learning learning learning model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training number number system system system system system system state results results units information information information information problem performance based based space linear linear case order order order order order order order shown shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems functions neurons neurons neurons neurons neurons approach approach approach approach pattern pattern single single single processing control control control control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns signal simple simple paper paper paper paper net work work work work cells cells cells cells cells step level current current cell cell cell cell cell cell cell cell structure response similar similar similar representation architecture architecture fixed rule general general general general general real real real term activity dimensional dimensional university threshold threshold threshold threshold computation research research research found found sequence sequence sequence sequence dynamics dynamics initial computer computer connections connections connections science science direction phase phase phase phase phase phase phase phase phase low frequency frequency frequency frequency frequency motion range range position components components components basis basis basis continuous abstract applied back back back back back back back find computational properties properties references procedure important important adaptive adaptive adaptive adaptive adaptive adaptive introduction introduction complex complex complex complex circuit circuit circuit behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior effect dynamic dynamic dynamic dynamic dynamic dynamic generated generated tion change complexity variable lower rules higher center center firing firing firing firing required required good good long conditions distributed distributed distributed distributed make length observed observed observed observed observed observed forward forward forward forward forward forward forward forward forward forward forward forward forward minimum resulting ing ing ing ing tasks tasks tasks simulation elements means potential potential potential potential made natural natural natural natural natural natural natural natural applications study study study artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial specific specific specific represented series series provide provide provide perform perform perform active active active experimental goal posterior connected gain gain motor motor motor motor motor motor motor brain brain brain brain voltage voltage contrast connection connection train dependent modeling report report synapses consists individual individual individual advances represents represents difficult scheme scheme addition addition addition cambridge environment environment environment environment environment environment additional additional design design design design design design design design design design design design design design design top top effects effects determine free basic basic basic basic con produce produce condition derived weighted developed robot robot robot controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller lines lines finally finally finally finally selected selected selected inhibitory constraint simply simply simply biological biological biological biological biological biological achieved normal describe arbitrary close complete excitatory stable stable implemented implemented implemented generate role role role role role eds square end end ability ability future future development simulated simulated simulated simulated typically underlying fully interesting interesting interesting york edge increasing head uniform operation call inhibition inhibition bottom early produced produced produced produced added added description architectures architectures membrane membrane membrane membrane membrane membrane membrane robust practical apply include period period side side side side side engineering interest varying varying varying volume works tions smooth studies studies studies studies address address address modified interval entire lead move move move generally flow conclusion greater conclusions depend depend depend central central central central central interactions interactions accurate suggest strong mechanisms mechanisms mechanisms presence cycle cycle characteristics characteristics characteristics characteristics demonstrated demonstrated solid labeled variety variety variety variety movements movements movements movements movements movements movements movements selective relationship relationship introduce manner force force appears appears construct construct produces produces produces longer longer ways generating generating transitions stability stability stability dept dept dept changing implement missing involves slightly slightly angle angle angle angle angle angle angle angle unique interaction develop mutual formed focus dependence review overlap overlap viewed detailed open controlled understanding understanding completely completely similarly suggested sign reasonable dashed delays add generation generation generation generation remains valid sufficiently sufficiently construction construction advantages coupling coupling avoid existing fire exploration includes currents currents currents currents currents currents currents bell bell prove prove coupled variations black black reason regular sensor sensor sensor sensor sensor middle middle middle closely capable capable capable capable capable capable capable driven driven successful successful literature literature literature fine reached capture excitation excitation kind procedures procedures strongly success interested issue duration bar play play dot backward backward backward backward wave wave wave wave highest highest principles principles principles deal load load load intrinsic intrinsic intrinsic intrinsic intrinsic situations bars body body body body body body body body body body body simpler simpler remain command command command command command command powerful american american american essential essential exhibit exhibit exhibit varied environments environments environments oscillators oscillators oscillators steady detail detail issues issues preliminary mass hall project project project behavioral behavioral behavioral plasticity analytically possibility reliable proper proper complicated fundamental phases phases phases neu adapt adapt adapt adapt opposite front front front front portion portion separated nervous nervous nervous nervous nervous nervous nervous nervous nervous nervous nervous nervous nervous nervous nervous nervous consist mixed simplest animal animal burst burst burst burst burst great developing crucial crucial crucial sensors sensors sensors sensors sensors sensors sensors agreement defining unstable phenomena adjacent adjacent biology biology biology caused tractable rapid sys producing producing producing producing forces forces desirable controls controls controls consequence scientific begin lowest annual cybernetics robustness apparent behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors freeman transient transient flexible embedded embedded capability autonomous autonomous treated continuously continuously continuously continuously continuously maintain requirement exhibits exhibits controllers controllers controllers controllers controllers controllers controllers controllers perturbations fall fall wind proven serve serve plan semi boston damage damage begins begins progress progress hints physiology sort primarily primarily generator martin temporally temporally animals animals animals animals dynamically controlling controlling homogeneous homogeneous homogeneous food discover flexibility interconnected receptors plays inspired inspired inspired inspired inspired inspired cellular cellular consideration consideration chance ranges interconnection chemical chemical intelligent abilities resulted resulted hope neurobiology neurobiology shifts responsible wilson wilson wilson wilson continue date exploring reliably reliably utilized reset reset falls periods encountered displayed pat mental enhance reproduce bases waves waves waves waves bursts bursts bursts insight repeatedly properly draw relies insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect designing speeds speeds speeds speeds speeds speeds speeds speeds speeds adopted escape escape skills reflex reflex reflex reflex reflex slight ter ter ter pointing hair solves ties emergent feeding theorems abstraction utilize lesions rhythm rhythm rhythm remainder lesion lesion leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg leg peripheral insights insights tems impose chapman gener generators uncertain uncertain mouth carefully careful careful plate emphasize argued synchronized increasingly rhythmic rhythmic rhythmic rhythmic rhythmic tied worth associates emphasized emphasized maintains tune ward ward supporting challenge worked tonic tonic triggered triggered triggered walk walk coordination circumstances locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion rarely reinforce copies bursting bursting bursting bursting handling instability inhibited virtually lated evolved evolved attempting puts loosely pearson pearson pearson pearson pearson supplied rons excited automation tactile tactile tactile heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous swing swing swing swing swing swing swing swing swing swing swing swing ultimate neurobiological complement reproduced falling falling inset periodically tations terminates terminates terminates comprised saturating robustly neglected translate cleveland selverston selverston silent subtle subtle experimented tivity rotate ted progresses bodies unaffected survival survival survival survival survival putational pull pull walking walking walking walking walking walking walking walking walking walking walking walking walking walking walking walking ample repeats apparatus extremes scribed patterned thumb sought sought pushed pushed begun begun insects insects insects insects insects insects insects insects impressive fulfilled exciting organisms organisms organisms serving cen inhibits necessity 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space space weights weights weights weights case case case vector shown shown shown shown shown shown shown systems systems systems systems values values probability probability probability probability probability probability probability probability probability noise noise noise noise weight weight weight weight weight weight weight weight functions method approach point point point point processing processing processing large large large large large test inputs inputs inputs signal signal signal signal algorithms algorithms algorithms algorithms simple small small size size size feature work work work work work work work task points points points points points field features current structure structure problems random random random random random random random high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory architecture rule vectors general real real real average average theory theory theory note note dimensional result computation research research research research research research research research independent defined defined estimate estimate estimate estimate estimate estimate standard standard standard standard computer computer computer distance distance science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left presented presented presented presented activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation low machine machine machine sets sets sets sets sets sets sets sets sets sets range press press learn learn abstract applied find find computational references due procedure important important important behavior behavior behavior behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical effect parallel search search search search tion tion assume assume measure measure measure representations chosen part part center center center center cases type multiple cortex good binary binary conditions conditions conditions conditions distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed make fact proposed probabilities errors ing ing sum performed performed performed called elements elements regions regions regions regions natural global applications study study study study knowledge obtain original artificial relative relative relative relative samples samples compared desired desired proc location location location location location location location location location location location location location location location location experimental related related related gain brain equal equal equal equal equal equal mit comparison connection connection source selection morgan report report report institute institute institute technique internal individual individual scheme scheme scheme framework framework cambridge equivalent experiment environment directly additional additional view estimates bit bit bit bit bit bit bit bit bit bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity full statistics world world world world estimated con condition weighted conditional conditional conditional conditional conditional developed developed area provided finally finally selected selected selected selected selected selected selected selected selected selected selected selected selected depends biological associative associative associative associative associative associative associative associative associative associative associative associative associative normal technical technical group limited close assumption finding amount nearest common common assumed assumed supported supported eds adaptation ability ability future future future makes makes makes development sensory sensory sensory including including kaufmann hopfield hopfield hopfield combination combination ratio special operation language call numbers stored stored stored stored bits normalized early combined sources light predict population improve correlations correlations separate ensemble apply include interest sufficient highly highly previously volume tions studies studies studies studies studies studies sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse address address address address address address address address address address address address address address address address address locations locations locations locations locations locations locations locations locations locations locations interval entire entire entire entire entire lead suggests suggests suggests suggests move occurs occurs runs row greater greater greater assumptions conclusions neighbor clear moody moody suggest propose hard largest california intelligence relationship reference reference reference reference reference explicit written written perception perception perception ann mathematical mathematical mathematical changing recall explicitly explicitly simultaneously averaging infinite physical remaining unique events predictive select john national reconstruction depending depending depending correlated correlated correlated viewed detailed operations restricted understanding completely partition partition allowed key spaces spaces sec combining purpose intermediate calculate calculate sufficiently sufficiently david david david david perceptual perceptual perceptual usa inter weighting weighting weighting memories memories memories memories memories memories determines illustrated identify genetic genetic ten ten refer refer graphs contained contained content sci gray involved write simplified board predictor predictor illustrates acknowledgments access access difficulty involving association limitations mass helpful ideas project combine combine proved statistically math reading reading reading man predicting extremely extremely extremely noted algo assumes nervous initialized improving improving improving defines averages animal animal percentage advanced advanced advanced advanced rows defining baum baum tive mathematics potentially begin cybernetics radius radius radius meaning meaning addressed percent double tional share variant variant variant ity calculating exhibits gains mod mod cal serve collective suited gave sums sums sums hamming hamming age damage damage summed extreme uncorrelated uncorrelated benefit writing writing rithm appropriately nat reconstructed discovery odor food food food addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses chance tools stated cerebellum cerebellum cerebellum los abilities viewpoint viewpoint fail filled filled filled meaningful mance cerebellar james entry equals equals perfor holland holland holland holland overview bad sphere uni counter counter counter counter counter counter counter counter counter counter counter darpa membership membership membership membership membership mem fitness rich informative informative informative informative informative informative informative informative informative informative informative informative informative informative informative storing storing storing partitioned projects discovered parents informa associations associations associations associations associations appeared ence unified constitute deriving ram cooperative emergent propagating arbor constitutes tor possibilities possibilities associate guess imagine activate activate degraded degraded mitchell maximally kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva guided topic topic termed breaks breaks register nasa nasa nasa nasa nasa esti grateful memo knowing els behaves correlate correlate correlate diagrams differently ble ble crude assistance designs savings jointly lated olshausen evolved albus albus conceptual fill condi agency meth ory ods randomness rel senses essence addressing twelve defense contents contents ized indi opinion opinion severely collecting judge predic topics activa proce bio albeit opportunity atoms mate ames 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#@Rogers_D,
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form form form form shows shows signal signal signal algorithms gaussian gaussian gaussian visual paper paper small small net net work task methods methods fig fig fig fig step step step step field field field field field field field field field field field field field process process process level current current current problems problems problems high high high high high high similar similar similar architecture show section section section section section section section section section line line line line images images images images images images images images images images images images parameter parameter parameter parameter approximation approximation approximation approximation average theory theory gradient gradient gradient term term term term term term term term note dimensional result result university university university university threshold computation computation computation solution solution defined found found found found sequence initial initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate standard standard computer science left presented presented map phase low low machine object maximum range range range range range range range range range range range range range range range range press press press press press abstract applied applied applied find find find find find find find computational computational convergence properties properties properties references stochastic stochastic stochastic stochastic ieee ieee ieee important adaptive introduction statistical statistical statistical statistical statistical statistical generated variance variance tion difference variable assume prior prior prior prior prior prior prior prior prior chosen center center center center previous good good good good binary conditions conditions bayesian bayesian expected markov fact techniques region region observed observed minimum minimum minimum minimum resulting ing total simulation eq eq eq eq called called optimization optimization optimization potential global applications knowledge knowledge knowledge original relative application application application cross cross provide provide provide define define define define objects proc perform perform determined constraints distributions discrete approaches comparison update descent descent descent dependent modeling proceedings report report report implementation technique kernel kernel represents represents represents final addition ai considered cambridge cambridge computing computing directly view solutions estimates design top detection conference conference upper requires requires requires choice statistics statistics statistics statistics vision vision vision pages con condition condition condition derived derived weighted levels area processes processes processes iteration iteration iteration simply simply measured normal technical technical technical describe arbitrary denote close inverse assumption complete surface surface surface surface surface surface surface surface surface surface nearest common assumed shape shape role theoretical journal journal end vlsi pixel pixel pixel makes noisy noisy objective simulated simulated probabilistic probabilistic typically smaller underlying reduced reduced functional functional fully block york edge edge increasing segmentation segmentation segmentation mechanism special squared direct making international depth magnitude minimize choose choose choose choose improved improve recent element reported strategy strategy strategy strategy strategy strategy strategy pixels pixels pixels quadratic quadratic quadratic highly conventional approximately solve smooth smooth smooth converge chain symmetric sensitive entire invariant occur deviation deviation derivative derivative locally deterministic occurs boundary generally starting critical critical critical reduce reduce segment operator valued valued valued editors accurate numerical faster temperature temperature temperature temperature temperature temperature temperature temperature temperature hard hard turn turn minimizing minimizing exist relationship derivatives derivatives derivatives derivatives manner minima annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing boltzmann appears edges edges edges describes mathematical explicitly consisting consisting equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium minimization minimization minimization minimization minimization letters independently reconstruction viewed solved variation variation variation variation soft constants calculation smoothing smoothing smoothing smoothing smoothing smoothing slow performing fitting iterative penalty interpolation interpolation initially visible sufficiently norm faces transactions transactions existing thesis priori priori formulation determines specifically absolute neighbors successfully successfully 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#@Bilbro_G,Snyder_W,
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weights weights case case order order order order order order order shown systems systems systems systems systems values probability probability probability probability probability probability probability probability probability parameters parameters parameters weight weight weight weight unit unit unit unit unit unit unit unit unit unit method method method approach approach approach point point point single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control control large local local local local local local local local local local local local local local optimal algorithms simple small size feature net net net net work points points process process process process process process level level current current problems problems problems problems random high high high equation equation line rule rule general real states states states states gradient result university solution solution solution solution solution solution solution solution solution solution solution solution solution research research defined defined found found found found found found found initial constant standard terms connections connections science left left present activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation low low machine machine machine machine machine machine machine machine sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press press continuous abstract find find find find references positive positive decision introduction effect parallel parallel search search difference lower lower lower lower higher higher part part part type type good good good good good good good good good long represent represent represent distributed make probabilities simulations simulations minimum minimum minimum minimum total simulation simulation human called times elements elements means means made natural global global global global global global global global global global global global global global global global global global global global applications knowledge negative negative relative relative represented represented provide determined determined determined goal related related constraints constraints constraints constraints constraints constraints constraints constraints connected connected connected connected connected power approaches approaches approaches mit comparison comparison comparison connection connection update update update update update update update update update update selection implementation difficult difficult difficult final final addition cambridge cambridge directly directly hinton solutions solutions solutions solutions solutions solutions solutions solutions upper upper upper requires basic condition condition developed levels criterion area area area area finally finally processes constraint constraint constraint constraint constraint simply simply simply achieved discussion normal normal normal normal increases increases increases increases increases tested close close close corresponds corresponds stable stable stable stable stable stable finding finding finding amount amount amount short shape shape theoretical main main end end end ability hypothesis hypothesis hypothesis easily easily easily makes makes makes rumelhart rumelhart increasing structures trials uniform uniform uniform representing max making description improved advantage movement movement practical practical practical practical practical practical moving machines sense sense sejnowski cognitive calculated calculated calculated works improvement sensitive parts suggests suggests trial locally move generally critical critical critical depend depend faster temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature largest largest cycle cycle cycle cycle cycle cycle cycle characteristics proportional proportional proportional start start start decrease annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing areas areas areas boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann ways stability mathematical changing infinite involves involves remaining remaining remaining remaining easy easy easy quality quality quality quality quality quality quality quality cycles cycles decreases decreases controlled updated updated understanding completely completely constants processor reasonable slow slow performing avoid figures activations activations determines automatic automatic automatic automatic automatic automatic automatic automatic automatic maximize absolute major determining closely importance maximal computationally paths mcclelland mcclelland characteristic quickly quickly quickly quickly quickly quickly procedures allowing running quantity hypotheses hypotheses processors attempt moves moves moves moves moves moves satisfies satisfies decreasing remain remain unlike schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule giving rest rest rest rest fundamental notion notion act extremely extremely extremely psychology illustrate obvious noted improving finds finds defines stop slowly slowly slowly slowly trivial trivial agreement agreement fairly worse processed processed satisfied directional commonly beginning gradually begin mellon mechanics requiring carnegie substantially poorly continuously biologically reliability reliability maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima summarized measuring pittsburgh replace decreased begins simultaneous extreme trade globally contribute consistently ordinary feasible feasible appearance summing pick perfectly tem generality accepted accepted satisfying satisfying analogy intelligent hit settings guide filled continue reliably reliably reset connect bad bad percepttons schedules schedules schedules ends agree avoiding explorations temperatures temperatures ure leaming benefits benefits benefits rejection employs smoothly resting resting resting resting resting beta param avoids avoids leg visited acting favor modifying continues maintained annealed distant considers rejected rejected spreading pos conversely importantly nal things handled cube cube rarely satisfaction satisfaction externally externally externally externally externally accordance savings compete clarity ackley ackley ackley minsky minsky goodness goodness goodness goodness goodness cold cold remained merit predetermined 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#@Leinbach_J,
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field features process process level current structure structure high memory memory memory memory memory memory memory memory memory memory similar show show equation equation equation equation equation equation fixed fixed fixed parameter approximation average states states states theory theory theory term term term term term note activity activity activity activity activity result university threshold threshold threshold solution research research independent independent independent initial initial constant table computer terms connections synaptic prediction phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation low low frequency frequency frequency frequency frequency frequency frequency frequency frequency object object range range press press components basis nonlinear nonlinear abstract analog properties properties properties references component component due due due due important important mixture mixture complex complex stimulus stimulus effect effect effect effect effect effect dynamic parallel tion difference difference variable signals signals signals signals signals higher part type required spike distributed distributed markov region errors errors errors finite simulation eq means means means filter filter relative objects perform active experimental gain gain cortical cortical cortical brain brain brain brain brain equal mit voltage voltage connection dependent selection version consists internal joint difficult difficult ai cambridge equivalent directly directly curve stimuli capacity basic basic basic produce coding actual evidence inhibitory inhibitory associative associative increases group group group assumption corresponds corresponds excitatory predictions short short short common main main main journal end hypothesis degree degree makes sensory sensory needed hopfield account account account dynamical functional functional transfer interesting structures principle max stored attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention sources neuronal property property property separate element similarity lateral lateral moving identical sense varying volume correspond studies interval entire amplitude amplitude expression invariant deviation loop loop loop white setting pass strength minimal greater depend modules modules taking integration integration integration integration external cycle exist selective selective selective decrease iii iii manner areas explicit perception plot describes transitions transitions transitions stability recall recall simultaneously simultaneously slightly consisting frequencies frequencies formed versus focus formation formation depending stationary stationary communication controlled controlled understanding processor sign diagram key partial tracking tracking tracking tracking tracking valid intermediate initially distances eeg eeg eeg existing existing combinations memories recognize major major major identified uniformly modification divided identify repeated strongly oscillations oscillations oscillations oscillations sci sci vary usual simplified wave wave leading thresholds thresholds automatically automatically modelling modelling trains law origin exhibit oscillators steady oscillator oscillator oscillator oscillator hall rise ideas oscillation hierarchy phases analogous psychology thought thought adjusted versions der precise detector detector nervous mixed simplest chaotic preference band crucial growing unstable unstable unstable unstable explanation explanation diffusion starts division located consequence ion ion hippocampal hippocampal hippocampal universal acad acad grossberg grossberg arises preceding virtual reflects composite car psychological ity schematic exhibits synthesis synthesis measuring collective boston shaped synchronization synchronization univ cor proportion acts controlling impossible cellular analogy analogy alpha alpha interpret serves shifts imply exceeds prentice prentice reset edelman periods loo dominant dominant dominant assembly hippocampus master locked locked concentration papers receiving ics mind radar unified unified listed ber reaction centre aij perceived perceived malsburg malsburg associate mismatch cns acting interact synchronized erp erp discusses locking locking elsevier elsevier ation union tune transients drops supporting develops diagrams picking drives remarks bursting bursting instability scalp tial agrees cliffs king neocortical neocortical neurol neocortex modalities modalities neurobiological comm connectionism counterpart essence subsystem subsystem subsystem indirectly facts facts mul supposed supposed medial gradual stems stems stems metastable metastable arousal arousal arousal arousal arousal arousal arousal arousal yon rhythms lifetime alization fukushima fukushima rom schneider schneider signalling thinking sky ell multiplexing functioning functioning thalamic multichannel reticular reticular reticular crick crick crick subsystems bears concluding emerging unitary unitary tha resembling theta theta freq attend treisman treisman sept bor bor bor abrupt party party breakdown phasic prin midbrain cocktail cocktail mountcastle arl numer ern urn pres russian russian russian voluntary acta hal sinc pulling taneously recency disc sti iol iol glue ussr ussr ential initiating moscow incoherent esis beating cyclical operative squ ator nonspecific ciple emanating odes citatory pll pll quencies nalysis anew nauka slipping engle 
#@Kryukov_V,
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shown shown systems systems systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons unit recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach pattern point image single single single single processing processing control control large local local local class matrix matrix matrix matrix matrix matrix matrix matrix form form form form shows shows simple simple visual visual visual visual visual visual visual visual paper examples work work task task methods methods process level level level level level level level level level level level level level level level level level level level level structure structure structure problems problems problems problems problems problems random high high high high high high high high high high high high representation representation equation equation fixed fixed fixed fixed line line rule general parameter parameter real real term term term term term term note experiments experiments experiments result result result university university university university university variables variables variables variables variables variables variables computation computation computation solution solution research defined found found initial computer computer computer terms terms terms distance distance connections connections synaptic low low low low low low low machine object object object object press press position position abstract abstract back find computational analog analog analog analog analog analog analog properties references due ieee ieee ieee introduction action complex complex statistical dynamic dynamic dynamic parallel cost cost cost tion difference complexity complexity variable variable part part part part part part part part part part part previous type required multiple good binary represent tree expected expected expected length length correct correct correct simulations minimum resulting ing sum called elements optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization orientation orientation orientation orientation knowledge knowledge knowledge obtain vol vol vol vol artificial artificial relative relative specific desired objects objects objects objects objects location location perform perform determined determined determined experimental experimental constraints constraints constraints constraints constraints constraints constraints gain cortical brain brain brain power approaches mit contrast proceedings report department department department technique technique consists represents final scheme addition addition graph graph graph graph graph graph graph graph graph graph graph ai considered framework computing computing computing additional view design design determine determine efficient requires choice world world speed vision vision vision vision vision vision vision vision vision vision vision pages con coding derived levels levels levels criterion area lines lines lines lines lines provided provided processes constraint constraint constraint constraint simply biological biological biological achieved technical describe describe denote denote denote transformation inverse surface surface finding short common shape supported require require main main main main square degree development including including including including objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective typically typically hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield reduced dynamical special consistent consistent consistent consistent matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform database database representing representing filters frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame polynomial minimize added improved reported reported include include include include subject side side hierarchical tions tions solve yields match match match match match match match match match match match match match match match match match match sparse sparse sparse organization organization organization organization organization organization organization organization entire increased grant grant grant parts parts parts parts parts expression invariant invariant occur occur deviation rotation correctly setting setting flow flow conclusion starting greater segment valued valued valued editors interactions differences measures constrained constrained characteristics solid intelligence intelligence regularization plane plane plane plane plane plane plane introduce manner scene scene minima minima base base base explicit index solving winner distinct distinct segments segments segments segments metric simultaneously physical involves involves transformations remaining integrated events minimization minimization minimization minimization minimization springer competition competition john communication controlled restricted frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames static static translation translation translation converges discrimination discrimination penalty penalty interpolation advantages transactions transactions avoid figures perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual coordinate coordinate coordinate formulation instances instances sciences recognize recognize extension illustrated activated neighbors neighbors structural efficiency efficiency capable encoded encoded schemes invariance invariance composed verlag graphs prob interpreted follow criteria criteria satisfy quantity involved relaxation absence paradigm paradigm correspondence attempt deal oriented minimized minimized involving involving involving involving hanson hanson hanson preliminary matches matches matches matches matches matches ideas links links links behavioral applicable plasticity relationships relationships relationships relationships relationships decisions hierarchy hierarchy fundamental hill act act circles circles editor editor psychology created der portion portion noted noted freedom initialized grouping grouping grouping grouping grouping grouping attempts great great smoothness turns widely organized potentially acknowledgement involve angles circle cybernetics integrating virtual prop prop prop understood consistency consistency flexible flexible introducing share formulated incorporating tank tank tank tank tank tank serve qualitatively suited achieves sums june arithmetic arithmetic arithmetic pyramid picture discontinuities discontinuities labeling forming tation restrict acts dynamically unity unity flexibility interconnected clamped platt platt fan held attractive imposed check mark reasoning methodology methodology hint guide carry spurious mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness governed displayed displayed displayed originally bases darpa recog foundations express express express ballard ballard robert counts onr lem metrics metrics yale yale yale yale converted cooperative formulate formulate formulate formulate forced nition abstraction abstraction abstraction connec junction personal malsburg malsburg hierarchies hierarchies hierarchies hierarchies hierarchies descriptions descriptions descriptions suppressed gene gene gene eric eric eric param shaded shaded shaded acting gated favor pami pami pami pami graphics afosr 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#@Anandan_P,Gindi_G,Mjolsness_E,
#t2
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probability parameters weight unit unit unit unit unit unit unit unit point point point point point point single single processing processing large local rate analysis shows paper paper paper examples small small small small size size net net work work points points points points points points points points field level random high high high high high high architecture show show rule rule rule approximation states states states obtained note note note note result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold solution research research independent dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant computer computer connections connections connections science science science science science left left left left left direction direction present activation low low low low low low low low machine machine machine maximum press outputs abstract find find find computational computational properties properties references component stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due important introduction complex complex behavior behavior dynamic generated parallel search search search search search search search search search search search energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference lower lower lower representations higher higher cases type type good binary conditions represent distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed make make make make fact region region correct total called regions regions regions means means true desired cross 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surface amount amount amount amount common shape supported supported supported role eds face end hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis future easily degree degree rumelhart development simulated typically hopfield hopfield combination dynamical york edge mechanism leads representing representing details making making inhibition inhibition early combined architectures improved improve directions ensemble ensemble takes takes reported moving identical machines machines machines sense sejnowski sejnowski cognitive cognitive highly volume axis axis smooth correspond symmetric symmetric grant horizontal lead suggests suggests wide predicted move touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky runs runs half half half half half strength strength conclusion starting starting starting place greater greater competitive competitive competitive modules modules modules modules peak peak peak peak temperature temperature temperature temperature temperature temperature temperature temperature hard hard physics largest external external external reduction characteristics labeled turn turn turn turn turn turn turn assuming variety start minima annealing annealing attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann appears edges edges winner winner winner winner winner winner winner winner winner winner ways ways transitions transitions transitions transitions vertical confidence simultaneously physical involves easy slightly slightly mutual mutual implies cycles cycles select competition decreases choosing national national focus influence controlled understanding understanding allowed diagram diagram diagram slow classical spaces spaces spaces spaces spaces spaces spaces remains initially 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large large large large large analysis analysis analysis matrix matrix inputs inputs form shows paper paper paper paper examples size size net work work task classification memory response show show show equation equation equation equation section section section section section section line line general generalization generalization real real real real real real real real real real real states states states states states states states states states states states states states states states states states states states states states states states obtained obtained obtained obtained term term term term note note variables research independent defined defined defined defined defined dynamics dynamics initial initial initial initial initial initial constant connections node node node node science presented present present low nodes nodes nodes nodes nodes nodes nodes components components components components components components components components components components components components components components components components outputs outputs continuous continuous continuous continuous abstract applied back find computational convergence convergence properties references component component positive positive positive positive positive positive important important decision introduction complex complexity variable assume higher part previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem type type type type type type type conditions equations equations computed respect sum sum performed made made study obtain obtain obtain obtain negative negative negative negative negative negative vol vol vol vol desired desired desired define proc gain gain gain gain gain gain gain gain gain gain gain equal equal equal equal mit comparison larger connection connection connection connection connection connection nets institute institute institute department loss implementation implementation connectionist addition directly solutions give condition condition condition condition condition derived developed types selected inhibitory depends discussion describe arbitrary denote close close close close close stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable proof proof proof proof proof proof short smaller needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield dynamical technology technology technology interesting increasing leads numbers numbers numbers numbers numbers numbers numbers numbers numbers max inhibition pair identical cognitive engineering sufficient volume solve yields yields yields yields correspond studies converge converge converge converge differential positions positions positions positions symmetric exists exists expression lead matrices setting setting conclusion critical 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algorithm output output output output output output output number number error error state state state state state state state state state state state state state state results results units units units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information information information information information hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case shown shown shown values values probability unit unit unit unit unit unit unit unit unit pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single processing processing processing local local local local test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis inputs shows shows signal signal signal algorithms simple simple simple simple simple simple simple simple simple paper examples small small small small small small small small small small work task step step step step step points features features features features process process current current current current current current current current current trained structure structure structure structure structure structure structure structure random random random random random random random random random response similar similar similar similar similar similar similar architecture architecture architecture show show show vectors average obtained note note experiments experiments experiments university university university university research defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial initial table table table table computer computer distance connections node node node node node node node science science science prediction prediction prediction prediction prediction prediction left presented presented presented presented presented presented presented presented presented present phase phase phase phase activation activation activation activation activation activation activation activation activation activation activation activation activation 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representations representations representations representations representations representations center previous previous required long long long represent make make make make fact fact proposed length length length length errors forward scale scale scale finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite total computed performed performed called called elements means potential made natural artificial specific represented represented desired determined constraints steps larger contrast contrast contrast dependent report report report report institute department internal internal internal internal internal code individual individual individual individual individual connectionist layers layers delay sequences sequences sequences sequences sequences considered considered experiment hinton hinton san top produce produce derived derived randomly randomly developed developed criterion path path path path path path path path path path path path path path path path path actual actual finally finally finally selected selected selected backpropagation nature constraint achieved technical technical technical technical describe denote tested limited limited corresponds corresponds stable stable predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions finding common common generate main journal end end end end end end end end end end cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster rumelhart rumelhart including smaller reduced reduced reduced fully trials language language max direct window stored bottom early early early early produced light predict predict predict architectures architectures element element typical introduced introduced moving subject identical hierarchical sense sejnowski sejnowski cognitive recently relevant relevant relevant relevant relevant relevant previously correspond correspond rl modified observation williams williams williams organization organization entire entire entire constructed lead predicted predicted predicted predicted predicted correctly correctly locally locally clusters clusters occurs occurs occurs conclusion starting minimal differences differences differences learns learns learns learns constrained encoding encoding encoding encoding encoding encoding drawn california labeled start start start manner groups groups program program question explicit appears factors sequential sequential sequential sequential sequential sequential sequential sequential distinct changing sensitivity explicitly infinite infinite infinite remaining slightly unique unique events implies letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters yield independently independently depending stages overlap influence influence showed margin completely allowed past epochs epochs epochs epochs epochs roughly string string string string string string string symbol symbol symbol david degrees figures figures figures activations activations strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings illustrated grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar tests regular letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter extra extra closely closely closely capable encoded encoded encoded encoded divided divided divided paths paths mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland presentation presentation presentation presentation comparing reached characteristic capture capture traditional refer kind repeated running automatically received principles illustrates subsequent explore simpler simpler diego experience replaced association association preliminary successive successive history proper encode encode encode encode encode encode phases phases phases phases examined naturally necessarily necessarily predicting predicting predicts predicts predicts predicts predicts predicts predicts predicts automata illustrate illustrate perfect recognizer recognizer prototype freedom epoch epoch epoch epoch epoch mentioned developing crucial answer closer division leaves immediately immediately consequence separately beginning implicit begin begin begin read demonstrates preceding preceding mellon mellon exemplars exemplars exemplars carnegie carnegie elman elman elman elman elman relevance cmu embedded conducted conducted fed 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#@Cleeremans_A,McClelland_J,Servan-Schreiber_D,
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state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results units information problem problem based based based based space linear case case order order shown shown systems systems systems systems systems systems systems values values parameters parameters functions functions functions neurons recognition recognition recognition approach approach pattern pattern pattern pattern pattern pattern point point image single single processing processing processing processing control control control control control control control large large large large large patterns patterns patterns patterns patterns patterns patterns matrix inputs inputs form signal simple simple simple simple simple visual paper paper paper examples examples examples examples examples small size net net net net net net net net net net net net net net net net net task task process process current current current current current current trained trained trained structure structure memory memory memory memory memory memory memory memory response similar representation representation representation representation architecture architecture architecture section rule parameter real states states states states states theory theory theory term term note experiments experiments experiments experiments activity activity activity activity variables variables variables computation defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial table table table table table table table table table table table table table table table table table table table computer terms node node node node node node node node node node node node node node node node node node node node node node node node node node node science presented presented presented present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine machine machine sets sets sets range range learn learn learn learn learn learn continuous continuous continuous continuous abstract abstract abstract references component component due ieee adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction introduction complex hand hand hand circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior behavior behavior behavior effect dynamic parallel parallel parallel complexity lower representations representations representations representations representations learned learned learned learned learned learned learned part previous previous cases type required required binary binary long long long represent represent represent make make fact length correct finite simulations simulations simulation simulation simulation sum elements elements elements elements elements elements elements elements mapping feedback feedback applications filter filter obtain artificial artificial artificial artificial artificial specific represented provide provide proc proc proc perform active active experimental experimental experimental goal motor comparison comparison larger fields fields nets nets nets nets nets nets nets nets selection report implementation implementation implementation version internal internal internal internal represents sequences sequences sequences sequences sequences sequences framework equivalent equivalent equivalent experiment experiment experiment experiment environment environment environment directly solutions transition transition transition transition transition transition bit bit bit capacity determine determine upper requires significant vision give give derived controller controller actual provided finally processes processes simply discussion feedforward describe describe fast limited limited complete circuits circuits common common implemented role main instance easily easily development noisy noisy noisy noisy noisy programming interesting special special mode mode principle principle operation operation operation operation operation representing details call numbers filters inhibition international normalized normalized normalized description description description description exact property robust separate element machines machines machines machines side sense sense inference engineering highly observations observations observations observations teacher match correspond modified entire entire constructed scaling occur extended wide matrices alternative correctly move column column column column column column column column column column column column column column column column column column column column column column column column column column hardware hardware runs runs row row row row row row conclusions sigmoid practice learns learns learns learns learns learns learns learns learns learns external iii iii identification identification identification base explicit explicit produces ways sequential sequential sequential sequential sequential sequential transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions label recall recall category physical physical physical transformations unique scales develop equilibrium equilibrium equilibrium equilibrium applying competition review labels organizing evolution activities activities completely partition partition allowed partial partial initially string string string string string symbol symbol symbol symbol symbol symbol assigned box box box box box box combinations priori strings strings strings strings strings strings strings strings strings strings memories recognize prove discuss discuss variations variations variations variations black black black black black black characterized characterized reason columns regular straightforward modification driven driven driven symbols symbols presentation identify ten composed composed composed composed composed soc conf conf contained split criteria satisfy absence consisted moves collection environments detail association pursuit respond respond respond respond respond tech investigated investigated decisions decisions math possibly automata automata implementations implementations queries versions precise observe explored store store consist arbitrarily arbitrarily rows rows developing developing capabilities lies tool reasons inside processed processed processed precisely forces leaves leaves grossberg grossberg grossberg grossberg grossberg grossberg integrating reflects relevance embedded simulate simulate share remove frequently operate controllers characterize eventually specifies contribute restriction restrict fix labelled labelled labelled labelled labelled jth jth jth jth bin partitions partitions partitions simplify held automaton automaton automaton automaton automaton automaton automaton automaton automaton observing observing settings disjoint alphabet repeat reset reset reset governed entry entry entry displayed overview guarantees expanded widrow widrow assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly entries entries entries winning membership stimulated stimulated ahead environmental environmental relies partitioned partitioned partitioned partitioned characterization characterization characterization characterization characterization characterization characterization intersection limitation outlined sequentially resonance resonance resonance resonance resonance resonance resonance resonance resonance associations associations associations gold gold gold gold corporation tables tables presenting forced convenience affects associate associate associate associate massively massively auxiliary mismatch mismatch mismatch graphics expand synchronized insertion constructs indexed indexed indexed distinguished distinguished discusses assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies intl intl tij siam algebra programmed tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin tin infinitely architectural info stores functionality regularities trainable inhibit inhibited inhibited suite east cornput kth integrates integrates operational operational dedicated dedicated heterogeneous ultimate characterizes characterizes optics recognizes recognizes appl robotic evolves memorized carpenter carpenter carpenter carpenter carpenter carpenter aic aic 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#@Winter_C,
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functions approach approach point point image image image image image single single single single processing processing processing processing processing local local local patterns analysis analysis analysis analysis analysis analysis shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal simple paper paper small small feature feature task cells step step points features features features features process level current structure structure structure structure structure structure structure random random random high high high high high high response response response response response response response response response response response similar similar show show line line line line line line line line images images images images images images parameter parameter parameter parameter parameter parameter parameter parameter real real real real approximation approximation term experiments activity threshold threshold computation solution solution research research log log log log found found found found found found distance left left present phase phase phase phase phase phase phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal range press press position components components components components components components components components basis nonlinear nonlinear outputs outputs outputs abstract back convergence convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties properties properties properties properties properties properties properties properties properties properties references component component due due ieee important introduction introduction complex complex hand circuit circuit circuit circuit circuit circuit circuit behavior stimulus stimulus dynamic generated parallel parallel parallel parallel change change change energy energy difference spatial spatial lower lower lower lower lower lower signals signals signals signals signals signals signals chosen higher higher higher part part center center good good long long long represent represent represent represent represent represent distributed distributed distributed distributed distributed equations make make fact fact fact fact proposed correlation correct observed observed observed observed finite finite finite minimum tasks tasks simulation simulation human human human respect elements elements elements elements elements elements elements elements elements elements regions means made made made study study study filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter obtain obtain original original original vol relative represented represented represented represented represented represented represented true cross series series provide provide provide provide compute compute compute location perform determined experimental connected discrete brain brain brain brain brain brain brain brain voltage voltage comparison comparison comparison source source loss version version version version internal internal represents represents represents responses responses difficult delay curve curve curve curve curve curve curve curve curve view curves curves curves curves curves curves curves curves curves curves curves design design transition effects effects detection full increase increase produce channel channel derived derived derived derived velocity velocity velocity types selected evidence evidence evidence simply achieved discussion increases group limited common effective role eds square square square end end end end end end end end end end end end end end end end end end end end end end development including auditory auditory auditory auditory auditory auditory auditory auditory typically needed account functional transfer transfer transfer transfer programming interesting york edge edge edge head head head consistent mode mode mode mode mode mode mode mode operation operation operation operation operation operation representing filters filters filters filters filters filters direct window window window window early magnitude idea produced choose choose denotes membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane directions resolution resolution resolution resolution resolution resolution property element element element element element element element element element element element element element element element element typical practical include side recently engineering interest interest dimensions compare observations approximately approximately works tuning tuning tuning tuning tuning correspond differential trans locations locations channels channels increased increased amplitude constructed constructed intensity suggests digital wide wide wide wide occurs occurs hardware hardware hardware hardware hardware hardware pass conclusion critical critical clear sound sound sound sound external external reduction cycle characteristics characteristics proportional pulse pulse pulse turn start relationship iii manner acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic force base construct edges edges edges edges edges edges produces produces longer solving mathematical dept dept segments implement coordinates simultaneously simultaneously electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical spectral spectral spectral spectral spectral spectral frequencies frequencies formed shift shift shift extracted independently formation review stages stages stages stages stages stages stages stages stages stages showed evolution evolution decomposition decomposition decomposition understanding spectrum partial roughly add valid valid filtering msec construction advantages advantages david expect building building building figures silicon currents plotted plotted structural structural major simplicity reason sensor middle middle aspects closely importance presentation identify build build computations computations ten excitation soc soc soc soc anderson anderson physiological device localization michael simplified simplified play wave wave wave wave wave wave wave wave wave delayed delayed cat cat processors moves extract acknowledgments deal software decreasing explore powerful wiley create essential essential essential exhibit exhibit mead mead humans accurately hall fourier relationships root proper complicated workshop analogous matched transmission transmission transmission transmission transmission transmission transmission possibly man analyze extremely extremely psychology illustrate equally front front front front front front front front impulse obvious obvious observe nerve nerve nerve nerve logic nervous fibers fibers fibers fibers simplest explain finds electronic seconds isolated animal mentioned indicating great advanced band band band band band band band band band band developing phenomena waveform waveform tool tool berkeley berkeley berkeley berkeley shared shared shared shared shared shared shared shared directional directional broad incorporate monkey afferent commonly cut beginning gradually recording bandwidth outer mechanics mechanics mechanics mechanics people percent cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear simulate experimentally share share passed incorporated resistive sharp sharp sharp sharp span span span operate extracting wind cal serve achieves achieves plan plan kinds decreased cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea realized ear ear ear ear ear ear ear ear ear accomplished amplifier driving animals animals velocities velocities velocities branches branches proceed proceed suppression khz imaging imaging resistance hope occurring removing exceeds corner wilson tap tap tap tap tap tap passive passive passive passive passive passive published tone tone tone tone tone tone irregular studying guarantees realization stereo uni enable enable enable thin insight eng eng smoothed repeatedly valuable receiving displacement mechanical mechanical mechanical discharge pressure pressure resonance leaving slight largely numerous incorporates sine hair covering creates opposed responds medium amplitudes spaced massively massively massively realize realize realize options argue preserved resistor resistor biophysical biophysical mammalian playing playing searches convert inverted inverted oct carefully carefully emphasize depicts depicts surrounding increasingly loading cubic slopes travel september rose shallow resembles species species acoust acoust acoust acoust simplification discretized traveling decided spring hearing hearing hearing impulses evolved aid lyon lyon inclusion drawing drawing acoustical acoustical acoustical acoustical acoustical acoustical acoustical acoustical wavelength push push preservation placement economic approaching approaching falling assp fin fin evolutionary lewis lewis lewis lewis lewis lewis lewis quick cutoff cutoff cutoff cutoff cutoff voice poles poles comer handbook compromise enters enters broadband carrying clues denominator ears ears ears ears 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#@Eisenberg_J,Feld_D,Lewis_E,
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neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate shows shows visual visual paper small small net net net net work work work work work field level cell problems problems problems problems high high high high high memory memory memory memory fixed real states states activity activity activity activity activity activity activity activity activity university university university threshold computation research synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science activation low low range range range range range outputs abstract analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references ieee positive introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit effect dynamic dynamic dynamic cost tion tion change variable lower lower signals signals higher previous firing firing firing firing firing firing firing firing firing firing firing represent represent represent distributed chip chip chip chip chip chip chip chip chip techniques length length resulting resulting classes total simulation simulation simulation elements potential potential potential potential feedback vol vol artificial represented proc proc proc proc proc active determined determined discrete power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage steps support nets implementation implementation implementation implementation synapses synapses technique technique technique consists code individual represents computing computing computing directly design design transition san stage bit bit bit conference conference conference conference conference upper upper full full full choice speed estimated increase con con channel area lines actual finally inhibitory inhibitory inhibitory inhibitory biological associative associative achieved achieved achieved describe describe arbitrary complete complete excitatory excitatory excitatory excitatory circuits circuits implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse require end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi ability ability instance instance instance makes auditory smaller fully fully fully technology technology ratio mechanism principle operation representing representing max inhibition inhibition inhibition inhibition inhibition stored stored added improved separate separate introduced moving include side array engineering varying smooth smooth modified channels gate gate storage storage storage storage storage increased constructed exists studied digital digital digital digital digital digital digital wide alternative locally width width loop column column hebbian hebbian strong external reduction intelligence pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse relationship acknowledgements areas generating dept dept dept implement implement implement integrated yield overlap controlled controlled fraction forms allowed sign diagram earlier topology precision precision silicon usa inter weighting determines illustrated illustrated gating gating successful computations schemes excitation excitation excitation excitation road road road conf physiological sci device nips cmos cmos cmos cmos cmos denker denker overlapping diego mead mead mead mead rapidly detail strengths mass behaviour behaviour postsynaptic postsynaptic postsynaptic rise giving int authors reliable stream stream stream complicated workshop presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic neu neu hill act implementations implementations logic store switching switching serial electronic charge charge charge charge charge devices devices ment asynchronous asynchronous asynchronous asynchronous asynchronous multiplication multiplication turns implementing ring style division division broad transistors transistors pulses pulses pulses pulses pulses pulses pulses pulses potentially involve acad grossberg summation integrating varies limits autonomous passed passed remove resistive psychological execution howard howard modulated fall proven proven collective simulator decreased implements begins wesley analogue proportion proportion addison oxford oxford amplifier linearity driving dynamically flexibility arrival multipliers multiplier multiplier multiplier multiplier multiplier smith smith adds murray murray murray murray murray overcome odd mos mos programmable programmable programmable programmable programmable programmable programmable programmable programmable mark splitting integrator synchronous capacitor capacitor capacitor capacitor capacitor capacitor arrays clock clock clock natl falls introduces widths buffer schwartz schwartz consequences jackel jackel nonlinearities tic tic bursts bursts eng eng eng offer broken tures receiving receiving acknowledge accumulated outlined discharge discharge discharge discharge ram ram removal ties smoothly tor edinburgh edinburgh edinburgh edinburgh increment subthreshold packets packets resistor hubbard hubbard tij tij resistors packet mimic removes removes electron stores beam functionality council hop hundreds suffers mahowald imple capacitors capacitors supply supply hamilton hamilton hamilton hamilton graf graf inverter inverter inverter inverter inverter converter converter ron connects rons devised operational architec alan arrives ory consumption creation ready elec elec enters aip aip aip united united united tory stan refine custom custom modulate ton rela minimise vdd vdd vdd 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#@Hamilton_A,Murray_A,Tarassenko_L,
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weights linear linear linear layer case shown shown shown systems values values probability weight weight weight weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit method method pattern single single single processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate inputs inputs form form signal algorithms algorithms algorithms simple visual paper small small small small net net net net net net net work work work work work work field process process level level level current current current current current current current current current problems high high high high high high memory similar show show equation equation equation equation fixed fixed fixed fixed line line rule rule general general approximation approximation approximation average gradient gradient obtained obtained obtained activity result result threshold threshold threshold threshold threshold computation solution solution found found found initial constant constant constant constant computer computer terms terms connections connections synaptic synaptic synaptic left activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation low low low low low low low low low temporal temporal temporal temporal temporal maximum range range learn learn learn learn components nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous continuous continuous abstract abstract back back back back back back density density density analog analog analog properties references ieee ieee ieee ieee ieee ieee ieee ieee ieee positive positive procedure procedure important important adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation propagation propagation introduction action action action action action action action circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior statistical effect parallel parallel parallel tion tion tion tion tion difference variable measure measure prior representations learned learned higher part part bound firing firing firing firing firing firing firing firing firing firing firing type type required cortex good binary binary binary spike spike long represent distributed expected equations equations equations equations equations chip chip chip chip chip region proposed observed observed observed simulations simulations ing total simulation multi sum times potential potential potential potential potential potential natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural feedback study vol vol artificial artificial artificial artificial relative represented represented true application define rates proc proc proc proc perform perform determined determined goal related connected gain equal power power power power power power power power power approaches approaches approaches approaches voltage voltage voltage voltage voltage voltage voltage voltage larger connection train train descent descent source source source source nets modeling implementation implementation implementation implementation implementation implementation implementation synapses synapses synapses synapses internal code represents represents bias computing equivalent directly directly hinton curve solutions solutions curves design design upper full requires requires approximate basic basic increase con con con channel derived derived derived derived derived weighted developed developed developed levels area area path path actual inhibitory biological associative increases arbitrary group assumption corresponds complete excitatory excitatory excitatory excitatory circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits implemented assumed assumed assumed synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse generate require vlsi vlsi vlsi vlsi future rumelhart rumelhart development development including including fit auditory simulated typically reduced functional functional technology leads leads principal numbers max pre early early idea attention neuronal architectures membrane membrane membrane membrane membrane membrane membrane membrane membrane discussed improve improve advantage typical practical practical practical include include include period period period period period period identical sense sejnowski sejnowski recently engineering dimensions varying conventional works tions tions yields correspond studies differential achieve background modified modified generalized generalized channels channels channels gate gate williams sensitive increased increased exists expression expression expression invariant invariant digital derivative width occurs occurs hardware pass flow flow flow conclusion starting greater depend interactions differences accurate accurate numerical numerical designed performs learns integration integration integration integration characteristics characteristics pulse pulse assuming exist manner configuration reference pro longer solving ways factors describes ann dept modeled simultaneously physical electrical electrical integrated formed shift shift potentials expressed expressed expressed stages communication open controlled organizing organizing centered forms approximated similarly purpose generation generation generation fire currents candidate variations phys phys partially major delta delta delta delta wij post post post post post online fine characteristic excitation excitation excitation excitation excitation excitation conf conf conf conductance follow follow cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos correspondence thresholds neighboring unlike xor xor collection requirements exhibit circuitry mead detail integral dual terminal biol stream func presynaptic neu neu act adapt onset onset onset configurations voltages voltages voltages implementations implementations implementations implementations implementations prototype impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse logistic logistic logistic logistic nerve logic logic nervous switching switching electronic electronic electronic electronic electronic electronic electronic charge asymptotically developing asynchronous ground derivation analytic analytical analytical floating turns turns turns turns rapid perspective arc arc arc closer transistors immediately ion ion ion ion ion ion axon axon involve beginning geometry geometry geometry questions reflect transient conducted frequently compares psychological operate prototypes howard exhibits rely differs reaches popular suited physiol differentiable differentiable arithmetic instantaneous irrelevant realized physiology investigation investigation amplifier summing summing summing refractory refractory refractory driving encoder connecting grows arrival extending spontaneous spontaneous cellular saturation smith murray murray difficulties mos attractive programmable responsible capacitor capacitor capacitor capacitor capacitor capacitor capacitor arrays substituting fires motivation studying equals moved washington evident schwartz schwartz jackel jackel artifacts artifacts artifacts artifacts modelled foundations express cerebral neuromorphic layout layout layout offer arrive late waveforms draw designing ignore summarize receiving receiving vari mechanical anns specification largely trigger trigger drain junction resting streams rectangular rectangular rectangular capacitance gated gated gated gated gated conduction resistor alternate interneuron goals continues potassium potassium potassium hubbard hubbard compatible rectangle cole cole cole cole switched investigating transconductance employing exchange interconnect amplifiers ation lippman examination hodgkin mann emphasis saturated saturated huxley impulses impulses coin imple imple establishes reflecting graf graf graf drawing fabrication fabrication eliminates rons rons operational repetition tance leakage communicate mosis amenable lewis lewis lewis tra translate dissipation dissipation dissipation dissipation hyperpolarization hyperpolarization hyperpolarization tory thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc thc gradual gradual imum depolarization depolarization depolarization applica plastic jack expresses activa gross gross fet fet fet fet fet fet fet fet fet fet fet fet fet fet fet fet fet fet fet fet vdd accu accu tran availability berger cir cir tiny sodium sodium sodium sodium offline offline offline viable emulate emulate emulate emulate desire desire facilitation synapfic theor hwang ions icnn icnn icnn kung kung adaptable sivilotti sivilotti conducting emulation embody micron micron designer grained opera flowing flowing experimen asymptote doubt conduc genera manifested lambda lambda cedure occupies occupies conflicts textbook initiation racy geometries 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#@Cole_C,Meador_J,
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shows signal algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper work points points points points points level current current current current current problems problems problems problems high representation show equation equation equation equation equation fixed line line line line line line line line line line line images images images general theory theory theory theory note experiments dimensional dimensional result computation solution solution solution solution solution solution solution research research constant standard standard computer computer computer computer terms node node node node node node map nodes nodes nodes nodes frequency range range press press components outputs outputs outputs outputs continuous sample abstract back computational computational convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references component ieee positive positive positive positive important introduction circuit circuit circuit circuit circuit circuit circuit circuit effect generated tion tion change energy energy energy energy energy energy energy energy difference difference representations representations represent represent expected equations equations chip chip chip chip chip chip chip chip chip chip chip fact techniques resulting total computed respect eq called times elements elements elements elements factor factor made feedback feedback feedback feedback feedback feedback orientation orientation orientation global negative negative negative negative negative negative negative negative negative negative represented true application application provide proc proc proc location location perform experimental experimental constraints constraints constraints constraints connected power power power mit mit voltage voltage voltage voltage voltage voltage voltage voltage voltage comparison comparison larger contrast support support support source institute implementation implementation implementation version version difficult difficult bias bias addition graph cambridge cambridge directly additional solutions stage detection detection detection detection conference conference determine requires choice choice speed vision vision vision vision vision vision vision vision vision vision vision con produce types types lines provided provided processes processes constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint measured measured arbitrary tested surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface circuits effective implemented implemented implemented implemented implemented require vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi development noisy sensory sensory simulated simulated typically combination technology york edge edge edge special consistent leads depth depth depth depth depth depth depth depth depth depth depth depth depth early early early early early early magnitude idea added sources sources architectures membrane membrane element identical conventional module solve solve solve smooth smooth smooth smooth smooth yields sparse sparse sparse sparse sparse sparse sparse chain modified modified grid grid grid horizontal horizontal scaling scaling digital wide derivative boundary conclusion operator operator modules designed designed constrained demonstrated california solid solid solid solid solid proportional proportional minimizing min min acknowledgements reference suppose produces written solving generating describes vertical vertical vertical confidence confidence implement implement implement implement implement implement explicitly explicitly consisting minimization minimization minimization john reconstruction reconstruction reconstruction reconstruction reconstruction squares open suggested allowed smoothing smoothing smoothing smoothing smoothing dashed dashed dashed dashed dashed measurements interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation calculate construction foundation advantages koch koch koch koch koch coupling coupling building building box box box box box box box box formulation currents determines extension coupled coupled coupled coupled coupled coupled variations successfully successfully straightforward straightforward straightforward poggio poggio poggio poggio build soc notice conf prob conductance conductance conductance conductance device device device device device device device built satisfy comp vary absence minimizes minimizes cmos cmos cmos cmos computes ill unlike poor circuitry mead mead mead mead mead mead mead mead dotted dotted graphical helpful terminal terminal terminal terminal terminal ideal transistor combine scaled authors office proper proper proper workshop surfaces surfaces act act circles possibly possibly reading voltages explored mapped submitted finds defines convolution convolution convolution smoothness smoothness slope slope slope slope slope slope slope slope slope slope slope slope slope analytic analytic analytic london forces directional directional directional incorporate arise commonly commonly circle computers author pure led generic generic fed lack orders posed resistive resistive resistive schematic limiting pasadena green green green plan implements implements yuille yuille june wesley lab discontinuities analogue addison fabricated formally reconstructed naval turned rigid held intuitively responsible adequate started sion washington stereo thin thin thin thin thin thin smoothed horn designing harris harris harris harris harris harris harris harris harris harris harris harris harris interestingly interestingly dense dense 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#@Harris_J,
#t2
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#*network network network network network network network network network network network network network network network network network network network learning model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output output output number number number system system system state state units information information information information models models based space linear linear linear linear layer layer case case case case shown shown shown systems systems systems values values noise functions neurons recognition pattern pattern point point point processing processing processing control control control large large patterns patterns patterns class class class inputs inputs inputs form form shows shows shows shows shows shows simple simple visual visual visual visual visual visual visual small small size feature feature net work fig fig fig cells cells cells cells cells field field field field field field features level level level level level level level level current current current cell cell cell cell cell cell cell cell cell cell cell cell high high high memory memory memory memory memory memory response response response response response response response response similar similar representation representation architecture architecture equation equation equation section general general general average theory theory term term term term term experiments activity activity activity university constant constant constant standard standard terms terms terms terms terms terms terms terms connections connections connections connections synaptic synaptic present frequency frequency temporal temporal temporal range press components components nonlinear abstract abstract applied applied computational computational analog analog analog analog analog analog analog analog analog analog analog analog properties properties properties properties properties properties references due due ieee important adaptive adaptive introduction introduction hand circuit circuit circuit circuit circuit circuit circuit circuit effect effect dynamic parallel parallel parallel parallel recurrent recurrent recurrent recurrent tion tion tion tion difference variable spatial spatial spatial spatial spatial lower lower lower rules chosen chosen higher higher part center center theorem bound required required good good represent expected equations equations chip chip make region region proposed length correct correct forward ing total eq eq eq elements potential made feedback feedback feedback feedback global global global applications filter negative vol vol relative specific desired receptive receptive receptive constraints connected gain gain discrete discrete brain approaches approaches voltage voltage voltage contrast contrast contrast contrast contrast contrast connection dependent source source nets nets nets nets nets department implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation version consists addition addition addition addition addition addition addition framework framework framework framework framework design design design design design design design stage stage stage stage stage stimuli capacity upper upper requires choice speed basic basic produce produce channel derived finally finally evidence inhibitory inhibitory inhibitory inhibitory depends biological achieved feedforward increases increases arbitrary tested excitatory excitatory excitatory excitatory excitatory stable stable stable circuits circuits short short short short nearest implemented implemented adaptation adaptation adaptation adaptation adaptation square square end hypothesis future makes sensory sensory sensory including account fully transfer interesting ratio york edge edge increasing special uniform uniform mode mode mode mode mode inhibition inhibition inhibition stored depth decay sources sources membrane membrane population population exact property property element lateral lateral introduced array engineering sufficient varying previously works module tuning tuning tuning axis axis tions studies achieve background gate gate gate organization storage storage sensitive constructed horizontal intensity intensity intensity intensity digital digital wide wide predicted feed width loop loop strength strength strength strength conclusions neighbor competitive central interactions interactions interactions exponential mechanisms integration integration external external solid proportional assuming variety variety variety variety connectivity areas relation pro construct edges produces optical stability stability tuned vertical mathematical implement implement sensitivity multilayer multilayer electrical angle interaction interaction equilibrium gaussians shift shift shift decreases formation dependence dependence dependence dependence codes densities organizing modulation completely processor additive normalization iterative advantages advantages dendritic includes silicon contour sciences automatic absolute characterized successfully simplicity compression extra capable suitable society efficiently compact showing showing conductance conductance oscillations content content content physiological device relaxation surround surround surround cmos cmos cmos cat automatically law american singh circuitry circuitry steady replaced behavioral behavioral applicable biol biol transistor transistor root root matched removed man extremely psychology front impulse portion logic logic nervous art art art art art simplest explain explain devices devices devices devices devices devices mentioned site preference preference agreement biology biology capabilities capabilities multiplication nonlinearity processed implementing tive transistors transistors transistors transistors transistors transistors transistors desirable desirable desirable controls mathematics grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg geometry cybernetics cybernetics cybernetics readily lack psychophysical cohen cohen biologically psychological operate operate exhibits suited suited coherent implements implements progress realized physiology feasible fabricated fabricated oxford enhancement enhancement enhancement enhancement enhancement grows generality fan fan fan cerebellum multiplicative multiplicative multiplicative multiplicative neurobiology capacitor preparation passive ranging sion conjunction buffer buffer buffer buffer buffer washington consequences interconnections interconnections interconnections nonlinearities bases hippocampus properly instructions cam cam cam fly robert robert resonance resonance shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting latency employs quantized capacitance mathematically compatible iso overhead sized electronics book placing interconnect applicability psychophysics psychophysics computa technologies technologies technologies cable inverter eral pronounced polarity polarity polarity seattle distinguishing lightness sen proposes core luminance luminance luminance contributes neocortex inefficient optics arriving 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#@Darling_R,Nabet_B,Pinter_R,
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#*network model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time networks networks networks networks networks networks algorithm output output output output output output output output output output output output output output system system system models models performance space order order order shown shown systems systems systems systems systems systems values values values values neurons neurons neurons neurons neurons neurons neurons neurons single single large large large local local local local local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis analysis analysis analysis analysis class inputs form form shows shows shows shows shows shows signal signal signal visual paper small small small small size feature net work work task step step features process level current current current current current current current current current current current current current current current current current current current current current current current current current current response response response response response response response response response response response response response response response similar similar representation equation equation equation equation equation equation equation equation section section line line line general general parameter parameter real real theory activity result result result computation computation computation computation computation computation computation computation research log defined dynamics dynamics constant constant constant constant computer science present present temporal sets sets sets range press press press press position nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous continuous abstract analog analog analog analog analog properties properties properties properties references component action action action complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior effect dynamic dynamic dynamic dynamic dynamic parallel tion complexity complexity complexity complexity complexity spatial spatial spatial spatial spatial spatial part previous bound multiple multiple good binary long represent represent represent represent distributed chip techniques region region scale finite factor potential potential global global global applications applications original original original vol relative relative desired series series compute compute perform perform perform active experimental experimental experimental experimental experimental experimental experimental related gain equal equal equal equal equal approaches voltage voltage voltage voltage voltage voltage voltage larger larger support source source source source source report report institute department implementation responses responses exp exp exp exp addition computing experiment experiment determine full full full condition condition derived area types lines provided nature nature inhibitory inhibitory inhibitory inhibitory technical increases tested tested limited stable stable predictions circuits circuits circuits circuits circuits circuits circuits nearest common common common theoretical theoretical theoretical require require vlsi vlsi vlsi development sensory sensory fit auditory auditory smaller functional technology transfer interesting mode operation operation operation operation max inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition normalized early magnitude magnitude magnitude magnitude added added added sources apply identical identical identical identical previously approximately yields yields yields correspond achieve modified modified gate gate gate gate entire entire intensity expression expression wide correctly locally locally conclusions designed designed designed exponential physics physics largest largest california solid solid solid decrease decrease produces solving solving solving winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner ways plot describes describes describes describes describes describes mathematical linearly physical physical physical scales integrated integrated integrated versus versus potentials potentials potentials john john influence evolution static completely constants diagram diagram diagram diagram diagram diagram smoothing sufficiently foundation topology david silicon currents bell determines plotted plotted absolute neighbors successfully differ modification symbols poggio efficiently computations plots receives receives compact compact repeated repeated showing showing showing conductance conductance oscillations localization localization cmos cmos cmos correspondence computes computes computes computes computes illustrates illustrates neighboring acknowledgments decreasing extend exhibit mead mead mead mead mead mead mead mead mead mead transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor office gates understand understand smallest circles circles circles reading predicts predicts predicts voltages voltages voltages impulse impulse impulse impulse extent defines synthetic devices devices mentioned ment ment phenomena spatially ring transistors transistors transistors transistors transistors transistors desirable circle optimize annual explained applies leave orders orders orders share compares compares schematic schematic schematic schematic schematic schematic maintain exhibits exhibits ordered pasadena suited boston age wesley extreme addison fabricated fabricated fabricated ratios driving naval connecting connecting caltech caltech platt saturation logarithmic logarithmic mos mos multiplicative serves mark exploit operates reasoning wire wire wire wire wire settings capacitor filled service ranging ranging ensures mental stereo darpa winning winning winning winning winning winning winning layout lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro variants explains logarithm logarithm logarithm logarithm encodes encodes encodes encodes encodes axe axe responds medium medium drain drain drain drain realize realize realize capacitance subthreshold subthreshold resistor resistor resistor resistor resistor resistor insights compensate crossover ization distant distant distant mask resistors interconnect interconnect likewise increments experi experi wider wider saturated losing losing losing losing losing losing mahowald mahowald mahowald mahowald mahowald mahowald mahowald mahowald supply clarity fabrication fabrication connects meeting triangles marr contributes carries symmetrical exploits volts vertically communicate mosis poles saturating media ically statements statements saturate winners sponsored rises hysteresis damped mediate controllable displaced asso inhibits parasitic explores ryckebusch ryckebusch ryckebusch ryckebusch ryckebusch ryckebusch supplies sponse narrower contributed volt volt abstracts tlx dave stereopsis realizing realizing logarithmically shed capacitances clocks wyatt unidirectional unidirectional sink sink sink highlighted confirming packard ciated diminishes inhibi designers locates inns hewlett capac swept gillespie supplement regulates ringing docu feinstein complezity hibition 
#@Lazzaro_J,Mahowald_M,Mead_C,Ryckebusch_S,
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#*network network learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set set set set set networks algorithm output output output output output output output output output output output output output number number number number number number system system system state results units performance performance performance performance based based weights weights weights linear linear linear case case shown shown shown shown shown systems systems systems values parameters parameters parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit recognition method pattern pattern pattern point single control control control control control control control control control control control large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test patterns patterns patterns analysis analysis analysis inputs inputs inputs inputs inputs inputs inputs shows shows signal algorithms algorithms visual paper examples size size size feature feature net fig fig fig fig fig fig cells step step process current current current current current current current current current high memory memory memory memory memory architecture architecture architecture architecture architecture architecture architecture fixed line line line general general general general speech speech real real real real real real approximation average obtained obtained obtained obtained activity university threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation research constant table table estimate estimate computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic direction phase activation low low low temporal temporal temporal machine machine machine machine machine machine machine machine machine machine sets motion motion maximum maximum maximum range range range range range range components components outputs outputs outputs outputs outputs abstract computational computational computational computational computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references ieee circuit circuit dynamic dynamic dynamic dynamic variable lower signals signals prior word word cortex represent represent expected equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip region length forward scale scale scale scale scale scale minimum minimum minimum minimum tasks tasks total total sum sum performed elements elements made knowledge filter specific specific application cross active determined connected connected connected gain gain gain gain gain gain gain gain gain gain gain gain gain discrete power power power voltage voltage voltage larger contrast contrast connection connection connection connection connection connection fields nets proceedings proceedings report implementation implementation version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses code code code individual individual responses bias scheme scheme addition addition considered equivalent directly curve additional solutions design design design design design design design design limit san bit bit bit bit bit bit bit bit bit conference conference conference world world speed speed speed speed speed weighted lines lines lines lines lines lines provided selected selected selected nature biological biological biological arbitrary limited limited limited limited limited limited surface circuits circuits circuits circuits circuits common common common common effective implemented implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse generate supported require require require end end vlsi vlsi vlsi vlsi vlsi degree development sensory needed block transfer transfer transfer transfer transfer transfer transfer programming special mode mode mode mode operation language leads leads numbers iterations direct direct inhibition stored stored stored bits bits international magnitude combined run architectures architectures architectures recent resolution resolution resolution resolution resolution separate separate separate separate typical typical reported include identical identical sense array array array engineering sufficient approximately module module module module module module differential modified horizontal scaling occur digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital setting pass pass runs runs flow greater greater central central measures modules modules modules modules modules modules modules modules modules modules modules modules modules modules retina numerical external characteristics solid labeled assuming acknowledgements areas van primary describes vertical dept dept segments linearly electrical events shift squares squares squares transform controlled controlled forms constants constants constants constants constants constants constants constants constants constants constants sign sign sign diagram diagram diagram earlier reasonable expansion combining purpose purpose purpose generation filtering david exploration exploration currents currents determines columns determining driven literature computations computations receives characteristic composed composed link receptor modular board cmos thresholds chips chips chips chips chips neighboring deal software routing routing routing receive situations diego mead mead relations relations circles reading opposite opposite prototype versions der logic switching switching serial serial serial electronic advanced rows developing sensors drive stanford lin straight implementing cut axon angles beginning axons annual nsf populations generic leave orders adjustable adjustable adjustable adjustable adjustable adjustable passed howard switch switch switch switch switch switch switch switch switch switch switch gains gains gains gains gains gains gains gains gains gains summarized serve serve serve simulator simulator simulator simulator simulator simulator simulator chose boston eventually simultaneous cochlea calls calls wesley summed trade primarily addison fabricated unity interconnected robotics robotics arranged arranged logarithmic logarithmic determination programmable programmable programmable programmable programmable programmable programmable programmable resistance resistance settings north north north north north arrays arrays arrays arrays arrays planar alspector alspector published ranging connect paul overview sides intended intended schwartz schwartz thomas multiplied cerebral neuromorphic neuromorphic layout layout lazzaro lazzaro route grants receiving switches switches switches switches switches switches switches onr compressed converted converted quasi adjustment adjustment capacitance exponent permits hubbard exceed exceed exceed rough register figs figs figs west west 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#*model model model model model input input input input input input function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set output output output output output output output output output output output output output output output output output number number number system state results results units performance performance based linear layer case order shown shown probability noise noise noise noise unit single control control control control control control control control large test inputs form form shows shows shows shows shows signal signal paper small small small small small small small small small work methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells process level level level current current current current current current current current current current current current current current current current cell cell cell cell cell high memory response response response response response response response response response response response response response response response similar similar show show show show show show general real approximation approximation note note note experiments activity result result result result threshold threshold threshold threshold threshold research log log log log log log log log log log defined defined initial initial constant constant constant constant constant computer computer terms terms distance science low frequency temporal temporal temporal sets range range range range outputs abstract back back back find properties properties properties properties references due action hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit effect effect effect effect effect dynamic dynamic dynamic dynamic parallel change change change change difference difference spatial part center type required spike expected chip chip make region region length correct correct scale scale scale scale resulting human human human human times factor factor made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications obtain negative relative relative relative relative compared compared compared compared series eye determined connected gain gain gain gain gain gain gain gain gain gain gain brain voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage comparison larger larger larger contrast contrast support source source source report institute words words version version technique consists consists represents represents responses responses responses responses responses responses responses responses responses responses bias equivalent directly directly curve curve curve curve curves curves curves curves curves top stage stage stage stage effects effects bit bit detection detection detection detection give channel levels criterion area area finally simply biological biological achieved measured increases increases increases increases increases increases describe assumption amount amount amount short supported require vlsi development including typically typically typically smaller technology technology interesting interesting interesting ratio ratio ratio mechanism trials trials mode operation operation operation operation operation leads call numbers direct bottom bottom early early early early early magnitude magnitude magnitude idea idea idea sources sources light light light light light light light light light light light light neuronal discussed improve property pair pair element element element element element element element lateral subject subject identical compare compare compare previously approximately works achieve background background background gate gate gate sensitive sensitive sensitive sensitive sensitive sensitive sensitive increased amplitude amplitude parts intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity expression expression trial trial trial hybrid loop loop loop half flow conclusion greater interactions peak exponential exponential exponential characteristics characteristics characteristics california proportional proportional proportional labeled labeled assuming variety manner base base base base acknowledgements produces produces optical optical ways ways describes ann sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity develop integrated equilibrium shift shift decreases decreases stages squares variation variation constants past past earlier reasonable sec roughly remains valid foundation includes silicon currents retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal extension sensor sensor capable differ included comparing tend characteristic characteristic capture refer strongly device surround delayed highest thresholds thresholds thresholds thresholds thresholds chips operating receive law law transformed mead mead mead mead mead mead steady dual helpful rise history rest rest rest rest transistor transistor transistor scaled scaled office office comparable tanh tanh hill smallest act closest analyze rev voltages voltages thought detector extent motivated electronic electronic electronic electronic electronic electronic electronic electronic isolated percentage percentage percentage percentage growth sensors agreement slope biology biology adapted caused ganglion ganglion ganglion spatially satisfied arc filtered filtered transistors transistors transistors arise arise arise potentially read recording recording outer varies led led led led led transient orders orders orders incorporated incorrect maintain gains gains limiting differs differs differs pasadena conductances gave substantial replace comments decreased room fabricated bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar amplifier amplifier amplifier amplifier amplifier amplifier amplifier naval receptors analogy logarithmic logarithmic determination determination familiar resistance resistance resistance height hit hope illumination illumination arrays arrays substituting started started falls equals expanded intended photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor arrangement sustained intersection intersection intersection dramatically drop encodes responds feeding feeding causing drain drain drain lit hundred hundred hundred hundred letting increment subthreshold subthreshold mammalian neurophysiological mediated transconductance transconductance transconductance transconductance transconductance flash nonetheless tively inversely inversely amplification amplification amplification amplification transients transients transients increments increments increments behaves photoreceptors ping assistance subjective diffuse thickness thickness operational obey obey dedicated cones cones cones intact symmetrical symmetrical symmetrical volts attenuation leakage mosis physically substrate tens decades unexpected mounted yellow asymmetry sat hysteresis hysteresis metal won fet vdd substituted substituted incident incident incident tran 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#*network network network network network network network network network network network network network network network network network network network network network learning model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set set set set set set networks networks training training training training algorithm algorithm algorithm output output output output output output number number number number number number number number number system system results units units information information information information information problem problem based based space space space space space space space space space space space space weights weights layer layer vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown systems systems systems systems probability noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method approach approach approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image single single single processing large large large large local local local local local local local neuron test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class class class class class optimal inputs form form form form form form shows shows shows shows shows shows simple visual paper examples examples small small small feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work task methods features classification classification classification classification classification process process process current trained trained trained trained trained trained structure structure high memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response response response response response response response response response response similar similar similar similar show fixed vectors images images general general general general general general speech speech real approximation approximation approximation term dimensional dimensional dimensional dimensional dimensional dimensional university university computation research research independent defined found found target table table table table estimate estimate computer computer computer distance distance distance synaptic left presented map map map map map map map map map map map map map map map map map map map map map map present phase phase low machine object object object object object maximum maximum maximum range press position position basis sample sample sample sample sample sample sample sample sample sample abstract abstract applied applied applied applied applied applied applied applied applied applied back find computational references important important decision propagation introduction action hand effect effect effect parallel parallel parallel parallel cost change change change assume measure measure measure measure measure measure representations representations word word word word word part part previous bound type required required multiple multiple good good binary binary binary binary binary binary long conditions distributed distributed make techniques proposed scale classes tasks tasks tasks tasks tasks simulation simulation human computed multi sum times times times times elements elements elements regions regions regions mapping made global global global global global applications samples samples samples samples represented true application application application application application application application application application application provide provide objects proc proc location perform perform brain brain comparison comparison fields fields words department implementation implementation implementation version technique technique technique technique technique technique technique technique joint represents difficult layers layers maps maps maps maps maps maps maps maps maps maps maps maps maps maps considered considered equivalent equivalent equivalent equivalent top bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit requires significant approximate approximate speed speed speed vision vision basic give give give give give produce produce produce coding coding coding coding randomly randomly randomly clustering clustering clustering levels area area product product actual processes associative achieved normal feedforward feedforward increases fast fast fast limited close assumption effective effective assumed shape supported require require require cluster cluster development development including objective smaller underlying needed combination character character character character character character projection york york york increasing uniform principle operation operation representing details pre window window window window window window window window window stored bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bottom expert early magnitude magnitude idea added perceptron perceptron perceptron perceptron discussed improve directions takes takes takes takes element similarity introduced identical pixels previously conventional conventional conventional conventional conventional unsupervised approximately yields match studies address address address address address address address address background organization entire parts invariant occur digital digital digital digital digital digital digital digital digital digital digital deviation rotation clusters clusters pass half assumptions reduce reduce conclusions clear performs exponential taking taking taking reduction drawn demonstrated start characters characters acknowledgements areas construct edges edges edges edges edges produces produces winner winner winner label distinct dimensionality dimensionality involves involves involves scales develop applying applying springer decreases decreases reconstruction depending labels labels labels labels forms allowed earlier performing performing reduces purpose purpose remains kohonen kohonen kohonen kohonen kohonen kohonen kohonen figures figures figures perceptual perceptual subspace subspace subspace memories illustrated automatic successfully successfully simplicity extra suitable effectively successful computations post projections projections projections orthogonal orthogonal orthogonal conf verlag strongly heuristic phonetic split running content strategies strategies comp dot dot subsequent extract approximating employed employed employed employed employed employed employed layered requirements requirements involving detail reducing giving giving combine decisions complicated circles adapt adapt reading thought thought assumes ith serial optimum advanced costs trivial coded adapted caused filtered incorporate separately circle calculations implicit demonstrates preceding fourth reflects apparent flexible readily effort employ employ incorporated berlin partitioning partitioning differs differs aim inherent summed corrupted corrupted corrupted analogue analogue proportion labeling labeling investigation extensive martin ordering ordering ordering ordering ordering ordering ordering hyperplanes labelled labelled labelled labelled labelled labelled labelled purely reconstructed reconstructed reconstructed reconstructed reconstructed addresses eliminate eliminated oja oja difficulties arrays corner corner respective moved topological topological bad fold johnson johnson johnson johnson johnson johnson johnson johnson centre ease england realize reconstruct quantized grouped mammalian mammalian permits permits interacting mask termed million million electronics commercial commercial milliseconds normalised normalised subspaces exploited saturated primitives unbounded textures east conversion tuple tuple labelling labelling labelling labelling labelling grids neighbourhood inspection resultant priming addressing addressing contents polar severely organisation organisation organisation organisation minute topologically suggestion centred centred centred centred unimportant fund inverses concentrates ordinates mips innovation kevin beneath lxt telecom realisation realisation realisation realisation realisation realisation realisation realisation concentric concentric organising organising organising organising organising organising organising adaption adaption generalise centering centering managed quantised redistribution technol flaw xxx moon moon moon moon moon moon recognise recognise microcomputer microcomputer 
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#*network network network network network network network network network network network network network learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set set set set set networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number system system system system error state results information information performance performance performance performance based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear case vector vector vector vector vector vector order order shown shown shown shown shown systems values values values weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight recognition recognition approach approach approach point single single single single single control control control control control control control control control local neuron rate rate test class class matrix inputs inputs inputs inputs inputs shows algorithms simple paper paper paper small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature net net work work cells features classification classification process process process process process process process process level current current current current current current current current current current current current current current current current current current current current current current current current current trained problems high memory memory similar similar representation architecture show equation section line vectors speech speech speech parameter approximation average term term experiments activity activity activity activity threshold computation computation computation research constant standard terms distance distance distance distance connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node node node node node node node node left left direction presented map map map map map map map map map map map map map phase activation activation activation activation low nodes nodes nodes nodes nodes nodes temporal maximum maximum maximum maximum range range range range range range range position position components components outputs outputs continuous abstract back computational density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references component due ieee ieee ieee ieee important important introduction hand hand hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior dynamic dynamic parallel parallel difference classifier classifier lower measure measure measure signals chosen higher part previous required required binary binary binary binary conditions represent represent expected expected chip chip chip chip chip chip chip make make region region region region region scale simulations simulations simulations minimum minimum minimum minimum resulting classes sum sum performed performed elements means potential potential potential made made global global global global global global policy negative original original original represented represented true true application desired desired desired cross cross rates rates proc proc perform perform perform determined constraints connected gain gain gain discrete discrete mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage steps accuracy comparison comparison comparison comparison connection connection connection connection dependent selection selection institute department implementation implementation implementation implementation version version version version version version version version version synapses synapses synapses synapses synapses synapses technique code individual addition equivalent directly curve curve view solutions curves curves curves curves curves estimates design design design design design design design design design design design design design limit top top top top top stage stage stage effects effects effects effects effects bit bit conference conference determine upper full requires requires significant approximate statistics basic basic increase produce channel channel channel channel channel channel channel developed levels levels area area area product product product product product product product actual actual provided provided provided selected selected selected selected constraint associative measured describe tested tested tested tested complete circuits circuits circuits circuits circuits circuits circuits amount amount short common assumed synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation end future makes functional fully fully technology block block block testing testing ratio edge increasing mechanism mechanism consistent operation operation operation operation operation operation operation operation operation operation operation squared squared representing max max max stored stored stored stored stored stored stored bits bits bits normalized normalized bottom bottom bottom bottom bottom bottom early magnitude magnitude frame combined produced produced produced sources description description description perceptron population discussed pair pair takes takes element typical typical similarity practical strategy include side sense array array array array array array array array approximately background modified gate gate gate organization storage storage storage storage storage storage storage storage horizontal parts parts digital digital digital digital digital hybrid hybrid occurs column setting setting hardware hardware hardware pass demonstrate place place row row greater greater conclusions operator operator competitive competitive central differences performs performs temperature external cycle cycle cycle cycle characteristics characteristics demonstrated proportional proportional proportional turn turn exist min decrease configuration force appears appears plot plot plot plot plot describes laboratory laboratory distinct implement easy integrated integrated integrated springer shift cycles select select expressed depending stages densities controlled controlled restricted restricted restricted organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing forms static static static updates processor past sign diagram diagram diagram earlier earlier earlier earlier earlier calculation slow neighborhood neighborhood neighborhood neighborhood initially euclidean euclidean kohonen kohonen kohonen kohonen kohonen views topology degrees existing box currents currents currents determines determines plotted plotted discuss variations absolute tests tests major selecting identified identified encoded modification modification effectively included included wij wij wij modes computations computations characteristic composed summary conf conf verlag graphs repeated contained stopping contribution device device built write write write write write write dot dot dot providing quantization quantization quantization quantization cmos computes computes automatically illustrates operating operating operating operating operating neighboring decreasing oriented oriented law simpler access access access access access access requirements experience circuitry circuitry circuitry circuitry circuitry circuitry exponentially limitations lippmann transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor comparable complicated coarse reading reading reading reading voltages voltages voltages voltages voltages implementations adjusted prototype prototype prototype prototype front quantities versions versions noted perceptton logic logic initialized serial isolated established charge charge charge massachusetts massachusetts years devices devices brown brown advanced ground diffusion producing choices transistors transistors transistors immediately immediately products products separately involve calculations begin read read read read author reflect reflect generic marked incorporated continuously howard modulated reaches monotonic serve simulator simulator simulator display decreased implements begins contribute initialization representative sensing sensing sensing accomplished accomplished accomplished writing writing fabricated fabricated fabricated fabricated fabricated amplifier amplifier summing drift drift drift drift drift drift drift drift member bin bin bin bin bin connecting connecting turned air saturation ranges ranges simplify held imposed programmable height wire wire wire wire wire monotonically capacitor capacitor capacitor capacitor modifications modifications exceeds date date james respective respective negligible sides schwartz schwartz facilitate offers arrangement arrangement neuromorphic bins bins bins offer route projects reverse reverse reverse characterization adopted accumulated boxes multiplying maintaining street leaving drop minus ram ram causing drain constitutes constitutes simulating rain realize adjustment quantized increment increment conduction conduction conduction subthreshold mhz continues guidance permits flash west intl intl gilbert gilbert gilbert gilbert gilbert gilbert permit permit holding holding completed completed mann mann mann mann mann mann mann mann served served drives accordance traveling monitor identifies evolved evolved dominates mirror mirror mirror mirror finer converter fabrication connects horizontally conversion conversion conversion conversion agency operational quantizer quantizer offsets contributes lying raises leakage leakage leakage leakage leakage leakage leakage leakage vertically vertically mosis mosis fin accommodate accommodate periodically adapts relaxed comer format pin doubling doubling doubling defense contents contents substrate prescribed registers refresh refresh refresh refresh refresh refresh refresh refresh refresh replaces sponsored linearities linearities degrade custom custom lincoln lincoln metal adjustments adjustments adjustments substituted traditionally decrement decrement berger berger package decides clocked cooling digitally wii converting responsive latch converters converters converters converters lowering wafer undergoing permission volt diode diode diode invoked official micron micron microns microns simplifications serially wood government clocks sel unary interfere kirchoff accessed duplicated duplicate raising opposing lexington lexington instrumental grounded reprinted refreshed refreshed serf serf permitting dram dram dram dram dram dram accessing adaption sram conserve coincident swept swept diminished organizes sectional mirrored ohmic ohmic ohmic bend tol 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output number number number number system system system system system system system system system system system system system system system system system system system system system system system system system state state state state state state state state state state results results information information problem problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer vector order order order order shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit distribution recognition recognition recognition recognition recognition recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single single single processing processing processing processing control control large large large large large large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate test test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns inputs inputs inputs form form form shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms simple simple visual visual examples examples examples examples examples examples examples examples small size size size size net net net net work task methods fig fig fig fig fig fig fig fig fig fig fig fig fig step step level level structure problems problems problems problems problems problems problems problems problems problems random random random random random high high high high memory memory similar similar similar representation representation architecture architecture section fixed line line rule rule rule general speech speech speech speech speech speech real real real states states states states states states theory obtained note note result university threshold threshold computation computation solution research found found table table table table table table table standard computer computer computer computer computer computer computer computer computer computer computer computer computer computer connections connections connections connections science science left left left left left left left presented presented presented presented presented presented present present present present present present phase phase phase phase phase phase phase phase phase phase phase phase phase activation low low machine machine machine machine machine sets range range press press learn learn learn learn learn learn learn learn learn learn components components components outputs outputs outputs abstract applied applied back back find analog analog analog analog analog analog analog analog references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due ieee procedure procedure important adaptive adaptive propagation propagation introduction complex hand circuit behavior effect effect effect generated parallel parallel parallel parallel change complexity complexity variable lower lower lower lower rules rules rules rules rules rules signals learned learned learned learned learned learned learned part part previous previous required required required multiple multiple good good binary binary binary long conditions conditions conditions conditions represent represent chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip fact correlation correlation correlation correlation correlation correlation correct correct correct correct correct scale scale scale simulations simulations simulations simulations simulations simulations simulations simulations simulation simulation simulation simulation sum sum performed called times times times times elements elements mapping factor made feedback feedback feedback applications study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge obtain negative negative negative original artificial artificial true true true true compared desired desired desired provide provide provide rates perform perform constraints connected connected connected connected connected gain gain gain gain gain gain gain gain gain gain discrete brain brain brain brain equal power mit accuracy accuracy accuracy comparison larger larger larger larger connection connection connection train source proceedings proceedings report words words implementation implementation implementation version synapses synapses synapses synapses synapses synapses synapses synapses technique represents difficult difficult difficult difficult final addition addition addition considered considered cambridge domain environment directly hinton curve additional solutions solutions solutions curves curves curves design limit stage stage bit conference upper upper full free free free free speed speed increase give give give produce condition channel weighted weighted weighted randomly area area types types lines provided selected nature depends simply biological achieved arbitrary fast fast inverse stable circuits amount amount effective effective synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse role require require adaptation end end vlsi vlsi vlsi vlsi vlsi vlsi future future auditory simulated simulated smaller smaller needed account unknown fully fully technology technology technology block block block block block interesting testing york mechanism special structures structures trials trials database pre direct making stored stored stored stored stored bits bits bits bits bits experts supervised supervised supervised expert expert expert magnitude magnitude decay idea run run improved directions recent correlations correlations correlations correlations advantage separate takes takes takes takes element typical similarity reported apply include machines hierarchical sejnowski cognitive cognitive interest interest highly highly highly highly previously conventional conventional unsupervised unsupervised unsupervised teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher solve solve solve solve speaker differential differential differential address address evaluation evaluation modified storage storage storage increased increased studied scaling scaling scaling suggests digital digital digital digital digital digital digital digital wide rotation rotation deterministic generally hardware hardware pass pass runs place reduce depend competitive competitive competitive competitive competitive competitive competitive differences performs performs performs faster faster faster faster learns learns temperature temperature temperature temperature temperature temperature temperature encoding encoding taking hard hard mechanisms mechanisms physics largest external cycle cycle cycle cycle cycle cycle cycle cycle demonstrated demonstrated demonstrated intelligence intelligence pulse start exist iii manner connectivity connectivity connectivity connectivity program annealing annealing annealing annealing annealing annealing annealing annealing annealing base boltzmann boltzmann boltzmann boltzmann boltzmann written solving winner ways transitions transitions ann changing student student student student student student student student physical physical physical physical physical physical remaining easy easy scales frequencies shift boolean cycles cycles stages correlated correlated correlated correlated correlated correlated correlated correlated correlated communication communication controlled controlled controlled controlled showed similarly translation translation sign sign diagram diagram diagram diagram partial slow measurements neighborhood purpose add generation building existing silicon silicon silicon perceptrons recognize recognize specifically specifically variations variations domains tests tests tests tests tests compression importance suitable suitable suitable society encoded effectively effectively included wij presentation presentation presentation presentation presentation presentation build build build ten reached reached reached composed capture capture traditional procedures strongly strongly contained link conductance conductance conductance classify classify running running running running oscillations device categories built built usual simplified modular modular modular board quantization cmos cmos highest leading leading chips chips chips chips principles consisted consisted operating software routing load tesauro presents presents law simpler remain schedule schedule schedule schedule layered xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor create circuitry exponentially updating varied varied strengths strengths strengths limitations limitations hall giving history ideas parity parity parity parity fault transistor relationships structured comparable tanh proved affect encode encode phases examined examined trace adapt adapt traffic extremely implementations adjusted portion portion nerve logic initialized initialized switching switching serial serial serial electronic electronic electronic electronic electronic electronic seconds charge charge integrate advanced growing unstable waveform waveform biology handle drive rapid rapid stanford berkeley berkeley arc easier easier organized organized strictly style style forces broad broad transistors leaves potentially separately sounds sounds calculations calculations read computers demonstrates robustness robustness fourth apparent improvements considerably percent percent double pseudo pseudo amounts conducted conducted capability capability fed compares maintain requirement switch switch limiting monotonic adjust adjust plan gave simulator simulator simulator logical eventually leaf summed yielding uncorrelated uncorrelated uncorrelated uncorrelated proportion generator generator generator generator generator generator generator fabricated fabricated amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier summing ratios driving approximates controlling count flexibility reaching arranged arranged arranged arranged clamped clamped clamped chance programmable loops viewpoint removing monotonically optic clock clock presentations presentations presentations selects hours alspector alspector alspector alspector alspector alspector alspector alspector alspector programs codebook expanded washington widrow captured counter counter counter counter arrangement initialize winning neuromorphic shortest record waveforms waveforms reverse speeds speeds discovered robert multiply multiply converted converted solves covering leaming bus break presenting presenting presenting responds feeding pointed chaos reports hundred letting increment exclusive exclusive exclusive deep mhz mhz thermodynamic annealed degraded expand picked books confirmed flip flip noting worth flash flash flash flash million million register denver accounted truth loading amplifiers thousands modifiable modifiable milliseconds milliseconds milliseconds things increments spite handling handling handling thermal allen allen allen allen allen allen allen allen allen vii trainable send settling settling settling settling settling thousand thousand loaded loaded loaded telephone inhibit inhibit connects wiring wiring inherently ackley seattle settle settle emerges accumulate edited edited convention bandpass amplified inset longest permanent teaching comer stabilize inaccurate assessed counted hoff dissipation monitored responded bidirectional modularity occasionally checked sends nov simulates plans vdd capacitive advice advice undesirable neurodynamics strongest billion challenges challenges challenges anneal anneal anneal anneal implementable rosenblatt digitally digitally clamping clamping clamping clamping clamping gupta gupta gupta gupta gupta gupta neti neti analyzer parentheses unix ire historical blank teach enormous incremented incremented disconnected bellcore flop telecommunications equipment equipment tri opening attack succeed alternately prepared instruments micron micron landauer joshua embodies synthesizer replications freeze freeze freeze transport manage kamm compressing minimally heating singhal oak oak amplify conservation aug morristown speedups microchip microchip microchip microchip microchip microchip microchip microchip defects flops oscilloscope oscilloscope spartan freezing inaccuracies inaccuracies electronically wescon decremented decremented vax photograph photograph microseconds microseconds dep accents slate technological graceful supercomputers releasing digitizing graduated comparably 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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data function figure figure figure figure figure figure figure figure figure figure time time set set networks networks networks networks networks networks networks networks networks networks networks training algorithm algorithm algorithm algorithm output output output output output output output output number system system system system error state state state state state state results information information models models models models performance based based based based based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights case case case case vector vector vector vector vector order shown shown shown shown shown systems systems systems systems systems values values weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight method single single single single single single processing processing control control control large large large large large local local local rate rate test test test analysis analysis analysis matrix matrix inputs inputs inputs signal signal algorithms algorithms algorithms algorithms algorithms simple small small small small small small size size size size size size size size net work work cells cells cells process process process level level level current current cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure high representation architecture architecture show equation section fixed fixed fixed parameter approximation average gradient obtained obtained obtained term term threshold threshold threshold computation solution defined found sequence initial constant constant constant constant terms connections node node node node node node science direction nodes nodes nodes maximum range range range range components outputs outputs abstract back back back density analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties properties properties references stochastic due due ieee ieee ieee ieee ieee ieee ieee positive positive positive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive complex complex complex circuit circuit circuit circuit effect effect effect effect dynamic dynamic dynamic dynamic parallel parallel cost search change change change change change change change change change change change complexity variable assume signals signals signals signals chosen higher type required required good good long long long long long long long represent represent represent represent distributed expected expected chip chip chip chip chip chip chip chip chip chip chip length scale minimum minimum minimum resulting total total computed respect multi factor dimension made made made made made feedback global global global global global applications study obtain obtain obtain obtain negative negative compared desired desired cross cross provide rates rates perform determined experimental experimental goal constraints connected connected connected connected connected equal equal power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger descent descent source source source modeling proceedings proceedings loss implementation implementation version individual individual individual individual individual advances exp bias scheme sequences hinton view curves curves design design effects bit conference efficient full speed increase channel channel channel channel channel channel channel channel channel channel randomly area area area controller controller lines lines lines lines lines provided provided sampling achieved discussion arbitrary group tested limited assumption corresponds corresponds complete surface predictions circuits circuits circuits circuits circuits circuits circuits amount amount amount common effective effective effective effective implemented supported supported journal journal journal journal journal vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi easily easily easily easily easily easily degree typically typically pairs needed needed reduced technology technology technology transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer interesting mechanism mechanism mechanism special special structures mode operation operation operation operation operation call call making stored stored stored stored stored stored stored stored bits bits bits bits bits international international depth magnitude magnitude magnitude magnitude decay decay decay decay decay decay decay decay decay decay decay decay decay run architectures recent resolution resolution resolution resolution resolution resolution resolution resolution property pair pair pair pair pair introduced machines machines sejnowski cognitive sufficient conventional approximately volume differential differential differential achieve evaluation modified gate gate gate gate improvement storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage entire entire increased concept digital digital digital digital wide width hardware pass pass reduce reduce conclusions designed peak peak exponential temperature taking external cycle characteristics characteristics sigmoidal demonstrated solid solid solid solid solid turn turn minimizing iii iii targets introduce minima configuration acknowledgements written written written implement implement consisting develop develop frequencies frequencies equilibrium family dependence dependence dependence depending detailed detailed evaluate evaluate operations controlled decomposition static static understanding approximated sizes updates allowed earlier fitting neighborhood purpose purpose iterative generation initially string string string string string string string transactions building silicon silicon silicon strings strings currents bell partially discussions tests middle extra capable capable suitable driven ten ten fine fine reached characteristic quickly repeated allowing allowing allowing heuristic heuristic follow device device device hold built built built bar bar usual absence cmos cmos cmos leading chips chips chips chips chips attempt attempt extend situations body body body simpler powerful access access essential circuitry exponentially optimized optimized mass hall helpful project incremental ideal ideal ideal ideal transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor authors maximizing gates variability complicated understand hill hill coarse measurement measurement coefficient transmission voltages voltages implementations obvious taylor separated initialized store simplest simplest simplest isolated charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge devices devices devices devices mentioned ment slowly agreement phenomena floating expensive nonlinearity drive tive organized directional choices worst worst transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors laboratories laboratories inversion optimize read read author geometry qualitative sun requiring people percent transient generic generic orders frequently howard howard howard howard howard howard switch rely proven achieves richard sophisticated summed globally fabricated fabricated guarantee tation narrow branches controlling circular mobile connecting turned turned turned turned multipliers multipliers multipliers multipliers fails multiplier multiplier saturation murray murray convenient tools mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos held programmable grow keeping wire capacitor capacitor capacitor clock clock clock clock clock corner wilson alspector prentice excellent separating james james james respective studying sides injection injection injection injection widrow schwartz schwartz schwartz schwartz schwartz schwartz facilitate neuromorphic environmental storing steepest steepest exploiting exploiting reverse papers speeds switches switches switches switches switches switches acknowledge robert robert robert robert limitation trading treat ccd escape multiplying multiplying minus minus session ram ram ram ram ram ram ram ram rejection die die medium exception acceptable ease ideally avoided eric eric manipulation rectangular capacitance capacitance capacitance capacitance capacitance increment increment packets packets packets mhz mhz mhz compensate decays decays decays hubbard hubbard hubbard hubbard hubbard hubbard searches disadvantage carefully eliminating concentrate switched overhead parallelism complementary transconductance transconductance attached turning turning turning turning turning turning gilbert gilbert exchange amplifiers amplifiers amplifiers page dsp milliseconds transients compu treating exploited increments signs examination tunneling mann mann spite demonstrating electron electron electron reversed reversed allen decided sake quadrant quadrant converging cliffs reversible diffuse capacitors capacitors capacitors capacitors capacitors capacitors capacitors capacitors capacitors capacitors capacitors graf fabrication cast wiring injected ackley holmdel meeting englewood separates measurable artifact isolation isolation isolation linearized losses william leakage leakage leakage leakage leakage leakage reproduced compensated fair remained locality pin substrate substrate inappropriate modest refresh cox linearities initiated jack elegant transferred vdd walker mention rescaling decrement berger package volatile volatile adap prohibitively clocked bruce bruce tially manipulating workers gupta samuel parasitic neglecting oxide lowering george george wishes disconnected volatility wafer kuo kuo granularity granularity charging multiplexed vittoz exceeding exceeding awi joshua millions grained serially transfers transfers transfers transfers transfers transfers transfers transfers transfers cycling isolate gte gte reversing differentially unreasonable incre microchip manipulate waltham assisted linearize linearize differen facilities followers bernard relay designers ida flux stearns bination crawfords linearizing buffered cascading cha inaccuracy electrostatic workings provisions provisions boltzman twin twin readout zeroed pumping antonio prospect layouts 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time networks networks networks networks networks networks networks algorithm output output output output output output number number number number number number number number number number number number number number number number number system state state state state results results results results results results results results results information information information space space space space space space space space linear linear linear linear linear linear linear order order shown shown shown shown values probability probability probability probability probability probability probability probability probability parameters parameters functions functions functions neurons neurons neurons method pattern pattern pattern pattern pattern pattern pattern pattern point point large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis inputs inputs inputs form form form form form shows shows shows shows shows shows shows simple simple simple simple simple small small small small small small small small small size size size feature net net net net work work work work work work work fig fig fig fig fig fig fig fig fig points features features process process current structure random random random random random random memory memory memory memory memory memory memory response similar similar similar representation show equation fixed fixed fixed rule rule rule rule rule general parameter parameter real real average average states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states obtained obtained term result result result threshold threshold threshold threshold threshold threshold threshold threshold research defined found found found found found found found found initial initial computer distance distance distance distance distance distance distance distance distance node direction direction presented present present phase phase phase phase phase phase low maximum maximum maximum maximum maximum maximum maximum range range range learn learn learn learn outputs abstract references due important important important behavior behavior behavior statistical parallel search tion tion change difference assume learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen center type type type type type type type type type type type type type multiple good binary long represent fact fact region region proposed probabilities errors errors errors errors errors errors simulations simulations simulations ing simulation simulation simulation simulation sum performed eq eq eq times factor natural em obtain vol artificial relative relative specific specific true desired provide define define proc perform perform perform related gain equal voltage voltage accuracy larger larger larger larger larger connection synapses synapses synapses synapses synapses synapses final directly directly curve curve additional additional design san bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine requires statistics con con channel channel randomly randomly types types types types nature nature simply achieved increases tested tested tested tested close inverse stable stable stable stable stable stable stable finding finding finding finding finding finding amount synapse synapse synapse synapse synapse synapse synapse synapse vlsi ability instance noisy including simulated typically smaller smaller needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield functional functional functional fully fully technology technology interesting interesting testing york york numbers pre pre direct stored bits bits bits choose light discussed discussed discussed robust typical period period varying previously address definition interval organization digital locally generally hardware demonstrate place hebbian hebbian central sigmoid sigmoid measures clear clear peak peak learns learns learns learns constrained propose propose hard characteristics characteristics characteristics characteristics proportional start relationship averaged question question construct longer factors implement decreases yield choosing open forms sizes completely partition allowed calculation dashed distances koch koch koch koch koch koch silicon usa weighting memories memories memories memories memories memories discuss phys tests successfully successfully successfully successfully successfully successfully capable capable capable divided divided successful successful successful situation essentially essentially conf repeated contained showing dis symmetry symmetry sci device device device built relaxation thresholds thresholds thresholds operating operating decreasing decreasing remain diego wiley essential put behaviour fewer int func func phases analogous opposite opposite extremely rev equally perfect perfect changed changed voltages voltages voltages voltages voltages ensure obvious explored explored explored hebb hebb hebb store message mixed finds finds attempts established devices devices spin slowly glass tractable handle easier desirable acad summation offset capability capability fed readily compares gen ordered qualitatively marginal hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming inherent attraction attraction attraction attraction attraction tolerance deviations summed trade picture investigation interconnected interconnected turned proceed saturation saturation occurred multiplicative multiplicative multiplicative multiplicative imposed imply exceeds natl utilized sompolinsky started corre pat pat intended intended realization thomas multiplied surprisingly probe probe considerations sequentially sequentially basin basin basin feeding conjecture utilize basins basins basins guess realize reconstruct argue attempted attempted ibm mathematically compatible emphasize emphasized utilizing utilizing opti ble sees lation inhibit utilizes dropped char eral incorrectly val peaked push retrieved retrieved governing tance inset inset era relaxed ranged approached approached watson responded sented sented ues tern tern tolerant tolerant tolerant heights mum enhancing enhancing viable pushed pushed implementable exceeded exceeded exhibiting amit functioning functioning functioning feel divides taught taught teach expects possi extraneous extraneous extraneous extraneous extraneous compactly retrieving probing straints shed gutfreund cated yorktown mosfet mosfet mosfet mirrors inhibiting acter incapable easiest serf monitors thrust thrust printing rea probed probed immunity reinforces pacity sonable struct avenues iei allo traction rors 
#@Hartstein_A,Koch_R,
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linear linear layer layer layer layer layer case case order order order order order order order shown shown shown shown systems systems systems systems values values values values values values probability probability weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions neurons method pattern processing processing processing processing processing processing processing processing processing large large large large large analysis optimal inputs form form form shows signal signal algorithms algorithms simple simple paper small feature net net net net net net methods methods methods methods fig fig fig fig points points features features features classification level level level level level level level level level level current current structure high high high high similar architecture architecture architecture architecture architecture section general generalization generalization real gradient gradient gradient gradient obtained obtained obtained obtained term term experiments result university university threshold threshold solution solution solution solution solution research found constant constant constant standard computer terms terms terms terms terms terms terms terms connections connections connections connections node node node node node node science activation low low low low low nodes nodes nodes sets sets sets press position components nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied back back convergence density references ieee positive important adaptive propagation behavior parallel search change spatial spatial spatial lower lower signals representations representations representations higher center center previous type required required multiple binary binary conditions conditions distributed distributed distributed fact proposed proposed proposed proposed proposed proposed proposed correlation scale total total elements elements elements elements elements elements elements elements mapping means means means negative artificial represented desired series series determined related constraints constraints connected connected connected connected connected connected connected connected connected equal approaches mit comparison connection support descent descent descent descent nets nets nets nets nets proceedings report implementation implementation implementation implementation consists internal internal internal internal individual responses layers layers layers layers layers layers addition addition addition considered equivalent equivalent equivalent equivalent equivalent hinton additional effects conference determine determine upper full significant significant produce coding clustering clustering types types types types lines product product actual finally finally backpropagation backpropagation backpropagation backpropagation biological technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward transformation transformation limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited limited complete common implemented implemented assumed require eds eds adaptation vlsi cluster cluster cluster degree typically reduced reduced reduced reduced functional fully fully fully fully fully fully fully fully fully fully fully technology edge increasing numbers numbers numbers filters direct direct direct direct direct international magnitude magnitude magnitude magnitude magnitude magnitude magnitude combined minimize minimize minimize perceptron perceptron perceptron perceptron architectures architectures architectures discussed element element element element identical identical identical identical identical identical subset sufficient highly highly volume works yields yields yields yields address address positions exists exists exists exists expression derivative width generally setting hardware hardware hardware hardware hardware pass pass greater greater greater conclusions sigmoid encoding characteristics solid derivatives derivatives scene connectivity connectivity connectivity connectivity relation relation solving dept develop develop springer formed decreases formation formation centers understanding completely completely constants expansion expansion reduces reduces initially degrees degrees degrees priori inter determines reason determining determining determining capable encoded mcclelland mcclelland mcclelland comparing comparing reached verlag procedures cmos overlapping overlapping routing employed layered layered layered wiley transformed collection collection collection collection collection collection requirements requirements exhibit detail limitations hall discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant pursuit mappings parity parity fault analytically possibility dependencies symbolic symbolic affect act implementations implementations implementations subsets subsets taylor taylor freedom freedom separated separated separated mapped perceptton arbitrarily motivated electronic synthetic synthetic synthetic synthetic synthetic synthetic synthetic developing trivial derivation analyzed biology nowlan adapted adapted implementing satisfied widely widely widely located hyperplane projected members arises computers mellon exemplars summation summation summation summation summation requiring carnegie employ continuously resource prevent prevent prevent suited replace redundancy tolerance implements june differentiable accomplished forming hyperplanes impossible eliminate connecting interconnected interconnected exemplar exemplar difficulties odd odd fan fan fan fan fan fan fan fan fan fan fan interconnection imposed programmable occurring occurring occurring exceeds arrays substituting prentice connect widths expanded dominant widrow widrow nonlinearities nonlinearities nonlinearities nonlinearities arrangement foundations neuromorphic neuromorphic layout layout considerations hart hart alternatively indirect basically expanding expanding seek malsburg affects duda duda magnitudes magnitudes magnitudes magnitudes magnitudes impose employing employing win win barrier electronics interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect interconnect permit expansions expansions thousand locate eliminates evenly executing functionally functionally placement placement aggregation vicinity dissipation dissipation dissipation dissipation proceeding propagates virtue walker 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#@Afghan_A,Akers_L,Haghighi_S,Walker_M,
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#*learning neural neural neural data data function function function figure figure figure figure figure figure figure figure figure figure set output output output output output output number system system system state state information information information problem problem problem models performance performance based based linear case order shown shown shown shown systems systems systems systems systems parameters functions neurons single processing processing processing large large local local local patterns patterns shows shows signal signal signal signal signal signal signal signal signal signal signal simple paper paper examples small small small small small small work work work work cells cells step points field field field field field field field field field field field field field field field field field field field field field field features process process level level current current current current current current current current current current current current current current current current current current current current current current current current current current structure problems high high response response response show show section section section note note note note activity dimensional university university university university research research independent independent found found found constant constant constant standard standard standard standard standard computer distance distance distance direction direction direction direction direction direction direction present low low low low low low frequency frequency frequency object object object object sets maximum maximum range range range press press press position position sample sample sample sample abstract applied applied analog analog properties properties references due due due ieee ieee ieee important introduction hand circuit effect effect effect effect effect effect dynamic dynamic spatial spatial spatial lower lower measure measure signals signals signals signals higher part previous cases cases type conditions conditions chip chip chip region region region region length total total total called elements elements elements elements elements elements regions potential made applications applications vol vol vol vol true true application application provide provide objects objects objects objects objects proc perform perform experimental experimental related related related related related related power power power approaches mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger fields fields fields fields fields support source source source source source source proceedings proceedings department implementation joint joint joint joint joint joint represents final bias scheme scheme scheme graph considered framework cambridge experiment environment directly additional stimuli stimuli stimuli stimuli conference conference conference world vision vision vision vision vision increase give channel channel channel channel channel channel channel channel criterion velocity velocity velocity lines provided provided processes processes depends simply biological biological biological associative measured measured discussion discussion discussion tested surface surface circuits circuits short implemented shape shape shape eds adaptation adaptation square square end vlsi vlsi vlsi vlsi vlsi ability ability development development development sensory sensory sensory sensory sensory sensory sensory sensory smaller underlying combination functional technology interesting head mechanism mechanism structures structures structures uniform mode mode mode mode operation operation operation principal direct direct direct direct expert magnitude magnitude magnitude run sources light light light architectures membrane discussed resolution resolution resolution element element reported moving subject machines side sense sense array array engineering engineering engineering interest dimensions dimensions varying compare axis axis correspond studies achieve trans channels gate gate gate gate gate gate sensitive sensitive sensitive sensitive sensitive sensitive sensitive increased exists horizontal parts extended width flow flow flow flow strength strength conclusions retina retina retina designed temperature mechanisms mechanisms mechanisms presence presence presence physics characteristics characteristics demonstrated california solid proportional variety variety exist plane relationship relationship program configuration force force force force denoted areas areas longer perception perception perception perception perception ways laboratory vertical implement sensitivity sensitivity linearly linearly electrical electrical electrical electrical electrical angle angle interaction develop integrated integrated integrated integrated integrated integrated formed yield dependence review review detailed controlled forms static static understanding discrimination key purpose exploration exploration includes perceptual silicon silicon silicon silicon silicon silicon silicon silicon currents currents currents currents memories plotted discuss discuss phys sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor included detect detect detect detect literature fine refer success split physiological device device device device device device device device device device device device device device device device receptor receptor receptor receptor receptor receptor receptor receptor receptor dot paradigm paradigm cmos cmos cmos cmos cmos principles operating operating acknowledgments deal extend employed employed production requirements circuitry mead mead mead mead mead steady dual hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall hall respond tech investigated terminal possibility transistor reliable comparable comparable workshop surfaces induction induction induction induction induction hill hill act voltages voltages observe observe fibers fibers simplest electronic electronic electronic electronic electronic electronic electronic electronic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic charge integrate devices devices devices devices devices devices devices devices devices devices devices devices devices devices devices devices devices devices great formula sensors sensors sensors sensors sensors sensors derivation phenomena diffusion sections strictly monkey consequence author author geometry raw robustness pathways flexible readily cohen cohen operate operate operate characterize fall qualitatively pasadena sophisticated cochlea cochlea wesley phenomenon sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing identifying identifying primarily addison generator generator sv sv fabricated fabricated fabricated fabricated bipolar bipolar bipolar oxford extensive conditioned angular receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors robotics caltech caltech saturation saturation khz logarithmic mos mos mos mos mos mos mos attractive biased biased biased operates responsible adequate adequate arrays arrays arrays passive utilized periods appendix offers arrangement specialized refers refers environmental contact contact extensively considerations reverse displacement johnson johnson johnson johnson robert speaking pressure pressure converted shorter revealed magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic terminals terminals terminals drain drain drain drain drain drain drain personal evoked avoided electrode perpendicular perpendicular perpendicular perpendicular subthreshold subthreshold convert convert mediated acquired guided guided transconductance covered funded barlow barlow electronics electronics placing amplification amplification tissue technologies architectural transducer transducer transducer transducer transducer transducer gratefully advantageous transduction transduction heavily skin skin skin skin conceptual hopkins hopkins hopkins fabrication fabrication fabrication rare dissertation partly andreou andreou andreou andreou andreou andreou andreou andreou andreou substitute offsets tactile tactile tactile tactile tactile tactile tactile tactile tactile tactile tactile disturbance cones periphery contacts contacts transducers transducers transducers arpa johns johns johns volts inset robotic mosis mosis mosis mosis permanent permanent permanent senses senses senses senses senses senses senses lewicki lewicki vicinity vicinity compromise feb deformation deformation baltimore baltimore percept problematic manual dissipation dissipation dissipation monitored degrades jenkins preprocessed sensed deeper touch biomedical biomedical andreas offered uniformity acknowledged biasing biasing biasing engineers electrically boahen mag parasitic parasitic functioning stretch fingers fingers earth motivate occasional vibration vibration imbalance micron microns proportionality proportionality skeletal skeletal transport originate services als beck scientists living living aug ken carriers carriers conformation conformation polysilicon permanently semiconductor audition cylindrical organs invited compensates amp benefited reverses bay island rods pouliquen lna chapel chapel organizational lamb digest psychophys chapters transverse transverse transverse disturbed imperfections goddard bulk microelectronic 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#@Konishi_M,
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based based based based based based space space weights linear linear linear linear linear linear layer layer layer vector order shown systems systems systems systems systems systems systems parameters parameters weight functions functions functions functions functions functions unit distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern single processing processing processing processing processing large large large rate patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis class class optimal inputs form form form signal signal algorithms algorithms algorithms algorithms algorithms examples small small feature feature net net work methods methods methods methods methods methods methods points points points points points features process process process level level current current current current current current current current trained structure structure structure structure structure random high high response fixed fixed line rule vectors vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter approximation states states states states states states states theory theory theory theory theory theory theory theory theory dimensional dimensional research research research research research independent found sequence sequence dynamics initial initial computer computer computer terms connections science map present present low frequency temporal temporal temporal temporal temporal press position position basis basis outputs continuous continuous continuous abstract applied back find find properties likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee ieee ieee ieee ieee ieee ieee important important adaptive adaptive adaptive propagation introduction hand hand estimation estimation behavior statistical dynamic recurrent recurrent recurrent recurrent recurrent recurrent search difference variable assume classifier signals signals word word learned higher theorem type long markov markov markov markov markov make techniques techniques techniques proposed probabilities probabilities forward forward finite resulting resulting classes classes ing tasks computed respect multi multi multi multi multi multi multi potential potential feedback feedback knowledge filter vol vol vol vol vol artificial application application desired cross series define proc proc proc proc proc proc proc perform related related posterior discrete approaches approaches approaches approaches approaches comparison update train modeling report words words words words technique technique technique internal internal internal internal internal kernel kernel connectionist connectionist connectionist connectionist difficult difficult difficult delay delay sequences equivalent environment directly transition san san classifiers full significant significant developed levels area types types types lines product actual processes processes backpropagation backpropagation nature describe hmm hmm hmm transformation transformation transformation fast limited finding nearest implemented assumed shape theoretical theoretical require eds eds adaptation instance instance future makes fit auditory probabilistic probabilistic probabilistic smaller combination unknown unknown programming interesting edge structures operation language language filters pre making window window early choose description predict perceptron correlations advantage typical reported include include machines machines hierarchical array cognitive relevant unsupervised volume works works speaker studies trans positions positions modified modified amplitude constructed lead lead digital feed feed generally flow minimal segment neighbor valued accurate designed clear constrained sound strong mechanisms characteristics drawn demonstrated radial radial user start relationship acoustic acoustic acoustic acoustic boltzmann boltzmann reference reference reference reference reference explicit pro perception label mathematical mathematical segments pruning multilayer physical transformations text applying john letters national review review depending viewed controlled soft discrimination discrimination discrimination processor past spectrum spectrum performing interpolation interpolation interpolation generation distances construction construction kohonen kohonen kohonen kohonen advantages building perceptrons perceptrons bell sciences automatic automatic automatic automatic automatic automatic automatic automatic straightforward suitable suitable encoded symbols successful successful invariance invariance score fine characteristic capture soc conf conf conf conf decoding decoding success moore moore moore phonetic phonetic phonetic phonetic phonetic dot realistic nips hypotheses chips situations simpler diego diego powerful powerful layered put humans detail recursive hall discriminant discriminant discriminant ideas tech links links detectors decisions working symbolic variability variability workshop scores waibel waibel plausible generalisation thought thought adjusted impulse art consist submitted isolated isolated great inequality asynchronous trivial explanation explanation adapted baum baum tool worse reasons comparisons sections producing sounds attribute meaning raw composite limits amounts spoken treated rep templates howard howard vocabulary vocabulary vocabulary spread popular phonemes extensions acoustics june june extreme bellman generator generator labeling concerned purely theories royal royal inspired inspired dealing dealing determination loops exploit bourlard bourlard symposium combinatorial inferior prentice combines governed decide overview percepttons percepttons arrangement arrangement claim enable foundations offer cpu erlbaum formant consonant insensitive treat radar radar unified unable accept presenting encouraging distinction welch smoothly icassp icassp icassp icassp icassp classic hillsdale adapting principled attempted cessing gained learnt compatible march careful kanerva kanerva cole paris ambiguous electronics intl intl memo programmed bridle bridle bridle bridle pineda november november rabiner laws laws beam acoust acoust regularities lowe lowe lowe generarive hearing interpreting inequalities optimisation russell usefulness rohwer arrives explanations explanations tracks watrous watrous assp assp amenable 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#@Bridle_J,
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#*model model input input input function function time algorithm algorithm algorithm output output output output output output output output output number number system system system system system system system system system system system system results results units units units units units units information information information information information information models based based space space space linear linear layer layer layer layer layer case order order order order shown shown systems systems systems parameters parameters parameters neurons neurons neurons neurons neurons neurons unit unit unit distribution point single single processing processing processing processing processing local patterns patterns analysis inputs inputs inputs form signal signal simple simple visual cells cells cells cells cells cells step features features level cell cell cell cell cell structure structure structure structure response response response response response response response line line general parameter parameter experiments experiments experiments activity activity activity activity university threshold research research independent log log log defined computer computer terms terms synaptic synaptic synaptic direction direction direction direction direction direction presented map map map map map map map range range range range position abstract computational computational computational computational properties properties properties properties properties properties references action complex complex complex stimulus stimulus dynamic parallel tion tion change measure higher higher higher higher firing firing type multiple cortex spike spike represent distributed proposed classes ing ing multi multi multi multi orientation study filter relative relative specific specific represented receptive receptive rates determined goal related cortical brain brain equal steps fields fields dependent modeling consists individual individual individual individual responses maps maps directly additional curves curves curves curves curves stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli detection detection detection detection determine determine full requires significant con channel developed velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types types nature nature inhibitory technical group excitatory excitatory implemented generate theoretical future development sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory pairs pairs pairs underlying underlying underlying functional functional functional testing ratio projection operation representing representing filters magnitude discussed directions directions directions directions recent array recently relevant relevant interest varying approximately approximately approximately approximately tuning tuning tuning tions studies studies studies studies studies separation organization sensitive sensitive amplitude amplitude amplitude spikes spikes occurs flow depend central retina mechanisms mechanisms characteristics sigmoidal california california factors primary primary distinct distinct sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity simultaneously simultaneously angle integrated frequencies frequencies formed versus versus versus potentials john john extracted review review overlap overlap influence variation centers centers roughly dendritic dendritic dendritic dendritic degrees currents currents currents weighting determines activated phys characterized characterized identified identified identified identified identified capable capable importance encoded encoded encoded miller miller miller miller miller miller miller ten ten graphs decoding interested interested neuroscience sin receptor receptor comp comp michael thresholds neurosci received overlapping operating operating preferred preferred preferred jacobs jacobs jacobs jacobs neighboring deal software trains carried transformed reducing project terminal plasticity relationships working encode encode understand topographic topographic topographic neu neu thought impulse portion precise mapped mapped nerve nerve nerve shapes nervous utility isolated animal great developing directed analyzed explanation interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons ganglion berkeley directional directional directional directional directional afferent afferent afferent afferent afferent afferent afferent axon begin res recording recording annual addressed researchers researchers orders recordings detecting span span span anti extracting wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind cal serve focused simultaneous lab accomplished accomplished accomplished animals velocities velocities velocities branches branches branches branches branches null repre theories receptors receptors spontaneous cellular systematic ranges ranges neurobiology preparation preparation preparation carry programs programs dendrites dendrites studying originally dif displacement displacement yielded hair hair hair hair sig shunting transmitted encodes encodes presenting uniquely employs acceleration acceleration sinusoidal sinusoidal interneuron interneuron interneuron individually electrodes electrodes electrodes electrodes electrodes lond selectively covered afferents afferents afferents afferents afferents afferents afferents intracellular knudsen knudsen ferent hundreds locate puts ron rons rons cord sen extracts laser vertebrate rel electrophysiological sentation antenna zones monitored monitored hypercolumn activates aims direc direc direc continuing synthesize extracellular extracellular tilt lay insects compartmental invertebrate charac tonal segregated sensitivities 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#@Miller_J,
#t2
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single single single single processing processing processing processing processing shows shows shows shows signal algorithms algorithms algorithms simple small task task fig fig fig fig fig fig fig fig fig fig fig fig points points features features features features process trained structure structure structure structure structure structure response representation representation representation representation section images images images images images images images images images images images general real experiments activity activity activity university research target target target target target target target target target target target target target target target target target target target target target target target target target initial initial initial estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate terms terms terms distance distance distance distance science left left map map map map map phase phase phase low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal object range range range range range range range range range range range range range range range range range range range range range range press press press press press press press press components components components components components components components components basis basis abstract convergence properties properties properties properties references component component component component component important complex complex complex complex complex complex complex complex stimulus stimulus stimulus change spatial measure signals signals signals signals signals prior representations representations representations part required good long conditions represent represent expected make fact techniques correlation correct computed called dimension dimension original relative specific represented represented represented true true cross series objects objects location location location location experimental related constraints discrete brain steps steps accuracy accuracy accuracy accuracy accuracy accuracy comparison support department consists consists code code code individual individual individual responses responses delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay graph graph graph domain domain domain domain domain domain domain domain domain domain domain domain domain experiment experiment experiment view view estimates top effects capacity capacity determine free world basic channel derived derived constraint biological measured measured increases corresponds corresponds corresponds corresponds corresponds excitatory short common shape shape shape shape supported role theoretical main including objective auditory auditory auditory auditory auditory auditory auditory auditory smaller edge edge operation leads representing filters bottom depth added added recent separate separate side side sense relevant dimensions dimensions sufficient previously conventional approximately tuning axis axis axis axis axis axis axis axis axis axis yields separation separation separation separation separation separation separation separation separation separation interval amplitude amplitude amplitude amplitude constructed parts occur suggests width width width pass critical place place central central central accurate peak peak peak peak peak sound sound sound sound encoding mechanisms integration integration integration integration integration integration integration demonstrated pulse targets targets targets targets targets targets targets targets targets targets acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic appears relation perception perception estimating ann tuned distinct distinct involves slightly slightly spectral spectral spectral consisting adding frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies events formed shift shift decreases expressed formation stationary overlap detailed transform transform operations forms discrimination discrimination discrimination discrimination discrimination discrimination spectrum spectrum spectrum spectrum partial earlier measurements delays intervals initially distances filtering filtering msec msec msec msec avoid perceptual absolute absolute absolute determining aspects identified encoded encoded identify detect detect computations computations computations computations computations computations comparing fine fine fine fine fine composed composed soc soc soc graphs contained allowing showing return lie sin physiological physiological timing timing timing timing timing timing timing comp comp play wave binding leading illustrates acknowledgments intrinsic receive explore transformed transformed existence successive behavioral referred cognition reading reading psychology rev thought separated separated nerve nervous consist explain integrate brown brown brown indicating site crucial crucial crucial track waveform waveform biology independence caused processed closer filtered division located located located located located located consequence separately sounds sounds sounds involve res demonstrates recognizing integrating reflects reflects apparent apparent composite reflect profile cochlear dark amounts capability poorly peaks peaks employ dots psychological psychological psychological exhibits limiting modulated occurrence occurrence occurrence chen chen chen achieves display physiol physiol physiol tile cochlea univ instantaneous instantaneous instantaneous shifted ear forming acts approximates reconstructed discovery harmonic arrival arrival arrival arranged adds imaging imaging imaging imaging imaging imaging ranges imposed replica exploit analyzing neurobiology fail shifts shifts receiver receiver receiver adequate carry composition inferior interference ambiguity ambiguity loo james enhance sim sim recovery arrive arrive colliculus waveforms merge insect grants onr trading trading trading fusion fusion discriminate discharge discharge yale emission unified largely largely numerous shorter accept latency latency latency latency latency latency inferred removal obstacles emerge perceived perceived perceived perceived perceived perceived perceived amplitudes spaced big big constitutes reconstruct reconstruct reconstruct reconstruct reconstruct echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo surrounding ultimately retain exceed sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sized supports sweeps sweeps sweeps sweeps sweeps modality indication flight milliseconds milliseconds reciprocal exploited echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes helps resembles resembles resembles acoust acoust acoust transforming hearing impulses impulses virtually spacing evolved aid reflecting reflecting reflecting medicine conversion conversion moss moss moss moss moss moss spectrogram spectrogram spectrogram spectrogram physiologically emerges extracts coincide arrives bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat bat arriving predictable format unusual jitter jitter jitter jitter jitter jitter jitter jitter prominent durations convey ears discriminating clutter intrinsically fundamentally recovers spectrograms spectrograms spectrograms spectrograms spectrograms spectrograms fight incident incident incident rectification simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons simmons machinery insects insects conveys nent grain providence perceive perceive ghost compound compound compound compound compound compound mammals embodied viewpoints acuity acuity acuity acuity acuity undergoing replicas replicas replicas farther revealing hyperacuity hyperacuity hyperacuity disparate emitted emitted nimh darkness orient discharges discharges discharges discharges discharges discharges transmits perceiving evidently evidently behaviorally trailing holes holes unification freedman freedman perceives perceives perceives perceives perceives perceives marking listening travels assembled airborne reception reception lives underlies griffin griffin intimately altos microseconds unify technological equency emit emit flying flying nyquist 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#@Simmons_J,
#t3
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#*model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input input input input input input input input input data data data function function function figure figure figure figure figure figure figure figure figure time time time time output output output output number number number number system system system system system system system system system results results units units units units information information information models models models models models models models models space space space space case order order shown shown shown systems parameters functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit distribution distribution method pattern pattern pattern pattern pattern pattern single processing processing processing processing processing processing processing control neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate patterns patterns inputs inputs inputs form shows shows simple simple simple gaussian paper paper examples small small feature work work fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step level level level level level level level level level level current cell cell cell cell cell cell structure response response response response response response response response similar representation representation show show show show show show show equation equation equation section real real real average average gradient gradient gradient gradient experiments activity activity activity activity activity activity activity activity result threshold variables variables variables computation computation computation computation computation computation research independent dynamics constant computer distance connections connections connections connections synaptic synaptic left left left direction direction direction direction presented map map map map map map map present present present present phase phase frequency frequency frequency frequency maximum maximum maximum maximum maximum range position position outputs abstract density density properties properties references introduction stimulus effect search difference difference difference difference difference difference difference spatial spatial spatial spatial lower chosen chosen higher higher center center center center firing firing firing firing firing firing firing firing firing firing type type type type type multiple multiple good spike spike spike represent represent represent distributed make make region length length observed observed observed observed simulations simulations simulations ing simulation simulation simulation simulation simulation computed computed sum sum times regions potential negative represented represented cross cross cross provide provide rates rates rates active determined related posterior motor brain equal equal voltage accuracy contrast connection connection dependent source source source source source source source source morgan technique code code advances responses responses responses responses responses responses responses responses responses delay maps maps maps maps considered computing curves curves curves curves curves curves curves curves transition san stimuli stimuli stimuli effects increase increase coding weighted randomly developed types types types actual inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply measured group tested excitatory excitatory excitatory predictions predictions amount assumed supported journal journal journal journal journal end end end end end end end end end sensory sensory kaufmann auditory auditory simulated typically smaller account interesting head head head mechanism representing details direct inhibition inhibition inhibition inhibition inhibition neuronal neuronal neuronal membrane discussed separate takes lateral lateral lateral side side interest approximately tuning tuning axis axis axis axis axis tions tions positions positions sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive increased horizontal parts intensity intensity intensity intensity suggests spikes spikes derivative derivative derivative touretzky half strength strength strength strength conclusion greater central central central central central central central differences sigmoid retina mateo sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound external sigmoidal sigmoidal sigmoidal sigmoidal proportional proportional targets appears describes tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned vertical modeled modeled linearly easy mutual shift shift versus john decreases dependence dependence dependence review depending stages stages stages variation forms sizes similarly suggested roughly add generation remains david bell inter sciences discuss black simplicity regular society society effectively driven post projections projections essentially essentially graphs kind strongly neuroscience neuroscience neuroscience neuroscience conductance cues cues bar bar bar involved vary usual localization localization realistic realistic computes ill thresholds disparity disparity receive receive presents trains bars bars bars investigate difficulty strengths strengths oscillator oscillator matches project project project possibility matched circles patch patch patch naturally plausible predicts predicts predicts predicts voltages thought mapped explain animal cart fairly fairly briefly processed closer closer precisely broad broad nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus projected sounds sounds sounds localized demonstrates geometry geometry varies varies varies percent cochlear experimentally poorly continuously sharp poisson poisson qualitatively qualitatively qualitatively conductances asymmetric enables semi kinds neuro shaped shaped owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl cochlea cochlea ear ear ear physiology physiology physiology sort forming forming princeton narrow harmonic contract removing shifts monotonically inferior inferior passive published published loo loo overview lengths consequences reproduce dif peterson april insight refers refers refers colliculus colliculus agree projects projects projects projects explains pressure pressure pressure land numerous numerous numerous numerous terminals comparative comparative comparative stem streams barn barn barn barn barn barn barn barn barn barn barn barn barn barn barn attempted capacitance increment increment perpendicular trends segregation interact interact interact afosr iso projecting complementary pos nuclei intensities conversely constructs dorsal dorsal dorsal dorsal dorsal dorsal dorsal dorsal dorsal dorsal dorsal dorsal dorsal dorsal responding knudsen knudsen slopes tissue increments ward unpublished worked acquire synthesized ferent confirm inhibit inhibit inhibited inhibited inhibited inhibited compete contralateral contralateral contralateral contralateral interaural interaural interaural interaural interaural pearson pearson pearson pearson pearson pearson calculates anatomy excited anterior konishi konishi konishi konishi konishi konishi konishi konishi konishi konishi konishi konishi ventral ventral ventral ventral ventral ventral ventral ventral ventral ventral ventral ventral ventral ventral triangles obey chan functionally tance leakage icl icl 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fujita fujita fujita ouput unambiguously cknowle dgement carr slab sarnoff tensity discharging projec inadequacy 
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patterns patterns patterns patterns patterns patterns analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form shows shows shows shows simple simple simple simple simple simple simple simple simple paper small small small small work work work work fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step process current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure response response response response response response response response response response similar show show section fixed fixed fixed fixed fixed fixed general general real obtained obtained activity activity activity activity activity university threshold threshold threshold research research defined defined found target target initial connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science left present present present present present present phase phase phase phase activation frequency frequency frequency frequency frequency frequency press press components outputs outputs continuous abstract applied applied computational computational properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties component due due important important important important mixture mixture introduction action action action action action action action action complex complex complex complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior stimulus stimulus stimulus effect dynamic generated change change variable rules part part cases firing firing firing firing firing type multiple multiple multiple multiple multiple multiple multiple good spike spike spike conditions conditions conditions conditions make fact fact observed observed observed ing tasks total called called elements elements potential potential potential potential potential potential study knowledge knowledge compared application application application application application application application active active active active active active active active active determined determined experimental experimental posterior motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor approaches accuracy support modeling synapses synapses synapses consists individual connectionist responses responses responses final final final addition addition experiment directly directly stimuli effects effects effects effects effects effects determine significant basic increase produce produce conditional conditional conditional levels types types actual provided finally selected inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply biological biological biological biological biological biological biological biological biological biological measured measured describe tested tested fast fast complete excitatory stable actions actions actions actions actions actions predictions circuits circuits circuits circuits circuits circuits amount synapse synapse synapse synapse generate generate supported role role theoretical require eds eds eds eds eds eds hypothesis easily sensory sensory sensory including underlying functional functional functional unknown fully block block block york york york mechanism mechanism special details numbers pre direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition early magnitude combined combined combined produced added neuronal neuronal membrane membrane membrane discussed property property element movement period identical identical recently sufficient varying varying works tions studies studies studies studies studies trans modified sensitive increased grant amplitude intensity intensity expression expression studied occur spikes occurs demonstrate strength strength strength strength conclusion conclusion place central central central central central central central central central interactions interactions interactions interactions interactions differences differences clear weak strong mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms presence presence presence presence presence cycle cycle cycle cycle demonstrated pulse turn variety variety variety movements movements movements movements movements selective targets identification question primary sequential generating generating changing changing infinite electrical electrical remaining text unique unique unique unique scales interaction interaction mutual mutual springer springer springer potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials cycles john john depending communication detailed showed modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation completely completely sign sign diagram earlier slow slow slow slow sec generation generation generation filtering msec coupling coupling expect fire fire combinations currents determines activated activated coupled coupled coupled major major major determining determining identified identified identified identified identified identified capable capable importance differ differ differ differ maximal spiking spiking spiking oscillatory post post post post post post situation miller miller miller excitation excitation verlag verlag verlag strongly strongly induced induced induced induced induced induced induced induced allowing contribution oscillations oscillations oscillations physiological physiological physiological physiological built receptor receptor receptor comp comp comp vary absence delayed cat cat cat neurosci neurosci neurosci neurosci neurosci neurosci neurosci acknowledgments deal intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic modelling simpler stimulation stimulation stimulation wiley wiley circuitry circuitry circuitry varied relations relations relations oscillators oscillators oscillator rest terminal plasticity plasticity muscle muscle muscle variability variability complicated oscillation understand understand understand understand presynaptic induction induction induction induction induction induction act naturally transmission transmission transmission transmission transmission transmission transmission changed changed aspect nerve nerve nerve nervous nervous nervous nervous nervous generates detected mixed explain seconds seconds isolated isolated isolated isolated isolated isolated isolated animal animal burst burst burst great slowly slowly majority capabilities caused interneurons ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion rapid rapid widely producing constructing nucleus controls controls consequence consequence axons axons axons recording apparent varies prop reflect understood pure tional capability quantitative cohen marked recordings recordings continuously release release release release release release release berlin berlin berlin summarized aim modulated modulated modulated gen physiol physiol physiol physiol physiol physiol traces extreme accomplished accomplished generator generator generator generator generator generator modify neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol eliminate flexibility flexibility flexibility flexibility flexibility receptors receptors plays eliminated cellular cellular cellular anatomical anatomical anatomical minutes minutes alpha chemical chemical chemical chemical chemical chemical chemical chemical chemical resistance efficacy efficacy efficacy neurobiology preparation preparation enhanced composition weakly weakly studying induce induce induce injection injection injection enhance heart claim infer bursts bursts stimulated mem extensively sons sons variants calcium harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris harris characterization ignore johnson johnson johnson fly lem mind cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic truncated graded graded graded graded graded graded graded graded removal feeding comparative regularity trigger causing causing resting resting rhythm rhythm rhythm rhythm rhythm rhythm suppressed spinal spinal argue trends subthreshold insights insights interneuron impose mammalian generators generators generators ocr oct oct oct oct efforts careful careful altered altered topic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic selectively monitoring importantly emphasized oscillating afferents responding intracellular induces induces induces induces modifiable computa inactive tonic tonic leech species emphasis reversal remarkable stimulating bursting bursting bursting bursting bursting bursting bursting bursting bursting bursting cpg cpg cpg cpg cpg cpg insufficient ongoing hundreds inhibit virtually evolved puts dominates tors transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter russell wiring anatomy physiologically plateau plateau plateau plateau plateau plateau plateau alan intact intact colleagues vertebrate vertebrate neurobiological enhances totally vivo vivo dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine marder marder marder marder marder ionic deter electrophysiological twelve nih stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory jan jan selverston selverston selverston selverston selverston ganglia ganglia ganglia ganglia tens actively silent silent subtle responded responded responded responded responded hyperpolarization hyperpolarization acetylcholine depolarization depolarization depolarization frog plastic ard ard unaffected unaffected altering altering altering altering altering elevation elevation elevation activates prolonged prolonged prolonged prolonged prolonged electrotonic adjustments activating extracellular modulating aimed warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick warrick stim bistable bistable tiny lasting vertebrates vertebrates vertebrates vertebrates vertebrates vertebrates vertebrates electrically electrically ronald epsps spontaneously participate exciting vitro excitability serving released released released released released invertebrate invertebrate invertebrate neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation enormous camp camp camp camp stretch lobster lobster lobster lobster lobster anatomically anatomically anatomically anatomically depolarized depolarized depolarized katz katz katz katz katz katz katz erties proprioceptive triggers mission complication modulates theme absolutely hen biochemical biochemical brane invertebrates invertebrates invertebrates cycling genera markedly markedly markedly markedly cornell crab crab crab neuromodulators neuromodulators neuromodulators neuromodulators neuromodulators neuromodulators neuromodulators neuromodulators isolate hyperpolarizing hyperpolarizing hyperpolarizing hyperpolarized hyperpolarized arose tives endogenous endogenous endogenous strengthening initiation alteration alteration alteration alteration depolarizing bibliography inhibiting gan pattems modulator modulator libraries silenced neuromodulatory restore underly transforma acute innervated pacemaker duces radically radically radically cease cpgs cpgs serotonin serotonin serotonin serotonin serotonin serotonin preparations alike ach ach synaptically unambiguously til pharmacological bal bal perspec mine modulators modulators modulators modulators modulators grossly naptic ithaca neurotransmitters 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output output output output output output output output output output output output output output number number system system system system results results results results units units units units units units units units units units units units units units units units information information information models hidden hidden hidden hidden hidden layer layer layer layer shown shown shown values neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit approach approach pattern pattern pattern single single single single single processing processing processing processing processing control control control control local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns analysis analysis analysis analysis analysis analysis analysis inputs inputs inputs inputs form form form form shows shows shows small small size feature fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells step field field field current current current current current current current trained trained trained trained cell cell cell cell cell cell cell cell cell cell response response response response response response response response response response response response response response response response response response response representation show fixed fixed real obtained experiments result result independent found found target target initial constant constant constant standard standard standard standard connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left left left left activation activation activation activation activation frequency temporal temporal temporal temporal press press position components components outputs abstract applied back back back back back computational properties properties properties properties properties references component component due due due positive propagation propagation propagation propagation propagation introduction hand circuit behavior behavior behavior stimulus stimulus parallel parallel recurrent recurrent recurrent recurrent change lower representations representations representations representations representations representations representations firing required multiple multiple multiple represent represent represent distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed make fact techniques region length observed forward simulations resulting sum performed called elements potential potential potential potential potential potential feedback relative specific specific represented represented represented represented desired desired receptive receptive receptive active active active determined determined determined determined determined determined determined determined determined determined determined determined posterior constraints constraints constraints constraints connected connected connected connected connected motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor brain voltage voltage comparison connection connection connection connection connection fields support train train train modeling modeling institute synapses synapses synapses synapses synapses synapses synapses responses responses responses exp exp delay addition additional view san stimuli stimuli stimuli effects effects effects effects effects effects effects upper significant significant produce produce produce produce produce derived randomly types types types types types types types types actual actual actual actual actual actual actual actual actual actual provided provided provided provided nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological biological biological technical denote fast fast fast fast fast excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory predictions circuits common implemented shape synapse synapse synapse supported main square sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory including fit simulated simulated simulated pairs pairs pairs pairs account dynamical dynamical functional functional consistent representing representing representing pre inhibition produced produced predict neuronal neuronal neuronal membrane membrane population population population exact exact similarity similarity lateral lateral lateral lateral lateral include side side subset subset subset sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently interest sufficient compare previously studies address modified sensitive amplitude amplitude amplitude amplitude amplitude amplitude occur suggests feed white white strength strength strength conclusion central central interactions constrained suggest hard sigmoidal proportional pulse pulse pulse pulse turn turn exist movements introduce connectivity connectivity connectivity connectivity identification identification acknowledgements construct laboratory implement electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical transformations unique potentials potentials potentials potentials potentials potentials potentials squares squares open restricted showed showed forms forms forms suggested constants constants constants partial slow slow slow slow slow epochs delays spaces sec assigned assigned assigned foundation foundation foundation coupling recorded recorded recorded recorded recorded box box box coordinate currents black black partially major middle aspects identified identified identified identified identified identified identified identified identified closely closely symbols included wij wij contained contained conductance issue physiological physiological physiological physiological physiological gray comp comp comp comp comp simplified relaxation absence realistic neurosci neurosci neurosci received received received receive oriented trains trains body body body body remain remain stimulation stimulation stimulation diego layered circuitry varied relations strengths strengths strengths oscillator postsynaptic postsynaptic postsynaptic matches matches fashion behavioral behavioral biol biol possibility possibility possibility muscle matched matched transmission transmission transmission analyze opposite adjusted adjusted adjusted adjusted obvious panel panel panel nerve nervous nervous mixed mixed explain indicating site site rows pairwise agreement adapted interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons reasons ganglion pool arises recording recording recording recording recording demonstrates qualitative summation behaviors reflect offset experimentally recordings recordings recordings robinson robinson release substantial substantial substantial shaped physiol physiol physiol physiol physiol physiol physiol physiol simultaneous simultaneous contribute accomplished appropriately arranged anatomical chemical chemical chemical chemical chemical chemical chemical chemical chemical chemical chemical imposed resistance resistance neurobiology roles salk intuitively responsible muscles muscles muscles loo 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#*learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set training algorithm algorithm system system system system system system system system system system results results results results results information information information information information information information information information information information information information information information information information information information problem problem problem problem models models models models performance performance performance based based based based based linear linear linear linear linear linear case case case order order order shown shown shown shown shown shown systems systems systems systems systems systems probability probability probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions neurons neurons neurons neurons neurons neurons neurons unit unit distribution distribution distribution distribution method method method method method approach approach approach approach approach approach approach pattern point point single single single single single single single single processing processing processing processing processing processing processing processing processing control large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis analysis class optimal optimal optimal inputs form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple simple simple simple gaussian gaussian gaussian visual visual visual visual visual paper paper small small work work work task task task methods methods methods methods methods methods fig fig fig fig cells cells step field field process process process level level level level level level cell cell cell cell structure structure structure problems random random high high high response response response similar similar representation representation representation fixed line line general general general real real real real real real real real real real real real real real average average average average term experiments experiments experiments experiments experiments experiments experiments experiments result result university threshold computation research research independent dynamics initial constant constant estimate estimate estimate estimate estimate estimate estimate estimate standard terms terms synaptic science direction presented present present low frequency frequency frequency frequency frequency temporal motion motion motion motion motion maximum range press press press continuous continuous continuous sample abstract applied applied back back back back find find find density density analog properties properties properties references important important decision decision context introduction introduction complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus dynamic generated generated difference spatial lower measure measure measure signals signals signals signals signals chosen higher part firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing required good good spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike conditions conditions conditions conditions represent expected expected make make fact correlation errors errors errors errors errors scale resulting resulting resulting resulting respect respect eq times times times times times times times times times natural study study study filter filter filter filter filter filter filter filter filter filter filter filter filter filter obtain obtain obtain negative negative true true true true cross define compute compute rates rates rates rates rates proc perform eye eye eye eye experimental experimental goal gain gain gain gain discrete discrete power approaches approaches approaches steps comparison train train train train train train train train train train train train train train train train dependent dependent dependent department department version consists code code code code code code code code code code code code code code code code code code responses responses responses responses layers delay delay delay delay delay delay delay addition sequences equivalent experiment experiment curve curve view view design limit limit stimuli stimuli stimuli stimuli stimuli stimuli detection detection determine upper requires significant vision estimated basic basic give produce coding coding coding coding coding coding coding conditional conditional conditional levels levels velocity finally constraint simply biological achieved achieved measured measured arbitrary arbitrary tested limited limited limited close close close corresponds complete excitatory circuits short short short effective generate supported supported supported theoretical theoretical require face face square end instance instance instance future easily noisy sensory sensory sensory sensory sensory sensory sensory sensory unknown unknown unknown coefficients york york increasing mechanism principle filters filters filters filters filters filters direct window normalized bottom minimize predict predict predict improved improve directions resolution resolution resolution resolution property property robust separate ensemble ensemble ensemble movement movement movement movement movement movement apply moving identical sense sense array array relevant varying varying varying varying varying varying varying varying conventional observations approximately calculated calculated solve correspond studies studies address address definition background generalized interval organization improvement improvement sensitive sensitive sensitive sensitive increased increased amplitude amplitude constructed constructed exists horizontal horizontal concept studied occur suggests extended wide wide spikes spikes spikes spikes spikes spikes spikes spikes width loop white white white generally half strength place place greater greater assumptions segment conclusions measures measures clear clear clear practice suggest suggest encoding encoding encoding encoding hard mechanisms integration integration physics external characteristics california california solid minimizing movements introduce introduce program explicit explicit appears appears appears relation van van van van van van van van van van construct longer longer longer ways estimating estimating segments sensitivity explicitly averaging averaging involves slightly spectral spectral scales develop frequencies quality quality quality national focus reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction static completely allowed spectrum reasonable reasonable measurements measurements delays delays expansion reduces combining add interpolation filtering calculate msec msec msec msec msec msec msec msec msec msec msec msec foundation david precision building existing priori inter specifically phys discussions discussions characterized identified identified identified encoded encoded encoded spiking spiking spiking identify computations computations comparing miller essentially essentially traditional traditional soc repeated repeated decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding link contribution content physiological follow strategies timing timing timing timing timing duration comp quantity write write absence absence realistic minimizes minimizes wave thresholds illustrates subsequent extract extract acknowledgments intrinsic receive trains trains trains trains trains trains trains trains trains trains trains explore simpler simpler carried carried carried carried requirements investigate exhibit circuitry relations limitations issues dotted periodic helpful behavioral behavioral behavioral behavioral applicable fault analytically combine decisions complicated understand understand understand fundamental matched transmission plausible editor reading reading reading reading reading reading reading opposite extremely eyes front front obvious precise explored nervous nervous regime explain averages established years formula crucial agreement convolution analyzed waveform waveform waveform waveform waveform waveform waveform coded coded coded biology biology answer briefly london processed berkeley berkeley mation scientific calculations begin res read read read lowest recording bandwidth bandwidth bandwidth bandwidth incomplete sun questions questions questions questions limits limits limits limits limits pure relevance tional simulate quantitative effort introducing introducing posed marked continuously continuously biologically reliability calculating operate rely characterize characterize popular occurrence occurrence achieves decreased redundancy redundancy redundancy redundancy redundancy physiol tolerance deviations summed instantaneous redundant sort accomplished angular angular recover recover recover approximates purely unity addresses impossible arrival arrival arrival proceed systematic systematic numerically imposed check moment hope star observing presentations moments infor meaningful bialek bialek bialek bialek bialek bialek bialek bialek bialek bialek studying studying negligible surprising pat moved photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor young smoothed smoothed arrive record matter waveforms waveforms observer statement characterization tures displacement displacement displacement displacement displacement fly fly fly fly fly lag outlined treat fired multiplying approx crossing land land visually sine fellowship achieving reaction reaction expanding tradeoff tradeoff tradeoff tradeoff generalizations hundred classic causal causal causal imagine massively molecular reconstruct insights graduate dominated emphasize emphasize guided ambiguous anal crossings suffer inverting fea flight corrections answers answers mea characterizing characterizing quantify spacing spacing dominates accomplish award horizontally manipulated carries characterizes vanish interpolate william faced faced steveninck steveninck steveninck steveninck steveninck steveninck steveninck steveninck decoded indicators surprise ruyter ruyter ruyter ruyter ruyter ruyter health talk noiseless stan tern decode ysis plenum linearities investigator tal tolerant judge accepting remarkably literal rieke rieke rieke rieke rieke saturates saturates mar dard manipulations opportunity hypothetical stim netherlands netherlands netherlands reconstructions reconstructions reconstructions reconstructions reconstructions reconstructions reconstructions reconstructions waiting lay insects conveys organisms bull correspondingly presidential insure organism organism organism organism organism organism organism organism blowfly blowfly blowfly fifty facing recon recon recon probing warland warland warland 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#*network network network learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural function function figure figure figure figure figure figure figure figure figure figure time time time time set networks number number system state state state state state results results information information information based linear linear case case case case order order order order order order shown shown systems systems systems systems neurons neurons neurons neurons neurons neurons neurons neurons point point point single processing control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate form signal signal simple simple simple paper small size size net net work work work work task cells level level level level level level level level response response similar similar fixed fixed line states states states states states gradient note experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result university university threshold threshold variables research research found sequence sequence sequence dynamics initial initial initial initial computer computer terms distance connections connections connections connections science science left left left presented presented presented presented present present phase phase phase phase phase phase low object maximum components basis basis basis basis basis basis continuous abstract applied properties references component component component component component component component component due due due positive positive positive positive positive positive positive positive important important adaptive adaptive decision introduction action complex complex complex hand hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus effect effect dynamic generated generated generated search search search change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference difference lower lower signals signals part center center center cases required conditions conditions make fact fact minimum resulting ing performed means natural natural feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation orientation study study study obtain obtain negative artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial compared active active experimental goal goal goal goal goal gain gain motor motor motor motor discrete larger connection connection connection support morgan proceedings report implementation implementation implementation implementation implementation technique consists consists internal internal internal internal internal internal internal internal internal internal internal internal internal advances joint responses responses difficult addition addition addition addition experiment environment environment environment environment environment environment directly directly directly san stimuli stimuli stimuli stimuli effects effects effects effects effects conference capacity capacity capacity upper upper full full full increase increase increase increase con con developed levels controller controller controller controller controller controller nature inhibitory inhibitory depends depends simply associative achieved achieved technical increases increases limited close close close inverse corresponds complete excitatory excitatory excitatory stable actions amount amount shape synapse synapse generate generate generate role role role role role square degree degree degree degree makes makes sensory sensory kaufmann simulated simulated simulated simulated underlying account account account interesting edge edge head mechanism leads leads inhibition inhibition international bottom produced architectures separate lateral identical side subset relevant engineering engineering interest interest interest sufficient sufficient sufficient approximately approximately works axis achieve definition interval interval interval interval interval interval entire increased increased exists intensity intensity intensity occur occur feed feed feed move touretzky loop loop loop loop loop loop loop demonstrate strength trajectories trajectories depend depend central interactions interactions differences designed clear mateo suggest presence presence external external characteristics characteristics characteristics drawn proportional proportional intelligence turn turn turn turn turn turn turn turn turn assuming movements movements movements movements movements decrease relationship relationship question reference pro ways factors factors factors plot plot distinct dept implement physical interaction interaction interaction decreases decreases decreases dependence depending open open open controlled completely diagram diagram earlier initially initially sufficiently sufficiently koch koch degrees avoid recorded fire extension gating gating successfully sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor identified capable capable capable differ identify detect build build build situation reached capture induced showing neuroscience neuroscience timing hold built comp involved play play absence highest attempt moves intrinsic decreasing oriented explore simpler simpler command command command command command command access essential requirements requirements exhibit exhibit exhibit exhibit circuitry environments detail issues rise rise examine examine examine successive successive project behavioral behavioral behavioral behavioral proper hierarchy understand removed act patch patch patch patch patch patch patch patch patch patch extremely thought front precise nerve nervous generates detected utility grouping grouping motivated motivated motivated motivated motivated motivated motivated motivated motivated motivated attempts animal animal animal animal animal animal animal animal animal animal animal animal animal animal animal animal animal animal animal crucial sensors sensors sensors sensors sensors publishers phenomena biology biology diffusion capabilities answer lies interneurons interneurons considerable turns beginning gradually patches patches patches qualitative addressed explained varies greatly behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors understood understood flexible spoken embedded capability fed fed fed autonomous effort continuously biologically exhibits controllers controllers controllers gen fall fall proven serve serve prevent prevent semi conclude decreased physiol begins begins begins begins begins begins begins modify extensive animals animals animals animals controlling controlling controlling circular odor odor odor odor odor odor odor food food food food food food food food food food food food food food food food food food food food food food food food food food food food food food food food food food food food food plays inspired inspired stronger occurred overcome chemical chemical chemical chemical chemical chemical chemical chemical chemical intelligent intelligent los nearby nearby responsible responsible corner fires fires continue motivation falls falls governed connect encountered conjunction exposure bursts environmental properly insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect insect 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insufficient insufficient builds designs agents hypothesized utilizes supply accomplish drawing possess dissertation automation automation tactile tactile tactile tactile tactile ref heterogeneous heterogeneous heterogeneous intact odors enhances complement frequent drastically fol comprised shaping modulatory modulatory antenna antenna cleveland shares explaining began initiated modulate survival arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal arousal preventing attracted transferred hysteresis hysteresis sensed excite terminate saturates reactive aimed possesses possesses hypothetical enabled sequencing sequencing insects insects insects insects insects insects insects spontaneously exciting hypothesize seemingly released feeds inhibits utilization correspondingly legs prototypical tational underlie behav persistence beer beer beer beer beer beer beer beer beer beer beer beer sponse triggers recognizable signif theme departments disabled maintenance scientists persist persist walks excites western western orient orient orient orient sect lows slowest erence patterning sensations ior closes pacemaker pacemaker cease hungry hungry hungry hungry hungry hungry hungry hungry explanatory releases petitive reserve reserve initiating emit pervasive erally icantly responsiveness responsiveness moti apl antennae antennae antennae tence consumes consume consume consume exhausted tur diffuses randall wandering wandering trolling occasions tually eliciting 
#@Beer_R,Chiel_H,
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#*network network network network network network network network network network network network network learning learning model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input function figure figure figure figure figure figure figure figure figure figure figure time time time time time set networks networks networks networks output output output number number number number system system state state results results results results results results results units units units models models layer layer layer layer layer layer layer layer layer layer layer layer order order shown shown shown shown shown shown shown shown shown shown shown shown values probability neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit distribution single single single processing large large large local local local local neuron rate rate analysis form shows signal gaussian visual visual visual visual size size size size size size size size size size size size size feature feature cells cells cells cells cells cells cells cells step field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field features process process trained cell cell cell cell cell cell cell cell cell cell cell cell cell random high response response similar similar similar representation representation representation representation architecture architecture show section section section fixed rule rule rule rule rule general parameter average obtained obtained term term term term term experiments experiments experiments experiments activity activity activity activity dimensional result threshold computation computation research research research research research defined sequence dynamics dynamics dynamics dynamics dynamics initial constant constant constant standard terms connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node left left left left left map map map map map map map map present present activation activation activation activation activation low low nodes motion maximum range press press press press continuous abstract computational convergence properties references adaptive adaptive introduction hand stimulus tion tion tion change change change change change change variable spatial signals representations representations representations center center center previous cases firing firing type type type type type type type required cortex cortex cortex cortex cortex cortex cortex cortex cortex long long long long long conditions conditions conditions region region correct observed observed observed observed simulations simulations simulations simulations simulations simulations ing ing ing total total simulation simulation simulation simulation simulation simulation respect performed elements regions regions regions mapping mapping mapping mapping optimization potential potential made made global study vol vol specific represented represented receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive proc location location location location eye experimental distributions cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain brain brain comparison connection connection connection connection fields fields fields fields fields fields fields dependent dependent dependent dependent dependent nets selection report report consists individual advances represents layers layers layers addition maps maps maps maps maps maps maps maps maps maps maps maps framework framework experiment experiment experiment experiment san san san san effects effects full full estimated basic increase increase con con con weighted criterion area area area area area area area area path path inhibitory inhibitory simply biological measured normal normal normal normal normal increases describe group fast inverse inverse inverse inverse inverse inverse excitatory excitatory excitatory excitatory excitatory excitatory excitatory surface surface circuits circuits generate supported role role eds hypothesis hypothesis instance sensory auditory auditory simulated pairs underlying account account functional projection projection projection york principle operation leads representing representing representing pre pre pre pre normalized decay decay decay run light light architectures membrane membrane membrane membrane discussed recent pair pair movement lateral lateral include period sense recently interest sufficient sufficient sufficient varying volume tions yields yields studies studies converge modified organization organization organization organization increased increased increased increased amplitude occur locally occurs boundary demonstrate strength strength conclusion critical critical hebbian hebbian valued competitive reward central central differences differences measures peak peak peak peak moody moody mechanisms reduction drawn drawn sigmoidal demonstrated variety movements decrease relationship relationship areas areas areas areas areas digit digit digit digit digit digit digit digit digit digit digit digit pro ways ways primary primary ann tuned linearly mutual mutual shift shift shift shift john yield formation formation formation formation review stationary detailed controlled controlled restricted restricted restricted restricted restricted organizing organizing forms forms digits digits digits allowed expansion normalization normalization initially initially initially kohonen kohonen kohonen kohonen figures includes perceptual specifically variations black phys discussions tests middle aspects modification driven included wij post post post post post post post post projections projections projections miller excitation excitation excitation summary soc strongly induced induced induced induced induced neuroscience neuroscience neuroscience neuroscience dis gray comp usual michael surround providing reach neurosci principles illustrates illustrates receive modelling modelling explore stimulation stimulation stimulation stimulation stimulation stimulation diego wiley steady detail strengths strengths strengths issues divergence preliminary pursuit helpful postsynaptic fewer fashion behavioral biol biol biol plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity maximizing tanh presynaptic topographic topographic topographic topographic topographic topographic topographic topographic topographic fundamental fundamental surfaces surfaces neu patch patch patch patch concepts concepts possibly predicts rev der der nerve nerve nerve nerve nerve nerve hebb amari amari contributions submitted submitted site site site developing distinguish drive tive tive closer sites organized organized monkey laboratories cut localized patches patches patches linsker linsker addressed summation reflects applies double double simulate simulate experimentally experimentally variant maintain maintain measuring incoming incoming incoming incoming incoming incoming incoming cal resource ordered qualitatively qualitatively inherent conclude decreased decreased neuro focused damage owl owl progress summed contribute shifted representative representative representative representative tation tation count food extending darken darken planar infor passive passive passive published representational representational representational edelman periods von von expanded enhance consequences monkeys monkeys monkeys monkeys monkeys monkeys originally soma reproduce tic barron francisco francisco emergence emergence modelled modelled cerebral cerebral stimulated stimulated stimulated stimulated offer matter contact contact partitioned variants variants grants fold vari discriminate schulten schulten largely shading focal focal focal nelson nelson willshaw willshaw connec lesions lesions lesions lesions corrected solely malsburg malsburg simulating lesion lesion lesion lesion mutually peripheral peripheral peripheral trends ibm cessing wall wall wall wall mammalian continues life distant expand met eliminating eliminating maximally confirmed surrounding surrounding surrounding lond noting noting represen represen cation refinement refinement refinement refinement refinement refinement refinement sized reveal descending descending descending descending son rotating elsevier indication modifiable bill compu ritter ritter topography capacities species covers syn drives gratefully expense stimulating stimulating continued insufficient insufficient skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin skin focuses lated somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory adult adult adult adult adult adult adult pearson pearson neocortical conversion neurol tactile lying restricting intact outgoing merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich synergy tance longest evolves fol tations inducing comprised acknowledges nih zones proceeding sur sur sur linking jose zone zone zone zone hypercolumn ard jenkins jenkins jenkins jenkins jenkins jenkins repeating converts stryker magnification magnification magnification magnification magnification magnification magnification magnification magnification magnification magnification magnification magnification magnification magnification contributing stand rela columnar checks adjustments impor relying opportunity nections undergoes patterned topologically lesioned fac terry disk disk finkel tational mammals recep tain fund facing neurophys wurtz wurtz entails microns strip conical regeneration ford ford heating hyperpolarized situated excites ken lows cyb cyb cyb supercomputer silenced silenced silenced silenced silenced silenced marion behaviorally behaviorally subcortical tude orm organiza patterning patterning aerospace reorganization reorganization reorganization reorganization reorganization reorganization reorganization reorganization tips subse injury surviving kaas kaas ampli universally sustain redistribution clearer renormalized quanti cynader mer additively cessation disambiguate coleman coleman rosci tative ticity quent malization tionship jen chemically kass multiplica pear prelim abnormally gall theoreti inary 
#@Grajski_K,Merzenich_M,
#t3
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#*network network network network learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural figure figure figure time time time time time time time time time time set networks networks networks number number number number number system system system system system system system system system system results information information information information information problem problem problem models performance performance based space space space space space space layer case case case case case case order order shown systems systems functions neurons neurons neurons approach approach pattern pattern pattern pattern single single single single single processing large large large large large large local local local local local local local local local neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs form shows shows shows shows shows simple paper paper examples small small net work task task task task methods methods fig fig fig fig fig fig fig fig fig field field process level cell cell cell structure structure structure problems problems problems high high response response similar similar similar similar section section general general general general average average experiments activity activity activity activity activity result computation computation computation computation computation computation computation computation computation computation computation computation defined defined found found computer computer computer computer computer computer computer computer computer computer computer terms terms terms terms connections science map map map map map map map map map map map map map map map map map map map map map machine maximum maximum maximum maximum maximum press press press continuous continuous continuous continuous continuous continuous abstract find computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational density density properties properties properties properties references important important mixture mixture context introduction introduction complex hand hand circuit dynamic dynamic parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel cost cost cost tion change energy energy difference spatial spatial spatial assume measure measure higher cases cases required multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex represent tree distributed distributed distributed equations make make make make techniques region region region region observed observed minimum minimum classes classes tasks total simulation simulation simulation human computed sum performed eq times regions regions regions regions regions regions regions regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping factor factor optimization optimization potential potential natural applications artificial specific represented represented proc proc location experimental experimental related constraints cortical brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain equal power power power approaches mit mit voltage voltage comparison update support dependent dependent modeling modeling modeling modeling selection proceedings institute department implementation version synapses synapses technique individual individual represents represents responses difficult difficult layers delay maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps computing computing computing computing computing computing computing computing computing computing equivalent equivalent equivalent equivalent directly view solutions design design design conference capacity efficient efficient efficient efficient efficient requires significant significant significant speed basic give give give levels types types lines actual finally processes evidence evidence nature nature depends constraint constraint constraint constraint achieved achieved group corresponds corresponds common assumed supported theoretical require eds eds eds eds easily degree makes development simulated simulated fully technology ratio uniform principle principle principal representing representing numbers making idea combined combined run neuronal neuronal neuronal architectures architectures architectures membrane membrane membrane membrane apply subset recently engineering approximately calculated works smooth smooth differential achieve channels organization organization organization organization organization organization entire increased constructed digital wide predicted generally assumptions conclusions interactions differences clear practice suggest california proportional proportional assuming variety relationship relationship relationship connectivity program program annealing annealing question areas explicit pro solving ways factors factors factors primary label vertical changing simultaneously interaction interaction interaction develop applying potentials john depending communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication overlap detailed organizing evolution evolution suggested processor processor processor processor processor processor processor processor processor processor earlier reasonable calculation calculation calculation calculation delays expansion remains assigned koch koch topology topology dendritic coupling avoid usa discuss variations characterized characterized efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency importance uniformly divided presentation identify computations computations computations computations computations computations computations computations computations computations projections projections projections tend tend tend tend tend fine prob neuroscience issue criteria sci hold categories categories categories receptor providing minimizes minimizes minimizes minimizes minimizes minimizes correspondence chips processors processors processors processors processors processors processors processors processors processors processors processors processors principles principles principles neighboring neighboring neighboring neighboring deal rat rat rat rat rat rat rat load load load load load load load load load load load load load load load load load load load load load load load load load load intrinsic body carried american wiley circuitry circuitry circuitry circuitry updating limitations hall rise rise rise rise giving ideas rest behavioral mappings mappings mappings applicable ideal ideal possibility relationships topographic topographic fundamental phases analogous neu neu measurement transmission extremely illustrate voltages voltages aspect olfactory olfactory olfactory olfactory olfactory olfactory mapped mapped nervous nervous nervous nervous nervous nervous nervous academic contributions contributions electronic great advanced ment ment ment cart costs costs costs costs analyzed phenomena biology capabilities spatially turns turns turns perspective organized division monkey arise arise arise arise arise afferent consequence cut cut potentially potentially scientific acknowledgement involve acad res localized arises computers computers computers computers computers computers computers computers computers computers computers computers computers computers computers recording nsf explained reflects reflects apparent apparent reflect understood effort effort share sharp sharp spread fall serve pasadena conductances conductances substantial logical electric kinds kinds kinds comments owl tile extreme pose sort accomplished acm optimizing resources resources resources perfectly neurophysiol neurophysiol odor odor connecting interconnected receptors caltech bower bower bower bower bower bower bower bower bower bower anatomical analogy balance balance balance balance mark ral north synchronous adequate carry heuristics natl date utilized prentice mance cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar james perfor pat holland dendrite bulb assembly interconnections bases similarities axonal cerebral ends draw hypercube sons considerations messages reverse davis balancing balancing balancing balancing interestingly influences acknowledge johnson lem largely corporation listed revealed nelson nelson nelson nelson nelson nelson nelson nelson tradeoff stem affects molecular capacitance peripheral peripheral favor favor grouped geoffrey geoffrey impose impose relate relate overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead overhead speedup speedup finger knowing october strict manuscript topologies topologies topologies reversal opti distortions distortions quantify terns ers suffers evolved attempting imple interpreting interpreting supply somatosensory somatosensory somatosensory somatosensory responsibility loosely broadly purkinje ron neocortical striking konishi konishi konishi kirkpatrick kirkpatrick push tactile tactile tactile tactile tactile tactile fox fox fox fox fox fox fox fox fox fox fox neocortex loads inefficient inefficient raises compartment compartment compartment compartment merzenich merzenich distorted physically delivery delivery correlates modern carrying cuts granule granule translate scattered scattered scattered scattered scattered scattered devoted putation putation hot incurred spots ular prolonged rela walker mentation mal lips compartments compartments compartments compartments compartments compartments compartments compartments compartments ecs gibson segev segev segev segev asso shepherd cen compartmental piriform brains unstructured communicating concurrent concurrent concurrent grain behav laminar comput rabbit partic deliver deliver imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance imbalance otto accompanied predominantly vecchi embodies distribute patchy patchy patchy patchy patchy discussing analogies ule programmer gelatt necessitates efficiencies efficiencies puting tradeoffs organiza ciated reorganization crn veloped overload hemispheres hemispheres hemispheres engineer origins suggestive munication microelectrode carr zornetzer tac changeux fects physio discernible equivalents ciency tionship isopotential disproportionately lau congruence cessors gether tma metabolism strikes tempt 
#@Bower_J,Nelson_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input data function function function function function function function function function function set set set set networks networks networks networks networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm output output system system system system system system system system system system system system system system system system system system state state state state state results results units units units units units problem models hidden performance performance based space space space weights weights weights weights weights weights weights weights weights linear linear linear linear linear case vector vector vector vector order order order order order order order order order order order order order order order order shown shown shown shown systems systems functions functions neurons neurons neurons neurons distribution recognition recognition recognition approach approach approach pattern pattern pattern point single processing processing large local local local local local local local local neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form form form form form form form shows simple simple simple simple simple simple visual visual visual visual visual visual examples size feature feature feature feature feature feature feature feature net net net net net net work work work work work cells field field features process level level trained cell cell cell cell structure structure structure structure random high high memory memory memory memory memory memory memory memory memory memory memory memory memory similar representation architecture architecture architecture show show show line rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors general general general general general general general general general general general real real real real real real real average average average states states theory theory theory theory theory theory term term activity activity activity activity activity dimensional dimensional variables variables computation computation research independent independent defined defined found found target constant constant standard terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic node left present phase phase phase phase phase phase phase phase phase phase temporal object object object sets range range range range range range range range range range range press components components components components nonlinear nonlinear nonlinear outputs outputs continuous continuous abstract applied find find density analog analog analog analog references component component positive positive positive adaptive decision decision introduction action complex complex complex complex complex complex complex complex circuit behavior stimulus effect dynamic generated recurrent tion complexity assume rules rules learned learned learned chosen chosen higher higher higher higher higher higher higher higher higher higher higher higher higher higher part theorem theorem theorem cases required required multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long long long long long long long long long long expected equations equations make make make techniques region correct observed observed observed observed scale simulations simulations resulting classes times regions regions means factor potential feedback feedback feedback feedback study obtain negative specific desired desired desired desired cross cross cross cross cross series objects objects objects proc proc location experimental experimental motor motor cortical cortical cortical cortical cortical brain power voltage connection support dependent nets modeling modeling synapses synapses synapses synapses synapses synapses joint responses final layers sequences sequences considered considered computing directly directly directly additional view view top capacity capacity capacity full full full full requires world basic give give give give give con derived randomly clustering clustering developed developed area area product product product product product actual actual actual evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological biological biological biological biological biological associative associative associative associative associative associative associative associative associative associative measured normal normal normal normal increases close excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable actions proof proof common effective effective effective synapse synapse synapse supported role theoretical require cluster future degree sensory sensory sensory hopfield hopfield hopfield hopfield combination reduced reduced dynamical coefficients block programming interesting projection projection projection projection projection projection projection projection projection projection projection projection projection york special structures principle operation operation operation operation operation operation direct direct making stored stored stored stored stored magnitude produced choose added added predict neuronal improved population population population discussed discussed directions recent exact pair pair pair separate lateral subject cognitive relevant engineering interest interest previously previously unsupervised smooth diagonal diagonal definition symmetric symmetric storage amplitude amplitude amplitude amplitude amplitude amplitude amplitude exists expression lead lead studied studied invariant occur suggests matrices locally generally flow strength minimal minimal minimal minimal minimal minimal minimal hebbian trajectories competitive competitive sigmoid sigmoid sigmoid modules designed learns mechanisms mechanisms sigmoidal sigmoidal sigmoidal sigmoidal pulse exist program attractor acknowledgements explicit explicit appears appears appears longer ways factors primary primary primary primary primary primary primary mathematical mathematical mathematical dept modeled modeled sensitivity category category linearly easy interaction springer blocks blocks formation viewed viewed viewed detailed densities operations operations restricted labels organizing evolution forms static static static static completely similarly suggested calculation additive expansion expansion reduces neighborhood roughly add initially dendritic dendritic dendritic dendritic dendritic degrees degrees degrees coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling expect expect perceptual coordinate coordinate eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues instances subspace memories memories automatic coupled variations absolute columns columns columns columns capable modification driven wij wij modes modes modes modes modes modes oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory attractors attractors attractors attractors attractors attractors attractors attractors identity composed conf conf kind kind kind kind success interested neuroscience neuroscience symmetry symmetry lie sin oscillations oscillations oscillations content physiological follow categories categories categories usual wave eigenvalue binding cat principles principles operating neighboring receive modelling explore origin origin perturbation create create essential investigate circuitry circuitry oscillators detail strengths association mass oscillator periodic periodic periodic periodic periodic periodic fewer fourier fashion project incremental int ideal ideal analytically analytically reliable structured eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors complicated complicated complicated tanh proved oscillation oscillation oscillation oscillation oscillation neu induction act math naturally transmission plausible editor man created voltages thought thought thought ensure rank prototype olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory bifurcation bifurcation bifurcation bifurcation assumes freedom freedom precise expressions nervous hebb hebb hebb hebb hebb hebb hebb academic store store store fibers averages established established animal animal cos directed guaranteed guaranteed guaranteed slope biology biology analytic analytic capabilities tractable interneurons nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity perspective berkeley berkeley preprocessing preprocessing preprocessing preprocessing preprocessing choices arise pulses pool projected axons axons axons axons axons exemplars outer outer outer outer researchers conjugate conjugate populations populations populations freeman freeman freeman generic incorporated biologically biologically maxima requirement synthesis characterize differs branch gen serve serve serve extensions collective collective collective singer coherent kinds kinds display fiber baird baird baird baird baird baird baird baird june realized realized contribute phenomenon uncorrelated secondary notes feasible accomplished equivalence forming modify investigation ratios linearity member perfectly branches impossible impossible connecting grows grey arrival establish saturation bower anatomical anatomical odd fan programmable loops los nearby ral intuitively spurious exploring contexts dendrites james corre guarantees guarantees expanded intended dendrite dendrite dendrite mel bulb bulb bulb bulb bulb bulb bulb interconnections interconnections nonlinearities nonlinearities multiplied recog waves waves infer axonal insight stimulated ends storing storing storing eigenvector eigenvector acknowledge dividing dense dense crossing leaving converted rigorous constitute basically removal opposed job emergent diverse nition spatio restrictions conjecture sigma causing amplitudes recurrence molecular realize clas argue argue magnitudes magnitudes interact interneuron permits convert expand expand afosr landscape landscape ultimately sketch weaker oscillating oscillating oscillating oscillating oscillating oscillating oscillating oscillating reveal reveal pools cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic page macroscopic programmed bill signs signs microscopic microscopic strict architectural sigmoids rats stores sponding lation traveling justified justified justified justification justification assistance hypothesized hypothesized hypothesized hypothesized evolved orthonormal orthonormal compete conceptual morris anatomy anatomy anatomy physiologically subtracted neocortex neocortex neocortex ultimate characterizes vanish degenerate daily suffice lewis fair relaxed lags lags positioning vicinity meant halves prominent addressable stacked substrate physica shares polar polar analyse cats arousal entering permutations macro hirsch imaginary entered tiny grown eralization cortico cortico standing standing haberly underlie anatomically contributed resonant emerging forest lend linearization invaluable siftcation ubiquitous disparate pleasure liapunov absorbed locus alteration wash axo trophic latest inferotemporal oscil clocking clever cartoon scalars conceivably unused cortices associational associational associational stemming stitute interconnec sociative citatory bulk proximately scopic endless tracts 
#@Baird_B,
#t3
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#*network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input data function function function function function function function figure figure figure figure figure figure figure figure time time time time time time networks networks number system system error error results results results results units units units units information information information models models models models models models based linear case case case case order order shown systems noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit approach approach pattern pattern pattern pattern single single single single single processing large large local local local neuron neuron neuron neuron neuron rate rate rate patterns patterns analysis analysis analysis inputs inputs signal signal simple gaussian visual visual visual visual visual visual visual visual visual visual visual small small small small feature work fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells field process level level level cell cell cell response similar similar similar architecture architecture architecture architecture show equation equation equation equation average average average average gradient gradient obtained note note activity activity activity activity activity activity activity activity dimensional result result result result university threshold computation computation solution solution research found dynamics initial initial initial initial initial initial constant constant terms terms connections connections synaptic synaptic synaptic science present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal object object range range range range press basis continuous abstract applied back find computational references stochastic due due due propagation introduction action action hand behavior behavior stimulus stimulus stimulus stimulus stimulus effect effect effect dynamic generated tion difference variable variable variable spatial chosen higher firing firing firing firing firing firing firing firing firing firing firing firing firing firing cortex cortex cortex cortex cortex cortex cortex cortex cortex spike long long long long long long conditions conditions conditions conditions represent distributed distributed fact fact region region observed observed resulting total multi performed eq times times times times regions regions regions regions potential potential potential feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation orientation orientation global global global global specific series define objects objects objects proc location location determined experimental connected cortical cortical cortical cortical cortical cortical cortical larger contrast contrast connection dependent words version internal code individual individual individual individual individual individual individual represents represents represents responses scheme solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions limit top top effects determine requires significant significant basic basic con coding coding randomly developed levels levels levels velocity lines nature nature nature discussion increases group group assumption complete excitatory excitatory stable stable stable stable finding nearest nearest nearest nearest nearest implemented assumed assumed role role require main ability ability ability easily degree degree simulated account account dynamical jordan significantly ratio mechanism mechanism special consistent trials leads representing details bottom bottom bottom decay description neuronal neuronal neuronal neuronal neuronal architectures architectures architectures architectures architectures membrane population population population population population population population discussed recent robust robust robust takes reported reported reported reported lateral lateral moving identical array array array recently highly highly highly highly highly highly compare tuning tuning yields converge differential address background background background background chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain channels interval interval sensitive sensitive entire entire increased amplitude amplitude amplitude amplitude amplitude horizontal parts lead lead occur extended trial trial trial deviation spikes derivative alternative feed width occurs occurs generally setting strength critical greater neighbor neighbor neighbor depend central central central interactions weak suggest strong integration presence demonstrated proportional turn exist exist averaged averaged manner groups groups groups groups groups groups groups connectivity force areas areas explicit derive stability stability stability stability stability stability stability tuned mathematical distinct distinct distinct dept sensitivity averaging averaging develop develop frequencies frequencies frequencies shift shift shift implies cycles cycles cycles cycles depending stationary communication variation labels static earlier slow slow additive delays delays reduces msec msec foundation foundation eeg koch koch koch koch koch koch coupling coupling coupling coupling coupling coupling fire fire perceptual usa inter plotted prove coupled coupled variations holds phys neighbors neighbors discussions simplicity simplicity middle middle uniformly maximal driven included oscillatory oscillatory oscillatory oscillatory ten excitation excitation excitation excitation strongly strongly induced superior issue sin oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations timing sci gray gray gray gray gray bar bar involved relaxation play realistic realistic computes reach cat neurosci rat intrinsic bars bars bars origin perturbation investigate exhibit exhibit exhibit exhibit circuitry rapidly rapidly rapidly rapidly oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillator oscillator oscillator periodic periodic existence existence project investigated biol biol relationships relationships relationships relationships office lgn variability encode fundamental phases phases phases math math gradients gradients possibly necessarily onset onset changed aspect olfactory der der assumes assumes taylor separated separated separated extent submitted asymptotically developing ground ground track coded analytical spatially rapid tive widely incorporate nucleus scientific acknowledgement acad begin nsf raw mechanics prop populations populations populations populations double freeman freeman pathways pure led led tional readily cohen cohen recordings slower maintain passes exhibits exhibits exhibits exhibits perturbations synchrony collective collective collective collective collective collective collective pasadena achieves singer adjust replace coherent coherent coherent conclude comments tolerance coherence coherence coherence coherence coherence coherence coherence synchronization synchronization synchronization cor cybern sort labeling investigation velocities homogeneous neurophysiol neurophysiol purely caltech plays lost lost cellular air bower bower numerically odd odd interconnection abilities shifts imply spot spot spot spot wilson wilson natl fires slice reset irregular james studying surprising von von dependency bulb dif ensembles young arrive arrive locked locked locked locked locked locked locked locked locked locked matter broken broken ignore receiving receiving maintaining fellowship wiesel wiesel ram perturbed malsburg malsburg tight algebraic algebraic conduction segregation compensate mammalian signatures maintained maintained generators argued argued confirmed synchronized synchronized synchronized synchronized synchronized exceed regimes investigating oscillating distinguished locking locking locking locking locking locking responding responding responding gilbert gilbert geniculate port circumstances syn tom mcdonnell ferent oscillate oscillate award fre excited excited excited excited excited excited excited excited excited concerns continuum settle isolation isolation establishing appl comm comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator comparator acknowledges bauer christof daniel diverge initiated investigator cats tightly spots biophysics quency incident ther tics awake perturbing synchronize synchronize synchronize holmes holmes holmes holmes holmes holmes holmes eckhorn eckhorn eckhorn electrically kammen kammen kammen kammen kammen kammen kammen theor neglecting presidential crick lock lock engel tain rabbit erties neurophys perceptually perceptually perceptually flanking tex markedly markedly cornell bet intriguing postdoctoral connors connors ermentrout kopell regulate illuminated rand propor diffusive synchronizing pertaining evoke cer kruse philip preparations ksnig anesthetized decouple decoupling ithaca brosch prompted munk portrait fmax rnsec attrac llin llin unperturbed devia recipient characteris subserve chem superposed perturbs reitboeck doo doo reformulating disrupts subserving sists neurobiologically chronization 
#@Holmes_P,Kammen_D,Koch_C,
#t3
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#*network network model model model model model model model model model model model model model model model model model model model neural neural input input input input input input input input data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time networks networks networks networks networks networks networks networks number system system system system system system results results results results results results results information information models models models models models models based space weights case case order order order shown shown shown systems systems values parameters functions functions functions neurons neurons neurons neurons neurons point point point single single single processing processing large large local local local local neuron patterns analysis analysis analysis form shows shows shows simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual feature net net work work work methods fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points field field features features features features current cell cell cell cell structure structure high response similar similar architecture architecture architecture show show general general average average average average obtained obtained activity activity activity activity activity activity activity activity activity activity activity activity result computation research independent found found found found initial computer computer computer computer computer computer connections connections synaptic synaptic science left left phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal range range range range range range range press press components continuous continuous continuous continuous abstract properties properties properties properties properties properties references component component due important important important propagation introduction action action behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect generated generated generated generated energy difference spatial lower lower prior center previous previous previous cases firing firing cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike long long conditions represent distributed distributed make make fact region region region region region region region region proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed observed observed observed observed scale scale finite simulations simulations simulations resulting ing ing total total simulation simulation simulation simulation simulation simulation simulation simulation computed respect performed regions regions regions factor potential potential made feedback feedback feedback global study original relative specific represented cross cross cross cross cross cross cross cross cross cross cross cross location determined experimental experimental experimental experimental experimental cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain power power mit voltage comparison comparison contrast fields modeling modeling modeling institute synapses individual individual responses responses delay delay addition addition ai cambridge cambridge additional transition stimuli stimuli effects effects effects determine upper upper statistics statistics estimated basic basic basic con produce developed developed area velocity types types actual actual actual actual actual evidence nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory discussion discussion describe fast fast limited limited complete excitatory excitatory surface common common supported role role role role eds square degree degree sensory sensory objective simulated simulated simulated reduced reduced functional functional jordan technology increasing increasing increasing mechanism consistent consistent consistent consistent consistent structures structures trials trials trials principle principle principle representing details details numbers direct inhibition inhibition inhibition bottom idea idea combined produced produced produced produced produced produced run light light neuronal neuronal neuronal neuronal neuronal neuronal neuronal architectures membrane membrane membrane membrane improved population recent correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations lateral lateral period period period recently interest sufficient highly compare observations approximately works tions tions sparse address address locations locations locations symmetric modified modified modified channels channels interval organization entire entire increased increased suggests suggests trial trial trial trial spikes column demonstrate demonstrate flow strength strength critical central differences differences peak peak peak weak encoding strong integration presence characteristics characteristics california relationship program base acknowledgements areas areas areas areas explicit appears relation van van produces produces primary ann ann modeled modeled modeled modeled modeled averaging mutual events events shift shift shift implies versus potentials potentials focus dependence dependence correlated showed completely completely diagram key slow measurements measurements delays fitting intervals intervals event intermediate intermediate intermediate msec msec msec msec msec msec msec msec msec msec msec construction eeg eeg eeg koch koch coupling coupling coupling coupling coupling coupling coupling recorded recorded recorded fire currents inter discuss activated coupled variations gating structural major middle differ differ effectively included presentation oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory projections projections projections projections characteristic characteristic procedures induced induced allowing conductance oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations gray gray gray gray gray bar bar bar bar bar bar bar bar simplified absence realistic providing correspondence cat cat neurosci neurosci received illustrates rat intrinsic intrinsic intrinsic intrinsic intrinsic receive extend bars body origin stimulation essential exhibit circuitry circuitry strengths association association association association association association association association association association association association association limitations periodic periodic examine successive fashion fashion biol relationships relationships relationships relationships referred referred referred proper variability presynaptic topographic topographic topographic examined measurement onset rev rev voltages olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory obvious separated nervous fibers fibers fibers fibers fibers fibers fibers pyramidal pyramidal baseline generates extent extent extent integrate years site site preference directed directed distinguish adjacent biology lies sites sites sites sites division nucleus afferent afferent involve involve axons axons axons recording recording recording demonstrates auto auto auto auto auto auto radius radius nsf reflects greatly populations reflect reflect reflect reflect freeman freeman freeman freeman freeman offset share recordings ity release calculating rely mod measuring modulated synchrony serve pasadena singer coherent coherent coherent coherent electric kinds display display display fiber fiber fiber fiber fiber fiber fiber physiol coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence findings traces summed synchronization univ displays instantaneous instantaneous instantaneous cor lot lot spectra spectra cybern primarily velocities neurophysiol neurophysiol neurophysiol theories establish eliminated eliminated extending cellular cellular systematic systematic systematic bower bower bower bower bower bower bower bower bower bower contract shifts shifts shifts shifts implications wilson wilson wilson wilson wilson wilson wilson wilson periods connect james james corre induce dominant intended evident bulb bulb bulb reproduce axonal cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral contact sustained broken broken onr corporation ties distinction pointed connec trigger tendency tendency simulating evoked shaded modifying modifying conduction insights decays mammalian mammalian distant distant activate retinotopic efforts projecting lond rhythmic weaker weaker locking locking gilbert gilbert geniculate tract round topography triggered architectural covers continued inhibit oscillate interpreting termination reflecting transmitter caudal pronounced essen essen anatomy arrives governing contacts compartment establishing establishing establishing senses absent remained electrophysiological thresh bauer modulatory counted replicate replicate linking columnar excite activating rostral holmes compartments segev eckhorn eckhorn chi kammen clin clin asso asso compartmental panels panels piriform piriform piriform piriform piriform piriform piriform piriform piriform piriform piriform piriform piriform konig haberly haberly haberly haberly haberly lations lations readers engel travelling rabbit particu restored correla collateral mediating mediating reactions simplifications axial eet assure intriguing ditions initiate stimulate tude activ sinc kruse principally oscil ampli synaptically electroenceph electroenceph mil adrian adrian assertion diminished matthew brosch larly cotterill munk transmembrane transmembrane transmembrane coordinating chem excursions reitboeck eled 
#@Bower_J,Wilson_M,
#t3
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#*network model model model model model model model model model model model model model model model model model model model model model neural neural neural data figure figure figure figure figure figure time number number number number system system system system results results problem models models models linear case case order shown shown shown shown shown systems values weight weight weight neurons neurons neurons neurons neurons neurons neurons distribution distribution control control large large local local local neuron neuron neuron neuron rate class matrix matrix form form form form form shows shows shows shows shows simple small net work fig fig fig fig fig fig cells cells cells cells cells process current cell cell cell cell cell cell structure high high similar similar show equation equation equation equation section fixed line line general average states theory theory theory term term experiments experiments experiments experiments experiments experiments activity activity activity dimensional result result university university threshold threshold research research found found found found found found found found target target dynamics initial constant constant constant constant computer computer connections connections connections synaptic synaptic synaptic synaptic science science science left left left left map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map temporal nonlinear abstract computational computational computational computational computational computational properties references important introduction introduction circuit stimulus effect effect generated tion tion tion tion difference complexity rules prior part part previous previous good conditions distributed distributed equations equations make make make fact observed observed observed simulations resulting resulting ing total total simulation simulation simulation simulation simulation sum called regions means means factor factor made made made made made obtain relative specific represented represented provide provide proc proc proc eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye posterior brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain support institute department synapses synapses represents represents exp exp bias addition maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps experiment experiment experiment experiment experiment experiment experiment experiment additional view solutions solutions solutions solutions top top effects effects effects effects effects effects choice area types provided provided finally evidence nature nature nature nature inhibitory depends biological achieved normal normal normal normal normal normal normal normal normal normal normal normal normal normal increases describe corresponds circuits circuits amount amount nearest nearest synapse synapse generate main square end end end end end ability easily degree development development development development development development development development development development development account account coefficients significantly mechanism consistent consistent consistent details details details details decay combined produced produced produced produced neuronal denotes reported lateral introduced recently highly observations correspond correspond studies differential trans diagonal diagonal diagonal diagonal diagonal modified modified entire occur extended matrices rotation correctly correctly half half half half half half half half half half half strength starting hebbian hebbian hebbian hebbian conclusions central interactions interactions interactions interactions interactions interactions interactions interactions measures retina retina retina retina retina retina retina retina retina retina exponential practice constrained demonstrated california proportional proportional variety variety exist exist exist decrease targets targets acknowledgements areas suppose suppose suppose appears winner mathematical involves remaining consisting interaction develop develop develop develop develop mutual blocks formation formation formation formation formation formation formation formation formation formation dependence squares influence controlled organizing fraction allowed partial earlier earlier reasonable classical expansion expansion neighborhood initially foundation foundation existing combinations retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal specifically candidate neighbors neighbors neighbors reason middle aspects capable modification driven included committee literature projections genetic tend tend tend tend soc soc soc soc interpreted lie receptor receptor comp comp comp absence neurosci subsequent intrinsic intrinsic intrinsic oriented oriented cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan replaced fashion fashion terminal biol biol biol biol plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity possibility relationships referred pathway pathway surfaces surfaces surfaces removed removed induction induction induction induction coarse coefficient adapt changed eyes eyes friedman friedman friedman friedman friedman der der obvious nerve nerve nerve nerve hebb ith ith ith ith ith fibers isolated established indicating growth growth growth growth growth growing fairly explanation answer lies ganglion ganglion ganglion ganglion ganglion considerable considerable purposes sites sites sites sites widely organized incorporate incorporate mathematics axon axon axon axon axon axon axon separately axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons res res res patches geometric apparent apparent apparent double simulate simulate simulate simulate formulated measuring anti anti modulated incoming incoming incoming incoming extensions replace physiol eventually univ globally sort forming forming rotated neurophysiol jth jth jth jth connecting theories interconnected fails fails fails fails ments chemical biased neurobiology fail imply optic optic optic optic modifications eqn eqn eqn eqn eqn eqn eqn contexts combines edelman edelman edelman corre von expanded expanded expanded expanded expanded expanded expanded topological topological topological topological fish fish fish specialized occlusion axonal axonal axonal axonal axonal axonal axonal gaze gaze gaze gaze specificity specificity specificity specificity specificity specificity contact contact contact contact contact contact roy roy roy roy projects harris harris explains explains discovered discovered discovered intersection material material influences outlined compressed compressed leaving outline incorporates graded wiesel willshaw willshaw willshaw willshaw willshaw willshaw willshaw terminals lesions ease malsburg malsburg malsburg malsburg tendency tendency hubel chicago chicago chicago possibilities possibilities possibilities molecular molecular molecular molecular illustration monocular mismatch mismatch mismatch peripheral preserved favor interact lobe permits inverted inverted inverted expand retinotopic retinotopic lond lond lond cij cij cij cij cij cij cij cij cij cij cij cij cij attached attached refinement molecules molecules molecules molecules molecules molecules tissue vice species species species species species species reversal versa sponding reversed ave compete compete diffuse establishes tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum contralateral contralateral contralateral contralateral caudal caudal kth illinois polarity polarity polarity polarity neurol neurol neurol markers markers markers markers markers markers markers markers markers markers markers markers markers markers markers comprising sij sij sij sij sij sij sij sij intact intact contacts contacts contacts contacts alto molecule molecule positional positional schmidt schmidt schmidt schmidt schmidt schmidt schmidt schmidt schmidt halves occluded stick stick stick stick stick stick stick stick inappropriate supposed replicate addi addi palo terminology terminology amer frog frog tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal expresses expresses disorder tal yon iris phil simulates simulates simulates rostral rostral respects devel ele mediate mediate comprises postulated postulated postulated subtract displaced vertebrates occupied concentrations exclude cooke cooke correspondingly meyer meyer meyer meyer meyer meyer meyer reproducing mature exposition plex expressing compound compound compound preferentially preferentially mediating mediating cited cited presumed presumed regeneration regeneration regeneration regeneration regeneration regeneration regeneration regeneration nasal nasal pnas fragments fragments yoon yoon patchy patchy biochemical prefers innervate cutting retinotectal axo axo axo axo axo axo axo axo chung chung onal marion hunt hunt collins collins reorganization reorganization tips tips scrambled retino retino retino retino retino retino retino eqns carded rig adhesion adhesion adhesion naptic schwarz schwarz fraser fraser innervating mediates dispersed regenerate superposed frogs frogs nonspecific contradict polarized adhering 
#@Cowan_J,Friedman_A,
#t3
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#*network network network network network network network network network network network network network network network network network learning learning model model model model neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set training training training algorithm output output output output output output output output output output output output output output output output output output output output number number system system system system system system system system system system system system results results results units units units units units units units units units units units units units units information information models models hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case shown shown shown systems systems values values values values probability probability probability probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution pattern point point single single single single single single processing processing processing neuron neuron test test test test patterns analysis analysis optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple gaussian gaussian gaussian paper paper examples net net net net net net net net net net net net net task task task task task cells cells cells step points level level level level level cell cell cell cell random random random random random random random random random random memory memory response response response response response response response response response response response response response response response response response response response response response response response response response response response similar representation representation show show show equation section fixed general general general parameter real states theory theory theory note note activity result result result result university threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables computation computation research research research research independent independent defined found sequence sequence target target target constant constant constant constant standard standard computer computer computer computer computer computer terms connections connections synaptic synaptic synaptic science science science science left left presented present present present present present present present activation activation activation activation activation activation activation activation activation nonlinear outputs outputs continuous continuous continuous continuous abstract applied computational density density references stochastic due positive positive procedure procedure introduction action behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect parallel recurrent recurrent recurrent recurrent change change change change change change change change change change variable variable variable variable variable variable variable assume assume assume measure signals prior part part previous theorem theorem theorem theorem cases firing cortex long conditions conditions conditions conditions conditions conditions represent represent represent distributed distributed distributed distributed distributed expected fact proposed proposed correct correct probabilities observed resulting simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation human human human called elements elements elements elements elements elements mapping means means means means made study obtain negative negative negative compared compared provide rates perform determined determined related distributions distributions distributions gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain motor motor discrete cortical cortical brain brain brain brain contrast connection train proceedings proceedings report report report words department version internal individual individual individual individual individual individual responses bias bias bias bias layers layers layers layers layers addition graph graph equivalent directly hinton curves curves curves top top stimuli stimuli effects effects effects effects effects effects effects effects effects effects effects detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection determine determine determine determine determine significant approximate increase increase increase con produce condition condition developed criterion actual actual finally finally processes backpropagation inhibitory inhibitory inhibitory inhibitory achieved discussion discussion normal normal normal normal normal technical increases increases increases increases increases increases increases describe assumption excitatory excitatory excitatory excitatory amount amount common common assumed assumed shape shape require require journal ability ability instance sensory including auditory typically account account account account account block significantly ratio ratio increasing increasing increasing increasing increasing increasing increasing increasing increasing increasing increasing increasing increasing empirical leads call call call call inhibition bottom bottom bottom attention attention attention combined added added added added added added added neuronal improve improve improve robust ensemble ensemble takes element element element typical reported reported identical sejnowski cognitive cognitive cognitive sufficient approximately subjects subjects subjects subjects subjects module module axis axis yields correspond correspond correspond studies chain chain chain chain chain chain chain chain chain chain chain chain chain chain interval improvement improvement improvement improvement sensitive entire increased increased increased increased increased lead lead deviation wide occurs occurs strength strength conclusion place assumptions assumptions reduce valued depend depend central central interactions measures suggest mechanisms presence presence presence presence presence presence presence presence presence presence presence drawn start decrease targets areas suppose appears relation relation van produces solving ann remaining events events potentials select letters letters decreases decreases decreases decreases national family family family dependence review review depending overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap modulation centered centered suggested converges converges converges constants discrimination additive performing event event false false false false false false false false remains remains intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate david illustrated illustrated variations major letter letter closely suitable society detect detect post receives receives excitation graphs graphs induced induced showing showing interpreted neuroscience physiological quantity vary write absence absence absence absence absence absence absence absence absence absence absence correspondence cat neurosci subsequent operating satisfies layered relations humans mass reducing school school behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral proved affect affect affect affect affect affect affect removed analyze predicts psychology psychology rev adjusted panel panel logistic logistic logistic logistic logistic nervous nervous consist baseline baseline improving improving explain motivated optimum mentioned convolution convolution analytical stress closer closer strictly strictly strictly strictly precisely monkey afferent afferent afferent arises arises cybernetics preceding mellon mellon fluctuations reflects improvements improvements improvements varies behaviors carnegie carnegie applies reflect freeman cmu simulate cohen cohen cohen cohen cohen cohen incorporated psychological release release release release release pittsburgh maximizes logical decreased findings differentiable distortion phenomenon phenomenon proofs primarily appearance member acts null enhancement enhancement children wrong analogy stated stated hit biased resulted analyzing fail monotonically affected affected adequate motivation tone tone tone induce displayed consequences consequences assembly arrangement modelled foundations young indicator extensively extensively impact impact projects projects ignore receiving receiving pdf pdf pdf pdf pdf pdf consecutive rms cooperative terminals copy copy solely evoked cns cns argue manipulation arising concentrated relate mediated relating careful relates academy amino reveal alarm scanning spite clinical circumstances payoff pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs monitor monitor agents adult dropped affecting alarms alarms alarms alarms alarms alarms alarms separates clark ignores inspection convolved acid dopamine dopamine dopamine lewis absent absent absent remained schreiber schreiber schreiber schreiber schreiber schreiber schreiber bauer convey servan servan servan servan servan servan putative hits detections modulate asymmetry drug rises arousal yon optimizes abnormal disorders bio reviews enhancing berger illustrating lasting convolving claimed translating jonathan diverges psy vigilance vigilance categorize administration mediating depict discriminability pathological presumed males misses misses misses misses misses misses misses investigators investigators ryan adults substances payoffs neuromodulatory harry bulletin steadily steadily freedman intuitions continous pharmacological implicated imbedded neurotransmitters neurotransmitters obscure rigidly awe psychiatry conventions olivier modula norepinephrine chology dividual 
#@Cohen_J,Printz_H,Servan-Schreiber_D,
#t3
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#*network network network network network network network network network network learning learning learning model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input function function function function function function function function figure figure time time time time time time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks output number number number number number number system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state results results results problem problem models based space space weights weights case case case case order order order order order order order order order shown systems probability probability probability probability probability probability probability probability probability probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution single single large large large local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns analysis analysis matrix matrix inputs form form form form shows shows simple simple simple simple small small small small size net net work work fig fig fig cells cells cells points features process process current current current current current current current cell cell cell cell cell structure high high high memory memory memory memory memory response response response response response response response response equation equation equation equation equation equation equation equation equation equation equation equation rule real real real approximation approximation average states states states states states states states theory theory theory term term term note note note experiments experiments experiments experiments dimensional dimensional result university threshold computation defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant standard standard terms terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic prediction direction phase motion motion motion maximum maximum press press press learn continuous continuous abstract abstract find find find find computational properties references stochastic stochastic introduction action action action action statistical statistical statistical statistical effect generated generated tion energy energy energy energy energy energy energy energy energy assume rules higher higher previous theorem firing firing firing firing firing firing firing firing firing firing firing type multiple good binary spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike equations make techniques length finite finite simulations simulations simulations minimum resulting ing total total computed computed multi multi sum sum eq eq eq eq regions means potential potential potential potential potential natural global global study obtain obtain original vol relative relative relative relative relative true application rates rates rates rates rates rates proc proc perform active active determined related constraints connected connected mit larger contrast connection connection connection connection train train dependent modeling modeling department department synapses final exp addition cambridge cambridge cambridge equivalent equivalent equivalent experiment additional view limit limit limit limit effects effects requires significant statistics weighted finally evidence nature biological biological biological associative associative discussion transformation limited close corresponds stable stable stable stable stable stable stable surface surface surface predictions circuits short effective effective effective effective assumed assumed assumed synapse eds journal instance makes makes including including fit auditory probabilistic probabilistic probabilistic needed hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield account dynamical dynamical coefficients fully transfer interesting interesting ratio ratio ratio character york mechanism mechanism special uniform pre direct direct stored normalized normalized idea choose description description description description description description predict neuronal neuronal neuronal recent advantage apply introduced introduced introduced sense sense sense sense relevant varying compare works tuning solve yields yields differential achieve achieve separation separation channels interval concept studied invariant suggests suggests spikes spikes spikes spikes spikes spikes spikes spikes spikes deterministic runs strength strength strength strength strength starting critical critical critical critical reduce conclusions depend depend central interactions sigmoid accurate numerical numerical clear exponential exponential practice temperature temperature temperature temperature temperature temperature taking strong presence physics cycle california relationship derivatives connectivity force force boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann monte carlo longer transitions stability stability explicitly explicitly explicitly slightly unique scales scales scales interaction interaction equilibrium equilibrium equilibrium equilibrium equilibrium formed implies blocks potentials potentials potentials yield stationary stationary stationary stationary stationary stationary stationary interpretation solved detailed detailed showed showed evolution evolution forms forms forms constants constants constants reasonable calculation calculation calculation reduces roughly generation intermediate coupling coupling coupling building existing fire coordinate usa usa currents currents currents currents currents weighting retinal memories memories memories memories memories prove coupled coupled coupled phys phys major driven driven included spiking spiking spiking spiking spiking spiking spiking post post post post post post post post post post post essentially fine strongly strongly strongly induced anderson symmetry sci sci write write usual michael relaxation relaxation relaxation relaxation realistic realistic realistic realistic observable received received attempt subsequent neighboring receive access strengths strengths strengths rise rise rise ideas ideas scaled func understand understand analogous analogous analogous analogous surfaces neu math coefficient naturally naturally predicts rev rev precise nerve hebb attempts isolated isolated isolated established devices asynchronous agreement convolution improves biology analytic diffusion tractable ganglion spatially berkeley berkeley closer precisely forces consequence ion acad acad describing describing opt opt calculations begin lowest recognizing qualitative qualitative fluctuations mechanics mechanics mechanics mechanics behaviors percent understood relevance relevance effort biologically ity poisson poisson poisson poisson poisson fall fall fall collective asymmetric conclude attraction attraction attraction attraction physiol deviations lim instantaneous physiology martin ratios ratios nat nat neurophysiol purely purely connecting theories adjusting adjusting adjusting adjusting balance balance abilities guide carry sompolinsky sompolinsky sompolinsky weakly falls bialek bialek bialek bialek bialek consequences captured hippocampus treatment clean speeds lett summarize convergent ics fired fired discharge approx emission rigorous deriving basin descriptions basins basins basins basins suppressed imagine molecular favor favor biophysical mammalian thermodynamic thermodynamic thermodynamic thermodynamic maintained elementary jij interacting interacting proba relate confirmed guided breaks happen inverting gordon treating microscopic mcculloch mcculloch mcculloch reversal simplification excess bility pitts pitts pitts agrees confirm confirm inclusion inclusion stay rons injected mcnaughton mcnaughton fastest william sity planck planck planck planck planck evolves edition granule ically dissipation inappropriate probabil damping asymmetry asymmetry altering obeys fractional eta topics invert fluctuation excitable imation schematically accessible quiescent quiescent biophys positively complexities amit amit bull symmetrically testable dynam fokker fokker fokker fokker fokker poten contiguous univer renders charging complication jii barnes amir amir amir theme brownian probabilistically absolutely experimen comment comment emitted gutfreund gutfreund gutfreund questionable inertial kybernetik alters alters alters alters stimulate necessitates increas diffusive lows friction folding kleinfeld dissipative elevated tally ive calibrate phenomenological realism gustafsson gustafsson dyi arranging taneous ike langevin langevin langevin excursions excursions specif diffuses gether kleinreid instan destroy destroy tials 
#@Bialek_W,Crair_M,
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#*model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure networks system system system system system system system system system system results results results results results results results results results results results results results results results information models based based based based based based layer layer case case shown shown shown shown shown systems neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern single single single processing control large large local neuron test test patterns patterns patterns patterns patterns patterns patterns inputs shows visual paper paper small small work work work cells cells cells cells cells cells cells cells cells cells cells cells cells cells step field features features features features features level current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure structure structure structure similar similar similar representation representation representation show section section general real real real obtained experiments experiments experiments experiments experiments experiments experiments activity activity activity activity activity result computation research found found found computer computer computer computer computer computer computer connections prediction left direction presented map map map map map map sets press press press basis sample abstract convergence convergence properties properties references positive introduction introduction introduction complex circuit circuit circuit circuit behavior generated spatial spatial spatial spatial spatial spatial representations center previous previous previous cases cases firing multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex represent represent represent represent represent fact fact techniques techniques techniques techniques techniques techniques techniques techniques region region region region region region region region proposed proposed correlation correlation correlation correlation scale simulations resulting resulting ing simulation simulation simulation simulation simulation respect respect called times regions regions regions regions regions regions regions regions regions regions regions regions mapping mapping made study study knowledge specific represented cross cross cross series receptive receptive posterior constraints cortical brain brain brain brain brain brain brain voltage contrast fields dependent dependent source source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling institute consists code individual layers addition maps maps considered experiment experiment directly view basic developed area area area area types finally biological describe describe limited limited assumption excitatory surface surface predictions common supported role hypothesis objective simulated simulated simulated simulated simulated simulated simulated simulated smaller account functional functional functional functional functional coefficients technology projection projection projection projection projection projection projection projection projection projection projection projection mechanism structures principle principal principal representing details direct direct light neuronal directions recent correlations correlations correlations resolution similarity lateral lateral lateral lateral include include subject engineering highly highly varying compare compare approximately approximately volume studies studies studies converge organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization entire entire grant constructed constructed horizontal parts extended extended clusters clusters clusters demonstrate conclusions accurate clear suggest suggest propose strong demonstrated california labeled exist exist movements plane plane relationship relationship targets manner groups program acknowledgements areas areas areas areas areas areas areas areas areas van van ways generating vertical modeled modeled involves unique scales springer focus review correlated correlated correlated correlated overlap influence influence influence detailed detailed detailed detailed open restricted restricted lee lee lee lee lee modulation understanding understanding understanding understanding understanding sizes activities suggested suggested suggested suggested partial partial roughly boundaries recorded figures figures figures figures figures figures coupled characterized structural major major determining included included oscillatory projections projections projections projections projections projections projections projections projections projections projections projections projections projections fine fine receives receives characteristic summary soc verlag procedures strongly showing showing interpreted physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological comp comp comp comp involved localization simplified cat cat cat neurosci neurosci neurosci neurosci principles attempt neighboring neighboring rat rat rat rat rat rat rat rat rat rat rat rat oriented oriented oriented extend extend presents body body body explore explore transformed exhibit detail divergence divergence project project project project biol relationships relationships variability variability topographic surfaces surfaces circles concepts concepts predicts olfactory portion assumes mapped nervous nervous academic fibers fibers fibers fibers fibers fibers submitted submitted electronic years site site adjacent adapted adapted adapted adapted briefly comparisons sites organized organized organized producing strictly nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus monkey arise arise afferent afferent afferent afferent circle res res res patches patches patches patches patches patches patches recording apparent apparent apparent greatly reflect profile pathways pathways pathways dark dark dark effort effort effort effort effort summarized serve pasadena conductances conductances simulator kinds fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber physiol physiol contribute contribute physiology physiology labeling labeling labeling labeling appearance appearance investigation caltech caltech climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing cellular bower bower bower bower bower bower bower bower bower bower bower bower anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical chemical cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum bands bands bands neurobiology neurobiology neurobiology unlabeled implications filled inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior inferior cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar james intended intended injection cerebral cerebral suggesting master master reverse davis receiving outlined shading shading shading users ram ram revealed revealed revealed diverse smoothly hundred tendency tendency tendency simulating spinal streams visualization peripheral publication publication trends grouped mammalian mammalian lobe lobe lobe lobe distant efforts efforts lond lond records nuclei sheet afferents afferents investigations places tract tract tract tract tract tract microscopic vice topography topography topography rats rats served electron fiat versa resolve resolve influenced influenced thousand thousand ferent king king somatosensory somatosensory somatosensory broadly purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje supplied essen essen anatomy anatomy conflicting anterior anterior anterior anterior couplings neurol neurol neurol neurol coincide tactile tactile tactile tactile tactile tactile tactile tactile chan chan interpretations functionally alan alan wisconsin ionic ionic electrophysiological nih unusual granule granule granule granule granule granule granule granule houk syst zones zones zones replicate medial adv zone replicates neurones neurones severely campbell campbell campbell campbell remarkably electrotonic ito ito enhancing des ago gibson gibson gibson genesis genesis genesis mossy mossy mossy mossy mossy mossy mossy mossy mossy mossy mossy mossy conflict conflict abstr vitro vitro bull responsive mosaic 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#@Bower_J,Lee_M,
#t3
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input function figure figure figure figure figure time set set networks networks networks networks training training output output output output output output output output output output output output output output output output number number number system system results results results results results units information information information information information information information models models models models models models based based based based based based weights weights case case order values values probability probability parameters parameters parameters noise noise noise noise functions neurons neurons neurons neurons neurons distribution distribution approach pattern pattern pattern point point image image image image image image single single single single single single single single single single single processing processing processing large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test patterns patterns patterns patterns inputs inputs simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper examples small size size cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field features features process process process current current cell cell cell cell cell cell cell cell cell cell cell structure problems random random random random random random random random response response similar similar architecture section fixed rule rule rule rule rule rule rule rule rule rule rule images images images images images general parameter parameter parameter average average average average average average theory theory gradient experiments experiments experiments experiments experiments experiments dimensional result threshold threshold threshold threshold threshold threshold independent independent found sequence constant standard connections connections synaptic synaptic synaptic synaptic presented present low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal motion maximum maximum maximum maximum maximum maximum maximum maximum press press learn learn learn learn learn learn learn position outputs abstract density analog properties references references stochastic stochastic stochastic positive positive positive important introduction behavior stimulus stimulus statistical parallel change energy energy difference variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume rules rules rules rules learned learned learned learned chosen chosen center center previous previous previous previous previous theorem cases cases type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long distributed distributed distributed make make region correlation observed observed observed observed observed scale scale scale simulations simulations minimum minimum resulting resulting sum sum sum called elements made natural natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global global filter filter filter filter filter filter filter negative negative specific represented receptive receptive receptive receptive receptive receptive receptive receptive compute proc location eye eye eye experimental experimental cortical cortical cortical cortical cortical cortical brain comparison larger contrast fields fields fields fields fields support dependent report version version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses individual advances represents represents exp addition computing equivalent environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment curve curve curves curves curves curves curves curves limit limit top stage stimuli stimuli stimuli effects effects effects effects effects effects detection detection conference determine choice choice choice choice free basic increase con condition derived randomly randomly developed developed criterion types types lines lines lines lines lines lines iteration nature nature inhibitory inhibitory biological biological biological biological discussion normal normal normal normal normal normal limited limited complete excitatory excitatory excitatory excitatory predictions predictions shape shape synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse generate end end end pixel pixel pixel pixel pixel pixel development development development development simulated pairs smaller ratio ratio york edge edge mechanism matching principle call iterations max filters direct bottom early decay decay decay combined produced choose run population population recent correlations property robust ensemble typical typical lateral period pixels subset array array array array array array engineering interest approximately calculated positions organization sensitive increased studied studied studied suggests deviation wide predicted width width white white half strength critical place place row row hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian conclusions depend central interactions differences retina retina learns suggest propose strong hard hard mechanisms physics external variety exist selective selective selective selective selective selective averaged groups configuration acknowledgements pro van van van edges edges edges generating laboratory tuned tuned tuned tuned vertical mathematical mathematical mathematical involves slightly slightly text text develop frequencies frequencies yield review depending correlated communication overlap viewed restricted organizing fraction evolution evolution forms sizes constants constants event event roughly closed intermediate filtering calculate calculate sufficiently foundation foundation koch usa retinal retinal retinal retinal retinal retinal determines variations black black reason importance differ modification modification modification modification effectively detect detect detect detect post characteristic characteristic characteristic characteristic summary quickly kind strongly allowing anderson anderson interpreted symmetry running content physiological strategies sci satisfy bar bar bar surround hypotheses thresholds thresholds cat cat cat principles attempt satisfies oriented oriented oriented oriented oriented oriented bars bars bars bars unlike unlike stimulation selectivity selectivity selectivity carried carried carried wiley production collection essential experience environments environments environments environments limitations periodic respond history mappings biol biol plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity structured structured structured structured structured structured structured structured structured structured structured comparable cover understand contours contours matched matched circles circles circles circles circles plausible predicts equally equally equally changed changed ensure adjusted portion assumes observe hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb academic initialized regime explain electronic averages developing trivial growth growth growth orientations orientations orientations orientations orientations orientations orientations biology biology adapted spatially straight straight straight straight arc arc arc arc filtered filtered filtered filtered filtered filtered filtered filtered desirable afferent products acad circle circle definite res lowest linsker linsker linsker linsker nsf explained apparent populations populations applies reflect pathways dark offset tional simulate simulate experimentally experimentally lack cohen adjustable adjustable treated sharp biologically calculating serve qualitatively curvature curvature pasadena pasadena adjust decreased shaped shaped shaped shaped shaped physiol implements yuille yuille yuille yuille yuille yuille univ consistently representative cybern secondary modify restrict ratios arguments animals animals animals animals animals animals circular circular circular circular harmonic jones jones jones jones theories theories grey caltech caltech caltech caltech spontaneous cellular primate striate striate striate efficacy efficacy shifts preparation exceeds arrays enhanced natl overlaps periods james appendix appendix induce induce induce displayed overview overview competing exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure laplace laplace laplace multiplied diameter emergence young insight reveals storing sons influences ence arcs emerge breaking alter constrain cns exponent community evolve alternate interneuron shannon shannon shannon mammalian mammalian activate regimes regimes rectified rectified million million maintains maintains responding accounted modifiable bill experi examination mann develops removes differently palmer palmer palmer palmer bienenstock excess excess excess mcdonnell rfs rfs rfs rfs jersey opponent stripes stripes stripes stripes stripes pictures pictures award illinois essen essen formulae fre polarity polarity exposed exposed exposed exposed exposed striking striking proposes proposes ref trol restricting ory decaying enhances enhances william lnp curved curved curved curved curved fol absent gence addressing thresh thresh thresh thresh acknowledges artificially substrate indi deciding ini ini ini ini christof saturate saturate daniel spanning refine urbana publishing plastic investigator movshon altering stryker stryker abnormal abnormal hirsch hirsch hirsch examines quadrature quency modulating thorpe postulated confirms remember wired kammen kammen kammen kammen kammen kammen kammen kammen kammen kammen kammen kammen lowing corresponded stripe stripe stripe distinguishes explores unstructured presidential softky softky softky softky softky mature mature mature mature mature mature fellow quences acuity rings rings rings resonant neurophys neurophys zucker debate depended portant collectively intro questionable overlaid postdoctoral conservation ezp documented florida envelopes envelopes divisions divisions annular annular vide weizmann overlapped barrow barrow occured exposures vidual orderly caution conse lobes lobes coincident distinctly naptic cynader expose ablex weaver weaver maturation immature emer reared illuminating bent abnormally exposing dobbins dobbins 
#@Kammen_D,Softky_W,
#t3
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model neural input input input input input input input input input function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks number system system system system state results results results units units units units units units units units units units units units units problem models models models models models models models models models models models models models models models models models 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small small net work work work work work work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells process cell cell cell structure structure structure structure structure structure structure structure random random random random random random high response response response response response response response response response response response similar similar similar similar show show show equation section section line line line rule rule general average obtained note note note note note note note note note activity activity activity activity activity activity activity dimensional university university university threshold computation solution solution dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant computer computer connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic science presented presented present present present present present activation activation frequency frequency frequency maximum maximum range range range range range press components basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied density density properties properties properties references references due due due positive positive complex complex behavior stimulus generated difference difference variable spatial spatial spatial spatial spatial spatial spatial spatial lower chosen chosen part part center previous firing firing type cortex cortex cortex conditions represent represent expected equations equations equations make make make proposed scale scale scale scale scale scale scale scale scale scale scale scale scale simulations simulations simulations simulations resulting classes total total simulation simulation simulation computed sum regions potential orientation applications relative specific specific provide provide rates rates eye related connected gain gain gain cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain equal connection connection connection connection connection connection connection connection connection connection connection connection connection connection fields modeling selection report report institute institute version synapses internal internal internal internal internal internal internal internal internal internal internal internal internal internal individual responses layers addition maps maps maps considered considered considered considered domain additional solutions curves limit upper choice basic con con developed types types provided provided inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological biological covariance covariance technical arbitrary group limited limited inverse complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable short short shape synapse supported theoretical theoretical adaptation journal journal hypothesis hypothesis hypothesis makes development development development development development development development development development development development development development development development development development development sensory including reduced account dynamical dynamical dynamical interesting york mechanism mechanism mechanism mechanism structures structures structures structures structures structures structures structures uniform empirical iterations iterations iterations pre pre inhibition inhibition inhibition inhibition inhibition inhibition inhibition decay decay decay attention description neuronal neuronal population population exact typical lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral include include period sejnowski sejnowski observations approximately approximately tions yields correspond correspond correspond trans address address positions separation symmetric organization organization organization sensitive grant grant exists parts occurs occurs generally column minimal greater greater hebbian hebbian hebbian hebbian hebbian hebbian hebbian depend depend modules modules modules modules peak peak moody moody moody moody moody moody moody moody moody moody moody moody moody moody moody suggest strong mechanisms presence sigmoidal sigmoidal sigmoidal sigmoidal demonstrated solid solid solid solid solid variety exist selective averaged groups connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity program program acknowledgements longer longer factors factors factors laboratory distinct linearly physical electrical scales scales scales scales scales scales interaction develop develop integrated integrated gaussians potentials john john john john john john focus focus formation formation formation formation formation formation formation stationary solved solved detailed detailed detailed transform densities densities densities densities restricted ocular activities activities activities dashed dashed dashed dashed additive additive additive additive additive additive additive additive additive additive additive additive purpose add add intermediate intermediate intermediate intermediate sufficiently foundation box activations activations dominance dominance color plotted illustrated illustrated coupled variations simplicity columns columns columns columns identified driven modes identify post post identity composed excitation excitation excitation excitation excitation soc interpreted neuroscience neuroscience neuroscience symmetry symmetry symmetry symmetry symmetry symmetry symmetry receptor receptor receptor relaxation relaxation relaxation relaxation modular modular modular modular modular modular modular modular modular modular modular modular modular realistic realistic correspondence cat attempt operating operating preferred preferred intrinsic cowan cowan remain american essential essential essential requirements requirements requirements requirements requirements exhibit exhibit exhibit exhibit put steady association limitations limitations dotted helpful existence existence rise rise fourier fourier giving biol plasticity scaled scaled scaled authors complicated complicated func topographic fundamental neu math possibly necessarily analyze analyze illustrate olfactory olfactory freedom nervous nervous nervous nervous hebb hebb hebb academic simplest submitted explain wta established established ment developing developing crucial adapted diffusion diffusion diffusion nonlinearity nonlinearity spatially spatially spatially drive stanford stanford mation afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent scientific universal medical medical localized localized localized localized localized localized behaviors populations substantially empirically offset lattice lattice peaks remove biologically howard howard exhibits exhibits exhibits gains gains incoming collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective enables enables comments phenomenon phenomenon phenomenon picture uncorrelated physiology temporally homogeneous homogeneous homogeneous homogeneous homogeneous jth purely spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous cellular cellular smith anatomical anatomical anatomical fan fan fan chemical neurobiology preparation carry edelman loo loo dendrites induce induce induce intended intended somatic somatic somatic emergence emergence emergence emergence emergence emergence axonal cerebral theoretically contact projects variants variants tures receiving onr yale yale yale yale yale yale neurophysiology geometrical email shunting shunting shunting shunting shunting shunting shunting shunting shunting reaction reaction reaction emerge emerge breaking breaking breaking breaking breaking molecular clustered biophysical mathematically graduate interacting interacting hughes hughes afosr frontal cation breaks breaks intl modality modality gordon struc develops drives stephen tial transforming solvable somatosensory somatosensory stripes adult december pearson pearson pearson pearson pearson alex alex eral anatomy station continuum continuum continuum possess functionally alan dog dog dog dog neutral neutral spa emerged zones col daniel modularity modularity modularity modularity modularity modularity modularity modularity modularity modularity modularity modularity modularity modularity modularity modularity tivity plastic plastic plastic boosted jack elaborate haven magnification magnification magnification magnification magnification magnification spots ular turing turing columnar columnar phil extrema hypothetical nonlinearly translational translational terry exhibiting ronald spontaneously hypothesize beckman shepherd laterally bimodal finkel idealized george gerald anatomically anatomically quantum blobs chemistry subdivided lat consequent wrap sidered tractability ported mountcastle ciently pursue electrophysiology hibitory ins timesteps tral abbreviated quently unavailable subse phe connectivities connectivities lective exci conjectured timescale ferred richness shunt taneous speculative spon operative operative elucidate velopment orga impetus hibition 
#@Chemjavsky_A,Moody_J,
#t3
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#*network network network network network network model model model model model model model model model model model neural neural input input input input input input input input input input input input input input input input input input input input input input input input input function function figure figure figure figure figure figure figure figure figure figure figure time time set set set set networks networks networks networks networks networks networks training output output output output number number number system state state state state results results results units units information information information information information models models models linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case order shown shown shown shown systems values parameters weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons unit method method single single single single single processing processing control large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate inputs inputs inputs inputs shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal visual visual small small work work fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells level level level level level level level cell cell cell cell cell cell cell cell cell cell cell cell cell cell response response response response response response response response response response response response similar similar similar show equation equation equation equation equation line line line line line line average average average average obtained activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold research independent independent independent defined defined found target initial initial initial initial initial initial initial constant standard standard computer terms terms terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic prediction prediction prediction left left present present activation frequency frequency frequency frequency maximum abstract applied find analog analog analog analog analog analog analog analog analog analog analog analog properties references due propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction stimulus effect effect effect effect effect generated change change change change assume signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals chosen higher higher previous firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing cortex cortex cortex good spike spike spike spike long conditions conditions distributed distributed distributed distributed distributed distributed proposed proposed correlation correlation observed finite simulations simulations simulations simulations simulations resulting simulation simulation computed eq eq times times times elements potential potential potential potential potential potential potential potential potential study vol relative relative relative relative cross cross receptive compute compute rates rates experimental cortical brain equal accuracy contrast fields source source source source source source report institute department department synapses code code code individual kernel represents layers layers layers layers layers layers equivalent equivalent curve additional additional additional top top top effects effects effects effects effects effects increase condition coding levels levels levels levels levels levels levels levels levels levels levels levels area nature depends depends simply biological biological biological measured measured measured measured discussion increases increases increases increases tested limited close corresponds circuits common common common common supported role degree degree degree underlying reduced reduced reduced account dynamical dynamical dynamical jordan significantly significantly significantly ratio ratio york mechanism mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode principal pre bottom bottom depth depth depth depth magnitude magnitude decay produced produced produced produced produced produced sources sources sources description description membrane membrane membrane membrane membrane membrane membrane membrane population population discussed recent correlations correlations correlations correlations correlations typical period period period period period period period period identical relevant sufficient sufficient varying previously observations studies observation generalized interval organization organization increased grant grant amplitude amplitude amplitude amplitude deviation deviation derivative predicted occurs strength strength strength strength row row trajectories trajectories designed peak peak peak peak asymptotic asymptotic asymptotic weak mechanisms mechanisms physics physics physics external solid solid solid solid manner areas areas relation relation relation relation longer factors primary primary primary mathematical changing changing modeled simultaneously simultaneously springer decreases yield focus dependence transform fraction modulation understanding approximated reasonable reasonable slow iterative msec msec msec msec msec msec msec msec msec msec msec sufficiently sufficiently sufficiently sufficiently fire fire fire fire figures figures figures specifically absolute absolute characterized identified divided effectively effectively modes modes modes modes modes modes spiking oscillatory repeated strongly interpreted oscillations physiological hold gray simplified simplified providing wave neurosci illustrates illustrates subsequent subsequent subsequent receive receive simpler american layered layered layered layered layered layered layered layered layered investigate exponentially rapidly rapidly dotted dotted mass existence rise examine successive successive respond giving authors office oscillation affect presynaptic transmission transmission transmission transmission transmission transmission predicts rev adjusted impulse impulse impulse impulse impulse impulse impulse baseline baseline extent motivated integrate integrate integrate integrate histogram asynchronous asynchronous asynchronous asynchronous asynchronous convolution phenomena interneurons drive tive widely consequence acknowledgement recognized involve attribute auto greatly considerably populations populations substantially effort share poisson poisson poisson poisson poisson poisson poisson poisson spread modulated modulated modulated synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony incoming singer substantial synchronization instantaneous instantaneous phenomenon physiology sleep fix refractory refractory refractory refractory refractory approximates neurophysiol jth naval grows accepted contract transforms synchronous synchronous synchronous synchronous synchronous enhanced falls combines governed governed governed washington enhance histograms den propagated propagated dif cerebral mem arrive record augmented eqs epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp projects propagate discharge discharge crossing sig sig tween convenience resting resting evoked sinusoidal sinusoidal molecular alter cns conduction subthreshold decays continues maintained intra surrounding synchronized synchronized records figs tij exhibited normalizing behaves mea tonic tonic correlogram correlogram syn drives characterizing influenced impulses impulses confirm abeles played char seattle subtracting partly meth concave concave arriving sity amplified amplified amplified amplified nih bauer prominent adequately adequately hyperpolarization firings depolarization modulate arousal biophysics simulates bio bio modulating modulating damped eckhorn delivered delivered engel cyber doctoral preferentially percentages brane nals amplify amplify succeeding sured ita voluntary kruse sustain gustafsson creased ferential asymptotes pertain nificantly amplifying larization understandable sinusoidally reitboeck physiologists 
#@Fetz_E,Kenyon_G,Puff_R,
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#*network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set networks output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number system system system system system system system system state state results results results results results results units units units units information information models models models models space space case case case case case order order order order order shown systems systems values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions neurons neurons neurons neurons neurons neurons unit method approach single single processing processing large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test analysis analysis analysis inputs inputs form form simple simple simple simple work work task points points level level current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current structure structure high high high high high high high high high high high high high high high high section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation obtained obtained note note note note note experiments activity activity activity result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables defined found dynamics dynamics constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant table table table synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science left left left direction present activation activation activation activation activation activation activation activation activation activation activation activation activation low low low low low low low low low low low low low low low low low frequency frequency frequency temporal temporal temporal range range range press press continuous abstract find find computational computational computational properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties references due due due due important introduction action action action action action complex effect effect effect effect effect effect effect effect effect dynamic dynamic change difference difference difference variable spatial spatial lower lower chosen chosen cases cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing required required binary spike spike spike spike long long represent tree tree tree tree distributed expected equations equations equations equations equations equations markov make fact fact fact observed observed observed observed observed simulations simulations minimum minimum minimum resulting resulting total total total performed times elements means means potential potential potential potential potential potential made study study study study study study study study study study study relative relative cross define rates rates rates rates location active active active active active determined brain voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage comparison comparison connection version version consists internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal individual individual individual final ai considered curve san effects choice choice basic increase increase increase increase increase increase increase increase increase increase produce channel channel levels levels types product finally nature depends simply simply biological biological measured measured normal increases increases increases close close close complete finding amount amount amount amount effective effective effective effective effective assumed assumed assumed shape shape shape shape shape shape shape synapse synapse synapse synapse eds square square square square square square square square square square ability degree degree including including smaller underlying functional fully transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer increasing mechanism trials trials trials trials uniform principle operation operation magnitude magnitude magnitude magnitude decay decay decay decay produced choose run description description membrane membrane membrane membrane discussed exact reported include period subject identical recently recently relevant relevant sufficient sufficient highly highly varying observations calculated volume volume volume volume differential differential differential observation channels channels sensitive sensitive sensitive sensitive entire studied suggests suggests trial wide spikes spikes spikes spikes spikes generally demonstrate strength conclusions sigmoid sigmoid clear clear exponential exponential exponential suggest suggest propose mechanisms mechanisms integration reduction reduction california proportional proportional proportional proportional proportional proportional proportional pulse pulse pulse turn turn turn turn turn assuming decrease targets manner base appears appears relation relation relation relation relation relation relation relation relation relation relation relation relation relation relation relation construct produces plot changing changing changing changing sensitivity sensitivity sensitivity sensitivity sensitivity explicitly electrical integrated integrated potentials potentials potentials potentials focus expressed expressed dependence review viewed variation variation variation variation variation detailed open modulation modulation modulation modulation modulation modulation modulation modulation completely suggested constants constants constants constants constants constants constants constants constants spectrum sec sec msec msec msec msec msec msec msec msec sufficiently sufficiently sufficiently symbol symbol dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic expect expect exploration currents plotted activated candidate coupled coupled coupled variations characterized structural simplicity effectively driven driven driven driven literature refer repeated strongly neuroscience conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance duration built built quantity vary simplified simplified simplified simplified simplified simplified relaxation realistic realistic realistic realistic realistic realistic wave wave wave wave highest leading thresholds thresholds subsequent modelling modelling modelling modelling employed explore stimulation command carried diego exponentially varied varied varied varied varied varied steady steady steady replaced replaced replaced fourier plasticity plasticity plasticity plasticity plasticity plasticity understand removed patch measurement measurement transmission necessarily thought explored explored nervous academic academic burst burst burst burst burst burst burst burst defining fairly tractable benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark turns drive strictly protein commonly pulses pulses pulses axon begin begin summation summation greatly conducted parameterized simulate experimentally marked employ employ biologically operate summarized characterize modulated modulated monotonic monotonic monotonic conductances conductances conductances conductances conditioning begins simultaneous picture notes notes proportion investigation summing fix refractory driving driving driving driving systematic systematic systematic systematic systematic systematic systematic systematic systematic dealing bower numerically held alpha alpha alpha alpha resistance resistance resistance check efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy hope effectiveness effectiveness adequate preparation exceeds fires exploring meaningful started governed governed governed governed governed governed paul surprising buffer buffer buffer injection enhance dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite den somatic somatic somatic somatic somatic somatic somatic interconnections soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma soma modelled modelled modelled modelled modelled bursts bursts bursts bursts bursts bursts surprisingly smoothed smoothed reveals rich rich epsp epsp epsp epsp epsp epsp epsp epsp epsp concentration concentration concentration concentration calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium dividing dividing fired fired unchanged resonance resonance leaving largely tables removal trigger resting resting resting resting streams publication preserved gated gated gated gated gated gated gated gated gated gated gated gated gated gated gated decays potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium potassium simplifying altered depicts ultimately ultimately retain host inversely inversely ation ation indication thousands things hodgkin strict drives accumulation accumulation accumulation accumulation accumulation accumulation accumulation accumulation accumulation accumulation accumulation accumulation accumulation externally bursting bursting bursting characterizing const const crude builds ongoing huxley envelope envelope envelope ave morphology supplied injected injected injected physiologically impedance striking systematically systematically systematically systematically substitution governing governing governing governing governing governing governing governing governing contacts compartment compartment compartment compartment compartment compartment compartment compartment compartment compartment protocol protocol protocol fidelity enforces doubling doubling raised artificially counted counted unexpected benchmarks aggregate dispersion modulate battery battery judge substituted modulating modulating modulating modulating modulating modulating modulating possesses possesses des courses compartments seeking pot membranes membranes elicited suppresses neglecting accumulating clamp kinetics timestep timestep multiplies multiplies rabbit govern volt volt volt volt render conducting buffers freq freq freq freq lumped millions modulates axial doubled kinase cai opened hyperpolarizing raising coloring effected effected fll profound faithfully intradendritic intradendritic intradendritic intradendritic intradendritic hawkins hawkins hawkins inp influx dose smearing spines unaltered olds olds dimensionless interrelated etal ded halved drove arborization 
#@Rhodes_P,
#t3
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#*neural neural neural neural neural neural neural neural neural input input input input input input input function function function figure figure set set output output output output output output output number number number system results results results results results results results information information information information information information information information information information information information problem problem linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case shown shown shown shown shown values values noise functions neurons distribution distribution distribution image processing processing processing processing rate rate rate rate rate rate rate matrix inputs signal signal signal signal gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual paper examples feature feature feature feature feature feature net net net net net net net work fig fig fig fig fig cells cells cells cells cells cells cells field field field field field problems similar architecture equation equation equation equation equation equation equation equation equation equation equation fixed line images images theory theory obtained note result variables variables variables solution solution solution solution solution solution solution solution solution independent constant constant constant standard computer computer distance connections direction presented present present present nodes maximum maximum maximum maximum maximum maximum press continuous continuous abstract density properties references references stochastic stochastic adaptive introduction behavior statistical statistical variance tion spatial spatial spatial spatial assume signals signals signals signals center center center multiple good conditions conditions conditions conditions distributed equations techniques correlation correlation correlation simulations simulations classes sum performed eq regions regions means dimension orientation study study obtain receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide proc location determined constraints discrete connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection fields fields fields fields nets nets loss synapses synapses responses layers considered directly solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions full statistics con condition condition derived derived derived derived entropy nature inhibitory inhibitory inhibitory inhibitory feedforward feedforward arbitrary close complete excitatory excitatory excitatory excitatory assumed assumed assumed main technology mechanism principle operation details making early population ensemble ensemble reported lateral subject subject identical identical works solve studies achieve symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric constructed lead invariant white strength strength strength strength strength strength strength strength strength strength strength accurate numerical numerical mechanisms mechanisms largest largest largest demonstrated selective iii configuration configuration denoted reference relation relation relation derive describes mathematical changing explicitly infinite formed formed versus formation formation formation formation formation formation formation formation communication solved evolution evolution evolution evolution evolution understanding understanding constants additive normalization normalization usa eigenvalues eigenvalues maximize absolute phys identified identified identified identified divided delta delta summary kind kind contained interested symmetry symmetry symmetry content sci involved surround eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue highest exhibit relations strengths strengths strengths strengths strengths integral integral integral integral integral parity parity parity analytically analytically maximizing plausible rev ith ith explain defines defines theoretic crucial agreement variances analytic analytic analytic analytic analytic analytic analytic analytic analytic briefly spatially drive straight organized precisely located mation acad optimize linsker linsker linsker summation posed treated passes anti anti maximizes maximizes univ appearance appearance lagrange appropriately labelled jth generality multiplier convenient analyzing natl infor corre evident agree eigenvector propagate summarize liu corporation constitute email equivalently breaking breaking breaking ary insights shannon shannon shannon superposition west ation hat hat austin mirror morphology morphology morphology morphology illinois equa 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#@Tang_D,
#t3
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#*network network network network network network network learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training 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recognition recognition recognition recognition recognition method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single single processing large local rate rate rate rate rate rate rate rate rate rate test test test test test test patterns patterns patterns patterns patterns patterns patterns analysis class class class class inputs form form form shows shows algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian small small size size size size size size size size size size size feature feature feature feature feature feature net net net net net net work task task methods fig fig fig fig fig step classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process current trained trained trained problems problems problems problems problems problems problems problems problems problems problems problems problems random high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response rule rule general speech speech speech speech speech speech parameter parameter parameter real real average average average average average gradient gradient experiments experiments experiments experiments experiments experiments dimensional university computation computation research research research research research independent log defined defined sequence initial initial estimate standard standard standard standard standard standard standard computer computer computer computer distance node node node node science science left left presented presented presented map map map map map map low nodes nodes nodes nodes nodes nodes sets sets press press press learn basis outputs sample abstract back back back back back back back back back back back back back back back back back back back back back back back back convergence convergence analog references due ieee ieee ieee positive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation mixture introduction complex complex complex complex complex complex complex complex statistical statistical statistical parallel parallel parallel parallel search tion tion tion difference complexity complexity complexity complexity complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower measure cases type required required required required multiple multiple multiple multiple multiple multiple good binary binary binary binary binary binary binary binary long long tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected make techniques techniques techniques region correct correct observed scale simulations minimum minimum minimum minimum classes classes classes classes classes classes ing tasks tasks tasks regression multi performed performed performed performed times times times times times times times elements regions regions regions regions regions regions regions regions regions regions regions regions regions potential dimension dimension global global applications study study artificial artificial artificial specific compared application desired desired desired cross cross provide rates rates rates rates rates rates rates rates determined determined determined goal constraints constraints gain mit comparison comparison contrast contrast train dependent selection selection selection selection selection selection institute institute words department department implementation implementation internal kernel responses difficult difficult difficult final layers cambridge cambridge computing equivalent equivalent view conference conference determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper full requires requires choice statistics pages pages pages pages increase validation validation randomly randomly developed developed area area types types types lines lines lines lines actual provided provided provided provided provided provided selected selected selected backpropagation depends biological measured covariance group group tested limited complete complete complete predictions finding amount short nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest implemented implemented implemented require require require require require main adaptation adaptation adaptation adaptation journal square square ability including fit typically reduced technology testing testing testing testing testing testing testing york york head trials trials trials language details details numbers pre stored international international international magnitude magnitude magnitude magnitude magnitude minimize added description improved improved discussed improve recent separate separate element element practical practical practical practical practical practical practical practical practical practical practical practical practical practical include side side trees trees trees engineering dimensions dimensions dimensions sufficient conventional conventional conventional conventional conventional conventional tions correspond correspond correspond achieve diagonal increased lead studied digital digital trial trial trial trial trial trial trial trial trial deviation deviation matrices alternative alternative hardware demonstrate minimal assumptions reduce reduce neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor depend depend editors differences differences modules bayes bayes bayes bayes numerical numerical designed faster faster faster practice suggest physics reduction cycle cycle cycle cycle characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics demonstrated solid solid radial relationship program program program program force force explicit digit digit digit digit digit digit pro factors laboratory tuned tuned mathematical segments segments pruning pruning pruning category averaging electrical dimensionality dimensionality dimensionality remaining formed formed formed versus versus versus versus versus select select focus depending codes evaluated updated updated updated lee lee lee lee lee lee lee centers forms sizes digits digits performing convex fitting purpose purpose boundaries boundaries intermediate intermediate intermediate classified classified classified transactions existing thesis selecting selecting middle middle society differ driven included presentation build efficiently vowel vowel vowel vowel vowel vowel vowel vowel vowel ten ten summary traditional road quickly prob classify criteria criteria criteria criteria criteria vary generalize highest overlapping jacobs software minimized minimized explore unlike powerful american poor requirements requirements requirements requirements experience updating updating rapidly rapidly issues lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann matches rest relationships office proper affect statistically fundamental surfaces circles coarse coarse measurement editor editor adapt adapt adapt implementations adjusted adjusted friedman friedman versions versions noted explored consist simplest serial serial serial attempts massachusetts stop costs guaranteed floating caused handle london comparisons rapid tive incorporate scientific angles calculations computers cybernetics sun exemplars exemplars conjugate conjugate greatly prop substantially led amounts tional axes axes experimentally readily poorly poorly orders orders orders orders orders frequently frequently richard richard richard june june converged converged converged trade trade trade trade contribute consistently room cooper interface lvq lvq lvq lvq lvq lvq lvq lvq resources resources 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model model neural neural neural neural neural neural input input input input input input input input input input input input data data data function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output number number number number system system system system error error error error results units units units units units units units units units units information information information information information information information problem problem models hidden hidden hidden hidden performance performance performance performance performance performance performance performance weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer shown shown systems values values parameters parameters noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method pattern pattern pattern pattern pattern point point point single processing control large large rate test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns optimal inputs form form shows signal algorithms simple simple paper paper paper examples small small small small size size feature feature feature work task task task task task task task task task task task task task task task step step field field features features features features classification current trained trained trained trained trained trained trained trained trained high high architecture architecture architecture architecture architecture architecture show show show equation equation equation section fixed rule rule general general generalization generalization speech speech speech speech speech speech parameter real average average average average states gradient obtained term term experiments experiments experiments experiments experiments experiments experiments activity university university university university research research research research research research sequence standard standard standard standard standard computer computer science science activation activation activation activation activation low frequency frequency frequency frequency frequency maximum position position components components components components continuous sample sample sample abstract applied back back back properties references procedure procedure procedure important decision propagation propagation propagation context context introduction hand generated generated cost cost cost cost cost cost cost cost cost cost cost cost cost energy energy energy energy difference difference complexity complexity lower lower prior prior prior prior prior prior word word word word word word word word word word learned learned learned learned chosen center center bound cases cases cases cases cases cases required good good good good spike conditions conditions represent markov markov markov make make make make fact fact fact fact techniques techniques region region proposed length length correct errors scale scale total human respect multi performed performed performed times factor factor factor made made knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge relative compared compared compared cross receptive receptive compute compute perform perform perform connected mit mit accuracy accuracy accuracy accuracy comparison comparison fields support modeling institute institute words words words words words words loss version version technique connectionist connectionist difficult final delay delay delay delay delay delay sequences domain equivalent hinton hinton hinton hinton hinton hinton hinton hinton view stage bit upper full requires free free free world estimated validation con channel randomly lines finally selected selected constraint achieved achieved measured increases tested tested tested limited close amount short common implemented generate supported main eds square instance easily noisy noisy noisy including objective objective objective objective objective objective typically typically smaller needed reduced testing testing testing testing ratio edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation mode mode details details details numbers pre pre making making window window normalized experts experts frame frame decay decay decay decay decay decay idea attention attention combined combined run improved improved improved discussed resolution resolution resolution resolution resolution resolution resolution advantage separate typical reported apply identical identical sense sense sense relevant relevant relevant relevant relevant highly highly highly highly highly highly conventional conventional conventional conventional axis smooth achieve definition definition background background positions modified modified generalized gate grant derivative derivative correctly feed setting hardware conclusion greater reduce conclusions neighbor accurate designed peak performs performs learns learns constrained strong largest reduction reduction reduction reduction reduction reduction reduction proportional assuming minimizing minimizing averaged program program acoustic acoustic force base acknowledgements construct transitions dept dept segments segments segments segments segments simultaneously dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality remaining slightly slightly text develop mutual frequencies letters letters extracted focus viewed influence influence influence variation frames similarly translation allowed discrimination discrimination discrimination discrimination key key earlier earlier smoothing smoothing performing intervals event roughly penalty msec msec msec msec msec msec advantages degrees expect expect building figures figures thesis priori usa recognize recognize determines automatic automatic automatic activated partially neighbors neighbors neighbors neighbors neighbors compression middle importance uniformly encoded included successful identify build build tdnn tdnn tdnn tdnn tdnn tdnn tdnn invariance score situation vowel plots plots essentially identity characteristic capture induced contained contained contained heuristic stopping classify duration cues cues cues cues cues built generalize highest ill attempt disparity extract neighboring neighboring decreasing employed employed remain poor create create accurately accurately accurately preliminary existence fewer reducing reducing reducing reducing rest rest rest detectors detectors detectors ideal office office complicated complicated waibel waibel created versions versions portion portion portion freedom speakers speakers baseline baseline baseline baseline baseline baseline baseline generates extent motivated phd attempts seconds isolated isolated mentioned burst burst brown brown brown advanced crucial smoothness independence worse sections sections sections precisely potentially toronto toronto localized localized localized read recording recognizing preceding mellon mellon mellon alignment alignment raw raw summation people percent percent percent percent percent percent percent percent percent carnegie carnegie carnegie led cmu spoken poorly poorly recordings recordings recordings recordings recordings detecting sharp sharp compares release release release release release vocabulary pittsburgh limiting prevent decreased segmented segmented focused viterbi viterbi utterances utterances utterances utterances utterances utterances utterances utterances traces traces traces traces traces summed irrelevant irrelevant irrelevant naive don classifying aligned aligned primarily princeton linearity narrow concerned controlling naval establish fails khz khz khz khz khz occurred logarithmic contract serves bands bands bands utterance utterance utterance utterance methodology methodology implications corpus corpus generalizes spurious spurious spurious spurious spurious spurious date performances lip ranging male pat lang lang lang lang lang lang lang lang lang accounts mel originally counter advance artifacts express stimulated creating smoothed smoothed matter properly informative informative canada consonant consonant consonant consonant consonant valuable valuable ignore ignore material material adopted treat discriminate yielded roc opposed rejection encouraging copy tradeoff hundred big constitutes suppressed reflected remote preserved care concentrated ibm ibm ibm geoffrey geoffrey gener convert challenging maximally differentiation names conversely indexed portions places exhibited ignoring worked scanning nec copies copies copies copies scanned scanned scanned scanned fortunately identifies trainable terns doesn locate locate locate proposal dissertation consonants discarded discarded capital tells isolation decaying drastically feldman ben meant addressing format format segmenting assessed devoted devoted microphone watson actively subtle mid clutter lisp retaining expresses meaningless attracted stand spectrograms spectrograms spectrograms spectrograms spectrograms tongue orig ontario ontario tiny tiny tiny distinctions mike named differed tums canadian conveniently unimportant fellow tony altogether waltz rejecting rejecting resort doctoral brute hoped told unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented penalize attend dft didn decayed kevin zee zee zee chart chart deduced vastly evidenced confusable transmits smeared died listeners thrown managed tax lots aren halting plagued iill iill appearances meaningfully blame correc forma 
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#*network network network network network network network learning learning model model neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data time time time time time time time time time time set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number system system system system system system system system system system system system system error error error error error state state results results results results results results results results results results results units units units information information information information models models models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based space layer layer layer case case case vector vector vector shown shown shown shown shown shown shown systems systems systems systems systems systems systems values values probability probability probability probability probability probability probability parameters distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach pattern pattern pattern pattern point point point single single single single processing processing processing processing processing processing large large large rate rate rate rate test test test test test test test test test test test test test patterns patterns analysis class class class optimal optimal inputs inputs shows shows shows signal signal signal signal signal algorithms simple simple simple simple simple simple simple simple simple simple small small small size size size feature feature feature work work work task methods methods methods methods methods points field features features features features features features features features features features features features classification classification classification classification classification classification classification classification level level level level level level trained trained problems representation show show section fixed rule vectors vectors general general generalization generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter approximation average average states gradient note note note experiments experiments experiments experiments experiments experiments experiments experiments result result solution research research research independent independent independent independent independent independent independent independent independent independent log log defined sequence sequence dynamics initial initial constant constant table table table table table table table table table table table table estimate estimate estimate estimate estimate estimate standard computer computer science science presented map map map map map map map frequency machine sets sets sets sets sets maximum maximum maximum maximum basis basis outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract back back density density likelihood likelihood likelihood references due due ieee ieee ieee ieee ieee ieee positive procedure procedure procedure procedure procedure procedure procedure procedure procedure propagation propagation mixture context context context context context context context context context context introduction complex complex complex complex hand estimation estimation estimation estimation estimation statistical statistical statistical statistical statistical statistical effect effect effect dynamic cost search tion energy difference assume classifier classifier prior prior prior prior prior word word word word word word word word word word word word word word word word word word word word word word word word part center required required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple good good good good good good binary markov markov markov markov markov make make correlation correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed errors minimum total multi performed called times factor factor factor potential applications applications knowledge original original original original vol vol vol vol vol vol artificial relative relative specific represented true application cross cross cross cross cross cross cross series provide provide rates rates proc proc proc proc proc perform determined experimental experimental experimental related discrete discrete discrete discrete equal equal power approaches approaches approaches approaches comparison larger support dependent dependent dependent dependent nets modeling morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan proceedings report institute institute institute words words words words words words words words technique consists consists advances represents connectionist difficult difficult difficult final scheme scheme scheme considered equivalent experiment experiment directly directly hinton additional solutions estimates estimates estimates estimates transition transition transition transition transition san san effects bit conference determine classifiers classifiers full full choice significant significant approximate estimated estimated estimated estimated estimated basic increase validation validation validation validation validation validation validation validation validation validation validation validation validation give conditional developed levels criterion criterion criterion criterion entropy entropy actual provided finally evidence evidence evidence iteration iteration iteration iteration iteration simply achieved measured normal technical feedforward feedforward describe tested tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited complete assumed assumed theoretical adaptation square hypothesis instance easily easily including kaufmann underlying needed reduced reduced fully technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp significantly york york segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation consistent consistent database language window window window window international international normalized supervised frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame produced sources sources sources description improved improved improved improved discussed improve improve recent advantage advantage reported include inference previously conventional conventional conventional observations calculated calculated speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker achieve trans modified generalized improvement improvement improvement improvement increased parts scaling scaling scaling hybrid hybrid width boundary column runs conclusion starting starting assumptions assumptions assumptions assumptions assumptions accurate bayes designed intelligence labeled labeled minimizing start start exist decrease targets manner program acoustic base denoted reference appears appears appears appears relation relation relation digit van ways sequential estimating estimating laboratory transitions modeled metric multilayer multilayer multilayer multilayer easy easy frequencies choosing choosing dependence review phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme estimator overlap densities evaluated updated labels fraction frames frames frames frames frames frames frames frames frames completely suggested spectrum reasonable measurements classical classical roughly iterative iterative valid avoid avoid expect box includes usa perceptrons perceptrons recognize automatic maximize priors priors priors priors priors priors tests tests structural major major hmms hmms hmms hmms hmms divided effectively schemes essentially essentially capture traditional traditional conf conf conf conf conf repeated procedures decoding decoding contained moore moore showing stopping phonetic phonetic duration duration comp quantity sampled simplified realistic providing reach extract approximating neighboring acknowledgments deal decreasing simpler simpler diego diego poor difficulty difficulty difficulty put optimized optimized limitations preliminary mass ml ml ml ml ml ml ml ml ml links possibility dependencies scaled scaled scores statistically removed waibel waibel math necessarily extremely prototype prototype observe perceptton perceptton perceptton initialized speakers speakers speakers speakers speakers improving explain sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences isolated isolated isolated developing costs costs coded capabilities capabilities independence independence berkeley style division division division incorporate incorporate incorporate incorporate incorporate potentially recognized sounds demonstrates alignment alignment alignment alignment improvements greatly reflect reflect led led led led bootstrap embedded remove requirement prototypes vocabulary vocabulary vocabulary rely incorporating phonemes phonemes phonemes phonemes acoustics acoustics acoustics acoustics acoustics boston segmented segmented windows windows viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi sentence yielding merging initialization consistently representative spectra benefit contextual contextual contextual contextual contextual contextual contextual labeling labeling labeling null royal extending khz ments logarithmic keeping bands utterance splitting bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard effectiveness modifications modifications modifications published embedding embedding embedding embedding embedding embedding male male male male lang percepttons mel mel offers recog recog recog mlps mlps mlps mlps mlps mlps mlps mlps insight smoothed offer offer exploiting stopped automated stone posteriori radar emission emission emission emission emission emission emission emission street outperform session session session session session session session equivalently nelson nition nition nition par acceptable acceptable ease hundred hundred hundred german german german female female warping edinburgh reflected clas quantized quantized mismatch gained gained convert met simplifying simplifying switched exceed intl intl intl intl intl intl intl esti ward sessions sessions gratefully continued assistance suite overtraining mining incorporation partly consonants fft interpolating measurable sliding watrous watrous statist statist binomial restrictive materials raised seg ous durations mle validated validated voiced repetitions repetitions explaining began wellekens wellekens wellekens wellekens wellekens ard dtw dtw stand checked pointers align shikano adjustments insertions insertions insertions helped terminated acknowledged silverman positively differed penalties penalties penalties necessity transcription succession succession permitted deletions deletions continu hanazawa nato accompanying discriminations discriminations icsi icsi hurt articles warped feedfor silence absolutely siftcation establishment phoneroes mated duplicated boutlard bush vocabularies substitutions unvoiced scotland ney ney malvern chuck asi moo shastri shastri belgium exit wooters brussels ignorance nem glasgow phonetically ucb mysterious ticularly 
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#*network network model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data function function function function function function function function function function figure figure figure figure set set set set set set set set networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output number number number number number number number number number number number number system system system system system error error error error error error error error error error error error error error error error error error error state results results results results results results results results results results results results results results units units information information information problem problem models models models models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based weights weights weights weights weights weights weights weights weights weights layer layer case vector shown shown systems probability probability parameters parameters noise noise weight functions functions functions functions functions functions distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern single single single single single processing processing processing processing processing processing processing processing processing processing processing processing large large rate rate rate rate rate rate test class class class class class class class class class class class class inputs inputs form form shows algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small small small small size size feature net net net net net net net net net net net work work work work task task task task task task task task task fig fig fig fig fig fig fig fig features classification classification classification classification classification classification classification classification classification classification classification level level level level level level level level level level level level level level level level level level level level level level level level level level level current current current current current trained trained trained trained trained trained trained trained trained trained trained structure structure problems problems problems high high similar show section section fixed general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real average average obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments experiments result university university research research independent independent independent sequence table table estimate computer node node node node node node node science science left presented low nodes nodes nodes nodes nodes nodes temporal temporal sets maximum maximum maximum maximum press components components components components components components components components basis basis basis basis basis basis outputs outputs continuous continuous continuous continuous continuous continuous abstract back back density density analog likelihood likelihood likelihood references due due ieee ieee ieee ieee ieee decision propagation propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context context context context context context context context context context introduction behavior effect dynamic variance parallel tion tion tion energy energy difference complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower word word word word word word word word word word word word word word word word word higher center center center required multiple good good good good good expected markov markov markov markov make techniques techniques techniques techniques correct probabilities observed observed errors forward scale classes classes ing total total total total total total total computed computed computed multi multi multi multi performed performed performed performed performed eq eq eq eq times regions means means means means means means means means means reinforcement factor factor factor factor potential study study study em obtain artificial relative compared desired provide provide provide provide provide rates rates rates rates rates rates rates rates rates rates rates rates rates perform perform perform determined determined experimental experimental experimental goal related related distributions distributions approaches approaches mit larger larger train dependent dependent dependent dependent dependent dependent nets nets nets nets nets modeling modeling morgan morgan proceedings proceedings report report institute words words words words words department department implementation individual individual individual advances connectionist exp addition addition equivalent directly directly directly additional additional solutions san stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage conference efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full requires significant significant world pages pages increase clustering clustering clustering clustering clustering clustering provided provided provided provided provided provided provided provided provided provided provided provided provided provided provided provided provided provided selected covariance covariance covariance technical technical technical hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited limited close close assumption assumption rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount amount nearest common effective effective shape generate require main journal end vlsi ability including kaufmann objective objective objective pairs underlying combination reduced unknown coefficients coefficients fully mlp mlp mlp mlp mlp mlp mlp testing testing testing testing testing york increasing increasing increasing increasing segmentation consistent matching matching matching matching database database database database mode pre pre pre pre pre pre pre pre international international frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame produced perceptron improved improved improved improved improved improved discussed discussed improve improve improve improve recent recent robust reported reported practical apply include conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional observations speaker speaker speaker speaker correspond studies studies diagonal address mixtures mixtures mixtures evaluation locations observation improvement improvement improvement sensitive increased increased increased increased increased lead lead matrices matrices matrices clusters clusters occurs minimal assumptions assumptions reduce segment neighbor depend sigmoid constrained constrained constrained constrained suggest integration characteristics radial assuming averaged averaged averaged acoustic acoustic acoustic force force reference reference describes laboratory label segments modeled multilayer dimensionality dimensionality dimensionality dimensionality involves slightly unique unique spectral spectral mutual integrated integrated applying expectation versus versus letters letters extracted focus review depending stages densities evaluated evaluate showed lee lee lee centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames static static digits discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination smoothing smoothing sec sec sec sec msec msec advantages advantages thesis perceptrons plotted illustrated automatic variations variations variations successfully selecting letter effectively symbols included wij post score score score summary strongly decoding decoding contained prob prob prob prob prob phonetic phonetic dis dis superior superior superior lie criteria strategies duration duration duration michael michael generalize backward providing maximization consisted consisted extend poor poor exponentially rapidly estimators estimators replaced lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann preliminary preliminary preliminary discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant ml ml ml ml fewer examine combine scaled scaled scaled office scores scores scores scores scores scores scores scores scores scores scores scores scores scores scores scores scores neu neu coefficient coefficient necessarily recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer singular portion explored explored art ith baseline baseline baseline baseline phd isolated isolated isolated isolated isolated isolated averages integrate integrate integrate integrate percentage brown histogram ment variances variances variances variances adjacent capabilities multiplication worse comparisons stress berkeley mation scientific lowest mellon mellon robustness integrating varies considerably carnegie carnegie substantially led cmu embedded peter share outliers maintain vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary rely mod ture spread spread spread extracting phonemes phonemes phonemes phone phone phone phone phone phone phone phone phone phone phone phone phone phone adjust richard richard richard richard sums replace decreased segmented segmented focused viterbi viterbi viterbi viterbi june merging consistently classifying classifying room tation jth jth air air promising resulted resulted utterance ral ral bourlard knn knn knn knn knn knn knn knn affected infor mance studying paul perfor decide mel multiplied multiplied tokens tokens tokens tokens tokens mlps april smoothed smoothed passing accumulated accumulated accumulated accumulated yielded ter shorter july forced axe icassp icassp utilize acceptable clas verified distri formance compensate compensate degraded degraded efforts efforts efforts tied tied tied tied tied tied tied tied tied tied tied denver esti behave els holding ignoring ignoring compu recognizers recognizers recognizers recognizers recognizers recognizers recognizers recognizers recognizers recognizers recognizers recognizers gauss gauss mix mix modal bution utilizing rabiner accumulation advantageous argmax january recogni outperformed outperformed outperformed outperformed svd partly huang huang huang huang huang huang huang juang correctness classi corrective corrective william william magazine dent dent indepen indepen indirectly unimodal unimodal unimodal discriminating talkers talkers talkers talkers sponsored retaining lincoln cepstral cepstral cepstral cepstral cepstral phones phones phones nov examines accu devel puter mmi differed accumulating accumulating accumulating accumulating accumulating talker talker talker talker talker talker talker hoped deliver implementa marcel dekker witbrock fii phoneroes mates bet consis extractors nodal lexington pseudoinverse boutlard kai kai oped resistant benchmarking benchmarking franzini franzini mclachlan levinson commu leaning rig sondhi ces sigrnoid skipping widening widening widening widening sifter mulated smoothes halved tracting tempt fying 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training output output output output number number number number number number number number error error state results results results results information models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based based based based layer layer layer layer layer layer layer case case order order order shown shown systems functions functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern single single single single single single single processing processing large rate rate rate rate rate rate rate rate rate rate rate form form form form form form form form shows shows signal signal signal simple small small size size size size size feature feature feature net net net net net net work task task task task task task task task task task task task features features features features classification classification classification classification process trained trained trained trained trained trained trained trained trained trained trained trained structure structure structure structure structure structure high high high high response response similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech states result result university university university university university university research research research research research independent independent found target initial table table standard computer terms connections connections connections connections connections connections connections connections connections connections connections connections connections connections science science presented map map map map present present frequency frequency frequency frequency frequency outputs outputs outputs outputs abstract back computational references references references ieee ieee ieee ieee procedure procedure procedure important decision decision decision propagation introduction action complex stimulus stimulus stimulus stimulus stimulus variance variance variance tion tion complexity classifier classifier lower representations representations representations representations representations higher higher type type multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple conditions distributed bayesian bayesian bayesian equations fact resulting resulting resulting resulting resulting tasks tasks total multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi sum called global global global global original original vol vol vol vol specific specific specific specific cross series rates perform perform perform perform experimental goal larger larger connection connection support support train dependent dependent dependent dependent dependent dependent dependent proceedings proceedings report report report report report report loss loss version version version technique internal internal individual individual individual individual individual joint joint connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult final final layers layers layers layers delay delay delay delay delay scheme scheme addition maps experiment hinton hinton additional design design design design design transition stage stage stage stage stage stage conference conference significant significant significant significant basic produce types entropy product provided finally processes technical technical technical technical technical increases group tested effective role ability degree objective objective objective objective objective objective typically typically typically smaller fully block block testing significantly edge mechanism structures database leads principal details direct direct making international international normalized combined added architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures improved improve improve robust robust identical highly compare approximately module module module yields speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker gate gate improvement improvement sensitive invariant scaling suggests conclusion reduce modules modules modules modules modules modules modules modules modules modules modules modules modules performs learns learns learns taking integration integration drawn selective selective manner identification identification acoustic acoustic acoustic acoustic acknowledgements reference reference explicit explicit explicit unique unique integrated integrated integrated integrated integrated integrated formed shift shift shift john national independently phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme viewed detailed detailed forms forms forms forms diagram diagram performing reduces reduces roughly foundation advantages topology transactions transactions david building figures activations activations bell recognize recognize recognize recognize recognize maximize variations major major major capable capable capable tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn invariance identity identity procedures link interested phonetic list sampled modular modular modular modular modular modular modular modular modular modular modular paradigm paradigm illustrates illustrates extend requirements strengths hanson fashion school tech mse detectors detectors investigated comparable comparable statistically waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers baseline baseline baseline baseline baseline integrate mentioned worse processed producing broad laboratories potentially attribute depicted mellon mellon mellon mellon mellon mellon integrating integrating integrating integrating integrating integrating considerably carnegie carnegie carnegie carnegie carnegie carnegie syllable substantially cmu cmu cmu cmu cmu cmu spoken spoken maintain operate pittsburgh limiting acoustics phone phone comments focused utterances utterances june irrelevant consistently redundant enhancement communications ranges adjusting multiplicative replica serves exploit intuitive constructive published combines male male male male male male male male male male lang lang washington tokens tokens tokens tokens insight pearlmutter formant ple corporation constitute constitute shorter super creates july employs responds tween additionally individuals female female female female constitutes descriptions descriptions adapting summarizes shifting degraded degraded pomerleau disadvantage disadvantage march march eliminating increasingly meta meta meta meta meta meta meta meta meta meta meta meta responding atr differing suggestions served expense stimulating sponding sponding stephen handling august recogni tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns crude crude designs designs attempting interpreting december december phonemic alex japanese burr integrates integrates conflicting exclusively exclusively exclusively dissertation governing assp assp presently counterpart sid sid sid sid sid sid sid lar lar replication dean rec daniel modularity modularity modularity shikano shikano gross conceptually hampshire hampshire hampshire hampshire hampshire hampshire hampshire hampshire ply ply ply ply ply tics conversations warp retrained intel formants supervision supervision inadequate prototypical bellcore hanazawa readers owing owing arbitration sponds inn inn appeal males males males nical eet phoneroes kamm knowl markedly criticism females registered barak rosenfeld 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training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output number system error error error state state state state state state information information information information information information information information information information information problem models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden performance performance performance based based based based based based based based based based based based based based based weights weights linear layer layer layer layer layer case case vector vector order order systems systems systems systems values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point processing processing processing processing processing processing processing patterns class class class class class class class class class class class class class class class class class class class class class class class class matrix optimal inputs form form form form form form signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian paper examples feature net task methods methods methods classification classification classification classification classification classification classification trained structure structure architecture architecture show show section fixed speech speech speech speech speech speech speech speech speech speech speech speech parameter real states theory theory gradient term note dimensional result university computation independent log log log log log log sequence sequence sequence target dynamics constant computer terms connections science science left temporal temporal temporal machine sets maximum maximum maximum maximum maximum maximum maximum maximum maximum basis basis outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous sample abstract back back find find density properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due ieee ieee ieee ieee ieee ieee positive positive procedure important adaptive adaptive propagation propagation introduction estimation estimation estimation estimation estimation estimation statistical statistical recurrent recurrent recurrent recurrent difference difference assume assume assume classifier classifier classifier classifier classifier classifier classifier classifier measure signals prior word word word word learned cases type required conditions expected expected expected markov markov markov markov markov markov markov make make make make proposed correct correct correct correct correct correct correct correct correct correct probabilities probabilities probabilities forward forward resulting classes classes classes classes classes classes classes computed computed computed respect multi multi multi multi sum sum sum sum sum sum sum called means means means means means means natural natural applications applications knowledge em obtain obtain relative relative relative relative relative relative true true true true true desired cross cross provide compute compute compute proc proc proc proc perform perform posterior constraints constraints distributions distributions distributions distributions distributions equal equal equal equal approaches approaches steps train selection morgan report department implementation internal advances joint joint joint connectionist final exp sequences sequences ai considered computing equivalent equivalent equivalent hinton estimates design transition san classifiers classifiers classifiers classifiers classifiers choice choice pages pages pages pages pages con con derived derived weighted weighted weighted weighted randomly conditional conditional conditional conditional conditional conditional conditional conditional criterion criterion criterion criterion criterion criterion criterion entropy entropy entropy entropy entropy entropy backpropagation backpropagation simply simply simply covariance technical feedforward describe arbitrary hmm hmm hmm transformation transformation transformation limited corresponds circuits common assumed require end ability instance instance instance kaufmann probabilistic typically pairs underlying transfer special special consistent mode operation squared squared squared squared details call call call numbers max supervised produced choose choose choose choose perceptron architectures architectures architectures pair pair separate include include identical machines sejnowski cognitive recently relevant engineering interest sufficient observations works address positions positions modified observation observation observation observation constructed constructed lead derivative alternative alternative feed move touretzky flow assumptions assumptions conclusions valued depend editors differences clear exponential exponential exponential mateo suggest physics largest demonstrated assuming relationship averaged targets targets introduce derivatives derivatives question question boltzmann boltzmann pro construct produces written index winner sequential generating mathematical distinct implement implement implement multilayer coordinates mutual mutual mutual mutual mutual mutual mutual gaussians events events springer boolean boolean john choosing choosing choosing choosing choosing family review stages communication communication squares interpretation interpretation densities densities labels labels labels labels soft suggested discrimination discrimination discrimination discrimination discrimination discrimination discrimination partial partial performing sec purpose distances euclidean includes perceptrons extension automatic prove priors priors priors successfully simplicity reason hmms hmms hmms build efficiently computations computations score score score score refer conf conf conf conf verlag kind procedures prob success success link anderson interpreted interpreted dis issue satisfy bar usual usual usual usual usual usual backward highest operating deal deal deal intrinsic parametric parametric layered involving replaced replaced replaced lippmann divergence divergence divergence ml ml ml giving ideas detectors int int int int transistor relationships workshop scores notion analogous editor editor generalisation generalisation generalisation equally ensure adjusted rank logistic logistic logistic logistic logistic logistic logistic perceptton perceptton multivariate multivariate attempts isolated brown brown great directed theoretic variances biology baum baum nonlinearity desirable read meaning mellon argument questions carnegie cmu lack lack red solla incorrect acoustics acoustics acoustics acoustics acoustics adjust asymmetric enables sums replace replace decoder conclude neuro specifies june june differentiable softmax softmax softmax ear modify investigation linearity pick jth discovery unity unity addresses royal kullback wrong odd attractive scoring scoring scoring ensures ensures bad spherical nonlinearities tic peterson recog recog mlps membership formant likelihoods likelihoods likelihoods designing pdf treat radar drop minus leibler july isotropic nition nition welch welch discriminative discriminative discriminative exception seek aij covariances big recurrence illustration param clas principled unseen levin mathematically mathematically life guided unconstrained option normalised normalised normalised bridle bridle bridle bridle bridle bridle mann picking picking tour preserves january pdfs pdfs justified trainable trainable firstly virtually optimisation recursion inherently tribution ackley corrective watrous sian fol subscript essence gaus modern inst indicators indicators february inform linearities entropies disadvantages minimise minimise availability mmi maximising maximising maximising silverman thinking mercer british maximise nonlin nonlin stochas generalised interpretable accelerated tributions ditional matters gersho optimise badly establishment variate specially specially optimising rault tual bush logs normalisation positivity bahl bahl bahl bahl ney malvern soulie patterning fleisher sifier ils wilczek discriminator parameterised lowed attractions attractions gopalakrishnan copyright ila emitting recommend tbr ifj normalise normalise 
#@Bridle_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output number number number number number number number system system system system system system system error error error error error error error error error error state results results results results results results units units units units units units units units units units units units units units units units units information information information information information information information information information problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based space space space space space space space weights weights weights layer layer layer layer case case order order order order order order order shown shown systems systems values values parameters parameters parameters parameters parameters parameters parameters parameters unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach processing processing processing processing processing large local local local local local local rate rate rate rate rate test test test test test test analysis inputs inputs signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple paper examples examples small size size size size size net net net net net net work work work work work task task task task task task task task step step features features features features features features features features features features features features features classification classification process level level level current current trained trained memory memory similar similar similar similar representation representation representation representation representation representation architecture equation section section vectors vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech approximation approximation approximation average theory theory theory gradient gradient gradient obtained obtained term note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments result university university university threshold threshold computation computation research independent independent independent independent independent independent independent independent independent independent independent independent defined defined found found sequence sequence sequence sequence sequence sequence sequence sequence target target initial initial initial constant constant constant constant constant constant computer computer computer terms terms distance distance connections science science science science science science left direction presented presented presented present phase phase frequency temporal temporal temporal temporal temporal temporal temporal range press learn learn learn learn learn learn outputs outputs outputs outputs outputs continuous continuous continuous abstract back back back back back properties references due ieee important important propagation propagation propagation propagation propagation propagation context context context context context introduction hand statistical dynamic variance variance parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion tion tion tion tion change change change change change energy energy complexity assume measure word chosen higher part previous previous previous type type type type good good binary long long long long conditions represent represent represent distributed expected equations make techniques proposed proposed length length length errors forward forward forward forward scale resulting resulting resulting classes classes classes ing human computed respect respect respect multi multi sum sum performed performed performed performed called times times times feedback knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge filter obtain obtain obtain original vol vol artificial artificial compared application application application application application application provide compute compute compute rates proc proc proc proc perform perform experimental constraints constraints constraints constraints constraints connected connected connected discrete discrete mit mit steps comparison larger support train morgan morgan report words words words internal advances joint joint represents difficult difficult delay delay scheme addition sequences sequences sequences ai maps computing computing experiment experiment directly hinton additional additional additional view design design design transition transition transition transition transition transition transition trajectory san san stage stage stage stage effects conference efficient choice basic con con coding coding coding coding coding coding coding coding coding coding coding coding coding coding derived derived weighted levels criterion criterion types lines provided processes backpropagation backpropagation backpropagation nature nature nature sampling constraint measured measured technical feedforward feedforward feedforward describe arbitrary arbitrary fast fast fast limited corresponds corresponds stable short short short square hypothesis hypothesis hypothesis hypothesis future future future easily easily rumelhart rumelhart rumelhart including including kaufmann kaufmann auditory needed needed needed reduced reduced reduced reduced coefficients coefficients coefficients coefficients fully fully interesting significantly character database database database representing filters filters filters direct direct direct window window window window international early frame frame frame frame frame frame frame frame frame frame idea idea combined produced improved improved improved improve apply introduced strategy strategy strategy strategy strategy strategy machines subset dimensions dimensions varying varying observations approximately works works tions speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker correspond definition generalized grid interval williams increased horizontal horizontal parts parts parts derivative feed touretzky loop loop generally generally generally setting pass pass pass pass half critical critical critical place place place place place place reduce trajectories sigmoid constrained constrained mateo encoding propose propose external reduction demonstrated demonstrated demonstrated intelligence intelligence manner connectivity connectivity acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic base explicit pro pro produces longer ways transitions transitions label vertical vertical vertical dept dept dept segments implement dimensionality slightly slightly spectral spectral spectral spectral spectral spectral spectral spectral frequencies formed extraction independently formation depending phoneme phoneme phoneme phoneme phoneme phoneme influence influence variation transform transform showed frames frames frames frames frames frames frames frames static static static discrimination discrimination discrimination discrimination past past past spectrum performing performing delays delays delays delays delays normalization remains initially advantages advantages advantages faces precision precision precision includes activations activations automatic automatic automatic automatic compression compression middle aspects extra included wij wij wij wij successful build build comparing vowel vowel vowel vowel tend identity reached reached receives refer compact compact compact phonetic phonetic phonetic phonetic phonetic follow device duration duration categories usual usual usual usual realistic backward backward reach attempt consisted moves preferred extract extract receive layered layered poor poor production requirements requirements put put put steady steady association fourier successive giving ideas links mappings possibility combine combine combine combine scaled stream proved cognition waibel waibel waibel waibel coarse recognizer subsets aspect aspect aspect quantities detector detector explored explored explored explored speakers speakers detected detected isolated isolated isolated isolated separable derivation handle handle preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing broad bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio mation mation recognized sounds pitch english recording meaning researchers varies spoken capability effort posed execution characterize ture ture gen synchrony synchrony synchrony synchrony phonemes phonemes phonemes phonemes phonemes phonemes gave enables enables chose boston expectations windows windows june sentence yielding instantaneous lot lot lot ear ear ear ear ear ear ear ear ear restriction ratios encoder tem flexibility inspired communications ments programmable loops loops loops loops abilities resulted generalizes vowels vowels motivation infor infor utilized utilized utilized started contexts contexts contexts periods sion male washington mel mel tic tokens tokens bursts canada pearlmutter pearlmutter designing material influences automated counts consecutive dramatically yielded ence ence microstructure shorter shorter recursively bank encouraging icassp regularity hundred female tor recurrence causal clas cessing permits unconstrained win crossings articulatory articulatory articulatory experi coming triggered architectural architectural architectural architectural copies characterizing ble august recogni recogni tdnns tial attributed imple tors phonemic alex realizations concerns mori mori mori mori mori mori mori mori mori mori mori mori mori mori mori mori mori mori equa accumulate architec architec architec fft fft fft fft fft fft fft plateau outgoing drastically nettalk fol demands articulation articulation articulation articulation articulation articulation bottleneck bottleneck meant dent robustly indepen clues ized ated ini montreal spec costly dow modularity nice richer cepstral preprocessed preprocessed timit neigh plexity turing phy compress subtasks eralization strongest inertia lpc supervision supervision supervision supervision supervision supervision supervision supervision machinery lowing wii wii wii wii wii poral mented canadian banks yoshua voicing owij poorer quences cap particu attack interna struction intend confer confer seneft seneft nasal nasal nasal nasal nasal nasal nasal nasal nasal nasal silence detec associ compressing compressing sification discrim vances mcgill mcgill mcgill ciently oxi oxi pute audition descrip acous tral cepstrum unfolding duces subsections coarticulation conserve fied nasals nasals trajec downstream discrimina larly stants accents discriminatory modi suffi gori gori gori ination detroit stead tural stra tories hor izontal ingful provid bors 
#@Bengio_Y,Cardin_R,De-Mori_R,
#t3
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#*network network learning learning learning learning learning learning learning learning learning model neural neural input input input input input function function figure figure figure figure figure figure figure figure figure figure training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number system system system system system system error error error error error error error error error error error error error results results information information hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based space weights case case case case case vector vector vector vector vector vector vector order order shown systems parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit recognition recognition recognition recognition recognition recognition recognition point point single single processing processing rate rate rate rate rate rate rate rate rate test test test form shows simple gaussian feature feature feature feature feature feature feature feature work work task task step step process process current structure problems high memory memory representation representation representation representation show fixed rule rule rule rule rule rule rule rule rule rule vectors speech speech speech parameter approximation approximation term term experiments activity activity activity activity activity threshold log defined constant terms distance distance distance synaptic presented map map map map map map map map activation learn abstract analog analog references due positive introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit dynamic tion tion difference difference measure word word word word word word chosen part required required required distributed expected chip chip markov fact region simulations ing simulation simulation simulation simulation performed performed made negative original relative represented rates determined related constraints constraints constraints connected connected gain gain discrete mit mit voltage voltage voltage accuracy accuracy comparison comparison connection connection connection source morgan department implementation implementation version technique consists advances graph graph curve additional additional san effects effects effects effects effects effects effects effects effects bit bit bit requires con developed area product product product product product product product product product product product product product nature depends associative measured tested tested tested hmm corresponds corresponds circuits implemented synapse synapse synapse synapse synapse supported adaptation adaptation adaptation end vlsi makes kaufmann needed reduced functional coefficients fully block increasing structures database database operation operation operation operation operation squared squared squared squared squared max making stored stored bits bits bits bits bits bits bits bits bits bits magnitude magnitude decay added sources improved similarity practical include include array array works speaker match gate gate gate organization storage storage storage digital digital digital correctly locally touretzky occurs hardware hardware strength strength critical measures designed performs performs constrained mateo integration integration integration characteristics demonstrated demonstrated proportional selective decrease program force areas appears pro written laboratory metric sensitivity slightly unique consisting consisting consisting springer depending variation variation restricted organizing organizing organizing approximations approximations approximations sign key calculation calculation calculation normalization boundaries remains euclidean euclidean euclidean kohonen kohonen kohonen kohonen kohonen precision precision precision precision precision precision plotted illustrated illustrated candidate variations characterized characterized tests included included included included modes computations essentially verlag dis lie contribution device device write dot dot dot dot dot dot dot dot dot dot dot quantization quantization quantization quantization quantization quantization computes thresholds thresholds operating circuitry circuitry circuitry circuitry varied limitations investigated ideal transistor transistor transistor transistor transistor transistor transistor transistor decisions variability variability understand examined examined integer voltages implementations prototype prototype front noted speakers speakers detected simplest simplest isolated isolated established charge charge charge charge ment ground track phenomena floating floating floating starts transistors read requiring virtual double conducted readily marked berlin vocabulary cal adjust globally fabricated fabricated fabricated tation drift linearity linearity dynamically turned reaching establish air imposed imposed modifications modifications degradation degradation degradation excellent loo dependency considerations subsequently std dramatically converted email session ram ties dec monotonicity causing drain drain realize adjustment representa increment increment increment magnitudes permits compatible efforts monitoring flash flash gilbert drops simplifies mann mann mann mann mann mann mann sessions accumulation recogni dropped converter conversion subtracted quantizer quantizer quantizer quantizer quantizer volts tance ready cess contents contents emerged proceeding repetitions refresh refresh gradual degrade proximation lincoln adjustments adjustments forgetting decrement decrement decrement decrement uniformity volatile volatile hypersphere penalties ana latch dev simu fell lations jim equipped wood zation straints compatibility clocks insures implemen lexington vth lends incre oot targeted ioo quantizing accessing gracefully relaxes quanti quanti petitive ohmic titions 
#@Mann_J,
#t3
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#*network network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data function function function function function figure figure figure time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm output output output number system system system system system error error error error error error error results results results results results results units units units units units units units units information information information information information information information information information information information information information information information information information information information information information information information information information information problem models hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based based based based weights weights weights weights linear linear linear layer case vector vector vector order shown shown shown shown systems systems systems systems values values parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach approach approach approach approach approach approach approach approach approach pattern image image image image image image image image image image image processing processing processing processing processing processing processing control large test test test test test test patterns analysis analysis analysis matrix matrix matrix optimal optimal optimal optimal inputs form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper examples feature net net task methods methods fig fig fig fig step step step step features level level level level current trained trained trained trained trained trained trained structure structure problems problems random high response representation representation architecture fixed line vectors vectors images images images images images images images images images images images images images images general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter real average average average average average theory gradient gradient obtained obtained obtained obtained obtained obtained obtained term term term term experiments experiments experiments university university university university computation computation computation computation research research research research independent independent defined defined found found found target estimate estimate estimate estimate estimate estimate estimate estimate standard standard computer presented presented presented presented presented presented presented map present present low press abstract applied applied applied find computational analog analog references component component ieee procedure procedure important propagation introduction parallel parallel parallel parallel tion tion tion lower rules rules signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals prior prior chosen previous previous required required multiple good long conditions conditions represent distributed distributed techniques techniques correct finite resulting computed performed called mapping mapping mapping factor made made study filter filter obtain original original vol relative relative true compared compared compared compared compared desired series series provide provide provide define define compute rates rates perform perform eye goal related related discrete discrete power power power mit accuracy accuracy accuracy accuracy comparison comparison contrast train descent source source source source source report institute words words department department technique internal individual individual individual represents represents represents final addition sequences maps considered cambridge directly directly directly hinton curve curve additional additional estimates estimates estimates estimates estimates estimates estimates san san top top top stage stage stage effects efficient full free speed estimated estimated estimated estimated increase produce produce produce produce produce condition channel channel weighted weighted weighted developed area path path provided provided provided provided selected selected backpropagation simply measured covariance technical feedforward feedforward feedforward transformation limited limited amount amount amount amount short short short short short short nearest nearest nearest common shape shape supported require eds eds face rumelhart rumelhart rumelhart noisy sensory fit auditory pairs underlying needed reduced account coefficients transfer transfer transfer significantly ratio ratio ratio ratio ratio segmentation matching principal squared squared representing making stored stored stored stored stored normalized normalized bottom early early frame combined combined combined combined combined combined combined combined combined produced produced produced produced produced produced produced produced sources sources description description architectures improved improved improved improve improve improve improve improve typical reported introduced introduced pixels sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski array engineering interest sufficient sufficient varying approximately approximately calculated calculated calculated calculated calculated works works tions smooth speaker speaker speaker evaluation channels channels channels williams improvement improvement increased grant amplitude amplitude constructed constructed digital alternative alternative alternative correctly hardware demonstrate demonstrate flow conclusion greater greater reduce neighbor accurate sound sound encoding encoding encoding integration integration presence presence physics physics largest characteristics characteristics demonstrated demonstrated california minimizing movements averaged identification configuration acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic force base acknowledgements pro produces perception perception perception perception perception ways laboratory laboratory distinct distinct modeled linearly physical electrical spectral spectral spectral spectral spectral spectral adding frequencies formation stages stages correlated squares estimator transform evaluated evaluate centered frames frames frames static similarly allowed allowed spectrum spectrum spectrum key partial performing epochs epochs combining combining combining combining combining combining combining combining intervals visible visible visible symbol strings bell inter weighting recognize automatic automatic automatic automatic automatic automatic automatic prove domains neighbors neighbors closely closely capable capable encoded encoded effectively symbols symbols mcclelland identify identify comparing vowel vowel vowel vowel vowel vowel traditional soc soc soc repeated procedures procedures heuristic video video video video superior contribution contribution contribution sampled sampled sampled vary cat automatically processors received attempt operating extract camera diego diego layered production production access essential updating environments humans humans humans limitations preliminary reducing mse mappings combine combine combine office decisions decisions decisions working comparable eigenvectors symbolic symbolic proved encode cognition gradients closest reading reading configurations perfect recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer changed observe mapped contributions serial attempts attempts residual great rows sensors sensors publishers publishers track improves biology sys preprocessing arise laboratories consequence scientific recognized sounds sounds bandwidth raw conjugate integrating integrating requiring requiring improvements varies greatly pathways empirically amounts poorly peaks passed remove incorporated templates vocabulary vocabulary rely incoming serve serve serve serve focused distortion spectra corrupted corrupted feasible ratios repre interconnected air chance knn salk corpus degradation vowels vowels vowels vowels vowels lip lip lip lip corre codebook male conjunction enhance consequences lawrence lawrence tic tic tic tic peterson peterson treatment insight pollack pollack pollack clean steepest extensively erlbaum erlbaum designing radar resonance audio microstructure sigma ease lit hillsdale hillsdale demon massively eric assess representa representa constrain preserved tems compensate degraded degraded degraded degraded degraded degraded degraded mouth mouth mouth afosr cole cole complementary categorization ambiguous ambiguous tract tract tract tract tract tract tract november handled served acoust acoust acoust sponding reversed resolve heavily hearing envelope envelope envelope envelope envelope hoc interpreting hopkins hopkins hopkins hopkins integrates tip acoustical exclusively proposes laser laser laser modalities systematically johns johns johns johns vocal vocal vocal vocal vocal vocal vocal complement comm absent remained magazine ranged ranged cess categorical categorical categorical baltimore baltimore tained ically translate translate massive talkers degrades comprehensive ambiguities jenkins jenkins jenkins jenkins jenkins predefined campbell cepstral sentations transferred erroneous tongue assoc assoc ther traditionally goldstein goldstein goldstein goldstein goldstein goldstein netherlands lips lips concurrently formants nation fuse serving barney barney lipreading lipreading lipreading lipreading jackson jackson susceptible poorer confused faithful categorized categorized categorized facing relied strated yuhas yuhas yuhas yuhas yuhas yuhas yuhas cate bernstein bernstein signif combi infrared fused fused articulators articulators articulators articulators accessed advocated teeth envelopes envelopes envelopes envelopes envelopes envelopes acous acous acous acous tremendous speeding preliminaries icant timation disc disc disc waste founda pletely supplement spect acoustically intelligibility intelligibility fusing hague laurel identifica 
#@Goldstein_M,Jenkins_R,Sejnowski_T,Yuhas_B,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training output output output output number number number error error error results results results units information problem problem hidden hidden based weights weights weights weights case order order order order order order order systems systems parameters unit recognition recognition pattern point point point single single processing control large large rate rate rate rate rate rate test test patterns patterns patterns patterns class inputs inputs inputs inputs inputs inputs inputs form shows shows shows signal signal signal signal signal simple paper examples examples examples examples small small net points points features trained trained trained trained trained trained trained trained problems random high response similar equation equation equation equation equation equation obtained university independent table table standard presented presented presented present position outputs outputs sample abstract applied back references important important propagation introduction complex complex generated difference difference lower signals signals signals signals signals chosen higher higher part center type type type long long long expected equations equations equations make make correlation length correct correct correct correct correct correct correct correct correct errors errors resulting resulting classes total respect sum sum sum made made made natural obtain original original original original original original original original relative samples samples application series series series series series series provide compute location constraints gain gain gain larger institute individual final addition equivalent experiment directly limit limit top top detection upper upper upper full significant produce produce produce derived area types types types discussion normal tested tested transformation fast short short short short short shape shape shape shape end end future typically typically pairs smaller unknown interesting testing york iterations window window window window window normalized bottom separate separate typical introduced introduced include sufficient calculated calculated calculated sensitive sensitive entire amplitude amplitude constructed constructed constructed constructed constructed invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant correctly occurs generally generally generally generally critical greater segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment depend differences encoding taking physics physics cycle drawn drawn start construct longer longer index laboratory segments segments segments segments segments segments segments segments segments segments segments segments segments sensitivity transformations remaining consisting applying choosing extracted extracted extracted extracted extracted extracted variation lee lee lee lee lee similarly translation translation translation translation translation translation translation translation translation translation translation translation translation translation slow slow slow slow recorded recorded recorded recognize recognize recognize illustrated automatic variations variations variations variations absolute characterized regular identified identified included included included included included presentation successful identify post invariance invariance invariance repeated contained classify vary vary generalize realistic wave wave giles giles giles attempt illustrates presents american create requirements difficulty replaced periodic periodic periodic stream variability trace trace trace trace trace extremely created perfect separated baseline arbitrarily seconds seconds seconds seconds seconds seconds devices percentage percentage percentage burst distinguish distinguish guaranteed phenomena fairly preprocessing broad recognized recognized recording author geometric generic generic lack substantial sums chose windows windows patients patients traces traces traces diagnosis diagnosis extreme shifted indices appropriately rotated count jth occurred transforms shifts presentations presentations presentations presentations presentations presentations patient patient patient patient patient patient patient patient patient patient patient patient patient patient patient patient patient moved moved heart heart ignore insensitive insensitive discriminate discriminate visually visually sine sine sine piece piece piece basically pieces pieces corrected additionally ideally resting rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm avoided examining attempted invariances translated care surrounding monitoring distinguished discusses discusses meet bridge fortunately parameterization twenty monitor thousand establishes hopkins morphology morphology inherently distinguishing distinguishing repetition digitized johns sliding constraining constraining differentiate comprised episode episode artificially artificially 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#@Lee_S,
#t3
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output number number number number number number system system error error results results information information information information information information problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case order order systems systems values values values values values values values values values values values values values values values values values values values values values probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight distribution approach pattern pattern pattern pattern pattern pattern pattern single single single single single single single single single processing processing processing processing processing processing processing processing control control control large rate patterns patterns analysis analysis class class class class class optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple gaussian gaussian gaussian gaussian paper paper paper small feature feature feature feature net net work work methods methods methods features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process level level current trained trained random high representation representation representation representation representation representation representation architecture architecture line line line line line general general speech parameter real real real real real real real real real real real real real real real real real real real gradient obtained note dimensional result threshold threshold threshold computation computation computation independent target target target target target target target target target target target initial initial constant estimate standard standard standard standard computer terms distance connections node node node node node node node node node node node node node node node node node node direction presented low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal machine machine machine sets position position outputs outputs outputs outputs outputs outputs sample abstract back computational likelihood references ieee positive positive propagation context context context introduction complex behavior statistical statistical statistical effect generated parallel parallel parallel tion change complexity spatial lower measure signals signals signals signals signals signals signals signals signals higher part part center previous type type type type type required required multiple conditions conditions represent represent distributed bayesian bayesian techniques correlation correlation correlation correct correct probabilities forward forward scale resulting resulting classes classes classes classes ing tasks tasks total computed computed respect respect multi performed means factor potential knowledge filter filter negative negative artificial artificial relative relative relative specific specific specific samples samples samples application application series series series provide provide compute compute rates perform determined determined connected distributions comparison contrast connection connection connection connection connection descent proceedings proceedings words version version consists code individual joint represents represents final final final layers layers layers layers layers addition addition framework computing computing domain additional additional estimates estimates estimates detection detection detection detection detection detection detection conference requires vision basic con derived randomly developed developed developed levels area area types actual evidence evidence evidence sampling achieved discussion normal normal normal normal tested transformation fast complete amount nearest nearest effective implemented implemented require require journal future future easily easily degree makes noisy simulated simulated simulated pairs pairs needed unknown unknown fully technology testing testing testing testing testing testing segmentation segmentation special matching matching matching matching matching matching matching mode mode leads representing representing representing iterations making window window window window window stored stored stored international normalized minimize improved improved improved improved discussed improve directions directions recent correlations correlations advantage pair pair separate separate separate separate takes similarity apply include include subject subject subject subject hierarchical recently recently engineering volume volume works tions tions match match achieve trans background background background background evaluation separation observation observation observation bounded sensitive lead deviation deviation correctly correctly feed feed white hardware pass pass pass pass runs starting place minimal segment conclusions conclusions operator neighbor neighbor sigmoid numerical numerical numerical performs performs taking presence presence characteristics characteristics characteristics characteristics characteristics intelligence intelligence iii targets targets targets targets program describes describes changing changing changing simultaneously simultaneously simultaneously linearly transformations transformations unique formed formed shift expectation extracted expressed transform transform evaluated evaluated updated modulation translation translation translation translation key reasonable normalization combining purpose iterative initially sufficiently assigned assigned assigned classified classified building template template template template template template template template template template template figures figures figures figures combinations priori assignment assignment uncertainty uncertainty domains domains absolute absolute sensor sensor sensor extra closely differ differ encoded detect computations computations computations situation tend tend receives receives traditional traditional kind procedures procedures contained prob contribution usual realistic thresholds automatically processors moves moves overlapping overlapping subsequent extract receive receive receive receive receive receive situations employed employed origin origin origin remain transformed transformed fourier fault fault fault dependencies dependencies matched matched adapt adapt adapt onset onset onset opposite created adjusted versions versions versions assumes consist consist generates submitted advanced derivation explanation explanation adapted adapted capabilities capabilities capabilities independence independence independence independence independence considerable considerable considerable snr snr snr snr snr snr purposes worst laboratories recognized optimize auto fluctuations reflect double items transient transient transient transient transient transient transient transient transient transient transient tional embedded embedded embedded capability simulate cohen share passed passed passed passed employ continuously templates templates templates templates templates templates templates templates passes gains differs popular acoustics enables electric age shaped deviations credit credit diagnosis diagnosis diagnosis summed contribute contribute representative accomplished accomplished extensive ratios ratios dynamically bin tem impossible enhancement arrival arranged dealing determination serves effectiveness symposium heuristics passive passive ambiguity corre overview dependency lengths april april express refers route likelihoods characterization accumulated fusion fusion fusion fusion fusion fusion radar radar radar radar radar crossing unable piece sig diverse classifications classifications classifications classifications classifications superimposed classifies warping transparent clas queue queue queue queue queue queue queue queue distri gas continues gener maintained maintained proba challenging efforts altered exceed exceed sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar sonar refinement outcomes avoidance permit nal transients prevents october inactive strict resembles bution lems lation handling bility corporate influenced jet transforming suite concern engine distinguishing spectrogram assessment fft propulsion classi deals deals intact governing explanations arriving totally sending enters enters prominent eighth sep sep merit merit merit merit merit massive unnecessary facilitates ted drawbacks prime transferred permutations optimizes suitably entered posi netherlands prohibitively differed ministry succession passage aver plex vation mexico adaptable handles albuquerque interna exceeding predominantly heuristically originated unmodified obser sification ship ship closeness closeness closeness possessing donald deviates deviates plates transforma underway sacrificing quently exposures exposures subse nection diluted bination discriminator lln recursions 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#@Malkoff_D,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural input input input input input input input function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set networks networks training output number system system system system system system system system system system state results units information information information based based based space weights weights weights weights weights weights weights weights weights weights linear linear linear layer layer layer layer case order systems systems parameters weight weight weight weight weight weight weight weight weight weight weight neurons neurons distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern point image image single processing processing control neuron neuron neuron rate rate rate rate rate rate rate patterns inputs form shows shows simple visual visual visual visual paper small small small small small small size feature feature work points field field level level current cell structure problems problems random random memory memory memory response similar representation representation representation representation representation representation representation representation architecture architecture architecture architecture architecture equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation section fixed line images speech parameter parameter term term term term term note activity activity activity activity activity activity activity activity activity activity activity dimensional result result university threshold threshold threshold threshold threshold threshold sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial constant terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node node node node node node node node node node node node node node node node node node node presented presented presented present present present activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object motion range press learn learn learn learn learn position position position outputs continuous sample abstract applied applied computational analog analog analog references positive positive adaptive adaptive adaptive adaptive introduction complex behavior dynamic search tion signals representations representations representations representations representations representations representations representations representations representations learned learned learned learned learned learned learned learned learned learned learned learned learned chosen part center previous required multiple multiple binary long conditions represent equations equations make scale finite simulations ing ing respect performed called called called orientation orientation orientation relative relative represented represented provide objects objects objects objects objects objects objects objects objects objects objects rates active active active active eye eye determined discrete brain approaches steps contrast modeling selection morgan proceedings report institute institute department implementation synapses synapses synapses consists internal represents represents final exp layers addition addition addition graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph sequences sequences sequences sequences sequences sequences sequences sequences sequences considered view view view view view view view view view view view view view view view view view view view view view view view transition transition transition transition transition trajectory san effects determine upper requires requires significant significant vision vision vision vision vision product product product processes processes evidence evidence evidence evidence evidence evidence evidence evidence depends depends constraint biological discussion limited complete complete complete stable short short short common common implemented shape synapse synapse synapse synapse synapse synapse synapse synapse synapse generate generate supported adaptation adaptation adaptation typically account dynamical functional technology significantly york mechanism structures leads call call max pre pre early decay decay decay decay decay decay attention added membrane discussed property separate separate separate introduced moving machines quadratic trees trees array array array array array array varying previously previously module module module module studies studies differential differential differential background organization organization entire constructed concept concept invariant invariant invariant invariant invariant invariant touretzky occurs occurs hebbian hebbian hebbian trajectories depend competitive retina designed faster learns learns mateo encoding solid assuming introduce scene force base appears appears van van van produces winner generating laboratory laboratory transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions category category category category simultaneously develop events implies extraction select competition competition competition competition competition competition stages overlap codes controlled organizing organizing evolution evolution evolution static static understanding understanding sizes activities activities activities activities activities activities activities activities activities activities activities activities activities activities similarly suggested partition key earlier convex intermediate initially initially sufficiently symbol symbol views views views views views views views views views views views dendritic 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aspect portion shapes art art art art detected extent extent grouping defines defines massachusetts massachusetts scenes scenes developing distinguish analyzed coded adjacent adjacent diffusion diffusion diffusion perspective organized preprocessing preprocessing preprocessing leaves arise arise mathematics ion ion axon recognized recognized recognized recognized grossberg grossberg grossberg grossberg grossberg grossberg grossberg axons axons cybernetics recognizing limits understood transient transient transient effort continuously rep partitioning fall attentional tile tile tile tile tile simultaneous realized contribute appearance appearance oxford fix saccadic concerned unity nonzero nonzero enhancement enhancement enhancement enhancement enhancement proceed proceed inspired air kaufman consideration convenient overcome simplify fan contract interpret hope illumination integrator arrays arrays arrays combinatorial alphabet alphabet exploring passive passive reset reset introduces governed governed ambiguity decide conjunction conjunction conjunction topological dendrite dendrite dendrite competing competing darpa winning recog axonal saccades sustained sustained storing horizon designing papers assigning accumulated resonance arcs arcs leaving shepard shunting shunting tween utilize additionally causing classifies avoids magnitudes decays continues activate relating maximally maximally maximally spreading relates represen paradigms confusion happen supports det exploited accumulation accumulation expense allen builds builds inhibit wins compete char emerges optics att recognizes syntactic periodically periodically experienced experienced experienced experienced adapts adapts tations doom doom doom carpenter carpenter allowable ard modulate modulate repetitive repetitive operated spario lincoln lincoln plexity deformations deformations resentation forgetting forgetting projective projective symmetries imagery imagery inhibits cad accumulating accumulating polyhedral permitted allocate nadel govern groupings disappears trim amorphous governs governs occluding occluding detec itive compressing insures investigators investigators decayed nodal vances lexington koenderink koenderink koenderink wash stimulate axo axo axo axo axo axo axo objec objec assures libraries runge ilar elaborated engaged lent lent aud aud ceases dxi kutta pioneered stark depiction featural formidable vie researcher reverberating signifying spon alized ctive noticing arid acteristic fignre pects constancies excit compet vhich stimulates 
#@Seibert_M,Waxman_A,
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information information information information information problem problem problem models models models models performance based based based based space weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector systems systems systems systems systems values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method approach approach approach pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single single single single single single processing processing processing large large large local local local test test matrix matrix matrix matrix matrix matrix form form shows shows simple simple simple simple simple simple simple visual paper examples small feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work task methods step points points field field features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features level level level level level level level trained trained problems problems problems random random similar similar representation representation architecture architecture architecture architecture architecture section section fixed fixed fixed fixed fixed fixed fixed images images images images images images images general parameter real real note experiments experiments experiments dimensional dimensional dimensional university university university university university university computation computation research research research independent independent independent independent independent defined target target target target initial estimate computer computer computer computer computer connections connections connections connections science science science science prediction map present present present present phase low low machine object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object sets sets sets maximum range press learn learn learn position position position position position position position components basis abstract abstract back back find find properties properties likelihood likelihood likelihood references component component component component important propagation propagation introduction complex complex complex hand hand hand variance variance parallel parallel parallel parallel search search search search tion complexity complexity complexity spatial spatial spatial spatial spatial assume lower representations higher center cases type type type multiple multiple multiple multiple good long represent represent represent represent represent represent represent represent represent represent distributed expected equations make make fact techniques region region region region correct correct scale scale scale scale scale scale simulations ing tasks computed computed respect respect respect called called called regions regions regions regions regions regions regions regions regions optimization optimization orientation orientation orientation orientation orientation study original artificial relative samples represented represented receptive receptive receptive objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects perform perform perform perform determined experimental experimental goal related constraints connected power larger larger connection fields train morgan proceedings report report report report report institute implementation technique technique internal code advances joint represents represents connectionist connectionist connectionist connectionist connectionist difficult difficult final layers layers layers layers layers layers layers layers layers scheme scheme scheme framework framework computing domain domain domain experiment experiment experiment experiment experiment directly directly directly directly directly directly directly directly hinton hinton hinton hinton hinton hinton hinton hinton additional view limit san san top conference conference determine determine determine efficient upper upper upper requires vision vision vision vision vision basic pages pages pages increase con derived derived weighted weighted area area types types types types types types types types types product product actual provided finally selected evidence nature sampling constraint constraint constraint biological discussion technical technical technical technical technical increases describe describe arbitrary arbitrary tested tested transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation limited limited assumption complete predictions predictions predictions common implemented implemented implemented implemented supported require main journal journal ability ability ability ability ability ability hypothesis instance instance instance instance future easily easily easily noisy fit probabilistic probabilistic underlying combination combination technology interesting testing testing testing testing york increasing segmentation mechanism consistent structures matching matching representing representing representing representing representing representing representing representing representing details details pre international international international normalized normalized bottom bottom supervised depth frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame combined combined produced run added description description description predict predict predict predict improved discussed discussed advantage pair pair takes apply include identical identical identical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical cognitive highly unsupervised unsupervised unsupervised unsupervised teacher tions smooth correspond achieve address positions organization organization sensitive entire entire grant grant invariant invariant invariant wide rotation predicted predicted predicted correctly touretzky occurs generally hardware pass demonstrate critical conclusions valued valued competitive accurate accurate mateo suggest encoding encoding encoding encoding encoding california intelligence turn relationship manner manner manner connectivity configuration areas reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference explicit relation relation edges written perception describes describes dept dept dept confidence confidence confidence confidence confidence confidence missing coordinates simultaneously simultaneously simultaneously averaging averaging involves transformations transformations transformations transformations transformations transformations angle angle angle mutual formed formed shift extraction extracted extracted focus expressed interpretation detailed transform transform transform restricted organizing frames forms forms forms digits key key key partial epochs measurements reduces combining combining false intermediate intermediate intermediate intermediate intermediate visible visible construction foundation foundation views views degrees precision avoid perceptual perceptual combinations coordinate instances instances instances instances recognize recognize recognize recognize recognize recognize recognize recognize recognize extension extension discuss mozer mozer mozer mozer mozer mozer mozer mozer candidate candidate candidate candidate domains partially structural structural structural structural aspects capable encoded identify detect build efficiently efficiently invariance quickly contained contained allowing allowing lie sin strategies cues built involved michael michael realistic correspondence denker denker highest hypotheses hypotheses consisted neighboring intrinsic intrinsic simpler origin diego requirements relations relations relations relations relations matches matches successive mappings relationships relationships structured working hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy fundamental notion examined plausible plausible editor traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic predicts recognizer aspect aspect versions freedom shapes shapes shapes academic academic grouping developing publishers coded multiplication handle handle london spatially implementing sections precisely constructing mation pool acknowledgement recognized recognized angles angles implicit toronto toronto toronto toronto toronto toronto lowest lowest patches cybernetics recognizing recognizing recognizing recognizing recognizing recognizing recognizing alignment raw robustness robustness consistency consistency consistency flexible tional capability fed introducing detecting slower frequently span howard synthesis ture aim extracting richard inherent boston sophisticated decreased segmented coherence deviations deviations baird sharing consistently pose pose discontinuities primarily forming forming forming tation perfectly zemel zemel zemel zemel zemel zemel zemel zemel zemel repre addresses discover impossible eliminate connecting connecting connecting robotics rigid rigid eliminated familiar primitive primitive viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint serves hope occurring nearby transforms removing star ral canonical corner spurious composition exploring exploring becker becker mjolsness mjolsness james corre expanded colorado stereo occlusion express express creating ballard ballard canada extends relies agree grants generalizing dividing assigns assigning sequentially numerous unable outline sine kluwer guyon recursively encodes uniquely employs poses tween adopt abstraction abstraction abstraction instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation assignments england massively henderson grouped geoffrey hubbard boulder individually ullman confirmed retain cosine increasingly increasingly selectively zip maintains likewise worked resembles resembles demonstrating appearing copies sponding lowe lowe lowe lowe impractical mcdonnell transforming builds ers pictures graf concerns concerns triangles architec ref lying carries sloan creation hough hough hough fication addressing occluded inst gardner neocognitron tern stems unaffected converts ton crg crg align locating tailored relying fukushima fukushima ontario accepts neurally sky sky anandan anandan mented stars stars stars stars stars stars contiguous suppresses tar gindi gindi spans allocate categorize viewpoints transfor highlights instantiations instantiations instantiations instantiations instantiations interna triples orienta unsegmented unsegmented unsegmented checking hin quired constrains composing loose implemen ont ont embed ject quicker erence triplets triplets barrow barrow penultimate publish xio xio frontiers sio alfred senting vancouver devia nce natu lates speci instan recognising manipu compounded actly 
#@Hinton_G,Mozer_M,Zemel_R,
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layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case order shown shown systems weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern point image image processing processing processing rate rate rate rate test patterns inputs form form form form form algorithms simple simple simple gaussian gaussian gaussian visual visual paper small size size feature feature feature feature feature net task task task points features features features features features classification process process process process process process level level trained structure structure structure structure random random high high memory memory memory response response response similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation fixed fixed rule images images images images generalization generalization generalization generalization parameter parameter real approximation approximation average theory obtained obtained note note experiments experiments experiments experiments experiments experiments experiments experiments activity activity activity activity result result result university threshold threshold threshold threshold computation computation sequence sequence target target target target target target initial initial initial initial constant estimate computer terms terms distance distance distance distance connections connections connections connections connections connections connections science left left presented presented presented map present present present activation activation activation activation activation activation temporal object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object motion range press press position basis abstract abstract convergence analog analog references due due important decision behavior stimulus stimulus effect effect variance parallel tion difference difference spatial lower measure prior representations representations representations representations representations representations learned learned learned learned part center center bound cases required required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple long represent represent distributed make fact techniques correlation correlation correlation correlation correct simulations resulting ing tasks human human human human human human human human human human human called called times made made natural natural feedback orientation orientation orientation orientation orientation global global relative specific specific specific specific specific specific specific specific represented compared application receptive provide provide define objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects active active active active active active active active related related connected connected brain mit mit mit mit mit mit comparison comparison comparison comparison comparison comparison connection connection connection connection connection connection fields support support dependent dependent implementation consists internal individual bias layers delay scheme sequences considered cambridge cambridge equivalent experiment directly directly curve view view view view view view view view view view view view view view view view view view view view view view view view view view view view view curves curves stage stage stage stimuli effects effects efficient upper upper requires vision increase provided nature depends biological biological biological arbitrary denote tested tested tested fast fast fast close close inverse finding finding amount amount shape supported eds square end ability ability ability ability ability easily degree sensory simulated simulated simulated testing testing increasing mechanism mechanism mechanism mechanism mechanism mechanism mechanism matching uniform principle principle operation details direct direct direct direct making making stored stored stored stored stored stored frame frame frame frame discussed lateral lateral lateral strategy strategy strategy strategy strategy subject subject sense cognitive cognitive cognitive highly compare unsupervised subjects subjects subjects subjects subjects subjects subjects works definition definition background locations modified gate storage entire increased horizontal occur rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation correctly locally pass demonstrate half half strength strength strength strength strength strength strength strength hebbian hebbian hebbian hebbian hebbian reduce depend measures clear peak performs moody moody practice practice practice practice learns strong mechanisms proportional radial turn turn decrease decrease decrease relationship manner appears appears appears appears appears appears appears appears perception perception winner winner winner winner describes tuned vertical vertical distinct dept modeled explicitly coordinates coordinates simultaneously linearly involves involves transformations transformations formed formed cycles decreases decreases dependence dependence dependence dependence dependence stages correlated interpretation interpretation interpretation interpretation variation organizing organizing organizing organizing organizing organizing organizing centered centered activities slow performing classical interpolation intermediate initially sufficiently views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views template figures activations priori coordinate sciences recognize recognize determines activated identified identified closely uniformly encoded computationally poggio poggio poggio poggio presentation presentation presentation identify schemes schemes projections projections essentially identity ten ten ten summary compact quickly kind kind classify list relaxation relaxation relaxation dot highest highest leading leading thresholds thresholds thresholds principles consisted decreasing decreasing extend law bars employed remain strengths strengths association association association association association association association accurately successive successive respond respond fashion fashion links rest investigated notion closest necessarily opposite psychology psychology created created perfect thought thought ensure panel panel panel panel shapes store attempts wta wta wta wta wta wta wta brown developing distinguish orientations growing phenomena phenomena turns perspective perspective closer commonly recognized recognized recognized beginning gradually localized localized recognizing preceding summation summation apparent people people led capability readily psychophysical adjustable employ employ rep rep psychological templates operate spread differs monotonic qualitatively substantial decreased findings findings realized trade phenomenon phenomenon secondary proportion cooper cooper cooper appearance appearance tation tation temporally girosi girosi controlling connecting enhancement rotations chance chance stronger chains darken darken difficulties proceeds fan multiplicative familiar familiar familiar familiar familiar familiar familiar viewpoint viewpoint serves wire wire wire wire monotonically monotonically monotonically hint canonical canonical canonical canonical canonical canonical canonical canonical canonical responsible enhanced presentations reliably edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman corre decide mental mental mental mental mental mental mental mental mental mental mental mental mental vertices vertices vertices enhance schwartz schwartz emergence surprisingly shortest storing erlbaum subsequently thresholding linguistic yielded associations geometrical outline shepard shepard shepard session session session session latency latency latency asked encodes encodes distinction aij spaced suppressed imagine adjustment assess representa favor grouped allocated thresholded thresholded thresholded thresholded represen selectively selectively selectively responding accounted familiarity memo memo memo rotating rotating elsevier exhibited intensive intensive demonstrating served served served palmer palmer sponding consuming bility prefer justification builds subjective subjective replicated replicated usefulness concrete evenly normalize goodness creation raised carrying substrate emerged winners winners dist dist tivity rotate rotate progresses resemble arousal blurred weinshall weinshall weinshall weinshall weinshall weinshall weinshall weinshall weinshall weinshall weinshall corr corr corr corr claimed responsive lose blurring succession succession psy providence perf sponse viewpoints viewpoints viewpoints attitude faithful unfamiliar foot pervised disappears conjunctions conjunctions signif resentations resentations stepwise strengthened subjected replicating regulated recruited recruited rock rock biilthoff biilthoff kandel kandel closeness unsu remembered judgement correlating prac pinker pinker sophistication chophysical baddeley vantage parallels progressive involvement capa disappearance viewer signify chase appearances icantly tice pends ceived abandoned congruence laxation bfilthoff anew 
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#*network model model model model neural neural neural figure figure figure figure figure figure figure figure figure figure figure figure set number number system system results units units information based based based based space space space space linear vector vector vector vector vector vector vector vector vector vector vector order shown systems systems values noise neurons recognition recognition recognition recognition recognition method method method method method method pattern point point point point point point point point point point point point point point point point point point image image image image image image image image image image image image image image image image image image image image image image single local matrix shows shows shows shows shows shows simple simple gaussian visual visual visual visual visual visual paper paper small small small small size feature feature feature net net net work work work task methods methods methods cells cells points points points points points points points points points points points field field field field field field field field field field field field field features features features features features process trained trained cell problems memory memory memory similar similar similar representation fixed fixed line line line line line line line line rule vectors vectors vectors vectors vectors images images images images images images images images images images images images images images general general general gradient gradient gradient gradient experiments experiments dimensional dimensional result result result threshold variables computation computation computation computation research research research research research independent defined defined defined defined initial constant table table table table table computer computer computer terms terms distance distance distance distance distance distance distance distance distance distance distance science left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction map map map map map map map map map map map map map map map map present low object maximum position position position components sample sample sample sample sample sample sample sample sample abstract back find find properties references component introduction hand parallel parallel difference difference difference difference difference difference difference assume representations representations representations word higher center center center cortex cortex cortex cortex cortex good good long long long long distributed make make make fact region scale scale scale scale finite resulting total total human human sum sum sum sum elements means means means made made made made specific specific specific specific specific specific represented compared compared compared provide define compute compute objects objects rates rates location location perform related related connected equal equal power power fields source report institute words words words internal code code code code code code code code code code code code advances maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps computing computing computing computing equivalent directly curve view san top top bit detection upper vision vision vision vision vision vision vision vision vision vision vision vision basic basic give produce randomly levels area lines lines lines lines lines lines lines lines lines lines lines finally sampling biological associative associative associative associative normal normal normal normal normal technical finding amount short common shape shape shape shape shape shape supported role main end end pixel pixel pixel pixel pixel easily degree makes makes kaufmann simulated needed testing special uniform uniform representing representing filters making bottom early early early early early early early early early early early magnitude magnitude magnitude magnitude magnitude magnitude magnitude idea idea combined run added light light light discussed directions directions directions directions machines pixels pixels pixels pixels inference array array compare approximately volume works works match correspond studies sparse positions modified generalized grid grid sensitive sensitive sensitive entire entire entire entire entire constructed horizontal horizontal intensity intensity intensity intensity wide touretzky white pass runs starting place place greater tangent differences practice mateo suggest suggest encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding mechanisms mechanisms drawn drawn california california proportional proportional proportional turn assuming variety manner characters identification identification force force force force force force force base acknowledgements areas digit digit edges edges edges written perception perception perception ways vertical segments text angle angle angle angle angle adding adding adding letters yield national stages viewed transform labels centers forms sizes similarly digits digits digits digits digits digits digits digits discrimination roughly roughly roughly purpose distances distances distances filtering euclidean david degrees degrees degrees degrees degrees degrees degrees handwritten color color color color color contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour memories memories memories recognize recognize recognize black discussions simplicity sensor sensor middle letter letter closely suitable suitable differ encoded encoded encoded encoded encoded encoded encoded encoded encoded computations comparing comparing ten composed composed kind interested running gray gray gray sampled sampled dot nips denker denker ill ill automatically oriented oriented oriented humans association preliminary preliminary mass mass mass mass mass mass mass rise scalar combine scaled scaled scaled encode encode encode encode contours contours contours contours contours circles coarse closest trace opposite opposite opposite equally perfect recognizer thought thought thought detector explored shapes shapes defines defines advanced rows stop sensors sensors sensors sensors agreement coded comparisons rapid closer widely forces forces directional directional leaves leaves controls recognized angles angles angles beginning ridge recognizing recognizing recognizing recognizing integrating people consistency dark dark dark dark howard parent parent curvature hamming kinds attraction attraction attraction attraction attentional baird perfectly concerned circular circular circular eliminate generality generality inspired overcome mail attractive attractive attractive intelligent handwriting resulted transforms fail salient corner excellent tone irregular regarded accounts jackel refers rich canada observer insensitive dividing assigns limitation limitation unchanged crossing leaving outline minus minus guyon cooperative job encodes encodes propagating propagating exception regularity ical guess henderson perpendicular perpendicular perpendicular perpendicular magnitudes stroke graphics hubbard douglas books kanerva kanerva kanerva kanerva kanerva kanerva zip zip covered inversely turning nasa nasa supports likewise places challenge reversal sake olshausen finer finer powers pictures pictures pictures pictures adult graf concern proposal codeword codeword meeting detects contributes strokes strokes strokes 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#@Kanerva_P,
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#*network network network network network learning learning learning learning learning learning model model model input function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time set set set networks training training training training output output output output output output number system system system system system system system system system system system system system system error error error error error error error state state results results results results units units units units units information information information information information information information information models performance performance performance performance performance performance performance performance based based based based weights weights weights systems systems values functions unit unit unit unit unit unit unit unit unit unit unit method approach approach approach approach approach image single processing processing processing processing processing processing processing processing control control large large rate rate rate rate rate rate rate rate rate rate rate analysis analysis analysis analysis analysis analysis analysis analysis analysis inputs inputs inputs form form signal signal simple simple simple simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual examples examples small small size work task task task task task methods fig fig process process process level current structure structure structure high high response response response response response response response response response response response response response similar similar similar rule rule images images images images images images real approximation approximation approximation approximation approximation approximation approximation theory activity activity result result result variables variables computation solution research research research research research found found initial constant constant estimate estimate estimate estimate estimate standard connections science direction direction direction direction direction direction map map map map map map map map map map map map present phase frequency object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range press learn position position basis basis abstract applied properties references due due due due adaptive introduction complex complex complex hand estimation estimation estimation generated generated generated generated generated tion change change change complexity complexity complexity spatial measure measure measure measure measure measure signals learned learned learned chosen chosen part part part center previous bound cases required required good good long make techniques correct correct correct correct correct observed errors errors resulting ing ing tasks human human human performed times times means made global artificial artificial artificial artificial artificial relative samples application provide rates rates perform perform perform perform perform active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye goal goal connected motor motor motor motor motor motor motor motor motor motor motor motor motor approaches mit mit mit accuracy accuracy contrast connection update update support train dependent report institute institute represents responses responses difficult difficult addition addition ai cambridge environment environment environment environment environment directly directly directly additional additional design design full requires significant significant significant vision increase robot robot robot robot robot robot robot robot robot robot area velocity velocity velocity velocity velocity actual provided finally processes processes processes processes processes processes processes processes processes nature achieved measured measured measured normal increases limited corresponds stable stable stable stable finding amount role adaptation adaptation adaptation journal hypothesis future makes including reduced reduced technology technology transfer transfer transfer transfer significantly head head head head head head head head operation operation leads representing call pre frame run sources predict improved robust robust takes takes typical movement moving moving side sense sense sense engineering engineering sufficient varying conventional approximately works axis axis axis axis smooth yields achieve modified modified modified observation grid sensitive sensitive sensitive constructed constructed exists studied trial wide wide rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation correctly correctly correctly loop loop demonstrate flow place place place reduce conclusions measures accurate retina retina retina performs performs performs learns learns learns mechanisms external external characteristics characteristics demonstrated demonstrated intelligence intelligence intelligence radial variety movements relationship scene scene configuration base base base base base base acknowledgements reference reference reference reference pro edges optical describes laboratory laboratory ann distinct coordinates involves angle events formed shift shift shift shift shift shift shift shift shift quality implies extraction extracted squares squares viewed detailed open open updated updated ocular ocular ocular ocular ocular ocular ocular ocular static static static approximated completely converges partial reasonable measurements measurements roughly generation initially initially initially msec construction construction construction degrees includes thesis retinal retinal partially aspects capable encoded encoded modification poggio poggio successful build computations comparing characteristic kind strongly video video neuroscience follow follow device device device cues built simplified absence board board correspondence neurosci principles moves camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera body body body body explore command command command command command command create create requirements environments steady limitations limitations accurately accurately hall reducing successive respond detectors detectors detectors applicable plasticity plasticity plasticity plasticity plasticity plasticity plasticity combine office office reliable proper variability statistically analogous act measurement measurement measurement measurement adapt adapt man opposite opposite rev eyes eyes eyes detector detector detector detector detector detected attempts animal massachusetts residual advanced vor vor vor vor vor vor vor vor vor vor vor growth navigation navigation tractable reasons reasons spatially rapid rapid rapid tive forces desirable pitch greatly axes capability peter autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous effort incorrect incorrect commands commands commands maintain maintain rely measuring characterize ture cal prevent prevent inherent begins cumulative cor cor benefit ear ear extensive saccadic driving driving animals velocities girosi vestibular circular mobile mobile naval naval plays inspired inspired inspired inspired inspired minutes minutes difficulties analogy contract contract contract observing observing wire shifts days hours continue prentice excellent mance combines ensures periods james paul perfor overview heart demonstration schwartz facilitate claim creating master matter motions motions motions motions motions motions motions considerations projects characterization ccd approx approx reflex ence numerous incorporates visually visually visually latency latency incrementally incrementally incrementally chapter tendency avoided chess eric adapting perpendicular intuition robots robots robots bounding hughes simplifying guided guided categorization rough rough rough monitoring oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor maintains esti book inverting inverting memo page elsevier applicability travel struc continually worked correlate correlate correlate correlate correlate correlate spite locomotion drives sees recogni vestibulo vestibulo vestibulo cliffs smoother viola viola viola viola viola calibration calibration calibration calibration attempting clarity cylinder conversion compensation agency settle sen contrary compensated lisberger adapts positioning positioning positioning positioning cess correlates kinetic stabilize stabilize motors motors motors motors lar modern defense inaccurate surprise platform platform unexpected stabilization stabilization stabilization stabilization stabilization stabilization publishing degrade plastic stabilizing tal putational walking blurred observes minute slip slip slip slip weakness imation imation saved adap mate displaced vertebrates vertebrates vertebrates neurally neurally neurally neurally stabilized bearing bearing functioning functioning circumvent susceptible glasses charac attitude attitude rejecting categorized particu wheel assist foot vehicles vehicles intervention signif wood rectly rectly autonomously traversing conscious conscious photo canals identi aging nystagmus nystagmus inertial inertial tomaso kandel miles miles miles hildreth succeeding calibrated calibrated sory terrain terrain inaccuracies counteract counteract counteract counteract navigational designers injury injury monitors compensating attaining attaining icant tection confirmation universally rection engineer ang ang tins vironment pacing batteries subunit motorola formidable marc wearing illness illness federico rim incorpo tactical entail disastrous nit looms rai monly rected engle 
#@Viola_P,
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#*network network learning learning learning learning learning model model model model model model model model model model model model model model model model model model model neural neural data data data data data data data data data data data data data data data data data data data data data data function function function set networks algorithm output output number number number number number number number number number number system system system system results information information problem problem based based based based based based based based based based based case order order order shown systems probability parameters parameters parameters noise distribution distribution distribution image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image control local local local 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dynamic generated parallel parallel parallel recurrent recurrent energy energy energy energy energy energy energy energy energy energy energy energy spatial spatial chosen part part previous type good good good represent represent represent represent markov markov proposed proposed proposed proposed proposed minimum minimum simulation human human human multi multi sum regions optimization potential potential potential orientation orientation knowledge knowledge filter filter filter filter filter filter filter filter filter filter original original original vol vol vol vol specific specific specific receptive define objects proc proc active determined experimental goal constraints fields report consists represents represents exp scheme framework equivalent equivalent equivalent hinton hinton solutions bit efficient efficient world vision vision estimated channel channel channel coding derived developed levels levels area types processes processes selected selected selected selected selected selected inhibitory inhibitory inhibitory depends sampling sampling constraint technical inverse shape auditory simulated block significantly ratio ratio segmentation mechanism special iterations filters filters filters filters filters filters filters filters filters filters bits early minimize property introduced introduced introduced introduced machines side side side pixels sejnowski sejnowski cognitive approximately works correspond studies achieve achieve trans increased lead derivative deterministic interactions interactions interactions interactions interactions constrained propose strong characteristics characteristics characteristics regularization variety configuration configuration configuration configuration configuration configuration annealing areas boltzmann boltzmann perception tuned infinite interaction minimization quality quality extraction competition family expressed reconstruction reconstruction communication communication centered sizes partition diagram 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#@Inui_T,Kawato_M,Miyake_S,Okamoto_T,
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process current cell cell cell problems response response response similar similar representation architecture architecture architecture show fixed line line real real real real real real theory theory theory theory theory theory theory theory theory theory theory theory theory experiments activity activity activity activity dimensional result university university threshold threshold computation solution solution research log defined found dynamics dynamics initial initial initial initial terms distance connections connections connections connections synaptic left left left direction presented presented map phase phase phase machine machine machine object object object object object object object object object object object object motion motion motion motion range range press press press press position position position position position position position components basis basis abstract find computational references positive important important adaptive adaptive adaptive adaptive adaptive action action hand hand effect dynamic dynamic dynamic generated parallel tion change energy difference assume lower measure measure signals signals signals signals higher higher higher required required cortex conditions conditions conditions conditions represent length ing tasks simulation simulation simulation human human elements elements elements mapping mapping means means feedback feedback orientation negative artificial artificial artificial artificial artificial artificial relative relative relative relative specific specific specific compared compared desired desired desired desired objects objects objects objects location eye experimental experimental experimental experimental experimental goal connected motor motor motor motor motor motor motor motor brain brain brain brain brain brain power mit mit mit mit selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection department consists joint joint joint joint joint joint responses responses delay scheme ai maps cambridge cambridge cambridge cambridge experiment environment environment curve view solutions design limit trajectory effects effects bit determine upper upper upper upper requires world world world world basic basic increase give con derived robot robot robot types lines actual actual finally processes processes selected selected nature biological measured group group group group group group group group group group group group group group group group group group group group fast fast fast fast fast fast fast close complete actions finding amount assumed shape shape shape eds eds eds journal end end end end end ability future future sensory sensory sensory sensory simulated typically smaller combination combination combination account dynamical functional york head matching matching empirical mode mode mode principle principle principle principle operation leads leads numbers idea added neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal population improve resolution typical typical typical movement movement movement movement apply strategy moving period subject machines array array array array cognitive engineering previously subjects match studies differential positions positions modified organization organization organization sensitive sensitive sensitive increased increased arm arm arm arm arm arm arm arm arm arm arm arm arm amplitude constructed constructed horizontal lead concept suggests extended wide wide alternative alternative move occurs generally generally hardware hardware critical place minimal reduce segment central clear peak peak performs temperature suggest presence presence proportional proportional intelligence intelligence intelligence turn movements movements movements movements selective selective selective selective selective decrease relationship iii iii iii iii iii iii iii groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups connectivity configuration configuration configuration question van longer perception perception perception perception primary primary describes dept implement electrical transformations angle angle unique unique consisting develop applying springer expectation versus controlled similarly similarly similarly classical remains sufficiently currents contour inter inter sciences recognize discuss discuss discuss discuss specifically structural major reason determining sensor sensor sensor sensor computationally computationally effectively essentially verlag quickly quickly kind link link link link showing interested contribution strategies device satisfy vary simplified paradigm paradigm providing correspondence ill reach reach reach reach reach principles attempt attempt oriented poor create essential requirements requirements experience experience difficulty varied involving strengths behaviour behaviour behaviour behaviour ideas ideas links links links links links links links rest applicable possibility muscle affect fundamental fundamental phases phases phases notion analogous matched hill adapt reading equally eyes ensure aspect der detector mapped mapped nervous nervous detected serial serial synthetic animal devices devices mentioned burst burst burst burst histogram histogram directed trivial trivial sensors sensors sensors sensors sensors orientations growing adjacent adjacent adjacent majority expensive handle reasons drive perspective straight closer division immediately controls angles angles implicit begin geometry researchers requiring greatly populations substantially led amounts tional generic generic autonomous introducing variant variant requirement operate measuring reaches substantial kinds shaped specifies calls wesley cor naive secondary secondary sensing analogue primarily addison appropriately member controlling addresses rotations interconnected robotics robotics robotics robotics robotics robotics robotics robotics rigid reaching arranged arranged automaton primitive primitive grow efficacy neurobiology roles effectiveness optimally adequate motivation date exploring cerebellar ensures edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman connect encountered paul lengths histograms lawrence arrangement arrangement modelled cerebral spatiotemporal suggesting ahead specificity specificity motions integers acknowledge mechanical mechanical mechanical mechanical mechanical mechanical mechanical boxes mind unchanged geometrical largely converted diverse responds responds responds seek perceived perceived perceived ical personal tor experiences possibilities letting edinburgh edinburgh edinburgh massively continuity manipulation acting shifting ibm insights gained robots mammalian execute life life distant distant playing intra intra retinotopic relating relating careful considers books differentiation ultimately player manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator diversity register enforce locking locking bring amplification amplification things intensive differing correlate develops coming coordination coordination stops stops circumstances species expense stephen quantify ping blake virtually attempting dominates developmental industrial russell striking tuple tuple proposes proposes loads comprising trol joints joints joints robotic evolutionary positional correlates correlates faced tra pin tim tim blocked limb mounted discriminating predetermined damping notions deeper lifetime touch touch couple avenue registration signalling signalling intel foveated paid effector effector manipulators manipulators manipulators neurology forrest strain comprise functioning brains historical driver touching george gerald gerald gerald gerald gerald organism organism organism lock proportionally braitenberg braitenberg repertoire repertoire repertoire repertoire repertoire repertoire repertoire repertoire repertoire repertoire repertoire jim jim shoulder premise proprioceptive selec lend instructed ditional antagonist antagonist suc ballistic ballistic ballistic ballistic ballistic manifest elbow rooted death structurally debate subsequences subsequences subsequences infrared infrared actuators crab crab crab crab agonist agonist agonist actuator actuator actuator actuator actuator actuator phasic reciprocally tuples rests mountcastle registered instabilities ser manipulate eleven eleven eleven biolog mol distinguishable schmitt radically translationally flux flux escaping organi stark stark hitting sharpness paral coordinating amplifying adversely moti gon favoured warm heed telligence join mechanically ditionally 
#@Donnett_J,Smithers_T,
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function function function figure figure figure figure time time time time time set set set set set set set set networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output number number error error error state units units units units units units units units units units units information problem problem problem problem problem problem models models models models models models models models hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear layer layer layer vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order systems systems systems systems values parameters parameters noise weight weight weight weight weight functions functions functions neurons unit unit unit unit unit unit recognition recognition method method approach approach approach approach approach approach approach approach pattern pattern point point point point point point single single single single single single processing control control control control control control control control large large local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local patterns analysis analysis class optimal inputs inputs inputs inputs form form form form form shows shows shows shows shows shows signal algorithms algorithms simple simple simple simple simple simple paper paper paper paper paper paper paper paper examples net work work work methods methods methods methods methods methods points points points points points points field classification process level current structure high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response similar similar architecture architecture architecture architecture architecture architecture show fixed line vectors vectors general generalization generalization real approximation approximation theory gradient gradient experiments dimensional university university computation research research research research research research research found found sequence sequence dynamics dynamics dynamics dynamics dynamics standard computer computer computer computer computer computer computer computer computer computer computer distance distance distance distance distance distance distance distance distance distance distance distance connections connections science science left presented activation machine machine machine machine machine machine machine sets range range press press press press press learn components nonlinear nonlinear nonlinear outputs outputs continuous continuous abstract find find computational convergence convergence convergence density density properties properties references ieee ieee ieee adaptive adaptive introduction complex complex complex hand circuit statistical statistical statistical dynamic dynamic generated parallel parallel parallel parallel search search search tion tion rules rules rules measure measure learned chosen chosen center previous previous type long long represent represent represent represent tree expected proposed proposed length length correct errors ing regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression performed mapping means means made feedback feedback feedback feedback feedback feedback global global global global global applications artificial samples samples samples samples samples samples samples desired desired desired desired desired desired desired cross series series series provide compute rates proc proc proc proc motor motor motor motor brain brain approaches approaches approaches approaches approaches mit mit mit comparison connection connection support support descent descent source nets modeling proceedings proceedings proceedings report report institute institute department department implementation version version technique consists consists kernel joint joint joint joint difficult bias layers layers addition ai cambridge cambridge cambridge equivalent equivalent directly directly curve curve curve curve curve curves curves curves estimates estimates design design design design design trajectory trajectory trajectory trajectory conference conference capacity capacity capacity statistics statistics statistics statistics free world weighted weighted weighted weighted weighted weighted randomly controller controller controller controller controller controller product product actual provided provided selected selected selected selected selected simply simply biological achieved feedforward feedforward arbitrary arbitrary fast limited limited inverse surface surface surface finding finding nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest common generate eds eds eds eds journal journal journal journal journal journal journal journal square fit fit fit fit simulated simulated simulated simulated simulated simulated simulated simulated simulated combination reduced unknown fully technology technology technology york york york special consistent structures empirical squared squared squared stored stored stored stored stored stored stored international international early polynomial polynomial polynomial idea produced predict perceptron improved robust robust movement movement movement movement movement movement movement moving moving moving include quadratic quadratic quadratic quadratic cognitive cognitive relevant engineering engineering engineering observations teacher tions smooth smooth smooth smooth trans address evaluation organization grant grant arm arm arm arm arm arm arm arm invariant digital matrices rotation alternative locally locally half half critical reduce neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor depend depend interactions numerical performs practice strong reduction intelligence intelligence minimizing user movements program force question pro winner winner describes laboratory laboratory metric metric metric implement coordinates physical electrical adding quality quality national national independently dependence squares squares squares forms suggested suggested key smoothing smoothing smoothing smoothing fitting fitting fitting fitting fitting fitting fitting purpose purpose interpolation interpolation interpolation foundation foundation euclidean euclidean euclidean euclidean query query query query query query query transactions transactions building sciences sciences sciences automatic automatic automatic automatic automatic phys neighbors neighbors neighbors neighbors neighbors neighbors tests society society differ refer refer quickly procedures running running running follow built quantity quantity paradigm minimizes minimizes computes highest highest leading leading approximating acknowledgments software cowan cowan cowan explore command parametric american american american american transformed poor requirements experience experience experience estimators estimators estimators association association association association issues mass matches matches history ideas office office referred maximizing func surfaces surfaces contours reading analyze predicting spline implementations friedman friedman portion taylor taylor taylor taylor taylor taylor taylor taylor taylor academic academic store multivariate multivariate multivariate contributions arbitrarily serial electronic electronic electronic chaotic chaotic optimum optimum optimum optimum optimum massachusetts massachusetts years guaranteed answer answer answer london drive implementing preprocessing mathematics scientific scientific computers computers computers author annual greatly consistency consistency lms atkeson atkeson atkeson atkeson atkeson posed sharp sharp rep compares robinson robinson polynomials kinds boston eventually summed lab college analogue analogue interface forming oxford acm velocities nat naval eliminate eliminate royal royal air fits fits smith smith mail logarithmic multiplicative contract biased serves nearby nearby guide symposium nonparametric nonparametric nonparametric nonparametric nonparametric planar planar selects analyses utilized interference interference programs negligible widrow widrow widrow sim lawrence treatment young surprisingly augmented augmented storing speeds automated stone stone stone stone stone rms metrics metrics metrics land annals annals annals annals fellowship torque die pointed sigma ical spaced spaced experiences experiences experiences experiences experiences experiences experiences experiences edinburgh massively avoids formance disadvantage afosr lookup lookup lookup proach son sta sta stuck stuck modifiable refined ward palmer palmer survey survey survey survey christopher australian australian australian send builds designs designs designs jersey drawing award award formulae devised att sloan interpolate sending iti iti est faced tra scattered scattered scattered cleveland cleveland cleveland cleveland cleveland health validated cox investigator erroneous approxima reviews biomedical resentation apparatus mason retrained cortico calculus engineers aware finkel finkel explores explores faculty presidential miiller allocate ulation fund ences proaches plications preceded marcel dekker extrapolate congress ric pollard pollard eubank eubank cheng cheng torques torques farmer farmer devroye devroye tered initiation clarendon tistical answered suf forget inevitable lancaster lancaster surveys hillis hillis keck referenced whitaker whitaker sidorowich sidorowich quarterly whittle whittle cga cga arti irregularly kelso alfred love ficiently boyd boyd evalua bentley bentley mathemat eco dth chui professorship ficial institution 
#@Atkeson_C,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input input data data data function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set networks networks training training algorithm algorithm algorithm output output output output output output output output output system system system system system system system system system system system system system system system system system system system system error error error error error error state state state state state state state state state state state state state state state state results results results units units units information information information information information information information information problem problem problem models models hidden hidden performance performance performance space space space space space space space weights weights weights weights weights case vector shown shown systems systems systems systems systems systems systems systems parameters parameters noise noise weight weight weight unit unit unit unit unit unit unit approach approach approach approach approach pattern control control control control control control control control control control control control control control control local local rate rate rate rate rate matrix matrix form shows signal signal signal signal signal signal signal algorithms algorithms algorithms paper paper paper size feature work work work work work task task task task task task task methods step points level current current current current problems problems problems problems random random random similar representation architecture architecture architecture section fixed fixed line general general parameter real average average gradient obtained obtained term term experiments university university variables variables variables research research research research independent log defined defined found found found target target dynamics dynamics dynamics dynamics dynamics dynamics initial estimate estimate estimate standard computer computer terms prediction phase frequency temporal temporal temporal temporal temporal temporal machine motion press learn learn learn learn learn learn outputs abstract applied applied find find properties properties properties references component ieee ieee ieee procedure procedure important important adaptive adaptive action action action action action action action action action behavior dynamic cost cost search tion change change change difference difference difference difference spatial assume representations learned learned chosen previous previous previous previous previous previous cases cases binary long long make make make make fact region region length correct forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward simulations simulations simulations minimum ing ing tasks tasks computed respect respect performed mapping mapping mapping mapping mapping optimization natural feedback obtain application application desired provide provide provide compute motor brain brain mit steps steps steps larger larger connection support train train modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling proceedings proceedings joint joint represents difficult bias framework cambridge environment environment environment solutions curves curves conference upper free estimated estimated con produce controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller path path path path path path path provided provided provided finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation depends depends depends depends feedforward describe arbitrary transformation transformation inverse inverse inverse assumption actions predictions predictions predictions predictions assumed assumed assumed supported supported require end future easily rumelhart rumelhart rumelhart rumelhart pairs needed functional functional jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan international supervised supervised supervised supervised idea attention minimize minimize minimize predict predict denotes population discussed advantage moving include cognitive teacher solve yields studies trans chain chain grant grant grant studied studied studied studied studied studied occur suggests derivative predicted loop loop loop white occurs occurs occurs occurs generally demonstrate runs runs runs runs half starting critical conclusions valued differences differences accurate numerical sutton sutton sutton sutton sutton sutton sutton sutton learns learns learns learns presence turn relationship derivatives derivatives derivatives derivatives minima identification program configuration force force base reference reference explicit longer longer longer transitions modeled modeled modeled coordinates coordinates coordinates coordinates coordinates simultaneously simultaneously transformations angle implies implies implies yield national correlated evaluate controlled controlled controlled updated understanding reasonable reasonable barto barto barto barto barto barto dashed performing closed closed closed sufficiently transactions degrees building activations priori priori coordinate coordinate coordinate coordinate assignment assignment sciences sciences sciences sciences maximize maximize successfully successful contained anderson anderson anderson anderson anderson anderson symmetry symmetry michael paradigm backward minimizes illustrates jacobs jacobs jacobs jacobs jacobs neighboring acknowledgments extend law origin origin origin detail integral mass mass existence existence existence tech incremental office phases notion naturally configurations configurations configurations man man changed changed changed changed quantities freedom separated plant plant plant plant plant plant plant plant massachusetts massachusetts cart cart cart cart cart cart track defining unstable unstable unstable unstable unstable unstable failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure briefly sections forces forces forces division ran sgn sgn sgn scientific separately angles author cybernetics cybernetics recognizing fluctuations varies varies consistency consistency parameterized lattice employ rep requirement controllers reaches reaches cal chose redundancy focused median converged converged credit credit differentiable instantaneous pole pole pole pole pole pole pole pole representative redundant redundant resources bin unity outcome air smith smith occurred siemens odd balance balance observing methodology methodology methodology implications preparation meaningful reset reset reset reset washington demonstration widrow widrow widrow widrow infinity infinity propagated propagated propagated bins pendulum erlbaum papers summarize balanced balanced robert specification corporation minus achieving exhaustive amherst amherst ical solely hillsdale jacobian rectangular favor werbos werbos werbos werbos inverted inverted afosr relates distal distal distal distal distal distal distal distal distal distal distal distal distal manipulator nonetheless applicability things differentiating fortunately excess twenty prefer dom kinematic kinematic disturbances automation trol coins smc evolves teaching stabilize backwards health meaningless broader saved puter proximal proximal proximal proximal restart restart inertia ixl endpoint conveys distinguishes specifications contin oft 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#@Jacobs_R,Jordan_M,
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#*network network network network network network network network network network learning learning learning learning learning learning learning model model model model model neural input input input input input input input input input input input input input input data data data function function figure figure figure figure figure figure figure figure time time time time time time set set networks networks training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output number number number number number number system system system system system system system system system system system system error results results results results information information information problem performance based based based based space space space space space weights weights weights weights weights weights vector vector vector vector vector vector vector vector vector vector vector vector vector vector order systems parameters parameters parameters parameters weight functions functions neurons neurons neurons neurons neurons unit distribution approach processing control control control control control control control control control control control control control control control control control control control control control control control control control large large large large local neuron neuron neuron neuron neuron neuron inputs form shows shows shows signal gaussian paper paper small small small size feature feature net net net net work work work work fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points points points points field field process process process process process process process process process process trained trained trained trained trained trained cell cell cell cell cell cell cell cell structure problems high memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response show show fixed fixed fixed fixed fixed vectors vectors vectors vectors vectors vectors vectors generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real real real real theory term activity activity dimensional dimensional dimensional dimensional result university university university research research found found distance distance synaptic synaptic direction presented presented presented presented presented map map map phase low maximum learn basis nonlinear nonlinear nonlinear abstract find find density density references component due due introduction stimulus stimulus stimulus stimulus stimulus effect effect effect generated generated search search search tion tion tion tion variable variable variable variable chosen part type type required cortex good represent distributed expected expected make techniques errors total simulation simulation computed elements mapping mapping factor optimization applications applications applications applications applications applications original compared compared desired receptive receptive receptive receptive receptive define compute active active active active active experimental constraints connected connected approaches steps steps steps steps comparison fields fields fields fields department department implementation implementation scheme scheme design transition stimuli stimuli stimuli determine basic basic increase produce produce coding coding coding coding area area area area controller actual processes associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative normal technical technical finding amount amount short nearest generate theoretical eds degree degree sensory sensory sensory sensory sensory needed unknown technology mechanism mechanism mechanism mechanism mechanism mechanism structures matching matching matching matching principle representing direct stored stored choose denotes denotes denotes exact advantage similarity similarity lateral lateral introduced previously calculated tions yields correspond evaluation positions organization organization storage storage storage grant concept concept concept loop loop loop loop loop loop conclusion greater mechanisms question acknowledgements areas areas areas longer generating recall predictive springer depending stages correlated influence updated organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing past kohonen kohonen kohonen advantages degrees coupling coupling coupling existing template template template template template template template template thesis usa memories memories memories activated tests major major aspects suitable differ divided verlag quickly allowing michael computes overlapping software unlike association association association association association association association association association association association association association association optimized preliminary behaviour ideas possibility working working working neu neu adapt adapt adapt equally changed algo mapped nervous phd years mentioned capabilities tive desirable localized virtual virtual capability capability red adjustable monotonic germany tile shifted ear ear extensive rithm concerned interconnected robotics robotics adjusting overcome serves symposium mance cerebellar cerebellar introduces ensures respective cmac cmac cmac perfor den searching indicator storing hypercube ence presenting german big adapting care grouped disadvantage memo memo memo modifiable advantageous lation ping hat inhibit albus albus accomplish ron rons sen deals ory arriving sity denmark setpoint setpoint setpoint dimen meant compromise merged lar maryland generaliza 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#@Hormel_M,
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error error error error error error error error error error error error results results results results results results units models performance performance performance performance performance performance performance performance based based space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer case case case case order order order shown systems systems systems systems systems values values values values values parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions distribution recognition approach approach pattern pattern pattern pattern pattern point single single single single single single single single single single single single single single single processing processing control control control control control control control control large large large large local local class inputs form form form form shows signal signal simple simple simple simple paper paper small small small small small small size size feature feature work work task task task cells step step step step points points field classification classification classification level level level level level current trained structure random random memory memory memory memory memory memory memory memory memory memory memory response response response response response response response response response response response architecture architecture architecture section section section fixed fixed fixed fixed fixed rule general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter real real real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation obtained term note note note note experiments experiments experiments experiments experiments experiments experiments dimensional result result university university threshold threshold computation found table computer computer computer computer distance distance distance presented presented map present present low frequency maximum basis basis nonlinear nonlinear nonlinear nonlinear abstract computational computational computational analog analog analog analog properties properties properties references due due due ieee procedure important important introduction introduction hand circuit circuit behavior effect effect effect effect dynamic parallel change change variable variable spatial measure measure prior learned learned part type multiple good good represent distributed make fact techniques region region observed scale finite resulting tasks tasks tasks tasks total total simulation times regions regions mapping mapping mapping mapping mapping mapping means natural global applications applications applications applications applications study study study study study study study relative specific true application application desired receptive proc proc proc proc location location location location location determined distributions motor motor equal voltage larger update dependent selection department loss loss loss loss loss loss implementation implementation implementation technique consists joint difficult difficult scheme addition considered considered considered equivalent experiment experiment experiment environment environment design transition transition transition limit bit choice choice significant free free vision increase produce produce produce produce produce developed controller controller types types types types types types types finally finally processes selected selected evidence simply associative discussion technical group tested transformation transformation transformation transformation fast fast close finding common common assumed supported role square degree development noisy typically typically pairs needed needed reduced unknown increasing increasing increasing increasing increasing structures uniform making stored stored stored stored magnitude magnitude magnitude magnitude magnitude magnitude magnitude attention added architectures architectures architectures improved discussed recent resolution property property property pair typical reported practical introduced introduced introduced introduced strategy strategy strategy strategy strategy subject sense subset engineering interest highly varying varying varying varying previously conventional conventional module module module correspond studies studies trans address address address address address address address locations locations locations locations locations locations locations bounded interval interval storage sensitive sensitive increased increased increased grant parts studied studied occur suggests suggests digital digital digital digital locally width setting critical place conclusions measures designed clear suggest presence cycle manner question acknowledgements areas sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity physical electrical transformations angle unique integrated versus yield dependence influence variation variation evaluated open open showed static sizes sizes processor key classical spaces add boundaries penalty initially foundation euclidean topology topology combinations instances batch prove activated activated activated activated activated activated activated activated activated absolute discussions tests tests tests reason reason determining straightforward effectively delta presentation presentation successful literature literature situation miller miller miller miller refer conf strategies device michael absence overlapping decreasing remain unlike poor create create investigate varied preliminary preliminary helpful rise reducing successive mappings investigated fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault authors referred referred root examined measurement extremely implementations thought adjusted subsets subsets subsets subsets aspect obvious obvious noted noted noted freedom observe separated separated mixed extent serial devices great great slowly distinguish smoothness coded coded coded failure reasons drive widely worst worst desirable consequence consequence attribute localized questions questions applies double transient conducted readily share adjustable adjustable adjustable adjustable adjustable incorrect perturbations limiting ordered suited hamming electric inherent tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance implements progress multidimensional multidimensional summed summed displays extreme arithmetic phenomenon shifted primarily accomplished accomplished accomplished generator generator generator generator generator generator generator investigation investigation concerned purely addresses addresses addresses enhancement exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar plays lost lost lost systematic held intelligent intelligent intelligent hope hope hope affected modifications symposium degradation degradation degradation cerebellar cerebellar ranging cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac bad reproduce reproduce young insight surprisingly refers impact impact impact impact impact valuable propagate generalizing adopted severe severe severe rms rms rms rms usage usage numerous rigorous session lane lane smoothly smoothly reports sinusoidal massively remote adjustment adjustment adjustment scenario arising trends shifting community gained robots faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults faults distant ultimately host lookup mask importantly manipulator manipulator manipulator register descending suffer placing placing placing likewise stuck stuck stuck stuck investigations gordon examination mix technologies architectural characterizing algorithmic demand saturated saturated saturated saturated saturated saturated saturated saturated discontinuous discontinuous discontinuous discontinuous discontinuous inconsistent tom continued albus albus albus concern concern injected operational operational operational operational operational operational operational deals placement placement placement placement placement placement spie robotic robotic robotic permanent articulation benign benign assessed problematic syst inappropriate tolerant attracted hampshire hampshire undesirable ascending ranked manipulators fil mac devise faculty reproducing multivariable multivariable cited illusion postulate 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output output output output output output output output output output output output output number number system system system system system system system system system system system system system system error error error error error state state state state results results results results results results results information information problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space weights weights weights weights weights weights weights case case case case case vector vector vector vector vector vector vector vector vector vector order shown systems systems systems values parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight method method method point point point point point point control control control control neuron neuron neuron neuron neuron neuron neuron neuron test matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs shows shows shows simple paper net work work work work work work methods points points points points points process trained problems memory memory memory similar show show show equation equation equation equation equation equation equation equation equation section section section line rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general generalization generalization generalization generalization real average theory obtained term term term term term term note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university computation solution solution defined sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics initial initial initial constant estimate computer distance presented map map map map map map map map map map map map map map present present phase phase phase phase phase phase activation activation activation activation activation nonlinear nonlinear outputs outputs continuous continuous continuous sample sample sample sample sample abstract applied applied applied find find find computational references ieee positive procedure procedure procedure procedure introduction behavior dynamic dynamic parallel tion tion difference assume rules measure measure chosen chosen chosen bound required required required binary conditions conditions equations equations equations equations equations equations equations equations fact fact fact techniques techniques techniques correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation errors errors simulations simulations resulting resulting resulting ing ing total simulation simulation simulation sum times mapping optimization optimization optimization global applications applications negative negative original specific specific specific samples samples samples samples samples samples samples samples represented true desired desired desired desired desired desired desired desired desired desired desired desired define define determined goal related discrete discrete steps comparison comparison train proceedings words version technique technique technique technique technique technique consists represents represents represents final final final final final scheme scheme maps considered considered curves curves curves curves curves curves curves trajectory trajectory trajectory trajectory effects bit bit determine determine choice choice choice choice choice approximate give give con condition derived derived derived path path path path product product product product product product product product product product product nature constraint biological associative associative associative achieved normal normal describe arbitrary transformation corresponds finding assumed end future objective objective pairs pairs pairs underlying underlying underlying underlying underlying hopfield hopfield hopfield hopfield hopfield unknown block block special consistent structures operation operation leads leads call iterations max stored magnitude idea minimize minimize choose directions pair element identical identical identical identical identical sense relevant engineering varying varying varying compare compare compare compare conventional solve yields differential differential differential diagonal diagonal symmetric storage storage extended extended matrices alternative correctly boundary boundary generally generally demonstrate flow starting conclusions valued competitive sigmoid measures measures clear clear performs performs performs performs constrained drawn drawn labeled labeled min min relationship program program program program program suppose suppose derive construct index index index index index index index index index index index index index index index index describes describes stability mathematical dept metric physical electrical angle angle consisting consisting consisting equilibrium formed blocks blocks yield yield choosing national formation forms suggested earlier neighborhood neighborhood tracking interpolation transactions recorded formulation sciences memories memories plotted illustrated maximize maximize absolute reason determining straightforward closely suitable differ included wij capture issue return return classify running michael generalize paradigm satisfies deal minimized minimized association integral integral accurately examine ideal analytically decisions func possibly man formal formal formal formal formal formal initialized store store extent motivated rows trivial defining analytical capabilities correction turns turns stanford stanford purposes sys sys sys closer forces products consequence grossberg cybernetics cybernetics meaning meaning outer outer outer outer outer outer outer outer outer outer outer outer summation reflects reflects empirically cohen requirement synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis monotonic tank collective attraction differentiable cor cor initialization lab ordinary corrupted corrupted corrupted indices ear writing equivalence formally lagrange lagrange acts approximates discover tem tem tem exemplar exemplar exemplar multipliers saturation tools proceeds interconnection abilities interpret transforms belong optimally mance perfor pat initialize initialize correcting correcting correcting designing generalizing fold default default yielded yielded outline vec ent equivalently emergent formulate suboptimal smoothly exception tor basins discovering decorrelation emphasize cosine cosine academy investigating investigating responding admissible algebra intensive examination completed completed remark capacities remarks remarks stephen ongoing ongoing solvable practically equa coincide comprising trol interpolate autoassociative autoassociative salesman smc constraining essence concatenated concatenated concatenated concatenated subsystem subsystem lar bear penalizes replication proceeding tern kailath kailath kailath kailath kailath instant coincides proce synthesize devel collect chi desire desire ordinate seeks nonlin abscissa euler subsystems subsystems travelling dembo dembo dembo dembo dembo concluding worthwhile sug lhe heuristically 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problem problem problem problem performance linear linear linear linear linear linear linear order order systems systems systems systems values values values parameters functions neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition method method method method method method method method method method method pattern processing processing processing large large large local neuron neuron neuron neuron neuron matrix optimal optimal optimal inputs form form shows signal algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple small small work work methods methods methods methods methods methods methods step points field field field field features level level structure structure structure problems problems problems problems problems problems problems problems response equation equation equation equation equation general general general approximation gradient gradient gradient note university university university university variables variables variables variables variables variables variables variables variables computation computation computation computation solution solution solution independent independent independent independent independent independent independent dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial distance direction direction presented presented presented present activation activation motion press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied applied applied computational computational computational computational convergence convergence convergence convergence convergence analog analog properties properties references ieee ieee procedure important important important decision decision introduction complex hand circuit circuit behavior dynamic dynamic dynamic parallel parallel parallel search change variable variable variable lower measure part binary binary conditions conditions tree distributed equations equations equations equations equations equations equations equations equations equations equations equations equations equations region region proposed minimum called factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization dimension applications applications study filter vol vol vol specific compared series proc determined determined determined determined related constraints constraints constraints constraints constraints gain discrete power comparison contrast update descent descent institute institute implementation version technique consists represents framework computing environment directly view solutions solutions design design design design trajectory efficient requires requires requires requires requires requires developed finally depends constraint constraint constraint constraint achieved transformation transformation transformation transformation fast limited close close corresponds corresponds stable circuits circuits effective implemented shape ability easily objective objective objective objective objective objective objective objective objective underlying hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield reduced reduced reduced reduced reduced unknown programming programming programming programming programming programming significantly significantly character york york increasing representing representing supervised minimize minimize produced produced robust element practical subject subject quadratic quadratic quadratic quadratic quadratic quadratic engineering engineering highly highly observations solve solve solve smooth differential differential symmetric generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized extended extended digital matrices locally locally locally demonstrate starting operator operator interactions interactions numerical designed designed clear constrained constrained constrained hard integration integration integration physics physics largest external demonstrated turn manner manner connectivity connectivity connectivity connectivity program acknowledgements explicit solving solving solving solving solving sequential dept dept dept explicitly simultaneously linearly electrical electrical unique quality influence solved solved solved solved solved solved solved solved updated converges processor delays initially initially transactions transactions avoid existing figures usa weighting weighting memories specifically characterized characterized major straightforward efficiently computations repeated heuristic anderson content sci correspondence denker reach processors processors processors processors received attempt employed american american wiley transformed transformed transformed transformed collection steady steady steady steady steady steady strengths limitations hessian fewer successive successive successive school tech rest authors complicated proved proved arbitrarily optimum optimum optimum optimum optimum inequality inequality inequality guaranteed majority tool tool rapid implementing satisfied satisfied producing inversion inversion acad optimize geometry geometry addressed integrating limits embedded effort formulated continuously rep execution switch tank tank tank collective inherent returns returns newton newton newton newton newton newton newton newton newton feasible feasible feasible lagrange lagrange lagrange lagrange lagrange lagrange optimizing interconnected interconnected eliminated multipliers multipliers multipliers multipliers multipliers multipliers extending numerically difficulties interconnection chemical chemical determination natl lyapunov lyapunov nonlinearities offers eng eng eng augmented augmented augmented augmented augmented augmented augmented passing steepest steepest hypercube implicitly subsequently papers adopted appeared unified solves graded goodman transmitted poses algebraic jacobian equality equality equality translated carefully unconstrained unconstrained unconstrained unconstrained unconstrained unconstrained unconstrained nonetheless attached tij tij programmed lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian algorithmic traveling hop hop hop hop converter exclusively optima inefficient inefficient tracks salesman feasibility cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy addressable sep bruck bruck predetermined trapped relax infeasible infeasible converts tenorio tenorio tenorio tenorio tenorio tenorio tenorio superiority burden adopting mented conveniently multivariable permission asynchronously communicated depict unknowns purdue purdue purdue purdue optimizer relaxing kennedy kennedy kennedy jeffrey jeffrey jeffrey solver manipulate cas tedious ian distributes famous marquardt publish lafayette lafayette lafayette chua chua levenberg interscience combinatorially parallelization algorithmically uncontrollable basics basics dictate 
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training training training training training output output number system system system error error results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based space weights weights order order order shown shown shown systems systems systems values values values noise noise noise noise noise weight weight weight unit unit unit unit unit unit recognition recognition recognition recognition approach pattern pattern point single single single single single single processing processing processing processing processing large large large large patterns patterns patterns form shows shows signal signal paper paper examples small small feature feature feature feature feature feature feature feature feature work work work work task task task task task task task task task task task features features process process level level level level level level level level level level level level level level level level level level level level level level level level level level level level level current current trained trained trained trained trained trained trained trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems high high similar similar representation representation representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture section section section fixed fixed general general generalization generalization generalization generalization generalization generalization generalization speech speech speech speech speech gradient note experiments university university university university computation research research research defined sequence sequence target target initial constant computer computer connections connections connections connections connections connections connections connections connections science science science science prediction prediction left presented presented presented presented presented presented present present activation activation activation activation activation activation activation activation low sets sets learn learn learn learn learn learn learn learn learn learn learn position abstract back back back references due ieee ieee procedure procedure procedure decision propagation propagation propagation context context context context context introduction action action action action complex complex complex complex complex complex complex behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent rules measure representations representations representations word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word learned higher part part center center center previous previous previous previous type type type required multiple tree distributed expected make techniques techniques correct errors errors errors errors scale resulting resulting ing tasks tasks multi performed called mapping mapping mapping mapping mapping mapping made made global relative relative relative relative application desired provide objects perform perform perform perform perform active active active active active constraints constraints connected connected approaches descent dependent morgan proceedings proceedings institute words words words words words words words words words words words words individual represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult final final final delay scheme addition maps domain experiment experiment hinton hinton additional design san san stimuli stimuli effects conference full full full choice significant significant speed speed speed increase con randomly conditional developed levels levels levels levels types types types types types types types actual actual processes processes associative discussion describe describe tested predictions predictions finding short short common common role role role role role role role role role require main eds hypothesis hypothesis makes noisy including fit kaufmann simulated simulated simulated underlying needed needed jordan jordan block block block block block interesting interesting testing testing language language language language language numbers direct international bottom bottom early minimize minimize produced produced produced produced produced description description discussed discussed robust separate separate reported hierarchical hierarchical sense subset sejnowski cognitive cognitive varying previously previously calculated module module module tions speaker correspond gate sensitive entire grant constructed constructed constructed parts parts predicted correctly correctly correctly touretzky touretzky occurs conclusion critical critical differences modules designed performs performs weak learns learns learns encoding strong california california relationship targets targets manner groups identification appears appears produces ways ways sequential sequential sequential sequential sequential sequential sequential describes label distinct modeled sensitivity explicitly simultaneously remaining integrated applying predictive predictive predictive predictive predictive predictive springer formed formed formed agent agent agent agent agent blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks expectation competition competition john john john national formation phoneme interpretation detailed detailed labels labels showed static static similarly updates diagram partial partial earlier reasonable initially initially symbol symbol assigned assigned construction foundation transactions coupling building building building includes dominance inter inter inter inter assignment assignment assignment extension illustrated illustrated automatic maximize specifically variations domains domains domains partially discussions grammar grammar characterized gating gating gating gating gating gating gating gating gating gating gating structural successfully successfully successfully major aspects efficiency differ modification included presentation presentation presentation presentation presentation attractors build build build plots fine capture verlag contained built list generalize generalize modular modular modular modular modular modular modular hypotheses hypotheses ill received acknowledgments remain diego diego difficulty detail detail limitations helpful fewer respond school school school tech tech tech tech incremental incremental incremental incremental incremental incremental incremental possibility relationships relationships relationships maximizing proper symbolic symbolic encode waibel waibel waibel waibel waibel waibel waibel waibel waibel act act act act possibly man analyze extremely singular portion portion mapped mixed serial defines sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences mentioned indicating trivial trivial publishers majority caused briefly processed processed processed processed processed perspective formalism formalism formalism formalism shared organized organized forces constructing constructing directional desirable immediately separately beginning beginning beginning beginning meaning mellon mellon exemplars requiring fourth percent carnegie carnegie reflect substantially elman elman cmu spoken spoken spoken embedded embedded embedded embedded embedded embedded simulate peter peter peter poorly introducing sharp rep rep rep pittsburgh ture ture modulated gen acoustics acoustics gave gave gave gave gave comments display expectations tolerance tolerance tolerance tolerance tolerance traces sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence semantic semantic semantic semantic semantic semantic semantic semantic sharing sharing sharing acquisition corrupted corrupted corrupted corrupted labeling labeling labeling labeling labeling labeling labeling labeling labeling assign assign forming modify tation dynamically dynamically dynamically arrival proceed extending promising familiar occurring roles roles roles roles roles roles roles roles belong clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase 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exhibited exhibited tune ignoring atr exploited struc inactive architectural deletion stimulating slot slot slot slot ate ate ate ate ate transforming slots phrases phrases phrases phrases phrases phrases phrases phrases phrases phrases phrases phrases phrases phrases phrases confirm confirm inhibit utilizes compete interpreting reflecting alex clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses jain jain jain jain jain jain jain jain jain jain incorporation architec interpretations interpretations conditionally dog dog dog dog dog substitution substitution quantitatively evolving syntactic syntactic syntactic syntactic noun inducing robustly statements emerged violated supposed verb verb verb dyer dyer rec rec rec subnetwork subnetwork snake snake snake snake snake snake repetitions repetitions lexical lexical modularity constituent subnetworks cons repetitive preventing shikano dominate constructions eralization miikkulainen miikkulainen parser 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representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture show section rule rule rule rule rule rule rule rule real real states theory theory theory theory theory theory theory theory theory note note university university university university computation research research research found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence standard computer computer terms connections science science science science left left left presented map present present press press press press press learn learn basis basis basis basis basis basis abstract applied back back back back back back back back back find computational computational computational computational computational computational properties references introduction complex complex hand hand behavior behavior effect parallel parallel parallel parallel parallel parallel parallel parallel search search change change change change energy energy rules rules rules rules rules representations representations word word word word learned type type required required multiple conditions conditions conditions conditions distributed distributed distributed length length length forward simulations minimum resulting human human human human human human human performed performed performed called called called elements elements elements elements elements elements elements elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping specific application application application application desired compute objects perform determined goal constraints constraints constraints constraints constraints discrete mit mit mit support modeling morgan proceedings proceedings proceedings report report department implementation implementation individual represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult final scheme scheme scheme sequences sequences sequences sequences sequences sequences maps maps maps maps maps cambridge cambridge cambridge computing computing directly hinton additional additional additional additional san san conference efficient full requires choice vision give give con condition condition condition derived derived clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering types types types actual finally finally finally processes processes processes processes processes processes iteration iteration nature constraint constraint discussion discussion technical feedforward describe arbitrary arbitrary surface surface surface predictions predictions common implemented implemented implemented supported eds eds eds eds eds instance cluster cluster cluster cluster cluster cluster cluster easily makes rumelhart rumelhart rumelhart rumelhart development including kaufmann simulated simulated simulated underlying underlying underlying underlying combination combination account account account account dynamical fully block interesting projection mechanism mechanism mechanism mechanism mechanism mechanism mechanism special matching principle language language language language language language leads details details making making idea description description predict perceptron takes element element element element element element apply apply sejnowski cognitive cognitive cognitive cognitive highly highly highly volume volume tions match bounded bounded bounded bounded entire grant occur alternative alternative alternative feed touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky clusters clusters clusters clusters clusters starting segment segment clear performs performs constrained constrained constrained mateo suggest drawn california turn variety iii introduce introduce groups annealing annealing annealing acknowledgements explicit construct produces produces sequential changing segments segments segments segments segments segments segments segments segments involves easy develop develop john john national operations operations operations operations controlled similarly past performing purpose iterative iterative iterative iterative iterative iterative intermediate initially string construction construction construction foundation david avoid avoid figures perceptual inter recognize determines straightforward aspects extra suitable society differ symbols included mcclelland mcclelland mcclelland mcclelland computations vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel repeated phonetic phonetic generative timing hold write relaxation relaxation relaxation relaxation relaxation relaxation correspondence illustrates subsequent operating satisfies extend diego american circuitry circuitry circuitry circuitry environments limitations limitations helpful giving ideas school school school applicable relationships office structured workshop workshop cover cognition cognition analogous examined naturally nervous academic grouping explain finds massachusetts massachusetts massachusetts languages languages languages languages languages languages languages directed crucial crucial derivation derivation derivation phenomena phenomena phenomena phenomena phenomena adjacent adjacent adjacent reasons stress stress implementing berkeley berkeley sys producing producing strictly immediately laboratories english read read annual preceding preceding preceding mellon mellon fourth carnegie carnegie applies cmu share marked marked operate rely pittsburgh pittsburgh pittsburgh differs phonemes utterances simultaneous simultaneous yielding acquisition writing purely tem naval smolensky smolensky smolensky proceed inspired analogy stated primitive intelligent height height height height contract contract mark harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony operates utterance utterance utterance utterance utterance vowels vowels vowels vowels vowels vowels vowels repeat overview overview buffer buffer buffer buffer buffer buffer buffer buffer buffer buffer heart accounts searching sim offers specialized foundations foundations omitted erlbaum reverse consonant consonant consonant adopted explorations explorations linguistic linguistic linguistic verify summer specification microstructure visually deriving gaps break break distinction trigger trigger trigger trigger trigger trigger trigger trigger perceived perceived chicago hillsdale reject param manipulation blocking intra hughes insertion insertion insertion insertion unconstrained covered breaks syllables eters round round round round round round round round round round round round round round round round round round round deletion deletion satisfaction unbounded unbounded justified ping slots slots virtually utilizes generafive attempting attempting clarity phonemic phonemic eliminates eliminates proposal settle proposes extracts consonants edited phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology reflection sian connectionism meant derives iterate mutation mutation mutation eighth undergo undergo undergo undergo undergo supposed verb operated tightly inserted excluded excluded sixth insertions inserting fight mar manipulations hypothetical constructions phonological phonological 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networks training training training training training training training training training algorithm output output output number number number number number number error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results information information information information information problem problem models models models models hidden hidden based weights weights weights weights layer layer layer layer layer layer case order order order order order order order order order order order order order order order order order order order order order order order order order shown systems systems values values values values values values weight weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit recognition recognition approach approach approach pattern pattern pattern pattern single single single single neuron neuron neuron neuron neuron neuron neuron neuron neuron rate test analysis analysis matrix matrix form form shows algorithms algorithms simple simple simple simple simple simple examples small size net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net work work work work methods fig fig fig step process level level level current current current current current current current current trained trained trained structure structure structure structure structure structure problems problems problems problems problems memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar representation representation representation architecture architecture equation rule rule rule rule generalization real states states states states states states states states states states theory theory theory gradient gradient gradient term note activity activity activity university computation computation research log defined defined defined defined defined defined defined found sequence target dynamics dynamics initial initial initial initial computer computer computer terms terms science science science presented presented map present present activation activation temporal temporal machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets range range range learn learn learn learn learn learn learn learn continuous continuous continuous continuous continuous sample sample sample abstract analog references positive positive important adaptive context context context context context context context context introduction introduction action action action action action action action action action action action action action action action complex complex complex complex parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change change change complexity rules rules representations learned learned learned learned learned learned learned learned chosen higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher part part part type type required conditions represent represent distributed length length length length length length length length length length length length length length length length length length length forward scale finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite simulations simulations simulations ing total simulation respect sum eq eq eq eq eq eq eq called mapping mapping mapping mapping optimization potential applications applications applications negative negative vol vol vol vol artificial samples samples samples represented true compared define perform determined connected connected connected connected connected connected connected equal equal power power approaches update descent descent descent dependent source nets nets morgan morgan proceedings proceedings proceedings report institute institute institute department version consists advances advances joint joint represents represents represents connectionist connectionist connectionist difficult final final final final final exp layers addition sequences sequences ai maps considered considered computing additional additional additional additional design transition transition san san san top top top top top top top top top top top conference conference conference requires requires choice free free free free free free free free con condition coding derived derived derived derived derived clustering developed types actual backpropagation depends biological discussion increases arbitrary arbitrary actions actions actions finding common common common common effective implemented generate theoretical require end end end end end cluster easily easily easily easily easily easily development including kaufmann kaufmann objective objective objective combination reduced reduced dynamical fully fully fully fully jordan jordan jordan interesting interesting testing testing significantly significantly increasing increasing operation operation operation language language details international international bottom bottom depth depth depth depth minimize added sources description architectures discussed discussed recent element movement include machines machines machines machines machines machines machines machines inference inference inference inference inference inference inference inference inference inference inference cognitive cognitive interest calculated solve yields studies definition modified bounded williams williams williams williams williams derivative move hybrid hybrid touretzky touretzky deterministic deterministic deterministic occurs minimal minimal minimal reduce conclusions numerical performs faster learns learns learns learns learns learns learns mateo mateo encoding encoding physics external external external external external reduction start start start relationship derivatives question attractor areas appears pro construct construct construct index sequential sequential transitions transitions recall recall recall multilayer multilayer infinite easy develop minimization yield extracted interpretation evaluated operations operations updated lee lee lee lee lee lee lee forms translation past past epochs epochs epochs remains remains string string string string string string string string string string symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol construction topology includes strings strings strings strings strings strings strings strings strings retrieval recognize recognize recognize recognize recognize prove phys grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar successfully simplicity regular regular regular regular closely capable society modification computationally effectively effectively effectively symbols symbols symbols symbols mcclelland wij wij wij wij wij wij wij wij wij wij procedures heuristic interpreted interpreted running write usual giles giles giles giles giles giles giles attempt consisted consisted extract deal presents remain diego powerful layered production relations relations recursive recursive recursive dual dual hall hall fewer mappings mappings terminal parity parity parity ideal structured encode hierarchy removed neu neu neu reading reading automata automata automata automata automata automata automata automata automata automata automata automata automata automata rev perfect perfect obvious formal formal formal formal noted assumes simplest simplest explain integrate languages languages great advanced independence perspective straight constructing recognized read read read read read read read read read read depicted recognizing sun sun sun sun sun sun sun sun sun summation argument questions questions simulate simulate readily employ continuously stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack vocabulary ture incorporating serve extensions extensions chen chen chen chen chen chen chen chen chen chen chen chen chen wesley college addison writing princeton acm acm member perfectly perfectly perfectly controlling connecting interconnected extending smith adds promising occurred proceeds interconnection automaton automaton automaton automaton automaton automaton automaton automaton automaton balance resulted resulted interpret ral ral ral implications adequate enhanced phrase grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars utilized prentice prentice sion respective buffer evident foundations mem pollack pollack pollack late grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical park erlbaum erlbaum eqs eqs eqs inductive lett discovered balanced empty empty empty empty empty mind zipser zipser liu liu ence misclassification accept emergent emergent formulate legal legal legal legal legal poses feeding amherst hundred hillsdale hillsdale graphics ullman ullman parallelism pop pop pop pop pop pop pop pop pop ation permit nal ward continually pineda pineda nec diagrams demonstrating removes primitives primitives primitives allen allen allen ping cliffs puts suffices recursion recursion recursion appealing integrates devised tuple tuple englewood englewood emerges architec push push push push push push push sym recognizes ory tended zipset zipset zipset minsky minsky syntactic teaching teaching teaching schreiber schreiber sparseness corn adequately inform maryland cleeremans emerged servan awij awij rent putation rec replaces ference proximation plexity turing proce ample couple inte recursire scribed concurrently pushed pushed designated parentheses ana earning recur recur owij owij concluded teach teach teach fifty extraneous extraneous chine chine chine chine iai iai formulating nected gramming cre ditional confer formalize unary dure parenthesis parenthesis parenthesis vocabularies manipulate illegal cou angluin intense pled effected surveys stringent hopcroft hopcroft ata devising chomsky init astronomy clude bol jli checker manipu tomata mite disposal rth 
#@Chen_D,Chen_H,Giles_C,Lee_Y,Sun_G,
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#*learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model data data data function function function function function figure figure figure figure figure set set set set set set set set set training training training training training training training algorithm algorithm number number number number number number number number number state state state state state state state state state state state state state state state state state state state state results results results results information problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models based based based based based space space case case case order order order order order order order order order order order shown shown systems probability probability probability probability parameters parameters parameters parameters method method approach approach approach approach approach image image processing rate test test test test test analysis analysis class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal form signal simple paper small size methods points field field features features features process current structure structure random random representation representation representation show show rule images general general general generalization speech parameter real real states states theory term term term term note note note note note note dimensional result university solution research research independent log log log log log log log log log log log log defined defined found found sequence sequence sequence sequence sequence estimate estimate estimate estimate computer terms terms terms terms terms terms sets sets maximum maximum maximum learn learn abstract properties likelihood likelihood likelihood references component stochastic stochastic due due procedure procedure procedure procedure procedure procedure important decision decision decision decision decision decision decision statistical statistical statistical statistical generated generated generated generated cost complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity spatial assume rules measure signals prior prior prior prior type binary binary binary bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make make fact fact length length length length length length length length correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed finite finite finite finite finite minimum resulting computed sum times regions factor made made study knowledge knowledge original samples samples samples samples samples samples desired define compute compute compute compute compute compute compute compute determined determined constraints distributions equal equal equal equal power accuracy source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source modeling modeling modeling modeling modeling modeling proceedings implementation joint represents sequences sequences sequences considered framework framework framework framework computing computing computing equivalent equivalent experiment experiment directly additional view transition transition transition transition transition transition transition transition limit bit conference conference efficient efficient efficient efficient statistics statistics estimated estimated estimated estimated estimated estimated estimated basic increase developed developed criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion simply simply describe denote tested tested transformation assumption assumption complete supported role require hypothesis hypothesis hypothesis hypothesis hypothesis easily development development including account unknown unknown unknown unknown unknown fully testing ratio segmentation special consistent language language language language language language language language max max max max max bits bits depth depth depth depth depth depth depth depth depth depth idea produced choose run sources sources sources sources sources sources sources sources sources sources description description predict denotes advantage advantage takes apply apply include inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference interest sufficient compare compare previously correspond definition definition observation observation observation generalized generalized generalized generalized risk risk risk risk entire entire grant exists exists exists occur occur alternative column demonstrate conclusion conclusion row greater greater greater valued measures bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes practice constrained taking taking largest largest largest largest characteristics proportional start introduce acknowledgements produces written primary plot plot laboratory laboratory transitions transitions mathematical recall recall unique consisting develop develop develop develop develop choosing choosing expressed expressed interpretation interpretation similarly reasonable initially string string string string string symbol symbol symbol symbol figures includes strings strings strings recognize candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate priors priors grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar structural structural structural structural structural texture texture texture texture regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular efficiency efficiency importance society divided symbols symbols symbols symbols included included miller miller miller miller miller miller miller miller miller refer kind procedures interested criteria criteria criteria criteria criteria notation gibbs quantity quantity quantity write write write michael play eigenvalue eigenvalue eigenvalue eigenvalue principles attempt attempt decreasing minimized american production production exponentially detail accurately terminal terminal terminal terminal terminal terminal terminal terminal int maximizing fundamental attributes examined reading assumes generates motivated electronic developing growth defining stress sites strictly probable potentially recognized begin begin recognizing nsf led incorrect calculating measuring differs maximizes maximizes incorporating acoustics enables logp sentence wesley indices primarily addison grows smith smith smith smith smith smith smith smith imaging stated stated stated grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars motivation representational entry entry studying washington counting viewing entries entries entries initialize treatment young express express infer grammatical discovered alternatively dividing assigns limitation consecutive incorporates annals inferred terminals examining examining suffer siam rewrite ignoring treating treating rewritten electron characterizing textures establishes inclusion award rissanen rissanen rissanen rissanen rissanen inferring inferring inferring inferring inferring sij bat implying rel nih segmenting discovers occurrences allowable ira publishing investigator expresses kolmogorov ece biomedical inte evaluates ting kurt presidential brings dictated albuquerque incidence incidence incidence incidence incidence incidence ams referring uncover igi igi apriori apriori apriori apriori apriori apriori bay combinatorics combinatorics combinatorics combinatorics bal casting louis itseft isl goto boo psi equiprobable parameterizing microscope quadruple 
#@Miller_M,Smith_K,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input input input input input input input input input input input data data data data data function figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training algorithm algorithm output output output output output output output number number number number number system system error error error error error error error error state results results results results results units units units units units units units units units units units units units units units information information information problem problem problem problem problem models hidden hidden performance performance based space space space weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer case vector order order shown systems systems systems probability parameters parameters parameters parameters parameters weight weight weight weight weight weight neurons neurons unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method pattern pattern pattern point point point image image image image image image image image image image image image image image image image image image image image single single single processing processing processing processing large large large large large large large large local local local local local local local neuron neuron neuron rate rate rate rate rate rate test test test test test test test test patterns class class optimal inputs inputs signal signal simple simple simple paper examples examples examples examples small size size size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work work work work task task task task task task step field field field features features features features features classification classification classification process level level level level level level level level trained trained problems problems problems similar representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show fixed rule vectors vectors vectors images images images images images general general generalization generalization generalization generalization generalization real real real real real real states obtained obtained obtained obtained obtained note activity activity activity dimensional result result result threshold threshold threshold computation solution solution independent independent independent target table table computer connections connections connections connections connections connections connections connections connections left direction presented map map map map map map map map map map map map map present present present low low machine object range learn position position abstract applied applied applied applied back back back back back back back back back back back back back back computational properties references due due important adaptive adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex complex complex hand hand hand hand hand effect effect parallel parallel difference difference complexity complexity variable assume prior representations chosen chosen chosen higher part part center previous previous previous cases required required multiple multiple multiple good binary conditions distributed chip make correct probabilities errors errors resulting resulting ing tasks tasks multi performed performed performed performed performed performed called times mapping knowledge knowledge knowledge original original artificial represented application application application application desired desired receptive receptive receptive receptive objects rates location location perform active active active determined constraints constraints constraints connected connected connected brain brain equal equal power power steps accuracy larger larger larger contrast connection connection fields train morgan morgan proceedings words version technique technique consists consists consists consists internal code code kernel kernel joint represents represents connectionist connectionist final bias layers layers layers layers layers scheme scheme scheme scheme addition addition maps maps maps maps maps maps maps maps maps maps framework cambridge equivalent environment directly directly hinton hinton additional additional design stage bit conference free free free free world world vision vision basic pages pages coding derived levels levels levels levels criterion entropy actual provided finally nature measured increases transformation transformation transformation limited complete complete predictions amount amount amount short common implemented shape shape role require main journal pixel pixel ability ability rumelhart rumelhart including including fit kaufmann typically smaller smaller hopfield reduced reduced reduced functional fully fully fully interesting interesting testing testing testing testing ratio character character character increasing segmentation segmentation segmentation segmentation segmentation consistent database database database database database database principle principle operation operation numbers direct international international normalized normalized normalized normalized idea minimize added resolution takes takes takes takes takes typical reported reported practical subject identical identical side pixels pixels pixels inference engineering highly varying unsupervised volume volume volume works module address background positions locations williams williams parts parts scaling extended digital digital correctly correctly touretzky touretzky white white boundary hardware half conclusion starting minimal minimal assumptions reduce editors measures modules designed designed designed peak performs performs performs performs performs practice practice constrained constrained constrained constrained constrained constrained constrained hard variety user plane plane plane plane plane characters characters characters characters characters characters groups groups digit digit digit digit digit digit digit digit digit digit digit digit written written written metric category category averaging averaging averaging averaging averaging remaining remaining slightly slightly shift shift blocks extraction extraction extraction boolean letters overlap codes detailed operations restricted showed centered sizes translation digits digits digits digits digits digits digits digits digits digits digits digits constants processor sign earlier performing normalization normalization combining neighborhood purpose add advantages classified precision avoid expect handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten priori bell inter assignment extension automatic automatic specifically black black holds neighbors neighbors discussions successfully reason reason successful post invariance invariance ten ten composed composed composed composed composed composed composed summary strongly cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun video interested strategies categories gray gray generalize realistic providing providing board denker denker denker denker denker denker denker denker denker denker denker denker denker denker reach thresholds consisted subsequent extract acknowledgments deal camera camera unlike unlike layered put humans preliminary preliminary reducing reducing mse mse scaled office complicated cognition removed neu editor editor recognizer recognizer aspect precise detector separated logic art ith store isolated percentage percentage great great convolution floating considerable considerable implementing tive shared shared widely preprocessing preprocessing preprocessing preprocessing preprocessing incorporate laboratories sun raw requiring varies people amounts fed readily leave effort backprop share share solla solla solla solla detecting passes passes passes howard howard howard howard howard howard howard howard howard howard extracting fall fall simulator simulator segmented redundancy attraction damage damage wang wang baird baird distortion sharing acquisition acquisition sort writing databases printed printed printed printed printed printed printed printed arranged arranged arranged plays kaufman occurred mail mail imposed tishby tishby operates ral shifts salient days service service service overlaps separating introduces washington schwartz jackel jackel jackel jackel jackel jackel jackel jackel jackel jackel scan specialized belonging passing relies broken designing designing influences unchanged multiply appeared slight numerous microstructure constitute visually session planes planes planes guyon convolutional opposed rejection rejection pieces discriminative year abstraction boser boser boser boser boser boser boser classifications classifications regularity classifies reject param remainder henderson henderson henderson henderson henderson henderson henderson henderson translated care shifting levin levin ization hubbard hubbard hubbard hubbard hubbard hubbard hubbard emphasize rejected books guided paris ambiguous ambiguous ambiguous translations zip zip zip emphasized million misclassified misclassified france denver denver elsevier commercial commercial dsp dsp dsp dsp dsp eters scanning coming demonstrating advantageous styles preserves distortions font marks attributed heavily heavily neighborhoods graf char bottou bottou holmdel devised normalize deals substitution squashing digitized distorted constraining connectionism bradford mis devoted gardner neocognitron neocognitron postal postal postal elaborate tolerant locating erroneous deformations fukushima fukushima ess reminiscent subsampling subsampling subsampling subsampling subsampling switzerland quarter named designated designated displaced gun gun implementable feel contiguous fogelman disconnected throughput throughput extraneous numerals instruments notable timal sparcstation extractors dig fonts fonts fonts acter miyake miyake overly atypical rejections rejections rejections faulty explo wittner zurich rations buffalo henry perspec srihari srihari zipcode zipcode zipcode zipcode superset steels supplemented redun europhysics discernible pfeifer hub esting schreter digitization extrapolating dant 
#@Boser_B,Denker_J,Henderson_D,Howard_R,Hubbard_W,Jackel_L,LeCun_Y,
#t3
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data function function function function function function figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number system system system system system system error error error error error error error error error error error error error results results results results results results results results results results information information information information information information information problem models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case vector order order order order order order systems systems systems systems systems systems systems systems systems systems systems values parameters parameters parameters parameters parameters parameters parameters weight weight functions functions functions functions functions functions functions functions functions neurons distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image single processing processing processing processing processing processing large large large large large large large large large large large large large large large large large large local local local local local local local local local local local local local local local local local local local local local local local local local local local local local rate rate rate rate rate rate rate rate rate rate rate test test test test test test patterns patterns patterns analysis inputs signal simple gaussian visual visual visual visual visual paper examples small small small small small size size size size size size size size size size size size size size size size size feature feature feature feature feature feature feature feature net net net net net net net net net net net net net net net net net net net net net net net net net net net net cells step points points field field field features features classification classification process process level current trained trained trained trained trained trained trained trained trained structure random high high high high high high high high high high high high similar similar similar similar representation representation architecture architecture section line line line line line line rule general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real gradient university university independent found found found found found sequence sequence initial initial initial initial constant constant table table estimate estimate estimate estimate estimate computer computer computer connections connections connections connections connections connections connections connections connections node node science science left presented presented low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal machine sets sets sets sets sets sets sets sets sets sets sets range range press learn learn position position position position position position position basis outputs sample sample sample sample sample abstract back find find find find find find convergence likelihood likelihood references due ieee positive positive important important adaptive propagation propagation complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand statistical effect effect effect generated parallel search search search search search search search tion tion tion tion tion tion tion difference spatial assume assume classifier classifier lower measure measure signals signals representations word learned higher bound bound cases required required required required required cortex cortex cortex good good good long represent represent represent distributed fact fact fact fact fact fact techniques region region correct errors forward ing ing ing ing tasks tasks total human human human human human human human multi multi times regions factor made natural natural natural orientation orientation orientation global global global global global applications applications negative samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples represented represented represented true desired receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide rates rates rates rates rates rates rates rates rates rates rates determined experimental goal goal constraints constraints constraints brain mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison larger larger connection connection connection connection fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields support train nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets selection morgan morgan morgan proceedings proceedings report report report report institute department department loss consists internal internal code advances advances advances connectionist difficult bias bias layers layers layers layers layers layers maps cambridge equivalent directly directly hinton hinton hinton hinton curve estimates estimates estimates estimates estimates design limit stage stage effects effects effects effects effects effects effects effects effects effects effects effects effects conference conference conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine upper upper full requires requires free free free free free free world speed vision basic randomly developed levels levels levels evidence backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature achieved achieved achieved achieved achieved achieved achieved measured discussion technical arbitrary tested transformation limited limited close close assumption corresponds amount amount nearest role role role theoretical require hypothesis degree rumelhart rumelhart rumelhart rumelhart typically typically typically typically pairs smaller underlying underlying underlying needed needed hopfield hopfield reduced reduced testing significantly significantly significantly ratio character character character character character character character character character character edge edge increasing segmentation segmentation segmentation principle principle numbers numbers numbers pre pre pre pre pre bits international international normalized normalized normalized normalized magnitude minimize minimize architectures architectures architectures architectures improved improved improved improve improve improve improve resolution advantage property robust reported reported reported practical practical practical practical practical practical moving pixels sense sense sense array array array array array relevant interest sufficient sufficient varying varying varying compare tions yields yields correspond achieve achieve achieve achieve achieve williams williams williams invariant occur suggests suggests suggests rotation correctly feed touretzky touretzky touretzky white white occurs flow minimal minimal greater reduce reduce reduce neighbor editors central central retina retina retina suggest suggest suggest suggest propose strong hard mechanisms physics largest largest variety variety exist selective selective characters scene connectivity connectivity connectivity connectivity connectivity connectivity acknowledgements areas areas areas areas explicit appears digit written winner ways generating category explicitly explicitly coordinates simultaneously slightly develop develop applying implies implies extraction select john letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters yield national extracted overlap viewed variation evaluate organizing understanding sizes sizes sizes sizes suggested digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits updates epochs fitting roughly roughly generation valid sufficiently sufficiently sufficiently sufficiently advantages topology topology topology topology topology topology topology avoid avoid perceptual perceptual usa sciences determines determines determines automatic prove maximize maximize variations variations black black tests reason reason selecting closely importance mcclelland comparing invariance invariance invariance invariance invariance invariance essentially receives receives cun cun cun heuristic heuristic anderson interested interpreted dis content strategies device categories categories gray write modular denker denker denker denker denker leading received principles overlapping overlapping approximating oriented oriented oriented oriented oriented situations presents minimized simpler american american layered layered layered wiley overfitting experience difficulty varied involving mass biases biases fewer fewer reducing reducing reducing reducing reducing successive tech detectors detectors detectors detectors detectors detectors detectors possibility combine reliable working affect func momentum examined examined plausible man man extremely perfect recognizer recognizer aspect panel panel assumes detector detected improving explain percentage indicating ment developing developing developing developing developing developing convolution fairly improves capabilities benchmark baum baum baum baum baum baum reasons reasons considerable considerable tive shared shared shared shared shared shared shared shared shared shared shared shared shared shared shared shared shared shared operators worst worst scientific scientific scientific projected calculations optimize optimize toronto computers linsker linsker linsker linsker linsker cybernetics recognizing recognizing recognizing recognizing recognizing recognizing preceding raw raw reflects people people people greatly greatly considerably reflect double collected substantially substantially relevance relevance relevance offset solla solla solla haussler haussler haussler haussler haussler haussler passed biologically requirement polynomials polynomials howard howard howard howard howard limiting limiting incoming extensions enables enables enables replace display display decreased segmented segmented segmented baird baird sharing sharing irrelevant consistently don don representative representative representative representative person contextual sort accomplished writing extensive martin martin martin martin martin martin narrow narrow optimizing resources resources approximates printed printed printed printed printed printed printed printed printed printed printed printed printed printed printed printed printed printed printed printed plays generality generality kaufman kaufman kaufman ments significance promising interpret keeping occurring removing fail implications imply analyses james negligible negligible pat regard washington schwartz schwartz den jackel jackel jackel jackel jackel offers emergence surprisingly refers draw impact impact sons hart hart discriminate informa converted corporation ter users achieving achieving wiesel wiesel wiesel guyon guyon benefits benefits emergent emerge emerge bank bank bank forced tween feeding abstraction copy reports flat constitutes hubel hubel hubel discovering discovering discovering discovering certainty reject reject reject reject visited visited arising henderson trends favor intuition gained duda duda distribu ization ization hubbard hubbard eliminating rejected depicts academy categorization zip million esti son thousands thousands thousands els gorithm worked helps spite diagrams circumstances topologies fiat appearing scanned scanned opti recogni inconsistent thousand austin oscillate evolved hid graf graf burr burr replicated replicated exposed mori mori ters manipulated push scenarios interpolate evolves evolves wisconsin rectangles rectangles rectangles ranged bauer bear indicators ically promise texas convey ized tens tens generaliza experimented gardner gardner col col linking began began tern spent discrepancy collecting judge crg blurred checks checks checks gross entered advice madison prohibitively boost biasing challenges sing unclear stabilized experimentation experimentation parentheses sults responsive underlie regularly standpoint standpoint charac kay premise premise proaches selec resembling raise raise proportionality backpropaga invaluable extrapolate grayscale grayscale grayscale mcc portant pittman pittman pittman pittman pittman pittman atlanta mates ade collects conflicts bitmaps georgia argues scientist invariants invariants invariants invariants loca bitmap typ demonstrations numeric numeric wittner wittner contradicts ceptive rejects lus duction determin printing reduc inch interactively sired mize janet promoting suits proces lev nology produc docu rele ncr ceived alized teresting gale affords sty 
#@Martin_G,Pittman_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output number number number number number number number number number number number system system system system system system system system system system system system system system system system error results results results units units units units units units information information information information information performance performance performance performance performance performance performance performance performance based layer layer layer layer vector vector vector vector vector vector vector vector systems systems systems systems recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method approach pattern pattern pattern pattern pattern pattern pattern processing processing processing large large large large large large large large large large large large large large large large large large large large local rate rate rate rate rate rate test test test test patterns patterns patterns patterns patterns patterns analysis visual paper paper examples small small small small small small small small small small small small small small small small small small small small small small size feature feature feature feature feature feature net net net net work task methods methods methods methods fig fig fig fig fig fig fig fig fig fig fig fig process level level level level current current trained trained trained trained trained trained trained trained structure structure high similar similar equation section line vectors vectors vectors vectors generalization obtained experiments result research independent defined constant computer distance distance distance distance distance distance distance distance distance distance distance direction present object learn outputs outputs outputs outputs outputs outputs abstract applied applied back computational density references references component component ieee important decision propagation introduction hand hand statistical variance parallel classifier measure chosen higher higher higher higher part part part type type type required good long long distributed distributed make make proposed proposed length correct forward forward scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale tasks total simulation performed called called means means made made made global knowledge knowledge filter original vol vol samples samples samples samples samples samples samples proc accuracy comparison larger fields support train train selection morgan morgan morgan report loss loss consists code difficult delay considered computing experiment limit capacity efficient full increase clustering provided selected nature normal group limited finding short short nearest common effective effective shape role role role makes kaufmann kaufmann kaufmann auditory smaller smaller needed needed character character character character increasing special database database call choose improved improve improve improve improve directions advantage advantage advantage advantage takes similarity reported reported strategy strategy strategy strategy strategy strategy strategy dimensions conventional conventional calculated diagonal diagonal separation modified modified modified constructed constructed constructed constructed horizontal horizontal horizontal parts extended deviation feed feed occurs conclusion greater segment neighbor designed propose propose integration integration integration integration integration turn start selective characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters groups groups groups base reference reference reference reference reference reference construct construct written perception vertical vertical category remaining easy integrated integrated integrated formed blocks select extracted extracted stages stages squares digits assigned construction kohonen building handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten recognize recognize recognize discussions divided build composed kind strategies strategies strategies categories categories categories categories categories categories categories categories categories modular modular denker denker acknowledgments layered collection ideas authors comparable waibel waibel waibel smallest closest adapt recognizer separated separated consist integrate devices mentioned answer arc easier filtered precisely constructing constructing constructing constructing laboratories recognized english computers computers recognizing recognizing integrating integrating substantially fed passed dots operate howard reaches kinds kinds baird june realized ordinary writing writing japan lvq lvq abilities selects exploring washington jackel facilitate multiplied snn snn snn snn snn snn belonging hypercube consonant valuable acknowledge discriminate dramatically maintaining outline guyon july retraining retraining retraining suppressed henderson grouped hubbard individually individually individually retain harder zip grateful knowing atr mix covers decided decided satisfactory assistance subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet phonemic graf alex japanese integrates integrates integrates devised mori mori mori mori mori mori mori mori mori mori contributes recognizes recognizes amplified cho gardner modest modest modularity saito saito saito subnets subnets subnets subnets subnets subnets subnets subnets subnets subnets subnets subnets erroneous yamada respects nth writers gun nent kyoto encouragement concurrent icnn altogether owing chinese chinese intend inn inn inn inn joe joe joe joe joe joe joe joe soraku seika miyake miyake numeric monolithic retrain integrative handprinted handprinted mcdermott diagonals erik 
#@Joe_K,Mori_Y,
#t3
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#*network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data figure figure figure time time set set set set set set set set set set networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number system system system system error state results results results results results results units units information problem problem problem problem models hidden hidden hidden hidden performance based based based based based based based layer layer layer case order order order order order systems values values functions distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach processing processing large large large local rate rate rate rate rate patterns analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class inputs form form form form form algorithms algorithms simple simple simple examples examples size size size size feature feature feature feature net fig features features features features features current trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure problems problems problems high high high similar similar similar similar similar similar similar representation architecture show general speech speech speech speech average obtained obtained obtained obtained dimensional university university university threshold threshold threshold threshold threshold threshold threshold threshold solution solution solution solution research research research research independent found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant table table table table table table computer computer computer distance distance distance distance science presented present present present present low low low low low low sets press press learn position position outputs outputs sample sample abstract applied applied back back properties references positive procedure important important propagation propagation introduction statistical effect dynamic generated generated generated parallel search search search search search search search search search search search tion tion lower rules rules measure chosen bound type type required required long long distributed region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region length length length correct correct observed observed total total human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human multi sum regions regions regions regions regions regions regions regions factor factor factor factor natural study knowledge knowledge vol relative specific specific application cross cross rates rates rates proc proc location experimental related related related constraints constraints constraints distributions brain brain mit larger institute department version consists internal advances advances joint addition sequences sequences sequences sequences sequences sequences sequences sequences sequences cambridge computing domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain hinton additional view design design design stage stage stage stage stage stage detection detection detection detection detection detection significant increase increase con con channel channel channel channel derived derived derived types nature biological biological discussion feedforward increases group group fast assumption corresponds corresponds complete complete complete surface surface surface surface surface surface amount short short common common common assumed generate supported easily rumelhart rumelhart including programming significantly character database database database database database database database representing details call numbers max pre pre pre window window minimize run added description light perceptron perceptron similarity similarity introduced include identical sense sejnowski sejnowski engineering highly previously works solve speaker correspond address positions chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain chain williams williams williams williams williams williams grant trial correctly hybrid touretzky generally runs starting starting starting starting critical critical greater designed designed designed designed designed designed weak learns strong presence proportional user exist iii groups groups groups groups identification identification program program program program program program program force explicit pro pro ann explicitly text text national review influence variation variation evaluated evaluate evaluate evaluate forms forms forms forms forms forms discrimination roughly false false false false false false false false false false false false false false valid distances distances sufficiently sufficiently foundation degrees usa usa perceptrons inter inter inter sciences recognize recognize automatic coupled variations variations domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains domains characterized characterized gamma gamma gamma gamma gamma identified identified identified identified efficiency efficiency efficiency efficiency computationally delta included identify detect detect detect detect detect detect detect efficiently score score score score score score score score characteristic characteristic composed traditional prob success sci sci hold built receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor list involved localization ill ill ill acknowledgments rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat origin origin layered poor xor access exhibit exhibit exhibit association optimized existence school applicable biol biol biol comparable stream scores scores affect statistically possibly necessarily predicting rev equally recognizer noted detected detected detected detected detected detected detected detected detected detected detected growth growth distinguish analyzed biology biology majority majority lies handle considerable rapid lin sites protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio ion ion recognized recognized acad acad members members res res localized localized sun considerably profile profile profile profile profile substantially pseudo poorly detecting detecting execution rely anti characterize gen gen gen gen cal occurrence incorporating suited decreased wang wang 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beta beta beta beta beta beta beta beta beta beta beta beta beta beta beta beta alter alter ary epsilon epsilon epsilon epsilon epsilon epsilon epsilon file file searches searches searches increasingly disease amino amino amino amino amino amino amino amino amino amino accounted sta programmed exhibited exhibited permit nil intensive strict scanning scanning handled species species served served moderate advantageous scanned scanned scanned stimulating stimulating council vii transforming transforming stochastically suffers lists eliminates possess possess mori mori comprising comprising positives positives positives positives positives positives positives positives positives positives degenerate degenerate acid acid acid acid wisconsin cutoff cutoff cutoff acids acids acids acids acids acids acids acids comprised sheets sheets lar rem rem rem fore montreal montreal montreal montreal col discriminating sorted sorted frog comprehensive searched eta align scans bio sition biomedical ver respects bonds schneider hypothetical hypothetical sodium sodium sodium sodium tentative tentative tie tie evaluates translational designated vast vast machinery exhibiting ously insects lowing strain strain previ scored scored scored parentheses ant ant ant penalties lacking comprise bearing bearing canadian banks ending ending ending ending yoshua succession gem expands rabbit categorized categorized conserved conserved conserved conserved conserved conserved conserved conserved conserved conserved conserved conserved violations handles hurt tang entails ehrenfeucht sug flanking reg subsequences subsequences subsequences gions portant kinase kinase pected collectively reacting reacting insignificant lambda lambda lambda lambda subregions subregions subregions subregions qian qian mcgill mcgill initiation ciently possessing substitutions ser ser patrick tistical neurological legend immune negatives negatives negatives negatives negatives mol mol mol helping fruit fruit fruit fruit 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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function figure figure figure figure figure figure time time time time time set set set set set set set training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number system state state state state state state state units units units units units units units units units units units units units units units units units units units units units units units units units information problem models models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based based based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer case case case case case vector vector vector vector vector vector vector vector order shown shown shown shown shown systems values values parameters weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single processing processing processing patterns patterns patterns patterns analysis inputs form form form form shows shows shows simple paper examples examples examples small feature work work work task task step step step process process process process trained trained trained problems problems problems random high memory response similar representation representation representation architecture architecture architecture architecture architecture architecture rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors general states states states states theory term note result university university solution research research research independent found sequence sequence sequence sequence sequence sequence initial initial initial initial constant table table table table table table computer computer connections connections connections connections connections connections connections science science science science presented presented presented present present present activation activation activation activation low sets press learn learn learn position position basis continuous abstract back computational references component component due due important important context introduction complex complex complex behavior behavior behavior parallel cost change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change change assume rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules representations representations representations representations representations representations representations learned learned learned learned part previous previous cases cases firing firing firing firing required required long long conditions represent represent distributed distributed distributed distributed distributed distributed make techniques length correct correct errors tasks tasks human factor made made knowledge knowledge knowledge original original original original original represented represented desired desired desired desired desired rates active active active active active active active active active active active motor equal mit larger larger contrast update source morgan proceedings proceedings words version version consists code code advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult difficult bias scheme scheme sequences ai maps maps cambridge experiment environment environment environment directly additional additional solutions solutions san effects bit bit conference conference determine determine choice significant produce produce developed types product finally selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation inhibitory discussion technical describe describe close close nearest common implemented generate supported supported role role role role eds instance instance future degree degree makes makes rumelhart rumelhart rumelhart development kaufmann pairs needed needed fully fully interesting edge edge mechanism mechanism mechanism special mode principle operation representing details pre bits normalized normalized normalized supervised supervised magnitude decay decay decay combined combined description predict architectures architectures architectures population robust separate separate separate apply apply apply subject subset cognitive cognitive cognitive cognitive highly teacher teacher teacher module match match match match match achieve rl rl rl positions positions positions positions positions positions improvement sensitive sensitive grant exists scaling occur wide correctly correctly correctly move move touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky greater segment segment segment segment segment segment segment segment segment competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive learns learns mateo encoding encoding external external intelligence intelligence variety exist iii introduce introduce manner program force acknowledgements suppose longer longer index winner primary primary generating describes implement explicitly slightly unique formed formed formed formed select competition letters letters yield national formation formation formation formation stages learner completely slow classical intermediate initially string string string string string string string string string symbol symbol assigned foundation advantages david fire fire fire fire fire fire fire fire perceptual combinations strings strings strings strings instances instances activated partially discussions successfully selecting letter closely suitable suitable society society differ symbols mcclelland presentation detect quickly repeated procedures strongly induced allowing showing split running running cue hold hold write play generalize minimizes thresholds overlapping presents production experience circuitry circuitry circuitry environments environments detail limitations helpful matches history school behavioral incremental office working symbolic symbolic symbolic proved cognition cognition cognition trace trace changed adjusted adjusted adjusted precise precise arbitrarily explain derivation derivation derivation track caused handle handle starts implementing satisfied satisfied satisfied closer producing producing laboratories pool pool pool pool pool read annual annual meaning mellon explained behaviors considerably carnegie applies applies applies fed backprop backprop share maintain switch exhibits pittsburgh reaches reaches prevent enables replace hamming hamming chose shaped returns implements focused eventually eventually eventually specifies contribute contribute shifted corrupted corrupted secondary writing assign assign assign forming discovery repre discover naval theories chains chains proceeds replacing check contract contract abilities splitting integrator responsible enhanced presentations presentations fires fires fires fires fires reliably interference interference interference interference combines representational ensures james mental buffer 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detects dedicated dedicated resolved phonology phonology cur cur william chunking chunking chunking chunking chunking chunking chunking chunking chunking chunking chunking permanent ready ready zeros enters feb raised request request seg seg seg seg successor derives mutation actively sented firings firings plastic plastic plastic plastic plastic plastic plastic plastic plastic plastic plastic boosted occasionally contributing examines saved waiting wheeler wheeler wheeler participate rosen temporary sorts lose ending taught permitted teach undergoing concentrates chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk chunk buffers chunks chunks chunks chunks chunks chunks chunks chunks chunks chunks chunks chunks chunks chunks chunks distribute requested manage eet chitecture assure composing eleventh eleventh ade ade ade ade ade ade ade ade ade ade ade ade ade ade ade recruited recruited accomplishes reversing 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system error error error error error error error error error error error error state state state state state state state state state state state state results results results results results units units units units units units units units units units units units units units information information information information information information information problem problem problem problem problem problem problem problem performance performance performance performance performance performance based based based based based space weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear case case case vector vector order shown shown values values values values values values values values values values values values values weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit approach approach approach approach approach approach pattern point processing large large large large large local local analysis matrix matrix matrix matrix matrix matrix form form shows shows algorithms simple simple simple paper small small small small small small net work work work work task task methods step step step level current current current current current current current current current current current current current current current structure structure structure structure structure structure structure problems random random random random random similar representation representation representation representation representation representation architecture show equation equation section rule parameter states states states gradient obtained term experiments experiments activity activity activity activity activity activity activity activity activity result result result result university university university variables variables solution solution solution research found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence initial table table computer computer computer computer terms terms terms distance connections connections connections node node node node node node node node science science science science science prediction left left left left left left left direction present present present activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal temporal machine sets press learn learn learn learn learn learn position position position outputs abstract applied back back back back back back back analog references stochastic due positive procedure procedure procedure procedure important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action complex complex behavior effect generated parallel parallel cost cost search tion tion change change complexity assume assume measure prior representations learned learned chosen previous previous previous previous previous bound bound required required binary long represent represent represent represent represent distributed make make make length correct correct correct observed observed observed forward finite finite finite finite finite resulting resulting resulting resulting resulting computed respect respect performed performed performed called called times times means means potential potential feedback feedback study knowledge knowledge obtain negative represented compared desired desired desired compute compute compute active goal goal goal constraints constraints constraints constraints constraints constraints constraints constraints connected discrete approaches steps steps steps steps steps steps steps steps contrast contrast contrast connection connection connection connection connection connection connection update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update train modeling modeling proceedings proceedings report institute institute department implementation consists consists internal internal internal represents represents represents represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult final final addition graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph sequences sequences sequences cambridge cambridge equivalent environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment directly hinton hinton hinton additional additional additional view limit determine determine efficient efficient upper upper full requires requires significant world world world world world world world world world world world world world world world world basic con con con produce developed developed developed robot robot robot robot robot robot robot robot robot robot robot robot robot area actual finally selected selected selected constraint constraint constraint constraint constraint simply measured measured technical describe describe corresponds complete stable actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions predictions predictions predictions amount shape supported require eds square square end future future makes makes rumelhart rumelhart rumelhart noisy sensory smaller combination technology significantly projection head head head head head consistent representing details call call direct international added description light light light light light light light predict predict predict predict predict improve improve exact advantage property property pair separate strategy strategy strategy moving include identical sense sense inference inference cognitive sufficient sufficient highly varying unsupervised tions tions tions converge achieve achieve address definition chain chain chain modified gate williams williams grant grant grant arm studied suggests suggests extended extended derivative matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices predicted predicted predicted predicted alternative alternative alternative alternative move move move loop loop deterministic white occurs flow flow flow flow flow strength strength strength strength critical critical row row valued designed sutton suggest suggest taking taking labeled labeled labeled turn turn assuming assuming start iii iii derivatives connectivity connectivity connectivity connectivity connectivity connectivity force force acknowledgements explicit appears longer longer ann modeled simultaneously involves involves adding events versus choosing interpretation updated updated updated updated labels activities activities activities activities activities activities activities activities activities activities activities activities activities completely suggested converges updates updates allowed allowed diagram diagram diagram earlier earlier earlier barto performing performing performing performing normalization purpose foundation foundation avoid exploration exploration exploration exploration exploration exploration exploration exploration exploration figures thesis extension activated mozer mozer mozer mozer mozer mozer mozer mozer mozer mozer mozer discussions tests tests tests reason modification mcclelland successful situation receives capture traditional traditional procedures contained allowing link link link link interpreted split contribution satisfy list involved michael michael correspondence hypotheses hypotheses hypotheses reach reach moves subsequent satisfies situations explore explore remain collection essential experience updating environments environments environments environments environments environments environments environments detail detail strengths strengths strengths strengths strengths replaced replaced preliminary helpful fewer history links links links links links links links links links links office symbolic symbolic symbolic workshop affect encode cognition notion notion analogous removed act concepts analyze predicting extremely automata automata automata illustrate rank formal algo algo initialized detected explain finds massachusetts massachusetts indicating indicating indicating indicating developing defining unstable fairly adjacent explanation starts perspective purposes satisfied satisfied satisfied formalism formalism formalism ran arise arise cut scientific beginning arises depicted annual fourth reflect empirically consistency consistency consistency readily car poorly introducing incorrect compares maintain switch switch ture incoming serve inherent median don shifted person room room room room room room room room room room room room room room room room room room room room room room room room room room room room room room room room room room sensing sensing sort assign equivalence forming temporally rithm rithm arguments linearity dynamically concerned circular smolensky outcome outcome outcome arranged fails air ments ments promising iiii iiii iiii tools automaton intelligent loops loops interpret serves fail intuitive date exploring schapire schapire schapire schapire schapire schapire schapire schapire schapire schapire schapire schapire schapire schapire schapire schapire schapire james paul surprising mental bad colorado colorado heart heart heart heart heart consequences consequences consequences consequences bulb propagated offers claim advance specialized foundations foundations infer shortest master record record record rich environmental environmental environmental environmental environmental environmental environmental environmental reverse discovered discovered propagate propagate insensitive explorations andrew appeared microstructure outperform outperform benefits benefits benefits benefits preserving failed forced feeding conjecture connec causing generalizations amherst superimposed superimposed discovering discovering discovering discovering 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arms legs news unfamiliar unfamiliar succeeded quence matters worthwhile quired quired rooms rooms rooms rooms tionist accomplishes bachrach bachrach bachrach bachrach bachrach iiiiii iiiiii connecfionist connecfionist connecfionist connecfionist connecfionist prince speedups zeroes ful armed rob sensations sensations sensations sensations sensations sensations sensations sensations sensations sensations unfolding cease contingent assured bachtach bachtach bachtach bachtach bachtach iiiiiiii complements complements clever renormalized worthy afb vironment fresh isn rigidly wander leamed elaboration struct complemented complemented trix bolling exchanging generali wandering blame formulates tivities 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data function function function function function function function function figure figure figure time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number system system system system system system error error state results results results results results results units units units units units units units information problem problem problem problem problem problem problem problem problem problem models models models hidden hidden hidden hidden performance performance performance performance performance performance performance performance based based based space space space space weights weights weights weights weights weights linear layer layer layer layer layer case case case order systems values values values values values values values probability parameters parameters parameters parameters parameters noise weight weight weight weight unit unit unit distribution distribution recognition recognition recognition recognition method approach approach approach approach approach approach approach approach approach approach approach point point point processing control large local rate rate rate test test inputs shows shows algorithms algorithms simple simple simple small small small small size feature net net net net net task fig fig fig fig field field field features classification classification process current current current current trained trained trained structure structure problems problems problems problems random random random high high response similar architecture architecture architecture show fixed rule rule rule rule images general general generalization generalization generalization parameter parameter parameter real real approximation approximation approximation average average average average average average average obtained term note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments university university university threshold threshold solution research research research research independent independent found target target initial initial initial initial initial initial initial initial initial estimate computer computer connections connections connections science science present low low machine maximum press components nonlinear abstract applied applied back back computational computational computational computational computational convergence density properties properties properties references component component procedure procedure procedure important important important important propagation propagation introduction hand effect generated generated generated parallel parallel cost cost search search search search tion tion complexity variable spatial classifier rules learned learned learned learned learned chosen higher higher required good techniques observed observed scale minimum ing human human computed computed sum performed called factor optimization optimization optimization optimization optimization optimization optimization optimization potential dimension natural applications applications applications applications applications applications applications applications artificial relative relative relative specific specific specific specific specific specific specific specific specific specific represented application application application application application application application application application application application application application application application application receptive receptive receptive perform active related constraints approaches approaches accuracy larger contrast connection connection connection connection fields fields update update support train source modeling modeling morgan proceedings report report report department implementation implementation implementation implementation version version version technique consists advances layers layers addition addition graph graph considered considered considered cambridge experiment experiment experiment experiment experiment directly hinton hinton hinton curve curve solutions estimates design design design design design design design design design san san stimuli stimuli bit detection conference efficient requires requires choice choice speed speed speed speed produce weighted randomly randomly randomly developed developed criterion area area area area area area area area area area actual selected backpropagation backpropagation backpropagation backpropagation depends sampling constraint technical technical feedforward describe arbitrary arbitrary tested fast fast limited limited corresponds common effective implemented generate role vlsi pixel hypothesis future future future future future rumelhart rumelhart development development development development including including including including including kaufmann objective typically needed unknown testing testing testing testing testing testing testing significantly significantly projection projection projection projection projection projection projection york edge structures structures structures structures structures structures uniform mode numbers iterations supervised magnitude magnitude decay decay decay decay produced produced produced produced produced produced produced produced run run description improved population population population population population discussed recent recent advantage advantage reported practical practical machines cognitive recently interest dimensions highly unsupervised works works works works works studies achieve address definition evaluation evaluation evaluation williams williams williams organization sensitive entire alternative hybrid hybrid generally hardware hardware hardware starting critical greater reduce segment segment clear faster faster mateo mateo cycle characteristics characteristics characteristics user user start start exist connectivity connectivity connectivity connectivity connectivity minima program configuration areas areas areas digit digit digit digit pro pro produces longer solving ways ways factors describes distinct segments multilayer simultaneously linearly linearly dimensionality scales develop detailed densities densities evaluated evaluated restricted restricted updated understanding earlier slow iterative penalty generation generation generation generation generation generation generation string norm expect existing exploration combinations weighting sciences extension candidate selecting aspects aspects aspects aspects aspects efficiency capable capable encoded committee projections projections genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic score tend tend online composed repeated strongly prob heuristic showing interested superior running running criteria criteria criteria criteria criteria criteria criteria involved realistic consisted subsequent load minimized employed unlike poor xor xor essential requirements updating steady optimized optimized optimized optimized optimized optimized optimized optimized optimized accurately behavioral ideal referred working proved scores affect momentum neu neu perfect prototype prototype aspect obvious algo algo algo consist averages slowly directed costs separable separable growing analytic floating floating capabilities tool reasons operators incorporate incorporate choices leaves desirable mathematics optimize localized computers radius radius robustness improvements evaluating evaluating substantially substantially conducted conducted conducted effort orders incorporated incorporated frequently variant requirement execution synthesis synthesis popular parent parent extensions substantial logical logical sophisticated neuro tolerance damage specifies progress wesley initialization initialization consistently interface interface extensive appropriately resources perfectly perfectly concerned controlling systematic systematic consideration tools hope hope north north arrays child heuristics continue date holland holland conjunction colorado surprisingly reader jolla fitness fitness fitness fitness fitness repeatedly vertex passing designing designing designing designing designing designing designing davis davis severe lem ics specification specification largely largely sch ter ter sine sine sine sine asked asked benefits encodes employs employs restrictions instantiation connec monotonicity individuals suppressed exclusive evolve werbos werbos oct retain investigating topic speedup cation covered emphasized emphasized alternatives distinguished permit nal intensive struc status continually strict ucsd syn moderate remarks lation discontinuous crude designs termination steven concern inherently ters partly manually goldberg goldberg goldberg sions appl cutoff cutoff feasibility feasibility bottleneck handbook addressing addressing addressing steve dent indepen acyclic prominent platform manual predetermined predetermined tivity custom cations appli appli marker putational eta eta eta eta eta generations save gross avenue ver week parame perturbing perturbing retention offline untrained terminated outlines golden golden cad cad convexity workstations supplies bypass bypass critically accelerate tly valley valley duced cate intend sole comparatively neur neur reg hue bor ger genera radii radii chart print ciently optimistic increas suf ash notoriously appreciated whitley whitley harmful vax symbolics symbolics symbolics popu abort immunity ingly fanout fanout fanout fanout fanout touretsky disabling disabling pause 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#*network network network network network network learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number number number number number number system system system system system system system system system system system system system state state state state results results units units units units units units information information information information problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based based based based based space space space space space space weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case vector order shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems values values values values values values values values values values values parameters parameters parameters noise unit unit unit unit method method method method method method approach approach approach approach point single single single single single processing processing large large large large large large local local test analysis analysis shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple small small feature feature feature feature feature feature net work work work work work work work work work points points field field field field field field field features features features features features features features features features features features features features features features features features process level level structure structure structure structure structure problems problems problems problems problems problems random random high high high high high high high high high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory representation representation representation architecture architecture show show show fixed rule rule general general real real real real real states theory note experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional variables variables variables variables research research research research research research found found sequence initial initial constant constant estimate estimate standard standard standard standard standard standard standard computer computer distance distance distance distance distance connections connections connections connections connections node science science prediction prediction prediction prediction direction direction direction presented presented presented present low low low low nodes nodes nodes machine machine machine machine range press press nonlinear sample sample sample sample sample sample abstract applied applied applied back find computational computational computational properties properties references due procedure procedure procedure procedure procedure important important important important propagation introduction statistical statistical statistical effect effect parallel search search search search search tion tion tion tion tion change change measure measure prior representations representations word chosen chosen part center center center multiple good good binary binary binary binary binary binary distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed make techniques correlation length errors forward scale scale scale scale sum performed performed called called times times elements elements regions dimension natural applications study study study knowledge original artificial artificial artificial relative relative relative specific specific samples samples samples samples samples samples samples samples samples represented desired location location location location location location location location location location location location location location location location location location location location location location location location location location location location location perform determined determined related connected equal equal equal equal power approaches mit comparison larger contrast contrast connection connection connection fields fields fields fields fields train dependent selection selection selection morgan morgan report report institute institute implementation technique technique consists internal code code advances represents difficult difficult layers layers layers layers cambridge domain domain directly directly additional view view san bit bit bit bit bit bit bit bit bit bit bit bit bit bit efficient world world world world world speed speed increase increase levels types provided finally finally processes processes processes processes selected selected selected selected selected selected selected selected selected selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature depends simply associative associative associative associative associative associative associative measured technical describe group tested effective supported eds adaptation end end ability ability ability ability future makes makes including fit fit fit kaufmann simulated underlying needed combination fully testing operation operation language call numbers pre making making stored stored stored stored bits bits combined improved population population population population population population population improve correlations correlations correlations property separate ensemble period period highly highly highly highly highly highly compare compare previously previously previously volume tions sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse address address address address address address address address address address address address positions locations locations locations locations locations locations locations locations locations locations locations locations improvement storage storage storage storage sensitive sensitive sensitive sensitive sensitive sensitive entire entire increased scaling scaling occur predicted feed move hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid starting place place row row greater greater segment conclusions central interactions differences measures designed designed designed designed designed clear clear performs mateo temperature temperature temperature temperature taking cycle cycle characteristics california proportional proportional intelligence user user user min min minima annealing denoted reference reference written written ways ann mathematical mathematical distinct changing changing recall sensitivity sensitivity sensitivity sensitivity simultaneously averaging physical physical physical dimensionality predictive predictive predictive formed select select national reconstruction depending depending detailed open open operations restricted organizing allowed past spaces spaces spaces spaces spaces spaces purpose string string string string string construction kohonen advantages david david david david expect box box box combinations formulation strings strings strings strings strings inter memories memories illustrated maximize specifically specifically specifically domains domains domains black black black absolute selecting middle importance effectively driven driven successful successful build genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic ten ten refer graphs graphs graphs contained contained success success success dis dis running gray involved sampled write nips board attempt consisted operating preferred preferred acknowledgments remain remain unlike powerful create create create create access access access access access put environments strengths association issues mass helpful fewer giving tech int referred proper scores func func cover cover cover cover removed removed hill coarse possibly reading reading reading analyze analyze predicting predicting predicting predicting predicting predicting predicting predicting predicting predicting predicting predicting predicts extremely extremely extremely created created created changed changed changed changed noted perceptton initialized switching finds years years percentage site advanced advanced advanced rows improves coded coded coded coded capabilities handle london tive tive sys sys closer easier style style day day worst desirable desirable desirable desirable commonly members members members members members members members members members begin radius radius radius addressed raw robustness reflects greatly reflect reflect collected conducted poorly poorly share incorporated variant operate measuring parent parent parent parent parent wind wind wind wind occurrence suited suited suited sums sums sums replace hamming hamming hamming june summed sharing primarily writing writing member member member member member dynamically dynamically reconstructed unity addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses addresses discover discover tem tem climbing inspired inspired air kaufman adds difficulties fan fan held held los scoring analyzing implications responsible hours hours hours hours hours hours hours hours hours embedding corre entry studying encountered holland holland holland holland holland holland holland holland holland holland bad forecasting den searching searching bulb bulb bulb bulb uni counter candidates darpa specialized surprisingly mem mem mem reader offer offer refers fitness fitness fitness fitness fitness fitness fitness storing relies projects davis davis davis davis davis davis discovered tures tures insensitive vari parents assigns pressure pressure pressure associations ence unified dna dna dna ple ple ter incorporates ram cooperative dec july july pieces tween year year year year utilize connec arbor possibilities england rain rain rain rain rain rain rain rain rain rain rain unseen exam intuition formance insights toy crossover crossover crossover crossover crossover crossover crossover file file mitchell oct individually kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva kanerva pos meta termed cation covered sam preserve nasa nasa nasa nasa grateful book memo memo memo fea fea applicability thousands thousands thousands els gorithm gorithm completed completed correlate correlate architectural advantageous scanned sponding payoff january january january august demand demand decided continued australian australian australian jointly hundreds envelope hypothesized olshausen hid station incorporation month month month month month month month month month month agency placement ory ory ory tance weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather weather evolutionary evolutionary evolutionary evolves demands twelve feb feb defense contents mul jan jan february february february sep discovers discovers massive shares stan stan publishing ard collections months months months tal newly judge predic align ables nov ness mar mar dard wait opportunity sible rated rated rated rated rated rated ranked ranked ames ames lay nation unclear rogers rogers rogers rogers rogers rogers rogers rogers rogers rogers rogers associating counters counters counters counters counters counters counters counters 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#@Rogers_D,
#t3
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data function function function function function function function function function function figure figure figure figure figure figure time time time time time set set set set set networks networks networks networks networks networks networks algorithm output output output output output output output output number number system system error error error error error state state state units units units units units units units units units units units units information information information information information information information problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden based space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights case case case case vector vector shown systems systems values values values parameters parameters parameters weight weight weight weight weight weight weight functions functions functions functions unit unit unit unit unit unit unit method method pattern pattern point point point point point point point point point processing large large large large local rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns inputs form form shows shows shows shows shows signal algorithms simple simple simple simple simple simple visual visual visual visual visual examples small small small small small small size net net work work work methods process process structure structure structure structure random random random random high high similar similar similar representation representation representation representation representation representation show show show show line line vectors vectors vectors vectors vectors general general general general general real real states theory gradient obtained obtained dimensional dimensional dimensional dimensional dimensional dimensional dimensional result threshold threshold threshold solution solution solution research research research research defined found found found found found dynamics dynamics dynamics dynamics dynamics initial initial computer computer computer computer node node node left left direction presented presented presented presented phase phase nodes nodes nodes nodes nodes nodes nodes temporal temporal press press learn position components components basis abstract applied back back back references due ieee positive positive positive important decision decision propagation propagation propagation introduction behavior dynamic dynamic parallel change change change spatial lower lower representations representations chosen part center cases required required good binary represent represent distributed expected make make make make make fact techniques techniques techniques techniques techniques correct correct correct errors scale simulations simulations simulations simulations total total simulation simulation simulation human multi multi sum sum sum regions made made made made made global global applications study study study negative negative relative represented application application application provide active active determined related connected connected mit larger contrast connection fields descent implementation internal internal code code code represents final final final final bias scheme addition cambridge computing computing environment environment environment environment hinton hinton curve additional solutions solutions trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory stage effects effects detection upper upper full requires choice basic developed levels area area lines lines processes depends normal corresponds require eds end easily rumelhart development development typically typically pairs pairs reduced projection uniform uniform representing representing representing call call window window window window window window window window bottom early early magnitude magnitude magnitude attention run run run improve directions directions pair pair introduced introduced include identical machines hierarchical sense sense interest interest conventional observations teacher calculated volume works axis solve yields match match match correspond converge converge achieve diagonal symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric spikes derivative alternative correctly move setting runs runs half strength conclusion critical critical trajectories trajectories trajectories trajectories central central designed suggest proportional user start plane plane introduce introduce configuration configuration configuration acknowledgements appears pro written solving ways plot distinct distinct segments explicitly simultaneously remaining unique interaction integrated integrated formed boolean boolean boolean decreases yield stages stages stages stages evolution evolution static completely diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram slow roughly initially initially initially topology includes color color plotted plotted major aspects aspects extra paths paths paths mcclelland identify detect detect notice heuristic symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry built received principles moves software tesauro tesauro tesauro tesauro tesauro decreasing extend layered poor collection investigate rapidly rapidly strengths graphical graphical behaviour behaviour giving project investigated investigated relationships decisions decisions complicated affect hierarchy understand understand cognition notion contours circles trace trace configurations opposite created changed adjusted obvious observe observe separated brown indicating distinguish distinguish majority majority majority majority majority majority adapted tool comparisons arc widely ran mation scientific scientific scientific scientific members outer researchers offset quantitative red marked treated dots rep anti anti anti anti differs proven simulator simulator simulator chose display display windows windows windows windows windows windows deviations instantaneous picture picture lab lab resources perfectly perfectly perfectly connecting grey ments tools tools tools observing infor programs displayed displayed lengths infer infer insight creating designing speeds explorations limitation geometrical microstructure pointing benefits presenting july feeding feeding obtains chaos blue generalizations perceived workstation workstation examining visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization ibm evolve insights gained magnitudes magnitudes learnt learnt graphics graphics graphics graphics graphics graphics graphics graphics graphics graphics graphics graphics graphics graphics interactive relates regimes thousands thousands travel signs signs article november diagrams diagrams diagrams diagrams diagrams diagrams diagrams diagrams diagrams emphasis identifies vis families aid optima triangles triangles triangles bond bond bond bond bond bond bond bond kirkpatrick carries totally totally resultant scott cess oscillates indirectly watson tens permutations permutations 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#@Tesauro_G,Wejchert_J,
#t3
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function figure figure time set set set set set set set set networks networks networks networks networks training training training algorithm output output output output output output output output output output output output output number number system system system error error state state state units units units units units units units units units units units units units units information information information information problem problem problem models models models models models performance based based based based based space space space space space space space weights weights weights weights weights weights linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer case vector order order systems values probability parameters weight weight weight weight weight functions functions functions neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit approach point single single single single single single processing processing processing processing processing control control control control local local local local local local local local local local neuron class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form signal signal signal signal algorithms simple simple gaussian gaussian gaussian gaussian visual visual paper examples small small small small small small size size size size size work work work work work task task methods methods methods fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells points field field field field field field features process level level level current cell problems high response similar similar architecture architecture architecture show line rule rule rule rule rule rule rule rule vectors vectors vectors general general generalization parameter approximation approximation average theory theory theory theory theory theory theory term term term note activity activity activity activity dimensional dimensional dimensional dimensional university university threshold variables computation research independent table table table table table estimate standard standard computer synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science science presented map map present present activation activation motion range range range press press learn components basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs abstract abstract applied applied applied computational computational properties references due positive adaptive introduction complex circuit behavior stimulus statistical dynamic parallel parallel parallel parallel difference assume assume assume assume assume rules rules rules rules signals learned learned cases type type type type type type type type type type type type cortex cortex cortex cortex cortex cortex cortex cortex cortex long long long long long long tree tree distributed distributed distributed make region proposed proposed correlation correlation total total total computed multi sum sum sum called elements elements elements elements means factor dimension orientation orientation global global specific specific specific represented represented desired cross receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive define proc proc proc location active active active active experimental goal distributions motor cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain equal mit mit voltage larger fields fields fields fields fields fields support support dependent dependent source nets modeling morgan institute institute words synapses synapses synapses synapses synapses synapses synapses synapses consists individual individual joint represents represents connectionist connectionist connectionist layers scheme scheme addition addition maps maps maps framework cambridge cambridge directly directly directly directly directly hinton view limit capacity capacity significant statistics vision basic increase channel channel channel weighted weighted weighted clustering clustering robot robot levels area area area area controller lines lines path product product product actual provided evidence evidence backpropagation depends simply biological biological biological biological associative associative associative associative associative associative associative associative associative associative discussion technical feedforward arbitrary group assumption assumption excitatory excitatory excitatory excitatory excitatory excitatory surface finding rbf rbf assumed synapse role role role role theoretical theoretical main eds eds eds eds hypothesis hypothesis cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster degree degree rumelhart rumelhart rumelhart rumelhart development development sensory sensory kaufmann pairs underlying underlying needed needed needed account functional functional unknown york york york york york edge mechanism mechanism operation principal squared representing pre pre pre pre pre pre making stored minimize description predict neuronal population population population discussed property property property takes element practical include sense cognitive recently recently recently engineering interest dimensions highly previously teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher address definition symmetric modified modified modified channels gate organization organization storage storage entire increased horizontal horizontal studied extended wide locally locally locally locally locally locally clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters occurs occurs column column hardware strength place place place hebbian conclusions interactions interactions interactions interactions moody moody moody moody weak learns encoding propose propose propose strong mechanisms physics physics largest demonstrated regularization radial radial radial variety minimizing exist exist selective iii iii iii iii iii groups program denoted denoted acknowledgements areas areas areas areas reference relation relation primary primary primary primary primary tuned vertical dept implement simultaneously simultaneously electrical angle interaction interaction adding john yield independently focus formation formation interpretation detailed open evolution centers decomposition suggested constants key key sec interpolation initially initially distances sufficiently foundation foundation koch koch koch koch koch koch koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic david thesis usa retinal retinal memories extension discuss maximize activated activated specifically discussions characterized major planning closely capable importance importance importance uniformly modification modification modification computationally driven driven driven mcclelland mcclelland mcclelland mcclelland poggio poggio poggio poggio identify identify computations schemes post post post post post post post post mackay invariance miller miller miller essentially essentially soc soc soc strongly strongly strongly strongly anderson anderson content follow timing localization modular paradigm realistic providing providing giles computes overlapping disparity preferred neighboring receive receive receive oriented origin remain remain unlike stimulation selectivity powerful powerful american american wiley transformed create access access essential put relations relations steady association association association association association association association association association association helpful rise rise examine respond fashion history school project plasticity plasticity ideal possibility possibility office maximizing pathway pathway pathway cognition induction act act math naturally transmission thought subsets assumes explored hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb fibers fibers fibers fibers fibers fibers fibers fibers pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal consist extent explain defines brown brown brown brown crucial growth growing coded adapted multiplication multiplication multiplication multiplication multiplication briefly interneurons nonlinearity nonlinearity spatially purposes widely widely strictly style afferent afferent commonly commonly involve axons axons localized localized geometry virtual virtual virtual virtual questions pathways understood pure pure relevance generic generic poorly atkeson atkeson item share biologically biologically operate collective pasadena suited richard physiol coherence specifies specifies simultaneous contribute physiology primarily primarily interface modify conditioned narrow girosi girosi girosi jth naval jones jones jones jones enhancement enhancement caltech plays climbing clamped inspired binocular darken accepted interconnection cerebellum multiplicative multiplicative multiplicative familiar interpret interpret nearby date exploring bartlett cerebellar cerebellar cerebellar governed dendrites dendrites dendrites dendrites dendrites james accounts dendrite dendrite dendrite mel mel mel mel mel mel mel mel nonlinearities nonlinearities entries multiplied diameter barron barron barron barron modelled specialized membership axonal axonal cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral cerebral stimulated ballard ballard ballard ltp ltp correcting projects implicitly generalizing generalizing generalizing generalizing generalizing thresholding thresholding thresholding acknowledge speaking summer ple numerous numerous numerous microstructure ter tables tables focal job connec sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma arbor additionally decomposed tendency classic massively clustered tight remainder exam robots biophysical biophysical chapman guidance potentiation potentiation thresholded douglas mediated individually projecting lond lond lookup lookup lookup lookup distal selectively manipulator afferents afferents pop memo lapedes lapedes modifiable normalizing durbin durbin durbin september lowe lowe lowe lowe accordance mcdonnell hypothesized virtually albus albus albus diffuse adult cylinder concern illinois inherently anatomy anatomy believed believed meeting nmda nmda nmda nmda marr marr marr marr neocortex neocortex cones optics cooperation cooperation neurobiological vertically vertically comm comm feldman feldman feldman bradford decoded addressable ensuring scattered scattered mesh massive allowable christof modularity modularity depolarization depolarization stems tivity plenum plenum lund occasionally unifying apical apical biophysics continuing columnar terminate hampshire enhancing parsimonious pyramids sible lasting clump segev pri workers neurally clus shepherd shepherd radially torre latch thalamic webb correspondingly mary maxwell enormous enormous multivariable underlie underlie ulation del rabbit broomhead broomhead broomhead broomhead selec lend rli sit cited trim abstractions rodney presumed pnas pnas pnas incentive unmodified bernander tionist locus peters peters peters peters contrasted situated butions ingredient clumps subcortical inevitably virginia schmitt farbet dentate optional ouput dennis glanz neurosc biosci extrinsic kelso kelso aggregated spines endowed kraft modelers modelers associational associational associational aggregates pyra pyra tstems tstems tstems multiplica cooperativity ofy bent midal midal neuroscientists reservoir 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#@Koch_C,Mel_B,
#t3
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input input input input input input input input input input input input input input input data data data data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number error error error error error error results results results units units units units units units units units units units units units units units units units units units units units units units units units units units information problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based based based space space weights weights linear linear linear layer layer layer layer layer layer layer layer case case case case case vector vector vector vector vector vector shown shown shown systems values values values values values values values values values values values values parameters noise weight weight weight functions functions unit unit unit unit unit unit distribution distribution method method method method method approach pattern pattern pattern pattern pattern pattern single single single processing processing neuron neuron neuron rate rate rate rate rate rate rate rate rate rate test patterns patterns patterns patterns patterns patterns patterns optimal optimal optimal form signal signal algorithms algorithms algorithms algorithms algorithms gaussian paper small small small size size size size work methods methods step points points points points field field field field field field field field field field field field field process process trained problems problems high high response response response response response response response response response similar representation representation representation representation representation show equation equation equation equation equation equation section fixed rule vectors parameter parameter real real real real approximation approximation approximation approximation theory gradient gradient obtained obtained note experiments dimensional result university independent defined defined found found target target initial estimate computer distance distance distance synaptic prediction presented presented presented presented presented map map map map map present present present present present present present phase phase low sets maximum range basis basis basis basis basis basis basis basis basis basis basis nonlinear continuous abstract references due due positive important important adaptive adaptive adaptive introduction hand effect variable rules measure measure measure measure representations chosen higher center center center center center theorem theorem theorem bound bound bound bound bound cases represent equations equations equations observed errors errors ing ing ing total simulation sum sum sum sum performed performed performed times times times regions mapping factor factor factor factor factor factor factor dimension applications obtain application series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive rates rates rates rates rates determined determined determined determined experimental equal equal equal equal comparison fields fields fields fields update descent descent descent morgan proceedings report institute technique consists individual responses responses responses responses responses responses considered considered considered computing hinton san stage stage determine upper upper upper upper upper choice con condition clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering bounds bounds provided finally processes backpropagation achieved close inverse proof proof rbf rbf rbf rbf rbf nearest nearest nearest nearest nearest nearest nearest nearest effective eds square square cluster cluster cluster cluster cluster future future degree kaufmann objective pairs combination combination dynamical functional technology technology significantly increasing special normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized supervised minimize added predict improved improved improved typical recently dimensions dimensions sufficient varying calculated works tuning tions improvement entire expression expression extended extended hybrid hybrid touretzky width width hardware hardware reduce conclusions neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor valued valued moody moody moody moody faster faster mateo radial radial radial manner areas index factors stability stability dept metric metric metric metric metric consisting quality john national squares squares overlap overlap overlap overlap overlap overlap overlap overlap overlap evaluated fraction centers centers centers centers decomposition updates updates updates updates updates slow intermediate assigned norm figures formulation sciences characterized determining determining suitable suitable suitable computationally poggio poggio presentation presentation build plots plots heuristic heuristic heuristic heuristic heuristic computes preferred decreasing decreasing situations xor xor essential put hall fashion school tech links links comparable closest closest predicting implementations implementations logistic logistic logistic logistic ith epoch epoch epoch epoch arbitrarily finds chaotic massachusetts indicating inequality crucial glass glass glass glass glass drive tive purposes organized potentially addressed exemplars exemplars summation pseudo employ spread sums implements appropriately girosi jth jth connecting establish darken attractive los nearby enhanced enhanced enhanced substituting substituting performances prentice connect james widths widths widths widths widths widths widths widrow widrow exploiting multiplying multiplying summer drop corporation ent leaming leaming expanding chaos conservative conservative unseen 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#@Keeler_J,Saha_A,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set set networks networks networks networks networks networks networks training training training training training algorithm output output output output output output output output output output number number number number number system system system system system system error error error error error error error error error error error error error error error state units units units units units units units units units units information information information problem problem problem problem problem problem problem models models models models models models models models models models models models hidden hidden hidden hidden performance based based space space space space space space space weights weights linear linear linear linear linear linear linear linear linear linear layer layer layer layer case case vector order order order order order order order order order order order order order order order shown shown shown shown systems systems values values values values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons unit unit unit distribution distribution distribution distribution distribution recognition recognition approach pattern pattern pattern pattern point single processing large large large local local neuron neuron neuron rate rate rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns class class class class class class class matrix optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows shows shows shows signal algorithms algorithms simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples small small small small net net net work work work work work task task methods methods step step step step step step step step classification classification classification classification classification classification process trained trained cell cell cell cell cell cell problems problems random random high high response architecture architecture architecture architecture show equation equation equation line rule rule general general speech speech parameter real real real real real average gradient gradient gradient obtained experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result threshold threshold variables variables variables variables variables variables computation computation computation computation computation solution solution solution solution independent log dynamics initial estimate estimate standard standard computer computer computer computer computer terms synaptic synaptic synaptic node node node node node node node node node node node node node node science science science direction presented presented presented presented presented activation low low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets press press learn basis basis outputs outputs outputs abstract abstract applied back back back back back back back back computational computational computational computational computational convergence density properties properties properties properties properties likelihood references component ieee positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive procedure procedure procedure procedure procedure decision decision propagation propagation propagation propagation propagation propagation context introduction complex complex complex circuit estimation estimation statistical statistical statistical statistical effect effect effect dynamic generated generated generated variance search change change variable classifier lower lower lower lower signals signals chosen higher higher higher higher higher higher higher higher higher higher part firing multiple good binary binary binary binary binary binary spike spike represent represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed distributed distributed distributed bayesian expected equations equations region correlation correlation length probabilities errors errors errors errors errors errors errors errors simulations resulting resulting classes classes ing ing tasks simulation sum performed called means means means means means means reinforcement reinforcement reinforcement reinforcement dimension dimension dimension made feedback feedback feedback global global global global global negative negative negative negative negative negative negative negative negative negative negative negative negative vol vol artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial application desired define define proc proc perform perform perform perform active active active active distributions distributions gain gain brain equal equal power mit mit voltage voltage voltage larger support descent descent dependent dependent nets nets nets nets selection report report synapses synapses synapses synapses consists consists represents connectionist connectionist difficult difficult delay scheme scheme scheme scheme ai equivalent directly hinton hinton view solutions solutions curves estimates limit top top top top top top top stage effects bit bit bit upper upper full full choice significant statistics statistics give give con con con channel channel channel derived derived derived weighted randomly conditional conditional conditional levels levels product product product actual provided backpropagation inhibitory depends depends achieved discussion covariance normal normal normal normal stable surface surface common shape shape synapse synapse generate generate generate require eds eds eds square degree degree degree degree degree degree rumelhart rumelhart development simulated combination combination account coefficients transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer interesting ratio edge increasing matching principle principle squared details numbers numbers making inhibition bits bits bits bits bits supervised depth polynomial polynomial polynomial idea idea choose run perceptron neuronal neuronal architectures membrane membrane membrane membrane recent exact property takes takes takes moving moving include quadratic quadratic quadratic quadratic quadratic quadratic trees trees trees trees trees trees trees trees trees trees trees trees trees interest dimensions dimensions sufficient highly highly highly calculated volume volume works tions tions tions solve solve solve yields converge converge differential address address address address observation channels channels channels channels channels constructed exists expression occur suggests spikes locally clusters half half conclusion place hebbian reduce depend interactions interactions differences sigmoid performs faster learns constrained suggest reduction drawn drawn sigmoidal sigmoidal intelligence radial assuming exist exist exist identification base question acknowledgements areas pro pro derive longer longer solving solving ways laboratory stability changing changing changing changing changing implement implement implement explicitly linearly transformations easy consisting gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians applying springer boolean boolean boolean potentials john choosing phoneme phoneme phoneme correlated correlated correlated viewed influence solved solved solved solved detailed operations organizing fraction showed lee approximated activities allowed sign epochs delays spaces spaces convex initially calculate calculate classified classified classified koch koch koch koch koch transactions dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic expect priori formulation bell bell bell bell bell bell bell bell assignment plotted plotted illustrated automatic black reason determining extra capable capable computationally computationally delta poggio poggio presentation presentation spiking successful build build computations schemes invariance fine fine receives receives composed verlag quickly quickly procedures prob interpreted neuroscience neuroscience symmetry lie contribution built comp giles giles computes reach automatically attempt illustrates approximating deal deal receive modelling modelling modelling modelling modelling modelling presents body schedule powerful wiley xor xor xor xor xor put discriminant behaviour rise scalar fewer respond fashion giving tech incremental boosting parity parity parity plasticity combine referred referred referred root workshop func notion measurement coefficient coefficient plausible generalisation generalisation generalisation extremely perfect perfect thought thought adjusted adjusted versions logistic logistic logistic observe separated perceptton logic logic hebb art multivariate multivariate speakers consist attempts seconds averages ment ment slowly separable variances defining defining defining explanation majority answer cascade cascade cascade worse starts reasons straight implementing purposes sites style ran leaves hyperplane arise commonly ion ion involve begin depicted author meaning sun fourth reflect cmu axes backprop backprop backprop backprop backprop span span polynomials operate anti anti gen monotonic monotonic parent cal serve phonemes adjust enables kinds sophisticated implements deviations leaf credit globally lab analogue notes assign summing linearity member member bin impossible exemplar exemplar air adjusting overcome simplify cerebellum moment occurring reasoning roles wire definitions adequate presentations presentations presentations filled hours moments substituting motivation ensures edelman dendrites respective lang lang lang demonstration propagated soma soma soma barron barron barron membership membership express axonal contact proteins concentration considerations variants calcium propagate receiving dividing lem speaking dna anns minus sig equivalently leaming formulate propagating centre sigma ical mutually attempted exponent deep cessing biophysical thick interact decays denoting altered altered altered altered considers ambiguous funded tively intracellular memo meet permit durbin hodgkin coming sigmoids circumstances cube lecture mcculloch pitts tial send multiresolution nested nested huxley lated optimisation purkinje determinant eral dom flows essen striking sparsely contributes push concert plateau archi optics squashing squashing tended arriving totally sliding falling falling statist absent thing reviewed dent unusual indepen translates ous dence indi massive formulas silent talk propagates freely percep linearities nice simula unifying biophysics biophysics tenorio tenorio tenorio broadcast broadcast excite yamada yamada electrotonic chang bio minimise excitable excitable apparatus cir des nth segev segev segev segev segev segev tecture positively positively positively positively positively initialised initialised throw thirty previ asso shepherd shepherd membranes membranes compartmental compartmental divides maxwell maxwell tony tony predicate travelling tain narrower almeida multiplexer multiplexer multiplexer multiplexer disappears arrived veto told grained grained adams quadratically dur hypersurface alterations optimising cedure kevin interac ors negatively sider polyno symp esprit pattems confusable supercomputer underly steadily ciated cer logically moidal vidual ellipses belgium cuits evi rall rall compelling arti ellipse steels symbolics popu spines spines spines spines routinely cotterill bivariate brussels usefully richness lined pfeifer nega construed nerves territory universiteit diffuses neuroscientists drove infinitesimally ling collaborative sluggish connectionists minded penetrate wegman 
#@Bell_A,
#t3
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input function function function function function function function function function function function function function function figure figure time time time time time time time time time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm output output output output output number number number number system system system system system system system system system system system system system system system error state state state state state state state results results results results results information information problem problem hidden performance based based based based space space space weights linear linear linear linear linear linear case case vector vector vector vector vector vector systems systems systems systems systems parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions neurons unit unit approach approach pattern point point point single single single single processing processing local neuron neuron neuron neuron neuron neuron neuron neuron neuron test patterns patterns analysis analysis matrix matrix form form shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper examples size work methods methods fig fig fig fig fig fig step points points points points trained problems problems problems random response response response response response response similar architecture architecture show show show equation section fixed fixed general general general general parameter parameter parameter parameter parameter parameter real real approximation theory theory theory gradient gradient gradient gradient gradient gradient obtained obtained obtained term term term term term activity dimensional result variables computation computation computation computation computation computation solution solution solution solution solution solution solution research independent defined defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant computer terms synaptic synaptic synaptic synaptic presented presented presented present phase phase activation temporal temporal motion press learn learn components components components components basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample abstract applied find computational computational computational computational computational computational convergence convergence convergence convergence properties references due due due ieee positive positive positive adaptive adaptive adaptive adaptive adaptive adaptive introduction introduction complex behavior effect parallel cost recurrent recurrent recurrent change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy complexity assume assume assume assume lower lower prior center center previous previous previous bound bound type required required conditions conditions represent equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations fact techniques proposed errors forward forward forward forward forward forward scale scale finite simulations simulations resulting ing computed respect respect respect respect respect respect performed eq eq eq eq eq eq eq eq elements elements mapping factor potential feedback feedback applications applications obtain obtain obtain obtain specific specific samples samples represented application application provide provide provide compute compute compute rates proc determined determined determined related constraints constraints connected connected connected gain gain mit fields dependent dependent source source source source source source source selection institute institute department department loss loss implementation internal represents represents represents represents bias bias bias bias bias scheme considered framework framework framework framework framework cambridge computing computing domain domain domain environment directly directly limit requires requires choice choice approximate basic con condition randomly randomly randomly developed developed provided finally finally selected selected selected iteration iteration iteration depends depends achieved discussion feedforward feedforward arbitrary denote denote denote denote fast fast stable theoretical require journal rumelhart rumelhart development development including including objective objective typically typically pairs pairs hopfield dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical functional fully fully fully fully technology technology technology principle principle iterations iterations iterations supervised supervised magnitude decay decay choose run denotes denotes denotes denotes denotes improved discussed discussed typical apply apply introduced include recently interest interest interest interest interest interest calculated tions tions solve yields yields yields differential differential differential definition definition definition williams williams constructed constructed exists expression expression concept concept concept concept digital derivative boundary boundary boundary generally generally generally demonstrate flow trajectories conclusions operator operator operator operator operator operator operator operator operator operator central tangent tangent tangent tangent numerical numerical faster faster faster constrained constrained encoding integration integration integration presence characteristics sigmoidal demonstrated california california assuming exist derivatives derivatives attractor attractor attractor attractor attractor attractor attractor explicit explicit pro construct solving solving solving laboratory laboratory laboratory laboratory stability stability stability mathematical mathematical recall recall recall sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity explicitly coordinates coordinates infinite infinite involves transformations unique scales scales equilibrium equilibrium equilibrium minimization minimization implies yield yield national national expressed expressed evaluated evaluated evaluate evolution evolution constants past sign earlier earlier additive spaces spaces spaces topology coupling figures includes formulation weighting sciences uncertainty specifically coupled coupled coupled simplicity straightforward straightforward selecting included included included identify attractors attractors attractors attractors attractors literature schemes characteristic notice notice heuristic contribution contribution contribution sin sin sin sin quantity involved sampled usual relaxation relaxation transformed xor xor requirements exhibit difficulty steady steady strengths strengths dual fashion fashion tech mappings mappings terminal terminal terminal terminal terminal terminal terminal terminal analytically office referred tanh tanh tanh affect topographic fundamental neu gradients integer illustrate singular quantities formal formal formal observe costs improves capabilities lies considerable considerable rapid straight satisfied strictly strictly operators operators operators operators operators operators operators operators operators operators worst acknowledgement involve grossberg opt opt opt opt opt opt opt calculations implicit implicit ridge ridge arises depicted qualitative preceding integrating considerably profile tional embedded lms cohen introducing posed requirement calculating gains synthesis mod perturbations differs pasadena enables conclude conclude neuro extreme extreme extreme identifying ear sv sv formally lagrange appropriately partitions unity proceed generality generality multipliers consideration tools simplify analogy interconnection efficacy efficacy hope reasoning methodology 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university university university variables variables variables computation research research research research research log log log log log log found initial standard standard computer computer connections science science science left left left left left presented phase phase low low low machine machine sets range press learn learn learn sample abstract applied back back computational properties references stochastic stochastic stochastic stochastic stochastic stochastic positive positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important important important important propagation propagation introduction generated generated parallel recurrent tion energy energy energy energy energy energy energy energy energy energy energy energy energy energy variable variable variable spatial measure prior representations higher higher higher higher higher center cases cases cases cases cases cases cases cases cases cases type required required binary binary binary binary binary binary binary binary binary binary represent represent distributed distributed techniques correct correct correct probabilities simulations simulations simulations simulations minimum minimum minimum resulting ing ing ing tasks tasks computed respect respect respect respect multi multi multi sum performed means made filter negative negative negative negative original represented true cross cross provide define compute compute perform perform perform related distributions mit train train train descent descent nets nets proceedings proceedings report report report report institute version technique technique internal individual individual joint joint joint joint represents connectionist connectionist layers layers layers layers cambridge directly hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton view bit conference efficient choice free free free free free free free free free free free free free free free criterion criterion criterion criterion entropy entropy entropy entropy entropy entropy provided backpropagation iteration discussion technical technical technical technical group group stable generate supported pixel degree rumelhart development fit fit fit objective objective objective underlying underlying hopfield technology technology representing details details details direct direct supervised supervised idea idea combined property ensemble machines sejnowski sejnowski cognitive engineering conventional conventional teacher calculated volume works module module module module module module module module module module module module parts expression invariant trial trial derivative derivative derivative correctly correctly deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic pass pass pass pass demonstrate valued depend central central modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules designed performs temperature strong physics external external external drawn assuming derivatives derivatives derivatives force boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann suppose produces dept dept explicitly explicitly averaging easy mutual mutual mutual mutual mutual mutual equilibrium shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift national national extracted extracted similarly allowed partial partial combining sciences maximize phys successfully society divided effectively mcclelland successful successful detect detect efficiently efficiently composed summary quickly procedures procedures anderson anderson paradigm extract extract extract extract extract extract extract receive difficulty rapidly rapidly varied replaced mass helpful fashion maximizing 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#@Galland_C,Hinton_G,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural input input input input input input input input input input input input input input input input input input input input input function function figure time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm 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pattern pattern pattern pattern pattern pattern single single single single single single single single processing control large large large local local local local rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns optimal inputs inputs inputs algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple simple simple small size size size size feature feature net task methods fig cells step step field process process process process process process process current current current current current current current cell random random random random random random random random high memory memory response response similar similar similar similar representation representation representation representation representation architecture architecture architecture architecture section section section section section fixed fixed fixed fixed line rule rule rule rule rule rule rule rule rule rule general general general general parameter parameter parameter parameter real average states states states states states states obtained obtained note note experiments experiments experiments university threshold threshold variables variables solution solution solution solution solution solution solution research research independent independent defined defined found found found found found target target target target target target target initial initial initial table table table table table table table table table table table table table table table standard computer science direction presented presented presented presented presented presented presented presented presented presented present present present present present range learn learn learn learn learn learn learn learn learn outputs outputs abstract applied applied back back back find find find find convergence references component ieee procedure procedure procedure procedure procedure important propagation propagation 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resulting resulting ing total total multi sum eq times elements means potential made made made feedback global study study obtain obtain vol relative specific desired desired desired desired desired desired proc proc proc proc determined determined determined determined goal related constraints discrete mit steps steps contrast connection fields update update train train train train source source source source source source morgan morgan proceedings report institute department implementation version version version version version version version version consists internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal individual advances joint connectionist bias bias layers layers scheme scheme scheme addition maps framework cambridge hinton hinton view san san stage stage stage stage bit bit efficient choice choice choice choice choice choice free basic basic basic basic basic increase con produce developed constraint simply simply achieved discussion describe describe describe describe arbitrary arbitrary tested tested inverse finding generate generate supported require require main eds eds adaptation future makes including kaufmann kaufmann simulated needed needed needed needed account interesting york increasing mechanism principle details pre pre making bits bits bits international idea idea idea added perceptron perceptron perceptron perceptron perceptron improved improve improve directions advantage ensemble takes typical typical typical reported reported reported practical apply apply apply introduced introduced introduced introduced introduced sense sejnowski recently recently recently recently recently relevant sufficient varying teacher teacher teacher teacher teacher calculated works works works works solve solve solve converge converge achieve definition modified modified modified modified generalized generalized generalized improvement entire increased grant exists exists studied studied feed feed feed feed feed feed feed feed feed feed touretzky touretzky occurs column hardware demonstrate demonstrate runs runs starting starting place minimal row row row reduce depend differences differences mateo mateo taking strong hard hard cycle cycle turn minimizing minimizing minimizing start iii iii manner manner groups annealing acknowledgements appears produces index index ways ways describes stability distinct involves involves applying applying applying formed cycles yield yield yield choosing choosing choosing family viewed solved detailed updated updated updated fraction completely completely suggested suggested allowed sign sign earlier reasonable epochs reduces purpose valid calculate sufficiently assigned advantages advantages views existing blind discuss phys phys phys partially tests tests simplicity extra capable importance included wij wij wij wij wij wij wij wij wij computations schemes kind repeated procedures procedures procedures procedures induced induced cun allowing success issue quantity relaxation thresholds thresholds principles attempt tesauro tesauro schedule layered layered layered experience updating updating updating updating updating replaced association preliminary preliminary preliminary school tech proper fundamental fundamental phases necessarily integer integer created created created perfect changed changed changed changed quantities algo precise perceptton perceptton perceptton store generates simplest finds attempts mentioned mentioned site rows stop developing directed directed guaranteed fairly nowlan briefly worse separately describing calculations gradually optimize recording recording mellon explained explained prop carnegie applies cmu introducing rep biologically price price limiting incoming serve sophisticated comments decreased implements median realized realized realized guarantee modify modify modify modify drift drift perfectly perfectly repre connecting eliminated wrong wrong wrong wrong wrong accepted primitive keeping krogh hertz published mance sion perfor washington widrow widrow percepttons searching viewing israel april ends draw relies considerations insensitive treat sequentially saad session exhaustive cooperative presenting presenting revealed corrected opper breaking guess guess imagine realize attempted increment modifying rithms rejected flip flip flip france electronics happen happen sweeps sweeps sweeps sweeps sweeps sweeps preprint preprint preprint treating unpublished completed suggestions resembles meir supplied supplied appealing connects venkatesh venkatesh venkatesh practically couplings disturbance rohwer totally minsky gmd sweep sweep sweep bonn cyclic shortly ated awij insert percep percep ference tal sentations pull entities entities teachers ver treats grossman grossman grossman 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#@Grossman_T,
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layer layer layer layer layer layer layer layer case case order order order order shown systems systems systems systems systems values values values values values values values weight weight weight weight functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition approach approach pattern pattern pattern pattern pattern pattern point single single single single single single single single processing processing processing processing large large test test test test patterns patterns patterns patterns optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows signal signal algorithms algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian examples small small small size size size feature feature feature feature feature feature feature net net net net net net net net net net work work work work points points points points field field features classification process process trained trained trained trained trained trained trained trained trained trained structure structure problems problems problems problems problems problems problems problems random random high high high memory similar similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture fixed fixed fixed fixed line rule rule rule rule rule generalization parameter real average average average average gradient obtained obtained obtained note note experiments result result university threshold computation solution solution solution solution solution research research research defined target initial constant standard standard standard standard computer terms terms connections connections connections connections connections connections connections connections connections connections connections connections node science science science science direction present activation activation activation activation activation activation activation activation activation machine machine machine machine sets motion range press nonlinear outputs outputs outputs outputs outputs outputs continuous abstract back back back back back back back back back back back computational computational convergence analog references positive positive important decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation mixture mixture complex complex complex complex complex hand dynamic dynamic generated parallel parallel parallel parallel search change difference complexity assume measure measure measure measure signals signals signals signals signals representations chosen chosen chosen higher part part part cases cases cases cases type required required required required multiple multiple 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update train train train train train nets nets morgan morgan morgan morgan morgan proceedings proceedings proceedings report report report institute implementation implementation version synapses consists internal individual advances advances advances connectionist final final bias layers layers delay addition addition computing computing environment hinton san bit conference requires requires requires requires requires requires choice significant world speed speed give con produce produce weighted weighted weighted randomly developed types types lines actual provided finally biological measured discussion covariance technical fast fast limited short nearest shape makes makes rumelhart rumelhart rumelhart rumelhart kaufmann kaufmann kaufmann kaufmann kaufmann simulated smaller smaller needed needed interesting testing structures trials trials trials trials empirical leads principal call numbers pre pre pre direct supervised depth depth magnitude magnitude magnitude idea run run run run run added added added added added added added added description perceptron perceptron architectures resolution takes reported reported strategy moving moving machines side cognitive cognitive works solve solve solve solve solve solve solve locations symmetric modified modified williams entire entire entire parts parts lead studied scaling derivative derivative feed move touretzky touretzky touretzky touretzky pass pass pass half half half greater greater reduce operator neighbor valued tangent differences sigmoid sigmoid sigmoid sigmoid sigmoid accurate moody moody moody faster faster faster faster learns learns learns suggest hard external reduction cycle cycle sigmoidal sigmoidal california radial minimizing min iii averaged averaged averaged manner connectivity identification annealing suppose relation pro winner ways primary vertical distinct changing changing changing simultaneously develop develop adding cycles national family communication controlled organizing lee lee sizes 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tesauro tesauro tesauro tesauro receive trains origin diego powerful create create varied varied varied relations fewer ideas school school school rest rest detectors detectors detectors detectors incremental investigated investigated parity parity parity parity parity combine affect cognition examined waibel waibel waibel waibel hill extremely created changed quantities algo precise detector detector explored explored explored logic epoch improving mixed mixed extent serial serial attempts residual residual residual residual residual residual histogram advanced stop developing formula formula derivation cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade briefly benchmark benchmark benchmark benchmark purposes satisfied producing producing precisely ran ran ran leaves immediately pool pool pool pool pool pool cut begin annual preceding mellon mellon researchers researchers requiring questions greatly considerably prop carnegie carnegie effort backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop adjustable employ passes stack pittsburgh popular incoming incoming incoming incoming incoming serve suited begins begins begins begins owl median progress pyramid extensive rithm pick acts discovery eliminate grows grows arranged climbing inspired inspired spiral adds adds wrong chance adjusting adjusting occurred iiii fan fan attractive contract contract obtaining roles roles generalizes constructive continue date date date combines ranging paul decide lang lang lang lang lang lang lang ascent widrow uni candidates candidates offers advance creating creating creating creating record repeatedly repeatedly repeatedly repeatedly properly properly projects consonant propagate propagate propagate alternatively fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fold fold explorations counts divide spirals spirals spirals spirals spirals spirals multiply summer summer microstructure solves creates smoothly classifies classifies hierarchies guess adjustment concentrated deep deep deep interact interact inverted expand eliminating ultimately speedup speedup speedup speedup speedup rough million million crossings crossings crossings crossings happen stuck places dramatic unpublished stops scanned sees sees sees hyperbolic trainable builds smoother attempting compete tors phonemic agency settle progressively progressively accumulate beneficial permanent creation creation creation creation scott differentiate sonn correlates unusual transmit defense syst backwards hoff actively stan sponsored lebiere lebiere lebiere lebiere lebiere lebiere gallant gallant gallant gallant preventing tenorio tenorio tenorio tenorio contributing broadcast plexity cancel frozen frozen frozen frozen frozen frozen repeats 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#@Fahlman_S,Lebiere_C,
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system system system system error error error error error error results units units units units units units units units units units units units units units units information information information information information information problem problem problem problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based space space space weights weights weights weights linear linear linear linear linear linear linear linear linear case order order shown shown shown shown shown shown shown shown systems systems systems systems systems values values values values values values values parameters noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method approach approach approach pattern point point single single processing processing control control control local local local local neuron rate rate rate rate rate rate rate rate analysis class shows signal signal signal signal simple visual examples examples small small small small size size size feature feature feature feature work task methods methods step points points points points features classification process process process level problems problems problems problems problems problems problems random random random random random random random random high high response response response response representation representation architecture architecture show equation fixed fixed rule rule rule rule rule rule rule rule general generalization generalization parameter parameter real real real real approximation average states gradient gradient gradient gradient gradient gradient note note experiments dimensional dimensional result result university variables solution solution research research defined defined found found target target standard standard standard standard standard standard standard standard standard standard terms terms terms synaptic synaptic synaptic node node node node node node node science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction present present present present present present present activation activation low low low nodes nodes nodes nodes nonlinear continuous continuous sample sample sample abstract back back back find computational convergence convergence convergence convergence convergence density density properties properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due ieee adaptive adaptive decision propagation propagation propagation introduction complex stimulus statistical variance variance variance variance variance variance variance variance variance variance variance variance search search search search search complexity complexity complexity complexity variable variable variable assume rules measure measure measure measure signals prior higher center type type required multiple cortex represent represent distributed equations fact region errors errors errors forward forward forward finite finite total computed respect times times means optimization made natural applications policy policy knowledge knowledge original vol relative samples samples represented compared rates rates perform related constraints constraints distributions distributions distributions distributions brain comparison larger connection connection connection connection connection connection update update update update train dependent morgan institute implementation implementation version synapses synapses consists individual advances connectionist connectionist responses final scheme domain environment solutions solutions solutions curves curves curves estimates stimuli stimuli stimuli bit bit bit bit capacity capacity capacity capacity significant world speed estimated basic basic increase increase increase increase produce produce produce randomly conditional product actual finally backpropagation nature nature nature sampling sampling sampling biological measured normal increases arbitrary group complete stable finding finding assumed synapse synapse require ability easily makes makes including kaufmann simulated simulated needed unknown transfer transfer transfer transfer transfer transfer transfer principle bits decay decay run run perceptron perceptron neuronal architectures population discussed recent advantage property separate typical identical identical identical cognitive dimensions dimensions dimensions varying previously subjects subjects studies trans modified modified interval sensitive constructed occur suggests deviation deviation deviation deviation deviation deviation deviation deviation deviation locally deterministic deterministic occurs pass pass pass runs runs runs runs runs runs runs runs half half strength strength critical critical minimal minimal minimal reduce conclusions central central measures weak hard mechanisms integration presence physics proportional pulse introduce groups annealing annealing appears written solving ways laboratory modeled implement implement sensitivity category averaging linearly linearly linearly dimensionality involves easy interaction formed depending stationary learner solved variation centered similarly updates updates sign key earlier calculation performing measurements intervals boundaries remains assigned construction advantages advantages degrees existing priori assignment determines uncertainty uncertainty uncertainty uncertainty uncertainty tests tests tests aspects efficiency efficiency modification delta delta delta delta delta delta wij essentially excitation repeated showing showing showing showing stopping split split content criteria categories categories vary usual dot absence providing hypotheses ill reach consisted policies operating modelling explore simpler parametric american poor poor rapidly varied environments strengths strengths hanson hanson hanson hanson hanson hanson hanson hanson hanson hanson biases discriminant discriminant reducing history history history history mappings parity parity parity parity parity parity variability complicated affect cover cover understand momentum coarse coarse coefficient transmission possibly possibly thought aspect freedom freedom nervous nervous initialized initialized chaotic isolated separable separable growth growth growth variances analyzed coded benchmark benchmark benchmark benchmark worse london producing producing producing producing producing precisely immediately hyperplane potentially projected involve involve involve involve computers incomplete considerably composite composite composite composite reflect 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#@Hanson_S,
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networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number number number number number system system system system error error error state results results results results results units information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models hidden performance performance performance based based based based based based based space space weights weights weights weights weights linear linear linear linear layer case case case vector vector order order order order order order order shown systems systems systems systems systems values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight functions functions functions functions functions functions functions functions functions functions functions functions neurons unit method method method approach approach approach approach approach point single single single single processing processing processing processing processing processing control large local neuron neuron test test test analysis matrix optimal optimal inputs inputs inputs inputs inputs inputs form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms small size net work work work work task task task task task classification classification level trained trained trained trained trained structure structure structure structure structure structure structure structure structure structure structure structure problems problems problems random high similar representation representation architecture architecture architecture architecture architecture show line rule rule rule general speech speech speech speech speech speech speech speech speech speech parameter parameter real real average average theory term term term term note experiments experiments experiments experiments result university university variables solution research research log log found found found sequence sequence initial estimate computer distance distance connections connections connections connections connections node node node node node node node node node science science prediction prediction presented presented presented presented presented present present present present present present activation activation activation low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine sets maximum press components components abstract back back back back back find convergence convergence density likelihood references references stochastic stochastic stochastic ieee ieee ieee ieee ieee ieee procedure procedure adaptive propagation propagation propagation propagation propagation context introduction complex circuit estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior behavior statistical statistical generated parallel recurrent search search search search search search search search search search tion energy energy difference complexity complexity complexity complexity complexity complexity complexity complexity variable variable signals signals signals signals signals prior cases required required required required required required good long distributed make proposed length length length correct errors errors minimum minimum minimum ing ing tasks tasks human respect respect performed performed called called times times elements optimization optimization optimization potential dimension made made made natural global study knowledge knowledge filter filter filter filter filter negative original original original vol vol vol vol artificial samples samples compared application application application application application series perform connected connected equal accuracy accuracy accuracy accuracy accuracy comparison comparison comparison connection train descent modeling selection selection selection selection report words version code individual individual advances represents difficult final final final final final final final final final final final final layers delay delay delay graph ai considered environment design design design design design design design design design conference determine full requires choice choice approximate statistics free free speed estimated estimated estimated increase increase give produce produce channel channel developed criterion criterion criterion criterion criterion lines processes backpropagation nature nature depends achieved covariance feedforward feedforward arbitrary arbitrary group group limited close inverse excitatory circuits finding amount generate main eds square future degree makes noisy including simulated simulated simulated simulated simulated smaller smaller needed reduced dynamical fully transfer transfer transfer transfer ratio ratio increasing special consistent consistent structures structures uniform uniform principle language representing details filters filters direct normalized normalized supervised supervised decay polynomial polynomial combined produced added added description description description description description description description architectures architectures discussed pair separate separate takes element reported reported practical strategy hierarchical hierarchical sense subset relevant engineering engineering varying varying compare previously observations observations observations works tuning speaker speaker trans trans trans trans address evaluation separation separation separation separation separation separation modified entire extended digital digital trial alternative alternative alternative move touretzky deterministic deterministic setting setting hardware pass demonstrate flow conclusion starting place minimal minimal trajectories sigmoid sigmoid sigmoid accurate designed designed designed performs faster temperature temperature temperature propose taking hard mechanisms characteristics drawn connectivity connectivity connectivity connectivity identification identification identification identification identification identification annealing annealing annealing annealing annealing pro construct construct index perception sequential generating plot describes laboratory electrical electrical easy quality select select john decreases decreases choosing extracted family family family family focus reconstruction reconstruction phoneme phoneme squares estimator variation open evaluate restricted organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing lee lee lee lee lee lee static completely similarly allowed partial performing sec sec sec sec sec sec sec penalty closed closed generation remains construction construction advantages advantages topology topology topology david box thesis priori priori memories recognize variations variations variations black characterized characterized successfully major major simplicity reason regular selecting modification included committee presentation presentation presentation identify literature efficiently post plots identity fine fine characteristic kind contained interested criteria criteria criteria criteria criteria strategies sci duration list paradigm paradigm realistic nips delayed delayed attempt jacobs deal explore explore simpler simpler parametric poor overfitting create requirements experience experience experience difficulty steady involving involving limitations limitations issues discriminant ml school school tech int decisions comparable symbolic symbolic func understand removed smallest configurations created prototype prototype prototype prototype prototype versions versions explored academic initialized message speakers speakers mixed mixed mixed arbitrarily submitted motivated optimum optimum optimum years stop track growing explanation tool tool handle reasons reasons purposes organized ion universal demonstrates questions questions apparent people pure led led flexible amounts readily posed compares polynomials polynomials synthesis summarized characterize achieves comments june converged cumulative cumulative trade trade trade phenomenon guarantee modify restriction extensive ratios linearity perfectly reconstructed air khz khz khz accepted accepted overcome imposed imposed effectiveness guide modifications selects hours heuristics exploring lip introduces studying male male expanded dominant intended captured originally emergence reader shortest shortest cpu environmental designing designing papers papers discovered tures interestingly integers vari indirect outline ter listed sig sig sig achieving asked transmitted july suboptimal terminals terminals terminals connec perceived mdl mdl mdl mdl mdl mdl mdl adjustment reconstruct reconstruct adapting unseen allocated searches oct careful host pos gender constructs apparently sam reveal son permit nal rewritten syn differently expense handling handling january instability justification invertible imple rissanen rissanen rissanen rissanen rissanen rissanen rissanen usefulness proposal excited striking tuple architec kirkpatrick sym smc smc smc fol creation voice voice voice sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn sonn comprised compromise ous iterate mid tivity tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio tenorio contributing disadvantages disadvantages rmse rmse rmse forthcoming trick mentation acceptance acceptance sible sought prohibitively biasing ting fuse gorithms tapped tapped tapped utilization gra implication charac duce recon emulation accompanied purdue purdue purdue purdue revealing fernando multilayered dient hypersurface specially party party party party party party party pursuing duffy duffy structed cocktail cocktail cocktail cocktail cocktail cocktail cocktail gelatt modem modem modem modem modem modem modem mahalanobis pled fruit inclusive hawaii tackle proposals franklin franklin reporting bolic radically lafayette lowed additively bivariate organizational tun river tstems motivating teristics notices farlow vantages autoregression sequent 
#@Kassebaum_J,Schaefers_C,Tenorio_M,
#t3
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number system system system error error error error error error error state results results results results results results results units units units units units units units units units units information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance space weights weights weights linear case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown systems systems systems systems values values values values values values values parameters parameters parameters noise weight weight functions functions approach pattern point single processing large neuron rate rate test test patterns patterns analysis inputs form algorithms algorithms algorithms algorithms simple paper small small small size net work work work task task step step step step step points structure problems problems problems problems problems problems problems problems problems problems random random random random random section section line line vectors vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter states states states states theory note note note university university university research independent independent found found sequence target table table table table table table table computer terms distance connections connections science science left direction direction phase low low temporal machine range range press learn outputs outputs outputs outputs outputs outputs continuous continuous sample sample abstract applied back back back back back find find references stochastic stochastic stochastic ieee ieee procedure important important decision propagation propagation propagation propagation hand statistical effect generated generated generated generated cost search search search search search search search search search search variable lower rules rules rules measure signals representations higher previous cases cases cases cases cases required multiple binary binary binary binary binary binary expected make length correct correct correct correct correct correct correct correct correct correct correct correct correct probabilities errors errors errors forward forward forward forward simulations simulations ing total simulation simulation simulation simulation simulation human performed performed performed performed called called called elements mapping mapping mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement feedback knowledge original relative specific compared compared compared desired cross cross provide compute compute location perform equal equal approaches larger update update dependent selection morgan report technique internal internal advances connectionist connectionist connectionist difficult difficult layers considered cambridge environment directly directly directly directly hinton solutions solutions solutions solutions solutions solutions san bit bit bit bit bit bit bit bit bit bit bit bit conference requires requires requires choice significant free speed speed basic basic produce produce produce produce produce produce criterion types lines backpropagation backpropagation backpropagation nature inhibitory depends depends simply associative associative associative associative technical increases group group tested inverse inverse inverse assumption assumption generate generate generate generate easily makes makes rumelhart fit kaufmann pairs pairs smaller combination reduced significantly increasing consistent trials uniform call call numbers numbers max direct making stored bits bits bits bits bits bits bits bits bits bits bits supervised supervised supervised added improved advantage advantage pair pair pair pair pair separate takes reported apply strategy identical array cognitive varying compare conventional yields correspond rl evaluation williams williams williams williams storage increased scaling scaling scaling scaling scaling scaling occur touretzky loop deterministic deterministic occurs occurs occurs runs runs minimal assumptions conclusions operator valued reward reward reward reward reward sigmoid designed designed designed sutton sutton performs performs exponential faster faster mateo taking taking taking start groups groups reference suppose suppose produces produces solving generating describes changing multilayer simultaneously linearly linearly linearly linearly linearly dimensionality dimensionality slightly agent family family independently correlated correlated squares viewed learner learner learner evaluated fraction sizes completely completely completely similarly digits updates spectrum barto barto barto barto performing spaces spaces spaces transactions david degrees figures priori assignment candidate middle middle middle middle middle aspects differ modification attractors attractors attractors attractors attractors attractors build genetic essentially reached prob success success anderson anderson anderson anderson interested interpreted interpreted stopping issue notation usual michael generalize absence paradigm paradigm paradigm computes reach automatically received extend employed employed explore unlike overfitting xor exponentially rapidly rapidly varied put put involving involving detail mass mass helpful parity possibility possibility decisions structured concepts integer man man automata aspect academic generates generates generates generates finds finds percentage indicating developing separable separable separable separable separable growth distinguish failure majority majority majority majority majority majority majority majority majority majority majority sys closer division division operators involve gradually begin cybernetics cybernetics recognizing reflects understood backprop slower slower rewards rewards summarized summarized mod adjust adjust hamming boston boston credit yielding displays displays displays displays extreme extreme arithmetic arithmetic arithmetic globally don uncorrelated college pick pick pick pick count count discover discover discover reaching fails ments stronger occurred occurred determination familiar grow interpret neurobiology observing modifications evident counting offer offer agree discovered discovered propagate propagate propagate generalizing generalizing generalizing generalizing generalizing generalizing dividing dividing counts lem solves kluwer propagating convenience copy copy copy copy copy copy copy amherst amherst reports certainty avoided summarizes increment increment magnitudes tems impose continues picked acquired ultimately ultimately lookup lookup complementary complementary nonetheless tively ation prevents compu differing signs wider answers answers littman littman littman littman stops advantageous regularities slot allen allen satisfactory families hundreds exper rare rare ackley ackley ackley ackley ackley ackley ackley ackley dissertation dissertation push cooperation exploits degenerate degenerate complement complement coins coins positional zeros propagates excluded excluded excluded excluded excluded adjustments shortcut shortcut possesses possesses opportunity evaluates bernoulli remember structuring agation hillclimbing temporary anandan anandan anandan violation divides notational tational bellcore stretch supplies regularly expects embodied interfering sketched accelerated folded scalable pairings pairings rewarded effec memorization morristown puting opportunities ccs dimensionalities returning returning profound iments slowed northeastern demonstrations judgment folds exit exit ruled outperforming precedence backpropagate distinctly sea decline inforcement inforcement pushes pushes rewarding rewarding punishment punishment punishment punishment acldey acldey tre neatly wisdom 
#@Ackley_D,Littman_M,
#t3
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#*network network network network network network network network network network network network network network learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number system system system error error error error error error error error error error error error error error error error error state state state state results results results information information information problem problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based space space space weights weights weights weights weights weights weights weights weights linear linear case order values values values values values values values parameters weight weight functions recognition method method method method method method method method method method method method method method point point processing processing control control control large large large local local local analysis matrix matrix matrix optimal inputs inputs form form form form form shows shows signal algorithms algorithms algorithms simple simple paper small net work work work methods methods step process current trained trained trained trained trained trained problems problems problems problems problems response similar similar architecture architecture show show show show fixed fixed fixed fixed generalization speech speech speech real average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term note experiments experiments result university variables variables variables variables variables variables computation computation solution solution research research independent independent log log defined defined found target target target target target target target target target target target dynamics initial constant constant constant estimate standard terms terms node node node node node node node node node node node node node node node node node node science left left direction presented presented presented present present present activation activation activation activation activation activation activation activation activation low low nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal temporal temporal temporal sets sets press press press components outputs outputs abstract back back back back back back back back back computational computational convergence references component component ieee ieee positive positive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction action complex behavior behavior dynamic parallel cost recurrent recurrent recurrent recurrent change change energy variable variable variable measure measure representations part previous cases type type type required multiple binary long distributed equations equations equations make techniques correlation errors errors forward simulations simulations simulations minimum minimum total computed computed respect respect respect sum performed called times times mapping optimization optimization made made feedback feedback applications applications knowledge specific represented application desired desired desired provide define define define proc proc proc proc experimental connected connected gain discrete discrete discrete equal mit steps steps accuracy connection connection update dependent nets report report version version version version technique internal internal represents bias bias addition cambridge computing computing hinton limit limit san detection detection full requires free basic basic basic coding derived developed developed types backpropagation normal feedforward feedforward feedforward feedforward feedforward increases describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote tested inverse common supported require require eds eds ability makes makes rumelhart rumelhart dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical fully fully technology york special special operation representing details call call making idea idea idea idea minimize run architectures directions directions correlations correlations pair separate reported reported practical practical moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving include period period quadratic highly teacher volume volume works works tions solve studies diagonal williams williams williams williams williams studied matrices matrices alternative strength minimal greater central central numerical numerical pulse relationship targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets derivatives derivatives derivatives derivatives manner minima minima denoted denoted acknowledgements appears appears estimating transitions transitions dept dept changing explicitly infinite unique unique frequencies events events events events events events events events events events minimization minimization minimization minimization minimization minimization minimization minimization minimization cycles cycles focus dependence dependence communication controlled decomposition static margin past event event event event event event remains intermediate symbol assigned classified exploration includes activations activations activations weighting weighting extension variations absolute absolute absolute reason straightforward suitable modification divided attractors detect literature plots success anderson interpreted dis issue notation vary write thresholds extend presents law law law minimized carried diego wiley difficulty varied put involving hessian respond ideas tech tech applicable applicable applicable parity parity oscillation fundamental analogous analogous neu concepts man singular singular formal separated academic art switching chaotic averages brown brown derivation defining sys formalism formalism pulses pulses scientific inversion inversion arises demonstrates author qualitative qualitative preceding conjugate conjugate pseudo amounts capability quantitative frequently robinson robinson switch limiting differs curvature curvature curvature gave richard progress progress differentiable calls oxford restriction temporally narrow acts purely difficulties difficulties difficulties proceeds odd city obtaining fail ral disjoint disjoint imply hint krogh krogh krogh krogh north north hertz hertz hertz exploring ambiguity displayed holland regarded regarded regard washington realization originally late cpu cpu cpu pearlmutter pearlmutter pearlmutter statement discovered accumulated treat treat zipser zipser achieving centre utilize tendency forcing edinburgh edinburgh representa toy tems ijcnn werbos werbos werbos file file file file dominated distant distant distant careful paris responding preprint stuck avoidance ward ward signs continually pineda pineda pineda resembles meir bridge remarks coin illinois usefulness ning attained attained rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer archi vanish curved gmd south essence aip unusual bonn corn emerged greatest kuhn kuhn objectives objectives objectives renals stems altering elegant fallside entered grossman grossman grossman grossman helped named tecture forrest forrest forrest deficit deficit deficit deficit deficit deficit deficit deficit participate divides notational icnn domany bears dreyfus concluding almeida almeida spelled spelled southern chir encourages havior linden resemblance feedfor feedfor secs secs secs multilayered referring recipes teukolsky philosophy quotient compar orlando flannery raining raining esprit florida vetterling scotland complez nordita infrequently wio thorbergsson thorbergsson disappeared ison itseft merical pie fletcher fletcher fletcher adoption lev sinha sinha discards hopes aleksander discourage preferring 
#@Rohwer_R,
#t3
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data function function function function figure figure figure figure figure figure figure figure figure figure time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output number number number number number number number number number number number number system system system system system system system system error error error error error error error error error error error error error error results results results results units units units information information information information information information information information problem problem problem problem problem problem problem problem problem problem hidden performance based based based based space space space space space space space space space weights layer case case case case case order shown systems systems systems systems probability probability probability probability parameters distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method approach approach approach point point point point point point point point point point single single single processing processing large large large neuron rate patterns analysis analysis class class class class class class class class inputs form form form simple simple visual paper paper paper examples examples examples examples examples examples examples examples examples examples examples small small small small small small size size size size net net work work task task methods points points points points points points points points points points points points classification classification classification classification classification classification classification process process process current current current trained trained trained trained trained trained trained problems problems problems random random random random random random random random random random random random random high high high representation architecture architecture architecture architecture show section section section section rule general general general general general general general general general general general generalization generalization generalization generalization generalization generalization generalization generalization real theory theory theory theory theory theory theory theory experiments experiments result result result university threshold research research research defined defined target target target target target initial initial standard standard computer terms terms connections node node science science presented presented present sets sets range learn components basis outputs outputs sample sample sample sample abstract applied applied find references positive positive positive positive positive positive positive procedure procedure important decision introduction effect effect effect parallel cost cost cost cost search search search search search search search search search search search search search search search search search search search search difference difference difference complexity classifier measure learned chosen chosen chosen part part center center center previous previous previous previous cases cases cases good expected expected make fact fact fact techniques region region region region region region region region region region region region region region region region region region region region region scale simulations simulations minimum minimum minimum resulting resulting ing tasks total respect sum sum regions regions regions regions regions means potential dimension natural natural global global global global global global applications filter obtain negative negative negative negative negative negative negative relative specific specific specific specific specific specific specific specific specific specific samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples true true compared compared compared application provide define define define define compute rates active determined determined experimental equal power power power power power power comparison support train train nets morgan morgan proceedings report report report implementation implementation implementation implementation implementation version version version version version version version version version technique technique technique technique technique consists consists connectionist connectionist connectionist connectionist connectionist connectionist connectionist considered considered domain domain domain domain domain domain domain domain domain domain domain domain domain curve additional additional view limit bit bit classifiers significant approximate world pages increase give give con produce derived weighted randomly randomly bounds area area area types types sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply simply simply achieved achieved discussion discussion feedforward describe describe arbitrary arbitrary arbitrary arbitrary arbitrary tested limited assumption assumption complete complete circuits finding finding amount amount implemented implemented supported theoretical journal square square square square ability ability hypothesis hypothesis hypothesis instance instance instance makes kaufmann kaufmann typically smaller needed reduced unknown unknown unknown technology transfer testing increasing consistent consistent consistent consistent consistent consistent consistent consistent consistent language representing international attention choose run run added description architectures pair subset subset subset interest works converge converge converge achieve definition background background symmetric modified bounded bounded improvement increased parts concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept studied studied suggests generally pass pass pass pass greater reduce reduce valued exponential exponential exponential drawn drawn drawn drawn drawn drawn assuming minimizing start selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective decrease connectivity minima minima configuration configuration configuration configuration configuration configuration acknowledgements produces describes label label stability dept dept dept dept dept changing confidence confidence remaining consisting applying decreases national learner learner learner learner learner static similarly similarly key partial earlier reasonable spaces roughly roughly remains valid valid filtering filtering filtering calculate sufficiently foundation query classified david david david david david contour instances instances instances instances instances vapnik uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty discuss specifically domains domains structural selecting efficiency efficiency efficiency efficiency plots plots fine capture interested lie classify classify classify classify sampled sampled sampled sampled sampled generalize generalize hypotheses leading thresholds deal load powerful difficulty exponentially limitations reducing examine tech tech tech incremental applicable analytically referred proper proper examined examined concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts plausible plausible plausible configurations opposite equally queries queries queries queries queries queries queries formal formal formal consist baseline baseline baseline improving defines brown great directed directed directed directed directed directed directed directed directed directed directed directed directed analyzed guaranteed defining failure failure majority majority majority baum baum lies tool inside inside inside inside stanford purposes widely producing recognizing improvements improvements greatly limits experimentally leave posed haussler haussler haussler haussler haussler incorporated frequently sharp passes passes passes passes passes rely fall suited richard inherent inherent shaped shaped tolerance specifies univ cumulative naive classifying pac modify restrict acm resources ordering proceed proceed generality communications promising proceeds logarithmic grow serves monotonically symposium intuitive passive falls iteratively negligible washington washington captured captured membership membership membership foundations refers warmuth properly draw park agree broken implicitly generalizing limitation limitation limitation learnable unchanged land drop specification specification specification corporation pointing chervonenkis benefits forced connec tendency classifies classifies examining examining valiant eric tight cohn cohn cohn cohn cohn cohn cohn ibm ibm realizable mathematically mitchell mitchell bounding rectangle confirmed selectively selectively selectively selectively worth discusses maintains maintains maintains loading loading applicability exhibited exhibited september october aaai shallow stephen thermal tom justified marks marks marks envelope attempting blum blum mining drawing drawing concern concern seattle exclusively assessment inefficient judd judd proves proves frequent rivest rivest amenable accommodate crl crl deter ings mis promise watson actively excessive atlas atlas atlas atlas atlas atlas relax security security security heights accu blumer blumer extremes decides ucsc ucsc ucsc ucsc disagree ronald manfred confident feel provably exclude accompanying imperfect useless departure ehrenfeucht appeal inexpensive notable conjunctive tionist batches contrasted yorktown les shrinks overly querying querying overload passively traversal sharkawi sharkawi steeper risks leslie tificial stretches rately secure secure sigrnoidal inductively asks asks believes analogues 
#@Atlas_L,Cohn_D,Ladnet_R,
#t3
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data data data data data data data data data data data function function function function function function function function function function function time time set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number system system error error results results results results results units units units units units units units units units units information information information problem problem problem models models models models models models models models hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space space space space space weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case vector vector vector vector vector vector shown systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters weight weight weight weight functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition method method method method method approach approach approach approach approach pattern pattern pattern pattern single processing processing processing control control large large large large large test test patterns patterns patterns patterns patterns analysis class class class class class class matrix matrix inputs inputs form form form form form form form form shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual paper paper examples examples examples examples examples small size size feature feature feature feature feature feature net net net net net work work work work work task task task task task task task task task task task task task task task task task methods cells cells step points points classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process level level level current current current current current current current trained trained trained trained trained trained trained trained trained trained problems problems random high high high high high memory similar similar representation representation architecture architecture architecture architecture show show show section section vectors vectors speech speech speech parameter parameter approximation approximation approximation approximation approximation approximation average average average average theory theory gradient gradient obtained obtained obtained obtained obtained activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university university university university university university computation solution research research research research independent independent log log log defined defined found found found target initial constant table table table table table table table estimate estimate estimate computer computer distance science prediction map map activation activation machine sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum learn position components components basis basis basis basis outputs outputs outputs sample abstract applied applied applied back back back back find find computational computational computational likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component due ieee ieee procedure procedure procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision propagation propagation propagation propagation mixture introduction complex hand hand statistical statistical statistical statistical generated generated variance variance parallel cost cost tion tion difference spatial assume assume classifier classifier classifier classifier classifier classifier classifier lower rules representations learned part part part part center center center previous cases cases cases type type type type type type type type required required required multiple cortex binary represent represent represent represent represent distributed distributed expected correct correct correct correct probabilities probabilities observed scale simulations simulations simulations simulations ing tasks tasks tasks tasks tasks tasks tasks tasks multi multi multi multi sum performed performed performed performed times means means means means means means means means means factor potential dimension made orientation applications applications study relative samples samples samples samples samples samples samples samples samples samples samples represented represented true compared application application application application desired series receptive receptive provide provide active determined distributions equal equal approaches mit larger fields fields update update update train descent descent morgan morgan morgan proceedings proceedings proceedings proceedings report report report report report institute department version version version version version version consists consists advances connectionist connectionist difficult difficult layers scheme addition addition addition maps maps maps cambridge cambridge computing equivalent equivalent equivalent directly hinton hinton hinton hinton hinton additional additional view view estimates estimates estimates san stage conference determine determine determine determine classifiers classifiers classifiers classifiers classifiers classifiers requires choice significant approximate approximate free free estimated basic basic pages pages pages pages give con coding weighted clustering developed developed developed levels levels criterion finally processes selected selected selected evidence sampling sampling simply biological biological discussion covariance covariance technical technical technical technical technical feedforward feedforward arbitrary group group group tested fast close assumption assumption rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount amount nearest nearest nearest nearest nearest nearest nearest nearest nearest effective implemented require adaptation adaptation journal square square easily easily easily makes rumelhart rumelhart development fit fit fit simulated probabilistic typically smaller smaller functional interesting testing testing york york head special uniform uniform uniform uniform principle operation operation language leads representing numbers making international normalized supervised supervised supervised supervised supervised idea minimize architectures improved directions resolution exact exact exact exact exact exact separate separate reported reported strategy strategy subject identical identical identical identical inference subset subset recently engineering interest interest highly compare previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised observations subjects subjects volume module module smooth smooth speaker speaker studies diagonal definition symmetric observation observation observation observation observation grid organization organization organization sensitive entire increased expression suggests extended extended hybrid hybrid hybrid hybrid hybrid hybrid hybrid touretzky touretzky touretzky generally pass demonstrate place greater reduce competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive editors modules modules performs performs moody moody moody moody moody moody moody moody moody moody moody exponential suggest propose strong hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard physics reduction reduction drawn drawn drawn demonstrated proportional proportional labeled labeled labeled radial radial radial radial variety variety manner groups scene acknowledgements boltzmann digit digit digit digit digit digit digit pro perception winner winner winner winner winner winner winner winner winner winner generating generating generating generating mathematical mathematical dept changing multilayer category category dimensionality dimensionality dimensionality adding frequencies gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians springer select competition competition competition competition competition competition competition competition competition competition competition john john national formation squares squares interpretation interpretation variation updated updated updated updated updated organizing lee lee centers centers centers centers centers centers centers centers soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft static sizes suggested suggested suggested suggested digits allowed discrimination discrimination spaces spaces spaces spaces normalization normalization normalization fitting fitting iterative iterative interpolation interpolation interpolation interpolation assigned kohonen kohonen kohonen kohonen advantages avoid perceptual thesis usa subspace subspace batch sciences specifically domains major reason determining capable uniformly society society divided effectively included included poggio poggio literature schemes comparing comparing 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comparisons tive organized incorporate mation laboratories separately universal grossberg grossberg implicit members toronto toronto toronto toronto toronto toronto localized localized computers linsker linsker linsker linsker author cybernetics cybernetics mellon summation greatly considerably considerably evaluating carnegie bootstrap bootstrap lms lms lms lattice lattice lattice lattice share frequently frequently frequently summarized gen popular popular prevent richard sophisticated sophisticated neuro focused softmax softmax softmax softmax extreme sharing sharing classifying proportion proportion optimality girosi girosi discovery theories convenient darken darken darken darken darken darken adjusting tools striate unlabeled unlabeled observing observing sanger sanger heuristics vowels vowels substituting substituting interference encountered negligible male regarded regarded regarded regarded von von den spherical spherical spherical spherical spherical spherical competing competing peterson peterson approximators winning winning emergence specialized reveals reveals reveals canada formant formant sons variants hart hart hart generalizing explorations dividing assigning limitation sequentially yale yale zipser zipser approx appeared summer summer microstructure incorporates maximized restrictions convenience connec connec ical malsburg malsburg female hierarchies clas duda duda rithms approxi generators books academy paris france universit son placing placing memo page places indication bridle bridle bridle bridle gauss gauss gauss gauss gauss gauss gauss gauss worked suggestions lowe lowe lowe impractical savings attempting compete hoc opponent hid responsibility responsibility responsibility steven keeler keeler outperformed dcs acoustical equa fij fij fij fij huang huang normalize placement neighbourhood digitized digitized maxi maxi america sity adjusts adapts adapts niranjan niranjan bradford adequately adequately lincoln elegant crg crg nents 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#@Nowlan_S,
#t3
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural input input input function function function figure time time time time set set set set set system system system system problem problem performance based based based based based based based space space space space space space space space space space case vector vector vector order order shown shown parameters neurons neurons recognition approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern point point point point point point point neuron neuron patterns matrix form form paper paper examples examples examples examples examples examples examples examples examples examples small net net net net net work fig fig fig fig fig fig fig fig fig fig step points points points points points points points points points points points points points points field field field field field random memory show equation equation line line line line rule vectors vectors general parameter parameter parameter approximation theory activity dimensional dimensional dimensional dimensional dimensional dimensional result research defined found found found dynamics initial initial constant constant constant constant constant constant table table computer distance synaptic synaptic synaptic synaptic synaptic node science phase phase phase phase phase activation nodes nodes learn position nonlinear nonlinear nonlinear abstract find find find convergence references ieee positive procedure adaptive action behavior energy energy energy energy energy energy difference difference difference difference chosen center center center center required long conditions represent represent equations equations proposed observed scale scale scale finite minimum simulation simulation eq eq eq eq eq eq eq eq eq elements study study obtain original original vol vol artificial represented perform determined goal goal gain support selection selection institute institute department final scheme considered considered trajectory basic con con condition developed developed area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines actual actual provided selected selected achieved role main end instance cluster cluster cluster cluster cluster cluster cluster cluster cluster development noisy including objective dynamical dynamical dynamical dynamical technology technology technology technology technology representing representing iterations iterations iterations iterations decay minimize improved discussed introduced introduced introduced introduced introduced unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised calculated calculated calculated calculated calculated calculated calculated converge converge converge differential differential organization sensitive concept concept concept concept clusters clusters clusters clusters clusters boundary boundary trajectories tangent numerical numerical numerical constrained integration california california turn force attractor attractor attractor attractor attractor attractor attractor suppose suppose laboratory laboratory dept coordinates coordinates transformations unique applying implies select letters decreases national formation static static static converges dashed measurements boundaries interpolation interpolation sufficiently assigned assigned assigned assigned coordinate inter assignment subspace subspace sciences illustrated coupled reason importance importance attractors invariance notice content providing carried create dotted periodic possibility office office math coefficient coefficient closest necessarily separated chaotic directed directed directed agreement analyzed caused reasons inside inside inside inside directional incorporate sgn sgn acknowledgement 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#@Toomarian_N,Zak_M,
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#@Abu-Mostafa_Y,Atiya_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time set set set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm output output number number number number number number number number number number number number number system system error error error error error error error error state state state results units units units information information information information information information information information information information problem problem models models performance performance performance performance based weights weights weights weights weights layer layer layer layer layer layer case vector vector vector order order order order order order order shown systems systems systems systems systems systems systems systems parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight functions unit unit unit recognition recognition recognition recognition recognition recognition recognition method method pattern point point single single single processing processing processing processing processing processing control large large large large large local local local test test test test test analysis analysis class matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows shows shows simple simple paper paper paper examples examples examples small small small small small small size size size size size net net work task task methods methods methods step points field classification classification process trained trained problems problems problems random high similar architecture show equation equation equation equation equation section fixed rule rule general general general general generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real approximation approximation approximation approximation approximation approximation approximation theory gradient gradient obtained obtained obtained obtained obtained obtained term term term term experiments experiments computation computation solution defined found initial initial standard computer terms terms terms terms terms terms terms connections connections connections connections left left presented low low learn components components basis continuous abstract applied applied applied back back back back back back back back back find computational convergence convergence references references references stochastic ieee positive procedure procedure procedure procedure procedure procedure procedure important propagation propagation propagation propagation propagation propagation propagation propagation introduction complex complex hand hand hand hand statistical statistical statistical statistical effect effect cost cost search tion change change complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume lower lower lower measure measure measure measure measure measure higher cases cases required good good represent expected equations equations make make make fact techniques techniques techniques proposed proposed length length probabilities scale minimum minimum minimum ing ing ing ing total total simulation computed respect respect respect respect sum sum sum performed called elements factor factor factor factor applications applications applications negative relative compared application cross series series define compute compute compute compute proc goal constraints connected brain brain brain brain brain brain brain brain brain equal power accuracy comparison larger larger connection train train morgan morgan morgan morgan morgan morgan morgan proceedings proceedings technique technique technique technique technique consists connectionist difficult delay ai ai ai ai ai framework computing computing computing computing computing directly hinton curve curve curve curve curve additional view curves curves curves estimates design design design limit san effects effects efficient upper upper approximate free free free free world world world speed speed basic basic basic pages pages pages pages increase increase increase increase increase condition derived weighted weighted actual backpropagation simply simply achieved increases increases increases increases tested fast limited corresponds surface amount amount implemented role theoretical require require main main hypothesis makes rumelhart rumelhart rumelhart rumelhart including kaufmann kaufmann kaufmann kaufmann objective objective objective objective objective objective objective objective objective objective objective objective objective objective pairs smaller needed hopfield interesting significantly significantly significantly significantly uniform database database empirical squared details details bits supervised magnitude magnitude magnitude magnitude magnitude magnitude decay decay decay idea idea idea minimize choose choose description description description predict architectures architectures improved improved improved improve property reported reported practical apply strategy strategy include side side side quadratic quadratic quadratic quadratic inference inference highly highly compare approximately approximately approximately volume volume volume volume volume volume works tuning diagonal diagonal diagonal diagonal diagonal diagonal definition chain increased increased increased derivative derivative derivative derivative derivative derivative derivative predicted predicted predicted correctly move move touretzky touretzky touretzky touretzky touretzky touretzky touretzky boundary setting setting half starting reduce conclusions valued editors editors central measures measures modules clear constrained constrained mateo suggest propose proportional minimizing start min averaged introduce introduce derivatives derivatives derivatives derivatives derivatives groups digit digit digit digit pro derive derive construct index category dimensionality remaining remaining easy slightly frequencies events minimization minimization extraction versus versus versus john decreases decreases extracted family formation communication solved evaluate controlled controlled approximations digits digits reasonable reasonable reasonable reasonable additive reduces reduces valid construction construction david avoid handwritten handwritten handwritten handwritten handwritten thesis priori bell sciences vapnik vapnik vapnik vapnik vapnik automatic automatic automatic mozer mozer mozer specifically reason straightforward wij wij literature literature literature schemes schemes schemes comparing comparing fine composed cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun cun prob allowing heuristic heuristic split content strategies usual usual play generalize generalize modular providing denker denker denker denker denker denker denker denker denker denker denker denker reach automatically principles acknowledgments decreasing situations carried overfitting perturbation perturbation experience involving hanson hanson hanson accurately hessian hessian helpful fewer reducing reducing giving ideas ideas school mse mse mse mse mse analytically structured structured complicated workshop notion removed examined waibel waibel saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency editor editor editor editor editor editor adapt obvious assumes assumes assumes taylor art improving motivated phd theoretic smoothness guaranteed caused caused caused baum baum tool tool reasons comparisons rapid tive shared arise laboratories scientific implicit begin annual improvements improvements relevance solla solla solla solla solla solla solla solla haussler haussler polynomials howard howard howard howard wind sums comments decreased segmented redundancy damage damage damage damage damage damage damage damage damage converged sharing ordinary sort perfectly printed smolensky smolensky smolensky kaufman kaufman kaufman tools tishby removing obd obd obd obd obd obd obd obd obd service becker becker equals equals expanded bad schwartz schwartz den uni jackel jackel jackel jackel propagated iterated rich theoretically contact extensively inductive variants consonant valuable tures trading informa outline ber chervonenkis chervonenkis chervonenkis retraining retraining retraining year icassp boser boser tradeoff tradeoff mdl personal param adapting henderson henderson levin chauvin chauvin chauvin num ization ization ization hubbard hubbard simplifying emphasize 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#@Denker_J,LeCun_Y,Solla_S,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input input input input data data data function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training output output output output output output output output output output output system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state state state results results results results results units units units units units units units units units units units units units units units units units units units units units models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case case case case case case case vector vector order order order order order order shown shown shown shown values values values values weight weight functions functions functions functions functions functions functions functions functions unit unit unit approach approach approach pattern pattern pattern pattern pattern point single single single single single single single single single single single single single large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test patterns patterns patterns analysis analysis analysis analysis analysis analysis inputs inputs form form form form form signal signal algorithms paper paper examples small small small small small small small small small small work work step process structure random random equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation section section section section section fixed line general general generalization generalization generalization generalization real states states states states theory gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained term term term term term note experiments experiments experiments experiments experiments experiments result university university variables computation solution solution research independent log initial initial constant constant constant constant constant constant constant standard standard standard standard computer computer terms terms terms terms terms terms terms science science science presented present activation maximum learn outputs outputs outputs continuous continuous abstract back find computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references positive positive procedure important important introduction hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior effect effect tion change difference difference variable variable variable assume assume representations chosen center center cases required multiple multiple good long long long expected equations equations equations equations fact fact proposed errors errors errors errors forward scale finite simulations simulations simulations simulations simulations resulting ing total sum sum times times times global study study study obtain obtain negative relative true desired desired desired cross cross provide provide rates power power power approaches approaches approaches mit comparison larger descent descent descent descent descent descent descent descent morgan proceedings proceedings report report individual individual represents represents connectionist connectionist final layers layers layers scheme considered hinton hinton hinton solutions solutions solutions transition transition transition limit san approximate speed speed speed speed basic basic basic increase con con randomly entropy entropy actual actual finally finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature simply discussion technical technical arbitrary arbitrary close finding finding common common eds future degree rumelhart development kaufmann typically smaller smaller combination transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer interesting consistent empirical empirical principle numbers numbers numbers making magnitude polynomial polynomial polynomial polynomial polynomial polynomial run takes takes typical practical side quadratic quadratic sense subset varying previously teacher teacher approximately approximately calculated solve yields yields yields converge differential rl williams williams increased lead studied scaling scaling suggests wide predicted feed touretzky runs conclusion starting valued depend differences sigmoid sigmoid numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical clear faster asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic mateo physics demonstrated assuming variety decrease decrease decrease decrease relationship reference appears appears written solving factors plot plot plot plot dept dept dept recall multilayer multilayer multilayer explicitly linearly slightly cycles focus stages controlled evolution sizes margin margin margin margin margin margin similarly constants allowed earlier earlier reasonable reasonable epochs epochs epochs epochs measurements measurements expansion valid expect expect box includes thesis thesis instances illustrated discuss coupled absolute differ modification schemes situation plots procedures cun issue return follow minimizes minimizes leading leading illustrates jacobs jacobs tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro decreasing extend law law employed remain detail examine school analytically analytically affect momentum momentum momentum momentum momentum momentum analyze subsets shapes logic extent extent arbitrarily indicating stop trivial slope slope analytic analytic analytic majority majority majority majority starts turns rapid straight berkeley purposes purposes calculations mellon addressed summation integrating argument percent carnegie empirically led cmu slower slower popular popular extensions prevent asymmetric attraction eventually univ univ cor indices driving driving driving resources lecun numerically numerically convenient logarithmic logarithmic moment definitions modifications modifications dominant dominant insight insight master late late late late theoretically summarize verify summer slight slight ent ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad expanding propagating convenience convenience 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#@Ahmad_S,He_Y,Tesauro_G,
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#*network network network network network network network network network network network network network learning learning learning learning model model model model model neural neural input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output output number number number number system system system system system system system system system system system system system system system system system system system system error error error error error error results results results results results results results results units units units units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based weights linear linear linear layer layer layer layer layer layer layer layer vector vector vector vector vector vector order order systems systems systems systems systems values parameters unit unit unit recognition recognition method method method method method method method method method method approach pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image processing processing processing processing processing processing control large rate test test test test test test test test test test test test test test test test patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class form algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual examples examples examples size size size feature feature feature feature feature feature feature feature feature net task task task task task task methods methods methods methods methods methods methods methods methods methods methods step features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process process level level level level problems problems problems problems problems problems problems problems high high similar representation architecture architecture architecture architecture architecture architecture architecture architecture show show rule vectors vectors images images images images images images images images images images images images images images images images images images images general generalization parameter real real real real real real real real real real real real real theory threshold threshold solution solution solution solution solution solution solution solution research research research research research research research research independent independent defined defined defined found found target constant table table terms terms terms terms connections left left phase phase phase activation low low low low low machine machine machine machine machine object maximum maximum maximum maximum maximum range press press components nonlinear outputs continuous sample abstract applied applied applied applied applied applied convergence likelihood likelihood likelihood likelihood references component ieee procedure decision decision decision decision decision decision decision decision decision decision propagation introduction complex complex complex statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical generated parallel parallel parallel cost cost tion difference complexity variable variable classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower representations center cases required required multiple binary binary distributed distributed distributed techniques region region minimum classes classes classes ing ing simulation performed performed performed elements regions regions regions regions made applications applications applications applications applications study study study study study study study study study study study study study study original original specific true application application application series series provide provide objects rates rates proc perform perform perform perform determined determined constraints connected power mit mit comparison larger connection selection selection report report report implementation implementation implementation consists advances represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult layers layers scheme scheme considered computing hinton view design san determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers requires choice choice choice significant free free world world world world world speed vision vision vision vision con con derived derived derived derived derived derived derived levels area area actual actual actual processes backpropagation associative achieved measured measured measured measured feedforward describe tested tested tested corresponds common implemented implemented implemented implemented require require adaptation adaptation adaptation adaptation pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel degree degree degree makes makes rumelhart rumelhart rumelhart development development fit fit underlying coefficients coefficients fully testing york segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism consistent representing representing making making supervised supervised supervised supervised supervised supervised polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial combined combined light architectures architectures architectures architectures exact property property separate separate element element element element typical reported apply strategy identical identical pixels pixels pixels pixels pixels pixels pixels pixels pixels quadratic quadratic interest interest interest varying approximately works solve correspond generalized williams entire entire entire entire entire entire entire constructed constructed digital trial trial alternative alternative alternative alternative alternative alternative hardware hardware hardware hardware demonstrate demonstrate greater greater assumptions assumptions conclusions editors bayes designed designed performs encoding encoding characteristics characteristics characteristics characteristics labeled labeled user user user averaged scene scene scene appears pro derive derive derive derive produces generating describes implement explicitly explicitly slightly applying springer quality quality extraction extraction extraction extraction extraction extraction evaluate updated sizes processor diagram performing measurements measurements classical classical classical classical remains advantages classified transactions transactions david david david priori priori black tests successfully successfully capable included mcclelland presentation presentation post comparing comparing comparing comparing comparing comparing comparing ten characteristic composed composed road verlag procedures success classify classify running running running satisfy satisfy paradigm paradigm paradigm paradigm highest reach reach automatically automatically software camera simpler parametric wiley production production requirements requirements exhibit detail biases int comparable statistically phases editor man man implementations front front front logistic massachusetts massachusetts theoretic analyzed adjacent adapted adapted handle choices describing cybernetics cybernetics qualitative qualitative robustness requiring applies cmu amounts readily quantitative employ summarized ture inherent segmented segmented tile tile converged representative classifying classifying extensive grey grey grey air fits held attractive determination exploit guide date james dependency belongs belongs viewing belonging exploiting hart unable rejection acceptable acceptable solely solely chapter workstation workstation reject reject reject reject ibm ibm ibm ibm ibm duda toy geoffrey pdp gas gas gas gas gas gas gas gas gas rejected rejected proach termed cation anal alternatives alternatives meet meet cubic cubic cubic exhibited mix architectural rarely prefer trainable trainable trainable december december inclusion cylinder cylinder cylinder dom eliminates incorporation classi poly poly syntactic smc connectionism feasibility feasibility seg lsi neocognitron jose ysis cox ard lisp nov italy fukushima viable classifica ronald experimentation outlines pared idealized delivered nectionist classifi chamber chamber deliver 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#@Blanz_W,Gish_S,
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#*network network network network network network learning neural neural neural neural input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output output output output output number number number number number system system system system system system system system system system system system error error error error error error error error error error error error error state results results results results results results results results results units units units units units units units information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based space space space space space space weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer layer layer case case vector order order order systems systems systems systems values values values values values values values weight neurons neurons recognition recognition recognition recognition approach approach approach pattern point image image single single single single single processing processing large large large rate rate rate rate rate rate test test test test test test test test test test test test test test test test test analysis class class class class inputs inputs inputs form shows shows signal algorithms simple paper paper examples examples examples examples small size size size work task task task methods methods step step points points points points points points points classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process level current trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure problems problems random similar show equation section line vectors vectors general general speech speech speech speech speech speech speech speech real real real real real real real average average states gradient gradient term note experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university university university variables solution solution solution solution solution solution research research research independent independent independent independent independent found initial initial constant constant standard standard computer terms node science science prediction prediction prediction left left left presented presented presented presented frequency frequency sets sets sets sets sets sets sets sets maximum range range range press basis nonlinear nonlinear nonlinear outputs continuous continuous continuous continuous sample abstract applied back back find convergence references due due due ieee procedure important important important decision decision decision propagation propagation propagation context context context introduction complex behavior statistical statistical statistical effect parallel search tion tion change change energy energy energy energy difference difference difference complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier lower rules representations representations chosen part center center cases cases cases cases cases cases required good good binary long represent represent represent represent represent tree tree tree tree tree distributed distributed equations equations equations make make fact fact techniques techniques techniques techniques techniques techniques region length correct observed observed scale finite classes classes ing ing ing ing total regression regression regression regression regression regression regression regression regression computed multi multi multi multi multi multi multi multi performed performed performed performed regions regions regions regions optimization optimization optimization optimization made made made made made made feedback feedback global applications applications applications study knowledge knowledge obtain artificial relative relative represented compared application application application application series provide compute rates proc proc proc proc experimental gain equal power power power power power power power power power power power power power power power power power power power power power power mit steps train train train nets nets selection institute institute words department department version technique technique technique technique technique technique technique consists internal joint represents difficult difficult difficult bias considered cambridge domain hinton additional solutions solutions solutions solutions design effects bit bit determine efficient efficient efficient classifiers classifiers classifiers classifiers classifiers classifiers full full choice choice significant significant significant significant approximate statistics statistics statistics statistics world world estimated con condition developed criterion area area provided selected selected selected backpropagation backpropagation nature constraint biological achieved achieved measured arbitrary arbitrary arbitrary arbitrary group fast close finding amount implemented generate generate generate supported theoretical end ability ability ability future future future easily easily makes rumelhart rumelhart rumelhart development fit fit pairs combination unknown coefficients coefficients coefficients coefficients technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp interesting testing testing testing testing testing testing testing testing projection projection consistent consistent database database database empirical empirical details numbers numbers iterations iterations iterations making making international normalized normalized normalized normalized minimize produced sources sources light light light predict predict perceptron perceptron perceptron architectures improve recent correlations advantage advantage advantage separate separate similarity include include identical side side trees trees trees trees trees trees trees trees trees trees subset recently engineering sufficient compare previously previously conventional solve solve smooth smooth speaker speaker speaker speaker match studies studies studies studies studies trans sparse background separation interval williams increased constructed trial wide wide correctly correctly correctly occurs boundary boundary half flow flow flow flow starting critical critical minimal trajectories segment conclusions operator operator valued depend differences differences differences accurate accurate accurate designed designed clear clear clear peak peak faster constrained temperature sound sound propose taking integration characteristics california turn variety plane decrease identification program acoustic acoustic question acknowledgements pro pro pro construct construct sequential generating label dept dept pruning pruning category category simultaneously linearly physical electrical easy spectral spectral spectral spectral develop formed formed versus national national independently independently interpretation interpretation influence variation evaluated evaluated showed static understanding understanding sizes completely partition past key calculation performing measurements measurements iterative boundaries boundaries boundaries boundaries boundaries interpolation generation generation generation generation assigned foundation foundation norm classified classified topology topology david avoid expect combinations combinations perceptrons automatic automatic prove black absolute partially discussions tests reason reason aspects extra efficiency efficiency capable importance suitable computationally mcclelland detect efficiently schemes comparing vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel tend fine composed soc conf contained phonetic phonetic phonetic phonetic phonetic split split split split superior superior superior superior symmetry usual reach thresholds thresholds received consisted consisted consisted consisted consisted consisted consisted consisted overlapping operating operating software load load load load load load load load load load load load trains schedule american poor overfitting steady detail accurately recursive mass pursuit pursuit helpful scalar successive successive successive tech links int ideal scaled authors authors reliable decisions variability variability variability workshop workshop affect statistically understand attributes circles circles coefficient concepts extremely perfect ensure ensure friedman friedman friedman formal fisher fisher separated mapped speakers speakers speakers consist consist utility years percentage brown great advanced ment ment cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart stop slowly piecewise piecewise piecewise piecewise band band band band separable growth defining answer worse reasons reasons comparisons comparisons comparisons comparisons comparisons stress turns rapid sections cut potentially english medical qualitative mellon conjugate conjugate apparent apparent percent carnegie syllable collected offset amounts quantitative remove sharp requirement partitioning partitioning popular proven ordered phonemes suited adjust gave gave electric electric chose conclude expectations implements utterances june converged diagnosis trade representative classifying spectra martin narrow member addresses impossible fits khz khz khz ments chance breiman breiman breiman breiman promising difficulties difficulties adjusting proceeds hyper hyper interpret operates splitting splitting splitting disjoint disjoint intuitively corpus corpus alphabet days days days days vowels vowels vowels vowels vowels vowels vowels vowels continue inferior mance contexts slice slice slice sion perfor washington washington washington washington washington washington washington realization forecasting forecasting forecasting forecasting forecasting percepttons percepttons uni uni offers darpa darpa darpa advance tokens mlps april young insight arrows partitioned splits splits splits splits splits splits grants intersection receiving thresholding stone robert sequentially sequentially informa radar ple specification planes planes bus break break diverse diverse suboptimal icassp utilize comparative stem descriptions verified acting cohn care trends trends concentrated exam exclusive exclusive exclusive exclusive pdp graduate graduate disadvantage careful careful careful careful paired paired cole cole cole cole cole cole surrounding noting proach investigating employing worth paradigms apparently book happen lippman tract treating experi oregon oregon oregon status status answers worked november picking january january recogni continued continued marks marks marks marks marks trainable trainable ongoing ongoing ers hoc routines hour award cally usefulness seattle sen assessment sparsely slices disturbance loads loads alan inefficient bat isolation vocal predictable prone company company cess february february inappropriate atlas atlas atlas atlas atlas atlas routine routine developments amer violate stat security security security security security security security security security connor connor connor connor connor timit marshall spectrograms fight fight reactive impor bird superiority nonlinearly tant belmont ronald impressive univariate converting feel hwang divides presidential beat analogously etienne comput olshen dam barnard barnard barnard barnard barnard barnard barnard barnard industry looked indicative duced nique unrelated comers sharper wadsworth pathological casey cot seneft regres dft dft heard interpolator gions gions readings variate variate bet forecast forecast ditions les muthusamy muthusamy muthusamy muthusamy muthusamy muthusamy muthusamy assisted interplay vide stuetzle stuetzle statisti vides beaverton listeners arbi listening professor coarticulation interests forecasts clever trary sharkawi sharkawi sharkawi sharkawi sharkawi displaying featural proceeded communities plagued volves inves secure secure tence underfitting brace stra firs carlos multipli jerome listener boot provid mak bought 
#@Atlas_L,Barnard_E,Cole_R,Connor_J,El-Sharkawi_M,Marks_R,Muthusamy_Y,
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#*network network network network network network network network network network network learning learning learning learning model model model model neural neural neural input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure time set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output number number number number number number number number number number number number number number system error error error error error error error error results results results results results results results units units units units units units units units units units units units units units units units units units information information information problem problem problem problem problem problem problem problem problem problem models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer case case case case case case case case case case case case case vector vector vector vector vector vector order order order shown systems systems systems systems systems values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise weight weight weight weight unit distribution distribution recognition recognition recognition recognition recognition recognition recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern point point point point single single processing processing control large large large rate test test test test test test test test test test test test test test test test test test test test test test test test patterns patterns patterns analysis class class class optimal inputs inputs inputs inputs inputs inputs shows shows shows shows shows signal signal signal signal signal signal signal simple examples small small small small small size size size size size size size size size size size feature net net net net net net net net net net net methods methods methods points points points points points points field field classification classification classification classification classification classification classification process level level level current trained trained trained trained trained trained trained problems problems random random random random random show show show fixed fixed rule rule vectors vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech speech speech speech speech speech speech speech parameter parameter parameter parameter parameter parameter parameter real real real real real approximation theory theory gradient obtained note note note note experiments experiments experiments dimensional result result variables computation computation research research research independent independent independent independent defined initial constant constant table table table table table table table table estimate estimate standard computer computer connections science presented object sets sets sets sets sets sets maximum range range range range range range press press basis outputs continuous continuous continuous continuous sample abstract back back back back back density properties references due ieee ieee ieee procedure procedure procedure important adaptive propagation propagation propagation propagation propagation propagation context context context introduction estimation estimation estimation estimation estimation behavior statistical statistical statistical statistical effect effect effect dynamic variance parallel parallel tion tion tion difference difference complexity complexity assume classifier lower lower lower rules measure prior learned learned learned learned learned chosen higher higher higher higher previous previous cases required required required required required required multiple multiple binary binary long represent represent distributed expected expected markov markov fact techniques techniques correct correct correct correct probabilities observed observed observed simulations simulations resulting classes ing ing ing ing ing total total respect multi multi multi performed times times times times dimension made applications study study study study study original vol vol vol vol specific samples samples samples samples samples represented application desired desired cross cross cross series provide rates proc proc determined related distributions discrete equal power approaches mit comparison larger larger larger larger larger larger larger contrast contrast connection connection train train train train train train train train train train dependent nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets modeling morgan morgan morgan morgan morgan report institute loss loss internal code difficult difficult difficult cambridge computing experiment experiment experiment directly hinton estimates design san effects effects bit conference classifiers choice significant significant significant significant significant significant validation validation validation validation validation derived randomly levels criterion criterion criterion criterion criterion criterion bounds entropy iteration iteration nature normal feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward group tested tested hmm limited complete amount short require require eds adaptation adaptation square instance instance cluster cluster cluster cluster cluster cluster cluster cluster degree degree makes rumelhart rumelhart rumelhart simulated simulated fully mlp mlp mlp mlp mlp programming testing ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio uniform uniform empirical empirical language numbers numbers numbers numbers iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations magnitude magnitude frame frame run run run added added added perceptron improve reported reported practical practical sense inference interest sufficient works tions tions tions speaker studies studies studies studies trans generalized williams improvement improvement improvement sensitive parts wide clusters generally generally half starting reduce conclusions valued valued valued differences bayes bayes bayes clear clear peak peak peak peak suggest hard hard hard presence largest drawn demonstrated minimizing iii iii averaged identification acoustic base base appears relation relation pro written factors estimating laboratory sensitivity sensitivity sensitivity multilayer easy easy consisting adding blocks yield dependence phoneme variation variation variation transform operations controlled controlled restricted updated fraction showed frames frames frames sizes sizes suggested discrimination past earlier smoothing measurements measurements measurements measurements measurements measurements classical classical event roughly roughly roughly valid visible classified topology avoid expect building usa perceptrons perceptrons inter variations regular mcclelland score situation ten reached reached conf repeated contained stopping issue criteria built vary generalize highest leading reach illustrates decreasing simpler diego layered poor poor overfitting create varied ml ml fewer project int referred structured variability proved workshop scores scores scores scores statistically statistically momentum measurement plausible man obvious algo arbitrarily sentences established advanced ment ground coded floating baum baum considerable snr snr snr snr snr snr snr tive berkeley sys sys broad potentially potentially sun raw greatly amounts amounts poorly solla haussler haussler biologically ity gains aim gen phonemes prevent acoustics inherent sophisticated decreased yielding contextual restriction acm rithm ratios resources dynamically establish lost lost lost stronger determination observing splitting bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard intuitively degradation degradation degradation degradation degradation started mance mance ranging surprising perfor perfor evident widrow widrow widrow mel mel den dif recog omitted suggesting suggesting explains stopped learnable discriminate discriminate arcs ple inferred suboptimal ease german german guess massively valiant valiant conservative representa quantized quantized quantized tems tems altered pearl pearl nonetheless france intl intl ation permit signs experi continued continued synthesized ongoing ferent confirm overtraining overtraining overtraining hid finer mining inherently usefulness autoregressive autoregressive tokyo comm binomial thing feldman feldman 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#*network network network network network network learning learning learning learning learning learning neural neural input input input data figure figure figure figure time time time time time time set networks networks training algorithm algorithm algorithm algorithm algorithm number number number number number system error error error units units units units units problem performance weights linear systems values values values values parameters weight weight weight unit unit method processing matrix matrix inputs inputs signal signal algorithms algorithms algorithms simple size size net net net net task task trained fixed fixed fixed rule real activity activity university computation solution research defined constant constant science machine machine sets press outputs abstract references propagation introduction effect parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent complexity complexity complexity complexity representations learned learned distributed fact simulation times times times factor factor potential original vol compared connected connected brain mit update update update update update nets nets nets nets nets department internal represents cambridge hinton hinton hinton san top produce backpropagation backpropagation feedforward feedforward feedforward feedforward describe group eds degree makes rumelhart rumelhart rumelhart reduced reduced dynamical dynamical fully fully fully fully fully testing structures idea added takes cognitive compare works works williams williams williams williams williams increased reduce faster faster cycle california assuming program consisting adding cycles operations operations activities past past past reduces reduces reduces add david illustrated gating computationally divided delta mcclelland running wave receive diego powerful difficulty cognition smallest obvious derivation growing growing turns beginning computers variant stack stack stack proportion rational balance candidates viewing record jolla speeds hart explorations zipser zipser truncated microstructure sine copy copy copy big big big grouped pdp generators continually copies copies sees consuming subnet mistakes zipset rtrl rtrl rtrl rtrl rtrl rtrl rtrl rtrl rtrl rtrl rtrl subnetworks subnets subnets turing turing emulate parentheses bptt bptt bptt bptt bptt bptt bptt bptt trouble kronecker succeeded succeeded tape collapse corrects predecessors recurrently biggest truncate backpropa confusing 
#@Zipser_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input input input input input input input data data data data data data data data data data function function function function function function function function function function function function function function function figure figure figure figure figure figure figure time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number number number number number number number number number error error error error error error error error error error error results results results results units units units units units units units units units units units units units units units units units units units units units units information information information information problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer case case case shown shown systems systems systems systems systems noise noise noise noise weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit distribution point point single processing processing processing processing processing processing local local rate test test test test test patterns patterns patterns patterns patterns patterns optimal optimal optimal form signal algorithms paper paper size size size size size size size size size size size size size size net net net work task task task task task task task task step points points points field classification classification classification classification level level level trained trained trained trained high similar similar representation representation representation architecture show equation equation equation equation section rule rule general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech speech speech speech speech parameter theory theory gradient gradient gradient gradient note note experiments dimensional university university university university variables solution solution independent defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant constant standard standard standard standard standard standard standard terms terms terms distance left presented map present present activation activation frequency frequency frequency frequency sets maximum press press press press press press press press components components components continuous sample sample sample sample abstract back back back back back back back back back back back back back back back back back back back back back back back back back back back back back back references component due due due procedure propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex estimation behavior behavior behavior behavior behavior statistical effect effect effect effect effect effect effect effect effect dynamic dynamic dynamic dynamic dynamic generated parallel cost cost tion tion tion tion energy energy energy energy energy energy energy energy complexity complexity complexity complexity variable lower representations representations representations higher higher cases type required long long distributed distributed distributed distributed equations make make proposed proposed observed observed observed observed observed observed observed observed observed simulations simulations minimum minimum minimum minimum resulting resulting resulting ing ing total regression computed computed computed multi times times times mapping mapping mapping made made global negative original original vol vol relative relative relative specific specific samples compared compared desired desired desired desired series compute perform constraints constraints constraints constraints constraints constraints constraints constraints constraints distributions distributions discrete mit accuracy comparison fields descent descent descent descent nets morgan morgan morgan morgan morgan morgan proceedings proceedings proceedings institute department department loss internal advances advances advances advances joint represents represents represents difficult layers considered considered considered considered cambridge equivalent directly hinton hinton curve curve san stage effects effects effects effects effects effects effects effects effects effects conference conference conference conference capacity capacity capacity basic increase product provided depends depends depends sampling sampling sampling constraint constraint feedforward increases increases increases increases inverse corresponds complete complete complete amount generate generate eds square square hypothesis degree degree makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart fit fit fit smaller hopfield reduced technology testing testing ratio york york increasing increasing squared squared international early early early decay polynomial polynomial polynomial run added description correlations correlations exact exact typical typical practical period period period period period sense engineering sufficient works solve speaker correspond differential observation observation interval interval interval interval williams williams entire entire entire entire entire entire entire entire increased occur occur derivative predicted predicted correctly touretzky touretzky touretzky touretzky generally runs runs minimal minimal minimal depend depend designed constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained physics reduction reduction characteristics california california decrease decrease decrease averaged averaged base acknowledgements appears relation solving changing segments electrical remaining easy slightly frequencies minimization springer extraction cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles decreases decreases independently phoneme phoneme stages communication interpretation interpretation variation showed showed approximations understanding spectrum partial fitting fitting fitting fitting interpolation interpolation interpolation remains remains construction classified classified david degrees degrees degrees activations activations activations bell inter illustrated automatic structural uniformly mcclelland comparing reached characteristic composed composed notice verlag quickly link contribution contribution categories receptor receptor involved sampled sampled usual wave computes denker denker attempt decreasing presents diego overfitting overfitting overfitting overfitting relations hanson hanson hanson hanson biases helpful reducing fourier matches successive rest func cognition notion examined examined act adapt adapt psychology singular logistic logistic fisher freedom freedom freedom separated academic generates improving explain percentage slowly slowly slowly piecewise smoothness phenomena phenomena phenomena phenomena worse stanford stanford stanford stanford precisely broad probable gradually understood pseudo lms lms lms lms lms lms poorly solla howard reaches reaches reaches cal occurrence phonemes richard comments decreased eventually june june cor realized contribute phenomenon phenomenon phenomenon labeling labeling labeling labeling reaching eliminated kaufman kaufman kaufman kaufman promising analogy fan bourlard bourlard preparation preparation infor started corre dependency washington washington schwartz infinity den sim jackel bins impact considerations generalizing interestingly baldi adopted explorations ics fitted fitted fitted fitted fitted appeared basically leaming forced personal avoided assess acting chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin ijcnn ijcnn continues ization discontinuity discontinuity discontinuity picked picked confirmed acquired hansen apparently unpublished unpublished unpublished manuscript manuscript manuscript served sponding acquire ping european suite interpolated overtraining overtraining overtraining overtraining overtraining overtraining overtraining overtraining hid phonemic val spectrogram pratt pratt pratt plateau plateau outgoing adjusts alto alto alto alto alto alto remained ance indepen talk explaining stan stan palo palo palo palo palo palo linearities linearities miyata prolonged spectrograms spectrograms spectrograms dead examines psaltis psaltis theo forgetting dard dard mal reminiscent holmes disappear stabilized golden golden golden dynam responsive behaved pierre gation cate snowbird observa ended crease dominating fred runge runge runge runge franklin propaga utah ulations propa yves leam retical thomson admitted introduc yoshiro erik tute dently microstructures gories theoreti vestigated 
#@Chauvin_Y,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural input input input input input input input data function function function function figure figure figure figure figure figure figure time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state state state state state state state state state state results results results results information problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based based based based space space space space weights weights weights weights layer layer layer layer layer layer layer layer case shown shown shown shown systems systems systems weight weight weight weight weight weight weight weight weight weight weight unit distribution distribution pattern point point point point point point point point point point single single single single single single single single single single single single processing processing large local local local local local local rate rate rate rate rate test test analysis analysis inputs inputs inputs inputs form form form form shows algorithms simple simple simple paper paper paper paper paper examples small small small size size size size size size size size size size size size size net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net work task task task task methods step step points points classification process level current trained trained trained trained structure problems problems random random similar similar show show equation section section rule rule rule rule vectors images general general general generalization generalization generalization average average average average average average average obtained dimensional result research defined defined defined initial initial initial initial initial computer terms terms node node science presented present present present present low nodes nodes nodes nodes machine sets sets sets press learn learn learn learn nonlinear outputs outputs outputs outputs outputs continuous sample abstract abstract abstract back back back back back back back back back back back back back back back back back back back back back back convergence properties properties references due due due ieee ieee positive adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction introduction complex complex behavior behavior effect effect effect effect generated variance parallel tion tion change change variable assume lower rules rules measure representations learned chosen chosen previous multiple multiple multiple multiple multiple multiple multiple multiple multiple conditions distributed expected expected fact fact fact length correct errors errors finite simulations simulations minimum minimum minimum minimum minimum minimum ing ing tasks called mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping made feedback feedback feedback feedback vol vol relative specific compared compared compared compared compared desired desired desired desired desired desired desired desired desired perform perform perform perform determined experimental related gain equal mit comparison comparison comparison comparison larger larger larger larger connection train dependent nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets department consists internal individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual bias layers layers considered cambridge computing computing computing domain equivalent transition transition san conference full significant estimated increase increase increase increase con randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering actual selected describe group group tested assumption complete finding assumed require ability instance cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster makes rumelhart rumelhart smaller smaller smaller underlying combination combination combination account interesting interesting significantly ratio ratio increasing increasing increasing increasing empirical direct international supervised supervised idea produced added description architectures improved recent advantage advantage advantage advantage advantage advantage advantage property apply introduced strategy period period period conventional teacher teacher teacher teacher teacher teacher teacher teacher teacher definition evaluation separation organization organization organization organization increased lead studied occur deviation deviation occurs pass pass pass pass pass starting assumptions conclusions central performs taking taking taking presence characteristics solid proportional turn start exist exist decrease decrease decrease connectivity configuration question pro perception ways laboratory changing averaging equilibrium versus versus versus decreases depending communication viewed viewed viewed interpretation open restricted centered completely completely constants past past performing performing performing convex convex convex intervals tracking valid initially sufficiently sufficiently sufficiently string string string string exploration figures figures formulation assignment determines determines plotted aspects extra differ differ delta delta mcclelland presentation schemes cun link link link 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representative mistake mistake mistake mistake mistake forming forming drift drift drift drift drift addresses adds adds significance occurred city los viewpoint fail generalizes continue periods equals sphere propagated propagated counter april indicator outlined verify microstructure ter leaming aircraft failed propagating feeding feeding feeding retraining retraining retraining retraining personal clustered clustered clustered clustered adjustment adjustment adjustment magnitudes pdp pdp faults faults faults faults hughes conversely denver investigations knowing lippman lippman exhibited failures failures failures advantageous bility sake ally synergy synergy synergy synergy synergy synergy synergy william company assp magazine dence ated indi ini ini degrade lincoln lincoln lincoln lincoln lincoln lincoln lincoln tolerant tolerant tolerant tolerant judge judge judge judge judge judge judge judge rela rela angeles topologically retrained retrained tially tially ously clus mented 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#@Lincoln_W,Skrzypek_J,
#t3
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#*network network network network network network network network network network network network model model model model neural neural neural neural neural neural neural neural data data data data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm output output system state state results results results problem problem problem problem problem problem problem models models models models models performance space case case case case case shown values values values values probability probability probability probability probability parameters parameters parameters noise noise noise neurons neurons distribution distribution distribution distribution distribution distribution method approach approach pattern point point point point image image image image image image image image image image image image image local analysis class class class class class form algorithms algorithms simple simple gaussian visual visual visual visual visual paper small work work methods step step step field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field process process process process process process process process process process problems random random random random random random random high response show show show show show equation equation equation equation equation fixed line line line line line line line line line images images images general parameter real approximation approximation approximation approximation average average theory theory theory theory theory theory theory theory theory gradient gradient obtained obtained obtained term term dimensional result result result result threshold computation solution solution solution solution solution solution solution solution solution solution solution research independent defined constant estimate estimate computer computer computer computer connections science machine motion maximum range range range press continuous continuous sample sample abstract applied applied applied applied find find find computational computational analog analog properties references stochastic ieee positive important important introduction statistical statistical effect variance variance variance parallel cost cost cost cost cost tion energy measure prior chosen theorem theorem required binary binary binary binary binary binary binary represent bayesian equations equations equations equations equations markov markov markov markov markov markov markov markov make make fact techniques techniques minimum minimum computed computed respect sum sum sum sum called called called means optimization optimization potential potential potential natural global obtain obtain obtain original artificial artificial artificial artificial represented true proc proc related posterior posterior distributions distributions discrete mit mit mit mit mit comparison larger connection fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields support dependent dependent dependent report department implementation represents represents represents represents represents represents ai framework cambridge cambridge cambridge equivalent equivalent directly estimates limit approximate speed vision vision vision vision vision vision vision vision vision randomly randomly conditional lines processes processes processes processes nature depends simply technical inverse surface surface surface surface surface amount amount common effective effective effective effective main main main face face square noisy noisy simulated simulated simulated probabilistic needed hopfield hopfield hopfield hopfield account dynamical functional segmentation consistent representing iterations iterations depth early early early early frame minimize produced membrane recent recent advantage property takes pixels dimensions unsupervised solve solve smooth trans sparse sparse sparse sparse sparse sparse sparse sparse address observation horizontal horizontal intensity deterministic deterministic deterministic deterministic white white starting modules bayes bayes bayes faster weak temperature temperature temperature temperature propose hard integration integration physics intelligence intelligence intelligence intelligence intelligence assuming minimizing decrease averaged averaged configuration annealing annealing force pro monte monte monte carlo carlo carlo edges edges laboratory laboratory laboratory laboratory laboratory label label vertical vertical physical physical interaction interaction equilibrium applying applying yield yield yield reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction depending depending estimator interpretation solved restricted updated understanding partition partition updates updates sign smoothing normalization neighborhood koch koch koch thesis formulation inter coupled coupled coupled coupled coupled coupled coupled coupled coupled coupled coupled poggio poggio poggio detect road notice running sci sci gibbs gibbs gibbs write write ill ill neighboring deal deal create mass tech tech investigated investigated analytically possibility authors surfaces contours naturally configurations configurations man created changed contributions defines integrate integrate years years site site site site tive sites precisely commonly acad acad describing cybernetics researchers researchers understood lattice lattice lattice introducing posed formulated dots prevent collective geman geman geman geman display yuille yuille yuille yuille discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities corrupted college saddle saddle writing labeling princeton girosi girosi girosi girosi girosi girosi girosi approximates reconstructed reconstructed enhancement robotics eliminated siemens interpret star combinatorial filled natl natl lip connect stereo tic smoothed smoothed constitute graded reconstruct reconstruct reconstruct pami discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity life life guidance proba drawback drawback geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger grateful memo coming factorized restoration august bility corporate justification blake blake blake east fill december harvard harvard fij fij kirkpatrick kirkpatrick kirkpatrick attained ory creation essence metropolis metropolis amer damping weinshall mft mft mft ample assoc mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs pay novelty brings depen asserts marroquin marroquin marroquin vecchi heaviside shadow suppressing tomaso resides zisserman zisserman zisserman cont invited ice specular attractions federico discretizing lla clifford mitter 
#@Geiger_D,Girosi_F,
#t3
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural input input input input data function function function time time time time time time set set set set training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number number number number system system system system system system system error state state results results results results results results information information problem space space space space weights linear linear linear linear linear linear linear linear linear linear linear case case vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters weight distribution distribution distribution distribution recognition method approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern processing large large patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis class class matrix matrix matrix matrix matrix optimal optimal optimal inputs form form form simple simple paper paper paper examples small small small work work methods methods methods step step classification classification classification classification classification classification classification classification classification classification classification trained trained problems problems random random random random random random random random random high high high high high high high high high high high memory memory memory show show show show fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general generalization generalization generalization parameter parameter real real real real real states states theory theory theory theory theory obtained note note dimensional result result result university university university university threshold threshold threshold threshold threshold variables independent independent independent independent log log log log sequence initial constant table table terms distance distance distance distance connections connections presented presented present sets maximum press press position outputs continuous continuous continuous abstract find find find computational computational computational convergence properties properties properties references ieee ieee positive introduction complex circuit circuit statistical generated complexity complexity complexity complexity complexity complexity assume assume assume assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower higher part part center theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound required good binary binary binary binary binary binary binary binary binary long conditions conditions distributed distributed equations fact length finite finite finite finite finite finite finite finite finite minimum minimum minimum minimum minimum minimum resulting classes classes classes classes ing total simulation called means dimension dimension dimension dimension dimension natural applications study negative represented true compared desired desired desired desired desired desired provide perform determined mit accuracy accuracy larger larger contrast support words department loss implementation joint difficult addition addition ai view bit bit efficient efficient efficient classifiers upper upper upper requires requires requires requires requires statistics pages increase give give give give condition condition provided provided provided nature depends achieved achieved normal increases arbitrary denote denote limited limited close assumption assumption complete complete proof proof finding common assumed assumed assumed supported require require vlsi vlsi vlsi makes probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic smaller underlying needed needed combination programming programming programming programming testing testing testing testing significantly york york uniform representing details details numbers iterations iterations max making stored bits bits bits bits bits bits bits bits bits bits early polynomial polynomial choose predict perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes recent takes takes takes practical practical apply sense sense subset compare volume solve solve converge converge achieve trans trans symmetric bounded bounded bounded bounded interval storage storage storage storage storage storage storage storage storage storage increased grant exists exists exists exists exists wide matrices matrices matrices matrices runs conclusion assumptions assumptions valued valued encoding reduction reduction exist exist introduce program force question suppose suppose pro solving ways ways ways ways sequential mathematical mathematical mathematical coordinates coordinates linearly linearly linearly linearly linearly linearly linearly linearly linearly linearly easy adding implies boolean select yield viewed lemma lemma lemma lemma lemma lemma open operations operations operations operations showed sign sign sign partial partial earlier classical expansion expansion event purpose sufficiently sufficiently classified classified precision precision precision precision precision precision precision precision precision precision precision precision includes coordinate coordinate coordinate retrieval batch sciences simplicity reason aspects aspects aspects extra uniformly uniformly society reached strongly dis classify classify sin device device satisfy satisfy list write computes principles attempt deal extend american requirements exhibit existence fewer proved proved cover cover editor integer equally singular singular singular portion portion assumes explored perceptton perceptton perceptton perceptton perceptton logic academic store electronic mentioned great pairwise separable separable separable separable separable separable separable guaranteed answer answer answer lies stanford stanford stanford stanford stanford stanford stanford stanford lin satisfied worst hyperplane hyperplane hyperplane products mathematics mathematics acknowledgement beginning beginning computers questions questions questions applies applies capability capability simulate simulate simulate cohen compares mod hamming conclude redundancy arithmetic arithmetic arithmetic arithmetic arithmetic classifying classifying lab lab lab proofs formally arguments grows grows generality air moment moment contract phrase constructive separating separating separating equals pat guarantees expanded percepttons infinity belongs uni counting thomas entries entries entries advance surprisingly discovered limitation treat geometrical rigorous outperform exhaustive ber theorems conjecture conjecture conjecture conjecture conjecture classifications classifications classifications classifications classifications possibilities intuition num proba emphasize books noting emphasized nasa answers bility inequalities inequalities siu siu siu siu siu rameters minsky minsky implying fol edition ready terminates raised raised inform inform inform inform brought tern percep kailath kailath kailath kailath kailath imum preferable elegant terminate compress ther cir neurodynamics versity unlimited fur tially rosenblatt rosenblatt army lowing logn papert dembo dembo dembo dembo dembo tributions plications lhe lhe lhe amir ficient plete services aeronautics misleading yeung calif calif calif fid kai surely spartan coordi famous navy tron cuits interests ify daal combinatorics combinatorics bilistic finitely finitely 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#@Dembo_A,Kailath_T,Siu_K,
#t3
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number error results results results results results results results results results results information information information information information problem problem problem problem problem problem performance performance space space space space space space space space space space weights linear linear linear linear linear layer layer layer layer case case order order order order order shown shown shown shown shown shown systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach point point point point point point single single processing large large large large neuron test class class class class class class class class class class class class class class class class class class class class class class class class class class shows algorithms algorithms algorithms simple examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples net work work work work work work methods step points points points points points classification current problems show show show show show show equation equation section section section section section section section section fixed fixed rule general generalization generalization parameter real real real real theory theory theory obtained note note note result university threshold computation solution research research independent independent independent independent independent independent independent independent independent independent independent independent log log log found target target target target target target target target target initial constant standard standard computer computer computer computer computer distance distance distance distance distance distance synaptic science direction direction presented present present present sets sets sets sets sets sets sets sets sets sets sets sets sets press learn learn learn learn learn learn learn learn learn learn position outputs abstract applied find find find find find find find find find convergence convergence convergence references stochastic positive positive positive positive positive positive positive positive positive positive procedure procedure procedure context context context introduction introduction complex behavior generated parallel parallel parallel tion change difference difference complexity complexity assume assume lower measure measure measure measure measure measure measure measure measure measure learned learned learned learned theorem theorem theorem theorem theorem bound bound bound bound bound cases cases good long expected make fact fact region region region region region proposed proposed scale finite finite finite finite finite finite minimum classes classes classes classes classes classes classes ing ing total called called called called called called times regions regions factor factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made made made natural natural natural natural natural natural applications negative negative negative negative negative negative negative negative relative specific desired provide define define define define proc perform determined related constraints constraints distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions equal equal approaches approaches mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy contrast update update update update update update update support support institute institute department loss cambridge computing view limit upper upper full requires choice world world world world world give produce condition randomly criterion criterion area area area actual processes simply simply discussion discussion feedforward arbitrary arbitrary arbitrary fast fast fast fast fast fast fast fast fast limited close assumption proof proof proof proof circuits amount supported theoretical journal square square square square end hypothesis hypothesis hypothesis hypothesis future easily including including probabilistic probabilistic pairs technology technology programming programming programming interesting york trials trials uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform empirical call call call call call call call call call call call call call iterations max making making depth depth depth early polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial attention choose choose choose choose choose choose choose choose choose choose description perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron takes takes reported apply apply apply apply apply apply apply side sense interest interest interest interest interest dimensions dimensions dimensions dimensions sufficient highly works axis tions solve yields converge converge converge converge converge converge definition definition definition definition definition definition definition definition definition definition symmetric symmetric bounded organization grant exists concept concept occur extended alternative correctly correctly correctly correctly correctly width width boundary boundary boundary half half half half half half half half half half half half half half place greater greater greater greater greater greater greater greater central differences differences differences differences accurate exponential faster faster faster learns propose strong strong strong largest cycle drawn drawn drawn drawn drawn california assuming assuming start program solving generating generating laboratory label confidence confidence confidence confidence confidence confidence recall recall linearly linearly linearly linearly linearly linearly linearly linearly linearly linearly linearly infinite infinite infinite infinite infinite infinite easy slightly applying springer formed formed formed formed formed formed boolean boolean boolean boolean boolean yield yield independently independently depending squares squares squares squares squares restricted fraction fraction fraction suggested converges converges converges converges converges updates updates updates updates updates updates updates updates updates updates updates updates updates updates allowed allowed sign reasonable reasonable spaces spaces spaces spaces convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex iterative valid valid sufficiently sufficiently construction construction euclidean classified classified classified classified classified classified expect expect expect expect includes sciences vapnik vapnik vapnik vapnik prove candidate candidate candidate simplicity modification modification modification build traditional notice verlag success return lie lie classify classify classify classify quantity write providing computes hypotheses principles preferred satisfies origin rapidly rapidly involving limitations tech applicable office gates gates proved proved proved proved proved notion notion notion concepts possibly automata equally changed observe mapped perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton arbitrarily arbitrarily serial serial serial serial band band band band band band formula formula theoretic separable separable separable separable separable separable separable separable separable separable separable trivial independence independence independence independence independence independence baum baum baum baum baum baum baum baum baum worse worse considerable inside inside inside inside inside inside processed purposes formalism closer worst immediately hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane acknowledgement involve begin author author geometry nsf relevance tional readily readily readily haussler haussler rep passes fall proven conclude conclude comments focused converged converged converged calls classifying classifying proofs proofs modify restriction restriction restriction fix princeton princeton acm acm acm arguments arguments arguments pick pick hyperplanes hyperplanes discover proceed generality inspired logarithmic hope imply imply presentations continue meaningful separating separating separating separating separating separating corollary appendix appendix appendix appendix appendix studying evident percepttons sphere sphere sphere sphere sphere sphere sphere surprisingly arrive warmuth kearns kearns empty learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable divide planes chervonenkis chervonenkis chervonenkis chervonenkis conjecture seek classifies classifies valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant valiant shaded argue argue concentrated distri proba learnability learnability books argued argued argued sketch sketch sketch adversary adversary adversary adversary adversary adversary adversary adversary portions sized exchange exchange exchange likewise induces union computa gorithm unpublished completed nec bution remarks bility demand demand demand prefer jet converging builds nested nested nested nested nested nested solvable suffices hull hull formulae horizontally condi sided meeting sen normalize propulsion lying cardinality cardinality cardinality tells shattered minsky minsky minsky sions suffice suffice suffice triangular vertically falling communicate inde comm dimen protocol protocol protocol protocol protocol crl cho restrictive restrictive restrictive restrictive dent indepen iterate ming pendent relax remarkably predic miss miss graphically blumer blumer blumer blumer blumer blumer separator conversations neurodynamics sible ucsc bernoulli translating rosenblatt rosenblatt unclear unclear seemingly subclass enormous intersecting intersecting successes discard calling papert papert trivially modulo integrand informal informal ehrenfeucht logarithmically restricts snowbird heard assure 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step step step step step step step step step step step step step process current current current current current current current problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random high high high high similar architecture equation equation equation equation equation equation equation fixed fixed fixed line rule rule rule rule rule rule rule rule vectors general speech parameter real real approximation approximation approximation states states states states theory theory theory theory gradient gradient gradient term term term term term term note university university university university computation solution research research research research research research defined defined sequence target target target target target target target initial initial table estimate estimate estimate estimate estimate estimate computer terms terms terms science prediction prediction prediction prediction prediction prediction prediction temporal temporal temporal machine machine sets press press press press press learn learn learn outputs continuous abstract computational computational computational computational computational properties references references stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due ieee ieee positive important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision context introduction introduction action action action action action action action action dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic cost cost search search tion change difference difference variable assume assume assume classifier classifier rules measure measure measure measure signals signals prior prior prior prior representations word word word part cases required required required required good long long expected expected expected expected expected expected expected expected expected expected expected expected expected equations equations markov fact fact probabilities probabilities probabilities resulting ing tasks tasks tasks tasks total computed computed respect sum performed called elements elements mapping means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor dimension natural global applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge knowledge knowledge knowledge knowledge knowledge obtain artificial artificial artificial represented true true true desired desired series provide provide provide provide provide define define compute compute determined related related related related related discrete discrete brain mit mit steps steps connection connection update update proceedings proceedings implementation version consists joint difficult difficult difficult delay delay sequences framework framework framework cambridge cambridge cambridge computing directly directly view solutions transition transition transition transition transition conference capacity requires significant significant approximate speed estimated estimated estimated estimated estimated estimated estimated estimated give con con produce condition condition condition developed developed developed developed controller controller types lines product actual actual actual backpropagation depends depends simply simply associative feedforward describe denote denote assumption complete complete complete complete actions actions actions actions actions amount amount amount amount short short common implemented implemented implemented implemented assumed supported role theoretical require require require require require journal end end future future makes makes development development objective objective objective underlying underlying underlying underlying underlying account dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical programming programming programming programming programming programming programming programming programming programming york york special special representing representing call call making making making making making international supervised supervised supervised supervised supervised produced predict improved discussed improve exact exact advantage takes element element element element typical introduced recently relevant relevant relevant relevant relevant highly teacher tions solve solve solve yields correspond studies address address evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation interval improvement studied extended derivative predicted deterministic deterministic hardware conclusion starting critical place editors editors differences modules modules accurate accurate numerical sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton exponential suggest intelligence intelligence assuming assuming assuming relationship relationship manner manner program force monte carlo produces longer solving solving solving solving ways primary sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential dept changing missing missing multilayer infinite infinite dimensionality slightly angle unique develop integrated formed expectation expectation focus viewed solved solved detailed evaluated evaluate approximations approximations understanding understanding approximated past barto barto barto barto barto barto barto barto barto barto barto barto barto barto barto barto delays spaces iterative transactions building includes includes includes includes thesis thesis thesis assignment assignment illustrated discuss discuss maximize specifically specifically successfully simplicity planning determining determining selecting selecting closely closely closely effectively included presentation identity identity reached receives receives refer heuristic moore moore anderson anderson anderson anderson anderson neuroscience neuroscience return return return return return return return return return return return return return return return return return return return return return return contribution strategies duration satisfy quantity usual usual play play absence delayed delayed delayed delayed delayed observable received received received received policies policies policies policies policies policies approximating approximating approximating approximating unlike collection difficulty environments environments environments involving involving game existence successive successive respond giving incremental incremental office decisions decisions decisions decisions decisions decisions decisions decisions maximizing understand concepts necessarily man man adjusted obvious noted assumes explored explored academic academic improving improving simplest simplest explain phd phd phd animal massachusetts massachusetts massachusetts great advanced ment cart slowly developing critic critic critic critic track analyzed improves failure failure briefly handle starts london considerable perspective perspective sys immediately immediately mation commonly watkins watkins watkins watkins watkins watkins watkins watkins watkins watkins watkins watkins watkins laboratories scientific acknowledgement involve cybernetics cybernetics incomplete requiring greatly tional parameterized parameterized autonomous formulated formulated rewards rely rely rely instruction maximizes maximizes cal prevent adjust adjust adjust plan richard expectations expectations begins credit credit calls calls univ cumulative cumulative cor pole pole pole pole bellman bellman bellman benefit secondary formally princeton temporally temporally optimizing approximates approximates approximates purely addresses proceed extending air fits satisfying moment moment occurring operates observing observing roles roles intuitively symposium phrase selects evaluations evaluations evaluations evaluations falls encountered equals regarded bad intended forecasting consequences consequences consequences consequences consequences consequences consequences consequences consequences chooses advance discounted discounted discounted surprisingly horizon horizon horizon extensively extensively subsequently grants balancing balancing cam assigns assigns assigns accumulated bertsekas bertsekas bertsekas multiplying truncated truncated truncated truncated truncated truncated truncated truncated truncated discount discount emerge dyna connec corrected corrected corrected corrected corrected generalizations amherst amherst amherst england letting ibm insights interact werbos werbos werbos werbos approxi continues continues uncertain uncertain interacting afosr afosr books lookup player topic alternatives discusses indication computa aaai reinforce bridge palmer payoff payoff payoff payoff payoff payoff payoff payoff payoff payoff payoff payoff payoff payoff payoff ase ase justification curse supply played cally ning concerns disturbances practically automation rangarajan ory adjusts ods fixing adequately ming hits rein assessing entering ace ace ace ace ace ace ace ton ton observes reactive formulations wait wait ross ross ross ross ross samuel samuel ponent tinuous earliest eval quences calling calling unrealistic peri forcement stud reachable neuronlike bucket interacts 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connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node direction direction direction direction nodes nodes nodes nodes nodes nodes maximum maximum range press position basis basis abstract computational density density density density density properties properties properties properties references component component component component component component component component component component component positive positive positive positive important important important effect effect effect change energy spatial lower rules rules rules rules rules rules rules higher theorem theorem theorem type type long conditions make correlation forward finite simulations simulations simulations simulations simulations simulations simulations ing total simulation computed computed respect sum sum factor negative negative negative negative negative negative negative negative negative negative negative relative relative compared 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learn learn learn components components components components components nonlinear continuous continuous continuous continuous continuous continuous abstract applied applied applied back find find find computational computational computational computational convergence analog analog properties properties properties properties properties references references component component ieee ieee adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation introduction hand estimation behavior behavior behavior behavior behavior generated generated parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change change change difference difference complexity complexity complexity complexity spatial assume measure measure representations learned learned learned learned part part center center previous type required required required required required multiple cortex distributed 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dependent dependent proceedings report institute institute institute words department implementation consists internal internal difficult final final final final exp cambridge domain hinton curve curve solutions transition limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san conference efficient efficient efficient requires requires requires requires requires requires choice approximate approximate basic condition condition condition condition derived derived developed product product product product actual actual provided provided provided provided provided finally finally backpropagation backpropagation backpropagation backpropagation backpropagation depends depends constraint constraint simply simply simply measured covariance feedforward fast fast fast inverse inverse corresponds corresponds proof amount amount amount amount amount implemented generate generate require eds eds journal journal 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activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university university threshold threshold threshold threshold threshold threshold threshold computation solution research research research defined defined defined defined defined defined found found initial constant computer terms terms distance synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node node science science science direction direction direction direction direction direction presented presented presented presented presented presented present low low nodes nodes press basis nonlinear nonlinear nonlinear nonlinear sample abstract applied applied applied find find find properties properties properties references component component component stochastic stochastic stochastic stochastic due due decision decision decision decision decision decision decision decision decision decision decision decision introduction hand estimation statistical statistical statistical statistical statistical dynamic dynamic variance variance parallel parallel parallel cost cost search spatial rules rules rules measure measure measure chosen chosen center center center cases firing type multiple multiple multiple multiple cortex cortex cortex cortex good good conditions conditions represent equations equations equations equations equations equations equations techniques techniques region correlation correlation observed scale finite simulations minimum resulting resulting resulting total total simulation simulation respect respect multi multi factor optimization optimization optimization potential made orientation orientation global global global global knowledge negative specific specific true compared desired provide define define define define define define proc location location perform related cortical larger larger larger fields fields descent modeling report loss loss loss loss loss loss loss 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structures leads leads principal principal principal inhibition inhibition inhibition inhibition inhibition inhibition inhibition polynomial polynomial idea idea minimize minimize minimize minimize added neuronal neuronal improved discussed discussed directions directions directions directions directions recent property property property robust takes takes takes lateral lateral practical period identical sense sense recently interest dimensions unsupervised unsupervised tuning smooth smooth yields differential differential rl definition definition definition symmetric bounded organization risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk exists studied invariant suggests suggests suggests suggests suggests deviation derivative deterministic deterministic critical place place greater assumptions accurate clear clear performs performs exponential faster presence reduction reduction reduction sigmoidal demonstrated radial turn turn start selective selective selective min iii iii averaged averaged introduce groups groups identification acoustic denoted relation pro index index index index index factors estimating ann stability dept segments sensitivity averaging dimensionality dimensionality dimensionality dimensionality involves interaction interaction interaction minimization minimization minimization minimization minimization minimization minimization extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction yield yield national extracted extracted extracted extracted family family formation review depending viewed viewed densities restricted sizes suggested processor past past smoothing performing performing classical classical spaces spaces normalization penalty valid foundation norm norm views topology coupling fire fire fire fire kernels priori usa formulation formulation formulation formulation formulation formulation inter inter coupled phys discussions major extra capable uniformly suitable society differ differ differ modification modification modification modification modification modification modification modification modification effectively driven presentation projections projections traditional compact compact compact notice allowing neuroscience physiological sci simplified simplified minimizes leading leading leading neurosci attempt mixing mixing mixing preferred extract extract extract receive receive receive simpler remain unlike selectivity selectivity powerful american experience detail replaced replaced replaced association graphical hall hall hall hall discriminant pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit rise giving school rest biol biol office office statistically topographic math spline friedman friedman friedman friedman friedman der der portion formal nerve multivariate multivariate amari amari simplest submitted serial isolated brown brown piecewise adjacent adjacent biology nonlinearity turns turns desirable mation mathematics mathematics projected acknowledgement acad calculations beginning demonstrates cybernetics argument relevance capability peaks detecting detecting continuously outliers differs serve phonemes replace coherent kinds inherent specifies differentiable yielding yielding yielding acquisition indices cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper linearity discovery naval jones jones interconnected binocular saturation oja oja oja promising proceeds striate attractive viewpoint star definitions intuitive natl moments meaningful meaningful saul saul von dependency barron barron specificity specificity specificity adopted annals annals munro munro removal tween retraining par exception seek seek intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator malsburg malsburg associate discovering eliminating emphasized emphasized anal siam esti exhibited exploratory exploratory exploratory exploratory exploratory exploratory exploratory exploratory computa unpublished modal opti bienenstock bienenstock bienenstock bienenstock bienenstock accordance families hat curse curse inhibit inhibit inhibited loosely bcm bcm bcm bcm bcm bcm bcm harvard affecting dissertation dissertation governing governing statist dimen rel electrophysiological bear bear minimizer proceeding decades tails correlational favors cox cox proximation substructures arousal yon columnar huber huber huber huber sparsity sought separability separability army analyzer analyzer fruitful analysed responsive responsive asymptotics providence providence emphasizing ore ore ore ore ore ore highlights doctoral concentrates normality normality mexican notations revealing overcoming unspecified scofield scofield scofield scofield regulated estimations kybernetik extractors rewriting rewriting sional sphering possessing 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algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number error error error error results results results units units units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer order order shown shown systems systems systems values values values values values values values values parameters parameters parameters weight weight weight weight weight weight functions 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standard standard terms terms terms terms terms terms terms terms terms terms terms terms terms terms connections connections connections connections left presented phase activation low low frequency frequency sets press learn learn position abstract back back back back back back back back back back back back back back back back back back find computational references propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction hand effect parallel cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost recurrent search search search search search tion change change energy energy energy complexity lower representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations chosen higher part previous multiple good good binary distributed equations equations equations make make proposed correct forward forward forward forward forward simulations simulations simulations simulations resulting ing ing ing tasks respect times times times times means optimization optimization optimization made made feedback feedback study obtain vol relative relative specific specific represented compared rates rates determined determined constraints constraints mit steps steps steps comparison comparison larger contrast connection connection connection connection connection connection connection connection train descent descent descent descent dependent institute implementation internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal difficult layers addition addition hinton additional solutions solutions curves limit limit limit limit limit limit limit limit limit limit limit efficient full choice increase con con produce criterion lines actual iteration simply measured measured describe tested fast fast fast fast fast corresponds corresponds surface finding effective generate eds easily rumelhart rumelhart rumelhart rumelhart including including reduced reduced fully interesting increasing special trials making run run added perceptron perceptron improved directions advantage advantage element moving include include identical side array recently varying varying varying conventional conventional volume volume tions solve converge converge generalized williams improvement lead studied feed feed hardware hardware runs runs runs runs runs runs runs strength conclusion starting reduce reduce faster practice encoding encoding encoding encoding encoding encoding cycle targets targets introduce denoted explicit explicit explicit explicit suppose pro construct ways plot plot plot describes describes tuned implement implement easy easy cycles cycles cycles cycles john review stationary interpretation updated updated updated updated updated updated updated labels labels labels completely completely suggested sign calculation slow slow slow add iterative advantages coupling coupling coupling coupling thesis activations activations activations perceptrons perceptrons perceptrons formulation formulation plotted variations variations delta mcclelland wij wij wij wij wij wij wij wij wij wij successful successful successful successful essentially kind cun cun cun success success success success success success success success success vary vary attempt minimized carried layered layered updating updating investigated parity parity parity parity parity 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control control control control control large large neuron neuron neuron neuron test inputs inputs inputs inputs inputs inputs form signal signal simple simple simple simple simple visual visual visual paper paper examples work fig cells step step step step step step field current current current current current current current current current response response response response response similar similar similar similar section section fixed fixed fixed fixed experiments computation defined found found target target computer computer science science science left direction direction presented presented presented presented presented present present present sets sets sets sets motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum maximum maximum learn learn learn basis outputs outputs outputs abstract analog analog analog analog analog analog analog analog analog analog analog analog references due due ieee adaptive adaptive adaptive adaptive 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voltage voltage voltage voltage voltage voltage voltage voltage voltage train proceedings institute institute institute department implementation implementation implementation implementation implementation version consists consists consists consists consists represents bias bias bias bias considered framework framework framework framework framework framework framework experiment environment environment environment environment directly limit top detection upper requires vision give give give give con velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity product product nature biological biological biological measured measured measured tested assumption actions circuits circuits circuits circuits circuits circuits implemented implemented generate generate require require adaptation adaptation 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correctly correctly correctly correctly correctly feed feed setting pass conclusions accurate accurate retina retina retina designed designed designed designed performs suggest cycle characteristics demonstrated california california california proportional proportional proportional pulse pulse pulse pulse user exist movements movements movements movements movements relationship relationship optical primary primary primary vertical modeled modeled implement implement coordinates linearly physical electrical integrated integrated integrated integrated extracted controlled ocular ocular ocular ocular ocular ocular ocular ocular ocular showed showed constants allowed allowed allowed sign diagram diagram sec combining fitting msec msec precision thesis thesis currents currents currents currents currents currents currents currents currents currents currents currents currents currents retinal retinal retinal retinal retinal retinal retinal retinal determines encoded schemes characteristic traditional allowing interpreted michael simplified simplified computes computes computes cat chips chips chips moves acknowledgments extend trains trains trains remain exhibit circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry mead mead mead mead mead mead mead mead environments accurately transistor transistor transistor transistor variability pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway adapt adapt adapt adapt reading changed voltages eyes eyes eyes adjusted impulse obvious generates generates generates improving plant plant plant plant site site slowly vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor growth biology interneurons interneurons drive rapid sys broad incorporate transistors monkey monkey monkey monkey monkey monkey monkey controls pulses integrating varies behaviors pathways pathways pathways pathways pathways pathways schematic schematic maintain robinson robinson gains gains gains gains gains pasadena pasadena pasadena richard inherent implements wesley summed summed primarily addison generator generator writing amplifier amplifier driving velocities velocities vestibular vestibular vestibular vestibular vestibular vestibular tem connecting minutes cerebellum hope exploit exploit salient capacitor capacitor presentations muscles hours mance sion displayed perfor moved moved facilitate deg creating environmental partitioned partitioned designing ball mechanical skills fitted mind multiplying reflex reflex reflex reflex reflex reflex reflex reflex reflex reflex ure neurophysiology converted converted converted encodes encodes junction adapting adapting attempted subthreshold interneuron execute convert convert convert disease oculomotor oculomotor oculomotor oculomotor turning turning indication suggestions stephen acquire vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo tial calibration mahowald king lyon steven purkinje supplied supplied connects connects sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor integrates integrates integrates subtracting operational operational correctness lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger adapts deweerth deweerth deweerth deweerth deweerth deweerth deweerth stabilize wires wires spec freely carver asymmetry converts converts magnification magnification walking slip slip slip slip slip slip slip slip slip slip slip slip slip slip ver lens mediate supervision ages organisms overshoot mag delbriick snyder snyder sponse multiplies compensatory proportionally proportionally proportionally volt sivilotti designer inspiration unmodified unmodified unmodified unmodified unmodified unmodified unmodified 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#@DeWeerth_S,Mead_C,
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analysis optimal shows shows shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual small small small small small small small size methods fig fig fig fig step step points field field field process current current current current current current problems high high response response similar show show fixed line line line images images general generalization generalization generalization real real real real real real real real real real theory theory theory theory theory gradient term term term dimensional dimensional variables computation solution research research research research independent constant standard computer computer computer computer computer computer computer distance distance node node node node node node node map low low nodes temporal object motion maximum range press press nonlinear nonlinear abstract applied applied find find computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties references stochastic due due ieee important important introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior effect variance variance variance parallel cost cost change energy difference difference difference difference difference difference center center type required required good binary binary binary binary binary binary long conditions bayesian expected chip chip chip chip chip chip chip chip chip chip chip chip simulations minimum resulting ing human computed sum eq elements elements natural orientation global true provide provide compute compute objects proc proc proc proc location perform experimental experimental goal goal related constraints discrete power power power power power power approaches mit mit mit mit voltage voltage voltage voltage voltage voltage voltage voltage voltage larger larger contrast nets proceedings report implementation version version final final ai ai framework cambridge cambridge cambridge computing computing equivalent environment environment environment environment curve curve curve additional view view design top detection detection detection detection conference free world world speed vision vision vision vision vision vision vision vision vision vision vision vision vision vision vision estimated developed robot robot controller finally processes processes nature depends constraint constraint constraint measured measured measured measured measured describe fast close close close corresponds surface surface surface surface surface surface surface surface surface surface actions circuits circuits circuits circuits circuits circuits circuits circuits circuits finding finding finding implemented implemented assumed assumed shape supported eds vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel pixel ability instance development noisy noisy noisy noisy including smaller underlying underlying functional functional functional functional functional functional fully ratio edge edge edge edge edge edge increasing segmentation segmentation special mode operation call making international bottom bottom depth depth depth depth depth early early early early early early magnitude magnitude magnitude minimize sources light light light light neuronal membrane advantage pair robust takes element movement movement movement movement include machines pixels quadratic quadratic array array highly varying approximately approximately smooth smooth smooth achieve trans sparse sparse sparse background background background evaluation positions locations locations locations grid grid amplitude amplitude horizontal intensity intensity intensity intensity intensity intensity lead extended digital digital derivative correctly width deterministic deterministic deterministic hardware hardware hardware demonstrate demonstrate demonstrate strength conclusion operator tangent retina retina retina designed designed exponential integration proportional regularization regularization regularization pulse minimizing minimizing exist plane relationship program acknowledgements edges edges edges edges edges edges edges laboratory laboratory laboratory laboratory laboratory laboratory vertical implement explicitly simultaneously physical physical electrical unique integrated integrated gaussians gaussians john formation formation reconstruction reconstruction stationary stationary stationary transform controlled controlled controlled controlled controlled controlled approximations modulation understanding approximated constants constants constants constants sign diagram smoothing smoothing smoothing smoothing smoothing smoothing additive additive convex sec sec purpose purpose tracking tracking tracking interpolation filtering advantages koch koch koch koch koch koch koch koch koch koch koch koch avoid building silicon silicon silicon silicon priori usa color inter illustrated activated black successfully successfully determining straightforward middle middle middle closely differ modification effectively driven poggio poggio poggio poggio detect detect build build soc soc notice notice success interpreted conductance conductance conductance conductance conductance dis content follow strategies sci device device device built built built built gibbs bar vary relaxation board cmos ill chips chips chips chips chips chips chips processors operating satisfies neighboring neighboring camera minimized explore requirements circuitry circuitry circuitry mead mead mead mead mead mead mead mead mead mead environments limitations terminal terminal variational variational variational office workshop circles reading illustrate voltages voltages voltages implementations implementations adjusted front mapped shapes arbitrarily serial finds isolated indicating indicating advanced slowly piecewise piecewise piecewise crucial sensors smoothness smoothness smoothness smoothness smoothness track track slope caused perspective implementing implementing formalism forces acad localized researchers robustness robustness robustness robustness behaviors limits lattice autonomous car car car posed detecting detecting resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive continuously schematic schematic price price differs resource pasadena geman geman green inherent segmented implements yuille yuille median traces wesley acquisition discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities sensing analogue addison fabricated investigation girosi girosi acts acts mobile mobile mobile mobile naval connecting enhancement robotics robotics robotics robotics robotics caltech logarithmic held stated attractive resistance vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle fail settings natl slice recovered studying bad photoreceptor photoreceptor scan facilitate foundations smoothed horn horn roy insect jump harris harris harris harris harris harris discovered thresholding andrew crossing crossing drop corporation kluwer aircraft ram smoothly utilize exception ease superimposed laplacian options rectangular resistor resistor resistor resistor resistor exclusive exclusive toy toy toy toy graphics generators discontinuity playing reflectance hughes argued ultimately transconductance transconductance anal breaks breaks geiger geiger maintains crossings crossings crossings crossings crossings crossings crossings crossings crossings resistors memo amplifiers steering radio demonstrating drives restoration hyperbolic identifies photoreceptors photoreceptors photoreceptors photoreceptors crude hat blake blake house mahowald mahowald mahowald utilizes utilizes utilizes utilizes reversible arrow micro fabrication incorrectly cast cast supplied usefulness tribution conflicting floor subtracting lightness subtracted triangles marr marr fij detects interpolating grids grids dog dog digitized tracks tracks decaying volts predictable robotic spirit physically demands rectangles fidelity deweerth deweerth deweerth saturating saturating saturating saturating steve foreground segmenting segmenting segmenting mach backwards mesh dissipation dij dij eeprom recovering christof mounted mounted mounted carver configured horiuchi horiuchi horiuchi horiuchi horiuchi operated cars cars demanding spots battery battery hysteresis bright bright bright relying availability mrfs reminiscent cir bair bair bair bair bair pay pay mediate retinas vast exceeded ages fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse fuse depths continuation continuation torre torre functionals functionals converters brooks brooks rising steep luo luo luo luo luo luo comput cheap ences volt assist vehicles vehicles vehicles vehicles vehicles vehicles embody mexican intend resistances resistances microprocessor marroquin marroquin cheaper logarithmically occlusions cumbersome ismail wyatt shadow shadow tape chart timothy hildreth hildreth loud loud puting exponentials methodologies hsu hsu hsu hsu hsu laid zisserman zisserman tremendous followers norwell abruptly ports bench bench hungry acquiring rockwell forwards cuit jin spell corrupt corrupt curious commercially convincingly cooperativity wyeth mounting mounting misha mobility 
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networks networks output output output output output output output output output output output number number number number number number number number number number number number system system system system system system system system units units information information information problem problem performance weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer case order order order shown shown shown shown systems systems systems systems systems values parameters parameters noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons unit unit unit recognition approach pattern pattern pattern point point point single single single single single single processing processing processing control large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate analysis matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form form form form shows shows shows shows shows shows shows shows algorithms examples small small size task cells cells field features classification process level level level current current current current current current current current cell cell problems problems problems problems problems problems high high high memory memory memory memory similar show fixed fixed vectors general real university threshold computation computation computation research independent defined found computer computer computer terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left low maximum maximum range nonlinear outputs outputs outputs outputs outputs outputs outputs outputs abstract computational computational computational density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due due due due ieee ieee ieee ieee ieee important adaptive introduction hand hand hand circuit circuit circuit circuit circuit circuit parallel parallel parallel parallel cost variable assume lower lower signals chosen part part center type type required binary long distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make forward forward scale scale total sum called called called elements means feedback feedback artificial application application desired receptive receptive provide provide provide provide provide define active active connected gain gain gain gain gain equal equal power voltage voltage voltage voltage voltage accuracy larger connection fields fields update update update update update morgan morgan morgan department implementation implementation implementation implementation implementation implementation version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses individual advances advances advances joint joint represents represents bias bias bias layers delay scheme scheme scheme scheme scheme addition addition framework framework equivalent equivalent environment solutions curves design design design design design limit san bit bit bit conference conference conference full full requires requires speed speed speed pages pages pages pages pages con produce weighted developed levels levels levels levels area area area area area area types actual actual provided selected nature depends achieved measured measured increases increases describe tested tested fast fast limited limited limited complete complete complete complete complete complete circuits circuits finding short implemented assumed assumed shape synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse 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#*network network network network network network network network network network network network network network network learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data function function function function figure figure figure figure figure figure figure time time time time time time time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training output output output output output output output number number system system system system system state state state state state state state results results information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance based based based based based based based based space space space weights weights weights weights weights weights linear linear linear linear linear case order order shown shown shown shown shown systems values values values parameters parameters weight weight weight weight weight weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach approach approach single processing large large large large large large large local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron matrix matrix matrix matrix matrix matrix matrix matrix inputs form form shows simple paper paper paper size size feature net net net net net net net net net net net net net net net net net net net net net net net work fig fig fig fig fig fig fig cells cells step step process process current current current current current current current current current current current current current cell problems problems random high high high response response response similar similar representation section fixed line vectors real real states obtained obtained obtained obtained obtained obtained obtained obtained term term term dimensional threshold threshold computation solution solution solution research found initial initial initial initial constant constant constant standard computer terms distance distance synaptic synaptic synaptic synaptic synaptic synaptic synaptic low low low sets sets sets range press nonlinear outputs outputs abstract computational convergence convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties likelihood likelihood references due due ieee positive positive introduction complex hand hand circuit circuit circuit circuit circuit circuit circuit behavior effect generated generated parallel parallel parallel parallel cost cost cost cost cost cost cost cost cost cost cost search energy energy energy energy energy energy energy energy complexity part center center cases cases cases cases cases type type required good good binary binary binary binary long long long long long long expected equations chip chip chip chip chip chip chip chip chip chip chip chip chip fact observed observed minimum minimum minimum minimum total total total multi performed performed performed times elements means optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization potential feedback feedback feedback feedback feedback feedback global global global global global global global global global applications study study obtain vol vol vol vol vol vol artificial application desired desired cross cross cross cross provide provide compute proc proc proc proc perform perform active connected connected distributions gain gain gain gain gain gain gain gain gain discrete equal voltage voltage voltage voltage voltage voltage voltage larger larger connection source nets nets nets institute institute implementation implementation implementation implementation implementation implementation version version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists consists consists joint bias bias bias addition computing directly additional additional solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions curves curves curves design design design design design design design design design design design limit limit trajectory bit bit bit bit bit bit bit bit bit bit statistics statistics statistics speed speed basic increase give channel channel channel channel channel channel weighted weighted weighted randomly randomly developed developed levels lines lines provided finally selected nature sampling simply simply associative achieved achieved measured measured arbitrary limited limited close corresponds excitatory stable surface surface common common common common common implemented implemented implemented implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse vlsi vlsi ability ability easily easily development development objective simulated typically hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield reduced dynamical dynamical fully fully fully technology technology technology technology block block block block transfer transfer transfer increasing increasing inhibition inhibition stored bits supervised depth minimize sources sources description light discussed discussed resolution resolution resolution element element typical lateral lateral quadratic array array array array interest highly calculated correspond address address positions gate gate gate gate gate gate increased digital digital digital digital digital digital digital digital digital digital digital digital digital deviation matrices alternative hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid generally column column column column hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware demonstrate strength strength row row row greater reduce conclusions taking strong external external external external external cycle characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics demonstrated demonstrated california california solid proportional proportional variety start minima minima program annealing annealing annealing annealing force acknowledgements appears solving solving solving solving laboratory laboratory stability recall consisting interaction interaction quality blocks blocks blocks john national depending variation updated fraction fraction static similarly similarly constants diagram diagram diagram diagram expansion purpose valid valid distances recorded building building building building priori inter assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment memories memories phys discussions capable importance encoded essentially excitation conf oscillations sci bar bar bar bar vary simplified simplified providing cmos cmos cmos cmos cmos chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips operating operating operating preferred employed employed investigate investigate investigate investigate exhibit circuitry optimized limitations biases biases biases biases investigated applicable biol possibility transistor transistor transistor transistor authors office decisions gates voltages implementations implementations ensure ensure ensure store store consist utility electronic electronic electronic electronic electronic electronic electronic electronic electronic optimum optimum optimum optimum optimum advanced slowly agreement floating capabilities multiplication nonlinearity located transistors transistors transistors desirable acad gradually annual considerably percent consistency consistency compares exhibits summarized incorporating incorporating incorporating incorporating incorporating tank tank tank tank tank collective pasadena suited suited suited gave simulator electric june cybern fabricated fabricated fabricated fabricated fabricated fabricated interface assign amplifier amplifier summing linearity nat controlling reaching arranged arranged establish consideration city city city city city city programmable programmable resistance los abilities combinatorial combinatorial excellent excellent evident permutation thin thin layout hypercube hypercube projects valuable fusion multiplying multiplying multiplying maintaining minus minus graded encouraging pointed monotonicity monotonicity drain ideally ideally assignments quantized quantized quantized capacitance favor resistor resistor resistor ijcnn convert figs tij resistors modifiable steering technologies helps spite tour corners corners traveling traveling traveling traveling traveling traveling quadrant quadrant attributed assistance jet jet trainable settling converging designs utilizes utilizes aid tsp tsp tsp tsp tsp tsp tsp fabrication conversion conversion conversion incorporation agency settle operational operational operational propulsion propulsion rating optics volts volts volts volts volts volts volts spie salesman salesman salesman salesman salesman salesman appl appl mosis evolves defense jan tim brought actively eeprom trapped sponsored custom ard decoders favorably fet fet mar angeles internally anneal electrically electrically vin vin vin latch converters emphasizes tours tours tours incremented incremented administration multiplexer micron nxn nxn aeronautics microelectronics microelectronics suppressing tam film film wash symp thakoor thakoor thakoor thakoor thakoor thakoor thakoor thakoor thakoor benson vss bromley jpl shaw interfaced latches permissible holler mirrored microcomputer unusually characteris castro tactical ohm readout 
#@Duong_T,Moopenn_A,Thakoor_A,
#t3
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#*network network network network network network model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set networks networks networks networks networks output output number system system system system system system error state information problem problem problem problem problem linear linear linear linear case order order order shown systems systems systems noise neurons neurons neurons neurons recognition method method method method method method method method method method approach processing processing large test matrix inputs inputs form paper paper paper paper work task points current current problems problems similar architecture equation equation section line line line line general general real gradient gradient gradient gradient university variables variables variables variables computation solution target target target constant computer terms science object press press nonlinear nonlinear abstract applied applied find find find find analog analog analog analog analog analog analog analog analog analog analog analog analog references positive positive introduction complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit parallel parallel change difference lower chosen multiple equations equations equations equations equations equations equations equations equations equations chip proposed observed observed observed minimum minimum minimum tasks tasks optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization made feedback applications applications negative specific desired location perform perform constraints constraints constraints connected gain voltage voltage voltage voltage descent descent dependent institute department consists advances considered computing san determine approximate basic basic con provided nature depends constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint simply close circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits implemented implemented square vlsi vlsi vlsi easily underlying needed hopfield hopfield hopfield technology programming programming programming programming programming programming programming programming programming programming programming programming interesting matching details minimize improved discussed practical subject subject subject quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic cognitive varying tions solve solve solve solve solve match match studies converge differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential address organization increased increased extended spikes correctly hardware hardware critical conclusions designed performs performs constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained california solid solid user min minima program program construct solving sequential generating plot plot plot plot describes stability stability changing infinite john yield formation codes constants diagram dashed dashed performing sec sec sec combining add box perceptual perceptual bell plotted successfully build road notice quickly decoding prob prob oscillations manifold manifold built built satisfy minimizes minimizes wave computes moves decreasing minimized circuitry circuitry circuitry circuitry mead mead mead mass examine rest biol decisions analogous reading man voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages thought academic simplest finds guaranteed caused london stanford stanford implementing sys ring forces forces acknowledgement gradually definite researchers transient frequently tank pasadena shaped implements implements simultaneous wesley analogue addison amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier summing repre platt platt platt platt platt platt platt platt platt platt platt multiplier multiplier multiplier multiplier multiplier multiplier multiplier multiplier multiplier adds murray capacitor capacitor mjolsness expanded ascent ascent originally dif creating refers correcting lem lem linked solves willshaw capacitance exam resistor resistor tems compensate labs flip flip flip flip flip flip flip flip flip flip flip flip transconductance transconductance transconductance transconductance transconductance transconductance transconductance transconductance resistors interconnect sta durbin durbin advantageous satisfaction lagrangian opti externally externally bility traveling spring spring inhibit suite arrow arrow inverter inverter equa impedance push economic salesman constraining fol enforces adequately undergo violated ming ming jose decode carver damping damping damping converts mization examines suitably damped cir bistable wright fulfilled fulfilled fulfilled fulfilled fulfilled temporary temporary anandan converting violation violation explores gindi gindi gindi flop flop flop flop flop flop flop flop flop flop flop flop fulfill fulfill fulfill fulfill travelling govern cyber temporarily temporarily snowbird abrupt funding synaptics synaptics straint oxi oxi oxi fulfills fulfills oscilloscope suddenly gill gill cuits abruptly barr sents ined clude ferential ringing ringing unusually digitization 
#@Platt_J,
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#*network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural figure figure figure figure figure time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks output output number number state state state state results information information models based based based based weights linear linear linear shown shown systems systems systems systems systems noise noise noise weight weight weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons approach pattern point single single processing processing control large large neuron neuron neuron neuron rate rate test analysis optimal form form form form form shows shows shows signal signal signal simple paper paper size size work work methods fig fig fig fig fig fig fig fig fig cells process level level level current current current current current current current current structure structure problems memory equation equation section section section fixed fixed line speech real states states term activity activity activity activity threshold research dynamics initial constant table table terms terms terms connections node science science direction presented present nodes frequency frequency frequency position continuous continuous abstract computational analog analog analog analog analog analog analog analog analog analog references ieee ieee ieee ieee positive decision decision context circuit circuit circuit circuit circuit circuit effect dynamic dynamic dynamic variable chosen part firing firing firing firing firing firing firing firing type type expected equations chip chip chip chip techniques techniques techniques techniques region length minimum sum performed factor factor made applications applications filter negative vol vol vol vol vol artificial represented application proc proc proc proc perform perform active determined determined determined related power power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger larger larger larger support source source source source source source source morgan implementation implementation synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses technique technique technique code individual individual difficult difficult addition equivalent environment directly directly directly directly estimates design conference full significant significant vision estimated estimated increase give developed developed area area area area area types lines product product provided constraint biological biological tested tested circuits circuits circuits circuits circuits circuits amount common synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse journal vlsi vlsi vlsi vlsi vlsi instance easily kaufmann dynamical unknown fully fully fully fully fully fully fully fully interesting significantly mechanism structures principle operation representing details details details filters direct inhibition inhibition inhibition stored early magnitude magnitude magnitude choose discussed separate reported reported apply array engineering interest conventional smooth address gate gate gate gate gate storage storage storage expression scaling digital digital digital digital digital digital digital spikes move hybrid width generally generally pass greater sigmoid clear encoding integration integration characteristics characteristics characteristics solid pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse relationship groups acknowledgements reference reference reference reference vertical distinct dept dept dept implement implement electrical electrical electrical text implies select letters letters family codes detailed controlled controlled controlled lee modulation modulation modulation modulation modulation modulation forms partial remains initially initially advantages advantages advantages advantages fire silicon silicon silicon silicon inter determines prove uncertainty specifically determining determining paths schemes projections essentially excitation excitation excitation road compact compact conf conf strategies device satisfy michael simplified simplified cmos cmos chips chips chips chips chips chips chips chips chips chips operating operating operating operating routing body circuitry detail replaced oscillator behaviour postsynaptic rise rise fewer giving investigated terminal int transistor transistor transistor transistor transistor transistor transistor authors stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream proved presynaptic presynaptic presynaptic act predicting extremely voltages voltages voltages voltages voltages voltages voltages regime regime motivated charge devices great developing asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous fairly coded multiplication nonlinearity implementing implementing easier easier producing transistors transistors transistors transistors transistors transistors transistors transistors pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses geometry raw robustness summation explained substantially pseudo pseudo lack remove remove variant maintain switch synthesis song song june june june univ univ univ arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic irrelevant analogue analogue feasible oxford oxford amplifier martin arguments count count count count exemplar robotics multipliers multiplier multiplier multiplier multiplier multiplier multiplier saturation smith smith murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray mos mos chemical attractive programmable programmable programmable programmable programmable los hope removing removing integrator integrator integrator synchronous capacitor capacitor capacitor capacitor capacitor capacitor capacitor capacitor capacitor symposium published financial overview buffer consequences nonlinearities eng eng eng layout layout waveforms park ignore receiving receiving insensitive switches benefits die die terminals drain drain drain drain ease constitutes edinburgh edinburgh edinburgh edinburgh edinburgh streams streams streams streams leg capacitance increment packets community crossover altered switched switched switched switched switched switched switched switched parallelism transconductance transconductance transconductance transconductance transconductance transconductance transconductance transconductance transconductance sized electronics electronics tij tij tij tij tij tij tij resistors grateful port oregon architectural architectural functionality council august european hundreds hundreds hundreds hundreds hundreds hundreds firstly supply micro hamilton hamilton hamilton hamilton hamilton hamilton hamilton carrier operational alan inefficient isolation volts predictable leakage sending resultant cox progresses cancel nov minimise minimise decrement signalling volatile topologically emulate clocked occupied implementable desire electrically oxide han han han han han han han han supplies tarassenko tarassenko tarassenko tarassenko tarassenko tarassenko tarassenko telecommunications telecommunications renders portland manifest inspiration regeneration clocks iee vas vas unwanted occupies mosfet mosfet mosfet mosfet esprit sink tsividis tsividis tsividis viability korea detrimental ful reekie reekie reekie reekie reekie reekie counteract arrange unsatisfactory tii hungry incidentally bra buffered attractions iiz admitted regenerate configure mobility 
#@Brownlow_M,Hamilton_A,Han_I,Murray_A,Reekie_H,Tarassenko_L,
#t3
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#*network network network network network model model model model neural neural neural neural neural neural neural input input input input input input input input input input function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set networks output output output output output output number number number number number number number number number system error error state state state state state results results results problem performance performance performance performance based based based weights linear case case case vector vector vector order order order order order shown shown shown systems neurons neurons recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image image large test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns inputs form form shows shows simple simple simple paper paper small work cells classification process current current current current current current current cell cell cell cell cell cell problems random random high high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory architecture architecture equation equation equation equation equation equation fixed fixed fixed fixed images images general general general general approximation obtained note result threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation computation constant constant computer terms node direction direction presented presented present sets maximum maximum range components components nonlinear outputs abstract back find computational convergence analog references due ieee positive procedure mixture hand hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit effect effect dynamic parallel change difference assume lower lower part theorem bound cases cases type good binary binary binary binary expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make fact region region proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length errors errors errors errors scale resulting simulation simulation computed sum sum times times made made feedback negative vol compared compared series proc perform voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage comparison larger connection connection connection source source source source source source institute institute department department implementation implementation implementation implementation implementation consists internal final final bias design design design design design design design effects effects bit bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine efficient speed speed basic basic basic basic weighted randomly product finally iteration iteration depends depends associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative achieved increases increases increases increases increases describe describe tested fast complete stable stable stable circuits circuits circuits circuits circuits circuits circuits circuits implemented implemented generate supported square square square vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi ability ability easily easily simulated simulated simulated simulated smaller hopfield technology technology testing character increasing increasing special special trials mode mode operation call stored bits bits bits bottom combined run improve correlations robust takes sense engineering engineering interest previously approximately approximately match differential address positions gate gate gate gate gate gate gate gate gate storage storage grant horizontal occur trial wide feed hybrid occurs conclusion greater conclusions designed designed performs exponential exponential exponential exponential exponential hard cycle california california proportional proportional program suppose relation optical solving winner vertical recall recall recall recall recall recall electrical electrical scales scales consisting consisting blocks versus select decreases national open open controlled controlled controlled controlled evolution evolution evolution evolution evolution static sign diagram performing expect includes usa currents memories memories memories plotted illustrated reason capable capable capable modes build essentially essentially reached reached reached notice conductance write quantization quantization cmos cmos computes computes computes xor exponentially exponentially exponentially updating mead mead ideal transistor transistor transistor transistor transistor working gates transmission transmission reading illustrate illustrate prototype prototype prototype assumes ith ith integrate asymptotically asymptotically asynchronous multiplication multiplication multiplication multiplication nonlinearity implementing transistors transistors transistors transistors transistors transistors sgn sgn sgn sgn products acknowledgement gradually read arises nsf addressed summation summation summation explained argument apparent pure fed experimentally leave incorporated variant branch branch pasadena wesley cor phenomenon addison forming amplifier summing summing pick branches unity connecting multiplier saturation mos programmable programmable monotonically synchronous carry equals dominant enhance uni specialized properly storing correcting correcting projects ignore goodman goodman goodman goodman goodman goodman ram opposed obtains drain drain drain drain subthreshold subthreshold continues wise switched flip resistors resistors amplifiers port port vice stores stores versa externally nonnegative loaded shot tors char supplied dissertation partly loads archi complement complement enter compromise brought unexpected degrade decoders vdd possesses possesses versity tecture asso icnn successes successes altogether temporarily settled rodney flowing exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation exponentiation replicating vth vth nondecreasing quantize vss vss vss vss vss vss vss vss nmos nmos nmos nmos nmos ciated divider contradictory limiter sociative mip notices acteristic transis 
#@Chiueh_T,Goodman_R,
#t3
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input data data data function function figure figure figure figure figure figure time time time time time time time time time time time time time set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number system system error error error error error error error units units units units problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case shown systems values values values values values noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit distribution pattern pattern pattern pattern pattern pattern pattern pattern point image image image single single processing processing processing processing processing large large local rate patterns patterns patterns patterns patterns patterns inputs inputs inputs inputs inputs shows shows shows signal algorithms algorithms algorithms algorithms simple simple paper paper paper examples examples examples small size size feature net net net net net net net net net work work work step step step step step points process trained trained problems random high memory similar similar section section section images images images images images general general general general generalization real approximation approximation theory gradient obtained term dimensional university university independent log log defined target target table table computer computer computer computer computer computer computer connections connections connections node node node node node node node node node node node node node node node node node node node node node node node node science science left left left left present activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets press outputs outputs outputs outputs outputs outputs outputs abstract applied back back back back back back back back back back back back back back back back back back back back back computational references ieee ieee important important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction behavior dynamic parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel change change difference variable assume assume lower representations learned higher higher previous previous cases required required long distributed make make techniques techniques techniques techniques errors errors forward forward forward forward forward forward forward forward total total total total simulation simulation simulation computed computed computed sum sum sum sum sum sum sum performed performed times times elements made study artificial artificial artificial provide compute compute compute compute compute compute perform active goal connected connected connected connected connected connected connected mit mit mit steps steps steps steps steps steps steps comparison comparison connection connection connection connection connection connection connection connection connection connection update update update update update update update update update update update update update update update update descent nets nets nets nets proceedings report report report department loss implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation consists consists internal joint final layers layers layers layers ai cambridge cambridge equivalent hinton san top bit bit bit bit bit conference efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient requires world speed speed speed basic increase produce produce weighted developed developed developed product product actual actual actual nature discussion discussion discussion technical increases increases increases group group denote amount amount short nearest nearest nearest nearest implemented implemented main main main end end end pixel pixel easily easily easily degree degree rumelhart noisy noisy needed fully fully fully fully block block block block programming character character character character character character special mode operation operation operation operation call max stored stored stored bits international produced run run architectures improve takes takes apply machines machines machines machines machines machines machines pixels subset array highly conventional works solve rl definition grid grid grid grid grid williams occur extended extended feed feed locally touretzky width width loop loop loop loop column hardware pass pass pass pass pass pass runs runs runs critical place row row row greater neighbor neighbor neighbor neighbor cycle intelligence turn user user user characters program reference reference suppose pro solving ways laboratory mathematical dept student implement implement implement implement implement linearly applying shift shift blocks blocks blocks blocks blocks blocks blocks cycles cycles depending communication communication communication communication communication communication communication communication communication communication detailed operations operations operations operations updated translation updates updates updates updates processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor additive convex roughly purpose add add add add add add add interpolation initially topology topology david david david includes inter inter sciences discussions columns columns columns columns columns columns columns straightforward straightforward differ encoded poggio efficiently efficiently essentially summary notice conf link link link link issue return running michael michael backward backward backward backward backward computes processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors processors moves software extend trains explore diego layered layered layered layered access updating updating updating reducing fashion fashion ideas tech links links int ideal ideal ideal ideal ideal ideal ideal momentum implementations implementations implementations implementations adjusted front front front portion store store store explain serial seconds seconds seconds languages guaranteed explanation floating adapted benchmark tool tool shared shared widely widely widely ran products acknowledgement separately beginning members read read read computers computers author sun sun researchers summation summation summation populations fed share share share share remove mod spread spread spread extensions singer adjust sharing cor lab corrupted proportion girosi recover rotated circular circular circular jth jth rotations interconnected arranged communications adjusting simplify odd odd odd odd interconnection familiar arrays repeat repeat repeat repeat recovered recovered zhang zhang zhang zhang zhang zhang studying guarantees intended colorado scan scan interconnections darpa darpa advance recovery omitted layout hypercube speeds speeds propagate propagate instructions mind multiply multiply multiply multiply multiply street corporation corporation corporation ent ber recursively ram presenting july july july copy copy copy copy sigma chapter simd massively massively massively massively massively increment num graduate permits pomerleau march million million million million memo rotating september cube copies copies copies copies copies copies copies copies tom rosenberg fill lists alex accumulate accumulate accumulate accumulate accumulate accumulate parti charles lar tenth replication replication dean gardner rotate rotate rotate rotate rotate rotate rotate lisp lisp lincoln sends sends italy helped helped helped warp warp thinking thinking thinking thinking rightmost conflict george allocate kung waltz waltz waltz waltz waltz waltz shi logarithmically distribute cleaned tomaso mckenna mckenna mckenna mckenna mckenna mckenna registered leftmost patrick waltham corp cray spends brandeis rot vax vax fortran rrr drafts symbolics symbolics accumulator louis federico jill jill rupted facility netwo igure nev lii 
#@Mckenna_M,Mesirov_J,Waltz_D,Zhang_X,
#t3
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number number error error error error error hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance space weights weights weights weights weights layer layer layer layer layer layer layer layer layer case case vector vector vector vector vector vector vector vector order systems systems systems values values values values values values values parameters weight weight neurons neurons neurons neurons unit unit unit unit method approach pattern point point point point single single single single single processing processing processing control control large large large large large local local local local neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate patterns patterns matrix matrix matrix matrix shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper examples small small small size net net net net net work work step step step field field field field field field features level level current problems problems random memory memory memory memory memory memory memory memory memory similar similar architecture architecture section section section section section section fixed vectors vectors vectors vectors vectors vectors vectors vectors general theory theory theory theory theory obtained obtained term term note note activity dimensional dimensional dimensional dimensional result result result result university computation log log log log log found found found sequence computer computer computer computer computer computer computer computer computer computer computer terms connections connections connections connections science phase phase activation activation activation activation activation low machine machine machine sets maximum maximum maximum learn learn learn abstract applied back back back back back back back find find find references due ieee important important important propagation propagation propagation propagation introduction hand effect effect generated parallel parallel parallel parallel parallel parallel parallel cost cost cost cost cost cost change change change assume representations previous type required required required required required required required multiple multiple multiple good binary conditions represent distributed fact errors errors errors errors simulations minimum classes total total total total simulation simulation simulation simulation simulation computed performed performed called called called times times times elements elements elements elements mapping mapping mapping mapping mapping mapping optimization optimization natural global applications applications applications applications obtain original original artificial compared application series provide compute compute rates rates rates rates rates rates rates perform perform perform active equal steps steps larger larger connection connection nets nets words words technique joint represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist layers layers layers layers layers layers addition addition addition addition addition addition addition considered considered considered computing computing hinton solutions bit bit bit bit bit efficient efficient full full requires requires approximate free free free speed speed basic basic derived developed finally finally nature achieved technical arbitrary fast close finding nearest assumed assumed assumed supported require require square square square end easily rumelhart development fit fit smaller smaller smaller smaller account technology block block block block block block block block transfer edge structures mode mode operation operation operation operation operation operation iterations direct direct stored stored stored bits bits bits bits bits bits depth added architectures architectures architectures architectures directions element element element moving moving machines machines machines subset sejnowski array array array array array array array array array array array array array engineering dimensions dimensions dimensions dimensions dimensions compare conventional conventional approximately calculated volume volume volume correspond sparse address address address address williams storage storage storage storage expression extended digital matrices matrices matrices matrices matrices rotation touretzky loop deterministic column column column column column column column column place row row row row row row row row row row row row row row greater reduce conclusions neighbor sigmoid accurate temperature temperature hard cycle cycle cycle intelligence plane plane plane decrease connectivity connectivity annealing annealing annealing annealing annealing annealing denoted denoted acknowledgements boltzmann suppose factors sequential changing electrical text equilibrium equilibrium blocks blocks blocks blocks blocks cycles cycles cycles decreases focus communication communication communication communication operations operations operations operations operations operations operations operations operations operations operations operations operations operations updated fraction sizes completely processor processor processor processor processor processor processor processor processor performing topology topology topology precision precision figures includes activations activations activations activations activations activations activations memories illustrated efficiency efficiency efficiency importance divided modes efficiently computations reached characteristic composed conf conf link anderson split contribution duration built write leading reach processors processors processors processors processors processors processors received overlapping software simpler simpler transformed access involving recursive issues scalar fashion school links links mappings int int stream phases phases phases phases hill integer obvious mapped expressions expressions expressions expressions expressions optimum optimum mentioned costs costs costs expensive multiplication benchmark purposes organized organized worst consequence implicit english computers computers computers computers computers computers computers computers outer summation explained flexible generic simulate frequently execution execution execution execution execution execution execution execution execution execution execution operate operate instruction instruction instruction cor lot indices perfectly perfectly rotated grows rotations rotations interconnected interconnected arranged clamped clamped clamped interconnection interconnection interconnection loops loops synchronous adequate adequate adequate arrays arrays arrays arrays arrays arrays clock clock clock substituting substituting overview scheduling peterson peterson hypercube partitioned partitioned propagate instructions instructions instructions material accumulated dense multiply multiply multiply multiply multiply shading planes propagating propagating exception exception decomposed decomposed simd simd simd simd simd simd simd simd simd simd simd simd simd simd simulating massively massively modifying grouped learnt execute execute execute allocated pomerleau parallelism worth option million register register west accounted sweeps commercial exploited increments demonstrating accumulation fortunately rosenberg rosenberg thousand savings outperformed val accumulate accumulate accumulate dedicated attained inefficient proves icl nettalk nettalk nettalk mcgraw addressing doubling doubling neglected mesh mesh mesh massive ues costly jose bodies spent spent spent spent spent spent pes pes pes pes pes pes pes pes pes pes broadcast broadcast broadcast broadcast broadcast broadcast broadcast remarkably mft mft mft mft mft mft mft mft mft mft mft mft mft mft recursire mention warp favorable ting ministry hwang aii subclass kung lock qualities tha simplistic purdue operands operands fernando concludes quadratically additions spend simi wrap eli education efficiencies efficiencies adder buses complez complez parison pipelined 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#@Fortes_J,Nunez_F,
#t3
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time networks networks networks networks networks networks algorithm algorithm number number number number number number number number system system results information problem problem problem problem problem models performance performance performance performance performance performance performance performance performance performance performance performance performance space linear shown systems systems systems systems unit approach approach approach approach approach approach approach approach approach approach approach single single single single processing processing processing processing large large neuron neuron neuron neuron neuron rate analysis class inputs form shows algorithms algorithms algorithms simple simple paper net net net task task task task task process process process process level level structure problems high memory memory memory memory memory similar similar architecture architecture architecture architecture architecture architecture fixed general general general general average obtained note note activity result result result result result result threshold threshold computation computation computation computation computation computation computation computation computation computation computation computation computation computation research independent initial initial constant standard standard standard computer computer computer computer connections connections connections connections science science science map map phase phase low machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine maximum maximum maximum press abstract computational references stochastic stochastic due ieee effect parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel cost cost cost cost cost cost cost complexity prior higher part required good good long conditions represent represent represent represent distributed length length scale finite simulations simulations simulations minimum minimum total simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation performed performed times times times elements elements elements mapping mapping potential made made natural global applications study study specific location active determined power approaches mit mit mit mit mit mit mit mit mit steps larger connection connection nets nets morgan morgan proceedings proceedings proceedings report report department implementation advances represents represents represents connectionist delay addition graph cambridge cambridge cambridge cambridge equivalent directly additional additional view view limit san san san effects conference conference requires world speed estimated estimated estimated increase developed developed path path path path path path product actual provided simply associative achieved achieved technical technical increases describe group group group fast close corresponds corresponds corresponds amount amount amount amount amount amount amount effective effective require require vlsi vlsi ability ability instance makes kaufmann kaufmann simulated needed programming programming programming programming interesting significantly special structures structures matching matching matching empirical operation operation operation operation language representing representing representing stored international international early combined run run architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures separate practical subject machines machines machines array recently engineering compare conventional tuning axis axis match match match match address gate organization improvement increased constructed horizontal alternative touretzky width white occurs hardware hardware hardware hardware hardware hardware critical critical critical critical critical reduce conclusions peak peak peak performs mateo mateo mechanisms mechanisms external cycle cycle cycle cycle assuming exist iii iii manner manner program program program program reference produces written optical ways sequential laboratory laboratory laboratory laboratory laboratory vertical explicitly simultaneously simultaneously infinite physical electrical slightly develop cycles review communication communication solved operations operations activities processor processor processor processor processor processor processor processor processor processor processor processor processor processor reasonable calculation delays expansion purpose generation advantages transactions transactions figures figures thesis illustrated prove discuss black absolute regular determining straightforward suitable driven included computations computations computations computations computations computations computations computations computations fine fine fine graphs graphs graphs graphs allowing split split split device built list realistic providing board delayed cmos cmos automatically processors processors processors processors processors illustrates diego powerful xor xor xor xor xor xor xor xor environments optimized optimized optimized examine fashion history school ideal ideal ideal ideal ideal dependencies encode phases possibly extremely illustrate implementations implementations implementations prototype observe store switching utility phd electronic years devices devices languages languages great asynchronous asynchronous asynchronous costs costs coded tool reasons widely division projected calculations optimize requiring limits profile profile profile profile profile profile profile profile profile substantially cmu flexible flexible flexible flexible flexible flexible flexible conducted effort effort peaks passed passed dots dots schematic schematic schematic execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution price switch gains instruction instruction instruction instruction instruction instruction instruction instruction incoming achieves simulator inherent returns eventually synchronization synchronization synchronization initialization initialization benefit sleep fabricated japan proceed proceeds proceeds interconnection programmable check arrays alspector alspector excellent excellent programs programs programs programs encountered darpa darpa darpa tokens tokens tokens specialized specialized specialized specialized specialized offer offer offer arrive partitioned instructions executed executed executed executed executed treat boxes linked summer corporation latency latency latency latency ram benefits abstraction profiles ease hundred hundred massively massively shaded queue queue ibm blocking continues token token token token token token token token token token token token token token token token token token token token token token pomerleau pomerleau overhead overhead overhead overhead overhead parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism exceed increasingly selectively termed million million million alternatives packet interconnect interconnect memo things treating technologies appearing allen justified impractical attributed attributed spacing micro exposed executing executing executing attained enhances thing bottleneck transaction transaction translates manual ira aggregate drawbacks lincoln lincoln tailored tag wait wait wait wait enabled waiting scheduled scheduled scheduled warp warp billion gun latencies gupta specifications executes bearing requests grain grain grain grain kung expressing wafer fifty fifty throughput occuring mips mips mips mips requested manage spend dyadic masking hammerstrom hammerstrom hammerstrom hammerstrom lexington tagged tagged tagged tagged tagged tagged tagged tagged tagged tagged tagged tagged tagged tagged initializations efficiencies remedy microchip elapsed eleven supercomputer supercomputer methodologies hillis hillis interpreter compensates engines engines compiled barriers fortran busy analogs operand operand operand operand expose motorola simulators mbytes supercomputers surpass surpass touretsky mflops mflops idle idle waits waits multiprocessor attributable ibaraki alu interleave executable compilation shai enumerated 
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probability probability probability probability probability probability noise weight functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit recognition recognition recognition method approach approach pattern pattern pattern pattern pattern pattern pattern point point single single processing processing processing processing control control control control large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis matrix matrix matrix matrix matrix optimal form form form form form form form shows signal signal simple simple simple simple paper paper paper paper feature feature work work work work work work work work work work work work work work work work work work work work task fig fig fig fig fig fig cells cells step field classification level current current current current trained trained cell cell cell cell cell structure problems problems random random high memory memory memory memory memory memory memory memory memory memory response response similar similar similar similar representation representation representation representation representation representation architecture show show equation equation equation equation equation fixed rule general general general real real real real approximation average states states states states theory theory theory theory theory theory theory theory theory theory theory theory theory theory gradient obtained obtained term note note activity activity activity activity activity activity activity activity activity result result university university university university university university threshold threshold variables variables computation computation solution solution solution research research research research research research research independent independent log log log found dynamics initial constant constant constant computer computer computer computer computer computer terms terms terms connections connections connections synaptic synaptic synaptic synaptic science science left direction direction direction present activation activation activation activation activation temporal machine machine object sets sets motion motion range range range press press press press press press press press learn learn components outputs outputs outputs abstract computational convergence convergence convergence analog analog analog analog analog properties properties properties properties properties properties properties properties properties references component procedure procedure adaptive adaptive propagation propagation mixture introduction introduction introduction action action circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical statistical statistical effect effect effect effect effect generated generated parallel parallel parallel parallel parallel parallel parallel search energy difference complexity variable measure signals part part theorem bound firing firing firing firing firing firing required required cortex good binary binary binary long long long long represent distributed distributed distributed distributed distributed distributed distributed distributed equations equations equations make make make region proposed proposed probabilities probabilities probabilities scale scale scale finite finite simulations classes tasks tasks tasks total simulation simulation computed respect called times times times elements elements elements elements elements elements elements elements elements elements regions regions regions regions regions regions regions made made made made made feedback feedback applications study study filter filter filter filter filter negative original original original original artificial specific samples represented true desired series provide define compute proc proc perform perform perform goal related connected connected connected connected connected connected connected motor motor motor motor brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain equal mit mit mit mit voltage connection support support descent nets nets institute words department department version version version synapses synapses consists consists consists consists individual final exp scheme scheme scheme scheme scheme scheme scheme addition framework cambridge cambridge cambridge cambridge computing computing domain domain equivalent equivalent equivalent additional solutions design stimuli stimuli effects bit bit bit detection choice significant free free con con produce condition condition coding weighted randomly randomly randomly conditional conditional conditional conditional conditional conditional developed lines provided provided provided provided provided processes selected backpropagation nature nature nature simply associative associative associative achieved achieved achieved measured measured increases increases group group transformation close corresponds stable stable proof circuits circuits circuits short common effective implemented implemented implemented implemented assumed synapse generate theoretical eds eds hypothesis hypothesis development noisy noisy sensory sensory sensory simulated probabilistic probabilistic pairs underlying hopfield reduced account account functional functional functional coefficients coefficients block interesting york york york york increasing increasing mechanism representing details details call making stored stored stored supervised depth depth depth depth early early early early early early early early early early early early early early early early combined minimize produced predict perceptron perceptron perceptron perceptron perceptron denotes denotes membrane takes element element element element element element element similarity introduced introduced introduced introduced introduced introduced introduced introduced period period machines array cognitive recently unsupervised approximately volume works solve smooth studies studies studies differential differential differential achieve trans trans diagonal positions chain symmetric symmetric observation observation channels organization organization organization organization organization organization storage sensitive entire grant constructed expression expression studied suggests extended feed deterministic white generally critical greater conclusions conclusions central central sigmoid designed clear exponential exponential learns learns learns encoding propose mechanisms mechanisms mechanisms presence external external demonstrated demonstrated proportional decrease averaged averaged introduce groups connectivity force force base acknowledgements areas suppose written written longer perception winner winner ways ways describes transitions mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical changing student implement implement implement implement implement multilayer physical physical electrical electrical electrical text consisting mutual equilibrium events events springer implies blocks potentials john yield expressed communication communication communication communication communication communication communication codes codes solved solved solved detailed open operations operations fraction fraction showed evolution centers activities suggested suggested constants discrimination past partial earlier delays event event event event purpose purpose closed initially calculate foundation eeg coupling coupling fire perceptual thesis perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons bell bell assignment assignment extension activated activated activated activated activated activated activated specifically black neighbors structural major reason reason reason aspects aspects extra capable capable modification computationally symbols wij wij wij wij wij wij wij wij committee committee committee presentation efficiently computations computations tend characteristic characteristic excitation excitation soc soc soc conf verlag repeated repeated strongly decoding contained showing conductance superior issue symmetry classify oscillations content gray built built receptor receptor receptor comp quantity involved localization localization simplified simplified realistic realistic realistic correspondence hypotheses received principles principles moves subsequent subsequent operating extend cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan carried carried wiley wiley collection exhibit exhibit exhibit put put involving detail association mass mass mass existence existence existence fashion fashion fashion history ideas ideas ideas ideas tech tech rest investigated biol biol biol int fault fault fault possibility transistor transistor transistor office referred reliable reliable reliable reliable working eigenvectors complicated complicated proved proved proved notion analogous analogous analogous math math math transmission concepts concepts plausible plausible plausible configurations man man opposite opposite automata automata automata automata rev rev created thought adjusted impulse portion formal formal noted noted noted noted logistic logistic taylor taylor taylor taylor taylor taylor taylor taylor taylor taylor taylor taylor taylor taylor taylor mapped perceptton nerve logic logic logic logic logic logic logic nervous nervous nervous nervous nervous nervous hebb hebb hebb hebb hebb hebb hebb ith ith ith message message message switching generates motivated serial averages established established integrate animal animal years years years years devices devices devices spin spin spin spin spin spin analyzed biology explanation explanation majority majority majority majority answer glass tractable lies lies correction london london london london reasons reasons style filtered forces pulses mathematics consequence universal universal calculations beginning beginning patches patches computers computers bandwidth geometry cybernetics cybernetics cybernetics cybernetics cybernetics mechanics mechanics mechanics fourth apparent limits pure led led lattice lattice lattice lattice lattice detecting formulated formulated sharp biologically reliability reliability reliability psychological switch berlin synthesis limiting differs fall incoming incoming ordered hamming hamming logical logical logical logical logical logical logical logical logical logical logical logical logical logical logical logical logical semi kinds age redundancy redundancy redundancy redundancy physiol tolerance tolerance tolerance implements damage damage patients conditioning conditioning conditioning eventually credit credit credit univ univ univ arithmetic cor proofs college redundant proportion accomplished equivalence forming formally gabor gabor gabor gabor princeton princeton nat count count neurophysiol jth naval receptors receptors arrival turned spontaneous wrong chance analogy analogy analogy height loops abilities neurobiology operates receiver imply synchronous preparation exceeds exceeds arrays planar days days days days days days days days days reliably reliably reliably tap published financial weakly recovered programs regarded von von von von von von von von von von von mental washington evident evident demonstration demonstration widrow widrow percepttons propagated assembly assembly counter counter counter waves specialized cerebral insight record matter late late contact roy roy correcting correcting correcting designing papers interestingly switches switches switches switches switches switches executed assigning lag onr mind mind mind mind mind mind mind associations neurophysiology outline rigorous pointing validity transmitted cooperative job job die magnetic magnetic magnetic magnetic smoothly year year year perceived personal personal classic chicago chicago chicago chicago chicago chicago chicago chicago chicago associate associate associate certainty reflected algebraic peripheral publication deep shannon shannon shannon pdp pdp mathematically execute elementary elementary efforts paired books argued confirmed synchronized lond lond topic topic paris sheet assemblies assemblies assemblies assemblies isi barlow barlow confusion book book book happen happen rotating algebra investigations investigations investigations investigations thousands modifiable modifiable modifiable modifiable modifiable permit nal things things tissue tissue tissue differing differing differing differing differing article failures continually unpublished mann worked students triggered triggered triggered triggered rewritten persistent persistent persistent rats lecture lecture mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch mcculloch laws laws remarkable remarkable neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann stimulating survey twenty traveling pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts pitts continued marks subjective impulses inhibit inhibit jersey ave virtually spins spins spins spins spins russell illinois connects returned proposal excited continuum continuum unreliable unreliable agency devised meeting kirkpatrick fox hamiltonian clark clark comprising comprising comprising comprising governing governing contacts colleagues convention implied minsky minsky minsky reproduced reproduced reproduced reproduced reproduced era era longest materials materials materials semantics modern shortly shortly syst syst hoff hoff wires began terminology developments comprehensive neurones damping sherrington wiener wiener wiener wiener wiener wiener elaborate elaborate spent gij biophysics attracted hysteresis hysteresis excite phil organisation thalamus regional excitable respects psych rigorously encourage conversations neurodynamics neurodynamics neurodynamics neurodynamics neurodynamics neurodynamics neurodynamics leaky quiescent quiescent comprises claims sought damaged damaged damaged atoms atoms atoms atoms atoms begun controllable remember thinking thinking workers calculus calculus calculus suggestion suggestion suggestion machinery rosenblatt rosenblatt rosenblatt rosenblatt rosenblatt biophys biophys clin syrup organisms bull bull bull theor multiplexing multiplexing taps wji walter walter executes functioning ire thalamic historical ferromagnetic psy lowering densely propositions propositions jackson jackson ghost organism vation skew skew papert papert papert papert acti volt organize story nected synchronously triggers multiplexed arrived emitter adaline publications eij postulate distribute ubiquitous debate focussed speak unary unary heaviside opened disordered disordered philosophy antecedent analogies analogies analogies hermitian symp modem modem vth vth vth propositional documented nand nand nand nand neurological pursue liquid liquid grandmother grandmother reprinted triggering spartan evidently wished creases garcia garcia famous navy appreciated appreciated elaborated requisite agencies warren pergamon tending tending tending stations wescon fifteen joined sensation nar cajal exert influential biosci pla conjectured technological slab paperr achievement invented invented clarified dyi complexes signaled signaled happened happened quantal equivalents emitting mildly lexp premature polytechnic embodiment embodiment supposedly fer stitute quest shades elicits multiplex congruence imperial chology deduction necess compounded computability weren immanent 
#@Cowan_J,
#t3
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#*network model model model model model model model model model model model model neural figure figure figure figure figure figure figure figure figure figure figure figure time time time set number number number number number system results results results problem models case case shown shown shown values weight weight weight neurons neurons neurons distribution distribution distribution control control control control large large large local local neuron neuron neuron neuron neuron rate matrix form form form form shows shows shows shows shows shows shows shows shows visual paper paper paper paper paper net work fig cells cells cells cells cells process current cell cell cell cell structure random similar show show fixed fixed line line general real average term note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments activity activity activity activity dimensional result result result result result university university solution research research found found found found found found target dynamics constant constant constant computer terms connections synaptic science science science left left left map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map abstract computational computational analog properties references due important important introduction introduction effect generated generated tion complexity spatial rules part previous previous previous previous previous previous previous cases conditions equations make make make fact techniques techniques observed observed simulations simulations simulations simulations resulting resulting resulting ing total total total simulation simulation simulation simulation simulation simulation simulation simulation simulation sum called elements means factor factor made made orientation specific specific represented represented series provide provide proc eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined distributions brain brain brain brain brain brain brain brain brain brain brain brain equal support dependent morgan proceedings proceedings institute department synapses synapses synapses synapses synapses advances represents represents represents exp exp exp exp addition addition ai maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment top stage effects effects effects effects effects effects effects determine choice produce area evidence evidence nature nature nature nature nature inhibitory depends normal normal normal normal normal normal normal normal normal increases describe describe surface surface circuits amount amount amount nearest nearest synapse synapse role square end development development development development development development development kaufmann simulated coefficients coefficients mechanism consistent consistent details details details details details details details details details early early decay produced produced produced denotes recent lateral introduced recently relevant observations observations smooth studies studies studies studies studies differential diagonal positions entire entire occur occur matrices rotation correctly correctly touretzky occurs half half half half half half half half half half half half half half strength strength conclusions central interactions interactions measures retina retina retina retina retina constrained strong presence proportional proportional turn exist exist decrease acknowledgements areas suppose suppose suppose winner mathematical involves involves remaining text text interaction develop develop mutual formed potentials formation formation formation formation formation formation formation dependence stages squares influence controlled organizing fraction showed forms forms forms allowed allowed key partial expansion expansion expansion neighborhood initially foundation existing combinations retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal specifically neighbors neighbors neighbors neighbors compression compression compression compression compression compression compression capable committee successful projections tend tend summary refer soc interpreted cues receptor receptor receptor comp play nips nips reach neurosci neurosci subsequent subsequent neighboring intrinsic oriented oriented cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan carried carried carried carried involving detail strengths biol biol biol plasticity plasticity possibility relationships referred complicated complicated surfaces surfaces removed removed induction induction patch coefficient coefficient eyes friedman friedman friedman friedman friedman friedman friedman friedman precise nerve nerve nerve nerve nerve nerve hebb ith ith ith ith fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers generates years years years years years growth growth growth explanation ganglion ganglion considerable considerable purposes sections sites incorporate immediately mathematics cut cut cut axons res patches patches geometric apparent pathways understood embedded simulate sharp release measuring modulated incoming incoming incoming incoming incoming parent extensions display fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber physiol eventually eventually univ instantaneous sort forming forming labelled labelled controlling neurophysiol jth jth jth jth connecting wrong neurobiology imply optic optic optic optic optic optic modifications eqn eqn repeat published edelman edelman expanded expanded expanded expanded expanded expanded expanded topological evident demonstration fish fish occlusion express axonal gaze gaze gaze gaze gaze specificity contact contact contact contact contact contact contact roy subsequently discovered intersection material material material displacement outlined outlined compressed compressed compressed compressed compressed compressed compressed leaving leaving smoothly year lesions tendency tendency tendency classic chicago chicago chicago possibilities possibilities molecular molecular molecular illustration mismatch mismatch mismatch mismatch mismatch mismatch mismatch mismatch acting peripheral preserved lobe permits interacting expand retinotopic plate confirmed lond lond cij cij cij cij cij cij cij cij attached attached molecules molecules molecules molecules tissue differing species species species reversal reversed reversed ave lated establishes tectum tectum tectum contralateral kth illinois polarity polarity polarity neurol neurol ooo markers markers markers markers markers markers markers markers markers markers markers markers markers markers markers carries sij sij sij sij sij sij sij sij sij sij intact intact contacts contacts contacts positional schmidt schmidt schmidt schmidt schmidt schmidt schmidt schmidt schmidt schmidt electrophysiological occluded stick stick stick stick stick inappropriate inappropriate supposed supposed aggregate terminology terminology amer depolarization frog noticed tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal tectal expresses attracted dominate manipulations edwards mediate comprises ago ago ago postulated postulated postulated subtract occupied disappear membranes exclude cooke cooke meyer meyer meyer meyer meyer meyer meyer meyer meyer meyer meyer reproducing fragment plex compound possi fifty neurotransmitter occupy tab tab disappears cited bilities presumed 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#@Cowen_J,Friedman_A,
#t4
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#*network network network network network network network network network network network learning model model model model model model model model model model model model model model neural neural input input input input input input input input function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time set set set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm number number number system system state state state state state state state state results units units units units units units units units based based space space space space space space space space space space layer layer layer layer layer layer layer layer case case vector vector vector vector vector vector order shown shown shown shown shown shown values values values values values values values probability probability parameters parameters functions neurons neurons unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution method pattern pattern pattern pattern pattern point image single large large large large large large large patterns patterns patterns patterns patterns form form shows shows shows visual visual visual visual visual visual visual visual visual visual visual small small small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells step field field field field field field field field field features features features features features features features features features features features features features features features features process structure structure structure structure structure structure structure structure structure structure random random high high high high memory response response response representation representation representation representation representation representation representation equation section fixed rule vectors vectors vectors vectors vectors vectors images parameter note activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university threshold threshold threshold research independent independent defined computer distance distance distance distance science science science left left left left map map map map map map map map map map map map map map map map map map map map map map present machine range position position position position position components components components continuous abstract properties properties properties properties properties properties properties properties properties references positive positive positive positive introduction stimulus stimulus stimulus stimulus stimulus generated generated variance parallel parallel parallel change change variable variable variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial rules representations chosen chosen part center center center center center center center previous previous multiple multiple cortex cortex cortex conditions fact region region length observed scale simulations minimum simulation eq times regions regions regions regions regions regions regions mapping mapping mapping mapping mapping mapping dimension dimension dimension dimension dimension dimension made made natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation applications study study study study study negative negative negative negative represented represented represented represented represented receptive receptive receptive receptive receptive receptive receptive receptive define proc proc proc location location location eye eye eye experimental constraints connected distributions cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical equal approaches comparison larger larger larger larger larger larger larger connection dependent institute institute joint final exp exp exp exp exp exp exp exp exp addition maps maps maps maps maps maps maps maps maps maps maps maps maps maps domain additional view stimuli effects determine determine full coding derived derived area area lines lines selected selected evidence nature nature nature associative achieved describe describe describe describe describe denote denote denote corresponds corresponds corresponds corresponds complete stable surface surface surface surface generate supported supported role role square square square pixel pixel development development development development development development development fit smaller smaller functional projection york edge increasing structures structures mode mode leads representing details max magnitude description denotes improve correlations correlations advantage separate ensemble ensemble similarity similarity similarity include subject hierarchical hierarchical hierarchical hierarchical hierarchical dimensions highly highly tions smooth smooth rl locations locations locations interval organization grant amplitude amplitude amplitude amplitude matrices white white white boundary column column demonstrate demonstrate half numerical strong largest exist selective selective selective selective selective min min plane plane groups groups acknowledgements explicit relation longer primary primary primary primary primary describes describes stability tuned coordinates coordinates simultaneously dimensionality angle equilibrium springer formed national national national formation formation formation formation stationary stationary stationary stationary stationary stationary stationary correlated influence variation variation organizing organizing organizing ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular approximations centers centers centers centers forms completely completely neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood iterative valid visible foundation foundation euclidean kohonen kohonen kohonen topology topology avoid combinations combinations combinations combinations combinations combinations combinations combinations coordinate usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance eigenvalues eigenvalues eigenvalues retinal black black neighbors characterized characterized characterized characterized characterized characterized characterized characterized characterized columns aspects divided driven modes modes modes modes modes modes orthogonal soc strongly interpreted interpreted interpreted interpreted dis contribution sin manifold manifold manifold sci gray gray comp relaxation dot absence wave wave wave neurosci neurosci principles preferred preferred preferred preferred preferred modelling extend origin origin selectivity relations relations relations relations preliminary periodic rise rise reducing reducing reducing reducing fourier fourier fourier fourier fashion giving investigated biol biol biol int authors hierarchy hierarchy hierarchy topographic topographic topographic topographic topographic topographic phases patch gradients closest plausible equally perfect changed eyes quantities quantities quantities der separated generates generates extent extent regime submitted preference preference preference preference preference cos cos derivation variances unstable unstable unstable caused drive rapid ring ring ring located located located located consequence consequence ion ion acad describing calculations patches fluctuations fluctuations fluctuations fluctuations fluctuations argument varies percent lattice lattice lattice marked dots biologically requirement requirement pittsburgh ture ordered qualitatively qualitatively shaped deviations tile displays displays displays realized shifted spectra spectra uncorrelated cybern cybern cybern secondary secondary secondary secondary secondary secondary tation repre arranged plays plays suppression binocular binocular binocular bower mark preparation natl published financial pat von infinity reproduce specialized specificity proximity proximity eqs explains interestingly lag ure ure ence schulten schulten schulten schulten schulten numerous wiesel nelson preserving preserving preserving isotropic isotropic willshaw medium amplitudes ical malsburg tendency hubel hubel reflected brightness brightness monocular monocular preserved preserved translated magnitudes concentrate lond topic represen sheet breaks figs figs universit fea obermayer obermayer obermayer obermayer obermayer obermayer port durbin round ritter ritter ritter ritter correlate species expense preserves distortions autocorrelation autocorrelation prefer vis hat developmental developmental stripes illinois illinois wavelength neurol preservation functionally functionally planck compromise compromise sentation translates denominator goodhill urbana urbana urbana diverge repetitive repetitive technische approxima proce proce icann devel blasdel blasdel pri ative froin beckman beckman ant fokker exclude mitchison ions mary mary helsinki charac govern oft tha resembling champaign mexican sharper ori bet bet dure kybernetik ffi swindale swindale neg enlarged crucially prespecified supercomputer scholarship bielefeld bielefeld subcortical retino vet continous continous continous tins pla diagonalized ull grinvald fonds supercomputing import fluctuate fluctuate eccentricity iei ffl anticorrelated salama aln vhich 
#@Obermayer_K,Ritter_H,Schulten_K,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input function function function function function function function function function function set set networks networks networks algorithm number system system system state state results results results results results results results information models models models models models models based based layer layer layer layer layer layer order order order order order order shown shown shown systems values values parameters parameters noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single single single processing large local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns form shows shows shows shows signal simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small small size size fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells points field field process cell cell cell cell cell cell cell cell cell high response response response response response similar similar architecture equation section average theory theory theory obtained obtained obtained obtained obtained obtained obtained experiments experiments activity activity activity activity activity activity activity activity variables research research initial initial constant computer computer computer computer computer distance connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left left left left left left left left left presented presented phase phase low low press position position basis abstract density properties properties references due positive introduction complex complex complex behavior behavior behavior stimulus stimulus effect parallel difference difference spatial spatial spatial spatial spatial spatial spatial assume center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center firing type type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex conditions tree tree distributed fact fact fact region proposed proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length length length observed observed observed simulations simulations simulations simulations simulations simulations simulation simulation simulation simulation simulation simulation respect performed performed means orientation orientation orientation orientation study filter obtain obtain negative negative specific represented represented receptive receptive receptive receptive proc active active eye eye eye experimental experimental related related connected connected distributions distributions distributions distributions cortical cortical cortical cortical cortical cortical steps steps comparison contrast contrast contrast connection fields fields dependent modeling morgan synapses advances represents represents represents final exp addition addition maps maps considered considered considered considered framework computing directly view transition san stimuli stimuli stimuli determine free condition types types types types types types finally inhibitory inhibitory achieved achieved normal group fast assumption corresponds excitatory excitatory effective assumed assumed assumed assumed assumed theoretical square square square development development development development development development development development development kaufmann simulated simulated simulated simulated smaller smaller account account account functional consistent structures structures structures structures leads inhibition bottom magnitude produced added description light predict neuronal neuronal recent takes typical reported lateral lateral lateral machines compare previously previously observations axis correspond rl rl trans positions positions observation grid grid grid organization organization organization organization organization organization increased suggests deviation touretzky white white boundary generally column pass pass pass conclusion conclusion row interactions interactions differences differences retina retina retina retina retina retina retina peak peak peak peak exponential mateo temperature temperature taking strong strong radial denoted areas appears appears monte van van van carlo edges winner primary primary primary primary primary primary describes describes mathematical mathematical distinct spectral consisting interaction interaction interaction interaction interaction interaction interaction interaction interaction equilibrium equilibrium implies competition competition formation formation formation formation formation formation correlated correlated overlap ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular showed showed understanding performing roughly filtering assigned degrees avoid figures figures usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance formulation formulation formulation color retinal determines discuss discuss discuss specifically domains domains domains black phys discussions simplicity columns columns columns middle middle identified closely closely differ included projections projections projections soc strongly anderson anderson anderson physiological sci comp surround surround surround surround surround correspondence cat cat cat cat cat neurosci neurosci decreasing stimulation stimulation stimulation selectivity carried carried carried carried exhibit experience project terminal terminal biol plasticity lgn lgn lgn lgn lgn lgn pathway pathway fundamental eyes eyes eyes singular panel panel panel observe separated fibers extent spin spin spin spin histogram trivial convolution analyzed ganglion comparisons spatially spatially straight widely nucleus nucleus monkey monkey afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent laboratories recognized separately separately acad calculations axons axons axons axons patches patches bandwidth bandwidth bandwidth bandwidth bandwidth author argument greatly profile profile pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways red red red red red red red red red treated treated treated calculating spread modulated modulated ordered ordered ordered green green green green green green green green green conclude fiber decreased physiol displays realized representative cybern japan narrow bin bin bin bin binocular binocular binocular binocular binocular binocular consideration anatomical striate striate serves bands monotonically natl analyses irregular irregular irregular irregular irregular regard dominant dominant dominant injection evident evident histograms histograms histograms histograms histograms monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys arrangement axonal reveals agree agree broken border adopted adopted balanced corporation wiesel wiesel wiesel wiesel wiesel wiesel wiesel cooperative revealed revealed terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals profiles tendency descriptions hubel hubel hubel hubel hubel hubel hubel monocular monocular monocular monocular monocular monocular trends segregation thermodynamic thermodynamic mathematically retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic lond harder amino superposition figs figs preserve responding supports geniculate nec arbors photoreceptors attributed send rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs opponent opponent tanaka tanaka tanaka tanaka tanaka tanaka tanaka tanaka tanaka tanaka tanaka stripes reflecting spins periodicity physiologically sharply wavelength neurol coincide hamiltonian grids grids acid reproduced reproduced counterpart counterpart electrophysiological electrophysiological electrophysiological vicinity metropolis metropolis metropolis emerged potts potts potts potts firings resemble cats cats cats cats cats cats cats cats cats cats cats transferred borders terminate fluctuation fluctuation fight fight fight fluctuating retinas retinas retinas retinas retinas retinas retinas retinas stripe synapfic synapfic lacking responsive originating visualize visualized acknowledgment looked segregated segregated segregated segregated ocularity ocularity ocularity ocularity ocularity ocularity ocularity ocularity ocularity ocularity ocularity ocularity ocularity ocularity ocularity 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#@Tanaka_S,
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#*network model model model model neural neural neural data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure networks networks number number system results results results models models models models models models models models models models models based space space weights linear vector vector vector shown shown shown shown shown shown systems unit distribution pattern pattern pattern pattern pattern large large rate patterns class form form form shows shows simple simple simple simple simple simple simple visual visual visual work work work methods features features cell cell structure similar similar similar show equation equation equation gradient gradient obtained note dimensional dimensional dimensional dimensional result result university university computation research research independent found dynamics initial constant science science left map map map maximum range range range range press abstract find find properties properties references introduction statistical change change energy energy energy energy energy part type cortex cortex cortex long long long long long long conditions represent equations equations equations fact proposed length length observed resulting regions regions regions regions regions orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study represented proc proc eye eye eye eye determined brain brain support institute institute institute department represents exp exp considered equivalent nature nature denote nearest generate generate theoretical development simulated simulated simulated simulated dynamical dynamical details details details max light recent recent recent introduced varying correspond correspond differential amplitude occur occur runs conclusions operator operator neighbor interactions interactions interactions interactions interactions moody moody physics physics plane relationship configuration configuration annealing annealing annealing annealing acknowledgements reference monte carlo plot changing changing changing easy springer formation correlated variation restricted ocular ocular ocular ocular ocular ocular evolution constants partial classical classical classical classical neighborhood foundation dominance dominance dominance dominance dominance dominance retinal recognize structural structural columns columns columns columns columns wij wij wij wij wij wij wij wij wij wij committee miller miller characteristic characteristic soc soc symmetry write minimizes minimizes cat cat cowan cowan cowan biol biol workshop smallest opposite eyes eyes singular singular singular friedman friedman friedman obvious academic ith fibers fibers fibers years spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin cos orientations orientations orientations orientations orientations orientations located mathematics recognized patches patches patches patches patches patches patches patches linsker linsker depicted dark lattice lattice lattice lattice lattice continuously continuously ordered univ discontinuities cybern cybern primate primate grow neurobiology published slice slice slice evident counter reproduce roy roy santa schulten schulten numerous alternating smoothly smoothly malsburg malsburg malsburg malsburg chicago chicago chicago breaking letting shaded iso iso iso iso iso iso iso singularities lond lond employing preprint preprint algebra drops durbin durbin differing differing increments dim hat hat hat ave tanaka tanaka spins spins spins illinois wavelength kirkpatrick kirkpatrick hamiltonian hamiltonian hamiltonian systematically materials rotate stryker stryker clockwise clockwise hirsch hirsch blasdel blasdel reproduces exhibiting mitchison mitchison singularity glasses ising keller keller mexican mexican mexican vecchi vecchi pnas disordered swindale swindale swindale swindale swindale swindale gelatt gelatt hamiltonjan barbara evidently hod hod hod hod hod hod hod hod physicists physicists physicists lectures stretches stretches treatments salama salama 
#@Cowen_J,Friedman_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input function function function figure figure figure figure time time time time time time time time time time time time time time time time time set networks networks training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output system error error results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden weights weights layer case order systems neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit pattern pattern image image processing processing control control control rate rate patterns analysis analysis optimal inputs inputs inputs inputs inputs inputs form signal signal signal signal signal visual visual visual examples net net net work work work fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig features process level level level trained trained trained trained random high high high response response response response response response response response similar architecture architecture architecture fixed fixed real activity result university research constant constant constant constant constant constant constant constant constant constant constant connections connections connections connections connections connections connections connections connections left left left left left left left presented presented phase phase phase low low low low low low low low low press nonlinear nonlinear nonlinear outputs outputs abstract back back back back properties properties references positive propagation propagation propagation complex behavior dynamic parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent lower lower lower signals signals signals signals learned learned higher higher higher higher firing firing firing long long long represent represent represent expected region observed observed ing sum sum times times times feedback feedback feedback feedback global study filter relative desired desired desired desired desired compute rates rates rates eye eye eye eye eye eye eye eye eye motor brain equal equal equal comparison larger larger larger contrast modeling modeling department loss synapses synapses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses exp delay directly effects increase con con con produce produce produce produce produce weighted developed developed levels velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity actual actual actual actual actual evidence inhibitory inhibitory inhibitory inhibitory inhibitory normal increases increases complete excitatory amount short supported sensory pairs pairs underlying account fully transfer york increasing head head head head head head head head mechanism operation direct direct inhibition inhibition inhibition inhibition inhibition inhibition bottom decay decay decay decay decay decay directions movement lateral lateral lateral lateral lateral lateral lateral introduced tions tions tions match correspond symmetric modified williams williams organization organization organization organization storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage amplitude amplitude amplitude amplitude amplitude amplitude horizontal horizontal horizontal horizontal horizontal horizontal occur suggests suggests rotation move pass pass pass pass conclusions retina peak faster faster constrained strong strong mechanisms mechanisms mechanisms cycle cycle cycle characteristics characteristics sigmoidal california california solid solid solid solid solid solid solid solid solid solid solid solid solid solid solid turn movements movements plane decrease decrease decrease configuration produces produces longer longer longer longer ann modeled modeled sensitivity sensitivity slightly interaction mutual mutual mutual integrated formed cycles cycles cycles cycles cycles cycles decreases ocular ocular ocular ocular suggested suggested constants constants constants dashed dashed dashed dashed dashed dashed dashed dashed dashed dashed dashed initially initially coupling figures inter inter retinal determines coupled absolute identified closely modification included plots tend characteristic strongly running running duration duration comp dot dot ill ill neurosci moves overlapping subsequent acknowledgments decreasing decreasing explore remain layered layered layered exhibit put detail dotted dotted dotted dotted dotted dotted dotted dotted respond school project project project project biol muscle muscle func opposite opposite opposite opposite rev illustrate equally impulse impulse impulse impulse versions baseline baseline baseline baseline baseline baseline baseline vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor developing interneurons interneurons interneurons interneurons interneurons interneurons purposes arc closer producing producing filtered forces ran nucleus monkey monkey monkey afferent afferent afferent afferent cut cut cut cut cut res demonstrates apparent pathways experimentally cohen incorrect robinson robinson operate operate summarized asymmetric asymmetric asymmetric returns cybern ear physiology modify angular animals vestibular vestibular vestibular vestibular neurophysiol neurophysiol neurophysiol jones jones jones jones jones rotations rotations rotations rotations receptors arranged arranged arranged arranged eliminated fails loops loops loops los analyzing presentations wilson wilson wilson wilson wilson muscles muscles muscles muscles date combines pat sides sides monkeys monkeys monkeys monkeys originally interconnections thomas nonlinearities nonlinearities arrangement arrangement arrangement tic insight repeatedly lag lag lag zipser zipser reflex reflex reflex reflex reflex reflex reflex reflex neurophysiology neurophysiology removal removal randomized transmitted forced connec medium medium obtains amplitudes amplitudes acceleration sinusoidal sinusoidal sinusoidal sinusoidal gained interact compensate mammalian rectified nuclei nuclei termed breaks afferents afferents afferents afferents afferents reciprocal reciprocal continually continually resembles vestibulo vestibulo vestibulo vestibulo inhibit utilizes puts contralateral contralateral reflecting medicine sharply peaked push squashing squashing sity brainstem brainstem brainstem brainstem raised rotational ipsilateral motoneurons motoneurons motoneurons motoneurons rent medial medial tern moderately plenum plastic pull anastasio anastasio anastasio anastasio anastasio anastasio anastasio slip lowered angeles rectification mediate retrained canal canal canal canal canal canal canal exciting stabilized preset dash dash recur faculty pared univer motoneuron motoneuron motoneuron mammals mammals compensatory compensatory compensatory skew skew permission fund southern southern sensitivities sensitivities sensitivities stant stant antagonist innovation originate pected canals canals canals commissural commissural commissural commissural commissural stabilizes agonist nystagmus alert alert interac cutting cutting tual semicircular semicircular semicircular lends accelerations inhibiting transmitting hibitory hibitory stretching acta tick tick tick relay relay relay gracefully skewed integrative exert steeper stants unaltered interrelated interrelated resembled moroneurons moroneurons moroneurons signifying contractions coor characteris subserve subserve excursions redrawn vestibuloocular disrupts disrupts coworkers 
#@Anastasio_T,
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#*network learning learning learning learning learning model model model model model model model model model neural neural neural input input input input input input input data function function function function function function function figure figure figure figure time time time set set set set set set set set set algorithm algorithm output state state results models performance based based based based based space space space space space linear order order shown systems values parameters weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single processing processing processing control large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis inputs inputs inputs form form form form form algorithms simple small small size feature fig fig fig fig fig fig cells cells cells points field process process process process current current cell cell cell cell structure structure structure random memory response similar representation equation equation line line line line rule rule rule general parameter parameter parameter average average average average obtained term term activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional university university computation computation computation research research research research independent initial initial initial constant constant constant estimate standard standard terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science left present present temporal maximum maximum range press press press basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied computational density properties properties references due due due due due due due due important introduction complex stimulus effect variance variance variance variance variance tion tion tion change change change complexity variable variable spatial spatial spatial spatial spatial spatial spatial lower measure measure measure measure prior higher bound bound bound type type long conditions represent represent tree distributed equations fact techniques region length observed observed observed observed observed simulations simulations simulations simulations simulations simulations simulations simulations minimum ing total simulation simulation simulation simulation simulation simulation simulation computed sum eq elements elements elements factor potential potential potential global obtain original original specific specific represented represented represented represented compute compute proc proc location active equal mit mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage contrast dependent dependent dependent dependent modeling modeling selection selection selection selection selection selection department version version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses represents represents represents represents represents represents responses responses final ai ai considered cambridge cambridge san top top stimuli effects effects determine upper requires significant increase give give con produce produce channel coding coding coding derived clustering clustering clustering clustering developed developed developed developed area types actual provided selected selected nature depends depends biological biological associative measured discussion increases fast amount amount synapse synapse synapse synapse supported role theoretical eds instance cluster cluster cluster typically smaller underlying functional functional functional functional functional functional interesting significantly projection head mechanism mechanism mechanism trials trials pre decay combined combined produced run neuronal neuronal neuronal neuronal membrane membrane membrane membrane membrane membrane membrane correlations property pair period subset subset subset compare previously tuning tuning tions differential sparse sparse sparse sparse generalized bounded channels organization organization organization organization organization organization organization organization organization organization organization organization organization sensitive sensitive entire trial trial trial trial trial clusters clusters clusters clusters occurs generally generally demonstrate flow strength strength strength critical greater hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian interactions interactions interactions interactions differences sigmoid measures clear peak peak peak peak peak constrained mechanisms mechanisms mechanisms mechanisms mechanisms presence presence presence sigmoidal solid solid proportional proportional variety relationship program force denoted ways sequential tuned tuned modeled modeled modeled modeled modeled electrical electrical electrical electrical electrical slightly text develop integrated formed formed competition formation formation formation dependence correlated correlated correlated interpretation detailed evolution forms forms suggested constants constants slow epochs epochs epochs measurements intervals initially msec msec koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic recorded usa usa color currents sciences determines plotted plotted plotted plotted illustrated illustrated illustrated illustrated activated aspects uniformly modification modification modification modification divided divided presentation presentation presentation computations soc soc strongly interpreted conductance conductance conductance conductance conductance sin sci sci comp localization michael realistic neurosci neurosci neurosci consisted illustrates acknowledgments explore stimulation strengths dotted dotted postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic rise rise respond respond int plasticity relationships relationships relationships scaled office office structured complicated affect affect presynaptic presynaptic presynaptic presynaptic presynaptic examined induction induction induction patch gradients naturally psychology rev voltages voltages portion precise explored nerve academic fibers pyramidal pyramidal pyramidal epoch epoch epoch epoch epoch epoch regime brown brown brown brown brown brown brown brown brown brown brown brown brown brown brown brown brown brown brown brown publishers variances phenomena correction london spatially spatially spatially purposes protein division arise pool consequence scientific hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal acad acad beginning beginning patches demonstrates sun apparent understood experimentally marked ture differs suited conductances conductances conductances conductances conductances conductances conductances conductances conductances simulator boston fiber age univ phenomenon ear oxford extensive temporally neurophysiol reconstructed reconstructed naval jones jones enhancement air convenient significance significance alpha efficacy resulted synchronous responsible modifications natl natl exploring passive passive passive passive dendrites dendrites dendrites pat regarded evident sim somatic thomas soma soma branching diameter winning hippocampus spatiotemporal mem mem ltp ltp ltp ltp ltp ltp ltp specificity concentration projects davis grants cam cam cam insensitive yale depression depression depression depression depression depression depression indirect kluwer revealed preserving connec arbor trigger superimposed affects resting workstation evoked assess biophysical biophysical biophysical biophysical biophysical biophysical interact blocking graphics life potentiation potentiation potentiation potentiation potentiation kanerva kanerva interactive interactive interactive regimes selectively distinguished figs tune differing struc strict tonic syn syn syn syn advantageous reversed twenty terns losing morphology morphology cally bilinear exclusively possess agency nmda nmda anthony heterogeneous functionally zador zador zador zador zador zador zador zador zador zador zador contacts compartment neurobiological inset remained ranged approached approached approached approached defense sentation mul texas emerged awij awij awij began winners depolarization eeckman tivity jack jack haven simula apical activa electrotonic electrotonic electrotonic bio fight excitable ities reconstructions proximal proximal mainen mainen mainen mainen mainen mainen mainen mainen compartments psp psp psp psp psp psp psp psp psp psp mossy electrically abstr abstr basal pattem synapfic synapfic synapfic synapfic steepness compartmental med functionals ions clamp clamp nonlin anatomically volt duce synchronously colored electro weakened zation strengthened strengthened strengthened debate brane ampa ampa ampa ampa conduc gle hines hines hines dition mech heterogeneity heterogeneity geometries annu tiple ful johnston johnston johnston johnston organiza appreciated collapsed nction crn crn pressed phe organi constituted biophysically analogs kelso kelso 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#@Brown_T,Claiborne_B,Mainen_Z,Zador_A,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time set set set set set set networks networks training training training output output output output number number system system system system error error state results results results results information information models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer case vector shown shown shown shown systems systems systems systems systems systems values values values values probability probability parameters noise noise noise weight weight weight weight neurons recognition approach pattern pattern processing control large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test test patterns analysis matrix matrix matrix inputs inputs inputs shows shows gaussian gaussian gaussian gaussian small work cells cells cells step field features classification classification classification classification level level level structure random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar representation show show show equation equation equation fixed rule vectors vectors vectors vectors parameter parameter parameter average average average average term experiments experiments experiments experiments experiments experiments experiments threshold threshold computation computation computation defined found dynamics standard standard standard computer computer terms connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic prediction presented presented presented presented presented present present present present present activation activation activation frequency maximum maximum range press press press press learn outputs outputs outputs sample abstract abstract applied applied computational computational computational computational computational properties references stochastic procedure important context introduction introduction circuit effect effect change difference lower measure measure learned part previous firing firing firing cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex represent represent represent distributed region minimum ing simulation human potential applications study study negative vol specific specific represented provide provide gain cortical cortical cortical cortical cortical cortical cortical brain brain brain steps steps steps steps larger larger larger larger larger update support modeling modeling modeling synapses synapses synapses synapses synapses individual exp ai ai ai ai ai ai ai ai ai ai ai ai ai considered san effects effects effects effects capacity speed estimated developed developed levels area finally evidence nature nature biological associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative increases tested tested tested excitatory amount amount amount amount effective synapse supported role role role theoretical eds eds adaptation adaptation end hypothesis noisy noisy noisy pairs pairs account account functional interesting testing testing testing york york york structures principle principle representing representing representing max inhibition inhibition inhibition inhibition decay run run run run predict membrane typical lateral identical recently engineering calculated calculated calculated axis axis studies differential trans symmetric symmetric storage grant horizontal deviation wide demonstrate demonstrate strength strength conclusion hebbian differences differences differences differences designed clear peak performs presence presence largest demonstrated assuming selective selective iii scene areas longer perception laboratory vertical recall recall scales gaussians gaussians agent potentials potentials potentials review review overlap overlap overlap influence influence updated updated updated showed modulation modulation modulation modulation modulation modulation modulation allowed allowed allowed allowed reasonable reduces combining purpose kohonen kohonen recorded retrieval memories black tests tests modification receives notice strongly showing anderson anderson anderson anderson anderson anderson anderson physiological michael simplified simplified simplified ill neurosci neurosci intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic stimulation diego wiley essential investigate varied optimized rise behavioral behavioral investigated affect neu neu transmission transmission transmission transmission transmission transmission adapt rev versions versions olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory explored nervous academic fibers fibers fibers fibers arbitrarily explain electronic averages animal years great asynchronous biology tractable sys easier widely afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent acknowledgement calculations radius dark quantitative recordings schematic pasadena pasadena pasadena substantial fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber neuro neuro deviations corrupted analogue analogue analogue analogue analogue restriction extensive neurophysiol purely odor odor odor odor jones turned turned turned caltech caltech caltech caltech caltech suppression suppression suppression suppression suppression saturation bower bower bower bower bower bower bower bower bower bower bower bower bower bower bower anatomical anatomical chance mail chemical chemical grow keeping hope ral implications preparation symposium wilson wilson wilson wilson continue service slice reset falls sion james conjunction enhance enhance enhance enhance enhance enhance enhance bulb bulb hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo cerebral cerebral creating concentration concentration concentration reverse davis hart hart intersection tures onr linked cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic leaving ideally descriptions suppressed evoked evoked cns trends duda duda tems picked selectively selectively selectively monitoring intracellular fea saturated quantify settling spring spring spring agents confirm hid morris morris transmitter suppress concern affecting settle normalize attained odors odors odors odors odors odors odors enhances enhances enhances adjusts cold cold cold rectangles rectangles rectangles handbook saturating categorical aip nih pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform pitiform deciding acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine plenum degrade unaffected rises hij hij hij quantified sends activating extracellular schematically schematically distinctive serving released released inhibits piriform piriform suppresses suppresses snyder haberly haberly neurotransmitter neurotransmitter reinforced mission preferentially psychol psychol bij bij contracts intriguing paragraph postdoctoral hyvarinen perfusion preclude harbor harbor harbor spherically spherically intemeurons pharmacological pharmacological iil andr zornetzer ritz ological physi lllll lllll lau presume cyclically flatten underneath 
#@Anderson_B,Bower_J,Hasselmo_M,
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#*model model model neural neural neural neural neural function function function function figure figure figure figure figure figure figure figure time time time time time time set networks networks number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system state results models models models models models models models models models models models based linear order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems neurons neurons neurons approach approach point point point point neuron test class class class class class class form form form form form form form shows shows shows signal paper small small work work fig fig fig step step features level current current current current current current current current current current current cell cell cell cell high high response response similar equation equation equation line line line line rule general general real approximation average average term term note university threshold variables variables variables variables variables variables variables variables independent initial terms presented presented present present present phase phase phase phase activation frequency frequency frequency frequency motion maximum range press abstract abstract abstract applied applied references introduction action complex behavior behavior behavior dynamic change change energy difference complexity complexity variable variable variable lower lower prior chosen cases cases firing firing firing firing firing firing firing good good binary long equations equations equations make make techniques techniques techniques simulations resulting classes classes total sum sum eq eq eq eq potential potential potential potential potential potential potential potential made made made made em original original original specific true application series series provide define proc proc location related equal equal power voltage steps comparison contrast dependent dependent modeling modeling proceedings department scheme scheme scheme scheme equivalent equivalent equivalent curve additional conference efficient full full full full full full full full choice basic give give produce derived weighted randomly lines lines path inhibitory depends discussion transformation inverse supported role theoretical degree smaller hopfield hopfield hopfield reduced reduced reduced reduced reduced dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical fully character mode direct depth polynomial combined choose description description membrane membrane membrane membrane membrane membrane advantage advantage introduced side side varying varying works axis solve smooth yields yields match differential differential chain modified interval grant grant amplitude expression suggests suggests suggests occurs setting demonstrate conclusion place place reduce reduce reduce depend differences differences sigmoid clear suggest physics external reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction solid solid solid solid derivatives manner program program produces mathematical dept dept dept modeled transformations transformations transformations equilibrium equilibrium equilibrium potentials potentials letters yield national national family expressed expressed expressed expressed formation dependence dependence variation detailed approximations evolution evolution constants allowed sign reasonable dashed dashed dashed dashed expansion expansion combining combining combining neighborhood neighborhood event msec msec degrees degrees degrees expect includes includes currents currents extension illustrated specifically coupled holds gating gating gating simplicity straightforward straightforward post situation situation plots refer kind procedures strongly showing showing conductance sci simplified simplified realistic realistic realistic realistic realistic realistic realistic providing leading illustrates command carried perturbation perturbation perturbation collection exhibit put detail accurately accurately dotted dotted matches respond investigated investigated biol relationships decisions root proper complicated removed coefficient coefficient coefficient trace onset adjusted bifurcation formal freedom consist utility submitted averages years mentioned biology biology tractable correction starts considerable drive tive tive sys incorporate ran immediately immediately axon acad describing members members qualitative fourth transient lack introducing branch plan physiol physiol phenomenon indices primarily saddle guarantee member nat dynamically concerned concerned generality generality systematic systematic balance contract obstacle analyses utilized recovered irregular irregular encountered mental intended injection thomas surprisingly matter augmented belonging eqs alternatively outlined neurophysiology latency latency latency benefits abstraction resting breaking representa constrain capacitance capacitance biophysical expand acquired singularities ultimately lond lond sketch meta abbott abbott abbott abbott abbott abbott abbott suffer likewise indication vanishes ignoring rose rose hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin expansions remark reversal simplification simplification preserves insufficient invertible ongoing huxley huxley huxley huxley huxley huxley huxley huxley huxley virtually focuses conceptual conceptual injected injected injected physiologically devised striking stevens stevens vanish hopf leakage marder marder marder marder marder experienced fidelity ionic differentiate profit denominator health health proceeding subtle hyperpolarization depolarization comprehensive connor connor connor connor connor connor connor connor sixth sixth excitable dealt rigorously biophys biophys walter indistinguishable expressing acknowledgment depolarized depolarized faithful inverses premise segregated cyber giant reductions reductions farther eps eps eps eps eps eps outward mono hyperpolarized hyperpolarized conservation conservation conservation forty ciently waltham facilitated suddenly laid brandeis institutes institutes fitzhugh fitzhugh fitzhugh joined renormalized seminal realism realism biophysically biophysically supplemented portrait portrait outset eve suffi telling tonically enjoyed climb sinusoids illustrations ordinarily greek 
#@Abbott_L,Kepler_T,Marder_E,
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#*network network network network network network network network network network network network network network network network network network model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input function function function function figure figure figure figure figure figure figure time time time time time set networks networks number system state state state state state state state state state state state state state state state state state state state state state state state state state state results units information problem problem space space space weights case case case case case vector vector vector shown shown shown shown shown shown probability probability probability probability probability probability probability functions functions neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution method approach approach point point large large large large neuron neuron rate patterns patterns analysis form shows simple paper paper net work work methods methods field field current current current cell cell cell cell structure structure random similar representation representation show show equation equation equation equation equation equation equation equation vectors vectors vectors vectors generalization real states states states states states states states theory theory obtained activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional university threshold threshold solution research research defined defined sequence initial initial initial initial initial constant synaptic synaptic activation activation activation basis basis basis basis abstract references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic introduction action complex statistical statistical generated generated generated change assume assume measure part part required conditions equations fact techniques correlation scale scale respect called elements means applications applications obtain represented represented represented provide rates rates rates related distributions brain voltage descent nets institute institute department department synapses internal difficult exp exp exp exp exp scheme scheme scheme ai ai transition transition transition transition transition transition effects statistics basic basic give derived derived path path path path processes simply measured describe group group group group group denote corresponds corresponds complete finding short assumed supported main main noisy probabilistic account york york york increasing special principle principle principle representing representing numbers making early description description description description description membrane membrane membrane ensemble takes takes relevant smooth symmetric symmetric observation generalized entire grant occur occur matrices matrices matrices matrices place conclusions operator operator practice integration physics physics cycle configuration configuration denoted acknowledgements van van written solving generating generating generating laboratory transitions transitions transitions transitions transitions transitions transitions transitions transitions mathematical mathematical averaging easy springer springer expectation national expressed expressed formation stages evaluate constants diagram smoothing smoothing remains remains david currents recognize activated activated activated activated phys phys gating closely closely suitable wij wij committee post lie lie lie lie lie content simplified dot cowan cowan cowan cowan simpler simpler wiley essential involving detail integral integral integral oscillator helpful existence giving office complicated act math bifurcation der formal spin spin spin spin spin spin site asynchronous asynchronous answer caused satisfied sites operators operators operators operators operators pulses probable mathematics calculations implicit fluctuations lattice lattice sharp summarized gen coherent coherent coherent coherent univ instantaneous analogue investigation refractory refractory refractory refractory refractory refractory acts labelled naval proceed reaching moment moment moment los efficacy efficacy neurobiology exceeds moments moments eqn eqn holland master master master steepest park santa cooperative markovian smoothly chicago chicago books algebra algebra lapedes mann lagrangian ave illinois neglect hamiltonian alan schmidt kinetic kinetic alamos analyse amsterdam wiener wiener neurodynamics neurodynamics neurodynamics neurodynamics neurodynamics quiescent quiescent quiescent quiescent menlo asymptotics lowering lowering lowering lowering physik quantum quantum skew safely rli chemistry presumed lat prog eli eli liapunov hecht hecht raising raising raising raising hermitian liquid evidently evidently evidently facilities navy distinguishable eqns carded ida physicists alp andr andr dai dai lagrangians lagrangians lagrangians lagrangians hospitality atl benjamin algebras cay andi 
#@Cowen_J,
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input figure figure figure figure figure time set set set networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm number number system system system system system system results information problem models models models models models models models models models models models models based space space weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear layer vector vector vector vector vector vector vector order order order shown shown shown systems systems systems systems systems values values values probability noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons unit distribution distribution distribution approach approach approach pattern pattern point point single single single processing processing large large large local local local local neuron neuron neuron neuron rate rate rate analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix optimal inputs inputs form form form form form form shows shows shows shows shows signal signal algorithms simple simple paper small small feature feature feature feature feature feature feature feature feature feature work work fig fig fig cells features features features random random response response response response response response similar similar architecture architecture show equation equation line line line line rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors speech approximation approximation approximation average theory theory theory theory gradient term term term term term note activity dimensional dimensional computation solution research independent independent found found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant computer computer terms connections connections connections connections connections connections connections connections synaptic synaptic node node node node node node node node node node node node node node node node node node node science science science left presented phase activation low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets sets motion motion motion motion range learn position components components components components components basis outputs continuous abstract applied convergence references component component component component component component component component component component stochastic ieee adaptive adaptive introduction hand behavior behavior statistical statistical statistical generated variance cost recurrent recurrent recurrent recurrent recurrent recurrent change lower lower rules signals signals signals signals higher part bound bound multiple multiple multiple conditions conditions equations equations equations equations equations techniques proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation observed forward forward forward forward forward forward forward forward simulations simulations simulations resulting ing performed performed called elements regions regions potential potential dimension made made feedback orientation study em em filter filter filter filter filter vol relative provide rates location location perform perform perform goal goal related discrete cortical equal approaches approaches connection connection connection connection descent morgan proceedings proceedings institute department department loss advances responses scheme scheme scheme addition framework directly directly solutions limit limit limit limit limit limit limit top conference determine upper full pages pages give give give con condition condition condition derived derived provided finally depends discussion normal increases describe fast close corresponds corresponds corresponds complete complete complete complete stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable short assumed assumed supported theoretical theoretical adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation journal development development dynamical technology block significantly york increasing consistent principle leads principal principal principal principal principal principal principal principal principal principal principal principal principal details max international international bottom supervised magnitude magnitude added description description light light denotes correlations correlations ensemble ensemble ensemble lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral sense array array engineering engineering conventional unsupervised tions correspond pca pca pca pca pca pca pca pca converge converge diagonal diagonal mixtures mixtures mixtures mixtures symmetric modified observation organization organization grant constructed horizontal horizontal studied studied suggests extended touretzky generally flow critical critical critical critical minimal minimal minimal minimal minimal minimal row hebbian hebbian hebbian hebbian hebbian hebbian hebbian interactions interactions interactions numerical clear performs constrained propose integration reduction drawn proportional selective min min plane plane averaged introduce groups connectivity minima program force force denoted denoted derive primary stability stability stability stability stability stability stability stability stability coordinates linearly linearly involves consisting equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium springer blocks extraction extraction expectation cycles cycles cycles cycles cycles cycles depending stationary correlated evolution activities activities constants spectrum spectrum diagram diagram diagram diagram diagram expansion reduces remains sufficiently topology david coupling coupling coupling coupling coupling coupling building combinations formulation eigenvalues eigenvalues eigenvalues subspace subspace discuss discuss suitable effectively post projections orthogonal receives notice verlag dis symmetry lie lie oscillations follow write simplified eigenvalue eigenvalue leading acknowledgments deal decreasing extend extend law employed carried carried strengths strengths strengths strengths detectors biol biol biol office referred eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors symbolic affect affect examined math math naturally editor necessarily configurations ensure bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation portion portion hebb hebb generates regime regime regime asymptotically asymptotically asymptotically developing unstable unstable unstable unstable unstable unstable biology reasons perspective incorporate inversion calculations calculations author qualitative researchers argument cohen introducing anti anti anti anti anti limiting limiting ordered qualitatively qualitatively acoustics replace shaped yuille yuille baird cor picture cybern cybern cybern leen leen leen leen leen leen saddle saddle optimality martin acts branches branches branches homogeneous homogeneous purely discovery discovery discovery discovery discovery discovery discovery discovery naval connecting nonzero extending oja oja oja oja oja oja oja oja oja tools mail contract sanger sanger sanger analyses analyses heavy heavy darpa reveals refers eigenvector projects alternatively tures mind schulten schulten vec super super break emerge emerge forced connec examining shaded exam evolve diag diag ijcnn graduate singularities regimes regimes anal oscillating responding reveal algebra tune bill subspaces oregon mix correlate develops diagrams replacement remarkable stimulating acquire todd confirm oscillate tors tells hopf hopf hopf hopf degenerate inspection appl inset cascaded cascaded sis schmidt penalizes violated violated equilibria equilibria equilibria equilibria equilibria equilibria equilibria equilibria equilibria equilibria equilibria equilibria equilibria equilibria spanning unifying locating simulates quadrature undergoes bifurcations bifurcations bifurcations kammen analyzer karhunen karhunen expects kung kung emerging loses rameter structurally imal liapunov prin structed instabilities preclude ita stringent beaverton generically ine parabolic parabolic coexist apex ull carlson carlson wine ticity mda jli kauffmann bottle cipal 
#@Leen_T,
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equation equation equation section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed vectors general real real real real real term term term term note experiments experiments dimensional dimensional result result university university variables variables variables variables variables variables research independent independent independent dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics standard standard standard computer computer computer computer science science present present temporal motion range press position basis abstract computational computational computational computational convergence convergence convergence analog references ieee ieee procedure decision introduction action circuit circuit circuit circuit circuit effect dynamic cost cost cost cost change change energy energy energy energy difference variable variable variable assume signals chosen chosen chosen part center previous good equations equations equations proposed finite simulations simulations simulations simulations resulting total respect performed means optimization optimization optimization optimization optimization obtain original original original original vol application proc active constraints descent descent descent nets nets nets report report department department version scheme graph graph ai domain equivalent solutions design limit trajectory trajectory trajectory conference choice significant pages increase criterion velocity selected constraint technical describe describe transformation transformation circuits effective assumed main future objective objective objective objective objective objective objective objective simulated smaller underlying hopfield hopfield hopfield hopfield hopfield hopfield hopfield dynamical dynamical functional functional functional block block block 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partitioned partitioned variants alternatively assigns limitation yale yale yale preserving conjecture simulating algebraic algebraic ibm pos indexed indexed indexed indexed enforce sized sized preserve exchange simplifies simplifies lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian imple dropped converter dcs station ning ters linearized nontrivial sliding deter charles kinetic kinetic kinetic unusual derives watson supposed favors favors derivations haven heights dard mentation parame sorts circumvent notational mined conserved rid indexes imitate itive namics coordinated subjected nonoverlapping nonoverlapping yorktown jumping jumping jumping objec ovi ovi ovi ovi ovi ovi ovi ovi ovi cas garrett garrett garrett garrett extremal dissipative dissipative dissipative optional ria ria ria ria ria ria ria yaleu lagrangians lagrangians afford itl focussing 
#@Miranker_W,Mjolsness_E,
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time networks networks networks output output number state state state state state state state state results results results information information information models based weights case case case shown systems probability parameters noise noise noise noise noise noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit distribution distribution distribution distribution pattern point processing large large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate patterns patterns patterns matrix matrix form form form shows simple simple simple simple simple simple simple simple simple gaussian net work work step step step field field field features features features features features process process level level level level level level current current current structure problems random high memory memory memory memory memory memory memory memory response response response response response response response similar similar representation representation show show show section rule general parameter parameter real real real real real states states states states states university university threshold threshold threshold threshold threshold threshold threshold solution solution solution solution solution solution independent independent defined found sequence dynamics dynamics dynamics initial initial constant constant standard standard standard standard standard connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic direction present low low frequency frequency frequency frequency maximum maximum range press nonlinear continuous continuous abstract abstract computational computational computational analog analog properties properties references references stochastic due due procedure procedure adaptive decision introduction hand behavior behavior behavior statistical statistical statistical difference variable variable assume measure learned learned firing firing firing firing firing firing firing spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long equations fact length length scale ing times elements elements potential potential potential potential potential made obtain negative artificial relative relative true compared compared application proc proc experimental related connected connected distributions distributions discrete discrete brain brain voltage voltage voltage voltage voltage voltage voltage steps steps larger larger contrast connection connection fields support train train train modeling department department internal internal internal internal exp addition cambridge equivalent curve curve additional view solutions solutions solutions solutions solutions solutions solutions limit effects bit bit determine full approximate approximate statistics world basic basic levels levels levels finally nature depends depends depends depends biological biological biological biological biological biological biological biological biological associative associative associative associative associative associative associative associative associative describe describe describe fast inverse assumption corresponds stable stable short short shape shape synapse main sensory including probabilistic hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield account account fully fully interesting interesting character principle details details making stored normalized early description description neuronal membrane membrane membrane correlations exact robust element introduced include period period period period period period period period period sense relevant highly compare calculated calculated works solve yields achieve diagonal diagonal address address modified interval interval interval constructed parts lead occur digital wide wide spikes spikes spikes spikes spikes spikes spikes spikes spikes strength strength critical critical assumptions assumptions hebbian conclusions depend sigmoid sigmoid exponential temperature suggest hard physics cycle characteristics characteristics california proportional assuming variety variety connectivity question attractor attractor explicit relation construct construct construct produces longer longer plot plot describes physical adding frequencies frequencies versus dependence depending stationary stationary overlap overlap overlap overlap overlap overlap overlap detailed forms completely delays intervals intervals event valid intermediate intermediate intermediate figures usa usa currents currents retrieval retrieval retrieval retrieval retrieval inter absolute absolute absolute absolute discussions regular regular straightforward encoded spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking capture capture excitation induced induced contained link showing interested symmetry sci sci duration write realistic realistic realistic realistic realistic received intrinsic trains trains trains trains remain remain essential exponentially ml behaviour behaviour helpful postsynaptic postsynaptic postsynaptic fashion history ideas analytically comparable tanh neu transmission trace perfect der formal formal formal formal formal nerve academic contributions regime regime integrate slowly trivial trivial track track fairly biology analytic analytic analytical tive berkeley berkeley berkeley sections closer incorporate ion acad acad preceding fluctuations fluctuations robustness varies generic generic generic quantitative introducing switch poisson incoming qualitatively qualitatively qualitatively collective collective replace replace comments attraction traces physiology assign refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory linearity linearity driving driving recover concerned tem arrival adds convenient significance overcome abilities efficacy neurobiology modifications natl natl service financial reset periods irregular irregular bialek reproduce bursts bursts late considerations acknowledge temperatures crossing crossing slight numerous graded graded basin transmitted emergent forced german verified preserved conduction jij jij crosses oscillating exchange interspike prevents hodgkin hodgkin hodgkin students coming replacement stimulating bursting bursting bursting bursting bursting bursting bursting bursting institut huxley huxley confirm spins stay rons sen carries gerstner gerstner characterizes decaying william cho thresh tory linking initiated initiated initiated notions andreas advice mention extremes amit amit conveniently conveniently flips emphasizes physik physik sume ising efficacies tailed simplistic ner ner jii momentary rests evoke alike muenchen muenchen theoretische influx disregard pending generous lasts hospitality initiates collec ifo 
#@Gerstner_W,
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output output output output output output output output output output output output output output output system system system system system system system system system system system system system state state state state state results results units units units problem problem models performance performance performance based space space space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear case case case vector vector vector vector vector vector vector vector vector order order order order order shown systems systems systems systems noise weight weight weight weight weight weight weight weight weight unit unit unit recognition recognition recognition recognition approach approach approach approach pattern pattern pattern pattern pattern pattern point single single control control control control large patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs form form form form form form form form form form form form form form form form form form form algorithms algorithms algorithms algorithms algorithms simple simple simple feature net net net net net net net work work work methods points points field classification classification classification level trained cell structure problems memory memory memory memory memory memory memory memory memory memory memory memory response representation representation representation architecture architecture architecture fixed fixed fixed line rule rule rule rule vectors vectors vectors vectors vectors vectors general real real real real states states states states states states theory experiments activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional variables computation computation independent independent defined found found sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial standard standard standard standard computer terms terms terms terms terms distance connections node node node node node map map map map phase phase activation nodes nodes nodes nodes nodes nodes nodes frequency temporal temporal temporal temporal temporal temporal machine sets sets learn learn components components components components components basis nonlinear nonlinear outputs continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied back back back computational convergence convergence convergence analog analog analog analog analog analog analog references references references component component positive important adaptive propagation introduction complex complex complex complex hand behavior behavior statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change variable spatial spatial lower lower representations learned learned learned learned learned learned learned chosen chosen chosen chosen chosen higher higher higher higher higher previous previous theorem required required required multiple multiple cortex cortex cortex binary conditions distributed distributed distributed equations equations equations equations equations chip region region region observed forward simulations total simulation elements reinforcement reinforcement dimension dimension dimension natural applications applications applications negative negative negative negative original specific specific samples samples application desired desired desired desired desired desired desired desired desired desired define rates rates proc proc perform determined motor motor discrete cortical power comparison larger larger larger connection fields support train nets version version version technique internal joint joint sequences sequences sequences sequences sequences sequences sequences maps maps maps considered considered considered equivalent environment environment directly design design limit trajectory trajectory san effects capacity determine determine determine upper upper full pages pages pages produce condition clustering path actual selected simply biological biological biological biological biological biological biological discussion normal normal normal normal normal normal normal normal normal normal normal normal normal normal technical tested transformation fast inverse inverse inverse finding effective implemented implemented implemented supported require main vlsi easily makes sensory sensory pairs pairs pairs pairs pairs pairs underlying combination dynamical dynamical dynamical dynamical dynamical dynamical coefficients fully block block block block block block block programming programming programming programming projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection york edge special special principle operation details stored stored stored stored stored stored supervised supervised supervised supervised combined combined produced choose choose added discussed directions separate separate include identical side hierarchical hierarchical inference engineering engineering varying conventional unsupervised module module axis correspond converge converge differential achieve diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal symmetric symmetric gate storage storage storage storage storage storage entire grant amplitude constructed constructed constructed constructed parts invariant invariant occur occur digital matrices feed move clusters occurs generally flow flow flow flow flow flow place place row row greater greater greater trajectories trajectories trajectories competitive competitive competitive competitive competitive competitive competitive competitive sigmoid modules modules modules modules modules modules modules modules modules designed faster weak encoding largest cycle cycle selective decrease introduce characters identification program attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor explicit appears digit derive winner winner winner ways describes laboratory transitions transitions stability stability dept dept category category category category explicitly explicitly coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates simultaneously linearly physical easy easy interaction interaction frequencies frequencies frequencies springer shift blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks competition competition yield yield choosing national independently overlap viewed transform updated evolution static static static static static static static static understanding sizes sizes suggested translation spectrum key key eeg advantages coupling coupling coupling coupling coupling coupling handwritten handwritten box coordinate coordinate coordinate coordinate eigenvalues eigenvalues subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace memories memories memories determines determines determines prove characterized planning columns columns columns columns columns columns columns columns columns determining middle middle aspects included modes modes modes oscillatory oscillatory oscillatory oscillatory oscillatory attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors identity conf conf kind kind symmetry symmetry oscillations content categories categories relaxation relaxation absence quantization binding leading cat employed origin diego transformed transformed transformed create put detail optimized optimized periodic periodic periodic periodic periodic periodic periodic periodic fourier fourier fourier fourier project incremental investigated int int fault analytically combine combine complicated tanh proved math naturally plausible possibly editor created created created prototype versions versions versions olfactory olfactory bifurcation bifurcation bifurcation taylor freedom observe hebb hebb store store chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic rows rows rows costs guaranteed guaranteed guaranteed biology lies lies nonlinearity lin tive berkeley berkeley pulses mathematics inversion projected acknowledgement angles describing patches patches geometry cybernetics conjugate conjugate behaviors fuzzy fuzzy freeman freeman freeman understood understood bootstrap bootstrap transient autonomous frequently biologically extensions chen replace coherent kinds chose attraction attraction attraction attraction attraction attraction baird baird baird baird baird baird baird june june semantic instantaneous proofs ear accomplished formally guarantee rotated signature purely nonzero interconnected interconnected interconnected establish establish lost adjusting tools hope north carry spurious spurious falls programs mouse holland moved moved moved mental realization widrow widrow widrow lawrence spherical nonlinearities entries entries entries entries entries entries entries entries entries multiplied winning winning winning advance advance route broken cam cam cam cam cam constitute constitute basin basin basin basin break break emergent forced spatio spatio spatio spatio terminals chaos chaos tendency tor basins basins basins basins basins molecular realize algebraic evolve evolve pij interact permits afosr paired projecting flip cartesian oscillating oscillating attached cubic cubic cubic cubic programmed programmed programmed programmed programmed programmed programmed programmed bill subspaces subspaces subspaces subspaces subspaces sigmoids stores interior assistance trainable impulses orthonormal compete compete compete supply morris accomplish fre fre archi retrieved hopf hopf bat transpose autoassociative autoassociative robotic evolves presently enter dent doubling indepen addressable hoff hoff physica polar eeckman eeckman eeckman eeckman subnetworks damping configured predefined assessing tolerant hirsch dominate centroids centroids holmes bifurcations clocked tecture organisms analysed walter feeds laterally frank pad flop isomorphic quences inverses inverses takens handles forest recognizable recognizable pervised peri implementa strange strange plications informal folded folded folded folded folded folded lesser dft invaluable torus governs governs associa pleasure liapunov plug unfolded unfolded wash autoassociation autoassociation incre exhaustively livermore livermore ruled guckenheimer petitive diagonalized attrac digitizing reconstructs parsed trix submodules ematical prohibits disrupting odic acknowl 
#@Baird_B,Eeckman_F,
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neurons point point point point point point point image single single single single processing processing large large large large local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix inputs inputs form form simple visual visual paper paper paper paper size size feature work work fig fig fig fig fig fig fig fig fig step points points structure response similar show show show show show equation section section section section section section section fixed fixed fixed fixed fixed fixed fixed rule rule rule rule rule rule rule general generalization average states states states states term note note note experiments dimensional dimensional dimensional dimensional dimensional result result result result university university research defined defined defined defined defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics table standard standard standard computer terms terms connections connections connections connections connections connections connections connections connections connections connections connections connections connections direction presented map map map map present phase phase phase phase phase phase phase phase low motion maximum maximum range press press position nonlinear outputs continuous continuous continuous continuous continuous abstract applied applied find find computational convergence analog properties properties properties properties references due ieee positive positive positive important important propagation introduction circuit effect dynamic dynamic parallel parallel parallel parallel parallel parallel parallel parallel parallel energy difference rules part part previous previous previous multiple multiple multiple long conditions conditions expected equations equations chip fact techniques region region region observed finite finite finite finite simulations resulting total sum eq eq eq eq eq eq eq eq eq eq eq eq eq elements regions regions regions mapping feedback global global global global global study study negative negative artificial artificial artificial compared define compute proc eye connected connected connected gain gain gain gain gain gain discrete discrete discrete discrete discrete discrete discrete discrete discrete brain power voltage steps comparison contrast connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection update update update update update support department loss implementation version exp delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay addition maps considered cambridge cambridge equivalent directly curves design design limit limit limit limit limit stage detection efficient free free speed speed speed vision vision vision vision condition criterion criterion criterion finally inhibitory depends depends depends depends simply biological measured transformation fast corresponds stable stable stable nearest nearest nearest nearest nearest nearest nearest common generate supported square square square square square square square square square square square square square square square square square square square vlsi vlsi instance instance instance future makes makes sensory including including including hopfield hopfield reduced dynamical dynamical transfer transfer transfer transfer interesting york increasing structures mode mode operation leads details max inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition normalized early discussed advantage advantage lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral practical apply include period array compare previously conventional calculated differential differential trans symmetric observation generalized generalized amplitude exists exists intensity studied wide boundary boundary setting setting hardware strength critical critical critical critical assumptions conclusions conclusions neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor retina retina retina numerical clear presence presence physics sigmoidal sigmoidal assuming assuming variety variety exist exist exist exist exist exist selective min min min min min min decrease relationship configuration attractor attractor attractor attractor attractor attractor reference appears edges written perception sequential stability stability stability stability stability stability stability stability stability stability stability explicitly explicitly text unique mutual adding quality communication updated forms converges updates spectrum delays expansion expansion closed calculate sufficiently advantages topology topology topology topology topology topology topology topology coupling coupling coupling usa formulation currents eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues instances sciences illustrated specifically coupled variations phys phys phys phys neighbors neighbors neighbors discussions characterized characterized simplicity straightforward aspects importance paths modes oscillatory oscillatory oscillatory oscillatory oscillatory attractors attractors attractors attractors attractors attractors attractors attractors schemes schemes schemes schemes situation characteristic excitation induced showing anderson conductance symmetry symmetry oscillations oscillations oscillations sci hold built satisfy relaxation relaxation generalize absence absence delayed delayed delayed eigenvalue eigenvalue eigenvalue leading leading operating operating satisfies neighboring acknowledgments presents origin origin origin remain create requirements circuitry updating updating updating updating updating updating mead mead mead mead varied periodic periodic periodic periodic periodic reducing fourier analytically analytically office tanh oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation smallest math reading onset onset configurations man rev rev rev rev academic regime electronic electronic electronic chaotic unstable slope slope slope analytic analytic analytic implementing satisfied satisfied organized division arise commonly acad grossberg grossberg describing begin questions greatly lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice cohen cohen price measuring differs gen collective suited asymmetric coherent coherent coherent physiol wesley addison guarantee extensive nat eliminate nonzero generality generality saturation satisfying odd odd loops contract contract contract serves intuitively intuitive carry continue recovered introduces ranging induce surprising surprising topological enhance accounts interconnections offers arrangement darpa iterated iterated iterated iterated sustained sustained sustained sustained sustained informative relies considerations onr leaving rigorous basin magnetic constitutes arising capacitance care ibm graduate afosr emphasize oscillating discusses denver figs barlow barlow reveal tij tij tij tij amplifiers ation behave vanishes dramatic reciprocal diagrams diagrams diagrams diagrams diagrams diagrams diagrams diagrams topologies characterizing characterizing characterizing agrees oscillate oscillate eliminates harvard harvard identically wiring marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus marcus triangle edited edited implied triangular triangular triangular triangular triangular triangular triangular triangular triangular triangular triangular triangular triangular triangular prone smc acknowledges aip oscillates oscillates westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt westervelt carver relax relax remarkably orig orig orig orig orig orig rescaling dissimilar challenges army organisms symmetrically steepness pal rescaled fellow fellow compound expands trivially emerging attracting lacks invertebrates wyatt wyatt liapunov insures crit crit crit crit crab postdoctoral orlando lattices lattices lattices lattices lattices lattices lattices lattices lattices irl irl audition famous persists permitting gauge extremal extremal coherently bob clocking dxi multiplicity coleman coleman dowling dowling fractals ide broaden approachable 
#@Marcus_C,Waugh_F,Westervelt_R,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural input input input input input input function function function function function function function function function function function figure figure figure time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number system system system system system system system system error error error error state state state state state state state state state state state state results results units units units units units units units units units units units units units units units units information information problem hidden hidden hidden performance based space space space space space space space space space space weights weights weights weights weights weights weights weights weights linear case case vector vector vector vector vector order shown shown shown systems systems systems systems parameters weight weight weight unit unit unit unit unit unit unit unit unit method method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point point processing control control control large local local rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis matrix matrix matrix matrix matrix optimal form form paper paper paper paper small small small small size size net net net work methods step points points points points points points points points points points points points points points points field field field problems problems memory memory memory memory architecture equation equation equation equation equation equation section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule rule rule generalization states gradient gradient gradient gradient gradient obtained obtained term note note university university threshold computation computation defined target target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant table table table estimate standard standard computer connections connections science science direction direction direction direction direction direction direction direction direction direction direction presented presented presented present phase activation activation activation activation activation activation activation temporal maximum maximum maximum maximum press learn nonlinear continuous continuous abstract applied computational convergence convergence convergence convergence convergence convergence properties references ieee positive procedure procedure procedure propagation propagation introduction complex dynamic dynamic dynamic parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent energy energy energy energy energy energy energy energy energy difference difference difference complexity complexity complexity complexity complexity assume signals learned learned chosen chosen chosen higher theorem type conditions equations equations equations make make make make minimum resulting resulting resulting ing tasks simulation computed respect respect respect mapping mapping mapping mapping mapping means means made made made global global global study obtain specific true application provide compute compute compute compute perform constraints connected discrete discrete equal power steps steps steps larger larger larger larger connection fields update update support train descent descent descent descent proceedings institute department implementation version consists consists internal represents represents sequences considered considered computing experiment directly additional solutions solutions trajectory top top conference efficient efficient requires requires free speed speed pages increase derived derived randomly finally finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation depends depends constraint associative achieved discussion discussion close assumption stable stable stable stable stable stable stable stable stable stable finding finding implemented assumed shape generate supported main journal square easily easily including including smaller hopfield fully fully interesting projection york york increasing representing iterations iterations making making making making bottom bottom combined combined choose run improved improved improve directions robust introduced introduced subject works solve yields correspond correspond converge rl diagonal evaluation symmetric generalized improvement storage grant expression predicted column column pass trajectories trajectories trajectories trajectories trajectories trajectories operator numerical faster faster faster mechanisms mechanisms physics largest largest largest largest largest largest turn assuming minimizing exist introduce derivatives force attractor written ways stability stability stability stability stability stability stability stability stability stability dept implement coordinates physical choosing national national review depending viewed solved variation evaluated evaluate updated evolution evolution understanding converges epochs expansion iterative iterative visible visible visible visible visible visible visible visible foundation advantages avoid thesis activations bell eigenvalues eigenvalues eigenvalues eigenvalues subspace sciences memories recognize plotted plotted illustrated illustrated aspects delta wij wij presentation attractors reached road repeated procedures allowing content content content content backward eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue illustrates neighboring presents american updating updating helpful possibility hill necessarily thought algo taylor academic phd defines indicating smoothness guaranteed guaranteed unstable unstable unstable unstable unstable implementing tive satisfied hyperplane arise laboratories simard simard simard simard simard projected projected acknowledgement reflects evaluating capability incoming incoming asymmetric simulator comments shaped attraction attraction attraction attraction progress differentiable saddle guarantee guarantee lagrange acts eliminated clamped clamped clamped multipliers simplify contract abilities hope corner spurious spurious spurious spurious spurious spurious spurious heavy introduces iteratively guarantees april omitted contraction contraction contraction contraction storing pearlmutter eigenvector eigenvector eigenvector eigenvector propagate alternatively avoiding convergent convergent material displacement limitation basin basin emergent expanding expanding expanding propagating propagating constitutes basins basins jacobian rithms carefully landscape landscape landscape landscape spreading academy iri unconstrained importantly anal france france france enforce discretization universit universit siam inverting rochester rochester rochester gauss pineda pineda gorithm fortunately morris suppress holmdel settle settle coincide anthony norms presently mcgraw shaping shaping shaping shaping addressable addressable addressable addressable cortes trapped noticed disadvantages hirsch llx llx evaluates clamping clamping wii gorithms henceforth pierre owij accelerate iai cedex cedex unitary unitary patrice 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#@Raysz_J,Simard_P,Victorri_B,
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output output number number system system system system system system system system system system system system system system system error error state state state results information problem problem problem hidden based based based space space space weights weights linear vector vector vector vector vector vector vector order order order order order order shown systems systems systems systems systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions functions neurons method method method method method method method approach approach approach approach approach approach approach approach approach pattern processing large large large large large neuron neuron neuron analysis analysis matrix matrix matrix matrix inputs form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper net net work work work task methods methods step step step step problems problems memory memory response response similar similar similar similar similar architecture architecture architecture architecture show equation equation equation parameter parameter parameter parameter real real approximation theory theory gradient gradient gradient gradient gradient obtained obtained obtained obtained term term term term term term term note activity result university variables computation computation computation computation computation computation computation computation computation computation computation computation computation solution solution solution research independent independent independent independent found found target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial constant computer computer terms terms terms terms terms synaptic synaptic synaptic synaptic synaptic science prediction presented presented presented presented phase activation activation activation activation activation activation activation temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal press press components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous abstract applied computational computational computational computational computational computational properties references references component ieee ieee procedure adaptive adaptive propagation context context introduction hand hand dynamic dynamic parallel recurrent recurrent recurrent recurrent energy energy energy energy energy energy energy complexity complexity complexity complexity complexity assume assume assume assume center center center previous previous type required conditions conditions conditions conditions conditions conditions conditions conditions conditions distributed equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations fact fact proposed proposed proposed forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward scale finite finite simulations resulting resulting total regression computed computed respect respect respect respect respect respect respect respect eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq times elements elements mapping mapping means potential potential global applications applications study obtain obtain artificial specific application provide provide define compute proc proc determined related distributions distributions distributions gain gain gain equal approaches approaches mit steps steps comparison update support dependent dependent dependent dependent dependent dependent source source source modeling institute institute department department implementation implementation implementation implementation implementation technique internal kernel represents represents final scheme scheme scheme sequences computing domain solutions limit limit trajectory stage efficient efficient requires requires requires requires requires requires choice approximate basic condition condition condition derived area finally selected backpropagation iteration depends measured discussion technical feedforward arbitrary fast fast amount amount amount amount require main ability easily easily makes makes rumelhart rumelhart development development including typically underlying needed needed dynamical dynamical dynamical dynamical dynamical dynamical functional functional functional functional fully technology technology technology principle principle principle details stored early decay decay attention choose run denotes denotes discussed discussed recent advantage sense recently relevant interest interest interest sufficient highly highly previously calculated works tions tions tions solve yields yields differential trans evaluation evaluation interval interval interval williams williams storage storage storage storage exists expression expression expression concept concept concept scaling suggests wide derivative derivative derivative derivative matrices alternative boundary boundary generally hardware hardware flow critical place minimal assumptions reduce trajectories conclusions operator differences numerical numerical numerical numerical numerical faster constrained encoding encoding integration integration reduction sigmoidal california california min iii introduce introduce introduce derivatives manner manner explicit written written solving solving solving solving solving describes laboratory laboratory stability mathematical mathematical sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity explicitly simultaneously involves involves involves transformations unique scales scales scales scales scales scales scales scales scales integrated integrated minimization minimization implies select select select national expressed stages solved solved solved solved solved solved solved evaluate restricted evolution static suggested suggested constants partial closed calculate symbol foundation advantages topology coupling thesis inter sciences sciences discuss specifically coupled phys discussions characterized major simplicity straightforward straightforward selecting selecting selecting capable importance computationally computationally computationally divided attractors schemes identity characteristic summary notice heuristic interested issue contribution oscillations notation quantity write paradigm backward acknowledgments decreasing oriented carried poor requirements requirements difficulty strengths integral helpful existence fashion school behavioral mappings mappings mappings terminal variational analytically authors authors authors office referred tanh func topographic fundamental neu math math math gradients gradients gradients concepts concepts quantities formal observe store submitted submitted integrate stop developing costs costs agreement derivation phenomena expensive expensive multiplication multiplication briefly lies lies considerable straight purposes purposes sys widely constructing operators operators operators operators operators operators operators involve opt opt opt implicit mellon addressed summation integrating carnegie limits cmu poorly formulated treated treated requirement requirement gains perturbations pittsburgh incorporating pasadena enables enables inherent focused focused univ identifying feasible sv appearance formally formally martin partitions naval proceed proceed consideration difficulties tools interconnection attractive moment observing ral methodology methodology methodology methodology monotonically lyapunov date combines governed interconnections enable enable enable neuromorphic eng eqs eqs pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter lett inf inf convergent adopted acknowledge severe zipser zipser multiply multiply multiply largely rigorous solves achieving encodes par obtains auxiliary auxiliary auxiliary algebraic illustration illustration evolve werbos werbos efforts cation drawback drawback drawback applicability dramatic port exploited differentiating continually pineda pineda pineda pineda architectural rewritten rewritten handling ase ase ase ase ase impractical jet jet lated adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint adjoint eliminates harvard val bilinear bilinear ning practically equa equa propulsion propulsion characterizes exploits exploits rameters zipset william appl appl firm 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#@Barhen_J,Toomarian_N,
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local local form simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual small size feature feature feature work fig cells cells cells cells cells field features cell cell cell cell cell cell cell response similar similar show show fixed general general real average average average theory theory obtained term term note note activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional university computation research defined defined defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial terms distance connections connections connections connections connections connections connections connections connections connections connections connections science presented phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase frequency frequency frequency machine object range range range range basis nonlinear abstract find properties properties properties references procedure introduction behavior behavior behavior behavior stimulus stimulus variance variance difference difference difference complexity spatial signals chosen chosen higher cases cases cases type cortex cortex cortex cortex cortex cortex long long long long distributed distributed distributed equations fact proposed correlation correlation correlation correlation total human computed multi sum sum performed eq times times times potential made orientation global global global specific series provide compute location eye determined connected connected connected connected distributions cortical cortical cortical brain power comparison larger connection connection connection connection connection connection connection connection connection connection connection connection connection support support dependent department loss responses exp scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme addition framework equivalent curve additional limit limit significant basic basic increase coding coding weighted randomly randomly randomly levels types product processes selected nature biological biological biological achieved measured discussion increases amount amount short nearest nearest nearest generate supported role role require eds square square auditory auditory typically pairs pairs pairs jordan significantly significantly mechanism mechanism uniform uniform uniform uniform uniform making early attention description neuronal neuronal neuronal neuronal neuronal neuronal pair robust robust movement reported reported introduced identical identical subset array array array recently interest interest interest highly tuning yields achieve sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse address address address locations separation separation grid grid grant constructed studied strength strength strength neighbor neighbor interactions differences differences numerical clear peak strong physics physics largest cycle cycle california solid variety variety groups connectivity connectivity connectivity connectivity connectivity connectivity force question areas appears longer longer ways plot plot transitions metric implement physical slightly text consisting interaction interaction interaction interaction interaction mutual frequencies equilibrium shift versus potentials national expressed expressed squares squares squares squares influence influence fraction evolution evolution centered neighborhood neighborhood neighborhood event distances foundation foundation foundation eeg eeg koch koch koch koch koch koch koch coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling figures perceptual coordinate inter plotted plotted plotted coupled coupled phys neighbors neighbors characterized aspects differ effectively wij oscillatory oscillatory schemes schemes schemes schemes schemes schemes receives verlag strongly strongly dis superior sin oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations gray gray gray involved play cat neurosci received neighboring rat intrinsic powerful exhibit exhibit rapidly rapidly oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator periodic biol office oscillation phases phases phases phases phases phases examined configurations opposite olfactory olfactory separated nervous isolated indicating site cos derivation considerable rapid rapid berkeley scientific acknowledgement begin geometry cybernetics cybernetics nsf reflects populations freeman freeman understood generic generic lattice lattice recordings incorporated slower ity pasadena singer singer singer germany coherent coherent coherence begins begins synchronization synchronization trade indices cybern primarily investigation ordering bin unity caltech systematic air biased excellent started ranging james lengths bulb bulb young locked impact impact variants summarize parsing slight slight slight numerous numerous sine fellowship exhaustive ram reaction magnetic flat evoked evoked sinusoidal massively neurophysiological jij jij jij interacting interacting interacting interacting interacting crosses concentrate fir synchronized oscillating locking locking locking locking locking locking locking locking universit dramatic signs signs signs signs regularities corners institut mcdonnell virtually drawing award wiring pronounced tribution peaked striking triangles emerges progressively sym nontrivial neurobiological curved ods sian evolves permanent permanent materials ruderman ruderman ruderman ruderman gaus acknowledges bauer prominent tenth massive christof probabil linking daniel daniel wagner wagner wagner investigator cats rij tightly schuster schuster schuster schuster schuster schuster schuster schuster remarkably columnar fiir incident awake tiny tiny niebur niebur niebur niebur niebur niebur consciousness eckhorn eckhorn kammen kammen kammen kammen kammen theor logothetis logothetis snapshots presidential crick crick physik poorer engel highlights rabbit conserved nected neurophys peri jii jii revealing prog cial clicks swiss frg postdoctoral separations separations separations separations diamonds diamonds opposing tiles ported lattices geometries geometries thouless thouless diffusive kiel kiel cou pled pertaining creases kruse radically artifi mathe click confine oid matically ksnig theoretische anesthetized physicists elect wid wid brosch ernst munk 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obtained term note note activity activity dimensional result computation solution solution solution solution solution solution solution solution solution research research dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant standard standard terms distance distance distance left present frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency press press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied back convergence density properties references due due positive propagation context introduction action complex complex complex hand hand circuit behavior behavior behavior behavior behavior behavior statistical effect parallel recurrent recurrent tion tion tion change change change change difference complexity variable variable variable variable variable variable variable spatial measure measure chosen chosen higher higher center center firing type required required good good conditions conditions distributed distributed distributed distributed distributed distributed distributed equations equations equations equations equations make fact fact fact fact fact correlation observed observed simulations simulations resulting simulation human human human respect eq eq eq eq eq eq eq eq eq eq eq eq eq called potential natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback study negative negative negative negative negative original vol relative relative compared series series determined experimental related related gain gain gain discrete equal comparison larger larger dependent dependent source proceedings institute words words kernel kernel kernel kernel kernel kernel kernel kernel kernel delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay scheme considered equivalent curve curve solutions limit limit limit limit limit limit limit effects approximate levels area area types finally inhibitory simply biological biological discussion increases increases group group fast corresponds corresponds stable stable stable stable circuits circuits short common supported supported role theoretical hypothesis makes noisy noisy noisy typically smaller combination dynamical dynamical transfer interesting significantly ratio leads inhibition normalized magnitude magnitude attention added added sources light light light light light light light light light light membrane population property property robust period side side sense sense engineering tions studies studies studies studies differential differential differential differential differential differential differential differential increased increased amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude intensity occur occur occur suggests suggests suggests deviation feed move deterministic deterministic deterministic deterministic occurs occurs occurs occurs occurs occurs occurs generally setting critical critical critical depend accurate numerical numerical numerical clear clear presence presence presence presence external external cycle cycle cycle cycle cycle cycle proportional iii construct laboratory laboratory ann stability stability stability stability infinite involves equilibrium equilibrium equilibrium equilibrium equilibrium springer implies implies versus versus choosing national national focus focus focus depending viewed variation fraction understanding understanding approximated sizes converges past past diagram earlier calculation additive additive delays delays delays delays delays delays msec coupling retinal retinal sciences sciences plotted illustrated specifically specifically coupled variations variations variations variations phys gamma determining aspects aspects encoded delta delta oscillatory oscillatory tend summary summary verlag strongly strongly induced interpreted dis oscillations oscillations oscillations oscillations physiological sci sci absence absence absence realistic delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed principles extract decreasing decreasing modelling modelling origin stimulation parametric parametric essential exhibit exhibit varied involving involving periodic school investigated biol biol biol biol biol muscle oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation affect understand math math math math math onset onset onset onset onset onset onset onset onset onset onset rev bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation der der der nervous detected mixed mixed extent extent plant plant histogram histogram histogram unstable slope slope slope glass glass glass glass nonlinearity organized division axon acknowledgement acad calculations auto author qualitative qualitative qualitative qualitative fluctuations fluctuations fluctuations fluctuations explained pathways pathways transient autonomous autonomous share passed frequently rep operate exhibits berlin occurrence serve suited wesley displays shifted ordinary cybern notes addison appropriately appropriately velocities impossible grows numerically stronger occurred occurred city los los los keeping keeping occurring monotonically monotonically affected responsible exceeds exceeds muscles muscles motivation weakly bad bad accounts infinity candidates enable modelled modelled modelled insight environmental canada reverse santa switches approx reflex reflex reflex reflex reflex reflex reflex reflex neurophysiology summer ties opposed forced conjecture par ease ideally ical affects forcing mackey mackey mackey mackey mackey mackey mackey mackey mackey mackey mackey conduction mathematically regulation regulation convert paris disease emphasized anal reveal reveal reveal siam sta intensive lecture externally ble council sees resolve sake oscillate diffuse affecting tribution practically settle equa regulatory comprising hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf hopf constancy prone amplified appl appl lags vicinity brainstem alamos alamos alamos prominent syst syst recalled undergo undergo unimodal 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#@Longtin_A,
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visual visual paper small small small size size size size feature work work work fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field features current current current current current cell cell cell cell cell cell high high response similar similar representation architecture show show show show show show show equation line line vectors general general general real real approximation approximation states obtained obtained experiments experiments dimensional dimensional dimensional dimensional university university university threshold variables variables computation computation computation computation computation computation research research research research independent independent defined dynamics dynamics dynamics dynamics dynamics computer terms distance distance connections synaptic synaptic synaptic science left presented presented present phase phase phase phase phase phase phase phase phase phase phase low low low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object object object object object object object object sets motion range range range range range press press position abstract abstract applied find analog analog analog analog analog analog analog analog analog properties properties references introduction action complex complex behavior statistical statistical statistical statistical dynamic dynamic change change energy energy difference complexity variable variable spatial spatial spatial spatial spatial lower measure measure measure signals signals signals signals signals part part part center center center theorem firing firing firing firing firing firing firing firing firing firing firing firing cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike long long expected expected equations fact fact fact region region region region correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length length length length length length length length length length length observed scale scale scale scale finite finite finite simulations simulations simulations simulations simulations resulting ing total total simulation computed sum eq eq eq eq times regions regions mapping mapping dimension dimension dimension dimension made made natural orientation orientation filter true receptive provide provide provide objects objects objects objects objects objects proc proc active active active connected connected connected connected connected connected cortical power power voltage voltage voltage voltage support train train train dependent source institute institute department synapses synapses synapses code individual responses exp exp bias scheme cambridge cambridge experiment directly view stimuli stimuli effects determine upper choice statistics free pages increase give area area types types actual evidence nature inhibitory simply biological biological biological measured discussion describe tested excitatory predictions predictions predictions circuits short short nearest nearest nearest nearest nearest effective effective effective effective shape shape synapse synapse synapse supported theoretical require journal square square easily makes including fit simulated pairs account jordan transfer interesting interesting significantly ratio character mode leads details call call call direct decay decay decay decay idea run added description description description predict predict predict neuronal denotes discussed recent recent correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations pair robust takes period sense sense sense array array array array array array array recently relevant relevant dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions highly observations volume tuning tuning tuning tions tions solve achieve rl address chain sensitive entire entire grant scaling scaling spikes derivative predicted locally locally clusters clusters clusters white pass strength strength critical critical critical critical critical critical critical critical critical critical critical critical critical critical critical critical critical critical critical critical reduce neighbor neighbor neighbor editors interactions interactions differences numerical numerical clear clear exponential exponential exponential temperature temperature temperature suggest suggest suggest suggest suggest encoding encoding physics external external external cycle characteristics california california proportional scene acknowledgements explicit relation describes transitions ann mathematical changing sensitivity infinite infinite physical physical electrical angle scales interaction interaction interaction implies potentials john national expressed dependence dependence detailed evaluate restricted showed forms static static sizes constants spectrum spectrum key key reasonable delays classical intervals add valid construction foundation foundation topology topology topology topology expect fire thesis usa currents eigenvalues eigenvalues sciences specifically absolute neighbors neighbors neighbors neighbors discussions major regular regular regular regular capable spiking spiking oscillatory oscillatory oscillatory oscillatory oscillatory build computations essentially essentially fine fine fine reached characteristic capture contained sin oscillations oscillations sci gray gray write simplified realistic realistic realistic wave delayed ill ill ill ill ill ill cat neurosci operating extract extract extract neighboring deal extend trains trains trains trains trains trains trains american essential exhibit exhibit exhibit exponentially exponentially helpful detectors biol int structured oscillation encode encode presynaptic act act editor reading man rev voltages assumes separated mapped mapped extent regime regime regime regime motivated phd finds spin spin spin spin spin spin spin spin spin spin spin spin histogram site great slowly cos crucial agreement phenomena independence glass london comparisons berkeley berkeley berkeley berkeley berkeley widely filtered filtered filtered precisely precisely broad broad located consequence consequence ion ion acad auto auto qualitative qualitative sun fluctuations mechanics lattice lattice peaks peaks operate perturbations characterize incoming qualitatively qualitatively qualitatively collective singer singer richard display tile tile tile tile tile tile traces realized trade cybern physiology addison princeton arguments arguments refractory nat interconnected arrival fits chains biased biased hope reasoning arrays 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#@Bialek_W,Kruglyak_L,
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time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output number number number system system system system system system system system system system system system error error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state results results results results units units units units units units problem problem problem problem problem problem problem models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based space linear linear linear linear linear linear layer layer case case case case case case case case case case vector vector vector order order order shown shown systems systems systems systems systems systems systems systems systems systems values values values values values values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise functions functions unit unit distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach pattern point point point point point single single processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control local test test analysis inputs inputs inputs form form form form form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms gaussian paper paper paper paper examples examples fig fig fig fig fig fig fig fig step step step step process process process process current trained trained trained trained trained structure structure problems problems random random high high similar similar similar representation representation architecture architecture architecture architecture architecture architecture show section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed vectors general general generalization speech speech speech speech speech speech speech parameter parameter parameter real real real real approximation average states states states states states states states states states states obtained obtained obtained obtained term solution research independent independent independent independent independent defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics estimate prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left left left left map map map map map map present present present present present present activation temporal temporal temporal maximum maximum maximum maximum maximum maximum range press press press learn learn position position nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous continuous continuous continuous sample sample sample sample abstract applied back back back back back find computational density properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due due due ieee ieee ieee procedure procedure procedure propagation propagation propagation propagation propagation propagation introduction estimation statistical statistical statistical generated generated generated generated generated generated generated generated generated generated parallel change change change difference complexity variable assume signals signals signals signals signals signals signals signals word word word word word word word word word word word word chosen part previous previous previous previous previous previous type binary represent represent distributed distributed markov markov markov markov markov markov markov markov markov proposed proposed proposed proposed proposed proposed proposed proposed proposed correct observed errors forward forward finite finite finite finite finite finite minimum resulting resulting tasks tasks tasks respect respect multi multi multi multi sum performed performed performed performed eq eq eq eq eq eq called times mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means potential made global applications applications applications applications applications vol vol vol vol specific samples samples samples samples samples true series series series series series series series proc proc proc proc experimental experimental related constraints connected connected connected connected connected connected connected connected connected connected discrete discrete equal mit accuracy accuracy accuracy comparison connection source source source source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling words words words words department technique consists consists internal joint joint joint joint represents represents represents exp layers layers graph graph graph sequences considered considered considered considered equivalent equivalent equivalent equivalent equivalent hinton additional additional additional stage approximate approximate approximate approximate approximate world estimated estimated estimated estimated estimated estimated basic produce derived criterion types actual processes selected iteration measured discussion covariance normal describe describe group tested tested tested hmm hmm hmm assumption finding common implemented implemented implemented implemented implemented main end ability ability hypothesis future easily rumelhart including including probabilistic underlying underlying account account account dynamical dynamical dynamical dynamical unknown unknown coefficients coefficients fully fully fully fully fully fully fully interesting segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism special special structures mode operation numbers max frame frame frame frame minimize produced produced produced produced choose choose sources description description predict predict denotes denotes denotes denotes denotes recent exact exact reported recently recently recently recently interest interest varying varying varying varying varying varying varying varying varying varying varying observations observations observations observations observations observations observations calculated axis axis speaker speaker speaker match match evaluation evaluation evaluation evaluation evaluation evaluation observation observation observation observation observation observation williams horizontal invariant invariant invariant extended predicted predicted predicted deterministic white pass pass minimal row segment segment valued sigmoid measures accurate characteristics characteristics sigmoidal assuming assuming minimizing minimizing minimizing groups identification acoustic acoustic appears digit digit digit digit digit produces produces generating estimating estimating transitions vertical distinct modeled modeled modeled modeled modeled modeled modeled modeled modeled implement simultaneously dimensionality consisting applying predictive minimization minimization minimization minimization minimization minimization yield choosing extracted focus dependence stationary stages overlap viewed interpretation solved solved solved solved variation evaluate restricted restricted frames frames static understanding approximated digits digits digits allowed past past past key partial intermediate msec msec string recorded exploration usa strings strings bell extension illustrated automatic candidate discussions discussions characterized simplicity closely closely capable maximal divided driven driven delta delta successful efficiently score situation reached capture capture summary soc procedures generative duration duration sampled write providing wave observable observable observable observable observable observable observable observable observable observable observable observable observable hypotheses maximization predictor predictor attempt consisted illustrates minimized remain parametric parametric parametric layered layered layered layered layered layered layered layered layered layered layered biases helpful matches matches detectors detectors maximizing variability variability variability variability complicated proved encode cognition hill math recognizer adjusted versions versions assumes logistic logistic logistic logistic logistic switching multivariate speakers speakers speakers arbitrarily arbitrarily chaotic chaotic chaotic years considerable inside arise controls laboratories probable separately sounds varies greatly spoken spoken spoken spoken capability solla continuously compares passes switch switch switch switch switch switch switch switch characterize differs modulated proven proven marginal adjust inherent comments implements implements implements implements implements viterbi viterbi viterbi viterbi utterances utterances june yielding distortion distortion accomplished optimality restrict driving driving perfectly murray khz accepted keeping tishby effectiveness obstacle spurious spurious spurious introduces 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time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output number number error error error error error results results results results results results results units units units units units units units units units information information information information information information information hidden hidden hidden hidden hidden hidden performance performance performance performance performance based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer case order shown shown systems systems parameters parameters parameters parameters parameters parameters parameters neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition method method approach approach approach approach pattern pattern pattern pattern point single single processing processing processing processing processing processing processing processing large large local local neuron neuron neuron neuron neuron neuron neuron patterns patterns optimal shows signal signal signal algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian small feature work work task task task task task task fig fig fig features features classification classification classification classification classification classification level trained trained trained trained cell problems random random random random high memory similar similar architecture architecture architecture architecture architecture show show section fixed fixed line line rule rule rule rule rule rule rule rule generalization generalization speech speech speech speech speech speech speech speech parameter parameter real gradient obtained obtained experiments activity activity activity university threshold threshold computation computation research sequence sequence sequence constant constant constant constant constant table table standard standard standard standard computer distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections science left activation low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal press press learn learn learn sample abstract applied applied back back back back find references ieee positive important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation propagation context context context context context introduction behavior parallel change change change change variable assume rules rules rules rules rules rules rules rules rules rules rules signals representations representations learned learned chosen higher center center previous cases spike spike spike long represent represent distributed distributed distributed make make proposed proposed proposed correlation length observed simulations simulations simulations tasks tasks computed respect respect respect respect respect respect sum times means means means means potential potential study study knowledge artificial artificial artificial artificial artificial artificial samples compared application provide compute compute rates connected connected brain brain mit mit steps comparison connection connection connection connection connection connection connection connection connection connection support descent dependent dependent morgan morgan proceedings proceedings proceedings proceedings implementation internal internal advances advances joint represents represents delay delay delay delay delay delay delay delay delay delay delay delay sequences sequences sequences sequences cambridge hinton hinton hinton hinton view san effects conference determine efficient significant significant speed pages pages increase increase derived derived derived weighted weighted levels area area lines discussion describe describe tested tested tested limited amount short effective implemented shape require main journal journal journal rumelhart rumelhart rumelhart kaufmann kaufmann smaller smaller needed needed needed hopfield combination testing testing significantly significantly leads representing window window window window window window window window window window window window window window window window window window window window window window window window window international supervised supervised supervised supervised added added added added architectures improve improve resolution resolution resolution resolution advantage robust typical moving recently relevant relevant relevant engineering varying compare compare observations smooth smooth speaker studies evaluation chain williams williams increased increased parts parts parts parts suggests suggests suggests deviation wide derivative derivative derivative derivative derivative correctly move width width width width width width width width width width width width width width runs runs place greater reduce editors designed solid proportional proportional variety variety decrease decrease derivatives program acknowledgements pro derive implement adding adding applying events events extraction independently independently depending phoneme phoneme phoneme phoneme phoneme evaluate centered centered understanding suggested partial earlier delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays add add initially construction foundation euclidean advantages transactions existing existing existing existing box perceptual combinations activations activations activations sciences determines activated activated activated activated activated activated activated importance society society mcclelland successful successful tdnn tdnn tdnn invariance situation vowel reached compact kind kind kind kind allowing interpreted neuroscience split classify cues modular cat automatically automatically automatically automatically automatically received carried diego powerful environments hanson hanson optimized optimized dotted dotted graphical helpful helpful postsynaptic rise ideas school investigated relationships authors comparable variability cognition waibel waibel waibel waibel waibel waibel waibel waibel plausible onset changed changed adjusted obvious explored initialized initialized initialized initialized motivated motivated motivated great stop stop slowly derivation derivation derivation explanation majority majority cascade caused starts formalism desirable laboratories mathematics axon axon describing axons axons mellon robustness robustness robustness robustness carnegie simulate music span pittsburgh ture tank phonemes phonemes phonemes phonemes phonemes phonemes achieves acoustics adjust enables enables decreased shaped shaped windows windows windows windows windows windows windows windows windows windows windows windows windows windows windows windows deviations june june irrelevant shifted spectra resources tem adjusting adjusting adjusting adjusting adjusting adjusting adjusting adjusting adjusting grow utterance 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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input function function figure time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks training output output system system system system system system system system system system system system system system system system state state state state state units units information information information models models models models models models models models models models models space weights weights linear linear linear linear linear layer layer layer layer case case vector vector vector vector order order order order order systems values parameters parameters parameters parameters weight weight weight weight weight weight weight recognition recognition method approach approach approach single processing processing processing processing processing local neuron rate patterns patterns matrix matrix matrix matrix matrix optimal form form form signal signal signal paper paper small net net net net net net net work classification structure structure structure structure structure structure structure structure problems memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar architecture show show equation equation fixed line line rule rule rule rule rule rule rule rule general general general generalization speech parameter parameter approximation approximation states states states states states states theory theory theory theory theory theory gradient gradient obtained term term note note dimensional dimensional dimensional dimensional dimensional result university university variables variables variables defined dynamics dynamics constant synaptic science present present phase activation temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine abstract convergence analog properties references due ieee procedure important adaptive introduction dynamic dynamic recurrent complexity assume rules rules signals signals signals word part type type type equations equations equations equations equations equations equations equations techniques proposed proposed correlation total computed sum sum eq means made applications obtain vol application application define compute objects objects proc related related related discrete discrete discrete approaches train dependent nets nets report words words department department consists kernel kernel kernel kernel connectionist delay delay delay delay delay delay delay delay domain equivalent equivalent directly solutions effects requires derived weighted area finally associative technical feedforward feedforward arbitrary limited close stable stable finding short short effective implemented shape shape supported adaptation easily hopfield hopfield hopfield hopfield hopfield combination combination functional functional functional jordan jordan jordan interesting direct direct direct stored normalized normalized normalized depth depth decay decay correlations correlations property reported introduced include cognitive engineering engineering conventional conventional conventional conventional conventional works yields yields differential differential differential differential diagonal generalized extended extended alternative locally occurs strength hebbian hebbian hebbian hebbian hebbian hebbian conclusions interactions interactions interactions peak exponential strong external question question attractor explicit explicit relation relation written written ways sequential describes stability mathematical physical electrical electrical involves develop expressed expressed expressed expressed operations restricted static static approximated suggested suggested past past past additive additive additive additive additive additive additive additive additive additive additive additive additive delays delays delays delays delays delays reduces valid existing existing existing kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels formulation formulation formulation weighting illustrated holds partially partially characterized successfully gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma regular regular encoded delta literature tdnn tdnn tdnn tdnn tdnn tdnn refer notice conf procedures procedures procedures oscillations criteria hold hold hold delayed delayed leading acknowledgments exponentially recursive links applicable int encode encode encode encode trace plausible adapt implementations formal hebb hebb arbitrarily submitted isolated isolated developing growth convolution convolution convolution convolution convolution convolution convolution convolution convolution derivation adapted answer cascade implementing incorporate consequence grossberg grossberg grossberg nsf elman elman elman lack cohen cohen incorporated formulated formulated polynomials tank tank tank tank tank substantial traces simultaneous simultaneous ordinary approximates concerned homogeneous flexibility establish multiplicative familiar generalizes lang lang spatiotemporal augmented augmented concentration grants lag associations associations basically basically super encodes utilize principe principe principe principe principe translated decays mathematically disadvantage parallelism differentiating rewritten topologies species junctions utilizes inclusion core substitution crl enabling completeness jose decompose vries vries nov substituted leaky evaluates ecs preset ies ies cse cse tapped tapped wtx simplifications nxn structurally postulate reformulated concentrating florida florida integrators bert recency recency collapses dispersive reverberating gainesville gainesville communicates odes odes odes biosciences affirmative 
#@Principe_J,de-Vries_B,
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set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output number number number number number system system system system system error error error error error error error error results results information information models hidden hidden hidden performance performance performance based space space space space space space space space weights weights weights weights weights linear layer layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector functions functions functions functions functions neurons recognition recognition method method method method method method method method pattern pattern pattern pattern pattern pattern pattern pattern point single processing local neuron test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns shows algorithms small small small size size net work work methods methods step features features features classification process level level level level level level level current current problems problems random random high memory memory response similar similar representation architecture architecture architecture architecture architecture architecture architecture show show fixed line line vectors vectors vectors vectors vectors real approximation approximation approximation approximation theory theory theory term dimensional result university university university research found found constant constant constant estimate estimate estimate estimate estimate standard standard standard computer distance distance distance distance node node node node node node node node node node node science prediction prediction low low nodes nodes nodes nodes nodes nodes nodes machine maximum maximum maximum maximum maximum maximum press press basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs abstract applied applied back back back back back back find find find convergence analog analog analog analog properties likelihood likelihood likelihood likelihood likelihood references stochastic ieee procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation introduction complex complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance parallel parallel prior learned chosen part part part part part previous previous previous previous bound cases cases cases cases type required good good good good distributed expected techniques techniques proposed proposed proposed correlation errors forward simulations simulations tasks tasks total simulation simulation simulation simulation performed called elements elements elements mapping mapping mapping means factor made made study original original vol vol artificial samples samples samples samples samples compared compared compared application desired provide define define compute location location goal connected connected discrete discrete discrete mit mit accuracy comparison train nets morgan proceedings proceedings proceedings department version version version consists consists code code code connectionist layers sequences maps cambridge cambridge domain domain domain domain hinton limit stage upper requires requires estimated basic increase increase con produce developed area controller processes processes processes processes processes selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation simply feedforward increases arbitrary arbitrary denote denote tested close stable amount short generate require main future future easily rumelhart rumelhart kaufmann pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs needed combination unknown unknown transfer transfer transfer transfer transfer interesting interesting significantly special mode mode mode mode call iterations making stored stored normalized normalized bottom bottom bottom supervised supervised supervised supervised supervised supervised expert magnitude idea combined run run description predict architectures advantage pair pair element element period previously previously works tions converge address background modified modified modified modified interval williams organization improvement entire entire concept concept occur feed flow flow flow flow flow flow flow flow conclusion performs faster practice learns learns hard largest reduction radial start identification program question construct construct category category category category category category unique adding formed competition competition family focus codes detailed updated organizing organizing centers centers understanding classical classical roughly roughly interpolation norm norm euclidean existing inter determines activated activated variations black determining extra modification divided poggio poggio presentation build comparing online online stopping classify criteria categories categories sampled generalize providing attempt acknowledgments origin origin detail recursive giving school incremental incremental incremental incremental incremental plasticity scaled scaled scaled proved func cover cover cognition smallest closest closest created obvious algo explored art art art art art art art art art art art art art art art 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accomplish optics quick ings steve cyclic carpenter carpenter carpenter carpenter carpenter huge subnetwork subnetwork subnetwork subnetwork subnetwork subnetwork plastic subnetworks subnetworks subnetworks subnets subnets subnets subnets disadvantages mason offline offline offline ant novelty george neighbouring neighbouring arma arma arma arma arma categorized categorized accelerate cate resemblance resemblance ljung ljung interpolator ryan ryan relearning wash wash liquid liquid liquid liquid liquid liquid liquid ifi conven analyzes bfgs sisting polation 
#@Sorheim_E,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input data function function time time time time time time time time time time time time time set networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm number number number number number system system system system system system system system system system system system system system system state state state state state state results results results results results results results information information information information information information models models performance based space space space weights case case case case case case case case case order order shown shown shown systems systems systems systems systems values probability probability probability parameters parameters parameters noise noise noise weight functions neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition approach approach approach pattern pattern pattern point point point single single single single single single processing large neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis class class matrix matrix inputs form form shows signal signal signal signal simple simple simple gaussian examples size size size feature feature net net work task task task methods cells cells step step step points points field process level level cell cell cell structure random random high representation representation architecture architecture fixed fixed fixed line rule general general generalization generalization average states states states theory theory term term note note note result variables computation defined defined defined found found found sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics terms terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic presented map present present present temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal motion motion motion continuous continuous abstract back computational references stochastic stochastic stochastic due due positive important important important important propagation context context introduction action hand behavior behavior behavior behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical parallel parallel change energy energy energy difference variable assume rules rules measure signals part firing firing multiple represent equations equations equations proposed errors finite finite finite finite simulations simulations simulations simulation respect respect times factor natural natural global applications applications study study study study study study knowledge obtain obtain original original original original artificial relative specific true true true compared provide define define define define proc proc proc perform connected brain equal equal equal equal approaches steps steps steps comparison connection support dependent institute institute department synapses synapses synapses synapses synapses synapses synapses technique consists joint exp exp exp delay delay delay delay delay delay delay delay delay delay delay scheme scheme sequences sequences sequences sequences sequences ai ai ai considered considered framework domain domain domain equivalent equivalent equivalent view solutions solutions solutions solutions solutions solutions estimates limit limit limit limit stimuli stimuli stimuli capacity capacity capacity capacity capacity capacity capacity efficient significant basic basic increase increase con derived lines lines product product actual finally depends associative associative measured discussion technical feedforward describe close close assumption corresponds corresponds corresponds corresponds excitatory stable predictions proof amount effective synapse synapse supported role theoretical theoretical theoretical main end noisy hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield reduced account dynamical dynamical functional functional functional functional functional functional functional functional functional functional functional character york mechanism special special special structures uniform principle principle principle leads leads direct stored stored stored stored stored stored normalized normalized denotes denotes architectures architectures directions correlations correlations pair robust takes takes apply apply period period period subject identical identical sense highly compare calculated tions differential achieve diagonal evaluation symmetric symmetric symmetric symmetric symmetric generalized bounded bounded gate organization storage storage storage storage storage storage storage storage increased grant studied studied scaling extended extended extended deterministic deterministic column column column setting hardware demonstrate demonstrate conclusion starting hebbian hebbian hebbian interactions interactions interactions numerical numerical numerical asymptotic asymptotic external external external cycle cycle cycle cycle cycle cycle cycle cycle cycle proportional intelligence labeled exist exist introduce introduce manner question attractor van van van van van van van derive derive derive written sequential ann sensitivity remaining develop equilibrium equilibrium equilibrium equilibrium equilibrium springer quality quality quality quality implies potentials potentials cycles cycles cycles cycles cycles cycles cycles john decreases focus focus focus focus stationary correlated interpretation interpretation influence detailed updated fraction evolution evolution static static static static static static static static static understanding activities activities activities partial delays delays delays delays delays delays delays delays delays delays delays remains includes priori usa usa usa retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval eigenvalues sciences memories determines extension prove prove holds phys phys phys phys phys phys phys discussions simplicity columns columns columns importance successful oscillatory oscillatory attractors computations schemes reached characteristic characteristic notice kind prob prob allowing allowing link interpreted symmetry symmetry symmetry symmetry contribution content physiological sci sci sci duration gibbs involved usual play generalize delayed delayed rat rat decreasing extend explore wiley create collection exhibit strengths association association association association periodic periodic helpful existence postsynaptic school links detectors detectors biol biol fault plasticity analytically comparable tanh tanh tanh neu act math transmission transmission integer integer analyze rev rev rev rev rev created changed implementations prototype versions der noted mapped hebb hebb hebb hebb store store great advanced rows phenomena analytic analytic formalism strictly division broad broad broad choices desirable sgn acknowledgement acad acad acad calculations axons definite arises outer mechanics mechanics mechanics mechanics mechanics mechanics mechanics mechanics argument applies double understood understood pseudo fed lack quantitative quantitative quantitative formulated operate switch switch mod differs ordered tank tank pasadena asymmetric semi sophisticated unbiased findings instantaneous shifted shifted shifted cybern cybern notes tation extensive princeton arguments angular receptors proceed caltech establish clamped dealing overcome efficacy replica synchronous synchronous intuitive natl natl natl lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov published overlaps sompolinsky sompolinsky sompolinsky recovered governed periods periods overview belongs reproduce iterated axonal reveals offer arrive arrive environmental passing passing storing extensively agree lett lett generalizing fold influences mechanical mechanical sequentially linked associations associations associations associations associations associations associations constitute session ram spatio spatio spatio spatio trigger generalizations ical possibilities demon scenario jij jij jij jij jij jij jij jij jij compatible mediated concentrate careful maximally wise landscape landscape drawback turning macroscopic macroscopic programmed modifiable permit compu microscopic microscopic resembles triggered sessions sessions sessions sessions covers lecture coolen coolen copies remarks nonnegative acquire satisfactory hop utilizes reflecting hemmen hemmen hemmen hemmen hemmen hemmen hemmen formulae rons incorporation exposed partly couplings couplings couplings marcus marcus obey hamiltonian gerstner vanish retrieved retrieved retrieved neurobiological evolves teaching brackets acknowledges westervelt westervelt cyclic cyclic facts neglected recalled noiseless elaborate tolerant settles suitably kanter kanter andreas des lasting quiescent reproduces heidelberg europhys europhys amit amit amit aware miinchen taught taught taught 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#@Herz_A,Li_Z,vanHemmen_J,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model input data function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number system system error error error error error error error error error error error error state state state state state state results results information information information problem problem problem performance based based based based based based based based based based based based based based based based based based space space space space space space linear case case case case case case case case case order shown shown systems values probability probability probability probability probability probability probability probability probability probability probability probability probability noise noise functions unit unit distribution distribution distribution distribution distribution distribution recognition recognition point processing control large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class form form form form shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small size size size work work work work task task step step points process process process current current current current current problems random random random random memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar equation section section section section section section section fixed fixed fixed fixed fixed line line line line line general general speech speech speech average average average average average states theory theory theory theory theory theory theory theory note result threshold research research research research research independent log log defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate computer science direction direction direction direction presented presented presented phase phase maximum maximum maximum maximum maximum learn learn learn components sample sample abstract abstract find computational computational computational convergence references due due ieee positive positive positive positive positive positive positive adaptive adaptive context introduction change change change change change change change change change change change change change change change change change change complexity complexity assume assume assume assume assume assume assume assume assume lower lower lower measure prior prior prior prior learned learned learned learned chosen chosen chosen chosen chosen chosen chosen higher higher previous theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound cases required required required expected equations markov markov markov markov make make make make make make fact fact length length length length correct correct correct correct probabilities probabilities finite finite finite classes classes classes classes classes called means dimension dimension dimension dimension dimension dimension dimension dimension made made made made made applications applications negative negative relative specific true true true provide provide define define define define define define rates rates rates active active active active active active active active active goal approaches mit mit steps steps steps accuracy update support support train modeling selection selection proceedings report words words consists individual individual responses scheme sequences sequences sequences sequences ai ai ai ai considered framework framework framework cambridge computing computing equivalent equivalent transition transition transition limit detection conference determine determine upper upper upper requires significant pages pages pages increase increase channel derived derived derived derived weighted randomly randomly randomly randomly randomly randomly randomly randomly robot bounds bounds bounds bounds types types types actual selected iteration iteration iteration iteration iteration depends depends depends achieved technical describe describe arbitrary arbitrary arbitrary denote assumption corresponds corresponds proof proof require main face face journal hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance instance instance instance instance instance instance instance instance future easily makes makes makes development including needed technology interesting interesting significantly york special special consistent consistent consistent consistent consistent consistent consistent uniform uniform operation call max direct window window window stored stored polynomial choose run recent recent recent recent recent recent pair apply introduced include include include subset subset dimensions sufficient sufficient sufficient varying varying varying varying varying varying varying varying varying approximately yields definition background chain chain observation bounded bounded interval interval grant grant grant grant arm exists concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept invariant invariant invariant occur occur suggests suggests extended extended rotation occurs occurs conclusions conclusions faster asymptotic asymptotic weak temperature largest largest drawn drawn drawn drawn drawn drawn drawn drawn drawn california labeled labeled labeled labeled exist identification base base question denoted pro produces written solving describes label label label label label label label label distinct distinct dept changing modeled coordinates infinite electrical slightly angle frequencies events formed implies implies implies implies boolean choosing choosing national focus focus overlap learner learner learner learner learner open restricted restricted updated updated labels showed showed forms static updates allowed allowed allowed spaces reduces intervals tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking closed closed closed closed closed sufficiently sufficiently foundation existing includes includes instances instances instances instances batch batch batch batch batch vapnik vapnik vapnik vapnik extension maximize straightforward sensor uniformly uniformly build receives receives road quickly quickly lie classify sci satisfy notation notation notation vary write usual computes hypotheses principles acknowledgments load extend extend situations presents explore remain access rapidly association preliminary periodic helpful incremental incremental incremental incremental incremental incremental incremental complicated phases examined hill transmission concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts analyze predicts predicts predicts facial formal algo assumes assumes speakers arbitrarily plant advanced slowly slowly distinguish track track track track track track track majority worse starts stress drive satisfied style worst circle circle circle circle implicit annual radius nsf applies haussler haussler haussler operate mod mod mod mod adjust inherent age age returns focused focused lim lim lim univ instantaneous lot trade lab pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac college feasible sort labeling mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake formally princeton acm acm drift drift homogeneous impossible communications communications siemens siemens siemens siemens logarithmic balance analyzing unlabeled definitions receiver imply modifications symposium exploring analyses heavy sion studying thomas chooses chooses chooses chooses chooses recog eng eng indicator indicator tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker warmuth warmuth warmuth warmuth draw extends santa intersection intersection intersection intersection learnable learnable learnable consecutive consecutive mind arcs drop corporation kinematics hair leaming chervonenkis chervonenkis chervonenkis chervonenkis restrictions theorems valiant valiant valiant realize conservative conservative conservative conservative conservative conservative remainder evolve rithms compensate continues proba learnability learnability learnability adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary misclassified maintains maintains abbott abbott grateful rotating unpublished removes learners learners gratefully inconsistent corporate ongoing east coin transmitter mistakes dichotomy sided sided petsche petsche petsche petsche petsche anthony anthony cardinality restricting littlestone littlestone littlestone littlestone littlestone tracks sliding sliding sliding rivest rivest rivest rivest rivest rivest dimen evolves fair crl cruz mcgraw voice voice acknowledges acknowledges gathered benign benign motors focusing statements allowable polar tit terminology terminology ceedings nice triple collecting continuing tracked tracked modifies modifies blumer blumer ucsc symmetries shrink disagree picks picks machinery scratch draws ronald ronald seeks constantly insure fatigue vcdim vcdim vcdim vcdim vcdim vcdim vcdim aperiodic quence told ehrenfeucht rotates rotates eet persons flipping kuh kuh kuh kuh kuh kuh irreducible collects conflicts malicious malicious malicious malicious malicious aro radians corp infrequent ccr hawaii hawaii randomization airborne bilistic wear pothesis lucky lucky leam leam mislabeled ofleee illness intelligently esis hypoth foregoing honolulu 
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networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output number number number number system error error error error error error error error error state state state state state state state state state state state state state state state state state state state state results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer case case order order order shown shown shown systems systems systems values values values probability noise noise weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition approach pattern pattern single single single single single single single processing processing processing processing processing large large test test test patterns patterns patterns patterns inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form shows signal simple simple simple examples examples examples small small small small small size size feature feature feature feature net net net net net net net net net work task task task task task task task task task task task task task task task step step step step step process process process level level current current current current trained trained trained trained trained trained trained trained trained trained structure structure structure structure problems random high memory memory memory response representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture fixed fixed fixed rule rule general generalization generalization generalization generalization generalization speech real real real approximation average average average average average average average obtained term term note note note note experiments experiments university variables variables computation computation solution research research research research independent defined sequence sequence sequence sequence sequence sequence initial initial table standard computer computer terms terms connections connections connections connections connections connections connections node science science science prediction prediction prediction prediction prediction left left direction presented presented presented presented map present present present phase temporal temporal machine machine sets sets sets sets range learn learn learn learn learn learn learn learn learn outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous abstract applied back back back back back back back references positive positive positive propagation propagation propagation propagation complex complex complex complex hand hand hand statistical effect effect effect effect recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change variable variable assume rules learned learned learned learned learned chosen part part center previous previous previous previous previous previous previous previous previous previous bound cases cases cases required required multiple good good long equations make proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length length length length correct correct probabilities errors errors errors forward scale finite finite finite finite finite resulting resulting resulting tasks tasks total total total computed computed respect multi multi sum called called times times times times study study study negative negative negative negative original original original vol represented true compared desired desired series series series perform perform active active active determined determined connected discrete discrete discrete discrete discrete equal steps steps steps steps larger larger connection train train train nets nets morgan morgan morgan proceedings report report report report report version version version version internal internal code code advances advances difficult difficult difficult final final layers delay scheme addition graph graph graph sequences considered computing experiment experiment additional additional additional transition transition transition transition san determine full requires requires requires requires requires choice free world give con produce weighted weighted weighted developed finally achieved achieved achieved increases arbitrary tested tested fast fast complete finding short short generate require require journal end ability ability ability ability future degree including fit kaufmann kaufmann kaufmann smaller smaller needed needed needed needed account fully block block block interesting testing ratio character edge increasing trials trials trials trials empirical empirical empirical operation international supervised depth combined minimize minimize produced choose choose choose run run run run run run added added added added added added predict predict architectures architectures separate separate typical reported reported identical side side studies address symmetric gate williams williams williams williams williams improvement entire concept studied trial trial trial trial trial derivative correctly feed move touretzky touretzky touretzky generally pass demonstrate demonstrate runs runs runs half half place minimal minimal minimal greater reduce conclusions tangent sigmoid modules faster faster practice learns suggest presence largest california user user start start derivatives characters connectivity connectivity force question edges sequential sequential sequential distinct distinct distinct distinct dept changing remaining remaining slightly slightly slightly scales adding events letters letters letters letters letters letters national dependence interpretation influence codes evaluated fraction showed past past past diagram diagram earlier slow epochs epochs epochs epochs epochs add add initially visible string string string string string string string string string string string construction construction foundation advantages advantages topology topology topology topology avoid building building building building existing existing formulation strings strings strings strings strings strings strings strings strings strings strings strings strings strings inter recognize recognize recognize automatic automatic prove maximize maximize maximize mozer mozer mozer mozer mozer specifically specifically candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate variations partially partially grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar letter letter letter letter letter letter letter letter letter extra encoded divided effectively paths included mcclelland mcclelland presentation successful successful build score score tend ten ten ten receives receives kind kind repeated procedures strongly link link link running timing hold built built built built comp vary usual dot modular automatically attempt acknowledgments deal explore diego powerful powerful layered poor production create create essential essential investigate difficulty fewer giving history school school tech tech detectors incremental incremental incremental incremental incremental incremental reliable scores neu waibel waibel waibel act automata psychology created equally perfect perfect perfect perfect thought adjusted greedy assumes assumes precise detector detector explored store epoch epoch improving explain attempts attempts averages residual residual residual advanced stop stop directed defining cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade reasons considerable widely style pool pool pool recognized separately begin begin english toronto mellon researchers researchers requiring requiring requiring reflects considerably composite carnegie elman elman elman elman elman elman elman elman elman elman elman elman embedded embedded embedded embedded embedded embedded fed leave poorly backprop backprop backprop dots passes passes partitioning pittsburgh incoming incoming adjust logical logical focused focused begins eventually univ univ cumulative perfectly perfectly perfectly perfectly perfectly count discover inspired smith smith smith smith smith adds adds adds adds loops loops contract contract operates ral clause presentations presentations reliably slice reset paul negligible negligible competing advance tokens shortest arrive repeatedly ends broken projects consonant propagate fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman adopted consecutive sequentially boxes zipser zipser zipser zipser zipser summer unable job legal legal legal legal legal incrementally guess activate altered retain retain flip rough harder apparently turning stuck dramatic ignoring increments suggestions resembles copies hyperbolic instability marks builds builds builds oscillate dropped phonemic accomplish alex clauses eliminates unreliable agency successively deals deals squashing symmetrical zipset evolving rtrl rtrl rtrl rtrl rtrl rtrl rtrl adjusts longest permanent crl creation scott ranged schreiber schreiber correlates defense contents successor successor successor tenth backwards cleeremans 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#@Fahlman_S,
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#*network network network network network network network network network model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output number number number number number system system system system system system system system system system system system system system system system system system system error error error state state state state state results results problem problem models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based based based based space space space case vector order order shown shown shown shown systems systems systems parameters functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach pattern pattern pattern point point point point single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing control control control control control control control control control control control control control large large large large large large large rate patterns analysis matrix matrix optimal optimal optimal inputs inputs inputs inputs shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms simple simple simple simple simple gaussian paper small small net step classification classification level level level level level current current trained trained trained high high memory similar architecture architecture section generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average theory note experiments experiments experiments experiments experiments experiments experiments experiments result university university research research research independent independent independent found found sequence sequence sequence sequence sequence target computer distance distance science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction present present machine nonlinear nonlinear outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract properties references ieee ieee ieee ieee ieee ieee ieee ieee ieee ieee ieee ieee positive positive positive procedure procedure decision mixture context context context introduction hand dynamic dynamic dynamic dynamic dynamic variance tion tion tion difference classifier word word word word word word word word word word word type required multiple good good good binary binary binary binary conditions bayesian markov make make make fact techniques region proposed correct errors errors errors errors errors errors forward forward forward forward forward forward finite resulting classes tasks tasks tasks tasks total computed computed computed computed multi performed performed regions regions regions made made made negative relative represented represented series compute compute compute compute proc proc proc proc proc proc proc proc proc proc perform determined experimental connected power steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy connection support support support train dependent dependent dependent nets nets nets nets modeling modeling modeling modeling modeling modeling words words words words words words technique consists consists connectionist difficult delay delay sequences domain equivalent directly hinton top stage stage stage conference conference conference conference conference conference conference conference conference conference upper significant approximate free speed speed con con produce produce area path path path path path path actual actual actual actual actual actual provided finally finally backpropagation achieved achieved achieved achieved describe tested tested hmm hmm hmm corresponds corresponds predictions predictions predictions predictions predictions predictions short short theoretical main main hypothesis hypothesis future easily makes including reduced unknown coefficients coefficients programming testing testing testing testing significantly segmentation database database database leads making window bits international international international international international international international international international bottom frame frame frame frame frame frame frame idea run architectures improved improved improved improve advantage typical similarity introduced sense varying works smooth speaker speaker speaker speaker entire entire studied invariant predicted predicted predicted predicted alternative feed pass pass pass pass pass pass conclusion reduce segment measures measures measures accurate accurate accurate performs faster faster integration intelligence labeled averaged acoustic acoustic acknowledgements explicit pro produces modeled modeled modeled metric multilayer category slightly slightly slightly spectral spectral spectral spectral integrated integrated predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive shift yield national phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme overlap densities evaluated frames frames frames frames frames frames frames forms similarly translation translation translation discrimination discrimination partial classical purpose msec foundation euclidean kohonen advantages classified topology topology transactions transactions recorded recorded instances instances illustrated discuss black successfully straightforward hmms hmms hmms suitable delta computations tend tend tend receives notice phonetic dis classify duration backward backward hypotheses predictor predictor predictor poor poor create varied strengths strengths replaced replaced replaced limitations discriminant school links analytically authors office decisions symbolic scores neu waibel waibel waibel waibel waibel waibel waibel waibel waibel circles versions obvious portion portion mapped mapped speakers speakers improving sentences ment distinguish fairly fairly nonlinearity comparisons lin sys sections strictly ran laboratories recognized english arises mellon alignment alignment alignment alignment alignment alignment alignment raw integrating integrating carnegie pure introducing recordings templates passes vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary pittsburgh modulated phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes curvature achieves acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics phone germany hamming conclude sentence yielding distortion distortion cor redundant ear lvq tem khz siemens replacing tishby utterance utterance utterance utterance ral bourlard canonical canonical canonical canonical responsible meaningful mance sion predictors predictors predictors predictors predictors predictors predictors predictors predictors predictors predictors predictors perfor lang percepttons candidates dif darpa april april april april april april april acknowledge accumulated unchanged linked linked linked linked linked linked linked linked linked yielded ence ple revealed warping warping levin levin cessing degraded carefully march iso concentrate sam sam suffer induces atr recognizers nec gratefully council recogni recogni savings ferent confirm interpreting fill december phonemic alex japanese jain eral spectrogram spectrogram spectrogram exposed triangles triangles fft specialization comprising digitized nontrivial presently concatenated acknowledges acknowledges corn indirectly watanabe inaccurate problematic saito wellekens spotting elegant accuracies dtw dtw align virtue virtue shikano shikano spectrograms spectrograms weakness saved registration puted proving univariate perplexity perplexity perplexity perplexity rendering circumvent tebelskis tebelskis tebelskis tebelskis tebelskis tebelskis tebelskis pared ration hanazawa granularity weaknesses weaknesses routed ist otto sev specialize specialize confer backpropagated backpropagated backpropagated males silence joe extrapolate pling multilayered linkage linkage linkage 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#@Petek_B,Schmidbauer_O,Tebelskis_J,Waibel_A,
#t4
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data figure figure time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output output number number number number number system error error error error error error error error error error error error error error error error error state state state state state state state state state state state results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based weights weights vector vector vector order order order order shown shown values weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition approach pattern single single processing processing large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test test patterns patterns analysis class simple simple simple simple paper paper small net net work task task task task task task fig step step step step step step points features features classification classification classification classification level level current current current trained trained trained trained trained trained trained trained trained trained structure high high memory similar similar architecture architecture architecture architecture architecture architecture architecture architecture section vectors vectors vectors vectors vectors vectors vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech average average average average obtained obtained obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments result result result result university threshold threshold threshold threshold threshold research sequence sequence sequence sequence sequence sequence sequence initial terms science science science science map activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation low frequency temporal temporal temporal temporal machine sets sets position position position position position continuous continuous continuous continuous continuous sample abstract applied applied references ieee procedure procedure procedure procedure important decision decision decision context context context introduction effect dynamic dynamic generated generated generated parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower prior word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word chosen higher higher part previous previous cases required required required distributed expected expected markov markov make fact fact techniques techniques length length correct correct correct correct correct correct correct correct correct correct correct correct observed observed observed errors errors errors errors scale classes classes classes classes classes classes classes tasks total total total total total total total computed computed sum performed elements elements factor factor factor made natural applications study study study study study original relative true true true compared compared application series provide provide provide provide provide rates rates proc proc proc proc proc proc location related constraints constraints connected distributions steps steps larger larger connection nets morgan morgan proceedings report institute words words words words words words words words words words words words words words words words words words words words words words words words words words words consists consists connectionist connectionist connectionist difficult difficult final final delay delay addition addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences considered experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment hinton additional additional design limit limit san top top top top top top top top stage detection detection detection detection detection detection detection detection detection detection detection detection detection capacity determine classifiers upper requires choice choice produce produce derived weighted randomly randomly randomly randomly levels levels criterion criterion criterion provided selected selected selected selected evidence discussion describe tested tested tested hmm limited limited finding amount implemented generate end end end future degree development development noisy noisy noisy noisy noisy noisy including typically typically needed jordan jordan transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer programming interesting significantly significantly database language representing representing making expert expert expert combined discussed improve improve directions recent resolution robust element element element element similarity strategy strategy strategy strategy strategy strategy subset subset cognitive cognitive cognitive sufficient highly approximately match studies studies trans positions positions positions locations locations locations locations modified modified constructed occur suggests correctly correctly correctly correctly correctly correctly correctly correctly occurs boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary demonstrate designed designed designed constrained suggest suggest suggest presence presence california variety identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification acoustic acoustic question reference longer longer primary sequential sequential sequential multilayer simultaneously remaining slightly unique unique unique consisting consisting integrated integrated phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme codes variation variation evaluated evaluate restricted updated updates past past past past past spectrum spectrum spectrum spectrum spectrum reasonable performing purpose false false false false false false false boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries initially assigned includes activations activations activations activations activations activations activations activations activations activations perceptrons strings weighting weighting instances instances instances instances recognize automatic prove specifically candidate candidate candidate candidate candidate candidate candidate candidate variations variations variations variations tests tests successfully successfully identified identified identified identified identified identified identified identified extra closely importance society differ differ divided included included successful identify identify identify identify schemes comparing situation miller procedures contained phonetic phonetic phonetic phonetic phonetic phonetic strategies realistic realistic highest highest highest highest highest highest ill attempt attempt consisted consisted subsequent extend presents remain diego american american issues helpful fewer fewer fewer reducing tech stream stream workshop momentum waibel waibel perfect adjusted explored explored explored mapped generates generates detected detected detected detected detected improving improving utility arbitrarily serial sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences years distinguish analyzed fairly handle choices choices choices located immediately english english demonstrates preceding researchers robustness explained integrating questions questions reflect syllable syllable elman elman spoken spoken spoken spoken spoken effort incorrect rep reliability span vocabulary vocabulary vocabulary vocabulary occurrence phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes prevent segmented utterances simultaneous june sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence semantic semantic yielding consistently classifying corrupted redundant identifying identifying identifying identifying identifying primarily primarily appearance summing chance chance chance resulted scoring scoring utterance bourlard bourlard corpus corpus corpus corpus corpus corpus corpus corpus corpus corpus phrase phrase heuristics substituting spurious spurious contexts reset ambiguity surprising lang candidates candidates candidates candidates darpa darpa darpa surprisingly suggesting papers dividing robert severe linguistic yielded yielded appeared appeared appeared users diverse encouraging icassp icassp icassp icassp generalizations warping recurrence recurrence certainty ijcnn efforts considers insertion deleted deleted deleted spanned accounted confusion confusion alarm alarm alarm alarm alarm alarm dictionary dictionary dictionary dictionary dictionary mimic drops increments recognizers demonstrating deletion replacement scanned distortions allen allen allen allen allen allen allen allen allen slots slots hypothesized hypothesized hypothesized hypothesized locate phonemic phonemic phonemic phonemic japanese incorrectly proportions proportions alarms substitution substitution isolation syntactic syntactic syntactic distorted company assp accounting remained feasibility durations unexpected talkers talkers talkers talkers moderately moderately moderately deleting predefined richer inserted inserted inserted occasionally spotting timit dtw locating locating locating shikano shikano fallside fallside insertions insertions insertions inserting compress substituted constructions emulate exceeded exceeded missed corresponded scored pronunciation transcription transcription transcription seventh seventh spans deletions bellcore bellcore persistence hanazawa poorer poorer proportionally lexicon identities identities prepared corpora corpora confusions confusions confusions seneft silence focussed kamm kamm kamm kamm kamm kamm kamm kamm discourse postprocessing postprocessing postprocessing postprocessing singhal singhal singhal singhal duplicated evidenced morristown morristown substitutions unsuccessful orthographic orthographic confusable overlapped levinson levinson coarticulation harrison harrison reserved answering unresolved unresolved sawai occasion padded retrospect anchor confusing 
#@Allen_R,Kamm_C,
#t4
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#*network network network learning learning model model model model model model neural neural neural neural input input input input input input input input input input input input input input input data data data function function function function time time time time time time time set set set set set set networks networks training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number system system system system system system system system system system system system system error error error error error state state state state state state state state state results results results results results results results results results results results results results results units units units units units units information information information information information information problem problem problem problem models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based space linear layer layer layer layer layer case case case case case case case case vector vector vector vector vector vector vector vector order order order shown shown shown shown shown shown shown systems systems systems values values probability probability probability probability parameters parameters parameters parameters noise noise unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern point point point single single single single single single processing processing control control large large large large local local local local local rate rate rate rate test test analysis analysis class inputs inputs shows shows shows signal simple simple gaussian gaussian gaussian gaussian paper paper small small size feature feature work work methods field features features features features features features features features features features features classification classification process process level level level current current trained problems high architecture show show show section section section section fixed line rule rule vectors vectors vectors generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter average states states theory gradient gradient obtained obtained obtained note note experiments experiments experiments experiments experiments experiments experiments dimensional result result threshold research independent independent independent found sequence dynamics initial initial initial initial initial initial initial constant table table table table table estimate estimate estimate estimate standard standard standard standard standard standard standard standard standard standard standard prediction prediction prediction prediction left left presented presented presented temporal machine maximum maximum basis nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract back density density likelihood likelihood references stochastic due ieee ieee ieee ieee ieee ieee ieee ieee ieee procedure propagation mixture context context context context introduction complex hand estimation estimation estimation estimation estimation statistical statistical effect dynamic dynamic dynamic dynamic generated generated generated variance variance recurrent search tion tion energy energy energy energy difference difference assume assume lower lower signals prior prior prior representations word word word word word word word word word word center previous previous previous previous previous previous previous cases cases required multiple binary binary binary markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov fact techniques techniques proposed proposed proposed proposed correlation correlation correlation length correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed observed observed observed errors errors classes ing ing multi performed called times factor optimization potential potential dimension dimension feedback applications vol vol vol relative represented compared compared application application desired cross cross cross cross cross cross series rates proc proc proc proc proc proc proc proc experimental experimental related related distributions discrete approaches approaches approaches approaches approaches comparison comparison comparison support dependent dependent dependent dependent dependent nets nets modeling modeling morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan institute words words words words technique technique technique advances joint connectionist connectionist connectionist connectionist connectionist connectionist final final final layers layers layers scheme scheme considered considered framework equivalent directly additional additional additional additional additional view estimates estimates transition transition san bit determine determine requires significant significant significant significant basic validation validation validation validation validation validation con con con con con con con con con coding derived conditional conditional conditional developed developed levels levels criterion entropy product provided provided provided processes processes evidence iteration iteration iteration simply achieved discussion covariance technical tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited limited assumption complete complete assumed generate generate generate theoretical theoretical theoretical theoretical main end ability ability ability hypothesis development development including kaufmann reduced coefficients fully mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp transfer programming programming interesting significantly significantly ratio character york york segmentation segmentation segmentation segmentation database database database database database database principle language language language language representing iterations bits normalized frame frame frame frame frame frame frame idea idea run run sources predict denotes improved improve improve improve improve improve improve improve advantage reported reported reported reported reported reported reported practical include side side inference recently varying previously previously previously observations observations calculated tuning solve speaker speaker speaker speaker speaker speaker speaker speaker speaker achieve achieve trans trans observation generalized improvement improvement improvement improvement lead alternative hybrid hybrid hybrid hybrid hybrid touretzky column column conclusion starting starting starting assumptions assumptions reduce bayes bayes clear mateo sound drawn intelligence assuming targets derivatives program acoustic acoustic acoustic acoustic denoted denoted reference explicit longer longer sequential estimating estimating describes transitions modeled multilayer multilayer multilayer multilayer multilayer easy slightly develop frequencies predictive minimization expressed expressed phoneme phoneme phoneme phoneme phoneme solved evaluated evaluated open restricted showed frames frames frames suggested discrimination discrimination measurements roughly add valid valid valid valid valid valid initially distances advantages classified avoid avoid expect usa perceptrons recognize prove prove priors priors tests major simplicity columns hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms differ divided delta capture repeated decoding contained contained allowing stopping phonetic duration duration built comp quantity simplified simplified generalize generalize quantization predictor predictor predictor presents simpler remain estimators optimized limitations preliminary preliminary preliminary preliminary discriminant ml ml ml successive successive links links applicable working working comparable waibel front portion portion algo fisher art speakers baseline baseline utility utility explain attempts sentences sentences sentences sentences advanced capabilities independence independence independence worse berkeley formalism formalism strictly division division incorporate incorporate leaves mation consequence recognized beginning optimize english english toronto computers alignment alignment explained improvements improvements improvements improvements substantially spoken cohen rep ity ity ity price prototypes vocabulary vocabulary mod resource resource resource resource incorporating phonemes phonemes viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi utterances sentence instantaneous instantaneous contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual sort primarily primarily accomplished interface interface japan restriction rithm driving driving count unity unity lost extending attractive bourlard bourlard bourlard north effectiveness modifications modifications embedding started predictors studying holland regarded intended percepttons percepttons percepttons mel mel counting darpa darpa iterated recog mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps april likelihoods exploiting unchanged linked emission emission emission emission unable sig ent nelson nition exception german warping causal adapting quantized quantized quantized quantized quantized quantized exponent levin gained alternate management management management management compatible compatible proba argued confirmed worth intl intl intl intl intl intl intl intl intl esti els ward spite bility recogni ers confirm confirm suite suffers overtraining puts december incorporation sen juang interpolating autoregressive autoregressive autoregressive autoregressive assp assp assp assp assp assp assp assp restrictive restrictive texas huge probabil developments moderately das violate wellekens wellekens wellekens dtw checked insertions posterjori plp thirty tinuous penalties bearing fogelman succession tebelskis permitted concluded deletions periments mexico mexico nato exercise lexicon weaknesses albuquerque albuquerque albuquerque tab bernstein warped neurocomputing kohn kohn feedfor incor ended rault pursuing boutlard boutlard boutlard boutlard boutlard boutlard boutlard boutlard vocabularies hermansky substitutions eckmiller chuck resented asi sri levinson cepstrum cepstrum belgium triphone dms memorandum wooters wooters wooters wooters wooters sondhi segmenta decipher triphones tricks tricks ormation nificant kobe overlooked sheer disappointing unfor porating tences tunately 
#@Bourlard_H,Morgan_N,Wooters_C,
#t4
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#*network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data data data time time time time time time time time set set set set set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training algorithm output output output output number number number number number system system system system system system system error results units units information information information models hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based based based based linear linear case case order systems values values values values values values values values values values values values values values values values values values values values values values noise noise recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition point point point point point single single single single single processing processing processing processing processing processing large large rate rate rate rate rate test test test test test inputs inputs inputs inputs form form signal signal signal signal signal signal simple simple paper small small size feature feature feature feature feature feature feature feature feature feature net net net work work work work work work task task features features features features features features features features features features features classification classification classification classification classification classification classification classification classification process process level current trained trained trained trained trained structure structure high high high response representation section section rule rule speech speech speech speech speech speech speech real average gradient experiments experiments research research research independent independent independent independent independent found found found found found found sequence sequence initial initial computer computer computer computer distance science science science map low low nodes nodes temporal maximum maximum range components basis outputs outputs continuous continuous continuous continuous abstract applied applied back back find find references due ieee ieee ieee positive positive procedure important propagation context context context introduction hand dynamic dynamic search search search search difference difference difference difference difference difference difference difference difference difference difference difference classifier classifier classifier classifier classifier classifier classifier lower lower rules rules rules rules rules measure measure measure measure measure measure representations representations chosen center center center center center center center center previous previous previous cases required binary binary tree tree correlation length correct correct probabilities errors errors errors errors errors forward scale scale resulting total total computed performed performed performed performed performed performed performed times natural feedback knowledge knowledge negative negative negative specific samples represented represented represented cross location location goal constraints connected equal equal equal approaches accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger train train train descent modeling selection proceedings proceedings proceedings proceedings proceedings institute institute institute words department consists individual advances joint joint difficult difficult final final final layers addition addition additional additional additional san top top conference conference conference conference conference classifiers classifiers classifiers classifiers full full choice validation con produce produce derived randomly developed developed levels provided provided provided selected selected achieved achieved achieved achieved measured measured measured normal feedforward tested fast corresponds supported require development development development including pairs coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients technology programming programming testing significantly segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation consistent consistent consistent database database database database database language language squared numbers window window window window window window window window stored international international international international normalized normalized normalized normalized expert frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame combined added added added added sources description recent resolution separate separate similarity movement reported apply period subject engineering engineering works smooth speaker speaker speaker speaker speaker speaker speaker speaker match match match achieve achieve evaluation locations locations locations modified interval interval interval interval entire grant amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude exists parts occur extended extended correctly correctly correctly feed feed locally width occurs boundary pass half half half segment segment segment segment segment segment segment segment segment peak peak peak peak peak peak peak peak peak peak peak peak peak performs presence largest largest largest largest largest largest largest drawn averaged averaged averaged averaged manner pro laboratory label tuned dept dept segments segments segments segments segments segments segments segments category category category category category category category category category category category linearly linearly linearly linearly slightly spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral extraction letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters extracted extracted extracted extracted extracted phoneme phoneme phoneme evaluated labels centered frames frames frames frames spectrum smoothing smoothing measurements measurements normalization intervals intervals boundaries boundaries boundaries boundaries boundaries boundaries boundaries tracking tracking tracking msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec classified classified classified classified classified classified classified classified transactions avoid thesis strings strings strings strings strings strings retrieval retrieval retrieval retrieval retrieval instances instances recognize specifically candidate candidate absolute grammar grammar grammar letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter differ paths efficiently score vowel vowel vowel vowel capture repeated phonetic phonetic phonetic phonetic phonetic classify classify duration duration duration categories categories list list sampled sampled usual simplified wave subsequent diego rapidly preliminary mass mass mass mass mass mass helpful matches root workshop scores scores neu smallest measurement naturally onset onset onset onset onset onset onset equally recognizer recognizer recognizer recognizer mapped speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers submitted isolated isolated isolated isolated isolated isolated isolated mentioned stop stop stop stop stop ground waveform waveform waveform waveform waveform waveform waveform waveform adjacent adjacent adjacent adjacent caused caused caused briefly inside inside inside widely filtered filtered filtered filtered filtered filtered filtered broad broad broad broad broad broad broad broad broad broad broad broad choices leaves acknowledgement pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch beginning begin english english english english english english toronto preceding preceding preceding nsf raw conjugate percent percent reflect syllable empirically tional spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken peaks peaks peaks peaks peaks peaks peaks peaks peaks treated treated vocabulary phonemes phonemes phonemes acoustics acoustics acoustics phone begins viterbi viterbi median median median median utterances june june spectra ear labeling labeling japan temporally impossible grows khz khz khz khz khz khz khz khz overcome scoring mark utterance utterance utterance ral alphabet alphabet alphabet vowels utilized slice periods overview overview overview expanded bad searching searching darpa darpa recog recog april april april indicator indicator master tracker canada formant formant sons sons jump consonant consonant consonant consonant consonant consonant consonant balanced assigns divide crossing crossing crossing crossing crossing crossing crossing minus minus misclassification session revealed nition nition tween distinction retraining retraining connec spaced classifies classifies attempted graduate graduate graduate carefully careful cole cole cole cole cole cole cole cole cole cole cole cole cole cole cole cole cole cole cole cole cole surrounding names names names names names names names names names names enforce crossings son son son son son son son son son son son son son son son son son son son son son son son son son son son son son articulatory indication tune refined things ignoring examination oregon oregon oregon rose rose november emphasis served august august august decided agrees ers micro routines sharply fft normalize classi retrieved retrieved recognizes isolation lowpass lowpass lowpass lowpass vocal fication closure segmenting prune modest ceedings tivity searched timit collecting insertions insertions delete fanty fanty fanty fanty fanty fanty fanty fanty fanty fanty fanty fanty fanty fanty enabled distinctions distinctions retrained notably begun begun ronald experimentation perplexity contiguous canceling divides voicing seventh deletions barnard barnard barnard spelled spelled spelled spelled spelled interna valley instructed arrived nasal dft dft dft dft dft dft dft dft dft dft dft dft dft pauses pauses pauses pauses slowing speak apple segmenter segmenter segmenter segmenter segmenter segmenter forty muthusamy substitutions resides finely msecs msecs beaverton locates coarticulation spelling devising tection thirds vided gopalakrishnan gopalakrishnan gopalakrishnan gopalakrishnan gopalakrishnan ptp pause pause cooperating sixty dozens failing kobe anchor 
#@Cole_R,Fanty_M,
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set networks training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number system error error error error error error error error state state state state state state state state results results results units units units units units units units units units units units units units information problem models models models hidden hidden hidden hidden hidden based based based based based based based based based based based based based based layer layer layer vector vector vector vector vector vector vector order shown shown values probability parameters parameters parameters parameters parameters parameters parameters unit unit unit unit unit unit unit unit unit unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach pattern pattern point point control large large large large large large large large large large local local rate test test test class matrix optimal optimal optimal form shows shows algorithms algorithms paper paper paper paper paper small feature feature feature feature feature feature feature feature feature feature feature feature feature net work process high similar similar similar similar similar architecture architecture equation equation equation section section section section section section vectors vectors vectors vectors vectors vectors vectors general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter average states obtained obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments result result result result result variables research research independent independent independent independent defined defined sequence sequence sequence sequence distance distance prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction map temporal sets sets sets nonlinear nonlinear continuous continuous continuous continuous continuous continuous abstract applied back back find computational convergence convergence references ieee procedure procedure important propagation propagation introduction introduction introduction introduction introduction effect dynamic dynamic tion tion tion tion difference word word word word word word word word word word word word word word word word word word word word word word word word word chosen chosen higher higher center center type type type type type type long expected expected markov markov markov fact techniques proposed proposed correct errors errors errors forward forward forward forward forward forward forward minimum minimum total total mapping means means optimization optimization made global obtain original original original original represented compared compared application application application application application desired compute proc proc proc proc proc proc determined experimental experimental goal constraints constraints equal accuracy accuracy accuracy accuracy accuracy accuracy accuracy support dependent dependent dependent report words words words words words words technique consists represents considered equivalent environment transition transition determine increase increase con con con criterion actual actual selected selected selected sampling discussion hmm hmm limited limited complete predictions proof amount amount amount amount implemented implemented end makes fit underlying dynamical technology technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp programming programming ratio segmentation segmentation segmentation segmentation segmentation segmentation segmentation numbers pre frame frame frame frame frame perceptron denotes improved improve improve reported introduced introduced period period subset dimensions conventional approximately calculated tions speaker speaker speaker speaker speaker speaker speaker definition definition evaluation interval improvement improvement improvement improvement improvement amplitude constructed expression suggests predicted occurs boundary half conclusion reduce segment start min min decrease groups configuration configuration configuration configuration configuration configuration denoted acknowledgements reference reference relation digit digit estimating laboratory changing segments segments multilayer multilayer multilayer explicitly involves applying predictive minimization phoneme phoneme solved evaluated spectrum diagram combining iterative iterative boundaries msec advantages advantages topology includes combinations formulation determines determines variations absolute characterized simplicity divided divided delta efficiently vowel vowel vowel vowel characteristic duration duration sampled backward backward backward backward backward backward backward backward backward backward minimizes predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor automatically presents presents presents presents presents presents employed carried carried production detail recursive examine tech applicable scaled scaled authors authors cover waibel configurations configurations obvious consist defines isolated stop formula analyzed improves improves adjacent adjacent caused nucleus laboratories members alignment syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable understood amounts amounts treated release vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary phonemes enables utterances utterances utterances utterances utterances utterances distortion consistently japan branches branches khz utterance effectiveness effectiveness effectiveness intuitively repeat repeat predictors male regarded regarded percepttons percepttons mel mel initialize recog mlps mlps mlps consonant consonant consonant balanced accumulated accumulated accumulated accumulated accumulated accumulated accumulated treat consecutive linked emission corporation basically validity nition icassp icassp icassp icassp causal verified levin levin iso iso iso iso iso iso iso iso iso iso confirmed confirmed confusion dictionary syllables applicability applicability mini nec topologies rabiner rabiner moderate accumulation recogni ping japanese japanese japanese japanese japanese japanese japanese recursion usefulness meeting fft manually successively articulation subscript closure concatenated concatenated concatenated concatenated concatenated media watanabe watanabe watanabe watanabe watanabe watanabe watanabe february applica cepstral cepstral mization accuracies accuracies tutorial predic predic tinuous transcription tebelskis tebelskis lexicon prepared prepared diction silence heuristically nical concatenation concatenation concatenation sudden cies causality causality fined absorbed tual quiet ken uttered concatenating ichi ieice segmenta jective backtracking backtracking phonetically 
#@Iso_K,Watanabe_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model neural neural neural neural input input input input input input data data data data data data data figure figure figure figure figure figure figure figure time set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training output output output output output output output output output output output number error error error error error error error results results results results units units units units units units information information information problem problem models models models models models models models hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance based based based based based based based based based based based weights weights weights linear linear linear linear linear linear linear linear case case case case case vector vector vector systems systems systems systems systems values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach approach approach approach pattern pattern processing processing large rate rate rate test test patterns patterns patterns patterns patterns analysis analysis class class class class class class class matrix matrix inputs inputs inputs inputs inputs inputs inputs form form form shows signal signal algorithms algorithms simple simple simple simple simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small small small feature net net work work work task methods fig fig fig fig step points points points points points points points classification classification process current trained high architecture show show fixed fixed fixed line line rule vectors vectors general general speech speech speech speech speech speech speech speech speech speech speech speech average average average states gradient gradient experiments experiments dimensional computation research independent independent independent independent independent log log log log log sequence sequence target target target target initial standard computer distance science map low frequency frequency maximum maximum learn position outputs outputs outputs outputs outputs outputs abstract abstract applied applied applied back back back back density density density properties likelihood likelihood likelihood likelihood likelihood likelihood references component component component stochastic ieee procedure procedure important adaptive adaptive propagation mixture context context introduction estimation stimulus statistical recurrent recurrent tion energy variable variable variable assume assume classifier classifier classifier classifier classifier classifier signals prior prior word word word word word word word word word word word word word word word word word good good conditions conditions conditions represent bayesian markov markov markov markov fact fact techniques correct probabilities probabilities probabilities probabilities probabilities probabilities errors errors forward forward forward scale classes classes classes human sum sum performed eq called times means means factor made applications knowledge knowledge knowledge obtain relative relative relative specific series rates rates rates proc posterior constraints constraints distributions distributions distributions distributions equal equal equal power power train descent morgan report words words words words words words words words words words implementation version technique technique technique internal individual individual advances difficult bias bias ai ai computing equivalent equivalent equivalent equivalent estimates design transition stage stimuli effects full significant significant produce produce channel coding derived criterion criterion controller types types entropy entropy product product constraint achieved measured covariance covariance technical feedforward feedforward feedforward describe arbitrary tested hmm transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation limited close assumption short short short common effective main adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation end end end end instance cluster future easily kaufmann probabilistic typically pairs pairs reduced unknown unknown unknown unknown unknown unknown unknown unknown coefficients technology edge special special consistent database database mode mode mode mode mode squared squared details call numbers supervised supervised supervised produced architectures improved discussed typical reported apply include subject side interest previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised works solve speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker differential diagonal evaluation positions improvement amplitude lead lead lead matrices feed feed locally place place place conclusions valued editors bayes bayes exponential exponential practice constrained sound propose largest largest reduction radial radial assuming assuming start decrease relationship targets targets targets targets derivatives derivatives derivatives derivatives groups acoustic acoustic acoustic acoustic reference reference reference reference reference suppose suppose suppose construct longer perception estimating transitions label transformations transformations transformations transformations transformations consisting mutual springer shift shift shift shift shift john letters communication viewed interpretation interpretation densities labels labels labels labels labels similarly digits allowed spectrum spectrum partial calculation euclidean kohonen recorded perceptual automatic simplicity aspects aspects hmms divided latent modes essentially identity identity soc conf verlag decoding interested interested issue duration write write usual ill simpler dataset giving ideas ideas project applicable int possibility relationships statistically adapt adapt equally thought adjusted front front front front logistic explored speakers speakers speakers simplest attempts isolated isolated isolated great improves coded london turns straight implementing purposes probable inversion implicit english english english applies double collected understood amounts amounts spoken spoken spoken backprop aim extensions acoustics adjust gave sophisticated sophisticated decreased age neuro utterances utterances utterances utterances utterances utterances simultaneous simultaneous simultaneous softmax softmax softmax softmax cor person room generator linearity pick labelled concerned jth royal dealing convenient alpha check hope exploit utterance utterance utterance utterance alphabet alphabet mance appendix perfor mel enable tokens matter likelihoods propagate propagate propagate balanced default outlined informa radar minus feeding terminals terminals discriminative copy classifications imagine illustration param labs concentrate names names ambiguous ambiguous ambiguous responding knowing bring tune tune normalised normalised eters bridle bridle bridle bridle bridle bridle bridle bridle walk lighting acoust stephen telephone supply optimisation stay practically labelling neighbourhood frequent unlabelled unlabelled unlabelled est bear february sex amer cox cox cox cox cox hood enforcing ace modifies trick trick apparatus imposing tentative maximising emulate displaced displaced hillclimbing british british british british converting confident encouragement maximise logn logn descriptive nato talker lbg generalised motivate interpretable likeli minimising minimising identities identities encouraged unambiguous disambiguation reductions preceded plied heard knowl persons specially rault sharpening normalisation normalisation normalisation normalisation normalisation normalisation normalisation uttered confusable telecom telecom malvern soulie pulls hunt asi listeners cepstrum ice pronunciations continous phantom phantom phantom phantom asr asr rum initialise sharpen forwards accents copyright recognise maximises alphabetic ada recognising 
#@Bridle_J,Cox_S,
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functions functions functions neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition method method method approach approach approach pattern point point point image single single single single single single processing control neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis class optimal form shows signal gaussian gaussian visual visual visual visual paper small feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net task methods methods methods field features features features features features features features features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification trained trained trained structure structure structure structure structure structure structure structure high high high high high high high memory similar similar representation representation show show section section fixed fixed fixed vectors images images images general general generalization speech speech speech speech speech speech speech speech speech average average average average theory theory theory theory theory theory theory theory theory theory gradient gradient note experiments experiments activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university threshold threshold threshold threshold threshold threshold computation computation solution research research research research independent defined defined defined defined found found found table table synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science left left left presented presented presented presented presented present present low low low low nodes frequency frequency frequency sets range press components components basis nonlinear nonlinear nonlinear nonlinear abstract back back back back back back back find find find properties properties properties references references due important important adaptive propagation propagation propagation propagation propagation propagation propagation context introduction hand hand hand statistical statistical statistical dynamic variance parallel search tion tion energy energy difference difference assume classifier classifier measure signals signals signals signals higher part part part center center cases cases cases multiple cortex good expected expected equations equations equations equations make make make make fact fact fact techniques region correct forward resulting resulting classes simulation simulation computed respect multi regions made made orientation knowledge negative original original specific compared desired provide define define perform experimental related related distributions distributions distributions cortical cortical cortical comparison comparison larger descent descent modeling morgan loss loss loss loss loss loss loss loss loss loss loss loss loss loss version consists advances represents represents represents difficult graph graph experiment experiment experiment hinton hinton hinton additional additional san top effects conference upper upper full significant statistics con levels levels criterion processes evidence depends biological biological achieved normal increases increases arbitrary close stable finding finding synapse supported main journal journal cluster makes development development development kaufmann objective pairs needed reduced account interesting interesting interesting interesting interesting projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection york special consistent structures mode mode mode principle language leads leads principal principal details details filters direct making window inhibition inhibition polynomial polynomial idea discussed discussed discussed directions directions directions recent property reported lateral lateral moving subject identical side sense recently interest sufficient sufficient compare unsupervised approximately works axis axis tions smooth yields speaker speaker speaker speaker speaker speaker speaker speaker correspond differential trans definition locations modified observation risk risk sensitive sensitive sensitive constructed studied studied invariant invariant invariant invariant invariant suggests suggests deviation move clusters clusters critical critical place place place place reduce reduce depend measures clear performs performs performs mateo suggest suggest suggest reduction reduction reduction reduction reduction reduction sigmoidal demonstrated scene base base written index index index index index index ann mathematical sensitivity sensitivity dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality transformations transformations easy interaction frequencies frequencies minimization minimization minimization implies extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction john national extracted extracted extracted extracted extracted family formation review review review review review phoneme phoneme phoneme overlap suggested allowed classical roughly tracking remains msec msec foundation topology formulation formulation phys partially simplicity straightforward importance society modification modification modification modification modification modification computationally projections projections projections projections projections projections projections vowel vowel vowel kind phonetic phonetic phonetic phonetic symmetry physiological paradigm providing neurosci preferred extract extract satisfies receive law selectivity american american wiley detail association graphical mass mass pursuit pursuit pursuit pursuit pursuit helpful fewer mse plasticity plasticity office office variability func statistically plausible plausible plausible plausible friedman friedman friedman precise speakers speakers speakers motivated defines percentage burst burst burst burst burst brown brown stop stop stop band distinguish distinguish agreement derivation defining nowlan nowlan straight preprocessing ran desirable desirable desirable projected projected projected projected projected projected acknowledgement beginning beginning addressed addressed explained evaluating relevance bootstrap remove continuously biologically outliers outliers release polynomials polynomials summarized measuring measuring characterize semi comments windows differentiable hints bellman bellman shifted acquisition indices indices aligned cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper princeton princeton naval generality binocular dealing attractive bands star intuitive corner corner child moments moments motivation motivation motivation meaningful falls saul sion male sides sides regard widrow uni similarities advance advance tokens tokens insight suggesting late specificity specificity extensively consonant consonant statement hart hart explains tures speaking consecutive linguistic linguistic linguistic mind annals misclassification munro munro munro munro opposed presenting stock distinction distinction connec seek seek intrator intrator intrator intrator intrator intrator intrator intrator solely female breaking concentrated concentrated concentrated concentrated insights duda duda emphasize cation happen fea modifiable exploratory exploratory exploratory exploratory exploratory exploratory article mann modal stops stops stops stops stops stops stops stops stops simplification simplification bienenstock bienenstock bienenstock characterizing heavily curse inhibit inhibited attempting tors bcm bcm bcm bcm bcm bcm bcm pronounced distinguishing distinguishing distinguishing distinguishing acoustical dissertation bss bss bss consonants consonants consonants governing governing america multimodal multimodal dimen articulation articulation articulation articulation electrophysiological format raised mis bear bear bear minimizer translates voiced voiced voiced voiced voiced tails appli richer richer omit miss huber huber huber huber huber conveyed forthcoming possesses devel versity reilly froin army seeks seeks bimodal asymptotics voicing voicing voicing voicing voicing providence mon emphasizing ore concentrates concentrates normality geoff notations departure native stepwise invaluable leon 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performance performance performance based based based based based based based layer layer layer layer layer layer layer order order order shown shown shown shown shown shown systems systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach pattern processing processing processing large rate rate test test analysis inputs shows shows shows shows signal signal gaussian gaussian gaussian gaussian gaussian paper paper paper paper work work work work classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification current current current trained trained trained response representation representation equation equation equation equation equation section section speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average obtained obtained term term experiments experiments experiments experiments experiments experiments experiments experiments experiments result result computation research independent independent independent independent independent found found sequence sequence sequence target table table table table table table table table table estimate estimate estimate computer distance connections science left left left temporal sets outputs outputs outputs outputs outputs continuous continuous continuous continuous abstract back computational computational references stochastic stochastic stochastic stochastic due procedure procedure important adaptive propagation context context context context context introduction estimation estimation statistical statistical generated search difference complexity assume assume classifier classifier classifier classifier classifier classifier classifier chosen chosen center bound type required binary binary binary binary binary markov markov make proposed proposed proposed correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities errors errors errors resulting resulting resulting resulting ing ing tasks total total multi multi multi multi multi multi sum performed regions optimization made applications study study knowledge knowledge vol artificial specific samples compared compared desired provide define compute proc proc proc proc proc proc proc perform determined determined determined experimental goal posterior distributions distributions distributions gain approaches mit accuracy accuracy comparison train train train train dependent morgan morgan morgan morgan proceedings report report report institute implementation technique advances joint joint connectionist addition framework framework framework framework framework framework framework cambridge computing estimates design detection detection detection detection conference determine determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full requires significant approximate statistics statistics free estimated estimated give finally finally simply simply achieved discussion covariance describe group denote tested corresponds corresponds amount amount require main end end future makes development including including kaufmann auditory typically underlying technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp testing testing testing testing testing ratio segmentation segmentation segmentation segmentation database database database database language language language representing numbers international supervised supervised magnitude magnitude frame frame frame frame frame frame idea perceptron perceptron perceptron perceptron improved improved improved improved discussed discussed discussed recent property include include identical hierarchical recently compare previously previously yields speaker speaker address locations entire exists parts lead occur occur matrices correctly hybrid boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary place assumptions reduce reduce segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment designed presence exist exist exist exist exist manner manner acoustic acoustic acoustic acoustic acoustic estimating laboratory ann ann label label distinct distinct segments segments segments segments pruning pruning pruning pruning pruning pruning pruning multilayer multilayer explicitly text belief consisting applying predictive extracted extracted extracted phoneme phoneme phoneme phoneme phoneme viewed viewed evaluated evaluated evaluated labels labels lee soft soft earlier earlier earlier earlier measurements normalization boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries valid valid valid intermediate string classified includes thesis usa usa usa perceptrons perceptrons formulation recognize extension automatic discuss discuss variations determining identify detect identity identity summary traditional soc procedures procedures phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic superior issue classify classify classify strategies strategies duration duration involved involved michael simplified modular highest highest highest highest automatically consisted deal modelling american poor requirements requirements put mass examine tech links detectors combine decisions decisions workshop workshop scores hierarchy hierarchy hierarchy hierarchy statistically attributes attributes examined waibel waibel detector detector detector explored mapped speakers speakers speakers speakers baseline baseline baseline motivated attempts sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences massachusetts massachusetts waveform majority glass glass glass glass glass glass sys broad located begin begin english incomplete flexible spoken spoken spoken spoken generic capability capability orders formulated schematic vocabulary summarized differs synchrony phonemes extensions achieves achieves viterbi progress initialization aligned aligned aligned aligned japan investigation nat discovery tem flexibility flexibility simplify exploit utterance utterance utterance utterance utterance settings bourlard bourlard bourlard bourlard corpus corpus corpus corpus corpus corpus corpus corpus corpus corpus corpus corpus corpus corpus corpus vowels vowels heavy james male male moved conjunction realization percepttons percepttons histograms offers dif darpa darpa tokens tokens tokens tokens recog recog recog suggesting offer extends papers adopted balanced metrics linked asked asked formulate nition nition nition adopt icassp icassp icassp icassp utilize female female stands stands clas clas community community token proba ultimately insertion diagrams stops emphasis deletion acoust ferent locate lated incorporation ters consonants substitution substitution inst february putation phillips phillips phillips phillips phillips phillips phillips phillips phillips amer wellekens leung leung leung leung leung leung leung leung leung leung leung leung leung leung timit timit timit timit segmental segmental segmental segmental segmental segmental segmental segmental segmental stand stand stand stand disadvantages insertions hong albeit parame multiplications phonological phonological favorable posterjori feel utilization transcription transcription transcription transcription tebelskis tebelskis tebelskis deletions altogether extraneous premise albuquerque albuquerque albuquerque corpora corpora bilities seneft seneft seneft seneft seneft silence siftcation phoneroes substitutions franzini bigram bigram victor afforded trigram trigram formu nasals phonetics aries pho ural discriminatory delineated fricatives netic sifter 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#@Glass_J,Leung_H,Phillips_M,Zue_V,
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case case vector order order order systems systems systems systems systems systems systems values parameters functions functions functions functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern single processing processing processing control control control control control rate test test analysis shows signal signal signal signal signal algorithms simple simple paper paper paper examples task task task task points features classification classification classification process process process process current current current current current current current trained structure structure structure problems high response response response response response response representation representation representation architecture architecture section section line rule speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real average term note result result result university threshold research research research research research research found initial computer computer computer terms distance science direction map map map nodes machine machine machine object object object object object object object components components basis continuous continuous continuous abstract back back back back back back back back find computational properties properties properties likelihood references component component component component component due due due procedure important important decision context context context context context introduction action action action effect generated generated generated generated generated generated generated search search search search search tion tion rules rules rules word word word word word word previous previous multiple good tree make region correct probabilities probabilities probabilities probabilities errors errors errors classes ing human human human human human human multi performed called called times means made natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural applications applications applications knowledge knowledge filter filter filter obtain obtain original vol artificial specific specific specific represented represented application application application application application application application application application application application provide provide provide provide provide provide provide objects objects objects objects objects objects objects objects objects objects objects objects proc proc proc proc proc proc proc proc proc proc location location location location perform active determined related constraints mit mit mit mit mit mit mit mit accuracy dependent source nets report report report report institute institute words words words words words words implementation version version version consists joint responses addition addition framework framework cambridge cambridge domain domain domain domain domain domain experiment environment additional additional additional additional design top top top efficient efficient requires free basic give con produce produce coding coding derived developed area area area area types types path provided provided finally finally finally finally processes selected constraint discussion technical describe describe describe describe describe describe group group tested fast complete actions finding finding finding short nearest nearest nearest nearest nearest nearest effective implemented generate generate generate supported role main main main square square end end end end end end end end hypothesis hypothesis easily easily makes development development development development development development development including including including auditory auditory auditory probabilistic probabilistic typically pairs needed unknown unknown fully fully technology technology increasing segmentation mechanism mechanism structures database database database database database language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language call call filters filters direct expert early attention produced description improve directions recent recent recent recent recent pair pair separate strategy strategy strategy strategy moving include include identical machines hierarchical hierarchical subset recently interest interest sufficient varying conventional subjects subjects subjects subjects solve achieve trans address address address evaluation evaluation evaluation locations correctly locally generally pass critical critical place interactions designed clear constrained propose turn variety user user user user user user user user user user configuration acoustic acoustic acoustic acoustic acoustic acoustic acoustic acknowledgements reference pro pro pro pro construct produces solving solving factors primary generating laboratory laboratory laboratory segments physical physical involves remaining remaining remaining text interaction interaction develop formed phoneme phoneme communication communication interpretation interpretation evaluated evaluated forms understanding understanding understanding understanding understanding understanding understanding understanding understanding understanding understanding understanding understanding understanding understanding past reasonable reasonable calculation performing false string assigned query david recorded building exploration exploration thesis retrieval determines specifically specifically specifically partially grammar characterized structural successfully successfully major suitable divided successful efficiently essentially essentially capture summary decoding stopping phonetic phonetic phonetic phonetic phonetic issue return return follow strategies list involved michael play realistic realistic realistic providing hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses ill automatically automatically automatically automatically automatically attempt consisted deal deal modelling command command command command command command command command access access access access collection essential requirements experience experience put environments environments involving humans issues issues issues preliminary preliminary hall hall matches history history history history school school school office referred complicated workshop workshop workshop workshop workshop workshop understand understand understand understand attributes act closest closest possibly illustrate equally recognizer recognizer recognizer recognizer recognizer recognizer queries queries queries queries queries queries queries mapped message message speakers speakers speakers improving extent arbitrarily arbitrarily sentences sentences sentences sentences sentences integrate integrate massachusetts massachusetts developing track analyzed phenomena navigation navigation navigation majority capabilities capabilities capabilities capabilities capabilities capabilities answer answer glass glass glass glass glass glass glass glass glass glass glass glass briefly briefly handle starts starts inside processed arc arc shared shared incorporate located located arise recognized involve describing begin begin computers computers incomplete incomplete meaning sun robustness people people reflect understood flexible spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken capability passed passed incorrect incorrect commands operate operate stack stack stack stack vocabulary vocabulary vocabulary synthesis fall synchrony incorporating serve phone enables inherent returns focused viterbi viterbi utterances progress progress june june sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence semantic semantic sharing naive room accomplished interface interface interface interface interface interface interface forming arguments acts databases null naval connecting printed theories spontaneous spontaneous spontaneous spontaneous spontaneous wrong city city city contract operates fail utterance utterance utterance corpus corpus enhanced date exploring evaluations evaluations analyses utilized james displayed male male male conjunction schwartz schwartz candidates candidates offers darpa darpa darpa darpa darpa darpa darpa recog refers refers augmented parse parse parse parse messages davis davis subsequently material counts linguistic linguistic linguistic linked street street street street arcs arcs largely converted rigorous transmitted rejection bank bank bank bank bank failed failed failed failed nition icassp icassp icassp icassp par seek ical female female female assess remainder constrain constrain acting unseen summarizes cessing maintained convert efforts efforts efforts acquired scope interactive interactive interactive interactive investigating ambiguous constructs importantly nonetheless supports meet ation places nil nil nil nil travel differing october october october status technologies syn regularities handling january slot slot slot resolve synthesized assistance assistance slots slots nested locate locate focuses fill december harvard harvard harvard returned returned diagnostic gram judged judged judged judged judged huang huang corrective screen destination syntactic syntactic pooling presently reviewed appro carrying request media media ically translate february unrestricted responded col phillips phillips phillips phillips phillips phillips phillips phillips phillips phillips lexical lexical lexical percep favors converts leung leung leung leung leung leung leung leung leung leung joseph collecting graphically proce inability hong plans entered rated phonological phonological pushed pushed designated designated designated begun judgments parser parser parser pronunciation pronunciation boards converting perplexity requests banks driver landmarks lexicon premise duce handles chinese chinese albuquerque albuquerque albuquerque chow chow simplistic seneft seneft seneft seneft seneft seneft seneft seneft seneft seneft seneft seneft inexpensive conscious didn didn interacts decade public discourse discourse discourse discourse discourse discourse dure vague vague embed straint testbed ken fulfills scotland vide highlighted conversation conversation querying typ referenced demonstrations bigram victor semantically buildings priate lives disciplines trons phonetics variabilities pho thirds realm textual clarified graceful reserved cently mediates parsed adverse ded incorpo commercially atten netic lected glasgow conversational conversational protection velopment seat paying inadequacy 
#@Glass_J,Goodine_D,Hirschman_L,Leung_H,Phillips_M,Polifroni_J,Seneft_S,Zue_V,
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data data function function function time time time time time time time time time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm output output output number number number number number number number number number error error error state results results results results results results results results results results units units units problem problem problem models models models models hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space weights weights weights weights linear layer layer layer layer layer vector vector vector vector vector order order systems systems systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise weight recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach pattern pattern point single single processing processing processing processing large local rate rate test test test test test test test test test test patterns patterns patterns class class class class class class optimal signal signal signal algorithms algorithms simple simple simple paper small size size size feature feature feature feature feature net net net net net work work task task task task task task task task task task methods methods cells features features classification classification classification classification classification classification classification classification classification process current current structure structure problems problems random similar similar similar similar similar representation representation architecture architecture architecture architecture architecture architecture architecture section fixed fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter average obtained obtained obtained obtained term experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional result variables research research research independent independent independent independent independent defined found found sequence sequence initial constant constant constant standard terms distance distance left presented presented phase low low low temporal temporal temporal temporal temporal temporal sets sets sets range learn outputs continuous abstract applied references references references references references references stochastic due procedure procedure procedure important important important important context introduction complex complex dynamic cost recurrent tion difference variable classifier classifier lower lower lower measure signals prior prior word word word word word word word word word word learned chosen higher previous previous previous previous bound required conditions markov markov markov techniques techniques techniques techniques length length forward classes tasks tasks respect respect multi multi sum performed times elements means means means means means means means means means dimension made made natural study knowledge knowledge filter obtain original vol specific compared compared compared compared desired desired desired cross provide provide provide perform perform determined related connected equal approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches steps accuracy comparison larger contrast train train train train nets nets nets nets nets nets modeling report report words words words words words words words words technique technique consists individual connectionist connectionist connectionist connectionist connectionist layers layers delay considered considered considered framework computing equivalent equivalent experiment experiment directly hinton effects effects detection detection efficient efficient efficient efficient classifiers classifiers classifiers classifiers classifiers classifiers full significant significant approximate free basic basic increase increase derived derived derived derived derived derived derived derived derived derived derived derived developed levels levels area path provided achieved technical technical feedforward arbitrary tested tested tested hmm transformation actions nearest nearest nearest nearest implemented supported main main main main adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation square degree makes including objective objective pairs combination combination combination account account account coefficients fully programming interesting testing segmentation segmentation database database database database database database mode mode mode details numbers numbers idea combined combined combined combined description description perceptron architectures architectures architectures architectures architectures improve property reported reported reported introduced introduced strategy identical side sense approximately module module axis solve speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker evaluation evaluation modified improvement improvement sensitive increased parts invariant deviation alternative feed hybrid hybrid width white white generally starting conclusions conclusions conclusions operator clear constrained constrained sound taking integration integration characteristics characteristics demonstrated assuming user user decrease relationship connectivity acoustic base acknowledgements reference reference reference reference reference reference solving factors sequential label mathematical mathematical multilayer averaging linearly involves transformations remaining slightly spectral spectral spectral consisting consisting integrated integrated integrated shift shift extraction extraction yield focus phoneme phoneme phoneme phoneme transform evaluated evaluated labels evolution evolution evolution frames frames digits digits delays classical classical classical classical classical normalization normalization normalization event roughly purpose boundaries boundaries initially distances euclidean recorded thesis combinations priori formulation inter extension illustrated automatic automatic variations absolute partially partially tests tests tests tests tests tests major middle aspects importance importance differ differ divided symbols tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn projections invariance score score score score essentially summary summary kind procedures procedures decoding phonetic phonetic phonetic phonetic phonetic phonetic phonetic split split superior superior superior built involved modular quantization leading automatically automatically overlapping deal load minimized remain remain carried carried carried powerful access collection environments environments detail existence examine examine tech tech tech project project project project project project project project project mappings mappings mappings mappings investigated combine scaled authors comparable comparable variability variability proved proved proved proved scores scores scores scores scores affect cover neu waibel waibel waibel trace trace trace equally recognizer recognizer recognizer changed thought aspect portion speakers speakers speakers speakers speakers consist consist improving phd sentences sentences sentences sentences sentences isolated isolated isolated isolated isolated isolated isolated isolated established charge failure adapted adapted adapted adapted adapted handle handle processed sections sections sections division located desirable immediately laboratories universal english recording depicted recognizing fourth items cmu consistency consistency consistency consistency tional conducted conducted conducted conducted conducted conducted conducted fed remove rep templates vocabulary summarized ture spread cal occurrence phonemes phonemes suited gave gave gave gave kinds sophisticated sophisticated sophisticated display neuro windows windows june june june summed initialization initialization initialization initialization initialization phenomenon phenomenon representative acquisition acquisition appropriately lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq databases databases databases repre turned proceed promising tools check fail utterance utterance ral enhanced alphabet performances mance perfor male expanded lang realization mel initialize multiplied advance recog mlps mlps mlps mlps designing summarize influences divide speaking speaking linguistic unchanged approx compressed compressed ber bank revealed forced nition encouraging par classifications warping demon assess constrain mismatch mismatch attempted num compensate intra oct carefully march relating proach paris paris paris paris hornik hornik hornik cation paradigms universit dictionary dictionary dictionary indication thousands margins atr exploited recognizers topologies distortions distortions tdnns tdnns tdnns european hundreds confirm concern concerns architec ref repetition measurable squashing cooperation rameters rameters sions protocol protocol connectionism ance carrying tained sentation discovers experimented cope discriminating tails repetitions lexical lexical objectives neigh aims topics shikano proce rom formulations offered warp endpoint endpoint british sults ies fogelman niques niques niques french namic namic neighbours delivered hanazawa cap classifi lexicon categorized lbg lbg lbg lbg lbg lbg lbg lbg rue quence prepared corpora warped neurocomputing neurocomputing neurocomputing silence innovation stinchcombe stinchcombe pauses manage sel phoneroes ficient borel frg strate gallinari esprit esprit esprit esprit ken deficiency suf uttered uttered telecom conven unsolved ichi agreed tackle tackle representatives bra bra bra bra stretched phonetics variabilities cantly aries maih spect unify programme war gies dures imate funahashi expecting rsre spain refs padded chitectures duplicating inadequacy resents 
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information information information information information information information problem models models models hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer order shown systems systems systems systems systems systems noise noise weight weight weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition pattern single single single single control control test test patterns patterns analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs form form shows shows shows shows shows shows signal signal simple paper paper small size feature feature feature feature net work work task task task task methods step features classification classification classification classification classification process process level level level level level current trained trained trained trained structure structure problems high high memory response architecture architecture fixed fixed fixed fixed vectors generalization generalization real real average average average average average theory theory theory theory note activity activity activity activity dimensional university defined target target target target target target initial initial table table table table standard standard standard standard connections connections connections connections connections presented presented presented present present activation activation low frequency frequency frequency frequency object object object object object sets range range press press press press press outputs outputs outputs sample sample sample sample sample sample sample sample sample sample sample sample abstract applied back back back back properties likelihood references stochastic ieee important decision decision decision decision decision decision decision propagation propagation propagation introduction behavior stimulus stimulus stimulus stimulus stimulus effect tion tion tion tion tion energy difference complexity variable variable variable variable variable classifier measure measure signals signals representations chosen center previous required required required required multiple multiple multiple multiple good expected length correct correct correct correct correct errors simulations total total total simulation computed sum sum performed called elements elements elements made natural natural natural natural natural natural applications study artificial artificial artificial artificial relative samples represented series series provide provide objects objects location active connected connected gain equal power accuracy accuracy accuracy comparison comparison comparison contrast contrast contrast update train train train train train train train train train train source source source source proceedings department individual represents layers delay addition environment additional stimuli stimuli stimuli stimuli conference conference conference determine world con con derived randomly developed levels criterion criterion criterion criterion criterion path actual processes processes processes selected evidence backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation sampling sampling sampling sampling sampling simply biological discussion technical fast assumption short shape role eds eds eds eds eds eds journal journal journal journal end ability development sensory sensory including auditory needed account transfer transfer testing testing significantly significantly ratio ratio ratio york york york york york matching matching matching matching matching matching matching details call making making attention produced produced added recent advantage strategy include include identical subset sejnowski sejnowski sejnowski sejnowski sufficient sufficient highly highly approximately match correspond studies achieve achieve horizontal suggests trial trial wide alternative correctly half greater assumptions sigmoid designed clear peak faster suggest sound mechanisms mechanisms integration characteristics characteristics solid start start start start start start selective targets targets targets targets identification pro solving sequential sequential sequential sequential sequential sequential describes laboratory vertical modeled confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence recall recall category category category category averaging text spectral spectral spectral spectral frequencies frequencies quality versus independently open suggested allowed sign sign sign earlier performing intermediate intermediate sufficiently assigned classified activations society society society identify identify identify identify identify identify detect ten reached reached kind contained contained contained moore moore moore moore moore moore moore moore moore moore moore moore moore moore moore moore return return classify classify classify classify classify classify duration categories vary vary absence delayed delayed delayed highest reach reach thresholds received received received consisted trains trains employed layered essential varied scalar scalar scalar scalar scalar examine matches successive successive successive successive successive successive successive behavioral working proper proper proper proper variability variability variability cognition removed plausible predicting psychology psychology front epoch submitted submitted attempts averages integrate integrate animal animal animal biology biology explanation implementing producing directional mation pulses recognizing integrating reflects substantially led led embedded autonomous backprop marked adjustable passed passed passed frequently schematic adjust sums redundancy cumulative cumulative spectra spectra spectra secondary identifying investigation ratios animals animals naval naval naval inspired rational adds khz khz khz multiplicative abilities abilities serves neurobiology integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator adequate filled spurious infor excellent mance reset reset reset combines combines cone cone cone cone cone cone studying studying paul perfor washington sphere sphere sphere sphere sphere sphere captured scan scan scan scan scan thomas thomas entries multiplied fish fish insight bins bins ends canada proteins erlbaum stopped receiving material automated vari johnson johnson assigning assigning assigning sequentially microstructure incorporates ent deriving planes ber ties emerge revealed tween causing amplitudes tor hillsdale molecular clas clas clas publication preserved concentrated cessing robots continues echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo categorization cation sonar sonar sonar sonar sonar meet investigations investigations things echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes echoes inactive scanning stops beam beam beam scanned hearing water water evolved 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#@Moore_P,Nachtigall_P,Penner_R,Roitblat_H,
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#*network network network network network network network network network network network network network network network network model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function time time time time time time time time time time time time time time time time time time time set set set networks networks networks output output output output output output output output output output output number number number system information information based based based based layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer order order order order order order order order order order order order order order order noise noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons single single processing processing processing processing processing processing processing processing processing processing processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns inputs inputs inputs inputs signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal examples work cells cells cells process process process process level level level level level level level current high high high similar architecture equation line line theory theory obtained term dimensional dimensional dimensional university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold defined defined found dynamics map phase activation low low low low low low low low low frequency frequency frequency frequency frequency frequency temporal temporal temporal machine press outputs outputs abstract abstract properties references due positive introduction action action action action action action action circuit estimation generated generated parallel parallel parallel parallel parallel difference difference difference variable spatial spatial signals signals signals signals signals higher higher higher higher higher previous firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type type multiple multiple multiple multiple multiple cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long conditions distributed correlation observed total computed sum sum called mapping mapping mapping potential potential potential potential potential potential potential potential potential potential potential potential potential potential study filter negative negative original original original original vol vol vol relative specific specific specific specific represented application cross series series proc proc location location experimental connected brain voltage voltage connection connection connection train train train train train train train train train train train dependent modeling proceedings proceedings words words words version code code code joint joint represents represents represents represents responses responses responses layers layers layers delay delay delay delay delay delay scheme addition addition addition considered stimuli stimuli stimuli stimuli effects effects effects detection conference conference capacity requires requires increase condition coding types lines lines evidence evidence evidence inhibitory inhibitory inhibitory inhibitory biological biological biological biological transformation excitatory excitatory excitatory stable supported theoretical eds including functional york mode operation representing representing call direct making window window international international added sources description neuronal neuronal denotes denotes denotes denotes membrane membrane membrane membrane membrane reported period period array array axis axis axis axis interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval increased horizontal intensity occur spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes width width width width width width width occurs pass pass pass pass pass place differences differences accurate encoding encoding mechanisms external external relationship iii iii introduce acoustic acknowledgements derive index index ways generating vertical sensitivity frequencies springer extraction potentials potentials potentials potentials potentials potentials potentials extracted extracted extracted extracted depending codes codes codes operations suggested suggested delays delays delays delays intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals generation generation generation generation filtering filtering filtering david fire fire fire fire fire coordinate instances variations domains society encoded encoded encoded encoded encoded encoded encoded delta modes modes modes oscillatory detect detect detect detect essentially capture excitation summary soc verlag decoding decoding neuroscience neuroscience split split superior oscillations content timing timing timing timing duration duration duration involved delayed delayed delayed delayed delayed delayed thresholds thresholds thresholds cat cat cat cat neurosci neurosci neurosci extract extract extract receive receive trains transformed circuitry circuitry oscillator periodic successive incremental investigated variability variability encode presynaptic naturally transmission thought ensure ensure mapped nerve switching baseline band band band band band band band band band band band band band band band band band band band band phenomena phenomena coded coded coded coded adjacent adjacent capabilities london london spatially spatially processed stanford stanford producing filtered filtered filtered division nucleus axon hippocampal read preceding double cochlear embedded embedded embedded embedded capability quantitative passed passed passed passed passed passed passed passed switch branch modulated modulated extracting extracting incoming occurrence conductances physiol physiol owl phenomenon college accomplished formally temporally temporally temporally temporally refractory branches branches neurophysiol neurophysiol neurophysiol neurophysiol eliminated eliminated clamped systematic consideration significance cerebellum contract occurring symposium wilson wilson wilson inferior inferior inferior inferior inferior inferior embedding cerebellar suggesting colliculus colliculus colliculus colliculus colliculus lett onr consecutive converted break transmitted trigger causing stem resting resting resting resting resting suppressed barn cns conduction lond interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike rose rose hodgkin hodgkin hodgkin hat hat hat hat huxley huxley huxley utilizes interaural interaural interaural interaural interaural suppress bcm medicine conversion konishi konishi detects detects chan chan chan chan chan successively sending irvine ionic electrophysiological decoded decoded hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization decode depolarization depolarization neurones prolonged prolonged prolonged rhythms hirsch ito rectification intervening intervening intervening heidelberg biophys vitro vitro serving elicited multiplexing multiplexing multiplexing multiplexing multiplexing multiplexing multiplexing multiplexing noises thalamic thalamic thalamic inactivation clue olivary olivary depolarized depolarized depolarized depolarized depolarized resonant giant multiplexed multiplexed multiplexed multiplexed anomalous primed primed biochemical topographically topographically topographically specially hyperpolarized hyperpolarized hyperpolarized hyperpolarized hyperpolarized tam tam tam tam tam tam tam tam tam pulsed depolarizing distributing triggering carr carr baylor yarom yarom yarom houston xlc oio oio arranging llin llin continual eur wideband moran moran 
#@Tam_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training output output output output output output output output output output output output output output number number system system system system system system system system system system system system error units information information information information problem problem problem hidden performance performance performance performance performance performance based space layer layer layer layer layer case order systems values noise noise noise noise noise noise unit recognition method method approach approach approach point image image image image image image image single processing processing processing processing processing processing processing processing processing processing processing large large local test analysis analysis analysis analysis analysis inputs inputs inputs form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms visual paper small small small small small small small small net net net net net net net net net net net net net net net net net net net net net net net net work work work work methods step points field field features features features features features process level current current current current current current current trained trained trained trained trained trained trained trained problems problems high high high high memory response fixed line line line line line line line images general general speech parameter real real real real real real real real average average average theory gradient note result threshold threshold threshold threshold threshold threshold threshold threshold research research research estimate estimate standard standard computer node node node left presented presented present present phase phase low low low low low low nodes nodes nodes nodes frequency frequency frequency temporal temporal machine press components sample sample sample sample sample sample sample sample sample abstract applied back references component component due ieee ieee ieee positive positive positive positive adaptive decision propagation mixture parallel cost cost cost cost energy difference difference complexity complexity complexity spatial measure measure signals signals signals signals signals signals signals signals signals signals word chosen part part center center good binary represent distributed region correlation observed observed observed simulations simulations simulations simulations resulting tasks tasks simulation multi multi performed performed performed called called called called times elements potential potential potential potential applications applications applications applications filter filter filter filter negative negative original original original relative samples samples samples samples samples samples samples samples samples samples samples samples samples true true true true compared application application series compute rates rates active mit comparison larger contrast fields train source nets nets nets proceedings words version consists final addition considered considered cambridge additional additional top stage bit bit bit detection detection detection detection detection detection detection conference significant significant vision con produce derived derived developed criterion lines lines lines lines lines simply normal technical group tested amount short nearest nearest implemented supported eds eds face vlsi rumelhart rumelhart development development noisy including simulated reduced technology york york york edge special squared filters pre bits bits bottom frame frame frame frame frame produced perceptron denotes moving pixels interest interest interest interest varying conventional conventional conventional conventional conventional conventional approximately works tions amplitude amplitude amplitude amplitude horizontal horizontal digital wide wide spikes alternative correctly correctly correctly width white generally generally column hardware hardware hardware pass conclusions sigmoid measures numerical designed peak performs suggest encoding hard presence presence largest largest reduction reduction cycle characteristics drawn demonstrated variety iii averaged configuration areas pro edges produces perception plot plot plot segments consisting applying formed quality quality versus john john john john depending correlated correlated communication communication variation fraction fraction fraction fraction showed showed showed centered centered centered frames frames suggested processor processor reduces intervals purpose false false false false false false false false interpolation interpolation filtering filtering visible transactions transactions transactions david precision color color color color color color color black absolute neighbors neighbors successfully identified identified mcclelland mcclelland detect post characteristic repeated contained video video video video video video video video video video video video video video video video video video video superior sampled modular modular computes chips chips processors principles principles operating neighboring neighboring parametric wiley wiley wiley transformed poor create essential experience experience varied replaced replaced mass mass successive ideas tech tech mse mse detectors detectors incremental cognition fundamental phases removed removed smallest transmission transmission illustrate eyes eyes eyes implementations impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse algo taylor detector detector detector detector detector detector detector detector detector detector detector detected detected detected detected detected established established band analyzed caused processed drive drive implementing implementing filtered broad broad desirable commonly products products products pulses acknowledgement computers computers bandwidth bandwidth conjugate composite composite composite composite composite composite composite composite fuzzy double pseudo fed quantitative red effort adjustable remove remove remove sharp passes stack switch switch spread modulated modulated instruction serve suited green green green gave replace replace simulator electric electric display display display median median median median median median median median median median median median arithmetic arithmetic arithmetic picture picture picture representative corrupted corrupted corrupted corrupted corrupted corrupted corrupted redundant redundant redundant sort fabricated princeton princeton princeton princeton princeton narrow robotics communications multiplier difficulties balance mark removing receiver receiver receiver salient responsible exceeds exceeds exploring tap elimination elimination embedding started displayed demonstration scan scan scan dif smoothed smoothed clean clean waveforms waveforms waveforms waveforms waveforms waveforms sons sons considerations adopted explorations market acknowledge consecutive consecutive consecutive outperforms roc roc roc roc roc roc roc microstructure corporation rigorous incorporates visually super tables bus removal removal removal removal removal employs spatio smoothly year par blue amplitudes amplitudes amplitudes amplitudes simd big big massively assess mhz mhz cessing rithms compensate permits altered proach investigating investigating library termed termed register geiger electronics electronics electronics electronics electronics det port radio corrections technologies technologies rarely replacement replacement replacement twenty christopher christopher identifies vii ongoing subjective impulses impulses impulses impulses impulses impulses impulses impulses impulses impulses impulses impulses impulses impulses impulses impulses interpolated interpolated pearson pearson pearson pearson pearson pearson carrier incorrectly incorrectly engine engine engine engine engine subtracting alarms luminance detects positives positives positives screen tended digitized receivers vertically confined feasibility feasibility ranged comprised motors decoded manual dean dean ated tory linking sented began decode ference triple simula ton broadcast stand blurred quadrature spence spence spence spence superiority gibson ronald clipping knight taps converting signaling psy grove insure mature nose nose jim economics emerging restored quantifies quantifies colored colored cre matters inexpensive ware interpolator doubled clay misses misses team als breakdown breakdown sidered contaminated registered prince patrick oscilla sparks sparks dictates reprinted rgb merits bernard ction mil strike allel staff fortran cartoon casting consumer consumer consumer consumer consumer falsely television television television television television ringing uncorrupted swets swets complicates verifies thomson exchanges samoff pictorial disregards 
#@Pearson_J,Spence_C,Sverdlove_R,
#t4
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural input input input input input input input input input input input input function function function function function function figure figure figure set set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output output output output output output output number system system system system results units units units units units units units units units units units units units units units units information information information information information information information information information problem problem problem models hidden based based space space space weights weights weights weights weights weights linear linear linear layer layer layer case case case case case case vector vector vector vector systems systems values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise weight distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method pattern image image image image image image image image image image image image image image image image image image image image image image single processing processing test patterns class matrix form form signal signal signal signal signal signal signal simple simple simple gaussian gaussian gaussian gaussian visual paper examples examples size size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature work task task features features features features features features features features features features features features features process process level current trained trained trained trained trained trained structure structure random high high high similar architecture equation fixed fixed fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images images images images images images images images images general general parameter parameter real average average states gradient term term note experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional university university computation research research research research independent independent log found found sequence computer computer computer science prediction left left presented present present present present low low temporal machine object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object sets press learn learn learn learn learn learn learn position position position position position position position position components basis basis basis basis nonlinear outputs outputs abstract references component component due positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important adaptive mixture mixture mixture introduction complex complex effect parallel recurrent difference difference spatial spatial spatial spatial spatial spatial spatial assume assume assume assume assume lower measure representations learned part center cases cases cases cases cases cases cases cases cases type type type multiple multiple good long represent represent expected make fact fact correct correct simulations tasks computed respect sum sum times mapping means optimization made made natural orientation orientation orientation orientation orientation orientation orientation orientation artificial relative represented represented compute compute objects objects objects objects objects objects objects objects objects objects objects objects perform experimental goal goal related constraints constraints connected mit train train train dependent morgan proceedings proceedings report report institute department version technique internal internal individual advances joint joint represents connectionist difficult difficult difficult scheme scheme addition framework computing directly hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton curve san conference conference upper full full requires requires requires significant speed vision vision pages pages pages increase con produce produce randomly clustering finally depends sampling constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint simply achieved covariance technical technical describe describe describe arbitrary tested transformation transformation fast close assumption assumption predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions rbf common shape shape shape shape shape shape shape shape shape role journal end end end end end end end instance instance instance cluster cluster cluster cluster degree noisy noisy kaufmann objective objective objective objective objective objective objective underlying underlying underlying technology significantly significantly consistent consistent consistent consistent consistent consistent consistent consistent matching details iterations making stored bits international international international normalized supervised supervised supervised frame frame frame idea idea combined produced added predict predict architectures robust separate separate separate ensemble ensemble ensemble ensemble ensemble moving hierarchical engineering varying unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised teacher volume module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module tions solve match match trans positions positions positions locations generalized organization entire entire parts parts intensity intensity intensity lead invariant invariant invariant invariant invariant invariant invariant rotation predicted predicted touretzky generally generally setting runs half half half half half half half half half half half half half assumptions valued competitive competitive differences modules modules modules modules modules modules modules modules modules modules modules accurate learns learns learns constrained mateo intelligence radial radial radial variety relationship relationship relationship relationship relationship relationship relationship relationship program force acknowledgements areas reference reference reference reference reference relation relation edges produces produces perception optical optical plot vertical simultaneously linearly transformations mutual mutual mutual mutual mutual adding adding formed extraction extraction extraction extracted independently independently expressed formation transform transform restricted showed frames sizes sizes sizes translation updates updates reasonable additive normalization intermediate initially advantages degrees degrees degrees avoid building perceptual instances instances instances instances instances instances sciences recognize recognize recognize recognize recognize recognize recognize recognize extension discuss maximize maximize maximize mozer mozer black discussions successfully letter suitable detect build efficiently comparing comparing invariance invariance score score score composed capture capture kind kind showing split dis vary dot modular realistic providing providing attempt mixing extract extract intrinsic extend extend presents explore simpler perturbation relations helpful giving relationships relationships relationships relationships relationships working maximizing maximizing scores scores scores scores hierarchy surfaces act circles editor editor traffic traffic traffic traffic traffic traffic versions versions obvious freedom freedom freedom shapes shapes shapes shapes shapes shapes shapes shapes shapes store generates extent finds finds finds indicating advanced agreement agreement agreement publishers orientations orientations orientations variances variances variances nowlan handle handle processed recognized separately separately describing optimize optimize toronto toronto toronto lowest robustness conjugate consistency consistency consistency consistency consistency consistency consistency parameterized share remove requirement passes mod measuring characterize characterize characterize characterize extracting fall achieves plan richard coherent boston sophisticated shaped coherence coherence coherence proportion fix zemel zemel zemel zemel zemel labelled discover discover discover tem eliminate connecting rigid rigid rigid rigid rigid extending significance adjusting interpret viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint analyzing star canonical exploring becker becker becker becker becker connect decide competing competing competing recog ballard ballard ends ends ends canada belonging agree agree agree agree erlbaum grants generalizing tures assigns assigns consecutive kluwer nition smoothly smoothly instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation covariances recurrence hillsdale discovering discovering discovering discovering reject reject param constrain magnitudes stroke geoffrey relates rbfs worth sweeps sweeps fea eters covers tail lowe lowe lowe lowe council sees sees corners agrees wins wins responsibility responsibility played determinant determinant characterizes rameters curved unlabelled unlabelled unlabelled unlabelled hough meant addressing halves halves halves halves halves halves halves halves halves halves halves halves halves twelve sweep steve lar artificially devoted experimented ira bootstrapping bootstrapping bootstrapping degrades crg stereograms ities ontario disagree disagree supervision responsibilities responsibilities responsibilities responsibilities responsibilities canadian augment fragment fragment fellow blobs instantiations particu unrealistic electro specialize specialize presumed apple assure roberts roberts ont ule ported descrip tains aca recoding recoding sibility semble sue vancouver telling imax imax imax noranda ame stances interleaving porally demic 
#@Hinton_G,Zemel_R,
#t4
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#*network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data function function function function function function function function function figure figure figure figure figure figure figure figure time time set networks networks networks networks networks networks training number number system system system system system system system system system system error error units information problem problem problem problem problem problem problem problem models models models models models models models based based weights linear systems parameters parameters neurons neurons neurons recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach point point point point image image image image image image image image image large large local local local neuron neuron neuron neuron neuron neuron analysis matrix matrix form shows shows simple simple visual small net net net net work task step points points points field field field field field field process structure structure structure structure structure structure structure high high similar similar architecture equation section fixed fixed line line line line line line line line line line line line line line line line line line line images images images images images images images images images images images images general general general parameter approximation approximation states states theory term term term term term experiments experiments activity dimensional dimensional dimensional dimensional dimensional dimensional university university university computation solution solution research log found found initial standard standard computer terms terms terms distance node node left left left left left left left left left left left direction presented presented present machine object object object object object object object object object object object object object object object object position position position abstract applied applied find find find convergence convergence convergence properties references due introduction complex dynamic generated parallel recurrent recurrent recurrent energy energy energy energy energy energy energy energy energy energy part part type type type type type type good binary equations equations equations equations equations equations equations make region length length length length length length scale human sum performed mapping optimization optimization orientation applications applications applications knowledge obtain vol true true true true true application objects objects objects objects objects objects objects objects objects objects objects objects active constraints constraints connected equal equal approaches steps train report report version represents graph considered considered considered considered equivalent view solutions design stage conference free speed vision vision vision vision produce derived derived developed types lines lines lines lines lines lines lines entropy nature constraint constraint constraint constraint discussion describe describe transformation transformation inverse corresponds complete complete surface surface implemented shape shape generate generate journal easily development simulated coefficients transfer ratio segmentation segmentation structures matching matching matching matching matching matching matching matching matching matching matching stored international international magnitude frame frame description description description description description description description architectures improved robust strategy moving identical hierarchical hierarchical dimensions sufficient approximately calculated calculated match match match match match match match match match match match match correspond correspond correspond evaluation positions separation organization grant constructed invariant digital rotation correctly correctly correctly deterministic column column column column column column critical row row row greater greater segment segment segment segment segment segment segment segment segment segment central interactions sigmoid designed learns temperature temperature temperature scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene minima identification annealing annealing annealing base base base base base base reference reference relation relation edges edges distinct segments segments segments segments segments segments segments segments segments segments segments missing explicitly coordinates coordinates coordinates angle angle quality solved solved updated translation allowed partial neighborhood visible assigned advantages views views views views degrees degrees perceptual activations eigenvalues eigenvalues recognize recognize determines partially determining identified identified poggio successful identity capture interested interpreted interpreted simplified minimizes eigenvalue correspondence correspondence correspondence correspondence camera camera situations minimized simpler transformed relations relations matches tech tech combine decisions contours matched matched matched matched matched matched matched front obvious portion separated multivariate extent contributions rows scenes scenes scenes trivial trivial agreement derivation unstable perspective sys satisfied ring acknowledgement recognized recognized recognized angles describing describing circle consistency peter measuring germany segmented neuro converged distortion shifted tresp tresp tresp tresp tresp appearance appearance tem robotics wrong siemens familiar primitive primitive primitive primitive primitive primitive definitions edelman edelman corre iteratively lengths lengths stereo stereo stereo stereo stereo stereo stereo stereo stereo peterson peterson contact belonging acknowledge assigning temperatures yale yale yale logarithm solves focal incrementally hierarchies descriptions descriptions certainty avoided gene gene gene gene gene eric eric eric eric leg leg pij magnitudes approxi interacting relating paris attached attached attached stuck knowing knowing indication drops eters sponding uniqueness acquire consuming compositional primitives primitives primitives primitives primitives primitives primitives primitives thermal industrial linearized linearized relational relational relational rectangles occluded occluded occluded lar ild mounted mfa mfa mfa mai retaining rij intrinsically mum enforced sition utans utans treats volker volker evaluates evaluates favorable vat heat machinery miinchen mac gindi gindi gindi gindi gindi gindi gindi gindi cameras endpoints endpoints 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#@Tresp_V,
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hidden based weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown shown shown systems systems systems systems values values values values weight weight weight functions unit unit unit unit recognition recognition recognition recognition recognition recognition approach approach pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image processing processing processing processing processing processing large inputs inputs inputs form shows simple visual paper examples small small size feature features features features features features features features features classification level structure problems high high memory architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show equation fixed fixed images images images images images general generalization obtained obtained obtained obtained term term term note note university threshold threshold computation computation solution solution research research research research computer computer computer terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms distance presented presented present present activation activation frequency frequency frequency frequency frequency frequency object range press position continuous abstract applied computational references due due introduction complex generated parallel parallel complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity spatial spatial spatial spatial spatial spatial lower lower lower higher higher higher higher higher higher higher center center required required required required binary binary binary binary distributed distributed distributed equations proposed scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale simulations total simulation respect multi sum sum sum performed factor made applications applications applications vol vol vol vol provide provide define compute location perform perform discrete equal equal equal power mit larger support institute institute department department implementation individual final bias bias layers addition cambridge computing computing directly directly directly additional stage conference determine requires approximate give give produce weighted associative associative achieved increases group corresponds require journal pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel rumelhart reduced reduced reduced reduced york york making international international architectures pixels pixels pixels relevant engineering engineering engineering dimensions works solve yields achieve rl definition definition definition grid grant constructed intensity concept invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation width width conclusions valued interactions performs performs encoding hard physics physics reduction radial assuming plane plane manner perception optical optical optical optical optical optical optical optical optical mathematical multilayer multilayer explicitly coordinates coordinates electrical scales scales frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies shift shift extraction review transform transform transform transform transform transform operations operations operations forms translation translation translation translation translation translation translation translation translation translation translation processor processor additive reduces calculate building combinations priori memories major determining mcclelland mcclelland mcclelland wij computations invariance invariance invariance invariance anderson anderson symmetry built built giles giles giles giles american american fourier fourier fourier fourier fourier fourier fourier detectors detectors scaled scaled cognition analogous possibly implementations implementations detector detector detector detector detector detector detector mapped explain distinguish defining multiplication comparisons ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring preprocessing mation mathematics angles nsf geometric greatly readily robinson limiting coherent simultaneous summing summing rotated rotated addresses rotations arranged difficulties simplify analogy multiplicative multiplicative multiplicative arrays arrays arrays infor zhang zhang colorado colorado park integers integers integers explorations thresholding acknowledge johnson johnson johnson johnson johnson microstructure fellowship opposed july restrictions amplitudes amplitudes classic invariances invariances invariances invariances invariances pdp labs disadvantage boulder boulder boulder retain paris mask mask mask translations permit vice emphasis mcculloch gratefully versa pitts pitts tial evenly subtracted laser archi optics inspection ance approached spa tan tan tory polar polar biophysics eta ito psaltis psaltis multiplications multiplications multiplications lens lens burden favorable tecture maxwell maxwell maxwell rings rings fid fid gte ovi bulletin reid reid reid invari nmnber griffin optoelectronic optoelectronic cdr television wechsler wechsler lel ological prohibits audi vll 
#@Goggin_S,Gustafson_K,Johnson_K,
#t4
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural input input input input input input input input input input input input function function figure figure set set set set networks networks networks networks networks networks training training training training training training training training number system system system error results results results units units units units units units units units units units units units units units units units units units units units units units units units information problem problem problem problem problem problem problem problem performance space space space space weights weights weights weights weights weights weights weights weights weights linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case vector order order order order shown systems systems values values values probability noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point image single processing processing processing large large large large local local local local local local local local local local local local local local local local local local local rate test test test test patterns patterns patterns patterns patterns patterns patterns patterns analysis inputs simple simple simple simple simple simple simple simple simple simple simple gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual examples small work work work fig fig cells cells cells cells cells step points points field field field field field field field field field field field field field field features features features level trained trained trained trained trained trained trained random random response similar similar similar similar architecture architecture architecture architecture architecture architecture show show rule rule rule rule rule rule rule rule rule rule real real average obtained term activity activity university solution solution solution solution solution independent independent independent independent independent independent independent independent found found found connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic science science direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented presented present present present present present present present activation activation temporal object sets sets sets motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum maximum range learn learn learn learn position position position position position position position position position position position position position position continuous sample abstract applied find properties references component positive important introduction complex complex complex complex complex complex hand stimulus stimulus stimulus stimulus stimulus stimulus stimulus generated generated generated generated generated generated generated change change difference complexity spatial lower rules signals signals learned learned chosen chosen higher higher higher higher higher higher part center center center center center center previous previous previous required cortex cortex cortex cortex cortex cortex long conditions fact correlation correlation correlation correlation minimum minimum total total total human sum times regions regions regions regions regions regions orientation orientation orientation orientation orientation orientation orientation study artificial relative specific true receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive objects proc location location location location location location location posterior constraints connected connected cortical cortical cortical cortical comparison larger larger contrast connection connection connection fields fields fields fields fields fields fields fields fields fields dependent dependent dependent dependent dependent modeling morgan proceedings advances connectionist responses responses responses responses layers layers layers layers equivalent directly curve curve curves curves curves curves curves curves curves transition transition transition san stage stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli detection detection detection conference full full full full requires approximate speed speed speed speed speed speed speed basic basic weighted randomly randomly randomly developed levels area area area area area area area area area types product actual evidence backpropagation biological achieved achieved discussion discussion normal feedforward feedforward feedforward feedforward tested excitatory stable effective shape generate generate generate main eds eds ability easily degree development development development development noisy kaufmann smaller smaller smaller functional mechanism structures structures structures structures structures structures structures max max max filters filters filters pre pre inhibition inhibition decay light directions directions directions directions directions directions directions directions correlations correlations correlations correlations correlations movement movement movement lateral moving moving moving moving moving moving moving moving hierarchical sense sense sense subset array cognitive cognitive interest unsupervised approximately tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning axis axis solve solve solve smooth smooth match locations locations modified channels organization organization organization sensitive sensitive sensitive sensitive increased constructed constructed constructed parts studied invariant invariant suggests rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation locally locally touretzky half flow strength reduce depend clear peak peak suggest strong mechanisms integration demonstrated california turn selective selective selective selective selective selective selective min min averaged scene acknowledgements areas areas areas areas explicit explicit pro written perception primary generating tuned sensitivity sensitivity sensitivity develop develop develop develop gaussians springer stages stages stages stages stages correlated overlap overlap solved solved fraction fraction showed showed showed modulation centered centered centered suggested translation translation translation translation translation translation updates partial partial partial partial earlier reasonable intervals views david recorded building template combinations contour blind blind subspace subspace subspace subspace subspace recognize discussions characterized texture determining capable detect detect detect detect detect post post post invariance invariance invariance essentially receives excitation soc soc soc verlag contained superior symmetry sci sci involved vary vary absence realistic surround neurosci neurosci neurosci neurosci neurosci received principles principles principles consisted moves receive body selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity diego transformed exhibit experience varied varied divergence divergence divergence divergence periodic successive respond respond fashion fashion project project detectors applicable scaled structured understand topographic contours contours gradients gradients naturally opposite opposite opposite changed adjusted obvious hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb generates detected indicating scenes piecewise distinguish publishers growing majority independence processed directional nucleus monkey arise arise involve acad acad beginning linsker linsker linsker linsker linsker linsker linsker annual summation substantially pure offset poorly dots dots dots characterize serve achieves simulator coherent coherent kinds kinds attentional displays displays displays picture discontinuities uncorrelated gabor martin animals narrow velocities velocities nat nat approximates circular rotations rotations rotations rotations rotations rigid rigid primate primate height balance nearby fail fail canonical optic responsible motivation reliably surprising monkeys originally parietal emergence emergence emergence emergence emergence jolla late ends motions motions motions extends broken projects davis davis speeds speeds speeds speeds learnable grating largely shading leaming emerge propagating smoothly smoothly copy medium regularity solely tendency experiences experiences breaking sinusoidal rain rain perpendicular perpendicular activate neurophysiological macaque macaque selectively translations translations translations importantly paradigms apparently sized rochester rotating rotating rotating rotating rotating rotating rotating rotating rotating geniculate exhibited exhibited bring prevents develops drives characterizing saturated satisfactory thousand mst mst mst mst mst mst opponent opponent tanaka adult cylinder horizontally practically nmda systematically tended zipset reproduced andersen andersen andersen amplified senses senses senses senses senses senses aperture aperture aperture aperture aperture aperture aperture indirectly gratings gratings percept backwards rotational responded responded responded responded rec newsome saito saito saito saito saito saito movshon movshon resemble tightly months primates primates align clockwise clockwise clockwise clockwise clockwise gross shear suitably apparatus reminiscent dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation dilation patterned ascending translational translational translational translational foveated translating translating translating supervision clipped clipped wired abstr abstr abstr pattem rationale foveal birth unstructured singularity singularity singularity sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno sereno fell mammals jour jour exercise emerging unrealistic wurtz wurtz wurtz selec resembling siegel siegel interrupted infant lacks counterclockwise counterclockwise subunits duffy duffy duffy irrespective mountcastle mountcastle contracting loc shaw translationally translationally magnocellular plaid warrant lined cla rigidly retinotopically pervasive granted granted firs goddard hikosaka retrospect arielson seelen neurophysiologists 
#@Sereno_M,
#t4
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data function function function function figure figure figure figure figure figure set set set set set set set set set set set networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number number system error error error error state state state state state state state results results results results results results information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based space space space space weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer case case case case order order shown shown shown shown shown shown shown shown shown shown systems values parameters noise weight method method approach approach approach approach approach approach approach approach approach approach approach point point image image image image image image image image single processing processing processing processing processing processing local analysis matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows signal algorithms simple simple simple paper paper paper paper examples examples size size size size net net net net net net net net net net net net net net net net net net work work task task task methods methods methods fig fig fig fig fig fig fig fig fig fig points points points points features process process process level trained trained structure structure structure structure random random random random random random random response similar similar architecture architecture fixed fixed fixed fixed line rule rule images images images images images images images general speech states states obtained term note note note note dimensional dimensional dimensional dimensional result university computation computation computation computation computation solution solution found initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial standard computer terms distance connections connections connections node node node node node node node node node node node node left left left left left direction presented map map phase nodes nodes nodes nodes nodes nodes nodes nodes machine object sets sets sets sets sets press learn learn learn learn learn nonlinear nonlinear abstract applied back back back find find computational computational density references due due ieee ieee ieee ieee ieee positive procedure procedure procedure important propagation propagation propagation propagation introduction complex complex complex complex generated parallel parallel recurrent search change assume rules rules rules representations learned learned learned learned learned learned learned learned learned part part previous cases cases cases cases type type good good good good represent distributed distributed fact techniques techniques region region region region proposed proposed proposed correct correct correct correct correct correct correct forward forward forward forward resulting resulting ing tasks total human human computed computed computed multi called elements elements elements elements elements elements regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means means potential made made study study study obtain negative vol vol vol vol relative relative relative specific represented true true true true true true application proc proc proc constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected connected connected connected connected connected connected connected approaches approaches mit steps comparison connection train train nets selection selection morgan proceedings report words department technique technique technique technique consists consists consists consists internal code represents connectionist difficult final final final scheme addition addition addition maps maps considered considered considered considered considered considered considered considered framework equivalent experiment hinton view limit san stage effects choice vision vision con con con con con weighted randomly developed developed developed levels levels levels area lines lines lines actual actual processes selected selected selected evidence evidence backpropagation inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory constraint constraint constraint constraint constraint constraint constraint constraint biological associative arbitrary denote denote tested tested tested tested tested transformation complete complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory surface finding finding common common implemented shape shape shape generate generate supported main main eds eds pixel degree rumelhart rumelhart rumelhart including kaufmann pairs pairs pairs underlying account unknown fully fully transfer york special structures matching matching operation operation international depth depth depth depth depth depth depth depth description discussed directions directions recent property pair pair pair pair pair pair element element element element element element typical include pixels pixels pixels pixels pixels subset sejnowski sejnowski sejnowski engineering varying compare previously conventional volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume works works solve solve smooth match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match match correspond studies trans generalized generalized williams grant constructed horizontal concept concept studied suggests extended trial trial wide matrices matrices feed feed feed feed feed touretzky white white half half conclusion row row row row row row row row row row assumptions reduce reduce neighbor neighbor differences sigmoid accurate accurate learns learns learns learns learns suggest suggest plane plane plane relationship manner scene scene acknowledgements perception perception perception perception solving laboratory ann vertical vertical vertical distinct modeled multilayer explicitly explicitly explicitly coordinates physical electrical involves involves integrated applying yield expressed review review stages stages overlap viewed influence solved solved lee lee lee lee lee lee lee lee evolution frames similarly suggested suggested constants past neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood false false false iterative iterative iterative iterative iterative remains distances distances advantages existing includes priori priori priori coordinate coordinate formulation formulation strings inter black black neighbors neighbors neighbors neighbors discussions characterized characterized structural successfully identified capable mcclelland poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio composed conf conf conf conf kind prob dis superior follow follow sci device gray gray dot dot dot dot dot dot dot generalize generalize correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence computes thresholds automatically automatically illustrates disparity disparity disparity disparity disparity disparity disparity disparity disparity neighboring receive oriented presents unlike carried diego american layered essential varied involving involving involving integral rise matches matches matches matches matches matches matches matches matches matches matches matches matches matches fashion rest applicable relationships referred proper surfaces surfaces surfaces circles necessarily man illustrate eyes aspect aspect portion algo algo consist consist consist explain attempts mentioned mentioned advanced rows rows rows rows ment distinguish distinguish publishers smoothness coded coded coded floating floating starts processed tive sections located located located scientific separately radius sun sun explained flexible flexible flexible flexible embedded psychophysical posed posed dots ity schematic requirement spread chen suited acoustics june don shifted shifted redundant labeling forming restriction rithm rithm linearity circular eliminate eliminate robotics systematic imaging imaging imaging difficulties analogy imposed imposed imposed imposed affected filled ambiguity regarded dependency stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo den darpa april april foundations record augmented augmented augmented extends subsequently adopted influences explorations limitation lem dense yielded ence unified microstructure planes exhaustive cooperative nition poses smoothly icassp assignments tendency examining transparent continuity care impose crosses crosses wise wise retain rough termed importantly drawback intl intl suffer happen els strict helps topologies survey uniqueness uniqueness uniqueness decided tial tial crude ping correspondences correspondences shot evolved hoc hid outperformed cast sparsely sparsely sparsely progressively marr marr marr marr marr marr marr marr marr marr marr marr marr automation restricting locality translates texas texas ini ini enabling hood upward ying ness impor stereograms stereograms stereograms stereograms stereograms stereograms stereograms stereograms stereograms ele internally cir tant sought stacking stacking displaced volumes volumes retains comprise utilization cog zhou zhou teach perceive cameras cameras disparities disparities viewpoints southern stant stereopsis stereopsis stereopsis stereopsis stereopsis stereopsis stereopsis stereopsis stereopsis inn inn inn straints straints sept downward qian sidered sidered chellappa chellappa itera rior psycho disc grams casting arti cussed incompatible indispensable subregion mda cles cles hor izontal 
#@Khotanzad_A,Lee_Y,
#t4
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#*network network network network network network network network network network network network network network neural input input function function function function figure figure figure time set set algorithm output number number number number number number number number number results results results information problem problem problem problem problem problem problem problem models based based based based based weights weights weights linear shown shown values values values values values values values values values values values values values values values recognition method approach pattern pattern image image image image image image image image image image image image image image image single single processing large local local local local local local local local optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form shows shows shows shows algorithms simple simple simple simple simple simple visual paper paper paper examples examples examples small size size size size net net net net net net work work methods fig fig fig fig fig step step process process process process process process problems problems high similar similar architecture show show show section fixed line line line images images images images general general real gradient note note note result computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation solution research independent independent defined defined defined defined defined defined defined found constant computer terms node node node node node node node node node node node node node node science left left direction map low nodes nodes object basis nonlinear abstract applied applied applied back find find find find properties properties references due positive positive procedure procedure important decision complex behavior parallel energy difference complexity assume assume assume assume measure measure measure measure measure measure measure measure measure measure measure part center bound bound bound type good good long long distributed fact length length length length finite resulting resulting resulting resulting total total total total total computed computed computed computed computed computed computed respect respect respect sum sum performed performed performed performed performed eq eq elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements factor optimization optimization optimization optimization optimization orientation global global applications artificial represented represented desired define define define define define define define define define compute compute objects objects objects objects perform determined determined determined related connected connected connected connected discrete brain equal equal steps steps larger update update update descent selection selection selection selection selection proceedings department loss implementation implementation consists difficult final scheme scheme graph graph graph graph graph graph graph graph graph graph ai ai ai ai ai ai ai ai ai maps cambridge computing computing equivalent curve curve curve curve curve curve additional curves curves curves curves curves curves curves curves curves curves curves curves limit stage stage stage stage stage stage detection conference upper upper upper vision vision pages increase give con con weighted weighted weighted randomly criterion path path path path product product finally finally finally selected iteration sampling simply measured increases increases increases describe describe arbitrary group group group group group group group group group denote close corresponds corresponds corresponds proof proof finding finding implemented shape supported role require end hypothesis hypothesis including pairs pairs account york edge edge edge edge segmentation structures structures matching uniform uniform uniform squared details details numbers iterations iterations iterations max max max max making early polynomial discussed property pair pair element element element element element element element element element element element element identical identical pixels trees trees sense subset cognitive interest interest highly observations smooth smooth smooth yields match correspond correspond converge definition definition definition background chain chain chain chain chain chain chain chain separation grid bounded organization increased grant exists exists parts lead studied extended alternative locally locally locally locally locally locally width width critical neighbor depend measures measures designed performs practice practice propose taking largest cycle cycle cycle cycle cycle characteristics demonstrated intelligence plane iii iii iii iii manner manner groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups scene suppose appears relation segments segments simultaneously remaining remaining angle mutual mutual mutual formed quality quality quality quality quality implies implies select select yield national formation stages stages stages stages stages stages influence influence evaluate approximated partition discrimination discrimination past reasonable calculation performing purpose add iterative degrees degrees coupling perceptual perceptual perceptual perceptual perceptual contour contour contour contour contour contour contour contour inter weighting determines illustrated illustrated maximize holds holds neighbors neighbors neighbors neighbors neighbors structural texture straightforward selecting selecting selecting closely maximal maximal maximal maximal maximal maximal maximal maximal maximal wij wij wij computations identity receives receives summary traditional graphs showing contribution contribution contribution contribution contribution contribution contribution quantity play correspondence correspondence computes highest neighboring acknowledgments decreasing oriented remain carried hall rise rise referred decisions decisions decisions decisions decisions decisions decisions maximizing notion notion notion notion contours contours contours contours contours contours contours contours contours contours induction induction induction saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency smallest circles circles math plausible necessarily spline illustrate subsets quantities mapped mapped detected grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping contributions motivated optimum inequality inequality formula ground agreement smoothness guaranteed adjacent lies straight immediately potentially potentially arises preceding preceding nsf autonomous car biologically exhibits partitioning maximizes maximizes curvature curvature curvature curvature curvature curvature curvature curvature display display display proposition proposition proposition proposition proposition globally lab equivalence forming forming forming linearity optimizing proceed proceed generality systematic convenient chains chains proceeds disjoint disjoint disjoint disjoint disjoint disjoint monotonically salient salient salient salient salient salient salient salient salient salient salient combinatorial selects filled prentice introduces governed governed equals vertices propagated facilitate claim claim iterated iterated iterated iterated iterated iterated permutation repeatedly repeatedly passing considerations implicitly propagate propagate accumulated arcs geometrical creates gaps gaps gaps gaps gaps gaps gaps emerge emerge exception arg arg stands pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing brightness brightness mutually exponent favor favor ibm elementary bounding paired maximally ullman ullman ullman ullman ullman landscape surrounding iri cij portions attached preserve cubic union priority compu round round exploratory scanning coming coming bution emphasis tour covers opti expense expense argmax argmax achievable achievable identifies prefer prefer agrees jersey house inequalities inequalities finer finer finer optima fij fij curved era filling filling iterating iterating concatenated segmenting undergo dij putation linking repetitive collections mization newly stand heights optimizes respects strongest strongest sing spontaneously spontaneously behaved surrounded tours tational fragment flowers groupings groupings groupings groupings perceptually fii fragments fragments fragments fragments fragments concatenation quadratically prefers decomposes visiting contradiction pairings pairings pairings pulled tual incre shashua shashua shashua shashua kom rounds contradicts contradicts taneously multistage cii cii shimon 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#@Shashua_A,Ullman_S,
#t4
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#*network network network model model model model model neural neural neural neural neural neural neural neural input input input data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set networks networks output system system system system system units units units information information problem problem problem problem problem based space space space space layer layer layer layer layer layer case case case order systems systems systems systems probability parameters functions distribution distribution pattern point image image image single processing processing control large local local local local local local local local analysis analysis analysis inputs inputs form form form form form shows signal signal signal signal signal simple simple simple simple simple simple gaussian gaussian gaussian visual visual visual visual visual visual visual visual cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field process level level level level level level level level level level level level level level level level level level level level level cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure problems high response response response similar similar representation images generalization theory note note note note activity activity dimensional dimensional university research dynamics dynamics dynamics dynamics computer direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction present activation low nodes frequency temporal object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range range range range range range range position abstract computational analog properties properties references component adaptive introduction complex complex complex generated generated generated generated generated generated parallel parallel tion tion change change change change change variable spatial spatial spatial lower lower signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals prior part center center center bound type required cortex cortex cortex binary long long long long long long make region region region region length length ing ing total total computed performed called called regions regions regions regions regions feedback feedback orientation orientation orientation orientation orientation orientation orientation global global filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter original desired receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide provide location perform determined goal related larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields fields fields fields fields fields support source words version consists consists individual difficult difficult considered considered domain domain view transition transition transition trajectory top stage stage stage stage stimuli full requires choice speed vision increase increase increase con coding coding area velocity velocity provided evidence nature inhibitory achieved achieved measured discussion normal increases group excitatory short short assumed shape generate generate generate supported require journal square end end end degree needed needed combination york edge edge edge edge edge edge edge edge edge increasing increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism consistent consistent consistent consistent call bottom depth early choose choose light light light light directions directions directions directions directions directions directions directions directions directions resolution advantage advantage advantage advantage advantage advantage property moving moving moving moving moving moving moving moving subject sense cognitive cognitive varying axis axis tions correspond diagonal diagonal diagonal diagonal background positions modified modified gate organization sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive entire exists horizontal horizontal horizontal horizontal horizontal horizontal occur occur locally locally locally loop loop loop loop loop loop loop loop occurs occurs boundary boundary boundary boundary boundary strength reduce trajectories segment valued competitive competitive competitive competitive competitive competitive competitive competitive competitive central measures peak weak weak strong mechanisms mechanisms regularization exist exist movements decrease decrease introduce program question question acknowledgements appears pro edges edges edges perception perception perception perception perception perception perception optical tuned tuned tuned tuned vertical vertical vertical vertical vertical vertical changing segments modeled simultaneously averaging averaging angle scales interaction formed implies competition competition competition decreases focus review stages codes evolution centers centers static static static static static static static static static static static static static static static roughly roughly boundaries boundaries boundaries tracking generation filtering includes perceptual contour contour contour contour contour illustrated illustrated absolute gating gating gating gating gating reason determining middle aspects identified identified identified identified suitable society differ maximal modification build computations computations projections projections situation tend soc soc soc soc induced prob contribution generalize surround surround leading preferred preferred preferred preferred preferred deal decreasing decreasing oriented oriented oriented oriented oriented oriented law stimulation exhibit issues issues successive detectors detectors combine combine combine referred structured fundamental analogous analogous contours contours contours contours contours contours act measurement possibly analyze opposite opposite opposite illustrate front front front freedom extent grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping isolated indicating preference preference preference preference ground orientations orientations orientations orientations phenomena phenomena handle rapid straight preprocessing directional directional arise involve grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg localized author summation transient transient transient transient dark dark dark completion completion continuously variant psychological span ture modulated coherent coherent coherent coherent coherent boston boston simultaneous simultaneous cor contribute aligned aligned proportion accomplished tation perfectly homogeneous homogeneous purely impossible enhancement arranged binocular stronger occurring nearby analyzing illumination north corner corner corner corner corner corner continue ambiguity conjunction lengths enhance infinity arrangement specialized occlusion layout sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained sustained ends arrows arrows reverse subsequently generalizing insensitive insensitive insensitive insensitive insensitive mind linked street ence sine sine accept sig cooperative cooperative cooperative cooperative cooperative cooperative perceived tendency suppressed monocular ary rectangular perpendicular perpendicular perpendicular gated favor cessing graphics elementary afosr rectangle rectangle rectangle mediated adelson adelson adelson surrounding ambiguous ambiguous ambiguous ambiguous conversely nonetheless investigations nal transients transients psychophysics psychophysics increments signs article diagrams lems tour stephen interior interior corners corners corners prefer jointly transparency hypothesized interpreting suffices accomplish horizontally horizontally horizontally luminance luminance luminance luminance luminance luminance luminance luminance luminance luminance luminance luminance functionally america sending curved vertically confined bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs pooling pooling pooling aperture aperture aperture aperture seg tained indicators spa registers actively excessive enabling detections hypercolumn movshon movshon movshon upward contributing contributing marshall marshall sends mentation posi stim scribed infinitesimal notably notably froin froin consensus continuation seeks fil henceforth earliest endpoints endpoints endpoints cap elongated revised gat perceptually unoriented ner illusion illusion manifest presumed mingolla mingolla mingolla mingolla mingolla mingolla mingolla mingolla mingolla mingolla survive lly discussing interac cooperate sharpening crease tering insensitivity evidently laid trailing logically polarities surviving nized joined collinear collinear sharpen reliance conceived segmen ulated erations conception operative investigative sus diagonally diagonally confound clarifies 
#@Mingolla_E,
#t4
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#*network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input data function figure figure figure figure figure figure figure figure figure figure figure time set set algorithm algorithm number number number system system system system error error error results results problem models based based based based based based based linear vector order shown shown shown shown systems weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern single single large local local local local local local local neuron neuron neuron patterns analysis optimal optimal optimal optimal optimal optimal algorithms algorithms algorithms algorithms gaussian gaussian visual visual visual visual visual visual visual visual paper size size size size methods methods methods cells cells cells cells cells cells cells step step step field field field field field field field field field field field field field field field field field field field field field field cell cell cell cell cell cell random random random random random response similar similar similar similar similar representation architecture architecture architecture architecture architecture architecture show show show equation section parameter parameter parameter real theory gradient obtained term term term experiments activity activity activity computation computation computation computation computation computation computation computation computation research independent log found found found sequence estimate estimate estimate estimate standard standard computer connections synaptic science science direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented presented presented map phase phase phase phase phase phase low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal object object object object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion press abstract computational computational computational convergence properties properties properties references component component component component due due important adaptive adaptive adaptive adaptive adaptive adaptive hand hand estimation stimulus effect effect effect effect parallel spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower lower lower signals higher center center center center center center center previous theorem type type type type type type multiple multiple multiple multiple multiple multiple make proposed proposed correlation correct scale scale scale scale scale scale simulations simulations total simulation human human human computed computed computed multi multi multi multi performed eq called factor potential potential natural original relative relative relative relative specific represented represented true compared series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide objects determined equal accuracy accuracy larger larger larger connection fields fields source source source synapses consists individual responses responses delay scheme scheme scheme scheme scheme computing computing directly view stage stage stage stage stimuli stimuli full choice speed vision vision vision estimated basic increase give give channel channel channel coding derived derived randomly developed developed area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types evidence evidence nature depends depends depends depends sampling sampling constraint constraint constraint measured measured measured measured normal increases assumption amount effective implemented require degree development simulated needed needed ratio edge mechanism leads numbers iterations iterations international international magnitude neuronal membrane improved population discussed directions directions resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution movement movement movement strategy strategy strategy strategy strategy moving moving moving moving moving moving subject pixels recently previously subjects smooth smooth sparse address background background background grid grid grid grid grid grid grid channels channels channels channels channels channels channels channels expression scaling suggests deviation derivative move move demonstrate flow flow flow flow flow flow flow flow strength conclusion conclusion greater operator operator operator operator accurate retina retina retina retina clear mechanisms minimizing exist selective selective selective relationship force acknowledgements written perception perception perception optical optical optical optical optical optical estimating simultaneously involves scales scales scales springer shift shift shift shift shift stationary stages influence open frames sizes sizes constants smoothing smoothing smoothing measurements classical classical classical sec neighborhood interpolation filtering filtering filtering filtering foundation classified koch koch koch koch koch koch koch koch formulation weighting retinal plotted plotted determining middle middle efficiency efficiency effectively plots fine fine fine fine fine fine fine capture capture capture capture capture capture capture capture capture capture verlag strongly superior issue issue satisfy dot surround surround surround surround surround surround surround computes highest thresholds preferred deal deal bars selectivity selectivity selectivity requirements humans matches dependencies dependencies reliable reliable complicated pathway circles circles circles coarse coarse coarse coarse coarse measurement measurement measurement measurement measurement measurement measurement reading opposite portion explain explain isolated optimum percentage percentage cos cos smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness explanation explanation explanation briefly ganglion implementing directional operators commonly controls ion res depicted bandwidth nsf researchers apparent varies greatly considerably evaluating applies embedded psychophysical psychophysical orders incorporated incorporated dots dots dots dots dots dots dots dots incorrect incorrect pasadena coherent coherent yuille yuille wang wang wang wang wang wang phenomenon phenomenon phenomenon phenomenon restriction velocities velocities velocities velocities caltech ranges primate primate primate guide enhanced filled motivation reliably james moved moved moved dependency dependency dependency injection captured stimulated surprisingly surprisingly extends summarize convergent influences displacement onr grating grating grating grating grating grating achieving shunting shunting spatio profiles superimposed superimposed tendency suppressed laplacian attempted life multiscale multiscale multiscale multiscale multiscale multiscale selectively termed monitoring discretization discretization discretization discretization intl supporting remarkable inconsistent influenced mcdonnell thousand thousand multiresolution multiresolution multiresolution multiresolution adaptively adaptively finer conflicting resolutions resolutions resolutions resolutions grids grids grids totally acknowledges gratings gratings christof newsome newsome movshon movshon primates primates primates primates rela erroneous erroneous enforced gross grzywacz grzywacz traditionally uniformity uniformity conflict conflict conflict conflict conflict circumvent perceive perceive coarser coarser coarser veto veto veto allman allman allman allman allman allman allman allman lambda lambda lambda antagonistic zlx surrounds surrounds conflicts speedups deviates profound deficiencies deficiencies manifestation mathur mathur mathur mathur mathur mathur ramachandran finest magnocellular multigrid multigrid multigrid multigrid multigrid rockwell rockwell rome signifies lion battiti battiti physiologists mounting adhere arielson arielson filed 
#@Koch_C,Mathur_B,Wang_H,
#t4
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#*network network network network learning learning learning learning model neural neural neural neural data data data data function figure figure figure figure figure figure figure figure time set set networks networks networks training training training number number number number number number number number number number system system system system system error error results results units information information information information information information information problem problem problem problem performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based space space vector vector order shown shown parameters parameters parameters parameters parameters parameters noise noise recognition recognition approach approach approach approach pattern pattern point point point point point point point point point point point image image image image image image image image image image processing processing processing processing large local rate rate rate rate rate patterns analysis inputs form shows algorithms algorithms algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual examples examples examples examples small feature net net work work task task task task task points points points points points points points points points points points points points points points points points points points points field field field field features classification process trained trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems similar representation representation representation representation representation architecture show show section section line line images images general general general general general general general real theory note experiments dimensional dimensional dimensional result result result computation computation computation computation computation computation computation computation computation computation computation computation computation computation solution solution research research defined found sequence sequence estimate standard computer computer distance science science science direction direction presented presented presented presented map map map map map present phase phase machine machine object object object object object object object object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range press press abstract applied back back computational computational computational analog references ieee ieee important important important introduction introduction estimation estimation estimation estimation stimulus stimulus stimulus effect effect parallel parallel parallel parallel parallel tion difference lower representations part part center previous theorem theorem theorem theorem theorem theorem theorem cases type type required good good good proposed length correct correct correct correct correct correct correct correct correct correct errors resulting total human human human human human human computed computed performed performed performed performed performed times factor knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge obtain artificial artificial artificial relative relative represented compared application compute compute compute objects objects objects proc location location location location location perform perform perform determined goal approaches mit mit accuracy comparison larger contrast proceedings proceedings institute words implementation implementation difficult difficult addition sequences sequences ai cambridge computing domain domain experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment directly directly directly curve limit stimuli stimuli stimuli stimuli stimuli detection determine full requires requires significant significant significant speed vision vision vision vision vision vision basic pages con produce condition condition types lines lines biological biological achieved normal describe denote fast complete complete surface surface surface surface surface rbf rbf rbf implemented shape shape shape shape shape shape shape supported supported theoretical theoretical theoretical main journal degree noisy account account account technology technology significantly significantly significantly significantly significantly significantly significantly projection projection york consistent trials trials principle details direct international supervised depth depth depth depth depth depth depth depth depth early magnitude frame frame frame frame frame frame frame frame frame description discussed discussed directions directions directions exact exact exact exact exact exact exact movement practical strategy strategy strategy moving moving moving moving moving moving subject identical identical sense sufficient sufficient subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects module yields studies address positions positions locations sensitive entire entire entire parts parts trial deviation wide rotation rotation rotation predicted locally flow flow operator operator depend editors retina designed designed moody moody taking intelligence intelligence regularization radial assuming min plane manner scene configuration configuration question question acknowledgements appears appears van van perception perception perception perception perception optical optical solving describes laboratory laboratory tuned distinct sensitivity multilayer involves text text formed select national focus focus expressed interpretation frames frames frames frames frames frames frames frames frames frames frames frames frames completely translation translation translation translation translation translation translation translation translation translation translation allowed sign sign sign sign sign sign sign sign sign sign sign sign sign sign sign sign partial performing expansion convex convex convex convex boundaries foundation foundation koch views transactions precision avoid expect recorded building includes coordinate coordinate instances extension plotted major middle aspects suitable society poggio poggio poggio identify build summary summary conf repeated heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic success success success interpreted interpreted cue cue dot ill ill ill consisted subsequent disparity extract camera situations presents bars collection requirements varied humans accurately divergence rise successive incremental investigated office maximizing affect surfaces closest plausible plausible plausible possibly configurations observe academic detected extent extent serial electronic massachusetts mentioned percentage directed navigation navigation navigation adjacent adjacent explanation answer answer lies london perspective straight purposes operators located projected projected implicit implicit patches qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative pure pure pure pure pure generic generic generic experimentally quantitative psychophysical posed posed posed incorrect incorrect incorrect biologically rely perturbations characterize limiting curvature curvature curvature curvature curvature curvature curvature curvature curvature curvature curvature curvature curvature curvature curvature curvature substantial semi inherent cor realized naive consistently uncorrelated pick girosi girosi recover recover repre naval eliminate rigid rigid rigid rigid lost wrong wrong imaging chance chance chance chance chance chance chance darken darken check hope analyzing planar obstacle reliably passive recovered recovered edelman ambiguity ambiguity ambiguity james studying encountered decide dependency washington infinity sim recovery recovery horn horn broken subsequently santa grants outlined verify geometrical geometrical geometrical incorporates fellowship nelson nelson acceptable affects graphics mathematically adelson ullman ullman ullman ullman ullman iri iri ambiguous ambiguous ambiguous responding memo meet knowing applicability psychophysics answers nec demonstrating uniqueness hyperbolic photoreceptors insufficient mcdonnell partly huang huang kirkpatrick correctness resolved explanations concave concave concave concave america spie curved sis ance doom doom february undergo recovering sented percep stems ference meaningless yon yon judge judge weinshall weinshall weinshall weinshall weinshall weinshall weinshall grzywacz stim undergoes translational translational translational ross puted puted differed clarify snapshots necessity psy perceive disparities disparities disparities disparities undergoing equiv relied renders appeal hyperacuity hyperacuity hyperacuity disparate imal misleading misleading beck postdoctoral reversals tual koenderink koenderink implausible hildreth hildreth hildreth shashua guessing guessing invariants judgement cylindrical ilar ulus alent professor plication rations attacked shortcuts curvatures parabolic collinear collinear parallax rosenreid configu elliptic surprised thai felt bent impoverished impoverished buildup questioned 
#@Weinshall_D,
#t4
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#*model neural neural neural data function function function function figure set set set number number system system system system system system system system state results information information information information information information information information information information information problem problem problem problem problem problem problem problem problem space space space space space space linear linear linear linear case case order order order shown systems systems noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions neurons neurons distribution approach approach approach point point point point point image image image single single processing processing processing processing processing control large large large large local local optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple simple gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small work work work task fig fig fig cells cells cells cells cells cells cells cells field field field field field field field field field field field field field field features features features level level cell cell cell cell cell cell structure problems similar architecture show equation equation equation equation equation fixed images images images images images images images images images images images images images images images images images general general general general real real real real states states states states states states states states states states states states states states theory theory theory theory theory theory theory term dimensional result result university university university computation computation solution research research independent defined defined defined terms terms terms terms science prediction prediction left present phase low low low low low low frequency frequency frequency frequency range range range press press outputs outputs sample sample abstract back find find find find find find find computational properties references component context context introduction complex complex statistical cost tion energy energy energy energy energy energy complexity variable spatial spatial spatial spatial spatial spatial assume assume lower lower lower lower rules signals signals signals chosen higher higher higher part part part part part center bound bound bound bound bound bound multiple cortex cortex cortex cortex cortex cortex cortex good long long conditions represent expected make make make fact fact region correlation correlation length observed observed observed observed observed scale scale scale scale scale scale scale finite resulting classes total total total total multi eq eq regions regions optimization optimization optimization optimization potential potential made natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation knowledge filter filter filter filter obtain original vol receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive determined experimental experimental related constraints constraints constraints constraints constraints gain cortical equal power power power power mit comparison fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields source source morgan institute department individual individual kernel advances layers considered cambridge computing equivalent experiment experiment view view solutions solutions solutions solutions solutions solutions solutions solutions solutions design limit limit san stage bit capacity capacity capacity capacity capacity capacity determine choice choice statistics free world pages give give con condition condition developed levels types provided finally sampling sampling sampling sampling sampling sampling sampling sampling constraint constraint simply biological biological achieved measured discussion limited limited surface predictions generate supported supported role role role theoretical theoretical theoretical theoretical square makes sensory fit kaufmann typically functional transfer transfer transfer interesting ratio ratio ratio ratio ratio principle principle principle principle leads details filters filters filters filters filters filters filters filters filters filters direct early produced choose choose choose discussed correlations correlations resolution ensemble reported lateral apply moving sense sense sense sense array array array recently tuning tuning tuning tions solve correspond correspond correspond studies address definition symmetric symmetric bounded channels organization sensitive increased grant exists exists invariant suggests predicted predicted touretzky white hardware hardware strength greater depend interactions measures measures retina retina clear clear peak asymptotic constrained mateo strong physics physics characteristics characteristics characteristics california california california california proportional minimizing selective connectivity acknowledgements reference derive construct primary mathematical implement sensitivity coordinates easy unique scales scales predictive predictive minimization select john national expressed stationary communication communication detailed detailed transform restricted centers similarly spectrum spectrum spectrum spectrum reasonable performing measurements measurements expansion expansion expansion normalization add penalty penalty construction construction construction foundation foundation avoid expect combinations combinations combinations formulation formulation eigenvalues retinal retinal sciences recognize variations discussions tests major simplicity regular extra efficiency capable successful oscillatory computations invariance invariance invariance invariance reached soc soc interested issue symmetry symmetry symmetry symmetry sampled sampled usual surround surround wave quantization eigenvalue correspondence preferred origin origin unlike selectivity selectivity selectivity selectivity selectivity selectivity selectivity carried essential essential issues mass helpful existence scalar fourier respond rest biol variational variational variational variational variational variational possibility combine scaled authors proper variability func understand momentum momentum momentum momentum momentum momentum momentum removed editor editor editor predicting extremely extremely extremely equally precise precise explored consist extent finds finds attempts site scenes theoretic orientations biology independence ganglion ganglion ganglion ganglion perspective snr snr snr snr tive berkeley berkeley berkeley easier preprocessing monkey monkey monkey mation consequence ion ion involve opt opt beginning begin localized localized localized lowest linsker qualitative nsf sun mechanics mechanics generic quantitative quantitative introducing introducing posed sharp rep biologically maintain maximizes maximizes qualitatively semi conclude redundancy progress wesley cor spectra spectra spectra cybern addison lagrange tation princeton ratios ratios angular angular angular angular angular angular angular angular angular angular angular angular driving optimizing impossible impossible proceed plays plays plays multiplier numerically proceeds attractive imposed moment hope hertz continue infor meaningful cone bialek bialek bialek bialek bialek photoreceptor infinity monkeys interconnections interconnections young surprisingly informative park santa santa santa adopted ure fellowship equivalently ties formulate isotropic ical constitutes tor imagine molecular rain var constrain constrain intuition shannon mammalian mammalian mammalian graduate careful proach weaker barlow barlow nasa particle page page knowing behave served served sees fractal jersey developmental powers award illinois rons optima striking atick atick normalize carries vertebrate william sions deter ruderman ruderman ruderman ruderman locality locality locality bear prominent dence eigenfunctions daniel urbana landscapes diverge diverge investigator cons remarkably phy cient imaginary resentation ver rom redlich possesses retinas sing vertebrates vertebrates vertebrates menlo ages foveal optimiza mined accord presidential jackson recep charac quantum quantum saving resemblance selectivities superpositions 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#@Bialek_W,Ruderman_D,Zee_A,
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distance distance connections connections connections node present object object object object object range range range range range range range range range range press components basis basis outputs abstract applied computational analog analog analog analog analog analog analog references component ieee important hand circuit effect effect effect effect effect dynamic dynamic dynamic dynamic parallel cost tion difference complexity complexity spatial spatial spatial rules measure measure center center center center center center center center center type type type required cortex good good good good conditions conditions conditions expected chip chip chip fact region region region region region region proposed proposed length length correct simulations simulations simulations simulations simulations simulation simulation human respect sum sum performed times times times regions regions regions regions natural study study original original original original artificial samples compared compared compared compared application desired compute objects rates proc location perform eye related contrast support support dependent dependent institute institute institute institute institute implementation implementation version version version version technique kernel kernel kernel joint computing additional design design limit top top top top stage effects effects effects effects bit efficient upper full significant approximate world world world vision vision vision vision produce condition channel channel weighted weighted developed area product evidence sampling simply normal technical arbitrary tested close close assumption assumption assumption assumption assumption assumption corresponds corresponds corresponds stable stable short nearest common implemented implemented supported face vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel ability ability ability reduced technology technology technology technology technology operation operation operation operation operation operation details details details details details call direct window bottom bottom bottom bottom magnitude frame minimize produced produced light light light light light light light light light light light light improved improved discussed recent separate reported practical practical practical subject subject subject subject subject subject identical identical pixels pixels sense array engineering dimensions highly varying conventional subjects works smooth yields studies trans address address background background background background evaluation modified modified grid grid grid grid grid grid grid grid improvement storage constructed intensity extended extended digital wide wide wide predicted alternative white white white white white white white white white half strength strength conclusion place neighbor central central central central tangent retina retina retina designed exponential weak sound taking strong mechanisms physics physics california california california california california variety variety variety plane plane derivatives scene scene scene scene scene scene scene scene scene scene scene scene scene program program configuration configuration question acknowledgements areas areas areas areas explicit suppose relation produces produces ways ann dept dept dept dept electrical john decreases decreases independently dependence review review viewed viewed detailed operations operations operations similarly allowed earlier calculation calculation smoothing reduces neighborhood roughly remains visible foundation silicon usa formulation color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color color weighting weighting weighting weighting weighting extension extension extension black black black black black black black black absolute holds discussions sensor middle importance effectively efficiently schemes situation ten composed capture soc quickly strongly strongly strongly video video video video video video video video video video video video video moore moore moore moore moore moore moore sci hold built built built built built surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround cmos cmos cmos chips illustrates neighboring neighboring intrinsic intrinsic intrinsic decreasing decreasing camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera remain carried carried american poor essential investigate experience mead mead mead mead mead varied varied humans strengths strengths strengths strengths issues issues preliminary ideal ideal office referred working analogous induction induction induction induction induction patch patch patch patch patch patch patch patch closest reading reading reading extremely rev rev perfect perfect adjusted front portion portion portion portion formal noted taylor explored switching extent electronic electronic electronic electronic electronic great scenes scenes slowly slowly band band sensors sensors sensors sensors sensors sensors convolution convolution fairly fairly biology answer correction correction correction correction processed processed processed widely transistors arise arise commonly scientific acad opt res patches patches patches patches raw raw raw raw raw explained reflects apparent varies varies limits dark dark dark dark dark dark capability fed quantitative red red red red red red red red psychophysical psychophysical passed remove resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive rely monotonic monotonic incoming pasadena pasadena pasadena pasadena green green green green green green green returns wesley lot consistently phenomenon phenomenon lab ordinary sort addison acts homogeneous purely naval eliminate enhancement grows grows grey grey grey grey grey grey grey grey grey grey grey grey grey grey grey grey grey grey grey grey turned reaching caltech lost lost fails fails imaging imaging hyper bands bands bands bands bands operates illumination illumination illumination illumination illumination illumination illumination illumination exceeds exceeds arrays filled natl recovered falls falls tone tone tone studying moved enhance captured nonlinearities darpa multiplied smoothed verification verification passing relies card card card observer observer papers fusion andrew dramatically dramatically land land land land land land land land land land land land land land land land land land land land land land land land leaving indirect corporation incorporates minus minus minus equivalently planes planes goodman goodman goodman goodman goodman revealed encouraging pointed pointed par corrected blue blue blue blue blue blue blue blue blue blue blue reports simulating demon realize subthreshold subthreshold deep geoffrey reflectance reflectance carefully carefully surrounding complementary complementary complementary complementary investigating conversely portions portions portions portions accounted grateful grateful placing retained holding compu psychophysics strict resembles lighting remarkable differently sees monitor thousand observers observers skin skin skin skin skin mirror mirror fabrication pronounced pronounced compensation subtracting subtracting lightness lightness subtracted subtracted subtracted subtracted subtracted subtracted subtracted subtracted subtracted subtracted striking proposes normalize fox fox fox fox grids grids grids grids ory colleagues 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#@Allman_J,Fox_G,Goodman_R,Moore_A,
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#*network network network network model model neural neural neural neural neural neural neural neural input input data data data data function function function figure figure time time time time time time time set algorithm output output output output output number number system system system system error results results results information information information information information information problem problem problem problem problem problem problem performance performance performance performance performance performance based based based based linear linear linear order shown shown systems systems systems systems systems systems probability probability parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise approach approach approach approach approach single single processing processing processing processing processing processing processing processing processing 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high response response response response response response response response response response response response response response response response response response show show show general general general general general general general parameter parameter parameter real real average average theory theory theory theory theory theory term term term experiments experiments experiments experiments result result result result university computation computation computation computation computation computation computation research research research independent independent defined dynamics dynamics dynamics constant constant estimate standard terms terms connections science prediction prediction prediction prediction prediction prediction prediction presented presented low low low low low low frequency motion maximum press position outputs abstract find find computational density density properties properties properties properties references component due important important decision introduction complex estimation estimation estimation estimation estimation estimation estimation stimulus stimulus effect tion tion complexity spatial measure signals signals signals signals prior higher higher center cases spike spike spike conditions conditions make make make make fact fact fact fact fact errors resulting resulting tasks tasks computed sum times elements elements optimization study knowledge knowledge filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter obtain series receptive define compute perform eye determined experimental experimental related brain approaches approaches approaches voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage comparison comparison contrast train dependent dependent source source modeling morgan morgan proceedings institute institute version version version consists advances responses responses responses responses layers framework experiment experiment experiment environment directly directly directly view view solutions estimates estimates design design design limit san san top stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stimuli stimuli determine determine determine significant free free free free free free world estimated estimated pages pages weighted conditional conditional levels nature nature depends depends depends depends depends biological measured measured measured measured measured limited limited close complete predictions predictions predictions predictions shape shape supported role theoretical theoretical theoretical theoretical theoretical theoretical adaptation square hypothesis makes sensory sensory sensory sensory sensory fit probabilistic probabilistic hopfield functional functional functional transfer transfer transfer transfer transfer transfer interesting ratio principle principle details numbers pre pre pre pre direct making early light light light light light predict predict denotes discussed discussed recent recent ensemble typical movement apply introduced strategy strategy identical sense sense sense array relevant varying varying compare compare conventional observations observations volume solve solve background background separation separation separation observation observation observation grant intensity intensity expression suggests extended deviation predicted predicted predicted predicted predicted touretzky touretzky occurs occurs hardware retina retina retina retina retina retina retina retina retina retina retina numerical mateo mateo suggest encoding physics physics physics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics california california labeled turn start start relationship scene scene question question reference pro van van solving estimating estimating estimating mathematical distinct recall linearly physical electrical involves involves spectral spectral develop develop predictive predictive extraction national national independently formation reconstruction stages stages stages stages stages correlated transform transform processor processor processor processor processor spectrum calculation calculation calculation expansion sec sec generation remains filtering filtering filtering filtering filtering filtering calculate precision coupling expect expect expect priori currents currents currents currents currents currents currents currents currents currents currents currents retinal retinal sciences specifically variations variations discussions discussions aspects identified efficiency spiking identify miller essentially essentially traditional soc success lie follow follow minimizes reach subsequent subsequent extract extract extract satisfies acknowledgments trains bars bars remain carried collection exhibit circuitry circuitry preliminary mass helpful fourier fourier respond ideas ideas rest behavioral behavioral analytically reliable complicated fundamental notion matched matched patch measurement naturally naturally editor editor editor adapt adapt reading predicting extremely extremely rev perfect voltages voltages voltages aspect impulse impulse precise precise detector nervous simplest regime regime motivated averages averages agreement agreement convolution adjacent biology analytic adapted adapted adapted adapted adapted adapted adapted answer answer independence ganglion considerable processed snr snr snr snr snr snr snr berkeley berkeley filtered filtered filtered precisely precisely ion involve universal universal universal universal universal opt opt calculations sun fluctuations argument questions limits limits limits dark dark dark dark dark experimentally quantitative quantitative lattice lattice recordings reliability reliability reliability reliability schematic characterize reaches extracting cal tank physiol physiol physiol deviations lim progress wesley sharing pose spectra spectra uncorrelated addison writing writing bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar princeton recover count count count connecting arrival arrival arrival arrival arrival arrival anatomical iiii imposed imposed occurring nearby observing illumination intuitively intuitively symposium presentations excellent bialek bialek bialek bialek bialek bialek bialek bialek bialek bialek studying photoreceptor photoreceptor photoreceptor photoreceptor counting specialized young layout passing insect considerations alternatively outline fellowship formulate formulate expanding expanding tween ical classic molecular realize adjustment cessing geoffrey mathematically graduate convert convert emphasize emphasize argued flash flash flash flash flash flash barlow barlow barlow intracellular intracellular rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod rod mea mea nec nec laws remarks dim dim dim dim dim lation thermal thermal photoreceptors photoreceptors photoreceptors photoreceptors agrees confirm jersey diffuse diffuse diffuse dominates fill fill award impedance atick atick atick emerges separates intact vertebrate william lewis ruderman tained steveninck steveninck derives ruyter ruyter health noiseless began investigator ular rieke rieke rieke rieke rieke rieke yamada incident redlich opportunity pri suggestion biophys biophys biophys ages testable torre ies divides divides presidential cleaning cleaning organism organism gem compound concluding volt fimction salamander salamander salamander salamander salamander salamander occuring stud larsen warland warland flowing gov departments ond imal identi bet hecht hecht funds zee calcu pursuing photon photon photon photon photon photon photon photon photon photon photon photon impedances impedances impedances kom fred sured overly dation helping completing cray absorption arbi decorrelate microsystems flux foun optim ang trary lln rods rods rods rods termined supplemented ces lectures excludes baylor surements photons photons photons photons photons inefficiencies lamb sfi ents ited flashes jen forin restilts theoreti liere 
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target constant computer computer computer computer distance synaptic synaptic synaptic synaptic synaptic synaptic science prediction left left low temporal temporal motion range abstract back computational computational computational properties properties properties properties properties properties references due introduction hand hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit stimulus effect effect generated generated generated generated generated generated generated change change change change change change change change change change change change change change change change change change change difference spatial spatial spatial spatial spatial spatial spatial part center center center previous cases type type required spike spike conditions represent represent distributed distributed make fact region region region region region proposed proposed proposed observed observed observed observed observed observed observed observed observed observed simulations simulations simulations simulation simulation simulation elements elements regions potential made applications filter filter compared receptive receptive receptive receptive receptive receptive proc determined experimental experimental brain voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage fields dependent implementation responses responses responses responses responses responses responses responses responses delay experiment experiment curve stimuli stimuli detection detection detection detection determine determine full full requires requires area area types types types processes processes inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory normal feedforward describe close excitatory excitatory excitatory excitatory excitatory predictions predictions predictions implemented implemented implemented implemented assumed generate generate eds hypothesis hypothesis degree including simulated simulated simulated simulated simulated simulated simulated smaller reduced reduced account account account block testing edge consistent consistent representing details details details call filters direct direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition bottom magnitude light light membrane discussed takes movement movement movement movement lateral lateral lateral lateral lateral lateral moving subject side array sufficient previously previously correspond sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive entire constructed horizontal horizontal horizontal occur wide wide wide wide wide wide wide wide wide wide wide wide wide wide wide wide wide wide predicted column column column pass pass demonstrate row row row central central central central central central central interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina suggest presence presence reduction characteristics turn iii manner appears van modeled modeled modeled sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity electrical scales interaction interaction integrated integrated potentials formation stationary stationary stationary stationary stationary stationary influence controlled showed suggested constants earlier reduces combining roughly generation msec msec recorded box box usa currents currents currents currents retinal retinal retinal retinal retinal illustrated illustrated illustrated illustrated simplicity simplicity spiking build receives excitation summary conductance physiological sci receptor involved involved vary surround surround surround surround ill leading neurosci neurosci neurosci overlapping illustrates illustrates illustrates receive receive receive receive receive extend body body body body investigate circuitry circuitry circuitry respond respond terminal terminal terminal terminal terminal terminal circles patch patch patch patch transmission transmission transmission perfect voltages thought thought extent explain integrate analyzed caused ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion comparisons comparisons spatially spatially spatially drive implementing berkeley berkeley widely located axon acad describing res recording depicted fourth apparent pathways consistency transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient amounts simulate simulate experimentally experimentally incorporated incorporated continuously maintain release release release release release summarized spread gen gen prevent conductances conductances conductances shaped physiol physiol traces traces simultaneous phenomenon lab lab room appearance bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar investigation narrow narrow narrow narrow narrow narrow narrow receptors receptors turned reaching anatomical height spot spot spot spot spot spot spot responsible natl continue dendrites dendrites dendrites accounts accounts accounts lawrence lawrence reproduce verification sustained sustained sustained sustained arrows arrows influences boxes truncated responds responds responds spatio spatio terminals terminals terminals profiles profiles causing simulating simulating simulating simulating suppressed visualization gated gated gated robots compatible thresholded mediated relating flash flash flash flash flash resistors tune wider coming coordination reversal hypothesized hypothesized transmitter transmitter accomplish contributes attained lying compartment compartment vertebrate reproduced presently ionic ionic meant enters enters format hyperpolarization depolarization eeckman eeckman eeckman plenum instant activates upward visuomotor hypothetical compartments electrically army mac feeds frank frank clamp clamp clamp clamp clamp clamp underlie visualize neurotransmitter neurotransmitter neurotransmitter neurotransmitter neurotransmitter depolarized copenhagen copenhagen arbib sensitivities salamander salamander salamander salamander salamander salamander salamander salamander salamander salamander succeeded mediating mediating reductions barnes barnes barnes barnes barnes flowing traced outward outward downward hyperpolarizing antagonistic 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#@Eeckman_F,Teeters_J,Werblin_F,
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line general obtained result result result university research independent log log log log log log log log log log defined found constant constant constant constant synaptic synaptic synaptic synaptic left presented presented presented present machine maximum range nonlinear continuous abstract back back properties properties references component component due due due due procedure procedure introduction action action circuit circuit circuit behavior stimulus stimulus statistical effect effect effect generated generated generated parallel parallel tion tion change change change change change difference assume assume assume measure signals signals part part center center center center center center center center center center center center previous previous type required long conditions represent observed observed simulation simulation potential potential potential potential potential potential potential potential potential potential potential potential feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback negative negative specific represented cross series series series receptive receptive receptive determined experimental experimental experimental related gain equal voltage voltage larger fields support support dependent dependent modeling consists internal represents represents represents represents responses responses responses exp domain domain domain domain domain domain equivalent equivalent environment curve curve curve curve curve curve curve curve curve curve curve additional additional additional additional curves curves curves curves curves curves curves curves curves curves curves limit effects effects effects effects effects full requires vision vision increase increase increase increase con produce produce channel derived derived developed provided finally evidence nature nature nature depends depends measured measured measured measured discussion normal increases fast limited limited close corresponds complete amount amount shape shape synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse role adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation hypothesis simulated smaller smaller smaller smaller underlying underlying underlying combination functional fully increasing increasing increasing increasing increasing increasing increasing mechanism mechanism mechanism mechanism special representing making depth early magnitude frame combined combined light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane reported lateral recently varying previously previously previously approximately approximately approximately axis studies studies studies channels channels channels channels channels channels channels organization sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive increased increased increased grant grant grant grant grant grant amplitude amplitude horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity invariant suggests suggests feed half reduce segment segment segment central central central interactions interactions interactions retina retina retina retina retina retina retina retina peak peak peak peak peak suggest suggest suggest presence presence drawn california california assuming decrease decrease relationship relationship manner identification identification base appears relation relation pro pro perception generating generating generating plot plot laboratory modeled sensitivity sensitivity electrical electrical spectral adding shift shift shift shift shift shift shift shift shift shift shift shift versus potentials potentials variation detailed open open controlled fraction showed static suggested key partial reasonable reduces add closed generation initially coupling recorded recorded recorded thesis combinations combinations currents currents retinal retinal determines plotted plotted plotted specifically compression compression compression middle middle aspects maximal maximal maximal maximal driven comparing reached reached reached characteristic characteristic characteristic interested conductance conductance conductance conductance conductance conductance conductance conductance conductance contribution criteria criteria involved involved involved simplified absence absence surround surround surround providing operating decreasing decreasing law remain unlike steady involving preliminary respond project examined circles circles adjusted portion portion explain seconds isolated isolated isolated averages site ment distinguish explanation tive berkeley sections ring day gradually res localized localized recording recording nsf outer outer outer outer outer explained varies limits empirically transient dark dark dark dark dark recordings span summarized spread branch branch branch branch branch branch gen gen physiol physiol physiol physiol physiol eventually contribute shifted shifted identifying bipolar neurophysiol neurophysiol fits saturation murphy ments significance minutes resistance resistance resistance resistance resistance los balance resulted resulted shifts shifts settings settings settings settings imply illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination spot spot spot spot spot spot spot spot spot spot spot preparation wilson filled passive reset cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone mental photoreceptor photoreceptor diameter diameter diameter diameter diameter fish stimulated sustained sustained concentration concentration calcium calcium calcium fold acknowledge onr fitted logarithm graded graded solely reports hundred resting resting resting evoked examining peripheral peripheral peripheral peripheral peripheral peripheral peripheral peripheral preserved gated shifting shifting shifting approxi hughes mediated mediated mediated mediated iso maximally argued argued surrounding lond lond intensities register superposition intracellular indication completed reversal reversal reversal stimulating lation saturated tial influenced synthesized insufficient lated micro transmitter transmitter transmitter chan cones cones cones cones cones cones cones cones cones cones cones cones cones cones cones cones cones cones cones cones cones cones periphery periphery periphery periphery vertebrate vertebrate fastest tance tance sity leakage leakage leakage leakage leakage drastically drastically falling ionic ionic cess seg tained cyclic undergo ira hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization hyperpolarization depolarization depolarization depolarization depolarization depolarization yellow ted resemble bodies battery battery battery battery battery battery battery modulating angeles cir sodium undergoes ecs nation abstr released released mag elicited elicited elicited elicited poten ions ions ions ions ism spans opens propositions abscissa abscissa abscissa abscissa recep sume prof salamander salamander salamander salamander quence peri mediating micron microns noticeable noticeable nucleotides annulus annulus annulus annulus annulus annulus annulus sug stepwise internet zation flowing gin lea conduc conduc kirchoff hyperpolarizing hyperpolarizing hyperpolarizing hyperpolarizing hyperpolarized antagonistic antagonistic antagonistic skrzypek skrzypek skrzypek skrzypek skrzypek skrzypek skrzypek skrzypek skrzypek skrzypek skrzypek ucla ucla ucla ucla photon crease illuminated depolarizing depolarizing depolarizing nels aro ambient urn iro resets calibrated legend annular annular annular annular annular annular annular 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threshold threshold threshold threshold threshold threshold computation research independent sequence sequence constant constant computer node node science science left left nodes nodes nodes object sets range abstract applied back analog analog analog analog analog analog analog analog analog properties references due introduction hand circuit behavior behavior behavior stimulus tion difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference lower center center center represent chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip proposed length length length simulations simulations simulations resulting ing simulation performed regions natural filter filter filter filter filter filter filter filter filter filter filter artificial artificial application proc connected connected power voltage voltage voltage voltage voltage voltage comparison implementation implementation version technique technique technique final final bias delay scheme additional view view design stage stage stimuli detection detection determine determine produce velocity measured tested tested finding finding finding finding finding implemented implemented implemented implemented implemented shape shape shape shape shape supported supported vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel easily block block edge edge edge representing filters filters bits international magnitude light light light light light advantage pair robust robust robust takes reported reported reported moving pixels pixels pixels pixels array relevant dimensions dimensions approximately works smooth smooth background positions locations locations locations gate gate gate gate gate intensity intensity intensity intensity intensity digital digital wide derivative move conclusion greater greater operator operator differences designed designed exponential exponential exponential exponential presence proportional proportional intelligence intelligence program acknowledgements edges edges edges edges edges edges edges edges edges edges edges edges edges edges edges edges longer laboratory implement implement implement gaussians gaussians gaussians gaussians gaussians john national independently focus stages approximated diagram smoothing smoothing sec filtering msec foundation advantages koch koch koch koch figures kernels silicon silicon silicon currents currents currents currents weighting extension partially detect characteristic characteristic characteristic capture soc quickly showing conductance follow device device device built built bar absence cmos cmos computes extend camera minimized xor circuitry circuitry circuitry circuitry circuitry circuitry circuitry mead mead mead mead mead mead environments accurately accurately accurately dotted biases biases ideal office reliable encode func trace trace trace reading voltages voltages voltages voltages voltages adjusted versions versions detector detected motivated finds charge indicating convolution track slope slope slope slope slope slope implementing purposes filtered filtered pulses demonstrates varies profile dark adjustable resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive compares differs incoming proven pasadena conductances green logical logical logical logical implements implements begins traces wesley displays room room addison appearance velocities naval caltech stronger logarithmic held held resistance resistance illumination illumination ranging photoreceptor photoreceptor smoothed smoothed smoothed roy arrows exploiting harris grants avoiding thresholding discharge crossing crossing crossing crossing crossing logarithm fellowship aircraft aircraft bank lit perceived reports reports superimposed spaced laplacian adjustment avoids rectangular exclusive graduate discontinuity crosses hughes hughes thresholded emphasize argued lond transconductance transconductance weaker weaker finger crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings crossings resistors resistors resistors placing minor amplifiers amplifiers amplifiers ation diagrams laws photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors hat hat hat hat hat usefulness settle subtracted subtracted marr marr marr detects detects detects dog dog dog dog dog dog symmetrical symmetrical symmetrical exploits digitized tracks decaying decaying decaying tance tance spirit mosis sian deweerth gaus saturating ings steve dissipation christof carver battery bright bright bright localize darker bair bair bair bair bair lens lens burden subtract ages wafer fingers fingers fingers volt charging mexican mexican mexican resistances resistances indoor conduc charges 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shows shows shows shows signal signal signal signal signal signal signal visual visual visual small small small small feature feature feature feature feature net cells step field field features process process level current structure problems random high high response response architecture architecture architecture equation section fixed fixed line line line line line line line images images images images real real real real gradient gradient note dimensional dimensional dimensional result university computation computation computation computation computation computation computation computation research research research research found initial constant constant constant standard computer distance science direction present low low frequency frequency temporal temporal motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range range range range range range range press press position abstract computational computational analog analog analog analog analog analog references due due due due due positive positive positive introduction introduction hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit stimulus stimulus stimulus stimulus statistical statistical parallel parallel tion tion tion change difference difference difference difference difference difference difference difference difference difference complexity variable spatial spatial spatial spatial spatial spatial lower lower lower measure measure signals signals signals signals higher part center center center center center center previous multiple multiple represent represent represent expected expected expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make techniques proposed correlation correlation correlation correlation correlation correlation correlation correlation length correct ing respect times times elements natural negative negative negative artificial specific specific specific samples provide location perform perform connected connected connected discrete approaches voltage accuracy larger contrast support support support morgan morgan report report institute department implementation version version advances final delay delay delay delay delay delay delay delay delay addition maps considered computing directly view design limit san san detection detection detection detection detection detection detection detection detection detection detection choice approximate approximate world speed vision vision basic increase produce channel channel channel channel channel velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines actual actual actual provided provided nature nature nature sampling biological measured measured increases arbitrary tested tested limited corresponds stable circuits short effective eds end vlsi vlsi vlsi vlsi vlsi vlsi pixel ability development sensory sensory kaufmann kaufmann typically smaller needed needed technology block block interesting testing testing york york edge edge edge increasing mechanism matching mode operation international early early sources light light light light light improve directions directions directions correlations correlations correlations correlations correlations correlations resolution resolution resolution resolution resolution robust takes moving pixels pixels pixels pixels pixels subset array array array array array varying address channels channels channels channels channels interval sensitive sensitive entire increased increased amplitude amplitude horizontal intensity intensity intensity intensity intensity intensity intensity occur occur occur occur extended digital derivative touretzky width setting pass half flow conclusion retina retina designed mateo mateo largest external drawn demonstrated california pulse pulse pulse turn start start start decrease decrease derivatives scene scene program denoted relation edges edges winner winner winner winner winner winner winner winner winner winner winner plot plot laboratory laboratory laboratory tuned changing confidence confidence confidence confidence sensitivity infinite text scales integrated frequencies frequencies events events shift shift john john interpretation labels sign diagram diagram sec sec sec event foundation koch koch koch koch koch fire box silicon determines determines activated neighbors successfully successfully successfully successfully successfully major closely poggio poggio detect detect schemes situation tend fine receives receives quickly moore moore moore showing interpreted interpreted interpreted strategies duration categories receptor quantity sampled providing wave delayed correspondence highest highest leading neighboring neighboring bars difficulty circuitry mead mead mead mead mead mead mead mead mead mead respond transistor office neu circles coarse measurement measurement measurement gradients trace reading reading opposite voltages implementations front academic academic generates detected detected electronic electronic indicating advanced scenes piecewise publishers publishers publishers navigation adjacent adjacent explanation inside rapid filtered filtered worst transistors pulses pulses pulses pulses pulses pulses axon axon axon axon axon axon axon axon axon projected axons axons axons axons axons axons lowest double collected tional adjustable passed passed passed slower slower slower incorrect incorrect measuring measuring fall pasadena logical decreased physiol focused begins owl traces traces cochlea cor addison fabricated fabricated fabricated summing summing temporally velocities velocities velocities velocities velocities velocities resources tem naval receptors inspired inspired ranges mos interconnection settings settings arrays clock fires reliably service financial financial corre sides photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor colorado colorado multiplied winning winning lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro ends passing passing motions projects statement speeds speeds speeds propagate propagate interestingly receiving fly andrew andrew andrew andrew sequentially boxes converted converted corporation kluwer aircraft ties alternating employs responds responds die causing acceptable reports affects barn translated trends subthreshold subthreshold activate expand boulder boulder barlow barlow placing meet meet meet rotating travel correlate reversal scanned scanned scanned externally bursting algorithmic transduction satisfactory photoreceptors photoreceptors synthesized mahowald lated spacing agency konishi konishi falling falling robotic mosis mosis mosis quick enter signed halves twelve twelve defense gratings gratings promise tim christof christof mounted mounted cope propagates plenum carver carver horiuchi horiuchi horiuchi horiuchi directionally aliasing aliasing grzywacz grzywacz tiny lens lens clocked insects poral multiplexing delbriick confident confident behavioural succession rising rising rising rising ryckebusch travelling rabbit rabbit multiples qualities lend multiplexed correlator votes ballistic manifest sudden ismail invertebrates race viii opposing detectable detectable lends increas polysilicon oscilloscope oscilloscope levick levick quicker slowest audition audition centrally delbrfick correlators correlators correlators correlators correlators packard norwell gracefully rectifying hewlett rockwell campus suffering zornetzer troublesome newspaper tradi nyquist ali manifests roscience denser 
#@Horiuchi_T,Koch_C,Lazzaro_J,Moore_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm output output output output system system system system system system system system system system system system error error error error error error error error error error error error error state state state state state state state state state results results results units information information problem problem problem problem models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance space space weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector shown shown shown shown shown shown systems systems systems systems systems systems systems values values parameters parameters parameters parameters parameters noise noise weight weight weight functions functions functions unit unit unit distribution approach approach approach approach approach point point processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large rate rate rate rate rate rate rate rate analysis matrix matrix matrix optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs form form shows shows shows algorithms algorithms gaussian paper net net net net work task task task task task task task task task task task task task task methods methods methods methods methods methods methods methods step field process process process process process process process process process process process process process process process process process trained trained structure problems random high high response response response response response response response response response response representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show equation equation equation general general real real states states theory theory gradient obtained obtained obtained term note note experiments variables variables solution solution research research research defined defined dynamics dynamics dynamics dynamics initial constant constant constant constant table table estimate standard standard standard terms connections present present present present phase phase phase phase frequency motion range press learn position position position position components components outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied back back back back back back back back back back back references component stochastic procedure procedure procedure propagation propagation propagation propagation propagation propagation propagation propagation introduction complex complex complex hand behavior behavior behavior statistical statistical effect effect dynamic dynamic dynamic variance parallel parallel cost cost cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change difference difference spatial assume measure measure signals signals signals signals learned part center center multiple multiple good good good conditions conditions conditions conditions represent represent represent represent represent distributed distributed expected equations equations equations equations equations make make fact techniques region proposed errors errors forward forward simulations simulations resulting resulting ing ing simulation simulation computed computed computed computed respect multi multi multi multi multi multi sum sum sum sum sum performed called means means factor optimization optimization feedback feedback knowledge knowledge knowledge vol relative represented represented application application application application application desired desired desired desired provide compute perform perform determined constraints constraints constraints constraints constraints distributions gain gain gain gain gain mit train train descent dependent modeling morgan morgan proceedings implementation implementation consists internal represents represents connectionist responses responses difficult final final layers maps framework cambridge equivalent equivalent equivalent environment environment environment hinton hinton hinton hinton hinton curve additional solutions design design design design transition trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san statistics world speed speed speed speed speed basic basic basic basic basic basic give con con con con con weighted weighted weighted weighted weighted weighted weighted weighted weighted developed velocity velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller path actual actual actual actual selected selected nature constraint constraint achieved measured measured discussion technical describe describe tested tested actions finding short implemented assumed supported theoretical main eds eds square degree degree rumelhart rumelhart rumelhart rumelhart rumelhart including objective objective simulated needed combination dynamical functional jordan jordan technology block block block interesting structures principle principle squared squared squared representing max filters making magnitude combined minimize minimize added added added architectures exact robust typical typical include period quadratic quadratic quadratic quadratic sejnowski previously observations axis tions tions smooth yields yields yields address williams williams williams sensitive entire entire entire constructed horizontal lead suggests extended digital derivative predicted feed touretzky white occurs generally generally generally generally trajectories trajectories depend reward sigmoid measures numerical numerical designed designed designed exponential practice practice mateo mateo suggest propose strong presence physics external characteristics characteristics characteristics characteristics characteristics sigmoidal demonstrated proportional turn variety minimizing min relationship introduce identification acknowledgements van construct written written index index index index index index index index ways ways ways factors estimating stability stability stability stability stability stability vertical mathematical implement physical easy angle angle angle angle angle angle angle interaction develop applying quality blocks blocks blocks yield transform evaluated operations controlled controlled controlled controlled approximations static margin reasonable additive classical classical classical sec sec purpose penalty penalty penalty penalty generation remains initially transactions box box priori priori determines automatic automatic variations characterized capable mcclelland modes oscillatory oscillatory literature ten composed cun cun follow strategies duration categories simplified illustrates jacobs modelling law law law law law law law minimized command collection updating varied varied put steady integral integral school links links mappings mappings structured structured structured structured func understand cognition fundamental phases phases changed ensure noted noted initialized switching switching switching consist consist generates plant plant plant plant plant plant plant plant plant plant agreement unstable slope slope adapted adapted capabilities multiplication sys widely controls controls separately universal pitch pitch pitch pitch pitch pitch pitch pitch pitch begin optimize optimize optimize optimize bandwidth auto geometry evaluating evaluating transient transient generic generic generic fed cohen passed formulated passes switch switch switch switch switch switch switch switch switch switch switch gains gains gains gains gains gains controllers controllers mod wind wind wind wind wind wind wind wind wind wind wind wind wind wind richard sums simulator chose sophisticated shaped begins deviations deviations extreme spectra indices indices optimality investigation velocities optimizing controlling repre unity multiplier kaufman kaufman numerically stated hit observing adequate adequate repeat excellent corre overview bad bad bad schedules schedules schedules schedules express augmented rich environmental motions propagate influences explorations switches switches mechanical severe accumulated unchanged grating land summer accept aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft tween acceptable ical examining shaded shaded gated chauvin chauvin chauvin chauvin formance tems distribu mathematically retain relates cation hansen nasa nasa flight commercial treating exploited modal modal modal modal laws laws laws functionality builds subjective suite imple loosely replicated integrates disturbances disturbances disturbances disturbances disturbances exposed ters linearized linearized alto alto setpoint fin elevator amenable essence ance ance saturating saturating saturating charles nominal lar modern modern modern modern neglected rent palo palo publishing damping damping damping damping damping damping damping damping spent miyata elegant sentations judge shear entered tailored inte mentation undesirable parame ames narendra narendra narendra landing landing landing landing landing landing landing landing landing landing landing landing landing landing landing landing landing penalties golden golden golden golden specifications turbulence turbulence turbulence turbulence turbulence plants plants plants recur categorize gerald attack gation electro sponds pilot simplifications probing foster foster downward referring simi subjected parenthesis coloring initiation troller parthasarathy parthasarathy effected tude feet intercept eee eee tains augmentation augmentation augmentation wil constituting bryson bryson fied decisive propa rea yves moffett modi sonable ules sched thomson blended sigrnoidal sisting yoshiro writ termine multipli trolling trolling ler ler maining microstructures trajecto 
#@Chauvin_Y,Golden_R,Henkle_V,Schley_C,
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#*network network network network network network network network network network network network network network network learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks training training number number system system system system system system state results results results information information problem problem problem problem problem performance based based weights weights linear layer case case case vector order order order order order order shown systems values functions neurons neurons neurons recognition recognition method method approach approach pattern pattern pattern point point point point image image single single processing processing processing processing processing processing control control control large local local rate test test test test patterns patterns patterns patterns optimal inputs shows shows shows signal signal signal simple simple visual paper paper size feature work work work work work task task methods cells process level level level level current current current cell structure problems problems problems response representation representation representation architecture equation equation equation section section section section fixed line line vectors vectors vectors general real real real real real real real real real real real real real real real real real real states gradient term note university university computation computation computation computation computation computation computation computation solution solution research research found found initial terms distance distance synaptic synaptic synaptic node node node node node node node node node node node node science science left left direction present present phase phase low low low frequency object motion maximum maximum range range range range range position position position continuous abstract applied applied computational computational computational analog analog analog analog analog analog analog references ieee decision introduction action complex hand hand circuit dynamic dynamic dynamic dynamic dynamic parallel parallel parallel parallel tion difference assume classifier classifier classifier classifier lower signals prior higher part previous cases firing required required binary represent equations chip chip region proposed correct finite minimum minimum minimum resulting simulation computed computed computed performed performed optimization potential potential made obtain artificial relative represented application application application compute compute compute objects objects objects rates perform perform goal goal goal goal goal connected connected motor motor motor motor motor equal power power voltage voltage voltage voltage voltage comparison support descent source source source selection morgan proceedings department department implementation implementation implementation implementation implementation technique advances ai domain equivalent environment environment environment environment environment environment environment environment environment environment environment environment directly view solutions design design design san top top detection detection conference determine efficient full full free free world world world speed con con derived developed robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot velocity velocity controller types path path path path path path path path path path path path path path path path path path path path path path path simply associative associative achieved describe group complete circuits circuits circuits short nearest nearest nearest nearest nearest nearest nearest nearest implemented implemented implemented implemented synapse synapse synapse vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi instance sensory sensory sensory including kaufmann account fully fully fully technology uniform principle leads pre direct early idea run description light light light light exact pair reported reported moving moving moving include machines sense array recently engineering engineering engineering compare conventional approximately module module module module module module module module tions solve solve solve achieve symmetric grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid gate amplitude concept digital locally move move hybrid touretzky width hardware hardware hardware hardware hardware demonstrate flow flow flow conclusion modules modules modules modules modules modules retina designed designed practice mateo taking hard largest external external demonstrated solid pulse pulse pulse pulse pulse derivatives scene derive optical optical optical optical solving winner laboratory laboratory metric infinite electrical develop applying letters solved solved evaluated evaluated open open open updated modulation static static static suggested partial performing measurements closed remains initially distances calculate euclidean advantages recorded recorded silicon silicon illustrated planning planning planning planning planning planning planning determining sensor sensor selecting middle middle identified identified identified identified capable capable paths traditional compact conf prob link follow write write localization localization localization localization localization localization localization localization michael realistic nips hypotheses chips chips chips processors received received principles moves mixing deal employed carried mead mead mead environments dotted preliminary preliminary discriminant discriminant discriminant scalar matches incremental applicable int fault ideal analytically transistor structured working working working stream stream measurement changed voltages voltages voltages thought quantities explored mapped mapped mapped detected devices devices great ment sensors sensors sensors sensors sensors navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation capabilities purposes transistors products cut acknowledgement angles members read read recording recording bandwidth sun sun people greatly evaluating understood capability red red red autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive rely measuring aim aim modulated suited plan tolerance arithmetic cor room identifying identifying identifying analogue analogue oxford oxford oxford oxford martin pick velocities resources concerned mobile mobile mobile robotics robotics robotics multiplier murray murray murray murray murray murray murray murray mos programmable resistance vehicle nearby nearby shifts optic responsible corner corner obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle continue published financial overview heart scan scan scan scan competing laplace laplace matter matter matter horn horn horn avoiding material automated switches acknowledge outlined lem dense linked drop workspace workspace ram obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles incrementally centre par copy ideally workstation workstation associate edinburgh edinburgh avoided reflected remote adjustment clas avoids shaded rectangular resistor resistor mhz learnt learnt distribu graphics parallelism guided sheet responding electronics electronics resistors resistors resistors resistors rotating avoidance avoidance avoidance avoidance avoidance flight flight programmed radio exploited gratefully council discretized discretized maze maze maze hundreds blake blake mahowald mahowald hamilton cord lightness automation alan trol grids grids approaching approaching permanent permanent planner planner planner planner tations gratings platform platform platform dissipation massive unexpected unexpected mounted mounted mid ard marshall marshall settles collision collision whilst advice notably vast workers environ neighbour neighbour neighbour neighbour taught han namic tarassenko tarassenko tarassenko tarassenko tarassenko tarassenko tarassenko tarassenko tarassenko ticular resolving vehicles vehicles intend hexagonal hexagonal hexagonal indoor adams ware siftcation walls focussed decoupled implemen pulsed enlarged esprit packages pute realisation malvern gabriel holes reekie demonstrations navigating wio wio circularly bra infra infra infra favour factory 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#@Brownlow_M,Marshall_G,Murray_A,Tarassenko_L,Tombs_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data figure figure figure figure figure figure time time time time time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output system system system system system system system system system system error results results units units units units units units units information information information information information problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden based based based based weights linear layer layer layer layer layer layer case case shown systems systems systems systems systems unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition approach pattern point image image image image image image image image image image image image image image image image image image image image image image image single single single single single single single single single single single single single single single processing processing processing processing control control control control test patterns patterns patterns patterns analysis analysis inputs inputs inputs form shows signal simple simple simple simple paper paper feature feature work task task task task task task task task features features features features features features features features process process process level level level level level current current current current current current current trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained problems problems problems problems problems high high high response response similar similar similar similar similar representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture section fixed fixed rule rule rule rule images images images images images images images images images images speech speech real real real real real real real real university computation computation research defined found sequence computer computer distance science science left left left left left left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented map map activation activation activation activation activation low low maximum range range range range press learn learn learn learn learn position position position position position basis outputs outputs abstract applied back back back back back back analog references ieee important important important important important propagation propagation propagation propagation propagation propagation introduction complex complex hand statistical parallel complexity rules rules representations representations representations learned learned learned learned learned chosen chosen chosen part center center center center center previous previous previous previous previous previous previous type required required required multiple multiple long conditions conditions represent distributed distributed distributed markov make fact fact techniques techniques techniques techniques techniques techniques techniques techniques techniques length correct correct correct correct errors errors forward forward tasks tasks tasks tasks total human human multi performed called times regions mapping potential made made feedback feedback orientation original original original original original vol vol artificial artificial artificial artificial artificial artificial artificial relative relative relative relative specific desired provide provide proc location perform perform perform perform active determined goal connected connected accuracy contrast update support train train train train morgan morgan morgan proceedings report report implementation version technique technique consists internal internal internal code individual individual individual individual advances advances represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult scheme scheme scheme scheme addition addition cambridge domain domain environment hinton hinton additional additional additional additional additional san san san effects effects detection conference determine determine efficient full requires requires free world world speed speed vision vision vision vision vision vision condition randomly developed developed developed developed robot robot area lines path path path actual provided finally backpropagation backpropagation nature depends achieved achieved discussion technical technical arbitrary tested tested transformation fast circuits finding short short effective assumed generate require eds face face journal end end vlsi ability instance rumelhart rumelhart development including including including including kaufmann kaufmann kaufmann simulated reduced reduced account fully fully jordan interesting significantly character york york edge edge principle iterations expert combined minimize architectures architectures recent recent recent resolution robust robust takes takes introduced side side side pixels array recently sufficient sufficient previously previously approximately approximately works module module match locations modified modified modified williams improvement sensitive entire increased grant parts intensity intensity intensity intensity wide wide rotation touretzky touretzky touretzky pass segment accurate accurate retina retina retina retina designed clear performs practice weak weak learns learns mateo mateo mateo cycle turn turn variety variety variety variety variety variety variety variety variety plane scene identification program acknowledgements explicit appears appears van van edges perception perception perception perception perception describes label distinct involves transformations develop adding competition focus phoneme correlated detailed operations controlled restricted restricted decomposition decomposition forms similarly translation allowed barto combining combining neighborhood add faces koch david degrees avoid building handwritten color domains domains domains domains domains domains successfully successfully reason determining determining determining determining sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor compression middle aspects closely capable driven driven included mcclelland presentation successful detect situation situation identity traditional road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road road conf quickly repeated allowing video video video video video video video video video video video success running content follow follow follow simplified generalize modular paradigm paradigm realistic backward nips highest jacobs deal deal software oriented camera camera camera camera situations situations situations situations situations situations situations situations situations situations situations situations situations simpler command command layered transformed transformed transformed poor create create create access access experience experience difficulty rapidly rapidly rapidly rapidly environments environments environments environments replaced replaced replaced replaced accurately accurately mass mass reducing school school project detectors detectors detectors detectors detectors detectors combine decisions symbolic symbolic symbolic cognition waibel waibel hill opposite versions assumes precise precise academic academic academic detected improving synthetic synthetic massachusetts scenes scenes stop ground publishers publishers publishers unstable navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation handle handle drive drive drive drive drive drive drive drive drive drive drive drive drive drive drive drive perspective straight straight straight straight straight straight implementing preprocessing projected projected gradually geometry mellon mellon sun sun sun exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars researchers apparent improvements carnegie carnegie profile cmu cmu cmu cmu cmu cmu cmu transient lack autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous poorly frequently frequently sharp sharp sharp sharp sharp maintain howard rely rely pittsburgh extracting serve extensions prevent prevent prevent prevent acoustics replace boston boston boston shaped univ consistently shifted shifted shifted shifted representative person person person person person person redundant redundant primarily primarily appropriately driving driving driving driving driving driving driving driving driving driving driving driving driving driving driving driving driving driving driving recover recover recover rotated rotated rotated rotated mobile addresses eliminate flexibility rotations lecun robotics robotics reaching generality eliminated eliminated extending imaging minutes minutes minutes vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle nearby analyzing shifts cottrell hours obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle encountered encountered decide lang buffer buffer jackel originally originally facilitate darpa enable tokens recog april insight ahead ahead ahead ahead ahead ahead rich cpu specificity sustained valuable harris speeds speeds ignore intersection avoiding explorations fly fly fly fly fly fly fly maintaining street land land land summer corporation kluwer kluwer kluwer lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane presenting obstacles obstacles nition distinction propagating utilize boser stem tendency adapting adapting adapting adapting henderson translated toy generators permits reflectance hubbard token token pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau march careful altered altered surrounding gender represen meta meta zip diversity diversity diversity funded maintains knowing avoidance avoidance avoidance avoidance avoidance steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering priority priority prevents travel corrections correlate develops helps coming circumstances circumstances circumstances drives drives drives lighting replacement differently august trainable transforming heavily emotion overtraining finer hour hour hour hour hour laser laser laser laser laser laser successively modalities modalities placement digitized tracks destination weather weather weather curved tations bradford charles charles charles sweep trend problematic dean unnecessary predetermined repetitive repetitive horiuchi occasionally preventing collision collision shikano dead hampshire puter thorpe thorpe thorpe thorpe thorpe warp warp prohibitively roads roads roads roads roads roads roads roads roads complexities tums comprise driver driver driver driver brooks stretch stretch live superfluous successes shortcomings luo hanazawa dictated dictated arbitration arbitration arbitration arbitration arbitration relied bicycle bicycle exceptions sharper prepared finder steer steer steer steer steer reductions reactions contracts autonomously autonomously imitate knowl holons notable collisions collisions intersections bringing undefined situated programmer darkness miles miles miles miles miles meters meters supercomputer forget latest hsu grounds terrain experimenting meter traverse fifteen foun monolithic lnt precedence older campus expose highway highway highway highway confronted lined lined lined lined dations daca daca daca watching watching stretches exchanging staying stray erratic bait imminent microstructures colliding naively 
#@Pomerleau_D,
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural data data data function function figure figure figure figure figure figure time time time time time time time time networks algorithm algorithm algorithm output output output output output number system system system system system system system system error error error error error error results results results results results results results results information problem problem problem problem problem problem problem problem problem problem models models models models models models based based based weights weights layer case case case case vector vector vector order order shown shown shown shown shown shown shown shown shown shown shown shown shown shown systems weight functions functions functions functions method method method method method approach point control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control rate class matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs signal simple simple visual paper paper paper paper small small small small fig fig fig fig fig fig fig fig fig fig fig fig fig level level level trained trained trained trained trained trained trained structure high similar similar equation equation generalization note note experiments experiments experiments experiments experiments result result result result solution solution solution research found found dynamics dynamics dynamics dynamics dynamics dynamics constant constant computer computer computer synaptic synaptic synaptic present object position position nonlinear nonlinear outputs outputs outputs outputs abstract applied applied properties properties properties references due introduction behavior dynamic dynamic dynamic dynamic generated generated generated generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel change change change change change change change change change change change change change change change change change variable variable assume part previous previous previous good proposed proposed proposed proposed proposed simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum simulation simulation human human human human human human human human human multi multi sum sum performed performed performed performed performed performed called called mapping made made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial desired desired desired desired desired desired desired desired desired determined determined determined related related related related related related related related related related related related related related constraints motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor train proceedings institute department consists consists consists joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint difficult delay scheme scheme addition framework computing experiment experiment experiment experiment environment directly directly view trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory determine approximate give produce derived derived derived derived criterion criterion criterion criterion criterion criterion controller controller controller controller controller controller controller controller controller controller controller finally processes selected depends depends biological biological biological discussion feedforward feedforward feedforward feedforward feedforward increases increases increases increases fast fast fast fast fast fast inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse stable stable role main journal journal journal journal end including objective objective objective objective objective auditory combination combination reduced account coefficients ratio mechanism mechanism principle squared iterations perceptron property pair pair takes movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement apply apply apply apply apply moving hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical sense cognitive engineering previously previously conventional conventional approximately calculated calculated calculated calculated calculated smooth studies increased arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm generally greater central central accurate accurate accurate accurate learns learns propose propose propose propose characteristics characteristics assuming assuming movements movements movements iii iii force force force force force force force force force force force force force force force force force force force force force force perception mathematical mathematical modeled simultaneously infinite easy easy angle angle angle equilibrium equilibrium equilibrium applying applying applying expressed formation depending communication solved controlled controlled controlled controlled organizing static static static allowed slow slow performing sec sec sec combining norm norm advantages advantages advantages transactions degrees combinations successfully determining efficiency efficiency efficiency efficiency suitable modification driven essentially moore moore moore neuroscience neuroscience physiological computes ill ill ill ill ill ill ill ill moves intrinsic intrinsic law law law law law law law law law law law law law law law law minimized minimized minimized minimized minimized command command command command command command command command command command command command command command command command rapidly humans integral reducing behavioral behavioral behavioral muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle oscillation measurement extremely noted freedom separated nervous nervous simplest explain explain explain motivated mentioned rapid rapid rapid rapid strictly forces monkey controls laboratories angles angles cybernetics explained integrating integrating virtual virtual virtual virtual virtual pseudo pseudo pseudo pseudo pseudo capability fed posed posed posed posed posed posed posed posed biologically commands commands commands commands commands commands gains reaches redundancy specifies simultaneous simultaneous simultaneous realized realized realized realized realized realized acquisition acquisition redundant redundant japan acts air air fits difficulties difficulties moment moment viewpoint viewpoint kawato kawato kawato kawato kawato kawato kawato kawato kawato hope symposium muscles muscles muscles muscles muscles muscles muscles muscles enable properly explains explains explains explains executed mechanical mechanical mechanical mechanical mechanical mechanical mechanical mechanical mechanical mechanical pressure basically basically torque torque torque torque torque torque torque torque torque torque uniquely uniquely uniquely realize jacobian jacobian manipulation interact compensate relate confirmed confirmed confirmed acquired acquired acquired acquired relates manipulator manipulator manipulator electronics minor atr tension tension tension tension tension tension tension tension laws laws laws laws laws laws laws laws laws laws nist acquire acquire resolve resolve resolve resolve ate spring firstly industrial japanese japanese japanese japanese calculates integrates impedance impedance impedance impedance impedance impedance impedance impedance impedance impedance manipulated resolved resolved cho positional prescribed uno uno suzuki suzuki fore expresses expresses reproduces untrained inertia effector gun engineers arms arms kyoto hogan hogan hogan hogan hogan hogan hogan hogan hogan hogan hogan ism ism ism ism ism ism ism ism ism ism ism ism ism ism ism ism ism ism ism ism ism succeeded hierarchically antagonist antagonist antagonist antagonist antagonist antagonist antagonist antagonist antagonist antagonist realizes penrose penrose penrose skeletal skeletal skeletal skeletal gravity soraku bizzi bizzi bizzi viscosity viscosity viscosity viscosity viscosity seika actuators actuators actuators actuators stiffness stiffness stiffness stiffness stiffness stiffness agonist agonist agonist agonist agonist actuator actuator actuator actuator posture posture posture finished stably rhesus friction voluntary voluntary lagged tensions tensions tensions tensions tensions mitsuo furukawa ame ame mechanically ascertained 
#@Katayama_M,Kawato_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data function function function function figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set networks networks networks networks training training training training training algorithm algorithm algorithm algorithm output output output output output number system system system system error error error error error error error error results results results results information problem problem problem problem performance performance performance based based based weights weights weights layer layer order order systems values values values parameters parameters weight weight weight distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point image image image image image image image image image image image image image image image image image image image image image image single single processing control control large large large large large local neuron rate test test test test test test test test test patterns patterns patterns patterns optimal inputs inputs inputs form form shows shows shows shows signal examples small small size size feature feature methods methods methods step features features features features features features current trained trained structure structure structure structure representation architecture architecture architecture show fixed line line line rule images images images general average average obtained obtained note experiments dimensional dimensional result result computation computation computation solution solution solution solution solution research found initial initial table table computer computer computer computer computer computer distance node node present present nodes maximum maximum range range components nonlinear nonlinear abstract applied computational computational computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties references positive positive procedure adaptive adaptive adaptive context introduction circuit effect effect effect effect effect effect dynamic generated energy energy energy difference variable variable spatial signals signals learned chosen chosen part center required required required required required required binary binary binary binary conditions expected equations chip chip chip techniques region proposed proposed proposed correct correct correct correct finite minimum minimum resulting resulting resulting resulting total simulation computed computed computed computed sum performed performed performed times times times times times times regions regions regions regions regions factor made made obtain negative negative negative negative negative negative original relative represented compared compared compared application desired desired desired desired desired compute compute compute compute compute perform active determined determined determined determined experimental experimental goal connected connected connected distributions discrete discrete voltage accuracy accuracy accuracy accuracy comparison comparison comparison larger contrast support train source source implementation implementation implementation technique technique consists internal code code code kernel kernel difficult difficult final cambridge cambridge cambridge cambridge cambridge cambridge equivalent equivalent equivalent directly stage effects effects bit bit determine determine determine efficient full full significant approximate speed speed speed speed speed speed speed speed basic increase weighted iteration iteration iteration iteration depends technical limited inverse circuits effective effective implemented assumed generate generate require require square pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel makes needed account coefficients consistent consistent consistent structures uniform uniform operation operation operation operation operation representing iterations direct making magnitude magnitude choose run added improved improved improved resolution advantage takes practical practical include include include identical side pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels array array array array array recently engineering interest dimensions dimensions sufficient address evaluation generalized improvement improvement improvement entire increased intensity intensity intensity intensity intensity intensity intensity expression lead suggests digital digital digital digital digital digital digital digital digital digital trial trial trial trial wide matrices correctly hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware demonstrate greater conclusions central accurate peak faster faster faster radial radial radial radial turn variety variety relationship relationship program configuration monte carlo written written written written written written mathematical mathematical averaging consisting shift shift shift evaluated evaluated operations showed showed static approximated sizes sizes completely suggested allowed processor processor processor processor sign diagram diagram neighborhood purpose iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative filtering precision building silicon bell bell bell bell variations phys discussions characterized tests simplicity closely delta computations comparing ten ten receives characteristic composed conf quickly contained contained contained contained success running sci sci built built write write board cmos operating acknowledgments software software receive limitations limitations dual fewer applicable int comparable comparable removed examined hill hill hill smallest voltages implementations adjusted prototype portion separated mapped shapes switching electronic seconds seconds isolated years devices indicating convolution convolution convolution convolution convolution adjacent adjacent analytical analytical analytical analytical analytical floating floating floating floating caused caused correction correction correction correction correction correction correction correction correction correction correction correction considerable considerable incorporate laboratories laboratories laboratories laboratories laboratories inversion calculations computers radius radius radius summation requiring greatly profile amounts amounts capability experimentally experimentally readily readily adjustable adjustable adjustable adjustable schematic schematic execution calculating passes rely summarized adjust kinds sophisticated decreased tolerance contribute gap gap primarily primarily amplifier summing summing summing summing approximates impossible impossible eliminate eliminate flexibility generality extending smith dealing murray murray murray minutes analogy determination resulted wire days days hours hours hours reliably started heavy combines iteratively buffer buffer buffer widrow widrow exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure thin record verification verification properly proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity relies lett instructions robert truncated truncated converted converted shorter benefits corrected corrected corrected corrected corrected corrected corrected corrected corrected additionally decomposed verified verified compensate surrounding surrounding sized sized resistors resistors resistors resistors resistors resistors inverting meet amplifiers amplifiers amplifiers amplifiers dsp dsp corrections corrections corrections corrections corrections corrections corrections corrections corrections corrections corrections corrections examination suggestions electron electron electron electron electron electron electron electron electron electron electron electron electron electron electron beam beam beam beam beam beam beam beam beam beam beam beam beam beam beam fortunately excess consuming resolve corporate loaded east adaptively adaptively fabrication hour inherently exposed exposed exposed exposed subtracted operational ray functionally resolved restricting convention scattered scattered scattered scattered scattered scattered scattered scattered scattered scattered scattered scattered substrate substrate substrate energies hoff hoff registers registers registers mountain mountain mountain imposes metal lynch lynch lynch lynch lynch lynch avenue avenue avenue incident incident incident incident cummings cummings cummings cummings cummings cummings cummings cummings billion prohibitively stabilized pattem pattem ire surrounded masks pad pad pad ore looked instruments instruments edward electrons manage cients wrap scattering scattering scattering scattering scattering scattering kevin film packages assisted exposures assembled resist resist resist resist resist resist resist resist prohibitive wescon memorandum constituted technol technol dose dose dose dose dose dose dose dose surroundings uncorrected motorola appreciable eighteen sem acceptably beams leamed mflops mage elliot grn quad appreciably 
#@Cummings_K,Frye_R,Reitman_E,
#t4
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input function function function function function function figure figure figure figure figure figure time time time time time time networks networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output number number number system system system system system system error error state state state state state state state state state results results units units units units units information information problem problem problem problem problem problem problem problem problem problem problem problem models models models performance based space space space space space weights linear linear layer case case case case order order order order order shown shown systems values parameters weight weight functions unit unit unit unit method method method approach approach approach point control control control large local patterns patterns optimal optimal optimal algorithms simple paper paper small small small net net net net work work work task task task task task task task task fig fig fig fig step step field process process current current current current current current current current current trained trained trained trained trained trained trained problems problems problems random random similar show show section general general real real real approximation average average states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained note note dimensional result result university university university university research research defined defined sequence sequence target target initial initial initial initial initial initial initial initial initial standard computer computer computer computer distance distance science science science science science science science prediction prediction prediction prediction prediction prediction prediction prediction presented present temporal temporal temporal temporal position position position position abstract applied applied applied applied back find computational convergence references due due due due ieee ieee procedure procedure procedure procedure procedure procedure procedure important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation context context context context context context introduction action action action action action action action action action action action action action action action action action action action complex hand hand hand hand hand hand hand hand hand hand estimation behavior behavior behavior effect effect effect recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search change energy energy energy energy energy difference difference variable variable variable variable assume assume chosen center center previous previous previous bound type required good good good good binary binary binary represent fact techniques proposed length observed observed forward forward forward forward finite resulting resulting resulting tasks simulation computed computed respect respect respect respect respect respect respect respect performed performed performed called mapping means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement optimization optimization optimization optimization optimization optimization made applications knowledge knowledge knowledge knowledge obtain obtain compared application desired desired compute related related constraints constraints constraints approaches steps steps steps steps steps steps steps accuracy accuracy larger update descent descent descent descent descent descent descent descent descent descent descent dependent proceedings proceedings report report institute department implementation technique technique technique internal internal joint represents connectionist connectionist connectionist connectionist connectionist final final scheme addition maps considered environment directly directly additional trajectory san san effects effects effects conference conference world world world world world world world world world world world world world world world world world world world world world world world world world estimated basic basic pages derived derived weighted randomly randomly robot robot robot robot robot robot robot robot robot controller controller controller controller controller controller finally backpropagation backpropagation backpropagation iteration measured measured discussion technical fast fast inverse actions actions actions actions actions actions actions actions actions actions actions predictions predictions predictions predictions finding finding finding finding short short generate main future future future future future future future easily makes makes makes including objective objective probabilistic account unknown unknown fully jordan interesting leads numbers iterations iterations making international decay decay minimize minimize run run predict improve improve typical movement movement strategy include sense sense cognitive cognitive cognitive sufficient works tions solve solve yields chain chain chain chain chain chain chain modified bounded williams arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm concept deviation predicted predicted feed feed feed deterministic white starting starting place minimal trajectories reward measures measures clear sutton exponential demonstrated demonstrated california minimizing minimizing exist movements manner minima identification identification configuration acknowledgements solving dept changing changing explicitly angle interaction interaction adding applying events springer quality agent agent implies implies national national stages influence labels showed past earlier barto reduces purpose purpose remains distances visible avoid thesis activations activations activations activations priori assignment assignment maximize candidate discussions planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning reason society society encoded committee reached repeated repeated repeated heuristic heuristic heuristic anderson interested interested strategies duration bar bar bar bar vary michael michael illustrates subsequent subsequent camera camera minimized diego diego powerful transformed investigate experience experience experience experience experience experience experience experience experience experience experience experience experience experience experience optimized optimized optimized optimized optimized optimized limitations dual scalar rest investigated applicable applicable analytically authors decisions decisions complicated proved fundamental act gradients gradients gradients gradients gradients gradients gradients gradients editor configurations predicting changed logistic explored simplest phd finds massachusetts massachusetts ment cart cart crucial expensive reasons tive cut gradually demonstrates annual preceding led led elman generic fed autonomous effort controllers controllers plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan sophisticated credit credit differentiable differentiable differentiable pole pole pole pole pole pole pole shifted formally angular optimizing optimizing optimizing approximates approximates grey turned robotics robotics robotics proceed establish convenient difficulties overcome overcome balance balance observing intuitively heuristics falls overview moved dependency washington lengths lengths lengths propagated lawrence advance smoothed ahead ahead ahead ahead ahead ahead ahead ahead ahead ahead relies pendulum erlbaum subsequently propagate balancing balancing balancing balancing adopted adopted ball ball ball ball ball ball ball ball ball ball ball ball ball assigning ics thrun thrun thrun thrun thrun thrun workspace workspace kinematics kinematics deriving munro retraining amherst german german hillsdale adapting modifying mathematically inverted pos pos pos pos conversely stuck vanishes september continually reinforce firstly solvable ning ning incorporation proposes progressively progressively progressively rameters joints approaching coins gmd gmd gmd lags lags lags magazine appro bonn bonn cuts rolling rolling stepsize ted predefined sebastian nov proce plans plans plans plans des alexander adap ninth fruitful cent completes correspondingly wanted wanted frank prevented gra accelerate reinforcements reinforcements tab linden linden linden linden linden roll sept unspecified doubled overcomes interacts dient frg frg frg frg dure danger sut sut sooner runtime kindermann nction pace trai trai ned complicates jor jor netj augustin augustin construc disturbed appropriateness appropriateness smoothes lue rth 
#@Linden_A,Moller_K,Thrun_S,
#t4
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time networks networks networks networks networks networks networks training training training training training training training output output number system error state state state state state state state state state state results units units units units units information information information information information information information information information information information information problem problem models models models models models models models hidden hidden performance based based based based based based based space space space space space space weights weights weights weights weights weights case order order shown shown systems systems values values method method processing processing processing control control control control control control control control control control control control large large local local local local test form form form form form shows shows shows shows shows shows shows signal simple gaussian gaussian gaussian examples small net net net net net net net net net net net net net net net net net net net work work task task task task task task task task task methods step step field field field level level current current current trained trained trained trained problems problems problems random random high high architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture fixed fixed line line line line line line line line real real states states states states dimensional dimensional university university solution solution research research research dynamics initial initial initial initial estimate computer computer distance distance distance distance distance distance distance science science science science left presented present phase temporal temporal temporal object object object object object object object maximum range range range range press press learn learn learn learn position position position position position position basis nonlinear outputs continuous continuous continuous abstract applied references ieee ieee adaptive adaptive adaptive decision action action action action action action hand hand behavior generated search tion tion change center center multiple good long expected proposed proposed length length length length length length length length length forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward scale scale scale scale minimum minimum minimum tasks total total respect respect sum performed elements mapping reinforcement reinforcement potential potential potential potential potential potential potential potential potential potential potential natural orientation orientation orientation global global global knowledge knowledge knowledge knowledge knowledge objects objects objects location location location location eye eye determined goal goal constraints constraints discrete mit steps contrast fields fields fields fields fields fields fields fields fields train train train train train modeling morgan morgan report report department department version technique technique technique technique consists consists consists advances advances represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult difficult difficult difficult difficult difficult difficult difficult difficult maps maps maps maps maps maps maps maps maps framework cambridge domain domain environment environment environment environment environment environment environment environment additional view view view view view view view view view curves trajectory top top conference efficient efficient efficient upper upper requires world world basic produce produce produce produce coding coding robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller path path path path path path path path path actual finally achieved discussion technical technical describe arbitrary group limited limited actions actions actions actions amount short short supported easily degree rumelhart rumelhart rumelhart sensory sensory sensory sensory sensory sensory kaufmann kaufmann simulated simulated simulated pairs pairs pairs pairs pairs needed jordan jordan jordan jordan programming representing making bottom bottom supervised supervised frame idea combined minimize added predict architectures architectures architectures architectures directions takes apply moving side cognitive unsupervised teacher tions solve evaluation evaluation evaluation evaluation evaluation positions grant grant exists exists trial wide move move touretzky touretzky white generally starting starting place trajectories trajectories trajectories trajectories trajectories valued competitive editors differences differences designed sutton sutton sutton sutton sutton learns learns learns hard hard hard hard hard hard hard hard presence radial derivatives minima minima minima minima force explicit explicit sequential plot plot plot tuned simultaneously involves involves expectation decreases national independently forms soft static static diagram diagram barto barto barto barto initially foundation views views views views transactions david david david avoid avoid avoid avoid building building existing exploration exploration box box box includes thesis priori priori contour contour contour contour contour assignment automatic discuss maximize black reason sensor sensor sensor sensor successful miller receives receives receives receives traditional anderson split michael modular realistic reach maximization automatically automatically jacobs jacobs simpler create access investigate environments environments involving successive ideas project incremental mappings office complicated neu editor editor man created created adjusted portion panel panel panel panel assumes assumes logistic extent submitted phd synthetic massachusetts massachusetts indicating critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic sensors sensors sensors sensors publishers publishers track unstable navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation briefly handle spatially straight straight straight straight closer easier easier forces division located watkins watkins laboratories scientific acknowledgement circle circle begin depicted depicted demonstrates radius radius radius radius radius requiring reflects reflects profile simulate introducing incorporating richard richard richard richard simulator simulator display display display credit differentiable room room room intractable grey grey grey grey grey extending air chance adjusting height height height height keeping wire planar planar obstacle obstacle obstacle obstacle obstacle evaluations evaluations equals paul overview colorado chooses viewing shortest tures material robert andrew informa ence geometrical incorporates kinematics shorter ber creates obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles amherst amherst superimposed home home home home home home home home home home home home home home home home home home ibm robots robots goals wall werbos werbos werbos afosr bump depicts distal sonar denver descending avoidance avoidance avoidance avoidance avoidance avoidance avoidance things durbin october differentiating architectural architectural impractical generafive aid bold wiring wiring inherently inherently evenly evenly architec archi cur alto alto smc bumps charles nominal watson rent palo palo facilitates comprehensive comprehensive prime ton direc align heights frozen dead dead tailored tailored bird bird ecs tecture jonathan jonathan wired wired wired wired wired accumulating visualized door door door farther attracting opaque lastly philosophy cated opposing displacements gte bachrach bachrach bachrach bachrach yorktown umass sut pres terrain terrain terrain terrain andy cylindrical cylindrical counteract critics critics mahadevan bed afb propel reckoning reckoning connell une bolling perimeter wheels colliding 
#@Bachrach_J,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input input input input input input input function figure figure figure figure figure figure figure figure figure figure time time time time set set set output number number number number system system system results units units units units units units units units units units information information information information information information information information information problem problem problem models models hidden performance performance based based based based based based space space space space case case case case shown systems systems values values probability functions functions functions functions unit unit unit method method approach approach point point point single processing control control control test optimal optimal form form form shows shows shows shows shows simple paper paper work work work task task task task task task task methods methods methods methods fig fig fig fig fig fig cells cells cells cells step step step step points points points points points points points current cell structure structure structure problems problems random random random random high similar similar representation representation representation representation representation representation representation representation representation representation representation representation architecture show section section section section section fixed general general general general real average average average average states note note note experiments university university university solution independent sequence initial initial initial initial table table estimate estimate computer science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left direction map map map map map map map map map map map present present low frequency temporal temporal temporal temporal temporal temporal temporal machine machine maximum press press learn learn learn learn learn position components continuous abstract applied back computational computational references references important decision introduction action action action action action action action hand stimulus stimulus stimulus effect effect dynamic generated parallel search tion difference difference difference difference difference difference difference spatial lower representations representations representations representations representations representations representations representations representations representations representations representations representations representations required distributed distributed distributed distributed distributed distributed distributed expected make make make fact fact fact techniques region scale finite minimum resulting sum times mapping mapping mapping mapping mapping means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor dimension dimension orientation orientation orientation orientation negative represented true provide location location location location location location location location location location location goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal related related related discrete mit steps steps steps steps steps steps steps larger dependent source morgan morgan morgan proceedings proceedings report department code code advances connectionist addition cambridge cambridge cambridge equivalent equivalent environment environment environment environment environment environment environment environment directly directly hinton additional additional curves curves san san san stage stimuli effects effects effects conference significant free world world world world speed speed con coding coding randomly developed developed controller lines path path path finally evidence constraint discussion discussion technical group close close complete actions actions actions actions actions actions actions actions actions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions require main journal future future makes makes makes sensory including kaufmann kaufmann simulated simulated dynamical dynamical dynamical dynamical dynamical programming programming mechanism mechanism consistent representing iterations iterations iterations iterations iterations iterations making making international supervised early added predict predict predict architectures improve advantage robust takes takes introduced moving moving moving subject sejnowski cognitive cognitive cognitive cognitive cognitive engineering interest dimensions dimensions highly works solve smooth rl locations locations locations symmetric grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid bounded improvement sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive arm constructed derivative move move move move move touretzky touretzky generally generally starting place place place place place place place place editors editors accurate retina retina retina retina clear sutton sutton sutton sutton sutton sutton sutton sutton exponential faster faster faster practice asymptotic mateo mateo mateo taking physics start program force base acknowledgements pro edges sequential generating changing metric averaging dimensionality dimensionality involves unique develop integrated agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent implies implies versus stages codes codes open restricted suggested suggested barto barto barto barto barto roughly closed generation remains initially visible visible visible visible assigned assigned construction euclidean classified classified transactions david avoid fire fire fire fire exploration exploration exploration exploration thesis thesis weighting prove mozer mozer coupled planning planning planning planning planning selecting extra extra extra closely closely differ computationally divided paths latent latent latent tend ten reached compact quickly quickly moore neuroscience dis running follow cue cue cue cue cues cues cues cues bar vary dayan dayan dayan dayan absence absence absence absence delayed hypotheses reach moves moves moves subsequent approximating rat rat unlike poor create essential exponentially graphical helpful helpful existence existence school referred workshop workshop removed act coarse coarse coarse coarse coarse plausible editor predicting opposite separated switching extent arbitrarily arbitrarily phd phd finds finds massachusetts ment ment slowly asynchronous fairly fairly navigation navigation improves coded coded coded coded coded adjacent capabilities briefly worse starts shared shared constructing leaves mation watkins watkins watkins watkins watkins watkins watkins watkins demonstrates addressed raw apparent apparent apparent substantially led elman peter share slower biologically variant compares rewards rewards ture ture aim reaches reaches richard substantial asymmetric sophisticated comments findings conditioning deviations sharing bellman discontinuities discontinuities college sort modify oxford oxford tation restriction angular angular pick repre addresses monotonically north optimally selects fires fires infor cerebellar studying cmac decide sides topological similarities hippocampus discounted discounted discounted discounted surprisingly ahead record receiving insensitive dividing limitation severe crossing summer largely solves benefits job responds dyna willshaw centre convenience amherst amherst england england discovering forcing edinburgh edinburgh edinburgh representa alternate alternate goals learnt pdp discontinuity discontinuity distant considers considers considers ambiguous constructs represen manipulator barrier barrier barrier barrier barrier barrier barrier barrier register funded west grateful normalised intensive struc mann species rats rats rats rats curse east albus king puts morris visit resolved arrives degenerate decaying ignores predictable totally sity amenable confined rel south articulation bumps inducing tra bear sentation scattered ming firings ambiguities altering tal ace directionally directionally directionally directionally directionally disadvantages ample reactive visits comprises environ environ tributed radially concluded univer neighbouring neighbouring neighbouring explosion nectionist nadel facing facing identifiable reinforced reinforced reinforced reinforced temporarily buckingham gramming reinforcements disappears manageable keefe lhe rotates chunks bucket bucket bucket bucket bucket experimen disabled markedly reacting jeffrey criticism tent bachrach bachrach kauf discounting mech navigate registered asme inconsistencies incapable incapable gabriel jay notoriously motivations stimu navigating navigating navigating navigating distinguishable dry lus harmful serc pavlovian traverses fictitious fictitious mazes mazes atively wander cjch cjch anism intelligently equivalents tate hump abandon 
#@Dayan_P,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model input input input function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set networks training algorithm algorithm output output output output output number number number number system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results results results results problem problem problem models models performance performance performance based based based based based based based based based based based space space case case case case case case shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values method method method approach single single single processing control control control control control control large rate rate rate test class optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form shows shows shows shows algorithms algorithms algorithms simple simple simple paper examples small task task task task task task task task task methods methods methods step step step step step step step process process process process process process process process level current current current current current current current current structure structure problems random memory memory similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show show show show rule general general general parameter real real real real real real real real real real real approximation average average average states states states states states states states states states states theory theory theory theory theory obtained term note experiments experiments experiments result result result university university research defined defined found found found found dynamics initial constant estimate science left direction presented presented presented presented temporal temporal temporal temporal machine machine machine machine machine maximum press press press press press press press learn learn learn components basis abstract applied applied back back back find find computational computational convergence references component stochastic stochastic stochastic stochastic ieee ieee adaptive adaptive adaptive adaptive decision introduction action action action action action action action action action action action action action action action action action action hand hand hand hand behavior behavior behavior behavior behavior behavior behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated cost search search search search tion change difference difference difference lower lower rules learned learned learned learned learned learned learned learned learned learned learned part cases cases type long long long long long long long distributed expected expected make proposed length probabilities forward resulting resulting ing simulation computed performed called called called times times means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge obtain obtain original artificial specific desired cross series provide location location perform perform goal goal goal goal goal goal goal goal goal brain equal equal equal approaches approaches approaches mit mit mit mit steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps comparison update update update update modeling modeling modeling modeling morgan morgan proceedings proceedings proceedings proceedings proceedings department technique consists consists represents connectionist addition addition addition graph graph sequences ai ai maps maps cambridge experiment environment environment environment environment environment directly directly hinton curve additional curves curves transition conference conference conference upper upper significant significant approximate approximate free world world world world world world world world world world world world world world world world world world world world world world world world world world world world world world world world world world speed increase con con produce condition condition randomly conditional developed developed developed robot path path path path path path path path path path path actual finally finally processes processes iteration iteration iteration iteration simply measured discussion describe group limited complete complete actions actions actions actions actions actions actions actions actions actions actions finding short short short short implemented assumed assumed generate generate generate theoretical theoretical eds square end ability ability instance degree degree makes makes rumelhart rumelhart including including kaufmann kaufmann typically needed combination fully programming programming programming programming programming programming programming programming significantly special structures trials trials call max making making making international international international international idea idea idea idea idea choose added description denotes architectures architectures architectures architectures architectures architectures architectures architectures pair pair separate movement movement reported apply identical side side side trees trees sense cognitive previously conventional volume match achieve achieve trans trans evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation locations modified grid entire trial trial trial trial trial trial trial trial trial trial trial trial loop deterministic generally generally generally runs runs half starting starting place conclusions reward reward reward reward reward reward reward reward reward reward reward sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton faster faster faster faster learns learns learns suggest taking taking taking external intelligence turn start start start start start relationship manner acknowledgements explicit pro pro monte carlo produces produces produces longer ways ways transitions distinct dept changing changing changing changing changing modeled explicitly explicitly simultaneously simultaneously involves easy slightly slightly unique integrated integrated integrated integrated integrated formed select choosing solved solved solved updated approximations static completely completely completely converges sign earlier barto barto barto barto barto barto barto barto barto barto barto spaces remains initially foundation building existing exploration exploration exploration exploration exploration exploration includes includes includes thesis thesis priori bell assignment uncertainty black holds planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning determining determining selecting middle closely suitable society maximal mcclelland mcclelland online reached receives receives summary compact kind kind heuristic heuristic heuristic moore showing anderson anderson anderson neuroscience superior hold hold sampled sampled relaxation relaxation relaxation relaxation relaxation relaxation nips delayed reach received policies policies operating approximating approximating approximating deal remain experience experience experience experience experience experience experience experience updating rapidly rapidly rapidly environments environments environments environments limitations limitations limitations mass hall scalar scalar incremental incremental incremental incremental terminal possibility relationships maximizing symbolic variability workshop cognition cognition fundamental analogous examined smallest act act adapt adapt adapt necessarily man extremely psychology changed portion explored simplest contributions arbitrarily phd phd integrate indicating critic critic track navigation navigation navigation slope slope slope adapted worse rapid lin lin lin easier watkins watkins watkins watkins watkins watkins watkins watkins watkins watkins laboratories gradually begin author annual incomplete fourth reflect pure leave marked marked incorporated incorrect variant rewards rewards rewards execution execution mod ture differs achieves adjust plan plan plan richard eventually credit credit univ cumulative bellman room benefit feasible optimality extensive extensive princeton conditioned pick smolensky adds consideration promising adjusting satisfying replacing attractive moment observing exploring exploring reliably evaluations prentice falls falls paul decide holland overview guarantees intended consequences propagated propagated lawrence approximators discounted ballard ballard ballard ballard ahead record record repeatedly arrows route route erlbaum hart explorations accumulated empty bertsekas bertsekas bertsekas bertsekas andrew speaking dramatically dramatically unchanged ence unable microstructure outline solves tables tables reaction dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna suboptimal tendency experiences experiences experiences experiences experiences experiences illustration shaded deep alternate blocking blocking blocking werbos werbos werbos pdp uncertain uncertain uncertain interacting considers argued ultimately meta barrier maintains maintains maintains mimic els prevents ward experi continually continually continually continually shallow chris gratefully fiat functionality excess lation insufficient maze maze maze maze maze maze maze suffers architec colleagues evolving totally coins kaelbling smc smc amenable essence acknowledges steve routes blocked blocked supposed freely began entering occasionally sixth plans entered shortcut shortcut shortcut shortcut ply hypothetical hypothetical hypothetical hypothetical hypothetical hypothetical hypothetical hypothetical hypothetical intel justify inadequate earning seventh seventh simu permitted ration quences quences almeida alternately alternately interrupted reactions trim bucket looo whitehead whitehead whitehead whitehead whitehead opened opened augmenting deterministically gte cesses cesses maxa elapsed weaken waltham brigade gabriel cont permitting quoted explo navigating distinguishable barriers strengthen shortcuts ventional expe ial mazes leslie slate sequently rumel evalua tabular trip 
#@Sutton_R,
#t4
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time set set set training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results information information information problem problem problem problem problem problem problem performance based based based based space space space space space weights linear linear case shown systems systems values values values values noise noise weight weight approach point point point point point point point point processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large rate rate rate rate test test test test test class optimal optimal form shows shows shows algorithms simple simple simple simple examples work work work step step points points process level level current current current current current current trained problems problems problems problems high high high high high similar representation representation representation show equation equation equation equation section section section section rule general average states states states states states states states term term term term note experiments experiments experiments experiments independent defined defined defined defined defined defined sequence sequence sequence sequence dynamics initial initial initial constant constant constant constant constant constant constant present machine range range range press learn learn learn learn learn learn nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous continuous continuous continuous continuous abstract applied find references component component component stochastic ieee ieee positive positive positive positive positive adaptive adaptive adaptive introduction action search search search difference variable variable variable variable variable lower lower lower learned higher center previous required required required multiple good binary binary binary represent represent equations techniques techniques region correct tasks tasks tasks called called called times times times elements regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement natural applications knowledge negative negative negative negative negative negative negative negative original vol specific specific specific specific represented desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired provide define define rates rates rates rates rates determined determined experimental experimental goal goal constraints gain gain steps update train modeling proceedings version difficult scheme scheme scheme scheme scheme scheme scheme scheme scheme sequences considered experiment experiment environment environment environment environment design trajectory trajectory trajectory detection conference upper upper upper requires basic basic basic basic coding coding coding derived derived developed area area controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller provided provided provided finally processes nature associative associative associative associative associative associative normal increases describe describe tested complete complete actions actions short short implemented assumed require eds ability instance easily degree development simulated simulated typically pairs technology interesting interesting significantly mechanism special trials trials trials trials trials uniform mode mode mode mode mode mode mode mode mode mode operation operation details window window window window window window window window run run run added added description improve improve improve recent resolution resolution element element introduced strategy strategy strategy strategy strategy highly solve solve rl rl rl rl rl address generalized interval increased increased increased constructed studied occur extended trial trial trial trial trial trial trial correctly move move occurs occurs setting runs starting greater trajectories conclusions conclusions valued reward reward sutton faster learns temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature encoding encoding encoding encoding encoding encoding encoding external demonstrated demonstrated demonstrated intelligence annealing annealing explicit longer solving primary plot plot dimensionality cycles cycles cycles cycles decreases depending controlled controlled controlled controlled controlled forms constants allowed allowed discrimination earlier earlier barto barto barto barto barto valid valid transactions degrees degrees avoid exploration figures prove prove absolute absolute absolute successfully successfully sensor schemes schemes situation plots reached reached composed refer quickly heuristic heuristic heuristic anderson anderson list delayed reach consisted operating operating operating operating operating operating operating operating operating law law employed explore explore remain unlike schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule exponentially updating varied varied examine successive possibility proper trace adapt man explored ith ith arbitrarily plant synthetic cart critic critic critic unstable coded failure failure failure failure failure failure nonlinearity starts drive forces incorporate worst watkins watkins describing beginning cybernetics researchers requiring fourth varies evaluating limits limits limits limits limits profile conducted conducted continuously variant variant variant variant rewards maintain maintain maintain maintain tank extensions tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance pole pole college accomplished modify investigation fails minutes minutes minutes held fail combinatorial heuristics embedding falls loo washington evident scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling facilitate schedules enable surprisingly shortest environmental environmental adopted thresholding thresholding executed unchanged maintaining shorter failed failed forced generalizations recurrence recurrence recurrence recurrence recurrence recurrence edinburgh avoided examining realize continuity visited learnt ijcnn maintained eligibility eligibility eligibility eligibility register meet steering september october interior january ase ase ase curse adaptively king devised dissertation regulatory beneficial successively daily setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint smc essence enters aip decoded monitored facilitates progresses progresses newly formulations visits cooling cooling cooling cooling cooling cooling heat positively rosen rosen rosen rosen rosen explosion explosion ixi handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped handicapped reinforced accelerated invoked reinforcements steer steer steer steer michie michie michie michie neuronlike setpoints setpoints setpoints setpoints setpoints setpoints setpoints setpoints setpoints setpoints heating heating heating heating heating heating heating heating forty forty negatively dale ambient ambient ambient ambient oliver invoking goodwin mathur deemed situ minneapolis sophistication encounters reinforcing reinforces punishment boyd flag promotes 
#@Guha_A,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input input function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number system system system system system system error error state state state state state state state state state state state state state state state results results results results information information problem problem performance performance performance performance based space space space space space space space weights weights weights weights weights shown shown shown shown shown shown systems systems systems systems systems systems values values values values values probability parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight neurons method approach processing control control control control control control control control control control control control control large large neuron neuron neuron neuron neuron test analysis class class optimal optimal optimal inputs inputs inputs inputs form shows shows shows algorithms algorithms simple gaussian gaussian gaussian paper examples feature work task task task task task task step level current current current current current current problems problems random random memory memory representation show show equation fixed rule vectors vectors general parameter parameter average average average experiments experiments experiments experiments experiments activity activity activity activity dimensional dimensional dimensional dimensional university university university research sequence dynamics dynamics dynamics initial initial initial initial standard standard standard computer computer computer science science science left left presented activation activation machine machine sets range range range range range range range range range range range range range range range range range range range range range range range range range range learn position outputs abstract computational density references due ieee adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction complex behavior behavior statistical effect dynamic dynamic dynamic generated search change difference difference difference signals learned chosen chosen chosen chosen part previous binary represent distributed distributed expected expected techniques region region region region region region region region region region region region region region region region region region observed minimum resulting tasks simulation performed times elements elements elements elements elements regions regions regions regions regions regions regions regions regions regions mapping mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement knowledge true true compared receptive provide rates rates active determined determined determined determined goal gain gain gain motor approaches approaches steps steps comparison comparison comparison fields selection selection report department department department consists code difficult difficult final maps considered computing environment environment curve additional significant approximate approximate speed coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding levels area lines lines finally associative associative achieved technical describe surface surface surface surface effective assumed assumed shape shape theoretical require adaptation future simulated smaller dynamical unknown unknown york increasing increasing mechanism trials trials trials trials trials trials trials trials principle squared magnitude decay decay run run run run run run discussed element element movement identical identical unsupervised solve solve address positions organization organization storage horizontal lead trial trial trial deviation move move move boundary boundary runs runs runs runs runs runs runs runs runs runs runs conclusion critical differences sutton sutton california intelligence intelligence turn user start movements movements averaged areas produces produces factors laboratory tuned tuned vertical gaussians springer springer depending evaluated updated organizing organizing showed static sizes partition partition earlier earlier barto barto barto barto barto barto barto barto barto barto dashed reduces intervals boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries generation initially kohonen kohonen kohonen kohonen kohonen kohonen topology transactions figures priori priori priori priori priori activated successfully major determining sensor differ differ successful successful successful successful tend fine verlag verlag heuristic success anderson anderson anderson anderson categories denker leading received consisted moves disparity neighboring receive situations explore unlike layered create optimized preliminary reducing successive successive tech mappings ideal decisions decisions decisions maximizing affect statistically hill adapt man adjusted impulse impulse initialized arbitrarily seconds massachusetts massachusetts cart cart formula critic sensors track analyzed coded adapted adapted arc arc producing describing computers cybernetics reflect adjustable frequently partitioning partitioning partitioning rely modulated shaped pole pole pole pole pole pole pole pole pole pole shifted generator resources resources dynamically robotics extending ranges ranges ranges ranges determination los los contract contract adequate exceeds generalizes performances heavy james respective respective topological topological vertices vertex vertex vertex vertex vertex vertex vertex environmental environmental partitioned partitioned subsequently balancing balancing balancing balancing balancing balancing balanced schulten schulten creates amherst amherst solely hundred edinburgh alter adapting concentrated allocated expand altered books overhead failures ritter ritter ritter served served laws accordance ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase ase adaptively albus albus albus reflecting evenly progressively seed seed adjusts coins coins experienced mcgraw shaping focusing counted promise modulate altering ace ace ace ace ace ace ace ace ace ace ace ace examines regional angeles angeles terminated terminated bruce differed rosen rosen rosen rosen stabilized conserving prism specifications brains fell successes vij vij vij vij succeed comparatively michie michie ballistic snowbird discriminated byte criticism attenuated alteration finely finely eckmiller coarsely oliver goodwin goodwin goodwin goodwin anticipated sacrificing chances utah alp rept boyd jacques partitionings 
#@Goodwin_J,Rosen_B,Vidal_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input function function function function function function function function function figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time set networks networks training training training training training training algorithm algorithm algorithm algorithm output output output output output output number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system state state state state state state state state results results results units units information information information information information information information information information information information information information problem problem problem problem problem models hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based layer order shown shown shown shown systems systems systems values values values values values values probability probability parameters parameters parameters parameters parameters functions unit unit unit distribution distribution distribution distribution distribution distribution method approach approach approach approach approach single single single control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control local local local local local local local local local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns inputs inputs shows size work methods fig fig fig step process process process process current current trained trained structure random response show section fixed fixed fixed fixed fixed fixed line line line line rule rule rule rule general general generalization approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average average states theory gradient gradient gradient gradient gradient obtained result result threshold threshold independent sequence sequence target target target constant standard standard standard node low range basis nonlinear abstract applied applied back back back back back back find find find references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee positive positive decision propagation propagation propagation propagation propagation introduction action action action behavior effect dynamic generated cost variable variable variable variable variable variable variable variable variable variable measure representations bound bound type required required long long long long distributed distributed expected expected markov markov markov markov markov markov proposed correct errors finite simulations computed respect respect eq eq times times times mapping mapping mapping mapping mapping mapping mapping factor factor made applications policy policy policy policy policy policy policy policy policy knowledge obtain specific application desired provide provide provide provide rates rates determined determined goal goal goal goal gain gain discrete discrete power approaches steps steps steps comparison comparison larger update update update update train descent implementation implementation implementation implementation internal addition considered framework environment environment environment environment environment hinton additional design design transition transition capacity determine determine full requires estimated estimated developed developed controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller provided provided processes nature depends depends depends achieved feedforward feedforward tested tested tested limited limited complete implemented implemented generate role require require require require ability easily rumelhart rumelhart typically smaller underlying underlying needed needed needed dynamical dynamical dynamical dynamical dynamical dynamical unknown unknown unknown unknown unknown unknown testing ratio increasing increasing mechanism mechanism call call call call call call call direct combined minimize run light discussed improve advantage advantage takes typical reported reported period subject interest varying varying varying varying varying varying varying varying varying varying volume correspond chain chain chain chain chain chain observation bounded interval williams deviation derivative derivative derivative loop loop deterministic place conclusions valued measures measures measures numerical constrained external drawn demonstrated assuming variety averaged question pro produces produces describes describes implement implement sensitivity sensitivity sensitivity sensitivity sensitivity minimization springer quality expectation expectation john independently independently dependence dependence stationary stationary stationary detailed open evaluate evaluate controlled controlled controlled controlled controlled controlled controlled controlled updated evolution static static static past past sign partial slow delays purpose tracking tracking closed closed assigned transactions includes includes bell extension automatic variations variations variations variations variations straightforward selecting capable capable driven build situation situation receives capture capture verlag prob prob duration satisfy quantity usual observable observable observable observable leading illustrates subsequent operating approximating neighboring load load load load load intrinsic decreasing minimized powerful powerful layered layered wiley exponentially exponentially environments environments optimized scalar history history ideas investigated analytically stream statistically measurement measurement traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic illustrate adjusted quantities track track adapted starts rapid sys immediately mation controls controls laboratories implicit arises arises depicted preceding preceding preceding fluctuations robustness apparent limits led amounts simulate lack lack solla solla solla requirement requirement controllers controllers controllers controllers poisson monotonic incoming serve implements implements implements deviations calls calls calls calls calls calls calls calls calls calls calls calls instantaneous instantaneous investigation fix dynamically controlling controlling addresses tem arrival arrival arrival arrival arrival arrival arrival arrival plays lost numerically overcome proceeds check keeping monotonically imply affected adequate exceeds exceeds exceeds corner composition infor service service service meaningful heavy combines loo induce guarantees enable tokens tokens tokens reveals arrive eqs sons empty empty outperforms specification specification accept guyon guyon guyon guyon rejection rejection bank bank bank bank bank revealed propagating ideally affects remote remote remote remote remote remote remote remote remote remote remote streams streams streams scenario scenario reject queue queue queue queue queue queue queue queue queue penalized execute token token token token token token token compatible careful rejected rejected unconstrained monitoring monitoring moderate ergodic expense regularities regularities excess handling confirm supply mining holmdel disturbances operational loads admission admission admission admission admission admission admission admission admission admission admission admission admission admission admission characterizes suffice randomness server server server server server stabilize assessed promise excessive monitored monitored monitored monitored propagates stan objectives dist frozen ample dard offered offered offered offered offered offered wait berger berger superiority accessible accessible waiting waiting waiting controllable spontaneously rendered birth neglecting spans queueing queueing queueing queueing queueing queueing kushner kushner blend arrivals arrivals arrivals arrivals arrivals arrivals arrivals exceeding death originated services services meets stabilizes regulated customer absorbed admit resides transmits vide sara rejections rejections rejections rejections telecommunication telecommunication overload crawfords satisfactorily queuing admitted admitted admitted uncontrolled queues trolled redefinition 
#@Guyon_I,Milito_R,Solla_S,
#t4
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number system system system system system system system system system error error error error error error error state state state state results units units units units units units units units units units units units units units units units units units units information information information information problem problem problem problem problem problem models models performance performance based based based based based space space weights weights weights weights weights weights weights weights linear layer case vector vector vector vector vector order order order systems systems systems systems systems values values values values values weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution method approach approach approach point point control control control control control control control control control local local local local local local rate rate test test analysis optimal inputs inputs inputs form shows algorithms algorithms algorithms algorithms paper paper examples small net work work task task methods methods methods step step step step step step step step step step step current current current current current current current current trained trained problems problems problems problems random random random similar similar fixed line line line rule vectors general real real approximation average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained note experiments experiments experiments experiments experiments dimensional result university university variables variables variables variables computation solution research dynamics dynamics dynamics initial science science prediction activation activation activation activation activation activation activation activation temporal temporal temporal temporal machine press learn learn learn learn learn position outputs outputs outputs outputs abstract find find references component component ieee ieee adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive context context context introduction action action action action dynamic dynamic dynamic dynamic dynamic generated variance variance parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent search tion difference complexity variable variable variable variable variable variable variable variable assume assume assume chosen previous previous previous previous previous previous bound required required long conditions distributed equations equations forward forward forward forward minimum minimum tasks computed computed computed respect respect sum performed called times times times mapping means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor potential made knowledge relative relative application desired desired desired desired desired desired compute compute rates proc perform perform experimental goal goal goal goal related connected connected gain discrete discrete brain approaches mit steps steps steps steps steps steps steps steps contrast connection connection connection connection connection update train descent descent descent descent descent descent source nets modeling morgan proceedings report report report report report report report report department version version version version version version version version version version version version version version version consists connectionist scheme sequences cambridge domain domain environment environment environment environment environment environment environment environment environment environment environment additional additional solutions solutions san san effects conference conference full full significant free world world world world pages pages con produce produce randomly criterion controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller actual actual provided backpropagation associative achieved discussion normal normal technical technical technical technical technical technical describe arbitrary arbitrary tested limited assumption assumption complete actions actions actions actions actions actions actions actions actions actions actions predictions predictions predictions predictions generate supported main main instance future makes makes including kaufmann probabilistic probabilistic probabilistic probabilistic typically needed combination combination dynamical fully fully fully fully fully jordan jordan jordan jordan jordan significantly increasing trials trials principle principle principle details iterations making international supervised supervised supervised supervised combined minimize minimize minimize run description description description predict predict predict predict predict predict improve advantage advantage reported practical introduced strategy cognitive relevant relevant relevant engineering engineering highly compare conventional conventional conventional teacher teacher teacher volume works works works differential differential achieve achieve modified williams williams williams williams williams williams williams williams improvement parts parts lead invariant extended extended trial alternative alternative feed loop loop loop demonstrate runs runs valued valued valued valued valued depend interactions differences differences numerical sutton sutton mateo suggest external external external turn variety minimizing introduce introduce introduce derivatives derivatives derivatives derivatives manner manner minima minima explicit pro derive construct edges written solving solving solving sequential sequential sequential sequential ann mathematical dept dept changing changing modeled modeled multilayer infinite electrical angle agent agent formation dependence stationary learner evaluated operations operations updated updated updated updated updated evolution understanding approximated activities past partial partial earlier earlier performing purpose boundaries boundaries valid visible visible advantages transactions degrees avoid expect building building building thesis activations activations activations activations assignment assignment extension absolute planning planning reason society paths paths driven driven delta wij wij wij wij wij wij wij wij wij wij wij wij wij wij wij wij build essentially reached anderson anderson anderson contribution contribution running running sci comp notation quantity quantity involved providing providing leading leading leading jacobs jacobs minimized minimized diego environments environments environments environments environments environments environments environments limitations limitations game issues scalar ideas school detectors relationships maximizing gradients gradients concepts man man predicting predicts perfect perfect perfect perfect perfect perfect changed versions observe ith ith ith utility phd finds massachusetts mentioned ment cart cart cart directed critic critic critic critic critic critic critic trivial track unstable failure capabilities answer reasons stanford straight tive tive constructing arise acknowledgement cybernetics conducted conducted conducted introducing employ incorrect robinson robinson robinson robinson controllers controllers differs serve extensions adjust sums germany kinds inherent sophisticated neuro expectations begins credit credit cumulative cumulative cumulative pole pole pole pole pole pole pole pole initialization notes generator generator interface acts acts addresses wrong convenient ments chance ranges adjusting siemens simplify fail belong belong imply responsible contexts realization realization consequences consequences consequences consequences discounted ahead reader offer environmental environmental environmental environmental environmental environmental discovered inf balancing balancing balancing balancing balancing balancing balancing avoiding executed executed severe zipser zipser zipser zipser zipser summer listed ent discount super markovian markovian markovian markovian markovian markovian markovian markovian markovian markovian spatio spatio tween connec arbor acceptable hundred affects affects forcing mismatch care schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber pij pij pij werbos werbos execute generators generators playing interacting interacting interacting flip flip flip flip universit universit universit son applicability behave behave failures failures continually continually students reinforce sees excess compositional instability institut institut institut institut termination kth dom automation accumulate push ultimate zipset sity reality coins iid iid informatik informatik informatik informatik informatik randomness randomness randomness longest experienced lags lags bumps enters appro stabilize tical episode episode february february backwards rent technische technische technische technische disadvantages fallside fallside fallside fallside fiir fiir fiir klaus klaus statis concurrently adap adap cued environ miinchen miinchen augment recur flop flop flop flop univer attack imperfect imperfect revised revised duced gation pain pain pain pain pain pain pain pain pain pain pain pain pain pain pain pain ner vised vised vised hochreiter hochreiter lacks indefinitely pleasure pleasure pleasure pleasure pleasure pleasure pleasure pleasure pleasure pleasure pleasure draft spend causality interfaces augmenting instabilities instabilities troller mfinchen scholarship infeng critics critics critics critics critics critics reporting tum propaga attacked differenttable fki fki fki muenchen propa josef josef vironment ilk flavor factory confronted diffi saves friendly ici forgets 
#@Schmidhuber_J,
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#*network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural data data data data data data data data figure figure figure figure figure figure figure time set networks training training training training algorithm system system system system system system system system system system system system system system system results results results results results results results results information information information models models models models models models models space space weights weights layer layer layer case order order order order order shown shown shown shown systems systems systems systems weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach approach approach approach pattern single single single single single processing processing processing control control control control control control control control local local test test test patterns analysis analysis analysis class class inputs inputs inputs visual paper paper paper small work work work work task cells cells cells cells cells features process level level current trained trained cell cell structure structure high response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar similar similar similar similar similar representation representation architecture architecture show section fixed rule approximation note experiments activity activity dimensional dimensional result result university computation research found found sequence initial initial initial initial initial initial initial computer computer connections connections connections connections connections connections science left left left left left left left left left left direction direction direction direction direction motion press components basis basis outputs abstract back back back computational properties properties properties properties properties references due due important important important adaptive propagation context introduction complex complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior effect parallel parallel tion change complexity complexity variable variable representations higher higher part previous firing type cortex represent distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed make make fact techniques correct observed observed observed observed observed forward forward resulting resulting resulting human multi performed means made made orientation knowledge em specific specific compared provide compute active eye experimental experimental experimental constraints constraints connected connected motor motor motor motor motor motor brain brain power larger connection connection train dependent source source modeling report consists code individual individual individual individual individual individual individual joint joint joint joint joint joint joint represents responses responses responses responses responses responses responses responses responses responses difficult addition addition considered experiment solutions curves stage effects full approximate free free speed basic con con produce coding coding derived actual actual finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature nature simply biological biological normal describe describe group group excitatory predictions circuits finding common effective supported role role adaptation adaptation end future sensory sensory sensory sensory including including simulated pairs pairs underlying underlying underlying underlying needed reduced functional functional fully fully fully interesting interesting significantly york special consistent consistent consistent consistent structures principle operation operation operation operation operation operation details details direct stored bottom run sources neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal population population population population population population directions directions directions directions pair movement movement moving include period identical side side side side side side cognitive recently relevant engineering sufficient compare approximately approximately approximately tions organization sensitive entire entire grant grant grant arm constructed intensity rotation move generally generally generally column column demonstrate runs segment conclusions constrained constrained constrained constrained suggest mechanisms mechanisms characteristics characteristics characteristics intelligence turn turn turn turn turn turn turn turn turn turn turn turn turn turn turn variety variety variety movements movements movements movements movements movements movements movements movements movements movements selective targets manner groups connectivity connectivity connectivity program appears appears appears tuned tuned tuned distinct modeled modeled angle angle formed extracted focus reconstruction detailed detailed controlled lee lee forms understanding similarly measurements msec degrees recorded existing activated specifically characterized structural successfully major major reason reason columns columns middle middle identified identified identified identified identified identified closely capable society encoded delta video interested neuroscience superior physiological physiological comp comp comp comp comp simplified simplified simplified play principles overlapping operating preferred deal receive body body body body body body body body body body body employed employed remain american american american essential essential essential exhibit circuitry circuitry circuitry involving detail integral limitations existence examine project project behavioral behavioral behavioral behavioral behavioral plasticity possibility possibility encode encode func analogous examined act onset onset ensure front front front freedom precise mapped nerve nerve nerve nerve nerve nervous academic generates generates integrate integrate animal animal animal animal great advanced directed crucial sensors orientations biology capabilities answer caused caused tool interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons turns turns turns turns turns turns turns turns turns turns turns turns rapid purposes sys strictly day day forces constructing directional located located immediately immediately controls acknowledgement involve angles angles angles angles angles angles members members read nsf questions questions questions prop populations populations populations populations populations pathways understood understood tional axes simulate effort share completion incorrect incorrect biologically biologically ity robinson robinson gen gen wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind proven serve serve representative representative redundant physiology physiology physiology physiology physiology sort proportion proportion modify tation saccadic appropriately velocities reconstructed reconstructed tem turned arranged plays extending cellular ranges adjusting accepted primate analyzing analyzing neurobiology neurobiology neurobiology cottrell responsible responsible adequate preparation preparation preparation muscles obstacle date exploring exploring utilized excellent ranging connect mental lengths evident schwartz offers reproduce reproduce reproduce similarities claim recovery recovery recovery recovery recovery recovery recovery offer pollack pollack pollack pollack pollack pollack contact colliculus insect insect insect insect insect insect insect insect insect insect insect onr escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape escape speaking neurophysiology largely largely largely hair hair fellowship validity removal cooperative cooperative uniquely retraining lesions lesions lesions lesions lesions lesions lesions lesions solely hundred simulating constrain lesion lesion lesion leg leg leg leg leg leg leg leg leg leg leg leg leg manipulation biophysical interneuron interneuron interneuron mammalian mammalian mammalian efforts plate emphasize individually ultimately termed oculomotor rod struc signs signs computa supporting experi unpublished completed modal leech vestibulo hundreds finer broadly broadly eral sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor kinematic kinematic integrates ventral ventral ventral ventral ventral ventral ventral intact intact joints joints neurobiological reproduced reproduced amenable demands comer comer addressing addressing nih lar cleveland cleveland ganglia freely refine refine plenum unaffected levy levy directionally excite anastasio anastasio deeper enforced forthcoming manipulations cir reconstructions coverage adap lesioned lesioned lesioned deficit thirty thirty ant responsive invertebrate invertebrate constantly legs legs legs legs legs legs legs legs legs prevented georgopoulos georgopoulos beer beer beer beer beer beer particu abstracts identifiable identifiable attack erties proprioceptive restored giant giant giant giant giant giant giant giant giant giant giant gation sudden neurosciences departments subjected wealth elicit innervate strained strained western rear rear rear rear sparks reorganization erating directionality thrust pulling cuits manufacturing propel popula predator reserve appreciable eighteen roach roach initiating grad backpropa evokes caveats antennae rer quires bns dozens tural hind endeavor elucidated kettner ploy suspended 
#@Beer_R,Chiel_H,Kacmarcik_G,Ritzmann_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm output output output output output output output number number number system system system error error error error error error error error error results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information hidden performance performance based based based based based based weights linear linear linear layer case case order shown shown shown shown shown shown systems weight weight weight weight functions functions functions functions neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution method pattern pattern pattern pattern pattern single single single single single single single single single single processing control control control control control control control large large large neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis inputs inputs form visual paper small small small size work methods methods methods fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points points trained trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random representation representation representation architecture architecture architecture architecture general real theory theory gradient obtained obtained obtained activity activity activity activity activity activity activity activity activity activity activity activity university university solution defined defined initial science presented presented present phase activation activation activation frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal range range range range press press learn outputs continuous continuous sample abstract analog references stochastic stochastic stochastic due important introduction complex complex behavior behavior statistical dynamic dynamic dynamic dynamic dynamic change spatial spatial spatial spatial spatial spatial rules rules rules measure prior prior prior representations part cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing required multiple spike spike spike spike spike spike spike spike spike spike spike spike proposed correlation correlation correlation correlation observed errors errors errors errors errors errors errors errors errors simulations ing ing ing total simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation sum sum sum sum sum sum performed performed times regions feedback applications study relative relative relative represented represented represented provide provide provide provide provide provide perform active active determined determined experimental connected motor motor motor motor motor motor motor steps train train train train train train dependent technique technique technique technique code individual individual individual individual exp bias bias addition sequences sequences sequences framework view effects effects detection significant significant produce coding derived derived developed velocity evidence backpropagation nature sampling biological biological biological biological biological biological biological biological biological biological biological discussion discussion complete effective effective assumed assumed generate main main main future degree simulated simulated typically underlying underlying needed needed needed account functional functional functional fully ratio york consistent consistent consistent consistent mode mode squared squared squared squared squared squared pre direct direct stored normalized normalized supervised decay run predict predict neuronal neuronal architectures architectures correlations exact typical include identical engineering dimensions highly highly highly calculated calculated studies generalized interval organization amplitude spikes spikes spikes matrices matrices matrices matrices predicted correctly width minimal minimal assumptions hebbian central interactions interactions interactions interactions exponential exponential characteristics characteristics sigmoidal turn turn turn averaged averaged averaged averaged groups connectivity appears primary primary primary primary describes simultaneously remaining remaining angle unique unique unique mutual events springer shift yield depending interpretation detailed controlled controlled past epochs intervals intervals roughly roughly roughly generation generation generation generation msec msec recorded fire thesis inter sciences coupled successfully reason middle importance importance driven spiking spiking spiking spiking post summary verlag contribution contribution criteria timing duration duration cues simplified neurosci operating operating trains trains trains command wiley production accurately accurately accurately accurately accurately hall rise history history history history behavioral biol biol biol encode statistically understand gradients analyze equally explored separated separated separated mapped nervous nervous hebb hebb contributions submitted submitted submitted submitted submitted synthetic seconds seconds integrate burst crucial analyzed analyzed analytical analytical majority caused caused briefly london ganglion spatially drive drive drive drive drive drive easier incorporate commonly controls potentially lowest recording recording addressed mechanics questions reflects reflect collected profile capability recordings recordings recordings incorporated berlin wind inherent inherent inherent simultaneous simultaneous simultaneous simultaneous simultaneous simultaneous contribute cybern cybern secondary secondary secondary physiology accomplished generator driving reconstructed spontaneous spontaneous spontaneous cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular occurred tools tools efficacy carry degradation degradation muscles evaluations analyses analyses analyses analyses analyses analyses analyses analyses utilized utilized utilized utilized utilized governed iteratively colorado colorado colorado assembly interconnections interconnections reproduce spatiotemporal record record environmental insect insect consecutive largely indirect presenting presenting adopt decomposed acceleration rhythm alter lesion lesion lesion verified verified verified verified acting chapman thermodynamic boulder boulder relate altered individually electrodes retain termed paradigms assemblies assemblies assemblies assemblies accounted flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight flight retained permit permit interspike tissue inactive resolve discretized discretized err caudal caudal caudal flows flows anatomy continuum episodes episodes episodes operational judged systematically intact symmetrical artifact neurobiological neurobiological neurobiological neurobiological 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#@Faller_W,Luttges_M,
#t4
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning model neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure set set set set set set set networks networks networks training training training training training training training output output number number number number number number state state results results results results results units units information information information information problem problem hidden hidden performance based based space layer layer layer layer case case case case order order shown shown values values noise noise noise noise functions neurons neurons neurons neurons neurons method method method method method approach approach approach approach approach approach approach approach single single single single processing large large local test analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form small small small work task methods methods methods methods methods methods methods methods process current current trained trained trained trained trained trained trained cell structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure random random random high high representation representation representation representation representation representation representation representation architecture show fixed general general experiments activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional university threshold threshold threshold threshold threshold threshold threshold threshold solution research sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics initial initial distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left presented presented map map map present low learn basis abstract applied convergence references due procedure procedure introduction hand statistical generated generated generated generated parallel parallel parallel parallel parallel energy energy energy energy difference spatial lower learned chosen part previous cases type good good binary binary binary binary binary binary binary binary binary binary binary binary binary binary long long long make length length length correct correct correct errors forward resulting classes ing ing ing called elements potential made study knowledge represented define proc perform determined determined determined experimental constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints equal accuracy accuracy accuracy accuracy accuracy larger train descent report institute loss version consists exp sequences sequences sequences sequences sequences sequences considered cambridge experiment directly hinton additional choice significant derived derived derived developed developed backpropagation backpropagation discussion technical describe group group close close surface predictions short generate generate main main square ability ability degree including needed account functional increasing structures structures structures structures structures structures structures structures structures structures structures structures structures structures empirical pre pre window window window magnitude idea produced produced produced added predict predict predict predict architectures recent resolution resolution robust typical reported introduced identical identical sejnowski recently recently interest approximately calculated diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal positions williams improvement sensitive exists exists exists invariant invariant invariant deviation deviation deviation deviation matrices matrices matrices matrices rotation rotation predicted predicted predicted predicted predicted predicted predicted alternative correctly correctly feed width width width generally half starting central accurate clear clear faster largest demonstrated turn minimizing exist configuration configuration question acknowledgements pro derive derive construct laboratory category category category coordinates angle develop minimization minimization minimization minimization minimization letters letters national reconstruction codes solved solved solved solved organizing centered suggested translation translation translation reasonable classical sec fitting generation distances distances distances distances usa usa formulation assignment illustrated illustrated specifically domains domains structural structural structural structural structural successfully aspects aspects capable importance included successful identify build schemes orthogonal traditional compact procedures contained dis dis symmetry classify running strategies sci hold hold categories categories involved generalize leading illustrates rat rat employed simpler essential preliminary rise biol biol biol biol biol biol root cover neu predicting predicts illustrate great band band band band band band band growing biology widely protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein broad recognized acad preceding explained prop collected led cohen rep anti anti aim fall occurrence windows deviations univ contribute contribute secondary secondary secondary secondary secondary secondary secondary secondary secondary assign tation reconstructed reconstructed reconstructed reconstructed enhancement grows accepted tools simplify determination loops ral salient presentations natl utilized entry uni assembly proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins steepest considerations subsequently grants discovered generalizing tures rms rms rms linked truncated bank bank encouraging distinction superimposed hundred hundred guess guess molecular beta reconstruct alter exam books acquired academy amino amino amino amino amino amino amino amino amino amino amino amino amino sheet sheet sheet distinguished investigations struc unpublished acquire ase tors stripes illinois ples ray ray ray ray ray lying functionally contacts contacts acid acid acid acid acid acid acid acid denmark denmark denmark denmark est bradford acids acids acids acids acids acids sheets sheets mutation emerged suzuki decades thc urbana tolerant tolerant tolerant insertions resentation posi helix helix helix helix atoms atoms atoms atoms atoms atoms nuclear lay fac biophys tributed unequal contiguous positioned positioned positioned taught taught brings deletions lira coil coil coil coil coil weeks today today today bears backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone backbone bigger story erties bohr bohr bohr bohr bohr bohr bohr bohr bohr bohr bohr bohr bohr depict native native resemblance apr rodney folded folded folded folded folded folded folded structurally prog cumbersome neurm qian chou straint kai blegdamsvej danish atom atom atom documented conformation conformation conformation conformation conformation conformation conformation conformation centrally centrally centrally mol mol mol mol mol folding folding folding folding folding steadily equ mately stories petersen petersen petersen trm trm trm trm trm trm trm trm homologous homologous homologous homologous athe improper engineer illus tioned pack alp inal lyngby cotterill cotterill cotterill cotterill cotterill cotterill achievement lasted ris ptp tertiary tertiary tertiary tertiary dicted ren stemming rummelhart stretches bridges dicting biochemistry dant 
#@Bohr_H,Bohr_J,Brunak_S,Cotterill_R,Fredholm_H,Lautmp_B,Petersen_S,
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output number number number system system system error error error state state results results results results units units units units units units units units units units units units units units information information information information information information information information problem problem problem problem problem hidden hidden hidden hidden hidden based based based based based based based based based weights weights layer layer vector shown systems systems systems values weight weight weight weight unit unit recognition recognition recognition recognition method method method method method method approach approach approach approach approach pattern point single processing processing large large large rate rate rate test patterns patterns patterns patterns analysis analysis class class class matrix optimal inputs form form algorithms algorithms algorithms algorithms paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small size net work task task task task task task methods methods methods methods cells cells points features features features features classification level trained cell structure structure random random similar architecture show fixed rule rule general generalization average theory theory theory theory obtained obtained note experiments dimensional result result university university university university research research research research research research research research research research research found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial initial table table table computer computer computer computer computer science science science prediction map present present present present frequency machine machine sets sets sets range learn learn position basis abstract applied applied find references due positive procedure procedure procedure procedure important important important important decision decision decision decision introduction complex statistical statistical statistical tion tion energy complexity variable lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules signals learned learned learned learned learned center center long conditions represent represent represent represent tree expected techniques techniques techniques techniques techniques correlation correct correct correct correct correct correct errors errors total human human human performed performed called regions made knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge negative negative negative negative artificial artificial artificial artificial artificial relative specific specific samples represented represented true true true true compared application application application cross provide provide provide define proc location location location perform active experimental related related connected connected brain approaches steps accuracy accuracy accuracy comparison connection support report department department consists advances advances represents represents represents represents represents connectionist final final addition addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences considered domain domain domain domain domain domain domain domain domain experiment curve curve curve determine determine determine determine requires significant free estimated pages pages pages pages pages coding derived derived derived weighted randomly randomly randomly randomly randomly randomly randomly lines lines lines lines lines provided finally finally nature nature biological biological biological biological discussion technical increases describe describe corresponds complete complete nearest supported journal ability ability future future makes including including needed combination reduced fully testing testing significantly significantly character special database empirical empirical empirical principle numbers numbers numbers making making window added added population population improve advantage reported reported apply introduced subject trees inference inference recently recently highly previously approximately approximately approximately approximately approximately correspond correspond correspond address definition positions positions locations locations improvement improvement grant grant grant parts expression expression expression occur occur alternative correctly hybrid hybrid hybrid boundary boundary demonstrate half conclusion starting reduce neighbor central differences faster practice taking strong hard presence demonstrated solid solid solid intelligence characters characters characters program configuration base base base base base base base base base base base base areas longer primary generating generating describes describes ann ann ann ann ann ann ann ann ann ann ann ann ann category category category category physical slightly slightly interaction develop national national depending interpretation detailed restricted similarly translation translation translation combining event roughly false boundaries initially string symbol foundation classified template weighting instances sciences sciences sciences recognize recognize recognize recognize recognize plotted automatic partially structural straightforward selecting identified differ included literature literature literature genetic genetic genetic genetic refer conf contained cun split split split superior classify criteria categories notation sampled usual usual realistic denker reach consisted illustrates unlike create humans accurately accurately recursive dotted dotted biases biases biases fewer fashion links links links links investigated dependencies dependencies office referred structured structured symbolic symbolic symbolic statistically understand removed removed removed neu predicting created created portion noted perceptton initialized initialized initialized initialized initialized initialized initialized initialized message extent defines percentage site stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop distinguish biology biology explanation explanation explanation cascade briefly briefly handle sites protein protein protein protein protein protein incorporate ran recognized computers demonstrates demonstrates incomplete recognizing recognizing recognizing fluctuations reflect substantially solla employ incorrect release differs incorporating suited boston windows findings damage specifies wesley don don don don don don don don don don don addison discovery naval theories theories cellular significance primate proceeds chemical grow resulted hope reasoning ral ral imply canonical canonical canonical alphabet spurious composition reliably repeat utilized falls combines intended bases bases bases entries initialize membership membership rich rich specificity properly proteins fahlman shavlik shavlik shavlik shavlik shavlik shavlik shavlik automated boxes boxes dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna dna anns anns anns anns anns anns numerous benefits pieces tween copy junction junction junction junction junction junction junction solely classifies constitutes molecular molecular molecular molecular gene gene gene options translated translated genes genes genes genes genes genes genes genes thick thick thick geoffrey surrounding surrounding relates investigating investigating names topic iri nuclei constructs refinement refinement sized lapedes lapedes molecules port manuscript topologies covers junctions junctions junctions junctions junctions junctions junctions junctions junctions junctions junctions junctions towell towell towell towell towell towell towell locate utilizes spacing exper hopkins clauses dom devised believed splice splice splice splice splice splice splice splice splice splice splice splice splice splice splice splice splice splice sym convention acid acid adjusts wisconsin wisconsin wisconsin absent creation acids acids acids acids translates translate eighth watson unexpected repetitions repetitions refine refine lebiere configured resemble richer notions farber plotting borders borders frozen weakness madison madison madison thumb ago intervening classifica shrink claimed positively craven numbered consensus ana feel kbann kbann kbann kbann kbann kbann kbann kbann kbann kbann kbann kbann kbann genome amples quences cate subscripts hierarchically hierarchically nucleotides nucleotides chemistry barnes folded consequent avail lighter subsequences concludes tunable acc acc acc acc acc acc acc acc acc acc acc decade initiative roberts pursuing negatively propositional documented intense undertaken evidently promoters promoters promoters promoters iments triplets disjunctive brunswick noordewier noordewier noordewier noordewier noordewier bolic discriminates bination coli substructure disjunction jude genetics genetics analogues nucleotide impetus gories 
#@Noordewier_M,Shavlik_J,Towell_G,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training output output output number number number number system system system system system system system system system system system system system system system system system error error error results results results results units information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space linear linear linear linear linear linear linear case case vector vector vector vector order order order order shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems unit recognition method method approach approach approach approach approach single single processing control control control control control control control control control control control control control control control control control control control control control control control control control control control large large rate test test test patterns analysis analysis analysis analysis analysis analysis matrix form signal algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper paper small small size net net net net net net work work work work work work work task task task task task task task task task task task task task task task methods methods methods methods methods methods methods fig fig fig step step step points classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process process current trained trained trained trained trained trained structure problems problems problems problems problems problems problems memory similar similar similar similar similar similar similar architecture architecture architecture architecture line rule vectors vectors real real real real real real real real real real real real real obtained obtained obtained obtained obtained note activity activity result university university computation solution solution solution solution solution research independent independent independent independent found found found found initial initial estimate estimate computer computer presented present present present nodes nodes sets sets sets sets sets sets sets range range range range range range range range range range range press learn learn basis continuous continuous continuous continuous continuous sample sample sample abstract applied applied back back computational computational computational references component due procedure important adaptive adaptive decision propagation introduction complex complex complex complex hand behavior behavior behavior statistical statistical statistical statistical effect dynamic dynamic dynamic dynamic dynamic cost cost tion tion change energy energy difference difference complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier learned learned part center previous type required required required required required required required required multiple multiple conditions conditions conditions conditions represent tree tree tree tree expected expected make fact fact techniques length observed observed observed errors errors errors errors forward forward simulations minimum tasks simulation simulation respect performed performed called called elements means means means means means means means means made made made applications applications study knowledge knowledge filter filter obtain artificial specific samples samples compared compared compared application application application application application application application desired provide provide provide provide provide provide rates rates perform perform perform active active active active active active active active active goal motor mit accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison larger train train nets nets nets selection morgan proceedings proceedings internal difficult difficult difficult difficult scheme scheme addition graph cambridge equivalent equivalent equivalent environment directly directly additional additional solutions solutions solutions solutions solutions solutions solutions solutions solutions estimates estimates design san san stage detection detection detection detection detection detection detection detection detection detection determine determine efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper requires choice significant world speed validation validation con con con con produce derived developed developed developed developed developed developed area area controller controller controller controller controller controller actual finally finally selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation simply simply normal normal normal normal normal normal group tested limited limited limited limited limited limited assumption complete complete complete surface nearest common common effective effective effective effective role role role require adaptation easily development development development typically smaller needed needed combination testing testing testing testing testing testing empirical empirical operation operation operation principal filters filters filters filters direct direct supervised supervised expert early produced produced produced description light predict architectures architectures improved improved discussed recent typical practical practical practical introduced introduced introduced strategy include recently interest interest previously previously conventional conventional conventional conventional conventional conventional conventional conventional conventional observations studies studies studies separation constructed constructed exists exists studied extended wide wide wide matrices matrices correctly correctly feed move occurs hardware hardware hardware conclusion reduce conclusions operator neighbor differences differences differences measures accurate accurate accurate accurate numerical mateo cycle cycle cycle cycle drawn drawn demonstrated demonstrated demonstrated california california variety start exist min min relationship introduce manner identification identification identification identification identification identification program explicit suppose tuned mathematical modeled modeled confidence infinite easy develop develop develop develop develop develop applying events quality quality agent implies select communication communication transform controlled controlled controlled restricted restricted forms static understanding understanding understanding understanding suggested suggested processor processor processor reasonable reasonable calculation performing measurements measurements intervals event iterative iterative initially avoid expect expect existing existing existing thesis thesis priori priori priori extension specifically specifically tests tests successfully sensor identified identified capable suitable effectively included successful successful identify identify identify identify identify identify identify detect detect detect build efficiently schemes situation miller summary traditional road compact compact procedures induced contained link link link link link link issue issue classify classify classify running quantity sampled play play absence absence paradigm paradigm board board board board board attempt attempt operating operating operating operating operating operating operating operating operating operating load employed employed explore explore unlike carried diego production production create access collection requirements experience put detail accurately issues preliminary examine examine examine links investigated investigated fault fault fault fault fault fault fault possibility reliable root complicated understand examined examined examined examined examined created implementations implementations implementations implementations prototype detector explored explored detected detected submitted serial serial serial plant plant plant plant plant plant plant plant plant plant plant plant established optimum massachusetts great developing developing developing developing developing developing developing developing crucial growth track failure failure failure failure failure analytic analytic briefly briefly considerable considerable rapid broad hyperplane arise arise beginning arises arises radius addressed addressed greatly prop evaluating limits limits applies collected collected collected flexible capability capability capability readily readily readily leave effort effort remove reliability requirement operate controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers semi deviations traces diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis realized shifted identifying sort investigation investigation extensive linearity driving narrow resources resources resources databases controlling controlling impossible eliminate proceed establish establish kaufman murphy occurred attractive vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle hope occurring obtaining transforms analyzing observing observing wire adequate hours service utilized utilized james encountered washington washington demonstration widrow widrow verification properly designing implicitly subsequently automated severe outlined outlined mind rigorous misclassification accept exhaustive obstacles failed encouraging utilize weiss weiss additionally additionally additionally acceptable acceptable acceptable acceptable reports stem experiences possibilities workstation conservative streams verified care care stroke management ijcnn ijcnn faults faults faults faults faults faults faults faults faults faults faults faults faults faults carefully efforts careful scope scope investigating constructs drawback nonetheless misclassified paradigms paradigms paradigms paradigms discusses confusion investigations investigations failures failures wider completed handled utilizing appearing handling demand demand satisfactory satisfactory satisfactory impractical trainable trainable compete accomplish accomplish concern replicated engine engine engine engine engine engine engine engine engine engine engine engine engine diagnostic diagnostic diagnostic diagnostic diagnostic diagnostic diagnostic diagnostic diagnostic diagnostic conflicting exclusively assessment linearized approaching establishing company fin experienced demands demands pin pin indicators emerged validated modest predetermined mid imposes operated operated cars demanding eta eta broader complications anticipate emulate emulate roads digitally spontaneously spontaneously adopting feel plants plants plants plants plants exclude michigan michigan michigan michigan rce rce rce rce rce permitted ans ans ans ans standpoint delivered altogether dam undergoing exercise exercise exercise asynchronously vehicles vehicles vehicles attain multiplexed encouraged prepared complication predominantly microprocessor microprocessor presumed opera opera standards standards tolerate diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics diagnostics focussed ford truck attainable paragraph contaminated accelerations tradeoffs tedious undertaken dictates kenneth wished wished wished obtainable feet companies underway judgment unavailable engines engines engines deemed backer infrequently infrequently bay diagnose staff sophistication precede superset routinely reserve endowed tabulated feldkamp mislabeled complicates chief intentionally puskorius detroit consumes sho exclusion exercised exercised multiplex broaden assembling impetus daunting intentional 
#@Marko_K,
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#*network network network network network network network network network network network network network network network learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data function time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number system error error error error error error error error state results results results results results results results results results results results results results results results results results units units units information information information problem problem hidden hidden hidden hidden hidden hidden hidden hidden performance based weights linear linear layer layer layer layer layer layer layer case case case case case case case case case vector shown shown shown shown systems values values values values values values parameters parameters parameters parameters noise weight weight weight weight functions recognition recognition recognition recognition recognition recognition recognition recognition method method method approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single processing processing processing processing large large large rate rate rate rate test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs shows shows shows signal signal signal signal signal signal algorithms simple examples small small feature feature methods points points points field field field field field features classification classification classification classification classification classification classification process process level level level level level level current trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained random high high high high architecture architecture show parameter real theory obtained term term threshold threshold threshold research research research independent independent defined defined found found found found sequence sequence target target target table table table table table table table table table estimate standard terms connections node node node node node node node node node node node node node node node science presented presented presented presented phase phase phase phase phase phase phase phase phase phase activation activation activation activation activation activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency frequency frequency frequency range range range range press learn learn basis abstract abstract applied applied applied back references due procedure propagation propagation introduction complex complex hand estimation estimation estimation estimation estimation estimation estimation effect effect effect generated generated parallel spatial classifier classifier classifier representations part part part previous previous cases cases cases firing type required required represent represent represent represent distributed fact fact fact techniques region region correct correct correct correct correct correct correct observed errors errors errors simulations simulations classes classes classes total computed computed sum sum performed performed performed called times elements elements elements elements elements elements means potential applications applications applications study study study study study study study study study study study study study study study study study study study study study study study study study artificial artificial artificial artificial relative represented compared application cross provide perform goal connected connected mit larger larger connection connection fields dependent dependent dependent source source source source source source source source source report implementation technique consists internal individual individual represents represents responses responses responses responses layers delay delay delay delay delay delay delay delay delay delay delay delay ai considered considered cambridge computing experiment experiment experiment experiment experiment experiment experiment experiment experiment hinton additional effects effects effects effects detection determine determine determine determine significant produce channel derived derived weighted weighted weighted developed levels levels levels criterion velocity product actual provided finally backpropagation backpropagation achieved measured measured normal normal normal normal normal normal normal normal normal normal normal normal normal transformation implemented assumed assumed generate future future easily rumelhart rumelhart including simulated simulated simulated fully fully technology mlp mlp mlp mlp mlp mlp matching matching matching matching mode mode squared squared window window window window window normalized depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth idea produced produced sources sources sources description description perceptron recent robust element include array array array array array array array highly varying calculated match match studies studies studies studies studies studies studies studies separation channels channels williams entire increased amplitude amplitude matrices matrices matrices generally row greater greater conclusions depend designed exponential sound sound hard physics largest characteristics sigmoidal demonstrated demonstrated demonstrated identification identification identification program written written index laboratory ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann multilayer involves involves angle spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral develop applying events events events events events events events events events events events shift shift versus john yield yield national focus focus focus focus review depending correlated transform evaluated evaluated centers understanding understanding discrimination discrimination discrimination discrimination discrimination discrimination discrimination past calculation smoothing measurements delays delays delays delays delays delays delays normalization normalization normalization event event event event event event event event event purpose purpose purpose distances msec recorded fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire combinations inter recognize recognize recognize automatic automatic specifically characterized selecting identified modes modes modes identify comparing excitation road soc soc soc kind procedures anderson superior issue return classify classify classify criteria criteria criteria criteria criteria criteria involved involved usual localization generalize wave highest ill consisted consisted extract extract deal minimized transformed varied varied replaced preliminary discriminant fourier fourier rest investigated investigated investigated affect affect phases momentum matched matched matched matched matched closest concepts concepts possibly analyze der der taylor precise explored explored explored initialized art submitted attempts synthetic synthetic synthetic synthetic optimum percentage percentage percentage rows waveform waveform waveform waveform majority tool tool division recognized recognizing exemplars exemplars percent percent populations embedded embedded simulate effort item incorporated incorrect incorrect characterize characterize acoustics gave windows coherence coherence spectra spectra spectra spectra ordinary modify velocities velocities bin connecting connecting royal exemplar exemplar establish convenient resulted resulted resulted obtaining obtaining methodology arrays arrays symposium studying dependency dependency dependency evident evident uni propagated lawrence darpa bins master theoretically verification propagate characterization characterization characterization characterization characterization characterization characterization characterization characterization characterization fired fired fired fired fired fired fired discriminate appeared anns anns anns anns anns anns anns anns anns anns numerous presenting presenting presenting presenting employs encouraging propagating classifications amplitudes conservative conservative conservative summarizes deep deep deep deep deep deep deep deep deep challenging douglas relating depicts attached superposition sweeps port unpublished november shallow shallow shallow shallow shallow shallow shallow shallow shallow shallow emphasis acoust acoust characterizing water water shot shot shot shot shot shot shot shot shot shot shot shot shot locate attempting attempting accomplish distinguishing operational economic economic economic transpose attenuation triangular triangular schmidt iterating approached unusual media february eigenfunctions experimented dispersion dispersion routine ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple ripple hij directionally regional regional regional regional regional regional regional regional regional regional regional regional regional regional regional hypothetical nth nuclear nuclear nuclear nuclear nuclear nuclear nuclear impressive depths depths depths depths depths bull comprise wanted wanted wanted wanted explosion explosion explosion explosion explosion explosion explosion explosion explosion relied recognizable intend anomalous anomalous anomalous anomalous anomalous anomalous anomalous anomalous anomalous anomalous anomalous modulations modulations modulations modulations decoupled gov multilayered emitted irrespective wash livermore livermore backpropagating virginia css oid communicates 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#@Baumgardt_D,Perry_J,
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#*network network network network network network network network network network network network network network network network network neural neural neural input input input data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number number error results results results units units units problem hidden hidden hidden hidden hidden hidden hidden layer layer layer layer layer vector vector vector vector weight unit unit unit recognition pattern pattern pattern pattern pattern pattern single test test test test test test test inputs inputs shows shows simple size size net net net net step trained trained trained trained trained trained trained high high architecture architecture vectors vectors vectors vectors average term term variables variables variables variables variables variables variables variables variables variables variables research found table table table standard standard low frequency press position position position abstract back back back back back references component component procedure adaptive propagation propagation propagation propagation propagation introduction parallel tion tion change previous previous cases required long long long long long long long long long long distributed errors errors errors errors forward minimum ing computed called made study negative artificial artificial desired desired desired active train train curve curve significant con con finally finally finally finally technical technical technical technical technical technical technical technical tested tested close short short short short short short short short short short implemented future future future rumelhart rumelhart increasing expert expert expert expert expert expert expert expert predict interest dimensions volume positions positions derivative feed column numerical relationship relationship targets targets plot plot plot ann ann ann ann ann ann ann ann ann ann confidence consisting consisting consisting john open open past roughly bell recognize recognize encoded encoded mcclelland denker consisted consisted consisted consisted consisted varied put encode encode fundamental fundamental fundamental fundamental fundamental momentum front noted agreement slope turns day day day day day day day day percent percent compares passes passes passes price price summarized wesley addison hit contract contract resulted modifications days days days days days days days days days days days tures market market market market market market market trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading speaking anns corporation vec year year year tor exclusive file labs fea tract tract round experi twenty allen agrees suite month month weather profit profit profit profit profit profit profit profit profit profit profit profit profit profit profit investment indicators indicators texas months joseph activa meanings buy buy cited varia varia elaborated sixteen optional yves rts rts rts rts eighteen eighteen eighteen calcula sell sell 
#@Collard_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input data data data function function function function figure figure figure figure figure figure figure figure time time time time time time set set set set set set networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output system system system system system system system error error error results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information information problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based space space weights weights weights weights linear linear layer layer layer layer layer layer layer layer case case case case vector vector order shown shown shown systems systems values probability probability probability probability probability probability parameters parameters noise weight functions unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image image image image image image image image single single single processing local local local local local rate test patterns patterns patterns patterns class class inputs inputs inputs shows signal algorithms algorithms algorithms algorithms algorithms simple simple paper size size feature feature feature feature feature net net net work task field field field field field field field features features features features features classification process trained trained trained trained problems problems problems random similar representation architecture architecture architecture architecture section section fixed fixed fixed rule rule rule rule rule rule rule rule rule images general generalization generalization generalization parameter parameter parameter parameter parameter parameter term term note note note note activity activity activity activity activity activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional university university solution research research independent independent log target target target target target target dynamics standard distance distance distance distance distance distance science left presented presented presented presented presented presented present present present present present present present activation activation activation activation activation activation activation activation activation activation maximum maximum press learn learn position position position position position position position outputs outputs abstract abstract applied back back properties likelihood likelihood likelihood likelihood references important decision propagation propagation introduction hand hand hand hand hand hand hand hand hand behavior behavior behavior stimulus stimulus generated parallel tion assume assume prior representations word learned center center cases type type type type type type type required required distributed make fact fact proposed correct observed forward forward forward forward forward scale scale ing ing human human respect sum called means factor dimension dimension feedback applications relative specific specific specific specific specific specific cross receptive receptive receptive receptive receptive receptive provide provide define compute location location location location location location location location location location location location determined experimental equal mit mit accuracy accuracy accuracy accuracy accuracy fields fields fields fields train train report department technique consists internal code individual difficult exp exp exp layers layers layers layers layers delay graph cambridge computing directly directly directly directly hinton hinton hinton hinton additional additional design design design detection significant basic con randomly conditional entropy finally finally finally backpropagation backpropagation backpropagation backpropagation nature depends simply simply biological discussion technical describe group tested limited assumption corresponds amount implemented require ability ability hypothesis degree rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart noisy noisy noisy fit objective pairs pairs pairs pairs smaller underlying underlying needed jordan jordan block block block interesting ratio ratio ratio ratio character character character character character character character character character character character character character segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism database representing representing window supervised supervised idea run added architectures discussed discussed exact exact exact pair pair pair takes include pixels sense array cognitive dimensions highly conventional conventional conventional teacher approximately approximately volume positions generalized generalized williams williams organization organization entire invariant occur occur suggests spikes spikes derivative correctly correctly correctly correctly feed feed occurs occurs hardware demonstrate strength strength place minimal greater segment segment segment segment segment competitive competitive competitive exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential learns constrained sigmoidal sigmoidal demonstrated proportional turn plane relationship targets targets characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters acknowledgements appears derive solving winner changing segments implement multilayer simultaneously simultaneously text text integrated integrated integrated integrated integrated integrated integrated integrated integrated integrated adding shift overlap overlap overlap overlap overlap overlap viewed organizing centers centers activities translation translation translation normalization normalization valid david expect handwritten combinations combinations activations activations recognize recognize recognize recognize illustrated discussions major aspects aspects aspects identified identified mcclelland presentation identify detect build build build tdnn invariance invariance invariance receives kind cun interested interested interpreted interpreted interpreted interpreted dis built built sampled providing computes denker principles overlapping overlapping deal deal deal receive situations presents investigate experience difficulty rise respond fashion fashion project detectors detectors scaled scaled workshop cognition waibel waibel extremely psychology thought aspect noted logistic detector isolated isolated advanced formula unstable coded majority independence independence reasons stanford stanford straight organized mathematics recognized localized localized localized localized demonstrates qualitative peter documents effort peaks solla detecting incorporated sharp sharp robinson howard proven richard segmented segmented segmented neuro attentional summed irrelevant don indices cybern labeling ratios member recover printed printed printed printed printed printed printed grey grey grey lecun occurred held height grow interpret interpret financial connect james equals displayed lang lang histograms jackel propagated offers peterson recovery recog foundations infer properly properly properly broken broken broken projects explorations displacement outlined linked linked linked linked arcs converted microstructure pointing convenience abstraction boser causing hundred affects examining eric reject shifting num pdp convert carefully carefully individually distal worth zip france sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet refinement enforce happen ation drops intensive durbin computa trainable thousand austin austin keeler keeler keeler keeler keeler keeler keeler keeler char ters tells recognizes recognizes tance positional positional positional positional bradford sheets sheets sheets sheets sheets sheets sheets charles enforces focusing artificially translates ous february texas dence neocognitron neocognitron replaces favors unaffected enforcing hij hij stand miss touch touch touch dealt dealt lowered fukushima fukushima respects translational translational translational vast shrink desire missed encounter functioning requests notational touching touching touching touching touching touching mart expects xij xij nato jim numerals numerals numerals numerals numerals numerals numerals organize organize handles occasional mcc mcc mcc mcc mcc portant xii exemplified favoring favoring bers sumption les labor leftmost acter acter acter acter acter acter acter exponentials tremendous serf wee ual leow leow leow leow leow leow nized hartman waterloo ventional designate designate designate zipcode individ organizes simultane usefully prep telling acters acters ncr reprint saves pects balcones 
#@Keeler_J,Leow_W,Rumelhart_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input data data data data data data data data function figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training output output output output output output number system system error error error state results results results results units units units units units units units units units units units units information information information hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based space space space space space weights linear linear layer layer layer layer layer layer layer layer layer layer layer order order order order order order order shown shown shown shown shown shown shown shown shown shown systems noise noise noise weight weight neurons unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern pattern point image image image image image image image image image single single single single processing processing processing processing large rate rate rate rate test test analysis analysis analysis class class matrix matrix optimal optimal inputs inputs inputs inputs form form form form small small size feature feature work work work work task task cells cells cells step field features features features features features features features features features features features features classification classification process trained trained trained trained trained trained trained trained trained trained trained trained trained cell cell random high memory response similar representation representation representation representation representation representation show vectors vectors vectors vectors images images images images images images images images images images images images generalization generalization generalization generalization generalization generalization average average states states states term term note dimensional dimensional dimensional university university university threshold threshold computation solution research found found found found found found found found found found initial initial constant table table table table table computer computer science science science left presented presented presented activation activation low temporal temporal object object maximum range range press learn components components components components basis basis outputs sample sample abstract back back back back computational properties properties references component due due due due positive positive positive positive positive procedure procedure procedure propagation propagation propagation introduction complex hand stimulus statistical variance variance parallel change difference lower representations representations learned chosen higher higher part previous previous previous required cortex good good represent distributed distributed distributed distributed distributed expected make make make fact techniques region region correct correct errors scale simulations resulting classes tasks total total human human human human human human human human human human human human human human human human multi sum performed performed times elements regions dimension dimension dimension study negative negative negative negative negative negative negative vol represented represented compared compared receptive receptive provide provide rates rates rates proc proc proc perform perform discrete equal mit comparison comparison fields support proceedings proceedings institute words department version internal internal joint responses responses responses responses responses responses responses responses responses responses bias layers layers considered cambridge cambridge environment hinton san san san effects conference conference capacity upper full full statistics give produce produce produce produce produce channel derived clustering clustering clustering developed developed levels levels area entropy actual provided finally selected nature nature simply simply simply associative covariance feedforward describe tested limited corresponds corresponds corresponds complete surface common require main eds face face face face face face face face face face face face face face face face face face face journal journal end pixel cluster easily degree rumelhart rumelhart rumelhart rumelhart noisy sensory reduced reduced block programming empirical operation leads principal principal principal principal principal principal squared squared call international normalized early frame decay idea produced produced light predict improved separate element element similarity apply subject subject subject pixels cognitive engineering dimensions sufficient sufficient compare compare unsupervised unsupervised unsupervised unsupervised unsupervised teacher approximately subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects correspond correspond correspond pca differential achieve diagonal definition definition definition observation williams organization horizontal expression scaling scaling scaling suggests suggests matrices matrices matrices predicted alternative clusters clusters clusters white generally column conclusions clear weak constrained reduction reduction sigmoidal demonstrated california california labeled selective manner appears perception optical factors vertical dept dept category category averaging linearly dimensionality dimensionality dimensionality remaining formed formed extraction extraction yield extracted extracted extracted extracted extracted labels showed showed showed suggested discrimination discrimination discrimination discrimination discrimination discrimination past past partial partial epochs epochs epochs epochs epochs reduces purpose initially distances kohonen kohonen kohonen faces faces faces faces faces faces faces faces faces recorded perceptual perceptual thesis activations activations instances subspace recognize automatic characterized tests columns compression compression compression compression compression compression compression compression compression aspects society society included mcclelland mcclelland mcclelland presentation presentation schemes tend identity identity identity identity identity identity soc conf conf quickly kind contained neuroscience superior classify criteria categories categories categories gray gray gray automatically received extract extract extract load extend extend diego diego diego poor investigate difficulty humans humans humans humans humans humans humans preliminary respond mappings investigated fault fault combine scaled reliable proper affect affect notion notion notion momentum matched circles psychology psychology psychology psychology psychology facial facial facial facial facial perfect perfect changed eyes noted separated expressions expressions expressions expressions expressions epoch epoch submitted submitted percentage rows band defining answer answer answer correction worse nonlinearity processed purposes producing preprocessing precisely monkey describing circle circle english localized demonstrates auto auto auto annual cybernetics meaning composite applies led offset axes poorly recordings detecting maintain span span extracting fall fall prevent kinds chose credit multidimensional summed extreme lot picture acquisition room room college aligned identifying restriction ratios narrow repre wrong oja fan abilities abilities interpret nearby sanger sanger cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell carry presentations motivation motivation inferior representational representational representational male regarded demonstration captured captured reproduce viewing entries entries express eng suggesting suggesting suggesting jolla informative thresholding outlined discriminate converted listed leaming tables maximized asked asked asked munro munro munro munro randomized randomized pentland pentland propagating regularity ideally female forcing brightness publication distant compatible compatible mouth maximally confirmed macaque names names paris gender gender gender gender gender gender gender gender gender gender portions confusion confusion intl pools minor tel tel unpublished students develops tour info expense regularities bility emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion conceptual autoencoder autoencoder fill developmental pictures eliminates russell russell russell russell russell russell russell russell russell russell seattle practically evenly extracts extracts correctness colleagues zipset zipset totally relaxed relaxed relaxed relaxed relaxed materials comprised unusual mis mis sex sex verb hits eigenfaces eigenfaces localist arousal arousal gross compress claims ninth quarter cued bruce numbered parentheses parentheses articulated ratings kyoto encouragement prevented reproduction extractor descriptive kanade kanade del del calling metcalfe metcalfe metcalfe metcalfe discriminations discriminations discriminations discriminations discriminations turk turk confusions confusions males emotions emotions emotions emotions emotions emotions emotions emotions emotions emotions emotions emotions emotions desimone desimone photo bullock bullock bor bor holons holons holons holons holons holons holons holons holons holons holons holons holons holons wrap insures tense verbs females wash ast ast heterogeneity resistant social social resorting expressive grandmother grandmother grandmother garrison sts sts judgements judgements distributes albright associator associator associator sixteen lnt participating emotional emotional emotional emotional emotional emotional happy 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#@Cottrell_G,Metcalfe_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input figure figure time set set set networks networks networks networks networks networks training training training training training training training training training training algorithm output output output output output output output number system system error error error results units units units units units units units units units units units units units units units units information models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance linear layer order order order order shown values values neurons neurons neurons neurons unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach pattern pattern pattern image image image image image image image image image image image single single processing processing control large neuron rate rate test test test test test patterns analysis analysis analysis inputs inputs inputs inputs inputs inputs algorithms simple simple simple visual visual visual visual examples feature net net net net net work work work task task task task cells features features features features features level level level trained trained trained trained trained memory similar similar similar similar representation representation fixed line images images images images images images generalization average average average average states gradient note university research research connections science prediction present phase temporal temporal temporal machine press press position components components basis nonlinear abstract back back back back back back properties references ieee ieee procedure procedure important important important propagation propagation propagation propagation propagation propagation introduction action complex hand behavior parallel tion measure prior representations higher part part cases cases multiple cortex cortex cortex cortex good good binary long long represent distributed fact correct errors errors errors errors errors scale resulting tasks human human human human human human human human human human human human human human human human regression performed performed performed performed means made made study original compared application application application desired provide connected connected brain mit comparison comparison train descent nets selection proceedings report institute institute institute internal individual individual responses responses final final final scheme ai cambridge computing experiment directly hinton hinton stage efficient statistics produce produce produce coding levels levels area evidence backpropagation biological discussion normal technical tested limited stable supported face face face face face face face face face face face face face face face face face face face face face journal pixel ability ability ability instance rumelhart rumelhart rumelhart sensory needed needed fully fully programming testing york head head special special principle making making normalized early improved population exact strategy strategy include identical identical machines pixels pixels pixels pixels sejnowski sejnowski sejnowski sejnowski sejnowski cognitive compare previously previously subjects match studies williams williams williams williams williams expression expression occur suggests trial correctly correctly correctly correctly white runs minimal greater depend differences clear performs faster taking mechanisms integration presence physics sigmoidal intelligence labeled variety exist exist selective selective averaged averaged manner manner identification force question reference appears van van sequential distinct distinct category physical physical angle blocks john decreases stages communication activities activities activities activities similarly digits discrimination discrimination discrimination discrimination reasonable purpose visible assigned assigned foundation faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces transactions sciences recognize recognize recognize tests compression compression compression compression compression compression compression compression compression compression compression compression identified importance differ mcclelland identify build comparing vowel miller miller identity identity ten fine fine traditional repeated allowing anderson anderson superior superior follow criteria strategies categories gray gray gray cues cues cues cues sampled generalize absence providing providing denker leading consisted extend selectivity american american wiley transformed essential difficulty varied humans humans humans humans humans humans humans humans humans humans humans humans humans humans humans humans humans preliminary preliminary mass hall biases fewer respond fashion behavioral parity scaled scaled decisions proper proved affect cognition matched matched man facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial eyes eyes eyes eyes eyes eyes eyes eyes eyes adjusted subsets portion portion noted expressions expressions expressions consist extent utility isolated established fairly coded failure tractable correction handle london spatially preprocessing preprocessing preprocessing style monkey monkey monkey monkey acknowledgement recognized recognized recognized optimize medical medical recognizing recognizing recognizing recognizing exemplars raw argument requiring people percent prop profile posed rep outliers extensions gave gave simulator age patients diagnosis yielding lot indices sort primarily animals animals rotated rotated encoder eliminate lecun children children children children chance significance difficulties difficulties tools analogy odd determination determination hope neurobiology imply affected salk cottrell cottrell cottrell cottrell guide prentice mance perfor male male male male male male male male male male male male male consequences monkeys lawrence lawrence lawrence reproduce young cerebral jolla sons reverse characterization explorations ics discriminate discriminate zipser zipser compressed compressed leaving unable unable microstructure visually hair hair hair munro munro benefits job encodes revealed encouraging distinction lesions personal individuals female female female female female female female female female female female female female certainty reconstruct brightness alter unseen translated perpendicular werbos werbos lobe graphics mouth mouth mouth mouth mouth efforts gender gender gender ambiguous selectively apparently accounted modifiable permit ucsd served served served served served lighting identifies identifies identifies identifies influenced emotion emotion emotion jersey observers locate adult harvard bottou rare devised extracts automation judged judged judged squashing intact screen william sions drastically company accommodate voice bottleneck handbook mis mis surprise clues problematic adequately adequately parker parker subtle sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex sex discriminating rotate jenkins jenkins locating favorably disorders men men resentation friesen friesen friesen goldstein goldstein subsampled unlimited untrained untrained neurology neurology neurology rolls rolls rolls rolls agation distinctive clipped participate cardiac distinguishes distinguishes encounter trouble prototypical neck karhunen yuhas yuhas accompanied lhe lhe lhe appeal males emotions indebted joining syndrome syndrome syndrome infants torrey pines females twofold relearning social stably resorting impairment golomb golomb golomb rhesus rhesus impaired neurological defects undertaken evidently helping expres persists neuroanatomical subjectively leonard leonard emotional discrimina hitherto louis erroneously confronted women women answering chase chase psychophysiology appearances adverse extensional genetics physi wrongly mimicked timetlon timetlon cropped drown audible recalls excel inpul abstracting 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data figure figure figure figure figure figure set set set set set set set set set set networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system results units information information information information information information problem hidden performance based based space weights linear linear linear layer layer layer layer layer layer vector shown systems systems systems systems systems systems systems systems values values values values values values values values values values values weight weight weight weight functions functions method method method method method method approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern test test test test patterns analysis analysis analysis inputs form form shows shows algorithms algorithms paper paper paper paper paper paper paper paper paper paper work work work work methods methods methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step process process level level trained trained trained trained trained trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure random representation representation equation section section section section fixed rule rule rule rule rule rule rule rule rule general general generalization real real real note dimensional university university university defined defined computer computer connections connections connections connections connections connections connections connections connections present present activation activation sets sets maximum maximum maximum maximum maximum maximum maximum press abstract references due ieee important important important important introduction action statistical effect effect generated generated search search rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules higher higher part part part part part part part part previous required multiple binary binary distributed distributed distributed distributed distributed equations proposed proposed proposed proposed proposed proposed proposed proposed proposed forward minimum minimum minimum minimum total sum performed performed called called knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge relative relative relative relative relative relative relative relative relative relative relative relative relative represented represented true true true true true application application proc proc proc proc proc determined determined determined determined determined determined determined connected discrete power steps accuracy accuracy accuracy accuracy contrast connection connection institute department department technique consists consists consists consists consists code represents represents connectionist connectionist connectionist bias addition framework framework framework framework framework framework framework determine determine determine determine significant give give give give give condition condition condition derived derived weighted randomly randomly developed developed developed provided provided selected selected selected selected selected selected selected selected backpropagation backpropagation discussion group group group group group group group group group group group group group group group group group group group group group group group corresponds corresponds amount implemented eds degree degree degree degree development unknown unknown unknown unknown unknown significantly database database iterations direct expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert run perceptron perceptron exact takes takes takes reported reported practical previously conventional conventional subjects subjects calculated volume evaluation evaluation expression lead correctly correctly conclusion propose propose taking taking external external reduction intelligence user iii manner manner manner groups groups groups groups groups groups groups groups groups groups groups groups groups groups configuration base base base acknowledgements primary generating confidence confidence electrical consisting springer extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction boolean boolean select select select select select select select select select select select select extracted extracted extracted extracted extracted extracted family interpretation influence evaluate showed lee lee diagram diagram partial measurements measurements roughly false false false false false intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate assigned assigned assigned transactions transactions activations activations activations activations activations assignment assignment sciences sciences prove prove prove uncertainty absolute absolute absolute discussions tests simplicity importance importance importance importance importance importance importance importance importance importance importance importance encoded included included wij presentation conf conf conf criteria backward providing ill automatically automatically automatically consisted illustrates extract extract extract extract extract extract extract extract extend employed production environments discriminant discriminant ml int int possibly possibly integer man noted precise logic stop handle handle processed satisfied widely consequence consequence consequence consequence consequence implicit medical medical medical medical medical medical author author qualitative meaning fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy items items substantially flexible capability capability capability quantitative item employ incorporated compares schematic schematic synthesis kinds conclude comments damage patients patients patients patients proposition proposition proposition proposition proposition proposition proposition proposition diagnosis diagnosis diagnosis diagnosis acquisition ordinary generator japan japan japan japan japan databases flexibility enhancement enhancement promising stated interpret reasoning reasoning reasoning north effectiveness effectiveness effectiveness symposium infor repeat holland widrow bases bases membership draw extends extends valuable integers automated automated automated automated automated automated automated automated automated automated automated automated automated limitation linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic users validity validity validity july july adopt associate certainty valiant unseen pub uncertain concentrate paris conversely conversely conversely conversely conversely conversely truth truth truth truth truth stephen vii vii trainable thousand subjective subjective barber termination termination termination engine diagnostic diagnostic diagnostic diagnostic diagnostic proposes proposes edited tokyo explanations twelve monotone birmingham supposed sex moderately moderately facilitates gallant gallant gallant gallant gallant gallant gallant gallant disorder sixth disorders disorders disorders disorders disorders disorders incident incident incident def excluding excluding cummings engineers wji wji wji med inferences wishes propositions propositions propositions propositions fifty crisp crisp crisp crisp crisp crisp crisp crisp crisp crisp crisp crisp crisp crisp shi shi liver liver diseases diseases hen biochemical biochemical ofp visiting antecedent antecedent antecedent antecedent antecedent antecedent antecedent antecedent antecedent antecedent antecedent llll confirming lll lll professor yer hospital frameworks ork fuzziness fuzziness diagnosed diagnosed diagnosed lion lth admitted informatics embodiment embodiment hitachi benjamin ibaraki ibaraki clinically inpul 
#@Hayashi_Y,
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#*network network network network network network network network network network network network network network network model neural neural neural neural neural neural neural neural neural neural neural input input set networks networks networks networks networks networks networks networks networks networks networks networks networks number number system system system system error error error results information information information models performance vector vector vector vector vector vector vector order order order shown shown shown shown systems systems systems systems systems probability probability parameters noise noise noise noise noise method point point point processing processing large large neuron rate rate rate rate rate class class class class optimal optimal optimal optimal optimal simple gaussian small small size size size feature net net net net net net net net net net work work task points points points points points points points points points points points points points points points points field process level current current high show section line line line line line line vectors vectors vectors general general real states states theory dimensional dimensional dimensional dimensional dimensional dimensional log found found found found initial table table table table standard terms distance distance distance distance distance distance distance distance distance distance node nodes nodes nodes nodes nodes nodes nodes nodes nodes sets maximum components components components components nonlinear nonlinear nonlinear nonlinear outputs continuous abstract back find analog analog analog analog analog analog analog analog likelihood references positive positive positive important decision introduction circuit circuit circuit generated parallel complexity assume assume part previous type required good binary spike spike chip minimum minimum minimum minimum minimum minimum minimum classes classes classes classes classes classes classes classes ing feedback obtain negative negative vol application perform perform perform perform experimental constraints constraints constraints constraints constraints connected power approaches comparison nets nets nets proceedings proceedings institute institute institute loss implementation consists consists consists code code code code code code code code code code code code code code code code code code advances connectionist addition considered computing hinton san bit determine channel channel channel coding area area area lines lines lines lines lines lines lines lines lines constraint constraint limited stable stable amount generate generate generate eds square end vlsi vlsi vlsi vlsi noisy noisy noisy noisy noisy noisy simulated pairs pairs hopfield hopfield reduced technology technology technology technology interesting language numbers bits discussed typical identical sejnowski array array engineering engineering previously previously converge positions bounded bounded constructed constructed constructed constructed constructed feed touretzky touretzky width white performs constrained suggest largest demonstrated california california california proportional proportional turn plane plane plane plane plane plane plane plane plane plane manner construct construct index winner winner winner label label dept dept implement implement electrical electrical remaining remaining scales integrated integrated formed select select family family family family family codes codes codes codes codes codes codes codes codes codes codes codes soft sizes additive roughly roughly thesis inter determines columns straightforward capable differ computationally composed summary decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding contained quantization denker processors received diego powerful detail school cognition closest closest integer analyze implementations phd asymptotically indicating rows analyzed capabilities implementing constructing involve experimentally pasadena pasadena hamming decoder decoder decoder decoder decoder pick reconstructed partitions eliminate interconnected lost generality platt platt disjoint receiver combinatorial embedding corre interconnections hypercube correcting correcting correcting metrics abu abu abu abu abu abu ence summer mostafa mostafa mostafa mostafa mostafa mostafa transmitted transmitted impose hughes mini technologies technologies cube sponding impractical families families families hop clarity usefulness codeword codeword nontrivial nontrivial feasibility aip winners prime decoders decoders decoders decoders decoders decoders decoders mum intersect intersect codewords codewords codewords codewords codewords projective projective projective projective projective projective projective projective projective froin numbered interconnectivity nected ruth embed yaser xve laid intercon decodes mainstream dictate decod 
#@Abu-Mostafa_Y,Erlanson_R,
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#*network network network network network network network network network network network network network network network network model input input input input input input input input data function function function figure figure figure set set set set set set set set set set set networks networks output output output output output number system state results units units units units units units problem problem problem based space space space space space space space space weights case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown systems parameters weight weight weight weight unit method point single processing processing processing processing processing processing processing processing processing processing processing processing processing large local local local local patterns analysis analysis analysis matrix matrix matrix matrix matrix matrix form form shows simple simple simple simple simple paper paper size work work points process level level level level level level level level level level level level level level current structure structure structure structure structure structure structure structure structure structure structure structure structure similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture show equation equation equation equation equation section section section section section rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general approximation theory theory theory note activity university computation solution research independent independent independent defined sequence sequence sequence sequence constant computer terms connections node science science science left left left left left left presented presented activation nodes nodes nodes sets sets position position basis basis basis abstract properties references context context introduction complex complex complex complex complex circuit effect generated parallel parallel parallel parallel energy energy variable assume lower lower lower lower lower lower lower rules rules measure representations representations representations representations representations representations representations representations representations chosen chosen higher higher higher higher higher higher higher higher center previous previous bound bound cases type type binary binary binary binary binary binary binary binary binary long long represent represent represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed distributed distributed distributed distributed distributed distributed distributed distributed make fact techniques techniques proposed length correct ing ing total computed multi multi sum performed performed performed elements elements elements elements elements elements elements elements elements elements elements mapping mapping factor natural global negative negative original artificial relative represented represented represented represented represented represented represented represented represented represented represented represented represented represented represented true application desired objects location active active active active goal power power accuracy connection dependent dependent proceedings proceedings report words department department implementation technique technique technique consists connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist exp addition sequences considered considered framework framework framework framework computing domain domain equivalent equivalent view view bit full choice free basic basic basic con con conditional developed developed developed developed developed developed levels levels levels product product product product product product product product product product product product product product product product constraint simply simply simply simply measured measured discussion arbitrary denote transformation limited inverse assumption implemented role role role role role role role role role role role role role role role role role role role role role role role role role role role role theoretical main needed fully fully fully fully fully fully fully fully fully fully special structures structures structures structures structures structures structures structures structures structures structures structures operation operation operation operation operation operation operation operation language language leads leads representing representing representing representing representing representing representing representing representing representing representing representing representing representing representing direct making depth depth depth depth depth depth depth depth depth depth depth depth depth choose added denotes discussed exact property property separate element subject trees trees trees trees trees trees trees trees trees trees sense cognitive cognitive cognitive relevant rl rl rl rl rl rl definition positions positions positions locations locations generalized sensitive sensitive constructed constructed constructed expression matrices matrices matrices matrices rotation locally setting demonstrate critical minimal greater central numerical taking taking taking intelligence turn turn assuming assuming question construct written written written sequential generating describes label linearly linearly infinite involves adding adding agent depending viewed viewed operations operations operations operations operations operations decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition soft soft similarly allowed spaces spaces spaces add string symbol symbol construction construction building strings strings strings extension illustrated illustrated specifically absolute grammar grammar grammar grammar grammar grammar grammar major simplicity determining straightforward aspects aspects capable capable symbols efficiently essentially traditional kind allowing success interpreted built involved usual generalize binding binding principles extend transformed involving replaced limitations accurately recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive dual preliminary fewer terminal terminal terminal authors structured root root root root root symbolic symbolic cognition cognition fundamental naturally illustrate implementations rank rank rank rank rank rank rank aspect portion formal formal generates arbitrarily arbitrarily motivated sentences sentences sentences sentences sentences developing trivial coded handle nonlinearity processed turns lin formalism formalism formalism closer immediately products consequence describing implicit english preceding meaning outer greatly applies embedded embedded car car car car car car car car car car incorporated rep extracting incorporating specifies specifies sentence sentence sentence sentence sentence sentence sentence sentence sentence extreme realized phenomenon member member labelled labelled labelled labelled labelled tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor purely harmonic harmonic harmonic harmonic harmonic harmonic connecting theories smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky children children children children generality analogy replacing replacing harmony harmony harmony harmony roles roles roles roles roles roles roles roles implications canonical canonical phrase alphabet alphabet grammars child child child child child passive passive passive passive passive passive passive analyses embedding embedding corre patient respective paul colorado captured captured branching branching enable creating contraction theoretically properly contact grammatical parse captures assigns assigning linguistic linguistic linguistic linguistic linguistic linguistic linguistic multiplying listed ent equivalently deriving maximized recursively adopt sigma superimposed assignments constitutes letting massively massively manipulation gated gated permits boulder fir preserve union supporting appearing sponding sees accordance transforming builds phrases savings doesn bindings bindings orthonormal orthonormal orthonormal filler filler filler filler filler filler filler filler accomplish meeting meeting dedicated contributes sym comprising governing isolation syntactic syntactic noun noun connectionism connectionism positional positional positional positional legendre legendre legendre legendre legendre legendre legendre legendre ated verb verb constituent constituent constituent constituent constituent subtree subtree subtree lisp lisp lisp cons cons cons cons cons cons cons cons cons cons cons cons cons cons cons cons cons cons cons cons cons simula miyata miyata miyata miyata miyata miyata marker marker obeys notions literal mum resentation recursire recursire recursire recursire recursire recursire recursire recursire recursire recursire recursire recursire constituents constituents constituents constituents dissimilar atoms atoms atoms atoms atoms atoms atoms atoms atoms atoms atoms atoms atoms atoms atoms atoms claimed calculus depths depths depths depths adopting adopting linguistics conveniently conveniently syntax formedness formedness formedness formedness formedness formedness formedness formedness formedness formedness prevented ons compose compose predicate ranks cheap equiv subtrees subtrees concentrates ist subscripts subscripts subscripts notations complication designer preceded ubiquitous unspecified para obeying obeying constrains genera fillers fillers accessed tual fodor fodor fodor fodor cording atom atom atom returning critics concatenating sacrificing bolic ive pylyshyn pylyshyn reside foun deeply wear wear wear optoelectronic cdr cdr cdr cdr cdr isn reserved dations struct zed conventions yoshiro har advocates alphabetical unordered isting 
#@Legendre_G,Miyata_Y,Smolensky_P,
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layer layer case case case order order shown shown systems values unit unit unit distribution approach approach approach approach approach approach pattern pattern pattern pattern pattern processing processing test patterns patterns patterns patterns patterns analysis analysis inputs inputs inputs form form form shows shows shows paper paper examples net net net net work work task task task task task task task features classification process current trained trained trained trained trained trained trained trained trained trained trained structure random response similar representation representation representation representation representation representation representation architecture architecture rule general average states theory theory note activity activity activity activity university university university research research research found sequence target target target target table table table table table table table table computer science science science science direction presented presented presented presented presented presented presented map map phase activation low temporal temporal machine machine machine machine machine object sets sets sets sets maximum press learn position components components components abstract back back find computational convergence references component component component component procedure procedure procedure important propagation propagation propagation context context context introduction hand parallel tion difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower measure representations representations representations representations representations representations representations representations learned chosen chosen part center cases binary represent represent represent distributed distributed distributed chip fact proposed correct correct correct errors errors errors errors errors errors errors errors errors errors errors errors forward scale simulations simulations simulations minimum resulting resulting resulting ing ing total total simulation simulation sum performed made vol relative relative relative relative application desired desired provide rates perform active active approaches mit connection support train dependent source source institute department consists consists internal connectionist connectionist responses scheme framework cambridge cambridge cambridge computing domain environment hinton hinton hinton hinton view san determine determine upper full free levels types lines actual provided selected simply measured discussion describe arbitrary transformation limited limited stable finding assumed assumed generate generate generate supported role eds future rumelhart rumelhart rumelhart development pairs edge edge language language language language language language language language language language language language language language language language language squared international description pair reported practical cognitive cognitive highly highly compare tions correspond generalized williams williams grant expression expression expression correctly correctly correctly constrained encoding encoding encoding california plane relationship relationship connectivity force acknowledgements relation construct generating ann ann missing sensitivity easy interaction formed formed interpretation translation translation translation translation translation translation translation translation translation translation translation translation translation translation performing event recorded includes combinations illustrated activated activated candidate tests tests society society delta mcclelland modes comparing capture traditional road conf conf decoding decoding success hypotheses extend diego put detail respond history school mappings ideal ideal ideal ideal ideal ideal understand cognition cognition matched concepts man illustrate separated expressions expressions expressions expressions expressions finds languages languages languages languages indicating indicating analyzed fairly glass processed involve english english english english english english english english english english english english english english lowest author author meaning meaning meaning nsf varies varies percent percent elman elman tional embedded share completion incorrect schematic pittsburgh pittsburgh suited converged semantic semantic semantic semantic semantic semantic semantic semantic semantic yielding consistently room identifying feasible generator investigation extensive appropriately driving databases count repre repre encoder encoder inspired wrong wrong city attractive keeping methodology corpus corpus corpus corpus corpus corpus phrase phrase phrase phrase meaningful financial weakly contexts paul enhance demonstration facilitate competing fish eng eng eng eng eng informative tures explorations linguistic summer microstructure constitute listed ber munro munro munro munro munro munro munro 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#@Munro_P,Tabasko_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input function figure figure time time time time time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training output output output output output system system system system system system system system error results results results results units units units units units units units information models models models models models hidden hidden hidden hidden performance weights layer layer layer layer layer layer case case case case case case shown shown shown shown systems systems unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image single single single single processing processing test test test test test test patterns patterns patterns patterns patterns analysis analysis inputs inputs inputs inputs inputs inputs form form form form form form form form form form form form form form form form form form form form form form form form shows simple simple simple simple simple simple paper paper paper size feature feature feature feature feature feature feature net net net work work work work task task task task task task task task task step step step step step step features features process process process process current current current current trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure memory memory memory memory memory memory memory memory memory response similar representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture rule rule rule rule rule rule real real real term term term term term term term note experiments result university sequence sequence sequence sequence initial initial initial constant constant table table computer connections connections connections science science science science prediction prediction prediction prediction prediction prediction left left left left left left presented presented presented presented presented presented map map present present present present present present present present present present present activation frequency temporal press learn learn learn learn learn learn learn learn basis basis outputs outputs outputs abstract find computational references important important important important important context context complex behavior behavior behavior dynamic dynamic generated parallel parallel recurrent recurrent recurrent recurrent recurrent change change rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules representations representations representations representations word word word word word word word word word word word word word word word word word learned learned learned learned learned bound bound cases cases type type type type type type type type required required required distributed distributed distributed distributed distributed expected expected expected expected make make make make fact fact fact fact fact fact fact correct correct correct correct correct correct correct scale simulations simulations simulations ing tasks simulation simulation human human human sum elements elements means made natural natural natural natural study knowledge knowledge knowledge knowledge vol artificial artificial artificial represented provide constraints constraints equal power approaches approaches approaches mit larger connection connection support morgan proceedings words words words words words words words words words words words words words words words words words words words words department version version version individual advances represents connectionist connectionist connectionist connectionist connectionist difficult difficult difficult final final addition sequences sequences considered cambridge directly estimates limit san stimuli bit conference capacity capacity requires world basic produce randomly area types types types types provided provided processes processes processes processes processes evidence evidence nature depends depends achieved discussion describe arbitrary arbitrary arbitrary tested limited limited corresponds corresponds complete complete complete finding short short short short short short short common common common shape generate generate generate generate generate generate require eds ability easily degree makes makes rumelhart rumelhart rumelhart rumelhart rumelhart kaufmann account unknown interesting significantly significantly language language language language language language language language language language language language language language representing representing representing representing representing representing representing call call pre making making window attention produced produced choose predict predict predict predict improved directions directions directions robust separate separate takes takes similarity include identical identical side sense cognitive cognitive cognitive cognitive recently relevant conventional unsupervised teacher works background symmetric studied occur occur predicted touretzky touretzky touretzky touretzky boundary boundary demonstrate demonstrate runs critical place segment segment conclusions depend clear clear clear clear clear performs learns learns constrained mateo targets base question reference explicit explicit relation perception perception perception perception ways ways factors sequential sequential generating generating generating describes distinct distinct segments consisting events events events yield yield squares lee lee lee lee forms forms forms forms forms forms forms forms forms forms forms forms forms forms forms forms forms past past past past past past past past past past past past past past earlier earlier epochs event event assigned advantages combinations combinations retrieval recognize recognize recognize recognize tests successfully successfully regular straightforward capable society society mcclelland mcclelland mcclelland mcclelland mcclelland build tend fine receives receives composed composed refer kind kind cun success interested phonetic issue issue follow involved involved michael generalize generalize generalize realistic attempt consisted consisted deal deal unlike production production production production production production production production production production production production production production production production access exhibit exhibit difficulty difficulty difficulty varied humans association limitations limitations fewer respond respond giving possibility combine referred decisions symbolic complicated encode hierarchy cognition cognition cognition closest necessarily predicting equally thought portion speakers extent arbitrarily serial established languages languages languages great track handle handle considerable style consequence recognized beginning english english auto annual annual preceding preceding meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning integrating items elman elman elman conducted item variant psychological ture gen gen extensions extensions phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone kinds focused yielding sharing acquisition acquisition oxford temporally appropriately addresses addresses discover discover fails chance held familiar interpret occurring occurring fail implications effectiveness adequate child games contexts contexts tone tone irregular surprising realization offers offer matter grammatical grammatical grammatical grammatical grammatical grammatical agree generalizing default default linguistic linguistic linguistic linguistic linguistic suffix suffix suffix appeared parsing ple basically asked convenience stem stem stem stem stem stem stem stem stem stem stem experiences associate associate associate forcing options preserved exam permits token interacting argued proach investigating apparently apparently apparently apparently port port things struc learners learners deletion deletion deletion deletion reversal reversal reversal reversal reversal reversal reversal acquire sees sees continued agrees suffers mirror realizations rare rare rare meeting chan phonology phonology phonology phonology phonology america accommodate connectionism connectionism connectionism voice ings twelve faced faced semantics semantics bear convey stm stm verb verb voiced voiced medial lexical lexical lexical stems stems stems phones phones phones phones phones phones phones phones phones accepting lookahead frozen sition devel copied copied phonological phonological phonological phonological phonological phonological designated wheeler wheeler meanings meanings meanings meanings meanings meanings meanings meanings meanings meanings clarify linguistics inadequate associating prefix prefix prefix prefix prefix prefix voicing voicing voicing successes successes shortcomings succeed hoped dave saving havior pilot preceded preceded suc indebted debate morphological morphological constrains cies tense tense tense tense tense tense tense tense tense tense tense tense tense tense tense isolate verbs verbs verbs fodor fodor oped prince prince mirrors opportunities anticipatory skip zeroes infrequent helping agreed hawkins hawkins hawkins compositionality associator pinker pinker indiana pylyshyn pylyshyn accommodated blackwell engage cessfully erate existent stretches asym suffixes ena phenom bloomington unaware 
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level current structure structure structure structure structure structure structure structure structure structure structure structure structure high memory representation representation representation representation representation representation representation representation representation representation architecture show show rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule parameter theory theory theory theory theory term term note dimensional result university threshold threshold computation solution solution research research research sequence sequence sequence sequence initial initial standard standard computer science science science left left left presented map map present present activation press press basis basis abstract abstract abstract abstract abstract computational computational computational computational computational computational computational references component important important important introduction complex complex complex circuit effect generated parallel parallel parallel parallel parallel parallel cost cost cost cost cost cost cost change complexity complexity assume rules rules rules rules rules rules rules rules rules rules rules rules rules representations representations representations representations representations word word word word word word word word word word chosen higher center previous required long long long long long long long represent represent tree make make make make make make fact forward computed computed multi performed mapping mapping mapping mapping mapping mapping natural natural knowledge knowledge original specific specific represented represented compared application application constraints constraints constraints constraints discrete cortical brain power power mit mit mit mit steps steps steps support modeling morgan words implementation implementation internal advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist final final addition addition cambridge cambridge environment directly additional san bit bit bit bit bit bit bit bit bit bit bit capacity determine requires requires produce derived clustering clustering clustering levels levels levels levels area types provided finally processes processes processes processes processes processes processes processes processes constraint constraint constraint constraint simply discussion increases increases increases arbitrary limited limited corresponds surface surface surface surface short short assumed synapse role theoretical require require eds cluster makes development kaufmann typically underlying underlying account account account account account dynamical interesting projection york mechanism mechanism mechanism structures structures operation operation operation language language language language language language language language language language language details pre pre pre pre pre pre bits bits bits bits bits bits bits depth depth depth depth depth combined produced added light discussed separate separate apply apply cognitive cognitive cognitive cognitive cognitive cognitive cognitive highly volume organization sensitive sensitive grant grant constructed exists occur alternative feed touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky occurs boundary boundary setting demonstrate demonstrate half half minimal segment segment measures constrained constrained constrained constrained constrained mateo propose mechanisms labeled turn exist targets introduce question acknowledgements explicit explicit appears pro perception ways segments segments segments segments segments segments segments metric metric metric metric physical physical easy slightly slightly consisting consisting interaction adding adding adding adding formed formed national independently influence detailed operations operations operations showed suggested purpose add iterative iterative boundaries boundaries remains intermediate string string string string string string symbol assigned construction foundation david existing existing formulation strings strings strings assignment assignment assignment assignment assignment illustrated illustrated activated activated activated activated activated grammar grammar grammar grammar grammar grammar grammar simplicity simplicity determining determining determining determining middle aspects identified extra society differ computationally computationally efficiently vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel essentially allowing anderson anderson phonetic phonetic phonetic phonetic follow generative hold quantity quantity play automatically principles principles preferred unlike american difficulty circuitry circuitry strengths replaced fewer school project relationships office structured working symbolic workshop encode induction plausible onset onset onset onset onset onset onset onset onset equally portion portion portion formal mapped logic logic academic speakers motivated motivated attempts chaotic languages languages languages languages languages languages advanced stop developing derivation derivation derivation derivation derivation phenomena phenomena fairly expensive handle stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress berkeley purposes shared strictly choices nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus projected universal universal describing english preceding preceding mellon apparent greatly greatly carnegie limits reflect double syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable introducing share marked rely pittsburgh ordered ordered phonemes replace conclude utterances contribute room feasible sort assign oxford oxford ordering ordering ordering ordering concerned count naval eliminate theories proceed eliminated wrong consideration significance chains chains chains analogy primitive primitive primitive contract harmony operates grammars grammars grammars grammars grammars vowels vowels vowels vowels vowels vowels vowels vowels vowels vowels analyses analyses heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy falls falls mental mental mental buffer branching tokens express matter refers grammatical correcting exploiting exploiting exploiting exploiting designing consonant consonant papers papers default assigns counts linguistic linguistic linguistic linguistic linguistic linguistic pressure parsing parsing specification largely corporation aircraft break connec trigger trigger chicago reject alter manipulation cessing maintained permits compatible hughes scope insertion insertion insertion insertion topic nuclei nuclei deleted deleted book son son son son son son syllables syllables syllables syllables syllables syllables syllables syllables syllables permit strict handled handled handled deletion deletion deletion deletion deletion deletion deletion deletion deletion justified european phonemic phonemic proposal dissertation consonants consonants consonants consonants push phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology phonology suffice presently demands voice feasibility enforces modern counted problematic mutation insert sponsored derivations derivations derivations derivations derivations derivations derivations tightly inserted fundamentally plausibility plausibility insertions gross delete courses distinctions distinctions phonological phonological phonological phonological intervening designated structuring structuring structuring structuring structuring structuring structuring wheeler wheeler wheeler wheeler wheeler wheeler wheeler wheeler wheeler wheeler wheeler wheeler wheeler rightmost diverges linguistics linguistics linguistics transcription voicing voicing voicing voicing voicing voicing voicing voicing voicing voicing george george george george deletions expressing heads del del confused violations doctoral triggers simplistic hierarchically cited reflections eet draft referring zky rewriting beneath danger leftmost illegal grounds grounds concatenating prosodic metrical metrical proposals proposals proposals penultimate penultimate penultimate penultimate penultimate penultimate psycho psycho psycho psycho psycho psycho disappeared optional collapsing precede precede chomsky phonetics frameworks blackwell blackwell indian hayes hayes hayes inserts attract straightforwardly introductory physio physio fanout elegance failing tiers weren repaired substring 
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state state state state state state state state state state state state state state state state state results results units units units information information information information information information problem problem problem problem problem problem models hidden hidden based space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear case case case case case vector order order order order order order order order shown systems systems systems systems systems systems systems systems systems systems systems systems systems values weight weight functions unit unit unit unit unit method approach pattern point point point image single processing processing processing processing processing processing processing processing control control control control large rate test test test patterns patterns class inputs inputs inputs inputs form form simple simple simple simple paper paper examples examples examples examples small small small small net net net work work work work work work work task task methods step points points points points points classification process level level level current current trained trained trained structure structure structure random random high response response response similar similar representation architecture architecture architecture architecture architecture architecture equation line vectors images images images parameter parameter states states states states states states states states theory term note experiments experiments experiments activity dimensional dimensional dimensional dimensional dimensional result university university threshold threshold threshold computation computation solution solution research research research research research defined defined found found sequence sequence sequence sequence dynamics dynamics dynamics initial initial initial initial initial table table standard terms terms connections science science science science science science map map present phase phase phase phase phase phase phase phase phase phase phase phase phase low low low machine machine machine machine object sets sets sets press press learn outputs outputs outputs continuous abstract applied back back back back back back back find find computational computational references positive positive adaptive decision propagation propagation propagation propagation propagation propagation propagation propagation context context context context context context context context introduction complex complex complex behavior behavior behavior behavior effect dynamic dynamic parallel parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change change change complexity complexity complexity complexity complexity complexity complexity complexity variable variable rules representations representations representations word higher higher higher higher higher previous cases cases cases cases cases long long conditions distributed distributed distributed distributed distributed expected expected make region region correlation length length length length length length correct observed errors forward forward forward finite finite finite finite finite finite finite finite finite finite finite finite minimum resulting tasks computed computed sum performed dimension dimension dimension dimension feedback feedback study negative negative negative vol vol artificial artificial artificial specific specific desired define compute determined experimental related gain discrete brain power power mit mit nets modeling morgan morgan morgan proceedings proceedings proceedings report report report report institute institute words words technique consists internal advances advances advances connectionist connectionist connectionist responses final bias bias layers graph sequences sequences ai considered considered cambridge cambridge equivalent directly hinton view view view transition transition transition transition transition transition transition transition transition limit limit limit limit limit limit limit limit limit san bit conference conference conference capacity capacity capacity capacity requires significant free produce condition entropy evidence evidence nature sampling simply biological achieved discussion arbitrary arbitrary arbitrary arbitrary group group tested transformation limited inverse corresponds complete finding assumed generate supported eds eds end hypothesis hypothesis hypothesis hypothesis rumelhart rumelhart rumelhart rumelhart development dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical unknown fully fully jordan jordan jordan interesting interesting interesting interesting interesting interesting projection consistent consistent principle principle principle language language language language language language language language leads representing bits international depth added description similarity identical machines machines machines machines inference inference inference subset cognitive cognitive cognitive cognitive cognitive recently dimensions varying previously teacher calculated yields correspond correspond studies studies converge converge separation williams sensitive grant constructed studied feed touretzky touretzky touretzky loop clusters white column pass minimal minimal assumptions sigmoid sigmoid measures learns learns constrained constrained encoding hard hard physics cycle cycle cycle intelligence intelligence intelligence relationship configuration question question question question question attractor attractor acknowledgements longer longer sequential sequential generating laboratory transitions transitions transitions transitions transitions transitions ann vertical mathematical mathematical mathematical mathematical mathematical changing implement implement infinite infinite electrical involves formed boolean boolean boolean boolean cycles cycles yield national communication overlap learner controlled showed lee lee evolution understanding diagram diagram earlier earlier performing epochs epochs spaces spaces spaces initially string string construction box figures strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings subspace batch recognize recognize determines illustrated illustrated phys partially simplicity reason regular regular regular regular regular closely capable capable capable society mcclelland mcclelland mcclelland wij wij wij wij wij wij attractors attractors receives characteristic characteristic characteristic composed traditional graphs moore link link link showing generative built usual giles giles giles computes computes illustrates simpler diego powerful layered difficulty rapidly environments recursive recursive recursive scalar fashion fashion fashion fashion ideas tech behavioral behavioral parity parity parity parity parity parity parity parity parity office proper cognition cognition momentum induction induction induction induction induction induction induction induction induction induction hill hill reading onset onset automata automata automata automata automata automata automata automata automata automata rev recognizer recognizer recognizer recognizer thought bifurcation bifurcation bifurcation formal precise precise observe mapped logic nervous epoch epoch epoch epoch improving serial serial chaotic chaotic chaotic established languages languages languages languages languages languages preference pairwise guaranteed answer benchmark stress processed perspective perspective widely organized style ran arise products cut cut recognized begin geometry annual sun exemplars exemplars exemplars requiring requiring fourth geometric freeman freeman elman elman pseudo parameterized measuring chen chen sums logical logical logical proposition converged wesley extreme don don don acquisition sort addison generator guarantee modify member dynamically naval smolensky arranged climbing climbing cellular cellular kaufman kaufman kaufman accepted accepted accepted overcome odd odd odd odd odd multiplicative los los los harmony disjoint implications phrase alphabet published embedding separating falls studying induce lengths den iterated tokens tokens foundations young young insight reveals pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack jolla matter theoretically theoretically grammatical exploiting subsequently balancing generalizing mechanical mechanical ics linguistic linguistic microstructure microstructure listed accept basically leaming leaming emerge propagating arbor chaos chaos personal hundred adjustment adjustment reject remainder visited care care exclusive pdp pdp file elementary token searches eliminating relating fsa fsa individually rejected rejected argued ultimately relates regimes academy hornik worth flash distinguished electronics thousands lapedes treating supporting examination recognizers recognizers recognizers recognizers recognizers recognizers ucsd mcculloch mcculloch algorithmic fractal fractal pitts pitts generafive evolved termination termination supply returned seattle proposal huberman huberman emerges governing exploits neurobiological evolving reproduced cascaded cascaded cascaded cascaded cascaded zeros inducing inducing schreiber schreiber cuts cuts tomita tomita tomita tomita tomita physica physica cleeremans brought servan servan subnetworks elaborate elegant biophysics farber accepting ohio ohio ohio graphically acceptance acceptance saved coincidence undergoes ninth thinking hillclimbing calculus engineers tums tums specifications brains taught mere expands descriptive categorized triples cis succeeded strange restarts theme subjected alternation parenthesis longitudinal columbus columbus 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#@Pollack_J,
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data figure figure figure figure figure figure figure figure set set set set networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number error error error error units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information problem problem problem problem models hidden hidden hidden hidden performance based based based based based space space space weights weights weights weights weights weights linear layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector systems parameters parameters parameters noise noise weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution recognition recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image single single single processing processing local local local local rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis matrix optimal optimal optimal inputs inputs inputs form form form shows signal signal signal algorithms algorithms algorithms simple simple simple simple size size feature feature feature net net net net net net work work work task methods cells cells step step step points points points points points features features features features classification classification level trained trained problems random random response response response response similar representation representation representation representation representation representation representation representation equation equation equation equation fixed rule rule rule rule rule rule vectors parameter average average theory gradient gradient gradient obtained term activity activity activity activity activity activity result result result university solution solution solution solution solution solution research independent sequence initial initial table table standard standard standard computer computer science science science science science left presented map present present activation activation maximum press press press learn position components components components continuous continuous continuous sample abstract back back back convergence convergence likelihood references component component component component stochastic ieee procedure procedure procedure adaptive propagation propagation introduction estimation statistical generated parallel cost search tion tion energy measure measure measure measure measure representations representations representations representations representations representations representations representations representations representations learned learned higher part part part center cortex good represent distributed distributed distributed distributed distributed distributed distributed distributed distributed proposed proposed correct observed resulting resulting ing ing ing ing ing ing total simulation simulation called elements optimization dimension dimension orientation orientation applications study obtain obtain original original artificial relative represented represented active constraints connected discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete approaches approaches approaches comparison connection connection connection update update train train descent descent descent morgan morgan proceedings proceedings institute department version technique consists consists code code code code code code code code code code code code advances joint represents connectionist difficult final scheme scheme maps framework framework computing computing environment additional solutions limit san stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage bit bit bit bit conference conference conference significant basic increase con con coding clustering levels levels product processes selected backpropagation constraint constraint simply simply simply simply simply biological achieved measured measured normal feedforward describe arbitrary arbitrary transformation transformation transformation transformation transformation transformation transformation transformation transformation finding finding supported require eds pixel pixel pixel pixel pixel pixel pixel pixel cluster cluster cluster cluster degree rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart development development kaufmann kaufmann objective underlying combination reduced account account programming ratio ratio ratio trials trials trials principal inhibition bits bits bits bits bits bits international international supervised idea idea idea idea idea idea idea attention minimize denotes architectures improved property takes element similarity apply introduced include identical side side hierarchical inference cognitive cognitive cognitive dimensions previously conventional conventional unsupervised unsupervised unsupervised unsupervised unsupervised axis axis tions yields achieve observation generalized generalized grid organization storage sensitive grant grant lead lead studied suggests suggests extended digital deviation rotation rotation alternative feed locally touretzky clusters clusters clusters clusters clusters clusters valued valued valued depend competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive clear performs performs mateo suggest suggest encoding encoding encoding strong external intelligence turn manner connectivity force force acknowledgements pro pro construct construct construct index index winner winner winner winner primary distinct explicitly explicitly involves transformations easy easy consisting develop develop develop mutual quality competition independently review reconstruction reconstruction stages stages stages stages stages stages stages stages stages stages stages stages viewed codes variation variation variation variation centered forms soft soft activities activities translation translation partition earlier performing performing sec purpose iterative iterative iterative initially foundation norm kohonen kohonen includes extension extension extension extension activated mozer mozer mozer mozer mozer variations reason reason compression compression compression compression compression compression compression compression compression compression compression compression compression selecting aspects aspects society encoded literature literature efficiently schemes post situation essentially essentially composed capture capture capture capture traditional compact compact compact allowing dis dis content content follow gray gray gray notation michael backward providing quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization moves subsequent extract software situations explore remain powerful powerful transformed varied put strengths strengths strengths strengths optimized helpful rise fewer tech detectors encode encode encode encode cognition patch patch patch transmission analyze analyze equally aspect der der noted algo explored detected detected attempts optimum mentioned distinguish guaranteed baum turns turns rapid perspective tive tive tive forces located mation pool pool pool pool pool pool consequence potentially universal grossberg grossberg describing gradually begin patches patches depicted depicted cybernetics nsf alignment raw readily readily variant ity partitioning partitioning summarized ture incoming extensions comments decreased specifies specifies summed consistently secondary secondary leen forming forming formally formally rithm rithm rotated concerned reconstructed discovery discovery discover discover eliminate smolensky inspired extending fails promising striate los interpret obtaining removing sanger sanger sanger sanger cottrell cottrell cottrell cottrell cottrell cottrell cottrell infor james iteratively iteratively paul surprising pat von von lang topological colorado heart captured captured captured captured captured originally dif viewing winning winning winning winning winning april augmented partitioned variants variants captures discovered generalizing avoiding vari dividing dramatically zipser zipser zipser zipser compressed compressed compressed compressed shading ter vec achieving munro munro presenting uniquely retraining connec malsburg malsburg classifies classifies tor experiences hillsdale discovering discovering discovering discovering reconstruct reconstruct representa principled principled quantized quantized mutually exclusive exclusive chauvin cessing cessing boulder rectangle rectangle rectangle retain iri win constructs constructs translations alternatives pools pools pools pools pools pools inverting permit durbin durbin bridle bridle served fortunately corners justification mcdonnell terns converging spring ferent todd virtually autoencoder optima subtracting subtracted ally ultimate zipset zipset convention proves neurobiological tance constraining icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl icl demands steve facts facts discovers discovers discovers discovers experimented elaborate putational virtue lynch lynch sixth compress mention dilation dilation leaky subtract solu numbered clus ponent adopting reconstructing subtraction proaches proaches recon struction stant nique invoked awi awi granger granger snowbird neur gary reformulation formalize nonoverlapping timal eleventh bringing kybernetik trast factoring quantize cod collapsed carded ach recoding loga utah sharkey rehfuss competi competi competi altos petitive supplement ablex iwi lwl spective norwood outper tivities 
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local local patterns patterns patterns patterns patterns patterns analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs form simple simple paper paper paper paper small work work task task task task task task task methods methods features process process process process process process process process process process process process process process process process process process process process process process level random high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response similar representation representation representation representation representation representation architecture show show show vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors theory term term note note note note note dimensional dimensional dimensional dimensional dimensional dimensional university university research research research research defined target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target dynamics initial table table computer computer terms terms terms terms terms terms terms terms terms terms terms terms science science science science direction presented presented presented presented presented presented presented present present activation activation activation low low low sets sets sets sets sets range range range basis outputs abstract find find find computational computational properties references important decision decision introduction effect dynamic generated parallel parallel parallel search search search search search search search search search change difference difference assume representations representations representations representations representations word word word word higher part part part cases required required required required binary represent distributed distributed distributed distributed distributed distributed distributed expected expected correlation correlation correlation correlation probabilities probabilities probabilities probabilities probabilities simulations simulations simulations resulting tasks tasks tasks tasks simulation simulation simulation simulation human human human human human computed multi sum sum sum performed performed times means means made applications study knowledge knowledge filter original represented represented represented represented represented represented compared application cross cross cross cross cross cross cross cross cross cross provide provide perform determined experimental experimental experimental related morgan proceedings report department implementation technique technique individual joint connectionist connectionist connectionist connectionist addition addition addition addition addition addition addition addition addition cambridge cambridge computing computing computing computing computing equivalent equivalent hinton hinton san stage stage stage stage determine requires requires requires choice approximate produce produce produce condition weighted weighted weighted weighted randomly levels product product product product product product product product product product product product product product product product product product product product provided provided processes processes processes processes processes processes processes processes processes selected selected evidence evidence evidence associative associative associative associative associative discussion discussion technical describe tested assumption finding short effective supported eds journal rumelhart rumelhart rumelhart kaufmann pairs pairs smaller underlying combination combination combination combination combination combination combination combination fully fully jordan interesting structures trials trials operation operation details pre direct direct direct direct direct direct direct direct stored normalized idea attention produced produced produced description advantage advantage separate separate separate include subject subject subject subject cognitive cognitive calculated match correspond sparse sparse address definition definition definition storage storage storage studied studied scaling scaling trial alternative alternative alternative alternative alternative alternative touretzky generally column demonstrate demonstrate demonstrate strength strength critical critical row weak weak constrained mateo taking strong strong strong characteristics demonstrated demonstrated proportional proportional targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets question acknowledgements appears longer perception winner ways sequential generating ann recall recall recall recall recall recall recall recall recall implement explicitly simultaneously slightly unique formed formed formed formed select select competition john national focus formation review review detailed transform operations operations restricted approximations sizes additive additive additive additive combining combining intermediate intermediate filtering foundation box box box combinations activations coordinate retrieval retrieval retrieval retrieval activated discussions major reason identified extra closely encoded mcclelland post situation orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal strongly strongly strongly strongly strongly strongly anderson anderson lie contribution cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues list involved michael michael michael dot paradigm paradigm paradigm paradigm surround consisted extend employed employed production production access access access access access access access access access access access access access access access access access access access access access access access access access access access access access investigate relations involving involving strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths strengths association association association association association association issues dual behaviour successive school ideal scaled scaled cognition cognition smallest act act naturally necessarily extremely psychology psychology psychology created created implementations rank rank preference preference distinguish multiplication multiplication multiplication multiplication multiplication implementing arc arc arc arc arc arc arc producing filtered filtered incorporate products implicit demonstrates auto auto auto auto auto auto auto auto outer outer outer outer robustness requiring requiring questions considerably composite composite composite composite limits simulate simulate lack psychological psychological psychological requirement calculating aim enables coherent comments semantic semantic semantic semantic don forming linearity tensor tensor tensor tensor tensor jones jones extending stronger occurred multiplicative operates weakly weakly weakly weakly weakly weakly respective dominant demonstration claim multiplied winning foundations creating arrows extends relies grants intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection intersection explorations default default empty mind multiplying multiplying multiplying associations associations associations associations summer microstructure logarithm rubin rubin fellowship email asked asked july incrementally medium arbor solely australia remainder mutually learnt paired host complementary associates associates paradigms paradigms union october simplifies answers served preserves council australian australian insufficient builds jointly orthonormal orthonormal conceptual award anthony retrieved retrieved retrieved retrieved retrieved retrieved retrieved explanations transpose transpose constraining iti iti creation feasibility categorical occurrences recalled recalled allowable talk wiles wiles wiles wiles wiles wiles wiles wiles wiles wiles wiles dyer dyer simon tit tit lexical decompose histories competence cancel cancel cancel disadvantages retrieve retrieve respects traditionally humphreys humphreys humphreys humphreys humphreys humphreys humphreys humphreys humphreys humphreys humphreys humphreys humphreys humphreys concurrently bind viable strongest strongest cued cued cued cued distinctive temporary temporary temporary temporary elicited analysed michigan psy isomorphic ghost ghost implication queensland queensland posner blend blend blend retrieving pauses departments intersections logarithms sussex accessing accessing associator associator associator associator wallace wallace dennis dennis dennis dennis dennis dennis dennis dennis janet ritz ritz stewart behaviours episodic procedural qld blends roland postgraduate 
#@Bain_J,Dennis_S,Humphreys_M,Wiles_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data data data data function function function figure figure time time time time time time time time time set networks networks networks networks networks networks networks output output number number number number number number number state state state state state state state state state state state state results results information problem models models performance performance performance performance performance performance performance based linear linear case case vector vector vector vector order order order shown shown shown shown systems values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability parameters noise noise noise neurons neurons neurons neurons neurons recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point control local neuron neuron neuron neuron rate test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix optimal optimal inputs inputs paper small size size net work work fig fig step field field field field field field field features features process process process level level random high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response similar similar representation show show equation vectors general general parameter parameter parameter average average states states states states states states states states theory obtained term note experiments result university university university threshold defined defined defined found found found found dynamics initial initial initial initial initial initial computer computer computer distance distance distance distance connections connections connections synaptic synaptic synaptic synaptic synaptic science science science left left presented presented presented presented phase phase phase phase phase phase phase phase low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency range range range range position components abstract find convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties references stochastic ieee context context context context context context context context context context context hand behavior statistical statistical effect effect effect effect effect effect dynamic generated generated generated generated generated generated change change change energy energy variable assume lower lower word word word word word word word learned learned learned learned learned learned learned learned learned higher higher higher previous firing required binary binary distributed expected correlation length length length length length length length correct probabilities simulations simulations ing ing tasks tasks total total simulation performed performed performed performed orientation relative relative represented rates proc perform determined experimental experimental experimental experimental experimental experimental goal related connected steps larger connection support dependent modeling modeling modeling modeling modeling selection report words words words words words words words words department department synapses consists exp delay delay addition considered considered considered framework framework equivalent curve additional additional additional limit effects capacity capacity significant free speed estimated estimated estimated basic basic increase increase randomly randomly randomly levels levels levels levels levels area selected evidence iteration nature depends depends associative associative associative achieved measured technical increases increases increases denote transformation inverse assumption corresponds stable stable stable stable stable stable stable nearest nearest nearest nearest assumed assumed assumed assumed main main main journal journal ability ability ability degree including including including simulated smaller hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield account account account account fully interesting significantly increasing increasing increasing mechanism uniform language language representing representing call numbers iterations iterations iterations iterations iterations pre stored stored stored stored stored stored stored stored stored stored stored stored stored stored stored bits bits bits decay minimize added sources description description discussed improve exact exact takes takes element include period period relevant sufficient approximately works studies converge converge modified bounded interval interval interval storage storage increased increased increased increased increased increased exists expression concept scaling wide wide predicted width demonstrate strength strength starting critical critical critical place differences differences faster temperature encoding encoding encoding encoding encoding taking taking external external external external external demonstrated demonstrated exist decrease decrease relationship minima question denoted attractor attractor attractor attractor attractor attractor attractor monte carlo longer solving estimating estimating ann ann ann ann ann stability stability mathematical mathematical distinct dept modeled modeled recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall explicitly infinite physical formed shift shift shift shift shift shift shift implies expectation decreases decreases decreases decreases yield expressed formation review review overlap overlap overlap overlap overlap overlap overlap overlap forms converges converges allowed reasonable classical iterative remains remains string assigned assigned transactions usa retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval inter inter sciences sciences sciences sciences memories memories memories memories memories memories memories memories memories memories phys phys characterized characterized characterized tests tests tests successfully successfully determining aspects aspects letter maximal presentation presentation presentation presentation presentation successful successful successful successful successful successful successful successful successful successful successful successful successful successful attractors literature post comparing situation reached reached reached composed strongly strongly prob success interested cue cue cues cues list list list list list list list correspondence leading load load load load load load load load decreasing presents access access relations relations association rise school school investigated biol cognition cognition cognition analogous examined coefficient possibly psychology psychology rev rev amari spin asynchronous asynchronous asynchronous growing phenomena phenomena slope failure failure failure failure failure explanation analytical glass considerable projected recognized acad describing beginning beginning recognizing radius radius meaning meaning explained people items items items items items lack quantitative quantitative poorly item item item item item completion completion psychological psychological psychological psychological psychological psychological psychological psychological psychological passes rely ture qualitatively qualitatively qualitatively collective collective hamming hamming decreased decreased age age attraction attraction attraction attraction attraction attraction attraction attraction findings findings findings begins semantic semantic semantic yielding phenomenon phenomenon phenomenon phenomenon cybern formally linearity nat occurred abilities monotonically monotonically monotonically motivation sompolinsky excellent corre equals pat sim originally enable enable enable israel israel recog mem mem reader refers storing storing proximity lett acknowledge ccd ics associations associations maintaining appeared shorter basin emergent emergent emergent presenting nelson nition obtains corrected resting basins basins basins basins basins basins examining demon acting modifying gained continues maintained allocated allocated allocated jij denoting rejected surrounding scope flip increasingly deleted termed accounted accounted accounted reciprocal supporting examination tel tel tel tel tel wider picking laws palmer externally terns hop hop hop hop hop hop hop ruppin ruppin ruppin ruppin ruppin exper venkatesh intact intact arrives ory frequent accounting encodings reviewed sid memorized bear ous aviv aviv aviv aviv aviv fore thc thc moderately distractor stabilizing severely meaningless tutorial tutorial stand retrieve deeper deeper examines examines activating decrement neurodynamics cued cued spontaneously mild lacking faculty faculty fragment fragment expressing strated posner mceliece weakened amir dur gutfreund linkage flipping flipping till till till aging aging recalling maintenance eytan estimations paragraph kom wei flipped pertaining pertaining prospects chronous ction phe parabolic older taining equency imental wet deteriorates associational rodemich asyn ena phenom timer shallower nomena cil tempera netwo controversial ilarity ove atio substring attenuate 
#@Ruppin_E,Yeshurun_Y,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input input input data data data data function function function figure figure figure figure figure figure figure figure figure time time set networks networks networks networks networks training training training training training training training training output output error error error error error results results results results information problem problem models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based based based based based based based based space space space space space weights weights weights weights weights weights linear layer layer case case order systems values values values probability probability probability parameters parameters weight weight weight functions functions unit recognition approach pattern single processing processing processing neuron rate rate rate rate rate rate rate rate patterns analysis optimal form form form form form shows shows shows shows shows algorithms simple simple simple gaussian paper feature work work work task task methods fig points classification level trained trained high high memory memory memory memory response response similar similar similar representation representation representation architecture architecture architecture architecture architecture architecture show show show show show equation equation equation fixed fixed fixed line line rule rule rule rule rule rule rule general general generalization real real theory theory gradient gradient gradient gradient gradient experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university university university university research research research research found constant constant constant constant standard standard standard standard standard standard distance node node node node node node node node node node node node node node node node science science science science science science left left left left presented map map map activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency press press press learn learn learn learn position position position basis basis basis continuous abstract applied back back back back back back back back back references positive positive adaptive adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation context introduction hand hand behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus parallel parallel parallel tion tion change rules rules rules representations representations representations learned learned learned learned learned learned learned learned part center cases cases cases cases cases cases cases cases cases binary binary distributed distributed fact probabilities observed errors forward ing human human human human human human human human human human human human human human human human multi multi multi multi sum sum sum called called called times mapping dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made applications applications applications negative negative vol vol vol relative relative relative relative represented represented compared compared series rates rates determined determined goal related constraints constraints connected brain mit mit mit comparison connection connection support descent descent morgan report report words department technique internal advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist exp exp exp exp exp exp exp ai ai considered considered cambridge cambridge hinton hinton san top top stage stage stage stage stage stage stimuli stimuli stimuli effects determine choice free increase con evidence corresponds predictions common supported main eds eds square rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart including including kaufmann probabilistic probabilistic combination combination account account unknown block significantly ratio york increasing mechanism structures structures structures language squared details call international bottom bottom early early magnitude attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention predict recent similarity similarity similarity similarity similarity similarity similarity similarity similarity cognitive cognitive cognitive cognitive cognitive relevant relevant relevant relevant dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions varying previously subjects subjects volume axis axis axis axis match correspond diagonal diagonal positions generalized williams williams storage grant exists horizontal horizontal scaling scaling scaling occur trial trial feed touretzky boundary boundary strength strength strength strength strength greater greater valued valued valued accurate exponential learns learns learns learns constrained mateo california radial radial decrease relationship identification program program program base base base base base base base base question denoted denoted denoted denoted denoted longer sequential vertical vertical metric metric metric category category category category category category category category category category category category category category category category category category category category category category category category category category category category category category category category category category category category linearly frequencies john national review detailed detailed open similarly suggested constants past past past spectrum dashed dashed fitting fitting remains initially euclidean advantages classified classified building activations activations usa retrieval assignment sciences activated activated mozer mozer candidate candidate domains reason regular determining determining encoded driven driven driven mcclelland mcclelland mcclelland mcclelland mcclelland situation tend orthogonal ten summary quickly strongly allowing dis classify categories categories categories categories categories categories categories categories categories categories categories simplified decreasing modelling modelling situations situations situations situations law simpler simpler unlike unlike unlike unlike unlike difficulty difficulty rapidly strengths strengths strengths association association association association association association association integral accurately fewer behavioral investigated cognition analogous concepts man psychology psychology psychology panel panel panel assumes explored separated separated mapped mapped mapped mapped mapped academic improving motivated motivated established established indicating separable separable track tractable comparisons perspective perspective berkeley easier easier broad universal english addressed exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars reflects apparent people people prop prop evaluating double double double profile relevance relevance axes cohen cohen posed marked marked dots dots psychological psychological psychological psychological psychological psychological psychological psychological psychological summarized incorporating adjust conditioning attentional attentional attentional multidimensional irrelevant irrelevant irrelevant irrelevant shifted shifted acquisition sort primarily writing summing discover smolensky smolensky exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar arranged multipliers fits fits bower bower bower bower bower bower bower bower difficulties difficulties occurred mail city city grow keeping corpus eqn motivation interference interference interference irregular irregular irregular sion intended demonstration arrangement arrangement reproduce dif specificity extends extends captures generalizing associations associations unable shepard shepard shepard shepard shepard shepard shepard shepard shepard covering covering covering encodes propagating classifications classic associate gated exclusive goals allocated carefully rectangle ullman gluck gluck gluck gluck gluck gluck gluck categorization categorization option behaves status challenge fat corners ferent hid hid harvard rare rare neglect neglect neglect neglect neglect dissertation assessment marcus marcus explanations frequent reflection connectionism connectionism presently scatter robustly catastrophic catastrophic indi health subtle verb verb verb jenkins jenkins campbell biomedical ver forgetting psych psych psych illustrating shrink dissimilarity agation rosen unequal trimming neglecting concluded allocate stretch susceptible acknowledgment doctoral doctoral exceptions exceptions exceptions occasional cate skeletonization attend lengthy mecha kruschke kruschke kruschke kruschke kruschke kruschke kruschke kruschke kruschke kruschke kruschke kruschke kruschke kruschke kruschke tense tense verbs verbs verbs verbs verbs verbs cated straint differentially undertaken wished quarterly institutes pinker indiana indiana indiana indiana monographs trail nism occurence oval psychologically challenged surpass wkj wkj jtn jtn jtn atten ena phenom construed construed exceptional exceptional bloomington alluded diagonally gories nia ove 
#@Kruschke_J,
#t4
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time set set set set networks networks networks networks networks networks networks training training algorithm number number number number system system system system system system results results results results results units units units units units units units units units units units units units units units units information information information information information problem models models models models models models hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based based based space space space space space space space weights weights linear linear linear linear linear layer layer layer layer case case order order order order order shown shown shown shown shown shown shown shown systems probability probability noise noise functions functions functions functions functions functions functions unit distribution distribution distribution distribution recognition recognition approach approach pattern pattern pattern point point processing control control control large large local local local rate test test patterns shows simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper size size size size size feature feature task task task task task task task task task task points field features features features classification classification classification classification classification classification level current trained memory memory memory memory response response similar similar similar similar representation representation representation representation representation representation architecture show show show equation section section fixed rule rule generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech approximation average theory theory theory theory theory theory theory theory theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained note note note note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university university university computation research research log log log found standard standard standard distance distance distance distance distance distance distance distance distance distance node science science science science left left present present present activation activation activation nodes nodes nodes range range range learn learn learn basis continuous continuous continuous continuous continuous continuous continuous continuous abstract back density density properties properties likelihood references component due important important important important important adaptive adaptive adaptive decision propagation context complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic search difference spatial assume assume assume assume assume assume assume assume assume measure prior learned learned higher center center cases cases cases represent distributed make fact region region region region region region region region region proposed errors errors finite minimum tasks tasks tasks tasks human human human human human human human human human multi multi regions regions regions regions regions regions regions regions regions regions regions regions mapping reinforcement reinforcement dimension dimension dimension dimension dimension made orientation global global global global global knowledge knowledge original relative relative specific specific specific specific represented represented compared compared compared compared series receptive receptive receptive receptive provide location location location active experimental constraints distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions discrete discrete discrete discrete brain power power comparison fields fields fields support support support support descent descent report report report report institute version version version internal internal represents connectionist connectionist connectionist difficult final final scheme cambridge computing domain directly curve curve curves top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects significant significant significant significant significant significant approximate approximate approximate speed produce derived derived weighted weighted weighted conditional levels controller lines lines provided evidence backpropagation measured technical technical technical arbitrary group fast close close close complete circuits rbf amount amount common common effective shape shape shape shape require main eds journal journal journal ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis probabilistic pairs underlying reduced account unknown character york special trials uniform empirical language leads representing representing representing max pre pre bottom bottom frame frame decay decay decay decay attention attention attention light advantage property property pair robust robust typical similarity similarity similarity similarity similarity similarity similarity similarity similarity reported strategy moving moving cognitive cognitive recently dimensions dimensions dimensions compare compare subjects subjects subjects subjects subjects volume correspond positions locations locations symmetric observation bounded increased lead lead invariant scaling wide correctly locally runs minimal assumptions assumptions conclusions competitive central differences measures moody moody moody exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential integration solid solid radial assuming assuming variety selective relationship iii iii groups explicit appears derive derive derive derive construct construct construct ways laboratory tuned implement implement multilayer multilayer multilayer multilayer category category category category category linearly linearly linearly linearly linearly linearly unique integrated events expectation competition competition competition competition competition competition competition yield dependence review squares overlap overlap densities open evaluate centers forms forms forms static sizes classical classical expansion expansion fitting event event event event event event event event distances distances transactions thesis thesis combinations priori color color inter weighting weighting sciences variations black gamma closely suitable society encoded delta presentation successful successful literature composed composed contained contained showing neuroscience cue cue cue cue cue cue cue cue cue cue cues cues cues cues generalize generalize generalize absence providing providing minimizes hypotheses overlapping overlapping deal law law unlike unlike american investigate investigate difficulty difficulty difficulty exponentially relations humans hanson hanson hanson hanson hanson hanson hanson hanson association integral limitations mass mass mass mass mass successive fashion project behavioral behavioral investigated reliable circles patch measurement gradients gradients gradients gradients trace possibly psychology illustrate equally equally equally subsets versions assumes logistic logistic shapes shapes switching extent electronic averages percentage separable separable separable separable separable separable separable separable separable separable orientations variances variances failure nowlan nowlan lies comparisons considerable stanford berkeley hyperplane hyperplane controls consequence consequence consequence consequence recognized involve involve universal universal toronto localized radius robustness geometric geometric evaluating items items axes lms backprop backprop psychological psychological psychological psychological psychological psychological psychological psychological differs monotonic resource curvature hamming hamming kinds expectations conditioning conditioning conditioning begins acquisition classifying proportion cooper cooper equivalence princeton princeton princeton arguments animals resources member hyperplanes food theories exemplar exemplar outcome rational allocation bower bower bower bower bower numerically darken darken darken siemens nearby mark reasoning implications implications implications effectiveness generalizes generalizes generalizes overlaps cerebellar heavy cmac widrow widrow spherical spherical spherical spherical spherical spherical spherical bases similarities contraction record contact impact implicitly dense discriminate metrics metrics associations unified slight shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard deriving deriving leaming leaming leaming leaming emergent propagating pointed medium classifications classifications classifications generalizations molecular constrain acting elementary activate bounding kanerva kanerva wise gluck gluck gluck gluck gluck gluck gluck gluck gluck gluck retain overhead categorization categorization categorization categorization categorization constructs constructs manipulator nonetheless drops radio dichotomies dichotomies dichotomies spite cube tail stephen corporate confirm albus albus burr burr burr wiring wiring rare lightness concert norms norms decaying concave convention convention adapts niranjan niranjan articulation resultant cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy cauchy compromise derives derives adequately hoff hoff tails tails wagner wagner jenkins jenkins crg fallside fallside broader activating extremes rescaling possesses possesses nonlinearly favorable cued engineers engineers separability pattem pattem hypersphere unequal encounter stars indistinguishable bellcore organism organism organism embodied reconfigurable rutgers adaptable attack comers conjunctions embodies integrations consequent shrinking hue kruschke shadow adults memorization radii contrasted differentially western pattems upwards easiest roger century shadows rescorla contingent reverses monographs pavlovian depiction leam jos hardest heavier heavier fare backpropogation newark unfavorable appleton crofts mathematica deduction conforms prokasy 
#@Gluck_M,Hanson_S,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural input input input input input input input input input input input input input input input input input input input data function function function function function function function figure figure figure figure figure figure figure figure figure figure set set set set set set training training training training training training training training training output system system error results results results results results units units units units units units units units units units units units units units units units units units units units units units information information information problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based space space space space space space space space space space space space space space space space weights weights weights weights weights weights weights linear linear linear layer case case case order shown shown values values probability probability probability probability probability probability probability noise weight weight weight functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution approach approach point point point single single single local rate test test analysis analysis class optimal inputs form form form form shows simple simple simple simple paper size size size net work methods methods features classification classification classification classification classification classification classification classification classification classification classification classification level level level level level level current current random response response response response response response response response response response response response response response response response response response similar representation representation representation representation fixed fixed rule rule rule general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter approximation average theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory gradient gradient gradient gradient obtained obtained obtained obtained result university university computation initial initial initial estimate estimate estimate distance distance distance connections connections connections connections science science science science direction presented presented present present present present present activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation object object object object object object object object object maximum maximum press press learn basis basis basis abstract back back density references positive positive positive positive positive positive positive positive positive positive positive positive positive positive important important adaptive adaptive propagation action complex complex behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus dynamic parallel change change change change lower measure prior prior prior representations learned learned higher higher higher higher part previous previous previous cases cases cases represent represent bayesian region region region region region region region region proposed probabilities probabilities probabilities probabilities probabilities errors scale simulations simulations simulations simulations minimum resulting simulation simulation simulation respect respect regions regions regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement factor potential potential natural natural natural natural natural natural natural knowledge knowledge obtain negative negative negative negative negative original artificial artificial receptive provide provide objects objects objects objects location location location experimental experimental experimental connected discrete power larger contrast connection connection connection connection connection connection connection connection fields nets selection morgan proceedings department department implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation internal individual individual individual individual individual individual individual individual represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist responses responses layers layers scheme addition considered considered cambridge cambridge hinton hinton hinton additional curves curves stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects conference choice choice choice world world basic increase con derived conditional lines entropy entropy actual finally finally nature simply close assumption corresponds corresponds corresponds finding amount assumed shape shape shape shape shape supported eds eds journal journal journal square ability degree rumelhart rumelhart rumelhart rumelhart rumelhart kaufmann account unknown unknown fully empirical empirical direct decay decay decay decay idea attention attention attention produced produced property takes similarity similarity similarity reported subject subset subset subset sejnowski array recently sufficient previously approximately volume volume tuning tuning tuning tuning tuning yields yields correspond locations locations generalized williams williams increased grant concept scaling scaling touretzky boundary boundary boundary boundary generally greater hebbian depend peak exponential exponential exponential exponential exponential exponential exponential mateo integration integration presence physics intelligence intelligence radial turn relationship manner identification identification acknowledgements sequential describes describes ann mathematical distinct metric category physical remaining consisting formed competition yield national national review depending stages overlap evolution evolution sizes sizes sizes suggested allowed allowed discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination reasonable reasonable epochs epochs spaces event purpose boundaries boundaries boundaries remains assigned assigned foundation david exploration includes priori extension uncertainty activated activated candidate differ delta presentation genetic situation situation situation situation miller miller miller ten fine fine fine fine fine compact compact compact kind kind kind repeated induced generalize absence absence principles principles principles illustrates illustrates subsequent situations presents law unlike american exponentially exponentially exponentially exponentially relations relations hanson hanson association association preliminary rise successive successive respond giving school notion math concepts plausible plausible predicts psychology psychology psychology psychology illustrate created panel panel panel panel panel panel panel panel panel explored shapes extent simplest submitted explain plant optimum optimum optimum integrate animal ment slowly derivation derivation phenomena explanation stanford stanford closer easier located probable consequence consequence consequence consequence consequence consequence consequence universal universal beginning arises author preceding empirically elman quantitative quantitative quantitative psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical slower treated sharp sharp biologically psychological psychological psychological psychological psychological psychological schematic gains summarized gen fall fall fall fall fall fall serve kinds kinds kinds conclude decreased shaped shaped shaped eventually multidimensional multidimensional multidimensional cumulative sharing secondary proportion proportion cooper member connecting outcome outcome outcome establish ranges analogy height height mark belong implications implications implications guide date exploring overlaps overlaps overlaps overlaps separating falls falls representational representational representational representational representational representational representational representational representational representational representational representational cone cone cone cone cone cone cone connect encountered encountered encountered induce mental uni facilitate spherical advance advance treatment considerations explorations explorations compressed summer drop drop shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard latency july emerge propagating classifications classifications arbor solely individuals simulating massively favor geoffrey gener gener mathematically guidance proba regularized relating gluck gluck gluck gluck categorization categorization sized tones differing differing wider challenge lecture fortunately remarks regularities regularities bility accordance accordance todd todd evolved steven russell russell harvard concerns concerns continuum continuum continuum sharply agency meeting successively successively successively cones systematically attenuation attenuation confined accounting approached discovers deciding propagates propagates propagates localist newly newly upward remarkably heights heights chang chang alization alization decrement mediate eralization sought latencies philadelphia jonathan justify michigan ism isomorphic concluding nadel superficial slowing outward comment asymptote decayed discrim bachrach sional advocated connecfionist connecfionist connecfionist connecfionist reid stretching roger tending interspersed mensional encounters encounters inpu progressive proceeded dispersed embodiment embodiment bns awj entail neurophysiologically neurophysiologically multidimen connectionists 
#@Kannappan_S,Shepard_R,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model model neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number number number system system system system system system system system system system system system error error error results results units units units units units units units units units units units units units units units units units units units units units units units information problem problem problem problem problem models models models based based based space space space space space space space space space weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear case case case case case case order order order order order order order shown values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method method method method approach approach single single single single control large large large large large large large large local local local local local local local test optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form shows shows signal simple simple simple examples small small small small small small size size methods methods step step step points classification process process level problems problems problems problems random high high high high high high response response response response similar representation architecture section section section section line generalization generalization parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average theory theory obtained obtained experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university variables variables variables variables computation computation independent target target target target target target initial initial constant constant constant constant estimate estimate standard standard computer science prediction prediction prediction prediction prediction left low low sets sets maximum maximum maximum press learn learn basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous sample sample sample sample abstract applied applied applied back computational properties references references component stochastic ieee procedure procedure procedure procedure procedure procedure procedure important important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction hand hand hand hand statistical statistical statistical effect generated variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable signals signals representations chosen chosen chosen part part center center previous previous previous previous previous previous required required multiple good good binary represent tree fact fact region region region region correct observed observed resulting total total regression regression regression respect respect sum sum called called regions regions regions regions regions regions regions regions regions regions optimization optimization optimization optimization potential potential potential global global global applications study knowledge vol vol artificial relative represented represented true true true compared compared compared application application cross cross cross series series provide provide define location perform determined goal goal goal goal gain power power accuracy accuracy accuracy accuracy accuracy larger support train train modeling selection selection selection selection selection selection selection department loss implementation implementation internal internal internal individual represents difficult difficult final final final final final final final addition addition addition considered framework framework framework additional san conference conference upper choice approximate approximate approximate statistics statistics basic increase validation validation validation con produce produce produce produce produce produce produce derived weighted weighted weighted criterion criterion criterion criterion criterion types product product product product product product product product product product product provided finally finally processes selected selected selected selected selected selected selected selected selected nature nature nature nature depends discussion discussion arbitrary fast close close inverse complete surface implemented ability future future future degree degree rumelhart rumelhart noisy including including including underlying underlying underlying functional coefficients york increasing special principal squared squared squared numbers max making international bottom supervised supervised polynomial idea minimize minimize produced produced produced produced choose choose run added added predict discussed improve improve improve advantage advantage advantage property property property separate takes typical practical practical introduced strategy strategy strategy strategy strategy strategy strategy strategy strategy quadratic trees subset subset subset subset subset subset subset subset subset relevant engineering interest dimensions highly varying approximately works works works works axis axis axis axis axis smooth address symmetric modified observation generalized generalized generalized interval improvement entire locally deterministic generally generally strength assumptions valued central interactions interactions interactions differences sigmoid sigmoid faster constrained taking taking characteristics sigmoidal sigmoidal radial radial radial radial radial decrease relationship relationship relationship relationship derivatives manner program program derive produces produces factors generating estimating describes dimensionality involves interaction interaction interaction interaction adding springer quality select select select select formation dependence squares viewed viewed interpretation controlled restricted approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations understanding understanding approximated completely partition partition partition spectrum diagram diagram earlier reasonable smoothing smoothing additive additive additive additive additive additive additive additive additive additive additive expansion reduces fitting intervals intervals purpose boundaries penalty penalty initially topology topology figures includes combinations combinations combinations characterized characterized characterized straightforward straightforward letter closely suitable computationally included successful successful successful literature literature post situation tend tend verlag repeated procedures allowing strategies quantity quantity highest leading automatically illustrates illustrates situations situations situations minimized minimized diego exponentially updating rapidly involving involving involving detail detail replaced limitations limitations limitations recursive terminal terminal necessarily spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline quantities friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman greedy greedy noted multivariate multivariate multivariate multivariate attempts seconds cart cart cart cart cart cart crucial defining briefly considerable stanford stanford stanford implementing purposes producing broad incorporate products products mathematics consequence consequence involve involve author nsf nsf sun outer argument reflects greatly flexible axes axes axes axes leave orders share marked adjustable splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines employ incorporated compares schematic operate partitioning partitioning gen popular popular ordered serve serve serve sums semi semi begins simultaneous realized realized realized contribute contribute bellman bellman ordinary accomplished restriction extensive princeton princeton tensor tensor tensor tensor tensor tensor tensor tensor tensor approximates flexibility nonzero nonzero nonzero grows interconnected eliminated fails minutes breiman breiman overcome moment resulted interpret serves serves serves hope settings settings settings disjoint affected guide selects selects selects hours elimination elimination elimination respective overview conjunction interconnections interconnections competing chooses multiplied partitioned vari stone stone severe severe ics speaking ence truncated truncated largely annals ber responds poses suboptimal regularity wahba wahba wahba stem mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars realize realize num compensate impose disadvantage disadvantage march individually complementary sized responding responding siam siam happen cubic cubic induces dramatic treating tin vice sigmoids sigmoids expansions stops topologies moderate moderate versa tial curse ave interpreting loosely industrial kth formulae contrasts triangles triangle triangle comprising rameters adapts restrictive comprised artificially denominator emerged nice observes topics ables synthesize regional regional impor conceptually conceptually extremes excluding tant belmont craven craven craven knots knots knots knots radially accelerator poten roots behaved knot knot subclass subclass wishes wishes wishes olshen olshen owing exercise numerator numerator interpretable duced confer ruth ruth badly gions intersections sparcstation forecast crease lends derlying adder adder adder adder adder adder preclude erated cbms cbms til aids fortran seldom delineated xli ination elim mathemat jerome chui chui unifies 
#@Freidman_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number number error error error error error state results results results results results results results units information problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer 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inputs inputs form form form form shows shows shows shows visual paper net net net net net net net net net net net net net net work fig fig fig fig fig fig fig fig fig fig fig fig fig fig points points points points points points points points points points field field field field field field field field field field field field field field field field field features level current structure problems response response response response response response response similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show rule general general general general general general general generalization generalization generalization generalization generalization generalization approximation approximation approximation approximation approximation approximation theory obtained university university threshold computation computation research independent initial initial standard standard standard standard standard standard connections connections node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node science left presented presented presented present activation activation low nodes nodes nodes nodes nodes nodes nodes learn basis basis basis nonlinear nonlinear nonlinear outputs outputs outputs continuous abstract back back computational computational computational computational computational properties properties properties references due due adaptive adaptive introduction introduction complex complex complex statistical effect effect generated complexity complexity learned learned chosen chosen higher part previous cases required required cortex represent represent represent represent equations equations techniques scale simulations resulting resulting resulting resulting resulting simulation simulation simulation human multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi sum eq eq eq eq eq elements regions global global global global global global global global global global vol vol vol represented desired receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive proc proc proc active active active active active determined connected discrete discrete discrete brain approaches accuracy larger contrast connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection fields fields fields fields fields fields support support descent nets report department version synapses represents connectionist responses difficult exp exp layers layers layers layers layers computing hinton hinton curve curve curve curve curve additional additional view determine determine significant statistics speed speed speed derived weighted developed developed controller provided iteration iteration iteration iteration nature nature feedforward feedforward feedforward feedforward arbitrary arbitrary group fast fast corresponds corresponds corresponds amount shape shape shape shape supported main eds square square square square degree degree makes development including fit fit fit typically reduced functional coefficients mlp mlp mlp mlp mlp mlp mlp mlp mlp special structures structures trials principle representing representing details details iterations iterations magnitude polynomial polynomial polynomial added architectures architectures advantage advantage typical typical similarity include quadratic sejnowski sejnowski cognitive recently sufficient varying solve modified interval interval sensitive grant constructed horizontal lead scaling scaling scaling locally touretzky touretzky white column column column column half conclusions moody moody practice suggest sigmoidal proportional radial start manner connectivity program acknowledgements construct construct tuned sensitivity scales interaction develop squares interpretation evaluate updated updated organizing approximations approximations approximations evolution evolution slow fitting fitting construction foundation dendritic dendritic david david degrees degrees perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons formulation formulation formulation formulation determines determines illustrated illustrated activated efficiency efficiency efficiency capable capable society included wij presentation presentation successful computations computations computations plots characteristic composed capture excitation conf split quantity cat consisted overlapping overlapping neighboring employed schedule schedule schedule schedule schedule schedule schedule experience exponentially updating school school mappings int combine combine affect analogous analogous coarse spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline psychology bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation freedom initialized initialized ith established indicating piecewise piecewise smoothness slope slope improves capabilities capabilities benchmark nonlinearity sys shared organized strictly located universal localized localized depicted fourth fourth prop conducted capability capability effort orders adjustable passed splines splines splines splines splines splines splines splines formulated span polynomials operate controllers incorporating incorporating enables boston june june summed realized lab physiology accomplished interface princeton princeton princeton princeton branches branches partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions nonzero exemplar spiral spiral spiral spiral binocular darken darken contract splitting effectiveness cerebellar cerebellar combines introduces james respective cmac cmac cmac lang lang lang lang percepttons percepttons percepttons percepttons propagated darpa approximators barron barron mlps mlps mlps mlps theoretically arrows steepest hypercube eqs impact jump speeds generalizing trading trading spirals spirals multiply summer summer incorporates wiesel wiesel lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane benefits pieces incrementally affects hubel hubel algebraic ijcnn projecting rbfs manipulator 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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural neural neural input input input input input data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set networks networks training training training algorithm algorithm algorithm output output number number number number number number number number number system system error error error error error error error error error error state state state results results results results results models models models models models models models models models models performance performance performance performance based based based based space space space space space space space linear linear linear case case case order shown shown shown shown shown systems values probability probability probability probability probability parameters weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution approach approach approach approach approach approach approach approach approach approach approach approach point point point point point point point point point point single single single single control local local local local local local local local local local local local local local analysis class class class matrix inputs form form form form shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual small size size work task task task task task task task task task fig points points points points points points points classification classification classification classification classification classification process current structure structure structure structure structure structure structure structure structure structure problems problems random random similar representation representation section section section general general generalization generalization generalization approximation approximation average states dimensional dimensional dimensional dimensional dimensional variables variables variables variables variables computation computation found constant computer computer terms terms distance distance node node node node node node node science science left presented presented map map map map nodes sets motion press learn components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear continuous sample sample sample sample sample sample abstract applied find find density density density density density density density analog references important important important adaptive adaptive mixture mixture complex estimation estimation estimation estimation behavior search search tion tion lower chosen chosen chosen chosen chosen higher higher center center center bound bound bound bound bound cases cases type required required good binary represent represent represent tree tree tree tree tree tree tree tree tree tree tree expected expected region region region region region region probabilities errors simulations classes classes ing tasks tasks tasks computed computed multi multi sum sum sum called called regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping factor factor natural natural natural natural global applications study study samples samples samples samples samples samples samples samples samples samples samples samples represented represented represented represented represented compared provide provide provide compute location location perform perform perform determined determined determined related related constraints constraints constraints constraints distributions approaches approaches approaches comparison larger larger update support support report report institute institute technique technique technique technique technique technique internal internal internal internal internal internal internal kernel kernel kernel joint connectionist final graph directly directly view san top capacity determine efficient efficient efficient efficient efficient efficient efficient classifiers classifiers full full requires speed vision estimated basic basic basic give con produce weighted weighted randomly conditional clustering developed robot robot robot robot robot robot robot criterion bounds product product finally constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint technical technical increases increases increases fast fast corresponds complete surface surface surface finding rbf nearest nearest nearest nearest nearest effective supported require require square square square easily easily including including fit fit fit fit fit fit pairs smaller smaller needed combination combination coefficients coefficients interesting york increasing special special structures structures structures structures structures structures empirical empirical empirical principle operation operation operation operation representing representing representing international international bottom decay idea combined combined combined choose improved discussed directions recent resolution pair pair pair typical typical reported include side side quadratic quadratic quadratic hierarchical hierarchical hierarchical trees trees trees trees trees trees interest interest interest dimensions dimensions axis tions tions tions smooth smooth smooth smooth smooth match achieve achieve achieve trans mixtures mixtures evaluation symmetric symmetric symmetric symmetric bounded bounded arm arm arm arm arm arm arm parts studied derivative width setting greater neighbor bayes clear performs faster faster faster faster strong largest largest largest external external drawn drawn california proportional radial radial radial radial radial radial radial radial radial 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computationally effectively identify build efficiently efficiently efficiently efficiently efficiently efficiently schemes comparing online summary compact quickly quickly kind kind kind kind kind repeated return timing bar generalize generalize approximating software camera situations situations presents origin diego powerful wiley access access access access access collection collection fewer fewer incremental mappings investigated relationships root root func func func fundamental analogous surfaces surfaces surfaces math coefficient extremely thought thought queries queries queries singular friedman friedman versions precise academic simplest simplest simplest contributions attempts attempts defines great slowly defining fairly expensive inside implementing implementing berkeley leaves leaves cut cut describing patches arises integrating geometric geometric geometric geometric geometric geometric geometric geometric evaluating empirically affine affine affine affine affine affine 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small size size size size net work methods methods methods methods methods methods methods methods methods methods methods methods step step step step points features classification classification classification process level level level level current trained trained trained structure structure structure structure structure structure problems problems high high high high memory response representation representation representation representation representation representation representation show equation fixed rule rule rule rule general general generalization generalization generalization generalization generalization approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states theory theory term term term term term dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result threshold threshold variables variables computation computation computation computation solution research research found constant constant constant constant computer computer terms terms node node science prediction prediction presented present present nodes machine machine maximum press press press press learn basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear abstract back find find computational computational convergence references references component due ieee ieee ieee important important adaptive adaptive adaptive adaptive decision decision introduction complex behavior behavior statistical statistical statistical variance variance variance variance variance variance variance search search tion change change change change change change change variable variable variable variable variable variable variable variable variable variable variable variable assume lower rules chosen higher part cases type required required good binary binary represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree expected techniques techniques techniques techniques techniques techniques techniques correlation finite finite finite resulting ing regression regression regression multi called called dimension dimension dimension dimension made natural natural applications study artificial samples application application application desired cross cross compute proc location perform determined related related related distributions brain mit mit mit larger train modeling selection selection selection selection selection selection selection selection selection selection selection morgan morgan morgan morgan morgan proceedings report report report institute institute institute department loss implementation technique technique technique technique code represents final addition ai framework framework framework cambridge cambridge equivalent directly hinton san stage conference efficient choice choice choice choice approximate approximate statistics pages pages pages pages pages increase increase validation validation con levels levels criterion criterion criterion lines path product processes technical technical arbitrary arbitrary arbitrary tested fast fast close inverse complete circuits generate supported require end ability instance development including including fit kaufmann kaufmann coefficients coefficients jordan technology significantly york york increasing increasing special structures structures squared squared squared squared call call call numbers max direct stored bits supervised depth depth polynomial polynomial polynomial polynomial idea minimize choose added advantage advantage robust include include trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees sejnowski cognitive engineering dimensions dimensions dimensions dimensions dimensions dimensions sufficient sufficient varying approximately studies converge rl trans trans trans generalized storage entire entire exists concept extended locally touretzky flow conclusion reduce depend depend depend differences differences moody practice practice learns mateo propose propose propose taking taking physics largest largest largest california intelligence radial exist min decrease decrease manner identification program force longer ways sequential sequential sequential estimating describes laboratory ann dept pruning pruning pruning electrical dimensionality dimensionality easy formed formed boolean select john national squares operations organizing organizing lee lee lee understanding partial additive spaces spaces spaces spaces purpose add iterative avoid existing existing existing existing includes combinations formulation sciences determines determines determines characterized tests aspects efficiency closely procedures anderson split split split split split split lie sin built write usual michael nips minimizes computes automatically approximating trains minimized powerful american essential essential environments recursive recursive recursive recursive scalar scalar scalar scalar scalar fewer fewer reducing fourier school school incremental int structured structured structured root root root removed induction adapt adapt integer man man man spline spline extremely subsets friedman friedman friedman algo fisher fisher switching multivariate generates attempts optimum massachusetts cart cart cart cart cart cart slowly piecewise piecewise cos separable separable separable separable separable separable growing growing growing growing growing considerable stanford leaves leaves products products products acknowledgement author cybernetics cybernetics sun sun sun explained people elman pseudo lms lms lms lms lms lms lms lms lms lms lms lms lms lack lack atkeson atkeson introducing splines slower polynomials polynomials maximizes parent proven chen adjust gave comments leaf leaf leaf leaf leaf leaf multidimensional univ univ univ univ bellman bellman bellman lab forming summing princeton princeton rithm resources member ordering inspired communications air minutes breiman breiman ranges odd grow grow grow los abilities sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger splitting games iteratively widrow widrow widrow widrow widrow searching searching bases multiplied barron barron barron eng record splits alternatively stone pressure approx summer truncated fellowship exhaustive incrementally arbor chapter mars mars mars mars mars mars mars avoided realize chess clas modifying alternate gener mitchell expand simplifying emphasize quinlan quinlan quinlan quinlan cubic cubic cubic aaai suggestions chris chris survey curse curse aid aid aid aid attempting fill recursion proposal incorporation maxi sions alto smc 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space space space space weights weights weights weights weights weights weights linear linear linear linear linear case case case case case case case case vector vector order order order order order order shown shown shown shown shown shown shown shown systems values values values values values values parameters parameters parameters parameters parameters noise weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions method method method method method method method approach approach approach approach approach approach approach approach large local local local test test test test test test test test test test test test matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs form simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small work work work work methods methods methods methods methods methods points points points classification random similar equation equation equation equation equation equation equation equation equation equation equation equation section general general general generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter approximation approximation approximation approximation approximation approximation average average gradient gradient obtained obtained obtained obtained obtained obtained obtained term note experiments dimensional variables variables variables variables variables variables variables variables variables variables variables variables research research research research log log found found found found found found found found found dynamics initial initial initial constant table table table table estimate terms terms distance distance distance distance distance distance distance distance distance science prediction direction presented present sets sets range range range press position basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract find find find find find find find convergence density properties properties properties properties properties properties references ieee ieee positive procedure procedure adaptive introduction complex estimation effect variance cost change change change lower chosen chosen center center center previous cases good good long conditions distributed distributed distributed distributed expected expected make techniques region length correct errors errors scale regression regression computed sum elements mapping optimization optimization optimization optimization optimization optimization optimization optimization made made natural global global knowledge artificial true true compared cross cross series series compute location location location constraints constraints brain equal equal equal mit larger support support train dependent modeling proceedings institute department technique consists joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint exp addition considered cambridge equivalent additional conference efficient choice choice choice choice approximate approximate approximate approximate approximate approximate approximate approximate estimated estimated estimated estimated validation validation con derived weighted randomly randomly randomly randomly criterion velocity types provided provided selected selected iteration measured describe tested tested tested tested tested tested tested transformation transformation fast limited close inverse inverse inverse inverse complete finding rbf rbf rbf rbf rbf rbf rbf square square ability ability easily pairs smaller combination reduced account functional coefficients coefficients coefficients coefficients technology significantly significantly significantly empirical iterations iterations iterations international normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized polynomial polynomial polynomial polynomial polynomial polynomial added added added improved improved improve directions directions directions exact exact exact exact exact advantage pair takes similarity reported subject cognitive relevant relevant engineering engineering compare solve studies converge converge diagonal diagonal diagonal locations locations locations symmetric modified observation generalized generalized generalized generalized sensitive entire grant grant arm arm arm horizontal horizontal scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling suggests matrices locally width width width width width conclusion conclusion accurate moody moody faster faster suggest suggest taking proportional intelligence regularization radial radial radial radial radial radial radial radial derivatives derivatives derivatives derivatives derivatives derivatives derivatives minima force pro pro estimating estimating laboratory tuned distinct changing modeled metric metric metric metric metric metric metric metric metric metric sensitivity adding adding gaussians gaussians formed versus national dependence review phoneme squares squares viewed showed centers centers centers centers centers centers centered approximated approximated approximated approximated approximated approximated approximated reasonable performing measurements expansion combining fitting fitting purpose add penalty interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation valid distances foundation foundation norm norm norm norm euclidean euclidean coordinate sciences sciences extension plotted absolute tests reason columns columns columns extra uniformly uniformly uniformly uniformly uniformly poggio poggio poggio poggio poggio committee identify efficiently refer repeated link dis sin sin sin sin criteria comp comp vary simplified generalize generalize ill principles approximating acknowledgments minimized explore poor poor optimized optimized optimized recursive recursive recursive mass mass fewer examine scaled scaled scaled office office referred proper affect affect func examined math measurement perfect singular taylor explored chaotic massachusetts cos cos cos cos formula crucial agreement agreement smoothness smoothness guaranteed improves tool desirable scientific angles optimize optimize definite raw greatly empirically orders atkeson atkeson atkeson atkeson splines splines splines polynomials polynomials polynomials expectations optimality modify oxford angular angular angular velocities girosi girosi girosi girosi girosi optimizing optimizing approximates naval air darken darken ranges attractive imposed hyper moment contract resulted nearby planar programs widths widths bad bad washington iterated young thin reader hypercube rms multiply approx approx fellowship torque torque torque wahba tradeoff spaced acceleration experiences experiences experiences experiences cessing disadvantage disadvantage afosr plate rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs inversely cubic worked worked differently lowe lowe christopher thousand routines dropped award award rohwer rohwer joints sloan contrary tance inde addressing fixing scattered scattered physica health routine renals renals ceedings cox investigator pendent invert biomedical mason reproduces inertia mac mac mac radially faculty presidential idealized idealized multivariable multivariable iix fund nonsingular broomhead broomhead normalizes tab lhe namics powell powell powell casdagli casdagli axi commun initiation prespecified clarendon accelerations friction ita keck whitaker marquardt subsections nts ils cga coef levenberg alg alfred grad scalings ficients hardy hardy hardy sino professorship ditionally 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data function function function function function function function function function function function function function function function function figure figure figure time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output number number number number number number number number system system system system error error error error error error error state results results results units units units units units units units units units units units units units units units units units units units units units units information information information information information information problem models performance based space space space space space weights weights linear linear linear layer layer layer layer layer layer case case case vector vector vector vector vector vector vector vector order systems systems systems systems values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit method pattern pattern pattern pattern pattern point processing processing processing processing processing large large large large local local local test test patterns patterns patterns patterns patterns patterns inputs inputs form form form form shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian paper paper examples small size size size size size size size work work work features features level level current trained trained high response response response response similar representation representation representation representation representation representation representation representation representation representation representation architecture equation equation equation equation equation equation equation equation section section fixed line line line line line line rule vectors vectors approximation approximation approximation average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term term term term dimensional university computation computation computation computation computation computation constant constant table table table table table table standard standard distance distance distance synaptic science prediction prediction prediction left presented presented presented presented presented presented presented maximum range press learn learn basis basis basis basis basis nonlinear nonlinear outputs outputs continuous abstract back back back back back back back back back find find find computational density references component important important adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex complex statistical generated tion difference difference difference complexity lower learned learned learned learned chosen part part center previous previous previous previous cases cases long represent represent equations make techniques region correlation correlation correlation length length length correct errors errors errors scale scale scale scale scale scale regression multi sum called mapping means means factor factor global global global application desired desired desired desired desired desired series series series series series receptive perform equal accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison larger larger larger fields descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent modeling morgan morgan morgan morgan report report department loss synapses synapses synapses synapses synapses consists consists advances advances advances represents represents connectionist responses responses difficult exp exp delay addition addition hinton additional san san san san san requires statistics speed increase condition condition condition condition derived weighted clustering levels area provided provided finally technical tested tested fast fast limited close circuits rbf rbf amount amount amount amount short nearest nearest nearest implemented generate require eds eds fit kaufmann kaufmann kaufmann kaufmann simulated simulated typically typically smaller smaller smaller smaller smaller needed york special max max max max making stored stored stored stored stored stored normalized decay polynomial polynomial polynomial polynomial polynomial polynomial added predict predict predict improve resolution resolution pair pair pair takes takes strategy sejnowski interest interest previously unsupervised approximately approximately works differential grid storage entire entire entire parts extended predicted locally locally move touretzky touretzky touretzky touretzky width hardware strength conclusions accurate accurate accurate peak performs performs performs moody moody moody moody moody moody moody moody moody moody moody moody faster learns learns learns mateo mateo mateo mateo strong hard presence largest proportional regularization radial radial radial radial min min min min decrease decrease decrease annealing construct index describes laboratory tuned tuned multilayer linearly linearly linearly easy adding formed versus versus cycles john john yield national formation review communication overlap overlap detailed updated organizing fraction lee lee centers centers centers centers centers reasonable epochs epochs combining combining combining combining fitting roughly interpolation interpolation interpolation interpolation interpolation existing existing silicon activated neighbors efficiency efficiency closely modes poggio poggio poggio presentation tend tend fine reached reached road compact compact compact compact compact compact compact compact compact quickly quickly categories generalize reach automatically mead optimized accurately accurately fewer fewer respond school tech comparable hierarchy hierarchy attributes smallest smallest coarse coarse predicting spline spline spline spline created created created thought adjusted friedman friedman store switching multivariate chaotic chaotic chaotic improves cascade cascade cascade glass glass glass glass glass glass glass starts starts reasons stanford ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran ran desirable immediately immediately gradually localized localized localized sun reflects reflect empirically empirically lms poorly poorly poorly poorly splines splines splines splines splines compares reaches reaches fall resource resource resource resource incorporating adjust comments comments windows coherence implements eventually eventually don oxford girosi girosi girosi approximates repre grows grows proceed platt platt platt platt platt platt 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networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number system error error error error error error error error error state results results results units information information information information information information information models models hidden hidden performance performance performance performance performance performance based based based based based based based based space space space space space space space space space linear linear linear linear layer case vector vector vector vector order order order shown values values values values values parameters parameters parameters noise noise functions functions functions functions functions functions functions functions functions functions functions method method method method method method method method method method method method method method method approach approach pattern pattern pattern point single single single processing processing control local patterns patterns patterns patterns analysis analysis class class optimal optimal optimal optimal form form form shows signal signal algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper net work work process process current trained trained structure random show show equation general general parameter parameter parameter parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states theory gradient gradient obtained obtained obtained obtained term term term term term note result result university university university university threshold threshold threshold defined found found found sequence dynamics initial initial estimate estimate estimate estimate estimate estimate terms distance node node node node node prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented presented presented map map map map map map map map map present present present present present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear sample sample sample sample sample sample sample sample sample sample abstract applied back find computational convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic procedure procedure important adaptive adaptive adaptive propagation introduction complex estimation estimation estimation cost cost cost cost cost cost cost tion change change change change difference variable measure signals prior prior prior higher previous previous conditions conditions proposed finite ing ing tasks respect multi performed called called elements mapping mapping mapping applications knowledge knowledge knowledge knowledge samples samples samples samples samples samples samples samples samples samples samples samples samples compared application application application series series series series series series series series series series series series series series series series series posterior posterior posterior posterior posterior posterior posterior posterior constraints constraints constraints constraints equal power steps accuracy train descent report report report report report report report department department department department department exp scheme scheme scheme scheme scheme scheme scheme scheme scheme addition ai ai ai cambridge cambridge cambridge cambridge domain additional curves san determine choice approximate free speed con derived weighted randomly developed developed developed area product actual iteration iteration iteration constraint constraint achieved achieved technical technical technical technical technical technical feedforward arbitrary close close complete stable rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf theoretical adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation square square end future makes makes noisy fit fit underlying underlying underlying underlying underlying underlying underlying underlying combination functional unknown block projection projection projection projection projection projection york increasing increasing increasing consistent consistent principle principle principle principle principle principle principle squared squared details pre choose choose predict predict predict predict directions takes takes introduced sense sense subset engineering engineering engineering engineering sufficient varying compare compare compare observations observations observations observations volume yields diagonal modified observation observation observation observation observation observation increased constructed constructed constructed constructed constructed constructed exists extended deterministic deterministic white white place place reduce conclusions numerical clear faster faster asymptotic propose reduction california radial radial radial radial radial radial radial radial minimizing pro construct construct sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential describes describes laboratory laboratory stability metric multilayer develop applying minimization minimization john choosing national national stationary stages viewed solved evolution centered converges past past past past penalty interpolation norm norm norm norm includes priori priori priori priori priori priori subspace subspace determines extension determining importance importance efficiently efficiently schemes projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections projections comparing comparing comparing quickly superior lie satisfy satisfy satisfy usual ill ill decreasing modelling minimized minimized diego wiley environments environments integral recursive examine successive successive successive successive successive successive analytically predicting predicting predicting logistic logistic generates improving chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic residual slowly developing improves adapted reasons implementing constructing incorporate incorporate hyperplane localized lms capability differs substantial sv investigation restrict royal fails los los los eqn eqn eqn repeat falls governed evident mem offer offer exploiting cam radar maintaining centre residuals residuals chaos constitutes employing memoryless memoryless reveal memo lapedes lapedes lapedes retained bridge lowe lowe lowe losing hilbert firstly autoregressive niranjan niranjan niranjan niranjan niranjan niranjan niranjan niranjan relaxed nonstationary nonstationary alamos alamos alamos tan stand eta eta fallside fallside fallside fallside fallside fallside fallside fallside infinitesimal cued cued cued pal recur mexico economics broomhead broomhead broomhead temporarily establishment hypersurface hypersurface farmer farmer darkness increas sive malvern steadily vides infeng infeng sidorowich sidorowich eqns farbet farbet adapta initialise eri halted halted rsre dicting trades iif servation succes 
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm output output output output output output number number number number number number number number number number number number number number number error error error error error error error error error error error error error error results results results units units units units units units units units units units units units units units units units units units units units units units units units information information information information problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based space space space space space space space weights linear linear linear linear case case case case case case case case case vector vector vector vector vector order order order shown values values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition method method method method method method approach approach approach pattern point image image image image image image image image image image image image image image image image image image image single single single processing processing large large large large local local local local local local local local local local rate test patterns analysis analysis analysis analysis analysis analysis analysis analysis class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal inputs inputs form form form form form shows signal algorithms algorithms gaussian gaussian gaussian gaussian paper paper examples small small small small feature feature feature feature net net net net work work work task methods fig points points points field field field field field field field features features features features features features process process process level level level trained structure random random high high high response response response response response response response response response response response architecture architecture show show equation section section section section fixed vectors vectors images images images images images images general general general general generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation gradient gradient term experiments dimensional dimensional dimensional university variables independent defined defined defined defined defined found found target initial constant constant constant table table table standard standard computer computer terms distance node prediction presented presented presented presented present present present present present low sets maximum learn learn components components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis abstract density density properties references component due due ieee ieee adaptive adaptive context introduction estimation behavior effect generated tion change variable lower rules rules rules rules chosen chosen higher higher part center center center center center center center center previous type type type type required required good equations fact region region region region region region region region observed observed observed errors forward scale minimum resulting ing ing total respect multi elements elements elements elements regions regions regions regions regions regions regions regions regions regions regions means means dimension dimension dimension dimension dimension dimension dimension dimension dimension made global global global knowledge original original vol vol vol vol samples represented represented represented represented desired cross series series series series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide define proc proc proc proc location determined determined determined determined equal power accuracy accuracy accuracy accuracy accuracy larger larger fields fields fields fields fields fields fields update descent descent nets report department individual individual individual kernel kernel kernel represents represents connectionist connectionist difficult delay scheme scheme scheme scheme addition addition addition ai considered experiment estimates limit top stimuli determine requires choice significant statistics free con con con con con coding coding coding coding coding coding coding randomly clustering developed levels levels finally backpropagation discussion technical increases transformation close corresponds surface surface surface surface surface finding rbf rbf rbf rbf rbf rbf rbf rbf rbf nearest shape role role square square pixel instance easily easily objective objective pairs pairs smaller underlying needed technology significantly character character special consistent uniform principal principal principal normalized normalized polynomial polynomial polynomial idea minimize choose added resolution resolution resolution resolution resolution advantage property property property property element element identical pixels quadratic hierarchical hierarchical array recently engineering sufficient sufficient works works tions tions smooth smooth smooth smooth match correspond correspond correspond correspond differential achieve address definition definition positions locations generalized bounded improvement entire entire increased studied invariant scaling scaling scaling scaling scaling scaling scaling scaling occur deviation deviation derivative rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation feed width width width column place row row greater conclusions neighbor valued measures designed designed moody moody reduction radial radial radial radial radial radial radial radial radial radial radial radial radial radial radial radial start introduce characters minima minima minima force plot plot tuned tuned dept metric metric linearly linearly electrical dimensionality transformations transformations slightly text text gaussians quality implies select john john yield yield choosing extracted extracted reconstruction correlated overlap interpretation influence influence influence detailed restricted forms forms approximated approximated approximated translation translation translation translation translation sec remains remains sufficiently sufficiently sufficiently norm euclidean euclidean avoid kernels kernels coordinate perceptrons illustrated maximize variations reason determining determining determining sensor suitable suitable divided poggio poggio schemes tend tend reached capture notice notice quickly repeated prob heuristic sin sin michael generalize subsequent oriented oriented oriented oriented oriented oriented oriented oriented oriented remain transformed poor collection exponentially estimators issues rise school school root proper hierarchy coarse perceptton shapes shapes grouping arbitrarily years formula growing glass considerable drive lin lin tive purposes purposes sections widely widely ran probable recognized localized localized varies collected cmu cmu readily readily readily posed posed rep compares polynomials ture limiting extracting extracting popular age begins multidimensional univ irrelevant ordinary ordinary primarily restrict fix fix girosi concerned jth grey consideration darken darken occurred determination hyper hyper hyper hyper hyper grow grow nearby transforms responsible motivation composition widths widths widths widths widths widths widrow captured approximators approximators bins bins partitioned alternatively tures approximator approximator baldi lem consecutive boxes informa multiplying approx ure summer summer corporation ter ter leaming opposed opposed algebraic illustration mackey exponent exponent modifying alternate alternate approxi permits permits met spanned superposition superposition west placing fea fea ignoring september architectural deletion tail advantageous differently opti grbf curse curse austin austin austin austin austin locate adaptively adaptively evolved tors lists tuple strokes dimen feasibility shaping tained texas texas ated rotational constituent rotate tal mization ece suitably imation parame parame illustrating kurt clipping pierre mere compose sponse sponse recep transfor tain jim interpretable chinese chinese spheres spheres spheres compactly tang tang tang reductions rameter orienta hyperacuity sept sept experimen christian christian christian christian gions mcc associ quired microelectronics hypersurface composing mations tomaso sidered elliptical bitmaps connecfionist dation bitmap bitmap bitmap linearize resented motivations popularity bernard ellipses ceptive sionality domly rot excessively mll mll mll mll mll lift madaline circumvented mension avenues scal scal vali alleviates mator balcones 
#@Christian_J,Saha_A,Tang_D,Wu_C,
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural input input input input function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training output output output output output output number number number number error error error error error results results results results units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space space space space weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer case case case case case case case case case case case case case case case vector vector vector vector order shown systems values values probability probability probability probability probability weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach approach pattern pattern point point point point single single processing large large large large local local local patterns matrix matrix optimal optimal optimal inputs form form form form form form shows algorithms simple simple simple simple simple gaussian gaussian paper examples examples small small size work points process process process process process cell problems random response similar similar similar similar show equation equation equation equation equation equation equation equation equation equation equation equation section fixed fixed fixed fixed fixed fixed vectors general general general general general general generalization generalization generalization generalization real real approximation approximation approximation approximation approximation approximation approximation theory theory theory gradient gradient obtained obtained term term term note activity dimensional result result computation computation solution solution solution solution defined defined defined defined defined found found found sequence sequence initial initial initial initial initial initial constant constant constant standard terms science presented presented frequency maximum position position continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous sample abstract applied applied back find convergence density density properties properties properties properties properties properties properties references important propagation propagation propagation context introduction introduction hand hand hand behavior stimulus tion energy variable spatial assume assume assume assume higher center previous previous theorem theorem theorem theorem bound bound type type good good long conditions conditions distributed distributed expected equations equations fact fact fact techniques region region correct errors forward forward finite finite simulation regression computed computed sum sum times regions optimization dimension natural orientation applications study negative vol true true application series series provide define location location related related related constraints discrete discrete equal equal equal approaches approaches approaches larger larger connection connection descent proceedings institute institute loss consists represents represents represents connectionist connectionist connectionist difficult difficult final final final final exp exp exp exp delay addition addition addition maps considered considered framework framework computing computing computing computing computing computing equivalent equivalent equivalent equivalent experiment directly directly additional view solutions curves curves curves limit limit conference significant increase increase validation give give weighted lines entropy provided finally finally finally processes nature depends biological biological biological feedforward fast limited close close corresponds complete surface proof proof proof proof proof proof finding finding finding shape shape supported square end instance instance instance instance instance instance instance cluster degree degree degree sensory probabilistic combination reduced functional technology technology transfer transfer transfer consistent consistent trials details normalized decay polynomial idea description light resolution resolution advantage property typical reported include period identical side sense sense array array relevant relevant relevant relevant dimensions dimensions sufficient highly approximately tuning axis smooth yields differential differential differential rl symmetric symmetric symmetric generalized bounded bounded bounded bounded interval interval interval increased increased grant exists exists lead suggests extended extended extended deviation feed feed locally move width white setting setting setting critical minimal assumptions sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid measures numerical clear clear clear moody moody constrained temperature temperature temperature temperature temperature temperature california california regularization regularization turn exist exist min derivatives derivatives minima minima minima question relation pro written longer solving laboratory transitions ann tuned tuned mathematical mathematical modeled metric multilayer multilayer infinite infinite easy easy easy easy unique unique consisting consisting gaussians gaussians gaussians gaussians springer john john john john john yield independently depending viewed viewed transform restricted approximations centers centers centers centered understanding approximated approximated approximated suggested partition spectrum spectrum partial partial partial reasonable reasonable reasonable reasonable reasonable slow convex convex purpose boundaries closed interpolation remains remains initially initially precision precision precision combinations bell bell bell bell bell bell bell bell bell bell bell bell bell bell bell bell bell bell inter weighting weighting extension holds discussions characterized characterized simplicity reason determining straightforward straightforward extra uniformly uniformly uniformly uniformly uniformly uniformly society maximal poggio poggio presentation essentially identity characteristic compact compact notice notice verlag heuristic heuristic success success interpreted lie duration write usual usual backward ill ill ill reach attempt moves approximating approximating minimized origin american wiley difficulty integral hall scalar scalar fourier ideas ideas detectors authors cover examined examined concepts integer integer extremely extremely created equally friedman friedman obvious logistic precise observe submitted isolated great inequality inequality trivial smoothness smoothness defining biology analytic analytic diffusion diffusion diffusion diffusion diffusion briefly briefly briefly lin precisely division commonly products products mathematics acknowledgement universal universal universal universal read cybernetics qualitative preceding nsf lms posed posed posed posed posed passed polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials price limiting limiting reaches incoming ordered pasadena adjust enables shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped shaped begins simultaneous differentiable yielding picture proofs ear tation girosi unity impossible enhancement generality darken satisfying satisfying hit contract interpret intuitively intuitively intuitively arrays arrays arrays arrays arrays constructive prentice ranging enhance sphere sphere sphere sphere uni entries approximators express hypercube concentration sons davis davis alternatively baldi baldi baldi baldi baldi baldi baldi baldi baldi baldi baldi onr treat temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures shorter equivalently feeding conjecture conjecture conjecture spaced letting imagine continuity publication conduction chauvin chauvin formance evolve learnt learnt mathematically elementary concentrate landscape landscape hornik hornik preserve tively mimic durbin durbin sigmoids rewritten remark tail remarkable jet invertible converging coin coin evolved broadly injected evenly propulsion periphery receivers appl binomial physically quick cess gaus backwards terminology collecting approxima suitably ther wait paid heat heat heat heat heat heat heat heat heat heat heat heat heat respec seeks convexity completes pierre densely successes successes stein sume sketched occupy asserts bernstein bernstein bernstein bernstein bernstein bernstein bernstein bernstein bernstein mat arrangements snowbird stinchcombe heiligenberg lengthy technically flipping till grand reversing reversing 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#@Baldi_P,
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#*network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural input input input input input data data data data data data data function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training algorithm output output output output output output number number system results information problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based based space space space space weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer case case shown systems systems functions functions functions functions functions functions method method method single single single single processing processing analysis analysis analysis analysis analysis analysis class form form form shows shows shows signal signal signal algorithms simple simple paper paper paper paper net net work methods methods methods features representation representation representation show equation section fixed line line images general general speech real real approximation approximation approximation approximation theory gradient obtained note note dimensional dimensional dimensional university university university university university threshold computation research research research research research research research log defined defined defined defined defined defined found found sequence sequence standard standard standard standard computer terms terms terms node science science prediction left map map map present present phase activation activation nodes nodes nodes nodes nodes nodes frequency frequency frequency frequency sets sets basis basis nonlinear continuous continuous abstract applied density density properties properties references due ieee ieee procedure procedure procedure introduction generated cost cost cost tion energy difference variable spatial spatial spatial spatial spatial spatial spatial assume measure signals learned chosen higher higher higher part center center center type required required required good conditions represent make fact region region forward finite simulations resulting classes simulation simulation computed computed computed respect called elements elements regions mapping mapping mapping mapping optimization dimension natural orientation orientation applications original original samples desired series series series series provide provide provide provide determined determined determined discrete discrete discrete discrete discrete discrete discrete discrete discrete power power power support descent modeling report report report report department department technique layers addition sequences framework framework framework curve curve curve solutions estimates estimates determine significant approximate approximate estimated give condition channel randomly developed product provided provided backpropagation backpropagation nature discussion discussion discussion technical technical technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward describe group denote denote inverse corresponds corresponds common generate generate supported supported eds square square easily easily typically account account unknown unknown unknown coefficients coefficients coefficients coefficients coefficients coefficients significantly empirical leads details magnitude frame frame frame frame frame frame frame frame combined choose architectures discussed discussed discussed property takes engineering engineering interest dimensions dimensions sufficient approximately works works trans definition bounded constructed constructed constructed constructed constructed constructed constructed exists suggests feed white setting assumptions conclusions operator operator operator valued designed designed clear drawn sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal demonstrated solid solid assuming minimizing exist plane relationship manner manner program force suppose index laboratory laboratory mathematical implement implement multilayer electrical involves remaining spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral develop predictive predictive minimization springer john choosing choosing choosing national national family family family review transform transform transform transform transform transform transform transform transform approximations centers frames frames frames frames static approximated similarly suggested translation constants spectrum dashed dashed expansion expansion expansion expansion spaces convex convex convex sufficiently construction foundation euclidean topology topology topology transactions transactions combinations combinations priori formulation extension domains domains simplicity determining suitable suitable verlag dis localization localization localization localization localization localization wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet providing approximating satisfies selectivity selectivity essential essential dual biases biases reducing fourier fourier tech mappings mappings mappings mappings authors office func integer illustrate precise grouping defines seconds seconds ment band defining defining defining briefly lies tool tool preprocessing choices scientific acknowledgement involve universal apparent applies understood affine affine affine affine affine affine affine affine affine tional introducing rep synthesis synthesis synthesis synthesis synthesis synthesis synthesis extensions acoustics inherent display multidimensional globally contribute indices college accomplished restrict fix arguments arguments bin naval air los contract transforms transforms transforms transforms transforms transforms transforms transforms transforms transforms analyzing analyzing definitions preparation guarantees bases approximators park concentration concentration valuable convergent isotropic isotropic spatio spatio spatio theorems avoids rectangular concentrated concentrated shifting shifting grouped afosr march hornik translations translations translations translations translations covered siam lapedes port exploited september examination sigmoids sigmoids sigmoids sigmoids sigmoids expansions expansions expansions expansions neumann discontinuous discontinuous justification invertible hilbert doesn doesn suffers orthonormal orthonormal orthonormal powers december december illinois wavelets wavelets wavelets wavelets wavelets wavelets wavelets wavelets tells sity sis sis locality locality alamos february maryland maryland maryland spec addi stan urbana stepsize stepsize spario farber decompositions dard grossman dilation dilation ames translating concentrations concentrations concentrations sults earliest univer ore cybenko cybenko compactly nical stinchcombe superpositions chitecture proximate hans vienna deviate tral professor professor mother mother mother mother mother mother mother cdr integrable mallat synthe synthe supercomputing pitfalls pings mml 
#@Krishnaprasad_P,Pati_Y,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model input data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm output number number error results units problem problem problem problem problem models hidden space weights linear layer layer layer case case order order order shown shown shown values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters noise noise noise noise noise noise functions functions functions functions distribution distribution distribution distribution distribution distribution distribution method method approach point point point point point point point point point point point large class class class form form form form shows algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small fig fig fig fig fig points points points points field field problems problems problems problems problems random random random random similar show show show equation section section fixed rule rule vectors general parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory theory theory theory theory theory theory theory gradient gradient obtained obtained obtained obtained obtained obtained term term term term note note dimensional dimensional result result result threshold threshold threshold variables variables variables variables variables variables variables variables solution solution solution solution solution solution solution solution solution independent independent independent defined defined defined found constant constant constant constant estimate estimate estimate computer computer computer computer science science direction map map press press position basis basis basis nonlinear abstract find computational references stochastic ieee ieee positive positive positive context introduction introduction effect variance variance variance variance variance variance parallel tion tion energy energy energy energy difference prior prior prior prior prior previous previous previous cases cases make fact techniques techniques resulting total eq eq eq called called called regions mapping means potential potential potential potential potential potential potential potential potential made natural natural knowledge knowledge obtain obtain negative negative negative negative negative negative negative negative negative negative negative negative negative negative vol artificial specific represented application define compute compute active experimental related related related related posterior posterior posterior distributions equal accuracy larger larger descent descent proceedings proceedings report institute technique consists consists consists joint represents final scheme addition graph ai ai considered computing computing equivalent equivalent view view view solutions limit choice choice choice significant statistics vision vision vision randomly randomly conditional finally selected depends sampling sampling discussion feedforward denote close corresponds corresponds amount common effective effective effective effective effective assumed face degree probabilistic probabilistic smaller smaller needed account account functional functional functional functional functional functional coefficients technology interesting york call call call iterations iterations international combined minimize robust introduced introduced quadratic quadratic quadratic sense previously previously approximately solve yields differential rl interval interval derivative move assumptions operator operator editors bayes bayes taking integration presence presence presence presence presence proportional intelligence regularization regularization regularization regularization regularization regularization regularization regularization radial radial turn assuming minimizing minimizing decrease relationship configuration force force acknowledgements suppose written solving ways laboratory vertical physical adding springer potentials choosing expressed expressed reconstruction interpretation influence controlled centered approximated sign partial smoothing smoothing classical expansion interpolation interpolation avoid priori contour absolute discussions characterized simplicity aspects closely suitable society delta poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio situation situation tend soc notice notice notice verlag quickly interested interested contribution vary write ill ill ill ill consisted approximating neighboring neighboring deal extend extend situations minimized minimized create access estimators rest variational variational variational measurement editor reading opposite spline front consist massachusetts percentage site cos cos smoothness smoothness variances variances variances fairly choices ion depicted integrating argument argument fourth fourth reflects lack lattice introducing posed posed posed splines outliers outliers outliers outliers polynomials berlin extensions extensions extensions extensions extensions prevent marginal green green green green tile tile tile trade lab lab notes equivalence equivalence oxford girosi girosi girosi girosi girosi girosi girosi girosi girosi girosi girosi girosi girosi girosi girosi null connecting connecting connecting dealing nearby nonparametric substituting regarded regarded regard bad washington realization infinity express reader extensively reverse papers papers papers outlined informa exhaustive maximized break break break par ical distribu denoting sketch weaker breaks geiger geiger particle particle particle particle memo knowing september manuscript lecture unbounded tial spring spring spring spring spring spring fill adjoint affecting unreliable unreliable unreliable unreliable unreliable push conditionally fol appro enforces enforces enforces trend neglected outlier outlier outlier outlier outlier recovering recovering sur fore stan particles particles amer cox hole attracted approxima italy substituted trick dard apparatus mrfs exceeded posterjori poten ions multivariable stretch tha fimction admits cre marcel dekker marroquin marroquin fii powell powell imal crit eubank eubank terzopoulos elongation elongation elongation elongation discounting closeness clarendon tikhonov tikhonov oper repulsive repulsive repulsive nction filnction monographs xll occurence zoo ial synthesizing bruno lion federico eccv tlt kass ator timer mitter fective winston ibr 
#@Caprile_B,Girosi_F,Poggio_T,
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data data data function function function function function function function function function function function function function function function function function figure figure figure figure set networks networks networks networks networks training algorithm algorithm output output output output output number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results units units units units units units units units units units units units units units units problem models performance performance performance performance performance based based space space space space space space space space space space weights weights weights weights weights weights weights weights weights weights weights linear linear linear vector vector vector order shown systems systems systems systems probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution point processing large large patterns patterns analysis form form form form form shows shows shows signal signal simple gaussian gaussian gaussian paper paper small small small small small small small size size size size size size task fig fig field field field field field field field field field field field field field field field field field field field field field field field field field field field field process process process current current current trained trained trained trained structure structure structure structure structure structure random high high high high high high high high high high high high high high memory response response response similar representation representation show equation section section section section section fixed rule general general general approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average term term note note activity activity dimensional dimensional result result result threshold threshold threshold computation solution target target target target target target target target target target constant distance presented present low frequency frequency frequency frequency frequency frequency frequency frequency frequency learn learn basis basis basis nonlinear outputs sample abstract density density density density density density density density density density density density density density density density density analog properties properties references due due procedure important important adaptive adaptive adaptive adaptive adaptive context complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical effect effect effect effect variance variance variance variance variance parallel cost tion tion spatial spatial spatial measure measure representations representations learned chosen higher part part center center center center previous type type type type required conditions represent distributed distributed distributed expected region region region region errors errors errors errors errors errors errors errors errors errors scale ing ing ing sum sum sum sum regions regions regions regions regions regions regions regions factor made vol artificial artificial relative specific desired receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive experimental goal constraints motor power steps steps accuracy fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields train source implementation version version technique consists joint addition maps considered framework cambridge domain domain hinton hinton additional additional curves design limit top effects effects effects determine efficient significant approximate approximate free free basic give condition coding coding coding weighted weighted lines sampling sampling biological biological biological biological associative achieved discussion increases describe fast fast assumption corresponds rbf rbf common shape shape generate role eds square ability future makes rumelhart noisy noisy noisy sensory sensory including fit fit fit fit pairs smaller needed reduced reduced account functional functional functional functional functional transfer interesting increasing increasing increasing increasing increasing uniform uniform principle squared squared squared squared squared details call call call numbers direct making supervised magnitude magnitude frame frame frame frame frame attention minimize minimize minimize minimize choose choose choose sources sources improved improve resolution typical introduced strategy strategy strategy strategy strategy strategy strategy quadratic relevant observations approximately match studies achieve address organization entire entire entire entire increased increased increased lead deviation wide wide derivative locally locally locally locally locally locally width width width width width occurs generally hardware half half greater conclusions central interactions moody moody suggest propose reduction reduction characteristics demonstrated proportional radial radial turn turn program factors factors factors tuned tuned tuned tuned averaging averaging involves text adding frequencies springer choosing dependence overlap overlap overlap overlap interpretation restricted approximations centers centers forms understanding approximated approximated sizes allowed additive measurements reduces reduces fitting neighborhood interpolation interpolation visible kohonen kohonen characterized aspects uniformly uniformly uniformly driven mcclelland identify mackay fine fine fine verlag kind kind repeated prob interested split dis contribution content content content follow involved sampled sampled vary highest highest attempt illustrates approximating satisfies intrinsic intrinsic remain stimulation powerful exponentially replaced rise fewer reducing tech mse mse mse biol biol referred affect affect affect affect affect func understand cognition fundamental matched matched matched matched act coarse coarse naturally analyze implementations ith attempts analyzed analyzed straight tive berkeley sections widely broad broad broad arise arise mation localized localized arises arises summation profile profile empirically lms lms lms lms lms leave peaks berlin popular ordered pasadena adjust replace kinds decreased contribute contribute benefit cybern cybern secondary resources resources resources resources perfectly dynamically count receptors caltech lost consideration darken darken serves splitting splitting adequate preparation exceeds exceeds repeat repeat bartlett recovered falls widths enhance mel mel mel mel den layout layout layout layout layout layout ballard ballard considerations omohundro omohundro omohundro omohundro explains baldi baldi baldi explorations severe severe unchanged maintaining ple microstructure profiles spaced var var mismatch mismatch mismatch cns manipulation concentrated concentrated exam interact shannon allocated allocated distinguished esti minor parametrized rewritten copies lowe lowe stephen tial heavily suite spacing spacing attempting broadly char affecting fre fre peaked sity adjusts sions curved implying dimen bradford doubling indirectly neglected spa proximation blurred approxima inability quency quency workers cad correspondingly blurring fell multivariable allocate iix recep icsi broomhead broomhead nique preferentially preferentially rli arrangements distribute hyperacuity xii xii investigates alters wash sparser persists acteristics vanishingly excessively broadening broadening broadening nyquist subfields unweighted accrue accrue accrue pends laying approzimation 
#@Mel_B,Omohundro_S,
#t4
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural input input input input input function function function function function function figure figure figure figure figure figure time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output number number error error error error state results results units units units units units units units units information information problem problem problem models models models models models hidden hidden hidden performance space space space space weights weights weights layer layer layer layer layer layer layer layer vector vector vector vector vector vector vector order shown shown systems systems systems probability probability probability probability functions functions functions functions unit unit unit distribution recognition recognition recognition pattern pattern pattern pattern image single single single single single single processing processing processing control control control control control control control large local local local local local local local local local local patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis matrix matrix inputs form algorithms algorithms gaussian gaussian gaussian gaussian visual paper work task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task step step step features classification classification level level current trained structure structure structure structure random architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show equation equation fixed fixed rule rule rule rule rule images general generalization parameter parameter approximation approximation approximation approximation approximation approximation approximation gradient gradient gradient term result result university threshold computation computation solution solution solution solution solution solution solution solution research research log log log log target target target target dynamics dynamics dynamics dynamics science prediction presented presented presented activation activation object object maximum press press press learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn position nonlinear nonlinear nonlinear outputs outputs continuous abstract applied applied applied find find computational likelihood likelihood likelihood likelihood likelihood references ieee procedure procedure adaptive propagation mixture mixture mixture mixture mixture introduction statistical statistical generated generated parallel cost change variable spatial rules rules learned learned learned multiple conditions conditions conditions distributed fact fact region correct probabilities probabilities ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks simulation simulation regression regression respect respect respect multi multi multi multi multi multi multi multi multi multi sum sum sum regions regions means global global global global global global global applications application application desired desired receptive provide compute compute compute objects location perform perform perform perform goal constraints connected gain gain gain cortical brain approaches mit fields morgan morgan proceedings report report institute department consists consists internal advances advances joint joint joint connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist ai cambridge cambridge cambridge cambridge computing hinton hinton hinton hinton hinton hinton view curves curves design design trajectory san san capacity vision vision vision con weighted weighted weighted clustering robot robot controller controller types provided provided selected evidence backpropagation associative associative associative associative associative achieved achieved discussion covariance technical technical feedforward feedforward describe arbitrary group nearest assumed assumed assumed assumed supported main eds eds journal square ability cluster rumelhart rumelhart rumelhart kaufmann kaufmann simulated simulated probabilistic probabilistic probabilistic typically typically fully jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan technology technology significantly york york york trials experts expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert polynomial light denotes denotes denotes denotes denotes architectures recent advantage advantage separate strategy inference cognitive cognitive cognitive cognitive relevant volume volume axis axis tions yields mixtures evaluation chain locations williams williams storage entire grant arm arm arm arm horizontal studied scaling derivative derivative move touretzky touretzky neighbor competitive competitive competitive competitive competitive competitive competitive competitive retina designed designed moody faster learns learns learns mateo mateo suggest sigmoidal variety derivatives scene connectivity program denoted denoted denoted ways generating vertical simultaneously linearly involves springer competition competition competition competition competition john yield yield formation interpretation interpretation interpretation detailed detailed restricted decomposition decomposition decomposition decomposition decomposition decomposition decomposition approximated partition partial earlier earlier barto barto barto epochs epochs combining combining intermediate intermediate transactions thesis activations priori retinal retinal sciences sciences illustrated maximize specifically specifically characterized gating gating gating gating gating gating gating gating gating gating gating gating successfully determining aspects closely capable capable differ mcclelland presentation presentation identify identify literature schemes schemes schemes vowel identity identity receives verlag cun cun prob neuroscience neuroscience superior strategies categories vary localization michael modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular received received consisted operating operating operating jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs receive law law wiley issues issues lippmann mass mass mass matches behavioral ideal possibility relationships authors root cognition possibly adjusted adjusted adjusted noted logic ith ith ith generates submitted plant plant plant plant plant plant plant plant massachusetts massachusetts years residual indicating piecewise piecewise publishers publishers nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan processed drive sys desirable acknowledgement involve author author nsf addressed addressed requiring requiring apparent understood bootstrap frequently exhibits controllers controllers mod asymmetric neuro softmax proportion investigation repre repre impossible robotics robotics robotics robotics allocation tools siemens attractive viewpoint belong heavy combines combines ascent widrow scheduling scheduling approximators foundations sons designing captures captures hart hart discovered approximator explorations robert posteriori posteriori posteriori corporation fellowship achieving ent tables employs medium acceleration 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#@Jacobs_R,Jordan_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data function function figure set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training output output output output output output output output output number number number number number number number number number number system system system system system system system system system system system system system system error error error error error error error error results results results results results results results units units units units units units information information models hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based weights weights layer layer layer case case case case case case case case case case vector vector vector vector vector vector vector order shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values values values probability probability probability parameters parameters parameters parameters parameters weight weight unit distribution distribution recognition recognition recognition pattern single single single single single single single single single single single single single single single single single single single single single single processing control large local rate test test test test test test test test class optimal optimal inputs form form form form form form form form form form form form form form form form form form form form form gaussian paper paper small small net net net work task task task task task task task task methods methods fig features features classification classification classification classification classification current current trained trained trained trained trained trained random high high high similar architecture architecture architecture architecture architecture architecture show show equation section vectors generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real average average average average average gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments dimensional result result university university university university computation research research research research log log defined found found initial constant table table table table table table table table table table table table computer computer computer terms terms terms science science science science low low frequency sets sets sets sets sets maximum range range range range range range range range range range range range range range range range press position outputs outputs abstract back back back back back back back back back back back back back back back back back back back back back find properties references 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total total simulation simulation performed performed means natural study knowledge negative original samples represented compared compared desired desired desired desired perform perform perform determined experimental experimental equal approaches comparison comparison comparison train descent descent descent dependent selection morgan report report report institute words department technique connectionist connectionist connectionist difficult difficult final final exp addition hinton hinton hinton hinton hinton hinton hinton hinton additional solutions san effects effects effects vision give weighted randomly randomly levels types types selected selected selected selected nature simply associative associative associative associative associative associative discussion technical technical technical feedforward feedforward group tested tested close effective supported adaptation adaptation adaptation adaptation journal end ability cluster easily degree makes makes including combination reduced jordan jordan jordan jordan jordan jordan jordan technology interesting interesting interesting testing testing testing significantly significantly head details details details numbers numbers making normalized normalized experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert magnitude magnitude added robust separate typical reported reported reported strategy hierarchical hierarchical cognitive engineering compare compare volume works works speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker correspond studies studies studies trans mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation evaluation evaluation evaluation entire entire lead touretzky generally pass demonstrate half row competitive competitive performs mateo encoding encoding strong variety averaged manner groups acknowledgements generating ann distinct dept pruning implement multilayer category linearly remaining remaining slightly adding frequencies frequencies frequencies frequencies frequencies frequencies frequencies gaussians competition choosing extracted focus overlap viewed evaluated decomposition decomposition decomposition soft suggested suggested barto barto slow performing performing normalization fitting fitting roughly initially initially initially degrees degrees building existing thesis priori bell sciences variations gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating tests determining straightforward selecting middle capable capable society divided divided divided effectively presentation schemes vowel vowel vowel vowel vowel vowel vowel identity identity identity identity identity identity identity composed composed summary repeated procedures strongly strongly contained contained contained contained contained contained contained contained contained symmetry cue cue categories categories categories categories cues cues list generalize modular modular modular modular modular received received received received received received consisted consisted consisted consisted mixing mixing mixing mixing mixing mixing jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs deal receive receive receive modelling poor poor overfitting exhibit varied school combine scaled authors comparable waibel waibel smallest naturally editor predicting predicting extremely created created subsets aspect front der portion algo freedom freedom explored initialized speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers grouping phd percentage advanced explanation nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan worse rapid tive purposes toronto toronto toronto toronto mellon mellon conjugate fourth percent carnegie carnegie cmu exhibits summarized pittsburgh pittsburgh gave segmented utterances utterances specifies multidimensional consistently contextual proportion proportion proportion proportion investigation labelled children fails utterance generalizes child child child child child child child vowels vowels vowels vowels vowels vowels vowels interference interference interference negligible negligible male male male male male male male originally competing competing competing competing competing competing peterson peterson advance tokens specialized reveals formant formant formant formant formant formant formant formant formant formant formant formant formant grants generalizing dividing assigns assigning audio leaving listed outperform sig sig break revealed forced female female female female female female female discovering reflected clustered clustered rithms grouped geoffrey labs meta reveal refined handled copies copies council excess twenty influenced puts hid hid hid steven proportions proportions acoustical striking classi ray raises tended tended tended america watrous watrous watrous watrous watrous fication spec hood localist localist crg crg decompositions spectrograms tongue subtasks subtasks hampshire hampshire ontario puter decides decides formants formants formants formants formants initialised initialised canadian barney barney fellow hierarchically kauffman males associa heard apple chitecture misclassifications ont females uttered uttered hod ciative noranda heed occasions hump 
#@Hinton_G,Nowlan_S,
#t4
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural input input function function function function function function figure figure figure figure figure figure figure figure figure figure time time set set networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output system system system system system system system system system system system system system system system system system error error error error error error state results information information information problem problem problem problem problem problem models models based based based based weights weights linear linear linear linear linear layer layer layer layer case case case vector vector systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems probability parameters parameters functions functions unit recognition recognition recognition recognition recognition recognition method approach approach pattern pattern pattern pattern pattern image single single processing processing processing processing processing processing processing processing processing control local local local local local local local local rate class class class class matrix matrix matrix matrix optimal optimal inputs inputs inputs inputs inputs inputs signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper examples examples examples examples examples examples examples examples examples small feature work task task task task task field classification classification classification process process trained structure problems random representation architecture architecture show show equation equation equation section section section speech speech parameter parameter theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient solution solution defined defined defined defined defined constant table distance distance distance distance distance connections science press press learn components components outputs outputs outputs outputs outputs outputs continuous abstract applied back back back convergence convergence density density density likelihood references stochastic stochastic stochastic stochastic stochastic positive positive important adaptive adaptive decision propagation propagation propagation introduction complex complex complex complex complex complex complex complex complex behavior behavior statistical statistical dynamic cost cost cost cost cost cost cost cost cost cost cost cost change measure measure signals signals conditions expected expected expected expected expected expected equations equations equations markov make correct correct forward forward forward forward forward minimum minimum classes tasks computed computed computed respect respect respect multi multi multi means means global global global global global applications study knowledge knowledge knowledge knowledge vol specific specific true compared application series provide define define compute compute perform goal goal goal goal goal constraints mit train train train descent descent descent descent descent nets morgan morgan morgan morgan morgan morgan proceedings implementation consists consists advances advances advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist delay delay graph framework framework framework framework framework framework framework framework framework framework framework computing hinton view design design san stage efficient world basic produce derived area product product iteration nature depends achieved achieved measured describe hmm complete finding nearest assumed supported theoretical require main eds eds eds adaptation square instance instance instance instance instance instance instance easily easily easily including including kaufmann kaufmann probabilistic probabilistic account functional functional unknown unknown unknown unknown coefficients mlp mlp mlp mlp mlp mlp programming leads minimize perceptron perceptron perceptron denotes denotes architectures architectures architectures architectures architectures architectures recent pair robust takes apply engineering observations observations volume volume module module module module module module module module module module module module module module module module correspond correspond correspond achieve address definition modified risk grant constructed expression concept concept studied studied extended wide alternative feed feed hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid touretzky touretzky touretzky touretzky white white pass conclusion depend sigmoid measures measures measures modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules faster practice external drawn drawn minimizing minimizing min min min min min relationship relationship introduce introduce introduce introduce introduce derivatives derivatives derivatives derivatives derivatives identification acknowledgements reference explicit digit derive produces estimating describes recall implement multilayer remaining unique unique minimization quality quality quality extraction expressed expressed stages detailed operations approximations approximations decomposition decomposition decomposition decomposition decomposition decomposition decomposition converges classical classical classical classical classical combining combining combining combining combining combining distances filtering symbol symbol advantages advantages topology handwritten thesis combinations priori priori priori formulation formulation formulation formulation assignment automatic structural structural suitable presentation build build build composed composed composed refer cun cun cun cun built write modular modular modular modular modular modular modular modular modular backward backward backward backward quantization quantization computes reach receive simpler carried diego parametric parametric parametric recursive ideas school mse combine combine combine combine reliable implementations formal formal perceptton perceptton academic mixed simplest phd defines convolution convolution guaranteed defining defining analytic analytical processed formalism formalism formalism shared incorporate incorporate products mathematics describing describing raw reflect empirically parameterized characterize eventually credit globally contribute initialization lagrange lvq lvq lvq lvq lvq lvq lvq kaufman kaufman promising bourlard bourlard optimally optimally adequate composition composition embedding overview belongs extensively extensively designing designing sequentially sequentially linked linked unified summer misclassification sig cooperative cooperative cooperative cooperative boser boser quasi quasi quasi interact interact interact interact mathematically careful depicts paris paris conversely france universit universit behaves resp resp resp resp lagrangian handling puts bottou bottou bottou bottou bottou bottou bottou cooperation cooperation cooperation cooperation cooperation connectionism acyclic devoted formulas formulas decades progresses subtasks subtasks def recursire meanings impressive feeds euclidian euclidian euclidian euclidian euclidian euclidian med chaining cedex subscripts adaline ljung ljung flamework convolutions cooperate les gallinari gallinari gallinari gallinari gallinari gallinari gallinari surely patrick shah recherche informatique wjk wjk equating laboratoire benveniste benveniste une apprentissage lipmann lipmann 
#@Bottou_L,Gallinari_P,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model neural neural neural input input input input input input input input input input data data data function function function figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output system error error results units units units units units units units units units units units units units information information information information hidden performance performance performance performance performance performance performance performance based based based based based based based based space space space space linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case vector order order order order order order order order order order shown systems systems systems values probability probability probability probability probability probability probability parameters unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution recognition recognition approach approach approach approach approach pattern pattern pattern pattern pattern pattern point point point single processing processing processing processing local local local rate test test test test test patterns inputs form form shows algorithms algorithms simple simple simple simple paper examples examples examples examples examples examples examples examples small size feature net work work work work task task task task task step step step step step step step step step step features features process level current current current trained trained trained trained trained trained trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems random random random random high high high memory response similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture architecture architecture architecture architecture fixed fixed line rule rule general generalization generalization 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activation activation activation activation low low frequency temporal temporal temporal maximum range range range range range range press press press learn learn learn components basis continuous sample sample abstract back back back back properties likelihood references component stochastic due ieee ieee procedure procedure procedure procedure procedure propagation propagation context context context context context context context context context context context context context context context context context context context context context introduction complex hand estimation statistical statistical statistical statistical generated parallel recurrent recurrent recurrent tion tion tion tion tion tion tion complexity complexity rules rules rules rules rules measure representations representations representations previous previous required binary represent distributed distributed distributed distributed distributed distributed markov make proposed proposed proposed proposed proposed proposed correct correct correct correct correct correct probabilities errors errors errors scale scale ing total simulation simulation simulation simulation simulation simulation human human called called elements potential dimension made made global global global global applications knowledge knowledge knowledge knowledge relative relative represented represented represented represented represented represented represented perform related constraints constraints constraints constraints constraints discrete equal approaches approaches approaches mit steps connection connection connection connection connection selection morgan proceedings report institute department department department technique consists consists internal internal internal code advances joint represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult final scheme scheme scheme addition sequences sequences sequences sequences sequences sequences ai considered cambridge computing computing computing experiment environment environment environment environment directly hinton hinton hinton additional additional additional transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition san san effects conference conference determine full choice choice statistics statistics con con con produce randomly criterion selected selected backpropagation nature simply simply simply associative achieved achieved achieved achieved measured discussion technical increases describe describe tested tested transformation predictions predictions finding amount short generate supported role eds eds eds face journal end end ability instance future makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart kaufmann pairs pairs account account fully transfer interesting testing york head mode mode principle representing pre making international international normalized expert magnitude produced produced run predict predict predict denotes architectures architectures improved directions similarity similarity similarity similarity apply inference array cognitive cognitive relevant relevant relevant relevant engineering dimensions sufficient varying varying compare approximately volume axis tions tions studies address generalized williams williams sensitive grant grant constructed constructed lead studied studied predicted alternative alternative alternative alternative correctly correctly correctly correctly correctly touretzky deterministic generally half half half half half strength strength strength critical critical valued central sigmoid designed exponential exponential practice learns mateo external external turn variety start manner denoted acknowledgements explicit pro pro produces produces written index index perception ways primary generating generating coordinates simultaneously electrical involves involves involves remaining scales scales scales scales scales mutual versus versus select extracted formation review transform transform evaluate approximations allowed allowed key key key key key roughly purpose string symbol assigned foundation norm euclidean kohonen kohonen kohonen kohonen kohonen kohonen kohonen faces avoid perceptual combinations coordinate coordinate extension automatic mozer mozer mozer mozer mozer mozer mozer mozer mozer mozer mozer mozer absolute absolute grammar grammar grammar grammar grammar grammar characterized major major major major straightforward selecting selecting aspects encoded encoded encoded included mcclelland build invariance ten ten reached composed capture capture traditional traditional refer refer kind prob allowing interpreted dis issue running follow criteria duration duration built built built notation michael generalize generalize denker highest highest consisted consisted consisted consisted neighboring deal law diego create collection essential difficulty exponentially exponentially rapidly strengths helpful rise matches matches tech tech rest relationships referred symbolic symbolic encode func func cognition notion analogous analogous circles circles man man predicting predicting created perfect adjusted algo observe motivated attempts indicating pairwise distinguish coded caused baum handle sys easier style style style style incorporate immediately universal describing circle circle circle circle circle pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch gradually begin lowest depicted depicted annual nsf researchers people people people evaluating collected items elman elman elman amounts fed readily psychophysical share completion incorporated music music music music music music music music music music music music psychological psychological psychological passes passes passes operate synthesis gen gen cal suited sums coherent inherent sophisticated comments coherence focused specifies specifies specifies naive notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes sort sort sort discover discover discover impossible smolensky proceed extending systematic difficulties logarithmic height height height height interpret hope operates corpus phrase phrase phrase grammars continue composition composition composition composition composition composition composition composition composition composition composition composition composition composition composition composition representational james paul induce pat expanded colorado colorado colorado captured facilitate facilitate candidates similarities entries foundations express creating offer proximity discovered discovered discovered explorations sequentially appeared geometrical ple unable microstructure logarithm shepard shepard shepard shepard shepard shepard shepard ter piece piece piece piece piece piece piece piece piece piece piece tables tables tables ties job presenting presenting pieces pieces pieces pieces pieces pieces encouraging possibilities hillsdale certainty examining musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical argue chauvin formance cessing rithms geoffrey tems boulder boulder boulder books books retain iri represen importantly drawback alternatives inversely suffer tones minor minor minor mimic likewise places indication behave bring bridle bridle examination walk walk walk lems heading remarkable regularities regularities regularities regularities preserves algorithmic algorithmic algorithmic accordance justification vii mcdonnell assistance todd todd todd todd spacing melody melody melody melody determinant resolutions contrasts extracts concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert concert ultimate restricting tended tance suffice bach bach bach accommodate voice tations deter bradford ings routes bear promise durations eighth tern publishing miyata marker judge judge lowered excluding eralization terminated quarter translating wired wii thirty retains lacking necessity melodic melodic melodic melodic melodic mined ponents rescaled spans perceive masks nectionist compose amples comput altogether altogether tonal tonal tonal selector contingencies contingencies equipped unrealistic nique octave octave octave ist embody silence straints 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#@Mozer_M,Soukup_T,
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#*network network model model model model model model neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data function function function function function figure figure figure time time time time time set set set set set set set set set set set set set set set training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output number number number number number number number number number number number number number number number number number number number error error error error error error error error error error error error error error error results results information problem problem problem problem problem problem problem problem problem hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space vector order shown shown systems systems systems values values functions functions functions recognition recognition recognition recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point single processing processing large large rate rate rate rate rate rate rate rate rate test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class class class class optimal shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net work work task task task fig fig fig field features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process problems problems problems high high memory memory memory memory similar similar vectors vectors vectors generalization generalization speech speech speech speech speech average obtained experiments experiments experiments experiments experiments result result threshold computation computation computation computation solution solution solution research research research log found found found found found initial computer distance science low low nodes machine machine sets sets maximum basis abstract applied find likelihood references important decision decision decision decision introduction complex complex complex complex complex estimation generated parallel parallel parallel parallel search search search search search search search search search search search search search search search search search search search search search tion tion complexity complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower measure word word word word word previous type required required required required required required required required required required multiple good good good good good good good good long long markov markov markov techniques techniques techniques proposed forward forward classes classes classes classes ing tasks tasks tasks tasks tasks total total total performed performed performed performed called times times times factor factor factor dimension applications applications study original original original original original original original original original original original original original original original original artificial artificial represented represented compared application cross provide provide provide provide rates rates rates rates rates rates rates perform determined determined determined goal related distributions approaches approaches approaches approaches approaches mit accuracy accuracy accuracy accuracy accuracy dependent selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection proceedings institute words department department technique technique consists advances advances difficult difficult difficult difficult final final cambridge experiment experiment directly solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions top stage stage stage stage stage bit bit bit bit bit bit conference classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers vision vision increase increase validation randomly randomly randomly developed criterion provided provided selected selected selected selected selected selected increases increases describe group tested hmm limited limited limited finding nearest nearest nearest nearest nearest effective effective effective effective effective effective generate require eds end ability makes development including including simulated typically typically typically smaller combination combination reduced reduced reduced reduced reduced reduced technology testing testing testing testing testing testing testing testing testing testing significantly ratio ratio increasing head head head trials trials database database operation operation operation operation details stored stored bits bits bits international international bottom polynomial polynomial polynomial produced run run run population population population population population population population population population improve improve improve improve improve improve improve advantage practical practical apply apply include identical trees trees subset subset subset subset engineering dimensions compare conventional conventional tions evaluation evaluation modified parts alternative correctly touretzky touretzky occurs occurs generally half starting minimal reduce reduce reduce conclusions neighbor neighbor neighbor neighbor neighbor depend moody faster suggest reduction cycle proportional intelligence radial user annealing force force acknowledgements areas reference reference sequential sequential sequential generating generating plot plot laboratory linearly electrical dimensionality dimensionality easy easy consisting adding frequencies select select select select letters stages stages influence evaluated static static approximated allowed allowed discrimination processor roughly roughly roughly purpose boundaries boundaries boundaries boundaries boundaries boundaries generation generation initially string string string string assigned classified thesis combinations strings strings strings strings strings strings strings strings strings strings determines automatic tests simplicity regular selecting selecting identified identified letter encoded encoded included successful genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic vowel vowel vowel vowel vowel vowel ten traditional decoding contained allowing heuristic heuristic heuristic heuristic success issue duration usual backward backward providing automatically consisted explore explore simpler powerful create create create requirements requirements requirements requirements exponentially rapidly replaced lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann fewer fewer fewer fewer reducing reducing incremental applicable office complicated proved created created created perfect recognizer changed subsets rank portion explored generates improving serial massachusetts percentage developing analyzed improves improves improves widely mation scientific english lowest computers computers sun exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars requiring applies tional leave leave leave poorly treated frequently maintain limiting parent parent parent prevent richard richard richard replace decreased viterbi eventually progress progress june converged benefit identifying identifying impossible grows exemplar exemplar exemplar exemplar exemplar exemplar exemplar air air allocation ments chance resulted resulted resulted hope knn knn knn knn knn knn knn knn knn knn knn knn knn knn responsible adequate alphabet days hours infor evaluations evaluations mance perfor overview bad washington reproduce creating creating creating offer master fitness fitness fitness fitness fitness fitness fitness waveforms formant parents pressure linked unable exhaustive exhaustive exhaustive comparative female female workstation eric eric alternate crossover crossover crossover crossover crossover crossover searches searches eliminating picked proach deleted portions portions attached ation nal experi moderate satisfactory impractical impractical impractical smoother hid hid hid char usefulness separates huang huang classi classi william creation creation creation creation creation creation fication fication signed adequately texas mutation mutation mutation mutation replicate degrades gradual sponsored hood hood hood degrade tightly lincoln altering enforced chang chang chang chang chang chang dominate exponents undergoes classifica ranked ranked begun gmdh preset ending workstations reproduction jour talker talker talker talker ror loses cre instruments heard heard heard lexington unreasonable condensed condensed manipulate eventual conven hod hod hod varieties acteristics whitley whitley spectrally 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#@Chang_E,Lippmann_R,
#t4
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural input input input function function figure figure figure figure figure figure figure figure figure figure figure figure time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number system system system system system results units units units units units information information information information information problem problem problem problem performance performance performance performance performance based space space weights weights weights weights weights weights weights weights weights weights weights weights layer layer case case case order shown shown shown shown systems systems systems values weight weight weight weight functions functions unit unit unit distribution distribution recognition recognition recognition recognition recognition approach approach approach pattern pattern pattern pattern pattern pattern point point single single large local local local rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns analysis optimal optimal optimal optimal inputs shows shows shows algorithms algorithms algorithms simple simple small small small task task fig fig process process process level trained structure structure problems problems problems high high high similar representation architecture show show images general real average average gradient gradient gradient gradient note note dimensional university university computation research independent defined initial initial initial initial standard connections synaptic synaptic synaptic present present machine sets press position position position position outputs abstract applied references stochastic introduction complex complex effect effect effect effect parallel search search search search change change energy energy spatial spatial lower learned learned learned chosen chosen chosen higher higher higher higher higher higher higher part center cases multiple good good represent represent represent distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed region simulations simulations simulations minimum total total simulation simulation times factor factor optimization optimization natural orientation orientation orientation orientation orientation filter artificial artificial artificial relative relative cross rates perform perform determined determined related connected connected connected connected connected equal equal approaches approaches connection connection descent descent descent dependent selection selection selection technique technique consists individual represents layers scheme scheme scheme scheme scheme addition considered environment directly hinton hinton curve curves bit determine upper choice significant increase increase randomly randomly randomly randomly processes selected selected selected nature depends biological biological measured discussion increases increases describe close corresponds amount amount amount amount amount amount amount amount amount require adaptation end pixel pixel rumelhart development including typically account fully fully significantly significantly significantly significantly structures trials trials trials uniform uniform uniform uniform uniform uniform uniform uniform language leads leads leads leads leads leads leads leads leads leads leads leads numbers numbers numbers filters filters bits supervised combined perceptron perceptron population population population population population population population discussed improve engineering sufficient conventional tuning solve solve studies converge positions grid grid improvement improvement increased exists lead lead correctly correctly correctly correctly hybrid hybrid hybrid hybrid hybrid hybrid occurs pass runs strength strength greater conclusions central central central interactions interactions performs performs faster faster faster demonstrated california proportional selective decrease scene minima minima minima force solving ways dept category category category category category electrical quality implies letters evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution slow slow slow slow generation generation generation generation generation generation generation generation generation generation generation intermediate intermediate intermediate intermediate initially advantages advantages classified david david avoid black discussions successfully determining closely identify identify identify schemes schemes schemes schemes genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic score score score receives receives receives road strongly strongly superior classify categories leading received received overlapping illustrates acknowledgments receive receive selectivity powerful american poor essential experience strengths detectors complicated affect contours contours contours contours attributes hill coarse reading equally equally perfect perfect changed detector detector detector detector detector perceptton detected arbitrarily submitted slope biology nowlan nowlan worse stanford stanford stanford closer pure slower decreased eventually wesley extreme classifying addison driving perfectly perfectly guide arrays combinatorial alphabet presentations presentations presentations presentations presentations presentations presentations presentations continue analyses holland holland bad offers reproduce reproduce reproduce reproduce reproduce reproduce peterson peterson 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#*network network network network network network network network network network network network network network network network network network network network network network model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data function function function function time time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training output number number number number number number number number number number number number system error error error error error results results units units units units information information information information information information information information problem problem problem problem problem models models hidden hidden hidden performance performance performance performance performance based based based based based based space space space space weights linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case vector vector vector vector vector shown systems values values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters weight functions functions functions distribution recognition approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point image image single single processing processing control large large large large large large large large large rate patterns class class class class matrix inputs inputs inputs inputs inputs inputs algorithms simple paper examples small small small size size size size size size size size size size size size feature feature feature feature feature feature net net net net net net net net net work cells cells cells cells cells cells cells cells points points points points points points points points points points points points features features classification classification classification classification classification classification classification classification classification classification level level current current cell cell cell problems random random random high response representation architecture architecture architecture architecture architecture architecture architecture architecture show section section rule rule vectors vectors vectors vectors vectors general generalization generalization generalization generalization parameter parameter real approximation average theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained dimensional result university threshold threshold threshold threshold threshold threshold threshold variables computation solution independent independent log log log log log defined found estimate estimate estimate terms connections connections node node node node direction direction presented presented low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency sets maximum position position components components components components components basis basis nonlinear nonlinear outputs outputs outputs outputs sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied find convergence references stochastic due ieee ieee ieee important important important important important adaptive decision decision decision decision decision context complex complex complex hand estimation behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical effect effect generated generated complexity complexity complexity complexity variable assume classifier classifier classifier classifier prior prior part previous theorem bound bound bound bound bound bound bound bound cases cases cases required required required required required good good good binary binary binary binary make make make make fact region region correct correct probabilities probabilities probabilities probabilities simulations classes classes classes classes classes ing simulation called elements regions regions regions regions means means means means factor dimension dimension dimension dimension dimension dimension made natural applications applications applications negative samples samples samples samples samples true application application application application desired desired series provide provide provide experimental goal goal posterior constraints distributions equal approaches accuracy accuracy larger support train source source source nets selection morgan individual individual individual advances responses responses responses difficult layers layers layers layers layers framework domain domain domain view estimates design design design limit limit bit capacity determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper upper upper upper full choice choice significant significant approximate free free con randomly clustering clustering clustering clustering clustering bounds bounds bounds bounds bounds bounds bounds actual actual provided provided provided processes selected selected depends simply achieved measured measured discussion covariance feedforward feedforward feedforward increases denote denote denote fast fast close close assumed generate require require require require pixel pixel pixel ability ability ability easily development typically underlying needed reduced account unknown significantly character character special empirical empirical principle leads direct direct direct making window bits bits bits magnitude attention choose sources sources denotes denotes denotes denotes improved discussed discussed directions exact typical reported practical include subset subset subset subset array engineering interest interest dimensions approximately calculated tions tions yields yields yields studies studies studies converge achieve trans trans address definition evaluation bounded bounded improvement constructed suggests suggests suggests wide touretzky width width deterministic clusters clusters clusters clusters clusters hardware conclusion conclusion critical conclusions valued central accurate bayes clear moody moody practice practice practice practice practice practice practice asymptotic asymptotic weak suggest suggest suggest suggest hard largest reduction drawn drawn sigmoidal assuming acoustic force base acknowledgements relation construct index generating mathematical distinct implement category category linearly electrical dimensionality dimensionality dimensionality belief belief unique consisting consisting springer springer formed boolean select select yield yield yield yield yield choosing family family formation viewed viewed detailed detailed restricted restricted approximations understanding sizes sizes partition partition partition discrimination partial reasonable calculation fitting event roughly boundaries valid calculate classified classified precision precision expect expect expect expect priori coordinate bell subspace subspace vapnik vapnik vapnik vapnik vapnik vapnik prove characterized selecting successful successful literature literature fine fine fine fine composed compact verlag verlag cun cun prob interested issue issue contribution categories absence realistic providing nips nips nips quantization quantization quantization quantization quantization quantization denker subsequent deal unlike carried powerful overfitting overfitting experience exponentially varied replaced limitations pursuit helpful fewer fewer ideas school terminal parity parity combine referred reliable reliable reliable workshop workshop possibly man equally recognizer ensure subsets subsets portion noted explored explored nerve ith fibers improving improving regime established devices inequality inequality directed theoretic separable growth growth growth derivation analytical majority adapted capabilities tractable baum baum lies rapid rapid perspective purposes forces constructing constructing worst worst worst worst worst involve members members preceding preceding meaning raw argument argument argument argument substantially transient flexible effort orders adjustable haussler haussler incorrect summarized limiting differs aim fall serve prevent richard substantial enables fiber focused irrelevant identifying sort optimality optimality assign assign restriction restrict summing arguments arguments arguments narrow hyperplanes labelled labelled concerned unity unity unity grows proceed rational kaufman dealing dealing dealing dealing consideration darken darken promising promising difficulties determination interpret hope exploit exploit optic guide adequate exceeds carry nonparametric analyses analyses analyses weakly equals overview thomas darpa enable enable insight repeatedly properly sustained informative agree considerations designing designing designing designing avoiding thresholding assigning empty discriminate approx unable listed annals annals accept guyon guyon chervonenkis chervonenkis chervonenkis chervonenkis adopt adopt adopt restrictions restrictions theorems seek acceptable tradeoff reports assess illustration quantized mismatch mismatch pub exponent community gained hubbard hughes hughes expand afosr march efforts terrence individually exceed exceed categorization sketch spanned nonetheless nonetheless enforce simplex union union union thousands dichotomies recognizers suggestions suggestions remarks excess excess excess excess curse hundreds inequalities inequalities concern proposal continuum exposed meeting quantizer quantizer lying resolved restricting restricting rameters occam approaching suffice implying meant prescribed inappropriate wagner wagner expresses derivations assessing argmin accepting topics preprocessor ness touch hoeffding dealt dependences albeit tentative prohibitively classifica tially occupied implementable unclear hypothesize widespread razor critically critically critically critically critically accompanying oft prepared exceeding reductions cited validate uninformative albrecht doubt collectively pollard pollard pollard pollard opened contradiction cornell minimally devroye devroye insightful urn quantize quantize generically quantizing nmnber imations alphanumeric til chernoff chernoff chernoff 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#*network network network network network network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function figure figure time set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm output output output number number number number number number number number error error error state state results results results results results results results units units units units units units units units units units units units information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space space space space space weights weights linear layer layer layer layer case case case case order shown systems systems values probability probability probability probability parameters parameters parameters parameters parameters functions recognition recognition recognition method approach approach approach approach approach approach pattern pattern pattern point image processing control large large large large large large large local rate test analysis analysis class class class class class class class class class class class class class class optimal optimal optimal form form algorithms algorithms algorithms simple simple simple simple paper paper paper paper paper paper paper size size feature feature feature work work task points points classification classification classification classification classification classification classification trained cell structure structure problems problems problems random architecture architecture show show rule rule general general general general general parameter real real average theory theory theory theory theory theory theory obtained obtained term term term term note note note result result variables variables solution research research research independent log log log log log log log log log defined defined defined defined defined found sequence constant estimate estimate estimate standard terms terms node node prediction left left map activation activation nodes nodes maximum maximum maximum maximum press continuous sample sample abstract applied applied find density properties likelihood likelihood likelihood likelihood references references component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due ieee ieee ieee procedure procedure decision decision decision decision context context context introduction complex complex hand hand hand estimation estimation estimation estimation estimation estimation statistical statistical statistical variance cost search search search search search tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable variable variable classifier classifier classifier classifier classifier lower measure measure prior prior prior prior prior chosen chosen part bound bound cases cases good good binary binary binary represent tree bayesian bayesian bayesian markov fact techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques region region region proposed proposed proposed proposed proposed length length length length length length length length length length length length length length length length length length length length length probabilities probabilities forward finite finite minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting classes classes total respect multi multi multi multi performed elements mapping mapping factor factor optimization optimization applications applications obtain negative vol vol artificial relative relative samples application application application application application cross cross provide provide provide provide define goal related related related posterior posterior constraints discrete discrete discrete discrete discrete larger modeling selection selection selection morgan proceedings proceedings proceedings proceedings institute institute words words technique technique consists advances difficult difficult final layers scheme scheme addition addition addition addition ai ai framework equivalent curve curve estimates estimates design design design design limit limit san stage bit conference conference determine efficient classifiers classifiers upper upper upper upper requires requires choice approximate statistics statistics basic produce condition coding coding coding coding coding derived conditional conditional criterion criterion criterion bounds bounds entropy entropy entropy entropy entropy entropy provided finally discussion feedforward describe describe assumption assumption complete surface finding finding amount amount short common assumed supported theoretical hypothesis hypothesis makes rumelhart including fit fit fit fit kaufmann objective typically typically smaller account technology technology york special special database principle principle principle numbers numbers numbers pre bits bits bits international international international normalized idea attention choose choose description description description description description description description description description description description description description description description description description description description description description description description perceptron exact takes practical practical practical trees sense sense inference inference inference inference subset recently interest interest interest interest conventional observations calculated calculated volume works axis correspond correspond trans trans definition definition background bounded bounded bounded risk risk risk grant exists lead lead suggests alternative correctly feed demonstrate conclusion conclusion critical minimal minimal minimal minimal greater depend bayes bayes bayes bayes clear practice practice practice practice mateo characteristics california california proportional proportional turn turn variety variety min introduce manner manner manner manner force pro construct factors laboratory label easy belief unique mutual mutual adding applying springer boolean decreases national national family family family interpretation interpretation detailed evaluated evaluate labels labels labels past past earlier earlier calculation calculation normalization boundaries penalty penalty penalty initially calculate calculate calculate assigned assigned classified precision precision existing combinations perceptrons sciences discuss discuss candidate candidate candidate candidate candidate major compression selecting selecting differ modification modification effectively successful literature literature miller fine reached capture traditional refer soc compact verlag prob prob success link link interpreted issue lie notation minimizes hypotheses automatically principles principles consisted moves acknowledgments intrinsic situations remain unlike poor poor collection rapidly limitations issues graphical hall biases ml ml examine incremental possibility office referred referred complicated workshop workshop affect cover cover fundamental notion notion notion notion notion attributes naturally possibly necessarily necessarily necessarily equally ensure obvious obvious greedy greedy ith ith extent motivated brown ground defining independence briefly lies london london considerable turns purposes formalism easier worst immediately arise arise scientific universal implicit medical medical preceding summation questions freeman freeman flexible orders frequently rep weigend pasadena achieves marginal inherent patients diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis intractable restrict arguments arguments narrow dynamically discovery eliminate eliminate royal eliminated communications air consideration consideration consideration consideration consideration consideration stated stated check grow contract star implications affected optimally exceeds alphabet motivation evaluations ambiguity patient lengths lengths searching originally barron barron barron barron insight cancer cancer reader shortest matter inductive inductive implicitly tures appeared equivalently goodman goodman pointed seek mdl mdl mdl mdl mdl mdl mdl scenario param clas clas ary ary argue translated insights chapman chapman afosr eliminating smyth smyth smyth smyth smyth smyth smyth smyth academy paris portions alternatives nonetheless nonetheless france inversely preprint truth admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible admissible 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#*network learning learning learning learning learning model neural neural input input input input input input input input input input input input function function function function function function function function function function function function function function function function function function function time time time set set set set set set set set set networks algorithm algorithm output output output output output output output output output output output number number number number number number number error error state state state state state state state state state state state state state state state state state state state state state state state state state results results results results units units units units units units units units units units units units units units units units units units units units units units units problem models models hidden hidden hidden based weights weights case case case case order probability probability probability probability probability probability probability probability probability probability probability probability probability parameters weight functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method method method method method method single single processing large local patterns patterns patterns patterns class class class class inputs form paper paper paper examples size size size size size size size net step step step step step step step step step step step step step step step step step points classification classification classification current current current structure problems problems problems problems high high high show show show show show show section section section section section section section section section section section section section section fixed fixed fixed rule general general general parameter parameter states states states theory note note note result result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables computation computation computation research defined defined constant constant constant constant computer computer computer computer distance distance distance node node node node node node node node node node node node science science science science map nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine maximum maximum maximum maximum maximum maximum maximum press press outputs abstract abstract convergence convergence convergence references stochastic ieee ieee positive positive procedure decision context context introduction hand hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit effect parallel parallel parallel parallel tion tion change change change change change change change change change change change change change change change change change complexity complexity complexity complexity assume assume assume assume assume assume assume assume assume lower previous theorem theorem theorem theorem theorem theorem theorem theorem required required binary tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed make fact fact fact length length simulation simulation computed computed computed computed called elements global global global global global global global applications applications applications desired series define define define define compute compute proc proc connected connected discrete brain equal power mit steps steps connection connection connection connection connection connection connection connection connection update nets department department consists consists difficult addition addition graph graph graph graph graph graph ai considered considered considered considered considered considered considered considered considered considered considered cambridge hinton hinton view view view design design design design design design bit conference efficient efficient efficient efficient efficient efficient efficient efficient efficient upper upper choice choice choice statistics speed speed speed increase condition bounds bounds types path nature depends achieved discussion increases arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary group fast fast fast limited proof proof circuits circuits circuits circuits common assumed eds end end end end end end hypothesis rumelhart simulated simulated pairs hopfield hopfield coefficients york york edge edge edge edge edge numbers numbers stored depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial choose separate similarity apply apply machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines sejnowski cognitive relevant relevant interest interest conventional converge converge converge converge converge definition definition definition definition definition symmetric symmetric symmetric bounded bounded bounded gate gate gate gate gate gate gate gate gate gate gate gate gate interval interval constructed constructed constructed exists extended occurs strength minimal depend depend temperature temperature propose hard labeled labeled labeled labeled decrease introduce introduce manner configuration configuration configuration configuration configuration configuration configuration annealing boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann appears construct edges edges edges edges edges written sequential sequential sequential changing simultaneously easy implies implies boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean john john family independently variation variation transform open approximations similarly converges remains remains valid sufficiently construction construction construction views strings assignment assignment assignment prove prove discuss absolute holds holds suitable suitable suitable society computations tend refer conf timing sci comp comp write write write write usual usual computes computes computes computes computes computes computes employed wiley wiley investigate strengths strengths strengths strengths strengths strengths strengths strengths strengths fourier fashion fashion applicable parity parity root gates gates gates gates gates cognition induction induction induction induction closest configurations obvious precise logic ith defines asynchronous directed directed directed directed directed directed guaranteed analytic turns easier division leaves arise mathematics consequence beginning beginning author annual preceding applies substantially understood simulate maxima ture replace replace hamming hamming hamming calls restriction fix jth maass maass maass maass maass clamped clamped rational determination check belong imply synchronous synchronous corollary decide washington belongs multiplied advance foundations sons sons considerations convergent integers integers explorations verify ple equivalently theorems connec chicago chicago chicago massively exam pdp relating parallelism parallelism parallelism parallelism parallelism parallelism siam minor status mann remark remark copies remarks remarks sorting hoc illinois visit concrete concrete ackley lying polynomially longest acyclic acyclic acyclic cyclic successor syst fore replaces undirected acceptance cir accepts constructions mediate unlimited unlimited unlimited unlimited unlimited suggestion clamping clamping gupta gupta gupta consensus consensus consensus consensus consensus consensus consensus consensus consensus subtraction constantly constantly ixi acknowledgment oft subtrees ein ein scalable scalable contradiction contradiction successors successors successors nen predecessors predecessors predecessors relearning oxi chines schnitger schnitger muroga unsatisfactory wolfgang cuits georg slate reserve cvs cvs chandra hajnal psi psi multiplica szegedy mulated microstruc stockmeyer vishkin 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural function function function function function function function function function function figure figure figure figure time time time time time time set set set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system error results results problem problem problem problem problem problem problem performance space space linear case vector vector vector vector vector vector order order order order systems systems systems parameters parameters parameters parameters parameters unit distribution distribution distribution recognition method control large large large large large large large large local local local local local local local local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis analysis class class class class class class class optimal optimal optimal optimal optimal optimal form signal algorithms algorithms algorithms simple simple simple simple paper paper paper paper paper small small small small small work work work work task task task task task task methods fig fig fig step step step points points field features features classification classification current current problems random random high equation line line line line general generalization speech parameter parameter parameter parameter parameter approximation approximation approximation approximation average average average average average average average average average average average average average average average average theory theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient term note note note note note experiments dimensional dimensional result university university threshold computation solution solution solution defined defined constant constant constant constant constant constant constant constant constant constant constant constant distance distance distance distance direction presented present phase low low machine nonlinear continuous sample sample abstract find find find find find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due ieee ieee adaptive adaptive adaptive adaptive adaptive context introduction statistical variance search search search search search search search search search search search search search tion tion chosen chosen previous cases type good good good good long conditions conditions conditions distributed distributed make make region observed observed minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting resulting ing ing tasks total simulation called called times means means means means means means means means means means means means means means means means means means means means means means means optimization optimization optimization optimization optimization optimization optimization global global global global global global applications study study study obtain obtain artificial specific specific compared application compute compute proc equal power comparison comparison comparison comparison descent descent descent descent descent descent descent descent descent report department technique joint difficult final equivalent directly directly conference determine full choice choice significant statistics speed speed speed con produce clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering backpropagation backpropagation depends depends achieved technical fast fast fast complete short short nearest nearest nearest assumed supported square square square square end instance cluster cluster easily including objective objective objective objective objective typically typically smaller unknown significantly head head head special uniform empirical empirical squared details numbers making international minimize choose choose choose run run predict improved recent advantage practical practical practical apply introduced engineering interest interest interest sufficient compare compare correspond converge converge converge converge converge converge converge converge converge converge converge converge converge converge converge converge converge achieve achieve achieve trans locations locations grid grant grant predicted deterministic deterministic white white white generally generally generally setting runs runs runs runs runs greater conclusions conclusions measures clear moody moody moody moody moody moody moody moody moody moody moody practice practice asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic california solid proportional labeled min decrease introduce introduce minima minima minima minima acknowledgements appears relation pro pro transitions ann stability linearly quality expectation john decreases decreases independently interpretation centers forms converges dashed measurements classical classical classical classical reduces visible assigned box figures includes includes plotted automatic characterized compression capable uniformly uniformly literature literature literature reached traditional quickly quickly prob prob issue running running running running running running running running running running running running minimizes quantization automatically moves satisfies law law minimized schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule poor limitations recursive dotted preliminary authors func math math ensure front shapes multivariate simplest simplest asymptotically asymptotically asymptotically residual residual great slowly slowly slowly slowly developing guaranteed guaranteed slope slope improves expensive expensive perspective berkeley located mathematics addressed exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars improvements understood lms lms lms quantitative poorly backprop dots proven extensions inherent age progress phenomenon optimality optimality guarantee member member exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar generality communications darken darken darken darken darken darken darken darken darken darken settings optimally optimally preparation degradation published bad schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules claim surprisingly indicator late onr yale yale yale slight outperform outperform ent email suboptimal additionally visualization community afosr scope nonetheless stuck drops drops rnn lems moderate council instability confirm locate usefulness station triangles implied quick stick began metastable metastable metastable preferable proximation stat stat haven vergence fractional llx goldstein goldstein tll conversations grown restart agation clus syrup aware stays aver live periments qualities southern robbins robbins robbins robbins illustrative illustrative hoped kauffman cited monro monro monro monro backpropaga ljung ljung shrinking christian portant obser pected lihood consis cedure 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systems systems probability probability parameters distribution distribution recognition approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point large large large large rate rate analysis optimal optimal optimal optimal optimal optimal optimal form form shows simple simple simple paper paper size work work methods cells cells points points classification classification classification classification cell cell random random show show show equation equation section section vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general approximation approximation approximation approximation theory theory obtained dimensional result result university university university university solution solution research research research independent independent defined defined sequence initial initial initial science presented present present present present components components continuous sample sample abstract convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density properties properties references stochastic stochastic stochastic stochastic ieee positive positive positive procedure adaptive decision decision decision decision decision decision decision decision decision introduction effect effect generated tion assume assume assume assume assume classifier classifier classifier classifier classifier classifier classifier prior chosen center center theorem theorem theorem binary conditions conditions conditions conditions conditions represent represent represent represent represent represent distributed bayesian bayesian bayesian equations equations techniques correct observed minimum resulting classes classes simulation times regions means means made made true location approaches comparison larger update update update update update update update update report department represents represents addition domain detection choice statistics con finally backpropagation iteration increases increases close close assumption complete stable stable stable stable stable proof finding nearest nearest nearest nearest nearest nearest nearest supported require underlying technology significantly significantly york york iterations discussed pair reported introduced moving subset engineering interest previously observations observations observations observations observations observations observations observations observations observations observations tions correspond studies converge converge converge converge converge locations modified modified modified modified modified modified modified observation observation observation observation observation observation observation observation observation bounded risk risk risk risk grant suggests locally locally move occurs occurs conclusions neighbor neighbor neighbor neighbor neighbor neighbor neighbor bayes bayes bayes bayes bayes performs practice asymptotic asymptotic constrained taking demonstrated manner scene acknowledgements suppose suppose suppose construct recall electrical consisting equilibrium equilibrium equilibrium springer john john national review estimator densities updated constants allowed past past sign calculation reduces assigned assigned foundation kohonen kohonen kohonen kohonen transactions determines prove prove prove prove discuss discuss specifically candidate determining suitable modification modification modification modification modification modification modification modification literature literature compact verlag showing interested hold hold notation notation quantization quantization quantization quantization hypotheses satisfies decreasing origin wiley divergence divergence divergence scalar tech office decisions decisions decisions decisions decisions decisions decisions statistically cover cover closest closest closest closest closest closest changed obvious algo initialized initialized averages phenomena majority majority majority majority majority majority majority correction considerable satisfied closer strictly strictly choices beginning passes berlin fall prevent adjust attraction lim ordinary college college identifying extensive rithm lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq concerned naval adjusting satisfying proceeds replacing effectiveness nonparametric lyapunov lyapunov lyapunov equals moved moved infinity infinity infinity park park agree agree agree agree sons hart hart hart hart convergent onr approx fellowship fellowship ease ease adjustment argue community duda duda picked concentrate paris unconstrained cation likewise likewise prevents infinitely voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi demonstrating dissertation vote vote vote vote vote vote vote anthony clark clark falling relaxed appro texas maryland maryland maryland maryland maryland analyse diverge coincides mason heidelberg pushed pushed pushed froin ell asso asso emphasizes helsinki iix lira occuring kushner kushner integrand instruments ilx ilx originated nical obser observa nonincreasing defect trl trl ciated ciated chances ool imations priate vations benveniste benveniste benveniste cdr verges modifi ameters reals forin forin doc 
#@Baras_J,LaVigna_A,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural input data function function function function function function function function function figure figure figure figure figure figure set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training output output output number number number number number system error error error error error error error error error error error error error error error error error error error error error error state state results information problem problem problem problem problem models models models performance performance based space weights linear case case case order order systems values values values probability probability probability probability probability probability probability probability probability parameters functions functions neurons neurons neurons approach point point single processing processing large neuron neuron neuron neuron test analysis analysis form shows signal signal simple gaussian gaussian gaussian gaussian paper examples examples examples examples examples examples examples examples examples examples examples examples examples size size size size net net net net trained trained trained trained trained trained problems problems random similar equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation section section section section fixed rule vectors vectors general general generalization generalization generalization generalization parameter average average average average average average average average average average average average theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory term experiments experiments experiments experiments experiments experiments experiments dimensional dimensional university university computation solution independent independent independent independent independent defined found target target target target target target target target target initial estimate estimate estimate prediction prediction prediction phase sets sets sets maximum maximum range press learn learn continuous continuous sample sample sample sample sample abstract applied applied find find find find density density density density density density density density density density density density density density density density density density density density density density density density density density density density references ieee ieee positive procedure procedure important behavior behavior statistical statistical statistical statistical statistical effect effect generated variance variance variance parallel search change prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen center center previous good binary represent distributed bayesian expected expected expected equations correct probabilities probabilities errors errors errors errors errors errors errors scale scale finite finite finite finite resulting ing total total total computed performed performed eq called called times elements dimension global study knowledge original artificial artificial samples samples samples samples samples samples samples samples samples samples samples true true true true compared application define perform determined determined posterior posterior posterior posterior motor equal approaches larger train train nets nets nets nets nets nets nets nets exp considered cambridge computing domain domain directly curves curves curves curves estimates limit limit effects detection conference determine determine choice choice significant approximate pages pages pages produce derived randomly criterion entropy entropy entropy entropy actual actual actual selected evidence depends sampling increases group predictions predictions predictions predictions predictions assumed assumed theoretical eds journal journal makes noisy needed unknown interesting ratio ratio ratio ratio york consistent consistent trials trials uniform uniform principle leads leads principal squared numbers international choose description denotes ensemble apply apply apply sense inference inference recently relevant engineering sufficient varying compare compare conventional conventional approximately calculated volume tions tions entire constructed constructed expression expression occur predicted predicted predicted predicted width occurs occurs generally conclusion conclusions depend competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive differences bayes numerical asymptotic propose largest drawn drawn drawn drawn drawn drawn drawn assuming exist iii configuration relation monte monte van van van van van van construct carlo carlo produces produces solving solving plot describes vertical vertical sensitivity unique interaction adding events implies versus versus independently densities densities densities evaluated evaluate restricted sizes additive additive normalization intervals valid construction david expect box box box box candidate characterized uniformly miller miller essentially identity quickly interpreted usual realistic realistic denker denker predictor layered poor exhibit rapidly relations relations replaced fewer examine fault structured induction integer analyze analyze predicting predicts adjusted portion shapes initialized simplest utility regime submitted averages averages averages histogram trivial derivation analytic tool formalism arc widely probable probable probable involve mechanics reflects greatly reflect substantially tional conducted experimentally experimentally solla solla solla solla solla adjustable remove differs qualitatively qualitatively suited specifies restriction lost communications communications saturation saturation dealing numerically numerically convenient ments accepted familiar tishby tishby tishby operates north north canonical moments moments schwartz schwartz den den den den den den treatment theoretically draw relies agree insensitive assigning mechanical mechanical treat unchanged exhaustive markovian acceptable ical adjustment unseen publication intuition levin levin levin ijcnn thermodynamic dominated elementary elementary elementary annealed integrals supports normalised unpublished capacities satisfactory families ning ning practically equa convention scatter denominator saturate imum 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output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number system system error error error results units units units units units units information information information information information information problem problem problem models hidden performance space space space space space space space space space space space linear layer case case vector vector vector vector order order shown systems systems systems systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters noise weight weight weight weight unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition method method method method pattern pattern point point image single processing processing processing large large local analysis analysis analysis class optimal inputs form algorithms algorithms simple gaussian gaussian gaussian paper small size size size size size size feature net net net net net net net net net work work methods methods methods points points points points points points points points classification classification classification level level trained trained trained trained problems problems random high high high response similar architecture equation equation equation equation equation equation equation equation section section section section section section section section section fixed fixed rule vectors vectors general generalization generalization generalization speech parameter parameter real approximation approximation average gradient note note note dimensional result result result variables solution independent independent defined found found target target target target target estimate estimate estimate standard standard standard standard standard terms presented present activation activation maximum range range range range range range range outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied back back back back back back find find convergence density density properties likelihood references stochastic positive positive important important important adaptive decision propagation propagation context complex estimation estimation estimation statistical statistical statistical statistical statistical effect generated variance cost tion tion tion difference assume lower prior chosen previous previous previous cases required multiple good represent represent represent distributed markov make fact fact techniques techniques techniques techniques region region region region region region proposed correct probabilities probabilities probabilities probabilities probabilities probabilities scale minimum computed respect respect multi multi sum sum elements elements regions factor factor factor applications applications original relative relative relative specific represented compared compared proc location perform determined goal distributions distributions distributions distributions distributions distributions distributions distributions gain gain discrete brain steps train train nets morgan morgan morgan morgan proceedings loss loss loss loss technique technique advances advances advances joint joint represents represents connectionist final exp exp exp exp exp scheme scheme scheme scheme computing directly directly hinton estimates estimates limit san conference determine determine upper choice statistics free world pages con produce produce weighted developed levels levels levels levels levels area lines actual actual depends constraint constraint constraint constraint simply achieved normal technical denote transformation transformation assumption corresponds complete predictions finding assumed shape shape shape theoretical theoretical main ability instance cluster cluster degree makes makes makes rumelhart rumelhart rumelhart objective probabilistic probabilistic probabilistic typically typically smaller needed hopfield unknown testing testing testing character character projection projection special special consistent consistent consistent consistent consistent consistent leads details numbers numbers numbers numbers making window window window international normalized idea idea idea idea combined combined run light denotes discussed discussed advantage advantage advantage ensemble ensemble ensemble element element element typical practical practical introduced sense inference subset dimensions dimensions dimensions highly conventional approximately calculated calculated volume volume volume works axis axis correspond converge definition separation symmetric interval interval increased expression expression expression expression expression lead wide wide derivative derivative locally touretzky touretzky touretzky width clusters starting assumptions depend depend editors clear clear exponential constrained mateo integration proportional proportional start exist exist plane plane targets targets derivatives characters scene configuration relation digit construct produces produces optical ways ways ways plot plot plot plot describes mathematical distinct segments confidence confidence confidence confidence confidence confidence confidence confidence implement sensitivity sensitivity category category category category category category category category category category category category category category category category linearly dimensionality text scales mutual quality quality extraction versus versus versus john john communication communication solved densities evaluated evaluate evaluate approximations approximations centers centered understanding similarly digits allowed processor reasonable reasonable calculation calculation calculation calculation additive classical classical expansion spaces reduces combining combining purpose closed valid calculate calculate calculate calculate calculate calculate assigned assigned assigned advantages expect handwritten figures figures formulation strings bell bell recognize determines plotted automatic uncertainty uncertainty discuss regular straightforward straightforward suitable modification efficiently schemes post plots tend tend summary cun cun cun cun prob strategies categories categories categories built satisfy satisfy quantity quantity bar usual usual generalize correspondence computes denker denker denker denker denker denker denker denker denker denker denker denker denker leading bars bars parametric layered wiley create exponentially put limitations hessian dataset successive ideas ideas ideas ideas ideas ideas ideas school applicable combine referred understand analogous editor editor editor extremely equally thought thought obvious taylor precise improving histogram indicating indicating formula formula formula crucial convolution track answer handle processed formalism formalism formalism formalism located mation laboratories laboratories probable probable probable describing describing describing definite arises argument prop prop prop prop limits applies understood axes lack item solla solla solla solla solla reliability requirement calculating calculating calculating calculating howard howard gains ture differs serve phonemes sums sums sums inherent sophisticated windows windows windows windows windows windows windows windows damage calls softmax softmax softmax softmax softmax softmax softmax multidimensional summed lot shifted sort guarantee summing summing perfectly circular lecun lecun lecun lecun lecun lecun lecun lecun arranged kaufman kaufman kaufman kaufman difficulties analogy proceeds multiplicative moment moment hope tishby tishby fail moments moments infor becker becker surprising washington schwartz accounts belongs jackel jackel offers modelled surprisingly probe contact contact draw statement statement hart hart hart discovered acknowledge outlined divide informa summer ple numerous outline constitute vec covering rejection boser personal personal constitutes tor suppressed guess guess imagine imagine clustered principled mutually henderson modifying exam levin levin exclusive duda duda duda goals parzen parzen parzen parzen parzen parzen ocr ocr ocr uncertain uncertain hubbard proba proba challenging statistic harder spanned denver denver denver outcomes son meet holding treating bridle bridle bridle bridle helps factored advantageous remarkable bility impractical transforming transforming transforming transforming transforming heavily curse calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration holmdel holmdel obey obey architec squashing vicinity faced scatter scatter scatter scatter scatter carrying vanishing ically scattered generaliza shares applica expresses tightly blurred preprocessor deeper weakness conversations collect sought yann ily gun gun fogelman fogelman elongated suit bilities shed absolutely pleasure zky touret exponentials wished tremendous typ wittner calibrate memorandum underdetermined underdetermined underdetermined fuzziness jnowski founded vanilla vanilla surprised 
#@Denker_J,LeCun_Y,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural input input data data data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm number number number number state state state results results results results units information information problem problem problem models models models hidden hidden hidden hidden hidden performance based based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear case case vector vector vector order shown systems systems systems systems systems systems parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions unit unit unit unit unit distribution recognition method method method approach approach processing processing large large local local local rate rate rate rate rate rate rate rate patterns optimal form shows shows shows algorithms simple simple simple paper paper paper examples small small size size size work work work task methods methods methods methods step step step step step step step step step step step points points points field field level trained trained trained structure high similar representation representation show show general speech parameter states gradient gradient gradient term note experiments experiments dimensional dimensional result result result result result university variables solution solution solution solution solution solution solution solution research research independent found dynamics dynamics initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial table table computer science left left left left map present low nodes frequency range range range press press press learn position outputs abstract back back back back back back back back back back back back back back back back back back back back back computational computational computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references due due ieee ieee adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex hand behavior behavior behavior behavior behavior behavior behavior effect effect effect generated parallel search complexity complexity lower lower multiple multiple multiple good long conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions distributed make fact techniques region region correct errors forward resulting classes classes classes classes tasks performed performed times means made made made global global applications study knowledge knowledge knowledge obtain obtain artificial specific samples samples rates rates rates location perform eye related related equal equal equal power approaches mit steps steps larger train descent descent descent modeling selection morgan proceedings department technique technique technique technique technique consists advances represents difficult final bias considered domain domain equivalent equivalent experiment experiment experiment environment environment environment environment hinton additional view view solutions solutions solutions solutions solutions limit limit limit limit limit san san bit conference determine efficient classifiers choice choice choice significant free produce condition condition condition condition levels area area path provided finally finally nature nature associative discussion increases tested close proof common generate supported theoretical journal pixel instance future future rumelhart rumelhart rumelhart rumelhart hopfield hopfield combination dynamical jordan interesting significantly increasing structures trials uniform database empirical empirical representing numbers numbers iterations iterations international magnitude produced choose added improved directions directions separate similarity reported pixels pixels cognitive engineering dimensions sufficient varying varying calculated axis axis axis axis axis smooth studies converge rl symmetric williams sensitive sensitive sensitive sensitive sensitive grant exists lead digital derivative feed touretzky deterministic deterministic deterministic white occurs demonstrate demonstrate runs starting place central interactions sigmoid faster weak mateo propose strong hard demonstrated intelligence plane relationship iii minima identification configuration configuration configuration question question attractor acknowledgements monte monte carlo carlo describes laboratory implement sensitivity sensitivity sensitivity sensitivity sensitivity linearly physical physical easy interaction formed boolean john letters letters national focus review depending forms approximated past sign epochs epochs epochs boundaries boundaries boundaries boundaries initially transactions figures figures figures figures figures figures figures figures figures figures figures combinations coordinate usa memories illustrated black reason aspects identified identified encoded effectively attractors attractors attractors attractors plots plots orthogonal refer issue symmetry symmetry symmetry running content list involved vary consisted body simpler origin origin origin remain diego poor exhibit experience experience difficulty varied varied detail recursive helpful existence existence rise examine successive giving links parity office variability complicated affect understand cognition momentum momentum momentum momentum momentum hill man extremely noted precise academic epoch epoch epoch arbitrarily arbitrarily explain chaotic chaotic chaotic chaotic years years percentage percentage great scenes trivial guaranteed phenomena worse inside purposes purposes closer precisely precisely arise scientific scientific auto cybernetics meaning sun researchers researchers researchers varies percent fuzzy axes axes peaks treated psychological schematic schematic collective substantial enables semi conclude display focused extreme extreme picture picture equivalence equivalence equivalence guarantee linearity resources partitions discover naval grey climbing kaufman convenient abilities exploit implications imply presentations date published utilized slice slice displayed percepttons claim claim initialize iterated iterated pollack pollack pollack pollack pollack pollack pollack pendulum projects statement explains discovered convergent convergent convergent influences default land gold gold minus leaming leaming break emergent forced forced propagating utilize chaos chaos chaos solely reports breaking basins tight alter argue exclusive exclusive exclusive exclusive community carefully argued academy likewise stuck stuck lippman lippman increments increments examination strict spite rarely appearing functionality fractal fractal fractal decided converging lists huberman triangles slices slices clark clark ultimate judd judd convention fastest minsky minsky reproduced triangular neutral demands ranged comer comer routes vanishing talk noticed bodies permutations ohio ohio ohio sixth availability collect claims claims claims symmetries symmetries confident mosaic explores surrounded rendering workstations regularly standpoint standpoint papert compactly cis cis matters strange specially public slows columbus answered factoring preclude nonconvergent nonconvergent speeding unsolved alike intemal rum prompted disregard storm storm paperr pervasive circumvented metaphor metaphor creative fractals impetus filed connectionists eliciting 
#@Kolen_J,Pollack_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning model neural input input input input input input input input input input input input function function function set set set networks networks networks networks output output output output output output output output output output output output output output output output output output problem hidden hidden hidden hidden space space space space space space space space space space space space weights weights weights weights linear linear linear layer case vector vector vector vector vector order order order shown values values values values values values weight weight weight neurons method method method method point point point point point point point point point point point image image image image image image image image image image image image image image image image image image image image processing control large large analysis class matrix matrix matrix matrix matrix matrix matrix matrix form form form form form form form form form signal paper small small work methods methods process trained trained trained random random architecture section section vectors images images general generalization real theory obtained obtained activity activity activity activity activity activity result result defined defined sequence dynamics dynamics dynamics activation activation activation activation activation activation activation activation range range range basis basis basis abstract applied applied properties references important important generated cost chosen part multiple multiple conditions region proposed forward forward forward forward forward forward ing eq eq eq eq eq eq eq eq eq eq eq eq called elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping optimization optimization dimension dimension obtain obtain obtain obtain obtain obtain obtain original original vol true application application application application application application desired constraints equal equal equal connection connection dependent nets proceedings technique technique technique individual joint layers addition maps domain domain domain domain domain san conference significant significant significant world produce produce produce condition product product actual backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation depends depends simply discussion normal normal describe inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse stable generate generate block block interesting projection projection projection projection projection special special operation operation direct magnitude magnitude produced produced produced added added discussed subject sense sense sense sense sense relevant sufficient varying previously calculated calculated module module module module module tions yields diagonal address address generalized generalized generalized generalized entire entire exists exists matrices matrices matrices feed column flow flow flow flow flow flow flow flow flow greater greater operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator sigmoid sigmoid sigmoid sigmoid sigmoid modules clear strong sigmoidal minimizing start exist exist exist exist exist exist exist exist produces describes stability stability unique expressed dependence operations restricted restricted decomposition activities calculation calculation calculation calculation combining add add iterative closed closed closed closed closed closed closed closed closed calculate calculate calculate symbol subspace extension reason columns columns columns straightforward importance orthogonal orthogonal summary moore issue follow satisfy satisfy satisfy michael subsequent operating satisfies diego perturbation replaced optimized optimized optimized optimized issues issues hall existence existence existence mappings mappings mappings possibly possibly rank rank rank singular singular singular singular singular singular singular singular singular singular portion portion portion logistic academic arbitrarily indicating derivation explanation answer briefly drive purposes producing operators operators operators operators operators ion inversion inversion inversion inversion inversion inversion annual addressed questions questions pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo backprop employ compares span perturbations bipolar bipolar bipolar linearity purely satisfying satisfying composition composition composition analyses prentice overview widrow widrow widrow propagated propagated propagated considerations considerations summarize ics sequentially outline perturbed par tor rectangular alternate alternate indexed ucsd uniqueness reversed cliffs svd svd svd svd svd svd englewood separates swing ory transpose resultant inappropriate ina cons favorably des reproduces reproduces reproduces agation solu participate dynam ire conveniently ticular inverses inverses inverses inverses inverses inverses inverses inverses unitary subscripts linden linden linden penrose opera opera chitecture orlando ors thereof consid fimctions lancaster lancaster lancaster lancaster guaranteeing verse verse ternational 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#@Rossen_M,
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#*network network network network network network network network network network learning learning learning learning learning learning model model model model model model model model neural input input input data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training algorithm output output number number number number number number number number number number number number system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results units units units units units units units units units information information information information information problem problem problem problem problem problem problem problem problem models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear case case case case order order order shown shown shown shown shown shown shown systems values values values values values values values probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution method method method method method approach approach approach pattern single control large large large large large large large large large large large rate rate rate test test test test optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs form form signal signal signal signal simple simple simple gaussian gaussian gaussian gaussian paper examples examples examples examples examples small small small small small small small small small small small small small size size size size size size size size size net net net net net net net net net net net net net net net task methods step points points level trained problems problems problems random high similar show show show equation section section section section section fixed rule general generalization generalization generalization generalization generalization parameter parameter parameter parameter real average average average average average average average average theory theory theory gradient gradient obtained term term term term term term term term term term term term term term term term term term term term note note experiments dimensional result result result university university university university computation solution solution independent log defined defined defined defined defined found target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics estimate estimate standard standard standard terms connections connections science science prediction prediction prediction prediction prediction left present present activation temporal sets sets maximum range range range range range range press learn learn nonlinear outputs outputs outputs sample sample sample sample sample sample sample sample sample sample abstract applied applied back back back back find find computational likelihood references stochastic positive procedure procedure procedure procedure procedure procedure procedure procedure procedure important propagation propagation propagation propagation mixture introduction action hand hand hand behavior behavior statistical statistical effect dynamic variance variance variance variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost search search tion change change difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity rules rules measure measure prior prior prior prior prior prior learned chosen higher part part center previous previous previous cases cases cases cases cases type good good long long long long long bayesian expected expected expected equations make make make fact region region region proposed proposed correlation length length length length length length length length observed errors errors scale scale minimum minimum minimum minimum tasks regression respect respect respect respect sum sum sum sum sum sum sum called called times times times times regions means means means factor potential applications knowledge knowledge knowledge knowledge negative negative negative original original relative relative relative specific true compared compared application application application application application desired desired desired cross cross series series series series series series series series series series series series provide define rates rates rates rates rates rates rates rates rates goal goal connected connected connected distributions equal power approaches larger larger larger larger descent dependent source nets nets nets nets nets modeling morgan morgan proceedings proceedings department department implementation represents represents connectionist connectionist connectionist connectionist connectionist connectionist difficult sequences framework framework experiment directly hinton hinton hinton curve additional solutions solutions curves curves limit top determine requires choice choice choice choice significant significant approximate statistics free world world estimated basic increase increase validation give give give con derived derived derived derived weighted developed developed developed levels criterion criterion criterion criterion criterion criterion criterion criterion types lines lines entropy provided finally backpropagation backpropagation iteration depends depends depends depends measured technical increases describe limited close close close assumption assumption corresponds corresponds corresponds corresponds corresponds complete stable actions actions predictions predictions predictions finding finding finding finding amount theoretical require eds eds eds eds journal square ability hypothesis hypothesis hypothesis future future future future easily easily makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart noisy fit fit kaufmann kaufmann smaller smaller underlying underlying underlying underlying needed reduced dynamical fully fully significantly significantly ratio mechanism special uniform empirical principle language squared squared details details details details pre pre making bits bits bits international normalized bottom early decay polynomial idea idea minimize minimize minimize choose added added description description description description description description description description description predict predict predict predict predict predict denotes architectures improved discussed discussed exact exact robust strategy strategy period side quadratic quadratic inference inference sejnowski relevant relevant compare compare compare observations approximately approximately works works correspond sensitive entire increased occur deviation deviation deviation wide predicted width width half critical minimal minimal minimal minimal reduce reduce central central measures measures clear peak performs performs hard hard hard physics drawn drawn sigmoidal sigmoidal solid solid proportional proportional start start decrease force question appears relation primary describes averaging remaining remaining easy slightly slightly slightly angle scales predictive choosing choosing independently focus focus focus expressed expressed formation dependence viewed viewed interpretation interpretation detailed evaluate centers centered similarly past past sign sign key reasonable dashed epochs epochs epochs spaces normalization normalization reduces fitting fitting roughly add add add add boundaries initially david david david david david precision precision precision thesis activations formulation weighting weighting mozer variations successfully simplicity reason aspects aspects importance importance importance importance driven presentation essentially reached procedures contained cun cun interpreted interpreted issue symmetry return return return return return device involved usual usual generalize minimizes minimizes denker extract approximating intrinsic situations remain powerful powerful overfitting overfitting overfitting overfitting overfitting overfitting experience exponentially hanson fewer reducing school analytically scaled root working comparable workshop encode momentum smallest coefficient analyze predicting predicting predicting predicting psychology equally perfect changed adjusted quantities quantities quantities precise epoch epoch epoch epoch improving simplest simplest explain phd finds averages devices devices residual preference slowly theoretic theoretic crucial analyzed growing growing fairly fairly fairly fairly fairly answer briefly benchmark lies worse worse starts starts reasons perspective perspective perspective perspective stanford stanford stanford stanford stanford closer day day day day day day day day division division broad probable probable cut cut scientific ridge lowest meaning meaning evaluating elman flexible peter solla continuously price price price measuring differs weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend reaches reaches prevent prevent richard richard attraction returns returns returns returns returns returns wesley yielding extreme irrelevant lot trade trade trade phenomenon addison forming oxford pick pick driving resources member acts acts dynamically discovery discovery unity unity unity eliminate grows grey smolensky smolensky outcome reaching eliminated eliminated inspired chance chance familiar balance interpret mark mark fail preparation exceeds generalizes days days days heuristics reliably elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination published published started paul expanded intended forecasting forecasting forecasting forecasting forecasting forecasting accounts lawrence counter counter viewing iterated foundations express insight surprisingly surprisingly creating late extends relies erlbaum inductive inductive inductive broken santa hart ignore summarize summarize interestingly receiving insensitive influences counts counts severe dense pressure summer logarithm logarithm achieving opposed randomized acceptable mdl solely german possibilities basins avoids increment increment trends intuition community chauvin chauvin gained toy goals dominated eliminating bump guided monitoring worth covered alternatives sized inversely exchange exchange exchange exchange exchange exchange exchange exchange exchange happen things prevents durbin walk sigmoids removes laws laws externally externally regularities reversed smoother blake focuses japanese rissanen rissanen huberman huberman huberman huberman huberman huberman huberman huberman extracts pratt deals ultimate occam enhances daily daily weather sending alto falling subscript twelve trend indicators artificially adequately penalizes palo trapped ton ton predic dead forthcoming psaltis andreas andreas andreas andreas andreas week albeit prices tong tong conversations grown grown grown desire clarify clarify cent golden feel canadian formalized incremented razor sunspot sunspot sunspot volatility justifies nato saving sharper cheaper cheaper manage swiss predictability eubank casdagli zky touret vague currency currency currency currency currency currency currency currency forecast finished sharpening yearly resorting trast wei wei sunspots sunspots sunspots notoriously famous hinges gauge benefited wil wil decremented bench enlarge deteriorate cheeseman cheeseman dollar dollar yves prompted smearing incrementing usefully inquiry ris ris rigidly bernardo bernardo bernardo bernardo interpretability rumel conception manages manages enlarging dicting dicting gently parc hopeless attaching attaching 
#@Huberman_B,Rumelhart_D,Weigend_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural input input input function function function set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system system system state state state state state results results information information information models space weights weights weights weights weights linear case case vector vector order shown probability probability probability probability probability probability weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons distribution pattern point point single large large large large neuron neuron neuron neuron neuron neuron matrix matrix form form form shows paper examples examples small size size size size size size size size size size size size size size size size cells cells step points points current structure random random random random random random random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory representation fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general parameter parameter parameter parameter parameter real states theory theory obtained note result result result university university threshold computation computation computation research research independent log log log log log log log log log log log log log log log log log found sequence dynamics constant terms connections sets sets sets sets sets sets sets sets position components components components abstract properties references component component component ieee ieee positive effect generated recurrent recurrent recurrent recurrent recurrent assume lower lower lower measure theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem conditions conditions conditions distributed distributed distributed expected expected probabilities errors errors errors classes classes ing total called elements elements elements elements elements applications obtain vol true application desired define define define define update support support report department loss loss loss loss loss loss consists code code code code code code code code code code represents graph graph graph graph graph graph graph graph considered equivalent equivalent estimates design san effects capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity efficient upper upper full choice randomly product product product product product product product evidence nature associative associative associative associative associative associative discussion technical technical increases increases describe denote denote denote corresponds complete complete complete complete complete complete stable stable stable short common generate require main main ability instance degree smaller hopfield fully fully block block block block block block block block block block block block block block block block block block block block block block edge structures uniform mode operation details details call call call call polynomial polynomial choose light denotes architectures advantage property property property property property pair robust robust takes include side subset subset engineering tions achieve trans trans diagonal sparse sparse sparse sparse sparse definition definition symmetric observation storage storage storage storage storage storage increased increased increased grant occurs setting setting critical trajectories depend exponential presence presence california introduce connectivity force base edges edges produces produces generating generating generating distinct linearly linearly electrical unique unique consisting agent implies blocks blocks blocks independently independently communication communication viewed codes codes codes codes codes codes codes codes codes codes codes forms sizes partition partition allowed allowed dominance dominance dominance dominance dominance memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories specifically holds holds structural regular suitable suitable wij wij wij wij wij wij modes efficiently orthogonal composed refer graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs interested interested interested interested lie content satisfy notation usual mixing satisfies satisfies situations diego collection collection investigate exhibit ml existence examine links links links links rest fault office notion notion attributes examined integer integer integer subsets subsets formal algo store simplest arbitrarily submitted failure choices choices choices ran commonly commonly scientific acknowledgement involve beginning attribute attribute attribute radius radius radius radius radius radius radius radius outer outer outer outer outer outer outer robustness robustness robustness robustness robustness robustness substantially capability capability effort ity exhibits ordered ordered ordered ordered ordered ordered ordered ordered ordered ordered extensions qualitatively damage damage damage damage damage specifies specifies phenomenon proofs indices indices indices indices equivalence equivalence formally formally formally formally formally guarantee rithm resources resources ordering grows grows grows interconnected interconnected generality air interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection stated los los removing disjoint disjoint affected synchronous intuitively degradation degradation continue contexts contexts corollary corollary corollary corollary corollary surprising surprising regard vertices vertices vertices consequences interconnections interconnections interconnections reader probe probe probe probe probe storing extends partitioned statement statement statement grants ignore integers integers dense dense dense usage usage drop sine sine equivalently super ber emerge theorems corrected associate imagine mutually mutually publication iff iff intuition num mathematically afosr retain flip increasingly complementary nonetheless tively placing admissible admissible admissible admissible admissible admissible applicability compu cube capacities capacities capacities capacities gratefully expense remarks remarks attributed dominates dominates dom venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh attained attained repetition carries retrieved approaching fol comprised format format lar catastrophic catastrophic inform inform rem merit allowable holographic retaining retaining collections security putational tolerant fractional rela permutations cient ness graphically dominate modulating sparsity sparsity sparsity sparsity sparsity sparsity sparsity sparsity sparsity acknowledged philadelphia lowing interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity interconnectivity exposition particu indicative posner posner asserts asserts pennsylvania mceliece mceliece embodies liapunov liapunov loose akin logarithms corrects odds odds localised urn urn urn urn urn prescription sparser devil devil devil devil devil devil devil devil devil grandmother rounding dation invoking invoking folk folk folk folk folk folk folk folk folk folk folk thrown bipartite bipartite bipartite characterised tln graceful santosh rodemich rodemich qua qua interconnec favourably sult imp uti 
#@Biswas_S,Venkatesh_S,
#t4
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#*network network network network network network network network network learning learning learning learning learning learning learning learning neural neural neural neural neural neural input input input input data data data data data data data data data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results units units information information problem problem hidden performance performance performance performance performance performance weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case shown systems systems systems values values values values values values parameters parameters noise noise noise noise weight weight weight weight weight weight functions functions distribution recognition approach pattern point image single single processing processing processing large large large local local rate rate rate rate rate patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal signal signal signal signal signal signal signal signal signal simple simple simple paper paper small size size net net task task task task classification trained trained trained trained trained trained trained trained trained trained show show show section section section general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech speech speech real theory gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained term note note dimensional dimensional university computation independent log log log found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial computer connections science presented present machine sets maximum range range range range press press press learn components components components components components components components components components components components sample sample abstract back back back back back find find convergence convergence properties references component component component component due ieee propagation propagation propagation propagation propagation context introduction complex complex complex complex complex behavior statistical statistical effect dynamic generated variance cost assume assume assume assume assume previous cases cases multiple multiple multiple long long conditions conditions represent represent represent equations make proposed length observed observed observed observed observed observed errors simulations simulations simulations simulations simulations simulations simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting resulting resulting ing total total simulation sum sum called times made made global applications applications applications applications study study study knowledge filter filter vol vol vol relative specific compared application desired compute compute compute compute compute compute rates rates perform determined goal related connected connected power power power power power power approaches descent descent descent descent descent descent dependent dependent dependent morgan morgan department represents represents represents connectionist final bias layers ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai considered considered considered framework curve curve solutions solutions curves curves curves design san san top top effects statistics statistics statistics free world increase increase increase increase validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation con bounds bounds bounds bounds lines lines lines provided provided provided provided finally iteration iteration discussion covariance covariance covariance covariance covariance feedforward arbitrary tested tested tested tested limited limited assumption corresponds complete stable stable stable surface predictions predictions predictions predictions predictions implemented assumed assumed generate generate generate theoretical theoretical theoretical theoretical theoretical theoretical theoretical main eds journal square square square future rumelhart noisy simulated fully interesting interesting principal principal call direct making international bottom bottom bottom bottom early architectures architectures architectures population population recent typical typical reported period quadratic quadratic quadratic quadratic inference recently sufficient observations observations works correspond evaluation exists scaling extended matrices matrices matrices matrices predicted predicted touretzky touretzky demonstrate runs minimal minimal minimal minimal minimal assumptions assumptions assumptions assumptions assumptions reduce depend depend depend numerical exponential asymptotic constrained mateo mateo suggest suggest solid turn assuming variety variety decrease decrease decrease decrease decrease decrease iii iii minima minima minima minima base base base question acknowledgements suppose suppose digit mathematical changing easy springer cycles cycles depending phoneme showed understanding understanding understanding converges spectrum spectrum spectrum slow dashed dashed valid valid sufficiently transactions handwritten dominance eigenvalues literature tend identity composed verlag quickly strongly cun cun cun interested sampled vary write write write write write write usual usual absence realistic realistic eigenvalue denker satisfies decreasing decreasing decreasing decreasing situations simpler remain overfitting overfitting overfitting helpful analytically relationships eigenvectors eigenvectors understand neu waibel waibel induction predicting predicts predicts psychology formal formal mapped explain residual explanation analytical analytical adapted baum baum starts stanford stanford strictly demonstrates varies varies applies substantially lms lms lms lms lms lms lms lack haussler maxima maxima maxima howard berlin weigend weigend weigend monotonic monotonic phonemes qualitatively qualitatively qualitatively acoustics sums germany comments progress yielding yielding phenomenon phenomenon phenomenon phenomenon uncorrelated intractable notes labeling labeling labeling labeling labeling labeling eliminate kaufman kaufman significance alpha alpha alpha alpha alpha alpha imposed hyper ral implications heuristics infinity jackel reproduce insight surprisingly late late rich rich eigenvector eigenvector considerations tures stopped baldi numerous numerous basically creates expanding dyna dyna boser forcing imagine imagine tight illustration henderson chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin gener hubbard scope nonetheless hansen knowing increments article rarely lecture sake suite overtraining overtraining overtraining overtraining hoc clarity phonemic phonemic phonemic phonemic huberman curved alto assp inde relaxed computable tained tained noiseless palo modularity linearities wellekens wiener imposes unaffected nents shikano spectrograms deeper alization albeit puter holmes pri impressive pierre almeida ori raise comment namics lai intersections raining sider necessitates insightful ful ioo anymore yves ellipsoids scent vmues overt thomson sawai ght pendently logx 
#@Chauvin_Y,
#t4
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural input input input input input input function function function function function function function function function figure figure figure figure figure figure time time time time time time time time time time time set set set set networks networks networks networks training training training training training training training training training training training training training output output output output number number number number system error error error error error error error error error error error error state state results results problem problem problem space space space space weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear layer case vector shown shown systems values noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight functions unit unit distribution approach approach approach approach approach approach pattern pattern point point point point single single large large large large neuron test patterns patterns patterns patterns patterns patterns matrix matrix optimal optimal inputs inputs inputs inputs inputs inputs inputs form shows simple simple simple simple simple examples examples examples examples examples examples examples examples small small size size size net work work step points points process level current trained trained problems random random equation equation equation equation equation equation equation equation section line line line line line line rule rule vectors vectors general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real average theory obtained obtained obtained obtained obtained term term term term term term term dimensional result result computation computation solution solution solution independent independent found dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial terms phase phase phase phase phase phase sets learn position components basis basis nonlinear abstract back find find density density density density references due important introduction action hand hand statistical statistical effect generated variance variance tion tion difference difference difference measure part part part binary binary binary binary binary long long long conditions fact fact correlation length length length probabilities finite resulting ing eq called called times times times times times means means factor factor study study vol relative proc power power power power approaches approaches approaches approaches institute additional transition transition transition transition transition transition transition transition transition transition limit limit limit bit capacity determine full approximate world produce randomly finally depends simply simply simply achieved measured fast inverse corresponds predictions amount common assumed assumed eds journal journal journal square square square ability ability ability ability ability ability ability ability ability ability ability easily easily makes objective pairs smaller dynamical testing increasing consistent leads leads leads leads leads call normalized decay decay decay decay decay decay decay decay attention choose perceptron perceptron perceptron recent takes reported practical side side inference inference dimensions sufficient sufficient teacher teacher teacher teacher teacher teacher teacher teacher works achieve diagonal diagonal storage sensitive entire entire conclusion critical critical critical critical critical critical critical place place depend exponential exponential asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic learns learns presence physics physics physics solid proportional assuming averaged averaged appears appears transitions averaging infinite physical physical integrated adding equilibrium boolean john letters letters letters independently focus expressed review solved solved evolution evolution forms spectrum spectrum spectrum calculation slow slow dashed dashed additive normalization reduces valid calculate sufficiently perceptrons perceptrons perceptrons bell eigenvalues eigenvalues subspace subspace subspace subspace subspace extension discuss discuss simplicity straightforward extra extra delta delta delta orthogonal orthogonal orthogonal orthogonal kind contribution follow follow quantity vary write relaxation relaxation relaxation relaxation relaxation relaxation generalize generalize generalize eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue denker reach situations law law law law simpler layered layered exponentially exponentially exponentially detail integral divergence dotted dotted behaviour fourier examine analytically analytically neu smallest smallest perfect perfect perfect perfect perfect perfect perfect perfect perfect perfect front perceptton ith simplest spin indicating growth agreement track briefly baum correction reasons desirable desirable immediately hyperplane hyperplane scientific qualitative meaning reflects understood understood pseudo introducing solla solla solla haussler frequently span span exhibits exhibits exhibits extensions extensions extensions green lot picture shifted restrict nonzero nonzero numerically numerically keeping tishby tishby tishby ral shifts krogh krogh krogh krogh krogh degradation hertz hertz hertz hertz hertz analyses sompolinsky separating governed washington evident percepttons percepttons schwartz spherical erlbaum severe unchanged ter piece exhaustive opper hillsdale levin levin ijcnn labs life degraded eliminating careful complementary spanned spanned preprint vanishes walk remarkable excess excess thermal agrees transforming obey normalize deals nontrivial inspection denmark denmark absent thresh approached carrying generaliza generaliza gardner imaginary sition couple tran manipulations diverges diverges diverges diverges diverges deformed roots signaling aii singapore copenhagen copenhagen imperfect imperfect rli bohr disappears awi pupil pupil pupil adaline adaline imitate imitate slowing slowing slowing tti tti relaxing prefactor blegdamsvej blegdamsvej succeeding kinzel divergent anders derrida nordita namical thorbergsson sumed dep ceptron niels eri europhysics europhysics mso 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#@Hertz_J,Krogh_A,
#t4
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural input input input input input input input input data function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output number number error results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information problem problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer case case case case case vector vector order order shown shown shown systems values values weight functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution method method method method method method method method method method point point point point single single processing processing large local local rate rate test test test test test patterns patterns class inputs inputs inputs algorithms simple paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size size size size net net net net net net net net net net net net net net net net net net net net net net net net net net net net task task methods step points points points points points points points points points points points points points level trained problems problems random random random random random random random random random high similar show section section line line line vectors vectors vectors generalization generalization generalization generalization generalization generalization generalization real real real approximation approximation average average average average theory gradient gradient obtained obtained experiments experiments dimensional result result threshold threshold threshold threshold threshold threshold threshold computation solution research defined defined defined found found found sequence target target target target target target target target target target target target target target target target initial initial initial initial table table standard distance node low sets sets press learn learn learn learn learn learn learn learn learn abstract applied back back find find find find find find find find find find references due due due ieee positive positive positive procedure procedure procedure procedure decision decision decision propagation propagation introduction behavior generated generated parallel parallel search search search tion tion difference assume prior representations representations chosen part theorem required required required required required good good good binary binary long distributed equations make fact fact proposed length errors errors errors forward scale minimum tasks computed computed computed computed multi mapping factor optimization made made study knowledge negative negative negative true compute compute compute location location perform goal mit accuracy accuracy accuracy accuracy comparison larger contrast train train source nets nets nets nets nets nets nets nets nets nets nets nets nets morgan morgan proceedings institute technique internal code advances connectionist maps computing experiment hinton hinton curve additional additional additional san top stage stage stage stage bit bit bit determine requires approximate approximate approximate approximate increase randomly randomly lines provided selected backpropagation backpropagation feedforward arbitrary arbitrary complete complete finding finding finding theoretical main eds future easily rumelhart rumelhart rumelhart kaufmann kaufmann pairs pairs pairs needed reduced programming head consistent consistent trials trials trials uniform uniform uniform uniform uniform uniform empirical empirical max max direct bits bits polynomial polynomial polynomial perceptron perceptron recent pair pair pair pair element relevant dimensions works works solve solve achieve achieve diagonal address definition definition positions observation bounded williams williams increased increased constructed suggests suggests trial touretzky boundary pass runs starting starting reduce reduce segment segment segment segment valued valued weak mateo suggest hard hard hard hard drawn drawn drawn drawn assuming start min min plane plane plane plane plane plane plane minima configuration question suppose suppose construct construct describes missing linearly linearly slightly adding boolean boolean learner learner codes restricted earlier performing boundaries valid sufficiently construction euclidean query query query query query query query query classified transactions avoid building existing existing existing existing figures assignment assignment assignment uncertainty uncertainty specifically tests middle uniformly divided mcclelland build efficiently plots tend ten summary heuristic heuristic heuristic success lie running built absence computes thresholds thresholds thresholds consisted illustrates load origin create essential detail fewer school mappings parity parity parity parity parity parity complicated complicated proved proved func configurations illustrate queries queries queries queries queries queries queries queries queries queries queries queries mapped baseline motivated attempts attempts rows separable separable crucial adjacent nowlan answer independence baum baum baum baum baum baum baum baum baum lies worse closer day constructing constructing constructing hyperplane hyperplane hyperplane hyperplane hyperplane arise arises geometry addressed conjugate conjugate requiring poorly backprop backprop backprop backprop backprop backprop backprop haussler haussler employ employ dots passes progress credit credit credit classifying classifying pac pac redundant intractable sort princeton acm approximates repre discover discover grey establish chance minutes check resulted resulted nearby nearby nearby fail methodology combinatorial generalizes hours hours heuristics started surprising lang lang lang lang lang den searching searching searching sphere sphere ahead repeatedly repeatedly cpu cpu draw passing discovered summarize intersection interestingly avoiding learnable spirals spirals spirals spirals spirals spirals spirals spirals summer unable shading shading piece planes planes planes planes planes planes alternating revealed revealed suboptimal propagating valiant valiant eric reject attempted attempted adversary misclassified misclassified misclassified sized accounted loading normalizing exploited infinitely vice nec cube cube drives versa fortunately january corners corners continued agrees locate locate blum blum blum hid mistakes rare floor proves rivest rivest rivest comm connectionism creation steve pin sentation promise terminology avg intersect intersect couple localize possesses imposing perturbing viable separability corresponded adopting lacking encounter slabs explosion amples oracle oracle oracle oracle rejecting succeeded succeeded unknowns backpropaga witbrock heuristically minimally kevin duplicate midpoint midpoint pare querying invoking knew knew decent committed bisection verifying tangents tangents prevalent pictured handful counterexamples 
#@Baum_E,Lang_K,
#t4
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure time time time set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output number number number number number number number system system system error error error error error error error error error error error error error error error error error state results results results results units units units units units problem problem problem models models models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance space space weights weights weights linear linear linear layer layer case case case case case case case case case case case order order order order order order order order order order shown systems values values values values values values values probability probability probability probability parameters noise noise weight weight weight functions functions functions functions functions functions functions functions unit distribution distribution distribution distribution distribution approach approach pattern pattern single single single processing large large rate rate test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns analysis analysis class optimal inputs inputs inputs inputs inputs inputs inputs inputs form form form form algorithms simple simple simple examples examples examples examples examples examples examples examples examples small small size size size size size size size net work task task methods points points points classification classification process process trained trained trained trained trained trained trained trained problems problems problems problems problems problems random random random random random random high representation fixed line general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter real real real real real real real real real real real real real real real real real real average average average average average average average average average theory theory theory theory theory obtained obtained obtained obtained note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation research research log log found target initial initial initial constant constant constant estimate estimate estimate standard standard standard left low low frequency frequency sets sets sets sets sets sets sets sets sets sets range press learn learn basis continuous abstract back back back find find find find find convergence convergence convergence convergence convergence properties references component due due due ieee positive propagation propagation propagation propagation introduction hand behavior behavior behavior behavior behavior statistical statistical effect generated generated generated generated parallel tion tion change measure measure chosen higher higher higher higher higher higher center bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases cases cases binary binary binary binary binary binary binary binary binary binary binary binary binary binary conditions distributed distributed expected expected expected expected expected fact fact correlation correlation correlation correct correct probabilities observed observed errors errors forward scale scale scale simulations simulations simulations minimum resulting classes ing ing tasks tasks tasks tasks tasks total total simulation regression regression regression computed computed computed sum performed times means factor factor potential potential potential dimension dimension dimension dimension dimension dimension made natural natural natural applications study study negative original original artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial samples compared series provide perform experimental experimental experimental experimental related connected mit comparison nets morgan proceedings report technique technique internal exp scheme scheme maps computing equivalent experiment hinton curve curve curve curve curve curve curve curve solutions curves curves curves curves curves curves curves determine determine upper choice choice choice significant significant significant significant approximate basic increase con produce coding randomly randomly developed levels criterion bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds finally achieved measured measured measured measured arbitrary denote tested close predictions predictions amount shape generate generate theoretical theoretical eds ability future rumelhart rumelhart fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit kaufmann typically pairs needed reduced functional functional functional functional functional functional coefficients fully interesting testing testing significantly significantly significantly increasing mechanism consistent consistent structures empirical making supervised polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial run sources sources predict improved recent apply apply apply include inference relevant interest varying previously previously yields converge converge converge williams exists concept studied scaling wide wide predicted predicted correctly feed touretzky runs runs runs runs runs runs runs runs half greater conclusions valued valued valued valued valued valued valued valued valued valued valued valued valued valued valued valued valued bayes bayes numerical numerical numerical numerical numerical numerical designed performs performs performs performs exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential faster practice asymptotic suggest drawn drawn sigmoidal california variety variety exist decrease manner question question appears appears appears dept changing confidence confidence averaging linearly linearly linearly adding boolean boolean independently focus dependence dependence squares solved open controlled restricted forms understanding sizes sizes sizes margin similarly suggested constants constants spectrum spectrum performing performing epochs fitting intervals roughly roughly roughly valid calculate visible classified david avoid box vapnik vapnik vapnik vapnik vapnik vapnik vapnik extension extension plotted variations absolute reason aspects closely closely uniformly uniformly presentation comparing score plots reached procedures contained interested issue issue issue symmetry lie classify sci hold comp generalize denker reach consisted tesauro tesauro tesauro tesauro tesauro tesauro tesauro extend law law law law law law law law bars bars powerful layered transformed xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor requirements exponentially preliminary school tech possibility reliable reliable affect affect momentum momentum examined examined coefficient coefficient coefficient plausible possibly predicting predicts opposite equally perfect perfect perfect perfect perfect formal initialized extent years asymptotically asymptotically asymptotically asymptotically separable separable improves analytic majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority majority tractable baum baum lies lies worse straight tive easier strictly broad worst worst worst worst worst opt addressed pure relevance capability solla solla haussler haussler haussler haussler haussler haussler haussler slower gen fall gave gave gave simulator simulator kinds conclude conclude decreased findings tile progress converged univ realized gap gap gap gap gap gap primarily appropriately appropriately approximates repre theories theories theories establish systematic fits ranges tishby tishby tishby observing methodology monotonically ranging ranging loo sion pat washington schwartz schwartz schwartz den eng warmuth warmuth inductive inductive santa speaking summer numerous visually visually ahmad ahmad ahmad exhaustive chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis opposed presenting failed failed theorems theorems theorems generalizations generalizations assess param alter alter attempted cohn cohn cohn cohn ibm levin ijcnn learnability carefully careful exhibited increments increments strict twenty terns hundreds overtraining overtraining hid concern seattle judged discarded discarded ooo lying littlestone linearized quantitatively protocol crl goodness goodness cruz cutoff cutoff thresh tra watson generaliza monitored repeating sentations rela plotting plotting plotting heights blumer blumer blumer blumer blumer blumer blumer eralization ucsc froin retains bearing behaved gerald predicate eter looked tha ehrenfeucht lea lea imal prefactor prefactor prefactor yorktown alters sepa figtire distinctly exten soo cautious surpass surpass disagrees disagrees nay inconclusive 
#@Cohn_D,Tesauro_G,
#t4
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural input input input input input input input input input input input input input input input input input input input data function function function function function function function function function function function function function function function function function function figure figure time time time time time time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training algorithm algorithm output output output output output output output number number number number number number system system system system error error error error error error error error error error error state state state state state state state state state state results results results results results results results results results results units units units units units units units information information information problem based based based space space space space space linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer case case case vector vector vector vector vector vector vector order order order order order order order order order order shown shown systems systems values values values probability probability probability weight weight weight functions functions neurons neurons neurons neurons unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method approach approach point point image single single single single processing processing large large large large large large local local local neuron neuron neuron neuron neuron neuron neuron analysis analysis analysis class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs form form signal algorithms algorithms simple simple simple simple examples examples small small size size size size size size size size size size work methods methods fig fig step step step step step step field field features process process level structure structure problems random high similar equation rule rule vectors vectors vectors vectors generalization generalization generalization speech average average states states theory gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained note note note note dimensional dimensional dimensional result result result result result university variables variables variables variables computation solution solution solution solution solution solution solution independent defined target dynamics dynamics dynamics dynamics dynamics initial constant constant constant estimate estimate estimate estimate synaptic prediction direction direction map present activation activation activation activation activation maximum maximum range range range range learn components components components nonlinear nonlinear nonlinear outputs continuous continuous continuous abstract back back find convergence convergence convergence convergence convergence convergence convergence convergence density density density properties properties properties properties properties properties properties properties properties properties references component component important adaptive adaptive adaptive propagation introduction behavior behavior behavior behavior effect generated variance variance cost cost cost cost cost search variable lower representations chosen chosen chosen part part part part center good good distributed equations techniques errors forward finite finite finite finite simulations minimum minimum minimum minimum resulting resulting ing tasks total computed computed computed computed computed respect respect respect respect multi multi multi multi multi multi performed performed eq eq eq eq eq called times times elements elements elements factor feedback feedback original specific true application desired desired cross cross provide rates experimental goal distributions gain equal equal equal equal approaches connection train descent descent descent descent descent descent source morgan department advances bias graph graph ai ai ai ai considered hinton hinton curve solutions limit limit limit effects effects efficient full full full full requires requires choice choice give produce produce randomly randomly bounds product actual provided iteration iteration nature depends discussion covariance covariance covariance covariance covariance covariance transformation fast limited close corresponds corresponds corresponds complete stable surface surface surface surface surface assumed role theoretical theoretical theoretical end easily easily degree rumelhart rumelhart kaufmann objective pairs needed needed needed combination dynamical dynamical coefficients fully ratio ratio trials trials uniform empirical mode leads leads principal principal principal principal principal principal iterations iterations iterations max max max filters magnitude decay minimize description architectures directions directions correlations practical quadratic quadratic interest highly yields converge rl diagonal diagonal diagonal diagonal diagonal symmetric symmetric symmetric observation observation bounded bounded interval interval interval williams williams constructed lead suggests suggests matrices rotation predicted predicted feed feed feed touretzky occurs occurs occurs critical minimal reduce conclusions tangent tangent sigmoid measures measures numerical numerical clear faster physics largest drawn drawn california proportional proportional proportional minimizing min min min averaged derivatives derivatives derivatives connectivity configuration derive estimating describes metric coordinates coordinates linearly dimensionality involves remaining spectral spectral spectral scales minimization minimization formed formed versus yield correlated squares squares viewed detailed open controlled controlled controlled controlled controlled evolution centered centered centered centered understanding translation constants updates updates updates allowed spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum calculation slow slow reduces iterative sufficiently assigned coupling coupling coupling perceptual coordinate coordinate coordinate usa usa perceptrons bell bell eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues subspace subspace batch determines extension discuss phys aspects identified uniformly delta delta wij presentation successful oscillatory literature reached receives characteristic composed composed induced contained cun cun cun cun cun cun symmetry contribution running satisfy bar involved relaxation relaxation minimizes eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue reach receive explore layered investigate exponentially updating hessian hessian hessian hessian hessian hessian hessian hall existence existence existence existence reducing investigated investigated applicable analytically eigenvectors surfaces surfaces surfaces surfaces surfaces smallest coefficient rev rank rank obvious logistic regime regime regime isolated isolated averages indicating crucial agreement analytic analytic explanation considerable sections sections mation commonly laboratories laboratories describing lowest demonstrates outer empirically empirically understood axes axes solla solla solla solla solla solla formulated exhibits exhibits reaches curvature adjust implements differentiable initialization gap newton uncorrelated investigation investigation restrict rotated controlling eliminate nonzero nonzero interconnected plays eliminated systematic numerically satisfying loops biased biased biased keeping krogh krogh responsible corner corner presentations hertz hertz infor published lip prentice encountered negligible surprising surprising dominant widrow widrow histograms accounts counting israel surprisingly hypercube eigenvector propagate characterization rigorous rigorous propagating propagating feeding decays searches inversely lippman rewritten rarely nonnegative nonnegative hyperbolic hyperbolic justified justification jersey focuses holmdel holmdel subtracting couplings couplings couplings ray sym sian pin prescribed prescribed indi damping rij quantified discrepancy amax amax amax amax amax amax amax amax lid remarkably kanter kanter kanter kanter kanter kanter availability yann lay lay counterparts diverges justifies accelerate reductions decoupled ifp elliptical rests gan accelerating slowest slowest slowest sara amin amin amin diverging vidual stearns stearns crawfords crawfords clarified rive collapses diagonalization ami wix hes nonsymmetric tma ido 
#@Kanter_I,LeCun_Y,Solla_S,
#t4
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model neural neural neural neural neural neural neural neural data data data data data data data data data data data data data function function function function function function figure figure figure figure figure figure time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training output output output number number number number number number number number number number number number number number error error error error error error results results results results units units units information information information information information information problem problem hidden hidden hidden performance performance performance performance performance performance based based weights weights weights weights linear linear linear layer case case case case order shown shown systems systems systems values probability parameters parameters noise weight functions functions unit distribution distribution recognition recognition approach point point point point point single single single single processing processing test test test test test analysis inputs inputs form form simple gaussian gaussian examples examples small small feature net net net net net net net work task task task points points points points classification classification classification classification classification trained trained trained trained trained trained trained trained trained structure random random random random random random high architecture fixed generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech average average average average average theory theory obtained obtained note note university university university university independent independent initial initial constant table table table table standard computer computer computer computer science science science presented map present present present phase machine sets learn position components outputs sample abstract abstract back find references component component stochastic stochastic stochastic stochastic due positive procedure procedure introduction statistical effect generated tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity classifier classifier classifier classifier lower lower chosen higher higher bound bound bound cases multiple binary conditions represent expected expected expected expected make fact fact techniques techniques errors errors errors finite finite simulations resulting resulting resulting ing regression computed sum times regions regions mapping dimension dimension dimension negative negative samples compared cross determined determined distributions power approaches support train train train train nets morgan morgan report report words technique technique consists internal individual individual individual individual advances advances final bias bias bias bias bias bias delay considered framework domain equivalent experiment hinton san san effects bit capacity choice approximate free pages pages validation randomly clustering levels bounds bounds lines entropy entropy backpropagation backpropagation backpropagation constraint constraint technical technical increases arbitrary arbitrary common implemented implemented implemented implemented end instance instance kaufmann kaufmann objective objective combination significantly empirical leads squared squared squared making making bottom decay idea minimize run run sources light perceptron perceptron architectures improved improve improve ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble introduced identical identical identical identical machines sejnowski engineering highly calculated works bounded interval interval increased increased constructed constructed correctly correctly touretzky touretzky boundary conclusion greater greater conclusions clear learns mateo mateo strong turn decrease averaged averaged averaged manner program program program program program program program boltzmann appears construct longer ways factors metric implement implement simultaneously simultaneously simultaneously simultaneously infinite infinite slightly adding applying extraction independently phoneme viewed learner learner centered discrimination sign performing roughly intermediate assigned david expect box box perceptrons black holds extra uniformly effectively contained superior issue symmetry symmetry symmetry symmetry classify usual generalize realistic attempt satisfies software receive xor collection detail reducing giving school school school mse mse mse mse mse mse mse parity reliable decisions root comparable waibel editor editor necessarily analyze predicts perfect perfect perfect implementations bifurcation freedom explored logic initialized improving regime arbitrarily attempts histogram stop stop inequality phenomena failure answer worse worse straight potentially potentially ridge mellon mellon mellon mellon exemplars exemplars exemplars exemplars exemplars researchers composite composite prop carnegie carnegie carnegie carnegie pure cmu cmu axes conducted outliers pittsburgh pittsburgh instruction instruction kinds conclude calls pac sort saddle acm perfectly count count purely grey lost lost communications ranges imposed balance knn knn knn generalizes generalizes representational regarded properly properly pearlmutter pearlmutter pearlmutter pearlmutter inductive inductive inductive inductive inductive broken broken broken broken broken learnable unified misclassification break break presenting copy intrator solely breaking breaking possibilities valiant tight principled exclusive geoffrey impose gener gener degraded crosses march efforts terrence overhead exceed exceed exceed regimes weaker million misclassified misclassified placing knowing behave behave programmed exploited advantageous satisfaction differently regularities reversed unbounded loaded loaded overtraining overtraining replicated replicated replicated replicated replicated replicated injected ackley striking systematically synergy resultant thing ically replication replication replication generaliza replicate replicate replicate replicate replicate percep lincoln lincoln kolmogorov kolmogorov kolmogorov kolmogorov putting couple hampshire hampshire alization alization illustrating billion symmetries symmetries symmetries symmetries symmetries jensen agation differed ronald complexities disk seemingly specifications taught calling bigger attack exceptions exceptions hurt hoped iden misclassifications entity augmenting diamonds skrzypek skrzypek barak rosenfeld rosenfeld rosenfeld confirming stdev stdev tron strike harmful josef discriminator pessimistic mislabeled mislabeled nctions delineated nathan eld failing tighten unduly accidentally 
#@Pearlmutter_B,Rosenfeld_R,
#t4
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#*network network network network network network learning learning learning neural neural neural neural neural neural neural input input input input input data data function figure figure figure figure figure time set set set set networks networks networks networks training training training algorithm algorithm output number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results information information information information information problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance space space space space space space space space space space space space space weights case vector vector vector vector vector vector vector vector vector order order order order shown systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters distribution distribution recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image single processing large large large large large rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class class optimal optimal optimal form shows algorithms small size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net task fig points field features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification structure problems problems problems problems problems problems random random random random response representation architecture architecture show rule rule rule vectors vectors vectors general general general generalization generalization speech real states states states theory theory theory theory obtained term note note note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result university university computation independent defined found constant estimate terms terms presented presented present present frequency learn basis sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract find computational convergence convergence convergence convergence convergence convergence density density references ieee important important decision decision decision decision decision decision decision context introduction hand behavior behavior statistical search assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier measure measure prior prior prior prior prior chosen higher higher theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem cases type required required conditions conditions represent distributed distributed region region region correct probabilities probabilities probabilities probabilities probabilities scale finite finite finite classes classes classes classes tasks total total regions regions regions regions mapping factor made applications obtain obtain obtain vol relative represented provide define compute rates proc posterior posterior posterior distributions distributions distributions distributions distributions discrete equal power approaches selection department consists exp exp bias sequences experiment additional estimates estimates limit limit limit limit limit san conference conference capacity determine choice free vision estimated increase validation validation give give con condition randomly conditional conditional conditional conditional developed criterion criterion lines lines selected selected selected selected selected backpropagation nature nature nature depends depends discussion normal describe describe arbitrary denote denote denote denote denote denote denote close nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest implemented role main pixel ability hypothesis hypothesis easily degree including fit fit typically typically typically smaller underlying underlying needed functional interesting interesting significantly york increasing increasing consistent trials principle magnitude magnitude frame denotes architectures recent recent recent element similarity strategy include side engineering engineering sufficient sufficient sufficient sufficient volume smooth smooth correspond achieve trans address definition bounded bounded bounded bounded bounded exists expression scaling scaling occur suggests suggests extended trial predicted correctly correctly neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor valued central bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes numerical numerical clear exponential practice asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak constrained reduction drawn drawn drawn proportional labeled turn assuming exist plane targets derivatives manner characters scene reference reference reference reference reference reference reference reference reference reference reference reference relation pro construct construct construct winner primary describes label label metric metric explicitly infinite infinite infinite infinite infinite infinite infinite electrical electrical dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality text consisting john decreases yield depending overlap viewed densities densities densities densities labels labels fraction centered understanding reasonable slow expansion expansion expansion spaces spaces spaces event valid sufficiently sufficiently sufficiently sufficiently assigned assigned euclidean expect handwritten formulation assignment simplicity simplicity selecting uniformly uniformly effectively identify identify identity induced induced classify strategies cues satisfy quantity generalize absence minimizes correspondence attempt attempt satisfies law parametric wiley requirements exponentially issues issues scalar fewer respond applicable working statistically cover cover cover cover cover cover cover understand fundamental fundamental analogous smallest coefficient closest concepts concepts noted expressions simplest arbitrarily attempts theoretic agreement smoothness smoothness smoothness analytic analytic analytic baum baum lies lies tive satisfied constructing implicit begin annual qualitative qualitative radius preceding freeman substantially pseudo readily orders haussler haussler compares requirement pasadena suited progress diagnosis diagnosis bellman bellman notes assign circular impossible nonzero grows caltech plays dealing numerically numerically stated hope imply affected enhanced combinatorial mance ranging ranging ranging sion encountered surprising perfor accounts belongs originally facilitate francisco omitted cancer cancer reader belonging proximity proximity extends sons hart hart hart hart convergent ball robert assigns assigns assigns assigning verify metrics dramatically dna ple largely numerous encouraging encouraging acceptable assignments classifies guess param clas exponent distri duda duda ization denoting crosses considers sketch conversely misclassified sam exchange happen ation vanishes reciprocal eters failures wider resembles bution electron info laws fortunately regularities achievable algorithmic agrees curse curse inequalities powers char appealing cally venkatesh venkatesh venkatesh venkatesh marr marr ref markers polynomially benign merit greatest decades cox intrinsically obeys proce weakness psaltis psaltis psaltis psaltis ther bernoulli fur philadelphia concise complexities complexities complexities poo poo poo poo malignant clue iix iix iix mon descriptive poorer multiclass pennsylvania depict iden siftcation slowing slowing slowing slowing unconditional chitecture collectively deci minkowski effec undefined slows slows resides yll creases erence vides hawaii requisite scalability scalability situ indications tumor satisfactorily peo pertain santosh dures erfc mension rim caveats orem pressing microscope unclassified tity acteristic 
#@Psaltis_D,Snapp_R,Venkatesh_S,
#t4
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#*learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data function function function function function function function function function function function function time set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training output output output number number number number results results results results results results results results units units units units units problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based space space linear linear linear layer layer layer layer layer layer case case case case case case case case case shown systems systems systems systems systems values values values functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition point point point point point single single single control control control control large large local local neuron analysis analysis analysis class class class class class class class class class class class class class class optimal inputs form form form form paper paper examples examples examples small net net net net net net net work work step points points points points points points points points points points points points points points points points points points points points classification classification classification classification problems problems high response representation show fixed fixed fixed line rule vectors vectors general general general generalization generalization real real real real real approximation approximation approximation theory theory obtained obtained obtained note note note note note note dimensional result result result university university threshold threshold threshold threshold threshold threshold threshold computation research independent independent independent defined sequence sequence standard standard standard standard connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections left map activation activation activation activation activation sets sets sets sets sets sets press continuous continuous continuous continuous continuous abstract applied applied back computational properties properties properties references references ieee ieee ieee positive important introduction hand hand behavior parallel tion change difference assume assume lower lower lower measure measure signals chosen higher part part center center center center previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound cases cases type type type make fact fact fact length finite classes tasks computed called called elements mapping factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made made feedback obtain negative true compared desired provide define proc proc proc gain power power power power power power larger contrast nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets proceedings report report implementation version version joint joint joint layers layers layers addition estimates conference upper upper full full choice approximate approximate approximate approximate approximate free give give give give bounds bounds bounds bounds bounds types lines product provided provided provided finally backpropagation backpropagation backpropagation backpropagation backpropagation achieved technical feedforward feedforward feedforward feedforward feedforward feedforward arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote close close complete proof proof proof proof implemented implemented assumed supported theoretical main main main main eds instance instance instance instance objective typically needed needed needed special principle details numbers numbers numbers direct direct direct direct direct direct direct direct direct direct direct direct direct direct bits idea choose choose denotes improved improve property robust robust robust robust robust takes element practical practical sense sense sense sense sense sense subset subset interest sufficient sufficient compare approximately achieve achieve definition definition definition exists lead lead white conclusion conclusion assumptions tangent sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid measures measures measures numerical clear practice hard largest largest largest largest sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal proportional exist plane introduce minima minima acknowledgements appears appears derive distinct changing implement implement multilayer multilayer coordinates coordinates infinite infinite infinite infinite involves remaining remaining easy easy easy consisting develop applying implies boolean boolean lemma lemma lemma lemma lemma lemma solved open open open open open showed approximated similarly similarly suggested partition allowed allowed allowed earlier additive classical interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation topology activations color color color vapnik prove prove prove prove holds holds holds holds aspects importance uniformly delta comparing situation tend conf conf conf strongly allowing sin sin sin sin hold usual dot generalize thresholds thresholds processors employed simpler perturbation exhibit existence rise rise rise scalar fashion giving tech links rest mappings int int int parity possibility authors authors complicated tanh tanh proved proved func math possibly possibly possibly possibly integer integer integer integer integer integer subsets quantities perceptton academic arbitrarily established piecewise piecewise piecewise inequality inequality inequality separable trivial distinguish slope analytic analytic capabilities capabilities capabilities capabilities baum baum baum baum inside precisely worst worst universal author geometry requiring questions considerably prop evaluating double double double lack variant june differentiable extreme globally gap proofs proofs rational rational dealing dealing stronger mail siemens analogy analogy abilities fail definitions definitions disjoint imply continue spurious spurious corollary respective washington washington realization vertices vertices percepttons percepttons consequences interconnections approximators recog april canada statement statement summarize convergent dense dense dense dense dense ence unable achieving basically basically equivalently equivalently chervonenkis alternating sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag sontag nition restrictions theorems theorems conjecture conjecture conjecture reports conservative tight verified equality equality equality alternate ijcnn permits denoting topic hornik hornik rough translations worth apparently dichotomies dichotomies dichotomies october signs sigmoids sigmoids sigmoids sigmoids sigmoids sigmoids sigmoids remark remark remark differently remarks remarks remarks remarks remarks remarks lation lation hyperbolic corporate families hilbert inclusion dichotomy dichotomy dichotomy dichotomy settle triangle separates separates cardinality cardinality cardinality cardinality cardinality rating nontrivial interpolate interpolate interpolate shattered shattered 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#@Sontag_E,
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural function function function function function function function function function function function function function function figure figure figure set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm number number number number number number number number number number number number error error error results results results results results results information information problem problem problem problem problem based based space space space space space space space weights weights weights weights weights weights layer layer layer layer case case order order order order order order order shown systems systems probability functions functions functions functions functions functions functions functions neurons approach processing control control rate class class class class class optimal optimal form form form form shows shows shows algorithms paper paper paper paper examples small net net net work work work work field level level level level level level current problems problems problems similar representation representation representation representation representation representation representation representation representation architecture architecture architecture architecture architecture show show equation equation general general general general general generalization parameter real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory theory term term dimensional dimensional result result result result university threshold variables variables computation research defined defined defined defined constant constant constant constant table table terms terms distance distance presented present nodes nodes nodes nodes nodes nodes nodes nodes sets sets sets sets sets sets sets sets range press components continuous continuous continuous abstract abstract computational convergence convergence convergence convergence density properties properties references component component positive important decision introduction complex estimation estimation estimation statistical parallel complexity complexity complexity complexity complexity complexity complexity complexity lower measure measure signals learned chosen part part theorem theorem theorem theorem theorem theorem bound bound bound type required required good represent represent represent represent represent represent represent represent represent represent make length errors forward minimum classes classes regression regression respect factor dimension dimension made global applications study negative artificial specific specific specific series rates rates rates constraints constraints constraints connected power accuracy accuracy accuracy accuracy accuracy dependent nets nets nets nets morgan proceedings proceedings proceedings proceedings department joint joint connectionist considered computing view san conference conference capacity determine upper significant approximate approximate approximate statistics statistics statistics statistics basic give con condition bounds bounds bounds bounds lines entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy processes backpropagation depends feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward arbitrary arbitrary arbitrary denote denote denote close complete supported theoretical main eds eds journal journal easily including fit kaufmann needed needed needed needed needed needed needed needed needed needed reduced account functional functional functional functional uniform uniform uniform empirical representing representing representing details making bits bits bits bits bits bits bits international idea idea description discussed introduced subject subset recently engineering engineering dimensions calculated volume volume works works studies achieve achieve achieve trans bounded bounded bounded interval grant exists parts scaling extended width white half place valued measures measures measures exponential mateo taking hard hard sigmoidal exist derivatives manner manner base question explicit explicit van index solving mathematical mathematical metric metric metric metric implement multilayer category infinite physical develop develop springer national family depending squares solved transform open open approximations approximations approximations approximated approximated suggested translation translation constants partial calculation spaces closed distances sufficiently construction construction david david box sciences vapnik vapnik vapnik discuss absolute discussions uniformly society society literature comparing comparing verlag satisfy ill ill principles satisfies remain parametric powerful american american estimators association existence ideas school mappings relationships proved proved workshop func cover cover notion neu smallest transmission possibly integer logic ith mentioned asymptotically indicating trivial smoothness smoothness smoothness capabilities straight worst hyperplane mathematics universal annual considerably tional haussler haussler gains berlin achieves tile tile tile notes oxford restriction fix approximates concerned jth consideration difficulties determination ral disjoint constructive constructive nonparametric date published combines sion realization originally originally approximators barron indicator shortest warmuth kearns statement adopted stone stone robert limitation andrew ics logarithm annals annals annals goodman chervonenkis chervonenkis chervonenkis suboptimal adopt theorems theorems convenience australia valiant tight illustration rectangular learnability rectangle cole hornik translations indication indication indication williamson williamson williamson williamson lecture achievable australian fill dropped concrete judged archi suffice dimen rectangles ben ben bruck gallant incurred kolmogorov kolmogorov plexity lipschitz lipschitz lipschitz blumer imposing machinery exciting inadequate lations implication cybenko tha inn mat ehrenfeucht ehrenfeucht ruth ruth stinchcombe canberra superpositions xii loose hecht neurm neurm erence stating hal nmnber nmnber arnold arnold figtire nielsen dickinson moscow nnmber funahashi iml iml radon mathemat odes yardstick unaware fiz tabulation probabilit 
#@Williamson_R,
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#*network network neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function set set set set set set set networks networks networks networks networks output output output output output output number number number number number number number number number number number number number system error error error error error results results results results results results results results results results results results results results results information information information information performance based based based based space space weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case vector vector vector vector vector vector vector vector shown systems systems systems systems values values weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions recognition method method method method method method method method approach approach approach approach approach approach approach approach approach pattern single single large analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix optimal inputs inputs inputs inputs inputs inputs form form shows shows simple simple simple simple simple paper paper paper examples small small small small size size size work work work process level level structure representation show show show equation equation rule vectors vectors general general general general real real approximation states theory theory theory note note note note note dimensional result university university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables variables variables variables variables computation research research defined found found constant computer distance present present present sets press components components basis basis basis outputs abstract applied applied applied properties properties references due ieee ieee ieee ieee positive procedure procedure procedure decision introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit statistical parallel tion complexity complexity complexity complexity complexity complexity complexity variable variable variable variable variable variable variable assume assume assume lower lower lower lower lower lower lower lower lower lower lower lower lower lower part part center previous theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound cases cases required required multiple techniques techniques techniques correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation resulting computed computed called called elements mapping applications obtain obtain negative provide define define proc determined related related gain discrete discrete power power power power approaches approaches comparison department technique technique technique technique joint represents difficult addition considered considered framework framework framework computing computing equivalent view view view design limit limit determine efficient efficient efficient upper upper requires approximate basic pages pages pages give con condition condition derived derived developed bounds bounds bounds bounds bounds types product product simply technical technical describe arbitrary arbitrary arbitrary close corresponds complete stable proof proof proof proof proof proof circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits amount effective effective implemented implemented supported require require journal journal easily including needed needed needed hopfield combination reduced coefficients coefficients coefficients programming significantly significantly significantly special special special special special special special details details details call call call max direct depth depth depth depth depth depth depth depth depth depth depth depth depth depth magnitude magnitude polynomial polynomial polynomial recent correlations correlations correlations correlations correlations takes practical introduced introduced introduced trees recently interest conventional tions yields trans trans sparse sparse sparse definition definition definition background generalized generalized generalized bounded bounded bounded bounded gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate grant exists lead lead column assumptions assumptions clear exponential largest largest proportional introduce introduce program force question acknowledgements relation pro derive derive derive construct laboratory laboratory laboratory distinct metric implement implement implement implement implement implement spectral spectral spectral spectral spectral spectral spectral spectral spectral mutual applying applying implies boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean john expressed expressed correlated correlated interpretation transform restricted restricted decomposition decomposition understanding allowed spectrum spectrum spectrum spectrum key earlier construction construction construction bell assignment sciences sciences memories determines prove prove prove prove prove specifically holds holds characterized reason columns efficiency closely literature orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal summary summary procedures procedures procedures procedures success showing showing interpreted sci sci comp comp write providing computes computes computes ill ill ill ill subsequent approximating approximating simpler simpler remain wiley investigate exponentially exponentially exponentially exponentially exponentially put detail limitations limitations preliminary fewer parity parity relationships office referred gates gates gates gates gates gates gates gates gates gates gates gates proved func cover smallest math coefficient coefficient concepts editor analyze analyze aspect logic store switching switching switching electronic asymptotically asymptotically majority majority answer multiplication lies comparisons considerable inside stanford stanford stanford stanford implementing easier division sgn sgn sgn hyperplane laboratories pool computers computers outer researchers geometric geometric geometric geometric geometric geometric geometric geometric questions considerably limits applies led share share polynomials polynomials mod proven proven proven proven logical tile tile tile tile tile tile tile tile tile tile tile cor cor uncorrelated uncorrelated proofs proofs proofs proofs proofs fix count harmonic harmonic harmonic harmonic harmonic nonzero maass air murray convenient tools tools tools tools tools tools fan contract contract hope analyzing definitions definitions definitions methodology effectiveness effectiveness effectiveness carry constructive constructive constructive spurious spurious corollary corollary corollary surprising counting viewing sons characterization generalizing outlined unified geometrical indirect pointing ber presenting mutually mutually num elementary bounding simplifying relating investigating termed inversely nasa siam siam siam algebra algebra algebra programmed nal reciprocal emphasis remarks uniqueness uniqueness uniqueness uniqueness quantify cornput siu siu siu siu siu siu poly polynomially polynomially polynomially polynomially polynomially polynomially sity lewis computable thresh thresh february bruck bruck unnecessary mountain kailath kailath kailath kailath kailath comprehensive collections incurred oil intersect avenue ther roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury constructions constructions constructions puted tially implementable implementable froin army army proving proving syrup syrup syrup syrup seemingly orthogonality exposition 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#@Kailath_T,Orlitsky_A,Roychowdhury_V,Siu_K,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data function time set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number system system system system system system system system error results results results results results results results results problem problem problem problem problem problem problem hidden hidden hidden hidden hidden performance performance performance based linear linear linear layer layer layer layer layer layer layer layer layer layer case case case case case vector vector vector vector order order order order order shown shown systems systems systems values values values values values probability probability probability probability parameters parameters parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution method method approach approach approach approach approach point processing control large local rate rate rate test analysis analysis class class class class class form form form signal signal algorithms algorithms 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similar similar representation architecture architecture architecture architecture architecture architecture section section section rule vectors general general general general general speech speech parameter parameter approximation average obtained note experiments university variables variables research research research research found found found found dynamics initial initial table table estimate computer terms distance node science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction direction presented presented presented present present machine machine machine machine machine sets press learn basis nonlinear nonlinear sample sample sample abstract applied applied applied applied back find convergence convergence convergence properties references ieee ieee important important important decision decision decision decision decision decision propagation introduction introduction complex hand hand hand generated parallel parallel parallel tion tion complexity assume classifier rules rules rules rules prior prior prior prior chosen chosen chosen chosen cases cases required good good good binary binary binary conditions tree tree tree tree tree tree tree distributed make make make fact fact fact techniques techniques techniques techniques techniques proposed correct correct probabilities probabilities observed errors errors errors errors minimum classes total total regression regression regression multi multi multi multi performed performed times times mapping mapping mapping mapping made made made made made made natural feedback study study knowledge knowledge knowledge knowledge artificial artificial artificial artificial artificial represented true true compared compared compared compared compared compared compared cross provide proc proc perform perform perform perform perform perform determined determined goal related equal equal equal power power mit steps accuracy accuracy accuracy comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison contrast train train department version version version version internal internal difficult layers addition addition considered considered considered considered considered considered equivalent san determine efficient significant approximate statistics statistics validation give give con condition clustering clustering clustering criterion depends measured feedforward describe denote assumption assumption predictions predictions finding finding amount generate theoretical require main main square end future makes makes makes makes rumelhart rumelhart underlying underlying underlying underlying underlying underlying underlying underlying underlying underlying combination combination unknown unknown mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp interesting testing testing testing testing testing york york increasing increasing leads call numbers iterations iterations iterations iterations iterations iterations iterations iterations iterations making expert idea attention run run run run run description predict predict perceptron perceptron improved improved improve recent recent separate practical practical practical trees trees trees trees trees trees inference subset recently recently sufficient compare compare compare observations volume axis studies studies studies entire occur predicted white occurs boundary generally assumptions assumptions assumptions assumptions assumptions assumptions assumptions assumptions conclusions conclusions conclusions accurate accurate designed designed clear performs performs faster characteristics characteristics drawn sigmoidal intelligence intelligence intelligence relationship groups groups force base question question explicit explicit appears ways ann ann tuned tuned tuned tuned distinct pruning multilayer category category category category category electrical text text consisting consisting applying applying extraction expressed lee understanding activities converges past performing performing combining purpose boundaries boundaries closed closed avoid avoid building priori priori perceptrons perceptrons automatic prove discussions closely divided mcclelland mcclelland efficiently comparing conf procedures procedures prob classify running running criteria criteria categories categories categories categories categories categories categories categories categories categories categories categories vary giles denker denker denker cat principles modelling carried diego wiley involving mass discriminant fashion tech rest incremental int possibility comparable proved proved cognition momentum momentum examined examined induction induction induction induction induction induction act math naturally possibly reading generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation predicts ensure aspect friedman versions noted noted assumes observe observe separated mentioned mentioned indicating cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart cart trivial capabilities capabilities reasons considerable purposes purposes purposes purposes closer desirable probable universal describing beginning implicit english qualitative qualitative axes axes axes axes adjustable frequently operate gen fall fall popular popular popular popular occurrence occurrence incorporating adjust sophisticated comments converged leaf wesley wesley acquisition acquisition acquisition classifying classifying addison guarantee grows interconnected wrong wrong wrong breiman breiman breiman breiman occurred occurred analogy interconnection methodology guide carry selects games performances performances performances performances performances performances performances performances performances performances performances respective intended washington forecasting forecasting originally approximators matter park variants statement statement statement dietterich dietterich stone default default default default default default default default lem metrics ence microstructure rigorous convenience australia australia chess param constrain unseen unseen unseen community mitchell books books cole academy topic hornik hornik cation cation quinlan quinlan quinlan preprint places lippman exhibited challenge circumstances remarks externally lowe lowe marks pearson pearson pearson pearson mistakes progressively classi classi lying frequent alto alto fol restrictive bradford fication fication nominal artificially statements statements brought tsoi tsoi tsoi tsoi atlas atlas atlas atlas predetermined palo palo appli campbell connor accuracies accuracies accuracies accuracies adjustments mention pursued pursued rigorously neurodynamics postulated nth clump rosenblatt rosenblatt hild lowing throw ies webb webb conveniently brooks maxwell maxwell queensland queensland olshen altogether classifi eter cybenko cybenko equi generalised minimising struction nique gation communicated wadsworth confer stud worthwhile neurocomputing stinchcombe utgoff utgoff cial superpositions doubt chitecture favoring hecht hecht optimised calif calif calif calif criticism sumption muthusamy bakiri comple contiguity contiguity clumps clumps latest spartan michalski michalski michalski ordinal erated popularity travels artifi ascertain ascertain lucia enjoy thirdly communities communities communities summarised carbonell refered introductory backpropa uneven defence isation mcdermott mcdermott desirability consulting pitfalls pitfalls har monterey 
#@Pearson_R,Tsoi_A,
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#*network network network network network network network network network network network network network network network network network network model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set set set set set set networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance performance performance space space space space weights linear linear linear linear linear linear linear linear linear linear layer order order order order order order order shown shown systems systems systems systems parameters parameters parameters parameters functions functions functions recognition recognition recognition recognition recognition approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single processing processing large large large large rate rate rate rate rate rate test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class inputs inputs inputs inputs form form form form form shows shows shows algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian small small small small size size work task task task task classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level structure problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems high high high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar line rule general general generalization speech speech speech speech real real average average note experiments experiments experiments experiments dimensional dimensional dimensional result research found standard standard computer computer computer computer science science presented low low low low nodes frequency range range basis basis basis basis basis basis basis basis sample abstract back back find computational references due due due due ieee procedure important adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision propagation propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex complex statistical statistical statistical statistical search search search complexity complexity complexity complexity complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier measure measure measure chosen part part center previous previous previous previous required required multiple good good good long long represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree 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advances represents difficult final layers layers layers addition ai cambridge cambridge cambridge equivalent curves limit determine determine determine efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers requires requires requires requires free speed estimated increase validation validation validation validation con developed developed developed developed types provided provided provided provided provided provided provided provided provided provided selected measured tested rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount amount nearest nearest nearest nearest nearest implemented implemented require require require require main eds square square including including including typically typically reduced reduced reduced reduced reduced technology technology testing testing testing significantly significantly significantly character increasing details numbers stored stored stored magnitude magnitude polynomial polynomial polynomial polynomial polynomial polynomial combined improved improved improve takes takes takes takes practical practical practical practical practical practical practical practical practical practical practical practical practical practical practical identical engineering engineering dimensions sufficient sufficient conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional calculated tuning smooth smooth match match studies studies studies achieve mixtures generalized deviation deviation wide predicted predicted alternative correctly touretzky touretzky width width width clusters pass demonstrate demonstrate conclusion reduce reduce neighbor neighbor neighbor neighbor differences differences differences differences modules moody faster faster suggest suggest reduction characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics demonstrated solid proportional radial radial radial radial radial relationship relationship force force acknowledgements digit digit digit digit digit digit digit digit digit digit digit digit digit longer longer longer plot laboratory tuned tuned electrical electrical dimensionality dimensionality adding formed formed formed formed versus versus select focus formation detailed densities evaluated evaluated lee lee lee lee lee lee lee lee centers centered digits allowed spaces convex roughly purpose boundaries boundaries boundaries boundaries boundaries intermediate intermediate intermediate intermediate intermediate classified classified existing thesis thesis neighbors extra differ differ differ differ computationally included included included genetic genetic vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel characteristic summary quickly repeated classify sampled vary vary generalize generalize generalize generalize extend minimized explore powerful powerful poor poor requirements requirements requirements requirements requirements requirements requirements exhibit rapidly lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann divergence discriminant office understand understand spline created implementations versions explored arbitrarily serial serial seconds massachusetts massachusetts theoretic theoretic improves scientific sun sun exemplars researchers greatly greatly substantially amounts amounts tional experimentally poorly poorly poorly poorly orders orders frequently polynomials richard richard extreme trade trade trade representative resources resources ordering hyperplanes exemplar eliminated communications air air fits significance significance grow disjoint disjoint disjoint disjoint knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn generalizes vowels mance loo sion widths perfor pat pruned pruned dependency mem master master cpu cpu properly formant considerations considerations variants fold sequentially usage usage usage usage usage usage usage usage usage restrictions 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#@Lippmann_R,Ng_K,
#t4
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#*network network network network network network network learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input data data data data data data data data data data data function function function function figure figure figure figure figure time time time time time time time time time time set networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number system error error error error error error error results results results information information problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden performance performance performance performance based space space weights weights layer case order order order order shown shown shown systems values values values values parameters noise method method method method method method point single single single single processing control large large large local rate rate rate rate rate test test test test patterns matrix matrix inputs form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper small small size size size size work work work methods methods methods methods methods methods methods step step step step step step step step step step step step step step step step step points classification trained problems problems problems problems problems problems problems problems problems problems problems random random random random high high show generalization speech approximation average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient dimensional university threshold variables variables research research defined defined defined found target target target target target target target target target initial initial constant table table table table standard computer computer terms terms node node node node node science science left direction direction direction direction presented present low nodes nodes nodes nodes nodes nodes sets maximum maximum maximum press press press learn basis nonlinear abstract applied back back find convergence properties properties references references component component ieee ieee positive important important adaptive propagation propagation context context context introduction action recurrent tion change variable variable variable variable variable variable variable measure chosen part previous cases type required required good good good binary conditions conditions techniques minimum ing computed multi sum regions optimization study study study negative compared compared desired connected descent descent descent morgan advances connectionist final cambridge cambridge computing solutions solutions design limit limit limit san san bit bit bit full speed basic produce types evidence backpropagation iteration measured arbitrary arbitrary tested fast inverse short generate supported theoretical eds eds eds makes kaufmann combination fully technology trials trials trials trials squared details iterations max pre early directions recent exact property pair separate introduced moving moving moving moving moving moving moving include subject quadratic quadratic highly approximately diagonal bounded sensitive studied studied scaling deviation derivative derivative derivative derivative touretzky width column column column runs runs runs conclusions numerical numerical numerical numerical numerical mateo suggest cycle cycle cycle drawn proportional pulse pulse pulse turn targets targets targets targets introduce derivatives derivatives derivatives derivatives derivatives minima base explicit produces longer sensitivity category remaining minimization minimization minimization minimization springer springer quality choosing influence detailed detailed approximations suggested allowed calculation calculation calculation calculation distances activations coordinate absolute absolute tests tests tests columns columns closely divided divided divided divided divided successful successful oscillatory detect computations schemes vowel tend conf verlag verlag quickly success success sin sin sin sin running follow criteria criteria strategies bar vary usual correspondence presents diego layered involving replaced association limitations hessian hessian preliminary investigated parity parity parity analytically decisions expressions art switching switching arbitrarily finds slowly formula analytic analytic analytic analytic nonlinearity nonlinearity nonlinearity perspective strictly precisely division sgn sgn pulses scientific acknowledgement calculations calculations auto author conjugate conjugate conjugate conjugate conjugate reflects improvements incorrect berlin berlin curvature curvature curvature curvature richard pose discontinuities notes notes arguments linearity acts lecun lecun lecun proceed lost lost fails systematic difficulties nearby north vowels evaluations evaluations holland regarded guarantees guarantees ascent ascent peterson peterson peterson peterson peterson omitted variants dividing consecutive boxes specification outperform tables break employs centre classifications acceleration edinburgh edinburgh avoided wise retain sized tively intl bring failures resembles lecture lecture differently bridge saturated suite proportions acoustical beneficial rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer maxi decaying america watrous watrous watrous connectionism cutoff cutoff firm south signed mis freely amsterdam wellekens wellekens resemble proximation mum save oooo abs abs abs barney barney barney barney accord 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#@Rohwer_R,
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural input input data data data data data data data data data data data data function figure figure time time time time time time time time time time set set set set networks networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number system system error error error error error error error state results results results results results units problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance based based space space space space space space space space space space space case case case case case vector vector vector vector vector vector vector vector order order order order order shown shown systems values probability parameters weight weight functions unit distribution distribution recognition method method approach pattern pattern pattern point point point point point point image image image image image image image image image image image image image image single processing processing large large large large large large analysis analysis optimal signal algorithms algorithms algorithms algorithms algorithms paper paper examples examples small small small small small feature feature feature feature feature feature feature feature feature work work work methods methods methods step points points classification classification classification process process current trained trained structure random high high similar similar similar similar representation section rule rule vectors images images images images images images images images images images parameter parameter real average theory term term term note experiments experiments experiments experiments result result university university threshold variables variables solution solution solution solution solution defined found found found found found initial initial initial initial initial initial initial table standard standard terms distance distance distance distance distance distance science direction presented presented presented map map map map map map map map low maximum press learn learn learn components sample sample abstract applied applied applied find find find computational computational computational convergence density density references due ieee ieee ieee context introduction introduction estimation effect effect generated tion tion difference variable lower measure chosen chosen chosen part center center center center center center required required multiple good good good long long conditions represent represent distributed distributed distributed make make make make techniques techniques techniques techniques techniques techniques techniques techniques region region correct errors minimum classes ing ing ing ing total human computed eq eq eq called times times times times times times regions regions regions regions regions means means means means means means means means means means means means means factor made made orientation orientation applications applications study original vol vol vol vol samples samples samples samples represented represented represented represented true true true application application application desired compute proc determined determined related connected accuracy comparison larger update update update dependent proceedings report report words department implementation code code final maps maps maps maps maps maps maps maps maps maps maps design design bit bit bit conference conference conference conference full full choice choice speed speed speed speed speed basic increase con randomly randomly randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering actual actual iteration nature nature biological measured discussion technical describe arbitrary arbitrary arbitrary tested tested fast assumption stable surface finding amount amount nearest nearest nearest effective require main vlsi pixel pixel pixel pixel pixel pixel cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster easily easily including typically typically typically smaller block block significantly uniform uniform details call direct making bits bits bits bits bits international international international idea produced run run run run run discussed resolution exact reported reported practical moving include period subject identical pixels pixels subset interest interest sufficient compare compare unsupervised observations approximately approximately calculated calculated axis axis converge converge converge trans diagonal sparse background background grid sensitive concept digital clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters generally runs runs runs greater assumptions assumptions competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive clear cycle solid variety decrease manner scene scene reference pro van van van van produces longer primary primary primary primary primary distinct distinct metric sensitivity slightly slightly adding quality quality quality quality quality quality formation depending solved updated updated updated organizing organizing centers centers centers centers centers completely converges allowed calculation performing epochs epochs epochs epochs classical reduces roughly penalty remains initially sufficiently assigned assigned assigned euclidean kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen faces faces topology david precision recorded figures formulation color color color color color color color color color color color color color color color color color color color color color color color color color color assignment assignment assignment candidate variations neighbors neighbors neighbors neighbors neighbors neighbors major compression closely uniformly uniformly differ literature comparing essentially ten strongly allowing heuristic dis dis dis running timing timing gray gray comp quantity play providing quantization quantization quantization quantization quantization quantization reach attempt deal decreasing body origin wiley difficulty updating updating updating rapidly hall fashion school referred referred referred complicated closest closest configurations extremely extremely facial facial facial equally changed eyes eyes eyes eyes eyes implementations observe academic initialized initialized store multivariate epoch epoch epoch epoch epoch baseline brown brown indicating great stop band fairly capabilities comparisons comparisons comparisons stanford berkeley organized choices choices located located desirable describing begin begin cybernetics exemplars pseudo pseudo red red red passed execution spread cal green green green green green gave gave substantial chose chose display eventually converged wesley assign assign assign concerned bin bin turned communications convenient minutes minutes determination bands north symposium symposium hours eqn exploring excellent started programs entry entry entry codebook codebook codebook guarantees moved moved dominant topological topological topological topological topological topological topological topological bad den den den den den sphere counter counter entries matter proximity proximity proximity proximity observer ball assigning assigning sequentially rms rms rms yielded ence schulten ter ter users opposed year comparative blue blue blue blue blue blue blue blue blue acceptable lit solely clustered wake rectangular increment increment evolve cessing march picked lookup win termed emphasized nonetheless tones book book minor thousands ritter resembles cube preserves ate ate traveling influenced subjective hundreds skin aid hoc pictures eral medicine ters judged quantizer classi attained economic tended fastest quantitatively tance tance salesman sions dimen colors colors colors colors colors colors colors fol thing fication approached files jan ized allowable subtle daniel searched tutorial plotting 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#@Bilbro_G,Nissman_D,Snyder_W,VandenBout_D,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data data function function function function figure figure time time time time time time time time time time time time time time time set set networks networks networks networks networks algorithm output output number number number number number number number number number number number number system system error error error state state state state results results results results results results results results units units information information information information information information information models models models models performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space space weights weights weights weights weights weights weights weights weights weights weights linear case case vector vector order shown systems systems systems systems systems systems systems systems systems systems systems systems weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions neurons neurons neurons neurons neurons neurons unit unit recognition recognition approach approach approach approach approach approach approach image single single processing processing processing processing processing processing processing processing processing processing processing processing processing control large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate patterns optimal optimal inputs inputs inputs inputs inputs inputs form form form simple paper paper small small size size size size size size size size net work cells step process process process level level level cell cell cell cell cell cell problems problems problems problems high high high high high high memory memory memory memory memory memory memory memory memory memory memory representation representation architecture architecture architecture rule rule rule vectors general general speech speech real gradient term note note result result result university computation independent sequence sequence table table table table table standard computer computer computer connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic direction direction direction presented low low low machine machine machine machine maximum maximum range range press learn abstract back computational computational computational density analog analog analog analog analog analog analog analog analog analog analog analog analog properties references due due due due due due ieee ieee positive important important important important adaptive adaptive propagation propagation circuit circuit circuit dynamic dynamic parallel cost cost cost cost tion change variable lower lower rules measure measure measure measure representations representations word higher higher higher higher higher higher higher higher bound firing firing type type required multiple good binary binary binary long represent chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make make fact observed errors errors scale minimum ing tasks tasks tasks total human human human human human human human multi sum sum sum called times times times times times times elements elements elements elements mapping means factor optimization made applications applications applications artificial artificial artificial artificial relative relative relative relative represented application compute rates proc proc perform perform perform goal related related connected motor brain brain equal power power power power power steps comparison comparison comparison comparison larger contrast connection connection morgan morgan words implementation implementation implementation implementation implementation implementation synapses synapses consists advances joint represents difficult final addition addition considered considered considered computing computing computing domain directly directly hinton hinton solutions solutions solutions design design design design design design design design design design design design san san san bit bit bit bit conference conference conference conference upper significant speed vision vision vision estimated basic basic basic give produce produce area area area area path product product product provided provided finally nature biological biological biological biological biological biological biological biological achieved achieved arbitrary group fast fast limited limited limited limited inverse circuits circuits circuits effective effective effective effective implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse require adaptation end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi future future degree makes makes development fit kaufmann kaufmann typically typically needed needed needed needed reduced dynamical fully fully technology technology technology transfer interesting interesting ratio ratio ratio ratio ratio character operation making making stored stored supervised early early frame frame frame frame frame frame frame frame frame discussed discussed discussed improve advantage advantage separate takes element element typical typical reported reported reported reported include include include machines machines machines machines machines array array interest interest interest highly conventional works tions solve achieve definition gate gate gate gate interval interval storage storage storage storage storage storage storage storage storage exists occur suggests suggests digital digital digital digital digital digital digital digital digital digital digital digital digital digital wide hybrid width deterministic white column column column hardware hardware accurate designed designed designed performs faster learns mateo mateo sound hard largest solid solid solid pulse pulse pulse assuming user user relationship introduce program boltzmann boltzmann boltzmann appears pro solving changing changing implement category simultaneously physical involves easy slightly integrated john review open operations operations restricted evolution sizes suggested updates processor calculation calculation calculation calculation performing purpose purpose penalty calculate calculate precision precision precision precision precision precision precision precision expect expect includes silicon activations recognize variations black divided included comparing comparing reached characteristic summary compact notice conf success issue running criteria criteria device device device built involved relaxation cmos highest chips chips chips chips chips chips chips chips chips chips chips chips chips chips processors processors processors processors processors processors attempt disparity put optimized limitations fewer reducing tech tech mappings int int int int fault transistor referred working maximizing stream stream fundamental neu examined smallest smallest smallest transmission adapt man changed changed implementations implementations implementations implementations implementations implementations implementations implementations implementations implementations implementations implementations prototype aspect aspect obvious noted art store store store store store consist serial attempts devices devices devices devices devices devices devices devices devices devices devices ment ground trivial floating majority capabilities answer multiplication processed rapid perspective sys worst leaves desirable products products products pulses calculations calculations calculations calculations lowest computers computers bandwidth cybernetics meaning summation varies flexible flexible flexible capability capability capability capability capability simulate quantitative continuously execution branch fall fall instruction cal cal cal conclude comments comments progress june trade trade trade don don don don representative representative uncorrelated college proportion primarily interface ratios arguments concerned count count count flexibility flexibility flexibility flexibility flexibility flexibility flexibility flexibility flexibility flexibility grows lost multipliers multiplier multiplier adds wrong consideration significance significance tools tools programmable programmable programmable handwriting balance resulted mark shifts arrays carry continue continue date alspector alspector programs von von von von von von von von von moved conjunction bad demonstration candidates tic enable francisco indicator horizon steepest santa santa automated thresholding executed counts accumulated accumulated ccd ccd ccd ccd ccd temperatures mind mind yale largely gold corporation minus shorter accept dec die die connec ease ease simd big big streams henderson henderson summarizes increment formance tems execute convert efforts drawback drawback drawback million sheet sheet diversity indication commercial milliseconds amplification round challenge mann spite suggestions stores accumulation neumann neumann neumann neumann neumann neumann neumann neumann neumann allen allen trainable designs designs designs micro micro micro micro puts loosely graf graf accomplish supplied calculates engine executing executing executing partly partly beneficial cur longest reviewed reviewed reviewed reviewed merit merit shares replicate refresh refresh pendent haven meaningless yon tolerant putting lowered availability availability accepts volatile volatile thumb thumb thumb sought intel intel intel electrically impressive seeks multiplexing brevity bellcore bellcore bellcore wafer reconfigurable today today useless mission attain multiplexed multiplexed multiplexed multiplexed multiplexed implementa millions jayakumar jayakumar synap business reed patterson patterson tam orlando hammerstrom cache semiconductor semiconductor semiconductor shortening corp noteworthy noteworthy refreshed refreshed dram offs sram mitsubishi decent decent traded grams yariv griffin worthy holler 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#@Holler_M,
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weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions approach approach approach approach approach approach approach approach single single single single single single single single control large large large large analysis class optimal optimal inputs simple small small size net net net work task field process level current current current current current current current current current structure structure problems high similar similar equation equation equation section fixed fixed fixed fixed fixed fixed vectors approximation note dimensional result result university university threshold threshold threshold threshold threshold threshold threshold computation computation computation computation computation computation research research independent found constant constant constant standard standard computer node science present low nodes press nonlinear nonlinear nonlinear nonlinear abstract applied computational computational computational density density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references positive positive positive important introduction circuit circuit circuit circuit circuit behavior behavior behavior effect effect generated parallel parallel tion tion tion difference difference chosen type required required long conditions conditions equations equations chip make make make make make fact region region region region region region proposed correct resulting tasks sum sum performed regions regions factor factor factor factor potential potential made feedback applications negative negative negative artificial relative relative desired desired desired cross provide provide provide compute perform perform perform active active active constraints approaches approaches approaches voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage accuracy source source selection proceedings department implementation implementation implementation implementation implementation synapses synapses difficult bias bias scheme scheme scheme addition addition addition addition addition computing computing directly curve additional additional additional additional additional curves curves top top top top efficient full requires requires significant significant basic increase increase produce channel weighted weighted weighted developed developed developed area area area area area area area product product actual simply measured measured measured measured measured normal normal technical common synapse synapse synapse synapse synapse generate require square ability makes development including simulated simulated simulated simulated typically typically typically needed needed functional technology technology programming programming programming programming interesting interesting mechanism structures mode operation leads stored stored bits minimize sources recent recent exact advantage advantage advantage advantage separate element element period engineering interest sufficient highly highly varying varying varying varying conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional differential differential differential modified gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage lead scaling scaling scaling scaling digital digital occurs occurs setting conclusions valued designed practice hard characteristics characteristics characteristics characteristics characteristics characteristics characteristics california california manner force areas reference ways factors mathematical distinct dept modeled modeled modeled implement implement implement electrical involves remaining easy unique applying blocks dependence dependence dependence depending depending overlap viewed controlled static sign combining combining sufficiently sufficiently sufficiently sufficiently advantages precision coupling coupling existing includes thesis weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting memories extension prove characterized characterized characterized major simplicity straightforward straightforward efficiency divided effectively included build efficiently essentially ten characteristic characteristic compact compact compact compact compact compact compact compact compact compact compact compact contribution sin sin sin sin sin sin device device device device device device device device device device device device device device device device device device device device device device device device device dot providing providing thresholds operating law essential circuitry circuitry limitations limitations helpful matches investigated ideal possibility possibility office gates reading analyze extremely voltages voltages implementations implementations obvious store simplest simplest motivated charge charge years devices devices devices devices devices devices devices devices devices devices devices devices devices devices slowly fairly slope floating floating floating floating floating floating floating floating floating floating floating floating floating multiplication multiplication multiplication multiplication multiplication multiplication nonlinearity nonlinearity implementing berkeley berkeley berkeley berkeley strictly transistors transistors scientific acknowledgement read depicted demonstrates requiring requiring greatly offset poorly requirement exhibits rely measuring monotonic proven proven conductances conductances inherent age accomplished sv fabricated fabricated guarantee amplifier summing linearity air saturation attractive programmable programmable contract hope capacitor capacitor capacitor capacitor capacitor date washington nonlinearities nonlinearities offers offers thin thin thin master storing storing storing designing captures captures discovered fold severe dense leaving corporation creates dec tween feeding drain drain drain drain drain drain drain drain drain drain drain drain drain drain drain drain drain drain drain drain massively rain capacitance capacitance capacitance capacitance capacitance capacitance capacitance capacitance disadvantage employing places behave programmed programmed programmed retained slopes inactive tunneling tunneling tunneling tunneling tunneling tunneling strict technologies technologies saturated saturated saturated saturated saturated const const quadrant quadrant quadrant quadrant quadrant quadrant quadrant quadrant quadrant trainable designs firstly house fabrication conversion subtracting impedance disturbance resolved artifact leakage unusual focusing mul tenth capturing eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom eeprom sponsored cox cox drawbacks configured altering cancel lifetime fet couple accu capacitive capacitive cir kramer kramer kramer kramer kramer kramer volatile intel intel electrically electrically vin vin parasitic parasitic parasitic parasitic parasitic parasitic canceling oxide oxide oxide oxide oxide oxide oxide widespread millisecond masks reconfigurable implementa implementa electrons sept vas 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#@Chu_R,Ko_P,Kramer_A,Sin_C,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set networks networks networks networks networks networks networks networks training training training training algorithm output output output output output output output output output output number number number number number error error error error results results results results units units units units units units units units units units units units units units units units units units units units units units information information problem problem problem problem problem problem problem problem problem performance performance performance based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown systems systems systems systems parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions unit unit distribution approach point point point point single single single single processing processing processing control control control control control large local local local rate rate rate test matrix inputs form form shows signal signal signal algorithms simple gaussian small small small size size size feature feature work task task methods points points points field field classification process process current current current current current current current current current current current current current trained trained trained cell cell cell problems problems response response architecture architecture architecture equation equation section fixed fixed fixed fixed line line line rule general parameter real real approximation gradient obtained obtained experiments dimensional dimensional dimensional result threshold variables computation computation computation solution solution defined found sequence target target constant distance connections prediction prediction prediction prediction low low range range range range press position position basis basis basis outputs outputs continuous abstract applied applied applied applied computational analog analog analog analog analog analog analog analog references due due ieee procedure procedure adaptive complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit effect effect generated generated variance cost tion change change change change change change difference variable variable representations center type type type type type multiple multiple long conditions distributed chip chip chip chip chip chip chip chip techniques techniques proposed length forward finite minimum ing multi multi sum sum performed performed called elements elements mapping means factor made made applications applications applications represented represented desired series series series series receptive receptive receptive receptive receptive receptive provide rates active active determined determined experimental experimental experimental experimental experimental experimental related related constraints constraints constraints connected connected connected connected connected discrete power power voltage voltage voltage accuracy accuracy comparison larger contrast fields fields fields fields support support descent source proceedings implementation implementation implementation version technique consists consists consists individual advances connectionist difficult bias bias bias bias bias bias layers directly curve design determine full requires approximate approximate free speed channel channel channel channel channel channel channel channel channel channel channel channel channel clustering area types types actual provided provided processes nature achieved discussion discussion arbitrary group tested fast limited surface circuits circuits circuits amount common effective implemented shape shape shape generate generate generate require require journal square vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi cluster future easily easily degree degree including fit underlying needed needed combination coefficients transfer interesting interesting ratio mechanism special uniform uniform direct making making stored international decay minimize produced added predict improved recent advantage property separate takes typical quadratic trees array array highly conventional conventional conventional conventional unsupervised tions smooth smooth smooth smooth match address address address evaluation grid grid gate gate gate gate storage storage digital digital wide wide feed locally locally locally locally touretzky width width width width width width width width width clusters generally hardware hardware pass pass pass pass pass pass pass pass pass pass strength conclusion place place place place place place place place editors clear sutton moody moody moody moody weak weak weak constrained encoding encoding encoding encoding encoding encoding propose cycle characteristics drawn sigmoidal demonstrated proportional radial assuming user exist min averaged acknowledgements appears plot tuned tuned tuned tuned distinct implement simultaneously simultaneously simultaneously averaging john stationary stationary overlap overlap overlap detailed fraction updates updates allowed earlier earlier reasonable barto slow measurements fitting roughly purpose interpolation interpolation interpolation generation initially advantages david degrees avoid avoid building existing currents currents currents currents currents currents determines maximize candidate simplicity closely closely capable uniformly suitable effectively effectively build efficiently efficiently computations excitation excitation excitation excitation excitation excitation follow timing duration duration duration quantity absence quantization cmos cmos cmos computes chips principles operating approximating neighboring intrinsic intrinsic body body simpler circuitry circuitry circuitry circuitry circuitry mead mead mead varied strengths helpful reducing reducing giving fault fault transistor transistor transistor transistor transistor transistor transistor authors gates predicting spline spline spline spline changed voltages voltages voltages voltages voltages voltages voltages voltages adjusted logistic freedom mapped shapes academic extent simplest simplest chaotic chaotic charge mentioned great slowly costs ground ground ground smoothness smoothness lies worse turns implementing tive easier located transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors desirable controls controls laboratories inversion inversion inversion demonstrates radius requiring applies offset lms lms lms autonomous peaks splines splines splines splines treated frequently sharp schematic schematic limiting limiting weigend resource resource resource adjust adjust richard decoder decoder sophisticated shaped tolerance tolerance wesley initialization initialization benefit addison writing fabricated amplifier amplifier amplifier amplifier amplifier amplifier amplifier resources resources approximates encoder flexibility turned arranged lost inspired platt platt allocation allocation allocation darken mos determination imposed primitive primitive hint capacitor capacitor tap tap passive excellent falls governed widths bad injection injection percepttons schwartz schwartz schwartz candidates smoothed layout park assigning speaking piece ram break encodes distinction terminals arg arg spaced spaced avoided constrain capacitance gated care compensate distribu mathematically execute bump bump bump bump bump cole surrounding spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading spreading complementary transconductance transconductance transconductance transconductance transconductance transconductance tied flash barrier register register superposition resistors suffer inverting amplifiers amplifiers amplifiers amplifiers amplifiers amplifiers amplifiers amplifiers amplifiers cubic programmed programmed lippman lippman exhibited exhibited ignoring examination tail tail remarkable functionality parameterization lowe excess ate marks crude aid aid imple capacitors converter realizations striking huberman offsets placement enhances leakage consumption implying aggregation bumps bumps bumps bumps bumps bumps bumps allocating registers actively inappropriate atlas atlas tails tails linearities ripple applica connor decoders adjustments tailored tran mentation tiny adap subtract biasing clump wired knots knots earliest laterally laterally multivariable allocate mere volt broomhead diode diode follower cited noticeable flowing tunable gte tiling advocated muthusamy comple sink sink sink remedy clumps waltham resets defects lancaster lancaster followers guaranteeing microsystems virtues evalu sharkawi proliferation budget tstems readout bitrary stiff 
#@Samalam_V,Schwartz_D,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training algorithm algorithm output output output output output output output output number number number number number system system system system system system error error error state state state state results results results units units information problem problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden performance performance space space weights weights weights weights weights weights weights weights linear linear linear layer layer layer layer layer layer order shown systems systems systems systems systems probability probability probability noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution method pattern pattern pattern single processing processing processing processing control control large large large large large large large large local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate test patterns patterns patterns patterns patterns inputs shows shows shows shows shows shows shows shows shows shows signal signal signal algorithms gaussian paper small size size size size size size size net net net net methods methods fig fig fig fig fig fig fig step field field field classification process level current current current trained problems problems problems problems problems problems problems problems problems problems random high high high high high high similar show show section section rule rule rule rule generalization parameter parameter average states states theory theory gradient term term note experiments computation computation log log found target dynamics computer computer computer computer computer computer connections connections connections connections connections science left direction presented present activation activation activation activation nodes temporal machine machine machine machine machine machine range range range range range range range range press learn learn learn outputs outputs outputs outputs outputs abstract back back back back back back back back back back back back back back back back back back back computational computational computational properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due due ieee ieee procedure adaptive decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex complex complex effect dynamic dynamic dynamic parallel parallel parallel parallel parallel parallel change change difference variable lower signals signals representations chosen center previous previous cases required required required required multiple multiple multiple multiple multiple good binary binary distributed chip chip chip chip chip chip chip make make make techniques techniques techniques correct forward forward finite simulations simulations simulations simulations simulations simulations simulation simulation simulation sum eq eq eq regions mapping means factor factor factor factor factor potential made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback global global global study vol represented compared application desired provide proc proc perform determined goal constraints distributions gain gain gain gain gain gain gain gain equal power mit voltage voltage voltage voltage steps comparison comparison comparison larger contrast connection update descent descent morgan words implementation implementation implementation implementation implementation implementation implementation implementation version version synapses synapses synapses technique technique technique technique technique internal individual advances difficult difficult cambridge equivalent experiment hinton hinton hinton additional additional additional curves curves bit bit bit efficient efficient upper full full choice free speed speed speed speed speed speed increase coding weighted area types actual actual achieved achieved measured measured measured feedforward arbitrary tested stable circuits amount amount common implemented synapse synapse synapse synapse synapse synapse synapse require eds end vlsi vlsi vlsi vlsi vlsi vlsi future future future makes rumelhart rumelhart kaufmann objective simulated probabilistic needed hopfield hopfield reduced account dynamical transfer transfer transfer transfer transfer interesting direct direct making making bits bits bits bits supervised supervised supervised supervised magnitude decay choose run added sources sources sources recent correlations correlations correlations reported machines sejnowski sejnowski array cognitive varying compare teacher teacher solve achieve trans trans sparse williams increased increased studied scaling scaling scaling wide wide feed feed touretzky width deterministic deterministic deterministic hardware hardware hardware hardware pass runs conclusion greater greater reduce measures designed designed performs performs performs exponential exponential faster temperature temperature temperature temperature temperature presence largest external external cycle proportional proportional variety annealing annealing annealing annealing annealing annealing annealing boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann explicit longer longer generating implement implement multilayer physical physical text text scales scales adding cycles cycles cycles letters family static static updates updates sign measurements roughly roughly expect usa usa currents retrieval absolute efficiency efficiency closely capable capable capable capable computationally paths paths driven mcclelland wij presentation post plots online identity kind kind strongly allowing showing anderson conductance sci sci relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation generalize board ill chips chips decreasing schedule transformed reducing matches matches parity parity parity parity parity parity parity possibility reliable tanh affect presynaptic cognition phases phases momentum analogous trace trace trace possibly adjusted prototype store electronic electronic electronic slowly answer implementing implementing implementing implementing implementing easier strictly sgn sgn acad acad implicit english questions questions pseudo orders completion adjustable adjustable slower slower slower monotonic phonemes collective adjust gave asymmetric asymmetric inherent chose chose chose chose findings summed extreme instantaneous uncorrelated uncorrelated uncorrelated feasible feasible generator generator generator fabricated modify summing linearity acts approximates promising proceeds proceeds imposed abilities disjoint affected corpus degradation natl natl alspector alspector alspector alspector started ranging representational ambiguity surprising percepttons tic peterson foundations steepest explorations dividing robert limitation microstructure incorporates leaming emergent adjustment manipulation exclusive annealed annealed differentiation parallelism electronics amplifiers continually meir meir meir stores externally externally interior accordance allen allen allen allen allen rosenberg settling loaded phonemic cast ackley anthony edited volts adjusts alto cascaded nettalk nettalk nettalk jan parker replication replication replication replication replication replication replication replication awij 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#@Allen_R,Alspector_J,Jayakumar_A,Meir_R,Zeppenfeld_T,
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data data figure figure figure figure figure figure figure time time time time time set networks networks networks networks networks networks networks networks training training training training training algorithm algorithm output output output output output output output output number number number number number number system system system system system system system state state state state state state state results units units units units information problem problem performance based based based based based based based based space space space space space space space weights weights weights weights weights weights weights weights linear linear case vector vector vector vector vector vector vector vector shown shown shown systems systems systems systems systems values values weight weight weight functions unit unit unit recognition recognition recognition recognition recognition approach pattern pattern pattern pattern single single single single single single processing processing control control control control control control control control control control control control control large inputs inputs inputs inputs inputs inputs shows shows signal signal simple simple work field field field field field field field field field field cell cell cell cell problems problems problems problems high high high high high high high high high memory memory memory memory memory memory memory memory memory response response response response response response response response response response response response similar similar similar fixed fixed vectors general general general generalization generalization parameter real real real real real experiments dimensional dimensional result university university threshold threshold research research independent independent independent dynamics standard computer computer computer maximum range learn learn components nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs continuous abstract back convergence references component ieee ieee ieee ieee adaptive introduction circuit circuit circuit dynamic dynamic generated parallel parallel variable variable part required multiple multiple multiple multiple multiple multiple multiple binary binary represent chip techniques techniques proposed proposed resulting total total total multi sum performed called called times times times times times times elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping applications applications vol vol vol vol vol vol vol vol vol application application application series series series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide objects rates proc proc perform experimental experimental goal connected connected discrete brain fields fields fields fields fields fields fields fields fields train proceedings proceedings proceedings institute department implementation implementation implementation implementation implementation implementation implementation version version final scheme cambridge design design design design design design design bit bit bit bit bit bit bit efficient speed speed speed speed speed speed speed speed speed vision vision vision vision con randomly developed developed developed robot robot robot robot robot controller controller provided finally selected nature associative associative associative associative associative associative associative associative associative associative associative associative associative associative group fast inverse circuits implemented implemented shape theoretical adaptation journal journal ability development sensory smaller technology technology technology special making stored international international combined produced architectures typical typical typical typical apply moving side relevant engineering dimensions axis studies studies trans sparse address address address address locations channels channels organization storage grant constructed studied width hardware hardware valued valued designed designed performs performs mechanisms cycle demonstrated iii acknowledgements pro produces produces solving primary laboratory implement implement implement simultaneously simultaneously physical electrical formed national overlap viewed operations static static purpose generation generation filtering sufficiently transactions box box box thesis successfully planning regular sensor sensor sensor aspects miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller receives traditional compact allowing video issue device device device device device device device device providing board board quantization cmos cmos cmos thresholds thresholds overlapping overlapping overlapping overlapping oriented camera circuitry varied recursive mass hall successive fashion project detectors detectors detectors detectors detectors detectors detectors detectors detectors detectors investigated office structured hill act measurement integer integer integer integer integer integer man implementations adjusted adjusted prototype detector logic logic logic logic logic logic logic logic logic initialized generates phd devices devices sensors sensors sensors sensors sensors sensors adjacent drive ran ion cybernetics addressed virtual virtual virtual virtual offset fed adjustable adjustable adjustable adjustable adjustable extensions sums logical logical logical implements summing summing addresses addresses addresses naval flexibility interconnected robotics robotics robotics communications communications adds intelligent intelligent intelligent programmable programmable serves arrays arrays arrays arrays symposium utilized cerebellar cerebellar james cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac buffer washington interconnections thomas april park park motions hypercube card card card automated onr sequentially sequentially sequentially summer kinematics basically bus bus bus bus bus ber recursively ram ram ram ram ram ram ram dec icassp theorems utilize adjustment adjustment mhz robots robots robots num interacting deconvolution host host investigating manipulator manipulator million million million million west placing supports union commercial commercial thousands september october accumulation accumulation accumulation accumulation interior august august ping hundreds albus albus albus albus albus industrial industrial excited excited excited excited operational automation automation dedicated inspection spie spie spie company company inde robotic robotic robotic robotic accommodate addressing tens maryland sponsored custom configured pendent nov hampshire hampshire hampshire devel manipulators manipulators manipulators manipulators vme vme vme vme vme vme vme vme vme boards converting specifications millisecond millisecond embodied duce industry standards cial philosophy hashing excites asme troller scotland pipelined brian mathe domly clocking glanz glanz glanz glanz glanz glanz glanz matical accumulator accumulator kraft kraft kraft erations opment glasgow manipu biosciences hts 
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#*network network network network network network learning learning learning neural neural neural neural neural input input input input input input input input input input input input input input input input data data function function set set networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output number error error error error error error results results results results results results units information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance space space weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer vector vector vector vector vector vector shown shown systems values values values values values values values weight weight weight weight weight weight weight weight unit recognition point point point point point point point single processing processing large large local local rate matrix inputs shows algorithms algorithms algorithms paper small classification process current current memory memory memory memory representation representation representation architecture architecture architecture show fixed vectors vectors general general general speech university computation table table table computer computer connections connections connections connections connections connections connections node node node node node left left left phase nodes nodes nodes nodes nodes nodes machine machine maximum range range press press learn position outputs abstract back back back back back back back back back back back back back computational computational references adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction dynamic parallel parallel parallel parallel parallel tion lower chosen required multiple multiple binary binary binary binary distributed chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip forward forward forward forward forward forward forward forward simulations ing total performed performed natural applications study artificial represented represented represented compared series connected mit steps comparison connection connection update update support train train morgan report institute implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation final layers layers layers addition cambridge directly additional solutions solutions solutions solutions solutions solutions solutions solutions san bit bit bit bit bit bit bit bit bit bit bit bit efficient efficient efficient requires speed product fast limited limited circuits finding common implemented instance including kaufmann typically transfer interesting special special mode mode mode mode bits bits bits bits international run run element element typical subset array array array array sufficient storage scaling scaling digital digital matrices feed feed feed feed feed feed touretzky hardware hardware hardware hardware hardware pass demonstrate flow critical greater sigmoid accurate accurate mateo hard user configuration configuration describes simultaneously cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles depending solved transform evaluate updated updated updates updates updates processor processor processor processor processor sign purpose purpose purpose intermediate assigned precision precision precision precision figures thesis successfully capable capable capable mcclelland efficiently computations summary allowing allowing dis running running timing backward board board chips chips chips chips chips chips processors processors processors processors processors processors processors processors processors receive requirements issues issues periodic fourier tech int comparable phases momentum momentum matched math math integer integer integer integer created implementations versions mapped logic submitted directed floating floating multiplication benchmark processed drive implementing implementing located controls calculations calculations computers computers computers preceding mellon sun addressed carnegie limits led cmu instruction instruction popular simulator simulator neuro arithmetic pose accomplished accomplished tation lvq resources multiplier held adequate clock clock clock clock ranging zhang darpa master integers integers leaving largely bus bus bus bus bus propagating propagating comparative sigma simd ijcnn graduate execute execute allocated overhead overhead lookup tied supports oregon suite eliminates identically seattle executing executing sparsely conditionally transpose transpose fair signed registers huge adv broadcast broadcast broadcast cient availability concurrently warp billion billion billion billion billion billion billion conserving contiguous bytes bytes embodied waltz accompanying neurocomputer neurocomputer neurocomputer implementa millions millions shifter witbrock baker baker baker ware fax investigators implemen duplicated mckenna adder buses dictates cray cray beaverton mcps mcps hal virginia pur effi leaning paral rummelhart innovations holt versatility 
#@McCartor_H,
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#*network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure time set set set networks networks networks algorithm output output output output output output number number system system system system system system system system system system system error state state results results results results results results results units information information information problem problem weights weights weights weights weights weights weights weights layer layer layer layer layer case case order shown systems systems values values values values noise weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition approach pattern pattern point image image image image image image image image image image single single single single single processing processing processing processing control control control large large large large local local neuron neuron neuron neuron neuron neuron neuron rate test matrix inputs inputs form form form form form form form shows shows shows signal signal signal signal signal algorithms algorithms small small size feature net net net net net net net net net net net net net net net net work work task task methods field field features features features features features features level level level level current current structure problems high memory memory memory memory architecture architecture architecture architecture architecture architecture architecture fixed images images states states obtained obtained result result result result result result result result threshold threshold threshold threshold threshold computation computation computation computation computation computation computation table table standard computer connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections left present maximum range abstract back find analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due due ieee important important adaptive mixture introduction complex circuit circuit circuit circuit circuit circuit circuit circuit effect generated cost signals signals signals signals signals signals signals part part part part part type required good binary binary binary binary binary binary binary binary binary long long chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make errors errors forward total total total multi multi multi multi multi multi sum performed means factor feedback orientation applications applications applications applications applications knowledge compared application application application application receptive receptive provide provide objects connected connected connected connected accuracy accuracy connection connection connection connection connection fields fields support nets nets nets nets nets nets nets morgan morgan implementation implementation synapses consists consists consists consists kernel advances advances represents represents final layers addition directly view view design san san bit bit bit bit bit bit bit bit bit determine determine full requires speed speed speed speed speed speed developed levels levels types types path provided selected describe group group fast fast fast limited limited limited corresponds circuits amount implemented implemented implemented implemented implemented supported require main main vlsi pixel makes makes makes fit kaufmann kaufmann typically smaller needed fully technology block block block transfer transfer transfer transfer programming edge special matching operation operation operation operation operation operation representing bits bits bits bits bits bits bits bits depth depth depth frame produced run run added added added sources resolution resolution resolution advantage takes typical moving moving pixels pixels pixels pixels array relevant compare approximately positions parts parts scaling digital digital digital digital digital digital digital digital digital wide touretzky touretzky width setting hardware hardware hardware half half minimal reduce segment measures designed designed mateo mateo hard integration external solid turn user averaged groups groups groups groups connectivity configuration acknowledgements reference reference reference reference reference van edges edges edges edges tuned implement simultaneously simultaneously simultaneously integrated integrated adding applying shift shift shift shift shift shift shift blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks extraction cycles extracted extracted extracted solved solved operations restricted lee lee lee lee approximated processor processor processor key key purpose building building building building building building building building building building building building kernels kernels kernels silicon currents currents bell discussions selecting extra extra suitable computationally computationally identify receives conf contained split split gray gray gray providing board board board board board board quantization quantization quantization cmos cmos cmos thresholds chips chips extract extract software receive receive optimized detectors int reliable structured comparable proper coarse reading configurations changed changed adjusted adjusted der switching detected contributions devices developing orientations diffusion expensive multiplication tool straight transistors laboratories recognized recognized members read demonstrates limits flexible amounts share schematic schematic limiting extracting extracting instruction simulator summed lot picture room uncorrelated uncorrelated fabricated summing summing summing summing connecting connecting flexibility interconnected arranged arranged multipliers multiplier minutes programmable programmable programmable programmable programmable contract mark wire wire wire wire corner reliably started connect multiplied alternatively switches acknowledge executed sequentially mind multiplying multiply listed bus bus bus bus bus bus bus convolutional connec workstation workstation henderson henderson henderson henderson henderson compensate crosses thresholded individually synchronized host host register register register register register register register register electronics placing loading loading loading intensive wider scanning sigmoids scanned scanned scanned scanned scanned stimulating corners corners corners corners quadrant designs loaded loaded loaded loaded loaded loaded loaded loaded loaded loaded loaded imple pictures pictures graf graf graf graf graf graf graf converter holmdel holmdel settle extracts archi poly drastically comparator comparator comparator comparator comparator comparator comparator comparator comparator registers registers registers registers registers registers registers registers registers registers registers registers registers registers registers configured operated contributing settles metal schematically multiplications multiplications billion tecture clipped vme vme vme mented converters reconfigurable reconfigurable reconfigurable reconfigurable reconfigurable reconfigurable reconfigurable throughput handles mueller mueller latched joining transport photo accumulates prin tsividis spiegel fills distributes photomicrograph mismatches digest ier ciple 
#@Graf_H,Henderson_D,Janow_R,Lee_R,
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#*network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input data data data function function figure figure figure figure figure figure figure figure figure time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number error error information information hidden performance performance performance performance weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer order order shown shown systems systems values values values values values values values values values parameters noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern point point point point point point image image image image image image image image image image image single single processing processing processing processing processing processing processing processing processing large large local local local local local local local rate test patterns patterns patterns patterns inputs inputs inputs form form signal simple simple simple visual small small small small small small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work work cells cells cells cells cells cells cells cells cells step field field features features features features features features classification classification classification process level level level level level level level level level level level level level level trained trained trained trained trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure random random random random high high memory architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture section line line line line line line generalization generalization speech speech real average dimensional university computation initial initial initial constant computer computer computer computer node node node node science science presented presented presented map map low low low nodes nodes nodes nodes nodes nodes nodes range range range range position position position components nonlinear abstract applied back back computational computational computational computational analog analog analog references ieee ieee procedure procedure procedure propagation introduction introduction complex hand effect effect effect effect generated parallel parallel parallel parallel parallel parallel parallel tion complexity spatial lower learned higher higher bound bound type required required required required good good equations chip chip chip fact forward simulations tasks simulation simulation simulation simulation simulation computed sum sum performed performed performed performed called elements study original original vol vol relative represented represented compared compared receptive receptive receptive receptive receptive receptive receptive receptive receptive compute rates perform perform connected connected connected connected connected equal connection connection fields fields fields fields fields fields fields update update update nets morgan morgan report institute department implementation implementation consists consists consists kernel advances advances responses delay delay delay ai ai ai maps cambridge computing domain directly hinton curve curve design san san top top top stage stage stage effects bit bit bit determine free speed speed basic increase produce weighted weighted developed developed levels area types lines lines product product product product product product product product product selected depends simply technical technical group group limited limited limited limited limited corresponds complete complete amount amount common effective implemented implemented generate supported pixel easily kaufmann kaufmann simulated simulated typically reduced fully technology significantly significantly operation numbers numbers window window window stored stored bits bits bits normalized bottom idea denotes practical identical identical identical pixels pixels pixels pixels array array array engineering previously previously conventional approximately correspond correspond trans modified modified modified modified modified modified storage storage increased increased digital digital digital correctly feed touretzky touretzky demonstrate flow row row reduce numerical performs performs performs constrained mateo mateo strong reduction plane plane plane plane plane plane plane plane plane plane plane plane plane groups connectivity connectivity force acknowledgements areas digit digit index laboratory laboratory laboratory tuned dept segments segments multilayer multilayer category explicitly coordinates electrical adding shift shift shift extraction extraction extraction extraction letters letters decreases decreases phoneme phoneme stages overlap viewed operations restricted restricted updated fraction digits processor partial performing performing performing normalization remains precision precision precision precision precision precision precision precision precision precision precision precision precision precision template template template template template handwritten handwritten handwritten thesis weighting candidate holds characterized successfully identified capable suitable modification identify efficiently efficiently computations computations invariance invariance reached excitation summary procedures cun cun cun cun allowing allowing interested contribution strategies device device device device device device device device built built notation michael computes denker ill overlapping software oriented access access collection requirements requirements put reducing reducing fashion detectors office comparable complicated complicated matched attributes waibel waibel thought obvious portion portion portion detected extent charge charge massachusetts devices ment fairly fairly improves improves adjacent floating floating floating majority spatially implementing purposes shared shared shared shared shared shared shared shared shared shared shared shared preprocessing desirable immediately immediately immediately products products products toronto attribute recognizing summation percent substantially substantially generic posed continuously schematic schematic schematic templates templates templates passes howard prevent suited suited acoustics sums implements june yielding arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic contribute shifted fabricated martin martin naval printed arranged air mail held imposed programmable programmable grow serves obtaining shifts clock clock continue date ranging negligible lang intended jackel darpa recog recog master implicitly papers assigning ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd unchanged unchanged multiplying planes planes planes planes planes planes planes planes planes planes break presenting rejection revealed nition nition pieces pieces restrictions boser boser var quantized quantized quantized henderson shifting shifting packets mhz compensate hubbard march march paired host translations tively holding holding computa supporting scanning corners twenty twenty twenty quadrant attributed loaded imple imple micro replicated replicated normalize successively archi tended inspection senses deformation contents neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron neocognitron stan lincoln lincoln lincoln crg shikano scans orig conceptually dard fukushima fukushima mentation mentation puter imposing multiplications multiplications burden billion clocked tecture clipped digitally deformed clipping converters tapped tapped visualized extractor extractor extractor extractor hanazawa chiang chiang chiang chiang chiang chiang chiang subdivided tolerate pittman pittman meets depart lexington beneath beneath beneath prespecified rejections isscc photomicrograph photomicrograph mil raster iil trons inal digest refered alluded dissipates 
#@Chiang_A,Chuang_M,
#t4
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure time time set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number system system system state results information problem based based space space weights weights weights weights weights linear linear case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown systems systems values values probability noise noise weight weight weight weight weight weight weight weight weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach approach single single single single single processing processing processing large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate test test test patterns patterns form form shows signal simple simple paper examples small small small small size size size feature feature step process level level level level level current current current trained trained structure problems random random random random random random high high memory memory memory memory memory memory architecture architecture architecture architecture architecture section section section line vectors vectors vectors vectors vectors vectors vectors vectors theory dimensional dimensional dimensional dimensional dimensional university threshold found table table computer distance distance distance distance distance distance distance distance distance distance distance distance distance left left left presented low frequency machine maximum range press learn learn position components abstract applied analog references component component component stochastic stochastic stochastic stochastic ieee procedure introduction action complex hand circuit effect parallel parallel search search search search difference difference difference difference signals word word word word word higher center multiple binary binary tree distributed chip chip chip chip chip chip region length length length correct correct ing total total total simulation simulation simulation multi performed elements elements elements elements elements elements elements made global global global global global global global global global knowledge original artificial provide compute determined connected connected connected mit steps comparison comparison larger larger update update update implementation implementation implementation implementation implementation implementation implementation implementation consists difficult final delay addition graph maps maps equivalent additional design design design design top stimuli effects effects bit bit bit bit bit bit bit bit conference speed speed speed speed speed speed basic pages pages conditional conditional area area area controller controller controller controller controller controller controller controller controller types lines path path path provided processes selected selected biological group limited close actions supported require vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi cluster makes rumelhart rumelhart fit simulated needed needed needed block block transfer operation numbers numbers stored stored bits bits bits international frame frame produced produced added added description element movement movement movement practical array array engineering highly calculated gate interval sensitive sensitive digital digital digital correctly width clusters hardware hardware hardware hardware hardware critical minimal greater greater greater greater reduce competitive competitive competitive competitive competitive competitive differences performs performs integration external cycle characteristics demonstrated proportional proportional averaged groups connectivity relation van van van van van winner winner generating describes dept changing implement coordinates electrical remaining remaining adding adding cycles cycles competition formation depending depending communication solved detailed operations operations operations organizing evolution completely similarly sign sign sign diagram diagram calculation additive additive spaces reduces distances distances distances norm kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen topology topology precision building exploration silicon silicon silicon silicon absolute absolute absolute absolute absolute neighbors closely encoded divided driven mcclelland wij build build comparing miller repeated built built built built built built write simplified board quantization automatically chips chips chips chips chips chips processors illustrates decreasing access requirements circuitry circuitry updating updating put fault reliable reliable working gates workshop affect cognition phases naturally closest closest closest integer integer integer integer logic logic logic logic store defines integrate slowly caused handle processed rapid rapid closer closer organized organized constructing worst transistors calculations calculations cybernetics tional readily compares modulated cal logical semi implements eventually eventually june diagnosis arithmetic realized shifted shifted uncorrelated fabricated controlling impossible connecting connecting communications fits adds check operates operates operates north clock clock clock carry carry carry carry reset expanded moved topological topological topological topological topological topological topological den den den den den den sim scan scan scan scan scan scan scan scan enable enable winning winning winning winning winning winning specialized creating layout layout storing extensively statement dense ple microstructure listed bus bus bus bus ram ties break markovian markovian spaced chapter hundred affects avoided massively clustered adjustment increment increment modifying mhz mhz mhz mhz mhz mhz gained ijcnn faults gener expand parallelism parallelism noting records win covered portions attached register register register register inversely investigations bring dsp simplifies failures status status status stores stores stores ping stochastically designs wins err calculates compo ning practically possess accumulate conditionally resolved complement complement adjusts cascaded mosis mosis mosis compromise pin wires tan tan enabling ripple ripple ripple ripple custom configured retaining broadcast broadcast broadcast broadcast broadcast broadcast broadcast broadcast broadcast nents accu alization centroids possesses decrement decrement enabled enabled enabled coverage topologically topologically intervening ting wired temporary testable testable testable parasitic densely pad crafted bout bout bout bout bout bout interna temporarily dave multiplexed saving pipeline inexpensive capacitances accumulates disabled disabled lets compiler compiler compiler pins pins pins resistant adder adder react buses markovjan ili concatenating carolina permitting numeric subtracts reside raleigh packed interconnecting latches accumulator topo simulators hinder diff diff plementation arranging disabling ezplorations cooperating alu sped practi broadcasts doug 
#@Melton_M,Phan_T,Reeves_D,VandenBout_D,
#t4
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#*network network network network network network learning learning model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set networks networks networks networks networks networks networks networks output output state state state state state state state state state state state state state state results information information information information information information problem models models models models models models models models models models models models models models models models models models models models models based based based based weights linear shown shown shown systems values values probability noise functions neurons neurons neurons neurons neurons neurons neurons unit unit approach approach approach approach single single processing processing processing control control control neuron neuron neuron neuron rate test analysis analysis inputs signal algorithms simple simple visual paper paper feature net work work cells cells cells step field field features features features features features features process process level level level level level level level level level level level level cell cell cell cell cell cell cell memory similar representation section section section line line images general real states states states states states states states states states states obtained term term term term activity activity university threshold computation research research research found constant constant computer terms terms synaptic science science present activation activation activation activation activation activation activation temporal range range press press press basis outputs outputs abstract applied back properties properties properties properties properties properties references important important important important introduction introduction behavior behavior dynamic dynamic generated generated change change change energy variable variable variable lower rules rules higher part part center firing firing type cortex cortex cortex long long long long long represent equations equations proposed proposed observed simulations simulations resulting ing ing respect times times means potential made made made orientation knowledge em vol artificial artificial relative relative relative relative relative relative specific represented cross provide provide rates active active active eye related related discrete brain brain brain brain brain brain brain brain brain equal approaches approaches larger dependent dependent dependent source modeling modeling modeling modeling modeling institute department department implementation consists individual individual responses scheme graph sequences considered cambridge view san san top stage effects effects effects capacity significant derived developed levels levels levels levels levels levels levels levels levels levels levels levels levels area processes nature inhibitory inhibitory biological biological associative associative discussion increases increases limited limited close excitatory excitatory actions short supported theoretical eds eds hypothesis hypothesis hypothesis degree development including fit fit fit fit typically smaller needed needed needed needed reduced account dynamical technology ratio character york mode mode leads representing details pre making making inhibition normalized bottom light neuronal neuronal neuronal neuronal membrane membrane membrane population population population population discussed discussed recent correlations separate movement movement lateral period cognitive cognitive cognitive cognitive cognitive cognitive recently relevant engineering dimensions dimensions dimensions dimensions varying previously subjects subjects subjects volume volume studies differential address storage sensitive grant studied occur occur width occurs generally generally generally conclusion assumptions assumptions assumptions central central interactions measures sutton sutton sutton sutton sutton sutton sutton sutton sutton suggest external cycle cycle cycle cycle cycle cycle cycle california solid turn variety variety min decrease iii base longer longer factors generating plot plot describes laboratory mathematical mathematical changing changing modeled electrical electrical involves transformations text text interaction interaction interaction develop implies implies cycles formation review review correlated correlated correlated detailed operations modulation modulation modulation modulation modulation modulation understanding completely suggested constants constants sign sign generation foundation recorded recorded existing figures perceptual dominance coupled variations structural structural determining aspects aspects aspects aspects identified closely build characteristic characteristic capture excitation excitation road soc notice graphs moore moore link showing oscillations content content content cues absence realistic nips highest neurosci principles attempt subsequent diego rapidly put oscillators oscillators oscillators humans dotted preliminary preliminary preliminary oscillator oscillator oscillator oscillator oscillator examine school rest behavioral behavioral behavioral plasticity plasticity understand understand cognition cognition cognition cognition cognition examined act thought thought noted noted nerve nervous academic attempts attempts integrate massachusetts mentioned burst histogram developing crucial biology biology independence rapid sections protein precisely incorporate desirable afferent mathematics potentially potentially scientific acknowledgement describing medical fluctuations populations populations populations populations populations populations populations populations pathways consistency parameterized experimentally effort recordings psychological psychological psychological span release synthesis synthesis synthesis synthesis summarized summarized characterize characterize incorporating logical boston display neuro physiol instantaneous college college sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep generator formally modify tation controlling discovery connecting theories receptors proceed moment moment contract efficacy keeping occurring occurring shifts affected modifications clock hours hours hours passive published tone periods mental consequences darpa hippocampus francisco waves specialized foundations insight extends davis subsequently balanced influences influences influences onr outlined mind mind mind mind discharge discharge dramatically linked linked cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic neurophysiology neurophysiology numerous minus shorter dec formulate rhythm demon wake wake wake wake wake wake wake alter continuity verified attempted mathematically mathematically discontinuity regulation neurophysiological neurophysiological interacting efforts efforts simplifying altered altered fir denver intracellular mimic mimic geniculate places dramatic reciprocal reciprocal reciprocal status status correlate species bridge bridge discontinuous instability mcdonnell ongoing nested inhibit routines harvard evenly compartment transducers sloan constancy daily fidelity handbook brainstem brainstem brainstem brainstem brainstem nih cyclic modulatory episode percept rem rem rem rem rem rem rem rem rem rem rem rem rem rem rem rem rem rem rem ized undergo proceeding proceeding silent acetylcholine acetylcholine plastic bodies tightly pew schema upward rhythms rhythms rhythms erroneous thalamus thalamus synthesize couple mentation mentation sequencing eog quiescent compartments fruitful excitability excitability excitability outlines feeds neuromodulation mitchison mitchison refining cog widespread widespread wanted wanted wanted wanted originating crick crick millisecond charac repertoire permission permission permission fund premise emerging chemistry revealing structurally transport downward biochemical biochemical collectively persons supplying alterations alterations borrowed linkage neuromodulators charged graphic phasic discussing adam prin prin jeffrey strate conservation vances mckenna mckenna mckenna education tered mountcastle bethesda neuromodulatory dream dream dream dream dream dream dream dream dream dream dream dream dream incapable raven faithfully voluntary whitaker whitaker void invited warren serotonin dictions dry dry ach ach trap modulators emotional connectivities inpu regulating clude zornetzer wet wet wet occipital psychiatry supra distin geniculo succinctly jected ciple informed norepinephrine realistically realistically biochemistry allan innovations teristic equip nore 
#@Hobson_J,Mamelak_A,Sutton_J,
#t5
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#*network model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number number results results results results results results results results results results results results results results results units units units units units units models models based based based based based linear linear linear linear linear linear linear linear case case order order order order order order order order order order order shown shown shown systems probability parameters noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution method method method method method method method method approach approach approach pattern point point point point point single local neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis inputs shows algorithms algorithms algorithms simple small feature feature methods methods cells cells cells cells cells points points features features features features process process process process process process process process process process process process process process process process level level current cell cell cell cell cell cell cell cell cell cell cell high high response response response response response response response response response response response response response response similar show show equation line line general parameter parameter real real real real real real real real real real real average average average average average average average average average average average average average average average average average theory term note note note note activity activity activity activity activity activity dimensional dimensional result result result result threshold computation research independent defined found target table table estimate estimate estimate estimate estimate estimate estimate estimate estimate terms connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic low frequency sets maximum maximum abstract density density properties properties properties properties likelihood likelihood likelihood references component stochastic stochastic due due due due due due positive positive introduction action action estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical effect effect dynamic difference measure measure center previous cases cases cases cases firing type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type type spike spike spike spike spike spike spike spike spike spike spike spike spike spike long conditions conditions expected fact correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed observed observed simulations simulations simulation simulation simulation regression computed computed computed computed computed computed computed computed sum sum performed times times elements elements made made made study study study negative negative relative compared compared cross cross cross cross cross cross cross cross series rates rates rates location determined determined experimental experimental goal related related related posterior discrete brain brain larger dependent source report words individual individual individual kernel kernel kernel kernel kernel kernel represents responses responses responses responses graph equivalent additional estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates trajectory stimuli stimuli stimuli effects effects effects effects effects significant estimated estimated increase increase derived derived derived derived conditional conditional area area area lines lines product product provided finally processes processes processes processes processes evidence evidence evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply increases describe describe tested transformation transformation inverse inverse inverse inverse inverse excitatory excitatory excitatory short short short assumed synapse supported require require hypothesis fit fit simulated simulated simulated simulated simulated simulated simulated simulated pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs underlying york mechanism mechanism mechanism consistent consistent consistent consistent consistent trials leads principal pre window window window window window inhibition inhibition inhibition inhibition combined pair separate separate separate element similarity reported reported period engineering compare approximately calculated address definition modified observation observation bounded interval interval interval interval interval interval interval interval interval interval interval organization entire grant amplitude constructed constructed horizontal intensity intensity expression expression expression studied suggests suggests spikes spikes spikes spikes spikes spikes spikes width column strength strength strength strength strength assumptions assumptions conclusions interactions interactions interactions interactions designed suggest suggest suggest suggest suggest suggest suggest strong strong mechanisms mechanisms labeled assuming assuming assuming decrease decrease relationship relationship relationship relationship relationship relationship relationship manner identification acknowledgements longer estimating estimating describes describes dept segments modeled simultaneously averaging linearly linearly linearly electrical involves interaction frequencies events events events springer versus versus versus potentials potentials yield independently expressed dependence dependence dependence stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary correlated squares estimator interpretation influence influence densities densities showed converges sec reduces event event event roughly roughly roughly initially msec msec coupling coupling coupling coupling coupling coupling coupling coupling coupling recorded recorded recorded priori inter inter sciences determines plotted plotted absolute regular modification divided driven delta presentation presentation post post post post post post tend characteristic summary traditional verlag strongly showing superior contribution physiological physiological physiological duration duration duration duration duration duration duration gray comp cat cat cat overlapping overlapping rat intrinsic intrinsic intrinsic decreasing trains trains stimulation stimulation collection investigate investigate estimators integral helpful postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic successive history school investigated biol possibility understand presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic examined coefficient coefficient possibly onset onset onset onset onset analyze analyze adjusted impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse assumes observe nerve multivariate consist consist explain motivated isolated isolated burst histogram histogram advanced developing convolution analyzed analyzed slope slope answer interneurons inside nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus immediately arise members res res depicted auto summation apparent collected collected profile profile cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear experimentally experimentally quantitative recordings compares compares compares poisson poisson poisson poisson poisson aim fall occurrence comments display windows windows conditioning displays distortion instantaneous phenomenon driving homogeneous neurophysiol purely bin eliminated eliminated spontaneous systematic smith moment efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy occurring mark analyzing analyzing effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness effectiveness modifications moments moments moments moments moments moments moments moments analyses tone tone tone tone tone tone tone tone histograms counting counting reproduce recovery recovery modelled young young young young young young young young young young young young young young bursts bursts bursts suggesting record colliculus belonging summarize dividing speaking fitted discharge discharge discharge yielded blood failed adopt restrictions solely suppressed evoked electrode electrode eric shaded shaded attempted pij thick interneuron impose electrodes electrodes surrounding dorsal dorsal dorsal dorsal dorsal dorsal dorsal dorsal afferents responding inversely inversely inversely tones mimic milliseconds milliseconds milliseconds milliseconds milliseconds interspike interspike interspike interspike interspike tissue reciprocal correlogram correlogram correlogram appearing hearing inhibit attempting supply hopkins medicine physiologically neurol alan johns vivo vivo distorted reproduced ranged nih nonstationary baltimore eighth maryland stationarity stationarity stationarity stationarity stationarity stationarity greatest silent repetitions spanning gradual modulate cats cats discrepancy dead substituted substituted avenue biomedical pursued qij clipping clipping clipping synapfic synapfic mild monosynaptic cumulant fatigue millisecond abscissa neurophys neurophys neurophys tlx innovation coordinated elicit hear aps aps assisted pres pres depletion dirac weakening correlograms correlograms eqns perturb neglects anesthetized pharmacological windowed windowed windowed extrinsic expose rii ringing nonstationarity nonstationarity nonstationarity dyn rhode rhode mount qua mic buted aptic ide digitization buildup intracellularly 
#@Sydorenko_M,Young_E,
#t5
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#*network network learning learning model model model neural neural neural neural function figure figure figure figure figure figure figure figure time time time networks system system system state results results results units units units models based based weights weights linear linear linear layer layer layer case case case case case case case case case case case case case vector vector vector order order order order order systems values values values values weight weight unit method large patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form shows shows shows shows shows simple visual visual visual examples examples small small small small small small small small small small cells cells cells cells cells field process current structure structure random similar architecture show equation equation equation equation equation equation rule rule rule vectors general general general general theory term note note activity university university university university variables computation computation solution solution found found found initial initial table table table table standard terms terms terms terms terms terms synaptic synaptic science science science science left direction sets sets components components components components components components nonlinear sample abstract applied applied applied references component component positive positive positive positive positive important introduction effect effect effect tion change change change change difference difference difference assume lower rules rules rules rules rules rules rules rules rules part cases required cortex conditions conditions conditions conditions expected expected equations make correlation correlation correlation correlation correlation simulations resulting simulation sum elements means natural orientation study study negative negative negative negative original specific specific application series receptive define define rates proc eye eye eye eye eye eye eye eye determined larger support institute version connectionist bias equivalent equivalent equivalent environment additional solutions solutions solutions limit san effects effects effects upper upper full full requires basic pages give condition iteration depends constraint covariance covariance covariance assumption stable stable stable stable stable stable stable assumed assumed shape theoretical require instance rumelhart development development development development development development development development including fit fit fit typically interesting projection special special structures empirical details details call call iterations magnitude predict predict predict population population population population discussed correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations pair separate separate separate apply identical cognitive cognitive recently relevant conventional approximately approximately tions studies studies rl address address symmetric symmetric symmetric sensitive grant exists expression expression studied studied studied studied occur occur matrices generally generally column setting starting starting place greater hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian conclusions editors differences faster constrained mechanisms mechanisms decrease decrease relationship averaged manner acknowledgements derive produces longer longer stability slightly slightly slightly develop develop implies competition competition independently communication solved ocular ocular ocular ocular ocular decomposition forms forms activities similarly sign sign key additive roughly calculate foundation david expect box thesis thesis usa usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues discussions differ driven driven modes modes projections projections projections projections mackay mackay mackay mackay mackay mackay mackay miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller miller reached neuroscience issue sci satisfy notation notation write dayan dayan dayan dayan dayan dayan eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue correspondence principles modelling selectivity diego production perturbation perturbation perturbation perturbation experience replaced helpful school terminal plasticity eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors affect affect understand presynaptic onset onset opposite opposite eyes eyes eyes eyes eyes eyes eyes eyes ensure versions assumes precise separated explain phd phd mentioned rows directed growth growth derivation growing growing growing growing turns stanford consequence acad medical linsker linsker linsker linsker linsker linsker linsker qualitative radius mechanics questions populations populations populations populations populations populations populations limits empirically amounts peter introducing introducing slower perturbations perturbations perturbations perturbations perturbations perturbations anti anti anti anti prevent substantial calls optimality fix fix nat concerned binocular binocular binocular saturation saturation affected affected salk lawrence reveals erlbaum eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector broken treat multiplying ure helmholtz pointing willshaw pointed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed centre centre arbor personal tendency affects edinburgh edinburgh monocular preserved geoffrey permits oct oct oct oct oct ultimately ultimately gluck relates grateful grateful happen page eigen normalised travel signs signs simplifies topography circumstances christopher vii vii vii agrees firstly inhibited suffices developmental developmental developmental clarity tors subtracting separates fastest fastest ance meant eigenfunctions enabling analyse analyse tit tit tit tit tit tit tit tit tit tit tit tit tit tit tit tit tit tit explaining saturate correlational correlational correlational correlational correlational correlational goodhill goodhill goodhill goodhill goodhill goodhill goodhill stryker collecting dominate perturbative treats devel perturbing perturbing perturbing perturbing tll radially unequal analysed analysed analysed converting responsive responsive mere quantum restored correla keller jii higgins iee relaxing degeneracy degeneracy fibres ken normalisation normalisation scotland sussex sussex inevitably borne ect cnl equating serc accommodated ixt ixt adopts popula complicate rti eel ris unperturbed unperturbed unperturbed covari opment bian delicate brighton heb obscured velopment swapped 
#@Dayan_P,Goodhill_G,
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#*network model model model model model model model neural neural neural neural neural input input input input input data data data data data data function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set output output number number number number system system system system system system system system system system system system system system system system system system system system system system error error error error results results results results results results results information information information information information information information information problem problem problem problem problem problem problem problem hidden performance performance performance performance performance performance performance performance performance performance based based based case case vector order order order shown shown shown systems systems values values values values values probability probability probability probability probability probability probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons distribution distribution distribution method method approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern point point point point single single single single single single single single single single single processing control large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis optimal optimal inputs form form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small size size size size size size size size work task task methods methods methods fig fig fig fig fig cells cells cells cells cells cells cells cells cells step step step step step step step step step step step step step step field field field field process process level cell cell cell cell cell structure problems problems problems random random random response response response response response response response response response response response response response similar representation representation representation representation representation line line line line rule rule parameter real real real real approximation average average theory theory theory obtained obtained obtained experiments experiments activity result result university university computation computation computation computation computation research research independent independent independent independent defined found sequence estimate estimate standard terms science left left left left direction direction presented presented presented presented presented presented present present low low temporal motion motion maximum press components components continuous sample abstract find find likelihood references stochastic due due due procedure decision decision decision context introduction behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical generated generated generated variance tion change difference difference difference difference difference spatial assume measure signals signals signals signals signals signals prior prior representations higher part previous firing firing firing firing firing firing firing firing firing firing type required multiple cortex binary binary binary binary binary binary spike spike spike spike spike spike spike spike spike spike spike spike long long conditions conditions conditions conditions conditions represent tree tree tree tree make make region correlation correlation correct correct correct correct probabilities probabilities probabilities probabilities finite ing ing tasks total total human computed computed computed computed computed computed computed performed performed times times elements means made made made natural natural orientation obtain vol artificial represented represented compared compared application application compute compute compute proc perform perform eye determined determined determined experimental experimental experimental experimental experimental related distributions distributions distributions discrete discrete cortical brain equal equal equal equal power power power approaches steps steps steps steps comparison comparison comparison larger larger update support train institute words consists code code code individual individual individual responses responses responses responses responses responses responses responses responses difficult difficult final delay addition addition sequences computing computing computing computing computing equivalent experiment experiment experiment experiment experiment experiment directly curve additional view view view solutions estimates estimates limit limit limit limit limit limit limit limit stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects detection detection detection detection detection detection detection detection determine determine choice choice significant significant significant significant statistics vision estimated estimated basic basic coding coding conditional levels levels levels lines finally evidence evidence simply biological measured measured measured measured measured measured measured discussion covariance describe describe group fast limited close corresponds finding finding finding finding finding amount short short effective effective implemented supported theoretical theoretical theoretical theoretical theoretical theoretical theoretical theoretical eds ability makes noisy noisy sensory sensory sensory sensory sensory sensory probabilistic smaller smaller needed account functional functional transfer transfer transfer transfer interesting ratio ratio ratio ratio york principle operation representing details details numbers direct making window window window bits combined combined choose choose description light light recent correlations resolution resolution pair typical movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement practical practical apply subject trees trees sense sense array array relevant highly varying compare compare tions yields studies studies rl trans address observation generalized interval interval interval interval interval sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive entire horizontal intensity expression invariant extended extended deviation wide wide wide spikes spikes spikes spikes predicted alternative correctly width width white conclusion conclusion assumptions depend accurate performs performs presence physics physics drawn solid turn variety averaged averaged averaged identification identification question question van van van van van van van van van van van van perception ways factors describes describes dept changing implement averaging averaging averaging easy slightly text belief angle unique develop events events events quality extraction independently operations operations restricted restricted understanding sizes sizes sizes sizes digits partition discrimination discrimination discrimination discrimination discrimination spectrum spectrum key partial earlier reasonable dashed dashed delays intervals intervals event purpose add remains recorded recorded recorded recorded thesis combinations retinal retinal sciences determines specifically variations black regular closely closely differ maximal encoded divided divided effectively poggio poggio presentation presentation presentation presentation presentation successful literature computations comparing comparing essentially essentially essentially essentially soc soc soc contained issue physiological timing duration categories built comp bar bar sampled vary absence leading reach cat cat cat cat attempt consisted subsequent preferred preferred trains stimulation powerful powerful wiley requirements exponentially humans graphical behaviour behaviour rise fourier successive successive successive fashion ideas behavioral behavioral biol ideal possibility possibility possibility authors authors referred reliable reliable reliable reliable reliable reliable decisions working variability proved pathway encode understand understand measurement concepts integer reading automata rev ensure detector explored nervous nervous nervous nervous nervous nervous nervous nervous nervous extent regime explain attempts electronic electronic animal formula phenomena slope waveform coded capabilities independence caused interneurons starts ganglion ganglion spatially turns constructing monkey monkey mation afferent afferent separately separately describing opt opt begin res computers recording geometry qualitative qualitative raw summation limits limits limits limits led pseudo quantitative quantitative quantitative psychophysical posed posed recordings formulated treated treated continuously reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability ity ity synthesis summarized characterize limiting modulated gen gen cal green green redundancy redundancy redundancy neuro neuro physiol physiol physiol physiol traces wesley realized picture shifted spectra indices cybern redundant redundant identifying primarily addison princeton princeton princeton ratios angular perfectly branches ordering homogeneous bin bin bin bin bin bin bin bin partitions unity unity grows interconnected outcome arrival arrival spontaneous adds anatomical ments overcome familiar familiar neurobiology preparation preparation presentations presentations presentations hours infor reliably meaningful periods bialek bialek bialek bialek bialek bialek bialek bialek bialek bialek bialek displayed surprising von von von realization photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor evident counting claim permutation thin stimulated stimulated bins bins bins bins bins repeatedly park alternatively adopted displacement fly fly fly fly fly fly fly fly fly speaking fired fired fired land land slight numerous rigorous latency latency maximized revealed forced responds convenience flat female imagine cohn peripheral trends favor favor shannon gener life convert neurophysiological neurophysiological ultimately lond guided rough emphasized apparently discretization barlow barlow barlow electronics parametrized psychophysics psychophysics psychophysics experi vice nec circumstances versa fat fat fat neumann neumann neumann characterizing discretized photoreceptors photoreceptors quantify quantify quantify quantify impulses shot shot focuses spacing interpreting broadly eral inherently inherently station unreliable unreliable subtracted plateau plateau periphery periphery periphery periphery optics digitized tracks william spirit randomness randomness crl faced approached raised steveninck steveninck steveninck steveninck steveninck steveninck steveninck steveninck steveninck steveninck assessed tenth parker parker parker ruyter ruyter ruyter ruyter ruyter ruyter ruyter ruyter ruyter dean occurrences ated stationarity massive subtle custom movshon biophysics excluded rieke conceptually wait des netherlands netherlands netherlands challenges eckhorn eckhorn biophys solu menlo organisms multiplexing widespread reichardt reichardt reichardt reichardt reichardt blowfly blowfly blowfly blowfly blowfly blowfly blowfly blowfly blowfly blowfly compound lock multiples wild discriminability discriminability discriminability discriminability discriminability warland revealing refractoriness quantifying hyperacuity sudden bullock bullock bullock discriminated heaviside meets investigators als kybernetik photon photon levick levick levick levick judgements rob correlators combina hinges cit hospital duplicates duplicates crt crt crt microelectrode lectures cautious photons swets swets sfi interchange signify jen equiprobable subvectors ery reli lect extracellularly intracellularly theoreti appreciably 
#@Bialek_W,de-Ruyter-van-Steveninck_R,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data function function figure figure figure set set set set set set set set set set set set set set set networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output number number number number number system results units information information information problem problem models models hidden performance based space weights weights weights linear linear layer layer layer case vector order order order order order order order order order order order shown shown shown shown shown systems systems systems systems probability probability parameters noise noise weight weight functions neurons neurons neurons neurons neurons neurons unit unit unit distribution distribution distribution distribution pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single single processing processing processing processing control control control control control control control control control control control control control local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis inputs inputs form shows simple simple simple simple simple simple visual visual paper paper paper size feature net net net net net net work work work task fig fig fig fig features features features classification classification classification process process level level current current current trained trained cell cell cell cell cell cell cell cell cell cell cell structure structure structure random random random random random random high high high response response response response response similar equation line rule rule rule rule rule images images general generalization average average average average average average average average average average average average average experiments experiments experiments dimensional threshold threshold threshold threshold computation computation computation computation research found sequence dynamics standard connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science left presented presented presented presented presented presented presented map present present present present present activation activation activation activation activation activation range press components components basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract abstract abstract computational density properties references component due due due important introduction action complex complex complex complex complex complex hand behavior behavior stimulus stimulus stimulus stimulus generated generated generated generated generated tion difference variable spatial spatial spatial spatial classifier chosen chosen chosen chosen chosen chosen higher higher higher higher firing type type type type type cortex cortex spike long conditions tree tree tree tree tree tree tree tree tree tree tree tree tree distributed expected expected equations equations make fact region region length length correct observed scale simulations ing total total total simulation simulation simulation computed computed respect multi multi multi called called times times elements potential potential potential natural global study study study vol vol relative specific represented compared provide provide location location active active active active active active active goal distributions distributions cortical cortical equal equal power power approaches voltage voltage voltage voltage voltage voltage larger connection connection connection connection support train dependent dependent dependent dependent dependent modeling modeling morgan morgan institute institute synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists advances advances represents connectionist responses responses responses responses responses responses responses final ai ai ai ai ai equivalent equivalent environment solutions san effects effects bit capacity capacity efficient full full full statistics statistics basic increase con channel weighted randomly randomly randomly randomly randomly types lines product product provided selected evidence backpropagation nature associative associative measured measured group group excitatory excitatory common effective effective effective assumed assumed synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse supported eds cluster cluster cluster cluster cluster cluster cluster rumelhart rumelhart kaufmann pairs pairs underlying underlying underlying needed technology increasing head mechanism principle leads numbers direct direct direct bits depth early idea idea idea run perceptron membrane membrane membrane membrane membrane membrane membrane membrane discussed recent recent property pair element typical reported include identical trees trees cognitive relevant relevant interest sufficient varying approximately tions studies differential sparse sparse definition definition locations locations locations locations locations locations channels channels channels organization storage sensitive sensitive sensitive intensity studied spikes spikes locally locally move touretzky clusters column runs strength conclusion hebbian hebbian hebbian interactions numerical clear moody constrained mateo encoding mechanisms integration presence california radial start exist averaged averaged averaged groups program program question question question acknowledgements relation relation tuned mathematical modeled modeled modeled sensitivity sensitivity sensitivity sensitivity sensitivity category category linearly consisting consisting formed shift boolean potentials john national dependence viewed variation detailed detailed detailed detailed open showed suggested discrimination discrimination performing epochs epochs neighborhood neighborhood neighborhood neighborhood neighborhood intervals remains remains foundation koch koch koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic degrees fire extension extension activated activated activated activated activated activated activated activated activated activated activated activated activated coupled variations black black neighbors neighbors discussions discussions discussions aspects closely capable uniformly encoded computationally driven presentation presentation post post post miller receives moore conductance conductance conductance issue lie contribution device categories categories categories michael providing extract neighboring body body body simpler origin unlike unlike stimulation powerful powerful layered layered poor access investigate relations strengths optimized issues issues lippmann discriminant discriminant helpful rise respond int scaled office working statistically statistically statistically analogous plausible necessarily noted freedom mapped perceptton nerve hebb hebb pyramidal pyramidal pyramidal epoch epoch simplest years brown brown scenes crucial crucial crucial crucial improves improves biology nonlinearity nonlinearity spatially purposes sys strictly division afferent afferent afferent afferent controls axon hippocampal axons virtual reflects understood relevance pseudo completion dots dots biologically variant mod mod characterize branch pasadena gave physiol globally phenomenon phenomenon primarily interface martin appropriately ordering ordering ordering ordering ordering ordering ordering count reconstructed naval caltech caltech establish inspired systematic anatomical convenient proceeds striate resistance resistance grow exceeds motivation reliably reliably excellent bartlett falls dendrites james mental enhance demonstration dendrite dendrite mel mel mel mel mel mel mel mel mel mel mel mel mel mel mel mel mel den somatic soma soma nonlinearities branching tic permutation cerebral surprisingly mem layout layout layout layout layout layout layout layout layout layout layout ballard ballard rich rich arrows calcium calcium calcium thresholding discriminate unchanged linked shading incorporates graded opposed abstraction abstraction abstraction abstraction connec sigma sigma arbor perceived hundred resting clustered clustered remainder alter cns cns manipulation manipulation subthreshold biophysical biophysical biophysical biophysical grouped degraded degraded degraded degraded potentiation thresholded thresholded douglas douglas douglas douglas switched switched switched selectively attached afferents inversely intracellular memo durbin durbin round elemental helps architectural circumstances rarely syn syn algorithmic mcdonnell diffuse diffuse puts cornput determinant neocortical neocortical neocortical neocortical neocortical injected nmda nmda nmda nmda nmda nmda nmda manipulated chan deals trol zador contacts contacts cur neurobiological tance alto remained feldman feldman stabilize prominent counted massive health christof rent palo linearities ted stabilizing newly opportunity rectification package ago untrained untrained mainen designated designated designated ting manipulating manipulating nation stabilized compartmental compartmental compartmental compartmental compartmental responsive visualized anatomically periments depolarized acti unfamiliar asynchronously groupings anomalous anomalous loses kauffman rodney inspiration traversing synap assump asymptote discriminated brane conduc exemplified hines hines hines injecting evidenced ken depolarizing geometries nels erm loci eling eling equ demonstrations wixi lent constituting ouput ive discrimi rectifier biophysically tivation spines simulta performer whitteridge neously combinatorially biotaed eccentricity cooperativity tur ctive vated inclined tempt troduced 
#@Mel_B,
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#*network network network network network network network network network network network network network network network model model model model model model model model neural input input input input input input input input input input input input input input input input input input input input input data function function function function function figure figure figure figure figure time time time time time time time time time time time time time time networks number number number number number system state results information models models space linear layer layer case case case case case case order order order order shown systems systems values values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters noise neurons neurons neurons neurons neurons unit method approach point point single single single single single single single single single single single processing control control control control large large large large local neuron neuron neuron rate rate analysis analysis inputs inputs inputs inputs inputs inputs inputs inputs shows signal visual visual visual visual paper paper small small small small small small small small size work fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells step step field current current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure random high high high high memory response response response response response show show show equation line line line line line line line average average note note note experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result threshold computation research research defined constant constant constant constant constant constant constant constant constant standard standard computer computer distance distance synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science left left direction presented phase phase activation activation activation activation activation low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal range press press components components abstract abstract computational computational properties properties properties properties properties properties properties references component due due due positive important introduction action action hand behavior behavior stimulus stimulus effect effect effect effect change change change change change change change change change change change change change change difference difference complexity variable spatial spatial spatial chosen higher previous firing firing firing firing firing firing firing firing type type cortex cortex cortex cortex cortex cortex spike spike long long tree expected equations make make fact fact length length length length length length observed scale simulations minimum classes ing ing total total total total total simulation human sum sum eq times times means factor potential potential potential potential potential potential potential made made study study negative negative negative relative compared receptive compute rates location active active active active active active determined distributions distributions cortical cortical cortical brain voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger larger larger larger larger contrast contrast contrast dependent dependent dependent dependent dependent dependent modeling institute words implementation version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses individual responses responses addition considered equivalent directly curve additional additional curves stimuli stimuli stimuli effects effects effects effects effects detection efficient requires significant significant significant significant basic increase increase give randomly developed types evidence inhibitory inhibitory inhibitory inhibitory inhibitory depends depends simply biological biological achieved measured measured discussion increases increases increases fast fast fast close corresponds corresponds corresponds corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory effective synapse synapse synapse synapse synapse synapse synapse synapse generate generate supported adaptation adaptation sensory typically smaller smaller smaller smaller smaller underlying needed needed needed reduced technology ratio increasing increasing increasing mechanism uniform uniform principle inhibition international magnitude added membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane discussed improve recent exact typical period period period trees relevant relevant relevant sufficient varying compare conventional tuning tuning tuning tuning axis tions studies definition background background background background background background background background background background background background background background background background background background background background background background background background background background modified interval organization sensitive increased amplitude spikes derivative derivative move setting minimal segment depend depend interactions weak weak integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration largest largest demonstrated california solid solid solid pulse pulse pulse decrease decrease iii program program program acknowledgements longer longer plot tuned distinct dept modeled modeled modeled sensitivity coordinates simultaneously simultaneously simultaneously simultaneously text adding frequencies events events shift implies blocks versus potentials potentials national independently depending viewed viewed influence detailed detailed forms static static static static constants slow slow slow slow dashed dashed dashed dashed delays add generation msec msec msec msec msec msec msec msec msec msec foundation foundation koch koch koch koch koch koch dendritic dendritic dendritic dendritic recorded recorded building fire fire fire includes usa usa currents currents currents currents determines determines determines determines activated activated activated activated uniformly computationally included spiking spiking spiking post post miller miller ten excitation traditional strongly induced induced contained anderson anderson conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance contribution sin comp bar vary vary vary absence absence providing delayed correspondence cat cat cat automatically illustrates disparity software rat receive receive body circuitry circuitry varied steady replaced replaced rise biol int office referred proper understand patch patch onset rev nerve nerve fibers pyramidal pyramidal pyramidal pyramidal pyramidal extent charge charge burst slowly crucial crucial crucial phenomena snr snr formalism consequence cut hippocampal hippocampal addressed integrating argument apparent varies fed leave slower mod spread spread spread spread branch incoming pasadena conductances conductances conductances conductances conductances conductances conductances simulator display physiol simultaneous summed shifted writing modify oxford tation martin martin narrow dynamically dynamically controlling neurophysiol purely naval receptors receptors reaching spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous binocular anatomical anatomical convenient significance alpha striate resistance resistance resistance resistance resistance resistance resistance shifts filled continue passive passive passive passive passive slice dendrites dendrites dendrites dendrites james dendrite dendrite dendrite somatic somatic somatic somatic somatic somatic soma soma soma soma soma soma soma soma soma soma branching tic tic spatiotemporal mem arrive epsp epsp impact calcium calcium fold fold influences fired fired fired fitted discharge opposed emergent spatio spatio spatio spatio medium trigger superimposed resting resting possibilities capacitance trends concentrated chapman potassium douglas douglas douglas douglas douglas douglas douglas douglas mediated careful synchronized synchronized synchronized distal selectively intracellular hodgkin spite tonic circumstances rarely reversal cable cable tom mcdonnell spring huxley cornput morphology adult cylinder neocortical neocortical neocortical fre injected injected injected tip nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda nmda neurol chan intact compartment compartment arriving vivo vivo tance attenuation compensated cold granule facts modulatory christof linearities initiated neurones neurones spario stryker apical contributing electrotonic electrotonic electrotonic electrotonic activating activating quency excitable ities traditionally traditionally pyramids sodium holmes holmes mike compartments unclear spontaneously syrup basal basal vitro excitability membranes henceforth functioning clamp stretch depolarized asynchronously electro rin rin leak leak superficial abstractions rodney gin gin synap synap bernander bernander bernander bernander bernander bernander bernander brane diameters morphological ampa ampa ampa dur conduc opened gle gpe hyperpolarizing overlaid graphic hines hines hines injecting pulled differentially shrinks shrinks orien depolarizing geometries exponentials assisted stretching harbor smeared johnston johnston activ barely paradox crn crn dentate rations anesthetized rectifier stretched converse desynchronized culture storm recomputed shut equency erage rnsec rnsec rnsec rnsec whitteridge biotaed grn quant impinging pharmacology eled 
#@Bernander_O,Douglas_R,Koch_C,
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#*network model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input input function function function function function function function function function function function function function function function function function time time time time set set networks networks output output output output output output output number number number number system results results units information information models models models models models based based linear linear linear linear linear linear linear linear case case case shown shown systems systems probability probability probability probability probability probability probability probability parameters parameters parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution distribution distribution distribution approach pattern pattern pattern pattern pattern pattern point point point single single single single single single single single single single single single single single single single single single processing processing processing processing processing processing processing control control large large large local local local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows algorithms small small feature work fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells points process process process level level level level level current current current current current current current current current current current current current current cell cell cell random random random random random random random random high high high high high response response response response response response response line line line rule general approximation average theory obtained activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional result result university university university university threshold threshold threshold threshold threshold threshold variables computation computation computation computation computation computation research research research research defined defined defined dynamics dynamics dynamics dynamics terms terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science direction presented present present present present present present present present activation activation low low temporal temporal temporal maximum maximum range range range range range press press press press press press press press press basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous sample sample sample abstract back back computational computational computational density density density density analog analog analog analog analog analog properties properties properties properties likelihood references component component component component stochastic stochastic stochastic due important important adaptive adaptive adaptive decision introduction action action action action action complex complex complex complex complex complex circuit circuit circuit circuit circuit behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect dynamic dynamic generated generated parallel parallel tion difference complexity complexity variable variable variable spatial spatial spatial spatial spatial spatial measure signals higher firing firing firing type type type type required required required spike spike spike spike long represent represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed distributed distributed region region region region proposed correlation correlation simulations simulations simulations simulations simulations minimum resulting resulting resulting resulting ing ing ing ing ing total total total total simulation simulation simulation sum sum performed times elements elements regions mapping mapping means potential potential potential potential potential potential study knowledge vol vol relative specific specific specific specific represented represented series series series provide define rates proc proc proc perform perform perform active active active active active determined experimental experimental experimental distributions discrete cortical cortical cortical brain power approaches voltage voltage voltage voltage voltage contrast contrast dependent dependent dependent modeling report synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists consists joint addition addition considered considered computing experiment additional additional estimates limit limit san stimuli full requires statistics statistics statistics increase increase give con channel channel channel channel weighted clustering developed evidence evidence evidence nature nature nature nature inhibitory inhibitory inhibitory inhibitory inhibitory achieved achieved achieved discussion increases increases increases fast fast fast fast fast excitatory excitatory circuits circuits implemented assumed assumed synapse supported role role main main eds eds eds eds noisy noisy noisy noisy noisy sensory simulated simulated pairs underlying underlying hopfield hopfield functional functional functional interesting interesting york york mechanism mechanism mechanism special special uniform mode principle operation operation details numbers direct direct making window window window inhibition inhibition inhibition early magnitude neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane population population pair separate separate separate element typical practical subject trees trees sense subset subset sejnowski sejnowski sejnowski sejnowski interest sufficient highly varying smooth studies background background background background background separation separation separation separation separation separation modified modified observation channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels gate organization organization organization entire increased increased increased amplitude intensity intensity occur extended digital digital digital digital digital spikes deterministic clusters clusters clusters flow flow flow strength strength critical greater assumptions assumptions segment conclusions interactions interactions interactions interactions constrained mechanisms mechanisms mechanisms mechanisms presence presence presence presence sigmoidal sigmoidal sigmoidal sigmoidal demonstrated solid radial radial radial selective relationship manner force suppose relation primary plot ann implement implement implement averaging electrical electrical electrical electrical electrical electrical text text unique consisting consisting formed potentials decreases formation dependence dependence dependence dependence dependence reconstruction reconstruction reconstruction correlated viewed variation operations operations operations showed showed forms forms static approximated approximated approximated completely suggested suggested suggested suggested discrimination key key neighborhood intermediate msec msec msec sufficiently sufficiently koch koch koch koch koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic usa usa bell bell retinal retinal sciences illustrated illustrated illustrated illustrated illustrated activated activated activated activated activated activated candidate coupled coupled characterized aspects suitable society computationally included poggio spiking spiking computations computations essentially reached capture soc strongly induced induced contained prob interpreted neuroscience conductance conductance dis dis physiological sci sci receptor comp involved involved michael dot dot absence absence absence absence realistic realistic providing highest neurosci neurosci consisted consisted consisted subsequent operating acknowledgments intrinsic explore simpler selectivity xor xor collection circuitry circuitry circuitry put strengths strengths strengths limitations dotted existence rise rise rise biol int plasticity possibility office office proper pathway pathway pathway pathway pathway fundamental neu neu circles circles patch patch patch patch patch math math gradients plausible psychology rev noted precise logic logic logic hebb academic academic pyramidal pyramidal pyramidal pyramidal pyramidal consist baseline baseline arbitrarily motivated isolated years brown brown brown brown brown brown brown brown brown brown brown brown brown brown brown advanced ment ground diffusion diffusion diffusion caused briefly nonlinearity london london ganglion spatially spatially spatially rapid stanford preprocessing strictly division directional arise mation pulses scientific recognized hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal involve involve acad acad circle localized depicted qualitative reflect pathways pathways pathways pathways pathways pathways transient transient introducing adjustable passed treated ity requirement summarized mod poisson poisson limiting differs branch branch branch gen monotonic monotonic qualitatively suited suited conductances logical age physiol physiol univ representative uncorrelated physiology physiology oxford oxford oxford extensive temporally appropriately branches purely purely purely purely naval jones jones outcome outcome eliminated eliminated cellular cellular air saturation anatomical resulted resulted resulted implications implications integrator spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot intuitive filled filled natl natl exploring infor passive passive governed ensures dendrites dendrites studying studying induce surprising washington mel mel mel uni somatic somatic somatic somatic somatic somatic somatic somatic somatic thomas soma soma soma soma soma soma soma soma nonlinearities nonlinearities nonlinearities modelled insight mem arrive augmented contact informative extends card projects davis davis grants fired fired fired fired fired fired yale yale ence ple converted listed equivalently ber creates ties tween utilize sigma trigger junction ideally ical imagine molecular reflected illustration alter attempted capacitance preserved gated resistor gained biophysical biophysical biophysical impose approxi life activate activate convert weaker distinguished geiger sized sized afferents tively resistors indication retained els supporting tel hodgkin hodgkin hodgkin hodgkin tonic triggered emphasis emphasis syn syn syn mcculloch mcculloch preserves pitts pitts justification insufficient huxley huxley huxley huxley puts morphology ron char dom injected agency nmda nmda ally dedicated anthony chan heterogeneous zador zador zador zador zador zador zador zador zador zador zador zador zador zador zador raises compartment compartment ignores ignores ignores complement implied implied cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold cold ionic locality handbook reviewed approached kinetic defense bauer granule tained texas syst ized emerged shares tory probabil amer linearities ted jack jack haven pes spots spots spots spots fundamentally rela excitable treats ities reminiscent hypothetical ele signalling signalling leaky mainen mainen mainen compartments biophys electrically electrically complexities bull pattem tributed tributed synapfic synapfic synapfic synapfic synapfic shepherd shepherd shepherd shepherd theor poo poo membranes torre abs clamp kinetics kinetics emphasizes concluded underlie graham graham graham rail rail cybenko cybenko volt synchronously synchronously neurophys uncertainties comers mediating cre veto veto veto strengthened strengthened assump brane ampa ampa gle gle subunits subunits nel arose hines hines kandel mckenna mckenna unreasonable unreasonable dig longitudinal longitudinal longitudinal longitudinal sive subpopulations cid pres interplay marion biolog lancaster lancaster lancaster lancaster stressed activ activ erated requisite requisite borne borne inhibi dozen nonmonotonic nonmonotonic nonmonotonic buffering buffering influx influx capac rall rall rall biophysically biophysically steeper extrinsic extrinsic exci spines tential diate chief pictured acterized tatory ronal incorpo fare fare aptic ican invariably perkel gion regenerative pas antonio dal focussing objection curred assisting formly pyrami 
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direction direction direction direction direction direction direction presented phase phase activation low low frequency frequency frequency frequency frequency frequency temporal temporal temporal machine motion motion motion maximum range range press press learn learn learn components components components components components basis outputs continuous abstract back computational computational computational convergence density density density density analog properties properties likelihood references component component positive positive important introduction action circuit circuit circuit statistical effect recurrent search search tion tion change energy energy energy energy energy complexity rules signals signals learned part cases type type type type good long conditions represent distributed expected make make make make fact proposed finite finite simulations simulations resulting resulting resulting resulting ing ing ing ing total sum sum potential potential potential negative negative negative vol relative specific specific represented true cross receptive receptive proc proc active active active active goal distributions cortical equal approaches approaches mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage fields fields support dependent dependent dependent dependent dependent dependent source nets nets modeling institute version version synapses consists consists consists consists represents bias addition ai ai considered considered considered considered experiment curve solutions solutions curves curves curves effects significant speed basic give con produce channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel coding derived weighted clustering evidence inhibitory inhibitory simply biological biological measured discussion corresponds circuits short effective synapse synapse synapse supported role role role theoretical eds square makes makes development sensory sensory sensory including including objective auditory underlying account account dynamical dynamical dynamical dynamical dynamical dynamical dynamical coefficients uniform empirical principle operation leads representing max pre frame attention neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane discussed sense sense sense sejnowski cognitive varying varying previously unsupervised unsupervised unsupervised tuning axis tions converge converge address chain channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels organization parts studied half flow strength place place place hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian segment segment segment differences clear peak faster mechanisms mechanisms demonstrated labeled assuming variety exist movements min plane plane manner program question question acknowledgements ways plot stability tuned changing electrical electrical involves involves mutual integrated integrated frequencies equilibrium competition choosing formation formation dependence communication influence densities densities densities open fraction evolution evolution static static understanding suggested constants constants sign sign sec combining closed koch koch dendritic usa currents currents currents currents bell bell bell bell bell plotted coupled coupled coupled domains gating successfully major simplicity reason determining closely spiking spiking spiking successful literature fine capture soc notice kind kind kind procedures induced induced showing conductance conductance conductance conductance conductance dis issue sci receptor quantity list write play play absence realistic nips wave cat neurosci received operating load intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic receive law simpler selectivity selectivity selectivity selectivity american create create investigate put behaviour behaviour rise biol biol possibility phases phases neu act coefficient coefficient gradients trace plausible created voltages implementations implementations adjusted impulse obvious nervous nervous hebb hebb hebb hebb hebb hebb pyramidal utility explain attempts established brown preference ment ment stop theoretic theoretic theoretic crucial biology biology diffusion diffusion diffusion capabilities tractable correction interneurons reasons perspective perspective purposes sys protein protein precisely leaves ion ion ion ion ion ion ion axon axon scientific acad res fluctuations argument argument populations simulate frequently schematic requirement span passes operate anti anti anti anti anti anti anti anti anti anti anti spread instruction popular resource curvature 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information information information problem problem problem models models models performance performance based based linear linear linear linear linear layer case case case case case case case case case case case shown shown shown shown systems systems systems systems systems systems values values values values probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons unit approach point point single single single single single single single single single single single single single processing processing processing processing large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate analysis analysis form form form form form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple simple simple gaussian visual visual paper small small small feature feature net net work work work work work work work work work work work work work methods methods fig fig fig fig points points points points points points points points field field features features features process process process process current random random high high response response response response response response response response 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frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal motion motion motion motion maximum maximum maximum maximum maximum maximum maximum maximum press press press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied computational computational computational density density density density density density density density density density density analog analog analog references component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic procedure procedure important important important introduction introduction introduction hand hand hand hand circuit behavior behavior statistical effect effect effect effect effect effect effect effect effect effect effect effect effect effect dynamic dynamic variance variance variance variance variance tion variable variable variable spatial assume lower lower lower lower measure measure signals center theorem theorem firing type type cortex spike spike spike long long conditions conditions expected expected equations equations equations fact fact fact fact fact observed observed observed finite finite simulations simulations minimum resulting ing ing total total total simulation simulation simulation simulation simulation simulation simulation simulation computed computed respect called called called times potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential feedback filter filter filter filter filter filter filter filter filter filter obtain obtain vol vol relative relative relative represented compared application series series series proc proc location location experimental experimental experimental connected connected connected distributions cortical equal power power power power power power power power power power power power power power approaches mit mit comparison comparison dependent dependent dependent dependent source modeling modeling modeling technique technique technique consists consists individual represents represents responses exp exp exp sequences considered considered considered framework framework cambridge cambridge computing computing equivalent equivalent experiment directly directly curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve additional curves curves curves curves curves transition limit san top top effects effects effects effects effects effects effects effects effects upper full full approximate free free basic con condition derived derived derived derived conditional developed developed area actual provided finally processes depends simply biological achieved achieved discussion increases increases increases describe transformation assumption corresponds stable stable stable finding finding effective effective effective effective implemented role role theoretical eds eds ability easily easily degree noisy noisy noisy sensory including auditory auditory auditory auditory hopfield hopfield hopfield hopfield hopfield hopfield reduced reduced reduced reduced reduced account account account dynamical coefficients fully fully transfer transfer significantly ratio ratio ratio ratio increasing increasing increasing leads leads leads leads leads representing details details details direct direct direct direct direct making bottom bottom bottom depth added light neuronal neuronal neuronal membrane discussed resolution exact exact exact takes takes element element reported practical include include subject subject side side side side recently recently recently interest approximately approximately approximately works yields correspond correspond differential rl background background background background locations modified modified observation observation observation interval interval interval improvement improvement grant amplitude amplitude amplitude constructed intensity intensity intensity intensity expression expression expression expression occur spikes alternative move width deterministic deterministic deterministic deterministic white occurs occurs occurs hardware flow flow flow strength greater depend central central central sigmoid sigmoid accurate numerical numerical numerical numerical peak weak weak weak weak weak weak weak weak weak weak taking taking strong presence presence presence presence presence physics external external external external external reduction cycle demonstrated demonstrated solid turn decrease decrease relationship introduce introduce introduce force acknowledgements reference explicit pro pro produces primary plot plot plot describes describes transitions dept changing changing changing modeled physical remaining text unique spectral spectral spectral spectral spectral spectral interaction interaction integrated equilibrium events events events events springer shift shift decreases yield yield depending stationary stationary stationary stationary correlated correlated correlated correlated influence influence solved transform approximations modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation spectrum spectrum spectrum spectrum spectrum spectrum earlier calculation slow dashed additive additive additive additive additive additive additive additive event purpose closed valid filtering construction koch koch coupling coupling coupling expect priori bell inter inter discuss coupled phys phys phys phys phys phys phys phys phys middle middle closely driven driven driven driven delta delta characteristic conf verlag kind induced induced induced anderson interpreted symmetry sin oscillations content content content follow sci sci quantity write absence absence realistic denker cat illustrates jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs decreasing trains carried diego essential steady steady detail strengths optimized dotted periodic periodic periodic periodic fourier fourier biol biol biol biol ideal ideal office referred tanh analogous neu examined coefficient transmission possibly rev rev rev rev rev rev rev rev olfactory bifurcation precise observe expressions expressions nerve nerve nervous nervous switching switching switching switching switching switching switching switching switching fibers utility electronic electronic chaotic developing agreement improves improves diffusion diffusion capabilities snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr tive purposes sys sys sys ring ring ring ring monkey monkey arise consequence recognized acad acad describing describing optimize bandwidth bandwidth preceding preceding fluctuations fluctuations fluctuations explained explained apparent considerably limits embedded readily readily readily readily peaks peaks peaks introducing treated treated maintain passes passes switch switch berlin measuring branch modulated modulated modulated modulated modulated gen cal qualitatively collective replace logical inherent display fiber age shaped shaped progress univ displays instantaneous realized realized phenomenon phenomenon writing amplifier driving driving bin harmonic unity tem naval naval enhancement grows interconnected turned fits consideration numerically adjusting odd replacing replacing multiplicative multiplicative multiplicative multiplicative multiplicative multiplicative multiplicative multiplicative height height height height height abilities occurring shifts north enhanced enhanced degradation natl natl eqn eqn elimination weakly introduces introduces ensures sion sion induce holland evident histograms histograms den den sim bulb offers offers reproduce reproduce locked roy roy roy roy draw passing agree agree davis davis davis davis davis lett lett lett outlined treat escape escape approx resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance ure schulten schulten schulten ple outperform sig graded deriving deriving ties cooperative emergent axe axe distinction quasi obtains chaos trigger trigger ical superimposed suppressed forcing sinusoidal demon reflected remainder remainder alter publication shifting tems tems mammalian buhmann buhmann buhmann barrier barrier barrier barrier barrier turning turning tones particle siam preprint preprint macroscopic macroscopic nal holding differing rose rose differentiating hodgkin cavity electron electron moderate expense tom autocorrelation stochastically huxley hop lated dominates played inclusion inclusion ron eral cast cast pronounced pronounced fre ning moss moss moss moss moss moss moss moss moss moss moss moss moss moss moss moss moss exposed floor floor striking couplings operational laser laser laser laser fft fft beneficial disturbance optics governing enhances sity sity reproduced andersen planck absent periodically periodically schmidt schmidt materials cess ings aip derives rem physica physica physica tan amsterdam stems wiener relax quantified transferred remarkably plotting graphically gross bio suitably fluctuating quency modulating modulating jung lowered lowered lowered tran extrema rigorously bistable bistable bistable bistable bistable bistable bistable bistable bifurcations segev segev philadelphia digitally excitability theor symmetrically fokker bimodal noises succession lowering zhou zhou zhou zhou zhou zhou zhou zhou zhou concluded aver mere embodied conserved conserved looked strated cyber cyber cyber assist struction alternately raise reactions kramers kramers kramers kramers kramers kramers kramers kramers kramers kramers kramers kramers kramers kramers observability wolf fax clocks neurosciences gle markedly funding csr shamma shamma shamma deterministically raising harmonics harmonics ermentrout ermentrout ciently instabilities erm adiabatic adiabatic adiabatic adiabatic adiabatic adiabatic adiabatic adiabatic assisted loca expres nance nance obt escapes sto sto ned louis reso reso suffi imate modu chem langevin tate hind hind multipli adiabatically approzimation succes 
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#*network model input input input function function function function function function function function function figure figure figure figure figure time time time time time time set algorithm output number number system system results results results results results units information information information based linear linear case case order order order shown parameters parameters functions functions functions pattern pattern single single single single processing processing control control control control control large local rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns analysis analysis analysis analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form shows shows shows shows shows shows signal signal simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual examples work work fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field level level level level level level level current cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure high high high high high high high high response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar similar similar similar similar show show show show show line rule general general parameter average average average note note experiments experiments experiments activity result result result result result university research research research research independent independent log log defined defined found found found found found found found found target dynamics constant terms synaptic presented presented presented low low low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal range range components basis abstract properties properties properties properties properties references component component component due procedure adaptive adaptive complex complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect dynamic dynamic generated generated generated generated generated recurrent tion tion tion change difference difference difference difference variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower lower lower lower lower signals higher higher part previous cases cases firing firing firing firing firing firing firing firing firing firing firing firing type type required required multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike long long conditions conditions distributed expected length length length length length length length correct resulting resulting resulting ing ing respect respect called times means orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global global global study filter filter negative specific true cross cross cross receptive receptive provide define define rates rates rates perform active experimental experimental experimental related gain gain gain gain gain gain gain discrete cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain equal comparison comparison contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast support support train train train dependent dependent dependent dependent dependent dependent dependent dependent dependent loss technique individual responses bias scheme sequences sequences considered experiment experiment experiment experiment experiment curve curve curves curves curves curves curves curves design stimuli stimuli stimuli stimuli effects upper upper upper full significant speed speed speed vision vision vision vision vision basic basic give con derived levels area area types lines lines provided nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends simply achieved measured measured measured measured measured measured measured normal excitatory excitatory excitatory short effective generate supported role role role face adaptation adaptation adaptation adaptation adaptation journal journal journal journal ability hypothesis easily degree degree including fit reduced reduced account transfer transfer interesting ratio ratio ratio ratio increasing mechanism mechanism mechanism mechanism consistent consistent consistent representing filters pre pre inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition added population recent recent pair separate takes lateral lateral introduced strategy side relevant engineering varying varying varying varying varying varying observations calculated tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning definition definition background modified bounded organization sensitive sensitive amplitude amplitude amplitude amplitude concept concept studied suggests suggests suggests suggests suggests spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes move width generally pass pass pass pass pass pass pass pass pass pass demonstrate half strength place depend central retina designed clear clear clear clear peak peak peak peak peak suggest suggest mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms integration reduction reduction reduction reduction characteristics characteristics characteristics solid solid assuming selective selective selective selective decrease averaged manner configuration base base base base base base question question question acknowledgements areas longer longer factors primary sequential sequential generating laboratory tuned tuned distinct dept electrical text unique unique frequencies frequencies frequencies frequencies quality implies focus expressed dependence dependence dependence depending squares squares squares influence influence influence variation variation variation variation open open open controlled showed showed showed modulation forms forms completely earlier performing epochs classical sec sec sec sec sec sec intervals intervals intervals remains remains filtering msec msec msec msec msec norm recorded recorded existing existing retinal illustrated automatic specifically specifically specifically domains characterized major gamma gamma gamma gamma gamma gamma gamma presentation presentation presentation presentation presentation presentation schemes post essentially orthogonal orthogonal orthogonal ten excitation excitation strongly strongly strongly neuroscience neuroscience issue physiological physiological physiological physiological device duration duration duration duration categories quantity involved vary vary vary usual usual absence cat cat cat cat cat cat cat cat cat cat cat cat intrinsic intrinsic decreasing trains trains trains remain stimulation stimulation stimulation stimulation stimulation stimulation selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity parametric powerful powerful rapidly varied varied varied steady limitations dual dual dual dual preliminary biases existence rise fourier history behavioral possibility lgn lgn lgn lgn lgn lgn lgn variability variability pathway pathway fundamental examined smallest act circles circles circles circles observe nerve generates mixed mixed contributions serial seconds seconds isolated burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst histogram histogram indicating band band band band band orientations orientations orientations analyzed phenomena fairly independence nonlinearity spatially spatially spatially spatially spatially rapid rapid organized organized day day day day broad bishop bishop monkey demonstrates demonstrates addressed addressed reflects limits limits reflect freeman freeman quantitative posed continuously polynomials polynomials ture differs fall popular incoming ordered serve findings yielding phenomenon phenomenon lab lab physiology primarily tation acts acts dynamically addresses enhancement suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression systematic saturation saturation adds striate striate striate striate striate striate striate striate striate imposed biased biased bands belong monotonically presentations filled filled filled filled periods periods injection injection enhance histograms histograms nonlinearities nonlinearities bases deg deg deg deg bursts bursts bursts bursts bursts bursts bursts bursts bursts bursts bursts bursts reveals indicator suggesting suggesting probe specificity properly waveforms impact broken vari thresholding thresholding sequentially grating grating grating grating grating grating grating yielded neurophysiology neurophysiology neurophysiology slight specification ter shorter shorter shorter shorter graded graded super creates opposed randomized randomized randomized reaction presenting emerge revealed restrictions corrected superimposed stem flat reject shaded shaded 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neurons neurons unit distribution pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point large large large large large local local local local local local rate test patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis form form shows algorithms simple gaussian visual small small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net fig fig fig fig fig fig fig fig fig fig fig fig cells step points points points points field field field field field features features features features features features features features process structure random high high high memory response similar similar representation show section line line rule vectors vectors vectors vectors vectors images images real real average average average average 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energy energy difference spatial spatial spatial spatial spatial spatial spatial chosen chosen higher center multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex conditions conditions conditions represent represent make fact region region region region region region proposed proposed correlation correlation correlation correlation correlation correlation length length length length length scale minimum simulation simulation simulation simulation simulation simulation simulation respect performed times elements elements elements regions regions regions regions regions regions regions regions regions regions regions regions regions dimension dimension dimension made orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global global global global global global global applications filter obtain samples represented represented represented represented compared compared compared compared compared compared cross receptive receptive receptive receptive receptive provide provide proc proc proc location location location location location location location location eye experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental constraints constraints cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain equal equal power power power approaches comparison comparison connection support institute institute consists code advances exp exp maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps design design stimuli effects determine requires approximate basic basic con randomly randomly randomly area area types lines lines lines lines entropy entropy processes selected selected selected selected evidence evidence nature nature nature nature associative normal increases describe denote denote close close corresponds corresponds corresponds corresponds corresponds surface surface surface surface surface surface surface surface surface predictions predictions predictions amount shape shape generate generate supported square end pixel pixel easily development development development typically smaller underlying projection projection york edge consistent mode principle principle principle principle principle numbers numbers iterations max direct normalized normalized description predict denotes directions directions directions recent recent correlations correlations correlations correlations correlations resolution resolution typical typical typical lateral period pixels recently recently dimensions dimensions sufficient highly highly compare unsupervised tuning tuning axis axis studies locations locations locations locations locations grid grid organization organization organization organization organization increased grant horizontal concept rotation locally locally locally locally width occurs boundary boundary strength strength conclusions valued measures peak peak strong strong reduction drawn start plane areas areas areas areas areas pro pro pro pro optical optical optical describes coordinates coordinates averaging averaging linearly linearly dimensionality dimensionality text text angle angle springer national national formation formation formation formation formation transform transform transform organizing ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular centers centers centers centers approximated completely suggested suggested suggested translation constants spectrum spectrum spectrum key spaces intervals iterative generation assigned assigned foundation kohonen kohonen kohonen kohonen topology topology topology topology topology topology topology topology avoid expect figures combinations coordinate usa usa usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance subspace subspace subspace plotted black black discussions characterized characterized characterized columns columns maximal maximal maximal divided invariance invariance tend tend tend miller miller orthogonal orthogonal orthogonal orthogonal characteristic summary soc soc verlag quickly showing interpreted manifold follow follow sci sci sci gray gray comp sampled vary wave wave wave wave cat neurosci neurosci neurosci preferred neighboring decreasing bars origin selectivity selectivity selectivity selectivity selectivity exhibit rapidly rapidly detail detail periodic reducing reducing fourier fourier fourier fourier fourier fourier fashion fashion school biol biol biol biol biol biol biol biol authors contours patch patch gradients closest plausible opposite equally changed singular front quantities quantities quantities separated mapped mapped mapped generates amari averages animal percentage rows preference preference preference preference preference preference preference preference slowly band reasons organized organized organized located located located located monkey monkey monkey monkey monkey monkey monkey monkey arise arise consequence consequence projected projected projected acknowledgement angles angles angles angles angles acad acad acad describing medical localized patches linsker radius nsf explained argument fourth reflects apparent applies reflect axes axes embedded experimentally quantitative quantitative quantitative lattice lattice employ dots biologically exhibits characterize gen inherent boston comments coherence coherence coherence findings yuille deviations deviations simultaneous displays picture acquisition spectra spectra spectra spectra discontinuities cybern cybern cybern cybern cybern cybern cybern cybern aligned proportion gabor gabor gabor gabor gabor gabor animals animals circular repre arranged arranged arranged imaging imaging imaging striate striate striate striate striate striate striate striate striate striate striate striate striate stated bands bands bands bands bands bands bands bands bands bands bands transforms transforms transforms mark reasoning corner planar natl natl natl repeat repeat repeat financial periods periods connect corre sides schwartz histograms histograms monkeys elastic emergence waves reveals reveals reveals reveals specificity eqs border intersection geometrical geometrical schulten schulten schulten schulten schulten schulten slight slight wiesel wiesel preserving preserving preserving preserving preserving preserving preserving isotropic preferences preferences preferences preferences preferences preferences preferences preferences preferences preferences preferences preferences preferences preferences preferences amplitudes spaced malsburg hubel hubel illustration param perpendicular mathematically retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic iso iso iso iso iso iso iso iso iso iso iso iso confirmed singularities singularities singularities singularities singularities singularities singularities singularities singularities singularities macaque lond spanned spanned spanned spanned cation funded obermayer obermayer obermayer obermayer obermayer obermayer margins durbin eters ritter ritter vice correlate correlate diagrams species versa autocorrelation sake agrees hat arrow arrow arrow arrow establishes stripes stripes adult adult char dom harvard harvard illinois illinois emerges neurol accumulate preservation baxter quantitatively quantitatively rectangles prominent prominent prominent zones zones zones zones zones zones zones ini dow urbana urbana urbana repetitive repetitive disorder disorder disorder disorder align borders intersect intersect intersect dominate hands centroids centroids ities blasdel blasdel blasdel blasdel blasdel blasdel blasdel blasdel sing tially kammen fruitful beckman beckman testable abs mitchison neglecting slabs slabs slabs slabs slabs slabs slabs slabs slabs slabs slabs slabs slabs lations steep visualized 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#@Blasdel_G,Obermayer_K,Schulten_K,
#t5
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#*learning model model model model model model model model model model model model input function figure figure figure figure figure figure figure figure figure figure figure time time system system system error error results results results results results information models models models based based based weights weights layer case case order shown shown probability weight weight weight neurons neurons neurons neurons distribution pattern pattern pattern single single control local neuron rate rate patterns patterns patterns patterns patterns patterns patterns analysis matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows gaussian gaussian visual visual visual visual visual visual visual visual size work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells current cell cell cell cell cell cell cell high high high similar similar similar similar show show equation section rule average average average term term term experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional dimensional result university research found found target target target initial constant distance distance connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science left left map map map map present present present position continuous continuous abstract computational references important introduction action behavior spatial lower lower signals part center center previous firing required cortex cortex long long represent represent represent region correct observed observed observed observed scale simulations simulations simulations simulations simulations simulations simulations simulations total total simulation simulation sum regions regions mapping mapping mapping mapping mapping mapping factor factor specific specific specific specific represented represented series provide provide provide active active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined experimental experimental related discrete cortical cortical equal steps steps connection connection support dependent synapses synapses synapses synapses synapses synapses individual represents represents difficult layers layers layers layers layers layers addition addition considered san san top effects upper significant significant significant increase produce produce produce weighted developed evidence evidence nature inhibitory depends depends biological biological normal normal normal normal normal normal normal normal normal normal normal normal limited assumption assumption assumption predictions predictions predictions amount synapse synapse supported supported supported role role role role role role require eds end makes makes development development development development development development development development development development development development development development development development development development development development development development development development development development development development development development development development development development development development development account account account account interesting significantly ratio york edge consistent leads pre pre inhibition bottom early early early early early early combined combined light light predict improve recent correlations correlations correlations correlations advantage advantage lateral lateral lateral lateral lateral moving period recently highly highly axis axis studies studies diagonal locations modified increased horizontal lead lead lead lead lead suggests wide wide wide wide wide wide width width width width occurs occurs occurs column pass pass demonstrate strength strength strength strength strength strength hebbian competitive interactions interactions interactions differences accurate retina retina retina retina retina retina retina suggest propose strong strong presence presence presence california targets base base acknowledgements areas longer optical generating vertical dept dept simultaneously simultaneously simultaneously simultaneously linearly formed formed formed blocks potentials competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition formation formation correlated correlated correlated correlated correlated correlated correlated squares ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular key earlier normalization roughly remains intermediate initially initially sufficiently david precision box dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance color retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal determines illustrated specifically neighbors determining modification modification wij wij wij wij wij wij post post projections projections projections projections projections projections projections projections projections projections projections projections projections projections miller miller ten ten summary sci gray cues receptor michael absence absence absence wave wave wave reach cat cat cat cat cat cat neurosci neurosci neighboring neighboring neighboring neighboring neighboring neighboring receive receive receive receive receive receive cowan cowan unlike stimulation stimulation stimulation poor essential essential essential helpful postsynaptic plasticity plasticity plasticity plasticity possibility lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn presynaptic presynaptic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic notion neu hill coarse coarse coarse coarse gradients predicts changed eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes aspect precise precise precise separated hebb established indicating developing developing growth growth growth growth growth growth growth growth growth adjacent majority adapted ganglion ganglion ganglion ganglion ganglion spatially rapid rapid stanford closer ring style precisely incorporate located nucleus nucleus nucleus axon axon hippocampal gradually gradually axons axons axons axons axons axons axons axons axons axons localized patches patches reflects dark dark experimentally experimentally experimentally lack treated treated treated treated differs ordered findings findings simultaneous simultaneous simultaneous don physiology forming driving animals animals animals narrow narrow ordering ordering eliminate connecting outcome arrival arrival arrival arrival arrival eliminated eliminated eliminated chemical imposed imposed grow neurobiology synchronous synchronous optic optic optic guide spurious slice slice widths conjunction conjunction competing competing branching branching multiplied treatment francisco francisco modelled modelled modelled waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves axonal axonal bursts suggesting arrive arrive arrive specificity park wolpert wolpert boxes boxes slight incorporates inferred stork stork stork stork stork alternating causing solely segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation blocking mammalian mammalian distant potentiation potentiation intra synchronized rough refinement refinement refinement refinement refinement refinement outcomes afferents intracellular likewise geniculate geniculate geniculate refined refined refined refined refined tract tract tract topography topography topography topography topography topography topography topography topography suggestions reinforce arbors justified suite compete diffuse diffuse contralateral contralateral contralateral contralateral contralateral contralateral contralateral contralateral contralateral contralateral contralateral stripes morphology adult steven inclusion inclusion cylinder ron supplied labelling ooo ooo alan ultimate arriving neurobiological vivo acid reproduced lisberger confined enter wong emerged ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral refine amer gradual cats drug drug stryker stryker stryker stryker stryker stryker stryker biophysics phy strongest strongest vertebrates menlo justify oooo dynam contiguous birth birth ricoh ricoh fifty segregated occupy ucsf keller antagonist weakened conical pnas strengthened topographically topographically wrap wrap replicating innervate innervate innervate meister meister meister retinotectal renormalization dominating crc sand underway underway ida orderly renormalized renormalized segregate segregate segregate gustafsson topo generous baylor wik wkj discernible righ liss arborization disrupts 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input function function figure figure figure figure time time time time set networks output output system system state state state state results units models based weights case shown shown systems systems parameters weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach pattern pattern pattern pattern pattern single single control control control large large local rate rate test patterns patterns patterns patterns analysis form small small size feature work fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells level level current current current current current cell cell cell cell cell structure similar similar similar activity activity activity activity activity university constant constant connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic direction direction direction phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase frequency frequency frequency frequency frequency frequency frequency frequency range range range range range range press press components basis abstract properties references due due introduction action action action circuit circuit behavior tion difference difference lower signals higher part firing firing type type required multiple spike spike spike long distributed techniques techniques length length length observed observed observed observed forward forward simulations classes classes simulation simulation multi multi multi sum factor potential potential made vol compared application provide provide provide active active experimental related connected connected connected motor motor motor brain larger connection connection connection dependent modeling department connectionist final delay delay scheme scheme addition considered additional curves top effects effects capacity capacity determine significant basic basic basic produce levels levels levels types types types types provided finally inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory achieved technical feedforward tested tested excitatory excitatory excitatory excitatory excitatory excitatory stable stable generate role role theoretical main eds adaptation ability ability ability pairs pairs pairs pairs account account functional significantly edge head head head mechanism consistent principal inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition bottom early produced produced added neuronal neuronal membrane membrane recent lateral lateral include period period period identical identical identical identical identical side recently sufficient observations studies studies studies chain symmetric williams williams williams organization exists lead lead occur occur wide wide occurs generally half half strength greater conclusions interactions interactions differences differences differences differences peak peak peak mechanisms mechanisms cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle demonstrated demonstrated variety movements selective relationship manner connectivity connectivity connectivity connectivity connectivity identification identification relation generating generating stability segments segments segments segments segments segments segments segments adding frequencies potentials potentials potentials potentials potentials potentials cycles evaluated fraction modulation modulation understanding activities sign slow intervals generation generation generation advantages coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling recorded fire coupled coupled coupled characterized characterized identified identified identified identified capable differ oscillatory oscillatory post plots tend miller ten reached excitation excitation soc soc induced induced showing oscillations oscillations criteria criteria timing duration receptor comp comp involved vary backward backward backward backward backward backward providing leading thresholds neurosci neurosci intrinsic intrinsic intrinsic intrinsic intrinsic body explore explore simpler stimulation production investigate exhibit exhibit relations relations oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators steady steady steady steady dual oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator periodic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic successive project biol biol possibility muscle root root root root presynaptic presynaptic presynaptic presynaptic phases onset opposite opposite opposite thought nerve nervous nervous fibers consist isolated isolated established established animal animal years burst burst burst burst advanced fairly biology interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons ganglion drive lin lin lin lin lin lin lin lin satisfied producing pulses cut axon axons axons axons axons axons axons axons res recording recording demonstrates prop experimentally cohen cohen cohen cohen cohen cohen peaks anti monotonic gave neuro shaped physiol physiol physiol progress simultaneous contribute don cybern physiology generator neurophysiol neurophysiol reaching cellular cellular cellular held resistance analyzing neurobiology shifts preparation preparation periods periods periods james sides sides sides injection histograms offers dif exposure fish fish axonal bursts bursts mem speeds propagate fold fold switches lag lag lag lag lag yielded ence ple piece achieving removal cooperative alternating alternating revealed pieces pieces medium amplitudes tendency resting resting simulating rhythm rhythm rhythm rhythm rhythm spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal spinal conduction alternate interact interact interact maintained generators generators mediated projecting projecting projecting proach rhythmic rhythmic oscillating locking dorsal sized descending intracellular intracellular intracellular thousands reciprocal reciprocal wider correlate correlate locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion tail tail tail bursting ate continued swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming oscillate aid exper termination contralateral morphology caudal russell russell rons cord cord cord cord cord cord cord cord cord cord cord cord cord cord cord cord cord cord cord cord ventral ventral ventral ventral ventral ally neurol neurol sym intact intact vertebrate vertebrate vertebrate constancy constancy constancy neurobiological neurobiological amenable electrophysiological handbook shaping oscillates stomatogastric carrying selverston selverston durations maryland ipsilateral ipsilateral motoneurons motoneurons motoneurons motoneurons motoneurons bidirectional cope saturate began depolarization ference operated segmental segmental contributing virtue vertebrates differed participate abstr vitro vitro vitro poten roots invertebrate invertebrate indistinguishable onsets brooks stuart concluded motoneuron lobster neurotransmitter stein swim erties ist ein ein ein ein ein originated depended tolerate pling brane phasic phasic endogenous initiate cording ezp ezp sect cou ccs ccs ccs ccs ccs pled hibitory acta coordi originates descend oscil dye preparations preparations reverses buffering buffering reside berg macmillan sea injections injections exci drawings imental coordinating moroneurons ships alepolarizing alepolarizing alepolarizing ceils tatory eur glutamate glutamate inhi locomotor locomotor locomotor promotes lon bition summa tials intracellularly hibition pharmacology 
#@Buchanan_J,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input function function function function function figure figure figure figure figure figure time time time time time time time time time time time set networks networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output system system system system system system system system system system state state state state state state state state results units units information information models hidden performance performance performance space weights weights weights weights weights weights linear layer case order order order shown shown shown systems systems systems systems systems systems systems parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight functions functions neurons neurons neurons unit unit pattern pattern pattern processing control control control control neuron patterns patterns patterns patterns patterns matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows signal signal algorithms paper paper small small net work task task task task step trained trained random similar similar show show equation equation equation section fixed rule rule rule rule average states gradient gradient obtained term term term term university university variables computation computation found target dynamics dynamics dynamics dynamics table table standard connections connections connections connections connections synaptic science left direction direction phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase frequency frequency motion motion motion motion maximum range press position nonlinear nonlinear outputs continuous continuous continuous abstract applied applied applied back back back back back find find find computational references positive positive positive procedure procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation propagation introduction hand effect generated recurrent recurrent recurrent recurrent recurrent difference assume lower signals signals previous required long represent represent equations equations equations equations equations make correlation forward forward simulations total respect respect multi called called times made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback obtain negative negative relative relative relative relative relative relative specific specific specific specific specific specific specific compared desired determined determined goal goal goal gain motor motor motor equal larger connection connection connection connection connection descent modeling morgan synapses advances represents difficult delay delay delay scheme equivalent additional curves san san san stimuli conference efficient efficient requires approximate speed speed basic produce derived derived velocity velocity nature biological biological discussion covariance covariance denote tested fast close close supported theoretical eds journal makes sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory kaufmann objective objective objective objective simulated smaller underlying dynamical coefficients fully jordan jordan mechanism call decay combined run architectures period period side sejnowski sejnowski dimensions works studies rl rl symmetric modified williams williams storage parts scaling deviation wide rotation rotation rotation rotation rotation rotation move touretzky setting runs critical trajectories central central central central weak mateo propose propose mechanisms mechanisms characteristics california solid relationship relationship relationship configuration configuration force force acknowledgements suppose pro derive derive derive index index index changing changing physical physical physical physical physical physical physical physical physical physical physical physical physical physical physical physical physical involves angle angle frequencies frequencies frequencies frequencies independently controlled sizes activities completely constants constants constants smoothing add coupling coupling coupling coupling coupling coupling coupling coupling figures usa determines coupled coupled identified identified wij oscillatory genetic ten composed composed sin sin sin sin sin sin sin sin running running nips delayed delayed delayed consisted moves jacobs jacobs satisfies deal intrinsic intrinsic intrinsic intrinsic minimized body employed command diego diego environments environments oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators dotted oscillator oscillator hall biases muscle relationships relationships authors tanh tanh oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation coefficient coefficient coefficient academic simplest simplest electronic seconds established animal animal animal cos cos cos cos cos cos ground ground track track unstable waveform waveform biology drive drive forces located afferent gradually radius radius radius radius pathways peter commands requirement anti modulated modulated gave comments specifies specifies synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization indices generator japan japan angular eliminate cellular cellular moment balance kawato kawato affected prentice started appendix appendix moved widrow widrow hippocampus waves locked locked locked jolla contact ends waveforms waveforms waveforms waveforms pearlmutter pearlmutter grants displacement largely sine july rhythm rhythm rhythm rhythm sinusoidal sinusoidal sinusoidal spinal realize leg leg cessing generators generators potentiation rhythmic rhythmic locking tune continually locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion bursting cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg doya doya doya doya doya doya doya doya doya allen swimming vii vii cliffs oscillate oscillate oscillate utilizes char partly englewood tokyo tokyo zipset zipset oscillates stabilize cyclic ganglia suzuki suzuki supposed subtle motoneurons noiseless neurones damping segmental walking rhythms rhythms clockwise modulating synchronize synchronize concurrently vertebrates vertebrates vertebrates rolls radially ministry neglecting legs legs masses stretch lock lock lock lock lock yoshizawa yoshizawa yoshizawa yoshizawa yoshizawa yoshizawa yoshizawa yoshizawa yoshizawa wheel wheel wheel wheel wheel wheel wheel wheel wheel wheel wheel wheel wheel wheel wheel wheel wheel proprioceptive accelerated ilx barnes barnes rotates autonomously coordinated coordinated coordinated invertebrates invertebrates stiffness inertial axi education bush finished slows pit pit pit synchronizing synchronizing finely slowed pacemaker cpgs cpgs cpgs cpgs cpgs kenji acteristics stearns stearns huji culture superscripts zornetzer fmax fmax fmax flying volves limiter locomotor rad wheels bunkyo destroy poster 
#@Doya_K,Yoshizawa_S,
#t5
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time networks networks output output output output output output output output output output output number number number number system system system system state state state state state state results results problem problem models models models hidden based based space space layer case case order shown systems values probability probability noise noise noise noise noise weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution processing large large large neuron neuron neuron analysis matrix inputs inputs inputs inputs inputs form form shows shows shows shows simple simple simple simple visual visual visual visual visual visual visual visual visual size size size feature feature feature feature fig fig fig cells cells cells cells step step step step field field process process random random random random random random response response similar similar architecture equation equation equation general average states theory theory note note note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables computation computation computation research research independent found dynamics dynamics dynamics initial initial initial initial initial constant constant computer synaptic science left present phase phase phase phase phase phase phase phase phase phase phase frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal sets motion maximum range range press press press abstract find find properties references component due due important important important adaptive context introduction action behavior behavior behavior stimulus stimulus stimulus effect effect effect effect dynamic dynamic dynamic dynamic generated parallel assume signals signals signals signals signals signals signals signals signals signals signals signals part part part previous firing firing firing type cortex cortex cortex cortex cortex cortex cortex cortex binary binary binary long long distributed distributed expected equations fact proposed proposed correlation correlation probabilities observed finite finite finite finite finite simulations simulations total total simulation computed respect eq eq eq eq eq eq eq eq eq eq times times times times times regions factor potential global global global global obtain specific specific compared receptive proc active related related cortical power steps larger larger larger larger dependent dependent nets institute words words consists consists represents delay ai considered directly limit limit top stimuli detection statistics statistics basic increase increase provided evidence nature inhibitory inhibitory inhibitory inhibitory depends depends discussion covariance increases increases increases increases corresponds corresponds complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory common common common common common supported supported role role role theoretical instance noisy simulated dynamical dynamical fully jordan technology interesting mechanism mechanism mechanism mechanism leads leads leads leads details details making inhibition inhibition inhibition inhibition normalized normalized bottom attention attention neuronal neuronal neuronal neuronal neuronal neuronal neuronal denotes population population correlations correlations correlations correlations correlations correlations correlations reported period period period period period sense recently recently sufficient tions solve correspond rl background observation entire entire increased amplitude parts expression studied occur occur suggests width width width conclusions depend interactions interactions peak peak suggest suggest strong presence external external california california averaged averaged introduce introduce manner manner program configuration force explicit written written explicitly explicitly simultaneously simultaneously simultaneously scales scales consisting consisting develop frequencies equilibrium equilibrium applying shift decreases national independently independently dependence dependence dependence dependence stationary correlated correlated correlated solved detailed updated fraction fraction fraction fraction fraction evolution centered completely completely completely completely completely converges processor spectrum diagram diagram earlier intervals intervals intervals remains remains remains msec symbol foundation foundation koch koch koch koch koch koch koch koch koch koch coupling coupling coupling coupling coupling recorded building fire fire fire fire fire fire fire usa usa inter prove discuss coupled coupled coupled coupled coupled coupled holds phys discussions effectively delta delta oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory situation essentially essentially notice showing dis issue oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations sci gray gray gray quantity vary relaxation play play absence realistic binding binding leading cat cat automatically neurosci neurosci moves subsequent subsequent operating receive simpler origin remain remain remain investigate exhibit exponentially updating put oscillators oscillators strengths game oscillator oscillator periodic periodic fashion ideas investigated biol biol biol int analytically office oscillation attributes smallest math integer opposite automata rev quantities olfactory olfactory der der detector pyramidal pyramidal pyramidal serial averages charge burst burst burst burst burst burst burst burst burst burst burst burst burst indicating cos cos asynchronous ground crucial crucial derivation defining phenomena interneurons considerable broad pool scientific acknowledgement acad describing describing auto qualitative addressed reflects reflects reflects reflects varies varies understood understood introducing biologically exhibits mod limiting limiting synchrony synchrony incoming occurrence qualitatively pasadena singer singer germany logical coherent semi begins lim yielding synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization cor uncorrelated uncorrelated uncorrelated uncorrelated uncorrelated cybern cybern cybern appearance amplifier summing drift acts controlling neurophysiol air bower bower bower anatomical numerically numerically ranges los monotonically synchronous synchronous synchronous synchronous wilson wilson wilson constructive natl date sompolinsky sompolinsky sompolinsky reset reset ambiguity loo irregular james realization monkeys similarities similarities iterated emergence emergence bursts bursts bursts bursts bursts bursts bursts bursts stimulated locked horn horn discharge numerous superimposed superimposed malsburg malsburg acting segregation biophysical biophysical grouped decays chapman douglas douglas douglas douglas douglas fir synchronized synchronized synchronized synchronized synchronized synchronized synchronized win emphasized apparently locking locking locking locking locking locking locking locking locking tively universit sta dsp els tin develops syn mcculloch mcculloch expense stimulating bursting bursting bursting pitts pitts institut satisfactory mcdonnell solvable solvable solvable solvable coin mirror neocortical excited coincide coincide detects exploits explanations decaying neurobiological sions evolves evolves electrophysiological thresh bauer christof linking linking linking wagner wagner cats tightly schuster schuster schuster schuster schuster schuster schuster schuster schuster schuster preventing yon yon attracted kolmogorov columnar coincides schneider schneider coincidence coincidence coincidence awake niebur niebur consciousness eckhorn eckhorn calculus biophys kammen bull poo poo poo poo poo latch usher usher piriform konig crick crick lations physik engel engel bears bears resort rid accompanied collaboration strengthened latched latched pling indefinitely tex heaviside lastly party mimics amplify bush bush bush bush cocktail inhibiting golomb kiel kiel cou itera oscilla underly faithfully speculate amplifies kruse kleinfeld oscil resetting resetting taneously ksnig theoretische simul connectivities brosch prompted coincidences mirrored munk olds sem repeatable eur rll anew immanent chronization 
#@Koch_C,Schuster_H,
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#*network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input function function figure figure figure time time time time time time time time time time time time time time time time time networks networks networks networks networks networks number number number number number system system system system system system system system system system system system system system system system results results results results results results results information information information information models models models models models models based based based case order order order order order order shown shown shown shown shown values values values parameters parameters parameters parameters functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit pattern pattern point point single processing large local neuron neuron neuron neuron neuron neuron neuron rate patterns patterns class inputs inputs inputs form form form shows signal signal visual visual small small size work task fig fig fig fig fig fig points process process level cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response similar show show equation section fixed fixed generalization speech average average theory obtained obtained obtained term term term term term term term term term term term term term note note experiments experiments experiments activity activity activity activity activity activity result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold variables variables research defined found sequence dynamics dynamics dynamics dynamics constant constant computer terms connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic science science left left present present present present phase activation activation activation low low temporal object object press components components components components basis continuous abstract applied find properties references component component component component component due due positive positive important introduction behavior behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus effect effect effect effect dynamic dynamic dynamic parallel change change variable assume assume assume assume chosen chosen chosen chosen part center previous firing firing firing type required required cortex good long long long long long long represent equations equations equations make make fact fact correct observed scale scale scale scale scale scale scale scale scale tasks sum eq eq times times elements elements means natural feedback orientation global global obtain negative original original specific represented compared rates proc perform perform perform active active active determined experimental related connected cortical brain contrast support dependent dependent institute words words words words version synapses synapses represents represents responses responses responses addition ai cambridge view view limit stimuli stimuli stimuli stimuli effects capacity capacity capacity capacity capacity significant vision basic increase processes processes nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological achieved discussion increases increases arbitrary denote denote limited limited limited limited limited assumption assumption excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory short short short short short short short short short short short short short assumed synapse role main main adaptation ability ability hypothesis makes sensory sensory dynamical dynamical dynamical dynamical dynamical dynamical dynamical segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism special matching matching leads representing representing representing numbers stored frame frame attention description correlations exact property property pair separate takes similarity introduced period subject subset recently relevant interest subjects works tions differential achieve address storage increased increased amplitude correctly feed flow strength place assumptions hebbian hebbian hebbian interactions numerical asymptotic mechanisms mechanisms physics external external demonstrated turn iii denoted attractor attractor attractor attractor relation relation pro longer longer longer longer describes ann mathematical dept changing slightly slightly slightly scales interaction adding adding implies versus competition letters decreases decreases decreases formation formation formation overlap detailed fraction fraction understanding activities activities activities activities activities activities activities suggested constants key performing purpose add add koch koch koch koch koch david coupling combinations usa sciences memories memories memories memories memories memories memories memories memories memories illustrated coupled coupled holds discussions major capable encoded driven included oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory literature post post post situation miller miller characteristic composed composed refer refer interpreted oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations content physiological follow follow sci hold duration comp comp comp comp comp simplified absence absence paradigm delayed binding binding binding binding binding leading thresholds thresholds thresholds thresholds thresholds neurosci received moves moves rat rat rat rat rat rat rat rat receive receive cowan cowan cowan origin stimulation carried investigate investigate oscillators involving strengths preliminary oscillator oscillator helpful fashion fashion school plasticity working oscillation affect understand presynaptic presynaptic phases attributes attributes attributes rev rev rev perfect changed der formal som observe mixed mixed mixed mixed mixed mixed motivated asymptotically percentage biology lies turns division monkey mathematics acad localized depicted argument populations populations items items items items capability capability fed psychophysical recordings psychological psychological psychological psychological release exhibits reaches reaches incorporating serve pasadena kinds kinds display display segmented attraction coherence findings findings wang wang semantic synchronization synchronization synchronization displays displays phenomenon refractory repre connecting turned turned turned turned turned caltech clamped clamped minutes ranges difficulties keeping keeping serves disjoint affected affected affected responsible responsible responsible responsible modifications modifications preparation enhanced enhanced carry wilson wilson wilson natl fires continue continue repeat sompolinsky falls governed induce pat von regard assembly assembly assembly assembly assembly assembly assembly competing competing israel israel creating creating horn horn horn horn horn horn horn horn horn horn horn horn horn properly sustained arrows arrows captures receiving material limitation maintaining depression minus fellowship basin presenting malsburg affects imagine continuity modifying continues maintained activate potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation simplifying synchronized buhmann option oscillating oscillating assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies locking turning investigations induces behave tel tel develops develops capacities terns arrow arrow flows exclusively couplings obey functionally proves neurobiological neurobiological permanent electrophysiological thresh thresh carrying tained stm stm stm stm stm stm stm stm stm stm stm stm stm stm stm stm stm stm stm stm aviv aviv tory tory tory illusory sented decompose recovers recovers recovers reminiscent stim holmes inertia inertia consciousness exhibiting exhibiting kammen disappear asso temporary poten usher usher usher usher usher usher usher usher usher usher usher usher usher usher usher faculty correspondingly konig konig konig konig psy crick crick crick crick fatigue fatigue fatigue fatigue fatigue fatigue fatigue fatigue fatigue fatigue namic plex raymond doctoral revised recognizable disappears disappears validate zucker zucker zucker zucker indefinitely neurosciences overcomes dates persist irrespective verbal acquires golomb oscilla oscilla sagi sagi sagi evidently weizmann quoted excita kleinfeld dissipative desynchronization ciative sustain lnt customary figtire bra quenched rehovot consecutively accomodate schillen schillen schillen schillen astronomy cotterill olds olds incoherent disappearance signifying recipient beverly sackler uli dra dies conclusive 
#@Horn_D,Usher_M,
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#*network network network network network learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data function function function function function function function function figure figure figure time time time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output number number number number number system system system system system system system system system system system system error error error error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state results units units units units units units units units units information information information information information problem problem problem models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based based weights layer layer layer layer layer layer case case case vector vector order shown shown shown shown shown systems systems systems systems systems systems systems systems values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight functions unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach pattern single single processing processing large large large large large local rate rate rate test analysis optimal optimal form signal signal algorithms simple simple gaussian paper paper paper paper examples small small net work methods methods methods fig fig fig fig fig step features classification classification classification classification classification classification classification classification classification classification classification process level level level level level level level level level level level level level level level level level level level level current trained trained trained trained trained trained problems problems problems random high high similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation section section section section section section section section section section fixed fixed line vectors speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average states states states states states states states states states gradient gradient gradient gradient term term experiments experiments experiments experiments university university university university research independent independent independent independent independent independent independent log log log log log log log found found sequence sequence sequence sequence sequence sequence sequence sequence target target constant table standard direction presented presented presented presented presented presented presented present present present phase phase phase phase phase phase maximum maximum outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample abstract applied applied applied applied applied applied applied applied applied applied back back back back back back density analog likelihood likelihood likelihood references due ieee ieee procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important important propagation propagation propagation propagation context context context introduction hand estimation estimation dynamic dynamic cost recurrent search tion tion tion tion difference variable assume prior word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word part part previous previous previous previous bound required multiple good good conditions conditions conditions represent expected markov markov markov make fact fact techniques techniques proposed proposed proposed correct correct correct correct correct correct correct correct correct correct probabilities probabilities probabilities probabilities probabilities observed observed observed errors errors errors errors errors errors errors forward forward resulting resulting resulting resulting classes classes classes classes tasks tasks tasks tasks tasks computed multi multi multi multi multi sum sum sum sum performed performed eq eq eq eq eq eq eq eq eq eq means optimization optimization global global global global global global knowledge knowledge negative artificial specific represented represented compared compared application desired desired desired desired provide rates rates rates rates active experimental goal connected connected connected connected connected connected connected distributions gain equal approaches accuracy accuracy accuracy comparison connection support train train train descent descent dependent dependent dependent dependent dependent dependent modeling modeling modeling modeling morgan words words words words words words words words words words words technique technique consists consists represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult bias bias bias bias bias bias bias bias delay delay delay delay delay delay delay delay considered considered framework framework framework framework framework equivalent hinton additional additional additional additional additional additional design design transition transition transition transition transition limit stage stage capacity capacity capacity efficient efficient requires choice choice approximate speed estimated increase give give con con con con developed developed developed developed criterion criterion criterion criterion path path provided provided selected depends simply achieved covariance increases describe describe tested tested hmm hmm hmm hmm hmm hmm hmm hmm hmm limited close close close corresponds corresponds complete complete amount role require main main end end end end end end end ability instance instance instance instance instance instance makes objective objective probabilistic probabilistic underlying needed reduced reduced account account account account coefficients coefficients programming testing testing testing testing testing testing testing segmentation database database database numbers max pre pre window window frame frame frame frame frame frame frame frame frame frame frame frame frame combined minimize minimize minimize description architectures architectures architectures improved advantage robust practical apply apply apply moving highly highly compare works tions yields speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker correspond trans modified sensitive parts invariant extended extended extended matrices move hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid boundary boundary boundary boundary generally generally generally runs critical critical place minimal minimal segment sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid bayes designed designed performs suggest suggest largest sigmoidal variety variety variety exist targets targets targets reference reference reference digit pro pro produces longer longer ways sequential sequential describes modeled multilayer explicitly explicitly explicitly remaining consisting shift shift letters letters letters letters letters letters letters phoneme phoneme phoneme communication interpretation variation labels lee lee lee lee margin similarly discrimination discrimination spectrum key reasonable performing event add add add boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries distances msec string string advantages transactions existing thesis thesis activations activations activations strings strings recognize determines extension extension extension maximize partially grammar successfully successfully straightforward letter closely hmms hmms hmms hmms importance maximal modification computationally computationally computationally detect tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn comparing score score score score score score score score score score identity reached receives receives summary traditional procedures procedures procedures procedures procedures procedures procedures procedures procedures procedures strongly interpreted phonetic phonetic phonetic phonetic issue quantity michael play backward minimizes attempt acknowledgments deal modelling extend extend extend presents presents unlike unlike unlike unlike powerful american difficulty difficulty association optimized helpful matches detectors applicable ideal combine authors reliable comparable proper proper proper proper proper scores scores scores scores scores scores scores scores affect func func surfaces waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel recognizer recognizer recognizer ensure subsets front front front front front front front formal noted precise observe speakers speakers speakers speakers consist baseline baseline baseline simplest phd finds attempts isolated optimum integrate asymptotically burst ment ment stop unstable fairly slope slope slope capabilities baum baum baum correction straight tive formalism formalism formalism formalism formalism formalism shared shared producing incorporate bengio bengio commonly laboratories potentially recognized beginning english toronto res recognizing preceding meaning mellon mellon mellon alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment robustness integrating integrating virtual greatly carnegie carnegie carnegie limits fuzzy fuzzy fuzzy cmu offset spoken conducted share treated incorrect incorrect incorrect incorrect incorrect incorrect incorrect incorrect incorrect vocabulary vocabulary vocabulary vocabulary vocabulary mod pittsburgh maximizes incoming resource phonemes extensions achieves acoustics acoustics phone phone phone phone phone phone phone phone phone phone phone phone phone sums replace viterbi viterbi viterbi viterbi june merging cor cor lot aligned feasible feasible writing modify modify modify extensive optimizing databases extending extending fits difficulties occurred overcome overcome resulted bourlard bourlard bourlard bourlard alphabet alphabet alphabet alphabet alphabet alphabet alphabet alphabet alphabet alphabet evaluations embedding combines combines ranging overview lang percepttons consequences den propagated dif darpa darpa specialized april express properly properly properly properly belonging likelihoods likelihoods consonant captures adopted balanced unified accept sig sig leaming july suboptimal welch welch welch icassp icassp possibilities imagine alter clas management token challenging names france enforce tune els september bridle bridle wider accumulation accumulation accumulation differently parameterization distortions recogni recogni pdfs tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns trainable trainable telephone hid phonemic alex gram sen sen separates separates functionally deals archi archi recognizes maxi articulation articulation cess closure dent feb indepen durations durations durations sep mle rec montreal stabilization bootstrapping bootstrapping bootstrapping bootstrapping routine hood discrepancy align align shikano mum frozen insertions insertions insertions proce posi copied tecture supervision supervision scratch tinuous penalties ending permitted deletions deletions deletions nectionist nectionist hanazawa spelled spelled interpretable icsi likeli albuquerque rect rect attain gramming gation witbrock wood haffner haffner haffner haffner haffner haffner haffner haffner haffner haffner zation siftcation manage nns nns nns accumulates overcomes dure discrim lets duplicated mcgill connecfionist connecfionist substitutions tectures patrick confusable vious franzini franzini franzini ney ney gathering triplets imm spelling filterbank backpropagate propa matical aries pho tence tence moid moid ognition ley triplet gratitude staged trip 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number system system system system system system system error error error error error error error error results results results results units units units units units units information information information information information information information information information information problem problem problem problem problem problem problem problem models hidden hidden hidden performance performance performance performance performance performance performance performance performance based space space weights weights weights weights weights weights weights linear linear linear linear linear linear linear layer layer layer layer layer layer case case case case case case case case order order order order order order order order order order order order shown shown systems systems systems systems values values values parameters parameters parameters parameters parameters noise noise unit unit recognition recognition recognition approach pattern pattern point single processing processing processing processing processing processing processing processing processing processing processing processing control local local test patterns patterns analysis analysis class class optimal optimal optimal optimal optimal optimal optimal shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal gaussian paper paper examples small small small size size size net net net net net net net net work work task task task step step process trained structure structure structure structure structure structure structure structure structure problems memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response similar similar similar architecture architecture architecture architecture equation fixed fixed line line line line line line speech parameter parameter parameter parameter parameter real real real states theory obtained obtained obtained term term term term term note experiments university university computation solution independent defined dynamics initial constant table table table terms terms terms science science prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented presented presented present present frequency temporal temporal temporal temporal temporal temporal temporal temporal machine press press press nonlinear nonlinear nonlinear continuous sample abstract applied back find computational computational analog properties references due due ieee ieee ieee ieee ieee positive procedure important important important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation context context introduction complex complex hand hand behavior generated parallel recurrent recurrent recurrent recurrent recurrent complexity complexity complexity complexity spatial spatial spatial spatial spatial lower measure signals signals representations word learned learned learned chosen chosen higher cases cases cases cases cases cases cases required required required good long long long conditions distributed equations equations make fact fact proposed proposed length correct minimum computed respect called times times elements elements elements factor optimization dimension dimension feedback feedback feedback global applications applications applications applications applications study study em filter filter filter filter filter filter filter vol vol vol vol vol specific samples samples samples represented compared cross series series series series series series series provide proc proc proc proc proc experimental experimental experimental power mit mit steps steps comparison comparison larger train train nets nets modeling modeling modeling modeling morgan proceedings report department internal represents connectionist delay delay delay delay delay delay delay framework framework equivalent equivalent hinton curve curves curves curves san stage stage stage efficient free free free validation criterion selected selected selected selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature biological achieved achieved technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward limited circuits finding short short short short implemented implemented implemented synapse supported theoretical eds eds adaptation adaptation square square square future easily easily easily easily rumelhart rumelhart rumelhart development including kaufmann smaller smaller hopfield hopfield hopfield reduced reduced dynamical jordan jordan jordan block block block transfer transfer interesting interesting mechanism mechanism special special special structures structures structures filters filters direct depth depth depth depth depth depth depth depth depth depth depth depth depth depth choose predict predict predict improved resolution resolution resolution resolution resolution advantage advantage advantage apply introduced introduced cognitive engineering varying varying compare compare conventional conventional works yields differential achieve definition generalized williams williams williams improvement increased increased grant studied extended touretzky white conclusion minimal segment segment conclusions measures performs moody mateo propose mechanisms characteristics plane plane plane plane iii iii iii iii identification identification identification identification identification identification identification configuration configuration attractor produces sequential stability stability segments modeled multilayer infinite electrical dimensionality versus select yield focus controlled restricted restricted restricted allowed past past past past past past diagram diagram epochs epochs epochs epochs delays delays delays delays delays fitting neighborhood eeg eeg eeg eeg eeg eeg eeg eeg advantages advantages topology topology topology topology topology transactions expect expect expect kernels activations activations mozer mozer mozer partially characterized characterized major gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma regular computationally effectively mcclelland wij identify tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn notice notice notice notice notice notice notice conf conf anderson physiological dot nips nips acknowledgments powerful experience detail recursive recursive recursive lippmann fewer mse mse mse mse mse int analytically oscillation understand adapt adapt implementations aspect impulse impulse freedom store store switching epoch epoch epoch epoch plant chaotic chaotic chaotic chaotic chaotic isolated established great unstable adapted adapted glass glass glass glass glass starts formalism formalism easier immediately controls controls controls ion depicted nsf addressed argument requiring fourth applies substantially elman elman lms lms poorly orders rep price price tank tank tank gave focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused focused traces traces displays sleep princeton establish accepted accepted iiii iiii loops keeping optimally lyapunov utilized utilized utilized utilized utilized utilized utilized utilized utilized utilized utilized utilized utilized utilized lang lang regard enhance enhance widrow widrow creating mem ahead matter proximity concentration considerations intersection outperforms outperforms sig planes chaos principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe adapting mackey mackey mackey mackey mackey publication publication concentrated deep gained ijcnn werbos werbos differentiation parallelism parametrized simplifies continually shallow helps diagrams topologies stores instability agrees savings conversion dissertation huberman hopf lowpass rtrl rtrl rtrl rtrl crl cutoff poles zeros approached corn hoff ming jose preferable wiener iir iir vries vries vries vries vries vries vries vries vries vries settles preprocessor intersect exponents iiiii iiiii paid paid conveys taps bptt bptt ire cse tapped tapped tapped tapped concluded kuo kuo kuo kuo kuo quantifies adaline adaline adaline adaline adaline adaline adaline concentrating pred insignificant ffi florida florida obtainable runge bert diminishes cit ensured ensured wescon outperforming versatile kutta iig hogg ork eel dispersive dispersive encompass elliptic gainesville recommend eeo lax 
#@Kuo_J,Principe_J,de-Oliveira_P,de-Vries_B,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data function function function figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number number system system system system system system system system system system system system system system system system error error error error error error error error error error error error state state state state state state state state state state results results results results results units units units information information models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based based based weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case vector vector vector vector vector vector vector vector vector order shown systems systems systems systems values values values values values parameters parameters parameters noise weight weight weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach pattern pattern single single single single single single single single single single single single single single single single single single processing processing control large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate test test test test test patterns class class class class class class matrix matrix matrix form signal signal signal signal signal signal algorithms algorithms algorithms simple simple gaussian gaussian gaussian gaussian paper paper paper examples examples size size feature feature feature net net net net net net net net net net net net net net net work work work work task task methods step features classification classification process trained trained trained trained trained trained structure structure structure structure structure structure structure structure structure high representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture show show show show show show equation section section section section section section section line line rule rule vectors vectors general generalization generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter states states states states states gradient gradient gradient obtained term experiments experiments experiments dimensional dimensional dimensional dimensional result threshold threshold computation research log log log log log defined found found found sequence target dynamics initial standard standard standard computer terms connections prediction left left presented activation activation activation activation activation activation activation activation activation activation activation activation temporal temporal temporal maximum maximum press learn components components nonlinear outputs continuous abstract abstract back back back back back back back back back likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component due ieee ieee positive important important decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation mixture mixture mixture introduction estimation behavior statistical dynamic dynamic generated generated parallel recurrent recurrent change change change difference difference complexity measure measure word word word word word word word word word word part previous cases type conditions conditions conditions represent distributed expected markov markov markov markov markov markov markov markov fact proposed proposed proposed proposed proposed proposed proposed correct correct probabilities probabilities probabilities probabilities probabilities scale minimum classes classes classes tasks computed computed computed respect multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi performed elements made made made natural applications applications knowledge original original vol vol vol artificial relative relative represented true application cross define define define define compute compute rates proc proc proc proc active determined determined experimental related related related connected connected connected connected power power power power power power power power approaches mit accuracy accuracy connection update train descent nets nets modeling morgan words words department version consists internal advances final exp bias bias bias layers layers layers graph ai framework framework framework framework framework framework computing computing equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent experiment experiment experiment experiment directly directly hinton transition transition transition determine upper choice estimated basic basic condition condition derived weighted weighted weighted criterion criterion criterion criterion criterion entropy selected nature nature discussion discussion covariance describe describe hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm close close corresponds corresponds corresponds role journal ability ability instance rumelhart including smaller account dynamical coefficients fully interesting testing testing projection increasing increasing mechanism special special special special operation operation operation language representing max max frame frame combined minimize denotes denotes denotes architectures improved improved improved discussed improve improve improve improve improve improve improve exact property element typical apply introduced include quadratic quadratic recently recently recently interest interest interest highly highly highly compare conventional conventional conventional smooth speaker speaker match match correspond trans diagonal diagonal mixtures separation separation observation observation observation williams improvement improvement increased exists suggests suggests derivative matrices correctly correctly hybrid hybrid hybrid hybrid hybrid hybrid column differences measures propose propose characteristics characteristics proportional labeled assuming minimizing targets identification explicit longer ways ways sequential plot plot plot changing modeled confidence confidence confidence implement multilayer multilayer dimensionality easy applying applying predictive decreases dependence communication interpretation interpretation densities evaluated evaluate restricted updated showed showed lee lee completely suggested discrimination discrimination discrimination discrimination discrimination normalization combining boundaries msec assigned advantages exploration figures figures figures activations activations usa bell subspace extension extension plotted automatic maximize characterized characterized selecting hmms hmms hmms hmms hmms hmms hmms hmms maximal delta included presentation presentation score plots plots tend composed composed composed summary summary soc allowing allowing allowing allowing link showing hold duration duration built built satisfy quantity involved sampled sampled simplified minimizes wave computes highest highest highest attempt deal deal receive parametric parametric layered layered layered layered layered layered layered investigate exhibit discriminant discriminant giving links links detectors detectors combine proper complicated proved cognition hill recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer formal formal formal perceptton initialized initialized initialized speakers baseline baseline baseline baseline baseline baseline baseline baseline improving improving isolated isolated isolated established established established developing benchmark tool handle handle handle nonlinearity considerable organized strictly strictly strictly choices laboratories recognized recognized describing english english english toronto qualitative reflect collected spoken conducted conducted experimentally introducing introducing solla treated incorrect vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary maximizes implements implements viterbi viterbi utterances utterances utterances utterances utterances june distortion contribute contribute classifying indices indices equivalence equivalence forming modify temporally establish inspired extending extending wrong murray khz tools tools alpha alpha utterance bourlard effectiveness effectiveness optimally optimally enhanced enhanced generalizes published entry regarded expanded dominant enhance enhance enhance percepttons competing initialize april april augmented late verification extends generalizing generalizing generalizing accumulated treat speaking outperforms emission microstructure misclassification leaming rejection rejection rejection rejection rejection rejection rejection preserving adopt discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative icassp conjecture arg warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping concentrated levin levin levin levin levin levin levin token token token token token token token token token concentrate concentrate rejected misclassified paradigms paradigms paradigms inversely minor ignoring bridle bridle rabiner rabiner acoust argmax argmax distortions marks adaptively aid pan pan distinguishing striking juang restricting recognizes transpose distorted constraining connectionism scatter scatter scatter scatter february prescribed enabling enabling mid wellekens wellekens expresses cepstral cepstral tutorial lpc adopting adopting fulfill albuquerque kauffman warped males nns gle arose chart boutlard females contaminated confusable confusable confusable rejections fleisher dummy representatives aiming subvector subvector ofleee rival sigrnoidal twin disregarding zxt 
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training training training training algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number system system system system system system error error error error error error error error error error error error error error state state state state state state state state state results results results results results information information information models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer vector order shown shown shown shown systems values values values values values values values values values values probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise weight functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach approach pattern pattern pattern pattern pattern pattern pattern processing processing processing processing processing processing large rate rate rate rate rate rate test test test test test test test test test test analysis analysis class class class class class class class class matrix matrix shows signal signal signal gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper size work task methods methods step classification classification classification level level level level level level level level trained trained trained trained structure structure structure structure problems high response similar architecture show equation fixed fixed vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter average average average average states states states states states states gradient gradient obtained obtained term note note experiments experiments result university computation research independent independent independent independent log log log found initial initial estimate estimate estimate estimate estimate standard standard standard standard standard computer connections node node node node node node node node node node node node science science left presented presented low nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency temporal sets range range range press position basis basis basis basis basis basis basis basis basis basis outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous abstract applied density properties likelihood likelihood likelihood likelihood likelihood likelihood references component ieee ieee ieee ieee ieee procedure procedure mixture mixture mixture mixture mixture mixture estimation estimation estimation behavior statistical variance recurrent tion energy difference difference difference difference complexity lower word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word chosen higher part center center center center center previous type required multiple good good good good conditions represent bayesian bayesian bayesian bayesian bayesian expected equations markov markov markov markov markov markov markov markov markov techniques techniques length correct correct correct correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities forward classes ing ing ing total total total total total computed computed computed computed respect respect multi sum sum sum sum sum performed performed performed performed times times times means means means means factor factor factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization global global global global global global global global global global global global global global study policy relative relative relative relative relative relative relative specific true true compared compared compared desired desired desired provide provide rates goal goal gain equal equal equal equal approaches mit accuracy accuracy comparison update train train train nets morgan morgan morgan proceedings proceedings proceedings report report institute words words words words words implementation technique technique technique technique consists consists advances advances connectionist difficult final final final final final addition framework computing additional additional estimates transition limit san san conference conference conference determine classifiers classifiers classifiers classifiers classifiers full estimated estimated pages pages produce condition derived derived derived clustering clustering clustering developed developed levels levels criterion criterion criterion criterion criterion bounds bounds bounds bounds actual selected constraint measured measured measured discussion covariance technical technical hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm fast limited close close close corresponds rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf short require square end fit kaufmann kaufmann account unknown unknown unknown coefficients coefficients coefficients technology mlp block block testing significantly increasing segmentation database database database database database leads squared iterations iterations iterations iterations window international international international normalized normalized normalized frame frame frame frame frame frame frame minimize minimize produced produced produced description improved improved improved improved improved improved improved improve correlations robust robust robust robust robust separate element element reported apply include identical identical recently conventional speaker speaker speaker speaker match match correspond studies achieve diagonal diagonal diagonal background background background background background background background observation interval scaling scaling suggests deviation deviation deviation wide hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid touretzky touretzky generally setting setting setting pass pass pass demonstrate greater greater reduce conclusions editors bayes bayes numerical designed designed moody mateo mateo hard characteristics sigmoidal proportional radial radial radial radial radial radial radial radial minimizing averaged force acknowledgements produces produces factors factors factors plot describes laboratory label label label multilayer unique mutual frequencies frequencies frequencies gaussians versus versus select select john expressed communication interpretation operations labels lee centers centers centers centers frames frames frames frames frames frames frames frames frames frames frames static static similarly discrimination diagram diagram diagram partial partial earlier reasonable performing measurements normalization normalization normalization normalization sec intervals intervals intermediate intermediate initially views expect priori priori priori usa maximize maximize priors priors tests successfully successfully letter letter capable hmms hmms score score tend composed summary refer decoding contained contained prob superior lie classify criteria quantity sampled michael simplified backward highest attempt consisted consisted extend unlike poor overfitting rapidly lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann preliminary preliminary discriminant discriminant fewer fewer school authors working comparable comparable comparable scores scores waibel hill editor created recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer quantities initialized initialized initialized speakers speakers baseline improving isolated isolated isolated isolated isolated isolated isolated advanced advanced variances variances variances waveform briefly snr implementing style bengio cut inversion inversion optimize optimize sun alignment alignment alignment alignment apparent considerably considerably reflect spoken spoken spoken spoken incorporated vocabulary vocabulary vocabulary cal acoustics acoustics acoustics singer singer singer singer singer singer richard richard richard richard richard richard richard conclude conclude begins viterbi viterbi viterbi viterbi viterbi viterbi viterbi deviations arithmetic labeling labeling assign martin member databases count bin bin bin bin bin unity unity connecting climbing communications fits khz significance minutes adjusting alpha abilities serves mark fail modifications modifications embedding mance combines combines iteratively iteratively perfor male male mel initialize tokens tokens tokens tokens tokens tokens april april bins bins properly canada partitioned projects assigns counts accumulated posteriori rms rms rms equivalently presenting nelson preserving failed expanding tween discriminative utilize comparative classifications seek female female avoided clustered streams graduate token token carefully carefully march individually cole noting exceed tied tied tied tied worth distinguished meet retained normalizing normalizing bridle oregon recognizers recognizers recognizers recognizers november accumulation opti opti subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet december alex ron hour integrates agency lying tracks binomial binomial sis goodness magazine appro defense unimodal unimodal unimodal formulas rec rec decode decode sponsored subnetworks lincoln cepstral cepstral cepstral mization mization subnets decoders decoders plexity accu fanty mike corresponded cse yoshua lowering incremented incremented mon plex periments succeed official sug government cies investigators sparcstation nodal nodal nodal grand lexington boutlard kai muthusamy racy skip franzini succeeds mial cepstrum cepstrum unnormalized priate gest reestimate elliot elliot frequen flit adjoining curred practi capitalize 
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output output output output number system error error error error state state state state state state state state state state state results results units units units units units units units units units information information information information information information information problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space weights weights weights weights weights weights linear layer layer layer case case case vector shown systems systems systems systems systems systems systems probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters weight functions functions functions functions functions functions functions unit unit distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach approach approach approach single single processing processing processing processing processing processing processing processing processing local local local local local local local class class class matrix matrix matrix optimal optimal form form signal signal signal signal algorithms algorithms simple paper paper work task task methods methods classification classification classification process current trained trained trained problems problems problems similar equation fixed fixed rule rule rule rule speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter approximation approximation states states states theory gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained obtained term term term note note note experiments experiments experiments experiments experiments experiments dimensional university variables solution solution independent log log log log log log log defined defined found sequence sequence sequence sequence sequence sequence sequence sequence initial constant constant constant estimate estimate estimate estimate estimate estimate standard computer terms present present maximum maximum maximum maximum maximum maximum maximum press basis basis basis basis basis basis outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous abstract applied applied back density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component stochastic stochastic due due ieee ieee ieee ieee procedure procedure important adaptive decision propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction hand estimation estimation estimation estimation estimation estimation statistical effect effect effect generated tion change variable variable classifier signals prior prior prior prior prior prior prior word word word word word word word word word previous required required required represent markov markov markov markov markov markov markov markov markov markov make make make make region proposed correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed forward forward forward resulting resulting classes classes ing ing ing ing tasks tasks computed computed computed computed multi multi multi multi sum sum means means means means factor factor global global applications study knowledge em obtain obtain obtain negative negative vol vol vol vol relative relative relative relative true compared compared application desired desired desired desired compute compute rates goal posterior posterior posterior posterior posterior posterior posterior constraints connected distributions discrete approaches train train descent source morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan proceedings proceedings proceedings proceedings words code individual advances advances advances advances joint represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist final final exp exp exp exp exp sequences cambridge computing computing domain domain domain domain equivalent directly estimates estimates estimates estimates transition san san san san san conference conference conference determine efficient efficient estimated basic basic con derived clustering levels criterion criterion criterion entropy entropy entropy finally finally evidence evidence evidence depends simply achieved achieved achieved discussion covariance covariance hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm transformation assumption corresponds complete rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount assumed generate theoretical require require eds eds adaptation instance makes including kaufmann kaufmann kaufmann kaufmann objective probabilistic typically typically typically typically typically typically pairs smaller functional coefficients coefficients coefficients coefficients coefficients coefficients fully mlp mlp transfer transfer transfer transfer transfer transfer testing significantly ratio ratio ratio ratio uniform database language language language language language language language language pre making stored international international international frame frame added perceptron discussed discussed discussed separate element introduced introduced identical side approximately calculated speaker match diagonal mixtures mixtures chain modified constructed lead extended matrices feed touretzky touretzky touretzky occurs generally conclusion assumptions differences differences differences sigmoid bayes bayes bayes numerical moody moody exponential practice practice practice constrained constrained constrained mateo mateo mateo mateo physics sigmoidal radial radial radial radial start relationship relationship targets acoustic acoustic acoustic acoustic acoustic construct longer longer generating generating transitions dept implement consisting interaction mutual mutual frequencies frequencies gaussians gaussians gaussians gaussians choosing national expressed review phoneme densities densities labels labels labels frames allowed discrimination additive performing interpolation interpolation interpolation interpolation valid topology topology topology topology transactions usa usa inter inter discuss discuss specifically priors priors priors priors priors priors priors variations partially partially partially grammar major straightforward hmms hmms hmms hmms hmms hmms hmms suitable computationally delta essentially procedures decoding interested phonetic dis superior criteria quantity quantity write michael backward backward attempt approximating modelling modelling modelling modelling modelling modelling situations employed simpler remain schedule powerful poor estimators estimators issues issues lippmann lippmann preliminary preliminary preliminary discriminant tech links ideal combine combine scaled surfaces gradients extremely ensure noted assumes assumes explored expressions consist consist extent attempts defines sentences variances guaranteed defining defining adapted answer lies reasons berkeley shared bengio desirable mathematics potentially acknowledgement separately toronto toronto arises alignment alignment alignment alignment robustness improvements fuzzy pure amounts lack cohen cohen cohen cohen cohen cohen frequently rep variant ity vocabulary proven acoustics acoustics acoustics acoustics phone phone phone replace semi semi viterbi viterbi utterances specifies simultaneous sentence softmax softmax softmax globally aligned formally labelled labelled concerned purely replacing replacing automaton imposed contract interpret interpret obtaining utterance utterance bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard responsible optimally substituting embedding ensures paul paul paul regarded regarded regarded regard percepttons propagated originally competing dif similarities darpa francisco modelled mlps infer theoretically steepest park likelihoods likelihoods likelihoods likelihoods implicitly implicitly alternatively convergent pdf pdf pdf dividing dividing inferred nelson forced axe discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative comparative additionally ideally decomposed tendency demon clas constrain mismatch mismatch mismatch mismatch arising convert relating relating careful differentiation retain relates rbfs rbfs rbfs rbfs rbfs rbfs rbfs rbfs investigating unconstrained tied tied tied tied tied tied tied tied tied tied tied tied tied tied tied tied funded book normalised bridle bridle bridle bridle bridle topologies lowe lowe resolve resolve recogni pdfs pdfs pdfs pdfs pdfs instability optimisation optimisation optimisation optimisation optimisation phonemic tribution gram labelling huang huang contributes correctness correctness correctness classi resolved syntactic unlabelled unlabelled unlabelled inde constraining resultant locality gaus fication steve raised raised mis fixing ous allowable huge experimented probabil renals renals 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#*network network network network network network network network network network network network network network network network network network network learning model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm output output output output output output output output output output output output output output output output output number system system system system system system system system system system system system system results results results units units units information information information problem models models models models hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based based based space space space weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case case case case case case vector order order order order order order order shown shown shown shown systems systems values values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight functions functions functions functions functions unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach pattern point single single processing processing control large local local local local rate test test test analysis analysis class matrix matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs signal signal algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper paper paper paper small net work task task task task task task task points points points points features features classification level level level level level level level level trained trained trained trained trained random random high similar representation architecture architecture architecture architecture architecture architecture architecture architecture show show equation equation equation section section section section line line line line vectors vectors vectors general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average gradient gradient gradient gradient gradient obtained experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional result result university university university university variables solution solution solution solution solution independent log log log defined defined found found found sequence sequence sequence target initial initial table table estimate standard computer computer computer computer connections connections science science science left left left direction presented map present low maximum maximum maximum maximum maximum maximum components components components components outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous abstract applied back back find density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic adaptive propagation propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical dynamic dynamic dynamic generated generated generated generated variance variance parallel parallel cost recurrent recurrent tion change change change energy variable variable variable variable variable assume lower lower lower prior prior prior prior word part part part part part part part center previous theorem good represent equations equations markov markov markov make make fact proposed proposed correct probabilities observed observed resulting resulting resulting classes classes ing computed respect respect respect respect respect respect respect multi multi multi performed performed performed regions mapping means optimization optimization optimization optimization dimension dimension dimension dimension dimension dimension dimension made global global global global study study study knowledge knowledge em obtain obtain vol artificial artificial artificial artificial samples samples samples samples samples compared application desired series series series series define define compute compute perform perform perform perform perform perform perform perform perform experimental related constraints constraints brain approaches accuracy update train morgan institute implementation version advances difficult final scheme maps considered considered cambridge equivalent experiment experiment experiment experiment experiment experiment experiment experiment directly curve view design design design conference approximate statistics free estimated estimated estimated estimated estimated basic con conditional levels levels criterion criterion criterion criterion criterion criterion criterion criterion product actual iteration depends depends depends depends simply covariance covariance describe describe hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm transformation transformation transformation transformation transformation transformation transformation transformation transformation close assumption proof short short assumed assumed role ability easily objective objective technology technology programming programming programming interesting significantly york database database database language principal principal principal principal representing details details details iterations international frame combined choose choose architectures population improve improve recent separate separate separate reported subject cognitive dimensions dimensions dimensions dimensions observations observations observations observations observations observations observations observations observations tuning tions yields yields speaker speaker correspond studies diagonal diagonal diagonal diagonal diagonal diagonal mixtures mixtures mixtures mixtures observation improvement improvement expression lead studied studied studied invariant invariant derivative derivative derivative derivative hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid touretzky white demonstrate conclusion starting place tangent designed clear performs performs learns suggest integration integration integration decrease relationship relationship introduce derivatives acoustic question suppose suppose appears relation pro ways estimating ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann tuned dept segments segments segments modeled modeled modeled modeled simultaneously simultaneously mutual mutual gaussians events select extracted depending stationary phoneme phoneme phoneme phoneme phoneme variation transform densities densities densities evaluated evaluate showed decomposition decomposition static discrimination processor processor processor delays delays reduces purpose intermediate initially initially initially initially initially initially string symbol symbol advantages topology kernels thesis thesis combinations perceptrons sciences recognize extension maximize maximize maximize maximize black simplicity columns hmms hmms hmms hmms efficiently efficiently post post post comparing situation tend orthogonal composed compact prob phonetic phonetic dis sin duration duration built notation vary write minimizes computes computes maximization attempt attempt mixing extend explore explore simpler parametric parametric layered layered transformed transformed optimized optimized integral integral preliminary preliminary preliminary hall ml ml ml ml ml ml school school maximizing neu possibly possibly man prototype singular der separated speakers speakers motivated phd finds sentences sentences sentences massachusetts years indicating variances analyzed briefly spatially sys preprocessing broad broad incorporate bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio projected recognized recognized sounds opt optimize depicted alignment raw explained improvements varies greatly empirically fed parameterized marked remove variant variant summarized mod phonemes phonemes phonemes acoustics germany findings don analogue acts addresses tem proceed establish nearby ral bourlard bourlard bourlard integrator intuitively substituting exploring displayed ascent ascent infinity den sim specialized specialized april theoretically canada canada likelihoods pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf assigns consecutive posteriori multiplying yielded yielded anns anns anns anns anns anns anns anns anns anns anns anns anns anns anns ple logarithm logarithm vec maximized ber comparative comparative comparative assess jacobian jacobian jacobian verified verified levin levin num relates integrals paris france universit articulatory knowing bridle bridle bridle bridle differentiating argmax recogni pdfs hyperbolic doesn exper hid tors determinant determinant determinant determinant determinant determinant determinant determinant determinant proportions bottou bottou bottou mori mori mori mori mori mori consonants separates 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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data figure figure figure figure figure figure time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training algorithm algorithm output output output output output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system state state results units units units information information information information information information information information information problem models models models models performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based vector vector vector vector order systems systems systems systems systems systems systems systems systems systems systems systems probability parameters noise noise noise functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach single processing processing processing processing processing processing processing processing processing processing processing processing processing processing control large large rate test analysis analysis shows shows signal signal signal signal signal signal signal signal signal signal algorithms paper paper small size net net work work task task task task features features process process process process level level level level level level level trained trained cell structure problems problems high high high high high high representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture rule general generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real real states states result result result result result university university university university university university university university university research research research independent independent found sequence sequence target target target target computer computer computer connections connections science science science prediction present present machine machine machine machine machine machine machine machine machine object learn learn learn components components components components continuous continuous continuous continuous continuous abstract back computational computational references component component component stochastic ieee ieee ieee ieee ieee ieee procedure important adaptive propagation mixture context context introduction hand hand hand hand hand hand behavior statistical statistical statistical dynamic dynamic dynamic generated parallel parallel parallel parallel parallel search tion energy difference difference classifier rules word word word word word word word word word higher higher part center center center bound required make techniques techniques techniques techniques techniques correct correct correct correct errors forward forward ing ing ing tasks tasks human human multi multi multi multi multi performed times elements mapping mapping potential made made applications knowledge knowledge knowledge vol relative specific compared compared compared compared compared cross cross cross provide provide compute rates rates perform experimental goal goal goal approaches approaches approaches accuracy accuracy accuracy comparison support train dependent dependent dependent source modeling modeling morgan morgan proceedings proceedings proceedings proceedings proceedings proceedings report report words words words words implementation version version version technique internal code advances advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult addition sequences ai computing domain domain domain additional san san effects detection conference conference conference conference conference conference conference conference conference conference conference conference conference conference conference conference efficient efficient requires con produce derived clustering developed developed developed types types provided finally achieved achieved achieved technical technical describe hmm transformation limited limited amount effective implemented implemented generate require require require face face face face adaptation hypothesis cluster development development noisy noisy noisy noisy including kaufmann kaufmann pairs needed needed combination combination reduced functional technology technology programming programming testing significantly increasing mechanism special database database database mode mode language language language language language language language language language language language language language language language language language language language language details direct international international international international supervised frame frame light predict discussed improve pair pair robust robust robust ensemble machines subset recently recently relevant highly highly approximately approximately volume works module module module module speaker speaker speaker speaker speaker speaker achieve achieve achieve address mixtures modified generalized generalized improvement parts lead lead alternative alternative hybrid hybrid touretzky generally generally generally hardware hardware hardware pass pass conclusion place greater greater valued modules modules modules modules modules designed performs performs moody moody faster mateo mateo external external characteristics characteristics labeled exist program program acoustic acknowledgements reference explicit appears pro pro produces produces written written written written written written ways distinct distinct distinct changing segments implement text text text text text text text text integrated predictive predictive formed formed formed formed formed versus select national focus phoneme phoneme phoneme phoneme phoneme phoneme communication communication variation evaluated restricted lee lee frames understanding understanding translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation translation diagram slow performing purpose boundaries generation generation generation generation msec msec foundation transactions thesis thesis strings automatic candidate coupled variations domains domains domains grammar grammar grammar grammar grammar tests planning extra successful successful tdnn capture traditional conf contained video strategies strategies strategies duration duration list generalize generalize providing quantization hypotheses hypotheses hypotheses hypotheses hypotheses ill ill ill automatically automatically automatically attempt attempt deal carried american create exhibit rapidly humans strengths hanson limitations limitations accurately issues lippmann lippmann school school tech possibility authors office office office structured structured structured symbolic symbolic workshop scores cover cover contours contours contours waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel waibel naturally adapt man recognizer versions versions formal academic message message contributions phd phd attempts synthetic sentences sentences sentences sentences sentences sentences sentences sentences devices devices languages languages languages languages mentioned mentioned publishers guaranteed coded coded expensive handle handle considerable considerable processed tive tive sys closer incorporate laboratories scientific recognized separately universal universal calculations calculations pitch pitch pitch pitch pitch pitch pitch english english english english english english english english english english english english read meaning mellon mellon mellon mellon mellon mellon mellon mellon addressed alignment robustness integrating improvements evaluating carnegie carnegie carnegie carnegie carnegie carnegie carnegie carnegie understood cmu cmu flexible tional tional spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken fed effort effort effort continuously continuously continuously ity passes vocabulary vocabulary vocabulary vocabulary vocabulary synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis pittsburgh differs gen gen phonemes achieves achieves acoustics acoustics acoustics acoustics phone plan germany germany decreased age age age tolerance eventually utterances sentence sentence sentence sentence sentence sentence sentence sentence calls semantic merging cor person person generator guarantee japan lvq lvq lvq lvq dynamically concerned tem flexibility flexibility flexibility flexibility spontaneous spontaneous air consideration promising difficulties siemens siemens siemens vehicle serves utterance utterance utterance utterance utterance settings affected canonical preparation preparation grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars constructive continue date date exploring service service evaluations evaluations mance introduces respective perfor pat conjunction uni facilitate candidates tic exposure recog smoothed smoothed offer tracker augmented augmented augmented properly grammatical parse parse extensively relies explains material automated acknowledge accumulated linguistic linguistic linked linked emission ence parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing corporation corporation corporation corporation users accept kluwer tables tables tables dec dec dec dec legal diverse forced forced utilize acceptable acceptable individuals simd german german german german german german german german german german german german german german german affects rhythm scenario tight reject pub pub translated translated translated translated translated mhz cessing alternate file file convert efforts efforts eliminating cole cation million paradigms distinguished register book memo macroscopic commercial programmed det milliseconds atr atr atr travel travel ward microscopic challenge modal modal nec nec emphasis gratefully beam functionality recogni satisfactory synthesized european ongoing telephone telephone telephone hypothesized utilizes aid interpreting interpreting interpreting hopkins phonemic alex japanese japanese japanese japanese japanese japanese japanese japanese jain jain jain jain jain eral pronounced conversion conversion compo compo huang huang interpretations tokyo cooperation cur enhances sity adjusts voice voice voice fidelity fidelity fidelity ance concatenated semantics robustly media tomita tomita tomita tomita translates statements translate unrestricted unrestricted talk talk talk talk ming rec bootstrapping lexical das saito lisp spotting predic nents nents shikano shikano ogi synthesize acceptance albeit traditionally accepts accepts registration registration registration registration registration registration versity coverage coverage adap retrained ranked notably intel vast challenges challenges challenges parser parser parser parser parser parser parser munich linguistics perplexity perplexity transcription syntax syntax tebelskis tebelskis tebelskis mature ungrammatical ism brings highlight univer nectionist tri barnard barnard contributed contin facing accent hurt interna rect duced nique ist disambiguation blend otto freq freq karlsruhe karlsruhe karlsruhe karlsruhe karlsruhe karlsruhe confer predominantly collaboration scripts 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#*network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time networks networks training output output number system system system system system system system system system system system error problem problem performance performance performance based based based based space layer case order shown shown shown values values values parameters parameters unit recognition approach approach point point point processing processing control control control control control control control rate test test test analysis analysis optimal inputs inputs shows shows signal signal signal visual paper small work work work task task step step points points points process current response response response response similar similar representation show generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter real real real real obtained obtained activity activity activity activity activity university research research sequence sequence sequence sequence target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial estimate science prediction prediction direction phase activation frequency frequency frequency temporal motion press position position position position position position position position position position position position position position nonlinear continuous continuous continuous continuous continuous sample sample sample abstract back computational computational properties properties properties properties properties properties references due important propagation propagation introduction complex estimation estimation behavior behavior behavior dynamic dynamic generated generated generated generated parallel parallel recurrent recurrent change change change change complexity lower lower lower lower signals signals signals representations learned learned learned previous good distributed distributed proposed correct observed observed observed observed observed forward forward forward forward forward forward forward forward forward forward forward forward forward scale minimum minimum minimum human human human natural natural natural global global applications study study obtain obtain obtain negative series series series provide experimental goal constraints constraints constraints connected motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor discrete discrete brain brain mit steps support modeling modeling modeling modeling modeling modeling modeling modeling morgan proceedings report institute institute department implementation internal connectionist responses responses final addition cambridge experiment hinton hinton estimates trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory bit upper full approximate approximate estimated basic increase increase increase criterion criterion velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types provided provided finally finally depends constraint biological discussion transformation transformation fast limited limited stable generate generate generate generate main ability ability future rumelhart rumelhart kaufmann auditory simulated simulated simulated simulated simulated simulated dynamical dynamical jordan jordan jordan jordan jordan jordan jordan jordan technology interesting ratio segmentation structures structures principle language produced perceptron perceptron recent correlations property movement movement movement movement movement movement movement movement movement cognitive cognitive engineering engineering previously smooth smooth speaker speaker positions positions positions positions channels williams williams grant arm arm arm amplitude horizontal horizontal predicted predicted predicted predicted predicted predicted generally generally demonstrate conclusion reduce trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories learns learns learns encoding propose characteristics characteristics characteristics demonstrated california movements movements movements targets targets targets targets targets acoustic acoustic acoustic acoustic acoustic acoustic reference relation perception generating vertical vertical vertical vertical vertical multilayer coordinates physical transformations develop integrated equilibrium equilibrium focus focus formation formation phoneme phoneme phoneme phoneme correlated transform understanding understanding approximated key reasonable reasonable smoothing tracking generation generation generation generation distances string assigned recorded strings sciences aspects importance vowel vowel tend physiological physiological physiological physiological physiological physiological satisfy michael absence paradigm realistic wave ill command command command command command command command command command command command command command production production production production production production perturbation perturbation perturbation access investigate limitations preliminary preliminary preliminary preliminary examine school rest rest rest biol biol muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle understand examined versions formal serial sentences isolated massachusetts publishers smoothness smoothness smoothness smoothness smoothness answer cascade cascade cascade cascade cascade cascade cascade spatially closer style incorporate laboratories laboratories acknowledgement attribute recording recording demonstrates offset capability experimentally experimentally quantitative posed posed incorporated incorporated compares commands commands commands commands commands release release synthesis perturbations perturbations perturbations ordered acoustics sums eventually utterances instantaneous realized cybern cybern bipolar japan temporally anatomical numerically difficulties kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato observing wire utterance utterance shifts symposium muscles muscles muscles muscles inferior inferior lip lip lip lip lip expanded intended elastic elastic elastic spatiotemporal spatiotemporal spatiotemporal smoothed gesture gesture gesture consonant consonant grants skills ics speaking speaking linguistic summer rubin torque torque alternating alternating revealed revealed diverse encouraging tendency acceleration eric assess articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator compensate neurophysiological efforts relating relating confirmed acquired acquired ultimately scope insertion insertion rectified rectified rough syllables syllables articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory atr coordination coordination tension tension styles attempting japanese kinematic kinematic tip anterior anterior anterior anterior partly couplings couplings couplings markers digitized emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg emg cho closure nih brought uno uno uno uno uno uno suzuki suzuki suzuki suzuki suzuki suzuki proceeding medial damping damping asymmetry marker insertions tongue tongue conceptually lips reproduces inertia gun conveys bateson bateson bateson bateson bateson kyoto encouragement lowering lowering nose resolving resolving opening differentiated differentiated entails antagonist skeletal skeletal skeletal soraku pauses speak jaw jaw jaw jaw viscosity seika articulators articulators articulators articulators articulators articulators raising hikaridai recurrently insightful intent facilities patterning prosodic listeners ichi offs coarticulation ool philip intention intention ensuing ensuing ooi ooi ooi mitsuo conceived chap schwarz equidistant elliot endeavor affords pioneering hfsp 
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#*network network network network network network network network network network network network network model model model model neural neural neural neural neural neural neural neural input data data data data data data function figure figure figure time time time time set set set set set set set set set set set networks networks training training training training training training training training output number number number number number number system system system system system system system system system system system system system error state results results units units units information information information information information problem models hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based based based based based linear linear linear layer layer order order order order order shown systems systems systems noise noise noise noise noise recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach processing processing processing processing large large large local local rate test test test test analysis analysis analysis analysis analysis shows shows shows signal signal signal signal signal paper feature feature feature feature work work task features features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level current current trained trained trained structure random high high high high similar speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech gradient experiments experiments experiments experiments experiments experiments solution research independent independent independent independent independent found found found found sequence sequence sequence sequence sequence sequence initial initial computer computer science presented present nodes nodes nodes sets outputs outputs sample sample abstract applied find references due due ieee procedure procedure important context context context introduction hand hand hand hand effect effect search search search search search search search search tion energy difference difference classifier classifier classifier classifier classifier classifier classifier classifier classifier rules prior chosen part center bound required good long represent tree correct correct correct correct probabilities errors errors errors errors forward forward human human computed performed performed performed performed performed performed performed regions made knowledge knowledge knowledge specific series series series rates location location location location perform perform perform constraints connected connected accuracy accuracy accuracy accuracy accuracy support train train train morgan proceedings proceedings proceedings report institute institute institute words words consists consists consists consists consists internal individual individual advances joint represents responses difficult difficult difficult final computing experiment design design san san top top top stage bit conference conference efficient choice choice choice choice choice free pages channel channel lines actual provided provided provided provided finally finally selected selected selected sampling sampling sampling sampling achieved discussion describe group tested tested tested limited complete amount short short short common generate generate supported makes development development including kaufmann auditory pairs needed reduced coefficients coefficients coefficients fully fully technology technology technology segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation database database database database database database database language language representing pre window window window stored international bottom expert frame frame frame frame frame frame frame frame frame frame frame frame frame combined produced produced added added sources description population improve improve resolution advantage separate separate reported strategy strategy sense subset subset sufficient sufficient subjects yields speaker speaker speaker speaker speaker speaker speaker match match match correspond achieve achieve achieve background background improvement improvement entire amplitude extended extended digital correctly feed feed touretzky boundary boundary boundary boundary boundary boundary boundary boundary boundary segment segment segment segment segment segment segment segment editors accurate accurate accurate accurate accurate accurate designed designed moody mateo sound integration labeled labeled variety averaged manner groups identification acoustic acoustic explicit explicit explicit pro pro ways describes transitions label label segments segments segments category category category category category spectral adding adding predictive predictive predictive quality quality quality letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters yield national phoneme evaluated evaluate labels labels labels labels labels labels labels centered centered frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames understanding allowed discrimination past past spectrum sign measurements measurements measurements boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries penalty intermediate initially msec msec msec msec msec msec msec msec msec msec msec msec assigned classified classified classified classified avoid recorded perceptual perceptual perceptual thesis thesis combinations retrieval retrieval retrieval retrieval retrieval inter recognize automatic determining determining determining letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter extra comparing score vowel vowel vowel identity ten fine characteristic capture soc contained phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic classify classify duration duration categories categories categories categories categories categories categories categories categories categories list list sampled sampled sampled automatically attempt extract receive diego collection difficulty accurately project combine variability workshop scores scores scores scores onset onset onset onset man speakers speakers speakers speakers speakers speakers speakers speakers consist motivated finds isolated isolated isolated massachusetts years burst burst burst burst histogram histogram great advanced advanced advanced stop stop agreement analyzed answer caused precisely broad choices optimize english english english english english english english english english english english english english bandwidth nsf questions offset offset spoken spoken spoken spoken spoken spoken spoken spoken spoken treated frequently compares release phonemes acoustics phone phone boston segmented focused focused viterbi viterbi viterbi viterbi viterbi calls calls classifying aligned proportion proportion recover eliminated dealing khz city city city grow resulted occurring scoring scoring mark analyzing utterance corpus alphabet alphabet alphabet alphabet alphabet alphabet alphabet alphabet alphabet ranging von overview darpa bursts master master record formant designing consonant consonant instructions tures assigns onr discriminate discriminate discriminate discriminate crossing converted corporation asked asked forced forced forced year profiles classifies workstation alter clas clas clas graduate graduate carefully cole cole cole cole cole cole cole cole cole cole cole cole confirmed guided names names names names names names names names names names names names names names names names names names names names names names names million attached distinguished distinguished west west fea programmed milliseconds refined oregon oregon oregon answers technologies technologies acoust neumann distortions recogni thousand telephone telephone telephone telephone telephone telephone telephone telephone telephone telephone telephone telephone telephone telephone hypothesized hypothesized locate locate locate routines concern rare ters manually slices slices placement placement placement retrieved retrieved recognizes closure compromise merged segmenting mul artificially durations durations durations microphone microphone occurrences timit locating locating locating retrieve insertions insertions insertions ogi fanty fanty fanty fanty fanty fanty fanty fanty fanty fanty distinctions coverage coverage ronald plp plp plp plp plp plp plp plp plp unix boards noises segmentations seventh deletions equipment news foreign calling duce spelled spelled spelled spelled spelled spelled spelled spelled 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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning neural neural neural input input input input input input input input input input input input input input input input input input input input input input input data data data function figure figure figure figure figure figure time time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training output output output output output output output output output output number number system system system system system system system system system system system system system error error results results units units units units units units units units units information information information information information information information information information information information problem problem hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based weights weights case case case vector vector systems systems systems noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight unit unit unit unit recognition recognition recognition recognition approach single single single processing processing processing processing processing processing processing processing processing processing processing large large local local test test test test test test patterns analysis form form form form form shows shows shows signal signal signal signal signal signal algorithms paper paper small small small feature feature net net work work work work task task task task task task features features features level level level level level trained trained trained trained trained structure structure structure structure structure structure structure structure problems problems high high similar similar representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture rule rule general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real obtained note experiments experiments experiments result result result university university university university university research research research research found sequence table table table table table table standard computer computer computer connections science science science science science presented presented machine sets learn learn learn learn learn learn learn learn learn learn position position continuous sample abstract back back computational references ieee ieee ieee ieee ieee important propagation propagation context context introduction action action complex hand hand hand hand hand hand hand hand cost tion tion tion tion tion energy classifier lower representations representations word word word word word word higher higher higher part part part center center center center previous previous previous previous previous required required multiple binary long length length correct errors ing tasks tasks tasks tasks human multi multi multi multi called called mapping made natural natural relative relative relative relative specific specific specific specific represented represented represented represented compared compared compared compared compared compared application application series define define location perform goal constraints approaches approaches steps steps comparison comparison larger connection support train train train source modeling proceedings proceedings proceedings proceedings proceedings words words words words department version version version technique connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult final final final delay addition sequences sequences environment hinton additional solutions san effects effects detection conference conference conference conference conference conference conference conference conference conference conference conference conference full free free basic basic con con con conditional developed levels area types types types types types types actual provided provided provided provided processes achieved achieved achieved achieved achieved group tested transformation limited limited complete generate role role require hypothesis hypothesis hypothesis hypothesis future degree development noisy noisy noisy noisy including including including needed combination technology block block block block block block block block special mode mode principle language language language language language language language language numbers international international international supervised early early early produced produced produced choose run run run added added sources denotes discussed directions recent advantage robust robust separate typical reported reported include subject hierarchical cognitive dimensions highly highly observations approximately module module module module module module module module module module module module module module module module module module module module module module module tions speaker correspond positions positions risk sensitive increased constructed correctly correctly correctly boundary boundary demonstrate demonstrate conclusion critical row row valued modules modules modules modules modules modules modules learns learns california groups connectivity connectivity denoted acknowledgements explicit pro pro produces factors primary primary primary generating generating generating generating describes distinct missing sensitivity explicitly explicitly explicitly transformations transformations predictive formed agent blocks blocks blocks blocks blocks blocks blocks national independently independently phoneme solved variation variation variation variation detailed transform evaluated labels labels labels showed forms forms understanding translation translation translation translation translation translation translation allowed partial performing sec sec generation generation msec msec transactions transactions coupling includes thesis thesis thesis strings automatic coupled coupled variations grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar tests successfully straightforward society society effectively successful build tdnn essentially essentially refer contained issue content strategies duration duration list involved generalize generalize modular hypotheses hypotheses automatically deal presents presents diego poor create exhibit exhibit difficulty humans strengths strengths replaced recursive issues issues preliminary respond school school tech tech tech incremental combine relationships office office structured structured structured structured structured symbolic affect contours contours contours neu waibel waibel waibel waibel waibel waibel waibel possibly versions versions formal academic phd synthetic synthetic sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences devices languages great rows developing costs costs trivial publishers coded coded coded coded coded coded majority comparisons processed sys shared preprocessing forces constructing broad incorporate immediately immediately laboratories involve pitch pitch pitch pitch pitch pitch pitch pitch english english english toronto localized author annual mellon mellon addressed researchers questions improvements people evaluating carnegie carnegie substantially substantially elman elman tional spoken spoken spoken spoken embedded embedded lack effort effort effort completion completion incorrect incorrect rep rep rep operate vocabulary vocabulary mod mod mod pittsburgh differs differs differs cal acoustics acoustics acoustics acoustics substantial substantial tolerance tolerance tolerance tolerance tolerance tolerance tolerance tolerance utterances utterances progress sentence sentence sentence sentence sentence semantic semantic sharing sharing cor shifted corrupted primarily accomplished writing labeling labeling assign japan japan extensive tem printed printed extending spontaneous systematic promising siemens resulted resulted roles roles roles ral disjoint preparation preparation corpus clause clause clause clause clause clause phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase generalizes grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars constructive constructive hours passive evaluations analyses analyses utilized mance mance patient patient surprising perfor perfor pat moved conjunction lang enhance sim sim assembly darpa darpa smoothed smoothed tracker augmented augmented augmented augmented augmented augmented grammatical parse parse parse parse parse parse parse extensively relies statement statement papers papers papers insensitive assigns sequentially linguistic linked appeared parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing parsing ple numerous accept sig kluwer job forced pieces utilize utilize utilize par par comparative hundred big affects tor mars mars reject representa summarizes translated translated translated modifying exam cessing cessing grouped pdp gener file file file distant writer writer cole acquired gender ambiguous constructs translations covered associates distinguished register register rochester macroscopic programmed nal nil prevents atr exploited microscopic modal modal modal nec develops emphasis emphasis info gratefully functionality recogni recogni twenty marks send send send send terns ongoing phrases phrases phrases ers doesn aid bold interpreting mirror clauses clauses clauses jain jain jain jain jain jain jain jain jain jain jain pronounced exposed unreliable gram gram sen ples sym dog dog dog tended cur evolving syntactic syntactic noun crl experienced positional ance brackets acknowledges twelve tra semantics robustly tomita tomita catastrophic ated indi indi supposed rent verb verb saito saito saito localist spent marker putational tolerant tolerant tighter shikano inability fight ogi modifies mal constituents tics fanty fanty constructions constructions constructions registration registration registration registration copied coverage coverage coverage coverage coverage coverage coverage coverage coverage miikkulainen miikkulainen ranked writers parser parser parser parser parser parser parser disagreement parentheses contiguous syntax tebelskis tebelskis tebelskis ungrammatical exposition emphasizes brings hanazawa weeks transfor heads barnard barnard lexicon crafted interna chunk unambiguous freq freq ditional chunks tolerate tolerate detec misses misses ade straint ule testbed corp corp ful conversation dollars dollars participants ilar unsolved bolic carded semantically phi determin alphanumeric alphanumeric decouple founda parses parses parses telephony predicates irregularities enhancements ances disambiguate morning morning prep parsed adversely attachment recipient cates cates shelf elusive conversational subordinate geared ovals assemble tences expecta overwhelming 
#@Jain_A,
#t5
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#*network network network network network network network network network network network network network network learning learning learning neural neural neural neural data function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks algorithm number number system system state state results units units units units units units units units units units units units units units units units units units information problem problem problem problem models models hidden based based based space linear case case case case case case case vector vector order order order order order order shown systems systems probability noise noise weight functions functions functions functions functions functions neurons neurons unit unit unit unit unit unit unit unit method method approach approach pattern processing processing processing matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form simple paper paper paper examples small size size task methods step step step step step step step step step step step step step field level level structure high response similar similar representation representation architecture architecture section section general general general general real approximation theory theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained dimensional dimensional result result result result result result result result result university university university university variables variables computation computation computation found found target constant constant computer computer computer terms connections connections connections connections science science science science left presented phase activation activation low machine press press learn position components abstract properties references due positive positive positive positive positive positive positive positive positive important introduction complex dynamic dynamic dynamic generated generated generated generated parallel parallel parallel parallel parallel cost cost search search search energy energy energy energy energy energy energy energy energy complexity complexity variable variable assume assume rules rules rules theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound type type multiple represent represent represent represent represent represent represent represent represent represent represent distributed distributed techniques techniques techniques length length length length length correct correct finite finite finite minimum minimum human sum performed called means means means means optimization optimization optimization made made natural global global global global global global applications knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge negative negative negative negative negative negative negative original original original original original original original original original original original original original original original original original artificial specific represented represented represented represented represented represented represented constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected connected mit mit steps steps steps contrast connection proceedings proceedings proceedings proceedings report report institute department department technique technique advances represents represents represents represents represents represents represents represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist bias bias ai hinton hinton hinton solutions conference efficient full basic give con con con weighted area area area area area area area inhibitory constraint constraint constraint constraint constraint constraint constraint constraint simply technical technical increases arbitrary limited complete proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof common generate role role end ability instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance rumelhart rumelhart pairs needed needed hopfield hopfield hopfield hopfield special structures structures structures representing representing representing representing representing representing representing representing details details pre minimize minimize added discussed improve resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution property pair pair takes apply include machines quadratic trees inference inference sejnowski sejnowski sejnowski cognitive relevant chain chain symmetric symmetric symmetric symmetric symmetric symmetric symmetric exists exists exists exists exists exists exists exists parts concept occur matrices touretzky occurs setting setting setting row row row row row row row row row row row row row row row row row practice encoding hard hard hard intelligence intelligence assuming minimizing minimizing user start start minima minima minima force force base base base base base base base base base base base base base appears appears longer longer longer winner generating generating implement implement missing unique minimization minimization minimization minimization minimization formed national national national extracted family expressed expressed expressed expressed expressed viewed soft soft soft soft similarly similarly constants constants constants allowed allowed allowed allowed allowed sign earlier earlier earlier earlier performing purpose add valid valid valid valid valid valid valid visible assigned query query query query query query query query query query query query query query query query query box thesis inter instances instances instances instances instances instances instances instances instances instances instances instances assignment sciences illustrated prove activated characterized major planning reason columns columns columns columns efficiency capable society differ symbols symbols mcclelland mcclelland successful identity fine composed capture summary traditional compact allowing allowing link list list list list list relaxation paradigm paradigm binding binding binding binding attempt preferred preferred deal minimized optimized limitations helpful rest rest rest fault fault reliable symbolic proved proved cognition cognition opposite opposite opposite assumes logic logic logic logic logic logic logic logic logic logic logic ith consist phd wta wta wta wta wta wta wta indicating indicating rows rows rows rows rows rows rows rows rows rows rows preference formula answer answer sys satisfied satisfied satisfied satisfied constructing constructing constructing constructing pool pool potentially res res res meaning mellon fourth composite carnegie cmu capability lack peter share adjustable monotonic ordered collective collective adjust logical logical comments tolerance proposition proposition proposition proposition sharing trade proofs proofs proofs proofs proofs proofs proofs proofs proofs proofs proofs proofs proofs proofs intractable arguments resources smolensky smolensky smolensky clamped clamped clamped clamped clamped allocation tools satisfying imposed imposed imposed imposed check biased harmony reasoning reasoning reasoning reasoning reasoning reasoning reasoning clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause clause filled mjolsness washington peterson peterson peterson treatment ballard ballard ballard ballard ballard pollack horn specificity reverse implicitly explorations explorations explorations ball trading associations appeared microstructure microstructure corporation shorter ent graded emerge forced forced forced restrictions restrictions copy copy copy copy copy copy copy copy copy copy copy assignments massively pij continues activate allocated allocated allocated allocated allocated searches searches considers acquired spreading academy names names names names supports cubic permit bill signs signs signs behaves triggered copies satisfaction satisfaction slot slot slot slot prefer trainable converging slots slots bindings bindings bindings ron clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses inherently resolutions emerges resolved ory syntactic syntactic syntactic accommodate accommodate fol fol fol fol fol ready unusual pointer allocating platform violated dij dij formulas formulas ini ini ini ini cope cope subnetwork stan publishing preferable rij imposes meaningless putational tolerant tolerant literal literal literal literal literal literal literal literal literal literal literal cancel cancel cancel cancel sydney enforced ness inability inability plans constituents encourage parsimonious copied copied copied copied dana calculus calculus philadelphia philadelphia wired clamping clamping proving participate participate participate participate anandan anandan anandan penalties inconsistency inconsistency inconsistency canceling canceling canceling violation violation ending syntax syntax syntax syntax syntax syntax syntax grain allocate propositions propositions propositions propositions propositions propositions expressing compound nectionist resolving resolving resolving acknowledgment predicate predicate predicate predicate predicate predicate predicate predicate kij kij sketched revised stant dave cis pennsylvania weakened sept instantiated dan prefers negated dition structed wash intractability propositional propositional propositional propositional propositional propositional propositional propositional binds cancels atomic atomic atomic atomic atomic atomic atomic atomic atomic weakening weakening unification unification unification faulty shastri shastri shastri hartman hartman hartman nonmonotonic nonmonotonic anymore foun predicates predicates predicates predicates predicates predicates campus ablex louis plagued dations participates participates tency boltzman boltzman laxation undoubtedly deduction constr 
#@Pinkas_G,
#t5
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model input input input input input input input input input input input input data data data figure figure time time time set set set set training training training algorithm output output output output number number number error state state results results results results results results units information information information information information information information information models based based based based weights weights weights layer layer layer vector order order shown shown systems systems systems systems systems systems systems systems systems systems systems values values values values parameters parameters parameters parameters parameters weight weight weight weight weight weight unit approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point single single single single processing rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class form shows paper paper examples small work work work methods step step level level trained trained random similar representation representation representation representation representation representation representation representation show section fixed fixed parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter theory theory theory theory theory theory theory note note note note note experiments experiments experiments university university university research research target initial initial initial initial initial table table table table table table table table table table table table table table table computer terms terms terms terms science science prediction prediction left left present machine range press learn learn components basis abstract abstract abstract abstract back computational computational computational computational computational computational references references references important important propagation propagation generated parallel tion complexity complexity complexity complexity lower rules measure representations representations word word word word word word higher previous cases required required required multiple multiple multiple multiple multiple multiple multiple good good good binary binary long long long long long long long long long long represent distributed distributed make make techniques correct correct errors simulations simulations simulations simulations classes simulation human respect called times times times times times times times times times times feedback artificial relative represented represented desired series provide provide provide provide mit connection connection modeling proceedings institute words words department internal connectionist connectionist connectionist connectionist connectionist connectionist connectionist final final scheme scheme scheme scheme scheme considered framework framework framework framework framework cambridge cambridge computing domain domain hinton bit bit bit conference determine determine produce levels levels levels levels levels levels actual actual provided evidence evidence nature discussion discussion discussion describe arbitrary group denote predictions predictions predictions assumed assumed generate supported theoretical theoretical theoretical makes rumelhart rumelhart rumelhart rumelhart fit account technology testing edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge empirical language language language language language language language language details details numbers bits produced run added description description description description light light light light light light perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron separate takes takes takes reported include array cognitive relevant relevant volume tions studies modified generalized bounded bounded williams sensitive sensitive entire grant lead studied suggests alternative touretzky touretzky touretzky touretzky touretzky touretzky touretzky column setting setting setting conclusion minimal greater greater differences drawn averaged targets targets denoted acknowledgements reference reference appears digit longer index index index index index index factors factors factors factors primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary laboratory changing explicitly develop develop implies variation detailed forms understanding completely suggested suggested partial partial earlier epochs epochs epochs epochs epochs iterative iterative closed closed closed string string string string string string string assigned david david avoid assignment assignment characterized determining determining middle uniformly society differ computationally mcclelland mcclelland presentation identify vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel receives receives summary traditional traditional traditional refer refer kind kind interested quantity quantity quantity quantity quantity leading consisted consisted decreasing access difficulty detail accurately preliminary preliminary helpful examine school office referred encode cognition momentum examined examined concepts concepts psychology perfect ensure adjusted versions perceptton epoch languages languages languages languages languages languages languages languages languages languages languages languages crucial distinguish agreement phenomena adjacent adjacent analytical analytical expensive stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress processed perspective purposes potentially read arises demonstrates author author annual preceding preceding preceding mellon mellon mellon considerably carnegie carnegie carnegie syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable empirically empirically led incorrect summarized summarized measuring pittsburgh pittsburgh fall incorporating logical kinds kinds secondary secondary secondary secondary secondary secondary secondary secondary secondary proportion primarily oxford investigation arguments arguments arguments arguments ordering impossible impossible naval air fits consideration consideration significance significance tools contract occurring analyzing settings settings settings settings salient responsible modifications analyses analyses heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy heavy regarded overview conjunction buffer buffer buffer dominant dominant lawrence offers similarities foundations reveals reader refers ends erlbaum consonant captures characterization characterization characterization insensitive insensitive insensitive default default default default default default acknowledge counts learnable linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic linguistic corporation listed aircraft employs distinction additionally ease ease chapter descriptions england hillsdale avoided reflected var eric alter alter representa representa alternate alternate alternate alternate alternate alternate pdp learnability learnability learnability learnability learnability learnability learnability learnability learnability learnability learnability learnability learnability learnability hughes relate scope constructs constructs constructs constructs constructs termed termed termed refinement syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables avoidance avoidance avoidance avoidance avoidance exhibited permit manuscript develops simplification characterizing inconsistent inconsistent inconsistent inconsistent unbounded unbounded suffices devised devised dissertation ref ref ref ref ref placement phonology phonology phonology phonology sliding positional positional feasibility steve repeating sixth superscript superscript superscript superscript repeats hypothetical hypothetical hypothetical lips mate wheeler gupta gupta gupta gupta gupta gupta gupta gupta gupta gupta gupta gupta gupta tums thirty linguistics linguistics ies permitted french french french french french french french descriptive ences chine doctoral exceptions foot native dan exemplified mono alternation alternation alternation alternation alternation alternation alternation succeeding succeeding refinements mas jay feet feet feet feet feet feet feet noteworthy alt alt alt alt alt alt alt alt alt alt alt brian facilities invoking logically logically metrical metrical metrical metrical metrical metrical metrical metrical metrical metrical evans penultimate penultimate penultimate penultimate invoke indiana suggestive unlearnable unlearnable revision sachusetts blackwell hayes hayes hayes fresh fresh tertiary tertiary tertiary ious concisely unweighted nate thirteenth exceptional undoubtedly deduction brad 
#@Gupta_P,Touretzky_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning input input input input input input input input input input input input input input input input input input input input input input input input figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training output output output output output output output output output output output output number number number number number number system system system system system results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer case order order order order order shown shown shown shown noise functions unit unit unit unit approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single single single single processing processing control control control large patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class form form form form shows shows shows paper small small small size net net net net net net net net task step step step step step step step step step step step step step step step step step features features level level level level level level level level level current trained trained trained structure structure structure structure problems problems problems problems high high high high high memory memory similar architecture architecture architecture line general general general note note note note note note note note note note note note activity university threshold threshold solution sequence sequence sequence sequence standard computer connections connections connections connections connections connections connections connections connections connections connections connections connections science science prediction left left left left presented presented presented presented presented presented present activation activation object object object object object object object object object object object object object object object sets sets sets press components components components components components components abstract applied back back properties references due procedure procedure important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction dynamic dynamic generated generated generated generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel tion word word word word word word learned previous bound bound bound bound bound bound bound bound bound bound type multiple multiple multiple multiple multiple multiple multiple represent represent represent represent represent represent represent represent distributed distributed distributed distributed proposed correct correct correct simulations resulting classes ing total simulation human human human human human human human human human human called potential natural natural natural knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter artificial artificial specific represented represented desired provide provide provide perform perform perform perform perform related connected connected brain mit steps connection connection connection connection train source source source source source source source source proceedings department technique individual individual joint represents represents represents represents layers layers layers cambridge hinton hinton hinton conference conference determine full significant basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic types lines lines lines finally backpropagation backpropagation associative associative group group group group group group group group group tested common implemented generate generate generate role role role role role role role role role role role role role role role role role role role role role role role role role role role role role role role role role role role role rumelhart rumelhart rumelhart smaller reduced fully significantly mechanism consistent structures structures language language language representing representing numbers filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters direct direct direct direct direct direct direct direct direct stored international idea description predict resolution resolution resolution resolution ensemble ensemble ensemble ensemble ensemble ensemble takes similarity subject subject subject subject subject subject subject subject subject subject subject subject inference inference sejnowski sejnowski cognitive volume works works works trans address modified modified gate sensitive sensitive entire constructed constructed concept concept concept occur occur white occurs occurs conclusions competitive competitive differences differences differences faster learns encoding hard demonstrated california intelligence intelligence manner groups groups groups connectivity connectivity sequential laboratory distinct distinct changing simultaneously consisting develop events formed versus reconstruction reconstruction communication communication viewed interpretation transform open open open open open open open forms understanding understanding understanding activities similarly similarly slow sec closed closed closed closed advantages instances instances recognize recognize determines black black black black black successfully simplicity society driven mcclelland mcclelland mcclelland composed traditional traditional refer quickly quickly success classify content content content content content content content content content content content content content content content content content content content content content content content content content involved michael generalize binding binding binding binding automatically illustrates illustrates routing routing routing receive receive receive employed remain remain remain transformed replaced issues issues dotted dotted reducing respond links links links applicable applicable fault structured proper proper proper encode act act circles circles concepts plausible plausible reading reading man man man man man man man man man man man man man man man man man man man man man man man man man man man man man man illustrate store store store message message message sentences sentences sentences animal animal animal animal animal animal animal animal massachusetts indicating developing considerable implementing actor recognized circle read read read read read annual meaning meaning meaning reflects people prop items items items dark backprop item music music music music music music music music music rep operate operate spread differs singer singer singer singer enables tolerance sentence sentence sentence sentence sentence sentence sentence sentence sentence semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic classifying accomplished acts acts nat repre encoder encoder addresses connecting connecting connecting connecting connecting connecting grey grey proceed inspired hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit los transforms transforms roles roles roles roles roles phrase phrase phrase phrase phrase phrase phrase phrase phrase generalizes motivation passive ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity connect pat propagated propagated propagated propagated propagated lawrence lawrence tic enable ensembles ensembles ensembles thin refers refers properly properly arrows arrows arrows arrows arrows arrows storing route erlbaum erlbaum papers propagate alternatively ignore generalizing sequentially maintaining leaving largely ter achieving propagating restrictions par chicago associate associate hillsdale hillsdale reconstruct reconstruct musical musical musical musical musical musical musical modifying thick pdp pdp pdp pdp pdp pdp pdp pdp pdp pdp pdp pdp ization douglas parallelism exceed ambiguous deleted discusses placing placing retained det status stores stores stores stores stores copies resolve resolve resolve resolve terns phrases phrases phrases bindings bindings filler connects connects striking resolved dog dog dog dog dog dog dog dog dog dog dog dog dog dog dog dog dog dog dog destination destination destination destination destination destination destination syntactic syntactic syntactic noun noun noun communicate physically deter addressing ings skeleton skeleton verb verb verb verb verb verb verb verb verb verb verb verb verb verb verb verb verb dyer dyer dyer dyer dyer dyer dyer dyer lexical lexical ambiguities ambiguities ambiguities ambiguities subnetworks subnetworks subnetworks localist subnets retrieve angeles constituents enabled enabled constructions decides sequencing sequencing sequencing sequencing sequencing copied copied copied bind bind structuring agation meanings meanings meanings ronald oooo oooo oooo oooo oooo oooo oooo temporary fil reconstructing associating inferences inferences exposition opens opens opens opens opens opens ticular selector selector selector selector selector selector selector selector selector selector selector selector selector selector routed routed routed routed folded ware collectively opened opened opened opened eleventh accessed lan ucla binds permitting propaga resent suggestive guage hitting hitting oval oval ural jnowski paral plagued performer performer performer performer punishment resolves resolves detroit thirteenth jagged dressed 
#@Dyer_M,Sumida_R,
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#*network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural input input input input input data data data figure figure time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output number number number number number number number number number number number system system system system system system system system system system system error results units units units units units units units information information information problem hidden hidden hidden performance performance performance performance performance performance based based based based based based based based based based based based based layer values values values values values values values values values values probability parameters parameters parameters parameters parameters noise noise point single processing processing processing large rate rate test test test test test test test test test test test test test test test test test test test test test test patterns patterns analysis form shows signal signal signal examples small small feature feature feature feature feature feature feature feature feature feature net net net work features features features features features features features features features features features features features classification classification classification classification process trained trained trained trained trained structure structure structure random high high architecture show show fixed speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average average average average average average average average gradient gradient obtained obtained obtained obtained note experiments experiments result research research research defined sequence sequence sequence sequence table table table table estimate standard standard standard standard standard computer computer computer terms distance science science science science phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal sets sets sets sets sets sets sets continuous abstract find references ieee ieee important decision introduction hand hand hand statistical statistical statistical effect effect effect generated generated generated search change difference difference difference difference difference assume classifier classifier classifier classifier classifier classifier classifier classifier classifier representations chosen chosen part part center center long expected region length length probabilities errors forward ing total total total total total total total total total total total total total computed computed computed computed computed performed performed performed optimization natural natural applications knowledge original relative samples samples samples samples compared series determined connected connected connected discrete equal equal steps accuracy accuracy accuracy accuracy accuracy accuracy larger train train train train train train proceedings report institute institute institute department department consists individual final final final final final final sequences sequences sequences computing domain estimates estimates design design detection detection conference choice choice choice world basic derived derived conditional developed developed area provided provided provided selected selected selected backpropagation sampling discussion technical feedforward feedforward group tested tested tested tested supported end end development development development development development development development development objective objective pairs pairs pairs pairs needed coefficients coefficients coefficients fully fully fully technology technology interesting testing testing testing ratio ratio segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation database database language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language numbers numbers numbers pre pre window window window window window frame frame frame frame frame frame frame frame combined produced pair separate include include relevant engineering varying approximately approximately approximately speaker speaker speaker speaker speaker speaker background evaluation evaluation entire grant grant grant amplitude deviation deviation deviation deviation correctly feed boundary pass greater assumptions segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment differences differences differences designed peak peak performs performs performs sound presence presence presence characteristics labeled iii iii averaged identification identification identification identification identification identification identification identification identification identification identification identification program configuration acoustic acknowledgements longer longer longer longer solving segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments category category category category category category category category category unique spectral spectral spectral spectral spectral spectral quality quality variation variation variation transform transform evaluated restricted labels labels labels labels labels labels labels fraction fraction centers centers centered frames frames frames frames understanding similarly spectrum key measurements measurements measurements sec intervals iterative valid distances classified transactions recorded recorded activations inter inter inter inter inter automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic absolute columns determining middle identified computationally post vowel vowel plots tend ten characteristic capture capture capture capture refer contained contained phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic duration duration duration duration duration duration duration duration duration duration duration duration duration categories categories categories categories categories categories sampled absence absence cat consisted consisted american american detail mass fewer fourier successive successive successive reliable scores coarse man ensure noted noted observe speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers consist consist extent sentences sentences seconds seconds seconds languages languages languages languages languages languages languages languages languages languages percentage histogram rows stop stop stop stop stop waveform waveform waveform waveform waveform adjacent stress rapid sys filtered filtered broad broad broad broad broad broad broad broad broad broad broad broad broad broad broad broad pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch english english english english toronto auto nsf conjugate conjugate questions led led consistency spoken spoken spoken spoken spoken spoken conducted simulate experimentally lack effort passes vocabulary vocabulary occurrence occurrence occurrence occurrence occurrence occurrence occurrence occurrence acoustics comments viterbi deviations utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances lab aligned aligned feasible labeling ratios tem khz khz determination bands bands scoring mark utterance utterance utterance utterance utterance utterance utterance utterance utterance utterance preparation days days vowels vowels vowels analyses performances mance periods perfor male male male male overview darpa surprisingly tracker ends canada formant assigns linguistic discriminate unchanged crossing crossing incorporates pointing asked tween year year amplitudes female female female female associate attempted summarizes concentrated ftp ftp graduate graduate graduate intra cole cole cole cole cole cole cole cole proach rhythmic iri unconstrained sam oregon oregon oregon rose mix stops opti continued satisfactory identifies spacing inclusion japanese japanese japanese japanese japanese japanese distinguishing progressively progressively consonants consonants consonants consonants correctness frequent remained vicinity concatenated concatenated concatenated segmenting february durations durations durations durations durations devoted devoted microphone occurrences voiced voiced spanning mid months months mization segmental exploitation checked week week fanty ronald scored parentheses canceling cse tonal barnard barnard chinese chinese chinese chinese chinese chinese triples triples triples encouraged native native nasal dft dft dft silence silence pauses secs secs speak apple standardized public lan lan segmenter segmenter segmenter segmenter segmenter muthusamy muthusamy muthusamy muthusamy muthusamy muthusamy pled beaverton prosodic prosodic prosodic prosodic prosodic prosodic bigram locates suffered subjectively ternational matically guage guage abe gopalakrishnan ptp ptp ptp ptp dle conversational conversational oratory 
#@Cole_R,Muthusamy_Y,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural input input function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number number number system system error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results units units information information information problem hidden hidden performance performance performance performance based based weights layer layer case vector vector order shown shown systems values values values values values values values probability probability probability parameters functions unit method point single single single single single single processing processing control control control control large local rate rate test test class class optimal optimal optimal optimal optimal shows shows shows shows shows shows shows shows algorithms algorithms algorithms paper paper paper paper paper paper paper paper paper net work work task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task methods step step step current current current current current trained trained trained structure structure structure random similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation equation equation equation section section section vectors general parameter real states states states states states states states states states theory gradient obtained term note note result university university computation solution solution research independent independent independent log log defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics table table table estimate estimate standard computer distance science science direction present present present low low temporal temporal temporal temporal machine machine machine sets sets sets press learn learn learn learn learn learn learn learn learn learn learn learn learn basis basis abstract likelihood references stochastic stochastic due due due positive positive positive adaptive decision decision propagation introduction action action action action action action action action action action action complex complex dynamic dynamic parallel cost cost cost cost cost search tion tion difference assume assume assume rules prior learned chosen chosen part required required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple long long conditions conditions conditions distributed expected expected expected fact techniques correct probabilities scale scale finite finite finite minimum resulting resulting tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks simulation simulation simulation simulation sum performed performed performed performed called called called called times elements elements reinforcement factor made made applications policy policy policy policy knowledge knowledge relative represented true true compared desired desired desired desired desired desired desired desired define define location location location perform perform perform perform goal goal goal goal discrete mit connection update update train train train descent nets morgan report department consists internal advances connectionist connectionist connectionist difficult final final final final final final final final bias bias bias bias scheme graph graph graph sequences sequences sequences sequences sequences sequences ai cambridge cambridge domain environment environment environment environment environment hinton hinton solutions solutions solutions solutions solutions solutions curves transition transition trajectory san determine efficient efficient efficient efficient upper requires requires choice approximate statistics pages produce condition weighted randomly randomly randomly developed developed robot robot robot robot robot robot robot robot robot provided provided provided selected selected backpropagation nature discussion technical feedforward feedforward assumption actions actions actions actions actions actions actions proof short common assumed assumed supported require require require main journal ability future makes rumelhart rumelhart rumelhart including kaufmann objective objective dynamical unknown unknown jordan transfer transfer transfer transfer transfer transfer transfer programming programming trials details details details details pre bits bits bits bits bits bottom experts supervised supervised expert expert expert produced added description description predict architectures architectures directions advantage pair pair separate separate reported strategy period works module solve solve solve solve solve solve solve solve achieve achieve mixtures locations locations bounded williams sensitive grant grant constructed scaling trial trial trial trial move loop column starting starting depend depend editors editors reward reward reward reward reward differences sigmoid modules modules sutton sutton performs performs moody faster faster learns mateo propose taking external labeled labeled radial iii force denoted solving sequential sequential generating describes label distinct dept simultaneously simultaneously infinite involves text text formed formed agent agent agent agent agent agent agent agent agent agent agent agent agent implies competition national independently solved updated decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition converges barto barto barto performing closed intermediate assigned assigned foundation faces building building thesis thesis determines extension extension prove holds gating gating gating gating gating gating gating straightforward middle computationally mcclelland successful schemes identity reached receives receives traditional graphs contained contained return return gray satisfy list dayan dayan absence modular modular modular modular modular modular paradigm delayed highest illustrates jacobs jacobs jacobs jacobs jacobs jacobs receive receive extend simpler simpler simpler command command command access singh singh singh singh singh singh singh singh singh singh singh experience environments lippmann mass ideas rest incremental possibility office referred structured structured structured encode cognition illustrate created greedy portion panel utility submitted phd phd massachusetts massachusetts massachusetts asymptotically asynchronous sensors sensors navigation navigation navigation nowlan adapted constructing watkins watkins watkins watkins watkins watkins scientific projected projected projected projected acknowledgement separately separately separately separately demonstrates radius considerably composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite 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subsequences subsequences interacts composing ended augmenting augmenting augmenting augmenting augmenting touret envi payoffs tempo leftmost testbed concatenating concatenating navigational icant traverse ronment bachtach bachtach bed bed afb vironment preparing formidable indispensable ezplorations bolling perimeter ero quential 
#@Singh_S,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural input input input input input input input input input input input input input data data data data data data data data data function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number system system system system system system system error state state state state state state results results results results results results results results units units units units units units units units units units information information problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear layer case case case case case case vector order order shown shown shown probability probability probability parameters parameters noise noise functions unit unit unit unit unit unit method method approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern pattern point point point single processing control control control control control control large local test test test test patterns patterns analysis class class class class optimal optimal optimal optimal optimal optimal optimal form signal signal signal signal algorithms simple simple paper paper examples examples small size size size size size size feature feature feature net net net net net net net net net net net net net net net net net net net work work work work task task task task task task task task task task task task task methods methods methods fig step step step step step points points points features features features features features features features features features features features features features features features features features features features process process process level level level level level level level level level level level current trained trained trained trained trained trained trained trained trained structure structure problems problems problems problems problems problems problems problems random random random high similar representation representation representation representation representation architecture architecture equation section fixed fixed fixed line line general general general general parameter parameter real real real average average average states states theory theory theory theory gradient gradient gradient obtained obtained obtained obtained obtained experiments experiments experiments experiments result result result result result variables solution solution solution solution solution research research research research independent found found found found found sequence sequence sequence sequence sequence target initial initial initial table estimate estimate computer computer computer computer terms distance prediction prediction prediction prediction prediction prediction prediction presented temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine machine machine machine machine machine press press learn learn learn learn learn learn learn learn learn position position position nonlinear nonlinear abstract applied applied applied back back convergence convergence references stochastic stochastic due due due positive positive positive positive positive procedure important important important important important important propagation context context introduction complex complex complex complex complex complex complex hand hand hand statistical generated generated variance parallel search search search tion change change difference difference difference difference difference difference difference difference complexity complexity complexity complexity spatial measure signals representations learned learned learned learned center previous cases cases required required good good good good good long represent represent represent represent expected expected expected expected expected make make fact fact proposed proposed proposed length length length length length length errors scale scale scale scale minimum resulting resulting tasks total total simulation simulation human human human human human human human human human human human human human computed respect times times times potential dimension made natural applications applications applications study study study study study knowledge knowledge knowledge knowledge knowledge knowledge negative negative negative negative artificial relative relative relative specific true true application application application application application series goal goal goal connected equal approaches approaches approaches approaches steps steps accuracy accuracy accuracy comparison comparison larger larger larger descent descent nets nets nets nets nets nets nets nets nets nets selection proceedings words advances represents represents connectionist connectionist difficult final final final final bias scheme scheme scheme scheme scheme scheme scheme sequences sequences sequences ai additional additional top top full choice significant free world world world world world world world world world speed basic increase give give coding developed levels levels levels controller controller actual finally finally finally finally selected selected evidence nature nature nature nature achieved feedforward tested tested limited limited close corresponds corresponds actions predictions predictions predictions finding amount amount theoretical theoretical theoretical theoretical theoretical theoretical eds end end end end ability ability ability development development noisy including smaller needed needed combination fully interesting interesting interesting testing increasing increasing increasing head head special consistent empirical mode leads pre making experts experts supervised supervised supervised supervised supervised supervised expert expert expert expert expert expert expert expert expert expert expert expert early magnitude combined combined combined run added description description predict predict improved discussed improve advantage separate takes typical typical practical practical practical practical practical practical practical practical practical practical practical practical strategy strategy strategy strategy include identical side sejnowski recently relevant interest conventional teacher teacher teacher tuning solve match match correspond studies studies converge converge converge converge definition evaluation evaluation positions positions positions locations observation entire entire increased lead scaling scaling scaling occur occur suggests alternative alternative locally move move move move hybrid touretzky deterministic white white white white white white white white white white white occurs occurs generally setting hardware half strength strength starting starting place place row greater conclusions depend reward reward reward differences differences accurate accurate designed designed clear clear sutton sutton sutton practice learns encoding encoding taking strong strong strong hard largest intelligence labeled labeled labeled user user iii program program program program configuration base base base question reference explicit explicit appears appears appears appears longer ways factors plot sensitivity multilayer explicitly linearly linearly linearly linearly dimensionality scales scales develop adding adding quality quality quality quality quality quality yield squares squares learner learner solved detailed evaluate showed evolution forms completely converges converges reasonable combining roughly purpose intermediate intermediate intermediate intermediate advantages existing existing box weighting weighting assignment assignment black black black black black black black black black black black black absolute absolute structural columns identified capable capable successful situation procedures procedures strongly contained contained prob heuristic showing interpreted issue running strategies strategies strategies built built built built built built quantity bar simplified play play play play play play play play play play play play play play play play play play play play play play play play play play play play play dayan dayan absence minimizes board board board board board board board board board delayed leading reach reach predictor predictor predictor moves deal intrinsic intrinsic tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro oriented oriented situations situations situations situations minimized unlike carried overfitting overfitting overfitting experience experience environments humans humans detail game game game game game game game game game game game game game game game game game game game issues issues issues issues issues issues issues issues issues issues issues examine examine possibility decisions comparable phases phases notion examined smallest adapt necessarily thought detector detector store baseline improving simplest serial averages mentioned percentage great rows defining fairly improves answer benchmark benchmark worse worse handle handle reasons spatially purposes organized style day author qualitative sun addressed exemplars exemplars raw raw explained questions improvements improvements applies substantially empirically empirically lack poorly adjustable passed measuring limiting maximizes proven substantial sophisticated progress credit credit credit naive globally globally contribute contribute representative intractable primarily primarily labeling labeling guarantee modify discovery discovery discover outcome outcome outcome outcome outcome establish plays plays ments difficulties adjusting stated hope monotonically north intuitively intuitive hours games games games games games games games games games games games games games programs programs programs programs surprising guarantees sides sides demonstration consequences thomas reproduce winning winning late cpu cpu cpu properly inductive discovered cam material mechanical lem dramatically yielded ure appeared appeared ple outperform basically opposed preserving pieces pieces pieces encouraging encouraging utilize preferences preferences hundred workstation workstation pairing pairing backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon visited home home equality care favor favor exam ibm ibm ibm ibm formance formance goals blocking ijcnn guidance playing playing playing playing playing challenging confirmed player player win win win win harder apparently apparently apparently apparently stuck indication commercial commercial behave frey frey bill infinitely moderate remarkable remarkable algorithmic algorithmic consuming continued thousand wins wins wins overtraining overtraining overtraining played played eliminates ning month believed progressively ultimate nontrivial contrary spirit positional players tical assessed rem convey watson watson brought massive massive massive massive inappropriate decades nice prime prime fundamentally lookahead observes observes disadvantages heights examines inability won won men men men men men ply ply ply puter quiescent volatile strongest confirms scratch samuel samuel samuel samuel samuel standing earning earning mon gerald emphasizing emphasizing poorer weeks dam opening bigger crafted crafted crafted attack tly suc suc manage quadratically knowl race compar farmer yorktown couples supercomputer descrip speculate noteworthy noteworthy prospects advan checkers checkers checkers microsystems engaged decent decent decent ison judging judging imitating worthy conceivably interpolates laborious ces cessfully cessfully thinks tage surpass inforcement watching tactical ero spective nalysis parameterizes ascertained dicate surpasses 
#@Tesauro_G,
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#*network network network network learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set set networks networks networks networks training training training training training algorithm output output number system system system system system system system system system system system error error error state units units units units units units information information information information information information information problem problem problem problem problem problem hidden performance performance performance based based based space layer shown shown functions functions functions unit approach approach approach approach processing processing processing processing local local local local local test test form shows shows shows algorithms algorithms algorithms algorithms paper examples examples examples examples small small size size net net net net net net net task task task task task task task task task features classification process level level level level current trained trained trained trained structure structure structure random representation representation representation representation architecture architecture show rule general speech real real approximation obtained note note note result university research found sequence target standard standard standard computer terms terms left left left presented presented machine sets learn learn position position position position position components components abstract back find find find convergence references component due important decision decision propagation context context context context context introduction statistical parallel parallel parallel parallel parallel tion rules rules rules rules rules rules learned learned learned part part part part part part part previous good distributed techniques proposed resulting ing tasks tasks total human respect respect performed called called mapping feedback feedback global applications study knowledge original vol vol relative specific represented proc eye determined determined goal constraints constraints constraints constraints power approaches approaches nets nets nets nets nets nets nets nets nets nets selection department version consists code code advances connectionist connectionist connectionist connectionist difficult scheme scheme sequences maps directly additional view design conference determine free world world coding coding coding developed levels finally backpropagation backpropagation backpropagation denote amount nearest common implemented generate generate eds journal end future kaufmann kaufmann typically smaller character york york special consistent making making window window window window window international expert expert expert produced produced light discussed reported side side side side hierarchical trees relevant relevant relevant dimensions previously previously conventional solve solve solve achieve definition parts parts parts hybrid touretzky demonstrate conclusions neighbor designed moody practice practice propose propose hard integration presence external external characteristics relation pro sequential generating describes explicitly easy easy text text quality boolean select extracted independently independently review viewed approximations decomposition decomposition decomposition understanding sizes key key key reasonable epochs reduces intervals add advantages box figures includes thesis mozer mozer mozer structural major major simplicity determining determining middle capable divided symbols build characteristic characteristic characteristic characteristic characteristic success nips leading reach subsequent lippmann giving applicable symbolic symbolic symbolic cognition attributes attributes aspect der contributions indicating great advanced majority lies starts stress sections easier producing producing style style style style style cut inversion inversion inversion inversion inversion acknowledgement separately pitch pitch pitch pitch pitch pitch beginning beginning english recognizing explained pure consistency flexible peter marked passed music music music music music music music music music music music music music music compares psychological characterize cal replace germany windows windows windows windows gap don lab ear notes notes notes notes appearance harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic theories outcome lost ranges accepted overcome harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony observing belong responsible responsible phrase phrase composition composition meaningful overview offer augmented augmented clean rich passing broken dietterich dietterich consecutive approx geometrical shepard shepard piece solves creates july employs pieces abstraction comparative additionally personal decomposed demon musical musical musical musical musical musical musical musical cessing expand concentrate concentrate considers depicts ultimately guided relates employing importantly universit minor places refined treating students resembles tension regularities algorithmic institut todd todd doesn melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody integrates dissertation judged sions suffice bach bach bach bach bach bach bach bach bach bach bach bach bach bach bach alto alto era gmd edition voice locality sweep promise capturing skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton skeleton eighth eighth eighth ized experimented ira ira ira insert developments sung preventing lookahead fiir subtasks winter anticipate quarter quarter plain chorales chorales chorales chorales chorales chorales chorales chorales chorales chorales chorales chorales chorales chorales chorales chorales hild hild hild hild hild hild fruitful chord chord chord chord chord chord chord chord chord chord melodic melodic correspondingly taught taught seventh plex compose braun depen proaches proaches modulo strated octave ist manageable comparatively karlsruhe karlsruhe abstractions votes bernhard shed und obeying composing melodies melodies frg predecessors bakiri tackled neces discus stressed roger famous menzel menzel menzel menzel menzel menzel dozen veloped buffalo decisive happy happy needing conceived routinely uka uka uka sical isn friedrich keys wolfram stylistic augustin creative sixteenth fischer adhering hermann voices obeyed chosing 
#@Feulner_J,Hild_H,Menzel_W,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output number number error error error error error error error error state results results results results results results units units units units units units units units units units units units units units units units units units units information information information information information problem problem problem problem problem problem problem hidden hidden hidden performance performance performance performance performance performance performance based based based based space weights weights layer layer layer layer layer case order order order shown shown systems systems systems systems values values values parameters weight unit unit unit unit unit unit unit unit unit unit unit unit approach approach approach approach approach approach approach approach approach approach pattern pattern pattern point point single processing processing processing processing control control large large large large large local local local local local local local local rate rate rate test patterns patterns analysis inputs form shows signal signal algorithms simple simple examples examples examples small net net net net net net net net net net net net net net net net net net net net net net net work work work work work work work work task task task task task task task task task task step points points trained trained trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems random random random high high memory response response response similar representation architecture architecture architecture architecture architecture architecture architecture equation equation section fixed fixed fixed line rule rule general general speech gradient term term note note note note experiments experiments experiments experiments activity activity activity activity activity result result university computation computation research research found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics initial initial constant constant table table table table table table standard standard standard standard standard standard standard computer terms connections science science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction left direction presented presented presented map present present activation activation activation activation low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine sets range range range range range range range press learn learn learn learn learn outputs abstract back back back back back back back back back back back back back back find computational references important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation context context context context context context context context context context context context context context context context context effect generated parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change difference lower lower lower lower lower lower lower rules rules rules representations learned learned learned learned chosen part previous previous previous cases multiple long long distributed make make fact proposed length forward scale scale simulations simulation simulation simulation simulation respect called elements elements means means means potential made global global global global global global global global global global global global global global knowledge original original perform perform eye discrete approaches mit steps larger larger larger train descent morgan morgan proceedings proceedings report institute department version version version version version version internal individual individual individual advances advances represents connectionist connectionist difficult difficult difficult difficult difficult layers scheme scheme graph graph sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences cambridge domain directly hinton curve additional view view solutions san san conference conference determine upper upper upper upper upper upper full choice choice choice significant statistics statistics world speed basic produce randomly criterion path processes processes selected selected selected simply simply achieved technical feedforward arbitrary arbitrary tested tested corresponds corresponds complete complete supported require require eds eds end end end end end end instance instance instance makes makes rumelhart rumelhart rumelhart including including kaufmann kaufmann pairs smaller needed reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced fully jordan jordan testing significantly special principle principle representing details call call call idea idea run run added description description description description description description description description predict predict predict predict predict predict predict architectures architectures architectures property property robust reported moving include period identical side hierarchical hierarchical sense cognitive cognitive cognitive recently relevant relevant relevant sufficient varying volume volume axis axis smooth correspond achieve address modified interval interval interval williams williams williams williams improvement grant grant horizontal studied studied extended extended wide derivative predicted predicted alternative locally hybrid hybrid occurs occurs pass flow trajectories designed moody practice practice learns learns mateo mateo suggest propose external external turn targets connectivity attractor acknowledgements explicit explicit explicit relation produces longer longer primary sequential sequential sequential tuned vertical recall averaging linearly involves involves involves slightly unique scales scales scales scales consisting events events formed versus versus letters focus review review viewed controlled fraction constants constants constants constants constants constants constants key key earlier earlier smoothing epochs epochs epochs epochs epochs reduces neighborhood intervals intervals intervals event roughly sufficiently sufficiently symbol symbol symbol symbol symbol symbol symbol symbol foundation views avoid building building box contour determines determines discuss mozer mozer mozer mozer mozer mozer mozer mozer mozer phys structural major major regular selecting aspects aspects aspects identified society society symbols symbols symbols symbols symbols symbols included mcclelland mcclelland mcclelland successful successful situation situation essentially ten ten ten fine receives traditional compact compact repeated repeated repeated success split return contribution running running criteria hold notation involved sampled michael correspondence consisted consisted consisted consisted consisted illustrates illustrates operating carried powerful powerful powerful poor difficulty difficulty varied put relations relations relations involving involving involving strengths limitations helpful examine history reliable decisions stream tanh understand cognition removed examined induction induction induction induction generalisation versions versions freedom observe separated store attempts slowly slowly distinguish fairly waveform waveform waveform waveform failure cascade organized style style style style filtered constructing ran immediately potentially sounds involve pitch pitch pitch pitch pitch pitch pitch optimize attribute depicted annual annual preceding nsf researchers requiring requiring requiring evaluating double pseudo generic readily detecting passed incorporated slower music music music music music music music rep variant compares psychological span span span passes operate operate operate ture ture qualitatively adjust gave coherent comments coherence focused begins extreme realized gap gap gap gap gap gap gap gap benefit notes notes notes notes notes notes temporally temporally pick dynamically ordering discover discover discover nonzero smolensky fails fails fails abilities occurring intuitively phrase phrase phrase phrase composition composition composition composition composition composition reliably reliably periods james encountered paul mental bad colorado propagated propagated propagated reproduce recog foundations young smoothed smoothed smoothed smoothed master contact erlbaum pearlmutter pearlmutter broken variants variants designing insensitive limitation yielded compressed compressed microstructure incorporates basically ber gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps benefits alternating dec nition pieces pieces pieces connec trigger trigger trigger trigger acceptable ical hierarchies descriptions descriptions hillsdale imagine representa avoids musical musical musical musical musical musical musical musical musical musical schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber mathematically permits boulder march books flip parallelism multiscale multiscale multiscale multiscale multiscale multiscale multiscale iri rough sketch constructs spanned drawback apparently minor tune drops holding exploited struc struc examination simplifies failures failures wider continually pineda pineda unpublished challenge manuscript excess handling twenty institut quantify mcdonnell assistance european phrases phrases phrases phrases phrases phrases phrases phrases phrases suffers attempting melody played award burr burr sharply optima devised concert concert rohwer tended zipset zipset bach informatik cascaded chunking presently bradford concatenated merged trend indirectly counted replication eighth eighth experimented spanning instant instant investigator technische inserted miyata miyata marker marker marker intrinsically ton putational resentation modulating bird scribed ascending ascending intervening intervening intervening terminated munich neti neti consensus distinguishes lacking devise indistinguishable overfit presidential ration compose periments news contingencies contingencies contingencies contingencies contingencies contingencies progression triggers replications replications hin ger melodies tape compositions compositions compositions walks detectable upwards complez descrip folding listeners sacrificing folk ual devising domly fki muenchen facilitating depicting compactness cially chromatic mathis reduc marginally revisited revisited individ contingency glance sical impression keys interrelated wander espe ezplorations responsiveness accom blended framed hardy ici 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#@Mozer_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks algorithm output output state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results units units units units information information information information information information information problem problem models models shown systems systems systems systems systems values values probability probability parameters noise weight neurons approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single processing processing processing processing control control large test patterns patterns patterns patterns inputs inputs inputs inputs inputs inputs signal paper paper small small net net net work work features features process level random high high high high memory memory memory memory memory memory memory memory show equation equation section rule rule general general real average average states states states states states states states states states states note activity activity activity result university threshold threshold threshold threshold threshold research research found sequence sequence sequence sequence sequence sequence dynamics initial initial standard standard computer terms distance connections connections synaptic synaptic synaptic present present present present present phase low low low frequency temporal temporal temporal temporal sets range basis abstract computational computational properties properties references stochastic important decision introduction complex complex complex complex behavior behavior behavior behavior effect effect effect effect effect dynamic dynamic dynamic generated parallel change change change change change assume lower measure chosen chosen chosen higher center firing firing firing firing firing type type binary conditions conditions conditions distributed equations probabilities observed observed observed simulations simulations ing simulation simulation elements elements elements elements elements elements elements means means factor factor potential made global study filter vol relative relative relative relative relative relative represented proc location eye eye determined gain motor motor brain brain equal steps steps steps steps larger contrast connection connection dependent dependent dependent dependent dependent dependent dependent modeling modeling institute department department consists consists individual difficult graph sequences sequences sequences sequences sequences sequences sequences sequences sequences ai cambridge transition transition transition transition san effects effects effects significant significant significant basic basic increase give produce area types types types lines lines path finally processes processes depends biological biological associative associative discussion close stable actions finding amount amount effective effective supported main main main eds cluster cluster cluster degree degree makes development including including simulated simulated simulated simulated simulated fully technology interesting ratio ratio character york york mechanism mode operation stored normalized neuronal neuronal membrane membrane membrane discussed recent correlations property property property takes movement movement reported cognitive cognitive cognitive cognitive cognitive relevant varying observations approximately volume works works tions yields correspond studies modified channels interval sensitive grant exists intensity intensity loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop clusters occurs generally demonstrate assumptions hebbian trajectories conclusions depend central interactions interactions sutton sutton sutton sutton sutton suggest mechanisms integration external external external external cycle cycle california exist exist exist denoted acknowledgements areas boltzmann longer ways factors sequential sequential generating plot plot plot laboratory transitions transitions transitions stability unique unique unique unique consisting consisting potentials decreases yield review correlated overlap overlap overlap overlap overlap detailed detailed fraction evolution centers modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation forms understanding activities suggested diagram reasonable delays generation generation remains intermediate initially initially construction foundation priori usa dominance inter memories memories memories memories memories memories memories memories memories extension coupled coupled variations holds partially characterized aspects presentation excitation road soc kind induced induced induced interested running timing sci duration duration absence absence absence neurosci neurosci principles intrinsic decreasing cowan remain remain wiley essential updating updating updating involving involving humans association dotted dotted rise school behavioral plasticity plasticity relationships relationships relationships referred reliable complicated affect notion analogous examined examined transmission possibly rev rev rev ensure bifurcation bifurcation nervous mixed motivated attempts integrate massachusetts burst improves caused baum considerable rapid rapid perspective desirable acad medical fluctuations fluctuations apparent apparent apparent greatly behaviors populations reflect embedded parameterized item schematic span release mod perturbations modulated asymmetric hamming logical kinds boston decreased decreased neuro attraction physiol begins instantaneous discontinuities discontinuities uncorrelated college college sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep arranged consideration loops loops loops loops loops loops loops loops balance contract occurring affected overlaps sompolinsky sompolinsky edelman induce induce induce induce overview sim bases darpa francisco foundations bursts bursts bursts rich epsp harris harris influences onr outlined linked associations cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic neurophysiology shorter basically basin opposed encodes alternating revealed diverse convenience superimposed affects hillsdale wake wake wake wake wake wake wake wake wake insights generators generators generators elementary neurophysiological neurophysiological intra intra simplifying altered altered investigating anal article correlate tonic tonic tonic locomotion bursting bursting bursting characterizing characterizing tial mcdonnell char harvard progressively sloan inspection dopamine marder marder confined absent cho fidelity fidelity resultant inducing inducing handbook brackets brainstem brainstem brainstem nih pin carrying cyclic modulatory modulatory modulatory prominent selverston selverston rem rem rem rem rem rem rem rem tory tivity spent repetitive disorder disorder disorder tightly pew remarkably dominate kanter kanter kanter warrick warrick sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing sequencing lasting mediate bifurcations bifurcations bifurcations cued cued cued pot epsps asso facilitation poo poo poo invertebrate neuromodulation neuromodulation neuromodulation neuromodulation lose cog widespread accord lowering highlight ulation readers klein highlights repertoire fund identifiable progression occasional resembling manifest serially pected gutfreund hypersurface neuromodulators neuromodulators neuromodulators phasic phasic persist adam jeffrey amplify kandel kandel education mountcastle bethesda transi neuromodulatory annu dream balances tude garcia ciated whitaker whitaker mezard mezard hawkins warren serotonin serotonin orderly orderly istic matically eff progressive progressive implicated implicated initiating asterisks occipital delineated ett ett acterized psychiatry motivating geniculo dra plicity formations locomotor modula 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#@Hobson_J,Mamelak_A,Sutton_J,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number system system system system system system system error error error error error error error error error error error error state state state state state state state state state units units information information information information information information information information information information information information information information information information information information problem problem problem problem hidden hidden performance based based based based based based based based space case case vector vector vector vector vector order order shown systems systems systems systems systems systems probability probability probability weight weight weight weight unit distribution recognition method method method method method method method method approach approach approach approach point single single processing processing processing processing processing processing processing processing control local local local local neuron test analysis analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper size net net net net net net net net net work task task task task task methods methods methods methods methods step step step step step step step step step step step step level level level level level level level level level level level level level level level level level level level level level level current current current current current current current trained trained structure structure structure structure structure problems response response similar similar similar representation representation representation representation representation representation representation representation architecture architecture show section section section section fixed fixed line line vectors vectors vectors general generalization speech real approximation theory theory gradient gradient gradient gradient term term term term term term note experiments experiments experiments experiments experiments university university university university university university university university university computation computation computation computation computation computation computation computation computation research research research defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target target computer computer terms connections science science science science science science science science prediction prediction prediction prediction prediction presented activation activation activation activation low temporal temporal temporal temporal temporal temporal machine press press learn learn components basis outputs continuous continuous continuous continuous continuous abstract applied back back back back back back computational analog references component due ieee ieee procedure important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation context introduction introduction introduction action complex complex hand dynamic dynamic dynamic parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent complexity complexity complexity lower lower rules measure signals representations representations representations representations learned learned higher higher higher higher higher higher higher higher part part part part center previous previous previous previous previous previous previous previous required required long long represent distributed distributed distributed distributed expected expected proposed proposed observed observed observed errors forward scale finite ing ing tasks tasks tasks tasks multi multi multi multi multi multi sum performed times elements means means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement potential potential potential potential global applications applications artificial artificial relative relative compared compared application desired provide define rates proc proc perform experimental goal related related related constraints motor discrete equal approaches mit steps steps steps steps steps contrast connection connection update update update update update update update train descent dependent nets nets nets nets nets morgan morgan morgan morgan proceedings proceedings report report report report report report report report report report report institute department loss version technique internal internal internal internal internal internal internal internal internal internal advances advances advances joint joint represents connectionist connectionist final final final delay sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences considered considered cambridge equivalent experiment environment hinton view limit san san san san san san stage bit conference conference conference efficient efficient free basic pages pages pages pages pages pages pages pages levels levels levels entropy simply associative associative technical technical technical technical technical technical technical technical technical technical feedforward describe tested fast fast limited predictions predictions predictions predictions proof finding short short implemented supported theoretical require journal instance makes rumelhart rumelhart development sensory including kaufmann kaufmann kaufmann kaufmann pairs needed needed reduced reduced reduced reduced reduced reduced reduced fully fully jordan technology increasing mechanism structures principle principle principle principle principle principle principle operation language details details details call numbers iterations pre window international international international supervised supervised supervised early attention produced description description predict predict predict predict predict predict predict predict denotes denotes architectures improve improve recent recent recent exact practical practical moving hierarchical hierarchical hierarchical hierarchical cognitive cognitive recently relevant relevant engineering highly previously conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional unsupervised volume volume volume works solve solve solve correspond observation williams williams williams williams williams williams improvement storage grant grant parts lead concept occur extended extended extended predicted predicted alternative correctly feed touretzky touretzky touretzky deterministic deterministic occurs runs strength critical critical place trajectories trajectories editors editors editors editors editors editors performs moody moody mateo mateo mateo strong external external external external california california intelligence turn start targets manner acknowledgements longer sequential mathematical dept dept changing confidence implement explicitly unique unique unique unique develop events events events events events events implies expectation review communication influence detailed updated organizing approximations decomposition completely updates past partial earlier earlier delays reduces event event event event event event event event generation construction construction foundation kohonen expect building existing box thesis thesis activations usa strings strings strings bell weighting weighting assignment assignment assignment memories memories memories automatic automatic mozer mozer mozer mozer mozer mozer mozer mozer grammar major planning compression compression compression compression compression compression compression compression compression compression efficiency society paths paths driven driven mcclelland build miller receives quickly quickly kind kind procedures procedures interpreted interpreted interpreted contribution sin running sci sci device comp comp involved michael giles delayed computes computes predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor principles overlapping deal receive receive receive receive situations remain unlike carried diego diego diego create create updating rise fewer fewer fewer fewer fewer fashion fashion fashion history history history history history history history history history history history history ideas ideas tech incremental incremental possibility referred working workshop hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy waibel induction editor necessarily man predicting automata adjusted adjusted adjusted versions formal algo separated ith improving utility serial phd defines defines massachusetts mentioned mentioned great crucial publishers failure caused starts processed sys ring ring ring organized forces forces worst potentially beginning beginning lowest auto auto annual nsf addressed explained behaviors prop elman fed fed fed autonomous psychophysical employ slower formulated formulated treated music rep robinson extracting incoming occurrence boston boston comments focused lim credit credit credit yielding univ don college college college redundant redundant modify rithm resources reconstructed addresses lost fails stronger difficulties adjusting adjusting accepted accepted accepted accepted occurred occurred occurred occurred hope mark removing monotonically north modifications carry carry composition meaningful ensures predictors predictors predictors james holland buffer buffer washington colorado colorado colorado colorado reproduce advance pollack pollack master matter theoretically theoretically environmental informative informative storing erlbaum erlbaum pearlmutter discovered discovered alternatively ignore ignore market lag outlined ics discriminate compressed shorter dec failed forced forced distinction distinction exception acceptable ideally amherst personal decomposed hundred hierarchies descriptions descriptions descriptions descriptions descriptions descriptions hillsdale hillsdale imagine mismatch mismatch publication publication publication publication schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber epsilon goals tems shannon werbos pdp gas disadvantage disadvantage boulder boulder boulder switched spreading multiscale iri employing drawback emphasized happen elsevier knowing knowing lippman lippman nal continually pineda unpublished coming stops reinforce bridge simplification institut justified mcdonnell thousand ongoing austin hoc suffices award sensorimotor medicine proposal practically contributes rohwer zipset zipset rtrl predictable predictable predictable predictable iid safe informatik chunking chunking chunking chunking chunking chunking chunking chunking rel crl teaching creation attended lags differentiate focusing focusing episode tenth texas eighth convey enabling unexpected unexpected unexpected unexpected unexpected unexpected unexpected discriminating ambiguities technische simula miyata fallside miss fiir conveyed reviews recursire pursued mike cued ative myers conveys aware miinchen theor bptt bptt exclude recur melodic quences confused conducting unambiguous unambiguous unambiguous unambiguous unambiguous unambiguous unambiguous linden hierarchically resentations bucket nical hochreiter hochreiter concatenation draft predictability paragraph prin criticism collapse collapse thereof instabilities instabilities tempo sive remedy ccs ccs brigade complez pression infeng collins critics critics critics northeastern northeastern kindermann commu peng unpredictable kangas inns inns collapsing collapsing collapsing mathis josef josef organi waste hierar unlearnable campus mismatches emit resembled stylistic nication augustin suffixes imperial wandering curred threefold 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data function function function function function figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm output number system error error error error error error error error error error error state state state state state state state state state results results results results results results results results results information information information information information problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models hidden performance performance performance performance performance performance performance performance performance performance space space linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case case shown shown shown shown shown systems systems systems systems values parameters parameters parameters noise noise weight neurons unit approach approach single single processing processing processing control large large test test analysis analysis analysis class class class matrix matrix inputs inputs form form form form form form signal simple simple paper size net net work work fig fig fig fig classification process process process process process process process process process trained trained trained trained trained structure problems random random similar representation representation representation show equation section section section vectors general generalization generalization real approximation average average average average average average average average average states theory gradient obtained term result university university computation independent independent initial constant table table table estimate terms terms terms science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction object sets sets maximum range range press press components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample abstract applied back analog properties properties references stochastic stochastic stochastic ieee positive procedure important important propagation introduction complex behavior statistical statistical statistical effect effect effect effect variance parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion difference difference complexity lower measure measure chosen part previous previous previous previous previous previous previous previous previous previous cases type type good good distributed markov markov techniques proposed proposed errors forward forward minimum classes total total total total total human sum mapping made made made natural feedback applications applications applications knowledge negative original vol compared compared series series series series series series series series series series series series series series series series series proc proc determined discrete power power power power power power power power power power power approaches mit accuracy accuracy comparison larger larger larger larger larger descent dependent dependent nets modeling modeling modeling modeling modeling modeling modeling modeling report internal advances difficult cambridge equivalent hinton estimates estimates design determine determine full choice choice approximate statistics world give conditional conditional levels types types types types product product actual finally processes processes processes processes backpropagation nature depends normal technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward tested limited inverse assumption complete predictions predictions predictions predictions predictions predictions predictions predictions predictions amount amount amount main eds square square square square square square square square ability ability future future future future rumelhart rumelhart including fit typically reduced unknown coefficients fully fully fully testing significantly significantly significantly increasing special details pre pre making experts depth added added added light light light predict predict predict predict predict predict predict denotes improved discussed improve advantage practical moving moving moving moving moving moving moving trees engineering interest interest highly observations observations observations observations observations works works smooth smooth achieve trans diagonal observation observation observation bounded williams williams williams entire entire constructed constructed predicted predicted predicted predicted predicted predicted predicted feed feed touretzky occurs occurs conclusion critical greater depend differences differences sigmoid measures peak peak peak peak asymptotic temperature temperature temperature temperature temperature temperature temperature temperature sound sound sound sigmoidal minimizing exist plane configuration base denoted acknowledgements written written winner ways laboratory laboratory dept dept modeled modeled modeled modeled modeled infinite infinite electrical involves predictive springer competition competition competition competition competition competition national national focus expressed expressed review depending stationary stationary solved transform approximated past past past past past past spectrum spectrum key earlier earlier roughly initially construction foundation advantages advantages box box illustrated partially discussions included included wij literature comparing plots tend summary traditional traditional verlag prob link superior superior superior superior lie running built built predictor predictor predictor predictor consisted load load load load load load load load load load load load load load load load load load load load load load load layered poor overfitting investigate experience varied accurately accurately accurately helpful int int working predicting predicting predicting illustrate noted noted algo perceptton multivariate simplest submitted established years years mentioned residual residual growth growth analyzed failure caused handle comparisons inside purposes sections day day day day day day day day day day day day day day circle preceding explained requiring apparent apparent percent limits profile profile profile lack peaks mod mod ture reaches monotonic extensions suited gave gave enables electric electric electric electric summed summed summed phenomenon identifying accomplished martin martin martin martin martin martin rithm impossible interconnected interconnected turned los los obtaining mark predictors negligible washington washington washington washington forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting nonlinearities nonlinearities nonlinearities express record robert temperatures temperatures temperatures zipser zipser yielded corporation ter ter listed listed outperform equivalently july july year year year par residuals residuals residuals residuals residuals descriptions descriptions avoided trends distant oct march march douglas relate concentrate interactive represen figs lapedes lapedes els els mini supporting continually november observables january august august demand demand marks attributed invertible invertible invertible adaptively outperformed hour hour hour hour hour hour hour hour hour seattle seattle seattle seattle exposed possess substitute autoregressive autoregressive autoregressive autoregressive loads loads loads loads loads loads loads loads loads loads squashing squashing daily company company company cold cold cold tations poles alamos alamos devoted stationarity atlas atlas atlas atlas atlas atlas atlas sponsored severely connor connor connor connor connor connor connor connor farber farber predic virtue mum save nondeterministic nondeterministic invert inability won week week week week week week availability availability enabled winter winter winter winter winter parsimonious parsimonious parsimonious sible rosenblatt ponents arma arma arma arma arma arma arma arma arma mexico indicative succeeded ner casey backpropaga diction lesser constrains forecast forecast forecast les danger vious acute holden nar nar sharkawi morning morning lel spell spon nem brace brace tempera por jerome petition autoregression weekly 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning model model model model model model model neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data function time time set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output number number number number number number number number number number number number error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results units units units units units units units information problem problem models hidden hidden hidden hidden hidden hidden hidden hidden performance space weights weights weights case case case vector vector vector vector vector order order order order order order order order order order order order systems values values values values values values probability parameters weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method method method method method method approach test test test form shows shows algorithms simple simple simple paper examples examples examples examples examples examples methods step process current current current current current trained trained trained structure random random random random random random random response representation architecture fixed vectors real approximation approximation approximation states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained experiments result university threshold threshold threshold threshold threshold threshold computation computation computation solution solution research research defined defined found found found found target target initial initial initial initial initial table table table table table table table table table table table table table standard science science science activation activation low low low low sets sets sets sets sets sets sets continuous abstract applied convergence references component positive positive decision decision propagation introduction complex hand effect effect dynamic recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search complexity measure measure chosen chosen higher center cases type required long long conditions conditions conditions correlation length length length length length length length length length length length length length length length length length length length length correct correct correct correct correct correct correct correct correct correct correct observed observed errors errors errors errors errors errors errors forward finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite minimum minimum resulting ing ing total total total computed performed performed made made made made made made made made global study obtain negative negative original vol represented desired compute compute perform experimental constraints power accuracy accuracy accuracy accuracy accuracy comparison larger contrast connection connection update descent morgan proceedings proceedings report report report institute loss consists advances joint connectionist final final final final addition considered considered domain experiment experiment additional additional transition transition transition transition bit conference conference approximate free pages pages pages condition weighted randomly developed criterion finally selected selected depends sampling technical technical increases arbitrary tested tested tested tested tested tested complete complete complete complete complete complete finding finding short require end end including including kaufmann probabilistic pairs smaller needed needed reduced dynamical fully testing increasing language language language language language language language language language language language language language language language language language language language language language language language language language language language squared iterations iterations iterations iterations iterations iterations iterations international international added predict element reported identical inference inference cognitive cognitive cognitive sufficient sufficient approximately tions sparse address definition definition generalized interval williams williams williams amplitude lead correctly correctly correctly correctly correctly correctly correctly correctly correctly correctly move move touretzky width width deterministic generally starting minimal minimal minimal minimal minimal minimal minimal row greater greater conclusions differences differences constrained demonstrated labeled labeled acknowledgements reference reference reference appears longer longer index label changing infinite slightly extraction extraction extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted interpretation interpretation interpretation showed lee lee lee completely similarly partition partition partition partition partition discrimination key intervals initially sufficiently sufficiently sufficiently string string string string string string string string string string string string string string string string symbol symbol symbol symbol symbol symbol symbol construction recorded recorded strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings recognize recognize uncertainty uncertainty uncertainty characterized characterized successfully uniformly society symbols included included included included included included included mcclelland mcclelland mcclelland mcclelland successful miller reached reached receives road road induced induced induced induced induced heuristic running vary generalize backward backward giles giles giles giles giles giles giles giles giles giles received receive minimized powerful varied optimized optimized optimized optimized optimized mse mse mse mse mse mse mse mse mse mse investigated investigated ideal dependencies decisions oscillation oscillation induction induction induction induction induction induction induction hill editor automata automata automata automata automata automata automata automata automata recognizer obvious mapped languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages percentage percentage histogram histogram histogram histogram histogram histogram histogram histogram adjacent caused starts starts starts processed widely potentially recognized recognized recognized recognized separately recognizing sun sun fourth led elman elman elman peaks remove summarized summarized summarized mod mod differs extracting extracting extracting chen chen chen chen tolerance tolerance tolerance tolerance tolerance converged sharing college princeton princeton perfectly perfectly perfectly perfectly null null null bin partitions partitions repre outcome climbing communications accepted accepted siemens odd odd automaton automaton mark fail generalizes corre induce surprising lang intended lengths consequences initialize initialize creating pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack record record grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical interestingly dividing empty ics dense speaking truncated listed listed listed listed accept accept accept accept rejection failed failed failed corrected reports recurrence pairing reject reject reject reject constrain constrain mathematically uncertain fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa ambiguous ambiguous covered covered indexed nal recognizers recognizers continually strict ucsd fiat opti opti sponding externally corporate east termination termination termination termination termination incorrectly injected acoustical believed sparsely seed seed seed seed seed seed seed seed seed seed seed seed seed seed seed seed seed zipset zipset zipset america watrous watrous watrous watrous watrous watrous watrous inducing inducing schreiber schreiber schreiber approached raised tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita tomita occurrences cleeremans cleeremans servan servan kuhn kuhn kuhn kuhn kuhn kuhn kuhn responded sented insert completeness mization ohio lowered acceptance terminated solu ages corresponded abs accumulating ungrammatical ungrammatical fell jour critically raymond succeeded subdivided subdivided seeds seeds seeds concatenation gary lan ume discussing byte cated succeeds mized collapsed collapsed marking ida bfgs marginally truncating tomira wrongly mans mans tomata 
#@Kuhn_G,Watrous_R,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input function function function function function figure figure figure figure time time time time time time time time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number number number number number number number number number number number number number number number number error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information problem problem problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance based space space space space space space space weights weights weights weights weights weights weights weights order order order order order order order order order order order order order order order order order order order order order order order order order shown shown systems values values values values weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit recognition recognition method method method method method method approach pattern large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate class class matrix inputs inputs form shows algorithms simple simple simple simple simple simple paper examples examples examples small small small small small small size size size size size size size size feature feature net net net net net net net net net net net net net net net net work work work work work methods methods methods methods step step classification classification process process process process process current current current current trained trained trained trained trained trained trained structure problems random similar similar representation representation representation representation architecture show show show show equation line rule rule rule general generalization generalization generalization parameter real real real states states states states states states states states states states states states states states states states states states states states states theory theory theory gradient gradient obtained note note note note note experiments dimensional university university computation computation computation computation research independent independent independent independent defined defined defined sequence target target target dynamics initial initial initial initial initial initial constant constant estimate standard standard computer connections node node prediction prediction prediction prediction presented presented machine machine machine machine machine sets sets maximum range learn learn learn sample sample sample abstract applied computational computational references due positive positive positive positive positive positive procedure context introduction introduction introduction complex dynamic dynamic dynamic generated generated generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion tion change complexity complexity complexity complexity complexity assume rules rules rules rules rules rules rules prior representations learned learned learned learned learned learned learned learned learned learned learned chosen chosen higher higher part part previous cases cases cases good good good good good long long long conditions conditions conditions represent represent represent tree distributed expected make fact techniques techniques length length length length correct correct correct errors errors errors finite finite finite finite finite finite finite finite finite simulations ing ing ing ing total called called regions regions regions mapping mapping mapping mapping mapping mapping made natural natural feedback orientation applications knowledge knowledge knowledge knowledge em obtain negative negative negative negative negative negative negative negative vol vol vol vol vol vol vol vol vol true desired desired define define define define define determined experimental experimental connected discrete discrete equal power power steps update support train descent source source nets nets nets nets nets nets nets morgan proceedings proceedings institute institute version consists advances joint joint represents connectionist difficult final final final final layers scheme addition maps maps considered considered computing equivalent equivalent directly directly transition transition transition transition san conference conference capacity capacity efficient full full full requires choice choice choice free give give give con con randomly randomly clustering clustering clustering product finally discussion discussion increases increases arbitrary tested assumption complete complete finding finding role theoretical theoretical journal end end end end hypothesis hypothesis easily easily makes makes kaufmann reduced reduced dynamical unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown fully fully interesting interesting character character character special language language details call numbers numbers numbers pre international international supervised choose similarity reported apply quadratic inference inference inference inference inference inference inference inference inference inference interest tions yields studies converge converge converge definition bounded bounded williams williams williams constructed constructed constructed exists exists exists expression derivative correctly loop deterministic deterministic clusters clusters occurs occurs demonstrate runs runs runs starting minimal minimal minimal minimal minimal minimal minimal row conclusions valued sigmoid measures practice learns learns mateo strong hard physics assuming assuming start start start exist relationship derivatives derivatives manner minima program program question appears pro pro pro pro construct longer generating generating transitions transitions transitions distinct dept pruning easy unique unique unique minimization minimization minimization formed extraction extraction extraction extraction extraction extraction versus versus cycles decreases extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted independently focus viewed detailed lee lee lee lee lee lee lee lee lee lee lee lee sizes partition partition partition partition partition partition partition updates diagram diagram partial dashed epochs reduces add sufficiently string string string string string string string string string string string string symbol symbol figures figures figures priori strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings batch batch extension illustrated discuss partially discussions grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar successfully regular regular regular regular regular regular regular regular regular regular aspects capable mcclelland wij presentation comparing miller miller miller miller miller miller miller reached summary prob heuristic classify running criteria criteria vary simplified generalize giles giles giles giles giles giles giles giles giles giles giles giles giles giles giles giles giles giles giles computes extract extract extract acknowledgments minimized minimized minimized minimized minimized minimized minimized minimized minimized production production production production production production production put put put detail recursive preliminary hall discriminant helpful reducing incremental terminal possibility authors authors momentum analogous neu induction induction smallest reading automata automata automata automata automata automata automata created created perfect perfect perfect perfect formal formal noted separated epoch epoch epoch epoch generates languages languages advanced fairly fairly fairly fairly fairly explanation capabilities capabilities independence baum tool nonlinearity starts arc constructing circle sun sun sun sun sun sun sun sun sun sun outer elman elman elman capability readily dots ity partitioning partitioning extracting extracting extracting extracting extracting extracting extracting extracting ordered ordered chen chen chen chen chen chen chen chen chen chen chen chen chen chen chen chen chen chen chen chose tolerance tile converged converged wesley wesley don representative classifying room college redundant addison equivalence equivalence forming modify princeton acm perfectly labelled partitions partitions partitions connecting establish fails smith smith smith accepted accepted city automaton automaton interpret fail krogh alphabet grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars hertz hertz filled prentice excellent excellent mance surprising perfor lang washington evident lawrence branching branching dif dif darpa recog infer mem pollack pollack pollack grammatical grammatical grammatical grammatical grammatical grammatical grammatical park extends erlbaum inductive discovered insensitive acknowledge acknowledge divide zipser zipser outperforms outperforms outperforms appeared ence arcs constitute accept accept basically inferred ber asked emerge tween par ease guess guess guess guess valiant reject reject shaded shaded unseen unseen unseen unseen unseen unseen pub publication publication num num permits afosr ullman ullman ullman indication programmed dsp computa computa computa recognizers continually unpublished nec nec lems served gratefully accumulation palmer ate vii trainable ferent ferent confirm cliffs lated ron val engine engine ning gram gram tuple englewood triangles ally ples ples ples ples extracts extracts ref classi sym parti occam zipset convention rtrl rtrl totally syntactic watrous watrous watrous watrous watrous watrous cho schreiber fication tained tomita promise ated ated physica maryland maryland cleeremans cleeremans cleeremans kuhn kuhn kuhn kuhn sur correlational benchmarks stan ues ceedings hot triple activates checked checked rela putting ample men mar ito dard decides tie yij associating maxwell razor proaches chine duced selec triples multiclass rameter lat didn acc redwood bers cedure ors vocabularies ven ven ast comple comple increas wei angluin quantize aining hopcroft hopcroft equ prac ulus scalability thi thi sary devising tition rejects alon alon ining ining ining ining ining ining ining ining ison goudreau fion verge trai ned astronomy sour ott cle leamed leamed whe unresolved bol conception tice ded tionship hem cles scl fies fect alphabetical alphabetical impetus presenta ove substring 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output output output output output number system system error error error state state state state state state state state state state state state state state state state state state state results results results units units units units units units units units units units units units units units units units units units information information information information information information information information information models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space space weights weights weights weights weights weights weights weights weights weights layer layer layer layer case case order order order order shown shown systems values parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point single processing processing processing processing test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis class class inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows algorithms simple simple simple simple simple simple simple simple paper paper work work task task task task task task task step step process process current current current current current trained trained trained trained structure structure structure problems random similar similar representation representation representation show show fixed general average states states states states theory term term term activity dimensional university university computation solution research research sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target initial initial computer computer terms terms terms connections science science science science science present present present present activation activation activation activation activation activation activation activation temporal machine machine sets sets sets press learn learn learn components components components components components components components components components outputs outputs abstract applied applied computational references component component component component component component component component component component propagation context context context context context context context context context context context introduction introduction action complex complex statistical effect effect effect effect effect effect effect generated generated generated generated generated parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change representations representations higher part previous previous previous type type required required required good good long represent distributed distributed region region proposed length length correct errors finite finite finite simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations resulting classes classes classes classes classes classes classes simulation computed computed computed computed computed computed computed performed called times regions regions regions regions regions regions regions regions potential feedback global vol specific specific specific specific represented represented represented provide provide compute compute compute compute objects mit morgan report report report institute institute words internal internal advances connectionist graph sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences framework framework cambridge computing computing equivalent equivalent hinton hinton additional transition san requires statistics randomly randomly developed levels criterion product provided provided provided selected backpropagation backpropagation discussion discussion technical technical technical describe arbitrary corresponds actions actions finding supported supported role eds cluster rumelhart rumelhart rumelhart development kaufmann functional fully jordan jordan jordan programming programming programming programming programming interesting testing operation iterations bits idea idea idea produced description description architectures recent separate separate apply cognitive cognitive cognitive interest solve match correspond studies williams williams williams williams sensitive sensitive sensitive entire correctly touretzky clusters clusters occurs column demonstrate minimal operator mateo integration turn targets program acknowledgements appears construct ways sequential transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions distinct distinct dept dept simultaneously consisting interaction boolean boolean boolean boolean boolean select john focus review viewed transform transform operations operations lee lee understanding reduces calculate box box figures figures activations strings sciences plotted discussions columns extra encoded encoded encoded encoded effectively mcclelland mcclelland mcclelland ten composed traditional traditional running follow play giles giles giles illustrates subsequent subsequent subsequent modelling simpler wiley xor xor xor xor xor xor xor xor xor xor xor xor investigate hall discriminant discriminant discriminant ideas structured structured stream stream encode cognition momentum act act act act closest necessarily generalisation generalisation automata psychology illustrate obvious separated separated separated art serial finds slowly developing phenomena caused caused caused perspective perspective operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators worst worst consequence projected projected projected projected describing sun sun argument argument argument understood elman elman elman elman elman elman item marked marked spread modulated chen chen chen chen gave specifies hints hints hints equivalence forming arguments arguments arguments arguments arguments arguments arguments arguments arguments arguments arguments arguments perfectly promising replacing scoring hint hint hint canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical carry wilson composition prentice started reset separating combines viewing similarities reveals sons papers papers grants insensitive explorations johnson johnson linguistic zipser appeared microstructure arg arg arg arg arg descriptions australia australia tight preserved intuition exclusive grouped learnt denoting denoting conversely preserve page page programmed bill continually completed ucsd ucsd ucsd diagrams diagrams council august australian australian converging thousand focuses steven award separates separates dedicated anthony zipset crl schreiber schreiber enters convey cleeremans cleeremans servan servan wiles wiles wiles wiles wiles simon analyse phillips terminology terminology bird bird symmetrically analysed timestep queensland queensland contributed cda cda collapse analysing ian jeff interpreter conventionally generalise dennis janet parems hayes stewart intentionally qld qld encyclopedia postgraduate 
#@Bloesch_A,Wiles_J,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number error error error error error error error error error error error error error error error state state state state state state state state state state results results results units units information problem problem problem problem problem problem problem hidden hidden space space space weights weights weights weights weights weights weights weights weights weights linear linear layer vector vector vector order order order order order order order order order order order order order shown shown shown shown shown systems values parameters weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution recognition recognition method method method method method method method method method method approach approach approach approach approach approach approach approach point single processing processing large neuron neuron rate rate rate patterns patterns analysis class class class class class matrix matrix matrix matrix matrix matrix form form algorithms algorithms algorithms algorithms simple simple paper paper paper paper examples examples examples small size size size size feature net net net task fig fig fig fig step step step step step step step step classification classification classification classification classification classification current trained structure random high high high memory memory similar show equation equation equation equation equation equation equation equation equation equation equation equation section fixed line line line line line line line line line line line line line line line line line line line line line line line rule vectors general general generalization parameter real theory gradient obtained obtained term term term term term note experiments activity activity dimensional dimensional dimensional dimensional result result result university university computation computation solution solution solution solution solution solution solution solution solution research independent defined defined defined defined defined found sequence sequence sequence sequence sequence target dynamics dynamics initial table table computer prediction left presented presented presented present present present present phase phase low temporal temporal press learn components components nonlinear abstract back back back back back back back find find find computational convergence convergence references due due due due procedure propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction behavior dynamic dynamic dynamic dynamic generated generated parallel cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search tion complexity measure signals signals representations chosen higher part part type required required required required good represent distributed distributed equations equations equations equations make make proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed correct correct correct forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward simulations classes simulation computed respect eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq called means optimization applications obtain original original vol represented compared application desired desired series series define rates rates goal related connected discrete mit comparison connection update update update update update update update train train descent source source source nets morgan proceedings report report report institute implementation implementation implementation implementation version internal advances joint represents final scheme scheme scheme considered directly hinton hinton trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory conference efficient requires requires requires speed speed speed speed basic basic condition derived derived derived derived randomly developed types types path path path path product product finally iteration nature nature depends depends sampling simply simply feedforward fast fast fast fast fast fast fast fast fast fast inverse proof implemented implemented implemented main main main end end end end end instance easily easily easily easily easily easily rumelhart rumelhart fit fit kaufmann objective pairs combination reduced functional functional functional fully fully fully fully block testing ratio ratio special representing representing call iterations iterations iterations iterations normalized magnitude idea attention run advantage property typical practical identical side recently compare compare calculated tions solve solve solve solve solve solve solve studies differential differential differential rl rl rl definition modified generalized generalized interval williams williams williams williams williams williams williams williams williams williams williams williams williams constructed constructed constructed studied derivative derivative alternative feed touretzky column demonstrate demonstrate conclusion starting trajectories trajectories trajectories trajectories trajectories operator operator operator operator operator depend sigmoid sigmoid numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical moody faster faster faster faster faster faster faster faster faster constrained taking taking taking integration external turn introduce introduce manner suppose appears construct written solving solving winner sequential laboratory mathematical segments implement sensitivity sensitivity multilayer explicitly simultaneously involves easy easy slightly develop develop adding adding blocks letters solved solved evaluate operations operations operations operations operations operations operations operations operations lee lee lee lee lee lee lee decomposition converges calculate symbol advantages avoid avoid thesis coordinate formulation sciences memories recognize phys straightforward straightforward straightforward selecting uniformly uniformly differ delta delta delta delta wij computations computations schemes essentially fine refer interested issue issue classify sin sin sin sin sin sin sin running comp sampled dot backward backward backward backward backward satisfies satisfies satisfies satisfies satisfies satisfies deal deal load load updating put integral integral integral lippmann dual tech tech mappings variational tanh affect neu neu math analyze rev perfect changed formal algo algo shapes shapes message seconds integrate indicating advanced cos cos cos formula analyzed briefly benchmark correction correction correction correction correction handle operators desirable sun sun sun sun sun sun sun addressed addressed researchers integrating integrating behaviors conducted fed adjustable slower ity requirement chen chen chen chen chen chen chen green green green green green green green green green green green green green green 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#@Chen_H,Lee_Y,Sun_G,
#t5
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output number number number system error state state state state state state state results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information models models models models performance based based space space weights weights weights weights weights weights weights weights linear case shown shown shown systems systems systems systems values values parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit approach point single single single single single processing processing processing processing local analysis inputs inputs inputs inputs inputs inputs inputs shows shows simple paper paper small small size size size size feature net net net net net net net net net net work work work methods process process level level level level level level level level level level level current problems high high memory memory show show fixed fixed theory term term term term term term note note note activity result university found found initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial constant constant constant constant constant constant standard computer computer connections connections connections connections connections connections connections connections connections connections connections connections connections node science science science presented activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation nodes nodes sets range range press press press abstract find find find convergence convergence properties references due ieee important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction complex hand hand hand hand effect dynamic dynamic parallel parallel search tion tion tion energy chosen higher higher part part part part previous cases required long conditions conditions conditions conditions conditions conditions conditions conditions conditions distributed distributed expected tasks total total total total total total total total total total simulation sum sum sum performed times times factor factor factor potential natural feedback feedback feedback feedback desired desired provide provide provide provide provide provide provide provide provide provide perform perform perform active active active active active active active active active determined goal goal goal goal goal equal power larger connection connection connection connection connection connection connection selection selection morgan morgan morgan proceedings proceedings department version advances advances advances advances joint represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist final final bias bias bias bias bias addition computing equivalent equivalent hinton hinton hinton view san san san top top effects conference determine basic basic increase increase increase increase increase con con produce condition condition condition condition levels levels levels actual actual provided finally inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply simply simply simply simply associative normal normal normal normal normal normal normal normal increases increases increases group group group tested excitatory excitatory excitatory circuits amount amount amount amount amount amount amount amount short role require adaptation end rumelhart rumelhart kaufmann kaufmann kaufmann simulated simulated typically typically needed account york mechanism language numbers direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition international international bottom bottom early idea combined combined added pair apply machines side cognitive cognitive sufficient sufficient highly highly highly highly highly highly highly calculated works works tuning tuning tions tions tions tions background organization sensitive sensitive lead lead trial correctly correctly hybrid touretzky touretzky touretzky touretzky touretzky touretzky touretzky setting critical conclusions competitive competitive clear mateo mateo mateo mechanisms mechanisms cycle california start start decrease decrease decrease decrease perception winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner plot tuned mathematical involves remaining text mutual springer versus versus versus cycles cycles select select select select competition competition competition competition decreases review depending depending stages viewed detailed understanding key purpose intermediate intermediate calculate calculate kohonen kohonen david david david avoid figures figures figures figures includes activations activations activations activations activations activations activations activations determines activated activated activated activated activated activated activated activated activated successfully middle middle middle letter differ driven mcclelland mcclelland successful successful plots plots plots plots tend essentially reached verlag quickly allowing heuristic success oscillations vary highest reach thresholds receive presents presents remain unlike production rapidly rapidly rapidly rapidly replaced biases biases biases rise rise fashion rest symbolic symbolic act act act editor editor editor extremely extremely serial attempts wta wta wta stop caused handle starts drive drive drive drive drive rapid closer precisely pool cut annual summation leave leave variant psychological berlin reaches gen fall maximizes incoming serve serve adjust sums sums sums simulator findings summed summed gap gap driving driving dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically circular grey adjusting adjusting grow los biased biased analyzing symposium ranging ranging ranging ranging ranging equals induce lawrence competing competing competing competing competing competing competing competing winning winning winning winning winning ballard ballard pollack erlbaum broken cam pressure pressure pressure unchanged unchanged abu abu land leaving mostafa mostafa shading deriving tween pointed seek causing hillsdale var mutually mutually magnitudes magnitudes differentiation interactive interactive win associates thousands tune simplifies simplifies continually worked drives simplification simplification vii inhibited inhibited bindings oscillate attempting attempting compete suppress suppress suppress suppress suppress calculates condi ning settle ally ally regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory heterogeneous functionally outgoing rameters adjusts falling falling differentiate feldman faced unusual robustly putation tory dyer dyer dyer bidirectional bidirectional addi winners winners winners winners winners winners winners winners winners landscapes lange lange lange lange lange lange lange lange lange lange lange lange lange activa activa mal darker angeles hypothetical scribed tant biasing biasing chi temporary temporary ant inhibits inhibits stays suppresses constantly rising rising perf closing hin cycling cycling ended suppressing suppressing nel graphic crease assures eventual assisted hibitory hibitory subsymbolic subsymbolic serf inhibi inhibi netw netw coincidences ablex competitors war searchers compe lake erally bridges interconnec quire failing wildly tre tunes norwood quential inpul 
#@Lange_T,
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#*network network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input function function time time networks networks networks networks networks networks networks output output output system system system system system system system system system system system system system system system system system error error error units units units units units units units units units units information information information information problem problem models models models models hidden hidden hidden hidden hidden hidden hidden hidden based space weights weights weights linear linear linear linear layer case case vector vector vector order order systems values functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit distribution distribution distribution method point image single single single single processing processing processing processing processing processing control neuron neuron neuron rate rate rate rate rate rate rate test matrix matrix matrix matrix inputs form signal signal signal signal simple simple simple simple examples small work cells cells cells features process level level trained cell random high high high high representation representation show equation equation equation fixed real real real theory obtained note dimensional university research target target initial constant constant synaptic temporal sets maximum range position position position position position position position position position position abstract find convergence properties properties properties references positive positive positive context introduction complex hand behavior behavior behavior behavior behavior behavior behavior effect dynamic parallel parallel parallel parallel parallel change difference spatial spatial spatial spatial assume signals signals signals signals signals signals signals signals signals signals signals firing long distributed distributed distributed distributed distributed distributed region region proposed proposed proposed proposed correct correct correct feedback feedback feedback feedback feedback applications applications study specific true compared application desired desired provide provide rates rates rates location perform eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye connected gain gain motor brain brain brain descent institute consists individual joint scheme addition design vision give produce velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity path path path actual finally biological feedforward feedforward feedforward feedforward describe close circuits finding amount generate supported supported including including typically combination combination coefficients technology block block block block block block block block block block transfer transfer head head head head head head head head direct direct making inhibition directions movement lateral moving sense recently engineering previously axis axis axis axis solve smooth studies converge differential background background background background interval williams organization organization grant studied trial wide spikes matrices matrices rotation rotation move central clear clear suggest integration external proportional proportional variety exist movements movements movements movements movements movements movements movements movements movements plane manner groups question question question acknowledgements explicit appears produces produces primary describes ann vertical vertical vertical vertical vertical sensitivity sensitivity sensitivity sensitivity sensitivity physical involves transformations transformations national national formation review ocular ocular ocular ocular ocular modulation modulation approximated allowed diagram diagram diagram diagram diagram diagram diagram sec david expect box combinations combinations coordinate coordinate coordinate retinal coupled major major simplicity aspects aspects differ encoded encoded encoded driven successful situation interested content involved write write cat neurosci attempt deal load load load modelling modelling origin command command command create create create create rapidly integral integral integral issues pursuit pursuit existence ideas school project biol biol biol biol biol ideal muscle muscle combine relationships working stream complicated complicated understand examined rev illustrate perfect eyes eyes eyes obvious nervous message fibers extent plant plant plant plant plant burst vor vor vor vor vor vor track answer lies interneurons interneurons interneurons inside straight nucleus monkey describing describing describing pitch pitch res recording geometry geometry addressed integrating integrating questions varies pathways pathways understood axes axes axes marked recordings commands commands commands commands robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson operate summarized neuro irrelevant pole realized benefit cybern cybern cybern cybern cybern physiology primarily saccadic linearity linearity linearity vestibular vestibular vestibular tensor concerned neurophysiol neurophysiol impossible rotations cerebellum nearby analyzing hint integrator integrator integrator integrator integrator integrator carry muscles muscles muscles muscles muscles muscles muscles meaningful negligible regard peterson record saccade steepest extensively relies jump statement discovered cam lag boxes rms mind discharge discharge discharge discharge discharge reflex reflex reflex reflex reflex reflex reflex neurophysiology leaving largely asked creates creates uniquely diverse pointed stem stem cns home perpendicular compensate compensate impose confirmed relates relates records nuclei conversely oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor afferents afferents behave things diagrams diagrams diagrams diagrams clinical utilizing mds vestibulo vestibulo vestibulo vestibulo vestibulo converging conceptual conceptual hopkins loosely purkinje caudal caudal caudal caudal caudal integrates medicine core push push loads tells raises raises johns vertically cutoff thing enter stabilize carrying baltimore baltimore brought health talk talk motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons limb freely rotate modulate nice converts converts pull pull remarkably topics anastasio anastasio anastasio anastasio disorders slip biomedical conceptually fukushima fukushima manipulations canal canal canal canal canal canal thompson neurally neurally neurally seemingly reticular concluded stretch motoneuron motoneuron motoneuron motoneuron shortcomings subsystems subsystems compensatory compensatory exercise exercise useless useless succeed mediating simplifications roll roll baker departments canals canals canals canals canals canals canals actuators misleading misleading misleading alert shamma intriguing zee zee oblique semicircular semicircular semicircular cancels innervation speculate equ equ bilateral intemeurons institutes relay randomization premotor premotor ports ils arnold arnold microelectrode microelectrode microelectrode forever conform flavor moroneurons moroneurons uncommon enjoyed subdivisions laying nerves worry vestibuloocular microelectrodes overlooked happening 
#@Robinson_D,
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#*network network network network network network network network network network neural input input input input input input input input input input input input input input data data data data data function figure figure figure figure figure figure time time time set set set set set networks networks networks networks networks networks networks networks training training training training output output output output output number number number number number number error error results results results results results results units units units units units units information information information information information information information information information information information information information information information information information information information information information information information hidden hidden hidden hidden based based weights layer case vector vector vector order order shown shown shown shown systems values values probability noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single single single single single processing control neuron neuron test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis matrix optimal inputs inputs inputs inputs form form shows shows shows signal signal signal signal signal signal signal signal signal signal simple simple gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual small small small size size work work work task task task task task fig fig fig fig fig fig cells step current current current current current current current current trained trained trained trained trained trained trained trained memory memory response response response response response response similar architecture show show show fixed generalization average average average obtained obtained obtained dimensional dimensional result research research research log found target target estimate estimate estimate estimate standard standard science prediction prediction prediction presented presented present present temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object sets sets range press components components basis basis basis continuous continuous sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract back back properties references propagation propagation context context context context context introduction complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect cost spatial spatial spatial lower lower measure measure signals signals signals signals signals signals signals signals signals chosen previous previous previous previous previous firing firing firing type cortex cortex cortex cortex cortex cortex spike spike spike spike spike spike spike spike spike spike conditions conditions conditions conditions conditions conditions conditions make fact region correlation probabilities errors forward finite resulting total computed computed respect performed performed made made made study knowledge represented true cross provide compute compute compute perform eye goal cortical cortical cortical equal mit support train dependent institute institute institute institute kernel kernel connectionist responses responses responses responses responses responses responses responses final bias bias layers layers cambridge experiment experiment experiment stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli capacity upper produce condition condition condition condition condition condition condition condition condition randomly levels entropy selected backpropagation measured measured measured measured measured measured covariance complete predictions effective supported role role square pixel pixel pixel fit testing significantly mechanism trials trials trials trials matching principal principal details numbers normalized idea minimize produced produced produced produced produced produced predict predict neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal architectures improved pair separate reported reported pixels array array highly calculated calculated calculated calculated calculated match match match match match match match match match match studies studies interval sensitive grant parts parts lead occur trial trial trial trial trial spikes predicted feed white white demonstrate half conclusion starting depend reward reward measures suggest encoding encoding averaged targets acknowledgements primary sequential laboratory laboratory laboratory explicitly explicitly averaging remaining text adding john national national national dependence dependence dependence correlated showed modulation allowed discrimination discrimination earlier earlier smoothing performing performing intervals purpose purpose msec msec msec avoid usa usa usa inter inter uncertainty black encoded encoded presentation comparing miller miller soc strongly decoding decoding decoding decoding decoding decoding contained contained contained contained bar bar bar bar sampled play absence neurosci received attempt subsequent trains trains trains trains carried varied preliminary examine giving rest behavioral behavioral behavioral behavioral behavioral mse investigated biol possibility working pathway matched examined onset predicting predicting equally adjusted multivariate utility submitted indicating pairwise analyzed immediately monkey monkey monkey mation ion separately calculations beginning begin medical cybernetics preceding apparent apparent varies relevance fed recordings howard summarized modulated chose unbiased temporally count count count neurophysiol neurophysiol neurophysiol enhancement proceed systematic anatomical primate held biased hertz hertz hertz hertz inferior inferior inferior inferior inferior inferior inferior inferior infor analyses analyses pat mental mental evident evident evident monkeys monkeys monkeys specialized surprisingly repeatedly waveforms waveforms discriminate ure appeared appeared appeared compressed incorporates visually inferred transmitted transmitted transmitted transmitted transmitted transmitted failed reflected equality neurophysiological hughes paired rose rose quantify terns terns thousand hat loaded pearson sensorimotor possess chan convolved denmark denmark halves nih transmit convey convey convey convey recalled health health sorted decode decode decode behaving crg conveyed awake lasting convolving quarter quarter sato sato abstr hypothesize elicited ana ending behavioural behavioural behavioural behavioural behavioural behavioural behavioural behavioural behavioural behavioural behavioural behavioural behavioural nato grasped copenhagen copenhagen discriminations discriminations discriminations discriminations ori pairings nel raining blegdamsvej blegdamsvej tempo bethesda bethesda bethesda coo remembered remembered remembered richmond richmond richmond richmond richmond richmond richmond richmond behaviorally msecs msecs msecs optican optican optican optican optican barely nordita nordita neuropsychology neuropsychology creased throwing barry reserved releasing releasing preprocess nations ier pause scholar collaborative 
#@Eskandar_E,Hertz_J,Kjaer_T,Optican_L,Richmond_B,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure set set set set set set set set set set set networks networks networks networks networks algorithm algorithm output output output output output system system system system error state results results information information information information information information information problem problem problem problem problem problem problem problem problem performance order order order shown shown shown systems systems values probability parameters parameters parameters parameters noise noise noise noise noise functions functions recognition method method approach approach pattern pattern point image image image image image image image image image image image image image processing processing large test class optimal form signal algorithms algorithms simple gaussian visual paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples methods step step points points points points points points points points field field field field field field field field field field process process process process process process process process process process process process process process process process random random similar representation representation show show show show show equation line images images images images images generalization generalization parameter approximation approximation states states theory gradient gradient gradient term term term term term term dimensional threshold computation research initial constant computer connections science map map map map map machine machine press learn learn learn learn learn learn learn learn learn basis abstract find find references references references stochastic ieee ieee statistical parallel parallel cost cost cost cost assume assume lower prior prior prior representations learned learned learned previous type type required good good binary represent tree bayesian equations equations equations equations markov markov techniques techniques techniques finite minimum minimum ing sum regions optimization optimization natural feedback global knowledge knowledge knowledge knowledge knowledge obtain obtain obtain obtain vol vol vol vol vol represented represented provide compute compute proc proc location posterior distributions mit comparison larger fields descent modeling selection morgan technique technique internal advances represents final final final final final addition addition ai ai ai considered framework framework framework framework cambridge equivalent equivalent equivalent equivalent hinton additional limit limit limit san bit bit detection full full full significant approximate approximate statistics statistics free vision estimated give condition types provided processes processes processes selected selected selected selected selected selected selected selected selected selected selected selected selected selected selected backpropagation nature constraint constraint constraint close assumption assumption surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface finding amount common assumed face pixel pixel instance rumelhart noisy noisy noisy noisy including kaufmann objective needed hopfield functional functional york edge edge edge edge edge segmentation segmentation consistent call numbers numbers iterations iterations iterations iterations supervised minimize choose added predict membrane membrane membrane discussed advantage pair robust robust introduced pixels relevant relevant relevant unsupervised unsupervised unsupervised teacher teacher teacher teacher approximately approximately approximately solve smooth smooth smooth smooth smooth smooth smooth differential sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse definition deviation predicted predicted predicted feed touretzky deterministic deterministic white boundary minimal minimal minimal minimal minimal minimal minimal minimal reduce operator bayes weak weak weak learns propose hard hard regularization minimizing minimizing plane introduce introduce introduce solving changing student student student student student multilayer physical adding applying applying quality quality blocks select select select select select john yield expressed reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction learner learner solved transform operations operations operations approximated approximated approximated approximated approximated approximated approximated approximated approximated partition partition key normalization reduces roughly add add add valid norm norm priori priori priori priori usa perceptrons discuss coupled coupled coupled black texture texture texture texture texture compression compression selecting selecting selecting selecting selecting selecting selecting selecting capable capable poggio poggio poggio poggio efficiently capture traditional refer notice notice conf prob running criteria criteria sci comp gibbs vary relaxation ill automatically automatically extend presents origin wiley mass fewer int workshop statistically surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces gradients adapt analyze predicting perfect mapped piecewise piecewise piecewise piecewise distinguish smoothness smoothness smoothness smoothness smoothness analyzed multiplication briefly baum precisely precisely forces leaves mation acad lattice backprop dots maximizes collective geman geman geman geman green yuille yuille yuille lim arithmetic arithmetic arithmetic discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities college redundant redundant redundant redundant saddle modify fix princeton princeton girosi girosi girosi girosi girosi girosi girosi girosi nat eliminate inspired fits siemens abilities keeping keeping selects selects selects selects filled infor francisco smoothed suggesting clean passing sons limitation lem dense multiplying multiply multiply emergent breaking massively reconstruct reconstruct reconstruct reconstruct modifying formance insights pami pami pami pami num impose discontinuity discontinuity discontinuity discontinuity concentrate careful cosine cation geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger geiger preserve fiat restoration hyperbolic corporate vis smoother blake blake east suppress cast cast proposal fij fij fij fij sij sij sij sij sij sions teaching outlier dij relax gij gij gij gij gij gij putational huber huber mumford mumford italy compress mrfs excluding lay machinery sky throw throw feeds reconstructing reconstructing teach teach teach teach teach teach teach teach teach teach teach zij jour discard kij kij iij iij assure mij compressing hypersurface hypersurface hypersurface lij lij lij bers pereira pereira pereira pereira pereira zisserman zisserman shah shah ili ili thrown dxdy dxdy coincident simulta dipartimento neously 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#@Geiger_D,Pereira_R,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set networks training training training training training algorithm output output output output output output output number system system system system system system results units units units units information information information information information information information information information models models performance space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear layer layer layer case case case case case case case case case case case shown shown shown shown shown shown shown shown shown shown shown systems values values values probability probability probability probability probability probability probability probability parameters parameters noise noise noise noise noise weight unit distribution distribution distribution distribution method approach approach image image image image image image image image image image image image image processing processing control large local local local local local local local local local local test optimal inputs inputs inputs form shows shows signal signal signal signal signal simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper small small small small feature feature net net net work work methods points points points points field field field field features features features features trained trained trained trained random random random random random high architecture architecture architecture show equation equation equation equation section fixed images images images images images images images images general general parameter parameter parameter parameter parameter real average average average average theory gradient term dimensional university computation research research research independent log log log log log log initial constant constant estimate standard computer computer distance distance science prediction left left left left left presented presented object range learn learn learn learn learn outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous sample sample abstract applied applied applied density density properties references ieee positive procedure procedure procedure procedure procedure important adaptive decision decision mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction generated variance variance variance variance variance variance variance parallel cost cost tion tion change change difference difference difference spatial assume lower measure signals signals prior learned learned learned learned learned learned learned learned chosen center previous cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases type type multiple good good good good represent expected expected make make make make make make make region region probabilities scale minimum computed computed computed computed multi sum sum times regions dimension made made study knowledge negative relative relative relative compared desired desired cross receptive receptive receptive receptive receptive define objects location location location location location location location related related constraints equal larger larger fields train morgan report institute institute department version version version technique advances exp layers computing directly hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton curve estimates estimates estimates estimates estimates estimates top top requires choice free world world speed vision basic basic pages produce produce produce derived weighted randomly randomly randomly controller controller controller controller controller controller controller controller actual backpropagation nature depends sampling constraint measured discussion normal technical assumption surface surface surface surface surface surface predictions predictions predictions predictions predictions predictions nearest nearest nearest common common common common common common common assumed assumed shape face pixel pixel makes sensory kaufmann objective objective probabilistic smaller underlying underlying underlying underlying underlying underlying underlying combination unknown jordan jordan ratio special uniform uniform principle leads squared squared representing iterations max making making normalized normalized normalized bottom experts experts experts experts experts depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert early minimize produced produced choose property property pair separate ensemble typical include identical side side pixels pixels pixels pixels pixels pixels pixels previously unsupervised unsupervised teacher teacher approximately works module module module module module module module module tions mixtures locations locations locations locations locations organization improvement parts parts parts parts parts parts parts intensity invariant wide wide predicted predicted predicted predicted predicted predicted predicted alternative alternative locally locally locally locally locally white starting valued central modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules learns learns learns learns taking taking hard presence presence presence presence external external external drawn plane averaged introduce derivatives derivatives derivatives force acknowledgements pro edges produces explicitly simultaneously averaging consisting consisting develop mutual formed select john extracted extracted extracted formation organizing showed soft sign earlier fitting remains filtering views avoid perceptual perceptual perceptual perceptual plotted maximize maximize maximize maximize maximize maximize maximize variations domains domains domains domains domains domains black discussions closely divided detect detect detect detect projections projections fine receives receives capture dis lie vary dot dot dot dot dot generalize absence modular predictor received received received overlapping disparity disparity disparity disparity mixing extract extract extract extract jacobs jacobs neighboring neighboring receive exhibit varied estimators replaced accurately accurately helpful rise reducing detectors applicable possibility relationships maximizing maximizing complicated surfaces surfaces surfaces surfaces surfaces surfaces surfaces patch patch patch patch patch patch patch patch patch predicting opposite spline spline created adjusted versions assumes detector detector separated separated shapes simplest attempts advanced advanced agreement agreement agreement agreement agreement agreement agreement publishers variances adjacent adjacent adjacent adjacent adjacent adjacent adjacent nowlan nowlan nowlan handle handle considerable spatially spatially easier filtered located gradually optimize toronto toronto patches patches patches patches patches patches patches patches linsker linsker conjugate considerably applies empirically pure pure splines treated treated continuously compares ity outliers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers characterize differs aim extracting extracting prevent adjust asymmetric logp coherent coherent coherent coherent coherent coherent coherent coherent coherent coherent coherent coherence coherence coherence coherence coherence coherence cor contribute contribute pose discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities corrupted contextual proportion proportion assign modify princeton zemel zemel discover discover discover eliminate rigid ranges viewpoint nearby nearby nearby nearby nearby nearby operates selects becker becker becker becker becker becker becker becker becker stereo stereo stereo stereo stereo stereo stereo stereo stereo competing competing competing tic specialized specialized canada agree agree agree captures grants discovered alternatively ignore summarize treat consecutive informa informa pressure maximized recursively gaps transmitted forced centre copy regularity ideally spaced discovering reject continuity continuity continuity continuity continuity continuity continuity continuity continuity constrain equality geoffrey ization discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity discontinuity march fixation spanned funded responding responding rotating modality cubic cubic cubic normalizing treating bridle develops rarely copies copies fortunately regularities regularities january interpreting tors tribution evenly atick atick interpolating interpolating interpolating interpolating interpolating interpolating interpolating interpolating interpolating interpolating interpolating modalities interpolate curved curved curved curved teaching steve transmit outlier scattered convey convey convey discovers discovers sur fore modest refine moderately unaffected touch ogy redlich redlich stereograms stereograms stereograms stereograms stereograms stereograms ontario ontario internally remember shrink conveys depths depths depths depths depths depths throw thirty rationale canadian nserc mon neighbouring neighbouring fellow rejecting rejecting strip strip strip strip strip restricts interpolator interpolator interpolator interpolator interpolator interpolator interpolator interpolator interpolator detec ont collapse kai implausible loca backpropagating invoke invoke collapsing striped figtire technol scalars throwing throwing hori gausstans gausstans noranda hatched zontal eco 
#@Becker_S,Hinton_G,
#t5
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training output output output output output output output output output system system system system system system system system system system system system system system system system system system system system system error error error error error state state state units units units units units units units units units units units units units units units units units units units units units information information information problem problem models models performance performance performance performance performance performance performance based based based space space space space space space weights weights weights linear layer layer layer layer systems systems systems systems values values parameters neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method approach approach approach approach pattern image image image image image image image image image image image image image single single single single single single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control control control control control control control control control control control control control control control large large large local rate test patterns analysis analysis inputs inputs inputs inputs inputs form signal signal signal signal signal signal simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small small small feature net net work work work cells step step step step step step step step field field field field field field field field features features features process process process process level trained trained trained trained trained trained trained structure structure structure structure structure random random random high high response response response similar representation representation representation representation representation representation representation representation representation architecture fixed fixed line line images images images images images images images real real real gradient gradient obtained activity dimensional dimensional dimensional university university computation found sequence target target target target target target target target target target target target target target target target target target target target target target target target target target target initial initial constant constant estimate estimate estimate estimate standard synaptic direction presented map map present low frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object object object object object object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum range range range position position components components components basis outputs outputs outputs continuous abstract computational density properties properties references component positive positive positive procedure important important adaptive adaptive introduction complex stimulus dynamic recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial signals center previous previous previous required cortex cortex good good good good distributed distributed distributed distributed distributed distributed distributed distributed techniques length observed simulations simulations resulting ing tasks total total total computed computed sum performed performed performed called times regions optimization dimension dimension made feedback feedback feedback feedback feedback feedback feedback feedback feedback study knowledge filter filter negative artificial artificial artificial desired receptive receptive receptive receptive receptive receptive receptive objects objects rates location perform perform active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye goal goal goal constraints gain motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor cortical brain brain brain steps accuracy comparison contrast fields descent descent institute institute institute department department version consists internal internal responses responses final delay delay delay delay delay delay delay addition addition maps considered considered experiment additional estimates design trajectory trajectory san san stage approximate approximate world world vision estimated basic con produce produce weighted weighted levels area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity controller controller controller types actual provided selected backpropagation backpropagation nature nature depends sampling biological feedforward denote fast limited complete complete complete complete stable stable stable stable predictions implemented journal pixel ability hypothesis instance easily makes sensory including including simulated simulated typically needed combination fully technology testing york head filters filters filters filters filters filters filters filters filters filters pre pre direct window bits combined minimize resolution resolution resolution separate separate moving moving moving moving moving moving moving moving moving moving pixels pixels pixels sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski array relevant engineering sufficient sufficient varying approximately smooth smooth smooth smooth smooth smooth match address background background positions locations generalized organization organization sensitive entire constructed constructed constructed constructed lead suggests wide wide wide wide predicted move move loop loop loop white occurs pass demonstrate runs flow conclusion greater trajectories trajectories trajectories editors central accurate accurate retina retina retina retina retina retina retina designed designed designed designed taking mechanisms presence presence presence california california solid proportional proportional proportional proportional intelligence intelligence pulse turn assuming variety variety variety variety variety movements movements movements selective selective selective selective selective relationship targets targets targets targets targets targets derivatives minima program areas relation construct longer perception perception perception optical ways primary laboratory ann tuned tuned changing physical transformations develop integrated frequencies frequencies decreases yield stages stages ocular ocular ocular ocular forms static activities constants calculation calculation slow dashed delays roughly tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking intermediate intermediate intermediate intermediate intermediate foundation degrees building existing box includes perceptual combinations coordinate retinal retinal retinal retinal retinal retinal retinal retinal retinal reason middle middle capable society detect detect build projections receives strongly neuroscience neuroscience neuroscience symmetry localization absence paradigm realistic realistic neurosci principles attempt moves moves subsequent extract extract rat simpler simpler carried diego put environments limitations pursuit reducing project project detectors plasticity proper complicated pathway matched matched plausible predicts rev equally eyes eyes eyes ensure explored academic generates generates extent submitted motivated plant seconds massachusetts band band developing separable separable separable separable separable separable distinguish track track track unstable phenomena biology shared shared ring sites organized producing filtered located separately separately circle medical demonstrates addressed populations populations pathways maintain robinson robinson howard fall incoming prevent prevent adjust simulator inherent chose implements attentional acquisition physiology physiology interface interface interface interface interface interface interface interface interface interface summing saccadic velocities vestibular perfectly flexibility theories interconnected interconnected arranged difficulties primate primate primate primate primate primate primate primate primate primate primate primate odd salk adequate days falls combines surprising moved francisco waves spatiotemporal stimulated ballard ballard saccades arrows motions motions reverse border speeds boxes reflex reflex reflex largely sine achieving ties emergent preserving responds poses spatio smoothly lesions lesions perceived stem tendency acceleration acceleration affects affects workstation shaded pub graduate convert hughes expand retinotopic retinotopic retinotopic adelson adelson adelson ultimately ambiguous conversely constructs oculomotor oculomotor oculomotor oculomotor rotating page ation transients simplifies worked covers drives drives interior interior instability vestibulo vestibulo vestibulo vestibulo photoreceptors settling viola viola viola viola calibration morris anatomy triangles bergen bergen bergen bergen raises cur bandpass america convolved bach lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger distractors distractors stabilize stabilize stabilize fovea fovea fovea inaccurate unrestricted rent newsome newsome began spots spots primates primates blurred directionally directionally frozen accu accu complications nation engineers complexities thirty rendered feel plants millisecond attain combi multilayered stabilizes inertial ship backgrounds stimulate stably impairment impairment accelerating pare pare aining collins keck compensating integrative extendable proceeded circumvented rately ejnowski hav staged synthetically 
#@Lisberger_S,Sejnowski_T,Viola_P,
#t5
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#*network network network network network network network network network network network network learning model model model neural neural data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set networks algorithm number number number number number number number system error error error error error error results results results results units units information problem problem problem problem problem problem models based based based based based based based based space case vector order shown shown shown systems systems values values values values values values values values values parameters parameters parameters noise noise noise noise functions functions distribution method method method method method method method approach approach approach approach approach approach approach approach approach pattern pattern pattern point point point point point point point point image image image image image image image image image image image single single single single control control large local local local local local local patterns optimal form shows shows shows shows signal signal signal algorithms algorithms simple simple simple visual visual small small small net net work work task task methods methods methods step points points points points points points points points points points points points points points points points field field process process process process process process process process process process structure structure problems problems problems problems problems random random random random random random memory similar similar representation representation representation representation representation representation equation equation section fixed fixed line line line line line line line line line images images images images images images general parameter parameter parameter parameter real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average theory obtained term term note experiments dimensional threshold computation computation solution solution independent defined found found found found found found found found found sequence sequence sequence sequence initial initial initial initial constant constant constant constant constant constant table estimate estimate estimate estimate estimate computer computer computer computer terms connections map map map map map map map map map map map map map map map nodes nodes nodes nodes temporal machine machine machine object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range press basis continuous abstract abstract applied applied find find find find find find find find computational computational convergence analog analog analog references stochastic ieee ieee positive positive important context introduction hand estimation behavior stimulus variance variance parallel tion difference difference spatial prior representations bound cases cases cases cases type type type multiple multiple multiple multiple multiple multiple good long represent represent represent represent represent distributed bayesian expected equations markov make fact fact region region region region region region region region region region region region region region region length observed forward finite minimum classes ing ing tasks human human regression regression computed computed computed respect performed elements regions regions regions regions regions regions regions regions regions regions regions regions regions regions factor optimization optimization dimension natural global global global knowledge negative specific samples represented true application compute compute compute proc active active active constraints connected connected connected connected discrete mit accuracy fields fields fields fields update support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support modeling institute implementation version individual final final sequences sequences ai ai ai ai ai ai ai ai ai ai ai maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps considered framework cambridge cambridge experiment experiment solutions estimates trajectory stimuli stimuli approximate approximate vision vision vision vision vision vision vision vision vision estimated increase con weighted randomly developed developed product actual provided provided finally finally nature constraint constraint simply describe group denote denote tested limited close close close inverse assumption assumption surface surface surface surface surface surface surface surface surface finding finding finding amount implemented implemented assumed shape shape shape generate supported supported supported supported supported supported supported theoretical eds square pixel pixel future easily makes noisy fit typically typically needed needed reduced account account unknown technology interesting projection projection york edge edge edge edge edge edge edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation consistent squared direct direct inhibition stored depth early frame frame frame frame frame frame combined added added description description description description predict membrane exact robust robust robust typical typical moving moving side quadratic subset subset subset subset subset array sufficient observations observations observations observations observations tions tions solve smooth correspond correspond converge trans trans trans sparse observation observation entire entire parts wide correctly locally deterministic hardware demonstrate starting critical place minimal minimal minimal minimal assumptions assumptions segment valued central sigmoid practice taking integration solid solid regularization regularization regularization regularization regularization regularization plane plane decrease averaged scene scene scene minima minima minima explicit explicit edges edges edges edges edges perception perception perception ways estimating estimating estimating plot describes distinct explicitly averaging slightly text text consisting consisting adding shift implies boolean john yield independently review reconstruction reconstruction reconstruction stationary squares overlap solved solved variation evaluated open open updated approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations centered frames frames frames frames frames approximated approximated completely similarly similarly translation translation reasonable smoothing smoothing smoothing reduces fitting false boundaries boundaries penalty penalty interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation valid valid initially visible koch koch avoid includes determines uncertainty candidate candidate candidate candidate candidate candidate planning regular selecting closely uniformly uniformly included poggio poggio successful build efficiently efficiently plots plots essentially essentially ten conf kind split split criteria built satisfy gibbs quantity quantity quantity sampled sampled sampled relaxation dot dot dot paradigm paradigm realistic minimizes computes ill attempt attempt consisted approximating neighboring neighboring origin unlike parametric powerful powerful wiley collection difficulty circuitry limitations limitations limitations accurately dotted scalar fewer successive successive tech rest reliable decisions complicated func cover cognition surfaces surfaces surfaces surfaces surfaces attributes smallest smallest smallest circles circles circles necessarily thought assumes assumes assumes shapes initialized initialized consist consist plant plant plant synthetic integrate integrate massachusetts residual residual residual residual residual residual piecewise piecewise piecewise smoothness guaranteed phenomena phenomena answer caused handle perspective straight sites ran ran leaves leaves mation involve universal lowest lowest patches patches populations limits empirically axes posed posed detecting resistive resistive resistive resistive dots dots dots rep polynomials rely synchrony serve prevent prevent geman geman geman geman coherent display decreased specifies displays person person person person lab discontinuities discontinuities discontinuities discontinuities corrupted japan linearity girosi girosi dynamically branches homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous reconstructed impossible nonzero overcome proceeds los belong belong disjoint disjoint disjoint salient exceeds exploring recovered recovered recovered recovered recovered moved viewing occlusion occlusion occlusion occlusion thin matter horn horn properly observer sons harris harris generalizing generalizing thresholding thresholding thresholding switches switches switches severe divide dense multiply approx approx street constitute shunting covering covering tables ber gaps rejection uniquely uniquely uniquely uniquely uniquely pentland pentland pentland pentland pentland adopt ideally reconstruct reconstruct transparent transparent transparent transparent shaded trends grouped grouped num approxi ization discontinuity discontinuity regularized plate intensities cij cij cij cij anal anal anal geiger geiger sam intl intl intl intl resistors esti placing placing supports meet meet avoidance port covers covers covers restoration attributed mrf correspondences blake blake observers transparency transparency neighborhoods interpolated interpolated alex cast usefulness tuple sparsely sparsely sparsely discarded heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous interpolating interpolating sij sij sij sij degenerate interpolate interpolate invisible andersen robotic rectangles rectangles thresh seg media outlier outlier scattered indi recovering recovering deciding insert ues began refine proximation rij rij converts collision excluded recovers approxima approxima lifetime resentation modulating imation puter parsimonious rightward darrell darrell darrell darrell darrell darrell intel ames translating fuse fuse corresponded continuation rendered mented reconstructing torre formalized refining niques segmentations prevented allocate grasping luo cov undergoing undergoing undergoing trevor chunk cate perceptually manageable chunks chunks stance straints overcomes abrupt decomposes opened mated intell intell minimally minimally shadow terzopoulos subregions subregions ered rosenfeld pled zisserman zisserman died treue contamination ual veloped imations combinatorics regularize ria sii corrupt flag multiplica scription ski osaka transparently 
#@Darrell_T,Pentland_A,
#t5
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#*network network network network network network network network network network network network network learning learning learning learning model neural neural neural input input input input input data data data data function function figure figure figure figure figure figure figure figure set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training algorithm algorithm system system system state state results results information information problem problem problem problem problem problem based based space space space space space weights linear linear order order order order order order order order shown shown shown shown systems systems systems systems systems systems values values values values probability probability probability probability probability probability parameters parameters parameters parameters weight functions distribution distribution distribution distribution distribution distribution distribution recognition recognition method method approach approach point image image image image image image image image image single single single single single single single single control control large local local local local local local local local local local local local local local local inputs inputs inputs inputs form form shows visual visual visual paper paper paper paper paper feature feature feature feature feature feature feature net net net net net net net net work task methods methods step field field field field field field field features features features features features features features features features process process level level level level level level level level level level level level level level level level level level level level level current structure structure structure problems problems random random random random random random random random random random random random random random random random random random high high high high high high high high high high high similar representation representation architecture show show show show show show show show show equation section fixed line line rule images images images general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter theory theory experiments experiments experiments experiments experiments dimensional university university university university threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables variables computation solution solution research research research independent independent independent log defined defined defined defined defined defined defined defined defined found constant constant estimate estimate computer computer computer computer computer terms connections connections connections node science science science left left left left direction present low low low low low low low low low low low low nodes nodes machine object object sets maximum press components basis basis abstract find find find find likelihood likelihood references stochastic positive important important decision decision decision decision decision decision decision decision decision decision decision decision decision introduction complex hand estimation generated parallel parallel tion tion energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy variable variable variable variable variable variable variable assume lower prior prior prior prior prior representations representations chosen higher higher higher higher higher higher higher higher binary binary binary binary represent represent bayesian bayesian markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make make make region correct probabilities probabilities forward forward minimum minimum minimum total sum sum sum sum sum sum sum called called elements regions regions optimization potential potential potential potential potential potential potential potential natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback global applications applications knowledge obtain negative artificial artificial specific represented application define define define compute active goal related posterior posterior constraints constraints constraints connected distributions distributions discrete discrete discrete equal equal mit contrast contrast fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields support dependent nets nets nets nets nets nets nets morgan proceedings report report report report institute institute institute department implementation implementation joint joint joint represents represents represents scheme addition graph graph graph considered framework framework framework framework framework framework domain domain equivalent equivalent equivalent equivalent equivalent solutions top top conference determine upper vision vision vision vision vision vision vision vision vision vision vision vision vision vision vision vision vision vision vision condition derived weighted weighted weighted weighted weighted conditional levels levels levels levels levels levels levels levels levels levels levels levels levels lines lines lines lines lines lines lines lines lines lines lines lines product provided evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence nature nature depends constraint biological technical technical technical feedforward feedforward feedforward feedforward limited inverse complete proof proof finding finding short implemented role require main journal pixel ability noisy noisy including simulated probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic pairs hopfield hopfield hopfield combination fully significantly edge edge edge segmentation segmentation segmentation structures matching mode mode representing representing max max making making making making making international international depth magnitude idea combined added property robust element lateral include subject identical side side hierarchical recently relevant sufficient highly observations observations definition definition definition background observation observation observation observation observation entire grant grant constructed constructed constructed exists exists exists exists horizontal horizontal horizontal horizontal feed feed white boundary demonstrate flow strength conclusion minimal minimal segment segment segment neighbor depend depend editors central bayes designed practice temperature sound integration characteristics demonstrated intelligence intelligence labeled assuming exist exist exist exist min scene scene scene minima configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration annealing denoted denoted denoted boltzmann explicit suppose pro derive construct edges edges edges edges edges edges edges edges edges edges edges edges edges edges written winner ways laboratory label label label label label label label label label vertical vertical vertical vertical distinct distinct dept changing changing changing changing segments segments segments confidence confidence confidence confidence implement missing explicitly simultaneously simultaneously easy easy integrated integrated potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials choosing focus expressed reconstruction interpretation interpretation interpretation lemma lemma lemma lemma lemma lemma transform transform transform transform transform transform transform transform transform transform transform transform transform transform labels labels labels labels labels labels reasonable convex sec reduces reduces neighborhood neighborhood neighborhood roughly add add remains intermediate intermediate intermediate construction construction foundation foundation advantages topology topology david building existing existing priori assignment assignment sciences sciences sciences determines uncertainty coupled neighbors characterized reason reason middle middle capable capable maximal build build schemes traditional traditional traditional procedures strongly strongly prob prob allowing allowing interested interested interested interpreted gibbs michael play providing computes highest highest hypotheses hypotheses hypotheses hypotheses received preferred preferred extract intrinsic intrinsic extend powerful layered xor essential integral existence existence existence existence ideas tech combine decisions decisions decisions encode encode surfaces surfaces removed removed removed circles plausible possibly configurations configurations configurations configurations configurations configurations aspect formal formal formal separated academic mixed mixed finds defines brown brown brown brown site site site developing crucial defining defining slope improves capabilities spatially spatially sys widely widely constructing constructing division incorporate incorporate leaves desirable desirable mation acknowledgement involve demonstrates nsf applies substantially flexible flexible embedded parameterized parameterized parameterized peter dots rep span tank tank tank serve geman geman geman geman geman geman geman geman logp simulator summed realized realized don acquisition cooper cooper cooper cooper cooper cooper cooper cooper labeling equivalence formally japan restrict tem impossible establish kaufman adds convenient tools intelligent keeping obtaining transforms exploit reasoning reasoning exceeds filled substituting representational representational representational representational representational ensures paul paul paul topological offers treatment express ballard ballard ballard offer offer offer offer offer likelihoods tures thresholding thresholding divide informa unified converted constitute clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique ter ter incorporates equivalently planes encodes dec abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction instantiation flat constitutes descriptions possibilities clas principled principled penalized ibm pami compatible compatible compatible compatible simplifying iri pearl pearl pearl pos represen voting voting voting supports rochester rochester fea ation normalizing september october simplifies november lems removes satisfaction bridge bridge bridge bridge bridge bridge bridge bridge functionality restoration restoration august justified justified christopher mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf mrf doesn doesn doesn neighborhoods hoc interpreting december jain jain cast replicated inherently vote vote detects contributes kirkpatrick kirkpatrick kirkpatrick interpretations functionally conditionally rameters establishing establishing andersen cliques cliques cliques cliques hough hough hough hough hough hough hough hough hough hough hough hough hough hough hough hough hough hough hough hough hough tations locality thresh thresh watson experimented jose relax richer richer richer intrinsically intrinsically intrinsically intrinsically exploitation fundamentally entities entities undirected men iiiii iiiii iiiii iiiii iiiii iiiii iiiii mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs mrfs parame puter tics beliefs cen functioning functioning inferences inferences optimiza explores concurrent stuart contributed contributed compactly matters votes votes votes resentations marroquin marroquin marroquin marroquin vecchi nical probabilistically unspecified occluding ond unary unary unary sic negated negated chou chou chou chou gelatt donald patrick intense invariants dictates behaviorally gathering intercept terior slx northwestern northwestern confidences istic determin imizing ils ils collinear incompatible eel eel swain swain swain existent surpass wlo evanston evanston tstems wrote ero consulting osaka scrutiny ergy ergy bridging hoods cedures 
#@Cooper_P,Prokopowicz_P,
#t5
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input input input input input function function function function function figure figure figure figure set set set set set number number error results results results results results results results information information information information information problem problem problem problem based space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case vector vector vector vector vector order order shown shown shown shown shown shown shown shown shown shown shown shown shown systems weight functions distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach pattern point point point point point point point point point point point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single local test analysis analysis matrix form visual visual visual visual visual visual visual visual visual visual paper examples small small work task task fig fig fig fig fig fig fig fig fig step points points points points points points points points points points points points points points points points points points points points points points points points points classification level level level level similar similar similar similar show show show show show section section section section fixed fixed fixed fixed line vectors images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general general parameter parameter approximation obtained obtained term result result result result result result result result result result result result result result threshold computation solution solution independent independent independent defined constant constant constant science direction direction direction direction direction direction direction presented object object object object object object object object object object object object object object object object object object position position position position position position position position position position position position position position position position position position basis basis basis basis sample sample sample abstract applied find computational computational computational computational references references component ieee positive important introduction complex hand effect generated generated generated generated generated generated tion tion change change change change change change change change change difference difference difference difference difference difference prior prior prior chosen chosen chosen previous cases required required required multiple good conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions represent represent distributed equations fact region correlation observed scale scale scale scale scale resulting human respect regions factor factor factor factor natural study negative artificial cross define define objects objects proc location location location eye determined experimental experimental experimental brain equal power power accuracy accuracy accuracy support source source source source source source source source source source source source institute institute institute department version technique difficult difficult difficult final final scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme cambridge directly directly view view view view view view view view view view view view view view view view view effects effects effects bit bit bit bit bit bit bit bit bit detection full full requires significant significant approximate con produce condition condition condition condition product provided provided biological normal normal normal transformation transformation transformation transformation limited limited complete stable stable surface surface surface surface surface surface surface proof proof proof proof proof finding common common shape shape generate supported eds pixel pixel degree degree including combination combination combination combination combination combination combination combination combination combination combination combination combination combination account unknown unknown coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients technology technology technology projection projection edge edge edge head matching details details details making bits bits bits bits bits depth magnitude idea attention combined minimize added sources sources sources sources sources sources sources sources light light light light light light light light light light light light light light light predict discussed directions recent exact property takes apply cognitive relevant sufficient sufficient sufficient sufficient sufficient varying varying previously previously approximately works solve solve smooth smooth smooth match match match match positions positions positions positions positions positions positions positions positions positions positions positions locations observation generalized bounded entire grant intensity intensity intensity invariant invariant suggests predicted demonstrate minimal row row row row row row row row operator operator practice practice taking taking taking taking demonstrated intelligence assuming assuming variety start iii iii manner scene scene scene question edges edges edges edges edges edges edges edges edges edges edges edges edges solving solving solving generating changing changing changing linearly linearly linearly transformations remaining remaining remaining text angle angle angle unique gaussians gaussians applying applying implies independently expressed review viewed viewed viewed viewed solved solved variation transform open similarly suggested constants allowed sign sign sign sign sign sign sign sign sign sign sign sign sign sign combining add boundaries boundaries remains visible visible visible visible sufficiently sufficiently faces views views views views includes combinations combinations contour contour contour subspace holds holds discussions major reason straightforward compression compression selecting selecting extra suitable poggio poggio successful identify literature literature literature literature schemes schemes schemes projections projections invariance summary traditional kind correspondence correspondence correspondence correspondence correspondence automatically acknowledgments situations origin remain wiley transformed transformed transformed transformed transformed transformed create difficulty humans lippmann discriminant scalar ideal ideal working variability variability variability variability variability proved cognition fundamental notion surfaces surfaces surfaces contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours gradients gradients analyze eyes simplest isolated massachusetts massachusetts massachusetts agreement convolution unstable handle purposes purposes leaves hyperplane hyperplane hyperplane hyperplane controls projected separately geometry nsf alignment alignment alignment alignment geometric geometric geometric geometric considerably reflect psychophysical introducing marked requirement span span rely incoming proven serve findings proposition proposition proposition proposition proposition proposition proposition picture lab discontinuities acm recover recover homogeneous rigid inspired chance satisfying replacing multiplicative familiar interpret illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination illumination generalizes separating separating separating separating recovered recovered recovered recovered edelman corre induce viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing occlusion border hart adopted adopted displacement displacement trading crossing crossing crossing crossing crossing crossing geometrical truncated personal flat reflected brightness brightness brightness brightness brightness brightness brightness brightness brightness brightness brightness duda compensate compensate compensate compensate reflectance reflectance reflectance reflectance reflectance mouth thresholded ullman ullman ullman ullman ullman ullman projecting scope frontal iri rough spanned spanned spanned attached attached figs crossings crossings crossings memo memo memo bring handled sponding accordance observers interpreting pictures pictures pictures cast cast cast tip compensation manually manually discarded triangulation dog dog assp comm compensated compensated compensated compensated compensated compensated compensated magazine closure ings merit brought modest cope cope cope relax richer direc align weinshall advice arline arline arline excluding displaced disappear standing reconstructing indistinguishable geometrically standpoint standpoint standpoint critically undergoing mooney mooney mooney mooney mooney mooney psychol incidence tolerate reflections decoupled shadow shadow shadow richards tomaso ditions shashua shashua shashua shashua shashua alent shadows shadows shadows compensating compensating munication specular ablex coping coping sharpness shimon viewer egg mage bracketed 
#@Shashua_A,
#t5
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#*network network network network network network network network network network network network network network learning model model model model model model model model model neural neural neural neural input input input input data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure set set set networks training training training algorithm output output output output number system system system system system system system error results results units units units units units units units units units units units units units units units units units units information information information information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space space space space space weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector vector shown shown shown values neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit recognition recognition pattern pattern pattern point processing processing processing processing processing processing processing processing processing processing processing large neuron test patterns patterns analysis optimal inputs inputs inputs shows signal simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual examples small task task task methods fig field field field features features features features features features features features features level level trained trained trained cell memory response response response response similar similar similar similar representation representation representation architecture architecture architecture architecture architecture equation obtained experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity solution research found found initial initial distance distance science science left left left left left direction direction direction direction direction direction direction direction direction direction direction direction direction presented map map map map map map map map present present low object object object object object object object object motion motion motion motion maximum press position position position position position position position position position position position position position position position position position position position position position position position position position position position position position nonlinear outputs abstract applied back find computational properties properties properties references due procedure important important important propagation propagation introduction stimulus parallel spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial signals signals representations representations higher part previous type type type type type required cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex distributed distributed expected techniques observed observed observed observed observed observed simulations tasks computed performed called factor optimization orientation orientation study study study obtain obtain represented receptive receptive receptive receptive receptive receptive receptive provide provide provide compute compute objects objects objects location location location location location location location location location location location location location location eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined goal posterior posterior posterior connected gain gain gain gain gain gain gain motor cortical cortical cortical cortical cortical cortical cortical cortical equal mit comparison comparison fields fields fields fields fields fields fields fields fields fields fields dependent dependent dependent institute internal code responses responses responses responses responses responses responses layers layers addition maps maps maps maps maps maps maps maps maps considered framework cambridge computing equivalent environment hinton effects determine upper upper vision vision pages increase increase developed developed developed developed levels area area area area area area area types types types types provided evidence backpropagation nature depends depends discussion feedforward group transformation transformation transformation transformation transformation stable predictions predictions finding shape end hypothesis hypothesis hypothesis rumelhart rumelhart sensory including typically typically needed needed fully testing testing head head head head head head head head head head head head head head head head consistent consistent trials call numbers early early early early early early frame attention produced directions directions recent movement movement movement movement movement reported reported side hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical subset sejnowski sejnowski sejnowski sejnowski recently sufficient compare previously previously observations volume solve trans trans background background locations williams increased suggests rotation move setting editors interactions sigmoid retina retina retina retina retina designed suggest encoding encoding strong proportional variety exist movements movements movements movements movements movements movements movements movements areas areas areas areas areas areas areas appears produces longer perception factors primary primary laboratory multilayer multilayer coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates simultaneously electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical transformations transformations develop implies john john independently depending stages stages stages stages stages communication influence evaluate restricted restricted restricted restricted showed modulation modulation modulation modulation centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered static static sizes sizes suggested suggested allowed earlier earlier earlier intermediate intermediate intermediate handwritten coordinate coordinate coordinate coordinate color color retinal retinal retinal retinal retinal retinal retinal plotted illustrated activated activated partially gating determining aspects aspects encoded encoded encoded encoded encoded mcclelland induced induced interpreted interpreted physiological physiological denker cat consisted preferred preferred preferred body explore explore stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation essential varied fashion lgn affect encode hierarchy circles circles circles transmission opposite perfect eyes thought adjusted fisher fisher fisher explain brown site site site distinguish distinguish shared shared closer organized organized organized monkey afferent ion res res outer integrating psychophysical psychophysical psychophysical backprop share recordings recordings howard gains measuring modulated modulated qualitatively simulator findings converged contribute primarily tation saccadic saccadic saccadic recover purely purely purely purely repre lecun lecun arranged anatomical significance primate interpret neurobiology monotonically corner lip lip studying dominant intended intended jackel reproduce parietal parietal parietal parietal parietal parietal parietal parietal stimulated stimulated stimulated stimulated stimulated stimulated stimulated stimulated stimulated gaze gaze gaze gaze gaze jolla saccade saccades probe projects designing implicitly receiving adopted balanced fusion zipser ure visually goodman goodman boser solely personal chapter evoked evoked evoked evoked evoked evoked evoked henderson goals pdp retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic terrence fixation guided pos pos zip weaker sweeps page page programmed compu 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weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit distribution distribution approach point image image image image image image image single single single single single single single single processing processing processing processing processing processing control control control control control control control control control large local local local local local neuron neuron rate rate patterns optimal inputs form form form form form form shows signal simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper paper size feature feature feature feature feature feature feature feature feature feature 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sequence target target target target target target target target constant computer computer distance connections connections science science science science direction map map map map map map map map map map map map map map map map map present present activation activation activation temporal object object object object sets sets sets sets motion press press components components components abstract computational computational computational computational computational properties references component context context introduction introduction complex complex complex behavior effect effect parallel parallel parallel parallel parallel cost search search search search search search search search search search search search search search search search search search search tion difference variable spatial signals signals higher higher higher part part center center firing firing required required multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good long represent represent make make fact region region proposed proposed ing tasks total human human human human human computed computed computed computed computed sum sum times means natural natural global global global global knowledge knowledge knowledge filter original specific represented desired receptive receptive receptive provide provide objects objects objects objects objects objects objects objects objects objects objects objects objects objects location location location location location location location location location location location location location location perform active eye eye eye eye eye eye eye eye eye eye eye experimental experimental experimental posterior posterior posterior posterior posterior posterior connected connected motor cortical cortical brain brain mit steps steps steps fields fields fields fields fields update support modeling institute institute implementation code individual individual individual represents connectionist connectionist connectionist responses difficult addition addition maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps cambridge computing computing directly directly view top top top top top stimuli stimuli stimuli stimuli effects effects effects effects detection detection conference efficient efficient requires requires requires significant significant speed basic basic increase increase give con weighted area area lines path actual processes evidence evidence evidence evidence nature nature inhibitory constraint simply biological discussion describe denote tested fast fast fast assumption corresponds actions finding implemented implemented shape role role require require main journal journal journal journal ability ability ability ability ability ability hypothesis hypothesis hypothesis hypothesis development sensory including including including auditory smaller underlying underlying functional unknown fully interesting york increasing mechanism mechanism consistent consistent consistent consistent consistent consistent uniform operation leads principal principal principal representing details details inhibition stored international international international bottom bottom bottom bottom bottom early early early early early early early early early attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention minimize minimize choose run sources light denotes directions recent resolution advantage advantage property property separate takes takes takes movement reported lateral lateral strategy strategy strategy pixels subset cognitive relevant previously previously unsupervised calculated volume module module correspond studies locations locations locations locations locations gate sensitive horizontal horizontal lead studied studied studied suggests move move move generally setting setting setting hardware flow critical minimal minimal minimal minimal minimal hebbian conclusions valued editors editors sigmoid modules modules modules modules accurate retina suggest suggest suggest taking strong integration presence presence largest external characteristics demonstrated demonstrated proportional exist exist exist movements movements selective selective relationship relationship targets manner manner groups connectivity configuration question areas areas areas areas areas areas areas areas areas areas areas areas pro van perception perception perception solving ways primary primary sequential sequential describes describes describes vertical vertical vertical vertical modeled implement coordinates coordinates simultaneously easy frequencies events shift shift shift shift shift select select national focus focus focus focus focus focus review review review communication influence influence detailed updated updated showed translation calculation neighborhood intervals add iterative generation generation intermediate fire fire thesis combinations activations color retinal sciences determines mozer discussions gating gating gating gating gating gating gating gating gating major aspects aspects closely closely effectively identify detect literature efficiently efficiently efficiently efficiently computations projections receives receives receives strongly induced anderson anderson neuroscience neuroscience neuroscience superior superior superior superior superior superior superior superior superior superior superior physiological physiological physiological physiological strategies list involved involved involved involved involved involved involved involved involved absence correspondence highest highest binding moves overlapping remain unlike production access essential difficulty updating updating detail detail examine matches matches matches rest rest possibility relationships relationships relationships relationships relationships authors authors decisions working gates lgn lgn lgn encode understand topographic topographic topographic analogous analogous neu smallest possibly possibly possibly man extremely psychology implementations thought adjusted precise separated separated nerve hebb academic fibers detected explain serial phd electronic integrate integrate scenes orientations fairly fairly slope coded explanation answer briefly spatially turns berkeley berkeley sections sections ring directional located leaves mation circle circle localized localized annual annual researchers researchers requiring people people people pathways understood relevance relevance conducted fed readily red psychophysical psychophysical recordings incorporated slower slower continuously continuously psychological psychological commands requirement extracting incorporating suited germany coherent findings findings implements focused damage damage patients patients patients patients patients attentional attentional attentional attentional baird displays phenomenon picture uncorrelated physiology physiology restrict restrict saccadic saccadic ratios pick dynamically dynamically circular count eliminate enhancement adds ments accepted primate primate siemens siemens reasoning shifts shifts monotonically spot optic responsible guide carry infor bartlett becker overview overview conjunction conjunction conjunction intended monkeys monkeys searching chooses chooses parietal parietal parietal parietal parietal parietal advance thin suggesting refers saccade saccades saccades saccades saccades colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus arrows horizon extensively extensively relies davis omohundro omohundro discovered assigns assigning discriminate 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psychologists moran cluding memorial 
#@Ahmad_S,
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visual visual visual visual visual visual visual visual visual paper small small small net net net net task task field field field features features process level level problems problems problems problems problems random random random random random random high high similar similar show equation equation section line line line line line line line rule rule images images images images images images images images general parameter real approximation approximation approximation theory theory theory note experiments dimensional university variables variables computation independent log found sequence sequence sequence sequence constant computer computer computer computer terms distance science science present present sets sets continuous abstract back find find find analog analog references due ieee decision introduction circuit statistical effect generated complexity complexity lower lower part multiple multiple multiple multiple good long long represent represent bayesian bayesian bayesian bayesian expected expected fact correlation correlation scale simulations resulting ing ing tasks computed respect sum sum sum performed means optimization optimization optimization optimization optimization natural orientation global global global global global knowledge original artificial relative represented compared objects objects location determined distributions discrete nets nets nets nets nets nets nets nets report department department version version internal joint joint final final final exp exp exp scheme scheme addition domain domain view curves curves curves curves curves design effects conference conference upper upper approximate vision vision vision vision pages derived derived derived lines actual processes nature simply achieved technical group transformation corresponds finding finding short instance instance instance degree makes including objective objective objective objective objective objective objective objective objective objective objective objective probabilistic probabilistic probabilistic unknown unknown unknown interesting segmentation matching matching matching matching matching operation operation stored international depth frame frame frame frame frame frame sources sources pair strategy include subject identical hierarchical inference inference inference inference dimensions dimensions dimensions sufficient previously tions match match match match trans trans positions locations locations locations locations symmetric generalized generalized williams williams williams horizontal horizontal horizontal horizontal horizontal parts studied studied rotation rotation rotation rotation rotation rotation deterministic deterministic clusters boundary flow starting place segment segment accurate accurate numerical performs strong hard physics intelligence assuming minimizing decrease introduce introduce scene scene scene configuration annealing annealing appears pro derive derive optical segments segments segments segments missing explicitly linearly involves involves consisting consisting shift quality yield yield national extracted formation reconstruction interpretation interpretation solved labels labels frames frames frames approximated translation translation translation translation translation key roughly add sufficiently euclidean figures inter instances assignment recognize grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar columns extra differ delta fine summary repeated dis generative usual dot dot dot dot dot dot dot dot dot dot dot dot minimizes leading principles illustrates illustrates mixing approximating decreasing camera camera camera simpler simpler exhibit replaced hanson hanson hanson matches successive root func hierarchy matched coarse equally versions consist grouping arbitrarily rows ment crucial agreement tractable worse starts processed straight formalism easier producing gradually optimize qualitative requiring pure flexible posed dots dots dots dots dots dots dots dots dots dots dots dots dots ture extracting monotonic yuille yuille yuille semantic shifted corrupted indices labeling optimizing repre rotations generality systematic iiii iiii proceeds replacing methodology optimally grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars recovered recovered recovered recovered recovered recovered mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness sim elastic elastic elastic recovery modelled permutation permutation permutation horizon displacement displacement displacement displacement displacement displacement yale yale formulate willshaw willshaw willshaw eric translated pami token eliminating proach translations fea durbin durbin durbin differing removes handled deletion argmax argmax argmax lated arrow arrow arrow err pictures dcs horizontally seattle rangarajan 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#@Mjolsness_E,
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visual visual visual visual visual visual examples examples examples examples size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net net work work work work work work task task task methods step field field features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features process process process process level level current current current current trained trained random random random random response response response response response response response response response response similar similar representation representation representation architecture architecture architecture architecture architecture architecture show fixed fixed line rule rule rule rule rule rule vectors images images images images images images images images images images images images images general generalization generalization generalization real real real approximation average average average average theory gradient experiments activity activity activity activity activity dimensional dimensional dimensional result university university university computation research research research independent target target target target target dynamics dynamics initial initial initial constant constant standard computer computer terms connections connections science science science left presented presented present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation activation activation activation activation activation activation activation activation frequency frequency frequency temporal machine object object object object object object object object maximum range range range press press learn position components components components continuous sample abstract back back back back back find computational computational properties properties references component stochastic due procedure adaptive adaptive propagation propagation complex complex complex complex complex complex complex complex complex stimulus dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated recurrent search tion difference difference difference spatial spatial lower lower lower rules measure signals learned learned part bound cases cases firing firing type type type type type required multiple multiple multiple multiple cortex cortex conditions represent make fact region region region proposed proposed proposed proposed correlation simulations simulations simulations resulting ing ing total simulation human human computed computed performed called called times elements elements means natural orientation orientation global artificial relative relative relative relative represented represented compared receptive objects objects objects objects objects objects objects objects objects objects objects location location perform perform determined determined related related related connected connected discrete brain equal approaches steps accuracy update proceedings report department implementation consists internal internal joint represents represents represents responses difficult difficult layers layers maps considered domain domain domain domain hinton view solutions san top top conference upper upper world vision vision vision basic con area types types types types types lines product actual iteration iteration iteration iteration iteration iteration iteration iteration nature biological increases describe group group group group tested corresponds stable proof finding amount shape shape supported including underlying jordan segmentation segmentation segmentation segmentation mechanism mechanism consistent consistent consistent trials uniform principle operation representing call iterations iterations iterations iterations max pre early frame idea attention produced light neuronal directions directions directions recent correlations property robust robust reported include hierarchical hierarchical subset array array array array array cognitive engineering dimensions sufficient varying previously solve match match match converge achieve diagonal diagonal background locations locations symmetric grid grid gate williams williams organization grant grant amplitude amplitude amplitude amplitude constructed horizontal horizontal lead lead studied occur trial trial spikes feed locally generally flow flow flow critical segment segment segment segment segment valued valued valued valued valued valued depend clear clear performs performs learns learns learns constrained constrained propose external proportional intelligence labeled labeled turn variety plane manner scene acknowledgements relation perception sequential label vertical vertical mathematical distinct dept dept dept segments segments segments segments simultaneously involves involves angle scales equilibrium letters national review overlap updated decomposition decomposition decomposition activities similarly suggested suggested updates allowed processor key earlier earlier performing reduces generation assigned construction foundation handwritten perceptual combinations contour contour assignment sciences discuss mozer mozer mozer mozer mozer coupled absolute absolute structural structural reason selecting aspects differ identify oscillatory oscillatory oscillatory detect detect detect detect projections essentially traditional refer repeated heuristic success interpreted symmetry symmetry sin running oscillations timing gray gray gray gray gray comp comp usual michael relaxation relaxation relaxation relaxation dot quantization highest binding binding binding binding binding binding binding binding binding cat principles principles principles principles overlapping overlapping overlapping overlapping neighboring neighboring intrinsic oriented presents minimized american exhibit rapidly limitations limitations periodic helpful examine examine matches respond respond investigated relationships workshop phases phases phases phases phases phases phases phases phases phases phases phases phases phases phases phases phases notion contours contours contours contours patch patch patch patch patch patch patch coarse plausible configurations configurations configurations configurations configurations configurations configurations man psychology psychology subsets der der der der panel panel explored shapes nervous academic utility grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping attempts attempts indicating scenes cos ground publishers phenomena london spatially processed perspective leaves pool pool scientific describing circle toronto toronto toronto toronto patches cybernetics cybernetics meaning nsf researchers researchers geometric reflects reflects people people freeman conducted capability capability capability readily completion incorrect biologically psychological psychological psychological fall incoming achieves singer adjust richard coherent boston comments display segmented synchronization synchronization globally accomplished labeling labeling labeling assign forming formally acts dynamically zemel zemel zemel null connecting arranged arranged arranged arranged arranged clamped clamped extending chance proceeds primitive primitive interpret interpret mark belong belong monotonically 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magic magic magic discovers discovers undergo massive greatest experimented illusory polar linking predetermined palo facilitates investigator bodies predefined unaffected unaffected unaffected tightly yon yon yon settles align align conveyed ontario ontario schneider schneider uniformity bind terminated eckhorn eckhorn picks clamping conveys panels tar faculty presidential psy tours permitted mart mart gra kanade kanade engel govern labelings segregated conducting groupings indicative aligning chemistry unsegmented koenig cleaned gestalt gestalt party rock rock reciprocally reciprocally diamonds diamonds diamonds diamonds diamonds ject cocktail succeeding synchronizing scholarship laid biolog oper iments underway anticipated tick thi kruse behrmann behrmann behrmann homologous hummel hummel segregate parses brosch segmenta munk multitude sed netj netj prevalent mand squ nput nput postgraduate 
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data figure figure figure figure figure set set set set set networks networks training training training training algorithm output output output output output output output output output output output output output output output output output output output output output output output system system system system system system system system system system system system system results results results results results results results information information information information information information information information problem models hidden based based based based based based based based based based based based based based based based based based based space space space space space space weights layer layer layer layer layer case vector vector vector vector vector vector vector vector order shown shown values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability weight functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image processing processing local local rate rate rate rate rate patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class inputs form form form gaussian visual paper examples feature feature feature feature feature feature feature feature feature feature feature feature feature work work work work work work work work work task task task task task task task task task task fig fig fig fig fig features features features features classification classification classification classification classification classification classification classification classification classification classification classification process process process process level level level level level high high high memory representation representation representation representation architecture fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors images images general generalization generalization generalization real real real average theory obtained dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result result university computation research research research log log log found found initial initial initial initial initial initial estimate estimate estimate computer node node node node left left left left presented presented presented presented presented presented presented presented presented presented presented presented presented map map map map phase phase phase phase phase low frequency frequency frequency frequency machine press learn learn learn basis continuous continuous continuous abstract find find computational references component ieee procedure decision introduction complex estimation behavior search tion tion variable spatial spatial spatial spatial classifier classifier classifier classifier classifier rules rules rules rules rules rules rules measure measure measure measure prior learned learned learned learned chosen chosen higher higher higher higher higher part part part part center center center previous cases multiple bayesian proposed proposed correct correct forward scale scale scale finite simulations classes classes classes classes classes classes classes classes classes classes ing simulation regions regions regions regions means dimension dimension dimension made natural natural natural natural natural natural natural natural natural natural feedback feedback feedback feedback feedback orientation applications applications knowledge knowledge original original vol vol artificial artificial artificial samples samples represented true application application desired desired provide define goal goal related posterior connected discrete support support support source proceedings institute institute department department version technique consists consists code code individual joint joint represents represents represents represents represents difficult difficult difficult difficult scheme scheme scheme scheme addition maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps considered framework framework framework framework framework framework framework framework framework framework framework framework domain domain domain domain domain domain estimates estimates estimates estimates estimates estimates estimates top top top top top stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage detection conference efficient world world vision give produce clustering clustering area area area area provided evidence evidence evidence evidence biological biological associative achieved achieved achieved achieved achieved achieved group complete eds journal square ability ability ability future future degree probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown technology block mode operation representing filters filters filters filters filters filters filters window bits international bottom bottom supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised early frame combined combined combined combined combined recent recent correlations correlations resolution advantage advantage property introduced hierarchical array recently engineering engineering interest interest dimensions dimensions dimensions unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised axis studies studies achieve achieve achieve trans channels grant invariant extended wide rotation correctly feed clusters clusters clusters white white demonstrate conclusion minimal reduce valued valued valued measures encoding strong mechanisms largest demonstrated demonstrated demonstrated demonstrated demonstrated demonstrated demonstrated california intelligence labeled labeled labeled labeled labeled radial iii scene scene identification identification identification identification areas perception optical laboratory label label label label label confidence implement electrical electrical involves scales scales consisting gaussians events springer shift extraction extraction extraction extraction extraction extracted family viewed viewed labels labels decomposition suggested suggested suggested suggested discrimination diagram smoothing smoothing smoothing smoothing boundaries filtering filtering filtering kohonen kohonen kohonen kohonen classified transactions degrees existing existing fire fire fire fire includes recognize extension prove black black structural successfully successfully texture texture texture texture texture texture 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capability exhibits spread modulated pasadena achieves enables enables enables enables enables enables logp pyramid pyramid pyramid contribute shifted representative college identifying labeling labeling tation gabor gabor gabor gabor gabor gabor gabor gabor databases discovery discovery discovery discovery discovery discovery discovery discovery discovery discovery discovery satisfying multiplicative attractive contract optimally utilized utilized utilized utilized sion respective evident evident darpa informative informative informative informative park valuable associations specification goodman goodman goodman goodman goodman goodman goodman goodman goodman poses encouraging distinction utilize utilize utilize sinusoidal laplacian laplacian clustered clustered quantized quantized quantized goals proba afosr challenging challenging adelson adelson differentiation differentiation smyth smyth smyth ultimately projecting noting multiscale relates win represen library library library 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#@Chellappa_R,Goodman_R,Greenspan_H,
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order order shown shown systems values values functions functions neurons recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method approach approach approach approach approach approach approach approach approach pattern point point image image image image image image image image image image image image image image image image image image image single processing processing analysis analysis matrix matrix matrix matrix matrix shows simple simple simple simple visual visual visual visual visual paper paper small small small small small small task task cells cells points points points points points points points points points points points process process process structure structure structure random memory memory memory response response similar similar similar similar representation representation representation representation show show show show show show show section section section section section vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images images images images images images images images images general general real real approximation obtained obtained obtained note note note dimensional computation research research research research research research independent independent independent independent defined defined found found constant connections science science left left left left left presented presented presented presented map machine object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object motion range range position position position basis basis basis basis continuous sample abstract applied applied back back find properties properties properties references due due ieee ieee important propagation introduction parallel parallel tion tion tion change assume representations representations representations part previous previous previous previous cases cases cases type type type required required required represent represent represent represent distributed fact proposed observed observed observed observed scale scale human respect called factor factor dimension obtain original vol vol artificial artificial artificial artificial artificial specific specific represented represented represented represented represented application application application define define compute objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc proc proc proc location location eye determined posterior constraints constraints constraints constraints brain approaches comparison comparison support report report institute institute words words words department department version consists internal difficult final scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme addition addition addition addition addition addition ai considered cambridge computing computing computing hinton additional view view view view view view view view view view view view view view view view view top top top top requires requires requires vision produce developed actual actual provided nature nature simply associative associative associative associative associative feedforward arbitrary arbitrary arbitrary transformation transformation limited inverse inverse inverse inverse predictions predictions proof proof common implemented implemented implemented implemented implemented implemented shape shape supported require square ability instance instance future smaller combination combination combination combination combination combination combination combination functional coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients technology technology technology interesting testing projection projection edge structures structures matching representing details call stored stored stored stored stored bottom bottom bottom early predict predict architectures architectures discussed directions recent exact exact property property separate takes apply quadratic quadratic quadratic subset cognitive recently interest sufficient compare previously tions smooth smooth studies trans trans definition positions positions positions modified modified observation bounded organization storage entire entire entire constructed exists scaling scaling suggests extended matrices rotation rotation correctly operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator accurate designed learns suggest suggest suggest suggest encoding propose california solid intelligence intelligence intelligence intelligence intelligence radial radial start exist exist introduce introduce identification identification suppose van van construct longer optical describes laboratory laboratory laboratory dept modeled modeled modeled modeled implement missing explicitly explicitly coordinates coordinates coordinates linearly linearly linearly linearly involves involves involves involves transformations transformations transformations transformations transformations develop applying applying applying applying expressed expressed expressed expressed viewed restricted updated approximations centered centered centered suggested suggested suggested translation translation performing measurements fitting boundaries valid valid intermediate filtering visible sufficiently sufficiently construction kohonen kohonen advantages advantages views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views existing existing template figures figures includes perceptual combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate recognize recognize recognize recognize prove variations partially middle aspects aspects capable differ poggio poggio build build computations schemes schemes schemes schemes schemes projections composed summary soc notice conf conf conf kind showing anderson lie follow follow follow hold hold involved paradigm correspondence correspondence correspondence correspondence correspondence correspondence correspondence acknowledgments extend simpler selectivity collection collection collection difficulty kalman tech biol int int office cognition notion surfaces contours math predicting created created changed front assumes academic pyramidal consist massachusetts advanced agreement orientations majority handle handle handle london london directional located scientific recognized recognized separately cybernetics recognizing recognizing alignment alignment alignment apparent applies affine pseudo pseudo pseudo embedded embedded embedded embedded fed car continuously sharp span span ordered boston returns returns returns implements pyramid pyramid pyramid phenomenon acquisition lab appearance appearance appearance appearance acm recover recover naval robotics robotics rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid communications oja oja ments familiar familiar familiar familiar contract viewpoint viewpoint viewpoint serves transforms transforms transforms transforms constructive obstacle reliably edelman edelman appendix appendix appendix appendix appendix appendix lawrence reproduce parietal viewing viewing claim claim claim israel recog occlusion occlusion occlusion erlbaum projects automated assigning verify informa abu abu mostafa mostafa kluwer opposed nition restrictions descriptions tor hillsdale unseen preserved life ullman ullman ullman ullman ullman ullman ullman ullman ullman ullman ullman ullman ullman lond rbfs rbfs unconstrained spanned spanned spanned associates memo indication programmed cube 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performance performance based based based based based based space space space space space weights weights case vector vector vector vector vector shown shown weight weight distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method approach approach approach approach pattern pattern pattern pattern point point point image image image image image image image single single processing processing processing neuron neuron neuron rate rate rate test test test test analysis matrix inputs inputs inputs inputs inputs shows 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representation representation representation show fixed vectors images images images images images images images images images general general general general general generalization generalization speech speech theory theory theory theory theory theory obtained obtained obtained experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university threshold solution solution solution research research research independent defined defined found found found found found target target target standard standard standard standard standard computer computer computer terms distance distance connections synaptic synaptic synaptic science science science science science science science science science science left left presented present present phase phase low object 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compared compared provide objects objects objects objects objects objects objects objects objects objects objects objects objects objects experimental related related related related connected cortical equal mit comparison larger support support support source modeling morgan proceedings proceedings institute institute institute institute implementation internal represents difficult scheme considered cambridge equivalent experiment experiment experiment hinton view view view view view view solutions solutions san stimuli stimuli effects choice significant statistics vision vision pages pages pages pages increase condition condition condition condition condition condition condition condition condition condition derived developed provided finally processes nature nature nature inhibitory biological biological achieved achieved discussion discussion discussion describe tested corresponds excitatory stable stable stable stable predictions finding generate supported role require main journal journal pixel pixel ability ability ability hypothesis cluster cluster easily noisy sensory kaufmann objective simulated simulated simulated technology technology interesting interesting testing testing testing testing testing testing significantly significantly character projection projection projection projection projection york increasing increasing consistent leads details details pre stored stored bits supervised attention combined neuronal directions directions recent recent recent recent resolution property element apply pixels hierarchical sejnowski array cognitive cognitive recently dimensions previously previously previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised subjects subjects subjects subjects subjects subjects subjects subjects volume axis axis correspond correspond studies studies locations bounded improvement increased amplitude constructed horizontal horizontal lead 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generalize absence paradigm paradigm paradigm neurosci consisted subsequent extract law explore origin selectivity carried american wiley involving humans association preliminary pursuit pursuit pursuit school applicable plasticity plasticity office office referred proved understand notion neu editor man analyze psychology equally friedman friedman extent utility submitted motivated motivated attempts synthetic massachusetts massachusetts brown brown brown distinguish agreement orientations defining caused briefly tractable tool worse arc arc style located located mathematics projected projected projected acknowledgement universal universal members lowest patches depicted geometry recognizing recognizing preceding meaning cochlear led led relevance amounts conducted readily psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical biologically psychological psychological berlin rely rely aim extracting asymmetric findings multidimensional benefit physiology proportion proportion cooper cooper cooper cooper impossible naval rotations rotations theories theories establish binocular ments ments chance stronger stronger replacing familiar familiar familiar viewpoint viewpoint viewpoint viewpoint wire wire wire ral imply affected illumination degradation mance mance mance edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman displayed perfor perfor perfor infinity sphere lawrence viewing israel deg deg occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion vertex specificity passing erlbaum hart summarize tures tures verify summer gold gold gold gold gold gold gold gold gold gold gold constitute shepard shepard annals pointing misclassification misclassification ent session validity asked munro randomized forced conjecture par comparative connec intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator spaced tor tor hillsdale examining examining examining clustered visualization favor formance duda duda graphics compatible hughes hughes guided academy emphasized familiarity memo memo minor fea fea modality indication exploratory exploratory psychophysics increments experi modal topography lighting appearing simplification bienenstock bienenstock vii jersey puts lists bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm pronounced replicated replicated usefulness distinguishing concerns equa extracts manipulated juang optics raises rel remained handbook handbook occluded occluded occluded occluded occluded occluded occluded occluded seg wires wires wires wires wires wires wires unexpected addi distractor asymmetry 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results results results units units units units units units units units units information problem problem problem problem problem problem problem problem problem problem hidden performance performance performance performance performance performance based based based based based based based space space space space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector vector vector vector order order order order order order order order order order order order shown shown shown systems systems values values probability parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions neurons unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method pattern pattern pattern image processing control control control rate rate test test test test test analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs form form form simple simple examples examples examples examples examples examples examples small small small small small small small small feature feature methods classification classification classification classification classification classification classification level trained structure structure structure structure structure structure structure structure structure structure structure structure problems similar similar similar similar representation representation architecture architecture architecture architecture architecture architecture show show equation equation fixed vectors vectors images general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter approximation theory theory theory obtained obtained obtained obtained obtained obtained term term experiments experiments experiments dimensional threshold computation computation independent log log defined defined defined defined found sequence sequence sequence initial constant table table estimate terms terms terms prediction maximum learn components components basis basis basis basis nonlinear nonlinear outputs abstract applied applied back find find properties properties properties properties properties references component component component component component due due ieee positive positive procedure procedure procedure procedure procedure procedure decision propagation introduction introduction estimation estimation effect effect cost cost cost cost cost cost cost cost tion change change change energy difference assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower measure chosen chosen higher higher higher higher higher cases cases cases good good good good good good binary binary binary bayesian expected expected expected proposed proposed correlation correlation errors minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting ing ing computed computed computed respect performed performed performed called elements elements factor factor factor factor factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension global global knowledge obtain specific compared desired cross cross define experimental goal related brain brain brain brain brain equal approaches train train selection morgan proceedings report implementation technique consists code kernel kernel advances joint difficult exp bias ai framework computing equivalent equivalent additional additional additional additional curves estimates design limit effects effects effects effects conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine determine determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper full free free estimated pages pages increase increase increase 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layer layer layer layer layer layer layer layer layer layer layer layer layer layer case order shown shown systems values noise noise noise neurons neurons neurons neurons neurons neurons neurons recognition recognition recognition recognition recognition recognition approach approach pattern image image image image image image image image image image image image image image image image image image image image image image image image image single single processing processing large large large large large large large large large large large large local neuron neuron neuron neuron neuron neuron analysis class class inputs inputs inputs form form form shows shows shows shows signal signal signal signal signal simple simple simple paper examples examples small size size size size size size size size size size size size size size size size size size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature 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machine machine object object object object object object object object object object range range range position outputs outputs abstract applied applied back back back find computational computational analog analog analog analog references propagation introduction complex complex complex dynamic search search search search search search complexity variable variable variable variable variable variable classifier classifier lower lower signals signals signals signals prior representations part part part part part part part part cases required required required required multiple good good good conditions represent represent chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make fact techniques techniques techniques techniques techniques forward scale scale scale scale scale scale scale scale finite classes ing ing ing tasks tasks total human elements means factor factor made made orientation orientation applications applications applications applications applications applications study knowledge obtain vol vol vol vol artificial specific specific specific true application application application receptive provide provide compute objects objects objects objects objects objects objects objects objects objects proc determined goal connected power power contrast connection connection fields fields fields fields train nets nets morgan consists kernel kernel joint responses responses responses difficult difficult final final maps maps maps maps maps maps additional estimates limit stage determine determine determine determine efficient classifiers upper upper requires requires choice speed vision vision vision produce produce developed area area area area area area area types lines lines lines lines lines lines depends constraint constraint arbitrary fast fast fast limited corresponds finding finding finding finding amount amount short effective implemented require main end end end easily makes typically typically typically typically typically pairs needed reduced account functional transfer character character character edge edge edge edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation special database principle operation details details numbers numbers numbers numbers numbers numbers stored normalized attention combined combined combined minimize produced light robust robust takes takes element practical practical practical introduced strategy include pixels pixels pixels pixels pixels pixels pixels interest interest interest interest interest interest highly varying conventional works works tions match address address background background positions positions positions positions generalized sensitive horizontal parts parts studied scaling digital digital digital digital digital digital wide wide wide wide correctly correctly move touretzky white white white hardware pass half flow flow conclusion critical row row reduce segment performs practice taking strong strong strong strong mechanisms presence presence presence demonstrated intelligence variety variety start selective iii iii iii iii iii iii introduce characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters groups scene identification identification identification identification identification program base areas areas areas areas digit pro edges edges written ways ways vertical vertical vertical vertical simultaneously simultaneously transformations scales scales scales scales scales integrated integrated quality quality blocks extraction extraction extraction extraction choosing choosing extracted extracted extracted extracted extracted focus focus estimator viewed solved variation variation variation variation transform transform densities densities evaluate static sizes sizes sizes sizes sizes sizes 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proper proper proper proved matched possibly necessarily reading reading reading reading analyze created created adjusted adjusted algo freedom shapes shapes shapes shapes shapes shapes detected extent extent seconds mentioned great great rows band directed crucial crucial convolution convolution analyzed answer expensive handle handle comparisons inside straight preprocessing operators located located controls laboratories projected projected read read robustness geometric varies varies substantially documents car car car car marked marked detecting passed maxima maxima schematic schematic schematic schematic schematic howard switch spread extracting extracting extracting cal tank gave display simultaneous picture identifying feasible sort investigation tation rithm member dynamically flexibility flexibility printed grows rotations lecun lecun arranged arranged suppression kaufman ments difficulties iiii iiii iiii mail alpha resulted bands mark operates corner corner corner heuristics 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information information problem models hidden performance performance based based based space space space space space space space space linear layer layer layer layer layer layer layer layer layer layer layer case vector vector order order order order order order shown shown shown shown shown shown shown shown shown systems values weight weight unit unit unit unit unit distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach pattern pattern image image image image image image image image image image single single single single single single processing processing processing large local test test test class optimal shows algorithms algorithms simple examples small small small small small size size size feature feature feature feature feature feature feature feature feature feature work work work work work work work task methods classification classification process process process level current current current trained problems high high similar similar similar similar similar architecture architecture architecture architecture architecture architecture line line line line vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images speech speech speech speech speech speech real gradient gradient gradient university university computation computation solution solution solution research defined initial table computer computer computer connections node science left direction direction direction direction direction presented map map present activation nodes press learn position position position outputs continuous continuous sample abstract back back back back find convergence references stochastic due ieee ieee ieee ieee positive procedure procedure procedure procedure procedure procedure propagation propagation propagation introduction hand statistical dynamic dynamic generated variance parallel variable assume lower rules word chosen chosen chosen chosen chosen chosen chosen part center center previous previous cases cases type required markov fact length correct correct correct correct correct correct correct correct correct correct correct correct probabilities errors forward forward forward resulting multi multi multi multi multi multi multi multi times regions regions regions reinforcement reinforcement natural feedback global applications applications applications negative negative negative original original vol true receptive rates rates rates rates rates rates perform constraints connected connected connected connected connected connected power fields support morgan proceedings proceedings proceedings proceedings report department department version code code code code code code code code individual individual advances represents connectionist difficult final layers layers delay addition graph graph maps maps maps maps maps maps computing equivalent hinton hinton additional view design design limit top top top conference determine efficient statistics speed pages give developed levels levels lines path path path product selected iteration constraint technical feedforward describe tested fast close corresponds corresponds finding assumed generate pixel pixel pixel pixel future future easily easily rumelhart rumelhart probabilistic combination reduced reduced unknown technology programming programming interesting testing character projection projection projection edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation call direct making international normalized normalized normalized bottom bottom magnitude frame combined combined combined combined combined architectures resolution separate pixels highly module module tuning axis solve achieve address background modified generalized constructed horizontal horizontal horizontal lead concept extended feed feed feed feed hybrid touretzky width width width white column column hardware pass pass strength segment segment segment segment segment segment segment segment conclusions editors editors moody exponential faster learns constrained constrained constrained constrained constrained constrained constrained propose propose hard largest reduction demonstrated demonstrated digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit construct edges written generating vertical vertical vertical segments segments segments segments segments segments segments implement multilayer slightly integrated applying applying applying springer john interpretation interpretation codes lee lee centers centered sizes digits digits digits digits digits digits digits digits digits digits digits digits digits digits reasonable roughly generation string string string classified handwritten handwritten handwritten handwritten handwritten handwritten handwritten kernels combinations strings strings bell batch recognize extension extension automatic candidate candidate candidate candidate candidate candidate candidate candidate coupled reason regular straightforward society driven tdnn efficiently score score score score score verlag cun cun cun cun cun cun cun cun lie oscillations follow built simplified denker denker denker denker denker denker highest highest highest reach overlapping overlapping extend explore parametric rise reducing giving relationships scores waibel waibel waibel waibel circles circles reading reading recognizer recognizer recognizer recognizer recognizer assumes art art isolated isolated isolated ground ground ground convolution answer considerable processed processed processed rapid stanford stanford shared preprocessing laboratories acknowledgement author recognizing recognizing recognizing mellon alignment alignment alignment alignment raw integrating requiring improvements percent percent carnegie cmu marked marked marked marked marked passed incorrect howard rely pittsburgh ture differs resource neuro viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi baird calls sharing newton redundant printed proceed kaufman adds adjusting overcome mail attractive height height height scoring scoring analyzing guide heuristics heuristics exploring exploring service repeat widths conjunction lang lang jackel jackel propagated candidates candidates candidates chooses chooses winning winning thin thin thin speeds displacement displacement displacement displacement displacement displacement displacement divide divide leaving numerous converted tables convolutional convolutional convolutional pieces icassp icassp boser classifications burges burges burges burges burges henderson alternate num file hubbard picked unconstrained termed zip zip zip zip zip zip zip zip zip responding sweeps sweeps truth truth truth lippman bridle bridle rabiner gratefully reinforce reinforce christopher keeler keeler replicated replicated replicated engine engine holmdel architec push interpretations recognizes prone longest cuts acyclic segmenting segmenting zones zones rec replicate replicate zone zone zone zone postal cations spent appli inserted ton tutorial save weakness reminiscent yann acknowledged thompson novelty fogelman segmentations discard narrower numerals haffner haffner cleaned cleaned decoupled misses rault ume segmenter segmenter beneath beneath beneath beneath matan matan matan matan matan matan matan strained loth lends franzini franzini franzini franzini soulie 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algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number system system system system system system system system system system error error error error error error error error results results results results results results results units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information information information problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based weights weights weights weights weights weights layer layer layer layer layer case case case order order order shown shown shown systems systems systems systems probability probability noise noise weight functions unit unit unit unit unit unit unit unit unit unit unit distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image image image image image image single single single processing processing processing processing processing processing large large large local local local local local local rate rate rate test test test test test test test test test test patterns patterns patterns patterns analysis analysis form shows shows shows shows simple simple simple examples examples examples small small small small small small size size size net net net net net net net net net net net net net net net net net net net net work work task task fig step step step step step step step field field field field field field field field field field field field field field field field field field field level trained trained trained trained structure structure structure structure structure problems high high high high memory similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture show section section rule rule rule rule rule images general general general generalization generalization generalization speech speech speech speech speech average average average gradient gradient obtained term term term note note note note note note activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional university computation solution research independent defined found found found found target target target standard standard standard connections connections left left presented presented presented presented present present present present activation activation activation sets sets sets learn position position outputs outputs outputs outputs continuous continuous sample abstract applied back back computational references due due procedure important important propagation propagation context context introduction complex hand hand hand hand hand hand hand hand statistical variance parallel tion difference difference difference assume rules measure signals signals prior word word part center center previous cases cases cases cases cases cases type type required multiple multiple good good good long markov markov make fact proposed length length length length length length length length forward forward scale scale scale resulting tasks total total total total total respect sum sum sum times factor factor factor dimension natural natural applications applications applications study relative specific specific specific samples cross receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive objects rates rates location location connected steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison larger larger fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields train train train train train train train nets nets nets nets nets morgan report report institute department implementation consists individual individual individual difficult difficult final layers layers delay computing directly directly hinton hinton curves san effects speed basic give give con coding criterion entropy finally nature achieved achieved discussion technical tested fast fast assumption common require square square square vlsi future easily rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart noisy noisy noisy noisy including including objective needed combination combination combination technology block block block block block block block block block block block block block block block block block block block block block block block testing testing significantly character character character character character character character edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation special database database database database database database database database database database database database mode mode representing numbers numbers numbers pre pre pre making stored combined combined run architectures improve exact property reported reported side quadratic sense sense highly conventional approximately approximately module yields achieve achieve achieve address locations separation organization organization improvement entire entire entire invariant spikes correctly correctly feed touretzky touretzky occurs boundary pass demonstrate strength strength assumptions assumptions segment segment segment segment segment segment conclusions competitive competitive competitive editors accurate peak performs moody exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential faster faster mateo taking mechanisms integration drawn sigmoidal sigmoidal sigmoidal demonstrated demonstrated proportional labeled start averaged targets characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters scene scene program reference suppose digit digit digit winner ways confidence category category simultaneously simultaneously simultaneously simultaneously slightly integrated integrated integrated integrated integrated integrated integrated integrated integrated shift shift shift shift shift shift competition john letters decreases national overlap organizing organizing organizing organizing organizing forms forms forms forms forms forms digits digits digits digits digits discrimination epochs normalization normalization normalization normalization normalization sec reduces boundaries valid intermediate david coupling handwritten handwritten handwritten handwritten box activations activations priori usa recognize recognize recognize recognize illustrated discussions reason aspects aspects extra differ included detect invariance invariance receives kind cun allowing running running running write write delayed denker highest overlapping deal receive presents powerful essential essential lippmann biases giving project project project ideal proper neu neu waibel waibel act extremely psychology noted precise isolated isolated integrate scenes publishers floating answer answer answer handle reasons reasons comparisons processed processed drive stanford stanford precisely mation products cut acknowledgement recognized recognized recognized involve localized recognizing apparent apparent collected effort peaks solla incorporated sharp howard ture incorporating incorporating serve prevent segmented segmented segmented segmented focused progress progress credit summed summed pose person person benefit writing labeling labeling investigation restriction martin martin summing summing summing summing printed printed printed grey grey grey lecun turned wrong ments chance difficulties accepted occurred attractive serves nearby nearby ral ral degradation infor document ranging ranging connect connect loo loo encountered encountered equals sides lang lang histograms histograms jackel competing rich properly broken broken broken broken broken broken projects severe boxes boxes boxes linked linked linked linked linked linked linked linked ure ure parsing parsing slight converted shorter removal dec rejection rejection rejection rejection pointed boser copy avoided demon dominated bounding careful rejected rejected rejected topic covered portions portions sheet enforce west confusion investigations places commercial answers helps handled covers fortunately nist nist nist nist nist nist nist nist nist nist algorithmic crude crude austin compete keeler keeler keeler keeler keeler keeler keeler keeler keeler keeler keeler engine unreliable ters detects architec normalize normalize recognizes positional positional positional positional positional positional restrictive bottleneck sheets steve seg seg segmenting segmenting devoted denominator supposed rec tails favors favors richer tighter dilemma borders touch inte mentation acceptance acceptance translational translational burden nation numbered outlines rationale converting requests insure touching touching touching touching touching touching touching touching touching charac jim facing numerals numerals numerals numerals numerals numerals strated kauffman unsegmented standards didn mcc mcc mcc mcc pittman pittman xlx xlx xlx duplicated duplicate smart smart labor ported exponentials exponentials violates wee agreed leow leow leow translationally discrimi printing staff designate designate zipcode extrinsic segmenta organizes organizes organizes throwing grated census quires reprint wrote alphabetic blame discern proximately balcones 
#@Keeler_J,Rumelhart_D,
#t5
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#*network network network network network network network network network network network network network learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set set set set networks networks networks networks training training training training training output output output output output output output output output output output output output number number number number number number number number system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error error state results information information information information information information problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based based based space space space weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems values values values recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach point point point point point point point image image image image image image single single single single single single processing processing processing processing processing processing processing processing processing control control large large large large large local local local local local rate rate rate rate test test test test test test test form shows visual visual paper paper paper examples examples examples small size size size size size size size feature net net net net net net net net net net net net net net net net net net net net net net net net work work task field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field features features classification classification classification classification classification classification classification classification process process process level current current trained trained trained trained trained trained trained trained trained trained trained trained trained high high high high high high similar architecture vectors images images general general generalization generalization speech real dimensional university university threshold threshold threshold threshold threshold computation research research independent independent defined found sequence sequence sequence target target target target target target target target target constant estimate estimate computer distance distance distance distance distance distance connections connections connections node node node node node node node node node science presented present present activation activation activation activation activation activation activation low low low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal machine object object object object object object object maximum maximum position position position position position position position position position position position position components basis abstract applied density analog references decision decision decision decision context action hand hand hand hand hand hand hand hand hand hand hand behavior parallel cost tion tion tion tion tion classifier classifier classifier classifier prior word chosen center center center center center center center center center center previous cases cases cases cases multiple multiple multiple multiple multiple multiple make fact region length length correct correct correct correct errors forward forward forward minimum minimum minimum ing ing tasks tasks total total human human human human computed computed respect respect multi multi performed called called times means factor factor made natural applications applications applications applications artificial specific samples application receptive receptive compute objects rates rates rates rates rates rates rates rates rates location eye eye eye related connected approaches approaches approaches approaches accuracy accuracy larger larger fields fields fields fields fields fields fields fields fields fields fields fields fields train dependent dependent morgan morgan morgan report institute words implementation implementation version version version version version version version version technique technique consists consists consists consists code individual individual individual individual advances advances advances final final delay addition graph considered computing computing domain design design san top top stage stage conference conference conference efficient efficient efficient classifiers classifiers classifiers classifiers classifiers requires requires requires significant vision vision vision vision con con con condition levels actual processes processes backpropagation backpropagation backpropagation nature depends simply achieved achieved technical technical feedforward feedforward increases increases group group tested tested limited close close corresponds corresponds amount common generate require require pixel pixel ability degree degree degree degree makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart development kaufmann kaufmann typically smaller needed needed needed block testing testing ratio character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation database mode principle representing details filters pre pre pre pre pre making making making making window window window window window window window window window window window window window window window window window window window window international normalized normalized normalized bottom bottom run architectures improved resolution resolution resolution resolution advantage reported reported reported reported apply include pixels pixels pixels sense sense sense sejnowski sejnowski relevant relevant engineering sufficient highly varying previously conventional conventional teacher tions correspond achieve achieve positions positions entire entire horizontal horizontal horizontal scaling occur occur correctly correctly touretzky touretzky width width width width clusters white white white pass half half greater segment segment segment conclusions depend accurate retina retina clear moody weak learns learns mateo taking hard mechanisms labeled labeled labeled movements movements characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters groups acknowledgements areas areas areas digit digit digit digit digit digit digit factors factors primary sequential describes describes label vertical vertical vertical sensitivity category category explicitly linearly electrical involves involves remaining develop integrated integrated integrated integrated integrated integrated integrated integrated integrated integrated extraction john john letters letters yield national focus focus depending stages stages operations operations organizing centers centers centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered forms forms forms forms sizes digits digits digits digits digits digits digits digits digits digits digits digits digits key performing normalization reduces roughly roughly purpose iterative initially distances filtering string string classified classified classified david david david handwritten handwritten box box includes includes includes usa inter inter recognize recognize recognize recognize recognize illustrated specifically variations variations domains discussions middle aspects efficiency efficiency effectively effectively symbols included included efficiently comparing comparing essentially essentially receives success classify running cue vary simplified nips nips nips denker denker highest highest automatically attempt consisted overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping subsequent operating operating extract software unlike create essential lippmann dataset dataset dataset helpful tech decisions decisions decisions stream stream workshop workshop scores notion waibel smallest smallest act closest trace necessarily reading reading created versions versions algo shapes shapes extent percentage advanced ment directed directed track navigation lies comparisons considerable sys shared shared shared located laboratories recognized recognized recognized read recognizing recognizing recognizing recognizing recognizing recognizing recognizing raw integrating integrating integrating improvements varies applies flexible offset tional fed autonomous backprop passed employ remove continuously passes passes passes howard howard vocabulary gen extensions achieves enables segmented segmented neuro windows windows begins sentence summed extreme lot identifying intractable accomplished writing labeling labeling martin martin martin martin martin martin martin summing fix saccadic saccadic saccadic saccadic saccadic saccadic resources eliminate connecting printed printed printed printed printed printed printed printed printed printed lecun lecun fails promising difficulties occurred simplify analogy height height height height handwriting falls mouse mouse moved dominant enhance scan scan scan scan scan scan scan scan scan scan scan scan scan scan scan scan scan scan enable recog recog creating saccade ends broken broken broken broken broken broken jump jump jump arcs parsing ple ple exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive dec rejection bank nition pointed year year year boser boser connec acceptable classifies classifies workstation certainty certainty reject reject avoids henderson henderson increment exam rithms tems chapman ocr ocr ocr ocr ocr ocr hubbard hubbard convert pomerleau pomerleau paired altered surrounding rough zip covered france france breaks tively placing places atr september computa supporting wider mann scanning scanning scanning scanning scanning scanning scanned scanned styles nist nist regularities regularities consuming handling recogni rosenberg rosenberg builds austin spacing interpreting hopkins hull phonemic keeler keeler keeler keeler drawing char char replicated replicated integrates val horizontally station carries corrective successively recognizes johns cur sliding company nettalk nettalk est robustly lar pointer seg seg seg seg mis mis february texas monitored rent rec ues modularity jack jack preprocessed shikano shikano scans scans scans scans scans scans scans scans checks minute touch touch weakness dealt mentation mentation mentation extremes decides intervening intervening puted jonathan jonathan cent executes correspondingly trouble segmentations touching touching touching blank blank blank blank spans compound nato numerals nected dave gation cursor ballistic ballistic standards restricts ware para mcc button pittman pittman pittman simi convolutions isolate duplicated reads aloud aloud kauf les vocabularies print navigate ered ken consid acter clumps clumps pres jay rejections rejections roger eecs navigational faggin faggin faggin erated judgment accessing wee sociated leow haft traded buffalo frontiers inch telephony segmenta segmenta segmenta pertain acters accesses nology sawai sawai conception jections ognition nize gale presenta trapezoidal navi 
#@Martin_G,Rashid_M,
#t5
#!
#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural data data data data data data data data data data data data function function function function function function figure figure figure figure set set set set set set set set training training training training training algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number results results information information problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models performance performance performance performance performance based based based based based based space space space weights order order shown shown systems probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight distribution distribution recognition recognition recognition recognition recognition recognition approach approach approach pattern point point point point image image image image image image image image image image image image image image image image image image image image image image image image image image single single single processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large large local local test test test analysis analysis class class class matrix shows shows simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small small small size net net net net net net task fig step step points points points points points points points points points points points points points points points points points points points points points points points points points points points field process process current current trained random high similar representation show equation equation section fixed fixed fixed line images images images images images images images images images parameter parameter real average average average states gradient obtained university computation research research independent log log log log defined defined initial initial initial initial standard standard computer terms terms terms science direction machine machine object object object object object object maximum maximum learn position abstract back find density likelihood likelihood references component due ieee procedure procedure procedure adaptive adaptive adaptive adaptive adaptive decision propagation mixture introduction hand hand hand hand hand hand hand hand effect effect dynamic generated generated generated variance variance variance variance variance variance variance cost cost cost search search tion change change change change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy assume prior prior part center center cases cases cases cases cases type required multiple good good good binary long represent represent make make make make fact correct correct probabilities errors errors forward simulations minimum resulting ing total total total simulation human computed sum sum sum times regions means means made orientation knowledge knowledge em em negative negative relative relative relative relative define define compute proc location location location location perform determined constraints connected distributions distributions steps update descent descent nets morgan department technique technique code code advances represents final final final scheme computing directly hinton hinton hinton hinton hinton hinton curve curve top determine efficient efficient efficient full requires requires requires approximate vision pages increase validation validation validation weighted weighted randomly criterion types iteration nature depends discussion covariance feedforward feedforward feedforward feedforward describe describe transformation transformation transformation transformation transformation close close finding finding nearest effective shape shape shape shape shape shape generate generate generate generate generate main journal pixel pixel pixel pixel pixel pixel pixel pixel ability instance instance instance easily noisy noisy fit fit fit fit fit fit fit fit fit fit kaufmann objective probabilistic pairs smaller coefficients coefficients coefficients coefficients technology technology character character character character character character character character segmentation segmentation segmentation segmentation matching matching matching matching uniform uniform database leads leads squared squared iterations bits normalized normalized bottom bottom bottom frame frame frame frame frame frame frame frame minimize minimize produced choose run improved improved improve advantage takes takes strategy moving include include include pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels highly previously conventional works yields match match achieve achieve trans positions positions locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations williams williams williams williams improvement parts invariant deviation wide rotation alternative alternative correctly feed move move move width width loop loop loop deterministic pass pass starting place minimal reduce reduce reduce segment segment neighbor central central differences differences peak peak performs suggest strong largest demonstrated proportional intelligence radial assuming assuming variety start start start decrease derivatives derivatives characters characters characters minima configuration configuration configuration configuration annealing annealing acknowledgements boltzmann boltzmann reference appears digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit longer winner ways generating generating generating generating generating vertical vertical changing changing changing changing segments modeled implement explicitly coordinates coordinates coordinates simultaneously involves transformations transformations transformations transformations easy easy easy belief gaussians gaussians gaussians versus cycles select decreases stages stages squares interpretation interpretation influence codes codes transform transform open operations approximated translation digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits updates updates sign slow normalization normalization normalization fitting fitting fitting fitting fitting fitting fitting fitting fitting add penalty penalty generation initially initially distances string handwritten handwritten box box includes coordinate weighting weighting instances instances instances instances instances instances recognize recognize recognize prove candidate variations variations variations variations planning determining letter importance uniformly uniformly uniformly modification driven included build fine reached capture capture soc kind kind repeated cun cun superior sin involved michael minimizes denker highest consisted operating mixing mixing preferred neighboring neighboring neighboring intrinsic remain schedule schedule poor difficulty put put integral dataset helpful helpful matches matches giving investigated ideal ideal ideal office structured complicated understand circles coarse adapt reading configurations spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline extremely equally changed obvious obvious portion shapes shapes explain explain defines isolated isolated residual residual great advanced stop developing variances variances variances variances variances fairly improves expensive handle easier preprocessing filtered forces forces forces forces mation recognized circle gradually toronto toronto lowest lowest incomplete recognizing recognizing recognizing recognizing alignment exemplars outer greatly greatly affine affine affine affine affine affine affine flexible poorly poorly peaks splines splines splines sharp prototypes howard mod cal incorporating extensions curvature curvature curvature richard logp kinds decreased decreased segmented segmented yuille yuille lot analogue proportion proportion generator appropriately pick pick pick pick pick pick labelled circular circular eliminate eliminate printed printed printed printed printed printed grey eliminated fits fits adjusting occurred height handwriting interpret affected exploring service repeat started governed governed edelman edelman topological jackel elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic modelled modelled express thin suggesting repeatedly properly ends ends canada roy steepest variants dempster dempster balanced thresholding treat fitted rubin rubin cooperative rejection willshaw willshaw pointed smoothly discriminative discriminative centre boser spaced big reject reject constrain avoids henderson home home home home home home home home home home home home home home modifying formance stroke geoffrey impose impose graphics generators generators hubbard rectangle rejected ullman ullman intensities win win harder laird laird zip zip zip zip flash flash portions funded placing cubic bring els durbin durbin durbin durbin durbin ignoring ignoring corrections helps picking tail fortunately generarive cursive christopher settling wins spacing cornput cornput responsibility burr burr burr rare thickness normalize recognizes strokes salesman salesman gaus deformation deformation deformation deformation deformation deformation deformation deformation deformation deformation deformation deformation deformation deformation seg tim penalizes united subtle revow revow revow revow postal postal elaborate stat preprocessed settles locating invert shear deformations deformations weakness mentation ontario ontario arline arline dilation registration usps topologically deformed deformed responsibilities confident deformable positioned knot ions segmentations ponents live travelling travelling extraneous elongated recognizable triples normalizes intend settled cheaper opera gravity prog doubled apple ink ink ink ink ink ink ink elongation elongation varia elliptical elliptical elliptical slant motivations experimenting pulling reverses optional influencing ellipse exert sians drawings blending jepson jor elaboration bend gently allan recompute recompute recycled deforming 
#@Hinton_G,Revow_M,Williams_C,
#t5
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input input input input input input input input input data data function function function function function function function function function function figure figure figure figure figure time time time time time time time time time set set set set set set set set networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output number number number system system system system system system system error error state state results results results results information problem problem problem models models performance performance performance based space space space space space vector vector order order order shown shown systems systems values values probability parameters parameters parameters parameters noise functions functions functions functions functions functions functions functions unit method method method pattern pattern pattern pattern pattern pattern point point single control control control control large large local local local rate rate test patterns patterns patterns patterns optimal optimal optimal optimal optimal optimal form form form shows signal signal algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small size feature work step points features process process process process level current current current current current trained structure structure problems random random random random high memory memory memory response response response similar similar architecture show show show show show show fixed line line general parameter parameter parameter approximation average average average theory theory theory theory gradient gradient gradient obtained term term experiments experiments activity activity activity activity dimensional dimensional university university university threshold solution research research research research independent defined found found sequence sequence initial initial constant table standard standard standard standard computer terms distance distance science science left left left left left map low temporal maximum maximum range range range press press press press learn position position position basis nonlinear continuous continuous continuous sample abstract applied back find computational computational density references component ieee positive important adaptive adaptive decision introduction action action action action action action action complex complex complex complex complex hand stimulus dynamic generated generated variance search search change measure signals learned learned chosen part part fact region proposed observed forward forward forward forward forward simulations simulations minimum resulting resulting simulation simulation simulation simulation simulation simulation simulation computed multi called elements elements regions regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement dimension made made made made feedback orientation policy policy policy policy policy policy policy policy policy policy policy policy policy negative negative negative negative original original artificial samples represented compared desired desired define rates perform goal related distributions distributions discrete discrete mit mit mit mit steps steps steps steps steps update support train descent source report report loss implementation technique consists consists consists internal individual connectionist responses responses responses responses difficult final final graph graph sequences sequences sequences cambridge cambridge cambridge cambridge cambridge environment environment environment environment environment environment environment environment environment directly view transition transition trajectory top stimuli stimuli stimuli requires free world world world world speed speed speed speed speed speed vision basic increase coding coding randomly developed robot robot robot robot robot robot robot robot robot robot robot robot robot velocity velocity velocity velocity controller depends simply simply biological biological associative associative associative technical technical fast limited close corresponds actions actions actions actions actions actions actions actions predictions short short short nearest effective effective generate supported eds square ability ability future future future degree degree degree sensory sensory sensory sensory sensory simulated smaller underlying underlying reduced programming interesting mechanism details pre pre making stored stored stored stored stored stored depth decay decay decay improved improved discussed recent element element element movement movement reported strategy moving moving recently engineering varying teacher approximately calculated solve correspond achieve sparse evaluation evaluation evaluation positions locations symmetric observation observation interval williams williams williams williams williams storage lead suggests extended deviation deviation deviation locally locally move move move move move move width width occurs occurs occurs runs strength conclusion starting starting minimal trajectories trajectories trajectories trajectories trajectories reward reward reward central central differences measures sutton sutton sutton sutton sutton sutton sutton sutton sutton peak performs faster practice practice learns constrained external demonstrated intelligence turn turn turn iii iii iii derivatives annealing annealing force acknowledgements areas sequential generating generating generating vertical mathematical explicitly slightly slightly angle angle consisting interaction interaction develop adding agent expectation expectation select john decreases stationary influence open evaluate updated approximated converges allowed allowed barto barto barto barto barto barto barto slow slow classical spaces generation initially euclidean transactions avoid expect recorded existing exploration exploration exploration box perceptual perceptual perceptual perceptual perceptual perceptual thesis assignment sciences illustrated automatic planning regular determining sensor selecting capable suitable encoded encoded divided paths paths driven summary quickly graphs graphs allowing moore showing anderson anderson anderson anderson anderson neuroscience stopping symmetry follow strategies strategies strategies list absence paradigm delayed principles overlapping policies policies operating preferred explore explore explore remain layered requirements experience rapidly environments environments preliminary behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour fashion giving ideas incremental scaled authors surfaces surfaces act circles math coarse coarse trace trace adapt configurations man psychology thought ensure mapped store store extent phd attempts attempts synthetic optimum animal massachusetts indicating stop slowly critic sensors fairly navigation navigation navigation lies considerable spatially implementing arise watkins watkins watkins watkins potentially angles angles implicit arises cybernetics cybernetics preceding researchers explained requiring offset axes adjustable adjustable variant rewards rewards maintain requirement requirement synthesis synthesis aim suited adjust plan plan asymmetric enables kinds boston conditioning eventually traces traces credit trade consistently college college secondary primarily mistake appearance forming conditioned angular angular angular narrow narrow velocities velocities circular mobile mobile mobile mobile mobile mobile mobile mobile inspired overcome primitive vehicle vehicle vehicle vehicle vehicle vehicle exploit operates effectiveness effectiveness obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle contexts cerebellar negligible cmac cmac cmac sides consequences propagated bins exploiting avoiding avoiding pdf associations maintaining maintaining break obstacles obstacles obstacles obstacles obstacles emerge restrictions centre centre trigger acceptable lit lit reports flat acceleration england avoided visited arising unseen rectangular iff robots robots goals werbos werbos werbos chapman chapman denoting crosses acquired acquired acquired acquired acquired acquired ltm eligibility eligibility eligibility enforce outcomes outcomes outcomes turning avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance exploratory exploratory exploited rose aaai wider circumstances rarely heading heading regularities regularities council agrees thousand thousand thousand thousand designs albus albus king cast stay sharply settle laser slices slices slices ray ray ray ray comprising tells spie frequent coins safe reflection reflection smc adapts firm comer faced capturing stm backwards simon simon rotate enforcing severely preventing elegant orbit competence collision collision collision collision collision collision whilst simulates fight minimise reactive apparatus ago notably remember workers wired depths depths explores maximise tony fifty fifty braitenberg braitenberg formulating safely vehicles occuring suit encouraged encourages encourages finder reactions reactions rotates neuronlike logarithmically indoor walls slowing cial doubled reflexive reflexive emitted disabled sheffield rewarded collisions collisions collisions collisions collisions attainable planned overlaid hashing economy tiles reversing reversing tiling initiate enlarged acquires ccs accelerating interplay gabriel promote experimenting occured occured northeastern artifi recency reverses reverses rig quantised pavlovian transferring casting realism biosci surroundings equidistant aat aat aat behaviours pie rewarding reflexes reflexes tactical unprocessed circumstance 
#@Mayhew_J,Prescott_T,
#t5
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input function function function function function function function function figure figure figure figure figure figure figure time time time time time time time time networks networks networks training training training training training training training algorithm output output number number number number system system system system system system system system system system error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state results results units units units units models models models hidden hidden hidden hidden hidden performance based based based based based space space space space space space space space space space space space weights layer layer case vector order order order order shown shown shown shown systems systems values values probability functions functions functions functions functions method method method approach approach processing control control control control control control control control control control control large large rate optimal optimal simple simple gaussian paper paper paper paper examples small size net net net work task task task task task task fig fig fig fig fig fig fig fig fig fig step step points points field field field field field field field field process process current current trained trained trained structure random random random random random random random random random high high high high memory rule general generalization parameter real real real real real real states states states gradient gradient gradient gradient gradient gradient gradient term term term term note note note note note dimensional result university university university university university university university research research research found found found found found found target target target target dynamics initial initial initial constant table table estimate estimate computer computer computer computer computer computer terms terms science science science science science science prediction prediction prediction prediction prediction presented presented presented presented presented map map map map map map map map map map map map map map map phase phase phase phase phase activation low low machine motion learn learn position abstract applied back back find computational references due due ieee ieee positive procedure adaptive adaptive adaptive adaptive adaptive propagation context introduction action action action action action action action action action action action action action action action action action action action action complex hand hand hand estimation behavior behavior effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated recurrent search search change energy energy energy energy energy energy difference variable chosen part part center center bound cases good long long long represent expected expected expected expected expected make make techniques techniques techniques techniques techniques region region region region observed observed forward simulations simulations simulations resulting resulting resulting resulting resulting resulting resulting resulting resulting ing ing ing tasks respect performed eq eq called called called regions regions regions regions regions regions regions regions regions regions regions regions regions regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor optimization optimization optimization potential potential potential potential potential potential potential potential study knowledge knowledge knowledge knowledge em em negative compared compared desired desired active active active active active active active determined goal goal goal goal goal goal constraints gain gain gain gain discrete discrete discrete discrete approaches approaches approaches approaches accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger larger larger support support descent descent descent descent descent descent selection selection morgan morgan proceedings proceedings proceedings report report report report report report report report institute department loss technique technique technique technique advances joint connectionist connectionist connectionist connectionist connectionist layers layers scheme scheme scheme addition ai cambridge equivalent environment environment environment environment estimates estimates san san san bit conference efficient efficient efficient efficient upper world world world world world world world world world world vision estimated basic increase con derived randomly randomly randomly randomly robot robot robot robot robot robot robot robot robot robot robot controller controller controller controller lines lines path path path actual actual selected backpropagation backpropagation sampling simply achieved achieved achieved measured discussion technical technical technical technical technical technical technical technical increases group denote close assumption stable actions actions actions actions actions actions actions actions actions actions actions actions actions predictions finding short short assumed assumed assumed require eds makes kaufmann kaufmann typically pairs pairs smaller smaller unknown unknown fully jordan jordan programming programming interesting significantly character increasing mechanism mechanism mechanism mechanism mode mode principle pre making international normalized supervised idea attention attention attention attention attention attention attention attention attention attention attention combined combined minimize minimize predict predict predict architectures improve directions pair pair typical strategy sense sense recently varying previously previously observations tions yields constructed constructed extended deviation predicted predicted predicted predicted touretzky touretzky deterministic demonstrate demonstrate runs runs runs runs runs starting starting trajectories trajectories valued valued valued valued depend measures accurate accurate sutton exponential exponential faster learns mateo mateo mechanisms largest demonstrated demonstrated minimizing minimizing minimizing minimizing minimizing minimizing start start selective selective selective selective selective selective averaged introduce manner identification identification identification identification acknowledgements relation factors generating stability dept dept confidence text integrated agent agent agent agent agent agent agent agent agent agent select select decreases national national focus focus focus focus depending depending stationary viewed influence evaluated evaluated sign reasonable barto barto barto performing spaces spaces intermediate assigned assigned avoid avoid exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration thesis color color color inter determines determines maximize maximize mozer domains domains discussions major planning planning planning planning determining straightforward selecting selecting middle middle identified maximal maximal paths paths paths paths paths paths driven committee schemes traditional heuristic moore moore leading principles policies subsequent preferred approximating deal explore diego singh singh singh environments environments environments environments environments environments environments optimized hall biases scalar school school authors proper proper proved notion notion waibel smallest gradients gradients adapt opposite extremely equally equally queries portion noted logistic explored explored explored switching switching switching switching switching phd defines massachusetts ment slowly asynchronous directed directed directed costs costs costs costs costs costs distinguish navigation navigation navigation navigation navigation improves expensive lin closer forces ran mation recognized beginning depicted depicted mellon mellon improvements behaviors behaviors carnegie carnegie pure pure pure pure pure relevance cmu cmu cmu dark dark generic lms lms lms leave autonomous poorly frequently compares rely pittsburgh pittsburgh prevent enables germany germany germany returns begins june differentiable realized don room feasible driving driving optimizing mobile outcome reaching establish inspired murphy chance mail siemens chemical familiar serves serves mark exploit observing monotonically optimally enhanced child heuristics obstacle obstacle obstacle obstacle obstacle obstacle obstacle exploring financial combines combines ensures ascent washington colorado mel mel uni uni propagated competing thin environmental arrows arrows park eqs adopted switches speaking summer indirect unable sch sch sch sch sch sch sch thrun thrun thrun thrun thrun thrun thrun thrun thrun basically benefits benefits cooperative failed smoothly smoothly german experiences experiences england discovering realize visited visited visited summarizes schmidhuber schmidhuber thick wall wall mitchell boulder march switched switched esti rochester rochester likewise ation ation ation flight bradtke rarely gratefully opti tom marks suffers establishes alex illinois stay conflicting progressively progressively inefficient squashing maxi coins randomness gmd gmd acknowledges bonn bonn inaccurate jan atlas unnecessary searched technische technische mization sebastian pull exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation exploitation attracted attracted competence competence competence competence competence competence competence competence competence competence competence competence competence competence competence competence competence competence competence competence competence collision disadvantages undirected nov reactive darker bistable bistable sible versity alexander satinder jonathan neurally fruitful seeks beckman miinchen recur seventh ration ore ore economics tab linden realizing walls guiding guiding pected whitehead visiting depart reacting collisions frg envi envi cutting bachrach bachrach finished aug relearning navigate sut sut sut sut sut sive exhaustively mfinchen corp andy andy erence sooner kindermann moo moo moo moo moo quently extremal tick explo subse differenttable differenttable fki ronment unnecessarily waste sharkawi mizing hinder moller sofge jor ormation awe augustin cobh appropriateness burn weighs acl acl controllet colliding preferring 
#@Moller_K,Thrun_S,
#t5
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#*network network network network network network network network network network network network network network network model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks output output output output number number system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results problem problem problem problem problem problem problem models performance performance performance based based space space space space weights case case case vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown shown shown shown shown shown systems probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach approach approach point point point point point control control control control control control control control control control control control control control control large large local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs form form shows shows shows shows signal paper paper paper small small size size net work task methods fig fig fig fig fig fig step points points field field field field field field field field field process process process level current current current structure problems problems problems problems problems problems random response response representation show equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation vectors general general real real real average states states states states states states states gradient gradient gradient obtained obtained obtained term term term note note experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity dimensional dimensional result result result result result result university computation computation solution solution solution solution solution research log defined sequence dynamics dynamics dynamics dynamics initial initial initial initial initial constant constant constant constant constant distance science direction direction direction low sets maximum range range range range range range range range range press position position position position position position position position position position position position position position position nonlinear nonlinear nonlinear outputs abstract applied applied applied applied applied find find find find analog analog analog analog analog references stochastic due due ieee positive important important important context introduction complex hand circuit stimulus effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated generated search tion tion tion change complexity assume assume assume assume assume assume assume assume measure chosen chosen chosen required long represent represent distributed distributed distributed distributed equations equations fact fact fact proposed proposed proposed proposed proposed proposed proposed length length observed errors simulations simulations simulations minimum resulting resulting resulting ing tasks simulation simulation simulation simulation simulation simulation simulation simulation computed respect respect respect respect respect respect respect respect respect eq called called called called called called called called regions regions regions mapping mapping mapping mapping means optimization optimization potential made global global global applications negative specific specific specific true application desired desired desired desired desired desired provide define compute location location location active active active active active active determined determined goal goal related constraints constraints constraints constraints approaches approaches fields fields fields fields fields fields fields fields support selection selection selection selection selection proceedings words words words words words loss implementation consists internal individual represents represents represents final final final ai ai maps directly directly curve solutions solutions solutions solutions solutions solutions solutions solutions solutions stimuli conference upper full choice free free free free free free free free free free free world world increase increase increase condition condition condition randomly robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels levels levels levels criterion criterion criterion area velocity path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path provided processes processes processes selected selected iteration iteration iteration nature nature simply simply simply measured discussion arbitrary denote denote circuits short nearest effective effective effective effective implemented implemented assumed assumed assumed assumed assumed assumed shape generate generate generate generate vlsi ability future easily easily easily degree noisy pairs smaller underlying underlying functional functional functional functional functional programming programming programming programming programming programming programming ratio principle representing representing max max max making bits bits bits bits bits bits early run run run light light neuronal neuronal neuronal denotes directions property pair takes takes movement reported reported reported lateral lateral lateral practical apply introduced introduced introduced introduced introduced strategy moving moving period sense array array recently engineering module solve solve yields differential rl trans diagonal diagonal locations generalized grid grid grid grid bounded grant horizontal horizontal studied extended trial locally white boundary boundary generally generally demonstrate strength starting greater assumptions assumptions trajectories conclusions neighbor neighbor competitive interactions interactions numerical numerical numerical numerical clear suggest strong presence largest largest external external external cycle characteristics turn exist movements min denoted denoted denoted acknowledgements areas areas produces longer solving solving solving solving solving ways label label vertical dept modeled sensitivity infinite electrical dimensionality minimization quality quality select national viewed solved open controlled labels labels showed evolution decomposition forms constants constants constants constants constants constants partial partial additive neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood penalty closed closed generation valid initially foundation norm norm norm norm norm norm norm norm norm figures figures figures weighting extension activated activated activated activated activated activated domains neighbors neighbors neighbors characterized characterized characterized planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning regular straightforward straightforward selecting capable uniformly modification paths paths paths paths oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory reached characteristic contained success return return return return return lie oscillations oscillations oscillations oscillations oscillations satisfy michael relaxation paradigm minimizes minimizes correspondence highest reach moves moves moves satisfies powerful collection collection requirements exhibit put dual behaviour behaviour behaviour scalar scalar fashion fashion terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal variational variational encode encode hierarchy extremely equally implementations noted freedom consist site preference stop stop stop guaranteed capabilities lies lies lies turns lin tive satisfied closer closer precisely choices controls controls controls controls preceding preceding nsf summation apparent varies prop applies dark amounts conducted parameterized effort resistive resistive maxima exhibits gen cal incorporating ordered ordered extensions prevent plan substantial boston conclude june globally globally globally globally bellman bellman bellman bellman bellman bellman optimality optimality optimality optimality forming investigation fix controlling controlling mobile unity unity unity addresses connecting turned arranged generality systematic consideration numerically numerically significance ranges interconnection interconnection stated abilities viewpoint definitions methodology imply synchronous corner degradation obstacle obstacle obstacle spurious spurious spurious spurious passive lip lip financial irregular equals equals induce surprising washington originally interconnections interconnections interconnections nonlinearities dif waves waves waves shortest shortest impact impact propagate acknowledge treat metrics metrics metrics metrics unchanged slight workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace solves cooperative cooperative cooperative cooperative obstacles obstacles obstacles obstacles obstacles obstacles acceptable simd examining realize reflected assess robots proach iri win oscillating sheet sheet discretization discretization sta sta sta sta sta sta sta sta sta sta sta sta admissible admissible admissible admissible places exhibited increments supporting inactive walk utilizing externally ping curse inhibited locate attempting hamilton hamilton integrates ning disturbances disturbances equa disturbance disturbance disturbance disturbance disturbance disturbance norms destination complement falling robotic amenable experienced feasibility planner thing thing meant enter enter oscillates faced catastrophic penalizes syst backwards dof dof publishing virtue subtasks thinking hjb hjb hjb penalties penalizing optimiza insure insure incremented endpoints embodied periments comput jacobi jacobi occupy snapshot comment reflections favored favored hemisphere initiate deviate pit pit cas detrimental aca 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neural input input input input input input input input input data function function time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output output output output output output output output output output number number number number number number number system system error error error error error error error error error error results results units units information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem models models models hidden hidden performance performance based based based based space weights linear case case case case vector vector vector vector vector vector vector order shown shown shown shown shown shown shown shown shown systems systems values values values values parameters parameters parameters weight weight weight functions unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach image control control control control control control control control control control control control control control control control control test test test patterns patterns patterns patterns patterns analysis analysis analysis analysis matrix inputs inputs inputs shows shows shows visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small net net net net net net net work task task task task fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step classification process level current trained trained trained trained trained trained problems problems random high similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show fixed line general parameter parameter parameter theory obtained obtained solution research research log found target target target target target target target target target target dynamics dynamics dynamics dynamics dynamics estimate estimate terms terms terms presented present phase temporal temporal temporal temporal temporal object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object sets motion press outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied applied applied applied computational likelihood references ieee ieee ieee important important adaptive adaptive adaptive decision mixture introduction hand estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical statistical dynamic variance variance variance parallel change assume representations representations representations learned learned chosen higher part part part previous previous previous required multiple multiple multiple multiple make proposed proposed proposed correct tasks tasks total simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation respect multi eq eq eq eq times times elements factor feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications vol vol artificial specific specific specific represented represented compared desired desired desired desired desired desired desired desired desired desired desired desired objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects rates rates proc proc experimental motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor mit comparison report report implementation internal internal responses difficult difficult final final scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme cambridge domain experiment experiment environment environment directly directly hinton hinton estimates trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory conference vision estimated estimated basic produce condition weighted randomly randomly randomly controller controller controller controller controller types actual actual actual actual actual actual actual actual actual actual actual provided selected selected selected selected selected selected selected backpropagation depends associative achieved discussion technical technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward denote tested limited limited inverse inverse inverse inverse inverse supported eds eds eds eds adaptation journal future auditory auditory dynamical dynamical dynamical dynamical functional unknown unknown unknown unknown coefficients coefficients jordan jordan jordan jordan uniform call direct experts experts supervised supervised supervised expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert combined produced produced choose denotes denotes denotes architectures exact exact exact exact exact advantage movement period period period hierarchical hierarchical sense sufficient compare conventional calculated solve achieve trans mixtures evaluation locations increased grant arm arm scaling scaling scaling predicted correctly correctly correctly move loop setting trajectories trajectories trajectories trajectories trajectories trajectories competitive competitive competitive sutton sutton learns propose characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics iii iii averaged averaged averaged averaged introduce identification identification configuration configuration configuration force perception perception ways estimating tuned category infinite physical physical physical physical physical physical physical physical physical physical physical slightly interaction interaction predictive select select competition choosing expressed expressed formation variation controlled controlled controlled controlled controlled showed decomposition decomposition barto barto barto sec sec sec sec sec sec sec sec sec closed advantages degrees retinal retinal retinal recognize recognize recognize maximize coupled coupled coupled coupled coupled coupled coupled coupled gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating identified suitable suitable identify identify identify schemes schemes schemes schemes schemes schemes schemes schemes schemes comparing miller identity conf anderson issue cue cues cues cues modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular nips nips nips correspondence correspondence correspondence correspondence automatically received attempt jacobs jacobs jacobs jacobs jacobs receive law employed employed employed employed command command command command command command command command command command command command layered layered essential experience environments involving issues lippmann lippmann lippmann preliminary mass mass mass mass mass mass mass mass helpful helpful tech biol int muscle reliable maximizing complicated examined examined measurement closest closest man changed changed freedom epoch epoch epoch integrate track nowlan nowlan nowlan nowlan handle considerable sys shared immediately laboratories laboratories consequence recognized toronto recognizing recognizing fed fed slower slower treated rep commands commands commands commands commands commands commands commands commands commands gains controllers controllers controllers semi simultaneous univ realized cybern cybern accomplished japan investigation acts perfectly perfectly perfectly perfectly robotics primitive kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato ascent somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic competing competing informative steepest considerations mechanical listed listed leaming leaming cooperative dec utilize quasi quasi quasi quasi quasi realize manipulation manipulation manipulation manipulation manipulation manipulation manipulation manipulation manipulation manipulation manipulation werbos emphasize acquired acquired acquired drawback atr atr coordination acquire acquire acquire acquire excess satisfactory compete disturbances impedance impedance impedance manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated manipulated interpolate coins coins smc remained cho inappropriate suzuki responded fore cope crg continuing dealt psaltis manipulating gun corresponded corresponded earning kyoto encouragement hogan hogan masses acknowledgment occupy neuronlike soraku viscosity seika stiffness nel gomi gomi gomi 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set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number system system system system error error error error error error error error error error error error error error error error error error error state state state state results results results units units units units units units units units units units units information information information information information hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based based based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear layer layer layer layer layer layer layer vector vector shown shown systems systems systems values values values values values values parameters parameters parameters parameters parameters noise noise weight weight weight functions functions unit distribution method method method method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach point processing control control control control control control control control control control control control control control control control control control control control control control control control rate rate rate rate test test analysis matrix matrix matrix inputs form form form shows shows signal signal simple simple simple simple simple simple gaussian paper examples examples small small small small small net net work work work work task task task task task methods step process process process process process process process process process process level level level level level level level level level current trained trained trained trained trained structure problems problems random random random random random random random response similar similar architecture show show fixed fixed fixed fixed generalization real real average average theory theory theory theory experiments experiments experiments experiments experiments experiments university university university university variables variables variables research research research initial initial initial initial initial initial constant table table table table table table table standard standard standard standard standard standard standard standard standard standard standard standard computer computer science science direction presented activation activation activation temporal sets sets sets range range range range range press press learn components basis basis basis nonlinear nonlinear nonlinear outputs outputs outputs abstract references ieee important introduction introduction introduction action action action action action action hand behavior statistical effect dynamic dynamic dynamic variance change difference difference difference rules rules measure signals prior learned learned required required multiple multiple good represent represent represent represent distributed equations equations equations errors errors forward resulting resulting tasks performed called feedback applications knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge vol artificial artificial true compared compared application desired perform perform determined determined determined experimental goal connected gain discrete mit steps accuracy accuracy accuracy accuracy comparison nets modeling modeling morgan department department department department internal internal advances represents represents difficult final final final final exp layers addition addition considered cambridge domain domain domain experiment experiment experiment experiment experiment experiment experiment experiment experiment design design design san determine determine determine determine determine determine determine choice significant significant significant significant significant approximate world basic increase con con con con condition randomly randomly randomly developed bounds area velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller actual actual finally finally finally finally processes backpropagation backpropagation backpropagation backpropagation nature tested actions actions actions supported main eds square square ability future future development kaufmann typically smaller jordan jordan testing testing testing testing testing significantly significantly significantly significantly york mechanism trials details numbers numbers numbers numbers pre magnitude idea idea improved improve improve apply recently relevant engineering engineering engineering varying compare tuning tuning tuning tuning tuning tuning tuning tuning achieve observation grant digital digital trial derivative derivative loop loop generally runs runs runs flow strength starting place conclusions interactions sigmoid sutton faster practice mateo temperature temperature temperature temperature temperature characteristics sigmoidal proportional proportional intelligence exist exist averaged derivatives manner configuration base question produces produces produces written written longer ways describes tuned mathematical confidence confidence confidence confidence confidence confidence confidence sensitivity involves formed national national national review variation restricted centered centered completely constants constants past past partial delays reduces initially calculate construction construction foundation topology topology topology topology topology topology topology topology topology topology topology topology topology topology existing existing existing instances instances instances instances instances instances instances instances instances instances instances sciences sciences black partially reason extra extra differ successful schemes miller miller traditional traditional traditional quickly showing issue lie contribution duration duration duration paradigm paradigm backward reach subsequent operating mixing extract jacobs jacobs extend create investigate exponentially steady steady steady integral integral hall biases fewer examine matches giving project project project relationships scaled office stream stream stream variability statistically statistically neu hill concepts man assumes explored initialized initialized initialized initialized initialized initialized initialized simplest plant plant advanced unstable improves lies reasons drive drive rapid closer producing acknowledgement computers requiring orders passed compares schematic maintain gains controllers controllers controllers controllers controllers controllers limiting tank tank tank tank tank tank tank tank tank tank tank tank qualitatively begins initialization initialization initialization initialization initialization initialization initialization initialization initialization consistently room acts controlling addresses naval enhancement theories eliminated adds consideration occurred chemical chemical chemical chemical chemical loops interpret ral continue repeat prentice ranging candidates initialize master park grants shavlik shavlik shavlik shavlik shavlik shavlik material johnson johnson boxes street ence largely fellowship sig removal presenting propagating summarizes summarizes summarizes magnitudes werbos graduate depicts paradigms paradigms paradigms refinement mimic aaai ongoing water water water water water towell towell towell cliffs eliminates calculates calculates calculates disturbances disturbances disturbances disturbances englewood pratt pratt correctness correctness ray ray ray ray ray ray ray ray disturbance disturbance disturbance disturbance trol governing company setpoint setpoint fol wisconsin wisconsin wisconsin wisconsin periodically cold mcgraw scott scott scott scott scott scott scott scott magazine appro fixing eighth refine configured extrapolation hot unifying oil psaltis psaltis madison madison madison differed differed menlo lowing initializing wji refining refining refining refining refining shell kbann kbann prevented multivariable embodied dictated illustrative interrupted confer gary multilayered setpoints setpoints 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training training training training training training training training algorithm output output output output output output output output output number number system system system system system system system error error state state state state state state state state state state state state state state state results information problem problem problem problem problem models models models models models models models models performance performance based based space space space space space space space space space space space space space space space space space space weights weights weights weights weights case vector vector vector vector vector vector vector vector vector shown shown shown systems systems systems systems parameters parameters noise noise method method approach approach point point point point point point point point point point point point single processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows signal signal signal simple simple simple simple paper paper examples examples examples small work task task task task task task methods methods methods methods current current current trained trained trained trained trained trained trained trained trained trained structure problems problems problems problems problems problems problems random high similar representation architecture architecture architecture architecture architecture architecture architecture architecture show equation equation equation line line vectors general real real real real real real real real approximation average states gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term term note note note dimensional dimensional dimensional dimensional result university variables computation solution solution defined defined defined found found estimate computer terms terms terms terms science prediction prediction prediction direction direction presented presented presented presented map temporal machine motion press press learn learn components components components components outputs outputs outputs outputs abstract applied applied references component due due due due due due ieee adaptive decision introduction action action action action action action action action action dynamic dynamic parallel search search tion change change change spatial lower signals signals signals signals cases cases cases cases required long represent represent expected expected expected equations make fact fact techniques techniques techniques proposed proposed proposed correct correct correct observed forward forward forward forward forward forward forward forward forward forward forward forward finite simulations ing ing called called called times times times elements means reinforcement reinforcement reinforcement factor factor factor made made natural study policy policy policy policy policy obtain obtain obtain obtain obtain obtain obtain original vol represented compared desired desired provide provide perform related mit mit steps larger train train train train source modeling modeling modeling modeling modeling modeling selection morgan morgan morgan proceedings report institute technique technique internal internal advances advances joint represents represents difficult difficult difficult final final final graph directly directly hinton curve curve curve curve additional solutions solutions curves estimates effects efficient efficient upper requires significant significant approximate approximate free world world world world world world world speed estimated estimated estimated increase con produce condition robot controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller lines lines provided backpropagation inhibitory simply associative achieved measured technical describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary tested transformation transformation transformation fast fast fast fast fast fast corresponds stable actions actions predictions amount implemented implemented assumed supported eds eds eds end end instance future future future future easily rumelhart rumelhart rumelhart kaufmann kaufmann kaufmann objective objective simulated simulated typically typically needed needed needed reduced account account unknown jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan technology programming programming edge trials trials trials empirical leads principal call making supervised supervised supervised supervised added predict predict predict architectures improve directions period identical sense sejnowski cognitive dimensions observations teacher volume volume solve solve differential achieve achieve address evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation modified modified observation improvement entire entire entire arm horizontal lead studied scaling occur suggests suggests trial trial predicted predicted predicted predicted correctly move touretzky touretzky touretzky occurs conclusion minimal conclusions valued valued valued valued depend accurate accurate accurate clear sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton faster faster practice propose drawn california solid solid turn relationship introduce program force suppose suppose relation construct longer longer longer sequential dept changing coordinates coordinates simultaneously simultaneously dimensionality dimensionality involves applying events predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive quality expectation independently solved evaluated evaluate evolution evolution allowed barto barto barto barto barto barto barto barto slow dashed intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate initially construction construction transactions avoid expect exploration priori batch prove extra closely differ modification modification paths paths presentation successful miller miller reached reached reached reached anderson anderson anderson anderson anderson dis lie manifold manifold manifold manifold manifold manifold follow device satisfy write providing leading reach predictor predictor predictor predictor policies mixing jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs deal explore fashion school project project applicable combine combine cover cover examined gradients gradients man predicting opposite algo explain seconds seconds seconds massachusetts mentioned ment cart cart cart cart cart cart slowly critic critic critic critic critic critic guaranteed explanation obs precisely forces desirable watkins watkins watkins acknowledgement separately angles beginning cybernetics argument questions led elman axes axes backprop introducing requirement pasadena richard redundancy redundancy redundancy redundancy redundancy redundancy eventually eventually eventually differentiable differentiable differentiable differentiable pole pole pole pole picture redundant redundant redundant redundant redundant modify modify modify modify concerned count eliminate proceed proceed caltech generality eliminated wrong wrong dealing mail balance balance hope modifications continue evaluations evaluations evaluations loo surprising widrow widrow surprisingly creating pendulum explains balancing balancing balancing fold fold interestingly balanced crossing summer covering encodes failed amherst breaking avoided argue rithms werbos werbos werbos werbos werbos interacting inverted crosses oct differentiation differentiation differentiation differentiation overhead overhead distal distal distal distal distal distal distal distal distal distal speedup cartesian termed attached sized preprint stuck applicability september differentiating differentiating differentiating continually helps stops remarks transforming curse drawing ackley ackley proposal concerns agency rohwer tracks coins smc hinge differentiate differentiate differentiate terminates enter faced problematic problematic indi analyse insert degrades rises ton minimise minimise weakness schematically schematically proximal concurrently endpoint endpoint environ tributed permitted nectionist vation mexico differentiated ences sketched minimising cate ordinates comparatively backpropaga neuronlike sept freeze looo obser truck brody brody brody brody brody minimisation crucially sut eleven answered cancels obtainable notoriously critics tangential tangential usable backer differenttable sustain backpropagate initialise nguyen nguyen minimised ormation interleave carlos flailing controllet 
#@Brody_C,
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state state state results results information problem models models models models models models performance performance performance performance performance based based based based based based based based based based based based based based based based based based based based based based space linear linear linear linear linear linear linear linear case order order shown shown shown shown systems systems values values probability parameters parameters parameters parameters noise functions method method method method method method method method approach approach pattern image image image processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large large local local local local local local local local local local local local rate rate rate test analysis analysis class optimal optimal inputs form algorithms algorithms simple simple simple simple visual paper paper paper small small small small size feature feature work work work task task task task task task task task task task task task task task task methods methods methods methods methods methods methods methods methods methods classification classification process process process current current problems problems problems random random random random random random high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory representation representation architecture architecture section fixed fixed line rule rule rule general parameter parameter parameter real real real real real approximation average states states obtained obtained obtained obtained obtained obtained experiments experiments experiments dimensional result result result university variables computation computation computation research log log defined defined defined defined defined found found found sequence initial initial initial initial initial table table table table table table table standard standard computer computer terms distance science prediction prediction prediction presented map present phase phase low frequency frequency temporal machine machine object object object object object range press learn learn learn position position position continuous abstract applied applied applied back find computational computational computational references component procedure procedure procedure procedure procedure important adaptive adaptive adaptive adaptive adaptive adaptive introduction action action action action action action action action action action action action action action action action action action action action action action action complex statistical effect effect dynamic dynamic parallel search search search search search search search tion change change change variable variable assume assume measure measure measure prior prior learned learned learned learned learned learned chosen chosen previous previous cases cases cases cases type required required required multiple good conditions expected expected make make make make make make techniques techniques techniques techniques techniques correct observed forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward minimum resulting ing tasks tasks tasks tasks tasks tasks tasks simulation simulation human human regression regression regression regression regression regression regression regression regression regression regression regression respect sum performed performed performed performed performed times mapping means optimization feedback global global global global global applications policy policy knowledge knowledge obtain obtain artificial artificial relative relative true compared application cross cross cross cross cross cross cross cross cross cross cross cross cross cross series provide compute perform perform perform perform perform determined experimental experimental goal goal goal goal goal related motor motor power approaches mit mit steps steps steps accuracy contrast update update update support support train dependent dependent nets selection morgan proceedings proceedings proceedings report report report implementation implementation version technique technique internal internal kernel kernel kernel kernel kernel kernel joint joint joint joint difficult final exp exp exp scheme addition ai maps cambridge cambridge experiment environment environment directly directly estimates trajectory effects conference conference conference determine efficient efficient full requires requires requires choice choice choice statistics statistics world world speed speed estimated basic validation validation validation validation validation validation validation validation validation validation validation validation validation con con produce weighted weighted weighted weighted weighted weighted randomly robot robot robot robot robot robot robot robot robot robot robot robot controller controller controller actual actual provided provided finally processes processes selected selected associative measured technical technical technical increases tested fast fast fast fast close close inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse actions actions actions actions actions actions actions actions actions predictions predictions finding amount nearest nearest nearest nearest nearest nearest nearest nearest common effective supported require require require journal square end rumelhart noisy noisy fit simulated simulated simulated typically typically pairs pairs combination combination jordan technology programming consistent direct direct international international international supervised supervised decay minimize produced choose choose run run predict predict predict predict predict improved improved discussed recent recent recent recent advantage advantage advantage robust robust robust robust robust robust robust robust robust separate takes movement apply apply introduced subject identical quadratic trees recently relevant observations teacher axis converge achieve achieve achieve achieve achieve observation observation grant arm arm arm scaling trial trial deviation deviation wide wide derivative derivative predicted predicted alternative locally locally width generally generally hardware hardware half place assumptions reduce editors accurate numerical numerical numerical numerical numerical designed sutton sutton weak taking hard hard hard hard presence cycle cycle cycle cycle cycle cycle intelligence intelligence variety start relationship iii scene minima minima force acknowledgements reference relation relation relation relation van longer describes laboratory laboratory laboratory changing multilayer coordinates coordinates coordinates integrated quality quality quality versus cycles cycles cycles cycles cycles cycles cycles cycles john national family family family family depending stationary stationary squares learner learner learner learner learner learner learner learner learner approximations forms updates updates updates updates updates partial partial reasonable slow iterative penalty interpolation initially assigned foundation query query avoid avoid avoid box thesis coordinate coordinate weighting memories illustrated uncertainty discuss maximize candidate candidate absolute tests tests tests tests major planning closely importance differ delta included included successful successful identify miller online online online ten reached excitation quickly quickly quickly repeated procedures success moore moore moore moore moore moore moore running content follow cue cue cue cue cue cue cue cue built vary absence minimizes ill automatically attempt subsequent subsequent subsequent subsequent preferred approximating approximating software decreasing camera camera camera camera powerful wiley wiley poor experience experience experience updating environments environments detail optimized preliminary behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour existence rest incremental incremental incremental incremental incremental applicable ideal office decisions proved func removed removed hill hill hill hill closest necessarily predicts opposite adjusted versions versions der noted noted observe observe observe ith motivated phd finds attempts seconds seconds years histogram great slowly trivial fairly expensive expensive caused starts drive sections formalism formalism producing mathematics scientific inversion inversion inversion inversion author author sun robustness requiring greatly greatly greatly considerably substantially amounts lms atkeson atkeson atkeson atkeson atkeson continuously frequently outliers outliers outliers requirement controllers controllers aim monotonic extensions sophisticated age age tolerance begins median june summed irrelevant discontinuities newton benefit indices sensing proportion investigation investigation fix arguments linearity optimizing member ordering circular discovery proceed climbing climbing air kaufman fits numerically numerically stronger intelligent resistance keeping obtaining removing adequate adequate adequate inferior meaningful introduces sion displayed negligible decide conjunction mental searching offers centroid dif young mem mem mem mem mem mem environmental relies sons considerations considerations variants implicitly implicitly omohundro hart instructions interestingly ball ball ball ball ball ball ball ball andrew constitute shepard fellowship ber removal removal removal removal torque july july axe incrementally encouraging comparative residuals obtains perceived hundred experiences experiences experiences experiences experiences experiences experiences experiences experiences experiences experiences experiences experiences experiences experiences breaking sinusoidal jacobian avoids acting robots duda werbos elementary disadvantage afosr overhead lookup increasingly distal meta cartesian selectively selectively worth discusses inverting inverting stuck stuck stuck milliseconds things ignoring october november learners learners moderate chris fortunately expense expense lation january discontinuous christopher ping thousand suffers shot shot shot shot reflecting concern award mistakes usefulness seattle huang ultimate sions quick mcgraw drifting enter benign benign foreground stick stick stick stick stick stick stick inaccurate outlier outlier outlier outlier addressable shortly scattered tens lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr awij putation tit insert trapped investigator ard progresses nice cations appli searched occasionally occasionally prime mir aims judge disadvantages optimizes coincides conceptually undesirable jumps pay helped offiine offiine offiine structuring counterparts experimentation experimentation aggressive aggressive outlines inadequate presidential enormous neighbours mere mere persistence successes successes successes nato inverses accompanying stant sole loses told millions collaboration regres inexpensive gravity dan deci wasted misleading mad mad reacting postdoctoral balls batches danger relearning alters xve xve xve xve sink recommended remembered argues troller detrimental prescription forget forget forget forget suddenly dation neighbout neighbout neighbout neighbout neighbout neighbout neighbout neighbout eat pushing datapoint verse benefited serc accommodated expe interpo hori cle behaviours bracket nearer cles vali flailing graphed ficult objection itly 
#@Moore_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks training algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number system error error state state state state state results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based space weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case vector vector vector order shown shown shown shown shown shown shown shown shown systems values values values parameters weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern pattern pattern point single single processing processing processing control control large large large large neuron rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns matrix matrix matrix matrix matrix inputs inputs inputs shows shows shows signal simple simple simple paper paper examples small small small small small size net net task task fig step step step step step step step points points points field features process level level trained structure problems problems memory architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show show equation equation equation equation equation equation section section section section fixed line rule rule rule general general general generalization speech speech speech speech speech states states states gradient gradient gradient obtained obtained obtained obtained obtained activity dimensional result university university university threshold computation found sequence sequence sequence sequence target target target target initial initial constant constant constant constant constant table standard terms terms connections connections connections connections connections connections connections connections connections connections connections connections connections science prediction left left left left left left left left left left left presented presented presented presented present activation activation activation activation activation activation frequency object learn learn learn learn learn learn position components nonlinear continuous continuous continuous abstract abstract applied applied back back back back back back references ieee propagation propagation propagation propagation propagation introduction hand hand dynamic dynamic parallel cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion change complexity lower lower lower lower representations learned learned learned learned chosen higher previous previous previous previous previous previous cases multiple multiple good long long represent distributed equations equations make fact fact proposed proposed proposed correlation correct forward forward scale resulting tasks total total simulation computed respect respect respect respect respect multi means means means means made natural global global applications em original original specific specific true compared application application application desired desired series series compute rates rates rates rates constraints connected connected connected connected connected connected connected connected connected connected gain gain motor motor motor discrete equal equal steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps larger larger connection connection update descent descent morgan morgan proceedings report report report institute implementation implementation version code code advances difficult difficult difficult layers layers layers layers delay delay delay delay delay delay delay delay delay scheme scheme sequences framework experiment experiment experiment directly hinton hinton hinton hinton curve additional curves design design trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san top top top top top capacity free pages increase give con produce produce condition derived derived robot lines lines lines actual finally backpropagation backpropagation backpropagation backpropagation iteration constraint constraint achieved technical technical technical describe arbitrary fast fast assumption corresponds complete short common implemented implemented implemented implemented implemented implemented generate generate generate generate generate theoretical main main main end ability ability ability instance makes kaufmann typically pairs combination combination fully fully fully fully fully fully fully jordan jordan interesting interesting character character character character character character special uniform database representing call call numbers making window window stored bottom bottom bottom bottom early idea minimize produced produced produced added perceptron architectures architectures improved improved resolution advantage advantage advantage typical practical strategy include subject identical hierarchical hierarchical sejnowski cognitive module module module module module smooth smooth speaker correspond differential differential differential differential differential differential diagonal diagonal positions positions positions modified improvement improvement sensitive extended extended derivative feed locally locally touretzky touretzky boundary half conclusion starting starting starting minimal trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories valued editors editors modules numerical designed designed faster practice learns encoding encoding reduction drawn drawn drawn derivatives characters characters characters program program digit digit produces written written written index solving generating stability vertical multilayer multilayer involves involves remaining remaining easy consisting adding frequencies letters letters letters letters letters letters decreases depending phoneme stages correlated influence solved variation variation variation updated updated completely suggested constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants updates earlier reasonable slow performing epochs add generation generation generation generation generation generation generation generation generation generation generation generation generation initially filtering visible advantages transactions avoid handwritten handwritten handwritten figures coordinate coordinate bell bell illustrated specifically variations variations variations successfully regular sensor sensor sensor middle middle letter letter letter letter letter letter letter letter letter letter letter letter letter capable importance differ wij tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn efficiently reached composed traditional compact compact quickly graphs graphs kind cun cun cun cun cun cun cun cun cun cun cun cun cun cun prob success strategies sampled generalize nips denker denker denker reach attempt consisted extract deal intrinsic minimized diego updating put put successive fashion ideas school terminal muscle hierarchy waibel waibel editor adapt adapt illustrate recognizer recognizer quantities versions noted precise precise initialized initialized art serial finds isolated indicating sensors orientations convolution unstable unstable capabilities starts starts reasons straight straight tive shared shared shared easier easier controls laboratories laboratories simard simard simard simard simard simard involve gradually optimize toronto auto recognizing preceding mellon requiring greatly carnegie limits cmu cmu effort dots dots execution howard howard synthesis pittsburgh pittsburgh gen gen cal prevent plan plan implements tile differentiable sharing sharing sharing sharing sharing lagrange resources controlling encoder encoder interconnected robotics multipliers kaufman ranges promising loops loops corner corner alphabet alphabet alphabet published programs programs ambiguity displayed negligible surprising lang lang lang consequences jackel jackel reproduce express shortest jolla draw draw draw draw draw pearlmutter pearlmutter pearlmutter reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse implicitly pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen dividing dividing ics summer unable piece equivalently guyon guyon guyon guyon convolutional opposed encodes boser boser connec decomposed stem big big warping letting adjustment jacobian acting unseen henderson henderson rectangular favor stroke stroke stroke hubbard hubbard picked lookup records unconstrained unconstrained unconstrained unconstrained denver discretization discretization elsevier milliseconds nal dramatic dramatic intensive ignoring coming resembles lems covers lagrangian lagrangian sees reversed reversed reversed monitor attributed adaptively drawing drawing drawing drawing drawing drawing flows bottou bottou bottou holmdel holmdel devised settle executing executing progressively progressively archi att att att fastest destination totally curved vertically vertically inde fol connectionism differentiate tra tra deciding deciding awij gradual preferable pendent shikano touch superscript superscript repeats repeats plans tailored subtasks mention tics subsampling subsampling subsampling subsampling subsampling subsampled subsampled subsampled subsampled subsampled subsampled subsampled subsampled switzerland yann notably lowing wii fogelman fogelman owij owij emphasizes hanazawa embodied differentiated differentiated nected recognizable resemblance albrecht genera bringing rests unfolded unfolded unfolded unfolded unfolded unsuccessful tectures transposed eration eration acous triplets plateaus crawford crawford zurich caution perspec zipcode steels instants tat tat parallels awl jectories oversampling reconstructs fort pfeifer jectory schreter curt begining 
#@LeCun_Y,Simard_P,
#t5
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data data data data data data function function function function function function function figure figure time time time time time time time time time time set set set set set set networks networks networks training training training training output output output output output output output output number number number number error error error error error error results results results units units units problem problem problem problem problem problem problem problem models performance based based based based space space space space space space space space space space space space space space space space space space space space space space space space linear case case case case order order order shown shown shown shown shown systems systems systems values values values values parameters unit unit unit method method method method method approach approach approach approach point point point point image image image image image single single control control control large large large local test test test patterns class form form shows paper paper paper paper paper small small work work work work task task task task methods methods methods methods step points points points points points points points points points points points points points points points points points classification trained high response representation line line vectors vectors general general real average average average gradient gradient obtained note dimensional dimensional dimensional result university computation computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research target target target target target target target target target constant estimate estimate estimate estimate computer computer science science direction direction direction presented map map map activation activation activation activation activation sets sets sets sets motion maximum maximum range range press learn learn learn position continuous continuous continuous sample sample abstract applied find find find computational references due due ieee procedure important important important important introduction introduction hand cost classifier classifier classifier classifier classifier classifier classifier classifier measure prior learned part part previous theorem multiple multiple multiple tree fact techniques region region correct errors forward forward forward forward forward finite finite finite finite ing computed computed respect multi sum called regions regions regions regions regions regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping factor made made orientation orientation global global global global global global applications original vol vol samples samples samples samples represented represented true provide define compute proc proc location connected connected gain motor equal equal approaches approaches larger train descent modeling modeling report consists individual joint joint joint joint joint joint difficult scheme maps maps computing directly solutions solutions solutions solutions solutions solutions solutions design san san determine efficient significant significant approximate estimated derived clustering developed developed robot robot robot robot robot robot levels path selected selected nature nature sampling sampling sampling achieved measured measured discussion technical feedforward feedforward group group tested fast fast inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse complete surface finding nearest common assumed assumed assumed supported require eds end end end ability easily rumelhart rumelhart development typically typically typically typically pairs pairs needed jordan jordan jordan jordan consistent consistent structures squared pre pre pre direct direct direct direct direct direct direct direct direct direct direct stored normalized supervised supervised supervised supervised supervised minimize choose run run run run run recent resolution resolution resolution resolution advantage property property property property practical strategy subset subset cognitive engineering previously previously unsupervised unsupervised teacher smooth differential differential differential differential achieve locations grid storage entire entire grant arm arm alternative correctly correctly locally locally generally demonstrate half critical critical critical critical critical critical greater greater reduce accurate numerical clear exponential taking regularization regularization labeled labeled labeled labeled targets targets targets introduce groups groups groups configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration base acknowledgements explicit construct construct estimating label distinct distinct distinct dept student explicitly physical physical electrical dimensionality remaining slightly angle unique consisting integrated formed john viewed solved open open controlled labels labels labels approximated approximated approximated partition partition partition performing neighborhood iterative iterative closed closed distances assigned construction advantages classified classified classified faces topology topology david david david degrees degrees degrees degrees expect thesis priori coordinate retrieval candidate domains discussions identified efficiency identify efficiently efficiently conf issue lie classify manifold manifold manifold michael michael providing nips ill ill ill ill neighboring origin diego diego requirements preliminary helpful existence existence fashion mse mappings analytically proper workshop cover surfaces surfaces surfaces surfaces surfaces examined configurations opposite implementations ensure subsets rank rank singular singular freedom freedom freedom freedom separated separated mapped fibers fibers fibers consist consist submitted motivated attempts massachusetts separable separable trivial expensive tractable lies stanford implementing style separately optimize author radius nsf geometric limits limits substantially bootstrap amounts posed posed posed posed slower branch branch branch branch branch branch fall suited kinds comments fiber redundancy redundancy traces wesley globally representative newton redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant identifying identifying proportion addison labeling assign restriction restriction restriction linearity resources branches branches branches branches branches branches branches branches branches partitions partitions robotics robotics robotics robotics robotics fails wrong mail mail interpret unlabeled unlabeled fail disjoint cottrell adequate separating introduces topological topological topological thomas young eng eng jolla jolla partitioned partitioned exploiting jump grants discovered ball ball ball ball assigning mechanical schulten workspace workspace workspace workspace workspace workspace workspace sine kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics achieving achieving ties benefits pieces pieces perturbed perturbed classifications seek acceptable amherst examining clustered clustered remainder remainder jacobian jacobian jacobian jacobian continuity unseen trends generators manifolds regularized individually individually singularities scope distal iri rough manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator intl nasa det travel ritter ritter ucsd ucsd coordination circumstances cube cube fortunately parameterization achievable excess resolve resolve invertible invertible invertible invertible neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods solvable award kinematic kinematic kinematic kinematic kinematic kinematic automation joints joints joints distorted coins drastically robotic amenable positioning positioning positioning positioning positioning positioning sweep investment problematic dof dof dof dof dof dof dof martinetz objectives investigator searched continuing ece erroneous regional klaus devel demers demers demers demers demers demers demers paid effector effector effector manipulators manipulators manipulators conserving singularity presidential fell resolving subsystems modulo attain ordinates comers loses loses elbow reachable torus torus torus gary misleading bundle viii viii regularizing invest balls balls balls balls education unreasonable closeness oped jacobjan jacobjan asme kenneth kenneth generically generically generically generically thrust attaining verse manufacturing regularize craig craig nguyen nguyen visuo wrist orienting usc singleton bootstrapped matics plicity joel joel kine helge 
#@DeMers_D,Kreutz-Delgado_K,
#t5
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#*network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input data data data function function function function function function function function function figure time set set training training algorithm output output output output output output output output number system system system system system system system system system system system system system system system system system error error error error error error error error error error error error error error results units information information information information information problem models models performance performance performance performance performance performance performance based based based space weights case case case case shown shown shown shown shown systems systems systems systems parameters functions functions neurons neurons unit image single processing control control control control control control control control control control control control control control control control control control control control control control large local rate test test test analysis analysis analysis inputs inputs form form signal signal signal signal signal signal signal signal simple simple simple simple simple simple simple simple simple simple visual visual visual visual paper small small small size size size size size feature net net net work fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells current trained trained trained trained structure structure structure structure structure structure random high memory memory similar similar architecture architecture architecture architecture equation fixed fixed line rule general general general average theory theory obtained term experiments experiments experiments result university solution research sequence target target target target target target target target target target target target target target target target dynamics initial initial initial initial initial initial initial initial initial constant constant constant constant table table estimate computer terms connections science science science science prediction left direction direction direction present present present frequency frequency range press press press learn learn position position position position position position position position position position position position position position position position position position position components components components components basis nonlinear abstract convergence properties references positive procedure important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction behavior effect generated generated parallel change change difference difference difference variable measure signals chosen part part part part required required required required required multiple cortex cortex conditions conditions conditions equations make make make region proposed correct observed observed errors simulations ing total simulation simulation human human human human human regions mapping dimension made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications applications study knowledge knowledge knowledge original original artificial artificial represented represented compared application desired desired desired series series rates rates rates location location eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye experimental experimental experimental related posterior posterior posterior posterior posterior constraints gain gain gain gain gain gain gain gain gain gain motor motor motor motor motor brain equal equal steps steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison dependent dependent nets nets morgan department internal internal internal internal internal individual advances joint represents addition ai ai ai ai solutions san effects effects effects effects efficient efficient requires choice speed vision basic basic increase produce produce produce coding derived derived robot robot robot robot area velocity velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller lines actual actual provided finally evidence evidence evidence evidence depends depends simply biological biological biological biological associative achieved measured measured normal normal normal feedforward feedforward arbitrary tested inverse corresponds corresponds predictions predictions proof amount implemented generate supported supported role require require main main main main main eds eds eds eds eds face adaptation adaptation degree degree degree degree degree development sensory including simulated simulated simulated simulated simulated pairs account functional unknown testing projection projection projection projection projection york increasing increasing head consistent structures structures structures structures trials trials trials trials matching mode principle representing details numbers direct supervised idea idea produced architectures architectures resolution resolution pair robust takes movement movement movement movement moving side subset cognitive relevant relevant relevant relevant interest interest dimensions compare previously calculated studies achieve evaluation positions positions positions modified increased amplitude amplitude constructed horizontal horizontal horizontal occur move touretzky loop loop loop loop loop occurs conclusion starting starting starting starting starting greater conclusions valued accurate accurate accurate accurate accurate accurate accurate accurate accurate retina retina asymptotic learns learns learns mateo suggest mechanisms mechanisms california proportional proportional intelligence turn variety start movements movements movements movements movements movements movements movements movements movements movements movements movements movements relationship iii iii iii averaged targets groups configuration force acknowledgements appears van van van van van van produces perception factors describes ann ann ann ann mathematical coordinates coordinates remaining remaining angle interaction interaction integrated quality versus john independently formation codes solved detailed ocular ocular showed similarly suggested constants constants diagram reasonable interpolation generation advantages combinations retinal prove activated absolute successfully major aspects identified delta efficiently projections miller miller characteristic kind kind superior superior superior superior superior superior superior physiological physiological physiological satisfy involved absence absence realistic attempt moves subsequent decreasing extend camera camera camera camera camera camera camera camera camera situations situations stimulation command command command command command command command command command command command command circuitry rapidly varied humans detail issues dotted giving ideas investigated biol int plasticity plasticity plasticity muscle muscle muscle muscle pathway pathway understand examined examined hill patch math coarse coarse measurement opposite psychology perfect freedom precise academic extent plant burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst advanced crucial publishers publishers publishers analytic considerable considerable rapid rapid rapid rapid straight widely producing incorporate located nucleus nucleus nucleus nucleus grossberg grossberg res computers people people experimentally quantitative cohen passed passed biologically schematic robinson robinson robinson robinson robinson robinson robinson robinson robinson span span gains controllers adjust gave gave gave substantial physiol damage damage patients multidimensional extreme arithmetic acquisition cybern physiology physiology generator generator generator generator generator generator generator generator generator generator generator generator generator oxford oxford extensive saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic appropriately animals animals acts concerned neurophysiol neurophysiol neurophysiol theories robotics robotics arranged climbing climbing kaufman anatomical primate primate primate primate primate primate primate primate primate primate cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum attractive kawato kawato kawato kawato kawato neurobiology neurobiology neurobiology implications implications north north north integrator muscles muscles muscles inferior inferior exploring cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar ensures paul cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac cmac pat holland holland holland regarded moved stereo stereo monkeys nonlinearities elastic offers offers similarities similarities similarities entries advance deg deg deg deg deg deg deg deg deg modelled ahead saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades colliculus colliculus colliculus colliculus colliculus colliculus displacement displacement displacement displacement displacement displacement displacement dividing anns anns anns kinematics kinematics covering retraining copy copy copy lesions england adjustment alter alter home home robots learnt relating books lookup lookup nuclei worth oculomotor oculomotor oculomotor oculomotor elsevier elsevier elsevier elsevier elsevier gordon supporting clinical clinical council accordance crude crude crude correspondences correspondences impulses albus albus albus albus adult adult responsibility anatomy anatomy anatomy disturbances goldberg goldberg goldberg goldberg corrective corrective corrective grids grids adjusts bach bach robotic adapts mcgraw terminates handbook brainstem brainstem brainstem brainstem brainstem brainstem brainstem brainstem brainstem brainstem brainstem compromise fovea fovea inaccurate assessed translate carpenter dean dean dean dean dean dean dean motoneurons amsterdam amsterdam months altering primates blurred sends sends recovers minimise accu hampshire rightward rightward rightward rightward untrained damaged damaged compartments lay lay manipulators mossy mossy wired initialised overshoot overshoot overshoot overshoot foveal testable lacking brains reticular mart mart olive olive olive cameras cameras anatomically olivary acuity qualities restored wurtz wurtz wurtz wurtz keller keller pilot leftward weakened told ballistic ballistic infant infant wolf debate infants infants sheffield sheffield initiative maintenance byte fibres fibres precludes eckmiller weakening weakening weakening optican optican optican optican organising collins collins midline midline saccarles pulling pergamon pergamon tissues universally rig rig neurobiol gielen acquiring glanz fibre fibre wear biosci gisbergen gisbergen gisbergen hitherto teaches teaches teaches ott ition inaccuracy kraft resembled maturation secure conveying rim shelf rro infancy favourably tate realistically confounded imperfections degrading inspect controllet mysterious italics 
#@Dean_P,Langdon_P,Mayhew_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time networks networks networks training training training algorithm output output output output output output output output output output output output output output output output output output output system system system system system results units units units units units units units units units units units units units units units units units units units units units units units units units units units models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer case shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown values neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit pattern point large neuron neuron neuron neuron neuron neuron neuron rate rate inputs inputs inputs inputs inputs inputs form form signal net work step step step step step step step step step step step process process process level level level level level level trained structure response response response response response response response response response response response similar similar architecture fixed fixed fixed fixed real real average average average average activity activity result result university solution found found sequence sequence dynamics dynamics constant constant constant constant constant constant constant constant constant connections connections connections connections connections connections synaptic synaptic synaptic prediction left left left left left left left left left left left left left left left left low low low low low press press press nonlinear nonlinear outputs outputs outputs outputs outputs continuous abstract back back back back back back properties references due due due positive propagation propagation propagation propagation propagation behavior behavior behavior behavior behavior behavior stimulus stimulus dynamic dynamic recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference difference lower lower lower lower signals signals signals higher previous firing type type represent expected expected expected fact observed observed observed observed observed observed observed observed simulations simulations resulting simulation simulation simulation times times made feedback study represented compared desired desired desired desired desired rates active active eye eye eye eye eye eye eye eye eye eye experimental experimental experimental experimental related constraints gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain motor brain brain equal equal equal comparison contrast contrast connection connection modeling institute loss loss loss loss loss responses responses responses responses responses responses responses responses responses exp exp exp bias bias sequences considered stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stimuli stimuli stimuli stimuli stimuli stimuli effects upper upper full full requires increase increase increase give produce produce condition weighted levels bounds velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines actual actual actual actual actual processes inhibitory inhibitory inhibitory achieved normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal increases transformation close complete amount short common supported role sensory simulated simulated simulated simulated simulated underlying reduced account fully york increasing head head head head head head head head head inhibition inhibition directions pair pair pair pair pair pair movement movement movement movement movement lateral lateral identical identical side side side side side side side previously previously match correspond correspond correspond correspond symmetric williams storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage increased increased increased increased increased grant amplitude constructed horizontal horizontal horizontal horizontal horizontal horizontal intensity studied suggests wide loop loop loop loop occurs occurs occurs generally half greater reduce interactions learns strong mechanisms integration sigmoidal solid solid solid solid solid solid solid movements movements movements decrease connectivity acknowledgements produces longer longer modeled modeled sensitivity interaction mutual mutual events cycles cycles stages stages ocular ocular ocular ocular ocular completely constants constants constants constants constants constants allowed allowed allowed dashed dashed dashed dashed dashed dashed dashed reduces purpose remains remains initially foundation degrees coupling figures extra closely driven plots essentially reached quickly quickly comp absence absence subsequent remain command layered circuitry dotted dotted dotted dotted dotted dotted dotted dotted dotted dotted rise rise rise rise rise rise fewer matches biol biol plasticity plasticity plasticity opposite impulse freedom extent explain indicating indicating indicating slowly vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor interneurons drive tive producing producing strictly nucleus nucleus immediately immediately monkey afferent afferent cut cut cut involve res res integrating integrating integrating integrating integrating reflects greatly greatly greatly substantially substantially substantially understood experimentally experimentally experimentally experimentally poorly cohen incorporated commands release passes passes passes passes gains gains rely sums decreased decreased findings begins extreme cybern physiology animals animals animals animals animals animals animals animals animals animals member vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular perfectly approximates neurophysiol neurophysiol jones jones jones jones jones flexibility rotations rotations receptors receptors receptors eliminated eliminated eliminated eliminated eliminated eliminated eliminated spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous balance balance occurring removing operates presentations wilson wilson wilson wilson muscles muscles muscles analyses sides sides sides sides dependency thomas recovery recovery insight reveals gaze passing balanced balanced balanced balanced zipser linked reflex reflex reflex reflex largely largely largely largely achieving removal removal removal removal removal dec retraining retraining retraining retraining solely acceleration acceleration constitutes simulating simulating simulating forcing sinusoidal sinusoidal adapting lesion lesion lesion lesion lesion lesion lesion lesion peripheral gained mammalian mammalian continues maintained inverted inverted eliminating mediated nuclei anal paradigms breaks breaks breaks afferents afferents supports modifiable modifiable modifiable modifiable reciprocal reciprocal continually strict develops species restoration vestibulo vestibulo vestibulo vestibulo vestibulo ave reflecting eliminates eliminates eliminates illinois anatomy compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation conflicting conflicting believed neurol push push squashing squashing intact intact intact intact zipset william reproduced compensated compensated compensated compensated compensated compensated compensated compensated compensated compensated compensated compensated compensated compensated accounting brainstem brainstem brainstem correlates brought brought rotational rotational rotational recovering silent silent motoneurons motoneurons motoneurons medial began urbana plenum plastic plastic plastic ted cats cats cats discrepancy pull pull stand recovers anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio extremes canal canal canal canal canal canal nuclear disagreement spontaneously spontaneously spontaneously spontaneously synapfic beckman testable functioning widespread motoneuron motoneuron expressing compensatory compensatory restored restored restored restored suit imbalance imbalance imbalance imbalance relaxing commissural commissural commissural commissural commissural commissural stabilizes crossed nystagmus nystagmus nystagmus nystagmus nystagmus nystagmus nystagmus nystagmus zee zee zee semicircular semicircular accelerations accelerations rhesus intense transmitting permanently silenced silenced silenced silenced silenced silenced silenced acute stretching persists whitaker bilateral bilateral bilateral bilateral relay lesioning deficits adopts exert compe reconcile disrupt disrupt subserve neurophysiologically restoring roedial roedial redrawn unilateral curiously 
#@Anastasio_T,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural data function function function function figure figure figure figure time time time set set set set networks networks networks networks training training training training training training training training algorithm algorithm output output output number system system system system system system system system error error error error error results information information information information information information information information information information information information information problem problem models models performance performance performance based based based space space space space space space space space space space weights weights weights weights weights weights weights weights linear case vector vector vector vector vector vector order order shown shown shown shown values values values noise weight weight functions neurons neurons neurons neurons pattern pattern pattern pattern pattern pattern pattern point point point processing processing control control control control control control control control control control control control control control control control control control large large large analysis analysis analysis inputs inputs inputs inputs inputs shows signal visual visual visual visual paper paper small task task task task task cells cells cells cells cells step points features process process level level level level level current trained cell structure structure random response similar similar similar representation representation representation representation architecture section line rule rule vectors vectors vectors vectors vectors vectors vectors general general parameter parameter states theory theory term term experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result result university university university university research research independent found target target target target target target target target target target target target target target target target target target target target target dynamics initial initial initial initial initial initial computer terms distance connections synaptic science science science left direction direction direction direction direction direction direction direction direction direction direction direction direction presented present present present present present present present phase phase phase phase phase phase phase phase phase phase phase phase activation activation activation activation activation low low low low temporal sets press press press press learn position position position components outputs outputs sample abstract applied back properties references component component due positive positive positive positive important adaptive propagation propagation context introduction action action action complex hand hand behavior generated generated generated generated generated parallel parallel parallel parallel parallel parallel parallel parallel parallel recurrent recurrent tion tion tion spatial spatial assume assume assume assume assume assume assume signals signals signals signals representations representations learned learned higher part center center center center cases cases cases type required required multiple multiple cortex cortex cortex cortex long long distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed expected expected expected expected expected fact length length length correct correct observed observed errors errors errors errors forward forward simulations simulations simulations simulations simulations simulations simulations ing simulation human human sum performed called elements regions regions made made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback original vol relative relative specific specific represented desired desired desired desired receptive provide provide location location location location location location eye eye determined determined goal related connected motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor cortical brain brain equal mit mit mit accuracy larger connection fields fields support dependent dependent dependent dependent selection selection selection selection selection selection selection selection selection selection report report report report institute institute department department implementation consists internal internal individual individual individual individual joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint responses cambridge cambridge cambridge cambridge cambridge hinton trajectory trajectory trajectory trajectory trajectory detection determine determine determine requires speed speed vision basic con developed velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines actual provided provided provided provided selected selected selected selected selected selected evidence backpropagation backpropagation nature nature discussion technical technical technical feedforward feedforward increases increases transformation fast complete circuits implemented shape generate generate generate generate generate generate supported supported role theoretical eds eds journal square end hypothesis hypothesis degree degree degree degree rumelhart rumelhart rumelhart rumelhart sensory sensory sensory simulated simulated simulated simulated simulated simulated simulated probabilistic probabilistic typically typically smaller needed dynamical jordan jordan technology programming york mechanism mechanism special consistent trials mode mode mode operation operation leads representing call numbers inhibition supervised magnitude magnitude attention attention produced description neuronal neuronal architectures population population population population population population population population discussed improve movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement reported subset array array array array array array array array array array array array array cognitive cognitive recently relevant highly varying teacher teacher volume works studies studies converge achieve symmetric generalized gate williams storage entire grant grant arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm amplitude amplitude amplitude amplitude parts lead concept scaling scaling scaling scaling occur trial alternative move move move move move move move loop loop loop loop loop loop loop loop loop loop loop occurs half starting starting starting starting starting starting starting critical trajectories trajectories trajectories trajectories depend central central modules modules modules learns learns learns learns suggest strong mechanisms integration characteristics california proportional proportional turn turn movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements plane targets targets targets targets targets targets targets targets manner manner manner manner program program program program program acknowledgements areas reference pro van van produces perception generating plot mathematical changing recall simultaneously slightly angle angle angle angle angle angle angle angle angle angle shift implies review influence influence detailed transform open open updated updated showed showed centers forms suggested suggested barto barto barto barto barto barto barto barto barto barto barto slow closed generation initially sufficiently foundation foundation foundation avoid fire fire fire instances recognize determines determines determines determines illustrated automatic selecting closely closely capable capable society mcclelland miller reached kind contained interested neuroscience neuroscience dis issue issue physiological follow timing sci duration simplified simplified simplified dot realistic backward providing reach cat automatically neurosci neurosci moves receive extend extend law body explore command command command command command command command american transformed transformed collection collection singh singh singh singh singh singh investigate circuitry updating varied varied accurately existence existence respond giving ideas ideas school muscle muscle muscle scaled proper pathway encode understand cognition phases phases naturally naturally naturally transmission concepts man man opposite rev adjusted subsets assumes fisher freedom freedom freedom freedom precise logic nervous fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers generates generates explain massachusetts massachusetts ment ment ment ment piecewise asynchronous directed caused correction correction turns rapid straight straight tive closer widely directional nucleus mation controls controls consequence consequence recognized angles angles gradually begin res medical read alignment alignment robustness greatly pathways pathways led led fed parameterized parameterized parameterized experimentally red posed recordings adjustable adjustable adjustable compares ity commands commands commands commands commands commands execution execution execution execution execution passes aim reaches reaches reaches gen fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber neuro shaped shaped specifies simultaneous simultaneous univ consistently aligned physiology physiology physiology physiology physiology feasible proportion accomplished accomplished recover receptors receptors turned reaching reaching reaching arranged climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing inspired inspired fails anatomical ments accepted simplify proceeds cerebellum cerebellum cerebellum cerebellum cerebellum loops loops loops moment efficacy resulted modifications adequate arrays arrays clock planar planar planar selects muscles muscles muscles inferior inferior infor passive started cerebellar cerebellar cerebellar cerebellar cerebellar programs programs programs programs james von moved intended advance specialized specialized specialized foundations spatiotemporal stimulated gaze gaze gaze saccades contact hart ignore stopped influences explorations displacement onr informa depression depression largely microstructure workspace workspace workspace workspace ter visually transmitted cooperative cooperative cooperative copy copy copy quasi trigger causing amherst superimposed descriptions tor chicago chicago chicago spinal spinal spinal spinal lesion gated interact werbos generators generators generators generators generators generators ization guidance convert relate books cosine cosine guided distal distal cartesian cartesian flash flash superposition superposition tively descending descending descending gilbert gilbert placing parametrized reciprocal simplifies worked resembles triggered triggered triggered coordination stimulating crude mcdonnell mcdonnell inhibit inhibited arrow termination developmental purkinje purkinje purkinje illinois sensorimotor sensorimotor sensorimotor kinematic kinematic kinematic kinematic kinematic kinematic anatomy anatomy anatomy anatomy cord cord corrective corrective corrective corrective corrective corrective corrective corrective corrective corrective corrective corrective corrective corrective corrective tended ignores vivo adjusts curved counterpart schmidt schmidt positioning bradford terminates handbook brainstem tra ically parker parker houk houk houk houk houk houk houk houk houk houk houk houk houk houk houk houk houk devoted ized inappropriate proceeding limb limb limb limb limb limb limb limb limb limb modulate resemble pew pew preventing ton yon direc terminate adjustments conveyed conveyed conveyed ito ito ito ito mussa mussa ther awake neurodynamics ascending ascending ascending ascending ascending ascending adap ivaldi ivaldi begun fur gibson endpoint endpoint endpoint endpoint cortico cortico cortico cortico wired hypothesize tributed cent cen symmetrically radially arms executes comprise brooks kinetics olive georgopoulos georgopoulos georgopoulos georgopoulos olivary news recep depolarized facing facing proprioceptive proprioceptive proprioceptive proprioceptive proprioceptive proprioceptive proprioceptive proprioceptive proprioceptive proprioceptive neurophys occasional selec ner probing farther adams adams adams adams probabilistically collaterals sor constrains alterations planned antagonistic nimh posture posture alters regulate stimulate bethesda sut trophic jacobjan triggering raven activ pacific tral northwestern northwestern northwestern ual gielen gielen microelectrode aiming gisbergen gisbergen unconscious equidistant jectories lished preparing cotterill sharpness erate signifies resembled proces moroneurons neuromodulator lection 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similar similar show equation equation equation equation equation equation equation line line parameter states obtained obtained experiments result university research independent independent independent found found found found sequence target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial table table table computer computer terms science science science science left left left left left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented present activation motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion press position position position position position position position position position position components components components basis basis abstract applied computational computational computational computational references component component component component component component component due due procedure introduction complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand estimation behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect generated parallel parallel tion tion change change change part previous previous required conditions conditions expected proposed observed observed observed errors simulations minimum minimum minimum resulting resulting resulting resulting resulting computed sum performed performed performed times means feedback study study study original vol vol vol vol relative represented represented represented represented represented represented compared location location location location location location location location location location location location location location location location location location location location location location eye eye eye eye eye eye determined determined experimental goal constraints motor motor motor motor motor motor motor motor motor larger larger larger larger contrast support dependent dependent modeling institute department version version version version version version version version version final final final final final final exp scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme addition addition addition addition ai ai equivalent equivalent directly trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory determine choice free speed speed speed vision vision vision give condition condition coding derived derived velocity velocity velocity velocity velocity velocity types types types path path actual actual measured measured measured measured measured measured measured measured measured measured measured measured measured measured measured measured discussion describe group tested tested fast fast short short common assumed assumed assumed assumed assumed supported eds journal end end end end end end end end end development sensory sensory fit simulated simulated simulated pairs smaller underlying account account account account account account account account account unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown coefficients coefficients coefficients block block increasing increasing mechanism mechanism mechanism mechanism consistent trials trials trials trials trials trials trials principle direct normalized early idea added neuronal population discussed pair typical typical typical similarity movement movement movement movement movement movement movement movement movement movement reported reported reported moving moving moving moving moving moving moving moving moving moving subject hierarchical cognitive previously previously previously observations subjects calculated calculated calculated correspond studies studies address positions positions positions locations locations locations locations locations locations locations locations locations locations locations modified modified modified modified modified modified modified modified modified modified modified modified modified modified organization entire entire increased grant arm arm arm arm arm arm amplitude amplitude amplitude amplitude amplitude expression occur suggests trial trial trial deviation predicted starting trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories differences differences clear constrained constrained suggest suggest taking mechanisms mechanisms mechanisms presence external start movements movements movements movements movements movements movements movements movements movements movements movements averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged targets targets groups configuration denoted denoted explicit van van van van van van van van van van van mathematical coordinates simultaneously averaging involves involves involves involves transformations remaining angle angle formed shift blocks choosing choosing extracted expressed dependence dependence stationary squares squares squares squares static similarly earlier intervals intervals roughly roughly generation intermediate intermediate intermediate initially initially initially initially initially initially initially msec msec msec msec msec msec msec msec msec msec msec msec msec construction foundation recorded building priori priori priori priori priori bell bell inter inter sciences successfully successfully successfully planning planning planning planning regular determining middle differ modification modification modification modification modification modification modification modification included presentation successful successful successful schemes schemes schemes schemes score induced induced success neuroscience lie lie physiological follow duration duration duration vary absence paradigm paradigm paradigm neurosci consisted subsequent presents minimized simpler command replaced successive rest rest investigated possibility muscle scaled complicated statistically statistically cognition analogous examined examined equally equally versions versions versions versions versions der der noted percentage directed directed directed directed directed directed track coded explanation independence straight straight probable probable mathematics acknowledgement gradually gradually gradually gradually res res res preceding double double double double double double double double profile profile profile substantially experimentally experimentally completion execution plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan replace shaped shaped deviations lot naive phenomenon shifted shifted shifted shifted shifted shifted representative physiology modify modify saccadic velocities purely connecting reaching reaching reaching reaching reaching ments ments occurred becker becker intended schwartz den similarities similarities israel israel israel infer saccade saccades saccades saccades saccades saccades motions motions motions motions motions motions motions motions motions motions motions motions motions motions motions motions motions motions motions motions motions motions alternatively alternatively tures displacement displacement displacement displacement displacement displacement specification shorter graded super inferred inferred inferred inferred inferred randomized reaction reaction reaction reaction par copy profiles lit perceived perceived amplitudes stem acceleration acceleration acceleration possibilities possibilities possibilities param continuity decays continues elementary guidance confirmed cartesian cation flash flash flash flash flash flash flash flash flash flash flash flash flash flash setup superposition superposition superposition superposition superposition superposition superposition superposition superposition superposition superposition superposition superposition superposition superposition tively isi isi isi isi isi isi isi accounted accounted accounted accounted accounted siam son fea elsevier eters completed elemental elemental elemental elemental elemental elemental coordination kinematic kinematic kinematic kinematic kinematic kinematic coincide obey curved pooling accounting accounting accounting quick remained vicinity vicinity tra durations durations united limb gradual amsterdam jerusalem instant cations levy occasionally plans plans mar internally internally internally internally internally internally internally internally internally enabled displaced respec rationale elicited vectorial vectorial vectorial vectorial tar aii hogan hogan analogously georgopoulos georgopoulos ticular news permission indicative pennsylvania rotates depended unmodified grasp planned planned jerk jerk jerk displacements displacements displacements initiation initiation derlying dii reprinted upwards weizmann wished loca ioo stimu marquardt marquardt pergamon ception gielen gielen gielen gielen rehovot aiming gisbergen gisbergen gisbergen abort abort abort abort abort abort tln cii modifi regan volves copyright chair career efference jectory modifica gon gon participated ceived bsf binational taxget taxget subserving kettner 
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generated parallel parallel parallel change change change change change change change change change change change change change change change change change change change change change change change change change change change change energy energy energy spatial chosen chosen part previous previous previous multiple good distributed expected techniques proposed proposed proposed proposed proposed proposed proposed length length scale simulations simulations simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum total simulation simulation simulation simulation simulation simulation simulation human human human human human human human human human human human human human computed multi multi multi performed called times optimization optimization optimization optimization potential natural global global global applications study study study study study study study study relative specific desired desired desired desired proc proc proc location perform active determined experimental experimental experimental experimental related constraints constraints motor motor motor brain mit steps larger update support proceedings report department department advances joint joint joint joint joint joint joint joint joint joint difficult final final final final considered view view view solutions curves curves trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory top top top top conference free speed estimated produce produce coding velocity velocity velocity velocity velocity velocity velocity controller path path path path actual actual processes evidence constraint constraint biological achieved discussion technical increases describe close assumption stable finding effective assumed generate supported eds eds end hypothesis hypothesis hypothesis hypothesis future including including auditory simulated simulated simulated simulated simulated simulated smaller smaller needed account account functional interesting projection principle iterations iterations iterations iterations pre pre pre stored international bottom minimize produced light discussed directions recent takes takes movement movement movement movement movement movement movement movement movement movement movement movement movement reported reported reported reported reported reported strategy strategy moving moving identical side side side side cognitive recently engineering engineering engineering subjects subjects tuning solve solve smooth studies positions organization organization grant arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm horizontal horizontal horizontal horizontal horizontal horizontal horizontal predicted predicted trajectories trajectories trajectories trajectories trajectories trajectories interactions numerical numerical numerical peak suggest hard hard physics regularization movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements plane program configuration force force question acknowledgements explicit produces perception ways sequential ann stability stability stability mathematical mathematical changing coordinates simultaneously simultaneously infinite slightly slightly slightly slightly slightly slightly slightly unique unique equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium springer john choosing choosing formation communication solved solved open organizing approximations static static static static approximated completely completely completely suggested suggested past key reasonable reasonable calculation convex convex convex convex roughly roughly roughly roughly iterative penalty generation degrees degrees includes usa bell bell middle paths paths paths paths paths paths paths modes reached verlag induced physiological strategies simplified simplified simplified realistic realistic realistic realistic realistic minimizes minimizes ill reach reach reach neurosci neurosci consisted deal minimized body body body origin command wiley create create collection steady humans preliminary hall reducing behavioral behavioral behavioral investigated biol biol muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle proper complicated complicated circles circles necessarily man ensure front front freedom nervous nervous nervous nervous nervous nervous generates explain explain electronic defines defines devices smoothness smoothness analyzed straight straight straight satisfied closer closer strictly forces forces forces forces forces forces monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey laboratories angles angles author annual cybernetics virtual virtual virtual virtual virtual virtual virtual double double double profile axes simulate simulate simulate experimentally cohen posed marked marked marked marked slower dots dots commands execution simulator logical shaped shaped attraction findings findings realized realized realized globally globally cybern cybern guarantee japan japan japan japan angular driving velocities acts controlling controlling eliminate reaching fails anatomical primate primate determination determination determination imposed moment kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato neurobiology preparation preparation symposium symposium planar filled muscles muscles muscles muscles muscles muscles muscles passive utilized irregular studying arrows sons valuable displacement workspace workspace workspace torque torque torque torque torque torque july comparative profiles profiles profiles profiles ideally tendency molecular considers confirmed unconstrained termed flash flash flash flash flash flash flash flash flash flash flash flash flash flash flash flash discusses dorsal atr atr atr coordination moderate tension tension tension tension tension tension tension tension tension tension tension tension tension tension tension tension tension tension tension tension tension smoother december japanese kinematic ventral proposes ray ray tokyo tokyo joints ignores ignores ignores curved curved curved curved protocol cho feldman feldman seg skeleton skeleton skeleton skeleton uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno uno suzuki suzuki suzuki suzuki suzuki suzuki suzuki suzuki limb gradual demanding biophysics primates insertions mussa mussa reproduces inertia inertia inertia ivaldi ivaldi gun ell arms faculty kyoto hogan hogan hogan hogan hogan hogan emphasizes del shoulder shoulder shoulder shoulder shoulder unrealistic intend elbow elbow elbow elbow soraku cleaned bizzi bizzi bizzi attracting attracting sel seika stiffness stiffness stiffness maintenance planned planned posture posture posture posture torques torques torques torques jerk jerk jerk jerk jerk jerk jerk jerk optimizations optimizations meters rhesus corp voluntary voluntary tangential virginia morasso morasso morasso morasso tensions tensions tensions tensions tensions curvatures frontier origins bra bra woo mitsuo criticized criticized criticized 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process process current trained trained trained high high high high high high high high high similar similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture average average average note note note note experiments activity activity activity result result result university threshold threshold threshold computation research defined found found constant table table table table table table distance presented presented low low low low low low low low press learn outputs abstract back density analog analog analog analog analog analog references due ieee positive procedure procedure important important decision decision decision decision decision decision decision decision decision decision decision propagation introduction action action action complex hand behavior effect generated parallel recurrent search tion tion energy difference complexity classifier classifier classifier classifier 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due due important introduction introduction complex complex complex effect parallel change spatial rules higher center cases multiple multiple multiple multiple expected make region correct correct forward total total human human multi performed regions means optimization optimization optimization made natural natural knowledge application application desired cross cross cross related related connected equal power steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger larger larger nets nets morgan report institute loss advances joint difficult difficult directly additional san top effects detection efficient upper upper full free free condition weighted weighted randomly developed levels levels levels levels area area types actual selected selected selected evidence achieved achieved achieved discussion normal technical common common shape role require end end pixel future kaufmann typically typically typically pairs fully significantly 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fewer reducing ideal possibility scaled comparable analyze detector detected detected extent averages averages separable distinguish majority answer answer ring commonly potentially medical medical medical medical conjugate conjugate conjugate apparent apparent greatly collected understood readily readily passes richard chose sophisticated decreased patients patients patients patients patients deviations diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis picture representative college secondary secondary physiology appearance circular fits imaging imaging imaging methodology continue date sion patient paul treatment specificity waveforms splits splits stopped ball ball severe severe lem dramatically resonance resonance resonance resonance resonance resonance resonance yielded maintaining blood blood slight unable ber forced encouraging magnetic magnetic magnetic magnetic magnetic magnetic magnetic year individuals classic num maintained graduate file uncertain cole 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hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance based weights weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer order shown shown values values values values probability probability parameters noise noise weight weight weight unit method approach pattern pattern pattern pattern pattern pattern point point single single single single single single single single control large rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis form shows shows signal signal small small small size task task task task task task task task fig fig fig step points field features features classification classification classification classification classification classification level level level trained trained trained trained trained trained trained trained random random random random high similar architecture line line line line line general generalization generalization generalization generalization generalization generalization parameter real average average average states states theory obtained obtained obtained obtained obtained obtained obtained obtained obtained activity activity activity activity variables solution research research research target target target target initial initial constant estimate connections prediction prediction prediction prediction prediction prediction left left presented present present low low frequency frequency frequency frequency frequency frequency maximum range range press components basis basis continuous continuous sample sample sample abstract applied back find computational references due due positive procedure procedure context introduction introduction stimulus stimulus stimulus measure measure measure signals prior part center previous previous previous previous cases cases multiple multiple good good long fact correlation correct correct correct correct correct correct correct correct correct observed errors errors scale simulations simulations minimum ing tasks tasks tasks total total simulation simulation simulation human computed performed performed performed times times made made made made study study obtain negative negative relative relative specific compared desired desired goal related related related related related related related related related motor brain brain brain power power power power power power power power power power power power voltage steps accuracy accuracy accuracy train report report institute institute department department department individual individual individual represents represents responses responses responses responses difficult addition considered considered san san san stimuli stimuli stimuli detection detection significant increase condition randomly provided backpropagation backpropagation achieved discussion technical technical feedforward feedforward tested limited close corresponds short short common common supported supported require square ability ability future sensory auditory auditory auditory auditory auditory typically combination reduced unknown testing testing testing testing testing york trials trials operation pre pre pre pre pre pre pre pre pre pre pre pre making window window window normalized normalized normalized idea attention attention attention attention produced choose predict predict predict predict architectures improve improve recent recent separate practical moving period period subject subject subject subject subject subject subject subject subject subject subject subject identical sejnowski sejnowski sejnowski sejnowski sejnowski cognitive cognitive cognitive cognitive cognitive highly varying varying varying compare previously subjects subjects subjects subjects subjects subjects calculated tions correspond studies background background background background evaluation interval interval interval improvement improvement entire increased grant amplitude amplitude occur suggests derivative predicted correctly pass runs runs half reduce operator measures measures accurate peak peak suggest suggest suggest strong strong solid solid pulse turn start min min decrease averaged averaged targets groups groups pro ways laboratory laboratory segments averaging averaging averaging electrical electrical involves remaining remaining remaining slightly spectral adding frequencies frequencies frequencies events predictive formed potentials potentials potentials potentials potentials potentials potentials select national extracted depending depending influence evaluated showed showed understanding similarly past spectrum spectrum spectrum spectrum spectrum spectrum sign performing epochs sec sec sec sec sec sec intervals intervals event event event event event event event event remains filtering msec eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg classified classified includes inter inter discussions identified society divided detect situation ten ten ten strongly cun neuroscience running physiological physiological physiological device bar bar bar bar generalize consisted decreasing diego diego diego poor difficulty difficulty dotted dotted discriminant discriminant giving int possibility root variability removed removed predicting predicting predicting predicts predicts predicts predicts predicts detector extent seconds seconds seconds averages averages indicating site site site band band band band ground agreement analyzed waveform waveform failure tool rapid widely filtered precisely desirable consequence recognized medical fluctuations fluctuations considerably double collected lack lack peter completion howard differs instruction occurrence simulator electric neuro coherence coherence attentional attentional attentional attentional extreme irrelevant irrelevant irrelevant irrelevant irrelevant initialization spectra spectra spectra spectra physiology sleep appearance naval air allocation chance minutes minutes minutes fan hit hit hit hit interpret bands bands bands bands mark analyzing removing neurobiology salk started ranging tone periods periods loo male heart heart dif locked jolla late probe probe sustained sustained ignore generalizing automated onr maintaining appeared appeared neurophysiology shorter shorter shorter session session latency alternating revealed additionally individuals tor causal causal causal evoked evoked evoked evoked evoked assess clas attempted grouped gener neurophysiological hughes terrence individually individually erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp monitoring monitoring monitoring monitoring monitoring sonar sonar tones lda lda lda lda lda lda lda programmed permit port intensive correlate sessions clinical clinical clinical demand monitor scalp scalp scalp ongoing virtually award bottou compo progressively operational operational repetition seed rameters william sis scott deter correlates indicators assessed united ated health hits hits plenum investigator jack simula nents excluded minute italy makeig makeig makeig makeig alization wright eog eog jackknife jackknife jackknife jackknife jackknife jackknife missed missed ministry alertness vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance vigilance enormous electro electro instructed opera invaluable associ sification public aging minimally grand grand scientist profound probes probes navy instrument instrument analy monitors resetting selections deflection designate neous preparing psychophysiology psychophysiology psychophysiology 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networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training output output output output output number number number number number number system error error error error error error error error error state state state state state state results results results results results results units units units units units units units units units information information information information information information information problem problem problem problem problem problem problem problem problem models models hidden hidden performance performance based based based based based space space space space space weights case case case order shown shown systems systems systems systems systems systems systems values values values values probability probability probability probability parameters noise noise noise noise noise noise noise weight weight weight functions distribution method method method method method method approach pattern point point point point point single processing processing processing processing processing processing processing control control control control control control control control control control control control large large large large large local rate analysis analysis class matrix optimal optimal optimal optimal optimal optimal shows shows shows shows algorithms gaussian gaussian gaussian gaussian gaussian paper examples examples small net net net task methods step step points points points points points points points classification process process process level trained trained trained trained high high high response response response response response response architecture architecture architecture architecture architecture architecture architecture architecture show equation equation equation equation section section section section section section line line line line line line rule vectors generalization generalization generalization generalization real approximation approximation approximation approximation states states theory theory theory theory theory theory theory theory theory theory theory theory theory gradient obtained note experiments activity university university university variables computation computation solution solution solution solution solution solution found initial constant constant table table table table table table estimate estimate standard standard standard computer computer distance science science prediction prediction prediction prediction direction presented present activation activation machine machine machine maximum maximum press basis basis sample sample sample abstract applied applied applied applied applied back convergence density properties properties likelihood references references component stochastic due adaptive adaptive introduction complex hand behavior effect effect dynamic generated generated generated generated generated generated generated variance change assume lower lower lower prior prior prior prior prior prior prior prior representations representations chosen higher higher higher part center center center center theorem theorem theorem type required multiple conditions represent tree distributed bayesian bayesian bayesian bayesian bayesian expected equations make fact fact techniques probabilities probabilities errors forward scale scale scale simulations resulting classes total computed respect respect respect respect multi sum sum performed performed performed times times regions regions mapping means means reinforcement factor dimension dimension made natural feedback applications knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge vol vol vol vol vol artificial relative relative relative specific specific specific specific specific specific specific samples represented represented true true application application application application application desired cross cross cross series receptive define proc perform determined determined experimental experimental related posterior posterior constraints brain equal mit mit mit accuracy accuracy comparison fields update train descent modeling selection morgan morgan morgan morgan morgan morgan proceedings report version consists advances advances advances advances advances advances joint connectionist connectionist connectionist connectionist difficult difficult difficult final exp exp bias bias ai considered considered framework framework framework framework domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain directly hinton view solutions design san san capacity determine efficient efficient full requires approximate approximate approximate world speed estimated validation validation give give give give give con derived derived weighted clustering bounds product actual actual actual backpropagation backpropagation nature constraint constraint simply achieved achieved achieved measured covariance covariance covariance technical technical describe group denote tested fast fast fast limited assumption assumption corresponds predictions predictions amount nearest assumed assumed supported theoretical eds eds eds eds eds eds adaptation adaptation adaptation adaptation adaptation adaptation hypothesis easily easily makes rumelhart rumelhart rumelhart rumelhart noisy noisy noisy noisy noisy kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann typically typically typically typically underlying reduced account dynamical functional coefficients coefficients coefficients mlp mlp mlp significantly significantly structures empirical empirical leads squared squared numbers numbers numbers numbers normalized normalized normalized normalized normalized experts sources light predict denotes architectures architectures architectures architectures resolution pair pair pair pair takes takes typical apply trees engineering interest sufficient highly conventional smooth yields studies diagonal diagonal sparse address positions locations williams improvement improvement improvement improvement improvement improvement lead extended derivative predicted locally locally locally touretzky touretzky touretzky touretzky width generally conclusion operator operator neighbor depend competitive bayes bayes bayes moody moody moody moody moody moody practice temperature temperature temperature suggest hard presence reduction reduction drawn sigmoidal sigmoidal sigmoidal sigmoidal proportional intelligence turn assuming assuming exist scene force force force force force force force explicit digit derive written written longer longer solving describes tuned tuned tuned tuned tuned dept dept recall explicitly physical dimensionality dimensionality remaining slightly integrated adding adding adding gaussians applying applying applying applying quality expectation expectation expectation choosing correlated squares influence detailed approximations centers centers centers centers centers centers centers centers centers centers centered suggested suggested constants updates past spectrum earlier additive measurements measurements measurements measurements measurements measurements normalization roughly interpolation interpolation valid distances distances construction foundation degrees degrees precision precision precision precision thesis thesis priori priori inter weighting priors domains holds phys determining selecting closely included poggio poggio poggio presentation successful successful identify mackay mackay essentially quickly kind strongly cun cun cun cun cun superior superior sampled paradigm eigenvalue denker hypotheses leading reach reach principles subsequent decreasing oriented minimized remain schedule diego diego wiley poor experience hanson optimized optimized biases fewer giving giving school project project authors reliable proved cover surfaces induction smallest act necessarily predicting extremely created equally noted noted freedom freedom art art art art art art improving extent extent extent submitted years preference preference preference costs smoothness variances guaranteed guaranteed guaranteed improves analytic analytic analytic analytic analytic analytic analytic analytic explanation explanation explanation nowlan nowlan adapted adapted adapted adapted expensive independence worse worse considerable processed perspective stanford closer precisely acknowledgement separately beginning optimize localized localized localized localized localized explained reflects varies percent percent led relevance lms parameterized readily solla solla incorporated incorporated incorporated reliability reliability reliability exhibits controllers partitioning partitioning partitioning partitioning partitioning weigend weigend reaches proven resource incorporating incorporating incorporating achieves substantial tolerance tolerance tolerance damage specifies initialization tresp tresp tresp tresp tresp tresp indices indices feasible feasible feasible martin girosi controlling controlling theories theories theories theories turned caltech lost platt platt darken darken darken promising overcome siemens siemens familiar contract abilities transforms fail optimally optimally optimally presentations substituting elimination slice recovered widths widths widths widths widths equals equals spherical spherical dif advance membership mem relies inductive considerations omohundro omohundro valuable papers hart grants shavlik material vari ball severe pressure outperforms summer propagating smoothly instantiation instantiation causing generalizations ical hierarchies edinburgh edinburgh avoided clustered clustered principled principled preserved intuition duda ijcnn ijcnn mitchell mitchell allocated bump simplifying plate plate plate plate emphasize individually considers guided cation drawback million sheet sheet apparently discretization tij tij memo lippman lippman refined hofmann hofmann october corrections mini simplifies suggestions circumstances syn accordance corporate corporate insufficient ferent curse suffers outperformed determinant supplied unreliable thickness thickness thickness thickness thickness thickness thickness operational automation automation beneficial ray successively cardinality mill mill mill mill mill mill mill mill archi archi economic syntactic safe spirit filling scott scott ance locality artificially derives allocating denominator huge decades validated rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling hot hot hot hot rein months preprocessed unifying putational argmin cancel entities entities cient metal kanter modifies week mal des volker helped 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#@Holmann_R,Roscheisen_M,Tresp_V,
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#*network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time set set networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm output output number number system system system system system system system system error error error state state state state state results results results results results results results results units units information information information problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based space space space space space space weights linear linear layer layer layer layer layer case case case case case vector vector vector vector order order shown systems systems systems systems systems systems systems values values values probability probability probability probability probability probability probability probability probability parameters parameters noise noise functions functions recognition recognition method method approach approach approach approach approach pattern pattern pattern point point point point point point single single single single single single processing processing control control control large large large large large local local rate rate test test test test test analysis analysis class class class class class class class class class class class class class class class class class class class class class class class class class matrix matrix inputs form form signal signal signal algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper size feature feature feature feature feature net methods points points points points points field field features features features features features features features classification classification classification classification classification classification classification process level current trained trained trained trained trained trained trained trained structure structure structure problems problems problems high high high response response response response response response response response response representation representation representation equation section line line rule rule rule vectors general general general generalization real real real real approximation approximation approximation states states states gradient obtained obtained note note note dimensional dimensional dimensional result variables research research research log log log log log initial initial initial constant table table estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard computer terms terms terms terms distance prediction prediction prediction presented present present present low temporal temporal temporal temporal sets sets maximum maximum maximum range range learn position components components components components components basis outputs abstract applied back density density density density density density density density density properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component component component stochastic due due procedure procedure procedure procedure important decision decision decision decision decision decision mixture mixture mixture mixture mixture mixture mixture mixture mixture context context context context context complex complex complex hand estimation estimation estimation estimation estimation statistical effect effect generated generated variance cost change variable classifier classifier classifier classifier classifier classifier classifier lower lower measure signals prior part conditions conditions conditions conditions conditions conditions represent represent tree equations markov markov markov markov markov markov markov markov markov markov markov markov fact fact fact fact techniques techniques proposed proposed probabilities probabilities observed observed errors forward resulting classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes multi multi multi multi sum performed mapping mapping potential potential potential dimension dimension dimension dimension feedback global applications applications applications applications em em em obtain original vol vol vol vol samples samples samples true true compared application application desired cross series series series location experimental experimental experimental posterior motor motor motor discrete discrete power accuracy accuracy contrast contrast support train train train proceedings institute institute loss implementation implementation version version technique consists consists individual kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel responses difficult difficult difficult addition addition addition ai ai framework domain equivalent experiment environment directly directly directly directly directly estimates estimates estimates estimates estimates estimates design transition transition trajectory san top detection detection determine classifiers upper upper full full full full choice significant statistics statistics world speed estimated estimated estimated estimated estimated estimated estimated estimated basic validation coding randomly levels lines product finally selected backpropagation backpropagation backpropagation nature nature nature nature simply measured covariance normal normal normal normal normal normal normal normal normal feedforward feedforward feedforward describe describe arbitrary tested hmm hmm hmm hmm hmm hmm fast limited corresponds rbf rbf common assumed assumed shape shape generate supported main end end end end hypothesis hypothesis degree makes including including including fit fit objective objective probabilistic typically typically underlying underlying combination unknown unknown coefficients fully technology technology interesting significantly significantly york special special database empirical mode squared numbers direct making window stored stored bottom early idea produced choose perceptron perceptron denotes improved improve recent recent advantage robust separate typical similarity reported practical practical introduced strategy side hierarchical sense sense engineering highly highly compare conventional calculated calculated calculated calculated volume works axis tions tions smooth studies diagonal address background evaluation locations channels sensitive entire grant lead alternative feed hybrid hybrid hybrid width loop loop clusters occurs occurs boundary boundary hardware flow critical greater competitive differences sigmoid accurate accurate bayes bayes bayes designed practice practice strong presence sigmoidal sigmoidal sigmoidal sigmoidal california california california california california radial turn variety manner manner denoted acknowledgements factors generating generating estimating plot laboratory label stability vertical implement involves unique integrated quality extraction expectation versus national national focus focus dependence dependence review depending correlated estimator densities densities controlled labels labels approximated completely discrimination past slow dashed intervals roughly false boundaries boundaries tracking calculate sufficiently sufficiently classified expect building kernels kernels currents uncertainty discuss discuss absolute absolute straightforward sensor sensor sensor sensor sensor sensor computationally included included detect detect situation tend kind link dis lie follow generative generative duration involved sampled providing observable consisted operating mixing mixing modelling modelling modelling extend simpler simpler unlike diego parametric transformed poor collection requirements experience hall behaviour successive respond respond giving history mappings fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault relationships referred reliable reliable attributes concepts voltages subsets aspect obvious obvious obvious assumes observe mapped switching consist detected contributions plant seconds seconds seconds seconds percentage site developing theoretic ground ground ground ground track variances failure capabilities expensive expensive lies rapid purposes sites constructing constructing located located commonly commonly potentially scientific arises computers bandwidth bandwidth demonstrates fluctuations conjugate fourth considerably limits applies collected axes generic generic lack red effort detecting detecting detecting treated commands calculating prototypes exhibits ture fall wind wind prevent pasadena replace inherent segmented windows windows windows windows tolerance damage specifies diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis merging merging instantaneous irrelevant representative acquisition lab benefit summing ratios conditioned linearity homogeneous establish communications ments chance difficulties chemical chemical contract viewpoint hope hope obtaining observing intuitively nonparametric degradation moments excellent loo iteratively widths guarantees belongs belongs centroid centroid centroid centroid centroid centroid darpa enable modelled april matter environmental likelihoods likelihoods likelihoods likelihoods omohundro omohundro ignore automated vari mechanical fusion divide outline pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing achieving exhaustive recursively discriminative discriminative discriminative discriminative discriminative ideally tendency causal australia remote summarizes deep deep deep deep ijcnn chapman faults faults faults disadvantage disadvantage afosr march iso smyth smyth smyth library monitoring monitoring monitoring nonetheless misclassified sam nasa siam esti esti amplifiers normalizing intensive radio mix mann november sigmoids drives beam simplification generarive monitor impractical jet jet jet calibration calibration transmitter char hour proportions proportions affecting condi station station disturbances ples alarms operational operational propulsion propulsion propulsion autoregressive autoregressive tells reality receivers positional ance categorical gathered transmit indirectly indirectly antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna manual monitored monitored health tory replicate maximisation developments amer facilitates linearities instant extrapolation operated severely ular elevation accuracies transferred tracked erroneous assoc orig walker walker centroids undesirable ele excluding kramer kramer coverage pushed watts silverman silverman initialised seeks outlines rendered comprise encounter confident bandwidths bandwidths azimuth ponents subsystems spacecraft spacecraft spacecraft spacecraft spacecraft undergoing steerable steerable partic earth earth administration administration southern temporarily electro steer ner signif manifest consequent initialisation aeronautics mated readings readings masked discrim criticism symptoms symptoms jeff faulty faulty jpl telecommunication mating deemed icant subjectively wil acteristics passively arx arx arx munications leonard leonard aero exogenous communica antennas inal shut ama complexes normalising padhraic labora spain weighs destroy oratory 
#@Mellstrom_J,Smyth_P,
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#*network network network network network network network network network network network network network learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural input input input input input input data data data data data data data data function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time set set set set networks networks networks networks networks networks networks training algorithm output output output output output output output output output output output output output number number system system system system system system system system system system error results results results results results results results results results results results results information information information information information problem problem problem problem problem problem problem problem problem problem problem problem models based based space linear linear linear layer layer layer layer vector vector vector vector vector vector order order order order order shown shown systems systems systems systems systems values values values values values values probability probability parameters parameters noise noise noise noise noise noise distribution recognition method method method method method method method method method method approach approach approach approach approach point point point point point point point point point point point image single single single processing processing processing processing processing processing processing large large large large large local test test test class optimal form form shows shows shows signal signal signal signal signal algorithms simple simple gaussian paper paper size task task methods methods methods methods methods methods fig fig fig cells points points points points points points points process process process level level level level level level level level level level level level level level level level level level level trained cell problems problems problems problems problems similar similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture show section section section fixed fixed rule general general general general general speech real real real real approximation approximation average gradient obtained obtained obtained obtained experiments result computation computation computation computation computation solution solution research defined found constant constant table table table table table table table table standard direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented map map present present present present present phase low frequency sets range range components outputs outputs outputs abstract back back likelihood likelihood references component stochastic due ieee procedure procedure important decision decision propagation propagation context introduction complex complex estimation statistical change complexity complexity lower measure learned learned higher cases type required good good good good good long long long represent techniques techniques proposed proposed correct correct probabilities observed observed errors errors errors errors errors errors simulations classes classes tasks simulation computed computed computed computed computed computed computed computed computed respect respect respect respect multi multi multi multi multi multi performed performed performed performed times made made made made global applications applications applications applications study study knowledge knowledge knowledge filter original vol vol artificial relative specific specific specific represented represented true compared compared compared compared application application application desired desired desired desired cross series provide compute compute compute compute compute compute compute compute perform active determined related related related connected power power steps steps accuracy accuracy accuracy fields train nets morgan technique consists consists consists consists advances represents represents responses difficult bias layers layers layers maps maps maps maps considered considered considered considered considered curve curve additional solutions solutions solutions solutions design design trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory determine efficient requires requires approximate free world world speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed estimated validation give coding randomly developed developed developed levels levels actual selected evidence nature depends describe tested limited assumption assumption corresponds complete complete surface amount journal easily easily noisy kaufmann simulated simulated needed reduced account account account account functional functional functional functional functional coefficients fully mlp mlp mlp mlp mlp mlp mlp transfer interesting leads representing call filters making normalized choose added added added predict architectures architectures architectures architectures architectures architectures architectures architectures discussed directions directions directions directions directions exact exact lateral introduced highly compare compare observations observations approximately module module axis axis solve yields yields correspond correspond correspond definition modified modified interval interval increased exists horizontal expression lead occur deviation predicted alternative touretzky white white conclusion trajectories valued depend depend central central modules modules modules modules modules modules modules modules modules accurate accurate accurate bayes bayes bayes numerical designed peak performs practice propose propose propose propose propose taking taking strong hard hard variety variety exist relationship appears digit vertical distinct physical remaining remaining slightly angle angle angle angle angle angle angle angle angle unique unique unique scales formed national dependence interpretation interpretation codes solved solved solved solved solved operations approximations measurements measurements measurements measurements measurements measurements measurements measurements measurements classical classical intervals interpolation advantages advantages transactions degrees degrees precision precision handwritten includes priori automatic prove discuss tests major reason middle closely detect build build build build build efficiently reached decoding decoding decoding decoding decoding decoding cun interpreted built built usual absence modular modular modular computes computes reach reach intrinsic presents powerful layered layered relations accurately discriminant discriminant ml ml successive successive successive successive ideas working proper variability complicated proved notion removed measurement measurement coefficient closest automata automata automata automata automata automata automata illustrate singular singular precise precise consist established years devices cos orientations track coded analytical briefly correction handle reasons perspective incorporate located arise inversion inversion involve involve sun empirically amounts generic generic generic experimentally peaks peaks peaks peaks introducing measuring differs wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind enables sophisticated sophisticated sophisticated specifies lot contextual sensing sensing sensing sensing sensing sensing sensing sensing martin approximates harmonic lecun establish dealing convenient difficulties automaton determination determination determination determination methodology methodology methodology modifications carry days performances performances performances performances performances performances performances performances performances performances performances performances performances recovered ambiguity decide forecasting reproduce reproduce correcting sequentially radar radar radar radar linked linked specification removal removal transmitted boser comparative quasi corrected constitutes realize remote remote remote remote remote remote remote remote options options options arising graphics permits inverted singularities paris paris paris paris ambiguous conversely france france universit universit suffer inverting bring differing september november beam beam discretized discretized twenty ers supplied station dedicated 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#@Badran_F,Crepon_M,Mejia_C,Thiria_S,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm output output output output output output output output output number number number number number number number number number number number number number number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results units units units units units units units units units units units units units units units units units units units units units units information information information information information problem problem problem problem models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear layer layer layer case case case case order order shown shown shown shown systems systems values probability parameters parameters noise weight weight weight weight weight functions unit unit method method method method method method method method method single single single processing large large rate test test test patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs form form shows shows shows paper paper paper small small small size net work task task methods methods methods methods methods trained trained trained trained trained trained trained structure random high high response representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation equation general general generalization generalization generalization generalization generalization generalization generalization approximation average average average average average obtained obtained obtained note note note note note university university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation independent independent independent defined defined defined defined sequence sequence target target target table table table table table table table table table table estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard standard standard standard standard computer computer connections connections science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left low low sets sets range press press basis basis nonlinear nonlinear sample sample sample abstract applied applied back find find density references ieee procedure procedure hand statistical statistical statistical effect effect generated variance parallel search search search change complexity variable variable variable lower measure measure measure measure chosen higher cases long distributed expected expected expected expected expected make make techniques proposed correct correct observed observed finite minimum minimum minimum minimum resulting resulting resulting resulting regression regression regression regression regression computed computed computed computed computed computed computed respect multi sum means applications applications study study knowledge original original original vol relative relative represented compared application application cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross series provide provide define compute compute compute perform perform related related connected connected connected brain brain brain brain equal comparison larger update modeling selection selection selection selection selection selection selection morgan proceedings department department version version technique consists internal internal internal internal advances final final final final final final addition maps considered equivalent directly directly curve estimates estimates estimates design limit conference conference determine efficient choice significant approximate statistics statistics statistics estimated estimated estimated validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation randomly criterion provided selected selected technical denote limited corresponds complete predictions short nearest nearest common effective effective assumed face journal ability ability ability ability ability ability ability future degree makes makes including kaufmann smaller unknown unknown unknown unknown fully fully fully transfer significantly york increasing increasing increasing special consistent database database squared squared squared squared pre international normalized magnitude decay idea combined combined choose description predict predict predict perceptron perceptron perceptron denotes denotes architectures architectures architectures architectures architectures discussed improve exact typical apply introduced introduced strategy include quadratic sense subset subset subset subset engineering interest interest varying observations observations observations observations observations calculated volume volume works diagonal diagonal generalized generalized generalized interval improvement improvement risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk entire constructed exists deviation deviation deviation deviation deviation deviation deviation deviation deviation deviation predicted predicted correctly touretzky column minimal assumptions assumptions reduce reduce editors measures accurate designed moody moody moody moody moody moody moody moody moody moody moody moody practice asymptotic asymptotic sound propose propose characteristics drawn sigmoidal intelligence regularization assuming targets identification factors factors factors estimating estimating describes ann pruning pruning pruning sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity category category electrical slightly predictive predictive predictive predictive predictive quality versus select select select select select john john john yield yield independently review stationary estimator estimator estimator estimator overlap influence variation detailed organizing approximations approximated sizes completely suggested key smoothing performing expansion reduces fitting roughly initially calculate assigned avoid box box priori priori perceptrons automatic automatic absolute absolute absolute absolute absolute characterized major determining selecting selecting selecting selecting society computationally divided essentially summary soc cun cun heuristic heuristic heuristic issue criteria criteria criteria hold categories minimizes denker predictor predictor predictor attempt attempt minimized explore american overfitting association 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#@Moody_J,Utans_J,
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#*network network network network network network network learning neural neural input input input input input input input input input input input input input input input input input input input input input input input function figure figure figure figure set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state results results results results results results results information information problem problem problem problem problem problem problem hidden hidden performance performance performance performance based space space space space linear layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown method method method method method method approach approach approach approach pattern pattern pattern pattern point point processing processing processing processing test test test patterns patterns patterns patterns analysis analysis analysis inputs inputs shows shows algorithms simple examples examples examples small small small small size size size work task methods methods methods step step field classification process level level level level level level level level level trained trained problems problems problems problems problems problems architecture architecture architecture architecture architecture architecture architecture architecture show vectors vectors vectors vectors vectors vectors vectors general generalization generalization generalization parameter real real real theory theory theory theory result solution solution solution solution solution solution solution solution solution solution solution research research research defined found found found found target target table distance distance distance distance distance distance distance connections science left left present activation nodes nodes nodes nodes nodes nodes nodes frequency frequency machine machine maximum maximum maximum press outputs abstract properties likelihood references due ieee ieee ieee important adaptive adaptive adaptive adaptive decision introduction complex complex complex complex complex complex complex statistical statistical statistical effect effect parallel cost cost complexity complexity complexity complexity assume classifier classifier classifier word word word word word word chosen chosen chosen chosen center type type required required required required binary binary binary binary binary binary long long distributed region region proposed length length length length correct correct correct correct correct correct correct observed errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors minimum total total total multi mapping mapping mapping mapping mapping mapping mapping made made made applications knowledge knowledge obtain original vol vol vol vol true determined determined goal goal constraints constraints equal mit connection proceedings report words words words internal code code code code code code code code code code code code code code code code code code code code code code code represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist final layers addition addition considered considered solutions solutions solutions solutions san top effects effects bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit determine efficient efficient efficient classifiers full choice free world world world vision basic basic basic basic increase increase channel coding clustering developed types actual provided selected selected selected selected selected backpropagation constraint constraint constraint constraint constraint constraint constraint measured feedforward describe tested corresponds amount effective effective implemented require eds instance degree rumelhart rumelhart development development development development development development noisy typically block segmentation pre pre bits bits bits bits bits bits bits bits bits bits bits bottom description perceptron advantage advantage separate separate separate separate separate separate strategy subset calculated tions tions solve achieve achieve trans background positions positions positions positions positions positions positions separation separation separation generalized williams increased increased increased constructed concept extended alternative touretzky hardware critical row row greater practice practice encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding exist relationship van longer primary multilayer slightly develop develop develop choosing choosing choosing codes codes codes codes codes codes codes codes codes codes codes codes codes solved solved solved calculation classical classical purpose add valid valid distances existing fire fire fire fire fire fire priori priori color illustrated prove uncertainty uncertainty candidate major major simplicity simplicity simplicity reason straightforward straightforward extra differ encoded encoded encoded encoded encoded encoded included mcclelland identify efficiently efficiently comparing road compact compact quickly graphs graphs graphs procedures decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding contained contained superior bar bar bar bar bar bar paradigm received received received received received received received received software schedule powerful difficulty put dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset rest referred decisions workshop encode cover measurement transmission possibly possibly portion logistic message burst burst burst burst burst developing publishers analyzed coded adjacent tractable correction correction correction worse arc easier division ran mation ion ion ion recognized addressed integrating generic generic capability readily rep anti incorporating serve hamming hamming hamming hamming hamming inherent decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder chose chose decreased decreased redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy june wesley corrupted intractable addison imposed height resulted north guide enhanced enhanced enhanced enhanced enhanced enhanced infor excellent programs holland candidates dif specialized creating reader proximity correcting correcting correcting correcting correcting correcting correcting correcting correcting correcting correcting correcting inductive dietterich ignore influences yielded parsing slight ter ber break july corrected corrected corrected chapter ibm ibm cessing gained gained gained gas degraded march lookup exceed book meet meet meet knowing prevents simplifies simplifies simplifies oregon challenge diagrams lems trainable trainable 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#@Blaum_M,Gish_S,
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#*network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training algorithm output output output output output output output output output output number number number system error error error error error error error error results results results results results results results results results problem problem models models models models models models models models models models models hidden performance based based based based based based based based based based based based based based space linear linear linear layer case case order order order shown shown shown values values values parameters parameters parameters functions neurons method method method method method method method method method method approach approach approach point single single control control control neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate analysis class class class class optimal optimal inputs inputs shows shows shows shows shows paper paper paper paper paper paper small feature methods methods methods methods methods methods methods methods methods methods methods points points classification classification classification classification classification classification classification process process process process process process process current structure structure structure structure structure similar architecture section section section line general general general general parameter real theory theory obtained obtained obtained obtained note university university variables variables variables research research research independent found found found found found found found found found found dynamics initial table table standard standard standard terms terms prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented machine machine sets maximum nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous abstract applied applied references due important adaptive adaptive decision decision introduction effect effect search change change energy energy variable variable variable variable variable variable variable classifier classifier classifier lower rules measure chosen chosen part center cases type type type type good good good conditions conditions tree tree tree tree tree tree bayesian bayesian bayesian bayesian bayesian bayesian fact fact fact region observed observed observed observed observed errors errors resulting classes classes classes classes classes regression regression performed called study knowledge filter filter filter filter filter filter filter original original original original artificial artificial artificial true compared compared compared application desired desired series series series series provide perform determined power approaches approaches accuracy accuracy comparison comparison comparison update train dependent institute department version technique consists consists individual individual represents difficult difficult final exp exp exp addition addition ai experiment experiment experiment directly curve view design conference full significant significant significant approximate estimated estimated basic give give give produce derived velocity velocity controller product evidence achieved achieved measured feedforward increases increases increases describe arbitrary arbitrary transformation limited limited inverse inverse inverse corresponds predictions predictions common assumed shape theoretical theoretical theoretical theoretical theoretical adaptation adaptation square degree fit fit fit fit fit fit objective underlying underlying reduced account functional functional functional unknown coefficients coefficients coefficients technology technology interesting testing testing testing testing testing testing testing testing testing testing special special consistent structures empirical mode operation details pre international early magnitude polynomial polynomial polynomial polynomial polynomial polynomial polynomial predict perceptron separate typical practical practical practical apply introduced trees trees trees sense engineering highly compare conventional conventional approximately tuning tuning tuning tuning tuning tuning tuning tuning tuning studies trans background improvement entire lead lead occur deviation deviation predicted predicted predicted predicted white setting pass runs strength strength conclusion accurate bayes performs performs performs temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature mechanisms characteristics exist decrease manner factors plot plot plot plot plot laboratory laboratory ann ann ann ann ann tuned tuned multilayer multilayer category category explicitly simultaneously electrical applying predictive quality quality quality versus versus versus versus versus versus competition yield yield yield yield yield yield yield yield yield yield yield yield yield yield yield yield yield yield yield yield yield yield expressed dependence dependence dependence dependence review squares interpretation influence understanding understanding understanding understanding constants constants past past diagram partial reasonable reasonable additive performing expansion fitting fitting fitting fitting fitting filtering figures thesis batch batch batch batch batch batch extension capable suitable modification divided situation online online online traditional traditional refer moore moore anderson anderson interested interpreted running involved vary vary providing providing providing providing nips modelling modelling modelling modelling modelling modelling modelling law law exhibit kalman kalman kalman kalman kalman kalman kalman kalman recursive recursive hall hall behaviour behaviour examine giving applicable dependencies authors induction induction induction measurement possibly generalisation man predicting spline spline extremely equally equally aspect friedman friedman friedman friedman friedman friedman friedman obvious noted taylor observe multivariate multivariate multivariate motivated phd years percentage cart cart cart cart cart cart cart cart cart cart cart cart piecewise piecewise piecewise piecewise adapted london considerable stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress stress processed purposes forces acknowledgement universal author considerably considerably understood experimentally readily lack splines polynomials passes passes passes passes passes operate gains serve deviations leaf consistently lab japan restrict controlling impossible plays extending consideration overcome resistance resistance resistance resistance star methodology guide preparation preparation prentice programs surprising captured captured captured approximators deg thin reveals reveals std std material material material material material material material material material influences vari stone market divide temperatures temperatures temperatures outperforms outperforms converted indirect incorporates sine sine sine piece piece recursively formulate superimposed superimposed superimposed mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars australia australia stands unseen unseen chapman convert convert convert simplifying relating plate plate plate plate plate plate plate plate plate plate plate plate ultimately hornik hornik quinlan quinlan quinlan reveal nasa cubic cubic cubic cubic cubic cubic ation places retained retained manuscript manuscript vice fiat versa demand demand hyperbolic hyperbolic hyperbolic assistance mill mill mill mill mill mill mill mill mill mill mill permanent permanent ready materials acknowledges deformation deformation deformation deformation deformation deformation indirectly prescribed tsoi tsoi tsoi tsoi experimented rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling rolling plastic plastic plastic hot hot hot hot hot fractional metal sydney forgetting buntine undergoes ames claimed belmont desire strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain strain abs knot slabs slabs slabs slabs implication readers queensland queensland olshen undergoing validate wood roll roll indebted stinchcombe specially steel steel steel steel steel steel steel steel steel steel viii finished polyno plates plates plates plates plates plates plates intense chung adaption mial stdev stdev petersen petersen petersen confirmation mentally lei lei staff older peculiar hitherto sinh sinh sinh lucia pendence slab riacs generous sation tural microstruc melbourne melbourne hump appreciably funda assisting 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure time time time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output output output output output number number number number number number number number system system system system error error error error results results results results results results results results results results results results results results results results units units units units units units units units units units units units units units units units units units units units information information information information problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based based weights weights weights linear layer layer layer layer case case case case case order order order shown shown systems systems systems values values values noise noise noise noise noise noise neurons unit unit unit unit unit unit distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach point point point point single processing processing processing processing local local rate test test test test test test test test test test test analysis analysis analysis analysis inputs inputs inputs inputs inputs inputs form form form form form form form signal signal signal signal visual paper examples examples examples examples examples examples size size feature net net net work work work task task task methods methods methods points points points points points points features features features features features features process process process process process level level trained trained trained trained trained structure problems problems random random random random random random random high high response response response response response response similar similar similar similar similar representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture show rule rule rule general generalization generalization generalization average states theory obtained obtained experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity result university university university threshold threshold threshold threshold threshold threshold threshold threshold research found found found found target target target target initial table table table table table estimate computer computer computer computer computer computer distance distance node node node node node prediction left presented presented presented present present present present phase activation nodes nodes nodes nodes nodes nodes temporal machine sets maximum maximum maximum range press continuous continuous continuous sample abstract applied applied back find find references ieee ieee positive positive important important important decision propagation introduction complex complex complex stimulus stimulus stimulus stimulus effect effect generated parallel search complexity rules rules rules measure measure signals signals learned chosen chosen cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases firing multiple distributed expected expected equations make make make make techniques techniques techniques correlation correct correct correct simulations resulting resulting resulting resulting ing total total total total total total total human human computed performed performed performed elements potential potential potential potential potential made made study knowledge knowledge knowledge knowledge knowledge knowledge negative negative original artificial represented represented true true compared compared compared desired series series series provide location location location location location location location location location location location location location location perform perform perform determined determined connected connected connected connected connected connected connected connected connected cortical brain brain brain brain brain brain brain brain brain brain brain brain power approaches mit accuracy accuracy comparison contrast contrast fields fields train source source nets modeling modeling modeling selection proceedings department version technique technique technique individual represents responses responses difficult difficult difficult difficult bias bias layers delay addition addition graph graph graph graph graph considered considered considered cambridge domain experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment curve stimuli stimuli stimuli detection detection detection detection determine determine determine determine determine determine requires requires significant channel developed area actual provided finally finally finally finally selected selected selected selected selected evidence sampling measured discussion normal normal increases group group group tested corresponds common shape supported require require require require require require require main journal end instance instance makes rumelhart rumelhart sensory sensory including auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory typically typically typically typically needed reduced reduced fully fully fully technology transfer testing increasing increasing head trials representing details pre making normalized experts experts experts experts expert expert expert expert expert expert expert expert expert early attention run light architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures discussed improve improve improve reported lateral apply moving include include subject subject identical identical machines machines side side side side side side side side side side side sense sejnowski sejnowski recently relevant engineering interest interest approximately solve match correspond studies differential trans background evaluation positions improvement grant amplitude amplitude amplitude amplitude exists occur suggests suggests extended digital trial derivative derivative derivative derivative derivative derivative correctly deterministic white generally starting starting starting place minimal greater assumptions conclusions valued valued valued central central central central sigmoid clear clear peak peak peak peak peak peak intelligence variety start decrease iii averaged targets targets derivatives identification identification identification identification identification identification identification identification identification program program acoustic acoustic acknowledgements appears construct written ways describes ann mathematical mathematical implement averaging averaging averaging electrical involves remaining remaining slightly belief consisting predictive formed potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials stages correlated estimator interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation forms forms forms activities diagram reasonable epochs intervals false false interpolation remains remains remains msec msec msec msec msec msec eeg eeg eeg advantages classified david recorded recorded recorded includes activations instances recognize prove domains domains phys discussions tests tests tests tests tests tests tests determining identified identified identified identified identified closely closely included included mcclelland mcclelland presentation identify identify identify identify identify post plots ten traditional refer conf graphs graphs repeated procedures superior issue contribution classify criteria criteria sci sampled sampled wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave ill ill automatically extract deal oriented origin unlike stimulation layered transformed create investigate difficulty issues preliminary graphical graphical graphical graphical graphical graphical graphical graphical graphical mass fewer fewer fewer fashion ideas school rest project investigated investigated comparable pathway removed examined examined examined examined possibly analyze opposite opposite psychology changed ensure prototype formal nerve nervous nervous nervous initialized initialized art epoch baseline baseline years advanced growing waveform adjacent failure explanation analytical analytical answer purposes easier widely preprocessing preprocessing located nucleus nucleus nucleus beginning beginning beginning medical medical medical computers recording author raw requiring freeman freeman freeman freeman cochlear pathways pathways transient peter effort peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks recordings recordings recordings sharp requirement pittsburgh pittsburgh pittsburgh anti characterize ordered extensions richard substantial substantial substantial simulator simulator electric electric boston boston boston boston boston boston boston focused patients patients patients patients patients patients progress diagnosis diagnosis distortion distortion cumulative ear ear ear ear ear ear physiology sort proportion primarily generator generator appearance forming martin martin arrival arrival arrival arrival extending spontaneous wrong resulted implications adequate alphabet alphabet presentations constructive degradation composition inferior utilized falls becker james patient patient paul sides evident originally facilitate waves waves surprisingly creating eng offer record colliculus subsequently automated automated automated automated dividing rms slight latency randomized failed corrected ease amplitudes amplitudes amplitudes amplitudes stem stem stem stem stem stem stem evoked evoked evoked evoked evoked evoked evoked evoked evoked evoked evoked evoked evoked evoked electrode attempted summarizes preserved conduction conduction intuition interact file generators distant expand terrence electrodes electrodes scope increasingly disease monitoring monitoring flash sonar attached attached distinguished placing geniculate intensive clinical clinical reversed consuming resolve resolve continued scalp scalp vii hearing hoc cornput somatosensory somatosensory contralateral contralateral contralateral contralateral contralateral contralateral contralateral contralateral contralateral contralateral contralateral mining incorrectly proportions proportions medicine medicine medicine diagnostic distinguishing subtracting judged discarded seed restricting contrary inspection william protocol protocol absent absent absent absent absent fidelity restrictive scott brainstem format files files files successor manual ears ears ears ears ears ears ears ears ears ears ears putative ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral ipsilateral medial severely occasionally prolonged abnormal abnormal abnormal abnormal abnormal abnormal disorders disorders fight saved saved des registration registration begun neurology latencies latencies latencies clin fuse surrounded transcription transcription encouragement encouragement wishes fell delivered olivary granularity neurophys collaboration seeds traversing clicks clicks clicks clicks cumbersome referring investigates expertise criticism chart chart reversing vastly labor donald gorman gorman attains effected gabriel gabriel slowed tucker tracing perez click click click diagnoses diagnoses electroencephalographic engineer mario hospital reliance tempting obscure obscure readable readable digitizing chief professional unusually mimicked digitization graphed progressed delivering biomed 
#@Freeman_D,
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point point point point image image image image image image image image image image image image image image image image image image single processing processing processing processing processing processing large local local local local local rate rate rate rate analysis form form simple visual visual visual visual visual paper paper paper examples examples net work work work work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods fig points features features features features process process process level level current structure structure random random random random high high response response response response response response response response response response response similar show show show images images images approximation theory gradient gradient gradient gradient gradient obtained term activity activity activity activity activity activity activity activity activity activity activity dimensional university university university variables independent defined defined defined found sequence sequence sequence constant constant constant computer distance distance direction direction direction direction direction direction direction direction direction direction direction present present present activation low temporal temporal temporal temporal temporal temporal temporal temporal machine motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion position position position components abstract convergence convergence references component due due due due introduction stimulus stimulus stimulus stimulus stimulus effect dynamic dynamic tion tion change change change energy energy energy energy energy energy energy energy energy difference variable variable spatial spatial spatial spatial spatial spatial spatial assume measure measure higher previous type type multiple conditions distributed distributed fact fact techniques techniques techniques correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correct minimum minimum resulting total human regions regions orientation filter filter filter filter filter artificial represented represented cross objects proc proc proc proc perform active determined experimental constraints constraints gain approaches approaches contrast words implementation consists consists joint responses addition sequences sequences sequences computing computing computing stage stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection determine determine determine determine speed speed speed speed vision vision vision vision basic basic give produce area velocity actual actual evidence nature nature biological group fast amount common common require main pixel cluster easily degree sensory sensory underlying needed combination account edge edge edge edge edge edge edge increasing segmentation matching principle operation details filters pre direct depth magnitude frame frame frame frame frame frame frame frame frame frame frame frame produced produced produced produced description discussed discussed discussed recent recent recent movement movement moving moving moving moving moving moving moving moving include include subset subset cognitive cognitive interest highly approximately tuning smooth differential achieve address definition background background background background background evaluation positions grid grid intensity intensity intensity intensity concept concept occur suggests rotation generally flow flow flow flow flow flow flow flow flow central clear peak suggest strong mechanisms presence min areas areas van van van edges edges edges edges produces perception perception optical factors describes tuned sensitivity sensitivity sensitivity averaging averaging averaging scales extraction extraction extracted depending stages communication variation variation frames frames frames frames frames diagram earlier expansion tracking tracking tracking tracking generation remains valid filtering filtering filtering filtering advantages degrees existing figures figures figures figures usa usa sciences sciences sciences activated gating texture texture capable capable suitable effectively identify detect detect detect detect soc soc conf conf conf receptor receptor receptor receptor receptor comp bar bar bar bar bar vary simplified dot principles modelling wiley essential varied detail reducing fourier successive respond school school school detectors detectors detectors int int int structured working workshop notion surfaces surfaces surfaces gradients plausible editor integer psychology psychology created front detector detector detector detector detector nervous detected established scenes separable distinguish track briefly processed processed arc producing directional controls opt opt opt gradually res qualitative fourth fourth lack lack lack psychophysical detecting continuously dots dots schematic popular coherent coherent coherent coherent coherent coherent coherent coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence simultaneous lot shifted discontinuities discontinuities guarantee temporally drift drift drift drift drift drift drift drift drift girosi unity arranged communications determination abilities reasoning optic optic optic degradation spurious spurious governed corre corre regard enhance searching occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion spatiotemporal spatiotemporal creating reveals motions motions balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced displacement displacement displacement displacement discriminate land validity personal spaced england brightness remainder alter shifting impose impose ijcnn adelson adelson proach paris rectified ambiguous constructs importantly france discusses responding reveal suffer differing mini removes fat lation autocorrelation vis micro micro affecting polarity polarity seattle evenly heeger heeger heeger heeger extracts autoregressive bergen bergen successively meth exploits reality ods irvine gence kinetic deformation segmenting percept problematic newly whilst whilst whilst whilst whilst whilst sixth sixth shear forthcoming illustrating web web web conver inertia british rosen blur laterally torre textured reichardt disparities pointwise hexagonal leftward leftward leftward leftward leftward leftward debate assump gestalt gestalt occluding occluding portant opposing crease crease argues sussex sussex sussex adaption adaption elaborated sir coherently reverses rectifying gradi nts landy landy landy landy underlies underlies nates smooths brighton glasgow brace 
#@Tunley_H,
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function figure figure figure figure figure time time time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm output output output output output output output output output output output output output output output output output number number number number number number number number number system system system system system system state results results results results results results results problem problem problem problem problem problem problem problem problem performance performance performance performance performance weights case case case order shown shown shown shown shown shown shown systems systems values values values values functions functions neurons neurons neurons neurons neurons neurons neurons method approach approach approach approach approach approach point point point point point single processing processing processing control large large large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron test analysis optimal optimal optimal optimal form shows shows paper small size size size size size size size size size net net work work work work work field current current structure structure problems problems random random random random random random random random random random memory memory memory memory memory memory memory memory memory response similar architecture show equation equation equation equation general average states dimensional dimensional university computation solution solution solution solution solution solution solution solution solution solution research research dynamics constant constant table table table standard computer computer terms terms terms distance distance distance connections connections connections connections left presented present present object sets sets sets continuous sample abstract applied find find find computational computational analog properties properties references due due ieee ieee ieee positive important introduction generated parallel parallel parallel parallel parallel search search search search search search search search search search change energy energy energy energy difference complexity assume chosen chosen bound bound bound cases cases type type type type type type required required multiple binary represent distributed distributed expected expected equations equations equations scale scale simulations minimum minimum ing ing simulation respect respect multi called elements optimization made global global global vol vol vol vol vol vol artificial represented represented compared compared application application desired desired desired desired desired desired desired cross provide provide proc proc perform determined constraints constraints constraints connected connected connected equal equal equal equal equal approaches approaches approaches voltage voltage connection connection connection source institute institute words implementation represents represents bias bias bias bias scheme scheme scheme scheme scheme ai ai computing computing solutions solutions solutions design stage stage stage stage stage stage stage stage stage stage stage stage stage upper upper upper approximate speed speed speed speed con produce randomly developed developed controller controller types types path actual finally selected constraint constraint constraint biological increases increases describe arbitrary fast limited stable finding assumed generate end ability simulated typically smaller needed hopfield hopfield hopfield hopfield hopfield hopfield combination combination combination combination combination reduced testing testing significantly york york increasing database database database mode stored minimize discussed takes element element element element practical subject quadratic array array array array array array array array interest compare conventional calculated calculated calculated calculated module module solve solve trans address address entire constructed occur alternative alternative locally column column critical minimal minimal row greater conclusions competitive sigmoid modules modules modules modules designed exponential faster faster asymptotic asymptotic suggest suggest largest cycle cycle cycle cycle cycle assuming exist manner manner minima minima force denoted areas appears solving ways implement implement quality quality quality blocks stages communication communication communication communication communication communication solved variation lee lee lee completely similarly constants processor valid valid usa currents currents inter partially columns regular delta oscillatory build schemes schemes schemes schemes tend essentially essentially essentially reached reached traditional traditional sci satisfy list list bar vary giles giles giles giles giles giles processors processors processors processors processors processors attempt moves subsequent routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing access access difficulty difficulty updating ml successive biol fault fault decisions working removed examined examined examined examined hill hill naturally voltages implementations rank obvious greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy logic message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message message switching established established established established brown brown brown brown great great independence independence handle handle sys shared shared easier widely broad worst worst acad beginning beginning cybernetics addressed behaviors empirically empirically calculating switch differs resource resource collective tolerance globally picture indices cybern investigation restriction restriction restriction princeton princeton princeton discover reaching establish establish convenient significance promising interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection hope obtaining mark synchronous synchronous degradation selects natl date analyses ensures ensures ensures ensures connect chooses entries claim route route route route route route route route route route route route messages messages speeds influences switches switches mind liu liu slight converted outperform graded bus exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive focal job july july legal legal legal legal legal legal encouraging affects acting ijcnn oct met setup rod rod packet applicability port port port port port nec nec moderate satisfaction sees consuming impractical converging converging hop aid aid establishes establishes calculates calculates conflicting conflicting conflicting huang huang resolved deals sij destination establishing establishing establishing establishing asset communicate comm mcgraw mcgraw routes routes routes routes routes routes routes routes routes routes routes routes routes routes routes routes routes began tolerant settles hysteresis virtue nov examines viable conflict conflict desire digitally mag utilization kronecker throughput routed routed routed routed concentrates hurt hoped siegel siegel stud requested itive liapunov specially suppressing conflicts conflicts commun methodologies methodologies ied multistage multistage multistage multistage multistage multistage multistage ports ports ports ports ports ports ports ports goudreau goudreau goudreau goudreau goudreau goudreau verge supposedly felt ees degenerates compet 
#@Giles_C,Goudreau_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural input input input input function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output number system error results results information information problem problem problem problem models based space weights linear linear linear linear case case order order order order systems systems systems systems parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions method method method single single single single processing processing processing processing test analysis analysis inputs inputs form form form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms simple paper paper paper work work work work work work work cells step step process process process process process high architecture architecture architecture architecture show show equation equation equation section section section line line line line rule rule rule rule rule rule rule rule rule images general general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real real states states states states theory gradient experiments experiments solution solution solution solution solution independent independent found found terms connections phase frequency press components outputs outputs outputs outputs outputs abstract applied applied applied applied back back convergence analog analog analog references ieee important adaptive adaptive adaptive adaptive adaptive adaptive adaptive mixture mixture introduction generated change assume lower lower rules rules rules signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals higher higher part part part previous previous cases type multiple multiple multiple multiple conditions represent represent proposed correct correct correct correct correct correct minimum minimum minimum minimum minimum minimum minimum minimum total performed performed performed called optimization optimization optimization optimization optimization made feedback feedback feedback feedback feedback feedback feedback global applications filter filter vol vol vol true true true proc proc proc perform perform perform power power power power power power power power power power power power power power power power power connection update update descent source source morgan proceedings implementation version advances difficult delay delay delay delay delay computing equivalent curve curve curve curves curves san san conference determine upper requires choice choice statistics con produce produce condition developed path path path path path path path finally finally achieved describe denote close stable stable stable stable amount amount amount short implemented assumed generate adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation square vlsi vlsi vlsi future future future future kaufmann needed account coefficients coefficients coefficients coefficients coefficients interesting ratio principle principle principle principle principle principle principle principle principle filters filters minimize minimize sources sources sources sources sources sources sources sources sources sources sources sources sources sources architectures exact exact exact separate practical apply apply apply identical identical quadratic subset subset subset recently recently interest interest compare approximately solve converge converge converge converge converge converge mixtures mixtures separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation williams suggests suggests extended derivative derivative feed white setting conclusions mateo sound propose propose propose taking integration solid assuming minimizing minimizing start start iii introduce identification acknowledgements stability mathematical modeled involves spectral develop mutual minimization john yield yield yield choosing independently independently independently independently forms forms understanding converges converges converges dashed dashed additive performing delays delays delays delays delays delays delays delays delays delays convex convex sec roughly roughly penalty penalty penalty filtering filtering filtering filtering filtering filtering david david avoid exploration blind blind blind blind blind blind blind blind blind blind blind blind blind extension specifically absolute absolute discussions capable mackay road notice quickly quickly quickly symmetry criteria generalize realistic minimizes minimizes minimizes delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed delayed cmos principles illustrates mixing mixing mixing mixing mixing mixing software situations access access put authors authors workshop workshop notion coefficient adapt adapt adapt created created adjusted adjusted academic initialized ith mixed mixed mixed mixed mixed mixed mixed mixed simplest isolated averages track adapted answer answer answer handle handle london reasons drive sections sections filtered filtered filtered mathematics sounds sounds sounds sounds lowest auto researchers fourth empirically empirically understood pure pure pure pure pure pure pure pure pure pure pure pure pure pure experimentally cohen cohen introducing adjustable adjustable music music music music music music music music music music incorrect extensions extensions prevent adjust converged gap room corrupted tation linearity purely proceed platt platt platt platt adds murray fail intuitively spurious interference interference interference interference interference interference interference interference interference 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#@Faggin_F,Platt_J,
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number number number number number number system system system system system state state results results models performance based based based based based based based weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer case shown shown systems systems values parameters weight weight weight weight weight weight neurons unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern point image image image image image single single processing large local local local local local local local neuron neuron neuron neuron rate rate rate rate test test inputs inputs inputs inputs inputs form form form form form shows shows signal signal signal paper size size feature feature feature feature feature feature net net net net net work work step features classification process process level structure structure high high memory memory response similar architecture architecture architecture line line line line line line line rule rule speech states note dimensional dimensional result threshold threshold threshold threshold threshold threshold computation computation computation research sequence table table connections connections connections connections connections presented presented presented low low nodes nodes nodes nodes nodes nodes nodes nodes temporal machine sets sets sets maximum range position nonlinear nonlinear nonlinear outputs outputs outputs abstract back analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due ieee ieee ieee ieee propagation introduction complex circuit circuit circuit circuit circuit circuit circuit circuit circuit dynamic generated parallel parallel parallel parallel cost tion difference classifier classifier lower word word word previous required conditions chip chip chip chip chip chip chip chip chip chip chip chip fact region proposed observed scale simulations minimum tasks tasks tasks computed computed computed computed sum sum sum performed performed means feedback applications vol vol vol vol artificial relative represented compute proc perform connected connected connected connected connected connected connected equal equal mit mit voltage voltage accuracy accuracy comparison contrast morgan proceedings proceedings proceedings report words words words version synapses synapses synapses consists consists individual advances responses final bias delay delay delay delay delay delay delay delay domain additional design design design design design design san stage stage stage stage stage bit bit bit detection speed weighted weighted weighted levels area area area area area lines product product product product product product finally selected measured discussion tested complete amount common common implemented synapse synapse supported end vlsi pixel ability kaufmann fully fully fully fully technology transfer transfer transfer character operation details call window window window stored stored stored bits bits bottom depth produced recent correlations element reported moving pixels pixels highly conventional calculated works works tions trans trans evaluation bounded gate gate gate gate gate gate gate storage storage storage storage storage amplitude constructed digital digital digital digital digital digital digital digital digital digital predicted locally locally touretzky column row sigmoid sigmoid sigmoid measures designed designed performs performs mateo integration cycle cycle sigmoidal sigmoidal sigmoidal sigmoidal demonstrated solid solid proportional force boltzmann digit pro pro produces laboratory implement implement multilayer multilayer multilayer integrated integrated frequencies shift shift extraction extraction cycles yield dependence phoneme phoneme phoneme stages controlled processor processor processor processor processor processor partial sec calculate topology handwritten memories memories memories memories memories memories prove coupled coupled holds tests efficiency differ computations composed composed composed summary compact compact cun strategies strategies device device device device device device device device device michael simplified nips board cmos cmos cmos cmos cmos cmos cmos computes computes chips chips chips processors processors processors processors operating detail tech tech scaled office func matched waibel waibel waibel trace adapt front generates serial serial charge charge charge charge charge charge charge charge charge charge charge devices devices devices devices devices ment cos cos cos cos floating floating floating diffusion briefly nonlinearity implementing shared shared shared preprocessing products products products products products acknowledgement read read computers depicted demonstrates incomplete addressed researchers double double capability red leave share adjustable schematic switch branch incoming incoming suited inherent age implements implements implements implements summed yielding realized lab fabricated fabricated fabricated ratios linearity naval lecun multipliers multipliers multipliers multipliers multiplier air khz fan fan held programmable programmable programmable programmable programmable programmable efficacy clock clock clock degradation expanded buffer injection nonlinearities darpa enable mem waveforms waveforms papers papers receiving receiving ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd sequentially multiplying street sig ent bus dec dec boser connec medium additionally ease amplitudes realize shifting deep mhz mhz mhz mhz mhz mhz mhz ijcnn ijcnn ijcnn ijcnn ijcnn ijcnn ijcnn march cosine cosine register packet places port port holding rewritten acoust tdnns quadrant quadrant trainable impulses fabrication compo concert arrives exploits exploits 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#*model model model neural neural input input input input input input input input input input input input input input input input input input data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set output output output output output output output output output output output output output output output output output output output output number results units units units information information information models linear order shown shown shown shown shown shown shown systems systems systems neurons unit image image image image image image image image processing processing processing processing processing processing processing processing processing processing processing processing large large rate analysis analysis analysis analysis shows shows shows shows shows shows shows shows signal signal signal algorithms 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adaptive adaptive adaptive adaptive introduction hand circuit behavior behavior stimulus stimulus stimulus stimulus change complexity spatial spatial spatial spatial lower higher firing expected chip chip make fact proposed finite minimum minimum resulting resulting resulting ing tasks respect performed performed performed means means means obtain negative desired series provide define proc perform determined related connected gain gain gain gain gain gain voltage voltage voltage voltage contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast connection connection support morgan proceedings institute synapses synapses synapses consists consists internal advances bias delay addition directly curve curve curve curve curves curves curves curves limit san top top top top stage stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli detection detection world world speed vision vision basic pages increase increase increase increase increase increase con condition levels levels levels levels velocity velocity velocity velocity velocity velocity velocity velocity velocity provided nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends simply simply biological biological biological measured measured measured measured measured measured technical increases describe arbitrary tested tested tested tested tested fast fast complete circuits circuits amount implemented vlsi pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel ability ability kaufmann hopfield reduced technology ratio edge edge edge edge edge edge increasing mechanism operation leads leads pre inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition 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insights guidance maximally maximally differentiation exceed selectively barlow barlow barlow barlow electronics memo rotating rotating computa scanned expense sees monitor photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors send inhibit mahowald mahowald accomplish fabrication pronounced excited striking andreou detects poly tells arrives vertebrate vertebrate spie spie leakage triangular alto mosis mosis adapts cutoff cutoff zones polar addi palo carver carver survival pull sends directionally directionally directionally recovers excite preprocessor preprocessor saturates ver incident rectification encourage quiescent retinas retinas retinas retinas retinas retinas desire ronald boahen boahen delbriick delbriick delbriick delbriick delbriick inhibits mosaic mosaic beat emphasizes abscissa travelling travelling rabbit rabbit visualizing freq flowing infrared orlando nakayama tiling hildreth precedes trast ambient prey legend vout vout levick 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world vision increase con produce channel channel channel weighted developed levels area area area lines lines actual provided processes inhibitory inhibitory inhibitory depends measured measured increases increases increases increases increases describe close excitatory excitatory excitatory circuits circuits circuits circuits circuits amount assumed synapse supported supported theoretical eds face face adaptation adaptation square end vlsi vlsi vlsi pixel pixel makes makes makes noisy including fit typically smaller smaller underlying account functional functional fully technology technology technology technology ratio ratio ratio ratio ratio york edge edge edge edge increasing increasing increasing increasing increasing increasing increasing increasing increasing increasing increasing head special mode mode mode mode mode mode mode mode operation operation operation operation call direct direct direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition 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#*network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure time time set networks networks networks networks networks networks networks networks output output output output number system system system error error state state state state state state state state state state state state state results results results results results information information problem problem performance performance based based based based based based space weights weights weights vector order shown shown systems systems systems systems systems values values values parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition method method pattern pattern pattern pattern point point image image image processing processing processing processing processing processing control large large large neuron neuron rate rate rate rate class class matrix matrix matrix form signal signal signal signal signal signal algorithms algorithms simple simple simple examples feature feature net task methods fig fig fig fig fig field features features level level level current high high high high memory memory memory memory memory memory similar architecture section section vectors general parameter real states states solution research table computer connections connections synaptic synaptic left left low object maximum maximum range components nonlinear abstract applied back back density analog analog analog analog analog analog analog references ieee ieee procedure procedure propagation introduction dynamic dynamic generated generated parallel parallel tion tion part previous required required chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make make region multi sum called called called called times times times times times means means factor feedback applications applications applications applications applications applications applications knowledge specific compared application application application application application application rates connected connected connected connected gain power steps larger support train morgan morgan morgan implementation version version synapses synapses synapses code code code code code individual difficult delay delay computing additional san san san bit bit bit bit bit bit bit bit bit bit bit bit bit detection upper full requires requires free speed speed speed speed speed speed speed speed speed pages con con weighted actual depends achieved fast fast limited circuits effective implemented implemented implemented implemented implemented implemented implemented implemented require main end end end end end pixel pixel instance easily makes makes makes rumelhart including kaufmann kaufmann kaufmann typically combination technology block transfer transfer transfer transfer programming programming programming testing testing testing testing character character character segmentation segmentation segmentation segmentation segmentation special special mode language call pre pre stored bits bits run run added added improve resolution advantage takes practical interest sufficient approximately volume volume volume trans sparse address address evaluation locations storage storage storage scaling digital digital digital digital digital digital digital digital digital digital wide wide wide matrices locally touretzky loop loop hardware hardware hardware runs runs flow conclusion starting greater segment editors editors performs performs moody moody faster faster mateo mateo mateo integration integration solid user user start start start characters characters characters program program program program program program acknowledgements digit digit digit digit digit digit written written ways primary physical text integrated shift shift shift shift shift blocks extraction john john overlap codes evaluate controlled organizing centered static static translation digits digits processor processor processor processor processor processor processor diagram partial calculation purpose purpose intermediate calculate string advantages advantages topology david precision precision precision building building building existing handwritten handwritten handwritten bell successfully suitable effectively paths tdnn post post ten road procedures procedures cun return running built built built write dot board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board board cmos denker denker automatically automatically chips chips chips moves software software software software load extend carried collection hanson hanson optimized issues helpful giving combine authors working symbolic func editor reading recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer logic logic store store store store store generates mixed simplest utility defines isolated charge mentioned mentioned stop stop crucial publishers publishers publishers convolution fairly floating floating multiplication implementing implementing transistors products laboratories calculations calculations demonstrates auto recognizing sun researchers evaluating double flexible generic readily passed slower howard instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction richard segmented implements calls calls synchronization arithmetic arithmetic arithmetic sharing realized writing interface interface interface guarantee summing addresses lecun lecun lecun lecun ranges promising tools programmable height moment fail responsible clock clock corner repeat repeat excellent combines programs connect histograms jackel jackel jackel jackel jackel jackel jackel jackel lawrence lawrence lawrence lawrence assembly assembly arrangement specialized mem storing designing subsequently instructions instructions instructions instructions instructions executed executed informa multiplying numerous converted users bus bus bus bus bus bus bus ram opposed job die retraining boser boser boser boser boser boser boser boser boser additionally ease workstation realize remote reject burges henderson increment packets mhz insights cessing approxi execute hubbard march overhead parallelism host host host host library library library library library monitoring importantly zip zip million million programmed programmed lippman lippman dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp dsp recognizers handled christopher capacitors supply micro micro micro micro micro micro micro micro december keeler keeler converter converter supplied replicated replicated concrete horizontally holmdel station sparsely anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna anna 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#*network network network network network network network network network network network network network network network learning learning learning learning neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function figure figure time time time time set set set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number number number number number system system system system system system error error error error state results results results units units units units units units units units units information models hidden hidden performance performance performance performance performance performance performance performance based based space space space weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order order order order order order order shown systems systems values parameters parameters parameters parameters weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons unit unit unit recognition recognition pattern pattern pattern pattern point point single single single single single single single single processing processing processing processing control control control large large large large large local rate rate rate rate test patterns class class class class class class class class class class class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper examples small small size size size size feature net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net work work step features features process level level level level level level level level level level level current current current trained trained structure structure problems high high memory memory memory memory representation representation representation architecture architecture show fixed line line general speech speech parameter parameter experiments result variables variables variables variables computation computation computation research research research independent defined sequence target table standard standard computer computer computer computer computer computer computer connections connections connections connections node node science science science science science science science left phase activation activation activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes machine machine machine machine machine object object object object object object object object object object object object object object object object object object object object object object object object object object object sets sets sets learn components components outputs continuous abstract applied applied back back back back back back back back back back back back back computational computational analog analog analog analog references references component stochastic ieee procedure procedure important propagation propagation propagation propagation propagation propagation propagation propagation propagation hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel change variable variable lower rules higher part part part part part part center type required required multiple multiple multiple multiple good represent represent represent tree tree markov make make correct correct probabilities errors forward forward forward forward forward forward forward classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes sum performed called called called called called called called called called called elements elements means potential made orientation global knowledge vol artificial artificial artificial artificial artificial specific specific application application application desired desired series define objects objects objects objects objects objects objects objects objects objects objects objects objects rates active experimental experimental experimental experimental experimental goal related related connected connected connected connected connected approaches steps steps connection connection update update update support support support train source source nets morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan proceedings report institute institute institute institute institute institute institute words implementation implementation version version consists consists consists internal internal internal internal code code code code code code kernel advances connectionist connectionist connectionist connectionist layers layers layers layers layers layers layers layers layers layers layers layers addition addition graph considered equivalent experiment environment environment environment environment curve additional view design design design design design design design design san top top top top effects conference determine efficient efficient full full requires significant significant statistics free speed speed basic derived derived developed developed levels levels provided selected depends measured describe tested fast complete complete complete complete complete complete implemented generate generate supported supported supported supported theoretical require eds square vlsi vlsi ability easily easily easily including including including fit kaufmann pairs pairs needed needed needed reduced reduced reduced fully transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer special structures database database database database database database principle operation language language language call call call call pre pre pre pre pre pre direct making making making making making making international international international international international international international international idea minimize minimize run run run run run run run run run run run run added predict pair pair separate takes practical apply apply apply include include include include include include machines side trees trees subset subset subset array array array array array array array array array array array array interest previously previously conventional works tions studies sparse address address evaluation modified improvement increased parts parts parts parts parts extended digital digital derivative touretzky loop occurs generally hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware pass pass pass pass pass pass pass pass pass pass pass runs runs runs flow place conclusions operator interactions sigmoid sigmoid designed clear peak peak peak performs mateo cycle cycle variety variety user user user connectivity program program program program program program program program program program configuration acknowledgements pro construct written written written primary ann ann ann ann ann ann ann ann ann ann ann ann changing changing implement missing physical scales decreases phoneme communication communication viewed viewed open open evaluate operations operations operations operations operations operations operations operations updated updated labels labels evolution static updates processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor partial partial partial partial reasonable sec add remains intermediate string advantages topology precision precision building existing includes includes activations activations activations activations activations activations usa assignment batch maximize specifically variations holds extra efficiency computationally divided build efficiently efficiently efficiently efficiently computations post post post post post post procedures procedures procedures split running running running running device hold built built built built built list write write write write backward backward backward backward backward backward backward board board board board board board computes highest automatically automatically automatically chips processors processors processors processors processors processors processors processors processors processors processors processors processors attempt operating software software software software software software software software software software software software software oriented oriented oriented oriented oriented oriented oriented oriented oriented oriented oriented oriented command powerful layered layered layered layered create access collection experience hall ideas tech tech tech tech tech rest int working comparable stream func phases math configurations created changed changed implementations implementations subsets versions noted mapped logic epoch epoch epoch epoch epoch generates utility contributions serial attempts defines languages languages languages indicating rows stop developing coded coded coded floating tool tool worse considerable berkeley ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring easier easier easier easier easier style day day constructing leaves leaves mation controls describing calculations localized localized read read read read lowest lowest computers computers sun sun researchers virtual greatly greatly greatly empirically flexible flexible flexible embedded simulate passed passed frequently rep rep rep rep rep execution execution passes partitioning instruction incoming incoming parent parent simulator simulator simulator simulator returns focused specifies calls calls calls synchronization arithmetic arithmetic sharing indices secondary redundant writing writing interface interface interface modify modify extensive restrict restrict princeton arguments conditioned databases databases databases branches repre interconnected interconnected interconnected communications communications interconnection programmable loops loops check balance transforms transforms shifts belong belong bourlard bourlard guide arrays arrays clock continue infor utilized prentice programs programs programs programs programs programs connect connect connect connect connect connect connect connect connect connect connect connect connect connect connect connect connect connect connect connect james overview overview moved realization assembly multiplied specialized specialized creating sustained passing card card considerations statement omohundro valuable propagate propagate propagate propagate propagate propagate default dividing accumulated 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#@Beck_J,Bilmes_J,Kohn_P,Morgan_N,
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#*learning learning model model model neural neural input data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time set set set set networks output output number system system system system system system system system system system error error error error error error error error error error error error error error state results results results results results results problem problem problem problem problem problem problem problem performance performance performance performance performance performance based based based based space order order order shown shown systems systems systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise functions method method method method method method method approach approach approach control control control control control control local test test test test analysis optimal inputs inputs form form shows shows shows signal signal algorithms simple simple simple simple simple work work work work task methods methods methods methods step step process process process process process level current current problems problems problems high response response response response response response response similar similar similar section section section section section speech parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter gradient gradient gradient gradient gradient gradient gradient gradient gradient note note experiments experiments experiments experiments experiments dimensional result university computation computation solution log log defined found target target target target target target target target target target target target target initial estimate computer computer computer computer computer computer computer computer computer computer terms distance left present frequency frequency frequency frequency frequency frequency range range range range press press press press press components outputs outputs abstract applied applied applied applied find find find computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references component ieee ieee ieee procedure important important important introduction complex complex complex complex complex complex complex hand hand hand hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior effect effect cost tion tion tion change energy difference difference difference difference assume measure measure measure measure signals chosen chosen part part part multiple good expected expected expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make techniques techniques techniques techniques region region scale minimum resulting classes multi multi performed elements elements factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization made natural natural knowledge knowledge knowledge knowledge knowledge filter artificial desired desired desired desired desired desired desired desired desired define compute compute compute proc perform goal goal goal goal goal goal goal goal goal goal goal gain gain power voltage voltage voltage voltage steps steps larger larger contrast support support descent descent descent descent descent descent descent selection institute institute implementation technique technique technique technique technique technique technique technique technique technique individual responses difficult difficult difficult difficult final bias bias bias bias cambridge cambridge computing computing domain domain domain experiment experiment experiment experiment experiment environment directly curve curve additional curves design design design design design design design design design design design design design design design design design choice approximate give con produce types path path actual actual actual actual actual provided backpropagation biological describe describe corresponds surface surface surface circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits finding effective shape supported require journal square square square square square square square square square end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi future degree development noisy including fit simulated typically combination combination technology technology interesting interesting testing mechanism special special special special operation operation operation filters filters normalized early minimize minimize minimize choose choose choose sources sources improved resolution robust robust robust takes takes element typical practical apply strategy strategy engineering engineering engineering engineering interest varying varying varying compare volume works smooth match converge trans sensitive entire entire constructed parts digital digital digital wide wide wide move setting setting setting setting setting setting setting setting setting setting setting setting setting setting setting setting setting setting setting setting trajectories trajectories conclusions conclusions differences accurate accurate accurate numerical numerical numerical peak peak learns constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained suggest characteristics california california solid variety exist introduce manner minima annealing relation produces solving describes tuned mathematical distinct dept confidence metric metric metric metric metric metric metric metric metric metric averaging physical physical physical electrical interaction quality select select john decreases choosing choosing choosing expressed expressed stages influence variation controlled controlled controlled measurements spaces sec views david precision expect building includes silicon silicon thesis combinations priori currents bell determines discuss successfully closely closely suitable driven identify build build build build composed composed composed conf quickly contained issue strategies strategies sci device providing providing computes computes automatically chips chips operating deal situations explore explore difficulty exponentially mead mead mead mead mead mead humans optimized integral accurately accurately helpful existence examine ideas ideas project behavioral transistor transistor reliable root root root root root root root root root proper measurement measurement measurement necessarily voltages voltages voltages ensure ensure precise explored academic art motivated finds attempts electronic electronic electronic electronic electronic integrate devices great slope capabilities cascade cascade lies tool tool tool tool drive perspective purposes sections producing desirable laboratories potentially scientific acknowledgement describing beginning gradually author nsf conjugate varies behaviors behaviors behaviors behaviors reflect generic posed adjustable frequently biologically compares differs pasadena adjust plan plan plan plan chose sophisticated findings deviations progress june cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea wesley newton addison interface acm narrow optimizing concerned caltech arranged platt platt platt platt fails multiplier murray minutes minutes adjusting tools programmable programmable fail methodology methodology settings settings guide enhanced tap tap tap tap tap tap tap tap tap tap tap document corollary encountered intended record captures ignore automated automated automated automated automated automated automated metrics fellowship july encouraging quasi causing decomposed affects adjustment adjustment alter care intuition goals goals goals graphics graphics landscape increasingly setup setup setup setup setup setup intl gilbert gilbert gilbert mimic tune mea worked opti acquire january ate quadrant lated aid attempting lyon lyon lyon loosely meeting automation alan lowpass cur quantitatively adjusts implying cascaded appro indirectly proceeding rent enabling developments moderately comprehensive comprehensive carver mization hysteresis optimizes avenue conceptually apparatus puter tics wright kirk kirk kirk kirk kirk watts watts watts watts watts kurt taps devise optimiza optimiza encouragement simu opens steep equipment equipment equipment cheap ences attack succeed safely valley valley valley havior instruments targeting embodies looo cumbersome lengthy recipes cies readings teukolsky flannery fleischer fleischer fleischer fleischer fleischer fleischer fleischer fleischer fleischer strained vetterling oscilloscope gill gill gill acous packard assembled numeric instrument instrument agencies manufacturing manufacturing manufacturing bart bart deepest barr barr barr barr hewlett priate tificial dations ambitious adoption frequen characteris lloyd tolerances opinions subproblems confidently assemble dress surement 
#@Barr_A,Fleischer_K,Kirk_D,Watts_L,
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#*network network network network network network network network network network network network network network network network network network network network network network network network model model model model neural neural neural neural neural input input input input input input data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time set networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm output output output state state results problem problem problem problem models models performance performance based space linear linear linear linear linear linear linear linear case order order shown shown shown shown shown shown shown systems systems systems systems systems values values values values noise noise noise noise noise functions distribution method method method method method point image image image single processing processing control large large large large local local local local inputs form form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian visual visual visual paper paper paper paper paper examples small small size work work work methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step step step step step step step points field features process process current problems problems problems problems similar show equation equation equation equation equation equation equation equation equation section line line line images images images general general parameter real real real states theory term term term term term dimensional dimensional result computation computation solution solution solution solution independent independent independent defined constant constant constant constant constant standard standard computer computer computer computer computer computer terms node science science left map low nodes press press press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous continuous continuous abstract find find computational computational computational computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties references stochastic ieee ieee important introduction complex complex complex complex complex circuit circuit circuit circuit circuit circuit circuit estimation effect cost cost cost change energy energy energy energy energy energy energy energy energy energy energy energy higher part previous required required required multiple good good bayesian chip chip chip fact techniques techniques techniques techniques techniques techniques region region region region region correlation observed scale finite simulations simulations minimum resulting ing total simulation simulation called times regions means optimization optimization optimization optimization optimization made made natural global original original artificial true application desired proc proc proc location perform constraints constraints constraints constraints gain power power power power power mit mit mit mit voltage voltage voltage voltage steps larger contrast support report report institute implementation version version technique joint difficult scheme ai ai cambridge cambridge cambridge cambridge curve solutions curves limit stage stage detection conference conference requires requires significant statistics statistics world speed vision vision vision vision vision vision vision vision vision vision vision vision vision pages con developed developed developed levels area area area processes constraint constraint constraint constraint constraint constraint measured measured technical technical limited limited close stable stable stable surface circuits circuits circuits circuits amount common vlsi vlsi vlsi vlsi instance degree noisy noisy simulated probabilistic probabilistic typically typically reduced reduced functional functional functional functional technology technology technology increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation special uniform depth early early early early early early early minimize minimize run neuronal discussed discussed exact exact exact exact robust robust robust robust robust robust robust robust element element typical side quadratic quadratic quadratic quadratic quadratic quadratic quadratic interest interest dimensions varying smooth smooth smooth yields converge sparse background background modified generalized improvement increased constructed constructed studied extended digital digital derivative width deterministic occurs hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware half conclusion starting reduce segment segment tangent clear constrained constrained constrained constrained constrained constrained constrained suggest hard physics characteristics demonstrated demonstrated demonstrated california california intelligence regularization minimizing minimizing decrease minima minima minima annealing annealing annealing annealing annealing pro construct edges edges laboratory dept dept student physical unique unique john interpretation influence influence solved controlled smoothing additive additive convex convex convex convex penalty penalty penalty penalty penalty penalty penalty interpolation construction advantages koch koch koch koch koch koch koch avoid avoid existing existing figures silicon thesis usa prove variations absolute absolute absolute absolute absolute absolute absolute absolute absolute absolute absolute characterized successfully successfully successfully reason regular delta poggio poggio poggio poggio poggio tend characteristic characteristic characteristic characteristic soc prob interested interpreted interpreted interpreted conductance oscillations content content content content content content content sci device device device built gibbs relaxation generalize minimizes cmos cmos ill ill ill ill chips deal software decreasing minimized minimized minimized origin unlike wiley mead mead mead mead mead mead mead mead replaced limitations tanh tanh tanh tanh tanh tanh tanh tanh tanh tanh tanh tanh tanh workshop notion notion editor necessarily extremely voltages voltages ensure obvious portion mapped academic phd synthetic synthetic smoothness smoothness smoothness smoothness guaranteed slope improves improves adapted reasons stanford implementing implementing strictly strictly commonly controls controls acknowledgement acad nsf researchers researchers greatly embedded posed posed posed posed detecting detecting resistive resistive resistive resistive resistive resistive resistive resistive sharp outliers rely pasadena pasadena geman geman geman geman segmented segmented segmented segmented segmented implements yuille lim tile tile wesley lab discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities analogue addison sv fabricated tation ratios narrow recover recover approximates homogeneous purely caltech caltech platt platt saturation murray familiar resistance height height height height hyper resulted interpret fail implications implications arrays intuitive enhanced natl lyapunov started ensures sides mental evident stereo surprisingly smoothed sons harris harris harris harris harris harris harris harris harris switches severe dense liu approx numerous piece piece piece piece piece piece piece fellowship fellowship kluwer aircraft july pointed theorems tradeoff simulating penalized resistor resistor resistor resistor resistor resistor resistor resistor resistor resistor intuition cessing gained graphics graduate ization hughes regularized relate wise wise wise wise wise wise wise retain lond statistic drawback resistors resistors resistors resistors memo compu ward resembles resembles lems utilizing gratefully scanned restoration const ping builds blake mahowald interpreting seattle dissertation obey interpolating consumption fidelity resultant saturating saturating saturating saturating saturating saturating saturating tra seg seg segmenting outlier outlier outlier outlier christof saturate carver heights heights heights phil huber huber assoc inte mentation tiny tiny tiny tiny tiny tiny tiny tiny wright acknowledged froin fulfilled fulfilled fulfilled fuse fuse fuse experimentation continuation continuation continuation continuation mag ant nent torre behaved feel formalized ration luo luo charac sivilotti fimction wild discarding blend marroquin marroquin ware tti tti tti tti tti ismail wyatt kirchoff arose wit pulled pulled possessing instabilities regu zisserman gill gill experimenting norwell designers bolic mathur aud subtracts figtire figtire older pioneered invented straightfor researcher plagued searchers dissipated dissipated dissipated imate discernible perimeter perimeter perimeter timetlon tute mitter fignre funda 
#@Harris_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural input input input input input input input input data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm output output output output output output output number system system state state results results results results results results results results results results results results results results units units information information problem problem models based based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights linear shown shown shown shown systems systems systems systems noise noise noise noise noise noise weight weight weight weight unit point processing processing processing processing processing processing processing large test test test test test test test test form signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple paper net work work cells current current current problems similar similar similar similar architecture architecture architecture section section section rule general speech speech speech speech speech speech real real real real real real real real obtained obtained note dimensional university university university threshold independent independent independent independent independent independent independent independent initial initial computer science presented presented present phase phase phase phase low frequency frequency frequency frequency frequency object press learn components outputs outputs abstract applied convergence convergence convergence convergence convergence convergence convergence analog analog analog analog analog analog analog analog properties references component due due ieee procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive mixture introduction complex complex circuit statistical parallel change rules rules rules signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals chosen higher part center type type required conditions chip chip chip chip chip techniques techniques techniques techniques proposed simulations ing sum performed factor potential applications original original original determined experimental power larger larger larger morgan proceedings proceedings proceedings implementation implementation implementation implementation implementation implementation implementation implementation synapses consists individual advances joint addition computing domain domain domain domain equivalent design design design san conference conference conference vision con produce channel weighted levels lines achieved describe describe describe tested tested circuits circuits circuits circuits circuits circuits circuits implemented assumed journal vlsi vlsi vlsi vlsi ability instance instance future easily kaufmann unknown technology technology technology testing york mode mode details international international magnitude sources sources sources sources sources sources sources improved separate typical introduced include recently engineering engineering compare approximately approximately approximately solve speaker match address background background background separation separation separation separation separation separation separation separation separation separation modified observation amplitude digital digital white white conclusion greater hebbian reduce trajectories segment segment segment designed designed peak performs mateo integration characteristics solid pro plot plot plot plot plot plot laboratory distinct segments segments electrical remaining slightly text text extraction john national extracted reconstruction communication updated evolution evolution spectrum spectrum measurements delays classical intervals filtering filtering msec msec msec eeg figures silicon silicon thesis thesis combinations priori usa blind plotted plotted tests tests tests successfully regular comparing procedures procedures showing sci wave delayed observable observable cmos cmos cmos cmos cmos correspondence denker operating extract extract employed wiley transformed circuitry involving detail workshop statistically necessarily implementations implementations implementations observe observe observe separated hebb hebb academic mixed mixed mixed mixed mixed mixed synthetic synthetic devices band band developing sensors publishers publishers adjacent handle rapid tive filtered filtered immediately involve beginning english read read recording auto auto auto auto auto auto auto auto auto auto auto annual improvements behaviors pure led capability cohen cohen cohen cohen cohen cohen cohen cohen cohen cohen cohen cohen cohen cohen cohen posed recordings recordings employ music music music bipolar tation ratios ratios interconnected turned reaching eliminated platt platt platt systematic mos mos mos resulted removing modifications symposium reset reset reset recovered encountered intended realization enable waves waves propagate audio audio audio sine sine sine kluwer employs medium spaced hundred evoked sinusoidal subthreshold subthreshold mhz mhz rectangle france universit elsevier exhibited jutten jutten jutten jutten jutten jutten jutten jutten jutten jutten oregon externally institut synthesized designs designs telephone adaptively capacitors hopkins hopkins hopkins calculates seattle spectrogram spectrogram andreou andreou andreou andreou andreou andreou andreou andreou andreou andreou extracts offsets offsets offsets edited digitized johns johns johns bandpass bandpass emg physically aip baltimore baltimore catastrophic maryland lsi lsi lsi lsi lsi analyse ceedings vergence herault herault herault herault herault herault herault spectrograms spectrograms organisation biomedical andreas andreas adap analyzer ration ration ences concentrates portland vittoz vittoz vittoz vittoz freq snowbird scalable party implemen crosstalk cocktail grounded sinusoid sinusoid methodologies neuromimetic hibitory ioo slowed faggin faggin norwell sepa sepa pressed pouliquen pouliquen pouliquen pouliquen pouliquen pouliquen pouliquen pouliquen stereoscopic marc plementation ambitious binations sinusoids ind kill greek buried 
#@Andreou_A,Cohen_M,Pouliquen_P,
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#*model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time set set set set set networks networks output output output output output output output output output output output state state information models models models models models models models models models models performance based shown shown systems systems systems systems systems parameters noise neurons neurons single single processing processing processing processing processing control control control control control control control neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate test patterns analysis analysis shows shows shows shows shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal work step process level level level current current current current current current current current current current cell cell cell cell random high high high high high response response response response response response response response response response response response response response response response response response response similar representation fixed fixed fixed fixed speech speech speech speech speech term experiments experiments experiments experiments activity result computation research research research research sequence standard computer science presented phase phase phase phase phase phase phase frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal maximum press press press nonlinear nonlinear outputs sample abstract computational analog analog analog analog analog analog analog analog analog analog analog analog references component due ieee ieee ieee ieee ieee important adaptive adaptive adaptive adaptive adaptive introduction action circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit difference variable lower rules measure signals signals signals previous firing firing firing firing firing firing spike spike spike spike spike spike spike equations equations chip chip chip chip chip region proposed ing original series perform determined goal connected brain mit mit voltage voltage voltage voltage voltage train train dependent source modeling modeling modeling modeling proceedings proceedings proceedings implementation represents responses responses responses cambridge cambridge experiment directly curve curve curve additional design design top top top conference conference conference conference full full con con produce coding coding coding levels biological biological biological biological tested tested tested circuits circuits circuits circuits circuits circuits circuits amount short shape shape eds adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation journal vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi sensory sensory including auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory functional block structures matching details making bottom bottom bottom architectures improve property element practical apply identical identical array engineering engineering axis match differential trans evaluation improvement amplitude amplitude horizontal horizontal intensity intensity spikes spikes spikes width width occurs occurs occurs half conclusion measures designed designed designed performs practice suggest cycle cycle cycle cycle characteristics drawn solid pulse pulse pulse pulse pulse averaged averaged averaged relation produces perception perception perception perception perception describes tuned averaging involves text unique spectral spectral scales integrated integrated integrated integrated adding frequencies frequencies potentials john national national variation understanding diagram key key sec sec intervals generation generation generation remains remains sufficiently foundation expect existing box box box includes silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon sciences sciences plotted specifically successfully compression middle middle aspects plots receives soc soc repeated repeated neuroscience sin duration localization localization localization localization localization wave cat chips remain circuitry exponentially mead mead mead mead mead mead mead mead mead mead mead mead mead mead mead mead mead mead limitations limitations hall transistor encode trace trace trace trace trace trace trace trace trace trace reading onset onset onset onset onset voltages implementations aspect aspect nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve academic fibers fibers fibers contributions electronic burst burst burst burst burst burst burst burst burst burst burst burst advanced ment publishers fairly waveform waveform improves biology ganglion ganglion ganglion processed perspective berkeley berkeley berkeley producing division laboratories pulses axon axon axon acknowledgement sounds sounds sounds describing pitch pitch pitch pitch pitch computers computers annual behaviors double cochlear pure pure pure transient marked marked biologically schematic mod qualitatively qualitatively fiber begins begins cochlea cochlea cochlea cochlea cochlea cochlea wesley instantaneous instantaneous instantaneous instantaneous instantaneous instantaneous addison generator fabricated fabricated fabricated fabricated tation tem eliminate connecting enhancement caltech spiral spiral spiral fails saturation adds khz khz khz khz khz khz khz khz khz khz height height serves operates capacitor capacitor capacitor enhanced tap tone tone tone tone tone tone tone tone tone tone tone tone tone tone tone tone tone tone tone periods 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#@Lazzaro_J,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set set set set set set set set set networks networks training training training algorithm algorithm output output output number system system system system system system system system system system system system system system system system system system system system system system system system system system system system state state state results information information problem models models models based linear linear linear case case case case case case case case shown shown shown systems systems systems systems values noise functions functions distribution approach approach approach approach approach pattern pattern pattern pattern pattern image image image image image image image image image image image single single single single single single single processing processing processing processing processing patterns patterns patterns patterns form form signal signal signal signal signal signal signal signal signal signal small feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net task task task cells cells step field field features features features features features features features features features features features structure high memory show vectors images images images images images images images images images images images images images images images images images general general states states states states theory theory university university research research research defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant standard computer terms presented presented presented presented presented present present present present phase phase frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency sets learn learn learn learn components basis basis nonlinear nonlinear nonlinear abstract back back back find properties references due due due due ieee adaptive adaptive introduction introduction complex complex circuit circuit circuit circuit circuit circuit effect generated generated energy energy energy energy energy energy difference spatial spatial measure measure signals signals signals signals signals learned learned learned learned learned learned chosen chosen part cases long long represent equations equations markov markov correlation correlation correlation observed observed scale finite ing tasks tasks simulation elements elements elements potential natural natural applications applications knowledge knowledge relative specific specific represented application desired cross cross provide define perform perform perform determined determined determined experimental experimental gain gain gain gain gain gain gain gain gain gain gain gain larger contrast contrast fields support support source source institute words words department implementation implementation implementation implementation implementation implementation technique consists internal joint exp exp bias environment design limit effects detection capacity capacity determine requires statistics speed speed speed con con criterion product provided provided simply biological biological associative achieved stable common common common require eds face end end makes smaller underlying dynamical dynamical coefficients coefficients interesting ratio ratio ratio character projection mode mode mode mode mode mode mode mode operation leads making stored supervised supervised idea choose light light light light light light correlations correlations property takes takes takes takes takes element similarity similarity period identical relevant interest sufficient sufficient conventional conventional unsupervised unsupervised unsupervised unsupervised unsupervised teacher works rl trans observation channels organization organization organization organization storage storage constructed constructed intensity intensity expression lead wide loop white white demonstrate demonstrate starting place valued competitive competitive competitive competitive competitive competitive competitive competitive weak learns learns learns physics external cycle demonstrated variety iii manner force force acknowledgements reference reference explicit van derive index 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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data function function function function function function function function function function function function function function function function set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output number number number number error error error error error error error error error state state results results results results units units information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden performance based based based based based based based based based space space space space space space space weights weights linear layer case case case case case case case case case case case vector vector order order order order shown systems values probability probability probability probability probability probability probability probability parameters weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition method method method method pattern processing control large local local local local local local local local local local local local local rate rate rate test class class class class class class class class class class optimal optimal form algorithms algorithms gaussian paper paper examples examples examples examples small small small small small small size net net net work task methods methods methods step step points features classification process process process process trained structure structure structure structure structure structure structure structure structure structure structure structure structure problems random response response response response response response representation architecture architecture architecture fixed fixed fixed fixed fixed fixed fixed fixed fixed rule vectors vectors general general general general general general general general general general parameter parameter parameter real approximation approximation approximation approximation theory theory theory theory theory theory theory note dimensional result result result solution solution solution solution solution research independent independent independent independent defined defined defined defined constant constant constant constant constant terms prediction prediction prediction prediction prediction prediction frequency frequency machine machine machine machine machine maximum maximum maximum components basis basis continuous abstract applied applied applied applied back back back find computational convergence convergence convergence convergence convergence convergence convergence convergence likelihood references procedure procedure procedure procedure important important decision decision propagation propagation propagation introduction introduction introduction hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation variance variance search search tion tion tion rules measure measure chosen bound bound bound bound bound bound bound bound bound required good good good good good binary binary conditions conditions expected expected expected region region proposed proposed errors minimum minimum minimum human respect sum sum elements regions dimension dimension dimension dimension dimension dimension global obtain relative true application application application receptive rates goal goal connected power steps steps steps fields nets selection morgan loss loss loss loss loss code code code kernel kernel kernel kernel kernel kernel joint joint exp exp exp layers considered considered equivalent additional solutions limit capacity full full full full requires requires requires requires requires free condition conditional developed developed bounds bounds bounds actual actual actual actual actual provided provided selected selected selected depends achieved achieved achieved achieved achieved increases increases increases increases increases increases increases describe group transformation transformation transformation fast limited close close corresponds nearest 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discussed ensemble takes element element element element element introduced introduced introduced introduced strategy quadratic interest dimensions sufficient sufficient sufficient varying observations approximately tions solve solve solve converge converge rl rl rl evaluation modified interval interval interval interval interval interval interval interval interval interval interval interval improvement improvement risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk increased increased constructed constructed lead extended deviation deviation touretzky width width clear clear characteristics drawn california introduce minima denoted denoted acknowledgements appears digit written ways ways mathematical mathematical confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence simultaneously simultaneously simultaneously infinite involves involves unique develop minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization springer implies implies decreases decreases decreases yield choosing independently communication communication communication communication estimator controlled centered centered centered understanding approximated translation digits smoothing smoothing classical classical normalization convex reduces reduces neighborhood neighborhood intervals handwritten includes usa formulation bell bell sciences vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik illustrated discuss holds holds neighbors neighbors discussions structural structural structural structural major simplicity selecting capable capable uniformly uniformly uniformly presentation characteristic verlag contained contained cun cun prob prob prob prob prob allowing built satisfy minimizes minimizes denker predictor predictor predictor principles principles principles principles principles principles principles principles minimized minimized minimized minimized replaced replaced ideas dependencies func notion induction induction induction induction induction necessarily illustrate subsets subsets obvious algo assumes precise simplest defines established inequality inequality inequality developing guaranteed guaranteed guaranteed tool stress implementing shared organized preprocessing worst worst worst mation mation controls laboratories simard simard members english questions questions questions improvements double consistency consistency lack quantitative posed solla formulated howard gains differs maximizes incorporating achieves adjust returns simultaneous trade trade trade generator guarantee lagrange fix rithm arguments appropriately approximates printed theories multipliers systematic ments difficulties stated monotonically ylx ylx modifications preparation selects pat forecasting jackel jackel indicator indicator indicator indicator offer refers theoretically statement statement statement statement incorporates chervonenkis formulate formulate year boser henderson rectangular rectangular exam community approxi approxi labs hubbard efforts academy zip zip zip book minor dramatic answers answers answers algorithmic recogni justified nested nested neighborhoods inequalities realizations bottou bottou bottou holmdel holmdel ples ples shattered fol vicinity neglected neglected devoted watson watson drucker drucker tern postal richer discrepancy srm srm srm srm srm predic deeper accessible implementable implementable lowing render private private private private invaluable avail leon chitecture degeneracy ilwll erm erm erm erm erm shatter sara russian bromley supervisor supervisor supervisor supervisor supervisor supervisor larry risks ussr princi moscow soundness pll minimiza nauka 
#@Vapnik_V,
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#*network network network network network network network network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training output output output number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error state units units information information information problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden performance based based space space space space weights linear case vector order shown systems systems systems values values values values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise weight weight weight weight weight weight weight weight weight functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution recognition method approach point single single single processing control control large large large rate rate test test test test test test test test test test analysis analysis analysis class matrix matrix form form form form shows shows simple gaussian gaussian gaussian gaussian gaussian gaussian net work work work work task task task task task task task methods methods methods methods methods step classification classification classification classification classification classification process level level level level level level level level level current trained trained problems problems similar architecture architecture equation line line line line rule rule rule general generalization generalization generalization parameter parameter parameter parameter approximation approximation approximation states states theory theory theory theory theory gradient obtained obtained obtained term term term term term term term term term term note note dimensional result computation computation computation independent independent log log log log log log log log log log log log log log log log defined defined defined defined defined defined found found sequence constant constant constant constant constant estimate terms terms science science prediction prediction maximum maximum maximum maximum maximum range press components basis basis basis nonlinear outputs abstract applied applied applied applied find find find density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due adaptive decision decision introduction complex complex complex complex complex estimation estimation statistical variance tion difference complexity complexity complexity assume assume assume assume measure measure prior prior prior prior prior prior prior prior prior theorem cases type good good good good good bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected fact fact techniques techniques correlation correlation correlation correlation probabilities probabilities probabilities errors errors scale ing total human regression regression regression regression respect sum sum times mapping factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor dimension dimension dimension natural natural obtain vol samples samples true true true true true compared cross rates rates rates rates proc active determined determined determined determined determined determined goal related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions gain steps steps comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison larger connection dependent nets nets nets nets selection selection selection selection morgan institute words loss individual kernel advances represents difficult difficult exp exp exp scheme graph ai ai ai framework framework framework framework framework framework framework framework framework framework framework cambridge equivalent experiment additional solutions solutions solutions solutions estimates limit determine choice choice significant free free validation con derived levels levels levels levels levels levels levels levels entropy entropy entropy evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence depends simply achieved discussion discussion discussion covariance covariance feedforward feedforward increases close inverse assumption assumption corresponds corresponds complete actions predictions finding finding rbf amount amount amount common common common effective effective effective effective effective effective assumed supported theoretical theoretical require require eds ability ability hypothesis hypothesis hypothesis hypothesis makes makes noisy including fit fit fit fit fit fit fit fit fit fit fit fit kaufmann objective objective objective objective objective probabilistic probabilistic probabilistic typically typically typically account account functional functional technology interesting interesting ratio character consistent uniform empirical principle leads details pre pre making making magnitude magnitude decay decay decay decay decay decay decay decay decay decay polynomial choose choose light architectures discussed recent recent recent practical practical include subject identical identical identical identical identical quadratic quadratic quadratic inference inference inference inference inference inference inference inference inference inference inference inference inference inference engineering varying compare compare compare compare calculated calculated volume volume volume tions achieve address locations interval risk risk risk risk expression expression concept scaling scaling scaling scaling scaling scaling predicted alternative alternative alternative alternative alternative alternative alternative alternative locally width width width setting assumptions assumptions central central central differences measures accurate bayes bayes bayes bayes peak peak peak moody moody moody moody taking strong drawn demonstrated california solid regularization radial assuming assuming assuming relationship relationship acknowledgements relation relation relation estimating describes tuned distinct involves involves consisting develop develop minimization expectation versus dependence communication estimator viewed interpretation interpretation interpretation interpretation evaluated evaluated evaluated evaluated evaluate evaluate approximations approximated approximated approximated approximated constants constants key earlier fitting fitting fitting fitting fitting penalty interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation david includes thesis eigenvalues eigenvalues vapnik extension uncertainty priors priors structural structural structural structural simplicity reason reason closely computationally computationally delta schemes mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay comparing characteristic traditional notice repeated procedures strongly cun cun prob showing interpreted interpreted dis quantity quantity quantity quantity quantity involved vary vary write denker denker hypotheses predictor automatically automatically received illustrates illustrates preferred satisfies modelling modelling bars bars bars bars bars bars bars bars bars bars simpler simpler parametric parametric powerful layered layered replaced hessian hessian hessian hessian lippmann dotted behaviour behaviour behaviour behaviour tech workshop func understand matched naturally plausible generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation spline extremely rank rank quantities quantities taylor expressions expressions utility submitted defines established preference derivation comparisons comparisons probable probable probable probable probable arises explained evaluating evaluating evaluating collected empirically empirically empirically led flexible flexible tional poorly backprop backprop backprop backprop backprop backprop solla solla solla splines splines splines polynomials gen monotonic cal curvature pasadena achieves logp specifies specifies univ trade college sort writing assign assign assign oxford resources theories caltech fits smith tools familiar height tishby tishby tishby dominant intended washington belongs chooses similarities ranking modelled infer infer infer surprisingly arrive inductive cam multiplying multiplying appeared ence ter solves kluwer guyon guyon guyon guyon expanding tween distinction boser mdl mdl personal decomposed hundred forcing imagine arising arising arising unseen levin levin levin ijcnn confirmed confirmed host increasingly alternatives breaks cubic det det compu differing differentiating mea covers inconsistent transforming nested families subjective interpolated hoc determinant bottou inferring interpolating occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam occam maxi quantitatively reviewed gathered akaike greatest linking developments preferable demanding demanding quantified phy heights mum minimise parame accessible accessible unlimited colt regularisation regularisation regularisation regularisation ranked plain interpolant interpolant interpolant interpolant interpolant tational razor razor razor razor razor razor razor readers poorer sume ror generalised minimising minimising minimising embody integrand sev embodies diction tti tti tti lastly optimised optimised minimisation minimisation quan implausible bibliography wld wld wld regu finely inevitably generalise generalise dictions alike unnecessarily serc misfit parameterised parameterised founda cussed dio stants invented dimensionless normalising normalising sed utilises recognise pear erates tity skilling skilling wla summarise 
#@MacKay_D,
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#*network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input data data data data data data function function function function function function function function function function function function function function function function function figure figure time set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training output number number number number number number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error results results units information information problem problem problem problem problem models models models models models models models models models models models models models models models models models performance performance performance based based space space space space weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear layer layer case case case order order order order order order systems systems systems systems systems systems values values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions approach approach single processing processing control control large large large large large local test test test test test test test test test test test test test test test test test test test test analysis analysis analysis class class class matrix matrix matrix matrix inputs form form form form form form form form form form form form signal signal signal signal signal signal gaussian paper paper examples examples small small size size size size size size task methods methods process current trained trained trained trained trained trained problems problems random high response response response response response architecture architecture architecture architecture architecture equation equation fixed general general generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter real real approximation approximation approximation approximation approximation average theory theory theory obtained obtained term term term term term note note note experiments experiments result result result result result result result result university variables variables variables solution research independent independent independent independent log log defined defined defined target estimate estimate estimate estimate estimate estimate estimate estimate standard standard computer terms distance science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented presented present sets sets sets sets sets sets sets sets sets sets sets sets sets maximum press learn components basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample abstract find density density density density density density density density density density density density density density density density properties likelihood likelihood references ieee ieee positive procedure important adaptive adaptive context estimation statistical statistical generated generated variance variance variance variance variance variance variance variance search search search search tion complexity variable variable variable assume lower measure measure measure prior learned higher type good good good long distributed expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected make correct correct observed errors errors errors errors errors errors errors finite finite finite resulting ing total regression regression regression regression regression regression computed computed computed computed respect sum sum sum sum called elements optimization made made knowledge specific represented true true true true true series define define compute location determined experimental related connected equal larger dependent modeling selection selection selection department version consists consists internal bias bias addition ai computing computing computing estimates estimates estimates estimates effects effects full full full full requires approximate approximate statistics statistics statistics free world estimated estimated basic derived weighted conditional conditional conditional conditional criterion product depends constraint arbitrary arbitrary denote denote close close inverse assumption assumption assumption assumption assumption finding finding finding amount common effective effective effective effective effective effective effective effective effective effective assumed assumed shape supported supported theoretical require future future easily rumelhart development fit fit objective objective objective objective objective objective typically typically pairs needed functional functional functional unknown unknown fully testing york york york york special uniform uniform empirical empirical principle principle principal squared squared squared squared squared squared squared call supervised decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay minimize denotes architectures discussed discussed exact exact robust robust robust ensemble ensemble apply introduced include subject quadratic quadratic quadratic quadratic interest highly previously observations approximately volume yields trans trans background generalized generalized generalized generalized risk risk risk risk risk risk risk risk risk grant grant exists expression lead occur predicted locally locally locally generally generally setting setting setting conclusion starting minimal greater assumptions assumptions reduce valued editors moody moody moody moody moody moody moody moody moody moody moody moody moody moody propose physics characteristics drawn regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization radial radial minimizing minimizing minimizing exist relationship relationship relationship relationship derivatives identification identification acknowledgements relation relation monte monte carlo carlo longer solving ways estimating estimating ann multilayer multilayer explicitly integrated formed quality expectation john yield choosing choosing dependence depending stationary viewed influence influence densities organizing understanding sizes calculation calculation smoothing smoothing additive classical classical expansion neighborhood intermediate box priori priori priori perceptrons perceptrons weighting extension extension automatic specifically reason closely importance included computations comparing heuristic criteria hold sampled sampled sampled sampled sampled eigenvalue predictor decreasing situations minimized wiley transformed detail estimators estimators estimators hessian hessian hall helpful authors func notion notion math predicting spline precise precise precise perceptton motivated established established crucial derivation smoothness smoothness variances perspective sys sections strictly desirable commonly calculations ridge auto author varies treated continuously incorrect perturbations ture differs differs differs differs curvature phone replace comments expectations unbiased unbiased don accomplished appearance linearity nonzero exemplar fits significance held familiar biased biased biased biased biased star preparation intuitive intuitive generalizes generalizes generalizes nonparametric nonparametric nonparametric nonparametric heuristics motivation introduces surprising evident enable barron barron barron barron barron barron barron alternatively onr andrew speaking fitted verify yale yale yale numerous deriving exhaustive adopt pointed perturbed medium preferences principled community formance tems chapman gener regularizer regularizer regularizer regularizer denoting afosr regularized emphasize relates constructs breaks sam tively intl knowing knowing union parametrized sigmoids sigmoids expansions removes topologies ble corporate agrees hat ers identically station ning architec bond juang archi rating linearized linearized linearized linearized linearized ignores convention implied implied implied iid restrictive brackets akaike akaike akaike akaike akaike akaike akaike akaike akaike inst penalizes penalizes penalizes aic aic aic unnecessary tit regularizers haven joseph argmin argmin chang huber huber huber utans utans perturbative conversations wright confirms respec syrup necessity subclass idealized wishes kung resort fpe fpe fpe subscripts peri arrived sse sse sse sse sse sse marcel marcel dekker dekker internet ric kamm gpe gpe gpe gpe gpe eubank eubank eubank eubank lambda zlx zlx 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#@Moody_J,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural input data function function function time time time time set set set set networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number error state state results results results results results information information information information information information information information information information information information information information information information problem problem performance performance based based space space space space space space space space weights weights linear linear layer layer case case case case case case case case case case case case case case case case case case case case order shown shown shown shown shown shown shown systems probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters noise noise noise weight functions functions functions functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution point large large analysis class class class class class class class class class class class optimal optimal optimal optimal form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper paper paper examples examples examples examples size size net work methods points field classification classification current problems random random random random random random random architecture show show show show show equation section section section fixed fixed fixed fixed fixed fixed fixed fixed rule rule vectors general general general general generalization generalization average average average average average average average average average average theory theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained note note note university university university threshold computation research research research research research research research log log log log log log log log log log log log log log log log log defined defined defined defined defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target target target target target target target constant computer computer computer computer terms terms terms terms terms terms terms science science science prediction prediction left presented machine sets maximum sample abstract applied find computational computational convergence convergence density properties properties properties references due ieee positive important context introduction complex complex estimation behavior behavior behavior statistical statistical statistical statistical statistical statistical statistical variable variable variable variable assume assume lower lower lower lower lower lower lower prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen chosen part part previous bound bound bound bound bound bound bound bound bound bound bound bound cases binary long conditions conditions conditions bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected expected expected expected expected equations fact techniques correct probabilities probabilities finite finite classes ing total respect respect respect respect multi multi multi sum called called mapping factor factor factor factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made natural natural applications study study obtain obtain obtain negative relative specific specific represented compared compared series provide define define define define define define define related related posterior distributions distributions gain gain gain gain gain gain gain gain gain equal equal comparison contrast morgan morgan proceedings proceedings report institute loss version version version version version joint framework framework framework curve curve curve curve curve curve additional view curves curves curves curves curves curves curves limit conference upper upper upper upper upper upper upper upper upper upper upper upper upper world basic pages give give give randomly randomly randomly randomly randomly randomly developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy finally simply simply simply technical technical describe arbitrary denote denote denote inverse complete predictions short common common effective assumed assumed assumed supported role theoretical main main main main main main main journal ability hypothesis hypothesis hypothesis hypothesis hypothesis instance instance instance instance instance instance instance instance instance easily makes makes kaufmann probabilistic probabilistic smaller unknown interesting ratio ratio ratio york special consistent consistent consistent consistent trials uniform uniform uniform empirical representing call max pre direct making international international early choose predict predict predict predict predict improved improved improve recent advantage robust takes element typical moving sense sense inference sejnowski interest interest previously volume volume volume volume volume address definition chain observation grant grant grant grant exists expression concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept studied trial trial predicted correctly correctly move move occurs setting setting setting setting setting conclusion place minimal assumptions assumptions conclusions valued valued depend depend measures bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes clear practice asymptotic temperature physics physics physics physics physics physics largest largest drawn drawn drawn drawn drawn drawn california california california iii iii denoted acknowledgements areas construct longer factors estimating estimating estimating estimating laboratory laboratory laboratory label label label explicitly averaging infinite infinite infinite infinite infinite unique interaction frequencies events springer extraction expectation expectation expectation letters independently dependence dependence review depending depending stages interpretation learner learner learner learner learner learner learner learner learner learner labels labels labels decomposition completely similarly partition partition partition partition partition partition partition reasonable reasonable calculation roughly roughly valid calculate david expect perceptrons perceptrons bell bell bell instances instances vapnik vapnik vapnik vapnik vapnik automatic prove priors holds discussions discussions closely importance differ maximal symbols receives receives refer refer verlag strongly prob link link showing return contribution hold hold notation gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs quantity quantity quantity vary write michael paradigm minimizes denker layered collection investigate detail limitations mass examine ideas ideas working workshop workshop fundamental analogous hill hill hill naturally concepts concepts concepts possibly possibly predicting predicting predicting predicts predicts predicts subsets versions perceptton attempts electronic spin inequality inequality inequality inequality inequality inequality inequality inequality inequality inequality inequality theoretic trivial crucial briefly baum tive precisely worst worst worst worst worst laboratories laboratories laboratories scientific beginning gradually author annual annual researchers mechanics fourth fourth greatly considerably evaluating applies conducted solla solla solla haussler haussler haussler haussler haussler haussler haussler haussler haussler haussler haussler ity howard popular popular germany sophisticated expectations expectations expectations instantaneous instantaneous instantaneous instantaneous instantaneous cumulative cumulative cumulative cumulative cumulative cumulative cumulative cumulative cumulative room proofs labeling labeling mistake mistake mistake mistake mistake mistake mistake mistake mistake optimality investigation fix member recover homogeneous theories theories theories plays extending murray murray murray convenient convenient convenient mail satisfying siemens contract interpret obtaining tishby tishby tishby tishby removing intuitively combinatorial combinatorial combinatorial motivation analyses performances sompolinsky sompolinsky schapire schapire schapire schapire schapire schapire schapire induce schwartz infinity sphere jackel darpa advance advance barron infer omitted reader warmuth warmuth kearns kearns kearns kearns kearns kearns kearns contact seung santa santa valuable papers robert onr andrew dense ure corporation logarithm deriving maximized asked chervonenkis chervonenkis chervonenkis dec diverse incrementally adopt opper opper opper opper opper opper opper generalizations letting letting tight tight tight favor levin gained gained shannon shannon ijcnn guidance bounding afosr afosr flip drawback drawback weaker algebra induces places mann suggestions stimulating dim dim dim dim dim dim dim dim dim dim dim dim dim institut families hop jersey jersey jersey suffers coin inequalities inequalities inequalities ron incorrectly incorrectly harvard mistakes mistakes mistakes mistakes measurable measurable restricting att littlestone littlestone littlestone rivest fair absent crl cruz cruz mis cti sented mountain derivations quantified unifying eta rela topics phil fiir avenue dependences extremes ele ele ele ele beliefs encourage ucsc ting terry draws manfred notational notational wanted physik glasses predicate admits omitting decomposing decomposing stud told subsequence ruth ruth ruth ruth ruth ruth indebted technically kauf aro insightful ied sara andy sauer abbreviated abbreviated wittner daal theoretische din nick includ seminal rti rti 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layer layer case case case case case case case case shown shown shown shown probability probability probability noise functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons approach point point point single single single processing processing processing processing large large large local local local local analysis analysis class matrix matrix matrix shows algorithms paper paper paper examples small size size size size size size net work work task task task task task task task task task task task task step points points points points field process current structure random random random response response response response architecture architecture architecture architecture architecture architecture architecture architecture architecture show fixed fixed fixed fixed fixed fixed line line vectors average obtained term term note note note note experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional computation computation computation computation computation computation computation solution solution research defined defined sequence constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant computer computer distance distance distance distance connections node node node node node node node node node node node node node node node node node node node node node node node node node node node node node left left left left map low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine sets sets press press abstract find find find computational computational references important introduction circuit stimulus stimulus generated parallel parallel parallel parallel parallel parallel parallel parallel parallel tion change change complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity measure measure higher higher higher higher part part part part part part part part part part theorem theorem theorem theorem theorem theorem bound bound cases cases required required required cortex cortex binary binary distributed expected expected expected expected expected expected expected make make make make region correct correct correct scale minimum resulting ing tasks tasks tasks called called times times mapping made made made natural global desired series receptive define define define compute perform perform perform constraints constraints constraints constraints connected discrete power mit larger larger support support support support support support support support support dependent dependent dependent nets represents connectionist connectionist connectionist connectionist responses responses responses difficult graph graph graph graph graph graph graph graph graph graph graph graph graph maps cambridge computing computing domain experiment experiment curve curve curve curve curve curve additional solutions curves curves estimates design design design stage stimuli stimuli bit bit bit bit bit bit determine upper upper choice free give give lines path path path path path path path path path path path path actual actual finally nature constraint biological biological measured fast fast inverse corresponds complete proof proof proof proof proof proof finding finding finding finding finding finding finding finding finding finding finding finding amount short shape shape face journal end vlsi instance instance instance easily degree makes makes objective objective pairs pairs reduced reduced unknown transfer significantly special consistent trials mode leads representing details details call making bits depth depth depth depth depth depth attention run architectures architectures exact robust takes takes takes practical machines side side relevant relevant relevant 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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data data data data data function function function function function function function function function figure figure figure figure figure figure figure time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm output output output output output output output output output output output output number number number number number number number number system system system system system system system system system system system system error error error error state state state state state state results information information problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden based based weights weights weights weights weights weights weights weights weights linear linear linear layer layer layer layer layer order order shown shown shown systems systems systems systems systems systems values probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution distribution distribution method pattern pattern pattern pattern pattern pattern pattern single single single single single processing processing processing processing processing control large local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns patterns inputs form form shows shows shows shows shows shows shows shows signal gaussian paper size size size size size size size net net work methods fig fig fig fig fig fig fig fig fig fig fig fig fig step step field field field field field field field field field field classification classification process level current current current current current trained problems problems problems problems problems random high similar similar similar similar similar representation rule rule rule rule rule generalization parameter real average average states states states states theory note note note note note note experiments experiments experiments experiments experiments university computation computation independent found sequence dynamics constant computer terms distance distance distance connections connections connections synaptic science left direction presented presented presented phase phase phase phase phase activation activation low low nodes temporal machine machine machine machine machine range range range press learn learn learn learn outputs outputs abstract back back back back computational analog analog analog properties properties properties references stochastic stochastic stochastic stochastic stochastic due due due due due ieee adaptive adaptive decision propagation propagation propagation propagation propagation propagation introduction complex complex circuit behavior parallel parallel parallel parallel parallel parallel change variable measure measure signals signals chosen previous previous cases required required multiple multiple multiple multiple distributed chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip length correct correct correct correct correct forward finite simulations simulation simulation sum eq eq eq times regions means potential made made feedback feedback feedback feedback feedback feedback study em vol represented application desired provide proc perform perform eye experimental experimental experimental experimental goal distributions gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain mit voltage voltage voltage voltage voltage steps steps comparison comparison larger larger contrast connection update morgan morgan report implementation implementation implementation implementation version synapses synapses synapses synapses technique technique technique technique internal individual advances advances difficult final delay delay cambridge equivalent experiment experiment hinton hinton view curves top bit bit bit efficient full choice free speed speed speed increase channel channel channel channel channel weighted area nature nature measured measured measured measured feedforward increases arbitrary tested fast limited stable circuits short implemented implemented implemented implemented assumed synapse synapse synapse synapse synapse synapse synapse supported require eds eds end vlsi vlsi vlsi vlsi vlsi makes rumelhart rumelhart rumelhart kaufmann simulated probabilistic needed hopfield hopfield combination reduced reduced dynamical transfer transfer transfer transfer transfer interesting operation representing window window bits bits bits bottom supervised early early magnitude run sources sources sources correlations correlations correlations correlations correlations separate separate takes machines sejnowski array cognitive varying previously teacher teacher calculated module trans address evaluation evaluation evaluation evaluation evaluation interval williams improvement constructed studied scaling scaling digital digital digital touretzky touretzky width deterministic hardware hardware hardware hardware pass demonstrate runs runs runs runs conclusion measures designed designed clear performs moody exponential exponential faster temperature temperature temperature external external cycle california proportional proportional user start start decrease annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann explicit sequential generating plot plot student student implement implement multilayer physical physical text scales scales yield family depending squares operations static allowed processor sign calculation measurements sec roughly roughly roughly roughly visible topology coupling expect building usa color color currents currents retrieval instances plotted partially closely encoded computationally paths paths mcclelland wij presentation presentation post plots plots online identity composed graphs allowing showing anderson conductance sci involved involved relaxation relaxation board leading chips chips software software software schedule powerful difficulty optimized lippmann hall matches rest mappings investigated parity parity parity parity parity parity parity parity parity possibility reliable proper tanh presynaptic cognition phases phases circles trace adjusted adjusted portion portion store electronic electronic electronic electronic slowly comparisons berkeley berkeley purposes arc easier sgn sgn controls ion acad implicit read percent percent percent percent percent limits offset offset offset offset pseudo orders completion adjustable adjustable outliers monotonic collective adjust asymmetric hamming hamming hamming simulator simulator chose chose chose display display shaped windows traces summed displays displays extreme instantaneous shifted uncorrelated generator writing writing fabricated interface interface summing summing linearity acts approximates clamped clamped clamped fits saturation saturation proceeds proceeds contract disjoint presentations natl alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector ranging displayed expanded percepttons peterson foundations waveforms waveforms captures captures speeds integers explorations boxes specification microstructure leaming bus bus emergent failed beta adjustment adjustment exclusive exclusive generators annealed annealed afosr figs electronics amplifiers signs continually utilizing meir stores externally externally allen allen allen allen settling settling loaded cast affecting ackley settle anthony volts volts volts volts volts volts volts volts volts volts volts volts adjusts alto alto cascaded permanent binomial tations signed jan parker replication replication replication replication replication replication replication replication replication replication replication replication awij bidirectional palo palo facilitates judge tighter cient mft saturates def analyzers occupied anneal vme vme digitally clamping clamping gupta analyzer latch latch disconnected bellcore supplies supplies volatility volatility volatility volatility poorer acknowledgment multiples volt unclamped joshua logarithmically jayakumar jayakumar jayakumar jayakumar jayakumar jayakumar photo accessed sparcstation duplicate sharpening morristown microchip microchip microchip ioo eecs scrambled lll instrument div panems dep sharpens isn pie negligibly bol pauern repr gannett haber wijsj rns 
#@Alspector_J,Jayakumar_A,Luna_S,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning neural neural neural input input input input input input input input input input input input function function function function function function function function function function function function function function function function function function function function time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training output output output output output output output output output output output output output number number number number number number number number error error error error error error error error error error error state state state state state results results results results results results results results results results results results results results results units problem problem problem models space space space space space space space space space space space space weights weights weights weights weights weights weights weights weights weights linear layer case case case case case vector vector order order shown systems systems values values probability probability probability probability probability probability probability probability probability probability probability parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions distribution distribution distribution distribution recognition approach approach approach single single single large rate rate analysis class class class class class class inputs inputs inputs inputs inputs inputs inputs inputs form algorithms paper paper paper paper paper paper examples examples examples small size size size size size size size size size size size net net work work task level structure structure high similar similar similar similar architecture show show show section generalization speech real real real average average theory theory theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained term note note note result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation log log log log log log log log log log defined defined defined defined defined defined defined target target target standard standard computer computer connections connections connections connections connections node node node node science science present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets sets sets press learn position position outputs outputs sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract abstract applied applied back computational computational computational computational computational computational computational properties properties references stochastic propagation introduction introduction action action effect effect generated search measure measure measure chosen chosen part previous previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound cases cases cases required required required required required required required required required required multiple multiple multiple multiple multiple binary binary conditions make fact techniques correct correct scale finite finite classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes total respect respect multi called called called times times means factor dimension dimension dimension dimension dimension dimension dimension dimension dimension natural natural natural knowledge em obtain obtain obtain obtain obtain obtain artificial samples application define define compute proc connected discrete discrete equal equal mit larger larger connection morgan proceedings report report department department technique technique connectionist exp graph sequences sequences sequences considered framework domain directly conference significant give give give randomly randomly bounds bounds bounds bounds bounds bounds bounds bounds bounds area types product finally evidence constraint technical technical technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward group group denote denote proof proof proof proof proof theoretical theoretical require main main main main main eds end ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis future development including kaufmann unknown consistent numbers numbers max max max idea improved improved pair reported introduced include subset subset previously approximately approximately tions match match definition definition definition background bounded bounded improvement increased expression expression expression concept concept concept studied extended extended correctly correctly correctly correctly correctly setting setting conclusion greater greater greater greater greater reduce constrained taking taking taking presence presence presence presence drawn drawn drawn drawn drawn drawn introduce introduce groups connectivity reference explicit suppose relation distinct confidence metric john john john john john john choosing choosing independently independently viewed lemma lemma lemma lemma fraction fraction fraction fraction fraction sizes sizes sizes sizes convex remains valid classified classified topology david david david building includes priori usa assignment vapnik vapnik vapnik vapnik vapnik prove prove major selecting suitable suitable tdnn tdnn invariance refer refer induced cun prob symmetry symmetry symmetry symmetry symmetry symmetry symmetry classify notation quantity bar simplified computes computes computes hypotheses hypotheses hypotheses ill automatically remain relations relations preliminary school reliable reliable func cover understand induction concepts concepts possibly editor generalisation generalisation generalisation generalisation generalisation formal formal taylor taylor taylor taylor taylor taylor taylor taylor taylor taylor taylor improving improving formula formula formula formula trivial growth growth growth growth growth growth growth growth growth guaranteed improves adapted baum baum baum london purposes precisely incorporate begin read mellon carnegie applies reflect cmu haussler haussler haussler haussler incorporated begins proposition don pac pac pac proofs college equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence guarantee restriction restrict martin martin martin acm count royal communications convenient ranges promising adjusting simplify mark definitions definitions definitions imply imply substituting expanded lang percepttons percepttons counting bases creating omitted extends tures cam learnable unified summer logarithm outline outline chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis preserving preserving expanding restrictions theorems conjecture obtains regularity assignments assignments associate certainty valiant valiant eric constrain distri formance bounding convert compatible proba proba learnability learnability learnability learnability termed indexed distinguished rochester algebra develops bution copies remarkable bridge preserves bility bility justified agrees loaded shawe shawe shawe shawe shawe shawe shawe shawe shawe shawe shawe attempting err incorrectly architec anthony anthony anthony anthony measurable measurable sym substitution minsky minsky approaching edition subscript freely completeness putational omit blumer blumer mal colt colt symmetries ously previ manfred lemmas wji exposition equipped vcdim pointwise ehrenfeucht iee holloway substitutions obtainable orbits orbits equiva wlog wlog wlog wlog wlog wlog din rhbnc fixes fixes conform leslie 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#@Shawe-Taylor_J,
#t5
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set networks networks networks networks networks networks training algorithm algorithm algorithm output output system system system system system system system system system system system system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results units units units units problem hidden hidden hidden based weights weights weights linear linear linear linear linear layer case case case case case order order order order order order order order order order order order order order order order order order shown shown shown shown shown shown shown shown shown shown shown shown systems systems values values parameters parameters parameters parameters weight weight weight weight weight unit method point point point point point point point point point point single single processing processing processing control control control local rate rate rate analysis analysis analysis analysis matrix matrix optimal optimal optimal form form form shows shows shows shows signal signal simple simple simple simple small small feature net random random high high high show show show equation equation equation section fixed vectors parameter parameter real theory theory theory theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term term term note dimensional dimensional computation research log found sequence dynamics initial constant constant constant standard computer science left left low maximum press nonlinear abstract applied back back convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties references stochastic ieee ieee procedure important adaptive adaptive adaptive propagation propagation propagation introduction complex complex circuit behavior effect dynamic dynamic dynamic parallel parallel recurrent tion tion tion change change change assume lower measure representations chosen higher center center bound good binary binary long conditions distributed expected make make fact techniques techniques techniques techniques region region region region region region region region region region region region region region region observed observed scale simulations simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum ing respect performed regions optimization optimization made global policy filter obtain relative series series rates rates location location perform determined equal equal approaches mit update descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent proceedings proceedings proceedings department technique internal exp exp graph graph ai ai ai equivalent hinton curve transition limit limit limit limit limit limit limit limit limit limit limit limit limit limit effects effects bit speed pages give give derived derived bounds bounds bounds backpropagation backpropagation backpropagation backpropagation backpropagation iteration sampling simply biological measured group fast fast limited inverse assumption corresponds corresponds stable stable stable stable stable surface surface surface surface circuits finding amount amount shape shape journal square hypothesis makes rumelhart rumelhart account account transfer special special leads squared iterations iterations max making international experts decay run run advantage practical period period period period period subject quadratic quadratic quadratic quadratic quadratic sejnowski recently volume works axis smooth smooth smooth converge converge symmetric modified bounded bounded bounded williams increased constructed constructed exists scaling predicted predicted predicted predicted predicted predicted predicted predicted predicted correctly occurs occurs setting setting hardware starting starting starting starting conclusions editors editors numerical clear peak peak performs faster faster practice practice practice practice practice practice asymptotic taking cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle characteristics sigmoidal sigmoidal turn variety min decrease targets program question attractor attractor attractor attractor attractor attractor plot vertical recall metric physical slightly slightly adding springer springer cycles review review squares detailed understanding converges converges converges converges converges updates past diagram earlier calculation epochs epochs epochs delays purpose add boundaries boundaries remains visible david box eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues contour batch batch batch batch batch plotted plotted plotted absolute characterized uniformly maximal mcclelland attractors build comparing online reached verlag verlag quickly quickly graphs repeated showing oscillations usual play leading reach automatically subsequent jacobs decreasing decreasing decreasing minimized minimized explore remain investigate updating hessian divergence oscillator rise rise giving eigenvectors oscillation workshop func cognition momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum analogous surfaces surfaces surfaces coefficient psychology changed bifurcation bifurcation bifurcation bifurcation algo assumes observe initialized epoch epoch regime regime chaotic asymptotically great slowly formula analyzed unstable unstable phenomena phenomena improves caused caused briefly lies rapid sections easier strictly strictly precisely incorporate ridge gradually gradually gradually read cybernetics qualitative fluctuations people limits empirically understood tional lms lms lms lms simulate passes passes gains spread reaches reaches popular adjust asymmetric asymmetric chose shaped begins june globally phenomenon phenomenon notes mistake tation rithm fails saturation adds adjusting adjusting analogy proceeds proceeds height analyzing analyzing settings settings settings settings monotonically capacitor symposium heuristics continue lip started started slice ranging ranging negligible regard widrow accounts accounts thomas foundations roy roy pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter splits speeds convergent convergent convergent convergent johnson robert yale yale associations microstructure shading achieving planes planes chaos chaos chaos chaos acceleration letting param ary shaded acting resistor geoffrey pdp terrence scope regimes speedup speedup portions breaks apparently nal transients slopes eters september october lecture achievable decided decided tom converging oscillate termination replicated station sharply progressively substitute sym plateau plateau fastest dimen gence restrictive enter saturating saturating saturating saturating saturating saturating nonstationary jitter doubling february devoted saturate saturate gradual wellekens rises tightly richer haven neigh obeys amax amax amax amax amax amax amax amax amax amax amax amax amax eta plotting saturates saved damped alexander conver conver adap confirms diverges aggressive optimiza clue justifies almeida accelerate progression progression interna raise strip backpropaga silva sional surely barak barak fang nonconvergent nonconvergent grounds atypical ating amin amin amin amin amin amin diverging explo oth rations practitioners ama ama scent ami ami ami erations erations rim speeded premature jagged gently doubles doubles yan mysterious feels borhood 
#@Pearlmutter_B,
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure time time time set set set set set set set set set set set set set set set set set training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output number system system system system system system system system system error error error results units units information information information information problem models models hidden hidden performance performance performance performance performance space space space space space space space weights linear linear linear linear linear layer case case case case case case case vector vector vector vector vector vector vector vector order shown shown shown shown values values parameters parameters weight weight weight functions functions unit unit recognition recognition recognition recognition recognition method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point image image image image image image image image image image image image single control large large large large large local local local local local local neuron rate rate rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns optimal inputs inputs form shows algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian paper examples examples examples examples examples examples examples small small small small small small small small small small size size task task methods fig fig fig fig fig fig fig fig fig fig fig fig step points points points points points points classification classification classification level level level trained structure problems high high similar representation show line line line line line rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images generalization generalization generalization speech parameter parameter parameter parameter approximation average theory gradient gradient obtained obtained obtained obtained obtained obtained term term experiments experiments dimensional dimensional result result result university variables independent independent found standard connections left left direction direction machine machine sets learn learn learn learn basis basis outputs continuous continuous abstract applied back find references procedure procedure procedure important adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation introduction hand effect effect generated generated generated cost tion difference measure learned learned part part part part part part part center center cases cases equations techniques forward forward forward forward forward scale scale finite computed respect respect respect respect respect respect respect respect respect eq called made made applications applications applications applications applications knowledge knowledge original original original original original original original original original original artificial relative compared desired desired desired desired desired desired desired desired desired desired desired compute perform constraints constraints connected equal equal equal steps comparison update update update report words words words implementation implementation version version consists consists kernel kernel represents final layers scheme scheme addition ai ai considered considered computing experiment experiment directly curve curve curve curve curve additional additional additional curves curves curves curves design top top top top top efficient efficient efficient requires requires approximate free speed pages derived derived types actual actual selected selected selected selected selected selected backpropagation backpropagation backpropagation backpropagation backpropagation depends constraint constraint simply achieved technical transformation transformation transformation transformation transformation transformation transformation transformation limited limited close stable amount amount amount amount amount implemented implemented implemented assumed generate generate require require pixel pixel pixel pixel pixel instance instance easily makes including including objective objective needed combination combination combination interesting character york segmentation special operation language bottom bottom bottom bottom bottom bottom magnitude magnitude idea idea combined choose denotes improved directions directions directions directions directions advantage advantage advantage separate typical moving pixels dimensions highly highly highly previously approximately smooth yields correspond definition locations storage increased exists horizontal horizontal parts invariant invariant invariant invariant invariant invariant invariant scaling scaling extended extended extended digital digital digital digital deviation derivative derivative derivative derivative derivative derivative rotation rotation rotation rotation rotation rotation locally locally generally column column setting half row row segment conclusions operator operator operator valued editors tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent measures designed clear faster solid solid regularization regularization regularization radial assuming minimizing minimizing user plane plane derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives groups groups digit digit digit digit derive written ways ways vertical vertical implement implement coordinates coordinates coordinates linearly involves transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations remaining angle angle adding adding implies versus versus john choosing choosing independently depending correlated correlated correlated squares squares evaluated evaluated open approximated approximated approximated sizes translation translation translation translation digits key reasonable smoothing smoothing dashed reduces closed interpolation symbol norm advantages handwritten handwritten combinations activations priori priori priori coordinate bell bell bell weighting instances determines extension tests structural successfully regular straightforward straightforward middle middle divided symbols symbols wij invariance invariance invariance traditional traditional traditional induced cun cun cun cun cun cun cun allowing lie lie lie lie manifold manifold strategies strategies gray gray usual usual usual backward denker denker denker denker denker powerful powerful wiley transformed transformed transformed access replaced dotted dotted scalar fashion incremental workshop func analogous hill coefficient necessarily illustrate illustrate recognizer adjusted consist separable convolution convolution answer tool lin tive tive tive formalism formalism formalism formalism formalism shared directional directional directional directional directional directional directional directional operators incorporate controls laboratories laboratories laboratories simard simard simard simard simard pitch toronto explained requiring varies greatly prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop conducted parameterized backprop backprop backprop span adjust age age age baird baird progress differentiable differentiable multidimensional distortion distortion distortion distortion distortion distortion distortion distortion distortion distortion distortion picture ordinary forming modify rotated rotated rotated rotated rotated rotated rotations rotations rotations rotations rotations rotations adds murray overcome proceeds shifts corner corner corner composition published document ensures negligible propagated propagated advance express smoothed agree subsequently vari limitation divide fitted fitted fitted fitted fitted multiplying multiply largely covering propagating tradeoff generalizations jacobian jacobian jacobian verified acting invariances invariances invariances invariances invariances invariances invariances invariances invariances invariances equality modifying shifting impose gener permits regularizer regularizer disadvantage speedup translations translations translations translations importantly importantly france enforce enforce tively universit sweeps sweeps rotating rotating algebra elsevier expansions rewritten emphasis distortions distortions distortions distortions distortions hyperbolic tial ave holmdel holmdel holmdel ters interpolating carries plateau inefficient linearized distorted distorted distorted connectionism sweep spa propagates drawbacks infeasible discrepancy ables deformations parame infinitesimal unlimited switzerland yann subtract named iter translating fogelman cedex patrice havior victorri victorri victorri victorri victorri nmse nmse exemplified effec tives compositions compositions propagations thereof deriva deriva objec defect puting divergent plateaus plateaus crawford crawford crawford bernard zurich perspec zipcode steels lots disagrees pfeifer scalings schreter osi binarized algebras greek tremendously 
#@Denker_J,LeCun_Y,Simard_P,Victorri_B,
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#*learning learning learning learning learning learning learning learning learning model model model model input input function function function function time time set set set set set algorithm algorithm algorithm algorithm algorithm algorithm state results results information information problem problem problem problem problem problem based space case order shown shown shown shown shown probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution shows examples small size size size size size size size size size work level problems random random random random representation representation show section section section section section section fixed fixed fixed fixed fixed parameter parameter parameter approximation approximation approximation average average theory theory obtained obtained result result result result result result result result research independent log log log defined defined defined defined defined sequence sequence constant terms terms terms terms terms present frequency frequency frequency frequency maximum maximum maximum learn learn basis outputs outputs sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references positive positive context context context context introduction tion tion difference difference complexity variable variable variable variable lower measure measure measure learned previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem conditions fact fact proposed correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities finite classes respect respect respect respect respect called elements means dimension dimension dimension dimension dimension made applications applications applications study study obtain obtain obtain obtain obtain relative relative relative relative relative relative relative relative relative relative relative relative relative relative relative relative relative relative relative specific samples samples samples define define proc proc related constraints distributions dependent dependent dependent dependent dependent dependent dependent dependent dependent framework framework equivalent upper free free free give condition condition condition condition condition condition condition condition condition condition condition condition condition derived derived bounds bounds entropy depends arbitrary denote close close close proof proof proof proof proof proof proof supported theoretical main main main main hypothesis hypothesis easily easily programming increasing consistent consistent uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform max max max max polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial produced choose denotes discussed discussed property property property property property property property introduced introduced relevant sufficient sufficient sufficient approximately yields converge converge converge converge converge converge converge converge converge rl definition definition definition bounded bounded bounded exists exists exists exists exists exists concept concept concept setting conclusions exist exist exist exist exist min min introduce introduce introduce introduce suppose relation relation relation index index solving confidence confidence confidence recall recall easy easy frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies applying events events events events events events events events events events events events events events events events springer implies implies implies implies implies implies implies expectation expectation expectation boolean boolean family family family family family family family family family family family family family family family family expressed lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma evaluated open open evaluate showed converges converges event event event thesis thesis vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik prove prove prove prove discuss holds holds holds characterized simplicity simplicity uniformly uniformly uniformly uniformly verlag induced prob interested interpreted notation attempt satisfies satisfies collection preliminary preliminary project working proved proved proved proved proved func notion notion notion notion notion notion notion automata precise observe arbitrarily languages inequality inequality briefly precisely worst immediately immediately consequence consequence consequence acknowledgement understood relevance readily readily haussler ity characterize characterize conclude conclude pac pac pac pac pac pac pac pac equivalence acm acm nat labelled labelled labelled communications convenient stated stated obtaining observing definitions modifications modifications adequate combinatorial substituting substituting corre studying uni refers warmuth learnable learnable learnable learnable learnable lem verify verify verify outline chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis quasi quasi valiant valiant valiant iff iff iff iff iff iff iff distribu elementary proba learnability learnability learnability learnability learnability relates exceed exceed tively minor minor covers sponding sake sake formulae anna polynomially polynomially polynomially polynomially polynomially polynomially polynomially polynomially shattered shattered appl fol request monotone probabil probabil italy italy blumer blumer blumer ities dnf dnf colt ixl ily respec cen sults propositions lira coil implication trivially notations notations bilities ehrenfeucht concatenation contradiction contradiction recalling estimations tered polyno polyno consid lows limt limt xla tral mial mial ixt mario converse paral dipartimento lfi formly 
#@Bertoni_A,Campadelli_P,Morpurgo_A,Panizza_S,
#t5
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number error error state state state state state state results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based based based space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer case case case case case vector vector vector vector vector vector vector vector vector vector vector vector order order order shown systems systems systems systems values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method pattern single single single single single single processing processing large large large large local local test test test test test test test test patterns analysis analysis analysis analysis class class class matrix matrix optimal inputs form form form form form form shows algorithms algorithms algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian paper examples examples examples examples examples examples small small small small small small feature work work work work methods methods methods methods methods methods methods step field field field field field features features process process structure structure structure structure structure structure structure structure structure random random random random random random random random random high similar show show show show show show equation equation section section section section vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images general general general general general general general general general general general parameter parameter real real approximation approximation approximation approximation approximation average states theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term term term term term experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional result university university university variables variables variables variables variables variables variables variables variables variables variables computation solution solution research independent independent log log log log log log log log log defined defined defined defined defined defined defined defined defined defined found found found found found found found found found found initial initial table table table estimate standard standard standard standard standard standard standard standard standard standard standard standard computer computer computer computer computer terms terms terms terms terms terms terms connections science science science prediction prediction left left direction direction direction direction present present present phase phase phase phase machine machine machine machine machine machine machine machine machine machine object maximum maximum maximum maximum press components components components components basis sample sample sample sample sample sample sample sample sample sample abstract find find find find find computational density density density density density density density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component stochastic stochastic stochastic stochastic stochastic stochastic ieee positive procedure mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context context introduction introduction complex hand hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical generated generated generated generated generated parallel search search search search energy energy variable variable variable variable variable assume assume assume measure measure measure higher part theorem type type type type type type good good good good good binary binary binary binary binary binary binary binary binary binary binary binary binary binary long represent represent distributed bayesian expected markov markov markov fact correlation correct observed observed errors errors finite tasks regression respect respect sum sum sum sum sum performed performed called called called times times means factor factor natural natural study knowledge em em em negative specific represented represented represented true true true true compared desired provide define define define compute compute compute compute compute compute compute proc perform active active experimental experimental experimental experimental goal goal goal connected distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions equal mit steps accuracy comparison larger contrast contrast connection connection connection fields train train train train train train nets nets morgan morgan morgan proceedings report report report department department implementation technique technique consists consists individual advances represents represents represents connectionist difficult difficult exp bias bias bias addition graph graph graph graph graph cambridge computing computing domain domain domain hinton hinton solutions estimates estimates limit san stage bit bit bit efficient efficient full requires significant significant approximate statistics world world estimated pages pages increase give give give weighted randomly developed bounds area types types types lines product product product product product product selected iteration nature discussion discussion technical technical technical feedforward group group denote fast fast limited close close assumption corresponds complete stable predictions finding finding finding generate generate require square square instance instance easily easily degree makes rumelhart noisy noisy kaufmann kaufmann kaufmann probabilistic probabilistic typically underlying needed hopfield hopfield hopfield hopfield hopfield combination reduced account unknown unknown unknown unknown unknown fully significantly significantly projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection increasing head head special special special special special structures uniform database representing iterations direct making bits bits combined choose choose run description predict improved discussed discussed directions directions correlations exact advantage advantage advantage typical typical similarity introduced include include machines machines machines machines machines machines machines machines machines machines side sense sejnowski sejnowski cognitive interest sufficient compare unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised volume volume correspond correspond studies trans symmetric improvement entire entire entire lead studied studied studied derivative touretzky setting conclusion reduce competitive editors central interactions interactions measures measures accurate bayes bayes bayes clear exponential exponential exponential mateo taking taking taking presence presence presence drawn california california proportional relationship relationship groups groups groups configuration configuration base denoted denoted boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann explicit suppose suppose appears appears relation relation digit written index generating ann tuned mathematical mathematical modeled modeled modeled modeled missing coordinates coordinates physical easy consisting interaction minimization quality extraction extracted independently independently reconstruction reconstruction depending squares squares interpretation influence influence transform transform restricted fraction digits digits digits slow slow slow epochs epochs epochs epochs epochs epochs measurements measurements measurements normalization normalization reduces purpose add add closed generation calculate david avoid expect expect handwritten handwritten handwritten handwritten includes combinations usa sciences sciences illustrated maximize maximize specifically specifically absolute holds holds simplicity reason middle maximal computationally mcclelland detect literature projections projections situation situation situation situation situation tend essentially capture soc kind kind kind repeated induced induced heuristic heuristic showing anderson interested sci hold comp gibbs dot dot absence absence computes reach thresholds thresholds attempt consisted preferred unlike carried powerful powerful create create investigate exponentially accurately issues mass hall pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit school combine combine dependencies dependencies scaled tanh proved cognition notion momentum attributes possibly editor configurations configurations analyze illustrate friedman friedman obvious greedy formal logistic ith ith ith ith detected arbitrarily finds finds finds finds defines defines synthetic synthetic synthetic cos pairwise pairwise formula formula formula ground nowlan capabilities tractable comparisons turns easier precisely products probable projected universal universal acad describing implicit members members begin toronto definite arises incomplete researchers people understood detecting haussler haussler haussler haussler variant variant variant execution prototypes summarized summarized measuring collective geman geman marginal sums eventually yielding univ extreme initialization gap person person lab indices intractable sleep sleep extensive summing summing narrow dynamically jth connecting smolensky generality clamped clamped moment abilities star star reasoning intuitive natl elimination displayed negligible ascent ascent ascent ascent ascent ascent ascent ascent ascent ascent ascent ascent ascent ascent ascent evident histograms searching sphere uni uni counting tic peterson claim advance roy santa santa santa santa santa dempster empty summer ple rubin creates removal removal emergent july freund freund freund freund tendency reconstruct avoids verified insights chapman approxi relating flip pearl pearl laird supports minor induces bill exploratory nist restoration ble ble ble consuming synthesized coin coin visit devised contrasts ultimate crl cruz cruz cruz cruz cruz est semantics stabilize shop shop shop shop shop recovering enabling amer amer unobserved unobserved retrieve nov huber dominate mar assoc assoc enhancing corr albeit ucsc ucsc bernoulli bernoulli tot nation devise formalized ons explosion alternately cis unclamped apr cial cial negation owi mad mad customers hines calif ucla social social fred fred yoav yoav stuetzle ful bipartite bipartite bipartite bipartite printing exert usefully entation stoch sitting negligibly acldey repr repr obscured interpre mgorithm synthetically csd ler formalizing daughter 
#@Freund_Y,Haussler_D,
#t5
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model input input input input data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number system error error state state state state state results results results results results results results results information information information information information problem problem problem problem hidden hidden performance performance based based based based based space space space space space space weights weights linear case case case case case vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown probability probability probability probability probability noise neurons unit unit distribution distribution distribution point point single single control neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test analysis analysis analysis analysis analysis analysis class class class class class class optimal form form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper examples examples examples examples examples examples small small small small small task task task methods step classification classification process current current current current random random random random random memory memory show show show equation section fixed fixed fixed line line line line line line line line vectors vectors general speech speech real average average theory theory theory theory theory theory theory theory theory note dimensional dimensional result university threshold threshold research research research research research independent independent defined defined defined defined defined defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence target target initial constant constant estimate computer terms distance science science direction direction direction direction direction direction direction direction direction direction direction presented presented presented present present present present present nodes maximum components outputs abstract applied applied back back back back back back back back find computational references due due propagation propagation propagation propagation propagation propagation introduction introduction hand behavior behavior behavior change change change change change change change change change change change change change change change difference difference difference difference assume assume assume lower lower lower lower lower rules measure measure measure learned chosen chosen chosen chosen chosen higher previous previous previous previous theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound good good good long long long long expected markov markov make correct correct correct correct correct probabilities probabilities forward simulations simulations simulations simulations simulations simulations classes classes classes classes simulation simulation simulation sum called called means means factor applications applications study compared desired define define define rates rates perform active active active active active active active active goal distributions equal mit steps update support support morgan proceedings report words words loss loss implementation version consists difficult layers addition sequences cambridge equivalent transition transition upper upper upper upper choice approximate free world estimated pages pages increase derived randomly randomly developed bounds bounds bounds bounds types types types types lines lines lines lines actual actual iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration depends depends depends normal normal normal normal normal normal normal normal normal technical describe denote tested tested close complete complete predictions predictions predictions predictions proof assumed generate theoretical theoretical theoretical theoretical theoretical require require require face hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance makes makes makes makes makes development including including kaufmann simulated simulated fully fully technology interesting leads call call iterations direct making stored choose choose choose run run predict improve recent recent recent reported apply apply include side side side side side recently engineering varying varying varying varying varying varying varying varying varying speaker match match background chain chain symmetric modified modified bounded grant grant grant grant exists exists lead concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept invariant extended rotation rotation rotation predicted predicted predicted predicted feed deterministic deterministic deterministic occurs occurs occurs occurs pass pass half half half half half half half half half half half half half half half half half half half half greater greater greater conclusions editors clear performs performs performs asymptotic asymptotic asymptotic asymptotic asymptotic constrained temperature drawn california labeled labeled labeled labeled turn variety minimizing movements plane plane plane plane plane plane decrease introduce denoted areas derive solving generating laboratory label label label label label label label dept changing modeled electrical slightly develop equilibrium national focus focus variation restricted restricted updated updated updated updated updated forms static allowed dashed spaces spaces spaces spaces tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking foundation euclidean perceptrons instances instances maximize holds sensor closely uniformly uniformly uniformly uniformly uniformly uniformly differ differ symbols orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal road interested interested dis lie notation vary usual minimizes hypotheses thresholds attempt subsequent acknowledgments extend explore explore origin origin origin origin existence existence matches incremental incremental incremental incremental incremental incremental ideal ideal working working workshop cover cover cover cover cover cover cover cover cover cover understand understand momentum closest concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts integer predicts perfect recognizer greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy simplest attempts plant advanced cos distinguish track track analyzed analyzed caused briefly lies handle stress 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adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary adversary abbott abbott behaves unpublished gratefully gratefully stores differently differently achievable achievable achievable corporate corporate hypothesized east incorrectly mistakes dichotomy petsche petsche petsche petsche petsche anthony anthony littlestone littlestone littlestone tracks tance rivest rivest rivest rivest rivest rivest fair crl cruz voice voice subscript restrictive drifting acknowledges acknowledges benign benign benign benign benign benign benign benign benign benign benign benign unrestricted modifies ucsc disagreement ronald ronald gorithms hypothesize hypothesize hypothesize devise augment fatigue helmbold helmbold helmbold helmbold rotates rotates rotates rotates rotates rotates rotates eet kuh kuh kuh kuh kuh kuh collects aro radians radians ccr hawaii hawaii airborne mislabeled mislabeled mislabeled mislabeled guesses guesses illness 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#@Kuh_A,Petsche_T,Rivest_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning neural neural neural input input input input data function figure figure networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training algorithm output output output output number number number number number system error error error error error error error error error error error error error error error error error error error error units units units units units units units units units units units information hidden hidden hidden hidden hidden hidden hidden hidden hidden based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case vector order order order order shown shown shown values values probability probability probability probability probability probability probability probability probability probability probability weight weight weight weight unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method approach approach approach approach pattern pattern pattern point single large large large neuron neuron rate rate rate rate rate rate analysis class class class class class class class class class class class optimal optimal optimal optimal optimal optimal shows paper small small small small small small small small net net net work work fig fig fig fig fig points points classification classification trained cell cell structure structure structure structure structure structure problems random random random random random random random random random random random random random random random random memory similar similar architecture show show show show equation equation equation equation section fixed vectors general general general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter real theory obtained obtained obtained dimensional dimensional result result result threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables independent independent independent independent log log defined constant constant computer connections present machine machine maximum range sample sample sample sample sample sample sample sample sample sample abstract applied applied applied find find find properties references due due ieee ieee positive important important important introduction estimation statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical parallel parallel parallel tion complexity complexity complexity complexity variable classifier classifier classifier lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower chosen chosen chosen chosen chosen theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases type type binary binary binary binary binary binary binary binary binary binary binary binary binary represent represent represent bayesian classes classes classes classes classes classes classes classes ing total total total called called called elements elements factor factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension natural applications study knowledge obtain obtain obtain negative vol vol samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples true true related related distributions distributions distributions distributions equal equal equal equal equal equal equal accuracy support train dependent institute institute department department represents represents represents represents considered considered considered equivalent equivalent equivalent curve view transition transition transition transition transition transition transition capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity classifiers classifiers upper upper upper upper upper upper upper upper choice approximate give con randomly randomly randomly conditional developed bounds bounds bounds bounds bounds bounds bounds bounds bounds types associative feedforward feedforward feedforward feedforward denote close close corresponds complete finding finding finding finding short implemented smaller smaller underlying needed needed hopfield reduced technology york special special structures empirical call stored idea idea idea perceptron pair pair pair pair pair pair takes practical subset subset engineering engineering interest dimensions compare works works works works correspond trans trans address definition bounded bounded bounded bounded bounded storage storage constructed constructed exists expression concept occurs hardware demonstrate place greater bayes bayes bayes bayes bayes bayes taking largest drawn drawn drawn drawn drawn drawn drawn california intelligence relationship relationship relationship relationship relationship relationship relationship relationship relationship relationship relation relation relation relation relation relation construct multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer electrical electrical consisting minimization springer versus versus versus versus versus select independently independently independently depending estimator overlap evaluated evaluate evaluate forms understanding allowed key key combining combining roughly roughly valid initially sufficiently sufficiently assigned assigned construction construction classified david priori inter vapnik vapnik vapnik illustrated automatic specifically specifically specifically discussions discussions structural importance suitable literature verlag quickly procedures contained showing notation quantity quantity quantity quantity quantity quantity quantity generalize thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds illustrates satisfies satisfies satisfies satisfies relations limitations matches mappings relationships authors presynaptic fundamental attributes integer integer integer integer integer equally implementations quantities obvious separated expressions ith ith generates arbitrarily motivated inequality trivial baum baum purposes probable acknowledgement universal universal universal universal universal universal addressed consistency capability capability capability capability lack haussler sharp sharp sharp sharp sharp sharp sharp rep ity ity requirement requirement characterize characterize fall fall pasadena tolerance irrelevant assign perfectly hyperplanes hyperplanes hyperplanes systematic satisfying stated interpret occurring obtaining fail methodology methodology methodology implications exceeds exceeds constructive constructive constructive constructive constructive constructive meaningful utilized corollary corollary corollary ranging equals regarded searching counting darpa properly properly properly belonging draw explains adopted speaking speaking abu mostafa planes formulate assignments assignments assignments assignments discovering stands tight illustration exam epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon gener afosr relates exceed proach sta gratefully achievable achievable achievable achievable incorrectly cally venkatesh separates characterizes characterizes littlestone littlestone littlestone nontrivial falling dent indepen inform generaliza psaltis psaltis psaltis psaltis alization dependences dnf dnf confirms acknowledged brings alternately posner mceliece mceliece eli memorization memorization memorization yaser structed devroye devroye devroye ered quan consid tistical memorize grandmother grandmother xls xls abound ine resent uninteresting memorizing memorizing memorizing naptic peo peo peo peo peo peo specifi fized rodemich concomitantly vith 
#@Ji_C,Psaltis_D,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure set set set set networks networks networks networks networks networks networks networks networks networks networks number error error error error units units hidden hidden hidden hidden hidden hidden hidden based based based space weights linear linear 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section section fixed fixed general general general general generalization approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average theory dimensional dimensional dimensional result result result result research research independent defined defined defined defined constant constant constant terms terms terms terms node node node node node science science direction direction direction direction low machine object sets basis basis basis basis basis basis basis basis basis basis basis basis basis basis continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied find convergence convergence convergence convergence density properties properties properties properties properties properties properties references important context introduction statistical statistical generated generated variance tion tion change energy energy difference difference rules measure learned chosen previous theorem bound bound cases cases type type required represent represent represent distributed distributed distributed distributed classes classes regression regression regression regression regression computed respect respect sum elements elements elements elements means natural artificial represented rates proc determined related related discrete mit accuracy larger support support proceedings institute words version technique kernel scheme scheme scheme scheme scheme scheme scheme scheme considered cambridge computing view approximate approximate approximate statistics con developed bounds types product product provided provided provided provided discussion feedforward feedforward feedforward denote limited inverse degree degree degree fit smaller underlying underlying underlying underlying underlying combination combination reduced coefficients technology interesting projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection special representing polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial choose denotes denotes architectures directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions advantage advantage property element element element element element element element element element element apply introduced engineering dimensions dimensions sufficient sufficient sufficient works works works works works works tions tions smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth address definition grant exists exists exists studied alternative generally conclusion conclusion conclusion operator operator operator numerical practice taking integration integration integration integration drawn drawn drawn sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal demonstrated intelligence radial radial radial radial radial radial radial radial derivatives derivatives force question pro monte monte monte derive derive carlo carlo carlo laboratory ann ann ann dept dept linearly infinite dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality develop formed expectation choosing national viewed lemma transform transform transform showed approximated allowed smoothing expansion reduces fitting foundation foundation avoid avoid avoid combinations combinations determines discuss discussions uniformly uniformly uniformly uniformly uniformly modes modes schemes schemes schemes projections orthogonal orthogonal orthogonal orthogonal orthogonal characteristic graphs kind kind dis sin sin sci usual ill acknowledgments rat replaced integral integral integral pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit fewer fourier fourier examine office proper proved proved oscillation func func neu math editor friedman friedman friedman friedman arbitrarily explain massachusetts cos cos smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness analytic purposes precisely mation mathematics scientific universal ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge peter peaks peaks peaks atkeson atkeson atkeson atkeson atkeson atkeson employ polynomials polynomials polynomials polynomials qualitatively univ extreme notes interface fix angular angular angular angular angular angular angular angular angular angular angular angular angular approximates circular circular harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic repre jones jones air star star star ral intuitively nonparametric nonparametric washington sphere sphere sphere sphere spherical spherical spherical spherical spherical spherical barron barron barron barron barron barron barron barron barron barron barron young matter properly generalizing rms rms ple ter ter fellowship ent restrictions conjecture associate avoided laplacian laplacian laplacian laplacian laplacian laplacian laplacian ijcnn distribu approxi gener afosr cartesian cartesian cartesian cartesian cartesian cartesian tij siam ation radio infinitely bution expansions lecture christopher justification curse curse curse curse curse curse curse curse award illinois formulae seattle poly systematically sloan sions statist statist statist statist dimen iti zeros zeros appro appro lar eigenfunctions amer urbana investigator proximation iir unifying ular cient ying huber huber huber huber quadrature quadrature quadrature assoc assoc biomedical corr extremes complexities seeks tributed tinuous orthogonality zhou donoho donoho donoho lations prof prof zhao zhao zhao zhao zhao zhao tly tly champaign muller muller muller cial superpositions ifp genera mates mono harmonics harmonics harmonics spe llll polyno polyno polyno ser stuetzle stuetzle johnstone johnstone johnstone ian ian fll keck oth nction mating usu iil cga duality mll alfred nctions sed diaconis diaconis whe mension jection zed zed radon reprint repr generali rre professorship wegman 
#@Atkeson_C,Zhao_Y,
#t5
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#*network network network network network network network network network network network network learning learning learning model neural neural neural neural neural neural neural input input function function function function function function function function function function function function function function function function function function function function function function networks networks networks networks networks networks networks networks algorithm algorithm number number number number number number number number number number system error state results results results results results results results results results results results results results results results information problem based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear shown weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions method single processing large large large large large large large large large large large large analysis analysis analysis analysis analysis analysis analysis analysis class class inputs inputs inputs inputs inputs simple paper paper paper paper paper small small small small small small small small small small small small size size size size size size size size size size size size size size size work work fig step field problems representation representation show show show show show show show show section general general real real real theory result result result result result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables computation computation computation research research research research research research log defined defined defined found found found found found constant constant constant constant constant constant constant constant computer computer terms terms left maximum maximum maximum range press abstract applied computational computational references ieee ieee ieee ieee ieee ieee important introduction hand circuit circuit circuit circuit circuit circuit circuit dynamic parallel complexity complexity assume assume lower lower higher part center center center theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound required fact fact techniques techniques techniques simulation simulation computed computed computed computed computed sum sum called elements elements elements elements elements elements elements elements elements elements elements elements factor factor made natural natural applications applications study obtain represented represented application application define define compute proc experimental experimental discrete discrete power power comparison comparison comparison comparison comparison comparison comparison report report words words department loss loss technique joint layers layers layers layers layers layers layers addition addition addition computing computing computing computing limit san bit bit bit bit bit bit bit bit bit bit efficient efficient efficient efficient requires requires basic increase increase weighted developed bounds area product product product technical technical arbitrary arbitrary denote denote denote fast fast limited proof proof circuits circuits circuits circuits circuits circuits supported require require main main main main main journal development simulated simulated simulated simulated probabilistic needed coefficients coefficients coefficients coefficients coefficients coefficients increasing principle representing numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers direct bits bits bits bits depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth magnitude polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial idea improved improve recent property element element element practical recently recently engineering tions tions yields trans trans trans trans trans sparse sparse sparse sparse sparse address definition definition observation generalized bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded gate gate grant exists reduce exponential california turn program force question question explicit explicit dept student explicitly explicitly electrical unique spectral spectral spectral spectral spectral spectral spectral spectral spectral develop implies boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean yield expressed lemma lemma lemma lemma lemma lemma lemma lemma lemma open showed showed forms approximated similarly sign construction construction construction norm norm norm norm norm sciences sciences prove prove prove characterized closely computations refer showing issue issue follow sci sci sci comp comp comp generalize computes computes extend powerful exponentially exponentially exponentially exponentially exponentially exponentially exponentially existence fourier giving rest referred gates gates gates proved proved proved func func math editor integer integer integer integer integer observe academic switching switching switching electronic electronic electronic electronic crucial growth growth growth growth majority majority majority answer tool stanford constructing division sgn sgn sgn sgn sgn commonly mathematics consequence consequence acknowledgement res computers computers computers computers simulate simulate simulate replace trade trade proofs restrict arguments harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic smolensky maass generality generality rational air smith tools stated stated grow grow contract motivation corollary studying studying counting integers integers integers integers integers appeared july theorems simulating associate iff ibm ibm ibm ibm ibm insights magnitudes magnitudes magnitudes learnability march nasa siam siam siam nal october unpublished manuscript november expense remarks sorting sorting sorting august cornput siu siu siu siu norms norms polynomially polynomially polynomially polynomially polynomially polynomially polynomially polynomially polynomially polynomially polynomially polynomially polynomially ready irvine irvine computable computable computable bruck bruck bruck bruck bruck bruck spec spec jose mention mansour prohibitively army proving syrup syrup ire subclass jour concluding services cients aeronautics yeung yeung kai kai symp tradeoffs schnitger muroga tral navy navy coeffi oth goldmann goldmann fro daal alon hastad hastad almaden almaden lti lti chandra hajnal szegedy ibaraki toda stockmeyer vishkin reducibility pudlak turan 
#@Bruck_J,Siu_K,
#t5
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data function function function function function function function function function function figure figure figure figure time time time set set set set set set networks networks networks networks networks networks networks networks training training training training training training training output output output output output number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error results results results results results units units units units information information information information information information information problem problem problem problem problem hidden hidden space space space space space space space weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems values parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit distribution recognition pattern pattern pattern pattern point point point processing processing large large large local rate rate rate rate test patterns patterns analysis matrix optimal optimal optimal optimal optimal optimal inputs form form form form shows shows algorithms simple simple simple simple simple simple simple simple simple simple simple paper paper examples examples examples examples small small small small size size size size size size net fig fig fig points points process current trained random random random random random architecture show equation equation equation equation equation equation equation equation equation section fixed line line line line line line line vectors vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter approximation average average average theory theory gradient gradient term term term term term term term note note experiments dimensional variables computation computation computation solution solution solution solution solution solution solution research independent independent independent defined defined found target target constant constant computer computer terms science science present present present machine learn learn learn learn components components components basis basis continuous abstract back computational references ieee positive propagation context introduction introduction complex complex effect effect effect variance variance parallel parallel parallel cost cost difference complexity complexity complexity complexity complexity assume assume assume lower lower measure measure measure chosen chosen chosen chosen chosen chosen part part center previous good long bayesian expected equations equations probabilities observed errors errors errors errors errors forward forward forward simulations simulations simulations simulations minimum minimum ing respect sum sum called called called called called means factor dimension dimension dimension dimension dimension made natural natural negative relative true application define brain equal equal equal equal larger larger update support selection morgan morgan proceedings proceedings institute words words words advances advances joint layers framework hinton additional view solutions solutions curves limit san san top top effects effects effects full full full full full choice free free free pages pages pages give con produce derived derived developed product actual actual finally depends depends depends covariance technical tested tested tested transformation corresponds corresponds corresponds surface predictions implemented assumed assumed assumed assumed assumed journal journal square ability instance instance easily easily rumelhart kaufmann kaufmann underlying needed interesting significantly projection york special consistent leads squared squared squared squared international international decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay idea choose choose run run perceptron perceptron discussed improve improve improve improve improve improve improve improve recent takes practical strategy sense inference sejnowski observations teacher teacher teacher yields yields yields match studies diagonal diagonal address improvement improvement improvement improvement improvement exists expression lead invariant feed feed feed occurs conclusion conclusions editors editors numerical numerical numerical clear moody exponential exponential asymptotic mateo mateo presence physics california proportional regularization min decrease decrease averaged averaged averaged targets targets targets targets targets targets targets targets targets derivatives force base denoted denoted produces written solving ways modeled pruning text angle adding adding minimization springer cycles john choosing choosing choosing choosing phoneme phoneme viewed fraction forms static static static static translation spectrum spectrum dashed epochs normalization fitting fitting fitting neighborhood neighborhood valid valid valid sufficiently norm norm eigenvalues eigenvalues eigenvalues eigenvalues subspace subspace subspace subspace subspace subspace subspace sciences prove characterized simplicity mackay situation orthogonal verlag kind kind kind strongly cun contribution contribution contribution manifold manifold manifold bar minimizes eigenvalue denker denker thresholds extend minimized layered detail lippmann dotted dotted dotted eigenvectors momentum smallest smallest smallest smallest smallest smallest smallest closest editor analyze analyze opposite rank rank rank rank rank perceptton improving extent simplest finds languages mentioned asymptotically growth analyzed defining growing improves baum lies inside tive widely strictly strictly projected acknowledgement recognized opt english lowest outer experimentally backprop solla solla solla haussler formulated span berlin weigend aim aim proven proven phonemes prevent gave conclude implements damage owl wesley summed univ irrelevant irrelevant irrelevant lot realized ear analogue notes addison mistake arguments pick wrong convenient city balance keeping tishby krogh krogh krogh krogh krogh krogh krogh hertz hertz hertz hertz hertz hertz hertz elimination connect connect studying expanded expanded bad washington forecasting evident schwartz treatment theoretically belonging draw santa santa explains tures entropic minus solves solves solves basically exhaustive expanding possibilities massively rain rain constrain argue penalized levin realizable realizable gener expand concentrate confirmed spanned denver denver happen page dramatic prevents infinitely picking lecture council council accordance rosenberg transforming transforming suppress suppress suppress pronounced unreliable huberman architec governing curved denmark denmark iti nettalk nettalk nettalk cruz cruz subscript acknowledges pin penalizes insert insert ference remarkably putting putting alization mal ucsc infinitesimal cse suppresses suppresses suppresses disconnected nonlin copenhagen copenhagen valley valley valley valley bohr awi linearization unrealizable unrealizable owi redwood loose zky touret ivl blegdamsvej blegdamsvej danish danish deriva anders folk valleys valleys descend nordita 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#@Hertz_J,Krogh_A,
#t5
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time set set networks networks networks networks networks networks training training training training training training training training algorithm algorithm number number number number number number number number system system system system system system system system error error error error error error error error error error error error error error error error error error error results results units information problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden performance based based based based based based based based based based based based based based based space space space space space space linear linear linear linear linear linear linear linear linear case order shown systems systems systems systems parameters parameters parameters parameters functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach point point point point point point point single single single single single processing processing processing local local local local local local test test test test test class class class class class optimal form shows shows shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper examples examples examples examples examples examples examples examples small small small small small small small net work work work methods methods methods methods methods methods methods step points points features classification process process structure structure structure structure structure structure structure structure structure random random high high memory memory similar representation representation representation representation architecture architecture show show show section fixed line general generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter real approximation approximation obtained experiments experiments dimensional dimensional dimensional computation computation computation solution independent found found constant constant table table estimate standard standard standard computer computer computer terms terms science science science science prediction presented presented present present low machine range learn components components components components components components components components components components components basis basis basis basis basis basis basis basis basis basis continuous sample sample sample abstract applied applied applied applied back computational computational density density density density density properties likelihood references component component component component stochastic important adaptive propagation context complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex estimation estimation estimation estimation behavior effect dynamic dynamic dynamic dynamic dynamic generated generated generated generated generated tion complexity complexity complexity lower rules measure measure measure prior prior prior prior prior prior prior prior prior prior prior prior prior representations representations learned learned learned chosen chosen chosen chosen chosen chosen chosen chosen chosen chosen chosen higher higher higher higher part center center center center represent tree distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected markov markov markov make make fact region region errors classes classes classes ing ing ing ing tasks tasks tasks total human human performed performed called times times times regions regions regions mapping mapping mapping means means means means means means means means means means potential potential potential dimension made made made made global global knowledge knowledge knowledge knowledge knowledge original original specific specific samples samples samples samples compared application desired desired cross provide objects objects objects location determined determined related posterior connected power approaches approaches steps larger larger larger fields fields train source source selection morgan report institute institute technique technique technique technique technique consists consists consists individual individual individual individual individual individual individual kernel kernel advances considered considered framework framework domain domain domain environment directly directly directly directly curve curve curve curve curve curve curve curve view curves curves curves san top top top top top top top determine efficient efficient efficient efficient efficient efficient efficient efficient choice approximate statistics free world world world world world vision increase increase validation conditional clustering levels bounds types processes processes processes evidence backpropagation depends constraint constraint constraint constraint simply technical increases describe arbitrary fast fast limited complete surface surface predictions rbf rbf amount amount amount nearest supported main eds square square pixel easily easily makes makes makes sensory fit fit fit kaufmann auditory pairs pairs pairs smaller underlying needed needed needed needed needed combination combination significantly york york segmentation structures structures structures structures empirical operation leads direct stored international international normalized bottom early early early early idea idea idea idea combined combined choose choose choose choose description architectures improved improve improve recent recent pair pair pair pair takes typical similarity similarity similarity similarity practical strategy strategy strategy strategy strategy strategy include subject subject hierarchical subset cognitive cognitive relevant interest dimensions dimensions varying volume axis tions tions rl sparse symmetric entire entire increased constructed constructed studied suggests wide wide wide locally touretzky width width width setting setting setting runs strength conclusion conclusion critical critical critical place row row segment segment segment segment segment segment segment segment sigmoid moody moody moody mateo strong reduction drawn drawn drawn california radial radial radial radial radial variety variety variety variety variety variety variety variety variety start start plane plane decrease manner manner scene base areas areas explicit appears appears appears appears longer longer factors primary estimating tuned segments segments segments segments segments segments segments segments modeled confidence metric physical slightly develop gaussians springer formed quality choosing choosing choosing choosing choosing choosing choosing choosing family family focus viewed viewed influence influence influence densities operations approximations centers centers centers centers centers centers centers centers centers centers centered centered partition allowed reasonable spaces spaces spaces combining fitting fitting fitting neighborhood boundaries initially initially construction construction construction construction construction construction construction faces avoid avoid building perceptual inter vapnik vapnik vapnik maximize domains domains domains major determining efficiency capable importance uniformly uniformly differ encoded computationally computationally computationally identify literature build efficiently efficiently mackay mackay situation essentially notice verlag quickly kind repeated induced allowing heuristic heuristic heuristic success stopping split dis criteria criteria generalize generalize minimizes highest received moves approximating approximating neighboring neighboring receive modelling modelling modelling modelling modelling extend situations situations situations law simpler origin parametric parametric powerful powerful wiley overfitting overfitting overfitting overfitting overfitting access access collection collection essential experience experience experience exponentially relations detail lippmann hall fewer successive incremental incremental mappings investigated applicable applicable applicable applicable ideal decisions decisions decisions decisions affect affect affect affect encode func hierarchy hierarchy fundamental phases phases phases surfaces removed removed removed induction smallest naturally naturally naturally naturally adapt adapt extremely extremely extremely aspect portion consist consist simplest grouping regime explain finds animal animal animal brown great piecewise pairwise publishers phenomena caused briefly starts processed straight implementing berkeley widely constructing broad choices choices located probable potentially potentially universal universal gradually members begin localized localized explained geometric geometric geometric geometric geometric geometric varies varies affine flexible parameterized parameterized parameterized backprop incorporated dots dots dots dots rep maxima compares psychological ity maintain maintain mod mod mod ture weigend weigend aim reaches ordered 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discovered discovered alternatively intersection stopped avoiding avoiding ball street appeared ence shepard shepard ter ent chervonenkis job job suboptimal smoothly smoothly ical tendency tendency experiences experiences possibilities discovering examining clustered representa continuity queue queue queue queue community gener interacting interacting proba surrounding lookup lookup proach constructs represen portions portions portions portions supports preprint sta applicability els els dramatic priority struc experi vice species versa regularities regularities stephen bility corners discontinuous justified prefer insufficient builds nested nested nested families cliffs doesn doesn suite shot puts puts mining inclusion proposes sparsely sparsely sparsely englewood triangles triangles accumulate successively successively successively meth deals arrives arrives rameters occam occam explanations decaying ignores contrary ods sian sian dimen rel sis locality locality locality inducing merged merged merged merged merged merged sparseness indepen seg allocating dence physica sur validated predetermined decompose violate cations imposes appli inserted checked plexity touch accu dependences coincidence cir buntine remember remember justify hypothesize radially penalizing workstations ism enormous razor organism organism plex plex susceptible endpoints organ perceptually comers bumptrees bumptrees sit sit validate validate validate validate gestalt para prefers misses decomposes bet merges merges balls balls balls balls balls balls radii sional devroye viability derlying typ dem tains complements expe expe collinear collinear analogs itseft intricate capa communities fun evant gles tolerances idealization fluence vali mulated mensions damental por dth resents 
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data function function function function figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number system system system system units units units units units units units units units units units units units units units units units units units units units units problem problem models models hidden hidden hidden hidden hidden performance performance performance performance performance based based based based based based based based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case vector order order order shown shown shown systems systems systems systems systems systems values values values probability parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit recognition approach approach pattern pattern single single processing processing processing processing processing processing processing processing processing local local local local test test test test test test patterns patterns patterns class class matrix matrix matrix matrix inputs inputs form form form form shows shows shows algorithms simple simple simple simple examples examples examples examples examples examples examples examples small net net net net net net work work work task task task task task task task task task points classification process process process level level level level level level level current structure structure structure high representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show fixed fixed fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors general general general general general generalization generalization parameter parameter real average states gradient gradient term term activity activity university university computation solution research research research research research research independent defined defined defined defined defined defined target initial constant table table table standard computer computer terms terms distance science science science left map map map present present present present present activation activation activation activation activation machine machine machine object object sets maximum press press learn learn learn learn learn learn components components outputs outputs sample abstract applied applied applied back computational references positive procedure procedure adaptive context introduction action action action action action action action action action action action action complex complex complex hand statistical generated parallel parallel cost tion tion tion classifier classifier rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules representations word learned learned learned learned higher higher higher higher part part center cases type type type type required multiple binary conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions represent represent distributed distributed expected fact length length length length length correct correct simulations simulations simulations simulations resulting resulting resulting classes ing tasks tasks computed computed performed performed performed called called called elements elements elements regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping potential natural knowledge negative original original original vol vol artificial represented compared compared compute perform perform perform perform perform perform perform goal constraints constraints constraints constraints constraints equal approaches approaches approaches approaches approaches mit mit steps steps steps comparison comparison connection train train train train train descent descent institute words words words department department version consists consists consists represents connectionist connectionist connectionist bias bias bias bias bias layers ai maps maps maps maps considered cambridge cambridge computing domain domain domain domain domain domain domain domain domain domain equivalent directly hinton hinton additional additional design capacity determine choice world con con con con con produce condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition clustering types types finally finally discussion describe describe describe describe arbitrary arbitrary arbitrary group group denote denote tested transformation close close close corresponds corresponds complete actions actions actions actions short nearest nearest generate generate generate generate generate generate supported role role role role role role square ability hypothesis instance instance instance instance instance instance instance instance instance instance instance instance future degree degree makes rumelhart rumelhart rumelhart rumelhart including smaller underlying combination combination functional functional fully fully jordan jordan block block block block block block block block block block block block block interesting testing projection projection projection projection projection projection projection uniform principle operation language language call direct window window window window experts experts expert decay idea minimize produced run added denotes denotes directions resolution takes element typical typical strategy strategy include subject subject subject sense subset sejnowski sejnowski cognitive cognitive cognitive cognitive cognitive calculated works tions match correspond correspond correspond diagonal diagonal mixtures grant grant grant concept studied alternative alternative correctly correctly correctly column column column demonstrate runs runs runs minimal row row row clear learns learns constrained hard mechanisms integration external intelligence labeled assuming variety start targets connectivity program program base denoted explicit explicit pro produces optical winner ways recall metric implement category category category category category category category category category category category category category category category category category category category category category category category category category category category category category simultaneously averaging involves remaining text unique integrated integrated integrated integrated integrated agent implies boolean competition extracted independently phoneme squares viewed transform evaluated labels evolution evolution evolution soft soft soft sizes activities completely completely allowed allowed past past epochs epochs epochs roughly add iterative iterative iterative string string string string string string string string string string string string string string symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol assigned foundation foundation euclidean degrees template template template template template template template template thesis strings strings strings strings strings strings strings strings strings instances instances instances instances instances assignment assignment assignment assignment assignment activated mozer mozer mozer mozer domains domains domains domains characterized gating gating letter capable suitable differ divided divided divided symbols symbols symbols symbols symbols symbols symbols symbols mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland identify identify literature genetic invariance essentially essentially identity identity identity identity traditional traditional compact repeated induced induced induced induced induced interested interpreted interpreted interpreted neuroscience classify content manifold categories categories categories categories categories categories categories categories categories categories categories categories categories categories categories categories categories involved write michael generalize generalize generalize correspondence correspondence correspondence leading automatically jacobs jacobs jacobs jacobs jacobs acknowledgments deal deal remain carried powerful essential exhibit exponentially put involving strengths strengths accurately examine respond respond rest rest project project incremental symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic func func cover cover cognition cognition induction induction induction induction induction induction act closest man created ensure ensure subsets obvious greedy portion formal formal logistic logistic fisher fisher freedom mapped mapped expressions epoch epoch epoch epoch epoch epoch motivated sentences sentences sentences fairly nowlan nowlan capabilities capabilities briefly comparisons tive sections satisfied satisfied incorporate incorporate ran pool pool pool pool projected implicit english english meaning nsf nsf nsf exemplars exemplars exemplars exemplars integrating apparent greatly applies tional parameterized readily readily backprop backprop templates templates templates templates templates templates templates templates templates templates templates templates templates templates templates operate operate switch exhibits limiting enables replace sentence sentence sentence sentence converged semantic semantic semantic yielding acquisition classifying writing guarantee tation restrict perfectly perfectly purely purely repre discover tem tem eliminate nonzero nonzero grows smolensky smolensky smolensky smolensky smolensky establish dealing imposed interpret roles roles methodology methodology methodology belong corpus corpus enhanced phrase filled falls combines governed governed governed governed ensures james patient patient patient paul induce induce induce holland moved moved moved conjunction colorado colorado colorado enhance bases bases bases permutation young refers grants discovered discovered explorations explorations assigning assigning outlined unchanged land land usage microstructure microstructure ter vec covering covering dec employs abstraction copy additionally ideally solely assignments tor remainder constrain constrain constrain constrain mutually argue manipulation manipulation gated exclusive cessing impose pdp pdp continues gener manifolds boulder boulder boulder thresholded eliminating books books projecting iri iri categorization categorization categorization represen covered covered anal attached esti pools pools pools pools meet induces inactive unpublished handled handled copies slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot slot ate ate ate font font ping rosenberg rosenberg mcdonnell slots slots slots slots slots slots slots slots slots wins virtually bold bold award stay injected condi devised subtracted extracts detects goldberg sym sym rating characterizes characterizes squashing sloan sity syntactic syntactic syntactic suffice noun noun inset periodically demands thing bradford inducing ranged ranged brackets categorical enforces discovers verb sented thc constituent stems investigator imposes predefined unaffected intrinsically intrinsically intrinsically intrinsically activates fundamentally fundamentally fundamentally ece excluded subtasks orig alization manipulations constituents encourage rightmost conflict devise presidential univer shortcomings equipped equipped cate encourages zation cleaned nouns nouns ford mated conjunctive conjunctive bet tense tense entity entity tives verbs verbs verbs rock crosstalk straint straint dition tiling twofold twofold alphabets alphabets mcmillan mcmillan mcmillan mcmillan mcmillan mcmillan mcmillan irl itera plates plates subsymbolic subsymbolic subsymbolic subsymbolic subsymbolic subsymbolic subsymbolic subsymbolic subsymbolic logically disjunctive instructive instrument bolic bolic bolic ries ries ries fork fork pronounce boy boy boy boy boy boy boy clayton substructure optoelectronic seldom aren aren inal criticized subvector disjunction disjunction lion netj malization incorpo acted engi submatrix submatrix generali estab uppercase neering brad strikes 
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number system system system error error error error error results results results results units units units units units units information information information problem problem problem problem problem hidden hidden hidden hidden based based based based based based weights weights weights weights weights weights weights weights weights weights weights case shown systems systems systems systems systems systems weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method method method method method method method method approach approach approach approach pattern point single single processing processing processing rate rate rate test patterns analysis analysis class class inputs form form form form form form form algorithms algorithms algorithms paper paper examples examples examples examples examples examples examples examples examples examples examples small size net work task methods methods methods methods methods methods methods methods methods methods step step step step step step features features classification process process trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure problems problems problems problems response similar similar representation show show show section section section section rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general generalization real real average theory note note experiments experiments experiments experiments result result result result result result university threshold threshold threshold solution solution research sequence sequence sequence sequence initial initial initial initial initial initial initial initial constant table table table table table table table table table standard standard standard computer computer terms terms terms distance science left machine machine machine machine sets sets sets sets sets sets sets sets sets press press learn position position position basis sample sample abstract applied back references due procedure procedure procedure important important important decision decision propagation propagation mixture context introduction behavior behavior effect effect cost search search change energy difference complexity rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules prior prior representations learned higher cases required required required multiple good long represent represent represent make techniques correct correct errors resulting resulting classes classes classes classes tasks tasks total sum called called times mapping optimization optimization knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge original original artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial relative specific specific true true true compared cross cross cross cross provide define rates location active active related related equal equal equal mit steps steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison comparison larger connection support support nets morgan morgan morgan proceedings proceedings proceedings proceedings proceedings proceedings department department technique consists internal code code code code individual advances advances joint represents represents connectionist difficult difficult difficult final bias bias bias bias bias bias addition addition sequences cambridge domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain directly directly directly hinton hinton hinton hinton additional additional additional limit san conference conference conference conference conference determine determine determine determine upper choice significant significant significant significant world pages pages pages pages pages pages pages pages validation validation validation produce derived derived weighted weighted weighted randomly clustering clustering clustering clustering lines lines lines entropy finally finally evidence evidence backpropagation simply biological biological measured discussion discussion group group group tested limited assumption assumption assumption assumption corresponds complete supported adaptation end ability ability ability hypothesis hypothesis instance cluster cluster cluster easily makes makes makes rumelhart rumelhart kaufmann kaufmann kaufmann smaller underlying underlying combination combination transfer transfer testing testing testing testing testing testing testing testing testing testing significantly significantly significantly character york mechanism matching empirical empirical empirical empirical principle principal call making international international international expert expert expert expert decay idea idea combined produced produced produced added added improved improved improved advantage property property pair takes introduced hierarchical trees inference subset subset subset subset subset subset subset subset subset subset subset subset subset subset approximately volume volume volume match match correspond correspond achieve chain williams grant grant grant occur suggests matrices correctly correctly correctly correctly clusters clusters clusters demonstrate assumptions assumptions assumptions assumptions reduce reduce conclusions editors differences measures accurate accurate accurate designed clear learns mateo propose strong hard solid intelligence intelligence intelligence intelligence intelligence labeled user user averaged groups groups groups groups groups groups groups groups groups groups groups groups connectivity base base base appears produces produces winner ann changing confidence implement category explicitly remaining remaining slightly slightly unique formed formed shift quality extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction boolean boolean national national national national extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted interpretation interpretation interpretation interpretation codes detailed detailed evaluated evaluate labels labels soft understanding approximated similarly suggested translation translation translation partial earlier calculation reduces initially foundation classified topology includes combinations combinations sciences recognize plotted illustrated domains domains partially tests tests tests major major determining identified closely importance importance importance included mcclelland presentation identify efficiently comparing plots tend summary refer repeated repeated procedures heuristic heuristic link link link link link link superior superior superior superior superior superior superior superior superior superior issue return return classify simplified thresholds thresholds illustrates extract extract acknowledgments situations presents presents trains bars simpler powerful wiley overfitting overfitting overfitting overfitting strengths accurately dotted biases biases dataset fewer links links links links links links links links links links links links links links links links links links dependencies dependencies office decisions symbolic symbolic symbolic symbolic symbolic symbolic workshop affect statistically statistically cognition matched induction act naturally concepts concepts concepts concepts extremely created perfect portion fisher academic simplest utility grouping grouping arbitrarily explain attempts defines percentage stop trivial defining biology biology explanation nowlan nowlan adapted worse worse handle reasons considerable satisfied closer widely style style style desirable members members optimize optimize medical meaning meaning meaning meaning meaning reflects reflects substantially empirically understood treated reliability summarized differs extracting proven prevent datasets adjust inherent boston boston returns returns specifies summed extreme sharing contribute classifying accomplished equivalence equivalence equivalence equivalence restrict purely addresses addresses addresses impossible impossible naval eliminate eliminate eliminate eliminate theories theories generality eliminated eliminated eliminated eliminated eliminated murphy simplify replacing determination determination determination interpret operates operates methodology knn knn knn knn knn knn knn knn modifications exceeds combinatorial constructive heuristics heuristics meaningful published analyses ambiguity guarantees enhance searching searching scan scan scan scan offers reproduce bases bases initialize membership foundations express thin indicator contact contact partitioned valuable discovered stopped fold fold fold shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik explorations leaving dna dna dna anns anns microstructure minus minus minus minus minus minus minus minus minus minus minus minus minus minus creates benefits retraining weiss weiss additionally additionally junction junction junction junction junction junction tradeoff solely molecular molecular assess community genes thick geoffrey pdp searches simplifying paired exceed exceed topic iri conversely refinement refinement refinement refinement refinement denver denver supports places applicability refined holding prevents examination inactive inactive rewritten deletion simplification august heavily towell towell towell towell towell towell towell towell confirm dropped dropped appealing stay affecting pronounced diagnostic believed assessment extracts extracts extracts extracts extracts extracts splice splice splice splice splice splice intact artifact explanations explanations wisconsin comer translates eighth eighth eighth repetitions noticed saito comprehensive violate configured configured repetitive modifies madison superiority reproduces ninth nakano suggestion consensus confident unimportant kbann kbann kbann kbann kbann kbann categorize shortcomings shortcomings categorized categorized render weaknesses looked rue oft oft oft mooney mooney gat tailed tailed consequent consequent promoter promoter promoter promoter promoter promoter promoter promoter promoter promoter guiding conjunctive eleventh antecedent antecedent arose orlando aug vastly conformation conformation eleven exhaustively freezing sacrifice disjunctive stating noordewier noordewier comprehensibility comprehensibility comprehensibility comprehensibility comprehensibility worlds combinatorics shortcoming predicates tat disregard refines enclosed inserts disjunction preconditions jude interpretability attach 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#@Shavlik_J,Towell_G,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output number number number number number number system system error error error error error error error error state results results results results units units units units units units units units units problem problem problem problem models models models models hidden hidden hidden performance performance performance performance performance based based based space space space space space space space weights linear linear linear case case case case vector vector vector vector vector vector vector shown shown shown shown values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters functions functions unit unit unit unit recognition approach approach pattern image single control large local local local local local rate test test patterns patterns patterns patterns class matrix form form shows algorithms algorithms algorithms algorithms algorithms algorithms simple visual paper paper paper paper examples examples small feature feature work work task task task task task fig features classification classification process process process process process process level level level level level level level level level structure structure structure structure structure problems similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation equation equation equation line vectors vectors vectors images general generalization generalization generalization generalization parameter approximation average gradient gradient gradient gradient gradient obtained term note dimensional result university variables computation research independent log log log log log defined found found found dynamics constant table table table terms terms terms terms science science presented presented map map map present present present present activation activation activation object maximum maximum press learn learn learn basis basis nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs abstract density density density density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component stochastic stochastic due procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision propagation introduction estimation estimation statistical statistical statistical effect generated generated parallel cost tion assume assume lower measure prior representations chosen chosen higher previous type type required binary binary binary tree tree tree tree tree tree tree tree tree tree tree tree equations equations techniques techniques techniques techniques region region region region region length probabilities probabilities probabilities probabilities probabilities forward finite simulations classes classes tasks tasks total simulation human human regression regression regression regression respect respect multi times regions regions regions regions regions optimization natural natural natural global global global global global applications obtain obtain obtain relative relative relative relative relative relative specific compared compared compared cross define define define perform related related posterior posterior posterior posterior posterior posterior posterior posterior brain approaches larger support dependent modeling report institute department technique joint joint joint joint joint joint maps cambridge computing environment hinton hinton hinton hinton additional top top effects classifiers choice choice significant approximate statistics validation give weighted weighted conditional robot levels levels levels levels levels levels levels levels types entropy entropy entropy finally processes processes processes selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation associative associative achieved discussion covariance normal normal feedforward arbitrary group rbf rbf assumed assumed generate supported theoretical eds pixel ability cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster degree degree development noisy fit fit fit auditory probabilistic probabilistic functional functional unknown unknown jordan jordan jordan jordan jordan jordan jordan jordan technology interesting york principal iterations making international experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts supervised supervised depth expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert early produced produced light light predict predict perceptron architectures architectures directions property separate separate separate separate separate separate apply pixels hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees trees trees trees trees cognitive unsupervised unsupervised volume yields correspond correspond achieve mixtures positions positions entire entire grant grant grant grant arm studied studied suggests derivative derivative locally move width clusters clusters runs practice learns learns learns learns learns suggest suggest suggest radial radial derivatives derivatives derivatives manner manner identification identification program base acknowledgements appears derive produces perception generating mathematical multilayer multilayer multilayer develop springer implies implies competition competition national dependence interpretation learner learner influence decomposition decomposition approximated margin similarly similarly partition partition partial partial partial earlier earlier additive measurements classical classical fitting roughly iterative valid foundation faces perceptrons color inter sciences discuss maximize candidate priors characterized gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating columns aspects aspects suitable computationally schemes comparing tend essentially essentially essentially fine fine composed verlag heuristic split michael modular modular backward overlapping extract jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs extend explore american overfitting collection investigate involving estimators recursive project mappings mappings combine relationships structured comparable comparable comparable func surfaces coarse coarse adapt equally friedman friedman friedman friedman algo algo logistic mapped mapped ith ith ith ith ith ith multivariate multivariate generates generates massachusetts residual rows cart cart cart cart cart cart cart cart cart cart cart cart cart stop developing nowlan nowlan nowlan nowlan tive tive incorporate ran leaves leaves laboratories arises auto author nsf robustness conjugate fourth percent percent percent items led affine affine affine affine dark readily backprop splines partitioning partitioning partitioning partitioning partitioning modulated gen adjust sums sums neuro leaf leaf leaf leaf softmax consistently restrict arguments velocities jth jth jth partitions partitions repre flexibility flexibility flexibility breiman breiman breiman siemens simplify multiplicative serves belong north generalizes utilized utilized corre sides ascent ascent sim competing competing arrangement entries young partitioned splits splits splits captures captures stone stone robert yielded ure corporation annals super ber recursively recursively ties medium tradeoff hundred acceleration hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies mars mars mars mars mars mars mars realize param deep rithms rithms num discontinuity discontinuity discontinuity convert surrounding iri sized nal normalizing ignoring atr eters treating bridle bridle differentiating species species sponding restoration regularities preserves ble acquire twenty twenty nested nested nested nested adaptively compete morphology award appealing archi arriving enhances adjusts edition differentiate bottleneck discovers discovers yellow investigator collections quantified quantified sentations decompositions favorably recursire arline arline viable adap ames tecture belmont agation respec yij yij yij yij yij yij yij yij fogelman presidential exposition masks masks masks olshen olshen fifty wadsworth worthwhile vised grayscale doubly exemplified exemplified rault oak oak oak torques forty forty accelerations gill acute acute acute soulie rounded rounded rounded parameterizations associator lobes frontier expe expe expe expe acquiring apex ulated truncate halted mso hier hier commonalities inclined pings 
#@Jacobs_R,Jordan_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure time time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training output output output output output number number number error error error error error error error error error error error results results results results results units units units units units units problem problem problem problem problem problem problem problem models models models models models models models models hidden hidden performance performance performance performance performance performance performance performance based based based based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer case case order order shown shown shown shown shown shown systems systems values values values values values values values values probability probability probability probability probability probability probability parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition method method method method method method method approach approach pattern pattern point point single single single single single control large large large large large large rate test test test test patterns patterns analysis analysis optimal form form shows simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small small small small small size size net net task task task task task task task task task step step step step step step points trained trained structure problems problems problems random high similar similar similar architecture architecture architecture equation equation equation section fixed vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization approximation average average average average average average average gradient gradient gradient obtained term term term term term term term term term term term term term note experiments result result university university university university threshold computation solution research research independent independent log log log defined initial initial initial initial table table table table table standard standard standard computer computer terms terms science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left sets sets sets press press press components components components basis nonlinear abstract back back back back find find computational density density density density density density density density references component component component component component component component due positive procedure adaptive adaptive adaptive adaptive adaptive propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex hand statistical statistical statistical statistical effect generated generated generated variance variance variance variance variance variance parallel parallel cost cost cost cost cost cost cost cost cost difference difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity lower measure measure measure measure measure prior prior prior word chosen chosen chosen chosen center center previous previous cases cases cases cases type required multiple multiple good good good binary binary long represent represent bayesian bayesian bayesian make techniques techniques techniques region correct correct simulations simulations simulations simulations simulations simulations simulations ing ing ing tasks tasks simulation simulation simulation regression respect multi sum sum sum sum sum performed performed performed called times means factor study negative artificial relative relative relative relative represented represented compared compared desired cross cross series series series series series series provide provide define proc perform constraints distributions equal approaches approaches steps steps larger larger train train train descent report report report institute institute institute institute department version version technique consists individual connectionist difficult final final final final final exp exp layers delay ai hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton solutions design limit limit san bit bit bit detection detection significant significant free estimated basic validation validation validation validation con weighted randomly criterion actual evidence depends simply simply achieved achieved technical technical group group fast close assumption predictions finding rbf rbf amount effective role theoretical theoretical adaptation journal journal ability ability cluster future future future future rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart typically reduced technology interesting uniform uniform leads squared squared details magnitude magnitude decay decay decay decay idea description predict architectures discussed discussed improve improve recent recent recent takes takes typical typical practical practical subset recently interest works works solve mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation evaluation symmetric lead studied invariant suggests deviation deviation deviation derivative derivative derivative predicted predicted locally demonstrate strength starting starting critical reduce reduce reduce competitive differences differences measures measures performs learns learns learns constrained propose strong hard largest california proportional proportional proportional radial assuming start relationship acknowledgements explicit ways factors generating laboratory laboratory distinct multilayer remaining spectral gaussians gaussians gaussians shift shift shift shift shift shift versus cycles choosing national communication squares squares squares open open evaluate updated centered centered soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft translation partial classical classical fitting add add penalty penalty penalty penalty closed closed valid string string degrees box figures thesis thesis weighting prove major determining extra extra importance society differ divided literature mackay mackay situation ten ten ten ten ten ten summary summary conf repeated contained cun cun prob showing interpreted neuroscience symmetry strategies comp comp comp comp usual usual generalize generalize generalize providing automatically mixing mixing mixing mixing modelling modelling bars explore origin unlike diego exhibit experience ml successive ideas school tech investigated investigated authors decisions comparable waibel waibel circles circles gradients adapt adapt adapt configurations configurations predicting predicting predicting created thought ensure ensure subsets subsets subsets subsets algo freedom precise academic baseline simplest simplest explain explain phd phd isolated averages averages years years languages great advanced costs variances variances variances improves improves coded nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan benchmark baum baum perspective division broad broad broad broad broad broad broad mation ion ion optimize optimize optimize toronto toronto toronto medical auto preceding mellon mellon conjugate conjugate improvements greatly considerably prop carnegie carnegie empirically cmu flexible offset amounts fed poorly share share share share share howard summarized summarized pittsburgh pittsburgh limiting weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend prevent pasadena tile tile sharing sharing sharing cor lot trade trade shifted shifted assign assign tation narrow narrow narrow narrow labelled labelled homogeneous flexibility royal eliminated eliminated los removing salk effectiveness responsible intuitive elimination elimination elimination elimination elimination lang lang iterated iterated iterated iterated modelled canada impact discovered discovered vari lem pressure pressure pressure ure ure leaving minus creates personal forcing massively clustered favor rithms geoffrey decays approxi gener playing hughes conversely tied tied funded inversely applicability lapedes lapedes lapedes normalizing compu differentiating excess lation justification influenced hat hat ave east responsibility responsibility responsibility responsibility responsibility responsibility steven dom proportions proportions proportions proportions proportions concrete bilinear huberman huberman huberman huberman fox constraining sian ance bumps tical cyclic penalizes began pull crg plexity optimizes terminate andreas ontario tics statis tong tong tong decides tie rated claims adap shrink froin adopting radially penalties canadian canadian nserc tar tar niques ponents simu lations lira lira sunspot sunspot sunspot sunspot sunspot sunspot fellow plaut plaut ditional tying tying tying tying tying tying lhe penalize penalize shrinking yearly yearly yearly cas tection aud circularly tio sinall sinall misfit misfit misfit deliberately ial algorit trai vanilla roach gausstans gausstans gausstans erations iml eindhoven apl nay squeeze 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#@Hinton_G,Nowlan_S,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input data figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set networks networks training training training training training training training training training training training training training training output output output output output output number number number number number number number number number number number number number error error error error error error error error error error error error error error error error error error error error state state state state state state results units units units information information information information information hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space space space space space space space weights weights weights linear linear layer case order order shown systems systems systems systems systems values values values values values values values values values values values parameters weight weight weight weight weight weight weight weight weight weight weight weight weight functions unit unit unit distribution distribution approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point single processing processing processing large large large local rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis shows shows algorithms examples examples examples examples examples examples examples small small small small small size size size net net work work task task task task task task task task task task task task task classification level level current current trained structure random random random high high high high response response similar architecture show show show fixed fixed fixed line rule rule rule vectors parameter real average average average average average note note note note note experiments dimensional result university university research research independent independent independent log defined defined defined found sequence sequence sequence initial initial terms science prediction left left left left left left presented presented presented presented presented presented presented present activation low low low low low low machine maximum range range range abstract back back computational computational convergence convergence references procedure procedure procedure procedure procedure propagation introduction action behavior behavior behavior stimulus effect effect effect effect effect effect parallel search tion tion change difference measure measure representations learned learned chosen higher part center cases required multiple good distributed distributed expected techniques observed observed errors errors scale simulations simulations simulations minimum ing tasks tasks tasks tasks tasks tasks tasks tasks total regression computed multi sum called times study negative relative compared compared desired desired desired cross active active constraints equal approaches mit comparison update support train selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection morgan morgan morgan department implementation technique technique technique individual individual advances advances advances connectionist responses responses final scheme scheme cambridge equivalent environment environment hinton hinton curve curve trajectory trajectory trajectory trajectory stimuli stimuli bit bit bit bit bit bit upper upper significant significant statistics world give con con condition randomly randomly criterion criterion criterion criterion criterion criterion lines provided selected selected selected selected iteration iteration nature depends sampling sampling simply simply measured measured measured measured discussion discussion arbitrary arbitrary arbitrary group denote tested corresponds surface implemented implemented implemented implemented supported require instance easily rumelhart rumelhart kaufmann kaufmann kaufmann simulated typically typically reduced reduced character trials trials trials trials trials trials trials trials mode principal squared squared squared squared squared squared iterations iterations iterations iterations iterations pre international supervised supervised magnitude attention advantage property pair pair typical introduced strategy strategy strategy strategy strategy side relevant unsupervised unsupervised unsupervised observations axis axis match correspond correspond studies converge converge converge converge definition observation interval williams williams improvement sensitive sensitive entire increased grant amplitude amplitude suggests suggests alternative alternative move boundary boundary critical critical minimal greater greater greater reduce reduce reduce trajectories depend depend measures performs strong cycle demonstrated exist selective averaged groups question acknowledgements pro vertical vertical implement category explicitly text consisting adding equilibrium equilibrium decreases yield independently depending depending stationary correlated correlated squares learner learner solved variation evaluate fraction converges sign remains remains intermediate sufficiently sufficiently classified david exploration batch batch batch sciences plotted plotted plotted plotted illustrated uncertainty mozer mozer absolute partially determining selecting selecting modification delta delta successful oscillatory schemes online reached repeated repeated repeated repeated repeated procedures strongly heuristic heuristic heuristic success success success oscillations strategies satisfy highest satisfies situations explore unlike schedule poor xor xor detail issues helpful investigated parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity workshop momentum examined plausible queries portion explored logic epoch extent motivated stop analyzed explanation baum baum strictly constructing broad ran author nsf addressed fourth apparent profile poorly backprop item item formulated maintain exhibits pittsburgh pittsburgh reaches decreased traces traces traces traces converged converged summed summed summed hints extreme extreme phenomenon phenomenon phenomenon benefit restrict encoder encoder encoder encoder encoder encoder children children eliminated wrong consideration ranges tools siemens odd odd stated determination methodology monotonically monotonically affected presentations constructive repeat repeat repeat repeat repeat repeat financial mance irregular corre paul perfor lang lang evident evident searching facilitate repeatedly designing statement intersection influences switches dramatically summer munro munro munro munro munro propagating conjecture profiles profiles profiles discovering reflected beta cohn cohn cohn perpendicular exam formance alternate interact werbos werbos continues gener iso iso overhead iri termed stuck bring dramatic experi unpublished drives drives differently stimulating sponding corporate identifies virtually bold bold harvard identically identically pronounced dissertation ples maxi contrary iid iid iid iid iid iid iid iid iid fair gence scott halves trend counted parker parker ized mesh mesh mesh proceeding atlas atlas addi zone zone zone zone zone zone zone zone trapped elaborate vergence notions lid lid lid orbit continuing recovers mum dead dead dead dead dead dead dead dead sixth repeats reactive decrement sequencing pushed lay iter positively seemingly seemingly pattem pattem divides behav behav encoders ences economics doctoral ations interrupted backpropaga iden indefinitely aaa mad bringing belew locus envi tual negatively ered prespecified pattems pattems intent ior tum selections domly abruptly ronment bachtach bachtach depicting origins exogenous strategic tically verge ates touretsky touretsky touretsky kindly swings lection pauern pauern norton anticorrelated fective cyclically 
#@Munro_P,
#t5
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time set networks networks training training algorithm algorithm algorithm algorithm number number system system system error error error error error error state results results results results information problem problem problem problem problem problem performance performance performance performance space space linear case vector vector vector vector vector vector systems systems parameters parameters parameters noise noise noise noise weight weight functions unit distribution distribution distribution method approach point processing control large large large large large large large large large large large large large local local local local local rate rate rate rate rate rate rate rate rate rate rate rate test class optimal optimal optimal form signal algorithms simple paper examples small small small small small small small small size work methods methods methods methods methods fig fig fig fig fig fig fig fig step process process process current problems problems problems random random random random random show fixed fixed fixed fixed fixed fixed fixed fixed line line rule vectors general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation approximation approximation approximation average average average average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term note note experiments dimensional university variables computation computation solution solution solution solution solution independent independent independent independent independent defined defined sequence initial constant constant constant constant constant estimate estimate standard standard computer terms distance science left presented phase phase low nonlinear continuous abstract find find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction introduction estimation behavior behavior behavior behavior effect variance variance variance search search search search search search search search search search search search tion change change change complexity variable variable measure chosen chosen previous theorem bound cases distributed distributed distributed fact proposed correlation scale finite finite finite finite minimum minimum minimum minimum minimum minimum resulting sum sum called times times means means optimization optimization optimization optimization dimension applications knowledge true compared compared compared compared define define compute rates rates rates rates location location perform determined power power power steps contrast update descent descent descent descent descent descent source nets selection report department technique technique technique advances difficult directly curve solutions curves trajectory trajectory trajectory effects bit determine determine choice choice approximate speed speed speed con produce condition clustering clustering clustering developed developed developed backpropagation backpropagation backpropagation depends depends depends normal technical increases denote fast common theoretical require require eds adaptation square end ability future noisy noisy objective objective objective typically smaller fully interesting ratio ratio increasing special empirical principle direct making supervised magnitude magnitude magnitude run discussed practical apply side recently recently compare compare conventional approximately approximately works tions smooth yields converge converge converge converge converge converge converge converge converge converge converge achieve bounded improvement storage storage entire increased deviation deterministic deterministic deterministic deterministic setting setting setting setting setting runs runs trajectories conclusions numerical moody moody moody moody moody moody moody moody moody faster faster faster faster practice asymptotic asymptotic asymptotic asymptotic propose propose taking taking taking taking taking presence presence demonstrated california proportional labeled user user user start minima minima minima minima force reference appears pro pro monte carlo sequential estimating estimating ann mathematical changing recall easy text springer quality implies john decreases yield choosing choosing independently stationary squares squares labels completely completely converges converges converges converges converges key slow slow performing measurements classical expansion reduces roughly purpose penalty penalty remains distances euclidean degrees precision expect box figures includes automatic automatic prove discuss candidate holds tests major major uniformly uniformly uniformly computationally delta delta delta delta delta delta literature literature schemes traditional notice notice verlag procedures strongly superior issue quantity bar bar bar usual usual minimizes eigenvalue eigenvalue automatically moves illustrates jacobs jacobs jacobs jacobs receive law schedule schedule schedule schedule schedule schedule schedule schedule poor poor hessian hessian tech possibility func fundamental notion smallest smallest math math measurement gradients opposite thought taylor freedom art arbitrarily arbitrarily years mentioned asymptotically residual indicating stop slowly crucial variances fairly expensive expensive widely precisely choices choices commonly mathematics involve qualitative fluctuations fluctuations fluctuations exemplars exemplars exemplars exemplars exemplars argument argument varies lms lms poorly orders posed calculating proven adjust display expectations lim lim optimality modify drift drift drift drift drift drift drift drift drift narrow printed grows exemplar exemplar exemplar extending darken darken darken darken darken darken darken darken darken darken difficulties simplify stated determination star observing definitions responsible optimally degradation published excellent encountered bad bad consequences schedules schedules schedules schedules schedules schedules schedules schedules schedules creating repeatedly theoretically agree statement statement ignore escape escape escape yale yale annals email benefits additionally affects formance toy discontinuity statistic investigating investigating rough apparently apparently figs figs figs figs figs siam dramatic dramatic rewrite walk persistent moderate algorithmic excess excess excess converging confirm aid bold kth kth meth ods sian sian vicinity brackets gaus unusual focusing ensuring scattered denominator denominator excessive metastable preferable haven demanding stand eta locating substituted tics statis goldstein goldstein illustrating anticipate paid outlines noises optimiza niques multiples numerator southern accelerated robbins robbins normality kushner kushner monro monro adaline pertinent christian stabilizes cedure ume ume ume elliptical forty slows slows vital attains pare unavailable disciplines ime uhlenbeck uhlenbeck uhlenbeck ornstein ornstein contrasting ology jagged hes restoring drb 
#@Darken_C,Moody_J,
#t5
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time set set set set networks networks networks networks networks networks networks networks training training algorithm algorithm output output output output output number error error results information information information information information information information information information problem problem problem hidden based space space space space weights weights weights linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case vector order order order shown shown shown systems systems weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions neurons neurons neurons neurons recognition recognition method approach approach pattern pattern point point point image image image single single single single processing processing large large local local local local local neuron neuron neuron neuron neuron neuron rate rate rate patterns patterns patterns patterns patterns analysis analysis analysis class class class class class class matrix optimal optimal inputs inputs form form form shows signal signal signal algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian examples small size feature feature feature feature feature feature feature net net net net work work work methods methods methods step step field field field features features classification classification current trained trained trained structure structure structure structure structure structure structure structure problems problems problems random random random random random random random random random high memory response response response response response response response response response response representation representation representation representation architecture architecture architecture rule rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images general general speech parameter real real approximation approximation average average average average average average average average gradient gradient gradient gradient gradient term term note note experiments experiments experiments activity result university computation log log dynamics constant standard computer connections node node science science science prediction prediction prediction left left direction present present activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal object maximum learn learn learn components components outputs outputs abstract applied find computational likelihood references component component component component component component stochastic stochastic positive context introduction stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect variance variance variance variance variance variance recurrent tion change change change difference spatial rules signals learned learned higher center cases type type required required cortex represent represent represent represent make make fact region probabilities probabilities scale classes classes tasks total total respect sum means optimization potential applications applications applications filter negative compared application receptive receptive receptive receptive receptive receptive objects rates location perform active active constraints equal equal power approaches accuracy fields fields fields descent descent descent descent morgan morgan institute words synapses technique technique individual advances advances represents represents connectionist connectionist connectionist layers layers layers layers sequences sequences framework framework framework hinton hinton hinton hinton hinton view curves san san san san stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli detection conference efficient efficient full requires free world world pages pages pages pages backpropagation backpropagation nature nature constraint simply simply simply biological associative achieved discussion covariance normal normal normal normal feedforward feedforward feedforward feedforward transformation transformation limited inverse finding implemented assumed synapse supported require adaptation journal journal end pixel pixel pixel instance cluster cluster easily noisy kaufmann kaufmann objective objective objective objective needed testing york edge mechanism special principal principal principal principal principal principal principal principal pre direct window window window window supervised supervised depth depth depth early magnitude magnitude magnitude magnitude magnitude decay decay decay predict predict population directions directions directions advantage advantage reported lateral lateral introduced strategy strategy moving identical pixels pixels quadratic hierarchical hierarchical sejnowski sejnowski sejnowski sejnowski cognitive cognitive recently sufficient sufficient highly highly unsupervised unsupervised unsupervised volume volume tuning tuning tuning tuning tuning tuning tuning yields studies differential differential achieve achieve rl trans address mixtures symmetric observation organization grant constructed lead invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant extended derivative move touretzky touretzky width width width clusters clusters clusters clusters clusters clusters boundary setting setting half half half half half assumptions hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian competitive competitive competitive competitive competitive competitive competitive editors editors moody faster practice learns learns learns constrained mateo mateo suggest suggest suggest strong strong demonstrated demonstrated california proportional proportional turn derivatives derivatives connectivity minima force acknowledgements explicit explicit derive laboratory tuned tuned tuned tuned mathematical distinct dept explicitly explicitly infinite dimensionality dimensionality transformations text text angle unique interaction mutual springer springer extraction expectation competition competition competition competition yield yield focus variation organizing forms forms soft soft soft soft sizes discrimination sign sign sign sign earlier performing normalization normalization normalization false kohonen kohonen kohonen bell eigenvalues subspace specifically specifically variations holds neighbors discussions determining aspects closely uniformly maximal maximal presentation presentation invariance invariance invariance invariance invariance invariance invariance tend tend verlag verlag interested lie lie built vary simplified dot dot dot dot dot paradigm paradigm paradigm nips highest highest maximization received consisted overlapping subsequent disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity extract extract extract extract deal receive extend presents diego diego investigate exhibit experience lippmann lippmann lippmann helpful giving detectors detectors detectors detectors detectors detectors relationships structured structured working eigenvectors encode encode encode encode surfaces neu patch closest editor opposite opposite equally perfect aspect detector hebb hebb hebb hebb submitted growth growth smoothness unstable slope biology nowlan nowlan nowlan implementing desirable desirable hyperplane hyperplane hyperplane hyperplane hyperplane mation patches author preceding integrating elman elman lack share remove span span berlin anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti characterize characterize extracting extracting maximizes popular popular prevent enables coherent coherent coherent coherent coherent coherent coherent coherent coherent sophisticated neuro coherence owl wesley pole pole shifted redundant leen leen leen addison generator investigation pick pick zemel zemel hyperplanes controlling discovery eliminate turned wrong oja oja oja oja oja oja oja promising logarithmic attractive familiar interpret viewpoint viewpoint removing neurobiology sanger sanger salk heavy introduces becker becker becker becker ascent intended evident evident stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo nonlinearities membership membership bins jolla jolla rich alternatively characterization ignore baldi baldi insensitive dividing severe fellowship removal presenting responds encouraging copy intrator intrator chapter discovering decorrelation decorrelation favor goals geoffrey decays discontinuity discontinuity discontinuity degraded degraded terrence maximally differentiation cosine exceed hornik hornik tied covered denver denver preserve barlow barlow accounted happen sweeps bring normalizing durbin travel exploratory computa develops develops ucsd served stimulating characterizing discretized mcdonnell suffers adaptively integrates polarity dichotomy positives sliding sliding sliding sliding edition differentiate vicinity steve discovers monitored enabling spanning schraudolph schraudolph schraudolph proximation pew plausibility formulations albeit stereograms stereograms stereograms stereograms stereograms stereograms clump plain machinery analyzer oooo parentheses novelty behaved mitchison mitchison mitchison densely rescaled karhunen karhunen karhunen kung kung disparities disparities tony transfor acuity permission particu violations attain awi awi attend negation survive owi intriguing reversing surely vital deficiency invariants invariants invariants invariants invariants eee counteract appreciated miall collapsing xiy jolliffe jolliffe larly 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#@Schraudolph_N,Sejnowski_T,
#t5
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#*network network learning neural neural neural neural neural neural neural neural neural neural neural neural function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure time time time time time time set set set set networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number system system system system system system system results results results results information information problem problem problem problem problem problem problem problem problem problem problem problem models performance based based space linear linear case case case order order order order order order order shown shown shown shown shown systems systems parameters parameters parameters functions functions functions functions functions functions unit method method method method method method method method method method method method method approach approach approach approach approach point point point point point point point single single single single processing large large large large large large local local local local local local local local local local local analysis optimal form form form form form form form form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple visual paper paper small small size feature net net net net net net net net net net net net net net net work work task methods methods methods methods methods methods methods methods methods methods methods methods step step points points points points points points points points points points points points field field field field field field field features features features features level structure problems problems problems problems problems problems problems problems problems problems random response similar similar similar show show show show show section fixed fixed fixed fixed fixed general general general parameter parameter parameter parameter parameter approximation approximation approximation theory theory theory theory theory theory obtained obtained obtained obtained term term term term term note result result result result university variables variables variables variables variables variables variables variables computation solution solution solution solution solution solution solution solution solution found found found dynamics dynamics constant table table estimate estimate estimate standard terms terms terms terms terms terms science presented presented present press press press components components components basis basis nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied applied find find computational computational computational computational computational computational computational computational computational computational computational convergence convergence convergence convergence properties references component component component stochastic due due due due ieee positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure adaptive adaptive adaptive adaptive context context introduction introduction hand statistical statistical statistical statistical statistical statistical statistical parallel parallel parallel parallel parallel change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference complexity variable variable variable chosen chosen chosen chosen chosen chosen part center previous previous cases cases required required required long conditions expected equations markov fact fact fact fact fact fact fact fact techniques techniques techniques proposed length length forward scale scale scale simulations simulations minimum minimum minimum minimum resulting classes total simulation respect respect performed called times regions mapping means means optimization optimization optimization optimization optimization optimization made made natural natural global global global global obtain original original true application series rates proc related constraints constraints constraints constraints discrete discrete discrete discrete power approaches mit accuracy larger contrast contrast contrast fields update descent morgan report report institute institute implementation technique technique technique technique consists consists internal individual advances represents represents represents difficult difficult final addition addition considered framework framework directly curve curve curve curve solutions solutions solutions solutions solutions solutions curves design trajectory determine determine efficient efficient significant approximate approximate free free free free free free free speed vision basic pages pages pages increase produce condition randomly developed entropy entropy entropy entropy entropy entropy entropy entropy entropy actual provided finally finally iteration nature constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint simply simply simply technical technical technical describe limited limited close corresponds surface surface surface finding finding effective generate theoretical require require require adaptation adaptation square end end ability cluster easily degree kaufmann objective objective objective objective objective objective objective simulated simulated simulated simulated simulated simulated simulated simulated typically typically typically typically typically smaller underlying underlying underlying underlying needed hopfield hopfield hopfield hopfield dynamical dynamical fully programming mechanism mechanism matching leads leads making international magnitude idea combined added architectures improved improved discussed discussed discussed discussed discussed improve exact advantage typical typical typical subject quadratic quadratic quadratic subset recently highly highly previously works tuning solve solve studies studies differential definition background background locations modified observation observation bounded improvement increased lead occur occur occur suggests alternative locally touretzky deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic setting conclusion critical critical critical critical critical critical greater trajectories depend differences differences numerical numerical numerical numerical faster practice constrained constrained constrained constrained constrained constrained constrained constrained constrained temperature temperature temperature temperature temperature temperature temperature temperature hard hard physics physics physics physics physics external solid turn turn exist decrease decrease decrease relationship introduce derivatives derivatives manner manner manner minima minima minima minima minima minima minima annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing areas explicit explicit appears appears construct written longer longer primary laboratory laboratory explicitly explicitly linearly physical transformations remaining easy slightly slightly text applying decreases yield national national reconstruction viewed restricted fraction approximations approximations approximations evolution evolution forms key slow additive convex convex convex convex combining roughly roughly roughly roughly add penalty penalty penalty penalty penalty penalty tracking valid valid initially assigned assigned construction degrees formulation instances instances illustrated illustrated candidate coupled successfully major reason reason regular straightforward extra extra extra extra efficiency efficiency efficiency efficiency suitable modification modification modification computationally paths included schemes schemes situation tend tend tend reached summary notice conf procedures procedures procedures procedures procedures contained prob heuristic heuristic heuristic heuristic superior superior superior superior issue contribution sin oscillations oscillations satisfy comp comp comp notation involved usual usual relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation leading leading automatically attempt simpler remain schedule schedule schedule schedule schedule schedule schedule powerful powerful transformed transformed transformed requirements difficulty involving replaced issues issues dotted dotted dotted dotted behaviour behaviour behaviour behaviour giving biol int authors authors decisions root complicated complicated statistically notion notion removed plausible editor editor adapt generalisation generalisation thought ensure ensure ensure bifurcation bifurcation obvious algo freedom explored expressions academic consist great ment piecewise distinguish improves adapted expensive stanford straight satisfied division broad immediately implicit lowest qualitative qualitative sun mechanics mechanics requiring improvements greatly substantially substantially empirically understood effort adjustable treated schematic requirement requirement limiting proven incorporating tank tank tank prevent substantial coherent sophisticated sophisticated display yuille eventually displays displays displays merging merging merging merging merging globally cybern analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue saddle saddle saddle saddle optimality lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange girosi resources approximates homogeneous homogeneous purely multipliers multipliers multipliers multipliers multipliers platt platt systematic multiplier multiplier multiplier multiplier multiplier multiplier multiplier multiplier consideration consideration consideration ments promising promising overcome satisfying city city city city city city city city imposed los los los occurring monotonically monotonically responsible modifications preparation enhanced combinatorial combinatorial combinatorial combinatorial heuristics heuristics heuristics heuristics heuristics embedding mjolsness ensures paul displayed ascent ascent ascent originally schedules elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic peterson surprisingly augmented augmented cpu cpu cpu santa santa santa convergent convergent convergent outlined outlined bertsekas escape temperatures entropic entropic shorter willshaw willshaw encouraging smoothly seek seek chapter avoided avoided algebraic care rithms approxi convert eliminating altered overhead overhead proach importantly importantly drawback alternatives barrier geiger exchange avoidance behave retained retained dramatic durbin durbin experi experi wider lems tour tour lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian externally externally externally externally externally accordance ers firstly blake suite tsp tsp tsp tsp tsp tsp tsp tsp tsp arrow arrow arrow hoc hoc optimisation optimisation optimisation optimisation optimisation optimisation optimisation optimisation optimisation optimisation optimisation loosely inclusion burr station floor floor floor floor obey kirkpatrick meth inefficient systematically rameters isolation inspection syntactic syntactic salesman salesman salesman salesman ods aip merged kinetic kinetic kinetic foreground investment investment alamos alamos alamos vanishing vanishing vanishing mul ensuring prescribed prescribed prescribed prescribed syst syst kuhn modest replaces drawbacks sparc occasionally notions plotting mft mft mft mft mft proce suitably lowered apparatus apparatus apparatus schematically tics undergoes ascending bifurcations terminated biasing volumes analysed dash dash deformable syntax lowering lowering tours tours travelling travelling travelling travelling inverses generalised generalised generalised trivially valley valley valley valley valley valley valley hoped hoped hoped sole entails vecchi inexpensive optimise optimise traced stolorz stolorz stolorz stolorz stolorz stolorz focussed cumbersome gle unwanted unwanted unwanted mecha philosophy philosophy mations inertial dure signifi minimisation pursuing strained gelatt crucially precludes interplay garrett tropy zisserman offering sight tucker quoted invari valleys valleys valleys valleys prohibitive barriers ensuing bart deepest trap barr trail nism ably distinctly peculiar minimises parallels confronted minimised tages sation ently trix combinatorially combinatorially inversions occasion occasion multipli laxation inher tackling tackling adaptations generalising obeyed uncon begining 
#@Stolorz_P,
#t5
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#*network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data function function function function function function function function function function figure figure figure figure set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm output output output output output output number error error error error error error results results results results results results units units units problem hidden hidden performance based based based based weights weights weights weights weights weights weights case case case case vector vector vector vector vector shown systems values values values values values values probability probability probability probability probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight functions functions neurons unit distribution distribution distribution distribution distribution distribution distribution method method method method method method method approach approach approach approach approach pattern pattern point processing control large local rate analysis analysis class class class class class class class class class class class class class class optimal optimal optimal shows examples small small net net net work task methods methods methods classification classification classification classification classification trained trained trained trained trained trained random random random random random random similar similar similar architecture fixed fixed rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general generalization generalization generalization parameter parameter parameter average theory obtained term experiments experiments dimensional result university computation computation research initial table table table table table table table table estimate estimate estimate estimate estimate estimate standard standard standard standard terms distance left left presented map present activation nodes maximum learn components components components basis continuous continuous sample sample sample sample sample abstract back density density density density density density density density density density density density likelihood references due ieee ieee ieee procedure procedure procedure procedure propagation introduction introduction complex estimation estimation estimation estimation estimation estimation estimation estimation statistical generated generated generated generated tion tion classifier classifier classifier chosen chosen chosen chosen cases cases type conditions conditions bayesian expected expected expected fact fact proposed probabilities probabilities forward classes ing total regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression mapping mapping mapping mapping mapping dimension natural natural obtain original original original original original artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial samples samples samples samples samples true compared cross cross cross cross cross cross receptive rates rates proc perform perform distributions discrete cortical equal equal equal equal connection fields fields train train modeling selection selection selection institute institute loss loss loss loss kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel connectionist layers considered considered experiment experiment experiment experiment experiment directly classifiers classifiers choice approximate statistics free pages pages validation validation validation validation validation produce conditional conditional conditional clustering criterion criterion criterion provided selected selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation sampling sampling normal technical feedforward feedforward feedforward denote denote denote fast actions amount common generate generate journal instance future easily rumelhart noisy objective simulated probabilistic uniform squared pre international magnitude magnitude magnitude magnitude minimize minimize minimize choose improve separate include quadratic recently recently compare works works smooth smooth trans trans modified sensitive expression expression lead deviation deviation deviation feed locally white white white conclusions performs moody moody moody practice asymptotic suggest taking proportional radial minimizing program suppose suppose suppose van produces index index generating generating generating estimating tuned pruning easy adding adding minimization minimization minimization minimization formed select select choosing estimator estimator estimator estimator estimator viewed densities densities suggested suggested suggested suggested converges discrimination smoothing smoothing smoothing smoothing smoothing additive additive additive additive additive additive fitting add add add add iterative transactions includes priori discuss uniformly schemes notice notice notice notice verlag procedures procedures procedures procedures success interpreted classify sin criteria generalize minimizes minimizes attempt attempt minimized poor overfitting overfitting estimators estimators estimators estimators biases discriminant scalar giving mappings possibility maximizing proved editor thought friedman friedman friedman logistic improving stop analyzed perspective mation separately localized bandwidth argument requiring evaluating consistency consistency flexible pseudo capability capability backprop dots variant weigend weigend weigend weigend gave chose begins darken darken darken hope nonparametric nonparametric hertz motivation started contexts den uni uni lawrence chooses creating draw erlbaum exploiting divide posteriori annals annals magnetic chaos reports associate associate evoked summarizes ijcnn parzen parzen denoting picked associates sam esti preprint experi ping partly huberman ples measurable characterizes characterizes appl minimizer watson watson watson watson watson physica validated validated repetitions repetitions repetitions repetitions wagner wagner wagner dow dow dow favorably orig tics statis parsimonious silverman silverman silverman plain agation rosenblatt theor mented mild analogously helsinki helsinki render adaptable adaptable yix suit resemblance stepwise ein finland borel optimizations devroye devroye devroye advocated wash argues yll overly specht specht specht specht specht marquardt nordita wien deteriorate iig inal irdle irdle devia technometrics blindly dicting valida puters feels discourage liere 
#@Holmstrom_L,Koistinen_P,
#t5
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#*network learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural function function function function function function function function function function function function function function function function function function set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks error error results results results results results results information information problem problem problem hidden hidden hidden hidden hidden hidden hidden space space space space space linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer case order order order order order order order shown shown systems systems values values probability probability probability probability functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution method point point single single single single single processing large large large local class class class class class class form form shows shows simple paper paper examples small small size net net net work work work methods methods methods methods step level problems representation representation representation representation representation equation section fixed fixed general parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory theory theory theory obtained obtained obtained term note note note note note note note dimensional result result result result result university university university university research research log log defined constant constant constant computer terms terms connections connections connections map machine press press press basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous sample abstract applied applied applied properties references component due due ieee positive decision introduction complex complex hand estimation estimation statistical statistical statistical statistical effect generated difference complexity complexity variable measure measure measure representations representations representations representations representations representations chosen chosen chosen part center previous theorem theorem theorem theorem theorem theorem theorem theorem theorem cases required required multiple multiple multiple conditions make proposed classes classes classes classes classes ing regression regression regression regression regression multi called called potential dimension natural applications applications study artificial relative series related connected distributions distributions connection connection connection dependent dependent nets report department department ai cambridge domain domain domain view bit determine free free free free free con condition bounds depends depends depends achieved measured feedforward feedforward arbitrary denote denote denote denote denote actions proof proof proof circuits supported supported main eds eds journal degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree makes needed unknown interesting ratio ratio uniform uniform uniform direct direct direct direct polynomial polynomial polynomial polynomial polynomial choose choose robust side subset subset engineering engineering interest dimensions observations works tions smooth trans definition definition definition positions positions positions improvement improvement studied studied suggests extended extended derivative generally generally setting conclusions operator operator valued depend sigmoid measures strong california user exist exist derivatives question acknowledgements pro written metric metric multilayer electrical unique springer choosing national expressed depending depending depending open open approximations approximations decomposition understanding approximated completely similarly translation partition partition partition constants classical classical spaces spaces spaces spaces spaces spaces spaces spaces spaces sufficiently sufficiently norm avoid sciences prove holds simplicity determining determining compression closely suitable literature situation identity compact compact verlag verlag interested hold quantity write wavelet board ill ill ill approximating approximating approximating american existence working proved func understand examined examined transmission possibly necessarily spline spline spline spline spline spline spline spline spline spline spline obvious obvious academic utility submitted defines great piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise theoretic theoretic smoothness smoothness smoothness worse turns purposes widely widely style operators immediately mation mathematics mathematics consequence author author understood understood understood amounts peter effort haussler splines splines splines splines splines splines splines splines splines splines splines splines splines polynomials calculating berlin partitioning partitioning popular boston pac pac benefit notes oxford restriction girosi flexibility rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational satisfying replacing efficacy canonical canonical canonical canonical published bartlett bartlett bartlett bartlett originally originally barron deg suggesting partitioned santa inf inf inf balancing cam robert piece theorems theorems theorems theorems par copy ideally ideally ideally generalizations generalizations ical chapter australia australia tight approxi wise flip topic barrier barrier barrier barrier barrier barrier barrier page page parametrized parametrized parametrized nal williamson williamson williamson williamson exploited ward rarely lecture remarkable bridge dim achievable achievable achievable achievable achievable achievable 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#@Bartlett_P,Williamson_R,
#t5
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training training algorithm algorithm output output output output number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden performance performance performance performance performance performance performance performance space space space space space weights linear linear layer layer layer layer case order order order shown shown values values values values values values values values parameters parameters parameters parameters parameters parameters noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution method method point point single single single large large test test test test test test test test test test test test test test test test test test optimal inputs inputs inputs inputs form shows shows shows algorithms simple paper examples examples small net work work points classification process trained trained trained trained trained trained trained trained trained problems problems problems problems problems problems problems high high high high high response response response response response response response response response response similar similar similar similar representation representation representation representation representation architecture architecture parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average gradient gradient gradient gradient obtained term term term term term term term term term dimensional dimensional dimensional dimensional result variables variables variables solution solution solution solution sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant table table standard computer terms terms terms science prediction prediction prediction prediction prediction direction presented present low low low low sets sets sets sets maximum range range range position nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract convergence references stochastic stochastic stochastic due context introduction complex complex complex complex complex complex estimation estimation estimation estimation statistical statistical variance variance variance tion energy difference difference difference variable variable assume measure measure measure measure learned learned learned learned learned chosen higher previous previous previous type type type type required required multiple good good represent fact fact region errors errors errors errors minimum classes classes total regression regression regression computed computed sum sum sum sum sum sum sum sum dimension negative negative vol compared compared compared compared compared desired series series series series series compute compute location perform equal comparison support descent descent descent descent nets nets modeling technique joint difficult graph graph graph graph ai ai considered domain curve bit determine approximate statistics free free give produce produce weighted weighted weighted weighted weighted robot robot robot robot robot robot robot robot robot robot robot robot velocity types provided iteration achieved normal feedforward feedforward tested tested limited limited close close inverse inverse inverse inverse inverse inverse corresponds amount journal square square ability easily degree degree degree degree degree degree degree degree degree degree degree degree degree degree makes noisy noisy noisy fit fit fit fit fit fit typically needed needed coefficients coefficients coefficients coefficients coefficients projection projection projection projection projection projection projection increasing increasing squared details details iterations stored normalized normalized normalized magnitude decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial added added improved discussed directions property separate typical apply trees highly volume works axis axis smooth smooth smooth smooth converge achieve bounded improvement improvement entire grant grant arm arm arm arm arm arm arm arm arm arm arm arm arm studied generally runs runs half half segment segment differences sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid measures moody moody moody moody characteristics sigmoidal sigmoidal acknowledgements produces longer factors metric multilayer easy slightly slightly consisting adding frequencies quality john john squares squares squares evaluated fraction fraction fraction approximated earlier intervals foundation degrees box absolute reason determining determining suitable suitable included ten ten reached composed graphs graphs graphs superior superior superior built vary computes highest highest highest highest highest highest highest reach american association optimized pursuit pursuit pursuit periodic fewer fewer fourier fourier fourier fourier fourier rest investigated scaled scaled scaled authors comparable tanh func phases coefficient extremely extremely friedman noted logistic epoch arbitrarily years years years asymptotically cos formula formula formula capabilities benchmark lies nonlinearity nonlinearity nonlinearity comparisons producing worst commonly separately universal exemplars explained explained explained apparent greatly substantially substantially pure pure pure flexible flexible flexible flexible flexible amounts amounts amounts tional poorly poorly atkeson treated polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials monotonic monotonic monotonic monotonic sums boston boston boston boston boston boston boston boston boston boston boston boston boston boston boston newton redundant ratios count count count rational rational rational rational rational rational rational fits breiman determination nonparametric hertz regarded regarded evident nonlinearities tic approximators deg deg deg permutation adopted acknowledge onr rms rms rms yale yale leaving annals fellowship ber torque torque torque torque revealed year exception amplitudes acceleration afosr cosine cosine cosine cosine cosine cosine cosine noting unconstrained cation worth covered superposition parametrized gauss housing housing housing housing housing housing housing housing housing housing sigmoids sigmoids sigmoids sigmoids sigmoids sigmoids sigmoids sigmoids moderate chris continued powers december station joints zeros meant twelve tained denominator denominator denominator denominator denominator denominator supposed tern extrapolation haven disadvantages disadvantages huber dealt monthly prices prices des helped manipulating thirty mild brooks clue stochas sunspot sunspot sunspot sunspot sunspot sunspot sunspot sunspot sunspot sunspot shoulder shoulder qualities wadsworth elbow extrapolate extrapolate restricts ric wei wei squaring stuetzle sunspots sunspots sunspots marquardt marquardt marquardt ool ool sixteen levenberg levenberg levenberg modifi alx mildly mildly proximations smooths whichever rationals rationals rationals prospect 
#@Moody_J,Yarvin_N,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural input input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number error error error error error error error error error error error error error error error error error error error results results results results units information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden based based based based based based based based based based linear linear linear linear linear linear linear linear layer layer case case case case case case case case case case case vector vector vector vector vector order shown systems values parameters weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit method method method method method approach approach pattern point point point point point point point point point point point point point point point point point point point point point point point point single single single single large local local local local local local test test test test test test test test test patterns patterns analysis analysis class class optimal optimal optimal optimal optimal optimal simple paper paper paper paper examples examples examples examples small small small size work work work work work methods methods methods methods methods methods methods methods methods methods methods methods methods fig fig step step step step step step step points points points points points points points field field current trained structure problems problems problems problems problems problems problems problems problems problems similar representation show show show section section section section section section line line line line rule rule vectors general general parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term note note note note dimensional result university university threshold solution research defined defined defined defined defined found sequence sequence sequence sequence sequence sequence sequence standard standard standard terms terms terms terms terms terms science science direction direction direction direction direction direction direction presented presented presented presented present present present maximum maximum maximum maximum maximum position position basis basis continuous continuous continuous abstract applied applied applied applied applied applied back find find find find convergence convergence convergence references stochastic due ieee ieee ieee positive positive procedure procedure important propagation context introduction introduction effect effect effect generated cost search search search change difference complexity part part previous previous previous theorem cases required required required required required required required required required good good good good long make fact fact techniques techniques techniques techniques region region region region minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum simulation computed computed computed called optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization dimension made natural study knowledge obtain obtain artificial desired series provide provide define define define define compute compute perform determined determined equal steps accuracy contrast descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent selection selection selection words version technique technique technique technique considered considered considered framework framework framework computing additional full choice significant basic basic basic produce condition randomly randomly randomly randomly criterion criterion criterion criterion criterion criterion criterion criterion criterion lines path provided backpropagation backpropagation backpropagation backpropagation backpropagation depends achieved achieved normal feedforward feedforward feedforward feedforward feedforward feedforward limited close assumption actions circuits short generate require require eds eds journal easily including fit technology transfer transfer transfer transfer transfer programming york york york york details details details max max max max max max max magnitude idea idea attention attention run added description description denotes discussed improve recent recent exact separate element element practical introduced include include include machines engineering sufficient varying works tions solve smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth yields converge converge converge achieve address chain generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized improvement storage exists expression expression expression expression expression expression lead lead concept concept concept concept occur occur occur occur occur derivative derivative locally locally locally locally locally locally locally deterministic occurs occurs occurs occurs demonstrate runs runs runs runs runs runs runs runs half starting starting conclusions numerical clear clear faster practice weak characteristics sigmoidal demonstrated proportional minimizing minimizing start exist exist plane decrease decrease manner denoted longer ways plot laboratory mathematical mathematical dept multilayer electrical involves adding adding applying springer shift boolean john john john yield choosing operations completely converges converges performing convex convex convex convex convex penalty sufficiently sufficiently norm norm norm norm norm norm norm norm norm norm transactions transactions transactions box thesis priori perceptrons contour extension discuss variations reason aspects aspects suitable suitable society delta wij literature literature situation reached reached characteristic compact verlag procedures cun cun success stopping stopping stopping stopping stopping stopping stopping sin involved involved involved minimizes received received received received approximating approximating satisfies satisfies deal minimized employed employed wiley wiley wiley poor xor xor xor create create discriminant discriminant behaviour behaviour giving ideas ideas tech possibility possibility complicated complicated tanh tanh func math gradients gradients naturally concepts initialized initialized initialized message improving phd electronic defines optimum great advanced piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise smoothness failure satisfied satisfied widely strictly strictly strictly division directional broad incorporate sgn sgn sgn sgn sgn arise ion implicit computers depicted author radius addressed addressed conjugate composite composite composite led lack lack treated frequently berlin marginal substantial replace replace tolerance june proposition proposition differentiable proofs indices notes optimality extensive concerned concerned null encoder encoder encoder impossible nonzero fails fails systematic consideration consideration difficulties difficulties difficulties difficulties difficulties overcome overcome replacing intelligent nearby fail north north motivation evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations encountered holland holland overview guarantees express matter repeatedly draw draw steepest steepest steepest sons sons sons ball ball outlined unchanged ure ure ure outline solves formulate employs convenience obtains arg australia australia continuity visited management met retain retain overhead relates employing termed siam happen simplex spite circumstances discontinuous satisfactory converging todd suffers conceptual hull incorporation coincide substitute neighbourhood neighbourhood minimax minimax accommodate edition oscillates oscillates amsterdam amsterdam stabilizing weakness dealt lips heidelberg calculus calculus wolfe wolfe itd canadian trouble trust trust trust trust trust trust trust trust trust trust vation queensland queensland comput succeed overcomes overcomes lastly misleading bundle bundle bundle bundle bundle bundle bundle bundle bundle bundle bundle arose arose cutting terminating viability viability dem descend clarke situ wio wio brady ive monographs nicholas downs downs downs downs fion fion adelaide surroundings texts smearing redefine multitude kan fletcher fletcher defence moti diffi staying org delicate llw lect discourage ifo 
#@Downs_T,Redding_N,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural input input input input input input input data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number error error error error error error error error error error error error error error error error error error error error error error error error error error results results units units units units problem hidden hidden hidden hidden hidden hidden hidden hidden based based based space weights linear linear linear linear linear linear linear linear linear layer layer case vector order order order order order order order order order order order shown systems systems values values probability noise noise weight functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit method method method method approach approach pattern image image image image image image image image single single single processing processing processing processing large large local test test test test test optimal optimal inputs inputs inputs inputs inputs form shows shows shows shows algorithms algorithms algorithms simple simple paper examples small feature feature feature feature work task task task methods methods methods methods step step step features features features features features features features features features features features features features features features features process process current trained structure random random high high high high high high high response fixed fixed fixed line images images generalization real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states theory theory gradient gradient term term term term term term term term term term term term term term term term term term term note note dimensional dimensional dimensional dimensional dimensional threshold variables variables variables variables variables variables solution research independent target target standard terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms science prediction presented present low nodes nodes machine machine basis basis basis nonlinear nonlinear nonlinear abstract applied applied applied references ieee ieee ieee procedure adaptive adaptive adaptive introduction complex effect parallel search complexity variable variable variable assume lower measure representations chosen chosen chosen higher higher part part part previous theorem type type type required tree tree tree expected make make finite finite finite finite finite resulting resulting resulting resulting classes ing regression regression regression regression regression regression regression regression regression regression regression regression regression respect called factor potential potential potential potential natural filter original original original original original original samples samples samples represented true application application application desired desired provide define compute compute compute proc proc proc perform determined goal related related brain mit mit steps steps comparison fields fields train descent descent modeling selection morgan report institute department loss version version version version technique technique technique consists advances joint joint joint joint joint final layers addition addition addition ai considered cambridge computing directly directly additional estimates top top top top determine determine determine approximate approximate pages pages pages con con coding developed lines product product product product product product product product provided backpropagation iteration measured feedforward describe arbitrary tested fast limited assumption predictions circuits implemented generate supported theoretical face square pixel pixel pixel ability future development including including including including kaufmann pairs pairs pairs combination combination combination unknown coefficients coefficients coefficients coefficients coefficients technology block testing significantly projection york structures structures principle leads leads squared squared squared squared squared squared bottom magnitude polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial minimize minimize choose choose choose choose added predict predict predict predict recent pair separate practical strategy include include include include include pixels trees trees cognitive recently engineering interest trans trans trans sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse entire exists exists lead lead suggests extended extended predicted predicted correctly touretzky flow row row greater reduce reduce operator valued accurate sutton sutton sutton sutton sutton sutton sutton performs moody practice suggest largest cycle cycle cycle cycle cycle cycle sigmoidal sigmoidal sigmoidal radial exist decrease decrease decrease decrease decrease decrease decrease decrease decrease relation pro sequential describes describes laboratory multilayer multilayer infinite infinite infinite involves remaining remaining adding adding gaussians applying blocks expectation potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials select choosing national organizing approximations approximations approximations approximations approximations approximated approximated approximated approximated similarly earlier spaces spaces intervals add iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative interpolation generation construction construction construction construction construction construction construction norm norm expect existing existing subspace sciences maximize included included included included included included successful efficiently orthogonal orthogonal orthogonal road road repeated induced heuristic heuristic interested dis contribution built write write nips computes computes leading leading predictor attempt approximating acknowledgments create create lippmann helpful helpful fourier successive successive mse mse mse mse mse applicable structured maximizing maximizing workshop cover coefficient man man predicting predicts thought switching utility finds attempts attempts attempts massachusetts residual growing growing processed drive purposes constructing products products products products laboratories laboratories laboratories universal depicted cybernetics preceding sun requiring led lms lms lms poorly incorporated incorporated incorporated incorporated incorporated polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials singer richard richard simulator comments irrelevant irrelevant irrelevant contribute room accomplished forming gabor gabor gabor member generality adds consideration minutes minutes sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger heuristics iteratively iteratively decide widrow widrow scan scan barron barron barron ahead ahead ahead ahead ahead ahead ahead record grants avoiding dense sequentially rms rms ence drop fellowship creates incrementally incrementally incrementally chicago avoids graduate individually denver intl siam drops continually gorithm correlate correlate suggestions stops fortunately opti christopher justification powers inclusion inclusion inclusion usefulness usefulness incorporation contributes measurable sij poly maxi proves arriving smc smc cho correlates nih defense united eighth hoff hoff subnetwork subnetwork subnetwork subnetwork subnetwork lisp deeper nth participate participate ell gmdh gmdh gmdh gmdh gmdh gmdh ire orthogonality orthogonality xlo justifies partic rect struction struction marcel dekker bizzi bizzi iee draft cook sparcstation xlx gte gte gte gte gte regressions polyno bibliography succeeding waltham waltham waltham xixj xixj pres mial monomials monomials monomials plication wescon arx arx arx arx arx craig karpinski xll xll xll symbolics depiction risks xxx integrable terence river lection mizes emilio farlow cony 
#@Matheus_C,Sanger_T,Sutton_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number system system system system system system system error error error error error error error error state results results results results results results information information information information problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based space space space space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case vector vector vector vector vector vector vector order shown shown shown systems systems systems values parameters parameters parameters noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions distribution distribution recognition recognition recognition recognition recognition method method method method method method approach approach approach approach approach approach pattern pattern pattern pattern pattern single single processing processing processing large large large large large large large large large local local rate test patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix optimal optimal inputs inputs inputs inputs inputs shows shows shows shows algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small small small small small small small size size size size size net work work work work work task task methods points field field classification classification classification classification classification classification classification current current current trained trained trained trained problems problems problems random random high high high architecture rule vectors vectors vectors speech speech parameter parameter parameter parameter parameter parameter parameter gradient gradient gradient term note experiments dimensional dimensional dimensional dimensional result result university university university computation solution solution solution solution research research research research research research research found found found initial initial initial initial estimate estimate estimate estimate standard standard standard standard standard node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node science direction direction direction direction direction direction direction present low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets maximum range range range press press press learn learn learn learn position position position position position position components basis basis outputs continuous sample sample sample sample sample abstract applied applied applied applied applied back back convergence convergence properties likelihood references component component component component component component component component component component component component stochastic adaptive decision decision decision decision decision mixture mixture mixture mixture introduction hand estimation estimation effect dynamic generated variance variance variance variance variance variance variance variance measure measure measure signals learned learned learned learned higher higher cases cases cases cases cases required required required required good good long long long long markov make make techniques techniques techniques techniques region proposed proposed proposed proposed proposed correct errors errors forward forward forward forward forward forward scale minimum minimum minimum respect respect multi multi multi multi multi multi sum sum sum sum sum sum elements means means potential made made made made negative relative samples samples true compared application receptive receptive receptive receptive receptive receptive receptive determined determined distributions distributions distributions gain brain comparison comparison comparison larger fields fields fields fields fields update train descent descent modeling morgan morgan morgan morgan report report institute implementation technique technique technique technique technique technique consists individual individual individual individual individual individual advances advances advances responses responses layers scheme scheme addition computing computing equivalent san san san san san san effects effects effects requires approximate approximate approximate approximate approximate approximate free world speed estimated pages pages pages pages pages weighted weighted clustering criterion criterion criterion criterion bounds area area product selected backpropagation backpropagation nature constraint simply achieved measured covariance covariance increases tested fast limited close close corresponds surface finding amount implemented implemented main end hypothesis future future kaufmann kaufmann kaufmann kaufmann smaller smaller mlp mlp testing matching matching leads leads leads principal principal principal principal principal principal principal principal principal principal principal principal principal squared numbers pre pre stored magnitude decay run added added perceptron perceptron perceptron perceptron improve directions directions directions directions directions recent recent correlations separate reported reported reported introduced introduced include include subject side side subset cognitive highly previously previously unsupervised calculated calculated calculated calculated calculated calculated calculated match studies studies converge achieve diagonal mixtures mixtures mixtures evaluation positions positions positions positions positions chain improvement sensitive sensitive increased increased parts parts lead occur occur occur deviation deviation deviation derivative derivative matrices alternative correctly correctly feed feed feed feed feed feed touretzky touretzky touretzky touretzky deterministic clusters boundary boundary boundary generally half place place greater conclusions central numerical clear clear moody exponential practice mateo mateo mateo mateo taking strong largest largest reduction demonstrated radial radial start derivatives derivatives derivatives derivatives groups groups minima identification appears appears pro pro ways generating generating estimating plot plot plot pruning pruning pruning pruning pruning pruning pruning pruning pruning sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity integrated equilibrium applying applying select john john john john yield independently review correlated evaluated updated updated updated showed decomposition decomposition decomposition forms sizes completely updates updates updates updates updates updates updates updates updates updates updates updates updates allowed allowed sign sign reasonable performing measurements measurements spaces fitting add iterative iterative iterative boundaries boundaries initially calculate david david david david degrees eigenvalues eigenvalues eigenvalues subspace mozer mozer mozer candidate gating gating gating gating determining selecting identified importance suitable suitable suitable modes identify build build comparing situation plots tend miller ten reached capture traditional road road road quickly kind repeated cun cun allowing allowing split split split split split split split split split split split split split criteria satisfy list eigenvalue eigenvalue denker denker leading modelling modelling modelling trains carried carried carried powerful collection exhibit varied detail detail detail detail detail detail replaced hanson hanson hessian lippmann divergence divergence preliminary helpful scalar tech possibility possibility possibility eigenvectors eigenvectors eigenvectors stream complicated oscillation oscillation oscillation oscillation oscillation cover cover coefficient coefficient gradients gradients trace trace trace trace editor editor editor editor editor generalisation created created created changed implementations singular quantities portion freedom perceptton art multivariate improving attempts attempts optimum optimum great publishers publishers publishers publishers variances variances variances variances failure caused caused implementing laboratories cut ion scientific acknowledgement circle circle circle circle begin author author incomplete greatly greatly led orders introducing marked solla slower dots calculating mod ture ture aim aim cal ordered curvature curvature curvature curvature curvature richard comments tolerance damage traces simultaneous summed contribute picture benefit benefit benefit proportion proportion member unity jones jones jones jones royal smolensky smolensky smolensky turned adds wrong consideration oja oja oja oja promising promising promising occurred multiplicative fail sanger splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting splitting constructive constructive constructive constructive constructive constructive constructive constructive constructive degradation continue date infor evaluations financial conjunction regard ascent dominant dominant dominant dominant spherical spherical offers advance mlps april april april offer jolla eigenvector splits splits captures valuable alternatively interestingly avoiding adopted insensitive influences pdf radar unable aston planes creates july july failed encouraging centre centre decomposed big examining reflected alter gained grouped decays crosses march bump surrounding overhead covered anal oscillating oscillating oscillating misclassified preserve esti places indication behave eigen normalised normalised increments ward september bridle bridle mix ucsd heading fat stephen stephen instability prefer insufficient smo smo reflecting supplied pronounced subtracted inferring push anthony attained seed seed colleagues approaching quick remained hinge hinge creation bumps steve scatter scatter scatter scatter scatter february greatest sur percep percep ysis ceedings diverge cox cox cox assessing newly aims prolonged clockwise frozen frozen slip slip advice advice mention mike mike mike yann initialised experimentation wii disk trimming encouragement han steep eval owing owing ror useless useless sensitivities hoped comparatively native plied annulus annulus annulus skeletonization nical indebted congress freeze lacks indefinitely establishment gions recipes sheffield initiative initiative mates teukolsky misclassifications modulus ode tives flannery pulled corrects cording deriva localised uation rounding ash ash ash sara malvern malvern companies slowed vet vet figtire trons seldom favour hayes enclosing jos disrupt rsre timetlon andrews andrews undergone disrupting 
#@Wynne-Jones_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number number number number number number number number error error error error state results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based space space space space weights weights weights layer layer layer layer layer layer layer layer shown systems systems systems systems systems values values probability parameters parameters parameters parameters weight weight weight weight weight unit unit unit unit unit unit unit unit recognition recognition recognition recognition method approach approach approach pattern pattern point point single processing processing processing processing processing processing control rate test test test test test test test test test patterns patterns patterns analysis class class class class optimal optimal optimal inputs form shows paper paper paper feature feature feature net work work work task methods step points classification classification classification level level level current trained trained trained trained trained trained trained trained trained trained trained trained trained trained problems random similar architecture architecture architecture architecture show generalization parameter average average average average average term note university university university university university threshold threshold log initial initial initial initial initial table table standard computer computer terms science science presented map present present activation activation activation activation activation machine sets sets press learn learn abstract applied back back back back back back back back references positive procedure procedure procedure procedure important important decision decision decision decision decision decision decision propagation propagation propagation propagation propagation propagation propagation introduction introduction effect dynamic parallel cost search difference difference difference difference difference complexity complexity complexity variable measure measure measure measure measure measure measure measure measure measure measure measure measure representations learned chosen higher higher cases binary conditions conditions represent represent tree tree tree tree tree tree distributed distributed fact techniques techniques techniques proposed correct correct correct errors simulations classes classes classes ing tasks total sum sum called called regions regions potential potential feedback study study original original original original original original original original original artificial true compared application application define perform experimental experimental experimental related connected connected connected gain brain mit comparison comparison larger update train train morgan morgan morgan morgan morgan words department department department technique technique consists advances advances advances advances advances bias ai ai ai considered cambridge cambridge hinton san san san san san determine significant significant approximate statistics speed speed speed increase derived randomly randomly area area nature measured tested assumption corresponds effective supported main journal journal end end end degree degree rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart fit kaufmann kaufmann kaufmann kaufmann kaufmann objective reduced reduced fully fully fully significantly significantly significantly empirical empirical empirical squared numbers making decay idea run improved improve improve separate separate separate separate introduced include trees subset subset engineering dimensions previously calculated works speaker speaker evaluation separation observation williams sensitive lead locally touretzky touretzky touretzky width demonstrate demonstrate conclusion minimal greater greater reduce valued editors differences moody constrained mateo mateo mateo mateo mateo reduction sigmoidal sigmoidal sigmoidal sigmoidal variety configuration acknowledgements confidence pruning consisting applying formed formed formed john john john national depending detailed evaluated evaluated showed lee lee updates updates updates updates updates updates earlier performing epochs epochs epochs epochs epochs epochs epochs epochs epochs intervals purpose add add construction topology david david david david activations activations activations inter automatic mozer mozer mozer holds partially tests society divided divided mcclelland mcclelland mcclelland presentation identify identify identify detect schemes schemes schemes vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel tend ten summary refer soc cun cun cun stopping split split return list list list list list list list michael simplified generalize denker reach reach software american wiley overfitting collection steady hanson hanson hanson lippmann biases fewer reducing reducing rest referred proper proper scores scores statistically statistically momentum analogous removed removed removed removed removed removed attributes induction induction induction induction induction circles editor editor editor editor generalisation generalisation generalisation created subsets finds isolated percentage theoretic improves caused worse strictly hyperplane hyperplane hyperplane hyperplane begin begin english attribute attribute attribute attribute addressed reflects relevance lack effort solla detecting remove slower robinson robinson robinson robinson robinson robinson robinson howard weigend weigend weigend extensions extensions adjust richard substantial substantial substantial chose comments damage utterances diagnosis diagnosis diagnosis diagnosis identifying fabricated ratios pick pick pick pick recover hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes count flexibility smolensky smolensky smolensky lost extending extending significance adjusting determination removing removing removing belong responsible responsible vowels vowels vowels vowels elimination performances recovered recovered programs james paul pruned heart heart heart heart heart heart heart jackel originally lawrence dif peterson peterson peterson peterson peterson peterson peterson peterson peterson creating arrows formant formant sons consonant stopped explorations robert andrew rigorous tables creates removal propagating par classifications classifications classifications acceptable acceptable chapter classifies constrain chauvin chauvin chauvin gained alternate goals degraded paired disease disease disease disease disease disease disease disease cation quinlan quinlan quinlan quinlan quinlan sized sized sized knowing nil drops tract status mea mea mea removes removes fat acoust simplification stephen tom ping ferent austin austin affecting affecting affecting pronounced acoustical dissertation triangles separates separates separates anthony pratt pratt pratt pratt pratt pratt pratt classi plateau plateau america watrous watrous watrous wisconsin handbook fication dent indepen ous texas fore repetitions dow dow dow jack andreas uniformity switzerland yann lpc exceeded british parentheses trimming trimming trimming trimming barney barney barney barney barney barney barney barney barney superfluous superfluous superfluous superfluous superfluous superfluous superfluous superfluous superfluous superfluous superfluous superfluous superfluous superfluous ticular rutgers classifi raymond reinforced siegel siegel siegel christian borrowed borrowed zky zky touret touret insightful sured sara brunswick zurich ensured generalise discriminates discriminates ramachandran ramachandran ramachandran ramachandran duction drafts drafts hospital casting bernardo jos paring ormation perturbs hirsh 
#@Pratt_L,Ramachandran_S,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model input data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set set training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number system system system error error error error error error error error error error error error error state results results results information information information information information problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models performance performance based based based space space linear linear linear linear linear linear linear linear linear linear order order systems parameters parameters noise noise noise noise noise functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit method point point single single single large local rate test test test test test test test test test test test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis optimal shows signal signal algorithms algorithms algorithms paper small small small size size size size size size size size size size size work work methods step step points field features process process process structure problems random high high high response response response representation parameter parameter real approximation average average average average average average average average note experiments experiments experiments dimensional dimensional university university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables research research research estimate standard standard standard standard standard standard standard computer science prediction prediction left left left left left left phase low sets sets sets sets sets sets sets sets maximum press components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis sample sample sample abstract find computational computational convergence convergence convergence likelihood references due due procedure adaptive adaptive adaptive introduction behavior behavior statistical effect effect effect generated cost search search complexity variable variable variable variable variable variable variable variable variable variable assume measure measure measure measure chosen higher higher higher part center cases type type good long conditions conditions conditions fact techniques techniques length length errors simulations minimum ing regression regression regression regression regression regression regression regression regression dimension made natural negative artificial relative samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples series perform determined experimental experimental goal related power power power power approaches comparison larger source modeling modeling selection proceedings report institute department loss technique code difficult final final final addition graph graph graph graph graph graph graph graph graph graph graph considered experiment experiment experiment experiment experiment additional additional additional additional additional additional san conference full requires significant statistics statistics free increase give derived derived randomly randomly randomly randomly randomly types types types types types types selected selected selected nature nature nature simply discussion technical tested tested tested close close close assumption complete common effective supported theoretical adaptation easily easily noisy including fit fit smaller smaller underlying underlying underlying underlying combination reduced reduced account functional coefficients coefficients significantly significantly ratio ratio special operation operation leads squared squared squared squared squared squared squared squared numbers direct international idea run added added description improved improved improved population population population population population population population discussed takes takes include quadratic quadratic previously previously studies improvement improvement improvement risk increased increased increased lead correctly hybrid hybrid setting reduce conclusions operator operator competitive faster suggest proportional decrease relationship program force question question question question question question question question construct produces written index index factors primary laboratory ann recall recall slightly slightly develop develop predictive predictive quality quality quality versus versus versus versus versus versus choosing national squares squares squares squares squares squares squares squares squares squares detailed operations operations operations operations operations operations operations operations operations operations operations operations operations operations operations operations showed showed sizes sizes sizes allowed smoothing smoothing additive intermediate calculate construction advantages david david building building combinations determines selecting selecting efficiency capable build build computations genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic score score score score score score score score score score plots plots plots plots plots plots plots plots plots plots compact graphs contained contained showing contribution sin sin involved minimizes predictor predictor automatically consisted acknowledgments minimized unlike diego overfitting overfitting overfitting overfitting overfitting overfitting collection collection rapidly put strengths replaced association issues fewer fewer fewer incremental incremental applicable comparable comparable proper scores spline spline spline spline created created created changed friedman friedman friedman friedman friedman friedman friedman friedman friedman art multivariate multivariate improving advanced slowly capabilities stanford sections shared constructing constructing operators operators operators operators worst cut author researchers robustness fourth reflects apparent greatly greatly reflect reflect reflect conducted conducted conducted lack lack splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines parent parent parent parent parent implements begins begins multidimensional trade contribute primarily fix purely discover discover eliminated eliminated consideration chance proceeds resistance affected inferior elimination elimination elimination elimination elimination repeat holland holland holland holland offers insight fitness repeatedly contact ends informative informative informative merge merge hypercube discovered discovered parents pressure multiplying usage usage truncated truncated truncated truncated piece creates creates cooperative july arbor causing preferences mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars mars molecular var var var var var var var var var var alter unseen penalized evolve crossover crossover crossover crossover crossover crossover continues considers deleted diversity sized inversely nasa nasa november removes stops deletion deletion ate august builds builds ave focuses hoc affecting fair filling goodness mutation mutation mutation mutation newly contributing contributing avg avg avg avg avg avg avg delete fight fight illustrating constructions ames scored rogers rogers rogers rogers rogers rogers unix michigan multivariable ranks weaknesses administration revised internet internet probabilistically wolf didn survive aeronautics ffi regressions regressions regressions regressions scientist counteract resist resist philip optional xil domestic ceases accommodated lse ncc ncc moffett agreements riacs riacs extendable extendable universities father squ squ formats doug 
#@Rogers_D,
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#*network network network network network network network network network network network network learning model model model model neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data data data data data function function function figure figure figure figure set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training algorithm output output output output output output output output output system system system system system error error error information information information information information information information information information information information models models models based based space space space linear linear case case vector vector vector vector vector shown shown systems values values values values probability probability probability parameters parameters parameters parameters parameters functions functions unit unit unit unit distribution distribution distribution distribution distribution distribution recognition recognition method method method approach approach pattern pattern pattern point point processing patterns analysis analysis analysis analysis analysis class class class class class class class class class inputs inputs inputs inputs form form shows shows shows algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples feature methods methods points points points points points points points points classification classification classification classification classification classification classification process level trained random response similar section fixed rule general general general general speech real average average average average average gradient gradient gradient gradient gradient obtained term note note note note result result computation research research independent independent independent log log log log log log log log log log log log defined defined target target initial terms distance node presented machine maximum maximum maximum maximum maximum learn components components outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied applied applied back back back find density likelihood likelihood likelihood likelihood likelihood references stochastic stochastic positive positive adaptive adaptive decision decision decision decision decision propagation mixture mixture context context complex complex behavior tion tion difference difference variable variable assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower measure type type required good good long conditions conditions bayesian bayesian techniques techniques techniques probabilities probabilities probabilities minimum resulting resulting resulting classes classes classes classes classes respect respect sum sum elements elements elements regions regions regions regions regions means means made natural global relative relative perform discrete equal equal equal larger descent morgan morgan institute code advances advances joint ai ai maps framework equivalent equivalent environment curve curve solutions design stage capacity classifiers classifiers classifiers classifiers classifiers classifiers upper full world give give derived derived clustering criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion controller types entropy entropy entropy backpropagation backpropagation backpropagation iteration depends simply covariance arbitrary transformation limited predictions require main end instance instance cluster cluster cluster easily objective objective objective objective technology special leads principal squared details details details call numbers numbers supervised supervised supervised supervised idea run architectures improve separate movement practical include identical highly unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised teacher tions achieve achieve definition positions expression expression lead lead lead lead matrices alternative move move generally generally starting depend measures clear performs exponential exponential taking hard presence drawn drawn drawn california proportional decrease targets targets targets targets targets targets derivatives derivatives derivatives derivatives boltzmann reference reference reference reference reference reference derive produces ways factors label label label changing transformations mutual mutual mutual mutual mutual mutual mutual mutual mutual gaussians gaussians john reconstruction reconstruction interpretation densities evaluate labels labels activities completely partition reasonable reasonable roughly purpose boundaries boundaries boundaries interpolation calculate assigned euclidean kohonen david building figures includes activations activations prove simplicity suitable computationally divided projections mackay mackay mackay mackay mackay ten road kind interested interested return criteria criteria categories ill modelling simpler rest applicable ideal plausible adapt necessarily necessarily ensure adjusted logistic observe ith submitted submitted motivated averages preference slowly trivial trivial fairly briefly tractable london turns turns producing probable consequence separately separately separately circle robustness requiring poorly poorly backprop maxima passes pasadena inherent comments simultaneous softmax softmax sort grey proceed adjusting grow interpret intuitively intuitively introduces surprising ascent propagated theoretically partitioned variants propagate severe andrew break job isotropic encouraging seek acceptable covariances imagine demon clas distribu convert retain enforce turning turning turning indication applicability normalised normalised drops normalizing computa bridle bridle bridle bridle bridle bridle strict heading heading heading bridge distortions hoc appealing usefulness agency quantizer anthony comprising tracks unlabelled unlabelled unlabelled iti fair fair fair firm firm bootstrapping cox notions minimise conveyed distinctions seeking froin devise lbg equi generalised recon strated struction recognizable encourages pervised doubled sification discussing unsu normalisation pursue malvern malvern aud aud wil weightings phantom phantom phantom phantom phantom phantom nts decisive peculiar lots founded copyright equivalents defence dxp bridges recommend dra rsre ofy illustrations fies kaufinann kaufinann simpli 
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning model neural input input input input data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output number number number number number error error error error error error error error error error error error error error error error error error error results results results results results units units units problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden performance performance performance based based based space space space weights linear linear linear linear linear linear linear linear linear layer layer layer layer case case vector vector vector vector vector vector order shown shown shown shown shown shown values values values values parameters parameters parameters parameters weight weight unit unit unit unit unit unit unit unit unit method method method approach approach pattern pattern pattern pattern point single single single single single processing control large large local local local local local local local local local local local rate rate rate rate rate rate class class class class class class class class class class class class class class class class class class class class class class matrix signal simple simple simple gaussian gaussian gaussian gaussian gaussian paper examples small feature feature feature feature feature net net net methods fig fig points points field features features features classification classification process process trained trained trained structure problems problems problems problems problems problems problems problems problems random random high response response response representation architecture architecture show fixed fixed fixed fixed rule rule rule vectors vectors vectors generalization generalization generalization generalization generalization generalization speech speech speech parameter parameter parameter average average average average obtained obtained experiments dimensional dimensional dimensional dimensional threshold solution solution solution solution solution research defined defined found initial estimate estimate standard standard standard distance distance distance distance left left direction direction presented frequency sets sets sets maximum maximum range range components components nonlinear nonlinear outputs outputs abstract convergence convergence convergence convergence convergence properties references component component component component component component due ieee procedure adaptive adaptive adaptive adaptive decision decision decision complex complex effect effect effect effect generated generated generated classifier lower rules measure measure measure higher part center center center bound cases required required multiple multiple good good long long long represent bayesian region region region region region region region region correct errors errors scale scale classes classes classes classes ing total respect multi multi times times times regions regions potential made global global relative relative relative relative cross cross receptive receptive receptive define rates rates rates rates rates rates proc proc proc experimental experimental distributions distributions accuracy contrast connection fields fields update update train dependent dependent dependent selection selection selection implementation version version technique internal represents represents responses difficult final exp exp exp exp layers addition addition sequences experiment experiment experiment directly solutions design stage stage efficient classifiers classifiers classifiers upper upper upper upper statistics estimated basic validation weighted weighted developed developed types backpropagation iteration iteration nature nature simply simply discussion normal normal normal normal normal normal increases tested fast limited limited close inverse assumption complete complete surface surface surface surface surface surface finding short nearest nearest nearest nearest effective effective effective implemented generate journal square square ability cluster cluster development development development including mlp mlp mlp mlp mlp mlp mlp mlp mlp significantly york edge segmentation segmentation mode principal representing making normalized bottom early magnitude magnitude minimize added added perceptron perceptron architectures improved resolution advantage pair pair pair pair pair pair pair pair separate separate separate movement reported practical machines side side side dimensions sufficient sufficient compare axis solve solve solve yields converge converge converge converge converge achieve rl sparse address separation modified generalized improvement sensitive entire entire amplitude constructed studied scaling scaling scaling scaling scaling scaling scaling scaling deviation wide wide locally width width width width width clusters boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary setting runs critical critical minimal minimal greater reduce neighbor neighbor sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid measures measures measures designed clear peak faster faster sigmoidal radial radial radial radial radial plane plane iii introduce edges edges produces index solving primary generating tuned distinct segments confidence confidence confidence pruning pruning pruning multilayer simultaneously linearly involves develop adding gaussians gaussians springer select yield focus squares squares squares squares solved variation centered completely completely translation converges discrimination discrimination discrimination discrimination discrimination sign performing normalization roughly roughly boundaries boundaries boundaries boundaries boundaries boundaries generation generation distances sufficiently construction construction classified classified includes coordinate weighting weighting batch extension illustrated candidate candidate candidate candidate candidate candidate neighbors successfully straightforward closely closely effectively effectively delta efficiently computations plots plots orthogonal orthogonal orthogonal fine road conf conf verlag repeated allowing heuristic heuristic link stopping contribution running running thresholds thresholds illustrates neighboring minimized origin origin origin origin remain poor optimized lippmann preliminary discriminant discriminant discriminant discriminant discriminant discriminant tech incremental incremental incremental incremental scaled affect affect momentum removed removed smallest coarse closest explored shapes initialized utility synthetic synthetic piecewise piecewise piecewise developing developing separable growth growth growth growing slope slope slope coded failure correction starts incorporate worst desirable hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane controls controls beginning localized localized localized localized localized localized localized localized localized localized localized lowest lowest demonstrates demonstrates geometry geometry exemplars summation geometric offset offset offset offset offset offset offset axes leave orders completion incorporated extensions prevent redundancy implements eventually merging initialization shifted shifted shifted college identifying primarily accomplished guarantee guarantee martin princeton appropriately narrow narrow narrow controlling discovery eliminate extending fails fails fails fails wrong wrong minutes minutes minutes minutes minutes siemens siemens siemens hyper keeping nearby fail settings knn knn knn constructive filled elimination utilized separating separating combines iteratively widths widths pruned overview moved lengths candidates candidates offers tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens tokens smoothed smoothed cpu cpu park consonant consonant consonant insensitive automated counts spirals spirals maintaining incorporates misclassification misclassification planes benefits alternating retraining convenience comparative sigma sigma obtains spaced spaced possibilities adjustment assess translated shifting gained magnitudes ijcnn discontinuity token token token token token token token token token token token token token harder covered covered intl rotating corrections mea removes covers advantageous consuming corporate insufficient trainable european converging nested nested nested east focuses inclusion polarity settle offsets markers seed seed seed seed seed plateau predictable comm permanent permanent accommodate rectangles resultant resultant ance comer sweep zones rec unnecessary dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion dispersion nice localize encourage illustrating grown retrained retrained conflict snapshots encounter ies utilization correspondingly grain insure emphasizing granularity ecg multiclass pain pain pain grained gravity gravity gravity alternates lambda midpoint midpoint midpoint midpoint midpoint discriminants discriminants discriminants discriminants discriminants discriminants geometries permanently obtainable easiest balances loc greyscale ellipses ouput aids halt localizing ups halted lamb accrue felt retrospect prospect exaggerated 
#@Glassman_M,
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#*network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural data data data data function function function function function function figure figure figure figure figure time set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number error state state results results results results results information information information information information information problem problem problem problem problem problem hidden performance performance performance performance performance performance performance performance performance performance performance performance based space space space space space space space space space space space space space space space space space space weights weights linear linear layer layer case case shown shown values values values values probability probability parameters parameters parameters parameters parameters parameters functions functions functions distribution approach approach approach pattern pattern pattern pattern pattern pattern point point point point single single large large large large large large test test test test analysis class class class class class class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal form form form form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian examples small small small small small size size size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work points features features features features features features features features features features features features features features classification classification classification classification classification classification classification classification classification process trained problems problems random similar similar similar show show equation equation equation equation equation section section section section section section section section section section section vectors general general generalization generalization generalization generalization parameter parameter theory theory theory obtained obtained obtained obtained term term term note note note note note note note note experiments experiments experiments experiments experiments dimensional dimensional solution solution defined defined sequence initial initial estimate computer computer terms terms distance distance distance distance distance presented map present nodes machine machine object object sets sets sets sets sets range range range press press abstract likelihood likelihood likelihood likelihood likelihood references ieee ieee ieee ieee ieee ieee procedure procedure procedure adaptive introduction hand statistical statistical statistical effect dynamic generated generated generated generated variance search search search search search search search search search classifier measure measure signals chosen part cases required multiple multiple multiple multiple good distributed make make fact fact fact techniques techniques proposed proposed correct probabilities probabilities probabilities errors errors errors scale classes ing ing total total total total regression regression respect respect respect respect respect respect respect respect sum sum sum performed performed called called called called called mapping optimization optimization optimization dimension made natural global original original vol vol vol vol relative relative true true true cross cross cross cross cross cross series define define determined experimental experimental related equal approaches approaches larger larger morgan proceedings technique technique consists code code code individual represents addition ai ai ai ai ai ai cambridge equivalent equivalent directly additional solutions san effects conference conference determine determine determine classifiers full requires requires choice choice free free increase validation validation validation validation validation give condition derived weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted randomly randomly conditional conditional developed robot criterion criterion criterion criterion area backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance feedforward describe arbitrary arbitrary arbitrary arbitrary denote denote transformation transformation transformation transformation transformation transformation transformation transformation transformation assumption predictions finding short short nearest nearest nearest nearest nearest nearest nearest nearest nearest supported theoretical theoretical main main journal future makes including including simulated probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically interesting significantly significantly ratio york increasing special empirical principle principle call numbers max max making making added population population population population population population population population population improve improve recent resolution resolution pair pair robust robust robust robust robust robust identical identical sense subset relevant relevant dimensions sufficient observations approximately works works solve diagonal diagonal diagonal diagonal diagonal diagonal diagonal evaluation evaluation evaluation evaluation evaluation evaluation evaluation symmetric modified modified modified entire constructed exists lead correctly locally locally runs reduce conclusions conclusions operator neighbor neighbor neighbor neighbor neighbor neighbor neighbor measures designed performs exponential practice practice practice mateo encoding encoding encoding encoding encoding encoding encoding demonstrated demonstrated intelligence min iii explicit van describes recall metric metric metric metric metric metric metric missing involves transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations consisting consisting gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians applying implies select squares evaluated evaluated evaluate evaluate evaluate restricted restricted restricted fraction centered translation constants constants partial partial partial partial reduces reduces roughly roughly remains sufficiently euclidean euclidean euclidean classified transactions transactions david degrees degrees degrees degrees degrees precision precision figures figures figures combinations coordinate coordinate weighting extension extension partially partially neighbors neighbors importance uniformly society society society encoded identify genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic score essentially identity identity ten ten ten ten ten ten quickly decoding contained heuristic heuristic success classify classify criteria criteria criteria hold generalize mixing oriented oriented extend extend poor essential difficulty steady steady optimized biases biases dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset giving ideas rest affect affect encode encode analogous possibly necessarily illustrate ensure ensure ensure subsets subsets quantities quantities freedom freedom freedom freedom freedom observe motivated optimum cart cart cart trivial distinguish derivation variances variances improves floating sections closer closer closer closer broad worst arise acknowledgement recognized optimize optimize optimize optimize optimize definite demonstrates exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars robustness robustness fourth greatly double affine affine affine affine affine affine affine affine affine affine axes axes axes axes lack lack effort backprop backprop backprop atkeson atkeson atkeson atkeson atkeson atkeson incorporated incorrect rely datasets datasets datasets datasets datasets sums replace inherent chose comments implements tile progress calls wesley irrelevant irrelevant irrelevant globally contribute contribute redundant redundant redundant addison modify modify restrict fix arguments arguments optimizing optimizing royal exemplar exemplar exemplar exemplar exemplar exemplar exemplar robotics proceed eliminated extending significance ranges ranges logarithmic held city los los contract viewpoint splitting disjoint hint modifications heuristics heuristics evaluations excellent falls corre entry encountered bad originally entries darpa fitness draw relies likelihoods likelihoods davis davis davis davis davis davis davis davis speeds fold integers stone stone stone stone onr verify metrics metrics metrics metrics metrics street leaving leaving leaving leaving validity encodes isotropic isotropic isotropic isotropic classifications individuals individuals individuals individuals covariances covariances covariances covariances covariances covariances covariances covariances covariances covariances big classifies reject transparent exponent diag diag pami compensate drawback sonar ation det det mann replacement replacement differently preserves nonnegative identifies identifies hundreds dropped incorrectly eliminates subtracting assessment automation discarded discarded goldberg goldberg norms compensated presently encodings encodings handbook ings enters format mul cia hood rein derivations amax amax arline arline claims claims anisotropic anisotropic anisotropic anisotropic anisotropic agation overfit shortcomings shortcomings tri likeli discarding discarding depict depict validate logarithmically redwood initiative loose alamitos alamitos kauf ken remedy fukunaga fukunaga tiple sacrifice specht specht onal equiva paradox marquardt compensates kelly kelly kelly kelly kelly lent evalu outperforming levenberg supplemented flaw flaw flaw flaw flaw newman 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#@Montana_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning neural input input input input input data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set networks networks networks training training training training training training output output output output output output output output output output output output output output number number system system system system error error results results units units units units units units units units units units units units units units units units units units units units units information information information information information information information information problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance weights weights layer layer layer layer layer layer layer layer layer order order shown shown parameters unit unit unit unit unit unit unit recognition recognition recognition recognition approach pattern pattern image single single processing large rate test test patterns patterns patterns analysis class class class class form form form form shows shows signal examples examples examples small small net task task task task features features features features level level trained trained trained structure problems problems problems problems problems problems random high high memory similar similar similar representation representation representation representation representation architecture architecture architecture section section vectors general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech speech average theory note note note note activity dimensional dimensional solution research research found target standard standard standard computer connections connections connections connections connections left left left left presented presented presented presented low low temporal machine press press press learn abstract abstract applied applied references propagation context context introduction hand behavior generated generated generated generated parallel recurrent lower representations representations representations representations learned cases type binary binary distributed distributed expected make fact fact fact region region region region region region correct errors errors ing human human regions regions made original vol represented represented represented represented related connected connected mit contrast connection connection internal internal internal code code connectionist connectionist connectionist connectionist difficult layers considered hinton hinton view san top bit requires basic basic produce coding derived provided provided backpropagation backpropagation constraint describe common shape shape generate supported require eds face journal square instance instance instance instance instance instance easily makes rumelhart rumelhart rumelhart rumelhart including including typically typically reduced fully fully character character database leads representing representing representing direct produced produced produced architectures architectures improved correlations correlations correlations separate separate element typical typical pixels subset recently teacher tuning tuning correspond diagonal sparse address grid grid grid williams williams constructed horizontal invariant invariant wide alternative alternative loop loop loop conclusion conclusions central designed designed designed designed clear performs strong reduction characteristics variety characters connectivity acknowledgements explicit optical generating generating tuned vertical distinct distinct dept confidence missing explicitly simultaneously electrical remaining remaining text integrated formed letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters letters restricted restricted restricted centers forms completely similarly epochs event event roughly generation generation generation david david david david figures color discussions successfully columns letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter effectively mcclelland presentation successful successful successful projections identity identity identity ten ten fine fine fine receives characteristic excitation repeated superior content dot generalize consisted illustrates decreasing explore poor production production production production production production production production production production production production production production production create exhibit humans strengths issues matches project project project project structured cognition cognition cognition fundamental fundamental notion momentum removed hill adjusted epoch consist simplest integrate integrate rows answer stress stanford stanford sections widely producing producing producing producing style style style style style style style style style recognized addressed addressed exemplars dark peter poorly share music music music dots howard serve prevent gave shaped physiology restriction perfectly interconnected analogy analogy city intelligent loops harmony roles guide alphabet presentations presentations spurious spurious composition composition composition meaningful meaningful connect surprising expanded reproduce francisco foundations reveals draw draw park projects stopped explorations mind microstructure inferred stork stork stork stork stork stork stork chapter chapter experiences chicago reconstruct unseen stroke stroke geoffrey intra intra crosses douglas douglas books projecting categorization categorization likewise prevents algorithmic font font font font font font font font font font font font font font font font font font font font font font font font font font font font font font font font font font font todd todd house house virtually melody adult ron ron ron judged judged comprising diamond diamond diamond strokes strokes strokes strokes strokes strokes strokes strokes implied reproduced experienced experienced essence twelve steve steve emerged shares severely meaningless meaningless fight schematically winter helped untrained thinking thinking menlo cen requests taught disconnected ricoh ricoh foreign recognizable recognizable foster exemplified graphic suspect inh inh unidirectional analogies deduced fonts fonts fonts fonts fonts fonts slant slant crc sand invariants informational informational evidently tremendous hunt hunt hunt hunt hunt judgment incidentally irregularities eighteen exc exc portrait portrait answering disrupt thai reprint compromised upside 
#@Grebert_I,Keesing_R,Mims_S,Stork_D,
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#*network network learning learning learning model model model model neural neural neural neural neural data data data data function function function function function function function function function function function figure figure figure time set set set networks networks networks training training training training training training training training training training training training training number number number number number number number number number number number number number number number number number number number error error error results results results results information information information models models hidden based based based space space space layer layer case case case case case case case vector vector vector vector vector vector vector vector order order order shown shown probability probability probability probability probability probability probability probability probability probability probability probability parameters functions functions functions functions distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point single single large large test analysis analysis class class class class class optimal optimal optimal optimal optimal optimal form simple simple simple examples examples small size size size size size feature feature feature feature feature feature feature feature work work task task classification process process trained trained problems random random random random random random high representation representation representation architecture architecture show show show equation equation fixed fixed fixed fixed fixed vectors general general general generalization real real real approximation approximation approximation approximation approximation approximation approximation approximation theory obtained term note note note note note result university university computation computation research research log log log defined found table table estimate estimate estimate standard computer computer terms terms terms prediction prediction presented present nodes sets maximum press basis continuous sample sample sample sample sample sample sample sample sample sample sample sample abstract abstract abstract find analog references ieee positive positive positive procedure context context introduction complex complex statistical statistical statistical statistical statistical statistical statistical effect variance variance search tion difference difference difference difference difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower lower measure measure measure representations theorem theorem theorem theorem bound bound bound bound cases required required bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected equations fact length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities finite finite minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting classes classes tasks computed multi sum made negative vol specific specific specific specific samples samples true true true true cross provide compute connected distributions discrete discrete approaches comparison comparison comparison larger larger contrast support train train train modeling morgan proceedings department department version joint represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist delay ai ai ai domain equivalent equivalent directly hinton additional view estimates san bit bit bit bit bit bit bit bit bit bit bit bit conference capacity classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper upper full requires requires requires requires requires choice choice choice choice choice choice choice significant significant approximate approximate estimated estimated estimated pages conditional bounds entropy product product product product actual nature nature achieved measured measured describe limited assumption assumption assumption complete predictions predictions predictions predictions predictions finding rbf rbf rbf theoretical theoretical theoretical theoretical theoretical require face face face face face face face face face face face face face face face face face face face face face face face face face face face kaufmann objective objective objective objective objective objective objective objective probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically typically needed needed needed needed functional functional functional functional functional functional functional functional functional significantly empirical empirical empirical empirical empirical empirical empirical leads leads leads squared max max max pre bits bits bits bits bits bits bits bits international supervised magnitude magnitude attention choose choose description light denotes architectures improved discussed robust practical strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy identical sejnowski recently engineering engineering interest compare compare works yields yields correspond differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential achieve rl rl rl rl rl rl rl rl rl rl rl rl definition definition interval interval interval interval interval grant concept extended wide correctly correctly correctly correctly correctly touretzky boundary demonstrate conclusion minimal minimal minimal minimal greater depend editors differences differences differences measures clear clear clear clear learns mateo largest largest radial min min relationship introduce connectivity force question question estimating estimating estimating mathematical modeled confidence confidence confidence confidence confidence confidence confidence confidence electrical electrical involves versus versus yield yield family phoneme labels translation discrimination discrimination discrimination discrimination discrimination sign sign sign sign sign sign sign iterative boundaries symbol classified classified faces faces faces faces faces faces faces faces transactions precision precision figures figures thesis vapnik extension extension prove prove prove prove holds partially straightforward closely symbols symbols identify identify identify identify identify identify identify identify identify identity traditional refer showing strategies strategies strategies strategies hold gray gray paradigm paradigm quantization quantization quantization quantization highest highest highest extend employed employed requirements requirements requirements requirements involving involving involving detail detail limitations accurately game game game game game game lippmann hall discriminant discriminant discriminant discriminant school authors office root cover notion notion notion analogous analogous analogous waibel smallest smallest transmission necessarily illustrate expressions phd asymptotically theoretic distinguish distinguish distinguish answer answer answer baum precisely located worst mathematics scientific acknowledgement definite recognizing meaning mellon mellon questions carnegie carnegie empirically elman relevance relevance cmu cmu dark quantitative posed marked marked haussler employ ity requirement pittsburgh differs richard semi conclude lim progress june proofs proofs proofs proofs proofs proofs proofs aligned identifying identifying identifying identifying identifying identifying equivalence arguments jth air chance definitions definitions generalizes motivation games games games corollary corollary corollary corollary equals evident creating reader reader shortest repeatedly repeatedly arrows pearlmutter designing integers acknowledge outlined posteriori posteriori posteriori posteriori linked linked linked validity formulate formulate die die die die die die die die die die die die die die die die die die die die die die die die die die die die die die die die die die distinction connec superimposed multinomial rain rain quantized searches afosr considers considers exceed employing funded turning meet page prevents infinitely gauss answers manuscript gratefully trainable recursion rissanen rissanen cally sided sided ultimate implied format jan occurrences occurrences occurrences merit mid kolmogorov kolmogorov ece mar hampshire hampshire hampshire hampshire hampshire hampshire hampshire hampshire classifica confirms paid seeking ixl ixl ixl indistinguishable brevity owing identifiable revised hoped rankings rankings realizes lesser focussed tionist discrim wit invalid connecfionist connecfionist arl arl arl arl arl arl arl arl arl arl arl arl dictates converse philosophical cision ceptron mer lsb lsb pertain 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#@Hampshire_J,Kumar_B,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input input input input input input input input data data data data function function function function function function function function function function function function function figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output number number number number number number number error error error error error error error error error error error error error state state results results results results results results results results results results results results units units units units units information information problem hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer case vector order order shown shown shown shown shown systems values values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions unit unit recognition method method method method method method method method approach point point single local local local local local rate rate test test test test test test test test test test test test analysis form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms gaussian gaussian paper paper paper paper examples feature feature feature feature feature feature feature feature feature feature feature feature net task task task task task task task task task task task task task methods methods methods methods methods methods methods methods methods methods methods methods features features features features features features features features features features features features classification classification process trained random similar architecture show show section section fixed general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech parameter real approximation theory theory gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained experiments experiments experiments result university university university computation research found found found found found found initial constant table table table table table table table table standard standard standard standard computer computer terms distance distance distance distance distance distance distance distance distance science science science presented map present present present low machine machine machine sets press press learn learn learn learn learn learn basis basis basis basis basis basis basis basis basis basis basis basis abstract applied applied applied back back properties references important important important important important important important important decision decision propagation propagation context introduction complex effect effect variance variance variance variance variance parallel search search difference prior prior word word word word word word word word word word word word word word word learned learned learned learned learned chosen center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center center cases required tree distributed make fact techniques correct correct correct correct correct correct correct correct forward scale scale scale minimum minimum resulting tasks computed computed computed sum called times times times mapping means means means means factor factor factor optimization optimization dimension made global global global global global applications applications study obtain obtain artificial artificial relative relative compared compared compared compared application application cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross series provide provide provide provide compute compute perform perform perform determined determined determined determined determined determined determined experimental goal mit accuracy comparison comparison comparison comparison larger train train train descent descent proceedings proceedings proceedings proceedings report report report institute words words words words words words department department implementation implementation version technique code code code code individual final bias bias bias delay addition ai cambridge cambridge computing computing domain domain domain domain domain domain experiment hinton hinton additional bit bit bit bit bit bit bit bit bit bit conference conference determine determine efficient efficient efficient full statistics increase validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation weighted weighted weighted weighted weighted weighted randomly clustering clustering clustering clustering levels levels criterion finally finally evidence backpropagation backpropagation backpropagation backpropagation achieved measured describe describe tested tested tested tested tested tested tested tested fast inverse inverse inverse inverse assumption finding rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf nearest nearest nearest nearest implemented supported role eds square instance easily typically combination unknown unknown testing testing testing testing testing significantly significantly consistent squared squared squared call call call making window window window bits bits supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised combined combined improved improve improve improve improve pair separate separate separate reported apply apply introduced period subject identical trees subset subset sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski previously previously unsupervised unsupervised unsupervised unsupervised observations approximately smooth correspond positions locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations locations modified observation generalized generalized generalized generalized improvement improvement improvement entire entire grant grant suggests suggests wide matrices alternative alternative alternative correctly correctly correctly correctly correctly correctly correctly correctly correctly feed locally locally generally column column setting setting starting row row row row reduce conclusions neighbor neighbor neighbor valued sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid clear peak moody moody moody moody faster suggest encoding drawn sigmoidal california intelligence intelligence radial radial radial radial radial radial radial radial radial radial radial radial variety user user minima minima minima minima program configuration configuration appears pro ways laboratory tuned mathematical metric metric metric implement simultaneously text text develop mutual gaussians gaussians letters letters letters letters letters letters letters letters letters letters letters yield yield choosing national national formation review phoneme phoneme phoneme phoneme phoneme phoneme influence codes codes codes codes codes codes codes codes evaluated open evaluate approximations centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centered suggested calculation performing performing purpose false distances string assigned assigned foundation norm norm norm euclidean euclidean euclidean euclidean euclidean classified classified classified classified classified classified combinations activations formulation activated domains domains domains neighbors tests determining letter letter letter letter letter letter letter letter letter letter letter importance importance society encoded encoded encoded divided poggio poggio poggio plots plots capture capture summary quickly procedures heuristic showing stopping stopping dis superior superior superior superior involved usual play generalize computes acknowledgments receive employed employed employed employed explore poor create varied optimized dataset matches fashion mappings comparable comparable scores scores encode statistically statistically understand momentum waibel waibel induction gradients plausible equally equally obvious assumes explored initialized multivariate improving improving improving improving improving isolated percentage percentage percentage percentage stop smoothness variances variances variances variances variances variances variances variances variances variances variances variances improves explanation explanation glass worse stress stress stress stress stress stress stress berkeley berkeley constructing located mathematics separately describing describing implicit english english english preceding conjugate conjugate conjugate percent substantially substantially pseudo pseudo conducted introducing adjustable adjustable passed rep prototypes summarized phonemes phonemes phonemes adjust substantial chose conclude conclude summed displays initialization gap gap room redundant girosi girosi girosi darken darken darken darken difficulties attractive attractive resulted methodology methodology methodology methodology disjoint symposium heuristics inferior inferior inferior inferior date elimination excellent programs studying widths surprising lang lang thomas surprisingly suggesting ends wolpert wolpert wolpert correcting correcting correcting correcting correcting correcting correcting correcting correcting correcting correcting inductive partitioned dietterich dietterich dietterich dietterich dietterich dietterich dietterich dietterich dietterich valuable vari achieving benefits encodes failed conjecture comparative assignments classifies classifies classifies classifies discovering remainder principled mackey cessing magnitudes graduate carefully cole cole exceed iri employing employing quinlan quinlan dictionary dictionary dictionary stuck oregon oregon oregon aaai aaai worked remarkable justification rosenberg rosenberg rosenberg rosenberg rosenberg rosenberg rosenberg grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf austin confirm virtually supplied proportions pronounced pronounced replicated replicated replicated explanations tance aggregation aggregation nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk nettalk deter ance violated recovering voiced spec began cations preventing ton ness devel ninth boost distinctive hild hild euclidian cse indistinguishable indistinguishable mined ration iix iix barnard barnard interpretable hurt attain tailed multiclass subdivided penrose penrose markedly twofold aha aha oped bakiri bakiri bakiri bakiri ovi unvoiced sumptions pronunciations mathe pronounce pronounce improper matical philosophical macqueen ified caught searchers configu corvallis corvallis 
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#*network learning learning learning learning learning learning learning learning neural neural input input input input input input input input input input input input input input input input input input data data data data data data data data data data function function function figure time set set networks algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number system system system system state results results results results performance performance performance based based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space weights weights case vector vector vector vector order order order values values values values probability weight weight distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method approach control large large rate test optimal optimal optimal form shows gaussian gaussian gaussian visual paper paper examples examples examples examples small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net net net work fig fig fig fig fig fig fig fig step step step step points points structure structure structure structure structure problems random high memory show rule vectors vectors speech speech speech speech speech speech speech speech dimensional dimensional dimensional dimensional result independent independent log found sequence dynamics table table distance node node node node left direction direction map map map map map map map map map map map map map map map map map map map map present phase low nodes nodes nodes nodes nodes nonlinear abstract applied find convergence convergence properties properties references due ieee ieee ieee introduction stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus dynamic variance change spatial classifier classifier lower measure measure word word chosen part part bound cases long long represent resulting resulting computed computed computed computed eq mapping mapping mapping optimization optimization optimization optimization dimension dimension dimension dimension dimension made made global applications specific compared application application provide define define proc proc proc perform determined distributions cortical approaches larger dependent dependent selection words words individual individual individual sequences maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps experiment experiment curve additional additional transition trajectory effects upper full choice choice choice robot robot criterion product product product product product product product product product product product product product product product product product product product product product product product finally finally associative discussion technical describe amount nearest nearest nearest nearest nearest supported square square degree fit underlying interesting ratio ratio principle principle principle denotes directions directions recent recent typical typical side dimensions varying varying varying works works yields speaker speaker speaker speaker match correspond converge trans trans evaluation symmetric organization arm arm lead lead lead suggests locally hybrid width boundary generally demonstrate trajectories trajectories neighbor neighbor neighbor neighbor differences measures measures exponential learns turn turn decrease averaged introduce reference reference suppose derive factors factors plot describes stability recall averaging dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality involves equilibrium springer shift expectation formation formation detailed detailed densities organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing suggested digits spaces spaces spaces spaces neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood roughly purpose distances kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen topology topology topology topology topology topology expect expect usa neighbors reason regular aspects importance effectively attractors attractors ten fine induced induced heuristic interpreted contribution follow sci hold notation minimizes quantization subsequent relations relations relations relations relations relations relations relations optimized helpful matches biol comparable complicated understand topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic smallest plausible possibly necessarily perfect aspect aspect aspect aspect aspect aspect quantities der separated mapped mapped mapped speakers submitted attempts chaotic chaotic synthetic isolated mentioned crucial derivation derivation derivation explanation explanation adapted multiplication caused briefly comparisons spatially spatially widely products acknowledgement acad optimize optimize optimize demonstrates fluctuations outer considerably fed quantitative orders rep compares measuring germany conclude decreased shaped expectations deviations deviations utterances utterances utterances wesley shifted addison modify ratios ratios ratios ratios ratios optimizing nat ordering ordering ordering concerned turned rational fits neurobiology north exceeds exceeds intuitive corre induce holland von regard regard topological topological bad uni eqs considerations considerations variants robert multiply schulten schulten schulten schulten schulten visually misclassification email preserving preserving preserving preserving german warping avoids publication preserved preserved perpendicular gas rectangle rectangle rectangle obermayer ritter ritter ritter ritter ritter ritter vice coordination topologies topologies topologies fiat resp resp resp versa sponding preserves institut neighborhoods neighborhoods neighborhoods puts compensation acoustical coincide coincide preservation preservation preservation preservation preservation deals deals suffice comm dimen rectangles rectangles 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#*network network learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input figure figure figure figure figure figure figure figure time set set set set set set set set set set networks networks networks networks networks training training algorithm algorithm algorithm output number number number number results results results results units information information information information problem problem performance performance performance based weights shown systems systems systems values values values values values weight unit unit recognition method method method approach pattern point single processing processing large rate test test test class class form shows algorithms algorithms algorithms algorithms simple examples examples small size size net net net net net net net net net net net net net net net work work features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level architecture show show rule rule rule general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech parameter real average average note experiments experiments university threshold solution solution research research defined found initial initial table table table table table table table table table table table table table table table table table estimate computer terms science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented present nodes machine machine machine machine machine machine machine machine machine object object object object object object object object object object object sets press learn sample sample sample sample sample sample sample sample abstract applied back find find convergence convergence convergence references procedure important adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision introduction hand behavior behavior behavior stimulus parallel tion tion rules rules rules rules rules learned chosen chosen center cases good tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed correct correct probabilities forward forward forward resulting classes ing total total total human human human human human human human human human human human human human human human human human respect performed performed performed mapping applications original original original original vol artificial relative samples represented compared objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects experimental related related constraints power mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison comparison fields fields fields nets nets nets nets nets nets nets nets nets nets modeling modeling modeling modeling modeling morgan morgan morgan report department individual individual advances advances connectionist scheme addition cambridge computing experiment experiment experiment experiment experiment experiment experiment experiment view solutions san efficient requires significant world basic coding randomly randomly criterion provided finally selected backpropagation backpropagation discussion close close predictions short short short supported eds end hypothesis hypothesis rumelhart rumelhart kaufmann kaufmann kaufmann interesting consistent mode principal representing representing representing details details magnitude predict perceptron perceptron discussed recent separate include trees trees trees trees trees trees trees trees trees sense inference recently recently interest tions tions studies studies locations generalized generalized grant lead lead correctly correctly correctly correctly correctly touretzky touretzky occurs runs runs conclusion starting minimal minimal minimal conclusions conclusions differences mateo propose strong strong intelligence variety variety exist exist relationship manner program areas pro construct construct remaining remaining remaining remaining remaining text predictive springer quality national independently focus viewed evaluated evaluate foundation classified classified priori perceptrons discuss partially tests importance mcclelland mcclelland computations computations comparing summary refer verlag graphs graphs procedures classify classify classify classify classify classify quantity backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward nips nips nips correspondence highest ill preferred preferred preferred preferred preferred modelling modelling employed exhibit varied humans humans humans humans humans humans humans humans humans humans humans humans issues fewer examine root root symbolic symbolic workshop workshop workshop notion attributes induction induction man analyze predicting illustrate equally eyes eyes eyes eyes formal observe observe consist generates explain averages years years years languages languages languages mentioned percentage brown brown brown brown cart theoretic analyzed briefly comparisons comparisons comparisons comparisons comparisons closer immediately probable mathematics acknowledgement separately calculations calculations calculations beginning english attribute attribute attribute attribute attribute attribute attribute qualitative nsf percent items items items profile substantially substantially dark dark dark red red ity berlin synthesis summarized gen extracting gave findings wesley sharing realized consistently addison investigation branches labelled stronger height height reasoning reasoning sanger implications intuitively games exploring meaningful respective expanded evident colorado dif informative inductive dietterich dietterich omohundro papers shavlik shavlik shavlik accumulated appeared hair hair hair hair hair tables tables asked asked tween year conjecture conjecture classifications classifications classifications classifications obtains profiles weiss weiss blue blue blue blue blue generalizations generalizations generalizations generalizations generalizations generalizations generalizations generalizations chapter classifies classifies classifies classifies classifies chess unseen attempted cessing ijcnn graduate ization mitchell boulder concentrate considers cole gluck gluck proach quinlan quinlan quinlan quinlan quinlan distinguished investigations investigations places ward computa students emphasis remarkable corporate prefer marks quantify ferent towell evolved puts seattle edited edited edited pratt pratt colleagues complement reproduced inde quick quick quick quick quick backwards tsoi atlas atlas atlas applica connor accuracies contributing proce ther rated eralization ago ross switzerland classifica fur hild hild amples barnard looked mooney tha revised arrived backpropaga percentages utgoff swiss unary persons subjected subjected muthusamy bakiri bakiri bibliography methodologies spectively suddenly michalski stressed underway optoelectronic cdr sharkawi pothesis carbonell dures sharpened crossvalidation curious agreeing norton norton arid pendently abil 
#@Bernasconi_J,Gustarson_K,
#t5
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function time time time set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output number number number error error error error error error results results results results information information information information problem problem models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based based based based based based based space weights weights weights weights weights weights weights weights weights weights linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case case case vector vector vector vector vector vector order order order order order order shown systems systems values values values parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit distribution distribution method method method method method method method method method method method method method approach approach single single single processing large large large large local local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test test test patterns patterns patterns patterns analysis matrix optimal optimal form form form form algorithms simple simple gaussian gaussian gaussian gaussian gaussian paper paper small small size feature methods methods methods methods methods methods points classification classification classification process trained trained problems problems problems random random random high high response similar similar representation equation section section fixed fixed fixed fixed fixed line general general parameter parameter real approximation approximation approximation approximation approximation approximation approximation theory gradient gradient gradient gradient note note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university threshold variables variables variables computation research independent independent independent independent independent independent independent defined constant estimate estimate estimate estimate estimate estimate estimate estimate estimate standard terms terms terms connections science science prediction direction direction presented presented presented activation low nodes maximum range basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract back back back back back back computational convergence convergence convergence properties references component stochastic procedure procedure procedure important important important important important propagation propagation propagation propagation propagation propagation introduction hand hand hand estimation statistical statistical generated generated generated generated generated generated variance variance variance search difference variable lower lower measure signals signals chosen chosen chosen chosen chosen part multiple good good good good represent represent distributed markov make fact fact fact techniques proposed proposed proposed proposed length length length observed errors simulations simulations simulations simulations simulations simulations ing ing ing simulation simulation simulation simulation regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect sum eq eq eq eq eq eq called called elements optimization optimization optimization optimization optimization optimization optimization dimension made made applications applications applications study obtain negative vol vol relative relative specific true true compared compared desired desired desired desired desired cross cross cross cross provide proc proc location determined determined determined determined determined goal constraints connected connected approaches accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison comparison comparison comparison comparison comparison comparison comparison contrast train descent descent descent modeling modeling modeling modeling modeling modeling selection selection selection selection report department department implementation implementation version version technique technique consists code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel bias layers addition ai estimates estimates choice choice approximate approximate approximate approximate approximate statistics statistics statistics statistics free free free free speed speed speed speed speed estimated validation validation validation validation weighted criterion area types types types types types actual iteration iteration technical feedforward increases group group group close close assumption complete complete complete amount common implemented assumed assumed generate supported theoretical theoretical require main degree degree noisy noisy typically typically pairs pairs smaller needed combination unknown unknown unknown unknown unknown unknown unknown character projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection increasing special structures uniform uniform mode principle leads squared squared iterations window magnitude minimize minimize perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes denotes denotes denotes discussed discussed improve improve directions directions directions recent advantage separate separate element reported identical varying varying varying compare observations smooth smooth smooth smooth studies studies converge achieve definition symmetric symmetric observation grid grid sensitive increased grant studied scaling deviation wide derivative derivative derivative locally locally setting pass pass half differences numerical designed performs practice learns constrained presence sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal radial assuming variety relationship groups groups force explicit suppose suppose appears pro pro longer factors sequential sequential sequential sequential estimating laboratory tuned mathematical distinct dept changing sensitivity multilayer explicitly simultaneously simultaneously averaging dimensionality involves adding adding quality select choosing national squares squares squares squares squares squares estimator evaluated fraction forms approximated completely updates updates updates updates earlier smoothing smoothing smoothing smoothing slow additive measurements sec event iterative valid foundation euclidean avoid expect expect expect kernels kernels priori perceptrons perceptrons perceptrons formulation formulation formulation bell batch batch batch batch batch batch batch specifically variations absolute partially successfully simplicity reason reason regular aspects identified extra efficiency efficiency efficiency efficiency efficiency differ divided divided wij presentation efficiently efficiently projections projections projections projections situation conf conf conf repeated procedures stopping strategies built write usual subsequent situations origin unlike unlike parametric parametric parametric parametric parametric parametric parametric parametric powerful updating updating updating updating updating updating updating updating updating estimators estimators hessian pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit fewer int scaled scaled working comparable comparable comparable comparable variability analogous opposite equally aspect friedman friedman friedman friedman friedman friedman friedman friedman logistic perceptton multivariate multivariate attempts defines stop smoothness smoothness smoothness fairly fairly capabilities starts comparisons considerable stanford tive easier choices mation acknowledgement separately implicit computers computers bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth robustness robustness explained argument reflects considerably considerably applies reflect conducted capability remove slower formulated outliers outliers outliers outliers outliers outliers outliers outliers span passes popular curvature curvature curvature asymmetric semi semi semi age shaped focused deviations contribute shifted newton newton newton newton newton newton newton newton restriction restriction martin martin martin martin martin martin martin martin arguments appropriately unity unity jones jones tools mail interconnection interconnection interconnection replacing replacing stated moment monotonically corner nonparametric date utilized heavy combines iteratively washington washington washington evident sim similarities reveals reveals refers ends extensively grants summarize approximator approximator approximator interestingly fitted linked linked ple incorporates users annals annals achieving creates employs employs smoothly conjecture comparative spaced translated deep approxi approxi mathematically douglas eliminating concentrate altered speedup zip enforce esti struc signs gauss gauss gauss gauss gauss gauss gauss gauss november november november sigmoids sigmoids removes nonnegative january jointly curse smoother smoother smoother eral identically inherently integrates seattle seattle seattle assessment assessment measurable inefficient rameters totally interpolate adjusts distorted iid lewis fair adapts vicinity sweep dent indepen tical focusing outlier outlier outlier mul translates monotone derives adequately manual unimodal modest cope unnecessary noiseless noiseless nice imposes lid virtue marginals graphically huber accu possesses parsimonious parsimonious parsimonious favorable ecs mate ting counterparts tially cent univariate noises noises overfit hwang hwang hwang hwang hwang hwang hwang hwang hwang hwang hwang hwang hwang grove grove donoho donoho multivariable abscissa abscissa visualized iix regularly gression viewpoints justifies jim render jacobi useless robbins suit tailed hierarchically sev monro fii fii fii fii extrapolate pertinent ond borel eli eli eli eli eli mated favoring nodal nodal nodal nodal nodal nodal mech racy prespecified solver nondecreasing carriers carriers sacrifice johnstone pacific pacific prac instructive pur confine xxt elect interprets pack timization consecutively consecutively consecutively magnified ilk engr asilomar asilomar parametrically parametrically parametrically parametrically protocols anism paring jection jection historically caveat sequen seidel jtn wix variates tural flit sensi ality cyclically vestigated 
#@Hwang_J,Li_H,Maechler_M,Martin_R,Schimert_J,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data function figure figure figure figure figure figure figure figure time time time time time time time set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number error results results results results results results results results results results results results results units information problem problem problem problem problem problem problem problem problem problem problem models models models models models models hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based weights weights weights layer layer shown shown shown systems systems systems values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters distribution distribution method point point point processing large large large rate rate rate rate rate rate rate rate rate rate test patterns analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal algorithms algorithms algorithms algorithms algorithms algorithms paper paper small work process trained trained trained structure structure structure problems problems problems problems problems problems problems problems problems problems problems random random random high response response similar show show equation section section section generalization parameter average average average average obtained obtained obtained obtained term experiments result university university university university threshold computation computation independent independent independent independent log defined defined defined found found found initial initial table table estimate estimate standard computer computer science science prediction prediction presented present present low low maximum range range range range range range range range range press learn basis abstract back back back back back back back back back back back convergence analog likelihood likelihood references ieee procedure propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction complex complex statistical effect effect effect parallel measure measure measure measure representations chosen chosen chosen higher higher cases cases required good binary binary conditions distributed techniques techniques techniques correct correct correct correct correct forward forward forward forward forward forward forward forward total total regression times times times times times times times times times times times times means study study obtain obtain artificial artificial compared desired provide provide define rates determined determined related connected gain equal mit comparison comparison comparison comparison comparison contrast contrast dependent dependent selection proceedings proceedings report report report report department implementation internal individual joint responses responses final layers graph graph graph graph graph graph graph graph graph graph graph graph graph considered considered considered considered considered computing computing computing equivalent equivalent directly hinton curve additional view curves estimates estimates estimates estimates limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit effects conference conference determine choice choice choice statistics speed estimated estimated pages pages pages produce produce derived developed provided processes achieved achieved discussion technical technical fast close stable predictions common shape adaptation journal easily rumelhart rumelhart rumelhart development including fit fit fit typically typically needed needed needed fully fully jordan significantly significantly ratio trials trials trials trials trials trials trials trials trials trials trials empirical empirical details international early decay produced produced run improved property separate typical reported include highly highly previously approximately solve achieve trans williams sensitive increased increased increased scaling trial trial trial trial trial deviation predicted correctly feed feed feed feed feed feed feed feed occurs occurs runs runs runs runs runs runs runs conclusion starting greater greater greater reduce reduce measures measures measures measures measures measures measures measures measures measures measures measures measures accurate peak peak peak peak peak practice asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic propose strong cycle characteristics demonstrated min min program base relation longer solving solving solving dept confidence confidence sensitivity infinite develop applying applying john john john yield yield yield depending estimator variation updated understanding suggested epochs epochs epochs epochs epochs measurements fitting fitting intervals intervals penalty remains recorded recorded existing existing combinations efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency suitable successful successful successful successful successful successful successful successful successful situation plots capture quickly graphs graphs strongly strongly strongly strongly allowing success success success success success success success success lie contribution vary realistic minimizes illustrates preferred preferred jacobs jacobs tesauro tesauro tesauro tesauro modelling extend presents employed employed unlike american accurately preliminary behaviour reducing tech applicable relationships scaled scaled reliable statistically statistically statistically momentum momentum measurement measurement measurement naturally man predicts predicts extremely portion precise epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch arbitrarily averages averages massachusetts indicating great great great failure answer benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark lies worse comparisons sections sections widely precisely broad desirable arise involve recording cybernetics mellon addressed questions questions varies considerably carnegie limits reflect cmu effort effort effort effort effort employ exhibits exhibits mod pittsburgh differs popular popular incorporating incorporating decoder decoder decoder decoder decoder unbiased unbiased median median median median median median converged wesley displays proportion proportion proportion proportion addison harmonic encoder encoder encoder encoder encoder adjusting biased biased biased reliably published evident modelled modelled modelled shortest shortest shortest shortest pollack pollack agree fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman fahlman robert metrics metrics drop slight unable incorporates solves benefits failed failed failed failed corrected corrected corrected corrected corrected amherst amherst chapter chapter affects australia australia exclusive exclusive exclusive exclusive exclusive exclusive exclusive exclusive epsilon epsilon epsilon epsilon epsilon epsilon dominated ultimately portions descending descending descending descending descending descending page investigations simplex simplex dramatic reciprocal reciprocal september tel tel tel failures wider wider wider resembles tail tail excess january satisfactory australian influenced movellan movellan optimisation believed proposes correctness tance approaching coins goodness goodness scott raised greatest searched pendent kolmogorov impor simmons simmons simmons holmes holmes jackknife restart restart restart maximise successes successes successes useless nique succeeded optimise initialisation asymptote imal wasted kruschke kruschke optimising optimised optimised optimised optimised byte restarted unsuccessful unsuccessful benchmarking benchmarking benchmarking benchmarking benchmarking benchmarking benchmarking nsw nsw unscaled leonard leonard javier lna encompass truncation speeded discards broaden 
#@Hamey_L,
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#*network network network network network network network network network network network network network network network network network learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data function function function function function function function function function function function time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm number number number error error error error error results results units units units units units information information information problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden performance based based based based based space space space space weights linear linear linear linear linear layer layer layer case case case vector vector shown systems systems systems values parameters weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions neurons distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method approach approach point image image image image single single single single single single processing processing processing large local neuron neuron neuron neuron neuron rate test analysis analysis class class class optimal form form form form signal gaussian visual visual visual visual visual visual paper feature feature net task methods methods methods points features features features classification classification classification classification classification classification classification classification classification classification classification process level level structure structure structure structure problems problems problems problems problems problems problems random high high high high high high high high high response response similar representation representation architecture architecture architecture architecture equation equation section section fixed rule images images images images images images general general general general generalization generalization speech speech speech speech speech speech parameter real approximation approximation average average average average theory theory theory theory gradient obtained obtained term term term term note experiments experiments experiments experiments activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university threshold threshold variables computation computation computation computation solution research research research research research research found found initial initial constant computer terms distance connections connections synaptic synaptic science science science science direction direction presented presented present present activation low low low low object object press press press press press press press press components nonlinear abstract applied applied back back back back back back back back back back back find computational computational computational convergence density properties references due ieee ieee ieee ieee ieee procedure important propagation propagation propagation propagation propagation propagation propagation context context context context introduction hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical statistical variance parallel cost cost cost search search tion energy energy energy difference complexity complexity complexity variable assume classifier lower measure measure measure measure measure prior prior prior prior prior prior chosen type type type required multiple cortex cortex good conditions equations equations make techniques forward forward ing ing ing total total regression regression regression regression regression regression regression regression regression regression multi multi sum sum performed mapping made orientation applications applications knowledge knowledge knowledge em negative original artificial specific specific specific specific specific represented application application application application desired desired proc location constraints constraints constraints constraints constraints constraints cortical cortical brain mit comparison fields morgan morgan morgan proceedings proceedings proceedings report institute department department implementation version version code advances connectionist difficult final delay addition considered experiment directly hinton hinton hinton additional additional additional additional additional san san san significant approximate approximate statistics statistics statistics statistics statistics world estimated pages pages pages pages pages pages pages con con con randomly clustering clustering area lines entropy entropy entropy actual backpropagation iteration iteration nature depends constraint constraint achieved achieved achieved discussion discussion discussion normal technical feedforward tested transformation transformation assumption assumption assumption surface finding finding effective implemented supported supported theoretical main face face face face journal journal journal journal degree development kaufmann objective smaller underlying underlying underlying needed combination interesting interesting interesting testing projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection york york york york special database database empirical empirical language leads principal details pre supervised supervised supervised supervised supervised polynomial idea minimize produced produced produced produced added added description improved improved discussed discussed discussed directions directions recent pair ensemble ensemble ensemble practical practical introduced introduced introduced pixels pixels sense sejnowski cognitive recently recently interest dimensions dimensions varying unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised observations approximately volume volume volume smooth smooth smooth differential observation generalized channels improvement risk risk risk risk lead scaling suggests deviation deviation deviation deviation feed feed locally hybrid hybrid hybrid hybrid hybrid touretzky touretzky clusters setting assumptions depend depend editors editors editors editors editors editors editors editors measures measures measures measures measures numerical performs moody practice practice mateo mateo suggest propose integration reduction reduction sigmoidal sigmoidal demonstrated minimizing minimizing minimizing minimizing explicit appears pro pro index index index index index index index index index index index index estimating estimating ann stability segments multilayer dimensionality dimensionality remaining interaction interaction adding adding minimization minimization minimization extraction extraction extraction yield national national extracted family review phoneme detailed detailed labels soft soft understanding converges sign partial smoothing performing expansion spaces spaces combining fitting purpose add penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty filtering foundation foundation norm transactions transactions handwritten formulation sciences extension specifically priors partially neighbors characterized compression compression compression compression efficiency capable differ modification modification modification included detect efficiently projections projections projections projections projections projections projections projections projections projections projections projections projections vowel vowel soc contained contained cun cun interested neuroscience phonetic contribution gray gray comp michael denker acknowledgments camera minimized minimized selectivity parametric parametric american american layered overfitting overfitting overfitting replaced association association lippmann lippmann graphical hall hall hall hall hall hall pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit reducing reducing school rest behavioral applicable applicable plasticity plasticity office office office workshop notion waibel waibel editor friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman academic academic multivariate multivariate motivated motivated motivated motivated brown stop stop stop agreement smoothness smoothness adjacent nowlan nowlan capabilities lies london processed shared ion ion ion ion potentially projected projected projected projected universal universal ridge ridge ridge ridge ridge ridge ridge computers prop prop prop cochlear cochlear cochlear cochlear embedded leave splines formulated biologically biologically variant variant polynomials howard measuring gen extracting achieves achieves geman acoustics semi comments tile tile tile tile tile cochlea multidimensional sharing sharing sharing lab indices indices indices indices cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper tation restrict nat reconstructed tem naval naval jones jones jones jones jones binocular imposed illumination nonparametric vowels composition composition elimination lang regard jackel tic israel tokens tokens specificity roy pearlmutter pearlmutter implicitly neurophysiology summer gold gold shepard ter annals annals annals annals super maximized munro munro opposed pentland pentland conjecture boser residuals intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator intrator avoided clustered henderson approxi hubbard token searches concentrate emphasize emphasize projecting proach paris hornik hornik represen library zip france reveal esti son preprint modality modality modality elsevier thousands parametrized normalizing exploratory exploratory exploratory exploratory exploratory exploratory exploratory exploratory exploratory exploratory tel helps served bienenstock bienenstock bienenstock corporate inhibited coin lyon lyon lyon lyon lyon bcm bcm pronounced distinguishing distinguishing incorporation consonants consonants slices juang ory synergy autoassociative assp statist rel goodness goodness feldman sparseness media bear aviv aviv eigenfaces favors plenum retaining lincoln lincoln timit timit shikano optimizes huber huber huber huber conveyed tailored aimed scribed conversations concurrently seeking disagree agation froin army fruitful seeks mild sults asymptotics ions concurrent emphasizes karhunen kung hanazawa pertone pertone tha tha normality normality normality normality suit suit turk turk aligning perrone vised stepwise lat leon apple kamm persons deprivation zky touret rio sidered skrzypek skrzypek spe dition xve derlying milton mammone uncover stuetzle stuetzle faithfully alt facilities freedman pur pur zeevi din decouple clouds init pla irregularities ces creasing rosenreid rosenreid multimodality rosci xvith diaconis diaconis rice devia jection cific ational hnage iml jections forin nathan seminar stu ada bfilthoff mator kaufinann israeli atio 
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#*network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure time set set set set training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number number number number number number number number state state state state state state state state state state state state state state state state state state state state state state state state results results results results results information problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance space space space space space space space space weights linear case case values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters functions distribution distribution distribution recognition recognition recognition method method method method method method approach approach approach approach approach approach approach point point point point single local local local local test analysis analysis analysis analysis optimal optimal form algorithms algorithms paper paper paper paper examples examples examples examples examples small size size size size size size size size size size size size work work task task methods step step classification classification classification process process process process current current structure structure structure structure structure structure structure structure structure structure structure random random random random random random random random similar similar similar show section fixed fixed fixed fixed fixed fixed fixed rule general general generalization generalization generalization generalization generalization generalization speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter real average states states states states states states states states states states states states states states states states states states states states states states states theory theory theory theory obtained obtained term term term note experiments experiments result result university university university computation computation research log log log log log log log log found found found found found found found sequence sequence sequence sequence sequence target target target initial initial initial initial initial initial initial initial initial initial initial initial constant table table estimate estimate standard standard standard standard computer computer computer computer computer computer computer terms science science science science science science direction map map map map map frequency machine sets maximum maximum maximum maximum maximum maximum basis outputs sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied back find find find find computational computational properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component stochastic stochastic stochastic due due ieee positive procedure procedure procedure procedure important decision mixture mixture mixture context context context introduction introduction introduction introduction complex complex hand hand hand estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical statistical effect effect dynamic dynamic dynamic generated cost search search search search search search search search search search tion change assume lower measure prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior word chosen higher center previous previous cases cases cases required multiple good long conditions conditions conditions distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov markov markov markov markov markov markov markov markov markov markov markov make make make fact proposed proposed length length length correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed finite finite finite finite finite finite minimum resulting resulting resulting classes total computed sum regions means means means means potential made natural global applications applications study obtain obtain negative artificial artificial relative relative specific specific samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples represented cross cross cross cross series determined determined related related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior connected distributions distributions distributions distributions distributions distributions discrete equal equal approaches approaches steps comparison comparison larger update update modeling proceedings report report report report institute institute institute department loss implementation version technique technique consists final final final bias bias bias bias bias ai considered considered considered computing domain equivalent estimates estimates estimates transition transition transition transition transition transition transition transition transition transition transition transition transition transition top conference determine efficient full full requires choice choice approximate statistics statistics statistics statistics statistics statistics statistics free free world increase increase increase give give produce produce produce produce coding coding weighted randomly conditional criterion entropy entropy entropy entropy entropy entropy entropy path path path path path path path product product product actual actual actual provided finally finally evidence evidence backpropagation iteration sampling simply simply technical technical technical technical increases describe denote hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited close amount shape shape generate generate require journal fit fit fit fit probabilistic probabilistic typically typically smaller smaller smaller smaller smaller account fully programming ratio character york increasing increasing mechanism special consistent trials trials trials trials uniform uniform empirical operation language language language language language language language details details call making making international international international magnitude idea choose added added description description denotes discussed pair robust takes similarity apply strategy strategy strategy identical identical hierarchical trees trees inference inference inference inference cognitive recently sufficient sufficient sufficient varying varying compare compare previously previously volume yields converge converge converge trans chain sensitive exists concept studied locally locally occurs minimal minimal minimal reduce bayes practice practice practice hard drawn california california proportional intelligence start start decrease decrease decrease iii manner connectivity force acknowledgements areas explicit explicit appears construct produces factors factors generating generating generating generating generating generating generating estimating estimating estimating estimating estimating describes describes transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions ann mathematical involves remaining unique unique adding adding frequencies springer formed implies decreases expressed formation formation viewed viewed operations approximations approximations approximated sizes sizes completely completely completely constants updates reasonable smoothing performing performing spaces purpose iterative penalty penalty interpolation generation initially initially initially string string string string string symbol symbol symbol construction construction topology topology topology topology topology david avoid includes strings strings strings strings strings sciences extension priors priors priors priors discussions grammar grammar structural regular regular extra hmms hmms hmms hmms hmms hmms hmms hmms hmms uniformly society society maximal paths paths paths paths paths paths driven symbols symbols symbols symbols literature efficiently computations mackay mackay situation compact verlag induced allowing heuristic stopping phonetic split split sampled generalize highest maximization received attempt attempt decreasing decreasing modelling simpler simpler carried overfitting overfitting create involving issues mass hall ml helpful fewer fewer giving giving incremental incremental incremental proved affect fundamental fundamental notion analogous induction induction induction induction induction induction induction induction induction hill reading automata automata automata automata automata automata adjusted adjusted greedy greedy formal noted generates generates generates generates arbitrarily finds finds languages languages languages languages stop stop biology caused briefly baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum starts starts inside turns stanford stanford berkeley berkeley berkeley berkeley berkeley berkeley arc shared shared easier protein protein division worst worst worst worst worst desirable probable universal implicit implicit implicit gradually depicted annual qualitative alignment conjugate explained integrating integrating virtual virtual virtual freeman freeman lack peter orders adjustable haussler haussler haussler incorporated maxima maximizes incoming incorporating ordered ordered adjust viterbi viterbi wesley merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging globally phenomenon phenomenon don don indices redundant feasible feasible sort sort addison equivalence forming acm driving royal climbing smith smith adds adds chance chains adjusting held replacing check keeping settings settings disjoint monotonically krogh krogh intuitively adequate carry carry generalizes grammars grammars continue reliably meaningful introduces governed iteratively respective induce induce overview young young express ahead refers augmented repeatedly repeatedly grammatical 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tells tells outgoing outgoing outgoing arrives occam occam convention assp compensated chunking accommodate crl accounting accounting goodness cruz feldman feldman feldman magazine bumps computable merged merged merged merged merged merged merged tomita tomita penalizes replicate costly costly infeasible entering notions transferred continuing insertions putting complications andreas berger berger rigorously buntine buntine buntine posteriors evaluates ucsc helped scratch temporary pronunciation penalizing provably deletions relied icsi icsi icsi revised occuring collaboration reuse sept merges summarizing regularizing walks opposing surgery exhaustively exhaustively angluin angluin uncover sacrifice surveys chuck hopcroft hopcroft tracing stolcke stolcke stolcke stolcke stolcke stolcke stolcke stolcke augmentation collapsing wallace wallace mcclure mcclure frontiers wooters cheeseman contingency practitioners flavor recomputed troublesome collapses complemented emitting imi imi jerry 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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training output output output output output output output output output output number number number number number number number error error state results results results results results results results results results results results results results results results results results results results results results results units units units information information models models based space weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer case case case case shown shown shown shown shown shown shown systems systems systems values values functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit approach approach point single single single processing processing processing processing processing control large large large analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class optimal optimal optimal optimal inputs inputs inputs inputs algorithms paper paper paper paper paper paper paper examples small small small size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size net work work work methods field features level structure problems problems problems problems random similar similar show show show show show show section fixed fixed fixed fixed fixed general general general real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states theory theory theory theory theory theory theory theory theory theory obtained note note result result result result result result result result result result result university university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables variables computation computation computation computation computation research log log log log log log log defined defined found found found found found constant constant constant constant constant constant constant constant constant computer science presented present present present low low low low low low low low low low low low press press basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied applied computational computational computational computational computational computational computational computational computational properties references due ieee ieee ieee ieee ieee ieee ieee ieee 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elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements factor factor natural natural applications applications study study obtain obtain obtain vol vol artificial artificial represented compared compared provide define define compute compute compute compute compute related related gain gain discrete discrete power power power power power power power power mit comparison comparison larger words words difficult layers layers layers layers delay addition addition addition addition considered computing computing computing computing computing computing computing computing computing computing computing computing computing computing computing computing computing computing domain equivalent equivalent additional additional additional additional additional view solutions solutions solutions bit conference conference efficient efficient upper upper upper upper requires requires significant significant approximate approximate basic basic basic pages pages increase give give give weighted developed developed bounds bounds bounds bounds bounds bounds bounds area path product backpropagation feedforward feedforward feedforward feedforward feedforward feedforward increases arbitrary arbitrary arbitrary group denote assumption assumption assumption complete complete proof circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits common common common common theoretical require require main main journal journal degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree makes rumelhart development simulated simulated pairs reduced coefficients 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approximations approximations understanding understanding approximated approximated approximated approximated approximated approximated approximated approximated approximated approximated approximated approximated approximated sizes sizes allowed allowed allowed allowed key earlier classical intervals intervals purpose remains valid construction construction transactions expect existing includes includes prove prove prove prove holds reason closely closely closely uniformly divided mcclelland presentation literature literature literature computations characteristic traditional refer compact success showing showing showing interested interested interested interpreted issue sci sci sci sci comp comp comp comp comp notation usual generalize generalize nips computes computes computes computes computes computes computes computes computes approximating approximating extend explore carried powerful collection exponentially limitations limitations periodic existence examine fashion school tech parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity referred gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates workshop func func func hierarchy fundamental fundamental notion math math math editor formal precise explored logic academic switching switching synthetic established established devices devices piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise costs majority majority capabilities answer multiplication stanford stanford implementing widely division division sgn sgn sgn sgn mation commonly commonly mathematics universal implicit computers annual annual argument geometric questions applies employ employ ity summarized characterize cal substantial coherent progress june arithmetic pose proofs sort restriction acm approximates concerned harmonic harmonic harmonic harmonic harmonic harmonic interconnected proceed maass maass rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational accepted tools tools tools logarithmic logarithmic logarithmic logarithmic odd definitions definitions definitions symposium symposium infor utilized thomas enable barron barron offer generalizing integers explorations limitation consecutive unified sig sig deriving sontag failed adopt pointed par monotonicity tight tight tight tight tight tight continuity pdp bounding singularities oscillating oscillating west siam siam siam union october october october computa remark remark remark expense august cornput siu siu siu siu siu siu siu siu siu siu norms nontrivial polynomially polynomially polynomially polynomially polynomially longest irvine irvine comprised ings bruck bruck bruck bruck kailath kailath kailath kailath kailath kailath kailath kailath proximation plexity deeper inte theo roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury concurrently infinitesimal colt ixl ixl ixl syrup syrup syrup syrup michigan niques seventh logn cybenko cybenko motivate modulo mat purdue lhe strengthened superpositions superpositions formalize timal modulus fined yeung dasgupta kai irrespective schnitger schnitger moidal moidal arrange wixi goldmann filnction lafayette stoc newman attacks cently chandra hajnal gon intensively szegedy analyti undoubtedly stockmeyer vishkin reducibility pudlak turan 
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#*network network network network network network network network network network learning neural neural neural neural input input input data function function function function function figure figure figure figure figure figure set set networks networks networks networks networks networks networks networks networks networks networks training output output output output number number number number number number number number number system state state state state state state state state state results units units units information information information problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based space space space space space space space space space space space space space space space space space space space space space space space layer layer case order order order shown systems systems systems functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit approach approach approach pattern pattern single single single processing processing processing large large large patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis class inputs form form form form simple simple simple simple visual visual visual paper small size feature feature feature work work work task task task task task task task task task task task task features features features features features features features features features process current trained trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure high high memory memory memory similar similar representation representation representation representation representation representation representation representation representation representation show show show show show real states states states states states states states states states states states theory theory dimensional dimensional dimensional university university university computation computation research research found found computer computer terms terms terms terms terms connections science science presented temporal temporal temporal machine machine machine machine machine object object object object object object object object object object object object press press position components components components basis basis outputs outputs outputs abstract abstract abstract abstract abstract applied find computational properties references component component component component component component due important important recurrent recurrent recurrent recurrent spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial prior representations representations representations representations representations representations representations representations word higher higher center previous type required required required required required represent represent represent represent represent represent represent represent techniques region region region region region region region region region region finite finite finite finite finite finite simulations simulations simulations simulations simulations classes classes tasks tasks tasks simulation simulation human multi multi elements regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions mapping mapping dimension study knowledge vol relative represented represented represented represented represented represented represented represented provide provide objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects location location location location eye related larger larger contrast support morgan morgan report words version consists consists individual individual individual advances advances advances represents connectionist connectionist connectionist sequences sequences equivalent equivalent equivalent equivalent additional additional view view san san san capacity efficient requires vision increase clustering clustering types provided provided processes nature nature technical increases group corresponds corresponds complete implemented shape shape shape shape shape shape shape shape shape supported supported require main eds eds face square square square square square cluster cluster future easily including kaufmann kaufmann smaller smaller needed functional interesting language principal representing representing representing numbers idea combined improved separate separate hierarchical hierarchical hierarchical hierarchical sense cognitive dimensions dimensions dimensions pca pca background locations locations locations separation separation entire constructed horizontal horizontal scaling extended alternative alternative alternative touretzky clusters clusters clusters clusters clusters demonstrate demonstrate demonstrate demonstrate demonstrate conclusion minimal minimal minimal minimal trajectories clear moody mateo mateo presence largest california exist groups groups groups groups groups groups groups scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene program acknowledgements ways label vertical vertical distinct distinct dept dimensionality dimensionality unique adding implies extraction extracted extracted extracted independently review squares squares squares interpretation interpretation variation variation variation variation showed showed showed showed showed showed showed showed lee lee lee key key key key key valid initially degrees expect recorded figures combinations combinations combinations combinations color color color color color color color color color color grammar straightforward aspects aspects aspects identified identified identified identified suitable encoded mcclelland mcclelland mcclelland identify identify identify projections projections plots orthogonal ten ten repeated contained showing interpreted cue categories involved simplified providing giles giles giles giles giles giles binding binding binding binding overlapping overlapping overlapping overlapping illustrates neighboring intrinsic extend explore diego xor create access access difficulty hanson limitations lippmann discriminant discriminant fewer reducing mappings encode circles plausible necessarily extremely automata psychology implementations aspect aspect freedom separated separated shapes shapes shapes shapes shapes multivariate grouping grouping sentences indicating scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes explanation adapted operators projected projected involve circle circle circle circle circle circle circle sun sun sun double items elman elman elman elman elman elman embedded embedded red red red red red red red red red psychological requirement partitioning extracting chen chen chen chen chen chen green green green green green green logical logical logical logical logical logical logical logical logical logical logical coherent inherent semantic trade lab identifying identifying equivalence labelled labelled tensor tensor encoder encoder flexibility lost mark exploit analyzing reasoning reasoning disjoint disjoint disjoint disjoint implications implications canonical canonical canonical canonical canonical canonical combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial grammars grammars grammars wilson analyses analyses analyses embedding separating conjunction demonstration competing arrangement tokens tokens grammatical grammatical partitioned grants intersection intersection intersection intersection intersection dividing linguistic mind compressed solves abstraction blue blue blue blue blue blue blue australia australia reflected clustered clustered clustered alternate alternate grouped grouped grouped grouped grouped learnt token maximally harder nonetheless exploited functionality council excess reversed australian vis reflecting steven triangles triangles triangles triangle triangle triangle triangle triangle lying functionally colors colors colors colors crl fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm schreiber schreiber schreiber cleeremans cleeremans cleeremans servan servan servan wiles wiles wiles wiles wiles wiles wiles wiles wiles simon phillips tightly entities albeit humphreys humphreys accessible concise concise perspectives corresponded contiguous idealized isomorphic isomorphic explosion emphasizing intersecting intersecting intersecting intersecting intersecting intersecting intersecting intersecting intersecting intersecting intersecting intersecting intersecting queensland tri reber reber groupings groupings emulation emulation hierarchically conjunctions conjunctions simplifications nouns analogical fsms intersections cda cda cda cda cda verbs orlando analogies analysing analysing florida legend completing tracing motivations legitimate drastic dennis expose janet unused ablex stewart episodic combinatorially procedural surprised qld vic brace norwood melbourne 
#@Ollila_M,Wiles_J,
#t6
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#*network network network network network network network network network network network learning learning neural neural neural neural input input input input input input input input input input input input data data data data data data data data function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number error error error error error error error state state results results results results results units units units units units units units units units units units units units units units units units information information information information information hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown systems values probability parameters parameters parameters parameters noise weight weight weight weight weight functions functions unit unit unit unit unit unit unit unit distribution distribution method method method method method approach approach approach single single processing processing processing processing large large large local local test test test class class class matrix matrix matrix matrix inputs inputs inputs inputs form shows shows shows simple simple simple simple simple simple simple simple gaussian paper paper paper paper size size net net net net net work work work task task task task task task task fig step step step step step points points points process process current trained trained trained trained trained trained trained trained trained trained trained trained structure structure structure structure structure structure structure structure structure random random random random random high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar similar similar representation representation representation representation representation representation architecture section section fixed fixed fixed fixed fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors parameter real average average average average average gradient gradient gradient gradient gradient gradient gradient term term term term experiments experiments dimensional dimensional result result university university university computation log defined defined defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target target target initial standard computer computer computer computer terms terms science science science left map present phase activation activation activation activation activation activation low nodes frequency frequency frequency temporal machine machine range learn position outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous abstract find properties references component component component due due propagation context context context context context context context context introduction complex generated generated generated generated variance parallel parallel cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search search change change difference difference variable lower representations representations representations representations representations representations representations representations representations representations chosen chosen chosen previous previous cases type required required required required required multiple multiple good good good long long long represent represent distributed distributed distributed distributed distributed expected expected expected techniques techniques techniques techniques length length length length length length length length length length length length correct correct finite finite resulting ing ing tasks total computed computed respect performed called times times times elements elements elements elements elements elements elements elements elements dimension dimension dimension made artificial artificial represented desired compute location perform active active active gain discrete discrete equal equal power power power power power power steps steps steps steps steps update train train descent descent descent descent descent nets nets nets nets nets nets nets morgan proceedings proceedings report report report department department version internal code code code code code code code code advances joint represents difficult bias layers scheme addition graph graph graph sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences maps maps cambridge domain hinton trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory bit bit conference conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine efficient approximate approximate approximate approximate speed pages pages give con produce produce produce produce produce derived derived randomly randomly path product product provided constraint simply associative associative associative associative associative associative associative associative associative associative associative associative achieved discussion technical technical increases increases denote tested tested fast limited inverse inverse inverse inverse inverse inverse inverse inverse inverse stable stable stable finding rbf amount short generate generate generate generate generate generate generate role role main end ability instance easily easily easily easily makes rumelhart rumelhart rumelhart noisy noisy noisy objective pairs pairs pairs pairs pairs hopfield combination reduced reduced reduced reduced testing significantly operation operation operation operation operation operation operation representing call numbers iterations window window stored stored stored bits international normalized magnitude produced run denotes improved improved improve improve exact exact advantage property takes element element element element element element similarity reported reported identical machines hierarchical hierarchical hierarchical sejnowski sejnowski sejnowski engineering sufficient varying compare compare conventional calculated volume works works symmetric symmetric symmetric williams exists expression scaling scaling scaling suggests derivative matrices correctly width generally runs runs conclusion greater trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories operator operator operator editors sigmoid sigmoid sigmoid designed designed moody learns encoding encoding taking intelligence intelligence exist relationship targets targets derivatives derivatives force denoted appears relation longer sequential sequential sequential sequential sequential sequential generating generating generating changing implement electrical slightly angle unique frequencies blocks versus independently focus correlated viewed codes codes transform operations fraction digits key key key key key partial partial roughly purpose add add penalty penalty penalty penalty generation generation generation generation generation generation generation remains remains symbol symbol euclidean euclidean euclidean precision handwritten activations activations activations activations activations activations activations instances memories memories memories memories memories recognize plotted grammar successfully identified extra suitable modification effectively symbols symbols symbols tdnn identity identity reached quickly decoding decoding decoding decoding decoding cun superior issue generative generative generative generative generative generative generative built satisfy list involved vary generalize nips computes subsequent situations poor poor production investigate difficulty difficulty involving hanson association association association association association association association recursive divergence biases scalar fourier fourier successive successive giving links links links applicable tanh tanh encode understand cognition analogous induction adapt extremely ensure aspect impulse obvious logistic extent extent averages percentage ment convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution multiplication multiplication multiplication benchmark shared closer style incorporate incorporate incorporate worst products simard simard simard simard calculations beginning toronto toronto toronto read outer raw conjugate conjugate varies greatly greatly considerably items items elman elman elman elman item incorporated compares passes passes passes passes passes ture serve suited gave asymmetric attraction windows softmax softmax softmax softmax summed summed summed ordinary generator restriction circular circular circular circular circular circular circular circular circular circular circular circular circular circular circular circular circular unity unity lecun lecun lecun turned kaufman numerically chance chance difficulties familiar serves transforms modifications grammars grammars inferior reset introduces induce regarded lengths den surprisingly omitted offer matter clean clean clean clean clean clean clean clean repeatedly late canada grammatical arrows storing storing storing correcting correcting correcting reverse interestingly pen explorations andrew multiplying ure associations associations appeared land unable microstructure shorter graded copy chapter recurrence associate forcing australia adapting adapting verified preserved modifying exclusive goals graphics disadvantage disadvantage plate plate plate plate plate plate plate plate plate plate plate plate altered books retain retain retain unconstrained represen nonetheless algebra modifiable lippman behaves challenge reversed compositional rosenberg rosenberg rosenberg aid overtraining puts hopkins powers powers powers identically tip judged architec johns curved bach nettalk nettalk tations thing bradford schreiber raised baltimore decoded decoded backwards 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abstract applied applied back find find references due due ieee ieee ieee ieee ieee ieee procedure procedure adaptive decision decision decision decision propagation introduction hand effect generated generated generated generated change difference difference difference difference difference assume classifier classifier classifier classifier lower lower lower prior prior higher higher higher higher center center center center center center cases cases required multiple multiple good good distributed fact techniques correct correct finite finite minimum minimum total total total respect respect respect multi multi called called called elements elements elements means factor factor factor made study obtain obtain obtain obtain original original original original original original original original original original original original original original vol vol vol vol vol vol artificial samples samples samples samples rates rates rates location location location determined connected discrete equal larger train train train train nets morgan morgan proceedings report institute institute institute implementation technique consists consists code kernel kernel advances advances difficult difficult difficult final exp layers scheme scheme scheme addition maps additional design san san effects classifiers classifiers upper upper upper full requires choice choice choice choice significant significant significant approximate basic increase validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation give give give give give produce produce produce randomly criterion criterion criterion criterion provided selected evidence backpropagation backpropagation backpropagation depends depends depends group tested tested close close assumption corresponds proof amount generate generate generate generate generate generate generate require eds journal square square square pixel pixel pixel pixel pixel ability degree degree degree degree makes makes development fit fit kaufmann kaufmann typically typically typically typically typically typically smaller needed combination reduced account fully technology technology interesting testing testing significantly character character character database database database leads squared details call numbers numbers international normalized normalized normalized supervised added added added added denotes architectures improved improved discussed improve improve ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble reported reported practical machines machines machines sense array array array array varying compare previously previously previously approximately approximately approximately approximately works axis axis axis axis axis axis axis axis differential achieve achieve trans trans diagonal diagonal address improvement improvement improvement improvement increased constructed intensity intensity scaling rotation correctly correctly correctly correctly pass pass pass pass pass half half half starting critical critical reduce conclusions depend tangent measures moody weak mateo mateo hard hard largest largest largest intelligence labeled labeled decrease derivatives derivatives derivatives derivatives manner manner manner characters characters acknowledgements suppose digit optical optical generating label label confidence confidence confidence confidence confidence recall simultaneously remaining consisting consisting adding adding adding adding formed letters national national national independently codes codes codes codes detailed labels showed centered soft similarly suggested translation translation translation digits digits digits digits digits digits digits digits digits digits digits digits constants constants sign key partial partial smoothing combining add add add add penalty penalty filtering assigned assigned construction construction norm classified classified handwritten handwritten handwritten handwritten coordinate coordinate bell bell bell recognize discuss straightforward selecting uniformly divided divided build essentially ten ten repeated procedures interested usual usual generalize minimizes highest poor hanson recursive lippmann history boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting combine combine proper workshop scores hill reading man man opposite equally recognizer observe consist consist generates improving improving improving improving improving improving arbitrarily arbitrarily finds years great theoretic publishers publishers expensive inside straight formalism shared incorporate commonly products laboratories laboratories laboratories simard simard simard simard simard simard simard simard simard potentially attribute cybernetics cybernetics incomplete recognizing raw percent percent prop evaluating double collected pseudo simulate passed passed passed passed passes reaches reaches achieves segmented segmented segmented segmented june credit differentiable differentiable sharing newton sort sort labeling labeling labeling mistake assign extensive martin martin summing databases databases printed printed lecun lecun lecun lecun lecun wrong wrong wrong murray numerically mail proceeds alpha alpha obtaining continue service service service published financial schapire schapire schapire schapire schapire schapire schapire schapire schapire respective iterated ensembles april smoothed smoothed smoothed smoothed smoothed smoothed theoretically agree agree broken statement harris border border summarize acknowledge robert dramatically slight constitute accept accept accept leaming presenting july july july retraining quasi ideally classifies classifies classifies classifies reject reject reject reject reject reject reject reject reject reject reject reject reject reject reject reject quantized invariances alternate continues convert learnability rejected rejected rejected rejected rejected flip unconstrained zip zip zip zip zip voting voting voting voting voting sized happen dramatic article picking emphasis nist nist nist nist nist nist august twenty twenty twenty decided send coin coin coin coin coin overtraining supply mining mining incorrectly incorrectly incorrectly incorrectly supplied holmdel holmdel conflicting thickness thickness vote push distorted distorted fair fair deformation deformation deformation deformation deformation deformation statements united united united proceeding proceeding tails tails drucker drucker drucker drucker drucker drucker drucker drucker postal postal postal converts pull deformations deformations conceptually usps usps usps usps usps convolving retrained retrained boost paid disagree disagree resampled consensus deformed deformed deformed deformed deformed deformed deformed deformed deformed deformed 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linear linear linear linear linear linear linear linear linear linear case case case case vector vector vector vector vector vector vector vector order shown shown systems systems systems parameters parameters functions functions functions distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point image image image image image image image image image image image image image image image image image image image image image image single processing large large large large large large large local local local local local rate rate rate rate rate rate test test test test test test test test test test test test test test 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minimum minimum minimum tasks tasks total human human computed computed computed computed computed computed computed computed computed computed computed computed respect respect respect respect respect respect respect sum eq times times optimization potential dimension dimension made made made made applications applications knowledge knowledge knowledge knowledge original original original original original represented represented represented represented represented true true true true compared application series define compute compute compute distributions comparison comparison larger contrast descent morgan report institute words loss implementation implementation implementation version version consists consists advances represents difficult ai computing computing computing computing computing computing computing computing experiment experiment curve curve curve additional additional curves curves curves san top top effects conference efficient efficient efficient efficient efficient efficient classifiers classifiers requires significant statistics speed estimated pages pages condition lines lines lines product provided provided finally selected selected selected selected iteration iteration depends depends constraint constraint associative measured measured discussion describe group tested tested transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation limited close close close close corresponds stable finding finding finding finding rbf amount amount nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest implemented generate generate require main face pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel instance easily easily typically smaller smaller needed combination combination technology interesting interesting character character character character character character projection increasing special matching database database database database database database database database database database database database principle representing details stored stored stored international normalized normalized normalized bottom bottom magnitude idea idea minimize added added improved improved improved improve resolution advantage property similarity reported apply introduced moving include machines side side pixels pixels pixels pixels pixels pixels subset interest dimensions dimensions highly highly volume volume volume tions tions solve yields yields yields correspond studies converge achieve achieve trans symmetric generalized organization sensitive entire increased horizontal expression studied invariant invariant invariant invariant invariant invariant invariant invariant scaling scaling scaling scaling scaling scaling scaling scaling deviation derivative matrices rotation rotation rotation rotation rotation rotation rotation rotation rotation locally locally locally touretzky white pass demonstrate conclusion critical minimal reduce neighbor neighbor neighbor neighbor neighbor tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent differences measures clear performs faster mateo propose hard hard hard hard labeled radial radial radial radial turn min min plane plane plane derivatives characters minima digit digit digit digit digit digit digit digit digit construct solving solving solving winner ways label changing changing sensitivity coordinates coordinates linearly involves involves transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations easy slightly slightly angle angle adding adding springer springer select competition competition john yield expressed depending squares squares squares viewed solved evaluate showed approximations approximations approximated approximated approximated translation translation translation translation translation translation translation translation translation translation digits digits key partial partial earlier smoothing smoothing smoothing spaces normalization neighborhood roughly remains distances distances distances distances distances distances distances distances filtering norm euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean kohonen kohonen classified classified classified classified existing handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten priori priori priori priori priori coordinate bell bell instances sciences plotted plotted illustrated discuss discuss variations black neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors reason columns regular middle middle aspects identified efficiency differ effectively symbols identify efficiently efficiently schemes post invariance invariance invariance identity orthogonal characteristic road soc verlag kind repeated procedures contained cun cun cun cun cun cun cun success success interested interpreted split dis dis superior classify manifold manifold manifold manifold manifold manifold gray dot dot nips quantization denker denker denker denker denker denker denker denker leading leading reach reach consisted approximating approximating transformed transformed difficulty fewer reducing reducing fashion giving ideas school tech scaled office referred affect func surfaces attributes closest closest closest closest closest editor necessarily extremely adjusted prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype quantities portion formal expressions expressions extent simplest submitted finds mentioned convolution fairly improves analytic analytical majority adapted expensive worse starts purposes closer closer organized filtered operators operators desirable hyperplane hyperplane products laboratories laboratories simard simard simard simard simard simard simard simard simard simard projected beginning members robustness geometric greatly greatly prop evaluating populations substantially amounts amounts amounts tional conducted parameterized readily leave leave orders incorrect templates span span prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes howard rely rely differs suited hamming windows eventually differentiable differentiable differentiable yielding extreme irrelevant globally consistently classifying classifying newton optimality formally lvq lvq databases databases databases databases rotated rotated hyperplanes eliminate rotations rotations rotations lecun turned kaufman adds adds promising mail transforms transforms unlabeled affected corner degradation substituting service meaningful respective respective surprising pat conjunction bad jackel candidates competing elastic express creating indicator shortest dividing empty unchanged multiply multiply yielded truncated slight visually solves ent planes planes planes planes planes covering uniquely boser big illustration clas henderson invariances invariances translated translated translated translated translated translated concentrated modifying parzen manifolds manifolds manifolds manifolds manifolds manifolds manifolds distant hubbard efforts considers translations translations translations translations sheet denver preserve confusion suffer truth port gorithm students coming picking fortunately nist nist nist nist nist nist nist lation hyperbolic decided terns hoc outperformed outperformed resampling holmdel thickness thickness thickness progressively progressively offsets norms digitized digitized digitized tance tance vertically statist concatenated excessive tan dist dist postal ted drawbacks inserted meaningless upward blurred decompositions intersect deformations imposing schematically netherlands collect usps usps yann named ting remember workers deformable ism transfor labelings patrice official official saving victorri victorri standards nical sification mations finished 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techniques finite finite finite minimum minimum minimum resulting computed computed computed computed computed computed computed computed computed computed computed computed computed computed computed respect multi sum sum sum sum sum sum sum called called elements natural natural study study study study vol artificial artificial specific application application define define define define define define compute compute compute compute compute compute proc related related related related related related related related discrete discrete brain power power mit implementation version represents represents represents layers layers layers delay delay delay delay delay delay addition addition addition addition addition addition addition addition addition addition considered considered computing computing computing computing computing computing bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit efficient efficient requires significant speed basic basic basic basic pages 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showed constants allowed key reasonable reasonable delays classical classical classical classical combining intervals building weighting sciences extension prove prove aspects computationally divided mcclelland build build capture traditional traditional traditional refer conf interested interested issue contribution sci sci sci comp comp comp comp realistic computes computes computes processors situations powerful powerful american exponentially limitations issues issues issues existence ideas school rest parity parity parity parity parity parity referred comparable gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates proved proved func hierarchy hierarchy understand fundamental neu math math possibly integer integer integer integer integer formal observe logic logic logic logic logic logic nervous motivated devices mentioned theoretic majority majority majority majority majority majority majority 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initial initial table table table table table table computer terms connections science science science presented presented presented presented presented presented presented present present activation activation activation activation activation activation nodes machine machine sets learn learn learn learn learn learn learn learn learn continuous continuous continuous continuous continuous abstract computational convergence properties references references positive positive positive positive positive positive positive important context context context context context context context context context context introduction introduction action action action action action action action action action complex effect recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change complexity complexity assume rules rules prior prior prior prior prior prior prior representations representations representations learned learned learned higher higher center cases required required required long conditions conditions conditions represent equations make make techniques techniques length length length length length length length length correct finite finite finite simulations simulations ing tasks tasks total performed called called called times elements mapping optimization made study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge obtain negative negative negative negative negative negative negative negative negative negative negative vol artificial artificial proc proc proc active experimental constraints discrete discrete larger train morgan morgan morgan proceedings report consists consists advances connectionist final final exp graph sequences sequences maps computing domain domain additional additional curves transition transition transition transition san san san top top top top top top determine determine efficient efficient efficient requires requires statistics statistics free free free free free free free free free free speed con clustering clustering clustering criterion criterion types product product provided provided provided selected depends simply discussion limited limited close corresponds corresponds corresponds actions amount short theoretical require require eds journal journal end end end end instance makes makes including kaufmann kaufmann kaufmann objective objective objective pairs needed reduced fully fully significantly character character character increasing special operation operation language language language language language language language language language language language language details details numbers numbers magnitude idea idea added sources description description discussed discussed recent exact element typical typical practical introduced period inference inference inference inference subset cognitive cognitive interest interest varying previously teacher studies rl modified williams williams improvement improvement concept touretzky deterministic deterministic deterministic deterministic deterministic conclusion starting greater reduce reduce valued performs performs faster mateo mateo mateo hard external external external external external demonstrated demonstrated intelligence intelligence labeled minimizing start start selective selective selective characters characters longer ways ways ways ways ways plot transitions transitions distinct dept changing extraction national depending detailed operations updated lee lee lee lee suggested allowed allowed partial partial earlier earlier epochs epochs epochs epochs epochs generation remains valid string string string string string string string string string string string string string string string string symbol symbol symbol symbol symbol symbol symbol symbol degrees building figures activations activations activations priori priori priori strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings strings extension discuss grammar grammar regular regular regular letter capable importance society computationally symbols symbols symbols symbols symbols presentation presentation presentation identify build miller reached reached reached reached reached refer conf conf conf conf kind induced contained success success success interpreted issue running built comp comp usual providing giles giles giles giles giles giles giles giles giles giles giles giles giles giles giles giles reach simpler unlike unlike essential essential limitations limitations biases history tech rest incremental incremental incremental incremental incremental incremental int structured structured structured proper proved matched induction induction induction necessarily reading reading automata automata automata automata automata automata 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words implementation implementation implementation implementation technique technique technique technique technique technique individual difficult final scheme scheme considered considered computing equivalent environment environment directly directly additional estimates estimates estimates estimates full choice choice choice choice choice significant approximate approximate estimated basic give con produce condition weighted weighted weighted developed criterion criterion criterion criterion types types types types actual actual provided processes selected selected depends measured denote close close complete surface common common common common generate generate generate supported journal end hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance instance instance instance instance easily degree degree including including including pairs pairs pairs pairs underlying needed unknown unknown unknown technology uniform uniform uniform uniform uniform leads leads leads representing representing representing direct direct direct direct making international international idea minimize minimize minimize minimize minimize minimize minimize choose choose choose choose predict denotes denotes discussed discussed discussed discussed exact exact advantage advantage property pair takes takes practical practical practical introduced identical side subset engineering varying observations approximately works studies achieve achieve achieve achieve rl address address definition definition interval grant invariant invariant invariant extended derivative rotation rotation rotation alternative deterministic generally generally runs conclusion assumptions valued depend measures measures measures numerical performs taking largest largest california proportional assuming assuming assuming start start exist introduce question acknowledgements explicit suppose suppose suppose relation pro produces written ways sequential generating describes recall implement simultaneously simultaneously simultaneously averaging averaging electrical unique consisting integrated minimization minimization minimization shift quality quality quality quality quality implies implies boolean independently independently independently expressed estimator evaluated forms translation allowed reasonable normalization event penalty penalty penalty penalty penalty penalty includes perceptrons batch batch batch batch batch batch batch batch batch batch illustrated discuss discuss simplicity selecting middle identified importance effectively comparing invariance invariance invariance invariance invariance invariance invariance situation situation situation situation situation reached reached heuristic superior criteria satisfy notation quantity list usual paradigm paradigm paradigm paradigm giles hypotheses hypotheses hypotheses reach reach reach automatically automatically attempt attempt moves approximating satisfies satisfies deal situations employed schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule access essential difficulty ml rise rise rest symbolic func notion notion smallest illustrate perfect eyes quantities quantities versions consist simplest simplest simplest attempts attempts inequality developing crucial distinguish agreement answer answer processed purposes organized preprocessing strictly forces arises author reflects reflect parameterized introducing treated treated requirement requirement passes popular incorporating incorporating pasadena achieves implements simultaneous simultaneous hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints 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#@Abu-Mostafa_Y,
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input input input input input input function function function function function function function function figure figure figure figure time time time time time time time time time time time time time time time set set set training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output number number number number number number number number number number system system system error error error error error error error error error error error error error error error state state state state state state state state state state state results results results results results units units units units units units units units units units units units units units units units units units units units units information information information information problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based based based weights weights weights weights weights weights 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current current current current current trained trained problems problems problems high response similar similar representation representation representation section fixed fixed real approximation approximation average average average average average gradient gradient gradient gradient note experiments experiments experiments result university university university university variables variables variables computation computation solution research research defined found found found sequence initial constant constant constant constant standard computer computer computer distance science science science science prediction presented present activation temporal temporal temporal temporal machine machine machine machine machine maximum maximum press learn learn learn learn learn learn position position outputs outputs abstract applied applied applied applied applied back back back back back find references component component due ieee ieee procedure procedure procedure propagation propagation propagation propagation propagation introduction action action action action action action action effect dynamic dynamic dynamic dynamic variance variance parallel parallel search search search search search tion tion difference difference difference variable lower measure measure measure signals representations part center multiple good conditions conditions conditions conditions equations equations fact region length probabilities observed errors errors forward resulting ing ing sum sum sum sum sum sum sum performed called times times elements reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor feedback study knowledge knowledge represented series define rates goal goal equal equal equal equal approaches approaches mit steps steps steps steps steps steps steps larger larger update train descent modeling morgan morgan morgan proceedings report report department department department version technique consists advances advances advances connectionist difficult difficult addition addition graph considered cambridge domain additional solutions curves estimates transition san san san top effects effects determine determine requires significant approximate pages pages pages pages condition derived weighted weighted weighted bounds bounds velocity velocity controller controller provided provided selected selected simply discussion technical technical tested tested tested fast limited complete actions predictions amount supported require future future kaufmann kaufmann kaufmann objective objective objective simulated simulated typically needed jordan jordan programming programming programming programming programming testing significantly significantly uniform squared details details max max max max making international normalized supervised supervised supervised early early early magnitude magnitude magnitude choose run run added predict discussed recent reported apply strategy conventional conventional volume volume solve solve studies modified modified modified modified grant grant expression occur deviation locally move touretzky touretzky touretzky width occurs runs runs runs runs runs runs conclusion starting greater greater editors differences measures sutton sutton sutton sutton moody faster learns constrained mateo mateo mateo largest demonstrated radial assuming assuming assuming start exist min plane decrease averaged averaged pro produces primary tuned vertical vertical multilayer involves angle angle angle integrated adding adding applying events implies versus versus decreases choosing choosing national focus stages stages stages overlap detailed controlled updated suggested converges past barto barto barto barto combining roughly interpolation remains initially initially calculate calculate foundation transactions transactions existing existing thesis assignment sciences extension maximize maximize mozer mozer mozer specifically domains domains major planning determining determining maximal modification computationally detect genetic reached compact compact anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson strategies timing usual dayan dayan generalize paradigm paradigm delayed received operating preferred jacobs jacobs presents explore unlike singh singh experience experience experience experience exponentially optimized optimized lippmann fashion giving ideas incremental relationships scaled workshop analogous removed removed neu editor editor man predicting psychology observe initialized improving utility utility utility phd attempts averages averages massachusetts cart cart cart cart asynchronous publishers track track track unstable unstable failure failure failure failure failure failure failure expensive glass lin lin straight sections widely ran ran ran ran ran ran controls watkins watkins watkins watkins watkins watkins laboratories acknowledgement optimize arises cybernetics cybernetics recognizing radius fourth prop led relevance rep rewards summarized resource resource resource sums june credit extreme angular velocities concerned discovery repre nonzero smolensky smolensky smolensky platt platt platt platt platt platt platt platt platt platt smith smith allocation allocation stated balance balance resulted fail ral symposium generalizes continue continue motivation published performances mance reset combines studying studying perfor washington colorado colorado widrow widrow counting foundations mem bins shortest pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum balancing balancing cam balanced balanced balanced balanced balanced balanced balanced discount removal corrected ideally amherst 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#@Anderson_C,
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hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based space space space weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case order order shown shown shown shown shown shown shown systems systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters noise noise noise noise noise noise noise noise weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution approach pattern pattern point point point image image image single single single single processing processing processing rate test test patterns patterns patterns patterns analysis optimal inputs inputs form form shows algorithms simple small net net net task task task task fig level trained trained trained trained trained trained trained trained structure random random random random random random high high response representation representation representation representation representation architecture architecture show show show line rule general average average average average average average average average average average states theory theory theory theory theory theory gradient term note note experiments experiments experiments experiments activity result result university university threshold solution research research research research research independent independent independent defined sequence constant table table standard standard computer terms distance distance distance distance distance distance distance distance distance distance synaptic node node node node node node node node science science science left presented activation low nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine sets sets press learn learn learn learn nonlinear nonlinear outputs outputs sample abstract back back back find convergence properties properties properties references component procedure procedure propagation introduction complex hand statistical effect effect tion tion tion classifier lower lower representations representations representations representations representations representations representations representations representations representations representations representations representations higher part part previous bound bound cases type required binary conditions conditions distributed distributed expected expected techniques region correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed errors errors errors errors errors errors errors forward forward simulations minimum minimum minimum minimum resulting ing computed multi sum performed performed factor factor potential potential applications artificial relative represented active active active related distributions equal equal approaches approaches comparison larger support descent source source nets nets nets nets morgan morgan proceedings proceedings proceedings words department loss technique consists consists code code code code code code code code code code code code code code code code advances advances represents layers layers layers layers layers considered computing computing experiment environment directly hinton hinton hinton hinton hinton additional additional solutions curves san san san san top stimuli stimuli bit bit bit bit bit capacity capacity efficient efficient upper upper full requires free increase increase increase increase con condition channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel coding coding coding coding coding coding weighted randomly randomly randomly randomly criterion bounds provided selected backpropagation backpropagation backpropagation backpropagation iteration nature depends constraint simply simply biological measured discussion normal increases increases tested tested transformation corresponds corresponds corresponds corresponds effective effective role theoretical require eds adaptation rumelhart rumelhart development noisy noisy kaufmann kaufmann simulated pairs needed fully fully block programming programming interesting york increasing increasing mechanism mechanism consistent uniform uniform uniform uniform uniform mode mode principle numbers direct bits bits bits neuronal architectures robust robust robust similarity introduced introduced include include machines subset subset subset subset sejnowski sejnowski cognitive cognitive sufficient varying varying works works correspond correspond studies converge symmetric channels williams williams storage entire lead lead suggests trial derivative predicted alternative feed feed boundary generally generally setting half half half half reduce tangent tangent sigmoid measures moody moody moody faster mateo mateo encoding encoding encoding encoding sigmoidal demonstrated demonstrated denoted denoted acknowledgements boltzmann boltzmann pro carlo carlo ways factors ann mathematical category linearly linearly remaining mutual decreases correlated correlated correlated correlated correlated communication communication squares viewed codes codes codes codes codes codes codes codes open completely allowed allowed dashed neighborhood roughly distances distances distances distances distances distances distances distances distances distances string string symbol symbol symbol assigned construction box includes combinations strings plotted 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strictly hyperplane potentially gradually begin author radius robustness robustness robustness applies items empirically introducing passed pittsburgh pittsburgh spread fall enables hamming hamming hamming hamming hamming hamming hamming kinds decoder tolerance tolerance tolerance tolerance tolerance simultaneous wesley naive uncorrelated uncorrelated college redundant addison guarantee princeton optimizing dynamically discovery repre encoder encoder encoder encoder encoder encoder encoder nonzero extending ranges siemens siemens siemens analogy resistance keeping methodology cottrell cottrell cottrell optimally enhanced alphabet alphabet alphabet filled reliably prentice interference mance introduces ranging paul induce perfor pat vertices enhance enhance sphere claim claim claim enable multiplied recovery specialized young young vertex passing extends hypercube correcting correcting correcting correcting correcting correcting correcting considerations partitioned designing valuable 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#@Judd_S,Munro_P,
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#*network network learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training algorithm algorithm algorithm algorithm number number number system error error error error state state state state state state state results results results units units units units units problem problem problem problem space space space weights weights linear linear linear layer layer layer layer layer order order order order systems systems systems systems systems systems values probability probability parameters weight method point single single control control local local test analysis class form form form form form form form form form form form form form form form form form form shows shows shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple size size size size feature feature work work task methods methods cells cells cells cells cells cells cells step process process process process process process process current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random similar similar architecture fixed general parameter real approximation approximation average average average average states theory theory gradient gradient gradient gradient gradient note experiments experiments dimensional dimensional dimensional dimensional university solution solution solution research research research research research research research defined sequence sequence initial initial initial initial initial initial initial initial table computer computer terms terms terms terms terms connections synaptic science science prediction prediction prediction prediction prediction left left left presented map present present temporal learn learn position basis nonlinear nonlinear abstract applied applied applied back find computational computational references adaptive adaptive context context introduction action complex complex complex complex complex complex complex complex complex complex complex complex hand behavior search search search search search search rules rules higher higher higher previous previous theorem type required good good good conditions expected techniques correlation length length length correct correct simulations simulations minimum minimum classes total simulation simulation multi performed performed performed performed called times optimization dimension dimension natural natural global original artificial relative relative compared desired desired desired desired cross series series series series series series series series provide provide provide define define proc proc proc proc active eye determined determined experimental brain steps update descent selection selection morgan morgan morgan institute technique technique technique internal individual individual individual individual individual advances advances advances connectionist difficult final final bias graph maps computing experiment curve additional view solutions design design transition san effects conference determine significant pages pages pages pages increase produce condition condition weighted randomly randomly randomly randomly randomly types types processes selected selected selected selected evidence nature nature nature depends sampling constraint simply simply arbitrary group close corresponds actions predictions finding effective assumed generate supported end hypothesis degree degree degree degree degree development development development development development development development fit kaufmann kaufmann pairs functional functional fully interesting york increasing head head mechanism consistent operation language numbers direct early early early polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial combined description population population population population population population population population population population population recent resolution property robust takes element typical reported introduced introduced identical side cognitive relevant dimensions conventional approximately works match achieve sparse background modified sensitive entire constructed constructed exists exists exists parts expression expression expression expression expression lead suggests suggests extended wide hybrid touretzky demonstrate half critical critical critical critical critical operator editors interactions accurate sutton moody suggest propose taking characteristics demonstrated california proportional proportional proportional variety start min appears appears appears appears longer longer sequential generating generating generating transitions tuned mathematical distinct dept changing changing changing recall missing coordinates slightly unique develop adding equilibrium formed formed formed select yield focus focus expressed expressed expressed expressed expressed formation dependence viewed variation evaluated operations showed approximations approximations evolution evolution evolution evolution evolution forms forms converges past performing expansion combining roughly false iterative generation generation generation generation remains string string symbol symbol construction topology precision combinations inter instances plotted neighbors neighbors grammar grammar grammar grammar grammar grammar successfully successfully major major importance differ maximal effectively effectively symbols symbols successful successful build genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic composed composed quickly quickly strongly contained contained prob allowing heuristic moore neuroscience list vary correspondence leading leading reach subsequent preferred cowan body explore explore origin remain diego production production access environments hanson preliminary preliminary history history history history terminal terminal analytically relationships complicated affect encode trace editor predicting predicting automata created subsets aspect friedman portion algo logistic logistic logistic explored nervous initialized extent arbitrarily finds attempts chaotic defines languages asymptotically ment developing developing growing phenomena adjacent adjacent answer cascade caused rapid perspective satisfied operators operators operators products products pool acknowledgement describing beginning depicted meaning apparent evaluating populations offset parameterized readily psychological maintain span polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials rely reaches gen ordered richard replace age redundancy redundancy begins eventually progress wesley cumulative consistently consistently physiology addison forming restrict rithm optimizing labelled concerned grows grows cellular cellular kaufman analogy automaton imposed sanger north clock clock clock clock alphabet grammars constructive constructive selects filled continue motivation contexts programs loo predictors predictors corre surprising holland guarantees guarantees conjunction dominant searching sim approximators deg deg jolla fitness fitness fitness fitness fitness fitness designing discovered instructions instructions fahlman material stone acknowledge fired pressure specification piece creates creates revealed die encouraging encouraging copy copy ical hundred individuals individuals individuals individuals individuals individuals individuals individuals individuals imagine gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene evolve genes genes genes genes genes genes genes genes genes genes genes genes interact gas gas gener life permits altered paris alternatives alternatives france placing supports lippman nal differing experi technologies ucsd lems demonstrating removes topologies topologies served info info info gratefully resp copies stimulating dim dim simplification algorithmic lation unbounded tial shot adaptively micro developmental developmental developmental developmental developmental developmental developmental developmental stay exposed manipulated manipulated ooo plateau plateau plateau plateau plateau plateau poly colleagues colleagues evolving reproduced neutral neutral neutral periodically doubling doubling doubling doubling derives mutation mutation mutation mutation mutation mutation mutation indi undergo ini mle amsterdam deleting schraudolph lebiere lisp 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#@Belew_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural input input input input input data data data data data data data data data function figure figure figure figure figure time time set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output output number number system system system system system system system system system system system system system error error error error results results results results results results results results results results results results results units units information information information information information information problem problem problem hidden performance performance based based based based weights weights weights weights linear layer layer case order order order order shown systems systems systems systems systems systems systems systems systems values parameters parameters weight functions functions unit unit unit unit unit recognition method method method method approach approach approach approach approach single processing large local test test test test test analysis form shows shows simple simple paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small work work task methods methods methods methods methods methods methods methods methods methods methods methods features features features classification classification classification classification process current current current trained trained trained structure structure problems similar representation architecture architecture architecture architecture architecture architecture line rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general real real real real approximation average theory theory theory theory theory theory theory theory theory gradient gradient obtained obtained note result result university solution solution research research research research independent defined sequence initial initial initial initial initial initial standard standard standard standard standard computer node node node node node node node node node science science direction presented present activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine range range press learn learn learn outputs abstract applied computational references due due positive positive important decision propagation propagation context introduction complex hand parallel complexity complexity rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure measure prior prior representations representations representations center previous cases required required multiple good long represent represent represent distributed bayesian equations make make fact fact techniques techniques techniques correct correct correct observed minimum ing ing ing ing ing ing ing tasks tasks human computed multi sum sum sum sum sum performed called called mapping mapping means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor optimization applications policy knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge obtain negative negative original vol artificial artificial artificial artificial specific true desired cross perform experimental experimental related connected gain gain gain approaches approaches mit steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison connection train descent descent morgan proceedings proceedings proceedings report words loss version consists internal represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult addition graph graph graph sequences sequences considered framework cambridge computing domain domain domain domain domain equivalent equivalent equivalent directly directly hinton curve curve additional san conference conference determine determine full full significant significant approximate approximate world world world basic pages pages pages pages pages con con produce condition developed developed levels levels area lines actual actual provided provided finally finally evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation simply simply describe tested limited limited short implemented implemented implemented supported main journal future easily degree rumelhart rumelhart rumelhart rumelhart development including fit fit kaufmann probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic combination fully testing testing testing significantly edge increasing trials trials empirical mode numbers max max international international expert expert expert expert expert expert expert expert expert expert expert expert idea idea combined combined combined combined minimize run added discussed improve improve recent separate takes introduced subject identical trees recently relevant calculated module correspond address locations modified modified williams entire grant grant grant constructed lead studied trial correctly correctly feed generally pass pass demonstrate demonstrate runs place place minimal greater conclusions conclusions valued editors editors differences accurate designed clear performs performs mateo temperature hard integration drawn solid intelligence intelligence variety min min min min min min program base base base base base base base base base base base base base base base base base produces index ways factors factors factors factors factors factors factors factors plot describes dept changing changing changing changing confidence metric category category category category category category category easy easy slightly belief belief belief belief belief adding adding adding adding adding applying predictive formed national national viewed evaluated restricted performing performing sec combining combining combining combining combining add add add intermediate string assigned assigned construction foundation advantages advantages classified classified classified classified existing strings strings sciences plotted automatic automatic maximize maximize specifically domains domains domains domains structural successfully successfully importance suitable modification symbols mcclelland build comparing traditional heuristic link link link link link return contribution classify criteria categories categories categories notation notation providing highest reach reach received attempt illustrates employed explore create updating detail association dotted dataset dataset dataset dataset helpful fashion ideas links links links links links applicable combine symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic workshop workshop statistically statistically phases removed removed examined induction induction hill created created created implementations aspect logic improving improving simplest utility attempts years indicating advanced developing distinguish explanation benchmark reasons considerable implementing tive sys sections formalism formalism easier protein style incorporate immediately immediately acknowledgement circle begin demonstrates demonstrates recognizing recognizing researchers summation requiring requiring fuzzy pure pure pure pure tional backprop adjustable adjustable passes reaches reaches datasets adjust enables boston age begins june june proposition proposition proposition proposition differentiable differentiable diagnosis diagnosis cor contribute acquisition classifying modify modify modify summing summing labelled purely purely purely tem theories theories theories proceed reaching climbing communications fails ments adjusting occurred intelligent biased resulted hope reasoning reasoning reasoning reasoning belong clause clause heuristics fires date date meaningful combines combines combines connect connect bases bases bases bases bases bases bases bases bases bases bases bases bases bases bases bases tic infer creating refers horn horn inductive projects dempster shavlik shavlik adopted outlined ence dna dna dna dna dna dna dna numerous converted converted converted removal july july pieces distinction year connec sigma weiss seek stem breaking certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty certainty var alter clas unseen ftp genes uncertain uncertain uncertain uncertain iri pearl pearl pearl pearl pearl employing disease disease cation quinlan quinlan quinlan quinlan misclassified misclassified breaks refinement refinement refinement refinement refinement maintains nasa applicability architectural deletion deletion appearing appearing inconsistent satisfactory towell towell towell towell towell towell towell towell austin integrates concerns meth explanations ods gence subscript terminates meant ings format texas texas eighth eighth eighth indi inappropriate modest linking refine refine deleting deleting comprehensive gallant gallant gallant gallant expresses repeats beliefs biasing ames machinery conflict desire positively retains blur lacking converting roots plants refining refining refining widespread kbann kbann kbann kbann kbann propositions emphasizing nectionist nectionist raymond contributed imperfect mooney mooney mooney mooney mooney mooney mooney mooney mooney mooney revised revised cate loses diseases diseases diseases nucleotides told publications seeds consequent consequent consequent consequent promoter promoter promoter promoter promoter cial ond knowl cycling supplying readings crit tionist antecedent antecedent accomplishes jeffrey negatively propositional propositional precedes opportunities binds archive promoters promoters promoters michalski michalski michalski revise revise revise revise revise revise revise noordewier noordewier diagnose utexas utexas rna ithaca ncc shorthand intelli revision revision revision technological soil ious revising revising revising revising revising curacy neuroprose evanston distin detroit ski formalisms hind lect 
#@Mahoney_J,Mooney_R,
#t6
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input function function figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number number number number number number number number number system system system system error error error error error error error error state state state state state state state state results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information information information hidden hidden hidden hidden hidden performance performance space space space weights weights weights weights weights weights weights weights weights linear linear order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown systems systems systems systems systems values values values values parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method processing processing processing processing processing processing control large large rate test test inputs inputs inputs form signal simple simple paper paper small small small size net net net net net net net work work task task task task task task step step step step step step step step step step step step step step step step step step points level level level level level level level level level level level level current current current current current trained trained structure structure structure random high high high high high high high high high high high high similar architecture equation equation equation equation equation fixed rule rule general generalization parameter parameter parameter real average average average average average gradient gradient term term term note experiments result result university university university university university threshold computation computation research found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target initial constant constant table table table table standard standard standard standard computer computer computer terms connections connections connections connections connections node node prediction direction presented presented activation low nodes temporal temporal temporal machine machine sets sets press press learn learn learn learn position outputs outputs outputs continuous continuous abstract back back back back properties references stochastic stochastic stochastic due due propagation propagation propagation propagation context context context context introduction introduction action complex hand hand effect effect dynamic generated generated parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change change change difference variable variable lower lower rules rules rules learned learned higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher center center previous previous previous previous previous previous type required required required required long long long long long distributed equations fact correlation correlation correlation correlation length correct correct correct forward forward scale finite finite finite finite resulting tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks computed computed sum performed elements means made made made feedback feedback feedback applications artificial represented compared compared perform determined related motor equal approaches mit steps steps steps steps steps comparison larger connection connection connection connection connection connection connection connection connection connection connection connection connection descent dependent modeling morgan morgan morgan morgan morgan morgan proceedings report report report department department department version internal advances advances advances advances advances final bias bias bias bias delay sequences sequences sequences ai considered considered considered considered cambridge cambridge cambridge computing directly hinton transition san san san san san san determine statistics pages pages pages pages pages pages pages increase con condition randomly randomly criterion finally finally simply simply achieved technical technical technical increases tested tested fast complete complete complete complete finding generate supported rumelhart rumelhart development sensory kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann smaller needed needed needed needed needed reduced dynamical unknown fully jordan principle principle language squared representing representing pre bottom magnitude minimize added added added added added sources predict predict predict predict predict directions directions takes element reported introduced introduced introduced introduced period identical side side side hierarchical sense sense engineering calculated calculated calculated works works solve solve correspond modified modified williams williams increased grant exists deviation deviation predicted predicted predicted correctly correctly correctly correctly correctly feed feed feed locally locally touretzky column runs starting row greater reduce reduce conclusions valued editors editors editors editors editors editors editors editors moody moody moody moody moody learns learns learns mateo mateo mateo mateo mateo largest demonstrated demonstrated california california california california california intelligence labeled turn decrease decrease characters characters program produces longer sequential sequential sequential sequential sequential laboratory transitions label student simultaneously linearly slightly adding adding adding adding adding adding adding events events john choosing depending depending variation lee past earlier epochs delays delays delays add add initially initially string string string string string string string assigned construction advantages classified david david building thesis activations activations activations formulation strings strings sciences sciences activated activated mozer mozer mozer mozer mozer mozer specifically candidate absolute discussions grammar grammar grammar grammar grammar grammar gating tests compression encoded encoded driven mcclelland mcclelland wij wij wij wij build build miller ten ten reached traditional traditional repeated strongly strongly strongly superior contribution running criteria duration built built usual michael simplified generalize giles highest leading reach attempt receive presents diego powerful create difficulty difficulty environments hanson hanson hanson hanson limitations lippmann lippmann ml helpful history incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental office referred decisions stream workshop affect affect affect hierarchy hierarchy hierarchy hierarchy hierarchy cognition removed removed induction induction induction possibly opposite automata created created created created created created perfect changed thought taylor ith utility arbitrarily phd averages massachusetts languages publishers publishers publishers publishers publishers publishers derivation growing cascade cascade cascade cascade multiplication arc arc arc ring ring ring ring ring ring ring ring acknowledgement beginning beginning gradually sun greatly behaviors collected items elman elman elman elman orders orders orders orders orders orders orders orders orders item item item item rep robinson mod extracting incoming occurrence proven prevent chen chen richard richard richard comments begins begins begins specifies specifies specifies june summed gap gap gap gap gap gap gap gap gap gap gap gap gap generator modify modify modify dynamically dynamically impossible jones jones arranged adds adds adds adds adjusting fan imposed height mark mark mark splitting settings settings imply presentations presentations presentations constructive contexts reset reset combines combines james decide intended lawrence april foundations creating pollack fahlman fahlman stopped influences explorations johnson robert zipser arcs arcs microstructure gaps gaps incrementally incrementally incrementally incrementally incrementally convenience utilize par exception hierarchies affects affects descriptions forcing eric alter preserved intuition schmidhuber schmidhuber graduate distant searches simplifying multiscale records nasa lippman lippman lippman recognizers continually continually completed technologies rewritten bridge bridge january continued austin austin austin steven inherently conflicting devised gram correctness outgoing rtrl rtrl destination sity watrous invisible crl scott schreiber signed indirectly february texas texas texas eighth denominator cleeremans servan kuhn awij awij awij awij awij awij awij awij unexpected sented began began replaces linearities inserted inserted inserted activa fallside organisation repeats repeats mar modifies modifies traversed traversed traversed opportunity tong simmons tiny mike unlimited anticipate remember remember cued jonathan ronald tinuous bateson notational univer ticular raymond reber reber reber reber reber alternately unambiguous hierarchically resentations avail gary concentrating collectively paragraph pulled pulled pulled jeffrey bachrach speedups stringent infeng collins quoted quoted quoted hartman ternational ify utexas drafts jiirgen substitutes generous searchers ceiling customized caveats califor nia 
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results results results results results units information information problem problem problem problem problem problem problem problem models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space space space space space space space linear case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown systems values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons 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properties references ieee important important important important important important introduction parallel parallel change difference difference difference complexity variable variable variable lower measure signals signals signals signals signals signals signals signals signals signals signals signals signals chosen chosen chosen higher higher higher part center previous type type good good long long distributed fact region proposed proposed proposed proposed proposed proposed proposed proposed length length correct scale simulations simulations simulations simulation simulation simulation simulation simulation computed respect respect respect performed performed called regions regions regions regions regions regions regions mapping mapping mapping mapping mapping mapping mapping factor factor optimization optimization potential dimension dimension dimension made natural applications applications study original vol artificial artificial specific specific specific specific specific specific specific compared compared application application application application application series proc proc determined determined determined determined related distributions distributions distributions distributions distributions distributions distributions distributions approaches steps accuracy comparison comparison comparison comparison comparison comparison comparison contrast modeling institute version version version consists internal difficult difficult final maps maps maps maps maps maps maps maps computing computing directly directly additional effects determine determine upper requires choice choice basic increase increase clustering clustering robot criterion criterion criterion criterion criterion lines product product biological biological biological biological achieved measured measured measured measured discussion technical arbitrary denote tested fast inverse corresponds amount nearest nearest nearest common common generate main eds eds adaptation adaptation 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kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen advantages advantages topology topology topology topology transactions building box usa determines neighbors neighbors neighbors neighbors neighbors neighbors tests successfully reason regular compression compression closely importance suitable divided identify build comparing situation reached prob stopping split split superior superior superior contribution criteria criteria criteria criteria criteria criteria criteria criteria criteria vary realistic realistic realistic quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization highest highest automatically automatically received received neighboring neighboring neighboring modelling modelling modelling modelling modelling modelling modelling minimized schedule exhibit difficulty difficulty relations relations relations accurately investigated fault stream symbolic complicated cover removed neu examined smallest versions taylor explored mapped initialized simplest motivated motivated trivial growth growth growth growth growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing adapted adapted caused briefly reasons inside berkeley organized choices desirable desirable commonly potentially implicit optimize computers demonstrates auto cybernetics cybernetics researchers robustness limits led effort variant variant variant mod ture fall resource resource resource resource resource resource resource resource resource resource resource resource suited damage semantic summed reconstructed connecting grows arranged dealing darken darken fail north north responsible combinatorial combinatorial ensures ensures irregular decide holland holland regarded moved topological 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space space space space space space space space space space space space weights weights layer layer layer shown shown systems values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise weight weight weight weight functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution recognition approach approach approach approach approach point processing processing processing processing processing processing processing processing processing processing large large local local local test test test patterns patterns class class class class inputs shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian paper examples examples small small size feature net net net net net net work work task task task task methods methods methods methods points points points features features classification classification process process process process level level level trained structure problems problems problems problems high high high response response response response response response response similar similar similar similar representation architecture architecture architecture architecture architecture section section section section fixed fixed fixed fixed fixed general generalization generalization generalization generalization parameter parameter parameter approximation average average average average gradient gradient term dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result university university computation computation computation solution solution solution research research research research defined target target initial initial standard computer computer computer science science science science prediction presented map activation low low sets maximum learn learn components components basis basis basis abstract applied back back find find find find computational properties properties likelihood references due positive adaptive adaptive propagation propagation context context introduction hand hand estimation statistical variance variance variance cost search tion tion variable variable variable variable rules measure learned center center center center center type required good long represent represent represent represent make techniques region region region region region proposed proposed correlation correct observed finite simulations simulations simulations simulations ing ing simulation simulation regression regression multi called called called elements regions regions regions regions mapping dimension made made global global global true series series series series compute location perform determined goal related constraints constraints constraints approaches approaches comparison contrast connection update descent nets nets selection selection selection selection morgan morgan morgan morgan report institute department department version individual advances advances advances represents responses difficult difficult difficult difficult difficult final bias bias bias ai maps framework framework computing computing computing equivalent directly hinton hinton additional additional additional solutions solutions solutions solutions solutions curves san san san san requires choice statistics free free free free free free free free free free free free free free free vision basic validation con con condition derived criterion nature constraint increases increases increases increases increases group group group group group group group group transformation fast fast assumption assumption assumption assumption assumption corresponds finding rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount nearest nearest nearest effective implemented shape supported main eds eds instance future makes makes makes makes fit fit kaufmann kaufmann kaufmann kaufmann typically smaller underlying underlying underlying underlying underlying underlying underlying underlying underlying underlying underlying underlying needed needed interesting increasing increasing principle call call normalized supervised supervised supervised idea idea idea combined run added added added added predict directions directions resolution advantage property property property property property robust robust element strategy include include include trees subset subset subset subset cognitive relevant relevant relevant dimensions dimensions dimensions dimensions dimensions unsupervised works axis solve solve solve match correspond achieve achieve rl rl sparse sparse sparse sparse sparse sparse sparse mixtures locations locations locations locations bounded bounded williams sensitive sensitive grant horizontal parts expression lead concept studied suggests deviation wide alternative alternative alternative alternative alternative alternative alternative locally move touretzky touretzky width width width occurs boundary runs strength critical place assumptions assumptions neighbor neighbor neighbor accurate moody moody moody moody moody moody constrained constrained constrained constrained constrained mateo mateo mateo mateo regularization radial radial minimizing exist averaged derivatives denoted denoted digit primary describes describes tuned changing multilayer category linearly interaction adding adding adding select select competition john decreases choosing formation phoneme squares centers soft soft updates updates key spaces neighborhood interpolation interpolation interpolation interpolation interpolation remains remains initially foundation kohonen kohonen kohonen kohonen kohonen advantages advantages advantages advantages advantages degrees degrees degrees degrees degrees degrees exploration includes mozer mozer mozer mozer mozer candidate domains neighbors neighbors discussions successfully reason determining selecting selecting extra closely computationally divided poggio efficiently ten reached composed refer kind prob heuristic split split split split split split split split split split split split superior classify follow strategies strategies built built built notation michael relaxation providing automatically automatically attempt employed explore explore remain poor poor create collection investigate updating updating hanson hanson lippmann lippmann helpful fewer fewer reducing tech authors func cover cover examined circles coarse necessarily predicting friedman friedman friedman friedman friedman freedom freedom freedom freedom freedom explored explored multivariate improving finds chaotic chaotic optimum optimum cart cart cart slowly nowlan nowlan nowlan nowlan expensive cascade glass glass glass starts inside implementing organized style forces choices ran ran ran ran ran ran ran ran ran ran ran ion acknowledgement gradually gradually gradually gradually gradually gradually members begin toronto toronto cybernetics nsf reflects apparent limits relevance flexible lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice introducing introducing marked splines rep variant compares partitioning partitioning resource serve geman geman logical implements eventually yielding ordinary ordinary ordinary ordinary benefit aligned sort tation girosi girosi optimizing resources resources flexibility smolensky arranged arranged arranged platt platt platt platt platt platt platt platt platt adds allocation darken darken breiman breiman breiman proceeds height nearby splitting splitting splitting splitting affected constructive constructive constructive constructive constructive constructive constructive constructive constructive constructive constructive constructive substituting date heavy introduces james widths widths widths widths paul colorado searching originally offers arrangement chooses ahead canada belonging arrows splits dietterich dietterich ignore fahlman fahlman stopped stone lem rms annals deriving ber forced par hierarchies mars mars mars argue mackey mackey mackey num allocated allocated disadvantage boulder boulder challenging picked rbfs iri meta nonetheless placing investigations compu stops tension tension tension tension chris info bienenstock agrees ping mcdonnell builds multiresolution multiresolution multiresolution multiresolution interpolated finer keeler award fre usefulness classi restricting interpolate interpolate interpolate dimen relaxed fication meant allocating 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error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results information problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based space systems systems values probability probability probability probability probability probability parameters parameters parameters parameters functions functions distribution method approach approach pattern pattern pattern pattern processing processing control large large local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class matrix optimal optimal shows shows shows shows algorithms algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian small small net work task task methods methods points points points points field features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification trained trained trained trained trained trained trained trained trained trained structure structure problems problems problems random random random high high high high high high high high similar similar show equation general general speech real approximation obtained term term experiments experiments experiments experiments experiments experiments experiments result threshold threshold threshold threshold threshold threshold computation independent found initial initial initial initial estimate left left left left presented presented nodes nodes nodes nodes nodes nodes nodes sets maximum maximum maximum range position basis basis basis basis basis basis basis basis outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous abstract applied find density references due important important adaptive decision decision decision decision decision decision mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex hand hand estimation estimation estimation generated generated variance variance difference difference difference complexity variable classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower measure signals chosen center center center center center center required required good binary conditions conditions represent distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian region region region region region region region proposed proposed correct probabilities probabilities probabilities errors minimum minimum classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes ing ing tasks tasks total total multi performed performed performed performed performed performed performed performed performed times regions regions regions regions regions regions regions regions regions mapping mapping means means means means means means dimension study study policy original artificial artificial desired cross receptive rates perform perform perform determined determined experimental experimental goal mit accuracy accuracy accuracy accuracy comparison comparison contrast train train train modeling modeling modeling selection morgan morgan report consists advances advances addition considered considered experiment estimates estimates san san determine determine determine determine determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers requires estimated validation con produce produce produce condition derived randomly randomly clustering clustering clustering clustering clustering clustering developed developed criterion criterion criterion actual actual selected selected selected selected achieved covariance covariance technical close close close finding rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf short generate supported eds eds journal square hypothesis cluster cluster cluster cluster cluster cluster cluster cluster cluster easily smaller functional mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp block block testing testing testing testing testing testing york trials database database database database database database squared squared squared squared squared squared call numbers combined choose added added added description improved improve improve pair pair pair pair pair pair practical identical subset varying conventional conventional conventional volume match converge achieve diagonal diagonal evaluation evaluation evaluation evaluation evaluation evaluation evaluation symmetric increased increased increased increased occur suggests predicted predicted predicted predicted touretzky touretzky clusters clusters boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary generally pass demonstrate conclusion accurate accurate accurate designed designed moody moody mateo mateo cycle cycle cycle characteristics radial radial radial radial radial radial radial decrease decrease relationship program pro laboratory tuned sensitivity sensitivity dimensionality dimensionality remaining mutual adding adding adding events formed formed formed cycles select choosing expressed overlap influence variation detailed organizing showed centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers similarly discrimination discrimination discrimination diagram diagram performing epochs epochs measurements purpose add add add boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries interpolation intermediate calculate assigned assigned advantages views avoid building priori priori usa automatic absolute successfully regular regular regular regular regular selecting extra extra uniformly society differ score vowel traditional traditional classify highest highest illustrates acknowledgments presents minimized explore overfitting overfitting overfitting exhibit difficulty varied varied accurately accurately lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann fewer fewer fewer ideal authors root affect phases momentum momentum examined editor illustrate consist consist great great stop distinguish variances variances waveform waveform worse worse located mation separately separately ridge gradually varies reflect empirically tional conducted poorly frequently ture fall prevent richard richard richard richard decreased decreased royal turned kaufman kaufman adds adds belong belong disjoint monotonically affected responsible constructive constructive vowels infor started ranging pat pat accounts mel mel dif peterson 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algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number system system error error error error error error error error error error error error error error error error results results results results results results units problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance based based based based based space space space space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer case case case case case case vector vector order order order order order order order order order order order order order order shown shown shown shown parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight functions functions functions functions functions functions unit unit unit recognition recognition recognition recognition recognition recognition method method method method method approach pattern pattern pattern pattern pattern pattern pattern single processing control large large large large large large large large large large large large large large large large large large local rate rate test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class class class class class matrix optimal optimal optimal optimal form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small feature net work task methods methods classification classification classification process level trained trained trained trained trained problems high high high high high representation representation representation representation architecture show show show equation equation equation equation section section section fixed rule rule rule vectors vectors images images images general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter real average average average average theory obtained obtained obtained experiments experiments dimensional dimensional result university university university computation computation computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution independent independent defined defined defined defined defined table table table table distance distance science presented present phase low low maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press press learn learn learn components components basis basis basis basis nonlinear nonlinear abstract applied back back find find find computational computational computational computational computational computational computational convergence convergence properties properties references due ieee positive positive important important important decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision propagation introduction estimation cost cost tion tion tion complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower rules measure representations part bound bound cases cases good good good good good expected fact techniques techniques proposed proposed observed finite minimum resulting classes classes classes ing ing tasks total human computed computed multi called called called elements optimization optimization potential potential potential dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension global applications obtain obtain original represented true true compared compared compared compared compared cross cross compute rates determined experimental experimental experimental goal goal constraints equal equal approaches larger train train morgan department loss loss loss loss loss loss technique consists consists consists code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel difficult exp exp exp exp exp bias bias considered framework cambridge cambridge equivalent experiment solutions design limit san san capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers requires choice free speed pages pages increase validation developed bounds bounds area area product actual evidence backpropagation backpropagation depends simply simply associative achieved achieved achieved increases increases tested tested limited limited inverse surface finding rbf rbf rbf rbf rbf rbf rbf amount amount effective effective effective effective theoretical theoretical square pixel instance instance instance including including including kaufmann smaller smaller smaller needed combination combination reduced unknown coefficients programming programming programming programming interesting testing ratio character york special structures database database database empirical principle squared squared max max making polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial idea idea minimize minimize minimize choose choose perceptron property property separate separate include include side side quadratic quadratic quadratic sense recently subjects works tuning tuning tuning tuning tuning tuning tuning yields match studies definition symmetric generalized generalized generalized bounded bounded bounded improvement risk risk exists suggests wide predicted white white boundary boundary boundary boundary boundary boundary boundary boundary boundary generally demonstrate half half starting starting conclusions editors numerical numerical moody exponential exponential practice constrained mateo presence largest largest largest largest california california regularization regularization regularization regularization radial radial radial radial variety minimizing minimizing exist min min min min scene minima question acknowledgements reference digit digit digit distinct recall sensitivity multilayer explicitly coordinates linearly linearly infinite infinite text unique minimization minimization minimization springer family solved evaluate restricted restricted restricted restricted labels margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin similarly classical expansion spaces spaces convex reduces reduces boundaries sufficiently euclidean avoid recorded recorded handwritten handwritten handwritten handwritten kernels kernels kernels kernels perceptrons perceptrons perceptrons formulation bell bell bell bell vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik extension automatic automatic automatic automatic automatic maximize holds discussions structural structural regular efficiency efficiency computationally computationally computationally wij poggio poggio literature efficiently efficiently ten ten quickly cun prob prob link lie lie lie quantity list dot generalize generalize paradigm providing providing nips minimizes minimizes computes denker automatically automatically satisfies trains wiley poor exhibit rapidly optimized dual dual dual dual dual dual dual existence ideas mse applicable biol maximizing maximizing comparable tanh workshop removed closest closest closest closest closest closest possibly editor integer adjusted adjusted adjusted adjusted quantities perceptton perceptton perceptton hebb hebb academic consist mixed finds years inequality inequality crucial tractable reasons reasons berkeley berkeley berkeley berkeley arise arise mation products laboratories laboratories consequence projected definite lowest arises annual argument understood pseudo experimentally solla solla adjustable adjustable adjustable adjustable adjustable adjustable adjustable adjustable adjustable adjustable haussler remove formulated rep outliers outliers outliers outliers outliers howard exhibits summarized pittsburgh reaches fall maximizes proven incorporating achieves green inherent inherent sophisticated comments wesley merging lot room benefit cybern intractable tation acm girosi grey grey eliminated wrong adjusting mail familiar intuitively substituting substituting infor performances separating separating falls introduces ensures iteratively equals equals expanded percepttons percepttons percepttons searching jackel candidates multiplied francisco membership foundations warmuth clean theoretically informative belonging designing border hart lem lem constitute shading shading listed listed listed guyon guyon guyon guyon guyon guyon guyon maximized chervonenkis july pieces pointed boser boser boser boser boser boser boser boser boser boser sigma sigma sigma obtains seek remote param clas henderson invariances formance duda labs labs ization hubbard investigating pos conversely conversely represen cation son eters mini supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting supporting examination recognizers gorithm suggestions expansions expansions gratefully advantageous advantageous styles stimulating factorized recogni impractical insufficient assistance envelope dropped concern cast bottou bottou cally rare polarity holmdel floor contrasts automation inefficient att att rameters colleagues minimax minimax minimax dent watanabe february generaliza huge huge fore unnecessary cortes stan imum elaborate predefined predefined meaningless tighter favorably proce mar resentation dard advice dependences dependences possesses classifica acknowledged seeks cleaning cleaning cleaning iix iix iix iix classifi depen equiv formulating safety admits admits chunks gin siftcation tunable tunable constrains hypersurface dure separations separations separations separations reciprocally ilwll methodologies pare eecs eecs lambert scarce extremal alent chances supervisor supervisor ifx ifx luenberger zipcode grossly grossly underdetermined underdetermined duality duality mizing roach encompasses pacity portrait portrait portrait mislabeled undesired sifiers elim qth vlad automati 
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input data data data data function function function function function function function function function function figure figure figure figure figure figure time time time set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm output output output number number number error error results results results results units information information information information information information problem models hidden hidden based based space space space space space space weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order shown shown shown shown systems systems systems systems values values values values parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight unit recognition method method method method method method method method method pattern pattern pattern pattern pattern pattern pattern pattern point image image single processing processing processing processing processing large large large large large large large large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns analysis matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form shows signal signal algorithms algorithms algorithms simple simple simple simple simple examples examples small small small small small small small small small small size size size size size size size size feature net work methods methods methods methods methods methods fig step step step step step step step points features process process current current current trained trained trained trained trained trained problems problems random random similar similar similar architecture equation equation section section section section section section line line line line line line line line rule rule images general generalization parameter parameter parameter parameter parameter parameter real average average average average average average average theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained term term term experiments experiments experiments experiments dimensional dimensional dimensional result university university research research found found target initial initial initial initial constant constant constant constant constant estimate estimate estimate computer terms terms terms connections connections connections connections connections prediction direction direction direction direction direction phase low machine sets sets sets sets sets sets press learn outputs abstract applied applied back back back find convergence convergence convergence convergence convergence convergence convergence convergence convergence references component stochastic stochastic stochastic stochastic stochastic ieee positive positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important adaptive adaptive adaptive adaptive propagation propagation propagation context introduction hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical cost cost cost cost cost cost tion part previous cases type required good good long make fact fact techniques techniques techniques proposed proposed proposed proposed proposed correct correct errors forward forward forward finite minimum minimum resulting resulting resulting ing ing total total total computed computed computed computed respect respect performed called called times means means factor factor optimization dimension global applications applications applications applications applications negative original compared compared application desired desired series compute compute compute compute rates perform perform determined connected connected connected brain brain equal equal power power accuracy accuracy accuracy accuracy larger update update update support descent descent descent descent descent descent descent descent descent descent descent descent nets morgan morgan morgan report words department implementation version version version version version version version version technique technique technique technique advances advances advances represents connectionist connectionist difficult maps computing computing computing computing computing computing computing computing computing computing equivalent equivalent equivalent estimates estimates top efficient efficient efficient full full requires approximate statistics free free free speed speed estimated basic increase give produce product product product product product actual backpropagation backpropagation backpropagation iteration iteration covariance technical group transformation close close inverse inverse inverse inverse inverse inverse corresponds stable surface finding finding short short short implemented generate supported require require main main adaptation square pixel makes including including objective objective objective objective objective objective objective typically smaller reduced fully ratio character projection projection increasing database database mode mode principal principal principal principal principal principal principal principal squared squared iterations iterations max direct direct normalized normalized normalized normalized bottom supervised expert early idea idea minimize minimize run run run added architectures directions directions exact takes typical reported practical apply introduced machines machines side quadratic quadratic interest interest dimensions approximately calculated volume tions yields converge converge converge diagonal diagonal diagonal diagonal diagonal symmetric modified bounded entire entire increased scaling derivative derivative derivative derivative derivative derivative derivative derivative derivative matrices rotation predicted predicted predicted locally locally touretzky touretzky loop generally setting setting pass assumptions editors differences sigmoid accurate accurate accurate accurate numerical clear clear moody faster suggest propose propose propose largest largest largest largest largest largest largest largest largest largest largest largest largest largest largest largest largest largest largest assuming assuming start exist decrease derivatives acknowledgements digit written ways estimating estimating estimating estimating estimating plot tuned vertical dept dept implement simultaneously simultaneously averaging averaging physical easy slightly slightly slightly slightly john letters yield yield choosing choosing extracted review depending estimator variation detailed updated updated updated fraction centered suggested digits constants reasonable slow slow epochs epochs epochs expansion expansion expansion roughly add filtering calculate sufficiently handwritten handwritten thesis thesis bell eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues contour batch batch batch sciences extension automatic automatic automatic automatic automatic absolute partially successfully reason regular regular regular straightforward computationally computationally presentation efficiently tend essentially orthogonal orthogonal orthogonal orthogonal procedures procedures procedures contained cun cun cun cun cun cun cun cun cun cun running running running oscillations notation bar usual backward backward backward nips nips giles eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue denker denker maximization maximization maximization maximization maximization subsequent jacobs jacobs cowan remain perturbation essential experience varied replaced hanson hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian divergence hall scalar fewer ideas applicable applicable scaled authors root eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors complicated complicated tanh surfaces smallest smallest smallest measurement editor editor changed ensure ensure versions obvious noted taylor taylor taylor store store store epoch improving explain phd phd attempts defines massachusetts formula formula formula costs crucial fairly adapted expensive considerable obs purposes sections shared shared shared controls controls controls laboratories simard simard simard simard simard members toronto nsf mellon fluctuations conjugate varies percent prop prop prop prop carnegie applies empirically axes axes backprop introducing solla solla solla slower passes passes howard howard rely perturbations pittsburgh serve curvature gave comments decreased unbiased damage converged differentiable yielding sharing newton newton redundant redundant pick pick pick pick optimizing lecun lecun lecun lecun lecun kaufman kaufman kaufman adjusting check intuitively adequate corner presentations presentations presentations presentations presentations obd elimination prentice becker becker becker ensures widrow widrow consequences uni jackel jackel iterated storing pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector border grants interestingly displacement onr verify outperforms session convolutional convolutional convolutional stork stork validity perturbed boser connec tradeoff tradeoff amherst decomposed hundred hundred acceleration jacobian principled principled henderson publication hubbard carefully eliminating emphasize projecting rbfs paris sketch portions denver denver denver esti eigen things intensive ignoring computa oregon sessions opti hassibi hassibi nist thousand routines holmdel subtracting progressively exploits coins drastically safe sian deter iterating iterating iterating surgeon seg inst derives stationarity excessive ues converts amax amax amax amax crg proce ample kanter kanter ver shortcut mal subsampled versity yann yann prohibitively ecs mate gun mented feel visualize cheap cheap accelerate useless unrealistic accelerated patrice patrice stabilizes propagations propagations barak barak ingredient restore eigenspace speeding beaverton agreed vmax vmax ellipses 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algorithm algorithm algorithm output output output output output output output output output output output output output output number number number number system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results units units units units information information information information information information problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based based based based based based based based based based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights 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recognition method method method method method method method method method method method method method method method method method method method pattern pattern pattern point point single single single single single processing processing processing control large large large large large large large large local local local local local local local local local local neuron test test test patterns patterns analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form shows shows shows shows signal signal algorithms simple simple simple paper small small small small small small small net net net net net net net net net net net methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods fig fig fig fig fig fig fig fig step step step step step step trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure problems problems problems problems problems problems problems problems problems problems problems problems high response response response response show show show equation equation section rule rule vectors vectors vectors vectors general general general general general general general generalization generalization generalization generalization generalization speech parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory gradient gradient gradient gradient gradient gradient term term term term note note note note note dimensional dimensional dimensional dimensional result university computation solution solution research defined defined found found found found found found sequence initial constant constant constant table table standard standard standard computer terms terms terms terms terms connections left left left left presented low machine machine press learn learn learn components basis nonlinear continuous sample sample abstract applied applied applied applied applied back find find computational computational computational computational computational references component component positive procedure procedure important propagation introduction introduction introduction complex complex effect generated parallel parallel parallel cost change change difference difference complexity complexity variable assume rules rules rules measure representations higher higher part center previous cases cases cases required multiple multiple multiple multiple long conditions represent distributed expected expected equations make fact fact fact length length correct correct correct correct correct correct simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting simulation regression respect respect respect respect eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq mapping means dimension dimension dimension global knowledge original original artificial relative true compared desired desired desired cross series define compute perform goal goal goal constraints brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain approaches mit accuracy accuracy accuracy comparison larger contrast contrast connection update train descent descent descent morgan morgan proceedings proceedings proceedings report department department technique internal represents final bias bias bias bias addition maps considered computing computing hinton hinton view san capacity efficient full requires significant significant significant significant statistics statistics world speed basic increase increase increase increase increase increase increase increase increase give give condition criterion criterion lines lines entropy actual provided finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation inhibitory inhibitory constraint simply achieved achieved discussion covariance covariance arbitrary denote close close inverse inverse inverse inverse inverse inverse inverse inverse corresponds excitatory surface surface surface surface short effective assumed supported eds eds square instance instance degree makes makes makes rumelhart rumelhart rumelhart including kaufmann kaufmann typically typically typically typically smaller needed reduced functional functional functional functional fully fully transfer testing significantly significantly character special special consistent leads leads leads principal representing call call call magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude decay decay decay decay decay idea idea minimize minimize minimize description description description denotes discussed improve directions side sejnowski sejnowski sejnowski relevant engineering sufficient compare calculated calculated solve solve solve yields yields yields yields achieve achieve diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal address definition williams williams improvement storage lead lead wide derivative derivative derivative derivative touretzky touretzky white occurs generally setting hardware pass starting minimal assumptions assumptions reduce reduce reduce conclusions depend competitive central differences moody reduction reduction reduction california solid regularization labeled turn variety minimizing min plane derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives minima acknowledgements boltzmann appears relation written optical sequential stability pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning simultaneously electrical remaining remaining text adding extraction competition expressed interpretation updated updates key calculation calculation calculation slow dashed dashed neighborhood add penalty valid valid calculate calculate david degrees includes candidate candidate black structural simplicity simplicity columns determining straightforward straightforward computationally computationally mcclelland successful literature reached road refer strongly strongly cun cun cun cun cun cun cun stopping criteria criteria hold generalize denker denker denker denker leading leading reach automatically illustrates subsequent modelling employed unlike wiley poor poor overfitting overfitting xor xor xor xor xor xor xor xor xor xor xor xor xor requirements investigate difficulty involving involving strengths hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian recursive lippmann hall scalar reducing successive giving incremental investigated investigated investigated authors decisions comparable analogous saliency saliency hill smallest smallest smallest plausible opposite equally perfect changed changed adjusted friedman assumes assumes assumes taylor fisher fisher freedom freedom optimum great rows stop formula formula crucial derivation benchmark benchmark lies nonlinearity obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs stanford stanford stanford precisely desirable inversion inversion describing begin begin english definite author mellon questions carnegie cmu axes axes solla solla solla solla employ employ remove incorrect incorrect calculating calculating calculating replace logical logical damage damage damage damage damage damage damage damage damage damage damage wesley yielding sharing newton benefit indices sort addison mistake guarantee lagrange extensive ordering eliminate eliminate eliminate eliminate proceed eliminated eliminated eliminated multiplier kullback wrong wrong wrong wrong wrong wrong overcome simplify hope scoring removing affected krogh krogh preparation generalizes hertz hertz obd obd obd obd obd obd obd obd obd obd obd elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination elimination meaningful utilized prentice recovered negligible negligible pruned pruned pruned pruned guarantees conjunction dominant washington enable francisco shortest refers refers late late park eqs eqs eqs grants explains ignore shavlik shavlik avoiding insensitive sequentially sequentially slight thrun thrun thrun thrun thrun leibler deriving stork stork stork stork stork stork stork stork stork stork stork employs isotropic retraining retraining retraining retraining retraining retraining retraining retraining retraining retraining retraining chapter imagine adjustment illustration deep magnitudes magnitudes magnitudes ijcnn permits permits permits afosr regularized eliminating singularities projecting conversely conversely deleted deleted deleted deleted deleted deleted importantly inverting thousands vanishes dramatic gauss removes removes removes lagrangian palmer palmer hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi simplification excess demand justified justified rosenberg rosenberg rosenberg assistance thousand towell towell suite pan mining outperformed recursion eliminates cast stay calculates rissanen rissanen seattle neglect thickness obey slices degenerate transpose adjusts nettalk nettalk teaching restrictive surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon cuts wolff wolff wolff wolff wolff wolff wolff surprise prune prune prune monk monk monk monk monk monk monk monk monk explaining began terminology terminology gradual kailath kailath kailath deleting deleting retaining pointers delete delete delete delete delete superscript jumps superiority superiority counterparts thinking menlo neti mag mag mag penalizing penalizing neglecting encouragement icnn insure unimportant kung kung ricoh ricoh ricoh accompanying wild wild inn millions criticism eft sect crc sand grounds helping stressed noteworthy llt llt daal curvatures pronounce retrain 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weight weight weight weight neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach pattern pattern pattern pattern pattern pattern point point image image image image image image single single processing large large large local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class matrix matrix matrix inputs inputs form form form form form shows shows shows simple simple simple gaussian gaussian paper examples examples examples small small small feature feature feature feature net net net net net work work work task task task task task points field field field field field field field field field field field field field field features features features features features features features features current random random random random random random random random random memory similar similar similar representation representation representation representation representation representation representation representation representation representation architecture show equation equation equation fixed fixed fixed line line images general general generalization generalization generalization parameter parameter parameter parameter parameter real real real real real approximation approximation approximation approximation approximation average states states states states states states states theory theory gradient note note note experiments experiments university university university university university variables variables variables variables variables computation computation computation computation computation solution research research research independent defined target target dynamics initial estimate standard standard computer computer computer computer computer terms connections science science science science prediction direction direction direction direction direction direction direction direction direction direction direction direction direction present present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase machine machine machine machine machine machine machine object object object object object object object object range range range range press learn learn learn learn learn learn learn learn components components sample abstract applied applied find find find find find computational density density density density density properties properties properties references component component component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due positive procedure important important important adaptive adaptive complex complex complex complex complex complex complex complex complex complex complex complex statistical statistical effect dynamic variance parallel tion tion tion energy energy energy energy energy energy energy energy energy energy energy energy energy difference variable variable variable variable variable variable variable variable higher cases required required required good binary binary binary binary binary binary binary binary represent represent represent represent expected expected expected expected expected expected equations equations equations equations equations equations equations fact proposed proposed length length length length length length length length length length scale simulations simulations resulting ing computed respect respect sum elements factor factor factor natural natural global relative relative samples samples represented represented application series define define define compute objects objects perform perform perform experimental goal related connected distributions discrete equal equal power approaches fields fields fields update support descent report version version version consists consists individual represents represents connectionist difficult layers addition considered computing domain directly directly directly directly directly directly directly directly hinton hinton hinton hinton hinton hinton hinton additional solutions capacity efficient requires approximate statistics free free free free free speed vision vision basic pages con con produce derived derived derived weighted randomly conditional robot robot entropy product product finally finally evidence nature depends depends simply associative normal normal normal normal normal normal normal normal normal normal normal normal technical describe describe describe describe describe group denote denote corresponds corresponds stable predictions predictions predictions implemented supported end ability ability ability degree degree noisy including objective objective typically underlying hopfield hopfield hopfield combination dynamical fully fully technology interesting interesting testing york edge segmentation special consistent consistent consistent consistent uniform uniform uniform empirical operation leads representing iterations making stored stored stored magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude idea idea minimize minimize run run sources architectures directions directions directions directions property property property property property property takes machines machines machines machines machines machines machines quadratic quadratic quadratic sejnowski sejnowski sejnowski cognitive axis axis axis solve match match differential differential diagonal sparse definition definition symmetric modified modified williams williams williams williams williams williams williams grant grant arm arm arm arm arm arm invariant invariant derivative rotation rotation rotation rotation rotation alternative alternative deterministic deterministic deterministic deterministic demonstrate flow reduce segment segment segment valued valued depend tangent numerical performs learns temperature taking proportional proportional labeled variety variety minimizing decrease relationship derivatives manner manner minima minima configuration configuration configuration annealing attractor acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann derive longer describes describes describes describes label label label dept dept dept segments segments segments segments segments confidence explicitly explicitly physical angle angle angle angle angle angle consisting equilibrium equilibrium equilibrium equilibrium applying applying decreases independently independently review stages communication labels labels labels labels labels labels labels labels evolution forms approximated completely updates discrimination key key partial earlier calculation performing normalization roughly calculate assigned foundation advantages advantages coordinate formulation formulation formulation contour extension discuss mozer mozer mozer mozer mozer mozer mozer mozer coupled coupled domains domains absolute absolute successfully texture determining capable suitable encoded attractors detect invariance invariance orthogonal orthogonal reached reached compact kind kind anderson anderson anderson symmetry sin sin sin michael relaxation dayan binding overlapping neighboring oriented essential updating rapidly oscillators steady integral integral accurately oscillator periodic helpful mappings mappings mappings combine combine relationships relationships authors symbolic symbolic encode phases phases phases phases phases phases phases phases act act act gradients naturally naturally configurations predicting aspect explored academic extent neal neal scenes cos cos agreement derivation phenomena nowlan lies handle london spatially formalism arc directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional directional angles angles angles circle circle circle circle members toronto toronto toronto toronto toronto toronto nsf outer mechanics conjugate conjugate reflects greatly consistency consistency peter completion completion completion treated dots characterize ture monotonic wind wind suited richard asymmetric kinds comments specifies globally corrupted saddle labeling labeling labeling assign assign equivalence tation angular zemel zemel zemel zemel zemel zemel zemel rotated circular circular circular circular circular circular circular circular circular circular circular circular circular circular repre connecting interconnected interconnected arranged arranged clamped clamped extending extending proceeds belong synchronous intuitively optic exceeds arrays intuitive generalizes generalizes days reliably falls becker james decide von expanded colorado propagated originally peterson peterson peterson peterson peterson enable young clean ends steepest agree concentration concentration concentration baldi temperatures incorporates maximized gaps emergent emergent emergent emergent magnetic centre year personal associate associate certainty certainty certainty certainty constrain concentrated evolve geoffrey geoffrey guidance boulder challenging considers iri conversely paradigms superposition reciprocal reciprocal reciprocal behaves meir meir regularities christopher mcdonnell settling settling lated routines award ackley ackley ackley devised settle huberman huberman autoassociative autoassociative autoassociative 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information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden space space space space space weights weights weights weights weights weights layer layer layer case case vector vector vector vector order order order order order order order order order order order shown shown shown shown shown shown shown shown shown shown shown shown shown shown systems values values values probability probability probability probability probability parameters parameters weight weight weight weight weight weight weight weight weight functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern point point point single processing processing processing processing processing processing processing large large local local local local rate rate rate rate rate test test test test patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis class class class class matrix form form shows signal signal algorithms simple simple simple simple simple paper paper examples examples examples small small small feature feature feature feature feature net net net net net net net work work work task fig fig fig fig fig fig step step step points features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process current current trained trained trained trained trained structure structure structure structure problems random random random random random memory memory memory memory memory memory similar similar show section section section section section rule rule vectors vectors general general speech speech speech speech speech parameter real states states states states states states gradient experiments activity dimensional result result university university variables variables variables computation solution research independent independent defined defined sequence sequence sequence sequence sequence target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial estimate standard computer computer terms terms terms terms distance distance prediction prediction presented present phase phase phase phase phase phase temporal temporal temporal temporal temporal temporal machine machine range range press learn learn learn learn learn nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied back back back find properties properties references due due due ieee ieee ieee positive decision propagation propagation propagation propagation context introduction introduction introduction complex hand hand estimation estimation behavior behavior behavior statistical statistical statistical effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search tion tion tion tion change change difference variable variable variable assume rules signals signals signals signals signals signals signals signals signals representations word learned learned learned chosen higher part good long long long distributed distributed expected equations markov markov markov make make fact proposed proposed proposed proposed correlation correlation length length length length length length length probabilities probabilities observed errors forward forward finite finite finite finite finite finite finite minimum classes classes ing ing ing ing total total simulation regression respect multi sum sum performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq called mapping mapping mapping mapping mapping mapping mapping mapping factor factor factor factor factor optimization global applications knowledge knowledge obtain negative vol vol vol specific represented represented represented represented compared compared compared compared desired series series series series define rates rates rates connected gain discrete discrete discrete discrete discrete discrete discrete discrete discrete power power power power approaches approaches mit steps train train train descent morgan proceedings proceedings institute loss implementation implementation version version version version technique technique consists internal internal internal advances joint joint represents connectionist difficult difficult difficult difficult final final final final final final final final delay scheme scheme scheme scheme sequences sequences sequences sequences sequences sequences considered directly directly directly hinton hinton curves curves curves curves curves transition transition limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san top bit conference conference capacity capacity efficient efficient requires statistics free estimated estimated basic con con con weighted weighted randomly randomly randomly randomly types path product product product selected iteration nature depends sampling sampling sampling sampling sampling simply simply feedforward feedforward increases tested tested tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm short short short short short implemented implemented generate generate generate generate generate main main square end end end ability ability ability instance easily easily easily rumelhart including including kaufmann pairs combination reduced dynamical dynamical fully fully fully programming programming programming programming programming programming testing testing testing ratio ratio ratio ratio structures structures structures uniform operation call iterations iterations max pre making bits international international normalized early frame idea minimize minimize minimize exact exact advantage typical include identical identical sense sense inference inference inference inference inference inference inference compare calculated tions correspond studies rl diagonal diagonal chain observation williams williams expression invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant occur occur occur derivative derivative matrices correctly feed feed touretzky deterministic column demonstrate conclusion starting minimal trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories valued tangent sigmoid sigmoid numerical numerical numerical numerical numerical numerical numerical learns mateo strong integration integration external start start start iii iii averaged introduce groups reference explicit explicit explicit pro written written longer longer winner sequential sequential laboratory mathematical mathematical category category category category explicitly easy unique adding choosing choosing expressed dependence dependence phoneme viewed variation variation variation operations operations operations lee lee lee lee lee lee lee frames frames understanding completely completely similarly key earlier slow spaces normalization roughly purpose purpose remains calculate string symbol symbol symbol symbol symbol symbol norm norm advantages advantages advantages advantages classified classified classified transactions transactions precision precision precision precision template template includes thesis priori coordinate strings strings strings weighting assignment sciences recognize recognize prove successfully successfully simplicity reason reason straightforward aspects closely uniformly suitable differ modification effectively effectively effectively paths delta symbols symbols symbols symbols symbols symbols symbols wij wij wij wij wij wij identify detect tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn schemes schemes schemes schemes schemes schemes schemes schemes schemes schemes invariance score plots traditional kind induced contained success classify sin sin sin sin sin sin sin sin running duration duration categories built built built built involved sampled sampled sampled write giles giles giles giles delayed delayed delayed highest ill reach reach deal deal deal intrinsic presents employed employed powerful layered transformed transformed integral examine examine history history history history history history history history mse ideal ideal referred tanh tanh tanh proved scores affect func understand understand neu coefficient editor analyze analyze analyze automata automata automata illustrate illustrate changed der obvious shapes shapes shapes store store consist mentioned advanced cos cos cos formula formula analyzed analyzed guaranteed adjacent adjacent failure failure benchmark benchmark lies correction correction correction correction handle handle handle handle handle handle handle handle starts immediately calculations sun sun sun sun sun sun sun sun summation summation considerably evaluating double spoken fed simulate remove treated rep templates gen occurrence chen chen chen chen chen chen chen chen chen achieves acoustics acoustics lim sentence converged credit contribute college assign assign guarantee tensor tensor connecting lost lost clamped saturation dealing numerically accepted tools replacing automaton check check mark fail ral belong grammars days date decide pat lang washington washington lengths infinity infinity propagated dif matter matter grammatical grammatical grammatical grammatical grammatical grammatical draw park eqs eqs jump severe consecutive informa zipser liu liu unified accept sig sig ent dec failed failed failed failed pointed aij aij aij aij aij aij ical warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping warping workstation forcing examining stands continuity continuity constrain exam evolve cessing werbos pdp convert jij march picked 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algorithm algorithm algorithm output output output output output output output output output number number number number number number number number number number number number number number number number number number number system system error error error error error error error results results results results results results results results results results units units units units units units units information information information information information information problem problem problem problem problem problem problem problem problem problem problem models performance performance performance performance performance performance performance performance performance performance performance based based based space space linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case vector vector vector vector vector vector order shown systems systems values parameters parameters parameters weight weight weight unit unit unit unit unit unit approach approach approach approach single single single single single processing processing control large large large large local local local test test test class matrix optimal optimal optimal optimal optimal form shows signal simple paper paper examples examples examples small small small small small small small small small small size size size size feature work work task task task task methods fig fig fig fig fig fig fig step step process process level trained trained structure structure memory architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show equation equation equation fixed generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real approximation average states term experiments experiments dimensional result university university computation research research independent independent defined target target standard node science science science science science prediction prediction prediction prediction prediction prediction prediction presented presented map map present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine sets sets sets sets sets sets sets sets sets sets learn basis nonlinear nonlinear sample abstract applied applied find computational convergence properties references due procedure procedure introduction hand generated parallel measure chosen chosen cases cases required good good represent expected make proposed correlation correlation forward forward resulting ing total total total performed performed called potential potential dimension applications study original vol artificial artificial relative samples samples samples samples samples samples application series series series series series series receptive provide objects proc proc proc proc proc determined determined determined related approaches approaches steps steps comparison larger larger fields train train modeling morgan department department individual advances joint joint represents connectionist bias layers layers layers layers layers layers layers layers layers layers layers layers layers layers graph maps maps maps maps maps maps additional additional additional curves curves san san stage effects conference conference choice approximate world vision increase con con condition randomly provided backpropagation nature constraint constraint constraint associative achieved achieved measured discussion covariance covariance increases increases arbitrary arbitrary denote tested limited nearest supported eds eds square makes smaller technology significantly significantly increasing empirical leads leads leads representing details details numbers numbers numbers numbers numbers numbers numbers normalized depth depth attention run predict perceptron denotes architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures improved improved discussed improve reported reported introduced introduced compare module module module module module module module tuning tuning yields differential differential achieve achieve achieve address evaluation organization risk risk grant lead suggests extended feed feed touretzky width width runs conclusions modules modules moody learns mateo hard integration proportional decrease attractor acknowledgements produces winner consisting consisting consisting consisting adding adding adding minimization springer springer springer versus dependence dependence dependence evaluate restricted organizing organizing organizing organizing organizing sizes similarly sign earlier epochs epochs epochs epochs roughly add construction construction construction kohonen kohonen kohonen advantages building perceptrons sciences recognize maximize suitable poggio successful literature comparing situation essentially ten fine graphs issue running running oscillations physiological generalize quantization correspondence maximization diego poor overfitting overfitting overfitting overfitting overfitting overfitting overfitting involving integral matches school incremental incremental applicable applicable authors root proper matched matched neu neu reading predicting taylor consist generates arbitrarily arbitrarily chaotic chaotic averages residual indicating publishers publishers publishers capabilities expensive cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade glass glass glass glass glass glass benchmark benchmark benchmark nonlinearity starts strictly broad broad broad consequence inversion opt opt localized virtual limits pure adjustable rely differs extracting extracting wesley yielding addison extensive narrow narrow grows kaufman chance darken abilities abilities abilities abilities abilities abilities mark exploit exploit ral ral north north symposium mance ranging edelman loo perfor holland holland uni uni facilitate iterated belonging extensively fahlman fahlman summer schulten schulten benefits benefits incrementally adopt chaos german avoided param pub mackey mackey mackey mackey mackey mackey deep iso iso iso iso landscape discusses figs figs elsevier elsevier lapedes lapedes bring nil nil ritter ritter ritter ritter ritter ritter ritter ritter ritter ritter mann shallow shallow shallow resp fractal grbf ers responsibility ning proposal cascaded cascaded cascaded cascaded cascaded cascaded cascaded cascaded cascaded cascaded cascaded cascaded baltimore contents 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problem models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based weights weights linear linear linear linear linear linear linear case case case vector vector order order shown systems systems values values values probability probability parameters parameters parameters parameters parameters weight weight functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method approach approach approach point single processing processing large large local rate rate test analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows shows shows shows shows simple simple simple paper small small small size size size size work work methods methods methods methods methods methods methods points problems problems problems random random random random random similar similar show show show section section section vectors vectors vectors vectors vectors vectors general generalization parameter parameter parameter parameter parameter real real real approximation approximation approximation approximation states theory note note experiments experiments university university university variables variables computation solution research research independent independent defined defined sequence initial initial constant table table table table table table table estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard computer science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction low low range press basis nonlinear nonlinear nonlinear nonlinear nonlinear sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied applied computational convergence convergence convergence convergence convergence convergence convergence convergence properties properties properties references component stochastic procedure procedure procedure procedure procedure procedure procedure introduction complex statistical statistical statistical statistical statistical statistical effect effect effect effect generated generated generated variance variance tion tion tion difference difference difference difference complexity assume lower higher higher part part center cases cases cases cases type type good good conditions conditions distributed bayesian bayesian expected expected region proposed proposed correct correct correct probabilities probabilities observed observed errors errors errors errors errors errors errors scale resulting resulting ing simulation simulation simulation simulation regression regression regression regression regression regression regression regression regression regression regression regression respect called elements elements regions potential potential dimension applications original original vol vol vol vol vol vol vol vol vol vol vol specific samples samples samples samples samples true true true true true true true true true true true true true true true true compared application desired desired cross cross series perform determined determined determined determined related related distributions distributions steps steps accuracy comparison comparison comparison larger larger contrast contrast nets selection selection selection selection selection morgan morgan department version kernel kernel kernel advances advances final bias bias maps considered considered cambridge cambridge experiment experiment additional view limit limit san determine determine determine full full full full full requires approximate approximate statistics statistics statistics statistics statistics statistics speed speed speed estimated estimated estimated validation validation con condition conditional backpropagation depends depends sampling sampling sampling sampling sampling sampling sampling sampling simply simply normal normal normal normal normal feedforward feedforward increases corresponds predictions predictions predictions predictions predictions predictions predictions predictions predictions finding short generate generate supported supported theoretical theoretical theoretical theoretical main eds eds eds journal journal journal square square square square square square instance noisy fit kaufmann kaufmann underlying underlying account account functional functional unknown technology consistent consistent consistent consistent uniform empirical empirical empirical empirical pre magnitude idea improved discussed discussed discussed discussed discussed discussed improve advantage takes reported practical practical practical practical apply strategy strategy interest interest volume works tions smooth yields yields correspond rl interval interval interval sensitive increased increased grant extended extended deviation deviation deviation deviation predicted alternative alternative occurs generally demonstrate assumptions central central central measures moody asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak mateo propose presence drawn radial exist relationship relationship denoted acknowledgements relation derive primary estimating confidence confidence confidence confidence confidence confidence confidence infinite involves predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive yield national independently review estimator estimator estimator variation fraction fraction showed key calculation intervals intervals intervals intervals intervals intervals intervals remains valid valid valid advantages precision box determines holds closely society differ literature literature mackay mackay situation situation plots summary summary soc notice repeated procedures procedures procedures procedures procedures procedures procedures contained contained heuristic interpreted hold list usual usual modelling situations simpler parametric parametric american american american xor xor exhibit exhibit exhibit relations estimators estimators estimators estimators hanson association association lippmann hall hall biases investigated reliable reliable complicated complicated proved notion concepts versions versions improving improving improving improving improving attempts defines residual great ment pairwise pairwise pairwise pairwise derivation derivation defining analytic analytic analytic caused tractable correction starts reasons turns purposes arise bandwidth fluctuations fluctuations reflects greatly substantially bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap consistency consistency amounts readily backprop backprop backprop backprop backprop reliability outliers requirement requirement spread spread spread differs differs gen replace germany chose median median median yielding cumulative secondary secondary intractable approximates royal royal mail fail intuitive nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric moments utilized sion sion dependency dependency offers indicator offer offer arrive extensively extensively pearlmutter pearlmutter subsequently valuable summarize cam liu liu liu liu ple ter annals annals annals annals annals annals uniquely forced tibshirani tibshirani tibshirani residuals residuals regularity tendency german german unseen distri approxi setup breaks discusses discusses discusses sam siam esti preprint preprint mimic investigations knowing applicability lippman intensive intensive bution replacement survey crude nested ers drawing identically resampling resampling resampling calculates contrasts coincide repetition occam iid fin gmd gmd reviewed tical assessed assessed prescribed unnecessary bootstrapping bootstrapping bootstrapping bootstrapping applica assessing assessing assessing assessing assessing kolmogorov approxima plans parame distributional tics statis statis eralization jackknife jackknife jackknife jackknife jackknife jackknife jackknife coverage coverage heidelberg heidelberg belmont philadelphia formalized utilization asymptotics asymptotics simu lations razor razor efron efron efron efron efron efron efron efron efron efron wild wild wadsworth articles plied regres regres ein ein observa mates federal thereof rosenfeld refinements calibrated freedman freedman freedman freedman freedman manifestation sistent gerhard deteriorate tential irdle irdle inspecting calibrating introductory inves devia augustin crossvalidation crossvalidation advocates mator promoted 
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networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number results results results results results results results information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based 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task task task task task task task task task methods methods methods points classification level level trained trained trained trained trained trained problems problems random random random random random high high high high high high high equation fixed line line line line generalization speech parameter parameter average average theory theory obtained note note note note experiments experiments experiments result result university solution research defined defined defined found found found found found target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target initial initial initial initial initial initial initial constant estimate standard computer computer computer science present activation low low low machine machine range press press press press learn position components outputs abstract back back back back back back back back back computational references ieee important important important adaptive decision decision decision propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction statistical tion change difference difference assume classifier lower measure learned learned center previous type required required required required good long conditions conditions conditions conditions conditions tree tree equations fact observed observed errors scale resulting resulting classes classes ing ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total total simulation multi sum called called called times factor factor factor natural applications knowledge knowledge knowledge artificial artificial artificial relative represented compared compared compared application application application cross related related constraints distributions mit comparison larger contrast connection update update train source source source source source source source source source source source source source source source source source source source source source source source source source source source source nets selection morgan proceedings proceedings report department synapses advances joint connectionist final equivalent directly san effects conference conference determine efficient requires significant significant significant significant speed speed speed speed speed speed speed speed pages pages pages pages pages validation give con randomly randomly randomly randomly randomly randomly randomly randomly randomly randomly randomly randomly randomly randomly randomly criterion criterion criterion criterion criterion criterion backpropagation simply measured measured technical tested tested fast limited surface amount amount effective implemented end kaufmann objective hopfield technology transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer significantly significantly significantly significantly ratio empirical empirical empirical empirical empirical squared details max pre direct magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude idea idea idea run discussed separate separate takes movement practical introduced introduced period period identical side side side subset subset subset subset subset subset engineering compare previously previously previously volume volume volume axis axis speaker studies studies studies studies converge trans address address evaluation evaluation positions positions modified improvement studied scaling alternative move move move demonstrate demonstrate runs conclusion place valued editors editors editors measures faster faster asymptotic asymptotic asymptotic asymptotic asymptotic mateo taking strong largest demonstrated california solid proportional intelligence intelligence intelligence assuming relationship relationship program question acknowledgements ways sequential sequential sequential sequential describes mathematical changing metric metric implement remaining shift shift john john national focus depending viewed evaluated evaluated evaluate controlled showed updates updates updates updates reasonable slow dashed epochs epochs epochs epochs epochs epochs epochs epochs topology avoid formulation sciences determines extension holds tests aspects uniformly uniformly society effectively effectively build build score situation situation situation situation vowel reached reached summary procedures prob prob allowing showing superior superior superior superior contribution criteria michael paradigm paradigm giles highest reach reach reach receive receive cowan situations unlike american american american put hanson hanson dotted helpful fewer fewer school scaled authors complicated scores scores scores understand momentum induction induction hill generalisation man psychology psychology assumes explored explored explored separated academic initialized initialized initialized initialized initialized initialized initialized initialized initialized initialized initialized initialized initialized initialized initialized initialized initialized epoch epoch epoch epoch epoch epoch speakers speakers baseline baseline baseline utility utility motivated neal mentioned indicating stop stop formula publishers defining defining defining defining explanation worse worse worse worse ran worst hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane cut english english author author evaluating evaluating evaluating substantially substantially relevance flexible cohen cohen cohen detecting detecting slower calculating ture ture reaches incoming achieves achieves substantial chose chose comments returns patients patients patients diagnosis initialization initialization don don shifted proportion martin martin martin martin hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes count count count climbing smith overcome logarithmic multiplicative hyper neurobiology methodology adequate motivation games interference reset separating separating falls loo entry displayed decide male washington colorado colorado heart heart heart heart heart reveals inductive inductive valuable mechanical mechanical lem yielded dna dna dna dna thrun thrun thrun corporation ter shorter sig sig planes sontag sontag sontag formulate seek female chess chess chess chess scenario visualization pub ftp magnitudes magnitudes magnitudes magnitudes magnitudes magnitudes magnitudes guidance mitchell mitchell mitchell crosses carefully disease meta quinlan quinlan quinlan million retained exploited aaai helps lems learners january tom ers ning equa pratt pratt pratt pratt pratt pratt pratt pratt pratt pratt pratt pratt pratt scenarios scenarios nontrivial rivest alto company cutoff addressing catastrophic catastrophic palo publishing degrade jack jack retaining inserted sebastian transferred literal literal literal literal literal literal literal literal literal literal literal literal literal literal literal literal mum modifies forgetting relying saved illustrating superiority ninth scratch engineers engineers wired british british justify initializing golden roots justifies eter wheel accent discriminability discriminability discriminability discriminability discriminability discriminability discriminability discriminability discriminability signif indexes indebted speak swiss swiss anonymous overcomes mcc vas vas vas microelectronics signifi females sider asme asme mammone mammone slowed prospects trm aca domly ternational zeevi engineer sharkey sharkey sharkey sharkey sharkey sharkey sharkey sharkey superset superset tat chap cantly nificantly eduardo xvith mines mines curacy rescale rescale sped hirsh gale gale rmeters recycled repaired ale upcoming magni 
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vector vector order shown shown shown shown shown shown shown shown shown shown shown shown probability weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method method method method pattern pattern point point point point single neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test analysis matrix optimal optimal optimal optimal inputs form shows paper small small size size size net task methods step step step step step step current current current current trained problems random random similar similar similar similar similar architecture show equation rule rule general parameter real approximation states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term note experiments activity activity university threshold table table table table table table terms terms synaptic node node direction direction direction direction direction direction direction direction presented presented presented presented activation activation activation activation activation activation range components abstract applied applied applied applied applied computational computational computational computational convergence convergence convergence convergence density analog references stochastic stochastic due due ieee ieee ieee adaptive introduction complex hand hand hand statistical cost cost recurrent search tion change change change change difference difference difference difference difference difference complexity complexity complexity complexity complexity complexity measure measure measure measure chosen chosen represent expected techniques correct correct correct correct correct forward forward forward forward finite finite finite finite finite simulations simulations simulations simulations simulations simulations simulations simulations total total respect respect respect respect respect respect performed performed optimization made made artificial represented represented true application series series series series determined determined determined experimental discrete equal steps steps steps comparison comparison larger larger update update update update train descent descent descent descent proceedings department implementation implementation technique technique technique technique internal code code represents directly directly effects bit determine significant approximate approximate approximate speed give randomly product product actual provided finally selected backpropagation backpropagation achieved achieved feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward describe limited limited limited limited generate require require require require square vlsi vlsi vlsi vlsi vlsi reduced technology transfer ratio ratio ratio ratio ratio trials mode mode mode operation bits combined added description description perceptron advantage reported apply introduced side side side engineering sufficient calculated calculated calculated calculated achieve improvement improvement improvement improvement improvement storage hardware hardware hardware hardware hardware hardware hardware hardware conclusion greater trajectories performs performs performs assuming assuming relationship averaged relation ann ann ann ann ann ann ann ann ann ann multilayer multilayer electrical applying applying implies versus versus versus 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural input input data data data data data data data data data data data data data data data data data data function function function function function figure figure figure figure figure figure time set set set set networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number error error error error error information information problem problem problem problem performance performance performance weights linear linear case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order shown shown shown shown systems values values values values values probability probability probability probability probability probability functions functions functions functions functions functions distribution distribution recognition method method approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern point point processing rate rate rate rate rate test patterns patterns patterns patterns patterns analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class optimal optimal optimal optimal optimal optimal optimal optimal form shows shows shows signal algorithms simple small size size size size size size size size size size size size size size size size feature feature feature work work step step step step step step classification classification classification classification classification classification classification classification random random similar show show equation equation equation vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general generalization generalization generalization parameter parameter real approximation approximation approximation approximation approximation theory gradient obtained note note note note note note experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional result university university university defined defined defined found found found sequence sequence initial initial initial estimate estimate estimate standard computer computer computer distance distance science science science science science science science left left left sets sets sets motion range press learn components sample sample abstract find density density density properties references stochastic stochastic stochastic stochastic stochastic ieee positive procedure procedure important adaptive decision context introduction statistical effect effect parallel parallel search tion change energy variable variable classifier previous cases type long conditions conditions conditions conditions conditions conditions conditions represent distributed expected make region region correct observed errors simulations minimum resulting classes classes classes classes classes ing tasks tasks tasks human regression regression regression respect multi sum performed optimization made negative artificial relative relative represented represented true application cross provide define rates perform goal goal constraints constraints constraints approaches approaches mit steps accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison update descent report department department department version version technique technique consists code code code represents graph graph maps maps considered experiment limit limit effects conference classifiers full approximate estimated pages pages pages condition condition coding coding coding weighted conditional conditional biological biological achieved discussion technical technical increases group proof proof nearest nearest supported theoretical square rumelhart rumelhart rumelhart rumelhart rumelhart development objective smaller needed account technology testing consistent consistent matching details numbers pre making window window window window window window window window window window window window window window window window window window window window window window window window window normalized normalized normalized normalized normalized supervised minimize minimize minimize minimize minimize run added improved separate machines engineering dimensions varying varying compare volume axis converge positions modified improvement improvement improvement increased grant grant parts occur suggests extended derivative move width width width clusters occurs boundary boundary runs runs runs place competitive competitive competitive competitive editors editors interactions bayes bayes sutton peak physics minimizing decrease decrease decrease averaged averaged program acknowledgements reference reference reference reference laboratory missing sensitivity linearly linearly linearly springer formation reconstruction reconstruction reconstruction reconstruction influence restricted organizing showed centered sizes suggested converges updates earlier normalization normalization normalization reduces reduces add distances calculate kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen transactions david priori priori extension plotted plotted holds tests compression compression middle extra mcclelland 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rochester rochester elsevier elsevier places ignoring travel mini worked november voronoi voronoi suggestions expense stephen recogni decided trainable losing ers tors tors steven steven obey quantizer quantizer quantizer classi classi classi classi classi classi placement unlabelled unlabelled unlabelled smc teaching gence resultant modest jack jack stat simula incurred obeys sentations borders borders oil orig llx encourage conver topologically dana formants seeks centred centred canadian nserc barney helsinki iix iix segregated segregated robbins robbins robbins monro monro monro monro worthwhile males attend additions draft identi misclassifications misclassifications misclassifications females argues legend scholarship rob virginia kangas publish declines sents frontier revisited alg xlc xlc complicates unweighted mizes microstruc warranted fewest 
#@Ballard_D,de-Sa_V,
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training training training training training training training training training training algorithm algorithm algorithm output number number number number number number error error error error results results results results results results results results results results results results results results results units units units units units information information models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based space weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer case case case case case systems systems values values probability parameters parameters parameters noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions neurons neurons neurons neurons neurons distribution method method method method method method method method method method method method method method method method method method single single processing processing test test test test test test test test test test test test test test test test test test test test test test test test class class optimal optimal optimal optimal inputs inputs inputs form form algorithms algorithms simple paper paper examples examples examples examples small small small small small small small size size size net net net net net net work task task methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step step step step step step step field field classification classification process process process process process process process process process process process process process process process process process process process process level trained trained trained structure structure structure structure structure structure structure random architecture architecture architecture architecture architecture show show show show fixed fixed fixed fixed general generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter average average average theory term term term term term term term term term term term term term term term term term term experiments experiments experiments experiments experiments experiments experiments experiments result variables variables variables variables variables variables variables variables variables variables computation research research independent defined initial constant constant constant constant constant constant table table terms terms terms terms terms terms presented presented activation activation temporal sets sets sets sets range range learn position position basis nonlinear nonlinear abstract back find computational convergence convergence convergence convergence convergence convergence convergence properties references stochastic procedure procedure propagation introduction complex hand hand hand statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical effect effect dynamic dynamic dynamic dynamic dynamic generated generated variance variance cost cost search difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable variable variable measure prior prior chosen chosen chosen higher center type long bayesian bayesian techniques techniques techniques techniques region proposed observed observed observed observed observed observed simulations simulations resulting classes ing simulation regression respect sum sum sum performed performed called elements elements potential natural specific specific true true compared compared compared compared application provide proc proc perform active active determined constraints distributions distributions brain brain brain brain steps comparison comparison larger update selection selection selection selection selection selection selection selection selection selection selection selection morgan morgan version version technique consists consists advances advances joint represents final final final final final exp exp exp exp exp exp bias addition considered considered considered considered framework framework domain domain domain experiment directly effects effects effects effects determine requires choice basic increase increase validation validation validation validation validation give give produce derived levels criterion criterion criterion criterion bounds types product provided finally finally finally processes processes processes processes processes processes selected evidence evidence simply measured discussion feedforward feedforward group group tested tested tested tested tested tested tested tested tested tested tested tested close assumption corresponds rbf rbf rbf rbf rbf amount short implemented generate theoretical theoretical require require adaptation adaptation ability rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart development including fit fit objective objective objective objective objective objective objective objective objective pairs combination reduced reduced reduced reduced reduced interesting testing testing testing significantly significantly significantly character head head empirical empirical empirical leads pre decay decay decay decay produced added improved recent practical introduced include include side quadratic sense array relevant relevant highly highly varying calculated calculated correspond converge achieve modified modified observation observation entire increased constructed extended extended extended extended extended extended wide derivative touretzky occurs generally generally column column setting strength minimal reduce reduce reduce reduce central differences measures measures designed moody constrained strong reduction regularization regularization regularization regularization regularization regularization regularization radial variety start relationship iii targets manner minima minima question denoted denoted denoted pro produces produces generating generating generating generating generating generating ann changing pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning category category category remaining adding formed quality choosing choosing independently dependence dependence dependence review estimator viewed controlled evolution suggested suggested updates reasonable additive epochs classical classical classical classical classical classical fitting fitting purpose penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty generation remains remains sufficiently symbol construction topology topology topology topology weighting weighting weighting discuss candidate variations tests tests tests tests regular efficiency modification modification divided divided included successful comparing situation identity identity ten ten reached reached conf conf repeated repeated procedures cun cun stopping stopping stopping stopping superior superior superior superior sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin categories list involved denker leading leading attempt illustrates deal overfitting overfitting overfitting overfitting overfitting overfitting overfitting essential investigate varied hanson optimized biases reducing fashion investigated investigated investigated int int referred referred tanh workshop analogous removed saliency naturally possibly adapt adjusted adjusted subsets versions versions consist consist established established percentage great directed explanation benchmark starts comparisons comparisons berkeley satisfied ring widely producing forces forces arise mation controls pool pool pool pool auto auto auto auto auto auto auto apparent greatly collected relevance conducted fed solla detecting remove frequently rep variant ity characterize differs weigend weigend weigend weigend weigend weigend weigend weigend prevent prevent datasets sums germany damage damage damage damage begins deviations converged irrelevant redundant sort extensive extensive ordering turned proceed extending kaufman kaufman consideration consideration significance significance significance significance siemens held held stated biased removing observing settings settings disjoint modifications modifications modifications enhanced enhanced enhanced obd obd obd obd infor elimination elimination elimination started mance falls corre appendix perfor pruned overview overview regard forecasting ranking ranking ranking iterated valuable stopped stopped stopped stopped stopped stopped stopped stopped stopped stopped stopped stopped stopped stopped stopped stopped stopped baldi accumulated dramatically ple specification listed listed tables tables tables tables tables tables expanding hundred var var remainder exam exam chauvin cessing ization searches statistic statistic interactive breaks diversity denver lippman inactive removes circumstances served resp resp resp resp resp sponding sees sees sees corporate continued continued doesn doesn overtraining overtraining overtraining overtraining establishes striking contrasts huberman ples pratt disturbance ings categorical categorical baltimore sented benchmarks benchmarks benchmarks regularizers fundamentally topics ther restart emulate emulate begun vast fur lay counterparts vat vat vat munich disappear fulfilled fulfilled penalizing singapore amples fifty zimmermann zimmermann zimmermann zimmermann zimmermann zimmermann zimmermann tain rankings rankings rankings quence otto steer restarts restarts restarts restarts restarts restarts innovation innovation finnoff finnoff finnoff finnoff finnoff finnoff finnoff consequent notable notable hahn danger deviate instrumental nonconvergent nonconvergent nonconvergent nonconvergent nonconvergent nonconvergent nonconvergent nonconvergent nonconvergent nonconvergent cer parametrization parametrization quantile quantile contradicts deteriorate pletely deteriorates lexp lear intensively reinitialized innovations hopes basing 
#@Finnoff_W,Hergert_Hergert,Zimmermann_H,
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output output output output output output output output output output output output output output output system system system system system system system system system system system system system system system system system system system system system system system system error state state state state state state state state state state state state state state state state state units units units units units units units units units units units units units information information information information information problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance space weights weights linear linear layer layer layer layer layer layer case case vector vector order order shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems values values values noise noise noise noise noise noise noise weight weight functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition approach pattern pattern point single single single single processing processing processing control control large large large local neuron rate patterns patterns patterns patterns patterns analysis analysis class class matrix inputs inputs inputs inputs inputs form form form form form form form form form form form shows signal signal algorithms algorithms simple simple simple simple simple gaussian visual visual visual paper paper small feature net net net net net net net work task fig fig fig points field process process level level trained trained trained structure structure problems problems high high high high high high high high memory memory memory memory memory memory similar similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show show fixed fixed line rule general parameter parameter parameter parameter parameter parameter real states states states states states states states states states states theory gradient note note activity activity activity activity activity activity activity activity activity dimensional university computation computation computation computation computation computation computation computation independent independent independent independent defined defined defined defined defined defined defined defined found found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial constant standard standard standard standard standard standard computer computer computer terms terms connections connections connections node science map present present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation activation low low low low frequency frequency frequency frequency frequency machine machine machine machine machine machine machine sets maximum range range range press press learn nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied find find computational convergence convergence analog analog analog analog analog analog analog analog analog analog analog references important important important important important decision context context context context context context context context context context context context context context context context context context context context introduction action complex behavior behavior behavior behavior behavior stimulus effect dynamic dynamic dynamic dynamic generated generated parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search tion tion tion tion tion change change change energy energy difference difference complexity variable spatial spatial assume lower representations representations chosen chosen chosen higher cases type type required cortex cortex cortex cortex cortex cortex cortex good binary binary binary binary binary binary binary distributed distributed distributed equations equations equations equations equations equations equations equations make techniques correct observed observed scale finite finite finite finite finite finite finite finite simulations ing ing total regions reinforcement potential made made feedback feedback feedback em filter artificial cross cross rates rates proc location active determined determined determined connected connected connected motor motor motor motor motor motor discrete discrete discrete discrete discrete discrete cortical cortical cortical cortical brain brain brain brain steps larger larger larger larger connection connection connection connection fields train dependent modeling implementation implementation synapses synapses individual joint responses final bias bias bias layers layers layers sequences sequences sequences considered computing computing equivalent view design design transition transition limit san determine choice choice choice choice significant free speed pages pages pages pages con produce coding coding randomly developed levels levels levels levels area area types types lines actual actual evidence backpropagation nature inhibitory simply simply biological biological associative associative associative associative associative associative associative normal normal normal normal normal normal normal normal normal normal feedforward feedforward increases assumption circuits amount common implemented implemented supported end ability ability easily makes makes sensory sensory sensory sensory auditory simulated underlying combination dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical fully fully transfer character projection projection york york edge increasing special mode mode mode mode mode mode mode mode principle principle operation operation operation operation operation representing representing call pre stored stored bottom polynomial predict neuronal architectures architectures discussed robust element element reported apply identical side side side side hierarchical inference inference inference inference inference inference subset cognitive cognitive relevant previously observations calculated works module module module module module module module module module module module module module module module module module module module axis axis axis axis tions match differential rl rl address storage storage entire entire increased grant amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude constructed constructed constructed constructed constructed constructed studied occur occur digital digital digital digital digital spikes matrices rotation predicted move occurs occurs hardware flow flow flow critical place minimal minimal valued sigmoid sigmoid modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules retina designed designed designed performs faster strong strong presence presence presence physics external external external external external cycle cycle cycle cycle cycle cycle demonstrated characters attractor attractor attractor attractor attractor attractor acknowledgements areas appears appears appears relation optical optical winner winner winner winner winner winner laboratory transitions transitions transitions transitions transitions transitions transitions stability stability stability mathematical mathematical dept dept implement explicitly coordinates coordinates coordinates coordinates coordinates coordinates coordinates infinite infinite slightly unique spectral interaction interaction interaction frequencies equilibrium equilibrium equilibrium springer formed expectation potentials cycles cycles competition competition competition competition competition competition competition competition competition competition competition competition competition choosing national communication viewed viewed influence variation variation evaluated open operations controlled lee forms static static static static static static static static approximated activities completely key additive neighborhood roughly intermediate string string symbol symbol symbol symbol symbol symbol construction construction foundation eeg advantages degrees coupling coupling expect building handwritten box figures strings strings inter memories memories recognize specifically coupled coupled domains holds grammar grammar grammar grammar grammar characterized reason regular aspects maximal effectively effectively driven symbols symbols symbols symbols symbols mcclelland wij wij modes modes modes modes modes modes oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors detect situation miller essentially identity identity reached composed traditional conf kind kind contained contained allowing neuroscience neuroscience superior superior superior symmetry sin sin oscillations oscillations oscillations gray gray gray gray built built giles giles giles giles giles giles binding cat principles principles operating operating operating operating extract load load intrinsic intrinsic receive employed explore explore diego create essential essential oscillators oscillators steady detail issues dotted oscillator oscillator periodic periodic periodic periodic periodic examine respond giving behavioral mappings int ideal analytically reliable reliable reliable reliable reliable proper proper proper proper proper oscillation oscillation oscillation oscillation oscillation affect affect examined math editor editor editor man automata automata automata automata equally equally thought thought aspect olfactory olfactory olfactory olfactory olfactory olfactory olfactory bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation algo assumes assumes expressions art consist consist generates generates regime regime chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic animal devices languages slowly cos cos coded capabilities capabilities benchmark benchmark inside implementing berkeley berkeley berkeley berkeley berkeley sys day forces broad transistors leaves arise controls mathematics mathematics cut projected recognized separately beginning begin patches computers geometry sun behaviors populations double freeman freeman freeman freeman freeman freeman freeman understood understood elman elman elman elman elman elman elman elman elman elman elman elman experimentally slower sharp sharp span operate mod perturbations perturbations perturbations reaches extracting serve collective chen chen singer singer singer enables coherent chose baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization irrelevant irrelevant cor gap shifted ordinary ordinary ordinary accomplished oxford rithm driving acts perfectly approximates approximates approximates circular tem lost clamped clamped clamped clamped clamped clamped clamped inspired adds tools alpha automaton automaton automaton automaton automaton analyzing north preparation clock clock clock clock constructive holland moved lawrence interconnections competing competing dif dif winning advance advance cerebral mem locked locked locked locked theoretically contact grammatical grammatical grammatical grammatical grammatical grammatical grammatical arrows impact impact messages speeds alternatively receiving cam divide leaving solves kluwer basin basin super break transmitted alternating emergent legal diverse tween amplitudes amplitudes amplitudes tendency tendency possibilities basins sinusoidal beta illustration remainder quantized quantized deep deep evolve gained grouped mathematically permits intra afosr picked rejected landscape landscape synchronized synchronized flip flip flip flip flip guided rhythmic option oscillating oscillating oscillating oscillating oscillating oscillating oscillating maintains sized inverting macroscopic macroscopic macroscopic behave behave behave programmed programmed bill computa examination microscopic microscopic microscopic behaves syn discontinuous justified assistance todd exper morris carrier anatomy continuum unreliable operational contributes neocortex neocortex recognizes recognizes ory bandpass complement emg evolves relaxed lags schreiber lar tical tomita substrate physica cleeremans cleeremans cleeremans cleeremans servan talk talk polar polar subnetwork subnetwork subnetwork subnetwork eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman tivity subnetworks subnetworks relax relax rises ular contributing primates macro hirsch bio ver lowered nections internally bistable synchronize synchronize holmes holmes holmes bifurcations bind topologically tilt tilt tilt tilt tilt clocked clocked clocked clocked thinking clamping asso released analysed walter behaved lose tilted flop flop flop flop isomorphic lock particu partic takens resonant resonant reber reber reber reber valley forest roi roi rli theta settled cot invaluable attracting gestalt disparate pleasure coordinated reciprocally midpoint coo transi recurrently recurrently flops quantize underly underly immune intent livermore livermore quantizing norwell bolic valleys valleys dissipative tition ciative namical reverses buffering clocking clocking clocking clocking clocking electromagnetic improper guckenheimer guckenheimer guckenheimer competi competi communica ferential ferential immunity portrait portrait ules compe prepare supra submodules dispersed subserve passband engi digitization adiabatically puters binarized petition petition neering effecting scopic acknowl 
#@Baird_B,Eeckman_F,Troyer_T,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data figure figure figure figure figure time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state state state results results results information information information information information information information information information information information problem models performance performance based based based based space space space space case case case case case case case vector vector vector vector order order order order shown shown systems systems systems systems systems systems values values values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise weight weight weight weight weight weight weight weight weight functions distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method method method method approach pattern point single single single single single single single single single single processing processing processing processing control control control control large large large local local local local neuron rate rate rate rate rate rate rate rate rate rate rate test analysis analysis analysis analysis analysis analysis optimal optimal optimal optimal optimal form form signal algorithms simple simple simple examples small small small small small small small small small small size size net net work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods fig fig step field field features features features process process process process process process level level current trained structure structure structure problems problems problems problems random random random random random random random random random random response response response response similar similar architecture equation fixed line line line line line line line line rule rule rule general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real approximation average average average average average average average average average average average average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term term term term note note computation computation computation computation computation computation computation computation computation computation computation independent independent defined defined found sequence dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial constant constant constant constant estimate estimate terms terms terms terms direction presented presented presented presented presented present present present activation low nodes maximum maximum maximum maximum maximum maximum maximum range press components components continuous abstract computational computational convergence convergence convergence convergence convergence convergence analog analog analog analog analog analog analog properties properties properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due due due due due ieee ieee ieee ieee positive positive positive important adaptive adaptive adaptive adaptive propagation context complex hand estimation statistical effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance variance variance variance parallel parallel parallel parallel parallel parallel parallel recurrent recurrent recurrent recurrent recurrent search tion change change difference complexity complexity complexity complexity complexity lower measure measure signals signals prior prior representations part part theorem required required multiple multiple binary binary long long conditions conditions conditions conditions conditions conditions represent distributed distributed distributed distributed distributed distributed distributed distributed expected expected fact techniques proposed correlation correct observed scale simulations simulations minimum resulting resulting resulting resulting classes ing ing tasks tasks total total total simulation respect respect multi performed performed performed times regions reinforcement factor factor factor factor factor factor factor factor factor factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization global applications knowledge knowledge knowledge obtain obtain obtain original original original vol vol vol vol vol vol vol vol vol vol vol relative relative relative specific specific specific true true compared application desired desired cross series rates proc related discrete discrete equal equal equal approaches approaches mit comparison comparison fields update update update update update update support descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent dependent dependent dependent morgan morgan morgan report institute institute institute implementation version technique technique technique technique technique consists internal internal internal internal internal code individual individual individual individual advances advances advances represents bias bias bias bias bias bias addition cambridge equivalent equivalent directly directly directly hinton additional view limit limit limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san san capacity efficient upper full full requires requires requires significant free free free free free free free free speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed increase increase give con condition channel channel channel derived randomly path path path actual provided provided provided provided provided selected selected selected backpropagation iteration depends constraint measured technical feedforward feedforward arbitrary fast fast fast fast fast assumption corresponds complete complete complete complete surface circuits finding amount effective effective effective effective effective effective implemented assumed generate require require eds square square end vlsi vlsi vlsi vlsi vlsi vlsi instance instance degree makes rumelhart rumelhart including typically needed reduced reduced dynamical dynamical functional functional functional functional functional functional functional unknown fully fully technology technology interesting significantly increasing mechanism mechanism consistent trials uniform uniform principle operation leads max max max direct bits normalized normalized supervised supervised supervised supervised supervised supervised minimize run sources perceptron improve improve directions directions correlations exact exact exact exact exact exact exact property typical typical period recently relevant dimensions dimensions varying varying varying previously conventional teacher teacher volume volume works works yields converge converge achieve trans trans address background evaluation modified modified modified channels interval williams williams improvement storage storage storage increased constructed constructed studied scaling scaling scaling scaling scaling scaling scaling scaling digital deviation alternative deterministic hardware hardware hardware hardware demonstrate runs runs strength strength conclusion starting minimal reduce trajectories central measures accurate numerical performs performs faster constrained mateo mateo mateo strong hard integration largest reduction demonstrated california california solid minimizing exist exist decrease decrease decrease decrease iii iii averaged minima minima minima acknowledgements reference reference explicit explicit explicit van construct longer longer factors sequential sequential sequential sequential sequential sequential sequential generating transitions transitions averaging averaging averaging averaging averaging physical physical remaining scales scales scales cycles cycles decreases decreases decreases decreases expressed dependence correlated operations operations operations fraction similarly suggested updates updates updates updates updates updates updates updates updates allowed calculation calculation calculation calculation calculation smoothing smoothing epochs epochs epochs delays delays reduces combining purpose boundaries generation valid sufficiently topology topology avoid includes formulation formulation instances instances sciences illustrated holds holds characterized successfully simplicity simplicity planning extra efficiency effectively effectively effectively mcclelland computations computations essentially orthogonal reached prob allowing anderson contribution contribution contribution running running follow satisfy satisfy involved involved involved involved modular paradigm ill reach thresholds received extract satisfies intrinsic decreasing unlike powerful perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation access access requirements investigate steady strengths issues issues ml rise rise scalar scalar scalar history history tech mse incremental incremental incremental investigated fault fault root statistically statistically statistically cognition gradients gradients necessarily necessarily analyze analyze equally implementations ensure formal formal algo assumes taylor perceptton epoch epoch epoch epoch epoch epoch epoch epoch epoch epoch consist contributions arbitrarily submitted serial finds years asymptotically histogram ment publishers publishers publishers analyzed guaranteed guaranteed navigation diffusion diffusion expensive expensive independence caused worse handle nonlinearity processed strictly strictly strictly strictly worst worst worst desirable desirable consequence consequence computers bandwidth auto fluctuations fluctuations fluctuations requiring applies substantially understood pure pure pure offset offset offset offset pseudo quantitative effort effort posed adjustable adjustable adjustable slower slower slower slower slower slower variant compares perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations measuring ture ture popular incoming serve pasadena suited achieves adjust enables comments tolerance tolerance converged calls summed yielding instantaneous representative uncorrelated uncorrelated uncorrelated extensive rithm arguments arguments proceed caltech inspired kaufman kaufman kaufman mail attractive analyzing synchronous intuitively intuitive substituting motivation alspector alspector alspector meaningful evaluations combines appendix appendix equals injection injection injection demonstration widrow sim tic reveals omitted matter matter refers steepest steepest steepest pearlmutter exploiting valuable speeds baldi baldi baldi avoiding balanced explorations sequentially mind multiply ure associations specification largely sig basically ber aircraft opposed opposed opposed formulate uniquely expanding distinction par regularity individuals jabri jabri forcing streams param avoids mutually mutually mutually equality increment favor schmidhuber num efforts relate relate simplifying parallelism importantly supports sta flower flower flower intensive increments increments increments struc differentiating continually continually gorithm spite suggestions sessions sessions removes picking meir reversal bility instability err err adjoint reflecting supplied burr compo concerns practically optima partly contributes contributes contributes rameters zipset frequent inde tations barhen cauwenberghs cauwenberghs cauwenberghs cauwenberghs correlates dent appro indepen fixing parker allowable putation unnecessary degrades kailath kailath kailath pendent derivations derivations omit direc upward upward nents excluded mum favorably reminiscent decrement decrement coincidence kirk kirk boost mate fur toomarian temporary steepness retains subtraction subtraction subtraction turbulence explores explores accumulating orthogonality namic stochas bypass spacecraft owing dembo dembo dembo eter rue yuhas occasional nique omitting unrelated exceeding ware jayakumar gert gert hue hue downward decoupled multilayered cumbersome interfere kerns kerns attainable attainable attainable stochasticity implemen injecting injecting fleischer contaminated pap ciently instabilities instabilities eft necessitates kom detrimental correlating balances stringent chu whitaker polarities jpl gracefully compensating virtues elevated nection allel yariv init parallels maih pertur thermore madaline madaline unperturbed vmue intentionally nificant plicity gannett haber stances mgorithm mgorithm aeronautical microstruc focussing effecting sensibly 
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#*network network network network learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks training algorithm algorithm output output output output number number number number number number number number number number number system system results results results information problem problem problem problem problem problem problem problem problem problem models based based based based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space case case case vector order order order shown shown shown shown shown systems systems values values values values values values parameters parameters functions functions method method method approach approach approach approach approach point point point point point point point point point point point point point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single single processing control control large local local local local local local local local analysis analysis class matrix matrix form form form form form shows shows shows shows shows simple paper examples small net net net work work work task task task methods methods methods methods methods methods methods methods methods methods methods fig points points points points points points points points points points points points points classification process structure problems problems problems similar similar representation representation show show show show images general general parameter parameter real gradient gradient obtained obtained note dimensional dimensional dimensional result result result result university university variables variables computation computation computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research found found initial initial initial constant computer computer distance distance node science science map map map map map map map map map map nodes nodes sets sets sets motion motion motion motion motion motion motion motion range learn position position basis nonlinear continuous sample sample abstract applied back find properties references component due ieee ieee adaptive propagation introduction introduction behavior generated generated parallel cost recurrent search tion tion variable assume prior learned chosen chosen part center bound type type required multiple multiple multiple multiple multiple multiple multiple multiple conditions fact region region region region region region region forward forward forward forward forward forward forward forward finite finite finite finite finite finite minimum resulting classes classes classes classes total total total computed multi called elements elements regions regions regions regions regions regions regions regions regions regions regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping optimization dimension made made made made made natural global global global global global global global global global global global global global global global global applications obtain vol vol vol specific specific samples samples application desired desired provide define proc location location location location location location location location location location location location goal constraints constraints constraints constraints constraints connected connected connected motor equal equal accuracy accuracy descent dependent source institute institute institute technique consists consists individual advances joint joint joint joint joint joint joint joint joint joint joint joint difficult maps computing domain equivalent equivalent equivalent solutions solutions solutions solutions solutions solutions design trajectory san san upper requires requires requires requires choice choice approximate approximate approximate con produce clustering clustering robot robot robot robot robot robot robot controller types path product actual selected nature sampling discussion feedforward feedforward arbitrary group group denote denote inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse finding finding nearest common effective implemented assumed assumed supported theoretical eds eds adaptation adaptation end end end end end end end end end end end end instance rumelhart rumelhart sensory fit fit objective typically typically typically pairs pairs jordan jordan projection projection consistent call pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre direct direct direct direct direct direct direct making normalized supervised run run run run discussed recent resolution resolution resolution property separate takes practical side cognitive cognitive recently engineering dimensions dimensions highly teacher tions smooth smooth differential differential differential differential differential differential differential achieve achieve achieve trans evaluation locations locations locations locations locations locations locations locations locations bounded interval arm arm arm constructed exists locally locally locally locally locally loop generally starting critical critical greater assumptions trajectories depend tangent tangent accurate accurate numerical designed moody exponential practice practice constrained california california california regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization exist exist plane derivatives derivatives groups configuration configuration configuration configuration base base question denoted acknowledgements construct ann ann ann ann mathematical distinct distinct dept dept dept student infinite physical electrical dimensionality dimensionality dimensionality dimensionality remaining angle angle angle angle unique unique consisting consisting adding select john choosing choosing choosing choosing expressed squares solved solved solved restricted restricted restricted restricted restricted organizing organizing approximations forms approximated approximated approximated sizes partition partition partition partial performing neighborhood iterative tracking closed closed closed closed interpolation valid assigned construction construction euclidean euclidean query faces views views views views topology topology topology topology topology topology topology topology topology david david david degrees degrees degrees figures thesis priori regular regular regular regular regular regular regular identified identified identified extra capable computationally effectively effectively identify identify efficiently tend tend reached compact compact conf quickly induced link link link neuroscience lie manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold criteria michael michael generalize providing nips computes ill ill ill ill ill ill ill ill attempt neighboring unlike diego diego transformed rapidly hanson issues lippmann existence existence existence existence existence mappings possibility scaled decisions surfaces surfaces surfaces surfaces surfaces circles circles plausible possibly configurations opposite extremely ensure rank singular der der obvious freedom freedom freedom fibers consist finds defines separable separable trivial trivial phenomena answer lies reasons inside inside stanford constructing constructing arise inversion projected separately angles arises author geometry geometry geometry geometry geometry nsf prop flexible generic generic parameterized parameterized posed posed posed posed posed posed posed partitioning partitioning branch branch branch branch branch branch branch cal serve qualitatively fiber fiber fiber fiber redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy globally consistently consistently phenomenon redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant redundant identifying accomplished accomplished accomplished optimizing branches branches branches branches branches partitions robotics robotics robotics robotics determination loops exploit belong disjoint disjoint disjoint disjoint disjoint disjoint canonical adequate planar planar planar planar planar separating separating separating topological topological topological lengths belongs thomas elastic elastic elastic initialize young jolla jolla augmented merge partitioned santa grants discovered mechanical divide schulten workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace workspace kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics preserving preserving poses smoothly restrictions conjecture convenience seek decomposed possibilities jacobian trends robots robots manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds regularized paired singularities singularities distal iri importantly manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator manipulator indexed intl union nal travel ritter coordination cube rarely resp fortunately parameterization parameterization parameterization parameterization parameterization parameterization parameterization parameterization achievable excess handling resolve resolve mcdonnell invertible invertible neighborhoods neighborhoods neighborhoods solvable industrial eliminates award kinematic sen tuple automation inefficient exploits joints amenable feasibility positioning positioning computable charles lar cyclic cyclic iterate iterate sep allowable snake dof dof dof dof dof martinetz martinetz daniel investigator repeating imposes pew fundamentally locating regional visuomotor klaus alexander unlimited sought sought topologically intel demers demers demers demers demers demers demers effector effector effector effector effector effector effector effector effector effector effector effector manipulators manipulators manipulators manipulators manipulators manipulators manipulators manipulators manipulators manipulators manipulators manipulators manipulators manipulators manipulators lowing behaved augment augment augment presidential visualize live transfor inverses inverses particu modulo erties rect linden linden reachable baker baker torus torus torus torus torus torus torus torus torus infant wrap wrap parameterize parameterize bundle bundle bundle regularizing education geometries geometries ambient annular kenneth kenneth marion stepping generically parameterizations parameterizations kindermann kindermann accessing unsatisfactory sistent manufacturing submanifold submanifold sumed physicists regularize regularize craig craig founda engr engr wrist redun fellowships matics inversions parameterizing joel joel kine nash configura doo direcfiy helge 
#@DeMers_D,Kreutz-Delgado_K,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system system system system system system system system error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results units information problem problem problem problem problem problem problem models models performance performance performance performance based based based based based based based based based space space space space space space space space linear shown shown systems systems systems systems systems probability probability probability probability probability probability probability method method method method method method method approach processing processing processing processing control control control control control control control control control control large large large large local class matrix optimal optimal optimal optimal optimal optimal optimal shows shows shows algorithms paper paper paper paper size task task task task methods methods methods methods methods methods methods methods step process process current problems problems problems problems problems random random random memory memory memory memory memory memory memory memory memory memory similar architecture section real real real real real real real real real real real real real real real real real states states states states states states states states states states states states states states obtained obtained term term experiments experiments result result university university university variables computation computation computation computation computation solution solution solution research research research log log sequence sequence initial table table table table table table estimate estimate estimate standard standard computer computer terms science science science prediction prediction prediction prediction prediction prediction prediction left left direction present present temporal temporal temporal temporal temporal machine machine machine maximum learn abstract applied find computational convergence likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee important important adaptive action hand estimation dynamic dynamic dynamic dynamic search search tion tion change change difference variable lower prior chosen center center previous previous previous previous cases required good long long tree tree equations markov markov markov markov make make length probabilities probabilities probabilities probabilities observed observed observed observed observed observed forward scale scale finite tasks computed performed times regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor potential obtain original artificial relative relative true goal goal goal related discrete mit mit mit mit steps steps accuracy support source morgan morgan morgan morgan proceedings proceedings proceedings report department version technique technique advances connectionist addition ai ai ai ai maps considered cambridge cambridge cambridge experiment directly additional estimates estimates estimates estimates estimates transition transition transition transition transition transition transition transition top top top top top conference efficient efficient efficient efficient efficient efficient full full full requires significant world world world world estimated give con randomly path path path path path path path provided finally iteration simply achieved achieved discussion technical describe tested tested fast fast close complete actions actions actions finding finding finding supported face square square kaufmann kaufmann reduced reduced technology technology programming programming programming programming interesting consistent trials call call max international international bottom early run run run predict predict recent recent resolution advantage robust practical recently engineering sufficient highly highly compare previously observations observations observations observations observations observations observations observations observations observations observations observations solve converge converge converge trans sparse observation observation observation observation observation observation williams williams williams improvement grant scaling deviation wide move touretzky loop deterministic white white white valued editors editors reward reward reward reward differences accurate designed sutton sutton sutton sutton sutton sutton sutton sutton moody learns intelligence start start start force acknowledgements areas areas areas areas explicit appears relation longer solving estimating transitions transitions transitions tuned tuned changing physical physical involves integrated national learner learner solved solved operations updated updated updated lee allowed allowed allowed earlier barto barto barto classical classical classical classical classical classical classical classical spaces neighborhood iterative initially assigned foundation foundation advantages advantages building existing exploration exploration exploration exploration exploration figures figures figures thesis thesis extension automatic uncertainty black black successfully planning extra closely included schemes ten ten ten ten quickly graphs heuristic heuristic heuristic success moore moore moore moore moore moore moore moore moore moore moore moore moore moore moore moore satisfy delayed subsequent approximating tesauro tesauro essential singh singh singh singh requirements experience experience experience difficulty difficulty environments detail hanson issues dotted fewer examine school incremental incremental incremental applicable terminal terminal terminal combine office decisions decisions workshop hill circles closest possibly editor man algo explored multivariate phd phd finds seconds seconds seconds seconds seconds answer lies processed stanford satisfied immediately immediately watkins watkins watkins scientific opt opt opt circle depicted depicted cybernetics requiring considerably embedded atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson remove slower rewards operate comments eventually june june june converged trade globally gap lab lab corrupted college college investigation rotated discover air kaufman kaufman chains promising siemens proceeds proceeds mark star guide preparation exceeds corner days heuristics continue motivation excellent mance mance reset reset reset introduces perfor perfor conjunction scheduling april young shortest shortest record rich subsequently summarize empty andrew andrew rms rms rms rms summer fellowship fellowship solves discount benefits dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna dyna conjecture experiences experiences experiences experiences experiences experiences experiences experiences associate constrain quantized visited queue queue queue queue queue queue queue queue queue queue queue translated ibm insights rithms continues afosr march concentrate guided sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping rod rod esti sweeps lippman priority priority priority priority priority priority priority priority priority travel gauss opti twenty christopher christopher vis converging maze maze maze maze maze prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized king award tells sloan kaelbling kaelbling kaelbling mcgraw sweep sweep sweep eighth blocked watson ini dof investigator rein elegant aims lifetime terminate avenue biomedical impor forgetting scribed tant backups backups backups quarter satinder sato sato sato qij pri pri pri experimentation absorbing preset earning earning dev presidential mary permitted ration allocate nato intend corpora forcement suc reachable requested secs secs portant draft mates philosophy reacting successors successors postdoctoral nilsson nilsson nilsson differencing differencing predecessors predecessors predecessors predecessors optimistic optimistic optimistic optimistic optimistic eventual promote promote collins keck northeastern absorption absorption absorption absorption cease peng peng peng sixteen prohibitive worlds bench serc cga mazes abe alfred ficiently ited fuller seidel servation ffl cessors eco occasions promoted professorship predecessor 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural function function figure figure figure figure figure figure figure figure time time time time set set set set set set set set set networks networks output number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system error state state state state state state state state state state state state state state state state state state state results information information information information information information problem problem problem models models hidden performance performance based based based based based based space space space space space space space space space case case case case systems systems systems systems values values values values values values values probability probability parameters parameters functions unit method pattern single single single single processing control control control control control control control control control large large local optimal shows shows shows shows shows algorithms simple paper examples examples size work work work work task task task task task task task task task task task task task task task task task task task task task task task task methods methods step step step step points level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level current current current structure high high high high high high high high high memory similar similar similar architecture architecture architecture architecture architecture section section section real real states states states result university university university university computation computation research found target standard standard standard standard standard standard standard standard standard computer computer science science prediction map map low low low low low low low temporal temporal temporal temporal temporal machine machine machine machine sets sets press press learn learn learn learn learn learn learn learn learn learn learn learn position basis abstract find find find computational computational references references component due adaptive adaptive adaptive decision decision decision context introduction action action action action action action action action action action action action action complex hand effect effect dynamic dynamic dynamic dynamic dynamic dynamic cost cost search search search change difference complexity variable variable variable lower lower lower lower measure representations learned learned learned learned learned higher higher higher higher higher part part cases cases multiple multiple multiple long long conditions represent expected expected fact region region length length length correct probabilities probabilities probabilities probabilities observed scale scale ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total multi multi sum times regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made made made natural applications study knowledge original compared desired provide location location perform perform active determined determined goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal related power power mit steps steps accuracy larger larger train dependent selection selection selection morgan morgan proceedings report report institute institute institute department department consists advances advances connectionist scheme graph ai maps considered considered cambridge directly hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton solutions transition transition trajectory san san san top top top capacity determine efficient efficient efficient choice choice choice choice choice world world speed speed give conditional levels levels levels levels levels levels levels levels levels levels area area path path actual actual selected nature depends constraint simply discussion technical technical increases arbitrary arbitrary actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions finding finding finding shape supported require require main main face square square instance instance instance instance future future degree fit kaufmann kaufmann smaller unknown jordan jordan transfer programming programming programming programming programming testing significantly york special special iterations iterations iterations direct making making making bottom bottom experts supervised early early choose choose choose choose resolution resolution resolution resolution resolution resolution resolution advantage advantage advantage takes practical side hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical sense previously solve achieve achieve address mixtures locations separation grid grid grid williams parts lead lead studied studied studied studied scaling move move move move move move generally generally setting setting place place conclusions valued editors editors reward reward reward reward central central sutton sutton performs learns learns learns learns learns learns mateo mateo taking external external proportional proportional turn turn manner manner program acknowledgements areas areas reference ways sequential sequential describes transitions transitions implement explicitly explicitly simultaneously slightly agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent choosing choosing choosing choosing choosing independently focus depending stages squares detailed updated decomposition understanding sizes completely completely suggested allowed key barto barto barto barto slow performing spaces spaces reduces intermediate initially initially initially initially initially calculate assigned exploration exploration exploration exploration exploration box thesis usa absolute partially discussions gating tests structural successfully major determining straightforward selecting aspects uniformly divided divided effectively effectively effectively successful build efficiently efficiently efficiently efficiently essentially composed road quickly quickly procedures allowing moore moore moore moore moore neuroscience split superior satisfy satisfy satisfy satisfy satisfy dayan dayan dayan dayan dayan dayan providing giles delayed highest highest highest leading reach received received principles moves moves moves moves moves jacobs jacobs satisfies satisfies rat tesauro tesauro cowan bars explore explore command command command schedule diego powerful create singh singh singh singh singh singh singh singh updating environments detail detail replaced hanson recursive issues ml behaviour behaviour behaviour helpful fewer matches successive giving complicated workshop hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy cover understand notion notion smallest act coarse naturally plausible editor necessarily generalisation generalisation illustrate illustrate academic multivariate submitted submitted phd averages integrate massachusetts advanced ment slowly separable fairly nowlan nowlan caused starts perspective satisfied satisfied closer ring easier easier forces division division division choices choices products watkins watkins watkins watkins watkins watkins separately circle circle implicit toronto toronto toronto medical lowest lowest arises radius radius meaning mellon composite carnegie cmu consistency peter leave leave effort atkeson atkeson share detecting passed incorporated slower psychological rewards rewards rewards rewards commands commands commands commands requirement howard gains instruction ordered achieves specifies softmax extreme pole college accomplished investigation restriction acts addresses tem impossible flexibility fails satisfying balance mark salk north responsible introduces periods decide moved demonstration consequences chooses chooses similarities enable advance foundations reveals late canada subsequently cam influences divide andrew boxes mind specification specification numerous thrun helmholtz achieving achieving super super super super super super super super super super markovian markovian expanding tween restrictions additionally amherst flat england forcing backgammon shaded care concentrated schmidhuber goals goals goals goals goals geoffrey learnt execute execute playing disadvantage hughes picked considers books ultimately conversely barrier barrier sweeping maintains tively grateful happen happen places bradtke bradtke dramatic exploratory strict strict completed elemental learners reinforce satisfaction satisfaction satisfaction bridge send builds maze maze maze maze maze maze maze maze maze maze agents agents doesn east prioritized interpreting finer finer finer finer ron concern flows returned ning concerns resolutions resolutions resolutions emerges emerges obey obey obey beneficial successively successively inefficient archi coins experienced south south bradford tra eighth inappropriate comprehensive cations searched altering sebastian rela manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager manager subtasks decides decides decides sought quarter satinder tecture picks draws poral contiguous canadian explores grain grain grain maximise maximise fellow bypass granularity granularity render embody communicated instruments coarser coarser backpropagated feudal feudal feudal feudal feudal feudal feudal feudal feudal feudal feudal feudal feudal feudal feudal feudal optimise wasted wasted composing rewarded rewarded rewarded occupies navigate navigate upwards intent gabriel speeding critics knew chronous preferably finest cnl sustain serc converse mazes mirrored jectories timescale bottlenecks bottlenecks inefficiencies solv decom cjch cjch punishment noranda asyn occasion subordinate competent dal confines 
#@Dayan_P,Hinton_G,
#t6
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training output output output output output output output output output output output number number number number number system system system system system system system system system error error error error error error error error error error error error error error error results results results results units units units units units units units units units units units units units units units units units units units units units units units units information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based linear linear linear linear layer layer layer case shown shown shown shown shown shown shown systems values noise weight unit unit distribution recognition approach pattern pattern pattern pattern pattern pattern pattern point point point image image image image image image image image image image image image image image image image image image image single single single single processing processing processing control local local test test test patterns patterns patterns analysis analysis analysis analysis class optimal inputs shows simple visual paper paper paper paper examples examples small feature net net work work task task task task methods points features features features features features process current current current trained trained trained trained trained trained trained trained trained trained trained trained trained trained high response response response response response response response response response response response response response response response response response response similar representation representation representation representation representation representation representation representation representation representation representation architecture architecture line line line line line line images images images images images images images images images images images images images images images images images images images images images images images images images generalization generalization real theory obtained experiments university computation computation research defined found found target target estimate estimate estimate estimate estimate estimate computer distance science prediction left left direction direction presented presented presented presented presented presented presented presented presented presented map map map activation activation activation activation activation activation activation low machine range learn learn learn position position position position components components components components outputs outputs outputs abstract back back computational likelihood likelihood references component component component due ieee important important important important important important adaptive propagation propagation mixture introduction estimation estimation estimation estimation estimation estimation estimation estimation effect variance variance parallel difference difference difference measure measure measure measure measure measure representations representations representations learned higher center multiple multiple multiple good good good good represent represent represent represent represent distributed expected fact fact fact techniques correlation correlation correlation correlation correlation correlation correlation correct correct correct observed errors forward ing ing tasks multi multi called called called potential potential orientation orientation applications applications knowledge original original vol artificial artificial artificial relative true desired desired provide proc proc location location perform perform constraints connected accuracy update support support support report technique technique technique technique technique internal internal internal internal internal internal individual represents connectionist graph considered considered cambridge computing domain hinton additional additional additional additional curves curves estimates capacity determine determine determine efficient upper requires world estimated estimated produce produce produce developed developed developed developed developed developed robot levels levels area types lines path product actual actual actual actual actual actual actual actual actual actual actual provided provided provided provided backpropagation simply biological measured discussion normal technical arbitrary arbitrary group group limited close close close close finding ability ability ability instance future degree degree degree makes makes development sensory including typically jordan interesting testing consistent principle principal principal principal principal principal principal principal principal details details details details experts experts experts experts expert expert magnitude combined predict improve robust separate separate include identical identical sejnowski sejnowski array array array array engineering dimensions approximately match match match trans mixtures entire increased invariant suggests suggests suggests touretzky column demonstrate differences sigmoid accurate accurate retina retina faster encoding encoding encoding integration demonstrated solid solid solid intelligence intelligence labeled labeled labeled labeled labeled labeled turn turn exist iii groups minima acknowledgements edges perception ways estimating describes describes dimensionality develop formed versus select reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction restricted dashed dashed dashed combining remains euclidean advantages degrees building combinations subspace recognize extension illustrated domains domains absolute absolute tests planning reason columns columns determining sensor selecting selecting closely closely closely capable capable driven situation situation situation situation situation situation reached reached road road road road road road road road road road road road road road road road road road road soc soc conf contained allowing sci hold vary modular correspondence correspondence highest automatically illustrates subsequent jacobs jacobs jacobs jacobs load camera situations situations employed unlike accurately accurately accurately accurately accurately accurately accurately accurately rise fewer matches school detectors reliable reliable reliable reliable reliable reliable symbolic symbolic affect encode encode encode encode encode topographic waibel waibel waibel waibel coefficient coefficient coefficient opposite extremely illustrate ensure simplest integrate rows developing formula ground ground navigation navigation improves nowlan capabilities independence handle starts drive tive strictly forces potentially potentially hippocampal linsker linsker linsker depicted demonstrates demonstrates mellon integrating varies carnegie empirically cmu conducted autonomous autonomous autonomous autonomous autonomous autonomous autonomous frequently frequently incorrect incorrect sharp rep reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability span pittsburgh ture prevent curvature deviations eventually univ irrelevant person person person linearity driving driving driving driving driving driving driving driving driving driving driving driving driving narrow acts acts acts acts reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed encoder encoder encoder encoder eliminate communications communications communications minutes familiar familiar vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle contract contract occurring reasoning cottrell cottrell cottrell cottrell effectiveness optimally corner reliably utilized interference representational representational percepttons propagated darpa hippocampus mlps mlps mlps eng indicator suggesting ahead ahead augmented relies erlbaum designing speeds intersection tures baldi baldi baldi baldi limitation street compressed compressed unable lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane munro munro munro munro ideally personal personal personal hundred simulating hillsdale forcing reconstruct reconstruct reconstruct reconstruct ibm guidance pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau terrence terrence wise wise depicts depicts gluck gluck gluck gluck gluck gluck gluck gluck hornik hornik rough meta meta confusion familiarity fea knowing indication indication indication steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering steering suggestions resembles resembles drives drives drives drives preserves autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder char hour mistakes exclusively architec markers exploits isolation proves inspection essence dean monitored monitored stems degrade ard discrepancy assoc resentation hampshire hampshire hampshire hampshire thorpe thorpe adap quarter myers myers myers myers roads roads roads army ponent reconstructing reconstructing encounter confident stretch stretch stretch stretch vation rutgers bears confused acti arbitration recon struction dave steer steer steer steer resemblance resemblance contracts photo interfere coder spe miles atypical atypical atypical faithfully chuck outdoor fork fork assertion decoupling arti coping daca adversely engi stead newark acteristic neering ficial confusing 
#@Pomerleau_D,
#t6
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number error error error error error error error state state state state state state state state state state state state results results results results results results units information information information information information problem models models models models models models models models models models models models models hidden performance performance performance performance performance based based based based based based based based based based based based based based based based based based based based based based space space space case case order order order order order order order shown shown shown shown systems systems values values values values values values values noise weight functions functions functions functions functions method method method approach approach approach approach point processing processing control control control control control control control control control control control control large large large local local local test analysis optimal optimal optimal shows shows shows algorithms algorithms paper paper paper examples examples examples examples examples examples examples examples size size net net task task task task task task task methods methods methods methods methods methods methods methods methods fig fig fig fig fig fig fig fig fig fig fig step step step step step step step step step step step points points points features features features process trained trained trained trained similar representation architecture show section section section section line rule general general generalization generalization generalization generalization generalization generalization generalization parameter real real real real real approximation approximation average states states states states states states states theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory gradient term note note note experiments experiments experiments experiments result university university university computation research research research research research independent independent defined found found sequence sequence sequence sequence target target target target target target target target target target target target target target target target target target target target target target initial initial initial estimate estimate standard computer computer terms terms terms science science science science prediction prediction prediction prediction prediction presented temporal temporal machine machine machine machine sets sets sets maximum press press press learn learn learn learn learn components components components components abstract applied applied applied find convergence properties references component component component component component component component component component component component stochastic due procedure adaptive propagation introduction action action action action action action action action action action action action action action action action action action action action action action hand estimation effect effect dynamic dynamic parallel difference difference complexity assume assume assume assume rules rules rules prior prior prior prior prior representations representations learned learned learned learned learned learned learned learned learned learned learned learned higher part center center center previous previous previous previous cases cases required long long represent distributed expected make proposed length correct correct correct correct correct observed observed observed observed observed observed observed observed observed observed observed observed observed observed errors forward tasks tasks tasks tasks computed respect respect respect respect eq eq called times reinforcement reinforcement reinforcement reinforcement factor factor policy policy policy policy policy knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge negative vol artificial specific represented represented represented represented represented represented represented represented true compared provide define location perform experimental experimental goal goal goal goal goal constraints discrete discrete discrete approaches approaches approaches approaches steps steps steps steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger connection update descent nets selection morgan proceedings report department version technique technique technique technique technique consists advances final final final final final final final final final final bias bias bias scheme scheme ai ai cambridge domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain experiment environment directly hinton curve additional additional view view view curves curves estimates limit san effects effects conference determine determine requires significant approximate approximate world world world world speed estimated estimated estimated estimated pages pages produce derived derived derived weighted weighted robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot product provided selected backpropagation backpropagation backpropagation backpropagation backpropagation nature achieved measured technical increases increases describe arbitrary group assumption complete actions actions actions actions actions actions actions actions actions actions actions actions actions amount nearest common assumed shape shape shape shape generate theoretical require require require main square square end end end ability ability hypothesis hypothesis instance instance instance future future rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart development fit fit kaufmann simulated simulated simulated typically typically typically underlying account jordan jordan jordan jordan jordan transfer transfer programming programming programming significantly ratio ratio increasing matching squared max max pre pre pre window international normalized combined combined minimize predict predict predict predict denotes architectures improve recent pair robust separate separate reported reported reported reported practical quadratic cognitive relevant highly previously previously previously previously previously teacher teacher approximately approximately approximately volume works axis correspond converge evaluation evaluation evaluation evaluation evaluation positions chain chain locations observation bounded williams grant constructed concept extended extended extended extended deviation derivative derivative derivative derivative derivative predicted locally deterministic generally runs conclusion starting starting starting reduce reduce valued valued valued editors editors reward reward reward reward reward reward reward reward reward reward reward reward reward reward tangent tangent tangent tangent differences measures measures accurate accurate accurate accurate clear sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton performs moody asymptotic weak weak mateo taking strong demonstrated minimizing iii averaged averaged averaged targets introduce derivatives derivatives derivatives force question denoted denoted denoted denoted denoted pro construct estimating describes describes vertical modeled modeled explicitly integrated applying agent agent agent agent agent agent agent agent select select john decreases decreases decreases decreases yield extracted extracted extracted extracted extracted extracted extracted focus dependence learner learner learner learner learner evaluated evaluated open open partition spectrum barto barto barto spaces reduces reduces combining fitting fitting valid distances sufficiently query david david david expect thesis weighting weighting instances instances determines extension extension maximize specifically specifically specifically domains domains neighbors discussions successfully successfully successfully major planning reason straightforward straightforward sensor importance encoded encoded mcclelland successful post post post post notice prob heuristic heuristic heuristic success notation michael generalize generalize generalize generalize generalize delayed denker leading automatically received illustrates subsequent extract extract extract approximating acknowledgments extend situations employed explore poor collection collection singh experience experience hanson accurately recursive recursive issues lippmann fewer fewer fewer school applicable analytically analytically combine symbolic symbolic symbolic symbolic symbolic cover analyze analyze analyze predicting illustrate greedy greedy separated logic arbitrarily submitted explain phd defines massachusetts asynchronous navigation slope slope slope slope slope slope slope explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation analytical analytical analytical analytical analytical analytical analytical analytical analytical baum baum handle obs drive lin lin lin lin lin formalism strictly division choices commonly watkins watkins watkins watkins watkins watkins watkins watkins simard simard simard angles circle depicted depicted preceding mellon addressed integrating questions reflects prop prop prop prop carnegie empirically pure pure cmu cmu amounts parameterized haussler haussler rewards operate measuring pittsburgh differs gen maximizes richard richard germany sophisticated conclude eventually june differentiable cumulative realized lab college analogue feasible acm perfectly purely purely purely purely grows theories theories theories theories theories theories theories grey lecun outcome generality air fits fits promising mail siemens simplify exploit analyzing observing monotonically monotonically guide guide generalizes generalizes obstacle obstacle obstacle combines introduces uni originally infer rich horn park extends extends impact inductive inductive inductive inductive inductive inductive inductive inductive inductive inductive inductive inductive inductive inductive inductive inductive explains approximator shavlik shavlik shavlik shavlik avoiding adopted executed severe accumulated learnable outperforms thrun thrun thrun thrun thrun thrun corporation minus achieving discount discount leaming super recursively july dyna suboptimal smoothly england valiant valiant valiant eric remainder invariances robots robots permits mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell learnability differentiation acquired fir increasingly distal distal slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes slopes differing aaai aaai suggestions chris august institut tom tom towell towell towell bold king steven outperformed clauses episodes episodes pratt pratt interpolating exploits explanations explanations explanations arpa coins informatik informatik teaching bonn bonn bonn successor ically episode episode episode episode episode episode episode episode episode episode episode episode explaining costly replaces sponsored ceedings degrade collections accuracies accuracies accuracies accuracies sebastian relying relying relying recursire illustrating wright wright mike yann named satinder scratch scratch menlo ronald inferences seventh gerald predicate raymond imperfect mooney mooney mooney keller victorri discriminability vised invaluable walls transfers misleading reacting collisions patterson deviate propositional sect maxa facto facto facto facto andy analyzes typ bernard gracefully gracefully intemal monolithic dejong dejong afb leslie jong lob lob lob lob jude jude undesired observ aeronautical navigates warranted mislead avionics 
#@Mitchell_T,Thrun_S,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system system system system system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state results results results results results results information problem problem problem models performance performance based based based based based based based based based based based based based based based based based based based based based based based based based based linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear vector vector vector shown systems systems systems systems systems systems systems systems systems values parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions distribution method method method approach point point point point processing control control control control control control control control control control control control control control control control control control control control large large class class class class matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form shows shows shows shows signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper feature work work work task methods methods step step step step step process process process process level current current trained trained problems problems problems problems problems problems problems problems problems problems random random random similar representation show show show show equation equation equation equation equation equation equation section section section fixed rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors general parameter parameter real approximation approximation approximation states states states states theory theory theory theory theory theory theory theory theory theory experiments dimensional dimensional result result result university university solution solution solution solution research research research research research independent defined defined sequence sequence initial initial initial table estimate estimate estimate estimate standard standard computer science science temporal temporal temporal machine machine machine machine machine machine learn learn learn learn learn learn continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied applied applied applied applied find find convergence convergence convergence convergence convergence convergence convergence convergence references stochastic ieee ieee ieee positive positive important important adaptive adaptive decision decision decision decision decision introduction action action action action action action dynamic dynamic dynamic dynamic generated generated generated variance cost cost cost cost tion change difference difference difference variable assume representations representations theorem theorem theorem type multiple good good conditions represent equations markov fact forward finite finite finite finite finite resulting resulting ing tasks tasks tasks total total respect sum performed called times elements reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor optimization feedback applications applications applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge represented represented application define define define define define compute discrete discrete discrete discrete brain steps steps steps steps steps steps contrast update update update dependent modeling morgan proceedings department implementation implementation implementation implementation implementation technique advances cambridge cambridge domain domain domain domain domain directly directly directly solutions solutions solutions solutions estimates san conference requires requires requires requires significant approximate estimated pages con produce condition developed developed controller controller controller controller controller controller controller controller controller controller controller controller processes selected backpropagation backpropagation iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration achieved normal normal describe describe describe describe describe describe describe describe describe describe group denote limited limited close close actions actions actions proof supported supported theoretical require require require future kaufmann needed dynamical dynamical unknown unknown jordan jordan mlp programming programming programming programming programming york matching representing numbers polynomial predict denotes improved improved improved improve recent recent exact exact practical apply apply quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic dimensions dimensions dimensions approximately yields yields converge converge converge converge converge converge converge converge converge trans definition symmetric symmetric symmetric improvement improvement improvement improvement grant grant exists invariant derivative matrices matrices locally locally locally deterministic deterministic white white column column setting conclusions differences differences accurate accurate numerical sutton sutton sutton sutton practice learns learns mateo taking minimizing min force acknowledgements areas written written written solving solving describes implement multilayer multilayer linearly linearly slightly slightly applying john national expressed expressed review squares squares squares squares squares estimator estimator viewed evaluate forms understanding converges converges converges converges updates updates key partial barto barto barto barto slow spaces spaces spaces spaces spaces spaces neighborhood iterative foundation norm norm transactions precision expect building existing exploration exploration exploration exploration thesis thesis combinations automatic candidate domains domains straightforward suitable computations refer notice strongly heuristic showing dis satisfy play play dayan dayan dayan dayan dayan dayan delayed principles principles attempt policies policies jacobs jacobs tesauro tesauro extend extend presents minimized explore wiley requirements involving involving recursive recursive recursive recursive issues hall scalar ideas office necessarily man man algo algo algo algo panel panel improving contributions arbitrarily phd attempts attempts defines massachusetts costs publishers track track track unstable starts lin lin sections precisely desirable watkins watkins watkins watkins watkins watkins watkins watkins watkins watkins watkins scientific involve definite definite demonstrates demonstrates author cybernetics requiring improvements flexible parameterized parameterized experimentally experimentally rewards howard howard howard characterize cal proven proven proven proven adjust plan focused focused specifies converged proofs rithm rithm arguments optimizing optimizing optimizing optimizing optimizing optimizing extending extending air promising preparation preparation preparation substituting prentice started percepttons approximators approximators approximators initialize initialize initialize initialize initialize mlps discounted ends sons approximator approximator approximator approximator approximator convergent convergent convergent executed counts bertsekas bertsekas bertsekas bertsekas andrew discount tables tables tables gaps markovian amherst acceleration england backgammon backgammon rithms rithms werbos werbos werbos regulation regulation regulation regulation regulation regulation regulation afosr concentrate lookup lookup lookup lookup meet meet bradtke bradtke bradtke bradtke bradtke bradtke bradtke bradtke bradtke exploratory exploratory worked demonstrating demonstrating rewritten beam beam discretized agents cliffs december steven ning englewood automation trol tells tells transpose teaching gence promise february supposed stabilizing stabilizing stabilizing stabilizing incurred lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr lqr argmin argmin approxima suitably suitably reactive recursire conver ecs designated controllable remember impressive exciting exciting ponent ponent aware earning ulation namic unknowns ner concatenation reg umass crete statisti markovjan markovjan hawaii afb forever forever ceptron factory sofge sofge inforcement bolling qua pitfalls pitfalls erik basics honolulu fori 
#@Bradtke_S,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set networks networks networks training training training training training training training training training training training training output output output output output output number system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state results results results units information problem problem problem models models models models models hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space weights weights linear linear layer order order order order systems systems systems systems systems parameters noise noise noise noise noise noise noise weight weight weight weight functions recognition method method method method method approach approach processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large rate rate rate rate rate rate test test matrix optimal optimal optimal inputs signal size net step step current current current current current current current trained trained trained trained trained structure structure structure structure problems random random random random high memory response response representation equation section section fixed fixed line line line line line line line line line line line line line line line line line line line line line line line line line line general parameter real real approximation obtained term result university solution independent dynamics dynamics initial initial initial initial estimate prediction direction presented map activation low temporal press learn position position components nonlinear nonlinear outputs outputs outputs abstract applied applied applied applied applied back back find computational convergence analog references due due adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision propagation propagation action behavior behavior effect generated parallel parallel cost recurrent recurrent recurrent recurrent recurrent search search search search search difference difference prior learned learned learned learned learned learned previous previous cases cases cases type type type required required good good good long distributed chip techniques techniques techniques techniques proposed observed errors errors errors forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward finite finite resulting resulting simulation regression computed computed computed performed performed performed called called mapping reinforcement reinforcement factor feedback feedback feedback feedback policy knowledge knowledge filter vol compared compared desired desired desired desired desired desired desired desired desired cross cross cross provide provide rates goal goal goal discrete approaches approaches approaches mit steps accuracy comparison update support train train train train modeling modeling modeling modeling modeling modeling modeling modeling morgan report report advances layers maps experiment directly solutions estimates estimates limit stage stage effects effects significant approximate speed speed estimated increase validation validation condition levels velocity velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller product actual provided achieved achieved achieved achieved measured measured technical group transformation transformation fast fast fast limited inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse complete stable stable actions actions generate generate generate require future future future noisy noisy noisy including kaufmann objective objective needed hopfield reduced reduced reduced unknown unknown fully jordan programming structures structures structures structures structures trials uniform mode mode mode mode mode mode mode mode filters pre direct direct direct direct direct direct direct direct making supervised supervised supervised supervised added added predict predict architectures architectures improved improve improve robust robust robust robust robust element element include side side side side side side side side side quadratic varying varying approximately volume tuning tuning solve correspond achieve achieve background evaluation positions improvement sensitive lead occur derivative derivative predicted predicted alternative feed feed feed feed feed feed feed hybrid touretzky occurs hardware starting greater assumptions reduce reduce reduce reduce reduce operator numerical sutton sutton sutton faster faster presence largest pulse user start force force reference reference explicit explicit appears solving primary sequential stability stability stability stability stability stability changing sensitivity sensitivity sensitivity coordinates interaction develop adding adding quality quality versus expressed dependence solved evaluated evaluated evaluate restricted updated sizes similarly barto smoothing slow slow measurements measurements measurements measurements measurements measurements combining intermediate box priori priori coordinate assignment determines specifically specifically candidate variations partially structural major sensor sensor differ modes modes modes modes modes modes modes modes computations score score score score miller reached capture summary traditional traditional traditional traditional traditional traditional traditional traditional traditional moore moore follow providing providing nips nips nips eigenvalue computes predictor predictor chips jacobs jacobs extend extend situations command perturbation perturbation hessian dual dual mass reducing incremental analytically eigenvectors stream scores removed hill measurement measurement measurement measurement adapt predicts changed implementations versions logistic explored shapes art generates plant plant plant plant plant plant seconds seconds seconds seconds seconds residual residual residual residual residual residual residual residual residual ground critic critic critic sensors sensors unstable unstable unstable improves caused correction worse forces commonly controls inversion separately incomplete robustness robustness greatly elman flexible flexible embedded embedded embedded autonomous autonomous effort effort remove slower slower slower incorrect controllers partitioning perturbations perturbations perturbations adjust age redundancy deviations credit univ pole newton newton newton newton newton newton newton newton newton accomplished extensive angular acts climbing wrong hit symposium continue continue continue service analyses demonstration searching enable enable young young smoothed smoothed augmented relies reverse balancing fold displacement displacement ball ball ball ball fusion yale indirect indirect indirect indirect leaming rejection incrementally corrected amherst experiences experiences massively auxiliary auxiliary remote jacobian compensate werbos werbos werbos dominated guidance searches searches boulder interactive distal distal monitoring breaks supports september differentiating modal justified christopher quantify insufficient adaptively aid december disturbance placement coins robotic compensated adapts fidelity resultant tra broadband stabilize antenna antenna antenna antenna antenna promise tenth replaces replaces erroneous sixth adjustments rom rom rom rom rom rom rom rom rom rom rom rom rom rom rom rom rom rom rom rom undesirable traditionally burden challenges narendra narendra stabilized stabilized scored scored scored necessity augment augment recur ions vigilance concluded susceptible spacecraft spacecraft spacecraft spacecraft spacecraft spacecraft tri vibration vibration vibration vibration lat slowing nns nns nns actuators actuators actuators brody brody actuator smart smart smart smart smart displacements unacceptable recommended aerospace ols ques reliance quanti fion halting recommendations ctive carlos controllet augments capitalize 
#@Bowman_C,
#t6
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set training training training training training output output output output output output output output number number number number system system system error state state state state state state results results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem problem problem problem performance based based weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector vector vector order order order shown shown shown shown values values values values neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition recognition method method pattern point image image image image image image image image image image image image image image image image image image processing processing processing control local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns form shows shows shows shows shows shows shows signal signal signal visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper size size net work task task task task task fig features features process process level structure problems problems similar similar similar representation representation representation representation representation representation show show show show equation equation equation equation equation equation equation section section fixed images images parameter real term term term term experiments activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional result result university university university computation computation computation computation computation computation computation computation computation computation solution research research research research defined defined defined found found dynamics constant table computer computer terms connections synaptic synaptic synaptic science science left left map map map present present phase phase phase phase phase phase phase phase phase phase phase activation activation activation activation activation activation object object object object object object object object object object object object object object object object object object object object object learn outputs outputs outputs abstract applied applied back references positive positive important important important important propagation introduction hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand behavior parallel tion tion tion change change energy energy energy measure measure signals signals signals prior representations representations representations representations representations representations representations representations part part type type required cortex cortex cortex represent represent represent represent represent distributed proposed proposed length forward minimum minimum minimum tasks simulation human human human human human human human human human computed multi performed times times optimization optimization optimization optimization optimization optimization optimization optimization optimization made made natural orientation study obtain represented define objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc active eye determined determined experimental related related related posterior posterior constraints motor motor motor motor motor brain brain brain brain brain brain brain brain equal support report words words words consists internal internal internal internal internal internal internal internal internal internal internal internal joint joint joint represents represents represents represents exp layers layers layers layers graph graph graph considered experiment experiment experiment view design design design stage requires basic con con developed developed criterion criterion criterion criterion criterion criterion criterion area types types types finally processes depends measured discussion technical increases corresponds corresponds complete stable finding assumed shape shape shape shape shape shape shape shape shape shape shape supported supported role require main pixel ability hypothesis future easily simulated simulated simulated simulated smaller interesting interesting representing representing call call iterations pre pre pre normalized bottom magnitude idea minimize produced produced produced description neuronal discussed discussed element element movement movement introduced include subject subject subject subject subject subject subject side side side side side side engineering engineering highly previously calculated solve solve solve studies differential differential address increased increased grant lead suggests move critical depend central clear learns learns integration integration proportional regularization minimizing minimizing movements movements movements movements movements movements movements movements selective plane plane configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration acknowledgements reference relation index index index index index optical ways dept integrated adding equilibrium equilibrium formed formed formed formed formed formed decreases decreases decreases expressed dependence depending depending operations operations static sizes roughly sufficiently recorded recorded perceptrons specifically specifically simplicity simplicity simplicity planning planning planning determining straightforward sensor compression compression closely suitable suitable suitable society divided divided projections identity identity identity conf graphs physiological criteria criteria timing relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation backward ill extract layered transformed essential investigate association association fewer project behavioral behavioral referred working complicated configurations configurations changed changed thought adjusted shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes nervous ith ith ith ith fibers established integrate integrate integrate developing sensors sections monkey controls laboratories laboratories projected recognized angles gradually res author recognizing integrating integrating integrating integrating integrating integrating fourth conducted fed fed fed fed introducing posed treated requirement suited kinds kinds kinds kinds shaped acquisition sensing modify japan japan japan japan japan japan japan japan tation tation circular circular circular circular circular circular circular circular circular circular jth jth robotics reaching plays communications fails ments primate kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato monotonically adequate programs decide regarded guarantees sides sides lengths lengths sphere sphere sphere sphere sphere somatic chooses reproduce reproduce parietal parietal parietal diameter diameter diameter diameter diameter diameter diameter diameter diameter repeatedly grants switches ure compressed corporation vec solves leaming leaming leaming uniquely pointed hundred realize realize manipulation manipulation manipulation manipulation manipulation guidance acquired acquired acquired acquired represen attached finger finger finger finger finger finger finger finger finger finger inversely electronics tract atr atr compu completed twenty thousand somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory tors cylinder cylinder cylinder kth japanese japanese japanese concerns concerns devised manipulated automation tactile tactile tactile tactile neocortex tokyo tokyo tokyo tokyo tokyo tokyo recognizes joints joints joints joints reproduced reproduced demands cho cho materials comprised twelve uno uno uno uno uno uno uno suzuki suzuki suzuki suzuki suzuki suzuki suzuki supposed rec percep murata tightly tightly schema schema obeys activa activa decides thumb topologically lay gun gun palm palm palm palm palm palm palm palm palm palm palm palm corresponded ordinate thirty hypothesize adopting preset prism ministry sual faculty faculty kyoto kyoto concluded pad pad pad pad pad pad pad pad abscissa georgopoulos grasping grasping grasping grasping grasping grasping grasping grasping grasping grasping grasping grasping grasping grasping grasping fingers fingers fingers fingers fingers fingers grasped grasped 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#@Fukumura_N,Kawato_M,Suzuki_R,Uno_Y,
#t6
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#*network network network learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data function function function function function function function function function function function function function function function function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks training algorithm algorithm algorithm algorithm system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state information information information information problem problem problem problem problem problem problem problem problem problem problem problem performance based based based space space space space case case vector vector order order systems values parameters parameters functions approach approach approach point point point point point point point point point point point control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large local local local local local local local local local local local optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form paper paper size size methods methods methods methods step step step step step step points points points classification process process process process trained structure structure structure problems problems problems high architecture architecture architecture architecture architecture equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation line line line line line line line line line line line line line line line line general general general general general general real real approximation approximation states states theory obtained obtained obtained obtained obtained obtained obtained obtained term note note university variables solution solution solution solution solution solution research defined sequence sequence sequence sequence sequence sequence sequence sequence sequence target dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial initial estimate estimate estimate estimate estimate estimate standard standard terms distance present machine maximum continuous sample abstract back computational convergence analog properties references ieee ieee procedure adaptive adaptive adaptive decision action action action action estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic cost cost tion assume assume lower measure chosen chosen center cases type multiple multiple conditions conditions equations equations equations equations fact fact fact techniques minimum minimum minimum computed computed computed respect respect elements reinforcement reinforcement reinforcement potential made feedback knowledge knowledge obtain obtain vol vol vol vol vol artificial artificial artificial samples true series provide define define compute compute active determined determined connected discrete discrete discrete approaches approaches steps steps steps comparison fields update support train words words department technique represents difficult final addition sequences sequences sequences sequences sequences sequences domain directly directly solutions solutions solutions estimates estimates estimates design limit limit trajectory choice choice approximate approximate approximate approximate approximate approximate estimated estimated give con con con condition developed robot controller lines path actual finally iteration iteration nature depends constraint constraint constraint simply associative achieved feedforward denote denote denote close complete actions actions finding common journal future future future easily underlying underlying programming programming programming programming programming interesting character special principle principle principle principle iterations iterations iterations pre international attention choose denotes architectures architectures architectures architectures resolution resolution resolution resolution resolution resolution exact advantage pair pair typical typical strategy subject sense engineering engineering engineering interest compare observations calculated solve solve solve smooth differential differential trans trans generalized generalized grid grid grid grid grid grid grid grid grid grid grid bounded interval interval interval interval interval interval interval interval grant lead boundary boundary boundary generally setting conclusion starting starting starting valued depend depend sutton sutton sutton sutton practice encoding integration reduction cycle variety start start start start min min min min min introduce derivatives manner denoted denoted denoted acknowledgements pro pro pro solving solving estimating stability stability mathematical integrated applying minimization focus dependence dependence estimator estimator solved solved solved solved solved solved updated approximations approximations lee lee converges updates updates sign partial partial partial partial calculation barto barto classical classical roughly iterative iterative interpolation box sciences discuss discuss holds planning planning sensor suitable differ build schemes schemes schemes miller miller miller essentially fine refer soc anderson interpreted interpreted interpreted issue criteria strategies strategies satisfy satisfy satisfy satisfy satisfy satisfy notation usual usual delayed leading satisfies situations law law law american estimators estimators estimators estimators estimators estimators estimators estimators replaced issues hall successive history history incremental int referred workshop patch math math coarse coarse coarse coarse coarse necessarily man plant plant ment critic defining sys directional broad controls controls watkins watkins involve calculations arises cybernetics integrating questions led amounts lack poorly formulated rewards controllers tolerance lim lim lim lim converged differentiable differentiable differentiable differentiable initialization initialization bellman bellman bellman bellman bellman college sort sort labeling optimality martin fix arguments count suppression determination hope heuristics obstacle continue started cerebellar cerebellar james negligible cmac cmac cmac cmac cmac peterson peterson peterson peterson peterson peterson peterson peterson peterson peterson initialize initialize ahead ahead repeatedly papers acknowledge approx approx land summer drop solves email conjecture convenience acceptable arg arg arg ease letting suppressed imagine arising alternate grouped tems werbos werbos werbos interacting relating manipulator nasa siam esti milliseconds september october rewritten discretized discretized discretized designs designs albus albus king hamilton hamilton hamilton hamilton hamilton resolutions resolutions trol trol implied smc robotic lewis articulation cess indirectly mesh mesh monitored dist dist dist dist ceedings discrepancy discrepancy tutorial argmin virtue terminate superscript imation pay ninth manipulators philadelphia implementable hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb hjb initializing articulated behaved notational notational supplies supplies jacobi jacobi jacobi jacobi jacobi alternately gramming vibration neuronlike gin viscosity viscosity viscosity viscosity ors spectively vious inevitably inevitably imations uij uij uij uij multigrid multigrid intimately verges carlson carlson automat differentiability ifj dispense mathematica 
#@Peterson_J,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural input input input input data data data figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time networks networks networks training training training training training training training training algorithm algorithm output output output output output system system system system error results results results results results results results results units units units units units units units information models hidden hidden hidden performance performance performance performance performance performance performance performance performance based based based based based based based based based space space weights case case order order order order shown shown shown systems systems systems systems systems systems systems values values noise noise noise noise noise noise noise functions approach approach approach approach approach pattern control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large large analysis analysis inputs inputs inputs inputs form shows shows paper paper feature work work task task task task task task task task task task task task task task task task task task task task task task task methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step step points trained random high high similar similar similar fixed fixed line line line line real real real real real real real average average theory obtained obtained obtained dimensional result university university computation research research research research constant table table table computer computer science science presented present motion motion motion motion motion motion motion motion motion motion motion motion press press press learn learn learn learn learn position position position position position position position position position position position position position position position position position position position position position position position position position position position position nonlinear nonlinear outputs outputs outputs abstract abstract applied applied back back find find references component stochastic stochastic stochastic due due due due due due due ieee ieee ieee ieee ieee ieee ieee adaptive propagation introduction action complex complex hand behavior behavior behavior behavior behavior dynamic generated tion tion change change complexity signals higher higher part long long conditions conditions conditions conditions conditions conditions conditions conditions conditions expected equations make techniques techniques proposed errors errors forward resulting classes tasks tasks tasks tasks tasks tasks tasks tasks simulation simulation computed computed computed computed respect times times mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement natural feedback feedback feedback orientation obtain samples samples compared application application desired perform perform perform perform active experimental goal constraints approaches mit mit steps steps steps steps comparison comparison nets proceedings proceedings proceedings proceedings report institute department version version joint joint joint joint connectionist difficult difficult difficult difficult final final final final final layers layers ai framework cambridge cambridge experiment environment environment environment environment directly curve curve curve curve curves curves design trajectory stimuli effects detection conference conference conference conference determine determine significant world world world world pages pages pages pages pages con condition condition robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels criterion controller controller controller controller controller controller controller controller controller controller controller controller actual actual actual actual actual actual actual simply associative associative associative associative associative measured discussion technical close assumption assumption actions amount effective implemented assumed supported supported require eds journal journal journal journal easily degree degree degree degree sensory sensory sensory sensory including simulated reduced technology testing mechanism trials trials trials trials trials operation details max max direct direct direct direct direct direct direct direct direct window window international international international international international international international supervised depth expert magnitude magnitude magnitude sources denotes improve directions robust robust movement strategy strategy strategy strategy strategy strategy moving moving include subject interest varying previously observations works works axis axis evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation positions positions positions positions positions positions positions positions positions modified interval grant grant arm parts parts parts studied studied occur wide wide feed loop loop occurs demonstrate greater conclusions valued valued valued editors editors interactions interactions clear learns strong mechanisms presence presence presence presence largest largest external cycle intelligence turn turn turn min min configuration configuration force force force force force force force force acknowledgements construct factors laboratory modeled physical physical physical springer national solved evaluated lee lee static suggested sign barto barto barto barto barto barto performing closed generation generation filtering filtering foundation transactions recorded thesis thesis usa automatic uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty discussions successfully major planning planning planning planning planning planning straightforward sensor sensor sensor sensor sensor sensor sensor society encoded modification successful successful successful fine fine fine fine traditional traditional verlag repeated repeated success showing running strategies strategies strategies strategies satisfy localization realistic automatically received received load load load load load load load load load load load load load load load decreasing situations command command requirements humans respond applicable ideal combine office measurement man illustrate illustrate adjusted versions formal taylor utility utility phd phd attempts massachusetts massachusetts massachusetts critic critic critic sensors sensors fairly considerable purposes closer widely forces forces forces forces forces forces forces forces forces forces forces controls ion scientific separately involve describing recording depicted cybernetics recognizing raw raw researchers geometric geometric geometric evaluating substantially capability slower continuously commands commands maintain execution synthesis popular incorporating suited kinds inherent extreme extreme extreme extreme extreme extreme consistently sensing ear notes primarily primarily forming forming appropriately controlling robotics robotics robotics robotics robotics robotics rigid air dealing dealing consideration intelligent moment occurring methodology canonical adequate symposium moments moments moments moments passive evaluations evaluations started ranging regarded washington washington assembly assembly assembly assembly counter diameter diameter recovery smoothed smoothed smoothed smoothed smoothed smoothed contact designing characterization instructions automated automated executed andrew consecutive consecutive consecutive consecutive consecutive sequentially ence indirect indirect kinematics ram ram ram ram ram ram presenting quasi ideally amherst amherst affects certainty representa acting attempted robots magnitudes grouped continues denoting interacting afosr march argued insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion insertion increasingly pos cartesian termed france distinguished margins gordon gordon gordon circumstances ate quantify spring loaded december char affecting progressively automation automation automation automation tactile ooo loads trol teaching positional positional positional ance robustly robustly indi actively degrade nice operated hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole hole inserted inserted inserted discrepancy sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed sensed insertions insertions insertions insertions insertions reactive reactive reactive reactive reactive reactive reactive mason ecs kim kim anandan anandan nonlin encoders encoders today gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli gullapalli proaches grasped equipped arbib rect lozano lozano lozano lozano exceeding quantifying quantifying readings ended posture prespecified donald donald elapsed servo servo cou pled pres cylindrical sensations virginia mating benefited perez perez perez brady acteristics passively appropri afb synthesizing wrist fmax fmax tificial commanded bolling evalua dln controllet mands compounded tomata assisting 
#@Gullapalli_V,
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training training training training training algorithm algorithm algorithm output output output output output number system system system system system system system error error error error error error error error error state results information problem performance performance performance performance performance performance performance performance weights case case order order systems systems parameters functions functions method method point point point point point single single single control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large rate rate analysis inputs inputs shows shows shows shows signal signal signal algorithms algorithms simple gaussian gaussian paper paper small small small small work task task task methods methods step step step step step level level structure structure high memory memory response response response response response response show fixed line line line line line general general general parameter parameter parameter parameter parameter parameter real real approximation approximation approximation approximation average average states states note note dimensional result result result result computation computation computation solution solution solution research defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial constant constant constant constant computer science science direction presented map present present low motion press press learn learn learn basis basis sample abstract applied applied convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties references due ieee ieee ieee ieee adaptive adaptive adaptive adaptive adaptive introduction complex complex behavior behavior behavior generated change change change change change change change change change difference difference variable signals signals signals signals signals signals prior prior learned learned learned theorem theorem theorem theorem required required conditions conditions conditions tree tree tree tree equations make fact techniques region region region correct errors errors errors errors errors errors errors errors errors ing ing tasks tasks total human respect multi multi performed called made made global knowledge represented represented true true application application desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired provide provide define define rates proc proc determined related motor motor discrete brain approaches mit mit mit mit steps steps accuracy connection train train report report institute department department technique joint joint joint represents difficult final ai ai ai ai maps considered cambridge cambridge domain trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory conference conference significant approximate approximate speed speed speed speed speed speed speed speed estimated estimated pages pages increase increase con con con produce robot robot robot robot robot robot robot robot robot robot controller controller controller controller types types path actual actual actual actual actual actual actual actual actual actual nature depends measured discussion increases fast close close inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse stable assumed generate supported theoretical theoretical journal future sensory sensory simulated unknown coefficients technology significantly significantly significantly increasing trials trials trials operation operation leads direct direct direct making stored stored magnitude idea minimize improve advantage pair robust element element movement movement movement movement movement strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy cognitive engineering engineering interest dimensions varying varying previously solve smooth smooth smooth converge differential achieve trans trans definition definition modified bounded bounded increased increased arm arm arm arm arm arm exists exists exists exists exists exists lead lead concept occur occur trial alternative alternative occurs conclusion greater greater assumptions assumptions assumptions assumptions assumptions trajectories trajectories trajectories trajectories trajectories trajectories trajectories operator designed faster faster practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice asymptotic learns solid solid movements movements movements movements movements decrease decrease decrease relationship relationship relationship acknowledgements derive produces longer solving describes laboratory ann stability stability stability explicitly easy slightly equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium yield yield national independently formation review review detailed controlled restricted understanding approximated similarly partition constants slow spaces sec reduces reduces intermediate intermediate intermediate includes coordinate coordinate coordinate sciences extension extension extension extension extension extension extension prove prove prove aspects successful schemes comparing summary traditional refer refer conf quickly repeated repeated strategies strategies strategies strategies sampled simplified nips leading leading subsequent trains simpler remain remain unlike command command command command command command command command command command command command american experience difficulty varied varied steady humans dotted dotted hall reducing int structured structured rev perfect perfect assumes submitted plant plant plant plant plant plant plant seconds seconds massachusetts stop separable smoothness smoothness unstable unstable explanation drive drive sys satisfied potentially calculations gradually gradually gradually gradually gradually gradually author requiring virtual people lms lms fed parameterized poorly atkeson atkeson atkeson atkeson commands commands commands commands maintain execution achieves boston comments neuro neuro june yielding phenomenon room modify modify modify optimizing grey grey robotics robotics proceed wrong simplify stated transforms sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger monotonically continue continue meaningful prentice claim multiplied multiplied speeds grants summarize kinematics fellowship break pieces smoothly smoothly theorems seek modifying robots robots tems graduate execute march ultimately manipulator maintains behave modifiable corrections corrections invertible jersey arrow subtracting automation automation trol ultimate nontrivial robotic subscript nih defense simon hood damping yamada yamada deeper lipschitz lipschitz lipschitz ness ample modifies subtasks subtasks tran mussa grown ivaldi controllable manipulators continuation hogan lock lock lock subtrees likeli quence trim bizzi bizzi bizzi bizzi bizzi 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#@Sanger_T,
#t6
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#*network network network network network learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm number number number number system system system system system error state state state state state state state state state state results results information information problem problem problem problem problem problem problem models models models based space space space layer case vector vector order order order order order order order order order order order systems systems systems systems values values probability weight functions functions neurons neurons neurons neurons unit distribution distribution pattern point single single single single processing control control local local local local local local local neuron neuron neuron neuron neuron neuron test test test test test patterns patterns patterns patterns patterns patterns patterns optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form simple simple paper examples examples examples small size size size size net net net net net net work task task task task cells cells step step step step step step features classification classification classification process level current trained trained trained cell cell structure structure problems random random high high similar representation representation representation representation representation representation representation representation representation representation representation architecture architecture architecture generalization generalization generalization generalization generalization generalization generalization generalization real real average states states states obtained term term term term term term term term term term dimensional dimensional university university university computation solution solution solution research log defined sequence target target dynamics dynamics dynamics terms terms terms terms terms terms terms prediction left left presented map map map present present present present present present present phase low low low temporal temporal temporal temporal temporal temporal temporal temporal temporal sets maximum maximum press press learn position position position position components basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous abstract applied applied likelihood references stochastic due ieee important important decision decision introduction action action action action action action action action action action action action complex behavior behavior effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated parallel cost cost recurrent search search tion complexity complexity representations learned chosen higher higher higher higher higher higher higher cases cases type binary long long long long long long long distributed distributed expected expected expected region region length observed forward forward forward forward forward forward forward forward forward finite simulations simulations minimum resulting ing ing ing ing ing tasks tasks total simulation computed respect performed performed mapping mapping mapping mapping mapping means dimension feedback global policy obtain original represented represented application desired desired desired cross cross series proc proc active active determined goal goal goal goal goal goal goal goal related related constraints constraints constraints distributions motor motor motor motor motor motor motor motor motor motor motor motor motor motor mit steps larger support train dependent nets nets nets modeling modeling institute department department version internal internal internal internal individual difficult difficult difficult considered considered considered cambridge computing environment environment environment environment environment environment additional solutions design design limit trajectory bit bit bit bit capacity capacity classifiers full approximate statistics free free world world world speed randomly robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot criterion bounds velocity velocity path path path path path actual finally depends discussion denote complete complete actions actions actions short short short effective effective effective supported theoretical theoretical eds adaptation adaptation adaptation adaptation future sensory sensory sensory sensory including simulated simulated account functional technology transfer programming programming programming programming programming programming programming programming programming programming testing character york york increasing increasing database representing numbers bits bits bits supervised supervised supervised run denotes architectures architectures discussed advantage robust robust robust separate takes takes practical moving moving moving subject subject subset array relevant relevant sufficient highly highly varying varying teacher teacher teacher teacher teacher module module module module axis axis tions yields sparse sparse sparse positions positions positions interval grant parts studied digital predicted alternative alternative feed feed feed feed feed feed feed feed feed move deterministic white occurs generally runs trajectories trajectories trajectories trajectories conclusions interactions interactions sigmoid modules performs exponential encoding taking hard physics external cycle minimizing decrease averaged targets scene scene identification base base question denoted van index perception perception winner winner sequential changing recall recall recall angle boolean boolean competition john decreases decreases independently focus focus learner evaluate updated forms sizes sizes margin partition spectrum spectrum epochs classical expansion generation generation faces degrees perceptrons assignment batch determines determines extension automatic discuss maximize coupled partially structural structural structural planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning importance encoded effectively effectively successful situation orthogonal reached receives receives compact notice conf repeated prob anderson superior symmetry built list usual generalize generalize providing consisted subsequent situations situations situations command command command command command powerful powerful american wiley requirements investigate investigate difficulty rapidly put environments environments detail mass project mappings mappings int fault working stream encode encode configurations extremely algo switching baseline generates extent serial devices ment directed directed costs growth growing growing fairly adapted adapted adapted capabilities expensive baum reasons desirable potentially acknowledgement arises depicted robustness percent understood generic embedded embedded fed fed lack orders orders orders orders continuously ity commands commands commands requirement exhibits mod suited plan plan germany germany inherent inherent shaped shaped findings findings focused deviations credit globally consistently don bellman bellman bellman bipolar extensive extensive princeton rithm velocities jth repre robotics allocation intelligent intelligent settings adequate carry combinatorial obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle eqn eqn exploring excellent excellent falls cone cone cone regard uni nonlinearities nonlinearities nonlinearities insight horizon horizon horizon horizon horizon horizon sons considerations limitation accumulated lem street crossing crossing specification workspace workspace workspace tables latency break obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles emerge spatio spatio spatio spatio par reports avoided realize acting unseen exponent care community insights robots goals goals werbos werbos continues distant insertion guided employing misclassified voting denver reveal admissible admissible admissible avoidance tel shallow expansions topologies functionality functionality discretized unbounded identifies impractical ping designs curse firstly firstly reflecting inclusion concern kinematic ning conflicting sparsely automation attained trol restricting minsky minsky minsky sions comm confined accounting planner planner planner planner planner planner planner planner planner planner tations handbook fication bonn bonn bonn bonn bonn counted percept occupancy occupancy emerged emerged excessive sented repetitions benchmarks costly spario spario spario spario spario inserted preventing checked collision excluded excluded fluctuating plans plans reactive icann ities posi encourage parsimonious parsimonious parsimonious parsimonious parsimonious atoms occupied environ ministry overfit gerald gerald opening papert renders safety exceeding ner incidence incidence incidence restricts distribute distribute fax plete obeying identi collisions federal cluttered donald accelerations oot eckmiller eckmiller eckmiller eckmiller eckmiller eckmiller collapsed assembled reporting reporting eqns monomials monomials forecasts wilczek decisive busy constituted tlo bed bed vironment neuroinformatics neuroinformatics neurocontrol neurocontrol neurocontrol neurocontrol neurocontrol sofge stemming existed fee brighton igure pings paying mml nostrand 
#@Eckmiller_R,Fahner_G,
#t6
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error error error error error error error error state results results results results information information information information information problem problem problem problem problem problem performance performance performance performance performance performance performance based based based based based based based based based based based space space space space space space space weights weights linear layer layer layer layer layer layer case order order order order order order shown shown shown shown shown systems systems systems systems systems systems probability parameters parameters noise noise functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions method method method method method method point point point point point point point point point point point single single processing control control control control control control control control control control control control control control control control analysis form shows shows simple simple simple simple visual paper examples examples examples examples examples examples small feature work task task step step field current trained trained cell cell cell cell cell cell response similar representation representation show show show show section section section fixed line rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general general general general parameter parameter real real approximation approximation approximation approximation theory theory obtained note note experiments experiments result threshold variables variables variables variables variables variables variables computation computation computation computation solution solution independent independent independent found found target initial initial initial initial initial constant constant table table table table standard standard terms terms terms connections node node node node node prediction prediction prediction prediction presented presented nodes nodes nodes sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum range range learn learn position position position components nonlinear outputs outputs abstract applied back find find find find computational computational computational computational computational properties properties references procedure procedure introduction complex hand hand hand estimation effect generated generated generated parallel parallel search search tion tion change variable variable variable variable variable variable variable variable variable variable variable variable variable rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure prior prior learned learned learned learned learned learned learned learned learned learned higher part part part previous firing firing firing type conditions conditions conditions represent represent represent distributed techniques techniques region proposed proposed correct correct probabilities forward minimum classes total simulation computed respect performed performed means made knowledge knowledge obtain obtain obtain obtain original original original original original original vol relative specific specific specific specific specific specific specific desired desired define compute perform perform experimental goal discrete discrete discrete discrete discrete discrete steps contrast dependent dependent dependent dependent proceedings institute department joint represents represents responses final final final final final layers layers scheme addition addition experiment trajectory effects effects conference efficient efficient efficient efficient upper upper upper upper upper upper upper upper full significant approximate approximate approximate approximate free speed speed speed speed speed basic give con con produce condition condition developed developed controller controller controller controller controller controller controller controller controller controller path product actual finally finally finally inhibitory inhibitory simply simply simply simply simply achieved describe describe describe arbitrary complete actions actions finding amount amount amount implemented supported require ability degree degree needed combination combination reduced fully technology call direct making international idea combined added added predict advantage takes lateral lateral lateral identical side side inference inference engineering varying varying tions tions match positions positions modified gate grant constructed constructed constructed constructed constructed exists horizontal suggests runs runs runs conclusion conclusion conclusion minimal minimal conclusions conclusions measures measures numerical designed performs performs performs learns suggest propose propose propose california user min manner acknowledgements construct construct construct construct construct solving estimating laboratory mathematical recall explicitly electrical slightly slightly angle angle angle frequencies decreases expressed expressed expressed expressed expressed expressed expressed interpretation variation variation controlled controlled decomposition margin completely partition allowed allowed allowed key performing convex combining purpose add add calculate calculate sufficiently advantages existing fire figures bell inter candidate holds holds determining compression compression compression compression 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representative accomplished rithm driving tem reaching lost simplify simplify keeping removing operates clause corner corner corner corner obstacle obstacle continue conjunction intended searching searching ranking darpa recovery membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership membership arrows approximator onr lem linguistic rms rms rms rms informa multiply compressed compressed compressed compressed goodman goodman goodman goodman goodman goodman goodman july responds smoothly perturbed perturbed associate attempted blocking 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#@Goodman_R,Higgins_C,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output output number results units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden performance based based space space space space weights weights weights weights linear linear layer layer case case case order order order order order order shown shown shown shown systems systems systems systems values probability probability probability probability probability probability probability parameters weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single processing processing processing processing processing large large local local local local local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class class class class class class class class class class class optimal optimal optimal optimal optimal inputs inputs signal algorithms simple visual visual visual visual visual visual paper examples examples examples feature feature net work work work step field features features features features features features features features features features classification classification classification classification classification classification classification classification classification level level current current cell cell structure structure structure structure structure problems random random random high high high high response representation fixed line line line rule rule rule rule images images general general general generalization speech speech speech speech parameter parameter average average average average average states gradient gradient gradient gradient term term experiments activity activity university computation computation solution solution research research independent log log defined sequence initial constant constant constant constant constant standard terms presented presented presented map present present present activation activation low low low low frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object object object object object object object maximum maximum maximum learn learn learn learn learn learn learn learn nonlinear outputs outputs outputs outputs continuous abstract applied applied applied applied back find properties references component stochastic stochastic stochastic procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important propagation introduction complex hand estimation tion change change complexity complexity complexity spatial spatial spatial lower measure measure signals signals representations representations learned learned learned higher higher center previous cases required cortex long long represent make proposed probabilities probabilities probabilities probabilities forward simulations resulting resulting classes classes classes classes classes classes classes classes classes tasks tasks total simulation human human human computed respect respect respect respect multi multi multi sum sum made orientation orientation orientation vol relative specific provide compute objects objects objects objects objects objects objects objects objects location location perform perform constraints constraints constraints constraints constraints discrete approaches steps steps steps steps steps steps steps steps larger contrast train descent morgan morgan morgan proceedings institute words department individual individual advances advances joint joint joint joint joint joint joint joint responses responses difficult difficult difficult final sequences domain directly hinton hinton hinton hinton hinton hinton hinton solutions solutions solutions trajectory trajectory trajectory san san stage stage detection requires requires statistics statistics statistics world world world pages pages pages increase produce produce weighted weighted randomly randomly randomly lines lines entropy entropy entropy entropy entropy entropy entropy entropy entropy selected evidence nature depends sampling constraint constraint simply simply biological discussion arbitrary arbitrary group group denote tested transformation transformation transformation transformation assumption assumption amount short short common shape shape shape require main end easily degree makes development development development sensory sensory sensory sensory sensory sensory sensory including kaufmann kaufmann kaufmann objective objective objective objective typically reduced block squared iterations supervised supervised early frame idea produced produced produced produced run sources discussed improve improve improve improve correlations correlations advantage pair separate separate ensemble typical reported reported apply moving moving pixels pixels hierarchical hierarchical interest interest interest highly unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised speaker achieve address modified storage entire entire exists parts intensity intensity intensity intensity lead invariant invariant invariant invariant invariant suggests feed locally move move touretzky deterministic occurs generally setting pass demonstrate half hebbian trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories segment conclusions competitive modules learns learns constrained constrained mateo mateo hard hard hard integration characteristics characteristics drawn demonstrated demonstrated assuming assuming variety variety averaged averaged averaged introduce scene identification question reference digit digit pro produces longer perception perception solving solving ways sequential transitions transitions tuned tuned linearly involves transformations transformations transformations transformations transformations remaining easy easy angle spectral scales scales scales scales scales mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual select national independently stages stages correlated overlap overlap overlap overlap overlap organizing showed understanding approximated similarly similarly suggested translation translation translation translation translation earlier expansion intervals handwritten kernels perceptual perceptual perceptual perceptual perceptual usa sciences maximize maximize maximize mozer mozer specifically discussions texture reason regular straightforward capable importance importance differ effectively detect detect build build build build invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance essentially identity identity ten composed capture kind contained cun cun classify classify content criteria cue cue cue cues localization dot giles giles denker consisted consisted consisted moves extract satisfies neighboring acknowledgments deal decreasing receive oriented modelling powerful powerful transformed poor create create biases biases postsynaptic reducing successive successive successive successive successive history ideas detectors detectors detectors applicable applicable maximizing maximizing presynaptic fundamental notion surfaces gradients trace editor editor traffic extremely psychology created changed quantities assumes logistic hebb ith ith ith ith ith store mixed extent established mentioned scenes slowly slowly slowly pairwise separable orientations adjacent adjacent reasons considerable considerable rapid easier widely widely filtered forces mation mation calculations gradually gradually members toronto conjugate conjugate varies considerably profile led effort introducing detecting detecting maxima operate howard maximizes phonemes prevent coherent coherent coherent coherent coherent coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence eventually softmax softmax summed globally globally globally shifted shifted classifying identifying assign forming temporally temporally temporally linearity optimizing perfectly zemel zemel jth repre discover discover impossible rigid rigid promising adjusting held held held held held familiar los abilities abilities viewpoint obtaining removing observing wire optimally vowels infor infor becker becker becker becker becker becker becker negligible pat lang lang ascent jackel bursts canada observer captures adopted assigning consecutive street ple shorter presenting july forced responds spatio boser classifications classifications classifications classifications classifications classifications classifications additionally perceived tendency certainty stands principled henderson equality translated exam hubbard maximally academy intensities drawback drawback enforce enforce enforce denver responding west stuck prevents normalizing ignoring bridle bridle worked helps spite regularities distortions recogni twenty textures ers developmental hamilton flows inherently optima optima consonants consonants tactile modalities optics predictable predictable sions drifting brackets segmenting segmenting capturing discovers undergo illusory tern trapped trapped drawbacks entropies cations spario sentations eta proce ample dealt ver fukushima fukushima stereograms ontario ontario angeles dilation intervening machinery exhibiting sky fruitful adopting earliest birth maxwell maxwell categorize categorize categorize categorize categorize disparities transfor classifi undergoing encourages encourages geoff stereopsis ori conjunctions vised iden incentive infant infant ubiquitous infants infants cumbersome portant abrupt concentrating wrap ijcai predictability predictability crossed mations tth zky touret cedure pit pit pit pit pit ries unpredictable publish clouds entation dures subproblem rudimentary invariably tity unsuper discourage probabilit trajecto 
#@Becker_S,
#t6
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#*network network network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model input input input input input input input input input input input function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training training output output output output output output output output output output output output output output number system system system system system system system system system system system system system system error error state state state state state state results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information problem problem models models models performance based based space space weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer case case order shown shown shown shown shown parameters weight weight weight functions functions functions neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit image image image image image image image image image image image image image image image image image image image image image image single single single single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing control large local local local local local local local local local local local local local local local local local local local local local local local local local test test test test patterns patterns patterns class optimal inputs form form form signal simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small size size size size net net cells cells cells cells cells cells cells cells points field field field field field field field field field field field field field field field field field field field field features features features features process process current current current trained trained trained trained trained trained trained trained cell cell problems random random response response response response response response response similar similar similar representation representation architecture equation equation fixed line images images images general average states states states states gradient note note activity activity activity activity activity activity dimensional result independent independent independent log found found found sequence sequence target target target target target target target target target target constant constant estimate estimate estimate estimate estimate estimate estimate computer science science science left left direction direction direction direction direction direction present phase phase frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal object sets motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range range press learn learn nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous abstract find computational properties properties properties likelihood references procedure procedure procedure important important important important mixture mixture mixture introduction complex complex complex estimation estimation stimulus effect dynamic generated generated parallel parallel parallel parallel parallel tion energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference difference difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower signals signals signals signals signals chosen chosen center previous previous cases cases multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex good represent represent represent represent represent represent represent distributed make fact region region region region region region proposed observed errors classes ing tasks tasks total human human human computed computed computed computed computed computed sum sum performed performed performed performed regions regions regions regions regions regions regions regions regions regions regions means means orientation orientation orientation global global global global global global global global global filter filter filter filter filter filter filter filter filter filter filter filter artificial artificial relative represented represented true compared desired desired receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide compute compute compute compute objects objects objects objects objects objects objects proc location location location location location location location location location active active active eye experimental constraints connected connected gain motor cortical cortical approaches larger contrast contrast contrast fields fields fields fields support support support support support support support support support descent dependent selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection report report institute institute department represents represents represents represents represents represents responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses final final final final exp bias layers layers layers layers layers layers addition addition sequences sequences sequences sequences sequences sequences sequences sequences computing computing directly directly estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates trajectory san san san stage stage stage stage stage stage stage stage stimuli upper speed produce produce produce weighted randomly randomly levels area area area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types product actual provided finally selected selected selected evidence evidence evidence evidence evidence evidence evidence evidence nature nature nature constraint constraint constraint associative discussion technical increases tested limited corresponds amount amount amount common common common implemented implemented implemented square ability objective objective combination edge edge mechanism mechanism squared representing representing filters filters filters filters filters filters filters filters filters filters pre experts experts experts experts depth expert expert combined combined description discussed directions directions directions directions directions directions recent pair separate similarity reported reported reported reported moving moving moving moving moving moving moving moving moving moving moving moving identical pixels subset subset sejnowski sejnowski sejnowski sejnowski sejnowski varying varying varying tuning tions yields yields match correspond address background background locations locations locations locations locations locations locations observation observation grid grid grid grid grid grid gate organization sensitive sensitive entire entire entire arm arm intensity intensity intensity intensity intensity invariant suggests locally locally occurs occurs generally flow flow flow flow trajectories trajectories central differences accurate accurate accurate designed learns learns constrained constrained suggest propose propose strong strong integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration integration largest largest intelligence intelligence selective targets targets targets targets targets targets targets targets targets targets targets targets targets manner manner scene scene areas edges produces perception perception optical optical solving primary generating generating generating generating generating ann tuned tuned tuned tuned vertical changing text consisting frequencies frequencies frequencies frequencies frequencies gaussians extraction select competition competition competition competition competition competition competition focus stationary stages stages stages stages stages stages overlap interpretation interpretation operations frames forms forms suggested diagram diagram diagram earlier smoothing measurements measurements measurements measurements normalization roughly tracking tracking assigned assigned assigned assigned box box combinations retinal maximize partially partially gating gating texture determining selecting selecting selecting middle aspects divided divided identify computations tend essentially soc soc soc soc strongly strongly strongly strongly strongly contained contained allowing interpreted split physiological physiological cue built realistic wave correspondence correspondence computes highest ill cat cat cat neurosci moves overlapping preferred neighboring deal receive receive receive oriented oriented oriented simpler unlike selectivity diego diego rapidly varied relations humans detail respond respond combine reliable proper pathway pathway pathway pathway pathway encode fundamental closest plausible plausible predicting rev thought subsets aspect aspect explored extent utility synthetic synthetic integrate integrate integrate integrate integrate integrate indicating band band phenomena phenomena phenomena fairly adjacent adjacent nowlan nowlan nowlan nowlan nowlan nowlan nowlan adapted cascade lies spatially easier organized organized organized organized producing filtered broad monkey pool pool pool pool pool pool pool pool pool pool pool pool pool separately separately opt opt opt optimize toronto patches preceding conjugate summation summation integrating profile profile profile pathways pathways pathways transient share share marked treated treated treated rep biologically ity operate ture serve coherent coherent kinds neuro coherence coherence focused yuille yuille yuille attentional softmax discontinuities sensing primarily primarily primarily primarily investigation gabor temporally linearity linearity narrow narrow velocities velocities velocities velocities velocities velocities velocities velocities convenient primate primate primate primate proceeds striate striate stated occurring salk salk enhanced exploring reliably combines ranging ensures moved intended accounts competing dif spatiotemporal smoothed horn horn motions motions motions extensively relies speeds speeds intersection intersection skills boxes grating grating grating grating grating grating grating converted shading planes ties presenting suppressed suppressed suppressed sinusoidal demon transparent transparent shaded shaded shaded shaded rectangular favor favor segregation mammalian maintained retinotopic challenging terrence altered adelson adelson adelson adelson adelson exceed pools pools pools pools pools pools pools differing supporting mix simplification heavily ferent observers transparency transparency stripes responsibility steven accomplish physiologically physiologically heeger heeger heeger heeger heeger luminance luminance luminance bergen bergen bergen deals tended tended sliding convolved sity vertically vertically remained drifting drifting ings tra aperture enforces enforces gratings gratings gratings gratings gratings percept watson watson responded shares polar newsome newsome newsome newsome newsome newsome jose aggregate began instant movshon movshon putational direc upward upward crg primates primates directionally attentive enforced intersect shear shear quadrature resentation conceptually ess grzywacz grzywacz schematically manipulating distinguishes permitted univer klein premise proaches neurophys accelerated indicative octave maunsell maunsell maunsell maunsell maunsell maunsell octaves sponses opaque opaque intersections intersections subunits synaptics iiiiii backgrounds loud extrastriate albright albright albright albright ramachandran cnl cnl plaid visuo parkway jectories born born fized integra orchard rained hancement mounting veloc 
#@Nowlan_S,Sejnowski_T,
#t6
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#*network neural neural neural neural neural input input data data function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time set networks number number number system results results results units information information information information information information information information problem problem problem models space linear linear case case case case order shown shown shown shown shown values values parameters parameters parameters parameters parameters neurons neurons neurons neurons neurons neurons neurons unit unit method method approach pattern single single single single single single single single single single single single single single single single single single processing processing large large neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate analysis analysis analysis analysis shows shows shows shows shows simple simple simple simple visual visual visual visual visual visual visual visual visual visual small small size task methods methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field field field field field field field field field field field field field process cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell high response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar representation line line line parameter activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional university university university variables computation computation computation independent found found found dynamics constant constant constant constant constant standard science direction direction direction presented presented map present present present present present phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal position components components components nonlinear abstract computational properties references component procedure introduction complex complex complex complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect dynamic generated variance variance variance variance variance variance variance variance parallel change change variable variable variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower lower measure measure higher center center center cases firing firing firing firing firing type multiple multiple cortex cortex spike spike spike spike spike spike spike spike conditions conditions represent expected expected fact correlation correlation scale resulting ing total total total multi multi multi multi performed performed dimension dimension dimension dimension dimension dimension orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study study represented represented receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive compute compute location location related related connected discrete discrete cortical cortical cortical larger contrast contrast fields fields fields fields fields fields fields train train dependent dependent dependent dependent dependent modeling institute institute department department department code individual individual joint joint represents responses responses responses responses responses responses responses responses responses responses responses responses final maps considered equivalent curve curve curve curve curve additional curves top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects upper significant significant significant significant world speed coding coding coding finally evidence nature nature biological measured measured describe describe group complete complete complete amount amount amount amount short common effective shape shape generate supported degree degree degree sensory sensory sensory account account account matching representing numbers window window window normalized normalized bottom bottom description description light neuronal neuronal neuronal neuronal neuronal neuronal neuronal population population population discussed correlations pair movement movement period dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions varying varying compare calculated tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning axis axis axis address definition generalized lead concept concept concept studied spikes predicted predicted width greater conclusions depend central interactions interactions interactions interactions interactions interactions interactions clear peak peak peak peak peak suggest suggest encoding encoding encoding encoding encoding encoding encoding propose propose propose characteristics exist exist selective selective averaged manner groups groups connectivity identification question question acknowledgements areas primary tuned tuned tuned tuned tuned confidence sensitivity simultaneously simultaneously simultaneously simultaneously linearly linearly linearly linearly slightly interaction interaction interaction frequencies frequencies frequencies frequencies cycles cycles cycles cycles national dependence dependence correlated variation showed modulation modulation modulation modulation modulation understanding similarly smoothing performing classical add valid msec msec msec msec msec msec foundation degrees degrees degrees degrees degrees degrees degrees degrees degrees expect recorded recorded recorded recorded fire template figures combinations color retinal retinal sciences sciences sciences plotted plotted uncertainty maximize variations discussions middle middle divided presentation schemes excitation showing gray bar bar bar vary generalize realistic highest cat cat neurosci overlapping oriented presents trains remain stimulation selectivity varied varied varied varied varied varied varied replaced limitations helpful fourier fourier school biol ideal ideal dependencies dependencies comparable encode encode fundamental notion patch concepts necessarily onset aspect portion separated percentage percentage percentage residual histogram histogram histogram indicating indicating separable separable separable separable orientations coded majority capabilities capabilities nonlinearity ganglion ganglion spatially directional directional monkey monkey describing describing describing medical recording raw fourth varies populations populations populations populations populations populations limits transient transient transient transient offset capability peter peaks peaks peaks introducing modulated modulated modulated modulated modulated prevent germany logical conclude display physiol physiol deviations multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional phenomenon picture picture picture cybern physiology proportion linearity linearity neurophysiol bin bin bin bin cellular significance stronger held height neurobiology neurobiology neurobiology implications implications meaningful analyses falls falls histograms histograms histograms monkeys monkeys israel israel israel israel israel israel spatiotemporal reveals bins sustained sustained sustained sustained arrows passing grants receiving robert counts counts counts grating grating grating shading encodes presenting residuals corrected sinusoidal sinusoidal sinusoidal sinusoidal electrode shaded life life emphasize emphasize fixation lond lond regimes academy rectified categorization institut quantify abeles abeles abeles continuum continuum slices carries arriving quantitatively sliding absent drifting drifting drifting raised raised gratings gratings gratings enabling repetitions jerusalem jerusalem jerusalem behaving quantified hebrew hebrew hebrew coincidence awake offiine fur separability separability separability palm palm palm participate ordinate utilization psth psth psth psth psth psth psth psth abscissa braitenberg ori ori ori peri conical conical edward prog depended vaadia vaadia vaadia vaadia vaadia alert mono subunits bergman beneath unreasonable aertsen aertsen aertsen aertsen aertsen aertsen aertsen aertsen aertsen deviates shapley shapley shapley hagai displaying coincidences gerstein neuroinformatik narrowly 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#@Aertsen_A,Hochstein_S,Stern_E,Vaadia_E,
#t6
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#*model model model input data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set networks algorithm algorithm algorithm algorithm output output output output output number number number number system system system system results results results results information problem problem problem models based based based based layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer order shown shown shown shown shown shown shown shown shown systems systems values values values values values values values values probability parameters functions distribution recognition method method method method approach approach approach approach approach point point image image image image image image image image image single single single single processing processing local local local local local local local local test analysis form visual small feature feature feature work methods methods points points points points points points points points field features features features classification process process process level level level current random random random random random random random random random random high high high high high high similar similar representation representation representation representation representation representation representation representation equation line line line rule images images images images images gradient obtained term term term term term term term term note note note note note note activity result result university university university university threshold threshold computation computation computation computation computation computation computation computation computation solution research defined defined constant constant constant computer computer science science science left left left presented presented machine abstract back find computational references stochastic due due ieee important important important introduction parallel parallel parallel cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost tion tion tion energy energy energy energy energy difference difference difference difference difference complexity variable lower measure measure prior prior prior higher higher higher part part center previous bound required required multiple multiple bayesian bayesian bayesian bayesian bayesian markov region region region region region region correct correct correct observed errors scale scale scale scale scale simulations simulations ing simulation simulation human computed computed computed computed multi multi multi multi multi performed performed performed regions regions regions regions regions regions regions regions regions regions regions regions regions factor potential potential potential natural natural knowledge knowledge obtain represented represented provide compute compute compute objects objects objects perform active goal constraints constraints constraints constraints constraints equal approaches contrast contrast support support support support descent report department department department consists layers layers layers layers layers layers layers layers layers layers scheme addition addition computing computing detection upper upper vision vision con produce conditional types types provided processes iteration constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint biological technical increases increases assumption assumption complete surface surface surface surface surface surface surface surface surface surface nearest nearest shape shape supported square square square square pixel pixel pixel ability noisy noisy sensory simulated pairs needed functional fully projection edge edge edge edge edge edge edge edge edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation consistent matching matching matching matching matching matching matching matching operation inhibition inhibition bottom depth depth depth depth depth depth depth depth depth depth depth frame frame frame idea description membrane directions directions separate separate include pixels pixels pixels pixels pixels pixels pixels pixels pixels quadratic quadratic quadratic recently observations solve solve smooth smooth match match match match studies trans diagonal sparse sparse background background background background background background background background entire entire horizontal parts parts parts intensity intensity intensity intensity intensity intensity intensity suggests derivative correctly correctly locally locally white boundary boundary boundary half half half half half conclusion place row row accurate bayes bayes bayes temperature propose propose reduction intelligence plane plane plane plane scene scene scene minima annealing force explicit explicit appears relation edges edges edges edges produces written perception perception perception solving factors plot plot label label label label label vertical distinct distinct missing missing simultaneously simultaneously simultaneously remaining unique mutual versus versus expressed dependence review labels labels labels labels labels labels labels sign classical reduces fitting neighborhood neighborhood add boundaries boundaries boundaries boundaries visible advantages classified faces transactions coupling avoid perceptual weighting weighting weighting assignment assignment activated activated activated priors absolute partially partially partially neighbors neighbors neighbors letter letter letter letter differ poggio poggio poggio computations excitation excitation excitation soc prob lie follow gray gray gray gray gray gibbs gibbs gibbs gibbs relaxation dot dot dot dot dot dot dot dot providing providing minimizes board board correspondence computes highest attempt overlapping disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity neighboring neighboring neighboring decreasing matches matches matches matches rest scaled surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces contours matched saliency configurations psychology front academic grouping grouping grouping grouping grouping grouping grouping site site ment costs costs costs crucial publishers smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness smoothness floating floating floating floating floating floating floating handle spatially straight straight sites sites forces directional incorporate commonly acknowledgement attribute attribute lowest percent lack psychophysical incorrect incorrect outliers requirement rely ordered geman geman geman geman geman geman geman conclude display yuille yuille yuille gap gap lab discontinuities indices primarily assign equivalence impossible flexibility inspired fails fails binocular accepted obtaining mark fail wire wire wire wire belong belong belong disjoint disjoint disjoint corner planar planar planar filled filled filled filled ensures ensures ensures ambiguity ambiguity ambiguity displayed pat moved stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo sim sim belongs captured occlusion arrive ends roy belonging agree captures captures fusion lem ics dense informa linked ence incorporates incorporates piece kluwer planes planes covering inferred removal cooperative forced pentland pentland pentland assignments associate transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent continuity argue formance discontinuity discontinuity discontinuity distant distant afosr rectangle rectangle rectangle wise ambiguous drawback enforce enforce placing bill bill normalizing normalizing inactive resembles fiat restoration uniqueness uniqueness uniqueness uniqueness uniqueness marks mrf mrf transparency transparency transparency transparency transparency transparency transparency transparency neighborhoods clarity cylinder cylinder gram sparsely triangulation 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#@Kersten_D,Madarasmi_S,Pong_T,
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#*network network network network network network network network network network learning learning model model model model neural neural neural neural neural neural input input input input input input input input input data data data data function function function function function figure figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training algorithm output output output output output output output output output number number number number number number number results results results units units units units units units information information information information information problem problem problem problem problem models hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance space space weights linear case case case case case case case case vector vector vector vector vector vector vector order order systems systems values values values probability probability probability probability probability probability probability probability probability probability probability probability parameters noise noise noise noise noise noise noise noise noise noise weight functions unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition approach pattern point point point image image single single single single processing processing processing control large large large large local local test test test test test test test test patterns patterns analysis class class class class class class class class class class matrix matrix optimal optimal optimal optimal inputs inputs inputs inputs inputs form form form form form shows shows shows simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper examples examples feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work task task task task task task task task task task step step features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification classification classification classification classification classification level trained trained trained trained problems random random random random high similar show show show show show show equation equation equation equation equation equation equation equation line rule vectors images images images general real real real approximation approximation average average theory theory gradient gradient note note note note note dimensional result result university computation solution solution solution solution solution solution solution solution research research independent independent independent independent estimate estimate standard standard standard computer computer distance presented object sets maximum maximum range range press press press learn position basis basis basis basis basis outputs outputs outputs sample abstract back back back density density density likelihood likelihood references component due positive propagation propagation propagation mixture introduction complex complex hand hand hand hand hand hand hand hand hand statistical variance variance tion tion tion assume assume assume assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier prior part center cases type type required good good good good good represent represent bayesian bayesian bayesian bayesian equations equations equations fact fact fact fact fact techniques techniques techniques region correct correct correct correct correct correct probabilities probabilities probabilities probabilities simulations resulting resulting classes classes classes classes classes ing ing computed computed computed performed performed eq regions regions means dimension dimension orientation orientation applications knowledge knowledge em em obtain obtain obtain obtain relative samples samples samples samples samples true true receptive compute compute compute objects objects determined determined determined posterior posterior distributions equal approaches accuracy comparison comparison larger fields update update train descent descent dependent nets modeling morgan proceedings technique advances advances joint joint connectionist exp addition graph considered cambridge cambridge computing computing domain directly hinton solutions solutions solutions solutions solutions estimates estimates estimates top top top classifiers classifiers classifiers classifiers classifiers classifiers full significant world vision vision vision vision vision vision vision pages pages con produce weighted weighted weighted randomly clustering clustering types product finally backpropagation depends depends simply simply measured measured measured measured discussion discussion covariance covariance covariance normal normal normal tested tested tested tested tested assumption complete complete complete complete rbf rbf rbf rbf rbf rbf rbf rbf rbf amount nearest nearest generate require end ability ability instance cluster development development noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy kaufmann combination combination account unknown unknown unknown testing significantly projection york uniform uniform uniform uniform uniform uniform representing numbers pre direct frame choose added denotes denotes denotes denotes improve advantage separate include side sense sejnowski dimensions dimensions dimensions dimensions sufficient highly highly highly highly calculated calculated achieve achieve diagonal diagonal diagonal positions positions interval interval entire entire grant lead extended deviation matrices predicted hybrid touretzky width demonstrate reduce neighbor competitive editors central central bayes bayes bayes numerical numerical moody moody moody exponential practice practice constrained constrained integration integration presence presence sigmoidal radial scene acknowledgements suppose monte carlo estimating missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing coordinates infinite dimensionality involves easy unique integrated gaussians gaussians gaussians select john decreases choosing extracted expressed densities densities densities evaluated approximations approximations centers centers forms soft approximated approximated approximated completely converges constants partial reasonable reasonable reasonable boundaries closed closed closed closed sufficiently advantages combinations weighting plotted discuss discussions characterized major reason effectively included efficiently score score score score score situation situation plots characteristic soc contained split dis issue classify write usual usual realistic providing correspondence highest highest deal deal deal deal deal situations situations situations carried wiley overfitting access estimators integral integral integral integral accurately lippmann lippmann lippmann mass helpful school rest project detectors complicated naturally adapt illustrate illustrate perfect art utility integrate integrate integrate percentage percentage trivial crucial variances nowlan nowlan nowlan independence benchmark perspective berkeley ring ring ran arise mation scientific localized depicted incomplete recognizing exemplars integrating evaluating substantially led dark lms poorly backprop measuring limiting extracting proven achieves marginal richard richard richard germany germany displays displays consistently tresp tresp tresp tresp tresp tresp tresp indices intractable assign assign assign guarantee guarantee guarantee arguments impossible theories royal exemplar rigid systematic wrong dealing dealing numerically darken darken darken ranges overcome siemens siemens siemens serves serves intuitively optimally substituting substituting substituting substituting date infor reliably loo perfor den occlusion occlusion omitted gesture gesture gesture gesture extends sons hart hart inf tures tures tures dempster dempster outlined posteriori posteriori informa grating summer ple shading ter rubin pointing pointing ahmad ahmad ahmad ahmad ahmad ahmad poses poses poses encouraging certainty scenario constrain preserved exam formance duda duda distribu distribu uncertain uncertain uncertain uncertain uncertain degraded picked picked careful regimes deleted laird finger finger esti fea fea fea normalizing ignoring exploited simplifies gauss gauss gauss gauss gauss gauss gauss gauss gauss gauss gauss gauss gauss gauss gauss utilizing gestures gestures gestures gestures ble ate insufficient invertible hid tribution ning unreliable substitute classi archi screen computable computable gaus faced unusual polar unnecessary rolling schuster substituted hands inte dealt volker thumb ranked mate agation scored scored wji indistinguishable comput ranks tain tly icsi otto otto proj validate und occlusions recipes teukolsky bet compar nodal flannery hahn hahn sider ported vital ser deficiency vetterling cer stolcke zfe zfe zfe shadows gracefully ual worlds domly managed ison malized fion sians subutai gaussi cil cil fier direcfiy 
#@Ahmad_S,Tresp_V,
#t6
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#*network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time set set set set set set networks networks networks networks networks networks networks networks networks algorithm number number number system system system system error error error results results results information information information problem problem problem problem problem problem problem problem problem problem problem problem models models models models models models performance performance based based space space space space space weights weights weights case shown shown systems systems values values values values values values values values values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise neurons distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach point point point image image image image single single single single single single processing control large large large neuron rate rate rate matrix matrix matrix shows shows gaussian visual visual visual visual visual net net net net work work work fig step step step step process level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level current current problems problems problems random random high high memory representation architecture architecture architecture architecture architecture show equation equation line line vectors general general general general parameter parameter parameter approximation approximation approximation approximation average average average term note note experiments experiments experiments experiments university university university university variables variables variables variables variables variables variables variables variables variables computation computation computation computation computation computation solution solution solution solution solution research found found found initial initial initial initial initial initial initial constant constant constant estimate estimate estimate standard computer computer computer terms terms terms terms terms terms terms terms terms science science science science left map present present present low low nodes object object object object object object object object object object object object object object object object object object object object object object object object object object object position position position position sample abstract abstract applied find convergence convergence convergence convergence convergence convergence convergence density analog analog analog analog analog analog references component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic procedure behavior behavior statistical variance variance variance variance variance variance variance variance variance tion spatial spatial assume assume assume assume assume lower lower prior representations representations chosen chosen higher higher higher part part part part part part part part part part part part part part part center center theorem cases cases cases cases type required good binary represent represent represent represent represent represent represent distributed distributed bayesian bayesian expected equations equations fact proposed length length correct correct correct correct correct correct correct observed observed observed forward forward forward scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale simulations simulations simulations simulation simulation simulation computed computed computed computed computed respect performed performed elements elements optimization optimization natural orientation applications knowledge obtain obtain original vol relative relative relative specific specific represented represented represented true application compute compute compute compute compute objects objects objects perform goal distributions equal approaches steps steps dependent nets nets morgan report report report institute department department department department department loss implementation individual advances joint joint represents final final exp scheme scheme addition addition graph graph graph ai computing computing computing domain equivalent additional solutions solutions solutions estimates estimates estimates estimates design limit limit san top top top top top stage stage choice approximate approximate speed vision vision estimated pages increase derived weighted weighted levels levels levels levels levels levels levels levels levels criterion lines lines lines actual actual constraint measured measured technical denote transformation close close close corresponds corresponds finding finding finding finding amount implemented shape shape supported instance instance instance makes kaufmann objective objective objective objective reduced reduced york segmentation segmentation segmentation segmentation matching matching matching matching matching matching matching matching matching uniform database operation leads leads leads representing iterations iterations max pre pre making stored stored stored stored stored stored stored international bottom frame frame added added added added description description description description denotes denotes resolution advantage advantage separate takes takes typical introduced include identical side side side side side side side side side side hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical sense inference inference inference engineering engineering engineering engineering sufficient highly compare compare approximately solve match match match match match match match match match match correspond converge converge address address generalized organization organization grant arm arm horizontal parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts studied deviation matrices correctly pass demonstrate flow starting place reduce reduce depend depend central bayes designed designed clear moody mateo temperature suggest propose physics solid labeled assuming minimizing min relationship relationship iii averaged scene scene scene base base acknowledgements appears derive derive derive index index index solving solving solving estimating describes describes dept segments recall recall explicitly explicitly explicitly coordinates coordinates coordinates coordinates electrical electrical electrical electrical involves involves involves text angle unique unique adding minimization select yield choosing independently expressed expressed variation detailed detailed evaluated updated centered frames frames frames frames similarly similarly translation converges earlier calculation reduces reduces reduces purpose intermediate intermediate intermediate intermediate intermediate intermediate intermediate assigned david box includes perceptual thesis coordinate coordinate formulation assignment assignment assignment recognize coupled coupled discussions grammar grammar grammar grammar grammar grammar structural structural structural simplicity simplicity aspects differ literature computations computations comparing identity identity identity identity identity reached composed composed composed capture repeated strongly prob prob success success interested stopping notation correspondence highest highest highest highest illustrates approximating neighboring bars simpler rapidly rapidly detail lippmann hall helpful successive relationships proved hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy notion notion notion matched matched matched matched circles coarse coarse coarse coarse coarse coarse coarse coarse concepts editor man equally implementations assumes shapes initialized improving improving improving improving grouping grouping grouping grouping grouping phd averages publishers track variances variances majority expensive berkeley berkeley style commonly probable describing describing optimize lowest lowest lowest lowest lowest lowest lowest lowest lowest depicted addressed raw integrating integrating reflect double collected freeman bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap introducing incorporated formulated incorrect differs serve yuille simultaneous converged converged converged hints initialization initialization initialization initialization initialization initialization initialization initialization consistently consistently redundant summing optimizing labelled unity unity arrival rigid lost generality stated determination obtaining observing belong settings grammars grammars reliably utilized prentice combines mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness loo belongs elastic elastic elastic initialize recog specialized permutation permutation permutation permutation permutation permutation permutation permutation omitted ahead summarize default assigns assigns lem temperatures yale yale yale yale yale ure street arcs solves recursively abstraction abstraction utilize arg assignments assignments hierarchies descriptions auxiliary gene gene gene gene eric eric eric principled preserved exponent grouped denoting afosr afosr considers represen placing struc lems simplification slot recogni compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional primitives crude influenced suite hypothesized aid bold bold bold imple finer inclusion outperformed outperformed dcs dcs station triangles triangles marr marr rangarajan labelling labelling labelling labelling labelling labelling labelling sity demands tations essence stick translates translates derives tim recalled ini mid ina ina ina violate unaffected haven haven utans utans utans utans utans utans utans utans mentation vast anandan anandan anandan anandan deformable blurring gindi gindi gindi gindi gindi gindi gindi gindi gindi univer icsi coarser abstractions abstractions structurally unspecified supplying consis tent joachim joachim joachim mth mirrors vious invari imize cult ably subparts subparts subparts subparts subparts subparts subparts sticks hierar yaleu parallels deteriorates advocate ignorance intentionally diffi blindly nizing tural mulation ovals 
#@Gindi_G,Utans_J,
#t6
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#*network network model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set output output output output number number number number number results results units units units units units units units units units information information information models models weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear layer layer layer layer order shown shown shown shown shown shown systems parameters noise noise noise noise weight weight neurons neurons unit unit pattern pattern point point point image image image image image image image image image image image image image image image single single single single processing processing patterns analysis analysis analysis inputs inputs form shows shows shows signal simple simple simple simple gaussian gaussian gaussian visual visual visual small fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field features features features process process process level level level level level level cell cell cell cell cell cell cell cell cell structure structure high high high similar similar similar similar similar similar representation section images images real real real real obtained obtained obtained note note note note note dimensional result threshold threshold computation computation computation computation computation computation found found dynamics dynamics estimate standard terms connections connections connections connections connections connections connections connections connections connections connections connections prediction left left left left left presented presented present low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency sets sets position position position outputs outputs outputs continuous abstract back back back back back back back back properties references due due due due positive important important introduction effect effect effect effect tion tion spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower measure part center center center center firing firing firing firing firing multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long long long long long long long long conditions represent represent represent make region proposed correlation length length forward forward forward forward forward scale simulations minimum ing simulation performed performed performed called times reinforcement factor made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation study study study filter filter filter negative original original original compared cross receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide provide proc location perform perform connected cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain contrast connection fields fields fields fields fields fields institute words synapses synapses synapses represents represents responses final exp exp exp exp exp layers scheme scheme scheme addition considered experiment view top stimuli stimuli effects effects detection detection detection full significant significant estimated estimated basic basic con produce channel channel channel channel channel channel channel channel area types types lines actual provided provided nature nature inhibitory inhibitory inhibitory inhibitory inhibitory simply simply simply discussion feedforward describe group tested close close corresponds complete excitatory excitatory excitatory excitatory stable short short short assumed assumed synapse synapse supported role role require end end end pixel pixel easily noisy noisy reduced reduced account account functional unknown technology ratio projection projection projection projection projection projection projection projection projection projection projection projection projection edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge mechanism principle principal principal details details iterations iterations iterations iterations direct direct inhibition experts combined produced produced added added light resolution robust robust robust robust takes reported lateral lateral lateral lateral lateral lateral include pixels pixels pixels pixels pixels hierarchical interest varying varying approximately tuning tuning tuning tuning studies achieve channels channels channels channels channels channels channels entire horizontal parts suggests deviation feed feed width loop loop loop loop strength place reduce reduce segment conclusions valued valued sigmoid retina retina retina retina retina retina retina retina clear performs weak weak suggest strong characteristics california turn assuming connectivity connectivity program acknowledgements areas areas edges edges edges edges edges edges edges produces tuned tuned tuned tuned tuned tuned tuned tuned segments segments modeled implement simultaneously simultaneously simultaneously linearly text text interaction interaction communication communication communication communication communication overlap centers centers suggested suggested constants diagram diagram reduces purpose remains initially filtering foundation koch koch koch degrees template template activations activations contour contour retinal retinal retinal retinal retinal illustrated illustrated phys partially major simplicity extra efficiency effectively detect summary summary summary soc showing stopping running physiological follow comp bar bar michael simplified simplified simplified surround backward backward providing observable cat cat cat overlapping overlapping overlapping deal receive oriented oriented oriented oriented oriented oriented extend bars bars bars unlike create rise reducing respond project project project project detectors biol possibility possibility possibility possibility possibility combine lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn tanh tanh pathway pathway pathway pathway pathway cover cover contours contours removed circles circles reading extremely illustrate noted logistic logistic precise precise detected detected detected detected detected extent attempts isolated established great preference slope slope improves biology briefly lies interneurons interneurons interneurons interneurons nonlinearity nonlinearity ganglion straight producing constructing nucleus nucleus nucleus nucleus nucleus nucleus monkey separately circle circle res res res res author radius integrating people considerably prop dark fed fed detecting detecting detecting detecting detecting detecting detecting completion passed passed schematic schematic passes spread ordered qualitatively pasadena gave richard physiol simultaneous cybern physiology physiology physiology extensive martin neurophysiol purely enhancement rotations rotations grey communications murphy anatomical accepted proceeds fan fan striate striate keeping nearby nearby observing optimally enhanced enhanced spurious utilized overlaps dendrites displayed enhance enhance facilitate dif late agree implicitly summarize stopped stopped mind informa crossing covering wiesel isotropic personal hubel certainty interact interact retinotopic mediated mediated mediated careful lond distal rough worth emphasized sheet crossings reveal gilbert pools pools pools pools pools pools geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate places manuscript reinforce reinforce reinforce ate inhibit smoother compete horizontally anatomy station intracortical intracortical neurol contacts enhances sending remained facts backwards backwards massive christof ference preferable cations elaborate sends phy excite excite simulates mumford mumford thalamus enhancing enhancing psych coincidence illustrating mediate nonlinearly helped cooling cortico cortico rightmost rightmost suggestion positively positively positively fulfilled stabilized rationale completes mexico erties unoriented orienta farther farther diction lesser baker flowing originated prog collaterals collaterals investigators brody brody brody brody brody summarizing malpeli unfolded terminating sillito leftmost stacks ain impaired hibitory neces originates stating relay innervated innervated principally principally sary printing reinforcing reinforces usefully ooooooo ooooooo ooooooo ooooooo retinotopically retinotopically mediates chase fellowships carlos volved inconclusive 
#@Brody_C,
#t6
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks training training output output system system system results results results results results results results information information information information information information information information information information information information information information based space space space weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer shown shown systems systems systems systems systems systems systems systems parameters weight weight weight functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution pattern pattern pattern pattern pattern image image image single single processing processing processing processing processing processing processing processing processing processing large large local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate test patterns patterns patterns patterns patterns patterns patterns analysis inputs form shows signal signal signal signal signal signal signal signal signal simple simple simple simple gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper examples work methods cells step step step step field field field field field level cell structure memory memory response response response response similar similar representation representation representation representation representation architecture architecture equation fixed fixed fixed rule rule general theory university research research research research research research research research research found found found sequence initial initial initial initial initial initial computer computer connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic science science prediction left direction direction direction direction direction direction direction presented presented present present phase phase activation activation activation activation activation activation activation activation object object object object object sets motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range range range range range range range range position position position abstract properties references stochastic procedure introduction circuit behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect generated change difference spatial spatial signals signals signals prior representations representations representations representations representations representations representations higher higher part multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long long long long long long long long long long long long represent tree tree region proposed correlation observed total simulation simulation simulation simulation simulation human human human human human human regions means means feedback feedback orientation relative specific specific specific specific specific specific specific specific specific represented represented represented cross receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide objects objects objects perform active active active eye eye determined experimental connected cortical brain brain brain steps connection connection connection fields fields fields fields fields fields fields morgan morgan proceedings proceedings proceedings proceedings proceedings report institute department consists represents represents represents responses sequences sequences sequences experiment directly design trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san top stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli conference vision vision vision vision vision vision vision vision increase area area area velocity velocity velocity lines evidence nature nature nature nature inhibitory inhibitory inhibitory sampling measured feedforward describe corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable predictions circuits shape generate generate generate supported main adaptation journal journal journal journal journal journal journal journal journal journal journal journal ability ability instance future future easily development development development development development development development development development development development simulated simulated typically smaller combination account functional functional fully mechanism consistent consistent structures operation leads leads representing max max max direct direct direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition international bottom bottom bottom bottom bottom early early early early early decay combined run run directions lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving include period cognitive sufficient highly highly approximately axis correspond correspond correspond differential background background positions positions chain chain chain locations locations locations modified organization sensitive sensitive sensitive horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal intensity suggests suggests suggests predicted move move move move clusters clusters clusters critical place row hebbian trajectories trajectories conclusions interactions interactions interactions retina exponential faster faster faster faster faster faster learns suggest strong strong mechanisms mechanisms mechanisms mechanisms integration integration integration presence presence external characteristics characteristics characteristics characteristics turn variety targets manner manner manner acknowledgements areas areas areas areas appears appears appears appears appears appears appears van van longer longer longer perception perception perception winner winner factors transitions tuned tuned vertical modeled modeled modeled modeled modeled modeled modeled explicitly simultaneously develop predictive national national independently focus formation formation stationary stationary stationary stages stages communication viewed viewed viewed viewed influence influence organizing organizing organizing organizing modulation modulation constants slow slow measurements measurements measurements delays classical combining initially initially distances activations sciences sciences plotted plotted uncertainty uncertainty uncertainty uncertainty activated domains regular regular identified society society differ effectively projections tend receives excitation excitation excitation excitation excitation excitation strongly contained anderson anderson neuroscience neuroscience neuroscience neuroscience neuroscience neuroscience lie built built localization delayed delayed delayed cat cat cat cat cat cat cat cat cat cat cat cat cat received moves moves moves illustrates subsequent subsequent intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic receive oriented selectivity selectivity diego experience put accurately dotted hall periodic existence matches matches successive combine combine relationships office reliable phases analogous neu hill circles measurement transmission transmission transmission illustrate ith ith pyramidal pyramidal generates grouping established integrate integrate integrate animal rows scenes analyzed phenomena phenomena briefly organized organized day directional located monkey potentially potentially grossberg grossberg circle ridge axons summation integrating fourth apparent pathways pathways lattice sharp sharp sharp sharp sharp biologically maintain maintain operate limiting serve chen singer singer singer singer shaped begins attentional eventually summed phenomenon ordinary aligned physiology forming martin martin martin martin martin martin martin martin temporally velocities perfectly null circular neurophysiol jth purely naval eliminate enhancement royal royal outcome outcome eliminated anatomical chains chains chains chains chains ranges primate proceeds striate striate striate striate striate striate striate striate striate biased exploit north spot spot spot spot spot days filled combines induce propagated propagated propagated parietal exposure exposure exposure exposure exposure exposure exposure exposure emergence axonal spatiotemporal repeatedly specificity arrows arrows propagate neurophysiology neurophysiology neurophysiology unable unable constitute shading shunting wiesel wiesel wiesel wiesel transmitted july july revealed revealed nelson nelson welch welch comparative comparative comparative comparative preferences perceived letting certainty clustered shaded shaded trends continues uncertain uncertain uncertain uncertain uncertain neurophysiological douglas douglas macaque macaque academy increasingly increasingly increasingly paris selectively flash france refinement refinement refinement refinement barlow barlow barlow gilbert gilbert gilbert gilbert gilbert gilbert gilbert modifiable refined refined steering species tail tail tail accumulation resolve resolve resolve crude crude influenced observers adaptively developmental developmental developmental suppress award burr burr burr burr burr burr burr burr burr burr burr burr burr burr essen essen horizontally exposed thickness thickness intracortical progressively manipulated ooo functionally mill mill resolved predictable predictable spie sonn carrying inaccurate inaccurate successor tim subnetwork propagates gallant gallant lund lund lund lund lund lund lund spots prime marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall columnar hirsch hirsch hirsch reminiscent blasdel blasdel rightward rightward rightward ross ross ross ross ross ross inertia inertia inertia challenges anisotropic anisotropic anisotropic neurology neurology neurology latencies latencies jonathan hypothesize facilitation blur laterally reconstructing mitchison mitchison faculty widespread accumulating communicating textured crick crick laminar persistence persistence smear smear smear smear smear smear smear smear smear smear smear smear smear smear smear smear katz katz katz katz katz katz katz sharper settled farther contracts tolerate asymptote accumulates oak kevin lets lets amplify axi duffy duffy orban orban sharpening sharpening excites mountcastle mountcastle perceiving incapable sts michalski michalski smeared smeared smeared smeared smeared smeared smeared smeared trailing rockland rockland rockland rockland rockland counteract carolina exposures invited guides directionality ramachandran ramachandran homologous emits sharpen sharpen sharpen cynader cynader lamina nonlocal nonlocal nonlocal nonlocal chapel reinforces ooooo retinotopically rnax postnatal postnatal whitteridge whitteridge whitteridge universities ological nonspecific impair corticocortical colliding suprathreshold 
#@Marshall_J,Martin_K,
#t6
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data figure figure figure time set set set set set set set networks training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system system state state results results results results results results results results results results information information information information information information information information information information hidden performance performance based based based based based based based based based based based based based space space space space layer layer layer layer layer vector vector vector vector vector vector vector vector vector vector vector order shown shown shown shown systems systems systems values probability probability probability probability probability probability noise noise weight recognition recognition recognition recognition approach approach approach approach approach pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image processing processing large local local test test patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class inputs inputs inputs form form visual visual visual visual visual visual paper paper paper examples examples examples examples size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work work work work work work work work task task task task task fig fig fig fig fig fig field field features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process level level current problems problems problems response similar representation representation representation representation representation representation representation representation representation architecture section section fixed rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors images images images generalization generalization generalization real real average average note note note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result computation research log log found found found initial initial initial initial initial initial initial initial estimate estimate distance node node node node left left presented presented presented presented presented presented presented presented presented presented presented presented map map present present present present phase phase phase phase phase low frequency machine machine range learn learn learn learn learn learn continuous continuous continuous continuous continuous sample sample sample sample abstract find computational computational references component ieee ieee ieee procedure decision decision mixture introduction complex complex complex hand estimation behavior statistical generated tion tion spatial spatial spatial spatial spatial classifier classifier classifier classifier classifier rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure learned learned learned learned learned learned chosen chosen higher higher higher part part part part center type required required required tree bayesian region region region region region region region region region proposed correct forward scale scale finite classes classes classes classes classes classes classes classes classes classes ing ing ing ing human human multi multi regions regions regions regions regions regions regions regions regions regions regions regions mapping means means means dimension made made made natural natural feedback orientation orientation applications applications knowledge knowledge knowledge knowledge original original vol vol vol specific specific samples samples represented true application application application desired provide define define experimental goal goal goal goal posterior connected discrete discrete discrete power support support support morgan institute institute department version technique consists consists consists consists consists individual advances represents represents represents difficult final final scheme scheme maps maps considered framework framework framework framework framework framework framework framework domain domain domain domain domain environment environment additional additional additional additional estimates estimates estimates estimates estimates san top top top top top top stage stage stage stage stage stage stage stage stage stage stage stage stage detection efficient efficient efficient world world produce channel clustering clustering clustering clustering developed area area area area area area area area area types types evidence evidence evidence evidence biological achieved achieved achieved achieved achieved discussion describe finding amount supported supported role require main eds pixel pixel pixel ability ability future noisy noisy noisy including kaufmann probabilistic probabilistic probabilistic unknown unknown unknown unknown technology technology block interesting testing segmentation segmentation segmentation segmentation segmentation segmentation mechanism mechanism structures structures matching database database mode representing representing filters filters filters filters filters filters window window window window bottom bottom bottom bottom bottom supervised supervised supervised supervised supervised supervised supervised expert expert expert frame idea attention combined combined light light light correlations correlations resolution resolution resolution resolution resolution resolution apply apply apply include include include include subset array array recently recently recently engineering interest dimensions sufficient sufficient previously unsupervised unsupervised unsupervised unsupervised unsupervised axis correspond correspond correspond correspond achieve grant intensity intensity intensity intensity intensity digital correctly feed clusters white white white white white pass demonstrate demonstrate place minimal minimal minimal segment segment segment valued valued valued valued performs moody mateo largest reduction characteristics characteristics characteristics characteristics demonstrated demonstrated california california california intelligence labeled labeled labeled variety exist selective scene scene scene identification identification question areas areas areas areas areas areas perception generating laboratory label label label category category category category category electrical involves spectral spectral spectral spectral spectral spectral spectral spectral scales adding frequencies applying extraction extraction extraction extraction extraction extraction extraction john extracted family stages stages stages viewed viewed open updated labels lee lee decomposition decomposition discrimination discrimination diagram iterative generation generation generation filtering filtering filtering filtering visible euclidean transactions transactions transactions transactions degrees avoid existing existing fire fire exploration exploration includes color bell extension specifically domains black black texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture major major major sensor sensor importance importance computationally computationally driven identify detect literature invariance miller characteristic characteristic summary compact prob anderson anderson issue contribution categories categories gray gray gray gray gray gray gray gray gray gray gray gray play surround wavelet providing extract software oriented oriented extend presents carried wiley investigate put detail strengths hanson preliminary links links possibility structured structured structured symbolic symbolic cover cover attributes attributes attributes hill hill closest man man man mapped mapped mapped art art pyramidal pyramidal arbitrarily submitted defines animal indicating indicating scenes scenes scenes band theoretic theoretic theoretic ground ground sensors sensors publishers orientations orientations track track growing navigation navigation navigation capabilities capabilities considerable purposes preprocessing preprocessing filtered filtered laboratories projected acknowledgement attribute attribute attribute attribute depicted robustness robustness robustness reflects dark dark dark dark dark capability experimentally autonomous autonomous autonomous autonomous autonomous detecting pasadena pasadena pasadena achieves enables segmented segmented age pyramid pyramid pyramid pyramid sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing identifying labeling labeling labeling labeling gabor gabor gabor gabor signature signature homogeneous homogeneous discovery air imaging ranges difficulties multiplicative check vehicle vehicle bands bands bands bands transforms spot enhanced corner utilized utilized combines evident enhance enhance stereo darpa enable enable contact informative informative informative sons hart hart material automated automated onr fusion fusion discriminate informa associations land specification minus visually fellowship achieving achieving goodman goodman goodman goodman goodman goodman goodman goodman goodman obstacles encouraging distinction utilize perceived classic clustered remote remote remote remote remote remote remote remote remote remote remote remote remote scenario quantized shifting duda duda proba challenging challenging challenging individually differentiation differentiation smyth ultimately guided relates topic rough rough rough rough library library discretization lippman slopes supporting covers characterizing bility tial textures textures textures textures jet jet multiresolution calibration utilizes focuses micro jain concrete distinguishing codeword automation propulsion propulsion classi modalities modalities modalities convolved suffice experienced fication appro segmenting derives convey spa satellite spec spanning elaborate ton ton ton ample codewords codewords inte enhancing darker pursued pursued subsampled coverage intel ously sky conveys imagery imagery imagery imagery imagery imagery contiguous unstructured textured greenspan greenspan greenspan greenspan greenspan greenspan greenspan greenspan greenspan greenspan greenspan greenspan greenspan confused rodney vised higgins unspecified gions infrared spend aerial bush bush bush bush bush bush detectable chellappa chellappa navigate meters sar quantize quantize cloud terrain succeeds eee gaining concatenating pacific surveillance jpl borne ice automate outdoor airborne airborne airborne landsat landsat landsat enlarge priate ably sea neous simultane soil atmospheric grated fusing fusing textural textural textural textural ban ech identifica 
#@Goodman_R,Greenspan_H,
#t6
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#*network network network network network network network network network network network model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input data function function function function function figure figure figure set set algorithm algorithm algorithm output output output output number system results results performance based space space space space linear linear layer layer layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector order shown shown shown values values parameters functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit pattern pattern pattern pattern point point image image image image image image image image single single single single single single single single single single processing processing processing large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix matrix matrix matrix matrix matrix form form form shows visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper net fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells step points points field field field field field field field field field field cell cell cell cell cell cell cell cell random random high response response response response response response response similar similar similar representation show show show show show show show show equation equation equation equation section fixed line line vectors vectors vectors vectors vectors general obtained note experiments experiments activity activity dimensional dimensional dimensional result result threshold threshold computation computation computation computation computation computation independent defined defined found found estimate distance connections synaptic synaptic left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented map map present temporal temporal object object object object object object motion motion motion motion range range range range range press position position position position position position position position position position components components basis basis abstract find find computational properties properties likelihood references component component component component component component component component component component component component component positive important introduction behavior behavior stimulus stimulus stimulus stimulus generated search change change spatial assume lower chosen chosen part part center type type cortex cortex cortex cortex cortex cortex cortex cortex long represent equations length correct correct simulations simulations resulting simulation human human human human human sum sum performed eq eq eq eq eq eq eq eq eq eq eq called called negative negative specific represented receptive receptive receptive receptive receptive compute proc location perform eye eye eye eye eye eye eye eye eye eye eye eye determined experimental experimental related connected brain equal steps accuracy comparison connection connection fields fields version consists individual individual individual responses responses responses responses responses layers addition addition considered computing environment environment environment curve stimuli detection detection upper world speed basic give condition developed area area area area area area area area area area area velocity types types types types types types types lines product provided finally finally nature measured complete common common common common common generate require instance easily degree degree degree degree pairs needed combination transfer interesting projection consistent consistent mode mode representing representing representing max depth depth combined neuronal neuronal neuronal denotes denotes denotes population population population population population population population population population population population population directions directions directions directions directions directions property takes element similarity movement movement movement movement movement moving include recently varying previously works works tuning tuning tuning axis smooth studies sparse address locations locations locations locations grid constructed constructed constructed constructed parts invariant invariant invariant wide wide matrices rotation rotation rotation rotation rotation rotation move occurs column column column demonstrate half half flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow strength conclusion minimal assumptions assumptions assumptions sigmoid sigmoid accurate retina designed peak suggest encoding encoding encoding encoding presence largest demonstrated assuming minimizing movements movements movements movements movements movements movements movements movements movements selective selective selective selective selective selective plane plane plane plane plane denoted areas van van construct written written perception laboratory tuned distinct coordinates linearly slightly angle consisting minimization versus choosing independently focus dependence depending stationary stationary correlated overlap evaluate restricted centered centered forms static static approximated activities activities suggested translation translation calculation measurements expansion spaces calculate calculate calculate visible visible koch degrees degrees includes combinations coordinate subspace subspace subspace subspace subspace holds characterized major simplicity simplicity middle suitable maximal maximal maximal maximal encoded effectively projections invariance situation situation situation orthogonal orthogonal orthogonal receives soc soc kind contained showing superior lie lie sin sci satisfy comp dot absence highest reach cat neurosci neurosci neurosci moves preferred extract deal body selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity exhibit exhibit varied humans strengths strengths strengths pursuit respond ideas biol int proper understand analogous matched plausible equally generates explain residual residual great cos navigation lies lies inside inside organized directional directional directional broad monkey monkey monkey acad res explained argument argument apparent populations populations double double double axes lack psychophysical psychophysical psychophysical share biologically biologically exhibits germany germany chose boston physiol findings wang wang summed proportion forming restrict animals velocities nat neurophysiol neurophysiol neurophysiol rotations rotations rotations rotations rotations rotations rotations saturation ments keeping shifts shifts shifts optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic substituting recovered ranging regarded monkeys multiplied deg deg modelled modelled modelled specialized contraction specificity observer observer observer eqs eqs splits reverse speeds stone stone pointing ties focal employs expanding expanding expanding expanding expanding responds preferences ease ease perceived spaced remainder shifting shifting compensate neurophysiological jij jij denoting compatible compatible retinotopic retinotopic emphasize maximally fixation fixation fixation fixation fixation fixation unconstrained translations dorsal responding universit rotating rotating rotating rotating rotating vanishes vanishes psychophysics resembles expansions picking locomotion locomotion covers heading heading heading heading heading heading heading heading heading heading heading heading heading heading heading heading institut quadrant quadrant observers observers mst mst tanaka tanaka broadly accomplish essen essen excited excited continuum exclusively possess proposes heeger heeger heeger detects complement complement andersen andersen andersen planck carrying fovea assessed dence tens rotational rotational rotational rotational rotational rotational rotational rotational favors favors saito saito triple triple triple triple triple triple yon upward upward directionally clockwise clockwise inserting inserting evaluates comprises translational translational gibson gibson displaced rightmost synapfic synapfic sual torre abs spans pertone depen wurtz wurtz wurtz wurtz unknowns unknowns predominantly maunsell maunsell selectivities selectivities selectivities fax originate counterclockwise counterclockwise counterclockwise counterclockwise allman allman kybernetik nimh elicit unidirectional markus occupies duffy duffy duffy duffy orban orban orban contracting contracting contracting contracting harmon cyb pertaining extrastriate iio warren warren mathur kaas kaas reverses rot rot rot organi halfway mer involvement houghton ofthe ofthe viewer jepson jepson jepson jepson contractions contractions etal eccentricity roedial ruhr maes intentional 
#@Lappe_M,Rauschecker_J,
#t6
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#*network network network network network network network learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input data data figure figure figure figure time time time time set set set set set set set set set set set set set set set training training training training training training training training training training training training training training training output output output output output output output output output output number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error state state results results results information information information information information information information information information hidden hidden hidden hidden hidden performance based based based based space space weights layer layer layer layer vector vector vector vector vector vector vector vector vector vector shown shown systems systems systems systems systems systems systems systems systems systems systems values values values values values values values values values values values values values weight weight functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach pattern image image image image image single single single single processing processing processing large large large local local local rate rate rate rate rate test test test test test analysis form simple simple simple visual visual visual visual visual paper paper paper paper paper examples small small size size size size size net net net 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distance distance distance distance distance connections connections node node node node node left direction present present present activation low low low nodes nodes nodes nodes nodes nodes nodes sets maximum maximum learn learn learn learn learn learn learn position position position position position position position position position components components components components abstract applied density density references component component component stochastic positive positive important decision action hand hand hand tion tion classifier rules rules rules prior word chosen higher higher part part part part part center center center center center center center center center center center center center center center center center center center center center center center previous required required multiple multiple multiple multiple multiple long represent distributed expected make make make make make make make make length forward forward forward forward total human human human human human human human human human computed computed respect respect multi called called means dimension dimension natural natural natural knowledge negative artificial artificial specific samples samples represented receptive receptive receptive objects objects rates rates rates rates rates location eye eye eye related connected connected connected connected accuracy accuracy accuracy accuracy contrast fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields morgan morgan morgan report report institute words version technique individual advances advances advances represents represents represents layers delay addition addition considered equivalent view view san san san stage stage conference conference determine determine efficient efficient efficient significant vision vision vision vision vision vision estimated con area area area area finally processes processes processes backpropagation backpropagation backpropagation simply simply technical describe group tested limited effective eds eds eds pixel pixel ability ability future makes rumelhart kaufmann kaufmann kaufmann typically typically typically typically typically smaller smaller underlying needed reduced fully fully technology technology testing testing ratio character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character increasing segmentation segmentation segmentation segmentation 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recognize recognize recognize recognize recognize recognize extension variations variations aspects efficiency effectively tdnn tdnn efficiently efficiently invariance tend essentially essentially identity fine fine reached cun dis dis classify classify running cue cues vary surround nips nips denker denker highest highest automatically moves overlapping subsequent decreasing oriented presents employed create varied hanson hanson hanson accurately accurately lippmann lippmann lippmann successive successive fashion fashion decisions momentum closest closest necessarily reading reading reading reading reading reading reading reading eyes aspect logistic art isolated integrate integrate years years percentage histogram histogram indicating indicating ment developing developing publishers publishers publishers navigation coded capabilities capabilities capabilities capabilities answer briefly starts comparisons drive sys shared shared shared shared style recognized recognized beginning beginning localized localized read read auto recognizing recognizing recognizing researchers integrating requiring fourth fourth questions people considerably considerably considerably collected backprop passed passed employ remove continuously passes passes passes passes enables decreased windows windows progress cor cor person classifying generator writing labeling martin martin martin martin martin martin martin martin connecting printed printed printed extending fails fails darken darken stated height obtaining operates operates operates fail filled heuristics falls falls falls sion james mental regard scan scan scan scan scan scan claim enable enable recog saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades informative extends extends broken broken jump jump jump jump displacement executed skills skills skills sequentially metrics yielded ter exhaustive exhaustive exhaustive exhaustive rejection employs employs forced obtains causing acceptable reports individuals individuals classifies adjustment adjustment reject reject constrain burges burges tems chapman chapman chapman chapman maintained ocr ocr ocr ocr ocr ocr paired rejected rejected fixation surrounding exceed placing mimic mimic increments corrections wider scanning scanning demonstrating scanned nist nist algorithmic austin locate spacing keeler keeler dcs char char char integrates horizontally horizontally horizontally horizontally corrective corrective corrective corrective corrective corrective corrective corrective corrective corrective successively periphery recognizes recognizes convolved tance seg contents contents mis mis tained texas indi sur enabling occasionally preprocessed activa fight fight touch ver lowered mentation jumps jumps des copied 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#@Chapman_D,Martin_G,Pittman_J,Rashid_M,
#t6
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural input input input input input input input input data data data data function function function function function function function function function function function function figure figure figure time time time time time time time networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm output number system error error error state results results information information problem problem problem based based space space space space space space space space space space space space space space space weights weights weights case vector vector vector vector vector vector vector vector order order order order order order shown systems systems systems systems values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions distribution distribution distribution distribution approach single single processing processing large local local local rate rate rate test analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal inputs inputs inputs inputs inputs form form form form form shows shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper 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machine motion press press press position basis nonlinear abstract applied find convergence density density density density density density density density density density density density density density density density density density density density properties references component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee important adaptive adaptive adaptive introduction behavior behavior behavior statistical statistical generated generated variance variance cost cost cost cost cost cost search search search tion tion difference difference variable spatial assume assume assume assume measure theorem cases multiple conditions conditions conditions conditions conditions conditions equations equations markov make make techniques correlation correlation correlation correlation length finite minimum minimum minimum resulting resulting ing ing ing total simulation respect called called called times times mapping mapping potential potential potential potential potential potential potential potential potential potential dimension dimension global global knowledge filter filter filter obtain obtain obtain relative relative true desired series series series provide provide define compute perform distributions distributions distributions distributions distributions distributions discrete power power approaches comparison update update update update update update update update update update update update update support descent descent dependent selection morgan morgan report institute department department version advances advances joint final ai ai ai maps framework cambridge cambridge computing curve design transition transition transition transition transition limit san san effects bit conference conference full significant free pages give derived derived conditional lines finally finally processes processes backpropagation iteration iteration iteration simply discussion discussion technical denote denote surface amount common effective effective effective effective effective effective effective generate supported supported theoretical theoretical theoretical theoretical eds end kaufmann kaufmann objective pairs pairs underlying reduced dynamical coefficients coefficients coefficients coefficients technology interesting york special squared international international depth choose description description denotes denotes denotes denotes exact exact pair ensemble ensemble ensemble movement quadratic quadratic sense engineering dimensions compare previously volume smooth yields differential diagonal evaluation symmetric generalized exists parts parts expression expression studied studied alternative alternative alternative move greater assumptions reduce neighbor depend depend editors interactions differences numerical moody moody moody moody moody moody mateo mateo integration integration physics drawn drawn sigmoidal solid proportional regularization assuming exist exist derivatives minima base acknowledgements boltzmann stability vertical explicitly coordinates physical physical remaining develop integrated equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium springer springer shift john john independently dependence stationary stationary stationary influence detailed densities densities densities densities densities densities densities densities densities densities densities densities densities evaluated evolution evolution evolution evolution forms understanding suggested updates updates sign sign sign sign sign earlier slow classical expansion expansion expansion expansion expansion expansion normalization normalization reduces reduces neighborhood closed closed valid calculate kohonen kohonen topology expect includes discuss variations suitable delta delta literature literature identity compact notice notice verlag verlag repeated strongly interested strategies satisfy satisfy gibbs gibbs giles extend cowan minimized origin powerful xor xor collection updating steady hanson hanson divergence hall biol analytically proper math coefficient algo algo expressions academic art consist defines optimum integrate integrate histogram formula publishers publishers publishers unstable phenomena phenomena analytic analytic analytical diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion tractable satisfied satisfied satisfied forces leaves mation scientific involve nsf mellon fluctuations exemplars mechanics fourth carnegie led cmu transient transient transient lms lms lms lms lms lms lms lms lms lms lattice formulated treated sharp berlin berlin pittsburgh differs progress progress june summed summed summed summed instantaneous contribute initialization newton indices cybern leen leen leen leen leen leen leen leen leen leen leen leen leen leen restrict rithm arguments drift drift drift drift ordering tensor theories exemplar exemplar proceed numerically convenient tools tools tools odd moment balance mark prentice slice studying von conjunction facilitate schedules chooses tic ensembles express master properly implicitly grants grants characterization displacement onr onr schulten schulten schulten truncated kluwer basin axe isotropic expanding classic breaking realize assess remainder avoids increment rithms graduate convert inverted expand afosr spreading spreading paris stuck det transients oregon gauss ritter ritter ritter fiat neumann simplification august thermal thermal todd todd todd cliffs suffers focuses settle englewood vanish orr orr orr orr orr orr orr orr planck planck planck planck planck planck planck planck planck planck planck sis edition gence handbook appro eigenfunctions generaliza equilibria equilibria equilibria equilibria equilibria simon tails rij rij schuster spots kolmogorov kolmogorov kolmogorov sition quadrature tran decrement conver ecs fokker fokker fokker fokker fokker fokker fokker fokker fokker fokker fokker insure stochas smear trivially kramers kramers kramers kramers kramers backpropaga cot appeal bij bij bij dropping recipes owi owi exemplified teukolsky flannery ivl sumption diffusive haykin haykin vetterling eventual factoring dirac spherically beaverton plateaus plateaus phi phi genevieve genevieve companion hopping anisotropy gaussi truncate vmues werner lipmann mong curiously sthe 
#@Leen_T,Moody_J,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural data data data data data function function function function function set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number error error error error error results results results results results results results results results results results results results results results units units information models models hidden hidden hidden hidden hidden based based weights weights weights linear linear linear layer layer layer case vector vector order order order shown shown systems values probability probability probability weight weight weight functions functions distribution pattern pattern single single single processing large local local local local local local local local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate matrix matrix matrix matrix matrix matrix inputs inputs inputs form algorithms algorithms simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper examples examples examples examples small small small small small small small small size net net work methods methods points process process process process process process process process process process process process process process process process process process process process process trained trained structure random random show show show show show show equation equation equation equation section section section fixed general parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation gradient gradient gradient gradient gradient gradient gradient term term term note dimensional result result result result variables computation solution solution solution solution solution research independent independent defined defined found sequence dynamics constant constant constant constant constant constant constant constant constant constant constant constant constant estimate standard direction present activation activation sets motion basis outputs continuous continuous continuous continuous continuous continuous abstract back convergence convergence convergence convergence convergence convergence properties properties properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due ieee adaptive propagation introduction statistical generated variance difference difference difference difference measure chosen part part part part part part theorem theorem theorem theorem theorem theorem theorem theorem theorem type required long long long conditions conditions expected expected expected expected fact region observed minimum sum elements mapping means optimization made knowledge original artificial application provide provide provide provide define define define define define define rates rates distributions discrete discrete discrete equal approaches contrast update update descent dependent dependent selection morgan version version represents represents final final exp considered considered experiment experiment directly directly limit limit limit limit limit limit limit limit limit limit limit san requires approximate statistics speed increase give con produce condition derived derived randomly developed bounds bounds bounds product product actual finally processes processes processes processes backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature covariance covariance covariance feedforward feedforward feedforward denote close corresponds proof proof proof proof proof proof proof rbf rbf generate require ability development kaufmann pairs character special structures uniform empirical details numbers making denotes denotes denotes 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thesis coordinate batch batch batch batch batch batch batch batch batch batch batch batch batch discuss wij literature literature situation situation essentially identity ten verlag repeated induced allowing sin sin follow notation notation hypotheses hypotheses hypotheses consisted decreasing law body parametric parametric requirements investigate exponentially fashion rest applicable combine combine comparable tanh necessarily versions portion noted noted noted improving finds defines averages trivial growth derivation phenomena diffusion diffusion diffusion diffusion diffusion diffusion diffusion worse reasons perspective sections ring widely producing products consequence recognized calculations preceding fluctuations fluctuations fluctuations robustness empirically empirically conducted fed documents backprop continuously rep variant ture ture limiting incorporating sums sums sums sums germany attraction deviations accomplished darken darken siemens held star definitions weakly 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#@Finnoff_W,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data function function function function figure figure figure set set set set set set set networks networks networks networks networks networks networks algorithm output number number error error error error results results results results results results problem problem problem based based based based based based weights linear case case vector vector vector vector vector vector vector vector vector shown shown shown shown shown shown systems values values parameters weight weight functions distribution distribution distribution recognition approach approach approach approach approach approach approach approach approach pattern image processing large large local local neuron rate rate rate analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix form shows algorithms algorithms algorithms algorithms simple simple paper paper paper examples small small feature work fig fig fig fig fig points points points points field field current problems random similar similar similar show show fixed line line line line line rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general generalization real real approximation approximation average average average theory theory gradient gradient gradient obtained obtained obtained obtained obtained obtained obtained term note experiments experiments experiments experiments experiments dimensional dimensional dimensional result result university university threshold computation constant computer terms direction direction present present present press press components components components sample sample sample abstract applied find likelihood references component component component component component component component component component component component component component component component component component component component stochastic stochastic ieee procedure important adaptive decision decision mixture introduction estimation estimation statistical statistical statistical statistical statistical statistical statistical statistical variance variance change energy energy energy energy energy energy energy energy energy energy energy energy difference variable rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules chosen chosen cases type type good binary binary conditions conditions bayesian techniques techniques proposed proposed proposed proposed proposed correct correct correct correct observed errors errors finite minimum minimum ing ing tasks tasks tasks sum eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq called factor factor factor factor made made natural natural global applications samples samples samples samples application define compute proc perform experimental related related related related distributions brain equal steps steps accuracy comparison contrast fields support descent descent descent nets nets selection institute version technique considered framework cambridge cambridge equivalent directly curve additional solutions curves curves curves curves limit choice choice significant statistics statistics vision estimated produce randomly developed types biological increases denote denote denote denote denote assumption finding finding finding effective effective square including including smaller smaller technology significantly significantly special principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal attention minimize minimize denotes population improve improve robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust separate lateral introduced sense sense sense sense cognitive recently recently previously previously conventional approximately axis axis axis correspond pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca studies converge converge trans address modified generalized generalized horizontal studied studied suggests alternative deterministic column critical hebbian performs practice temperature propose taking presence presence physics physics physics physics physics physics physics largest largest turn variety minimizing minimizing minimizing minimizing minimizing exist plane plane minima annealing force reference solving solving solving vertical dept dept easy easy angle angle develop applying minimization extraction decreases yield reconstruction squares interpretation detailed organizing organizing organizing organizing organizing organizing organizing organizing organizing centered partition convex fitting existing existing existing existing existing existing priori priori priori formulation subspace subspace subspace subspace subspace subspace subspace batch sciences sciences extension prove specifically compression closely capable literature literature literature projections success sin satisfy gibbs gibbs list generalize generalize generalize generalize minimizes eigenvalue satisfies origin essential relations detail estimators estimators replaced issues issues mass ml int hill math math naturally adapt reading versions versions versions versions portion portion portion portion observe extent massachusetts mentioned residual residual track implementing purposes closer ring widely division located mathematics ion acknowledgement angles angles cybernetics improvements considerably axes poorly introducing treated outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers maintain span asymmetric sophisticated yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille wesley lot saddle addison formally angular acts air consideration oja oja oja oja oja oja oja oja oja oja oja oja oja satisfying multiplicative obtaining obtaining sanger sanger sanger modifications performances performances performances performances ensures connect regarded regard infinity yang darpa indicator eqs eigenvector papers 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#@Xu_L,Yuille_A,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input input data data data data data data data data data data data data data data function function function function figure figure figure figure figure time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output number number system system error error error error error error error error error error error error error state state state results results results results results results results results units units units problem problem problem problem problem problem problem models models hidden hidden hidden hidden hidden performance performance performance based based space space space space weights weights weights weights weights weights weights weights weights linear case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown systems values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method approach approach approach approach point point point single single single large large large test test test test test test test test test test test test test test test test test optimal optimal optimal inputs inputs inputs form shows shows shows shows shows simple gaussian gaussian gaussian gaussian small size size size size size task methods methods methods methods methods methods methods fig fig fig fig fig fig fig fig step step step step step step step points points level problems random random random random high architecture show equation fixed line vectors vectors vectors vectors vectors vectors vectors vectors general general generalization parameter parameter parameter real real real real approximation approximation average average average average gradient obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained term term term term note note university university computation computation solution log log defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant constant constant constant estimate estimate standard standard standard standard standard standard computer computer terms terms science science prediction prediction prediction prediction prediction phase phase phase low low machine sets maximum maximum range learn position components outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs sample sample sample sample sample sample sample abstract back find find find find likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due procedure propagation complex statistical effect tion tion tion tion change change change change energy energy energy energy energy energy assume assume prior prior prior prior prior chosen chosen chosen chosen part theorem bound cases cases cases cases cases cases cases required good good good good long long distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations markov markov markov techniques region correct probabilities probabilities probabilities observed observed observed errors errors scale scale scale scale scale simulations simulations minimum simulation simulation computed computed sum regions regions mapping factor factor potential potential potential made obtain obtain obtain obtain vol vol vol vol vol true true true desired cross provide define define rates determined posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions discrete equal steps steps steps steps steps steps steps steps steps steps larger larger connection dependent dependent modeling department loss individual joint joint difficult difficult difficult final exp exp exp exp exp exp bias bias bias bias bias bias bias scheme framework computing equivalent equivalent equivalent view solutions limit trajectory top full choice approximate free validation validation validation validation validation validation validation give give give give give give give con con derived randomly randomly randomly conditional robot robot lines lines lines lines actual selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration sampling sampling increases increases group tested tested fast close close corresponds corresponds surface surface predictions predictions predictions finding finding amount assumed require journal journal end future degree degree fit fit objective objective probabilistic probabilistic smaller needed dynamical dynamical unknown unknown testing uniform mode leads squared squared squared squared squared details iterations iterations iterations iterations iterations iterations iterations iterations iterations pre early early early early decay decay decay decay decay decay decay decay decay minimize minimize produced produced choose run run run run run run run run run run run added light discussed improve exact advantage robust separate separate separate separate practical practical apply introduced introduced introduced introduced include machines inference inference interest dimensions conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional approximately approximately volume tions tions tions achieve achieve chain chain chain chain grid increased arm arm lead lead invariant deviation deviation deviation deviation hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hardware runs runs runs runs runs starting greater trajectories trajectories valued valued valued valued competitive bayes temperature taking integration physics physics physics drawn sigmoidal solid solid assuming averaged question monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo factors factors factors dept category category category category averaging averaging slightly consisting predictive predictive select letters independently stationary stationary stationary stationary stationary solved variation evaluate evaluate sizes converges constants constants constants constants constants dashed performing reduces valid initially initially avoid avoid avoid expect inter weighting batch batch uncertainty uncertainty candidate priors variations identified importance uniformly included mackay mackay mackay mackay mackay reached repeated anderson stopping split sin sin categories categories sampled minimizes highest reach reach attempt attempt consisted consisted subsequent approximating approximating explore simpler unlike poor overfitting overfitting overfitting create integral integral dotted dotted giving giving comparable proper affect momentum momentum analogous analogous circles plausible aspect quantities portion portion consist generates finds defines neal 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#@Neal_R,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input function function function function function function figure figure time set set set set set networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number error error error error error error error error error error error error error error error error results information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem models performance performance performance space space space space space space space space space space space space space space space space space space space space space space space space space space space space space linear case case case case vector order shown shown shown systems values probability probability probability probability probability probability probability probability probability probability probability functions functions functions functions functions functions functions functions functions functions functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method point single processing large large test analysis class class class class class class class class class class class class class class class optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small size size net work work work work work work work work work methods trained problems problems problems problems problems problems problems problems random random random random random random random random random random random random random random random random random random random high high high high high high high high high high high high high similar similar show show show show show show section section section section section section section section section section section fixed fixed fixed rule general general general general generalization parameter approximation approximation average average theory theory theory theory theory theory obtained obtained experiments experiments dimensional dimensional result result result result result university university university university computation research research independent independent log log defined defined defined found found sequence sequence sequence target target target constant constant constant computer computer computer terms distance science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left direction direction present present low low low low low low low low low low machine press learn learn learn basis continuous sample sample abstract applied computational computational computational density density references component ieee positive positive positive positive positive positive positive positive positive important adaptive decision decision introduction complex complex statistical change complexity assume assume lower lower lower lower lower lower lower lower lower lower lower lower measure measure prior prior prior prior prior prior learned chosen chosen chosen chosen chosen chosen chosen part part center previous previous theorem theorem bound bound bound bound bound bound bound bound bound bound bound type type required required required good conditions distributed bayesian bayesian bayesian bayesian bayesian expected expected expected expected expected expected expected expected expected expected expected expected expected expected fact fact proposed correct correct probabilities probabilities finite finite finite finite resulting classes classes classes classes ing ing respect respect respect multi eq called called called mapping dimension dimension dimension dimension dimension dimension dimension made made study em filter filter filter filter filter filter negative negative specific specific cross provide define define define define define determined experimental goal goal posterior posterior posterior posterior posterior gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain equal equal power power power power larger contrast contrast support proceedings proceedings institute institute institute words version version version version version version version version version version version version version version version version version version version version version version version version version version version version consists consists advances connectionist exp framework equivalent equivalent experiment experiment additional additional curves design design limit limit san san bit bit bit upper upper full choice free pages pages pages give con con derived derived derived randomly randomly bounds bounds bounds area types product product provided provided depends sampling discussion normal normal normal normal feedforward increases increases increases group tested fast fast close assumption assumption corresponds complete proof proof common assumed assumed shape main main square ability hypothesis future makes noisy kaufmann kaufmann pairs reduced functional unknown technology transfer ratio york york consistent consistent consistent uniform uniform uniform uniform uniform uniform uniform details filters filters pre bits bits supervised polynomial minimize denotes denotes architectures discussed improve exact exact takes typical strategy dimensions varying teacher teacher teacher teacher teacher teacher calculated volume volume volume axis axis smooth smooth smooth smooth smooth achieve trans bounded bounded bounded bounded bounded interval interval grant constructed 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learner learner learner learner learner learner learner learner learner learner learner learner learner learner detailed open open open labels labels fraction centered understanding understanding understanding suggested suggested suggested converges expansion spaces spaces spaces convex convex convex convex convex convex convex add remains filtering filtering filtering filtering filtering filtering calculate symbol construction construction construction construction foundation query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query query thesis coordinate coordinate bell batch sciences prove prove discuss holds holds discussions tests successfully selecting uniformly maximal maximal committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee literature literature mackay reached receives summary summary kind contained split manifold gibbs gibbs gibbs gibbs gibbs gibbs gibbs paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm paradigm realistic hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses received attempt illustrates acknowledgments decreasing decreasing body body body body body origin layered access access exhibit exponentially exponentially exponentially exponentially rapidly rapidly game game game game game game game helpful fewer rest rest applicable analytically comparable stream stream stream proved workshop workshop workshop analogous hill smallest math naturally concepts concepts necessarily necessarily analyze analyze automata created queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries mapped perceptton perceptton academic art amari improving phd defines inequality trivial guaranteed failure expensive baum lin lin organized strictly filtered precisely constructing constructing hyperplane hyperplane mation mation laboratories cut members members lowest depicted geometry annual annual annual radius radius integrating argument fourth questions questions behaviors applies relevance axes fed fed haussler ity fall cal cal cal pasadena achieves achieves achieves achieves enables yielding instantaneous cumulative cumulative cumulative cumulative cumulative cumulative naive gap gap pac pac pac pac mistake restriction fix acm acm acm ratios pick member member member hyperplanes murray convenient stronger stronger accepted accepted accepted tishby tishby tishby tishby tishby tishby tishby unlabeled unlabeled unlabeled unlabeled constructive constructive constructive planar games infor infor repeat published utilized sompolinsky contexts governed governed schapire corre infinity chooses chooses chooses israel membership membership surprisingly warmuth kearns informative informative draw seung seung seung seung seung seung seung seung statement statement santa generalizing receiving ball ball learnable learnable consecutive consecutive logarithm logarithm entropic constitute pointing accept basically asked preserving opper opper generalizations freund freund freund freund freund freund avoided valiant valiant avoids argue perpendicular intuition formance gained shannon realizable annealed thresholded thresholded thresholded rectangle rectangle rectangle concentrate maximally sketch constructs placing vanishes parametrized behaves behaves spite suggestions suggestions learners learners learners learners sponding sees inconsistent jersey cornput eliminates inefficient cones arrives concave concave nontrivial nontrivial rivest rivest statist comm randomness remained cruz cuts cuts tained atlas noiseless ceedings 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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure time time time time set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output system error error error error error error error error error error error error error error error error state results results results results results results results results information information information problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based space weights weights weights weights weights weights weights weights weights weights weights weights layer layer case vector order order order shown shown shown shown shown shown shown systems values values probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise 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term term term term term term term term term term term term term term term note note experiments experiments dimensional result result university university solution solution research target dynamics constant table table standard terms terms terms terms terms terms terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node node node science prediction prediction phase phase low nodes nodes nodes nodes nodes nodes sets sets sets press learn position basis outputs abstract back convergence convergence density analog analog analog analog analog properties properties references stochastic stochastic ieee ieee important propagation context introduction complex statistical effect effect effect effect effect cost cost cost cost cost tion tion change classifier classifier classifier lower lower lower representations chosen higher higher binary long distributed distributed equations chip errors forward simulations simulations simulations simulations simulations simulations simulations simulations simulations minimum resulting resulting ing ing tasks simulation simulation simulation simulation simulation multi times times means made made natural applications applications study negative vol vol vol vol vol vol vol artificial location perform eye eye eye eye eye eye eye eye eye eye eye eye eye eye connected contrast connection update update update train source implementation version version synapses synapses synapses synapses synapses technique technique internal code final domain additional additional additional solutions solutions solutions solutions estimates trajectory trajectory trajectory trajectory trajectory trajectory effects bit full free world world vision increase levels levels levels levels levels levels levels levels area actual provided selected backpropagation backpropagation nature nature depends simply simply biological measured increases tested tested surface predictions predictions predictions predictions predictions circuits finding generate vlsi ability ability ability ability ability ability ability ability ability ability ability ability ability noisy noisy smaller underlying combination combination reduced reduced reduced account mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp character character character character character character character character consistent uniform early early magnitude magnitude produced produced added added description light perceptron perceptron perceptron perceptron improved improved improved property robust robust takes typical introduced include pixels engineering engineering engineering highly previously approximately calculated tions achieve trans trans improvement improvement entire entire increased increased increased increased increased increased increased increased increased lead studied wide derivative derivative derivative derivative derivative correctly feed locally hardware conclusion place reduce reduce sigmoid clear clear clear faster faster constrained suggest taking reduction characteristics characteristics characteristics demonstrated proportional start start averaged averaged targets targets derivatives manner characters acknowledgements factors plot mathematical mathematical mathematical distinct distinct dept dept multilayer multilayer electrical electrical involves adding quality quality implies letters dependence stages correlated viewed influence detailed updated forms sizes sign earlier smoothing epochs epochs epochs expansion expansion expansion reduces add penalty penalty penalty valid valid classified classified existing variations variations straightforward straightforward effectively driven delta delta schemes tend tend tend quickly graphs dis issue issue classify highest thresholds software presents carried carried perturbation perturbation perturbation perturbation perturbation perturbation rapidly put involving detail hanson hanson hanson hanson behaviour rise giving biol 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proportion extensive perfectly perfectly encoder encoder encoder encoder encoder encoder encoder enhancement enhancement enhancement enhancement exemplar turned spontaneous murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray consideration promising overcome held held balance ral implications optimally enhanced enhanced enhanced constructive degradation degradation meaningful financial ranging loo displayed expanded expanded expanded injection injection injection injection injection injection evident sim competing tic infer infer infer ahead augmented augmented verification verification passing ignore avoiding verify verify verify dramatically leaving largely outline visually super emerge expanding incrementally smoothly medium acceptable edinburgh edinburgh acting unseen unseen increment ijcnn faults faults faults relate mediated mediated mediated mediated altered projecting noting importantly electronics grateful stuck 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#@Edwards_P,Murray_A,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure time set set set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output state state results units information information information information information information information information information information information information information information information information information information information information information information information information information hidden hidden based based space space space space space weights weights linear linear linear layer layer layer layer layer layer layer layer case case vector vector vector vector vector vector vector vector vector order shown values values probability noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons unit distribution recognition approach approach pattern image single single single single single control large large large local local local neuron patterns patterns patterns patterns patterns optimal inputs inputs inputs inputs form shows shows shows algorithms simple simple gaussian gaussian gaussian gaussian visual small small size size feature feature feature feature net net net net net net net net net net net net net work work work work methods methods methods features process trained problems random random random random high high response architecture line line rule rule rule rule rule rule vectors images general generalization real average average theory gradient gradient gradient gradient gradient gradient obtained term note note experiments activity activity activity dimensional result university computation computation solution solution research research independent log log log dynamics dynamics dynamics initial initial initial initial initial initial estimate estimate standard computer computer node node node node node node node node node node node node node node node node node node science prediction direction direction direction direction direction present present phase phase phase nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency sets press learn nonlinear nonlinear outputs abstract back back computational references component component component component due ieee positive positive important important adaptive mixture mixture mixture introduction complex estimation behavior behavior effect dynamic variance cost search change change change change change difference variable variable variable rules prior prior representations center center previous multiple cortex binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary conditions conditions conditions conditions conditions make make techniques region region correlation length scale resulting resulting resulting respect respect respect multi multi means optimization optimization optimization optimization optimization optimization made orientation applications study knowledge knowledge negative negative relative provide perform active goal related related posterior distributions distributions distributions gain gain gain gain gain gain gain gain gain gain gain gain gain gain equal mit contrast contrast update source institute technique technique technique joint represents final final bias bias framework framework framework cambridge equivalent experiment experiment hinton hinton curve additional solutions curves curves design san san san detection conference efficient efficient significant approximate world estimated estimated pages pages condition weighted lines lines entropy entropy product actual actual evidence backpropagation nature biological achieved discussion covariance covariance increases tested limited common implemented supported require face adaptation adaptation journal journal journal instance cluster future degree makes makes makes development objective objective probabilistic smaller smaller needed reduced fully mechanism empirical principle principal principal principal principal details max pre pre pre international produced sources sources predict denotes improved directions directions robust robust separate lateral lateral lateral strategy identical identical sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive sufficient highly highly highly varying unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised volume yields speaker studies converge achieve achieve address symmetric modified observation observation organization entire expression lead suggests extended extended derivative derivative derivative derivative clusters clusters clusters clusters clusters setting demonstrate demonstrate half half half starting critical critical place minimal hebbian operator operator editors central central sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid performs performs exponential suggest integration demonstrated demonstrated california solid proportional derivatives manner force denoted acknowledgements derive derive produces longer factors plot plot plot plot plot laboratory stability mathematical mathematical dept confidence implement implement explicitly explicitly averaging averaging easy text interaction interaction mutual minimization minimization extraction competition extracted reconstruction estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator interpretation interpretation interpretation codes controlled organizing approximations soft completely similarly suggested discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination reasonable slow expansion purpose intermediate initially sufficiently degrees existing perceptual batch batch batch batch batch extension plotted maximize maximize maximize maximize priors discussions successfully successfully straightforward straightforward aspects aspects aspects aspects efficiency closely capable society maximal projections projections projections vowel vowel essentially orthogonal orthogonal success anderson anderson anderson anderson neuroscience neuroscience dis running running dot dayan reach maximization remain selectivity selectivity diego diego diego access involving estimators estimators estimators replaced limitations discriminant discriminant discriminant helpful respond combine office maximizing maximizing maximizing maximizing presynaptic notion notion surfaces coefficient necessarily illustrate equally ensure front front greedy logistic precise hebb utility isolated averages preference theoretic trivial derivation derivation derivation biology nowlan nonlinearity nonlinearity tive preprocessing implicit localized patches linsker linsker depicted summation improvements greatly understood flexible peter introducing share remove maximizes resource incorporating plan asymmetric asymmetric coherent redundancy unbiased unbiased utterances traces gap proportion cooper cooper zemel discover naval eliminate flexibility flexibility eliminated extending extending binocular saturation convenient attractive grow neurobiology observing observing splitting splitting salk generalizes vowels vowels vowels becker becker ensures appendix appendix appendix regarded ascent ascent ascent ascent ascent ascent demonstration peterson peterson peterson shortest jolla repeatedly rich specificity informative informative storing formant splits discovered infomax discriminate discriminate informa incorporates munro munro munro munro gaps gaps responds tween distinction smoothly intrator intrator superimposed superimposed clustered clustered clustered clustered clustered adapting factorial favor schmidhuber schmidhuber gained gained gained gained interacting terrence eliminating relate emphasize selectively preserve happen meet indication simplifies mix vice ucsd ucsd picking picking versa fortunately stimulating bienenstock bienenstock bienenstock saturated saturated mcdonnell utilizes aid bcm bcm acoustical evenly evenly evenly settle separates preservation heterogeneous concert carries substitution squashing occam occam maxi america complement unlabelled unlabelled asset amplified accommodate adapts relaxed steve scatter scatter baltimore prominent discovers discovers proceeding rent rent discriminating schraudolph schraudolph schraudolph schraudolph rotate pew severely demanding quantified aims lid alization respects stereograms reminiscent volatile nonlinearly seeking seeks serving bimodal bimodal barney barney barney conveniently razor razor dictated discriminations discriminations discriminations tributions discarding weakened flanking flanking neurocomputing disparate predictability predictability predictability discriminants discriminants discriminants discriminants discriminants eft rosenfeld rosenfeld biometrika refinements lib reprinted ita anticipated anticipated backpropagating deemed centering recoding recoding collapsing discriminator mizing escapes engr timescale commitment weakest ctive graphed confidently nici 
#@Schraudolph_N,Sejnowski_T,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural input input input input data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm output output system system system system error state results results results results results information information problem problem problem problem hidden performance space space space space space space space space space space space space space space space weights weights weights weights weights weights weights case order order order order order shown shown systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight distribution distribution distribution distribution single single processing processing large large large local local local local local local local local local local local local local local local local local neuron rate rate rate rate rate rate rate patterns optimal inputs inputs form shows shows shows shows shows shows shows algorithms algorithms algorithms simple simple simple gaussian paper paper paper examples examples examples examples examples examples examples small small small small work methods step step step step step process trained trained problems problems random random random random similar show show equation equation equation equation equation equation equation equation equation equation equation equation section section section line line line rule vectors approximation approximation approximation average theory theory theory gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained note note note dimensional dimensional dimensional variables variables computation computation solution solution solution research independent sequence target target dynamics dynamics dynamics dynamics initial initial initial constant constant constant computer terms terms distance science science direction direction map motion motion learn learn sample sample sample abstract back find computational convergence convergence convergence convergence convergence density density density density density density density density density density density density density density density density density density density density density density density properties properties references component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee important propagation hand behavior behavior statistical statistical statistical cost cost cost cost cost cost cost search search search search search search tion tion difference variable assume chosen higher higher center required required required required required required required good spike spike markov region region forward finite simulations simulations simulations ing ing simulation times times times times times times times times times times times times times times times times optimization dimension dimension global global global global global global global global global global global global global global study study obtain obtain obtain obtain artificial true true true true true application cross series series series provide provide rates rates location experimental distributions distributions power power larger contrast contrast update update update update update descent descent descent descent descent descent descent dependent nets selection morgan morgan institute department advances advances joint final maps maps framework framework transition transition transition san san top effects conference conference upper full significant estimated pages give give condition condition lines entropy path path path finally finally finally finally selected backpropagation backpropagation backpropagation iteration iteration iteration iteration iteration simply simply measured discussion discussion discussion denote denote complete stable predictions predictions predictions predictions supported theoretical theoretical theoretical theoretical theoretical theoretical theoretical theoretical eds makes noisy noisy kaufmann kaufmann simulated simulated simulated pairs coefficients fully technology principal iterations direct direct making international international supervised supervised supervised supervised early frame frame frame added description predict predict recent exact exact exact ensemble ensemble ensemble ensemble takes apply subject engineering compare compare unsupervised calculated calculated volume solve converge differential expression invariant occur predicted predicted feed move move width white white occurs boundary boundary pass pass pass pass pass place assumptions reduce competitive competitive competitive competitive competitive numerical numerical moody moody moody moody moody moody asymptotic asymptotic mateo mateo integration integration integration solid targets minima minima configuration annealing acknowledgements monte construct carlo describes stability averaging remaining remaining integrated equilibrium minimization springer shift shift john john expressed dependence stationary densities densities densities densities densities densities densities densities densities evaluated evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution frames frames converges expansion expansion neighborhood valid intermediate initially calculate calculate kohonen topology expect subspace batch batch characterized straightforward uniformly delta invariance verlag induced dis simplified backward backward backward giles satisfies intrinsic decreasing decreasing cowan remain poor xor xor xor xor xor xor xor xor xor hanson graphical graphical graphical examine biol office proved understand notion notion removed math math coefficient coefficient necessarily analyze analyze illustrate academic initialized initialized initialized initialized initialized initialized switching contributions optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum asymptotically histogram histogram slowly agreement agreement publishers publishers track phenomena phenomena biology diffusion diffusion handle drive tive formalism formalism widely leaves mation recognized fluctuations exemplars integrating integrating integrating questions transient parameterized passed passed passed passed dots dots berlin focused cybern leen leen leen leen leen leen leen leen leen leen drift narrow naval exemplar fails oja oja numerically darken darken logarithmic held stated height obtaining intuitive corner substituting substituting excellent started slice slice governed sion von expanded schedules schedules tic ensembles infer reader arrive late passing concentration grants summarize summarize receiving escape escape escape schulten ple ple minus ent basin basin basin basin basin basin ties expanding theorems theorems superimposed superimposed basins basins verified exam distribu approxi mathematically graduate crosses rectangle rectangle spreading paris sam siam transients travel subspaces oregon ritter ritter neumann sees agrees todd todd todd recursion recursion recursion optima optima optima optima optima optima optima optima optima optima optima optima settle peaked ultimate orr orr orr orr orr orr orr orr complement planck planck planck planck planck planck planck planck planck planck appl constraining handbook brackets dence spa equilibria equilibria degrades derivations schuster 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#@Leen_T,Orr_G,
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#*network network network network network network network network network model model model model model model model neural neural input data data function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time networks output number number state state state state results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem models models performance based based based case case case case case case case case case case case case order order shown shown shown shown shown shown shown shown systems probability probability probability probability probability noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit method method method method point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point single processing large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis visual paper small small work methods level structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure similar similar equation line line line line line line real real states states theory theory theory theory theory theory theory obtained obtained obtained obtained obtained obtained obtained obtained obtained activity dimensional university research research research independent independent log log defined found found found found dynamics dynamics table table table table connections synaptic synaptic synaptic synaptic synaptic science presented temporal temporal maximum press press nonlinear abstract find find references due positive positive positive positive positive positive positive positive positive procedure procedure procedure introduction action action action action action hand circuit estimation estimation estimation estimation estimation effect tion measure cases firing firing firing firing firing firing multiple cortex cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long long expected equations equations equations equations techniques techniques region proposed correlation correlation correlation probabilities simulations ing total total simulation simulation performed means potential potential potential potential potential study negative negative negative negative negative negative negative relative represented represented true compared application application perform determined experimental experimental related connected discrete equal mit steps connection connection connection connection connection connection connection dependent modeling synapses technique technique difficult difficult delay delay graph sequences ai ai ai ai ai considered considered considered considered considered directly bit bit detection capacity capacity capacity capacity capacity determine determine significant significant significant estimated give give produce condition condition channel channel channel channel channel channel conditional conditional conditional conditional conditional bounds bounds lines processes processes inhibitory inhibitory measured discussion describe limited limited corresponds corresponds complete excitatory finding amount amount effective effective future including simulated simulated simulated simulated combination combination reduced transfer mechanism consistent structures structures produced description neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal denotes discussed pair pair reported practical apply previously conventional calculated trans channels sensitive occur spikes spikes strength strength strength strength central central central central measures peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak weak encoding variety plane relationship iii iii iii iii iii iii manner connectivity connectivity connectivity connectivity identification suppose laboratory laboratory laboratory mathematical simultaneously unique consisting consisting interaction mutual mutual mutual mutual mutual mutual mutual integrated potentials depending communication overlap codes modulation understanding completely similarly similarly calculation calculation calculation delays delays delays delays delays delays delays koch koch existing figures usa bell phys major major major efficiency presentation trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains carried powerful powerful difficulty circuitry relations detail issues graphical graphical existence postsynaptic postsynaptic successive applicable biol biol biol biol working statistically statistically presynaptic neu transmission quantities quantities quantities quantities quantities multivariate contributions submitted theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic theoretic distinguish agreement fairly briefly tool shared easier calculations author apparent quantitative peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks calculating characterize electric electric electric proposition cybern cybern japan investigation extensive impossible interconnected interconnected interconnected difficulties difficulties primate overcome interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection interconnection analyzing inferior published utilized interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections interconnections yang yang omitted offer reverse 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#@Matsumoto_K,Nakashima_M,Shiono_S,Yamada_S,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural input input input input input input input input input function function function function function function function figure figure figure figure figure figure figure figure figure figure time set set set networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output number number number number number number number system system system system system system error error error error error error error error error error error error error error error error error 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weight weight weight weight weight weight functions unit unit unit unit unit distribution method method approach approach approach approach approach pattern point point point point point single processing large large large large large large large large large large large large large large large large large large large large large local inputs inputs inputs inputs inputs form form form shows shows shows shows shows shows shows shows simple simple simple simple simple simple simple simple simple simple examples examples examples examples examples examples examples small small small small small small small small small small size size size net net work work points process level level trained high high high high similar similar similar architecture architecture architecture architecture architecture architecture architecture section section fixed line line line line line line line line line line line line line line line line line rule rule vectors vectors vectors vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter approximation approximation approximation approximation approximation average average average average average average states states theory theory theory obtained obtained obtained obtained term term note note note dimensional dimensional dimensional solution solution solution solution solution solution solution solution solution solution solution research defined defined found found found found found target target initial terms science science left present present phase phase phase phase phase phase phase phase phase phase phase low low machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets sets sets sets sets sets sets outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied find find find find properties references stochastic stochastic due procedure procedure decision decision introduction behavior behavior behavior behavior statistical statistical statistical statistical statistical statistical generated tion energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference lower rules measure higher previous previous previous cases cases good good good good binary binary binary binary binary binary binary binary binary binary binary binary long long tree tree tree tree tree tree tree tree tree equations make make region region region region region correct finite finite finite finite finite simulations simulations simulations simulations simulations simulations simulations simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum total total simulation performed performed called times regions factor made natural global global global global global applications study study study obtain negative compared compared compared compared compared cross receptive receptive receptive location connected connected connected connected connected connected connected connected discrete approaches comparison larger contrast contrast fields fields fields fields support support nets morgan institute version individual advances framework curve additional additional curves transition transition transition transition transition transition transition transition transition transition limit limit limit limit limit limit limit san capacity choice free free free free free free free free free free free free free free free world weighted lines entropy entropy path finally simply achieved technical arbitrary close corresponds corresponds corresponds corresponds corresponds complete predictions predictions common implemented assumed shape theoretical square ability ability ability easily degree including including including including kaufmann fully fully fully fully fully fully fully fully ratio york increasing operation leads details details normalized perceptron perceptron perceptron perceptron perceptron perceptron perceptron correlations correlations correlations exact reported practical include include subject machines machines sufficient previously teacher teacher teacher teacher teacher teacher calculated works smooth yields yields yields yields yields yields match achieve address locations locations symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric entire increased increased increased increased studied wide correctly loop occurs occurs occurs runs starting critical critical critical assumptions assumptions moody asymptotic asymptotic mateo temperature temperature temperature physics solid solid solid solid solid solid proportional assuming minimizing exist averaged averaged averaged appears monte monte monte monte carlo carlo carlo carlo laboratory transitions transitions student student student student student student implement linearly linearly mutual equilibrium boolean john yield dependence review review overlap overlap overlap influence solved evaluate restricted partition sign diagram diagram calculation calculation calculation calculation dashed dashed dashed dashed performing performing remains remains remains valid initially calculate sufficiently expect priori usa perceptrons perceptrons phys phys phys phys phys phys committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee situation receives allowing symmetry symmetry symmetry symmetry symmetry symmetry sin sin gibbs involved leading deal load load load load decreasing decreasing receive remain poor poor poor poor poor exhibit exponentially replaced hanson integral lippmann dotted dotted dotted dotted dotted dotted existence parity possibility hill predicts rev rev rev rev perfect perfect perfect perfect perfect der formal freedom expressions arbitrarily defines spin asymptotically residual indicating slowly ground separable separable agreement analytic analytic analytic majority majority correction starts scientific acknowledgement calculations calculations calculations gradually qualitative qualitative mechanics mechanics mechanics mechanics mechanics mechanics mechanics limits tional quantitative poorly poorly share adjustable adjustable incorrect compares calculating exhibits exhibits exhibits exhibits ture cal extensions qualitatively qualitatively decreased implements yielding phenomenon picture uncorrelated saddle saddle saddle saddle restriction perfectly 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gardner gardner percep replaces metastable metastable metastable metastable metastable metastable metastable hysteresis ansatz translational schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze europhys europhys europhys biehl singapore analogously barkai barkai barkai barkai glasses engel engel recep contin copenhagen copenhagen bohr disappears accompanied specialize uous parga parga parga ger nonoverlapping nonoverlapping nilsson nilsson nimh blegdamsvej blegdamsvej danish danish bethesda propor transi kinzel freezing freezing differen derrida tron neuropsychology algebraically arccos arccos rau agreements programme niels lnz nonvanishing culated misclassifying 
#@Hertz_J,Schwarze_H,
#t6
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#*network network network network network network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural data function function function function set set set set set set set set set set set set set set set set set training training algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system error results results results results results results results information problem problem problem problem models models performance performance based weights weights weights weights case case case order order order order order order order order order order order order order order order order order shown shown shown values values values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability weight weight functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method approach approach pattern pattern pattern pattern pattern single processing large rate rate rate rate test test test test test patterns patterns patterns class class class class class class optimal form form shows shows simple paper paper paper work work work task methods methods classification classification classification classification process random random high memory representation show show show show equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation general parameter real real real approximation approximation approximation approximation approximation approximation average states states states theory theory gradient gradient obtained obtained term term note result result result result result result university university variables solution solution research independent independent independent defined defined defined constant table table table table estimate estimate computer terms science presented presented presented presented present low low frequency machine machine machine machine machine machine sets maximum maximum maximum press outputs sample sample sample sample abstract applied references due important introduction complex complex hand hand hand estimation estimation estimation estimation estimation parallel tion change energy energy energy energy energy energy energy energy energy energy energy energy energy energy assume classifier classifier classifier classifier classifier prior chosen higher part part part theorem represent represent distributed distributed expected equations equations equations equations markov correct probabilities probabilities probabilities probabilities probabilities probabilities finite finite resulting sum sum sum sum sum called called called called called called called times times elements mapping mapping potential potential potential potential potential potential potential potential applications negative original vol vol artificial samples samples samples true define define define define rates perform experimental experimental distributions distributions distributions discrete discrete equal mit comparison contrast contrast fields fields train train train descent descent nets modeling modeling modeling morgan morgan proceedings proceedings institute institute department implementation implementation version technique joint joint joint joint joint difficult scheme maps maps cambridge equivalent equivalent equivalent experiment directly directly hinton hinton estimates estimates san conference conference efficient efficient full approximate statistics statistics statistics statistics statistics statistics statistics estimated basic give weighted entropy entropy finally processes iteration simply simply technical increases describe tested transformation transformation transformation transformation inverse proof proof proof assumed theoretical journal instance easily makes including kaufmann kaufmann probabilistic underlying underlying needed combination unknown unknown technology technology special consistent trials trials trials database database database database database database database database database database database database database database database database database database database database database empirical empirical empirical empirical empirical principle principle numbers stored stored international international normalized idea choose exact exact advantage separate separate element element typical identical identical identical machines side side side subset sejnowski engineering sufficient sufficient sufficient compare compare works yields background background grant parts concept occur trial trial predicted occurs occurs setting setting conclusion greater assumptions accurate accurate designed practice mateo california california california california intelligence variety variety variety start configuration configuration configuration configuration configuration boltzmann boltzmann relation pro written mathematical dept electrical unique unique adding frequencies frequencies frequencies events potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials john choosing choosing stationary viewed interpretation lemma lemma lemma lemma lemma transform labels approximated similarly reasonable normalization iterative calculate calculate assigned building thesis thesis bell weighting instances assignment assignment assignment assignment assignment activated activated reason selecting society literature efficiently miller miller miller miller miller miller miller identity summary quickly showing classify satisfy satisfy notation gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs observable american create create collection collection exponentially association accurately mappings scaled scaled attributes attributes attributes attributes attributes attributes attributes configurations configurations configurations created separated baseline defines formula formula formula defining implementing broad probable inversion inversion inversion acknowledgement begin attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute summation summation geometric double double collected collected orders remove calculating extracting pasadena marginal datasets datasets acquisition primarily tation databases databases databases databases databases databases count count count count unity addresses grows murphy murphy los substituting published published representational zhang zhang entry surprising sides sides sides sides ranking darpa creating creating cancer cancer record record counts counts onr empty ics uci uci truncated truncated truncated outline goodman goodman goodman goodman goodman weiss weiss assignments adjustment adjustment quantized verified pub distribu convert inverted proba relate relating noting records records records tied tied voting funded inverting prevents normalizing replacement bility breast breast house interpreting inclusion inclusion outperformed outperformed subtracting substitute repository repository icl icl icl icl icl irvine irvine irvine prescribed energies energies microsoft microsoft collecting iris iris iris collision recovers invert invert excluding collect collect subtract ninth outlines unequal sults providence 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#@Goodman_R,Miller_J,
#t6
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#*network neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data function function function figure figure time set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training output number number number number number system system error error error error error error error error error error error error error error error error error error results results results results results results results problem problem problem based based based based based weights weights weights case case case case case case vector vector vector vector order order systems values values values noise noise noise noise noise weight weight weight weight weight approach approach point point point single single large large large large large large test test test test test test test analysis analysis analysis form form shows shows simple simple gaussian gaussian paper paper paper paper paper examples small small small small small small small small small small small net net net work work methods methods step level current problems architecture equation equation equation equation equation equation section fixed fixed line parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states gradient gradient term term term term note note note note dimensional dimensional dimensional result result result result result result result result computation solution research independent independent independent independent independent independent log log target dynamics initial constant constant constant constant constant constant constant constant estimate estimate estimate estimate estimate estimate computer computer terms terms presented map map map map map map map map map low sets maximum maximum maximum maximum maximum range press learn components abstract applied back back find find likelihood likelihood likelihood likelihood references component due positive positive positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important important propagation propagation complex hand hand hand estimation behavior behavior effect effect tion tion tion change change change change change difference assume assume assume assume assume assume prior prior prior prior prior prior prior prior chosen part part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem required good good good good good conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations equations equations make make region region region proposed proposed correlation correct correct correct correct correct correct correct correct minimum resulting ing respect multi sum sum times times means means means means means means means factor factor factor factor made negative relative samples true true true 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simply discussion discussion increases close close proof proof proof proof proof proof finding finding finding common assumed assumed supported makes pairs underlying needed interesting matching uniform uniform uniform uniform squared max max pre direct magnitude decay combined choose light light exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact advantage advantage separate takes reported reported practical practical introduced introduced side sense recently recently interest interest interest sufficient sufficient compare calculated works tions tions smooth smooth definition modified bounded bounded bounded bounded interval interval grant exists expression lead suggests derivative width width starting assumptions assumptions assumptions bayes numerical numerical clear clear peak peak peak peak peak peak peak peak peak peak peak peak peak peak exponential exponential practice practice practice taking characteristics proportional proportional assuming assuming minimizing exist iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii averaged introduce introduce manner question appears appears factors factors changing explicitly applying decreases expressed dependence dependence communication squares viewed learner evaluated open evaluate evaluate evaluate evaluate evaluate approximations approximations centered approximated approximated approximated approximated approximated similarly constants allowed allowed allowed reasonable reasonable reasonable reasonable calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation additive performing normalization fitting penalty penalty penalty closed closed interpolation valid valid valid valid valid valid calculate sufficiently sufficiently david expect determines prove prove prove prove priors priors priors priors priors coupled holds holds holds holds holds holds tests major major reason reason extra importance differ maximal mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay essentially essentially essentially essentially essentially essentially procedures lie lie lie lie lie classify running hold hold hold hold hold hold hold hold quantity quantity quantity quantity quantity vary vary vary write usual usual providing acknowledgments deal deal deal employed simpler simpler unlike poor poor poor poor poor difficulty involving integral integral integral integral scalar examine giving tech combine reliable complicated understand act integer opposite created noted assumes logic arbitrarily submitted explain finds finds attempts slowly formula formula trivial publishers publishers failure failure answer answer answer answer answer answer answer answer answer answer answer answer answer answer answer answer tool starts easier easier mathematics consequence cut cut calculations implicit implicit implicit lowest author reflects reflects reflects reflects varies varies varies greatly evaluating evaluating applies peaks orders remove sharp weigend weigend weigend fall maximizes popular hyperparameters hyperparameters irrelevant irrelevant trade trade don corrupted intractable assign formally formally formally investigation fix addresses establish generality extending extending fails wrong wrong dealing difficulties alpha alpha stated check viewpoint reasoning reasoning preparation exceeds date falls corre equals negligible negligible negligible negligible negligible negligible negligible surprising surprising sides consequences sim claim infer arrive matter wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert santa santa alternatively alternatively summarize posteriori fitted unchanged multiplying approx entropic entropic rigorous solves ent kluwer kluwer validity restrictions chaos flat flat big guess guess guess guess reflected scenario scenario scenario scenario scenario scenario scenario equality equality equality iff exponent modifying distri intuition continues carefully met met met met met singularities ultimately integrals pos discusses apparently things signs behaves behaves correlate cube rarely stimulating lation demand justified justification justification subjective subjective subjective doesn doesn doesn doesn puts val condi condi sharply sharply sharply sharply peaked peaked peaked peaked peaked peaked peaked peaked tells tells tells scenarios scenarios governing occam decaying sian sian absent subscript brackets modern raised raised tim dence dence dence dence ized developments argmin checked proce modifies imation advice offered puter opportunity cir buntine buntine buntine posteriors evaluates infinitesimal claimed pri justify ponent tums tums stays exposition wishes expects amples depen accompanying oft estima rect stant nique sponds private proportionality proportionality proportionality pathological backpropaga diction incor wolf wolf badly ofp sufficiency sufficiency sufficiency sufficiency sufficiency sufficiency ifp dure absorbed graphic suspect invalid invalid calcu logarithms dition unreasonable butions neg illegal illegal cancels quicker quicker wll wll terior generically generically offs evi evi evi trail marginalization til fixes malized convincing laborious suits sfi sfi ofw orem elucidate plicity nax nax illuminating skilling believes disappointing proximately objection foregoing weren basing incurring 
#@Wolpert_D,
#t6
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#*network network network network network network network network learning model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input function function function figure figure figure time time time time set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output number number number number system system system system system system system state state state state state state results results results units units information models models models space weights weights weights weights weights weights case order order systems values values values noise weight neurons neurons unit unit unit unit unit unit unit distribution distribution approach pattern point point point point point point point point point processing control control control large large large neuron neuron neuron neuron neuron class class class matrix matrix shows gaussian gaussian visual examples small size size size size size feature fig fig fig fig fig step points points field field features features random random random random random random random random random high similar architecture architecture architecture architecture fixed fixed fixed fixed fixed fixed fixed general general parameter parameter parameter parameter parameter parameter real real real real real real states states theory theory obtained term activity dimensional dimensional dimensional result variables research research independent independent independent independent independent independent independent defined found dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant constant constant table standard computer connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left presented phase activation low low low frequency frequency frequency frequency temporal range press continuous continuous continuous abstract find convergence convergence convergence density properties properties references due due due due due due due positive important important important introduction complex complex complex complex behavior behavior behavior behavior behavior behavior stimulus statistical effect effect dynamic dynamic dynamic dynamic variance variance variance variance variance variance parallel recurrent recurrent energy energy complexity variable variable assume chosen higher part cases type type type cortex conditions conditions expected make observed observed observed finite simulations simulations simulations human computed sum sum performed made global global global global study study study study study obtain negative series provide connected connected connected connected connected connected discrete discrete brain brain brain equal larger connection connection dependent loss loss internal responses view view transition transition limit limit limit limit limit effects effects full approximate free world produce derived randomly randomly types types product processes processes processes processes selected nature nature simply biological biological biological biological achieved increases increases increases increases increases increases increases increases corresponds corresponds stable stable stable stable stable supported role role theoretical theoretical hypothesis makes dynamical dynamical dynamical dynamical dynamical fully fully fully fully transfer interesting interesting interesting testing projection increasing increasing structures uniform uniform uniform leads call max max max max stored normalized normalized normalized magnitude attention neuronal recent exact property period sense cognitive cognitive cognitive cognitive engineering sufficient highly varying previously approximately axis studies symmetric symmetric studied studied studied studied occur occur occur suggests extended deviation matrices matrices correctly occurs occurs occurs occurs flow strength strength strength conclusion critical critical depend depend numerical numerical weak strong cycle cycle sigmoidal plane introduce connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity program acknowledgements stability stability stability stability sensitivity simultaneously infinite slightly spectral spectral scales versus cycles decreases decreases reconstruction depending stationary stationary stationary influence influence showed converges spectrum normalization reduces remains intermediate intermediate sufficiently eeg coupling coupling coupling coupling coupling coupling figures eigenvalues eigenvalues sciences variations phys phys phys phys characterized maximal oscillatory oscillatory attractors attractors attractors genetic reached notice notice strongly prob interpreted symmetry symmetry oscillations oscillations sci gray gray built relaxation play eigenvalue eigenvalue eigenvalue observable observable leading leading cat received decreasing modelling modelling law law law simpler investigate investigate exhibit periodic periodic periodic periodic periodic periodic existence int authors tanh oscillation understand analogous math math plausible onset onset onset onset rev rev bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation explored nervous regime submitted chaotic chaotic chaotic chaotic chaotic chaotic chaotic established established established spin spin slowly distinguish slope slope tool afferent arises arises arises arises qualitative radius radius conjugate reflects apparent freeman freeman transient transient sharp biologically span occurrence occurrence qualitatively qualitatively singer asymmetric asymmetric chose chose findings focused spectra spectra spectra cybern proportion proportion appearance appearance branches circular nonzero reaching plays lost numerically simplify keeping service sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky separating ranging ranging studying dominant entries rich theoretically sustained route route route route route route route route route route route route route statement lett lett lett convergent convergent convergent resonance resonance geometrical emergent emerge pointed centre centre convenience quasi quasi quasi quasi quasi quasi quasi quasi chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos chaos possibilities thermodynamic thermodynamic 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#@Cessac_B,Doyon_B,Quoy_M,Samuelides_M,
#t6
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model model neural neural neural neural neural neural input data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks number number number number number number system system system error state state state problem performance space space space space linear order order shown shown shown shown shown systems systems values values values values values values values values values values probability probability probability parameters parameters parameters parameters parameters parameters weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution recognition recognition recognition method approach approach approach approach approach pattern pattern pattern pattern pattern point point point point point point point point control large large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns class class class inputs inputs inputs form shows shows shows simple simple gaussian paper paper paper small small small small size size size net net net net net net net work work fig step step step points points points process process process level level level level level level level level level level random random random random random random high high high high high memory similar similar similar show show show show show show equation equation equation equation equation fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed general parameter parameter parameter parameter approximation approximation approximation average average average average average states states states states theory term note note note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional university university threshold threshold threshold threshold research research defined defined sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial estimate standard standard terms terms connections connections connections connections map map phase phase activation activation activation activation activation activation activation low low temporal object range range range range abstract computational references stochastic stochastic due due ieee context introduction complex complex complex complex complex complex complex complex complex complex behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical statistical effect dynamic dynamic dynamic dynamic generated generated variance variance recurrent recurrent tion tion complexity complexity variable variable assume prior prior part center firing firing firing firing firing firing firing firing long long conditions represent distributed expected equations equations equations make region region region region region region region length finite ing ing total simulation called elements elements elements regions potential global global global applications study obtain obtain specific desired desired series series define rates proc location active active active active active active active determined related connected brain larger connection connection nets modeling modeling department department consists individual individual represents represents graph graph sequences sequences considered limit limit effects significant con condition condition developed criterion area finally sampling sampling constraint associative associative increases describe group group close close corresponds complete excitatory excitatory stable stable short short supported underlying hopfield hopfield dynamical dynamical fully interesting interesting interesting projection increasing empirical empirical empirical leads leads leads call max inhibition inhibition inhibition inhibition combined discussed recent practical period identical identical side sense subset interest works works works works solve yields correspond correspond achieve trans trans sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse definition symmetric symmetric studied studied studied suggests predicted predicted predicted predicted predicted predicted deterministic deterministic occurs setting setting conclusion tangent tangent differences clear strong presence cycle cycle turn assuming start min averaged averaged introduce introduce connectivity connectivity acknowledgements pro plot plot plot vertical vertical physical unique cycles john independently review review depending organizing evolution understanding activities reasonable remains calculate fire fire fire box usa subspace sciences memories memories phys phys phys characterized regular effectively effectively effectively effectively effectively effectively attractors situation tend excitation soc graphs dis issue return sci sampled sampled write absence bars bars simpler varied association investigated tanh notion neu neu math math possibly predicting predicting predicting predicting predicting predicting predicting predicting extremely rev amari amari amari amari finds chaotic years devices devices devices histogram histogram histogram histogram indicating defining unstable forces broad ran mation hippocampal acad describing arises computers qualitative qualitative researchers behaviors composite transient flexible posed variant maintain switch switch gen gen fall qualitatively collective asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric kinds kinds kinds focused focused deviations deviations eventually proportion appropriately nat ranges fan fan fan fan fan fan fan fan familiar abilities biased substituting sompolinsky sompolinsky falls regard regard histograms insight insight lett switches ure largely largely shunting 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#@Levy_W,Minai_A,
#t6
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#*network network network network network network network network network network network network network network network network network network network network neural neural neural input input input input input input input input input input input input input function function function function function function function function function function function function function figure figure figure figure time time time networks networks networks networks networks networks networks networks number error error error error error error error error error error error error error error error error error error error results results results performance performance performance performance performance performance performance performance performance performance performance performance based based space space space layer layer layer layer case vector vector vector vector order values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability neurons neurons neurons neurons distribution distribution distribution distribution distribution recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single single single single single neuron neuron neuron neuron neuron neuron neuron rate rate patterns patterns patterns patterns optimal optimal optimal optimal optimal optimal optimal inputs form simple simple paper small size size size size size size net work classification process random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory representation show section fixed dimensional result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables independent independent log initial table table standard standard standard standard distance distance connections connections connections connections connections presented presented presented activation maximum abstract convergence density density references due due due due ieee introduction effect generated generated generated tion difference complexity complexity measure representations type required multiple correct correct correct correct correct probabilities probabilities probabilities probabilities probabilities resulting ing respect sum factor obtain obtain obtain obtain original original original original original original original relative desired desired compute compute proc perform perform experimental experimental experimental experimental related connected connected equal equal equal mit accuracy comparison comparison larger nets report version internal final exp exp exp exp exp exp exp exp exp exp exp exp sequences bit bit capacity capacity capacity determine classifiers classifiers requires choice approximate approximate give randomly types processes iteration iteration iteration iteration iteration iteration iteration iteration simply biological associative normal normal normal normal technical arbitrary arbitrary denote denote denote denote close typically hopfield fully ratio special iterations max stored stored bits magnitude attention choose recent exact similarity similarity similarity similarity similarity similarity similarity similarity practical identical sense compare calculated calculated yields yields trans organization storage storage parts expression expression derivative predicted predicted correctly conclusion minimal numerical performs performs moody exponential propose integration physics start connectivity relation winner winner winner winner laboratory tuned mathematical sensitivity sensitivity consisting consisting springer versus letters expressed overlap lemma lemma lemma lemma lemma lemma lemma lemma lemma variation variation transform approximations approximations completely similarly converges converges converges expansion reduces reduces iterative calculate topology sciences sciences plotted activated gamma gamma gamma selecting society maximal identify composed verlag vary received satisfies presents requirements detail detail replaced integral integral integral integral lippmann lippmann graphical existence examine examine matches school smallest closest closest integer integer analyze analyze analyze analyze versions taylor taylor taylor wta wta wta wta wta wta wta wta optimum years growth analyzed failure failure baum baum worse london ran ran calculations depicted varies considerably prop incorrect berlin limiting maximizes maximizes cal replace replace hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming extreme cumulative cor proofs proportion proportion primarily bin bin bin royal wrong alpha alpha alpha selects selects evident originally israel multiplied omitted properly storing considerations convergent integers gold convenience classifies classifies letting scenario tight clas increment epsilon epsilon epsilon epsilon integrals minor nil tel tel accordance subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet ruppin ruppin ruppin ruppin calculates calculates practically lnp approaching approaching distorted distorted drastically drastically binomial binomial differentiate aviv aviv winners lincoln subnets activa extremes heidelberg claimed cortico standing thalamic faculty lira domany domany discard discard meilijson meilijson meilijson raymond erties integrand exceeding rectly eytan probabili divergent rhs quantile wilczek equate displaying pacity summand isaac 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#@Meilijson_I,Ruppin_E,Sipper_M,
#t6
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#*network network network network network network network network network network network network network network model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input function function function function function function function function function function function function function function function figure figure figure figure figure time time time set set networks networks networks networks networks networks networks networks networks networks output number state state state state state results results results units models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space linear linear linear linear linear case case case case order order order shown shown systems values values probability probability probability probability probability probability probability probability parameters parameters weight functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution approach approach approach approach point single single single single single single large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns optimal optimal optimal optimal optimal shows shows signal signal signal signal signal signal signal signal signal signal simple gaussian paper small net net work field field field field field field field field field field field level level current current current current structure random random random random random random random random high high high high memory memory memory memory show show fixed line rule rule rule rule rule rule general parameter average states obtained term activity activity activity activity activity activity university threshold threshold threshold threshold variables variables independent independent independent independent independent independent independent log defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial constant constant constant table table standard connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic direction presented presented present present activation activation activation activation activation activation activation activation activation activation activation activation activation activation low low low low low low sets range range range basis sample abstract back find find likelihood references due positive important introduction variance tion tion assume rules rules rules rules signals signals prior chosen higher previous bound firing firing firing firing firing firing cortex cortex good spike conditions distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian make fact correct correct correct probabilities scale scale finite simulations ing human regression means optimization optimization potential potential potential study policy obtain negative original specific true true compared provide rates rates proc active active active active active active active active active active active active active determined determined experimental experimental posterior posterior connected connected connected gain cortical cortical cortical cortical cortical cortical brain brain power contrast connection connection fields fields fields update dependent dependent dependent dependent dependent dependent dependent dependent dependent consists represents final final final exp exp exp ai ai framework framework equivalent view limit san capacity upper choice statistics basic con channel randomly conditional actual actual processes evidence iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration inhibitory biological biological associative achieved achieved achieved measured normal normal normal group group close assumption assumption assumption corresponds corresponds complete predictions common assumed synapse synapse role role theoretical theoretical theoretical hypothesis hypothesis future typically smaller hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield combination combination combination testing testing ratio ratio ratio mechanism trials details iterations iterations iterations iterations iterations iterations max magnitude magnitude magnitude neuronal neuronal denotes denotes denotes architectures architectures membrane improved improved correlations exact pair takes typical similarity similarity similarity similarity similarity recently varying works module yields diagonal diagonal diagonal sparse sparse definition observation generalized generalized generalized generalized generalized generalized channels channels interval interval interval interval interval interval interval interval sensitive exists exists horizontal expression expression suggests spikes predicted predicted hybrid hybrid hybrid hybrid hybrid strength starting hebbian depend numerical numerical suggest mechanisms characteristics sigmoidal sigmoidal sigmoidal sigmoidal averaged derivatives connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity identification attractor attractor attractor attractor attractor attractor attractor attractor explicit ways plot ann ann ann ann mathematical mathematical physical belief belief belief belief belief belief belief develop develop applying choosing independently independently independently expressed review depending depending depending influence lemma lemma lemma detailed densities evaluated evaluated evaluated evaluated open evaluate fraction understanding converges constants past sign sign sign reasonable slow combining event event assigned degrees fire fire combinations combinations priori usa sciences sciences memories memories memories determines determines activated absolute absolute characterized determining selecting included wij modes modes identify identify post post post post essentially receives receives strongly strongly superior superior contribution follow sci involved sampled observable correspondence correspondence received illustrates preferred neighboring receive law remain updating updating history history history history history history history history history history history history history school decisions working working working maximizing notion examined plausible plausible possibly opposite opposite illustrate equally obvious expressions pyramidal motivated seconds formula asynchronous ground variances variances fairly improves analytical tool interneurons considerable turns perspective broad ran sgn sgn involve acad apparent quantitative effort marked biologically biologically maintain span mod incoming collective conductances replace extreme contribute gap don narrow narrow nat neurophysiol enhancement significance analogy odd moment abilities keeping exceeds exceeds heuristics mance perfor infinity belongs entries israel express indicator indicator assigns posteriori posteriori posteriori posteriori anns achieving emergent adopt adopt restrictions convenience letting letting examining var var assess acting formance mammalian activate activate activate activate relate synchronized proach memoryless examination tel tel tail tail tail tail tail tail tail tail ruppin ruppin ruppin ruppin adaptively 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image image single single single single single single single single processing processing processing processing large local local test test test patterns analysis analysis analysis analysis analysis analysis matrix matrix inputs shows shows shows shows shows shows signal signal signal signal signal algorithms examples small small small small size size size feature feature feature feature net net net net net net task methods points points features classification process structure problems high high high representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture architecture architecture architecture show equation equation equation equation fixed line vectors vectors images images images images images images images images images images images images images parameter parameter parameter parameter theory gradient obtained obtained term experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university threshold threshold threshold threshold threshold threshold variables variables computation found found found found found target initial initial initial initial initial initial constant constant estimate estimate estimate estimate standard computer connections connections connections science science left presented presented map activation activation activation activation low low low low sets maximum maximum learn components components components components components components components components components components components nonlinear outputs sample abstract applied applied find find find find computational computational references component component component stochastic due important introduction hand estimation estimation generated variance variance variance variance variance variance variance variance variance search lower lower representations representations representations representations representations representations representations representations representations representations representations chosen chosen chosen chosen higher part bound good conditions make fact region correlation correlation length correct simulations minimum minimum minimum minimum human respect respect respect multi elements means optimization dimension dimension dimension dimension made global global original original original original original original original original vol artificial artificial desired series series series series series provide provide proc perform determined constraints connected equal larger larger train train nets institute institute loss loss loss loss technique technique technique consists internal individual advances final layers layers layers layers layers layers layers layers layers layers layers delay delay delay addition graph ai ai considered cambridge directly solutions solutions san bit bit determine full choice approximate estimated basic give coding selected backpropagation backpropagation simply achieved covariance covariance feedforward feedforward feedforward describe denote inverse amount supported require eds eds eds face face face face face face face face face journal pixel pixel pixel pixel pixel pixel objective underlying needed needed reduced reduced reduced unknown programming interesting interesting significantly principal principal principal principal principal principal principal principal principal principal principal principal principal direct making stored bits bits bits bits magnitude magnitude run resolution typical subject subject subject cognitive dimensions dimensions approximately subjects subjects subjects solve smooth pca differential differential achieve achieve bounded interval interval interval interval sensitive entire increased increased constructed extended derivative correctly touretzky pass minimal minimal reduce conclusions operator measures performs moody exponential encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding propose reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction california california regularization regularization user relationship minima minima identification question question question acknowledgements suppose appears longer primary generating dept pruning simultaneously dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality remaining remaining develop minimization minimization extraction extraction expectation choosing review reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction depending controlled showed static reasonable reasonable smoothing convex fitting add add closed interpolation foundation kohonen kohonen classified faces faces david david david avoid avoid activations priori color eigenvalues eigenvalues assignment subspace recognize partially reason determining compression compression compression compression compression identified identified efficiency capable capable encoded encoded encoded effectively driven delta essentially identity identity compact compact compact repeated repeated decoding decoding decoding decoding decoding decoding decoding decoding decoding allowing superior lie classify manifold manifold manifold sampled thresholds automatically consisted consisted consisted consisted extract extract extract extract software intrinsic intrinsic intrinsic intrinsic diego humans lippmann scalar scalar reducing project mappings eigenvectors eigenvectors eigenvectors encode encode cover cognition examined equally rank greedy portion precise mapped epoch arbitrarily arbitrarily arbitrarily finds optimum theoretic variances failure glass glass glass glass glass inside processed tive commonly projected circle circle circle circle circle circle lowest auto author preceding addressed raw geometric embedded embedded backprop decoder decoder decoder decoder decoder redundancy multidimensional yielding consistently consistently analogue formally guarantee jth reconstructed reconstructed reconstructed encoder encoder encoder eliminated eliminated oja oja resulted resulted resulted mark 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#@Cottrell_G,DeMers_D,
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problem problem hidden based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer case case vector values values values values values values values probability probability parameters weight weight weight weight weight weight weight weight weight functions functions functions functions functions unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method single single single single single single single single single single analysis class class class class class form form form form algorithms simple simple simple simple paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples size size task task fig fig fig step step step step step step step step step points points problems architecture generalization parameter parameter real real approximation states theory theory theory theory obtained obtained note note note note result university university university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables research research research research research defined defined defined defined defined target target target target target target target target target target constant estimate estimate estimate estimate estimate estimate estimate estimate computer science direction presented machine machine learn learn learn learn outputs continuous sample sample sample sample abstract abstract find computational computational references positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive procedure important important introduction tion complexity variable variable variable variable variable variable variable variable variable variable assume assume assume assume assume assume assume assume measure part center theorem theorem cases good binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary represent distributed make fact fact fact fact correlation correlation correlation probabilities probabilities probabilities finite finite minimum respect respect eq eq eq eq eq eq eq called dimension study negative negative negative negative negative negative original original original original vol vol vol vol vol vol vol desired proc proc proc proc active related related connected connected connected connected connected distributions distributions distributions distributions distributions distributions steps steps steps accuracy update nets morgan morgan report institute institute final bias bias bias bias computing computing directly view view capacity capacity determine determine determine determine full full approximate estimated give conditional bounds area depends simply simply simply simply simply technical arbitrary arbitrary arbitrary denote denote denote limited assumption complete proof proof proof proof supported supported theoretical theoretical main hypothesis hypothesis hypothesis degree development probabilistic needed reduced reduced reduced unknown fully fully technology interesting york special uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform empirical representing call polynomial polynomial polynomial polynomial attention choose description perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron correlations correlations property reported reported reported practical apply sufficient sufficient sufficient yields achieve storage grant grant grant exists suggests setting hardware runs runs conclusion starting reduce reduce reduce valued valued editors learns learns suggest suggest suggest suggest hard physics physics california labeled introduce connectivity connectivity connectivity question denoted denoted acknowledgements written written generating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating dept changing changing changing confidence student multilayer applying boolean choosing influence influence influence influence lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma open open approximations understanding earlier reasonable reasonable reasonable reasonable expansion event precision precision avoid perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons inter vapnik extension prove major determining straightforward identify literature road showing return return return notation quantity write computes reach thresholds simpler investigate limitations complicated workshop workshop func math concepts concepts integer ensure queries quantities obvious greedy perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton submitted motivated established inequality guaranteed majority majority lin lin tive easier easier ion read nsf nsf conducted share share haussler haussler enables enables gap gap gap pac pac pac pac pac proofs college equivalence restriction princeton acm acm acm acm generality kaufman kaufman difficulties siemens simplify proceeds proceeds exploit star definitions methodology belong belong intuitively symposium obstacle substituting inferior decide decide realization 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parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters distribution method method method method method method method method method method method method method method method method method method method method approach approach point point point point point point point processing large test test analysis analysis analysis optimal optimal optimal form form form form form form form form form simple paper paper paper paper paper small size work methods points random random random random response architecture equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation section section section section general general general generalization approximation average average average theory theory theory obtained obtained obtained obtained obtained obtained term term term term term term term term result result result result result result result university university variables research independent independent independent independent log log log log log sequence constant constant estimate terms terms terms terms distance distance left presented presented presented presented presented present maximum press nonlinear nonlinear abstract find computational computational properties likelihood likelihood likelihood likelihood likelihood likelihood references procedure adaptive decision context introduction estimation statistical statistical effect cost cost tion difference difference variable variable variable variable measure measure prior prior chosen higher higher higher higher part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem multiple bayesian bayesian bayesian fact proposed probabilities observed minimum resulting regression regression regression regression regression regression regression respect respect respect respect called called called factor optimization optimization optimization optimization optimization optimization optimization optimization optimization dimension obtain obtain obtain obtain obtain obtain obtain negative negative negative negative original original specific true true true true true cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross posterior posterior posterior gain brain brain equal approaches approaches approaches approaches approaches approaches dependent selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection morgan proceedings institute institute institute department technique advances equivalent equivalent equivalent directly directly limit choice choice choice choice approximate estimated basic pages pages validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation give condition criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion discussion discussion denote denote corresponds corresponds corresponds predictions proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof amount amount effective effective effective assumed supported fit fit fit fit kaufmann technology special special mode principle squared squared squared international idea idea combined denotes takes introduced introduced side interest compare observations calculated definition definition generalized generalized bounded bounded risk risk derivative derivative derivative derivative derivative editors editors moody moody moody moody moody moody moody moody moody moody moody moody moody asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic physics california regularization relationship derivatives derivatives derivatives explicit written estimating estimating ann ann modeled recall infinite infinite infinite infinite infinite infinite predictive predictive predictive predictive springer expectation yield choosing review squares estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator influence lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma detailed detailed detailed evaluated evaluated evaluated key calculation additive expansion expansion expansion expansion expansion normalization combining penalty penalty penalty calculate box thesis extension prove prove prove regular selecting selecting mackay mackay miller miller miller summary soc soc soc verlag repeated link notation quantity michael minimizes hypotheses satisfies satisfies parametric put detail estimators hanson issues lippmann helpful mse proved proved func math editor reading taylor taylor taylor taylor taylor ith phd mentioned asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically brown great formula formula formula expensive strictly acknowledgement implicit members author author nsf summation summation summation argument bootstrap consistency readily readily readily formulated substantial comments comments age unbiased unbiased unbiased lim differentiable ordinary proofs proofs cooper equivalence equivalence equivalence equivalence equivalence equivalence ratios optimizing optimizing consideration ylx ylx ylx symposium sion equals equals decide schwartz schwartz multiplied roy roy roy likelihoods grants ignore ignore ignore stone stone stone stone stone stone stone stone stone stone onr speaking liu liu liu liu liu theorems theorems theorems intrator chicago auxiliary mutually publication ization denoting deleted deleted deleted deleted deleted algebra behave vanishes vanishes rewrite ignoring rewritten remark remark served deletion const continued continued ters assessment proves 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#@Liu_Y,
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input function function function function function function function function function function function figure figure set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm output output output output output output number number number number number number number number number error error error error results units information information information information information problem problem models models models models models hidden weights weights weights case case case case order order order shown shown systems systems values probability probability probability probability parameters parameters parameters noise noise functions neurons distribution distribution distribution distribution distribution distribution distribution distribution method method method method approach pattern point processing large large large large large large large large large local analysis optimal optimal optimal optimal optimal optimal optimal optimal form form form form shows shows shows signal paper paper paper examples examples examples examples examples examples examples examples small small size net net work work methods methods fig fig step step step step step step step trained trained trained random random similar representation representation architecture architecture architecture show show show show show show show equation general general generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation average average average average average average theory theory theory theory term term term note note note result result university university university university university computation log log defined sequence sequence sequence initial constant science present present components basis nonlinear outputs sample sample sample sample sample sample sample sample sample sample abstract applied back find properties properties properties references stochastic stochastic stochastic stochastic ieee ieee ieee positive procedure important important adaptive propagation introduction hand behavior statistical statistical statistical statistical statistical statistical statistical generated generated variance variance variance variance variance variance variance search tion complexity complexity complexity complexity complexity complexity complexity complexity complexity variable variable variable assume assume assume rules measure measure learned learned chosen previous previous previous theorem theorem theorem cases type good represent distributed distributed distributed expected proposed probabilities respect respect multi multi multi multi called called called called called called elements natural study obtain artificial artificial true true true true application application define define define proc related related related distributions distributions descent descent selection selection selection selection selection selection selection selection selection selection morgan report words loss 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typical typical practical introduced introduced hierarchical sense sense engineering compare conventional calculated works correspond trans trans definition definition exists matrices matrices conclusions operator depend moody moody moody moody asymptotic asymptotic mateo integration physics characteristics solid solid regularization regularization radial minimizing exist min minima identification relation relation relation relation relation relation written sequential estimating mathematical dept dept changing averaging averaging physical predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive expectation expectation expectation decreases choosing family independently review depending lemma lemma lemma lemma evaluated evaluated operations sign earlier dashed dashed expansion roughly purpose purpose valid valid kohonen includes thesis prove phys determining selecting differ modification included satisfy satisfy quantity quantity quantity quantity sampled sampled sampled sampled usual minimizes thresholds automatically satisfies satisfies satisfies minimized minimized origin origin layered layered layered layered layered relations relations relations replaced hanson lippmann divergence divergence divergence divergence ml giving proved math coefficient coefficient coefficient naturally naturally quantities quantities amari amari amari amari amari amari submitted phd optimum asymptotically asymptotically asymptotically publishers smoothness variances baum baum mation ion ion ion researchers researchers mechanics reflect tional parameterized solla haussler plan expectations expectations tile tile tile tile tile tile specifies ordinary japan japan japan summing fix fix kullback mail analogy abilities tishby tishby belong intuitively ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx adequate sompolinsky holland regarded regarded guarantees expanded regard realization eng seung seung 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#@Amari_S,Murata_N,Yoshizawa_S,
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#*network learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function set networks networks networks networks networks networks networks networks networks networks networks networks networks networks output number number number number number number number number number number number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state results results units units units units information performance performance performance weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer case case vector order systems weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons single single processing control large large large class class class class class class class class inputs inputs inputs form gaussian examples size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size net 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threshold threshold computation computation computation research log log defined constant constant constant constant constant constant constant constant standard standard standard standard standard standard standard standard standard standard standard computer computer computer terms terms terms distance science science science phase phase activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation maximum components basis basis basis nonlinear continuous continuous continuous abstract computational convergence analog analog analog analog properties properties properties references due introduction hand hand circuit behavior tion complexity assume assume assume assume assume assume assume assume assume lower measure measure measure signals part part part previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound required good good binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary make resulting classes classes classes classes ing simulation computed computed respect respect respect respect respect respect respect respect respect respect respect respect respect respect multi sum sum called times mapping factor factor factor natural obtain obtain obtain obtain artificial relative represented compared application series proc proc proc proc proc proc proc goal power power power power power power power power power power power power power power power comparison comparison comparison comparison larger support nets nets nets 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increase increase increase increase increase increase weighted criterion bounds bounds bounds product provided provided finally finally backpropagation achieved feedforward feedforward feedforward feedforward describe describe fast fast fast proof proof proof circuits circuits implemented assumed assumed require main journal square instance easily easily degree degree degree degree degree degree including simulated simulated smaller smaller coefficients coefficients coefficients ratio edge edge special call numbers numbers numbers numbers numbers bits bits bits bits bits bits international international international international international polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial sources discussed advantage property property property property separate subset interest sufficient compare compare previously approximately approximately works tions smooth smooth definition definition definition definition definition separation generalized generalized bounded bounded bounded bounded gate interval interval increased exists exists exists lead concept white white white conclusions valued sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid numerical exponential suggest sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal proportional intelligence labeled radial radial radial turn introduce base acknowledgements edges stability multilayer involves unique scales applying quality quality implies extraction versus boolean boolean boolean boolean boolean boolean decreases national transform approximations approximations approximated approximated approximated approximated approximated approximated approximated approximated allowed allowed allowed sign partial add sufficiently assigned assigned assigned assigned construction norm includes inter discuss absolute absolute absolute absolute absolute holds holds discussions reason determining efficiency efficiency capable capable importance suitable suitable suitable suitable suitable differ poggio poggio efficiently efficiently efficiently efficiently comparing tend essentially essentially receives allowing showing interested interested dis list involved generalize computes computes thresholds thresholds thresholds thresholds thresholds thresholds approximating approximating approximating approximating approximating approximating satisfies deal carried powerful powerful powerful powerful powerful powerful powerful powerful layered collection investigate integral helpful mappings root gates func notion notion math math integer spline spline spline observe observe observe observe multivariate mentioned great trivial trivial crucial smoothness smoothness capabilities considerable satisfied shared universal author annual annual nsf questions greatly considerably applies applies simulate splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines requirement polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials gains extracting resource specifies proposition sv assign assign equivalence equivalence equivalence equivalence equivalence restriction girosi girosi approximates approximates approximates grows proceed maass maass maass maass maass maass rational rational rational rational rational rational rational stronger mail fan abilities generalizes corollary decide realization vertices vertices vertices percepttons accounts counting approximators foundations suggesting vertex vertex vertex vertex properly roy park statement valuable severe multiply approx approx approx approx linked logarithm listed sine sine sine sine email sontag sontag sontag additionally tight cosine hornik hornik sketch superposition inversely nal remark remark remark gratefully resp 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#@DasGupta_B,Schnitger_G,
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#*network network network network network neural neural neural neural neural neural neural neural neural neural neural neural function function function function function function function function function function function function function function function function function function function function function set set set networks networks networks networks networks networks networks networks number system system system system state results results information problem problem problem hidden space space space space linear linear linear linear linear linear linear linear linear linear linear layer case case case case case vector vector vector order order order order order order order order order order order order order order order order order order systems systems systems systems systems systems systems systems systems functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions image single single control local matrix matrix matrix matrix matrix form form form simple simple simple simple paper paper paper paper paper examples size size size work points points field field field field representation representation representation representation show show show section section vectors general generalization real real real real real real real approximation theory theory theory theory theory theory theory theory theory theory theory obtained note note note dimensional dimensional dimensional dimensional dimensional result result result result result university university variables variables research research independent defined defined defined defined defined defined defined sequence sequence standard standard standard standard standard standard terms terms terms connections direction map map activation activation continuous continuous abstract properties references ieee introduction introduction complex complex complex complex complex complex complex hand parallel tion change variable variable assume assume representations representations representations representations representations representations representations representations representations part theorem theorem theorem long long conditions conditions conditions make fact length length length finite finite finite finite finite finite finite finite finite called called dimension dimension dimension dimension dimension made applications study obtain obtain relative specific series series define define define compute related connected power power connection connection connection connection department department version version ai ai ai ai ai maps maps considered domain domain domain curve curve curves stage full requires condition condition condition condition condition condition product simply feedforward arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote denote close complete assumed supported main main main easily degree degree degree typically combination combination dynamical dynamical dynamical dynamical functional coefficients jordan transfer transfer transfer york york matching details numbers numbers numbers attention denotes discussed include side sense subset subset subset subset subset subset recently engineering interest solve achieve address definition definition definition definition definition definition definition definition definition definition generalized interval interval interval exists exists exists exists lead generally minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal reduce conclusions operator operator operator operator valued sigmoid sigmoid exponential drawn drawn sigmoidal sigmoidal sigmoidal ica exist exist exist plane plane plane relationship derivatives question question question question denoted suppose suppose written solving generating generating generating generating generating generating generating generating generating generating generating generating generating mathematical mathematical distinct distinct distinct distinct linearly infinite infinite infinite involves transformations unique unique unique springer springer shift implies john national interpretation lemma lemma lemma open open approximations forms forms understanding constants partial partial partial classical purpose closed closed closed interpolation interpolation transactions combinations combinations eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues contour extension domains holds holds holds holds straightforward literature essentially summary summary refer verlag verlag kind contained contained contained prob moore anderson satisfy satisfy write board observable observable correspondence satisfies satisfies satisfies satisfies oriented explore explore perturbation kalman kalman integral issues hall helpful existence existence existence existence existence scalar scalar possibility proper cover notion hill rank rank rank rank rank formal formal formal taylor precise observe observe consist contributions established theoretic theoretic analytic analytic analytic analytic analytic analytic analytic analytic considerable strictly operators choices mathematics consequence author geometry conjugate conjugate conjugate conjugate conjugate conjugate questions questions questions generic orders berlin berlin characterize sums germany comments proofs equivalence equivalence formally rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational fails fails consideration stronger canonical meaningful prentice corollary corollary corollary sion realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization realization counter permutation omitted extends fold robert lem equivalently aircraft sontag theorems solely australia conversely electronics algebra union commercial det parametrized parametrized williamson williamson williamson williamson williamson williamson expansions remark remark remark remark remark dim dim dim uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness council interior australian australian australian invertible cliffs realizations realizations realizations realizations realizations realizations realizations realizations realizations realizations realizations realizations realizations realizations realizations realizations realizations periodicity englewood coincide substitution nontrivial implied mcgraw monotone cia cia kailath publishing attracted topics clockwise coincides nonlinearly controllable controllable continuation continuation roots nonsingular arbib admits triples canberra compositions telecom ima acta cer parametrization parametrization parametrization ati haft munications spect spect enclosing ail eduardo tence restated textbooks quadruple 
#@Helmke_U,Williamson_R,
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural data data data data data function function function function function function figure figure time time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm system system system system system system system system system system system system system system system system system system error error state state state state state state results results results results results units units units units units units units units units units units units units units units information information information information problem models hidden space weights weights case case case case vector order order order order order order order order shown systems systems systems systems systems systems systems systems systems systems systems systems systems weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons unit unit unit unit unit unit unit unit unit unit single single single processing large large large local local local local local test test test test test test test test test patterns patterns patterns patterns patterns class class class class class class class class class class class class class signal simple simple simple simple simple examples examples examples examples examples size size size size feature net work work task task fig fig level trained trained trained trained structure problems random rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule generalization real states theory gradient obtained obtained note experiments dimensional dimensional dimensional dimensional dimensional dimensional result result result threshold variables variables computation computation computation computation log log defined found found found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial initial initial constant terms connections prediction left present activation activation activation object motion range range press learn learn learn learn learn learn learn learn learn learn learn learn learn basis basis nonlinear nonlinear continuous continuous continuous continuous abstract find find properties references procedure introduction complex complex complex complex complex complex complex hand hand dynamic generated generated generated recurrent difference difference variable variable variable variable rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules learned learned learned learned chosen chosen chosen higher higher part part previous cases cases cases cases binary binary binary long long long long long conditions conditions conditions conditions conditions make fact region length length scale finite classes classes classes classes ing simulation made natural global global study study study study study knowledge knowledge obtain original original original original original original original original original original true cross series series series series provide perform constraints constraints gain gain discrete mit steps steps steps steps steps steps steps steps steps steps steps larger contrast update descent nets institute version difficult difficult bias computing limit top full full choice significant free world give give con con produce condition condition randomly levels levels levels entropy nature nature simply achieved achieved discussion tested tested tested stable finding short short short short nearest implemented implemented assumed generate main square square end end future future easily degree rumelhart including including simulated simulated simulated typically smaller underlying underlying underlying underlying underlying underlying underlying dynamical dynamical dynamical dynamical dynamical fully interesting interesting head uniform principle representing bottom run run added predict architectures period sense sense relevant interest interest dimensions sufficient sufficient sufficient conventional tions studies achieve rl address chain chain modified entire constructed lead lead lead lead lead lead studied studied occur occur occur suggests suggests digital correctly correctly correctly locally boundary boundary generally pass starting starting critical place valued depend differences accurate asymptotic asymptotic asymptotic asymptotic constrained exist groups connectivity configuration configuration configuration question attractor attractor attractor attractor attractor attractor attractor attractor suppose laboratory laboratory implement implement missing sensitivity infinite dimensionality easy easy easy unique consisting consisting implies boolean boolean letters yield focus depending viewed labels labels evolution evolution evolution evolution updates updates measurements intermediate degrees degrees expect includes priori priori priori usa extension specifically characterized characterized identified identified capable capable suitable divided delta successful successful attractors attractors attractors attractors attractors attractors invariance situation online reached composed kind allowing success moore interested lie usual paradigm paradigm received consisted subsequent modelling situations situations access access access access access exhibit difficulty updating updating put game game game preliminary preliminary behaviour behaviour behaviour behaviour behaviour behaviour behaviour periodic periodic rise history history history history history history history history history history history history history history history history history history history history history tech int proved proved proved proved proved proved analogous naturally possibly configurations configurations configurations configurations configurations automata automata automata automata automata automata automata automata automata portion portion formal formal formal freedom simplest chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic site site site site site site site distinguish answer sites sites sites sites day precisely division ran sgn immediately scientific universal universal universal universal beginning begin begin qualitative fourth questions questions questions understood transient transient transient transient transient transient transient transient transient transient transient tional generic capability simulate simulate simulate simulate lattice lattice lattice lattice lattice lattice lattice lattice treated variant exhibits weigend instruction chose conclude eventually simultaneous sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing globally globally indices sort labeling formally investigation arguments homogeneous impossible impossible eliminate cellular cellular cellular cellular cellular cellular cellular cellular automaton automaton automaton automaton automaton automaton automaton automaton los los north arrays hertz hertz hertz hertz hertz hertz continue continue continue continue continue continue started connect studying holland evident insight late rich rich hypercube learnable learnable dramatically unable emergent formulate legal emerge failed connec reports hundred imagine evolve evolve life life life life life life life life life harder apparently turning turning investigations investigations knowing lapedes exhibited permit permit permit transients transients transients transients transients transients transients october answers worked characterizing demand doesn neighborhoods possess huberman lying neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood restricting raises proves nontrivial nontrivial quantitatively implied implying denmark denmark evolves confined alamos alamos fixing physica physica extrapolation extrapolation histories histories histories histories histories histories histories histories histories histories relax neigh neigh continuing continuing checked cient coincides distinctions accessible lived dissimilar translational fur europhys forrest implementable distinguishes biehl taught simu ons looked copenhagen copenhagen succeed bohr ergodicity extrapolate extrapolate imitate subjected nimh ditions blegdamsvej irrespective bethesda stringent died died conventionally nordita farbet neuropsychology adatron pending thermore niels rept wolfram wolfram wolfram wolfram ymptotic awj neighbouts neighbouts meaningfully reinitialized conjectures 
#@Hertz_J,Wulff_N,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural input input function function function function function function function function function function function function function function function function function function function function set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks number number number number number number number number number number number number number state results results results results results results results results results results results units units units units units units units units units units units units units units units units units units units problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer case case case case case case case vector vector vector vector order order order shown values probability probability probability probability probability probability weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit recognition approach pattern point image single processing neuron neuron class class class class class class class class class optimal form form signal algorithms simple simple simple paper paper paper paper examples examples examples examples small small small net task task step step step step points points points points points points points points points points points points points points points points structure memory representation representation representation representation show show show show show section section fixed fixed fixed fixed fixed vectors vectors general general general general general general speech real approximation approximation approximation obtained obtained term note note note note note note note result result result result result result result threshold threshold threshold computation computation research research independent defined defined defined found constant estimate connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic direction present activation range range range range position position position position position position position position basis continuous continuous continuous continuous abstract back find density properties properties references ieee ieee ieee propagation context introduction complex complex estimation statistical complexity complexity variable variable variable variable variable variable assume assume assume measure measure measure chosen higher higher higher higher part part part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound type multiple multiple good good make make forward forward forward forward forward forward forward forward finite finite finite finite finite finite finite finite classes classes ing tasks tasks tasks tasks tasks tasks respect called called times mapping mapping means means means dimension natural applications obtain artificial artificial artificial artificial artificial specific specific compared desired provide define compute compute determined accuracy accuracy accuracy accuracy comparison support support train train dependent selection selection proceedings loss implementation implementation implementation consists final exp layers layers layers layers considered considered considered considered considered considered computing domain domain domain domain equivalent directly curve curve solutions estimates estimates estimates estimates estimates estimates estimates limit top top top capacity capacity capacity capacity capacity capacity capacity capacity efficient requires significant approximate approximate approximate pages pages give con randomly randomly levels bounds selected selected selected associative associative discussion feedforward denote denote denote transformation transformation transformation stable proof proof proof proof proof proof proof proof proof short implemented theoretical require require main journal future easily including typically combination ratio ratio york special special structures structures empirical numbers early magnitude magnitude idea combined combined perceptron perceptron perceptron denotes recent recent recent advantage property property property property typical typical subject sense subset subset subset subset subset subset subset subset subset subset subset subset recently relevant interest interest interest sufficient sufficient sufficient sufficient observations approximately volume works differential achieve achieve trans improvement constructed exists exists exists exists exists exists exists wide wide feed feed feed feed feed feed feed feed hardware hardware minimal minimal minimal assumptions central sigmoid sigmoid measures exist iii iii iii introduce manner identification index optical optical ways ann segments implement implement implement implement implement implement implement implement multilayer multilayer multilayer multilayer multilayer multilayer category category linearly dimensionality remaining easy unique springer shift implies implies implies family family depending depending viewed influence lemma detailed open open open open restricted fraction approximations completely past partial classical classical classical classical classical classical convex convex convex convex reduces combining closed closed closed sufficiently sufficiently sufficiently norm euclidean kohonen topology transactions perceptrons formulation subspace memories extension extension discuss specifically candidate candidate domains domains holds tests tests simplicity simplicity suitable maximal poggio presentation identify road compact verlag kind kind showing showing showing split hold categories categories built built built built built comp notation write nips ill leading satisfies deal deal decreasing situations perturbation biases helpful fewer links investigated applicable proper proved proved proved cover cover cover cover cover analogous smallest editor integer equally implementations thought subsets singular obvious obvious observe observe perceptton logic logic logic store arbitrarily devices devices trivial trivial crucial improves capabilities benchmark benchmark baum lin precisely constructing broad broad sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn laboratories laboratories acknowledgement involve involve argument applies relevance adjustable adjustable adjustable adjustable adjustable adjustable treated continuously continuously continuously perturbations gen popular ordered comments june proposition proposition proposition proposition proposition proposition proposition proposition proposition differentiable differentiable irrelevant proofs proofs girosi count eliminate generality stronger stronger satisfying fan abilities implications imply phrase obstacle corollary appendix appendix entry equals regarded topological percepttons belongs belongs belongs counting counting counting counting entries matter repeatedly passing park relies statement material ball empty dense dense dense geometrical leaving outline outline rigorous uniquely poses theorems theorems exception exception tor australia australia australia adjustment adjustment tight tight argue preserved ijcnn singularities attached loading loading elsevier union union union subspaces subspaces dichotomies dichotomies dichotomies dichotomies infinitely develops bution capacities capacities covers gratefully achievable achievable inequalities determinant eral dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy tuple huang huang cardinality cardinality squashing squashing squashing squashing computable closure elec kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk vanishing vanishing shortly shortly devoted talk proximation elaborate assessing assessing direc kolmogorov kolmogorov kolmogorov virtue intersect hong couple psaltis def def superiority acknowledged separability necessity necessity convexity genuine rising lira isomorphic permission adaptable sakurai sakurai sakurai intend pathological publications strengthened sufficiency genera contradiction viii adam pseudoinverse corrects deduced tuples tuples telecom telecom grounds trl iiw diverging diverging rst contradicts virtues publish differenttable differenttable downs eff decisive clayton madaline fized fized plying blackburn orem hitachi vic complezity controversy 
#@Kowalczyk_A,
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#*network network network network network learning learning learning learning model model model model model model model model model model model model model neural input input input input input input input input input input input input input data data data data data data data figure figure time time time time set set set set set set set set set set set networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number 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based based based based based based based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case vector vector vector order order order order shown shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight functions functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern point point single single processing control large large large large local local rate rate rate rate rate test test test class class class class class class class class class class class class class class class class class class class class optimal optimal inputs inputs inputs shows shows signal gaussian paper paper examples examples examples size net net net net net net net work work task features features features features features features classification classification classification classification process level level level level level level level level level trained trained trained trained trained trained trained trained trained structure problems memory memory similar similar similar similar representation representation representation architecture architecture architecture architecture show section section section section rule vectors vectors vectors general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter average average states states states states states states states states states states states states states states states states states theory gradient experiments experiments result result result result result result result university computation computation computation solution independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent log log log defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target dynamics initial initial initial initial initial initial initial constant table table table table table estimate estimate estimate estimate standard standard standard standard computer science left left left left left presented presented presented map present present phase phase phase low sets sets sets sets sets maximum range press learn nonlinear outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied find computational computational computational density likelihood likelihood references stochastic stochastic due due due positive procedure procedure procedure procedure procedure propagation mixture mixture mixture mixture context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context introduction introduction estimation estimation estimation estimation estimation estimation statistical variance parallel parallel search search tion tion tion tion tion change change change energy energy energy prior representations representations word word word word word word word word word word word word word word learned higher higher higher higher part previous cases cases type required required required required multiple multiple multiple multiple multiple multiple multiple binary binary long distributed distributed distributed distributed bayesian markov markov markov markov markov markov make make fact techniques proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed forward forward forward forward finite finite minimum minimum resulting resulting resulting resulting resulting classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes ing ing ing tasks computed computed computed computed performed factor factor factor factor made applications obtain negative original original vol relative specific specific specific specific specific specific specific specific specific specific specific specific specific specific specific application desired cross cross cross cross cross cross cross provide provide compute compute compute compute compute perform perform posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions distributions distributions distributions distributions power mit accuracy larger train train train train train train train descent descent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent source nets nets modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan words words words implementation implementation technique internal individual individual individual connectionist connectionist layers layers layers layers layers layers addition addition addition addition addition computing directly hinton view estimates estimates estimates estimates transition transition trajectory san san effects effects effects effects determine determine efficient approximate estimated estimated increase validation validation validation validation validation validation validation con condition weighted developed developed levels criterion criterion entropy entropy provided provided provided finally backpropagation nature nature achieved discussion increases increases describe hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited corresponds amount amount common common effective supported eds eds journal journal end instance future rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart including including including fit probabilistic typically needed reduced reduced coefficients coefficients coefficients technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp significantly increasing special database database database database iterations making window international international international normalized frame frame frame frame frame frame combined combined run architectures improve recent pair pair pair robust robust robust robust separate separate separate separate separate separate separate reported apply moving identical subset array array recently relevant highly highly previously previously approximately tuning tions smooth speaker speaker speaker correspond converge achieve achieve sparse evaluation observation observation observation observation observation observation observation observation generalized generalized generalized generalized generalized generalized generalized williams increased increased increased lead suggests suggests extended extended alternative feed feed hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hardware place greater assumptions reduce reduce conclusions bayes performs performs performs practice practice suggest suggest suggest sound strong reduction reduction characteristics sigmoidal labeled assuming decrease acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acknowledgements pro produces index generating estimating label segments segments segments modeled multilayer multilayer explicitly averaging linearly consisting focus dependence dependence dependence dependence dependence communication overlap viewed influence detailed detailed densities evaluated labels frames frames converges allowed discrimination processor processor earlier earlier earlier smoothing smoothing smoothing smoothing smoothing smoothing reduces combining purpose boundaries interpolation valid string string string advantages advantages topology david degrees degrees degrees activations perceptrons perceptrons bell weighting extension automatic partially discussions grammar grammar grammar grammar grammar grammar grammar tests tests tests tests tests tests tests tests middle middle extra hmms hmms hmms hmms hmms hmms importance delta delta symbols included mcclelland computations comparing vowel capture capture capture traditional allowing allowing stopping phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic dis dis dis categories categories categories involved michael generalize backward backward highest attempt consisted overlapping overlapping mixing load load extend presents presents simpler simpler simpler production requirements experience experience put limitations dual discriminant discriminant ml ml helpful fewer reducing tech scaled referred referred maximizing hierarchy hierarchy cognition adjusted front versions algo initialized art art consist improving mixed mixed mixed mixed sentences sentences sentences years asymptotically ment stop stop waveform improves improves improves independence starts rapid stanford stanford tive berkeley ring ring producing broad desirable immediately recognized preceding robustness improvements improvements percent percent substantially substantially pure pure pure pure conducted poorly cohen cohen cohen cohen cohen cohen cohen cohen cohen price vocabulary vocabulary resource resource resource resource resource resource resource acoustics phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone adjust substantial substantial chose viterbi viterbi viterbi viterbi viterbi viterbi sentence sentence sharing sharing sharing sharing sharing sharing sharing initialization spectra aligned aligned aligned rithm conditioned conditioned conditioned conditioned conditioned resources resources count proceed allocation proceeds replacing contract resulted hope bourlard bourlard bourlard bourlard north adequate adequate adequate exploring tap contexts contexts contexts contexts contexts combines combines ranging representational representational decide holland realization schwartz mel counting counting tic darpa darpa darpa darpa darpa initialize francisco francisco recog mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps mlps foundations smoothed smoothed theoretically specificity belonging likelihoods likelihoods likelihoods explorations displacement mind discriminate discriminate discriminate discriminate converted microstructure vec tables tables benefits nelson forced axe nition incrementally discriminative retraining icassp icassp icassp icassp icassp personal tor unseen peripheral gained management management management management management management proba deleted tied tied intl stuck compu exploited october factored rabiner recogni interpolated attempting attempting finer finer finer supplied practically ters extracts attained archi restricting syntactic sian articulation tations restrictive gaus correlates concatenated concatenated tra dent feb feb robustly indepen mul february tim sep sep sep sep syst ized occurrences shares ming spanning renals renals renals renals renals amsterdam hood pendent phones phones phones phones phones phones mir rela broader accu parame posi posteriors phonological rap rap tecture mercer mercer menlo corresponded retains perplexity beer tri del mexico mexico icsi icsi likeli likeli chir franco franco franco franco franco franco tributions cri makhoul sharper chow bernstein bilities kohn assump manage relaxing deci deci observa beck planned tives accomplishes boutlard ditions vocabularies logs cording racy deriva refinements factoring factoring factoring acous abrash abrash abrash abrash 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#@Abrash_V,Cohen_M,Franco_H,Morgan_N,Rumelhart_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set networks networks networks training training output output output output output number number number system system system results results results results information information problem models models performance performance performance performance performance based based based based based based based based based based based layer layer layer case order order order order shown shown shown shown shown systems systems values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions unit recognition approach approach processing processing processing processing processing control control control test test test test test test test patterns patterns analysis analysis analysis analysis analysis analysis analysis inputs inputs form shows shows shows shows signal signal simple simple simple simple visual paper paper paper small small size net work work task step step step process problems architecture show section generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter real real real real real real real real real real real real real obtained obtained experiments experiments activity activity activity result university research research research sequence sequence sequence target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial terms science presented presented low low frequency temporal sets motion motion motion motion motion motion motion motion range learn learn learn position position position position position position position position components outputs outputs continuous continuous continuous continuous sample sample abstract back back back computational properties references ieee important propagation introduction action complex estimation estimation estimation estimation behavior behavior behavior behavior behavior behavior dynamic dynamic dynamic generated generated generated generated generated generated generated parallel parallel recurrent tion change change complexity complexity lower signals signals signals representations learned learned learned learned good good good long distributed distributed techniques techniques correlation observed errors errors errors errors forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward scale minimum minimum ing ing ing human human mapping mapping factor dimension dimension dimension made natural natural global global study filter obtain obtain original specific specific samples samples samples samples represented compared compared cross cross provide rates experimental experimental experimental experimental experimental experimental related constraints connected gain motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor discrete larger support source source source source source source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling morgan report institute implementation advances difficult final final delay scheme scheme addition computing experiment hinton hinton additional trajectory trajectory trajectory trajectory trajectory san top stage effects upper full full estimated estimated estimated produce criterion criterion area area area velocity velocity velocity velocity velocity provided finally nature constraint discussion technical technical increases group transformation limited limited inverse corresponds surface surface implemented shape shape shape shape shape generate main eds eds journal ability degree rumelhart rumelhart including kaufmann auditory underlying dynamical dynamical coefficients jordan jordan jordan jordan jordan jordan jordan jordan interesting increasing head head empirical empirical representing direct window bottom early attention combined produced produced run added added sources predict predict perceptron improve movement movement movement movement movement movement movement reported introduced introduced introduced include subject inference cognitive recently dimensions trans positions positions positions channels channels williams williams entire entire increased increased grant arm arm amplitude parts parts suggests extended digital predicted alternative move boundary generally generally pass trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories numerical moody learns constrained mateo sound sound sound hard mechanisms integration integration integration characteristics demonstrated movements targets targets introduce introduce acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic areas areas relation relation perception primary laboratory label vertical vertical vertical modeled implement simultaneously unique develop integrated springer formation formation phoneme phoneme phoneme phoneme phoneme correlated correlated transform transform modulation spectrum partial sec generation generation initially filtering string degrees recorded recorded recorded recorded recorded recorded strings strings reason reason aspects suitable suitable differ computationally situation ten summary verlag graphs physiological physiological physiological device vary simplified paradigm paradigm wave wave wave wave predictor predictor subsequent subsequent acknowledgments employed command command production production production production production production production put put hanson limitations issues lippmann preliminary preliminary matches mappings biol biol muscle muscle muscle muscle reliable variability examined closest plausible possibly predicting freedom precise perceptton initialized generates motivated serial electronic seconds residual residual residual residual residual ment publishers smoothness waveform waveform cascade cascade tool tive sections sections producing bengio bengio commonly laboratories laboratories laboratories ridge begin recording demonstrates apparent improvements greatly double collected collected collected profile offset effort effort effort cohen cohen recordings commands commands commands commands commands commands commands commands berlin synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis limiting aim cal incorporating serve acoustics acoustics acoustics acoustics acoustics acoustics acoustics inherent chose sophisticated utterances utterances utterances utterances utterances utterances utterances utterances progress progress simultaneous sentence sentence converged summed instantaneous cumulative cor cor cor lot realized acquisition acquisition cybern cybern interface japan japan japan driving velocities recover perfectly controlling repre resulted kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato wire utterance utterance utterance utterance utterance utterance utterance modifications muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles vowels vowels lip lip lip lip intended consequences enable spatiotemporal insight suggesting ahead record contact waveforms motions erlbaum formant formant formant formant reverse grants limitation severe speaking linguistic audio specification numerous torque torque encouraging propagating par par reports acceleration acceleration acceleration acceleration acceleration hillsdale causal eric param attempted concentrated articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator relating relating differentiation acquired acquired scope proach pos responding articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory applicability tract tract tract tract tract tract tract atr eters coordination stops served gestures drives styles opti acoust acoust preserves acquire acquire acquire ate distortions transduction synthesized synthesized synthesized synthesized synthesized heavily loaded pan pan conceptual concern tip tip physiologically physiologically physiologically physiologically physiologically anterior markers functionally intact governing rameters vocal vocal vocal vocal vocal vocal vocal emg emg emg emg emg emg emg emg emg emg cho articulation articulation articulation nih uno uno uno uno suzuki suzuki suzuki suzuki proceeding spec medial developments modularity saito saito saito saito assessing sentations plexity insertions tongue tongue tongue tongue tongue tongue tongue tongue tongue tongue tongue weakness synthesize synthesize mal tics rectification enabled patterned lips lips lips lips adap gun desire outlines distinguishes bateson bateson bateson bateson bateson bateson kyoto succession encouragement lowering rce permitted namic jackson jackson closing closing closing poorer quences opening opening opening hoped entails antagonist skeletal skeletal synthesizer soraku snowbird speak jaw jaw jaw jaw jaw jaw jaw jaw jaw jaw dan ond namics abrupt seika articulators articulators raising accelerations accelerations hikaridai recurrently insightful overly acous stringent facilities prosodic ichi tick listening intention ify skilled ensuing ensuing ensuing utah conse appropri electromagnetic electromagnetic optoelectronic optoelectronic phonetics extrinsic mitsuo underestimate sectional schwarz suits jor ology pause produc ological physi fricatives audible progressed mands hfsp placements 
#@Hirayama_M,Honda_K,Kawato_M,Kioke_Y,Vatikiotis-Bateson_E,
#t6
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input data data data data function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set networks output output output output output output number system system system results results information information information information information models models models models performance based linear case order order order shown shown shown shown shown systems systems systems parameters parameters noise functions method processing processing processing processing processing processing processing processing processing patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis form form shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal paper paper small feature work work work methods methods cells cells cells features process cell cell structure structure structure high high high high high high high high high high response response response response response response response response response response response response response response response similar similar representation representation representation representation representation representation section section speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real theory theory obtained term term result result result university university computation log log found constant constant constant estimate standard standard computer computer terms prediction left presented presented map present present low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal range range range components outputs abstract applied applied find density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties references component component ieee ieee procedure introduction complex complex hand circuit estimation estimation effect dynamic dynamic dynamic generated tion tion difference variable measure signals signals signals signals signals signals signals representations word word higher higher higher firing firing firing firing firing required multiple good good good good long fact proposed length scale simulations simulations ing tasks simulation simulation simulation performed performed performed times elements regions natural applications study filter filter filter filter filter filter filter filter filter filter obtain obtain relative specific represented represented compared provide rates rates rates rates rates determined determined related related constraints power comparison institute department implementation implementation synapses synapses consists consists consists responses responses delay delay scheme scheme considered considered considered computing domain domain domain domain directly directly additional curves design top top top choice estimated basic give channel channel channel coding developed developed nature nature biological biological discussion group group group limited close short short short effective effective implemented implemented synapse main adaptation adaptation adaptation vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi development fit fit auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory pairs pairs pairs pairs pairs smaller functional fully technology technology uniform principle operation language representing direct window window window window window window window window window window bottom bottom magnitude minimize architectures membrane resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution advantage pair pair pair pair robust reported period identical identical relevant engineering engineering engineering engineering varying varying conventional conventional conventional speaker speaker match studies trans trans address locations channels channels channels channels channels amplitude amplitude amplitude concept scaling alternative width hardware conclusions depend modules modules clear peak peak peak peak peak peak performs practice constrained suggest strong characteristics demonstrated california plane manner base base question pro plot laboratory stability tuned tuned tuned vertical vertical changing changing simultaneously physical physical physical electrical electrical spectral spectral spectral spectral spectral spectral spectral spectral frequencies frequencies frequencies frequencies frequencies events implies extracted focus stationary stages communication communication viewed detailed transform transform transform transform transform transform lee understanding completely similarly earlier additive delays intervals intervals intervals generation precision exploration silicon silicon silicon silicon usa usa inter inter inter determines uncertainty variations absolute compression middle aspects closely closely closely importance suitable effectively literature efficiently situation vowel fine characteristic characteristic characteristic capture summary refer soc soc soc dis running physiological duration receptor vary localization realistic realistic wavelet wavelet wavelet chips subsequent subsequent operating software software software software software software parametric parametric mead mead mead mead rapidly rapidly limitations limitations accurately accurately fourier fourier fourier fourier fundamental fundamental fundamental fundamental notion transmission trace trace trace man illustrate front obvious obvious precise separated nerve nerve nerve nerve nerve nerve nerve nerve fibers fibers fibers fibers fibers fibers fibers fibers extent extent electronic synthetic synthetic synthetic synthetic synthetic synthetic synthetic languages histogram histogram histogram histogram band analyzed tool nonlinearity london reasons rapid rapid tive widely precisely broad desirable scientific sounds sounds pitch pitch pitch pitch pitch res read arises depicted bandwidth bandwidth bandwidth bandwidth cybernetics researchers mechanics fourth apparent considerably composite cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear flexible spoken spoken spoken incorporated frequently exhibits exhibits cal hamming hamming fiber windows cochlea cochlea cochlea calls wesley instantaneous instantaneous instantaneous gap ear addison gabor harmonic caltech arranged fails smith smith imposed obtaining analyzing affected adequate adequate tone tone tone tone tone tone tone loo loo male male regard lengths histograms histograms sim enable insight reveals lazzaro lazzaro ends formant formant limitation discharge liu liu liu liu liu liu hair hair hair hair shorter equivalently lane gaps gaps benefits bank bank bank bank bank ideally tradeoff tradeoff tradeoff tradeoff german representa representa pub cessing mammalian mammalian mammalian neurophysiological neurophysiological hughes careful emphasize win discusses tones tones tones tones sweeps compu examination wider resembles picking laws advantageous acoust acoust acoust acoust parameterization parameterization survey preserves reversed transduction tom autocorrelation autocorrelation builds multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution hearing envelope spacing spacing imple hopkins hopkins lyon lyon stripes fre compo spectrogram spectrogram spectrogram spectrogram spectrogram spectrogram spectrogram spectrogram acoustical dissertation resolutions andreou andreou andreou andreou andreou periphery periphery periphery characterizes johns johns communicate voice broadband broadband broadband broadband broadband broadband broadband broadband broadband broadband broadband broadband broadband baltimore eighth maryland maryland dissipation voiced voiced dow resemble demanding spectrograms spectrograms spectrograms gross bio alization andreas walker walker pursued rectification goldstein goldstein goldstein goldstein goldstein illustrating package watts watts lpc formants formants mented basilar nent ana ana bandwidths workstations workstations workstations beat behav jackson neurotransmitter revised interconnects interfaces interfaces insignificant shamma shamma harmonics harmonics harmonics harmonics ered lution consid refinements calibrated ney ior ulations duty perspec bot olution olution apex reso pervasive challenged taneous adequacy beating engi compressive tationally quencies instan reservoir neering periment substance 
#@Andreou_A,Goldstein_M,Liu_W,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning neural neural input input data data function function function function function function function function function function function time time time time time time time time time time time networks networks networks networks networks training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output number number number number number system system system error error error error error error error error error error error error error error problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance based based based based based space space space space space space space space weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case vector order shown shown values values probability probability probability probability probability probability probability probability parameters noise noise noise noise weight functions functions functions functions distribution distribution distribution recognition method method method method method method method method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern point point point point point processing processing large large local rate rate rate rate rate rate class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal gaussian gaussian gaussian gaussian gaussian paper small size size feature feature feature feature feature feature feature feature feature methods methods methods fig fig fig fig fig fig points features features features classification classification classification classification classification classification current trained structure structure structure structure problems problems problems problems problems problems problems random high high high high high high high memory similar similar similar equation equation section fixed line line rule rule rule rule rule general general general general general approximation approximation gradient note experiments experiments experiments result result result result threshold threshold threshold computation computation computation solution solution research research found found sequence terms terms distance distance distance distance node node node node phase phase low nodes nodes nodes nodes nodes nodes nodes nodes nodes press basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs sample sample sample sample sample abstract applied back convergence convergence convergence convergence properties references stochastic due due due ieee ieee procedure procedure procedure important adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision mixture introduction introduction complex complex complex complex statistical tion complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier lower signals signals signals chosen center center center theorem cases good binary binary long long long tree tree tree tree tree distributed make fact techniques proposed proposed proposed length length observed observed forward classes classes classes ing ing computed computed computed computed multi called regions means made made vol vol samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples represented represented compared compared compared compared application application desired desired desired desired series series provide provide provide location perform determined experimental goal posterior constraints discrete equal equal equal approaches approaches comparison comparison train train train implementation version version represents exp layers scheme sequences considered considered considered considered considered framework equivalent experiment design design design design design design design design design design design design design design design design efficient efficient significant speed increase give con con produce channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel weighted weighted weighted conditional developed developed developed product discussion fast fast fast limited close close amount amount assumed role theoretical theoretical theoretical require square square makes smaller smaller needed needed combination reduced reduced dynamical dynamical dynamical dynamical unknown mlp mlp mlp mlp testing testing york york increasing increasing increasing increasing increasing increasing structures structures mode operation operation operation numbers direct direct idea idea idea idea produced produced perceptron denotes improved discussed robust separate separate typical reported reported reported reported practical include achieve achieve achieve achieve rl trans trans separation generalized channels channels improvement storage grant grant amplitude amplitude constructed constructed constructed constructed expression suggests extended digital feed hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid width width width width width boundary boundary boundary boundary boundary boundary boundary boundary runs strength conclusion greater reduce reduce reduce valued accurate bayes bayes bayes bayes bayes bayes bayes bayes numerical exponential exponential practice suggest propose propose strong reduction demonstrated radial radial radial radial radial radial radial radial radial radial pulse relationship produces written written written written modeled recall multilayer multilayer easy integrated implies john reconstruction depending communication squares interpretation solved evaluated lee lee lee lee centers modulation modulation centered suggested suggested partition allowed spectrum diagram reasonable combining boundaries boundaries boundaries boundaries symbol symbol assigned advantages advantages classified david combinations bell batch determines automatic automatic automatic prove major major reason efficiency closely symbols symbols symbols symbols symbols symbols symbols orthogonal fine fine dis contribution classify classify satisfy correspondence correspondence received received consisted consisted neighboring neighboring deal cowan cowan cowan trains layered collection collection rapidly put replaced investigated combine authors authors structured structured structured structured structured complicated complicated hill coefficient closest closest closest closest closest transmission adjusted impulse academic ith explain established integrate residual residual piecewise piecewise waveform analytical reasons lin lin straight snr tive located desirable inversion inversion inversion inversion inversion inversion inversion summation summation summation explained collected conducted lms adjustable formulated ity partitioning partitioning partitioning partitioning partitioning partitioning partitioning gen chen chen chen chen chen chen adjust adjust shaped lot trade classifying classifying classifying ear ear accomplished princeton resources recover partitions enhancement interconnected communications communications adjusting overcome viewpoint reasoning receiver imply tap interference interference separating recovered combines introduces sion decide expanded sides percepttons offers mlps properly passing designing adopted adopted limitation divide consecutive dramatically geometrical ter sig leaming asked transmitted transmitted transmitted transmitted adopt solely forcing clas equality distri elementary proba deconvolution march fir synchronized sam sam isi isi ation bution lation bility distortions justification justification ers finer pearson pearson pearson pearson concern eral proposes ples ples push siu distorted distorted iid company feasibility thresh jitter denominator neigh turing proce proce quadrature equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization equalization traditionally traditionally adap classifica gibson gibson gibson gibson gibson asso taps tapped concluded iix xij proportionally confused confused confused confused confused confused numerator recon struction siftcation deci bet fused nals dure dure overlaid aug wei fukunaga fukunaga fukunaga oper ciated decent lxi llxi llxi llxi dispersive dispersive dispersive dispersive dispersive plugging cept ofa rearranging distort samoff boring undo 
#@Lee_W,Pearson_J,
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#*network network network network network network network network network model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data data data data data figure figure figure set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training output output output output output number number number number number number number number system system system system system system system system system system system system system system system system error error state state state state results results results results results results units units units units units units units units units units information information information information information information problem models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based layer case case case order shown shown shown shown shown systems systems systems systems probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach point single single processing processing processing processing processing large local rate rate rate test test test test test test test test test test analysis inputs signal simple simple paper size size net net net net net net net net work work work work work work work work task task features features features features features features features features features features classification classification classification classification classification process level trained trained trained trained trained trained trained problems high representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech note note note experiments experiments experiments experiments experiments result result computation independent independent independent independent independent independent independent independent independent independent independent independent independent log log table table estimate estimate estimate estimate estimate estimate estimate standard standard computer science direction presented map present frequency frequency temporal machine sets sets sets press press outputs continuous continuous continuous continuous continuous continuous abstract find properties likelihood likelihood references ieee ieee ieee context context introduction estimation estimation estimation estimation statistical statistical dynamic cost tion energy energy difference representations word chosen chosen center previous previous multiple multiple multiple binary binary binary binary bayesian markov markov markov markov techniques proposed length probabilities probabilities probabilities probabilities probabilities observed observed resulting total total computed computed multi potential natural applications study study artificial compared application cross cross proc proc proc proc goal goal related related related related constraints connected steps steps accuracy contrast contrast support dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent source nets nets nets nets nets nets modeling modeling modeling modeling modeling modeling modeling modeling morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan report institute words individual advances advances advances joint connectionist connectionist connectionist final scheme additional estimates estimates estimates limit limit san san san conference significant significant significant estimated basic pages validation validation give con con provided sampling constraint constraint constraint simply achieved achieved achieved discussion discussion discussion group hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited short common assumed assumed generate adaptation ability ability hypothesis future future rumelhart including kaufmann combination coefficients mlp mlp mlp mlp mlp mlp mlp mlp mlp consistent language making making window window international international international frame idea minimize description description architectures architectures improved improved improve improve recent separate separate separate separate separate separate separate separate separate reported calculated calculated volume speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker improvement improvement improvement improvement alternative hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid touretzky hardware starting critical assumptions editors mateo mateo california assuming exist averaged derivatives derivatives acoustic question acknowledgements reference reference explicit pro pro ways estimating estimating tuned changing multilayer multilayer explicitly explicitly integrated applying blocks blocks versus choosing expressed phoneme phoneme phoneme phoneme overlap viewed influence evaluate lee frames frames frames forms sizes similarly earlier reasonable expansion normalization msec msec msec building building existing usa usa perceptrons recognize extension discuss maximize specifically priors variations variations partially grammar extra divided build tdnn tdnn computations score essentially summary conf conf repeated prob phonetic phonetic phonetic phonetic classify duration michael giles highest software cowan parametric hanson issues helpful investigated int combine dependencies dependencies comparable workshop workshop statistically statistically fundamental fundamental waibel waibel waibel waibel waibel editor editor predicts predicts recognizer recognizer recognizer recognizer recognizer recognizer art speakers speakers baseline baseline baseline baseline explain attempts attempts sentences sentences sentences sentences sentences sentences sentences sentences integrate distinguish fairly explanation answer worse berkeley producing incorporate incorporate incorporate recognized recognized recognized calculations members lowest researchers fourth improvements pure led consistency consistency consistency consistency consistency consistency consistency consistency consistency consistency spoken lack cohen cohen cohen cohen cohen cohen cohen cohen cohen cohen share variant variant switch rely summarized resource resource resource resource resource resource resource incorporating phonemes acoustics phone phone phone phone phone phone chose conclude comments comments viterbi viterbi june june sentence sentence sentence sentence sentence merging sharing sharing realized realized princeton conditioned conditioned flexibility kaufman khz contract resulted utterance utterance utterance utterance bourlard bourlard bourlard bourlard bourlard bourlard bourlard north corpus corpus degradation published male male male male male male male male male male male male male male male male male holland lang mel mel darpa darpa darpa darpa darpa darpa francisco mlps augmented canada park balanced linguistic emission street nelson female female female female female female female female female examining param clas management management management management management management management oct oct march gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender gender rough rough meta meta meta funded intl tune permit permit tract eters october october worked helps recogni insufficient transforming jersey ave suite hypothesized hypothesized suppress suppress huang huang huang archi rameters vocal totally factorization twelve steve feb feb doubling doubling baltimore ensuring maryland experimented experimented shares shares enabling percep renals renals renals renals renals ceedings cepstral cepstral cepstral disadvantages phil hampshire hampshire hampshire hampshire scribed phonological rap tecture lpc menlo experimentation fruitful pronunciation perplexity konig konig konig konig konig konig konig konig nectionist nectionist jim depen accent attack icsi franco franco franco franco franco franco gramming males males males kohn siftcation consequent doubled beck females females females hermansky uttered uttered factoring abrash abrash abrash abrash abrash abrash abrash chuck factorize sri sri sri victor suffered wooters wooters wooters decipher decipher mda malization mainstream 
#@Abrash_V,Cohen_M,Franco_H,Konig_Y,Morgan_N,Wooters_C,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output number number number number number number number system error error error results results results results results results results results results units units information information information information information problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based space space weights weights weights linear linear linear layer layer case case case shown shown shown shown systems systems systems values probability noise noise noise noise noise noise noise noise noise noise noise noise distribution recognition recognition recognition recognition approach approach approach approach approach approach pattern pattern pattern point point point point point point single processing processing processing processing control large large local rate rate rate test test test test test test test patterns patterns patterns patterns patterns analysis analysis class class class class class class class optimal optimal optimal optimal form shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal paper paper examples small feature net net net net work work work work step step points features features classification classification classification classification classification classification classification classification level trained trained trained trained problems problems random random random random random random random random random high high memory similar similar similar representation architecture show show show line line line line line rule rule rule rule rule rule rule speech speech real real approximation approximation average average theory theory theory gradient gradient term term activity activity activity activity result result result result university university threshold threshold computation solution research defined defined defined found found found found found target target target target target target target target target table table table table table table computer terms connections node prediction prediction prediction prediction prediction prediction prediction prediction presented presented presented present present present low nodes nodes nodes nodes frequency sets sets range press learn learn learn nonlinear outputs continuous sample sample sample sample sample abstract applied applied computational properties references due due due ieee ieee ieee ieee important important important important important important adaptive decision decision decision decision decision decision decision propagation introduction introduction hand stimulus statistical effect dynamic dynamic dynamic dynamic parallel cost recurrent recurrent recurrent search search search search search variable spatial classifier signals signals signals representations learned learned chosen chosen chosen chosen bound cases cases required spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike represent represent represent represent distributed distributed distributed make fact fact techniques length correct correct correct errors forward classes classes human human human human respect performed elements regions regions optimization study study filter filter filter filter filter filter filter filter filter filter vol vol vol artificial artificial samples samples samples samples samples samples compared application application application application desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired provide provide proc proc proc proc proc proc experimental goal related connected brain brain equal approaches comparison comparison larger dependent dependent selection morgan department implementation consists consists consists internal individual connectionist difficult difficult bias bias delay delay considered considered cambridge directly hinton view design limit effects bit detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection requires requires choice approximate give produce produce channel levels criterion criterion area provided provided selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature nature sampling simply simply biological biological biological close corresponds complete surface amount short common shape shape shape shape shape shape shape shape synapse supported role theoretical require require main eds adaptation square easily makes rumelhart rumelhart rumelhart rumelhart kaufmann typically smaller needed needed hopfield fully fully mlp interesting ratio york mechanism consistent matching empirical mode principle principle filters pre window window window window window normalized normalized normalized supervised supervised supervised supervised expert expert expert produced choose added added predict perceptron architectures improved improved discussed improve reported reported strategy include sense sense sense recently relevant relevant engineering sufficient sufficient varying compare conventional conventional conventional speaker studies trans address background background background background background background background background background background background background background background background background background background background background background background background background background background background background bounded williams williams williams improvement sensitive amplitude amplitude constructed exists extended spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes derivative conclusion segment conclusions differences sigmoid sigmoid bayes bayes bayes bayes performs performs performs faster practice learns cycle assuming exist iii iii iii iii minima configuration configuration configuration explicit explicit digit construct construct factors laboratory ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann changing segments implement multilayer averaging averaging averaging electrical consisting events events events events springer formed versus versus stationary correlated communication updated updated static static static static static static static sizes discrimination partial performing normalization normalization sec reduces purpose false false false false false false false false false false false false filtering filtering msec msec eeg eeg eeg eeg topology degrees expect template template template template template template thesis priori determines extension extension extension automatic automatic discuss variations partially reason aspects uniformly uniformly effectively included mcclelland presentation attractors detect tdnn schemes characteristic refer soc notice allowing interested interested issue running strategies duration duration comp sampled simplified paradigm paradigm paradigm delayed predictor operating preferred acknowledgments decreasing employed employed unlike powerful wiley poor poor poor create create create difficulty issues issues issues issues biases biases discriminant discriminant existence fewer fewer school detectors detectors proper variability variability workshop cover momentum matched matched matched matched matched matched matched matched matched matched matched examined naturally necessarily configurations equally voltages thought olfactory olfactory freedom detector explain chaotic averages established stop agreement agreement agreement waveform waveform waveform waveform analytic explanation lies correction tool worse nonlinearity processed straight commonly recognized begin medical nsf exemplars robustness reflect reflect freeman freeman transient transient transient transient transient transient transient transient transient transient transient transient embedded embedded embedded experimentally experimentally readily readily quantitative poorly poorly marked detecting continuously extracting occurrence occurrence tank achieves electric decreased yielding don primarily generator gabor gabor princeton appropriately resources resources resources neurophysiol neurophysiol fails saturation promising promising difficulties simplify balance receiver adequate presentations meaningful utilized utilized utilized utilized decide bad bulb bulb assembly thomas thomas waves waves waves waves waves master matter augmented theoretically properly waveforms belonging concentration concentration grants fahlman fahlman stopped automated zipser outperforms summer roc anns sig sig removal classifies principe principe principe principe principe care care werbos werbos compatible picked picked emphasize speedup unconstrained unconstrained monitoring portions setup barlow barlow happen transients continually clinical acoust consuming decided decided quantify supply suffices converter detects normalize positives positives positives positives positives positives positives positives positives ultimate odors enhances watrous watrous longest longest compromise nonstationary nonstationary surprise kuhn detections detections detections detections detections detections detections jose pes deeper superiority ecs clocked palm clin clin disappear rationale taps cse refining teach implication organize makhoul makhoul makhoul backpropagated manifest discriminated morphological morphological suspect weber symp aertsen florida florida pertaining raven minneapolis electroenceph outperforming accommodated delve enforcement unnikrishnan whe universe gainesville artifical nput degrading neuroengineering nol dobbins extrapolating 
#@Principe_J,Zahalka_A,
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#*network network network network network network network network network network network network network network model model model neural neural neural neural neural neural neural neural neural neural neural input input input data data function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm number number number number system system system system system system system system system error error error error error error error error error error error error state state state state state results results results results results results results units units units units units units units units units units units units units information information problem problem models models models hidden hidden hidden performance performance performance performance performance performance based based based based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer layer layer case case case vector order order order order shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems parameters parameters parameters parameters parameters parameters weight weight functions unit unit unit unit unit unit unit unit unit unit unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern single processing processing processing control control large large large large large large large large large large large large large large test test test test test test matrix optimal optimal inputs signal simple paper paper small small small small small net work task task task classification classification classification classification classification classification level level level level level level level level level level level level level level level level level level level level level level level level level level level level current current trained trained trained trained trained trained problems high representation architecture architecture architecture architecture architecture architecture section fixed speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech states states states note note experiments experiments experiments experiments university university university solution independent independent independent independent independent log log found found found found found found found found target target target target constant constant constant table table table table computer science science prediction present present activation activation activation activation activation maximum outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied properties references positive positive adaptive adaptive mixture context context context context introduction behavior dynamic difference difference classifier classifier classifier classifier classifier word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word learned learned learned type multiple multiple multiple binary make fact fact fact correct correct errors scale resulting resulting resulting tasks total total multi multi multi multi sum sum sum performed performed performed performed performed called factor factor made negative negative negative negative negative original relative true compared compared application cross series define compute proc proc proc proc proc proc perform perform perform perform determined experimental experimental connected approaches accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison support train train dependent dependent dependent modeling morgan morgan morgan report words words words words words words words version version technique technique consists advances advances connectionist connectionist connectionist connectionist bias bias bias bias layers layers delay delay delay addition equivalent experiment experiment directly directly design design design conference conference conference conference conference requires free free give give con condition criterion criterion criterion criterion criterion criterion criterion area entropy path path actual backpropagation iteration sampling simply simply technical tested tested hmm hmm hmm hmm hmm limited limited close close corresponds amount effective end future makes kaufmann kaufmann typically unknown coefficients mlp mlp mlp mlp mlp mlp testing testing testing testing testing testing testing testing testing testing segmentation special consistent consistent consistent consistent database database database database database database database database database operation leads squared squared pre stored international normalized normalized bottom early early early early magnitude frame frame idea added improved improved improved improve separate apply quadratic hierarchical recently recently tions yields speaker speaker speaker speaker speaker speaker address address symmetric modified improvement entire entire scaling hybrid occurs demonstrate half conclusion segment sigmoid designed practice suggest suggest suggest sigmoidal sigmoidal sigmoidal ica exist targets targets connectivity connectivity connectivity program acoustic acknowledgements reference reference pro longer longer explicitly explicitly infinite remaining slightly adding adding predictive predictive national independently focus review depending depending phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme influence densities evaluated lee frames frames forms suggested discrimination discrimination discrimination discrimination delays sec boundaries boundaries remains intermediate intermediate sufficiently foundation avoid expect recorded existing includes thesis activations activations illustrated illustrated discuss specifically straightforward letter mcclelland tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn score score tend online fine prob prob showing phonetic dis criteria criteria criteria hold duration quantization highest highest leading leading cat cat cat cat cat cat cat cat cat subsequent simpler transformed difficulty updating optimized preliminary preliminary preliminary biases biases biases helpful matches successive giving school mse authors structured comparable proper proved waibel waibel waibel waibel waibel waibel waibel waibel opposite perfect perfect obvious assumes observe initialized phd sentences sentences sentences isolated great publishers publishers defining defining majority expensive expensive purposes sys sys sys shared shared shared shared ran consequence ion english attribute arises preceding mellon mellon mellon addressed alignment alignment alignment alignment alignment integrating varies carnegie carnegie carnegie cmu cmu cmu cmu consistency consistency cohen backprop introducing posed recordings treated frequently incorrect incorrect incorrect vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary pittsburgh modulated incoming incoming resource resource resource incorporating phonemes phonemes phonemes acoustics focused sentence sentence sentence consistently ordinary primarily primarily investigation lvq lvq lvq lvq dynamically tem tem wrong held utterance date excellent corre negligible male enhance enhance viewing darpa recog properly balancing balancing balanced acknowledge counts lem lem speaking discriminate discriminate discriminate outperforms outperforms linked linked yielded nition suboptimal suboptimal discriminative retraining icassp icassp icassp icassp icassp comparative connec arising management management management tems ultimately noting tied worth apparently minor correlate correlate tonic sigmoids emphasis moderate gratefully fiat preserves resolve resolve resolve tdnns continued impractical trainable trainable designs suffers alex outperformed outperformed dom integrates sen archi establishing promise promise microphone merit ming spec discriminating bootstrapping bootstrapping bootstrapping bootstrapping modulate spotting spotting dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw accu conceptually enhancing registration registration registration copied copied phonological favorable begun vast tecture hild hild stabilized inconsistency inconsistency inconsistency inconsistency inconsistency inconsistency inconsistency perplexity perplexity tebelskis tebelskis tebelskis tebelskis tebelskis tebelskis tebelskis fulfill resolving resolving resolving handicapped motivate icsi franco encouraged hierarchically mat backpropagated backpropagated backpropagated joe reg phoneroes phoneroes phoneroes discriminated mono racy unbalanced confusable inconsistencies inconsistencies inconsistencies inconsistencies inconsistencies vious vious asymp franzini abrash eee tral sri lll inevitably pushing pushing sistent compensating rea nectivity cla rion resolves bootstrapped bootstrapped crite spond wilh presume outper disrupting tences overwhelming 
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#*network network network network network network network network network network network network network network model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data function function function function figure figure figure figure figure time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output number number number number number number number number number number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error error error error error error error error error error error error error error state state state state state state state state results results results results information information problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer case order order shown systems systems systems systems systems systems systems systems values values values probability probability parameters parameters parameters parameters parameters functions functions functions unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach point single single single single single single processing processing processing processing control control control large large large large local rate rate rate rate rate rate rate rate rate rate rate test test test test test test test test test test test test test test class class class matrix form form shows signal signal signal signal signal algorithms simple simple simple simple feature feature net net net net net net net net net net net net net net net net methods methods step step step points features features features features features features process process process level level current trained trained trained trained trained structure structure structure high representation representation representation section fixed fixed fixed fixed fixed vectors general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average obtained obtained term term experiments experiments experiments experiments result university computation computation computation computation independent independent independent independent independent independent independent independent independent log log log sequence sequence sequence sequence sequence sequence initial initial table table table table table estimate terms terms left left left left left presented presented present present sets sets sets sets sets sets sets sets sets sets maximum range basis basis basis basis basis nonlinear outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous abstract computational properties likelihood references due due ieee ieee ieee ieee ieee positive procedure important decision context context context context context context context context context context context context context context context context context context context context context context introduction estimation statistical search tion difference variable variable assume measure measure measure measure measure measure measure word word word word word word word word word word word word word word word word chosen chosen chosen higher previous cases required required multiple multiple good long conditions conditions represent markov markov markov make fact techniques techniques techniques correlation correlation length length length length correct correct correct correct probabilities probabilities minimum resulting total multi multi multi sum performed performed performed called times made made made made natural natural natural obtain negative original original vol artificial relative relative samples samples represented compared compared cross provide provide rates proc perform determined determined experimental posterior posterior discrete discrete power power approaches approaches approaches steps steps accuracy comparison train train train dependent dependent nets nets nets nets nets nets modeling modeling modeling modeling modeling modeling modeling selection morgan words words implementation version version technique individual individual joint final addition considered considered cambridge cambridge cambridge additional estimates design san san top top top top stage stage stage conference efficient classifiers full full full requires choice choice significant approximate estimated increase increase validation give give produce weighted conditional conditional developed developed developed developed criterion criterion criterion criterion criterion entropy entropy product actual provided selected sampling sampling sampling sampling simply achieved covariance feedforward describe tested tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm close assumption complete complete finding finding amount implemented implemented generate generate require main square hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis degree makes development development development development kaufmann objective probabilistic typically combination combination combination combination combination reduced reduced account coefficients coefficients coefficients coefficients coefficients technology programming segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism special consistent structures language language representing call call iterations window international frame frame frame frame combined combined minimize produced improved improve recent advantage advantage advantage advantage property separate typical reported introduced include identical recently previously conventional speaker speaker achieve improvement improvement improvement improvement improvement improvement constructed exists exists exists parts concept concept alternative hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid occurs segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment conclusions differences sigmoid designed taking taking taking integration presence largest reduction reduction sigmoidal demonstrated regularization regularization regularization regularization regularization regularization regularization regularization radial minimizing minimizing exist decrease iii minima reference produces estimating label segments segments segments segments segments segments simultaneously simultaneously slightly unique integrated adding minimization depending phoneme phoneme phoneme phoneme phoneme phoneme stages detailed transform transform transform labels showed frames frames frames frames frames frames frames frames frames frames frames frames frames frames understanding understanding suggested allowed diagram smoothing smoothing normalization reduces combining combining roughly purpose initially perceptrons recognize recognize extension extension automatic candidate candidate grammar tests selecting selecting selecting aspects efficiency hmms hmms divided included included successful score score score score score score score score score score score score score score score score score score score identity identity notice conf conf conf conf conf decoding phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic duration duration duration duration duration list list list list list list list list vary usual usual paradigm paradigm paradigm paradigm paradigm paradigm providing highest highest hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses automatically attempt consisted neighboring modelling modelling employed remain diego diego powerful xor limitations limitations limitations limitations ml ml behaviour scalar mse mse mse mse int int int int combine combine proved workshop scores scores scores scores scores scores scores scores cover neu ensure portion precise initialized art art art art art art art art speakers speakers speakers consist baseline attempts attempts sentences established mentioned mentioned histogram histogram ment stop publishers explanation capabilities answer answer independence independence nonlinearity nonlinearity reasons purposes producing incorporate controls consequence sounds gradually toronto researchers improvements composite composite spoken incorporated continuously incorrect incorrect incorrect schematic gains vocabulary vocabulary vocabulary differs resource resource serve phonemes phonemes phonemes phonemes extensions acoustics acoustics phone gave boston sophisticated utterances utterances utterances utterances utterances june sentence sentence sentence wesley distortion distortion distortion distortion distortion newton addison labeling tation restrict linearity turned proceed proceed dealing ments overcome resulted serves scoring scoring scoring scoring scoring removing utterance utterance utterance utterance utterance utterance utterance ral corpus corpus mance reset perfor male male conjunction regard bad schwartz schwartz schwartz schwartz schwartz schwartz mel searching darpa darpa darpa initialize initialize multiplied barron april smoothed snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn canada considerations fold adopted limitation treat discriminate diverse discriminative quasi quasi quasi quasi exception female female warping warping warping stands summarizes management convert oct oct oct march efforts efforts cosine cosine insertion gender drawback prevents september experi technologies technologies technologies stops acoust acoust decided austin hypothesized overtraining overtraining overtraining dropped dropped accomplish lists lists lists integrates incorporation floor conditionally comprising interpolate approaching drastically triangular falling inde constraining feb feb feb feb feb feb feb feb doubling seg tained decoded ous february february february durations sep sep sep sep occurrences unexpected cope trapped pendent cepstral cepstral cepstral segmental segmental segmental segmental segmental segmental segmental segmental accu mentation availability mention mention mention convolving positively scored released penalties penalties penalties encounter exclude segmentations grove continu mere bigger zhao zhao zhao zhao makhoul makhoul makhoul makhoul makhoul strange worthwhile apr apr warped manage phoneroes overcomes csr csr csr csr csr csr csr csr csr csr bringing suspect elliptical elliptical elliptical negatively deviate gish racy unsuccessful methodologies mas bbn bbn bbn bbn bbn bbn bbn pacific northeastern imm popularity advan requisite radically minneapolis luenberger happy sachusetts lift triphones segmen deterioration truncate tage adoption ameliorate flames excursion 
#@Makhoul_J,Schwartz_R,Zavaliagkos_G,Zhao_Y,
#t6
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#*network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output system system system system system system system system error error error error error error error error error error error state state state state state state state state state state state state results results results results results units units units units units units units units units units units information problem models models models hidden hidden hidden hidden hidden performance performance performance performance performance based based weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case vector vector vector shown shown shown shown shown systems systems systems systems values parameters weight functions unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach processing processing processing processing processing processing processing processing large large rate rate test test test test test test optimal optimal form shows shows shows shows signal signal signal signal signal signal simple paper small small size net net work task task classification classification classification classification classification classification process level level level level level level level level level level level level level level level level level level level level level level trained high high high high high similar architecture architecture architecture architecture architecture fixed fixed speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech states gradient note experiments experiments university independent independent independent independent independent independent independent independent independent independent independent log found found found found found sequence sequence sequence target target target target constant table table table standard standard computer distance connections connections connections connections connections science science left left presented presented present present phase sets sets nonlinear continuous continuous continuous continuous continuous continuous continuous abstract applied find find references due ieee ieee ieee ieee ieee ieee ieee ieee ieee ieee ieee ieee positive positive procedure procedure important important context context context introduction effect effect effect dynamic search tion change lower word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word part previous previous bound markov techniques techniques techniques techniques techniques techniques correct correct correct correct correct correct correct probabilities errors errors errors minimum ing tasks tasks tasks multi multi multi multi multi multi multi multi multi multi applications applications negative relative specific specific specific specific specific specific specific specific represented represented cross cross compute compute proc proc proc proc determined experimental related connected connected connected connected connected connected connected connected power accuracy accuracy accuracy accuracy accuracy accuracy accuracy support train train train train descent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent nets modeling modeling modeling modeling morgan proceedings proceedings proceedings words words words words words words words words words words words technique consists internal individual connectionist connectionist connectionist connectionist layers delay delay delay delay delay delay delay delay delay delay delay addition sequences experiment directly directly hinton additional additional additional curves curves stage stage stage conference conference conference conference conference classifiers choice free free free basic pages pages validation con con con coding derived developed area entropy path path path path path path path backpropagation backpropagation backpropagation backpropagation iteration iteration iteration iteration simply simply simply achieved achieved achieved hmm hmm short short effective square end end end future future degree degree makes including objective objective objective coefficients programming testing testing testing testing significantly significantly ratio segmentation segmentation special special database mode mode mode mode mode representing representing international international international international frame frame frame frame added architectures architectures improved improved improved improved improve exact typical reported reported reported apply introduced machines subset highly compare previously previously approximately tions tions speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker entire parts invariant hybrid boundary boundary half propose proportional targets targets derivatives identification base acknowledgements pro modeled remaining easy formed shift letters letters letters letters letters letters letters national phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme influence evaluated approximated suggested diagram delays delays boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries penalty penalty msec string string foundation classified transactions transactions avoid avoid building activations activations activations usa strings recognize determines extension extension maximize maximize absolute discussions characterized straightforward straightforward letter letter letter letter letter letter letter letter letter letter letter letter letter capable importance paths paths tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn score score score score summary conf kind prob phonetic phonetic classify running duration duration duration duration duration duration gray nips nips delayed highest receive receive extend essential essential put involving biases ideas school mse int combine authors proper proper proper phases waibel waibel waibel waibel waibel waibel waibel waibel waibel recognizer adjusted front front front algo freedom art speakers speakers speakers speakers speakers speakers speakers baseline baseline improving improving improving improving sentences sentences sentences sentences sentences sentences isolated great improves capabilities starts starts lin shared shared broad desirable ion recognized recognized beginning english english toronto depicted demonstrates recognizing recognizing recognizing mellon addressed alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment robustness integrating integrating integrating improvements carnegie collected cmu cmu pseudo spoken spoken spoken continuously continuously incorrect incorrect incorrect outliers templates vocabulary vocabulary vocabulary mod pittsburgh resource resource phonemes achieves acoustics acoustics acoustics acoustics acoustics acoustics acoustics sophisticated windows june sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence pose classifying aligned aligned ear forming rithm narrow databases unity addresses extending kaufman wrong occurred balance keeping optimally selects excellent started started started mance perfor male male male male male lang washington infinity darpa darpa treatment specialized specialized april canada pen pdf acknowledge accumulated approx outperform outperform sig july forced suboptimal discriminative connec female female female female female classifies shaded summarizes management management ijcnn mathematically crosses challenging march cole cole cole cole insertion insertion insertion insertion insertion names names gender gender gender gender gender gender gender gender gender gender gender cation maintains denver nal differing worked november deletion deletion deletion deletion gratefully tdnns doesn alex fft fft huang sliding approaching approaching prone iti problematic ized merit freely freely bootstrapping bootstrapping bootstrapping subnetworks spotting phones subnets subnets subnets dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw dtw activa shikano enforced enforced touch mar inte hampshire aimed aimed aimed pooled ontario fanty fanty fanty enabled copied ative ously hild hild hild hild hild seemingly tinuous penalties penalizing surrounded hwang tebelskis ration continu nonlin hanazawa spelled spelled spelled spelled spelled spelled nected sit backpropagated collaboration haffner silence joe phoneroes chitecture philosophy tionist neurm neurm neg patrick confusable confusable insightful franzini ney ney ney ney rob experimenting aries ified gopalakrishnan transac spell spell spell bootstrapped crossvalidation crossvalidation submodules fee codings tute arthur sheer hermann outper identifi 
#@Hild_H,Waibel_A,
#t6
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#*network network network network network network network network network network network network network learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data figure figure figure figure figure figure figure figure figure time time time time time time time time set set networks networks networks networks training training training training training training algorithm algorithm output output output output system system system system system system system system error error error error error error error results results results results results results results results results information information information information information problem performance performance performance performance performance based based based based based based based based based based space space space weights weights layer layer layer case systems systems systems probability distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method pattern pattern pattern point point point processing processing processing processing control large large local local rate rate test test patterns class class matrix inputs form shows signal algorithms algorithms simple simple paper paper examples examples examples examples small size size feature net net net net net net net work work work task methods methods methods methods methods methods methods methods step step points points points points features process process process current trained trained structure structure similar similar similar representation representation architecture architecture show show section section section fixed line line line line line line line line line line vectors speech speech obtained obtained obtained obtained obtained obtained obtained obtained experiments experiments university computation solution independent found found found sequence sequence sequence sequence sequence table table table table table table connections connections connections node node node direction map present present present present present low nodes learn basis outputs outputs outputs abstract computational computational references ieee ieee ieee introduction complex hand hand hand hand hand hand hand hand hand hand dynamic dynamic search tion tion spatial spatial lower representations word word word word word word word word word word word word word word chosen higher cases long expected markov fact techniques techniques proposed length length errors scale ing human multi performed factor dimension orientation orientation orientation orientation orientation orientation negative application define rates perform perform experimental connected connected distributions approaches steps steps steps comparison comparison comparison comparison comparison comparison larger contrast support modeling morgan morgan report institute words words words words words words words words words words words words words words words words version technique technique advances advances layers layers delay delay delay scheme addition graph graph graph graph graph graph graph graph graph graph graph considered directly hinton hinton hinton curve additional design trajectory trajectory trajectory detection determine basic pages pages give levels path path path path path path provided processes selected evidence nature constraint simply technical describe group denote corresponds short implemented main end pixel instance easily rumelhart rumelhart rumelhart kaufmann combination reduced account technology programming programming testing character character character character character character character character character character character character character character character character character character character character character segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation database database database mode principle call call numbers direct window window bottom decay combined produced produced run run run advantage separate separate include subject identical relevant relevant compare conventional volume module module module yields address definition grid interval improvement entire horizontal horizontal alternative alternative alternative correctly loop loop loop column starting starting critical conclusions designed designed designed performs performs performs performs moody exponential learns constrained drawn relationship characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters denoted digit digit written index optical optical ways transitions transitions confidence confidence pruning coordinates coordinates remaining slightly integrated integrated expectation letters letters letters letters letters letters extracted extracted independently phoneme communication overlap overlap interpretation interpretation interpretation interpretation interpretation interpretation similarly allowed processor spaces intervals purpose generation valid string transactions avoid expect handwritten box figures strings strings strings bell bell recognize recognize illustrated automatic absolute discussions regular identified letter letter letter letter letter efficiency differ differ driven identify identify tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn post score score score score notice kind contained cun cun cun cun cun cun cun heuristic success content device duration duration duration duration duration built list list sampled simplified simplified providing providing denker denker denker denker hypotheses hypotheses chips overlapping acknowledgments extend explore poor collection exhibit difficulty lippmann helpful successive successive giving investigated terminal scores scores scores scores scores scores cognition removed waibel waibel editor editor recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer versions detector separated separated consist grouping submitted motivated trivial capabilities handle starts processed purposes preprocessing preprocessing choices immediately laboratories consequence cut cut recognized english english english english english recognizing mellon people considerably carnegie reflect double double collected substantially empirically cmu poorly marked howard howard rely poisson ordered prevent prevent prevent acoustics returns viterbi viterbi progress calls hints hints identifying writing mistake tation tation princeton databases databases databases approximates printed printed printed printed printed printed printed printed printed grey grey inspired communications wrong wrong stronger handwriting handwriting keeping scoring symposium alphabet heuristics date performances lang lang lang searching jackel jackel jackel similarities recog shortest ends relies relies relies relies discovered summarize pen pen pen pen pen pen pen pen pen pen pen pen pen approx shading ent tables guyon guyon guyon guyon guyon guyon guyon guyon guyon guyon guyon convolutional convolutional convolutional transmitted legal legal legal nition boser boser boser weiss reports spaced spaced stands burges burges burges henderson henderson henderson henderson henderson henderson henderson penalized exam stroke grouped ijcnn labs ocr ocr ocr ocr ocr permits hubbard hubbard march writer individually ultimately insertion sweeping voting denver denver dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary grateful page commercial commercial commercial commercial commercial commercial nil nil nil nil nil nil nil nil nil october recognizers recognizers recognizers mann november nec spite suggestions gratefully styles preserves algorithmic recogni recogni pitts cursive cursive cursive cursive satisfactory attributed heavily jersey spacing graf keeler keeler char char char char char char bottou cally engine engine engine engine holmdel holmdel distinguishing thickness ples interpretations repetition capital capital capital strokes strokes totally complement magazine ben ben gathered lar baltimore cuts cuts segmenting jan durations rec facilitates enforcing meaningless preprocessed shikano checks sixth touch substituted advice ess mention mention darker tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative tentative yann acknowledged writers gun gun ration pad expects hanazawa discard bears numerals private albrecht indebted cleaned swiss simi schenkel schenkel schenkel schenkel schenkel schenkel postprocessing federal parenthesis kauf matan matan matan darkness nohl nohl nohl nohl nohl 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#@Guyon_I,Henderson_D,Nohl_C,Schenkel_M,Weissman_H,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model data data data data figure figure time time time time time time time set set set set set set set set set set training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based space case case case case case case case case case case order shown shown systems systems systems systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters noise unit distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach approach approach approach approach approach point point image image image image image image image image image image image image image image image image image image single single processing processing processing large test test test test test test analysis analysis analysis class class class class class class matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal shows shows shows shows signal algorithms simple simple simple gaussian paper paper paper small size size size size size work task task task task task methods fig points classification process level level current structure structure structure problems random random random random high similar similar representation representation representation show section section section section section section section fixed fixed images images images images images images images images images images images general generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real states states states states states states states states states states states states states states states states states states states states states states states states states states obtained obtained obtained obtained note note experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional solution solution solution independent independent defined defined defined found found found found found sequence sequence sequence sequence sequence sequence sequence sequence initial table table computer terms terms terms left left left left left left presented present present phase frequency frequency temporal temporal sets sets sets continuous sample sample sample abstract applied find computational density properties properties properties likelihood likelihood references references stochastic stochastic due due due ieee ieee ieee ieee ieee ieee ieee procedure procedure procedure procedure procedure important introduction hand hand hand estimation behavior behavior behavior statistical statistical statistical statistical statistical dynamic dynamic generated generated parallel search search complexity complexity variable variable rules signals signals word word word chosen chosen chosen higher previous cases cases type binary binary conditions conditions conditions conditions conditions equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov techniques region proposed probabilities probabilities probabilities probabilities probabilities probabilities observed errors errors errors errors errors errors errors errors minimum tasks tasks tasks computed computed respect respect performed performed performed called called called regions means means global applications applications applications knowledge obtain vol vol vol vol vol vol samples samples samples samples samples represented represented represented represented application application application define define proc proc proc perform perform active active active active active active active constraints constraints constraints constraints constraints constraints constraints constraints connected connected connected connected connected discrete discrete discrete power accuracy accuracy accuracy contrast fields fields update source source source modeling modeling modeling modeling modeling modeling modeling proceedings proceedings proceedings words words words individual joint joint joint joint joint joint represents addition sequences considered computing experiment experiment design transition transition transition transition transition transition stage stage stage stage conference efficient efficient full choice significant significant approximate estimated estimated basic increase condition condition levels bounds processes processes selected iteration iteration achieved achieved discussion increases describe describe describe describe describe describe describe describe denote denote denote denote tested tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm transformation corresponds finding finding finding finding effective effective role role main square pixel pixel pixel pixel ability makes noisy noisy fit needed account programming significantly significantly significantly character character character character character character character character increasing increasing increasing increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation consistent trials uniform database mode language leads leads call numbers iterations direct making normalized normalized bottom bottom bottom bottom polynomial polynomial polynomial polynomial polynomial produced choose sources discussed advantage advantage advantage property property property property property property typical typical introduced subject pixels pixels subset subset subset recently recently dimensions dimensions sufficient sufficient sufficient conventional conventional observations observations subjects axis rl trans address definition observation observation generalized generalized generalized generalized entire exists horizontal concept suggests matrices white neighbor valued depend central performs exponential exponential practice suggest propose propose hard hard hard hard exist exist exist exist exist introduce characters characters characters characters acoustic acoustic acoustic reference digit digit digit digit digit digit written written written written written index optical optical optical optical optical solving sequential generating estimating estimating vertical segments modeled modeled sensitivity explicitly coordinates simultaneously text text text develop integrated decreases independently independently expressed stages stages stages squares interpretation solved solved solved evaluated restricted showed lee lee lee centered centered forms understanding sizes similarly similarly similarly similarly similarly digits digits reduces combining generation advantages transactions transactions expect expect expect handwritten coordinate formulation bell extension automatic automatic black black characterized characterized characterized successfully simplicity reason hmms uniformly maximal divided effectively effectively identity summary summary traditional traditional traditional quickly decoding dis symmetry duration satisfy gibbs involved write observable observable observable observable observable ill leading leading leading maximization consisted neighboring decreasing extend origin involving preliminary mass successive comparable variability variability variability hill coarse naturally plausible ensure subsets subsets generates generates improving improving grouping grouping grouping grouping grouping submitted defines isolated isolated isolated isolated isolated isolated isolated isolated isolated isolated trivial guaranteed caused stress closer widely widely strictly located laboratories probable recognized describing alignment alignment alignment alignment alignment alignment alignment alignment raw geometric composite composite reflect collected axes lattice documents vocabulary differs incorporating incorporating acoustics segmented viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi utterances converged semantic distortion distortion initialization phenomenon aligned writing writing forming guarantee guarantee optimizing member recover count count flexibility printed grows grey plays plays murray convenient satisfying simplify check roles roles monotonically optimally optimally corpus generalizes generalizes constructive planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar elimination elimination elimination equals enhance belongs elastic elastic elastic elastic elastic elastic elastic april april kearns kearns grammatical grammatical grammatical extends likelihoods messages valuable explains stopped fold insensitive fly assigning boxes linguistic linguistic drop exhaustive exhaustive asked break encodes markovian markovian suboptimal suboptimal aij warping stands constrain mutually mutually rectangular levin levin levin levin levin levin levin levin levin levin levin levin levin levin levin exclusive pami pami ocr ocr ocr degraded degraded degraded intra intra intra intra eliminating eliminating writer rectangle noting unconstrained harder harder worth memoryless parametrized parametrized atr september recognizers unpublished november rabiner rabiner rabiner rabiner january august distortions distortions distortions distortions distortions distortions distortions distortions distortions cursive textures doesn ave realizations eliminates comprising comprising restricting governing nontrivial enhances enhances enhances assp assp constraining feb mountain noticed spent spotting spotting tolerant tutorial align mar imposing blur textured segmentations segmentations kuo dam handles aligning sharper overcoming concatenation sudden unspecified chellappa chellappa loth eft markovjan markovjan markovjan markovjan argmaxp argmaxp parametrization keywords kelly kelly goldman lnt deteriorate jelinek jelinek neous keams keams deterioration emitting elliot elliot skipped aligns lap eurospeech join chosing 
#@Levin_E,Pieraccini_R,
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#*network network network network network network network network network network network model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data data data data data data data data data function figure figure figure figure figure figure time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number system system error error error error error error error results results results results results results results results problem problem problem problem problem problem problem problem models models models models models models models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based space weights linear linear linear layer layer layer case vector vector shown systems systems systems values values values parameters noise noise functions functions unit distribution method method method approach approach approach point point single single single single single single control large large large large large large test test test test matrix matrix matrix inputs inputs inputs form shows algorithms algorithms algorithms simple gaussian paper small small size feature feature feature feature feature feature feature feature feature feature feature feature feature net net net net net net net net work work work work work task methods methods methods methods methods methods methods step features features features features features features features process process process process level level level level level level level current current current current trained trained trained trained trained trained trained trained problems random high high high high response response similar representation architecture architecture architecture architecture section section section fixed fixed fixed vectors vectors general general general generalization generalization parameter parameter parameter approximation average average gradient gradient gradient obtained obtained obtained obtained term term term term term note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university variables variables variables variables variables variables variables computation research independent found initial initial initial table table table table table table estimate standard terms terms direction direction direction present phase low low nodes nodes nodes nodes nodes nodes sets sets sets sets sets sets sets sets sets components components components nonlinear nonlinear outputs outputs sample sample abstract applied applied applied find find computational convergence references component ieee ieee ieee procedure important context introduction statistical statistical statistical variance parallel recurrent search search search tion difference complexity complexity complexity variable variable variable prior representations chosen part previous previous previous cases type type type good good good good good long conditions distributed distributed distributed make make techniques techniques proposed proposed proposed observed errors errors minimum resulting ing ing ing regression regression regression regression regression regression regression regression regression regression regression eq eq called times factor potential dimension dimension dimension dimension dimension made made study knowledge em artificial true application series provide proc proc proc determined experimental related distributions power power power power power power power power power approaches approaches comparison larger contrast support train train train source modeling selection selection selection selection department implementation implementation version version consists consists individual individual kernel difficult bias scheme addition view curves estimates stage stage stage stage full requires requires choice significant approximate approximate statistics basic basic basic basic increase give weighted conditional conditional area area types types provided provided provided backpropagation backpropagation backpropagation backpropagation depends depends depends achieved achieved achieved measured covariance tested tested limited inverse inverse inverse inverse circuits finding finding finding amount short short short short short implemented implemented implemented implemented journal square ability ability ability instance easily fit fit objective needed reduced functional interesting testing testing testing projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection structures matching uniform operation representing direct making window idea combined produced predict architectures architectures directions directions directions directions directions recent recent recent advantage advantage pair pair reported reported reported practical practical include quadratic recently recently relevant relevant engineering highly compare observations calculated works correspond studies trans address generalized improvement grant constructed occur suggests matrices rotation runs numerical peak peak peak peak peak constrained temperature temperature temperature temperature taking reduction reduction reduction reduction reduction reduction drawn turn minimizing minimizing minimizing minimizing minimizing plane relationship relationship iii introduce identification base base acknowledgements appears pro pro index index index index index index index index factors primary plot mathematical implement implement implement implement physical electrical electrical consisting consisting integrated adding implies expectation expectation cycles cycles select choosing family family focus squares evaluated evaluate controlled updated centered decomposition sizes suggested suggested past key partial earlier earlier earlier earlier reasonable smoothing smoothing smoothing smoothing additive fitting fitting fitting roughly initially avoid exploration box inter weighting subspace determines plotted illustrated candidate absolute absolute absolute discussions tests determining closely literature literature efficiently projections projections projections projections plots plots orthogonal fine fine fine fine fine fine fine conf quickly repeated heuristic success showing superior lie running running follow criteria sci simplified relaxation relaxation generalize providing providing nips eigenvalue predictor predictor attempt operating load load load load load load load load load load load employed employed employed employed explore carried american rapidly replaced hessian hall pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit fewer reducing reducing reducing reducing reducing fashion school combine comparable eigenvectors notion momentum smallest plausible implementations implementations implementations ensure subsets subsets friedman friedman friedman logistic logistic logistic baseline baseline improving utility utility utility defines years percentage percentage percentage percentage stop developing failure expensive benchmark benchmark nonlinearity comparisons arc easier day day constructing incorporate ran mathematics projected separately preceding nsf reflect led led conducted peaks peaks peaks peaks peaks employ span rely cal incorporating adjust green gave substantial electric electric electric electric electric electric electric electric electric electric shaped shaped summed univ sharing extensive martin princeton homogeneous connecting proceed rational proceeds balance ylx nonparametric nonparametric days days days days hours hours service service service slice sion encountered dependency intended washington forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting enable smoothed ahead relies eigenvector considerations considerations partitioned variants variants executed consecutive fitted temperatures temperatures temperatures temperatures rms leaving largely annals ent employs tibshirani tibshirani residuals exception intrator intrator individuals hastie hastie hastie magnitudes grouped goals chapman denoting efforts efforts efforts terrence picked individually unconstrained spanned grateful meet intensive exploratory exploratory computa computa info expense achievable consuming demand demand demand demand demand demand demand demand demand demand demand demand demand demand demand demand demand demand demand demand satisfactory marks justification heavily subnet subnet subnet subnet subnet subnet termination industrial affecting pronounced exposed believed operational slices autoregressive meth loads deals predictable daily daily daily daily daily weather weather ods demands demands twelve twelve scatter scatter scatter atlas enabling stan dispersion dispersion dispersion dispersion dispersion amer amer jenkins stat connor connor accuracies accuracies subnets subnets subnets subnets subnets subnets subnets subnets subnets subnets subnets contributing utilities utilities utilities huber huber gross gross repeats reviews assoc apparatus week albeit extremes extremes extremes extremes devel encourage winter scribed mmi burden ecs gorithms seemingly cen symmetrically fil trimming historical hwang buy prevented discard cities cities prof sketched occuring occuring suit fii fii fii regres intro cornell cornell forecast forecast forecast tered oped symp testbed deviates benchmarking ern corp statisti freedman prospects quantizing sir sir sir sir sir sir extremal devising pur tionally infrequently calibrate forecasts forecasts forecasts forecasts slicing slicing slicing slicing uninteresting decoupling ithaca sharkawi thirteen thirteen prompted morning morning morning morning diaconis fourteen jection lam lam jen ican ducing 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#*learning learning learning learning learning learning learning learning learning model model model model model model model model model model data data data data data data figure figure figure figure figure figure figure figure time time set set set training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number state state state state state state state results results results results information information information information problem models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden based space linear linear case case case case case order order values probability probability parameters parameters parameters distribution distribution distribution recognition recognition approach approach approach large rate analysis analysis matrix matrix optimal signal signal algorithms algorithms algorithms algorithms algorithms algorithms simple examples net methods cells cells features classification classification classification classification current trained trained trained trained trained cell cell structure problems random random random representation representation architecture architecture fixed line line line line line general general speech speech speech parameter parameter approximation approximation approximation approximation approximation approximation average average average states states states states states states states states states states states states experiments experiments university university university defined defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target dynamics initial initial estimate computer left left left left present low sets maximum maximum press abstract applied applied applied applied applied computational properties properties likelihood likelihood references stochastic ieee procedure procedure procedure procedure important important important important important important adaptive adaptive introduction statistical statistical dynamic generated variable variable variable lower prior chosen part part previous cases cases multiple multiple multiple multiple multiple multiple multiple multiple good represent represent tree tree expected equations equations markov markov markov markov markov markov markov region region region length length length length length length length length length length length probabilities observed observed forward forward forward scale minimum minimum resulting tasks tasks tasks tasks computed respect regions regions regions potential natural applications applications applications applications applications applications applications applications applications knowledge em em compared application provide define related constraints equal update update modeling modeling modeling modeling proceedings report report institute institute institute institute department department consists consists advances addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences ai computing computing computing domain experiment additional additional additional additional transition transition transition transition transition upper choice statistics statistics statistics basic basic basic derived derived derived randomly types entropy entropy entropy entropy entropy path path path path path product processes selected biological biological biological discussion technical technical describe hmm hmm hmm hmm hmm corresponds complete proof common common common main main main main main main journal end end end end instance easily easily including including including including including typically underlying needed needed account functional technology technology technology programming special special consistent database mode mode mode details max bottom produced added architectures architectures discussed discussed advantage typical include include identical subset subset subset subset recently highly highly highly highly previously calculated tions smooth smooth correspond converge rl rl positions positions constructed lead invariant suggests place segment clear mechanisms presence california california california california california start start start exist iii introduce characters identification identification identification base base base base boltzmann pro primary primary primary primary plot laboratory transitions transitions mathematical modeled consisting frequencies expectation expectation letters letters letters letters letters family family family family family family family family family family family independently reconstruction reconstruction stages communication viewed variation similarly classical symbol symbol symbol batch batch batch sciences plotted coupled variations domains domains holds characterized characterized structural letter hmms hmms hmms hmms hmms hmms hmms hmms paths paths symbols included wij wij detect detect efficiently computations characteristic capture capture induced contained contained receptor gibbs involved usual usual absence modular backward backward cmos cmos cmos cmos cmos binding binding reach maximization maximization unlike powerful essential exponentially dual terminal proper removed examined naturally psychology adjusted portion academic percentage indicating site biology biology biology biology biology biology biology biology biology biology biology briefly briefly baum baum baum baum tool tool stanford snr snr sites sites protein protein protein protein protein protein protein protein protein division division located transistors beginning members alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment marked marked adjustable haussler haussler haussler remove treated incorporating pasadena viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi utterances displays displays gap representative representative aligned aligned identifying sort accomplished resources perfectly cellular consideration significance chains ranges determination loops resulted salk krogh alphabet alphabet heuristics reset corre lengths sim lawrence lawrence reveals suggesting late specificity specificity proteins proteins proteins proteins proteins proteins proximity park likelihoods likelihoods santa characterization baldi baldi baldi baldi baldi baldi baldi baldi baldi baldi convergent emission emission emission emission emission emission dna dna dna super ber opposed welch welch welch welch exception arg molecular molecular molecular molecular molecular molecular gene visited chauvin chauvin chauvin chauvin chauvin num maintained searches insertion insertion ambiguous termed cation importantly amino amino amino diversity tij tij tij tij molecules treating gorithm remark served rabiner rabiner deletion resp resp resp resp sponding vii vii vii jet thousand families families families families families families families lated val discarded propulsion heterogeneous acid acid acid acid lnp evolutionary evolutionary crl cruz irvine tim awij awij insert insert insert ues hood hood applica lqr tutorial save enforced insertions insertions insertions insertions delete delete impor bonds jumps sible tie ucsc tant bind notably effector reilly reilly menlo consensus gorithms symmetrically penalties stars pierre prototypical prototypical han birds ans deletions deletions deletions mammals foreign classifi backbone backbone conserved conserved conserved conserved conserved conserved emerging recognizable private fragments eij eij eij eij emitted emitted kinase kinase kinase kinase kinase kinase kinase kinase abrupt imal mij mij mij mij nij nij nij nij nij viii viii ala detectable arl normalisation regu divergent wee wee wee wee wee tection ive mcclure mcclure mcclure mcclure mcclure mcclure phe rna downstream yves accomodate accomodate alignments alignments inserts emit tertiary struct stitute peptide hanks hanks nucleotide respon 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data data data data data data data function function figure time time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm output output output number number number number number system system error state results results results results units units units units units units units units units units units units units information information problem hidden performance performance performance performance performance based based based based based based based space weights weights weights weights weights linear layer layer layer layer layer layer layer layer case case case case case vector order order order order systems systems values values values values values probability parameters weight unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution method method approach approach pattern pattern image image image image image single single single single single single single single single processing processing processing processing large rate rate rate rate test test patterns analysis analysis analysis analysis algorithms gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual small small feature net task methods step field features features level level level level current current trained trained trained trained trained trained trained problems random random architecture fixed fixed fixed rule rule rule rule rule vectors vectors images images images images images images general generalization generalization obtained experiments result result university university university threshold threshold threshold threshold threshold threshold variables computation computation research research defined found found found found target initial table standard standard standard standard standard computer computer computer computer computer computer computer computer computer science science left left left left map present present activation low sets sets sets maximum press press press basis outputs abstract applied applied applied back computational references due due due due due due due ieee ieee ieee ieee positive positive positive procedure adaptive adaptive decision decision decision propagation context introduction complex complex statistical effect generated parallel parallel parallel tion classifier lower measure learned higher part part center center center center center center previous previous cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases multiple multiple multiple multiple multiple multiple good conditions distributed distributed make make region region region length length correct observed resulting resulting ing total total total human computed multi sum performed called regions regions regions regions regions regions regions regions regions factor made applications applications study negative artificial artificial artificial artificial artificial compared compared application application application application application cross cross provide location eye determined determined related posterior constraints constraints approaches mit accuracy accuracy comparison comparison larger contrast connection support train nets selection proceedings report department department department department technique technique internal individual individual difficult difficult exp delay delay delay delay considered considered cambridge experiment curve additional additional additional view view view detection detection detection detection detection detection conference determine determine efficient full significant approximate free world pages pages pages pages pages validation produce condition levels levels levels levels area selected selected backpropagation backpropagation backpropagation backpropagation sampling achieved measured normal normal normal normal normal normal normal normal technical technical group group tested tested limited limited complete complete circuits rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount require journal journal journal journal journal journal journal pixel ability future degree makes rumelhart rumelhart rumelhart noisy including typically smaller smaller combination reduced account testing significantly ratio york york representing representing representing details details numbers pre pre pre making making making normalized normalized experts supervised supervised supervised expert expert expert expert expert expert expert expert idea combined combined improved improved improved population directions exact exact lateral lateral lateral lateral lateral include period period period identical subset sejnowski sejnowski sejnowski recently interest interest highly compare previously previously unsupervised unsupervised approximately approximately volume volume volume works studies studies studies address background positions locations risk increased scaling occur digital digital correctly width occurs generally generally setting conclusions competitive competitive competitive competitive competitive editors editors editors editors interactions differences differences numerical moody learns learns learns learns learns learns presence presence physics intelligence labeled labeled radial targets groups identification acknowledgements areas pro pro pro index index winner winner winner estimating confidence confidence confidence sensitivity sensitivity sensitivity sensitivity angle unique consisting applying versus review overlap interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation completely suggested discrimination smoothing epochs epochs epochs epochs normalization add add assigned assigned views views views views views david perceptual perceptual combinations inter inter plotted plotted automatic specifically partially partially tests major planning gamma aspects closely suitable society society society society society society maximal encoded encoded divided delta delta delta included included mcclelland wij build essentially essentially characteristic refer interpreted interpreted criteria involved sampled play generalize generalize absence delayed leading consisted moves operating software tesauro tesauro camera employed explore american american investigate varied strengths accurately preliminary mass matches matches matches fashion history history history history possibility muscle muscle authors referred reliable reliable variability variability variability variability scores scores scores scores scores scores scores scores momentum momentum examined closest editor reading predicting psychology implementations initialized initialized switching mixed extent utility phd indicating distinguish distinguish agreement caused caused tool reasons considerable stress stress stress stress stress stress processed processed tive closer closer ring widely immediately immediately cut ion angles angles medical medical medical medical computers computers annual annual annual qualitative sun alignment explained improvements percent percent fuzzy profile profile led lms lms lms quantitative quantitative leave leave effort effort detecting incorporated treated variant compares extensions semi inherent patients attentional diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis irrelevant representative acquisition acquisition aligned proportion gabor appropriately discovery discover lost eliminated eliminated eliminated dealing anatomical imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging minutes promising accepted occurred city abilities interpret interpret interpret interpret interpret interpret interpret scoring mark shifts receiver affected preparation planar planar planar planar planar planar planar planar planar planar planar filled hours hours inferior sion corre patient widths mental dependency regard regard washington heart heart heart heart heart heart heart heart widrow widrow reproduce israel israel israel israel francisco francisco artifacts artifacts occlusion record augmented specificity specificity specificity observer observer observer observer observer observer observer observer observer observer observer impact hart dividing limitation counts severe severe severe severe severe severe severe accumulated unchanged zipser yielded roc unable ter visually visually annals maximized randomized utilize lesions profiles profiles profiles ical hundred england backgammon lesion lesion lesion translated decays mammalian intra intra expand march relate relate acquired acquired host distal distal distal distal distal gender disease disease disease disease disease disease disease disease disease ambiguous win happen sweeps page page exhibited tissue increments examination technologies clinical clinical clinical clinical clinical clinical clinical clinical clinical meir moderate moderate moderate moderate moderate august continued tial ping insufficient insufficient insufficient rosenberg rosenberg rosenberg rosenberg rosenberg rosenberg rosenberg rosenberg rosenberg assistance heavily breast breast breast breast agents austin observers observers reversible reversible dropped mining illinois val cally medicine medicine medicine medicine medicine medicine medicine medicine medicine medicine medicine medicine medicine medicine diagnostic diagnostic distinguishing anterior anterior anterior meeting meeting meeting assessment assessment marcus marcus marcus ooo ooo ooo attained interpretations interpretations interpretations modalities archi rating zipset zipset convention inspection protocol remained cho cho positional positional differentiate positioning inducing charles categorical mis hoff hoff rotational generaliza spec ceedings ceedings urbana jerusalem jerusalem jerusalem jack disorder segmental segmental biophysics biophysics cancel hebrew hebrew scans scans favorably favorably abnormal abnormal italy regional regional mal posi pursued devel cir enabled package proximal proximal proximal proximal viable viable terminated boost vast nuclear nuclear nuclear nuclear nuclear nuclear nuclear nuclear nuclear nuclear nuclear nuclear nuclear remember claimed tecture bruce terry deficit spontaneously consensus scored scored bull cardiac cardiac cardiac cardiac cardiac cardiac cardiac cardiac ant ant ant mild mild mild mild mild subtraction ire ire contiguous cad cad cad ratings ratings ratings ratings mined poorer exercise ecg administration roi champaign encouraged diseases ner confusions death lat lat lat wolf wolf wolf christian gions gions anonymous departments imal cedure elicit subregions favored duplicated suspect pulled oblique oblique oped western rodriguez perfusion perfusion perfusion perfusion perfusion perfusion perfusion perfusion defect defect defect defect defect defect defect defect defect defects defects defects defects defects defects assisted acute biolog profound garcia garcia garcia garcia garcia garcia garcia garcia distributes collins menzel severity severity severity fujita fujita deemed usable tissues wescon diagnoses utah redistribution redistribution diagnose staff grams hospital tioned individ agreements chap imaged thirds spect spect spect clude apex apex educational ctl haim netj aided lake rumel drs reviewers physician physician physician occasion instrumentation shin roland lvi ually moshe maining automati jacob 
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#*network network network network network network network network network network network network network network network network network learning learning learning learning model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set networks networks networks training training output output output output output output output output output output output output output output output output output output output output output number number state results results results units information based space space weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector order order shown shown shown shown systems systems values values values values values values weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons recognition recognition recognition method method point image image image image image processing control large neuron neuron neuron neuron neuron neuron neuron test test test test inputs inputs inputs inputs inputs inputs form form shows shows shows shows shows shows algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples size work work work work points features features process current current current current current current trained problems problems high high high high high memory response architecture architecture architecture architecture show show equation equation equation section section line images general real real approximation average average average gradient term experiments experiments experiments dimensional dimensional dimensional dimensional threshold threshold threshold threshold threshold threshold threshold computation computation standard computer distance distance distance distance distance distance synaptic science prediction left left left left map map present low range range press basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs outputs abstract applied density analog analog analog analog analog analog analog analog analog analog analog analog references due introduction introduction complex complex circuit circuit circuit circuit effect effect parallel parallel parallel variable lower measure higher center center previous type required required multiple good long equations equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make region ing ing total simulation simulation simulation computed multi sum sum sum called elements mapping mapping mapping dimension dimension applications applications filter filter vol vol vol represented represented application application compute compute compute compute compute compute location perform perform equal power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage support descent morgan version version version version synapses synapses synapses synapses synapses synapses synapses synapses kernel advances difficult exp bias bias addition computing computing computing computing equivalent limit san san top full requires requires requires choice approximate speed speed speed speed speed increase produce produce produce weighted weighted weighted lines backpropagation simply measured measured measured increases arbitrary arbitrary group tested tested tested fast close circuits circuits rbf rbf rbf rbf rbf rbf amount nearest implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse theoretical theoretical eds eds end end end end end end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel future future future future noisy kaufmann simulated smaller combination combination programming interesting character character character character character stored stored stored stored stored stored stored stored idea produced choose added discussed resolution resolution robust element quadratic quadratic quadratic quadratic quadratic quadratic sense sense sense sense sense sense sense sense sense sense sense sense sense sense array varying works works axis axis solve yields yields match match match address modified gate gate gate gate gate intensity intensity studied scaling suggests suggests deviation wide alternative locally touretzky width width setting setting hardware hardware hardware hardware hardware hardware hardware hardware hardware place conclusions neighbor designed peak peak peak moody moody moody moody moody exponential mateo hard physics drawn solid proportional proportional regularization radial radial radial radial radial radial radial radial radial radial radial radial radial radial radial radial radial radial decrease averaged introduce characters digit pro optical tuned mathematical mathematical implement implement implement multilayer simultaneously dimensionality gaussians gaussians gaussians john john yield expressed review operations operations lee lee centers static suggested partition partition partition partition partition diagram diagram partial slow reduces combining roughly interpolation interpolation david handwritten memories discuss discuss holds successfully middle letter suitable poggio poggio poggio build compact notice quickly success anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson running device cmos cmos computes computes computes computes computes approximating software software explore create create create investigate circuitry circuitry circuitry mead mead mead mead mead mead mead mead mead integral integral accurately accurately preliminary respond transistor transistor transistor transistor transistor tanh matched naturally editor reading ensure store attempts charge ground ground explanation floating floating floating floating floating multiplication turns easier transistors transistors desirable laboratories mathematics acknowledgement localized read researchers robustness fuzzy share adjustable splines dots outliers outliers measuring anti anti pasadena adjust adjust adjust adjust adjust gave implements wesley wesley lot don benefit addison addison fabricated fabricated fabricated oxford amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier linearity linearity linearity linearity linearity linearity girosi perfectly approximates approximates approximates jth unity unity unity unity unity printed robotics caltech platt platt platt platt platt platt platt khz darken adjusting mos mos attractive occurring capacitor adequate exceeds intuitive injection injection injection infinity lazzaro divide medium ideally subthreshold subthreshold wall graphics graphics rbfs rbfs rbfs rbfs rbfs rbfs setup setup discusses discusses sized turning amplifiers amplifiers amplifiers page union programmed programmed programmed programmed programmed lippman differing tunneling tunneling tunneling nec suggestions electron allen allen decided rosenberg interpolated spacing mirror steven inverter inverter inverter inverter inverter core core beneficial volts volts convolved convolved fair saturating appro mis scattered dissipation saturate jose aggregate cox carver hot operated hij hij hij hij heights capacitive advice mason coverage coverage kirk kirk kirk kirk kirk ramp exponentiated correspondingly multivariable rail rail rail rail adaptable follower follower follower follower follower blend micron votes votes votes exponentiation powell powell ink memorization synaptics negatively fonts darkness cid fimctions fimctions packard followers faggin faggin amp amp divider ampli veloped patent patent patent hewlett priate swept parkway blending blending federico orchard smooths sho ality 
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#*network network network network network network network learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training algorithm algorithm output output output output output output output output output output output output output output output output number number system system system system system system error error state state state state state state state state state state state state state state state results results results results results results results results units problem problem problem problem problem hidden performance performance performance performance performance performance based based weights weights linear layer layer layer case vector order order order shown systems systems systems systems systems systems systems values values noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight functions neurons neurons neurons neurons recognition recognition method point point point point single single single processing processing processing large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate test patterns patterns patterns inputs inputs inputs inputs form form form form form shows shows shows shows shows shows shows signal signal signal signal signal paper paper small size size work work task points points points classification process process process process process level current current current trained trained cell problems problems problems problems high high response similar representation architecture section section section fixed fixed vectors vectors images general speech real real real real states states obtained note note note experiments experiments activity activity activity activity activity activity activity result result university university university university computation computation computation computation computation computation computation research research independent constant constant constant table table table standard standard standard computer computer computer connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science presented presented presented presented presented presented activation frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal maximum maximum maximum maximum maximum range range range learn basis outputs outputs continuous abstract applied applied applied analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog likelihood references ieee ieee ieee ieee important important introduction circuit circuit circuit circuit circuit circuit circuit dynamic generated generated generated parallel recurrent recurrent tion tion tion difference variable variable variable higher previous previous firing type conditions represent distributed expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip region correct forward simulations resulting resulting ing ing ing tasks tasks total respect multi multi called times times elements regions factor natural feedback feedback applications applications applications applications applications original vol vol vol vol represented represented compared application application desired provide provide rates proc proc proc perform perform determined constraints gain gain gain power power power power power power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage accuracy larger larger contrast contrast connection support train dependent dependent dependent dependent source implementation synapses synapses synapses synapses technique difficult scheme addition addition graph computing computing equivalent directly additional additional curves curves design design design design design design design design design design design stage stage stage stage effects bit conference full world world world world speed speed vision vision basic basic developed levels criterion product actual finally finally finally processes nature nature nature nature constraint achieved achieved achieved measured technical describe arbitrary arbitrary tested limited circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits common effective shape synapse synapse synapse synapse synapse synapse synapse synapse synapse generate main main square end vlsi vlsi vlsi vlsi vlsi vlsi instance easily makes development development smaller fully technology mlp mlp block transfer transfer transfer edge mechanism uniform database operation operation leads representing filters filters direct bits international magnitude combined architectures architectures improved discussed discussed robust element practical apply period subject subset array engineering engineering engineering engineering sufficient varying varying previously conventional axis axis tions differential differential differential achieve trans evaluation gate storage increased horizontal concept digital digital digital digital digital correctly correctly width width width width width width width width width width column column pass pass conclusion critical conclusions sigmoid sigmoid sigmoid designed designed designed practice practice strong cycle characteristics characteristics characteristics characteristics sigmoidal sigmoidal sigmoidal demonstrated proportional pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse variety user targets targets manner groups acknowledgements reference reference reference reference pro edges solving solving describes describes vertical dept dept dept dept confidence implement implement implement linearly remaining easy integrated integrated integrated integrated formed versus versus letters yield communication variation densities evaluate controlled controlled approximations lee evolution modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation forms completely processor earlier calculation calculation epochs reduces initially advantages classified transactions precision silicon perceptrons currents currents inter inter inter inter illustrated illustrated variations variations variations variations tests successfully columns straightforward capable capable capable encoded effectively included included modes modes identify post post post post situation vowel vowel vowel vowel plots plots characteristic characteristic characteristic composed graphs induced contained success classify criteria device device device satisfy vary cmos cmos cmos chips chips principles subsequent operating software load load oriented employed carried circuitry put issues oscillator reducing tech ideal ideal transistor transistor authors comparable stream stream stream stream stream stream proved oscillation workshop func phases matched removed attributes act generalisation extremely illustrate voltages voltages voltages voltages voltages implementations implementations prototype impulse noted perceptton switching switching switching epoch speakers generates regime charge charge mentioned mentioned percentage percentage scenes stop band asynchronous asynchronous asynchronous asynchronous asynchronous crucial sensors fairly coded coded coded biology adapted multiplication multiplication implementing implementing sections transistors transistors transistors controls pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses sounds attribute auto explained virtual virtual greatly reflect double double double double transient flexible offset offset offset spoken generic generic generic generic fed completion employ ity gains incoming incoming germany inherent inherent comments segmented deviations june june arithmetic arithmetic arithmetic instantaneous globally analogue analogue fabricated fabricated interface guarantee guarantee oxford amplifier martin arguments linearity multipliers multipliers inspired multiplier multiplier multiplier multiplier smith smith murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray murray consideration ments mos stated stated programmable resistance resulted removing integrator synchronous capacitor mance widths perfor sides injection tic tic multiplied omitted waveforms subsequently subsequently subsequently temperatures mind discharge multiply appeared specification specification specification accept sig sig basically ram employs die causing drain tor edinburgh edinburgh edinburgh edinburgh unseen home packets epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon approxi intra disadvantage crosses eliminating cole transconductance transconductance transconductance employing million sheet diversity tively electronics grateful tune transients transients experi completed sigmoids sigmoids syn advantageous simplification stephen stephen ble ble council continued sake european ers spacing evolved king king king supply supply supply micro puts hamilton hamilton hamilton hamilton hamilton hamilton clarity tors inverter fabrication fabrication cally station station sided sided ray ray alan poly symmetrical symmetrical symmetrical baxter baxter baxter baxter baxter baxter baxter baxter tracks tance cascaded fair crl resultant comparator addressing elec elec elec ensuring ated dissipation experimented addi hip mid mid mid drawbacks cations cations elaborate appli appli sparc sparc tolerant tolerant tolerant cancel whilst whilst metal metal proce vdd vdd tran cir cir notably lay respec munich british synapfic synapfic ramp ramp ramp retains specifications banks circumvent driver communicating supplies supplies aver tarassenko tarassenko tarassenko facing renders embody imbalance depict invaluable lat sponses associ vas vas sor microelectronics microelectronics supplying markedly 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#t6
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#*model model neural neural neural input input input input input input data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output units units units information information information problem problem order order order order order shown shown shown shown shown shown shown shown systems systems systems values values values noise noise unit unit unit unit unit unit unit unit unit unit approach approach point image image image image image image image image image image single single single processing processing large large local neuron optimal optimal inputs inputs inputs shows shows shows shows shows shows shows shows shows shows signal signal signal signal algorithms algorithms algorithms algorithms simple visual visual visual visual visual visual visual small small work work work work work fig cells step field features features features features level level current cell cell cell high high high high high response response response response response response response response response similar architecture architecture line images parameter parameter parameter parameter real real real gradient obtained note threshold computation computation computation computation computation computation computation computation computation computation computation solution research research found found found computer distance distance distance distance node left left left left left direction direction direction direction direction direction direction present present present present low low low low frequency frequency temporal temporal temporal temporal motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion press basis outputs outputs outputs outputs outputs outputs outputs abstract analog analog analog analog analog analog analog analog analog analog references due due due ieee positive positive positive positive positive positive positive introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit estimation behavior behavior difference difference variable spatial spatial spatial spatial spatial lower measure chosen higher center center firing required conditions represent represent represent chip chip chip chip chip chip chip chip chip chip chip chip chip correlation correlation observed total total computed made natural applications filter filter filter negative negative negative negative negative vol compared series compute compute compute proc location location location location location location active active active active active active active determined experimental experimental experimental experimental constraints motor motor motor motor approaches approaches voltage voltage voltage voltage voltage comparison comparison comparison larger contrast contrast support morgan report report institute version version version internal kernel advances final bias bias delay delay delay delay delay delay delay delay delay delay delay scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme computing computing computing computing computing domain curve curve curve curve curve curve curve curve curves transition transition san bit detection efficient requires speed speed vision vision vision condition velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity provided measured increases increases fast fast fast corresponds surface circuits circuits circuits circuits circuits circuits finding amount implemented implemented implemented implemented implemented generate generate supported theoretical eds eds journal end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi easily including fit fit kaufmann needed needed technology edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge increasing operation operation operation operation details details details window window depth early light light light directions robust robust separate typical apply moving moving moving moving period side side pixels sense sense array array works tuning tuning tuning tuning tuning tuning tuning yields yields yields yields yields yields correspond correspond locations locations sensitive sensitive sensitive sensitive intensity occur rotation feed touretzky width width width width width width width width width width width width width half half half half flow conclusions competitive designed moody mateo hard presence physics california california pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse start program program program denoted acknowledgements pro pro edges edges edges edges edges edges edges edges edges edges edges edges optical laboratory tuned tuned tuned implement integrated integrated potentials potentials decreases yield focus dependence dependence stages overlap solved operations controlled controlled controlled controlled slow delays sec sec sec generation remains koch koch koch koch koch koch koch koch silicon thesis currents plotted prove activated coupled discussions sensor identified importance importance symbols detect detect computations schemes schemes schemes schemes tend receives composed soc compact compact quickly prob moore superior timing built built absence paradigm paradigm delayed delayed delayed delayed computes computes chips chips chips overlapping operating operating operating operating preferred receive origin remain selectivity create create circuitry circuitry circuitry circuitry circuitry circuitry mead mead mead mead environments environments rise fashion detectors detectors detectors detectors detectors detectors relationships office circles naturally plausible onset onset onset onset man opposite opposite voltages voltages voltages voltages voltages der der detector detector detector detector detector separated separated baseline detected detected phd defines years indicating ground sensors sensors adjacent adjacent adjacent adjacent adjacent biology expensive multiplication caused implementing satisfied filtered filtered division directional transistors pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses axon axon axon axon axon axon axon axon involve describing demonstrates demonstrates radius raw evaluating fed fed marked marked marked marked detecting detecting detecting detecting detecting detecting resistive sharp sharp monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic pasadena pasadena pasadena suited conductances logical fiber decreased implements implements implements implements implements begins lot don lab lab physiology amplifier amplifier angular angular angular refractory refractory velocities labelled labelled naval arrival caltech inspired inspired height fires evaluations loo loo bialek photoreceptor photoreceptor facilitate facilitate facilitate facilitate facilitate deg neuromorphic stimulated lazzaro environmental contact ends waveforms waveforms passing passing grants acknowledge fly fly boxes boxes crossing crossing crossing crossing crossing graded graded encodes responds trigger trigger trigger trigger trigger trigger trigger trigger trigger trigger trigger trigger amplitudes translated cessing cessing segregation concentrate ullman ullman differentiation lond ambiguous harder crossings crossings crossings crossings crossings crossings intl mimic investigations signs inactive technologies correlate correlate correlate correlate correlate spite triggered externally externally externally reversed transduction photoreceptors photoreceptors inverter cylinder cylinder cylinder fabrication wiring excited excited subtracted progressively marr offsets grids bandpass bandpass bandpass bandpass william robotic compensated mosis robustly rotational christof bidirectional analyse zone carver horiuchi horiuchi converts dead bright bright conceptually traversed ities bair bair bair bair bair bair bair des sodium lens lens watts 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#*network network network network network learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time set networks networks networks networks networks networks networks algorithm algorithm output output output output output output output number error error error state state results results results results results results information information information information information information problem performance performance weights case case case shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values probability probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight functions unit method approach approach approach processing processing processing processing local local local neuron test analysis inputs inputs inputs inputs inputs shows shows shows shows signal signal signal signal algorithms paper paper small small small work work work work fig fig fig fig fig fig fig fig step points features process process process process process process structure random high high high response similar similar similar architecture show equation rule vectors general parameter real approximation average average theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result variables variables variables variables computation computation solution research found target initial initial estimate estimate estimate estimate estimate estimate estimate estimate estimate computer computer node left left left direction presented present low low low low low range press position position components continuous continuous continuous continuous continuous abstract applied back convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties references stochastic stochastic stochastic ieee ieee ieee ieee ieee ieee ieee important important important important adaptive adaptive context introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation tion tion difference complexity lower signals signals signals signals chosen higher part part part previous multiple multiple represent distributed chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make techniques techniques region correlation correlation correlation correlation errors errors forward scale scale scale scale minimum minimum minimum simulation simulation computed multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi sum eq eq elements means factor optimization optimization optimization optimization optimization optimization optimization optimization potential dimension global global applications applications applications applications applications filter filter vol vol vol vol vol vol represented compared application application provide provide perform perform perform related discrete discrete discrete discrete discrete approaches mit larger contrast support descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent dependent source source source source morgan morgan morgan morgan morgan morgan proceedings institute institute institute institute implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation version technique technique technique technique technique technique technique technique technique technique technique technique advances advances advances advances advances joint represents represents addition computing directly curve additional additional curves curves curves estimates estimates estimates san san san san san effects conference efficient classifiers upper choice approximate approximate approximate approximate free free world estimated increase produce produce derived path path path actual provided processes backpropagation measured measured measured measured measured measured measured discussion describe describe describe tested tested fast surface surface surface actions circuits circuits circuits circuits circuits circuits circuits circuits implemented implemented implemented synapse supported theoretical main vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi easily typically needed needed technology technology technology block block interesting ratio character operation operation leads details filters filters international supervised magnitude magnitude sources sources description architectures similarity side dimensions dimensions dimensions dimensions varying volume smooth smooth match trans chain bounded improvement sensitive entire increased amplitude amplitude parts scaling extended derivative feed touretzky loop loop setting setting hardware hardware hardware hardware pass pass pass pass pass pass pass pass runs runs critical assumptions reduce trajectories conclusions conclusions operator operator accurate designed constrained constrained mateo mateo mateo taking hard integration integration integration integration integration california california california assuming minimizing derivatives derivatives minima annealing annealing annealing annealing annealing annealing acknowledgements reference explicit pro pro produces written generating estimating distinct metric metric implement implement integrated adding expectation expectation expectation john expressed correlated detailed detailed operations operations approximated approximated diagram diagram partial slow performing performing performing performing closed valid views transactions transactions transactions transactions david david david coupling box includes thesis thesis bell extension extension extension specifically variations differ compact compact kind anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson contribution providing nips nips wave computes computes automatically chips chips approximating approximating decreasing minimized minimized minimized unlike schedule schedule diego diego layered perturbation perturbation perturbation circuitry mead mead put integral existence scalar scalar scalar scalar ideas working tanh fundamental fundamental fundamental gradients gradients necessarily voltages precise submitted submitted advanced publishers derivation derivation derivation improves multiplication multiplication multiplication multiplication perspective implementing implementing producing style filtered filtered filtered operators operators operators desirable laboratories scientific gradually author nsf nsf raw raw greatly reflect fed continuously continuously dots variant perturbations limiting pasadena adjust boston findings june june wesley summed extreme don uncorrelated addison fabricated fabricated amplifier linearity caltech caltech caltech caltech multipliers platt platt systematic systematic multiplier multiplier multiplier kaufman kaufman kaufman kaufman kaufman adds mail multiplicative hope operates integrator alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector document combines sides intended washington injection colorado reproduce darpa smoothed grants summarize informa multiplying fellowship dec july utilize monotonicity ideally decomposed jabri jabri jabri jabri demon realize visualization ibm cessing cessing compensate graphics graphics graphics douglas douglas douglas bump bump bump bump bump bump differentiation differentiation differentiation sketch denver memo flower flower flower flower flower meir january allen christopher converging steven seattle triangle manually offsets offsets offsets offsets alan alan spirit deweerth cauwenberghs cauwenberghs cauwenberghs cauwenberghs contents mul parker kailath ted carver drawbacks intrinsically nov capacitive undesirable puter kirk kirk kirk kirk kirk kirk kirk kirk kirk kirk kirk kirk designated chi gupta kurt kurt beckman delbriick delbriick delbriick delbriick subtraction closing gra embodied leong dembo dembo dembo differentiated differentiated differentiated yuhas rid rid kauffman plications ventricular ware jayakumar gert apple dient kerns kerns kerns kerns kerns kerns kerns kerns kerns kerns kerns kerns kerns kerns kerns strate fleischer fleischer fleischer fleischer fleischer fleischer contaminated contaminated microchip correlating integrators packard chu permitting agencies rhs ual bart barr barr barr barr barr hewlett pacemakers individ escapes apex additively additively caught recommendations egg oyi larity gannett haber dimensionm opinions tobias 
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#*network network network network network network network network network network network network network learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data function function figure figure figure figure time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm output output output output system error error error state state state results information information information information information information information information information models models performance based space vector order order order shown systems systems systems systems values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight functions functions functions functions functions neurons recognition pattern pattern pattern pattern point point single single processing processing processing processing control control control control control control control control large large large large patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis class inputs inputs form form shows signal algorithms algorithms algorithms algorithms paper examples examples examples feature feature feature net net work work fig points field field features features process process level level current current trained structure structure structure structure structure structure structure structure structure high high high high architecture show vectors vectors vectors vectors general general speech real obtained obtained note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments university computation solution solution research research research research research defined defined found table computer computer connections node node science science science science map map map map map map map map map map map activation activation activation object object object object object object object object components components outputs outputs abstract abstract abstract abstract abstract abstract computational properties properties references ieee ieee ieee important propagation introduction action action action complex complex complex complex complex complex complex complex statistical statistical statistical statistical tion tion chosen part part center cases type multiple multiple multiple multiple equations make proposed proposed errors simulations classes classes classes classes classes classes ing ing ing ing simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation respect performed performed called called elements means means reinforcement potential natural natural natural applications applications applications applications artificial artificial application provide provide provide provide provide provide provide provide provide provide define define compute rates perform determined determined experimental related constraints constraints constraints approaches connection update support train source nets nets nets nets nets morgan proceedings proceedings proceedings report implementation version consists consists internal internal internal code advances joint joint connectionist connectionist layers layers layers maps considered framework framework framework framework framework framework framework framework framework equivalent experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment environment environment environment additional additional additional view design design design design design design design design san conference conference conference conference conference conference efficient full world vision basic basic basic basic basic basic pages pages pages pages con con coding derived randomly conditional clustering robot robot robot robot robot robot robot levels levels levels controller types types types lines lines path provided provided provided finally processes backpropagation constraint simply simply normal technical describe arbitrary arbitrary arbitrary group complete complete complete complete complete complete complete proof finding short common implemented implemented main main main future future easily easily degree degree development development development kaufmann objective functional functional block block block 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configuration configuration configuration base base appears pro pro construct primary ann mathematical mathematical dept implement missing multilayer multilayer multilayer multilayer averaging dimensionality transformations easy text unique unique develop integrated integrated formed implies blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks cycles national formation communication communication communication communication transform operations controlled controlled controlled organizing sizes sizes updates sign diagram earlier performing performing normalization combining combining add symbol construction construction 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built built satisfy list involved modular paradigm nips nips nips nips automatically automatically acknowledgments deal software software software software software software software oriented oriented oriented oriented oriented oriented oriented oriented oriented command command command command command diego powerful access access rapidly put environments issues preliminary graphical graphical graphical graphical graphical graphical existence links links links links terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal structured complicated complicated encode hierarchy possibly editor editor configurations illustrate created prototype prototype formal formal store generates utility utility explain explain defines synthetic years years brown site site advanced ment ment distinguish publishers derivation growing adjacent briefly tool tool inside sites sites sites constructing consequence consequence consequence optimize computers annual researchers researchers improvements collected consistency generic generic generic generic parameterized share incorporated ity execution switch spread parent parent enables germany simulator simulator kinds display display windows hints arithmetic lot lot redundant redundant interface interface interface interface interface interface interface interface interface interface interface flexibility flexibility flexibility flexibility interconnected inspired bower ranges ranges imposed primitive primitive primitive loops check check moment north guide wilson obstacle evaluations contexts connect iteratively pat holland washington facilitate offers specialized specialized april matter rich captures subsequently valuable papers propagate tures approximator approximator leaving specification largely numerous workspace workspace workspace users deriving deriving obstacles propagating abstraction instantiation instantiation arbor german hierarchies hierarchies hierarchies tor simulating simulating possibilities visualization manipulation manipulation modifying ftp ftp community cessing impose ijcnn pdp file file file interactive names paris sketch library library library setup setup paradigms paradigms paradigms paradigms paradigms denver universit supports rochester rochester elsevier programmed refined refined holding struc experi november diagrams deletion satisfaction functionality functionality functionality interior handling handling august demand insufficient assistance loaded transparency transparency imple routines routines inclusion loads spie experienced gmd gmd demands demands planner planner planner planner cess baltimore files files statements manual cope cope tern decode developments developments amsterdam ceedings lange predefined predefined substructures substructures derivations simula miyata elegant tutorial utilities utilities plotting erroneous dealt offered saved saved saved saved accessible accessible offline genesis ily missed unix unix inconsistency arms executes comprise subtraction workstations constantly unstructured simu visualize fulfill eval endpoints compose highlights administration administration revised illustrative struction buffers intend linden linden linden linden linden linden plications suc scripts scripts scripts scripts scripts scripts scripts scripts scripts scripts opera trigonometric reuse reuse reuse supplying contradiction philosophy philosophy composing eleventh accessed lan script weber weber weber weber weber mech increas packages refinements refinements libraries inconsistencies eckmiller uation coordi coordi facilities cont runtime runtime adaption collapsed collapsed assembled ternational interactively interactively interactively interactively guage nates nates simulators simulators inheritance inheritance inheritance reused reused kraft menting professional professional augustin scribe 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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data function function function function function function function function function function function function figure figure figure figure figure time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training output output output number number number number number number number number number system system system system system system system system system system system system state state state state state state state state state results results results results results results results results problem problem problem problem models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space space space weights weights weights weights weights case case case order order shown shown systems values values values values parameters parameters noise noise noise noise noise noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution recognition method method approach approach approach approach pattern pattern pattern pattern point point point point single control control large large local local local local local local local local local local local local local local neuron neuron neuron neuron neuron neuron neuron test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis matrix matrix optimal optimal optimal optimal optimal optimal optimal shows shows shows shows signal algorithms simple simple simple simple gaussian paper size size size net net net work work work task task task cells step step step step step points points points points points features process process process process problems random random random memory memory memory memory memory memory memory memory memory architecture show section section section fixed fixed fixed fixed fixed rule rule rule general parameter parameter parameter parameter parameter states states states theory theory obtained term term activity result result threshold threshold threshold threshold variables variables variables variables computation computation computation solution solution solution solution solution independent defined defined defined found dynamics dynamics dynamics dynamics initial initial estimate terms terms terms connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left direction presented phase phase phase activation activation temporal maximum maximum range outputs abstract find computational computational computational computational computational properties references due due propagation propagation propagation propagation introduction complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior statistical statistical statistical statistical statistical effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance parallel parallel parallel parallel parallel parallel parallel cost cost tion change energy energy assume lower higher part bound required multiple good binary binary binary long long long represent represent distributed expected expected equations equations chip chip chip chip chip chip chip region proposed correlation correlation errors finite simulations simulation computed computed respect respect respect respect respect respect sum sum sum performed performed performed means means means factor factor factor potential feedback feedback global study study study study study study study artificial cross cross cross cross cross define perform perform perform perform active active goal related related constraints connected gain larger fields fields fields selection selection selection selection proceedings proceedings implementation implementation implementation implementation implementation implementation implementation implementation version version version version synapses synapses synapses synapses internal internal internal code code final final final delay delay scheme computing equivalent equivalent directly view solutions design transition transition transition transition transition limit effects bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity upper full full choice choice choice world speed basic basic increase increase give give con produce levels finally selected selected inhibitory inhibitory inhibitory inhibitory depends depends simply associative associative associative associative associative associative associative associative associative discussion discussion increases describe describe fast fast fast fast limited corresponds corresponds complete complete complete stable stable stable circuits circuits short short effective implemented implemented assumed supported role role role role role theoretical require main main end future easily makes typically hopfield hopfield hopfield hopfield hopfield hopfield hopfield dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical fully block transfer transfer transfer transfer transfer interesting interesting ratio ratio ratio special special structures operation details numbers inhibition inhibition inhibition inhibition inhibition inhibition inhibition stored stored stored stored stored stored bits bits decay decay decay attention description description neuronal architectures discussed discussed discussed discussed discussed correlations correlations resolution advantage takes takes takes typical typical identical side array interest interest interest sufficient sufficient volume works works tions correspond trans definition definition evaluation modified gate improvement storage storage storage storage storage storage increased increased increased grant parts lead studied studied extended digital digital digital matrices deterministic hardware hardware hardware conclusion critical critical critical critical critical critical minimal hebbian trajectories depend central interactions interactions numerical numerical numerical clear performs faster physics external external external external reduction cycle cycle characteristics characteristics assuming variety minimizing configuration configuration attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor acknowledgements appears relation longer sequential sequential sequential sequential stability stability recall implement implement implement implement implement infinite physical physical electrical electrical integrated integrated integrated minimization minimization quality blocks blocks blocks blocks blocks cycles cycles decreases family stationary stationary stationary correlated correlated correlated overlap overlap overlap overlap interpretation operations updated fraction evolution evolution static static static static static static static activities partition allowed past additive delays classical classical spaces precision existing retrieval retrieval retrieval retrieval retrieval subspace subspace subspace subspace subspace subspace memories memories phys phys partially characterized selecting aspects divided identify build computations schemes orthogonal characteristic characteristic composed traditional kind allowing moore interpreted symmetry symmetry symmetry symmetry follow device device device device device quantity quantity list simplified simplified relaxation relaxation correspondence correspondence correspondence ill reach chips chips software law minimized minimized diego investigate exponentially exponentially updating updating updating updating put limitations preliminary behaviour behaviour behaviour behaviour project project analytically possibility possibility scaled scaled scaled referred referred reliable gates gates gates gates gates understand configurations configurations configurations rev thought prototype versions formal observe observe expressions logic logic logic logic logic logic logic logic logic hebb hebb hebb hebb store serial finds chaotic chaotic chaotic chaotic defines years devices devices devices spin spin spin site ment unstable unstable unstable analytical capabilities glass glass multiplication multiplication reasons spatially inside implementing precisely choices sgn pulses scientific separately describing opt res fluctuations fluctuations mechanics mechanics mechanics generic capability lack quantitative quantitative effort slower slower mod ture reaches monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic qualitatively conductances sums unbiased implements implements progress realized realized don don feasible saddle assign fix acm dynamically grows saturation wrong numerically stated programmable programmable programmable programmable programmable programmable replica replica replica replica replica responsible preparation preparation clock clock clock clock enhanced enhanced combinatorial selects performances sompolinsky mance governed connect studying perfor decide decide pat belongs offers belonging storing explains limitation ber ram ram ram ram revealed monotonicity breaking breaking breaking mutually care exclusive mhz formance impose ijcnn jij jij jij books retain tij book preprint commercial els transients transients compu subspaces subspaces subspaces subspaces subspaces subspaces subspaces october remark appearing decided decided decided decided trainable terns lated capacitors capacitors played played couplings couplings architec ref ref fastest fastest relaxed addressing memorized memorized memorized memorized memorized memorized monotone devoted devoted recalled registers talk talk gardner gardner fore subnetwork developments custom subnetworks subnetworks relax entering fractional observes fluctuation simulates italy italy capacitive multiplications undergoes emulate nakano yij yij clarify amit tational namic concluding yoshizawa resort multiplexed implementa jii worthwhile fii neurocomputing itive namics abrupt gutfreund analogical timal lets collapse twofold resorting adder aerospace derrida ieice brunel brunel emulates capac quenched ceptron endowed endowed endowed dipartimento dipartimento italian ihi ihi interconnec quote tractor disposal 
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functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method method pattern pattern single processing control control control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate inputs shows shows shows signal signal small work methods fig fig fig fig step step step step step step step current current current current current current current current current current memory similar parameter real real real real real real real note experiments activity activity activity activity activity result university university university university threshold threshold research found standard computer computer computer computer computer computer computer computer computer computer computer connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science direction present present activation press press press components abstract computational computational computational properties properties properties properties references procedure important important introduction action action action action action action complex complex circuit circuit circuit behavior effect effect effect dynamic dynamic generated change change complexity complexity measure higher part firing type conditions conditions conditions equations equations equations equations make minimum resulting total human computed computed times elements potential potential potential potential potential potential potential potential potential potential potential made study study artificial artificial artificial artificial artificial artificial relative compute determined determined determined experimental goal connected connected connected connected connected mit mit voltage steps modeling modeling department department department department synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists internal individual individual individual individual represents cambridge cambridge computing experiment experiment curve additional additional effects bit determine speed speed increase increase increase increase developed actual inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends sampling sampling biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological measured group fast limited complete circuits circuits circuits circuits circuits effective implemented implemented synapse synapse synapse supported role main eds eds end ability ability simulated typically typically underlying needed block block increasing increasing increasing mode details stored polynomial produced run neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane advantage reported lateral lateral moving period highly differential differential differential address address channels channels increased increased increased increased increased amplitude amplitude digital digital correctly hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid occurs hardware demonstrate demonstrate runs runs critical critical place conclusions interactions faster taking mechanisms integration integration integration physics physics external cycle cycle cycle selective iii connectivity connectivity connectivity program configuration force force construct construct construct primary plot mathematical changing changing electrical slightly spectral consisting consisting consisting integrated integrated potentials potentials potentials potentials potentials potentials potentials potentials decreases depending completely processor diagram diagram diagram diagram sec sec fitting add generation generation msec koch koch precision recorded fire currents currents currents currents currents currents activated coupled coupled coupled identified identified differ maximal maximal showing neuroscience neuroscience conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance contribution timing built simplified realistic realistic realistic realistic providing board board board board board board board board board board board delayed delayed delayed acknowledgments software software command access oscillators optimized graphical postsynaptic postsynaptic postsynaptic postsynaptic understand presynaptic presynaptic onset onset created created perfect adjusted adjusted precise store switching burst burst burst burst burst biology biology tool tool ganglion ganglion ganglion ganglion ganglion ganglion drive drive describing describing recording nsf raw considerably transient lack recordings recordings recordings slower sharp sharp biologically schematic maintain release release conductances conductances conductances display specifies simultaneous simultaneous arithmetic contribute interface driving concerned controlling controlling establish tools chemical chemical chemical operates affected adequate preparation preparation clock clock clock connect displayed injection offers record harris harris harris fired fired neurophysiology neurophysiology neurophysiology neurophysiology tables ram emergent simulating simulating evoked assess assess biophysical biophysical interacting interacting interacting interacting interacting relating synchronized rhythmic france france abbott abbott abbott abbott abbott universit universit intracellular programmed dsp dsp dsp dsp dsp dsp dsp dsp reciprocal reciprocal reciprocal hodgkin manuscript rarely reversal reversal reversal discontinuous cable huxley agents injected injected anterior screen reality marder marder marder marder marder marder marder marder marder marder marder marder periodically ionic ionic stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric files translates selverston hyperpolarization mounted investigator investigator investigator investigator preferable retaining transferred warrick warrick warrick opportunity package synchronize segev segev electrically electrically exciting mac mac mac mac inadequate converters clamp clamp inactivation lobster lobster olivary cedex 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#*model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time networks output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number system system system system system system system system system state state units units units units units units units information information information problem models models models models models models models models performance performance based case shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition method method method method approach point point point single single processing processing processing processing processing processing processing processing control control control control control control large neuron neuron neuron neuron rate rate analysis class inputs form shows shows shows shows signal signal signal signal signal signal signal simple paper paper paper examples methods methods fig process level high response response representation representation representation architecture architecture architecture architecture line line line line line line line line line line line line line line line line speech speech real real note activity result research research research research found constant computer computer computer computer computer computer computer computer presented present present present present low low low temporal press position position position basis abstract computational analog analog analog analog analog analog analog analog analog analog analog analog references ieee ieee ieee important introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit generated parallel parallel parallel energy energy energy energy energy energy energy energy assume signals signals signals signals signals signals signals signals representations part firing binary binary binary binary spike spike spike spike spike spike spike spike long tree tree tree tree tree chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip ing total performed potential global em represented application define perform goal connected connected brain power voltage voltage voltage voltage connection support source institute implementation implementation implementation code code final addition addition additional transition san stage stage stage stage stage stage bit efficient efficient efficient efficient efficient efficient increase con coding coding coding coding developed criterion area lines lines lines lines lines lines lines lines simply biological biological biological biological biological biological technical describe group limited complete complete actions circuits circuits circuits circuits circuits circuits implemented implemented require vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi including auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory fully fully block block transfer edge operation details details direct window recent correlations resolution takes takes lateral trees array array array array array array array array array array array array engineering dimensions axis tions rl address address address address address address address address address grid gate parts suggests digital digital digital digital alternative locally width occurs column column column column column column column column column column hardware hardware hardware place place row row row row row row row row row row row row row designed clear sound sound sound encoding encoding encoding hard external reduction characteristics california california pulse pulse groups identification base acknowledgements acknowledgements explicit appears produces produces produces produces laboratory explicitly remaining unique develop integrated integrated adding implies blocks blocks john john national review review communication communication communication communication communication communication codes operations operations fraction static static static static completely allowed diagram diagram diagram dashed event event event event event event event event event event event event event event event event initially distances foundation foundation includes includes silicon silicon silicon silicon silicon silicon silicon thesis thesis compression letter suitable suitable encoded encoded encoded encoded driven spiking spiking spiking spiking spiking spiking schemes schemes identity reached receives traditional refer issue lie strategies strategies sci device list list list list list list list simplified board board board board computes computes processors processors processors processors processors processors processors principles software rat load create access circuitry circuitry mead put put detail integral graphical mass tech transistor transistor reliable root working stream neu act onset onset onset man implementations precise nerve nerve logic logic logic logic logic logic logic message message switching switching indicating ment asynchronous asynchronous asynchronous asynchronous asynchronous ground ground ground ground tool inside inside berkeley berkeley berkeley sys arc organized producing division transistors pulses pulses ion ion ion ion axon axon axon acknowledgement acknowledgement acknowledgement acknowledgement axons computers bandwidth bandwidth nsf 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#*network network network network model model model neural input input input input input input input data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set networks networks algorithm output output output output system problem performance based based based based based based based linear linear linear case shown shown shown shown shown systems values recognition recognition method pattern point point point point point point point point point point image image image image image image single single single processing processing processing processing processing large large large local patterns patterns patterns form shows shows shows shows shows signal algorithms simple simple simple simple simple visual visual visual visual visual visual paper examples small small small small small size work work fig fig fig fig fig fig fig fig fig step step points points points points points points points points field field field level level level level level level current current current current current current current response fixed line images images images images images real real states gradient gradient gradient gradient note dimensional dimensional computation computation computation research research defined found constant computer terms distance node node node node node node science science science left left left presented presented map present low nodes nodes machine object object object object object object object object object object object object object object object object object object sets outputs abstract analog analog analog analog analog analog analog analog analog analog analog properties references component due due due ieee ieee important important action hand circuit circuit circuit circuit circuit circuit behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic difference assume assume assume lower chosen chosen higher part part center center center center center center center binary binary binary binary represent represent chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip proposed length length length length length length length length length length length length length length length scale total human regions made global global applications vol vol artificial application series series series compute compute compute objects perform perform connected connected connected connected equal mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger larger larger dependent source proceedings institute consists internal represents responses bias considered considered cambridge environment additional view view view design limit limit top top stage detection conference determine upper full requires requires vision vision vision vision vision vision vision vision vision vision vision vision con coding levels levels area area lines lines selected measured measured measured increases increases describe describe arbitrary arbitrary limited corresponds corresponds complete complete complete circuits circuits circuits circuits circuits circuits amount common common implemented implemented supported supported journal square vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel ability noisy noisy pairs smaller smaller smaller technology technology technology edge edge edge edge structures international international bottom bottom early decay choose denotes discussed property property property robust separate separate ensemble introduced side pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels array array array array array previously correspond achieve background background background locations locations grid grid grid grid grid grid grid grid grid grid horizontal intensity intensity intensity intensity studied occur digital wide wide wide wide locally move width width white white boundary boundary boundary boundary half flow flow flow conclusion row central central central differences encoding presence presence california intelligence labeled labeled turn relationship groups groups appears appears edges edges edges longer longer winner winner plot plot laboratory distinct segments segments implement electrical unique select competition competition competition john national communication communication open open open evaluate operations restricted restricted labels labels labels labels labels completely completely smoothing smoothing boundaries boundaries boundaries closed closed closed foundation koch koch koch koch koch box box box silicon contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour illustrated black black black black partially partially neighbors structural structural successfully effectively included notice notice conductance gray comp surround surround providing cmos cmos automatically chips chips chips chips circuitry mead rapidly mass rise ideas office working encode cognition contours contours contours contours contours contours contours contours contours contours contours contours saliency saliency gradients possibly voltages thought prototype aspect isolated isolated isolated charge ground ground ground ground ground ground ground ground ground ground floating capabilities inside inside inside inside inside inside inside inside implementing shared strictly located acknowledgement incomplete incomplete incomplete incomplete nsf limits collected profile pure share share marked marked completion completion resistive resistive resistive resistive frequently curvature pasadena pasadena inherent age globally gap gap gap fabricated acts impossible naval connecting fails resistance occurring exploit wire wire wire wire wire wire wire wire salient responsible capacitor capacitor excellent reset decide sides enable broken broken broken broken harris harris harris harris harris harris harris alternatively switches switches switches switches switches switches switches fly discriminate liu liu liu liu liu liu liu outline fellowship shunting shunting gaps break break break encodes encodes uniquely die shaded shaded rectangular rectangular resistor resistor segregation segregation segregation grouped thresholded challenging ullman ullman ullman ullman tied tied breaks breaks 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#@Harris_J,Koch_C,Liu_S,Luo_J,Mathur_B,Sivilotti_M,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input function function function function function figure figure figure figure time time time time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number number number number number number number number number number number number number number number number error error error error error error error error error error error error error error error results information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer case vector vector vector order order order order order order shown shown shown systems systems systems systems systems systems values values probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons unit unit distribution distribution method method method method method method method method method method method pattern pattern pattern pattern pattern pattern point single single single single single single single processing processing processing processing processing large large large large large large local neuron neuron neuron neuron rate rate rate rate test analysis analysis optimal inputs inputs inputs shows shows shows shows signal signal signal algorithms simple simple simple gaussian gaussian paper paper small small size size size feature net work work work work work work work task task methods methods methods fig fig fig fig fig fig fig fig points field level problems problems problems problems problems problems random random random random random random random random high high high memory similar similar architecture fixed fixed fixed line rule vectors general general approximation approximation approximation approximation average average average theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term term term term term term term note note note note note note note note note result university threshold computation independent constant estimate estimate estimate estimate estimate estimate estimate standard standard standard computer computer terms terms synaptic synaptic science science direction direction direction direction direction direction presented present present present activation activation activation activation low motion motion motion press press press continuous continuous continuous abstract back back computational computational convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties references component stochastic stochastic stochastic stochastic stochastic stochastic due ieee ieee ieee positive important important adaptive propagation propagation propagation introduction estimation behavior statistical effect generated generated variance variance variance variance variance variance parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel recurrent recurrent recurrent tion change change change change change change change change change difference complexity complexity complexity variable variable measure chosen higher higher part type required required multiple multiple multiple multiple multiple binary binary conditions conditions distributed distributed distributed distributed chip chip make make techniques correct errors errors scale scale simulations simulations simulations simulations resulting resulting ing simulation respect respect sum sum performed performed eq eq eq eq eq eq times means means means optimization natural study knowledge vol vol vol vol vol true true true true compared application provide provide proc experimental related gain power power power approaches mit mit comparison update descent descent descent descent descent descent descent descent descent descent descent descent dependent source modeling modeling morgan morgan morgan morgan proceedings implementation implementation implementation implementation implementation implementation implementation implementation implementation version synapses synapses synapses technique technique technique technique technique technique technique technique technique technique technique technique internal code advances advances advances advances difficult exp layers cambridge cambridge computing domain hinton additional curves curves curves limit san san san san bit bit determine efficient requires requires free speed estimated increase condition area area product product actual finally finally backpropagation nature measured feedforward describe describe fast fast surface surface circuits effective effective effective implemented shape synapse synapse synapse synapse synapse supported require main eds eds journal end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi future makes rumelhart rumelhart noisy noisy kaufmann needed needed reduced technology technology significantly york york edge edge edge leads leads leads representing representing numbers iterations iterations iterations iterations iterations iterations iterations pre making stored bits normalized supervised early magnitude magnitude added sources sources improve improve directions directions resolution exact advantage advantage ensemble takes typical similarity subject cognitive relevant dimensions approximately works converge converge converge achieve trans trans address address evaluation bounded gate williams storage storage entire expression scaling scaling scaling scaling suggests deviation derivative hardware demonstrate runs conclusion critical critical critical critical critical critical critical critical critical place row reduce reduce reduce sigmoid measures moody weak weak constrained mateo mateo mateo mateo taking hard external cycle proportional turn assuming variety variety start decrease decrease averaged averaged derivatives derivatives derivatives derivatives annealing force generating mathematical dept dept implement implement multilayer simultaneously physical easy easy angle scales applying springer expectation expectation letters dependence dependence depending correlated detailed detailed sizes converges sign sign sign sign sign diagram diagram calculation calculation slow additive measurements measurements expansion reduces roughly generation calculate calculate symbol advantages precision precision precision precision includes plotted plotted plotted partially discussions importance uniformly suitable suitable delta mcclelland presentation presentation presentation presentation literature plots identity composed verlag quickly repeated issue follow follow device device gibbs vary dot dot nips quantization leading leading leading software law schedule perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation access requirements circuitry varied varied varied hanson lippmann giving parity parity parity parity parity parity parity parity parity possibility proper affect understand understand cognition momentum gradients closest equally implementations implementations algo taylor precise precise precise precise perceptton improving serial charge years asymptotically cos directed directed publishers publishers publishers publishers analyzed phenomena floating considerable considerable implementing sys potentially involve involve involve angles angles angles angles calculations geometry geometry qualitative integrating varies varies greatly applies double double slower calculating perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations measuring measuring measuring popular ordered serve adjust substantial hamming hamming hamming shaped summed uncorrelated notes fabricated oxford extensive summing summing rithm drift drift drift repre kaufman kaufman kaufman adds proceeds proceeds mos held check hyper contract bands capacitor capacitor guide presentations alspector alspector alspector alspector alspector alspector alspector alspector alspector corre pat buffer buffer widrow widrow percepttons counting tic israel advance foundations agree valuable papers hart dividing dramatically multiplying summer microstructure outline outline die pointed perturbed copy obtains jabri jabri jabri shaded resistor tems afosr cosine speedup speedup emphasized inversely flower flower flower applicability thousands ignoring cube meir meir meir meir consuming appealing calculates venkatesh venkatesh core clark poly implied suffice binomial relaxed cauwenberghs cauwenberghs cauwenberghs cauwenberghs comparator elec indepen translates jan parker replication replication replication replication dissipation technion tern refresh refresh refresh refresh particles particles kailath stepsize nice repeating sentations broadcast continuing avg avg plotting perturbative perturbative perturbative def reminiscent perturbing perturbing perturbing perturbing perturbing perturbing perturbing volatile kirk kirk watts anneal anneal anneal implementable parentheses feel shell shell kronecker teach bellcore lations steep steep stochas embodied quantum acknowledgment dembo dembo dembo dembo dembo dembo looked yuhas yuhas yuhas yuhas yuhas kushner kushner intend loses indexes brownian brownian jayakumar jayakumar jayakumar jayakumar jayakumar jayakumar gert knowl kerns haifa fleischer slows morristown speedups barak insightful correlating speculate chu nmnber bart bowl bowl justin justin incidentally vantage pertur sulting madaline rumel ezplorations lam langevin gannett haber dently 
#@Alspector_J,Jayakumar_A,Lippe_D,Meir_R,Yuhas_B,
#t6
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#*network learning learning model neural neural neural input input input input function function function function time set set set set set set set networks networks networks networks networks networks networks algorithm number number system system state state results information information problem problem problem models hidden hidden case case case vector vector order order order order order order shown systems systems systems systems systems systems systems systems probability weight functions functions neurons neurons approach approach approach pattern pattern single single single processing processing processing processing processing local local local local patterns matrix form form form form form form form form form algorithms simple paper work work field process level level level level level level level level level level level level level level level structure structure structure structure structure structure structure structure structure structure problems problems memory response representation representation representation architecture section rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors general general general general real theory theory theory theory theory theory theory theory theory theory gradient activity activity result result result university university university university university university university computation computation computation research research research research research defined defined defined defined defined standard computer computer computer computer terms terms node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node science science science science science science science science science left left left left left left left left left presented presented present present activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine maximum maximum range press press press press press press press press press position position abstract applied applied back find computational computational computational computational properties properties references stochastic ieee positive positive positive positive context context context context context introduction complex hand hand hand parallel parallel parallel parallel parallel change energy difference variable variable lower lower lower lower lower lower lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules representations representations representations representations higher higher higher higher higher higher higher higher higher part cases type required required binary tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed distributed distributed distributed proposed correct forward ing ing ing total total total total human computed computed multi multi sum sum called means optimization made made natural natural natural natural global study negative negative negative negative negative original artificial artificial artificial application application desired determined constraints constraints constraints distributions brain equal equal equal power approaches mit mit connection connection selection morgan morgan proceedings proceedings proceedings proceedings proceedings proceedings proceedings proceedings proceedings report report report report report report institute department department department version version technique technique advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist framework cambridge cambridge cambridge equivalent hinton hinton hinton hinton solutions san san conference conference conference conference conference determine requires free free free free free basic basic basic pages pages pages pages pages pages pages pages pages con con con con con condition condition types product product product product finally processes processes processes constraint simply simply simply simply simply biological discussion normal normal normal normal technical technical technical technical technical technical describe group group denote corresponds complete proof generate generate supported role role role theoretical degree makes makes makes rumelhart rumelhart kaufmann kaufmann pairs pairs pairs pairs hopfield hopfield dynamical special structures structures structures structures structures language language language numbers numbers numbers early magnitude idea description description pair pair pair pair pair pair pair apply apply introduced strategy include machines machines side side side quadratic trees trees trees trees trees sense inference sejnowski sejnowski sejnowski sejnowski sejnowski cognitive cognitive cognitive cognitive cognitive cognitive recently conventional volume volume correspond generalized generalized generalized storage entire entire entire entire grant alternative feed feed touretzky touretzky half competitive editors editors editors editors editors editors editors measures numerical numerical designed clear sutton mateo mateo intelligence intelligence intelligence turn start start start start start exist introduce connectivity program boltzmann explicit suppose construct written stability mathematical mathematical mathematical missing missing missing missing missing missing category simultaneously simultaneously physical remaining slightly unique unique interaction integrated adding adding formed formed formed formed formed letters national national national national evaluate evaluate evaluate evaluate decomposition soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft similarly similarly similarly 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binding binding ill ill ill ill ill leading principles principles principles satisfies extend production production collection collection involving involving replaced recursive recursive helpful ideas school links links links links links links links links terminal terminal terminal terminal terminal terminal terminal terminal terminal root root root root symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic understand cognition cognition cognition cognition neu naturally possibly editor necessarily reading man automata psychology psychology illustrate formal formal formal formal formal formal formal formal formal formal ith detected simplest contributions contributions contributions contributions contributions contributions contributions contributions serial defines established languages languages languages languages languages languages languages languages languages languages languages languages ment pairwise pairwise pairwise pairwise directed directed directed crucial analyzed analyzed analyzed analyzed analyzed defining defining defining tive berkeley berkeley berkeley formalism arise mation acknowledgement separately grossberg grossberg annual annual annual annual cybernetics cybernetics nsf requiring virtual evaluating double cohen cohen introducing introducing completion rep requirement ture ture ture fall maximizes parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent collective enables replace replace leaf wesley realized contribute contribute notes addison optimality optimality oxford appropriately labelled labelled labelled labelled tensor tensor tensor tensor count count harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky 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bindings lated evolved conceptual fill suffices filler filler kth kth harvard connects tribution tribution meeting meeting core contributes contributes sym sym alan alan comprising outgoing outgoing phonology phonology phonology phonology phonology phonology syntactic suffice connectionism connectionism absent adapts bradford bradford legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre semantics shop counted unrestricted unrestricted unrestricted tim linking constituent constituent constituent amsterdam comprehensive triple assessing miyata miyata miyata miyata miyata miyata miyata miyata schema unifying upward upward upward upward upward cancel turing undirected undirected checks conceptually complications trick constituents constituents constituents constituents constituents constituents constituents constituents constituents constituents parser occupied suggestion froin froin froin tributed 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#@Smolensky_P,
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#*network network network network model model model model model model model model model neural neural neural neural neural neural neural neural neural neural data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time networks networks networks networks networks networks algorithm number system results results units information information information problem problem models models models models models models models models models models models models performance based based based based based case vector order order order shown shown systems systems systems systems systems probability recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single single single single processing processing processing control local local rate rate patterns analysis form visual paper paper examples examples size size feature work work work task task task methods features features features features process process process process process process level level level level level current trained structure structure structure structure structure structure structure structure structure structure structure problems high high high memory similar similar similar similar similar similar similar similar similar similar representation representation representation representation representation representation architecture show line vectors vectors general states states states obtained obtained result result university university university solution research research research research found found found target target terms connections science science science science science left left left left left left presented presented presented presented presented presented map present present activation activation low object object maximum press press press press press press components sample abstract find computational properties references component component important important important introduction complex hand hand hand hand hand hand hand behavior search complexity variable variable representations representations representations representations representations representations representations representations representations representations representations representations learned higher higher higher higher part part part part type type type multiple multiple multiple good binary long represent represent distributed expected make make make make fact fact fact fact fact tasks tasks human human human called mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping made made made made natural global applications study study study study study knowledge artificial artificial artificial represented represented compared cross cross cross cross series objects objects objects objects objects objects objects objects determined experimental constraints connected comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison contrast contrast selection proceedings department department connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist framework directly top top top top top top stimuli stimuli stimuli stimuli determine determine determine requires significant free world world world world world world increase developed robot robot criterion product finally processes processes selected selected evidence evidence evidence evidence evidence depends constraint simply simply describe group group group tested surface surface predictions predictions finding finding finding finding common common common role role role role theoretical journal journal ability degree degree degree development development development development development development sensory including pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs underlying underlying hopfield hopfield functional functional functional character projection consistent consistent consistent structures structures structures structures matching matching matching matching matching matching matching matching matching matching matching matching matching matching empirical operation operation bottom bottom idea choose predict recent property pair pair pair pair pair pair pair pair takes similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity hierarchical trees array cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive highly compare compare previously subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects match match match studies studies studies sensitive sensitive grant suggests suggests suggests suggests suggests suggests suggests extended extended extended predicted predicted predicted predicted move move clusters occurs generally generally demonstrate conclusion critical place place central central central central accurate faster suggest suggest suggest taking taking taking largest largest demonstrated demonstrated intelligence intelligence intelligence connectivity configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration base question question question relation relation relation relation relation relation relation relation van van van van perception perception perception optical ways ways distinct distinct segments modeled physical involves involves involves involves involves shift letters yield yield national extracted focus review review review review review review communication viewed interpretation interpretation interpretation interpretation solved variation open open controlled centered understanding similarly suggested key key key key classical symbol figures figures figures figures figures perceptual perceptual perceptual recognize recognize specifically structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural determining determining middle aspects aspects importance symbols successful successful successful identify build comparing comparing situation capture summary notice kind success anderson anderson anderson interpreted interpreted interpreted issue symmetry running list list correspondence binding binding preferred acknowledgments situations exhibit exhibit exhibit relations relations relations relations relations relations relations humans integral recursive recursive examine matches matches matches mappings mappings mappings mappings possibility structured structured structured structured structured structured structured structured structured structured symbolic symbolic symbolic symbolic symbolic cognition cognition cognition cognition cognition cognition cognition analogous attributes examined configurations configurations psychology psychology psychology psychology psychology psychology front mapped mapped mapped mapped mapped mapped mapped scenes stop crucial track phenomena phenomena phenomena caused caused comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons comparisons perspective implementing sections choices arise arise potentially involve involve circle circle circle circle circle circle circle circle attribute attribute attribute attribute attribute attribute read demonstrates addressed alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment alignment explained geometric geometric questions people people people people limits double collected items items items items items items items items elman elman flexible flexible flexible readily leave item item item item item item share completion completion completion completion completion completion completion completion completion psychological psychological psychological psychological psychological psychological psychological psychological psychological psychological summarized monotonic collective substantial kinds inherent chose chose chose comments age age findings findings sentence sentence classifying aligned aligned extensive tensor jones jones flexibility flexibility flexibility flexibility flexibility flexibility flexibility printed smolensky smolensky smolensky children children children plays adds analogy analogy analogy analogy analogy analogy analogy analogy analogy analogy determination determination check abilities roles implications child filled ambiguity evident captured similarities similarities similarities similarities similarities similarities similarities similarities similarities similarities tokens young suggesting suggesting pollack pollack probe summarize interestingly onr linguistic leaming asked asked asked asked asked asked asked asked asked asked emergent pointed personal decomposed chicago chicago causal causal causal causal causal examining acting preserved intuition robots robots robots maintained playing permits relate academy names ambiguous ambiguous selectively quinlan quinlan weaker discusses page places places permit things round differently palmer palmer palmer palmer ate compositional compositional compositional compositional compositional compositional prefer prefer insufficient correspondences correspondences doesn bindings bold bold conceptual conceptual conceptual arrow king king appealing engine triangle triangle interpretations interpretations interpretations interpretations interpretations functionally functionally functionally implying implying relational relational relational relational relational relational relational relational relational relational relational connectionism connectionism connectionism materials concatenated categorical surgeon surgeon wolff facts facts facts facts facts capturing united united united shares shares sponsored stems deleting phil inability entered respects traditionally rated claims distinctive distinctive conflict exhibiting meanings conveys conveys corresponded organisms ratings taught analogously george george highlight looked story story story story story unambiguous rocks pilot pilot told theme attend attend attend structurally structurally transport analogical analogical analogical antecedent antecedent antecedent antecedent antecedent adults intriguing rock rock rock suspect bush bush bush bush fodor fodor fodor fodor connecfionist social social stacks highlighted subsymbolic promote completing prospects northwestern northwestern stories stories stories stories stories compositionality compositionality compositionality richly guides waterloo pylyshyn pylyshyn depicting assertion pessimistic older storm storm ritz ritz criticized war war war war war war nations comprehension evanston evanston jon adequacy metaphor metaphor bns pauern commonalities commonalities arthur promotes mounting metaphors transparently endless 
#@Gentner_D,Markman_A,
#t6
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set networks networks networks training training training training training training training training training training training algorithm number number number number number number number system system error error state state results units units units units units units units units units units units units units units units units units units information information information information information information information problem problem problem hidden performance performance performance performance based based based weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer case case case case case vector vector vector vector vector vector order order shown probability probability probability probability probability parameters parameters noise weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution recognition approach approach pattern pattern pattern pattern point single single single single single processing processing processing processing processing control test analysis class class class form form form form form form form shows algorithms algorithms simple gaussian examples examples examples examples examples examples examples examples small small small net net net net net net work work work task step process process process process current current trained trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure high high memory memory memory representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture fixed rule rule rule rule vectors vectors general general generalization generalization generalization states gradient experiments experiments activity activity activity result result university research research log defined defined sequence sequence sequence sequence dynamics dynamics dynamics initial initial constant table table computer terms distance connections connections science science science science left left presented presented present present present present present present present phase activation low temporal machine sets sets sets sets maximum maximum maximum range press press press learn learn learn learn components outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample abstract back back back back back likelihood likelihood references component component stochastic due positive positive positive positive positive positive positive procedure propagation propagation propagation propagation context context context context context context context context context context context context context context complex complex hand hand hand hand estimation behavior behavior statistical generated generated generated parallel recurrent change change lower rules rules rules rules rules rules rules rules rules prior prior representations learned learned learned learned higher higher part previous cases cases firing firing required required required required required multiple multiple good conditions represent tree tree tree distributed bayesian markov fact fact fact length length finite minimum ing ing ing ing tasks total total total total computed computed computed respect sum performed performed called called times optimization made natural knowledge obtain negative negative negative negative negative negative negative specific represented desired perform active active active active active goal discrete discrete discrete discrete approaches approaches mit steps steps larger connection selection morgan morgan morgan morgan morgan institute department implementation version version consists internal internal internal individual joint represents connectionist connectionist connectionist connectionist connectionist difficult difficult final bias bias sequences sequences framework cambridge domain hinton hinton hinton hinton additional additional view san san san san san top top top top top top top top top top top conference conference conference upper requires requires significant significant free free free free free free free free free free free free free free weighted randomly levels provided provided selected backpropagation nature simply achieved discussion arbitrary denote denote limited amount implemented supported role require require require eds eds eds eds ability makes makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart including including kaufmann kaufmann kaufmann kaufmann kaufmann objective objective objective objective objective underlying combination combination reduced reduced reduced fully transfer special special structures structures matching matching uniform operation language language language representing representing representing representing call making international normalized bottom run improved recent pair pair takes reported introduced moving side side side hierarchical hierarchical hierarchical trees inference inference inference subset cognitive cognitive cognitive cognitive interest interest varying previously volume volume volume works tions match generalized interval interval williams williams entire increased grant lead studied extended extended derivative move touretzky generally demonstrate strength reduce numerical numerical designed designed clear performs moody moody exponential practice learns mateo mateo mateo mateo mateo sound encoding strong external external reduction reduction reduction variety targets denoted denoted written written longer perception primary primary sequential infinite involves transformations transformations mutual adding formed formed formed competition letters letters focus formation interpretation transform operations operations operations operations updated fraction lee lee lee understanding sizes activities allowed key partial spaces reduces combining event event roughly string string string string string string string string string string string symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol foundation advantages degrees building fire fire fire exploration template strings strings strings strings strings strings strings strings strings recognize maximize mozer mozer mozer mozer mozer mozer mozer domains holds partially partially grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar characterized successfully successfully successfully simplicity straightforward identified encoded symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols included mcclelland presentation successful detect tend essentially identity identity identity identity identity identity receives strongly strongly allowing allowing allowing allowing interpreted contribution classify follow criteria hold write michael simplified giles giles giles giles giles giles giles giles giles giles computes leading remain unlike powerful environments replaced replaced hanson hanson preliminary biases helpful scalar reducing examine matches matches respond respond respond root root symbolic symbolic symbolic symbolic symbolic symbolic affect encode understand cognition removed induction induction necessarily automata recognizer recognizer portion formal formal assumes explored initialized generates generates explain explain attempts languages languages languages languages languages languages indicating preference defining capabilities capabilities briefly perspective perspective tive sys ring ring organized style acknowledgement recognized involve gradually gradually read read read annual annual nsf sun sun sun sun sun exemplars robustness summation integrating behaviors behaviors composite composite composite composite composite composite composite composite composite composite composite composite composite composite items items items items items substantially pseudo capability readily orders item item item item item item completion adjustable music stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack stack summarized extracting proven chen chen chen chen plan sophisticated comments specifies progress sentence differentiable merging primarily accomplished forming forming investigation perfectly concerned null discover discover tem tem tem tem smolensky plays promising replacing automaton automaton height interpret methodology responsible phrase phrase phrase grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars grammars fires fires fires motivation reset james iteratively entry paul induce regard ascent colorado advance advance advance advance advance advance advance young express express ahead reader theoretically theoretically grammatical grammatical grammatical grammatical parse parse parse parse parse erlbaum erlbaum omohundro propagate balancing default default default default default default default fly fly fly limitation unchanged multiplying parsing parsing logarithm shading shorter achieving achieving incrementally propagating exception causing big hierarchies descriptions descriptions mars hillsdale hillsdale hillsdale demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon demon 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imposes transferred contributing observes proce proce proce proce recursire recursire darker perturbing tentative copied remember claimed scratch theor presidential pad embodied interpretable attack sketched identities identities identities unambiguous sole inspiration doubt cumbersome itive unary entity embed parenthesis bachrach twofold ingredient marion stolcke stolcke fourteenth thi thi unfolding discriminates sac sac bachtach transferring achievement multilevel multilevel fresh parsed parsed pushes pops ded nega staged feat affords deliberate limita bols 
#@Das_S,Mozer_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure figure figure figure set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output output output output number number number number number number number number number system system system system system error error error error error state state state state state state state state state results results units units units units units units information information problem problem problem problem problem problem hidden performance performance based based based based based based based based based based based space space space space space space space weights case case case case case case vector vector shown systems systems systems values values values values values probability probability probability probability probability probability probability probability probability parameters parameters parameters noise weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit distribution method method approach approach approach processing processing control control control control large local local class class class class class class optimal inputs inputs inputs form form form form shows shows shows simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small small feature feature task features features classification classification process trained structure high response architecture architecture architecture architecture show equation equation equation equation equation equation section line line line rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general generalization generalization generalization generalization parameter parameter parameter real approximation approximation average average average average average average states states gradient gradient gradient note activity dimensional result threshold computation computation solution research research research found initial initial initial initial initial constant table table standard terms terms prediction prediction prediction prediction prediction left left presented map present present low low learn learn basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs continuous continuous abstract applied back find find density density properties likelihood references ieee positive positive procedure procedure important adaptive adaptive mixture mixture mixture introduction hand variance complexity complexity complexity complexity complexity complexity assume assume assume assume assume classifier lower lower lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure prior prior prior prior prior prior prior prior prior learned chosen higher higher part center center cases required required required good binary conditions represent distributed distributed expected expected expected make region correct correct correct finite finite ing human regression sum sum regions mapping mapping mapping mapping means factor natural applications applications applications applications applications knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge em obtain obtain obtain obtain vol vol vol vol artificial artificial relative application application define define active active experimental related distributions distributions distributions equal equal equal accuracy support descent descent descent dependent modeling proceedings internal advances joint difficult final exp exp exp bias addition ai considered domain domain domain equivalent directly directly hinton hinton additional solutions conference approximate approximate approximate world vision estimated estimated basic give derived weighted randomly clustering actual evidence simply achieved achieved achieved measured normal increases increases describe describe denote fast limited close corresponds corresponds corresponds corresponds corresponds corresponds complete predictions amount common implemented supported eds adaptation easily degree makes makes noisy including probabilistic probabilistic probabilistic probabilistic probabilistic typically typically smaller underlying jordan jordan increasing special leads normalized normalized normalized normalized normalized experts experts experts supervised expert expert expert expert expert expert expert decay polynomial minimize predict population improve improve advantage advantage typical reported strategy trees subset subset relevant relevant engineering dimensions sufficient previously teacher teacher teacher approximately approximately approximately approximately approximately approximately approximately volume achieve address mixtures mixtures mixtures grant expression concept deviation deviation locally width occurs demonstrate demonstrate conclusion conclusion conclusion conclusion conclusion conclusion conclusion assumptions conclusions central central central moody moody faster learns suggest integration largest reduction reduction demonstrated proportional intelligence assuming start relationship introduce identification monte carlo ways ways generating describes describes describes tuned pruning pruning pruning pruning pruning missing belief gaussians gaussians extraction extraction national extracted extracted extracted extracted interpretation interpretation interpretation interpretation interpretation interpretation solved evaluate centers forms approximated approximated partition constants reasonable reasonable additive reduces neighborhood event boundaries penalty valid valid calculate calculate sufficiently symbol advantages transactions existing formulation weighting sciences priors discussions importance encoded effectively situation allowing follow illustrates subsequent mixing jacobs jacobs employed experience integral dotted authors reliable complicated removed smallest smallest smallest adapt adapt adapt adapt man predicting ensure ensure taylor freedom expressions logic initialized multivariate years percentage cart cart cart stop variances analyzed nowlan nowlan adapted correction ring ring ring incorporate potentially acknowledgement beginning beginning medical cybernetics reflects fuzzy fuzzy generic quantitative car remove remove incorporated price rely rely summarized gen occurrence occurrence germany germany germany logical boston boston boston deviations specifies specifies specifies specifies specifies tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp proportion primarily formally formally formally driving resources resources recover theories theories numerically darken darken breiman breiman breiman overcome mail siemens siemens siemens siemens interpret removing ylx ylx ylx ylx started pruned infinity valuable shavlik shavlik interestingly acknowledge accumulated sequentially fellowship ahmad ahmad ahmad ahmad ahmad ahmad ahmad maximized ber formulate formulate legal preserving aij ical associate certainty certainty certainty certainty home home preserved preserved preserved num altered relates refinement refinement elsevier xly permit refined refined hofmann hofmann hofmann hofmann status housing housing housing institut subjective towell ers dominates industrial inclusion kth kth neuneier substitute successively rating informatik rectangles cauchy skill artificially translate prune prune penalizes lsi validated rolling amsterdam plexity fiir fiir extrema volker structuring structuring structuring structuring concise miinchen miinchen miinchen brooks kronecker ralph premise premise premise premise bicycle bicycle encouraged otto otto otto wadsworth pupil told penalize bij extrapolate freeze freeze und manage tti assure itive rooms rooms lij hahn hahn hahn spe deviates deficiency mfinchen sinusoid sinusoid forget specht xls xls xls sooner hollatz hollatz hollatz hollatz hollatz hollatz hollatz erated noordewier noordewier retrain probab malized jiirgen init init subutai unobservable cific riding mathemat disastrous yls aleksander formulates 
#@Ahmad_S,Hollatz_J,Tresp_V,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input data data data data data data data function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time algorithm output number number system system system system system state state state state results information problem problem problem problem problem problem performance performance performance performance based based based space space space space space space linear linear case vector vector vector vector vector vector vector vector vector vector vector order order order values values values values parameters parameters parameters noise noise noise noise noise recognition recognition recognition recognition recognition recognition recognition recognition recognition method pattern point single processing processing processing processing processing processing processing large test test test analysis analysis matrix matrix form form form signal signal signal signal signal signal signal signal simple visual visual visual visual visual visual small size size size size task task methods features process level level current response response representation representation representation representation representation representation representation representation show show fixed fixed fixed rule rule vectors vectors general parameter real theory theory note note dimensional result result threshold threshold threshold threshold threshold threshold threshold threshold threshold research found sequence sequence target target target target target target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics terms distance presented presented presented presented presented presented presented presented presented activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation temporal temporal temporal temporal temporal temporal maximum position components nonlinear abstract properties properties likelihood references due due due due due due due positive positive procedure important important decision decision introduction complex estimation stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect dynamic dynamic dynamic dynamic dynamic parallel energy variable variable lower lower signals signals signals signals signals representations representations representations representations representations word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word part previous type multiple multiple binary long long long conditions conditions conditions represent distributed distributed make make fact fact fact fact fact fact fact length length observed observed observed observed observed observed errors forward scale minimum human times times natural natural filter filter filter filter filter filter filter filter filter filter filter filter filter relative specific specific represented compared compared compared compute objects determined determined determined determined determined experimental experimental related constraints constraints constraints brain mit steps larger dependent dependent institute institute words words words words words words words words words words department individual final sequences cambridge experiment environment additional view solutions curves curves curves curves transition stage stage stage stage stage stage stimuli effects effects effects detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection requires requires choice significant significant significant significant basic basic increase increase condition condition conditional developed developed developed developed levels finally processes processes nature nature nature constraint simply increases increases increases increases increases increases increases increases increases describe describe describe denote fast close finding finding finding finding finding finding short effective main main adaptation journal end easily noisy smaller needed account account dynamical dynamical dynamical dynamical dynamical dynamical dynamical unknown unknown unknown unknown unknown jordan jordan jordan jordan jordan jordan technology programming programming programming programming character character york york increasing mechanism trials trials trials trials language language leads numbers filters filters pre pre making normalized magnitude attention description recent recent recent recent separate separate typical similarity similarity similarity similarity similarity similarity period subject identical identical identical identical side trees trees cognitive cognitive varying subjects subjects subjects subjects subjects solve background interval interval sensitive increased increased increased grant grant lead scaling scaling scaling scaling correctly move white white occurs occurs hardware flow strength strength critical critical critical assumptions conclusions suggest presence presence characteristics manner manner identification identification identification identification explicit pro van van perception factors factors laboratory recall sensitivity angle angle scales events implies implies versus letters letters letters letters decreases decreases decreases decreases focus dependence dependence dependence stages stages stages stages stages overlap overlap overlap viewed viewed codes restricted centers modulation similarly constants earlier classical classical classical classical remains filtering sufficiently construction foundation building figures perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual priori inter inter inter inter sciences determines absolute absolute neighbors neighbors neighbors characterized tests structural middle middle aspects aspects identified identified letter presentation presentation presentation presentation presentation presentation presentation presentation presentation detect detect detect literature literature tend identity ten capture capture repeated repeated allowing neuroscience duration duration duration list list michael michael backward leading thresholds thresholds acknowledgments decreasing explore origin origin origin wiley wiley rapidly scalar history behavioral behavioral behavioral behavioral behavioral behavioral behavioral decisions cognition cognition matched matched matched matched matched matched matched matched naturally naturally onset onset psychology quantities impulse impulse baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline detected detected detected detected detected detected detected detected finds massachusetts residual costs phenomena phenomena phenomena phenomena phenomena failure explanation briefly shared shared shared organized filtered choices projected projected arises arises preceding meaning fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations varies items items items items empirically embedded detecting detecting rep psychological passes passes occurrence occurrence serve prevent semi age multidimensional multidimensional multidimensional bellman acquisition corrupted corrupted optimality dynamically repre significance significance significance significance stronger difficulties adjusting proceeds imply salk responsible intuitive enhanced enhanced overlaps reset reset reset accounts accounts accounts accounts accounts captured mem arrive jolla erlbaum sons captures captures captures captures interestingly lag yielded sig asked bank year warping suppressed hillsdale clas avoids subthreshold cessing segregation continues distant token convert inverted maximally maximally projecting increasingly mask mask mask mask mask termed termed termed quinlan quinlan tied superposition superposition funded accounted confusion happen vanishes bring bring bring bring bring bring bring bring bring bring bring bring nal prevents prevents psychophysics ucsd sessions appearing algorithmic corporate mcdonnell mcdonnell inhibit inhibited utilizes utilizes utilizes filler judged repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition repetition characterizes ory tracks establishing cascaded iti iti iti iti iti permanent connectionism priming priming priming priming priming priming priming priming priming priming priming priming priming priming priming priming priming priming priming priming priming reviewed correlates nominal sentation durations durations durations durations recalled indi sented repetitions repetitions detections detections pew pew prime prime prime prime prime prime prime prime prime prime prime sentations heights preprocessor fluctuation fluctuation fluctuation fluctuation ample humphreys humphreys humphreys humphreys humphreys lasting lasting lasting dissimilar dissimilar missed facilitation facilitation hypersphere hypersphere onsets onsets blank blank blank blank blank blank masks lexicon interfering identifiable identifiable renders unrelated unrelated quence conscious conscious conscious formalize xii masked masked masked masked masked masked masked masking masking sional crease prince prince precedes orthographic orthographic orthographic orthographic orthographic orthographic facilitated facilitated facilitated facilitated inevitable parison ioo diminishes judgment manifestation proposals recency neuropsychology pinker pinker influencing ork sical episodic episodic rudimentary specifics alphabetic writ cluding formalization looms ingful hindered 
#@Bavelier_D,Jordan_M,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm number number number number number number number number number number number number state state state state state state results results results results units units information information information information information information information information information problem models based based based based based based based based based based based based based weights case vector shown shown shown shown systems systems values values values values point point point processing processing large test test test test test test test test test test analysis form form shows simple visual paper paper examples examples examples examples examples examples examples examples examples examples examples examples small small small size feature task task fig fig fig points features features process level level trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure structure structure problems problems problems problems random high high response response response response response similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar representation show show section section section section section rule rule rule average average average obtained note note experiments result result result result result result result university variables research research research research independent independent initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial table table table table table table table table table table table table table table table table table standard prediction direction direction presented presented presented present sets sets sets sets sets sets sets sets sets range press learn learn learn learn learn learn position basis basis sample abstract find properties properties properties properties properties properties properties properties properties properties references due important important important important decision decision decision decision decision introduction introduction action complex hand hand effect effect effect effect effect generated generated parallel parallel parallel parallel parallel difference difference assume rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules prior prior prior prior prior prior learned learned learned learned learned type good good good good long long conditions represent expected make make make make make correct correct probabilities probabilities times mapping potential made made made made made made knowledge knowledge knowledge knowledge knowledge knowledge knowledge artificial artificial specific specific compared series provide gain equal equal equal equal equal equal equal equal equal equal accuracy accuracy accuracy comparison larger contrast train train selection morgan morgan implementation implementation version version consists individual advances advances represents responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses difficult final addition addition addition addition addition addition sequences sequences sequences sequences sequences experiment experiment experiment experiment experiment experiment experiment experiment view design design transition transition transition transition effects effects effects determine efficient significant pages pages increase give produce derived weighted weighted developed developed developed area area lines lines lines lines lines finally processes processes selected simply simply simply simply simply discussion describe describe describe describe describe describe proof short short short common effective shape shape shape shape shape ability ability ability hypothesis hypothesis hypothesis instance instance instance instance instance instance instance instance instance instance instance future development kaufmann kaufmann pairs pairs pairs pairs pairs pairs pairs pairs pairs underlying combination interesting testing testing testing york york trials principal representing numbers pre pre pre making making making attention produced added added description description predict predict predict predict predict predict predict improved improve directions advantage property property property pair pair pair pair pair pair pair separate typical typical similarity similarity similarity similarity reported include subject sufficient compare conventional conventional conventional conventional conventional conventional teacher approximately volume volume match match match positions positions modified modified observation sensitive constructed lead concept suggests suggests suggests correctly column column conclusion starting starting row row conclusions differences differences accurate clear suggest suggest propose propose hard drawn demonstrated solid start manner base explicit van van van derive perception ways ways ways estimating describes explicitly involves remaining angle unique unique unique develop develop select yield choosing stages squares interpretation labels showed showed understanding understanding understanding understanding understanding understanding understanding understanding understanding understanding translation translation translation discrimination discrimination dashed dashed expansion convex valid valid initially advantages topology expect existing figures figures figures figures figures figures figures figures perceptual instances instances instances instances instances instances instances instances instances instances instances recognize maximize characterized tests tests major reason identified importance importance divided presentation identify comparing essentially road refer refer repeated repeated repeated success link superior symmetry involved involved predictor consisted software trains unlike american collection investigate detail replaced association accurately accurately accurately accurately accurately matches matches matches matches school links links decisions decisions structured symbolic encode encode cognition matched attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes hill math concepts concepts concepts possibly editor predicts opposite opposite opposite psychology equally equally formal formal formal shapes shapes shapes shapes shapes shapes shapes academic initialized initialized initialized generates extent utility utility finds mentioned analyzed adjacent answer briefly briefly briefly tool tool reasons reasons turns lin formalism shared shared precisely probable mathematics angles angles angles angles angles angles angles angles angles angles angles angles attribute attribute attribute attribute geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry geometry annual recognizing geometric geometric geometric geometric applies items lack frequently templates templates instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction richard conclude expectations returns begins representative representative college identifying identifying princeton appropriately concerned purely impossible impossible outcome children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children children lost chance chance accepted occurred tools siemens siemens determination determination hope reasoning reasoning reasoning reasoning reasoning methodology effectiveness salient guide modifications presentations child child child respective encountered surprising surprising decide expanded sides sides sides sides sides sides sides sides sides intended sim sim sim sim sim reproduce similarities similarities insight horn correcting valuable ignore shavlik shavlik shavlik interestingly material material johnson counts treat boxes boxes verify verify linked appeared dna unable listed asked uniquely revealed failed medium medium associate examining examining pairing translated genes geoffrey elementary names names names names names names names conversely apparently denver denver responding west minor things things differing differing differing answers answers answers answers mix modal modal modal modal modal modal fat acquire corporate attributed agrees agrees agrees towell towell towell towell towell towell towell towell east fill fill fill fill clarity clauses incorrectly val val val diagnostic meeting contrasts triangles triangles judged mill att att att att att att att att att att att att att convention convention convention convention convention reality reproduced wisconsin binomial mcgraw materials materials materials materials materials materials materials materials materials differentiate translate comprehensive richer adjustments teachers teachers dominate madison treats pay dissimilar tilt claimed judgments positively knight unimportant unimportant kbann kbann kbann teach weeks weeks weaknesses hoped hierarchically informal informal informal informal informal informal informal informal attend invaluable nicely subsection subsection subsection pairings grade grade grade grade grade grade grade grade grade grade grade grade grade grade adults duplicated negatively textbook textbook textbook textbook textbook textbook textbook textbook textbook textbook textbook slant propositional propositional guessing odds answered wisc deficiencies judgment noordewier alike alike alike alike alike deficits generous revising educational educational love appearances paring conception textbooks 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#*network network learning learning model neural neural neural neural neural neural neural neural neural neural neural input input input input input input data figure figure time set set set set set set set set set networks networks networks networks networks training training training training training training algorithm algorithm algorithm number number number number number number number system system system error error results results results information information information information information information information information information information information information information information information information problem models models models hidden performance based based based based space space space space space space space space space space space space space space space space space space space space space linear linear case case case case case case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown values values distribution distribution distribution recognition recognition method method method method method approach approach approach approach approach approach pattern processing processing processing processing processing processing processing control large large large large large large large large large local rate rate test test test test test analysis analysis class class class matrix matrix matrix matrix matrix matrix matrix inputs form form form shows shows shows shows paper paper paper paper small small small small size size feature net net work work task step step features features features features features features features features features classification classification process trained structure problems problems problems problems problems random random high high similar similar similar similar similar representation representation representation representation representation representation representation show section section section section section fixed line line line rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general speech speech real approximation term note experiments experiments dimensional dimensional dimensional computation computation computation computation computation research defined defined defined defined found sequence target target target initial table table table table table table table table table table terms terms node science science left presented map map present present present phase frequency frequency frequency frequency frequency machine sets sets motion press position sample abstract applied applied back find references ieee important important decision context context context context context context context context context introduction action complex hand hand hand statistical parallel tion tion tion complexity lower lower lower lower lower lower lower lower lower representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word learned higher part part part center center cases required represent distributed distributed distributed distributed distributed bayesian make make correlation length correct scale scale scale resulting classes classes classes ing ing ing ing ing tasks total total regression computed computed computed respect respect sum sum sum sum sum performed performed performed times times times times times times times times elements regions means natural natural natural natural natural global applications applications applications applications study knowledge original original original original artificial artificial artificial relative relative represented true compute objects perform determined goal goal goal related related related related related related mit contrast contrast train nets nets modeling selection morgan proceedings proceedings proceedings proceedings proceedings proceedings proceedings words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words individual individual individual joint connectionist connectionist final sequences ai considered cambridge computing experiment directly directly directly directly san san conference conference conference efficient efficient upper upper upper upper upper upper upper upper statistics statistics statistics statistics increase derived derived clustering clustering clustering clustering area finally selected selected selected selected selected nature nature depends depends biological measured measured discussion describe arbitrary group group limited limited close close close close close corresponds corresponds complete surface surface surface surface amount nearest nearest nearest nearest nearest nearest require eds eds journal journal square instance instance cluster cluster easily degree makes rumelhart fit smaller reduced reduced fully fully fully interesting interesting york york york york york york york head special structures uniform language language language language language language language language language representing representing numbers window window window international international normalized normalized normalized idea attention added description resolution resolution property separate similarity similarity similarity similarity similarity similarity similarity similarity movement reported reported practical pixels sense sense sense sense sense sense sense sense sense sense sense sense cognitive interest dimensions dimensions dimensions dimensions dimensions highly varying compare unsupervised unsupervised calculated volume volume works tions tions yields achieve sparse evaluation positions sensitive constructed occur occur occur occur extended wide wide move clusters occurs occurs occurs occurs occurs occurs occurs conclusion reduce reduce segment neighbor neighbor differences performs mateo suggest sound mechanisms reduction characteristics intelligence variety variety targets characters characters program question acknowledgements relation index describes describes segments dimensionality dimensionality text text text text text text text text scales quality letters letters extracted extracted extracted formation depending interpretation lemma lemma lemma lemma lemma detailed evaluate centered decomposition decomposition decomposition decomposition decomposition decomposition forms forms forms forms similarly similarly slow performing classical normalization purpose purpose boundaries filtering filtering string assigned construction construction kohonen kohonen expect retrieval retrieval recognize automatic automatic variations neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors discussions characterized major major reason columns letter closely society encoded encoded divided included included mcclelland mcclelland mcclelland latent identify literature efficiently computations schemes schemes tend ten ten ten ten fine fine capture traditional traditional strongly success success interpreted content categories dot hypotheses ill cat automatically deal presents presents diego american poor access collection collection accurately hall rest applicable applicable combine reliable symbolic complicated cognition coefficient coefficient closest plausible opposite singular singular singular singular singular singular singular taylor separated finds plant sentences percentage brown brown derivation derivation derivation derivation track analyzed phenomena london stanford widely organized organized preprocessing preprocessing protein bishop mation commonly cut pitch auto incomplete meaning outer percent percent reflect reflect collected collected items freeman bootstrap tional tional axes documents item completion employ rep psychological vocabulary ture weigend popular occurrence occurrence occurrence tank suited suited kinds june sentence semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic multidimensional summed summed cor realized realized don don person college redundant formally martin martin resources lost significance significance promising occurred occurred occurred occurred occurred overcome mail odd odd vehicle keeping keeping occurring roles ral methodology disjoint cottrell cottrell cottrell corpus corpus corpus corpus corpus corpus degradation infor service contexts contexts contexts contexts document document document programs ambiguity cone corre entry decide sides regard searching tic entries entries fish treatment pollack pollack matter refers properly proximity proximity characterization characterization insensitive stone market assigning assigning counts counts counts counts counts counts counts counts counts empty dense yale dna blood microstructure listed vec deriving ber opposed job legal employs poses distinction exception amherst hierarchies tor stands clustered clustered representa representa ibm num management pdp graduate distant distant interactive topic topic topic rough ambiguous ambiguous ambiguous ambiguous ambiguous conversely deleted deleted deleted deleted million amino misclassified discusses apparently confusion confusion confusion confusion nasa fea bring bill intensive october october mann manuscript emphasis sponding ate send heavily water hop micro dominates lists lists fre usefulness rare rare unreliable gram gram gram core carries carries inefficient dog frequent frequent frequent frequent syntactic drastically senses senses senses senses senses connectionism filling remained deter zeros magazine inducing semantics scatter sparseness shop contents bear counted problematic problematic jan dean occurrences huge indexing lexical lexical lexical lexical lexical lexical lexical terminology degrades stems stems stems moderately deleting hood linearities gallant gallant gallant gallant nice hot localist collections cars cars months months months topics oil synthesize forthcoming forthcoming andreas constituents tics scribed distinctions mike named rolls workers mercer perspectives rationale lemmas lemmas lemmas lemmas lemmas lemmas lemmas lemmas inadequate neglecting teach deletions lobster successes eval news kay waltz waltz interpretable useless interna interna occupy suit suit ist unrelated disambiguation disambiguation disambiguation disambiguation disambiguation disambiguation disambiguation disambiguation disambiguation disambiguation disambiguation disambiguation disambiguation manageable corpora articles lumped predominantly berry berry berry grained uninformative government indebted concludes nouns disabled intro wasted crab lai melodies beck discourse hecht living verbs byte cutting cutting ship kauf vocabularies vocabularies ule labor labor columbus ain supercomputer supercomputer uation jobs coarsely neces cod pulls roger rob topical intercept gather ste ste ste ste ste ste surveillance quently duces ice sary trec dry kelly semantically semantically neuropsychology phi anymore domestic domestic domestic nyu grams grams resent cheeseman cheeseman pipelines exert hitting incompatible factory nielsen riacs halting inheritance graceful river newspaper sigir inspecting 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#*network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data function function function figure figure time time time time time time time time time time set output output output output output number number number system system system results results units units units units units units units units units information information information information information information information information information information problem problem problem models models models models based based based based based based based based based based based based based based based based based based based weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case order order order order order order systems values values values probability noise noise weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach pattern pattern pattern pattern pattern point point processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control control control large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns analysis analysis analysis shows simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper small size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work task task task field field field field field field field features features features features features process process process process process level level current current current trained cell cell high memory similar representation representation representation representation architecture architecture line rule images general average theory term term activity activity activity university computation computation computation solution solution defined defined defined sequence target dynamics initial initial initial constant standard connections connections connections connections connections science left left presented presented map map map map map map phase phase phase phase phase phase phase phase phase phase activation activation activation activation activation temporal object object object object object object object object object object object object object object object object object object object object object object object object object object object object press press press position position position position position position position position position position position basis abstract applied back computational properties references due important important important important decision decision decision propagation introduction complex complex complex complex complex complex complex complex complex behavior behavior behavior stimulus stimulus dynamic dynamic dynamic dynamic parallel recurrent recurrent search tion change spatial spatial spatial spatial spatial spatial signals representations representations representations part part center previous bound firing firing firing firing firing type type type type multiple multiple multiple multiple cortex cortex cortex cortex cortex conditions conditions represent represent represent represent distributed equations make region region region region proposed proposed proposed correlation length length length length length length length simulation computed computed respect multi called regions regions means orientation orientation orientation global global global global study knowledge knowledge knowledge obtain vol relative specific specific specific represented represented provide compute compute objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc location location location location location location location location location location active determined determined experimental goal constraints cortical brain brain brain approaches mit mit contrast dependent selection selection selection selection selection report department synapses consists consists internal internal internal internal code code code code code individual individual connectionist connectionist connectionist responses layers layers layers layers layers layers ai ai ai ai ai maps maps maps maps maps maps maps maps considered considered cambridge computing directly hinton hinton additional top stage stage stage stage stage stage stage stage stage stage stage stage stage stage stimuli detection basic produce levels types types finally finally processes processes processes selected selected selected selected selected selected evidence nature nature depends depends simply biological biological achieved feedforward tested transformation transformation limited limited limited corresponds predictions short short implemented assumed shape shape shape shape supported role role role theoretical main eds eds journal journal ability including combination functional functional jordan interesting york york segmentation segmentation segmentation segmentation mechanism mechanism mechanism mechanism mechanism special consistent consistent consistent empirical empirical representing representing representing window stored bottom early early early early idea idea attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention combined sources neuronal neuronal population population recent resolution resolution exact separate typical similarity lateral period period period period period period period period period period period hierarchical cognitive recently varying conventional module module module module module module module module correspond positions positions gate gate gate gate gate gate gate gate gate gate gate williams williams organization sensitive entire exists exists exists horizontal horizontal parts lead studied invariant invariant invariant invariant invariant invariant wide rotation width loop occurs setting flow conclusion segment segment segment central retina retina performs suggest mechanisms cycle sigmoidal turn assuming variety variety movements movements selective selective selective selective selective selective selective groups scene scene connectivity connectivity force question acknowledgements areas relation relation relation pro pro van van van perception tuned tuned vertical distinct distinct dept segments segments missing explicitly simultaneously simultaneously transformations transformations transformations transformations consisting integrated shift extraction select select select select select select independently focus formation depending stages stages stages codes variation detailed detailed detailed open understanding earlier normalization roughly roughly roughly add includes perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual usa usa color color color color contour retinal retinal retinal retinal recognize recognize recognize recognize recognize determines determines determines mozer mozer mozer mozer mozer coupled coupled coupled coupled coupled coupled variations absolute absolute discussions columns determining determining selecting selecting aspects letter computationally wij wij oscillatory oscillatory oscillatory oscillatory oscillatory invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance receives receives quickly kind strongly allowing anderson anderson symmetry oscillations oscillations oscillations oscillations oscillations timing cue sci gray gray gray cues cues michael simplified play computes computes binding binding binding binding binding binding binding cat cat received received received principles principles overlapping operating oriented stimulation stimulation stimulation stimulation exhibit rapidly oscillators oscillator oscillator oscillator oscillator oscillator respond ideas project possibility gates gates stream stream oscillation pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway attributes saliency saliency saliency saliency saliency saliency saliency possibly necessarily opposite psychology psychology psychology rev changed der der logistic separated store extent grouping grouping attempts attempts integrate mentioned scenes scenes scenes scenes scenes distinguish derivation analyzed growing ganglion stress tive organized organized producing filtered forces nucleus mation recognized acad cybernetics populations flexible simulate simulate experimentally peter psychophysical psychophysical psychophysical completion commands ture ture reaches reaches serve singer singer singer singer adjust green germany coherent segmented segmented findings findings findings findings findings implements attentional attentional attentional attentional tile tile tile tile tile synchronization extreme cor globally globally forming forming refractory refractory zemel zemel circular jones theories caltech establish plays plays suppression dealing promising primate imposed familiar familiar los neurobiology neurobiology operates operates operates definitions salient optimally selects natl fires fires sompolinsky sompolinsky falls von von overview lang lang counting assembly arrangement parietal viewing viewing cerebral stimulated stimulated bins locked locked locked locked locked proximity projects valuable instructions outlined informa ple maximized ber focal encodes feeding additionally malsburg malsburg experiences breaking simulating avoided cns acting gated cessing segregation biophysical num continues elementary retinotopic books acquired retain synchronized interactive importantly oscillating oscillating grateful memo fea induces behave holding exploited mann bursting ble oscillate oscillate olshausen olshausen imple establishes establishes broadly connects integrates integrates essen essen essen couplings cooperation isolation neurobiological distorted falling communicate attended attended attended bradford ance meant routes bauer uno illusory linking linking linking addi ceedings plenum exploitation transferred contributing excluded entities entities deeper organisation organisation organisation organisation organisation organisation thalamus fukushima fukushima psych possesses possesses schneider angeles bind nth sing eckhorn eckhorn eckhorn eckhorn eckhorn eckhorn eckhorn positively positively positively clamping neti neti fruitful mented feeds inhibits snyder surrounded cog ration ons viewpoints subsystems blobs transfor del spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight spotlight groupings posner posner ner confusions conjunctions conjunctions chemistry pnas wolf desimone gestalt gestalt tex tex ijcai xii entity entity bringing peters negatively negatively terminating stimulate golomb elapsed resets perceiving perceiving perceiving perceiving underly extrastriate shortening coarsely invari century kruse kleinfeld desynchronization tionally ksnig ksnig ksnig mil behrmann neurosc brosch schillen schillen munk emit proces retinotopically retinotopically demanded mpi werner moran moran reitboeck reitboeck desireone appleton crofts shorten abstracting accidentally 
#@Goebel_R,
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control control control large patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix form shows shows shows simple examples small size work cells step points points points level level structure response equation equation equation section fixed vectors parameter approximation approximation approximation gradient obtained obtained term experiments experiments experiments experiments experiments experiments experiments experiments activity activity activity activity activity dimensional dimensional university solution solution research found dynamics dynamics dynamics dynamics dynamics dynamics dynamics estimate estimate estimate standard computer terms connections connections synaptic synaptic synaptic left left map activation activation activation activation activation frequency frequency object motion motion motion motion motion motion motion range press position nonlinear nonlinear nonlinear outputs outputs abstract applied find references due ieee adaptive complex complex circuit circuit circuit circuit circuit behavior stimulus stimulus effect effect effect dynamic generated parallel parallel change change difference variable part previous firing firing spike represent equations length length length length length length length length length length length observed errors forward scale simulations ing tasks total simulation respect performed elements mapping mapping mapping mapping mapping potential feedback feedback study obtain represented represented cross series provide objects determined determined determined determined determined related connected connected motor motor motor motor motor brain approaches mit larger update descent modeling modeling modeling proceedings department consists joint represents represents represents difficult difficult difficult exp considered considered cambridge equivalent experiment curve view design design trajectory san stimuli effects effects effects determine determine approximate free speed pages pages pages con derived velocity velocity controller types nature inhibitory inhibitory biological biological measured measured discussion inverse surface circuits assumed generate supported main journal journal journal journal end end future makes sensory sensory sensory typically smaller dynamical functional fully york york york mechanism empirical normalized produced description predict predict neuronal element element typical typical movement movement movement movement movement movement movement reported lateral lateral lateral lateral lateral lateral period subject side subset engineering engineering interest axis axis axis studies differential positions positions symmetric generalized generalized organization organization organization grant constructed constructed parts studied rotation rotation rotation rotation rotation predicted predicted predicted locally runs assumptions editors editors editors central central central interactions exponential exponential strong mechanisms mechanisms largest external characteristics characteristics characteristics characteristics california assuming movements plane iii iii configuration configuration force force force force force force force force base question acknowledgements construct ways modeled modeled modeled physical physical physical physical angle angle integrated integrated frequencies springer springer springer springer potentials interpretation controlled modulation forms static static static static understanding approximated activities activities activities activities translation constants closed closed generation generation generation construction transactions transactions degrees recorded recorded coordinate formulation automatic society society maximal modes composed composed composed verlag verlag verlag verlag induced induced video video neuroscience physiological physiological physiological physiological relaxation backward binding intrinsic camera camera body employed employed diego poor oscillator postsynaptic project behavioral behavioral behavioral behavioral behavioral behavioral behavioral ideal muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle combine office root oscillation oscillation oscillation oscillation oscillation func removed removed removed hill hill hill hill hill hill measurement changed freedom nerve nerve nerve nervous nervous nervous nervous nervous fibers fibers fibers simplest submitted submitted explain serial serial electronic seconds isolated isolated isolated isolated isolated isolated isolated isolated isolated established animal animal mentioned mentioned pairwise analyzed fairly biology biology nonlinearity london london ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion inside perspective forces forces forces located located mation controls controls cut cut cut cut cut angles angles mechanics considerably understood understood flexible flexible axes simulate simulate lack quantitative posed incorporated incorporated berlin modulated modulated qualitatively fiber neuro neuro shaped shaped instantaneous don physiology generator naval royal royal receptors rigid rigid spontaneous spontaneous spontaneous anatomical anatomical ranges balance balance wire intuitively preparation preparation muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles muscles reliably utilized studying regarded regarded regarded lengths lengths lengths heart enable stimulated contraction contraction contraction contraction contraction record record jolla ends extensively concentration calcium calcium harris harris mechanical neurophysiology neurophysiology neurophysiology kinematics torque pieces pieces pieces feeding quasi quasi ical chapter chapter resting resting resting resting resting rhythm rhythm electrode electrode molecular stands jacobian gener plate rhythmic rhythmic rhythmic rhythmic anal attached attached attached dorsal dorsal dorsal dorsal rod rod esti macroscopic mix tension tension tension bursting ate doya doya doya doya doya allen decided crude vii agrees spring spring skin loosely integrates injected thickness impedance partly loads mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill mill intact marder rel elec stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric selverston selverston selverston selverston selverston selverston selverston selverston selverston selverston selverston selverston selverston selverston selverston selverston ganglia supposed medial medial medial medial medial medial refine ysis modulate upward ogy apparatus warrick warrick stim quiescent mike heat ative facilitation cardiac cardiac mary hogan hogan namic motoneuron lobster lobster lobster lobster lobster lobster lobster lobster lobster lobster lobster lobster acti duce abstracts antagonist skeletal skeletal skeletal chunks ware viscosity muscular muscular muscular commissural identi stiffness stiffness neuromodulators neuromodulators neuromodulators initiate teeth teeth teeth teeth teeth teeth teeth teeth shortening onal runge midline pacemaker tissues tissues tissues sac sac kenji fied kutta dose philosophical sea extrinsic woo woo expose ulated attachment attachment attachment attachment evokes squeeze squeeze peptide ator mathemat roedial roedial lso xiv aln elucidated disrupting suspended 
#@Boyle_M,Doya_K,Selverston_A,
#t6
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#*model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time output output output output output output output number number number system system system system system system system system system system system system system system system system system system system system system system state state state state state state state information based based based layer case case case order order order order shown shown shown shown shown shown shown shown shown shown shown values values values neurons neurons neurons neurons neurons neurons neurons neurons neurons point single single single processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control neuron neuron neuron neuron neuron neuron neuron patterns analysis analysis class class inputs inputs inputs inputs inputs form form shows signal signal signal signal signal signal signal algorithms simple simple visual visual paper paper small size feature feature net work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field features level level level current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell high high high response response response response response response response representation show show show equation equation section fixed line line line line line line line general note note experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result university threshold independent independent found target target target target constant constant constant constant constant constant terms terms distance connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic prediction prediction present phase activation low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal object maximum range range components components components basis abstract back find find find find properties properties properties properties references component component due adaptive propagation introduction complex complex circuit circuit circuit circuit circuit circuit behavior stimulus stimulus stimulus effect effect dynamic generated parallel tion change change change change change difference complexity variable spatial spatial spatial assume signals signals higher part type type required cortex good conditions conditions conditions represent represent represent represent tree equations make make make make make fact proposed proposed proposed proposed proposed proposed observed classes classes classes ing ing total total total total total total total total total total total total total total total total total total total total means means potential potential potential potential potential potential potential potential potential natural feedback filter filter true desired provide provide provide objects objects objects objects proc location active experimental experimental experimental experimental goal goal goal posterior posterior gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain cortical brain brain brain voltage voltage dependent dependent dependent dependent institute words synapses synapses synapses synapses synapses synapses synapses synapses synapses individual individual addition addition considered equivalent equivalent equivalent equivalent experiment environment directly directly directly directly additional stimuli stimuli stimuli effects effects effects full requires significant significant significant increase increase give give con con produce condition levels levels levels levels levels levels levels levels levels types path path provided provided evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory achieved discussion feedforward tested excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable amount effective synapse synapse synapse supported role role role eds face ability degree makes makes sensory sensory sensory sensory auditory smaller underlying underlying functional fully fully transfer interesting york increasing mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism principle direct inhibition inhibition inhibition normalized magnitude idea idea light predict membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane population recent lateral lateral lateral lateral lateral lateral lateral moving moving sense sense sense subset array achieve achieve background background background channels increased amplitude amplitude amplitude parts parts intensity intensity invariant occur occur wide loop occurs occurs pass pass pass demonstrate strength strength suggest suggest propose mechanisms mechanisms integration proportional turn relationship acknowledgements perception solving ways ways primary primary primary primary primary describes changing changing modeled modeled sensitivity simultaneously electrical electrical electrical electrical electrical scales frequencies frequencies frequencies events potentials decreases dependence depending viewed influence influence influence variation open controlled controlled centers activities suggested constants diagram key reasonable delays normalization sec filtering msec msec koch dendritic dendritic includes includes usa automatic automatic variations holds discussions tests determining straightforward aspects identified extra spiking detect detect projections projections tend essentially identity receives receives capture excitation excitation excitation excitation excitation allowing interested conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance contribution contribution criteria sci categories gray comp comp comp comp comp comp comp involved simplified absence providing reach neurosci subsequent extract receive receive body unlike unlike unlike carried powerful wiley essential essential circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry steady steady steady steady steady steady steady involving rise rise rise rise giving referred pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway affect cover understand fundamental circles circles changed thought adjusted freedom observe shapes logic nervous nervous pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal baseline baseline baseline baseline baseline extent contributions regime mentioned ground interneurons implementing sys nucleus nucleus nucleus afferent afferent afferent afferent afferent afferent afferent afferent involve involve acad axons recording meaning fluctuations varies varies varies greatly considerably prop reflect reflect pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways understood understood tional capability capability capability experimentally experimentally experimentally resistive schematic maintain maintain perturbations perturbations characterize differs achieves conductances conductances conductances conductances conductances conductances conductances electric electric electric electric electric electric electric electric electric electric electric electric electric electric fiber decreased age physiol physiol physiol physiol physiol summed instantaneous instantaneous sensing identifying accomplished martin acts acts discovery tem receptors receptors plays lost inspired inspired spontaneous adjusting adjusting adjusting familiar resistance resistance resistance resistance resistance resistance mark affected preparation filled natl elimination passive weakly weakly weakly weakly slice cerebellar cerebellar dendrites dendrites dominant injection injection dendrite dendrite dendrite dendrite dendrite dendrite diameter fish fish fish fish fish fish fish fish fish fish fish fish specialized spatiotemporal specificity impact characterization influences discriminate discharge discharge ence pointing nelson nelson nelson nelson nelson reports resting experiences molecular manipulation arising acting capacitance peripheral peripheral peripheral segregation segregation interneuron interneuron interneuron interneuron compensate lobe lobe lobe lobe lobe lobe lobe dominated activate activate activate regulation regulation regulation regulation regulation douglas mediated paired paired echo altered differentiation surrounding retain intensities intensities monitoring worth sonar maintains inversely inversely inversely descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending descending intracellular meet holding tonic tonic tonic demonstrating rewritten species reversal reversal reversal reversal fortunately cable photoreceptors water water morphology played purkinje purkinje illinois fre rons excited possess impedance impedance ventral neurol periphery characterizes characterizes bat arriving arriving arriving tance leakage confined experienced cutoff cutoff cutoff electrophysiological electrophysiological granule blocked massive sur cope urbana apical apical apical activates remarkably cient terminate adjustments ver capacitive ther manipulations opportunity undergoes segev tot tot tot participate ell ell ell ell ell ell ell ell ell ell ell ell exciting basal basal basal basal vitro beckman rogers basilar testable widespread live story erties leak leak resistances ner pupil inspiration presumed joe heiligenberg heiligenberg bernander bernander modulations assump bullock bullock emitted emitted morphological conduc conduc mecha nimh inh inh inh inh inh unreasonable regulate regulate regulate regulate navigate darkness propor prey regu efferent silenced vss vss vss hibitory speculate noteworthy tances descend descend perimental regulating 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#@Nelson_M,
#t6
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#*network learning learning learning learning learning model model model model model model model model model model model model model model model model input input input input data data data data figure figure figure figure figure figure time time time time time time time time time output output output number number number number number number number number system system results results units units information problem performance performance performance based based space linear case vector vector shown shown shown shown shown shown values unit unit unit unit unit pattern pattern single single single single single processing large large local local local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns analysis analysis form shows shows shows shows simple simple visual paper paper small small small small size size net net net net net net net task fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step points points field field field field field field field field field field field field field field field field field field field process level current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell problems problems random random random high memory memory representation representation show show line parameter average gradient term term experiments activity activity activity activity activity activity activity dimensional result university threshold research independent found found found found found dynamics constant estimate terms distance distance distance distance connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented map map map map map map map map map map map map map phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation frequency frequency frequency temporal temporal temporal object object object object object object object motion press position position position position position position abstract properties properties references positive positive introduction action complex complex hand estimation generated tion tion tion change change change change difference variable spatial spatial spatial spatial spatial spatial assume classifier rules rules measure higher part part previous firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing multiple cortex cortex good spike spike spike spike long long region correlation correlation length scale scale simulations simulations total total total simulation computed respect sum sum times times times reinforcement knowledge negative artificial relative relative relative relative specific specific compared compared cross define objects objects objects rates rates rates rates rates rates location location location location active active active active active active active active determined goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal connected motor motor brain brain larger connection connection connection fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields update department synapses synapses synapses code code code joint scheme addition graph maps maps maps maps environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment trajectory trajectory effects bit requires significant approximate free speed estimated estimated estimated coding coding coding coding coding coding weighted weighted weighted provided finally evidence simply increases group group group group limited limited close close corresponds excitatory excitatory stable surface surface surface predictions amount short implemented synapse require journal square ability simulated simulated simulated simulated simulated smaller interesting edge edge head head head head head consistent consistent leads numbers max max max max pre pre pre direct making bottom run description predict neuronal neuronal neuronal neuronal population directions directions directions directions directions directions takes element typical typical typical typical similarity movement movement strategy moving moving moving moving moving moving period cognitive cognitive recently relevant relevant sufficient previously background positions positions positions positions locations locations locations locations locations locations locations separation separation grid interval entire arm arm constructed parts extended spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes predicted occurs occurs occurs occurs runs runs runs runs starting starting starting place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place trajectories trajectories depend competitive reward central central central accurate clear learns propose cycle cycle cycle cycle cycle cycle characteristics proportional movements movements movements relationship relationship iii iii iii targets groups groups groups groups groups question longer primary sequential estimating vertical vertical explicitly simultaneously involves shift shift shift implies versus john decreases decreases independently review depending depending stages stages overlap open controlled restricted restricted updated fraction similarly earlier earlier initially eeg eeg eeg eeg eeg eeg eeg eeg classified avoid recorded fire fire fire fire fire exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration box box figures includes successfully successfully middle aspects differ divided driven latent build post post tend reached receives receives excitation refer refer notice notice notice notice strongly induced allowing showing neuroscience strategies cue built built built michael delayed neurosci neurosci neurosci moves moves moves moves moves subsequent subsequent rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat modelling remain rapidly rapidly environments preliminary behaviour fewer examine successive incremental reliable phases phases phases phases phases phases smallest plausible reading equally changed portion simplest seconds site site site site site site crucial track defining navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation coded worse worse interneurons london london spatially lin straight sys closer closer ring sites ran ran immediately immediately hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal involve beginning res recording simulate quantitative quantitative leave recordings recordings recordings continuously psychological spread modulated reaches achieves age progress simultaneous shifted room college oxford investigation investigation investigation acts acts circular food food food food food food food food food food food food food food food food food food food food food food food primate primate iiii overcome mail moment mark shifts north north north north north north north guide corner obstacle obstacle obstacle obstacle obstacle obstacle obstacle fires fires fires fires fires fires exploring exploring published cone encountered encountered encountered encountered encountered encountered encountered encountered encountered encountered induce decide moved moved ascent schwartz consequences consequences searching searching searching searching enable enable hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus modelled ahead ahead ahead passing passing route exploiting exploiting exploiting exploiting designing subsequently displacement fired fired fired fired fired fired fired fired leaving minus piece piece piece piece piece piece ent covering opposed alternating obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles revealed pieces centre centre centre centre rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm england avoided visited visited goals goals goals potentiation potentiation crosses crosses switched switched switched switched switched switched switched switched harder portions portions superposition figs dorsal west west west west crossings travel correlate rats rats rats rats rats heading heading european envelope envelope east east east east east east diffuse char returned anatomy excited physiologically evenly peaked peaked peaked peaked peaked peaked vote vote successively mcnaughton fair centres south south south south south south resultant resultant enters enters oscillates approached raised cuts backwards backwards greatest addi freely freely freely freely hip modulate resemble entering entering newly collision examines saturates minute men posi displaced initialised aware earliest centred centred behavioural behavioural behavioural behavioural ration timestep timestep timestep timestep georgopoulos georgopoulos travelling nadel nadel burgess burgess burgess burgess burgess burgess gation preferentially muller muller muller theta theta theta keefe keefe keefe keefe keefe keefe keefe keefe keefe keefe keefe keefe keefe keefe keefe barnes barnes barnes postulate cai diameters recruited tered closeness navigate crucially clarendon sinusoid electrophysiology parison died timesteps navigational navigational explo dentate characterised accommodated leonard encounters encounters encounters suggestive sitions downstream vironment telling stricted encountering encoun navigates navi kettner 
#@Burgess_N,O'Keefe_J,Recce_M,
#t6
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model input input input input input input input data data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm output output output system system system system system system system system system system system system system system system system system system system system error error results results results units information information information problem models hidden based based space space space space space space space space weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown systems values pattern pattern pattern pattern pattern single single single processing processing processing patterns analysis inputs inputs inputs inputs inputs inputs inputs form form form form form form shows shows shows signal signal simple simple simple simple paper feature task task task task task task task task task task task task task task task task points points features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification level level level level level level current current current current trained trained trained structure structure high memory memory memory memory memory memory memory memory memory memory response response response response response response response response response response response response response response response response response response response response response response similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture show show show show fixed fixed fixed fixed fixed fixed fixed line line rule rule general generalization generalization generalization generalization generalization generalization generalization real states theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory gradient term term activity dimensional result university university university research research research independent independent found initial terms terms node science science prediction prediction left presented map map map map present present present phase phase phase phase phase phase phase nodes nodes temporal temporal range range range range press press press press press press press learn learn learn learn learn learn abstract computational computational computational computational computational computational references references adaptive adaptive adaptive adaptive adaptive adaptive propagation context context context context context context context introduction complex behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect effect parallel change change change spatial spatial lower lower signals representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations learned learned learned center previous cortex long long long represent distributed expected expected make region region region region region region region region region region region region region region region proposed proposed observed finite tasks tasks tasks human multi multi multi multi multi called regions mapping reinforcement reinforcement dimension study original vol artificial relative desired series provide perform eye eye experimental experimental constraints constraints cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain mit contrast contrast dependent dependent proceedings institute loss version internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal represents connectionist connectionist connectionist connectionist responses responses bias layers layers delay considered framework cambridge cambridge equivalent experiment directly hinton hinton hinton hinton top stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects effects effects determine determine upper upper upper full choice choice basic produce developed developed developed provided finally processes evidence backpropagation backpropagation nature inhibitory constraint constraint constraint simply associative associative normal normal increases corresponds corresponds complete complete predictions predictions predictions circuits finding amount short role role role role require eds eds eds journal journal journal journal journal ability makes makes rumelhart rumelhart rumelhart development noisy noisy sensory sensory sensory including including including simulated account account functional transfer transfer transfer transfer transfer york york york increasing mechanism consistent consistent structures trials trials trials trials trials empirical empirical empirical empirical representing pre pre pre pre pre pre pre pre pre pre pre inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition bottom light light light light light light predict predict predict predict membrane membrane recent advantage takes similarity reported apply period cognitive cognitive relevant sufficient sufficient sufficient highly previously previously studies studies studies studies address address background background observation interval williams williams increased suggests suggests trial trial trial trial trial wide wide wide occurs occurs generally place conclusions faster faster learns learns learns learns learns constrained suggest encoding encoding propose strong hard mechanisms mechanisms presence presence external solid intelligence relationship iii suppose van van derive construct construct factors distinct changing changing implement sensitivity simultaneously involves remaining easy slightly slightly text interaction interaction develop predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive formed shift implies independently independently independently formation formation review review review depending viewed interpretation interpretation interpretation interpretation restricted similarly translation partition partition discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination slow dashed classical classical classical classical classical classical classical reduces reduces closed remains classified classified classified classified classified activations activations activations activations color retrieval memories determines plotted variations black characterized compression compression compression compression compression capable society mcclelland latent latent latent latent latent latent latent latent latent quickly procedures contained moore moore moore interpreted interpreted neuroscience neuroscience neuroscience neuroscience neuroscience issue lie classify physiological physiological physiological physiological physiological strategies timing cue gray gray cues cues cues cues cues cues notation involved simplified absence absence paradigm observable subsequent subsequent subsequent receive modelling situations simpler remain unlike access access access exhibit association association accurately biases successive successive respond respond behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral mappings investigated investigated working comparable encode cognition cognition attributes trace trace predicting predicting predicts predicts predicts predicts psychology psychology psychology psychology psychology psychology rev der der precise separated academic switching generates simplest simplest attempts electronic animal animal animal animal animal animal animal years slowly slowly developing developing developing phenomena navigation biology biology implementing sites sites easier easier widely forces hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal gradually res arises arises geometric behaviors behaviors empirically flexible lms readily red cohen cohen slower continuously psychological psychological psychological partitioning characterize popular extensions redundancy redundancy redundancy redundancy redundancy damage damage conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning progress irrelevant irrelevant irrelevant consistently acquisition classifying benefit contextual contextual contextual contextual contextual contextual redundant redundant forming modify modify oxford oxford conditioned conditioned conditioned conditioned conditioned conditioned animals animals animals animals animals animals animals animals animals animals resources resources resources resources resources resources odor eliminate theories theories theories arrival plays eliminated fails air grow abilities abilities biased mark removing effectiveness presentations elimination cerebellar cerebellar cerebellar cerebellar representational representational representational representational representational representational tone tone tone tone tone tone loo enhance widrow widrow accounts facilitate facilitate facilitate reproduce exposure exposure exposure exposure exposure exposure exposure exposure exposure hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus modelled foundations cerebral creating arrive record repeatedly environmental informative ignore explorations stone lem discriminate compressed unified constitute shepard shepard removal incrementally comparative comparative classifications lesions lesions lesions lesions lesions lesions associate molecular clustered lesion lesion lesion evolve activate allocated allocated emphasize altered maximally maximally differentiation differentiation differentiation differentiation differentiation acquired gluck gluck gluck gluck gluck gluck gluck scope complementary harder conversely selectively paradigms dorsal likewise behave radio ignoring develops rats reversal reversal reversal reversal reversal reversal differently differently acquire acquire acquire acquire reversed twenty ers autoencoder autoencoder autoencoder autoencoder eliminates ning distinguishing continuum orr orr intact intact intact intact intact intact intact intact intact intact intact intact intact convention convention evolving evolving evolving distorted neutral demands demands demands differentiate tra devoted devoted stm hoff hoff wagner wagner hip mid severely severely lid enhancing dard psych berger berger concurrently scheduled lesioned lesioned lesioned lesioned lesioned lesioned lesioned lesioned lesioned lesioned lesioned lesioned lesioned 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classically psychiatry nay elusive tbr psychobiology instantiate disrupted rll elicits newark hirsh hirsh bloomington appleton crofts disrupts impair deduction occupying prokasy 
#@Gluck_M,Myers_C,
#t6
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#*network network network network network network network network learning model model model model model model model model model model neural neural neural neural neural data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure time time set networks training training training training training training training number number number number number number number state state state state state state state state state state state state state results results results results units units units units units units units units units units information information information information models models models models models models models models hidden hidden hidden hidden hidden hidden performance based case vector vector vector vector vector order shown shown shown shown shown shown probability probability probability probability probability probability probability probability functions neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution method method method method method approach approach approach pattern pattern point single single single single single single single single processing large large local rate rate rate rate rate test test patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis visual visual small small small size size task task task task cells cells cells cells step step process process process process process process process level level level level trained trained trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell response response similar similar similar similar fixed general general speech parameter parameter average average average average average average average states states states states states states states states states states states theory obtained obtained term note experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional university university university university university computation research log log defined sequence sequence estimate computer terms terms distance distance science science left left presented present present low temporal sets maximum press continuous abstract find references stochastic stochastic due due due important important important introduction hand estimation behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical effect effect effect generated generated change difference difference difference spatial spatial lower lower measure measure measure prior learned higher higher higher higher part center cases cases cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good spike spike spike long distributed markov markov markov markov markov markov markov fact techniques region correlation correlation correlation correlation length correct correct correct correct correct probabilities observed observed ing multi multi multi multi multi multi multi multi multi multi sum performed performed eq called called times times made natural study study obtain obtain obtain relative compared application application desired rates rates rates rates location location perform perform active determined determined determined determined experimental goal goal distributions distributions cortical cortical cortical brain brain contrast support train train train dependent modeling modeling modeling modeling modeling report institute code individual individual individual individual individual responses responses exp delay delay addition sequences sequences sequences ai ai cambridge directly curve additional additional view curves curves curves estimates top top top top stimuli stimuli determine upper requires requires choice significant significant significant significant statistics estimated basic increase con channel channel channel channel randomly clustering clustering clustering clustering clustering clustering developed entropy entropy processes processes processes selected selected nature nature depends simply simply associative associative associative associative associative associative associative measured tested assumption complete complete complete predictions short implemented generate supported main main ability ability hypothesis instance cluster cluster cluster cluster cluster cluster easily noisy underlying interesting testing significantly significantly york york segmentation segmentation segmentation segmentation segmentation segmentation segmentation special special trials trials trials trials trials trials empirical empirical mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode call pre window window window window window supervised frame frame frame frame frame attention light light correlations correlations correlations correlations advantage typical reported reported include include period period subject inference cognitive recently sufficient highly highly previously unsupervised unsupervised observations correspond achieve rl observation organization grant trial trial trial spikes spikes spikes clusters clusters clusters clusters clusters clusters demonstrate demonstrate assumptions assumptions segment segment central central clear clear clear propose external external external external external external external drawn labeled variety iii iii iii iii iii introduce manner manner question construct estimating plot distinct modeled simultaneously averaging electrical develop develop events events events events springer quality focus focus focus correlated correlated evaluate labels organizing centers centers centers centers frames frames frames frames frames soft activities activities activities activities similarly discrimination discrimination discrimination key key key performing performing measurements measurements measurements measurements normalization sec event remains valid distances msec foundation recorded recorded recorded recorded formulation instances instances determines determines plotted phys discussions characterized characterized modes modes modes modes modes modes modes modes modes modes modes modes modes characteristic capture capture notice notice verlag repeated allowing dis hold paradigm delayed delayed correspondence correspondence correspondence ill ill ill ill overlapping trains trains trains trains trains origin carried parametric wiley wiley difficulty exponentially association association divergence divergence divergence divergence divergence divergence divergence respond school school rest behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral detectors reliable variability statistically statistically statistically cover understand examined measurement measurement possibly rev aspect front front nerve hebb hebb multivariate multivariate multivariate multivariate extent seconds seconds seconds seconds seconds established asymptotically histogram indicating pairwise pairwise pairwise pairwise agreement purposes day day day monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey monkey mation laboratories probable probable medical medical recording recording recording recording recording recording depicted fuzzy reflect collected understood led consistency quantitative marked recordings recordings recordings recordings completion release switch switch switch exhibits poisson poisson poisson poisson poisson poisson poisson poisson poisson characterize characterize characterize spread cal comments windows simultaneous simultaneous simultaneous simultaneous simultaneous yielding sharing consistently picture uncorrelated aligned aligned aligned lagrange tem interconnected turned multipliers cellular cellular chains tishby tishby tishby tishby tishby tishby tishby observing shifts belong spot infor reliably utilized started recovered ensures corre pat histograms monkeys monkeys monkeys monkeys monkeys monkeys facilitate assembly assembly assembly assembly thomas centroid centroid centroid claim israel cerebral bins belonging characterization characterization characterization accumulated accumulated accumulated accumulated discriminate yielded drop drop numerous logarithm exhaustive encouraging tween icassp aij aij ideally solely big reflected alternate relating careful fixation fixation fir guided frontal frontal frontal anal setup assemblies assemblies assemblies assemblies preprint preprint preprint indication thousands bring tissue treating examination manuscript vice sessions tour versa remarkable stimulating terns smoother hypothesized hypothesized aid abeles abeles abeles abeles abeles exper finer horizontally markers markers markers markers systematically sliding sliding electrophysiological elec lsi technion unexpected repetitions repetitions lights routine routine ysis jerusalem behaving behaving behaving behaving behaving behaving initiated unobserved ted marker marker marker marker marker discrepancy nents hebrew hebrew hebrew hebrew touch extracellular extracellular accu iiiii ogy distributional distributional undergoes eog collect remember tributed poral henceforth signaling encouragement touching underlie lations quences relied reinforced gat gat gat gat gat electro prepared straints flamework vaadia vaadia hardness rewarded living bergman bergman bergman bergman bergman surgery crease pereira rhesus rhesus statisti divergences divergences profound illl conventionally discriminates anesthetized technol iil iil hagai huji engage naftali imental negligibly pops jill jli cooperativity corticonics pressing exceptionally bsf binational microelectrodes looms concomitantly moshe israeli margalit 
#@Gat_I,Tishby_N,
#t6
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model model neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function figure figure figure figure figure figure figure time set set set set networks networks algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number system system system results results information information information information information information information information information information information information information information models based space space space space space space space space weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case case vector vector vector vector vector vector vector vector vector vector vector order order order order order order order order order order shown shown shown shown shown shown shown systems systems systems values values values values values probability parameters noise noise noise noise noise noise noise noise noise noise noise weight functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach image processing processing processing processing processing processing processing processing processing processing large large large large large local local patterns patterns patterns analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form form shows shows shows shows shows shows signal signal gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual paper paper examples small small small small small feature feature feature feature feature net work work work methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells field field field features features features features structure structure structure structure random random random high high high high high response response response response similar similar similar representation representation show show show show equation section fixed line vectors vectors vectors vectors vectors images general general general real real real average average average average average average states states theory theory obtained term term term term term term term term term note note note note note note activity activity activity activity activity activity activity dimensional dimensional result variables computation computation computation computation solution solution solution solution solution solution solution research independent log log defined defined defined found found found found found constant constant computer terms terms terms distance distance connections connections synaptic node node node node left left presented presented present present present present phase phase phase low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency frequency sets sets sets maximum maximum range components components components basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous abstract applied find find density density properties properties properties properties properties references component due positive important introduction statistical statistical statistical statistical statistical statistical statistical effect dynamic variance variance variance variance tion change spatial spatial spatial spatial spatial assume lower lower lower rules measure prior representations representations representations representations learned chosen chosen chosen higher higher higher higher higher higher higher part center previous cases type type type type type type type type type multiple multiple multiple multiple multiple multiple multiple multiple multiple cortex good good conditions conditions represent expected make make region region region observed scale scale resulting resulting resulting resulting total computed respect sum sum sum sum sum sum sum sum eq eq eq eq eq eq elements elements elements mapping mapping mapping mapping mapping means means factor optimization potential natural natural orientation study filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter obtain relative represented application desired receptive receptive receptive receptive receptive receptive define define define proc goal goal related related related related related related constraints gain gain gain gain gain gain gain gain gain gain gain gain equal equal power power power approaches mit mit larger contrast contrast connection connection connection fields fields fields fields fields morgan loss loss version advances joint maps domain domain curve additional solutions solutions solutions solutions solutions solutions solutions solutions curves limit san stage stage determine full full choice choice choice choice choice statistics statistics statistics statistics statistics increase increase condition coding coding coding coding coding randomly criterion criterion criterion criterion types types types types types types types types types types types types types types entropy entropy entropy entropy actual actual actual depends constraint constraint constraint constraint constraint biological biological discussion discussion discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance increases denote denote denote denote limited inverse amount implemented generate require square degree makes development sensory including kaufmann block block interesting ratio ratio projection increasing special principle principle principle principle principle principal squared squared squared squared squared squared details call filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters stored stored early early magnitude choose predict denotes denotes denotes improve correlations correlations correlations correlations resolution resolution property ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble strategy subject subject subject subject subject quadratic interest interest highly previously unsupervised unsupervised unsupervised unsupervised yields yields yields rl diagonal diagonal sparse definition locations modified organization sensitive entire expression expression invariant invariant invariant scaling scaling matrices matrices touretzky setting starting place place greater greater hebbian valued valued depend measures measures retina retina numerical peak weak mateo encoding encoding encoding encoding taking presence presence presence presence presence drawn drawn drawn drawn turn selective averaged averaged suppose suppose suppose suppose relation construct produces produces produces produces longer ways ways plot plot mathematical sensitivity sensitivity linearly involves text text angle unique scales scales mutual mutual mutual mutual mutual adding adding adding frequencies frequencies shift shift shift shift extraction versus independently focus formation depending stages overlap detailed transform transform fraction centered understanding activities activities similarly translation allowed allowed allowed spectrum spectrum earlier earlier calculation smoothing measurements spaces spaces roughly distances kohonen advantages box perceptual priori retinal retinal determines determines plotted plotted plotted maximize maximize maximize maximize maximize maximize absolute absolute partially characterized tests simplicity simplicity efficiency closely delta included presentation invariance tend allowing heuristic issue satisfy satisfy quantity quantity quantity wavelet wavelet highest maximization extract extend law access replaced limitations limitations divergence dotted dotted pursuit fewer fewer reducing reducing fourier fourier fourier fourier fourier mappings mappings analytically relationships maximizing maximizing maximizing encode topographic phases phases phases phases phases phases phases neu patch patch trace equally equally aspect aspect portion multivariate multivariate multivariate utility site site site site site site site scenes pairwise pairwise pairwise theoretic agreement convolution derivation derivation analyzed coded coded coded adjacent caused correction nonlinearity nonlinearity nonlinearity nonlinearity reasons turns rapid snr sites mation cut implicit localized localized localized localized lowest linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker preceding argument requiring tional axes quantitative share share remove span span partitioning partitioning partitioning partitioning summarized limiting differs maximizes maximizes maximizes maximizes coherent conclude age redundancy coherence pyramid pyramid pyramid irrelevant shifted intractable sort lagrange lagrange lagrange modify modify gabor ratios optimizing proceed extending multiplier multiplier multiplier kullback replacing replacing replacing stated stated stated keeping keeping transforms transforms ral salient presentations infor lip weakly loo loo appendix appendix equals equals pat arrangement artifacts ensembles ensembles omitted omitted concentration summarize infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax infomax ence outline sine deriving deriving deriving deriving maximized emerge emerge expanding obtains seek intrator intrator flat breaking breaking breaking continuity constrain avoids principled principled mismatch acting concentrated favor favor ibm distri gained shannon crossover bump bump selectively spanned nonetheless breaks breaks figs cubic cubic det det det parametrized exploited resembles resembles bution moderate differently preserves justified identifies justification justification justification influenced multiresolution envelope sen atick atick atick atick atick sparsely progressively preservation wavelets ooo carries substitution artifact maxi bandpass transpose spie lnp lnp suffice cho cutoff cutoff bumps bumps brackets comprised enter inst mul surprise surprise watson addi tern adv favors favors ripple continuing ansatz ansatz ansatz ansatz heights save superscript superscript perturbative enhancing redlich redlich redlich redlich redlich possesses subsampling subsampling dilation comprises conveys kronecker spans brevity aver standpoint vation ralph illustrative heuristically heuristically reg looo looo discriminated degeneracy degeneracy degeneracy degeneracy favored accomplishes harmonics yorktown tiling tiling ject deriva resistant urn sisj pres tropy rhs imize mizing antisymmetric interrelated signaled definiteness controt mildly expecting defi skipped partitionings pects 
#@Linsker_R,
#t6
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time output system system system system system system system system system error error error error error error error error error error error error error error state results results information information models models performance based space space linear case order shown shown shown shown shown shown shown systems systems values values values values values parameters parameters parameters parameters neurons neurons approach image image image image image image image image processing control local local local local local local local local local local local local rate rate rate rate rate rate rate rate rate rate rate analysis analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small small small small small small cells cells cells cells cells step process level level cell cell cell cell cell similar representation representation show section rule rule rule rule images general parameter parameter parameter parameter parameter parameter parameter parameter parameter theory theory obtained obtained term term term term term term term term note activity result university university research defined defined target dynamics initial constant constant constant constant synaptic node node node node node node node node node node node science left left left left left direction present phase phase nodes nodes object object object object motion motion press position basis basis abstract back computational computational references due due due ieee positive positive adaptive adaptive adaptive adaptive adaptive introduction behavior effect effect recurrent recurrent recurrent change change change difference difference lower lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure signals signals signals signals signals signals signals chosen chosen part part center previous firing firing firing firing firing firing firing firing firing firing firing firing firing multiple cortex good long long long long long long long conditions conditions conditions represent distributed expected expected equations proposed proposed proposed correlation observed observed observed finite simulations simulations simulations simulations simulation simulation means made feedback study filter negative negative negative relative relative represented represented represented compared compared compared desired desired desired desired desired desired desired desired desired desired desired provide provide rates rates eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye constraints gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain motor motor motor motor brain equal equal equal steps steps larger larger morgan report institute institute department version synapses synapses synapses advances represents represents represents responses responses responses responses responses responses final delay addition graph directly curves curves curves san san san san san top top top effects upper significant vision pages increase increase increase increase con velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types provided selected evidence evidence iteration iteration iteration iteration inhibitory depends depends biological biological discussion technical feedforward increases increases increases increases increases increases transformation limited close close predictions short short short assumed synapse supported main main adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation journal journal end hypothesis hypothesis easily kaufmann smaller combination reduced dynamical transfer transfer ratio head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head mechanism consistent leads leads squared bottom bottom early magnitude magnitude magnitude magnitude magnitude choose added ensemble ensemble movement moving moving period period sense sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently previously observations volume smooth smooth smooth smooth smooth achieve trans address modified modified modified modified gate increased increased increased amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude constructed parts lead studied suggests locally move occurs occurs occurs occurs occurs occurs conclusion greater depend editors central interactions interactions differences retina retina retina moody faster constrained mateo mechanisms mechanisms physics cycle cycle california california california turn turn turn turn turn turn movements movements decrease decrease decrease decrease scene program explicit appears longer factors describes laboratory ann dept modeled sensitivity simultaneously slightly scales scales scales equilibrium letters decreases decreases influence influence controlled ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular modulation static static understanding constants allowed sign sign diagram earlier slow delays delays tracking valid calculate foundation classified avoid expect box retinal determines determines variations aspects letter capable society differ modification driven driven driven delta symbols included reached reached soc induced neuroscience neuroscience neuroscience neuroscience contribution physiological physiological categories reach reach reach neurosci subsequent acknowledgments decreasing decreasing remain stimulation carried diego diego diego experience steady association integral pursuit pursuit pursuit pursuit pursuit int plasticity plasticity plasticity possibility affect affect encode math plausible plausible plausible plausible plausible editor predicts opposite opposite rev changed explored nervous fibers fibers fibers fibers fibers fibers fibers fibers fibers extent asymptotically asymptotically vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor publishers analyzed analyzed starts turns turns turns drive drive drive rapid rapid rapid arc sites sites day nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus afferent calculations medical cybernetics cybernetics explained pathways consistency dark dark dark experimentally recordings biologically biologically biologically biologically biologically commands robinson robinson howard gains gains gains gains gains gains gains differs boston fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber fiber decreased physiol physiol traces simultaneous univ physiology proportion proportion proportion animals animals animals animals animals vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular jones jones climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing eliminated anatomical anatomical ranges primate primate stated cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum multiplicative keeping kawato kawato neurobiology shifts monotonically salk integrator effectiveness effectiveness preparation days days fires fires cerebellar cerebellar cerebellar cerebellar cerebellar studying equals equals conjunction monkeys reproduce peterson peterson recovery jolla passing adopted adopted skills multiplying reflex reflex reflex reflex reflex reflex reflex reflex reflex reflex reflex reflex maintaining neurophysiology neurophysiology drop depression depression indirect constitute minus helmholtz email responds solely solely solely stem chapter acceleration resting resting resting pairing adapting trends compensate compensate potentiation neurophysiological hughes terrence lond lond investigating oculomotor oculomotor hansen apparently afferents afferents afferents lippman coming tonic tonic tonic tonic tonic demonstrating served drives replacement reversal stephen vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo viola viola albus albus purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje purkinje jain proportions exposed meeting ventral marr marr neurol carries capital totally vivo lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger lisberger absent fovea ipsilateral correlational altering converts magnification transferred transferred settles primates phil slip slip slip ito ito ito ito ito concurrently rightward suggestion mossy mossy mossy mossy mossy mossy mossy mossy mossy diverges vitro vitro overshoot overshoot overshoot overshoot overshoot overshoot overshoot overshoot overshoot nserc stays concurrent glasses glasses compensatory sakurai sakurai leftward baker baker straints restricts stabilizes phasic phasic gomi gomi corrects miles miles miles miles miles crc interplay organs keck fujita fujita elevated inp premotor arnold arnold contradictory fibre fibre ime biosci magnified wearing wearing moroneurons uts negligibly reconcile diminishing diminishing glutamate olivier olivier vestibuloocular respon 
#@Coenen_O,Lisberger_S,Sejnowski_T,
#t6
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model input input input input input input input input input input input input input input input input data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time networks output output output output output output output output number system system system system system system system system system system system system error error error error error error state results results units units information information information information problem weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case vector order shown shown systems systems systems systems noise noise noise weight weight weight weight weight neurons neurons neurons pattern pattern point point single single control control control control control large large large local rate rate rate inputs inputs form form form shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper examples examples examples examples examples examples small small size size net net methods cells cells field level current current current current cell structure random random random high high response similar similar architecture architecture architecture equation equation equation equation equation section fixed fixed fixed fixed rule rule rule rule rule rule rule rule rule parameter average theory theory theory theory note experiments experiments activity activity activity activity activity activity activity activity activity activity activity result result university variables variables independent independent independent target target target target target target target target target target target target target target initial initial constant constant estimate computer terms connections connections connections connections connections synaptic synaptic synaptic synaptic science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left left direction presented map map map map map map map map present temporal temporal temporal temporal temporal temporal machine sets motion range range learn learn position position position position position position position position position position position position position position position position position position position position position position position position position position position abstract applied convergence references positive important adaptive decision context introduction complex dynamic dynamic dynamic dynamic generated change change change difference difference difference difference assume lower rules measure measure measure measure signals signals signals signals signals signals signals signals signals signals signals signals prior representations learned higher center center previous firing firing firing firing required required required multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex represent represent distributed expected expected make make region region region region region region region correct observed minimum resulting resulting classes ing ing sum called called times times times elements regions mapping mapping mapping mapping mapping mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made natural feedback relative relative relative specific receptive receptive provide provide provide objects active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye related gain gain gain gain motor motor cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain brain brain brain brain brain brain larger larger contrast contrast contrast connection fields fields dependent dependent dependent source source modeling selection proceedings report institute internal internal code individual represents responses responses responses responses bias layers layers layers layers layers layers layers layers layers layers scheme maps maps framework framework framework framework framework framework framework framework framework framework top top conference determine upper upper requires requires significant approximate approximate world world increase give condition coding derived randomly randomly conditional conditional developed area area area path actual actual selected selected selected nature nature biological biological biological achieved achieved technical transformation excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory predictions predictions predictions predictions predictions predictions predictions predictions common effective role role journal pixel future future future future future future future future future future future future future future future future degree degree makes makes makes development development development development development development development development development development development development development development sensory sensory sensory sensory including including auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory pairs pairs combination account account account fully programming projection increasing increasing head head head head head mechanism mechanism mechanism structures structures structures structures structures principle representing filters pre pre making making making window normalized frame combined sources sources predict predict predict predict recent correlations correlations correlations separate separate movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement pixels subset sejnowski sejnowski sejnowski sejnowski sejnowski array array cognitive highly varying varying unsupervised approximately tions rl rl rl rl rl sparse positions organization organization organization organization organization organization organization sensitive amplitude occur occur occur occur suggests suggests predicted predicted correctly correctly correctly move move occurs occurs setting place assumptions hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian reward reward reward reward reward reward reward reward reward reward differences differences measures accurate retina sutton sutton sutton sutton sutton sutton weak learns learns suggest propose presence largest external external external external external labeled start exist movements movements movements movements movements decrease decrease targets targets manner manner connectivity connectivity question areas areas reference appears sequential describes changing changing coordinates linearly text scales develop develop develop equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium events events events events events predictive shift shift expectation cycles cycles cycles cycles independently expressed review correlated correlated viewed interpretation influence influence influence influence codes detailed controlled controlled controlled organizing modulation centered centered centered centered centered static static static activities barto barto barto barto barto barto classical classical classical event roughly remains intermediate initially initially initially initially initially initially box combinations combinations combinations combinations coordinate usa color retinal retinal retinal retinal absolute major middle middle middle closely capable society modification effectively effectively driven driven driven driven driven successful successful post projections projections receives kind link superior superior superior superior built involved dayan dayan dayan dayan dayan absence absence surround providing leading automatically moves illustrates illustrates illustrates decreasing presents body employed explore unlike stimulation command command access experience experience experience experience varied existence postsynaptic scalar scalar scalar scalar scalar respond behavioral mappings mappings mappings mappings plasticity muscle muscle muscle muscle relationships working working working working pathway pathway pathway statistically predicting predicts illustrate illustrate illustrate illustrate assumes assumes separated extent simplest utility defines slowly slowly directed directed directed directed explanation nowlan nowlan nowlan nowlan nowlan answer lies reasons drive drive drive drive drive drive drive drive drive drive drive drive sys incorporate ran nucleus nucleus nucleus nucleus nucleus immediately monkey watkins separately implicit begin begin begin axons read arises demonstrates annual fluctuations alignment requiring reflects pathways pathways dark passed incorporated incorrect incorrect psychological rewards commands commands maintain modulated modulated modulated reaches qualitatively qualitatively singer singer sums kinds display findings conditioning conditioning conditioning conditioning conditioning specifies extreme extreme cor globally feasible primarily tation extensive appropriately controlling repre tem arrival eliminated primate primate balance balance balance balance occurring salk north salient guide selects muscles muscles muscles muscles muscles muscles ensures sion moved lengths accounts accounts parietal parietal parietal parietal parietal parietal parietal parietal axonal suggesting suggesting suggesting jolla colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus informative projects projects projects projects implicitly convergent balanced balanced balanced balanced ence neurophysiology incorporates helmholtz sig super utilize causing amherst imagine scenario representa acting segregation permits bounding relates pos nuclei nuclei nuclei nuclei nuclei nuclei nuclei nuclei mask selectively covered oculomotor oculomotor maintains happen permit permit experi continually topography develops develops demonstrating circumstances persistent drives drives drives externally crude synthesized pouget pouget pouget pouget pouget calibration diffuse diffuse diffuse diffuse diffuse diffuse developmental tors adult adult adult played cast sensorimotor sensorimotor rare seattle proposes judged modalities comprising vertebrate vertebrate vertebrate vertebrate fastest predictable dopamine dopamine multimodal delivery delivery delivery delivery delivery delivery delivery delivery enforces modern fovea fovea fovea bear bear sentation facts modulatory modulatory inappropriate motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons acetylcholine acetylcholine correlational instant plastic rein rein broadcast align thalamus anticipate ninth supervision picks stabilized basal basal foveal foveal foveal unequal brains quadrants passage salience stretch stretch motoneuron motoneuron motoneuron motoneuron motoneuron motoneuron visualized delivered delivered delivered delivered delivered delivered recep organize contingencies contingencies contingencies contingencies contingencies contingencies contingencies contingencies relied proprioceptive aperiodic aperiodic aperiodic aperiodic deliver deliver deliver deliver ordinates foveation foveation foveation foveation foveation foveation foveation foveation foveation foveation foveation foveation foveation foveation mediating comparatively reactions forcement forcement vised topographically topographically montague montague montague montague montague originate originate tex neuromodulators nals torrey pines antagonistic antagonistic antagonistic innervate innervate delivers delivers midbrain midbrain instrumental slows slows acquires unbalanced unbalanced unbalanced unbalanced sparks sparks calibrated calibrated neuromodulatory neuromodulatory neuromodulatory mas subcortical subcortical subcortical subcortical subcortical jay jay hinges reporting tensions serotonin dictions contingent contingent cnl calibrate calibrate awt bal malized sachusetts schultz shut expec cjch neuromodulator neuromodulator neuromodulator conveying disrupt grab excursions norepinephrine foveate foveate territory staged concomitantly tration uti mak 
#@Dayan_P,Montague_P,Nowlan_S,Pouget_A,Sejnowski_T,
#t6
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#*network network network network network network network network network network network network model model model model model model model model model model model model model model model model neural input input data data data data data data data data function function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time networks networks networks networks algorithm algorithm number system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state results results results information information models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden case case case vector vector order systems probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit distribution distribution distribution recognition method method approach approach approach point point point point point single single single single single single single single single single processing processing large large local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns analysis analysis analysis matrix matrix shows simple simple simple simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual feature feature methods fig fig fig fig fig fig step features process process process level level level level structure structure structure structure high memory representation show show show equation section section fixed fixed fixed fixed line general speech parameter average states states states states states states states states states states states states theory note experiments experiments activity activity activity activity activity activity result threshold threshold threshold threshold dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant constant terms terms synaptic presented present present phase phase phase phase phase phase phase phase phase activation frequency temporal object maximum maximum components components basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract abstract back find find find find find density density density density density properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee procedure introduction action hand hand hand hand stimulus stimulus stimulus stimulus statistical tion tion tion change spatial assume signals signals signals chosen part firing firing firing firing firing firing firing firing firing type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike conditions represent markov markov markov make correlation correlation correlation probabilities probabilities probabilities probabilities observed observed observed observed observed observed observed observed multi multi multi multi multi elements elements means means means means potential global applications em obtain obtain relative specific represented true compared compared application application define proc experimental experimental experimental experimental experimental experimental connected cortical cortical cortical brain approaches approaches approaches approaches approaches larger train dependent morgan proceedings report institute synapses internal internal internal internal individual individual represents represents represents responses responses responses responses responses responses responses responses framework directly directly directly directly directly directly transition limit limit limit limit san effects full choice estimated estimated estimated give finally selected nature measured measured describe describe corresponds corresponds corresponds corresponds corresponds proof amount common shape shape synapse theoretical theoretical main eds easily easily easily including underlying underlying underlying underlying underlying underlying reduced reduced dynamical dynamical functional jordan increasing mechanism mechanism consistent consistent details details call max description description description description description description neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal denotes element typical typical lateral lateral introduced include period period relevant calculated calculated calculated calculated calculated observation interval interval lead predicted assumptions interactions sigmoid designed peak moody strong external external external external external external external cycle cycle cycle cycle characteristics demonstrated start manner scene program relation relation relation relation derive derive derive ways describes distinct interaction interaction interaction interaction interaction adding extracted extracted independently dependence depending depending influence detailed detailed transform evaluate fraction fraction fraction showed evolution activities activities activities activities activities completely completely earlier reasonable measurements measurements event event purpose remains remains valid koch coupling coupling coupling expect fire fire fire fire fire includes combinations formulation inter inter inter coupled regular aspects aspects differ spiking spiking spiking spiking spiking spiking oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory attractors projections projections characteristic capture excitation excitation excitation excitation excitation summary soc kind repeated contribution contribution oscillations oscillations follow gray gray gray gray receptor bar binding cat cat cat cat cat cat cat cat cat cat cat cat neurosci preferred trains trains trains trains stimulation exhibit exhibit exhibit exhibit detail hanson accurately lippmann behaviour existence successive rest biol biol oscillation oscillation oscillation func understand phases phases phases phases measurement transmission analyze ensure bifurcation bifurcation formal formal formal formal observe observe switching switching switching switching switching switching switching switching switching switching switching switching switching switching switching consist contributions contributions contributions contributions regime submitted submitted explain explain motivated isolated integrate years burst burst burst burst burst burst burst burst burst burst burst burst burst histogram band agreement phenomena phenomena phenomena baum baum turns strictly broad incorporate monkey fluctuations fluctuations reflects reflects reflect reflect reflect reflect experimentally experimentally quantitative quantitative passed switch switch switch exhibits exhibits synthesis characterize characterize characterize collective collective pasadena singer singer singer coherent coherent inherent synchronization synchronization phenomenon equivalence refractory refractory narrow purely caltech numerically accepted striate synchronous synchronous synchronous adequate preparation exceeds excellent reset falls periods irregular irregular irregular irregular corre sides uni assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly assembly nonlinearities reproduce reproduce treatment francisco bursts reveals master considerations considerations captures captures explains discovered switches robert incorporates alternating emerge revealed tween welch welch convenience par chaos ical ical malsburg electrode illustration cns cns cns mutually evolve evolve biophysical alternate interact ization concentrate electrodes complementary complementary assemblies assemblies apparently apparently locking investigations microscopic mann triggered remark correlogram syn syn observables bility bility institut autocorrelation autocorrelation stochastically solvable exper suffices episodes episodes peaked nmda emerges emerges coincide resolved hopf hopf quantitatively contrary predictable planck falling evolves permanent iterating bauer bauer bauer bauer bauer bauer bauer bauer bauer bauer bauer physica brought talk linking expresses relax schuster schuster schuster tutorial columnar ansatz ansatz ansatz miss fiir icann klaus bistable bistable accessible reproduces bind ago heidelberg confirms eckhorn abstr excitability excitability excitability excitability excitability excitability excitability excitability excitability excitability excitability excitability excitability poo distinguishes dynam lations physik ticular engel engel pawelzik pawelzik pawelzik pawelzik pawelzik pawelzik pawelzik pawelzik pawelzik pawelzik sketched quantifies chemistry governs modulations namics frg stochasticity initializations transi coexistence dominating cyb cyb subpopulation subpopulation subpopulation subpopulation subpopulation chronous kruse ksnig ksnig ksnig ksnig theoretische thalamocortical neglects str phenomenological phenomenological phenomenological grams coexist brosch tat schillen schillen creased munk imental paral lel interchange interchange renewal renewal discretizing brighton destroy sfb backed lax corticocortical gsttingen tivities 
#@Bauer_H,Deppisch_J,Geisel_T,Pawelzik_K,
#t6
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#*network learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input data function function function function function function figure figure figure figure figure figure figure figure figure figure figure time set networks training algorithm output output number system system system system system system results results results results results results units units units units units units units units units units units units units units units information problem models models models models models models based weights weights weights weights weights weights linear layer case case case case order shown shown shown systems systems probability weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit pattern pattern pattern pattern pattern pattern point point processing processing large test test patterns patterns patterns patterns patterns patterns analysis inputs inputs form form form form form shows simple gaussian gaussian gaussian visual visual visual paper small small size size net net net work work cells cells cells cells cells step points points field field features level structure random random random memory similar similar similar representation architecture show fixed rule rule rule general average average gradient note note note experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional university university found found target constant constant constant standard standard terms distance distance distance connections connections synaptic science science science science left left left left left left left left direction presented presented presented presented presented presented map map map map map map map map present present frequency range position position position basis continuous abstract back back computational references positive positive positive positive positive positive positive important important important introduction action effect effect effect effect effect effect generated generated tion variable spatial assume rules center previous previous previous previous previous type type required cortex cortex cortex cortex cortex cortex cortex cortex cortex represent represent represent distributed distributed distributed distributed region proposed correlation correlation correlation correlation correlation correlation minimum total total total simulation simulation sum sum natural natural natural orientation obtain negative artificial specific specific represented represented represented represented represented application application series receptive receptive receptive receptive receptive proc proc proc eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined experimental experimental connected connected cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain brain power larger connection fields fields fields descent version consists advances joint represents exp bias layers addition addition addition maps maps maps maps additional additional effects conference con lines finally evidence inhibitory constraint biological biological associative achieved discussion normal increases complete finding finding amount short assumed theoretical theoretical theoretical theoretical require journal square square pixel instance instance instance instance degree degree degree degree degree development development development development development development development development objective account account functional interesting increasing mechanism mechanism structures leads representing iterations pre inhibition international bottom bottom bottom bottom attention produced description light correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations takes typical typical similarity lateral lateral lateral introduced identical cognitive recently interest varying smooth studies studies trans positions positions positions positions grid grid grid grid organization organization expression lead lead studied occur suggests deviation deviation locally width width width width width white white white occurs occurs occurs occurs column setting strength strength place place assumptions assumptions competitive central interactions retina retina retina retina retina retina retina retina retina retina retina clear clear mechanisms mechanisms mechanisms mechanisms largest drawn turn exist decrease decrease relationship iii averaged averaged manner connectivity question acknowledgements appears produces factors ann mathematical modeled explicitly simultaneously interaction interaction develop develop develop springer formed potentials competition decreases formation formation formation formation formation formation formation formation dependence stages correlated correlated correlated correlated correlated correlated correlated correlated transform ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular activities activities activities suggested spectrum key earlier earlier earlier normalization reduces boundaries boundaries boundaries initially euclidean kohonen david david existing box thesis dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance retinal retinal retinal retinal retinal retinal retinal domains black black black simplicity aspects projections tend tend miller essentially capture excitation refer soc soc soc soc strongly strongly strongly induced showing showing showing contribution follow vary dot surround wave cat cat cat neurosci neurosci received principles deal receive modelling modelling cowan law strengths replaced mass behaviour helpful postsynaptic postsynaptic postsynaptic fourier mappings mappings mappings investigated investigated applicable biol lgn lgn complicated topographic topographic topographic topographic examined induction rev eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes aspect aspect friedman der der der der precise nervous hebb extent extent simplest motivated phd established established great ment ment ment developing growth convolution phenomena phenomena fairly majority ganglion sys producing day nucleus monkey arise axon gradually res localized addressed summation experimentally experimentally marked formulated formulated variant price berlin mod ture gen ordered ordered comments eventually eventually specifies specifies specifies cor picture discontinuities discontinuities uncorrelated cybern primarily optimality investigation pick perfectly circular discovery repre addresses tem grey grey arranged spontaneous binocular binocular binocular stronger stronger striate bands imply synchronous guide arrays corner corner corner von von von von dominant dominant dominant dominant dominant dominant accounts belongs counting elastic elastic elastic waves bursts reveals environmental roy proximity extensively projects dividing assigning unchanged appeared neurophysiology outline fellowship wiesel wiesel opposed encodes alternating july willshaw willshaw willshaw willshaw willshaw terminals centre centre malsburg malsburg malsburg malsburg hubel hubel edinburgh edinburgh monocular cns trends concentrated segregation segregation segregation segregation segregation segregation geoffrey mammalian maintained ization relating individually argued macaque lond lond lond rough indexed indexed sheet sheet sheet refinement register sweeping funded accounted geniculate els struc worked topography topography topography topography topography topography topography topography topography topography topography topography topography topography topography topography topography topography develops firstly smoother exper termination stripes stripes stripes stripes stripes stripes stripes stripes stripes stripes stripes stripes eral dom calculates periodicity seattle subtracting lying convolved edition sheets doubling wong tical artificially sented correlational goodhill goodhill goodhill goodhill goodhill goodhill goodhill goodhill refine frog tectal severely stryker marker aims phil enforced enforced advice manipulations nections patterned convolving confirms divisive positively positively positively stripe stripe stripe stripe stripe stripe stripe stripe stripe stripe lose birth blurring neighbouring neighbouring neighbouring neighbouring neighbouring anatomically weeks narrower narrower narrower opening opening opening progression ocularity ocularity ocularity keller raise regeneration folded shed establishment draft postdoctoral graphic minimisation meister retinotectal retinotectal innate fibres fibres fibres implausible harry scotland laid sussex erence barrow retino innervated folds nance serc satisfactorily topo baylor imental colour postnatal domi studentship fuller reared frogs inance postgraduate doubles 
#@Goodhill_G,
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#*network model model model model model model model model model model neural neural neural neural neural data data data data data data data data data data data data data function time time time time time time time time time time time time time time time time time time time set networks number number system system system system system system system system system system system system system system system system system system results results results results information information information information information information models models models models models models based based based based based based based linear order shown shown shown shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution point point point single single single single processing processing large large neuron neuron neuron neuron neuron rate rate optimal shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple simple simple simple simple simple gaussian visual paper examples small small feature feature work work work methods fig fig fig fig fig fig fig fig cells cells cells cells points process cell problems random random random high high high response response similar similar show show show fixed fixed fixed parameter parameter theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained note note experiments experiments experiments experiments activity university university university threshold solution research defined defined defined defined found sequence dynamics dynamics dynamics constant constant constant constant standard standard terms connections left left presented present low low low frequency frequency frequency frequency temporal motion maximum maximum range range press press press components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied density analog analog analog analog analog analog analog analog properties references component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due introduction action action complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical statistical statistical generated tion energy difference variable variable variable variable variable variable variable variable lower lower chosen cases firing firing firing firing firing firing firing firing firing firing type type required good spike spike spike represent correlation correlation correlation observed forward simulations simulations simulations simulations simulations simulations ing simulation simulation human eq eq called times times means potential potential potential potential potential potential made made study knowledge specific represented represented compared objects rates rates determined experimental brain brain equal power power power power power power power power voltage voltage voltage larger larger larger contrast morgan proceedings proceedings proceedings department department department implementation internal internal code individual advances exp sequences sequences cambridge experiment experiment directly transition transition limit limit san stimuli stimuli effects upper upper significant significant vision vision con condition actual provided provided finally processes evidence nature depends simply biological biological measured measured measured measured measured measured discussion increases fast fast fast fast circuits supported role ability ability easily easily noisy noisy sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory including fit fit kaufmann auditory typically typically smaller dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical interesting ratio ratio details call magnitude magnitude added added added membrane recent recent robust typical similarity period period period period sense recently recently recently compare previously studies background background background interval interval interval grant amplitude amplitude constructed intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity studied studied studied studied occur occur occur spikes spikes spikes touretzky deterministic deterministic white white occurs boundary pass demonstrate strength critical editors editors measures clear peak peak peak peak moody weak weak weak weak weak mateo suggest integration presence physics physics physics physics external external demonstrated demonstrated demonstrated turn variety relationship manner base question question question acknowledgements pro van sensitivity physical electrical equilibrium events events versus cycles john decreases review depending interpretation interpretation interpretation interpretation detailed transform densities controlled fraction approximated suggested constants constants past spectrum spectrum spectrum spectrum spectrum spectrum spectrum diagram slow slow measurements measurements intervals intervals event event event koch koch figures inter retinal determines discuss phys phys phys phys identified identified driven driven detect detect essentially essentially essentially induced induced prob showing sin sin oscillations physiological physiological physiological built quantity sampled usual play chips consisted trains collection investigate varied accurately periodic periodic periodic behavioral possibility possibility office analogous matched naturally transmission integer rev rev subsets bifurcation bifurcation bifurcation der panel panel panel panel separated separated nerve regime motivated electronic analyzed biology biology biology ganglion ganglion comparisons comparisons snr snr snr snr snr snr snr snr snr sys strictly broad monkey pulses res res res demonstrates fluctuations mechanics behaviors embedded orders recordings adjustable frequently sharp rep maxima schematic execution operate exhibits measuring modulated gen gen maximizes occurrence simulator simulator simulator simulator simulator simulator simulator simulator simulator simulator simulator coherent coherent coherence phenomenon spectra spectra ear physiology amplifier refractory refractory refractory refractory naval multipliers spontaneous spontaneous minutes adjusting stated familiar familiar height interpret occurring integrator integrator integrator preparation clock clock enhanced hours passive analyses reset periods decide pat moved enhance demonstration histograms searching reproduce tic recovery recovery bursts stimulated stimulated stimulated stimulated stimulated stimulated stimulated stimulated stimulated sustained canada canada motions relies reverse reverse lett discovered mechanical accumulated resonance resonance resonance resonance resonance resonance resonance schulten schulten hair hair hair piece ent ber ties randomized transmitted spatio perturbed par quasi quasi weiss alter neurophysiological neurophysiological neurophysiological douglas douglas careful ambiguous worth oscillating oscillating barrier barrier barlow barlow barlow barlow accounted particle siam mimic applicability lippman travel psychophysics lems demonstrating transducer transduction photoreceptors terns terns designs lated caudal inherently fre fre cally moss moss moss moss moss moss moss moss moss moss moss moss moss moss moss moss moss exposed subtracting operational edited edited edited ooo ooo ooo modalities ultimate raises digitized sity reproduced periodically periodically periodically periodically periodically periodically periodically periodically electrophysiological reviewed transmit shop tens col frog stat stat phy heights extracellular quency excitable excitable excitable excitable excitable excitable forthcoming forthcoming ontario bistable bistable bistable bistable bistable bistable bistable bistable bistable bistable bistable bistable bistable ages lacking nserc webb webb frank emphasizing multiples nato nato correla colored raise cot bernander bernander bundle masked living living pol hear ottawa ottawa wells trast efferent electrophysiology assisted correlating resented quently stimu kaplan kaplan kaplan kaplan fitzhugh fitzhugh fitzhugh fitzhugh ice preparations electromagnetic satisfactorily louis louis simulators dynami tac incoherent dimensionless renewal ois characteris chem residing inten mimicked riding sinusoidally transduced vols excit tronic excursion 
#@Douglass_J,Longtin_A,Moss_F,
#t6
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#*network network network network network network network network network network network network network network network network network network network network learning learning model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks state state state state state results results information shown values values probability probability probability probability parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit distribution approach pattern point point point point point single local neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns form visual examples small methods cells step step classification random memory response show fixed fixed images average states theory obtained activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university university university university threshold threshold research research found target target target target target target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial computer computer computer computer computer distance distance distance distance connections connections connections connections science low temporal temporal range range press press nonlinear abstract convergence properties properties references propagation propagation propagation introduction introduction complex complex complex hand hand generated generated tion spatial spatial spatial cases cases firing firing firing multiple multiple cortex conditions conditions conditions conditions conditions represent region region simulations simulations simulations simulations simulations simulations minimum simulation performed times elements potential potential made study study artificial artificial relative relative represented series active determined related related connected connected connected connected connected connected brain steps support source source source source source source source source source source nets department department department code difficult exp layers efficient free increase randomly randomly provided provided provided iteration discussion increases increases increases corresponds corresponds excitatory stable stable stable assumed role eds square makes including including typically functional york uniform uniform uniform details magnitude decay produced neuronal membrane membrane membrane typical reported period period period sufficient previously previously previously observations observations observations correspond trans interval organization organization increased amplitude amplitude amplitude constructed constructed studied studied occur occur occur occur white occurs occurs occurs boundary critical critical critical critical central central central central interactions clear exponential suggest suggest demonstrated assuming variety decrease connectivity connectivity connectivity connectivity connectivity connectivity appears appears plot stability text formed formed formed formed potentials john decreases decreases national formation formation formation formation formation formation fraction fraction fraction fraction evolution modulation constants constants slow generation generation initially initially sufficiently foundation eeg euclidean fire fire fire fire fire fire fire figures figures figures figures color activated black absolute partially discussions major regular capable suitable suitable tend composed excitation excitation soc sin criteria gray comp play wave wave wave wave wave wave wave wave principles decreasing cowan cowan cowan cowan stimulation stimulation stimulation stimulation exponentially replaced replaced replaced issues mass periodic periodic periodic periodic rest rest rest rest authors office examined math transmission onset onset illustrate ensure front bifurcation bifurcation bifurcation epoch established integrate integrate integrate integrate integrate integrate years slowly unstable phenomena phenomena phenomena glass spatially arc closer organized located ran ran arise arise arise pulses mathematics consequence res arises arises sun fluctuations fluctuations fluctuations populations transient simulate readily readily lattice cohen continuously perturbations spread spread asymmetric coherent begins begins eventually eventually representative appearance princeton princeton refractory refractory refractory refractory refractory naval turned arranged spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral smith ments significance occurred occurred occurred financial ranging irregular washington realization recovery recovery waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves waves roy acknowledge acknowledge spirals spirals spirals maintaining break break spatio spatio spatio propagating chicago chicago chicago chicago chicago imagine conduction evolve gener maintained maintained emphasize spreading lond pos breaks tively exchange ation differing unpublished unpublished continued tip tip tip resolved clark clark clark clark hopf hopf hopf governing inspection presently periodically remained elec media media media monitored health propagates propagates propagates dispersion initiated initiated jack tightly tightly sparc entering generations plotting phil excitable excitable excitable undergoes leaky quiescent quiescent quiescent ago neurology respec differed spontaneously thirty cardiac arms regularly travelling identifiable preceded slowing gle investigators disordered inhomogeneous inhomogeneous ermentrout kin irl milton milton milton milton transmits suddenly centrally centrally centrally centrally chu chu chu chu institutes kaplan kaplan kaplan distinguishable pergamon domly abruptly biosci conceivably shut hinder drs biotaed dispersed ronal forma 
#@Chu_P,Cowan_J,Milton_J,
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#*network network network network network network network network network network network network network learning learning model model model model model neural neural neural neural neural neural input input input input input input input input input data function function figure figure time time time time set set networks networks networks networks networks networks networks training training training output output output number number number number number number number number number number number number number system system system system system system system system system system system system system results information information information information information models models based based weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case vector order order order order shown shown shown shown systems values values parameters parameters parameters parameters parameters weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution method method pattern pattern pattern pattern pattern pattern point processing processing large large large neuron neuron neuron neuron patterns analysis analysis class inputs inputs shows gaussian visual visual visual visual visual visual paper paper paper small size feature feature feature feature feature feature feature feature feature feature feature feature feature work work work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells classification classification level trained cell cell cell cell cell cell cell cell cell cell cell cell structure problems random random random response similar representation architecture architecture architecture equation equation equation equation equation equation equation equation equation equation line line rule rule general parameter parameter approximation approximation average average average average average average average average average theory obtained term experiments activity activity activity activity dimensional dimensional result university university computation research defined found found found target constant constant connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic low low sets maximum range range range outputs abstract find density density properties references due due important important important adaptive context introduction action statistical effect effect effect parallel change difference spatial spatial spatial assume assume lower lower lower lower lower rules rules chosen chosen chosen higher center center center center center center center center center center previous bound bound type required required required cortex cortex cortex cortex cortex cortex good binary equations region region region correlation correlation forward simulations simulations simulations total total simulation respect respect multi times times regions regions means means means made made made made made orientation orientation applications study obtain obtain negative original original artificial receptive provide experimental cortical brain brain equal equal equal larger fields train dependent proceedings proceedings proceedings synapses individual represents difficult exp layers layers layers layers layers layers layers layers layers addition graph ai ai ai ai maps directly curve curve limit effects effects effects upper choice vision basic basic basic give produce condition coding weighted developed area types types finally nature nature inhibitory depends depends biological biological biological biological biological biological biological increases arbitrary denote close assumption assumption assumption corresponds excitatory amount short short assumed assumed synapse synapse synapse theoretical theoretical theoretical require journal journal easily development development development development development development development development development development development development development development development development development sensory sensory sensory sensory sensory sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory smaller smaller smaller reduced functional unknown ratio ratio edge special uniform mode mode pre pre pre pre pre pre pre pre pre pre pre inhibition idea idea attention produced produced light perceptron correlations ensemble ensemble takes takes movement lateral moving period subject array recently sufficient sufficient sufficient approximately approximately approximately approximately calculated tuning axis yields sensitive sensitive sensitive sensitive sensitive sensitive sensitive constructed expression expression expression occur feed move width half conclusion starting starting place place assumptions hebbian hebbian hebbian weak constrained constrained constrained presence external assuming selective plane plane decrease averaged connectivity connectivity connectivity reference written longer longer index interaction interaction develop develop develop develop develop develop develop potentials yield national national national expressed formation formation formation formation formation formation influence controlled understanding earlier reasonable calculation add boundaries sufficiently david box box figures priori usa usa usa eigenvalues batch sciences sciences sciences domains holds holds columns aspects aspects divided divided divided presentation genetic genetic mackay mackay mackay mackay mackay miller miller miller miller miller excitation refer refer kind lie follow realistic realistic realistic surround nips nips cat cat principles principles principles attempt subsequent subsequent deal deal deal simpler carried create detail behaviour existence giving detectors detectors detectors detectors authors variability understand fundamental examined examined extremely ensure der detector mixed mixed regime established established years great great developing growth growth diffusion considerable considerable spatially sections closer choices nucleus nucleus nucleus nucleus potentially axon axon axon scientific universal grossberg grossberg grossberg grossberg linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker cybernetics cybernetics cybernetics radius radius addressed summation summation varies varies considerably limits limits pathways pathways pathways detecting biologically biologically ture aim reaches sums conclude decreased tolerance tolerance findings begins cochlea cochlea cochlea cochlea cochlea physiology physiology cooper cooper acts unity theories binocular ranges fan fan stated chemical keeping presentations presentations presentations presentations presentations presentations reliably governed von claim artifacts emergence environmental environmental extends extensively designing ics boxes schulten hair hair wiesel wiesel reaction terminals pointed centre connec arbor arbor malsburg hubel hubel england england examining rectangular fir regimes regimes academy academy academy million million dorsal fea obermayer obermayer compu ritter expense agrees agrees hearing firstly aid aid opponent tanaka morphology december concrete continuum core centres gence gence subscript schmidt brackets approached derives eigenfunctions amer tivity cats plausibility organisation examines superscript apparatus apparatus intel paid thirty analysed sual birth pared mature mature tational mammals mammals mammals mammals concentrates ocularity ocularity coarser indexes morphological morphological fundamentals proximate questionable insignificant retinotopy manipulate kom organising organising intercept intercept quoted deemed recoding mensional unsuitable extendable utilised morphologies maturation maturation maturation emer emer hem ican normalise infers adhering lue 
#@Bisset_D,Walton_L,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input figure figure figure figure figure figure figure time time set networks output output output output output output output number number number number system system system system error error error results results units units units units units units units units units units units units units units units units units based based weights weights weights weights linear layer layer layer layer order shown shown shown values weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit pattern pattern pattern control control control control control control control control control control control control control control control neuron rate shows signal signal signal gaussian visual paper paper paper work work cells cells cells cells cells cells cells cells cells cells cells cells cells field process level current cell cell cell cell memory response architecture architecture architecture architecture equation section activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university computation computation research research found found found target target target initial computer connections science science science left left direction presented map map map map map map map map map map map activation temporal position position position position position position position components components components abstract back back back back computational references due important introduction action action behavior dynamic dynamic recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference signals signals signals signals signals part part part part part center center center firing firing firing required represent represent represent represent represent represent represent equations proposed proposed proposed correct simulations simulations simulations resulting simulation computed computed sum performed called called means made feedback feedback receptive provide rates rates location active active active active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye experimental experimental experimental related related constraints motor motor motor motor motor motor motor motor motor motor motor motor motor motor accuracy larger connection fields modeling department department version internal code represents represents represents represents represents represents represents experiment top top free vision vision produce produce produce produce coding coding derived area area area area area area area area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity actual selected nature increases increases describe transformation supported role role role eds eds journal journal journal square square square end end ability ability ability pairs account dynamical ratio head head mechanism mechanism mechanism mechanism bottom bottom bottom combined description population population directions pair pair pair movement movement movement movement movement movement movement movement movement lateral lateral moving identical array array array array array array array array array array array array array array array engineering observations observations observations observations axis axis correspond studies differential positions organization grant arm horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal concept extended spikes white demonstrate demonstrate assumptions trajectories trajectories conclusions performs mechanisms demonstrated assuming movements movements movements movements movements movements movements movements movements movements movements movements movements plane relationship connectivity connectivity connectivity configuration acknowledgements van produces produces produces describes vertical vertical vertical vertical vertical vertical vertical vertical vertical implement averaging electrical angle angle equilibrium shift shift shift versus letters decreases national expressed detailed ocular ocular ocular ocular ocular ocular showed lee lee centered generation generation generation generation generation intermediate intermediate intermediate msec foundation activated activated specifically black gating gating gating gating straightforward selecting society driven tend neuroscience neuroscience neuroscience superior superior superior superior superior superior superior superior superior physiological physiological hold hold built relaxation cat automatically moves moves presents presents stimulation stimulation stimulation stimulation stimulation stimulation carried carried carried exhibit circuitry circuitry exponentially issues fashion fashion rest project project project analytically topographic topographic concepts opposite opposite eyes eyes eyes assumes logistic nervous academic contributions submitted submitted submitted submitted plant plant burst burst burst burst burst burst burst burst burst burst burst burst site site site site ground publishers starts starts sites organized monkey monkey consequence angles author varies profile dark dark conducted fed fed quantitative continuously biologically commands maintain robinson robinson robinson robinson robinson robinson robinson robinson execution reaches qualitatively curvature phenomenon shifted physiology physiology saccadic saccadic saccadic saccadic angular velocities velocities outcome outcome arranged plays inspired inspired anatomical grow splitting shifts shifts shifts integrator integrator responsible muscles started reset reset ensures studying arrangement arrangement arrangement arrangement reproduce reproduce reproduce express stimulated gaze gaze gaze gaze saccade saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades saccades colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus sustained motions sons projects exploiting sequentially neurophysiology neurophysiology neurophysiology specification kluwer graded graded spatio copy decomposed freund chicago chicago evoked spinal trends shifting maintained fixation fixation fixation fixation fixation fixation fixation fixation fixation fixation fixation oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor nil differentiating coordination copies copies copies send calibration contralateral caudal sensorimotor physiologically push push push push goldberg periphery curved bcs colors electrophysiological handbook brainstem brainstem brainstem brainstem brainstem translates devoted devoted devoted medial pull pull pull pull upward orbit orbit orbit sends rostral rostral rostral reactive visuomotor avenue imposing rightward army army spontaneously unequal vectorial brooks brings brings anatomically abstracts wurtz wurtz antagonist antagonist leftward downward topographically topographically viscosity stiffness agonist stimulations alert innervate oblique oblique oblique discharges efferent efferent efferent efferent sparks sparks integrators integrators integrators northwestern saccarles saccarles curvatures cynader cynader gisbergen shut orienting brighter 
#@Massone_L,
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#*network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input input data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set algorithm output number number number number number number number number system system system system system system system state results results results results results results results results results information based based based space space weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case order order order order order order order systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single single single single single single processing processing processing local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis inputs shows shows shows shows signal signal signal signal simple simple simple simple simple simple simple simple gaussian paper paper paper small work classification trained cell structure random random random response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar architecture architecture architecture architecture show show show show show show equation equation fixed fixed rule parameter parameter parameter average average average average average average obtained obtained obtained obtained university threshold threshold threshold threshold threshold threshold threshold threshold variables computation research constant constant constant connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic presented present present present low low low low low low low frequency frequency frequency frequency frequency frequency frequency temporal temporal maximum maximum range press components components components components components components components components basis continuous abstract computational properties references component component component component component component component introduction action action behavior behavior stimulus stimulus stimulus stimulus statistical statistical statistical effect effect effect generated variance search assume classifier classifier lower signals chosen chosen higher part cases cases firing type type type long make make make make make proposed correct observed observed simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations classes classes classes simulation simulation simulation simulation computed computed called called means potential potential potential potential potential potential made made made made natural feedback feedback feedback orientation vol specific compared compared define define perform determined constraints distributions distributions distributions brain brain equal equal approaches comparison comparison synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists code code code individual represents responses responses responses responses responses responses responses responses responses responses responses responses layers layers layers layers layers delay delay delay curves curves curves transition limit stimuli stimuli upper full condition coding coding coding coding coding coding derived types types types types types lines inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends biological biological biological biological biological biological biological biological feedforward describe transformation assumption assumption assumption excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory predictions amount amount synapse synapse synapse synapse supported supported main main future development sensory probabilistic probabilistic account ratio projection projection projection projection uniform uniform direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition decay sources predict predict membrane membrane membrane membrane membrane membrane membrane membrane typical typical typical relevant compare differential differential bounded interval organization sensitive grant grant amplitude occur occur runs conclusion row row row assumptions assumptions reduce central central central central designed designed suggest propose presence demonstrated variety exist selective selective selective selective iii iii iii iii averaged connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity acknowledgements reference suppose pro longer longer ways describes modeled modeled electrical predictive expectation expectation potentials john john review detailed approximations approximations approximations evolution understanding similarly constants allowed discrimination discrimination delays delays delays delays delays valid valid valid david fire fire combinations sciences automatic middle importance importance importance uniformly spiking spiking spiking spiking spiking spiking spiking spiking oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory reached receives receives receives receives receives excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation allowing contribution classify oscillations physiological physiological follow follow duration receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor comp comp simplified hypotheses ill ill ill ill received received received receive receive receive receive receive explore stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation wiley investigate exhibit existence postsynaptic respond respond respond respond respond respond respond respond respond project investigated analytically analytically analytically analytically analytically analytically oscillation pathway statistically presynaptic presynaptic presynaptic presynaptic cognition plausible olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory formal formal formal formal formal formal observe observe perceptton mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed mixed percentage percentage site agreement analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical capabilities capabilities tractable tractable interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons comparisons satisfied broad afferent afferent afferent afferent afferent afferent cut cut meaning meaning questions behaviors populations pathways pure pure pure exhibits fall physiol cumulative physiology oxford odor receptors anatomical chemical chemical chemical chemical loops exceeds published governed governed governed connect connect male belongs relies agree insect insect insect insect insect insect insect sons receiving divide discriminate discriminate rigorous covering exhaustive exhaustive validity reaction responds responds responds responds responds responds female descriptions interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron interneuron lobe lobe lobe lobe lobe lobe crosses relate relate relate mediated regimes paris paris france france france france diversity diversity diversity minor species institut inhibited neglect excited excited bat odors odors odors odors reproduced senses senses senses binomial oscillates neglected antenna sur sex sex ted gallant obeys invert reviews kramer des des latencies concentrations insects insects insects gupta mammals dreyfus dreyfus dreyfus dreyfus dreyfus permission rue rue rue personnaz personnaz personnaz personnaz personnaz blend blend blend blend blend blend blend blend blend blend blend blend percentages morphological stimulations stimulations compar inh pulsed pulsed grand ingredients recherche intemeurons relay michel laboratoire laboratoire laboratoire inl bal bal bal satisfactorily vanishingly illill ernst ernst courtesy cnrs cnrs pads blends blends blends lil excit 
#@Dreyfus_G,Kerszberg_M,Linster_C,Marsan_D,Masson_C,Personnaz_L,
#t6
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#*learning neural neural neural input input input input input input data data data data figure figure figure figure figure figure figure time time time time time time time time time time time time set output output error error state state state results results units units information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem based layer case case order order order systems values probability probability probability probability probability probability neurons neurons approach approach approach approach approach approach point single single single single single processing control control large local neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns inputs inputs inputs form form shows shows shows simple simple simple visual visual visual visual visual visual visual visual visual visual visual small small small work methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points field field field field current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random random random random random random high high high memory similar representation show show show equation equation section approximation average average average average average average average average theory theory theory theory obtained obtained obtained note note experiments experiments activity activity activity activity activity activity activity activity activity dimensional university variables variables variables variables defined found sequence constant table table estimate estimate standard terms left left left left direction direction direction direction direction direction direction direction low low temporal position basis basis sample sample abstract applied applied back find density density properties properties references important adaptive introduction stimulus effect generated change difference difference variable variable variable variable variable variable variable variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower lower rules measure measure measure measure measure higher higher higher higher center center previous previous firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type cortex good good good binary spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long long conditions distributed expected expected fact observed observed observed scale scale total performed times times regions mapping means means factor natural applications study study study study study knowledge obtain relative specific samples represented represented compared application series define rates rates rates rates rates location location location location location location location location location location location location location location location location location location location location location location location location active active determined experimental related discrete discrete discrete cortical cortical cortical brain brain power larger larger fields fields fields fields fields fields fields fields fields fields train train train train train train train dependent technique code code code code code represents final addition ai ai maps maps maps maps maps maps experiment experiment experiment experiment environment environment environment environment environment environment environment environment environment environment environment environment environment estimates top top bit bit bit significant significant statistics speed speed speed speed speed basic give give con channel channel coding derived randomly randomly randomly bounds types types lines depends depends measured measured measured discussion normal describe complete stable amount amount amount amount short short short short shape shape shape supported hypothesis pairs smaller combination combination account significantly head head head head head head special trials leads call numbers numbers bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bottom bottom idea minimize light light light light light light light population population population population discussed robust typical typical identical identical identical sense cognitive highly compare previously calculated studies achieve trans background locations locations locations interval interval interval interval interval sensitive grant arm arm constructed trial spikes spikes spikes spikes spikes spikes half half half half half half place place place place place place place place place place place place place place place place place place place place place place place valued reward interactions differences differences differences accurate designed designed faster practice suggest suggest encoding strong strong integration radial selective selective decrease relationship introduce configuration question suppose suppose suppose suppose appears appears derive derive longer index ways primary plot plot plot mathematical distinct changing simultaneously simultaneously simultaneously slightly mutual applying versus versus expressed formation dependence dependence dependence stationary communication influence influence fraction fraction showed understanding calculation measurements sec sec sec neighborhood event msec sufficiently sufficiently precision recorded recorded recorded recorded recorded recorded recorded recorded fire fire fire fire combinations sciences plotted black black black major straightforward aspects aspects divided effectively included spiking spiking detect computations plots plots ten receives receives compact kind video neuroscience running running running running running content content content content content cue cue cue cue cue cue cue cue cue cue cue gray cues cues cues cues cues cues cues cues cues cues cues cues cues absence wave neurosci neurosci consisted moves neighboring deal deal deal rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat receive camera situations situations requirements experience environments environments environments environments detail detail preliminary helpful helpful rise examine respond giving behavioral circles circles naturally integer equally aspect obvious portion precise observe separated separated expressions pyramidal pyramidal pyramidal pyramidal submitted averages integrate animal great great formula formula formula formula formula formula formula formula formula formula formula formula formula theoretic theoretic theoretic theoretic theoretic theoretic distinguish derivation derivation explanation answer caused briefly spatially spatially inside inside easier precisely mation controls pool potentially hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal res recording recording recording meaning considerably populations substantially pathways dark dark dark dark dark dark dark dark dark experimentally lack dots maintain requirement requirement measuring aim modulated serve chen electric decreased redundancy deviations shifted lab room room room pick concerned circular neurophysiol bin bin food food turned turned systematic systematic minutes minutes occurred primate loops moment keeping nearby north salient spot spot adequate adequate arrays fires fires fires fires fires fires fires infor published falls decide arrangement dif parietal diameter diameter hippocampus hippocampus hippocampus bins clean specificity specificity ends proximity partitioned summarize interestingly fired fired fired fired discharge drop drop ter visually opposed amplitudes tendency possibilities imagine transparent visited manipulation alternate interneuron wall wall wall life distant electrodes electrodes distal distal distal distal distal distal distal attached turning algebra milliseconds milliseconds bill article expansions circumstances rats info info consuming twenty maze maze maze hat virtually virtually cylinder cylinder cylinder cylinder cylinder cylinder visit tactile tactile successively mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton william absent absent thing granule scattered platform platform platform platform platform convey convey convey convey silent silent silent lights lights moderately ference nice tracked blurred conveyed conveyed conveyed conveyed conveyed conveyed conveyed extracellular traversed treats patterned patterned proximal proximal proximal proximal proximal proximal proximal proximal proximal proximal quarter bruce occupied differed conveys conveys conveys conveys conveys conveys fulfilled abstr abstr distinguishes arms arms alertness unstructured prevented millisecond fifty heads landmarks facing facing mission yix cards cards muller theta microns barnes barnes barnes farther walls walls opaque opaque nonoverlapping aging nimh markus markus markus markus markus markus logarithms ditions detectable darkness possessing ezp richmond richmond dangerous optican optican arizona arizona inferotemporal spends tips directionality deemed leonard downstream sutherland perimental ceiling overestimates conveying psychobiology informed wandering tucson controversy 
#@Gothard_K,Markus_E,McNaughton_B,Skaggs_W,
#t6
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data function function function function function function function function function function function figure figure figure figure figure time set set set set set set networks networks networks training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output number number number number number number number number system system error error error error error error error error error units units units units units units units units units units units units units units units units units information information information information models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown shown shown systems systems values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise weight weight weight unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method approach approach approach approach approach approach image image image image single single single processing control control large large local local analysis analysis analysis class class optimal optimal optimal optimal optimal form form algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples examples net net work work work work methods points points field current trained trained trained problems random random random random random random random random representation representation representation representation show show fixed fixed fixed fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images general parameter real approximation gradient gradient obtained term term note activity university university computation research research research independent independent independent log log log log log log log log log log defined standard standard standard standard computer computer terms terms terms terms terms distance science science activation machine sets maximum maximum learn learn learn components components components components components abstract applied back computational computational properties likelihood references component component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic procedure important mixture mixture mixture mixture mixture mixture introduction statistical statistical effect generated generated variance variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy complexity complexity complexity assume assume lower measure prior prior prior prior prior representations representations learned chosen chosen chosen chosen chosen chosen higher higher center theorem theorem bound bound bound bound bound bound type required required required required required required required required required good good represent distributed distributed distributed distributed distributed distributed distributed distributed expected expected expected expected expected expected expected expected expected expected make make fact fact fact fact fact techniques techniques length length length length length length length length length length length length length length length length length length correct correct correct correct correct probabilities probabilities observed observed observed observed errors forward simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting ing ing total total computed computed computed computed respect respect respect sum sum sum eq eq eq eq called mapping mapping means dimension dimension natural em em artificial specific represented true true true compared application desired define define define define compute compute compute compute compute compute compute compute compute compute compute compute perform related posterior posterior posterior posterior distributions distributions distributions distributions distributions gain equal contrast descent descent morgan institute institute institute department department version version consists code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code code advances connectionist final bias scheme scheme addition framework framework framework framework computing computing computing computing computing equivalent directly hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton curve additional view curves limit limit limit san bit bit determine determine efficient efficient efficient efficient efficient upper upper upper requires requires choice choice choice choice approximate approximate approximate approximate approximate free free free free free free free free free world basic coding coding coding coding coding coding coding coding coding coding derived randomly clustering area entropy provided selected depends depends constraint simply simply simply simply simply simply simply discussion describe describe describe describe describe group denote fast limited close assumption corresponds corresponds corresponds corresponds amount implemented generate generate supported require eds pixel including kaufmann objective objective objective underlying underlying technology block block interesting special principle principle principle principle principal principal principal squared squared squared squared making bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits bits idea combined combined minimize minimize produced choose choose added description description description description description description description description description description description description description description description description description description population population exact advantage pair separate separate ensemble apply apply include machines pixels sense relevant unsupervised unsupervised unsupervised approximately approximately works pca pca pca positions positions observation bounded williams intensity lead lead concept concept suggests deviation wide derivative derivative alternative alternative feed width width deterministic white generally generally generally generally demonstrate runs row segment competitive differences differences differences differences clear performs exponential weak weak mateo suggest encoding physics intelligence assuming assuming assuming assuming variety minimizing minimizing start relationship derivatives derivatives derivatives derivatives derivatives minima configuration configuration force question acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann suppose appears monte derive carlo produces index winner ways ways factors laboratory vertical segments segments explicitly physical physical dimensionality involves remaining easy slightly slightly equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium gaussians gaussians gaussians gaussians gaussians gaussians formed implies blocks choosing choosing reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction correlated communication communication viewed viewed codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes approximations activities activities activities activities activities activities similarly suggested slow performing fitting fitting fitting penalty string assigned degrees thesis formulation maximize variations discussions successfully major straightforward aspects encoded schemes situation online road road procedures cun allowing interested neuroscience generative generative generative generative generative generative dayan minimizes minimizes quantization quantization quantization quantization quantization quantization observable reach tesauro cowan situations presents minimized minimized minimized powerful powerful poor difficulty difficulty exponentially exponentially detail replaced limitations accurately game game dataset dataset helpful incremental ideal combine authors maximizing complicated complicated complicated complicated complicated encode analogous smallest spline spline spline spline spline equally equally obvious obvious obvious freedom freedom precise simplest arbitrarily phd defines defines neal neal neal integrate residual residual residual advanced developing crucial derivation variances fairly coded expensive independence caused caused caused caused briefly tractable tractable tractable tractable tractable worse reasons reasons purposes easier easier choices choices pool pool scientific separately toronto toronto toronto lowest argument argument amounts peter aim adjust richard display expectations college intractable feasible restrict pick pick pick pick pick pick recover recover acts acts perfectly zemel zemel zemel zemel zemel zemel zemel zemel zemel count purely purely reconstructed reconstructed reconstructed reconstructed reconstructed discover robotics kullback wrong convenient convenient ranges adjusting attractive intelligent height receiver receiver receiver receiver receiver receiver receiver receiver receiver receiver salk north lyapunov lyapunov lyapunov lyapunov alspector slice recovered negligible competing jolla matter canada variants grants ignore ignore ignore baldi baldi assigns treat divide fitted specification converted helmholtz helmholtz helmholtz helmholtz helmholtz deriving suboptimal suboptimal suboptimal suboptimal suboptimal suboptimal smoothly mdl mdl mdl mdl mdl mdl mdl mdl imagine reconstruct reconstruct reconstruct reconstruct factorial factorial factorial factorial factorial factorial factorial factorial factorial factorial quantized quantized distri geoffrey geoffrey shannon shannon convert convert convert convert convert convert picked picked hornik hornik conversely worth alternatives alternatives pools wider manuscript factored bution picking picking picking picking chris fortunately excess excess thermal send send stochastically stochastically stochastically stochastically stochastically stochastically stochastically stochastically stochastically stochastically generafive generafive generafive generafive generafive generafive king autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder connects rissanen rissanen rissanen quantizer contributes outgoing outgoing sending communicate communicate communicate encodings essence inaccurate energies sur predetermined proximation observes save ontario encourage reconstructions anticipate yann thinking canadian nserc conveniently singapore communicating communicating communicating communicating communicating communicating communicating communicating fellow ogp justifies contributed faithful chaining compactly communicated communicated communicated communicated communicated communicated communicated communicated communicated communicated encourages blend galland galland overestimate overestimate radford torrey pines vague sender sender sender sender sender sender sender cooperate autoencoders autoencoders autoencoders autoencoders autoencoders autoencoders liebler finely agreed inevitably wasteful publish unnecessarily seldom inquiry noranda waits 
#@Hinton_G,Zemel_R,
#t7
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set networks networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number system system system error error error error error results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space weights weights weights weights weights weights weights weights weights weights linear linear linear layer layer layer layer case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order shown shown systems systems systems parameters parameters parameters parameters weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method method approach approach approach approach approach pattern pattern pattern point point point point point image image image image single single processing test patterns patterns analysis analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples size size size size size feature net net net net net net work task methods methods methods points points field field field level level level current trained trained trained structure structure structure random random random random high high similar similar similar representation representation representation representation representation show show show fixed fixed fixed fixed fixed fixed line vectors vectors vectors images images images images general general real average average gradient term note note note experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university research research research independent log log found target target standard standard standard standard computer computer terms terms distance distance science science left presented presented map map present present low low low low machine object range learn learn learn learn position position position position position position position position position position position position position position position position position components basis nonlinear nonlinear continuous abstract applied find find computational properties properties properties references stochastic due ieee important complex effect generated variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost search tion energy difference difference complexity assume assume representations representations learned learned learned higher higher center center center center center center center center cases type required required required multiple multiple multiple represent represent represent represent represent represent expected make make fact length length length length length length length length length length length correct errors errors errors minimum minimum minimum classes ing ing total total total computed mapping means means means dimension dimension dimension dimension dimension orientation orientation orientation orientation obtain relative samples represented represented represented represented represented receptive receptive receptive define compute objects location location location perform active determined determined experimental goal related constraints connected brain approaches accuracy accuracy train morgan institute institute institute department department version version code code code code code code code code code code code code code code code code code code code code code code advances represents connectionist difficult exp exp exp exp bias layers layers layers addition addition addition addition maps framework computing computing computing experiment experiment experiment hinton hinton hinton hinton hinton hinton hinton hinton additional additional limit limit san top determine determine determine determine full approximate free free world coding coding coding coding coding coding coding derived derived weighted randomly developed levels levels levels levels levels levels types actual actual actual nature nature depends depends constraint constraint constraint constraint constraint constraint simply simply biological biological discussion describe group limited assumption corresponds corresponds corresponds complete rbf rbf short implemented shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape supported role require eds pixel instance instance instance instance instance instance easily degree fit kaufmann objective objective objective objective underlying underlying underlying underlying needed technology interesting interesting interesting ratio principle principle principal squared details call bits bits bits bits bits bits bits bits normalized normalized minimize minimize produced produced choose description description description description description description description description description description description population population population population population population population population population population population population population population population population population population population population population population directions property robust separate ensemble include hierarchical dimensions dimensions dimensions dimensions highly highly varying unsupervised unsupervised unsupervised unsupervised smooth match correspond correspond correspond correspond correspond correspond pca pca positions positions positions positions positions positions positions grid constructed exists horizontal horizontal horizontal parts lead occur deviation derivative derivative predicted predicted predicted alternative width setting hardware conclusions valued depend competitive competitive competitive retina retina exponential learns encoding encoding reduction drawn solid proportional intelligence radial minimizing minimizing minimizing minimizing start min derivatives connectivity acknowledgements explicit suppose suppose derive produces winner plot plot describes tuned tuned vertical vertical vertical coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates dimensionality dimensionality develop develop develop develop mutual gaussians minimization formed formed formed independently independently formation formation formation reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction correlated communication communication viewed codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes detailed activities activities activities activities activities activities activities activities activities activities activities activities activities activities allowed earlier earlier earlier epochs epochs spaces neighborhood neighborhood neighborhood assigned kohonen kohonen kohonen kohonen kohonen advantages topology topology topology transactions existing thesis coordinate coordinate inter weighting instances determines extension neighbors discussions determining differ encoded symbols tend identity kind contained contained interpreted bar bar play dayan minimizes minimizes quantization quantization moves illustrates extract extract extract extract tesauro cowan minimized bars employed unlike varied relations relations accurately accurately issues helpful reducing respond mappings fault working variability encode topographic topographic act opposite perfect perfect panel panel explored mapped message message epoch epoch epoch epoch arbitrarily defines advanced developing developing developing developing developing costs crucial variances coded failure adapted caused organized style forces scientific separately involve describing implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit implicit toronto toronto toronto cybernetics conjugate explained reflect understood peter marked adjustable limiting aim aim suited achieves datasets gave richard enables enables redundancy redundancy redundancy tolerance converged converged redundant redundant analogue fix appropriately appropriately zemel zemel zemel zemel zemel zemel zemel zemel zemel zemel ordering reconstructed reconstructed reconstructed repre flexibility flexibility robotics fits intelligent height serves serves nearby receiver salk north exceeds corner corner alspector falls moved moved intended intended elastic elastic viewing similarities winning advance francisco jolla canada grants alternatively ignore assigns limitation pressure helmholtz ent inferred creates responds responds willshaw willshaw smoothly smoothly instantiation instantiation mdl mdl mdl mdl mdl mdl mdl mdl mdl realize reconstruct representa factorial factorial pub geoffrey geoffrey bump bump bump bump bump bump bump bump bump bump bump bump bump bump bump bump bump depicts rbfs intensities spanned covered nonetheless durbin durbin ignoring mea topography develops coming discontinuous attributed autoencoder autoencoder autoencoder autoencoder autoencoder broadly rissanen rissanen possess lying ignores sending salesman communicate communicate communicate communicate positioning bumps bumps addressing responded began hip imum resemble richer sentations save aimed ontario topologically blob blob blob conveys corresponded canadian nserc singapore communicating communicating communicating communicating fellow viewpoints bears travelling cheap formulating recon communicated communicated entails saund saund signif backpropagated backpropagated gravity gravity hyperacuity torrey pines recruited autoencoders autoencoders factorim factorim ttt ttt ttt backpropagating cnl caption misfit misfit concisely struct noranda cheaply communicates squeeze squeeze prevalence aforementioned economical manipulates 
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data function figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number number number number number error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results units information information information information problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance based based based based space space space space space space space space space space space space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer case vector order order order order order order shown shown shown systems systems systems systems values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise weight unit unit unit distribution distribution distribution approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern point point single processing processing processing processing processing processing large large large local rate test patterns patterns patterns patterns analysis analysis class class class class class class inputs form shows algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples examples examples examples examples examples small small small net net net net net net net net net net net net net net net net net net net work work work work work task task task task task task task task step step step points process process process process level level current current current trained trained trained trained trained trained trained structure structure random random random response representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show section section fixed line line rule rule general general general generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter real average states states states states states states states states states states states states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained note activity activity activity activity activity activity activity activity result result university computation computation computation computation research sequence target target target target dynamics dynamics dynamics dynamics initial initial initial initial initial standard standard standard standard computer computer science science science science left left left presented presented presented map map map map map map machine machine machine machine machine machine machine machine sets maximum maximum maximum learn learn learn components continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied back convergence density density density likelihood references due due positive positive positive positive positive procedure procedure procedure procedure procedure procedure procedure procedure important adaptive adaptive decision mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction behavior behavior effect dynamic dynamic generated generated variance cost cost cost cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search tion difference difference complexity complexity assume assume assume assume assume assume rules measure measure prior prior prior representations representations representations representations representations representations representations representations representations representations representations representations representations word learned learned chosen chosen chosen higher part center center required required multiple distributed distributed distributed fact region length observed observed observed observed observed observed observed observed scale finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite simulations ing ing tasks total simulation simulation computed performed called times regions regions regions mapping mapping mapping optimization natural global study knowledge negative negative negative negative negative artificial specific specific represented true true true true true true true true true true compute location perform perform perform determined related posterior discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal equal approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches larger larger connection descent descent descent descent descent descent descent descent descent nets morgan morgan morgan morgan proceedings report department version version version version version version technique technique consists consists consists internal internal internal internal internal internal internal internal advances advances advances advances represents represents difficult exp exp exp bias bias layers layers layers graph ai maps maps computing domain domain domain equivalent environment directly directly directly hinton san san san san conference requires requires significant approximate world produce produce condition clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering criterion entropy actual actual finally selected selected selected nature simply feedforward describe describe describe group tested assumption assumption corresponds corresponds corresponds corresponds complete surface predictions finding nearest assumed supported theoretical require eds eds eds eds end cluster cluster cluster makes rumelhart development noisy noisy noisy noisy kaufmann kaufmann kaufmann kaufmann typically underlying needed special uniform mode mode mode mode mode mode mode operation operation language language language language language language language language language language language leads squared call making making supervised supervised supervised supervised supervised supervised minimize run denotes recent robust robust typical include machines machines side side side cognitive cognitive engineering dimensions dimensions highly compare previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised module module module module axis tions correspond studies converge converge achieve williams improvement grant constructed horizontal studied alternative alternative alternative alternative correctly clusters clusters clusters clusters clusters clusters occurs runs half half conclusion minimal greater assumptions assumptions assumptions assumptions accurate bayes moody moody moody learns constrained mateo mateo mateo mateo temperature strong solid regularization regularization start plane manner connectivity annealing base appears construct produces longer primary vertical changing dimensionality involves involves involves involves scales scales integrated integrated integrated gaussians gaussians applying extraction versus decreases formation depending estimator estimator estimator estimator estimator estimator interpretation variation open lee evolution soft soft soft activities activities earlier earlier earlier roughly initially initially string string string string string string string string string string string string string symbol symbol symbol symbol symbol symbol symbol symbol symbol construction foundation foundation classified avoid exploration box includes includes strings strings strings strings strings strings determines discuss mozer mozer mozer mozer mozer mozer mozer mozer mozer mozer specifically priors priors domains domains domains domains regular compression identified efficiency society maximal effectively symbols symbols mcclelland presentation presentation presentation successful successful successful successful identify schemes post miller ten ten fine procedures heuristic issue lie bar michael giles giles giles giles quantization quantization quantization quantization quantization quantization quantization quantization quantization computes subsequent software software decreasing cowan transformed difficulty varied varied involving replaced hanson hanson hanson hanson integral limitations limitations lippmann lippmann maximizing comparable comparable symbolic understand cognition matched matched induction induction induction induction induction induction induction induction induction induction induction induction induction induction hill circles predicting automata automata illustrate adjusted adjusted adjusted versions algo algo explored explored explored explored initialized multivariate defines years languages languages languages languages improves processed purposes incorporate ran desirable acknowledgement optimize depicted depicted annual meaning nsf sun exemplars researchers argument fourth elman elman generic generic generic passed ity schematic schematic partitioning partitioning spread aim extracting incorporating chen chen deviations converged differentiable cor consistently corrupted corrupted corrupted rithm rithm member member recover nonzero smolensky rigid rigid climbing overcome odd odd hyper replica methodology methodology disjoint corpus corner loo james corre colorado belongs belongs schedules young infer pollack ends arrows hypercube inductive inductive partitioned designing summarize shavlik shavlik consecutive consecutive pressure unified unified unified unified drop incorporates incorporates incorporates misclassification accept goodman goodman goodman emerge encouraging feeding utilize classifications additionally superimposed flat affects possibilities discovering clustered alter evolve boulder eliminating landscape depicts smyth smyth smyth iri categorization nonetheless reveal happen examination infinitely mann coming discretized continued mcdonnell towell towell neighborhoods hoc broadly outperformed outperformed award incorporation characterizes characterizes characterizes watrous watrous sian goodness goodness quick fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm fsm zeros bumps bumps drifting schreiber gaus faced tomita ous cleeremans servan kuhn kuhn probabil unnecessary unnecessary repetitions replaces moderately das das das das das das das das das das das das investigator progresses progresses elaborate stabilizing observes enforced reactive pursued encourage encourage tie emulate emulate emulate designated motivates posterjori posterjori experimentation presidential continu contin premise motivate emulation emulation gation cri encourages pervised sponds depict uous replications replications looo fsms fsms unsu mcmillan mcmillan quantize quantize oot judgement underly subsymbolic quantizing principally bachtach bachtach propa depiction depiction aren inaccuracy inaccuracy lipp tomira isodata substring 
#@Das_S,Mozer_M,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set networks training training training training training training training algorithm output number error error error error results results results results results results units units units units units information information information models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based space weights weights weights weights weights linear layer layer layer layer layer layer layer layer case vector vector vector vector vector order shown shown shown shown systems systems systems values values values values values noise weight functions functions functions unit recognition pattern pattern point single single processing processing processing control large large large local test test test test test test test test test test patterns patterns analysis analysis class class form form form form form shows paper small net net fig step points points features classification trained structure structure structure structure structure random random random response response similar similar representation representation representation representation representation architecture architecture fixed vectors vectors vectors vectors vectors vectors vectors images images approximation gradient gradient note activity activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional result result variables variables computation research independent independent log found found initial initial initial standard standard terms prediction prediction prediction prediction prediction left left left left left presented presented presented present present low machine machine maximum position position components components components components components sample abstract applied likelihood likelihood references component procedure mixture mixture mixture mixture mixture mixture context introduction hand hand hand statistical statistical statistical statistical generated tion lower lower measure representations representations representations representations center center center center center center center center center multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple binary binary binary binary binary binary binary binary binary represent make make techniques correct observed observed observed observed observed errors errors resulting ing computed computed respect multi sum sum sum sum means dimension dimension global knowledge obtain specific samples samples samples samples compute active active active active experimental distributions contrast train morgan morgan morgan internal individual advances advances advances responses equivalent san san san bit full requires requires requires give weighted weighted weighted levels processes processes processes processes processes biological biological discussion feedforward assumption corresponds predictions predictions predictions predictions predictions predictions predictions predictions common generate generate eds square pixel ability ability cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster degree noisy noisy noisy noisy including including objective objective objective objective underlying underlying underlying account functional fully york principle principal principal principal principal principal iterations pre magnitude predict advantage robust takes side subset dimensions dimensions dimensions sufficient varying unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised achieve sparse mixtures mixtures mixtures mixtures expression occur predicted touretzky clusters clusters white white white boundary demonstrate strength conclusion starting hebbian competitive sigmoid sigmoid numerical designed moody constrained mateo mateo mateo encoding encoding encoding encoding encoding iii characters characters scene boltzmann boltzmann explicit explicit ways mathematical distinct multilayer linearly linearly belief consisting predictive centers centers centers centers centers centers centers centers centers centers decomposition activities activities activities activities activities activities converges sign key performing combining combining perceptrons formulation formulation formulation formulation domains black black black black black successfully middle middle suitable differ computationally identify success issue issue criteria criteria criteria bar write paradigm ill ill illustrates illustrates mixing mixing mixing mixing mixing mixing mixing mixing presents minimized unlike wiley difficulty hanson association giving mappings combine dependencies encode statistically statistically hill circles measurement measurement possibly man predicts created equally singular attempts indicating ment formula formula crucial nowlan independence independence tractable lies nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity tive purposes purposes controls consequence ion optimize auto cybernetics cybernetics reflects share haussler haussler employ employ incorrect operate anti popular coherent coherent coherent coherent coherent inherent specifies sharing don don don don don don don don optimality forming tation tation controlling encoder discover nonzero printed grey grey grey grey turned simplify fail fail sanger sanger bourlard bourlard salient intuitively responsible respective displayed displayed sides ascent ascent accounts belongs centroid centroid offer arrive clean variants variants exploiting hart hart discovered discovered outlined outlined pressure pressure ure ple shading employs adopt seek ical freund freund causal causal causal causal eric reconstruct arising care care care duda duda interact permits permits uncertain rectangle bump flip represen represen represen barlow reveal turning turning meet lippman subspaces gorithm demonstrating served regularities regularities compositional twenty twenty focuses responsibility responsibility reflecting reflecting inherently conflicting ters interpolating interpretations squashing squashing sions prone alto alto dimen neutral accounting tations palo palo judge entities weakness compress iiiii iiiii formulations offered extremes darker beliefs beliefs tll reconstructions reconstructions reconstructions nonlinearly disagreement exhibiting clus adopting confident bearing associating idealized independencies rni rni rni rni rni deliver pointwise kauffman kauffman saund saund saund saund saund lighter portant obeying zky touret registered alterna numer unsatisfactory dictions kamp kamp assertion adopts obscure cancelled pertain combinatorially observ delivering sensibly 
#@Saund_E,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data function function function function function function function function function function function figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results units units units units information information information problem problem problem problem models models hidden hidden performance performance performance performance based based based based based based based based weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case vector vector order order shown shown shown shown systems systems systems systems values parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight functions functions functions functions functions neurons neurons neurons unit distribution distribution method method method method method method method method method method method approach approach approach point processing processing processing large large large large large large large large local local neuron rate rate test test test test test test test test analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs form shows shows signal signal signal algorithms simple simple simple gaussian paper small small small small size feature net work work work task methods methods methods methods methods methods methods points points process process trained trained trained trained trained trained similar equation section section section section line line general generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter approximation approximation approximation approximation approximation approximation approximation approximation average average average gradient term term term term note note activity activity dimensional variables variables variables variables variables variables research research research research research defined found dynamics standard standard computer terms node node node science science prediction prediction prediction prediction prediction prediction presented presented presented present activation low low low nodes nodes nodes nodes nodes nodes sets range components components components components components components components components components components components basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs sample abstract applied applied computational computational computational references component component component stochastic due due ieee procedure procedure procedure context context introduction statistical effect effect effect effect effect effect effect effect generated generated variance variance variance variance variance parallel cost cost cost tion tion tion change change variable assume assume assume assume assume classifier lower measure measure measure learned higher center previous bound bound cases required required represent expected expected techniques techniques proposed proposed proposed proposed proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed observed scale minimum minimum resulting resulting resulting resulting ing total simulation regression regression regression regression regression regression regression regression regression regression regression regression sum sum sum eq called elements elements elements factor factor factor dimension dimension applications obtain original compared application application application series series define perform determined related connected brain brain brain brain power comparison contrast contrast support support descent nets morgan morgan morgan proceedings proceedings report institute institute department technique technique technique advances advances advances joint represents final final bias bias layers layers layers layers ai ai computing computing directly curve san top top effects conference efficient full full full full full requires requires significant significant approximate approximate statistics statistics world speed basic basic pages pages pages pages pages increase increase increase increase increase increase validation validation validation weighted criterion bounds actual provided backpropagation simply achieved discussion discussion covariance technical feedforward feedforward denote denote fast fast fast fast fast assumption assumption assumption assumption complete short effective effective effective effective effective effective effective require require main ability ability future future makes rumelhart rumelhart noisy noisy including including fit fit fit fit fit kaufmann kaufmann kaufmann objective underlying underlying underlying underlying underlying underlying account account account functional functional fully block block block block block block significantly special special special empirical principal principal principal principal principal principal principal principal principal principal principal principal principal principal squared squared squared squared squared squared representing numbers international supervised supervised supervised supervised early early early early decay decay decay polynomial polynomial polynomial polynomial combined predict denotes denotes discussed discussed improve improve directions recent correlations correlations property practical introduced moving identical engineering observations calculated volume volume volume correspond pca pca pca pca diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal background bounded sensitive grant grant grant exists exists lead extended deviation matrices matrices matrices matrices touretzky touretzky column demonstrate runs runs runs half starting minimal greater hebbian reduce reduce reduce reduce conclusions operator operator editors differences measures numerical moody moody moody moody moody moody moody moody moody moody moody moody mateo propose propose reduction drawn sigmoidal sigmoidal california solid solid regularization regularization regularization regularization start relationship relationship averaged connectivity identification force acknowledgements relation index index index ann pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning implement implement implement multilayer multilayer coordinates coordinates easy consisting adding springer implies john yield yield review depending stationary viewed interpretation variation detailed evaluated sizes activities activities activities completely suggested dashed additive normalization reduces reduces norm degrees expect expect existing box activations priori priori coordinate subspace mozer mozer holds discussions columns columns determining straightforward efficiency uniformly differ computationally effectively reached verlag cun cun success stopping stopping stopping stopping contribution contribution running satisfy quantity generalize eigenvalue denker predictor approximating bars simpler unlike transformed transformed poor production production replaced hanson hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian dotted dotted preliminary biases examine successive applicable office office reliable proper proper eigenvectors eigenvectors eigenvectors tanh affect func removed removed removed removed examined saliency saliency saliency smallest math coefficient possibly editor editor editor predicting predicting subsets rank rank rank freedom improving improving years advanced inequality inequality crucial derivation fairly improves expensive briefly benchmark tool tool starts obs obs obs obs obs obs obs obs obs obs obs obs scientific projected involve involve ridge lowest exemplars evaluating applies substantially understood relevance backprop solla employ remove calculating passes spread differs differs weigend weigend weigend aim gen extensions extensions electric sophisticated unbiased unbiased damage damage cor redundant leen leen leen leen leen leen leen interface interface guarantee guarantee approximates discovery naval connecting flexibility smolensky smolensky systematic air adds wrong convenient promising analogy efficacy serves serves transforms removing removing removing star affected salient symposium obd obd obd obd obd obd obd obd obd obd obd obd obd motivation motivation exploring analyses financial mance mance perfor perfor pruned pruned pruned pruned forecasting contraction properly horizon park projects projects acknowledge onr leaving constitute piece stork removal removal retraining retraining retraining spaced equality equality levin levin levin levin levin levin compensate continues graduate eliminating eliminating eliminating eliminating eliminating relating individually scope deleted deleted spanned denver lippman eigen eigen eigen eigen eigen oregon spite sigmoids removes removes removes rewritten rewritten gratefully fat stimulating hassibi hassibi excess excess january january january ate ase identifies impractical todd orthonormal finer december industrial outperformed ning month agency triangle judged beneficial sij economic economic linearized linearized sions dimen ance acknowledges surgeon surgeon akaike wolff inaccurate inst indicators penalizes eigenfunctions eigenfunctions eigenfunctions generaliza costly replaces months andreas monthly relying relying eralization ranked menlo complexities univariate trimming ricoh altogether cheap cheap cheap economics fpe fpe fpe fpe portland manageable worthwhile cheaper skeletonization skeletonization cumbersome gpe saliencies mono hammerstrom prin optimizations ilwll trailing trailing combina lagged mial monitors inns athe jolliffe jolliffe rehfuss richness nonstationarity ike ike covari prunes ducing exercised cipal 
#@Leen_T,Levin_A,Moody_J,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural input input input data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number system system system system system system system system system system system system system error error error error error error results results results information problem models models models models performance performance performance performance performance based based based based space space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear linear linear case case shown systems systems values values values values values values values values values values values values parameters noise functions functions recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach point point point point point point point point point point point point point point point image image image image image image image image image image image single single single processing processing processing control control large local local local local local local local local local local local local local local local local local rate rate analysis analysis analysis analysis class inputs form form form shows shows shows shows shows shows shows shows shows shows signal signal simple simple gaussian visual visual visual paper examples size size feature work task task task task step step points points points points points points points points features features features features features classification classification classification process current structure random representation representation representation representation representation representation architecture show show show vectors images images images images images general general generalization speech speech speech speech speech real approximation average gradient gradient gradient gradient gradient gradient gradient term experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university variables variables variables variables variables variables variables variables variables variables research research research found sequence initial initial initial initial estimate estimate estimate estimate estimate computer computer computer computer distance science science science prediction prediction presented low maximum range range range learn position position components components components components components components components nonlinear nonlinear nonlinear nonlinear outputs sample sample abstract applied back find find find density analog analog references important important context complex complex hand hand effect generated generated variance search energy energy energy energy energy energy energy energy energy energy energy lower representations learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen higher part part center center previous good conditions region correct minimum resulting classes tasks tasks tasks regression computed sum performed performed performed times mapping mapping mapping mapping means means optimization dimension dimension dimension dimension dimension dimension dimension made made applications applications applications applications knowledge knowledge knowledge em filter negative specific samples samples samples samples samples samples samples provide proc proc proc location perform active determined determined determined determined goal constraints connected approaches approaches approaches approaches approaches approaches steps accuracy larger larger support support descent morgan report institute institute institute words technique technique consists internal internal internal internal internal advances connectionist connectionist difficult difficult final final addition sequences maps curve curve curve curve curves san determine determine efficient efficient full free free free world vision vision estimated estimated estimated give randomly randomly clustering clustering robot lines depends constraint constraint constraint constraint constraint constraint achieved technical describe hmm surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface finding finding finding nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest shape shape shape supported face journal square pixel fit kaufmann auditory typically smaller combination reduced mlp projection projection database database empirical principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle squared squared representing international normalized magnitude idea minimize minimize discussed improve improve improve improve robust robust takes reported quadratic cognitive dimensions dimensions dimensions dimensions dimensions sufficient compare compare compare conventional conventional volume works axis axis smooth smooth speaker speaker match match pca pca observation grant studied invariant occur wide correctly correctly hybrid touretzky width width boundary demonstrate starting reduce conclusions neighbor neighbor tangent moody mateo propose taking presence largest largest largest largest largest external external external external drawn drawn drawn demonstrated california labeled variety derivatives characters minima construct produces longer describes coordinates coordinates coordinates remaining easy gaussians gaussians applying applying formed decreases influence influence influence operations controlled centers centers centers centers centered partition partition key earlier performing performing convex reduces neighborhood neighborhood neighborhood tracking tracking tracking tracking tracking tracking tracking tracking interpolation interpolation interpolation intermediate initially query query query query query contour contour contour contour contour contour contour contour contour contour contour contour contour contour uncertainty neighbors neighbors neighbors neighbors determining selecting aspects letter capable computationally included included identify build efficiently efficiently efficiently projections fine conf conf conf kind kind strongly video video neuroscience symmetry symmetry return lie lie lie lie lie quantity relaxation generalize modelling powerful lippmann successive project mappings mappings mappings int int int relationships root surfaces surfaces surfaces surfaces surfaces surfaces contours contours contours removed waibel waibel waibel circles patch patch naturally naturally naturally closest closest closest closest closest reading configurations spline spline recognizer implementations queries queries queries queries queries queries queries queries queries queries queries queries prototype prototype prototype prototype prototype prototype prototype prototype separated improving improving extent simplest utility attempts synthetic synthetic synthetic advanced growth track coded starts starts london reasons straight berkeley berkeley division ran acknowledgement gradually patches patches patches fourth geometric collected collected empirically axes axes embedded embedded embedded parameterized quantitative completion completion maintain templates templates templates span span span polynomials prototypes measuring phonemes acoustics acoustics replace focused yuille yuille merging cumulative globally don aligned aligned forming restrict acts repre unity unity discover discover tem rotations exemplar robotics extending imaging ranges ranges proceeds contract exploring reliably embedding lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip combines introduces studying ascent ascent sphere sphere sphere chooses omohundro omohundro omohundro omohundro omohundro omohundro omohundro omohundro omohundro vari dramatically street land drop piece leaming ber additionally reports spaced continuity constrain constrain num ocr bounding plate altered projecting cation translations funded esti supports stuck refined supporting lighting stephen corners crude crude quantify jointly smoother suite alex incorrectly dom illinois evenly agency bregler bregler bregler bregler bregler bregler bregler bregler bregler interpolate relaxed relaxed robustly energies snake snake snake snake snake snake snake snake snake snake linking sented decompose decompose urbana relax magnification ables broader invert undesirable lips lips lips lips lips topologically manipulating hild hild deformable deformable deformable deformable konig konig grain lipreading lipreading lipreading lipreading lipreading lipreading lipreading lipreading classifi champaign bumptrees torus extrapolate portant fundamentals mates terzopoulos graylevel rations minneapolis lnt glue adelaide christoph researcher configu scalings neuroinformatik kass kass stricted dimensionm 
#@Bregler_C,Omohundro_S,
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#*network neural function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number error results results results results results results results information problem problem problem problem problem performance performance performance performance performance based space linear order order order order order order order order order order order order order order shown shown shown shown shown systems systems systems probability probability probability probability probability functions functions functions distribution method method method point point point single single single single single single single single single single large large large large large large rate rate rate rate rate test analysis analysis analysis analysis analysis analysis class class class class class optimal optimal form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple simple simple simple simple paper paper small small small small small size size size work work work work work methods methods methods fig step step step step points features features features features features features features features features process level level level level level level level level level level level level level level level level level level level level problems problems random random random random random high high high high high high similar similar similar fixed general general general general general general general real real real real real approximation approximation average average average states note experiments experiments experiments experiments experiments experiments result result university university university university computation solution independent independent independent independent independent independent log log log defined defined defined defined defined defined found found found found found found found found found constant table table table table estimate standard standard computer computer science science direction presented presented low low low maximum maximum maximum press press position nonlinear sample sample sample sample abstract find find find find find find references procedure procedure procedure adaptive adaptive adaptive introduction behavior behavior parallel search search search search search search difference lower lower lower chosen chosen chosen chosen higher higher higher higher higher part previous previous previous previous bound bound bound required conditions expected expected expected expected expected expected expected expected expected expected expected expected expected markov make make make techniques techniques region region length length length observed errors total respect respect sum performed called times regions means factor factor factor optimization optimization made natural applications obtain obtain original original original artificial artificial relative relative samples samples samples samples samples samples samples samples samples compared compared desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired perform perform perform experimental goal goal equal mit mit comparison comparison larger larger larger larger contrast support selection selection selection selection morgan morgan morgan proceedings proceedings proceedings institute institute institute loss version consists consists bias scheme cambridge directly solutions design design san san san effects effects bit bit bit bit bit bit bit bit bit bit bit conference conference upper requires significant significant approximate approximate speed speed speed speed give randomly developed levels levels actual selected depends sampling sampling achieved discussion fast fast limited close finding finding short short main eds eds eds adaptation hypothesis hypothesis hypothesis instance instance instance instance instance instance instance instance instance instance future makes fit fit fit kaufmann kaufmann kaufmann simulated simulated typically typically reduced block block block block block block block block block block block block programming testing significantly significantly significantly uniform principle leads pre making bits bits bits bits international international depth idea idea idea run run added predict denotes architectures population population population population population population population population population pair reported apply identical relevant relevant relevant sufficient highly highly compare compare approximately approximately works works works works works works yields studies evaluation evaluation evaluation evaluation positions positions positions positions positions positions positions positions positions chain modified modified interval grant parts parts parts expression expression studied studied scaling occur occur move runs runs runs runs runs runs runs runs runs runs conclusion greater measures designed designed designed designed faster faster faster faster faster practice mateo mateo mateo temperature suggest taking strong hard mechanisms program annealing question question question question explicit suppose suppose suppose monte carlo longer longer ways primary ann ann ann mathematical mathematical dept dept explicitly explicitly explicitly simultaneously simultaneously slightly blocks blocks blocks blocks blocks blocks blocks expectation john national independently communication communication variation detailed evaluated evaluated evaluated showed completely similarly suggested earlier earlier earlier slow slow purpose intermediate initially initially string string string string string string string string string string string string string string string string string string string string string string string string string string string string string string string construction foundation foundation expect building building building building building combinations priori strings strings strings strings strings strings strings strings instances instances instances instances instances instances instances illustrated discuss variations absolute partially discussions successfully major major reason reason determining suitable included identify identify identify identify schemes genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic comparing ten reached reached reached reached receives traditional road road road road road road road road road quickly quickly quickly kind repeated success sin follow criteria cue list sampled sampled simplified realistic reach reach principles principles principles moves overlapping subsequent acknowledgments modelling simpler create detail detail optimized optimized preliminary preliminary preliminary preliminary helpful rise matches possibility combine working working comparable proved understand understand understand hill hill hill hill hill hill hill hill hill hill hill hill hill hill hill hill hill hill hill coefficient integer analyze analyze psychology algo separated consist simplest simplest isolated optimum optimum optimum optimum optimum optimum optimum percentage slowly slowly developing distinguish analyzed improves adjacent biology majority answer answer answer independence baum reasons comparisons comparisons comparisons inside purposes constructing ran worst desirable desirable calculations implicit implicit implicit implicit begin lowest lowest fourth fourth empirically led poorly posed incorporated slower slower variant maintain maintain poisson characterize ture spread prevent suited richard comments expectations implements median median median median instantaneous sharing contribute contribute proportion proportion discovery discovery discovery discover discover discover jones royal royal royal royal royal royal royal royal royal royal royal reaching climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing systematic wrong determination balance balance balance carry exploring evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations analyses analyses analyses mance combines representational negligible perfor holland holland holland holland holland holland holland holland holland holland holland holland expanded ascent ascent counting claim iterated foundations suggesting ahead ahead fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness fitness theoretically steepest card davis davis implicitly santa santa santa santa santa grants discovered discovered discovered ignore cam balanced parents acknowledge maintaining ence rigorous outperform outperform outperform outperform outperform outperform outperform outperform outperform outperform outperform achieving equivalently job sigma arbor arbor arbor personal personal personal mutually increment rithms goals crossover crossover crossover crossover crossover crossover crossover gas gas execute life mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell mitchell compatible carefully carefully careful landscape landscape landscape parallelism parallelism parallelism topic iri iri speedup preserve likewise knowing struc mea unpublished worked gratefully heading appearing bridge palmer palmer opti agrees assistance european converging suite suite dominates dissertation striking meth sloan evolving ods quick edition bottleneck meant meant doubling ous mutation mutation mutation mutation mutation mutation mutation discovers replaces landscapes landscapes landscapes landscapes landscapes landscapes landscapes schema schema schema schema schema schema schema schema schema schema schema schema schema schema schema schema schema preventing mum ness huber huber inserting orig saved rigorously excluding helped lay forrest forrest forrest forrest forrest forrest forrest forrest forrest forrest forrest forrest forrest forrest forrest forrest roads rosen previ parentheses parentheses michigan michigan michigan flips idealized idealized idealized idealized idealized reproduction euler mexico doctoral albuquerque attain wild confer confer confer confer confer innovation wasted wasted wasted crossed linkage maintenance belew belew locus locus slows vastly ered complez balances balances spends elaborated whitley cially instantaneously trail conserve mutations mutations mutations mutations munication jong jong alfred espe viously underscores recombined 
#@Forrest_S,Holland_J,Mitchell_M,
#t7
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input data data data function function function function figure figure figure figure figure figure time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number number number number number system error error error error error error error error error error error error error error error error error results results results results results units units information information information problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models hidden performance performance performance performance based based based based based based based space space space space space space space weights case case vector vector order order order systems systems systems values probability probability probability parameters parameters functions method method method method method method method approach approach point point point point point point point point point point point processing control control control control control large local local local local rate rate rate test test test test test test test test test test test test test test class class inputs shows algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper small size size size size size net net net work methods points points points points points points points points points points points points points points points features classification classification process level level current current current trained structure structure structure problems problems problems problems problems problems problems random high high memory memory memory memory memory memory memory memory memory memory similar architecture show section section section line line vectors approximation states theory gradient gradient gradient experiments university university variables computation initial initial initial initial initial initial constant constant table table table table table table estimate estimate estimate estimate computer computer distance science science prediction prediction prediction prediction prediction prediction prediction prediction left left left left range press press press learn outputs sample abstract applied applied find find find find find computational computational computational computational computational convergence references stochastic ieee adaptive decision introduction complex hand hand statistical cost search search search search search search energy energy energy difference difference difference assume lower chosen chosen previous previous previous bound bound bound bound bound bound bound bound cases required good good good good good equations make make make make correct correct correct correct forward scale finite minimum classes ing tasks total total regression regression computed times mapping factor made made made global global applications artificial artificial relative true true true true true cross cross cross cross cross cross cross cross cross cross compute rates perform perform power power power mit mit mit accuracy accuracy accuracy accuracy accuracy accuracy larger connection update descent descent descent selection selection selection selection selection selection morgan proceedings proceedings report institute institute words words words words department loss technique advances final addition cambridge curve curve top conference conference upper upper upper full significant statistics estimated estimated increase increase validation validation validation validation validation validation validation validation validation validation weighted weighted randomly randomly robot robot robot robot robot robot robot criterion criterion bounds actual actual processes iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration simply simply discussion discussion describe denote tested tested tested fast close close stable proof finding finding finding finding amount nearest nearest nearest nearest nearest common effective effective generate main journal journal end future makes fit kaufmann smaller smaller needed technology ratio special database call numbers numbers iterations iterations iterations making international bottom idea choose run run description description predict predict predict predict architectures robust include period subset relevant compare volume axis axis bounded bounded improvement entire increased arm constructed constructed exists expression wide locally locally hybrid loop greater neighbor editors editors editors clear sutton moody reduction drawn drawn proportional intelligence intelligence variety start relationship minima minima minima force force force force force force force force force force force force question suppose appears derive solving ways describes laboratory distinct confidence confidence confidence confidence confidence confidence confidence confidence confidence metric metric averaging slightly consisting springer select independently independently expressed communication learner learner learner learner open completely smoothing combining fitting fitting intervals generation calculate query query david building building box box box box box box box box box box box box box box box box box box box box box box includes kernels thesis combinations instances instances memories automatic prove discuss black neighbors neighbors neighbors neighbors discussions selecting selecting selecting computationally miller reached verlag quickly quickly contained success moore moore moore moore moore moore moore moore moore moore moore moore dis content highest predictor automatically attempt load extend trains american collection hanson hanson association preliminary helpful helpful fewer examine ideas school tech applicable decisions decisions cover attributes hill hill hill configurations spline extremely equally ensure queries queries queries queries queries queries queries queries queries queries obvious formal noted utility arbitrarily phd finds massachusetts inequality inequality inequality formula theoretic smoothness smoothness biology answer expensive worse starts starts reasons stanford closer preprocessing protein protein protein protein broad ran worst pool pool pool pool acknowledgement demonstrates mellon robustness improvements varies carnegie empirically embedded lack leave leave leave leave leave leave effort atkeson atkeson atkeson atkeson atkeson atkeson atkeson haussler haussler haussler incorrect compares requirement requirement requirement mod measuring pittsburgh spread popular cal sums chose returns returns june trade don discontinuities pac proofs secondary secondary sensing nat addresses eliminate eliminate outcome robotics climbing inspired communications communications wrong wrong wrong wrong wrong wrong wrong wrong wrong dealing reasoning repeat combines zhang zhang zhang bad bad bad searching searching sim approximators april omitted reader omohundro omohundro omohundro tures approximator stopped market market johnson ball andrew boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes boxes rigorous visually outperform pieces wahba wahba wahba perceived molecular argue summarizes robots epsilon impose werbos proba eliminating careful flip proach importantly weaker fea stuck applicability lippman tune els intensive rewrite treating differentiating aaai chris expense expense stimulating stephen stephen consuming bility discretized shot focuses inequalities fill december concern eliminates eliminates eliminates returned ning concerns schaal automation petsche correctness correctness judd kaelbling kaelbling kaelbling goodness goodness feasibility thing meant artificially tenth derives addressable united stan winners noticed plexity tighter hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding hoeffding ply viable viable cooling picks asso divides niques french waltz cheap cheap duce brute brute brute brute brute brute brute brute brute brute brute brute omitting private instantiated concentrating pollard pollard kingdom flipping collisions race race maron maron maron maron maron strate plug accelerating accelerating accelerating accelerating devil juggling stringent famous meila disjunctive disjunctive numeric ciative managed queried pessimistic ural greg encompasses wold wold wold gies solv happened pricing inves climb ees marina occasions pumping smoothers 
#@Maron_O,Moore_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function figure figure figure figure figure figure figure time time time time time time time set set set set set set networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output system system system system system system system system system system system system error state state state state state state state state state state state state state state state state state state state state state units units units units units units units units units units units information information information information information information information information information problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden weights linear linear layer layer layer layer layer layer layer layer layer layer layer vector vector order order shown shown shown shown shown systems systems systems systems systems systems values values values noise noise noise noise noise noise noise noise noise noise noise weight weight functions functions neurons neurons unit unit unit unit unit unit unit unit unit unit unit recognition pattern pattern pattern point single single single processing processing processing processing processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control large large local patterns patterns patterns patterns patterns patterns patterns analysis class matrix matrix matrix inputs inputs inputs inputs inputs inputs form form form form form form form form form form form shows shows signal signal algorithms simple simple simple visual visual visual visual visual paper paper paper paper feature net net net work task fig fig field field level level level trained structure structure structure problems random random random high high high high high memory memory memory memory memory memory memory memory similar similar similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show fixed fixed line parameter parameter parameter real real states states states states states states states states theory gradient obtained activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result university computation computation computation computation computation computation computation computation computation independent defined defined defined defined defined found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial standard standard standard computer terms connections connections node left direction presented present present phase phase phase phase phase phase phase phase phase phase phase phase phase low low nodes frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal machine machine machine machine machine object sets maximum press learn components nonlinear continuous continuous continuous abstract applied back back computational analog analog analog analog analog analog analog references important context context context context context context context context context context context introduction complex hand behavior behavior behavior behavior behavior behavior behavior stimulus effect effect dynamic generated parallel recurrent recurrent recurrent tion tion tion energy difference difference complexity spatial spatial lower representations representations learned learned learned chosen higher part previous bound required cortex cortex cortex cortex cortex cortex cortex cortex binary binary binary binary binary distributed distributed distributed distributed equations equations equations equations equations equations observed scale scale finite finite finite simulations ing ing tasks mapping mapping potential made study filter define define objects objects active active determined connected connected connected connected motor motor motor motor discrete discrete discrete discrete discrete cortical cortical cortical cortical cortical cortical brain equal steps larger connection connection fields train dependent source source morgan implementation consists consists consists internal internal code code individual advances connectionist responses bias layers layers layers layers layers layers layers graph graph sequences considered equivalent additional additional additional transition transition transition san san choice choice choice significant free pages pages con con coding coding coding coding coding coding coding randomly developed levels levels levels levels levels area types lines selected selected evidence evidence backpropagation backpropagation simply biological associative associative associative associative associative associative associative associative associative normal normal normal normal normal normal normal normal normal normal feedforward group group group amount common effective effective implemented implemented implemented generate generate supported square ability hypothesis future easily easily easily easily sensory sensory including simulated underlying underlying dynamical dynamical dynamical dynamical functional fully fully fully transfer character projection projection york york edge increasing mechanism special special special special special special mode mode mode principle principle operation operation operation operation representing representing representing call direct direct direct making bottom magnitude magnitude attention attention attention attention attention attention attention attention predict neuronal architectures discussed discussed separate ensemble ensemble element element side side side side inference inference inference inference inference inference inference subset subset subset subset subset cognitive sufficient varying previously previously previously previously observations works module module module module module module module module module module module module module module module module module module module module module module module module axis axis tions solve solve correspond differential differential channels gate organization storage entire entire grant amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude constructed constructed constructed constructed constructed constructed studied studied suggests digital digital digital rotation deterministic hardware pass demonstrate flow flow flow flow flow flow flow flow flow valued editors editors sigmoid modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules designed designed designed performs performs constrained strong presence presence external external external cycle cycle cycle cycle cycle turn turn start start start start start start exist selective selective selective selective plane averaged introduce manner groups connectivity program program program program program program attractor attractor attractor attractor attractor attractor areas areas areas appears relation construct longer winner winner winner primary sequential generating laboratory transitions transitions transitions transitions dept dept changing changing changing modeled modeled implement explicitly coordinates coordinates coordinates coordinates coordinates coordinates remaining unique consisting interaction interaction frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies equilibrium springer potentials cycles cycles select competition competition competition competition competition competition competition competition competition competition national focus focus communication communication communication communication communication viewed codes codes variation variation variation evaluated operations static static static static static approximated completely completely discrimination key earlier roughly purpose add remains string symbol symbol symbol symbol symbol symbol symbol symbol construction construction foundation eeg advantages views degrees box strings strings strings memories memories memories memories determines illustrated discuss activated coupled coupled phys grammar grammar grammar grammar grammar grammar differ divided driven symbols symbols symbols symbols symbols symbols included mcclelland modes oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors detect computations situation identity identity reached composed traditional refer contained prob showing neuroscience neuroscience issue symmetry sin oscillations oscillations oscillations content content gray gray gray gray built giles binding cat principles illustrates acknowledgments intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic cowan perturbation create essential investigate put relations oscillators detail hanson issues issues dotted preliminary oscillator periodic periodic periodic periodic periodic examine respond respond rest behavioral behavioral reliable reliable proper proper proper oscillation oscillation oscillation oscillation affect affect phases notion math editor editor man automata automata automata automata illustrate equally changed subsets olfactory olfactory olfactory bifurcation bifurcation bifurcation freedom switching consist consist generates generates chaotic chaotic chaotic chaotic chaotic chaotic chaotic animal cos cos band capabilities briefly benchmark spatially turns drive implementing berkeley berkeley berkeley day broad choices transistors leaves mathematics separately separately begin begin begin begin computers addressed fluctuations fourth fourth freeman freeman freeman freeman freeman understood elman elman elman elman fed fed recordings employ mod mod mod ture synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony serve singer singer singer singer coherent chose attraction attentional attentional attentional attentional attentional attentional attentional attentional attentional baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird traces traces synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization irrelevant ordinary ordinary accomplished appearance oxford investigation driving driving acts perfectly branches branches branches controlling circular tem interconnected lost lost clamped clamped clamped kaufman bower automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton moment serves operates monotonically north selects reliably introduces irregular holland monkeys lawrence competing viewing francisco francisco recog cerebral locked locked theoretically grammatical grammatical grammatical grammatical grammatical grammatical grammatical messages receiving lem ure constitute sig ent kluwer break transmitted job emergent revealed tween chaos amplitudes amplitudes assignments tendency constitutes possibilities basins sinusoidal molecular quantized quantized arising deep deep gained ization intra afosr picked landscape synchronized synchronized synchronized synchronized synchronized synchronized synchronized flip flip macaque guided rhythmic pos selectively oscillating oscillating oscillating oscillating oscillating enforce apparently maintains sta page places macroscopic macroscopic behave behave nal bill exploited struc computa examination behaves demonstrating syn assistance todd todd oscillate ave establishes finer morris carrier flows cally ning continuum sen contributes contributes neocortex siu loads hopf tended vertebrate communicate communicate randomness attended lags schreiber reviewed robustly seg substrate physica cleeremans cleeremans cleeremans cleeremans servan rent polar eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman eeckman notions activates contributing phy oil hirsch lowered perturbing perturbing perturbing perturbing bistable synchronize patterned sible holmes holmes bifurcations bifurcations emulate tilt tilt clocked thinking asso walter recur communicating frank namic tilted flop isomorphic chine resonant resonant resonant resonant resonant resonant segregated reber reber reber reber valley forest roi ucsf havior rli modulates invaluable experimen gov pleasure emitted wells subgraph subgraph subgraph subgraph subgraph subgraph subgraph subgraph subgraph subgraph subgraph subgraph subgraph crosstalk crosstalk crosstalk crosstalk crosstalk crosstalk crosstalk crosstalk crosstalk structed ule transi recurrently oscilla binds binds flops sory livermore livermore oscil dissipative perturb exit emulates emulates ampli ciative reverses tally processin clocking clocking ooi ooi ooi guckenheimer guckenheimer guckenheimer competi thirteen thirteen desynchronized desynchronized synchronizes suppl dynami incoherent ules ules investi learnin lating attending ternal dispersed subserve exchanging passband directs perturbs nize mans binarized acknowl chronization 
#@Baird_B,Eeckman_F,Troyer_T,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data function function function function function function function figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm 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hidden hidden hidden hidden performance performance performance based based based space space space space weights linear layer case case case case vector order order order order order systems systems systems values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise weight weight weight functions functions unit unit unit unit unit distribution distribution distribution distribution recognition recognition method approach approach point point image control large local local local local local local local rate rate test analysis analysis analysis analysis analysis class class matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs inputs form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper paper examples small small small small size size net work task methods methods methods methods methods step step step points features classification classification classification classification process current current trained problems problems problems problems problems problems random random random random random similar architecture architecture show show show show show section section fixed rule rule vectors speech parameter parameter parameter approximation average average average states states states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained term term term term term term experiments experiments experiments experiments experiments experiments activity activity threshold threshold threshold variables variables variables variables computation solution log defined defined found found found found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target dynamics dynamics dynamics dynamics initial initial constant table table table table table standard science prediction left direction presented presented map map map map map present present activation nodes temporal temporal maximum maximum maximum press press learn learn learn learn learn nonlinear outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous abstract applied back back back back back back back back back back convergence convergence likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic ieee positive important important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation context context context introduction estimation behavior cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search search search search search tion tion change change assume assume assume prior learned chosen chosen chosen chosen previous theorem theorem theorem theorem cases cases required long long long long long long long long conditions conditions represent represent distributed markov markov make fact region region region region proposed length length length length length length length correct probabilities probabilities probabilities forward forward finite classes ing tasks tasks tasks tasks tasks tasks tasks tasks tasks computed computed computed respect respect respect respect respect respect respect respect multi multi sum sum performed performed performed performed performed elements optimization optimization optimization global global global global applications applications applications knowledge em em em em em em em em em em em em em em em em em obtain vol vol artificial compared compared desired desired desired desired compute proc perform perform perform perform perform perform experimental experimental constraints connected connected discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete approaches steps steps comparison contrast update train train train descent descent descent descent descent descent descent morgan loss consists connectionist difficult difficult difficult difficult final final final final delay sequences sequences sequences sequences sequences sequences sequences sequences sequences maps considered considered considered framework domain domain domain directly hinton curve transition transition transition transition bit bit bit full requires free free basic increase con con derived weighted weighted weighted weighted weighted weighted weighted weighted randomly randomly conditional conditional criterion criterion criterion criterion criterion types types finally evidence backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration simply feedforward increases increases increases arbitrary fast fast inverse corresponds complete short implemented theoretical theoretical theoretical require eds end end end end ability easily simulated simulated simulated simulated simulated simulated simulated simulated simulated simulated probabilistic probabilistic probabilistic needed combination dynamical dynamical dynamical dynamical fully fully jordan jordan interesting significantly ratio ratio trials trials uniform representing representing details numbers stored bits bits bits bits experts supervised magnitude idea idea idea produced added added predict architectures architectures architectures improved advantage robust separate takes element reported reported practical practical introduced introduced machines hierarchical subset sejnowski compare previously unsupervised volume volume works yields studies converge trans diagonal sparse sparse definition mixtures generalized grid grid bounded improvement sensitive increased increased constructed exists studied trial matrices alternative alternative alternative alternative locally touretzky loop loop generally generally column flow conclusion starting minimal reduce reduce reduce central sigmoid clear clear performs performs faster constrained taking presence external minimizing exist targets targets targets introduce derivatives derivatives connectivity connectivity connectivity minima minima minima annealing annealing annealing annealing annealing annealing attractor attractor attractor acknowledgements pro winner ways transitions mathematical mathematical mathematical dept missing missing transformations text belief expectation expectation yield independently interpretation interpretation interpretation influence solved evaluated open controlled controlled showed centered static understanding understanding understanding similarly constants allowed slow additive intervals intervals remains remains remains transactions avoid activations coordinate bell assignment assignment assignment assignment subspace batch memories recognize prove maximize maximize absolute reason regular extra hmms hmms hmms hmms hmms uniformly paths paths successful attractors efficiently situation capture soc cun cun prob allowing interpreted stopping stopping dis issue contribution classify manifold criteria duration vary write modular backward backward backward backward reach maximization maximization attempt moves jacobs jacobs software decreasing parametric parametric parametric powerful poor production essential difficulty difficulty difficulty exponentially exponentially exponentially exponentially updating varied put involving hessian fashion school parity parity parity parity parity parity analytically dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies structured structured understand fundamental gradients gradients gradients gradients possibly analyze adjusted subsets quantities quantities algo algo assumes explored explored explored store store store store improving attempts averages optimum cos guaranteed unstable improves diffusion diffusion independence worse worse inside perspective tive sys producing bengio bengio bengio bengio bengio bengio bengio bengio bengio arise consequence simard simard simard simard simard gradually definite arises incomplete prop prop prop prop prop prop prop prop pseudo pseudo pseudo pseudo pseudo pseudo pseudo conducted autonomous autonomous introducing introducing formulated maxima span span span span span rely perturbations extensions qualitatively curvature decreased age attraction attraction credit credit credit credit credit credit credit credit credit credit softmax softmax phenomenon pose newton newton newton newton newton newton newton proofs restrict restrict acm rithm optimizing tem royal lost kaufman consideration ranges promising difficulties difficulties accepted odd grow interpret occurring fail splitting carry presentations presentations reliably reliably evaluations evaluations performances becker becker irregular encountered ascent ascent ascent sphere captured propagated propagated propagated propagated propagated suggesting repeatedly theoretically correcting propagate propagate dempster dempster assigning assigning lem ics yielded appeared incorporates rubin rubin basin basin tables tables markovian propagating propagating instantiation comparative auxiliary auxiliary stands jacobian constrain quantized gated rithms labs convert challenging met picked rejected confirmed increasingly laird laird alternatives alternatives alternatives alternatives alternatives alternatives universit stuck ward helps sigmoids topologies fiat hyperbolic prefer frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi converging confirm err err err err determinant determinant holmdel optima proposes kirkpatrick kirkpatrick push plateau vanish vanish vanish drastically falling multimodal robustly robustly metropolis vanishing successor durations backwards backwards backwards brought brought montreal subnetwork subnetwork propagates propagates tit replaces linearities subnetworks subnetworks stat italy trick theo hypothetical llx accepts supervision anneal anneal anneal anneal dynam latch latch latch latch yoshua han gem gem gem instantiations cheap contingencies looked patrice awi subsequence vecchi vecchi latched assump tunable tunable successors wit wit gelatt gelatt alterna resistant resistant ern crete markovjan recherche informatique plateaus plateaus preferably multigrid multigrid multigrid multigrid nectivity decoupling mer wards wards cle tricks iim scent informatica retical montrdal universitd prescribes blame blame ilu diffused 
#@Bengio_Y,Frasconi_P,
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural input input input input input input input input input input function function function figure figure figure figure figure figure figure time time time time time time time time time time time set networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output system error error error error state state state state state state state units units units units information information information information problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based case case vector values probability probability probability probability probability probability probability probability parameters noise noise noise weight functions unit unit unit unit unit unit unit recognition recognition recognition recognition approach approach single processing control control local local local local rate patterns optimal optimal optimal form shows shows shows shows signal signal signal signal signal signal simple gaussian gaussian paper paper paper paper net work work work work work task task task task process process process trained trained trained trained problems problems random random random response response similar equation equation equation rule rule rule vectors generalization speech speech speech approximation average average average average average states states states gradient gradient gradient obtained obtained obtained obtained note university university variables computation computation independent independent independent log log log sequence sequence sequence constant constant standard standard computer distance distance science science science phase activation activation machine motion motion press press learn learn learn learn outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample abstract density likelihood likelihood references component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due generated generated parallel parallel parallel tion difference variable classifier rules measure signals part part center bayesian expected expected expected expected equations equations equations equations equations equations equations markov markov markov markov fact probabilities probabilities simulations resulting computed respect sum reinforcement reinforcement potential applications knowledge obtain obtain obtain negative artificial specific specific represented desired desired desired desired define compute distributions motor motor discrete discrete discrete steps steps train modeling department version version joint connectionist responses sequences sequences ai ai equivalent transition transition transition transition transition limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san top effects estimated estimated increase con conditional robot robot entropy product actual processes depends achieved fast fast inverse require require ability easily simulated smaller needed needed coefficients interesting york representing max making bottom minimize produced sources improved improve recent recent advantage takes typical typical period period machines machines machines cognitive cognitive engineering calculated differential differential differential differential differential achieve symmetric interval interval entire grant grant digital wide derivative deterministic hardware flow row greater trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories practice practice taking california variety variety start decrease derivatives acknowledgements boltzmann boltzmann boltzmann boltzmann pro pro transitions belief transform transform densities evaluated evaluated controlled key additive epochs initially assigned activations activations mcclelland mcclelland wij computations refer prob interpreted follow follow notation received consisted intrinsic situations situations presents presents diego put oscillators integral fourier fourier respond applicable applicable ideal combine scaled func statistically gradients gradients gradients implementations logistic multivariate epoch epoch epoch neal neal indicating indicating indicating great diffusion diffusion diffusion diffusion diffusion diffusion diffusion desirable gradually computers mellon carnegie limits limits consistency fed continuously calculating pittsburgh asymmetric asymmetric asymmetric drift drift jth flexibility spontaneous simplify obtaining receiver receiver started governed governed locked jolla fitness fitness environmental partitioned papers consecutive inferred markovian adopt convenience guess sinusoidal options toy oscillating funded continued vii movellan movellan movellan movellan movellan movellan phonemic accumulate loads era cess approached progresses progresses derivations derivations derivations ito spontaneously spontaneously notational owij emitter emitter emitter emitter emitter emitter emitter emitter emitter emitter brownian brownian brownian owi unwanted lai nimh supercomputer sinusoid ita pression judgment aca javier dai 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#@Movellan_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number system system state state state state state state state results results results results results units units units units units units units units information information information information information information problem problem hidden hidden hidden hidden hidden hidden hidden performance performance space space space space space space weights order shown shown shown systems systems systems systems systems systems probability probability probability probability noise weight weight point point point point point single processing processing processing processing processing processing control control control large large local rate optimal optimal inputs inputs form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple gaussian gaussian paper paper net net work work task task task task task task task task task task task methods methods methods fig step step step points points points points process structure structure structure random random random random high response response architecture architecture architecture architecture architecture show show fixed fixed fixed fixed fixed fixed fixed general generalization states states states experiments dimensional result university university university university threshold solution research research research defined found sequence sequence sequence sequence sequence sequence dynamics initial initial initial computer computer computer connections connections node node node node node node node science science science left left left left activation low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine sets maximum maximum range press press position position position position position sample sample abstract applied references stochastic stochastic ieee ieee introduction action complex complex complex complex hand behavior behavior behavior behavior behavior behavior dynamic variance recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search search search search search search tion tion change change complexity complexity assume measure signals signals signals signals signals representations distributed correlation correlation correlation length forward minimum classes ing performed mapping optimization optimization natural feedback artificial artificial artificial artificial artificial artificial artificial artificial constraints connected connected brain brain approaches mit steps steps steps steps contrast connection connection morgan morgan morgan morgan morgan proceedings proceedings proceedings report report report report institute department department technique technique internal advances advances advances advances advances advances represents connectionist connectionist difficult final cambridge directly directly additional limit limit limit limit limit trajectory san san san san san conference determine determine full approximate free pages pages pages pages pages pages pages increase provided finally selected backpropagation biological normal technical technical technical feedforward tested limited limited close assumed supported adaptation square square kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann simulated simulated underlying needed dynamical fully jordan programming structures structures max max making international international international international supervised run run run run run run run added light denotes denotes improved population population population population similarity reported period unsupervised unsupervised calculated works solve studies positions positions generalized grid grid grid grid grid grid grid bounded improvement entire move move move move move move move move touretzky touretzky touretzky touretzky touretzky place place conclusions operator editors editors editors editors editors sutton moody mateo mateo mateo temperature temperature temperature presence cycle cycle cycle california california solid intelligence intelligence turn turn variety user user user start start exist iii derivatives connectivity program program annealing attractor attractor attractor attractor attractor pro generating laboratory ann pruning pruning slightly adding adding applying john operations controlled restricted evolution evolution evolution evolution evolution evolution evolution evolution allowed barto barto dashed epochs add add add initially initially transactions thesis combinations combinations combinations combinations maximize mozer mozer candidate partially structural structural structural structural structural structural structural structural structural structural structural middle middle capable uniformly attractors attractors genetic genetic genetic genetic genetic genetic genetic genetic genetic miller reached graphs graphs induced induced cun cun allowing link link interpreted follow sci gray vary absence giles giles giles giles denker denker reach acknowledgments cowan diego diego parametric parametric collection collection hanson hanson hanson lippmann mass tech links links links links links links links links links links links links behavioral behavioral behavioral behavioral behavioral office workshop workshop workshop workshop removed induction induction coarse editor editor editor editor reading recognizer front algo taylor taylor taylor initialized initialized art epoch ment ground ground cascade cascade cascade cascade mation describing read demonstrates demonstrates sun behaviors relevance lack peter solla solla employ remove rely monotonic parent parent chen chen chen chen shaped damage begins wang wesley wesley acquisition cooper accomplished accomplished addison addison dynamically food food food food food food food food food food food food food food food naval smolensky smolensky loops loops efficacy monotonically guide modifications modifications corner constructive constructive constructive constructive exploring infor published falls introduces becker programs encountered induce induce holland holland uni april pollack pollack pollack pollack pollack pollack pollack pollack tracker tracker tracker tracker fitness fitness fitness fitness repeatedly grants ignore fahlman fahlman fahlman fahlman fahlman empty empty ure ence stork stork break encodes emerge employs failed forced pieces pieces pieces pieces pieces pieces incrementally arbor chapter individuals individuals recurrence alter visited visited deep alternate rithms num num num num num num crossover werbos annealed life life life life fsa fsa unconstrained deleted constructs constructs induces transients architectural moderate fat hassibi hassibi survey christopher evolved finer flows supplied supplied stay exclusively assessment rasmussen rasmussen progressively kirkpatrick kirkpatrick evolving evolving evolving company evolutionary evolutionary evolutionary evolutionary demands creation inducing inducing reviewed charles semantics surgeon prune dyer bidirectional ceedings deleting deleting das publishing lebiere lebiere triple severely generations generations generations ohio ohio ohio ohio ohio delete incident relying extremes perturbing illustrating versity ranked anneal anneal nation solu ant ant ant ant ant ant ant trimming executes executes executes reproduction superfluous vation flowers acti cyber cis sole entails door grained grained vecchi theme skeletonization indebted structurally traversing traversing alternates supplying questionable belew belew pol farmer collects gelatt columbus columbus gan barbara ash ash collins saunders saunders saunders saunders saunders saunders saunders saunders mor omlin omlin whitley whitley unnecessarily trail trail trail 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#@Angeline_P,Pollack_J,Saunders_G,
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#*learning learning learning learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural input data data function function function function function function function function function figure figure figure time time time time time set set set set set set set set set set set set networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm error results results results results results information problem problem problem problem problem problem problem models models performance based vector order systems systems values values values values values values values probability parameters noise noise functions functions functions functions distribution distribution recognition recognition recognition method method method pattern pattern pattern point point point point point point point point point point point point point point point point point point image image image image image image image image image image image image image image image image processing local rate test test test analysis matrix matrix matrix matrix matrix matrix matrix form form shows algorithms gaussian visual visual visual visual visual paper small feature feature feature feature work methods methods points points points points points points points points points points points points points points field field features features structure problems problems problems random random random random random similar similar similar representation fixed fixed fixed fixed line vectors images images images images images images images images images images images images images images images images images images general generalization average theory theory theory obtained note experiments experiments experiments dimensional university university threshold variables variables variables variables solution independent log log defined defined defined dynamics dynamics dynamics dynamics dynamics initial initial initial constant standard computer computer terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance science science science science present phase phase phase phase phase phase phase phase phase phase machine object object object sets sets sets sets sets learn learn position sample abstract applied applied applied find find find find find find find find find find find computational properties properties properties properties references stochastic procedure procedure mixture mixture mixture introduction complex statistical generated generated generated generated generated generated generated variance cost tion energy complexity variable lower rules measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure prior center center center center center center previous previous bound type required required required good distributed bayesian expected techniques techniques techniques correlation minimum resulting resulting resulting resulting ing ing tasks total computed computed computed computed respect respect respect respect respect times times mapping factor optimization optimization optimization optimization optimization optimization orientation global global global em em em em em original artificial specific specific specific specific specific specific specific objects determined experimental experimental goal related constraints constraints constraints constraints constraints constraints distributions approaches mit update descent descent descent descent descent descent descent descent descent descent descent descent morgan report report report department department technique technique technique consists exp exp exp exp graph graph graph ai ai maps maps considered domain domain domain domain domain domain domain domain domain domain domain domain domain equivalent equivalent estimates san conference efficient efficient statistics speed vision vision increase produce produce produce produce derived derived derived randomly randomly randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering levels finally finally selected selected iteration iteration constraint constraint technical technical technical describe transformation transformation corresponds finding amount common shape supported theoretical eds journal square square end end cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster degree degree noisy including kaufmann objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective probabilistic probabilistic pairs needed jordan jordan special matching matching matching matching matching uniform database representing call call pre international normalized normalized normalized experts supervised minimize minimize minimize minimize minimize minimize produced run run run run description pair pair separate separate typical similarity apply introduced hierarchical hierarchical inference cognitive varying varying conventional unsupervised unsupervised calculated calculated calculated calculated calculated volume match match converge trans sparse mixtures increased increased increased increased grant grant constructed constructed parts invariant invariant invariant invariant scaling deviation derivative matrices rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop deterministic clusters clusters occurs column column column setting setting starting starting critical critical critical row row row row reduce competitive measures measures measures measures measures measures measures measures measures measures faster mateo taking mechanisms presence physics intelligence labeled min averaged averaged derivatives manner minima annealing annealing annealing annealing annealing derive derive derive derive construct produces solving solving generating laboratory distinct distinct distinct transformations transformations transformations consisting consisting consisting develop adding applying minimization minimization minimization expectation expectation letters expressed expressed reconstruction depending interpretation updated updated updated organizing centers centers centers centers centers centers centers centers centers centers centers centers centered similarly translation translation translation translation translation translation translation translation translation translation converges constants constants partial partial reduces add tracking initially distances distances distances distances distances euclidean figures figures coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate plotted plotted plotted domains domains domains domains partially grammar grammar grammar grammar grammar successfully columns columns determining selecting efficiency uniformly included projections comparing invariance invariance invariance invariance essentially ten fine summary traditional graphs repeated cun cun prob sin sin sin sin running notation bar localization relaxation nips nips giles correspondence correspondence correspondence computes computes computes denker denker maximization maximization jacobs jacobs cowan minimized minimized minimized minimized employed unlike carried powerful essential varied varied hanson optimized accurately accurately fourier matches fashion incremental analytically working phases phases phases phases phases phases phases coarse created created ensure prototype prototype prototype prototype prototype der der greedy initialized indicating rows rows rows cos cos cos analytic glass glass handle straight arc closer easier preprocessing commonly simard simard projected projected acknowledgement beginning begin begin english lowest outer outer outer outer outer outer outer outer outer outer outer outer greatly applies fuzzy fuzzy reflect substantially generic generic formulated formulated formulated formulated operate prototypes prototypes fall incorporating incorporating inherent yuille yuille begins attentional softmax softmax softmax softmax softmax distortion distortion distortion saddle saddle saddle saddle labeling formally lagrange lagrange investigation tation extensive recover recover rotated rotations robotics multipliers multipliers minutes proceeds proceeds held held replacing loops loops occurring occurring unlabeled fail adequate clock grammars hours composition repeat falls mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness iteratively iteratively iteratively respective von overview ascent ascent ascent captured peterson peterson darpa initialize initialize enable iterated membership membership membership membership membership permutation permutation permutation permutation permutation permutation permutation speeds summarize assigns onr divide lem mind yale yale gold gold gold gold maximized maximized recursively employs employs malsburg malsburg workstation avoided avoided reflected clustered eric translated permits inverted proba afosr projecting translations barrier enforce enforce preserve rotating drops increments increments architectural drives remarks tial nested nested nested hoc steven harvard rangarajan rangarajan rangarajan rangarajan seed seed spie amenable amenable deter enforces potts potts tan unnecessary objectives haven yon enforced enforced repeats repeats repeats saved traditionally registration registration reconstructions clocked clocked clocked clus ages initializing xij xij xij xij xij xij calling relied formulating formulating quantifies plied seeds seeds consequent mia mia mia mia mia mia mia jects kosowsky kosowsky raising spe optimizations irrespective mahalanobis memberships memberships memberships succeeding tering laid speeding sgi rota ministic anand bilistic rnj fuzziness fuzziness lagrangians preprocess ust concisely concisely cific proximations parallelization formations kll 
#@Gold_S,Mjolsness_E,Rangarajan_A,
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#*network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function figure figure figure figure figure set set set set set set set set set set set set set networks networks networks networks networks networks networks networks algorithm algorithm algorithm output number number number number number system error error error state state results results results information information problem problem problem problem problem problem problem problem problem based based based space space space space space space space space layer layer layer layer layer case case case vector vector vector vector vector order order shown shown systems values values values probability probability parameters parameters parameters parameters parameters parameters parameters noise noise noise noise functions functions neurons neurons neurons distribution distribution distribution distribution distribution distribution approach approach approach approach approach point point point point image image image image image processing processing processing processing processing rate class matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal shows shows signal signal algorithms algorithms algorithms small small small size size size size size feature feature feature feature work work task methods fig fig fig fig step points points points points points points points features classification process level current structure memory representation representation architecture equation fixed fixed images images images images general general general speech speech parameter real approximation approximation approximation approximation approximation approximation approximation average average average average states theory gradient term term term term term note note activity dimensional dimensional dimensional dimensional university variables variables variables variables variables computation computation solution solution solution solution solution solution solution solution solution solution solution research independent log log log defined constant estimate estimate estimate terms terms distance distance distance distance science present phase low nodes nodes sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press position abstract applied find find find density analog analog properties references references stochastic due due due ieee ieee ieee ieee ieee procedure important important important important context introduction hand estimation estimation estimation estimation estimation estimation statistical statistical generated parallel cost cost cost cost cost cost cost cost energy energy energy energy energy energy energy energy energy energy energy energy complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable assume assume lower lower lower lower lower measure measure measure measure measure measure measure higher higher higher center bound bound bound bound bound cases cases conditions conditions conditions conditions distributed expected expected expected expected equations equations equations equations equations techniques proposed length probabilities probabilities probabilities probabilities errors errors errors errors errors minimum resulting resulting resulting respect respect respect respect respect respect eq means means means means means factor optimization optimization optimization optimization optimization global study original original original original artificial specific specific represented application define determined determined goal constraints distributions brain equal approaches mit larger contrast connection connection loss implementation implementation joint exp exp exp exp exp exp exp scheme scheme maps maps maps maps maps maps maps maps considered framework framework framework framework cambridge cambridge equivalent experiment additional solutions solutions estimates design design design limit limit bit determine efficient choice choice choice choice approximate statistics free free free free free free free free free free world basic increase condition condition derived derived derived derived conditional clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering criterion criterion entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy depends constraint biological associative covariance denote denote denote denote tested fast close close inverse complete stable circuits short nearest nearest common effective supported vlsi vlsi cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster objective probabilistic reduced reduced reduced coefficients coefficients coefficients ratio york special special consistent mode principle principle leads leads normalized supervised frame decay minimize choose sources improved discussed robust robust robust separate strategy quadratic quadratic quadratic quadratic sense inference relevant dimensions varying conventional solve yields yields yields yields yields studies positions chain chain separation generalized channels organization expression expression studied scaling scaling scaling scaling suggests suggests deviation alternative alternative loop clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters hardware hardware conclusion minimal minimal minimal neighbor neighbor depend competitive competitive competitive competitive competitive competitive competitive central central central central central central central central central central central central central central central central interactions interactions measures measures peak asymptotic weak constrained temperature temperature temperature temperature encoding propose physics external reduction assuming variety minimizing start decrease averaged averaged derivatives configuration configuration configuration explicit derive derive derive edges edges produces produces written index index index index index index solving winner winner factors transitions transitions transitions transitions transitions transitions transitions coordinates coordinates coordinates coordinates coordinates coordinates coordinates simultaneously simultaneously simultaneously simultaneously physical physical unique interaction adding gaussians minimization minimization minimization springer implies expectation letters dependence review review reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction communication solved solved variation variation densities organizing organizing organizing organizing organizing organizing centers centers centers centers centers centers approximated partition partition calculation distances distances distances distances assigned kohonen kohonen kohonen topology topology topology topology topology transactions transactions transactions transactions precision precision combinations weighting weighting assignment assignment assignment assignment assignment assignment determines determines determines determines maximize black absolute discussions characterized compression compression compression compression compression compression compression compression efficiency schemes invariance traditional refer interpreted stopping split dis dis dis symmetry gray gray gray gray gray gray gibbs gibbs quantity vary vary usual wavelet wavelet wavelet wavelet minimizes quantization quantization quantization quantization quantization neighboring intrinsic receive modelling parametric perturbation perturbation exponentially optimized optimized optimized optimized optimized optimized optimized optimized optimized optimized optimized rise fashion fashion fashion links mappings variational variational variational variational analytically maximizing maximizing complicated proved analogous neu transmission configurations implementations adjusted prototype prototype singular aspect improving regime finds averages pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise costs costs costs costs costs costs costs costs costs costs costs costs costs derivation analytical adapted caused considerable considerable snr located mation commonly acknowledgement opt optimize demonstrates cybernetics mechanics explained percent fuzzy fuzzy amounts amounts embedded embedded embedded fed treated treated rep prototypes prototypes prototypes prototypes prototypes berlin partitioning partitioning partitioning acoustics acoustics logp germany decreased specifies wesley multidimensional multidimensional multidimensional multidimensional displays distortion distortion distortion distortion distortion distortion distortion distortion distortion distortion phenomenon picture indices indices addison sv assign restriction ratios angular optimizing ordering homogeneous addresses communications ments accepted analogy logarithmic logarithmic mos tishby fail splitting combinatorial generalizes infor embedding embedding embedding embedding embedding contexts codebook negligible topological topological topological topological topological thomas centroid centroid tic membership april permutation permutation compressed schulten schulten entropic ber uniquely preserving preserving preserving tradeoff decomposed assignments constitutes avoided clustered clustered algebraic quantized quantized increment favor subthreshold num shannon impose harder buhmann buhmann buhmann buhmann buhmann buhmann buhmann buhmann buhmann preserve reveal obermayer hofmann hofmann hofmann hofmann signs rose rose rose ritter ritter removes removes covers preserves preserves distortions institut continued solvable establishes establishes rons ters sparsely sparsely andreou andreou quantizer fox vanish contrary informatik gence magazine brackets compromise bonn fixing vanishing penalizes stationarity martinetz favors jenkins imposes unifying plexity theo centroids centroids centroids ities parame manipulations imposing conver occupied amit amit tums boahen stars euclidian euclidian euclidian euclidian euclidian euclidian ministry pared densely emphasizing ogp discard duce quantifies resembling complication penalize mia mia lly chou chou joachim oxi insightful tropy gurewitz faithfully preferably quantizers pouliquen ature reestimation reestimation excessively reestimate tln fuzziness friedrich refered refered levine acterized temper mic interleaves necess unifies 
#@Buhmann_J,Hofmann_T,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural input input input input input input input input input input input data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number system system system error error error results results results results results results results results results results results information information information information information information problem problem problem models hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance space space weights weights weights weights linear linear linear linear linear linear linear layer layer layer layer case case case vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown shown shown systems probability probability probability probability weight weight weight weight neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition method approach pattern pattern pattern pattern pattern pattern pattern pattern point point point image single processing processing processing processing local neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class class class class class class class class class class class class class class class class class class class class class class optimal optimal optimal shows shows shows shows shows signal signal signal signal algorithms visual visual paper paper paper examples feature feature feature feature work task task task step step step step step points features classification classification classification classification classification classification classification classification classification classification classification classification classification process current structure structure structure random random random random random random similar show show show show vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images speech speech speech approximation average obtained obtained obtained note note experiments experiments dimensional dimensional dimensional university research initial initial initial initial initial initial table table standard computer connections science activation range press learn learn learn components outputs outputs outputs sample sample sample abstract find find find density density references due adaptive context introduction effect parallel parallel cost tion classifier classifier classifier classifier classifier classifier classifier classifier rules rules rules measure measure measure measure measure signals signals signals signals prior chosen chosen part previous good good represent represent represent represent represent represent distributed expected make fact fact correct correct correct scale minimum resulting classes classes classes classes classes classes classes classes classes ing ing ing tasks human human multi multi multi performed performed times natural obtain obtain specific samples samples application cross cross cross objects objects goal related distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions power power power mit steps steps accuracy accuracy accuracy update update modeling morgan proceedings department version consists internal code code advances joint joint joint joint joint joint represents represents connectionist final final final final final sequences ai maps experiment directly directly directly directly hinton view curves stage stage stage effects conference conference determine classifiers classifiers classifiers classifiers significant approximate world world world pages pages pages pages pages increase increase con con produce coding derived randomly randomly conditional robot actual actual iteration iteration iteration depends sampling biological biological achieved measured measured measured discussion arbitrary group transformation limited close close close close close corresponds complete finding nearest nearest main instance future easily rumelhart rumelhart rumelhart rumelhart development sensory sensory kaufmann pairs needed consistent trials leads representing details details iterations iterations making making international international supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised depth idea idea minimize minimize choose run run light improved improved improved improve advantage takes introduced moving moving unsupervised unsupervised unsupervised unsupervised unsupervised volume volume volume positions positions parts occur occur extended deviation correctly move move move touretzky setting demonstrate runs runs runs greater reduce competitive competitive competitive competitive competitive competitive editors editors editors performs sound external labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing ica ica ica decrease averaged averaged acoustic question acknowledgements explicit appears derive derive derive label label label label label label label label label label label label missing simultaneously linearly text text consisting agent formation reconstruction stages correlated communication updated labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels fraction showed approximated similarly updates key earlier spaces combining boundaries boundaries boundaries boundaries boundaries initially kohonen kohonen kohonen kohonen kohonen kohonen advantages classified classified david david david figures illustrated maximize mozer tests regular extra mcclelland presentation presentation presentation presentation comparing invariance vowel vowel vowel vowel vowel vowel vowel vowel vowel tend ten receives receives summary refer notice repeated repeated repeated repeated allowing dis lie classify classify classify gray gray minimizes minimizes giles quantization received received received received moves overlapping cowan situations presents presents minimized powerful powerful transformed collection collection experience difficulty difficulty environments hanson limitations accurately preliminary dataset dataset dataset helpful ideas school detectors ideal reliable reliable cognition circles closest closest closest closest closest closest configurations changed versions assumes separated mapped speakers speakers mentioned slowly piecewise piecewise piecewise piecewise piecewise piecewise piecewise trivial derivation defining nowlan nowlan expensive lies comparisons organized constructing mation sounds sounds universal grossberg grossberg grossberg implicit cybernetics cybernetics raw apparent apparent apparent percent reflect elman dark conducted peter autonomous ity weigend fall suited suited marginal marginal marginal marginal marginal marginal marginal marginal gave initialization initialization sensing proportion labeling labeling labeling labeling labeling labeling labeling labeling labeling labeling labeling labeling labeling labeling labeling labeling temporally lvq lvq lvq discovery repre addresses smolensky children occurring unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled belong filled filled vowels vowels vowels vowels vowels repeat started mance separating james respective respective respective codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook induce induce perfor pat originally peterson peterson initialize enable permutation ballard ballard ballard ballard refers erlbaum formant border discovered receiving receiving explorations zipser zipser zipser crossing crossing summer microstructure visually super stork stork stork stork stork personal experiences letting letting pairing pairing robots learnt learnt ijcnn ijcnn pdp approxi ization met paired paired paired paired individually associates misclassified misclassified misclassified book book rochester rochester rochester likewise modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality modality vice vice voronoi modal helps suggestions heading versa versa stephen sees terns hearing hypothesized hypothesized hypothesized bold steven sen substitute modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities modalities placement placement placement placement tended steve wolff derives manual putation sensed borders borders borders borders schneider darker lips strongest topologically dana dana disagreement disagreement disagreement disagreement disagreement disagreement disagreement formants barney barney positioned positioned neighbour lipreading neighbours occuring tributions geoff vised males lighter ric misclassifications misclassifications misclassifications misclassifications misclassifications females quan implausible increas sory sight jeff sensations moo moo unavailable virginia virginia virginia recoding sensation sensation sensation expe greg tabulated levine propriate nately tabulation sequent 
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function figure figure figure time time set set set set set set set set set set set set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output system system error results results information information information information information problem problem problem problem problem problem problem problem models models models models models models models models models hidden performance performance based based based based based based based based space space space weights linear linear vector vector vector vector vector vector vector vector shown systems systems systems values values values values values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters distribution recognition method method approach approach approach approach approach approach approach approach approach approach approach approach approach pattern point point point point point point single single single single single single processing large local patterns patterns analysis analysis class class class class class class class class class matrix inputs inputs form form form form form form shows shows algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper paper paper paper net work work work methods methods methods methods step step step step step step step step step step step step step step step step step step step step points features features features classification classification classification classification classification classification classification classification classification classification process current current current structure problems problems problems problems problems problems problems problems random high high similar similar similar representation representation architecture architecture equation equation equation equation equation equation equation equation section section section line rule images images general general real real real real real real real real real approximation approximation approximation approximation obtained obtained term note note note dimensional dimensional dimensional dimensional result university variables variables variables variables variables variables variables computation computation research research independent log log log log log log log log defined defined target target target estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard terms terms terms terms terms science science presented presented presented presented map present present machine object sets sets sets sets maximum maximum maximum maximum maximum range learn learn learn components components components components components basis abstract applied applied density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component stochastic stochastic ieee important adaptive adaptive adaptive adaptive decision mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical statistical generated generated generated generated generated tion tion variable variable variable variable assume assume assume rules learned part previous multiple binary binary represent tree expected equations make techniques observed observed observed observed classes ing ing ing tasks regression regression regression regression regression regression regression computed sum sum elements mapping means means means made applications applications em em em em em em em em em em em em em em em em em em em em em em obtain samples samples compared application application application application application series compute compute compute goal posterior discrete discrete discrete discrete discrete brain equal equal approaches approaches steps steps train morgan proceedings institute department individual advances joint joint joint joint joint joint joint joint connectionist difficult final exp exp maps considered framework framework framework framework cambridge computing computing computing computing directly hinton solutions solutions estimates estimates estimates estimates estimates san full statistics statistics statistics statistics statistics world estimated estimated estimated estimated basic con derived derived derived weighted conditional conditional conditional conditional conditional conditional conditional conditional clustering clustering developed controller types types product finally sampling sampling simply simply achieved achieved measured discussion covariance covariance normal arbitrary arbitrary group denote inverse inverse inverse inverse inverse assumption complete complete complete complete complete complete surface finding common assumed supported require adaptation easily easily noisy fit probabilistic needed needed reduced unknown unknown jordan jordan jordan jordan jordan jordan jordan jordan interesting testing york york matching principle principle principle call international experts experts experts experts supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised frame added predict architectures discussed advantage takes takes similarity hierarchical trees inference cognitive recently relevant relevant dimensions dimensions dimensions dimensions sufficient sufficient sufficient varying unsupervised unsupervised unsupervised unsupervised calculated tions yields trans mixtures mixtures mixtures mixtures mixtures arm wide matrices generally generally generally generally valued valued valued valued valued valued valued valued competitive editors interactions clear learns mateo taking turn assuming start denoted denoted denoted denoted acknowledgements explicit explicit relation relation relation written perception solving solving solving ways ways estimating estimating estimating estimating estimating estimating label label distinct modeled modeled missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing explicitly linearly involves involves gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians formed expectation expectation expectation expectation expectation expectation expectation expectation expectation yield independently squares squares estimator estimator estimator estimator estimator estimator viewed viewed solved densities densities densities densities densities densities evaluate labels labels labels labels fraction approximations forms soft similarly similarly partition classical convex convex combining fitting iterative generation foundation foundation advantages advantages david assignment assignment sciences discuss maximize maximize priors priors selecting society divided divided literature literature comparing composed traditional heuristic interested classify notation vary michael simplified modular giles computes highest maximization maximization maximization maximization maximization maximization consisted mixing extract extract approximating jacobs jacobs jacobs jacobs jacobs jacobs cowan parametric parametric parametric parametric wiley wiley access relations environments involving estimators replaced hanson helpful school school project applicable applicable combine combine office attributes attributes naturally man spline subsets aspect friedman friedman friedman friedman portion portion noted algo assumes multivariate mixed mixed finds integrate massachusetts cart sensors sensors publishers derivation defining analytic nowlan nowlan independence benchmark lies handle handle sections arise laboratories ion involve involve involve involve involve involve incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete mellon outer summation requiring requiring evaluating carnegie cmu flexible tional readily lack splines operate operate pittsburgh ture ture differs suited adjust enables kinds comments expectations expectations expectations returns tile specifies credit credit yielding ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani tresp tresp tresp sensing proportion writing guarantee databases branches approximates naval flexibility flexibility royal generality fails dealing dealing numerically breiman breiman breiman siemens intuitively intuitive nonparametric nonparametric planar moments substituting utilized utilized den belongs indicator indicator indicator indicator erlbaum hart hart grants ignore dempster dempster dempster dempster dempster dempster stone uci summer largely corporation corporation outline outline rubin rubin rubin kinematics deriving ahmad maximized maximized tween distinction distinction covariances covariances multinomial multinomial mars hillsdale causal arising arising cohn intuition intuition duda duda rithms goals permits denoting disadvantage proba expand laird nonetheless esti esti inverting parametrized rewrite atr exploited simplifies failures mix mix completed argmax argmax bility sake mcdonnell clarity proportions compo substitute substitute deals parti zoubin repository sity robotic ready essence iterating categorical categorical tory cope thc ted derivations pew hij hij hij hij hij hij hij intrinsically fundamentally iris iris iris rela nents superscript substituted substituted pursued puter bernoulli bernoulli bernoulli structuring picks froin froin ponent outlines ponents zij zij zij xlo ogp olshen tain tlx pervised wadsworth marcel dekker ein unconditional occlusions plete ric genera mated mated lihood xii xii xii xii xii xii kauf lends kom titterington specht specht cod incom greyscale mclachlan mclachlan aud lse lse lse lse lse decouple basford basford lxi superscripts coping stoch stoch subvector subvector subvector alx xlc circumvented subvectors 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#@Ghahramani_Z,Jordan_M,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output number number number number number number number number error error error error error results results results results results units units units units information information information information problem problem problem problem hidden performance performance performance performance performance performance performance performance based based based weights weights linear linear linear linear linear case case case vector vector vector vector shown shown shown systems systems systems systems values probability probability probability probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight functions functions functions functions distribution distribution recognition method approach approach pattern pattern point point point processing processing processing large large large test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class class class class optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form shows shows shows shows shows signal signal simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper feature task task task points points features features features features features features features classification classification classification process current trained trained trained trained trained trained problems random random random random random random similar similar show show show equation equation equation equation equation equation equation equation equation equation section section section section rule vectors vectors general generalization parameter parameter real approximation approximation approximation average gradient gradient gradient gradient gradient obtained obtained obtained term term note note result variables variables variables variables variables computation solution solution research research research independent independent independent independent independent log log log log log log log log log log defined found found target target estimate estimate estimate estimate standard prediction prediction left left left presented maximum maximum maximum range learn basis basis basis basis basis basis outputs continuous continuous sample sample abstract back back computational density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due procedure procedure procedure propagation propagation mixture mixture introduction complex hand hand estimation statistical generated variance variance cost tion tion tion change difference difference complexity variable variable variable variable variable variable variable assume assume assume assume classifier lower prior higher center cases cases cases cases cases cases cases required binary bayesian expected equations equations equations equations fact finite finite regression regression regression regression regression respect sum mapping dimension applications knowledge knowledge em em em em em obtain obtain obtain obtain obtain obtain obtain original vol vol specific specific samples samples samples samples true true true true true true true true true compared application cross series define location experimental goal posterior distributions equal mit update update train dependent dependent modeling morgan morgan implementation consists kernel joint joint joint joint represents graph considered considered computing experiment additional additional solutions solutions solutions solutions solutions solutions solutions estimates estimates estimates san san top classifiers requires significant approximate approximate world vision vision give con derived weighted weighted weighted levels entropy processes processes selected normal feedforward feedforward feedforward feedforward increases arbitrary denote denote denote fast assumption corresponds complete complete complete complete complete complete complete complete complete complete stable finding assumed require main eds eds ability makes noisy noisy noisy including including kaufmann kaufmann probabilistic typically underlying underlying underlying account account unknown unknown unknown unknown unknown unknown unknown unknown unknown jordan jordan significantly significantly york special special special special squared numbers normalized bottom description predict denotes improved improved population discussed typical typical introduced strategy include include sense sense sense cognitive relevant dimensions dimensions varying varying approximately calculated volume axis smooth converge address mixtures mixtures mixtures mixtures interval interval sensitive amplitude locally width column setting setting demonstrate half half conclusions conclusions depend central central bayes moody moody mateo mateo integration integration integration assuming assuming relationship relationship relationship averaged scene appears monte carlo plot describes describes tuned vertical recall missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing explicitly physical dimensionality remaining consisting consisting adding gaussians gaussians gaussians gaussians expectation john independently depending stationary solved densities approximated approximated similarly allowed dashed dashed additive measurements sec closed closed closed closed closed valid calculate degrees figures includes includes combinations sciences uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty discuss reason reason aspects importance society computationally computationally included included contained contained interested contribution built notation notation vary giles giles predictor consisted consisted approximating deal cowan cowan wiley transformed access access put replaced hanson hanson integral integral integral integral integral integral dotted dotted analyze predicting ith ith averages slowly formula convolution convolution convolution improves expensive expensive briefly worse reasons satisfied formalism formalism closer mation potentially projected incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete meaning addressed varies percent incorporated incorporated reliability requirement price weigend weigend gen extensions germany germany naive ghahramani ghahramani tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp feasible assign recover approximates approximates jth jth jth royal darken darken siemens siemens siemens siemens attractive resulted affected ylx ylx heuristics substituting substituting substituting infor surprising mental consequences den occlusion gesture sons hart hart alternatively ignore dempster dempster outlined outlined approx corporation rubin rubin ent ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad stands realize duda duda uncertain uncertain uncertain uncertain uncertain uncertain uncertain uncertain uncertain deconvolution deconvolution relate laird laird page page computa status housing prefer attributed agrees hat hat kth neuneier neuneier neuneier neuneier neuneier eral equa equa substitute substitute contributes mill sij sij tells symmetrical sity alto lar palo unobserved rela cient miss substituted substituted tics buntine buntine scribed volker structuring aware miinchen miinchen blur gra sume sume ralph ralph cheap yix alternately validate 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#*network network network learning learning learning learning learning learning learning neural neural neural neural input input input input input input input input input input input input input input data data function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure set set set set set set networks networks training training training training training training algorithm algorithm output output output output output output output number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system results units information problem based based based space space space space space weights weights linear linear linear linear linear linear linear case case case case case case vector vector vector vector order order order order order order order order order order shown shown shown shown systems systems systems systems systems systems values values values noise noise weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution method method approach approach pattern pattern pattern image image processing processing large large large local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form shows signal algorithms algorithms visual paper paper examples examples feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work methods methods methods methods step step features features features features classification classification classification classification classification classification process process process structure structure problems high high response response response response response response response response response response response response response response response similar architecture show show show show show show show show equation line line line rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general parameter parameter real real approximation theory gradient gradient gradient term term term note experiments experiments experiments experiments experiments experiments experiments university university university university computation solution solution solution solution solution solution solution solution solution solution research independent found initial initial table table table table standard computer computer distance distance connections node science direction low low low low low low sets sets sets maximum maximum range learn learn learn learn components components components components components components components nonlinear nonlinear nonlinear abstract applied find find convergence convergence properties properties properties properties properties references references references component component decision introduction hand statistical variance variance variance variance parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel search search search tion tion energy energy energy difference complexity assume assume rules rules measure measure measure measure word learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned higher higher previous type type binary binary binary long conditions equations chip fact techniques techniques techniques techniques proposed proposed correlation correlation correlation correlation correlation correlation length length length length classes classes classes classes tasks total regression computed respect respect respect performed elements optimization optimization optimization optimization optimization optimization global applications applications filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter negative negative negative negative negative negative samples samples samples compared application desired series define perform determined goal related related constraints cortical equal equal equal equal equal power power power comparison contrast contrast support support train dependent report version consists internal difficult considered computing curve curve curve curve curve additional solutions solutions solutions solutions design detection determine statistics statistics statistics statistics world speed vision con produce condition condition derived derived criterion criterion product product product product selected selected iteration iteration iteration simply achieved measured measured measured covariance covariance describe describe describe arbitrary arbitrary arbitrary arbitrary inverse inverse amount amount common assumed supported require main end cluster cluster cluster degree makes makes objective smaller smaller needed needed combination coefficients coefficients technology technology technology block block projection uniform uniform database mode principle leads leads principal principal principal principal principal max filters inhibition normalized normalized normalized normalized supervised supervised supervised magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude idea attention minimize produced directions recent exact robust robust robust typical typical typical typical typical typical similarity lateral apply strategy strategy include include include identical recently sufficient sufficient conventional unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised observations approximately approximately volume works pca pca studies converge achieve diagonal diagonal diagonal definition grant expression lead wide derivative matrices rotation rotation rotation rotation rotation rotation hebbian hebbian sigmoid measures numerical numerical designed clear learns learns learns learns learns hard largest largest largest largest largest largest largest largest largest largest largest reduction solid solid proportional turn selective selective iii derivatives derivatives derivatives acknowledgements relation derive construct produces optical optical primary primary describes laboratory laboratory laboratory stability distinct dept dept dept explicitly coordinates linearly dimensionality angle consisting quality quality quality quality quality quality quality quality quality quality quality quality quality quality quality quality quality quality implies implies extraction extraction extraction extraction extraction extraction extraction extraction extraction select extracted extracted extracted extracted extracted extracted extracted extracted dependence depending communication controlled showed centers centers centers approximated discrimination discrimination discrimination sign sign partial partial partial partial dashed expansion expansion expansion reduces fitting closed valid norm figures thesis combinations formulation formulation color color color color color color color color color eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues batch sciences discuss maximize maximize suitable differ modes identify computations tend tend identity orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal refer notice symmetry classify wave maximization chips chips received principles principles principles principles principles attempt attempt extract extract oriented origin parametric american investigate investigate put replaced hessian hessian dotted preliminary preliminary hall pursuit scalar scalar scalar scalar scalar examine respond tech tech plasticity eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors coefficient opposite motivated defines advanced advanced distinguish variances variances briefly lies sys sys sys easier incorporate choices desirable products products products demonstrates requiring fourth fourth fourth fourth fourth pure pure pure axes embedded red red incorporated span summarized maximizes maximizes incorporating extensions extensions datasets green green lot spectra spectra spectra spectra newton newton uncorrelated cooper cooper linearity linearity optimizing tem suppression rational oja oja oja oja contract observing moments prentice sion corre pat ascent ascent ascent ascent ascent ascent nonlinearities nonlinearities dif belonging belonging steepest steepest steepest steepest eigenvector eigenvector concentration robert divide divide largely maximized tween kurtosis quasi quasi blue 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#*network network network network network learning learning learning learning learning learning model neural neural neural neural input input input input data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number system system system system system error error error error error results results units units problem problem problem problem problem hidden hidden hidden hidden performance based based based linear linear linear linear linear linear linear layer layer layer layer case case case case case vector vector vector order order shown shown shown shown systems values values values values noise noise noise noise noise noise noise unit unit method single single processing processing control control control control control rate matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form shows shows shows shows shows signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms examples small work methods methods points trained structure random random random random random similar similar representation representation representation representation equation equation equation equation equation equation rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors approximation approximation approximation average gradient term note variables variables variables variables computation solution research constant science left left left left left left left presented present sets press learn learn components components components components outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs sample sample abstract applied applied find find find find convergence convergence convergence convergence convergence convergence convergence convergence convergence properties references component component component due ieee important important important important adaptive propagation introduction behavior effect variance variance parallel parallel tion difference rules learned learned learned part theorem theorem represent distributed equations equations equations equations equations equations equations techniques proposed forward forward minimum ing tasks computed computed elements elements elements elements elements elements mapping mapping mapping mapping mapping mapping dimension global applications obtain original samples samples samples samples true define compute compute perform goal related related gain motor motor motor brain mit mit mit update train train descent report words department technique technique internal internal cambridge computing computing computing equivalent equivalent directly hinton curves efficient significant significant approximate approximate approximate approximate pages pages channel channel channel randomly product product selected backpropagation backpropagation depends measured measured arbitrary arbitrary transformation transformation transformation close inverse inverse inverse stable surface proof proof circuits finding finding finding supported theoretical rumelhart rumelhart sensory sensory sensory smaller combination unknown unknown unknown special mode mode leads principal principal produced added predict advantage property property apply include hierarchical cognitive engineering varying varying unsupervised converge converge converge converge converge converge diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal symmetric symmetric generalized generalized generalized generalized generalized generalized generalized generalized williams occur matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices loop generally setting runs hebbian hebbian hebbian hebbian hebbian hebbian operator learns learns learns propose presence largest reduction exist exist relationship averaged averaged averaged averaged attractor suppose appears van van van written describes laboratory laboratory distinct metric simultaneously remaining remaining minimization formed extraction yield national squares transform approximations decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition slow additive additive combining iterative iterative iterative iterative iterative intermediate transactions thesis eigenvalues sciences determines determines determines coupled variations columns columns determining modes modes modes modes modes modes modes computations score situation identity identity orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal write usual computes attempt operating extract approximating approximating approximating approximating minimized minimized graphical graphical respond authors eigenvectors smallest transmission transmission singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular academic switching submitted phd finds plant plant plant plant plant plant plant plant plant plant plant animal rows rows rows track tool drive snr choices choices choices choices acknowledgement author argument reflect double double double double double double double pseudo lms lms lms poorly passed variant pasadena asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric uncorrelated uncorrelated writing oxford oxford narrow null encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder nonzero sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger north widrow widrow widrow widrow arrangement record eigenvector eigenvector grants multiply fellowship transmitted forced forced chapter realize graduate depicts represen memoryless inverting algebra eigen ward cursive autocorrelation autocorrelation jet svd svd svd svd svd svd svd svd svd svd svd svd subtracted propulsion governing vertebrate ignores robotic tations bottleneck bottleneck bottleneck nih enforces defense hoff hoff proceeding decompose behaving proximation invert invert scribed named ire orthogonality grove inverses feedfor bizzi bizzi autonomously ric dur oak graphic accomplishes succeeding wescon depiction conv rts ull terence ptp signify loan loan loan asym uncontrollable uncontrollable nonsymmetric emilio 
#@Sanger_T,
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#*network network network network network network learning learning learning model model model neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure time time time time time time time time time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number error error error error error error error error error error error error error error error error error error error results results results results results results results results results information information hidden hidden hidden performance performance performance based space space space space weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector vector order order order order order shown shown systems systems values parameters functions recognition recognition method approach image image image image image image image image single processing processing local local local local local local local local local local local local local local local local local local local local local test test test test test matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal form form shows shows signal signal signal algorithms algorithms algorithms algorithms paper examples feature feature net work work work task task task cells classification trained trained trained cell cell cell cell cell cell cell cell cell structure structure problems high memory memory response similar representation representation representation representation architecture architecture architecture architecture show show section section line vectors vectors vectors vectors images images images images images images images images images images speech speech speech speech speech speech speech speech speech speech parameter parameter parameter gradient gradient note experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional university computation research research defined defined defined target table table table table table table computer terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance node science science science left presented present present low low nodes nodes nodes nodes nodes nodes frequency sets range press press press components components nonlinear nonlinear outputs continuous sample abstract find computational references component component stochastic ieee ieee ieee introduction statistical statistical search search tion difference lower lower lower lower lower lower measure measure measure measure measure measure measure representations representations chosen higher higher center good long represent represent distributed expected expected expected techniques techniques techniques techniques region proposed errors errors errors errors forward ing simulation respect respect respect multi multi times times times times times regions regions mapping mapping mapping mapping mapping mapping optimization dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension orientation global global global global global global global global study obtain obtain original original original vol artificial relative represented represented represented represented represented provide provide provide provide provide compute compute perform perform perform perform determined experimental experimental experimental experimental goal power steps steps accuracy comparison train train train train train train descent descent nets nets nets nets nets selection selection morgan morgan proceedings institute institute department technique technique technique technique consists consists consists advances advances layers layers layers layers layers layers layers layers maps cambridge cambridge computing directly design limit san stage stage bit conference requires significant approximate free speed pages pages pages pages pages validation validation validation validation validation validation produce produce produce clustering clustering clustering clustering clustering clustering clustering lines lines depends biological associative associative associative associative associative associative associative associative covariance covariance covariance covariance covariance covariance feedforward feedforward describe describe fast fast fast fast fast fast fast fast corresponds complete surface surface implemented supported face pixel fit fit kaufmann reduced reduced coefficients coefficients technology significantly significantly projection projection projection projection projection york database database database mode language principal principal principal principal principal squared squared squared call numbers international normalized magnitude magnitude magnitude minimize choose denotes architectures architectures architectures architectures improve improve directions recent correlations takes reported apply recently engineering dimensions dimensions dimensions dimensions dimensions varying compare compare pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca achieve achieve modified modified generalized improvement storage sensitive expression suggests alternative feed locally hybrid touretzky demonstrate half reduce competitive competitive competitive editors editors central accurate accurate performs moody faster faster faster mateo encoding encoding encoding propose propose reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction drawn solid solid averaged configuration force reference reference reference reference produces produces written index ways multilayer coordinates coordinates coordinates coordinates coordinates coordinates dimensionality slightly extraction expectation john extracted extracted independently reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction decomposition understanding activities partition partition partition slow slow performing reduces construction norm norm norm euclidean euclidean euclidean euclidean euclidean euclidean euclidean faces faces david box activations coordinate perceptrons subspace batch compression compression middle middle encoded divided divided detect computations vowel identity capture summary refer compact compact compact notice decoding induced dis criteria gray gray gray gray gray built built built providing providing minimizes giles quantization quantization quantization leading leading leading approximating acknowledgments cowan trains trains layered poor requirements requirements hanson association accurately lippmann project mse mse authors office referred eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors workshop closest transmission trace singular fisher fisher explored explored explored academic art speakers motivated seconds seconds seconds indicating great rows publishers publishers hyperplane hyperplane scientific scientific calculations lowest lowest lowest patches auto auto auto auto auto auto auto auto auto auto cybernetics researchers conjugate fourth people spoken conducted orders posed posed operate partitioning partitioning summarized achieves gave gave electric utterances merging distortion distortion distortion distortion distortion distortion distortion distortion distortion cor representative newton identifying leen leen leen leen leen leen reconstructed fails air oja oja khz ments ranges ranges ranges proceeds utterance bourlard bourlard north cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell preparation vowels introduces holland centroid centroid darpa darpa recog formant grants tures specification kluwer nition pieces quasi obtains obtains reports realize avoids shaded summarizes graduate dominated eliminating projecting gender spanned covered anal responding suffer grateful elsevier eigen oregon status mea voronoi voronoi voronoi voronoi builds builds emotion todd orthonormal exper optima architec quantizer colleagues prone alto assp encodings encodings encodings encodings encodings encodings encodings encodings encodings magazine twelve stan palo spanning trapped ysis drawbacks incurred incurred timit ogi dard superiority demers demers demers demers demers demers demers demers demers demers desire tributed parentheses neck expects metcalfe metcalfe recon recon recon recon struction portland ordinates ilx dft gersho gersho grayscale gary holons recipes teukolsky hemisphere hemisphere flannery autoassociation incre vetterling kambhatla kambhatla kambhatla kambhatla kambhatla kambhatla trailing trailing iments multistage multistage prohibitive prohibitive kamp kamp submanifold bfgs bfgs bfgs bfgs bfgs reduc swept redundancies redundancies merical lloyd speeded kauffmann kll bottle 
#@Kambhatla_N,Leen_T,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number system system system system error error error error error error error error error error error state state state state state state state results results results results results results results results results results information problem problem problem models models models models models models models models models models models models models models performance performance based based based based based space space space space space space weights weights linear linear linear linear linear linear linear linear linear linear case case case case vector vector vector order order order systems systems systems parameters parameters parameters parameters parameters parameters parameters noise noise weight weight weight weight functions functions functions unit unit distribution method method approach approach approach point point point point point point point point point point point point point point point point processing control control control control control control control control control control large large local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local test test test patterns analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix optimal optimal optimal inputs inputs form form shows shows shows shows algorithms algorithms algorithms simple gaussian gaussian paper small small small small work work work task task task task task task task task task task task task task methods methods methods methods methods methods methods methods methods methods methods fig step step step step step step step points points points points points points points classification process current current current current current trained problems random random high high high high high high high high memory memory memory memory memory memory memory memory memory memory show section section section section section fixed generalization real real real approximation approximation average states theory obtained note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result threshold threshold threshold threshold threshold threshold computation research found dynamics dynamics initial initial initial constant constant constant constant estimate estimate standard distance distance science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left left presented presented presented phase low frequency frequency frequency range press press press press press press learn position position position nonlinear nonlinear nonlinear outputs continuous continuous sample abstract applied applied applied applied computational density density density density density properties properties references procedure procedure important introduction action action action action action action action complex complex complex hand hand hand hand hand hand hand hand estimation behavior behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical effect dynamic generated generated generated variance variance search tion tion difference complexity variable lower measure measure measure measure measure measure learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen chosen higher part center previous bound required good good long long represent represent expected techniques techniques errors errors errors forward forward forward forward scale scale classes ing tasks simulation simulation regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression computed respect respect respect performed performed eq eq eq eq called called elements regions regions regions regions regions regions means factor optimization optimization feedback global global global global global global global global global global applications knowledge knowledge obtain vol vol relative samples true true desired desired desired cross cross cross cross cross cross cross cross cross series perform determined goal goal goal goal goal goal goal related related motor discrete discrete brain approaches approaches mit mit accuracy accuracy accuracy comparison larger larger contrast update support support support support support support modeling modeling modeling modeling selection morgan institute department implementation implementation version version version individual kernel advances final exp exp bias bias bias graph graph ai ai cambridge experiment directly curve curve curve additional trajectory stage stage stage stage efficient statistics statistics statistics statistics statistics world world world world world speed speed speed increase validation validation validation validation validation validation validation give give give con con produce weighted weighted weighted weighted weighted developed developed robot robot robot robot robot robot robot robot robot robot robot bounds area velocity velocity velocity controller controller controller actual provided finally sampling sampling sampling simply achieved achieved arbitrary arbitrary fast limited close corresponds actions actions nearest implemented require eds eds eds journal journal square end ability ability future easily noisy noisy noisy fit fit fit fit fit fit fit fit fit kaufmann reduced account technology technology significantly significantly significantly york york trials trials trials mode operation squared representing pre pre making making frame minimize description property pair robust separate takes typical strategy moving side subset cognitive dimensions dimensions dimensions sufficient works tuning correspond correspond achieve diagonal sparse sparse address definition definition definition definition positions generalized interval interval interval sensitive entire entire constructed horizontal predicted predicted predicted predicted alternative correctly locally locally locally locally locally locally locally locally locally move move demonstrate runs place place place greater reduce conclusions depend tangent tangent tangent measures measures measures performs performs reduction intelligence assuming assuming start exist plane plane averaged introduce force acknowledgements areas van solving plot plot laboratory changing modeled confidence confidence student explicitly explicitly explicitly averaging dimensionality dimensionality remaining slightly scales develop minimization springer springer formed shift quality quality quality quality quality quality quality quality quality quality quality quality select competition choosing national focus controlled updated updated showed soft approximated completely suggested suggested suggested smoothing smoothing additive classical spaces spaces reduces fitting fitting fitting fitting fitting fitting fitting intervals intervals intervals intervals intervals intervals purpose purpose generation initially initially calculate calculate calculate msec foundation foundation foundation query query query query query query query query query advantages faces degrees degrees avoid avoid building exploration exploration exploration exploration exploration exploration exploration exploration exploration contour contour weighting weighting sciences determines illustrated illustrated illustrated automatic neighbors characterized tests tests tests tests tests planning closely closely suitable differ encoded computationally computationally computationally detect build tend essentially essentially traditional quickly quickly repeated strongly moore moore moore contribution sin follow hold sampled sampled board approximating deal tesauro extend cowan law explore origin command parametric american american transformed collection requirements steady humans association association optimized hall rise tech investigated scaled office proper proper affect affect affect examined smallest predicting spline illustrate illustrate created adjusted versions versions obvious portion freedom freedom explored academic multivariate arbitrarily arbitrarily chaotic established massachusetts residual residual site piecewise cos band directed directed directed defining expensive briefly lies lies correction tool tool starts starts starts drive drive implementing implementing tive sites widely day precisely controls ion scientific scientific angles calculations gradually optimize optimize optimize optimize localized bandwidth annual requiring requiring questions questions evaluating collected parameterized leave leave leave leave leave car car car car car car car car car car car car car car car car atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson slower formulated commands outliers requirement controllers berlin perturbations cal serve chose sophisticated unbiased wesley lot contribute contribute shifted shifted representative ear notes forming narrow narrow optimizing recover acts controlling controlling outcome outcome outcome communications air fits fits accepted tools tools tools siemens fan fan fan city hyper hyper hit moment los biased resulted bands bands shifts shifts north exceeds exceeds nonparametric nonparametric nonparametric nonparametric moments continue alspector analyses started started reset falls ensures sion holland von guarantees moved forecasting originally young thin mem ahead storing proximity implicitly interestingly default consecutive fitted fitted metrics ence corporation outline constitute ter vec annals email planes ties tibshirani tibshirani tibshirani tibshirani tibshirani pointed wahba wahba lit german tor experiences experiences imagine adjustment assess assess assess illustration avoids shifting shifting shifting shifting shifting hastie hastie hastie hastie hastie chapman approxi searches convert met relate landscape landscape landscape retain statistic statistic lookup lookup lookup discusses son places det dsp port exploited mini mini experi infinitely unpublished vice architectural architectural architectural architectural architectural lecture versa christopher christopher builds exper pictures accomplish dom hour award calculates mistakes val cally diagnostic diagnostic meeting schaal schaal schaal schaal schaal schaal schaal schaal detects raises ory cur consumption tube tube setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint setpoint compensated constraining dimen goodness creation deter magazine compromise feb modern stick outlier outlier cleveland cleveland cleveland cleveland cleveland lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr lwr rent dyer dyer col cope cope addi hits ues costly costly mountain mountain mountain mountain mountain mountain mountain mountain mountain mountain mountain decompose stems investigator extrapolation assessing assessing assessing assessing assessing assessing assessing mization contributing predic excluded cient coincides terminate graphically repeats sition hands hoeffding ther week tics tics statis statis jumps jumps alexander biasing fur ative myers myers myers unclear throw throw throw correspondingly presidential miiller permitted analogously french behav gression discard stein tain backbone proaches trivially renders stefan stefan duced nique tailed normalizes pointwise regres diction nicely requested sudden gions setpoints setpoints mated redwood eubank casdagli ade maron maron farmer farmer cooperate sional longitudinal deriva ingredient suf suf suf accelerating scholarship devil devil devil devil devil juggling juggling juggling juggling juggling juggling juggling juggling juggling suddenly dation cer dem sidorowich mized mcreynolds mcreynolds thrust multistage effi ction decent fied ine pessimistic cga sticks fion kelso econometrics milllet wold wold irdle mxm mines ficiently ficiently leamed oss dle curacy commitment wix lected jagged trolled fluence vali artifical valida throws throws unfavorable drove inspect tually attaching smoothers simpli rors iment 
#@Atkeson_C,Schaal_S,
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#*network learning learning learning neural neural input data function function function function figure figure figure figure figure time time time time time set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number system system error error error error error error results results results information problem problem problem problem problem performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space linear linear linear case case case vector vector vector vector order order order order order shown shown systems values probability probability distribution recognition recognition recognition recognition recognition recognition method method method approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image large large large large large test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class optimal optimal optimal optimal optimal optimal optimal optimal shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple simple paper paper small task methods methods points classification classification classification classification classification classification classification classification classification classification classification classification process process process process process process process level level current structure structure high high high high high high high memory memory memory representation equation section section section section section section vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images general real approximation approximation approximation average theory note note note experiments experiments dimensional result result result result result threshold threshold threshold threshold computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation solution found initial constant constant table table computer distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance left left left left low machine sets sets maximum maximum range press abstract applied applied applied find find find find computational computational computational computational computational computational references due ieee ieee introduction complex complex complex complex complex complex complex complex complex complex parallel parallel cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search search search search search difference complexity complexity complexity complexity complexity complexity complexity complexity complexity lower lower lower lower measure chosen part previous previous good good good good good tree tree tree tree tree expected make techniques resulting resulting classes ing total total computed computed computed computed computed computed computed computed computed computed computed computed computed computed computed computed computed performed performed times times elements means factor factor optimization optimization optimization dimension made made made knowledge filter filter obtain true compared compared compared application application application compute compute compute compute compute compute determined determined goal accuracy accuracy accuracy larger larger technique consists difficult difficult final final final addition considered computing computing computing computing computing computing computing computing computing additional curves curves san stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage determine determine determine determine efficient efficient efficient efficient efficient efficient efficient upper upper full full full full full choice significant world speed speed speed speed speed basic pages validation validation validation give derived developed types product provided selected selected selected selected nature achieved discussion increases increases increases group transformation transformation transformation transformation limited close finding finding nearest nearest implemented implemented require require main pixel pixel instance instance instance easily makes smaller smaller smaller reduced account unknown unknown unknown unknown unknown unknown unknown unknown unknown interesting character character projection increasing increasing increasing increasing increasing increasing increasing database database database database database database database database representing making early early magnitude magnitude idea idea idea idea combined added improve resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution advantage pair separate element period side side side pixels pixels pixels pixels pixels pixels pixels pixels hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical sense recently sufficient sufficient compare observations observations volume trans evaluation evaluation observation invariant scaling wide alternative locally column column column column setting half half half starting reduce neighbor neighbor tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent accurate accurate accurate accurate faster mateo taking california intelligence labeled decrease decrease averaged averaged groups index solving solving ways changing confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence pruning metric sensitivity sensitivity category transformations transformations remaining remaining easy adding adding implies versus select select decreases decreases choosing depending depending stages stages stages stages stages stages stages stages variation variation transform evaluate approximations decomposition decomposition decomposition approximated approximated sizes completely completely similarly translation digits reasonable reasonable add iterative intermediate distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances filtering filtering filtering filtering filtering filtering filtering filtering filtering filtering euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean advantages classified classified transactions avoid handwritten bell automatic candidate straightforward selecting selecting identified efficiency society computationally included included successful computations projections projections invariance score score score score score score score orthogonal reached reached summary quickly repeated showing split dis dis strategies dot dot dot wavelet wavelet wavelet wavelet quantization computes denker denker denker denker reach consisted consisted subsequent subsequent remain create requirements requirements rapidly involving ideas incremental incremental comparable scores scores hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy phases smallest closest closest closest closest closest closest closest closest closest changed subsets subsets prototype prototype prototype prototype prototype prototype obvious algo separated store simplest simplest defines percentage percentage stop fairly fairly improves improves expensive expensive expensive expensive expensive expensive expensive expensive expensive worse closer closer desirable hyperplane hyperplane products products products laboratories simard simard simard simard simard simard simard simard potentially recognized optimize addressed raw raw raw raw fourth greatly generic leave orders orders passed remove prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes rely measuring ordered suited windows tile leaf wesley extreme lot feasible addison extensive lvq optimizing databases hyperplanes hyperplanes eliminate grows rotations lecun lecun lecun lecun proceed adds adds adds consideration stronger attractive los transforms knn knn evaluations performances mance separating ranging respective negligible perfor perfor pat sides dominant searching searching searching bases extensively executed metrics metrics metrics metrics metrics metrics metrics unchanged multiply multiply yielded maximized recursively recursively recursively rejection hierarchies hierarchies avoided attempted rithms parzen parzen dominated degraded increasingly speedup translations suffer det cube survey hyperbolic crude crude terns multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution orthonormal proportions holmdel thickness resolutions resolutions resolutions wavelets wavelets wavelets ham norms fastest halves halves halves mul problematic ming sorted sorted sorted dist dist dist noticed noticed degrade plotting sixth graphically graphically deformations deformations copied exceeded froin brings news conserved fimction fimction patrice tang inexpensive intro exemplified alamitos puting skip quicker slowest hopcroft hopcroft tances tances nction dozen aud duction processin probab hierar dasarathy dasarathy reused reso putationally mallat mallat proto proto prod formations skipped ici ici chosing 
#@Simard_P,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural data data function function function function function function figure figure figure figure figure figure figure time time time time time set set set set set set set set set set set set set set set set training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number system error error error error error state state state state state state state state state state state state state results results information information information information information problem problem problem models models models models models models models models models models models hidden performance performance based based based based based based based based based based space linear case case case case case vector order order order order order order shown shown values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters noise noise functions distribution distribution distribution distribution recognition recognition recognition recognition pattern point single single large large large large rate test test analysis class class simple paper paper small small small small size size size size task methods methods methods fig fig fig fig fig fig step process process process process process process process process process process level level current trained structure structure structure structure structure random random high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar architecture show show fixed fixed rule speech speech speech speech parameter states states states states states states states states states states states states states states states states states states states states states states states states theory theory theory obtained term note note result result university computation solution research log log log defined defined defined defined defined found sequence sequence sequence sequence sequence sequence dynamics initial estimate estimate computer distance node node node node node node node node node node node node node node science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left left left present present present nodes nodes nodes nodes nodes nodes nodes temporal temporal machine continuous sample sample sample sample abstract applied applied applied applied applied applied find find properties properties likelihood references stochastic stochastic due ieee ieee context context introduction complex hand hand hand estimation estimation behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical dynamic generated difference difference difference complexity complexity variable variable variable variable variable measure measure measure measure measure measure measure measure prior learned learned part center cases cases multiple good good good good binary long long long long long long long represent represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov fact proposed length length length length length length length length length length length length length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities scale scale scale finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite total human human respect multi multi called called called called called called regions regions means potential potential natural natural natural natural natural natural natural applications knowledge original original original vol relative true compared desired define related related distributions power power power power power accuracy accuracy larger support source source source source source source modeling modeling modeling modeling modeling modeling modeling modeling modeling institute consists internal internal final final final sequences sequences sequences sequences equivalent equivalent equivalent transition transition transition transition transition top top top stage stage stage efficient efficient efficient full requires requires significant statistics free free free free free free estimated produce condition coding coding conditional types lines lines entropy path processes processes processes processes processes processes nature measured measured arbitrary arbitrary denote denote denote denote denote denote denote denote tested tested hmm hmm hmm hmm hmm hmm transformation close corresponds proof short short short short short theoretical require main end ability future degree noisy noisy including probabilistic probabilistic pairs smaller needed programming testing character york edge increasing mechanism special structures empirical empirical empirical empirical language language language language language language language language language language language call normalized bottom bottom bottom depth depth polynomial idea attention produced run run added added description predict correlations correlations property property property property typical practical apply machines machines hierarchical trees trees trees trees sense calculated tuning trans trans definition definition symmetric modified modified observation observation observation observation bounded bounded bounded bounded bounded bounded bounded bounded exists exists extended generally demonstrate demonstrate demonstrate runs starting starting starting conclusions measures measures accurate accurate exponential propose propose propose taking labeled labeled labeled labeled labeled labeled labeled labeled assuming minimizing start manner base base base denoted denoted denoted denoted denoted denoted appears edges edges edges edges written ways estimating transitions transitions ann ann mathematical changing segments implement slightly slightly slightly slightly text text text text text text text text text text text text text unique scales scales scales scales consisting consisting adding applying springer letters stationary stationary communication viewed transform lee similarly key dashed dashed reduces roughly add add add sufficiently sufficiently string string string string string string string string string string string string string string string string string string string string string string string symbol symbol symbol symbol symbol symbol symbol construction foundation david avoid building includes strings strings strings strings strings strings strings strings strings strings strings strings strings strings plotted plotted prove specifically specifically candidate candidate discussions characterized successfully simplicity reason reason letter letter closely uniformly differ maximal effectively effectively symbols symbols symbols symbols symbols build identity identity reached reached characteristic capture capture capture capture refer compact compact verlag kind kind kind kind kind decoding induced induced interested interested superior built satisfy involved providing giles cat automatically approximating software carried powerful wiley requirements replaced divergence divergence divergence divergence divergence divergence helpful tech root root root comparable comparable proper proper complicated complicated statistically statistically notion notion notion naturally integer predicting predicting automata automata automata automata automata automata automata automata created obvious obvious generates generates finds years theoretic derivation growing caused correction correction organized precisely leaves leaves leaves leaves leaves leaves probable probable universal universal english english depicted depicted depicted depicted depicted depicted tional haussler haussler remove rep requirement calculating differs differs gen parent parent singer singer singer singer leaf leaf leaf yielding yielding yielding yielding instantaneous instantaneous cor corrupted corrupted corrupted redundant labeling labeling labeling labeling labeling equivalence pick optimizing branches impossible impossible outcome outcome extending systematic kullback kullback kullback chains difficulties tools satisfying automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton automaton check handwriting grow grow resulted resulted tishby tishby tishby tishby star observing observing observing observing definitions belong krogh krogh alphabet alphabet alphabet alphabet alphabet alphabet continue schapire iteratively equals expanded lengths laplace initialize israel mem mem kearns belonging belonging captures captures parents counts empty empty empty speaking suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix appeared appeared land land land dna dna dna dna dna dna rigorous constitute shorter ber markovian convenience freund constitutes letting unseen ibm deep genes gained toy num expand altered scope investigating names constructs reveal son sta induces induces induces bring bring bring completed walk walk info sees adaptively bold bold err err ron ron ron ron ron rissanen rissanen neglect tuple sym seed seed poly outgoing outgoing att ory ory syntactic assp longest crl decoded decoded surprise surprise surprise manual addi predetermined jerusalem hebrew plotting cient tag grown ucsc ucsc dana prefix prefix prefix prefix prefix prefix prefix ending succession blank blank cleaning cleaning acknowledgment earth earth earth earth earth earth earth gat notations lhe lhe lhe absolutely cleaned predictability lan walks nll nll nll tistical liebler liebler yoram gathering gathering gathering fruit fruit fruit fruit fruit fruit anders grass grass grass conventionally spelling aca dry dry dry deepest deepest deepest weigh coli coli coli coli coli coli acquiring cga jelinek stoc recurslye guage tat amnesia amnesia amnesia amnesia amnesia naftali ancestor erate isl appearances bol suffixes suffixes rupted xex nomial tracting 
#@Ron_D,Singer_Y,Tishby_N,
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#*learning learning learning learning learning learning learning learning learning learning learning learning neural neural input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number number number number number number number number error error error state state results results results results results results results results information performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space space space space space space space space shown shown shown shown systems values values values values values values values values values values values values values values values values values values values values values values values values values values values parameters noise noise noise noise noise noise noise distribution method method method method method method method method method method pattern pattern pattern pattern pattern single single single single single single single large large local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class class class class class class class class class class class class class class class class class class optimal shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper examples examples examples examples examples examples size size net work work task task methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods points points points points features features features features features features features features features classification classification classification classification classification classification classification classification classification level level trained memory similar similar similar similar show show section line line line line generalization parameter parameter parameter parameter average average average average obtained obtained note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments result university university university computation research initial constant constant table table estimate estimate estimate standard standard standard computer computer computer science presented machine machine machine machine machine machine sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets maximum maximum range range press learn abstract computational computational properties references due due ieee ieee procedure procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive decision introduction behavior statistical parallel parallel difference complexity assume assume classifier classifier classifier lower measure chosen part part cases good distributed make fact techniques correct correct correct correct correct probabilities classes classes classes classes classes tasks tasks tasks tasks total total computed computed computed computed computed computed called times times times regions regions regions means means means global global global global global global global applications applications applications applications applications study em original relative relative specific specific specific specific compared compared compared compared compared compared cross cross cross cross cross cross cross cross cross cross cross compute compute compute perform determined determined determined determined determined determined determined experimental approaches approaches approaches accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison larger larger morgan report report report words department version graph graph graph graph graph domain experiment experiment experiment experiment experiment experiment experiment experiment curve curves curves san top top detection determine determine determine determine determine determine determine determine determine classifiers classifiers significant significant significant significant free estimated basic basic basic validation validation validation validation validation validation validation validation validation validation validation give randomly clustering clustering clustering lines lines lines actual selected evidence depends simply biological measured measured discussion technical technical tested rbf amount nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest assumed supported require require main journal ability instance cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster future makes kaufmann smaller smaller needed reduced account interesting significantly significantly significantly significantly significantly significantly significantly significantly significantly significantly significantly increasing call numbers pre stored stored bottom bottom bottom supervised combined combined combined combined combined combined combined choose run run run discussed discussed advantage advantage separate separate separate separate apply introduced identical identical relevant varying varying varying varying varying varying compare unsupervised approximately approximately solve correspond modified entire entire grant grant constructed constructed constructed constructed constructed constructed constructed constructed constructed constructed constructed constructed constructed constructed constructed constructed parts parts parts parts lead lead alternative correctly correctly locally locally locally locally locally locally locally locally locally clusters clusters clusters clusters clusters clusters clusters generally generally generally runs reduce neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor competitive competitive differences differences differences differences performs performs mateo propose largest characteristics characteristics drawn california california california variety groups groups acknowledgements construct construct solving distinct distinct distinct distinct pruning pruning implement sensitivity category simultaneously physical remaining easy predictive depending variation evaluated evaluated evaluate evaluate evaluate labels labels showed showed lee centers centers sizes sizes sizes sizes sizes performing measurements measurements neighborhood neighborhood neighborhood sufficiently assigned assigned assigned construction query query query query query query query query query query query query query classified classified classified classified classified transactions combinations vapnik domains domains domains domains domains domains domains domains neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors tests reason straightforward straightforward letter letter letter letter letter letter uniformly society modification effectively computations repeated superior superior superior lie classify classify classify classify classify classify classify categories list list list list list vary vary wave computes moves subsequent subsequent bars employed employed remain american collection exhibit helpful fewer comparable comparable comparable proper proper proper statistically statistically attributes attributes attributes attributes extremely ensure subsets subsets subsets queries queries queries versions versions algo separated initialized percentage percentage percentage percentage percentage percentage histogram ment publishers waveform waveform waveform waveform explanation majority majority majority majority glass glass considerable rapid tive tive desirable commonly commonly commonly commonly commonly commonly commonly describing nsf sun researchers improvements varies percent percent led led led led led relevance conducted conducted lack leave leave leave leave leave fall gave conclude comments display display display display display irrelevant irrelevant irrelevant databases databases purely eliminate wrong murphy murphy oja significance iiii methodology belong belong belong belong belong settings knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn knn modifications inferior inferior date mance introduces respective displayed displayed perfor pruned pruned pruned pruned pruned pruned pruned belongs thomas initialize recog recog insight surprisingly ends impact dietterich dietterich dietterich dietterich explains uci outperforms outperforms outperforms ter listed sine sine outperform outperform outperform par classifications classifications weiss weiss spaced classifies classifies penalized penalized rithms searches eliminating paired overhead iri pos covered covered voting voting nasa minor molecules bill experi oregon manuscript stores stores stores lists lists outperformed outperformed bottou bottou val meth meth meth norms repository repository repository frequent ods ods ods irvine irvine irvine twelve twelve cleveland cleveland unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted repetitions repetitions ues cations appli collections neigh iris iris sible adap ames complexities experimentation hypothesize ies indistinguishable periments dam dam tailed stud presumed bor aging ors aha aha aha aha ven recommended recommended flipped flipped complez packard distinguishable ect microsystems hewlett representatives representatives stretched revision dasarathy dasarathy paragraphs attrac wine wine researcher readable rival rival rer rer rer rer recommend prunes consulting fewest corvallis ployed 
#@Dietterich_T,Wettschereck_D,
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#*network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function 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distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method approach point point point point point point processing processing large large large large large test test analysis analysis analysis analysis matrix matrix optimal form form paper small small feature feature net net net net net net net net net net net work work work work methods step points points points points points points points points points points response architecture architecture show equation equation equation equation equation equation equation equation equation section section section section section section section vectors vectors vectors general general generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real approximation average average theory theory theory term term term term term result result result university research research independent log log log log log log defined estimate estimate estimate estimate terms prediction prediction maximum maximum maximum nonlinear outputs abstract back back back convergence density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due due due adaptive decision propagation propagation propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical generated generated generated variance variance tion change change measure measure prior prior prior prior prior prior prior prior prior prior word part previous previous cases multiple multiple good good good good distributed bayesian bayesian bayesian bayesian expected expected make fact region correct errors errors forward finite simulations simulations simulations ing regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect respect respect respect respect respect respect performed optimization dimension dimension natural em em em em em em em em negative negative negative negative negative vol true true cross cross cross cross cross cross cross goal posterior distributions distributions distributions brain comparison comparison comparison comparison nets modeling modeling selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection morgan morgan proceedings institute institute department advances advances exp exp layers considered considered computing equivalent equivalent equivalent equivalent additional view estimates limit efficient efficient full full requires choice choice choice choice choice choice choice choice choice statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics estimated estimated estimated estimated estimated estimated basic pages pages validation validation validation validation validation validation condition condition condition condition randomly conditional criterion criterion provided depends simply discussion discussion discussion discussion covariance covariance normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal denote denote denote denote denote denote close surface predictions proof amount effective supported role theoretical main ability easily degree degree degree degree degree makes noisy fit fit fit fit fit fit fit fit fit fit fit kaufmann kaufmann underlying underlying underlying combination functional technology significantly projection york consistent empirical principle international normalized idea combined choose choose choose choose denotes denotes discussed discussed exact property property robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust takes side sense conventional conventional conventional observations observations observations observations observations calculated calculated tions yields yields yields definition definition definition evaluation generalized bounded bounded bounded bounded bounded derivative generally editors editors editors moody moody asymptotic asymptotic presence physics sigmoidal sigmoidal sigmoidal california regularization denoted estimating estimating estimating ann ann missing missing missing infinite easy springer shift implies expectation yield yield independently squares estimator estimator estimator influence influence influence influence influence influence influence influence influence influence influence influence influence influence influence evaluate forms forms calculation calculation calculation calculation calculation smoothing smoothing iterative iterative penalty penalty calculate expect box thesis weighting weighting extension prove discuss discuss discuss priors tests reason straightforward included mackay situation situation soc soc soc verlag link dis issue sin sin sin criteria criteria criteria criteria criteria write minimizes giles extend cowan body wiley wiley perturbation perturbation perturbation investigate hanson hanson lippmann mass mass rest rest rest mse func func math predicting spline portion portion freedom freedom freedom submitted submitted phd brown brown variances variances variances turns straight tive satisfied arc broad choices acknowledgement implicit author author incomplete meaning nsf robustness robustness robustness robustness robustness robustness detecting outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers popular unbiased unbiased lim extreme lot lot lot corrupted corrupted cooper equivalence kullback kullback fits fits fits dealing consideration significance overcome overcome biased star star star star star star intuitively symposium heavy iteratively surprising holland holland regarded regard regard schwartz infinity roy roy roy grants explains characterization dempster stone stone fitted dramatically liu liu liu liu liu liu liu liu liu rubin achieving leibler leibler wahba flat flat tor stands param cns verified publication publication concentrate deleted laird article fiat tail tail unbounded influenced influenced ers identically usefulness usefulness tribution believed assessment assessment accommodate accommodate goodness akaike akaike outlier aic favors noticed noticed miss abnormal abnormal abnormal abnormal huber tics statis berger jackknife remember chi craven ages conveys providence eter oft estima illustrative illustrative illustrative penalization penalization penalization penalization penalization penalization cre perrone rameter leon sufficiency variate variate cook commun deriva ylz ylz ylz ylz ylz numer upwards leverage statisti balances tending caption improper improper influential erage validatory yil reweighted reweighted reweighted technometrics heavier yla turbation ale 
#@Liu_Y,
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#*network learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input data data data data function function function function function function function function function function function function function function function function figure figure figure set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training output output output output output output output output output output output output output output number number number number state state results information information information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based based space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear layer layer layer layer case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order systems systems systems systems values values values values values values values values values values values values values probability probability probability probability probability probability probability probability weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution distribution image single single single processing large large large large large large local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns analysis analysis analysis analysis class class class matrix matrix matrix matrix optimal form form form form shows shows shows gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper paper small small small small size feature feature feature feature net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net problems random random random random random similar architecture architecture architecture architecture architecture equation equation equation equation section fixed vectors vectors vectors vectors vectors vectors vectors vectors general general general general parameter parameter parameter real real real approximation average theory theory term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term note note note dimensional dimensional dimensional variables variables variables computation solution solution research independent independent independent independent defined defined found found target dynamics constant constant estimate estimate terms terms map map map map map map map map map map map map map map map map map low low low low maximum maximum basis abstract back back find find find find find find density density density likelihood likelihood likelihood likelihood likelihood likelihood references references component component stochastic stochastic due procedure procedure procedure decision decision propagation propagation introduction introduction introduction complex hand effect cost cost cost cost change change difference complexity variable variable variable variable variable assume assume assume assume assume lower lower rules measure measure prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen theorem cases cases good bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian make make make fact fact techniques probabilities finite finite finite finite minimum resulting resulting ing ing regression respect respect respect multi multi multi sum sum elements elements mapping mapping mapping mapping means means means means means means means means factor factor factor dimension dimension dimension dimension made global knowledge original vol true true compute location related posterior posterior brain equal approaches accuracy larger larger larger train dependent nets nets nets nets nets nets nets nets nets nets nets nets modeling selection selection morgan morgan proceedings report report institute words words words version difficult difficult final exp exp exp exp bias bias layers layers scheme addition addition graph framework directly hinton hinton hinton hinton curve curve view curves top effects effects full approximate approximate approximate approximate world world basic con con conditional levels finally selected selected evidence evidence evidence backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation depends measured discussion discussion normal denote assumption assumption assumption assumption assumption assumption corresponds corresponds surface surface surface common assumed theoretical theoretical require eds eds eds square makes kaufmann pairs pairs pairs pairs pairs combination uniform empirical mode mode call pre pre bits bottom supervised magnitude decay decay decay decay decay decay decay decay decay decay attention combined minimize minimize minimize choose added description description architectures architectures architectures exact property pair pair pair pair pair pair pair element practical apply apply include subject identical identical identical identical identical machines sense sense conventional conventional conventional conventional conventional conventional axis axis axis tions correspond diagonal evaluation modified modified modified modified modified modified horizontal horizontal lead lead lead concept suggests suggests suggests suggests suggests derivative derivative matrices alternative alternative alternative alternative feed locally generally row row assumptions assumptions reduce valued valued valued depend depend accurate bayes peak peak peak practice practice practice encoding taking taking strong hard integration proportional turn turn minimizing minimizing start iii introduce derivatives minima acknowledgements pro pro ways ann vertical changing changing changing pruning pruning pruning metric metric explicitly linearly infinite infinite infinite involves easy consisting consisting adding gaussians gaussians quality quality quality letters letters expressed communication viewed densities densities densities densities densities densities densities densities densities evaluated evaluated evaluate evaluate evaluate evaluate evaluate evaluate evaluate soft sign sign partial partial reasonable reasonable reasonable expansion spaces add interpolation valid calculate euclidean euclidean euclidean euclidean euclidean euclidean david david avoid avoid avoid figures figures figures includes priori priori priori illustrated automatic automatic holds simplicity columns columns differ differ differ delta delta modes mackay mackay mackay mackay situation situation identity fine procedures induced induced induced interested dis manifold notation quantity vary vary write usual usual nips denker denker leading leading automatically attempt deal deal situations situations minimized unlike difficulty involving detail estimators estimators estimators estimators estimators hanson hanson integral integral integral accurately hessian hessian hessian hessian biases biases fewer successive giving tech tech applicable applicable working maximizing maximizing tanh tanh tanh tanh tanh tanh tanh workshop affect func neu neu neu induction possibly integer analyze illustrate illustrate implementations ensure singular singular singular singular singular aspect quantities quantities quantities quantities der formal formal noted mapped mapped perceptton consist finds finds neal neal devices mentioned rows rows rows rows slowly variances nowlan nowlan nowlan nowlan correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction starts reasons shared shared precisely choices choices arise arise probable probable probable probable probable probable involve involve implicit begin read arises computers argument argument argument argument argument argument argument argument varies applies empirically empirically leave leave leave peaks backprop backprop backprop backprop orders remove remove incorporated treated treated maintain calculating calculating measuring characterize differs weigend weigend weigend weigend weigend hyperparameters sums kinds kinds kinds kinds wesley sharing sharing sharing irrelevant cor cor don sort addison equivalence equivalence modify modify restrict conditioned impossible grows theories lecun lecun fails adds hope removing removing implications imply affected affected intuitively enhanced enhanced enhanced enhanced enhanced meaningful ensures corre appendix equals equals equals pruned pruned lengths lengths den chooses entries entries refers refers wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert implicitly santa santa characterization insensitive empty speaking mind unchanged ence leaving ple ple ter vec vec stork stork validity validity par mdl personal constitutes constitutes constitutes constitutes tor tor scenario jacobian jacobian jacobian jacobian pub care favor favor favor favor favor exam ftp distri cessing cessing approxi ization searches regularizer expand simplifying depicts depicts singularities singularities singularities singularities regimes integrals win win emphasized lippman det det things things differing coming rarely differently fortunately stimulating hassibi hassibi justification justification justification transforming transforming loaded doesn doesn doesn hid suffices loosely ron determinant concern concern concern incorrectly cast rissanen rissanen affecting affecting rons rons val rare compo compensation concerns push capital tells restricting degenerate resultant relaxed compromise enforces surgeon bear ues favors favors stat gij gij newly nents ohio won won advice treats extrema dependences buntine buntine buntine buntine buntine emulate symmetries symmetries symmetries ixl ixl ixl ixl ixl ixl ixl ixl ixl ixl workers justify rosen diverges absorbing cen reconstructing exclude circumvent accord accord succession kronecker hyperparameter multivariable live ticular ixi ixi ricoh vation gation cis sponds kauffman grained unmodified unmodified unmodified unmodified unmodified iwl iwl iwl iwl iwl iwl iwl iwl iwl iwl iwl iwl unary unary lihood parameterize mations funding absorbed ume favored embed butions pit pit condensed guessing regu crc cancels dirac archive easiest easiest zeroes zeroes zeroes zeroes counteract conventionally cosh compensates rection rection trail designate iol uninteresting encounters ature fixes equate peculiar laborious aren uncorrected ingly isn asterisks hessians hessians redefine confuse sfi sfi sfi tricks backpropa guesses ently pushes pushes iwi bian neuroprose fer samoff redefining absorb parameterizes direcfiy redefinition 
#@Wolpert_D,
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#*network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training output output output output number number number number number error error error error error error error error error error error error error state units units units units units units units units units units units information information problem problem problem problem problem models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer case case case shown shown systems systems values values values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit distribution distribution distribution distribution distribution distribution method approach approach approach single single single large large test test test test analysis analysis optimal inputs inputs form simple simple gaussian gaussian gaussian gaussian paper paper examples small small small net net net net net net points level level level level level level level level level level level level level level level level level level level trained trained random high high architecture architecture architecture architecture architecture architecture architecture architecture architecture section section line line general general general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real approximation approximation approximation average average average states obtained obtained obtained obtained obtained obtained result research log log log log log log log log log log log log log log log log log log log log log log log log log log log log log defined defined defined found dynamics initial estimate estimate standard standard connections connections connections connections connections prediction prediction prediction presented present low maximum maximum maximum maximum maximum maximum range range components components abstract applied back likelihood likelihood likelihood likelihood references component component stochastic due ieee important propagation action action action action action complex generated variance cost cost cost tion assume assume assume lower lower measure prior prior prior prior prior prior prior cases cases good binary bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian make make make make region length correct probabilities errors errors scale scale scale scale minimum total total total total total regression computed computed computed computed computed respect respect sum called called called called times times means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor potential natural study negative vol artificial relative samples compared application application application application application define compute determined determined determined determined determined determined goal posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior connected connected connected connected connected distributions approaches comparison comparison larger larger larger larger contrast connection connection train train nets nets nets morgan institute consists difficult exp exp exp exp bias ai framework framework framework framework framework framework framework equivalent equivalent additional solutions solutions san determine determine statistics free free world increase give con weighted levels levels levels lines product actual selected selected evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence backpropagation backpropagation backpropagation describe group assumption predictions predictions predictions predictions predictions predictions predictions square end instance instance instance makes including including fit fit fit probabilistic typically needed account account account fully principle principle principal principal principal principal details numbers direct early decay decay decay decay decay decay decay decay decay decay decay description light denotes architectures architectures discussed typical practical practical include identical inference inference inference inference compare volume volume volume volume tuning tuning axis tions evaluation symmetric symmetric channels expression suggests extended derivative correctly correctly width measures measures bayes bayes designed mateo integration largest proportional turn assuming groups minima denoted appears relation pro monte carlo factors factors factors describes tuned tuned tuned tuned tuned pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning averaging remaining slightly slightly belief belief belief scales scales scales integrated quality implies select select select select decreases review correlated viewed interpretation detailed fraction approximated margin spectrum spectrum spectrum sign remains valid sufficiently construction topology transactions avoid expect recorded eigenvalues eigenvalues weighting determines illustrated illustrated uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty simplicity simplicity extra differ maximal divided included committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay comparing notice repeated interpreted stopping split superior symmetry symmetry contribution content content content comp giles computes highest highest ill leading automatically approximating modelling modelling modelling extend cowan bars bars bars bars bars bars overfitting varied hanson integral accurately accurately accurately hessian hessian hessian dotted biases rise giving giving root complicated neu generalisation configurations equally changed assumes simplest contributions arbitrarily arbitrarily submitted neal neal band formula formula answer worse perspective purposes choices probable probable probable separately members members members members members meaning integrating integrating argument fourth reflects applies reflect poorly backprop backprop backprop backprop backprop backprop backprop share adjustable formulated differs weigend weigend hyperparameters adjust converged trade trade phenomenon spectra primarily pick optimizing acts acts count theories lost fits analogy familiar ral preparation negligible negligible pruned pruned pruned pruned pruned pruned multiplied express extends extends limitation outlined inferred inferred inferred transmitted sigma gene param pub cessing alternate decays life picked picked meta barrier suffer eters mea mann bution fat fat fat prefer firstly err dominates appealing formulae ning believed sparsely sparsely sparsely sparsely sparsely rameters explanations william adjusts compensated goodness enter enters dence sep sep sep sep stan comprehensive ace permutations approxima ohio minimise conceptually dard respects buntine buntine deduce permuted tot solu justify ponent datum hyperparameter industry renders nected uncertainties uncertainties uncertainties uncertainties uncertainties minimising cis raise combi tunable infrared infrared infrared hans economy committees committees collapse kauf danish wld wld archive sight generalise virtues virtues subjectively evi calibrate compelling evidences evidences attach neuroprose nir underfitting favoured optionally 
#@Thodberg_H,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural input data data data data data data data function function function function function function function function function function time time set set set set set set set networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output error state state results results results results results information information information problem problem problem problem problem problem problem problem problem problem problem models models models hidden performance performance performance performance performance based space space space space space space case vector vector vector vector systems systems values values values values parameters unit recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method method approach approach approach approach approach pattern point point single processing processing large large local local local local local test test class class class class class class class class matrix form shows shows shows shows algorithms algorithms algorithms paper paper examples examples examples size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work task task task task task task methods methods methods methods methods methods methods methods features features features features features features features features features features features features features features features features classification process process process process current trained structure structure high high similar similar similar similar representation show fixed fixed fixed fixed line vectors vectors vectors vectors vectors vectors vectors real approximation approximation gradient gradient gradient note note experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional university computation defined defined found initial initial table table table table standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left direction low low low low low object sets maximum maximum learn learn learn nonlinear abstract applied applied applied find find find find convergence convergence analog properties properties likelihood references positive procedure procedure important important important important adaptive adaptive decision decision propagation propagation mixture context introduction hand hand hand hand dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic tion tion change change change change energy energy energy energy energy learned learned learned learned learned learned learned learned chosen previous bound required required good represent make make make make make techniques techniques region region region proposed correct correct correct correct observed observed errors errors forward forward forward forward scale scale scale classes classes classes ing tasks tasks computed computed computed computed respect respect respect respect respect respect respect respect respect called times regions optimization made orientation orientation em em em obtain artificial specific compared compared application cross cross cross cross cross cross series define compute compute compute compute compute compute objects location location location active active active active active active active active determined determined determined experimental constraints power approaches mit accuracy comparison comparison comparison comparison comparison comparison support descent modeling selection morgan morgan technique consists internal internal advances advances difficult difficult difficult difficult difficult final final addition addition addition graph graph graph graph graph considered cambridge computing computing design design design design design design san san san stimuli effects determine determine efficient full approximate approximate validation validation validation give give con developed selected selected selected backpropagation backpropagation iteration iteration iteration depends constraint constraint constraint constraint constraint measured measured measured describe describe describe describe group transformation close assumption assumption corresponds surface surface surface surface surface predictions predictions predictions predictions predictions predictions finding nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest common shape shape shape eds eds journal square ability ability hypothesis development including fit kaufmann kaufmann typically underlying unknown technology testing character character character character character character character character structures structures principal details iterations iterations max supervised supervised frame frame minimize choose added predict predict predict separate apply moving side side subset subset dimensions sufficient highly highly varying compare previously works studies converge chain improvement studied invariant invariant invariant invariant invariant scaling rotation rotation rotation rotation predicted predicted predicted predicted predicted predicted feed feed feed generally column starting starting critical critical neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor valued depend depend depend depend tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent interactions interactions interactions sigmoid accurate accurate accurate moody practice learns mateo mateo taking strong hard mechanisms drawn intelligence minimizing start exist min plane plane introduce characters minima minima force reference reference suppose digit digit van produces written written optical laboratory label metric multilayer coordinates simultaneously physical physical unique select john john yield choosing extracted extracted family focus review review communication viewed viewed viewed densities showed activities translation translation translation translation digits digits digits allowed discrimination discrimination reasonable performing performing initially distances assigned norm euclidean euclidean euclidean euclidean david degrees degrees existing existing existing template template handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten maximize neighbors structural structural selecting identify identify identify identify computations invariance invariance situation identity capture soc quickly graphs graphs contained contained cun cun prob heuristic dis dis dis superior superior manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold criteria gray receptor usual giles computes denker denker denker denker denker denker highest binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding subsequent extract approximating camera cowan requirements difficulty put hanson hanson lippmann dual giving project relationships authors func analogous neu act possibly predicting predicting equally changed der assumes freedom freedom shapes art simplest contributions submitted submitted attempts site site site site site site site site site site site defining growing fairly expensive briefly benchmark comparisons perspective formalism shared sites producing constructing pool pool pool pool simard simard simard simard simard simard simard acknowledgement describing localized arises arises arises demonstrates demonstrates geometry recognizing preceding alignment people percent percent prop prop prop prop prop prop prop applies collected substantially substantially substantially understood tional axes embedded poorly effort posed share employ employ incorporated variant compares compares exhibits synthesis rely maximizes maximizes gave richard substantial logical kinds attraction simultaneous displays pose pose pose pose pose pose pose pose pose pose pose pose pose pose pose pose pose pose pose pose picture ordinary aligned feasible labelled odor odor odor odor odor odor odor addresses addresses discover tem lecun lecun lecun lecun rigid adds dealing held chemical chemical chemical ral guide guide exceeds composition published excellent iteratively iteratively displayed ascent searching thomas chooses francisco belonging park dietterich dietterich dietterich dietterich dietterich fold fold fold lem discriminate discriminate outperforms approx slight slight corporation corporation corporation corporation planes super uniquely diverse forced poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses poses adopt adopt exception ideally personal superimposed guess molecular molecular molecular molecular molecular molecular auxiliary jacobian mutually invariances exam community chapman chapman chapman manifolds manifolds manifolds manifolds manifolds manifolds manifolds ocr convert regularizer efforts efforts efforts plate suffer siam induces permit molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules drops holding holding oregon inactive inactive inactive deletion argmax remarks recogni tial synthesized hundreds suite hypothesized aid exper accomplish jain jain jain jain jain jain jain jain jain jain jain incorrectly kinematic concerns thickness ally ples judged bond bond bond bond bond bond bond ray meth meth digitized cur tance tance tance safe ods ods senses molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule south vicinity enforces bauer bauer bauer focusing focusing cyclic translates translates translates translate skeleton energies tens discriminating addi dist dist rotate resemble resemble resemble drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug drug searched excluded save bio weakness impor complications walker walker bonds bonds opportunity mike tant bind ross iterates deformed poten deformable positioned george namic compound amples concluding katz proaches conducting visualizing victorri victorri lozano lozano lozano lozano lozano chemistry chemistry vised iden rotates rotates rotates traced formalize ford standardized standardized standardized mations charged optimizations ject atom atom conformation conformation conformation conformation attains binds iments roger acta intersects money permitting cease fujita fujita perez perez perez perez perez pergamon tally discrimi barr sensation imitating ellipse pothesis committed rigidly biologists chem tighten exceedingly corvallis rently vlad brad augments blvd troduced iiv accidentally imating 
#@Dietterich_T,Jain_A,Lathrop_R,Lozano-Perez_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data function function function function function function time time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training output output output output output output output number system system system system system system system system system system system system system system system system system error error error error error error error error error error results results results results results results results results results results results results units problem problem problem problem problem models hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based based based based based space space space weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer case case case case vector shown shown systems systems systems systems systems values values values values values values values values values values parameters parameters parameters parameters parameters weight weight weight neurons neurons neurons neurons neurons distribution distribution distribution method method method method approach approach approach approach point point single large large neuron neuron rate rate rate rate rate rate rate test test analysis analysis analysis analysis analysis analysis analysis analysis inputs inputs inputs simple simple simple paper examples examples examples small small small small net net work work work task task task task step step step step points points points trained trained trained trained trained trained trained trained structure structure random memory similar representation representation architecture architecture architecture architecture show rule vectors vectors general general general parameter average average average average obtained obtained obtained obtained term term term term term term term term term term term term term note note note activity result university threshold solution solution solution solution solution solution defined defined found found sequence initial table table table table table table table table table table table table standard standard terms connections connections connections connections connections connections connections science prediction prediction prediction prediction prediction prediction prediction presented presented presented present present sets range range basis continuous abstract applied back back back back find find find find computational convergence references procedure procedure procedure procedure procedure procedure procedure adaptive propagation propagation propagation mixture introduction complex complex complex complex complex complex complex complex complex complex hand statistical statistical variance variance tion complexity complexity variable variable assume chosen chosen higher previous previous cases type type type type multiple good long long long long long long long long conditions represent equations length length correct errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors minimum minimum resulting resulting ing tasks regression regression regression regression regression regression regression regression regression regression performed performed eq eq elements means made applications study study original original original original original original artificial artificial relative true true compared application desired cross series series series series series series series series series series series series series series series series define rates rates rates rates perform perform perform experimental related power steps steps train train train technique connectionist difficult final bias addition equivalent hinton hinton view solutions solutions limit limit efficient free validation produce condition randomly provided nature nature depends constraint simply biological achieved achieved discussion feedforward increases assumption predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions finding short short short short common implemented assumed generate journal journal future future future easily rumelhart rumelhart smaller needed reduced account dynamical functional functional functional functional testing testing significantly increasing principle leads direct direct direct direct normalized normalized idea idea combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined minimize minimize produced choose run run predict predict predict predict perceptron perceptron perceptron perceptron denotes improved improved improve improve improve correlations correlations correlations correlations exact element typical apply strategy include recently sufficient compare tions match correspond correspond correspond correspond differential improvement constructed constructed expression studied deviation deviation predicted predicted predicted alternative alternative alternative demonstrate demonstrate runs starting starting reduce reduce depend numerical designed performs faster faster weak propose propose propose propose propose propose physics reduction reduction sigmoidal sigmoidal sigmoidal sigmoidal minimizing start exist averaged manner question relation relation longer primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary linearly slightly unique gaussians predictive quality quality quality quality implies cycles expressed stages stages stages correlated viewed viewed viewed fraction soft allowed earlier slow performing performing performing expansion expansion reduces roughly add penalty valid string construction construction david degrees expect expect includes includes includes includes includes includes formulation strings holds characterized tests major simplicity selecting selecting capable reached receives soc kind strongly success lie follow comp comp notation vary leading reach predictor predictor predictor trains carried investigate updating school int int combine complicated complicated cognition smallest math closest predicting predicting implementations taylor taylor freedom observe perceptton perceptton nervous improving improving chaotic averages years years mentioned residual residual residual residual ment agreement guaranteed phenomena nowlan nowlan correction correction correction correction correction correction worse worse worse processed sys describing beginning considerably considerably reflect led capability effort remove incorporated compares weigend weigend weigend weigend weigend weigend weigend gen geman geman deviations deviations deviations lim extreme sharing realized secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary labelled eliminate systematic systematic systematic analyzing star disjoint elimination elimination started periods regarded regarded guarantees forecasting israel modelled express horn horn horn horn horn horn correcting alternatively lag lag consecutive consecutive consecutive session break feeding residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals corrected corrected corrected big letting representa modifying gained tems met simplifying worth nonetheless corrections corrections corrections corrections corrections corrections tel tel completed resembles advantageous bienenstock focuses huberman huberman iterating aviv aviv brought modest searched iris dilemma favorably activating ele tong tong nth nth completes refining faculty emphasizes lira gression charac raymond handles cate primed primed primed primed primed raise philosophy doursat yearly uncover sunspots sunspots sunspots sunspots sunspots quoted quoted bined unpredictable equate astronomy advocate chapters beverly sackler cyclical recast ematical collec teristic autoregression 
#@Ginzburg_I,Horn_D,
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural input input input input data function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number error error error error error results results results results results units units units units units units information problem problem models performance performance performance performance performance performance performance performance performance performance performance performance performance weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case order shown shown systems values values values values values values values values values values values values values parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution recognition recognition recognition pattern pattern pattern pattern pattern pattern point point point single single processing processing large large large large large large large large local rate rate rate rate rate rate rate rate rate rate rate rate test test test test patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis optimal shows shows signal algorithms small small small small size size net net work work cells points classification process process process process process trained trained trained problems problems random high high high high high memory memory memory memory memory memory similar architecture architecture architecture show show equation equation equation equation section section section fixed line images general real approximation approximation average average states states states states states states states states theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term result result result threshold computation computation computation computation independent independent found target constant constant constant estimate standard standard standard standard standard standard standard standard standard standard computer distance left left left left left present present activation activation activation activation activation low low machine machine nonlinear abstract applied back back back convergence convergence convergence analog analog analog references stochastic stochastic stochastic stochastic stochastic due ieee ieee ieee ieee ieee procedure important decision propagation propagation propagation propagation introduction hand circuit circuit circuit circuit circuit behavior effect effect effect effect effect effect effect effect effect effect dynamic variance variance variance recurrent tion change change variable variable assume assume assume lower lower rules type required good good binary long long long represent represent chip chip chip chip chip chip make make fact fact fact fact observed forward forward forward forward forward simulations simulations minimum minimum ing computed computed computed respect respect multi sum sum elements mapping means made obtain original original artificial represented represented true compared application application desired provide compute rates rates discrete discrete discrete equal equal power power power power power power power power power power power power power power accuracy comparison larger update update update update update update update train descent descent descent selection morgan morgan morgan loss implementation implementation version technique technique represents final final layers ai ai ai ai considered considered experiment experiment experiment experiment additional view curves design design limit top effects bit bit bit bit bit bit bit bit bit bit bit bit bit full full full full requires requires choice significant speed speed speed speed speed basic area area provided processes backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation depends simply simply measured discussion feedforward feedforward fast fast fast limited limited inverse assumption assumption nearest nearest nearest nearest nearest nearest nearest implemented implemented implemented implemented implemented implemented assumed theoretical require require main end vlsi vlsi vlsi instance instance easily makes makes including fit typically smaller reduced reduced account technology transfer interesting testing testing testing testing significantly character character increasing uniform database operation operation operation operation leads squared numbers numbers numbers stored stored stored bits bits bits bits bits bits bits bits bits bits bits bits bottom bottom magnitude added description architectures discussed resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution robust reported practical introduced introduced introduced introduced introduced identical sufficient sufficient volume converge converge achieve trans trans trans trans evaluation modified modified storage exists digital digital digital deviation deviation deviation deviation deviation deviation deviation derivative derivative derivative derivative derivative derivative derivative derivative derivative touretzky white white boundary generally hardware hardware hardware hardware hardware pass pass pass pass pass pass runs reduce reduce reduce sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid performs faster hard hard largest external external reduction demonstrated proportional proportional assuming decrease decrease digit written written longer factors changing confidence multilayer multilayer multilayer easy easy slightly shift shift shift shift shift shift shift implies depending stages correlated correlated correlated squares viewed influence solved evaluate evaluate operations operations operations operations operations operations operations restricted static completely digits digits updates updates sign sign sign sign sign diagram partial slow slow epochs epochs epochs reduces reduces add add add precision precision precision precision precision precision precision avoid expect handwritten handwritten silicon bell bell batch variations tests middle middle suitable modification divided divided delta computations computations contained cun built simplified simplified backward backward denker reach operating routing poor poor perturbation perturbation requirements circuitry reducing reducing transistor structured comparable comparable affect affect circles gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients editor noted assumes explain explain electronic mentioned asymptotically asymptotically asymptotically histogram histogram histogram histogram histogram histogram piecewise piecewise piecewise piecewise formula derivation analyzed guaranteed improves floating floating capabilities multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication worse considerable lin lin implementing implementing filtered ran worst worst worst transistors transistors arise commonly products products laboratories laboratories simard simard simard simard ion potentially computers depicted depicted depicted depicted recognizing meaning raw researchers researchers researchers summation integrating greatly considerably considerably peter orders slower howard limiting suited sums decreased decreased age age neuro tile tile differentiable summed summed extreme arithmetic uncorrelated benefit aligned summing driving count reaching multipliers multipliers multiplier ranges simplify multiplicative attractive check keeping shifts monotonically affected days filled reliably performances utilized introduces corre negligible negligible negligible negligible negligible surprising perfor regard jackel propagated multiplied multiplied matter executed executed executed executed empty unchanged slight piece boser copy amplitudes jabri jabri quantized verified henderson exponent exponent exponent exponent exponent exponent exponent exponent shifting mhz formance compensate execute hubbard carefully confirmed speedup speedup million denver discretization 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hans minimally orlando wit wit reversals sumption raining speedups dominating rounding rounding rounding rounding rounding dirac dangerous cont aud filnction duction packed titis underestimate vanilla eri discretize xvith xvith tricks discretizing netxvork netxvork rri compromises lyi alu multipli tricky resolu 
#@Graf_H,Simard_P,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time time time time time time set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number system error error error error error error results results results results results results results results results results results results units units units units units units units units units units units information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based space space space space space space space space space space space space space space space space space weights weights weights weights linear layer layer layer layer layer layer case case case vector order order order order shown shown shown shown systems systems systems values values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit recognition method approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern point single single processing processing local local local rate test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class matrix matrix optimal optimal form shows algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian paper paper small small small work task methods points classification classification classification classification classification classification process level level level level level level level level level current trained trained structure structure structure structure structure problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random random similar architecture architecture architecture architecture architecture show show line general speech parameter parameter real average average average average average theory obtained obtained obtained obtained experiments activity result university university threshold research defined defined found found found found found found initial initial initial initial initial initial initial table table table table standard standard standard standard standard standard standard standard computer computer terms terms science science prediction presented presented present phase activation activation activation activation activation activation activation low sets sets sets sets sets range range press position basis basis basis basis basis basis basis outputs sample abstract applied applied applied computational references procedure procedure procedure procedure important important adaptive adaptive decision decision propagation introduction complex hand parallel variable classifier classifier classifier lower measure measure signals representations chosen higher type type type required required required required required required required required required required multiple multiple multiple good good binary tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed fact techniques techniques correct observed classes tasks total multi multi multi multi multi multi multi multi multi multi multi multi multi times times means dimension dimension dimension dimension dimension dimension dimension dimension made natural global study study study study study study study study study original vol vol artificial represented compared compared desired series receptive provide provide active active active active active active active active active active active determined determined determined determined determined determined determined determined approaches mit comparison comparison contrast connection fields train dependent dependent proceedings proceedings proceedings report report report institute department implementation implementation implementation technique technique technique technique technique technique internal internal individual individual individual advances final exp bias bias bias bias bias bias bias bias bias addition addition considered considered cambridge hinton additional solutions solutions design conference determine determine efficient efficient efficient efficient efficient requires world give give produce produce weighted randomly clustering clustering developed levels levels levels bounds area area area area area types types types types actual provided finally finally finally finally backpropagation backpropagation constraint constraint achieved achieved achieved achieved achieved measured discussion technical technical describe inverse inverse inverse corresponds rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf effective effective square rumelhart rumelhart including including underlying reduced dynamical functional jordan mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp interesting increasing mechanism structures structures structures squared iterations iterations iterations making international international added added perceptron perceptron perceptron perceptron perceptron perceptron architectures architectures architectures improved improve improve separate element introduced introduced quadratic quadratic quadratic quadratic quadratic quadratic hierarchical trees trees trees trees relevant interest interest interest interest dimensions dimensions dimensions highly highly varying compare compare calculated calculated calculated calculated studies studies studies studies studies studies studies studies achieve achieve locations modified modified modified modified modified williams williams williams sensitive sensitive exists expression lead studied studied studied deviation wide wide matrices matrices matrices alternative alternative correctly correctly correctly generally runs runs runs conclusion place greater differences moody suggest encoding characteristics characteristics demonstrated radial radial radial radial radial radial averaged derivatives manner manner minima question areas areas reference sensitivity sensitivity remaining slightly consisting gaussians phoneme viewed viewed influence detailed decomposition partition partition partition allowed past calculation classical iterative iterative interpolation valid initially calculate calculate assigned assigned assigned assigned assigned assigned assigned construction euclidean euclidean classified classified classified classified figures assignment activated successfully determining determining determining determining selecting efficiency suitable differ modification computationally divided effectively effectively presentation genetic genetic vowel essentially ten summary traditional compact allowing list involved paradigm highest highest automatically principles attempt attempt consisted deal modelling situations employed employed employed employed employed employed xor xor xor xor xor xor xor access access collection difficulty difficulty rapidly issues behaviour fewer fashion incremental parity parity parity parity parity parity possibility possibility referred root root root root root root comparable comparable proved proved momentum removed examined examined generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation perfect singular singular portion ith ith ith ith ith simplest utility years percentage percentage percentage considerable perspective division mathematics inversion inversion inversion acknowledgement members localized lowest lowest radius radius radius radius geometric geometric substantially empirically empirically led led pseudo pseudo conducted conducted lack share splines requirement calculating partitioning partitioning partitioning branch branch branch parent parent parent gave gave gave gave richard richard conclude leaf diagnosis redundant investigation investigation restriction extensive extensive concerned concerned jth jth encoder encoder encoder encoder encoder encoder encoder royal fails dealing consideration darken difficulties overcome settings settings settings affected exceeds symposium constructive continue published performances financial encountered holland forecasting offers thin thin thin cancer cancer offer arrive arrive impact partitioned partitioned omohundro omohundro omohundro omohundro omohundro omohundro omohundro omohundro adopted adopted adopted adopted parents acknowledge assigning assigning radar outline aston benefits emerge revealed employs centre centre comparative comparative comparative classifications solely england england continues guidance degraded allocated allocated oct plate plate plate increasingly investigating employing employing employing covered alternatives placing investigations retained normalised normalised gauss gratefully lowe lowe lowe resolve satisfactory satisfactory influenced insufficient assistance firstly skin skin shot dcs connects attained attained alan resolved rohwer rohwer inspection centres centres centres centres goodness goodness relaxed positioning feb assessed birmingham renals renals degrade collections iris offered encourage superiority comprises viable confirms responsive webb encouragement fell susceptible diabetes broomhead accelerated minimising bumptrees bumptrees bumptrees subdivided cial establishment iee iee arose discussing radii pth pth pth pth irrespective undertaken malvern carded principally suffered artifi memorandum worthy cfi yaleu macqueen enclosed attract aft eindhoven eindhoven wholly rsre favourably quad whichever 
#@Bostock_R,Harget_A,
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#*network network network learning learning learning learning learning learning learning model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure time time time set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number error error error error error error error error error results results results units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem models performance performance performance performance performance performance based based based based space space space space space space space space space space space weights linear linear linear linear linear vector vector vector vector vector vector order order shown systems values parameters parameters noise noise noise weight functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution method method method method method approach point point point point processing processing large large large large large large large large local local local local local local local local rate rate rate rate rate rate test test analysis analysis optimal optimal optimal form signal algorithms algorithms algorithms algorithms gaussian gaussian paper examples size size size size net net work methods methods methods methods methods methods methods methods methods methods step step step step step step step step step step step points points points points points points classification process process current trained trained structure structure problems problems problems problems problems problems problems memory response show show show show equation equation fixed fixed vectors general general generalization generalization approximation approximation average average average average average average average gradient gradient note note note experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university variables variables variables variables variables variables variables computation solution independent independent independent independent independent independent found initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard computer distance science presented presented presented presented map map map map map map map map map map map map map map map map map map map map map map map map map present present present low range basis nonlinear sample sample sample sample sample sample sample abstract applied applied applied find find find density density density properties references due due due ieee procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction complex hand estimation estimation behavior statistical statistical statistical generated generated tion complexity variable variable variable variable assume measure chosen higher center center center center center center type multiple good good distributed fact fact techniques techniques techniques region proposed observed forward ing total regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect respect called times regions regions regions regions regions regions regions regions regions mapping mapping mapping factor factor optimization dimension dimension dimension dimension dimension made global original original original original original original original original original original original original original samples samples samples true true true compared application provide location location location determined goal constraints discrete equal approaches steps comparison descent dependent modeling department department technique kernel kernel kernel kernel kernel kernel difficult difficult final final final exp exp exp addition maps maps maps maps domain domain equivalent directly additional estimates estimates determine approximate approximate free estimated estimated estimated estimated estimated estimated estimated increase increase produce randomly product actual provided finally iteration iteration nature depends depends associative normal arbitrary arbitrary tested transformation fast surface surface surface surface surface surface surface finding finding rbf nearest implemented easily easily makes makes noisy typically typically typically underlying underlying underlying account account functional unknown unknown unknown unknown coefficients coefficients coefficients projection projection matching matching matching matching matching uniform uniform uniform uniform empirical empirical empirical normalized polynomial produced description improved improve directions recent takes movement movement practical practical practical introduced strategy strategy strategy strategy include include identical trees sense subset recently engineering highly compare volume works works solve solve achieve achieve achieve rl rl positions positions locations locations locations locations locations locations modified modified modified modified modified modified modified modified modified modified modified modified modified modified modified modified modified observation grid interval interval organization organization organization organization organization organization organization sensitive increased suggests suggests deviation derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative rotation locally locally move move move width width generally critical place neighbor neighbor valued depend editors clear performs performs moody constrained constrained constrained presence drawn drawn proportional proportional proportional regularization radial start iii averaged derivatives minima denoted appears pro estimating estimating estimating estimating ann ann tuned tuned mathematical coordinates coordinates coordinates electrical remaining minimization springer springer formed formed formed quality independently viewed influence solved evaluate organizing organizing showed centers centers partition smoothing smoothing smoothing smoothing smoothing additive measurements convex convex fitting fitting neighborhood neighborhood iterative iterative iterative closed interpolation kohonen kohonen kohonen kohonen kohonen kohonen building existing figures coordinate coordinate formulation subspace subspace subspace subspace specifically neighbors neighbors uniformly suitable modification modification effectively effectively driven poggio verlag verlag return sin follow strategies notation involved providing correspondence predictor predictor predictor predictor moves neighboring neighboring neighboring extend rapidly relations recursive recursive analytically reliable statistically matched matched gradients gradients closest closest closest closest spline spline equally implementations friedman friedman algo som som assumes multivariate residual residual residual residual cart piecewise adjacent straight closer closer closer closer organized located commonly controls gradually pure affine flexible flexible splines incorporated summarized summarized achieves achieves adjust age feasible forming investigation rithm girosi approximates flexibility flexibility flexibility darken breiman overcome mail proceeds stated determination familiar biased biased settings responsible guide nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric heuristics falls introduces sion iteratively conjunction topological topological topological topological topological topological topological topological topological topological topological topological initialize considerations considerations border alternatively stone outperforms sine sine sine seek seek spaced spaced mars impose challenging bump employing constructs algebra indication mea handled lowe crude crude telephone hoc practically normalize placement placement placement placement placement placement placement placement placement placement placement placement placement inde wisconsin edition positioning positioning positioning positioning positioning iterate mesh tan refine ceedings pendent fallside parsimonious belmont silverman concise univariate knots knots knots knots knots knots knots knots knots knots knots knots knots knots knots knots knots knots knots knots knot knot knot knot knot knot knot knot knot knot knot knot knot knot knot knot knot knot knot knot knot correspondingly multivariable aver kung olshen critically faithful handles broomhead fimction normalizes regres kamm alternates predictability nel fined regu vladimir loca minnesota minnesota ker pulling pulling minneapolis aud filnction allocates allocates fied interprets piscataway fool modi river technometrics larization mulation smoothers recycled 
#@Cherkassky_V,Najafi_H,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural input input input input input input input input input input input data data data data data data data data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm output output output output output output output output number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information problem problem problem problem problem problem problem problem problem problem problem models models hidden hidden performance performance performance performance based based based based based space space space space space space space weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer case case case case case vector vector vector vector vector vector vector vector shown shown shown systems systems probability parameters functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition method method method method method method method approach approach approach pattern single single single single single single single single processing processing large local local local local local local local local local local local local local local rate test test test test test patterns class class class class class class optimal form shows shows signal signal algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples examples examples examples small small small size net work task task methods methods fig fig fig cells step step step step step points points points points points points points points points points classification classification classification current current current current cell cell cell cell cell cell cell cell structure structure structure structure structure structure structure problems problems problems problems problems high similar similar similar similar architecture fixed fixed rule rule vectors vectors general generalization approximation gradient gradient obtained note experiments dimensional dimensional dimensional dimensional dimensional dimensional result university variables variables variables computation defined defined initial initial initial constant table table standard standard computer distance distance connections science science present present present phase activation activation activation activation low frequency maximum maximum maximum maximum position position position position position position basis basis basis basis basis basis basis basis basis continuous continuous abstract find computational density density density density density references stochastic due procedure procedure important decision decision decision decision propagation introduction behavior dynamic generated change change difference variable variable variable assume classifier lower signals higher higher part center center center center center center center center center center center center center previous cases good good good distributed bayesian expected make make fact techniques region region region region proposed proposed proposed correlation correlation correlation observed observed observed errors errors forward simulations simulations resulting classes classes total simulation regression regression multi sum performed performed called regions regions regions regions regions regions regions means means means factor factor made global global original specific cross receptive compute compute compute compute perform perform perform perform determined determined goal connected connected approaches steps steps steps steps steps comparison larger contrast connection connection connection connection fields fields train descent descent morgan morgan morgan morgan proceedings proceedings institute version version consists consists advances advances connectionist connectionist connectionist difficult final layers scheme scheme cambridge cambridge equivalent directly directly directly hinton hinton estimates san san san san top determine determine determine determine determine determine determine determine approximate approximate basic con derived weighted weighted weighted randomly clustering developed lines lines entropy backpropagation denote denote inverse corresponds nearest nearest common eds eds eds eds adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation square square degree degree makes makes makes makes kaufmann kaufmann kaufmann kaufmann pairs pairs smaller needed fully interesting interesting significantly structures structures structures structures structures structures structures structures matching matching matching matching principle leads leads numbers direct direct direct direct direct direct direct making international international supervised supervised supervised supervised supervised supervised supervised idea minimize choose choose added perceptron denotes denotes improve resolution property pair pair typical reported reported reported reported practical identical subset sejnowski sejnowski sufficient varying conventional unsupervised unsupervised unsupervised unsupervised unsupervised works achieve positions positions positions positions positions positions positions positions positions positions positions exists occur deviation alternative correctly feed locally move touretzky touretzky touretzky touretzky width width width width width reduce neighbor neighbor neighbor neighbor competitive accurate moody moody moody moody learns mateo mateo mateo mateo propose hard hard hard sigmoidal sigmoidal demonstrated demonstrated regularization radial radial radial radial radial radial radial radial radial start plane denoted construct multilayer simultaneously linearly linearly linearly infinite dimensionality dimensionality easy consisting consisting consisting gaussians gaussians cycles cycles cycles choosing communication influence solved restricted updated labels organizing centers centers forms soft similarly constants epochs epochs epochs spaces convex neighborhood neighborhood purpose interpolation interpolation interpolation interpolation sufficiently sufficiently kohonen existing existing existing thesis thesis activations activations perceptrons perceptrons perceptrons activated specifically specifically partially neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors reason reason reason suitable suitable suitable suitable delta delta wij poggio situation vowel tend quickly induced moore lie generalize generalize computes overlapping neighboring essential investigate difficulty lippmann dotted school school incremental incremental incremental investigated stream complicated removed coarse closest necessarily queries aspect mapped consist consist submitted phd mentioned indicating separable separable distinguish publishers publishers growing growing growing growing growing growing growing growing growing adjacent adjacent adapted cascade cascade cascade caused caused benchmark benchmark baum baum baum lies nonlinearity berkeley purposes easier widely constructing choices localized localized localized considerably prop items items items items readily poorly poorly poorly effort peaks peaks continuously frequently robinson robinson robinson gen resource adjust germany chose conclude extreme room girosi girosi count arranged platt platt spiral spiral spiral spiral spiral spiral darken darken darken north constructive constructive eqn eqn connect respective widths holland lang lang topological topological topological topological topological topological topological topological topological topological percepttons percepttons facilitate chooses initialize multiplied matter fahlman fahlman fahlman severe accumulated accumulated accumulated accumulated accumulated accumulated accumulated accumulated spirals spirals spirals summer summer schulten schulten unable covering incrementally personal stem classifies alter clas gas gas distant activate picked insertion insertion insertion insertion insertion insertion harder covered universit algebra simplex article challenge voronoi voronoi voronoi topologies simplification lation institut interpolated interpolated interpolated suffices hull triangles core accumulate accumulate triangulation placement placement placement dent allocating huge awij insert insert insert insert insert insert insert martinetz martinetz terminology amsterdam lebiere lebiere lebiere repeating elaborate inserted inserted inserted simula ular borders borders borders insertions fiir italy icann 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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural input input input input data data data function function function function figure figure figure figure figure figure time time set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results units units information information information problem problem problem problem problem problem problem problem models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based based space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear case vector vector vector vector vector order order order order order order order shown shown shown shown systems systems systems systems probability parameters parameters noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit distribution recognition method method method method method method method method method method approach approach approach pattern pattern pattern pattern pattern point image image single single processing processing processing control control control control control large large large large large large large large large large local local local local local local rate rate test test test test test test test test test test test test test test test test test test patterns patterns class class matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows signal algorithms gaussian gaussian gaussian small small small small net net net net net work task task methods methods methods methods fig fig step step classification classification classification process level level trained trained trained structure problems problems problems problems problems problems problems response show show show show show equation section line vectors vectors vectors general general general general general generalization generalization generalization generalization generalization parameter real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average theory theory theory theory gradient gradient obtained term term term note note note dimensional dimensional dimensional result result result university computation computation solution research log found found found found constant table estimate estimate estimate computer terms terms terms terms distance distance distance science left left left left direction presented phase low low sets range press nonlinear abstract applied applied applied applied back find find computational computational computational computational density references due due due ieee procedure important important important important introduction complex estimation statistical statistical generated cost tion tion change change complexity lower lower lower prior prior chosen higher center bound type required required multiple good long expected fact observed errors errors errors scale simulations simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting ing total total sum sum eq eq eq eq eq eq eq eq elements elements means means dimension dimension study study em obtain obtain original original true compared application cross cross define perform distributions brain brain brain brain brain brain brain brain brain brain brain brain equal voltage voltage steps steps comparison comparison larger larger contrast contrast support support train train dependent source nets morgan morgan morgan proceedings report department version technique technique advances advances advances difficult difficult difficult difficult maps considered computing computing curves san san san san full full full full requires requires choice significant approximate world world basic increase increase increase increase validation validation validation validation validation validation validation validation give weighted randomly criterion criterion bounds entropy entropy actual backpropagation backpropagation constraint simply technical feedforward arbitrary close close inverse inverse inverse inverse corresponds amount common eds eds journal end instance easily makes noisy including including kaufmann kaufmann kaufmann typically typically typically needed reduced reduced reduced functional block interesting significantly consistent empirical empirical leads leads leads leads squared squared squared max international international magnitude magnitude decay produced denotes improved improve exact exact typical include identical sense sense engineering highly highly works yields achieve diagonal diagonal diagonal diagonal diagonal address storage storage storage increased lead lead lead extended wide wide matrices predicted touretzky occurs occurs generally critical reduce reduce reduce reduce conclusions measures measures clear performs practice practice mateo mateo mateo temperature largest largest california assuming variety minimizing user exist derivatives acknowledgements appears factors factors mathematical dept pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning category electrical remaining remaining slightly unique gaussians quality decreases decreases stages updated showed approximations approximations decomposition decomposition decomposition decomposition suggested suggested key epochs classical reduces roughly roughly roughly valid initially norm norm norm norm david expect recorded eigenvalues eigenvalues eigenvalues eigenvalues subspace subspace subspace automatic priors successfully simplicity reason reason reason straightforward differ effectively successful computations comparing comparing reached reached road graphs induced interpreted interpreted stopping stopping lie criteria criteria categories generalize giles giles eigenvalue denker denker cat consisted consisted subsequent modelling extend cowan cowan bars employed explore explore explore simpler powerful poor overfitting overfitting overfitting requirements requirements put hanson hanson hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian recursive hall behaviour fewer fewer reducing fashion authors reliable eigenvectors eigenvectors workshop affect fundamental removed removed saliency saliency hill smallest smallest smallest smallest smallest smallest plausible created equally subsets subsets rank rank algo fisher fisher fisher logic store mentioned great stop stop stop benchmark reasons comparisons comparisons comparisons comparisons comparisons obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs stanford stanford sys widely desirable probable simard simard universal gradually meaning mellon carnegie fuzzy fuzzy led cmu poorly share solla solla continuously incorrect span reaches popular extensions extensions extensions extensions chose decreased damage damage damage damage differentiable differentiable consistently consistently college forming tation restrict rithm lecun lecun lecun lecun kullback dealing proceeds proceeds intelligent keeping scoring scoring scoring removing removing removing removing krogh intuitive generalizes obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd inferior inferior document pruned pruned pruned pruned pruned pruned pruned pruned pruned pruned pruned pruned pruned dominant dominant dominant dominant dominant bad consequences belongs claim francisco informative storing park eqs pearlmutter pearlmutter grants ignore stopped stopped avoiding dividing speaking rms rms approx approx thrun thrun outperform leibler stork stork stork stork stork stork stork stork stork stork stork stork stork employs failed isotropic retraining retraining retraining retraining retraining retraining retraining retraining retraining retraining retraining utilize copy covariances covariances clas avoids avoids diag diag diag interact tems afosr plate conversely hansen breaks sized reveal likewise vanishes permit behaves continually mea demonstrating reinforce hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi suite virtually december loosely industrial kth recursion station meth contrary transpose sity drastically ods nettalk teaching restrictive surgeon surgeon surgeon surgeon surgeon surgeon surgeon surgeon wolff wolff wolff 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output output output output output output output number number number number number number number number number number number number error error error state state state state results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance weights weights layer layer case case case shown systems systems systems systems systems values values values values values values values unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method method method method method method method method method method method method method method approach pattern pattern pattern pattern pattern pattern pattern pattern pattern point processing processing processing processing large large local local rate patterns patterns patterns analysis analysis analysis analysis analysis analysis class class optimal inputs shows simple simple paper paper paper paper small small small small small small small small small size size net net methods process problems problems problems problems problems problems representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture architecture show section section section rule rule rule generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter average theory obtained obtained experiments experiments experiments experiments activity activity activity result university research defined defined defined defined defined defined defined target target initial initial initial initial initial table table table table table standard standard standard distance distance distance connections connections connections connections connections connections connections connections connections science presented present frequency frequency sets maximum maximum press outputs outputs outputs abstract applied applied applied applied applied applied back back back back computational references procedure procedure important important propagation propagation propagation propagation propagation context introduction hand hand hand hand hand statistical generated generated variance variance variance variance variance parallel cost recurrent tion tion change change change energy difference difference rules measure representations representations representations representations representations representations representations representations representations representations multiple multiple multiple good good good good binary conditions conditions conditions represent represent distributed distributed distributed distributed expected expected make proposed observed observed observed observed observed observed forward minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum classes ing ing computed respect respect respect respect respect respect performed called called called called elements means obtain obtain obtain obtain obtain obtain obtain obtain obtain obtain original original original original original original vol vol vol vol vol vol vol artificial specific specific specific samples compared compared compared compared define determined determined experimental mit update update internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances advances advances represents layers layers addition addition addition addition addition considered cambridge equivalent hinton san san san san conference choice significant give give produce coding derived criterion entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy finally finally finally finally backpropagation inhibitory discussion group transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation role main eds eds eds eds easily easily easily objective objective smaller smaller smaller smaller significantly significantly increasing increasing representing call call international normalized attention minimize produced architectures architectures architectures improved improved improved improved improved improved improved improved improved improved improved improved improved improved improved improve improve element similarity introduced moving works works tions solve williams improvement improvement increased increased increased constructed correctly feed touretzky touretzky touretzky conclusion row row reduce competitive competitive competitive competitive competitive differences sigmoid mateo mateo mateo mateo propose strong characteristics characteristics demonstrated minimizing minimizing targets targets targets targets identification identification denoted denoted denoted explicit suppose construct produces laboratory changing changing changing changing explicitly explicitly explicitly easy frequencies frequencies frequencies minimization minimization minimization quality letters letters letters letters interpretation transform transform transform completely generation generation generation generation intermediate intermediate intermediate intermediate intermediate intermediate sufficiently assigned activated activated activated activated activated absolute major divided delta delta mcclelland wij wij detect tend tend ten ten ten ten ten composed composed summary summary kind strongly showing superior strategies automatically minimized minimized minimized minimized minimized minimized minimized employed transformed transformed create create relations respond respond ideas referred referred referred understand understand understand phases examined smallest equally equally perfect changed ith ith ith ith explain explain averages mentioned mentioned briefly briefly producing producing gradually lowest lowest meaning meaning meaning meaning meaning exemplars summation greatly behaviors behaviors behaviors behaviors incorporated rep rep rep rep rep summarized adjust adjust hamming hamming hamming kinds decreased decreased decreased decreased decreased tile extreme japan appropriately appropriately appropriately appropriately appropriately repre turned turned turned turned eliminated interpret interpret obtaining obtaining obtaining roles alphabet hertz ranging den reproduce waves waves creating extensively compressed saad outline sine sine maximized maximized maximized formulate formulate terminals attempted chauvin pdp gener activate playing carefully differentiating transforming exper autoencoder autoencoder autoencoder autoencoder autoencoder hid archi tended creation sentation awij unnecessary dow imum entropies searched impor resentation resentation resentation resentation resentation grossman tant tecture thirty thirty thirty accord owij owij owij unimportant chir succeeded sse sse sse sse iden zky touret finished ovi ovi ain mas tropy complez fifteen fifteen fifteen mizing sachusetts imental interpretability interpretability interpretability sixty sixty minimiza rived 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number number system error error error error state state results results results results results results results results units units units units units units units units units units units units units units units units units units units units units information information information information information information information information problem problem problem problem hidden performance performance performance performance performance performance performance based weights weights weights weights weights weights weights weights weights weights layer layer layer layer case case vector order order order shown shown systems systems systems systems systems values values values values values values values values values values values values weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight neurons neurons neurons neurons neurons unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method approach approach approach processing processing processing processing processing large neuron neuron rate patterns analysis class class matrix optimal optimal inputs inputs algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper paper paper paper examples examples small small small small size size size size size feature net work work task task task task task step step step classification process process current current trained trained trained structure problems problems problems random memory memory representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture show fixed fixed fixed speech speech speech speech speech speech speech speech speech real average average states theory gradient obtained term term result university university computation computation defined found found found sequence sequence sequence sequence initial initial standard standard standard standard standard standard computer computer terms terms node node node science science presented presented present nodes nodes nodes nodes nodes nodes temporal temporal sets maximum maximum press outputs continuous continuous continuous abstract applied applied applied applied applied back back back computational properties properties references component due ieee ieee ieee ieee propagation propagation propagation propagation propagation context context context context context context context context context context context context context context context context context context context context context context context context context context context context introduction behavior statistical statistical statistical parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent complexity variable assume signals prior word previous previous required required required required good good long long distributed fact proposed proposed proposed proposed correlation correlation correlation correlation correlation correlation forward forward forward finite finite simulations simulations simulations minimum resulting resulting tasks tasks simulation simulation multi multi multi multi multi multi sum called times times times times factor made feedback applications knowledge knowledge obtain original artificial specific represented compared compared compared application application provide provide determined related connected brain larger larger contrast update update update update update update update update update update morgan morgan morgan morgan proceedings report institute department implementation internal internal internal internal internal internal advances advances advances advances advances connectionist difficult difficult final layers addition addition sequences sequences directly directly curve curve additional additional additional design san san san san san stage detection conference conference determine determine determine efficient requires requires significant significant significant world speed speed speed increase produce weighted developed area provided provided backpropagation backpropagation backpropagation nature simply discussion normal technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward increases finding short short common role main eds adaptation adaptation journal makes rumelhart development noisy including fit kaufmann kaufmann kaufmann kaufmann typically smaller reduced fully fully fully jordan jordan technology significantly special database database empirical empirical mode mode mode principle operation language principal details stored international international early attention produced produced added added added discussed recent reported reported apply identical cognitive relevant engineering engineering previously previously works speaker studies sparse address improvement storage storage constructed lead studied extended deviation deviation deviation deviation derivative correctly feed feed feed touretzky touretzky touretzky touretzky setting starting depend faster faster practice mateo mateo mateo mateo strong strong reduction start start exist iii manner manner minima identification acoustic acoustic question areas laboratory distinct distinct distinct pruning pruning implement electrical consisting adding extraction cycles decreases decreases national focus depending depending phoneme phoneme phoneme variation evaluated approximations lee converges updates updates updates past past calculation epochs epochs epochs epochs epochs fitting add add add add add boundaries valid initially calculate advantages degrees instances batch batch batch batch automatic partially partially partially partially partially grammar grammar selecting efficiency closely computationally divided effectively mcclelland detect detect summary cun cun heuristic heuristic heuristic phonetic phonetic split criteria giles denker highest leading subsequent extract load receive trains diego requirements rapidly hanson hanson hessian behaviour behaviour fewer school applicable authors referred referred affect neu neu examined examined automata created aspect aspect algo freedom store store epoch baseline detected detected detected detected detected serial mentioned analyzed growing growing majority cascade cascade cascade cascade cascade cascade starts constructing division mation potentially implicit mellon sun researchers prop carnegie empirically elman elman elman elman elman cmu conducted peaks peaks peaks peaks solla detecting frequently maxima maxima maxima maxima maxima maxima maxima maxima ity robinson robinson robinson operate ture spread chen chen chen suited adjust adjust adjust adjust decreased damage eventually consistently redundant rithm jones jones jones jones grows proceed adds adds significance determination grow ral splitting splitting adequate grammars constructive constructive constructive constructive constructive constructive constructive constructive constructive constructive moments infor started contexts contexts ensures regard darpa recog reader erlbaum papers discovered fahlman fahlman fahlman fahlman fahlman fahlman accumulated leaving solves nition jabri jabri jabri jabri hillsdale australia werbos werbos allocated acquired oscillating preserve modality modality modality modality modality modality modality modality indication correlate modal modal nist resolve decided insufficient attempting attempting rons partly automation detects architec modalities modalities modalities resolved nontrivial experienced schreiber maryland cleeremans cleeremans servan rent predetermined stan dow dow lebiere entering entering entering timit timit newly fallside fallside fallside sydney sydney adjustments dard rom copied conflict seemingly retains recur unimportant prevented concluded resolving tri contin erties reber reber uous iden standards manifested duplicated persist marwan conflicts conflicts conflicts conflicts conflicts conflicts conflicts conflicts twofold crease verbal verbal nsw pertaining automate goudreau duplicates piscataway tivation unsuitable criticized disabling disabling elaboration paring narrowing 
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output system system system system system system results information information information problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models hidden hidden hidden performance performance based based based based based based based layer case case case case case vector shown shown shown shown shown systems values values probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise weight weight unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method approach pattern pattern image image image single single single single processing processing processing large local local local analysis class class matrix matrix form form form shows shows algorithms simple gaussian gaussian visual visual visual visual examples examples examples size feature work work methods field features features features classification level level level level level level level level level level level level level level level level level level level level level level level current current trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems random random random random similar similar similar similar representation representation representation representation representation architecture architecture architecture architecture architecture architecture equation line rule rule general general parameter parameter parameter parameter real real real average obtained obtained obtained term term term term note note experiments experiments result university university university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation computation computation research independent independent independent independent independent defined initial initial initial initial estimate computer computer computer computer computer distance distance connections node node node node node node node node node node node node node node node node node node node node node node node node node node node node science science science science science science left present present present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine machine machine object object object object object object object object object object object object object object object object object object object object object object maximum learn learn position position position position position position components components abstract applied applied find find computational density density likelihood references stochastic stochastic stochastic stochastic stochastic due due ieee important mixture mixture mixture mixture mixture context context context context context introduction introduction complex complex complex hand hand estimation statistical effect generated generated generated generated generated generated variance variance parallel parallel cost tion variable assume lower lower lower learned learned learned learned chosen chosen chosen higher higher higher higher higher part part part part part part part part part part part part part part center center type multiple multiple multiple binary binary represent represent represent represent represent represent represent represent represent tree tree tree tree tree tree tree distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian fact techniques techniques proposed proposed proposed proposed proposed correlation correlation correlation correlation length probabilities probabilities probabilities observed observed observed observed observed observed forward forward forward forward scale scale simulations simulations minimum resulting resulting classes human respect performed performed means means optimization made orientation global applications study em em em em em obtain obtain relative relative relative specific represented represented represented represented represented represented true desired provide compute objects objects objects objects objects objects objects objects objects constraints distributions distributions distributions distributions mit dependent nets morgan morgan morgan morgan proceedings proceedings report report report report report report report institute institute institute department department implementation implementation consists consists internal internal code individual individual advances advances advances joint joint joint represents represents represents represents represents represents represents represents represents difficult final exp layers addition addition graph graph graph graph graph graph graph graph graph graph ai considered computing equivalent equivalent directly hinton hinton additional additional estimates estimates san san san san top top top top top top top stage conference efficient efficient requires choice choice statistics world vision vision estimated estimated estimated estimated estimated condition condition condition conditional conditional conditional conditional conditional conditional conditional conditional developed levels levels levels levels criterion lines lines provided backpropagation constraint constraint constraint discussion covariance normal normal normal technical technical technical technical technical describe describe denote denote transformation transformation assumption assumption corresponds finding finding common assumed assumed shape shape shape shape shape supported require eds eds square square ability instance instance instance instance cluster cluster cluster cluster cluster noisy including kaufmann kaufmann kaufmann objective probabilistic probabilistic probabilistic typically pairs account unknown coefficients coefficients coefficients coefficients jordan jordan interesting york structures matching matching matching matching matching principle leads leads representing representing details making making stored stored stored stored stored stored stored international international international bottom experts experts supervised early frame idea idea choose added added description description improved correlations correlations robust typical typical typical reported include subject hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical sense inference inference cognitive engineering engineering interest sufficient previously previously unsupervised unsupervised calculated match match correspond correspond sparse mixtures mixtures positions organization entire entire entire entire entire grant arm arm constructed exists parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts studied studied invariant invariant extended feed feed touretzky touretzky clusters strength starting segment segment valued central central measures designed designed clear performs moody constrained mateo mateo mateo mateo propose hard hard physics exist relationship question acknowledgements reference appears relation digit digit digit construct edges index estimating tuned dept modeled missing sensitivity multilayer explicitly explicitly coordinates coordinates electrical transformations transformations text belief belief unique interaction interaction gaussians applying events focus expressed dependence dependence stages overlap interpretation restricted restricted updated centers centered centered soft approximated convex convex reduces reduces roughly remains valid intermediate intermediate intermediate intermediate intermediate intermediate assigned construction advantages transactions avoid handwritten handwritten box perceptual thesis thesis coordinate coordinate formulation instances instances instances assignment assignment assignment recognize uncertainty mozer mozer holds discussions grammar grammar grammar structural structural structural importance suitable differ presentation literature invariance identity reached composed soc interpreted superior contribution criteria generative generative satisfy dot dot dot dot dot dot absence giles observable observable observable correspondence denker denker denker denker approximating jacobs jacobs deal cowan origin production overfitting hanson lippmann preliminary hall helpful project project relationships relationships scaled decisions structured root workshop hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy notion notion contours contours induction circles concepts plausible traffic traffic implementations prototype prototype generates grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping submitted phd phd attempts inequality pairwise directed publishers publishers publishers independence independence independence independence independence caused spatially berkeley berkeley arc arc arc arc preprocessing constructing constructing constructing leaves arise simard simard potentially angles angles describing optimize lowest lowest lowest lowest lowest lowest lowest author incomplete recognizing exemplars exemplars exemplars exemplars exemplars exemplars robustness reflects reflect freeman led led parameterized treated dots dots prototypes prototypes howard howard summarized parent parent parent parent parent parent parent parent parent cal extensions marginal plan display display yuille yuille leaf leaf semantic sharing benefit cooper cooper cooper cooper assign extensive conditioned conditioned pick recover zemel zemel rotated connecting royal lecun lecun lecun lecun exemplar kaufman difficulties overcome attractive intelligent viewpoint star star star star observing observing reasoning preparation grammars child child child child child child child child spurious prentice recovered mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness ambiguity induce regarded regarded regarded dependency regard jackel jackel elastic augmented belonging belonging captures captures implicitly omohundro omohundro omohundro summarize tures dempster dempster onr verify discriminate yale yale multiplying arcs arcs arcs constitute rubin rubin solves ent leaming recursively uniquely incrementally encouraging boser boser ease mdl reports hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies descriptions descriptions possibilities causal clustered henderson henderson equality pij toy interact grouped grouped grouped graduate hubbard hubbard allocated relating maximally multiscale multiscale pearl pearl pearl pearl pearl pearl pearl pearl laird laird zip accounted preprint rochester knowing refined oregon factored emphasis deletion observables observables stores parameterization reversed distortions compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional compositional reflecting dcs connects sparsely marr marr triangle offsets offsets conditionally conditionally conditionally governing concave concave alto statist locality inducing inducing inducing inducing inducing sparseness sparseness acyclic prominent penalizes suzuki suzuki dij dij palo comprehensive ina ina ina ina ina ina ina ina ina substructures substructures substructures substructures substructures substructures substructures substructures substructures substructures substructures substructures substructures substructures substructures substructures substructures haven coincides deformations ogi ogi utans utans utans utans utans utans utans utans utans utans utans utans utans utans utans utans traversed relying respects accessible concurrently structuring parentheses anandan anandan anandan anandan cse positioned gindi gindi gindi gindi gindi gindi emphasizes emphasizes emphasizes dictated hoped portland encouraged bumptrees departure saund saund manifest ijk dag stolorz 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#@Utans_J,
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#*network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input function function function function function function figure figure figure figure figure figure figure figure figure figure figure time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm output output output output number number system error error error error error error error error error error error error error error error results results units units units units units units information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem models models models models models hidden hidden hidden hidden hidden based based based based based based space space space space weights weights weights weights case case case case order order order order shown shown systems systems probability probability probability probability probability probability parameters parameters parameters parameters weight weight unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method image image image image image image processing processing control control large local local local class matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal form shows shows shows paper paper work methods methods methods field structure show show show show show equation images images images generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter average average theory theory theory theory obtained term term note result university computation log log found found found found found found found dynamics dynamics initial initial initial initial initial initial initial initial initial constant standard distance prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction sample sample abstract applied applied back find find find find convergence density density likelihood likelihood likelihood references ieee ieee positive introduction estimation statistical statistical statistical statistical statistical variance tion complexity chosen chosen part center theorem theorem theorem theorem theorem cases long conditions expected equations fact proposed proposed proposed proposed proposed proposed length errors errors resulting eq eq means optimization optimization optimization optimization optimization optimization dimension made made global original vol vol vol vol vol vol artificial artificial artificial artificial samples samples samples samples samples samples samples samples samples true true true true true true true true true true true true true compared application application application application define define define objects objects active experimental experimental connected connected equal larger descent selection selection selection morgan report loss loss advances advances exp exp exp ai ai ai equivalent equivalent curves san full full statistics speed condition condition coding derived conditional criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion actual selected selected backpropagation discussion normal normal technical arbitrary arbitrary proof common effective effective role theoretical pixel simulated testing testing testing uniform uniform empirical empirical empirical empirical empirical empirical numbers frame decay choose added added description discussed discussed property takes practical practical practical practical subject conventional calculated calculated calculated trans trans background modified modified modified modified modified modified modified generalized generalized exists studied deviation conclusion bayes mateo temperature cycle minimizing minimizing minimizing min identification annealing annealing acknowledgements relation relation pro estimating pruning pruning pruning simultaneously simultaneously simultaneously expectation choosing family family family family family family reconstruction communication estimator estimator converges calculation fitting neighborhood sufficiently sufficiently priori automatic discuss partially discussions essentially ten procedures contained contained contained contained contained contained contained heuristic sin criteria criteria criteria satisfy minimizes minimizes minimizes minimizes ill satisfies satisfies layered layered layered layered layered layered layered optimized optimized optimized optimized biases biases biases tanh affect formal fisher fisher separated perceptton amari asymptotically formula caused tive universal definite author understood understood experimentally experimentally quantitative mod ordered ordered tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile differentiable differentiable ordinary formally modify japan approximates controlling controlling controlling nonzero plays kaufman imaging overcome definitions effectiveness effectiveness forecasting theoretically theoretically steepest annals mdl mdl mdl mdl mdl mdl mdl mdl big rain rain ibm eliminating eliminating esti ation ation thousands mini tail restoration restoration restoration tial ers doesn filler proposes proposes tokyo degenerate degenerate totally est akaike akaike tical watanabe watanabe watanabe watanabe watanabe aic aic aic aic aic aic aic aic aic aic aic aic aic aic thc murata preventing oil ily froin inconsistency lira ricoh ricoh yoshizawa prof prof prof fimction restored restored restored restored selec neurm xve xve famous prac ieice lyl amp nmnber imize dxdy dxdy sinall yokohama yokohama perspec bic bic bic bic mizing ial schwarz ified hess seminar nodel nodel yilxi shin nator eeo ult fignre ahnost ahnost vlx clarifies 
#@Watanabe_S,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural input input input data data data function function function function function function function function time time time time time time time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results information information information information information information information information information information problem problem problem problem problem problem problem models hidden performance performance performance performance performance performance space space space space weights weights weights linear linear linear linear linear linear linear linear layer case case case case vector vector vector vector vector vector vector vector vector vector order order order order order order order order order order order order order shown shown shown systems probability probability probability probability probability probability parameters parameters parameters noise noise weight weight weight weight functions functions neurons neurons neurons neurons neurons distribution distribution distribution approach point point point point point large large large large neuron neuron neuron neuron neuron neuron rate rate rate test analysis analysis analysis class class class matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form shows algorithms simple paper paper paper examples examples examples examples examples examples examples examples small small size size size size size size size size size size size size size size size size size size size size size size size size size size size work methods methods methods process process process process process process process process process process process process process process process process process process process process current trained trained trained trained structure problems random random random random random random random similar show show show show equation equation equation equation equation equation section section section section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed rule vectors vectors vectors general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real real real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory theory theory theory gradient gradient gradient gradient gradient gradient obtained term term term term term note note experiments dimensional dimensional dimensional dimensional result university university variables solution solution research research research research research research independent independent defined defined defined defined defined found found target dynamics dynamics dynamics dynamics initial initial initial initial initial initial constant constant constant estimate standard terms terms distance distance science prediction prediction direction map phase phase phase phase phase phase phase phase phase phase phase phase temporal machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets learn learn basis basis nonlinear nonlinear outputs outputs outputs outputs continuous sample sample sample abstract find find find find find convergence density density density properties properties likelihood likelihood likelihood references stochastic stochastic due positive procedure decision context context introduction complex estimation estimation estimation behavior statistical statistical statistical statistical effect effect effect effect generated tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable variable variable variable assume assume measure learned higher higher part part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound cases type good long long conditions conditions conditions represent distributed expected equations make fact fact fact region region region region observed errors finite finite finite finite finite finite finite minimum minimum minimum minimum minimum minimum minimum minimum total regression multi called called dimension dimension dimension dimension dimension dimension dimension made global global global global global global global global global applications applications applications study study study knowledge vol vol relative specific specific samples samples true true true true true true compared compared application application series provide define define define define define define determined determined determined goal goal goal goal related related posterior distributions accuracy comparison comparison comparison larger larger larger larger support support descent descent descent descent descent nets selection selection selection selection selection selection selection selection selection selection selection department department loss loss implementation individual joint ai ai computing equivalent view estimates estimates limit limit limit limit limit limit limit limit limit limit limit limit capacity capacity capacity capacity capacity capacity capacity capacity capacity upper choice approximate statistics statistics increase increase give criterion criterion criterion criterion criterion criterion criterion criterion criterion bounds provided provided provided provided provided finally finally processes processes depends simply achieved covariance normal normal feedforward feedforward feedforward increases increases increases describe describe arbitrary arbitrary arbitrary denote denote inverse assumption assumption finding finding effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective assumed supported role theoretical theoretical main journal journal square square square square end end end hypothesis hypothesis hypothesis hypothesis degree degree degree degree rumelhart including fit fit smaller smaller smaller needed reduced account dynamical unknown interesting ratio york consistent structures uniform empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical principle principle principle language leads squared call call numbers iterations iterations iterations international early magnitude minimize minimize perceptron discussed recent exact ensemble ensemble practical practical introduced machines machines machines machines machines machines machines machines machines machines sense recently recently engineering varying compare compare tuning studies definition definition definition generalized generalized bounded interval interval interval improvement grant exists exists parts parts parts lead lead concept concept concept concept concept concept concept concept concept concept concept studied studied occur occurs occurs generally starting starting starting starting critical critical minimal minimal assumptions assumptions assumptions central central differences numerical clear clear clear encoding taking presence drawn drawn sigmoidal proportional proportional proportional radial assuming minimizing minimizing min min decrease decrease decrease relationship force suppose relation relation relation produces written longer primary distinct distinct distinct physical electrical unique minimization shift implies implies expectation john decreases decreases decreases decreases decreases choosing choosing independently focus review depending communication squares viewed learner detailed open open restricted evolution evolution centers forms converges converges earlier earlier reasonable reasonable epochs reduces reduces fitting fitting fitting fitting fitting fitting fitting fitting fitting fitting fitting tracking remains valid valid sufficiently foundation euclidean eigenvalues vapnik extension extension prove holds holds holds discussions characterized aspects identified uniformly uniformly uniformly society reached reached reached reached summary induced stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping issue criteria criteria criteria criteria criteria sci hold hold notation quantity quantity quantity eigenvalue eigenvalue principles approximating acknowledgments decreasing minimized carried detail issues ml ml scalar scalar rest authors office proper cover understand phases phases phases phases notion notion hill smallest smallest smallest smallest smallest naturally possibly necessarily integer thought front formal noted noted fisher fisher precise precise observe epoch epoch epoch epoch epoch explain averages averages years asymptotically stop stop stop theoretic theoretic theoretic trivial defining phenomena answer caused turns purposes satisfied satisfied strictly desirable consequence scientific definite limits effort introducing haussler treated frequently polynomials measuring differs weigend marginal sums conclude comments unbiased unbiased begins tile tile tile tile tile tile tile tile wang wang wang wang wang wang wang lot trade trade trade pac pac college interface interface formally princeton addresses theories royal plays generality air kullback consideration siemens siemens analogy definitions monotonically monotonically monotonically monotonically monotonically monotonically imply imply affected affected north north intuitively symposium symposium generalizes generalizes generalizes elimination started corollary corollary corollary corollary corollary falls governed corre holland regarded schwartz infinity infinity sphere sphere sphere chooses surprisingly eng reveals reveals reveals concentration captures explains stopped stopped baldi ball ure ure summer largely numerous logarithm incorporates incorporates incorporates annals achieving leibler break dyna dyna dyna theorems sigma regularity regularity seek causing arg solely letting rain stands var chauvin num dominated picked argued relates relates weaker hansen breaks confusion esti son preprint preprint preprint truth eigen treating remark opti remarks sponding stephen ate accordance corporate corporate tom justified east overtraining compete inequalities inequalities dominates appealing identically rissanen venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh concerns inferring deals tells judd judd judd judd judd occam occam occam maxi quantitatively america approaching approaching mcgraw carrying akaike akaike akaike akaike facts statements statements aic aic aic aic aic aic aic aic aic aic aic aic aic brought amsterdam initiated applica meaningless eta heskes avenue aimed parame accepts counterparts conflict philadelphia philadelphia utilization analogously razor justifies concluding nonsingular tha chow pennsylvania pennsylvania kappen nicely lly nilsson nilsson kai surely surely observational prescription facilitated effected revise anders bert nction intuitions nmnber optional assertion disregard integrable econometrics lars santosh suming ambitious timetlon nodel interchangeable nax nize nit pects hopeless algorith vhich 
#@Judd_J,Venkatesh_S,Wang_C,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data function function function function function function function function function function function function function function function function time set set set training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number number number system system system system error error error error error error error results results results results information problem problem problem problem problem problem problem problem problem hidden based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer case case case case case case case case order order order order order order order systems systems systems systems values values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method control large large analysis analysis class class class class class class optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs form form form form form paper paper examples examples examples small small size size net net net net net net net net step step step step points process level problems problems random random random high high architecture architecture architecture show fixed fixed fixed fixed fixed rule general general general real real real states theory theory theory theory theory theory term term note note note result result variables variables variables variables variables variables variables variables variables variables computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation solution solution solution log defined defined defined defined target target target target constant constant constant computer terms node node node node node node node science prediction phase activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine range press learn learn learn learn learn learn learn learn learn learn learn learn learn learn components nonlinear nonlinear nonlinear outputs outputs outputs outputs sample sample sample sample sample abstract abstract abstract back computational computational computational analog analog analog analog analog analog analog references positive positive positive positive decision context complex effect parallel parallel parallel parallel parallel parallel tion change complexity complexity assume assume assume assume assume assume assume assume assume measure measure theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem type required required long long conditions conditions tree expected fact fact length correct finite finite finite finite finite resulting resulting resulting classes ing computed computed computed computed computed respect respect multi multi eq eq called called times optimization optimization optimization optimization optimization optimization optimization optimization optimization dimension dimension dimension dimension dimension dimension dimension dimension global applications negative negative original original original vol vol vol specific specific specific true true true true true desired define define define compute compute proc proc proc proc proc proc equal power mit steps steps steps steps nets nets nets nets nets nets nets nets nets nets nets morgan institute words implementation version version version consists consists individual individual represents bias bias layers addition graph ai ai ai ai ai ai considered cambridge computing computing domain domain equivalent additional view view solutions solutions design design san bit conference efficient efficient efficient requires give give levels bounds actual provided finally simply achieved normal normal feedforward feedforward feedforward describe describe describe describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote transformation transformation close assumption corresponds complete proof proof proof proof theoretical journal journal journal end end instance easily degree sensory kaufmann needed coefficients programming programming programming programming programming special special special operation principal details details details details call numbers numbers numbers numbers numbers numbers max bits depth depth depth polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial minimize choose architectures architectures advantage property property property apply quadratic subset interest previously previously correspond achieve definition definition bounded bounded bounded bounded bounded bounded gate gate gate gate gate gate gate gate interval exists exists expression concept concept scaling scaling scaling scaling scaling occur extended extended white occurs minimal assumptions valued valued depend competitive exponential asymptotic asymptotic mateo reduction drawn exist program question question acknowledgements pro construct edges edges edges edges written longer longer index solving describes linearly adding implies expectation boolean boolean boolean boolean choosing family independently learner transform operations restricted constants allowed processor purpose add sufficiently sufficiently sufficiently symbol construction construction construction construction views degrees combinations priori coordinate assignment assignment assignment assignment assignment assignment assignment assignment assignment vapnik extension holds holds computations computations computations situation receives receives receives refer refer kind contained satisfy involved write write write realistic realistic realistic realistic computes computes computes computes computes computes computes processors processors processors satisfies satisfies remain carried carried transformed transformed detail limitations recursive hall biases biases helpful rise reducing reducing successive possibility referred gates gates gates gates gates gates gates workshop workshop analogous math automata changed algo consist consist consist arbitrarily arbitrarily submitted explain defines mentioned piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise theoretic costs adjacent answer multiplication briefly sgn sgn sgn arise annual preceding preceding preceding applies substantially pseudo pseudo pseudo pseudo pseudo amounts parameterized simulate peter haussler haussler haussler haussler employ employ compares requirement polynomials replace replace replace pac pac pac pac pac pac pac pac pac pac notes guarantee investigation fix acm acm acm acm acm rithm arguments labelled labelled labelled maass maass maass maass maass maass maass maass rational rational rational rational rational rational rational rational ments ranges mail fan fan fan fan fan fan fan programmable programmable programmable programmable programmable programmable programmable programmable programmable programmable programmable exploit definitions imply canonical symposium carry combinatorial prentice corollary schapire sion regard regard regard regard infinity multiplied kearns kearns verification exploiting inf inf inf inf integers treat learnable unchanged multiply approx outline piece piece solves recursively chervonenkis employs employs employs forced pieces pieces pieces pieces pieces convenience generalizations auxiliary valiant valiant valiant valiant valiant valiant publication mathematically bounding disadvantage inverted expand expand wise wise employing employing refinement computa architectural architectural architectural architectural architectural remark remarks sees cliffs inequalities inequalities inequalities inequalities inequalities inequalities inequalities inequalities blum suffices suffices drawing formulae englewood goldberg sym judd nontrivial polynomially polynomially polynomially polynomially polynomially polynomially rivest comm dimen computable computable computable brought amer deleting technische demanding plexity phil coincides claimed picks gorithms permitted altogether chine fimction fimction agnostic agnostic agnostic agnostic agnostic agnostic agnostic gramming graz graz graz freeze para para para austria lets duplicated predecessors predecessors auer meters meters yll yll yll yll yll fimctions fimctions lll igi wolfgang hal varieties meter ivi finitely equate ellipsoid imately wards nctions fized volves yil speeded psi psi ican lul 
#@Maass_W,
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#*network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training output output number number number number number number number number number number number number number error error error state results results results results information problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden space weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer case case case case case case case case case order order order order order order order order order order order order order order order order order order order order order order order order order order shown systems parameters parameters parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons point single single single single single processing control neuron rate class class class class class class class class class class class class class matrix matrix optimal optimal optimal optimal inputs form shows shows signal algorithms simple gaussian paper paper paper features process process trained similar show show section section section section section section section section section section fixed vectors general general general general general general general general general real real real real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states theory theory theory gradient obtained obtained obtained university variables variables variables variables variables research research independent independent independent independent independent independent log defined sequence target target target target table table table estimate estimate estimate estimate estimate standard terms terms terms terms terms connections science activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation maximum components basis basis basis basis basis basis basis basis nonlinear nonlinear outputs outputs continuous continuous continuous continuous continuous abstract applied applied applied computational convergence properties references due ieee ieee ieee positive positive introduction tion complexity variable variable assume assume assume assume assume signals higher higher part center theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem cases type type required required conditions conditions fact finite minimum minimum classes multi sum sum sum sum times times times elements dimension dimension dimension dimension made applications study knowledge em obtain artificial artificial relative desired desired provide provide provide define define define rates proc determined equal equal power accuracy accuracy accuracy accuracy accuracy accuracy contrast connection dependent department individual advances advances advances represents exp layers considered equivalent equivalent view estimates estimates estimates estimates conference determine approximate approximate approximate approximate approximate world estimated condition condition bounds bounds bounds bounds bounds discussion feedforward feedforward feedforward feedforward describe describe describe denote denote denote close assumption assumption assumed assumed supported require require main main main eds eds square degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree including objective combination combination reduced coefficients coefficients coefficients coefficients coefficients coefficients york special uniform uniform leads numbers max international normalized magnitude magnitude decay polynomial choose choose choose choose choose choose choose denotes denotes discussed apply apply apply introduced include interest smooth yields achieve achieve trans definition bounded bounded bounded bounded bounded bounded grant constructed constructed constructed exists expression studied extended matrices white generally place row conclusions operator operator valued depend depend central measures measures designed largest sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal california regularization radial radial radial radial radial radial radial radial radial exist min min min iii iii derivatives derivatives derivatives derivatives derivatives derivatives manner question question denoted denoted denoted denoted explicit explicit suppose pro construct construct construct construct estimating multilayer explicitly explicitly explicitly explicitly infinite consisting consisting develop develop yield review review depending depending transform showed centers approximated constants partial reasonable classical valid norm norm norm norm box combinations combinations priori priori formulation formulation discuss discuss discuss specifically absolute determining poggio poggio identity compact conf interested interested interested interested interested sin sin sin sin sci notation notation quantity quantity quantity involved involved involved involved usual usual thresholds approximating approximating approximating approximating satisfies satisfies investigate investigate dual dual periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic fourier fourier fourier fourier fourier applicable int authors proved proved proved notion analogous analogous math possibly necessarily integer integer integer integer integer integer thought ensure quantities quantities quantities versions observe explain formula formula formula formula growth smoothness smoothness capabilities briefly briefly mation commonly mathematics mathematics mathematics mathematics acknowledgement universal universal universal localized evaluating evaluating evaluating formulated continuously continuously span polynomials polynomials howard summarized enables replace differentiable differentiable differentiable proofs girosi girosi approximates approximates arranged arranged satisfying satisfying los viewpoint modifications preparation evaluations evaluations entry belongs entries approximators barron barron theoretically subsequently inf inf inf cam integers integers integers truncated connec summarizes ibm ibm approxi afosr relates hornik superposition superposition minor knowing ward infinitely manuscript manuscript replacement remarks sake smoother smoother cornput accomplish accomplish practically comprising comprising norms norms norms poly squashing squashing contrary transpose appro corn facts facts prescribed watson watson deciding formulas formulas aims heights angeles constructions constructions constructions ixl functionals subclass logn lira kung vation acti cybenko exceeding plied trigonometric trigonometric trigonometric trigonometric feedfor yoon stinchcombe superpositions multilayered kamm pii pii pii proximate tionist hecht lets yorktown advocated chellappa iin vides ifx ifx nmnber universally sequel customary customary customary taining xll truncating encompass judiciously lxl sigrnoidal concreteness backpropogation logk logk iif approzimation mathematica publ nomials 
#@Mhaskar_H,Micchelli_C,
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural input input data data data data function function function function function function function figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results information problem problem models models performance based based based based based based based weights weights linear linear linear linear linear linear layer layer layer layer shown shown shown shown shown shown systems values values values values values values values values values values parameters parameters parameters parameters parameters weight recognition recognition recognition method method method method method method method method method method method method method approach point point point single large large large large large large large large large large large rate rate rate rate rate test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns shows shows shows simple simple simple simple paper examples size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size feature feature net net work work task task task task task fig fig fig fig fig fig fig fig fig fig fig fig fig points points points points trained trained trained trained trained representation representation architecture architecture equation equation line line line line line rule general generalization real real real real approximation obtained obtained experiments dimensional dimensional result result result result solution research log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log found target constant constant constant estimate estimate estimate standard standard terms prediction prediction prediction prediction prediction prediction left left left left left left low sets range abstract back find computational computational convergence convergence convergence convergence convergence convergence references due due positive procedure procedure procedure procedure procedure decision decision decision decision propagation mixture mixture introduction behavior statistical statistical statistical effect cost search search change difference difference difference difference difference difference difference difference difference difference classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier rules measure chosen cases type good good good good expected expected expected expected make proposed proposed proposed proposed proposed correlation correlation correlation correlation observed observed errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors finite finite resulting resulting ing ing ing tasks tasks tasks multi multi multi multi sum sum sum sum sum sum sum sum sum sum sum dimension dimension applications applications relative compute perform connected connected connected gain equal power power power power power power power power power power power power power power larger larger larger larger larger support support train train train train train modeling modeling modeling modeling modeling modeling selection morgan institute advances difficult maps maps considered considered framework additional additional curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves estimates estimates stage determine efficient efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full full full full full full full full full full full full requires requires choice choice choice choice approximate free estimated pages give give weighted lines lines lines lines lines lines lines finally constraint measured measured measured measured measured describe describe tested tested tested limited assumption assumption assumption assumption assumption surface predictions finding amount common common common assumed assumed theoretical theoretical theoretical theoretical theoretical theoretical theoretical ability easily makes fit smaller smaller needed reduced fully fully technology special database database database database database database database database database database database database database database squared squared normalized normalized early decay decay decay decay decay decay combined sources typical typical practical practical practical practical strategy strategy subject observations volume works tuning studies converge converge separation symmetric observation interval improvement amplitude amplitude amplitude deviation deviation predicted predicted predicted predicted predicted half strength reduce reduce measures numerical numerical numerical asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic suggest suggest propose propose demonstrated minimizing base reference appears appears digit digit pro ways plot plot plot plot plot plot plot plot plot plot confidence implement physical develop develop predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive formed expectation expectation versus versus boolean boolean boolean boolean cycles john choosing national extracted extracted extracted extracted independently review evaluated forms sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes suggested digits digits digits key performing valid valid intermediate intermediate intermediate intermediate intermediate assigned foundation foundation norm existing handwritten handwritten handwritten bell vapnik vapnik vapnik vapnik vapnik illustrated illustrated illustrated illustrated characterized suitable modification modification computationally computationally ten summary quickly procedures procedures strongly cun heuristic follow follow hold hold denker denker denker denker denker denker ill reach illustrates operating extract extract extract situations law law law law law law law law law poor poor referred referred reliable reliable reliable surfaces surfaces surfaces circles circles predicting changed obvious expressions expressions regime regime regime asymptotically asymptotically crucial agreement agreement agreement slope slope explanation straight straight straight straight straight straight straight straight straight straight straight implementing implementing implementing choices choices desirable desirable commonly commonly laboratories calculations demonstrates mechanics mechanics applies experimentally quantitative solla solla solla solla solla slower slower howard characterize characterize resource sophisticated tile tile tile tile naive naive feasible resources resources resources resources databases databases databases databases ordering eliminate kaufman promising intelligent tishby effectiveness adequate inferior inferior exploring sompolinsky excellent falls decide jackel jackel jackel jackel jackel jackel candidates candidates candidates candidates cpu seung intersection intersection intersection convergent mechanical unchanged numerous validity validity validity validity revealed poses boser medium medium avoids principled principled principled principled henderson exponent exponent exponent exponent exponent exponent exponent exponent exponent formance cessing decays decays life life life life hubbard termed termed termed accounted accounted applicability laws laws laws nist nist simplification characterizing demand quantify utilizes usefulness holmdel sparsely triangles triangles judged classi fair tra devoted huge cortes cortes cortes cortes cortes costly datapoints extrapolation extrapolation extrapolation extrapolation demanding continuing dilemma exponents froin strain strain strain explosion weeks ror suit standards extrapolate extrapolate extrapolate unrealizable unrealizable unrealizable questionable asymp vladimir sara oll suitability suitability filnction iog iog corinna freed totic tiers 
#@Cortes_C,Denker_J,Jackel_L,Solla_S,Vapnik_V,
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#*network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data function function function function function function function set set set set set set set set set set set networks networks networks networks networks training output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number system system error error results information information information problem problem problem models hidden hidden hidden hidden hidden hidden hidden space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer case case values values values weight weight functions functions functions neurons neurons point point point point point image single single single single single control large large large large inputs inputs form form form shows shows simple simple paper paper small small small small small small small small net net net net net net net net net net net net net net net net net net net net net net net work work work task points points points points points structure structure structure structure structure architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation equation fixed fixed line vectors vectors general real real real real real states note note result result university variables research research research research research research defined defined defined defined found found sequence sequence constant standard standard terms node node node node node node node node node science presented map map map map map map map map map map map map map map map map map map map map map map map map map map map nodes nodes nodes nodes nodes nodes nodes nodes nodes sets sets sets sets sets nonlinear outputs outputs outputs outputs abstract find find find references positive introduction complex complex complex complex hand hand hand change change variable variable variable variable assume assume assume assume assume assume assume center center center theorem theorem theorem theorem theorem conditions conditions conditions conditions conditions conditions make make fact fact forward forward forward forward forward forward forward forward finite sum called called called called made natural natural natural natural natural natural applications study study study study study knowledge knowledge obtain obtain true true define define compute determined determined determined related equal equal equal accuracy nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets consists bias layers layers layers layers maps domain domain domain domain domain view view view solutions solutions determine determine determine full choice approximate finally depends simply discussion technical feedforward feedforward arbitrary complete complete surface proof proof proof proof proof proof proof assumed assumed assumed supported supported require main main main main main square hypothesis hypothesis instance instance easily easily makes including needed unknown technology interesting ratio special principle leads numbers numbers numbers numbers depth idea attention attention produced description practical introduced sense subset highly observations solve yields address definition definition expression expression lead studied suggests feed feed feed feed feed feed feed feed setting critical minimal minimal assumptions sigmoid asymptotic asymptotic asymptotic asymptotic largest reduction reduction reduction start plane force question acknowledgements reference suppose suppose suppose suppose suppose pro distinct dept involves transformations unique unique applying national family family focus squares squares squares squares open open fraction fraction constants allowed sign sign sign key key neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood construction foundation david david david avoid avoid expect box recognize determines determines discuss absolute simplicity simplicity simplicity reason determining determining differ maximal literature comparing identity interpreted return return sin hold satisfy satisfy notation write simplified dot nips hypotheses hypotheses hypotheses thresholds thresholds thresholds thresholds thresholds thresholds thresholds remain collection essential essential analytically analytically analytically analytically analytically office complicated tanh tanh tanh tanh tanh proved surfaces induction induction induction induction smallest math integer perfect singular obvious obvious obvious obvious freedom precise observe nervous nervous contributions arbitrarily advanced formula formula trivial crucial distinguish defining analytic analytic analytic analytic analytic analytic analytic analytic analytic analytic analytic briefly purposes widely precisely immediately arise mathematics scientific begin read read read read read read geometry qualitative geometric reflects reflect understood generic generic generic generic generic generic generic generic generic introducing posed dots dots sharp chen replace kinds specifies specifies arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic pole pole pole pole pole pole picture picture picture fix fix fix fix princeton princeton princeton princeton princeton princeton pick approximates proceed spiral spiral air mail analogy odd odd check moment contract definitions definitions adequate continue continue entry overview consequences originally reproduce theoretically projects statement ignore integers integers integers integers integers integers integers empty empty appeared outline sontag sontag sontag uniquely uniquely uniquely uniquely uniquely adopt pointed theorems theorems home alternate impose continues continues continues mathematically relate singularities singularities singularities singularities singularities singularities singularities sketch grateful union union union union union union union union ignoring signs signs signs infinitely sigmoids accumulation accumulation accumulation accumulation fortunately uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness continued influenced jersey jersey ave pearson agency accumulate accumulate accumulate accumulate architec carries complement complement complement iid poles poles poles poles poles poles poles poles poles poles poles scott scott brackets brackets enter charles charles defense facts fixing ically united monitored recovering recovering recovering recovering recovering stan permutations cancel virtue checks touch dard symmetries symmetries sing sing sing sing sing sing sing sing sing sing sing sing sing sing clarify disappear disappear continuation continuation continuation arms arms reconstructing exclude asymptotics completes singularity accumulating isomorphic isomorphic isomorphic today contin imperfect oft modulo progression progression progression progression progression iij iij iij iij iij iij iij asserts government distribute concludes iia hecht hecht scientists lets wit les uation evidently completing cont sacrificing wjk wjk ruled disciplines finitely mutations sigrnoid sarnoff sarnoff copyright pictured countable countable scription samoff samoff interchangeable counterexamples counterexamples 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#@Fefferman_C,Markel_S,
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function figure figure time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number error error error error error error error error error error state results results results results results units units units units units units units units units units units units units information problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based based space space weights weights weights weights weights weights weights layer layer layer case order order order order order order shown systems systems values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions unit unit distribution distribution distribution distribution recognition method method method method method method method method method pattern pattern point point point point control large large large large large large rate rate rate rate rate test class optimal optimal optimal optimal inputs inputs inputs form shows algorithms algorithms algorithms algorithms simple simple examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small size size size size net net net net net work task task task task methods methods methods methods methods methods methods methods methods methods methods methods step step points points classification classification classification classification classification process level level level level level level level trained trained trained trained trained trained trained trained trained trained trained random random random random random random random random high high high high similar similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture show section fixed fixed line line rule general generalization generalization generalization generalization parameter parameter approximation average average average average average average average average gradient obtained obtained obtained term note note note result result result threshold threshold computation independent defined target target target target target initial initial initial initial table table table estimate standard standard standard distance distance distance distance distance distance distance distance distance prediction prediction prediction prediction prediction left presented presented presented present present machine sets sets sets sets range learn learn outputs abstract applied back back back find find computational references stochastic procedure important important adaptive adaptive adaptive decision decision decision decision propagation propagation introduction complex complex hand estimation estimation behavior behavior behavior statistical variance cost tion change change change difference difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower measure chosen part part part part previous cases cases good good good good good binary binary binary tree expected expected proposed length correct correct correct observed forward forward forward finite minimum resulting classes classes classes classes ing ing tasks tasks performed means means factor obtain original original original original artificial artificial specific desired desired desired desired desired cross cross cross cross cross provide provide define define define define proc experimental experimental goal related constraints discrete approaches accuracy accuracy accuracy accuracy accuracy contrast contrast connection update train train nets nets nets morgan institute words represents connectionist bias layers addition experiment experiment experiment experiment experiment curve top determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full full requires choice choice choice approximate approximate approximate free free free free free free free free world basic validation validation validation validation validation validation validation validation give con produce produce produce randomly levels levels levels levels levels criterion criterion actual simply measured measured discussion describe group group limited limited limited close stable predictions predictions predictions predictions predictions circuits amount effective require eds instance degree noisy noisy noisy noisy noisy noisy noisy fit fit kaufmann kaufmann typically typically smaller smaller smaller smaller smaller smaller needed needed functional functional functional functional functional unknown testing testing significantly significantly increasing uniform uniform principle principle representing call bottom polynomial minimize produced produced choose choose choose description description perceptron perceptron perceptron architectures architectures architectures architectures improve advantage pair separate apply apply apply introduced include subject quadratic trees relevant compare teacher teacher teacher teacher teacher calculated calculated works tuning tuning match achieve achieve background sensitive exists occur deviation alternative feed feed feed touretzky touretzky boundary boundary boundary generally demonstrate reduce reduce conclusions depend depend sigmoid measures measures numerical clear clear suggest taking external drawn iii averaged connectivity acknowledgements produces tuned changing pruning pruning pruning pruning sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity applying predictive boolean boolean boolean boolean select select yield choosing expressed dependence viewed influence detailed evaluate fraction fraction fraction forms approximated sizes sizes suggested calculation convex fitting add penalty penalty penalty penalty penalty penalty penalty penalty penalty calculate calculate classified classified classified david degrees avoid avoid avoid avoid includes includes instances determines plotted illustrated mozer holds partially discussions major aspects aspects closely capable differ differ computationally computationally identify identify schemes score score score situation plots capture soc cun cun stopping stopping stopping classify oscillations follow follow criteria quantity usual usual michael nips nips denker highest extract software situations situations situations bars unlike unlike parametric poor overfitting overfitting overfitting issues issues lippmann dotted behaviour school reliable momentum trace created created created changed changed changed quantities quantities quantities quantities friedman algo observe regime stop stop stop formula distinguish expensive expensive starts producing producing choices scientific recording explained elman solla ity calculating switch exhibits weigend weigend weigend qualitatively suited inherent comments tolerance tolerance tolerance contribute representative classifying optimality rithm signature signature signature signature signature signature signature signature signature smolensky consideration analogy los los observing methodology inferior decide bad bad bad bad bad realization evident candidates roy wolpert erlbaum considerations santa santa generalizing stopped influences stone stone dense fitted summer specification ent distinction mdl hillsdale realizable signatures signatures signatures associates outcomes suffer ation lapedes lapedes lapedes lapedes parametrized parametrized parametrized parametrized parametrized parametrized parameterization characterizing consuming assistance subjective realizations realizations realizations realizations realizations rissanen rissanen practically huberman edited alan scenarios statist presently alamos alamos adv adv terminology preferable tal disadvantages delete relying grossman grossman grossman grossman grossman prohibitively prohibitively classifica aver mexico cheap safely wild prepared perrone invaluable lets parenthesis ser aged sooner rob scrambled scrambled scrambled scrambled scrambled scrambled fractions distinctly memorizing inquiry rummelhart ternal sensitiv devi prepare guidelines delicate complezity 
#@Grossman_T,Lapedes_A,
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#*network network learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural input input input input input input input input data function function function figure time time time time time set set networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number system error error error error error error error error error error error error error error error error error state results results results results results results information information information problem problem problem problem problem problem problem problem problem problem problem problem performance performance based space space space space weights linear linear linear linear case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector order order shown shown systems systems systems systems values noise noise noise weight weight weight weight weight weight weight functions functions functions recognition approach pattern pattern pattern point point point processing control control control control control control control control control control large large large large large large local local local rate rate rate rate rate patterns patterns analysis class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper small small small work methods fig problems show show show section section fixed line line line vectors vectors vectors vectors general real real approximation approximation states theory theory theory gradient gradient term term note note note note note result result result result result result result university university university solution solution solution solution solution solution solution solution research research defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial initial constant constant estimate estimate estimate estimate estimate terms terms prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction direction direction presented presented maximum maximum maximum press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied find find find convergence convergence convergence properties properties properties references due due due ieee ieee ieee positive procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision context introduction complex complex estimation estimation estimation estimation estimation statistical parallel cost tion tion change energy energy energy energy energy energy energy energy difference signals signals chosen part part part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound cases type long long conditions distributed distributed expected expected make make fact fact fact fact observed observed observed errors errors errors errors errors errors errors errors errors errors errors errors minimum minimum resulting resulting resulting ing sum called called means means means means made made made feedback applications study knowledge filter filter filter filter obtain obtain true true true true true compared desired desired provide define compute compute rates gain equal mit larger larger train modeling words words version responses addition addition sequences sequences maps maps maps maps cambridge curve additional estimates estimates san san determine upper upper approximate approximate approximate approximate give give con channel randomly criterion criterion bounds entropy entropy entropy product provided provided backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation discussion increases increases group denote denote denote denote denote transformation close close close close close close corresponds stable circuits supported theoretical theoretical main face square end rumelhart rumelhart including including objective underlying underlying functional unknown unknown unknown unknown unknown transfer transfer transfer transfer transfer transfer transfer transfer interesting ratio ratio ratio ratio york special leads squared squared details filters pre pre international normalized early minimize minimize denotes denotes exact robust robust takes introduced introduced strategy strategy include recently recently recently observations observations observations yields correspond converge trans definition observation observation observation bounded risk risk sensitive sensitive grant exists exists suggests suggests predicted predicted predicted alternative locally locally locally locally locally column column setting setting demonstrate conclusion conclusion assumptions assumptions assumptions operator operator operator operator operator operator operator operator valued central faster faster hard california minimizing exist introduce derivatives minima force force suppose suppose suppose suppose suppose index laboratory laboratory dept sensitivity minimization john yield yield yield choosing family squares squares squares squares estimator estimator estimator estimator estimator estimator interpretation variation showed showed converges converges updates updates reasonable dashed measurements spaces tracking remains initially filtering filtering sufficiently sufficiently norm norm norm norm norm norm norm norm norm norm norm norm norm norm includes formulation extension illustrated automatic discuss discuss mcclelland mcclelland literature reached capture conf conf criteria criteria criteria criteria comp notation write absence minimizes minimizes attempt modelling modelling extend extend situations situations minimized command wiley estimators estimators estimators estimators estimators estimators replaced recursive recursive recursive dotted dotted mass hall behaviour behaviour behaviour scalar scalar applicable int office cognition smallest math gradients concepts plausible thought ensure algo precise observe ith ith switching arbitrarily arbitrarily arbitrarily arbitrarily preference formula derivation guaranteed lies reasons stanford stanford stanford stanford sections satisfied satisfied satisfied widely widely widely filtered worst worst worst worst worst arise scientific acknowledgement opt opt opt opt begin arises meaning meaning robustness robustness robustness reflects reflects apparent lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms lms readily lack lack poorly poorly backprop introducing formulated gen achieves inherent chose lim instantaneous instantaneous instantaneous proofs proofs optimality optimality optimality optimality optimality optimality optimality optimality guarantee rithm connecting connecting nonzero air air multiplicative resistance hit hit contract implications implications intuitively motivation prentice excellent excellent corollary corollary corollary ensures encountered surprising regarded regarded guarantees guarantees guarantees expanded widrow widrow originally thomas reader repeatedly storing sons statement santa santa explains inf inf inf inf inf inf explorations ball ball microstructure solves recursively opposed opposed causal causal causal guess guess guess conservative argue insights pdp afosr considers considers wise exceed exceed stuck behaves behaves sigmoids rewritten hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi accordance justification justification vii cliffs eral recursion disturbances disturbances disturbances disturbances disturbances disturbances disturbances englewood disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance linearized linearized presently elec facts minimizer texas texas hoff hoff rec kailath kailath kailath kailath kailath kailath kailath kailath obeys obeys omit 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input function function function function function function function function time time time time time time set set set set set set set set set set set set set networks networks networks networks networks networks networks 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weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit recognition approach single processing processing control large large local inputs inputs inputs inputs inputs inputs inputs form form form form form algorithms algorithms simple paper paper paper paper paper paper paper paper paper paper paper size size size size net work work field structure problems similar similar similar architecture architecture architecture architecture show show equation equation equation equation section section general general general general generalization speech states states states states states states states states states states states states obtained term result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables computation computation computation research log log log log log log log log log log log log log log log log log log log log log log log log log log log defined defined defined found found initial constant constant constant constant constant constant standard terms terms terms terms node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node left left left left nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine maximum maximum maximum range nonlinear outputs outputs outputs outputs outputs continuous continuous abstract back back back computational references due due ieee ieee important important adaptive propagation introduction complex complex hand 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equivalent directly additional transition limit determine efficient efficient efficient efficient upper upper upper upper upper upper upper upper upper upper world basic basic pages pages coding weighted bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds area provided finally finally finally simply achieved technical technical feedforward feedforward feedforward feedforward feedforward arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary limited limited limited limited proof proof proof proof proof proof proof proof proof proof proof proof circuits circuits amount implemented implemented implemented implemented implemented implemented implemented implemented implemented implemented implemented implemented implemented implemented implemented require require ability easily easily easily including fit typically needed dynamical fully fully fully fully fully fully interesting special matching language representing max direct bits bits bits bottom depth magnitude polynomial idea idea combined choose perceptron perceptron perceptron architectures architectures discussed improve improve recent element practical apply subject machines machines machines machines machines machines machines machines machines side side side trees trees subset subset subset interest tions solve solve yields yields match match trans trans definition background bounded gate exists exists exists expression expression expression lead lead extended feed feed generally minimal valued performs performs performs practice encoding encoding hard hard external assuming assuming variety connectivity identification question question question denoted derive derive derive derive ways ways ways ways ways primary dept dept implement implement implement implement implement implement implement implement implement multilayer multilayer multilayer multilayer multilayer multilayer multilayer 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interested comp comp providing giles thresholds thresholds thresholds thresholds thresholds receive explore explore powerful wiley optimized optimized hall matches matches tech tech terminal possibility referred gates proved proved fundamental neu concepts editor extremely automata implementations implementations implementations implementations implementations implementations implementations aspect explored perceptton perceptton perceptton logic logic logic logic logic logic logic logic logic logic logic logic logic logic logic logic logic logic logic logic switching baseline devices devices inequality inequality inequality guaranteed guaranteed independence nonlinearity turns implementing implementing sys sys arc choices worst universal acad meaning argument generic fed fed simulate leave leave ity robinson synthesis synthesis limiting limiting popular popular collective marginal gave gave inherent extreme don primarily investigation investigation investigation restriction restriction 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural input input input input input data data data function function function function function function function function function function function function function function figure time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training output output number number number number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer vector vector vector vector shown shown shown shown shown systems systems probability probability probability probability probability probability probability probability parameters parameters weight weight weight weight weight weight weight weight weight functions functions unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method processing large large large large large large large large large large large large large class class class class class optimal optimal inputs inputs form form form shows shows algorithms simple gaussian paper small small size size net net net work work work work work work methods trained random random random random random random random response architecture architecture show equation equation equation section fixed fixed general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter approximation approximation approximation average theory theory theory theory obtained obtained obtained obtained obtained obtained term term term term term term term term term term term term term term term term term term term term term term result result result result variables computation research research independent defined defined found found target constant constant constant estimate estimate estimate estimate estimate estimate terms terms terms terms terms terms terms distance science prediction presented sets sets components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous abstract applied find references due positive mixture mixture introduction introduction estimation estimation estimation estimation statistical effect variance variance variance variance variance variance variance variance variance variance variance variance variance tion tion energy energy energy energy complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable measure prior prior prior prior prior prior chosen chosen chosen chosen previous previous previous previous theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound type good good good conditions conditions expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected equations make fact fact fact region region region region forward minimum resulting total total called elements elements regions dimension dimension dimension dimension made applications applications original original vol artificial samples samples samples samples compared application series provide provide define define define define proc proc proc determined determined determined determined distributions distributions discrete larger larger larger larger support dependent dependent selection loss loss version consists individual joint represents bias bias bias bias bias bias bias bias bias bias considered domain directly hinton additional curves estimates limit effects conference choice approximate estimated estimated estimated estimated estimated increase increase increase give developed criterion bounds actual actual actual depends depends normal feedforward describe denote denote close corresponds corresponds corresponds corresponds common effective effective effective effective effective effective effective effective effective effective effective effective assumed assumed theoretical theoretical ability instance makes rumelhart smaller smaller needed combination account unknown ratio york york special empirical empirical leads squared squared details details direct international supervised magnitude decay minimize minimize choose exact takes practical quadratic interest works trans background bounded bounded bounded bounded bounded bounded bounded bounded interval expression expression lead lead lead scaling extended feed assumptions depend central central central sigmoid sigmoid sigmoid sigmoid measures measures measures accurate clear peak moody practice practice drawn drawn sigmoidal sigmoidal sigmoidal sigmoidal proportional regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization relationship relationship pro longer longer index index index primary plot dept pruning category explicitly explicitly explicitly develop develop adding applying springer expectation expectation expectation john national independently independently independently expressed expressed open open open evaluate evaluate soft completely expansion reduces reduces reduces event closed closed foundation norm degrees existing formulation eigenvalues extension plotted specifically specifically priors discussions characterized characterized effectively effectively effectively effectively effectively effectively effectively effectively effectively effectively effectively effectively effectively effectively delta refer strongly content satisfy comp gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs generalize generalize generalize generalize generalize nips minimizes minimizes operating operating operating satisfies deal minimized wiley optimized optimized fewer tech analytically analytically workshop presynaptic presynaptic act naturally equally equally noted taylor freedom amari inequality inequality explanation explanation explanation nowlan independence briefly reasons arc ring widely strictly sgn commonly commonly commonly commonly probable actor ion ion acknowledgement implicit explained questions questions questions apparent empirically quantitative quantitative introducing posed solla solla sharp operate characterize characterize characterize weigend fall incoming incoming incoming incorporating geman generality consideration motivation introduces equals barron barron barron barron emergence vertex vertex hypercube hypercube sons subsequently onr ure ber axe convenience arg big big affects affects rain rain rain rain tight tight illustration penalized penalized distri magnitudes dominated ization regularizer proba efforts relate simplifying relates indexed happen applicability modifiable normalizing answers utilizing gratefully survey bienenstock ble bility dominates sharply peaked equa triangle triangle comprising characterizes degenerate degenerate iid 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general general general general general general general general general parameter real states states states theory term note note note experiments dimensional result result result result result result threshold threshold threshold threshold threshold threshold threshold threshold threshold research research research research research independent log log log log defined defined defined defined defined found constant constant constant constant constant estimate estimate terms terms terms connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic left low low sets learn position position position position position position position position position components components components components components components components continuous abstract find find find computational density properties properties references component component component due ieee ieee positive introduction hand estimation statistical complexity variable assume lower lower lower lower measure measure measure higher higher part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound cases cases cases required binary errors forward finite finite finite multi multi multi multi multi multi multi sum called times means factor factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made made natural natural applications obtain obtain true true compute connected connected connected connected connected connected connected connected connected connected connected approaches accuracy comparison comparison larger contrast contrast contrast connection connection support morgan proceedings proceedings proceedings version individual advances layers layers layers sequences considered directly curve additional estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity efficient upper upper upper upper upper choice basic basic basic basic pages randomly randomly randomly developed bounds bounds lines provided selected selected selected biological achieved achieved discussion technical feedforward feedforward feedforward feedforward denote denote corresponds proof proof proof proof proof circuits implemented implemented assumed theoretical theoretical require main main main journal journal ability ability ability ability ability hypothesis hypothesis easily pairs pairs pairs fully fully fully fully technology significantly special special special empirical operation leads leads details details call numbers numbers depth polynomial attention combined perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes improve recent recent recent property property introduced subject side sense sense subset subset interest dimensions previously volume works works achieve trans address observation interval interval storage storage storage exists exists exists parts feed locally half critical critical minimal greater assumptions valued valued weak weak largest turn start exist exist exist min iii iii iii derivatives identification question question relation relation relation relation relation confidence confidence recall recall implement implement implement implement implement multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer infinite easy springer implies implies implies boolean expressed dependence dependence lemma lemma lemma solved open open open open controlled controlled key expansion reduces sufficiently sufficiently sufficiently sufficiently sufficiently sufficiently symbol david perceptrons perceptrons perceptrons perceptrons vapnik vapnik vapnik extension holds holds reason efficiency maximal maximal maximal maximal maximal included comparing comparing composed road refer verlag prob heuristic showing showing split split split split symmetry hold built built comp notation localization realistic nips layered perturbation perturbation essential rapidly hanson biases biases rest analytically proved proved workshop cover cover cover cover cover cover cover cover cover cover cover cover cover cover cover notion neu concepts editor generalisation generalisation generalisation generalisation generalisation generalisation generalisation der der der observe expressions perceptton perceptton perceptton perceptton logic logic logic logic logic logic logic logic store amari advanced ment publishers derivation capabilities caused baum stress immediately hyperplane hyperplane laboratories acknowledgement arises annual cybernetics argument affine adjustable adjustable haussler continuously gains gen semi june gap gap lab pac indices indices investigation acm ratios hyperplanes turned turned kaufman consideration chance significance satisfying odd odd hope obtaining obtaining ral imply imply imply preparation exceeds exceeds reliably corollary corollary corollary corollary corollary corollary corollary corollary corollary percepttons counting counting counting counting counting counting counting counting counting counting warmuth extends relies impact splits integers dense dense linked geometrical usage outline outline uniquely axe decomposed big australia australia australia algebraic options options arising equality preserved iff ijcnn learnability oct fir drops durbin dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies manuscript vice spite capacities capacities capacities gratefully versa unbounded justification ave imple inequalities determinant compo dichotomy dichotomy dichotomy dichotomy exclusively believed tuple tuple tuple tuple tuple tuple tuple tuple tuple tuple tuple tuple huang huang proves amenable presently binomial cutoff ben elec kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk dyer terminology aims judge tighter retrieve sixth minute blumer complications forthcoming dependences claims acknowledged fur implementable implementable implementable standing outlines nent mitchison mitchison cap cap cap cap cap cap cap cap altogether permission bigger bigger sakurai sakurai sakurai sakurai sakurai sakurai sakurai ehrenfeucht ams hen adam tuples tuples tuples tuples telecom trl rst abbreviated hal varieties selections dye dye dye dye dye publish pessimistic clayton ilk ilk managing blackburn hardest hitachi crux crux vic director satis complezity oratory probabilit 
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data function function function function function function function function function function function function function function function function set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number error error error error error error error error error error error error error state state state state results results results results results units units units units units information problem problem problem problem problem models hidden hidden hidden hidden hidden hidden based space space weights weights weights layer layer layer case case case order order shown systems systems systems probability noise weight weight weight weight functions functions recognition method method method method method approach approach approach approach pattern point point point point point point point point point point point point point single single single processing processing processing large local rate rate rate rate rate patterns analysis analysis analysis analysis analysis analysis analysis analysis class class matrix form shows signal algorithms algorithms algorithms simple examples examples examples examples examples examples examples examples examples examples small small small net net work work methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step step step step points process level problems similar similar similar show section section fixed fixed fixed line general generalization generalization real real approximation approximation theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term term term term term term term term term note note note note note note note note note dimensional dimensional result result result university solution research research defined defined sequence sequence sequence sequence sequence sequence table table computer terms science science direction direction direction presented map present sets sets sets sets press press press learn continuous continuous abstract convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee ieee positive important adaptive propagation introduction introduction complex estimation statistical generated generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel tion tion variable assume representations chosen part theorem theorem theorem theorem type type binary long conditions conditions represent distributed distributed fact techniques techniques proposed proposed errors finite finite computed sum performed elements means factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization natural global global global applications applications knowledge knowledge obtain negative negative original artificial artificial artificial artificial artificial desired series series compute compute compute rates rates rates rates related related mit contrast descent descent descent descent descent morgan proceedings department consists consists consists internal advances represents connectionist addition sequences ai ai framework cambridge computing computing computing equivalent hinton hinton hinton hinton hinton hinton additional view view san san conference conference full full choice choice approximate approximate increase give give condition randomly criterion criterion bounds provided backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration iteration iteration iteration iteration iteration iteration iteration iteration nature depends achieved feedforward feedforward denote proof proof assumed assumed supported theoretical main journal journal journal future easily easily makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart kaufmann objective objective objective objective objective objective typically typically programming projection projection york details numbers iterations iterations international international supervised decay decay decay decay decay attention minimize choose added description architectures separate element practical introduced subset sejnowski sejnowski cognitive recently interest volume tions smooth smooth yields achieve modified modified modified grid bounded bounded bounded bounded bounded williams williams williams entire grant grant scaling deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic white white white white white generally setting row assumptions assumptions valued editors editors editors numerical numerical clear performs asymptotic mateo california intelligence regularization turn start start start exist min min decrease decrease decrease manner minima minima program force explicit suppose suppose pro pro pro derive index index index index ways primary label mathematical mathematical mathematical mathematical mathematical explicitly averaging infinite text minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization springer versus cycles choosing national dependence stationary stationary stationary stationary stationary squares viewed converges converges converges converges partition processor processor processor processor processor processor partial partial partial partial slow slow epochs classical reduces event assigned foundation topology avoid box box batch batch sciences automatic successfully major major major major major major major simplicity simplicity reason columns society modification mcclelland literature computations tend online online online online online online online online refer refer compact verlag kind cun cun interested stopping stopping issue issue strategies notation notation notation generalize giles maximization thresholds thresholds automatically processors processors attempt overlapping software software software software software load cowan remain remain remain american perturbation difficulty hanson association hessian ideas applicable possibility office eigenvectors func cover fundamental momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum coefficient coefficient gradients concepts editor integer predicting equally thought ensure adjusted subsets versions academic art epoch epoch epoch serial serial serial serial serial serial serial serial attempts established massachusetts asymptotically rows stop stop stop guaranteed guaranteed handle purposes sys satisfied widely division immediately simard simard scientific acknowledgement english annual meaning addressed researchers robustness conjugate prop continuously incorrect ity price berlin perturbations perturbations weigend weigend weigend fall proven enables damage differentiable wesley multidimensional synchronization synchronization synchronization ordinary ordinary proofs redundant addison generator assign equivalence guarantee fix fix recover concerned purely repre establish establish air stronger imply modifications modifications symposium published published published published reset ensures zhang zhang appendix appendix regard tic recovery francisco foundations passing hypercube erlbaum pearlmutter pearlmutter summarize balancing convergent material multiplying multiplying arcs rigorous email july perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed classifies hillsdale community tems denoting challenging emphasize noting unconstrained unconstrained unconstrained worth minor minor minor minor mini mini infinitely remark remark remark remark remark remark remark remark remark remark covers accumulation accumulation accumulation advantageous nonnegative nonnegative handling justified prefer justification justification rosenberg rosenberg converging jersey cast appealing huberman huberman huberman cardinality nontrivial establishing wisconsin periodically barhen barhen iterate iterate eighth replaces ceedings sentations attracted lipschitz lipschitz lipschitz madison madison rigorously iterates iterates iterates iterates iterates iterates paid claimed permuted permuted diverges diverges 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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data function function function set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output number number system error error error error error error error error error error error error error error error error error error error error error results results results results results results results results results information information information information information problem models performance performance performance based based space space space space space weights weights weights weights weights weights weights linear vector systems systems systems systems values values values values probability probability probability probability probability probability probability probability parameters noise noise noise weight weight weight weight functions distribution distribution method method method single processing processing processing large large large large test analysis analysis analysis analysis matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs shows examples examples examples examples examples examples examples size size size size size size size size size net work work work task task task methods methods points points points process process process process trained trained trained random random random random random random similar architecture architecture architecture architecture architecture show show show show show show equation section fixed fixed rule general general generalization generalization generalization generalization average average average average average average theory theory theory obtained obtained obtained obtained obtained obtained obtained obtained note note experiments result result result result result result result result university university computation computation computation solution independent defined sequence constant estimate estimate estimate estimate estimate estimate estimate estimate computer science presented map sets sets sets sets sets sets sets sets sets maximum range press press press nonlinear nonlinear nonlinear continuous continuous sample sample sample abstract applied convergence convergence convergence convergence convergence convergence convergence convergence convergence density density density density density density density properties likelihood references stochastic due ieee positive complex complex complex complex estimation estimation estimation estimation estimation behavior statistical variance variance variance variance tion tion complexity complexity complexity assume assume measure measure measure measure measure measure measure measure measure measure measure measure measure measure learned theorem theorem theorem theorem theorem multiple good conditions conditions conditions conditions expected expected expected make make make techniques probabilities observed observed errors errors finite finite resulting ing ing regression regression regression mapping means dimension made made made made natural natural applications obtain obtain artificial artificial application application cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross series series provide provide define define proc proc location related discrete mit accuracy comparison comparison selection selection morgan morgan morgan report institute department department department version version version version version kernel kernel kernel advances advances advances joint joint bias bias cambridge computing computing equivalent additional curves estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates design design san san san san conference conference determine efficient efficient choice choice choice choice choice choice choice approximate approximate statistics statistics statistics statistics statistics statistics statistics estimated pages validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation con condition derived conditional conditional conditional conditional conditional conditional conditional criterion criterion criterion criterion criterion criterion selected depends depends sampling sampling technical denote denote denote denote denote limited assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption predictions common effective supported eds eds eds journal square easily degree including including including fit kaufmann kaufmann probabilistic probabilistic smaller underlying testing york york york york consistent consistent uniform empirical empirical leads leads squared squared squared squared squared squared squared squared squared squared squared squared squared squared squared squared squared numbers numbers max direct window international minimize denotes architectures architectures takes takes element apply inference subset subset subset subset subset subset engineering interest observations observations observations tions converge converge observation observation generalized generalized generalized generalized generalized bounded entire grant exists exists wide alternative deterministic white white white white white white white white white white white demonstrate demonstrate conclusion row row assumptions assumptions assumptions assumptions assumptions assumptions assumptions assumptions assumptions assumptions assumptions measures measures measures measures measures measures measures moody moody moody faster practice asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic mateo mateo mateo strong strong strong presence intelligence regularization minimizing min min relationship relationship averaged averaged targets introduce suppose suppose relation relation written index index index sequential generating generating estimating ann mathematical distinct metric averaging unique integrated integrated integrated integrated integrated springer quality expectation expectation expectation expectation expectation expectation expectation select select john choosing choosing formation formation squares squares squares squares squares estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator lemma evaluate restricted soft similarly reasonable reasonable smoothing smoothing smoothing fitting sufficiently faces transactions david avoid avoid expect building box priori uncertainty holds discussions successfully determining straightforward straightforward selecting selecting closely uniformly essentially orthogonal summary refer soc soc compact verlag strongly criteria sci sci hold hold hold hold hold hold hold hold hold hold hold hold hold hold hold hold hold hold comp sampled write write usual providing providing giles observable ill satisfies satisfies tesauro extend cowan cowan law minimized minimized diego wiley wiley overfitting estimators estimators estimators estimators estimators hanson optimized lippmann hall hall dataset dataset dataset dataset dataset existence scalar giving mse mse mse mse mse mse mse applicable applicable possibility authors cover analogous surfaces surfaces neu neu smallest math math measurement concepts necessarily spline spline spline equally subsets quantities quantities freedom observe academic academic ith ith ith ith multivariate optimum asymptotically asymptotically asymptotically asymptotically publishers publishers publishers glass caused perspective strictly mation commonly consequence potentially acknowledgement ridge begin author nsf nsf exemplars integrating evaluating evaluating evaluating evaluating consistency peter peter splines ity prevent geman geman datasets expectations unbiased unbiased unbiased unbiased unbiased unbiased unbiased unbiased unbiased unbiased proposition proposition proposition proposition representative accomplished optimality optimality optimality optimality interface equivalence equivalence modify appropriately establish kullback chance stronger stronger grow obtaining mark mark mark mark star star ral ral definitions north cottrell nonparametric nonparametric degradation infor analyses separating holland guarantees realization histograms den iterated clean roy wolpert variants valuable inf inf stone stone stone stone empty ics liu ence specification minus annals annals annals annals annals annals annals solves solves july convenience convenience convenience additionally wahba assess avoids verified mackey intuition formance impose permits march relate iri deleted weaker siam siam esti esti son sta likewise avoidance behaves mann manuscript opti opti bienenstock uniqueness correspondences converging designs losing supply cornput clarity kth appealing appealing appealing condi assessment anthony measurable measurable measurable measurable suffice statist charles charles categorical akaike akaike jan inappropriate sur validated validated deleting deleting deleting deleting deleting deleting jack stat stat schuster ular dilemma delete delete delete delete delete delete delete delete delete delete inte mal tics statis jackknife mate thompson philadelphia concise justify aware mild plutowski plutowski plutowski plutowski plutowski plutowski plutowski plutowski ire provably asymptotics michigan notational stuart han gerald gression gression periments xij klein economics economics partic estima yix selec deliver deliver cri chow confer plications joshua marcel dekker larsen assump unconditional unconditional unconditional downward assure borel borel mates cornell minimally consis delivers doursat ship timothy kauf regulate symp donald bibliography ser patrick patrick tistical biometrika biometrika biometrika biometrika liebler garrison iiw jeff bert bert ker ker hal hal cbms fedorov halbert halbert halbert halbert grace afforded adrian adrian adrian gregory validating integrable econometrics mally terion ise grated validatory validatory validatory validatory validatory abundant abundant singleton amine tency underfitting mathemat yilxi yilxi ley andrews dispense lect 
#@Plutowski_M,Sakata_S,White_H,
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural input input input input function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output number number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error error error error state state state state results results results results results results results results results results results results results results units units units units units units units units units units units units units information information problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer case vector vector vector order order order order order order order order order shown shown systems values values probability parameters parameters parameters noise weight weight weight weight weight unit unit unit unit distribution distribution distribution distribution approach approach approach approach approach approach approach point point point single single processing processing large large large large large large large large large large large large local local local rate analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows shows simple simple simple paper examples examples examples examples examples examples examples examples examples examples small size net work work work work task task features classification process level trained trained trained high similar architecture architecture architecture show show fixed line line line line line line line rule vectors vectors vectors vectors general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter approximation approximation approximation average average average average average average average average average theory theory theory theory obtained obtained obtained obtained note experiments result result university computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research independent defined defined defined defined found found found target initial standard standard science science science prediction left left left left presented present phase phase phase phase phase phase phase phase phase phase phase phase phase low low machine machine machine machine machine machine sets components nonlinear outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract find find find find find properties properties properties references stochastic stochastic due procedure decision introduction introduction behavior behavior behavior behavior behavior statistical statistical statistical statistical variance energy energy energy energy assume lower representations chosen higher previous previous good binary binary binary binary binary binary binary binary binary binary binary long long tree tree equations make fact fact region correct correct correct errors errors errors errors finite finite simulations simulations simulations simulations simulations minimum minimum minimum minimum ing tasks tasks multi performed times times mapping mapping factor made natural global applications study study study negative compared compared desired receptive compute proc location location location location goal constraints connected connected connected connected connected approaches approaches comparison fields support train morgan morgan morgan institute version version advances advances layers considered framework framework curve curve curve solutions transition transition transition transition transition transition transition transition transition limit limit limit limit san san san upper requires requires free free free free world randomly lines lines entropy entropy entropy finally backpropagation backpropagation backpropagation technical feedforward feedforward feedforward describe close close predictions predictions predictions theoretical theoretical theoretical theoretical theoretical main eds ability kaufmann kaufmann kaufmann combination unknown unknown fully fully fully fully technology york increasing increasing consistent details normalized description description description predict perceptron denotes architectures correlations ensemble ensemble apply machines machines machines machines machines machines machines machines machines machines recently compare previously teacher teacher teacher calculated tions smooth yields rl locations symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric grant studied studied studied scaling occur suggests deviation predicted predicted correctly runs runs runs conclusion critical assumptions numerical performs performs moody asymptotic asymptotic mateo mateo mateo temperature temperature temperature physics drawn proportional proportional decrease averaged averaged averaged introduce connectivity acknowledgements appears appears monte monte carlo carlo transitions transitions transitions transitions transitions vertical dept student student student student implement multilayer multilayer equilibrium quality implies decreases yield independently dependence dependence overlap influence variation open restricted soft soft soft understanding sizes sizes partition sign calculation calculation calculation dashed epochs purpose closed remains valid calculate sufficiently includes priori perceptrons discuss phys phys phys phys phys phys phys discussions differ symbols symbols included included committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee allowing allowing symmetry symmetry symmetry symmetry symmetry symmetry symmetry follow follow gibbs gibbs gibbs gibbs gibbs generalize load extend parametric investigate exponentially hanson lippmann existence existence possibility authors referred tanh tanh workshop func circles rev rev perfect quantities versions formal perceptton simplest arbitrarily spin residual residual agreement guaranteed improves analytical analytical majority majority sys formalism formalism formalism widely scientific qualitative qualitative alignment mechanics mechanics mechanics mechanics argument considerably quantitative quantitative poorly poorly poorly poorly poorly effort solla solla adjustable incorrect schematic mod mod gen qualitatively qualitatively qualitatively findings wesley saddle saddle saddle addison concerned connecting fails city check replica replica replica replica replica replica replica tishby tishby tishby tishby tishby tishby krogh krogh krogh carry hertz hertz hertz hertz hertz hertz hertz hertz hertz hertz hertz hertz hertz hertz hertz sompolinsky sompolinsky sompolinsky ensures connect respective respective regarded regarded infinity specialized specialized specialized specialized park broken broken seung seung generalizing generalizing generalizing generalizing generalizing escape temperatures temperatures temperatures temperatures geometrical drop drop smoothly convenience utilize par par breaking reflected care concentrated favor levin levin tems decays realizable realizable thermodynamic gener annealed annealed hansen hansen misclassified breaks preprint els signs gorithm students diagrams diagrams palmer council council discontinuous discontinuous discontinuous discontinuous discontinuous discontinuous thermal thermal tial triangles vote specialization specialization specialization edited carries scenarios scenarios nontrivial denmark acknowledges gardner gardner gardner gardner trapped trapped trapped metastable metastable metastable metastable metastable lund lund lid permutations ansatz teachers teachers teachers teachers reviews alization eralization schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze schwarze europhys europhys fruitful biehl biehl singapore ticular glasses copenhagen rid accompanied accompanied hin parga parga redwood flipping nilsson nilsson blegdamsvej danish danish korea kwon salamon sumptions nordita algebraically rau quenched quenched seminal programme watkin nonvanishing nonvanishing nonvanishing sweden lapping 
#@Hertz_J,Schwarze_H,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output number number results results information problem performance based weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case case vector vector order order order order order order shown shown shown shown shown shown shown systems systems probability probability probability parameters weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point point single processing control control large large large local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix optimal inputs form form form form form form form signal algorithms algorithms algorithms simple simple simple simple simple gaussian paper paper small small size size feature work methods methods methods methods points points points points points points points features features structure structure random random high high memory response equation equation equation equation section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule rule rule rule rule rule rule rule rule rule rule general general generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter average average average average average average theory dimensional dimensional result university threshold threshold threshold threshold computation solution solution found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial computer terms science direction direction presented activation activation activation activation activation activation activation activation activation activation activation activation activation low frequency frequency sets learn learn learn learn learn learn learn learn learn learn learn learn learn learn components components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied find find find find find find find density likelihood likelihood references component component component component component component component component component component stochastic important important mixture introduction introduction estimation statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical variance variance tion tion tion change energy energy measure measure measure measure learned learned learned chosen chosen higher part center previous cases cases required multiple equations equations equations equations make fact techniques techniques proposed proposed proposed correlation correlation correlation correlation correlation length correct tasks computed multi sum sum sum sum performed times means optimization optimization made global applications knowledge em negative artificial artificial application desired compute compute rates perform perform perform perform perform perform perform perform determined determined determined determined distributions equal power power power power proceedings proceedings department technique individual individual individual exp maps equivalent equivalent additional solutions solutions solutions solutions solutions solutions solutions solutions curves curves limit limit effects detection determine determine determine determine free world world give produce weighted simply feedforward describe stable stable stable stable stable finding assumed shape shape shape supported theoretical cluster easily objective objective objective objective objective objective objective objective dynamical interesting principle principal principal principal principal principal principal principal principal principal principal principal details predict predict neuronal denotes denotes discussed directions correlations correlations quadratic quadratic subset dimensions highly previously previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised calculated tions solve correspond pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca studies trans address generalized grant studied studied clusters clusters clusters critical critical hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian conclusions competitive editors editors sigmoid sigmoid sigmoid sigmoid clear learns learns learns learns learns learns learns propose presence drawn proportional relationship relationship relationship relationship relationship relationship question solving tuned tuned tuned implement unique correlated correlated correlated correlated correlated correlated correlated overlap solved solved solved organizing organizing organizing organizing showed approximations forms understanding suggested calculation kohonen batch determines extension discuss maximize phys phys closely differ literature situation interpreted notation usual simplified correspondence correspondence extract law law law essential optimized optimized optimized integral hessian hessian respond int maximizing maximizing maximizing complicated func understand understand neu neu act math predicting implementations thought obvious taylor taylor taylor taylor ith ith ith finds finds finds defines distinguish analyzed tive precisely controls controls controls acknowledgement definite fluctuations mechanics mechanics mechanics mechanics mechanics mechanics mechanics understood understood pure maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima partitioning partitioning partitioning partitioning partitioning partitioning maximizes attraction attraction attraction wesley addison formally lagrange lagrange linearity acts approximates homogeneous fails multiplier oja oja oja oja oja oja oja oja oja oja oja oja oja sanger sanger krogh krogh north north phrase hertz hertz weakly weakly governed ambiguity studying holland holland viewing partitioned outlined dense associations numerous minus basin basin basin responds incrementally basins basins sinusoidal sinusoidal algebraic perpendicular thresholded argued statistic ambiguous breaks breaks reveal likewise subspaces differently palmer palmer opti rons rons compo optima optima devised sen equa extracts normalize parti tells squashing degenerate statist cho reviewed reviewed reviewed generaliza linearities mization optimizes bio men psp jonathan jonathan jonathan jonathan kammen kammen kammen kammen solu analyzer nent analysed associating softky softky softky softky karhunen bennett bennett bennett bennett bennett bennett bennett bennett bennett bennett bennett bennett portland portland 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#@Prtigel-Bennett_A,Shapiro_J,
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#*learning learning learning model model model model model model neural data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure set set set set training training training training training error error error error error results information problem problem models models models performance performance based based based based based space space space space space linear linear linear layer case case case case vector vector vector vector vector vector values values values probability probability probability probability probability probability parameters parameters parameters parameters parameters functions functions functions functions functions functions functions functions functions functions distribution distribution distribution method method method point single control large large large large large analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix form form form shows simple simple simple gaussian gaussian paper examples examples examples examples examples examples examples examples examples small small net work work work methods methods step points points classification classification classification classification classification classification classification classification classification classification process problems random random random representation show section section section fixed fixed vectors vectors vectors vectors vectors generalization generalization generalization generalization generalization generalization parameter parameter real real approximation approximation theory gradient obtained obtained obtained obtained term result university university university university university variables variables variables computation solution log log log log log log log log log log log log log log log defined defined defined defined found constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard terms terms terms distance distance distance distance left left left left present low machine machine sets maximum press basis basis basis nonlinear continuous sample sample abstract applied find find computational convergence convergence likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references references references component stochastic procedure procedure important context context introduction estimation estimation estimation estimation estimation estimation estimation estimation variance variance variance variance variance variance tion complexity variable assume measure measure prior prior prior prior learned chosen chosen chosen chosen higher cases multiple good good good good good long conditions conditions represent distributed bayesian bayesian bayesian bayesian expected fact region region proposed proposed proposed correct errors ing ing regression regression respect respect sum sum means factor factor potential made study study study study obtain obtain negative vol vol true true true desired cross cross cross cross cross cross cross cross cross cross series series provide define define define define compute compute compute proc proc proc determined determined goal goal related posterior posterior comparison train modeling selection consists kernel represents bias bias graph view estimates estimates estimates estimates estimates estimates conference full choice statistics statistics statistics statistics world world world estimated estimated estimated estimated estimated estimated validation validation validation validation validation randomly levels criterion lines product processes selected iteration iteration iteration iteration iteration iteration iteration iteration sampling constraint describe describe describe describe describe fast close close rbf assumed assumed generate supported eds eds eds ability future degree degree degree makes development development noisy noisy combination unknown coefficients interesting testing structures details details supervised early polynomial minimize minimize minimize minimize minimize minimize minimize choose choose choose population population population advantage property robust side side quadratic relevant relevant relevant interest interest sufficient observations approximately approximately subjects subjects calculated volume tuning smooth smooth smooth smooth smooth studies diagonal evaluation generalized generalized generalized generalized generalized interval interval risk risk risk risk risk risk risk risk risk risk risk risk risk lead extended extended trial trial trial deviation deviation predicted generally half half reduce operator depend measures bayes bayes numerical practice asymptotic suggest taking strong regularization regularization regularization radial assuming assuming variety minimizing minimizing minimizing start iii groups base index solving ways estimating estimating plot ann ann ann dept dept dept dept dept confidence confidence confidence confidence involves remaining easy develop expectation choosing choosing family dependence review evaluate fraction fraction showed showed soft soft soft soft soft soft soft soft soft soft suggested reasonable reasonable smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing expansion reduces reduces fitting neighborhood neighborhood intervals intervals intervals iterative iterative penalty penalty penalty penalty expect expect figures kernels instances sciences automatic priors variations successfully reason suitable suitable suitable suitable differ divided score soc procedures prob sin satisfy usual generalize correspondence predictor predictor approximating oriented oriented body overfitting overfitting relations hessian issues preliminary graphical mass ml ml ml ml relationships reliable structured workshop func contours contours contours attributes attributes attributes attributes attributes attributes math math trace possibly necessarily onset predicts spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline rank quantities versions versions panel panel separated academic ith multivariate multivariate arbitrarily years smoothness smoothness smoothness smoothness adapted adapted sections sections precisely mathematics acknowledgement ridge members attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute definite medical medical read nsf nsf varies people pseudo marked marked splines splines span polynomials gave age age age age age age age age age age age age unbiased unbiased unbiased unbiased unbiased median median wang wang wang wang wang wang wang converged wesley summed don person newton newton newton newton newton newton addison optimality assign controlling outcome outcome outcome outcome biased adequate generalizes substituting continue analyses sion patient patient entry entry entry regard forecasting heart bases thin thin arrive late wolpert likelihoods davis santa fitted leaving leaving leaving leaving blood numerous leibler maximized randomized randomized alternating alternating alternating alternating uniquely smoothly wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba tradeoff tradeoff tradeoff decomposed chapter letting letting letting shaded pub pub penalized penalized penalized penalized penalized penalized penalized ftp ftp ftp file file proba plate plate wise records disease indexed portions outcomes outcomes outcomes west siam lapedes retained examination mea bility families families hilbert smoother lated cornput moss believed partly partly petsche successively governing statist statist statist wisconsin wisconsin wisconsin wisconsin thing computable computable computable computable meant nih minimizer minimizer minimizer minimizer minimizer minimizer minimizer iterate iterate stacked greatest inappropriate stat continuing decompositions decompositions conceptually madison madison madison madison albeit bernoulli bernoulli bernoulli vat craven craven craven ronald penalties penalties functionals beat reproducing reproducing klein klein klein klein klein klein klein klein klein klein klein klein klein permission interpretable attack zhao unrealistic diabetes diabetes progression progression progression progression progression progression progression tha selec cited purdue incidence indexes pima regres anova anova anova anova anova anova anova anova anova 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#@Gu_C,Klein_B,Klein_R,Wahba_G,Wang_Y,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number number system error error error error error error error error error error error error error error error error error error results results results results results results units units units units units units units units units units units units units information information information problem problem problem problem problem models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space linear linear linear linear linear case case order order order order order shown shown shown systems probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions unit unit unit distribution distribution method method method method method method method method method method method method method method method method method point processing large large large large local local local local analysis class class matrix optimal optimal optimal optimal optimal inputs form form form form form shows shows shows shows shows shows shows shows shows simple simple simple simple paper paper examples small points structure structure structure show show equation equation equation equation equation equation equation equation equation section line line line line line general generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter approximation approximation approximation theory theory theory theory theory theory theory theory obtained obtained term note note experiments result computation solution independent independent log found found found found found found sequence target target target table table table maximum maximum maximum maximum press nonlinear nonlinear nonlinear sample sample sample abstract applied find density likelihood likelihood likelihood likelihood likelihood likelihood references procedure procedure procedure introduction hand estimation statistical statistical statistical statistical statistical statistical statistical statistical complexity assume center theorem theorem theorem theorem theorem theorem conditions conditions equations equations equations fact proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed errors errors errors errors errors finite finite finite minimum minimum regression regression regression regression regression regression regression regression regression regression regression regression regression sum eq eq called mapping means optimization optimization global artificial artificial artificial artificial artificial artificial artificial artificial artificial samples samples samples samples true true true true true application define define define define determined determined experimental experimental experimental experimental experimental experimental experimental larger larger selection morgan advances difficult difficult exp exp exp exp exp exp exp sequences ai ai ai ai ai ai ai ai ai equivalent equivalent equivalent equivalent curve curve curve solutions curves san determine estimated estimated estimated estimated estimated estimated estimated basic increase con conditional lines backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation discussion discussion normal arbitrary arbitrary proof rbf role square square square square square square end ability easily smaller mlp testing york increasing choose perceptron denotes improved recent property reported practical subject machines quadratic quadratic quadratic inference conventional calculated calculated solve studies differential differential differential differential differential differential differential differential definition definition bounded interval exists exists exists exists studied studied white conclusion operator operator operator operator operator operator central sigmoid asymptotic mateo physics radial minimizing minimizing start exist exist decrease minima minima suppose relation relation relation construct construct construct solving sequential mathematical adding cycles cycles cycles cycles cycles independently independently communication estimator estimator estimator estimator estimator solved transform decomposition decomposition decomposition approximated spaces sufficiently expect characterized reason reason reason prob satisfy wavelet wavelet wavelet wavelet reach minimized minimized minimized parametric layered layered layered layered relations optimized optimized optimized optimized optimized optimized optimized optimized recursive recursive fourier tanh fundamental hill coefficient analyze analyze analyze predicts algo fisher precise perceptton academic amari submitted asymptotically phenomena perspective closer strictly precisely leaves optimize optimize mechanics lattice backprop globally ordinary ordinary ordinary ordinary ordinary proofs japan abilities analyzing corollary corollary corollary tone sion yang enable permutation theoretically lem lem speaking uniquely uniquely adopt theorems theorems hundred algebraic algebraic num playing book det solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable solvable ning proposes attained baxter baxter degenerate degenerate degenerate iid iid company mcgraw watanabe watanabe watanabe watanabe watanabe watanabe rem tan tan tan tan murata agation inconsistency fell ricoh ricoh yoshizawa equiv equiv strange regres didn didn didn mono neurm ors structed ain yokohama yokohama ivi hnction hnction clarified sho shin ici stood aset contradict contradict ahnost toda 
#@Watanabe_S,
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input function figure set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number state results results results results units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem based space space weights weights weights weights weights weights weights linear linear vector order order order shown shown shown shown systems values values weight weight unit unit unit unit unit unit unit unit approach pattern pattern pattern single analysis class class class form signal signal signal signal signal signal signal algorithms simple simple simple simple simple simple simple simple small small net work work task task task task task task task task task fig fig fig step structure problems problems problems problems problems problems problems architecture architecture architecture architecture architecture show show show equation equation equation equation general general general general general general parameter real states theory theory theory term term note note note note note dimensional result result result result result university university university threshold threshold threshold variables variables variables variables variables solution solution solution solution solution research sequence sequence dynamics initial constant computer computer terms connections connections node node science science left presented map activation activation low machine machine sets maximum maximum press press press abstract find find computational computational computational properties references positive decision decision decision decision decision hand hand behavior behavior behavior behavior behavior behavior recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference complexity complexity complexity complexity complexity complexity variable variable variable lower signals signals signals signals signals signals signals higher higher higher part theorem theorem theorem theorem bound cases type type long represent equations equations equations equations equations fact fact correct correct correct correct correct forward forward forward forward classes sum called called elements mapping negative negative original original original original artificial artificial represented desired compute perform perform determined determined related related related related related connected equal equal equal power power mit mit steps larger larger contrast connection connection connection update train nets institute difficult final final final final exp exp framework cambridge cambridge equivalent equivalent solutions solutions solutions solutions design design top top top bit conference determine statistics pages pages pages pages con condition weighted weighted types product finally depends simply technical close corresponds complete complete complete complete stable proof proof proof proof supported theoretical theoretical theoretical main main instance instance instance degree including smaller smaller smaller needed dynamical coefficients york york representing max bottom bottom polynomial polynomial architectures architectures architectures discussed discussed property takes side quadratic sense relevant volume works module solve solve solve solve correspond rl definition evaluation interval grant constructed constructed constructed constructed exists exists exists exists exists exists exists lead feed feed feed setting setting setting demonstrate conclusions central modules modules modules modules modules modules modules modules modules modules strong largest demonstrated intelligence exist iii configuration configuration configuration configuration base question question question reference suppose relation construct construct construct construct solving mathematical mathematical mathematical infinite consisting develop springer implies choosing depending static static updates classical construction construction construction construction construction david david david box thesis formulation instances instances instances instances determines prove prove holds phys aspects aspects closely society refer verlag return hold usual michael michael correspondence received deal deal intrinsic investigate recursive existence existence existence existence workshop fundamental notion neu math math coefficient editor integer integer integer integer integer integer integer integer der formal formal mapped phd attempts massachusetts massachusetts trivial trivial trivial track multiplication tractable starts london stress lin lin lin straight satisfied closer constructing commonly acknowledgement universal universal universal universal universal universal universal universal acad circle computers author freeman simulate formulated robinson operate exhibits berlin synthesis incoming incoming replace conclude conclude summed realized indices intractable equivalence equivalence oxford oxford restrict martin martin impossible impossible fails accepted mail moment interpret hope ral definitions definitions imply guide symposium started reset corollary corre decide decide decide decide decide multiplied shortest extends davis davis davis davis davis davis integers johnson johnson johnson johnson johnson johnson johnson counts linked solves leaming leaming sontag sontag sontag formulate uniquely uniquely restrictions chapter england demon arising march loading loading loading loading loading loading loading loading loading loading loading page elsevier drops things september vice vice versa versa sponding stephen hilbert hilbert hilbert hilbert hilbert hilbert hilbert hilbert hilbert hilbert hilbert hilbert hilbert solvable blum blum blum stay concrete concrete seed outgoing judd judd judd judd judd judd polynomially rivest rivest rivest scott computable computable handbook transmit tenth tenth tenth tenth tenth tenth tenth tenth occurrences ira completeness completeness developments amer amsterdam putational turing sends phy monthly netherlands evaluates colt colt ronald disappear preset han siegelmann siegelmann siegelmann mere predicate synchronously strated emitted unary cients hardness austria austrian austrian vienna vienna jeffrey tractability intractability famous famous knew coeffi wien garey garey garey garey accumulator accumulator catalog unaltered eduardo informatica fonds zur pauern nalysis schottengasse computability 
#@Wiklicky_H,
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#*network model model model model model model model neural neural input input input input input data data data data data data data data data data function function function function function function figure time time set algorithm number number number number number system error state state results results results results results information problem problem problem problem problem problem models models models models performance based based space space linear case case case case vector vector order order shown shown shown shown systems systems systems systems values values values values values values values values probability probability probability probability parameters parameters parameters method method approach point point point point point point point point point point point point point point single single control large large large large large local test analysis analysis analysis analysis analysis analysis analysis analysis inputs inputs form form form form shows shows shows shows shows algorithms algorithms algorithms simple simple simple examples size size size size size size size size size size size work task methods methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig field classification process problems problems problems problems problems problems problems problems problems problems problems problems random random random random random random random random random random random random random random random similar similar similar similar show show section fixed rule parameter parameter parameter approximation approximation approximation average average average states theory theory theory theory theory theory obtained obtained obtained obtained obtained obtained obtained note note experiments university university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables computation computation computation solution solution research independent log log defined defined found found found found table table table table table estimate estimate computer computer computer computer computer terms terms science science left left present phase phase phase phase phase phase phase phase phase phase phase maximum range range range continuous continuous abstract applied find find find computational computational computational computational computational properties references procedure procedure procedure important important introduction complex behavior behavior behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical generated generated generated generated generated generated generated generated generated cost cost cost cost cost search search search search search search energy energy energy energy difference complexity complexity complexity complexity complexity variable variable rules rules part center center center previous bound required good good good good good binary represent expected make fact fact region region region proposed correlation length length length length length length observed observed observed scale scale scale finite finite finite finite finite finite finite finite finite finite minimum ing tasks human sum called called times made natural natural natural study obtain vol vol vol vol specific samples samples true cross cross provide define define define proc proc proc proc proc perform determined determined determined experimental experimental experimental experimental experimental distributions discrete equal steps accuracy larger larger larger support proceedings institute institute institute institute implementation consists internal difficult difficult graph sequences ai computing computing experiment curve curve curves curves curves curves curves curves curves curves curves transition limit limit limit effects effects effects determine determine upper requires world world give give give derived derived randomly randomly randomly randomly randomly randomly randomly randomly lines lines entropy entropy entropy entropy finally finally processes evidence evidence evidence evidence constraint simply discussion normal technical increases group denote close inverse complete complete predictions predictions finding finding shape theoretical require main instance cluster cluster fit fit probabilistic pairs smaller smaller smaller needed reduced account testing ratio ratio ratio increasing increasing increasing structures empirical details numbers max direct expert expert polynomial description correlations correlations resolution element practical include identical identical side recently relevant sufficient highly compare calculated works match address evaluation evaluation observation observation entire increased parts parts parts studied studied studied invariant invariant scaling scaling scaling scaling scaling scaling scaling scaling suggests digital wide correctly width boundary boundary critical critical critical critical critical critical critical conclusions interactions interactions interactions numerical clear exponential exponential constrained temperature taking strong hard hard hard hard hard physics physics physics physics physics physics physics largest largest characteristics characteristics proportional assuming identification configuration configuration configuration configuration appears written solving solving factors factors generating plot transitions transitions transitions transitions transitions transitions ann distinct distinct metric averaging easy scales scales scales scales shift shift shift shift expectation boolean boolean boolean boolean focus dependence dependence depending correlated overlap overlap solved detailed evaluate organizing fraction fraction fraction fraction fraction understanding similarly partition sign sign diagram calculation combining remains construction foundation expect expect building figures usa bell instances instances instances instances assignment sciences automatic coupled holds determining closely capable differ computationally computationally modes identify efficiently tend ten ten characteristic capture strongly prob heuristic heuristic success anderson symmetry lie strategies comp simplified play absence providing leading thresholds thresholds thresholds thresholds deal deal modelling bars schedule carried production exhibit exponentially optimized existence giving int analytically scaled authors root comparable understand phases analogous math math trace plausible configurations configurations thought quantities quantities obvious taylor taylor precise expressions expressions contributions arbitrarily submitted years years spin spin spin spin spin spin spin spin mentioned formula formula formula formula formula directed ground ground growth track defining phenomena phenomena phenomena phenomena slope slope biology explanation glass glass glass glass glass glass lies correction london reasons rapid sys satisfied satisfied style precisely worst immediately scientific scientific universal calculations lowest mechanics mechanics mechanics mechanics mechanics mechanics mechanics questions behaviors percent items consistency experimentally lack orders introducing marked employ sharp sharp characterize characterize limiting popular proven proven proven collective logical logical inherent credit wesley consistently shifted sort addison generator extensive extensive ratios arguments theories theories extending extending fits ments ranges satisfying satisfying check replica replica replica keeping tishby tishby tishby tishby tishby roles shifts imply salk clause clause clause exceeds symposium combinatorial combinatorial combinatorial combinatorial combinatorial selects exploring overlaps weakly ranging ranging ranging studying conjunction lengths heart accounts originally candidates israel israel specialized foundations matter repeatedly proteins arrows arrows card broken davis davis davis valuable characterization vari treat temperatures crossing outline rigorous clique ter pointing pointing cooperative stock conjecture attempted publication ibm ibm interact tems crossover crossover labs annealed annealed annealed annealed annealed annealed annealed annealed annealed annealed permits mitchell mitchell mitchell mitchell mitchell challenging relate individually increasingly increasingly employing sketch portions amino accounted son truth commercial applicability molecules slopes signs supporting experi aaai aaai aaai lems moderate copies satisfaction satisfaction satisfaction satisfaction satisfaction ping mcdonnell converging spring subjective aid arrow powers industrial spins spins clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses clauses formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae formulae huberman huberman ally coincide kirkpatrick kirkpatrick kirkpatrick kirkpatrick kirkpatrick kirkpatrick kirkpatrick kirkpatrick kirkpatrick characterizes att colleagues ignores acid salesman salesman alto permanent accounting ready materials scott vicinity ranged doubling vanishing inform watson watson formulas decades completeness completeness completeness jerusalem jerusalem jerusalem searched disorder pew tal connor quantified sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat sat eta literal plexity ables hebrew hebrew heights deeper assoc rescaling parisi evaluates anticipate kirk kirk atoms heat workers machinery complexities syrup banks neglecting singapore rescaled rescaled rescaled rescaled buy glasses equipment stein travelling attack ising franco franco reactions mat replicas replicas replicas collaboration business manage reed reed negation hardness visiting 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#@Gyorgyi_G,Kirkpatrick_S,Tishby_N,Troyansky_L,
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#*network model model model model model model model model model model model model model neural neural neural neural function function function function function function function figure figure time time networks number system system system system system system system system system system system system system state state state state state results results models models space case case case case case order order order order order order order order order order order order order order order order order shown systems values values probability parameters parameters parameters noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution method approach pattern pattern point point single single large local neuron neuron neuron neuron neuron rate patterns form form form form form simple simple simple gaussian paper examples small step field field field field field process process process random random random response response equation fixed line line rule generalization generalization parameter parameter parameter real real average average average average average states theory theory theory theory theory obtained term term term term note activity dimensional university variables variables variables research independent independent log defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics terms terms terms synaptic synaptic science left presented present present present phase phase phase phase maximum range range range learn continuous abstract find find find references stochastic stochastic stochastic stochastic due complex hand statistical statistical statistical dynamic dynamic dynamic dynamic variance recurrent change energy energy energy energy difference lower lower lower higher higher cases type type long expected markov make fact fact region correlation scale finite finite ing respect dimension natural study obtain negative negative negative specific specific compared application define determined related connected connected gain comparison larger fields fields fields fields fields fields support source loss version consists exp exp exp exp exp considered equivalent transition transition transition transition transition transition transition transition transition transition limit limit limit top full choice choice free free free free free world basic produce randomly developed types types finally processes discussion transformation fast fast fast fast fast fast fast fast fast fast inverse inverse assumption corresponds stable stable surface actions effective effective effective theoretical adaptation pairs smaller underlying dynamical functional ratio ratio ratio york leads leads leads leads details details max pre direct making magnitude combined choose choose discussed introduced introduced side sense engineering varying observations tuning studies separation symmetric symmetric symmetric generalized organization organization grant lead lead studied studied studied scaling scaling extended locally white critical critical critical critical greater hebbian hebbian valued interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions differences practice asymptotic temperature temperature temperature presence physics physics external external external external external solid proportional manner characters connectivity identification acknowledgements boltzmann boltzmann boltzmann explicit van factors generating generating transitions stability dept changing averaging infinite infinite physical physical scales interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction adding adding equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium implies choosing communication viewed influence influence variation detailed labels evolution completely partition partition partition partition partition slow slow slow slow slow slow slow slow formulation inter inter inter discuss coupled coupled coupled coupled coupled coupled coupled coupled coupled coupled coupled coupled coupled coupled phys phys phys phys phys phys phys phys phys phys characterized characterized suitable effectively effectively post situation characteristic characteristic road symmetry symmetry symmetry symmetry quantity bar write usual usual absence deal modelling presents remain layered wiley perturbation perturbation varied involving involving replaced replaced dotted behaviour behaviour analytically analytically removed math math math math math math math naturally integer onset onset rev rev der assumes separated hebb averages spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin slowly analyzed glass glass glass glass glass glass glass glass glass glass glass glass glass briefly briefly turns perspective sections sites precisely immediately scientific describing qualitative meaning fluctuations alignment mechanics relevance quantitative lattice introducing exhibits exhibits exhibits anti anti characterize gen gen gen gen gen gen cal ordered ordered enables replace lim lim lim simultaneous instantaneous picture college analogue analogue analogue oxford oxford oxford acts controlling generality inspired spontaneous dealing imposed grow balance replica replica replica replica replica replica replica replica replica replica replica replica replica replica modifications substituting financial consequences tic refers refers grants summarize vari mechanical treat temperatures temperatures temperatures breaking breaking breaking community evolve evolve thermodynamic thermodynamic dominated annealed jij jij jij jij jij jij jij jij jij jij jij jij jij jij jij jij interacting concentrate flip relates exchange induces tissue challenge correlate gratefully coolen coolen coolen coolen coolen coolen coolen coolen characterizing characterizing council thermal instability instability instability const const continued european solvable dominates spins replicated tip devised believed fij obey bond kirkpatrick kirkpatrick kirkpatrick hamiltonian arrives evolving subscript ranged ranged enters routes sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington rises disorder ables ansatz trick trick trick reminiscent reminiscent parisi infinitesimal acknowledged workers clarify ferromagnetic ferromagnetic ferromagnetic singapore zij namic lira stochas glasses kij kij kij almeida almeida ising ising ising efficacies rli private replicas replicas replicas replicas complication jii jii disparate extremum substitutions thouless thouless virasoro zard zard zard gauge til lln quenched quenched quenched quenched superscripts shinomoto shinomoto recognise thermodynamics thermodynamics physi langevin langevin lnz rri rri curious gon pretation sell esting nit adiabatically 
#@Coolen_A,Penney_R,Sherrington_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input function function function function function function function function function function time time time time time time time time time time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output output number number number number number number number system system system system system system system system error error state state state state state state state state state results results results results results results results results results units units units units information problem problem problem space space space space space space space space space space weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case case vector vector vector order order order shown shown systems systems systems systems systems systems systems systems systems values parameters parameters parameters noise weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons unit unit unit point point point point point point point point point point image image image single single control control control large local matrix matrix matrix matrix matrix inputs form form simple simple paper paper examples small small small small small small net net net net net net work cells cells cells cells step step step points points process process cell cell cell cell cell problems problems random similar show equation section section section section section section section section section section section fixed fixed fixed fixed fixed fixed line line rule general general general general general general general general general general general real real real real approximation states theory theory theory obtained term term note dimensional dimensional dimensional result university university threshold threshold threshold computation solution research research defined defined defined found sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics initial constant table computer computer computer computer terms terms terms distance distance distance synaptic map map map map map map map map map map map map map map map map map activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation sets sets range range range range range range range components continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog properties likelihood references component component component due due positive positive positive important important important introduction action action complex hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior recurrent recurrent recurrent tion tion difference assume assume assume assume assume assume assume chosen higher higher previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem cases type type type type type long long conditions conditions conditions conditions conditions fact fact fact fact fact fact fact fact fact length length observed errors errors errors errors errors finite finite finite finite finite finite finite finite finite finite finite finite finite simulations simulations simulations total total simulation simulation called called called means means natural natural natural global global global global global global obtain original represented true true true series proc determined connected gain discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete comparison contrast support nets nets nets nets nets nets nets nets nets nets nets report institute department loss loss loss implementation implementation implementation difficult exp exp exp exp exp addition ai ai ai ai maps maps maps maps maps maps maps maps maps equivalent equivalent equivalent equivalent solutions solutions trajectory conference conference determine upper requires choice free give give give give condition condition condition types types product product actual finally finally finally processes iteration iteration nature technical feedforward feedforward feedforward arbitrary arbitrary arbitrary arbitrary transformation inverse actions proof proof proof proof proof proof proof proof proof proof proof common common common common implemented assumed require main main main face end instance easily makes makes simulated typically combination dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical jordan block block transfer projection york increasing principle operation representing call max making idea choose run sources sources sources denotes denotes denotes denotes exact property property property property property property property property property property property pair element element element apply introduced include side pixels sense sense sense sense recently interest dimensions sufficient sufficient sufficient sufficient tions tions converge trans diagonal diagonal diagonal diagonal diagonal address definition background chain generalized bounded bounded bounded interval interval interval interval interval entire grant exists expression invariant invariant invariant digital digital rotation rotation rotation locally locally locally deterministic deterministic setting conclusion minimal trajectories segment segment segment segment segment segment segment valued tangent tangent sigmoid sigmoid numerical practice strong hard hard hard hard presence external sigmoidal sigmoidal sigmoidal sigmoidal variety exist derivatives configuration configuration configuration configuration question question question denoted denoted attractor attractor acknowledgements suppose appears ways factors mathematical mathematical changing recall metric metric metric metric metric metric simultaneously infinite infinite infinite remaining easy easy easy consisting springer springer quality blocks blocks boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean family family lemma lemma lemma lemma detailed open open updated fraction showed approximations evolution evolution decomposition approximated approximated key classical classical spaces spaces spaces reduces roughly roughly purpose valid distances sufficiently euclidean euclidean euclidean precision includes combinations activations activations activations activations activations activations coordinate formulation eigenvalues eigenvalues eigenvalues sciences determines prove partially characterized characterized aspects uniformly suitable society essentially identity identity identity identity identity receives characteristic capture compact compact compact compact verlag verlag showing follow device notation involved vary observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable thresholds thresholds moves satisfies satisfies presents explore remain american perturbation investigate exponentially detail strengths replaced limitations limitations fault ideal ideal ideal ideal referred referred proper tanh tanh notion surfaces math math measurement possibly configurations perfect implementations thought logistic logistic precise precise precise observe explored ith message extent simplest motivated established rows piecewise trivial fairly explanation multiplication multiplication lies reasons strictly precisely precisely leaves leaves leaves hyperplane arise arise universal author geometry nsf addressed robustness robustness robustness conjugate conjugate conjugate argument argument questions people applies applies reflect pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo autonomous autonomous autonomous continuously summarized perturbations perturbations perturbations perturbations characterize chen chen inherent tolerance eventually eventually traces differentiable cor globally globally globally globally ordinary drift acts acts acts nonzero rigid establish establish establish generality generality generality difficulties odd intelligent observing definitions definitions definitions definitions canonical lyapunov composition composition composition meaningful negligible negligible surprising regard topological intended consequences infinity claim permutation reader contraction properly passing hypercube hypercube hypercube hypercube inf propagate characterization characterization characterization dense dense metrics multiply listed creates opposed sontag sontag sontag sontag sontag uniquely nelson poses restrictions sigma exception tradeoff auxiliary rain jacobian acting home iff sketch sketch sketch conversely cartesian france discusses electronics minor preprint likewise likewise ation bring subspaces sigmoids sigmoids remark characterizing uniqueness interior saturated saturated saturated saturated primitives hyperbolic hyperbolic hyperbolic hyperbolic european virtually imple puts suffices loosely determinant concerns possess coincide accumulate optics evolving totally totally reflection evolves facts devoted ated notions notions orbit orbit orbit orbit orbit orbit orbit orbit orbit orbit orbit orbit orbit orbit orbit orbit orbit activa cient cient broader deeper regional netherlands iterates wii mented idealized providence disconnected disconnected contin iai oft trivially useless synchronously exceptions exceptions admits pointwise implementa observability observability observability observability observability observability observability observability observability observability observability observability observability observability observability observability observability observability observability ams consequent consequent traced traced fax obser obeying misleading hecht hecht tent contaminated print jacobjan preclude inevitable inevitable oper ccr orbits orbits orbits orbits orbits orbits orbits equiva franklin franklin cbms distinguishable concomitant evalu weigh island worthy worthy peculiar instants redundancies nielsen icy fool cnrs endowed endowed kan kan rhode rupted distort lwl perturbs exceptional noi ordinarily determinants lently 
#@Botelho_F,Garzon_M,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model model neural neural neural neural neural neural input input input input function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time networks networks networks number number system system system system system state state state state state state state state state results units information information information information information information information information information information models models based based based space linear case case case case case case case case case case case vector shown shown systems systems probability probability probability probability probability probability noise noise noise noise noise noise noise weight functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution approach pattern pattern pattern pattern pattern point single processing processing large large large large large large local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns analysis inputs form form form form shows shows simple visual small net work work fig fig fig fig fig fig fig fig fig fig fig fig fig cells step points level level structure structure problems memory memory response response response response response response response response architecture show show equation section section fixed fixed rule rule rule rule general general general general general parameter average states states term term note note note note note note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result threshold threshold threshold threshold threshold threshold threshold solution defined defined found dynamics dynamics dynamics dynamics constant constant constant constant constant constant constant standard synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic frequency frequency frequency temporal temporal temporal nonlinear nonlinear abstract back back find find references important important important introduction introduction action behavior behavior stimulus dynamic tion tion tion tion tion assume assume assume assume assume assume assume chosen higher higher part cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike distributed distributed distributed equations equations equations equations make make fact fact fact correct correct finite simulations simulations total total simulation sum eq eq called means means factor potential potential potential potential potential potential potential potential potential potential potential potential potential vol relative specific specific receptive define define define define rates rates rates rates rates rates rates rates active active active active active active active connected connected connected equal approaches contrast connection connection fields train train dependent modeling morgan words department consists code code code code code code code code code code code kernel kernel advances difficult difficult exp exp exp exp exp delay delay delay delay scheme graph sequences equivalent equivalent equivalent equivalent environment san capacity capacity full statistics statistics free free condition coding weighted conditional conditional conditional finally inhibitory depends depends biological associative associative discussion describe describe describe describe describe arbitrary arbitrary arbitrary fast inverse corresponds excitatory excitatory stable stable stable stable amount short short effective effective assumed synapse supported theoretical theoretical theoretical theoretical kaufmann reduced functional fully fully york york special principle principle leads pre pre pre pre pre pre window window description description description description description description description neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal denotes denotes denotes membrane membrane membrane membrane recent recent exact exact ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble typical typical typical period period period period period period period subject identical subset relevant relevant sufficient sufficient highly highly varying approximately calculated yields yields yields yields correspond rl interval interval interval interval organization increased increased increased grant amplitude amplitude amplitude amplitude parts parts occur spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes locally touretzky occurs occurs occurs hebbian hebbian hebbian conclusions depend moody exponential mateo hard integration integration external reduction reduction pulse pulse turn start start averaged averaged averaged averaged averaged averaged averaged averaged question acknowledgements relation relation van van van van van van van van van van van van van van van van van van van index describes describes stability stability simultaneously averaging averaging involves interaction interaction interaction interaction springer springer potentials formation formation dependence stationary stationary stationary stationary stationary stationary stationary stationary stationary interpretation interpretation transform activities activities activities activities activities activities activities activities similarly past past earlier earlier reasonable dashed delays intervals intervals intervals false remains intermediate construction fire fire fire fire fire fire retrieval inter inter inter determines plotted absolute phys partially characterized simplicity columns differ encoded driven driven included spiking spiking spiking spiking spiking spiking spiking spiking spiking oscillatory build build post post post post post mackay mackay identity identity identity identity receives excitation traditional verlag verlag induced contained contained link neuroscience contribution oscillations oscillations oscillations oscillations timing involved write write usual delayed cat preferred neighboring deal trains law origin wiley transformed rapidly put relations lippmann postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic biol structured oscillation oscillation oscillation oscillation oscillation func presynaptic notion transmission transmission necessarily necessarily rev perfect adjusted der portion noted nerve hebb hebb hebb hebb defines ment slowly defining unstable phenomena analytical immediately immediately immediately immediately pulses pure passes berlin berlin limiting synchrony collective collective germany coherent coherent coherence lim lim simultaneous instantaneous cor globally globally globally contribute cybern appropriately refractory refractory refractory refractory refractory recover labelled neurophysiol fails binocular analogy chemical attractive efficacy keeping definitions belong fires fires fires fires started reset dominant infinity sim belongs assembly assembly assembly assembly assembly assembly assembly dif ensembles ensembles ensembles ensembles ensembles modelled axonal axonal stimulated locked card card card card eqs eqs eqs eqs epsp epsp considerations lett inf alternatively intersection fired fired fired fired mind emission schulten schulten ent wiesel wiesel reaction spatio spatio spatio ical tendency hubel hubel suppressed jij synchronized assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies locking induces induces things atr atr atr atr atr mcculloch mcculloch differently characterizing sake insufficient builds ferent arrow eral hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen hemmen concerns ref edited edited edited gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner resolved inspection communicate gathered stabilize noiseless meaningless biophysics srm srm men couple infinitesimal heidelberg heidelberg biophys bull miinchen miinchen zij physik regularly domany domany stein stein efficacies efficacies sev superficial joe refractoriness refractoriness integrations exponentiation prefactor momentary harmonics harmonics situated thereof dfg leo transi cou pled hsu evoke deutsche descrip descrip descrip bined coherently coherently elevated disappeared disappeared raster raster raster creased impression ritz semble incoherent incoherent incoherent incoherent emitting tlt tlt tlt tlt sii hem sembles 
#@Gerstner_W,vanHemmen_J,
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#*network network network network network network network network network network network network network network model model model model neural neural neural neural neural neural neural neural data function figure figure time time time time time time time time time time time time time time time time time time time time time networks networks networks number number number system system system system system system state state state state state state state state state state state results results results results results units units models models models linear case case case order order order order order order order shown shown systems systems values values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons point point point point point point point point point point point point point point large large large large large large large large large large local local local local local local local local neuron neuron neuron rate rate analysis analysis matrix form shows small small size work work fig fig points points field field high similar similar similar similar show fixed fixed fixed fixed fixed fixed fixed fixed general general parameter parameter parameter parameter parameter real real average average average average states states states states states states states theory obtained note activity activity activity activity result university university university threshold computation computation dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant constant constant constant constant constant estimate connections connections synaptic science low temporal range press press basis abstract find properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic important important important introduction behavior behavior behavior stimulus dynamic recurrent recurrent recurrent recurrent tion difference chosen part part part center cases firing firing firing firing cortex cortex cortex cortex cortex spike represent represent represent represent represent expected expected equations equations equations equations equations equations equations correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation probabilities observed observed observed observed ing means study study study study study vol relative relative relative compared cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross provide define rates rates rates rates perform active experimental connected cortical cortical cortical cortical cortical equal equal comparison comparison comparison comparison comparison fields fields dependent modeling institute represents exp exp exp exp delay delay ai cambridge solutions solutions solutions solutions solutions transition limit limit limit requires statistics statistics con con levels types finally inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply measured inverse inverse inverse inverse corresponds corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable circuits assumed assumed supported theoretical theoretical theoretical theoretical pairs pairs pairs account functional coefficients coefficients fully testing testing mode magnitude magnitude decay neuronal neuronal neuronal neuronal neuronal neuronal neuronal denotes denotes denotes denotes population population population population population population population recent correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations exact pair interest approximately studies definition symmetric amplitude amplitude amplitude studied studied studied extended conclusion conclusion critical critical critical critical depend interactions interactions differences weak weak strong presence physics physics cycle sigmoidal exist averaged averaged averaged averaged averaged connectivity denoted acknowledgements relation written solving stability consisting consisting equilibrium equilibrium cycles focus focus focus focus dependence dependence dependence dependence depending depending stationary stationary stationary stationary stationary correlated overlap detailed evaluated evaluated approximations forms sizes activities activities activities activities activities activities activities activities activities activities constants constants constants remains foundation coupling coupling figures usa eigenvalues sciences memories memories plotted plotted discuss coupled holds holds partially discussions characterized modes oscillatory oscillatory oscillatory characteristic oscillations oscillations oscillations physiological hold hold hold hold leading cowan cowan cowan trains carried exhibit relations detail divergence helpful school rest biol possibility tanh tanh tanh tanh statistically statistically analogous analogous neu bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation der expressions regime averages years cos cos ground ground growth growth growth growing unstable localized auto auto auto auto auto fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations populations populations populations populations populations populations populations populations quantitative slower aim collective collective coherent coherent coherent cor cor phenomenon phenomenon cybern homogeneous purely jones grows outcome spontaneous saturation smith smith check definitions imply wilson wilson wilson overlaps sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky equals assembly israel israel israel cerebral cerebral extensively eqs eqs eqs summarize break amplitudes magnitudes dominated dominated interacting interacting interacting regimes cij cij assemblies assemblies sta investigations investigations indication macroscopic macroscopic macroscopic vanishes holding tel tel microscopic lation thermal thermal inconsistent neighborhoods neighborhoods abeles abeles abeles abeles abeles pronounced rons exposed obey neocortex neocortex edited comprising comprising hopf hopf hopf hopf hopf approached approached nonstationary nonstationary nonstationary nonstationary aviv aviv wagner wagner jerusalem plenum schuster schuster iris hebrew damped damped nections tentative bifurcations bifurcations bifurcations bifurcations diverges lacking faculty raymond aperiodic resembling slowing slowing als peters quiet correlograms ker kleinfeld nized autocorrelations autocorrelations linearizing popu astronomy cii cii cii eri haim beverly sackler concreteness ero racah corticonics binational orga extracellularly 
#@Ginzburg_I,Sompolinski_H,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural input input data data function function function function figure figure figure time time time time time time time time time time time time time time time time time time time time time time time networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm error error error error error error error error error error error error results results results results results results results results results results results results information information information models based space space space space linear linear case vector vector order order order order systems systems systems systems systems values probability probability probability probability probability probability weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions approach approach processing processing processing processing large large local local local local local neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form form shows shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian paper work work methods fig fig fig process process trained trained structure random random show show show show show show show equation equation equation equation equation equation equation fixed general general general parameter parameter parameter parameter parameter parameter approximation approximation approximation average average gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term note dimensional dimensional dimensional dimensional result result university computation solution solution solution research research independent independent independent independent independent log log log log log log log log defined found dynamics dynamics dynamics dynamics constant constant constant estimate estimate computer terms terms terms science science prediction left left left left present motion range components continuous continuous continuous continuous continuous continuous abstract find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density density density density density density density properties references references component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee positive procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical generated variance cost cost search search search search search search search variable assume lower measure chosen higher previous previous previous previous required multiple conditions conditions conditions conditions equations proposed correlation correlation correlation correlation correlation correlation correlation probabilities probabilities observed simulations simulations simulations simulations simulations simulations ing simulation simulation simulation respect sum performed times times times times times times elements optimization optimization optimization dimension natural study study obtain obtain obtain obtain negative vol vol vol artificial relative true series series define define define define define rates rates rates determined goal related discrete discrete discrete discrete discrete discrete power power power approaches update update update update descent descent descent descent descent morgan morgan morgan proceedings proceedings report institute institute words department loss advances advances advances connectionist exp exp scheme scheme addition graph graph ai ai equivalent directly directly directly additional additional solutions solutions curves curves curves curves curves curves curves curves estimates san san san top top top determine determine upper upper significant statistics speed speed give give con con developed path finally simply achieved covariance technical describe fast predictions predictions predictions circuits effective effective effective effective assumed supported theoretical theoretical require eds eds eds eds journal square square square square end easily noisy including kaufmann typically smaller smaller unknown coefficients technology york squared squared squared squared squared details call max max international bottom bottom decay attention denotes denotes improved discussed ensemble ensemble ensemble ensemble practical apply engineering interest dimensions dimensions previously previously previously teacher yields correspond correspond correspond converge differential achieve achieve diagonal diagonal diagonal increased parts suggests alternative alternative touretzky deterministic white white critical greater greater trajectories operator operator depend moody moody moody moody moody moody moody moody moody moody faster asymptotic asymptotic asymptotic asymptotic asymptotic mateo mateo mateo suggest propose physics drawn california solid solid minimizing minimizing min min targets targets minima force appears relation derive ways plot mathematical mathematical dept coordinates coordinates averaging physical remaining easy develop minimization springer john john john decreases review depending densities densities evaluated evolution evolution evolution evolution understanding similarly dashed expansion expansion reduces neighborhood purpose valid initially initially norm norm norm box eigenvalues eigenvalues batch extension extension extension extension mozer specifically coupled characterized simplicity maximal identify literature identity identity summary verlag quickly link interested lie follow involved involved giles giles reach automatically satisfies acknowledgments cowan cowan simpler unlike schedule requirements hanson hanson hanson hessian hessian dotted dotted school authors office referred momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum coefficient coefficient trace trace formal algo algo initialized improving defines optimum optimum optimum asymptotically asymptotically asymptotically asymptotically asymptotically slowly slowly trivial trivial publishers publishers publishers derivation slope diffusion sections formalism mathematics scientific involve opt opt lowest lowest integrating understood elman tional lms lms lms lms lms lms lms lms fed treated compares calculating calculating measuring weigend curvature achieves achieves adjust adjust electric displays instantaneous instantaneous leen leen leen leen leen leen leen leen leen leen leen leen leen leen optimality equivalence restriction arguments drift nonzero smolensky establish generality air darken darken darken darken darken proceeds moment optimally symposium generalizes moments falls governed governed governed iteratively studying schedules schedules express reader master master master late late late late late late late late late roy roy route grants executed treat leaving summer minus annals achieving basin basin ease auxiliary auxiliary rithms rithms graduate annealed annealed expand expand retain spreading spreading statistic statistic statistic regimes regimes unconstrained cij esti behave transients drops drops drops drops drops oregon oregon differentiating mann mann walk opti ble tom todd todd adaptively sharply peaked clark clark orr orr orr orr orr orr orr orr interpolate adjusts evolves evolves adapts vicinity equilibria facilitates retaining derivations vergence mization fundamentally heskes heskes heskes cient won theo formulations imposing goldstein goldstein mate draws diverges gorithms asymptotics asymptotics asymptotics neglecting insure exposition passage lations southern robbins robbins normality normality normality normality kushner kushner portland depict kappen monro monro kramers kramers christian insures insures crit crit crit crit crit crit crit walks ivl ivl ivl ivl ivl kauf kauf strained propor dii asymp asymp amin bert coeffi oscil confine halbert continous eff eff eff larry genevieve crt hopping xtx cii retical totic totic ali spective dispense lipmann drb 
#@Leen_T,Orr_G,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time networks networks networks networks networks networks networks networks networks networks networks output number number number number number state state results results results results results information information performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based case case vector vector shown shown systems values values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution method approach pattern pattern pattern pattern single processing large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal gaussian gaussian small small small small small size size size net work work field field field field field field field field field field field field level level level level current high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory similar similar architecture architecture architecture show show show show show section fixed fixed general general general average average average states term activity activity activity activity activity activity activity activity dimensional result result university university threshold threshold threshold threshold threshold computation independent log found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial standard computer terms connections connections connections connections synaptic synaptic science presented presented presented present activation activation activation low low low low low low low press basis continuous abstract applied applied applied applied applied applied find find analog analog analog analog analog analog analog properties properties references due due positive decision introduction behavior behavior stimulus effect generated variance search search tion spatial lower lower signals signals prior prior prior higher higher previous previous previous previous previous previous bound bound bound firing firing firing firing firing firing firing firing firing firing firing long conditions distributed bayesian bayesian bayesian bayesian region proposed length correct probabilities observed observed observed scale simulations resulting simulation multi potential study study obtain true true provide define proc perform active active active active active active active active active active goal posterior posterior connected connected connected connected connected connected connected discrete cortical cortical cortical cortical cortical cortical cortical cortical equal larger connection fields dependent dependent dependent dependent dependent dependent dependent dependent version version version version synapses final final final final final final final final addition ai ai framework framework framework framework limit limit effects capacity capacity capacity efficient efficient efficient efficient efficient upper full choice choice statistics basic pages increase con con channel randomly randomly randomly randomly iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration nature inhibitory simply simply biological biological biological associative associative achieved achieved achieved achieved achieved achieved achieved achieved measured normal increases arbitrary arbitrary denote limited shape shape shape theoretical main adaptation makes typically smaller hopfield hopfield hopfield hopfield hopfield hopfield hopfield account fully fully fully significantly iterations iterations magnitude idea neuronal neuronal denotes architectures architectures architectures architectures membrane directions exact typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity identical subset subset subset previously conventional conventional approximately works correspond correspond achieve sparse background symmetric modified generalized generalized generalized generalized organization increased increased increased exists expression expression half greater depend editors sigmoid sigmoid sigmoid sigmoid sigmoid numerical clear sigmoidal sigmoidal sigmoidal sigmoidal decrease connectivity connectivity connectivity connectivity connectivity connectivity connectivity attractor attractor attractor attractor attractor attractor relation relation plot ann ann ann tuned mathematical dept explicitly physical slightly belief springer formed versus expressed expressed expressed dependence review depending depending overlap viewed influence restricted fraction forms constants allowed sign sign sign sign sign additive initially initially initially initially initially assigned assigned david building fire fire usa formulation formulation currents sciences sciences illustrated illustrated illustrated maximize identified capable uniformly computationally wij essentially characteristic composed summary verlag heuristic follow sci computes received received illustrates illustrates load load load load intrinsic receive receive receive extend updating accurately rise examine respond history history history history history history history history history history history history history school investigated decisions tanh func notion neu possibly equally perfect subsets noted academic pyramidal amari defines residual preference agreement fairly explanation analytical correction interneurons considerable spatially perspective broad acad describing describing calculations geometry varies marked ity span cal collective achieves conductances asymmetric enables decreased findings findings eventually displays cumulative sharing cor phenomenon newton forming investigation investigation restriction fix arguments resources nat neurophysiol numerically numerically held abilities observing ral intuitive intuitive continue repeat pat pat evident evident evident offers entries israel properly storing davis tures receiving posteriori fired fired anns anns anns anns anns sig emergent diverse restrictions abstraction hundred tendency tendency big letting gated formance formance goals synchronized spreading investigating sketch memoryless memoryless discretization supports differing tel tel spite deletion achievable discretized discretized discretized discretized discretized tial send terns converging ruppin ruppin ruppin ruppin ruppin ruppin ruppin ruppin ruppin neocortical cally anatomy sharply sparsely sparsely architec rameters distorted distorted fidelity fidelity fidelity fidelity ionic differentiate twelve mul monotone monotone aviv aviv maryland silent silent silent silent silent ini shares opinion tern mid expresses enforced reminiscent superiority signalling signalling signalling signalling signalling signalling signalling signalling signalling signalling signalling signalling signalling proximal quiescent quiescent quiescent quiescent quiescent seemingly fil henceforth signaling constantly faculty conveniently clue expressing meilijson meilijson meilijson meilijson meilijson meilijson meilijson meilijson meilijson braitenberg braitenberg braitenberg raymond yoshizawa yoshizawa yoshizawa nected iij lesser governs manage tex simi eytan tam tam tam connors connors connors mckenna contrasted twofold modulator prescription silenced unavoidable nonmonotonic emits nectivity tins displaying zornetzer ands llxi llxi isaac investi beverly sackler moti larity nce sociative imizes methodological vated tractor criti worsen 
#@Meilijson_I,Ruppin_E,
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components components components components components components components components components components nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied back computational convergence convergence convergence analog analog analog analog properties references references component component component component component component ieee important adaptive propagation context context introduction introduction hand hand effect generated parallel parallel tion change energy energy assume chosen theorem theorem theorem theorem theorem theorem theorem cases cases type type type type type type type binary conditions conditions distributed distributed distributed distributed distributed distributed equations equations equations equations equations equations equations make fact fact fact forward simulation simulation respect called called called times times times times times times times times times times times times times times times times times times times means means global global global global global global global global global global study knowledge obtain obtain original original original compared application provide define define define rates proc proc related constraints discrete discrete discrete discrete equal contrast connection connection connection update update modeling proceedings proceedings report department department department department department department loss implementation implementation implementation version version version consists consists delay delay delay delay delay delay delay delay delay delay delay delay delay delay scheme scheme scheme scheme scheme ai ai maps maps maps maps maps considered computing computing computing equivalent environment directly limit limit san conference requires statistics pages con condition condition condition condition condition condition randomly product provided provided provided finally finally iteration constraint constraint constraint constraint simply biological biological biological technical arbitrary arbitrary transformation assumption proof proof proof proof proof common main main journal instance makes fit needed hopfield hopfield hopfield hopfield hopfield dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical functional functional functional functional york york york increasing mechanism special special special call call call numbers iterations iterations iterations iterations international decay idea denotes denotes recent property apply identical interest volume works works tions tions studies studies converge differential differential differential differential differential differential trans definition definition symmetric symmetric symmetric bounded channels concept studied studied studied studied derivative matrices matrices occurs hardware conclusion trajectories trajectories differences numerical numerical asymptotic asymptotic hard hard presence external sigmoidal sigmoidal california california california california exist iii iii iii relation stability stability stability stability stability stability stability mathematical mathematical mathematical mathematical mathematical explicitly physical physical easy unique applying springer implies implies versus versus family family focus review communication communication communication communication communication communication communication communication communication communication communication communication communication communication viewed evolution converges converges allowed allowed partial partial reasonable additive additive additive additive additive additive delays delays delays delays reduces iterative iterative iterative iterative norm euclidean existing existing includes includes thesis usa usa formulation formulation sciences memories discuss partially major aspects closely uniformly uniformly uniformly wij wij wij oscillatory oscillatory computations schemes schemes schemes schemes schemes schemes schemes schemes situation situation compact notice notice notice notice verlag kind strongly strongly strongly strongly induced induced interested interpreted issue issue issue content follow follow sci sci categories satisfy usual simplified relaxation relaxation absence delayed delayed delayed delayed satisfies satisfies software extend diego transformed requirements association issues preliminary preliminary hall periodic mappings possibility relationships variability oscillation oscillation func analogous act math concepts possibly ensure ensure ensure subsets bifurcation assumes nerve academic simplest motivated motivated attempts chaotic chaotic asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous caused tive sys shared precisely desirable mathematics mathematics mathematics mathematics mathematics mathematics acad acad grossberg computers cybernetics addressed outer reflects applies consistency tional effort cohen continuously gains gains incorporating ordered collective asymmetric inherent inherent wang wang wang wang wang wang wang wang wang wang wang wang differentiable differentiable synchronization synchronization synchronization synchronization globally globally globally globally ordinary ordinary identifying fix refractory nat nat tem impossible theories generality consideration consideration satisfying los los los los abilities definitions definitions imply imply synchronous synchronous synchronous synchronous synchronous synchronous synchronous synchronous synchronous clock clock clock continue prentice corollary corollary corollary governed ensures periods respective guarantees dif waves eng ahead contraction sustained tsitsiklis tsitsiklis tsitsiklis tsitsiklis exploiting implicitly convergent convergent convergent convergent convergent convergent bertsekas bertsekas bertsekas ics graded validity cooperative cooperative emergent par quasi monotonicity obtains amplitudes letting massively evolve diag diag diag convert concentrate careful emphasize wise parallelism exceed investigating importantly enforce discretization preserve preprint parametrized computa unpublished nonnegative lation august discretized discretized invertible families ferent cliffs blum blum blum blum blum blum blum blum blum blum blum blum inclusion condi englewood marcus marcus marcus edited norms characterizes evolves barhen barhen barhen closure westervelt westervelt westervelt 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#@Blum_E,Li_Q,Wang_X,
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural input function function function function function figure figure figure figure figure figure figure figure figure time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training algorithm output output output output output output output output output output output output output number number number number number number number number number number number system system system system system system system system system system system state 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processing processing processing processing processing processing processing processing processing processing control large large rate rate rate rate analysis class class inputs form form form shows algorithms algorithms algorithms algorithms simple paper paper paper examples examples small small feature net net work work work work work task task task task task methods methods methods methods methods methods methods methods methods step step points points points points points points points points field current current current current structure problems problems problems response response representation show equation section fixed fixed fixed fixed fixed line vectors states states states states states states states states states theory theory theory gradient note dimensional university threshold computation computation computation computation computation research research research research independent defined sequence sequence sequence sequence sequence sequence sequence sequence target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial initial initial initial initial initial standard computer computer terms distance distance science science science science science left left left left left activation activation activation activation machine machine machine machine machine sets maximum maximum range press press press press press basis nonlinear continuous continuous continuous continuous continuous continuous sample abstract applied computational computational computational computational computational computational computational references positive decision decision decision decision context context context context context context context context context introduction introduction introduction complex hand hand hand hand circuit behavior behavior behavior behavior generated parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search search tion tion complexity complexity complexity complexity complexity complexity complexity complexity lower rules measure representations representations learned learned part center cases multiple multiple multiple long long conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions distributed make fact techniques techniques techniques proposed observed observed forward forward finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite resulting resulting resulting classes classes ing ing respect respect regions regions regions regions regions regions dimension made natural negative artificial artificial artificial specific provide location perform experimental related constraints discrete discrete discrete discrete discrete approaches approaches mit mit descent dependent morgan morgan morgan proceedings proceedings department technique technique internal internal internal internal internal internal internal internal internal individual individual advances advances advances connectionist responses difficult final bias bias sequences sequences sequences sequences ai cambridge cambridge computing domain equivalent additional solutions transition transition limit limit san san conference upper full free free free free basic give produce clustering clustering clustering clustering clustering clustering clustering velocity velocity velocity velocity entropy actual iteration iteration iteration iteration sampling sampling sampling sampling sampling measured arbitrary group transformation assumption stable finding finding short common assumed shape shape generate generate generate generate supported theoretical eds eds eds eds eds journal end cluster future future rumelhart rumelhart rumelhart including underlying underlying underlying underlying dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical unknown programming programming edge mechanism structures empirical language language language language language language language language language language language language language language language language language language call iterations iterations iterations iterations iterations iterations iterations iterations run run run sources description description predict discussed typical reported moving machines machines machines machines machines machines machines machines machines machines side side side sense sense cognitive cognitive cognitive engineering varying volume works tions correspond trans trans definition definition definition observation bounded improvement sensitive sensitive sensitive sensitive sensitive grant constructed constructed concept digital wide rotation feed feed move move hybrid touretzky deterministic deterministic clusters clusters white occurs occurs boundary boundary boundary boundary demonstrate conclusion trajectories trajectories trajectories trajectories competitive competitive performs moody moody exponential exponential mechanisms mechanisms mechanisms physics demonstrated intelligence intelligence start exist introduce manner manner identification force question attractor attractor attractor attractor attractor attractor attractor appears edges edges produces produces longer solving sequential describes laboratory transitions transitions mathematical mathematical sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity category infinite physical physical physical physical physical physical physical angle angle minimization minimization implies extraction extraction extraction extraction extraction extraction extraction john john john extracted extracted focus formation viewed lee lee completely partition measurements spaces spaces neighborhood initially visible symbol symbol symbol symbol symbol symbol assigned construction foundation classified recorded strings assignment determines plotted illustrated mozer mozer mozer mozer specifically domains grammar grammar grammar structural major regular regular aspects society differ differ computationally symbols symbols symbols mcclelland mcclelland situation miller ten characteristic traditional traditional notice induced induced induced contained neuroscience split return strategies notation write write dot dot giles giles giles giles quantization illustrates operating extract acknowledgments intrinsic tesauro modelling cowan presents explore remain unlike carried diego collection exhibit exponentially hanson hanson association divergence divergence mass rise school behavioral mappings applicable analytically dependencies office tanh pathway hierarchy understand understand understand induction induction induction induction act reading onset automata automata automata automata automata automata automata automata automata automata automata queries versions formal formal formal formal formal formal academic speakers extent arbitrarily chaotic sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences devices languages languages languages languages languages spin trivial trivial growth tractable purposes sys involve beginning annual incomplete radius preceding sun researchers researchers researchers apparent apparent understood elman elman elman simulate employ remove operate partitioning mod characterize spread spread differs weigend extracting extracting extracting extracting extracting extracting fall chen chen richard richard logical inherent comments focused focused eventually eventually specifies wesley proofs intractable addison addison addison velocities ordering circular partitions discovery naval eliminate rotations rotations smolensky reaching communications kaufman kaufman kaufman saturation saturation replacing automaton abilities nearby nearby operates fail disjoint imply corner alspector repeat induce induce induce regarded demonstration accounts claim claim iterated iterated iterated francisco young young young young young pollack pollack pollack pollack pollack pollack pollack matter hypercube erlbaum designing ball ball ball ball ball dividing zipser zipser summer gold gold gold gold gold gold goodman validity emerge revealed distinction corrected chaos reports individuals individuals descriptions hillsdale imagine examining constrain quantized epsilon epsilon tems pdp gener ullman ullman smyth topic pos employing associates sheet apparently discretization discretization pop rod likewise likewise rotating rotating simplex simplex union lippman lippman recognizers suggestions walk regularities interior interior interior interior unbounded justified thousand families observers observers powers steven steven concern affecting ning sen separates push preservation specialization interpretations artifact explanations ignores syntactic watrous watrous watrous confined fol periodically remained fsm fsm fsm fsm fsm fsm fsm gence deter differentiate inducing schreiber ated cleeremans cleeremans cleeremans servan rotational rotational rotational rotational rotational rotational kuhn kuhn kuhn allowable rent illusory rec rec simon simon simon spec diverge das das das jack orbit broader ohio ohio nondeterministic nondeterministic nondeterministic nondeterministic orig trick def relying internally burden begun begun begun machinery clus sky landing recur syntax ulation gerald shortcomings fifty swim wheel bicycle elongated embody cis comers abstractions joshua subsequence mecha fsms fsms fsms questionable lan locus embed rests columbus newell newell newell tering observational angluin angluin eventual divergent grounds cloud evoke loca descrip dangerous saunders hopcroft hopcroft paradox paradox fifteenth thrown ries istic ministic ascertain nism lln chomsky chomsky chomsky chomsky guage lowed intelli inal greg fool fool fool fool cha inquiry researcher confuse discretize watching uct prod formations fractals hague counterexamples nately tences trajecto 
#@Kolen_J,
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#*network network learning model model model neural neural neural neural neural neural neural input input input data function figure figure figure figure figure figure figure time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks number number number number number system system system system system system system state state state state models models models weights shown systems systems systems neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution pattern pattern pattern pattern pattern pattern pattern single processing control control control control control control control control control large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns patterns patterns patterns patterns inputs inputs inputs inputs inputs inputs inputs form simple small feature work work task fig fig fig fig cells cells cells current current current current current current cell cell memory memory memory show show states term term term term term activity activity activity activity activity activity activity activity activity activity activity university threshold research found sequence dynamics connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science science left phase low frequency frequency frequency frequency frequency temporal temporal range range press press press outputs abstract applied find properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties references important introduction action action action action action action action complex complex circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior effect effect dynamic dynamic dynamic dynamic dynamic change rules part center cases firing firing firing firing type multiple multiple multiple multiple multiple multiple long long long scale scale times times potential potential potential potential potential made made artificial artificial application application proc active active determined motor motor motor motor motor motor motor approaches mit voltage voltage voltage voltage voltage voltage contrast connection dependent dependent dependent dependent dependent dependent modeling selection synapses synapses synapses synapses synapses synapses synapses synapses individual exp ai cambridge environment environment transition top stimuli effects effects effects effects determine determine choice choice significant increase increase give produce produce produce conditional conditional evidence nature nature nature depends depends biological biological biological biological biological biological biological describe group fast fast fast close stable stable actions actions actions circuits circuits circuits circuits circuits circuits circuits amount short short short short short common common synapse generate supported role sensory sensory sensory sensory sensory including typically dynamical functional functional functional functional functional functional interesting significantly mechanism mechanism principle operation operation operation operation details bottom decay produced produced produced produced neuronal neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane discussed recent property lateral include period subject subject subject conventional tuning smooth studies rl mixtures modified modified modified modified modified modified modified channels channels channels channels channels organization amplitude amplitude lead occur occur wide strength strength strength depend depend depend depend central differences retina retina suggest strong mechanisms mechanisms mechanisms integration pulse pulse pulse pulse variety variety variety variety variety variety exist decrease identification acknowledgements produces produces generating generating generating transitions distinct electrical electrical scales scales scales events potentials potentials potentials potentials potentials potentials potentials potentials potentials independently expressed open open controlled controlled modulation modulation modulation modulation modulation modulation modulation modulation forms activities slow slow slow slow combining construction coupling recorded fire fire usa usa currents currents currents currents currents currents currents discuss activated activated activated activated activated activated capable modes modes modes modes modes oscillatory oscillatory characteristic characteristic characteristic characteristic kind induced allowing showing oscillations sci duration duration comp simplified absence absence neurosci neurosci neurosci principles illustrates illustrates rat intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic receive simpler environments oscillators oscillators strengths strengths oscillator oscillator oscillator postsynaptic postsynaptic postsynaptic respond behavioral behavioral terminal biol biol biol biol dependencies dependencies presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic fundamental induction trace panel panel panel nerve nervous nervous nervous nervous nervous nervous nervous art switching fibers seconds seconds burst burst slowly slowly ganglion ganglion ganglion ganglion rapid rapid rapid rapid rapid sites protein ion ion ion ion ion ion axon hippocampal acad recording recording demonstrates considerably empirically understood flexible car recordings employ release release operate operate switch switch switch characterize modulated modulated modulated conductances conductances conductances conductances conductances conclude display display display physiol physiol physiol traces synchronization displays extreme cybern cybern cybern generator modify modify oxford extensive branches branches neurophysiol lost minutes ranges balance balance balance balance efficacy efficacy transforms implications salient preparation natl fires reset displayed bursts bursts bursts cancer cancer cancer theoretically sustained sustained sustained sustained impact harris harris harris harris harris alternatively alternatively fusion fired fired dramatically multiply reflex depression depression depression depression terminals junction rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm evoked remote alter gated care subthreshold insights biophysical interact mammalian generators activate potassium oct oct rhythmic rhythmic constructs amino amino oscillating figs dorsal abbott abbott abbott abbott electronics intracellular intracellular geniculate tune milliseconds milliseconds milliseconds milliseconds dramatic examination bursting bursting bursting bursting bursting ongoing agents hundreds hundreds virtually transmitter transmitter stay plateau plateau plateau plateau mill clark clark clark contacts vertebrate enhances vivo dopamine dopamine invisible marder marder marder marder marder marder marder marder marder marder marder marder marder marder marder marder marder marder marder absent molecule molecule molecule quick electrophysiological electrophysiological terminates acids acids stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory modulatory selverston durations monitored monitored silent silent silent hyperpolarization depolarization depolarization depolarization remarkably extracellular warrick warrick warrick warrick warrick perturbing bistable signalling signalling lasting lasting mediate kirk counterparts facilitation facilitation facilitation facilitation facilitation facilitation facilitation released monosynaptic neuromodulation neuromodulation succession kinetics inactivation inactivation neurotransmitter opening repertoire depolarized depolarized katz katz mediating sse skeletal adams adams neur neur somers somers crab crab crab crab crab crab crab neuromodulators neuromodulators alternation hyperpolarizing hyperpolarizing hyperpolarizing hyperpolarized substances substances substances substances substances substances substances substances substances substances substances substances substances substances substances substances elicit kandel kandel kandel deduced kopell kopell ast ast depolarizing depolarizing depolarizing stably modulator waltham neuromodulatory neuromodulatory neuromodulatory neuromodulatory underly overly gill motivations brandeis relay evans serotonin serotonin serotonin serotonin pergamon ach ach ach thalamocortical lse modulators messenger messenger mccormick mccormick mccormick courtesy storm storm neurotransmitters neurotransmitters programme lasts dickinson dickinson coleman coleman sem eve dowling dowling llin llin alepolarizing tonically amine glutamate peptide peptide riding elicits elicits aln substance suprathreshold 
#@Marder_E,
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#*network model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function figure figure figure time time networks output output output output output output output output output output state state results results results results results models models space linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown shown systems values functions neurons neurons neurons neurons neurons neurons neurons unit method single single processing control control control control large large neuron neuron neuron rate rate rate rate rate rate analysis analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form shows shows shows signal signal signal simple simple simple simple visual visual visual visual visual paper paper small small work task methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells points current current current current current current current current current current current current current current current current current current current current current current current current current current current current cell cell cell cell cell cell cell cell cell cell high high high response response response response response response response response response response response response similar similar similar similar line line line line line average obtained obtained experiments experiments result threshold threshold threshold computation computation research research research independent independent independent target dynamics constant constant constant synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node node node science science activation activation activation activation activation activation low frequency frequency frequency frequency maximum maximum range range press press press continuous abstract back computational density properties properties properties properties references due important important important introduction action action complex circuit behavior effect effect generated parallel parallel change change assume assume assume chosen part center firing firing required required required cortex cortex cortex cortex cortex cortex cortex cortex good binary spike spike spike spike long tree tree tree tree distributed distributed expected make correlation resulting resulting resulting ing human computed potential potential potential potential feedback feedback feedback study study negative provide provide rates location location perform active active active active experimental experimental experimental goal gain gain gain gain gain gain motor cortical cortical cortical cortical cortical cortical cortical cortical brain brain voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage contrast support dependent dependent dependent dependent dependent dependent dependent modeling institute institute institute version synapses synapses synapses synapses synapses synapses individual represents represents represents responses layers layers layers layers layers layers layers layers layers layers layers addition computing equivalent curve curve view curves curves curves curves estimates stage significant estimated pages increase derived derived derived derived derived derived derived area area evidence evidence depends depends achieved increases transformation transformation fast close excitatory excitatory stable amount common effective effective shape supported role degree including underlying combination technology technology increasing mechanism mechanism mechanism mechanism mechanism principle principle leads leads leads leads direct international light neuronal neuronal neuronal membrane membrane membrane membrane membrane membrane membrane membrane recent correlations exact exact include hierarchical recently relevant highly conventional observations studies channels sensitive sensitive increased constructed expression lead concept studied suggests wide spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes predicted predicted occurs setting demonstrate half place depend editors suggest propose propose strong mechanisms integration presence presence sigmoidal california california solid solid proportional proportional labeled variety relationship relationship relationship relationship relationship relationship relationship relationship averaged averaged targets manner manner program program base acknowledgements relation relation pro pro van van derive derive derive primary dept explicitly infinite electrical slightly interaction adding events events quality potentials potentials national dependence detailed detailed detailed fraction constants diagram slow dashed dashed dashed measurements event add boundaries msec koch koch koch koch koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic thesis usa currents currents inter activated activated black simplicity simplicity straightforward middle included spiking spiking literature projections comparing reached excitation traditional induced induced anderson neuroscience neuroscience neuroscience neuroscience neuroscience conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance contribution comp simplified simplified play realistic correspondence reach reach cat cat cat cat neurosci rat rat receive extend law stimulation access exhibit rapidly steady steady involving postsynaptic reducing reducing terminal analytically relationships office complicated proved affect presynaptic removed act act trace concepts rev friedman academic pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal extent submitted established site ment ment agreement agreement derivation derivation slope slope caused interneurons nonlinearity london spatially spatially drive located located monkey axon hippocampal medical localized sun addressed explained reflects substantially pathways offset simulate introducing introducing introducing introducing posed marked recordings recordings variant release exhibits spread branch cal incorporating tank tank tank tank qualitatively pasadena conductances conductances conductances conductances conductances conductances conductances conductances conductances conductances boston fiber yielding contribute physiology physiology physiology proportion oxford amplifier amplifier amplifier amplifier martin martin driving driving reconstructed reconstructed naval eliminate grey eliminated clamped clamped fits saturation saturation saturation saturation saturation bower bower anatomical imaging primate analogy resistance hyper resulted spot adequate reliably passive passive passive passive slice cerebellar cerebellar loo dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites conjunction mental mental dependency dependency dependency dependency injection injection accounts dendrite infinity somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic somatic soma soma soma soma soma soma soma soma soma soma soma soma soma soma nonlinearities arrangement dif tic cerebral cerebral cerebral thin thin sustained sustained route extensively epsp calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium discharge discharge discharge discharge neurophysiology neurophysiology depression graded graded deriving validity alternating nelson causing chapter evoked argue acting capacitance thick thick interneuron mammalian distant potassium potassium potassium potassium potassium potassium potassium convert crosses douglas douglas douglas douglas douglas douglas douglas douglas douglas iso relating confirmed projecting macaque distal distal distal distal distal distal distal distal rough weaker reveal abbott abbott intracellular minor page amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification experi triggered triggered persistent persistent persistent syn moderate council arbors justification hypothesized powers powers morphology morphology adult transmitter purkinje purkinje purkinje flows neocortical neocortical neocortical neocortical essen essen evenly nmda neurol slices slices neocortex neocortex neocortex ray functionally resolved compartment compartment compartment linearized linearized linearized linearized losses losses vivo vivo complement attenuation amplified amplified amplified constraining fin fin fin fin fin electrophysiological electrophysiological electrophysiological saturating robustly united health christof gradual depolarization tivity neurones hot connor apical apical apical apical apical apical apical apical apical apical apical apical apical apical apical apical apical apical apical notions notions activates fractional rela electrotonic electrotonic activating saturates saturates ample ogy mason mason sodium kim kim kim rightmost abstr basal basal vitro clamp ons mere delivered delivered delivered anatomically del repertoire resembling electro leak leak resistances superficial superficial superficial superficial superficial superficial superficial informal linearization linearization rodney axial axial flowing flowing flowing flowing incor synap bernander bernander bernander bernander bernander bernander bernander bernander formalize morphological ampa ampa conduc kingdom mecha favoring elicit connors connors connors connors connors connors connors connors amplify amplify amplify conservation kandel kandel mckenna leftmost leftmost sive ain electrophysiology innervation vide pulls intradendritic intradendritic intradendritic sight linearize linearize rockland rockland counteract ass plateaus amplifies amplifies unsatisfactory tances synaptically frontier nism linearizing linearizing linearizing linearizing sea kan llin amplifying amplifying amplifying amplifying whitteridge ology reconcile eur areal ohm partment regenerative pas ficult impinging porating pharmacology 
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#*network network learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data data data data data function function figure figure figure figure figure figure figure figure figure figure figure time output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number system system system system system system system results results results units units units units units information information information information information models models models based based based based based linear layer layer layer layer layer layer layer layer shown systems probability probability probability probability probability probability probability noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit distribution distribution distribution distribution method approach pattern pattern pattern pattern image single single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control local local local local local local local local local local local local local local local local local local local local local neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns analysis inputs form signal signal signal signal simple gaussian paper feature feature feature feature feature feature feature cells cells cells cells cells cells cells cells cells cells cells step step step step features features features process level cell cell cell cell cell cell cell cell cell cell cell high high high high high high memory memory memory memory memory memory response representation representation representation architecture architecture show show show equation images images general general average average average states obtained obtained term experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional result result threshold computation computation target dynamics dynamics dynamics dynamics constant connections connections connections connections synaptic synaptic synaptic presented map map map map map map map present phase activation activation activation activation activation activation activation low low low temporal temporal press components components components components components components abstract computational computational computational computational density density properties references due due due due due due due due due due due important important mixture introduction complex complex complex complex hand circuit behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus difference spatial spatial spatial spatial spatial spatial spatial spatial spatial signals signals signals chosen part firing firing firing firing firing cortex cortex binary represent distributed equations equations region region region proposed probabilities observed forward simulations performed performed performed performed performed performed elements elements elements elements regions regions regions natural feedback global global global global global global global global global global study study study study study specific represented represented represented represented represented compared provide provide provide location active active active active active active active active experimental experimental related related related distributions cortical brain brain mit steps steps steps steps comparison contrast contrast contrast connection connection connection modeling modeling modeling modeling selection implementation synapses synapses synapses synapses synapses code individual individual advances represents represents responses responses responses responses responses responses responses difficult delay addition maps maps maps maps maps maps maps stage stimuli stimuli stimuli detection detection detection detection upper requires coding randomly levels levels types types types types provided finally processes evidence nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends sampling sampling sampling sampling sampling sampling sampling biological biological associative associative associative achieved discussion increases corresponds excitatory excitatory excitatory excitatory stable stable stable stable short common synapse role role role role role role main eds eds adaptation adaptation journal sensory sensory sensory including fit simulated underlying underlying hopfield hopfield hopfield hopfield functional projection projection increasing increasing increasing increasing increasing mechanism uniform uniform leads representing direct direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition international predict membrane population population recent recent separate takes lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral array array highly varying varying varying tuning studies differential differential sparse sparse mixtures mixtures mixtures mixtures mixtures organization storage exists concept occur suggests suggests feed strength strength strength conclusion central central central central central central central central suggest propose propose mechanisms mechanisms mechanisms mechanisms presence reduction reduction demonstrated assuming exist iii introduce introduce program acknowledgements areas areas areas appears distinct recall recall category category averaging quality extraction extraction extraction extraction extraction select competition competition competition competition competition competition competition competition focus expressed review overlap restricted evolution centers modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation activities activities similarly suggested constants allowed discrimination discrimination discrimination key key delays dendritic david degrees degrees degrees coupling recorded figures sciences activated activated activated activated activated activated activated activated discussions characterized identified identified maximal included presentation presentation presentation presentation presentation spiking spiking spiking spiking spiking oscillatory oscillatory literature tend essentially essentially fine reached receives excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation induced neuroscience oscillations oscillations follow categories categories categories receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor comp involved simplified simplified realistic realistic realistic correspondence principles overlapping operating neighboring intrinsic decreasing decreasing decreasing receive receive receive receive stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation investigate investigate exhibit circuitry circuitry circuitry circuitry circuitry circuitry circuitry updating involving strengths strengths preliminary postsynaptic respond respond respond respond ideas project project project investigated investigated plasticity authors comparable oscillation oscillation pathway pathway trace onset predicts predicts equally olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory olfactory der formal formal precise precise submitted plant established established indicating crucial agreement unstable phenomena phenomena majority majority majority interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons london lin closer preprocessing located located afferent acad axons axons axons res localized localized localized localized localized localized localized cybernetics meaning sun sun sun sun sun sun explained populations populations populations fuzzy fuzzy fuzzy freeman pathways pure pure amounts recordings compares fiber decreased physiol eventually sharing representative spectra spectra investigation branches branches branches homogeneous homogeneous odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor enhancement enhancement spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous bower anatomical anatomical chemical chemical chemical determination abilities interpret neurobiology belong synchronous arrays wilson analyses governed dendrites respective induce enhance enhance enhance bulb bulb bulb bulb uni uni hasselmo hasselmo winning emergence belonging arrows insect insect insect projects projects projects davis interestingly interestingly dense indirect constitute transmitted emerge comparative individuals tendency molecular peripheral translated interneuron interneuron grouped mammalian mammalian mammalian lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe lobe permits permits paris paris paris win france france diversity intracellular grateful molecules molecules molecules tissue triggered resp institut inhibit inhibited inhibited inhibited inhibited oscillate wins focuses hamilton morphology stay stay proposal incorporation excited excited excited neurol heterogeneous heterogeneous ooo 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#@Kerszberg_M,Linster_C,Marson_D,Masson_C,
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#*network model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input data function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set set networks networks networks output output output output output output output output number number system system state state units based based based order order order order probability parameters parameters noise noise noise noise noise noise neurons neurons neurons neurons unit distribution distribution single single single single single single single single control control large large neuron neuron neuron rate rate rate rate rate rate rate patterns patterns optimal inputs inputs inputs shows shows shows signal signal signal signal signal simple simple small small work work cells cells cells cells step step level level level level level level level level level current current current current current current current current current current current current cell structure random high high response similar show show show parameter activity activity activity activity activity activity activity activity result result university university university university threshold threshold threshold threshold threshold threshold threshold threshold research target target initial constant constant constant computer connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic phase activation activation activation activation activation activation activation activation activation activation activation activation activation low low frequency frequency frequency frequency frequency maximum range range range range press components abstract applied applied properties properties properties properties references component due due due due introduction action behavior stimulus effect effect effect effect effect effect effect effect effect dynamic dynamic generated generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change change change difference difference spatial lower lower lower lower lower measure higher higher firing firing firing firing firing firing firing firing firing firing firing firing firing firing spike spike equations correlation length simulations minimum minimum ing ing ing ing ing ing ing total total total total simulation simulation times times regions means factor potential potential potential feedback feedback feedback feedback feedback feedback feedback feedback feedback study negative specific cross series series series rates rates rates rates active active experimental gain gain motor motor motor motor motor motor motor motor brain power power comparison larger modeling modeling modeling report synapses consists individual individual addition maps curve limit san effects effects effects effects effects effects effects effects effects effects effects effects efficient significant significant significant estimated increase increase increase produce produce channel randomly levels levels levels levels lines lines inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory discussion increases increases amount common assumed assumed supported role theoretical simulated simulated reduced coefficients significantly increasing mechanism mechanism matching direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition magnitude magnitude magnitude decay produced produced produced added added added added added added description predict membrane membrane membrane membrane membrane population population discussed ensemble ensemble typical reported include engineering engineering sufficient sufficient sufficient sufficient sufficient sufficient varying compare observations observations observations match match differential address definition modified grid interval interval amplitude suggests suggests suggests suggests trial spikes spikes spikes derivative derivative move loop loop generally column setting pass pass strength strength strength row reduce reduce reduce measures peak peak peak peak peak performs weak weak weak weak strong strong characteristics solid decrease decrease relationship connectivity connectivity program force force force force force force force force force force force force force appears relation relation van van produces longer plot plot dept dept dept dept modeled confidence simultaneously linearly spectral spectral scales adding formed implies potentials potentials potentials dependence correlated communication variation open forms static constants constants past past spectrum spectrum spectrum spectrum smoothing dashed measurements reduces boundaries boundaries boundaries boundaries visible construction fire fire thesis currents plotted activated activated coupled columns columns maximal computationally post post plots plots reached receives excitation soc conductance conductance conductance superior physiological physiological timing receptor simplified realistic realistic realistic thresholds thresholds thresholds thresholds cat cat cat cat cat cat cat neurosci acknowledgments remain remain diego exponentially relations relations steady steady behaviour existence reducing examine tech biol biol biol biol muscle muscle muscle muscle muscle muscle muscle authors pathway pathway affect statistically statistically statistically presynaptic matched examined measurement coefficient coefficient coefficient transmission changed adjusted nervous academic switching finds integrate asymptotically percentage rows rows asynchronous adapted interneurons interneurons interneurons filtered forces forces broad nucleus pool pool pool pool pool pool pool pool pool pool pool pool pool axon axon res res preceding simulate quantitative peaks peaks peaks schematic synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony ordered conductances substantial boston physiol physiol physiol physiol physiol physiol summed room cybern cybern cybern cybern physiology physiology physiology physiology investigation neurophysiol purely bin arranged establish spontaneous mail resistance resistance loops contract neurobiology roles shifts synchronous synchronous synchronous synchronous fires service published negligible negligible surprising realization arrangement multiplied suggesting agree impact impact reverse lett grants fold robert limitation counts fired fired rms discharge discharge reflex street quasi chapter resting chicago chicago chicago chicago chicago workstation spinal spinal spinal spinal spinal spinal cns ibm mitchell mitchell regulation crosses mediated maximally synchronized synchronized synchronized option inversely descending pools interspike interspike removes tension tension instability tom send hat hat impulses east injected cord excited sharply sharply plateau plateau plateau governing vivo cutoff comer comer handbook reviewed shaping nih adequately cleveland cleveland cleveland cleveland houk actively actively motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons motoneurons medial firings firings firings firings firings firings extrapolation excite biomedical biomedical pooled ross ross ross clump numbered synapfic ramp inhibits brooks stuart stuart fell stretch stretch motoneuron motoneuron motoneuron motoneuron motoneuron implication graham graham fifty govern indebted prog bullock bullock fused suppressing mimics phasic persist adam adam adam inhomogeneous excites excites bethesda cas synchronizing synchronizing synchronizing synchronizing synchronizing synchronizing synchronizing inevitable northwestern northwestern northwestern northwestern intemeurons desynchronization desynchronization desynchronization desynchronization desynchronization intention discrepancies waterloo hospital desynchronized desynchronized desynchronized synchronizes discernible stretches evanston roedial 
#@Druzinsky_R,Heckman_C,Maltenfort_M,Rymer_W,
#t7
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#*network learning model model model neural neural neural neural neural data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure time time time networks networks system system results results results information models models based linear linear linear linear linear linear linear layer vector order shown shown shown shown shown systems systems systems values values values pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern processing large large large local local patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis form form shows shows shows shows shows shows shows signal signal signal signal visual visual visual visual visual visual visual visual visual visual visual visual paper feature work fig fig fig fig fig fig fig cells cells points points points features features features features features process process structure structure structure high high high similar similar representation representation show show section section section images images images states obtained note experiments activity result result university university solution research found found found constant table table table table estimate distance distance science science left left direction presented map map map map map map map map map map present present present present present frequency frequency frequency press press abstract density density density density references component important adaptive introduction introduction complex complex complex statistical parallel parallel parallel tion tion change change energy spatial spatial spatial spatial spatial signals representations higher part center center center previous previous previous previous cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex expected make fact fact fact fact fact techniques region region region observed total times elements elements regions regions regions regions factor dimension natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation artificial artificial represented true provide provide provide proc proc location eye experimental experimental cortical cortical cortical cortical cortical cortical cortical cortical brain equal power power voltage comparison comparison morgan institute institute institute institute department advances sequences maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps framework requires vision vision vision basic basic pages pages pages pages increase increase increase derived area area area area area area area area area area area area area area types lines lines lines lines lines lines provided provided processes processes evidence evidence evidence evidence nature nature depends biological normal normal technical increases increases denote denote close close close close close close close close corresponds corresponds stable surface surface finding finding shape require require pixel pixel hypothesis hypothesis development development development development development development development development development development development development development development development development development development development sensory kaufmann pairs needed account functional york york consistent consistent consistent principle principal squared details details details numbers normalized early early early early early predict correlations correlations correlations correlations correlations correlations correlations resolution resolution robust typical typical reported period sejnowski observations approximately approximately approximately axis axis tions studies studies studies differential interval organization organization organization organization organization sensitive increased parts suggests touretzky white strength strength strength strength hebbian conclusions editors editors editors peak suggest strong strong presence reduction radial exist decrease relationship relationship areas relation pro optical optical optical plot plot plot coordinates averaging slightly angle develop develop formed shift john letters independently independently formation formation formation formation formation stages stages transform ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular showed centers centered suggested past spectrum spectrum calculation calculation calculation intervals intervals intervals intervals initially foundation recorded recorded recorded recorded recorded recorded recorded recorded recorded recorded recorded figures usa usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance color contour contour contour inter black phys characterized major columns columns columns columns columns columns columns columns columns columns modes characteristic characteristic characteristic characteristic characteristic summary summary strongly induced dis physiological follow sci comp comp comp dayan modular neurosci neurosci modelling modelling origin selectivity selectivity selectivity wiley exhibit experience experience experience strengths fourier fourier fourier fourier school investigated investigated biol possibility possibility possibility relationships relationships func contours naturally editor editor rev assumes taylor taylor observe fibers established established established animal animal years percentage percentage percentage percentage preference preference preference preference preference preference preference preference preference preference preference preference preference band developing growth growth growth growth agreement publishers publishers publishers growing analytic lin lin closer organized monkey monkey monkey monkey monkey monkey consequence consequence acknowledgement angles angles angles acad acad medical medical medical geometry explained questions apparent apparent limits dark quantitative peter recordings howard howard exhibits aim cal ordered adjust adjust adjust boston comments age age age age age age age age age age age age age age age age findings findings findings simultaneous cor spectra indices cybern saddle saddle saddle oxford extensive extensive animals animals animals zemel grows turned anatomical imaging imaging primate primate primate primate striate striate striate striate striate striate striate striate striate bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands bands neurobiology guide natl natl repeat analyses excellent ranging ranging connect overview monkeys monkeys monkeys monkeys monkeys arrangement young thin thin reveals jolla late rich border border border border intersection interestingly mechanical liu linked ence schulten schulten schulten slight visually shorter wiesel wiesel alternating emerge revealed tween preferences preferences preferences preferences preferences preferences preferences amplitudes tendency hubel hubel england brightness brightness remainder representa continuity perpendicular perpendicular perpendicular perpendicular segregation segregation thick thick hughes hughes efforts iso iso iso iso iso iso iso confirmed singularities singularities singularities singularities singularities singularities singularities singularities singularities singularities macaque macaque macaque macaque macaque relates cartesian covered covered covered covered apparently funded reveal reveal rod preprint elsevier elsevier obermayer obermayer obermayer obermayer obermayer obermayer obermayer obermayer obermayer lippman durbin wider ritter manuscript accordance autocorrelation prefer assistance ongoing hat confirm spacing spacing spacing spacing spacing spacing arrow arrow developmental contralateral adult adult adult adult adult adult adult adult dom dom harvard pronounced wavelength settle neurol neurol neurol inspection tance colors sis handbook pin pin trend zones zones zones zones zones zones zones simon tivity movshon movshon align align align columnar borders borders borders borders bright intersect intersect intersect intersect intersect intersect won klaus week week blasdel blasdel blasdel blasdel blasdel blasdel blasdel blasdel blasdel alexander alexander pri blob terry standing lacking mitchison behavioural slabs slabs slabs slabs slabs slabs expands mammals weeks weeks weeks weeks weeks weeks weeks weeks weeks weeks weeks weeks blobs blobs narrower acuity progression selec mexican ori orienta zation infant infant infant infant infant infant percentages gary gions gions infants infants tex coordinated cies mates adults adults adults adults elliptical swindale innate innate enlarged sect wavelengths wavelengths wavelengths wavelengths wavelengths dation steadily barrow barrow midline midline preferably analy neglects foun optically nance organi precede stretched neurosc pothesis realm anisotropy lished entation coleman grinvald grinvald cortices dicted postnatal firmly immature immature immature domi frequen rro ali deprived levay wheels inance inance gion velopment eeo aligns estab salama 
#@Blasdel_G,Kiorpes_L,Obermayer_K,
#t7
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#*neural neural data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set output output output output system system system system system units information information information information information information information information information information information information information information information information information information space linear linear linear linear case order order shown shown shown shown shown systems values probability probability probability probability probability probability parameters noise noise noise noise noise noise neurons unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution point point point image image image image image image image image image image image image image image processing processing processing processing processing control control control control control control large local local local local local local local local local local neuron rate test analysis optimal form form shows signal signal simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual paper size work task cells cells cells field field field process level level current cell cell structure structure problems random high high response similar similar similar representation fixed line line line line images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images approximation average theory theory gradient gradient note note note computation research independent independent log log log log log log log log log log log log log log log log defined defined found dynamics constant standard standard standard terms left left left left left left left left frequency frequency frequency components nonlinear sample abstract applied find find find find find properties properties references component positive procedure procedure important introduction statistical dynamic variance variance variance variance variance change change change change spatial spatial spatial lower signals signals chosen part center center center theorem bound bound bound bound type good long distributed make fact fact region region region region length length scale scale scale scale scale scale scale scale scale scale scale scale scale ing ing total human sum means means made natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural filter filter filter filter filter filter filter filter negative represented receptive receptive define define define objects objects objects objects proc location perform experimental constraints distributions gain gain gain gain gain gain discrete cortical power power power power power power power power power power approaches comparison comparison comparison comparison comparison contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields fields institute consists advances exp graph graph cambridge environment directly view view curves design limit limit limit stimuli capacity capacity capacity determine upper upper upper upper upper statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics vision validation produce produce channel coding coding area entropy path finally finally processes depends sampling simply simply biological measured measured measured measured measured limited limited close predictions amount shape supported role role theoretical eds pixel ability hypothesis degree degree degree degree makes sensory sensory including including ratio ratio character principle inhibition bits bits bits bits bits early early magnitude frame combined choose light recent resolution property ensemble ensemble ensemble pixels pixels pixels pixels trees array array array array recently highly highly volume volume address channels amplitude intensity intensity invariant invariant invariant invariant invariant invariant scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling deviation deviation touretzky white occurs pass critical place place assumptions conclusions central central retina retina retina retina retina peak peak peak moody exponential exponential exponential exponential suggest sound taking physics characteristics demonstrated solid solid averaged averaged acknowledgements reference van van van produces plot plot plot plot plot plot plot plot plot plot plot laboratory averaging infinite angle angle scales scales scales integrated predictive implies cycles cycles cycles cycles john focus formation stages correlated understanding spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum dashed dashed dashed additive measurements normalization remains distances distances filtering filtering filtering filtering filtering foundation avoid avoid box color invariance composed graphs graphs graphs video dis lie lie physiological receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor comp quantity quantity quantity quantity surround surround surround attempt attempt consisted overlapping extend camera camera camera law create relations dataset fourier examine respond stream lgn encode understand understand analogous analogous analogous removed gradients gradients gradients gradients gradients closest analyze quantities quantities explored consist consist histogram histogram histogram histogram histogram histogram histogram scenes scenes scenes scenes scenes scenes scenes scenes scenes slowly formula ground orientations independence nonlinearity ganglion turns snr snr snr snr snr snr precisely opt localized patches fluctuations fluctuations evaluating axes red lattice lattice lattice effort effort remove remove music music ity requirement passes characterize spread adjust green coherent semi semi semi semi semi semi semi redundancy physiol displays gap gap sort princeton angular angular acts receptors receptors receptors minutes primate nearby transforms imply hertz bialek bialek bialek bialek bialek bialek bialek appendix appendix photoreceptor lengths histograms histograms deg ensembles express spatiotemporal creating characterization fly dividing rms rms rms street appeared fellowship maximized ram focal focal focal encodes blue blue blue amplitudes england guess distri mammalian signatures thermodynamic distant playing surrounding lond relates increasingly importantly barlow placing rotating places places lippman nec excess fractal photoreceptors send vis jersey played val tribution possess atick atick contrasts luminance luminance normalize normalize functionally tells optics optics optics optics enhances william cutoff ruderman ruderman ruderman ruderman ruderman ruderman gathered ruyter decades decades decades tails tails tails tails daniel ues stand conveyed conveyed aliasing incident redlich redlich rescaling lens ages sky conveys conveys foveal knight snapshots lacking passage passage tilted equipped forest rocks hexagonal logarithmically grayscale wasted breakdown woods woods woods woods woods woods woods zee butions evidenced quiet quiet loud loud calibrated calibrated gather kaplan laughlin laughlin laughlin cie coherently parabolic capac convolve fresh hateren sony cropped 
#@Bialek_W,Ruderman_D,
#t7
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#*network network network network network network network network model model model model model model model model model model model model neural neural input input input input input input input input function function function figure figure time time time set output output output output output output output output number system system system results results results results results results units units units units units units units units units units units units units units units units units units units information information information space space space space space layer layer case values values values values values values noise noise noise functions functions functions neurons neurons unit unit unit unit unit unit point image image image image image image image image image image image image image image image image image image image image image single processing processing local local local local local local local local neuron neuron rate optimal inputs inputs inputs signal signal signal signal signal visual visual visual paper feature methods fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells process level current cell structure high high high high high high high high high high high response response similar architecture show fixed fixed fixed fixed fixed line images images images images real average average obtained obtained obtained obtained obtained obtained obtained result research found constant constant computer computer distance distance connections synaptic synaptic left left left presented presented presented present present low low low low low low low low low low low frequency temporal temporal temporal temporal temporal range range position position abstract analog properties properties references ieee adaptive adaptive adaptive adaptive adaptive introduction action action action action action complex behavior stimulus stimulus stimulus effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect variable spatial spatial spatial center firing type required good good good good spike spike conditions fact simulations simulations simulation simulation means potential potential global study filter filter filter filter filter obtain obtain compared compared proc perform perform connected connected connected connected contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast connection dependent synapses synapses addition experiment environment stage stimuli effects capacity efficient vision vision give types types types types nature depends depends biological biological biological measured discussion tested limited nearest nearest nearest implemented synapse generate role adaptation adaptation pixel makes noisy simulated simulated simulated simulated simulated simulated simulated simulated reduced account account dynamical dynamical dynamical dynamical dynamical dynamical functional functional ratio ratio edge mechanism filters direct direct inhibition inhibition inhibition international international early frame produced light light light light light light light membrane membrane takes lateral side pixels relevant works tuning tions studies background background background grid increased increased constructed horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal intensity intensity intensity intensity intensity lead studied occur occur spikes spikes locally white white white pass pass pass pass pass pass pass pass pass pass pass conclusion starting central retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina performs suggest mechanisms external decrease iii program areas areas areas areas areas appears van van edges produces produces produces ann tuned sensitivity averaging averaging averaging quality quality extraction extraction extraction extraction extraction decreases focus depending stationary stationary stationary communication detailed showed evolution modulation allowed initially filtering filtering filtering filtering filtering filtering filtering filtering filtering filtering avoid recorded includes contour contour contour contour contour contour retinal retinal retinal retinal black black characterized regular middle aspects extra extra extra extra included spiking post post conf strongly induced conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance dis physiological physiological receptor localization localization received received consisted consisted extract decreasing modelling law explore remain stimulation stimulation carried poor investigate behaviour respond plasticity plasticity plasticity plasticity plasticity pathway pathway pathway pathway pathway pathway transmission transmission transmission plausible ensure panel nervous slowly coded adapted diffusion diffusion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion sections preprocessing preprocessing preprocessing day involve optimize addressed behaviors behaviors double transient dark dark quantitative psychophysical biologically release release release release release release release characterize ture reaches enables logical display neuro neuro focused phenomenon gap gap gap gap gap gap gap gap gap gap gap gap gap gap bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar acts acts count reconstructed enhancement grey receptors cellular cellular cellular cellular adds anatomical bands removing roles optic cone cone displayed displayed displayed photoreceptor photoreceptor photoreceptor sim modelled modelled modelled modelled modelled stimulated stimulated stimulated horizon dramatically appeared indirect junction junction junction junction ical affects eric brightness brightness brightness brightness brightness brightness trends trends mammalian mammalian mammalian mammalian retinotopic paris paris distinguished rod expense reversed lation photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors junctions junctions junctions junctions junctions junctions junctions junctions junctions junctions adult played played pronounced exclusively architec inefficient vertebrate vertebrate evolving dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine dopamine reproduced molecule unusual lar fovea fovea fovea mach mach mach mach mach mach mach mach mach mach mach mach mach mach mach ous hyperpolarization subnetwork wagner wagner subnetworks tal neigh bio reviews compress extracellular undesirable darker darker darker illustrating undergoes ously disk disk disk disk released released released released rendered neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation neuromodulation rendering rendering rendering rendering rendering rendering simu brings brings brings brings underlie continu abscissa fifty neurotransmitter neurotransmitter owing rue cedex ordinates antagonist hexagonal modulates illusion ubiquitous lighter lighter photo neurosciences conduc stimulations living elongation axo illuminated modulator modulator levick shortening holden tances frontier imbert imbert diminished adaptivity adaptivity adaptivity adaptivity redundancies pho simultane progressive ulated dowling indispensable ois jean neuromodulator mage hateren hateren chemically glutamate diffuses diffuses hermann hermann hor izontal 
#@Boussard_E,Vibert_J,
#t7
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural data data data data data figure figure figure figure figure figure figure figure figure time time time time time time time time time time time set networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output system system system error error error error error error error state state state results results models models models models models models models models models models based based based based space space space space weights linear linear case order order order order shown shown shown systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions distribution approach pattern point single single neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate test patterns patterns matrix matrix form form shows shows algorithms algorithms algorithms simple simple simple small small work cells cells points points current current current current current current current current current current current current current current current current current current current current current current current trained trained cell cell cell cell cell random high similar similar similar show equation equation line line line general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real average average states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient experiments experiments dimensional dimensional university university threshold threshold variables variables variables variables variables solution solution found found target target target target target dynamics initial initial constant table table table table table estimate estimate estimate standard standard computer computer synaptic science activation activation activation activation activation activation activation maximum maximum range range range continuous continuous continuous continuous abstract applied applied back references ieee positive positive positive positive positive important adaptive propagation introduction hand estimation estimation behavior behavior behavior statistical effect effect effect recurrent recurrent recurrent recurrent search search change change difference variable variable part cases firing type type type type type type type type type type type type type type required good spike spike spike spike spike spike spike spike represent represent represent represent equations equations region proposed simulations simulations resulting resulting total respect elements optimization potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential feedback feedback feedback feedback feedback feedback study negative negative negative negative negative original original application rates perform perform active experimental experimental experimental experimental goal voltage voltage voltage voltage voltage voltage voltage larger connection update update descent descent descent descent descent descent descent descent descent dependent modeling modeling proceedings report institute department version individual represents connectionist connectionist difficult scheme scheme curve curve curve view curves curves curves curves curves trajectory trajectory trajectory san san san efficient requires free estimated estimated estimated estimated estimated pages pages con channel channel derived randomly levels product actual discussion covariance covariance technical arbitrary tested fast fast close circuits common effective assumed assumed supported role role role role journal journal journal journal journal journal underlying underlying combination dynamical coefficients coefficients york mechanism mechanism mechanism trials principal international normalized normalized normalized normalized bottom minimize description neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane recent takes takes lateral apply period period recently dimensions varying teacher teacher teacher teacher approximately tuning tuning match match match studies differential address channels channels channels channels channels williams grant lead suggests deviation deviation white setting critical place trajectories trajectories trajectories trajectories trajectories interactions sigmoid sigmoid faster learns learns learns learns learns propose mechanisms mechanisms physics cycle california solid targets manner derive derive estimating tuned tuned mathematical changing averaging physical slightly implies cycles cycles dependence squares variation variation variation detailed evaluated updated modulation forms similarly suggested constants constants diagram diagram slow slow slow slow slow slow slow slow slow slow slow slow slow normalization reduces generation msec msec msec msec msec degrees box usa currents currents currents currents currents currents currents currents currents currents currents currents currents currents batch sciences automatic automatic activated black gating gating successfully successfully identified identified identified identified identified maximal maximal spiking spiking spiking spiking oscillatory efficiently excitation conductance conductance conductance conductance conductance running running physiological providing thresholds diego diego diego perturbation essential updating steady steady steady dotted dotted oscillator oscillator periodic authors oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation oscillation neu neu integer olfactory nerve seconds isolated isolated slope biology ganglion ganglion ganglion ganglion ganglion ganglion ran commonly axon acknowledgement describing axons conjugate conjugate integrating quantitative peter autonomous slower slower formulated popular conductances conductances chose chose traces gap college physiology japan repre impossible proceed multipliers bower bower settings salk symposium carry days exploring pat dependency dependency injection bulb mem jolla calcium calcium balanced default default default default onr rms zipser neurophysiology neurophysiology neurophysiology unified ple ter annals basically validity revealed tween ideally covariances rhythm forcing forcing forcing forcing capacitance conduction exam magnitudes biophysical biophysical wall ijcnn potassium potassium potassium potassium potassium academy pos apparently tune slopes ward hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin hodgkin resembles utilizing drives reversal externally bursting doya doya doya doya doya doya doya allen terns junctions huxley huxley huxley huxley huxley huxley huxley huxley huxley huxley huxley hundreds rons injected unreliable obey systematically rameters marder marder ionic ionic ionic ionic ionic ionic ionic ionic ionic ionic ionic ionic ionic ionic deter ings oscillates stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric stomatogastric granule selverston selverston selverston selverston selverston selverston selverston manual tens tens hyperpolarization replicate acetylcholine rotate cations repetitive connor exponents excitable excitable parame sodium sodium sodium sodium leaky bifurcations quiescent calculus calculus initializing membranes walter ana mined clamp clamp kinetics inactivation inactivation inactivation inactivation inactivation inactivation lobster lobster susceptible kay yoshizawa alternately havior subscripts leak eij outward outward outward outward itive brane crab questionable agonist endogenous batches ccs spectively integrators rob northeastern lecar pacemaker cosh cnl kenji ooi ooi multiplicity stants lob modifi historically nodel speci fies sinauer rived 
#@Doya_K,Rowat_P,Selverston_A,
#t7
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#*network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model input input input input input input input input input function function function function function function function function function function figure figure figure figure figure figure time set set set set set networks training training training output number system system system system system system system system system system system system system system system system system system system system system error results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem models hidden based weights weights weights weights layer layer layer vector shown shown shown values values parameters weight functions functions functions neurons neurons neurons neurons neurons neurons neurons unit unit unit distribution distribution pattern point single single processing processing large large patterns analysis class class inputs inputs inputs inputs inputs inputs gaussian examples examples examples examples examples feature work work task task cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field level trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell problems high high high high high high high high response response response response architecture architecture vectors real real gradient activity activity activity activity result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold solution solution research found found found initial initial initial table terms distance distance connections connections connections synaptic science left left left left left left left left left left left left left left left left left direction direction direction direction direction direction direction direction phase phase phase phase phase phase activation activation low low low low low frequency motion motion motion motion motion motion motion motion motion motion motion press position components components nonlinear nonlinear abstract back find computational computational computational computational computational density properties properties properties properties references component component component due positive positive positive positive positive positive procedure important decision decision propagation propagation propagation propagation context introduction circuit behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus effect dynamic generated generated generated generated generated search tion tion change difference difference measure signals signals learned part part cases cases cases cases cases firing good spike conditions conditions conditions represent represent distributed distributed distributed distributed classes classes ing total sum times elements elements means orientation knowledge negative negative negative negative negative negative negative original relative compared cross cross receptive provide provide provide perform perform active active active active experimental distributions brain brain brain brain equal contrast fields support source department version consists consists code individual represents represents connectionist connectionist connectionist connectionist connectionist responses bias layers delay addition addition equivalent directly additional additional additional solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects full requires significant basic con randomly randomly developed levels types entropy actual backpropagation backpropagation nature inhibitory inhibitory inhibitory inhibitory inhibitory technical group fast fast fast predictions predictions predictions finding implemented synapse supported role role role role eds eds future easily degree degree degree noisy sensory sensory sensory sensory sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory pairs functional projection york increasing increasing increasing consistent consistent consistent consistent consistent consistent consistent consistent consistent mode principle operation representing call direct direct direct direct making inhibition idea minimize description membrane improved population discussed directions pair introduced include include include side side side side side side side side sense dimensions sufficient sufficient highly highly previously tuning axis axis axis tions solve separation gate gate gate gate gate sensitive sensitive sensitive sensitive increased grant intensity suggests suggests alternative occurs demonstrate demonstrate demonstrate demonstrate minimal minimal minimal minimal minimal conclusions operator operator differences exponential constrained constrained constrained suggest suggest sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound encoding propose taking strong mechanisms integration presence characteristics sigmoidal demonstrated demonstrated turn turn turn start start exist plane targets targets introduce derivatives manner acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic base acknowledgements pro primary primary generating tuned sensitivity unique frequencies equilibrium springer national depending depending interpretation influence codes solved solved evaluated controlled static understanding discrimination discrimination partial earlier expansion roughly calculate msec msec msec msec degrees degrees degrees degrees expect fire exploration includes includes combinations activations inter batch uncertainty activated activated activated candidate variations discussions compression uniformly included projections projections tend identity receives soc quickly procedures interested dis oscillations physiological physiological physiological gray receptor comp involved localization localization localization localization play absence paradigm realistic realistic wave wave hypotheses thresholds neurosci preferred decreasing decreasing decreasing receive receive receive receive extend body explore explore simpler stimulation stimulation experience rapidly varied mass biases giving project project project behavioral biol gates gates neu transmission onset analyze psychology equally thought thought thought ensure versions obvious nerve nerve nerve nerve nerve nerve logic logic logic logic logic fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers fibers detected mixed mixed mixed crucial fairly biology explanation tractable handle handle handle handle reasons rapid directional directional directional directional directional directional directional located immediately afferent commonly controls pool pool pool pool pool sounds sounds sounds sounds sounds members axons recording conjugate fourth varies greatly populations populations populations reflect recordings recordings recordings recordings recordings treated maintain serve substantial logical logical logical logical logical logical logical logical logical fiber fiber fiber decreased physiol contribute contribute consistently pose don ear ear ear ear ear ear ear physiology sort primarily primarily primarily approximates controlling theories arrival inspired platt platt air wrong ranges resistance interpret interpret analyzing neurobiology roles salient fires fires ambiguity encountered colorado colorado fish fish fish fish fish fish fish fish fish fish fish fish fish fish fish stimulated clean relies designing explorations displacement displacement displacement displacement displacement displacement displacement dividing robert lag lag escape escape escape escape escape escape pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure pressure linked appeared hair hair hair hair hair hair hair hair hair hair hair hair hair hair latency uniquely medium trigger stem possibilities spinal gated exclusive insights segregation boulder boulder boulder efforts mediated maximally acquired projecting cosine alternatives afferents intracellular intracellular intracellular particle particle particle particle particle particle particle particle particle particle particle particle particle grateful pools pools pools pools truth investigations treating ward simplifies inactive coming triggered transducer species simplification transduction inconsistent assistance hearing hearing hearing hearing hearing hearing hearing water oscillate interpreting reflecting japanese sensorimotor rons polarity polarity polarity cord evenly exclusively neurol tended tended tended brainstem brainstem ically prominent eighth emerged ears ears ears greatest health motoneurons began zone particles particles simula ton direc sensed sixth fight plans conveyed reviews mar assoc localize localize relying nections perturbing mediate pushed vertebrates exhibiting ponent abstr responsive seventh rce ishii ishii live plex swim swim swim chamber organ organ looked interpretable segregated assist duced deliver resembling collateral collateral collateral prepared backpropaga feedfor collaterals commissural commissural linkage shadow consis inertial elicit innervate pulled displacements displacements displacements displacements tent initiate regulate vastly unsuccessful nand intense intense electrophysiology coarsely raven acute organs bilateral logically unsolved midline institutes travels commu descend cosh reception homologous mathis deflection deflection sensation escapes escapes escapes furukawa furukawa hori acoustically preparing initiating asymptotes physio initiates nication ceils supra supra behar behar debugging outpu realistically transduced deserve redefinition curiously mechanically suspended 
#@Eaton_R,Guzik_A,
#t7
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#*model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data function figure figure figure figure figure figure figure figure time time time time time time time set set set set output output output output output output output output number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error error error results results models models models models models performance performance based based space linear case order order order order order shown shown systems systems systems systems systems systems parameters noise functions neurons approach point point image image image image image processing control large large large large large local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron inputs inputs inputs inputs inputs inputs shows signal signal signal signal signal signal signal signal visual visual visual visual visual visual visual visual visual paper small small small work methods fig fig fig step step step step features process level current current current current current current problems problems memory response response representation show show line line vectors parameter parameter real real real real real real average average average term term note note note activity activity activity university university computation research research research found target target target target initial initial initial estimate standard computer science left left left direction map map low low low low frequency temporal maximum range position position position position position position position position position position position position position components outputs outputs outputs abstract analog analog analog analog analog analog analog analog analog analog analog analog properties properties references component component adaptive adaptive introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior stimulus stimulus effect dynamic generated tion tion change change change signals signals signals representations representations higher part center center center center center center center center previous firing firing type spike long represent represent chip chip chip chip chip chip techniques scale simulations ing ing computed multi elements elements feedback feedback orientation applications study negative relative samples desired desired provide provide objects objects location location location eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye goal goal related gain motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor power power power approaches voltage voltage voltage voltage voltage accuracy contrast contrast selection institute institute institute institute version code difficult final final final layers layers layers layers addition considered computing computing environment directly directly additional design design design design top stage stimuli stimuli detection world world world vision coding weighted developed developed area area velocity velocity controller lines processes processes processes nature simply biological biological biological biological achieved discussion increases increases describe group fast complete complete surface circuits circuits circuits circuits circuits circuits short short common implemented generate supported supported end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel degree degree degree degree sensory including auditory auditory auditory simulated account technology technology technology technology technology technology significantly mechanism mechanism special numbers international bottom bottom early early attention run sources light population population discussed discussed pair pair pair robust robust movement movement movement movement movement identical side sejnowski array array array array array array array array array array interest interest interest approximately works smooth smooth smooth achieve organization storage grant constructed horizontal intensity digital digital deviation wide spikes spikes spikes derivative locally move move loop loop loop loop occurs setting hardware hardware hardware hardware demonstrate starting critical retina retina clear peak performs constrained mechanisms integration sigmoidal california california california solid proportional proportional pulse pulse pulse pulse pulse pulse pulse pulse turn movements movements movements movements movements averaged targets targets targets program force acknowledgements areas areas longer laboratory ann mathematical changing sensitivity sensitivity physical interaction integrated integrated equilibrium stages solved forms understanding understanding constants diagram diagram key slow dashed delays sec purpose closed closed closed initially msec msec construction construction advantages koch koch koch koch koch koch degrees degrees degrees degrees coupling coupling building building silicon thesis thesis currents retinal retinal automatic discuss coupled variations absolute holds partially successfully middle uniformly driven literature build build receives receives composed capture traditional traditional compact compact quickly moore superior superior superior superior superior superior superior superior superior superior superior superior superior issue strategies hold duration built built involved sampled localization simplified simplified cmos cmos computes computes computes ill chips chips neurosci moves software trains command command command command carried investigate circuitry mead mead mead mead mead rapidly rapidly pursuit pursuit pursuit project behavioral biol int analytically muscle muscle office office reliable working variability variability understand topographic trace trace plausible onset rev changed eyes eyes front portion freedom freedom freedom nervous nervous explain plant plant plant plant plant seconds burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst burst indicating vor vor vor developing asynchronous directed lies drive drive drive drive forces forces located laboratories laboratories angles integrating reflects double understood led red effort effort effort passed biologically schematic maintain passes pasadena plan age begins attentional attentional attentional wesley cybern addison generator generator generator generator generator generator generator generator generator generator oxford saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic angular linearity driving mobile impossible naval naval robotics caltech saturation imaging primate primate primitive replica serves operates salk integrator integrator integrator integrator integrator integrator integrator integrator capacitor capacitor arrays arrays intuitive carry carry muscles exploring service passive becker photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor centroid centroid centroid centroid arrangement deg deg foundations neuromorphic stimulated lazzaro saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus designing grants balancing metrics discharge dramatically dramatically numerous ter visually visually visually creates emerge obtains trigger trigger trigger trigger causing remote brightness shifting interact mammalian maintained maintained douglas douglas fixation fixation fixation fixation guided guided oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor figs dorsal bring holding tissue compu exploratory ucsd tonic tonic rarely drives lighting photoreceptors photoreceptors photoreceptors photoreceptors attributed mahowald mahowald mahowald evolved somatosensory morris char fabrication harvard wiring injected acoustical luminance luminance contributes modalities clark falling mosis lisberger lisberger physically adapts quick quick deweerth deweerth brainstem stabilize motors motors motors fovea fovea ically translates platform tim rotational silent christof refine sponsored carver horiuchi horiuchi horiuchi horiuchi horiuchi horiuchi horiuchi survival vergence rela sends disadvantages attentive deeper deeper gross capacitive jumps jumps bair lens notably begun cen delbriick delbriick delbriick brooks tational closing mammals owing prof hoped intend microns superficial superficial collaboration government pauses sudden reflexive reflexive viscosity viscosity agonist antagonistic midbrain timothy pursue friction sory intent audition pulls amplifies surveillance electronically pulling acteristics integrative bishofberger bishofberger bishofberger bishofberger bishofberger rockwell shut multitude flashed mimicking initiates ame centtold mans fabricate 
#@Bisofberger_B,Horiuchi_T,Koch_C,
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#*model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure time time time time set set set set set set set set set set set set set set set set set training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number number number number error error error error error error state results results results results information information information information information problem problem problem problem problem models models models models models models models models models models models models models models models models models models models performance space linear case case vector shown shown systems values values values values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters noise noise noise functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution recognition method method approach approach approach approach single single single processing large large local local neuron neuron neuron neuron rate analysis class class class matrix optimal form form form form shows signal signal signal algorithms simple gaussian gaussian gaussian small work task task task methods methods methods methods methods cells step classification classification classification classification classification classification classification classification classification classification classification classification classification level cell structure structure problems problems problems response similar similar show show show equation equation section section fixed line rule rule general parameter real approximation approximation approximation theory theory theory obtained obtained obtained obtained obtained obtained obtained term term note note activity dimensional result threshold computation computation solution solution solution solution solution solution research sequence sequence sequence sequence sequence table table table standard standard terms terms present frequency sets maximum maximum maximum maximum position sample sample sample sample abstract applied find properties properties references component component component due due ieee positive procedure procedure procedure procedure mixture introduction action action action action action action action action complex dynamic generated search search difference complexity rules signals signals signals signals signals signals prior previous previous previous previous previous firing multiple multiple multiple spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike conditions distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected make fact techniques region region correct probabilities probabilities probabilities observed observed observed errors resulting resulting resulting classes classes classes classes classes total total times times times times times times times times times times elements means means potential potential potential made study obtain obtain obtain obtain artificial relative specific true true true true true true provide compute perform eye determined posterior posterior posterior posterior posterior posterior posterior posterior equal equal approaches approaches voltage voltage accuracy accuracy dependent dependent modeling modeling modeling modeling modeling modeling modeling modeling modeling institute individual individual difficult difficult difficult difficult difficult difficult final exp exp exp addition addition sequences sequences sequences directly solutions estimates estimates estimates detection determine determine determine determine determine efficient efficient efficient efficient increase increase con weighted conditional clustering clustering clustering types types lines lines lines finally finally selected evidence evidence evidence evidence iteration simply discussion arbitrary denote denote tested tested limited limited limited assumption circuits finding finding assumed shape shape shape supported hypothesis instance instance makes makes development fit fit fit fit fit objective objective probabilistic probabilistic typically typically pairs smaller underlying underlying account account account unknown unknown technology programming significantly leads leads squared iterations making window normalized combined added description description neuronal neuronal neuronal neuronal denotes advantage apply period period identical trees inference inference inference inference engineering highly compare previously calculated tions yields trans sensitive entire grant parts lead deviation deviation spikes spikes spikes spikes spikes spikes spikes spikes alternative alternative alternative correctly clusters row assumptions interactions interactions interactions accurate accurate accurate accurate accurate accurate accurate bayes bayes clear peak practice hard presence california solid turn turn assuming program force generating distinct distinct distinct distinct distinct distinct modeled modeled modeled explicitly adding events events events events events events events events events events events potentials potentials potentials potentials potentials choosing independently overlap overlap overlap overlap overlap overlap overlap solved solved evaluate controlled decomposition decomposition decomposition decomposition decomposition soft soft approximated completely allowed calculation fitting fitting fitting fitting event event event event event event event event event event event event false interpolation assigned classified transactions david fire combinations priori priori priori priori determines plotted plotted uncertainty uncertainty variations absolute discussions major reason determining determining determining determining determining determining determining determining determining determining determining computationally efficiently mackay mackay mackay mackay composed composed procedures prob success success dis criteria list sampled michael providing hypotheses ill overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping overlapping preferred extract software software minimized minimized overfitting overfitting essential essential investigate investigate optimized integral accurately helpful matches analytically reliable maximizing proved affect math equally friedman friedman obvious algo observe detector separated separated shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes generates detected defines seconds seconds seconds residual residual pairwise smoothness defining defining waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform handle perspective satisfied precisely commonly probable probable probable probable probable probable probable probable probable probable probable probable probable acknowledgement fluctuations evaluating populations collected red posed posed splines incorporated frequently ity summarized summarized poisson poisson extracting occurrence occurrence qualitatively pasadena replace eventually classifying classifying identifying intractable primarily assign investigation extensive rithm conditioned eliminate caltech caltech wrong convenient convenient minutes difficulties logarithmic moment methodology heuristics overlaps overlaps overlaps overlaps iteratively encountered belongs dif infer infer infer thin indicator record cpu waveforms fired largely tables tables exhaustive inferred inferred inferred inferred inferred inferred inferred inferred inferred inferred decomposed certainty electrode electrode alter cns thick neurophysiological electrodes differentiation superposition superposition isi applicability milliseconds prevents normalizing wider utilizing circumstances quantify synthesized synthesized synthesized ferent virtually hoc kth tip tip extracts inferring frequent sian lewicki lewicki lewicki lewicki electrophysiological terminates gaus nih inaccurate inaccurate dence deciding deciding formulas decompose facilitates sparc demanding fluctuation superscript extracellular extracellular extracellular extracellular biomedical uniformity conver ting missed missed missed finkel penalizing overfit fell enormous ranks depen formulating brute quantifies stant decomposing decomposing decomposing decomposing decomposing compositions compositions atiya atiya aps aps aps aps aps aps aps aps aps aps derlying notoriously demonstrations demonstrations taneously collapsing sumed simul div distinctly discriminator reestimation lime popula obscure abilistic fellowships stereotyped ivy lap isj compounded isolating 
#@Lewicki_M,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data function function function function figure figure figure figure time time time time time time time time time set set set set algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number system system system system system system error error error error error error results results units units units units information information information information information information problem problem problem based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer case order shown shown systems systems systems systems systems systems systems systems values values values values probability weight weight weight weight weight neurons neurons neurons neurons unit method method method pattern point point single processing processing processing control control control control large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate analysis optimal inputs inputs form form form form shows shows shows signal signal signal signal simple simple simple simple simple visual visual paper small small net net work task task task fig fig fig fig fig cells points points points points process current current problems problems high response similar similar architecture architecture architecture architecture architecture show equation equation equation equation equation equation equation fixed fixed fixed line rule rule rule rule rule rule rule rule rule rule rule rule general real real real real real real real real real real real real real real real real real real real average average theory obtained term term term note experiments experiments experiments activity activity activity activity activity activity dimensional result university university university university university university research research research target target target constant constant constant constant constant constant constant constant constant constant computer computer terms connections connections connections synaptic synaptic synaptic science science science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left presented present present present frequency temporal temporal temporal temporal temporal temporal temporal temporal sets press press press learn learn basis outputs outputs abstract computational computational likelihood references component stochastic stochastic ieee positive adaptive adaptive decision context context action action action action action action action action action behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus dynamic variance variance variance variance energy difference difference difference difference difference variable variable variable variable variable variable variable variable variable variable variable variable assume assume measure measure prior prior prior representations higher part center firing firing firing type type type type type long conditions conditions expected expected expected make make make fact correlation length observed observed errors simulations simulations computed performed regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor made made made made artificial samples represented compared application series compute active determined experimental experimental related constraints constraints connected motor brain brain brain brain brain brain brain equal approaches larger larger connection connection dependent selection selection selection selection selection selection selection selection selection selection selection morgan proceedings report report report report institute institute institute version version version advances represents represents final bias bias bias cambridge cambridge cambridge equivalent experiment experiment experiment environment environment environment environment environment environment environment directly additional limit san san stimuli stimuli stimuli conference requires choice choice choice choice significant world derived levels types types lines actual evidence nature sampling simply biological associative discussion discussion technical technical describe assumption assumption assumption excitatory actions actions actions actions actions actions actions actions predictions predictions predictions predictions predictions predictions predictions predictions predictions finding amount amount short common shape supported supported role role journal journal ability instance future future future future future future makes makes development sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory kaufmann probabilistic underlying functional functional programming testing york york consistent structures trials trials representing representing details direct window inhibition inhibition magnitude produced choose choose sources predict predict improve pair reported lateral apply strategy sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive engineering engineering varying previously approximately approximately volume volume volume volume volume studies modified observation organization organization sensitive sensitive entire increased constructed occur occur suggests suggests suggests trial trial trial trial trial trial derivative derivative predicted predicted predicted occurs generally demonstrate demonstrate assumptions hebbian hebbian hebbian hebbian hebbian hebbian hebbian conclusions editors editors editors reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward accurate retina retina clear sutton sutton sutton sutton sutton sutton practice mateo suggest suggest sound presence presence presence demonstrated solid proportional variety exist relationship relationship iii averaged program acknowledgements explicit suppose suppose pro produces winner sequential plot changing implement implement remaining remaining text text text develop adding predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive springer shift expectation competition yield choosing choosing national review review stages influence influence influence influence restricted restricted updated showed showed modulation approximated suggested past diagram calculation barto barto barto barto barto barto classical classical classical classical classical event sufficiently sufficiently construction construction transactions david degrees thesis thesis usa formulation color color color color color color color color weighting sciences specifically specifically black reason selecting identified closely capable society driven delta successful identify literature literature projections receives verlag quickly induced induced contained contained contained contained allowing allowing showing anderson neuroscience neuroscience return physiological strategies quantity sampled simplified dayan dayan dayan dayan dayan dayan dayan absence giles subsequent cowan diego american singh updating varied strengths strengths hanson hall hall biases biases biases biases helpful postsynaptic scalar respond rest project project project behavioral behavioral behavioral plasticity plasticity plasticity relationships reliable comparable variability presynaptic presynaptic analogous matched removed examined act circles circles circles editor editor man illustrate equally equally changed adjusted adjusted taylor hebb switching extent seconds seconds massachusetts massachusetts massachusetts mentioned preference preference preference preference preference slowly ground nowlan london london ganglion drive purposes widely division choices controls controls watkins scientific circle beginning axons medical read read demonstrates annual annual cybernetics preceding reflects apparent reflect reflect dark embedded peter slower biologically variant psychological psychological rewards rewards rewards rewards howard berlin berlin ture spread modulated adjust richard substantial germany inherent comments conditioning conditioning conditioning conditioning conditioning conditioning conditioning lab college secondary feasible sort proportion proportion proportion oxford oxford conditioned conditioned animals animals animals resources zemel controlling odor odor food allocation anatomical chance adjusting neurobiology salk enhanced filled fires reliably utilized prentice mental enhance demonstration widrow consequences captured captured viewing viewing viewing suggesting suggesting jolla arrows horizon insect concentration considerations projects projects convergent influences influences appeared land land unified drop slight shorter feeding blue blue blue blue blue blue blue blue blue blue blue blue blue blue blue blue tradeoff amherst amherst reports england england england associate associate adjustment alter visited trends favor ibm chapman mathematically distant playing permits permits uncertain uncertain uncertain uncertain uncertain uncertain hughes terrence paired paired cole wise switched switched switched switched switched projecting projecting nuclei harder harder harder enforce flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flower flight flight flight bradtke steering steering steering tissue drives drives council reversed inconsistent prefer prefer ongoing pouget pouget envelope cliffs utilizes bold diffuse diffuse diffuse diffuse diffuse diffuse diffuse developmental steven bcm harvard visit visit medicine concrete seattle possess devised striking executing substitute substitute anthony restricting outgoing colleagues vertebrate approaching dopamine colors teaching delivery delivery delivery delivery delivery delivery saturating substrate substrate health acetylcholine correlational correlational correlational correlational bee bee bee bee bee bee bee bee bee bee bee bee bee bee bee bee bee bee bee wagner plenum yellow yellow yellow yellow yellow yellow yellow yellow yellow rein survival sensed simulates modulating forgetting offered availability availability visits visits visits visits visits visits visits visits visits mediate reproduces postulated ninth biasing biasing vertebrates vertebrates justify samuel samuel landing landing landing landing landing landing landing organisms encounter encounter encounter encounter brains brains widespread reproducing wtx wtx flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers flowers neurotransmitter neurotransmitter neurotransmitter neurotransmitter premise abstracts contingencies contingencies robbins deliver bohr steer steer forcement berry wood consequent montague montague montague montague montague montague neurosciences neurosciences chitecture invertebrates invertebrates mates torrey pines stochasticity delivers delivers amplify kandel alexandre instrumental instrumental instrumental alters supercomputer neuromodulatory legend legend wavelengths grounds distributing armed iio menzel menzel century hawkins rescorla contingent magnocellular stearns reinforcing reinforcing flies schultz neurotransmitters baylor houston houston dowling exerts cjch rewarding prepare reflexes antennae provision pitman txt checker norepinephrine encountering appleton crofts inadequacy engle prokasy predators 
#@Dayan_P,Montague_P,Sejnowski_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure time time time time time time time set set networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output system system system system system system system system system system system system system system system system system system system system system system system error results results results units units units units units units units units information information information information problem problem models models based based space space space space space space space space space space space space weights weights weights case case case vector vector vector vector order order shown shown shown shown systems systems systems values values values values values values probability probability probability probability probability probability probability probability probability probability probability weight weight weight functions neurons neurons unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution approach pattern point point analysis analysis analysis analysis analysis inputs inputs form shows shows shows shows signal signal signal signal signal signal signal signal visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual net net work work task methods cells cells field process process process process level level level level level level level level current trained trained trained trained structure response response response response response response response response similar similar similar representation architecture architecture architecture equation equation equation equation section section section section fixed rule rule rule rule rule rule rule rule rule real average average theory theory theory theory theory theory term term term term term term term term term term term term term note experiments experiments experiments experiments activity activity activity result result university university university computation independent log defined found found target target target target target target target target target dynamics constant table table table estimate standard standard standard standard standard terms terms connections connections science science left left map map map map map map map phase phase activation activation activation activation range press press learn learn components outputs abstract back back back back computational computational properties properties properties references component component important adaptive adaptive decision decision propagation propagation propagation introduction hand hand circuit estimation behavior behavior stimulus effect variance variance cost search search search tion tion change difference difference difference difference difference complexity complexity spatial assume assume assume assume assume signals signals signals signals signals signals signals signals signals signals signals prior prior prior learned learned center previous previous good good represent distributed bayesian bayesian bayesian expected expected equations region simulations simulations computed elements made natural natural natural applications study knowledge knowledge specific specific true compared cross provide define compute compute compute location location location location location location experimental goal goal goal goal motor cortical brain accuracy support train train train dependent dependent source source source source source proceedings report institute department department department technique represents represents represents represents represents represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist responses difficult final final addition maps maps maps maps maps maps computing equivalent experiment environment environment environment curves design design design san stimuli determine choice world world vision vision derived derived derived derived weighted types entropy provided processes backpropagation backpropagation nature depends depends measured discussion describe transformation assumption assumption complete predictions predictions shape supported theoretical theoretical eds journal journal journal journal journal journal journal ability ability ability ability ability future future future makes makes makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart development development development development sensory sensory sensory sensory fit fit auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory simulated simulated simulated simulated probabilistic pairs pairs pairs pairs pairs technology head head head trials leads pre pre making inhibition international early idea minimize choose predict predict denotes denotes architectures recent recent pair takes element lateral lateral apply period identical side sense array highly varying varying tuning tuning studies studies address address locations locations bounded bounded sensitive sensitive sensitive amplitude exists horizontal intensity expression trial trial trial trial trial trial derivative derivative derivative derivative predicted setting flow critical critical place place place place assumptions reduce central differences differences differences accurate accurate bayes designed designed designed sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound taking taking external drawn sigmoidal california california labeled labeled relationship relationship targets targets acoustic relation derive ways ways ways factors tuned tuned vertical mathematical mathematical changing changing changing modeled modeled develop choosing national formation stages interpretation interpretation evaluated evaluated restricted restricted updated centered understanding diagram remains david precision activations discuss maximize maximize maximize specifically priors priors priors major simplicity determining middle society included detect mackay mackay induced induced showing showing interpreted neuroscience neuroscience neuroscience neuroscience neuroscience return follow cues cues cues cues cues built built involved vary write write write write localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization computes leading principles principles principles unlike essential experience experience experience experience experience experience put accurately accurately accurately biases respond respond fashion giving behavioral plasticity plasticity plasticity relationships maximizing maximizing affect encode encode encode understand adapt adapt adapt adapt predicting predicts psychology psychology facial adjusted logistic logistic precise precise precise nervous attempts animal animal animal animal animal animal animal animal site developing developing defining biology biology reasons spatially drive stanford stanford stanford stanford stanford stanford sys style precisely nucleus immediately sounds describing gradually meaning alignment researchers greatly peaks exhibits exhibits weigend weigend weigend weigend reaches reaches maximizes maximizes monotonic ordered ordered ordered qualitatively pasadena adjust neuro owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl realized physiology primarily summing appropriately appropriately appropriately angular angular discover tem grows grows fits ments ments simplify neurobiology observing optic optic optic optic optic optic optic optic optic optic guide guide inferior inferior inferior elimination periods periods overview accounts accounts lawrence advance francisco occlusion young environmental colliculus colliculus colliculus captures discovered ignore ignore dramatically neurophysiology neurophysiology numerous numerous logarithm logarithm visually achieving deriving deriving maximized maximized removal encodes encodes presenting responds poses connec letting hillsdale eric adjustment adjustment adjustment adjustment barn barn barn barn barn barn barn barn barn principled chauvin chauvin chauvin goals blocking degraded expand concentrate altered academy nuclei nuclei nuclei nuclei nuclei nuclei nuclei associates knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen mimic mimic mimic mimic bring tune durbin durbin experi experi mea unpublished completed architectural remarkable ave calibration calibration tectum tectum tectum tectum tectum tectum tectum tectum tectum developmental developmental developmental interaural interaural interaural interaural dropped lists calculates exclusively dissertation konishi konishi konishi konishi huberman huberman core progressively disturbance systematically systematically lnp lnp adjusts accounting binomial binomial adapts subscript subscript skill ild ild ild ild ild denominator ears ears ears rec stan daniel survival altering altering altering elevation newly newly settles observes localize dard manipulations buntine buntine blasdel blasdel begun begun yij yij clarify clarify rosen rosen rosen rosen itd itd itd itd itd itd itd testable testable golden golden prism prism prism prism prism prism retains shell shell shell azimuth mature originating oij oij binaural binaural genome genome coil abstracts doctoral ucsf backpropaga presumed originated originated tionist accomplishes ffi chart plug plug plug darkness lends orient prey prey audition keck diminishes diminishes diminishes diminishes bilateral guides principally tum prisms prisms mil diate neuroanatomy localizes interme midway asterisk 
#@Knudsen_E,Rosen_D,Rumelhart_D,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set networks networks networks networks networks networks networks networks algorithm algorithm output output number system system system system error error results results results results results results results units units units units units units units units information information hidden performance based linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer case case case order order order shown shown shown shown shown shown shown systems systems systems systems values values values functions functions functions functions unit recognition recognition method pattern pattern single control control control control control control control large rate class matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple feature work work methods features level level structure structure random random random high representation representation representation representation representation representation representation representation representation show show vectors vectors general general general general general approximation approximation states states theory theory theory theory theory theory note experiments experiments experiments experiments dimensional result result variables variables variables variables computation computation computation solution solution research independent defined found found dynamics initial constant computer science science left left left left direction direction direction direction presented present low low sets sets motion motion motion range press learn components components components components components components basis basis basis basis basis basis basis nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs outputs abstract back find find find find computational density properties properties properties properties properties properties properties references component due due ieee ieee important important important important important important adaptive adaptive adaptive adaptive adaptive introduction complex hand behavior statistical statistical generated tion assume assume lower lower signals prior representations representations representations representations representations representations representations representations learned chosen chosen theorem theorem theorem cases cases cases long long long long long conditions represent tree fact fact proposed proposed proposed proposed proposed correct observed resulting resulting resulting resulting simulation simulation simulation simulation simulation simulation simulation simulation respect sum sum performed called elements mapping mapping made natural orientation orientation orientation orientation orientation applications knowledge artificial compared desired desired desired desired desired desired desired perform determined determined determined determined experimental related related constraints connected connected gain gain motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor brain equal mit selection report words department internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal responses responses difficult maps maps maps maps maps framework domain domain experiment environment environment environment environment environment solutions solutions stimuli determine determine upper upper upper choice statistics statistics world world produce channel coding coding developed nature biological biological biological biological biological biological biological feedforward describe arbitrary transformation inverse inverse inverse inverse inverse inverse inverse inverse assumption surface predictions predictions circuits circuits finding finding rbf short short short short short short short assumed generate supported adaptation journal hypothesis makes development development sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory reduced reduced unknown block block projection projection head head head head head head head head head head head head head head head head head head head head head head special special consistent making international supervised polynomial polynomial polynomial polynomial polynomial polynomial minimize minimize minimize choose description predict predict directions directions directions directions directions directions directions advantage typical movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement period subject identical cognitive recently relevant engineering sufficient unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised approximately volume tuning tuning axis axis axis axis axis tions achieve trans trans trans diagonal diagonal generalized channels channels channels channels channels channels channels channels channels interval interval interval exists horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal lead lead concept concept occur matrices predicted move move move move move move move move move move move move move loop loop demonstrate half half half half conclusion starting assumptions assumptions hebbian operator operator accurate asymptotic suggest taking mechanisms physics external external external radial radial exist exist exist movements movements movements movements movements movements movements manner groups appears relation pro pro produces describes laboratory laboratory tuned tuned tuned vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical distinct distinct distinct dept coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates physical electrical dimensionality mutual implies blocks national formation formation formation depending detailed transform transform transform controlled controlled controlled showed understanding approximated approximated approximated allowed reasonable spaces intervals intervals iterative iterative iterative iterative closed closed intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate sufficiently kohonen kohonen degrees degrees expect box box figures thesis coordinate coordinate sciences determines determines extension discussions successfully successfully successfully reason determining modes modes modes computations computations computations tend essentially orthogonal orthogonal orthogonal orthogonal orthogonal repeated allowing interested symmetry symmetry symmetry symmetry symmetry lie criteria criteria involved involved automatically moves moves oriented oriented oriented minimized stimulation stimulation command production detail helpful existence existence existence existence reducing respond ideas project mappings mappings investigated int muscle structured maximizing eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors adapt predicts predicts predicts predicts illustrate singular singular separated mapped explain phd attempts attempts plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant ment ment theoretic distinguish sensors sensors sensors orientations orientations adjacent answer drive sites sites sites organized located mation controls scientific acknowledgement toronto linsker linsker bandwidth bandwidth author cybernetics qualitative alignment alignment argument questions questions improvements double axes axes axes axes simulate posed incorrect commands commands commands commands commands commands commands schematic summarized extracting maximizes ordered serve prevent pasadena chen asymmetric coherent redundancy owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl univ extreme aligned aligned aligned optimality optimality guarantee refractory refractory refractory refractory animals controlling encoder receptors ments simplify height height transforms sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger optic responsible muscles muscles muscles muscles muscles moments infor meaningful becker becker studying intended belongs claim infer infer grants maintaining slight fellowship achieving session planes latency latency latency barn barn barn barn barn barn barn barn barn barn barn barn barn barn barn representa graduate inverted cartesian distinguished distinguished isi isi isi isi isi isi knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen nal ward develops sessions remarkable fortunately ble tom autocorrelation autocorrelation autocorrelation jet broadly broadly pronounced horizontally compo propulsion raises tended vertically dimen nih defense rotational responded unobserved simula upward align align directionally nents invert possesses rightward dissimilar topologically inertia intel controllable controllable controllable ily hypothesize sults plants quadrants grove neck neck neck neck permission permission unrelated ordinates pervised gravity feedfor bizzi bizzi lly oak rests stimulate unsu reprinted reprinted succeeds vides sionality discrepancies discrepancies capa terence transverse musculature aligns emilio 
#@Sanger_T,
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#*network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input figure figure figure figure figure figure figure figure time time time time time time time time time time time networks networks networks output output output output output output output system system system system system system system system system system system system system system system system system system system system system system information information models models models weights shown systems systems systems systems systems systems values neurons neurons neurons neurons neurons neurons neurons pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point processing large local neuron neuron form form form shows simple simple paper small cells cells cells cells cells cells cells cells cells step points level current current current cell cell structure response similar similar similar similar similar line parameter real real approximation note note activity activity activity activity activity activity university university computation research independent connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic presented present phase phase phase phase phase phase phase phase phase phase phase phase phase frequency frequency sets sets range range abstract analog analog analog analog analog analog analog analog analog analog analog analog references positive important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation introduction action circuit circuit circuit circuit behavior behavior behavior change spatial spatial multiple spike conditions represent distributed observed scale scale scale scale scale scale scale respect respect elements elements means potential potential natural feedback represented provide provide provide active determined experimental experimental related related posterior posterior connected larger connection modeling modeling modeling morgan institute department department implementation synapses synapses synapses individual individual individual advances represents represents delay delay delay delay addition framework framework additional design design design san full speed produce levels levels levels levels lines inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends biological biological biological biological biological biological biological biological biological biological biological biological discussion group tested tested close complete excitatory excitatory excitatory circuits circuits circuits implemented implemented implemented generate role theoretical eds journal journal journal vlsi vlsi vlsi vlsi vlsi vlsi vlsi future sensory including kaufmann typically smaller functional functional technology technology block block interesting interesting significantly projection projection york head making inhibition inhibition inhibition magnitude magnitude produced neuronal membrane membrane exact strategy moving include include identical engineering engineering interest highly varying approximately studies address locations organization organization organization organization constructed digital wide wide spikes touretzky width loop strength critical central central central central central central central central central central central central designed mateo mechanisms mechanisms mechanisms mechanisms integration cycle cycle cycle cycle cycle cycle demonstrated california exist relationship groups groups groups appears appears generating laboratory segments segments segments modeled explicitly electrical electrical interaction interaction interaction interaction integrated frequencies frequencies potentials potentials detailed suggested diagram diagram delays delays delays delays delays generation generation generation generation generation generation generation generation generation construction building building fire includes includes silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon coordinate determines coupled coupled coupled coupled coupled coupled successfully successfully identified identified identified included oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory projections characteristic characteristic excitation excitation notice notice neuroscience neuroscience oscillations device involved simplified simplified simplified simplified play absence realistic realistic wave wave wave wave delayed delayed delayed principles operating acknowledgments intrinsic body body body body body explore explore explore explore transformed essential mead mead mead oscillators detail integral oscillator rise successive successive successive successive successive successive behavioral ideal relationships phases phases phases analogous analogous measurement transmission plausible plausible reading equally implementations implementations thought nerve nervous nervous nervous nervous nervous nervous nervous nervous generates generates motivated motivated motivated stop biology interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons interneurons ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion potentially arises recording demonstrates cybernetics apparent behaviors behaviors behaviors behaviors behaviors behaviors behaviors understood embedded autonomous orders adjustable adjustable adjustable employ biologically biologically biologically biologically biologically biologically span exhibits exhibits fall qualitatively qualitatively qualitatively pasadena sophisticated segmented wesley synchronization addison generator generator fabricated conditioned animals inspired cellular bower significance significance mail height hope hope neurobiology operates operates responsible responsible responsible guide excellent excellent governed respective somatic somatic somatic similarities fish recovery recovery recovery recovery express axonal axonal bursts bursts captures captures captures lag lag lag yale yale reflex constitute constitute employs employs employs incrementally encouraging spaced constitutes rhythm rhythm rhythm clustered arising capacitance shifting conduction conduction evolve wall compatible increasingly rhythmic maintains dorsal supporting tonic tonic tonic tonic tonic leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech leech locomotion locomotion locomotion tail cpg cpg cpg cpg cpg cpg cable swimming swimming swimming swimming swimming swimming swimming spring spring impulses utilizes evolved inclusion inherently integrates cord anterior anterior anterior anterior ventral artifact vertebrate spirit cold cold adapts counterpart counterpart counterpart counterpart ready ready correlates subsystem subsystem platform platform platform selverston selverston ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia ganglia undergo comprehensive comprehensive modulate haven discrepancy rhythms repeats aliasing friesen friesen friesen friesen friesen friesen friesen friesen friesen friesen friesen friesen friesen friesen friesen friesen friesen counterparts organisms retains invertebrate invertebrate invertebrate invertebrate beat spans ryckebusch ryckebusch tri tri repertoire repertoire swim swim swim swim swim swim swim swim swim swim swim swim swim elongated muller siegel siegel siegel siegel siegel marcel dekker invertebrates phasic phasic endogenous oscilloscope shortening harbor harbor stepping guides homologous homologous homologous participating biophysically biophysically extrinsic flavor technological encompasses coordinating contractions intentionally pauern riding illuminating imprecise igure undoubtedly 
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#*network network network network network network network network model model model model model model model model model neural neural neural neural neural neural neural input input input input data data function function function function figure figure figure figure time time time time time time time networks networks networks networks number number system system system system state state results units units units units units units units units units units units units units units space layer order order shown shown systems systems systems systems values probability probability noise noise noise noise noise noise noise noise noise noise noise weight functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution pattern pattern pattern pattern pattern point point point single single single single single single single single single single single single single control large local local local local local local local local local neuron neuron rate rate rate rate rate rate patterns patterns patterns analysis analysis matrix inputs form form form form shows shows signal simple simple gaussian gaussian gaussian visual visual visual visual visual small small small size size size size size feature net work fig fig fig fig cells cells cells cells cells cells cells cells cells cells step field field field field field field field field field process process process process process process level level current current current current cell cell structure random random random random high high high high high similar show show fixed fixed fixed fixed fixed fixed fixed general general real approximation approximation theory note note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional result result threshold threshold threshold computation computation computation research research research research log log found dynamics dynamics dynamics dynamics constant constant constant table table terms distance connections connections connections connections connections science science left present present phase low low low low low frequency frequency frequency temporal temporal temporal temporal motion motion motion maximum range range range range range range press press press position position position position nonlinear abstract back find properties references component component component due due ieee circuit stimulus statistical statistical effect recurrent tion tion spatial lower chosen chosen higher higher part center center center theorem firing firing firing firing firing firing firing firing firing firing firing firing firing type type cortex cortex cortex cortex spike spike spike spike spike spike spike long long long long long long conditions distributed fact techniques correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation scale scale scale finite finite simulations resulting total simulation simulation multi sum sum sum eq eq times potential potential potential potential potential potential potential potential dimension feedback global study study relative relative samples compared cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross series receptive rates rates rates rates related connected connected connected connected distributions gain cortical cortical cortical cortical brain equal power power power power power power power power power power power power power power power power power power power power power power power power power power power voltage voltage contrast connection train train dependent institute institute institute loss consists consists individual individual individual individual represents represents represents responses exp exp exp delay addition graph equivalent curve transition top upper approximate increase con developed area area processes evidence iteration iteration nature inhibitory inhibitory inhibitory inhibitory inhibitory measured measured increases denote limited corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory short short common effective generate supported cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster makes auditory hopfield functional fully technology character york mechanism consistent uniform empirical leads leads leads leads inhibition inhibition inhibition inhibition magnitude frame frame decay decay decay decay decay decay decay decay description neuronal neuronal neuronal membrane membrane membrane correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations ensemble ensemble ensemble ensemble typical typical typical typical lateral lateral lateral lateral moving moving period period period period highly varying tions trans grid interval interval interval amplitude lead lead scaling scaling trial spikes clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters occurs boundary generally generally demonstrate strength strength interactions peak peak peak peak peak peak peak exponential asymptotic constrained constrained suggest integration presence physics external external external external california pulse turn turn assuming decrease relationship averaged connectivity connectivity force attractor areas areas reference reference longer longer primary dept modeled simultaneously scales consisting interaction develop frequencies frequencies frequencies frequencies frequencies frequencies frequencies equilibrium applying events events events potentials john national independently independently formation formation formation dependence review depending transform transform centered centered approximated constants constants spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum key slow sec sec intervals roughly distances visible msec msec msec msec msec msec msec foundation eeg eeg koch koch koch koch koch koch koch koch koch koch koch coupling expect expect recorded recorded fire fire fire fire currents currents phys phys characterized planning driven spiking spiking spiking spiking spiking spiking spiking spiking oscillatory oscillatory literature characteristic excitation excitation excitation notice neuroscience symmetry symmetry oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations hold gray gray gray michael relaxation surround surround surround cat cat cat cat neurosci neurosci neurosci neurosci moves satisfies neighboring acknowledgments rat cowan cowan cowan trains trains trains trains law law law law law remain remain investigate exponentially varied relations relations relations issues dual hall rise rise fourier fourier fourier fourier fourier giving int relationships office office variability variability variability presynaptic neu hill hill rev rev illustrate olfactory explored separated separated nerve nervous consist generates generates seconds integrate integrate integrate integrate histogram histogram slowly slowly band fairly navigation biology explanation diffusion diffusion diffusion diffusion london ring broad monkey monkey monkey monkey pulses cut scientific res medical localized recording bandwidth auto auto auto auto geometry geometry radius radius fluctuations fluctuations fluctuations fluctuations mechanics mechanics mechanics freeman freeman freeman freeman empirically understood generic quantitative lattice lattice lattice lattice lattice lattice lattice recordings slower frequently sharp sharp sharp sharp ity howard mod poisson poisson poisson reaches reaches pasadena singer singer singer singer coherence deviations summed summed synchronization synchronization synchronization synchronization synchronization phenomenon spectra spectra spectra spectra spectra extensive martin refractory refractory refractory driving circular homogeneous homogeneous homogeneous naval spontaneous spontaneous cellular air stronger simplify chemical transforms transforms transforms weakly reset reset irregular corre captured israel eng offer vertex merge interestingly outlined consecutive discharge neurophysiology slight slight fellowship ties randomized transmitted reaction emergent nelson nelson nelson quasi flat flat classic resting breaking breaking examining var constrain mutually mutually pub exponent exponent decays decays decays chapman dominated neurophysiological hughes paired surrounding synchronized macaque sheet superposition isi isi isi isi isi isi isi isi isi isi isi isi amplification interspike interspike interspike interspike behaves behaves walk walk walk laws ergodic reversed fractal fractal fractal fractal fractal fractal inconsistent autocorrelation oscillate stripes stripes pronounced subtracting optics arriving william sions lewis lewis lewis bauer corn cyclic prominent prominent substrate christof newsome eeckman eeckman eeckman behaving behaving cox cox cox wiener simula occasionally tracked broader broader tsodyks tsodyks tsodyks awake awake awake bair bair leaky niebur eckhorn eckhorn eckhorn vat vat cortico terry epsps amit amit amit usher usher usher usher usher usher usher usher usher softky softky softky softky aver cancellation mon engel quantum narrower correla sponds hexagonal hexagonal hexagonal hexagonal retrieving chemistry fluid fluid fluid fluid indebted traced bernander bernander bernander pling lighter looo whitehead whitehead whitehead mimics interac mech newell newell newell cou insightful interplay weizmann discus aged noteworthy coordi activ repulsive richly ksnig anesthetized emits nectivity quanti rehovot nates ernst lished jnowski munk renewal renewal renewal renewal multaneously britten biotaed fluctuate fluctuate ronal shades wyeth diffuses bait bait diffused tre neuroreport disrupts cay 
#@Koch_C,Olami_Z,Stemmler_M,Usher_M,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural input function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time set set set set set set set set set set set set set set set training algorithm algorithm number number number number number number number number system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information problem problem problem problem problem problem problem problem problem problem performance performance performance based based based based space space space space space space weights weights weights weights order order shown shown shown systems systems systems systems systems systems systems values values values values values values values values values values values values values values values values values values values values values values values values values values values values values weight weight weight weight weight weight weight weight approach approach approach approach approach approach point point point point point point point point single processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large rate optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form form form shows shows signal algorithms paper paper small size size work work task task step step step points points points points points process process process process random random memory memory memory memory memory memory memory memory memory memory memory memory memory response equation equation equation equation equation equation equation general general generalization real real states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states dimensional result result result result result result result result university university university university university defined found sequence dynamics initial initial initial initial left left left low machine machine maximum learn learn learn learn learn position position continuous continuous continuous continuous abstract applied applied applied applied applied applied find convergence convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee positive adaptive introduction action action action action action action action action action action action action action action action action action action action action action action behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic cost cost cost cost variable variable lower rules learned learned learned learned learned learned learned learned learned part previous required required required required required required required expected equations equations region region region region region region region region region region region region ing total performed called times elements regions regions regions regions regions means reinforcement reinforcement factor potential dimension made made made policy policy policy policy policy policy policy policy policy policy vol vol vol artificial represented represented represented represented represented compared compared compared application desired proc proc proc determined determined related constraints approaches update modeling morgan morgan report words implementation version technique consists advances joint connectionist addition addition addition addition addition maps cambridge curve solutions design transition transition transition transition transition transition transition transition transition transition transition transition san san determine determine determine determine determine determine determine full requires significant basic basic increase con con randomly randomly velocity depends associative achieved technical arbitrary arbitrary group group limited limited close assumption complete complete surface actions actions actions actions actions actions actions proof proof proof shape supported role theoretical theoretical main main main main main eds future makes makes makes kaufmann kaufmann combination reduced jordan programming programming programming programming programming programming programming programming programming programming programming testing trials trials uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform pre direct direct direct direct early idea idea description resolution resolution exact advantage advantage advantage advantage takes typical typical typical typical movement movement movement movement practical practical practical practical practical practical practical practical practical practical practical practical practical practical include include hierarchical engineering engineering highly conventional conventional conventional conventional solve achieve sparse address evaluation evaluation evaluation positions positions positions positions positions modified modified modified increased grant arm parts lead concept concept occur trial trial move occurs occurs occurs boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary pass pass conclusion starting starting minimal minimal minimal minimal minimal minimal minimal minimal reduce reduce valued designed performs mateo taking external reduction reduction reduction intelligence turn exist exist min explicit explicit transitions transitions dept dept dept changing simultaneously simultaneously infinite electrical electrical electrical dimensionality adding shift shift shift john review depending variation updated centered converges barto barto barto barto barto epochs epochs epochs spaces spaces spaces roughly add boundaries closed advantages existing existing existing exploration figures thesis thesis memories specifically determining determining middle identified suitable modification modification modification modification modification modification effectively efficiently reached conf conf quickly heuristic moore moore neuroscience return running content dayan quantization delayed delayed reach consisted policies policies policies policies policies illustrates operating tesauro employed employed employed remain powerful transformed singh singh difficulty updating updating updating rapidly association accurately preliminary reducing incremental int int ideal ideal possibility proper workshop removed possibly ensure adjusted multivariate epoch epoch consist simplest utility attempts massachusetts asynchronous costs costs publishers publishers track track track track track track track track adjacent reasons comparisons rapid located located watkins watkins watkins watkins watkins watkins watkins watkins watkins potentially localized lowest lowest arises computers annual led readily peter car car car car car car car atkeson remove treated rewards requirement operate controllers controllers proven proven suited substantial inherent deviations jaakkola jaakkola consistently benefit modify modify controlling determination determination hyper removing operates operates operates operates modifications modifications modifications modifications modifications modifications continue utilized loo encountered facilitate facilitate lawrence lawrence lawrence lawrence lawrence lawrence tic francisco discounted repeatedly canada canada canada horizon discovered cam boxes usage usage usage drop slight kinematics achieving basically discount session removal removal lit acceleration experiences england associate rain adjustment assess avoids quantized shaded shaded shaded attempted attempted modifying wall chapman chapman maintained maintained maintained maintained simplifying proach cation sweeping locking son bradtke prevents exploratory continually develops bridge discretized discretized ongoing savings curse mining thickness assessment assessment assessment assessment assessment resolved trol trol coins kaelbling deter routes routes routes routes routes routes assessed assessed assessed addressable merit excessive excessive facilitates facilitates initiated rein assessing incurred continuing disadvantages sydney entered entered illustrating concurrently concurrently intervening inertia inertia iter ative british british british nserc nserc constantly concurrent concurrent concurrent incremented superfluous premise accompanying reductions reductions forcement worthwhile heuristically indefinitely additions imal subjected race race race race race race aug aug fulfills scholarship kenneth sooner sooner abstracted pacific ttt commu optional decremented decremented sinall cknowle dgement mer stoch specifi columbia columbia columbia vancouver vancouver circumvented negligibly responsiveness rim finishing finishing finishing engi postgraduate wildly commerce swapped swapped progressed neering ack 
#@Buckland_K,Lawrence_P,
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data function function function function function function function function function function function function function function function function function function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number system system system system system system system system error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results units information information problem problem problem problem problem models based based based space space space weights weights weights linear linear linear linear linear case case case order shown shown systems systems systems systems values values values values values values values values values values values values values noise noise noise noise noise noise noise noise noise functions distribution distribution method method method method method method approach approach point point point point point point point point point point point point point point point point point point point point point single single processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large large large large local local local rate rate rate patterns patterns analysis matrix matrix matrix inputs inputs inputs form form form form signal simple gaussian paper paper paper examples small small small small small small small small small feature work work work task step step step step step step step points points points points points level current current current current current trained trained trained trained problems problems random random random high similar representation representation architecture show show equation equation equation section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line rule rule rule general general generalization parameter parameter parameter parameter parameter real real real real real real approximation average average average average average states theory theory theory gradient gradient term term note note experiments experiments experiments experiments dimensional dimensional dimensional result result result university university variables variables computation research research research independent defined defined found target target target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant estimate computer computer terms terms terms distance distance distance distance science science science science science prediction prediction prediction prediction left left left presented map map map map map map map map map map map map map map map map map low motion maximum range press press basis basis basis basis basis nonlinear nonlinear nonlinear outputs outputs outputs sample abstract back references component due due adaptive propagation introduction generated variance recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change variable assume rules rules signals chosen part part part center previous previous previous previous previous previous previous multiple good spike spike long long represent equations equations equations equations equations equations equations equations equations equations equations make make fact techniques techniques techniques techniques techniques region region proposed proposed correlation length observed forward forward forward forward forward simulations simulations simulations ing simulation respect respect respect performed times mapping means global global study knowledge knowledge knowledge knowledge true compared application desired desired series provide define define define define define compute compute compute location location determined experimental experimental experimental experimental goal constraints constraints mit comparison contrast connection update update update train train train train train train train train train train descent proceedings report institute institute department version technique technique technique technique technique consists consists joint represents connectionist final exp exp scheme scheme cambridge cambridge computing computing experiment additional view estimates trajectory trajectory top stage stage stage conference requires requires requires requires approximate free free world pages give give produce randomly randomly controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller finally backpropagation iteration constraint simply technical describe describe denote fast fast limited assumption corresponds rbf rbf rbf rbf rbf rbf rbf rbf rbf amount nearest effective assumed supported end instance future future future future future easily easily rumelhart rumelhart noisy fit fit objective objective objective objective objective objective typically smaller needed dynamical unknown unknown unknown unknown unknown unknown jordan jordan mlp mlp mlp testing york edge special special special operation details details international normalized supervised supervised magnitude magnitude idea combined minimize minimize choose perceptron discussed directions separate introduced moving moving period identical identical quadratic recently recently highly teacher calculated works tions solve yields correspond studies converge achieve modified williams improvement increased grant constructed intensity studied invariant extended extended extended spikes feed locally demonstrate conclusion starting minimal row greater greater conclusions measures measures numerical numerical numerical numerical designed moody moody hard presence physics physics cycle cycle radial radial radial turn minimizing minimizing minimizing minimizing minimizing introduce derivatives derivatives manner force force force force attractor attractor attractor attractor acknowledgements derive construct produces produces index index index ways tuned mathematical distinct modeled modeled multilayer multilayer physical consisting cycles cycles letters focus review stages solved controlled controlled lee lee lee lee lee lee lee lee evolution centers forms approximated converges allowed partial partial earlier epochs epochs measurements combining purpose purpose add add add add add visible advantages precision coupling avoid priori priori extension illustrated discuss specifically specifically discussions tests successfully reason reason capable capable schemes reached composed summary quickly success success success return hold notation generalize realistic giles computes ill automatically law powerful american american perturbation requirements experience rapidly detail accurately preliminary preliminary helpful fewer fashion history history understand gradients editor necessarily spline portion mapped epoch epoch consist consist utility plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic great trivial crucial derivation unstable unstable unstable unstable unstable unstable coded analytical benchmark reasons considerable drive drive drive drive perspective tive purposes sections sections easier strictly forces desirable beginning sun sun sun sun sun argument understood fed fed experimentally passed compares rely summarized proven chen chen chen chen chen comments eventually specifies contribute newton college temporally pick pick driving driving acts controlling controlling controlling discover jones jones adds darken darken simplify familiar keeping keeping methodology published james widths guarantees searching facilitate facilitate offers initialize advance clean park exploiting exploiting exploiting exploiting discovered discovered generalizing acknowledge limitation maintaining numerous job adopt chaos chaos chaos chaos chaos chaos chaos chaos additionally additionally additionally additionally additionally hundred forcing imagine alternate alternate carefully afosr distal cation maintains happen places tune tune transients transients differentiating pineda chris gratefully sees august trainable locate locate locate usefulness fft fft fft artifact zipset rtrl rtrl rtrl evolves lewis fair differentiate differentiate differentiate vicinity enforces indirectly prominent plasma promise iterate maryland campbell elegant ogy ogy ogy ogy ogy ogy ogy ogy ogy ogy ogy unlimited perspectives cardiac cardiac bptt functionals functionals discard proaches unrealistic occasional ergodicity ergodicity strange barnes barnes distribute hen nns gary knowl recipes ifp ifp teukolsky flannery qian unfolded vetterling skip roger yee sensation sensation communica modifi ott ott ott ott unfavorable prospect 
#@Chen_H,Flake_G,Lee_Y,Sun_G,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set set set algorithm algorithm algorithm algorithm number number number number number number system system system system state state state state state state state state state state state results results results results results results results results units problem problem problem problem problem problem problem problem hidden performance performance performance performance performance performance performance performance based space space space space space space space space space space space space space layer layer layer vector order shown shown shown shown systems values values functions functions functions functions functions functions unit method method method method approach point point point point single control control control control control control control control control control control control control control large local rate optimal optimal optimal optimal optimal optimal shows shows shows shows shows shows shows shows shows algorithms paper paper paper net work work work work task task task task task task fig step step step step points points points level level level level level current trained structure structure structure problems problems problems problems architecture show show show show show show show show show equation equation equation equation equation equation line line line line line line line line line line line vectors general general general parameter parameter real real real approximation average average average average states states states states states states states states gradient gradient gradient note note note dimensional result university university university solution solution solution solution research research research independent defined found found found initial computer computer computer terms terms distance distance science science science science science left direction present present low low low low machine machine motion motion motion motion motion motion motion motion motion motion motion maximum maximum learn learn position basis sample sample sample sample abstract abstract abstract abstract find find references component component due ieee important adaptive decision mixture mixture mixture context action action action action action action action action action action hand hand behavior behavior dynamic dynamic dynamic generated generated generated parallel parallel cost cost search search tion tion difference spatial prior learned learned learned chosen chosen higher higher higher part center bound cases cases cases conditions conditions conditions make techniques region region region region region region region region region correct finite finite simulations minimum minimum minimum resulting resulting resulting resulting resulting resulting tasks tasks simulation simulation computed computed sum performed called called times mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor dimension applications applications applications applications applications applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge artificial relative relative specific compared desired desired series define compute objects location location location perform perform determined determined goal goal goal goal goal goal goal goal goal goal goal goal constraints constraints constraints constraints connected brain mit update descent proceedings report report institute department department department implementation consists consists connectionist final maps maps considered framework framework cambridge cambridge cambridge domain domain domain domain environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment directly curve curve curve curve curve solutions solutions solutions solutions solutions curves design design trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory conference approximate approximate approximate statistics statistics statistics world speed pages give give produce derived randomly randomly developed robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels criterion criterion bounds velocity velocity velocity velocity velocity velocity velocity controller types types lines path path actual actual processes constraint achieved normal technical technical arbitrary denote close surface actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions finding finding common generate supported journal ability future simulated simulated simulated dynamical dynamical dynamical dynamical fully technology technology transfer programming programming projection trials trials trials trials trials trials trials trials details details direct international added improve improve advantage robust robust robust robust practical practical apply moving sense cognitive dimensions dimensions approximately tions tions solve differential achieve achieve rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl locations locations locations locations locations locations williams risk grant horizontal lead lead trial loop loop loop loop loop loop white white white boundary boundary boundary boundary boundary boundary boundary boundary hardware conclusion starting starting starting starting starting starting starting starting minimal greater reduce trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories sutton sutton practice practice learns learns suggest propose taking taking taking hard demonstrated solid solid solid intelligence labeled labeled labeled labeled labeled labeled radial start relationship relationship averaged averaged minima minima configuration configuration configuration configuration denoted reference perception solving solving factors modeled modeled explicitly simultaneously simultaneously physical involves formed agent agent agent agent agent agent agent agent agent agent agent national national stationary solved solved solved solved open similarly partial partial barto barto barto barto barto barto barto barto barto slow dashed dashed performing convex reduces boundaries closed closed closed closed closed foundation foundation advantages precision exploration exploration exploration exploration exploration exploration exploration figures figures thesis thesis formulation formulation sciences determines automatic specifically black black black planning planning planning planning planning planning planning planning planning planning planning selecting capable paths paths paths paths paths paths paths plots plots tend tend summary kind moore moore interested follow follow follow hold hold delayed reach reach reach reach reach policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies mixing mixing mixing mixing mixing mixing mixing mixing presents presents explore american singh singh singh singh singh singh singh singh singh singh singh experience experience rapidly rapidly environments dotted dotted mass rise fewer successive successive successive fashion possibility proper affect func removed act act circles circles circles circles circles circles circles circles circles circles coefficient coefficient gradients gradients configurations extremely illustrate illustrate ensure ensure greedy panel panel panel panel panel panel panel panel panel panel panel panel panel ith store store generates improving improving mixed phd phd massachusetts massachusetts massachusetts massachusetts ment ment defining failure failure analytical expensive worse worse inside strictly division watkins watkins watkins inversion acknowledgement arises author addressed researchers researchers robustness geometric greatly collected pure pure pure pure pure pure pure pure pure pure pure pure flexible offset conducted conducted autonomous atkeson atkeson marked marked marked marked marked marked marked formulated formulated rewards summarized prevent plan boston shaped shaped specifies univ cumulative room room room room room room room room room secondary proportion proportion proportion proportion guarantee restriction mobile mobile mobile harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic flexibility grey grey grey robotics robotics reaching reaching consideration numerically imposed primitive primitive primitive intelligent check mark mark mark mark exploit symposium planar filled filled filled filled filled filled filled filled filled obstacle obstacle exploring mance appendix appendix perfor decide dif laplace laplace designing grants alternatively executed andrew outperforms outperforms maintaining workspace accept discount formulate obstacles obstacles obstacles obstacles suboptimal acceptable acceptable acceptable acceptable tradeoff amherst amherst acceleration acceleration england avoids argue care ibm formance robots robots robots wall execute topic dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet iri iri sweeping maintains meet meet ation bradtke failures gauss mix elemental neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann neumann expense payoff interior ate christopher ferent agents spacing prioritized condi executing judged judged judged ooo vanish vanish safe safe safe safe safe safe robotic rel terminates enters catastrophic watson mesh rein heights erroneous darker darker darker posi psyche ecs satinder designated environ environ snapshots snapshots snapshots stars stars stars stars stars ending ration contributed accelerate formulating prof prof safety safety safety accelerated exceptions forcement arrangements inexpensive walls namics rooms composing cda envi jerk yorktown accelerations trophic unacceptable unacceptable unacceptable oxi asymp loca markovjan mahadevan mahadevan explo ensured guaranteeing intuitions ction afforded appropri expe tivation excludes excludes connell impression controt totic finishing quential formulates 
#@Barto_A,Connolly_C,Ginpen_R,Singh_S,
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#*learning learning learning model function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set set training algorithm algorithm algorithm number system system system state state state state state state state state state state state state state state state state state state state state state information problem problem problem problem problem models models models models models models models models models based based based based based space space space space space space space space space space space space linear case vector order order order order shown systems systems functions functions functions functions functions approach approach approach approach approach approach point point point point point point point point point single control control control control large local local local local local local local local local local local local local local local local local local local local local local local local local local local test optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form shows shows shows shows algorithms algorithms simple simple paper paper examples size task methods cells cells cells step step step step step step step step points process process process process process process process process current current current cell cell cell cell cell cell cell cell cell cell problems problems problems similar similar representation representation representation fixed general general states states states states theory university threshold threshold computation computation computation research research defined found found dynamics dynamics dynamics initial initial initial initial initial initial initial constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant estimate estimate standard node science present phase phase low press press learn learn position nonlinear nonlinear continuous abstract applied applied find find find references stochastic adaptive adaptive adaptive action action action action action action complex complex complex dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search search spatial spatial assume representations learned chosen center center type good conditions conditions equations make fact techniques length correct errors forward ing total human computed respect sum sum sum regions regions regions means reinforcement optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization made natural global global global global global global global global global policy policy policy policy policy policy policy policy policy policy policy policy policy artificial true provide compute compute location determined goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal motor discrete brain approaches mit support support institute department implementation version joint difficult difficult difficult ai cambridge computing environment directly directly directly additional estimates design limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory requires approximate approximate approximate world speed speed speed speed estimated increase increase con produce produce developed developed controller provided provided iteration iteration depends depends simply measured describe fast limited stable surface surface surface surface surface surface actions actions actions actions actions generate generate generate generate role require require face square future future future future makes simulated typically underlying reduced technology technology programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming york york york increasing increasing consistent consistent consistent consistent leads making magnitude minimize produced produced choose added improved resolution resolution resolution resolution resolution resolution resolution pair separate separate takes element typical quadratic quadratic quadratic cognitive volume volume volume volume volume volume volume tions match converge differential differential sparse modified grid grid grid grid grid grid grid grid grid grid increased increased increased grant parts correctly correctly correctly locally locally locally locally locally locally locally locally locally locally locally locally locally locally deterministic boundary boundary boundary boundary starting starting starting starting reduce trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories segment segment segment neighbor clear clear taking intelligence turn start start start decrease derivatives derivatives derivatives derivatives program force base explicit construct longer index index ways laboratory segments segments segments dimensionality dimensionality dimensionality dimensionality dimensionality slightly slightly text develop integrated equilibrium applying blocks national solved solved solved solved solved solved solved solved solved solved solved approximated approximated completely completely completely completely key key reasonable performing performing performing spaces combining initially foundation avoid avoid avoid building exploration exploration figures includes includes contour inter sciences plotted illustrated candidate planning planning computationally computationally driven summary procedures procedures procedures procedures dis follow criteria built play backward minimizes moves moves approximating neighboring neighboring neighboring situations estimators limitations hall ideas rest rest office surfaces surfaces contours contours contours contours contours contours predicts versions obvious academic plant plant integrate integrate massachusetts stop costs costs growing growing unstable adjacent adjacent expensive caused lies tool starts inside straight straight immediately controls laboratories scientific acknowledgement gradually lowest requiring greatly consistency consistency leave atkeson atkeson atkeson atkeson atkeson maintain maintain controllers mod achieves plan chose deviations globally globally globally globally globally globally globally globally globally bellman intractable intractable princeton princeton air siemens serves methodology methodology guide guide exploring prentice started separating separating representational iteratively consequences young ahead contact pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum assigns bertsekas corporation pointing achieving creates arg forcing forcing avoids increment increment increment increment evolve inverted afosr surrounding surrounding suffer suffer elsevier union els atr answers helps stores accumulation inconsistent christopher marks marks curse curse curse cliffs adaptively focuses dropped award englewood interpolating swing swing grids grids contacts contacts tube tube planner thing sweep oscillates penalizes backwards sur tory ming dyer dyer refine instant investigator searched optimizes plans plans plans plans grown solu volumes volumes volumes volumes volumes presidential checking quadratically pump torques script optimizations swinging sparser laid laid speeding knew valleys mcreynolds mcreynolds guaranteeing guaranteeing optimizers optimizers optimizers optimizers optimizers cga cga trajec swings swings polation progressed 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number system system system system system results results results units units information information information information information information problem problem performance performance performance performance performance performance performance performance performance based based based based based shown values parameters parameters approach approach approach approach approach pattern point point point single single processing control control control control large large local local local local local local rate patterns patterns patterns patterns patterns analysis optimal optimal optimal optimal optimal shows signal algorithms algorithms algorithms simple paper paper paper paper paper size net work work work task task field level level level level level level current current random random high high high high high high high high high representation equation section section speech parameter average experiments experiments experiments experiments result result university university university university university university variables research research initial initial initial table table estimate estimate estimate estimate estimate estimate estimate computer computer computer computer computer computer distance node node node node node node node node node node node node node node node node science science science science science science science science left left left direction direction low low low low low low nodes nodes nodes temporal machine press learn abstract applied back references ieee adaptive adaptive decision decision context context context introduction behavior effect effect tion tion tion difference difference lower learned learned higher part part part center center bound cases long conditions conditions conditions conditions conditions conditions represent distributed distributed distributed make make techniques techniques length scale scale simulations ing ing ing tasks total total total total simulation simulation simulation times times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement potential natural natural applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy negative compared application application cross perform related related connected discrete approaches steps contrast connection update support dependent report department version technique represents scheme scheme scheme cambridge cambridge domain domain directly curve estimates estimates estimates top efficient efficient upper upper full full full full full full full significant statistics statistics basic basic basic increase con channel levels levels levels levels area path path path path path path path path path path path path actual actual finally measured measured discussion technical increases increases group group denote tested tested close corresponds stable actions amount common role face adaptation instance future including including including fully interesting significantly york trials operation language leads leads leads call stored minimize improved discussed directions advantage robust separate takes similarity practical practical period period period period cognitive cognitive engineering varying module tuning solve rl grid grid grid grid increased grant lead white generally conclusion critical minimal neighbor neighbor neighbor editors central measures accurate performs performs performs learns learns learns learns learns labeled variety minimizing min program question acknowledgements van longer describes changing changing changing changing changing changing changing changing changing remaining select select national national communication communication learner detailed updated updated static static suggested allowed allowed past diagram delays delays event add initially visible foundation topology topology topology topology topology transactions david avoid exploration exploration exploration exploration thesis thesis thesis plotted specifically neighbors characterized successfully reason straightforward aspects modification paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths delta successful efficiently efficiently efficiently efficiently schemes plots tend online online fine fine summary quickly quickly quickly quickly quickly quickly success vary michael relaxation generalize modular realistic delayed policies policies policies approximating routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing 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adjacent majority adapted adapted caused worse lin widely day incorporate immediately watkins mathematics potentially recognized demonstrates demonstrates auto mellon mellon mellon apparent evaluating carnegie carnegie carnegie fuzzy cmu embedded slower continuously compares compares rewards pittsburgh reaches popular qualitatively adjust plan replace simulator simulator returns median converged contribute bellman bellman bellman college princeton dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically discover discover extending communications adds overcome intelligent continue performances prentice loo irregular irregular irregular irregular irregular surprising captured advance reveals shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest master ends passing route route route route route route route route hypercube approximator dramatically outperforms maintaining unable thrun fellowship diverse suboptimal suboptimal exception tradeoff recurrence discovering adapting backgammon queue queue queue queue queue summarizes packets packets packets packets packets packets packets packets packets community robots continues graduate echo echo echo echo echo echo echo considers switched switched iri drawback drawback oscillating packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet tune answers diagrams diagrams littman littman littman littman littman littman topologies learners january send telephone oscillate king flows boyan boyan boyan boyan boyan boyan boyan manually loads loads loads inefficient trol ignores proves destination sending sending adjusts elevator randomness periodically edition edition bottleneck bottleneck delivery delivery delivery delivery delivery delivery delivery delivery delivery delivery delivery handbook halves halves routes routes routes routes raised request request defense ous propagates drawbacks cations spent appli simula neigh sebastian sends erroneous tailored lowered grown viable requests constantly rising disconnected bellcore bellcore standpoint asynchronously deliver deliver settled settled tolerate unmodified slowing concludes overestimate bor spend ford ford ford strate morristown donald eventual parison gathering balances revise rior experimenting quarterly telecommunication distinguishable shortcuts shortcuts shortcuts sustain justin ceases irregularly centralized nonadaptive precomputed bottlenecks sulting inefficiencies inefficiencies gies sofge inefficiency continual pictured queues trip reinhold inconclusive nostrand 
#@Boyan_J,Littman_M,
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output 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optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs form form simple simple simple simple simple gaussian paper paper paper paper examples examples examples examples examples small net net work work work task task task fig step step step step step step points points points points points points points field classification classification process process current current current trained trained trained problems random random random random random random random high high high architecture architecture architecture architecture equation equation equation equation section section section section section section fixed fixed parameter parameter parameter approximation approximation approximation approximation approximation average states theory gradient gradient gradient gradient note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional result university computation computation computation computation computation solution solution research research research research research found dynamics initial estimate estimate estimate estimate estimate estimate estimate standard terms science low machine sets sets maximum maximum maximum press learn learn position basis nonlinear nonlinear sample sample abstract find computational computational computational computational computational computational convergence likelihood likelihood likelihood stochastic stochastic stochastic due ieee important mixture introduction action action action action action action action estimation estimation behavior statistical statistical effect effect effect dynamic variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance parallel cost cost cost cost search search tion tion change change change change change change change change change change change variable lower learned required good good good expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected make make make make fact techniques techniques techniques proposed proposed correlation length correct correct forward forward simulations minimum ing ing ing tasks human human regression computed sum performed elements mapping reinforcement optimization optimization optimization made study em em filter specific true compared application application define compute compute active active active experimental experimental gain gain gain gain gain gain brain steps steps steps steps steps steps steps comparison update selection selection morgan morgan morgan technique individual advances advances advances joint joint joint joint connectionist cambridge computing computing computing domain domain domain experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment environment estimates estimates estimates design design design design design design design design design design design design design design design design design trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san san determine full requires requires requires significant significant world estimated produce randomly randomly robot controller controller controller lines actual actual actual actual actual actual actual actual actual actual actual actual provided finally selected evidence backpropagation nature sampling sampling discussion feedforward feedforward describe arbitrary limited limited limited assumption assumption assumption corresponds corresponds corresponds actions actions actions actions actions finding amount role eds adaptation end future rumelhart fit kaufmann kaufmann kaufmann objective pairs pairs reduced unknown unknown jordan jordan jordan jordan jordan technology block transfer interesting significantly york squared squared squared squared squared direct making making supervised supervised combined minimize minimize minimize minimize minimize choose choose choose added sources description light predict predict architectures discussed improve correlations correlations correlations resolution movement strategy strategy strategy moving subject identical side cognitive cognitive relevant interest highly teacher volume volume correspond studies trans diagonal improvement improvement improvement improvement entire entire grant arm arm arm arm arm arm arm parts parts parts predicted predicted predicted alternative alternative locally move move touretzky white white demonstrate runs starting greater greater assumptions assumptions reduce trajectories trajectories trajectories trajectories trajectories trajectories trajectories editors sigmoid measures accurate designed moody practice asymptotic constrained strong drawn demonstrated assuming minimizing minimizing selective selective decrease decrease decrease decrease decrease decrease averaged minima minima identification identification acknowledgements areas reference reference reference reference reference produces plot describes dept confidence confidence confidence confidence sensitivity sensitivity coordinates involves adding adding gaussians versus select select select decreases decreases decreases decreases decreases yield learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner evaluate approximations approximations approximated translation translation allowed allowed slow additive spaces spaces sec intervals generation sufficiently query david david expect building exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration box coordinate batch sciences plotted illustrated automatic automatic discuss discuss discuss maximize maximize maximize black successfully selecting selecting selecting selecting selecting selecting uniformly suitable computationally delta delta identify build build build efficiently mackay mackay mackay mackay mackay reached repeated allowing heuristic moore moore link dis lie strategies hold hold michael minimizes highest leading predictor automatically approximating neighboring situations situations situations presents explore explore explore explore simpler put environments involving involving detail hessian hessian game lippmann hall successive rest mse mse mse mse mse mse mse incremental mappings int act act editor predicts queries queries greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy assumes explored explored academic utility arbitrarily attempts massachusetts great costs costs costs costs variances variances variances variances variances variances variances variances fairly adapted expensive expensive expensive expensive baum baum tool processed perspective strictly constructing incorporate incorporate choices mation laboratories inversion angles angles begin optimize toronto geometry incomplete nsf integrating limits led leave incorporated maxima gains gains gains gains rely measuring cal extensions simulator logical expectations multidimensional extreme realized realized realized ghahramani ghahramani intractable feasible linearity concerned robotics climbing fails wrong promising siemens check fail implications intuitively guide guide guide corner corner moments spurious infor passive iteratively iteratively guarantees lang lang viewing francisco francisco francisco surprisingly clean theoretically informative draw horizon designing avoiding ure leaving thrun thrun kinematics kinematics kinematics kinematics kinematics kinematics kinematics outperform piece ber suboptimal retraining covariances covariances covariances covariances var var remote reject adapting mismatch cohn cohn cohn cohn cohn cohn cohn community num chapman gener token maximally distal cartesian worth manipulator emphasized alternatives discusses funded discretization bring bring atr computa differentiating spite coordination opti corporate heavily stochastically builds confirm virtually imple inherently tip tip settle manually correctness inefficient parti ignores tance prone robotic robotic amenable amenable gathered inst promise translate ized ated mle mle mle mle mle atlas routine preferable occasionally settles treats ess mal undesirable perturbing retrained vat hillclimbing concise draws unclear exciting fruitful confident plutowski plutowski masses brevity cov cheap conserved entails cheaper indebted asymptote guiding crossed inertial cda batches bibliography intent underway gather gather quantizing arbi abbreviated fedorov fedorov instantaneously trary menting xerion bridges dimensionm writ flailing flailing fewest unexplored 
#@Cohn_D,
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#*learning learning learning learning learning learning learning learning learning data function function function function function function figure figure figure figure figure figure time time time time set set set set set number number number number number system system system system system system error error error state state state state state state state state state state state state state state state state results results information problem problem problem models based based based based based based based space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case vector systems systems systems systems systems systems systems systems systems systems systems values values values values values probability probability distribution method method method method method method method method method method method method method method method method method approach approach approach single single control control control control control control control control large large large large large large local rate rate rate analysis analysis analysis analysis class class matrix matrix matrix matrix matrix matrix matrix matrix optimal form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple paper paper size size size size feature feature work work work work work work work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step points features process process level problems problems problems problems problems problems problems problems problems random random random random similar similar representation show equation equation fixed fixed fixed line vectors general parameter real real approximation approximation approximation approximation average average average states states states states states obtained term term term note university university variables variables variables variables computation computation computation computation solution solution solution solution solution solution solution solution independent independent log log defined defined defined defined defined defined defined dynamics initial estimate estimate estimate estimate standard standard standard computer computer terms terms science science science temporal temporal temporal machine machine sets press learn components components components components components sample sample sample sample sample sample sample abstract computational computational computational computational convergence convergence convergence convergence properties properties properties properties properties references component component component component component stochastic stochastic stochastic stochastic important decision decision decision decision decision decision introduction estimation estimation estimation estimation statistical statistical effect effect dynamic dynamic dynamic dynamic dynamic generated variance variance variance variance tion tion tion difference difference complexity complexity complexity complexity complexity complexity complexity complexity complexity variable measure theorem required required required required required distributed expected expected expected expected expected expected expected equations equations equations equations equations equations equations equations equations equations markov markov markov markov markov markov markov markov markov markov markov markov markov make fact fact fact techniques techniques techniques techniques techniques proposed proposed length length length length observed scale scale finite resulting classes ing ing simulation respect respect respect sum sum sum regions regions means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor policy policy policy policy knowledge knowledge samples represented true compared compared desired series series series series compute compute compute determined equal mit accuracy comparison comparison connection connection department department technique technique scheme scheme addition maps considered considered cambridge computing computing computing solutions solutions solutions solutions estimates estimates estimates transition transition transition transition transition transition transition limit trajectory trajectory trajectory determine efficient efficient choice approximate approximate approximate approximate approximate estimated produce condition weighted weighted randomly conditional criterion bounds path path path path actual actual actual actual provided finally processes iteration iteration iteration discussion discussion describe describe arbitrary inverse corresponds amount amount amount effective assumed supported theoretical theoretical theoretical require require simulated simulated underlying programming programming programming programming programming interesting significantly york york consistent trials trials numbers making making predict denotes discussed improve separate takes practical practical include include identical sense relevant relevant observations observations tions yields converge rl rl rl rl rl rl rl rl rl rl rl rl rl evaluation evaluation evaluation chain chain chain chain chain chain interval sensitive grant scaling scaling scaling suggests suggests matrices occurs starting place reduce reduce trajectories trajectories trajectories operator reward central differences clear sutton sutton sutton sutton sutton suggest reduction reduction reduction reduction drawn relationship relationship explicit explicit suppose pro monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo produces written solving solving solving solving solving solving solving solving solving solving solving estimating estimating transitions transitions confidence confidence recall averaging infinite infinite unique applying versus versus versus versus versus national family family family focus expressed stationary estimator viewed key barto barto barto barto barto barto barto barto slow slow slow classical classical event iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative remains sufficiently sufficiently foundation weighting plotted determining capable capable computationally paths paths paths paths plots plots summary repeated repeated interpreted stopping stopping stopping return return sampled sampled sampled michael relaxation automatically policies approximating tesauro tesauro tesauro unlike wiley wiley essential singh estimators issues mass mass successive successive tech notion math math implementations versions obvious noted noted precise arbitrarily submitted motivated defines massachusetts massachusetts mentioned asymptotically formula formula asynchronous guaranteed improves analytic analytic lies lies reasons perspective producing producing constructing worst inversion inversion inversion inversion inversion inversion acknowledgement describing arises geometric consistency effort share requirement howard howard limiting differs achieves sophisticated conclude returns returns returns returns begins begins representative appearance arguments arguments arguments approximates grows arranged establish significance significance attractive serves implications imply preparation symposium substituting governed governed loo von von discounted discounted discounted discounted discounted insight mem augmented horizon horizon variants material assigning andrew multiply truncated truncated truncated leibler leibler covering leaming tables tables ties break break markovian uniquely utilize corrected amherst perceived perceived algebraic backgammon publication preserved cessing proba statistic statistic player ation bradtke exhibited gauss gauss gauss develops develops advantageous neumann neumann neumann neumann neumann neumann correspondences ongoing establishes establishes establishes establishes cornput cornput recursion rare practically equa tical focusing focusing focusing focusing subtle stan yon virtue approxima save suitably suitably dard multiplications favorable terminated ecs duff duff duff duff duff duff duff solu posterjori gorithms gorithms oooo sorts converting prefix unimportant barnard barnard barnard jacobi rtdp rtdp rtdp rtdp comparatively suc originated ficient variate bers walks labor condensed efficiencies absorption prac recency tending intention aids aids evalu marginally probab probab probab probab rept solv recast recast seidel seidel evalua tee lue uti burdensome 
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural function function function function function function function function function function function function function function function function function function function function time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information information information information information performance based based based based based based based based based based based based based based case case case case case case vector vector shown shown shown systems systems systems values values values values values values values probability probability probability probability probability probability probability probability probability probability parameters functions functions distribution method method method method method method single processing processing control control control control control control control control control control analysis analysis matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper paper paper paper paper examples work work work work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step process process current current current problems problems problems memory similar similar show show equation equation line general general general real real real real real approximation states states states states theory term term note note experiments result result result result result result result result result result result result result result university university university university university computation computation computation computation computation computation solution research defined defined initial table table table estimate estimate estimate computer computer computer terms science science science direction present temporal temporal machine machine maximum maximum maximum maximum maximum learn continuous abstract convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties likelihood likelihood likelihood likelihood likelihood references references stochastic stochastic due due important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision introduction action action action action action action action action action action action action action action hand estimation estimation estimation behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated parallel cost tion tion difference measure measure measure theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound required required long long conditions conditions conditions distributed expected expected expected expected expected expected markov markov markov correct probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed finite finite finite finite ing tasks called called times times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor optimization policy policy policy policy policy policy policy policy policy policy policy policy obtain obtain original artificial relative specific true true true true true true true true series define determined goal steps steps update update update selection selection morgan proceedings report report report department department version advances advances scheme sequences framework cambridge cambridge computing equivalent environment environment environment environment directly directly directly estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition limit limit limit san conference conference determine determine efficient requires requires significant approximate approximate basic pages con con condition condition condition condition condition controller actual provided finally finally finally processes selected selected selected iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration nature nature simply discussion technical arbitrary arbitrary denote denote denote denote complete actions actions actions actions actions proof proof proof assumed generate supported require journal future easily makes kaufmann simulated probabilistic typically underlying needed needed programming programming programming programming programming significantly special special special trials operation call max max direct direct direct direct direct direct direct direct making stored international attention attention attention attention minimize produced produced produced predict denotes denotes denotes denotes denotes discussed discussed improve directions recent pair practical subset subset recently conventional observations works correspond converge converge converge converge converge achieve address evaluation modified bounded bounded bounded williams williams williams williams increased increased grant grant exists trial trial trial matrices place place conclusions editors reward reward reward reward differences accurate numerical clear clear sutton sutton practice practice mateo taking assuming start identification identification identification identification identification identification identification denoted denoted pro pro solving estimating transitions modeled modeled explicitly infinite infinite infinite involves interaction agent agent implies implies implies implies implies select focus review controlled controlled controlled updated updated updated updated updated updated understanding understanding completely similarly similarly converges converges converges converges converges converges updates updates updates earlier earlier barto barto barto barto barto barto barto barto barto barto barto barto barto barto barto barto performing classical valid valid valid valid norm norm classified existing existing existing thesis priori extension prove prove partially discussions planning efficiency presentation computations computations repeated prob prob moore moore moore moore moore moore link anderson dis issue issue issue contribution notation gibbs dayan giles delayed observable received received policies policies policies operating operating approximating approximating tesauro tesauro cowan remain singh singh singh singh singh singh singh singh singh singh singh singh experience environments environments environments hanson issues mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp hall examine incremental applicable combine induction act adapt adapt integer analyze analyze ensure ensure ensure versions der algo algo algo store store store utility utility utility phd integrate massachusetts massachusetts massachusetts mentioned inequality asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous critic publishers analyzed fairly considerable sys satisfied watkins watkins watkins watkins actor acknowledgement incomplete incomplete incomplete incomplete nsf addressed researchers researchers reflects items embedded embedded peter atkeson atkeson atkeson atkeson atkeson atkeson posed formulated rewards rewards rewards rewards rewards rewards execution execution characterize maximizes extensions suited kinds boston baird baird trade trade trade college identifying equivalence forming forming forming restrict ordering systematic promising observing substituting substituting prentice appendix appendix appendix studying studying belongs approximators discounted infer indicator environmental horizon tsitsiklis tsitsiklis variants receiving receiving convergent material material acknowledge executed executed executed executed executed executed mdps mdps mdps mdps mdps mdps mdps bertsekas bertsekas andrew verify outperforms indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect discount exhaustive randomized markovian employs axe dyna dyna pointed amherst amherst amherst england certainty param queue rithms rithms rithms tems afosr afosr met anal sweeping sweeping sweeping sweeping sweeping sweeping sweeping isi isi siam sweeps sweeps bradtke bradtke bradtke bradtke bradtke bradtke bradtke bradtke bradtke priority priority eters september infinitely infinitely infinitely infinitely infinitely lems lems circumstances emphasis emphasis served gratefully survey ble cliffs prioritized prioritized prioritized prioritized prioritized prioritized prioritized eral sided executing executing executing executing executing englewood trol trol adapts restrictive cess successor counted proceeding unnecessary objectives ysis preferable preferable simula reactive reactive formulations concurrently ecs 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural function function function function time algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system system system system state state state state state state state state state state state state state state state state state results results results results results results results problem problem problem problem based based based based based based based based space case case shown shown systems values values values values values values values values probability probability probability probability parameters parameters parameters parameters parameters distribution distribution method approach approach approach approach control control control control control control large rate rate class class class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper methods methods methods step step process process process process process process level current problems problems problems random random high similar show show show equation equation equation equation equation section section fixed line line line line line line line line line line line rule rule general general approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states states theory theory theory theory theory obtained obtained note note note note university university university variables computation computation solution solution solution independent defined defined defined found sequence sequence sequence sequence constant estimate estimate estimate estimate estimate estimate estimate standard computer science prediction prediction prediction presented presented temporal machine machine machine machine maximum maximum maximum maximum maximum maximum maximum press learn abstract applied applied applied find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due due due due important decision introduction action action action action statistical statistical effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance variance variance variance variance parallel parallel cost cost cost tion change difference difference difference previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem required required required required conditions conditions conditions conditions conditions conditions represent distributed expected expected expected markov markov markov markov markov fact techniques techniques techniques region correct correct probabilities probabilities probabilities finite finite finite finite finite ing tasks respect respect respect times mapping mapping mapping mapping factor made made made made made policy policy knowledge knowledge obtain obtain obtain obtain specific specific application desired define determined constraints distributions brain equal equal mit update update update dependent proceedings institute institute department department version version version version version addition addition sequences sequences cambridge cambridge environment environment environment directly directly additional view estimates estimates estimates estimates transition transition transition transition limit san upper requires statistics statistics free basic derived derived weighted weighted bounds bounds bounds types provided finally finally processes processes processes processes processes iteration iteration iteration iteration iteration nature depends achieved denote transformation complete actions actions predictions predictions predictions predictions predictions predictions predictions predictions proof proof proof proof proof proof proof proof role theoretical theoretical end future future future easily including underlying needed needed needed account account unknown jordan jordan jordan jordan jordan jordan technology programming programming programming programming programming programming programming programming programming increasing increasing max making attention light predict predict predict denotes property property property property property property pair practical practical apply include sejnowski sejnowski cognitive recently recently interest previously calculated tions chain chain chain chain observation bounded bounded bounded bounded bounded williams williams exists exists exists lead lead studied suggests extended extended deterministic generally generally starting assumptions conclusions operator operator operator depend central differences differences numerical sutton sutton sutton taking strong california variety manner relation pro produces written mathematical mathematical mathematical missing linearly slightly slightly slightly applying applying implies viewed learner learner learner solved controlled forms understanding converges converges converges converges converges converges converges converges converges converges updates updates allowed allowed past past past classical spaces iterative iterative iterative iterative iterative iterative iterative iterative valid assigned norm norm norm norm norm norm norm thesis formulation formulation formulation batch batch batch batch batch batch batch batch batch batch batch sciences prove specifically specifically simplicity importance uniformly uniformly uniformly uniformly uniformly uniformly uniformly schemes showing showing showing interested satisfy satisfy satisfy satisfy satisfy notation notation quantity write usual michael relaxation relaxation dayan dayan dayan dayan minimizes delayed observable policies policies policies extend extend remain unlike diego powerful singh singh singh singh singh singh updating updating updating updating environments environments environments involving involving involving replaced recursive hall hall behavioral applicable applicable applicable terminal terminal terminal authors affect cover cover naturally closest possibly analyze versions versions versions versions obvious algo submitted submitted phd massachusetts asymptotically developing asynchronous asynchronous asynchronous costs costs costs costs costs costs crucial variances guaranteed defining purposes strictly immediately controls watkins watkins watkins involve begin begin geometric understood readily readily lack maxima rewards rely rely mod characterize occurrence conclude unbiased jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola bellman bellman proofs proofs identifying accomplished controlling establish establish plays generality generality belong salk symposium prentice prentice falls iteratively iteratively guarantees sides sides similarities enable discounted ahead contraction contraction contraction contraction contraction contraction contraction contraction contraction contraction contraction refers tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis characterization convergent executed bertsekas bertsekas bertsekas bertsekas divide verify rigorous annals munro convenience utilize england forcing forcing stands var var visited verified pij pij rithms interact goals impose bounding interacting proba relate relating relating emphasize ultimately tively preprint applicability vanishes els covers bility converging converging converging cliffs cliffs realizations subtracting englewood englewood evolving implying fin fin rem maxq ira enabling incurred unifying checked theo constructions psyche mmi subtract satinder paid respec absorbing absorbing absorbing tommi tommi robbins robbins monro 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number system system system system system system system state state state state state state state state state state state state state state state state state state state state state information problem problem problem problem problem performance space space space space space space space space space linear linear shown shown shown shown shown systems systems values method method approach approach approach point point processing control control control control control control local local local local optimal optimal shows shows shows shows shows shows paper work work task task task points process level level level level level level level level current current problems problems random random high high high high high high high high high high high high high memory similar similar show show fixed fixed real real real real real real real states states states theory obtained experiments experiments experiments dimensional dimensional dimensional dimensional dimensional university university university university university variables variables computation solution solution solution solution solution solution solution research research found dynamics dynamics dynamics initial initial initial constant estimate standard standard computer distance science left left direction low low nodes temporal machine machine machine maximum maximum press learn position position position continuous continuous continuous continuous abstract find find find computational convergence convergence properties references ieee decision decision action action action action action action action action complex dynamic dynamic dynamic tion tion change change change complexity variable variable variable variable variable variable spatial lower rules prior learned part part part part part part center center center center previous cases required good good tree tree tree expected expected markov make techniques techniques region region region length length length length length probabilities observed ing tasks total total times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement policy knowledge knowledge desired series provide compute compute compute compute perform goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal constraints connected steps steps steps larger morgan morgan proceedings report report advances joint difficult final final final delay maps considered cambridge domain hinton hinton hinton limit trajectory trajectory trajectory top top full full requires choice world increase increase increase increase increase con derived robot robot robot robot robot robot criterion velocity velocity controller controller controller controller controller controller lines lines path path path path path path path path path path provided finally discussion technical technical increases arbitrary tested tested corresponds complete surface surface actions actions actions actions finding finding amount short nearest shape journal end end end future degree development including kaufmann simulated probabilistic typically unknown block programming programming programming ratio ratio edge trials trials trials trials trials trials trials trials uniform database database database numbers international depth magnitude choose run improve resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution property robust takes movement reported include include side side trees sense subset dimensions highly studies trans trans observation grid bounded entire arm horizontal lead trial trial trial trial trial trial move move move width deterministic runs starting starting critical place assumptions trajectories trajectories neighbor valued valued valued editors editors editors reward sutton sutton sutton constrained cycle user start start start start start iii manner program configuration force force base areas areas van edges edges transitions mathematical distinct dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality slightly text angle angle angle versus versus select communication interpretation detailed restricted updated updated partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition updates allowed past sign diagram diagram earlier barto barto barto spaces spaces spaces spaces spaces spaces roughly remains remains initially sufficiently degrees degrees precision exploration exploration exploration exploration exploration exploration exploration exploration exploration figures thesis thesis bell assignment automatic planning planning straightforward extra uniformly build efficiently efficiently reached quickly quickly allowing moore moore moore moore moore moore moore moore moore moore moore moore link link criteria criteria strategies built play dayan dayan dayan absence giles delayed delayed delayed delayed policies neighboring neighboring neighboring software cowan explore explore essential singh singh singh exponentially exponentially exponentially involving humans hanson game game game game game game game game game game game game game game game game game game dotted rise matches ideas school links links incremental scores contours hill hill coarse necessarily man created thought friedman friedman friedman greedy greedy greedy greedy greedy greedy greedy algo algo freedom freedom freedom multivariate consist phd phd massachusetts massachusetts asynchronous theoretic theoretic theoretic costs explanation tractable spatially inside inside turns easier controls watkins watkins watkins ridge ridge members lowest computers mellon behaviors carnegie applies applies empirically axes atkeson atkeson atkeson passed remove remove rewards rewards rewards passes controllers controllers partitioning partitioning partitioning partitioning pittsburgh aim aim aim aim extensions prevent plan shaped begins eventually eventually specifies june converged credit multidimensional multidimensional hints pole pole globally gap gap bellman bellman discontinuities college guarantee investigation restriction princeton princeton acm rithm rithm member partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions addresses discover outcome outcome plays climbing kaufman minutes promising promising occurred proceeds logarithmic automaton intelligent check hit hit splitting splitting splitting splitting intuitively planar planar started slice ranging moved assembly record route route agree broken splits border border stopped ball andrew crossing workspace recursively obstacles obstacles incrementally restrictions restrictions par amherst amherst personal experiences imagine illustration mutually ibm robots robots robots wall chapman chapman chapman concentrate altered noting guided records harder harder adversary adversary adversary manipulator barrier barrier barrier barrier barrier barrier barrier barrier barrier sweeping sweeping maintains outcomes outcomes outcomes rod rod rod rotating stuck stuck stuck bradtke permit september october laws sees consuming august discretized discretized twenty losing losing losing maze maze maze ers curse curse curse prioritized prioritized king 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#@Moore_A,
#t7
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input input data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set networks networks networks networks networks training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error state state state state state state state state state state results information information information information information information problem problem problem problem models models hidden hidden performance performance performance performance performance based based based based weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer vector order order order order order order order order order order order order order order order order order order order shown systems systems systems systems systems systems systems systems systems systems systems systems systems probability probability probability parameters parameters noise weight weight unit unit method method approach approach point point single processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large local rate rate rate rate rate test test test class inputs inputs inputs form algorithms algorithms simple simple simple gaussian net net net work work task task task task task task task step step step points points classification process process level current trained trained trained trained trained trained problems random random high high similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture equation equation section line general parameter approximation approximation average states states states gradient gradient note note note result result university university computation computation computation log log log log log sequence sequence sequence sequence target target target target dynamics dynamics estimate estimate standard computer distance left left presented present frequency frequency object object object object object object object object object object object object object object object object press learn learn learn learn learn learn learn position outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs sample sample sample abstract applied back back convergence convergence convergence analog likelihood likelihood likelihood likelihood likelihood references stochastic ieee procedure procedure procedure procedure procedure important adaptive adaptive propagation propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction complex complex complex behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical statistical dynamic parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference assume assume assume learned chosen part part previous previous previous cases cases required required multiple multiple multiple conditions equations markov markov markov markov markov markov make make proposed proposed proposed correct forward scale simulations minimum resulting ing ing ing ing tasks tasks tasks tasks tasks tasks computed computed computed computed respect respect sum performed times times times potential made global applications em em em original original original original true compared compared application desired desired desired desired desired define compute determined experimental gain gain power mit steps update train train descent descent descent report department department technique represents represents represents connectionist final exp exp sequences sequences sequences sequences sequences directly hinton additional additional solutions solutions transition trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san determine determine determine efficient con con con derived derived weighted randomly conditional conditional conditional velocity velocity controller controller controller controller controller controller controller controller actual actual provided provided provided associative discussion technical feedforward increases describe assumption assumption assumption effective implemented require ability future degree development noisy fit pairs smaller underlying combination dynamical dynamical unknown jordan jordan jordan jordan jordan significantly significantly ratio mode mode mode mode mode mode mode mode mode mode mode mode leads squared call direct experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert produced produced choose denotes architectures improve reported introduced strategy identical hierarchical highly observations teacher teacher works axis axis achieve mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures modified modified generalized generalized horizontal expression lead studied suggests suggests derivative derivative pass pass pass greater assumptions trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories competitive differences designed designed designed sutton sutton faster learns demonstrated california turn turn turn turn turn assuming assuming targets targets derivatives derivatives derivatives force explicit derive primary transitions transitions stability vertical distinct explicitly explicitly explicitly simultaneously select choosing family stationary stationary stationary stationary stationary stationary stationary squares detailed controlled controlled updated updated decomposition decomposition decomposition approximated activities activities activities completely past partial partial epochs iterative tracking tracking initially assigned priori formulation determines extension extension extension extension extension illustrated uncertainty gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating successfully successfully successfully successfully extra extra capable capable importance modes modes modes modes modes modes modes modes successful successful identify detect miller miller online contained interested interested strategies strategies strategies sci vary modular backward backward providing observable observable automatically automatically received received consisted operating operating operating operating operating jacobs jacobs jacobs jacobs jacobs jacobs deal modelling modelling modelling law law diego exhibit exhibit exhibit difficulty updating rapidly respond ideal ideal ideal ideal ideal ideal ideal dependencies decisions maximizing affect removed removed closest changed algo explored switching switching switching switching epoch epoch plant plant plant plant plant plant plant plant piecewise piecewise derivation track nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan independence tractable lies drive straight implementing sys sys producing producing incorporate controls controls controls controls describing toronto preceding integrating requiring greatly behaviors behaviors behaviors behaviors frequently incorrect variant switch gains controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers ture ture proven eventually softmax softmax instantaneous identifying appearance appearance investigation rithm linearity linearity controlling controlling controlling tem establish extending fails fails adequate performances interference scheduling scheduling scheduling originally competing jolla partitioned jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump designing designing tures tures receiving switches switches dramatically ure ence ple revealed employs failed recurrence recurrence 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#@Cacciatore_T,Nowlan_S,
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#*network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural data data data data data data data function function figure figure figure figure figure figure figure time time time time time time time time time time set set set set set networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system system system error error error error error error error error error results results information information information information information problem problem problem problem problem models models models models performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based based based based based space space linear case order shown shown shown shown systems systems recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method pattern pattern pattern point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point single processing processing control control control large rate optimal form shows shows shows shows shows shows visual paper paper feature work fig fig fig fig fig fig fig fig step step step step points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points points features process process process process process level trained memory representation representation representation representation representation representation representation show show show show show show equation equation rule speech speech speech speech speech speech speech speech speech real approximation theory theory theory theory theory theory theory theory theory theory theory theory experiments experiments result result result result result threshold threshold threshold threshold threshold solution solution research independent independent found found found found found sequence target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant estimate left present present temporal object object motion motion motion maximum maximum maximum position position position nonlinear nonlinear continuous continuous sample abstract applied back find computational computational computational computational computational computational computational computational computational references procedure procedure procedure procedure important important important important propagation context introduction hand hand hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation dynamic generated generated generated generated generated generated generated generated generated generated generated generated generated generated change change change change change change change change change change change change change change spatial lower measure part previous previous previous required good good good long long conditions represent proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed forward forward forward forward forward minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum human human human human human human human human human human computed mapping mapping optimization optimization optimization optimization made made natural natural applications knowledge represented compared desired compute location location determined related related constraints constraints constraints connected connected connected motor motor motor motor motor brain equal steps morgan version advances joint joint joint represents difficult difficult final final final final final final final considered equivalent experiment curves estimates trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san top top determine determine choice estimated estimated estimated estimated estimated estimated estimated basic condition criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion velocity velocity velocity velocity velocity velocity velocity lines lines lines finally finally selected selected depends sampling constraint constraint measured group group group group denote transformation close inverse inverse inverse inverse finding finding finding implemented assumed assumed generate generate eds journal journal journal square square square square square square kaufmann objective combination character character character character character character character character character character character character character character character character character character character character character character character segmentation segmentation consistent principle principle principle principle principle principle principle principle principle principle principle representing numbers normalized normalized idea minimize minimize produced produced added denotes movement movement movement movement movement movement movement movement movement movement movement movement movement movement subject identical side side quadratic previously module module module module module module module module module module correspond studies address positions positions positions arm arm arm arm arm arm arm horizontal studied extended derivative move move white white boundary boundary generally hardware hardware starting starting starting starting greater trajectories trajectories trajectories trajectories trajectories trajectories trajectories segment central clear mateo suggest propose propose propose propose propose propose hard hard demonstrated solid minimizing start start start start movements movements movements movements movements min min min decrease targets characters characters characters characters groups acoustic acoustic acoustic acoustic areas index perception vertical vertical vertical vertical mathematical mathematical infinite infinite infinite angle angle angle unique unique unique unique minimization minimization minimization minimization minimization minimization minimization extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extracted extracted extracted extracted extracted extracted extracted extracted expressed formation formation formation formation formation formation formation formation formation formation formation formation formation formation formation formation formation formation formation phoneme phoneme phoneme phoneme phoneme centers static approximated approximated completely suggested sec generation generation symbol symbol symbol assigned assigned assigned assigned assigned classified template handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten combinations priori assignment illustrated candidate candidate black planning planning reason regular compression compression identified identified identified identified letter society computationally literature comparing summary repeated strongly link neuroscience timing timing timing timing duration write relaxation relaxation relaxation ill ill ill reach reach extend cowan command command transformed production production production essential difficulty put humans hanson integral oscillator oscillator examine biol biol biol biol possibility stream oscillation oscillation cognition cognition examined circles plausible spline psychology nervous generates explain finds stop agreement agreement agreement publishers smoothness waveform satisfied producing located located laboratories recognized circle circle qualitative fourth questions profile profile spoken fed experimentally quantitative quantitative posed posed posed incorporated biologically passes synthesis reaches extracting extracting phonemes phonemes phonemes acoustics segmented sentence realized realized realized lab cybern cybern cybern generator optimality japan japan perfectly perfectly tem reaching reaching reaching reaching reaching reaching reaching attractive determination determination handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato preparation lip edelman edelman iteratively iteratively bad bad bad accounts thomas candidates reproduce late assigns assigning crossing corporation listed kinematics basically opposed torque torque torque torque torque torque torque torque torque torque torque torque torque torque torque pointed reports acceleration acceleration acceleration possibilities eric cns articulator articulator mathematically argued confirmed confirmed flash flash flash flash flash flash flash flash sam sam articulatory ation atr coordination gestures resolve cursive cursive cursive cursive cursive cursive cursive cursive cursive cursive cursive cursive cursive hoc kinematic tip spectrogram compensation concerns concerns acoustical physiologically extracts extracts inferring ray raises strokes strokes america reproduced cho firm firm firm firm firm articulation articulation uno uno suzuki suzuki ira completeness repeating repeating levy schema schema sat sat activating tongue tongue mussa mussa mussa imposing inertia ivaldi ivaldi ivaldi gun parentheses bateson bateson bateson bateson bateson bateson kyoto hogan hogan hogan hogan numerals hochberg revised soraku jaw seika actuators steel actuator actuator lly compar overlaid locus jerk jerk jerk finished ovi hikaridai cup tangential morasso morasso morasso snap phonetics mitsuo ned ition procedural intensively ilu preassigned 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data data data function function function function function figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number system system system system error error state results results results results results results results units units units units units units units information information information information information information performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based space weights weights linear linear linear linear layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown systems values values values values probability probability probability parameters noise functions unit unit recognition recognition recognition recognition recognition recognition method method method method pattern pattern pattern pattern pattern point point point point point point processing large local local neuron rate test test test test test test test test test test test patterns patterns analysis analysis form shows paper paper examples small small size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work task methods methods fig step step points points points points points field field features features features features features features features features features features features features features features classification classification process level trained random random memory similar similar representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture fixed line vectors vectors vectors vectors vectors vectors vectors vectors general generalization speech parameter real real obtained note experiments experiments dimensional dimensional result university university university threshold threshold research research independent independent found found found found found found target constant table table estimate estimate estimate standard standard computer computer distance distance distance distance direction direction direction direction present low sets sets range range learn position position position position position outputs outputs outputs outputs abstract find density density density density density references component introduction effect effect dynamic dynamic dynamic variance variance tion tion tion difference difference difference variable spatial spatial assume lower lower rules signals chosen chosen chosen chosen higher higher part cases represent represent make make make make make proposed length correct total total simulation computed called means means dimension dimension made made made made study study original artificial specific samples represented represented desired receptive receptive receptive receptive provide proc experimental approaches comparison larger contrast fields fields fields fields report report report report department loss version consists consists consists consists represents connectionist difficult layers delay delay delay delay delay delay delay delay graph equivalent hinton hinton estimates design trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory requires significant world world speed speed speed validation validation validation con developed developed velocity provided finally backpropagation iteration sampling constraint constraint measured normal normal normal technical technical technical group tested tested corresponds complete surface amount assumed shape shape eds eds easily easily makes noisy fit fit typically pairs pairs pairs pairs pairs pairs pairs needed needed technology testing testing testing character character segmentation matching representing making stored stored stored stored stored normalized normalized run description architectures improved improved improved directions resolution resolution resolution resolution pair robust separate takes typical typical similarity movement reported reported identical identical identical identical identical pixels subset interest dimensions compare previously calculated calculated calculated achieve modified improvement improvement storage storage lead lead invariant occur trial deviation deviation deviation greater trajectories trajectories trajectories trajectories trajectories conclusions tangent tangent measures accurate numerical designed constrained hard hard variety iii scene scene identification acknowledgements written describes describes dept coordinates coordinates coordinates averaging averaging averaging averaging remaining angle angle angle develop john john letters extracted independently squares evaluated open updated sizes completely similarly discrimination past sign sign sign sign sign normalization add closed interpolation recorded handwritten handwritten box box bell bell bell bell bell automatic variations absolute simplicity simplicity regular compression aspects closely successful detect detect build comparing comparing essentially essentially ten capture capture summary summary cun cun cun cun heuristic success moore sin sin sin sin sin sin strategies device device satisfy write denker denker leading attempt consisted consisted extract extract extract carried carried carried american american wiley collection collection collection investigate varied varied helpful reducing project project project project investigated terminal int scaled authors reliable structured func statistically removed neu act circles circles measurement opposite equally recognizer multivariate consist generates detected detected extent devices percentage percentage percentage cos cos cos cos cos cos convolution slope slope coded majority majority inside closer closer easier producing producing preprocessing preprocessing preprocessing directional laboratories laboratories laboratories laboratories scientific members toronto res lowest mellon sun sun people people people people people people people people people people people people people people people evaluating carnegie collected collected cmu simulate effort effort effort effort effort remove remove treated frequently dots dots compares requirement requirement requirement requirement calculating passes passes passes passes passes passes passes passes passes passes measuring pittsburgh ture ture differs aim aim aim aim incorporating incorporating prevent curvature curvature curvature gave simulator chose comments redundancy credit credit credit consistently consistently consistently person person person person person person person redundant writing tation signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature signature eliminate lecun lecun lecun lecun air air minutes accepted accepted accepted handwriting handwriting hope removing removing removing ral north effectiveness guide carry days mouse entry displayed lang lang demonstration sim captured originally elastic surprisingly eng verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification canada proximity card card card sons hart hart pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen pen baldi baldi insensitive dividing mind pressure liu liu liu leaving converted unable corporation sine sine pointing covering guyon guyon guyon guyon guyon guyon guyon guyon guyon convolutional asked magnetic tween perturbed boser comparative copy copy copy copy reports acceleration acceleration acceleration acceleration big breaking rhythm workstation workstation transparent verified henderson ibm chauvin chauvin duda duda learnt signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures signatures labs life hubbard writer rejected rejected rejected rejected rejected cosine cosine cosine cosine cosine cosine interactive names harder cartesian preserve sta elsevier commercial compu signs examination worked continued agrees european telephone spacing puts resampling proportions returned holmdel subtracting normalize beneficial att screen screen strokes strokes strokes strokes america company positional signed signed signed signed signed signed signed signed signed thresh gathered ically surprise penalizes capturing monitored subnetworks sparc sparc sparc crg miss touch italy compress package collect yann differed encouragement wanted touching bytes bytes bytes bytes bytes bytes bytes genuine genuine genuine genuine genuine genuine genuine genuine genuine genuine genuine 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network model neural neural neural neural neural neural neural neural neural neural neural input input input data data data figure figure figure figure figure figure figure time time time set set set set set set set set set set set set networks networks networks training algorithm output output output output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system system information information information information information information problem problem problem models performance performance based based based based weights weights weights weights linear layer layer layer layer layer layer layer layer case shown shown shown systems systems systems systems probability probability parameters parameters noise weight weight recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach pattern pattern image image image image image image image image image image image image image image processing large large large large large local local neuron neuron neuron test test test test test test test analysis shows simple simple simple simple paper paper paper paper size size size size size feature feature feature feature feature feature feature work work task step step step field field features features features features features features features features features features level level level level trained trained trained trained trained trained high high high high response architecture architecture architecture architecture show show line rule images images images images images images images images images images general general real real average note activity computation computation found found standard computer left map map low low low machine machine machine object object object object object object object object object object object object object object object sets range range learn position outputs outputs abstract abstract abstract abstract abstract abstract applied find find find find find find computational likelihood references ieee introduction complex hand effect generated generated parallel cost cost tion tion complexity spatial lower lower rules rules rules rules prior prior prior part center previous bound cases required required required represent chip length correct correct probabilities scale scale scale scale scale scale classes tasks total regions mapping factor knowledge knowledge filter filter negative original specific specific cross receptive compute objects objects objects proc proc proc location location location location location location location location location location perform perform perform perform steps steps contrast fields train train implementation consists code code code code code advances represents difficult difficult final final final final layers addition maps maps maps maps maps maps domain domain additional san top top top stimuli conference conference conference upper requires requires statistics free speed speed vision basic validation validation validation produce lines lines lines lines lines provided backpropagation backpropagation biological discussion tested complete complete finding finding finding finding amount amount amount amount amount amount implemented shape shape shape shape shape shape shape generate pixel pixel pixel pixel pixel easily degree typically pairs technology technology technology block block block block block block block block block block block block block block block block block block block block block block block block block block block block block testing significantly character character character character character segmentation segmentation segmentation segmentation segmentation mechanism bottom combined architectures resolution takes typical relevant dimensions dimensions highly previously conventional conventional module tuning yields correspond trans address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address background background entire entire horizontal parts intensity occur suggests wide width white hardware hardware pass reduce conclusions accurate designed performs suggest turn variety min iii characters characters characters explicit construct construct produces optical optical describes confidence confidence remaining easy text text text text text develop integrated frequencies shift blocks blocks blocks blocks blocks blocks blocks john extracted correlated organizing centered completely allowed allowed past reasonable reasonable epochs reduces combining purpose classified handwritten box box box box box figures figures figures figures color recognize recognize specifically candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate black absolute absolute middle identified effectively detect detect detect detect build invariance invariance identity compact compact notice notice notice quickly contained success built list list vary vary vary vary modular denker hypotheses hypotheses hypotheses overlapping operating deal deal software decreasing unlike requirements varied optimized combine authors stream examined aspect portion great great advanced advanced advanced ment convolution reasons purposes sys shared preprocessing preprocessing preprocessing preprocessing preprocessing day located acknowledgement demonstrates cybernetics recognizing raw considerably considerably evaluating substantially fed remove maxima maxima maxima howard enables sophisticated age windows windows windows irrelevant lot sort generator generator generator martin martin ratios jth addresses printed printed printed printed printed grey lecun lecun lecun platt platt platt platt platt platt platt mail mail mail mail mail mail mail mail mail mail mail mail contract serves fail corner corner corner corner hours service sides enhance histograms jackel jackel candidates candidates candidates candidates candidates candidates candidates candidates candidates candidates candidates candidates recog smoothed cpu ignore boxes dramatically truncated ter piece piece piece piece convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional nition pieces pieces pieces pieces pieces pieces pieces boser boser ideally tight henderson publication tems ocr ocr hubbard bounding bounding bounding bounding bounding bounding convert convert challenging challenging rectangle zip zip zip funded preserve thousands wider sorting sorting corners corners corners corners recogni justification impractical trainable hundreds envelope hypothesized hypothesized anna detects archi enhances enhances destination destination destination ranged delivery delivery delivery tens neocognitron jose postal postal postal postal postal applica custom unaffected tightly preprocessed preprocessed preprocessed omit locating locating preprocessor preprocessor preprocessor preprocessor advice fukushima fukushima encourage subsampled usps usps usps usps usps usps usps tecture scratch draws suppresses subsample pad stretch equipment equipment equipment charac discard blobs ralph confused extraneous assist wolf wolf wolf wolf wolf unmodified ink ickinger ickinger synaptics duplicate duplicate ffi ffi ffi ffi delivers 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#@Platt_J,Wolf_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training 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based based based based space weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector order order shown shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems parameters unit unit unit unit recognition recognition method method point point image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single single large large large large large test test test test test test test test test test test test test test test test test test analysis analysis inputs inputs simple simple gaussian gaussian gaussian paper paper paper paper small size size size feature task task task methods points points features features features current current current trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure structure random random random random random high response similar similar similar similar similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show section section section section section section section section section line line line line line line line line images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images speech average average average average average average average experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments university university computation research research research found found found target target initial initial constant table table table table table table table table standard standard standard computer computer computer computer computer distance connections connections science science science science prediction prediction prediction left left left direction direction presented presented present present activation low machine machine sets sets sets sets sets sets sets sets sets sets sets sets sets sets motion motion position position position position position position position position position position position position position position position position position position outputs outputs outputs continuous sample sample sample abstract back back references due due procedure procedure procedure important propagation propagation context introduction estimation behavior search tion tion tion tion tion difference center center previous previous required required required required multiple techniques techniques region region errors errors errors forward forward ing ing total simulation human human human respect respect respect performed performed performed performed performed times regions potential potential made made applications study artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial relative relative relative relative samples provide provide location location location location location location perform eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined determined goal related connected connected gain steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger train train train train train source selection selection selection morgan proceedings report department implementation individual represents represents represents represents represents final delay addition addition addition addition graph computing experiment experiment environment additional estimates limit detection conference determine determine efficient requires speed vision vision basic increase produce developed robot path path path path path path actual finally evidence achieved achieved achieved measured tested tested tested tested tested tested tested tested limited assumption assumption corresponds predictions common supported supported require require require require eds face ability ability ability degree makes noisy kaufmann pairs pairs pairs pairs needed needed needed reduced reduced account fully fully fully testing testing testing testing testing testing testing testing testing testing testing testing testing edge head head head head head head head head head head head head head head head head special special special trials empirical representing numbers making window window window window stored international frame frame combined combined light light light light light light light light predict architectures architectures architectures architectures architectures architectures architectures architectures improved improved improved resolution resolution resolution separate separate separate takes typical reported reported moving moving moving period subject subject subject subject pixels pixels sejnowski interest varying compare previously approximately approximately approximately approximately approximately approximately subjects calculated works axis axis axis axis axis axis studies studies achieve achieve evaluation positions positions positions positions positions increased grant exists horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal parts predicted predicted feed move hardware pass runs greater greater reduce conclusions conclusions accurate accurate accurate accurate accurate retina retina retina peak peak performs performs encoding user user user user user user user user user user user user user user user user user user movements movements manner manner areas pro perception ways factors primary describes ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann vertical vertical vertical vertical vertical vertical vertical vertical vertical sensitivity coordinates coordinates coordinates remaining remaining slightly slightly interaction interaction decreases national national extracted extracted independently expressed reconstruction stationary stationary viewed updated lee forms static sizes sizes sizes allowed diagram additive performing performing epochs epochs epochs epochs epochs epochs epochs epochs epochs epochs epochs sec fitting tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking generation construction foundation foundation views degrees degrees degrees degrees degrees coordinate coordinate tests successfully selecting selecting divided divided divided divided divided divided divided successful comparing comparing traditional traditional traditional road road repeated contained allowing showing interpreted device device generalize generalize generalize modular giles automatically attempt moves moves policies acknowledgments camera camera camera camera camera camera camera camera cowan remain unlike unlike collection detail detail detail hanson accurately accurately accurately issues reducing school school rest authors authors office matched attributes attributes examined waibel waibel reading predicting predicting created changed eyes ensure noted noted assumes explored explored academic mixed mixed mixed attempts attempts devices mentioned mentioned mentioned mentioned ment ment track expensive independence correction tool tool handle reasons processed tive sys organized located located located potentially circle arises recording mellon mellon sun fourth fourth carnegie carnegie collected collected collected collected collected collected collected collected collected collected collected cmu cmu cmu dark offset offset offset offset offset offset offset offset autonomous autonomous autonomous autonomous effort employ slower reliability maintain pittsburgh pittsburgh ture cal extensions gave replace display shaped windows wesley picture benefit addison appearance tation restrict mobile tem naval minutes minutes intelligent analyzing analyzing analyzing operates shifts filled performances performances document ranging mouse mouse respective decide expanded moved moved moved moved moved moved washington den searching sim creating gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker tracker contact observer designing consonant valuable valuable balancing automated acknowledge onr yielded visually visually visually visually visually visually users users users users users vec fellowship kluwer session session benefits nelson restrictions tor letting workstation examining attempted attempted cessing baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja approxi graduate guidance pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau terrence concentrate paired wise surrounding setup setup distinguished modality modality elsevier corrections experi infinitely worked develops sessions sessions sessions gratefully ers hypothesized hypothesized lated aid aid aid exper hid finer phonemic horizontally horizontally horizontally horizontally seattle subtracting architec manually manually screen screen screen screen screen screen screen digitized tracks cur implied vertically vertically vertically reflection reflection reflection reflection reflection reflection creation gathered gathered gathered gathered gathered gathered gathered ous dean deciding deciding freely publishing 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#@Baluja_S,Pomerleau_D,
#t7
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#*learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural data data data data data data data function figure figure figure figure set networks networks networks networks networks networks training training training training training training training training training training number number number number system state state results results results results units information information problem problem problem problem problem models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based order order order shown shown systems values probability parameters parameters parameters parameters parameters parameters weight distribution distribution recognition method method approach approach pattern pattern pattern pattern point processing large local test test test test patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis signal algorithms algorithms algorithms algorithms simple paper examples small feature net task methods methods methods fig fig fig fig fig step classification process process process level level level current current trained trained trained trained trained trained cell structure structure structure structure problems problems random random random random random high high similar similar similar architecture show show line speech real real average average average states states states states states states gradient gradient gradient obtained note note experiments experiments experiments result result result university university university university university computation computation research research log log found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial table standard standard standard standard standard computer terms terms science prediction left left presented present present phase phase low machine machine press press learn learn learn learn position position position position continuous continuous abstract applied computational likelihood likelihood references references ieee positive procedure procedure context introduction complex statistical statistical statistical dynamic dynamic search variable variable rules signals signals signals prior representations learned higher center center previous bound type required multiple good markov markov markov markov markov markov markov markov markov markov markov fact fact techniques techniques region region region region length length length length length length length length length length length length probabilities scale classes ing total human human human human human human human human human human human human human human human called called times regions regions regions regions regions regions regions regions regions regions regions regions regions means factor applications applications applications applications negative negative represented true compared application application application experimental related related related discrete accuracy accuracy connection descent descent descent modeling modeling modeling modeling modeling modeling morgan proceedings proceedings report institute institute institute institute department consists consists internal code code code code advances addition addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences experiment directly directly additional additional solutions san effects detection detection conference requires significant significant statistics free free pages con coding coding coding coding coding coding lines 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simultaneous wesley sharing lot sort addison interface assign systematic promising difficulties city los operates ral implications implications krogh krogh krogh krogh krogh krogh krogh krogh krogh krogh krogh krogh responsible grammars composition composition reliably reliably weakly lengths den belongs interconnections elastic francisco surprisingly reveals rich proteins proteins proteins proximity parse reverse subsequently santa santa harris baldi baldi baldi baldi baldi baldi baldi baldi baldi baldi baldi vari emission emission dna dna dna dna dna dna dna dna dna dna dna parsing parsing parsing parsing parsing parsing parsing numerous removal encouraging ease ideally hundred constitutes constitutes molecular molecular molecular molecular gene gene gene chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin chauvin genes genes genes genes genes genes genes genes genes genes genes genes genes searches confirmed investigating harder tied tied tied tied tied tied amino electronics knudsen knudsen lapedes molecules tract remark species algorithmic reversed twenty vii insufficient jet junctions junctions junctions thousand families families locate hid integrates optima striking striking propulsion splice splice splice splice splice splice splice splice splice splice artifact acid acid denmark denmark denmark denmark denmark denmark evolutionary evolutionary crl presently cruz acids acids acids tra trend tory rec insert converts intrinsically farber contributing checked terminate sixth insertions insertions delete deformations entered sequencing ucsc wired consensus consensus consensus consensus seemingly organisms nent lacking converting comprise contiguous snyder snyder pierre mature han deletions deletions ons mart genome genome genome genome genome genome genome periments fifty backbone conserved peri shapiro tying nucleotides nucleotides nucleotides nucleotides nucleotides nucleotides nucleotides nucleotides nucleotides nucleotides nucleotides 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#@Baldi_P,Brunak_S,Chauvin_Y,Englebrecht_J,Krogh_A,
#t7
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#*learning model model model neural neural neural neural neural input input input data data function function function function function figure figure figure set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm output system system system system system system system system system system system system system error results results results results results information information information information information information information models models models performance performance performance performance performance performance performance based based based based based layer layer vector vector vector vector vector vector shown shown systems systems systems systems systems systems systems systems values parameters noise noise functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method pattern pattern pattern pattern pattern point image image image image image image image image image image image image image image image image image image image image image processing processing processing control control large large large local local local local local local local local local local local local rate rate rate rate rate rate rate rate rate test test test test analysis optimal form shows shows signal signal gaussian gaussian size size feature feature feature feature feature feature feature feature feature feature feature feature work task task task task fig cells cells cells cells cells cells cells cells cells points points features features features features features features classification classification classification classification classification classification classification level level cell structure high response similar architecture architecture architecture line vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images images parameter average average average theory term experiments experiments experiments experiments experiments experiments dimensional threshold threshold computation research defined constant constant table table table table standard standard computer computer terms connections science left left low low machine object object object object object object object object object object object object object maximum range range range components abstract analog analog analog analog analog analog references component due due due ieee ieee ieee ieee ieee ieee positive positive positive positive positive procedure important adaptive adaptive adaptive decision decision introduction behavior effect effect effect dynamic dynamic dynamic dynamic cost cost cost cost search difference measure measure measure measure measure prior higher part center center center center cortex cortex conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions distributed expected expected expected expected expected expected chip chip chip chip chip chip chip correlation length correct correct scale respect multi eq eq factor potential potential potential natural feedback global applications study knowledge filter filter filter artificial artificial represented represented receptive receptive provide provide compute objects rates rates rates rates proc proc perform determined gain gain gain brain power power power voltage comparison larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields fields descent proceedings report report version version synapses synapses technique internal represents responses exp exp exp layers graph graph graph graph graph graph graph graph computing experiment experiment experiment experiment environment environment design limit limit stage effects significant significant statistics free vision vision vision vision vision vision pages pages pages increase con weighted developed levels levels levels criterion criterion criterion provided provided selected inhibitory inhibitory depends biological biological biological achieved increases transformation fast limited assumption corresponds excitatory excitatory amount nearest shape generate generate supported face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel pixel pixel ability ability makes sensory including simulated reduced account unknown unknown unknown unknown unknown coefficients technology technology technology technology ratio ratio character york edge edge matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform database database database database database database max inhibition stored combined minimize choose description description light light light denotes membrane membrane improved improve improve directions directions resolution resolution resolution resolution resolution advantage robust separate separate typical similarity similarity similarity similarity similarity reported lateral strategy strategy strategy identical side side side side pixels pixels hierarchical sense sufficient highly compare conventional conventional conventional conventional conventional approximately calculated yields match match achieve trans trans background background grid grid organization organization sensitive sensitive sensitive sensitive sensitive sensitive increased increased increased horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal parts intensity invariant invariant invariant invariant invariant invariant invariant invariant deviation deviation rotation locally column column setting hardware demonstrate demonstrate runs runs place minimal conclusions interactions retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina designed designed designed designed weak taking strong intelligence labeled minimizing iii connectivity minima program construct edges edges edges edges edges produces produces index index perception laboratory laboratory laboratory changing changing changing changing metric metric sensitivity sensitivity sensitivity sensitivity explicitly explicitly simultaneously simultaneously electrical electrical angle scales interaction integrated versus select yield national national communication viewed interpretation influence influence influence influence detailed controlled labels labels centered centered sizes suggested translation discrimination spectrum performing convex reduces reduces neighborhood false false false false false generation initially filtering filtering filtering visible classified classified faces faces faces faces faces faces faces transactions degrees coupling coupling expect template template handwritten box kernels kernels silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon retinal retinal automatic maximize coupled coupled coupled variations variations variations neighbors discussions compression encoded poggio poggio identify identify invariance situation fine graphs graphs repeated strongly strongly strongly strongly heuristic link link interpreted conductance symmetry classify sci sci simplified paradigm surround surround surround wavelet wavelet providing nips minimizes wave cmos correspondence correspondence chips chips chips chips extract extract deal camera camera camera camera camera camera camera camera camera camera camera camera camera camera employed explore american poor poor mead mead mead mead mead mead environments environments detail matches matches matches fashion fashion fashion detectors maximizing affect encode matched matched saliency naturally plausible facial facial recognizer recognizer recognizer adjusted adjusted prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype versions der der der der der der separated expressions expressions devices devices devices great cos costs costs costs costs costs sensors sensors orientations orientations convolution defining adjacent adjacent capabilities caused perspective perspective perspective perspective perspective straight purposes purposes sys preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing filtered filtered filtered filtered filtered consequence scientific acknowledgement computers demonstrates demonstrates recognizing outer robustness percent percent percent percent percent percent substantially substantially dark dark generic generic parameterized autonomous autonomous adjustable reliability templates templates prototypes switch reaches gen serve qualitatively suited adjust adjust adjust adjust adjust adjust enables germany germany germany inherent yuille yuille deviations wesley extreme distortion distortion distortion distortion distortion distortion distortion person person person spectra benefit addison fabricated fabricated martin tem receptors receptors receptors receptors receptors receptors receptors saturation wrong significance significance significance significance promising attractive primitive intelligent settings illumination illumination illumination illumination illumination optimally planar reliably published weakly document recovered respective pat von von von von von von moved washington vertices vertices vertices vertices evident enhance accounts originally lawrence lawrence interconnections elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic viewing viewing cerebral eng ahead refers vertex vertex vertex vertex vertex horizon steepest acknowledge assigns mechanical ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd dramatically neurophysiology numerous accept shunting ram removal rejection revealed employs pentland pentland comparative comparative causing malsburg malsburg malsburg malsburg malsburg malsburg german imagine assess rectangular summarizes preserved robots robots magnitudes ijcnn ijcnn interacting challenging altered switched ultimately cosine multiscale ambiguous buhmann buhmann buhmann buhmann buhmann buhmann buhmann buhmann buhmann cation setup setup attached attached figs figs figs mimic tune reciprocal reciprocal removes emphasis lighting lighting lighting lighting lighting lighting lighting lighting lighting lighting lighting lighting lighting lighting lighting stimulating distortions distortions distortions distortions distortions distortions distortions distortions distortions institut institut institut identifies attributed quantify correspondences mahowald mahowald spacing establishes pictures burr burr andreou andreou luminance offsets cones cones vertebrate bandpass enhances enhances drastically planck informatik mosis vicinity correlates format deformation bonn mach penalizes spec eigenfaces lights eeckman eeckman eeckman eeckman facilitates lange lange rotate carver elaborate tal preprocessed iris blurred bright enhancing pursued excluding registration concurrently retinas retinas intel biophys electrically digitally fulfilled deformed boahen boahen boahen imagery ministry exclude explores deformable cog cog frank cameras expands classifi critically faithful particu equipped hurt vehicles turk turk leak hierarchically checking ubiquitous ubiquitous pleasure persons persons persons persons persons antagonistic joachim registered illuminated illuminated illuminated iip inevitable livermore livermore livermore organs gaining bilateral surveillance lades lades lades lades lades lades lades lades lades drastic drastic discrepancies ventional adaptivity adaptivity seminal larly conv drawings christoph brunelli brunelli friedrich promises neuroinformatik chem uncontrolled innovative compromises neuroanatomy erates fluence unclassified reli smoothes smoothes flit ruhr collaborators deforming 
#@Buhmann_J,Eeckman_F,Lades_M,
#t7
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#*network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set networks networks networks networks networks networks networks training training training training training output output output output number system system system system system system system system error error error error error error error error state state results results information problem problem problem problem problem hidden hidden performance performance based based based based based based based based based based based based based space space space space space space linear linear layer layer case shown shown shown systems systems values values recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method approach approach approach approach approach pattern pattern pattern pattern pattern point point processing large rate rate rate rate test test class class class class matrix matrix matrix matrix matrix inputs form form signal paper paper paper paper paper examples examples size size size size size size size size size size size size size size feature feature work step points points points points points features features features features classification process process process process process level current trained trained trained structure problems problems random random high similar similar architecture architecture architecture architecture architecture show line line line line line line line line line line line line line line line general real average note experiments experiments experiments experiments experiments result university university independent defined found found found found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial computer computer distance science presented presented map low sets sets sets sets learn sample sample abstract abstract abstract back references due due important decision propagation context context introduction hand hand hand dynamic generated generated generated variance search search search search search search search search search search search search search search search tion tion variable variable spatial classifier classifier classifier word word word word word word word word word word word word word word word word word word word word word learned chosen higher higher previous multiple represent represent represent expected make techniques length length correct correct correct forward forward forward forward forward forward forward minimum multi performed performed performed times mapping mapping made natural natural filter original original original original vol vol vol vol vol vol artificial artificial samples samples samples samples samples samples represented represented cross cross receptive receptive perform perform determined constraints constraints constraints connected connected steps fields fields fields fields dependent dependent morgan proceedings words words words words words words words words words words words words department consists consists consists consists consists consists code code code code code individual individual individual individual advances represents sequences maps maps computing domain experiment design san top stage bit bit conference significant speed vision levels velocity velocity velocity velocity lines lines lines product actual provided provided finally constraint achieved tested tested transformation corresponds complete effective supported eds journal end ability ability development development kaufmann block block block character character increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation uniform database database database principal principal window international normalized bottom produced run denotes directions directions recent robust separate include side hierarchical varying approximately correspond differential evaluation evaluation positions grant occur extended alternative alternative alternative feed feed column column column column pass demonstrate row row segment central designed designed performs performs performs learns learns mateo drawn demonstrated intelligence intelligence variety variety exist produces written written perception generating describes vertical distinct distinct coordinates coordinates coordinates coordinates coordinates coordinates remaining remaining easy angle angle angle applying applying events events letters letters letters letters letters letters letters letters letters letters letters letters letters letters national stages overlap overlap overlap codes evaluate organizing organizing organizing sizes sizes reasonable reasonable performing epochs boundaries boundaries boundaries boundaries interpolation faces expect box recognize recognize recognize recognize recognize recognize recognize illustrated illustrated illustrated illustrated illustrated candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate absolute major regular identified identified letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter efficiency suitable encoded divided included successful identify identify identify tdnn score score score score summary repeated cun split classify sin sin follow device list sampled dot backward backward giles delayed delayed delayed delayed delayed delayed denker automatically illustrates illustrates satisfies cowan presents presents employed employed poor varied put humans detail hanson accurately graphical terminal terminal stream stream stream stream stream stream stream variability variability variability encode removed waibel waibel waibel closest reading reading reading recognizer recognizer recognizer improving mixed isolated cos cos developing improves processed straight shared preprocessing preprocessing preprocessing style style directional immediately arise mation acknowledgement recognized recognized recognized recognized recognized describing beginning english english english english english lowest lowest computers recognizing recognizing recognizing recognizing recognizing alignment raw requiring fourth greatly collected flexible leave poorly remove prototypes extensions extensions enables hamming kinds segmented progress pyramid pyramid gap writing writing writing writing writing writing interface appropriately angular angular repre printed printed ments significance handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting biased scoring scoring scoring methodology disjoint disjoint effectiveness spurious contexts introduces programs edelman edelman edelman ambiguity equals pat expanded lang lang lang candidates candidates candidates candidates candidates candidates candidates dif thin smoothed verification verification verification verification passing motions correcting correcting correcting inductive partitioned dietterich dietterich dietterich pen pen pen pen pen pen pen pen pen pen pen pen pen outlined linked suffix converted guyon guyon guyon guyon exhaustive exhaustive maximized gaps encodes legal legal legal legal legal diverse poses classifications classifications classifications regularity acceleration descriptions descriptions descriptions demon remainder henderson henderson gained stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke stroke thick impose maintained hubbard searches writer writer writer writer writer writer picked picked ullman proach unconstrained employing employing employing employing employing sized dictionary admissible prevents normalizing recognizers challenge styles styles cursive cursive cursive cursive cursive cursive cursive cursive cursive cursive cursive cursive ping ferent eliminates correctness strokes strokes strokes strokes strokes strokes strokes strokes strokes strokes strokes strokes strokes strokes cur tations terminates files sorted tern spanning spanning initiated meaningless preprocessed preprocessor shear shear touch touch translational ninth writers writers resampled resampled resampled cent ramp confident prefix prefix prefix prefix explores faculty segmentations segmentations fragment fragment fragment fragment fragment fragment fragment fragment fragment fragment fragment subsystems transfor lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon multiclass finder subsequence albrecht fragments fragments fragments fragments fragments fragments fragments fragments fragments orderings schenkel schenkel schenkel schenkel strate script script slant bakiri bakiri bakiri necessitates nohl nohl quicker interpreter interpreter interpreter assembled unavoidable morasso morasso morasso morasso nary nicholas utah utah srihari srihari usu segmenta segmen sively digitizing uncommon coor restoring alphabetic advent forma rns conforms 
#@Flann_N,
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#*network neural neural neural neural neural neural neural neural neural neural neural data data data figure figure figure figure figure figure figure figure time time time set algorithm number number system system system system system system system system system system system system system system system system system system system system system system system system state state results results results results results results results results information information information information problem problem problem performance performance based space layer case order order order order order order shown shown shown shown systems values noise noise noise noise noise noise noise noise noise noise noise approach approach point image image image image image image image image image image image image image image image image image image image image image image image image image image image processing processing processing processing control large large large large large large rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis form form form shows signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper examples examples small small small size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net net net net net net net net net net net net net net net net net net net net net net net net net net net task task points points features features features features features features features features features features features process process process process process process level level level level level level problems problems high high high high high high high memory response response response response similar representation representation representation show section section section line line line line line line line line line line line line line line line line line line line line line line line line images images images images images images images images images images images images images images images images images images images images images images real real states states states obtained obtained obtained obtained obtained obtained result result result result result threshold computation computation computation computation computation computation computation computation solution research found found found found found found sequence sequence sequence standard computer computer distance left left direction map map map map map present present present present low machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine maximum range position position components continuous continuous abstract applied applied applied find find find find find find find find density analog references component component component due ieee ieee important introduction action complex hand hand circuit effect generated search complexity complexity classifier classifier classifier lower lower measure chosen part part part part bound bound cases cases type type required required good good good good good binary long conditions represent represent chip chip chip make make fact fact fact techniques techniques correct resulting tasks human performed elements elements factor orientation knowledge obtain original original vol vol true compared compared application provide compute compute compute proc location location location location location location location location location location location location location location location location location eye constraints connected connected connected connected power steps steps accuracy accuracy accuracy accuracy larger nets words words words implementation technique technique technique technique consists internal code code code code code code code code individual kernel kernel kernel represents responses responses difficult final final maps maps maps maps maps maps maps maps maps maps maps maps maps maps framework environment additional additional additional additional top bit bit detection determine determine determine determine determine upper requires requires choice choice world speed speed speed speed weighted clustering clustering clustering clustering developed developed area lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines lines actual provided selected depends depends sampling achieved group group group tested tested fast circuits circuits circuits finding finding finding finding finding finding finding amount common implemented implemented require main end end end end pixel pixel cluster cluster easily makes development noisy noisy noisy noisy noisy including including objective typically typically typically smaller account unknown technology block block block block block block block block block block block block block block block block block block ratio character edge increasing special special special operation representing numbers numbers stored stored stored stored bits bottom bottom magnitude idea combined combined produced produced light light improve improve resolution resolution resolution resolution advantage advantage robust separate typical apply machines pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels recently sufficient conventional works module module solve solve correspond achieve address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address address background evaluation positions horizontal horizontal horizontal parts lead digital digital digital wide wide correctly correctly width width white white boundary hardware hardware hardware hardware hardware hardware half conclusion minimal reduce segment segment segment measures modules modules modules designed clear faster presence presence presence solid solid variety variety variety characters characters characters groups groups edges edges produces produces written written describes tuned tuned tuned vertical segments segments segments segments segments metric simultaneously simultaneously text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text angle angle angle angle angle integrated integrated applying quality quality quality quality quality quality blocks blocks blocks blocks blocks blocks blocks blocks extraction extraction extraction extraction extraction extraction extracted extracted focus depending stages communication communication interpretation interpretation interpretation interpretation interpretation influence sizes discrimination processor processor processor processor processor processor processor processor processor processor processor key slow slow dashed spaces purpose purpose purpose purpose distances string degrees degrees existing handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten box box box box includes includes kernels kernels kernels kernels kernels combinations priori usa usa bell determines automatic candidate black black black black black tests tests texture texture texture texture texture texture major major major reason identified divided divided paths detect tend tend road compact conf conf quickly quickly success split content categories write modular board board board board board board board board board board board board board cmos chips chips chips chips chips processors processors processors received attempt illustrates subsequent extract extract extract decreasing camera poor poor exhibit rapidly respond project detectors detectors detectors detectors detectors detectors detectors detectors detectors int combine reliable reliable proper proper proper coarse reading reading reading reading reading reading changed detector detector detector detector mapped art consist detected mentioned advanced developing distinguish distinguish orientations convolution convolution convolution convolution convolution convolution analyzed analyzed lies handle starts starts reasons inside inside processed straight widely preprocessing preprocessing preprocessing preprocessing style style located laboratories describing describing read read researchers robustness robustness robustness requiring people percent evaluating led dark dark dark lack peter orders marked marked passed passed schematic schematic schematic extracting serve suited suited segmented lot corrupted sensing writing writing writing writing appearance addresses printed printed printed printed printed printed printed printed printed printed printed printed printed printed turned turned difficulties mail city height height height moment transforms analyzing fail guide reliably reliably reliably reliably service service service started heavy introduces introduces irregular irregular decide overview overview captured candidates surprisingly surprisingly layout layout layout layout layout indicator reader reader reader reader reader reader reader reader reader reader reader reader reader reader reader clean clean clean clean clean clean clean properly arrows extensively relies exploiting executed executed executed empty boxes discriminate multiply street geometrical geometrical solves bus gaps gaps pieces obtains spaced big remote eric tight tight tight tight henderson henderson stroke stroke stroke stroke stroke bounding bounding bounding thresholded thresholded considers rejected host drawback zip zip zip zip zip zip zip zip zip alternatives minor sta places dsp dsp dsp intensive intensive handled handled covers covers scanned styles styles differently consuming distortions corners heavily envelope envelope envelope envelope graf graf graf graf graf graf graf industrial cast affecting holmdel thickness executing extracts extracts systematically strokes strokes strokes fastest destination destination destination destination destination destination destination destination totally sending drastically hough bottleneck comer comer format merged cuts platform platform platform united united united analyse analyse postal postal postal postal progresses sparc sparc sparc sparc sparc checked locating heights entered ess ess billion ames vme vme throw boards surrounded surrounded readers reconfigurable throughput throughput throughput blobs skew skew skew skew skew skew ranks operands cleaned accumulates lea convolutions convolutions hans cutting print slant darkness detrimental companies assembled biggest biggest caution skewed facilitating buffering deteriorate srihari crawfords judging drawings drawings smearing smearing lightly mbytes mbytes digest ren stretches recipient sla dozens syste layouts buried 
#@Cosatto_E,Graf_H,
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training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number number number number number number number system system system system system error error error error error error error error error error error error error error error error error error error error error error results results results results results results results results units units units units units units information information information problem problem models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based based based based based based weights linear linear linear layer layer layer layer layer layer layer layer layer case case case case case case vector vector vector vector order order order order systems systems systems systems systems values probability weight weight functions unit unit unit unit unit unit unit distribution distribution approach approach approach approach approach approach pattern point point single processing processing rate test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis class class inputs inputs form simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian paper size size size size size size size size size size net work work points points classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level level structure random high high high high high high high high high similar similar representation representation representation representation architecture section section line vectors generalization real obtained obtained note experiments experiments experiments experiments dimensional result result threshold variables variables variables computation research research research independent independent log found initial initial table table table table table table table table table standard standard terms terms terms terms terms distance distance distance distance distance prediction left presented present phase phase phase phase low low low low low low low sets sets range learn nonlinear outputs continuous sample sample abstract applied likelihood references component component component due ieee ieee ieee ieee ieee ieee positive procedure important important decision complex complex complex complex hand cost cost tion difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier learned learned higher previous type type type type type type type type type type type type type type type type type type required long represent represent represent represent represent represent distributed make techniques techniques techniques correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation errors errors errors errors errors errors forward forward forward forward forward forward forward forward forward minimum minimum minimum minimum resulting resulting resulting classes classes ing ing total total total regression regression performed performed performed called times regions made made natural feedback feedback applications study study study study study study study study study study study original original vol vol vol vol vol vol vol vol samples samples samples samples samples samples samples samples compared compared application cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross provide provide proc proc perform perform perform determined experimental distributions distributions accuracy accuracy accuracy comparison comparison comparison comparison comparison comparison train train nets nets modeling selection selection selection morgan morgan loss version version internal internal internal code code code code individual individual individual advances advances represents connectionist difficult bias addition considered considered considered considered experiment experiment view view stage stage detection detection classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers approximate statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics free increase validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation con con produce produce randomly developed developed developed developed developed area lines lines product actual selected selected achieved measured measured normal arbitrary arbitrary tested assumption complete complete predictions predictions implemented implemented implemented role require main journal square end future future development development development development development development development development development development fit kaufmann kaufmann kaufmann objective needed reduced reduced functional technology testing testing testing special consistent consistent trials empirical empirical empirical principle principle language details pre pre early early early early early frame produced added added predict perceptron perceptron improved improved improved discussed improve typical reported reported practical machines engineering engineering compare compare previously approximately calculated module module module module module module module module module module correspond studies trans trans trans trans trans trans modified modified modified modified modified improvement risk entire constructed constructed constructed constructed constructed constructed studied studied studied scaling deviation feed feed feed feed feed feed feed feed feed touretzky touretzky occurs column half half half half conclusion greater assumptions assumptions reduce operator valued measures measures measures modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules accurate numerical constrained suggest suggest suggest suggest suggest hard reduction reduction reduction cycle cycle cycle cycle cycle cycle characteristics sigmoidal sigmoidal demonstrated decrease relationship relationship program program program program program program program program program base construct written longer estimating mathematical metric metric metric metric metric multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer category category category category category category category category category category category category category linearly dimensionality transformations remaining remaining remaining remaining remaining remaining easy easy text adding adding adding minimization quality implies versus select extracted stages stages stages influence evaluate evaluate evaluate evaluate fraction fraction soft soft soft static static static static static sizes suggested suggested earlier purpose purpose assigned assigned construction construction avoid recorded existing columns columns columns columns selecting identified identified capable capable suitable divided score tend tend orthogonal summary summary refer refer repeated repeated interested interpreted issue classify classify follow categories categories categories categories categories categories categories usual consisted illustrates subsequent software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software software intrinsic tesauro tesauro decreasing parametric transformed transformed exhibit exhibit varied issues issues preliminary preliminary preliminary preliminary discriminant discriminant discriminant discriminant discriminant rest int int fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault reliable proper proper variability workshop understand attributes examined integer prototype prototype algo perceptton perceptton perceptton perceptton perceptton perceptton perceptton explain motivated percentage residual residual residual developing separable growth growth growth growth growth cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade tool tool perspective lin producing incorporate products medical bandwidth raw researchers considerably considerably tional conducted conducted effort effort remove reliability reliability reliability reliability reliability compares maintain release mod characterize ture limiting incorporating asymmetric asymmetric sophisticated unbiased deviations progress extreme extreme room identifying identifying identifying identifying identifying identifying identifying identifying identifying identifying ear investigation investigation rithm resources resources controlling jth imaging ments ranges mail logarithmic check check efficacy resulted resulted methodology belong belong implications constructive heuristics motivation inferior exploring exploring alspector passive programs programs iteratively realization enhance lawrence assembly initialize foundations eng eng eng eng eng eng eng belonging erlbaum projects statement valuable border fahlman fahlman fahlman fahlman fahlman stopped stopped std std std std std std dividing metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics metrics street constitute incorporates misclassification misclassification sig revealed encouraging medium medium constrain intuition deep faults faults faults faults faults faults efforts relate categorization categorization mask constructs constructs represen alternatives sized indication commercial commercial applicability applicability applicability struc experi correlate shallow develops circumstances tail inconsistent identifies routines usefulness measurable transpose sions prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone prone cascaded constraining constraining sian south tations gaus allocating validated addi objectives violate lebiere lebiere lebiere asymmetry manager devel classifica rationale bellcore bellcore nectionist telecommunications readers charac skew categorized normality normality normality discarding discarding iden regres ware ware ware percentages percentages chitecture constrains misclassifications investigates nilsson nilsson sumption oped morristown symp rodriguez rodriguez rodriguez rodriguez gan moidal mor crawford crawford interspersed whitley whitley validating fortran waste releases conform texts sulting ules releasing chapters curious teristics deliberate 
#@Kamnanithi_N,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data function function function function function function function function function function function function function function function function function function function function function function figure figure time time set set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training output output output output output number number system system system system error error error error error error error error results results information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem based based based based based based space linear linear linear linear layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector order shown systems systems values parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit distribution method approach approach approach approach approach approach approach approach point point point point single processing processing processing rate test analysis analysis form form shows shows shows paper paper paper examples work work work work task task fig fig fig points points process process process process problems problems problems problems similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show show show equation section section section section rule rule rule rule vectors vectors general generalization generalization generalization parameter real approximation obtained obtained obtained experiments experiments solution solution research research research defined defined initial standard terms terms node node node node node left left left left left left left left direction presented presented present present phase maximum press learn learn learn components components abstract applied applied applied applied find find convergence convergence convergence convergence convergence convergence convergence references due due positive positive procedure procedure procedure important important decision decision context context introduction hand hand behavior parallel parallel cost tion change difference difference difference rules rules measure learned learned learned learned learned chosen center previous previous previous type type type type required good good good represent distributed make resulting resulting ing ing ing human multi multi multi multi multi called called called mapping factor factor potential potential potential potential potential made made applications applications study study knowledge knowledge obtain obtain obtain negative negative artificial artificial relative specific specific represented compared desired provide equal mit comparison comparison comparison comparison comparison comparison comparison update update morgan morgan proceedings proceedings consists consists consists consists advances advances represents connectionist delay scheme scheme graph graph ai cambridge equivalent equivalent view view view limit san san conference conference capacity efficient requires choice choice choice choice choice choice choice choice choice choice significant give coding coding criterion types types actual finally finally finally backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation describe group group finding finding finding finding short supported require main eds adaptation end end ability degree rumelhart rumelhart kaufmann kaufmann account account technology significantly increasing operation squared call making making international international bottom expert expert expert expert expert expert expert expert expert expert expert expert expert expert choose choose architectures improve improve improve improve improve property property property takes similarity apply apply strategy strategy strategy period period sejnowski sejnowski sejnowski recently relevant relevant sufficient sufficient compare compare calculated solve solve correspond converge evaluation evaluation generalized generalized generalized generalized organization improvement increased digital derivative derivative derivative derivative derivative derivative derivative derivative move touretzky generally generally conclusion conclusion minimal greater reduce tangent sigmoid sigmoid sigmoid sigmoid learns mateo mateo suggest propose propose taking taking hard reduction characteristics intelligence intelligence decrease relationship introduce introduce identification suppose construct solving factors factors factors factors describes describes laboratory laboratory stability stability stability stability mathematical mathematical mathematical recall missing unique adding applying events events quality choosing interpretation interpretation interpretation influence solved solved evaluated evaluate evaluate decomposition approximated activities activities past partial partial partial partial partial delays delays remains calculate calculate priori formulation formulation retrieval illustrated candidate simplicity simplicity planning planning efficiency efficiency importance importance differ modification delta delta delta delta mcclelland mcclelland identify identify build comparing comparing comparing comparing comparing comparing comparing comparing comparing comparing score score score score score kind procedures prob prob success contribution follow strategies list list list involved play absence absence paradigm paradigm minimizes minimizes board ill approximating acknowledgments deal software rat tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro cowan law law law unlike schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule perturbation experience association association game game game dual dual dual dual dual dual dual dual dual dual dual dual hall possibility decisions working circles math reading illustrate rank rank consist contributions integrate costs adapted adapted answer tool starts reasons reasons organized day precisely immediately hyperplane hyperplane hyperplane pool pool pool pool pool pool consequence separately implicit members members optimize lowest lowest meaning fourth fourth reflects considerably profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile profile substantially effort perturbations perturbations limiting proven suited suited asymmetric replace replace replace returns returns calls formally modify optimizing member member member member signature signature royal lecun tools stated occurring scoring scoring scoring scoring scoring scoring scoring analyzing adequate selects days days hours hours games games alspector ensures ensures connect corre scheduling scheduling scheduling scheduling scheduling schedules schedules schedules schedules schedules candidates chooses ranking ranking ranking advance advance verification impact impact impact impact implicitly implicitly valuable explains tures onr lem lem consecutive multiply geometrical geometrical geometrical microstructure constitute solves guyon perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed year profiles profiles profiles profiles profiles profiles profiles profiles profiles profiles profiles profiles acceptable preferences experiences possibilities associate backgammon backgammon backgammon argue mathematically permits retain player academy topic associates associates associates france france pools pools fea flight flight flight architectural resolve justified identifies morris hour integrates month proposes operational substitute substitute substitute substitute manually inefficient rating rating substitution rameters rameters fastest contrary company company company magazine corn fixing ated asymmetry security attentive men couple couple dealt respects psp psp psp psp psp psp psp psp psp psp psp psp psp notably sing permuted suggestion froin regularly regularly braun braun braun braun accelerated sponds pilot pilot pilot pilot pilot pilot retrieving prog associ specially merges team team team team team team team team team team team funding expertise expertise duplicate ule couples couples couples couples couples social unacceptable equity equity equity memorize shah stressed companies companies bromley bromley bromley unavailable associator belgium belgium rations filnction filnction filnction filnction filnction disappeared figtire contradictory steels steels steels pertur reserve reserve brussels jnowski sched flying occupation paring nearer ematical timetlon timetlon europe universiteit universiteit parc 
#@Keymeulen_D,de-Gerlache_M,
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data function function function function function figure set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output number number state results results results results results results results results units units units units units units information information information information information information information information information information problem problem hidden hidden hidden hidden performance based space space weights weights weights weights weights weights layer shown systems systems probability functions functions neurons neurons unit method method pattern large local local local local local local local local local local local local local local local local local local analysis class class class class class class class class shows algorithms simple simple paper paper paper examples examples examples examples examples examples size feature net net net net net net net net net net net net net net net net net net net net net net work work work work work work work work work methods methods methods fig classification classification classification classification classification classification classification classification classification classification classification classification classification classification trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems random random random random random random random high similar representation representation representation representation representation show show show section rule general general general real states states states states states obtained obtained obtained obtained obtained obtained term note note note note result result university university university variables solution research research independent log defined defined defined defined defined defined defined defined defined defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial initial initial initial initial constant standard standard standard standard standard standard computer computer terms terms synaptic science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left left left left left left left left left left presented low low temporal machine machine sets press press press press basis basis outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied find computational properties references due due ieee procedure important important important important adaptive mixture context context context complex complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand behavior statistical effect variance tion change energy complexity spatial rules rules rules rules rules measure measure representations chosen higher part part previous previous previous previous previous required required multiple long long conditions conditions conditions conditions conditions represent represent represent fact correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation simulations simulations minimum minimum resulting classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes ing tasks multi performed performed called mapping mapping made natural orientation negative artificial artificial relative represented provide define define define compute objects proc perform experimental goal goal related related related related constraints discrete mit accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison train train train train train train train nets nets modeling morgan morgan proceedings proceedings report institute institute words words department department department individual joint joint difficult maps maps equivalent hinton hinton additional san san effects bit detection conference conference conference determine significant significant significant significant increase increase con con produce condition derived clustering clustering finally finally backpropagation backpropagation backpropagation nature constraint constraint simply describe group group tested effective implemented shape supported require require require easily easily degree development including kaufmann objective objective objective objective objective objective typically needed interesting significantly significantly significantly significantly york special database database database representing details details numbers numbers pre pre pre pre window window window window window window window window window window window bits international supervised early choose predict predict predict predict predict predict predict denotes architectures improved discussed pair pair introduced introduced identical identical sejnowski sejnowski cognitive engineering sufficient highly highly highly highly highly conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional unsupervised unsupervised subjects tions studies achieve definition definition definition definition definition positions positions chain studied extended predicted predicted alternative alternative alternative locally occurs occurs occurs setting starting starting conclusions editors editors differences differences differences measures measures measures accurate clear mateo demonstrated california intelligence intelligence variety minimizing minimizing minimizing exist min relationship groups minima minima minima minima minima minima question acknowledgements explicit relation relation pro derive produces primary primary primary mathematical distinct changing implement category explicitly explicitly simultaneously simultaneously simultaneously physical angle angle develop mutual mutual mutual mutual mutual adding springer national national formation stages correlated correlated correlated correlated viewed variation variation labels showed evolution evolution soft sizes completely allowed discrimination discrimination past past past sign sign key sec sec roughly boundaries remains symbol symbol construction degrees degrees avoid avoid figures perceptual thesis bell inter extension discuss maximize maximize discussions structural structural structural structural structural structural extra closely capable suitable maximal divided situation situation situation essentially verlag quickly contained success contribution sin strategies sci vary vary usual generalize paradigm highest thresholds thresholds received principles attempt consisted software presents poor replaced preliminary graphical fashion ideas tech project investigated biol biol biol biol authors maximizing stream complicated notion coefficient coefficient coefficient coefficient coefficient coefficient coefficient coefficient coefficient editor analyze predicting predicts predicts extremely equally ensure versions noted algo extent utility utility phd attempts defines cos theoretic trivial trivial agreement agreement agreement agreement agreement agreement guaranteed biology biology biology biology answer reasons implementing tive sys widely widely protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein desirable desirable angles angles angles angles acad calculations toronto toronto toronto computers meaning addressed tional tional cohen employ employ employ maxima ity anti anti anti anti ture ture ture maximizes popular occurrence chose display windows windows windows unbiased progress representative secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary accomplished investigation tation restriction rithm angular perfectly nat repre eliminated extending ranges difficulties alpha alpha alpha alpha alpha alpha alpha alpha alpha alpha alpha alpha alpha alpha alpha intelligent los los resulted definitions definitions definitions definitions definitions definitions definitions definitions definitions methodology eqn eqn date analyses becker becker becker becker becker becker becker becker becker zhang zhang zhang zhang zhang zhang encountered negligible regard evident colorado den sim similarities ends ends canada proteins proteins proteins proteins passing park extends extensively agree agree agree agree wolpert projects reverse captures santa santa santa harris shavlik shavlik avoiding adopted default acknowledge robert robert robert assigns counts counts dna ple numerous maximized opposed classifications classifications classifications classifications classifications classifications classifications solely classic discovering forcing molecular molecular molecular molecular molecular beta beta beta beta beta beta beta beta beta beta beta mutually attempted exam schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber evolve evolve pij pij pij pij tems impose dominated degraded denoting efforts maximally maximally ultimately ultimately employing associates associates emphasized amino amino amino amino amino amino amino amino sheet sheet enforce enforce suffer suffer grateful preprint investigations lapedes lapedes lapedes lapedes lapedes lapedes lapedes lapedes lapedes lapedes lapedes lapedes compu struc struc struc aaai aaai mea mea utilizing rarely rarely fortunately expense regularities sees twenty twenty prefer evolved hid clarity clarity pearson periodicity dichotomy dichotomy alan alan evolving evolving evolving predictable predictable predictable predictable predictable predictable predictable predictable predictable predictable predictable predictable predictable predictable predictable predictable totally acid acid acid acid acid prone compensated constraining acids acids bear alamos alamos assessed tenth sented jose adv trapped ceedings cations demanding newly farber farber farber farber farber farber farber predic optimizes won def comprises helix helix helix helix helix helix helix helix helix helix helix helix helix helix viable ninth classifica menlo comprise tational mart coil coil coil coil coil coil coil coil coil susceptible susceptible classifi mexico waltz waltz backbone backbone chine trivially geoff sole kauffman barnes joe nical compatibility ware stolorz stolorz stolorz stolorz stolorz stolorz stolorz stolorz stolorz stolorz unary strand strand strand strand predictability implemen qian qian qian qian qian qian chou chou chou defect exhaustively intense mol mol conven conven combina quoted appreciated agreed farbet farbet farbet farbet imization ventional ventional ulations ine berg uninteresting uninteresting explanatory peculiar princi usefully senting tertiary hospitality sue sue imax peptide dicting pert teresting subsumes 
#@Farber_R,Lapedes_A,Steeg_E,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural input input input input input input input input data data function function function figure figure figure figure time time set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training algorithm output output number number number number system state state state results units information information information information information problem problem problem hidden hidden hidden performance performance performance performance based based based based space weights weights weights layer layer layer case vector order order shown shown shown shown shown systems systems systems systems values values probability probability parameters weight weight weight weight weight weight weight weight weight functions unit unit recognition recognition approach approach approach approach approach approach approach approach approach pattern pattern pattern point point point point point single single single control control large local local local local rate patterns analysis matrix matrix optimal optimal form form small small size size feature feature work work task task methods methods methods points field field features features features features features features level level level level trained trained trained trained trained trained trained structure problems random random random random random random high high high similar representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture fixed fixed line images general general generalization parameter parameter real average states theory obtained obtained note note experiments university university university computation computation computation research found found found found initial standard standard computer computer computer distance node science prediction left map map map map low low nodes temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine machine machine machine machine machine machine range press learn learn learn learn learn learn position position position position position position position position position position position position position position position position position basis basis basis outputs sample abstract applied applied applied applied back computational computational computational computational properties references component stochastic ieee ieee positive important adaptive propagation context introduction introduction complex hand generated search search search search search change difference difference difference difference difference difference difference difference difference complexity spatial spatial spatial rules measure signals prior learned learned learned learned learned learned learned learned center cases type required multiple good good long long represent represent tree tree tree bayesian make make make make fact techniques correlation correct minimum ing human human human human human human respect respect sum called elements mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor optimization optimization made natural policy knowledge knowledge knowledge knowledge knowledge knowledge negative artificial compared receptive receptive provide provide provide compute active related constraints connected distributions approaches mit contrast support train train source report report report institute institute implementation technique technique code kernel connectionist connectionist difficult difficult final final bias bias bias bias layers layers layers layers maps maps domain domain domain domain domain domain domain equivalent experiment directly hinton additional san effects efficient full full significant free world world speed estimated estimated basic produce developed levels area area provided provided backpropagation backpropagation backpropagation backpropagation nature inhibitory sampling constraint constraint constraint constraint constraint constraint biological measured discussion discussion technical group group group limited limited predictions predictions predictions predictions predictions effective generate generate require require main face adaptation journal square end instance future degree degree makes makes development development objective simulated simulated typically smaller needed reduced reduced account account account fully fully transfer transfer transfer transfer transfer transfer interesting significantly character projection edge edge edge mechanism mechanism special matching principle operation leads direct supervised expert early early magnitude attention produced produced predict predict predict predict predict predict predict architectures architectures improved improve advantage advantage advantage advantage takes similarity lateral lateral practical strategy strategy strategy strategy subject sejnowski sejnowski sejnowski sejnowski sejnowski cognitive sufficient sufficient highly compare conventional conventional conventional conventional conventional teacher approximately solve yields match studies studies achieve address evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation positions positions positions positions positions positions symmetric modified grid organization risk invariant invariant invariant suggests wide wide rotation rotation rotation predicted predicted alternative alternative alternative alternative locally move move move move move move move move move move move move hybrid deterministic deterministic deterministic deterministic white white white white white white generally pass pass demonstrate demonstrate strength competitive central interactions interactions differences sutton sutton sutton sutton sutton faster practice practice weak temperature temperature propose hard mechanisms external proportional intelligence intelligence turn turn turn turn variety variety start selective selective derivatives groups groups groups groups connectivity connectivity connectivity connectivity connectivity program program program program program program program program program program program annealing annealing annealing question acknowledgements areas explicit appears monte carlo edges edges edges ways ways laboratory stability tuned changing changing implement explicitly linearly remaining easy adding adding predictive predictive quality quality implies versus versus yield choosing focus influence evaluate evaluate evaluate evaluate forms static sizes sizes margin suggested translation translation translation translation translation past past reasonable barto barto slow fitting purpose generation advantages advantages advantages faces faces faces faces faces faces faces transactions transactions expect expect recorded existing exploration handwritten kernels kernels kernels kernels silicon thesis thesis priori color color color color color assignment assignment coupled black black black black black black black absolute partially neighbors discussions gating successfully straightforward selecting aspects identified extra efficiency efficiency capable suitable suitable computationally build projections projections invariance invariance invariance invariance score reached capture procedures cun cun allowing anderson neuroscience issue symmetry symmetry symmetry symmetry running criteria strategies strategies strategies strategies strategies strategies hold comp comp comp comp gibbs gibbs gibbs gibbs relaxation play play play play play play play play play play play play play play play play play play play play play play play play play dayan dayan dayan dayan dayan dayan dayan dayan modular modular surround providing board board board board board board board board board board board board board board board board board board board board board board board board board board board board denker moves moves moves moves moves moves moves moves moves illustrates tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro situations situations explore remain remain unlike unlike unlike diego poor exponentially steady humans humans detail strengths game game game game game game game game game game game game game game game game game game game game game game game issues helpful scalar giving investigated structured symbolic proved encode removed naturally plausible man extremely perfect eyes ensure ensure quantities noted panel freedom switching improving contributions phd massachusetts separable trivial convolution convolution improves adjacent adjacent multiplication starts starts reasons considerable considerable considerable inside processed perspective sections incorporate controls simard recognized beginning res medical localized arises computers cybernetics mellon raw integrating carnegie reflect reflect cmu bootstrap peter completion adjustable compares howard howard rely popular prevent prevent achieves geman geman geman geman geman geman plan enables enables inherent redundancy credit credit instantaneous sharing sharing phenomenon benefit proportion generator generator summing summing appropriately pick pick pick pick labelled tem outcome outcome outcome stronger promising primitive loops nearby neurobiology observing salk salk salk salk obstacle games games games games games games games games games games games games games games games exploring reliably ranging programs programs programs programs programs encountered consequences jackel captured branching branching arrangement exposure exposure treatment suggesting ahead offer offer master master ends informative arrows extensively agree exploiting intersection adopted stone stone stone stone empty empty boxes outperform randomized legal suboptimal pieces adopt boser amherst affects forcing reflected chess chess chess chess backgammon backgammon backgammon backgammon backgammon verified henderson invariances ibm deep alternate interact wall file file file file file file file file file file generators playing playing playing playing playing playing playing playing playing hubbard hughes carefully terrence eliminating surrounding retain player player player player investigating investigating records win zip sam grateful placing happen commercial commercial bring intensive intensive intensive inactive challenge manuscript manuscript scanning demonstrating reversal reversal satisfaction satisfaction satisfaction restoration acquire ping mcdonnell assistance stochastically thousand doesn adaptively opponent opponent opponent opponent opponent opponent supply fill played reflecting accomplish concern eliminates integrates ally obey kirkpatrick kirkpatrick beneficial inefficient raises squashing complement rivest rivest unlabelled reflection reflection reflection constraining randomness amenable teaching remained players players players players players players players players players server server bottleneck format skill gammon gammon gammon gammon successor successor prominent tim spa talk modest mid stems schraudolph schraudolph schraudolph schraudolph schraudolph infeasible pew richer prime fundamentally lookahead lookahead favorably won won forthcoming trick ply ply ply ply accessible grown dissimilar coverage viable viable ago burden occupied occupied samuel samuel disk scored scored poral nserc overfit augment succession beat beat stochas eval bears opening opening weaknesses modulo patrice recognizable ucsf ucsf ucsf ucsf ucsf geoff intend intend loses ergodicity modulates casey vecchi neuronlike internet internet internet internet internet internet internet restricts pling manage anonymous anonymous anonymous anonymous cumbersome sampler tex convolutions public public intersections planned expertise grand occupies vastly western gelatt illegal uation barely invited richly checkers checkers tum tum tum istic skilled skilled trap serc propa combinatorics multiplicity intimately pla tically newman newman newman routinely reserve teaches antisymmetric readable protocols aided ignorance rewarding elusive china reprint disproportionately checker hampered territory territory competent competent mechanically sluggish plies mous erry 
#@Dayan_P,Schraudolph_N,Sejnowski_T,
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#*network network network network network network network network network learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure time time time time time time time time time time time time time networks networks training training training training training training algorithm algorithm output output number number number system system system system system system system system system system system system system system system system system system system system system system system error state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results units units information information information problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based based space space space space space space space linear case case vector order order order order shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters functions functions distribution recognition recognition recognition recognition recognition recognition method method method approach approach approach approach pattern pattern pattern pattern pattern point single processing processing processing control large large large large local rate rate analysis analysis class class class class class matrix form form form form signal simple simple simple simple simple gaussian gaussian gaussian gaussian paper paper paper paper examples small size feature feature feature feature feature feature work methods methods methods methods methods step step points features features features features features features features features features features features features classification classification classification classification classification current current trained trained trained trained problems problems memory memory similar similar show equation equation equation fixed line rule rule rule rule general general general speech real real states states states states states states states states states states states states states states states states states states states states states states states states states theory theory theory gradient obtained term term term note dimensional dimensional threshold computation research found found sequence sequence estimate estimate estimate estimate standard computer terms presented presented present phase activation low temporal press press press press position components basis basis continuous continuous sample abstract applied applied computational density density density density density density density density density properties likelihood references component component component component due ieee important adaptive decision decision mixture mixture mixture mixture mixture context context complex complex hand circuit estimation estimation estimation statistical statistical effect effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated variance cost change change classifier classifier classifier classifier classifier lower prior prior prior prior prior prior prior prior prior prior prior prior chosen part cases multiple long conditions conditions conditions conditions conditions conditions bayesian bayesian bayesian expected expected equations equations equations markov markov markov markov markov markov markov fact fact techniques proposed proposed proposed proposed proposed correlation probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed forward scale finite resulting resulting classes classes classes classes classes classes classes ing ing sum performed optimization potential made natural feedback applications applications applications applications knowledge knowledge knowledge knowledge knowledge filter original vol vol vol vol vol relative specific samples samples true true application application application application application application application application application provide provide perform experimental experimental goal related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints motor discrete mit steps comparison larger morgan morgan report report institute institute loss loss loss loss loss implementation implementation individual kernel kernel advances advances final scheme scheme framework framework framework cambridge experiment environment directly directly directly directly directly estimates estimates estimates estimates estimates estimates estimates estimates design design transition transition transition san san detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection determine efficient classifiers classifiers classifiers full choice choice choice choice significant significant significant significant statistics estimated estimated estimated estimated estimated con con produce condition derived levels criterion bounds provided provided provided finally nature nature nature sampling achieved normal normal normal normal normal normal normal normal normal technical feedforward feedforward denote tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm assumption assumption assumption corresponds stable short common common effective implemented assumed assumed assumed supported main eds eds eds eds ability ability ability ability ability future makes noisy noisy fit kaufmann kaufmann simulated probabilistic probabilistic probabilistic probabilistic probabilistic typically typically typically typically underlying unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown coefficients coefficients technology technology block interesting testing significantly projection york mechanism mechanism details direct window window frame idea minimize minimize added added discussed robust typical typical practical practical practical practical practical include sense sense subset dimensions highly highly highly highly previously previously previously conventional correspond background bounded sensitive grant constructed exists scaling occur occur occur alternative feed hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid boundary hardware hardware conclusion critical assumptions valued valued bayes bayes bayes designed designed designed moody practice practice practice practice weak mateo mateo integration characteristics characteristics sigmoidal california california california turn variety exist manner identification configuration explicit pro construct construct longer primary generating describes describes laboratory laboratory laboratory distinct category category explicitly dimensionality belief consisting develop integrated frequencies events choosing national extracted dependence correlated viewed detailed densities densities densities densities operations operations controlled labels suggested discrimination discrimination past diagram earlier earlier reasonable calculation smoothing smoothing intervals event event purpose false false tracking tracking symbol classified classified classified classified classified transactions recorded figures activations subspace determines priors simplicity determining determining straightforward sensor sensor identified extra extra hmms hmms included detect detect detect literature miller miller online online online online heuristic link dis running generative generative generative generative generative generative generative generative generative generative generative generative duration duration duration duration built built sampled usual backward giles observable ill thresholds automatically automatically consisted extract software software software modelling modelling cowan origin origin origin origin remain unlike parametric poor estimators hanson hanson hanson limitations issues lippmann lippmann lippmann lippmann hall discriminant behaviour behaviour pursuit fashion project detectors fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault fault reliable cover induction necessarily equally voltages aspect aspect portion noted assumes assumes detected detected detected plant seconds seconds mentioned site site theoretic ground ground ground ground sensors track phenomena failure failure failure failure analytical tool worse drive rapid purposes purposes sys operators desirable desirable mation commonly potentially acknowledgement medical author author incomplete incomplete conjugate reflects considerably reflect collected empirically empirically transient transient transient generic fed poorly introducing posed detecting rely mod fall occurrence occurrence pasadena pasadena suited richard richard windows progress simultaneous diagnosis diagnosis diagnosis diagnosis trade acquisition acquisition acquisition acquisition primarily assign amplifier appropriately conditioned conditioned conditioned perfectly dynamically encoder tem stronger minutes minutes minutes minutes minutes minutes contract occurring operates methodology belong disjoint receiver synchronous infor prentice paul consequences searching originally tic modelled omitted record matter late kearns informative omohundro omohundro automated thresholding discriminate discriminate drop specification specification pointing pointing pointing pointing pointing basically goodman goodman exhaustive exhaustive exhaustive exhaustive exhaustive inferred creates july failed discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative australia remote mutually mutually unseen exclusive exclusive deep deep deep faults faults faults faults faults faults faults smyth smyth smyth smyth smyth smyth smyth smyth smyth smyth smyth smyth smyth smyth smyth smyth smyth noting interactive win monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring worth worth weaker nonetheless nonetheless accounted minor thousands normalised transients ignoring failures failures fiat generarive impractical assistance jet jet jet jet solvable incorrectly hour hour station compensation believed alarms alarms operational judged obey petsche propulsion propulsion propulsion propulsion autoregressive autoregressive meth clark clark arpa inspection rivest ods rel delivery indirectly antenna antenna antenna antenna antenna antenna antenna antenna antenna antenna problematic problematic translate february blocked manual backwards cti monitored health health subtle experimented analyse anomaly anomaly anomaly anomaly anomaly months accepting gross minimise minute weakness accu undesirable beliefs scheduled posterjori novelty novelty novelty novelty novelty novelty novelty novelty necessity multichannel communicating pared frank frank grove ons lock kay kay spacecraft spacecraft spacecraft narrower equipped resonant administration illustrative struction anomalous anomalous ditional designer comment pii pii ifp aeronautics oak servo servo servo uncover acute confirming vides jeff stolcke stolcke jpl ction wil discriminator tlo antennas antennas antennas antennas antennas complexes atively lth guidelines facility spain ult llo califor nia 
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values values probability probability probability probability probability probability probability parameters parameters parameters parameters distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach pattern pattern pattern single single single single control control control control control control control control control control large large large patterns analysis analysis analysis analysis optimal optimal optimal form form shows algorithms algorithms simple simple simple simple simple paper paper paper examples examples examples examples small small small small small size feature feature task methods methods methods methods fig fig fig fig fig points field field process process process process process process level level level level level current structure structure structure structure structure high high high high high high high high high similar representation representation representation representation architecture architecture show show show section section section section fixed fixed line line line rule general speech speech speech parameter approximation average states states states states states states states states theory theory obtained obtained experiments experiments activity result result result university university computation computation research log log log log log log log log defined defined found sequence sequence sequence sequence sequence sequence sequence dynamics dynamics initial initial initial constant estimate estimate computer computer science presented present present phase phase phase phase phase phase phase phase phase phase low frequency temporal temporal temporal motion motion motion maximum maximum maximum position components components continuous continuous abstract applied back back find find likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due ieee ieee positive procedure important important important important important adaptive adaptive adaptive introduction introduction action hand hand estimation estimation estimation estimation estimation statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated variance parallel tion tion change complexity assume lower lower prior word word word word word word word word word word higher higher higher higher part center center center previous type required good equations equations equations markov markov markov techniques proposed proposed length length length length correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed finite finite finite minimum resulting total human sum performed performed performed called times mapping dimension dimension natural applications applications study study em obtain negative original original original relative relative true true true true compared series provide define compute proc proc location determined determined motor motor motor motor discrete discrete discrete discrete discrete discrete discrete discrete discrete power power power power update support train train source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling report institute words words words words words words words words technique technique code individual represents final final layers scheme scheme scheme scheme scheme scheme scheme scheme scheme graph graph sequences sequences sequences sequences sequences sequences sequences ai considered computing additional transition transition transition transition transition transition transition transition transition trajectory trajectory trajectory trajectory trajectory trajectory trajectory top top stage conference efficient efficient upper full requires free world vision estimated estimated estimated estimated estimated basic basic basic pages con channel channel coding coding coding coding coding coding developed levels levels levels levels levels levels levels levels levels levels velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines lines lines entropy path product product actual actual provided selected achieved achieved normal normal technical technical describe describe describe denote hmm limited limited assumption assumption assumption complete complete complete finding short assumed role role theoretical require require main adaptation adaptation end end end end end end future rumelhart probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic needed dynamical dynamical dynamical fully fully technology technology programming programming programming programming interesting ratio edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism database empirical principle language language language details call numbers bits bits normalized normalized normalized bottom bottom run added added description description description description description property pair pair robust ensemble typical similarity movement movement machines inference relevant relevant dimensions sufficient sufficient previously previously observations observations approximately approximately approximately calculated calculated volume correspond correspond correspond rl positions positions locations locations locations locations locations locations symmetric modified grid grid interval entire amplitude amplitude amplitude horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal occur occur occur occur correctly correctly occurs setting hardware critical place place minimal assumptions trajectories segment conclusions measures measures practice encoding encoding encoding encoding encoding encoding encoding propose strong hard hard cycle drawn demonstrated demonstrated regularization regularization assuming assuming start movements movements movements denoted suppose edges edges written written written index index estimating transitions vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical segments modeled modeled dimensionality easy scales adding equilibrium applying applying applying predictive minimization quality implies cycles letters letters letters letters letters letters letters letters letters letters letters letters letters review reconstruction communication viewed viewed evaluated restricted restricted updated lee modulation similarly past key reasonable dashed dashed dashed performing intervals intervals tracking intermediate string string string string string symbol symbol symbol symbol foundation existing handwritten figures coordinate strings strings strings strings strings inter plotted plotted automatic uncertainty uncertainty variations discussions determining selecting identified identified letter letter letter letter letter letter letter encoded divided symbols symbols symbols symbols symbols symbols oscillatory oscillatory efficiently efficiently efficiently score score online online online composed composed capture capture soc compact compact compact compact conf decoding decoding decoding decoding induced induced contained contained prob success sin oscillations oscillations oscillations oscillations oscillations oscillations built built built vary vary simplified play paradigm providing giles quantization correspondence highest automatically received acknowledgments deal software presents simpler experience issues preliminary preliminary ml rest investigated reliable variability variability variability oscillation oscillation oscillation scores scores encode encode encode encode cognition phases phases adapt adapt automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata created created implementations front front message switching generates utility regime motivated years indicating cos growing coded briefly sections precisely incorporate located commonly probable beginning gradually begin english english depicted depicted depicted incomplete incomplete recognizing robustness virtual greatly collected transient amounts amounts fed marked remove incorporated dots requirement operate synthesis synthesis synthesis occurrence ordered singer singer singer singer singer singer singer singer enables segmented segmented segmented segmented segmented 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transmitter transmitter transmitter ron ron rissanen rissanen excited tuple manually resolved deals trol frequent frequent statist accommodate lags inducing inducing tra feb transmit acyclic acyclic acyclic acyclic indicators indicators sep jerusalem jerusalem drawbacks cations spotting spotting spotting tutorial locating hebrew hebrew plotting cient markets bio entered modifies equalization availability concurrently dana writers writers writers vast challenges absorbing transcription transcription succession stochas resolving altogether adaptable emerging progression cri antagonist scripts scripts scripts scripts scripts scripts scripts scripts imitate clocks muscular agonist intriguing strate script script slave terminating ingredients slant comple ingredient cyb yoram adaptability adaptability coarticulation effi halt amnesia naftali mally ups automatica recalculated pis jectory dri arate mentary 
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure time time time time set set networks networks networks networks networks training training output number number number number number number system system system state state state state state state state units units units units information problem problem problem hidden hidden hidden hidden performance performance performance performance performance performance performance space linear layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown systems systems systems systems values parameters parameters functions functions functions functions functions recognition pattern pattern pattern point point image image single single single single single single single processing processing processing processing large rate test test test test analysis class class class class class class class class class class inputs inputs shows simple gaussian paper paper examples examples feature work work work task classification classification current current problems problems high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response architecture architecture fixed fixed fixed 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difference difference variable variable variable part long long represent represent tree distributed distributed equations chip chip chip chip fact techniques length length correct forward minimum minimum minimum minimum resulting total computed multi sum sum sum sum performed performed performed performed times times elements elements elements elements elements elements dimension made global global global applications applications applications applications applications applications vol vol vol vol represented compared receptive receptive receptive compute compute proc proc location perform perform perform connected connected power mit mit comparison comparison connection connection fields fields fields morgan words department code code advances represents maps cambridge cambridge equivalent environment environment environment design design san san san bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit efficient classifiers full requires vision vision vision vision basic conditional controller controller controller actual actual backpropagation nature biological feedforward feedforward arbitrary tested transformation fast fast complete complete rbf rbf rbf nearest nearest nearest nearest nearest nearest common effective effective effective effective implemented supported square vlsi vlsi including including fit kaufmann needed needed technology block block programming programming programming programming york operation operation operation operation operation operation language language numbers direct bits bits bits bits bits bits bits bits magnitude combined added architectures element typical machines array array array array array engineering highly highly highly compare match match match match correspond achieve address address storage entire entire grant grant locally touretzky width neighbor neighbor neighbor neighbor neighbor differences sigmoid peak peak performs moody moody moody faster taking reduction sigmoidal sigmoidal demonstrated radial radial variety iii scene identification program program program program pro pro pro pro longer describes describes tuned metric implement simultaneously simultaneously electrical easy easy unique boolean cycles cycles select family formation review evaluated operations operations operations operations operations operations organizing organizing organizing organizing approximations approximations processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor processor diagram diagram reasonable performing performing sec purpose purpose add add distances msec msec msec msec msec msec msec msec msec msec msec msec euclidean kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen degrees precision precision precision includes inter instances absolute absolute absolute suitable included miller miller miller miller road return return return running running running built vary localization michael computes automatically chips processors processors processors processors processors processors diego wiley scalar scalar scalar scalar giving int root scores act closest implementations freedom art art art switching switching serial serial serial serial defines advanced convolution track track implementing implementing implementing implementing organized operators operators operators operators acknowledgement grossberg computers bandwidth bandwidth cybernetics sun exemplars exemplars exemplars flexible switch switch switch switch switch switch instruction instruction instruction instruction popular proven logical windows june arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic realized ordinary assign acts flexibility interconnected robotics rational rational significance darken alpha alpha alpha alpha interconnection interconnection performances performances performances thomas dif francisco francisco card card projects hart instructions instructions instructions integers integers integers integers onr sequentially metrics listed listed listed listed listed listed kinematics bus bus bus copy simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd massively massively massively massively massively massively massively massively transparent mhz mhz mhz mhz cessing duda duda ijcnn execute searches compatible compatible compatible host host host host host host host host speedup speedup speedup speedup library library library library library sheet paradigms paradigms register register register placing supports programmed programmed lippman milliseconds port mini spring inherently station agency gram gram functionally inefficient arpa sheets sheets carpenter carpenter registers neocognitron neocognitron neocognitron neocognitron routine sparc sparc sparc sparc sparc pes pes pes pes pes pes neigh align align mum hampshire puter topologically subtract named watts abstracts accelerate saving mips mips mips mips mips additions bor hammerstrom hammerstrom programmer programmer manipulate manipulate resides resides resides hillis hillis dram managed holler holler overflow overflow saves alu alu alu cessors chitectures ficult dissipates 
#@Glover_M,Miller_W,
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set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training algorithm algorithm output output output output output output output number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error error error error results results results results results results results results results results results results results results results results results results results units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based space space space space weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer systems systems values weight functions functions functions neurons neurons neurons neurons recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method approach approach approach pattern pattern point point point single single processing processing large neuron neuron neuron neuron neuron test test test patterns optimal inputs inputs inputs inputs inputs inputs inputs inputs form form shows shows shows shows shows signal signal signal gaussian gaussian paper paper small size size feature methods methods methods methods methods cells step process current current current trained trained trained trained trained trained trained cell cell problems problems problems high high high similar similar similar similar similar architecture equation section fixed line line speech speech speech speech speech speech speech speech speech speech speech speech parameter gradient obtained obtained obtained obtained obtained experiments result computation computation computation computation computation solution research found table standard terms terms terms terms low low low low low low low low low low low range learn basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs outputs outputs continuous sample abstract applied applied back back back back back analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due ieee ieee ieee positive important propagation propagation propagation introduction circuit circuit circuit estimation estimation estimation estimation statistical statistical statistical dynamic generated parallel cost cost cost cost cost search search tion energy energy difference difference lower signals learned learned center center previous previous required represent represent chip chip chip chip chip chip region correlation errors minimum minimum simulation simulation computed computed sum sum performed mapping mapping mapping mapping mapping means potential potential applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications obtain vol vol vol artificial specific compared compared compared compared compared compared application application application application application application application application application application application application application application application application application application series series series series series series series compute compute compute perform power power power power power power power power power power power power power power power approaches approaches approaches voltage voltage voltage accuracy accuracy accuracy comparison comparison comparison comparison proceedings proceedings institute department department department implementation consists individual individual represents difficult difficult layers layers layers layers layers delay delay delay computing computing computing domain domain domain domain domain experiment solutions curves curves bit bit bit conference conference classifiers requires requires area area area area controller actual actual provided provided nature nature constraint achieved achieved achieved tested tested tested tested fast fast limited limited inverse inverse circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf common implemented implemented implemented implemented implemented require require require require require journal square vlsi vlsi vlsi vlsi vlsi future easily makes development development development development fit simulated simulated combination combination reduced technology technology technology transfer testing testing significantly significantly significantly operation operation operation squared details filters making stored bits bits international magnitude produced produced produced produced produced produced produced produced predict predict predict improved improved improved discussed improve advantage advantage array varying varying previously previously previously previously conventional conventional conventional conventional conventional conventional conventional approximately solve match achieve improvement improvement improvement improvement improvement constructed exists digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital predicted locally hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid width hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware critical row reduce reduce conclusions differences sigmoid sigmoid sigmoid designed clear performs moody moody exponential faster faster temperature reduction sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal demonstrated demonstrated california solid solid intelligence radial radial radial radial radial radial radial radial radial radial radial radial radial radial radial minimizing ways ways plot describes laboratory tuned student implement implement category slightly unique applying john john john national national phoneme phoneme phoneme phoneme phoneme phoneme phoneme variation variation completely completely completely completely completely completely completely completely key key key dashed reduces interpolation advantages topology topology topology david precision precision precision precision precision precision currents retrieval recognize coupled absolute absolute absolute absolute absolute absolute discussions major sensor closely tdnn tdnn tdnn tdnn computations comparing comparing reached reached traditional traditional traditional quickly allowing success anderson anderson superior content content content content content content content built providing nips board board board board board board board board board cmos automatically illustrates operating acknowledgments software software software software software requirements mead mead dotted giving possibility authors proved workshop matched neu waibel waibel waibel waibel waibel waibel naturally naturally predicting implementations implementations precise explored chaotic chaotic chaotic sensors sensors floating floating glass glass glass glass glass glass glass glass glass glass glass glass glass benchmark implementing watkins watkins watkins watkins watkins watkins watkins watkins watkins potentially medical bandwidth bandwidth raw requiring requiring requiring double capability fed orders detecting passed remove passes passes howard resource pasadena pasadena acoustics chose implements wesley don representative benefit sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing feasible addison fabricated fabricated restriction restriction princeton acm caltech caltech multipliers multipliers multipliers multipliers multipliers multipliers platt platt platt platt platt platt multiplier multiplier allocation consideration minutes darken darken attractive bands mark symposium enhanced enhanced meaningful falls combines paul paul paul overview lang offers offers recog jolla jolla jolla cpu hart executed executed rms rms rms rms rms rms rms rms pressure pressure pressure multiplying multiply multiply summer summer converted fellowship ties benefits benefits benefits transmitted transmitted july profiles hundred remote remote remote remote remote remote remote remote remote remote remote remote remote remote remote remote eric mackey mackey mackey mackey mackey mackey mackey mackey mackey mackey mackey mackey mackey subthreshold ijcnn graduate execute degraded degraded degraded oct eliminating altered parallelism parallelism parallelism lookup nasa gilbert gilbert gilbert gilbert gilbert placing lippman dsp dsp dsp dsp dsp dsp tune october technologies november ucsd ucsd ucsd demonstrating rats gratefully advantageous consuming jet send thousand water water water water water water water water steven steven converter ron fabrication rons conversion conversion conversion accumulate accumulate propulsion poly retrieved retrieved weather consumption consumption consumption consumption amplified sis sis feasibility feasibility feasibility feasibility acknowledges steve steve allocating greatest satellite satellite satellite satellite satellite discriminating mid sponsored custom custom carver severely prime battery ece ece shikano nov alexander kirk kirk quarter acknowledged wired plutowski plutowski plutowski plutowski dash cse hanazawa earth neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer neurocomputer administration administration saving micron settled neurocomputing fernando phoneroes phoneroes infrared aeronautics aeronautics microelectronics kerns portable portable portable portable portable portable fid thakoor calibrated rnns targeted targeted targeted moidal 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#@Chau_P,Lambrigsten_B,Plutowski_M,Tawel_R,Watkins_S,
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neural neural input input input input input function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output system error error error error error error error error error error error error error error error error error error error error error error error state results results results information information information information information problem performance performance performance based based space space linear linear linear linear linear vector vector order order order order order shown shown shown systems systems systems systems systems systems values values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons method method method method method approach point point point single single single single processing processing processing processing control control control control local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate test optimal inputs inputs inputs shows shows shows shows shows signal signal signal signal signal signal signal signal algorithms simple simple simple small small small size size net methods cells cells cells cells features process process process process process level current current current current current current current current current current trained trained trained trained cell cell cell cell cell cell structure structure structure random random random random random random random high high high high memory architecture architecture architecture architecture architecture show fixed fixed fixed line parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation approximation approximation approximation states gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained obtained obtained obtained term term term term experiments dimensional dimensional dimensional result university threshold threshold threshold variables computation computation defined defined defined found sequence target target target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial constant constant constant standard terms terms distance distance connections connections synaptic synaptic synaptic synaptic direction presented present present present present phase phase phase activation activation activation low low low frequency frequency frequency sets range range range press components components nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied convergence convergence convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due ieee ieee ieee positive positive positive introduction action action complex behavior stimulus statistical effect dynamic dynamic dynamic dynamic generated parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion difference signals signals signals signals signals signals signals signals signals signals learned learned chosen higher cases multiple binary long long long conditions conditions conditions chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip techniques region region region proposed probabilities observed errors minimum ing total multi multi performed performed performed means means optimization optimization feedback feedback feedback feedback global global global global global applications applications filter filter negative vol vol vol vol vol vol vol vol vol vol specific application cross cross provide location active active determined experimental related connected discrete equal equal power voltage voltage voltage voltage voltage voltage voltage voltage larger larger contrast connection connection connection connection connection update update update update update support descent descent descent descent descent descent source source morgan morgan morgan morgan institute department implementation implementation implementation implementation synapses synapses technique consists internal internal advances advances advances advances bias bias bias delay delay scheme sequences sequences experiment experiment experiment directly additional trajectory trajectory trajectory trajectory san san san san san top effects bit bit bit bit bit bit bit conference efficient free free free con con derived randomly levels levels lines lines product product provided nature achieved achieved achieved measured measured technical fast fast limited corresponds corresponds proof circuits effective implemented implemented implemented implemented implemented shape shape synapse synapse synapse synapse synapse synapse synapse generate generate generate generate supported end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi including simulated smaller needed dynamical functional fully fully technology york increasing mechanism consistent consistent mode principle principle principle principle operation operation operation operation operation representing iterations iterations stored stored stored stored bits bits bits bottom supervised supervised supervised magnitude decay decay run added added sources description improve directions resolution resolution exact pair pair robust element element typical include period identical array array recently engineering sufficient varying teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher works tions differential differential differential differential trans diagonal diagonal address background evaluation evaluation evaluation observation gate gate williams organization storage storage storage storage storage storage storage storage amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude constructed lead extended deviation wide wide feed locally column setting hardware pass strength strength strength conclusion starting row row row greater trajectories valued sigmoid performs weak weak learns constrained mateo mateo mateo mateo strong strong strong strong strong hard external external external external cycle cycle cycle characteristics characteristics sigmoidal california pulse pulse minimizing decrease averaged introduce minima configuration annealing denoted attractor attractor reference reference explicit longer sequential generating generating tuned dept metric metric explicitly averaging infinite electrical dimensionality dimensionality integrated integrated integrated applying springer shift shift dependence communication detailed controlled evolution static static updates updates updates sign diagram calculation smoothing slow dashed sec sec sec purpose purpose purpose generation generation initially initially msec msec construction foundation norm norm coupling coupling avoid recorded recorded figures activations currents currents currents extension illustrated automatic activated activated absolute structural extra delta wij wij wij wij oscillatory oscillatory fine notice verlag sin running running running oscillations timing satisfy simplified simplified simplified relaxation absence providing nips cmos cmos cmos cmos thresholds thresholds thresholds approximating acknowledgments origin poor perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation requirements requirements circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry strengths strengths strengths oscillator oscillator oscillator periodic periodic rise reducing giving incremental incremental transistor proper stream affect voltages voltages voltages initialized initialized multivariate contributions arbitrarily established established charge charge charge charge residual residual residual ment ment slowly cos trivial distinguish defining phenomena fairly fairly fairly waveform majority starts rapid strictly day forces transistors transistors desirable cut gradually depicted nsf outer requiring fourth double collected pseudo pseudo embedded conducted experimentally adjustable adjustable resistive requirement span stack perturbations perturbations perturbations perturbations serve pasadena implements specifies traces traces simultaneous summed summed summed distortion initialization uncorrelated uncorrelated uncorrelated bipolar drift driving driving circular circular harmonic flexibility flexibility interconnected caltech caltech generality extending spontaneous spontaneous multiplier kaufman kaufman kaufman kaufman khz ranges mail interconnection resistance serves fail monotonically imply capacitor capacitor capacitor modifications clock selects service alspector alspector financial periods iteratively negligible expanded expanded conjunction conjunction demonstration facilitate offers arrangement darpa francisco waveforms waveforms waveforms pearlmutter variants limitation sequentially leaving largely converted rigorous constitute basically session forced forced perturbed perturbed perturbed perturbed sigma exception junction ical jabri forcing forcing forcing forcing forcing forcing forcing forcing forcing forcing forcing forcing forcing forcing forcing forcing streams avoids verified verified capacitance increment increment iff exclusive exclusive decays gener relating switched retain complementary complementary complementary transconductance transconductance transconductance unconstrained covered register preserve minor minor flower simplifies continually completed triggered sessions sessions sessions sessions sessions removes persistent meir drives fiat fiat functionality externally externally externally externally ate accordance satisfactory settling calibration capacitors supply hopkins suffices adjoint converter suppress fabrication supplied periodicity replicated injected polarity polarity polarity polarity polarity horizontally sided impedance impedance dedicated clark squashing symmetrical zipset johns leakage sions vertically inset communicate mosis accommodate accommodate accommodate accommodate periodically barhen cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs baltimore parker prescribed registers dissipation undergo rent freely refresh refresh refresh refresh refresh trapped ripple configured elaborate predefined repetitive operated vergence vergence discrepancy observes ece virtue activating activating quadrature quadrature quadrature perturbative apparatus formulations decrement decrement internally illustrating undergoes volatile volatile volatile kirk toomarian wii released multiplexing dynam feeds functionals optimiza tar tar recur constantly communicating orthogonality interconnectivity proportionally trivially synchronously yuhas assist kushner diode tang probing opera 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#@Cauwenberghs_G,
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#*learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set networks output output output output output output output output output output output output output output number number number system system system system system results information information information information information information information problem problem problem problem problem performance linear linear shown systems systems systems systems systems systems systems neurons neurons unit method method pattern pattern pattern image processing processing processing processing processing control control large neuron test test test test inputs inputs form form form shows shows shows simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small size size feature feature feature feature feature feature feature feature feature feature task cells cells cells field field field field field features features features features features features features level current current current cell cell cell cell cell random high high high high memory response response representation representation architecture architecture architecture line line line line line line line line line rule images average average average average average average average theory dimensional result university university threshold computation computation computation computation computation solution research log found target target target target target target target target target target target computer computer computer left direction present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low low temporal temporal temporal temporal object object object object object object object object object object object position position position position position position position outputs outputs outputs outputs outputs abstract analog analog properties references due ieee positive positive important adaptive propagation introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit stimulus stimulus stimulus tion difference difference assume assume representations center bound type required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex binary binary long distributed distributed distributed chip chip chip chip chip chip chip chip chip chip chip make make correlation correlation correlation correlation correlation length simulations simulations simulations minimum tasks total simulation simulation elements feedback feedback orientation global original vol specific receptive receptive receptive receptive receptive receptive provide provide objects objects objects objects objects objects location location location location active active eye related connected connected connected connected connected cortical brain power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage morgan department department consists code code advances responses responses responses addition maps considered computing san top determine determine requires speed vision lines lines provided provided provided provided nature biological associative associative measured discussion discussion group group group group group group group group group group group group tested complete stable circuits circuits circuits circuits circuits nearest nearest nearest nearest common role require vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel easily degree smaller combination functional technology york segmentation segmentation mechanism mode making bottom neuronal architectures architectures architectures architectures architectures architectures recent correlations robust separate separate movement lateral pixels engineering engineering compare smooth match correspond correspond correspond correspond achieve achieve trans chain chain modified gate gate storage amplitude exists occur wide touretzky pass neighbor neighbor neighbor neighbor neighbor neighbor neighbor valued central sigmoid retina performs performs mateo cycle cycle cycle proportional proportional pulse pulse pulse pulse pulse pulse pulse turn groups groups groups groups groups groups groups groups groups connectivity connectivity acknowledgements generating plot plot describes averaging averaging averaging averaging averaging averaging averaging averaging infinite electrical electrical easy easy easy slightly develop frequencies yield communication communication codes controlled modulation modulation suggested discrimination processor slow dashed sec sec intervals intervals tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking koch koch koch exploration combinations currents inter instances memories coupled neighbors neighbors gating texture middle identified extra capable driven spiking spiking oscillatory oscillatory oscillatory detect soc split oscillations oscillations physiological physiological duration gray gray gray gray play cmos cmos cmos binding binding cat cat cat neurosci extract intrinsic intrinsic minimized carried american requirements requirements exhibit circuitry circuitry circuitry circuitry mead mead mead mead rapidly rapidly oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators 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#@Andreou_A,Edwards_T,
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#*network network network network network network network network network network network network network network network network network model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data figure figure figure figure figure figure figure figure figure figure figure figure time time networks training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output system system system system system system error error results results results results units units problem problem problem problem problem hidden hidden hidden hidden hidden performance performance performance based based weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer case case case shown shown shown shown systems systems values noise noise noise noise noise noise noise noise weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons single control large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test patterns patterns inputs shows shows shows signal algorithms algorithms paper paper paper paper paper small small size net work work work work classification classification classification classification classification classification classification classification process level current current current current current current current current current current current trained trained trained trained trained trained trained trained problems problems problems problems random high high architecture architecture architecture fixed fixed fixed general parameter real average obtained university threshold found found table table table table table standard standard presented present low low low low low low low low maximum maximum maximum range range basis nonlinear nonlinear outputs outputs abstract back convergence references references component due due ieee introduction circuit circuit circuit effect effect effect effect effect cost search search tion energy energy energy energy energy energy energy energy complexity variable classifier classifier lower lower chosen chosen part part part previous cases required conditions chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip fact techniques techniques techniques techniques techniques length correct scale minimum simulation simulation multi multi multi multi performed called called called times times elements artificial specific samples compared compared application cross cross cross cross cross active related constraints connected gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain power power power power power power comparison comparison connection connection connection connection connection connection connection train source source source source source proceedings department department synapses synapses synapses synapses synapses consists individual individual difficult difficult bias bias layers delay addition environment environment environment design design design design design design design design san effects effects bit bit bit bit detection detection conference requires free world increase weighted weighted developed developed area area area lines lines lines selected achieved measured measured normal feedforward feedforward limited limited limited circuits circuits circuits common common effective implemented implemented implemented implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse generate vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi development including simulated smaller combination combination reduced fully technology technology mlp testing testing testing testing significantly ratio edge mechanism mode mode operation operation operation leads iterations iterations iterations max bits decay combined produced run perceptron perceptron resolution separate separate typical typical typical reported period identical trees sense array array engineering engineering previously previously module module converge differential achieve address address address storage increased lead scaling suggests digital digital digital digital digital digital deviation wide wide wide width loop loop loop loop loop loop loop loop loop boundary column hardware hardware hardware demonstrate conclusion row row greater reduce reduce reduce numerical numerical numerical peak characteristics characteristics characteristics pulse variety annealing reference reference appears describes laboratory sensitivity electrical electrical electrical electrical electrical integrated integrated shift versus influence variation variation evaluate showed allowed allowed diagram diagram diagram measurements purpose advantages precision precision precision avoid usa currents determines activated coupled coupled tests modification delta literature summary induced contribution running timing board cmos cmos cmos cmos consisted software software modelling diego perturbation access access requirements requirements circuitry varied environments tech parity parity parity parity parity transistor authors hill measurement generalisation generalisation voltages separated academic serial drive sys worst ion potentially acknowledgement bandwidth demonstrates sun summation transient transient flexible offset resistive reliability operate gains gains gains gains gains gains gains gains gains gains reaches plan plan richard coherent patients converged analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue driving count tem saturation proceeds mos fan biased capacitor capacitor capacitor capacitor arrays arrays symposium clock clock clock reset reset separating sion patient patient intended evident sim counter peterson peterson peterson april april offer discovered influences switches acknowledge verify multiplying multiplying leaving leaving ter email kluwer ram die feeding jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri tor rhythm edinburgh edinburgh australia australia australia assess modifying subthreshold subthreshold intra switched switched switched switched switched switched register funded nasa suffer meet flower transients transients transients transients differing september appearing achievable achievable font assistance trainable trainable trainable trainable trainable trainable trainable trainable designs designs designs jointly capacitors capacitors supply morphology morphology morphology morphology morphology morphology morphology optimisation connects burr burr burr station floor floor automation offsets offsets offsets classi archi consumption mcgraw fication steve tra pin february registers talk talk talk talk talk mounted imum custom simula continuing rhythms sydney vdd regional opportunity package signalling named classifica tecture vme cardiac cardiac cardiac specifications neglecting pad implication leong leong leong leong leong leong leong del industry adaptable charging charging charging buffers buffers buffers buffers resistances suc ventricular ventricular ventricular axial publications canberra capacitances modulations comment clocks clocks deci optimised reads marwan marwan marwan cated crosstalk xie xie xie tsividis tsividis urn scotland scotland assisted realisation tachycardia tachycardia tachycardia oth pacemaker photomicrograph photomicrograph ultra philip pace sedal sedal sedal interfaced cult pacemakers pacing sto routinely cessfully 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#@Coggins_R,Jabri_M,
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#*network network network network neural neural neural neural neural neural neural neural neural input input function function function function function function function function figure figure figure figure figure time set networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm output output number state information information information problem problem problem problem problem problem linear linear linear vector vector vector vector order systems systems functions functions neurons neurons neurons neurons unit unit distribution method point image image single processing processing control local local matrix optimal inputs inputs inputs inputs inputs form form form algorithms algorithms algorithms simple simple simple paper paper paper paper work task methods methods field field process current current problems problems problems random high similar similar show show show show equation vectors parameter real theory theory theory gradient gradient gradient note note dimensional result computation solution research research defined found found dynamics dynamics dynamics constant constant computer computer science map map map map maximum press press components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs abstract find convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties properties properties properties properties properties properties references stochastic important important context introduction hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior statistical statistical statistical parallel parallel energy energy complexity complexity variable chosen center theorem binary distributed region region proposed minimum ing ing elements elements elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping optimization optimization optimization optimization optimization potential potential made natural global global study vol compute proc eye related connected distributions discrete mit mit voltage voltage voltage dependent source nets morgan proceedings institute institute implementation implementation implementation implementation implementation implementation implementation advances represents responses exp exp graph ai considered considered framework cambridge cambridge additional view solutions design design san upper speed vision vision vision vision pages pages give developed entropy entropy backpropagation constraint constraint constraint constraint constraint constraint constraint denote fast circuits circuits common supported role theoretical main journal vlsi vlsi vlsi vlsi vlsi vlsi instance instance cluster rumelhart rumelhart rumelhart hopfield hopfield hopfield hopfield technology technology programming interesting matching mode representing numbers numbers max max max international early early combined combined combined added architectures discussed takes element element element element element element element element element element element element reported practical quadratic quadratic volume solve correspond definition separation symmetric modified generalized bounded gate grant exists expression locally locally clusters hardware hardware hardware conclusions editors sigmoid constrained temperature suggest propose strong physics physics characteristics sigmoidal acknowledgements explicit pro derive solving solving winner winner winner winner winner winner ways laboratory laboratory laboratory stability distinct implement implement implement explicitly remaining easy implies competition competition competition national independently review open controlled converges convex symbol foundation koch box figures silicon usa currents currents currents currents currents eigenvalues assignment assignment assignment assignment assignment prove discussions discussions efficiently content content content content content content content content content sci gibbs gibbs paradigm eigenvalue cmos computes satisfies satisfies carried diego essential mead mead mead mead mead mass helpful helpful giving int transistor gates workshop fundamental naturally concepts editor voltages voltages voltages voltages implementations implementations singular noted academic wta wta wta wta wta massachusetts massachusetts theoretic theoretic theoretic publishers derivation derivation derivation defining nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity implementing transistors acad mechanics mechanics detecting resistive resistive resistive resistive resistive resistive cal collective sums implements implements yuille yuille yuille softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax wesley discontinuities addison assign assign formally tation nat robotics plays kaufman saturation adds imposed wire lyapunov passive passive passive passive passive passive passive vertices facilitate peterson peterson peterson peterson peterson enable lazzaro lazzaro vertex eigenvector harris harris harris harris harris harris harris assigns boxes boxes boxes entropic sig kluwer graded encodes incrementally incrementally medium drain drain drain drain jacobian subthreshold subthreshold resistor cessing gener interacting carefully challenging library library geiger geiger geiger geiger enforce tively electronics electronics memo preprint sta simplex simplex simplex nal normalizing reciprocal reciprocal reciprocal reciprocal reciprocal reciprocal reciprocal reciprocal reciprocal reciprocal reciprocal reciprocal 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#@Elfadel_I,Wyatt_J,
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#*network network network network network network learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure figure figure time time time time time time time time time set set networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number system system system system system system system system system system system system system system system system system system system system system system error error information information performance performance performance performance performance performance performance performance performance performance performance weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer case case case vector vector vector order order order shown systems systems systems systems systems parameters weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons distribution approach point point point image image single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing control large large large local local local local local rate patterns patterns shows shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper small size size net net net net net net net net net net net net net work work work work work cells points level level level cell high high high memory memory memory memory architecture architecture architecture architecture line line real real real theory theory note note experiments experiments experiments experiments experiments activity activity dimensional result variables computation computation research research research research research sequence table table table table table table standard standard computer computer computer computer computer computer computer computer computer connections connections science left phase low machine machine sets maximum maximum press learn learn learn components nonlinear continuous continuous abstract applied back back back back back back back back back properties references ieee ieee ieee ieee ieee ieee ieee important important important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation circuit dynamic dynamic parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel search tion tion change difference variable signals chosen chosen part part part part part part previous cases cases type required multiple multiple multiple good good distributed expected errors forward forward forward forward forward scale simulations simulations simulations resulting resulting ing ing total simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation elements elements elements elements elements elements elements elements elements means means means factor made made made applications applications applications applications knowledge specific compared compared compared application series series provide experimental experimental experimental experimental experimental experimental goal connected connected connected connected connected gain equal power steps comparison larger connection connection update update update update support support support support train train source nets nets nets nets nets nets nets nets nets nets nets modeling morgan morgan morgan institute institute implementation implementation implementation implementation implementation implementation implementation implementation internal code code code code code individual individual individual advances advances layers scheme framework cambridge computing computing computing environment environment environment directly hinton additional additional design limit san san san bit bit bit bit bit conference conference conference conference determine efficient choice world world world speed speed speed estimated estimated estimated basic basic basic basic basic basic basic basic basic basic basic basic basic basic pages pages pages pages pages pages pages pages conditional conditional conditional developed controller lines lines path path path path path actual actual actual iteration biological measured measured technical technical fast fast fast limited corresponds complete complete complete complete complete actions circuits circuits amount amount amount short implemented implemented require face end end instance instance instance easily makes makes rumelhart rumelhart including fit kaufmann kaufmann auditory needed needed reduced fully technology technology block block block programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming significantly ratio ratio special special structures structures mode principle language language language language language language language language language language squared numbers numbers direct stored stored international international magnitude idea combined combined produced run run run run run run run run added perceptron takes element element element element element element reported reported machines subset array array array array array array array dimensions highly conventional conventional volume module converge trans locations gate williams storage storage increased parts extended digital wide locally touretzky touretzky occurs hardware hardware demonstrate runs conclusions depend editors editors editors modules peak peak peak moody faster faster faster mateo mateo physics cycle california california user user user user program program program program program program program program program program program program program program question acknowledgements reference reference van construct construct written sequential sequential describes laboratory ann label label implement multilayer category easy easy easy easy easy shift blocks blocks cycles john communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication communication overlap interpretation controlled restricted updated updated static sizes sizes completely updates processor processor processor processor processor processor processor processor key measurements measurements neighborhood purpose purpose remains assigned foundation transactions david david david david david precision avoid existing existing perceptrons batch determines illustrated automatic holds neighbors neighbors importance society mcclelland literature build efficiently allowing video video video interpreted return running running running involved write michael michael michael paradigm backward backward backward backward nips nips board board board board board board computes automatically processors processors overlapping software receive receive receive oriented law simpler simpler simpler simpler simpler command command command command command carried diego access access collection requirements requirements experience put hanson issues lippmann mass links project project project terminal combine working stream proved cognition fundamental editor editor editor created implementations implementations implementations subsets subsets front front algo consist contributions serial defines optimum devices mentioned great publishers defining floating floating floating capabilities tool drive drive lin lin ring ring ring ring ring ring widely producing desirable scientific computers computers bandwidth sun sun sun sun sun sun researchers virtual flexible flexible flexible tional embedded capability experimentally peter peter peter effort effort music music music music music music music music music music music music music music music music music music music music music music music music music music music music frequently commands requirement stack partitioning summarized spread instruction instruction richard simulator simulator kinds neuro neuro neuro neuro neuro synchronization realized realized don don shifted ordinary interface interface interface interface interface interface interface interface interface interface tation acm rithm branches branches branches flexibility flexibility flexibility arrival extending cellular cellular cellular cellular cellular cellular saturation alpha city intelligent intelligent programmable loops loops balance affected north responsible clock clock clock carry degradation motivation published mance programs james james zhang perfor holland overview overview overview realization realization counting yang yang tokens april express cpu passing projects valuable propagate propagate propagate instructions explorations executed robert usage microstructure ter achieving achieving achieving super bus bus validity ram ram ram july nelson forced year copy simd simd simd simd workstation workstation workstation workstation workstation workstation stands stands gene transparent mhz mhz mhz mhz mhz graduate token pomerleau books parallelism host host host host host host host host interactive interactive interactive interactive exceed speedup speedup speedup speedup speedup represen meta library million setup setup attached register funded electronics exchange meet likewise loading elsevier dsp port port october october october october worked november students nec nec august decided send european spring ers doesn neighborhoods suite suite interpreting exper micro steven station fastest consumption invisible invisible comm comm comm comm comm comm comm ready ready scott magazine bradford format pointer investment mul dean huge propagates replicate insert amsterdam operated pes pes manager manager manager phil klaus week wait copied switzerland warp warp named named classifica rap cooling cooling gun munich continuation boards walter walter walter 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#@Gunzinger_A,Kocheisen_M,Muller_U,
#t7
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data function function function figure figure figure figure figure figure figure set set set set set set set networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number system system system error error state state state state state state state state results units units units units units units units information problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden performance space space space weights weights weights weights weights weights weights weights weights weights weights weights layer layer order order shown shown shown systems systems values values values values values values probability probability probability probability probability weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single processing control control control control large local local local local local neuron neuron rate rate rate rate rate rate test patterns patterns patterns patterns patterns patterns inputs inputs inputs inputs inputs form form form shows shows shows simple size work methods methods step step step field field field field field process current current current current current current trained problems problems problems problems problems problems problems problems problems problems random high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory architecture general general parameter states theory theory gradient gradient note result university variables computation computation solution solution research research independent independent found found initial initial table table computer terms distance science left left left phase phase phase phase phase phase phase phase phase activation activation activation activation activation activation activation activation activation activation activation activation activation activation low low nodes frequency machine machine machine machine maximum range press press outputs outputs outputs outputs outputs continuous abstract back back find find analog analog references stochastic stochastic stochastic stochastic due due ieee ieee important important introduction circuit circuit circuit dynamic dynamic dynamic parallel parallel parallel parallel parallel tion tion change change energy energy energy energy energy lower lower lower lower signals higher part center previous binary binary represent represent represent distributed chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip fact finite simulations minimum classes total simulation simulation multi multi eq eq called called means means means optimization global global applications specific application desired desired cross provide compute compute rates proc perform experimental constraints constraints constraints constraints constraints connected power power power power power power power voltage voltage steps connection connection update update update update update update update update update update update support support descent descent descent morgan department loss implementation version synapses consists consists code advances final final final final final delay computing directly directly hinton hinton hinton hinton hinton hinton hinton view design design design design design san top bit bit conference capacity efficient full full free free speed speed speed speed give con randomly developed developed area lines entropy actual provided depends constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint achieved arbitrary arbitrary fast fast fast limited inverse corresponds complete circuits circuits circuits amount effective theoretical require main main main eds eds eds end end end end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi instance future easily kaufmann simulated simulated simulated typically reduced functional functional functional functional fully technology block block block transfer testing testing york edge special mode operation operation operation operation leads stored bits international bottom depth early attention minimize run light improved recent typical machines machines machines side sense array cognitive engineering teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher calculated volume module tions tions solve evaluation locations symmetric modified gate organization storage storage storage storage storage storage storage grant lead digital digital digital digital digital digital digital digital digital digital deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic occurs generally hardware hardware minimal reduce conclusions valued sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid modules designed performs performs performs moody mateo temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature external external external california solid proportional assuming minimizing user user minima minima minima minima program annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann appears written solving confidence recall recall recall recall recall student student student student student student student student student student student student student student implement simultaneously electrical electrical electrical electrical remaining unique frequencies blocks yield independently stages communication updated updated updated soft static static updates updates allowed allowed processor processor diagram diagram partial slow slow sec sec sec sec sec roughly roughly purpose sufficiently topology topology topology david precision avoid silicon activations activations activations activations activations activations activations activations activations activations activations activations activations activations memories candidate candidate black efficiency effectively effectively wij successful road repeated running hold duration built vary vary write write michael board board board board board board board cmos chips chips chips processors processors processors processors processors processors processors processors processors processors processors processors received software software software explore schedule schedule schedule schedule powerful wiley perturbation perturbation difficulty circuitry circuitry steady detail hanson limitations limitations lippmann hall hall reducing rest mappings relationships scaled working phases phases hill concepts extremely implementations implementations implementations versions versions mapped logic initialized store store store store store store mentioned great great ment slowly crucial crucial slope slope stanford stanford implementing berkeley purposes incorporate transistors products gradually read read read lowest lowest lowest sun raw explained virtual virtual passed instruction monotonic instantaneous room interface interface interface interface interface interface interface modify extensive extensive martin linearity linearity linearity circular flexibility interconnected clamped clamped clamped clamped communications murray murray murray murray murray accepted held held attractive programmable los los imply responsible adequate arrays symposium clock clock clock clock clock alspector alspector prentice prentice reset james buffer schwartz schwartz schwartz schwartz peterson peterson peterson peterson peterson peterson multiplied layout repeatedly late sustained sustained steepest park card inductive fold avoiding explorations sequentially sequentially temperatures unified stork stork stork stork stork stork stork ram benefits bank bank bank bank revealed employs die die die ease capacitance mhz mhz mhz insights annealed annealed annealed annealed annealed annealed annealed annealed annealed annealed permits convert overhead host host lookup nasa supports minor rotating rotating rotating rotating transients reciprocal corrections supporting inactive rarely gratefully satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction satisfaction fortunately council excess august allen insufficient assistance send loaded loaded loaded loaded loaded 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#@Boonyanit_K,Burr_J,Kritayakirana_K,Leung_M,Murray_M,Peterson_A,Schwartz_E,Stork_D,Watanabe_T,Wolff_G,
#t7
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#*network network network network network network network model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time set networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number system system system system system units information information information performance performance performance performance performance based space space space weights order shown shown shown systems systems systems systems systems systems values values probability probability probability neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution method method single single single processing processing large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns analysis shows shows shows shows algorithms simple visual visual visual visual visual small small small size size size size size work work work task methods fig fig fig cells cells cells cells cells step step step step step step process level current cell cell cell cell cell cell cell structure structure random high high memory representation architecture architecture architecture general real average average average average theory obtained obtained obtained obtained obtained note note note activity activity dimensional variables computation computation computation research research research independent independent log found dynamics dynamics estimate connections connections connections connections connections connections science present present low temporal temporal temporal temporal machine machine machine machine machine press abstract back computational references due due due ieee important important propagation propagation propagation propagation introduction action action behavior effect parallel parallel parallel parallel parallel parallel tion change difference difference difference difference difference complexity complexity lower lower rules higher part part part previous cases firing required required required cortex cortex cortex binary binary spike spike spike spike spike spike spike spike spike spike long distributed expected expected equations fact fact observed scale simulations tasks total simulation simulation simulation simulation simulation simulation simulation simulation computed performed eq eq eq eq eq mapping factor factor factor factor potential study study obtain artificial represented represented compared compared cross provide provide rates rates active determined related cortical cortical equal approaches mit larger larger larger contrast connection connection support dependent modeling modeling morgan proceedings institute implementation implementation implementation implementation synapses synapses synapses code responses scheme cambridge computing computing computing experiment curve additional additional additional additional additional curves curves curves estimates san efficient efficient efficient efficient efficient efficient efficient efficient efficient upper full pages pages pages provided provided biological biological biological biological biological biological increases denote limited limited limited short nearest implemented implemented implemented implemented synapse synapse synapse synapse synapse generate supported role require main instance makes kaufmann simulated simulated simulated simulated simulated reduced functional fully technology significantly ratio ratio ratio increasing head structures operation representing details numbers numbers direct direct direct direct direct direct neuronal neuronal neuronal neuronal neuronal architectures improved discussed discussed advantage takes trees array interest highly highly highly compare previously approximately trans storage storage storage storage scaling spikes spikes spikes spikes spikes spikes spikes spikes touretzky deterministic column column conclusion neighbor editors editors interactions retina numerical clear peak mateo encoding integration largest characteristics california connectivity connectivity force van primary primary laboratory laboratory vertical changing explicitly slightly text scales scales consisting consisting events events events potentials national national expressed communication communication communication partition partition partition partition processor processor processor processor processor processor processor earlier delays penalty foundation koch koch koch koch koch koch koch transactions expect fire fire usa usa inter determines determines coupled black partially discussions major identified efficiency maximal maximal maximal maximal effectively effectively delta spiking spiking spiking spiking oscillatory efficiently essentially essentially fine follow hold simplified realistic realistic realistic providing delayed delayed highest cat neurosci neurosci processors processors processors processors processors processors processors processors processors processors trains powerful rapidly accurately helpful postsynaptic ideal ideal ideal ideal office office func neu smallest editor algo generates integrate advanced agreement growing analytical drive implementing located monkey scientific describing incomplete virtual virtual tional simulate simulate completion biologically biologically biologically compares ity execution execution execution poisson limiting spread aim gen cal occurrence occurrence pasadena pasadena singer singer datasets simulator simulator simulator simulator simulator indices tation rithm ratios ratios resources neurophysiol neurophysiol partitions partitions partitions partitions partitions unity addresses addresses naval interconnected interconnected caltech spontaneous air bower bower occurred primate los los efficacy performances mance irregular zhang zhang perfor evident accounts sim propagated scheduling modelled modelled arrows hypercube hypercube stone acknowledge dividing basically isotropic propagating simd simulating simulating massively massively massively massively stands disadvantage crosses crosses overhead overhead overhead overhead macaque speedup speedup speedup speedup speedup speedup speedup speedup speedup speedup speedup speedup speedup speedup signs challenge stimulating allen attributed thousand impulses impulses hamilton carrier essen rons rare rare ally inefficient nontrivial communicate communicate fair tations bottleneck alamos alamos tained dean addi moderately rises demanding broadcast continuing touch wait wait awake niebur niebur niebur niebur niebur intel genesis segev epsps softky softky originating dong timestep vation waltz mission publications absolutely quired asymmetrical implemen implemen diamonds diamonds diamonds grand mckenna crucially transposed transposed transposed transposed transposed transposed transposed transposed transposed transposed transposed richmond richmond legend optican optican subcortical infrequent erating commu sistent decisive munication ernst supercomputers nication communicates mildly facility refs puters holt 
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural input input input input input input data data function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number system error error error state results results results information information information information information information information information information information information problem problem problem problem problem models performance performance performance based based based based space space shown systems values values values values probability noise functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons recognition recognition recognition method approach approach approach approach approach approach approach point point image image image image image image image single single single processing processing processing large large test test test patterns patterns patterns patterns patterns patterns class class inputs inputs inputs form form shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper examples examples examples examples examples examples examples examples examples small size size feature feature feature work task step points field field features features features features classification classification process level level level level level current cell problems problems problems problems problems random high high high similar similar representation representation architecture show show section fixed images images general general general real average average theory gradient obtained obtained experiments threshold variables variables variables variables variables variables variables variables solution solution solution research research independent independent log defined found found found target target target target target table table standard standard standard distance node node node node node node node node node node node node node node node node node node node node node node presented nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine sets sets maximum press learn learn outputs outputs outputs sample abstract find find find analog analog analog properties references stochastic ieee procedure decision decision decision decision decision decision decision decision decision decision decision context introduction complex complex complex complex complex complex hand generated generated cost cost search search tion complexity complexity complexity complexity complexity variable variable variable variable variable variable variable measure measure measure representations higher center cases cases cases type type required required required binary binary binary binary binary tree tree tree tree tree tree tree techniques techniques proposed proposed proposed proposed correlation correlation length probabilities observed observed errors scale resulting resulting ing tasks tasks tasks multi multi performed performed performed called called called times times regions optimization made natural global applications applications applications applications applications applications applications applications applications applications study knowledge knowledge obtain original original artificial specific specific samples true true true compared desired provide provide active active active active equal equal power approaches approaches accuracy accuracy accuracy accuracy larger larger support train descent modeling selection morgan morgan proceedings proceedings code code code code advances joint scheme scheme graph graph domain domain equivalent equivalent experiment experiment additional solutions design design design design san san bit bit conference efficient full choice statistics speed speed speed basic pages pages pages pages pages increase con randomly area types entropy selected selected selected selected selected selected nature normal technical tested tested tested tested tested tested limited complete complete circuits finding finding amount short effective implemented assumed generate generate generate generate supported theoretical require main main journal journal vlsi pixel pixel ability makes makes development noisy kaufmann kaufmann objective objective underlying reduced technology interesting character character character york edge consistent consistent database empirical empirical language max max pre pre pre direct international normalized supervised idea added description description description description improve improve improve improve improve improve improve exact advantage takes trees trees trees trees volume works works works correspond achieve evaluation generalized grid gate gate sensitive increased increased grant digital digital digital digital digital digital alternative alternative touretzky runs runs runs starting minimal row valued valued depend depend measures designed performs faster mateo mateo encoding encoding encoding encoding taking hard solid intelligence labeled labeled labeled labeled labeled labeled labeled pulse pulse minimizing characters program pro derive edges edges written primary describes label label distinct dept implement explicitly remaining remaining mutual mutual mutual mutual mutual predictive boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean select select select select select select select letters national reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction viewed viewed codes solved evaluate evaluate operations restricted labels labels labels labels labels modulation similarly digits digits digits partition partition partition slow performing add false false generation valid initially initially construction precision handwritten handwritten handwritten thesis bell illustrated prove uncertainty uncertainty uncertainty maximize candidate domains selecting identified suitable maximal maximal encoded identify build reached reached reached reached characteristic compact compact compact compact compact graphs prob heuristic heuristic success success success success success return return classify classify running gray built built built list list list list generalize generalize generalize paradigm computes processors consisted routing simpler xor xor xor investigate exhibit put detail matches applicable terminal terminal terminal terminal combine root stream stream encode attributes induction induction smallest act act act act act act act act act act act act act act act act act act act act act act act act act act act closest editor implementations implementations implementations greedy greedy greedy algo logic switching improving phd rows asynchronous directed failure floating expensive expensive cascade cascade lin lin lin lin berkeley berkeley berkeley sections arc commonly attribute attribute attribute attribute attribute attribute computers improvements composite freeman flexible pseudo pseudo poorly posed haussler haussler haussler haussler haussler haussler compares partitioning partitioning measuring aim maximizes maximizes suited logp hamming segmented age implements implements calls arithmetic consistently corrupted corrupted corrupted benefit identifying sort sort sort restrict fix rithm reconstructed discovery repre exemplar fails fails fails fails smith smith smith wrong murray murray murray programmable keeping definitions splitting disjoint guide modifications preparation arrays carry selects selects hours published programs yang yang yang iterated warmuth informative correcting correcting correcting inductive inductive dietterich dietterich dietterich fahlman fahlman fahlman stopped johnson johnson johnson informa listed annals accept accept accept accept accept ram failed comparative additionally additionally descriptions descriptions descriptions certainty auxiliary concentrated formance individually quinlan quinlan quinlan quinlan alternatives sized electronics minor exhibited dsp aaai mea technologies lems fortunately nist preserves identifies identifies ongoing designs doesn rissanen rissanen rissanen codeword automation dedicated anthony alan inefficient placement outgoing outgoing occam occam occam explanations fastest acyclic derives february inappropriate sented sorted completeness ceedings custom lebiere lebiere lebiere unifying sentations plexity blumer blumer blumer dnf dnf dnf package package ninth prohibitively counterparts sorts boards razor razor razor routed multiclass comparatively ehrenfeucht plied rooted avail services occupies carl bakiri bakiri bakiri intractability hadamard slowest eecs runtime merits tains designers nmnber rot rot compactness compactness garey garey garey xiy xiy str str greedily 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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time set networks networks networks networks networks networks algorithm algorithm algorithm algorithm output output output output output output output output output number number number number state information based based weights linear layer order shown shown shown shown shown shown shown shown systems systems systems systems systems noise weight weight weight weight weight functions functions functions functions functions neurons neurons point image image image image single single single processing processing processing processing control control control control control control control control large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test test patterns inputs inputs inputs inputs inputs shows signal signal algorithms algorithms simple work work work fig fig fig fig fig fig fig fig fig fig fig fig fig field field classification process process level level level level level level current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure high high high high high high memory memory memory memory memory memory memory response representation architecture architecture architecture architecture fixed rule rule rule real real real real real experiments activity result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables computation computation computation computation research research research found found found initial constant constant constant connections connections connections connections synaptic synaptic synaptic synaptic science left present low outputs outputs sample sample abstract applied applied applied applied back back density analog analog analog analog analog analog analog analog references due due due ieee ieee ieee ieee ieee positive important introduction action circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior effect effect generated generated search change change complexity variable variable variable variable variable variable variable variable variable variable signals signals signals signals signals learned part part previous previous previous multiple multiple multiple multiple binary binary binary binary binary binary binary binary represent represent represent chip chip chip chip techniques resulting sum sum sum sum sum called called factor potential potential made made made feedback applications applications applications negative original vol vol vol vol vol vol vol represented represented compared application proc location perform determined determined experimental equal equal power voltage voltage voltage voltage voltage voltage voltage larger larger connection connection connection dependent source source source source source source institute department implementation implementation implementation implementation implementation implementation version joint directly directly directly directly directly directly design design design design top top top stage stage detection conference full basic basic basic basic basic basic con channel channel weighted weighted weighted weighted weighted developed developed developed lines provided processes backpropagation backpropagation nature inhibitory inhibitory inhibitory inhibitory simply biological biological biological biological biological associative associative associative associative achieved measured measured measured measured technical technical technical increases increases excitatory excitatory actions circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits short common common common common effective effective implemented implemented implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse supported main main main main vlsi pixel instance instance instance easily easily degree development smaller functional functional functional functional functional functional functional functional functional functional functional functional technology technology technology programming programming programming programming programming interesting interesting interesting interesting ratio edge structures matching matching matching matching mode mode principle principle operation operation operation details call pre pre pre pre pre pre direct window stored stored bits bits international bottom bottom bottom magnitude combined neuronal neuronal architectures pair similarity similarity similarity similarity similarity practical identical array array engineering highly conventional conventional conventional conventional conventional yields studies studies differential differential trans trans trans trans trans modified gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate organization sensitive grant grant constructed intensity occur digital feed width loop hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware demonstrate flow strength valued competitive competitive modules peak taking largest largest external reduction reduction reduction reduction characteristics characteristics characteristics characteristics characteristics demonstrated demonstrated demonstrated demonstrated demonstrated demonstrated intelligence intelligence intelligence intelligence pulse pulse turn turn turn turn averaged manner configuration configuration configuration areas winner winner winner winner winner factors laboratory implement simultaneously electrical unique integrated integrated integrated integrated integrated integrated formed boolean boolean extracted depending communication operations operations forms soft soft soft soft soft soft diagram key key slow msec msec coupling coupling coupling coupling coupling coupling building building template template silicon silicon silicon silicon silicon silicon inter weighting weighting activated coupled coupled coupled partially characterized characterized simplicity reason regular sensor sensor sensor modification paths build build computations post tend tend essentially composed summary cun allowing allowing allowing issue device device device device device device simplified play wave cmos cmos cmos leading thresholds automatically principles overlapping software employed employed carried carried powerful powerful xor xor xor xor essential essential essential difficulty circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry exponentially updating updating updating updating updating varied association dual giving ideas ideas tech tech tech tech tech rest terminal terminal terminal terminal terminal terminal plasticity plasticity transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor gates symbolic matched matched matched math created changed changed voltages noted logic logic logic logic logic logic logic logic logic logic logic logic logic logic logic nervous hebb arbitrarily finds electronic electronic electronic electronic electronic wta wta wta optimum charge devices devices devices devices devices great floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating capabilities turns implementing implementing implementing implementing implementing transistors transistors transistors transistors transistors transistors transistors transistors pulses pulses pulses cut scientific scientific read lowest apparent apparent double conducted conducted capability capability capability fed peaks schematic synthesis synthesis logical electric sophisticated conclude june yielding sharing realized pose room fabricated bipolar bipolar japan japan linearity linearity count flexibility flexibility flexibility enhancement inspired imaging significance adjusting mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos intelligent intelligent intelligent intelligent intelligent intelligent intelligent intelligent roles exceeds symposium fires motivation exploring excellent injection dendrite dendrite facilitate interconnections interconnections creating clean verification papers papers papers papers receiving counts fired fired crossing indirect ent super creates terminals terminals drain simulating simulating electrode electrode electrode manipulation capacitance capacitance capacitance learnt elementary oct simplifying parallelism parallelism complementary complementary figs figs inverting loading amplification dramatic dramatic dramatic article tunneling tunneling tunneling tunneling tunneling tunneling 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#*network network model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks output output number number number system system system system system state state state results results information information models models performance linear shown shown shown shown shown shown shown systems systems systems systems systems parameters parameters parameters parameters parameters parameters parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons pattern pattern single single processing large large large large large large large neuron neuron neuron neuron neuron neuron 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complex complex complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior generated generated tion change variable spatial prior prior part firing firing firing firing type required spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike distributed make scale ing total simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation elements elements elements elements optimization potential made feedback feedback feedback applications negative artificial relative represented desired series define compute perform constraints cortical cortical cortical cortical mit mit voltage voltage dependent dependent dependent modeling proceedings institute institute institute implementation synapses synapses synapses synapses synapses synapses synapses synapses consists bias delay sequences cambridge directly san san top top stimuli stimuli conference efficient efficient full basic produce channel channel channel coding developed developed developed levels inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological biological biological associative tested fast fast fast assumption excitatory excitatory excitatory circuits circuits circuits circuits circuits circuits circuits short common synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse supported supported eds adaptation adaptation journal journal end end vlsi vlsi vlsi vlsi vlsi vlsi future including including auditory auditory auditory simulated simulated simulated typically combination technology technology transfer york mechanism structures principle run predict predict membrane membrane improve movement include period period period hierarchical hierarchical varying varying varying previously correspond studies studies studies sparse sensitive increased amplitude intensity lead spikes spikes spikes spikes loop runs conclusion trajectories central central designed designed designed sound sound physics external california labeled labeled pulse pulse pulse pulse pulse turn user program program acknowledgements pro van written plot laboratory distinct implement slightly text consisting integrated integrated frequencies events events john john john john review detailed detailed detailed labels fraction diagram key reasonable delays delays delays event event event event event event event event event event event event symbol symbol topology david david fire fire includes silicon silicon thesis strings currents currents currents currents inter memories plotted plotted plotted plotted characterized capable society society driven driven driven driven driven driven 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input function function function function function function function function figure figure figure figure time time time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number system system system system system system system system system system system system error error error error error error error error error error error error error state state state state results results units units units units information information information information information information information problem problem models models models models models models hidden hidden hidden hidden hidden hidden based based based based based space space space space space weights weights layer layer layer layer layer layer layer layer case case case case case case case vector vector vector vector vector vector order order shown shown shown shown systems systems systems systems systems values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight neurons unit distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach pattern pattern point point point image image image image image single single single single single single single processing processing processing processing control large large large large large large local local local local local local local local local local patterns patterns patterns patterns class class inputs form signal gaussian paper size size size size size feature feature feature feature feature feature feature feature feature points points points points points field features features features features features features classification level level level level level level level level level level level level level level level level level level trained trained trained trained trained trained trained structure structure structure structure structure problems high high similar representation representation representation representation architecture architecture architecture architecture architecture architecture equation section line line line line line line line line line line line vectors vectors vectors vectors images images images general generalization generalization speech speech speech parameter parameter average gradient gradient gradient obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained experiments experiments experiments experiments experiments dimensional university threshold variables variables independent independent independent independent independent independent log log log log log defined found found sequence sequence sequence sequence sequence target standard standard standard node left direction direction low low temporal sets motion motion range position position position position position position position outputs outputs outputs outputs sample abstract applied applied back back find convergence density density density references stochastic ieee ieee ieee procedure important important propagation propagation mixture mixture mixture context context introduction hand dynamic dynamic generated parallel cost cost cost search search tion tion complexity spatial spatial assume classifier lower lower lower lower lower lower lower lower measure prior representations representations representations representations representations word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word chosen chosen chosen center previous previous required multiple multiple multiple long represent represent distributed expected markov markov markov markov markov techniques proposed correct correct correct correct correct correct probabilities probabilities observed observed errors errors errors errors errors errors errors errors forward tasks total computed computed computed respect respect respect multi multi sum performed performed performed performed performed performed performed called called called called called means optimization dimension natural natural natural orientation global global global global global em em em em negative relative relative relative relative relative represented cross series series rates rates rates rates proc proc location location determined determined experimental constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected connected distributions equal approaches accuracy accuracy comparison larger fields descent morgan morgan report words words words words words words words words words words words words implementation version 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robust element element element identical identical side subset array array highly observations observations volume volume module smooth smooth smooth smooth yields correspond trans positions positions locations locations locations observation observation observation observation observation observation generalized williams organization sensitive entire entire entire entire constructed parts parts extended correctly feed hybrid boundary generally generally strength conclusion assumptions trajectories trajectories segment segment segment segment depend editors editors editors modules designed performs moody practice constrained mateo propose propose propose taking taking strong drawn demonstrated minimizing minimizing targets introduce characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters connectivity minima minima minima configuration base digit van derive construct produces produces produces written sequential sequential sequential generating transitions transitions vertical vertical vertical dept segments segments segments segments sensitivity multilayer coordinates transformations transformations slightly angle interaction mutual adding frequencies gaussians springer yield extracted extracted dependence viewed viewed interpretation interpretation interpretation interpretation solved variation transform evaluated evaluated centered translation translation digits processor processor processor past earlier performing normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization reduces fitting fitting fitting neighborhood generation distances assigned euclidean advantages transactions avoid handwritten handwritten handwritten handwritten handwritten handwritten handwritten box box kernels kernels kernels combinations priori priori strings bell bell bell recognize recognize recognize maximize candidate candidate candidate candidate priors priors coupled absolute grammar grammar grammar grammar tests tests hmms hmms hmms hmms computationally paths paths paths symbols detect tdnn post post post post score tend ten compact verlag cun cun cun cun cun cun cun cun cun cun cun cun cun allowing interpreted contribution follow strategies built delayed computes denker denker denker denker hypotheses maximization overlapping extract presents unlike essential essential relations optimized integral integral discriminant discriminant discriminant reducing successive terminal analytically combine reliable decisions decisions maximizing proper variability scores scores scores scores cover cognition gradients possibly editor recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer thought detector art baseline baseline baseline baseline generates generates mixed finds isolated integrate devices devices costs crucial publishers convolution convolution convolution convolution coded correction spatially perspective sys arc arc shared producing preprocessing preprocessing preprocessing style incorporate located bengio bengio bengio bengio bengio bengio bengio controls cut separately separately separately toronto definite lowest depicted geometry recognizing recognizing recognizing raw raw robustness requiring geometric improvements improvements improvements greatly greatly flexible parameterized readily share share incorrect rep maxima maxima maxima howard spread spread prevent curvature curvature curvature curvature suited asymmetric sophisticated segmented segmented deviations baird sentence multidimensional multidimensional yielding sharing irrelevant globally globally globally globally globally picture writing writing writing perfectly ordering ordering approximates concerned repre tem connecting printed rotations lecun arranged kaufman tools city stated height height handwriting handwriting handwriting handwriting handwriting handwriting handwriting exploit exploit observing optimally enhanced published excellent ensures jackel jackel propagated propagated candidates elastic dif recog recog shortest likelihoods likelihoods pen pen pen pen pen pen pen pen cam explorations displacement displacement displacement boxes fitted fitted informa associations arcs geometrical geometrical geometrical geometrical geometrical drop drop drop drop microstructure ter piece accept guyon guyon guyon convolutional convolutional convolutional convolutional convolutional convolutional ties nition nition boser decomposed classifies associate forcing auxiliary auxiliary representa constrain burges burges burges henderson henderson henderson henderson henderson henderson stroke stroke stroke stroke stroke pami ijcnn labs labs labs intra crosses compatible writer writer writer writer writer simplifying books proach unconstrained ambiguous 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#*network network learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model input input input input input input input data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set training training training training training training algorithm algorithm number number number number number number number system system system system system system error results results results results units units units units units units units units problem problem problem models models models models models models models models models models models models hidden performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based space space space space space space space space linear layer layer layer vector vector vector vector vector order shown shown shown values values parameters parameters unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method approach approach approach image image image image image image image image image image single single single single processing processing local rate rate rate rate rate rate test analysis inputs form form shows shows shows shows shows shows shows signal signal simple simple simple simple gaussian gaussian visual examples examples examples examples small small small feature feature feature feature feature feature feature net work work task task task task points points features features classification classification classification classification classification classification classification classification process level current trained trained high response response response response response similar similar similar similar similar representation representation representation representation representation representation representation representation representation representation representation fixed fixed fixed fixed line vectors vectors vectors images images images images images images images images images images images general general general speech parameter parameter parameter real real real real real real real real real obtained obtained dimensional dimensional dimensional dimensional threshold threshold threshold threshold threshold threshold computation computation independent found found found found found found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target dynamics initial estimate terms distance distance distance distance distance distance left direction present present low low low low low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine machine machine machine machine object object object object object object object object object object sets motion maximum maximum range press learn learn position position position position outputs outputs outputs sample sample abstract applied find find properties properties references due ieee ieee ieee ieee ieee procedure important adaptive adaptive adaptive context context introduction complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand stimulus dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated variance variance cost search search variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial classifier classifier classifier classifier classifier classifier classifier classifier word learned center previous cases required good good good long conditions represent represent distributed distributed distributed distributed distributed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed scale minimum tasks human human human computed computed respect multi multi performed regions optimization made made applications applications applications obtain vol vol vol vol vol relative specific specific true desired cross series provide objects objects objects objects objects objects rates proc proc location perform perform perform constraints approaches mit mit mit steps larger train technique represents responses responses responses responses difficult difficult final scheme scheme scheme sequences sequences sequences sequences sequences sequences sequences sequences ai computing computing domain domain domain experiment directly directly directly curve additional view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view curves stage stage stage stage detection efficient classifiers full full statistics statistics free free vision vision vision vision con condition coding randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering robot bounds types actual actual actual provided provided selected nature sampling simply achieved group group tested transformation transformation surface surface surface actions finding finding nearest implemented implemented shape generate journal pixel pixel pixel ability ability degree degree degree degree including needed needed combination reduced fully fully mlp mlp mlp programming programming testing york segmentation special special structures trials trials matching matching matching principle representing normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized supervised supervised supervised depth frame frame frame idea produced run perceptron perceptron advantage advantage ensemble side side side side sense subset cognitive relevant relevant relevant relevant dimensions previously conventional conventional unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised approximately works tuning tuning tuning axis axis axis axis axis match converge converge achieve achieve achieve trans diagonal sparse sparse locations storage entire entire entire increased constructed horizontal parts parts occur trial rotation rotation rotation rotation correctly demonstrate runs half half conclusion greater reduce reduce reduce learns demonstrated labeled turn user user user user user minima base base explicit derive construct construct index plot plot describes tuned vertical metric metric physical dimensionality dimensionality dimensionality transformations remaining angle angle angle angle angle interaction develop extraction yield family focus dependence reconstruction stages communication communication interpretation solved variation transform updated frames forms static static completely processor processor performing performing spaces convex convex reduces roughly roughly purpose false false false false tracking tracking tracking tracking tracking tracking tracking advantages faces views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views degrees degrees degrees degrees recorded existing box box box box figures perceptual perceptual combinations instances instances instances instances subspace recognize recognize plotted automatic major aspects aspects maximal poggio poggio poggio build score score score score score score score score plots capture traditional neuroscience classify running follow strategies strategies cues list involved vary wave wave quantization quantization automatically illustrates subsequent extract extend camera camera camera body body simpler powerful collection difficulty matches behavioral applicable eigenvectors workshop workshop workshop workshop workshop scores scores scores scores scores scores matched act coarse man created created thought aspect established sensors track analyzed fairly expensive considerable sections broad ran commonly recognized recognizing recognizing qualitative qualitative composite collected empirically empirically flexible offset spoken passed continuously templates templates span span synthesis rely characterize differs extracting synchrony gave converged yielding univ pose pose pose bellman person classifying classifying classifying classifying lab lab lab feasible appearance interface princeton princeton rotated repre rotations rotations rigid rigid rigid rigid imaging held held city hit hit hit illumination illumination salient adequate edelman encountered overview overview overview intended demonstration viewing recovery recog infer gaze gaze gaze gaze gaze record vertex gesture gesture gesture gesture gesture gesture gesture gesture gesture automated ccd users kinematics pointing failed failed pentland pentland pentland pentland pentland pentland nition poses poses poses poses spatio spatio spatio spatio spatio spatio spatio classifications additionally warping warping warping warping examining conservative acting summarizes pami ullman ullman acquired interactive intensities nonetheless alarm alarm memo rotating rotating rotating rotating rotating stuck covers gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures gestures lated attempting establishes interpreting broadly alex unreliable alarms alarms interpolating characterizes joints interpolate interpolate interpolate suffice assp dimen dimen articulation materials merged media media sentation derives adequately eigenfunctions eigenfaces spotting dtw tracked tracked excluded gross hands hands hands hands hands localize localize coverage darrell darrell darrell darrell darrell prohibitively articulated accelerator exclude workstations spans fingers fingers undergoing trevor turk turk makhoul warped interfaces interfaces gish advocated shashua finely sionality sionality semantically mase parallax interactively taining wrist beymer affords facets 
#@Darrell_T,Pentland_A,
#t7
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#*network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model neural neural neural input function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure networks number number system system system system results results units units units units information information information problem models models models performance performance based based based based based based space space space space space linear linear linear order order order order order order shown shown shown shown systems noise noise noise noise noise noise noise functions distribution distribution distribution method pattern point image image image single single processing local local local local local local local local local local local test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns form shows shows simple gaussian visual visual visual visual visual work cells cells step cell random random random random random response similar similar show show show show equation images images images images images images images images real real real real real real real approximation average gradient gradient obtained experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional result university computation computation research left left left direction phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency machine maximum maximum range press press press position position components components components components abstract computational computational computational computational computational density properties references component component component component ieee ieee introduction complex complex complex generated generated generated generated generated change change change change change change energy difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume lower lower higher part part center center center cortex good distributed techniques techniques region region region region region region region region region proposed forward simulations simulations minimum simulation human human human human human human human human computed computed computed respect eq regions orientation orientation orientation orientation orientation orientation global global global study obtain vol vol vol artificial artificial artificial specific specific specific specific objects proc proc determined determined experimental constraints cortical approaches mit comparison contrast descent modeling institute department technique consists consists individual responses difficult cambridge domain domain domain domain domain domain view view curves top top top stage stage stage stage stage stage stage stage stage stage stage stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects detection determine determine vision vision vision vision vision vision produce produce condition randomly randomly area path actual actual processes evidence nature biological denote tested tested transformation transformation transformation limited assumption corresponds corresponds surface surface surface surface surface surface amount implemented shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape supported journal including including including simulated simulated underlying account technology character projection segmentation mechanism mechanism mechanism mechanism mechanism mechanism max max direct making inhibition inhibition inhibition inhibition inhibition normalized normalized normalized normalized normalized bottom bottom bottom bottom bottom depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth early early early early produced produced recent takes lateral lateral lateral lateral lateral identical identical cognitive observations smooth address positions channels channels channels constructed constructed horizontal suggests suggests feed locally locally white white white white white white white boundary half conclusions peak peak peak peak peak peak constrained suggest suggest propose propose propose taking taking taking strong mechanisms integration integration integration integration integration integration characteristics min plane plane plane averaged averaged averaged averaged averaged program question denoted relation relation relation relation edges perception perception perception perception perception perception perception perception perception perception perception optical tuned vertical vertical vertical vertical physical spectral consisting frequencies frequencies frequencies frequencies extraction extraction extraction independently stages stages viewed controlled decomposition approximated discrimination processor spectrum normalization normalization normalization normalization normalization foundation avoid coordinate sciences determines plotted texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture major major major major major regular regular regular regular regular regular regular compression compression compression compression compression compression compression compression compression compression compression compression compression compression middle aspects invariance soc video showing neuroscience physiological cue cue cue cue cues cues bar wavelet wavelet computes computes acknowledgments oriented oriented camera camera employed simpler carried carried carried access environments humans humans integral accurately preliminary periodic fourier fourier fourier fourier fourier fourier examine biol office momentum surfaces measurement gradients psychology created created academic academic consist detected detected cos agreement agreement agreement agreement orientations orientations orientations capabilities spatially spatially spatially spatially processed perspective perspective closer constructing arise opt res lowest lowest lowest lowest qualitative qualitative alignment alignment integrating affine embedded conducted quantitative quantitative quantitative psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical biologically schematic schematic rely characterize serve simulator begins spectra spectra spectra spectra spectra spectra spectra spectra spectra indices cybern aligned aligned naval anatomical imaging determination determination determination determination determination determination determination moments motivation utilized utilized loo irregular irregular irregular dominant accounts infinity steepest considerations grants characterization characterization characterization characterization johnson ccd street kluwer kluwer planes planes planes planes super super perceived realize illustration illustration relating adelson adelson frontal nonetheless normalizing psychophysics characterizing textures textures textures agrees mcdonnell todd todd todd confirm ave observers pan pan accomplish cylinder cylinder cylinder cylinder cylinder spectrogram extracts manipulated manipulated detects detects carries bergen bergen dog characterizes curved vertically south parker parker undergo undergo tan validated decompose eeckman pew stand manipulating manipulating manipulating philadelphia standing finkel finkel finkel finkel finkel finkel finkel finkel finkel malik malik masks tilted tilted normalizes integrand pennsylvania turner turner sajda sajda subunits subunits skrzypek slant slant slant cvpr cvpr neurological perona perona johnston whitaker preattentive norwell norwell discriminates orderly landy agreements ellipsoids ellipsoids ellipsoids ellipsoids ellipsoids ellipsoids gerstein gerstein upenn upenn viewer eccentricity eccentricity 
#@Finkel_L,Sakai_K,
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#*network network network network network network network network network network network network network network learning learning model model model model model model model neural neural neural neural input input input input data data data function function function figure figure figure figure figure figure figure time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm output output output output output output output output output output output output number number number number number error error error error error error results results results results results units units units units information information information information information information information information information information information problem problem problem problem problem models models models models models models hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based based space space space weights case case case case case case case vector vector vector vector order shown shown shown systems systems systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability weight weight functions functions functions functions unit distribution distribution recognition recognition recognition recognition recognition recognition recognition method method method method method method method method approach approach approach approach pattern point image image image image image image image image image single processing processing processing control local test test test patterns class class class class class class class class class class matrix optimal optimal optimal optimal optimal optimal optimal inputs form shows shows simple gaussian gaussian gaussian visual visual visual visual paper paper examples feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work task task task task task task task task task task methods step step points features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification current current trained trained trained trained trained problems problems random random random random random random high similar show show show equation section vectors images general general general general approximation approximation average average average theory theory gradient obtained term note note experiments experiments experiments experiments solution solution solution solution research independent constant constant table table table table table estimate estimate estimate standard standard computer computer computer computer computer computer computer map map present present object object object object sets maximum maximum maximum press learn learn basis basis basis basis basis basis nonlinear sample sample abstract back density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references ieee ieee important propagation introduction complex complex hand hand hand hand hand hand hand hand hand statistical generated tion assume assume classifier classifier prior prior prior chosen higher higher previous previous previous previous cases required required required required good represent bayesian techniques techniques techniques techniques correct correct correct correct correct correct correct correct correct correct correct probabilities errors errors resulting classes classes classes classes ing tasks computed times regions mapping means factor potential made orientation orientation applications knowledge knowledge knowledge knowledge em obtain artificial specific specific specific samples compared compared compute compute compute compute compute objects objects objects objects objects objects perform experimental posterior posterior posterior approaches approaches approaches approaches support nets selection selection proceedings report version technique consists advances advances advances joint joint joint joint represents represents represents exp addition addition sequences considered considered computing computing computing computing computing computing equivalent equivalent equivalent equivalent hinton hinton additional view solutions solutions estimates san san conference determine classifiers full requires choice approximate approximate vision vision vision vision vision vision give condition weighted weighted weighted randomly randomly randomly randomly clustering finally selected selected selected selected selected backpropagation nature simply measured measured measured measured measured measured discussion denote denote denote denote denote denote tested close close common common generate eds eds journal ability ability ability noisy noisy noisy unknown unknown unknown unknown unknown interesting edge edge matching matching matching matching uniform principle representing details numbers max max normalized depth frame frame choose added denotes denotes denotes denotes denotes denotes denotes advantage typical strategy strategy strategy sense recently interest dimensions dimensions dimensions dimensions dimensions dimensions dimensions highly compare unsupervised axis yields match correspond diagonal positions locations interval williams williams constructed constructed suggests correctly correctly touretzky boundary boundary place competitive central bayes learns propose propose presence solid intelligence exist decrease configuration denoted acknowledgements suppose written index generating generating describes missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing simultaneously transformations transformations easy slightly consisting applying select select select choosing choosing extracted viewed densities densities densities densities densities densities densities showed soft completely completely allowed allowed reasonable normalization purpose closed assigned assigned assigned assigned advantages degrees degrees includes combinations color weighting weighting weighting assignment assignment assignment assignment recognize recognize candidate discussions characterized successfully successfully determining determining selecting selecting selecting selecting selecting society society maximal maximal maximal effectively wij poggio poggio poggio score situation plots plots plots road refer soc prob success classify list vary providing giles correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence highest highest subsequent deal deal deal deal cowan unlike diego perturbation experience hanson reducing reducing examine tech project project mappings applicable applicable maximizing affect matched neu adapt perfect regime submitted neal neal percentage percentage percentage percentage crucial crucial publishers orientations adjacent nowlan nowlan benchmark perspective perspective sys arise projected depicted recognizing fourth reflects evaluating evaluating substantially substantially axes conducted lack lack incorrect ity switch berlin mod ture fall fall maximizes maximizes maximizes maximizes maximizes popular proven incorporating yielding cor consistently pose classifying tresp tresp tresp tresp tresp mistake appearance arguments pick recover zemel concerned theories royal rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid wrong dealing consideration overcome mail siemens siemens ral optimally symposium intuitive corner edelman edelman decide chooses recog recog permutation permutation occlusion surprisingly surprisingly reader gesture gesture gesture gesture gesture variants generalizing dempster assigns severe informa outperforms corporation rubin pointing pointing graded ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ber nition poses poses poses poses suboptimal encouraging assignments assignments assignments assignments classic possibilities imagine principled principled shaded community formance num tems degraded ullman ullman argued projecting regimes topic laird attached finger finger finger supports fea page els aaai aaai gestures gestures gestures gestures info lowe lowe ping correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences correspondences ers substitute meth mill deals screen ods alto remained lar dence dence probabil rolling palo dealt volker thumb puted froin ages wji clamp idealized justifies instantiations rni particu unrelated occlusions occlusions occlusions lea plete formalize pected ger timal vital pute deficiency biometrika xla brady brady correspon correspon correspon correspon publish ternational alc alc alc alc alc connell subutai alx alx xlc xlc xlc iance hnage hnage kaufinann 
#@Ahmad_S,
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#*model model model model model model model neural input data data data data data data data function function function function function function function set output output system system system error results information information information information information information problem problem problem problem problem problem based space space space space space space space weights linear case vector vector vector vector vector vector vector order order order order order order order order order order order order neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons point point point point processing large large local local local local neuron neuron neuron neuron neuron analysis analysis analysis shows gaussian visual visual visual visual visual visual visual paper work fig fig fig fig fig fig fig fig fig fig fig points points field field field field field field field field field field field field field structure structure structure structure random high response response response response response representation show show equation vectors gradient gradient term term term note activity dimensional dimensional computation independent defined defined defined found found found found found constant constant estimate estimate standard standard standard distance distance distance distance distance distance synaptic left left left direction direction direction direction present low low frequency frequency temporal temporal temporal temporal temporal temporal object object object object object object object motion motion motion motion motion motion motion motion motion motion components components nonlinear outputs outputs continuous continuous continuous continuous abstract applied applied applied properties properties properties properties properties properties properties properties references component component due introduction complex hand hand stimulus stimulus change difference spatial spatial spatial spatial assume assume lower measure center center center center center center center center center center center center center center center cases conditions represent represent equations equations equations fact observed scale resulting human human computed respect eq eq regions mapping mapping factor natural orientation orientation orientation orientation orientation orientation global filter filter filter filter filter relative relative relative specific represented desired series series receptive receptive receptive receptive receptive receptive receptive receptive provide objects objects objects eye goal related gain discrete cortical brain equal power power comparison larger fields fields fields fields institute institute represents responses responses responses responses responses responses responses exp computing computing computing computing domain environment curve curves curves curves curves curves curves trajectory san top stimuli stimuli stimuli stimuli stimuli detection full speed speed speed vision levels area area area area area area area area area area area area area area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types types types types types lines nature biological normal normal normal normal normal normal normal arbitrary tested tested assumption assumption corresponds surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface common effective assumed shape shape shape shape shape shape shape supported role role role role role role role eds ability hypothesis reduced functional coefficients transfer interesting ratio ratio ratio ratio ratio ratio projection projection increasing increasing principal principal principal principal squared filters filters filters filters filters filters filters filters filters filters filters filters filters filters bottom bottom depth choose neuronal recent property typical reported introduced moving moving moving recently relevant interest varying approximately calculated tuning tuning tuning tuning tuning tuning tuning tuning tuning axis axis smooth yields yields correspond correspond differential differential differential differential differential achieve organization grant grant horizontal invariant scaling suggests wide rotation rotation pass pass half flow conclusions operator operator operator central interactions sigmoid suggest propose integration demonstrated california solid assuming movements selective relationship averaged introduce derivatives derivatives acknowledgements areas areas areas relation relation perception perception perception perception perception solving solving solving estimating plot laboratory ann involves develop frequencies gaussians gaussians gaussians applying extraction national extracted extracted independently depending variation showed translation translation constants additive performing classical expansion reduces boundaries tracking interpolation interpolation interpolation interpolation interpolation calculate foundation foundation norm norm precision recorded box perceptual combinations coordinate coordinate retinal retinal retinal plotted discuss partially discussions characterized simplicity straightforward middle middle middle middle middle divided presentation detect capture soc allowing superior symmetry cue cue bar involved play surround surround surround surround surround surround surround surround surround surround surround surround surround providing providing nips wave neurosci neurosci neurosci neurosci decreasing decreasing oriented oriented oriented body origin selectivity diego powerful essential essential essential investigate relations preliminary helpful scalar fashion project possibility combine combine stream stream surfaces surfaces surfaces surfaces surfaces surfaces plausible possibly predicts rev thought singular quantities quantities quantities versions shapes band ground crucial agreement navigation navigation nonlinearity perspective filtered constructing directional directional operators operators operators operators operators monkey monkey monkey monkey res radius radius addressed geometric fuzzy reflect profile profile profile axes axes generic embedded readily psychophysical passed dots requirement extracting fall curvature curvature curvature curvature curvature curvature curvature replace comments shaped shaped shaped patients owl owl deviations lab discontinuities equivalence velocities approximates neurophysiol nonzero spontaneous systematic primate primate primate primate primate logarithmic logarithmic obtaining monotonically monotonically monotonically implications salk optic planar date ambiguity zhang widths induce monkeys captured viewing enable diameter recovery deg deg specialized observer observer observer speeds speeds speeds largely helmholtz expanding quasi lesions simulating laplacian laplacian continuity manipulation manipulation segregation discontinuity neurophysiological simplifying iso fixation fixation differentiation differentiation surrounding macaque macaque macaque supports investigations vanishes slopes normalizing travel round unpublished rewritten stimulating characterizing const rfs rfs rfs rfs rfs rfs rfs mst mst tanaka tanaka tanaka physiologically extracts interpolating acid andersen andersen positional correlates gathered silent sur analyse sponsored behaving saito omit plotting hypothetical rectification translational convolving lesioned abstr abstr vectorial convexity idealized george perceive elongated elongated proprioceptive siegel annulus annulus flanking desimone erf erf asymmetrical allman allman allman antagonistic antagonistic antagonistic surrounds surrounds surrounds surrounds surrounds surrounds surrounds surrounds surrounds surrounds surrounds surrounds surrounds surrounds nakayama slant orthographic rhesus perceiving scholarship judgement tangential treue albright albright albright albright albright albright albright confine curvatures curvatures curvatures curvatures deficits parallax scalars truncating involvement born born born redefine unresolved redrawn redrawn redrawn redefining analogues hikosaka poster 
#@Albright_T,Buracas_G,
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#*model model model data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure set system system system results results results results information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem based based based case case vector vector vector vector values probability probability probability parameters noise distribution distribution distribution distribution distribution distribution recognition method method method method approach approach approach approach pattern point point image image image image image image image image image image image image large large large local local local rate matrix matrix matrix shows shows shows algorithms simple visual visual visual visual visual paper paper examples examples examples small size size size size feature feature feature work methods field field field field field field field field field field field field field field field process process problems problems random random random high high high high high high similar show section section section images images images images images images general parameter parameter real approximation average note note note note note note experiments dimensional dimensional result result variables computation research research defined defined defined constant constant estimate estimate estimate estimate estimate estimate computer computer science direction direction direction direction direction direction low low object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion press press press abstract applied references component component component component component stochastic due due due due due ieee ieee ieee ieee important important decision introduction introduction estimation estimation variance variance variance parallel parallel cost search tion energy energy spatial measure measure measure prior prior chosen higher cases cases required binary binary bayesian expected equations equations markov markov markov markov techniques techniques region region region proposed correct correct errors minimum minimum total human human computed respect respect sum called times regions regions regions regions regions regions regions regions regions factor optimization natural natural global global global study obtain obtain vol vol artificial application desired provide define objects goal related posterior posterior constraints distributions equal approaches approaches mit mit mit larger larger larger fields fields fields fields institute institute technique technique represents represents final final exp bias bias bias bias sequences sequences sequences considered framework cambridge cambridge view solutions estimates estimates estimates estimates estimates estimates san stage detection detection vision vision vision vision estimated estimated give give con produce condition conditional velocity velocity velocity velocity processes constraint constraint constraint constraint discussion covariance covariance describe inverse inverse assumption surface common effective assumed shape main square square square square square square square square square square pixel pixel pixel pixel pixel pixel pixel pixel including account account block block block block block block block block block block block projection york edge edge edge edge edge edge edge edge edge segmentation matching matching matching matching matching matching matching matching matching matching matching matching matching matching iterations window window idea minimize run discussed directions directions directions property introduced moving moving side side side side pixels pixels pixels pixels pixels pixels pixels pixels module solve solve smooth yields yields correspond correspond correspond trans address address background background background background separation parts intensity intensity intensity intensity intensity intensity intensity occur occur occur extended rotation rotation rotation rotation rotation rotation rotation locally deterministic white white occurs occurs boundary half flow flow flow flow flow flow flow neighbor neighbor interactions measures measures measures measures measures measures measures measures retina bayes clear temperature propose taking strong integration integration proportional minimizing minimizing exist min plane averaged introduce introduce introduce scene scene annealing annealing annealing relation edges edges edges edges edges edges edges edges edges edges edges edges edges perception optical optical optical optical optical optical optical solving describes dept confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence explicitly springer formed boolean select yield extracted reconstruction reconstruction reconstruction reconstruction reconstruction stationary stationary stationary interpretation interpretation interpretation frames translation translation translation translation translation translation translation partition measurements measurements normalization convex convex convex convex convex neighborhood neighborhood neighborhood neighborhood roughly roughly iterative closed distances assigned thesis formulation formulation eigenvalues eigenvalues eigenvalues contour inter uncertainty uncertainty uncertainty uncertainty uncertainty discuss discuss maximize coupled coupled black texture simplicity determining capable poggio poggio capture conf verlag symmetry contribution follow gibbs localization localization localization localization localization localization relaxation moves receive presents law schedule create involving humans mass mass rest rest rest int eigenvectors eigenvectors measurement trace configurations thought front phd synthetic synthetic massachusetts asymptotically indicating site piecewise piecewise ground ground distinguish agreement smoothness smoothness smoothness smoothness smoothness smoothness inside inside inside inside inside straight organized precisely precisely forces beginning arises arises author reflects improvements lattice introducing measuring geman geman geman geman display shaped yuille yuille eventually eventually lim univ discontinuities discontinuities discontinuities discontinuities discontinuities newton college saddle investigation princeton pick velocities girosi homogeneous homogeneous binocular wrong ments stronger overcome siemens siemens corner corner corner corner separating ambiguity decide guarantees sides sides sides sides sides sides sides sides sides moved moved stereo stereo propagated propagated chooses francisco occlusion occlusion horn horn belonging displacement displacement informa street preserving utilize par quasi ideally amherst brightness mutually exclusive pami pami pami impose discontinuity concentrate emphasize considers ullman ullman depicts employing cij cij cij geiger geiger geiger geiger geiger geiger geiger geiger geiger inversely tij esti coming restoration resolve resolve resolve august corners corners corporate sake mrf vii vii vii correspondences blake blake east cornput coincide fij fij fij fij fij fij fij obey resolved concave concave concave cur contrary complement coins gence occluded occluded occluded aperture aperture aperture aperture foreground neglected dence cti cti cti ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities rij hole hij hij hij hij gij gij gij gij gij gij erroneous mumford mumford men lowered mrfs ities mate translating translating mercer anandan anandan functionals convexity convexity textured oij perceive ticular resolving resolving resolving resolving resolving resolving resolving vij vij eij occluding occlusions occlusions occlusions obeying nij nij nij nij nij backgrounds hildreth zisserman zisserman correlating confi shah shah helping elf confidences confidences nyu interprets intelli alg reinforces isaac adoption eccv lnz lla 
#@Diamantaras_K,Geiger_D,
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#*network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural data data function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure set set set set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number state results results problem problem problem problem problem problem problem problem problem problem problem problem problem problem based based based based space space space space space case case vector shown shown parameters parameters parameters parameters noise functions recognition recognition method approach approach pattern point point point point point point point point point point point point image image image image image processing large local local local local analysis matrix matrix optimal optimal optimal optimal form form form shows algorithms gaussian gaussian gaussian gaussian visual paper small feature feature feature net work methods methods methods points points points points points points points points points points points points field field field field field field features features features features features problems problems problems high representation representation representation representation representation representation representation fixed fixed line line line line line line line line line line line line line line line line line line line line line images images images images images real approximation approximation approximation approximation theory theory theory theory gradient note dimensional dimensional dimensional dimensional dimensional dimensional result university variables variables variables variables variables variables variables variables variables solution log log log found found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant computer computer computer distance distance node science science science left left left left direction present phase low machine object object object object object object object object object object object object sets maximum press components continuous abstract applied find analog analog references stochastic due ieee introduction estimation statistical search change change energy variable variable spatial assume assume assume assume chosen binary long conditions tree tree tree tree bayesian make techniques proposed correlation correlation correlation correlation correlation correlation correct scale scale scale finite resulting resulting ing ing computed sum sum sum sum sum means optimization optimization optimization optimization optimization optimization original artificial specific represented represented represented represented application objects location determined constraints constraints approaches mit steps accuracy contrast descent descent descent descent descent nets report department department version represents exp scheme cambridge directly directly top top efficient world vision vision pages pages give produce derived derived clustering developed levels actual constraint constraint constraint achieved achieved discussion technical tested tested transformation transformation transformation transformation transformation transformation transformation transformation corresponds corresponds finding short effective effective effective effective supported square instance instance instance easily objective objective objective objective objective objective objective objective objective objective objective objective simulated smaller underlying hopfield hopfield unknown edge edge special matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching representing bottom improved robust robust subject hierarchical hierarchical inference previously conventional approximately calculated works tions tions solve solve match match match match match match correspond trans trans locations locations generalized generalized generalized grant parts matrices rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation deterministic segment segment segment segment segment segment segment segment segment segment segment valued numerical constrained propose propose physics intelligence turn minimizing minimizing scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene connectivity minima annealing annealing annealing acknowledgements derive winner segments segments segments segments segments segments segments segments segments segments segments segments segments segments pruning pruning coordinates transformations angle angle angle gaussians gaussians applying minimization formed extracted extracted extracted extracted formation dependence communication squares viewed interpretation solved solved transform transform transform evaluated centers soft soft similarly translation translation translation translation translation translation translation translation partial partial convex convex intervals intervals roughly penalty tracking closed euclidean euclidean avoid template coordinate coordinate assignment plotted illustrated candidate coupled variations black partially successfully reason effectively fine fine fine fine fine fine fine procedures prob dis gray satisfy notation vary write localization localization localization localization localization localization relaxation correspondence correspondence correspondence correspondence correspondence correspondence correspondence hypotheses overlapping approximating camera simpler transformed transformed transformed transformed collection collection essential updating put replaced optimized optimized integral fewer matches matches analytically maximizing tanh func surfaces matched matched matched matched circles coarse coarse coarse coarse coarse coarse closest configurations thought greedy detector ith wta synthetic massachusetts scenes defining adapted tractable processed turns producing style located grossberg optimize arises incomplete recognizing double substantially parameterized readily readily treated treated continuously frequently dots dots outliers outliers baird cor pose pose saddle summing recover bin rigid rigid clamped fits loops illumination clock grammars spurious spurious mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness lengths demonstration searching captured darpa iterated specialized april permutation onr ccd lem dense dense temperatures temperatures temperatures yale yale equivalently covering formulate big pairing eric eric graphics searches relates relates integrals ambiguous cation indexed enforce differently opti january discretized tom ping correspondences correspondences nested nested dcs believed equa vote ory spie implying edition hough hough hough brackets occluded transaction inaccurate indexing indexing appli tightly haven blurred locating locating locating mft mft extrema llx jumps tll tll clocked continuation continuation positioned positioned endpoints endpoints endpoints crisp aligning lozano private rameter rameter overcoming congress mia mia mia mia mia mia mia mia mia occlusions obeying strained uncover garrett garrett grimson perez compactness bot vantage mize localizing yaleu sinh lagrangians trapping acceptably scent ila transverse jittered interpre subproblems undergone tunes uncon 
#@Lu_C,Mjolsness_E,
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#*network network network network network model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time number system results results units units units units units units units information problem problem based based based based based based based based case vector order shown shown shown shown shown shown shown shown shown shown systems values values values values neurons neurons unit unit unit unit unit unit method pattern pattern point image image image image processing processing large local inputs inputs inputs inputs shows shows shows shows gaussian visual visual visual visual visual visual visual visual visual visual visual paper paper paper paper small feature work work points field features features features process process process process level level level structure high high similar similar similar representation representation representation architecture architecture architecture architecture show line line line line line theory theory note note activity activity activity activity activity activity activity activity activity activity result university threshold computation computation independent independent independent independent found constant computer terms distance distance connections connections connections science science science left left left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction phase phase activation activation activation activation activation activation activation activation activation low frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object range range position components components outputs abstract back computational properties properties references component component component component due important context context context context circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit stimulus stimulus effect effect parallel parallel parallel parallel parallel parallel parallel search search tion change spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial prior representations representations representations representations higher previous bound bound bound bound cases firing firing type multiple cortex cortex cortex long represent represent represent region region region region region region region region region region region region proposed correlation scale simulations simulations simulations simulations simulations simulations simulations classes simulation simulation simulation simulation human computed computed computed computed computed computed computed computed computed computed computed sum elements regions regions mapping potential orientation orientation orientation orientation orientation orientation orientation relative relative relative relative specific specific specific represented represented represented define compute compute compute compute compute objects objects objects objects objects objects location active active related cortical cortical brain approaches contrast contrast connection dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent proceedings report institute institute department department individual represents responses scheme scheme considered computing computing computing domain domain environment environment directly curve additional view view top top stimuli detection determine determine upper requires free free con con area area types types finally processes nature nature depends depends depends discussion technical describe transformation transformation transformation limited limited limited corresponds complete surface surface surface surface surface surface surface circuits circuits circuits circuits circuits circuits circuits amount amount shape shape generate generate generate supported role role role role role role square square square square square pixel underlying functional interesting segmentation segmentation segmentation segmentation segmentation mechanism mechanism mechanism mechanism consistent principle representing representing details call max depth depth depth depth depth depth depth depth depth magnitude magnitude magnitude magnitude magnitude neuronal neuronal neuronal neuronal neuronal membrane directions directions resolution advantage advantage property typical similarity similarity similarity similarity side side side side side side side side cognitive subjects subjects tuning observation bounded organization organization horizontal predicted alternative locally column column column column column column strength conclusion segment segment segment segment segment segment segment segment differences numerical propose mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms largest characteristics proportional selective selective selective selective selective selective decrease relationship relationship relationship scene scene scene scene scene program configuration force force acknowledgements areas areas areas construct perception perception ways primary plot plot segments segments segments segments segments simultaneously consisting integrated events events implies implies national extracted focus dependence squares squares activities activities activities activities constants constants discrimination discrimination discrimination closed intermediate intermediate intermediate construction construction foundation koch koch figures perceptual perceptual perceptual perceptual perceptual perceptual usa contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour determines illustrated illustrated illustrated domains columns columns columns columns columns determining determining determining aspects comparing comparing tend tend tend tend orthogonal receives characteristic traditional traditional strongly allowing link interpreted neuroscience neuroscience lie lie contribution contribution contribution oscillations oscillations cue cue cue gray gray cues cues cues play play play play play binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding cat overlapping overlapping illustrates illustrates operating operating preferred neighboring oriented unlike carried carried create access essential circuitry dual dual dual dual dual dual dual existence relationships relationships relationships relationships relationships oscillation affect affect topographic topographic topographic topographic topographic fundamental surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces contours contours contours contours contours contours contours contours predicts illustrate illustrate rank rank der der obvious mapped utility grouping integrate ground ground ground ground ground distinguish orientations phenomena explanation diffusion purposes closer organized producing forces angles implicit incomplete varies varies varies populations transient completion completion completion rep operate operate mod characterize differs differs resource resource resource resource resource ordered singer singer germany coherent segmented segmented segmented neuro shaped shaped shaped shaped shaped shaped shaped attentional cor realized discontinuities secondary secondary assign assign summing temporally temporally ordering repre arranged stronger striate efficacy neurobiology operates fail filled falls paul von mental accounts consequences belongs facilitate offers occlusion occlusion occlusion occlusion occlusion occlusion occlusion infer infer thin thin thin locked proximity proximity proximity proximity proximity grants interestingly thresholding assigns assigning onr discriminate linked street pointing distinction perceived perceived malsburg malsburg classic argue summarizes biophysical biophysical thick grouped grouped grouped disadvantage retinotopic mediated considers considers argued academy complementary complementary complementary complementary complementary rough conversely cij cij cij selectively weaker register els normalizing increments increments topography utilizing served ate mcdonnell junctions converging converging observers utilizes utilizes bold char believed resolutions inferring concave quantitatively neurobiological vivo implied inset accounting south inducing brackets closure closure closure closure closure closure closure closure occluded foreground tical segmenting greatest greatest illusory illusory illusory illusory illusory illusory illusory illusory dof dof dof dof dof dof dof dof dof dof dof dof dof dof pew yon contributing contributing columnar ness puter illustrating proximal bind consciousness pri philadelphia serving finkel finkel finkel finkel finkel finkel finkel finkel finkel finkel convexity convexity convexity mary crick crick perceive organize segregated pennsylvania chemistry grayscale grayscale discriminated discriminated sajda sajda sajda sajda sajda sajda sajda sajda sajda sajda referring mecha coexistence neurological binds divisions sory extrastriate extrastriate proposing speculate whitaker preattentive orderly ify acteristics sents nism organizes organizational viewer strat ternal dle dle untilled resolu 
#@Finkel_L,Sajda_P,
#t7
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#*network network network network network network network learning learning learning learning learning learning learning learning model model neural neural neural neural neural input input input input input data data function function function function function function function figure figure set set set set networks networks networks algorithm output output output output output output output output system system system system system system system system system system system system system system error units units units information information information information information information information information information problem models models hidden hidden based based space weights weights linear linear linear linear linear linear layer case case case case case case shown systems values probability probability probability probability parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise functions functions neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach approach approach approach approach pattern processing processing processing large large large large large large local local patterns patterns patterns patterns analysis matrix inputs inputs inputs inputs inputs inputs form form form shows signal signal signal signal signal signal signal signal signal signal simple gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual paper paper small work work work work methods fig fig fig field features process structure structure problems random random random similar similar similar similar similar equation equation equation images images images images general general generalization speech approximation theory theory theory theory theory theory theory theory term term term term term term term term term activity result university university university university university variables computation solution research independent independent independent independent log log log log log log log log log log log log log log log log log log log log log initial constant constant constant constant estimate standard computer computer terms terms distance distance distance distance connections synaptic synaptic science science map present nodes object maximum maximum press press learn position outputs outputs outputs outputs outputs outputs outputs outputs continuous sample abstract applied applied computational computational properties references stochastic stochastic stochastic stochastic important important introduction statistical effect variance variance tion tion energy energy energy energy difference complexity variable spatial spatial spatial spatial spatial spatial spatial assume assume assume assume assume assume measure measure measure prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior learned chosen part theorem theorem theorem good bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov make make make make make make proposed correct correct forward scale resulting classes human respect respect respect multi performed performed natural natural filter filter filter filter filter filter filter filter filter obtain obtain obtain obtain obtain negative vol vol vol vol vol relative represented true true true application receptive receptive receptive define objects objects perform perform perform determined goal goal related related constraints distributions distributions distributions distributions distributions distributions brain equal power mit contrast contrast connection connection connection fields fields fields update train train descent report implementation implementation version individual individual joint joint joint scheme scheme cambridge cambridge equivalent equivalent directly hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton additional solutions solutions solutions san determine determine requires approximate approximate world world world world world vision vision vision vision vision vision vision vision vision vision basic give con condition condition derived derived derived derived derived criterion criterion criterion criterion criterion criterion entropy entropy entropy entropy entropy product actual provided provided provided backpropagation nature nature nature sampling constraint associative achieved technical increases describe describe describe close close close close inverse inverse inverse assumption corresponds corresponds surface finding implemented assumed assumed assumed assumed face square development sensory fit fit probabilistic typically needed interesting interesting mechanism mechanism special principle principle principle principle principle principle leads squared representing max pre making early early early magnitude idea idea idea idea idea minimize minimize minimize choose choose sources light predict perceptron neuronal neuronal denotes denotes recent advantage pair similarity similarity strategy highly highly teacher teacher teacher calculated tuning correspond correspond achieve definition organization organization organization organization organization organization organization organization organization parts intensity intensity intensity intensity intensity expression suggests feed white demonstrate conclusion starting minimal assumptions assumptions assumptions assumptions assumptions assumptions competitive bayes bayes bayes constrained temperature physics regularization assuming assuming assuming assuming variety minimizing minimizing averaged introduce introduce scene scene scene force force force force force force suppose appears relation relation relation derive written perception perception optical ways ways ways estimating estimating laboratory laboratory dept dept recall recall implement implement multilayer explicitly dimensionality involves easy unique mutual mutual mutual mutual mutual mutual mutual mutual gaussians applying minimization extracted expressed expressed formation estimator estimator viewed interpretation transform transform restricted organizing organizing organizing organizing organizing converges spectrum key additive additive additive additive normalization normalization filtering filtering filtering filtering sufficiently koch koch david avoid sciences sciences discuss maximize maximize maximize maximize priors priors priors simplicity capable society divided effectively poggio poggio poggio identify detect detect traditional anderson interpreted dis dis dis dis dis dis quantity write dot ill maximization automatically received principles principles overlapping disparity disparity disparity disparity extract extract extract modelling humans strengths integral behaviour fourier fourier ideas detectors analytically relationships root maximizing maximizing maximizing maximizing maximizing maximizing maximizing variability variability complicated surfaces surfaces surfaces surfaces act plausible possibly adapt thought ensure ensure adjusted assumes precise observe expressions expressions academic arbitrarily scenes slowly formula trivial trivial derivation analytic analytic tractable london spatially spatially spatially spatially perspective perspective tive forces forces division division choices commonly commonly probable mathematics acknowledgement universal integrating evaluating applies freeman consistency readily posed adjustable rep calculating aim fall prevent coherent coherent boston boston age coherence coherence coherence coherence yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille representative room uncorrelated pick concerned impossible theories theories theories robotics binocular binocular binocular binocular air kullback kullback kullback kullback kullback kullback kullback convenient imaging imaging promising adjusting adjusting held held stated attractive contract abilities abilities viewpoint hope obtaining disjoint disjoint moments substituting exploring becker becker becker becker becker becker becker becker becker becker becker becker becker becker becker becker becker becker becker stereo stereo stereo stereo claim darpa approximators enable advance francisco eng steepest variants variants variants alternatively ignore generalizing fusion leibler leibler leibler leibler leibler leibler kluwer formulate conjecture arg generalizations flat stands realize illustration argue argue distribu proba relating argued relates proach investigating hornik hornik intensities enforce barlow barlow barlow preprint det september mini develops fortunately ble lation bility december harvard harvard harvard harvard harvard concrete tribution atick atick atick atick proposes marr marr neocortex alan clark clark clark clark neighbourhood ory maxi maxi america tance company spirit goodness relaxed deter sid sid sid jan discovers kong kong entropies entropies wiener wiener wiener wiener distractor distractor months unifying ansatz mumford mumford mumford mumford hong hong theo redlich redlich redlich redlich stereograms reminiscent coincidence encourage pot workers picks picks unclear poo poo poo poo torre birth ism sereno perceive disparities organize organize sketched chinese encourages implementa resentations infants dan nakayama nakayama contrasted deriva liebler perceiving appreciated ries imization formu lei lei iog mizing mizing mizing creasing genetically mines dordrecht birkhauser encyclopedia clifford reformulating scholar bldg 
#@Smimakis_S,Xu_L,Yuille_A,
#t7
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#*network network network network network network learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training algorithm output output output output output output number number number number number number system system system system system system system system system system error error error error error error error error state state state results results results information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem models hidden performance performance performance space space space space space space space space space space space space space space space space space space space space space space space space space space space weights weights linear linear linear linear linear linear linear linear linear linear linear linear layer layer case case case case vector vector vector vector vector vector vector vector vector vector vector vector order order order order shown shown systems values values values values parameters parameters parameters parameters noise functions functions functions unit unit unit unit unit unit unit recognition recognition recognition recognition recognition method method method pattern pattern pattern pattern point point single single processing processing processing processing processing processing processing large local local local test patterns analysis analysis analysis analysis analysis analysis class matrix optimal optimal inputs shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple paper paper paper size size size net work task task task methods methods features features features classification trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response representation representation architecture show show equation equation fixed fixed fixed line line line line line line line line line line line general general general general general speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real real real real average states theory gradient gradient gradient gradient obtained obtained term term term term term term term university computation computation solution solution independent defined sequence sequence dynamics dynamics dynamics terms terms terms distance science prediction prediction presented presented presented presented present low temporal temporal temporal temporal machine object position basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous abstract abstract back back back find find find computational computational references ieee ieee ieee procedure important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision context context context context context introduction complex complex complex complex complex complex complex complex dynamic dynamic recurrent recurrent recurrent search assume signals signals signals signals signals signals signals signals word part part center center previous cases type multiple multiple long conditions conditions represent represent proposed length observed finite finite tasks respect respect called called mapping mapping mapping mapping means means means means means made natural global study filter filter filter filter obtain vol vol vol vol artificial artificial relative samples represented application series provide provide provide define define define define compute proc proc proc proc proc proc location perform determined goal goal goal related comparison descent descent descent nets department implementation version internal kernel kernel kernel represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult layers delay delay delay delay delay delay delay delay delay delay delay delay delay delay considered domain domain domain domain domain domain domain domain directly san efficient full full choice free world world world speed speed produce condition condition criterion criterion types types provided provided provided backpropagation backpropagation backpropagation backpropagation nature depends feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward close corresponds stable finding finding finding finding short short short short short short short common effective synapse supported require adaptation adaptation adaptation adaptation square square square ability easily easily degree fit coefficients coefficients coefficients jordan jordan transfer projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection increasing increasing mechanism special special special structures structures structures structures structures structures structures structures structures structures structures structures structures structures structures structures structures principle operation operation leads representing call filters filters filters filters filters pre making window window window normalized depth depth depth depth depth depth depth depth depth depth perceptron architectures discussed improve improve recent resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution advantage advantage advantage pair element apply introduced moving include cognitive recently relevant relevant engineering interest varying varying varying varying varying axis axis axis match converge trans definition definition definition modified modified generalized generalized generalized generalized generalized generalized bounded storage grant constructed exists studied rotation feed move setting pass conclusions operator operator operator operator operator depend faster constrained constrained external characteristics drawn minimizing decrease relationship minima minima identification attractor appears relation relation ways ways sequential generating laboratory stability stability changing changing changing implement multilayer multilayer multilayer linearly electrical dimensionality dimensionality dimensionality easy minimization decreases review correlated transform open restricted showed static static static static suggested processor past sign additive spaces spaces intervals purpose construction topology topology topology kernels priori perceptrons weighting memories memories memories memories memories memories memories memories memories memories memories memories memories extension partially successfully simplicity gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma selecting extra society divided tdnn essentially orthogonal characteristic traditional notice notice notice notice conf conf conf procedures interested issue manifold manifold modular minimizes highest acknowledgments oriented minimized explore origin powerful powerful create requirements experience recursive recursive recursive recursive recursive recursive recursive recursive recursive preliminary mass mass periodic periodic rise history ideas school project combine proved workshop waibel circles gradients concepts adapt adapt man created created implementations thought quantities impulse impulse freedom mapped perceptton store chaotic crucial convolution convolution convolution defining growing growing analytical adapted adapted adapted adapted cascade stress choices choices projected projected involve circle calculations annual nsf addressed researchers geometric improvements applies axes axes axes experimentally lattice lattice lattice span span extracting windows implements implements focused focused focused traces traces proposition pole pole pole trade trade newton corrupted accomplished assign equivalence modify princeton appropriately rigid systematic fits accepted moment salient carry tap tap tap tap tap tap tap tap tap tap tap tap utilized utilized representational representational representational studying studying moved widrow bases bases francisco bursts extends subsequently valuable mind summer unable creates creates opposed alternating alternating uniquely icassp icassp icassp warping causal principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe principe realize constrain concentrated interact manifolds echo echo projecting parallelism unconstrained meet meet likewise likewise likewise indication signs worked worked november topologies topologies topologies topologies topologies topologies fortunately envelope adaptively adaptively adaptively adaptively adaptively recursion wiring usefulness obey dedicated autoregressive ultimate lowpass lowpass nontrivial quantitatively rtrl adapts poles poles poles poles poles poles poles poles zeros reviewed faced translates scattered tsoi tsoi tsoi ming cope jose trapped decompose wan wan demanding newly vries vries vries vries enforced recursire parsimonious accepts accepts ecs seeking taps taps taps narx bptt cse spans spans cancellation cancellation visualized arma kuo kuo kuo kuo kuo kuo bears equipped decomposing adaline adaline lacks unspecified unspecified wealth tape silva silva silva silva silva florida hsu hsu hsu hsu hsu tremendous lagged devising intimately asilomar coping indispensable gainesville framed discards neuroengineering versatility versatility 
#@Hsu_H,Kuo_J,Principe_J,
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#*network network network network network network network model model model model model model model model model model model model model neural neural neural input input input input input input input input input input data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set set set networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number number number number number system system system system system system system error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results problem models models models models models models models models models hidden hidden hidden hidden hidden hidden performance performance performance performance performance weights weights weights linear vector vector vector order shown shown shown shown shown shown shown systems systems systems systems values values values values values values probability probability probability probability parameters weight weight weight weight weight weight weight weight weight weight functions functions unit unit unit distribution approach approach approach approach pattern pattern single large large rate rate rate rate rate rate rate rate rate rate rate rate test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class inputs inputs inputs inputs inputs inputs inputs form shows shows shows gaussian gaussian gaussian gaussian gaussian gaussian examples feature feature work work task task points points points points classification classification classification current trained trained trained trained trained trained structure problems problems problems random high high high high high high high high high high high high high similar similar equation equation equation equation equation fixed fixed fixed vectors vectors vectors vectors images images general general speech speech speech speech speech speech speech speech speech average average states states states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient experiments result university threshold threshold threshold threshold threshold threshold threshold threshold threshold research log log log log log log log defined found sequence target target target target target target target target target target target target target target target target target target target target initial estimate estimate standard distance node node node node node node node node node node node node left presented presented presented low low low low nodes nodes nodes nodes nodes maximum range range range range position components basis basis basis basis basis outputs outputs outputs continuous continuous abstract applied applied applied applied applied back back back likelihood likelihood component component component component positive positive positive important propagation mixture introduction complex complex hand effect effect effect effect generated generated generated cost cost cost cost tion tion change change change change change change change difference classifier classifier measure measure signals signals word word word word word word word word word word word word word word word learned part center center long conditions represent bayesian bayesian markov markov markov length observed observed errors forward resulting classes classes ing tasks tasks tasks tasks tasks computed computed computed computed computed respect performed performed performed eq eq eq eq called called called called times means means policy negative negative relative relative specific true true true true true true true true true true true true true true true true true true true true application desired compute compute rates location location experimental posterior approaches mit accuracy accuracy accuracy accuracy larger train train train modeling modeling words words words words words words words words implementation technique represents difficult difficult difficult difficult difficult final ai ai cambridge directly directly directly directly curve curve curve curve curves curves curves curves curves curves curves curves transition stage detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection classifiers classifiers classifiers requires requires significant approximate estimated pages pages pages increase produce developed developed actual actual provided backpropagation backpropagation backpropagation nature covariance normal increases hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm fast fast complete finding rbf rbf rbf rbf short short common common shape generate generate generate generate require require require adaptation easily noisy smaller reduced account account account account account account unknown block block database database language squared squared squared squared representing representing max normalized normalized normalized frame frame frame frame added added improved improve improve recent moving include identical interest interest interest interest interest conventional calculated calculated calculated calculated calculated volume volume volume tions tions match correspond diagonal address mixtures mixtures background background background background background background background background evaluation evaluation evaluation evaluation evaluation evaluation modified modified modified modified observation observation increased increased increased increased increased increased increased occur occur occur suggests deviation wide derivative derivative derivative derivative derivative matrices move move move hybrid hybrid hybrid hybrid hybrid hybrid occurs occurs occurs pass minimal segment differences sigmoid sigmoid sigmoid measures accurate peak peak sound sound hard cycle characteristics sigmoidal radial radial radial radial radial variety targets targets derivatives acoustic base generating laboratory distinct segments metric linearly text gaussians gaussians versus versus versus decreases expressed evaluated evaluated updated centers centers centers frames frames frames frames frames frames frames frames frames sizes updates discrimination past diagram key normalization normalization roughly roughly roughly false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false penalty calculate assigned assigned assigned assigned assigned views includes usa instances maximize maximize successfully extra extra importance identify detect detect tdnn comparing score score score score score score score score score score score score score score score score plots summary procedures strongly strongly strongly decoding prob phonetic split split split running duration duration duration list list list list vary backward providing computes thresholds thresholds thresholds thresholds thresholds automatically operating poor overfitting varied varied humans accurately accurately lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann analytically scaled authors complicated scores scores scores scores scores scores scores scores affect matched waibel gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients extremely created adjusted front versions shapes detected detected detected improving attempts isolated charge percentage percentage percentage advanced distinguish variances analyzed caused closer acknowledgement separately separately demonstrates addressed alignment alignment raw reflects varies prop reflect reflect reflect embedded embedded embedded car car peaks share detecting detecting frequently maxima maintain passes passes passes passes mod fall fall maximizes prevent singer adjust richard decreased viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi credit credit credit credit credit credit credit credit credit credit credit credit cumulative initialization aligned aligned sort proportion proportion forming modify resources resources printed saturation ranges adjusting check check check check check check hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit hit nearby scoring scoring scoring scoring scoring scoring effectiveness spot corpus corpus ranging loo male male male young smoothed smoothed card card card card card card card card card card card card card card card card card card card impact impact impact projects thresholding thresholding lem posteriori posteriori dramatically linked tween icassp icassp acceptable female female female var eric adjustment quantized faults graphics file allocated careful careful insertion portions alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm alarm sta els dramatic normalizing ward ward picking nist sorting discontinuous jointly doesn routines routines filler filler filler filler recursion eliminates hour hour stay fre month agency ters sen alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms alarms normalize sij drastically assp steve problematic occurrences occurrences merit merit merit merit merit merit merit merit merit merit merit excessive satellite putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative putative hits hits hits hits hits hits hits hits hits hits hits hits hits hits hits hits hits hits hits hits hits hits sorted talkers talkers talkers talkers insert sponsored stepsize stepsize cars lincoln inserted inserted spotting spotting spotting spotting spotting spotting spotting spotting spotting spotting spotting spotting spotting spotting spotting spotting spots plotting spectrograms spectrograms spectrograms chang chang chang chang chang accu conversations conversations conversations conversations conversations conversations conversations conversations dissimilar ative cen correspondingly prototypical mon gra eval official government fragments detec discriminated mij mij dient observa fillers ended lexington neg bibliography ied conversation conversation money quently richly richly keywords keywords keywords keywords keywords tection backpropagate dollar cash reestimation reestimation houghton tative tative rately supplementary tence nput servation optionally dividual 
#@Chang_E,Lippmann_R,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data function figure figure figure figure figure figure figure figure time time time time time time time time time set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training output output output output output output output output number system system system system system system system system system system system state results results results results results units units units units units units units units units units units units units information information information information information information information information information information information information problem models hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance based based based space weights weights weights weights linear layer layer layer layer case case case case case order shown shown shown systems systems systems probability probability probability probability probability parameters noise noise noise noise noise functions unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach pattern pattern image image image image image single single processing processing processing large rate rate rate test test test test patterns analysis matrix matrix matrix optimal optimal inputs inputs shows shows signal algorithms simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small feature work work task methods methods methods methods field features features features features features features features features features features features features features features features features classification classification classification classification process level level trained trained trained trained response response response similar similar representation architecture architecture architecture architecture architecture equation section fixed line line rule rule images images images images generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech theory term note note university threshold computation computation research research research research independent independent independent independent independent independent independent found found sequence sequence target target standard standard computer distance left left left presented presented presented present low low low low frequency temporal temporal temporal temporal machine sets motion motion motion maximum range press position position position position position outputs outputs outputs outputs outputs outputs abstract properties likelihood references component ieee decision decision context introduction statistical statistical dynamic variance tion change change spatial lower lower lower signals signals signals signals signals signals signals representations center center center previous previous multiple good good long long conditions conditions bayesian bayesian expected fact region region correct correct correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities errors scale ing tasks total total human human human human human sum eq times regions means means made filter filter filter obtain obtain obtain obtain vol vol relative relative relative samples cross cross receptive receptive provide provide provide rates rates rates proc proc proc proc perform eye determined determined constraints distributions steps accuracy accuracy larger fields support source words department consists consists code individual individual individual joint represents represents responses difficult difficult final final final final exp delay delay delay delay delay addition ai ai estimates top stage effects upper upper upper full statistics statistics speed vision basic give con conditional conditional developed developed entropy entropy product product evidence backpropagation nature nature nature achieved measured increases assumption complete amount amount common shape shape role require require eds eds pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel future future easily easily makes makes noisy noisy sensory sensory sensory sensory sensory sensory including auditory auditory typically pairs pairs combination coefficients transfer transfer testing testing significantly significantly york edge segmentation special consistent matching mode max pre pre direct direct window window normalized normalized bottom frame frame frame combined combined combined combined combined minimize description improved improved improved improved improve improve recent correlations advantage advantage advantage pair reported reported pixels sejnowski array relevant relevant engineering interest interest highly highly highly subjects subjects calculated smooth yields speaker speaker speaker speaker speaker diagonal diagonal diagonal background evaluation positions positions positions separation separation separation modified modified channels channels interval interval sensitive entire entire entire entire horizontal horizontal horizontal horizontal intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity lead deviation matrices matrices matrices predicted hybrid hybrid width occurs occurs generally generally column pass pass pass pass flow row row row reduce reduce conclusions central central bayes peak exponential sound strong hard integration integration integration integration integration integration integration integration integration presence sigmoidal california california california proportional labeled labeled assuming relationship targets derivatives manner acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic appears edges edges perception perception perception perception perception perception perception optical optical estimating describes label vertical vertical vertical vertical segments missing missing category category category category category averaging electrical consisting predictive springer formed versus versus independently review variation open open open operations frames frames frames frames frames frames frames frames static understanding activities activities sec combining combining roughly roughly closed closed closed calculate visible visible visible visible construction advantages classified david recorded weighting automatic automatic automatic simplicity straightforward sensor identified letter letter extra importance society computationally detect detect build tdnn computations vowel vowel vowel vowel tend miller miller identity capture capture road road road notice verlag strongly video video video video video video video video video video video video video video video video video video video video video video video video phonetic issue contribution contribution contribution timing hold categories categories categories quantity modular correspondence automatically automatically received received received received attempt attempt consisted consisted overlapping extract extract extend camera presents collection rapidly environments humans humans accurately fewer reducing successive rest rest combine scaled complicated encode encode cover fundamental waibel waibel waibel hill hill hill naturally reading reading reading reading reading reading reading onset onset psychology equally recognizer recognizer recognizer eyes eyes eyes detector art speakers speakers speakers speakers speakers detected seconds seconds percentage burst indicating indicating indicating rows distinguish distinguish distinguish fairly adjacent independence independence independence tractable stanford stanford shared shared preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing desirable recognized recognized separately separately describing lowest lowest radius collected profile profile profile profile substantially spoken spoken cohen cohen cohen peaks peaks peaks marked remove remove incorporated requirement differs extracting synchrony serve qualitatively datasets green green sums sophisticated coherence findings utterances utterances utterances utterances utterances utterances utterances utterances utterances june distortion contribute spectra aligned identifying kullback adds mail fan height efficacy bands utterance utterance utterance utterance utterance utterance corner lip lip lip lip lip lip lip bad enhance enhance captured lawrence candidates offers enable recog late properly belonging park park park erlbaum consonant fold interestingly insensitive automated assigns treat consecutive consecutive consecutive grating audio audio audio audio audio compressed visually visually achieving leibler stork stork stork stork stork stork stork stork stork forced pentland pentland nition utilize classifications profiles profiles solely hillsdale argue unseen compensate ijcnn mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth thresholded efforts eliminating complementary complementary gender conversely distinguished confusion confusion confusion confusion confusion confusion confusion refined nil normalizing psychophysics psychophysics simplifies recognizers recognizers vice modal utilizing lighting versa recogni hearing hearing hearing suite suite suite suffers locate hoc replicated engine venkatesh bregler bregler bregler marcus luminance conditionally conditionally modalities recognizes vocal contrary america drastically vertically inde pooling pooling voice computable closure subsystem subsystem wolff wolff wolff wolff wolff wolff wolff wolff wolff indirectly segmenting aic aic opinion opinion moderately drawbacks jenkins repeating pendent campbell campbell judge tracked cancel tongue tongue inte inte extrema psych berger berger goldstein registration subsampled lips retention phonological hild menlo menlo menlo proving disk bimodal refining circumvent icnn ponents opens lipreading lipreading lipreading lipreading lipreading lipreading lipreading lipreading lipreading ricoh ricoh ricoh ricoh ricoh ricoh ror yuhas yuhas valley valley roi roi roi roi roi vibration comers manageable manageable confusions confusions confusions confusions grayscale grayscale grayscale reflections phoneroes isolate estimations teeth teeth crc crc crc confusable confusable impaired sand sand sand rounding easiest notoriously valleys valleys compensates ida prasad prasad prasad prasad prasad prasad trices gregory mase mase convolve convolve convolve convolve concen acoustically acoustically acoustically acoustically probabihty confuse automat trate descriptors intelligibility grated promises levine levine levine distin equiprobable convincingly sheer tle 
#@Hennecke_M,Prasad_K,Stork_D,Wolff_G,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data function function figure figure figure figure figure figure time time set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm output number number number number number number number number error error error error error error error error error results results results problem models models models models models models hidden hidden performance performance performance performance performance performance performance performance performance based based based based based based based based space space linear linear layer layer vector vector vector vector vector vector vector order shown systems systems systems systems systems probability probability probability parameters weight weight recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach pattern point single processing processing large test test test test test analysis class class class class class class class optimal form signal signal signal signal algorithms paper paper paper size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature task methods methods step features features features features classification classification classification classification classification classification process level level level level level trained trained trained trained trained trained structure structure memory architecture equation equation section section section section section fixed fixed rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors speech speech speech speech speech speech speech approximation average obtained obtained obtained note experiments experiments experiments experiments experiments experiments experiments university university threshold threshold threshold threshold threshold independent independent independent independent independent independent independent found found sequence sequence constant table table table table estimate distance node node node node node node node presented presented presented nodes nodes nodes nodes frequency machine machine sets maximum press press abstract applied applied applied applied applied computational properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due ieee positive procedure adaptive decision decision decision decision decision decision decision decision decision decision decision introduction generated generated parallel cost cost cost cost search search tion classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier measure measure measure measure center binary represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed bayesian proposed correct forward forward forward forward forward simulations minimum ing tasks regression computed respect multi performed performed called called called regions means optimization knowledge knowledge filter obtain obtain negative original artificial specific specific compared compared compared application desired rates rates proc experimental experimental posterior equal equal equal mit steps comparison support dependent dependent modeling proceedings proceedings technique consists consists consists consists individual individual represents addition addition addition addition addition considered considered considered cambridge cambridge computing equivalent equivalent experiment experiment experiment experiment curve curves curves stage determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full statistics vision estimated pages con derived derived developed levels product selected selected backpropagation sampling simply group tested assumed require degree rumelhart objective objective typically coefficients coefficients fully mlp mlp mlp mlp testing significantly ratio ratio uniform database database database database numbers pre pre window international normalized normalized normalized supervised supervised supervised supervised frame polynomial minimize minimize minimize perceptron denotes architectures improved improved population advantage element element similarity introduced strategy hierarchical hierarchical trees trees trees trees trees trees trees trees trees trees subset recently varying unsupervised unsupervised unsupervised unsupervised approximately approximately speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker match modified modified modified modified modified modified modified modified concept invariant feed demonstrate demonstrate conclusion reduce differences sigmoid measures measures bayes largest labeled labeled minimizing identification identification identification identification identification identification identification identification identification identification identification identification denoted denoted acknowledgements solving winner sequential describes label label label label label label label confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence pruning pruning pruning pruning pruning pruning pruning pruning implement multilayer multilayer multilayer remaining text text text text text text text text text predictive quality extraction extraction extraction extraction extraction yield yield extracted extracted extracted extracted depending evaluated evaluated evaluated evaluated evaluated evaluated evaluated evaluate evaluate labels labels lee sizes completely partition key smoothing normalization normalization false false false false closed closed assigned assigned norm norm norm norm advantages classified classified transactions building figures thesis perceptrons perceptrons retrieval retrieval recognize illustrated automatic automatic specifically identify score score score score score tend identity identity characteristic capture summary traditional traditional road repeated split classify criteria duration duration categories backward backward minimizes minimizes quantization quantization quantization computes computes operating operating operating rat rat varied limitations hall discriminant discriminant discriminant discriminant discriminant reducing authors decisions structured comparable stream scores scores scores scores scores scores scores scores scores phases examined induction hill closest subsets subsets subsets friedman noted academic speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers consist consist consist phd defines sentences seconds seconds cart cart cart growing london processed organized preprocessing leaves leaves leaves commonly laboratories ion ion ion ion ion ion computers demonstrates fourth people populations summarized summarized mod ture differs richard hamming utterances utterances leaf leaf leaf leaf leaf leaf leaf leaf consistently representative person person person person acquisition homogeneous children khz khz breiman ranges ranges logarithmic logarithmic hit hit contract obtaining removing utterance utterance utterance utterance utterance utterance splitting belong salient modifications corpus exceeds enhanced phrase utilized combines ranging codebook codebook codebook codebook codebook pruned pruned regard belongs belongs entries darpa recog mlps mlps verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification stone acknowledge verify outperforms ure incorporates vec vec outperform outperform misclassification accept accept accept recursively opposed rejection nition discriminative icassp icassp classifications england england clustered clas clas verified verified exclusive formance chapman oct oct march met met simplifying individually rejected cation cation quinlan quinlan option associates discusses discusses sized tively confusion nasa struc mea rabiner gratefully lagrangian const rosenberg rosenberg jersey focuses imple tors tors core ally edited juang juang juang voice fication comprised concatenated twelve sented predetermined stan percep cepstral cepstral timit timit timit 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algorithm output output output output output output output output output output system system system system system system system system system system system system error error error information information information information information information information information information problem models models models models performance based based based based based weights weights shown shown shown shown shown systems values values parameters parameters parameters parameters parameters parameters noise recognition recognition recognition recognition method method method method approach approach approach approach approach pattern point point processing processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control test test test test patterns patterns analysis optimal optimal optimal inputs inputs inputs inputs shows shows shows signal paper paper paper paper small methods points points points points points points points points classification problems random architecture show section line speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter real approximation average average theory obtained obtained obtained obtained obtained note activity dimensional result university computation research research sequence sequence target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial distance science science prediction map activation activation activation activation frequency temporal temporal temporal temporal object object object sets motion maximum range range range learn position position position position position position position outputs outputs outputs continuous continuous continuous abstract applied applied computational properties references due important introduction complex estimation behavior behavior dynamic dynamic dynamic generated generated generated generated generated generated generated generated parallel tion tion change change lower signals signals signals signals signals signals signals signals signals learned chosen chosen part part previous multiple long distributed make proposed proposed correlation forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward simulations minimum ing human mapping mapping mapping mapping mapping mapping means potential made made made natural natural natural natural natural feedback feedback feedback applications study original original original original original relative specific specific specific specific specific specific specific specific compared compared compared desired desired desired series series experimental experimental experimental experimental experimental related constraints constraints constraints motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor discrete discrete discrete discrete support source source source source source source source source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling morgan morgan institute implementation implementation implementation technique advances difficult final scheme scheme scheme scheme environment trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san top determine determine upper requires produce derived area area velocity velocity velocity velocity velocity velocity velocity controller actual actual actual actual provided constraint constraint constraint constraint constraint biological biological technical feedforward feedforward limited inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse effective generate role main eds journal journal journal future future rumelhart rumelhart rumelhart noisy sensory kaufmann pairs needed coefficients coefficients fully jordan jordan jordan jordan jordan jordan transfer transfer mode mode principle direct direct direct direct international supervised supervised supervised choose sources sources sources sources sources predict improved improved improved discussed exact advantage separate typical movement movement movement movement reported reported include cognitive relevant engineering previously previously previously previously teacher works tions smooth converge achieve positions positions positions positions modified channels improvement improvement arm arm horizontal extended alternative pass conclusion trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories differences differences accurate moody faster faster learns constrained constrained constrained mateo mateo sound sound mechanisms reduction characteristics characteristics characteristics demonstrated pulse minimizing exist targets targets targets targets targets targets configuration acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic pro solving solving plot plot laboratory vertical modeled coordinates text unique interaction integrated adding adding applying minimization focus formation phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme transform controlled controlled controlled static activities completely updates key partial reasonable reasonable delays generation string classified degrees determining compression aspects suitable society society society driven driven included characteristic kind issue physiological physiological physiological physiological physiological gray gray relaxation relaxation relaxation realistic realistic wave wave giles cowan unlike command command production production production perturbation essential essential put hanson hanson issues lippmann applicable muscle muscle fundamental measurement extremely electronic sentences seconds distinguish distinguish publishers publishers smoothness smoothness smoothness smoothness smoothness phenomena cascade cascade cascade caused caused caused closer filtered located mation laboratories pulses cut sounds sounds recognizing capability experimentally readily compares commands synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis rely mod incorporating incorporating serve acoustics acoustics acoustics neuro focused tile tile tile tile tile tile tile tile tile tile tile tile tile utterances utterances progress progress sentence sentence sentence calls realized japan japan japan investigation velocities velocities velocities velocities plays viewpoint kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato muscles muscles vowels vowels vowels infor lip recovered cmac pat thomas chooses smoothed contraction passing motions motions consonant grants balanced linguistic yielded ence shorter basically diverse reports acceleration acceleration eric articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator permits relating acquired ultimately distal rectified rough cartesian manipulator sam sam pop articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory nal port tract tract tract atr mea syn syn tension gestures excess ping ping synthesized synthesized synthesized telephone albus albus clarity japanese japanese japanese val tip acoustical acoustical physiologically anterior sen consonants consonants consonants consonants inferring ray rameters rameters vocal vocal vocal 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system system error error error state state state results results results results results results results results units units units units units units units units information information information information information problem problem models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case order order order shown shown shown systems systems systems systems systems systems systems systems systems values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach single processing processing processing processing large large local local local rate rate test test test analysis class matrix matrix inputs form shows signal signal signal algorithms simple simple simple gaussian paper small small size feature feature feature net net net work task task task task task methods step step step step points features features features process process process process process process trained trained trained trained trained trained structure structure structure structure problems problems random random high memory memory memory memory memory memory memory memory memory memory similar similar representation representation representation representation architecture architecture architecture section section line line line line line line line line line line line line line speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter real real average gradient obtained obtained note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments university computation research independent independent independent independent independent defined found sequence sequence target target target target target target target target target target target initial initial constant constant table table table table table table table table table table table table estimate estimate estimate standard standard standard terms terms connections prediction low low frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal sets sets sets press press outputs continuous continuous continuous continuous abstract applied back back back back back properties likelihood references component ieee ieee ieee procedure important important important important adaptive adaptive adaptive propagation propagation propagation propagation context context context context context context context context context context context context context context context context context context context context context context introduction action estimation statistical effect recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent energy energy complexity lower lower lower lower representations representations representations word learned learned higher higher higher higher part previous previous required multiple expected markov markov markov markov markov markov markov make make techniques proposed proposed length correct correct observed forward forward forward forward forward forward forward forward forward total regression computed multi multi multi multi performed performed factor made feedback knowledge filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter vol relative relative compared compared compared application series provide determined determined constraints connected discrete comparison contrast dependent dependent nets morgan morgan morgan proceedings department loss kernel kernel advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay maps framework cambridge cambridge equivalent equivalent equivalent directly additional additional estimates estimates estimates estimates san effects conference determine significant estimated estimated estimated basic increase increase give produce produce produce produce conditional developed levels levels finally nature simply discussion hmm hmm hmm hmm hmm hmm hmm limited limited assumption corresponds stable amount common assumed supported supported supported require require eds eds adaptation end end end end end end future future future future future future future future future future future future future future future future future degree kaufmann typically smaller account coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients fully technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp testing ratio increasing database database database database database database database language language leads filters filters filters filters filters filters filters filters filters window window window supervised depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth frame frame frame frame frame frame frame frame frame frame description perceptron perceptron perceptron architectures architectures architectures architectures improved resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution element reported introduced include include identical identical recently engineering speaker speaker speaker speaker speaker speaker speaker speaker speaker correspond chain chain chain improvement improvement improvement grant lead derivative derivative feed feed feed feed feed feed feed locally locally hybrid hybrid hybrid touretzky generally demonstrate minimal greater greater greater greater central designed moody practice mateo characteristics characteristics drawn demonstrated variety averaged introduce derivatives derivatives derivatives acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic base base base base base base base base base explicit explicit ways distinct segments segments explicitly explicitly explicitly explicitly infinite scales interaction adding events family expressed dependence dependence dependence communication restricted showed frames frames frames frames frames frames frames frames frames frames static static static understanding past past past smoothing smoothing smoothing smoothing smoothing epochs epochs delays filtering filtering filtering foundation transactions transactions transactions kernels kernels kernels perceptual priori perceptrons extension illustrated automatic discuss mozer mozer partially partially grammar grammar grammar gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma hmms divided symbols included tdnn comparing traditional allowing interpreted running duration duration backward providing nips delayed delayed delayed delayed delayed delayed delayed delayed automatically deal modelling modelling modelling employed employed schedule investigate detail estimators replaced accurately accurately recursive lippmann preliminary rise fewer giving giving project possibility dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies referred referred referred analogous waibel waibel coefficient naturally adapt adapt necessarily generalisation predicting adjusted front front front front front front front front art speakers speakers speakers speakers baseline baseline baseline baseline baseline baseline motivated sentences sentences sentences sentences sentences great great advanced trivial guaranteed unstable waveform adjacent adjacent adjacent adapted adapted rapid filtered filtered filtered incorporate incorporate potentially acknowledgement addressed improvements substantially pure led amounts spoken spoken cohen employ incorporated robinson robinson robinson robinson robinson robinson robinson robinson robinson release passes berlin vocabulary weigend resource incorporating prevent phone phone phone phone phone phone phone phone phone phone phone enables hamming hamming hamming decoder comments focused viterbi sentence wesley displays merging merging merging merging merging merging merging picture addison fix labelled reconstructed adds ments adjusting replacing city attractive attractive resulted adequate enhanced date tap tap tap contexts governed displayed regarded regarded regarded sides regard mel schedules darpa darpa modelled modelled modelled modelled mlps mlps smoothed ends ends subsequently cam speaking audio incorporates fellowship fellowship failed expanding incrementally 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number number number number number number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error error error error error state state state state state state state state results units units units units units units units information information problem problem problem models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based based based based space space space space weights weights weights weights weights weights weights weights weights weights linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector order order shown shown shown shown shown shown shown systems systems systems systems probability probability parameters parameters parameters parameters weight unit distribution recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach point single single single single processing processing processing processing control large large large large large rate rate rate test test test test class class class class class optimal optimal optimal optimal optimal inputs form shows shows signal signal paper small size feature net net net net net net net net net net net net net net net net net net net net work work work task methods methods cells cells cells cells cells cells points features features features level level current current trained trained trained trained trained trained trained trained structure structure structure structure problems random high similar similar representation show section section fixed fixed fixed rule rule rule generalization speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter approximation gradient gradient obtained term term term note experiments dimensional dimensional dimensional computation solution research research research independent independent independent independent independent independent log found sequence sequence initial initial initial initial initial table table table table table estimate estimate estimate terms science left left left direction low sets sets range nonlinear outputs continuous continuous continuous continuous continuous continuous continuous abstract applied applied back back find density properties references due ieee ieee ieee procedure procedure decision decision decision propagation context context context context context context context context context context context context context context context context context context context introduction statistical statistical statistical statistical tion difference variable variable measure measure measure measure measure word word word word word word word word word word word word word word word word word higher part previous previous multiple represent markov fact fact techniques proposed length length length length length minimum resulting classes classes performed regions regions optimization optimization optimization optimization optimization optimization optimization knowledge em em obtain original artificial samples samples samples compared cross cross cross cross cross cross cross cross series compute compute compute compute rates rates rates determined experimental experimental goal posterior power power accuracy larger larger larger contrast contrast train train train train train descent dependent dependent dependent dependent dependent dependent dependent source nets nets modeling modeling modeling modeling modeling modeling modeling selection morgan morgan morgan words words department implementation implementation version technique technique technique technique consists consists advances advances difficult final final layers cambridge domain experiment estimates san san conference classifiers estimated basic basic validation validation validation validation validation con weighted conditional developed developed developed criterion criterion criterion entropy entropy entropy iteration iteration sampling achieved achieved achieved measured measured tested tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm inverse assumption complete eds eds journal journal journal easily makes rumelhart development development development kaufmann kaufmann objective probabilistic combination reduced reduced technology technology technology interesting interesting 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bayes designed mateo mateo hard presence reduction reduction sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization groups acoustic relation produces index index plot describes distinct distinct segments minimization select john independently phoneme phoneme phoneme phoneme phoneme phoneme squares squares squares squares squares viewed evaluate frames frames decomposition decomposition decomposition forms understanding completely converges partition reasonable smoothing reduces reduces combining combining combining combining iterative norm euclidean transactions avoid expect includes combinations recognize recognize recognize recognize discuss specifically grammar grammar grammar grammar grammar grammar tests successfully major selecting hmms hmms literature build projections comparing score score score score score traditional traditional conf conf kind prob phonetic phonetic phonetic phonetic phonetic phonetic usual paradigm paradigm paradigm giles giles consisted acknowledgments cowan cowan presents employed parametric overfitting overfitting overfitting difficulty hanson hanson limitations hessian pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit int combine scores scores affect neu spline adjusted singular singular singular explored initialized art art art art art art art art consist baseline baseline improving grouping grouping attempts asymptotically indicating advanced advanced rows publishers publishers smoothness capabilities independence implementing sections shared shared easier incorporate controls mathematics gradually optimize read nsf integrating capability cohen atkeson vocabulary 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systems systems systems systems systems systems systems systems neurons recognition recognition recognition recognition recognition approach approach pattern image single processing processing processing processing processing processing processing control local patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis inputs inputs inputs form shows signal signal signal signal signal algorithms simple simple simple visual visual visual visual visual visual visual paper paper work work work work work work task task methods fig features process process level current current trained cell structure problems problems problems memory representation representation architecture general speech speech speech speech speech speech speech speech speech speech speech real real theory theory theory theory theory theory term activity activity activity dimensional dimensional result university university university university university university university threshold threshold computation computation computation solution research research research found found estimate estimate estimate computer computer computer computer terms science science left left left low frequency frequency temporal machine machine range press press press press press components components components components components components components nonlinear outputs abstract back find find computational computational computational computational computational computational computational computational computational computational analog analog properties properties references component ieee ieee ieee ieee ieee ieee ieee important important important important mixture context introduction introduction complex statistical effect effect effect effect effect effect dynamic dynamic dynamic tion tion tion tion difference spatial spatial spatial spatial spatial spatial lower signals signals signals signals signals signals signals signals signals representations representations word chosen part center required multiple multiple cortex long distributed proposed proposed correlation correlation correlation resulting resulting tasks tasks tasks tasks tasks tasks tasks tasks tasks simulation human human human performed called called potential natural natural orientation applications applications vol vol vol vol vol vol vol vol vol vol vol vol vol vol vol artificial specific cross cross provide provide provide objects objects objects proc proc proc proc proc location perform experimental gain discrete approaches mit mit mit contrast source source source source source source source modeling modeling modeling morgan morgan morgan morgan report department department department department individual individual advances advances joint connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist delay addition addition maps maps maps cambridge cambridge cambridge cambridge cambridge environment environment environment environment environment environment environment environment environment additional san san san san san san conference conference determine determine determine full requires choice significant world world world vision vision vision vision vision vision basic basic basic basic basic basic con con developed developed developed levels lines finally processes processes evidence biological arbitrary group group short short common common common common common effective shape supported main eds eds eds eds eds eds eds vlsi vlsi easily rumelhart rumelhart development development noisy sensory sensory sensory kaufmann kaufmann auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory 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transactions david existing includes perceptual perceptual perceptual silicon usa color extension automatic phys determining aspects identified importance importance paths driven soc soc soc soc soc soc soc conf conf verlag procedures anderson anderson anderson anderson dis superior superior superior symmetry follow timing cue sci duration cues cues cues cues built comp localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization wave delayed correspondence chips chips processors received received principles principles principles principles principles moves tesauro modelling modelling cowan cowan law law employed origin wiley wiley wiley mead mead mead mead kalman relations environments humans humans humans humans accurately accurately hall hall periodic investigated int stream 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interaural interaural interaural interaural pearson fre fre seattle spectrogram spectrogram physiologically exposed believed believed dissertation dissertation dissertation konishi konishi englewood marr anna offsets juang juang modalities colleagues arriving iid iid iid iid iid company assp communicate accounting edition remained magazine brainstem brainstem brainstem reviewed skill problematic devoted ears ears recovering putation col cope medial stan stan jose jose began firings diverge bregman bregman bregman bregman bregman bregman initiated ference converts ular elevation elevation elevation elevation elevation elevation elevation elevation tenenbaum topics entities organisation spence spence quency quency conceptually localize schneider schneider hypothetical ago begun vast fur distinctive neti neti rosen rosen fuse fuse itd itd itd itd aware earliest earliest comprise onsets cooke cooke cooke cooke cooke cooke cooke bandwidths constantly azimuth azimuth azimuth azimuth azimuth 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produce condition coding derived derived robot robot robot robot robot robot robot robot robot robot levels criterion velocity velocity velocity controller controller controller controller controller controller controller path path path product product actual actual provided provided evidence nature biological biological achieved measured transformation fast fast limited limited inverse inverse assumption assumption assumption stable actions circuits circuits circuits circuits amount implemented implemented supported supported adaptation adaptation adaptation adaptation end end ability hypothesis hypothesis hypothesis makes sensory sensory underlying needed combination combination dynamical dynamical unknown unknown coefficients transfer transfer significantly significantly significantly significantly consistent trials representing representing representing call call direct making stored magnitude idea idea produced produced produced produced produced choose predict neuronal neuronal 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generalize generalize generalize generalize generalize paradigm paradigm paradigm leading reach reach reach reach attempt acknowledgments intrinsic decreasing receive law simpler unlike rapidly humans accurately lippmann mass hall existence links biol biol biol int possibility possibility combine structured comparable affect encode encode encode encode encode understand analogous transmission trace trace onset man illustrate changed portion freedom nervous generates submitted plant plant optimum growth sensors adapted adapted adapted capabilities turns rapid perspective perspective straight straight straight straight sys sections producing strictly forces forces forces forces forces forces forces forces forces forces forces forces forces broad broad incorporate describing circle gradually gradually definite res localized localized bandwidth bandwidth cybernetics virtual virtual virtual virtual virtual geometric geometric geometric geometric geometric geometric geometric greatly led led 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task step features features features features features process process process level level trained trained trained trained structure structure structure structure structure structure structure memory memory memory memory response similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation architecture line vectors vectors generalization generalization average states states states term note note note note note note note note note note note note note note activity dimensional dimensional university university university university university university university variables research research research research independent log sequence sequence sequence sequence target target target target dynamics initial constant computer computer computer computer computer computer computer terms terms science science science science science science science prediction prediction prediction prediction present present present present activation activation activation activation activation activation frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal press press position position components components components components components components components components components components components components components components components components components outputs abstract back properties properties properties properties properties references component component component component component component component important important important context context context context context context context introduction statistical statistical statistical effect effect generated generated generated generated parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent change complexity lower rules prior representations representations representations representations representations representations representations representations representations representations representations representations word learned learned learned learned learned learned learned learned learned higher part part center type type represent represent distributed distributed expected expected expected expected expected region region correct correct correct probabilities observed observed errors errors errors errors simulation human human human human human respect performed regions regions regions regions regions made made made global applications study study study study specific specific represented represented represented represented represented represented represented compared application provide experimental experimental constraints mit mit steps comparison comparison comparison contrast contrast nets modeling modeling morgan morgan morgan morgan proceedings proceedings proceedings institute department department code code code code code code code code individual individual individual advances advances advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist bias bias bias graph graph sequences sequences sequences sequences framework framework framework cambridge cambridge domain domain environment environment environment environment environment environment hinton additional additional additional view design design transition trajectory san san san san san stage effects effects conference conference efficient upper significant developed developed developed area path actual actual actual finally processes processes processes processes evidence evidence simply discussion feedforward group limited close close assumption predictions predictions common effective assumed supported eds eds eds eds eds eds eds journal journal journal journal journal journal rumelhart rumelhart development development development including kaufmann kaufmann kaufmann kaufmann typically pairs pairs pairs pairs pairs combination account account jordan jordan block block block block interesting projection projection increasing mechanism mechanism consistent structures structures database principle language representing call early early early early polynomial polynomial attention produced description predict predict predict property typical movement machines hierarchical sejnowski cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive relevant dimensions compare teacher rl rl rl rl rl rl positions entire amplitude constructed occur suggests predicted predicted predicted predicted predicted predicted predicted predicted touretzky clusters half half half half half critical conclusions interactions interactions designed moody moody moody exponential exponential weak weak weak weak weak weak weak learns mateo mateo mateo strong strong strong strong strong strong strong strong mechanisms mechanisms california california averaged targets groups groups groups program denoted denoted attractor acknowledgements explicit construct perception perception perception perception perception perception perception factors sequential generating transitions transitions transitions transitions changing modeled metric metric averaging physical remaining consisting interaction interaction interaction develop frequencies frequencies events events events events events events events events events events events events events events events predictive extraction extracted independently focus depending stages stages stages communication communication viewed codes showed showed evolution static approximated completely similarly epochs epochs spaces spaces event event event event event event event event event event initially string construction construction expect recorded recorded perceptual perceptual combinations activations activations priori priori contour memories illustrated mozer mozer mozer mozer mozer mozer specifically coupled variations variations grammar regular aspects aspects capable importance society society encoded modification modification divided mcclelland mcclelland mcclelland mcclelland attractors reached characteristic characteristic characteristic characteristic induced success interpreted interpreted timing timing timing timing timing timing timing timing timing duration duration duration duration duration duration duration duration duration duration duration duration duration duration duration bar bar bar bar bar vary michael absence paradigm paradigm paradigm providing observable observable highest highest predictor bars diego diego american american investigate relations relations relations relations hanson hanson hanson association association lippmann lippmann lippmann dual mass mass biases discriminant discriminant behaviour behaviour school tech tech rest rest rest relationships relationships authors authors reliable structured structured structured stream encode hierarchy hierarchy hierarchy hierarchy cognition cognition cognition cognition cognition cognition fundamental induction act reading reading psychology psychology psychology psychology psychology psychology psychology created created created aspect aspect aspect separated epoch epoch epoch epoch epoch epoch epoch epoch epoch extent extent submitted explain serial optimum devices histogram histogram histogram developing theoretic phenomena phenomena phenomena coded adapted adapted lies correction starts considerable sections style operators located involve describing pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch beginning implicit gradually gradually members recording recording depicted demonstrates author annual annual virtual fourth reflects reflects composite substantially elman elman elman elman psychophysical backprop incorporated incorporated music music music music music music music music music music music music music music music music music music music music music music music music music music music music music music music frequently rep rep psychological psychological psychological psychological psychological psychological occurrence occurrence occurrence kinds inherent comments decreased decreased notes notes notes notes notes modify japan recover labelled purely harmonic harmonic jones jones jones jones jones smolensky smolensky systematic systematic significance occurred familiar roles canonical canonical canonical canonical canonical canonical responsible combinatorial combinatorial composition composition composition composition composition composition composition composition composition composition composition contexts programs tone tone tone tone tone paul regarded washington washington evident lawrence bases bases recovery reveals reveals master specificity park erlbaum erlbaum alternatively intersection intersection explorations default mind summer specification numerous shepard shepard piece piece piece fellowship inferred reaction revealed feeding adopt quasi quasi blue blue blue blue blue generalizations superimposed classic hierarchies rhythm rhythm rhythm hillsdale hillsdale forcing guess australia australia reflected reflected musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical musical interact learnt learnt ijcnn learnability relate scope multiscale complementary rhythmic rhythmic rhythmic rhythmic discusses tones tones tones tones refined psychophysics suggestions rarely styles styles styles regularities regularities regularities regularities council australian australian phrases phrases todd todd todd todd todd todd melody reflecting inherently incorporation couplings regulatory separates lying repetition stevens stevens stevens stevens stevens stevens stevens stevens placement bach fin connectionism connectionism crl essence priming handbook comprised comprised durations durations durations durations durations massive wiles wiles wiles wiles wiles wiles wiles wiles wiles phillips phillips organisation psych reminiscent anticipate untrained quarter quarter quarter quarter quarter quarter quarter acknowledged notably judgments chorales hild hild menlo ordinate facilitation bptt explores divides melodic melodic behavioural psy beat abscissa intersecting intersecting equipment queensland queensland queensland queensland queensland tonal tonal tonal tonal tonal tonal tonal tonal tonal tonal tonal tonal tonal tonal tonal tonal opening waltz waltz waltz waltz waltz accent accent accent accent accent accent accent accent accent accent accent accent accent accent accent accent accent accent accent accent identifiable plaut plaut emulation octave octave octave octave instruments designer octaves octaves departments cda cda cda postdoctoral funds akin rests fodor fodor western western western western western divisions menzel menzel listeners gauge manifestation generalise characterised 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#@Stevens_C,Wiles_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data data function function function function function function function function function figure figure figure figure time time time time set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output number number number number number number number system system system error error error error error error error error error error error error error error units units units units units units units information information information information information information information information information information information problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based based based based based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer case vector order order order order order shown shown systems systems systems systems systems systems values values values values values values values values values values values parameters parameters parameters weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit recognition recognition recognition recognition approach approach approach approach approach approach pattern pattern point point point single processing processing processing processing large large large large large large neuron neuron neuron neuron neuron neuron rate test test test patterns patterns patterns patterns patterns patterns analysis class class class optimal inputs form form shows algorithms algorithms algorithms simple simple simple paper examples small small small small small small size feature net net net net net net net net net net net net net net net net net work work work task task task task task task task task task task cells features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process level level current trained trained cell structure structure problems problems high representation representation representation architecture show equation rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general generalization generalization generalization parameter real real real real states states theory theory gradient gradient gradient gradient gradient term term term term term term term term term term term term note experiments university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation solution sequence sequence sequence sequence sequence sequence sequence sequence target target constant table table estimate standard computer computer terms terms terms connections node node node node node science science prediction prediction prediction prediction left left direction present activation activation activation activation activation activation activation activation activation nodes nodes machine machine machine machine machine machine machine sets range position position position continuous continuous continuous continuous abstract applied find computational computational computational references component component component component due ieee ieee ieee positive positive important important important adaptive adaptive decision decision decision decision context introduction introduction complex complex behavior behavior behavior effect effect generated generated search tion difference complexity classifier classifier rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure chosen part part cases cases cases type type type type good good good good good binary binary represent distributed distributed make make fact fact fact region region region classes tasks tasks tasks tasks total total total human computed regions means factor factor factor factor made applications applications applications applications study knowledge knowledge obtain obtain negative negative original vol vol vol relative samples represented true application application desired cross cross cross cross series series series series series define rates rates rates rates rates rates rates rates rates rates proc proc perform active determined connected power power power power power power approaches approaches larger larger contrast contrast connection descent descent descent descent descent nets nets nets morgan morgan morgan morgan proceedings proceedings proceedings department consists code advances advances advances advances joint represents represents connectionist connectionist difficult final bias bias bias bias bias scheme scheme addition sequences domain domain equivalent equivalent equivalent additional transition transition san san san san effects effects conference conference capacity determine choice free world world increase increase increase validation validation validation validation produce produce produce coding randomly criterion types types provided backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation depends biological achieved measured feedforward transformation transformation transformation close close predictions circuits amount amount amount amount nearest common generate supported require eds end future future easily easily development kaufmann kaufmann kaufmann objective objective objective smaller smaller underlying underlying reduced reduced reduced fully fully block transfer testing empirical numbers making international international normalized experts expert expert expert decay decay decay decay decay idea combined combined minimize minimize minimize perceptron denotes practical apply strategy include subject subject identical side trees relevant relevant relevant interest interest interest interest interest interest interest interest interest interest sufficient sufficient previously calculated works solve yields yields match match converge address address positions observation interval grant parts move touretzky demonstrate conclusion conclusion conclusion conclusion conclusion conclusion conclusion critical reduce reduce neighbor valued valued designed designed designed moody learns mateo mateo mateo mateo strong characteristics drawn sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal demonstrated california minimizing start decrease decrease decrease reference reference relation pro produces distinct changing implement multilayer simultaneously simultaneously slightly extraction extraction extraction versus boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean yield depending influence solved transform transform transform transform restricted fraction showed understanding understanding approximated approximated allowed reasonable slow dashed performing measurements intervals add penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty generation generation generation generation generation sufficiently classified classified topology david expect box box weighting weighting recognize determines determines prove black absolute phys discussions successfully capable uniformly genetic tend miller miller essentially ten composed compact quickly graphs heuristic dis superior classify notation providing providing reach thresholds extract layered transformed transformed create exhibit difficulty replaced limitations lippmann biases biases biases ml rise rise rise rise reducing examine matches school incremental investigated applicable decisions symbolic symbolic symbolic symbolic symbolic tanh tanh tanh proved notion neu induction act math adapt adapt thought expressions motivated motivated years site stop slowly theoretic failure majority adapted capabilities caused handle handle inside mation commonly consequence acknowledgement describing beginning implicit medical medical annual raw researchers percent fuzzy pure pure amounts backprop backprop introducing marked compares compares calculating gen fall fall fall serve germany germany logical inherent tolerance tolerance diagnosis wesley semantic yielding displays classifying tresp accomplished addison restrict restrict restrict databases databases databases nonzero nonzero nonzero nonzero grows grows turned maass maass kaufman dealing murphy murphy murphy ments adjusting overcome siemens siemens proceeds odd fan fail ral krogh krogh adequate symposium hertz hertz infor mance falls perfor regard intended initialize modelled mlps foundations insight surprisingly relies broken shavlik shavlik shavlik integers influences automated default severe ics uci uci uci verify mind informa summer dna dna dna dna dna ahmad goodman goodman goodman job sontag sontag adopt restrictions year junction junction junction junction junction german german affects imagine stands scenario param unseen pub penalized iff ftp genes impose ijcnn pdp smyth smyth exceed exceed exceed quinlan discretization discretization discretization discretization discretization discretization mimic applicability eters sigmoids advantageous remarkable palmer palmer simplification justified transforming towell towell utilizes interpreting hancock hancock medicine seattle conversion diagnostic month 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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural input input input input input input input data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm output output output output output output number number number number number number error error results results results units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space space space space space space space weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case order order shown shown shown systems values values values values probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method approach approach pattern point image image single processing large large local local local local local local local local local local local local patterns patterns patterns patterns patterns inputs inputs form simple gaussian small small size feature net work task task task task task methods points points points points field features features process process process process process level level level current trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems random random random random high memory memory memory memory response similar similar similar representation representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture show show obtained note experiments experiments experiments experiments activity activity activity activity activity university university university variables research defined standard standard computer computer terms distance distance distance distance synaptic node node node node node science science science science science science science left left left left map map phase phase phase phase phase phase phase phase low low low low low nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal temporal temporal temporal temporal temporal sets press learn learn outputs outputs abstract applied applied applied convergence properties properties properties references positive procedure important important introduction introduction estimation behavior behavior effect effect effect recurrent tion tion change complexity spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations learned chosen higher previous cases cases cases cases type required represent make techniques techniques correct correct observed observed forward forward forward scale scale scale resulting ing ing computed respect regions mapping mapping mapping mapping mapping means factor factor natural global global global global global global global global global global global global global global global global global global global global global global study study study knowledge knowledge knowledge knowledge negative vol vol vol vol vol vol represented cross receptive receptive receptive location location active experimental experimental experimental experimental goal constraints constraints constraints constraints connected steps fields fields train nets modeling morgan proceedings proceedings report report institute words department department department version technique internal internal internal internal individual advances advances represents connectionist connectionist responses responses layers layers layers scheme graph graph graph graph graph graph maps maps maps maps maps maps considered considered considered domain environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment directly directly directly directly hinton hinton hinton additional additional view solutions design san effects conference full full choice choice estimated increase give con con developed developed developed levels levels area lines lines actual processes selected backpropagation iteration depends constraint biological discussion technical technical stable finding effective effective implemented implemented main eds eds journal journal journal square square end degree development development development development development including kaufmann typically smaller york york consistent consistent consistent structures uniform leads squared representing details iterations international early magnitude combined added added recent pair robust robust robust robust separate separate reported reported introduced introduced subject machines subset subset sejnowski cognitive cognitive cognitive cognitive sufficient axis tions correspond studies studies studies converge chain locations locations locations grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid bounded bounded bounded organization organization sensitive sensitive horizontal studied studied rotation alternative alternative feed feed feed locally move touretzky white white white reduce tangent sigmoid asymptotic mateo mechanisms integration integration presence characteristics proportional relationship derivatives configuration configuration acknowledgements boltzmann reference reference reference relation relation edges longer ways factors plot vertical distinct sensitivity explicitly linearly dimensionality dimensionality dimensionality dimensionality involves involves involves remaining scales develop develop integrated formed select formation formation formation formation formation formation review influence influence influence codes open showed activities activities allowed sign spaces spaces sec neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood purpose distances distances distances distances kohonen kohonen degrees avoid avoid exploration exploration exploration exploration exploration exploration exploration exploration exploration extension plotted plotted activated activated mozer candidate absolute partially neighbors neighbors characterized determining middle middle middle society successful comparing plots plots essentially characteristic capture capture procedures moore moore showing contribution strategies duration built usual giles correspondence illustrates illustrates neighboring neighboring intrinsic cowan presents layered layered wiley essential exhibit put relations relations environments environments environments environments environments hanson preliminary graphical matches school incremental relationships structured comparable proper affect topographic topographic topographic topographic topographic topographic topographic topographic topographic cognition cognition cognition cognition cognition phases phases notion examined circles circles circles circles coarse necessarily psychology psychology psychology illustrate versions obvious explored separated separated separated hebb hebb academic initialized extent mentioned mentioned ment ment ment ment ment directed separable crucial crucial phenomena adjacent spatially spatially berkeley sites organized strictly strictly forces constructing broad ran circle beginning gradually res annual cybernetics mellon reflects greatly carnegie reflect reflect reflect reflect elman elman elman cmu tional axes axes readily introducing continuously incorrect rep variant span pittsburgh pittsburgh pittsburgh pittsburgh pittsburgh ture weigend proven qualitatively comments focused converged cor globally globally acquisition acquisition acquisition restriction rotated circular repre repre repre encoder encoder encoder connecting smolensky reaching arranged systematic ranges proceeds imposed resistance exploit affected child constructive representational representational paul mental topological topological evident evident emergence emergence emergence emergence emergence emergence suggesting route route erlbaum correcting valuable hart hart alternatively influences vari pressure associations associations associations associations associations associations associations associations associations associations associations associations maintaining ence arcs arcs summer indirect constitute ber munro munro munro munro munro munro munro munro munro munro munro ties emerge emerge responds conjecture causing solely hierarchies chicago associate hillsdale hillsdale examining reflected alter representa representa representa visited visited visited num neurophysiological relate acquired acquired investigating represen represen drawback tively reveal reveal grateful supports supports behave struc mea topography architectural regularities survey stephen hyperbolic correspondences subjective neighborhoods neighborhoods dom injected ackley ackley unreliable emerges beneficial ooo grids judd judd tended tations tations positioning priming priming comer comer comer sentation capturing wiles wiles wiles sented landmark landmark landmark landmark landmark landmark landmark landmark landmark landmark landmark landmark progresses cations cons frozen activating impor encourage tant manipulating environ environ environ environ environ ant cog orthogonality underlie cap landmarks landmarks landmarks 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#*network network network model model model model model neural neural neural function figure figure figure figure time set set set set set networks algorithm number number number number number number system results results results information information information problem problem problem problem problem problem models models models models models performance performance based based space weights weights case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order order order order order order shown shown shown shown shown shown shown systems systems values values values distribution recognition method method processing processing large large large test test patterns optimal optimal simple simple paper paper paper paper examples examples examples examples examples examples small size size size size size feature feature feature feature feature feature task task features features features features features features features features features features features features features features process process structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems random random high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar representation representation representation representation representation representation representation representation representation architecture fixed fixed fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general term term term term experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional university threshold solution solution found found found constant table table table table table table table table estimate estimate estimate estimate estimate standard computer computer node science science activation low low low low low low low low low object object object object object object object object object object object object object object object object object object object object components components outputs continuous abstract analog analog analog likelihood references due ieee important important important context context context context context context context introduction complex complex effect effect effect effect dynamic variance variance variance search variable lower rules measure measure measure representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations chosen chosen higher higher higher higher higher higher type multiple multiple multiple good good long long long long conditions conditions conditions conditions represent represent distributed distributed distributed distributed distributed distributed distributed distributed make make scale tasks tasks sum performed called called called times times times elements elements elements elements elements mapping mapping mapping mapping mapping means potential dimension dimension dimension dimension obtain artificial artificial artificial artificial relative represented represented represented represented represented represented represented represented true true compared cross compute objects objects objects objects objects objects objects objects objects objects objects objects location location perform perform perform equal approaches approaches comparison comparison larger selection morgan morgan proceedings department technique code advances joint represents connectionist connectionist connectionist connectionist connectionist responses addition ai maps considered considered experiment experiment experiment experiment experiment experiment experiment experiment experiment view estimates estimates estimates estimates san san stage stage stage stage stage stage stage stage stage stage stage stage stage bit bit bit bit bit bit bit bit bit bit bit conference conference efficient full full full requires choice approximate approximate free pages pages pages give give produce coding coding types types types types lines product product product product product product product product product product product product product product product product product product product product product product product product provided provided selected constraint associative discussion normal increases describe describe describe fast fast fast fast fast inverse inverse corresponds stable surface surface surface surface surface surface surface surface surface surface surface surface common assumed shape role role role role role role role role role role role role require main ability degree degree degree degree degree degree degree development development including kaufmann kaufmann underlying underlying reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced account transfer increasing consistent consistent consistent structures structures structures structures structures structures structures structures structures structures structures structures structures operation operation operation numbers making making bottom run run added denotes discussed discussed pair element typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity subject cognitive cognitive cognitive calculated works solve match match match studies studies diagonal improvement sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive constructed constructed constructed constructed exists scaling wide wide width width occurs column column runs runs runs runs greater editors editors central designed exponential mateo mateo encoding encoding encoding presence demonstrated intelligence intelligence intelligence intelligence variety variety relationship manner force base base base base relation relation relation relation relation relation relation relation relation pro construct solving ways ways estimating estimating estimating estimating estimating estimating changing changing recall recall recall sensitivity explicitly involves involves agent select competition john john john john john john john john john john decreases independently expressed expressed review stages stages estimator estimator estimator viewed viewed influence evaluate controlled suggested performing normalization purpose false false false remains advantages transactions existing retrieval retrieval retrieval retrieval retrieval illustrated absolute structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural middle aspects aspects aspects aspects aspects aspects identified identified importance society encoded encoded computationally computationally computationally detect efficiently situation situation decoding involved simplified dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot absence nips giles highest highest binding binding binding binding binding cat cat cat illustrates mixing deal software receive cowan command access varied relations relations relations relations relations relations relations relations relations relations relations involving hanson matches mappings investigated ideal ideal ideal relationships reliable symbolic scores scores scores scores scores scores scores scores scores scores scores scores encode cognition analogous analogous analogous analogous analogous analogous analogous attributes attributes attributes circles psychology psychology changed ensure adjusted adjusted aspect der noted mapped mapped mapped mapped mixed growth distinguish distinguish distinguish convolution convolution convolution convolution convolution convolution convolution convolution improves adapted expensive multiplication comparisons comparisons comparisons comparisons strictly products products products products products products products products products products products products products pool pool involve calculations toronto toronto attribute attribute attribute attribute attribute attribute attribute author annual fluctuations alignment alignment alignment alignment alignment alignment alignment alignment alignment outer outer outer outer researchers argument reflects apparent varies people people people people evaluating reflect reflect items items items items items items flexible flexible flexible flexible tional share rep psychological requirement incorporating adjust adjust sums deviations consistently person person person person ordinary ordinary ordinary ordinary ordinary ordinary ordinary redundant appearance arguments ordering ordering tensor tensor circular circular circular circular circular circular circular count impossible flexibility smolensky proceed adjusting analogy analogy analogy analogy analogy analogy analogy analogy analogy analogy analogy analogy fail reasoning roles roles roles roles roles roles roles implications affected spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot intuitive selects tap separating governed mouse mouse mouse intended counter candidates similarities ranking tokens tokens tokens permutation matter probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe probe canada erlbaum insensitive influences associations associations compressed compressed compressed arcs email nelson preserving causing causing causing causing causing causing causing causing causing causing causing causing ease ideally superimposed classifies constitutes affects hillsdale reflected reflected remainder alter token token searches plate plate plate plate plate plate plate plate plate plate plate plate retain spreading represen suffer algebra xly xly 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function figure figure figure figure figure figure figure time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number error error error results results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance space space space weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer case case shown systems systems values values values values values values values values weight weight weight weight weight weight weight weight weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit pattern pattern pattern pattern pattern pattern pattern point point image single processing processing processing processing processing large large large local test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix inputs inputs form form shows algorithms algorithms paper small small small small size feature net net net net net net net net net net net net net work methods points points points points points points points features features features process process process level current trained trained trained trained trained structure structure problems problems problems problems problems problems problems problems problems problems problems problems high high similar similar representation architecture architecture show show equation section line general average states term term term experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university university variables solution solution solution solution solution solution research research research research research research defined defined defined defined defined defined found target target target target target target target target target target target target standard standard standard standard standard terms distance connections connections connections connections connections connections connections connections science science science science prediction direction present present present activation activation activation activation activation activation activation activation activation activation activation activation activation sets range range range press press press press press press learn learn learn learn learn learn components components components components components components components components components components components components components components components components components components components components components components components outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied applied applied applied back back back properties references component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component due positive positive positive positive positive positive positive positive important important propagation propagation propagation propagation introduction complex complex statistical statistical generated variance variance variance parallel parallel parallel parallel parallel complexity assume measure representations representations representations representations representations representations learned learned center center center cases cases cases cases cases type type required multiple multiple multiple good binary represent represent represent represent represent distributed distributed distributed distributed distributed distributed distributed distributed distributed expected make make make make make fact fact fact fact techniques correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correct correct correct correct correct forward simulations simulations simulations simulations minimum tasks tasks human human computed multi multi multi multi multi multi sum performed performed times natural natural orientation knowledge obtain negative negative negative negative negative negative negative negative relative relative specific application application application application cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross provide provide provide provide define perform goal related related constraints constraints constraints connected connected connected connected connected connected connected connected connected connected connected connected connected equal equal equal equal equal equal equal equal equal approaches mit mit steps comparison comparison comparison comparison comparison comparison larger contrast contrast contrast connection nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets modeling modeling morgan morgan proceedings report department department version version version technique technique technique technique technique technique technique technique technique technique technique internal code code individual individual advances represents represents connectionist connectionist connectionist connectionist difficult difficult difficult difficult bias layers layers layers layers addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition addition cambridge hinton hinton hinton hinton hinton view view solutions solutions solutions solutions design san san stage determine determine determine full full requires significant significant significant free speed produce randomly randomly randomly randomly randomly types types product product product provided provided finally selected selected selected selected selected nature nature nature simply achieved discussion discussion technical describe close finding finding common effective shape shape generate supported role role role main eds eds eds eds end end end end cluster cluster cluster degree degree makes rumelhart rumelhart rumelhart development development development development development including including fit kaufmann kaufmann typically typically typically pairs pairs pairs pairs pairs pairs smaller needed combination combination account account fully fully interesting interesting interesting york consistent empirical operation operation operation language language principal principal principal principal representing representing representing numbers direct combined combined improve correlations correlations advantage pair pair pair pair separate separate separate separate separate reported apply apply apply apply include include subject machines sense sejnowski sejnowski sejnowski sejnowski sejnowski array array array array cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive engineering interest interest interest interest dimensions sufficient sufficient highly highly varying compare approximately volume volume yields yields yields yields yields pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca separation williams sensitive constructed exists scaling scaling suggests suggests extended extended rotation rotation predicted feed clusters demonstrate half starting starting critical critical greater greater greater greater greater greater greater greater greater greater reduce valued interactions sigmoid sigmoid designed designed clear clear clear faster learns learns learns learns taking largest california california targets targets targets targets targets targets targets targets targets groups groups identification appears construct construct written factors primary plot recall explicitly involves text unique unique adding adding adding yield yield yield yield focus focus focus focus depending depending stages influence codes codes variation variation variation variation variation variation variation operations operations operations operations operations restricted static static understanding understanding similarly similarly discrimination sign sign sign sign sign sign sign partial earlier additive performing epochs add remains valid assigned construction foundation advantages degrees degrees figures activations activations activations activations activations activations activations activations activations sciences plotted plotted plotted domains simplicity middle middle identified suitable encoded mcclelland mcclelland mcclelland mcclelland plots plots plots plots plots plots essentially capture capture repeated success success symmetry symmetry contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution contribution generative generative categories play realistic eigenvalue automatically extract acknowledgments load origin diego diego layered layered xor xor xor xor xor xor xor xor essential difficulty difficulty difficulty relations involving detail association helpful fashion school rest behavioral scaled comparable variability scores scores scores scores scores scores scores scores scores scores scores understand understand cognition cognition cognition cognition cognition analogous examined examined examined naturally closest trace integer integer analyze predicting opposite opposite opposite opposite psychology psychology ensure multivariate multivariate multivariate generates contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions explain inequality developing distinguish distinguish distinguish distinguish distinguish fairly adjacent adjacent analytical analytical adapted adapted answer answer cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication correction comparisons comparisons comparisons considerable precisely ran commonly products products potentially involve involve begin begin english english english researchers requiring fourth reflects apparent apparent understood understood elman elman elman elman elman elman elman elman elman elman spoken employ psychological psychological characterize proven suited sums inherent comments progress wesley yielding yielding extreme extreme extreme extreme arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic contribute contribute picture picture sort proportion primarily accomplished oxford restriction linearity perfectly rotated rotated rotated rotated rotated rotated eliminate connecting connecting reaching reaching eliminated spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral systematic difficulties tools familiar analyzing analyzing analyzing analyzing analyzing neurobiology fail roles roles roles sanger sanger sanger sanger sanger sanger sanger sanger sanger implications implications carry filled filled date analyses analyses slice separating separating representational respective lang lang accounts facilitate thomas similarities multiplied multiplied multiplied foundations foundations reveals matter ends informative canada canada relies erlbaum exploiting summarize fahlman fahlman fahlman fahlman fahlman fahlman explorations explorations dividing assigning treat spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals multiplying multiplying multiplying multiplying multiply summer unable microstructure microstructure covering leaming emerge revealed distinction distinction centre comparative comparative comparative comparative comparative aij aij stem descriptions hillsdale principled equality insights insights insights distant convert disadvantage argued confirmed interactive nonetheless placing likewise places indication retained bring ignoring signs examination examination answers answers answers answers answers answers answers answers answers answers answers answers unpublished challenge mann coming coming coming ucsd diagrams topologies served expense council justified identifies quadrant insufficient rosenberg rosenberg confirm inhibit generafive generafive interpreting mirror developmental morris accomplish accomplish drawing concern appealing distinguishing distinguishing possess possess operational separates separates slices push push ooo correctness lying deals deals symmetrical enhances sending sending sending sending sending sending sending sending sending sending adjusts nettalk connectionism crl crl accounting accounting schmidt schmidt scott differentiate differentiate focusing problematic derives supposed simon began mountain mountain linearities lebiere lebiere lebiere lebiere lebiere triple occasionally competence plotting psych distinctions distinctions distinctions distinctions distinctions distinctions retention intervening symmetries symmetries claimed army complexities experimentation distinguishes distinguishes unequal responsibilities responsibilities signaling quadrants quadrants quadrants quadrants mined mined taught incremented tilted superfluous bypass emphasizing skew sector sector sector sector sector sector sector sector renders succeed buckingham buckingham resembling cited witbrock witbrock ijk ubiquitous cumbersome subjected subjected subjected subjected subjected wrap notable isolate recruited recruited recruited jeffrey opposing mcgill mcgill mcgill fodor fodor relearning grounds unscaled unscaled unscaled inclusive inclusive inclusive wjk wjk principally afforded afforded afforded pylyshyn pylyshyn slicing loadings loadings loadings loadings pronounce lesioning lesioning pioneered downstream supplement leam obscure leamed interpretability bol underscores unduly impair undoubtedly 
#@Elman_J,Shultz_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model model model model model model model model model model model neural neural neural neural input input input input input input input input input data data data data data data function function function figure figure figure figure figure figure set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training output output output output output output output output output output output output number number number number system system system system system system error error error error error state state state state results results results results results units units units units units units units units units units units units units units information information information information information information information information information information problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case shown shown shown shown systems values values values functions method approach approach pattern pattern pattern pattern pattern point image single single processing processing large local rate test test test test patterns patterns analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix paper paper paper examples small feature feature work task points points points field field field field field field field field field process process level level current trained trained structure structure structure structure structure structure structure problems random high high high representation representation representation representation representation representation representation representation representation representation section section section section section fixed fixed fixed fixed fixed vectors general general general general general approximation approximation states theory obtained obtained obtained note note activity result result result university university computation solution solution research defined defined defined defined sequence target initial table table table table standard computer computer computer terms node node node node node node node node node science science science presented present activation activation activation activation activation nodes nodes machine learn components components components components abstract applied applied back computational convergence convergence analog analog analog analog properties references component component component component component due due procedure procedure procedure procedure procedure procedure procedure procedure important introduction complex complex hand dynamic dynamic generated search difference variable lower representations representations representations representations representations representations representations representations representations representations representations representations representations representations higher part part part part part part theorem theorem theorem theorem theorem theorem type required good binary binary conditions conditions conditions represent represent represent represent tree tree tree tree tree tree tree tree tree tree tree distributed distributed make fact fact fact fact fact proposed proposed correlation length correct observed errors errors errors errors forward simulations minimum ing tasks total total respect respect multi performed performed performed performed performed elements elements mapping factor potential dimension made made natural natural global applications knowledge obtain original artificial artificial artificial represented represented represented represented represented represented represented represented represented represented true desired experimental goal related related constraints constraints connected equal connection connection fields fields fields fields fields fields dependent report institute department department implementation version consists consists advances represents connectionist connectionist connectionist connectionist connectionist connectionist graph graph graph graph graph graph graph graph graph graph graph graph considered considered considered considered considered considered computing computing directly hinton hinton solutions bit efficient approximate free pages validation validation coding randomly developed developed levels levels product actual actual backpropagation biological achieved discussion discussion covariance technical technical increases transformation transformation transformation fast fast fast corresponds complete stable stable stable stable stable stable stable stable stable stable common effective implemented generate role theoretical ability ability ability instance easily makes smaller smaller hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced interesting projection structures structures structures structures structures structures structures trials language principal principal representing representing representing representing representing iterations direct direct direct stored stored bits bits bits international idea run light advantage property element reported introduced introduced introduced introduced identical hierarchical trees trees trees relevant sufficient sufficient previously previously conventional volume works solve solve converge achieve background bounded lead concept extended matrices correctly feed touretzky touretzky column setting pass demonstrate conclusion conclusions conclusions clear clear constrained constrained encoding encoding encoding encoding encoding encoding propose cycle cycle cycle cycle cycle cycle cycle cycle cycle characteristics intelligence intelligence intelligence intelligence labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled assuming minima configuration configuration question explicit derive longer index generating label label label label label label label label label label label label label label label label label label stability stability stability stability stability stability stability stability multilayer explicitly explicitly simultaneously remaining remaining remaining unique implies cycles cycles cycles cycles choosing depending correlated transform restricted updated labels labels showed showed decomposition static key key key key key key epochs epochs roughly closed symbol symbol symbol symbol advantages activations perceptrons retrieval retrieval retrieval subspace memories extension extension extension extension extension discuss domains domains partially simplicity reason aspects aspects encoded encoded encoded encoded encoded encoded encoded encoded encoded encoded detect build build efficiently identity reached reached compact graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs kind procedures procedures procedures procedures procedures procedures procedures decoding decoding decoding decoding decoding decoding decoding decoding decoding success success success issue issue content content content content content content content content content list list nips binding hypotheses automatically attempt presents employed powerful transformed access access access access access access access access access access access access access access access access access access access access access access access access access access association recursive recursive recursive dual dual existence reducing respond respond ideas terminal possibility possibility relationships structured structured eigenvectors symbolic symbolic symbolic symbolic encode encode encode encode encode encode fundamental naturally configurations perfect subsets subsets rank rank singular aspect versions freedom store store epoch epoch synthetic years asymptotically asymptotically asymptotically asymptotically directed coded capabilities capabilities briefly berkeley berkeley berkeley easier strictly located located leaves leaves potentially beginning toronto arises auto cybernetics researchers integrating considerably lack posed share occurrence proven proven asymmetric logical decoder decoder findings sentence sentence wesley contribute consistently don addison labeling labeling labeling labeling labeling labeling labeling acm acm tensor repre encoder encoder encoder encoder discover discover smolensky smolensky children clamped clamped extending wrong wrong wrong wrong ments satisfying proceeds imposed exploit fail bourlard bourlard modifications spurious spurious performances performances corollary representational encountered facilitate branching specialized pollack pollack pollack pollack pollack record belonging belonging belonging storing extends statement statement implicitly pen baldi baldi linguistic mind compressed compressed compressed arcs recursively preserving feeding terminals theorems corrected reports hierarchies constitutes possibilities letting discovering jacobian care relating plate plate plate distal records hornik hornik harder nil nil nil nil nil nil nil nil nil nil nil nil nil exploited sigmoids sigmoids survey handling demand saturated sake invertible firstly doesn suffers conceptual conceptual imple termination fill lists possess manipulated tells retrieved retrieved outgoing outgoing symmetrical symmetrical connectionism pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer pointer sentation cyclic decoded fixing surprise allocating allocating enabling dyer dyer dyer holographic holographic relax crg pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers pointers retrieve entities erroneous ness ness italy synthesize claimed perspectives clamping diverges experimentation rationale knight knight icsi icsi checking cial philosophy accessed accessed accessed accessed accessed accessed pol stacks surveys surveys unification unification void void void void void void void void void void compositionality artifi kamp kamp ablex descriptors beled corso multidisciplinary neuroengineering 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model neural neural neural input input input data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error state state state results results results results results units units units units units units units units information information information problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space space space space weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case order order order order parameters noise unit unit unit distribution method method method method method method method method method method method method method method method method method method method method method method method approach approach approach approach approach point point point point point point single single single single single single processing control control large test test test test test test test test test test matrix optimal inputs inputs form form shows shows shows shows shows shows signal simple paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small size size size size size size size size size net work task task task task task methods methods methods methods methods methods methods methods methods methods methods methods step step step current current current current current current trained trained trained trained problems random random random random random high similar representation representation architecture architecture architecture show equation equation equation fixed line line line generalization generalization generalization generalization parameter parameter approximation average average average average average gradient gradient gradient gradient gradient gradient obtained obtained obtained note note note note experiments experiments experiments experiments dimensional university computation computation solution target initial initial standard standard standard computer terms terms terms terms distance science science prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left sets sets sets sets sets sets sets sets sets sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum nonlinear abstract back find computational likelihood references component due due due ieee procedure introduction hand generated generated generated generated variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search tion difference complexity complexity complexity lower lower measure measure previous previous type required required required required required required required required required required make techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques observed observed forward scale ing ing ing total total total total total total total total total total regression respect respect performed performed performed performed performed performed performed times times times times times optimization dimension study obtain compared compared desired desired desired desired desired desired desired desired desired desired series series series series series series series provide provide compute compute compute compute compute perform active active active active active active active active active active active active active goal equal equal approaches steps steps steps steps steps steps steps steps accuracy comparison comparison comparison comparison comparison comparison comparison larger train train train selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection report report report institute department department implementation technique technique technique technique technique technique code code code individual difficult final bias bias bias layers addition graph equivalent directly additional additional solutions solutions san effects requires requires requires requires approximate give condition randomly randomly developed criterion criterion criterion criterion criterion provided provided finally selected selected selected selected selected selected selected selected selected selected selected selected selected sampling sampling technical technical arbitrary denote denote denote denote denote close close close close close close close predictions finding implemented generate supported require require ability fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit objective typically typically typically typically typically typically typically typically smaller needed significantly special uniform uniform uniform uniform uniform uniform uniform uniform squared squared squared squared details max max max max making normalized early magnitude magnitude minimize minimize choose added added property separate typical reported practical apply apply include sense subset subset subset subset subset engineering highly compare compare compare compare compare compare previously conventional conventional works diagonal grid grid grid grid grid grid grid grid entire entire entire entire entire grant suggests suggests deviation deviation feed feed width width loop loop white white white white white white white white white white white demonstrate demonstrate runs runs runs runs runs runs runs runs runs runs half flow place reduce reduce conclusions depend clear performs performs practice learns presence demonstrated california california solid proportional minimizing minimizing user start introduce manner denoted acknowledgements derive ways sequential estimating dept sensitivity involves easy slightly slightly slightly slightly integrated integrated integrated integrated integrated adding adding versus versus versus versus versus versus select select select select select select select select select select decreases choosing choosing correlated interpretation evaluated evaluated evaluated evaluate operations restricted showed approximations sizes sizes suggested suggested calculation calculation fitting fitting fitting intervals valid sufficiently sufficiently euclidean transactions plotted maximize candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate partially tests tests tests reason regular straightforward straightforward compression selecting selecting selecting selecting selecting selecting selecting uniformly computationally delta detect detect comparing comparing comparing identity composed composed refer refer heuristic physiological follow minimizes automatically automatically subsequent modelling bars bars simpler diego varied varied environments involving dotted preliminary fewer fewer reducing giving giving history analytically referred root maximizing maximizing maximizing maximizing comparable comparable comparable oscillation necessarily predicting ensure greedy initialized explain chaotic distinguish growing growing growing growing growing growing growing growing improves floating floating expensive expensive glass glass glass glass glass glass glass glass glass worse worse comparisons comparisons rapid sys closer easier easier easier easier ran worst cut opt beginning beginning begin nsf exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars exemplars outer conjugate requiring fourth considerably compares compares requirement passes reaches gave tolerance median median globally consistently consistently consistently shifted representative feasible appropriately count exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar proceed fits fits fits adds adds accepted occurred occurred occurred attractive attractive familiar grow los mark mark mark cottrell cottrell cottrell cottrell cottrell optimally nonparametric selects selects selects selects continue continue excellent respective uni competing competing competing chooses chooses initialize iterated iterated iterated iterated iterated iterated infer arrive jolla jolla clean informative relies robert consecutive sequentially dramatically dramatically outline incorporates minus minus minus minus minus achieving validity presenting incrementally distinction chaos additionally arg spaced spaced reject reject reject penalized mackey mackey mackey mackey mackey mackey mackey mackey mackey increment modifying tems permits denoting challenging scope overhead overhead overhead iri worth million million sta lapedes lapedes exhibited ignoring ucsd sigmoids picking replacement fractal demand justified marks justification heavily savings spacing spacing suffices appealing evenly equa triangles beneficial alan exploits tended tended terminates doubling alamos ensuring greatest noiseless routine replaces datapoints severely occasionally ton tighter rmse rmse rmse rmse rmse rmse rmse rmse rmse rmse rmse possesses decrement decrement grown restart picks desire concise concise concise concise henceforth comprise plutowski plutowski plutowski plutowski plutowski plutowski plutowski plutowski plutowski plutowski cse divides succession brevity amples multiplies multiplies multiplies multiplies multiplies multiples economics looked attain deliver worthwhile restarts restarts restarts millions 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#@Cottrell_G,Plutowski_M,White_H,
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layer layer layer layer layer layer layer layer layer layer layer layer layer case vector vector vector order order order order order values weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method approach point point point point image single large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron class class class class class class class class class class class class class class class class class class class class class class class class class class class class optimal form form algorithms paper examples examples examples feature feature feature feature feature feature feature feature feature feature feature work methods methods methods methods methods methods methods step field features features features features features features features features features features features features features features features features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process current current trained trained trained structure structure structure problems memory memory memory memory similar similar similar similar similar representation representation section line line rule rule rule rule vectors vectors general general generalization generalization obtained obtained obtained dimensional dimensional university independent found found found table table table table standard standard distance synaptic synaptic synaptic synaptic node node node node node left direction presented presented presented presented presented presented presented map map present present present phase phase phase phase nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency sets sets maximum maximum press learn abstract back back back back find references due due due due ieee propagation propagation propagation propagation introduction stimulus stimulus assume classifier classifier classifier classifier classifier lower rules rules rules rules rules rules rules rules rules rules rules rules rules signals signals signals signals word word higher part part previous previous previous cases cases firing type multiple binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary represent represent represent represent represent represent represent represent represent represent represent represent represent represent represent represent correct observed forward forward forward classes classes classes classes classes classes classes classes classes classes classes classes classes tasks total total human human computed multi multi multi multi multi multi performed called called applications applications applications applications knowledge specific specific represented represented represented represented represented represented compared compared cross cross cross cross objects perform active determined related related connected distributions larger train words words department synapses synapses consists consists individual represents represents final layers layers layers layers layers scheme scheme maps maps considered considered considered considered considered environment environment environment environment environment environment environment design stimuli bit determine classifiers classifiers upper basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic randomly lines actual processes processes selected selected backpropagation inhibitory inhibitory inhibitory associative associative associative associative associative arbitrary denote tested tested fast excitatory excitatory actions nearest nearest nearest nearest nearest common synapse synapse synapse end pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel smaller underlying needed needed combination combination combination testing testing significantly mechanism special mode mode representing representing representing representing details numbers pre bits bottom added added added light light light improved exact advantage practical practical pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels sense previously observations approximately approximately match match match correspond background evaluation positions interval entire exists intensity occur correctly correctly feed feed boundary boundary boundary boundary boundary boundary generally column place row neighbor neighbor neighbor neighbor neighbor depend learns taking mechanisms physics largest demonstrated start introduce scene scene scene scene scene scene scene scene scene scene reference index index ways ways category category coordinates involves easy spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral consisting consisting consisting events events events events events blocks select family family independently depending codes evaluated updated diagram intervals event event event event event event event event event purpose purpose visible assigned assigned euclidean classified classified classified classified classified classified classified classified classified classified classified classified classified transactions recorded recorded recorded building existing combinations combinations activations retrieval retrieval memories memories activated activated activated characterized tests regular identified identified differ effectively included included identify post comparing situation ten kind contained contained list list list vary highest leading reach reach thresholds consisted consisted consisted consisted illustrates satisfies neighboring situations situations employed carried parametric rest rest relationships relationships reliable reliable reliable affect encode hierarchy hierarchy hierarchy hierarchy cover cover cover cover closest implementations noted precise consist consist mixed submitted animal scenes scenes scenes scenes scenes scenes scenes scenes stop band band band ground ground ground ground ground ground growing growing cascade cascade tool handle comparisons inside sections widely cut auto auto auto auto auto explained percent percent collected collected items consistency consistency red red red red red red red red red red red lattice lattice car item item item item item item item item item item item item item item item item item item item item item item item item item marked formulated treated compares compares howard rely incorporating serve serve green green enables classifying identifying ordering bin food turned turned arranged lost systematic adds wrong ranges grow serves bands bands adequate preparation performances started ensures ambiguity james washington washington belongs arrangement enable specificity specificity belonging relies propagate propagate propagate default assigning limitation outlined sequentially verify land land land land land land pointing encodes presenting presenting presenting presenting classifications classifies associate reflected remote activate activate activate simplifying intensities intensities cartesian turning turning happen ation treating housing housing utilizing covers covers mcculloch discretized pitts identifies influenced send water loaded shot shot industrial stay core operational diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond diamond frequent vicinity carrying pointer corn corn clues clues clues clues clues clues clues clues clues clues clues clues clues clues 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#@Salu_Y,
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#*network network network network network network network network learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks training training algorithm algorithm output output output output output output number number number number number number number system system system error error error error state state state state state results results results results results results results results results results results information information information information information problem models models models models hidden hidden hidden hidden hidden hidden hidden based based weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown systems systems systems parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition recognition recognition method method approach approach pattern processing processing processing processing processing processing processing large local neuron neuron neuron neuron test analysis analysis analysis analysis analysis analysis analysis class class class class matrix matrix matrix matrix inputs form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms simple gaussian paper paper paper paper paper small small feature feature feature feature feature feature feature feature feature feature feature feature feature work work work work work work task methods methods features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process current trained trained trained trained structure high high response similar similar architecture equation section section section section vectors vectors vectors vectors general speech average average average average states theory theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained experiments activity activity result result university threshold threshold threshold threshold research research research research defined found found found found found dynamics initial constant table table estimate standard standard computer connections synaptic synaptic synaptic prediction direction presented presented presented presented present present activation activation activation low low frequency frequency frequency frequency frequency frequency frequency frequency press learn components nonlinear nonlinear outputs outputs abstract applied applied find find references ieee ieee ieee introduction introduction introduction hand estimation effect effect generated variance variance assume rules signals signals signals signals signals signals chosen chosen chosen chosen chosen higher part previous cases cases cases cases type type type good good good good good good long long conditions conditions represent equations fact fact techniques techniques techniques techniques techniques techniques techniques techniques length length observed observed observed observed errors forward minimum resulting classes classes classes total human human human human human respect multi multi multi multi performed called elements made made applications applications applications applications filter original vol vol vol artificial artificial artificial artificial artificial artificial artificial artificial artificial desired desired series series series series perform perform determined experimental experimental connected connected gain discrete brain brain brain brain brain brain brain accuracy accuracy accuracy support support train train nets morgan morgan morgan proceedings department department synapses technique technique technique technique consists consists consists advances advances advances advances advances represents responses addition addition maps considered considered computing domain domain domain domain domain domain domain domain domain domain domain view san san san requires free basic basic basic give give give condition channel channel channel channel channel criterion criterion types discussion normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal feedforward describe describe fast limited short effective assumed assumed instance degree makes noisy noisy fit kaufmann kaufmann kaufmann underlying underlying underlying underlying underlying underlying combination unknown unknown unknown unknown coefficients technology technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp testing character york segmentation representing representing representing representing representing representing pre pre pre pre direct direct window experts experts frame frame frame frame frame frame frame frame frame frame frame perceptron denotes architectures advantage typical typical moving moving period subject subject subject subject subject subject sense recently engineering highly varying approximately subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects works tions studies studies studies converge diagonal diagonal channels channels interval interval interval digital matrices matrices predicted correctly touretzky touretzky touretzky touretzky touretzky touretzky width pass pass assumptions reduce segment conclusions tangent sigmoid sigmoid performs moody faster practice mateo mateo mateo minimizing averaged averaged averaged introduce question relation produces ann ann ann ann ann ann modeled multilayer averaging averaging electrical electrical electrical electrical spectral spectral spectral spectral frequencies frequencies frequencies frequencies frequencies formed quality extraction extraction extraction extraction extraction potentials potentials national extracted extracted extracted extracted stationary interpretation interpretation variation transform transform frames activities spectrum spectrum spectrum spectrum partial partial performing valid foundation eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg classified expect recorded handwritten perceptrons contour inter inter inter automatic automatic automatic discuss simplicity capable delta literature tend traditional classify content duration sampled sampled sampled vary vary wave ill extract extract extract acknowledgments modelling employed parametric parametric parametric parametric parametric poor investigate updating steady lippmann lippmann lippmann lippmann lippmann lippmann preliminary preliminary preliminary hall hall discriminant discriminant discriminant rise fourier fourier rest rest possibility muscle complicated plausible possibly generalisation generalisation generalisation generalisation man facial changed perceptton perceptton consist attempts attempts seconds seconds seconds seconds distinguish unstable explanation capabilities capabilities capabilities capabilities capabilities nonlinearity reasons considerable considerable perspective purposes filtered medical medical computers recording recording recording recording recording author author raw raw researchers considerably recordings anti popular popular acoustics logical windows diagnosis diagnosis diagnosis diagnosis diagnosis wesley representative classifying classifying classifying classifying classifying classifying classifying classifying cooper cooper cooper cooper addison mistake mistake modify concerned harmonic discover connecting inspired spontaneous alpha alpha city check hope transforms krogh krogh krogh krogh north intuitively intuitively hertz hertz hertz hertz published prentice prentice financial financial ensures sion patient patient surprising holland dominant dominant percepttons artifacts smoothed smoothed contraction late subsequently harris harris tures vari acknowledge acknowledge mechanical severe severe fitted neurophysiology anns largely basically job german classifies evoked australia beta param unseen unseen unseen unseen unseen unseen unseen unseen unseen unseen favor mathematically file convert denoting acquired employing sonar pop fea investigations elsevier elsevier indication eters differentiating clinical clinical clinical served advantageous palmer palmer palmer palmer council council hyperbolic scalp scalp scalp sake australian australian attributed envelope usefulness gram contrasts fft fft fft fft autoregressive autoregressive autoregressive autoregressive screen artifact transpose leakage magazine enter modern modern files files files files files files files files files convey tsoi tsoi tsoi tsoi tsoi health proceeding experimented putation drug disorder disorder disorder disorder ular accuracies nov biomedical walker traditionally berger parsimonious holmes holmes holmes claims classifica lay henceforth azimuth wishes concluded arma arma arma queensland queensland kay kay kay kay kay kay kay kay assist indicative rid cri theta redwood fundamentals xii hans suppressing calif calif calif calif screening undertaken pertaining expres levinson travels wixi hnear generalise alike neuropsychology din laborious suffering suffering suffering suffering lucia glance routinely diagnosed terion herrmann herrmann psychiatry ological abandoned rla generalising summarise 
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#*network network network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model input input input input input input input input input input input input input input input input input input input input input input input input input data data data data function function function function function function function function function function function figure figure figure figure time time time time time output system state results models models models based based space weights linear linear order order order shown values values parameters weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit point point point point point processing large large neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate test test test test test analysis analysis analysis optimal inputs inputs inputs inputs inputs inputs inputs form shows simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper small small small small small small fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells field field field field field features current current current current current current cell cell cell cell high high memory memory response response response response response response response response response response response response response response response response response response response response similar similar similar similar show show show show section section fixed fixed fixed fixed average term term dimensional university threshold threshold threshold solution research research found dynamics initial initial constant connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction present present low low low temporal motion motion motion motion motion range range position nonlinear continuous abstract convergence properties properties properties properties properties properties properties properties properties properties references due important important context introduction action action circuit circuit circuit stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus parallel change change spatial spatial measure center firing firing firing firing firing firing firing firing firing firing cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good good long proposed proposed forward simulations simulations resulting resulting ing ing total total total times feedback feedback orientation negative compared receptive receptive receptive receptive receptive receptive provide define eye experimental related constraints connected cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical power larger larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast connection connection institute synapses synapses synapses synapses synapses synapses synapses consists responses responses curve curve curve curve curve curve curve curve curves curves curves curves curves curves stage stimuli significant con con condition area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity provided nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends measured measured feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward increases increases increases group denote tested fast fast limited excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory circuits amount short short generate supported role including including simulated underlying combination account account transfer transfer transfer transfer transfer consistent consistent consistent mode mode mode mode mode mode operation operation pre inhibition inhibition inhibition inhibition inhibition inhibition early early magnitude description neuronal membrane population population directions directions recent property moving moving moving moving moving include pixels pixels array array array recently compare approximately module smooth match match studies positions positions amplitude occur suggests feed loop generally pass strength strength conclusions retina peak peak peak peak faster weak weak weak weak strong strong mechanisms presence drawn selective selective selective selective program program acknowledgements pro produces index primary primary primary primary plot plot mathematical modeled transformations remaining slightly consisting equilibrium equilibrium springer versus versus versus potentials potentials potentials national national depending detailed detailed open operations diagram key key slow classical sec sec filtering filtering symbol foundation foundation koch koch koch koch koch recorded fire fire fire fire includes retinal activated tests tests differ symbols symbols symbols modes detect schemes post excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation strongly strongly strongly strongly induced neuroscience conductance conductance conductance conductance conductance conductance physiological bar bar bar bar simplified realistic surround providing reach reach cat cat cat operating operating preferred preferred preferred preferred preferred preferred preferred body origin stimulation stimulation stimulation stimulation stimulation selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity investigate circuitry steady detail strengths limitations dual rise respond respond respond analytically possibility office lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn understand fundamental neu circles ensure portion portion shapes pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal explain explain seconds mentioned mentioned indicating slope slope spatially arise improvements populations reflect pure embedded simulate experimentally experimentally recordings biologically maintain maintain berlin cal incorporating prevent pasadena pasadena substantial substantial physiol physiol cor physiology physiology physiology physiology oxford oxford amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier martin martin martin martin linearity linearity narrow velocities velocities velocities velocities labelled labelled null null null null null null null null null null null null null null neurophysiol neurophysiol purely naval caltech caltech saturation anatomical anatomical striate attractive balance canonical canonical filled filled overlaps reset connect loo loo loo loo loo loo injection somatic somatic somatic somatic nonlinearities deg deg cerebral late specificity epsp displacement discharge discharge dramatically grating grating grating appeared shunting wiesel wiesel ber presenting failed sigma causing hubel hubel cns cns insights gained interneuron num douglas douglas douglas douglas douglas douglas douglas douglas douglas douglas douglas mediated mediated mediated superposition superposition superposition afferents afferents intracellular intracellular geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate amplification amplification amplification ward mcdonnell hamilton hamilton morphology suppress wiring rons usefulness physiologically exclusively nmda contrasts intracortical intracortical intracortical intracortical intracortical intracortical triangles triangle capital compartment quantitatively bandpass totally vivo amplified saturating tical gratings substrate massive massive massive silent christof christof christof christof christof moderately ton biophysics hysteresis hysteresis hysteresis hysteresis saturates saturates nections goldstein tong pyramids pyramids courses compartments psp psp displaced displaced cortico cortico cortico exceeded symmetrically feeds ana thalamic steep steep persistence anatomically proportionally critically invoked rameter ipsp rodney rodney rodney rodney rodney selectivities albrecht albrecht albrecht albrecht albrecht feedfor straints originate originate namics abrupt peters peters amplify orban orban orban orban excites ferster originates persists victor victor retino proposals proposals ampli discrepancies rection rection includ fied underlies intimately mer creased ferred corti ents suarez suarez suarez suarez suarez whitteridge ently gon gon geisler geisler compressive dal affer neurophysiologists pyrami suprathreshold 
#@Douglas_R,Koch_C,Suarez_H,
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#*network network network network network network network network network network network network network network network model model model model model model model neural neural neural input input input input input data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set set set set set networks training training training training training training training output output output output output output output output output output output output output output output number number system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results units units units units units units information information information information problem problem problem problem problem problem problem problem models models models hidden performance performance performance performance performance space case order order order noise noise unit unit unit recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern point point point point point single processing processing processing processing processing large local local patterns inputs inputs form form form form shows shows shows shows simple simple simple simple visual visual visual visual size size size net net net net net work work work work task task task task task task task task step step step step step step step step step step step points points points process process process process process process process process process process level level current current current trained trained trained trained trained trained problems problems problems memory response response similar similar representation representation architecture architecture architecture architecture architecture show show show show rule general generalization generalization generalization generalization generalization average states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states theory theory theory theory theory note experiments activity activity activity activity activity activity activity result result result result result result result result result university university computation computation solution solution solution solution solution solution solution solution solution solution defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target dynamics dynamics initial constant constant computer connections science science left left map present activation activation activation activation activation activation activation object object press press press learn learn components outputs continuous abstract back computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational convergence properties references procedure important decision decision decision decision context context context context context introduction action action hand behavior behavior effect parallel search search search search search change spatial spatial assume prior representations representations representations representations word word word word learned learned part previous required required required required required required multiple long long long conditions conditions represent distributed make make make make make make correct correct correct correct correct errors simulations simulations resulting resulting resulting ing tasks tasks tasks tasks simulation simulation simulation simulation simulation simulation human human respect performed elements regions mapping mapping mapping mapping mapping mapping mapping mapping mapping made made knowledge knowledge knowledge vol relative specific specific represented represented represented represented represented represented compared desired objects perform perform perform perform perform active active active determined experimental goal goal constraints connected motor motor brain brain brain brain brain brain brain brain brain mit mit steps steps steps steps steps steps larger larger contrast update modeling modeling modeling modeling report institute words department consists consists consists connectionist connectionist final final addition addition addition addition addition addition addition sequences sequences sequences sequences sequences sequences ai ai ai maps framework framework framework framework framework framework framework framework cambridge cambridge cambridge domain domain domain domain domain equivalent hinton hinton hinton curve curve additional solutions transition transition trajectory stage stage determine choice choice choice choice choice choice choice con con condition condition condition area processes processes processes nature simply simply simply simply associative feedforward feedforward feedforward feedforward feedforward feedforward feedforward tested transformation transformation fast close corresponds complete complete actions predictions role role role role role theoretical theoretical theoretical theoretical require require eds journal ability ability hypothesis hypothesis degree rumelhart rumelhart rumelhart auditory underlying underlying needed account account account functional interesting projection projection projection mechanism mechanism consistent empirical principle operation numbers iterations making supervised frame idea attention run run run run architectures improved exact property pair pair element introduced include cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive sufficient highly unsupervised module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module solve correspond correspond studies studies address interval alternative correctly locally occurs conclusions central differences sigmoid modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules clear suggest sound encoding propose propose propose propose propose propose strong mechanisms turn assuming assuming exist exist force question question question denoted attractor attractor attractor attractor attractor attractor attractor attractor attractor areas suppose appears relation digit digit digit digit digit digit digit digit digit digit pro solving winner winner sequential transitions modeled implement simultaneously unique interaction adding events formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed formed versus select focus overlap operations updated updated understanding understanding activities digits digits digits digits digits digits allowed key key partial partial partial partial partial partial partial partial reasonable performing performing roughly purpose iterative boundaries valid intermediate initially sufficiently sufficiently construction koch koch avoid existing existing combinations priori determines activated mozer mozer mozer mozer mozer mozer mozer mozer partially partially mcclelland mcclelland presentation identify attractors situation tend essentially ten strongly showing showing neuroscience issue sin sci usual michael michael michael michael michael relaxation relaxation relaxation relaxation relaxation generalize modular ill ill ill ill ill leading reach reach attempt attempt consisted subsequent approximating situations explore american access access experience experience experience experience varied periodic examine fashion incremental decisions decisions gates proper affect hierarchy understand cognition cognition cognition cognition notion neu coarse psychology psychology rev created thought precise mapped mapped initialized consist consist utility utility utility utility utility utility utility utility explain explain explain sentences indicating cart cart track phenomena improves answer cascade lies drive drive drive perspective straight shared organized mation mation pool pool pool pool pool pool pool pool scientific scientific describing gradually questions questions questions questions people people behaviors percent transient transient transient slower psychological psychological operate mod aim reaches achieves coherent neuro neuro semantic semantic arithmetic irrelevant don don don don person person ordinary contextual identifying forming investigation temporally acts perfectly perfectly theories smolensky smolensky smolensky reaching clamped clamped clamped clamped anatomical imaging imaging promising stated moment keeping optic symposium intuitive carry carry carry carry carry carry generalizes continue motivation infor infor meaningful meaningful falls conjunction mental mental regard colorado colorado colorado consequences consequences consequences treatment specialized creating clean clean passing erlbaum statement statement statement statement intersection influences influences influences counts mind specification specification rigorous solves achieving basin basin presenting lit solely decomposed forcing imagine imagine alter argue pdp maintained dominated activate activate activate boulder boulder individually acquired ultimately refinement enforce pools pools pools pools investigations compu answers resembles coordination demonstrating persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent differently primitives marks justification settling settling ongoing subjective incorrectly integrates concrete neglect dedicated beneficial lying functionally comprising ultimate ultimate squashing proves neurobiological constraining amenable rel connectionism cess enter enter enter contents inaccurate lexical lexical modularity predefined preventing observes entities ness ness ness plans subtasks psych scribed illustrating accepts undergoes claims consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness consciousness rightmost wired perspectives perspectives aware testable testable lacking feeds completes faculty cog crick crick crick crick crick unimportant tational formedness formedness cleaning persistence persistence persistence persistence interpretable temporarily plaut plaut posner posner encourages native tolerate conscious conscious conscious conscious conscious conscious conscious conscious conscious conscious conscious ficient chitecture persist essay initiate fodor fodor verbal leftmost donald donald donald donald donald suf binds evoke inaccuracies inaccuracies diverging helping helping persists neuroanatomical sistent semantically semantically assured mentally behrmann behrmann mathis mathis mathis mathis mathis mathis lesioning operand creased unconscious unconscious unconscious ules cently preconditions exerts jective blending ships commitment commitment regenerate behar degenerates 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#@Mathis_D,Mozer_M,
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input data function function function figure figure figure time time time time time time time time time set set networks networks training training training training training training algorithm output output output output output output output number number system system system error error error state state state state state state state state state state state state results results results results results results results results results information information information problem problem problem models models models models performance performance performance performance performance performance based based based based space space space space space space space space weights weights weights weights linear linear case vector order order order order order shown shown shown shown shown systems systems values probability probability probability parameters parameters approach approach approach pattern point single processing control control control control control control control control control control control control control control control control large large rate rate test test test test inputs inputs form signal signal signal signal simple paper paper paper paper small work work work task task task task task task task fig fig fig fig fig fig points field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field process process process process level level current current current current current current trained trained high memory memory memory memory similar representation architecture architecture architecture architecture architecture architecture architecture architecture show section fixed fixed fixed fixed line line line line line line line rule average states term term term term note note note note experiments experiments activity result result result result computation research found found sequence target target dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial standard computer terms terms connections connections connections connections connections connections prediction direction presented presented presented presented presented map present present present present present phase phase low temporal temporal press press learn learn learn learn learn learn learn learn learn learn learn learn position position outputs outputs outputs outputs abstract abstract applied applied applied applied applied back computational computational computational properties likelihood references ieee important adaptive adaptive adaptive adaptive adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture context context introduction hand hand behavior behavior effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated change change change change difference difference variable measure signals prior learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen higher higher part part part previous previous previous previous previous previous required multiple multiple long long long conditions conditions conditions conditions conditions conditions conditions conditions represent fact fact proposed correlation correct correct observed forward forward forward minimum resulting resulting resulting resulting tasks tasks tasks tasks tasks human human human human human computed computed sum called called times elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping factor study study em negative negative negative negative negative negative original compared compared compared desired desired desired desired desired desired series series compute compute rates proc location perform perform active active experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental posterior posterior motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor brain brain mit mit fields fields fields fields fields fields train train dependent dependent dependent dependent modeling modeling words words consists consists internal internal internal joint joint joint joint joint joint represents represents difficult addition ai ai maps maps maps maps maps cambridge experiment environment environment environment directly curve curve curve curve curve curve curve curve curve curve curve curve curve curve curves curves curves curves curves curves curves curves curves effects capacity capacity determine significant approximate free world produce produce produce produce condition condition condition developed robot velocity velocity velocity velocity velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller lines lines path actual processes processes evidence evidence evidence evidence evidence evidence evidence nature biological measured feedforward feedforward group group group group group group group group group group group group group group group group group tested tested tested tested fast fast fast fast fast fast fast fast inverse inverse inverse inverse inverse inverse inverse inverse corresponds complete actions circuits circuits short assumed end end ability ability ability degree rumelhart rumelhart sensory simulated needed account account account unknown unknown fully jordan jordan jordan jordan jordan jordan transfer transfer transfer transfer transfer transfer significantly significantly significantly consistent pre direct stored stored experts experts experts experts experts experts experts experts experts supervised supervised supervised expert expert expert expert expert expert expert expert expert expert magnitude produced light light light light light architectures discussed exact pair pair pair pair separate separate separate separate similarity movement movement movement movement movement apply introduced subject subject subject subject subject subject subject subject subject subject subject subject subject hierarchical cognitive previously teacher approximately subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects volume volume tions smooth studies rl trans modified modified improvement improvement improvement storage storage storage increased increased arm arm arm arm arm arm arm arm lead suggests suggests deviation predicted move move move move move move move pass half half minimal row row trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories conclusions faster faster practice practice practice practice practice learns learns suggest suggest propose external movements movements movements movements movements targets targets introduce introduce manner groups groups groups force force force force force force force force force force force force force force force force force force force force force force force force force force force force force force force question question question explicit appears produces longer longer longer longer solving laboratory mathematical distinct dept dept changing changing changing changing changing changing modeled implement coordinates adding predictive shift select select correlated correlated transform open updated soft static suggested allowed allowed allowed allowed allowed allowed allowed allowed key slow slow slow performing convex convex sec intervals initially initially recorded retrieval inter inter inter batch sciences extension plotted plotted gating gating gating aspects suitable effectively literature computations situation plots identity identity ten soc link return strategies sci cues comp involved sampled modular modular modular paradigm paradigm paradigm observable computes leading leading neurosci neurosci neurosci neurosci moves moves overlapping subsequent operating jacobs jacobs jacobs jacobs deal load load load presents employed explore explore explore essential investigate experience experience rapidly humans humans humans humans preliminary successive successive mappings mappings mappings mappings mappings referred comparable affect notion circles possibly adapt man opposite opposite changed aspect der portion assumes assumes observe explored nervous store baseline baseline baseline extent explain plant plant plant plant seconds slowly piecewise separable worse handle handle starts straight day day day day day day day day day day day day day day day day day day day day day day day day day precisely forces forces forces forces forces forces forces ran desirable immediately immediately immediately immediately angles describing describing depicted meaning people dark dark dark dark dark flexible experimentally lack poorly psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical slower ity partitioning anti anti incorporating serve suited plan gave findings findings univ phenomenon phenomenon sleep forming forming velocities recover imaging minutes minutes minutes minutes minutes occurred imposed moment moment resulted resulted resulted occurring operates operates guide modifications planar planar planar selects hours hours moments interference interference interference interference interference interference interference interference interference interference interference interference interference mance heavy displayed perfor consequences counter counter dif dif eng arrows reverse emission solves solves email session session benefits randomized torque torque torque torque torque torque torque torque presenting causing alter representa attempted compensate compensate interacting met paired paired confirmed scope retain retain retain retain distal distal distal cartesian flash flash setup figs figs minor retained holding holding psychophysics coordination sessions circumstances circumstances monitor tom tom tom tom ferent ferent exper hopkins dom sensorimotor sensorimotor returned functionally loads screen johns protocol protocol physically adapts demands demands electrophysiological correlates twelve twelve skill baltimore catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic substrate inform dence undergo undergo undergo inappropriate unexpected medial sented explaining adv ference ference plastic plastic jenkins jenkins resemble primates clockwise clockwise clockwise clockwise entities biomedical mussa mussa mussa mussa mussa respects decrement decides retention retention retention retention offline ivaldi ivaldi ivaldi ivaldi ivaldi challenges scratch arms wanted hogan hogan millisecond poorer compensatory proaches cyber deliver cursor pnas muscular interfere depart torques torques jerk accelerations resistant elapsed sagi sagi todorov todorov todorov todorov todorov immune immune linearize jhu perturb suffered evi fifteen backpropagate sired bme engage organizational resembled practiced practiced practiced love limbs limbs limbs destroyed whichever emo proximately undo tea 
#@Brashers-Krug_T,Shadmehr_R,Todorov_E,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input input input data function function figure figure figure figure time networks networks networks networks networks networks networks networks networks networks networks algorithm output number number number number number number number number results results information models models models models models models performance weights weights weights weights weights weights weights weights layer layer layer layer case case shown systems systems parameters unit distribution distribution distribution pattern single processing rate rate rate inputs form form form shows simple simple paper paper small small feature feature feature net work work task task field field field field field features features classification classification classification classification classification classification classification classification classification classification process current current current current current structure structure structure structure structure structure memory memory memory show show line line rule theory gradient gradient gradient gradient gradient note university university computation research research research defined sequence sequence sequence sequence sequence sequence sequence initial constant table table table table table table computer terms node node node science left left left left direction presented activation nodes nodes nodes machine object object maximum abstract back back references positive positive context context context context context context context context context hand generated generated generated recurrent tion rules rules rules rules rules rules rules rules rules rules rules rules representations representations word word word word learned learned part previous previous distributed equations correct observed errors ing tasks tasks simulation simulation simulation simulation simulation human respect called natural natural knowledge knowledge relative relative compared goal related constraints motor discrete connection morgan morgan proceedings proceedings proceedings proceedings words words words words words words words words words version consists connectionist connectionist addition ai ai maps maps environment hinton hinton design design top top top top top classifiers basic derived randomly controller controller path actual selected selected discussion normal tested limited limited finding generate supported theoretical require ability future sensory including kaufmann objective reduced block testing york head head structures principle language language language language direct direct supervised supervised combined added added added denotes recent recent recent recent recent recent recent recent recent pair pair pair pair pair pair include include identical identical cognitive cognitive cognitive unsupervised teacher works works works match observation organization parts correctly feed feed feed touretzky touretzky conclusion reduce reduce reduce reduce editors editors editors learns encoding external external reduction min min identification force acknowledgements explicit explicit dept category category category category category category category category category category category explicitly mutual applying springer formed formed shift shift shift shift john john john extracted expressed codes evaluate operations organizing organizing organizing organizing organizing organizing organizing organizing organizing forms forms forms forms activities activities diagram reduces reduces purpose purpose symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol assigned construction construction kohonen kohonen kohonen kohonen classified classified classified includes includes priori activated discussions grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar symbols symbols symbols symbols symbols symbols symbols symbols symbols mcclelland mcclelland mcclelland verlag categories categories categories categories categories categories categories categories categories reach cat receive situations presents unlike carried production production production production production production production production production production production production relations humans recursive recursive examine school school office structured structured proper induction plausible predicts extremely singular singular motivated finds sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences sentences agreement agreement track adjacent adjacent biology handle processed scientific grossberg grossberg grossberg grossberg read author author meaning explained requiring elman elman elman elman amounts fed fed cohen marked completion treated frequently ity occurrence occurrence boston boston boston eventually progress sentence sentence sentence sentence sentence sentence sentence sentence sentence acquisition acquisition contextual contextual notes equivalence arguments count air accepted accepted stated familiar los los occurring removing utterance shifts corpus clause clause phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase phrase utilized contexts contexts contexts contexts contexts appendix washington lengths offers exposure reveals record record grammatical grammatical grammatical grammatical grammatical grammatical parse valuable harris consecutive suffix suffix suffix street summer summer parsing parsing ple email tables incrementally terminals terminals terminals connec copy causing suppressed stands cns trends exam goals ijcnn ijcnn token token token token token afosr rejected acquired acquired acquired acquired acquired scope guided names topic categorization categorization categorization pop pop pop induces induces examination wider wider status completed ritter ritter ritter ritter walk chris lecture acquire phrases phrases phrases phrases phrases phrases phrases phrases subjective clauses seattle judged repetition dog dog syntactic noun noun noun noun resultant deter artificially verb verb verb dyer dyer dyer cats cats cats accepting competence lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead teachers plans forgetting mike miikkulainen miikkulainen miikkulainen myers steepness feeds feeds feeds feeds feeds syntax syntax syntax ungrammatical ungrammatical exposition wishes live live live live live categorize mere mere mere categorized organ prof prof prof chunk kauffman reductions awi nouns nouns nouns bullock dan tionist verbs verbs verbs walks carl acquires preclude ses fll bigram exposures ifx lives lives ably mine boy boy cash cash cash altos altos parses agreements agreements organizes ork mer sigrnoid xlc xlc xli ctl grad chase chase chase chase whe subfields comprehension nem conversational algorithmically transitive transitive abc reli subordinate optionally ually 
#@Negishi_M,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks number number number number number number number number number number number number number state results results results results results results results results results results results results results results results units units units units units units units units units models models models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based case case case order shown shown shown systems systems values values values values values probability parameters noise neurons unit unit unit unit unit unit approach pattern pattern point single single single single single single processing large large large large large large local local local rate patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis inputs form form form shows shows shows simple simple simple simple gaussian paper paper small small size size size size size size size size size size size size size size size size size size size size size work work field features features level level level level level level level current random memory memory memory memory memory memory memory memory memory memory memory memory memory memory response similar similar similar similar similar similar architecture show show show section section section section fixed rule rule rule rule rule rule rule general general general general average average average obtained obtained obtained term note note experiments activity activity activity activity activity activity activity dimensional dimensional result result result result result university university computation computation computation research independent defined defined found dynamics constant constant standard standard computer computer terms distance distance connections synaptic science science left presented presented presented presented present low low temporal object range press abstract find find computational properties references ieee positive important introduction action effect effect effect effect effect effect effect effect effect effect spatial spatial spatial assume lower rules rules measure higher bound bound type multiple multiple multiple multiple multiple multiple cortex cortex long conditions represent make region region correct observed simulations simulations simulations simulations simulations simulations resulting resulting resulting resulting ing total total simulation simulation simulation simulation simulation multi multi multi multi multi sum performed elements elements elements factor study study study study study study study study relative specific specific specific specific specific true compared series rates determined determined goal related related related connected connected connected connected connected cortical cortical cortical brain brain brain comparison larger larger larger larger larger nets modeling modeling report institute department department loss individual connectionist final exp framework framework framework framework equivalent equivalent curve curve view curves curves curves curves effects effects effects effects effects effects effects effects effects effects effects effects effects effects effects capacity upper significant approximate increase increase increase con randomly randomly levels area area area area area area area area area area area area area area area area area types actual actual actual finally selected depends depends associative associative associative associative associative associative associative associative achieved achieved achieved measured discussion normal increases increases describe limited assumption predictions circuits amount short shape shape shape shape shape shape shape shape shape supported role role theoretical theoretical theoretical main face square square square square hypothesis including fit fit underlying hopfield account functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional interesting significantly significantly significantly significantly significantly ratio ratio edge increasing increasing increasing consistent trials principle representing pre stored early magnitude light light light light neuronal denotes denotes denotes denotes discussed separate separate similarity identical array array cognitive cognitive recently recently recently interest interest varying varying compare compare compare approximately approximately calculated volume works correspond studies studies studies studies trans sparse symmetric williams organization storage increased parts expression expression lead lead lead studied scaling occur occur trial predicted hardware critical greater interactions numerical numerical numerical numerical numerical strong mechanisms mechanisms external characteristics demonstrated proportional turn assuming assuming variety decrease decrease decrease decrease averaged manner connectivity connectivity connectivity connectivity denoted attractor attractor attractor attractor areas relation derive edges factors primary estimating modeled involves remaining scales interaction interaction decreases review overlap overlap variation detailed detailed fraction fraction fraction fraction fraction showed approximations approximations understanding understanding understanding understanding understanding suggested converges past past classical neighborhood valid initially sufficiently sufficiently existing retrieval retrieval retrieval inter memories plotted plotted plotted illustrated illustrated domains neighbors neighbors characterized characterized structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural structural determining determining plots receives composed composed induced anderson interested neuroscience cue hold hold cues modular thresholds load presents presents presents investigate association limitations accurately accurately mass examine examine examine relationships root root working func examined plausible plausible man man thought precise expressions baseline extent motivated devices site advanced slowly developing growing failure analytic analytic analytic explanation analytical analytical analytical analytical analytical analytical analytical majority caused caused reasons considerable spatially spatially spatially spatially spatially spatially tive tive organized organized organized organized organized organized organized acknowledgement describing describing gradually localized cybernetics qualitative robustness reflects led dark dark tional quantitative lattice formulated formulated biologically psychological maintain span span price limiting spread reaches incoming cal cal cal enables decreased shaped damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage patients progress displays college secondary primarily primarily primarily primarily forming formally investigation circular eliminate lost generality clamped consideration anatomical significance stronger primate held multiplicative nearby nearby analyzing definitions enhanced wilson degradation governed james james james james james studying studying displayed surprising sides sides evident offers surprisingly theoretically horn park border border adopted mind shading shading shading shading pointing fellowship ber validity focal focal focal focal focal focal focal focal 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frontal disease disease disease disease sketch weaker accounted parametrized clinical clinical clinical clinical clinical clinical capacities capacities capacities remarkable characterizing accordance accordance ruppin ruppin ruppin ruppin ruppin ruppin ruppin ruppin ruppin hypothesized diffuse diffuse diffuse diffuse diffuse diffuse diffuse diffuse diffuse diffuse diffuse diffuse micro pronounced cally compensation couplings neocortex characterizes intact intact symmetrical frequent sions smc handbook reviewed memorized mul maryland maryland degrades gradual nice rises assessing columnar borders disorders disorders disorders disorders conceptually tsodyks tsodyks viable viable postulated postulated damaged damaged lesioned lesioned lesioned europhys neurology neurology cued deficit clamping ordinate ordinate ordinate mild bearing functioning usher accompanying elongated elongated progression discarding pathological death torus structurally associa associa shed wolf traversing flamework portant portant concentrating markedly manifested eytan eytan eytan eytan eytan tth tth prefrontal les les twofold ule symptoms impairment impairment detrimental neurological innervation acute acute parison differen gaining invited neuroanatomical severity severity neuropsychology goldman ceases lesioning organi chronic chronic equidistant deterioration deterioration deterioration herrmann specifi retrieves rudimentary thomson prevalence prevalence prevalence prevalence sheds hier analyti adhere chology looses bldg 
#@Reggia_J,Ruppin_E,
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#*network learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input data data function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set set networks output output output output system system system system system system system system system system system system system system system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results information information information information information models models models models models models models models models models models models hidden based based based based based based based space linear linear linear vector vector vector shown shown shown shown parameters parameters noise noise noise noise noise approach pattern point point image processing control control control control control control control control control control control control control large test matrix matrix matrix matrix matrix matrix optimal optimal inputs inputs inputs form form shows shows shows simple visual visual visual visual visual visual visual methods methods field process process process process process process process process process process process process level current current current problems representation equation equation line line line line images images general theory dimensional result research research independent independent target target dynamics dynamics dynamics initial initial initial initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard computer distance distance distance distance distance distance science prediction prediction prediction prediction left present temporal press press learn position position position position position position position position position position position position outputs outputs abstract back computational computational computational references component positive procedure important adaptive adaptive propagation propagation propagation propagation propagation propagation propagation propagation introduction introduction action action action action hand hand hand hand hand hand hand hand hand hand hand hand hand hand estimation estimation estimation estimation estimation estimation estimation estimation behavior behavior behavior dynamic dynamic dynamic dynamic dynamic dynamic generated variance variance variance variance variance variance variance variance variance variance variance variance variance variance tion tion change change difference assume assume assume measure measure signals signals signals representations chosen higher cases required conditions conditions conditions equations make make region proposed proposed correct observed observed observed errors errors errors errors forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward scale simulations simulations resulting ing tasks simulation simulation simulation simulation simulation human human human human human performed factor potential dimension dimension dimension made made natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback study study filter filter filter filter filter filter filter filter filter relative relative specific specific true desired provide provide provide compute location location location location location location eye experimental experimental experimental experimental experimental experimental gain gain gain motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor brain mit mit mit mit accuracy larger fields update support dependent institute department consists internal internal internal internal internal internal internal internal internal internal internal internal joint represents represents represents represents final final final bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias framework framework cambridge cambridge experiment experiment experiment directly view estimates estimates estimates transition transition effects effects effects effects effects effects effects full full approximate vision vision vision estimated estimated estimated basic basic increase increase validation produce condition randomly randomly developed velocity velocity lines lines lines path actual actual actual actual actual finally processes processes processes selected evidence evidence discussion covariance covariance covariance normal tested transformation transformation inverse actions predictions effective theoretical theoretical main journal journal square square end end ability degree degree rumelhart rumelhart rumelhart sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory fit simulated combination fully fully jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan technology interesting projection projection york york head special consistent consistent trials uniform empirical representing representing details direct direct making making supervised combined choose sources sources sources sources light light predict movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement moving subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject hierarchical cognitive cognitive cognitive engineering engineering engineering teacher subjects subjects subjects subjects subjects smooth differential differential rl observation generalized generalized organization increased increased grant arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm horizontal horizontal concept studied suggests trial deviation matrices matrices predicted feed move move move move white white generally demonstrate flow conclusion starting reduce editors central sutton sutton peak practice strong integration integration integration integration integration integration integration external external external external external external external external solid movements movements movements plane plane plane relationship relationship targets configuration configuration force force force force force force force force force force force force force force explicit construct produces written perception solving factors estimating distinct distinct distinct dept coordinates simultaneously consisting interaction integrated expectation select focus stationary estimator viewed transform controlled controlled updated similarly sign key barto barto barto smoothing dashed additive additive additive performing delays combining filtering filtering foundation degrees recorded thesis sciences plotted uncertainty major planning aspects importance driven tend tend identity neuroscience dis sin sin timing duration duration duration duration duration duration duration michael michael michael michael michael michael dayan absence absence paradigm paradigm paradigm providing observable observable reach predictor principles moves body command command command command command command carried create investigate rapidly kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman involving accurately accurately dotted mass mass mass hall hall pursuit existence existence examine rest project biol biol muscle combine office referred func fundamental phases phases notion coefficient reading predicting predicting predicts rev freedom freedom nervous academic contributions contributions seconds massachusetts site analyzed correction correction correction correction correction starts london rapid forces forces forces forces forces forces forces choices laboratories consequence projected projected projected acknowledgement gradually nsf integrating virtual virtual prop populations applies dark dark simulate simulate lack peter psychophysical peaks splines resistive resistive resistive resistive resistive resistive sharp rep commands commands robinson robinson synthesis rely modulated semi semi decreased damage patients wesley trade trade contribute ghahramani ghahramani ghahramani ghahramani ghahramani cybern cybern addison null null null neurophysiol purely naval receptors outcome outcome outcome robotics reaching establish smith siemens held held cerebellum cerebellum cerebellum imposed loops kawato kawato planar planar prentice started tone tone patient appendix appendix moved moved moved moved mental mental lengths bulb reproduce reproduce young suggesting probe wolpert wolpert wolpert wolpert wolpert wolpert wolpert wolpert observer observer observer observer observer observer erlbaum captures grants stopped balanced balanced mechanical skills linked maintaining appeared leaving unable corporation visually visually visually pointing pointing recursively torque torque torque tibshirani tibshirani copy solely tor simulating possibilities causal reflected reflected constrain cns cns cns cns acting unseen hastie hastie chapman projecting topic distal monitoring setup setup finger accounted placing mimic gordon gordon atr article experi manuscript suggestions externally reversed monitor mcdonnell mcdonnell cliffs arrow mirror mirror mirror sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor kinematic kinematic integrates tribution sen englewood ally zoubin zoubin zoubin zoubin zoubin zoubin zoubin screen screen screen screen screen accommodate handbook motors motors motors modern assessed emerged suzuki mounted daniel daniel daniel daniel daniel daniel gradual investigator damping unaffected infeasible pew pew discrepancy ton sensed cancel dead dead simulates resentation ito ito ito localize damped psyche psyche psyche thumb thumb thumb thumb thumb thumb thumb thumb anticipate agation sults feel ies accumulating accord presidential perceive embodied embodied stein proprioceptive proprioceptive havior instructed psychol cursor cursor stud debate heard overestimate formalize investigates mimics torques ported illuminated couples sut rear rear ingredient asme 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#@Ghahramani_Z,Jordan_M,Wolpert_D,
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#*learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model neural neural input input input input input input input input input input data data data data data data data function function function function function function function function figure figure figure time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set algorithm output output output output output output output output output output output output output output output output number number number number system error error error error error error error error state state state state state information information information information information information problem models models performance performance performance weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer order order order order order order shown shown shown shown shown shown systems values values values values values probability probability probability probability probability probability probability probability probability noise noise noise noise noise weight neurons unit distribution pattern point processing rate rate rate rate analysis analysis inputs inputs form form shows shows signal signal signal signal signal simple simple gaussian gaussian gaussian visual visual small size size net work work fig fig fig fig fig fig fig fig step step step step step step process process process level level current current problems random memory memory memory memory memory memory memory memory memory memory similar similar similar similar similar similar similar similar similar representation architecture show show show show show speech speech speech speech parameter parameter parameter average states states states term term term term term term term term term term term term term term term term term term term term term term term term note note university university research research standard standard connections connections connections connections connections connections connections node node node node node node node prediction left presented presented presented presented present present present phase activation activation activation activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal sets press press learn learn position position position position position position position position position position position position position components components components components components abstract applied references component component component component component component due due due due due context context context context context context context context context context context context context context context context context context context context context context context context context context context context introduction estimation estimation estimation effect effect effect effect effect effect recurrent tion difference variable variable lower prior prior prior prior prior representations representations word learned chosen part part previous previous previous previous type long long long long long long long long long long long long long long long fact proposed proposed proposed length length length length length length correct correct correct correct probabilities probabilities probabilities errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors simulations simulations tasks simulation human sum eq elements factor factor factor factor natural feedback negative artificial relative relative specific specific specific specific represented define rates active active active active experimental experimental constraints connected motor brain connection connection connection connection connection connection connection connection connection connection selection selection selection selection selection selection selection selection selection morgan report words words words words words words words department implementation consists advances connectionist connectionist connectionist connectionist exp layers layers layers addition addition addition ai ai ai ai ai ai maps cambridge curve curves curves curves curves san stimuli stimuli effects effects effects effects full full full approximate free estimated estimated estimated estimated basic increase increase increase increase increase increase con coding weighted levels area types types types lines lines lines lines selected selected selected selected selected selected selected evidence nature depends depends discussion increases increases increases increases increases corresponds corresponds excitatory excitatory predictions short short short short short short short short short short short short short short short common shape supported role role eds end makes development development kaufmann combination account functional mechanism mechanism mechanism mechanism mechanism trials trials trials trials language language language language language language leads leads representing details max pre inhibition inhibition inhibition inhibition inhibition inhibition inhibition decay decay decay decay idea idea idea added added recent exact advantage similarity similarity similarity similarity similarity sufficient varying varying varying varying previously approximately approximately calculated match correspond studies address address positions storage increased expression occur occur occur suggests deviation deviation wide predicted predicted correctly correctly correctly correctly correctly touretzky loop loop loop occurs occurs occurs conclusion starting hebbian hebbian reduce competitive competitive mateo taking strong presence presence presence characteristics sigmoidal turn variety decrease relationship relationship relationship iii averaged acoustic acoustic acknowledgements areas relation digit winner winner winner winner winner winner winner winner winner stability distinct changing recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall missing simultaneously involves involves remaining slightly interaction interaction interaction interaction versus versus select select select letters letters letters letters decreases phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme completely similarly suggested digits digits digits digits digits partial dashed generation existing combinations activations activations activations activations activations extension extension activated activated activated activated activated specifically absolute discussions successfully major planning selecting selecting extra extra extra society encoded modification modification wij wij wij wij wij wij presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation presentation post tend tend receives notice repeated strongly allowing showing showing neuroscience timing timing timing duration list list list list list list list list list list list list list list list list list list list list list involved involved absence receive bars bars american production production production varied detail association association association association association behaviour successive tech incremental plasticity plasticity plasticity plasticity plasticity plasticity referred working working act circles circles predicts predicts psychology psychology psychology psychology thought hebb hebb academic store store store store store grouping grouping grouping submitted serial serial serial serial serial serial serial serial serial serial serial serial serial serial wta wta wta wta seconds seconds seconds brown improves majority adapted adapted london london london implementing arise involve addressed varies varies reflect items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items items experimentally item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item item span span span span span span span span span span span span span vocabulary vocabulary rely ordered ordered ordered ordered ordered ordered ordered ordered ordered serve phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes prevent phone replace begins softmax softmax acquisition acquisition college primarily recover royal plays suppression suppression suppression wrong mail odd imposed familiar familiar familiar familiar familiar familiar familiar familiar familiar presentations presentations filled published ensures corre buffer accounts winning winning winning winning winning winning recovery recovery modelled modelled modelled suggesting refers refers storing erlbaum subsequently receiving empty consecutive multiply associations emission fellowship super alternating corrected affects rhythm rhythm england suppressed reflected avoids increment translated translated modifying tems decays decays impose gener mathematically maintained activate activate associates figs familiarity familiarity familiarity familiarity familiarity familiarity familiarity grateful articulatory articulatory articulatory articulatory page prevents inactive accordance tom crude vii inhibit inhibit wins wins wins shot solvable solvable solvable reflecting phonemic phonemic phonemic phonemic phonemic phonemic phonemic lists lists lists lists lists lists lists lists lists lists lists lists lists lists lists lists lists lists anatomy ooo ooo ooo markers markers comprising decaying decaying decaying decaying vocal vocal articulation articulation articulation articulation locality enters routes stm stm recalled recalled greatest repetitions replaces distractor repeating activates checked virtue saturates nections scribed mediate mike phonological phonological phonological phonological dissimilar dissimilar dissimilar dissimilar george brings neighbouring graham unfamiliar unfamiliar unfamiliar unfamiliar unfamiliar unfamiliar chaining chaining burgess burgess burgess burgess burgess burgess burgess burgess burgess burgess burgess burgess sponds ucl serially serially serially serially spreads pauses decayed recalling recalling recalling recalling viii wit mech verbal verbal dale clarendon ezp elapsed localised quarterly principally recency recency recency tally explanatory baddeley baddeley baddeley baddeley baddeley baddeley consecutively incompatible ates committed committed houghton houghton houghton houghton houghton houghton normalising postulates overestimates anism repeatable repeatable repeatable queuing queuing favoured interchangeable hum recalls recalls presenta 
#@Burgess_N,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output number number number number system error error error error error error state results results results results results results information information problem models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden based weights linear layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown shown systems values parameters parameters parameters parameters parameters weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons method method approach pattern single single single single single processing processing local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test patterns patterns optimal optimal shows shows shows shows shows signal algorithms algorithms algorithms paper size size size work work task task methods cells cells cells cells cells step step step points process current trained trained trained cell cell cell cell cell cell cell cell structure structure structure response response response response response response response response response response response response response response response response similar similar similar show show show equation generalization parameter parameter parameter parameter result solution defined defined found found sequence constant left presented activation activation activation low press components abstract applied find computational computational computational references adaptive adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction action action action action complex complex complex complex complex behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect effect effect effect generated tion change difference complexity complexity higher higher higher bound bound bound bound type required binary binary binary binary binary binary binary spike spike represent equations proposed proposed proposed observed observed observed observed observed errors forward forward scale simulations simulations simulations minimum resulting classes total total total simulation simulation simulation simulation simulation simulation simulation simulation simulation sum sum sum sum eq times elements elements means means means means potential made artificial artificial artificial relative relative specific specific specific series provide rates experimental experimental experimental experimental experimental experimental mit larger train dependent dependent proceedings version consists represents represents represents responses responses responses responses responses responses responses responses responses responses responses responses responses layers layers layers ai ai ai ai ai ai ai ai ai ai ai equivalent solutions solutions stimuli effects effects effects effects full full full free pages pages pages produce channel channel randomly developed levels types types types types types types types types types types types types types types types types actual provided processes processes processes backpropagation backpropagation backpropagation inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory achieved achieved describe fast corresponds corresponds corresponds excitatory excitatory excitatory excitatory surface amount amount supported theoretical sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory fit fit fit simulated simulated smaller smaller combination unknown consistent numbers direct membrane membrane improved element element element element element sufficient sufficient sufficient sufficient sufficient sufficient highly varying previously approximately correspond correspond mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures channels channels channels channels channels constructed spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes feed feed occurs occurs column column demonstrate runs greater conclusions depend competitive competitive competitive editors interactions interactions faster strong mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms characteristics characteristics introduce perception perception ann ann ann ann ann ann mathematical changing sensitivity interaction interaction interaction interaction applying applying applying applying springer springer implies potentials potentials potentials expressed depending transform open restricted sizes sizes additive epochs fitting fitting fitting generation generation box combinations combinations formulation activated activated activated activated activated activated activated activated activated discussions tests identified importance differ divided build build ten kind neuroscience conductance physiological receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor comp generalize observable computes binding binding reach acknowledgments modelling minimized simpler powerful powerful transformed overfitting create investigate rapidly varied mass rise giving possibility possibility smallest measurement editor editor changed olfactory olfactory olfactory olfactory olfactory olfactory olfactory initialized cart capabilities cascade cascade cascade cascade caused tool sites sites sites protein protein protein protein protein protein protein protein protein protein protein protein protein located ion ion ion ion ion ion ion depicted recognizing summation summation summation summation simulate simulate simulate simulate simulate simulate simulate simulate introducing recordings recordings recordings berlin berlin berlin germany germany physiol deviations martin martin martin martin martin animals animals odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor odor eliminate receptors spontaneous mail mail logarithmic chemical chemical chemical chemical chemical neurobiology ral settings corre pat regarded thomas thomas thomas thomas thomas reproduce stimulated proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins insect insect eqs concentration concentration concentration concentration concentration concentration davis grants material divide fitted anns anns anns anns anns minus reaction reaction reaction reaction reaction reaction reaction feeding chapter tor molecular gated gated activate activate activate activate crosses mediated universit universit molecules molecules molecules molecules molecules molecules molecules diagrams transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer covers simplification simplification transduction transduction hyperbolic hyperbolic twenty institut institut institut substitution substitution substitution odors odors odors odors odors odors odors odors odors odors odors transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers senses senses ionic ionic cyclic antenna ira ira opinion bee bee bee bee bee bee depolarization activates entities optimizes fiir extracellular schematically signalling volatile volatile bind bind ting vertebrates vertebrates workers concentrations concentrations concentrations concentrations concentrations concentrations fruitful shepherd shepherd shepherd icnn kinetics kinetics analogously analogously blank ons camp compound recep fifty braun braun braun braun depolarized kij sponds reactions reactions reactions reactions reactions karlsruhe karlsruhe karlsruhe ijk und und und reformulated invertebrates invertebrates ger stimulations hyperpolarized substances elicit dfg react react react sory deutsche rprop rprop rprop influx influx reception reception reception reception reception reception reception reception messenger messenger messenger messenger messenger messenger rall carr carr involvement uka uka complexes complexes complexes complexes complexes forschungsgemeinschaft antennae chem chemically biochemistry nucleotide cular 
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#*network network network learning model neural neural neural neural neural neural neural neural input input input data data function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set networks algorithm algorithm algorithm number number system system state state results results results based space space space space space space space space linear order shown functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution method method approach approach approach approach approach point point point point point point point point point point point point single single processing processing processing processing processing processing neuron neuron neuron neuron neuron neuron neuron neuron analysis analysis analysis analysis analysis analysis analysis analysis analysis inputs inputs inputs inputs inputs form form form form form shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal simple simple paper net net work work work task methods methods methods cells cells cells points points points points points points points points level level level level current current current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure high response response response similar architecture architecture architecture architecture show equation general real real theory theory theory theory theory theory theory theory theory theory obtained dimensional dimensional dimensional result university university university university computation computation independent found found dynamics initial constant constant computer distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left left left direction direction direction direction direction direction direction direction direction direction direction direction present activation activation activation low frequency frequency frequency frequency frequency frequency maximum press press abstract applied find computational computational computational computational properties properties properties properties properties properties properties properties properties properties properties references important important important important propagation propagation propagation propagation propagation propagation introduction complex hand circuit effect effect parallel recurrent difference difference complexity spatial spatial spatial rules signals signals signals signals prior representations representations part part center required required good good long long distributed equations make fact length length length length scale finite finite finite finite classes classes simulation regression respect respect respect sum performed elements elements elements elements elements mapping potential potential potential potential orientation study original vol artificial artificial artificial artificial artificial relative relative relative relative relative relative represented compared application series define define define define compute compute location experimental discrete brain brain brain brain brain brain equal approaches voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage accuracy accuracy accuracy larger fields dependent dependent dependent dependent dependent nets nets nets nets department department department synapses synapses synapses synapses individual difficult difficult addition ai domain domain equivalent equivalent equivalent directly directly estimates design design design design design san effects effects determine efficient full choice basic increase give derived developed developed path path path path finally finally depends depends biological biological biological biological biological associative associative associative discussion increases increases describe transformation transformation transformation transformation transformation transformation transformation transformation transformation surface circuits circuits circuits circuits finding synapse synapse synapse synapse supported role theoretical theoretical theoretical theoretical eds square easily makes development development development pairs combination reduced ratio projection york york consistent consistent uniform uniform operation representing iterations direct direct direct direct making inhibition magnitude decay idea attention minimize run neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal architectures membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane directions directions resolution resolution advantage property pair pair separate element element similarity lateral practical practical apply strategy subject identical identical trees trees relevant relevant engineering interest interest interest highly highly previously teacher teacher teacher teacher teacher teacher teacher approximately calculated definition definition definition background separation grid grid grid grid grid increased constructed suggests extended flow flow critical greater hebbian hebbian reduce segment segment segment conclusions interactions interactions interactions interactions interactions interactions interactions accurate designed clear exponential exponential exponential weak taking strong mechanisms integration integration physics characteristics characteristics proportional relationship relationship relationship program program reference reference reference reference reference reference suppose suppose suppose suppose suppose appears construct ways primary primary primary primary primary plot changing segments metric metric metric metric student student student student student student student student student student student simultaneously linearly infinite infinite infinite physical physical physical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical electrical easy interaction frequencies frequencies frequencies cycles depending viewed interpretation influence detailed transform transform transform transform transform transform transform transform transform evaluate showed showed forms understanding understanding understanding completely similarly constants dashed additive additive classical distances calculate dendritic dendritic dendritic dendritic dendritic expect building figures figures currents sciences illustrated coupled variations characterized simplicity simplicity reason middle middle efficiency closely differ computations plots essentially receives excitation summary soc soc soc compact quickly neuroscience neuroscience neuroscience neuroscience criteria device vary neurosci neurosci principles principles operating acknowledgments deal rat rat rat unlike essential circuitry steady steady strengths limitations limitations recursive graphical graphical helpful existence ideas terminal terminal plasticity plasticity affect patch gradients concepts opposite opposite psychology psychology psychology illustrate illustrate created impulse obvious noted nerve nervous academic academic pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal extent utility utility contributions electronic electronic electronic seconds charge brown brown brown brown brown brown brown brown brown brown indicating growth adjacent analytical benchmark tool tool tool tool reasons spatially sites division directional located located hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal circle begin res computers computers depicted demonstrates sun reflects reflects apparent applies relevance transient tional embedded readily quantitative quantitative quantitative orders recordings treated calculating rely spread spread spread branch branch branch branch branch branch achieves asymmetric simulator logical kinds attraction physiol instantaneous instantaneous contribute picture physiology extensive extensive branches branches branches branches branches branches neurophysiol neurophysiol nonzero turned establish inspired cellular consideration anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical significance logarithmic chemical imposed resistance viewpoint transforms transforms transforms transforms transforms transforms transforms transforms transforms transforms exploit analyzing intuitive filled hours hours passive passive analyses analyses dendrites dendrites dendrites dendrites dendrites irregular entry guarantees lengths evident accounts dendrite dendrite dendrite dendrite dendrite dendrite consequences consequences captured facilitate thomas thomas thomas thomas thomas soma soma soma soma soma soma soma soma branching arrangement diameter diameter diameter infer neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic thin spatiotemporal spatiotemporal mem late arrows extends reverse davis characterization influences lag onr severe treat pressure yale yale yale yale unchanged drop logarithm logarithm logarithm logarithm presenting restrictions big affects affects imagine massively remote remote mutually arising capacitance capacitance capacitance preserved favor insights biophysical impose life met relating relating relating relating parallelism spreading spreading spreading speedup disease preserve reveal inversely turning intracellular exchange loading port port port vice laws versa reversed consuming ate hyperbolic cable cable cable cable cable cable cable cable cable cable cable cable designs conceptual conceptual morphology cylinder cylinder anatomy anatomy anatomy sharply exposed settle impedance core beneficial zador zador zador compartment arpa attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation attenuation reality invisible evolutionary quick counterpart ionic electrophysiological handbook enters modern granule bear facts clues derives shortly texas convey massive subtle decades propagates began jack sparc months haven haven haven apical apical apical apical apical apical apical apical putational electrotonic electrotonic electrotonic electrotonic electrotonic electrotonic electrotonic 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#@Brown_T,Camevale_N,Claiborne_B,Tsai_K,
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input data data function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set networks networks output output output output output output output number system system results results results results results information information information problem models models models models models models models based space linear layer layer layer layer case shown shown shown shown shown systems systems functions neurons neurons neurons neurons neurons approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single processing control local neuron neuron neuron neuron neuron neuron neuron rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis matrix form shows shows shows shows simple simple simple size net work work methods cells cells cells cells step step field level level level level level current current current current current current current current cell cell cell cell high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response response similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show section rule real average average theory theory obtained obtained obtained obtained term term note experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university threshold threshold threshold threshold variables computation computation research sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left presented presented presented presented presented presented activation activation activation activation activation activation activation frequency machine sets press press press press press press continuous abstract computational computational computational computational computational references due due due due ieee adaptive context introduction effect effect recurrent recurrent recurrent tion tion tion tion tion tion tion tion tion variable representations representations representations representations representations representations representations representations representations representations learned learned learned higher center previous previous previous previous firing firing type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long long represent distributed equations techniques region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region proposed proposed observed simulations simulations simulations simulations simulations simulations ing ing total total simulation simulation simulation simulation simulation simulation simulation regions potential potential potential potential potential potential potential feedback feedback feedback feedback feedback feedback feedback feedback specific specific specific series provide active determined experimental experimental constraints cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain brain brain brain mit voltage comparison comparison comparison contrast dependent dependent dependent dependent modeling modeling version version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses represents represents addition ai framework cambridge cambridge environment hinton top stimuli stimuli stimuli stimuli effects effects effects full full full full full full full full full full requires developed levels levels levels levels levels lines path path path path path provided finally evidence evidence evidence evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory associative associative associative associative associative associative associative associative associative associative discussion feedforward tested tested excitatory excitatory excitatory excitatory excitatory stable circuits amount effective supported role theoretical require eds eds eds adaptation adaptation hypothesis including simulated combination combination york mechanism consistent structures structures pre pre inhibition stored stored stored stored stored decay decay combined neuronal neuronal neuronal membrane membrane membrane membrane membrane membrane membrane population recent robust separate separate highly highly highly previously previously previously previously works tions smooth studies rl trans address bounded interval organization organization organization organization organization organization organization storage storage storage storage increased increased increased increased increased grant occur touretzky touretzky width width strength strength strength place row greater greater hebbian sigmoid performs performs constrained strong strong strong strong strong mechanisms mechanisms external external characteristics characteristics demonstrated demonstrated proportional proportional proportional intelligence selective decrease decrease manner connectivity connectivity acknowledgements areas primary sequential sequential dept changing modeled recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall explicitly consisting events formed formed formed versus potentials potentials potentials potentials decreases formation formation formation formation formation review influence detailed evaluated modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation forms forms forms allowed combining recorded recorded box plotted illustrated illustrated black tests aspects modification modification modification modification wij presentation presentation presentation presentation spiking post identity identity orthogonal excitation soc strongly induced induced contained allowing allowing allowing allowing allowing allowing allowing moore anderson neuroscience physiological physiological physiological follow comp michael michael michael michael michael simplified simplified dayan dayan providing ill ill ill ill neurosci neurosci neurosci neurosci overlapping overlapping overlapping overlapping overlapping overlapping overlapping subsequent rat rat rat rat intrinsic intrinsic intrinsic remain stimulation selectivity selectivity circuitry association association association accurately matches giving behavioral analogous matched neu transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission man psychology rev versions versions versions olfactory explored nervous academic academic fibers pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal neal animal animal massachusetts ment growth publishers diffusion caused interneurons rapid rapid tive tive organized organized organized organized organized organized afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal res res recording recording recording auto auto addressed addressed questions apparent experimentally recordings completion schematic schematic summarized summarized mod mod spread reaches cal fiber fiber fiber decreased decreased focused conditioning traces displays physiology zemel neurophysiol neurophysiol neurophysiol neurophysiol repre enhancement enhancement theories suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression bower bower bower bower bower bower bower bower familiar familiar familiar hit resulted resulted keeping ral implications exceeds exceeds passive published utilized utilized weakly weakly slice slice slice slice slice falls pat injection injection injection enhance sim hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo tic hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus foundations mem suggesting properly roy storing concentration concentration concentration calcium calcium calcium calcium calcium calcium calcium calcium calcium ics sequentially sequentially informa associations associations associations cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic helmholtz ent ent kluwer responds responds connec exception causing suppressed suppressed suppressed suppressed evoked evoked eric eric eric eric eric representa arising arising trends trends robots biophysical life potassium potassium potassium degraded degraded degraded degraded degraded potentiation regulation regulation regulation regulation regulation neurophysiological altered gluck gluck projecting projecting disease disease selectively weaker intracellular intracellular intracellular intracellular intracellular familiarity interspike prevents prevents atr reciprocal experi demonstrating rats syn drives lation tial marks justification terns inhibit utilizes morris morris morris morris morris suppress suppress harvard harvard award neocortical anatomy proposal mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton ory arriving enhances enhances autoassociative absent cho dent sentation prominent pitiform pitiform recalled rent tory medial medial medial linking acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine eeckman plenum levy levy levy wan ace preventing activates activates remarkably excite phil dominate dominate dominate extracellular assoc assoc illustrating mediate myers myers mossy ously ously previ previ pattem synapfic elicited elicited novelty dynam poten poten ana neuromodulation piriform suppresses snyder recur prevented prevented behav behav ulation ulation ulation mart mart laminar barkai barkai barkai barkai barkai barkai barkai barkai barkai barkai vation acti depen unfamiliar interfering interfering interfering buckingham buckingham buckingham burgess burgess selec mediating keefe pilot joshua joshua joshua joshua associa depended collaterals collaterals collaterals synap cai cai aging agonist agonist regulated regulated regulated nimh orlando bergman bergman subregions subregions subregions ffi ffi terminating longitudinal wash consid perfusion hetero hetero suf entorhinal entorhinal entorhinal entorhinal entorhinal entorhinal entorhinal entorhinal entorhinal entorhinal entorhinal gabriel organiza organiza ilar dem redish intemeurons intemeurons intemeurons intemeurons norwell hawkins dentate dentate dentate dentate dentate dentate preparations preparations preparations nized nized ciative ach ach ach ach interspersed adapta adapta adapta adapta pressed influx nance imitating senting edi edi edi edi edi ficiently modu subregion runaway org aptic stood rla orga orga forma intracellularly affer 
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#*network network network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data data function function function function function function function function function function function function figure figure figure figure figure figure time time time time time time time set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training algorithm output output output output output output output output output output output output output output output output output output output output output number system state state state results results units units units units units units units units units units units units units units units information information information information information information models models models models models models models models models hidden hidden performance performance based space space space linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector order order order shown systems systems systems probability functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit approach approach approach pattern pattern pattern single single single single single single single single single single processing processing processing processing processing processing processing processing processing large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate analysis optimal inputs inputs inputs form form shows signal signal signal signal simple small net net net net net net net net work work work methods methods fig fig fig fig fig fig cells cells step step step step features level trained trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure problems random random random high high memory memory memory memory memory memory response response response response response response response response similar similar representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture section section section line vectors general general real real approximation average theory gradient term activity activity activity activity dimensional dimensional result university university threshold threshold threshold solution research found found sequence sequence sequence sequence target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics computer terms terms connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node node node node node node node node node node node node node node node node node node node node prediction map present present present nodes nodes nodes nodes frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal range range press press press learn position components components components components nonlinear nonlinear nonlinear outputs outputs outputs continuous abstract applied applied applied applied applied back computational computational computational computational computational computational computational computational computational properties properties references component procedure important important adaptive propagation introduction action action action action complex complex complex complex complex complex behavior behavior statistical dynamic generated recurrent search tion tion tion complexity variable spatial spatial spatial assume lower lower lower lower lower lower rules measure higher center center firing firing required cortex cortex cortex spike spike spike spike spike spike tree distributed equations chip make forward finite simulations simulations resulting total total simulation simulation multi called called times times times times elements elements elements elements regions regions regions regions mapping mapping mapping mapping mapping mapping mapping means feedback feedback feedback feedback feedback feedback feedback study study study filter filter filter filter filter filter original artificial artificial compared series perform perform active active active active determined determined determined experimental experimental experimental connected connected connected connected connected discrete discrete cortical cortical cortical cortical brain brain voltage voltage voltage steps train train train train dependent nets modeling morgan department implementation implementation implementation synapses synapses synapses consists consists internal internal advances represents connectionist connectionist difficult layers delay graph graph graph graph graph graph sequences sequences sequences sequences maps maps maps framework cambridge environment directly additional additional view san top top capacity capacity efficient upper upper upper upper full full requires con con con channel channel developed types lines finally processes evidence depends sampling sampling sampling sampling biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological biological discussion feedforward describe describe describe arbitrary arbitrary arbitrary arbitrary assumption predictions short common implemented implemented synapse synapse synapse synapse supported role theoretical theoretical theoretical theoretical eds eds vlsi vlsi vlsi vlsi ability future future kaufmann typically typically underlying dynamical dynamical dynamical dynamical functional mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp transfer transfer transfer transfer transfer transfer transfer transfer transfer interesting interesting projection mechanism trials numbers pre bottom bottom frame decay decay perceptron perceptron perceptron neuronal neuronal neuronal architectures architectures membrane membrane membrane membrane property property property element include period period period identical identical subset interest highly previously conventional observations observations approximately calculated calculated works works works axis axis tions tions studies studies differential sparse locations channels channels storage sensitive horizontal horizontal studied occur trial spikes spikes touretzky flow place minimal hebbian hebbian segment interactions accurate accurate numerical designed designed performs performs moody faster mateo suggest suggest propose mechanisms mechanisms physics labeled connectivity program question acknowledgements areas pro solving ann label vertical vertical modeled modeled multilayer multilayer multilayer explicitly physical involves remaining text unique develop develop events events events events events events potentials potentials potentials formation review viewed viewed evaluated understanding suggested constants past past past diagram key key delays event event event event event tracking initially advantages dendritic dendritic recorded building fire fire fire fire fire fire fire fire fire fire box activations activations sciences illustrated discuss mozer mozer mozer mozer coupled characterized major gamma gamma gamma gamma middle extra efficiency modification computationally computationally computationally included efficiently schemes reached receives receives composed capture anderson neuroscience neuroscience neuroscience oscillations physiological timing device device sampled modular realistic realistic realistic realistic received attempt body simpler powerful essential investigate varied detail lippmann preliminary mass postsynaptic rise rise plasticity scaled affect phases neu neu trace trace trace trace predicting psychology implementations implementations thought hebb ith consist utility seconds seconds isolated biology analytical answer expensive comparisons considerable filtered incorporate afferent afferent afferent axon axon hippocampal members axons arises geometry raw raw conjugate explained apparent collected empirically axes axes fed fed fed effort treated continuously continuously biologically biologically schematic schematic weigend incoming incoming cal suited conductances sophisticated sophisticated implements focused focused wesley multidimensional cor don accomplished addison labeling labeling extensive extensive appropriately refractory refractory refractory acts dynamically approximates neurophysiol jth discovery repre repre repre tem inspired adds murphy murphy murphy murphy bower bower anatomical promising city wilson wilson passive passive passive passive published analyses separating mental mental somatic somatic somatic soma offers hippocampus infer cerebral characterization cam fly accumulated yale yale largely numerous converted exhaustive expanding spatio spatio spatio spatio spatio spatio abstraction stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem stem assignments molecular principe principe principe principe attempted cessing biophysical biophysical biophysical mammalian efforts surrounding topic rough meta maintains afferents mimic modifiable challenge tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau tau served syn stores bridge functionality recogni continued morphology ron calculates rons possess equa huberman sparsely measurable functionally archi compartment compartment compromise enters format wong wong tical sentation sentation translate pitiform greatest sented spario haven tal biophysics vries vries vries vries activa preprocessor preprocessor preprocessor bio plans avenue albeit burden compartments genesis genesis lay tecture poral compartmental compartmental compartmental compartmental compartmental compartmental compartmental compartmental compartmental compartmental compartmental compartmental compartmental compartmental vectorial vectorial vectorial reconstructing comprise shell kinetics compose handicapped dave implementa conical conical edward edward edward edward structurally incor debate redwood gershenfeld nodal sional quiet precludes roger experimenting synaptically versatile biophysically hogg ceptron stants multitude dispersive porated paring incorpo artifical multidimen direcfiy unexplored stiff 
#@Kairiss_E,Murphy_S,
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#*learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure time time set system state state results results information models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models based based based based based space space space space linear linear linear linear case case case vector vector vector vector vector vector order order systems systems values values parameters noise functions functions functions functions functions functions functions distribution distribution pattern pattern pattern pattern pattern pattern pattern pattern pattern point image processing processing large local local local local local local local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class shows shows shows shows shows algorithms visual visual visual examples small feature feature feature feature feature feature fig fig fig fig points points points field field features current current structure structure structure high high response similar similar representation show vectors parameter parameter parameter parameter parameter parameter real real gradient gradient obtained experiments experiments activity university university computation solution independent found found table table table table table table distance distance distance science left left left left left left left left left left left left map map map map map map present present range components abstract abstract find properties properties properties properties properties properties properties references component due important complex generated generated generated generated generated generated generated generated parallel change difference difference difference difference difference spatial spatial lower rules chosen center center cases cases type cortex cortex cortex cortex cortex cortex cortex good conditions conditions equations make fact fact fact correlation correlation correlation correlation correlation observed observed resulting elements elements elements elements regions regions regions potential made orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global global global global global global global global study true compared compared compared receptive receptive provide proc proc proc eye eye experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental related constraints cortical cortical cortical cortical cortical equal power power power power power power power approaches approaches comparison comparison comparison comparison comparison comparison comparison fields support dependent morgan institute institute institute version individual advances bias bias bias bias layers maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps considered additional top top con con con derived area area area area area lines lines lines actual finally nature nature biological discussion describe describe predictions predictions predictions predictions predictions proof implemented generate generate require main future easily makes kaufmann underlying underlying account account special consistent numbers pre pre normalized normalized bottom bottom early early decay combined combined run description description predict predict predict denotes directions directions directions directions directions directions recent correlations correlations correlations correlations correlations correlations correlations property property property property robust typical typical reported include include machines interest sufficient approximately match studies studies achieve achieve trans address evaluation evaluation evaluation locations modified organization organization exists exists exists horizontal invariant extended wide rotation predicted predicted predicted predicted predicted correctly correctly white boundary pass conclusion critical critical critical critical row row row row hebbian hebbian hebbian competitive competitive competitive differences differences differences mechanisms presence presence exist exist iii iii iii iii iii iii averaged acknowledgements reference pro ways laboratory vertical vertical coordinates text text angle spectral spectral develop develop formed focus formation formation formation formation correlated detailed densities evaluated evaluated organizing ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular lee centers suggested suggested suggested allowed spectrum reasonable reasonable neighborhood neighborhood neighborhood roughly advantages avoid recorded recorded figures perceptual usa usa usa usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance plotted plotted black phys characterized characterized tests structural columns columns columns columns columns columns columns columns differ symbols symbols tend miller miller miller miller orthogonal orthogonal ten summary soc soc soc soc issue contribution contribution sci sci categories categories gray vary simplified wave neurosci neurosci neurosci neurosci neurosci neurosci principles principles principles principles principles principles principles principles principles principles principles illustrates preferred preferred preferred preferred preferred modelling modelling cowan origin fourier fourier project project investigated investigated biol biol biol biol biol biol relationships relationships authors predicts predicts rev som som assumes explored academic generates generates regime regime regime regime percentage preference preference preference preference preference preference preference preference preference agreement publishers phenomena fairly fairly coded independence briefly reasons rapid closer organized filtered consequence angles angles acad acad linsker linsker linsker linsker qualitative apparent prop experimentally readily lack share treated ity exhibits exhibits summarized summarized aim gen fall fall cal singer shaped findings yuille yuille yuille yuille sharing spectra spectra spectra spectra spectra spectra spectra discontinuities cybern cybern cybern cybern cybern cybern aligned aligned saddle saddle appropriately angular angular angular animals nat nat circular repre robotics fails bower imaging stronger striate striate striate striate striate hope bands bands bands bands bands intuitive date pat schwartz schwartz branching reproduce reproduce reproduce reproduce reveals layout specificity specificity roy roy arrows extensively agree tures interestingly mind ure schulten schulten schulten schulten schulten schulten schulten listed listed listed listed kluwer wiesel wiesel wiesel tables tables tables emerge emerge tween preferences preferences preferences preferences hubel hubel hubel breaking continuity continuity continuity monocular monocular constrain perpendicular iso iso singularities singularities singularities singularities singularities singularities macaque macaque macaque macaque macaque macaque macaque lond lond cartesian cartesian sheet diversity diversity diversity diversity diversity universit ation obermayer obermayer obermayer obermayer obermayer obermayer obermayer obermayer obermayer obermayer obermayer durbin durbin experi status status ritter species species opti satisfactory autocorrelation autocorrelation autocorrelation hat ers bold bold tanaka tanaka tanaka developmental developmental developmental developmental dom harvard illinois illinois vanish baxter baxter baxter lowpass quantitatively bandpass bandpass bandpass bandpass bandpass reproduced lar sentation prominent prominent zones zones zones zones zones spec tern dow dow eeckman urbana urbana disorder disorder disorder disorder disorder technische tal tal stryker obeys align align nents phil intersect blasdel blasdel blasdel blasdel niebur niebur niebur reproduces lay anisotropic anisotropic anisotropic kim disagree concise fulfilled beckman beckman beckman abs abs mitchison mitchison singularity orthogonality reproducing slabs slabs underlie aver descriptive braitenberg braitenberg braitenberg braitenberg segregated erties fimction gation keller mexican tab tab tab quence superficial indebted experimen experimen focussed mecha deprivation favoring frg paragraph elliptical swindale swindale swindale swindale cesses loci bielefeld bielefeld bielefeld tropy tropy aged stringent coordi erated unsolved preferably varieties fro dictions conse optically str evalu realism neous nates incompatible anisotropy anisotropy homogeneity hospitality sequently sed dicted elliptic elliptic drs coor gles orthog orthog nodel levay inance prohibits salama nore 
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set networks networks algorithm algorithm output output output output output output output output number number system system system system system system system system system system results units units units units units units units units units units units information problem models models performance performance based based based based based space space space space weights weights weights weights weights case order order order order shown shown systems weight weight weight weight weight weight functions functions neurons neurons neurons neurons distribution pattern pattern pattern pattern image image processing processing control control control control control control control control control test patterns patterns analysis matrix matrix inputs inputs inputs form shows signal signal signal simple simple gaussian visual small small task field field process process current current current trained structure problems random random random random random memory response response response similar similar similar similar representation representation representation show show show line line line line line line line line line line line images parameter real real real real real average average average gradient gradient gradient gradient gradient result variables variables variables variables research sequence sequence target initial estimate estimate estimate estimate computer computer connections synaptic synaptic synaptic synaptic synaptic synaptic direction direction direction direction direction present present present phase phase phase activation activation activation frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal press learn learn components components basis abstract find computational computational computational analog properties properties references component component component stochastic stochastic ieee adaptive adaptive adaptive adaptive mixture introduction complex complex complex complex circuit effect dynamic generated generated variance search search search change difference difference variable variable spatial assume measure measure signals representations representations representations learned learned learned learned higher higher part part part part center type type expected make fact region proposed observed resulting resulting ing ing simulation human human respect sum sum called elements elements mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement dimension made feedback feedback study filter filter original original original artificial specific specific specific represented compared compared determined determined experimental constraints motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor brain brain brain brain mit steps accuracy accuracy connection connection connection source proceedings institute institute synapses consists consists internal internal internal individual individual responses responses responses responses responses difficult difficult difficult final delay delay delay delay sequences sequences sequences sequences framework cambridge directly curves transition san stage stage stage stage estimated con produce channel channel coding coding weighted developed area area area area area area area area area area area area area area provided provided evidence biological biological discussion inverse assumption stable circuits short assumed assumed assumed assumed assumed supported role theoretical theoretical theoretical journal journal journal journal journal journal end end hypothesis hypothesis cluster easily development noisy sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory needed needed functional programming projection projection mechanism consistent trials trials trials trials trials matching matching matching matching matching principal pre direct direct direct stored stored normalized normalized normalized supervised early attention attention combined sources neuronal membrane membrane membrane membrane membrane recent recent robust separate lateral strategy period period side sejnowski sejnowski sejnowski sejnowski sejnowski dimensions highly unsupervised observations tuning solve studies studies sparse evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation channels storage amplitude amplitude amplitude constructed constructed exists parts wide alternative locally white generally strength strength critical assumptions hebbian accurate accurate sutton learns suggest suggest suggest sound sound sound sound sound sound sound encoding encoding propose propose mechanisms mechanisms mechanisms mechanisms mechanisms solid solid proportional variety selective selective groups identification acoustic acoustic areas areas produces produces produces primary primary primary sequential sequential sequential generating transitions tuned averaging linearly involves interaction develop national depending stages stages evaluated evaluate controlled controlled updated modulation margin suggested allowed barto barto barto slow dashed dashed generation generation generation generation generation generation construction faces transactions expect recorded exploration exploration template template template template template template template template template kernels kernels kernels combinations combinations usa usa assignment sciences specifically candidate coupled discussions major reason gamma gamma closely importance suitable encoded encoded driven schemes orthogonal orthogonal fine reached receives composed anderson neuroscience neuroscience neuroscience phonetic duration gray involved involved involved involved involved hypotheses acknowledgments explore simpler remain selectivity selectivity command command diego transformed production production perturbation perturbation perturbation perturbation essential experience dotted dotted helpful behavioral plasticity structured working pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway encode fundamental phases phases momentum matched plausible man separated nervous established established critic analyzed fairly coded coded coded biology processed drive organized organized preprocessing located nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus laboratories separately separately sounds sounds medical cybernetics behaviors syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable pathways dark capability simulate poorly biologically biologically commands commands commands commands schematic templates templates templates templates howard perturbations perturbations aim modulated modulated maximizes song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song replace credit acquisition acquisition accomplished interface japan controlling harmonic harmonic harmonic air significance minutes check contract viewpoint serves neurobiology implications salk responsible enhanced phrase phrase phrase muscles muscles evaluations evaluations started programs male male overview ascent accounts consequences reproduce specialized young young young suggesting arrows arrows harris harris interestingly adopted resonance spatio spatio comparative comparative lesions lesions lesions lesions profiles profiles decomposed hundred simulating principe principe lesion trends guidance hughes terrence terrence terrence terrence terrence mediated simplifying projecting cosine cosine cosine academy investigating nuclei nuclei nuclei nuclei nuclei nuclei nuclei pools syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables thousands atr failures correlate correlate develops ucsd resembles walk species species species tension tension remarkable doya doya doya doya doya primitives establishes developmental adult adult adult replicated station spectrogram compensation anterior anterior anterior anterior konishi konishi konishi konishi konishi nmda nmda ventral vocal vocal vocal vocal vocal vocal vocal vocal vocal bandpass dopamine implying marder smc lewis lewis lewicki lewicki stomatogastric substrate selverston replication tens ears opinion opinion replicate medial medial modulate sparc months vries vries checked spectrograms undirected abnormal thalamus thalamus reviews bird bird bird bird bird bird bird bird bird bird bird bird warrick warrick opportunity favorable lesioned lesioned lesioned sing sing sing neurology deficit membranes kyoto birds birds birds birds birds birds birds motoneuron bypass kuo organ imperfect mooney mooney mooney mooney vibration snapshot casey casey neuronlike synthesizer imitate focussed topographically neurosciences unary seika ryan hear midbrain midbrain structed innate social hikaridai onal easiest organs persists songs songs songs songs songs songs assembled neuroanatomical perturb perturb sac kenji kenji kenji kenji kenji magnocellular arnold origins deficits deficits imitating stretched stretched memorizing reinforcing regulates neurotransmitters genetically resembled contrasting practiced elaboration father orthog neuroanatomy perturbs perturbs norepinephrine perkel drove quential impair mands 
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#*network network network network network network network network network network network network network network network network learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input input input input input function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set set networks training algorithm number number results results information models models models models models models models models based based based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear case case case case case vector order shown shown shown shown shown shown shown shown values weight weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach pattern pattern pattern single single single large local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns patterns patterns analysis analysis inputs inputs inputs inputs inputs form form form shows shows shows shows shows simple simple simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small small small size size size feature feature feature feature feature feature feature feature net work cells cells step step step field field field field field features process process process process cell cell structure random random high response response response response response response response response similar similar similar similar similar similar similar architecture architecture show equation images images parameter approximation activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional result result result university computation research dynamics dynamics initial initial constant computer computer distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic science science science left left left left left left left left presented presented map map map map map activation activation activation low temporal range range range range range range range range range range press press learn learn position position basis abstract computational computational computational computational properties properties properties properties properties properties properties properties properties references due ieee ieee positive positive introduction statistical dynamic dynamic dynamic dynamic dynamic recurrent recurrent tion tion tion tion change change difference spatial spatial assume assume higher part part part center center center center previous previous firing type multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long long long long long long long make region region proposed correlation length length correct observed observed observed scale scale simulations simulations total total simulation simulation simulation simulation human sum called regions regions regions regions orientation orientation orientation orientation orientation orientation orientation orientation study em original vol relative represented receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive location eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined connected connected cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical equal equal equal connection connection connection connection connection connection connection connection connection connection connection fields fields fields fields fields fields fields fields fields fields fields fields dependent dependent modeling selection proceedings proceedings proceedings proceedings proceedings department synapses consists joint represents responses final final exp addition addition maps maps maps maps maps maps framework san stimuli conference determine full significant world con con con con con con randomly randomly area area area product provided processes processes processes processes inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends biological biological measured discussion normal normal normal normal normal limited close excitatory excitatory excitatory excitatory excitatory excitatory stable surface predictions circuits circuits short short short common assumed supported role main journal journal journal journal square future development development development development development development development development development development development typically smaller smaller smaller underlying account functional projection york mechanism mechanism structures structures structures uniform representing inhibition inhibition inhibition international normalized early early idea produced produced run light light neuronal neuronal neuronal correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations property typical typical lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral include side highly highly previously previously unsupervised unsupervised observations observations approximately tuning tions smooth match modified generalized organization organization organization organization organization organization organization organization organization organization organization organization sensitive grant horizontal horizontal parts parts occur suggests suggests suggests suggests extended wide width width clusters white white white column column demonstrate strength conclusion hebbian hebbian editors interactions interactions interactions interactions sigmoid retina retina retina retina retina retina retina retina retina weak weak weak weak suggest strong strong mechanisms external labeled start relationship groups groups connectivity connectivity connectivity connectivity connectivity areas areas areas areas areas areas areas areas areas areas areas areas pro longer optical primary primary primary primary laboratory tuned tuned mathematical mathematical changing modeled implement explicitly explicitly explicitly simultaneously simultaneously physical scales interaction interaction interaction develop develop develop develop develop develop develop develop develop develop develop develop develop develop develop equilibrium equilibrium gaussians formed competition decreases decreases national national national formation formation formation dependence review review depending stages correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated overlap organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular forms converges constants partial expansion normalization neighborhood neighborhood initially initially distances distances distances foundation kohonen kohonen kohonen degrees figures perceptual activations activations activations activations usa usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance retinal retinal sciences sciences sciences determines activated black partially neighbors columns columns columns columns columns columns columns columns columns columns columns columns columns determining closely closely closely wij wij presentation detect projections tend tend miller miller miller miller miller receives excitation excitation excitation excitation induced link link link link link neuroscience neuroscience neuroscience neuroscience neuroscience dis return follow follow gray built receptor receptor vary dot realistic wave wave binding binding cat cat cat cat cat principles principles principles overlapping neighboring neighboring acknowledgments intrinsic intrinsic intrinsic receive receive receive receive remain wiley experience experience strengths strengths scalar matches matches respond detectors plasticity plasticity plasticity affect encode func presynaptic topographic topographic neu hill adapt adapt predicts opposite opposite perfect eyes eyes eyes eyes eyes eyes adjusted der der der der der der som som hebb extent grouping grouping preference preference preference preference preference preference preference preference ment piecewise adjacent adjacent biology caused starts spatially drive closer organized organized organized broad broad located afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent consequence potentially potentially scientific projected recognized begin patches patches patches patches patches patches patches patches patches demonstrates demonstrates annual annual cybernetics cybernetics cybernetics radius simulate experimentally quantitative share marked continuously continuously continuously dots ity ity mod pittsburgh spread cal ordered ordered singer singer singer singer singer singer singer singer singer substantial coherent boston shaped coherence coherence focused focused eventually specifies cor uncorrelated primarily primarily primarily primarily forming dynamically connecting grey interconnected interconnected receptors receptors receptors eliminated eliminated binocular binocular binocular binocular binocular binocular binocular binocular binocular anatomical imaging stronger primate striate striate familiar nearby neurobiology neurobiology roles spot spot spot spot spot spot spot responsible exploring ranging connect iteratively pat pat pruned von von von von dominant sim assembly arrangement dif treatment francisco specificity grants explains tures mechanical ence schulten shorter ent kluwer wiesel wiesel cooperative encodes alternating emerge revealed forced tween tween abstraction lesions lesions profiles preferences preferences preferences ical malsburg malsburg malsburg malsburg malsburg big affects simulating demon stands illustration adapting adapting adapting adapting monocular monocular monocular monocular monocular monocular monocular lesion concentrated exclusive exclusive mammalian maintained expand concentrate altered surrounding academy academy iri iri weaker sheet assemblies afferents afferents tij tij gilbert gilbert gilbert gilbert gilbert fea obermayer obermayer obermayer retained nal inactive topography develops expansions served drives prefer terns spring spring spring rfs austin austin austin neighborhoods spacing reversible developmental stripes eral dom medicine sharply wavelength wavelength wavelength wavelength meeting neocortex evolving vivo amplified evolves cold cold vicinity cess charles tra lar lar texas brought health replicate goodhill goodhill goodhill goodhill plastic plastic progresses progresses cons stryker spots spots ular ular yon yon joseph joseph joseph joseph joseph columnar columnar nections nections nections nections nections nections synchronize blasdel patterned patterned patterned patterned patterned patterned patterned patterned retinas retinas topologically miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen confirms lesioned lesioned pri pri iter fuse laterally sual birth mary mary engel tain narrower katz katz katz organize organize concentrates concentrates correla ocularity keller iij comers ations settled predominantly abstractions farther amir lat eij eij congress gestalt tex namics public entity kybernetik retinotopy regulate biolog harbor harbor harbor targeted activ abstracted serf reorganization ilar worm inhibi surviving coherently adapta strengthen strengthen utexas piscataway injections conceived grinvald corti bernardo cently ronal dordrecht inance strates anticorrelated anticorrelated corticocortical affer hibition eled repaired 
#@Miikkulainen_R,Sirosh_J,
#t8
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#*network learning learning learning input input input input input input input input input input data data data data function figure figure figure figure figure figure figure figure figure figure time set set set set networks algorithm output output output number number number number number number number number number number number number number number system system system system system error error error error results results results results units units information information problem problem problem problem models models performance performance based space weights linear linear linear linear linear layer shown shown shown systems systems systems values values values probability parameters noise noise noise noise functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit recognition pattern point point image single single single processing processing processing processing large neuron test patterns patterns patterns patterns optimal optimal optimal inputs inputs inputs inputs inputs form form form shows signal signal algorithms gaussian gaussian gaussian visual visual visual visual visual visual visual examples examples small size size size size size size size size size size feature task cells cells cells cells cells cells step points features process level level trained high response response response response response response response response response response response response response similar similar architecture architecture architecture architecture architecture architecture architecture architecture show show show equation equation section section section line images images images images general approximation approximation approximation average average theory theory theory obtained obtained obtained obtained experiments experiments activity result computation computation independent independent defined defined defined defined defined defined found found found found found found constant computer computer computer distance connections connections connections connections connections connections connections connections connections science science science science science left left left left presented present motion motion maximum range range range press learn position basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs continuous sample abstract find computational computational density properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties references ieee stimulus stimulus effect generated generated generated energy energy assume signals signals signals signals required required required cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long conditions tree tree distributed distributed distributed distributed expected fact correlation observed simulations simulations simulations simulations simulations simulations resulting ing tasks tasks tasks tasks simulation respect elements mapping made orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation em original original specific samples represented compared desired desired desired cross cross receptive receptive receptive receptive receptive provide define location location perform determined goal related discrete discrete discrete discrete discrete cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain equal equal equal equal accuracy comparison larger fields fields fields fields fields support proceedings institute individual responses responses exp maps domain domain domain equivalent equivalent environment stage stimuli effects determine upper approximate vision pages give randomly area area product product provided nature depends sampling sampling sampling sampling sampling sampling sampling biological biological biological increases arbitrary limited surface finding rbf amount amount short role role require journal journal journal ability hypothesis hypothesis hypothesis degree sensory pairs combination combination combination combination combination combination functional functional functional functional functional functional functional coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients ratio ratio ratio ratio ratio ratio ratio projection projection projection york structures matching matching matching matching matching matching matching matching principle principle principle operation leads leads details filters filters filters filters filters idea combined run sources light neuronal neuronal neuronal neuronal neuronal neuronal denotes population population population population recent advantage property subject identical recently recently interest approximately calculated calculated calculated tuning tuning tuning tuning smooth smooth smooth yields match match match achieve separation grid organization organization organization improvement entire horizontal horizontal lead extended derivative feed clusters column column column column setting demonstrate minimal minimal assumptions interactions clear peak suggest suggest taking presence proportional proportional proportional regularization radial variety minimizing selective relationship relationship groups areas areas areas areas areas optical optical optical solving generating tuned tuned tuned tuned tuned vertical mathematical distinct modeled modeled modeled multilayer coordinates transformations slightly angle angle angle develop adding formed formed shift national formation formation review overlap overlap variation organizing organizing centered sizes sizes sizes sizes sizes sizes activities suggested allowed spectrum dashed intervals purpose generation valid transactions dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic usa inter inter plotted domains domains domains domains domains domains domains domains holds simplicity columns columns columns columns columns columns columns columns regular determining closely suitable maximal maximal poggio poggio literature projections projections projections projections projections projections tend tend tend receives composed capture summary allowing link physiological bar sampled localization maximization maximization maximization cat cat principles overlapping overlapping overlapping overlapping overlapping mixing preferred preferred neighboring neighboring intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic receive extend origin origin selectivity selectivity selectivity selectivity carried wiley biases periodic rise fourier matches matches successive rest detectors incremental maximizing lgn lgn proved func topographic fundamental fundamental notion notion neu patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch possibly editor equally precise precise pyramidal explain devices percentage histogram histogram histogram preference preference orientations orientations orientations orientations adjacent spatially snr implementing implementing sites sites organized organized precisely located located located monkey mathematics separately angles calculations patches patches patches patches patches patches patches patches arises arises bandwidth outer apparent percent double freeman profile tional conducted peaks incorporated spread aim cal proposition proposition shifted aligned physiology labeling forming driving girosi girosi receptors binocular binocular anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical anatomical imaging imaging imaging significance primate striate striate striate stated obtaining neurobiology neurobiology shifts edelman edelman edelman edelman edelman edelman dendrites encountered regarded dependency dominant demonstration histograms somatic israel diameter diameter diameter diameter axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal cerebral cerebral cerebral creating bins matter considerations subsequently discovered receiving receiving outlined ence neurophysiology wiesel wiesel wiesel wiesel wiesel maximized ram revealed revealed revealed diverse feeding par comparative profiles arbor arbor arbor arbor arbor arbor arbor preferences preferences spaced tendency tendency hubel hubel hubel hubel streams perpendicular trends trends shifting shifting shifting shifting compatible adelson argued confirmed macaque noting multiscale academy cartesian selectively diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity reveal inversely inversely gilbert modality elsevier geniculate geniculate steering steering steering steering steering steering round gorithm species species species arbors arbors arbors arbors arbors arbors arbors arbors accordance const quantify rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs rfs hypothesized interpolated broadly continuum continuum striking heeger ally manipulated attained attained attained maxi maxi vivo vertically era era accounting sis resultant faced faced scatter carrying prominent scattered substrate aic ini polar linking freely freely simoncelli simoncelli explaining lund lund lund lund lund lund lund mization mization putational columnar columnar columnar borders borders borders sition uniformity compartments confirms tially participate seemingly mosaic widespread ticular steerable steerable steerable steerable stereopsis stereopsis steer amir ein originated originated shed patchy patchy patchy patchy patchy patchy patchy patchy patchy neurosciences neurosciences diameters crossed radii sional aertsen pres weizmann weizmann targeted rockland rockland originates tracing manifestation coef rehovot levitt injections slab ttm vidyasagar vidyasagar vidyasagar grinvald grinvald grinvald corti shimon shimon shimon shimon shimon mani nce imprecise multidimen substantiate wisdom 
#@Edelman_S,Malach_R,Spector_K,
#t8
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural input input input input input input input data figure figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set networks networks training training training training training training algorithm output output output system system system system system system system system system error error error error error results results units units units units units units units units units units information information based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer shown shown shown shown shown systems systems values values values probability probability probability probability probability probability probability weight weight weight weight weight functions neurons unit unit unit unit unit unit unit approach pattern pattern pattern pattern single processing processing processing processing processing control control local patterns matrix matrix inputs inputs inputs form shows signal signal signal signal signal signal signal visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper examples examples examples small work work work methods cells cells cells cells cells field field field field process trained trained structure random random response similar similar similar similar similar representation representation architecture architecture architecture architecture architecture show equation section fixed fixed rule rule rule rule rule vectors vectors general gradient experiments activity result university solution solution solution solution solution solution research independent found found found found found target target dynamics initial initial connections synaptic synaptic synaptic synaptic synaptic science map map map map map map map map map map map map map phase phase frequency frequency frequency temporal temporal sets sets sets press position position position basis continuous abstract back find convergence convergence convergence references stochastic stochastic stochastic ieee positive procedure important important important propagation introduction action hand behavior stimulus stimulus generated parallel parallel search search tion tion tion change change change change change change change change change difference spatial spatial spatial spatial spatial spatial spatial spatial signals signals signals signals learned learned learned part part previous previous required distributed expected fact observed simulations simulations simulations minimum resulting resulting ing simulation respect sum sum called times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement feedback global global global original original compared series receptive receptive receptive compute objects objects proc location location location location location location location perform active active active determined determined experimental connected brain brain brain brain approaches mit accuracy contrast contrast contrast connection connection connection fields fields fields update dependent morgan morgan report report institute institute department synapses synapses synapses synapses synapses synapses synapses internal advances advances connectionist responses final layers layers addition addition maps maps maps maps maps maps maps maps maps maps maps maps maps cambridge directly hinton additional view solutions limit san san san stage free free vision vision vision vision pages increase weighted weighted lines evidence evidence evidence backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature simply simply biological discussion group close assumption assumption actions actions actions finding finding amount synapse synapse synapse synapse generate adaptation journal journal hypothesis easily rumelhart rumelhart rumelhart development sensory sensory kaufmann kaufmann auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory simulated probabilistic typically typically needed combination functional jordan projection projection projection increasing head head mechanism mechanism consistent structures squared bottom bottom supervised early frame frame combined sources discussed recent separate movement reported reported lateral introduced subject identical hierarchical sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski compare observations teacher volume volume volume volume tuning tions diagonal chain locations modified williams organization organization amplitude trial trial wide matrices predicted alternative correctly deterministic white occurs setting half place place place place place place editors editors central differences differences sigmoid sigmoid constrained mateo mateo suggest suggest sound sound sound encoding strong strong strong mechanisms mechanisms external external california turn exist movements decrease introduce derivatives minima configuration acoustic reference reference explicit appears optical optical winner generating tuned modeled simultaneously simultaneously interaction interaction interaction interaction shift shift shift shift shift shift shift blocks competition choosing independently independently expressed formation stages stages communication controlled controlled updated updated evolution evolution activities activities activities allowed allowed allowed allowed allowed allowed diagram diagram diagram partial barto intermediate intermediate coupling coupling expect existing determines illustrated prove activated activated discussions major major reason society mcclelland wij comparing receives conf induced induced contained interpreted neuroscience neuroscience superior issue issue physiological cues involved involved vary localization michael dayan dayan absence absence wave giles reach automatically consisted illustrates subsequent acknowledgments cowan unlike diego layered create experience humans hanson helpful scalar rest project int plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity possibility closest plausible adapt adapt predicts predicts predicts predicts predicts illustrate changed changed eyes thought adjusted adjusted explored hebb hebb animal site site site site site site site site site site site site site site site site site directed growth distinguish unstable biology biology nowlan starts spatially nucleus consequence consequence sounds medical localized read demonstrates questions greatly pathways pathways pathways pathways pathways pathways readily peter recordings adjustable passed incorporated sharp biologically schematic schematic perturbations incoming prevent prevent adjust conclude findings owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl owl simultaneous simultaneous converged converged cochlea consistently consistently shifted shifted shifted shifted shifted shifted primarily restrict appropriately appropriately animals controlling receptors systematic systematic proceeds multiplicative multiplicative multiplicative multiplicative multiplicative imposed keeping shifts salk salk salk salk optic optic optic optic optic optic optic optic optic optic guide inferior inferior inferior inferior inferior inferior inferior inferior inferior ensures young young surprisingly reveals suggesting jolla colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus relies agree projects projects forced sigma ical personal chapter tendency simulating eric adjustment adjustment barn barn barn barn barn barn barn barn barn barn barn barn barn barn barn barn barn barn representa mismatch mismatch gated gated favor insights pdp hughes terrence terrence terrence terrence terrence paris nuclei france register register knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen knudsen supports page nal prevents examination unpublished diagrams triggered resolve attributed ping send converging pouget pouget pouget pouget pouget pouget calibration calibration tectum tectum tectum tectum tectum tectum tectum tectum tectum interaural interaural alex stay stay injected nmda core raises raises cooperation reproduced constraining teaching teaching delivery delivery delivery raised raised transmit convey ears responded awij addi trapped imposes imposes rein rein broadcast sends activa activating aliasing aliasing localize pooled helped displaced terry fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr fbr clipped spontaneously neti neti neti neti neti rosen foveal prism prism thalamic exclude shell owij abstracts relied rue reinforced aperiodic preferentially unambiguous collateral foveation foveation raise forcement forcement predominantly remap remap remap collaterals topographically montague montague originate interacts favored favored favored alexandre alexandre alexandre alexandre alexandre slows vastly prey prey audition relay guides guides wjk ensured tum prisms prisms prisms unambiguously ecole unaltered genetically normale servation eyi 
#@Deffayet_C,Pouget_A,Sejnowski_T,
#t8
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#*model model model model model model model model model model input input input input input input input input function function function figure figure figure figure figure figure figure figure figure figure figure time time time time set number number number system system system system system system system system system system system system state state state state state results results layer layer layer layer layer layer case order shown systems values values values parameters parameters parameters noise noise neurons neurons neurons neurons neurons neurons pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point single single large large local local rate rate rate patterns patterns patterns patterns patterns patterns inputs inputs form form form form form form form shows gaussian visual visual visual visual visual visual visual small small size size size size size feature work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step points points field field field field field field field field field field field field field features process process process process cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure random random random similar similar similar similar similar representation representation section fixed fixed fixed fixed images general general general parameter states term term term term term term dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university variables variables variables variables variables variables variables research independent defined found dynamics dynamics dynamics dynamics dynamics initial initial initial terms terms distance distance distance synaptic science left left present present present maximum position position position position position nonlinear abstract find properties properties properties properties properties properties properties properties properties properties properties references stochastic due due positive positive important propagation propagation propagation introduction hand behavior behavior dynamic tion change change change change change variable variable spatial assume representations representations chosen chosen part part part part part part center center type type type type type type type type type required cortex represent represent distributed distributed make fact fact observed resulting total eq eq eq called times means global global global global study negative negative negative negative negative represented receptive receptive receptive receptive location location eye eye eye eye eye eye eye eye eye eye eye eye experimental posterior brain brain equal equal equal equal equal steps steps fields fields fields fields fields fields dependent modeling institute institute institute department synapses synapses synapses synapses synapses consists exp exp exp exp layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers maps maps maps considered view transition transition transition transition transition transition transition transition transition transition transition transition top top stage determine determine upper upper free clustering clustering types types types types types types types types types types types types types types lines provided nature depends depends simply simply biological measured denote close close corresponds stable stable stable surface surface surface predictions assumed shape shape shape synapse generate supported role role role main main hypothesis development development development development development development development development development development development development development development development development simulated simulated typically typically underlying functional functional functional functional functional functional functional functional functional ratio projection projection projection projection projection projection structures uniform principle minimize neuronal neuronal neuronal denotes denotes exact exact lateral lateral lateral lateral lateral lateral lateral lateral lateral subject subject side side side side side sense dimensions dimensions dimensions sufficient sufficient compare observations calculated calculated calculated calculated volume axis axis axis axis axis converge rl locations locations grid interval interval organization organization organization organization organization organization organization organization organization organization entire horizontal parts parts parts parts occur occur extended extended extended extended trial trial move deterministic clusters occurs column column column column column column strength starting critical critical critical critical depend central interactions interactions interactions interactions differences differences retina retina retina retina retina retina asymptotic propose presence external external external external external external external external external external characteristics labeled start exist plane plane plane configuration force force denoted acknowledgements produces produces factors factors factors factors primary generating transitions transitions label vertical distinct distinct distinct distinct modeled modeled explicitly interaction interaction interaction interaction interaction develop formation depending depending influence influence densities lee lee centers forms completely completely completely completely completely completely similarly allowed allowed allowed past key reduces roughly roughly intermediate intermediate initially distances visible sufficiently sufficiently sufficiently classified classified classified topology color blind blind blind blind blind blind blind blind blind blind blind retinal retinal retinal retinal retinal retinal determines coupled coupled characterized successfully columns columns columns columns columns uniformly uniformly differ effectively projections projections essentially ten reached reached reached receives receives characteristic summary refer refer induced allowing symmetry symmetry lie lie contribution contribution contribution hold comp notation realistic realistic realistic wave wave wave wave wave wave wave wave wave wave wave wave reach reach principles preferred preferred neighboring receive receive receive receive oriented explore origin origin layered perturbation investigate replaced existence rise examine fashion lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn affect topographic surfaces neu predicts opposite opposite opposite opposite opposite opposite psychology equally eyes eyes eyes eyes eyes adjusted front front front front front quantities separated mapped mapped nerve contributions contributions explain established crucial growth growth coded adjacent caused caused caused starts reasons ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion spatially drive forces incorporate sgn nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus monkey cut cut involve describing describing gradually gradually axons localized localized localized localized localized geometry geometry meaning fluctuations explained reflects prop limits limits limits limits pure pure pure passed passed incorporated exhibits exhibits perturbations spread modulated occurrence ordered curvature curvature curvature chose shaped gap gap gap gap gap gap indices proportion driving driving narrow narrow narrow narrow neurophysiol establish establish plays plays spontaneous spontaneous spontaneous anatomical anatomical accepted occurred occurred occurred grow grow serves nearby roles belong belong imply spot spot spot spot spot spot spot spot spot spot spot optic continue started slice ensures connect dendrites irregular appendix appendix appendix appendix induce induce propagated competing competing specificity specificity specificity specificity specificity specificity specificity specificity specificity extends merge eqs jump captures grants propagate propagate stopped receiving influences influences influences maintaining schulten schulten schulten schulten schulten gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps die trigger solely possibilities options peripheral peripheral peripheral peripheral peripheral peripheral peripheral peripheral peripheral peripheral peripheral perpendicular perpendicular segregation mammalian singularities singularities singularities macaque macaque macaque macaque macaque iri cation weaker register maintains dorsal dorsal supports sweeps sweeps sweeps geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate prevents signs strict strict triggered functionality functionality functionality sorting acquire acquire acquire inconsistent continued compete developmental developmental developmental developmental developmental developmental contralateral contralateral contralateral morphology illinois illinois illinois proportions rons polarity polarity polarity polarity polarity polarity polarity polarity polarity polarity possess thickness thickness ventral emerges neurol coincide interpretations reality sions drastically curved dimen permanent permanent inducing inducing nih fovea prominent counted counted capturing ipsilateral ipsilateral propagates gradual urbana urbana metastable hole stabilizing tightly joseph joseph joseph joseph joseph primates primates sends columnar sition klaus klaus klaus klaus klaus tran schematically retinas retinas intervening favorable differed numbered ell beckman beckman beckman foveal foveal foveal foveal foveal foveal foveal foveal foveal foveal foveal foveal singularity mature mature mature mature mature laminar laminar laminar laminar laminar laminar laminar laminar laminar laminar mon spheres champaign tab theta ein baker baker depended namics vas vas vas stabilizes eli allman malpeli malpeli malpeli malpeli malpeli malpeli malpeli malpeli malpeli malpeli malpeli cutting retinotopy retinotopy transi rhesus rhesus diverging holes stressed polarities polarities ceptive kaas kaas magnocellular magnocellular coincident enforcement pertur intricate ext organizations maturation maturation immature ternal lam behar phs shades degenerates promotes midway darkest vhich 
#@Malpeli_J,Schulten_K,Tzonev_S,
#t8
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#*network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set networks networks networks training training training training output output output output output number number system system system system system error error error state state results results results results units units units units units units information information information information information information information information information information information information information information problem models models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space weights weights weights weights weights layer layer layer layer layer layer order order order order order shown shown systems values values probability parameters parameters parameters parameters noise noise noise functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons unit unit unit unit unit unit distribution approach pattern pattern pattern pattern pattern pattern pattern processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control control control control large neuron neuron rate rate test patterns patterns patterns analysis analysis form shows shows signal simple simple simple gaussian paper paper small size feature net work task task task task task task task task task task task task task task task task task task task task task task task task task step step points current current trained cell cell structure random high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response response response response response response response response response response response response response similar similar similar representation architecture show show show show equation fixed fixed general generalization parameter parameter parameter real real states states term term term term activity activity activity activity activity activity activity activity result threshold threshold threshold computation research research found found found target target target target target target target target target target target target target target dynamics dynamics dynamics dynamics constant constant constant estimate standard standard standard standard computer connections connections synaptic science prediction presented present present activation activation low frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal press press press press components basis continuous continuous continuous continuous continuous continuous abstract computational computational computational computational computational computational computational computational computational computational computational computational properties references stochastic stochastic due positive procedure procedure procedure important important context context context context context context context context context context introduction action behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect generated parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent difference measure measure signals prior prior prior prior representations representations representations representations representations representations representations representations representations higher higher previous previous previous firing firing type type required required cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good long long long long long long long long long long long long long long conditions conditions conditions conditions conditions conditions conditions conditions represent distributed expected make make fact fact correct correct correct correct correct correct observed errors errors errors errors scale simulations simulations simulations ing tasks tasks tasks tasks tasks tasks tasks total total simulation simulation simulation simulation simulation simulation simulation simulation human human human respect times times times times times times factor made made made natural study study study obtain negative relative relative relative specific specific specific specific specific specific specific compared provide provide perform perform perform active active active active active active active active active active active active active active active determined determined determined determined experimental experimental experimental related constraints constraints connected distributions gain gain gain gain gain gain gain gain gain gain gain gain gain gain motor discrete brain brain steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger connection support train modeling morgan version version version represents connectionist responses responses responses responses responses responses responses responses bias bias delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay addition addition graph considered framework framework framework framework framework framework framework equivalent directly additional san top stimuli stimuli stimuli stimuli stimuli effects effects effects effects effects effects effects effects conference capacity choice free increase produce produce condition condition condition condition condition condition condition developed developed developed developed developed developed developed area area types provided processes evidence evidence evidence backpropagation inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory constraint measured normal normal normal normal normal normal normal describe fast limited assumption excitatory excitatory predictions predictions predictions predictions predictions short short short short short short short short short short short short short short short short implemented assumed supported supported role role role role role journal ability ability ability hypothesis makes makes development development fit fit fit simulated simulated underlying needed combination reduced reduced reduced reduced reduced reduced reduced reduced account dynamical dynamical dynamical fully fully interesting interesting testing significantly significantly significantly character york york increasing mechanism consistent trials trials trials trials trials trials trials trials trials trials trials trials trials trials trials trials trials trials trials trials matching empirical language making inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition bottom decay attention produced run run added neuronal discussed resolution exact robust lateral introduced period period subject subject cognitive cognitive recently relevant dimensions sufficient highly highly previously subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects module module module module module module module module module module module module module module module module module match match correspond correspond studies studies studies address evaluation modified scaling occur suggests trial trial trial trial trial trial trial trial deviation wide correctly touretzky occurs occurs occurs occurs generally strength strength critical reduce trajectories trajectories conclusions central differences modules modules clear constrained mateo suggest strong mechanisms mechanisms integration characteristics variety decrease decrease relationship targets manner connectivity connectivity areas appears pro produces produces produces produces produces longer longer solving ways ways primary laboratory distinct dept dept dept changing simultaneously simultaneously simultaneously remaining slightly integrated adding events events events competition letters formation review squares influence detailed detailed evaluated updated forms understanding activities suggested diagram diagram earlier slow performing delays delays delays delays delays delays delays delays delays delays delays delays fitting event msec msec msec msec msec msec david david david david fire determines maximize activated specifically specifically specifically successfully planning middle letter letter letter letter letter society effectively presentation presentation presentation presentation presentation presentation presentation literature build comparing comparing tend identity ten reached reached composed capture capture repeated neuroscience dis superior physiological physiological cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue duration duration duration duration involved play play absence absence paradigm paradigm paradigm providing providing providing providing delayed delayed reach principles consisted consisted illustrates bars employed explore explore explore simpler simpler remain carried american essential circuitry involving limitations preliminary biases reducing reducing examine examine matches respond respond respond behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral analytically scaled reliable structured working examined act act act measurement naturally trace plausible predicts opposite psychology psychology thought adjusted versions nervous nervous baseline generates explain animal mentioned mentioned biology tractable tractable worse comparisons arise commonly controls controls cut describing qualitative mellon mellon apparent behaviors carnegie carnegie populations populations double simulate simulate simulate cohen cohen cohen cohen cohen cohen cohen cohen cohen cohen introducing completion incorrect incorrect incorrect incorrect incorrect variant compares psychological maintain maintain calculating pittsburgh pittsburgh pittsburgh pittsburgh ture qualitatively age findings implements focused focused damage patients univ univ univ cumulative cor benefit college contextual analogue physiology sort formally temporally appropriately appropriately animals receptors plays extending cellular kaufman occurred primate overcome overcome roles responsible responsible guide modifications exploring analyses utilized representational governed tone tone periods periods loo decide pat consequences consequences captured facilitate facilitate assembly offers offers multiplied reveals rich rich probe probe probe probe probe probe probe probe probe probe probe probe probe sustained sustained sustained card pearlmutter pearlmutter captures limitation ics unchanged zipser zipser maintaining maintaining neurophysiology ter incorporates latency asked reaction reaction reaction reaction reaction reaction reaction forced forced forced tween distinction par lesions lesions solely superimposed tendency tendency tendency tendency simulating examining lesion attempted modifying cessing lobe execute regulation neurophysiological maximally argued argued noting frontal frontal selectively weaker maintains responding responding suffer supporting failures demonstrating clinical syn reversed demand terns todd todd todd todd todd inhibit inhibit hypothesized hypothesized aid reflecting transmitter flows rare tip disturbances believed believed meeting striking striking assessment inferring intact screen explanations zipset dopamine dopamine dopamine dopamine dopamine wisconsin handbook schreiber schreiber schreiber schreiber schreiber schreiber schreiber schreiber schreiber schreiber schreiber gathered distractors stabilize indirectly focusing modulatory adequately durations capturing emerged servan servan servan servan servan servan servan servan servan servan servan servan inappropriate inappropriate responded decades explaining progresses modulate preferable distractor tightly adjustments disorders inability accu manipulations opportunity mediate latencies latencies latencies jonathan jonathan jonathan jonathan jonathan consensus temporary cen testable testable novelty dynam specifications confident panels panels functioning functioning functioning feel neuromodulation neuromodulation neuromodulation tapped accumulating behav behav cap tri reinforced instructed reductions cited preceded hen jects syndrome acc acc instantiated reflexive button button guiding tex quired impulsive investigators investigators crossed als deterministically prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal prefrontal instrumental mech racy bethesda quan inhibiting neuromodulatory neuromodulatory neuromodulatory benson benson benson benson raven raven behaviorally probes permitting ior agreed confirmation neuropsychology goldman goldman goldman goldman sustain lobes deficits compelling convincing probed engage neurotransmitters involvement involvement changeux changeux fects interpretability levine levine psychiatry dehaene dehaene distin anisms promotes clinically ticularly 
#@Braver_T,Cohen_J,Servan-Schreiber_D,
#t8
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#*network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data function function function function function figure figure figure figure figure figure figure figure figure time time time set networks networks output state state state state state state state state state state state state state results results results results results results results results results units models models models performance based weights weights shown systems probability parameters noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons unit distribution distribution distribution distribution distribution distribution pattern pattern pattern pattern pattern pattern point point large neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis inputs paper paper examples small net work work work points field field process process level level level level level level level level level current current random high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response similar similar show show show equation section section section fixed fixed line rule rule real approximation average theory theory theory theory theory theory theory obtained obtained term activity activity activity activity activity activity activity activity activity activity university university threshold computation computation research research defined defined found dynamics dynamics initial initial initial constant computer connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science prediction direction presented present present phase activation activation low low frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal press basis abstract back find computational computational computational references component component due due positive important introduction introduction hand hand behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus effect effect effect effect effect recurrent tion variable chosen firing firing firing cortex cortex cortex cortex cortex binary long represent represent represent distributed proposed proposed correlation correlation correlation simulation simulation sum performed times times elements regions factor potential global global global study study study study study study negative specific specific specific specific active motor cortical cortical cortical cortical cortical brain brain brain brain brain comparison larger support dependent dependent dependent dependent dependent dependent dependent modeling modeling department loss loss synapses synapses synapses synapses internal internal internal internal internal internal internal internal internal internal internal represents connectionist responses difficult final final exp directly curve additional additional additional stage stimuli effects effects effects capacity requires significant basic increase increase con derived randomly levels levels levels bounds area area associative associative achieved measured measured measured measured increases denote tested limited assumption assumption corresponds stable predictions finding synapse supported role face face face journal journal end degree including including auditory hopfield account account functional block projection structures structures trials trials trials trials trials trials trials trials uniform uniform leads leads leads representing representing iterations pre pre stored stored stored stored stored stored stored stored early early magnitude magnitude magnitude frame combined neuronal denotes denotes recent recent recent recent include include period subset cognitive cognitive cognitive cognitive cognitive recently interest highly volume module module module module module axis axis studies studies studies converge organization storage increased increased increased increased increased increased increased increased increased lead occur occur correctly generally strength strength place place hebbian hebbian hebbian hebbian conclusions conclusions editors central sigmoid measures modules numerical suggest taking taking physics external external external external external external external external external external external external external external external characteristics demonstrated plane manner manner manner manner attractor attractor attractor attractor attractor attractor attractor attractor areas relation ann ann tuned modeled modeled modeled modeled metric implement interaction events formed formed formed formed versus focus formation formation review review stages stages overlap overlap overlap overlap evolution suggested converges converges slow expansion add add remains eeg eeg dendritic david david david david david david building perceptual retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval memories memories memories memories memories memories illustrated illustrated absolute delta wij presentation post projections projections projections projections projections projections projections projections projections projections comparing tend tend tend characteristic refer kind prob showing dis physiological cue cues cues cues receptor receptor absence absence absence modular wave delayed highest binding leading receive presents remain remain stimulation updating humans association preliminary biases examine examine examine examine history school behavioral behavioral investigated plasticity notion necessarily onset onset man man analyze predicts store fibers fibers fibers baseline generates mixed mixed mixed extent contributions explain motivated years developing ground growing fairly analytic analytic analytical analytical sites sites monkey acknowledgement hippocampal res apparent apparent reflect autonomous item slower slower frequently frequently biologically variant psychological ity schematic maintain maintain calculating synthesis mod limiting gen incoming incoming occurrence occurrence qualitatively kinds decreased attraction findings findings findings findings findings patients patients eventually eventually eventually converged displays phenomenon indices college investigation homogeneous homogeneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous spontaneous proceeds biased biased biased biased biased occurring occurring occurring enhanced enhanced days continue passive published overlaps james james james james james patient displayed monkeys searching branching israel hippocampus hippocampus treatment emergence emergence emergence emergence young mem master late late environmental horn horn horn horn horn horn horn park erlbaum lett receiving receiving ics consecutive maintaining fellowship basin emergent emerge trigger trigger ical hundred tendency tendency recurrence england england examining illustration preserved preserved deep stroke lobe lobe maintained denoting intra concentrate concentrate acquired frontal frontal frontal frontal frontal frontal frontal frontal frontal frontal frontal frontal frontal frontal frontal disease disease disease disease preserve preserve page macroscopic macroscopic nal tel tel microscopic triggered tau clinical clinical capacities capacities capacities capacities capacities persistent persistent rats externally preserves accordance accordance accordance ruppin ruppin ruppin ruppin ruppin ruppin ruppin ruppin ruppin diffuse diffuse diffuse char medicine medicine tribution compensation compensation compensation episodes sharply peaked neurol neocortex neocortex stevens stevens stevens stevens stevens stevens stevens stevens stevens retrieved retrieved retrieved retrieved ory decaying quantitatively establishing dopamine evolves evolves sis handbook reviewed gathered memorized memorized memorized facts carpenter aviv aviv ized maryland undergo shares col linking linking sented sented plastic progresses progresses disorder months meaningless continuing columnar columnar plausibility macro abnormal abnormal disorders disorders dominate reactive reactive reactive reactive tsodyks tsodyks undergoes quiescent quiescent postulated europhys neurology cued cued cued cued cortico spontaneously spontaneously spontaneously testable functioning percepts psy underlie compensatory compensatory compensatory compensatory compensatory compensatory compensatory formulating story unrealistic invoked anomalous intervention intervention weakened pathological pathological pathological pathological pathological pathological regeneration regeneration regeneration portant concentrating wealth adults eytan eytan eytan eytan eytan cutting strengthening strengthening strengthening verbal symptoms symptoms symptoms symptoms symptoms symptoms rhesus arch arch ating weakening bulletin subcortical explo invited neuroanatomical severity rations neuropsychology goldman acteristics concomitant ports lobes lobes neous consecutively parallels astronomy involvement orienting wander nations retrieves jin inves taneous adversely adverse rice mani spon psychiatry sinha esis hypoth hypoth regenerative regenerative wijsj chology looses overwhelming 
#@Horn_D,Reggia_J,Ruppin_E,
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#*network model model model neural neural neural neural neural input input input input data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure set networks algorithm output output error results results units units units units units units problem models hidden space space space space weights weights linear linear linear linear linear linear linear linear linear linear linear layer case case case vector vector vector vector vector vector vector vector vector vector shown shown shown shown shown systems systems functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit method approach pattern single single single single single processing control neuron neuron neuron neuron patterns analysis analysis inputs inputs inputs inputs inputs form form shows shows simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper examples work work cells cells cells cells cells cells cells cells points points field field field field field field field field field field field field field field field field field field current cell cell response response response response response response response response response response response response response response similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show show show show show equation section fixed fixed fixed fixed rule vectors vectors vectors general general approximation approximation approximation approximation approximation average theory obtained experiments experiments activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional result result university variables variables variables computation defined found table science science prediction prediction prediction prediction left left direction direction direction direction direction direction direction direction direction map map map map map present present activation object object object object maximum range position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract back find computational computational computational properties properties properties references component important propagation introduction hand hand hand behavior statistical statistical effect effect tion spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial signals prior representations representations representations representations representations representations representations representations representations part previous cases required multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good good conditions represent represent represent correlation observed observed observed simulations total total human computed respect sum eq eq called called called called called regions mapping means study specific represented represented represented receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide provide compute compute compute objects objects objects objects objects objects objects objects objects objects objects objects objects location location location location location location location location location location location eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye experimental experimental related posterior posterior posterior gain gain gain gain gain gain gain gain gain gain gain gain motor motor motor motor motor cortical brain brain fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields support institute institute department code code code joint represents represents responses responses responses responses difficult difficult scheme scheme scheme scheme scheme addition addition addition maps equivalent directly curves san san top top conference determine efficient approximate approximate approximate approximate increase give con condition coding coding product product actual evidence evidence nature nature discussion arbitrary transformation transformation predictions predictions predictions generate supported role role role role journal journal journal journal hypothesis hypothesis hypothesis degree makes makes sensory sensory sensory sensory simulated typically typically typically combination fully fully interesting projection projection projection head head head head head head head head head head consistent consistent consistent consistent consistent consistent structures operation leads representing max direct international bottom bottom frame frame produced predict neuronal population directions directions recent typical typical movement reported lateral strategy moving identical identical side side subset sejnowski sejnowski sejnowski sejnowski sejnowski array cognitive highly approximately tuning tuning tuning tuning tuning tions smooth smooth correspond studies studies positions positions positions positions positions positions locations arm arm amplitude exists exists horizontal horizontal horizontal parts studied suggests rotation alternative alternative move touretzky demonstrate conclusion conclusion critical central central central sigmoid sigmoid sigmoid sigmoid retina clear peak encoding encoding encoding encoding propose propose strong integration sigmoidal sigmoidal demonstrated california movements movements plane averaged reference reference reference reference reference reference appears perception perception perception vertical modeled modeled modeled modeled modeled coordinates coordinates coordinates coordinates coordinates simultaneously involves transformations transformations transformations transformations transformations angle angle integrated gaussians gaussians gaussians gaussians review stages codes operations approximations centers centered centered centered centered centered centered centered centered centered centered frames frames frames frames decomposition forms activities purpose remains valid valid intermediate degrees expect exploration coordinate coordinate coordinate coordinate bell retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal illustrated illustrated black characterized uniformly suitable encoded computationally computationally delta poggio literature computations schemes schemes schemes situation situation plots capture strongly neuroscience neuroscience neuroscience dis superior involved sampled play dot computes computes leading attempt subsequent preferred preferred preferred preferred preferred preferred preferred approximating approximating acknowledgments body body simpler stimulation stimulation diego diego access requirements put involving accurately helpful respond respond fashion investigated possibility possibility muscle muscle working working encode encode encode encode encode circles circles circles plausible necessarily predicts predicts opposite eyes thought thought adjusted attempts charge site piecewise distinguish navigation biology biology multiplication nonlinearity perspective precisely desirable monkey monkey products pool pool medical demonstrates annual radius outer explained readily lack quantitative peaks biologically howard characterize aim modulated modulated modulated modulated monotonic monotonic richard sums kinds shaped patients patients patients physiology extensive arguments narrow spontaneous saturation primate salk salk salk adequate arrays planar planar planar inferior published published published recovered representational patient widths accounts monkeys monkeys uni nonlinearities nonlinearities parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal multiplied hippocampus deg specialized suggesting jolla colliculus arrows extensively extensively subsequently multiplying multiplying zipser zipser zipser zipser indirect rigorous minus sig equivalently goodman goodman encodes comparative lesions lesions lesions lesions profiles junction tendency sinusoidal sinusoidal lesion argue interact neurophysiological neurophysiological neurophysiological hughes retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic terrence terrence terrence terrence terrence met individually cosine cosine cosine lookup cartesian emphasized programmed programmed rewrite sigmoids sigmoids coordination coordination coordination handled synthesized spring pouget pouget pouget pouget pouget contralateral alex eral sensorimotor sensorimotor sensorimotor sensorimotor neglect neglect physiologically believed believed sym raises andersen andersen andersen andersen andersen andersen andersen andersen andersen andersen andersen andersen sian neutral confined confined cold essence gaus meant format emerged recovering limb polar imum wan ular gross posi nections conversations nonlinearly neurology terry vectorial vectorial vectorial vectorial vectorial vectorial vectorial vectorial vectorial canadian idealized lations georgopoulos georgopoulos anatomically partic ordinates siegel siegel entails modulates presumed selectivities selectivities syndrome syndrome syndrome hemisphere alexandre alexandre alexandre alexandre alexandre neurological neurological neurological loca harbor redish borne premotor premotor premotor behrmann downstream lished etal disregarded subdivisions corticocortical pharmacology stimulates 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function figure figure figure figure figure set set set set set set set training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number system error error results results results results results results units units units units units units units units units units units units units units units units units units units units units units units information information information information information models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based based based based based space weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer vector order shown shown shown values parameters parameters weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution approach pattern pattern pattern pattern pattern point image image image image image image image single single single single single processing processing processing processing large large large local local local local local local local local local test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis inputs inputs inputs inputs inputs inputs inputs inputs form shows shows shows signal simple simple visual visual visual visual visual visual visual visual visual visual visual visual paper examples small small size size net methods methods fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field field field field field field field field field field field field field field field field field field field field process process process current current trained cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure random random random response response response response response response response response response response response similar similar representation architecture architecture show line rule vectors images images images images images images images images images images generalization approximation gradient gradient note experiments experiments activity activity activity activity activity activity dimensional result result university university computation computation computation research research research research independent independent independent independent independent independent independent independent independent log found found found found sequence sequence sequence sequence sequence initial standard standard standard connections prediction direction direction direction direction direction direction direction direction direction present activation activation temporal temporal temporal object object object object object object object object object object object object object object object object sets motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range press learn position position position position components components components components components components components components components sample abstract applied applied back back back find computational computational properties properties properties properties properties properties properties properties properties references stochastic stochastic due due procedure procedure procedure propagation introduction complex complex complex estimation estimation behavior stimulus stimulus stimulus stimulus dynamic generated generated generated generated generated generated cost cost cost cost tion spatial spatial assume measure signals signals signals representations representations higher part part part part center center previous previous type type type multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex binary conditions represent expected expected make techniques region length observed minimum minimum resulting ing ing tasks total simulation simulation computed computed multi potential dimension natural natural natural natural knowledge artificial relative relative relative relative relative relative relative relative specific specific specific samples desired cross receptive receptive receptive receptive receptive provide objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects location location location active active eye eye eye determined determined experimental goal goal related distributions cortical cortical brain equal comparison fields fields fields fields fields fields fields fields modeling selection institute department synapses technique technique consists individual individual represents represents represents represents represents responses responses responses responses layers scheme scheme sequences sequences considered framework environment environment environment curve additional view view estimates san stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects detection determine determine full full statistics world speed speed vision vision con produce derived randomly randomly area area area area area area area area area area area area velocity types types types types types entropy actual selected evidence evidence nature sampling discussion normal describe describe group tested tested assumption assumption assumption corresponds corresponds surface nearest common assumed shape shape supported role journal journal journal journal journal journal journal ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis degree including fit objective simulated probabilistic underlying underlying underlying underlying underlying combination combination combination combination reduced account account account block interesting interesting segmentation consistent consistent consistent consistent database operation leads principal iterations making making attention produced produced produced produced run description light neuronal population population directions directions directions directions recent recent recent resolution exact property property ensemble element movement movement reported lateral lateral apply moving moving moving moving moving moving moving moving moving moving moving moving include include identical sense sejnowski sejnowski sejnowski sejnowski sejnowski array recently relevant dimensions unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised approximately approximately approximately approximately tuning tuning tuning tuning tuning match match correspond studies studies studies studies achieve positions positions positions locations locations observation sensitive sensitive sensitive sensitive entire constructed exists invariant occur suggests suggests suggests wide derivative rotation rotation alternative width width generally demonstrate half half flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow place assumptions assumptions assumptions hebbian hebbian hebbian depend depend competitive designed clear performs encoding encoding encoding encoding propose mechanisms presence characteristics drawn sigmoidal demonstrated intelligence variety movements movements movements movements selective selective selective selective selective selective selective plane averaged manner manner manner scene scene scene scene connectivity connectivity connectivity identification program force base question question areas areas areas areas areas areas relation construct produces perception optical optical optical optical optical optical optical estimating plot describes stability tuned tuned segments modeled sensitivity sensitivity sensitivity sensitivity sensitivity angle develop develop adding applying implies competition yield yield extracted independently independently focus depending showed centers centers static suggested translation earlier earlier smoothing smoothing expansion expansion expansion spaces combining tracking box includes thesis combinations combinations combinations combinations combinations activations formulation retinal discuss specifically successfully regular regular selecting selecting aspects aspects aspects aspects closely capable encoded effectively included invariance invariance invariance situation situation ten reached receives composed capture induced contained allowing neuroscience neuroscience neuroscience superior superior superior physiological criteria cues sampled sampled relaxation play dayan dayan dayan realistic attempt moves moves disparity disparity disparity disparity disparity preferred preferred preferred extract extract oriented extend extend camera camera situations situations situations situations selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity carried diego essential exhibit updating varied relations relations environments detail divergence pursuit helpful matches matches respond respond respond respond respond detectors office decisions stream complicated encode cover neu examined act patch plausible man psychology created eyes thought portion portion portion portion portion portion grouping grouping grouping grouping grouping grouping grouping phd attempts synthetic animal animal indicating preference scenes scenes ground derivation smoothness track caused monkey monkey monkey monkey arise mation consequence acknowledgement pitch pitch toronto localized patches arises radius mellon conjugate reflects carnegie cmu flexible simulate simulate peter share share employ biologically maintain switch pittsburgh occurrence qualitatively suited richard richard richard richard richard asymmetric logp coherent coherent coherent coherent boston comments findings findings implements multidimensional summed pose primarily accomplished tation zemel zemel zemel zemel zemel zemel zemel zemel zemel zemel discover naval extending spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral fails ments primate held fail salk salk optic optic optic optic periods zhang zhang paul conjunction intended intended accounts accounts accounts facilitate thomas fish fish emergence spatiotemporal contraction contraction gaze gaze gaze specificity roy roy motions motions motions motions motions observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer discovered propagate stone stone ball ure maintaining maintaining neurophysiology neurophysiology neurophysiology parsing incorporates sig asked cooperative presenting presenting revealed expanding responds responds responds preferences perceived spaced simulating simulating gene reconstruct arising translated translated shifting grouped gener neurophysiological neurophysiological terrence terrence terrence terrence terrence fixation differentiation projecting macaque macaque selectively portions dorsal dorsal dorsal dorsal placing placing rotating avoidance retained experi correlate coming heading heading heading heading heading differently reversed reversed lation generarive prefer quantify agrees rfs rfs rfs rfs rfs rfs pouget viola mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst mst compete tanaka tanaka interpreting autoencoder flows flows flows compo continuum evenly evenly ray ray ray systematically andersen faced dent robustly fovea fovea indepen segmenting derives ated undergo undergo responded polar medial medial newsome newsome diverge saito rotate resemble unaffected walking nents invert simulates subsampling dilation cir package tie gibson gibson pri movie movie movie movie movie movie movie depths adopting adopting tinuous testable signaling singularity mary simu sereno sereno persistence mammals undergoing undergoing proaches recon wurtz wurtz wurtz wurtz wurtz wurtz indicative resembling preferentially encourages encourages intend sit perrone perrone selectivities selectivities selectivities selectivities shrinking traced swiss sponses prefers investigators investigators nals envi alexandre duffy duffy duffy duffy orban backgrounds backgrounds mech thereof contracting harmon extrastriate extrastriate sts movies sight tracing navigational albright warren warren cnl ronment localizing conform houghton anism struct scribe eccentricity hikosaka controversial maes cular erry 
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#*network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data function function function function figure figure figure figure figure figure figure figure time time time set set set set training training training training training training number system system system system system system system system system system system system system system system system system system system system system error error state state units information information information information performance based based weights weights weights linear layer layer case case order order shown systems values weight weight weight weight functions neurons neurons distribution method method pattern point point single single single single single control control control control control control control control control large large neuron rate rate rate rate rate rate rate rate rate rate analysis inputs inputs inputs inputs form shows simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small small small feature feature feature feature feature feature feature feature feature feature feature feature net work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points field process level current trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell problems random high memory similar representation architecture architecture architecture show show rule rule rule general general parameter real theory theory note note experiments experiments activity university threshold found dynamics dynamics dynamics dynamics initial distance connections connections connections connections connections connections connections connections connections connections synaptic prediction prediction left left left left left left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction activation frequency motion maximum range range press press position components basis basis basis basis basis abstract abstract applied applied properties properties properties properties properties references important behavior behavior stimulus effect effect parallel change change variable rules signals higher part center cases firing firing firing firing firing firing firing firing required multiple cortex cortex cortex cortex cortex cortex cortex long conditions represent expected fact fact region proposed proposed proposed correct correct observed observed respect respect respect made orientation study negative specific specific specific specific specific specific true compared series provide rates rates location location location perform active active active active active active active active active eye eye determined experimental related posterior posterior posterior gain gain motor brain brain brain brain brain brain equal mit connection connection fields train dependent dependent dependent dependent internal individual difficult final exp exp layers addition addition cambridge directly curve curve curves curves limit stimuli effects effects bit significant free world speed pages increase increase coding coding area velocity velocity types types evidence evidence evidence nature inhibitory discussion group group group tested limited complete excitatory excitatory excitatory stable stable stable predictions amount amount assumed assumed shape shape supported role role main hypothesis cluster cluster degree makes development sensory sensory including auditory underlying underlying needed account interesting interesting york edge edge edge head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head mechanism mechanism mechanism mechanism mechanism mechanism mechanism special consistent consistent structures numbers pre pre direct depth frame frame frame sources sources description light neuronal improved population directions recent resolution property separate typical typical typical typical lateral moving moving moving side side sense sense sense sense sense sense sense sense sense sense array recently previously previously observations approximately works works tuning tuning tuning tuning tuning tuning tuning axis axis locations modified williams williams williams organization organization parts intensity studied occur suggests extended spikes rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation correctly move move move white half half flow strength place place place place place hebbian hebbian hebbian neighbor editors clear peak peak peak peak peak peak peak peak peak peak weak weak sound strong strong strong strong strong strong mechanisms mechanisms mechanisms integration external sigmoidal sigmoidal proportional proportional turn exist exist movements selective decrease relationship iii introduce manner manner groups groups groups groups attractor areas areas suppose suppose suppose suppose suppose suppose relation ways stability stability stability sensitivity simultaneously simultaneously simultaneously simultaneously linearly easy slightly angle interaction develop develop applying springer shift shift shift shift shift implies competition formation formation dependence depending depending stationary influence influence influence influence influence influence influence influence influence operations restricted modulation centered completely translation earlier intervals roughly purpose add initially advantages degrees degrees degrees degrees recorded recorded recorded recorded recorded recorded recorded recorded fire fire sciences activated activated activated specifically absolute absolute absolute reason straightforward modification modification attractors build projections projections plots receives receives receives excitation soc soc soc strongly strongly allowing superior superior superior superior symmetry symmetry follow cue cue cue cue cue cue cue cue cue cue cue cue cue duration gray cues cues cues cues built neurosci neurosci neurosci neurosci neurosci neurosci neurosci neurosci moves illustrates illustrates neighboring neighboring neighboring neighboring rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat intrinsic intrinsic intrinsic intrinsic oriented situations stimulation selectivity wiley experience experience rapidly humans strengths periodic helpful postsynaptic postsynaptic postsynaptic respond respond behavioral behavioral detectors detectors detectors applicable plasticity authors referred working variability variability complicated complicated understand presynaptic presynaptic neu plausible possibly predicts predicts thought front der detector detector simplest contributions explain isolated integrate animal animal animal animal animal massachusetts crucial navigation explanation caused caused caused caused correction considerable considerable turns turns lin lin division directional directional directional directional directional directional directional broad located nucleus potentially hippocampal hippocampal circle circle circle circle circle circle gradually gradually gradually res res localized recording recording recording recording recording recording alignment alignment alignment alignment prop populations reflect pathways dark dark dark flexible effort detecting detecting detecting formulated maxima commands maintain perturbations aim prevent chen chen chen chen chen singer singer green green sophisticated sophisticated physiol implements focused deviations deviations deviations eventually cumulative consistently room aligned sort cooper saccadic drift angular angular animals vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular perfectly rotated rotated circular discovery food rotations theories turned cellular anatomical anatomical stronger stronger stronger minutes primate imposed operates shifts shifts north salient enhanced wilson moments fires continue inferior date passive weakly weakly james james james james james moved mental accounts interconnections nonlinearities parietal hippocampus bursts surprisingly ltp specificity specificity colliculus colliculus colliculus colliculus belonging card card card card card card card card card projects subsequently interestingly influences linked leaving numerous indirect indirect constitute session session session covering munro emerge responds poses copy causing molecular manipulation manipulation preserved deep life distant activate nuclei nuclei nuclei selectively importantly worth weaker weaker portions refinement outcomes dorsal dorsal dorsal dorsal west accounted turning turning turning investigations modifiable things things bill travel exploited behaves inactive unpublished topography sessions species rats rats rats rats rats rats rats rats rats rats rats rats rats rats rats rats rats tail bienenstock bienenstock water virtually broadly cylinder cylinder cylinder cylinder cylinder cylinder anterior anterior anterior anterior neocortex neocortex mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton william william william william william reality sending prone reflection cold experienced experienced essence brainstem reviewed stick facts facts vanishing adequately selverston ears silent silent polar freely freely freely landmark landmark landmark landmark landmark landmark landmark lights rotate rotate rotate plastic hot tightly intrinsically putational sends directionally dead dead minute dominate thalamus thalamus thalamus thalamus thalamus thalamus respects manipulations devel schematically rightward begun bruce bruce bruce bruce bruce bruce conflict environ outlines testable necessity responsive bearing bearing bearing bearing abs abs abs functioning thalamic stays correspondingly mature concluded mammals susceptible landmarks facing earth erties synchronously unitary recognizable sponds muller muller sole weakened knierim knierim knierim knierim knierim knierim knierim knierim knierim knierim barnes barnes rotates shed remap imal decade aging inertial markus markus markus markus markus emd excites ingredients darkness quan ingredient sparks sparks inevitable arizona arizona arizona arizona arizona integrators integrators sooner directionality directionality pur passively ruled halfway intimately lamina reckoning reckoning breadth richness happened rosci ternal opment efference disrupt dispersed erratic tucson dictate impair subserving compromising 
#@Knierim_J,Kudrimoti_H,McNaughton_B,Skaggs_W,
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#*network network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input function function function function function function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training output output output output output output output output output number number number number number number number number number number system system error state results results results results results results results units information information information information problem problem models models models models models models models models models models based space space space weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear case case case case case case case case case case case case order shown shown systems systems systems systems systems systems values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit recognition pattern pattern single processing processing processing large large neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis analysis class class inputs inputs inputs inputs inputs inputs inputs form shows shows shows algorithms algorithms algorithms simple simple simple simple simple paper examples examples size size size size size size size net net net net net net net task task task cells cells step step step process current current current current current structure structure problems memory memory memory memory response response response response response response response response response response response response response response response representation show show section section section section section fixed fixed fixed fixed fixed parameter real real real real real real real real real real real real real real real real real real real real real real real real real states states states states theory theory theory theory note result result result result result result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation computation computation computation computation computation computation computation computation log log log defined defined defined defined defined found sequence sequence sequence sequence initial initial initial constant constant constant constant constant constant constant constant computer computer terms terms terms terms synaptic synaptic synaptic science science direction phase phase phase phase activation activation activation activation activation activation frequency temporal temporal temporal temporal machine machine machine machine machine machine machine sets press press press basis outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous sample abstract abstract abstract abstract abstract applied back computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational analog analog analog analog analog analog analog analog analog properties references references important important adaptive decision propagation context introduction action action hand behavior behavior effect generated recurrent recurrent recurrent difference difference difference difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume assume assume assume assume assume assume assume assume assume assume assume lower lower lower lower lower lower chosen part part previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound firing firing firing firing firing firing firing firing firing firing firing firing firing type required multiple cortex cortex binary spike spike spike spike spike spike spike spike long tree tree tree make fact fact length length length length length finite finite finite finite finite finite simulations simulations simulations minimum classes classes classes tasks simulation simulation simulation simulation computed sum sum times times times times times times times times times times elements elements factor factor potential potential potential potential potential potential potential potential potential potential dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension applications negative vol vol relative specific specific specific specific specific provide provide provide define compute rates proc proc location determined related related related discrete discrete discrete discrete discrete discrete brain brain brain equal power power power power power power power power power power power power power approaches mit mit steps steps larger larger contrast train train train dependent dependent dependent dependent nets nets nets nets nets nets nets nets nets nets nets nets nets nets morgan report institute words version version version synapses synapses consists consists consists advances final delay delay graph framework cambridge computing equivalent transition bit bit bit bit bit bit upper upper upper upper significant significant significant basic basic basic basic basic basic increase increase give coding coding coding coding derived weighted levels levels levels levels bounds bounds bounds bounds bounds bounds bounds bounds bounds finally evidence inhibitory simply biological biological biological biological biological biological biological biological biological biological associative associative associative associative associative describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary limited limited assumption corresponds stable proof proof proof proof circuits short short common common shape synapse synapse synapse generate theoretical theoretical require require ability easily degree including kaufmann simulated simulated typically needed needed needed needed interesting interesting interesting segmentation special special matching details details details details numbers bits supervised polynomial polynomial attention membrane membrane membrane recent exact property element element reported reported introduced include period machines machines machines machines machines side sense subset subset sejnowski sejnowski interest previously unsupervised works sparse sparse sparse sparse definition bounded bounded bounded bounded gate gate gate interval storage exists exists exists parts studied invariant invariant invariant invariant invariant occur occur occur extended extended extended extended spikes spikes spikes spikes spikes spikes spikes spikes spikes deterministic deterministic demonstrate conclusion minimal assumptions assumptions assumptions assumptions assumptions assumptions assumptions assumptions segment segment valued valued valued valued valued valued valued valued valued valued valued valued depend depend differences numerical peak weak weak weak encoding propose mechanisms mechanisms presence pulse variety decrease decrease relationship relationship introduce explicit appears van van van construct construct construct produces longer solving factors describes mathematical mathematical mathematical mathematical linearly linearly linearly infinite infinite involves easy scales frequencies implies implies boolean boolean potentials potentials potentials independently focus depending depending viewed solved solved solved detailed evaluated open operations modulation modulation sizes similarly delays classical classical distances construction norm precision precision precision precision precision precision precision precision fire assignment assignment vapnik prove prove prove prove holds discussions tests simplicity simplicity aspects aspects aspects closely closely closely suitable suitable suitable suitable differ encoded encoded spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking build computations computations computations computations computations computations computations computations computations computations comparing traditional refer refer refer refer link showing interested interpreted interpreted interpreted oscillations content content physiological timing timing timing timing timing timing timing timing timing timing timing timing satisfy satisfy satisfy satisfy satisfy involved involved vary realistic realistic realistic realistic realistic binding binding received trains trains trains carried carried create essential investigate investigate exponentially rapidly oscillators replaced integral helpful existence postsynaptic postsynaptic postsynaptic biol biol analytically analytically possibility relationships relationships relationships gates gates gates workshop presynaptic presynaptic notion notion transmission plausible integer opposite automata formal formal formal assumes precise shapes shapes consist consist arbitrarily arbitrarily submitted motivated defines established established ment piecewise piecewise piecewise piecewise piecewise piecewise directed theoretic trivial analyzed phenomena phenomena phenomena benchmark processed processed processed turns rapid consequence axon axon axon axon acknowledgement involve annual preceding reflect pseudo pseudo pseudo pseudo pseudo tional simulate simulate simulate quantitative recordings haussler haussler passed employ biologically biologically exhibits measuring differs collective substantial logp logp logp logp logp logp logp logp logical realized pac cybern cybern investigation restrict acm arguments arguments arguments arguments refractory refractory count grows establish maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass rational rational rational rational rational rational rational rational rational rational rational rational rational rational rational saturation mail chemical grow transforms definitions definitions definitions imply adequate adequate exceeds symposium carry fires lip combines periods overview sim offers dif claim modelled axonal cerebral snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn snn matter epsp epsp epsp epsp inf inf inf schulten schulten schulten piece piece recursively chervonenkis transmitted sontag sontag forced spatio theorems theorems theorems theorems generalizations assignments resting resting possibilities algebraic algebraic algebraic publication file considers considers wise wise investigating buhmann buhmann oscillating apparently investigations elsevier permit refined drops compu article article article article article article mann spite demonstrating differently fortunately remarks survey sake sake sake ferent abeles abeles imple cornput reflecting hemmen concrete ters sen gerstner gerstner gerstner gerstner gerstner poly poly poly poly squashing judd judd handbook statements firings modulate rises technische notions remarkably turing turing turing turing turing turing turing turing turing turing sends simulates bio parame unlimited ago concentrations subclass siegelmann siegelmann tational subsystems proportionally multiples ences chine unrelated ipsp ipsp graz graz graz graz technically austria substances tape tape tape tape ivl tractability logs polyno aertsen vout vout archive rounded rounded occured institutes extremal igi wolfgang wolfgang wolfgang wolfgang wolfgang mial coherently ivi deliberately intricate ritz interrelated neuroprose conventions iei corticonics rationals bitrary 
#@Maass_W,
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#*network network network network learning learning learning learning model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input function function function function function function function function function time time time time networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output error error error error error error error information information information information information information problem problem problem problem problem problem problem problem problem performance based space space weights linear linear linear linear linear linear linear linear linear linear linear linear layer case case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order shown shown shown shown systems systems systems systems systems systems parameters parameters noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions method method method method pattern pattern pattern point point point processing processing control control control control control large large large local local local local local local rate rate rate class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian paper paper small small small small small small small small small net work work methods methods step step step structure structure problems problems random random random memory similar show equation equation equation equation equation equation equation equation section section section section section fixed fixed fixed fixed vectors vectors vectors general generalization generalization generalization parameter approximation approximation approximation approximation states theory theory theory theory gradient gradient obtained obtained note note note note note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result university university university variables variables variables solution solution solution solution solution research research research independent independent log log log found found sequence sequence sequence sequence sequence sequence sequence initial initial initial initial initial initial initial initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction direction direction presented maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum range press components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs abstract find find find properties properties properties properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood references references due due ieee ieee positive important adaptive adaptive adaptive adaptive adaptive context context introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical parallel cost cost energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy complexity assume assume assume assume assume signals signals signals chosen higher part previous previous previous previous previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound cases cases cases required good long distributed expected expected expected expected expected equations equations make make fact fact fact fact errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors finite finite finite finite finite finite finite finite finite minimum minimum minimum resulting resulting resulting resulting resulting ing respect multi called called called means means means made feedback global global global global global global applications applications study study study knowledge knowledge knowledge knowledge knowledge knowledge knowledge filter filter filter filter filter obtain obtain obtain obtain obtain obtain obtain negative vol specific true true true true desired compute distributions gain gain gain gain gain gain gain gain mit morgan words words version advances difficult sequences ai maps considered considered cambridge computing view view view solutions solutions estimates estimates estimates estimates estimates estimates estimates estimates upper requires requires requires requires requires approximate approximate approximate approximate approximate statistics con condition condition condition condition derived criterion criterion criterion criterion criterion criterion criterion bounds entropy backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration iteration iteration iteration iteration iteration nature nature simply simply discussion group denote denote denote transformation close close close close assumption assumption stable circuits finding assumed supported require require square end end rumelhart rumelhart including including including kaufmann underlying unknown unknown unknown unknown unknown unknown interesting ratio increasing special call idea attention minimize minimize minimize minimize minimize minimize choose denotes recent recent recent exact exact property robust robust robust robust robust robust robust practical practical introduced strategy include subject sense sense sense recently interest interest previously works tions solve solve solve solve solve solve yields yields correspond achieve trans trans address bounded bounded bounded bounded bounded sensitive constructed exists lead lead wide wide wide locally column column setting setting conclusion assumptions assumptions sigmoidal demonstrated variety variety minimizing exist exist exist min iii derivatives derivatives derivatives force force question question question acknowledgements suppose suppose suppose suppose suppose suppose relation relation relation relation derive derive construct construct longer index laboratory laboratory laboratory recall sensitivity infinite infinite infinite infinite infinite infinite infinite dimensionality involves belief applying implies implies yield depending squares squares estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator solved solved updated updated approximations approximations approximations approximations approximations approximations approximations approximations earlier smoothing smoothing measurements measurements classical reduces filtering filtering filtering norm norm norm includes priori priori priori formulation automatic automatic variations mcclelland refer dis dis lie criteria strategies satisfy quantity minimizes minimizes minimizes received attempt satisfies modelling modelling modelling modelling modelling modelling minimized command investigate updating updating updating environments estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators replaced mass hall ideas applicable office office cognition smallest math assumes observe observe observe ith ith ith ith ith switching arbitrarily mentioned preference variances variances growing expensive stanford stanford stanford stanford stanford stanford stanford satisfied satisfied widely widely filtered constructing constructing constructing immediately mation mation consequence scientific opt opt opt opt opt opt opt arises author preceding robustness robustness robustness questions reflects reflects led lms lms lms lms lms lms lms lms lms lms lms lms lms lack lack lack poorly backprop cal phone instantaneous instantaneous newton newton newton newton corrupted ear optimality optimality optimality optimality optimality optimality optimality optimality guarantee guarantee proceed air air ments mail stated stated stated multiplicative contract contract intuitively date lip prentice contexts studying surprising guarantees guarantees widrow widrow thomas thomas thomas thomas thomas surprisingly matter contact explains explains inf inf inf explorations ball ball microstructure vec diverse suboptimal generalizations tor causal causal guess guess conservative pdp uncertain afosr fir fir fir exceed alternatives esti esti applicability behave gauss tail appearing remarks hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi accordance satisfactory crude vii cliffs connects condi neglect disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances disturbances englewood disturbance disturbance disturbance contrary contrary minimax faced dent raised indepen ous hoff hoff violated rec kailath kailath kailath iir obeys obeys obeys observes ogi ogi ogi ele agation army exciting exciting exciting exciting exciting gorithms previ ire plants nonlin inverses uncertainties uncertainties intend intend intend unknowns unknowns cial fax doubt ivl spe ditions raphson raphson raphson haykin haykin derlying xlw conceivable conceivable daal wescon ensuing finitely worthy worthy exogenous exogenous accomodate specializes llw imizes iie boundedness scrutiny cony 
#@Hassibi_B,Kailath_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks number number number number number system system system system system system system system system state state state state state results results results results results results results results information problem problem models based based space weights case case case case case case shown shown shown shown shown shown shown values values values parameters parameters parameters noise noise noise noise noise weight weight functions functions neurons unit unit distribution approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern point point point image image image image image image image image single single single single single single single processing processing processing control large local local local local local local local local local neuron rate rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class inputs form form form form form form form shows shows shows shows shows shows shows algorithms simple gaussian gaussian gaussian visual visual visual visual visual paper paper small small small small feature feature feature feature feature fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells field features features process process process process level current cell structure problems random high similar representation architecture architecture architecture show show show section fixed fixed images images images general parameter parameter parameter parameter real real approximation theory theory theory theory theory theory term term term activity activity activity activity activity activity activity dimensional dimensional result result university university threshold threshold threshold threshold threshold threshold threshold solution solution solution defined defined defined defined dynamics dynamics constant standard standard computer computer computer computer computer computer computer terms terms distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic science science left left left left presented presented presented present phase phase phase phase phase phase phase phase phase phase activation temporal temporal temporal temporal temporal temporal temporal temporal object object object object object object object object object object object object object object range range range press press continuous abstract applied back find computational computational computational properties properties references due due due due due ieee ieee positive introduction hand hand behavior behavior stimulus stimulus effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated parallel difference assume word chosen chosen chosen part part part center theorem theorem theorem theorem firing multiple multiple multiple multiple cortex cortex cortex cortex cortex binary binary long long conditions represent equations make fact techniques techniques techniques techniques techniques region region proposed proposed proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation simulations total simulation simulation simulation simulation eq eq called times elements elements regions regions regions means natural natural feedback global global global global global global global global global global global global global global global global applications study vol vol vol vol vol vol vol vol relative represented represented represented true compared compared desired provide provide provide provide objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc proc perform active active active active active active active active experimental experimental connected connected connected connected connected connected brain brain brain equal steps steps connection connection connection connection connection connection support dependent modeling modeling report words department department implementation consists internal represents represents represents represents responses responses responses exp scheme considered framework framework framework curve solutions curves limit trajectory efficient upper upper vision vision vision vision basic basic basic give give produce produce condition condition coding randomly randomly finally processes selected nature nature inhibitory inhibitory inhibitory achieved discussion arbitrary group group group group fast corresponds corresponds complete excitatory excitatory excitatory excitatory stable stable stable short short short nearest nearest nearest nearest nearest effective effective effective effective effective effective supported supported role theoretical theoretical vlsi pixel pixel pixel pixel ability ability ability easily noisy sensory sensory auditory simulated typically underlying dynamical block block block block block block block segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism representing representing representing details max direct inhibition inhibition inhibition inhibition inhibition inhibition normalized normalized bottom bottom combined combined description denotes denotes robust takes lateral lateral lateral introduced introduced introduced period period subject sense sense subset cognitive recently engineering engineering engineering interest dimensions conventional solve studies differential achieve achieve trans trans separation grid grid grid grid grid grid grid grid grid gate gate organization organization organization organization entire entire entire grant grant amplitude amplitude lead studied extended extended locally locally locally loop clusters boundary boundary generally demonstrate demonstrate strength critical greater greater segment segment segment conclusions neighbor neighbor sigmoid sigmoid performs exponential encoding propose strong integration external external external external external cycle turn turn selective selective selective selective plane plane iii groups groups scene scene scene scene scene scene scene scene scene scene scene scene scene connectivity connectivity identification question produces perception perception ann stability simultaneously simultaneously simultaneously physical unique unique scales blocks blocks blocks blocks blocks blocks blocks cycles cycles cycles competition competition formation review stages solved lee evolution evolution evolution evolution evolution modulation activities activities activities activities activities activities activities activities processor past normalization normalization normalization normalization boundaries boundaries remains sufficiently foundation advantages david david david david david coupling coupling coupling coupling building perceptual perceptual perceptual perceptual perceptual perceptual usa usa usa inter determines activated activated activated coupled coupled coupled black black neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors neighbors gating gating gating gating major simplicity reason middle aspects aspects importance modification included spiking oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory computations tend reached receives receives composed composed excitation excitation summary summary traditional refer refer soc conf quickly quickly interested interpreted interpreted lie oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations criteria sci sci gray gray gray satisfy satisfy list relaxation relaxation play binding binding cat cat received received principles neighboring acknowledgments intrinsic receive receive receive extend stimulation stimulation stimulation exhibit exponentially rapidly rapidly rapidly rapidly oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators steady humans limitations oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator periodic periodic periodic rise successive fashion rest rest rest rest rest applicable biol biol biol analytically referred reliable tanh oscillation oscillation affect fundamental fundamental phases phases phases math trace trace man illustrate ensure singular der der der der der separated separated mapped mapped initialized simplest simplest utility grouping grouping grouping grouping arbitrarily isolated established established established ground ground ground ground analyzed analytical starts considerable rapid rapid satisfied mathematics acad circle circle beginning beginning beginning beginning beginning attribute nsf nsf addressed robustness reflects apparent greatly limits readily lack recordings exhibits exhibits rely branch branch synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony achieves singer coherent coherent display segmented segmented wang wang wang wang wang wang wang wang wang wang wang wang wang traces traces converged synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization extreme instantaneous globally picture proofs cybern cybern cybern cybern feasible forming formally formally ordering discovery outcome reaching numerically chance promising synchronous intuitively intuitive heuristics natl exploring representational edelman connect von von von von dominant dominant assembly offers diameter stimulated stimulated stimulated stimulated stimulated stimulated stimulated stimulated surprisingly reader belonging belonging extensively jump receiving adopted onr slight largely basically encodes emergent pointed pointed ease perceived superimposed malsburg malsburg malsburg malsburg malsburg simulating suppressed reflected community segregation segregation segregation segregation segregation biophysical graphics maintained elementary distant distant activate emphasize cole synchronized synchronized iri covered covered locking pop cubic cubic cubic investigations intensive ignoring inactive triggered interior distortions institut continued evolved cornput cornput suffices suppress inherently proposal gram ooo symmetrical cooperation cooperation planck falling remained segmenting shortly shortly shortly shortly scattered syst physica actively silent silent linking instant preventing yon orbit columnar excluded plausibility ohio ohio ohio ohio ohio ohio ohio oil intersect intersect dominate schneider schneider synchronize synchronize tiny dissimilar eckhorn eckhorn positively ell oooo feeds inhibits inhibits opens descriptive engel renders triggers cis asserts shapiro shapiro shapiro snapshot snapshot snapshot snapshot snapshot snapshot chemistry spreads fragments somers somers alternates exemplified party frg llll llll llll llll llll llll jumping jumping jumping cocktail kopell kopell coo coo leo columbus columbus permanently spends unsolved lll lll closes desynchronization desynchronization 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#@Terman_D,Wang_D,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input input input input input input input input input input input data data function function function function function function function function function function function function function function function function function function function function figure figure figure figure time time time time set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output system system system system error error error error error error error error error error error error error error error error error error results results results results results results results results results results problem problem models performance based based based space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector vector order order order order order shown shown shown shown shown systems systems systems values values values values values values noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight distribution distribution distribution distribution method method method method method method method method method method method method approach approach approach large large large large large large large test test test test test analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form shows shows simple simple simple simple gaussian gaussian examples examples examples examples examples small small small small small size size size size size size size size size size size size size size methods step random random random response response response response response response response response response response response response response response similar similar show show show show show equation equation equation section section section section section section section section rule vectors vectors vectors general general general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter real real real real real approximation approximation approximation average average average average average average average average average average average average average average average average average average average average average average average average average average average average average average average gradient gradient obtained obtained obtained obtained obtained obtained obtained obtained obtained term term term term term note note dimensional result result result result result result result result result result result result result result result result university variables variables solution research independent independent defined defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial constant standard computer terms terms terms terms terms terms presented present present present phase sets range basis outputs outputs outputs outputs outputs continuous abstract find properties properties references positive procedure important introduction complex statistical effect generated variance variance variance tion energy assume assume assume prior prior chosen previous bound cases good good long long distributed distributed bayesian expected equations equations make fact fact fact fact correlation correlation correlation correlation correlation finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite simulations resulting total performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq called times mapping means means means means obtain obtain obtain obtain obtain negative negative relative specific true compared application series series series series location determined determined distributions distributions power larger contrast support descent descent dependent department represents exp exp exp exp exp exp ai considered considered directly curves curves limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit limit effects effects effects effects effects effects determine determine full statistics free world world world world basic pages give give con condition condition condition derived derived randomly randomly finally finally finally evidence iteration depends simply achieved discussion discussion discussion denote denote inverse finding assumed assumed assumed assumed theoretical main makes makes noisy pairs smaller smaller reduced functional functional unknown interesting york york consistent consistent leads squared details normalized decay decay decay decay decay decay decay decay attention attention added predict perceptron perceptron perceptron perceptron perceptron perceptron denotes discussed discussed discussed exact exact exact exact apply identical quadratic quadratic quadratic inference relevant relevant relevant relevant previously teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher approximately calculated calculated calculated calculated yields yields differential differential differential differential rl rl symmetric modified observation bounded exists expression deviation correctly setting starting starting critical critical greater editors peak peak exponential exponential asymptotic asymptotic taking presence physics physics largest drawn drawn drawn labeled labeled plane areas explicit relation relation relation relation van derive solving plot plot transitions student student student student student student student student explicitly explicitly explicitly explicitly explicitly averaging averaging averaging averaging averaging averaging infinite infinite spectral spectral spectral spectral adding springer springer implies john john letters independently expressed expressed dependence dependence dependence correlated solved solved forms sizes sizes sizes constants spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum key partial partial partial additive expansion expansion expansion expansion expansion expansion expansion expansion expansion normalization combining fitting add add penalty valid valid valid valid valid valid calculate calculate calculate calculate avoid perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons eigenvalues eigenvalues extension discuss discuss discuss discuss priors priors phys phys phys phys phys determining determining straightforward straightforward suitable identity identity characteristic summary summary refer strongly contained interpreted interpreted issue lie quantity write write write eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue extend simpler remain wiley transformed investigate investigate relations detail replaced replaced accurately behaviour examine analytically root root analogous smallest coefficient trace predicts quantities perceptton perceptton multivariate simplest simplest submitted spin variances fairly fairly fairly correction correction correction correction correction correction starts turns leaves commonly cut ion calculations calculations calculations implicit definite read lowest arises fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations fluctuations argument limits limits limits readily readily peter peter peter peter peter peaks peaks peaks orders schematic calculating calculating calculating calculating berlin branch gen hyperparameters extensions extensions extensions extensions prevent conclude conclude implements begins lim pole corrupted sv investigation nonzero systematic numerically height replica hope occurring obtaining exploit krogh krogh krogh krogh krogh krogh krogh krogh preparation generalizes hertz hertz hertz hertz hertz hertz hertz weakly contexts recovered sides sides percepttons reader arrows eqs exploiting learnable unchanged multiply ure saad schulten truncated validity isotropic isotropic expanding obtains obtains opper opper opper opper edinburgh edinburgh arising penalized distri community thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic gener relating singularities singularities singularities sollich sollich sollich sollich sollich likewise algebra parametrized rewrite corrections corrections corrections corrections corrections corrections corrections corrections corrections bution remark const agrees hundreds solvable barber barber barber powers eral recursion recursion recursion recursion recursion neglect contributes scenarios scenarios scenarios pin pin derives tens generaliza huge modest insert percep clutter collecting heights broader fluctuation fluctuation inserting inserting teachers men alization deduce anisotropic anisotropic anisotropic anisotropic anisotropic proving widespread aver domany sume sume sume admits identities identities slowing focussed ofp cumbersome heaviside sumption sumption ditions acquires kinzel kinzel squaring marion amin amin amin slowed quoted trm trm trm thorbergsson confine physicists iog vanishingly vanishingly scalars trons broadening broadening broadening europhysics ymptotic ymptotic hem ale 
#@Sollich_P,
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#*network learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural data figure figure time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training number number number number number number number number number system error error error error state results results results results results results information problem problem problem hidden based space space space space space space space space linear linear linear linear layer layer case case case case case case case case case case case vector vector order order shown shown values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters functions functions functions functions functions functions neurons distribution distribution distribution distribution recognition method pattern point point point large neuron neuron neuron neuron neuron analysis class class class form shows simple paper paper paper paper paper paper paper examples examples size size size size fig fig fig fig fig fig fig level current current trained random random random random high high similar similar similar architecture show show section section fixed general general general general real average average average average average theory theory theory theory theory note note note note result threshold threshold threshold threshold threshold threshold computation computation research research research independent independent log log defined defined defined target target target target target target target target target constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate direction direction phase low low machine sets sets sets sets press basis continuous continuous continuous sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract abstract abstract abstract abstract abstract abstract find find computational computational computational density density density properties properties references references ieee positive introduction complex estimation estimation statistical statistical statistical generated difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume assume assume assume lower lower lower lower measure measure measure measure measure measure chosen higher previous theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound cases cases cases binary distributed region region region region observed finite finite finite ing ing called called called elements dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made applications obtain obtain obtain obtain samples samples samples samples samples samples samples samples compared application application desired desired series provide provide define define rates proc proc determined determined determined distributions distributions distributions distributions distributions discrete power approaches accuracy accuracy selection report words ai ai cambridge curve curve curve additional view curves estimates estimates estimates estimates estimates estimates estimates estimates transition transition stage stage stage stage capacity capacity capacity determine upper upper upper upper upper upper significant significant world basic pages give con produce condition condition derived randomly bounds bounds bounds bounds bounds bounds bounds bounds bounds lines backpropagation backpropagation depends depends achieved discussion technical feedforward feedforward feedforward feedforward feedforward increases group denote transformation close assumption assumption assumption assumption corresponds predictions proof proof proof proof proof proof short theoretical main main main journal journal hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance easily probabilistic needed fully technology significantly increasing special special consistent consistent consistent uniform uniform uniform empirical max max max predict improved advantage property takes takes element interest dimensions approximately volume yields rl trans improvement improvement exists concept concept concept concept concept concept scaling width occurs minimal minimal conclusions peak strong hard physics sigmoidal proportional radial exist min min min introduce introduce introduce manner denoted pro derive transitions confidence confidence recall implement multilayer multilayer linearly infinite infinite infinite transformations applying predictive springer implies letters family family family stages viewed interpretation lemma lemma restricted showed showed sizes digits constants classical reduces boundaries sufficiently sufficiently expect expect includes vapnik vapnik vapnik vapnik vapnik discuss discuss discuss discuss discuss uniformly maximal maximal modification projections projections projections plots road verlag strongly cun allowing heuristic showing issue hold comp comp notation notation notation realistic providing hypotheses hypotheses hypotheses leading reach attempt mass ml ml ml fashion links possibility proved cover cover fundamental concepts concepts concepts concepts necessarily integer integer generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation predicts predicts perfect perfect perfect perfect quantities versions bifurcation bifurcation bifurcation obvious obvious perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton explain crucial agreement improves analytic analytic analytic analytic capabilities reasons satisfied satisfied formalism formalism formalism formalism formalism formalism mation laboratories potentially acknowledgement universal universal annual meaning mechanics argument empirically haussler haussler polynomials measuring proposition ordinary proofs sort restriction martin acm promising occurring transforms tishby imply imply combinatorial combinatorial eqn eqn eqn date infor separating corollary corollary corollary corollary corollary appendix appendix appendix equals equals negligible regard regard uni warmuth kearns kearns belonging belonging agree impact seung implicitly intersection dividing divide geometrical outline rigorous equivalently chervonenkis chervonenkis chervonenkis sontag formulate forced restrictions theorems possibilities imagine australia australia australia valiant tight options shaded iff levin learnability oct relate noting rough sketch worth weaker anal discusses preserve drops dichotomies resembles gratefully laws achievable recogni tial crude crude crude virtually hoc inequalities cornput tuple anthony attained cardinality substitution substitution shattered shattered falling binomial ready elec thresh kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk linking terminology repeating predefined tighter tighter sition blumer lowered tran dependences uniformity uniformity uniformity uniformity uniformity constructions versity implementable clarify syrup ordinate poten icnn abscissa permission rni rni attack sakurai intend ehrenfeucht ehrenfeucht 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#@Ferra_H,Kowalczyk_A,
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function set set set set networks networks training training training training training training training training training training training training algorithm output output output output output output number error error error error error error error error results results results information information information information problem problem models models models models models space space space space space weights linear linear linear linear case case case case vector vector vector order order order order order shown systems systems systems systems values values values probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise weight weight weight weight weight weight weight weight weight weight weight weight functions distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition method approach approach approach pattern pattern pattern pattern image image single processing processing processing processing processing large large large large patterns class matrix optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form form form form form shows simple simple simple paper paper paper examples examples examples examples examples examples small small small small work methods random random similar similar show show equation section section line vectors general general general parameter parameter parameter parameter parameter parameter approximation approximation average average average gradient term term term term term term term term term term term term term term term term term term term term term note note note result computation target dynamics dynamics constant constant constant estimate standard computer terms terms terms science science left direction presented nodes nodes machine machine machine components components outputs outputs abstract back find density density density density density density density density density references positive procedure adaptive propagation action generated variance variance variance variance variance variance variance variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost tion tion change difference difference difference assume assume assume learned higher higher part part part previous theorem conditions conditions distributed distributed expected fact proposed correlation correlation correlation correlation correlation correlation correlation minimum minimum minimum minimum minimum regression regression regression regression respect sum elements elements elements elements elements elements regions global global applications knowledge obtain original original original original original original original original vol vol compared desired desired desired desired desired series provide related constraints distributions distributions distributions distributions distributions equal equal equal power approaches approaches approaches approaches approaches connection support morgan morgan morgan institute institute department technique advances advances advances addition ai considered equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent additional effects effects full choice pages pages pages pages increase con con condition condition condition derived finally finally finally selected simply achieved discussion covariance describe arbitrary group group group group group group group group group group group group group group denote denote transformation transformation transformation transformation transformation transformation transformation transformation limited close corresponds effective assumed assumed supported square square square easily makes fit kaufmann kaufmann kaufmann technology interesting character special special squared squared squared magnitude magnitude minimize added added denotes recent correlations correlations ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble apply apply introduced introduced include include machines quadratic sense subset subset engineering approximately yields correspond achieve trans trans trans diagonal modified generalized bounded grant grant grant exists parts expression invariant invariant invariant invariant invariant invariant invariant scaling scaling matrices rotation rotation alternative alternative occurs occurs occurs strength strength assumptions assumptions editors editors tangent tangent tangent tangent measures measures measures moody encoding hard mechanisms integration presence physics physics proportional regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization minimizing minimizing minimizing minimizing minimizing minimizing plane decrease averaged targets targets targets targets targets targets targets introduce introduce derivatives groups groups denoted suppose suppose digit van derive construct longer longer ways vertical implement infinite transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations adding adding adding adding adding adding adding adding adding adding adding adding adding applying springer formed formed john john expressed correlated correlated squares squares evaluated operations operations restricted showed forms completely smoothing smoothing smoothing expansion reduces reduces reduces reduces fitting fitting neighborhood add penalty degrees handwritten includes extension holds holds discussions simplicity straightforward delta invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance identity identity identity summary verlag repeated procedures cun cun showing lie lie lie lie satisfy notation quantity vary giles giles giles correspondence denker denker satisfies satisfies acknowledgments cowan origin remain remain carried american transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed exhibit detail hanson hanson hessian hessian hessian lippmann helpful helpful func statistically coefficient gradients editor der obvious assumes assumes freedom precise arbitrarily arbitrarily isolated trivial publishers derivation analytic analytic analytic stress inside sections satisfied satisfied satisfied satisfied formalism precisely precisely incorporate bishop bishop bishop bishop leaves leaves simard simard simard simard simard implicit lowest geometry raw mechanics geometric prop prop prop prop parameterized effort howard exhibits datasets gave gave richard comments unbiased unbiased unbiased unbiased unbiased unbiased summed hints hints distortion distortion distortion distortion distortion distortion distortion distortion sharing sharing uncorrelated indices leen leen leen leen leen equivalence equivalence equivalence equivalence equivalence equivalence equivalence arguments approximates rotations rotations lecun dealing satisfying satisfying satisfying satisfying obtaining shifts imply hint hint hint hint hint intuitively intuitively intuitively optimally intuitive intuitive intuitive intuitive intuitive intuitive enhanced enhanced enhanced enhanced enhanced enhanced enhanced enhanced carry substituting substituting substituting introduces governed equals regard regard enhance jackel suggesting rich passing alternatively onr unchanged unchanged multiplying abu abu linked maintaining maintaining leaving mostafa mostafa expanding expanding pointed boser ideally eric param remainder alter henderson invariances invariances invariances invariances invariances invariances modifying modifying impose graduate life hubbard regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer afosr regularized relates translations translations translations translations breaks grateful vanishes vanishes vanishes vanishes eters simplifies oregon oregon develops chris bridge bridge stimulating ble distortions distortions distortions distortions invertible todd todd todd todd todd steven continuum sharply subtracting peaked restricting vanish vanish orr distorted distorted spirit brackets brackets steve carrying neglected fixing unrestricted penalizes penalizes penalizes penalizes penalizes penalizes dence regularizers regularizers regularizers retaining wan cient ogi enhancing enhancing enhancing walker infinitesimal infinitesimal infinitesimal infinitesimal yann wired ponent cse indistinguishable indistinguishable insure maxwell expects embodied equiv nonsingular trivially tlx tlx tlx tlx tlx tlx tlx tlx tlx tlx tlx patrice patrice victorri ditional ditional preceded linearization reg ficient pth tikhonov tikhonov detrimental dictates dirac spherically beaverton bernard nction trm correspon coe athe genevieve griffin intimately fdx rehfuss coef ned weaver father dxp reviewers algebras summa enumerated liere greek 
#@Leen_T,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data data data data function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training output output output output output output output number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state results results results results results results results units information information information information problem problem problem problem hidden performance performance performance based based space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear layer case case case shown shown shown shown shown shown shown shown shown shown shown shown shown systems values weight weight weight functions functions functions distribution distribution distribution distribution distribution method method method method method approach pattern pattern pattern point image single single processing processing large large large large test test test test test test test patterns analysis matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs form form shows shows shows shows shows shows shows simple simple simple simple simple paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size size size size size size size size size net task methods points points points classification classification classification classification trained trained trained trained trained trained problems problems problems random random random random random high similar show show show show equation equation equation equation equation equation line line line line line line line line line line line generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech real real approximation average average average average average average average average average average average average average theory theory gradient term term term term term term note note experiments experiments experiments experiments university variables computation solution independent independent defined defined found found target target target initial estimate estimate estimate estimate estimate estimate estimate estimate prediction left low low low low machine sets sets sets sets sets sets sets sets sets sets learn learn basis outputs outputs continuous continuous sample abstract back find find find find computational references ieee positive important important propagation mixture mixture context introduction hand hand generated generated generated variance variance variance variance variance variance variance tion tion tion tion tion variable assume lower lower learned chosen higher bound type type required required good good good good good make make techniques correlation correlation correlation errors errors errors errors errors errors errors errors errors errors errors errors forward minimum regression regression sum sum sum sum called called called times means optimization optimization optimization optimization made applications knowledge obtain obtain obtain negative true cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross define active active active active active active active active active active active active active active active active active active experimental constraints constraints equal equal equal accuracy accuracy larger larger train descent morgan morgan proceedings institute consists individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual advances final final final bias bias bias bias bias delay scheme scheme scheme experiment experiment curve curve curve curve curve curves curves estimates estimates estimates estimates estimates san san top conference efficient full choice approximate approximate estimated estimated estimated estimated estimated estimated estimated estimated basic pages increase increase increase validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation give give weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted randomly developed developed area types types provided finally finally selected depends depends constraint simply technical increases tested close predictions finding common assumed assumed square square square square instance instance including kaufmann kaufmann smaller smaller needed combination combination combination combination combination unknown programming interesting testing testing testing significantly significantly significantly increasing increasing uniform uniform uniform uniform squared bottom idea idea attention combined minimize choose added added improved improved discussed discussed discussed improve improve improve correlations advantage ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble strategy include subject identical identical identical quadratic quadratic calculated volume works tions smooth yields yields interval improvement entire expression suggests derivative feed setting runs runs half conclusion starting minimal valued valued valued central measures mateo mateo suggest propose strong largest largest drawn california solid solid solid solid solid solid intelligence regularization labeled turn decrease averaged denoted denoted areas relation pro derive plot plot label implement easy easy text belief adding minimization select independently depending correlated squares overlap overlap learner variation restricted showed approximated completely calculation dashed dashed dashed dashed neighborhood query query query query query query transactions david expect building illustrated holds discussions discussions tests tests letter maximal committee committee committee committee committee plots essentially essentially refer notice notice kind kind strongly strongly follow hold bar michael michael dot generalize generalize nips wave wave wave correspondence poor detail estimators optimized limitations dotted dotted dotted hall fashion ideas rest investigated authors authors reliable reliable root complicated workshop workshop measurement editor necessarily perfect obvious obvious noted extent averages averages averages great trivial crucial agreement improves analytical majority expensive turns easier desirable desirable immediately members members members members members members lowest lowest author addressed addressed fluctuations applies experimentally peter dots dots calculating gen geman gave enables chose comments converged yielding yielding lot lot lot benefit cooper fix fix member member iiii held biased tishby unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled imply krogh krogh krogh krogh krogh krogh passive passive passive passive passive sompolinsky ensures ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity predictors predictors corre approximators approximators israel ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles insight agree wolpert wolpert seung seung valuable papers drop numerous email session conjecture conjecture conjecture opper tradeoff tradeoff individuals individuals individuals freund constrain exam community insights gained gained chapman oct individually relates weaker million hansen hansen setup electronics supports preprint algebra holding holding vice circumstances rewritten topologies meir versa scanned bienenstock acquire consuming lation converging imple december subtracting equa ples separates contributes capital tells denmark denmark denmark scatter pin jan stacked devoted indi indi actively generaliza formulas technion ambiguities expresses contributing predic dilemma putting dealt mentation rigorously eralization disagree disagree disagree disagree disagreement disagreement disagreement disagreement unclear dash overfit idealized aver aver calling pertone copenhagen estima quantifies gramming quantifying assump leon borrowed aging committees doursat kai blegdamsvej vedelsby vedelsby vedelsby 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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output number number number number number number number number number number number number number number number number number system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state results results results results results results units units units units units units units units information information information information information information information problem hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space space space weights weights weights linear layer layer vector vector order shown shown systems systems values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise functions functions distribution method method method method method method method pattern pattern single processing processing processing large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test test test test test test test test test test test test test test test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis class class class class class class class class optimal optimal form shows shows shows shows simple paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size size size size size size work task task task task task task task task task task task task task task task task task points classification classification classification classification classification classification level level level level level level trained trained trained trained random random high high high high high high high high high high high high high high high similar section section fixed fixed fixed fixed fixed line vectors vectors vectors vectors vectors vectors general generalization generalization generalization generalization parameter obtained obtained obtained obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments experiments experiments result result result result result university university threshold threshold research independent independent defined defined estimate estimate estimate distance prediction prediction prediction prediction phase low low low low low low machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets sets sets sets sets learn continuous abstract applied applied applied applied applied applied applied back convergence properties references due due ieee introduction action complex complex hand hand hand behavior behavior behavior statistical statistical statistical statistical statistical statistical tion difference difference difference difference complexity complexity complexity complexity complexity complexity classifier classifier classifier classifier classifier classifier classifier measure signals higher higher part type long long long make proposed proposed length correct errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors minimum minimum ing ing regression performed performed called mapping mapping mapping means means dimension made made made made applications applications study study knowledge em negative true true true compared application series series provide proc experimental experimental connected accuracy accuracy accuracy accuracy larger contrast train train nets modeling selection morgan morgan report implementation technique technique technique internal code individual advances advances experiment curves curves estimates design limit limit top top bit bit bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity classifiers classifiers classifiers classifiers classifiers classifiers full choice choice choice free free free free free free free estimated estimated estimated estimated estimated basic pages pages increase increase increase increase increase produce channel channel channel channel randomly criterion path path path path path path path path path path path path path path provided depends depends achieved achieved achieved measured measured measured technical feedforward increases increases increases increases group limited close complete complete predictions predictions amount amount amount amount amount short short implemented supported theoretical end end end end ability ability ability instance future future easily fit typically typically smaller underlying needed unknown fully character character york increasing increasing increasing increasing increasing increasing increasing increasing increasing increasing database database database database database database database database database database principle principle details call window stored stored bits bits bits bits bottom bottom frame frame frame frame attention produced run sources description predict recent resolution takes typical typical typical typical typical reported reported strategy include include include period period identical machines machines machines machines machines machines machines machines machines machines varying compare previously volume volume volume smooth match match correspond studies achieve modified channels channels interval improvement increased increased constructed lead correctly white occurs generally setting demonstrate conclusion critical minimal greater depend differences measures measures measures measures measures measures measures measures measures measures measures measures measures accurate accurate designed designed performs practice asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic constrained propose propose largest largest characteristics drawn demonstrated demonstrated labeled labeled labeled groups base appears construct produces longer longer optical ways primary estimating estimating estimating label label implement implement missing multilayer averaging averaging infinite infinite physical physical physical physical dimensionality involves involves slightly text adding quality quality quality quality quality quality quality quality quality quality quality implies john decreases decreases decreases decreases decreases extracted extracted extracted extracted extracted extracted extracted review review communication communication labels labels labels fraction completely completely reasonable measurements purpose false initially filtering sufficiently kohonen advantages includes thesis perceptrons bell vapnik vapnik plotted plotted illustrated illustrated discuss discuss discuss discussions extra capable capable capable divided paths paths paths paths paths plots plots fine reached characteristic characteristic characteristic capture notice notice conf induced criteria device vary quantization denker highest leading reach thresholds thresholds automatically received illustrates acknowledgments intrinsic intrinsic intrinsic intrinsic intrinsic poor overfitting collection collection collection collection requirements requirements exhibit difficulty difficulty varied varied humans replaced optimized dotted helpful rise rise rise fewer matches matches history history history links links links investigated int authors authors reliable proved statistically examined concepts necessarily traffic predicting predicting ensure ensure adjusted baseline amari arbitrarily arbitrarily phd seconds seconds seconds seconds seconds seconds seconds mentioned mentioned asymptotically asymptotically asymptotically indicating agreement failure failure failure tool starts starts implementing implementing day constructing constructing choices laboratories cut universal universal universal calculations members members begin mechanics robustness limits limits limits limits limits collected solla continuously continuously maintain maintain summarized summarized characterize limiting limiting limiting limiting limiting limiting limiting limiting limiting limiting reaches reaches reaches suited adjust kinds fiber windows implements eventually eventually eventually traces yielding synchronization picture corrupted redundant labeling formally lvq lvq lvq lvq resources member databases databases count impossible reaching eliminated kaufman kaufman minutes minutes city city imposed imposed imposed imposed imposed imposed imposed los resulted resulted resulted tishby receiver degradation days days days days days hours continue service service service sompolinsky mance mance periods irregular entry entry codebook codebook codebook codebook codebook paul perfor perfor jackel jackel jackel jackel jackel jackel approximators recog record matter belonging seung harris alternatively material automated thresholding acknowledge approx transmitted transmitted formulate revealed revealed nition conjecture conjecture conjecture medium medium medium opper big constitutes examining eric scenario care trends exam ijcnn continues switched exceed exceed exceed hornik monitoring misclassified apparently book minor rochester exhibited exploited failures gratefully expense regularities survey excess cable cable marks quantify ping ping ping ping ping insufficient termination loosely transmitter holmdel holmdel ters ples bss contributes carries carries corrective explanations daily reproduced prone dent dent indepen indepen mis media tained catastrophic brought monitored cortes cortes cortes cortes cortes cortes cortes drucker murata imposes expresses expresses histories histories histories months wan wan wan wan minute minute ample parame angeles subsampled unlimited unlimited chi engineers clipped ronald preset walter inadequate overfit constantly mined trouble trouble trouble trouble trouble trouble trouble trouble trouble trouble trouble trouble trouble trouble perf mon amples equipment chiang chiang chiang chiang yoshizawa cybenko sketched accompanied checking transport lengthy cornell manifested logs increas guessing guessing kinzel benchmarking memorize vladimir sara inaccuracies commit surveillance telecommunication telecommunication telecommunication declines declines domestic iog iog decline decline complicate irregularities committed hinder corinna corinna corinna corinna corinna corinna entirety jective imate historically underfitting eeo logged inadequacy upcoming 
#@Chiang_W,Cortes_C,Jackel_L,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input data data function function function function figure figure figure figure figure set networks training training training training training training output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number system results results results results results units units units units information information information information information information information information information information information information information information information information information information information information information information problem problem hidden based based space space space space space space space space space space space space space space weights linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case case case case case case case vector vector vector order order order order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown values probability probability probability probability probability probability parameters parameters parameters noise functions functions neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method processing neuron test analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix inputs inputs inputs form shows shows signal signal gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper paper feature work fig fig fig fig fig fig fig features features process structure structure structure structure random similar similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation section section section rule rule rule rule vectors general general general general general general generalization generalization generalization theory theory theory theory theory theory gradient obtained obtained note experiments experiments experiments dimensional dimensional dimensional result variables variables computation computation research independent independent independent independent defined defined defined defined defined defined constant constant terms connections connections connections synaptic presented presented map map map present low components components components components components components components components components components components components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs abstract find find find find references component component component component stochastic due due due due due due important important important important introduction statistical statistical statistical statistical statistical statistical generated cost cost cost cost cost cost cost cost cost cost tion tion tion assume lower rules rules signals signals higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher previous cases conditions conditions represent distributed fact fact fact fact fact fact proposed proposed proposed proposed correlation correlation correlation correlation correlation correlation correlation correlation forward simulations minimum minimum resulting sum performed performed performed performed performed performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq called called elements elements elements elements elements means means means means means means dimension dimension obtain obtain original original application define define define define define perform goal goal goal related distributions distributions distributions distributions distributions distributions brain equal equal equal equal equal equal equal update descent loss loss loss loss loss loss loss loss loss implementation technique consists joint represents bias considered equivalent equivalent experiment experiment curve curve curve curves effects upper basic basic basic con con con condition derived conditional developed developed entropy entropy entropy entropy entropy entropy entropy entropy processes achieved covariance covariance describe arbitrary denote transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation inverse generate role role theoretical main easily development noisy noisy noisy sensory reduced reduced account account coefficients interesting york principle leads principal principal principal iterations iterations direct supervised early polynomial polynomial polynomial polynomial polynomial idea idea minimize minimize minimize choose denotes denotes architectures architectures architectures lateral strategy sense sense recently recently relevant unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised calculated volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume works tions tions pca pca achieve achieve achieve rl diagonal diagonal definition background generalized generalized expression expression derivative feed conclusion conclusions central sigmoid performs performs performs performs performs performs performs performs propose strong reduction reduction reduction reduction assuming minimizing minimizing derivatives pro derive construct written ways plot describes implement multilayer multilayer multilayer simultaneously linearly linearly dimensionality dimensionality involves involves easy mutual mutual mutual mutual minimization minimization minimization minimization minimization yield extracted extracted independently independently expressed expressed expressed dependence correlated transform transform evolution forms expansion expansion expansion expansion expansion expansion expansion sec reduces reduces reduces calculate symbol coordinate coordinate holds major simplicity straightforward straightforward compression extra closely delta build kind contained interpreted follow bar involved paradigm paradigm paradigm paradigm extract satisfies satisfies satisfies satisfies xor put put fourier fourier fourier successive fashion fashion ideas func statistically statistically statistically statistically statistically statistically statistically statistically cognition cognition hill transmission concepts necessarily necessarily analyze automata automata automata equally perfect aspect aspect versions logistic logistic nervous ith mixed theoretic theoretic variances analytical independence independence independence independence independence perspective satisfied satisfied satisfied formalism ring preprocessing mation mation mation beginning summation summation fourth fourth fourth fourth orders orders orders orders orders orders posed remove formulated polynomials anti aim aim extracting extensions asymmetric asymmetric asymmetric asymmetric germany germany logical redundancy redundancy redundancy redundancy redundancy redundancy multidimensional yielding yielding yielding yielding don ear ear ear ear tensor tensor tensor tensor unity impossible theories cellular cellular cellular cellular rational rational siemens automaton generalizes moments infor introduces sion corre corre guarantees eqs eqs eqs lem compressed leaming transmitted formulate formulate demon decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation jacobian jacobian jacobian jacobian factorial factorial equality equality impose manifolds manifolds manifolds manifolds inverted expand concentrate cij cij tively barlow barlow barlow barlow barlow barlow rewrite mini expansions expansions handled remark remarkable factorized lation institut transforming lated lated reversible reversible reversible reversible reversible mining determinant determinant determinant eliminates condi ning equa atick atick proposes triangular triangular informatik edition mcgraw facts nice asymmetry expresses technische transferred sat graphically putting dependences redlich redlich redlich redlich redlich redlich redlich redlich redlich rigorously fac respec munich munich deco deco deco deco deco serving conserving conserving conserving conserving conserving conserving conserving conserving conserving conserving conserving conserving conserving conserving conserving pal cumulant cumulant cumulant cumulant cumulant cumulant cumulant cumulant cumulant cumulant karhunen ons nonlin nonlin nonlin nonlin transfor transfor transfor conserved strated duced otto factoffal factoffal factoffal factoffal factoffal factoffal factoffal vised cot ijk decorrelated decorrelated decorrelated decorrelated decorrelated decorrelated decorrelated cumulants cumulants zation probabilistically assure intro pol hahn conservation conservation finished polyno eft assures marion papoulis papoulis papoulis mized decorrelate decorrelate decorrelate mathe assured matically conserve exten inpu concen princi excludes rive diagonalization summand summand summand trate ise sequently volves uct matfix ctive unsuper minimiza mands 
#@Brauer_W,Deco_G,
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#*learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural input input input input input input input data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set networks networks training training training training training training training training training training training algorithm algorithm output output output output output output output output output output number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results information problem problem performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space space space space weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case case case case case case case case case case vector vector vector vector order order order shown shown shown systems values values values probability probability probability probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method point point point point point point processing large large large large large large large large large local test analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows shows shows shows shows shows gaussian gaussian paper examples examples examples examples examples examples examples examples examples examples examples examples small small feature methods methods points points field level level level level level level trained trained trained random similar similar section section section fixed rule rule rule rule rule rule rule rule rule rule vectors general parameter parameter real real real approximation average average average average average average theory obtained note note note note dimensional dimensional university research defined constant estimate estimate estimate prediction sets sets sets maximum maximum learn components nonlinear outputs outputs outputs abstract find likelihood likelihood references component component component stochastic due due due due procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important context introduction action statistical statistical statistical statistical statistical effect effect generated generated variance variance variance variance variance variance variance variance variance cost energy difference difference complexity assume assume rules rules rules rules rules measure measure measure measure measure measure measure measure measure measure measure measure prior prior prior prior chosen part conditions bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian make fact finite finite minimum minimum resulting respect respect respect respect sum sum times mapping factor made study obtain artificial relative relative true compared application define define define define perform determined posterior comparison larger contrast dependent morgan words department advances exp scheme scheme addition addition graph graph graph graph maps framework equivalent curve curves curves curves curves limit limit limit san effects determine free estimated give entropy finally finally finally finally evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence sampling sampling sampling constraint simply simply discussion normal increases increases increases denote tested tested limited close assumption predictions effective effective effective effective effective effective supported theoretical eds ability ability hypothesis hypothesis hypothesis instance easily objective probabilistic underlying underlying reduced account increasing leads leads squared squared details supervised supervised magnitude magnitude decay produced produced produced predict perceptron perceptron perceptron perceptron perceptron perceptron denotes improve improve typical practical practical introduced include hierarchical sense inference inference relevant teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher calculated calculated definition evaluation increased increased expression expression expression occur deviation deterministic setting setting conclusion greater assumptions assumptions measures measures measures measures measures measures measures measures measures measures measures measures accurate bayes bayes clear practice asymptotic asymptotic asymptotic learns mateo suggest taking integration presence physics physics reduction drawn plane decrease iii iii iii iii iii iii averaged introduce question generating generating plot confidence pruning student student student student student student student student student student student student student student student student student student student student student explicitly adding adding adding versus independently independently review earlier reasonable calculation calculation calculation reduces fitting fitting interpolation calculate calculate david david david david david priori assignment determines plotted plotted plotted discuss specifically specifically absolute phys phys phys phys discussions major simplicity identified successful literature post post post post post post post mackay mackay mackay mackay mackay mackay refer graphs repeated strongly interested interested dis lie comp comp quantity write usual usual paradigm acknowledgments extend cowan situations bars explore essential steady rise examine examine examine examine analogous examined math math math possibly necessarily generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation predicting rev noted extent extent simplest regime regime regime attempts averages asymptotically percentage percentage percentage percentage preference preference agreement nonlinearity starts starts formalism formalism incorporate desirable controls controls probable opt opt opt begin mechanics mechanics questions reflects composite percent limits understood consistency consistency consistency consistency consistency consistency consistency consistency generic peter poorly backprop backprop backprop measuring gen gen gen hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters qualitatively deviations deviations displays trade corrupted corrupted corrupted indices aligned appearance linearity linearity linearity linearity recover acts acts fails fails viewpoint tishby fail krogh krogh krogh guide guide guide degradation degradation degradation hertz hertz hertz published sompolinsky mance mance surprising perfor perfor regard enable ensembles reveals matter wolpert wolpert seung seung seung mechanical mechanical learnable learnable learnable learnable learnable multiplying saad saad saad saad saad saad saad saad saad saad saad saad saad logarithm kluwer validity seek seek assignments assignments edinburgh edinburgh scenario principled mismatch mismatch distri thermodynamic termed sollich breaks grateful mimic students students bution circumstances picking const influenced firstly firstly firstly supplied tribution unreliable coincide coincide coincide coincide coincide coincide rameters decaying convention interpolate interpolate implied lnp pin fixing dence dence percep preferable whilst coincides coincides minimise teachers teachers maximising bruce bruce bruce bruce bruce bruce picks picks maximise maximise maximise hyperparameter hyperparameter razor razor standpoint minimising minimising minimising optimise optimise optimise optimise optimise optimise badly comment misleading misleading misleading misleading optimising optimising optimising attainable modulus breakdown lambda minimisation summations normalisation pursue marion marion marion marion marion marion marion steadily unsatisfactory evi evi eff eff eff rrr parameterised fixes unlearnable unlearnable unlearnable behaviours studentship kauffmann normalise advocates fective hump accommodates 
#@Marion_G,Saad_D,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data function function function function function function function function function function function function function function function function function function function function time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results results results results results units problem problem problem problem models hidden hidden performance performance performance performance performance performance performance performance based based based based space space linear linear linear layer case case case case case vector vector vector vector vector vector vector order order shown shown shown shown shown shown systems probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise weight weight weight functions functions functions neurons distribution distribution distribution method method point point point large large local local local rate analysis class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form shows shows algorithms algorithms algorithms algorithms paper paper paper examples examples examples examples examples examples examples examples examples size size size size size work work work work work step step points process process process process process process process process process process process level trained trained trained trained trained structure problems random random random random similar similar similar similar similar show equation equation equation equation section section fixed fixed fixed fixed vectors vectors vectors general general general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory gradient gradient gradient gradient gradient obtained term term term term note note note experiments dimensional result result result result result university university university solution research research independent log defined defined found sequence sequence target dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial constant constant estimate terms terms distance map map phase phase activation temporal temporal temporal temporal machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets nonlinear nonlinear nonlinear sample sample sample abstract abstract find find find find density density density properties properties properties properties likelihood references component due due positive procedure introduction hand hand estimation estimation estimation behavior statistical effect generated generated tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume assume assume assume part part previous theorem theorem cases cases required conditions conditions conditions conditions distributed expected fact techniques techniques region region length correct finite finite finite finite finite finite finite finite finite minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum ing ing regression regression computed respect sum means dimension global global global global global global global global global global applications applications applications study study obtain obtain obtain original relative specific specific true true true true define define determined determined determined goal power larger support support train descent descent descent descent dependent dependent dependent proceedings proceedings department department loss loss loss loss loss loss loss loss loss loss loss loss loss loss joint represents connectionist equivalent directly estimates stage effects capacity capacity determine determine basic give conditional types entropy entropy provided finally backpropagation iteration depends depends sampling simply simply achieved achieved measured measured covariance feedforward increases describe denote denote denote denote denote denote limited assumption amount effective effective effective effective effective effective effective effective supported theoretical theoretical require main main main main adaptation square square square square end end hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis degree development including including fit typically typically pairs smaller reduced dynamical functional functional unknown unknown unknown unknown interesting york increasing special special uniform uniform empirical empirical empirical empirical empirical empirical empirical empirical empirical language leads details iterations direct normalized frame idea denotes denotes denotes denotes denotes denotes improved recent exact property ensemble element practical practical machines machines machines machines machines machines machines machines machines side side subset engineering engineering varying studies converge differential trans diagonal interval grant exists exists exists exists lead concept studied deviation deviation wide locally occurs demonstrate conclusion starting starting critical assumptions assumptions assumptions assumptions operator depend central numerical weak suggest strong reduction reduction reduction reduction reduction reduction drawn regularization minimizing minimizing minimizing exist min min min decrease force question question denoted acknowledgements explicit suppose relation relation relation relation produces written longer factors factors generating generating describes sensitivity electrical easy unique unique unique minimization minimization springer quality expectation decreases decreases yield family focus depending depending viewed viewed interpretation open open evolution evolution decomposition forms forms completely completely suggested converges constants constants earlier additive additive additive spaces reduces reduces fitting fitting neighborhood neighborhood purpose iterative iterative penalty valid euclidean includes thesis eigenvalues determines vapnik vapnik extension extension mozer specifically candidate major major major major major major regular uniformly maximal modification situation essentially essentially orthogonal soc compact compact verlag contained link interested interested interested interpreted stopping stopping stopping stopping stopping stopping stopping stopping content content criteria notation notation quantity quantity quantity involved write write write write write write nips approximating situations situations situations presents law law minimized minimized parametric overfitting perturbation existence scalar fashion giving school rest rest analytically office referred referred affect affect affect notion smallest smallest math possibly analyze noted precise precise ith ith epoch epoch epoch epoch epoch epoch epoch epoch generates explain mentioned inequality theoretic phenomena adapted caused tool nonlinearity tive satisfied strictly precisely precisely precisely operators arise commonly consequence consequence scientific opt radius applies readily introducing adjustable continuously limiting limiting limiting weigend gen extensions replace deviations wang wang wang wang wang wang wang wang simultaneous differentiable trade optimality tation generality air difficulties tools simplify familiar interpret roles roles definitions methodology settings monotonically monotonically monotonically intuitively optimally optimally phrase generalizes generalizes selects selects heuristics exploring governed governed governed entries artifacts clean proximity extends erlbaum characterization characterization characterization stopped stopped stopped adopted fly ball approx summer slight rigorous rigorous rigorous achieving leibler equivalently opposed monotonicity regularity regularity regularity arg ideally recurrence hillsdale diag distribu ization ization relate argued increasingly indexed associates likewise truth applicability gauss rewritten laws opti remarks achievable interior attributed overtraining finer finer played played suppress venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh partly substitution judd occam occam arriving evolving suffice era goodness fication comprised enter enters monotone amer gradual incurred mization discrepancy intrinsically kolmogorov entered entered imation dependences enabled eralization philadelphia philadelphia henceforth henceforth functionals razor concluding chine nonsingular invoked deliver pennsylvania pennsylvania pennsylvania pathological zation governs overcoming fax contradiction effec implemen wit closeness answered asymp persists sequel ang pioneered modi upenn upenn refered santosh santosh santosh santosh santosh seidel idealization totically 
#@Venkatesh_S,Wang_C,
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#*network network network network network network network network network network network network network network model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input figure figure figure figure figure time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks number number number state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results information information space space weights linear case case case case vector vector vector vector vector order order shown shown shown shown shown systems systems systems values probability probability probability parameters parameters parameters parameters noise weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach point single processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis analysis analysis analysis form paper work methods field level level level level level current current current problems representation representation representation representation representation representation representation show equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation section section fixed line line parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average states states states states states theory obtained obtained obtained note note note note note note dimensional dimensional university university variables variables variables research defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics standard computer connections connections science present activation motion basis basis abstract references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic important introduction behavior difference assume assume representations higher part part previous multiple represent equations equations equations equations equations finite simulations simulations simulations simulations simulations simulations simulations resulting total total simulation simulation respect sum performed performed natural study study obtain obtain obtain obtain vol represented compared define define define rates rates rates rates active active active active equal comparison comparison morgan proceedings department advances scheme graph ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai solutions transition transition transition transition transition san conference basic con derived product product product product product product product product product limited assumption predictions finding assumed synapse supported theoretical easily including kaufmann needed dynamical fully increasing special leads leads direct direct normalized produced description description advantage takes typical apply introduced introduced introduced identical interest compare compare compare tions correspond studies studies definition improvement grant studied matrices touretzky conclusion operator depend accurate numerical moody mateo cycle solid labeled introduce introduce introduce introduce introduce denoted acknowledgements monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo produces laboratory transitions transitions dependence influence controlled fraction approximations approximations approximations evolution activities constants past dashed classical classical classical extension extension extension activated coupled phys phys phys phys neighbors simplicity wij wij wij wij schemes schemes schemes schemes comparing composed notation notation involved sampled write quantization quantization modelling extend extend cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan cowan body body employed remain essential varied relations examine office hierarchy hierarchy hierarchy hierarchy hierarchy neu math math configurations rev der explored ith ith ith ith spin indicating site site asynchronous publishers analytical diffusion briefly comparisons sys formalism formalism ring ring ring precisely operators mathematics calculations outer outer outer outer outer mechanics orders item dots differs gen analogue japan refractory refractory refractory refractory refractory labelled jth jth tem naval eliminated ranges analogy analogy moment moment moment moment moment moment moment moment moment moment moment moment moment moment moment moment moment moment definitions moments moments moments sim sim master master master master master master master master master master master master park robert ple ter fellowship sig smoothly chicago chicago chicago transparent publication iri iri particle investigations macroscopic lippman mann diagrams australian kth rons equa tokyo modern ous analyse jack jack jack jack jack stat terminate ply neurodynamics neurodynamics neurodynamics neurodynamics quiescent quiescent quiescent cummings neurology menlo previ wji physik gem quantum sakurai sakurai duced reactions jects interacts intro lai lai lai lai lai lai lai lai rio sil mas uncover lib dirac markovjan navy ria mccormick intricate lal ail ail ail nificantly netxvork benjamin sony sony isj 
#@Cowan_J,Ohira_T,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural input input input input input input input input input input input input input input input function function function function function function function function function time time time set set set set set set set set set set set set set set set set set set set set set set training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number system error error error error error results results results results information information information information information information space space space space weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability noise weight weight weight weight functions functions functions functions functions functions neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method large patterns analysis analysis class class class class class class class algorithms algorithms algorithms algorithms simple simple simple simple simple paper examples examples examples examples examples examples examples examples small size net work task step points field classification classification classification process problems random random high show show fixed fixed rule generalization real real approximation theory theory theory theory theory obtained obtained result university university university threshold variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation independent independent independent independent defined defined defined defined found sequence target target target target target target target constant table table estimate estimate standard standard computer terms distance presented map present present present activation activation activation activation activation activation activation activation activation activation low machine sets sets sets sets press press press learn learn learn learn learn components basis basis basis basis outputs sample sample sample abstract find find find find find find find computational computational computational references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due ieee positive positive positive positive positive positive decision decision introduction hand hand behavior statistical statistical statistical generated generated generated generated tion tion tion complexity variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable assume assume rules measure center theorem cases cases cases type type required good binary binary conditions represent markov markov markov markov markov markov markov make make fact fact fact fact fact fact fact techniques proposed probabilities probabilities observed observed finite classes classes classes classes regression respect performed eq called natural natural applications filter obtain vol vol vol vol vol vol vol specific represented desired compute compute compute proc goal constraints distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions mit larger larger contrast contrast nets modeling morgan proceedings institute institute loss consists represents exp addition ai ai considered considered framework framework cambridge domain domain directly design design conference efficient efficient efficient significant free world world vision estimated estimated give give criterion criterion product product provided nature simply simply biological technical arbitrary arbitrary arbitrary denote denote denote denote denote denote close complete proof proof proof proof proof supported supported main eds journal journal square pixel ability ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance instance instance noisy kaufmann probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic needed needed needed needed needed unknown unknown unknown testing projection special trials empirical empirical principle call call call making making polynomial polynomial polynomial combined combined perceptron perceptron perceptron denotes denotes denotes recent exact advantage property property property property robust reported include pixels subset recently recently recently sufficient sufficient sufficient works studies studies trans definition definition definition definition definition chain chain chain chain bounded grant exists concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept studied studied extended extended deterministic deterministic deterministic deterministic setting setting setting setting minimal minimal minimal neighbor central sigmoid practice practice learns learns learns hard hard physics physics physics physics largest largest radial radial radial turn introduce denoted pro written estimating estimating confidence confidence confidence confidence confidence confidence recall remaining consisting formed boolean boolean family family family family family family family family family family correlated learner learner learner learner learner learner learner learner influence influence lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma solved variation restricted expansion neighborhood neighborhood neighborhood purpose purpose classified classified classified expect perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons formulation assignment assignment assignment sciences extension prove prove holds discussions straightforward presentation presentation efficiently prob prob prob prob interpreted dis return return contribution hold usual usual attempt satisfies neighboring neighboring acknowledgments deal decreasing situations american access replaced association dual affect affect func func statistically statistically statistically notion notion induction naturally concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts reading reading analyze changed ensure subsets expressions perceptton perceptton perceptton generates simplest motivated attempts established years devices inequality inequality inequality trivial analyzed lin lin precisely precisely located members lowest summation behaviors parameterized effort haussler remove monotonic monotonic monotonic monotonic monotonic proven extensions enables sums sums comments returns cor pac pac pac pac pac pac pac pac proofs writing oxford restriction restriction restriction restriction restrict acm acm member member ordering discover discover discover discover nonzero establish generality keeping serves observing observing observing observing observing definitions disjoint affected affected intuitive carry schapire schapire schapire schapire schapire schapire schapire ensures sphere originally tic kearns kearns kearns kearns canada canada ignore avoiding vari learnable speaking verify rigorous break reaction adopt adopt perturbed generalizations superimposed discovering valiant valiant valiant valiant argue argue iff iff iff exam blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking proba learnability learnability learnability sketch sketch sketch sketch harder superposition expansions expansions rarely bility shawe solvable err err err err err err err err err err err err inequalities loosely hancock kth kth connects wiring returned returned returned neglect ples triangle anthony prone comm fixing fixing unrestricted inform dence blocked blocked emerged proximation unaffected ables hoeffding hoeffding hoeffding hoeffding hoeffding impor klaus mansour tant bernoulli colt nserc stochas ogp render handles stefan rect ist tributions chow chow chow chow concatenation unconditional negation hardness ont ont ottawa ottawa ottawa ottawa ottawa ottawa criticism malicious kin kin nonincreasing nonincreasing nonincreasing nonincreasing succeeding nondecreasing nondecreasing nondecreasing nondecreasing nondecreasing nondecreasing vide returning returning smeared arrange wixi wixi wixi wixi wixi wixi nary anymore ivi mario mario mario mario mario mario permissible unlearnable ceptron pothesis eurocolt abilistic abilistic marc inspecting mazimum worry unnatural taxget publ 
#@Hadjifaradji_S,Marchand_M,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural input input input input input input data data data data function function function function function function figure figure figure figure figure figure figure figure set set set set set set set networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results information information information information information information information information information information problem problem problem problem models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case vector vector vector vector vector vector vector shown shown shown systems values values probability probability probability noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach large large large large large large test analysis matrix matrix optimal optimal optimal inputs inputs inputs inputs inputs inputs form form shows shows gaussian paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small size task trained trained structure structure structure structure structure structure structure structure problems problems problems problems problems problems problems problems problems random random random random random random random random random random random random random random random random random random random random random random random random random random response similar similar show show section section section section section section fixed line rule vectors vectors vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter real average average average average average average average average average average theory gradient gradient gradient gradient obtained obtained obtained obtained term note note note dimensional dimensional result result result result result university log defined defined found found found found constant constant standard prediction direction direction direction maximum maximum maximum maximum maximum range range learn learn learn learn learn learn components components components basis outputs outputs outputs continuous abstract find find find references component component due due due due due positive mixture context introduction hand hand statistical effect effect effect effect effect effect generated variance difference assume lower measure prior prior chosen chosen chosen chosen higher higher higher previous required good good binary binary binary binary binary binary binary expected expected make fact length length length finite finite finite minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting resulting resulting resulting resulting ing eq eq eq eq eq eq eq factor factor factor factor made feedback feedback feedback study study study relative relative relative true true true true compared compared define define perform posterior distributions gain gain gain gain gain gain gain equal equal equal approaches approaches comparison comparison larger descent descent dependent morgan department version version version version version version version version version version version version version version version exp exp exp exp considered curves curves curves limit limit limit limit limit san effects effects effects efficient choice significant significant significant significant approximate approximate approximate approximate approximate approximate approximate approximate approximate free world speed pages pages pages increase give con derived randomly randomly entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy provided selected selected evidence depends constraint simply achieved achieved achieved achieved discussion discussion covariance increases increases denote denote tested close corresponds corresponds amount assumed easily easily makes noisy noisy fit fit kaufmann functional unknown unknown unknown unknown significantly ratio york uniform squared squared details call max normalized normalized normalized supervised decay decay decay decay decay decay decay attention produced added added perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes improved improve improve improve pair pair element practical practical introduced identical sense sense varying compare compare 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situations minimized minimized minimized minimized employed simpler simpler simpler simpler overfitting investigate investigate exponentially exponentially exponentially exponentially replaced hanson dotted investigated investigated proper affect integer rev queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries der perceptton perceptton extent extent spin asymptotically great slowly agreement guaranteed worse worse worse reasons sections widely widely precisely sgn hyperplane hyperplane arise mation consequence ion scientific opt calculations improvements improvements readily lack lack peter peter peter peter peter marked marked slower frequently aim qualitatively qualitatively qualitatively prevent replace kinds conclude progress progress progress benefit benefit analogue writing sv sv acm perfectly perfectly perfectly perfectly perfectly perfectly perfectly nonzero nonzero consideration ments significance proceeds efficacy efficacy efficacy replica replica tishby tishby tishby tishby tishby exploit krogh krogh optimally intuitive intuitive hertz hertz motivation motivation motivation analyses sompolinsky bad bad percepttons infinity facilitate tic omitted reader seung seung seung seung splits generalizing learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable lem mind saad saad saad saad saad saad outline sine sine benefits benefits obtains freund freund freund edinburgh edinburgh scenario scenario algebraic verified verified publication perpendicular perpendicular perpendicular exam decays thermodynamic thermodynamic thermodynamic approxi gener ization maximally sollich sollich sollich sollich sollich sollich sollich sollich sollich sollich sollich sollich sollich sollich happen permit mea students students students picking picking achievable achievable achievable achievable achievable const stochastically firstly virtually usefulness subtracted subtracted ples progressively beneficial restricting decaying deter ben halves dent pin statements translate greatest percep percep imum ceedings das eta eta align ying teachers teachers forthcoming alization strongest colt translating hypersphere indistinguishable singapore prototypical prototypical unimportant glasses readers justifies news news news sume narrower rue signif shrinking misleading insignificant summarizing discussing sidered raining raining shrinks incre analysing dominating tropy neces querying sary tron wallace wallace weigh rau rau rau vanishingly encounters sired deliberately deliberately deliberately steeper hnction 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#@Saad_D,Sollich_P,
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#*network network learning model model model model model neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function time set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training output output number number system error error error error error error error error error error error error error error error error error error error results results results results results results results problem problem problem problem problem problem problem models performance performance performance performance based based based weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector order order order order order order shown shown shown shown shown shown values values values values probability probability probability parameters parameters parameters noise noise noise noise noise noise noise noise noise weight weight weight functions functions unit distribution distribution distribution distribution distribution approach point point single single single single single single single single single single single single single single single single single single processing processing large large large large rate analysis class matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal form form form form form form signal signal simple simple simple simple simple simple gaussian gaussian paper paper paper paper examples small small small small small small small small small small size size size size size size size size size size size size size work work work work work task methods level level trained trained problems problems problems random random random random similar show show show equation equation equation section section section general general general general generalization generalization generalization parameter parameter average average average theory theory theory obtained obtained obtained obtained term term term term term term term term term term term term term note note note note note note note note note dimensional dimensional result result result result variables variables variables variables variables variables computation computation computation computation computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution independent independent independent independent independent independent independent independent independent independent independent independent defined defined found found target target target target target constant terms terms sets sets sets sets sets sets sets sets sets sets sets sets sets sets learn learn components outputs continuous sample sample sample sample sample sample sample sample sample sample sample sample sample abstract back find find find properties properties references due due due due positive important mixture mixture mixture mixture introduction complex complex hand estimation estimation estimation estimation estimation behavior statistical statistical statistical effect effect effect effect effect effect effect effect effect variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance tion tion complexity variable variable variable variable assume assume assume assume assume lower rules measure learned chosen center previous theorem cases cases multiple multiple multiple distributed distributed expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected equations equations equations make make fact fact fact correlation correct errors finite finite finite finite finite finite finite finite minimum minimum resulting resulting resulting regression regression regression regression computed computed computed computed computed respect respect respect respect respect multi multi sum sum eq called called factor factor potential dimension dimension made global study study study study obtain obtain relative specific specific specific series define define compute compute compute compute compute goal related related distributions distributions equal approaches larger support dependent source words department difficult difficult bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias scheme computing computing directly directly directly curve view solutions solutions solutions curves curves limit limit limit limit limit limit effects detection efficient full full full full full full requires requires choice choice statistics free estimated basic basic increase increase increase produce weighted criterion lines finally finally depends depends depends simply simply simply simply simply covariance covariance covariance covariance normal normal increases increases arbitrary denote inverse inverse corresponds complete complete complete complete complete complete amount common common effective eds ability easily easily degree noisy noisy noisy fit objective pairs smaller combination combination combination combination combination combination combination combination combination combination combination combination reduced unknown fully fully interesting interesting significantly significantly increasing increasing increasing increasing uniform uniform uniform empirical empirical empirical empirical principle leads squared squared direct direct making normalized experts supervised magnitude decay idea attention combined combined produced improved improved improve recent correlations exact exact exact separate typical strategy identical identical identical quadratic subset subset subset recently recently relevant engineering engineering compare previously solve yields yields studies converge mixtures mixtures evaluation separation modified increased increased exists parts expression expression expression studied studied scaling matrices matrices demonstrate conclusion conclusion minimal minimal reduce reduce conclusions conclusions central measures clear clear clear performs asymptotic taking strong hard physics physics reduction drawn assuming minimizing minimizing minimizing minimizing decrease decrease decrease decrease averaged averaged manner minima question question denoted explicit explicit explicit explicit explicit van produces produces produces written longer index recall category explicitly explicitly electrical electrical easy easy slightly unique unique unique unique scales springer formed formed formed quality quality choosing independently focus focus expressed expressed dependence review review correlated squares squares squares squares squares squares squares squares squares squares squares squares squares squares squares squares squares squares estimator estimator estimator estimator estimator estimator estimator estimator 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decreasing extend situations situations situations layered detail estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators hessian helpful helpful helpful rise reducing fashion referred notion smallest smallest smallest necessarily rev subsets subsets subsets subsets subsets subsets subsets subsets subsets rank singular singular singular aspect quantities quantities quantities obvious noted precise observe observe expressions expressions expressions contributions regime regime regime regime arbitrarily finds finds finds finds massachusetts years mentioned mentioned trivial variances analytic independence independence independence briefly turns turns immediately potentially acknowledgement separately calculations calculations read lowest arises arises author mechanics apparent pseudo poorly posed remove berlin partitioning partitioning summarized summarized gen fall popular popular geman geman conclude conclude expectations expectations expectations unbiased focused focused wesley extreme extreme addison linearity concerned impossible proceed proceed proceed tools satisfying replacing balance keeping obtaining splitting splitting splitting disjoint monotonically ylx ylx financial weakly predictors heart dif claim israel insight late draw passing passing passing route agree eqs eqs broken broken broken balancing dividing mind unchanged unchanged schulten indirect obtains opper opper opper opper covariances scenario remainder mismatch community distribu thermodynamic thermodynamic thermodynamic approxi denoting denoting expand efforts individually ultimately pos option vanishes vanishes helps meir meir meir meir meir advantageous expense expense bienenstock twenty ferent solvable attempting attempting dominates tors eral identically hemmen neglect exposed bss bss bss bss bss bss coincide beneficial beneficial scenarios degenerate quantitatively drastically implying subscript meant statements devoted devoted technion technion unaffected demanding eta dilemma couple albeit rescaling possesses sible pay manfred inadequate faculty brevity domany resort estima replicas penrose penrose penrose penrose penrose penrose granger granger granger granger unrealizable unrealizable unrealizable unrealizable lengthy eli mates discussing forecast haifa kinzel kinzel kinzel undertaken sts wll conversation analyzes wasteful xxt xxt concomitant concomitant forecasts underdetermined underdetermined coexist xtx econometrics tempting afford prevalent 
#@Meir_R,
#t8
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data function function function function function figure figure figure time time time time time time time time time time time time time time time time time set set set networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number number system system system system error error error error error error error error error error error error error error error error error error error error error state results results results results results results results results results results results results results results results results results results problem problem problem problem problem performance performance performance performance based based space space space space weights weights weights weights linear layer layer case case case case case case case case case case case case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector order order order order order order shown shown shown systems probability probability probability probability probability probability probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach point point point point point point point large large large large large large local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test analysis analysis analysis class class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs form form form form form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small small small work task task task task methods step step step classification level level trained problems problems random random similar similar similar show equation equation equation equation equation equation equation equation section section section section section section fixed fixed fixed fixed fixed fixed fixed line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general general general general general generalization generalization generalization generalization generalization generalization generalization generalization approximation approximation approximation average average theory theory theory theory gradient gradient obtained obtained term term note note note note note dimensional result result result result result university university variables solution solution solution solution solution solution solution research independent log defined defined defined found found target target target target target target target dynamics dynamics initial initial constant constant constant constant constant standard terms prediction prediction prediction direction direction direction presented presented presented present present present present present low machine machine machine motion learn learn sample sample abstract applied find convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties references stochastic stochastic stochastic stochastic stochastic due due due important important decision decision decision decision introduction introduction action hand estimation behavior statistical generated generated variance parallel change change change change change change difference complexity complexity assume assume rules rules rules rules measure learned chosen chosen higher center center center previous previous cases cases cases cases binary binary long long conditions equations equations equations equations equations equations markov markov fact fact fact errors scale finite finite finite finite finite simulations minimum ing ing tasks simulation simulation simulation respect respect eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq called times times factor made natural study study study obtain obtain relative compared compared provide rates proc determined distributions distributions distributions distributions equal power power power power power power steps dependent dependent dependent dependent dependent institute institute loss difficult exp exp exp exp exp exp exp framework equivalent equivalent curve curve curve curve curve curve curve curve curve curve curve curve additional solutions curves curves transition limit limit limit limit limit limit limit limit limit limit limit determine upper full choice choice choice choice approximate free basic condition condition condition bounds types types provided finally finally processes processes depends depends depends depends depends depends depends depends simply achieved achieved measured measured discussion arbitrary fast fast fast fast fast inverse inverse complete stable stable stable finding effective supported theoretical theoretical theoretical theoretical require easily degree including smaller reduced fully york special special special special special uniform uniform empirical mode operation leads leads normalized normalized normalized normalized normalized supervised supervised early magnitude magnitude magnitude magnitude polynomial attention choose perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes denotes denotes discussed directions recent advantage typical apply apply machines sense dimensions sufficient teacher teacher teacher teacher calculated smooth smooth smooth smooth smooth smooth smooth smooth yields yields yields converge converge converge converge converge differential differential differential achieve achieve rl rl rl symmetric modified modified modified modified generalized generalized generalized exists lead studied studied studied scaling extended extended correctly occurs boundary boundary boundary boundary generally half half half minimal minimal minimal minimal greater reduce conclusions operator numerical numerical clear exponential asymptotic asymptotic asymptotic asymptotic asymptotic constrained suggest propose propose integration physics physics physics physics cycle drawn drawn solid solid proportional proportional assuming variety plane plane decrease decrease relationship iii minima minima acknowledgements van van construct construct construct written solving label label label changing student student student student student student student student student simultaneously averaging linearly linearly unique scales frequencies equilibrium equilibrium equilibrium springer springer shift implies decreases decreases yield dependence depending stationary stationary overlap overlap overlap overlap overlap viewed learner learner updated labels labels evolution evolution centered centered forms understanding similarly similarly converges converges converges converges converges converges converges converges converges converges converges converges allowed allowed reasonable dashed dashed dashed normalization normalization normalization neighborhood roughly remains remains remains valid valid sufficiently formulation bell bell batch batch batch batch batch batch batch sciences vapnik vapnik vapnik holds phys phys phys phys phys phys partially discussions simplicity simplicity regular straightforward efficiency presentation orthogonal summary verlag success success interested dis issue symmetry classify running generalize realistic leading leading leading overlapping decreasing extend situations situations presents presents law law law law unlike unlike schedule schedule schedule schedule schedule schedule schedule optimized behaviour behaviour helpful incremental parity parity parity analytically scaled complicated proved fundamental hill coefficient coefficient analyze rev rev rev illustrate perfect changed ensure queries noted noted perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton store amari amari arbitrarily averages averages asymptotically asymptotically residual slowly cos separable agreement agreement agreement baum baum baum baum baum baum correction worse reasons stress formalism sgn sgn sgn sgn sgn sgn sgn sgn laboratories laboratories separately involve calculations begin optimize lowest mechanics requiring reflect requirement berlin limiting differs proven decreased focused deviations differentiable multidimensional yielding yielding yielding yielding realized shifted corrupted corrupted pac uncorrelated acm homogeneous homogeneous addresses nonzero wrong murray held grow replica replica tishby imply north overlaps sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky excellent separating governed schapire equals holland guarantees israel israel treatment repeatedly kearns eqs seung seung seung seung seung seung seung seung seung seung summarize pen thresholding limitation learnable multiplying converted solves solves deriving uniquely isotropic isotropic isotropic freund valiant valiant argue shifting shifting ijcnn realizable realizable realizable realizable realizable realizable gener gener ization ization thresholded thresholded thresholded thresholded thresholded confirmed academy unconstrained drawback hansen hansen hansen paradigms grateful behave vanishes dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies corrections gorithm demonstrating laws laws cornput cornput incorporation clark vanish vanish retrieved att nontrivial implied implying brackets addressing appro pin neglected problematic denominator cope noiseless jerusalem jerusalem incurred obeys cancel hebrew hebrew heskes heskes heskes heskes heskes lowered dependences possesses poo behaved barkai barkai barkai barkai barkai fund numerator kushner kushner kappen kappen chemistry overcoming iwl iwl asymptote unrealizable unrealizable unrealizable unrealizable obeying ger bringing lly prefactor inhomogeneous malicious commun ule coo coo stressed salamon fujita virtues optim usu fibre supplemented gaussi gaussi cle sched haim shinomoto shinomoto shinomoto huj huj mso nonvanishing ifil hes racah racah adiabatically adiabatically disregarding israeli recycled arts 
#@Barkai_N,Seung_H,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training output output output number number number number number number number number number number number system system system system system system system system system system system system system system system system system error error error error error error error error error error error error state state state state state state results results results information information information problem problem models models models hidden performance space space space space linear linear linear layer layer case case case case vector order order systems values parameters unit method method method method method approach approach approach approach approach point point point point point point point point point single single single single single processing processing control large local rate analysis analysis optimal optimal inputs shows shows shows shows signal signal signal signal signal signal signal signal signal signal algorithms simple simple paper paper paper paper paper paper paper paper small size size net net work work work work methods methods step step step step step step step step step points current trained trained trained trained trained trained trained trained problems high high memory memory representation architecture architecture show show equation equation equation equation section line rule real real average average states theory theory theory obtained obtained obtained obtained term term term term note note dimensional university university computation computation solution found sequence sequence sequence dynamics dynamics dynamics dynamics dynamics initial initial initial estimate estimate estimate estimate estimate estimate distance distance science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented presented map map map map map map map map map map present low frequency basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs sample sample sample sample sample sample sample sample sample sample sample abstract applied back find find computational properties properties properties references due due due ieee positive procedure important important introduction introduction complex estimation behavior behavior behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search rules measure measure signals signals higher part previous previous theorem theorem type type required required long long long long long long long conditions expected fact region region region proposed proposed proposed proposed proposed proposed correlation correlation correlation length length length length length length length length length length length length length length length length length length observed errors errors errors resulting resulting resulting computed computed computed called times times regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means means means factor factor dimension dimension dimension dimension natural feedback feedback global global global global study study obtain original original original original original original original vol vol artificial artificial artificial artificial artificial samples samples samples samples samples samples samples samples samples samples true true series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series define experimental experimental goal goal constraints constraints steps steps steps steps comparison comparison larger larger train train train train train train train nets modeling modeling report implementation connectionist final final delay delay sequences sequences sequences sequences equivalent curve view design limit limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san full requires choice approximate estimated estimated estimated estimated estimated estimated estimated produce weighted developed developed developed developed criterion criterion provided selected selected selected backpropagation backpropagation backpropagation backpropagation backpropagation iteration iteration iteration sampling simply achieved discussion technical feedforward describe describe arbitrary assumption corresponds finding short implemented assumed synapse generate generate generate supported theoretical theoretical theoretical main main journal journal square square future future rumelhart fit fit underlying dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical unknown unknown unknown coefficients mlp mlp mlp interesting testing testing testing mechanism principal principal iterations iterations iterations iterations iterations iterations max max max max max max max filters international international normalized produced produced produced produced produced choose predict predict discussed apply sense recently varying varying compare conventional approximately axis axis match studies address separation separation interval increased grant exists extended trial predicted predicted predicted predicted predicted feed feed loop loop setting trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories segment conclusions sigmoid constrained suggest suggest propose hard mechanisms integration largest largest largest largest largest largest characteristics characteristics assuming assuming minimizing minimizing averaged identification identification attractor attractor attractor attractor attractor attractor appears produces laboratory laboratory ann segments segments multilayer multilayer averaging unique develop predictive predictive predictive predictive predictive predictive predictive quality versus select select select select decreases national independently expressed expressed depending overlap overlap overlap controlled showed showed showed static static static past past spectrum key reasonable sec fitting neighborhood iterative iterative norm topology topology topology topology topology topology topology topology topology topology avoid box figures perceptrons weighting batch uncertainty uncertainty uncertainty uncertainty uncertainty partially successfully successfully regular identified identified capable successful identify identify literature build tdnn tdnn tdnn tdnn tdnn efficiently fine capture capture capture capture notice notice notice notice repeated success showing showing interested issue issue return follow quantity sampled paradigm predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor neighboring neighboring neighboring acknowledgments modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling minimized create requirements rapidly rapidly detail optimized optimized issues divergence divergence divergence divergence divergence existence existence successive mse mse mse workshop understand fundamental momentum gradients adapt predicting quantities quantities perceptton initialized generates improving chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic established trivial waveform waveform adapted glass glass glass worse handle closer closer closer day choices choices universal describing nsf understood autonomous autonomous autonomous autonomous autonomous requirement weigend replace median credit wesley instantaneous instantaneous lot picture addison guarantee guarantee reconstructed addresses addresses nonzero establish systematic dealing consideration promising accepted city imposed imposed los los nearby nearby transforms methodology methodology methodology krogh enhanced hertz lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov eqn eqn eqn reliably embedding embedding utilized utilized utilized predictors predictors predictors predictors predictors decide forecasting captured captured nonlinearities iterated iterated iterated iterated iterated francisco mlps creating impact considerations captures stopped limitation onr anns shorter basically job conjecture conjecture chaos chaos ease guess principe principe principe principe principe realize constrain constrain constrain argue mackey mackey mackey exponent exponent exponent exponent exponent exponent exponent impose carefully met careful scope topic covered breaks discusses lapedes lapedes reciprocal topologies palmer dim instability instability instability instability distinguishing conflicting exclusively dissertation huberman accumulate autoregressive seed seed seed nontrivial rtrl totally reality presently goodness alamos alamos surprise iterate iterate brought ming ming ming ming ming jose jose jose jose jose dist dist dist diverge jenkins extrapolation farber putting exponents corr iterates iterates iterates ecs displaced tums seeks taps necessity bptt explores kuo kuo kuo kuo kuo kuo kuo kuo proportionally proportionally mexico takens takens pointwise constrains redwood predictability casdagli casdagli instabilities vital florida florida invariants invariants runge holden orbits preferably farbet kutta magnified colinear fluctuates gainesville neuroengineering lays 
#@Kuo_J,Principe_J,
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural input input function function function function function function function function figure figure time time time time time time set set set set set set set set set set set set networks networks number system system system system system system system system system system system system system system state state state state state state state state state state results results results results results models models based based space space space space space space space space space space weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector order shown values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight functions functions functions functions functions distribution method approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point point point point point point point point point point point large large large large large large large patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs form form form gaussian paper paper paper paper small small small small size size work fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells points field process cell cell cell cell cell structure problems random random architecture show equation equation equation equation equation equation equation equation fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule rule rule rule vectors general general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation average average obtained note university university research independent independent defined defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial table table standard computer terms terms distance connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic prediction left presented present present sets range range range range learn position nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract density density density density density properties references component due ieee ieee positive positive positive positive important introduction hand hand hand behavior behavior behavior effect variance parallel change difference difference difference assume assume assume rules part center center center center center center center center center center center theorem theorem cases type type type type type type type type type long long long conditions conditions expected equations make fact proposed correlation correlation correlation observed observed scale simulations simulations simulations ing simulation simulation respect potential made obtain obtain negative negative negative negative negative negative negative vol relative relative specific specific specific specific compared application application series receptive receptive receptive receptive provide provide define proc proc perform determined determined determined determined goal related connected gain connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection connection fields fields fields words department loss synapses synapses synapses difficult exp exp exp layers layers layers layers layers framework equivalent san effects effects determine determine determine basic give con con condition condition condition condition condition developed criterion criterion lines provided inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory constraint constraint covariance covariance covariance covariance covariance normal feedforward feedforward group denote assumption complete complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable stable stable stable stable stable stable stable stable stable predictions proof short supported supported role role theoretical easily makes development development development development development development development including underlying underlying underlying underlying dynamical dynamical dynamical fully fully fully mechanism mechanism special principle principal principal principal max max normalized idea idea idea description predict predict advantage property separate ensemble side sense engineering sufficient sufficient varying previously unsupervised unsupervised unsupervised approximately definition symmetric symmetric symmetric organization organization organization organization sensitive grant studied occur deviation strength strength conclusion critical critical critical critical hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian depend numerical numerical clear propose taking mechanisms presence presence largest largest largest largest largest characteristics exist min min min min plane plane decrease relationship iii iii introduce program attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor acknowledgements explicit derive derive derive longer longer index index primary describes stability stability stability stability mathematical changing explicitly averaging electrical easy develop develop equilibrium implies implies decreases national independently focus formation depending influence variation evolution evolution evolution evolution understanding activities activities activities similarly similarly sign sign key key performing purpose purpose avoid fire perceptual combinations usa formulation eigenvalues subspace determines prove partially neighbors characterized texture suitable divided attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors literature mackay mackay miller miller reached reached receives notice conf kind kind kind kind absence absence surround satisfies oriented oriented oriented oriented origin origin carried carried difficulty steady steady strengths limitations existence school project applicable int relationships referred structured structured structured structured structured structured structured structured structured structured structured structured proved fundamental removed smallest smallest smallest adapt changed ensure ensure ensure der precise precise precise hebb hebb regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime regime submitted defines inequality inequality band crucial slope slope slope slope slope adjacent analytic explanation majority majority tractable nonlinearity satisfied precisely precisely division division arise afferent afferent acad describing localized localized localized linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker linsker qualitative qualitative preceding preceding preceding preceding preceding nsf behaviors applies dark parameterized parameterized item item incorporated summarized characterize reaches gen occurrence occurrence proven sums eventually extreme extreme extreme extreme extreme picture picture uncorrelated proofs equivalence restriction grey plays climbing generality saturation consideration stronger stronger ranges stated attractive attractive check check obtaining monotonically exceeds natl analyses dominant belongs belongs treatment francisco emergence emergence emergence emergence emergence eng hypercube hypercube approx approx approx rigorous rigorous rigorous rigorous rigorous rigorous rigorous rigorous rigorous rigorous rigorous constitute constitute fellowship emerge emerge emerge diverse centre theorems theorems theorems convenience arbor arbor tor basins basins concentrated insights dominated confirmed exceed proach regimes regimes regimes regimes regimes regimes regimes regimes regimes regimes regimes regimes regimes west reveal eigen fortunately remarks saturated saturated saturated saturated saturated tial sake pan pan pan pan pan pan pan pan pan pan pan pan pan pan played eral core core progressively gence vicinity computable motors stabilization noticed italy italy def mention roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury comprises favorable ecs designated designated designated qij qij deduce deduce poten sual ies faculty originating originating concluding chinese mat purdue purdue purdue embodies multilayered ficient specially specially dition coexistence coexistence coexistence coexistence coexistence suf intercept intercept intercept ili circularly circularly circularly rig lafayette coexist coexist piscataway assert rome rome stants attrac ier lxl emer limiter limiter limiter limiter bian nonempty heb kll arborization unifies 
#@Feng_J,Pan_H,Roychowdhury_V,
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#*network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural input input input data data data data data data data data data data function function function set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training output number number number number number number error error error error results results information information information problem problem problem problem problem problem problem problem problem performance performance performance based space space space space space weights linear case case case vector order order order order order values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability weight weight weight weight weight weight functions functions functions functions unit distribution distribution distribution distribution distribution method method method approach approach approach approach point point point point point point single large large large large large large large large large large rate analysis analysis class matrix inputs form form shows shows shows algorithms simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian small small small size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size net net net work work methods methods points points points points field field field features process process process process process process process process process process process level level level level level structure random random random random random high high high high high similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show equation equation section section vectors vectors general general general general generalization generalization generalization parameter real approximation approximation theory theory theory gradient obtained obtained term dimensional dimensional dimensional dimensional result result result result solution independent independent log log log defined initial constant constant constant constant constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate terms terms terms terms left activation activation activation low maximum maximum range range basis continuous sample sample sample sample sample sample sample sample sample sample sample sample abstract applied find find find find find computational convergence analog properties references stochastic stochastic due ieee positive positive positive mixture introduction complex hand hand hand estimation behavior behavior effect variance variance variance variance variance variance variance variance parallel search tion tion tion complexity complexity variable variable assume classifier lower lower chosen chosen chosen higher center center center center center theorem theorem bound bound bound bound bound bound bound bound bound bound bound required good good long fact techniques region region proposed correlation correlation correlation correlation correlation probabilities probabilities probabilities errors minimum resulting resulting ing total simulation simulation computed computed computed respect sum sum performed called times regions regions means factor factor factor potential dimension dimension dimension dimension obtain obtain obtain obtain original original vol samples samples samples samples compared application desired define compute compute compute proc determined goal larger larger train source nets nets nets nets nets nets technique individual represents represents exp exp exp exp exp cambridge computing equivalent directly directly estimates estimates estimates estimates estimates estimates limit limit classifiers classifiers classifiers upper upper choice choice significant approximate approximate approximate statistics estimated estimated pages give give con condition condition derived weighted conditional conditional bounds bounds product provided provided finally processes processes processes processes depends depends sampling sampling sampling measured covariance covariance covariance covariance normal normal normal technical feedforward feedforward feedforward feedforward feedforward feedforward group limited actions proof finding finding finding role main face square ability smaller smaller smaller needed functional functional unknown unknown unknown special uniform uniform uniform empirical empirical empirical empirical empirical squared representing details call normalized magnitude magnitude perceptron recent resolution resolution advantage typical similarity similarity practical practical practical introduced introduced side sense recently engineering engineering sufficient highly highly varying approximately approximately approximately approximately calculated volume volume volume volume volume volume volume volume volume volume volume volume volume axis smooth smooth smooth smooth yields yields yields yields yields studies studies entire expression studied studied occur correctly touretzky occurs occurs conclusions central accurate exponential exponential faster practice practice asymptotic asymptotic asymptotic asymptotic taking largest turn min min derivatives derivatives derivatives force force force question explicit suppose suppose suppose relation monte monte carlo carlo factors factors estimating estimating estimating ann vertical recall electrical electrical involves unique unique unique unique unique interaction applying applying events springer springer springer expectation expectation expectation select select yield dependence dependence dependence dependence correlated correlated correlated viewed interpretation lemma lemma lemma lemma lemma lemma transform restricted approximations approximations centers centers centers centered approximated sizes sizes sizes similarly key reasonable performing expansion expansion convex combining roughly remains valid valid valid degrees avoid expect existing coordinate coordinate vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik holds holds determining importance computations tend fine fine fine fine fine fine fine summary soc heuristic heuristic heuristic heuristic heuristic issue contribution classify comp quantity quantity michael michael michael michael michael generalize absence realistic nips leading leading decreasing presents law bars origin powerful requirements requirements requirements requirements requirements investigate experience difficulty exponentially exponentially exponentially integral integral integral integral integral integral hessian hessian hessian discriminant matches giving reliable reliable func fundamental fundamental fundamental act math illustrate ensure ensure ensure ensure freedom perceptton shapes academic simplest regime regime finds indicating slowly growth smoothness guaranteed analytical baum baum tool purposes located worst arise potentially geometry outer argument argument geometric evaluating items empirically parameterized orders orders haussler haussler haussler employ continuously continuously compares operate poisson poisson poisson poisson poisson poisson poisson poisson poisson characterize differs fall occurrence occurrence occurrence sentence yielding univ univ univ cor contribute gap equivalence japan conditioned narrow unity unity unity dealing consideration replacing nearby exploit fail imply exceeds substituting substituting negligible decide percepttons laplace laplace multiplied multiplied treatment reveals warmuth probe sustained informative arrows arrows partitioned reverse ball equivalently chervonenkis chervonenkis expanding die pieces adopt monotonicity arg arg letting letting avoided acting playing bounding disadvantage learnability terrence terrence terrence terrence terrence concentrate retain noting integrals integrals setup apparently reveal sta drops expansions remark remark remarkable remarkable differently algorithmic nonnegative interior interior const satisfactory justified crude transforming stochastically jointly finer finer determinant condi striking anthony anthony archi amenable accounting raised wong wong mach neglected scattered inform capturing fore hits imum moderately bodies mum favorably dominate assoc tailored blumer blumer extrema extrema formulations dependences undesirable anticipate anticipate clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump clump tecture ily ily seeks expressing cov jour numerator numerator tly sharper ehrenfeucht probing farther overestimate pollard pollard sification sification cornell cornell cornell cornell sider tistical tradeoffs clumps clumps clumps clumps clumps clumps shatter evidently closes supremum supremum supremum supremum attacked unnormalized differenttable parabolic casting ithaca ithaca intern practitioners biggs biggs fresh enclosing vie mazimum disagrees suming restated excursions tur complezity excursion ditionally 
#@Fine_T,Tunnon_M,
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural input data function function function time time time set set networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm error state results results results results results results results information problem problem models hidden hidden hidden based based based based based based space space weights weights weights linear layer layer layer case case case case case case case case case case vector vector vector vector vector vector order order order shown shown shown systems values values values values values probability probability probability probability probability weight weight weight weight weight weight functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach pattern single single processing processing processing processing processing large large local local rate rate rate test test test test test test test test test analysis analysis analysis analysis analysis analysis analysis analysis class matrix optimal optimal inputs inputs form form form form shows signal algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small small small small small small small small small small small small size net net methods step classification process process process process process process process process level level level trained structure problems random random random random random random high high show equation equation equation section section fixed fixed fixed fixed fixed fixed fixed fixed line vectors general general general general general general general general parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation states theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained term note dimensional dimensional dimensional result result university university university research independent independent independent log log log log log log log log log log sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics initial initial constant constant constant constant constant constant constant constant constant constant constant terms terms node node presented presented present activation activation activation activation press continuous continuous sample abstract applied convergence convergence convergence properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due ieee ieee positive positive positive positive positive positive positive important propagation introduction introduction behavior behavior generated generated variance variance variance variance parallel tion tion tion variable assume assume higher higher part previous theorem theorem cases cases required multiple good good conditions conditions distributed markov markov markov markov markov markov markov markov markov make fact techniques techniques techniques finite finite finite simulations resulting resulting simulation computed respect times elements means reinforcement dimension made study study study study em obtain obtain original vol vol vol vol samples true compared application application series define compute rates goal distributions discrete discrete discrete approaches approaches mit contrast support descent descent descent descent dependent morgan morgan morgan words loss version version advances difficult sequences sequences sequences sequences sequences sequences considered cambridge hinton estimates estimates limit limit limit limit san san san san efficient choice choice statistics basic basic basic basic give give condition developed criterion product actual processes processes selected normal normal feedforward feedforward feedforward denote transformation close assumption assumption assumption assumption assumption proof finding common assumed assumed assumed assumed supported theoretical hypothesis hypothesis hypothesis easily easily rumelhart rumelhart development kaufmann kaufmann kaufmann pairs pairs york york consistent trials trials empirical mode mode numbers max max max max direct normalized normalized normalized supervised choose run run run exact pair pair pair reported engineering engineering sufficient sufficient sufficient compare solve rl rl trans trans definition chain observation bounded bounded bounded bounded interval williams entire grant exists exists exists suggests deviation wide matrices matrices matrices white white white generally runs conclusion starting assumptions assumptions conclusions conclusions operator operator depend editors editors bayes clear moody moody moody asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak mateo mateo mateo strong sigmoidal turn assuming assuming assuming assuming exist min min min min min min min min derivatives derivatives minima acknowledgements suppose suppose pro stability mathematical recall metric multilayer multilayer infinite electrical electrical involves easy unique unique unique applying applying springer springer formed implies implies expectation independently dependence dependence stationary stationary estimator lemma lemma lemma detailed densities densities evaluated approximations forms forms neighborhood iterative interpolation valid sufficiently sufficiently norm norm norm norm norm norm norm euclidean euclidean thesis eigenvalues batch batch batch prove holds holds holds holds holds holds partially tests tests tests major uniformly paths mcclelland literature literature tend fine fine fine fine fine reached verlag verlag kind prob showing showing follow criteria criteria hold hold quantity quantity nips nips giles cowan law updating updating updating put estimators hanson recursive existence existence existence existence existence existence scalar examine successive giving ideas school school combine proved analyze ensure taylor expressions expressions piecewise piecewise inequality inequality publishers publishers guaranteed diffusion diffusion independence day forces definite definite nsf argument fourth considerably understood affine peter backprop passed passed passed passed remove continuously continuously calculating limiting limiting limiting limiting limiting limiting limiting limiting limiting limiting limiting limiting limiting limiting limiting gen gave conclude differentiable differentiable yielding cumulative classifying leen leen leen leen leen intractable intractable restrict null homogeneous homogeneous unity nonzero nonzero nonzero nonzero establish establish establish establish fails dealing chains simplify stated balance hope star moments moments moments moments moments moments moments lengths francisco agree lag verify basin failed failed failed kurtosis kurtosis kurtosis convenience seek ease recurrence rain rain leg leg leg leg leg leg pub chapman distribu permits terrence terrence terrence terrence terrence investigating hornik hornik represen indication applicability exhibited ward ward infinitely infinitely expansions removes autocorrelation autocorrelation establishes establishes eral neglect equa attained sym orr orr linearized linearized proves implying appl tations cess jitter vanishing vanishing unrestricted inform merit stationarity equilibria linking adv adv adv deleting kolmogorov kolmogorov kolmogorov topics approxima fluctuation suitably tran berger berger berger claims iterates iterates iterates iterates iterates iterates iterates iterates jensen iter agation gorithms gorithms lemmas asymptotics asymptotics asymptotics circumvent neglecting ore equiv oft unrealistic tha normality normality normality yix linearization linearization linearization linearization feedfor feedfor finnoff finnoff finnoff finnoff finnoff foster foster hen lea dates iia cornell cornell cornell cornell cornell consis persist surely skewness skewness skewness mina mina mina mina mina mina holden downsampled downsampled downsampled downsampled downsampled downsampled tally customary ine trices ithaca ithaca ithaca hopping decimation integrable awl marc ates ficiently existed semidefinite reconcile tlt lishers upto frobenius 
#@Fine_T,Mukherjee_S,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural data function function function function function function function function figure figure time time time set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number state state state state state state state state state state state state state state state state state state results information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem models hidden performance based based based space space space space space space space space space space case case case case case case case case case order shown shown shown shown systems values values values values values values values values values values values values values probability probability probability probability probability parameters functions functions distribution distribution method method method method method approach approach approach approach approach approach approach approach processing processing control control control control control large local local local local local local rate analysis analysis analysis analysis class class matrix form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper examples examples small work methods methods methods step step step step step process process level level level current current current current current current current current problems problems problems problems problems problems problems problems problems problems random similar similar show show equation equation equation equation section section section line line general general generalization generalization approximation approximation approximation average average average average average average average average average average average average average average average states states states theory theory obtained term note note result result result result university computation solution research research defined defined found found found found sequence constant constant estimate estimate estimate estimate terms terms terms terms terms science left direction presented present present temporal machine machine machine machine machine machine maximum maximum maximum maximum maximum maximum continuous continuous continuous continuous sample abstract find find convergence convergence convergence convergence convergence analog references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due procedure procedure decision decision decision decision decision decision decision decision decision decision decision introduction action action action action action action hand estimation estimation behavior effect effect dynamic dynamic dynamic dynamic variance variance search search change change change change change change change difference assume assume assume assume measure prior prior chosen chosen higher higher higher higher higher part previous theorem theorem theorem theorem theorem theorem theorem type type long expected expected expected expected expected markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make make fact fact fact proposed proposed correct probabilities probabilities probabilities probabilities observed observed observed errors finite resulting ing ing total human computed computed performed eq eq times mapping means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor potential applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge obtain obtain obtain true compared provide define define define define compute perform goal related distributions discrete brain equal approaches approaches approaches mit mit mit steps dependent dependent dependent morgan proceedings proceedings institute department version version version version advances bias bias bias addition sequences sequences framework cambridge cambridge domain equivalent environment environment environment environment environment environment directly directly additional additional estimates transition limit limit limit limit san conference conference requires requires approximate increase give condition bounds bounds bounds bounds provided processes nature nature depends depends achieved achieved achieved technical increases describe denote denote hmm hmm hmm transformation assumption assumption assumption assumption assumption actions actions actions actions actions proof proof effective assumed supported theoretical theoretical theoretical theoretical end instance easily easily kaufmann probabilistic underlying underlying underlying underlying underlying underlying underlying underlying underlying account unknown jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan technology programming programming programming increasing increasing max max max direct direct direct direct making making early attention combined choose choose predict predict discussed improve improve improve recent practical practical side cognitive recently observations observations calculated works solve yields yields correspond converge converge converge converge address definition definition evaluation evaluation evaluation evaluation chain generalized generalized bounded improvement improvement improvement improvement improvement improvement improvement improvement improvement grant grant grant grant exists parts expression expression lead lead lead suggests alternative deterministic deterministic deterministic generally setting setting setting setting setting setting setting conclusions reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward differences sutton sutton sutton performs faster practice mateo sound propose propose taking taking drawn variety question explicit appears monte monte monte monte monte monte monte monte monte monte monte construct carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo produces written solving ways estimating changing changing averaging involves slightly expectation yield yield yield yield focus stages viewed viewed viewed learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner transform restricted updated updated forms allowed allowed past partial earlier earlier calculation barto barto spaces normalization false iterative foundation advantages classified expect thesis weighting instances assignment batch batch sciences extension extension extension partially partially partially partially characterized simplicity simplicity simplicity computationally computationally computationally computationally effectively efficiently efficiently schemes comparing online composed refer interpreted satisfy notation quantity quantity involved write michael michael michael michael michael michael dayan dayan dayan dayan generalize providing providing delayed observable observable observable observable observable observable highest policies policies policies policies policies policies policies policies policies policies policies policies acknowledgments unlike schedule access access access singh singh singh singh singh singh singh singh singh singh singh singh updating environments environments environments environments replaced replaced recursive recursive mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp hall rise giving project authors office maximizing statistically analogous removed removed analyze automata perfect changed changed quantities noted algo precise observe message message message message message message message message phd averages averages massachusetts years indicating asynchronous asynchronous analyzed analyzed guaranteed guaranteed fairly tractable tractable tractable purposes arise watkins watkins watkins watkins laboratories inversion separately separately involve gradually nsf greatly considerably considerably applies readily treated rewards rewards rewards rewards calculating rely mod maximizes occurrence occurrence enables enables age jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola lim credit yielding yielding bellman intractable feasible feasible assign tation summing impossible naval occurred tools satisfying siemens replacing stated pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp operates synchronous carry generalizes continue analyses analyses analyses prentice started started appendix appendix guarantees lengths schwartz schwartz schedules schedules young discounted indicator refers rich theoretically theoretically tsitsiklis tsitsiklis messages messages messages messages messages messages messages messages messages statement convergent material bertsekas bertsekas bertsekas indirect indirect corporation pointing solves discount discount ties markovian incrementally constitutes constitutes england letting avoided var assess avoids equality rithms management refinement refinement refinement els refined refined atr exploited ward resembles rewritten appearing payoff survey characterizing identifies mcdonnell heavily converging cliffs utilizes clarity recursion recursion cast appealing possess devised partly partly englewood restricting implying facts facts vanishing tenth occupancy occupancy occupancy merit merit refine stems investigator infeasible pew cancel wait illustrating psyche psyche psyche concurrently concurrently satinder satinder satinder satinder satinder controllable paid duff duff tommi tommi tommi tommi tommi tommi completes accord presidential aver successes motivate observability reachable eleventh pol jumping discounting discounting discounting discounting revise unfolding cease guaranteeing resist usable concomitant weightings terministic flavor icy undiscounted expec stricted 
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural data function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time set set set networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system system system system system system system system system system system error error error error error error error error error error state state state state state state state state state state state state state state state state results results results results results results results results results results results information information information information problem problem problem models performance based space space weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear case vector vector vector vector order order shown systems systems systems systems systems systems weight weight weight weight weight weight functions functions functions point point single processing control control control control control control control rate rate rate rate matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form form form form form form form shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper small small small small small size size work task step step step step step step step step step step step process process current problems problems random random high show show show equation equation equation equation equation equation equation equation line line general general general approximation approximation approximation approximation approximation approximation states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term experiments dimensional dimensional dimensional university solution solution research research research defined defined defined found found dynamics dynamics initial initial initial table table table estimate estimate terms terms distance distance distance distance presented temporal machine machine maximum learn learn learn learn position continuous continuous continuous continuous abstract applied applied applied applied applied find convergence convergence references stochastic decision action action action action action action action action action action action action action behavior behavior dynamic dynamic dynamic dynamic cost change change change difference lower lower representations learned learned learned chosen center center bound cases cases long long conditions expected expected equations equations equations equations equations equations equations equations markov proposed correct correct correct correct correct errors errors errors errors errors simulations simulations simulations resulting resulting total total total total simulation simulation simulation simulation simulation simulation simulation simulation simulation respect sum sum sum sum performed performed performed performed performed performed called times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement policy policy policy policy policy policy policy policy policy policy policy policy policy negative negative relative relative specific true true true compared compared compared application define rates rates rates rates rates rates rates rates perform perform experimental steps steps steps comparison comparison comparison comparison update update update descent descent descent proceedings proceedings proceedings report report report institute implementation consists joint represents final final final graph considered cambridge cambridge cambridge equivalent equivalent experiment experiment experiment hinton hinton transition san effects conference conference conference requires choice significant significant significant significant increase randomly developed velocity types product backpropagation iteration nature associative technical technical technical technical technical actions actions actions actions actions short generate generate supported journal ability ability future easily degree rumelhart rumelhart simulated needed needed reduced technology programming programming programming programming interesting york squared squared squared squared squared representing representing numbers iterations max max stored stored stored international international normalized magnitude combined minimize run architectures advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage advantage pair practical include period identical quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic sense recently dimensions compare calculated calculated solve converge converge converge converge converge differential differential differential differential differential differential differential differential differential differential differential definition definition modified williams williams williams increased increased horizontal matrices matrices matrices deterministic deterministic deterministic deterministic deterministic conclusion starting sutton sutton faster faster taking solid turn plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane iii iii iii iii iii averaged program force force force force force base base base base digit derive derive longer laboratory laboratory laboratory laboratory laboratory laboratory metric category integrated john extracted independently estimator evaluate evaluate controlled forms forms forms forms forms forms forms completely digits converges converges converges converges calculation performing performing performing fitting calculate advantages degrees includes thesis thesis sciences maximize planning planning comparing comparing receives composed composed composed repeated allowing superior return duration duration duration duration duration duration satisfy notation dot delayed approximating acknowledgments tesauro tesauro tesauro employed diego wiley updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating updating optimized optimized game game game game game game game game game game game issues dotted mdp hall pursuit incremental combine office maximizing necessarily changed ensure initialized defines massachusetts residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual residual rows guaranteed guaranteed guaranteed guaranteed unstable unstable navigation answer answer satisfied ran watkins watkins scientific circle annual parameterized poorly adjustable adjustable rewards calculating maximizes decreased unbiased baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird baird simultaneous june bellman bellman bellman bellman bellman bellman bellman bellman optimality optimality modify extensive grows air air air air air numerically simplify wire preparation preparation games games games games games meaningful prentice mance mance mance mance mance ensures discounted discounted discounted master environmental sons bertsekas bertsekas appeared unable unable unable shorter tables aircraft rao rao dyna comparative residuals residuals residuals residuals acceleration acceleration acceleration acceleration england avoids backgammon life guidance regulation player player academy turning bradtke bradtke exhibited october unpublished demonstrating cliffs suite station station englewood minimax minimax minimax minimax minimax minimax minimax players players players defense defense durations united amax amax nondeterministic invert wright wright wright wright wright wright wright wright wright wright klopf klopf klopf klopf klopf klopf seeks seeks seventh accelerate doctoral millions seeds reacting patterson patterson patterson patterson pursuing accelerations accelerations maxa maxa maxa maxa maxa harmon harmon harmon harmon harmon harmon harmon squaring urn harry harry harry harry harry backpropagating keywords prasad prasad mil mil mil rau rau rau rau punishment mathematica avionics bldg 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural function function function function function function function function function function function function function function function function function function function function function function figure figure figure set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number system system system error error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results information information information problem problem problem hidden based based based space space space space space space space space space space space space space space space space space space linear case case case case case case order order shown shown shown shown systems values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters weight functions functions single processing processing control control control control control control large large rate test test analysis analysis matrix form form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper examples small size size size work work work methods methods methods step step step step step step step step step step step step step process process process process level level level current current current problems problems problems problems problems problems problems problems random similar representation representation representation representation representation show equation equation equation equation equation equation section section section section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed line general general general general general general generalization generalization parameter real real real real approximation approximation approximation approximation approximation approximation approximation states states states states states states states states theory theory theory theory theory gradient note note note result result university variables computation computation solution solution solution solution solution solution solution research defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant table table table standard computer terms science presented presented presented presented presented presented present present present present temporal machine machine machine machine machine basis basis continuous sample sample sample sample abstract applied applied applied applied applied applied find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic ieee positive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision introduction action action action action action estimation effect effect dynamic dynamic dynamic generated variance variance search change change difference variable assume assume assume assume representations representations representations representations representations learned learned part previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem cases required good good conditions conditions conditions conditions conditions represent represent expected expected equations equations equations equations equations markov markov markov markov markov markov fact proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities finite ing human computed computed sum called elements mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor policy policy policy policy policy policy policy policy policy policy policy specific provide provide define define define compute discrete discrete brain equal equal mit mit mit steps steps larger update dependent dependent proceedings proceedings report report department version version version individual individual advances difficult final addition ai ai maps maps cambridge domain domain directly curves transition transition transition transition transition limit conference determine requires world world estimated pages pages pages con con randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed processes processes iteration iteration iteration nature nature sampling discussion technical describe arbitrary arbitrary arbitrary arbitrary arbitrary assumption assumption proof proof proof finding implemented assumed supported theoretical end cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster future future future makes objective typically smaller underlying unknown unknown jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan programming programming programming interesting increasing special special empirical empirical empirical squared squared representing iterations iterations max max making making making international international attention minimize minimize produced produced produced predict architectures improved improved resolution advantage separate takes apply quadratic sense sejnowski sejnowski cognitive conventional works tions tions solve solve solve solve converge converge converge converge converge rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl address address definition evaluation evaluation chain bounded bounded bounded bounded grant grant grant constructed constructed constructed constructed scaling scaling extended wide deterministic clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters runs reduce reduce valued differences sutton sutton sutton sutton sutton practice asymptotic asymptotic constrained constrained strong hard demonstrated variety averaged acknowledgements derive solving solving transitions dept averaging infinite infinite text agent agent agent implies independently stationary communication communication communication restricted approximations forms soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft understanding understanding converges converges converges allowed partial barto barto spaces combining combining iterative foundation building priori batch batch batch batch batch batch batch batch batch batch sciences extension extension prove prove maximize partially partially partially planning uniformly symbols symbols efficiently plots essentially online online online online online online online online online ten summary compact compact compact compact compact compact compact compact compact compact compact heuristic heuristic heuristic moore moore anderson anderson issue issue notation notation quantity usual usual michael michael michael michael michael michael dayan dayan dayan dayan dayan dayan dayan observable observable satisfies extend presents presents presents unlike carried singh singh singh singh singh singh singh singh singh singh singh updating steady preliminary preliminary preliminary mdp mdp mdp mdp mdp mdp hall reducing project applicable workshop naturally possibly adapt adapt adapt analyze thought ensure quantities quantities quantities algo assumes observe multivariate generates finds finds massachusetts asymptotically asynchronous crucial crucial defining improves explanation caused sections widely widely commonly watkins watkins watkins laboratories potentially potentially nsf requirement mod characterize limiting limiting cal plan plan semi semi semi semi semi semi semi jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola summed bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman picture proportion proportion modify rithm chains accepted accepted satisfying satisfying siemens attractive belong intuitive intuitive intuitive generalizes generalizes generalizes continue prentice corollary corollary corollary corollary combines appendix belongs belongs initialize young discounted indicator contraction theoretically horizon tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis exploiting exploiting approximator approximator approximator approximator assigns mdps mdps mdps mdps mdps mdps outlined bertsekas bertsekas bertsekas dramatically approx corporation discount tables tables randomized markovian markovian markovian markovian abstraction amherst personal personal personal forcing adapting representa representa regulation proba lookup lookup lookup lookup lookup supports meet bradtke bradtke vanishes parametrized els holding atr develops ergodic ergodic advantageous payoff payoff payoff sees mcdonnell proposal dissertation executing trol coins aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation aggregation smc maxq maxq eighth ira investigator pew conceptually psyche psyche psyche satinder satinder satinder satinder satinder proving ell exciting exciting tommi tommi tommi tommi tommi presidential xlo xlo chine iai exceptions gation specialize bilities neuronlike debate asa asa asa asa asa asa asa asa interfere eleventh pol absorbed collects collects structed payoffs payoffs payoffs payoffs xls xls xls xls xls xls trl slx slx slx yee yee iyi slo slo aggregated icy ylo 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number error error error state state state state state state state state state state state state state state state state state state state state state state results results results results results units problem problem problem models models hidden performance based based based based based based space space space linear linear linear linear linear linear linear layer case case case case order shown shown values values values values values values values values values values values functions functions functions functions functions functions functions functions method method approach approach point single control control control control large local local local local local test test analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form shows algorithms algorithms algorithms simple simple paper paper small net net net work work task methods methods fig fig step step step step step step step step points points points points points process current trained trained trained trained problems problems problems high memory show section fixed general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states states states states states states states states states states states term note note note note experiments experiments experiments dimensional dimensional university university university university university threshold computation computation computation research defined defined target dynamics table table table table table table estimate computer science prediction left present present low temporal temporal machine machine machine maximum maximum learn learn basis basis nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample sample sample sample sample abstract applied back back computational convergence convergence convergence convergence convergence convergence convergence convergence references due procedure decision decision context introduction action action hand hand behavior behavior behavior behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost difference assume assume assume assume lower representations learned chosen center previous bound cases cases required required multiple good good good good long represent represent represent distributed expected markov fact techniques region region region length errors errors finite finite finite simulations simulations simulations minimum resulting resulting resulting resulting resulting resulting classes ing ing tasks total total regression regression regression regression regression regression regression regression regression regression regression regression sum called regions regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement potential potential made natural global policy policy policy policy policy policy policy policy policy policy policy policy specific true true compute compute goal goal goal goal goal goal goal goal goal goal goal goal goal goal related gain discrete discrete discrete discrete discrete discrete discrete steps accuracy support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support train train train train dependent morgan morgan proceedings proceedings report report report report department loss technique represents represents final final bias cambridge cambridge domain domain domain domain domain domain domain domain environment transition upper upper requires approximate approximate approximate world world world world world speed produce derived derived weighted weighted weighted weighted randomly bounds bounds area velocity types path path path actual actual processes backpropagation backpropagation iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration nature technical technical technical technical assumption complete stable stable actions actions short theoretical require face future future including including including fit fit fit fit fit fit fit kaufmann kaufmann smaller combination combination mlp programming programming programming programming programming programming programming leads representing call iterations iterations iterations iterations iterations iterations making polynomial polynomial polynomial polynomial produced produced run added added added light predict advantage robust robust robust robust robust robust robust takes practical practical include quadratic quadratic quadratic quadratic quadratic quadratic quadratic sejnowski array recently highly compare compare conventional axis smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth converge converge converge converge converge converge achieve sparse grid williams williams williams grant lead suggests correctly correctly locally deterministic deterministic deterministic occurs demonstrate demonstrate conclusion starting starting starting editors editors differences designed designed sutton sutton sutton sutton constrained reduction reduction demonstrated variety variety min introduce explicit construct produces longer sequential transitions changing changing changing explicitly explicitly dimensionality easy slightly adding adding adding agent versus independently restricted lee approximated similarly converges converges barto barto barto smoothing smoothing performing performing epochs spaces fitting fitting purpose add add add intermediate intermediate intermediate assigned advantages figures includes thesis thesis thesis combinations bell recognize automatic prove discuss domains simplicity simplicity straightforward straightforward straightforward middle capable computationally paths successful successful successful schemes reached reached characteristic summary prob success success moore moore moore moore moore return follow strategies comp sampled michael dayan absence modular nips nips giles delayed delayed computes reach reach principles principles policies approximating approximating approximating approximating approximating tesauro tesauro tesauro tesauro cowan cowan poor collection collection singh singh singh replaced hanson accurately accurately accurately accurately recursive game game game issues issues divergence divergence divergence divergence divergence divergence divergence divergence divergence dataset ideas school school tech neu hill hill hill hill hill act man opposite illustrate implementations greedy greedy greedy greedy greedy greedy greedy algo assumes phd phd established massachusetts advanced stop costs costs costs costs trivial analyzed guaranteed growing growing expensive expensive expensive caused reasons lin lin lin lin producing incorporate worst desirable watkins watkins watkins watkins mathematics ion acknowledgement nsf mellon mellon fourth fourth behaviors carnegie carnegie substantially empirically cmu cmu car car car car car car car car backprop backprop frequently rewards rewards maintain polynomials passes pittsburgh anti popular enables replace replace conclude progress converged univ univ contribute bellman bellman bellman ear intractable optimality assign guarantee investigation rithm perfectly repre grows grows reaching extending fails allocation wrong wrong grow grow grow grow grow grow grow grow grow grow grow grow grow grow grow grow grow hope hope ral corner corner games reliably alspector repeat repeat connect connect appendix appendix appendix surprising bad schwartz schwartz schwartz tic tic approximators approximators master augmented theoretically reverse generalizing generalizing generalizing approximator approximator approximator approximator approximator approximator approximator approximator approximator approximator approximator approximator approximator approximator approximator fahlman outlined andrew andrew andrew andrew andrew verify approx summer summer thrun thrun thrun fellowship tables tables benefits propagating abstraction big scenario tight assess backgammon backgammon summarizes ibm robots robots compensate discontinuity regulation expand overhead lookup lookup lookup lookup iri pos pos harder importantly nonetheless indication bradtke bradtke bradtke gordon prevents prevents compu september worked suggestions littman lems stops stops stops fiat appearing nonnegative discontinuous attributed converging curse adaptively opponent clarity concerns boyan boyan boyan boyan boyan boyan boyan boyan executing substitution recognizes coins coins safe scott comer terminates legendre benign benign robustly inaccurate sentation problematic cleveland cleveland cleveland watson allowable lwr lwr lwr lwr lwr lwr costly imum schraudolph schraudolph schraudolph diverge diverge diverge diverge diverge diverge rein argmin exploitation nondeterministic terminate terminate inserting imation jumps backups backups backups puted iter iter iter iter iter iter iter iter impressive diverges absorbing aggressive inadequate trouble trouble mary tational stochas mon eval relied imperfect imperfect safely safely safely safely succeeded geoff exceeding forcement suc farther ams reachable cheaper extrapolate nical dates assure instabilities ccs divergent uation mas immune ifi concentric diverging stepping aea quantizing northeastern yee yee yee yee yee yee mahadevan mahadevan mahadevan rection justin justin justin justin justin enlarge fibre subroutine oval magnified verge sachusetts lucky lucky lucky cessfully marc connell connell connell roach tac diate inforcement neously vmue underestimates manages apl erro bend jasa interme reap 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural input input data data data function figure figure time time time time time time time time set set networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results information information information information information information information information problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based based based based based based based based based based based space space space space space space space space space space space space space space space space space space space space space linear linear linear case case case case case case case order order order order systems systems values values values values values values values values values probability noise noise noise noise noise noise functions recognition method method approach approach approach approach approach approach approach approach approach approach approach point point point point point point point single single single processing control control control control large large large large local rate analysis optimal optimal optimal optimal inputs algorithms algorithms algorithms algorithms simple simple simple simple simple paper paper paper small small feature work work work work work work work task task task task task task task task task methods methods methods methods methods step step step step field current current current current current current current structure structure structure structure structure problems problems problems random random random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar representation representation representation representation representation representation section section fixed line line line line line rule rule states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states term term term term term term note note result result university university university university solution solution solution defined defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial constant constant standard computer computer computer computer distance distance distance science science science science prediction low machine machine machine sets maximum range range press press press learn learn learn learn nonlinear outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied find find find find computational references references stochastic stochastic stochastic due due important important adaptive adaptive decision decision decision context action action action action action action action action action action action action action action action action action action action action action action action behavior dynamic dynamic recurrent recurrent recurrent recurrent recurrent variable variable measure representations learned chosen chosen chosen chosen chosen higher previous previous previous previous previous bound required required good good good long long represent represent represent tree expected expected markov markov make techniques techniques techniques length length length length length length correct correct probabilities finite finite finite resulting ing tasks tasks tasks tasks simulation respect called called regions regions regions regions mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made made policy policy policy policy policy policy represented represented compared compared application application application application cross perform determined experimental experimental goal related related related connected gain approaches approaches approaches approaches mit steps steps steps steps steps steps steps steps steps steps steps steps steps update update update update modeling morgan morgan proceedings proceedings proceedings department department implementation version technique technique technique technique consists consists consists internal internal internal internal internal individual advances advances difficult difficult final delay sequences sequences ai ai ai ai considered cambridge cambridge equivalent environment environment environment environment view solutions limit conference conference conference determine efficient choice choice significant statistics free world world world world world world pages increase give randomly robot robot robot robot levels lines path path path depends depends simply simply simply discussion transformation limited complete actions actions actions actions actions actions actions actions actions actions actions actions actions amount short short short short short nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest common supported theoretical require end instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance future future future future future makes noisy noisy including fit kaufmann kaufmann underlying underlying needed needed needed needed combination account unknown jordan jordan programming programming programming programming head trials trials trials matching representing details details call max window window stored bits international international international magnitude magnitude magnitude idea attention choose choose choose choose description light improved improved recent resolution exact exact advantage robust separate takes takes similarity apply trees varying varying works works works works solve match match match match match correspond correspond trans definition background chain chain chain chain chain separation bounded improvement improvement storage grant grant parts parts trial deterministic deterministic deterministic white critical neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor valued depend editors reward reward reward reward reward reward reward reward reward reward reward differences differences learns learns learns learns learns learns learns learns learns learns demonstrated demonstrated demonstrated proportional turn averaged averaged identification identification identification identification identification identification identification identification identification identification denoted areas produces longer perception perception perception perception perception changing changing metric metric metric metric metric metric metric explicitly explicitly averaging averaging involves involves easy interaction adding adding agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent select choosing detailed open restricted evolution completely past key key earlier performing spaces spaces spaces spaces spaces spaces combining neighborhood neighborhood neighborhood neighborhood roughly roughly distances distances string string euclidean query query query query query query avoid avoid recorded building exploration exploration includes perceptual perceptual perceptual perceptual perceptual perceptual perceptual thesis thesis thesis thesis retrieval instances instances memories memories prove discuss variations domains partially neighbors neighbors neighbors neighbors neighbors neighbors discussions reason reason regular straightforward uniformly uniformly maximal divided divided driven identify literature genetic genetic comparing situation fine receives conf quickly success moore moore moore moore moore moore interpreted dis issue hold gray gray built michael michael michael providing delayed observable highest reach policies policies policies policies policies policies policies approximating acknowledgments load load situations presents unlike create singh singh singh singh requirements experience experience experience experience experience experience experience experience experience experience exponentially limitations limitations game existence scalar fewer fewer fewer fewer matches matches history history history history history history ideas school structured closest trace trace editor man predicting perfect academic store utility utility utility phd phd phd phd finds finds averages established indicating crucial distinguish distinguish sensors sensors sensors publishers adjacent lies handle handle handle turns lin lin lin lin closer immediately watkins watkins watkins potentially involve involve begin res arises recording recording cybernetics incomplete preceding preceding preceding preceding nsf mellon raw raw raw raw geometric geometric improvements carnegie amounts amounts atkeson atkeson atkeson incorrect incorrect incorrect incorrect incorrect rep rewards rewards rewards rewards calculating limiting differs extracting incoming singer inherent sophisticated sophisticated sophisticated windows windows jaakkola jaakkola jaakkola jaakkola progress traces wesley lot naive addison formally animals nat addresses inspired inspired adds wrong wrong wrong biased resulted keeping tishby fail splitting north reliably separating surprising mental forecasting counter offers chooses occlusion discounted insight creating ballard record record passing storing instructions material adopted bertsekas bertsekas bertsekas andrew andrew andrew andrew andrew andrew andrew andrew andrew andrew mind discriminate suffix suffix suffix ence geometrical geometrical solves markovian markovian markovian markovian uniquely bank failed failed tween distinction distinction distinction distinction distinction obtains chapter experiences experiences experiences experiences experiences increment evolve robots alternate chapman execute execute disadvantage disadvantage iri records records records records cation indexed memoryless barrier register voting maintains sized sized sized west suffer rochester rochester rochester rochester rochester rochester knowing dramatic experi worked november walk littman littman littman chris advantageous january slot ate inconsistent christopher attributed builds losing nested maze agents east suffers suffers suffers steven steven ron proportions visit returned vote vote parti colleagues evolving kaelbling creation south fication gathered nih faced faced faced faced tical percept percept percept percept percept percept tenth tenth tory predefined histories triple disadvantages ness inability aliasing aliasing aliasing undesirable schneider distinctions distinctions distinctions distinctions dana satinder satinder kim executes tommi tommi pal pal formalized lose augment tapped percepts percepts percepts percepts percepts percepts percepts percepts wanted emphasizing successes discard bears granularity granularity granularity granularity proaches imperfect mccallum mccallum mccallum mccallum mccallum mccallum mccallum mccallum mccallum perceptually perceptually simplistic snapshot grained overcoming probabilistically accumulates whitehead whitehead whitehead whitehead wasted identi eubank casdagli timal eleventh augmenting deterministically delivers ship finished predecessors unacceptable memorize finely uncover uncover laid dangerous markovjan cup eee jeff sensations prac shadows designers benefited harmful ception sensation olution chrisman chrisman chrisman chrisman mazes mazes mazes disambiguate reused cautious lion inforcement chief chief inefficiency commitment phs cepts degenerates wildly advocates ceptual resents identifi 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural function function function function function function function function function function function function function function function function function figure figure figure time time time time time time time time time time time time time set set set set networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results information information information problem problem problem problem problem problem problem problem problem problem models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space space space space case case case case case vector order order order order order order order order order order order shown shown shown shown shown systems systems values values values values values probability probability functions functions distribution approach approach approach point single single single single single single single single processing control control large large large local local rate rate rate optimal optimal optimal optimal optimal optimal optimal form form form form shows algorithms algorithms algorithms simple simple simple simple simple paper paper paper paper paper paper paper paper paper small small small small small task task task task task task task task task task task task task task task task task task task task task task task methods methods methods fig fig fig fig fig fig cells level level current current trained structure structure structure structure structure structure structure structure structure problems random random random random similar similar representation representation representation equation section section line rule rule general general general generalization generalization generalization parameter parameter real real real real real approximation states states states states states states states states states states gradient obtained term term term experiments result result result university university university university variables variables solution solution research defined defined defined defined defined defined defined found found found target constant table table computer computer computer computer terms science science science science left direction low temporal temporal temporal machine machine machine sets sets press press press learn learn learn learn abstract abstract abstract abstract abstract applied applied applied applied find find find convergence references stochastic stochastic stochastic stochastic stochastic ieee important important adaptive context introduction action action action action action action action action action action action action action action action action action action action action action action action action action action action complex complex complex complex complex complex behavior behavior dynamic dynamic dynamic change difference complexity assume assume rules rules rules measure measure representations learned learned learned learned learned learned chosen chosen part part previous previous required required required required multiple multiple multiple multiple multiple multiple multiple multiple multiple binary long conditions represent represent represent represent expected expected expected markov make fact techniques region proposed length length length length length length length length length length length length length length probabilities probabilities scale scale minimum minimum minimum resulting resulting resulting tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total total total total simulation respect sum sum sum eq eq eq eq eq called called times mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor made natural global policy policy policy policy policy policy policy policy policy policy policy policy knowledge artificial artificial artificial artificial specific specific specific specific specific specific represented represented represented compared define perform determined experimental experimental experimental goal goal goal goal goal related related related related related gain discrete discrete brain approaches approaches mit mit mit steps steps larger larger larger update update update descent selection selection morgan morgan proceedings proceedings proceedings report department department department loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss individual individual individual individual individual advances represents connectionist scheme addition addition sequences sequences ai maps cambridge domain domain domain domain domain domain domain experiment experiment environment environment environment environment environment environment environment hinton solutions solutions solutions transition transition conference conference conference determine efficient requires requires significant free world world world world world world speed give give produce weighted randomly randomly robot robot levels types actual selected selected constraint discussion technical describe describe denote close close complete complete stable actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions finding finding finding finding finding amount nearest effective assumed face future future future makes development kaufmann kaufmann probabilistic typically typically typically needed needed combination reduced account unknown unknown fully jordan transfer transfer transfer programming programming increasing mechanism mechanism empirical empirical leads leads representing representing details numbers international international normalized normalized magnitude magnitude combined minimize minimize description description description description description description description description description description description description description description denotes denotes improved improved directions recent resolution takes takes takes reported reported practical apply apply apply apply moving include identical identical hierarchical subset subset cognitive recently previously previously previously approximately volume solve converge sparse positions positions chain modified generalized generalized generalized grid grid grid grid grid grid grid entire entire parts lead studied scaling occur derivative locally move touretzky occurs generally generally starting starting greater reduce reduce reduce reduce neighbor valued editors editors editors differences measures measures accurate designed sutton moody faster faster learns mechanisms drawn drawn intelligence intelligence minimizing minimizing minimizing minimizing minimizing start exist exist iii manner denoted denoted denoted denoted denoted denoted denoted denoted denoted suppose suppose suppose derive construct produces solving solving sequential dept easy applying agent agent agent agent blocks select select select national family family expressed overlap overlap learner learner learner learner learner learner learner learner learner learner evaluated open open completely completely partition spectrum key key partial barto performing spaces spaces add iterative closed remains initially initially initially initially faces faces faces expect building exploration perceptual thesis thesis thesis color assignment assignment sciences recognize extension maximize maximize maximize mozer specifically specifically specifically domains domains domains domains domains domains domains domains domains domains black partially partially partially characterized characterized successfully planning planning determining straightforward middle importance differ delta successful successful identify identify build comparing fine compact notice notice notice repeated interpreted built play dayan generalize generalize generalize absence modular minimizes minimizes delayed delayed delayed delayed policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies illustrates approximating neighboring tesauro receive presents presents presents minimized employed employed employed employed simpler origin unlike unlike carried powerful transformed poor collection singh singh singh singh singh environments environments environments hanson optimized issues issues lippmann preliminary helpful helpful scalar scalar scalar school school incremental applicable applicable decisions decisions decisions hierarchy hierarchy hill act act circles gradients gradients editor configurations opposite opposite opposite illustrate illustrate changed quantities greedy freedom precise observe academic initialized initialized extent phd phd phd finds defines defines massachusetts years ment costs crucial distinguish derivation derivation navigation navigation navigation navigation adjacent capabilities capabilities tractable stanford stanford stanford lin shared ring widely precisely operators operators desirable arise watkins recognized separately depicted depicted mellon researchers researchers argument argument argument questions behaviors considerably carnegie empirically elman marked adjustable incorporated slower frequently rewards execution price operate controllers vocabulary partitioning rely weigend maximizes maximizes maximizes maximizes replace germany inherent chose findings findings findings focused jaakkola credit credit merging cumulative pyramid room room college pick pick animals discovery discovery addresses addresses discover discover discover discover discover connecting smolensky establish plays lost climbing climbing generality chance mail definitions settings optimally corner corner corner corner generalizes date meaningful governed ensures paul schwartz schwartz schwartz schwartz schwartz schwartz schwartz consequences uni counter candidates approximators approximators approximators advance membership membership discounted discounted infer indicator refers passing erlbaum eqs eqs eqs partitioned discovered discovered discovered ignore balancing generalizing generalizing approximator skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills skills 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acquire heavily savings firstly focuses king micro supplied calculates affecting inherently exclusively exclusively exclusively exclusively boyan executing slices raises adjusts drastically kaelbling informatik goodness skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill skill bonn bonn bonn tenth tenth prescribed prescribed maxq maxq discovers discovers proceeding favors instant notions sebastian sebastian sebastian sebastian sebastian entities sition reactive pay pay pay pay pay pay pay pay pay pay pay pay pay pay pay comprises controllable structuring plain plain plain plain experimentation experimentation experimentation seeks seeks absorbing rationale henceforth executes completes unstructured unstructured grain unimportant bytes bytes bytes bytes bytes kronecker enormous gullapalli ranks safely gation door door door abstractions abstractions abstractions abstractions feudal probabilistically utgoff rooms whitehead decayed composing doors doors byte byte collapse collapse dictates sacrifice ses ses sooner abstracted commit mahadevan offs franklin conceivable ool compactness interleaved acquiring precede greedily conceivably forever suffering glance warrant connell redefine staircase staircase commanded decompo commonalities trades navi 
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state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results units units units units information problem problem problem problem problem problem problem models models performance based based space space space space case order order shown systems systems systems systems values probability probability probability probability probability probability probability probability parameters parameters parameters functions functions distribution distribution distribution method method method processing control control control control rate rate rate rate rate rate optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper feature work work methods methods methods methods methods methods methods methods process process process trained problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems high similar equation equation equation equation equation equation equation equation equation fixed line line line rule rule rule rule rule vectors general general real real real real approximation approximation approximation approximation approximation states theory gradient obtained result university university university university threshold threshold computation computation solution solution solution solution defined defined sequence sequence dynamics estimate estimate estimate estimate estimate estimate standard computer computer computer science science science left temporal temporal machine machine press basis continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample sample sample sample sample abstract applied applied applied applied applied applied applied find find computational computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee ieee ieee procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision context introduction action action action action action action action action action action action action action action action action dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated cost cost search search tion difference assume lower prior chosen chosen type conditions distributed distributed expected expected expected expected expected expected equations equations markov markov markov markov markov markov markov markov markov markov markov make fact fact techniques proposed probabilities probabilities observed observed finite finite finite resulting total total total total respect times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor optimization applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge obtain artificial true true application application desired define define compute compute perform perform goal discrete discrete discrete discrete discrete discrete mit update update update update selection selection proceedings report version version version consists represents represents represents represents represents represents represents difficult difficult cambridge cambridge cambridge domain domain domain domain experiment experiment solutions estimates estimates design transition transition transition transition transition transition transition transition transition transition transition transition transition limit limit san free speed estimated con derived derived conditional developed developed developed processes processes selected selected backpropagation simply discussion discussion discussion feedforward arbitrary denote denote limited corresponds actions actions actions actions actions actions proof finding assumed supported square square objective typically underlying needed needed combination jordan programming programming programming programming programming programming programming programming uniform mode mode leads representing max max max direct choose choose predict denotes discussed property property pair practical apply apply identical subset sejnowski recently recently axis axis tions solve converge converge diagonal diagonal diagonal definition chain grant deterministic white white occurs occurs occurs demonstrate reward reward reward reward reward differences clear sutton sutton sutton moody faster faster asymptotic temperature temperature temperature temperature propose intelligence start decrease program base boltzmann boltzmann suppose pro derive factors laboratory laboratory transitions transitions modeled infinite infinite infinite consisting interaction applying applying select choosing national review updated similarly converges updates updates updates updates barto barto barto slow slow spaces spaces event iterative initially foundation advantages thesis thesis priori color black black holds characterized structural structural determining straightforward straightforward selecting build traditional traditional notice notice return running satisfy involved sampled sampled sampled sampled michael michael michael michael michael dayan minimizes minimizes delayed received received attempt policies satisfies satisfies satisfies satisfies routing routing routing routing explore unlike singh singh exponentially issues mdp mdp mdp mdp mdp mdp hall scalar ideas ideas tech incremental mappings analytically analytically decisions structured complicated complicated workshop analogous act ensure versions greedy greedy panel panel panel assumes observe initialized utility motivated phd phd massachusetts massachusetts massachusetts ment asynchronous asynchronous asynchronous directed defining adapted tive widely style day day watkins watkins watkins watkins involve gradually members rewards rely poisson incorporating semi semi semi semi semi semi semi semi conclude conclude decreased jaakkola extreme bellman bellman bellman bellman proofs proofs proofs optimality optimality optimality optimality count arrival arrival extending extending darken accepted proceeds monotonically service service repeat prentice governed respective intended originally originally schedules schedules tic approximators initialize francisco april discounted discounted contraction shortest horizon route route route route tsitsiklis approximator bertsekas andrew discount discount discount axe axe axe axe axe axe incrementally amherst amherst england realize visited queue queue queue queue queue exam maintained interacting investigating enforce tively siam applicability applicability bradtke bradtke bradtke bradtke bradtke bradtke bradtke bradtke exploratory circumstances circumstances rewritten reinforce opti builds ongoing cliffs tsp steven steven steven steven steven identically englewood heterogeneous heterogeneous trol governing constraining evolves inaccurate derives adequately maxq generaliza ming refine approxima chang sition lowered tran mal ross adap named ecs duff duff duff duff duff duff desire gorithms stochas queueing queueing queueing queueing owing routed rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp rtdp gramming arrivals arrivals plied crites nical unspecified interacts customers customer ors ffi raising umass nondecreasing itera spectively ses holden chronous lll unsatisfactory professor professor bob stations ining slicing cknowle dgement forever lids usefully usefully tac reviewing inspecting leaxning leaxning fort asyn queues queues analogues join 
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algorithm algorithm algorithm algorithm algorithm algorithm number number error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results based based based based space space case case case order order shown systems systems systems systems systems systems systems values values values values values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters functions functions distribution approach control control large rate rate analysis analysis class class optimal optimal optimal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms examples examples methods methods methods methods methods step step step step step step step step step process process process current current current current current problems problems random architecture architecture architecture show show line vectors general parameter parameter real real approximation states states states states obtained note note note result university university university university university computation research research defined defined found estimate estimate estimate estimate estimate estimate computer computer computer science science science science direction presented presented present present temporal temporal temporal machine machine machine machine machine sets sets maximum maximum range press continuous abstract back back back find computational computational convergence convergence convergence convergence convergence convergence convergence convergence references references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee positive positive adaptive adaptive adaptive decision decision decision decision introduction action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action dynamic dynamic dynamic dynamic parallel parallel change change difference assume lower learned part theorem theorem cases cases multiple conditions distributed distributed expected expected expected markov markov markov fact probabilities probabilities probabilities probabilities probabilities probabilities probabilities finite finite finite finite ing ing sum sum sum performed performed times elements means reinforcement reinforcement factor factor factor made feedback feedback feedback policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy obtain negative artificial relative relative provide provide provide location location determined discrete mit mit steps update update update update update update proceedings report report department department difficult addition addition ai maps framework cambridge equivalent equivalent equivalent equivalent equivalent equivalent directly directly estimates estimates estimates estimates transition conference determine determine requires significant estimated estimated increase con con randomly randomly bounds types provided processes processes iteration iteration iteration iteration iteration simply achieved technical technical denote denote corresponds complete complete actions actions actions actions proof proof amount supported theoretical require require ability future including objective simulated pairs underlying needed fully jordan programming programming programming programming ratio york increasing increasing increasing increasing mechanism empirical details call call making stored international idea produced run light predict architectures architectures architectures exact advantage property pair pair pair strategy strategy strategy strategy strategy include include cognitive recently solve match studies converge evaluation locations modified modified modified modified modified modified modified modified modified modified modified modified modified modified modified williams williams storage entire increased grant exists studied alternative move deterministic conclusions depend editors editors reward reward reward reward reward differences differences numerical sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton performs practice learns constrained constrained constrained constrained temperature temperature encoding encoding intelligence variety exist decrease relationship relationship program annealing force question question boltzmann boltzmann explicit appears pro construct solving ways ways sequential estimating estimating infinite remaining unique integrated adding adding agent agent agent agent implies expectation select detailed open operations updated updated updated updated updated updated understanding similarly converges converges converges converges updates diagram diagram key barto barto barto barto barto barto barto barto barto barto barto barto barto barto performing performing classical iterative calculate construction construction construction norm transactions exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration thesis thesis priori assignment prove prove prove holds discussions planning reason determining determining selecting differ encoded computationally literature online receives traditional kind allowing success moore anderson anderson interpreted neuroscience return return dayan dayan dayan policies policies policies illustrates approximating decreasing decreasing employed collection singh singh investigate exponentially game mdp mdp mdp mdp hall helpful incremental incremental incremental incremental office hill act man implementations implementations thought versions precise store store store motivated motivated phd phd attempts attempts massachusetts massachusetts asynchronous asynchronous critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic guaranteed lin lin lin strictly strictly watkins watkins watkins watkins watkins watkins watkins watkins probable probable probable probable probable actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor scientific acknowledgement gradually computers mellon carnegie generic generic generic readily poorly slower rewards rewards rewards rewards pittsburgh maximizes proven achieves decreased implements jaakkola jaakkola baird baird progress credit calls proofs proofs college notes accomplished accomplished equivalence equivalence restrict appropriately air adjusting adjusting accepted modifications optimally selects date prentice initialize initialize foundations foundations discounted discounted ahead late rich verification horizon tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis variants valuable cam executed executed executed executed executed executed dividing robert robert robert robert robert assigns assigns mdps mdps bertsekas bertsekas andrew andrew andrew andrew verify converted converted outline discount discount ties dyna dyna amherst amherst tor tor letting param visited robots num execute execute convert convert interacting sweeps ation bradtke det permit eters infinitely behaves behaves behaves behaves spite coming bridge opti ase invertible cliffs establishes supply val executing englewood cur adapts adapts mcgraw resultant feldman indirectly rent discriminating ues infeasible vergence ace observes recovers recovers modifies mal ities traditionally devel illustrating concurrently desire desire samuel samuel samuel converting lowering seventh gullapalli equiv resort cri neuronlike crites crites crites crites crites crit bers umass umass strained ven cesses ccs react gabriel northeastern chronous alent nction nction checkers optim optim usu probab cision collapses verifying suming maa maa asyn sheds checker commutative bypassing 
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training training training training training training training training training training output output output output output number number number number number number system system system error error error error error error results results results results information information information information information information information information information information information information information information information information information information problem problem problem problem problem models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based case systems systems systems systems parameters noise noise noise noise noise noise noise noise noise weight recognition recognition recognition recognition method method method method method method method method method approach approach pattern pattern processing processing processing large large rate rate test test test test test test patterns analysis analysis inputs inputs inputs inputs inputs form form shows simple simple simple simple simple simple simple simple paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small feature task methods step points process process process process process process process process level level random random random high high representation show show section section section section section section section section line general generalization generalization real real real real real approximation average average average average experiments result result target target target target target target target target target target target target target target standard terms prediction left range range range range range range range range range range press learn nonlinear outputs outputs continuous sample abstract applied applied properties references due propagation introduction introduction hand behavior effect effect effect effect parallel cost cost cost complexity rules rules rules measure prior learned learned learned learned type type good good good good good good good good long represent represent represent represent represent represent represent distributed make make make fact fact correct ing total times means applications applications applications applications applications applications applications applications applications policy knowledge negative artificial represented application application application application application cross compute experimental experimental experimental experimental goal related mit contrast contrast train morgan morgan morgan proceedings report institute internal advances advances advances final bias experiment experiment hinton additional additional additional solutions determine efficient upper significant significant significant basic give give give condition condition levels types types types types types evidence evidence backpropagation nature constraint describe limited limited limited limited limited close close amount common common common common common common effective generate role role role role require eds eds eds eds journal hypothesis hypothesis hypothesis instance instance instance instance future makes makes rumelhart rumelhart rumelhart rumelhart noisy noisy noisy noisy kaufmann kaufmann kaufmann objective objective pairs pairs pairs pairs needed needed needed technology character character special consistent consistent representing representing details numbers making window normalized expert idea choose run added improved improved improve recent advantage property pair pair takes takes takes takes typical typical typical movement reported moving include period period identical sense sense sense subset relevant relevant works differential differential differential differential williams improvement improvement improvement invariant invariant correctly move occurs demonstrate runs runs half half conclusion place place minimal moody moody moody learns california california regularization regularization regularization regularization assuming minimizing minimizing minimizing start averaged averaged acknowledgements suppose pro produces longer optical ways generating ann modeled confidence involves easy easy slightly events shift implies versus versus versus versus versus detailed restricted evolution similarly past combining fitting roughly add false false false false false generation valid valid valid filtering formulation extension discuss discuss holds holds major major major simplicity reason extra included invariance invariance invariance plots plots plots notice notice notice notice interested symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry return return return content content content content hold list bar paradigm providing hypotheses hypotheses hypotheses consisted policies software law poor overfitting overfitting create experience difficulty put put detail hanson lippmann reducing history history referred statistically statistically fundamental notion notion neu math illustrate versions observe art explain explain explain attempts percentage crucial distinguish defining fairly fairly independence worse purposes organized day day day broad incorporate ran inversion read preceding explained virtual virtual virtual virtual virtual virtual virtual reflects applies applies simulate effort employ incorporated incorporated rep price price price spread weigend gen monotonic resource pasadena chose returns returns credit credit hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints cumulative lot trade shifted person person formally restriction approximates concerned concerned proceed caltech establish plays plays systematic systematic saturation saturation saturation consideration odd hit hit resulted resulted viewpoint viewpoint mark mark mark mark mark star ral monotonically affected hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint hint canonical canonical corner days days days days days elimination financial financial financial financial financial financial financial financial financial financial financial mance negligible perfor pat bad bad bad forecasting dif claim enable enable enable treatment treatment april infer reader reader fitness informative informative agree agree agree impact valuable characterization market market market market market market market market market market market market market market acknowledge limitation trading trading trading trading trading trading speaking abu abu abu abu abu abu abu abu abu abu abu abu mostafa mostafa mostafa mostafa mostafa mostafa mostafa mostafa mostafa mostafa mostafa mostafa poses poses year monotonicity monotonicity monotonicity personal german german german german german illustration illustration illustration argue cessing picked picked ultimately ultimately exceed exchange exchange grateful knowing dramatic november november picking remarks sees japanese japanese pronounced pronounced settle contrasts contrasts huberman sym autoregressive capital ultimate characterizes losses daily sliding ready akaike transaction transaction transaction inst translates shortly stationarity stationarity huge modest modest tern ference elaborate enforcing enforcing months markets markets markets markets markets markets markets markets markets markets markets markets markets markets checks aimed coincidence prices prices prices eralization british british formalized formalized teach closing closing implication readers readers news weeks foreign foreign asserts asserts asserts asserts asserts resentations uninformative uninformative amir restricts cial hin swiss swiss negation fundamentals isolate paragraph regularizing currency expertise expertise duplicate duplicate atiya forecast forecast forecast yaser yaser yaser yaser yaser yaser nondecreasing detrimental money money amplifies ouput harmful outperforming decisive validating dollar dollar dollar dollar dollar maih simulta uncommon uncommon ike neously disastrous diminish bought 
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure time set set set set set networks networks networks networks networks training training training training training training training training training training training training training training algorithm output output output output output output number number system system system error error error error error error error error state results results results information information information information problem problem problem problem problem problem problem problem models models models performance performance based based based based based based based based based based based based based based based based based based based based based based space space space space weights linear layer case case case case case case case vector vector shown shown systems systems systems systems probability probability probability parameters parameters noise noise weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit distribution distribution distribution recognition approach approach approach approach approach approach pattern pattern pattern single processing processing processing large large local local local analysis matrix matrix matrix optimal optimal inputs inputs inputs inputs form form form shows algorithms simple simple simple simple gaussian gaussian gaussian gaussian visual paper paper paper small small small size feature feature feature net work work work task methods step step step features features current trained trained trained trained trained trained trained trained trained trained representation show show show equation equation equation equation equation equation equation equation section section section section rule rule rule rule vectors general general general general general generalization generalization parameter approximation approximation approximation approximation theory gradient obtained note note note note note note experiments experiments dimensional university university variables variables variables computation solution solution solution solution solution solution solution research research research independent independent independent independent found found constant constant constant constant constant table table estimate estimate estimate estimate estimate estimate terms prediction prediction prediction direction presented presented presented map sets sets sets sets sets sets sets motion motion motion basis continuous continuous continuous continuous abstract computational computational density density density density density density density density density references component adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction action action complex complex complex complex hand estimation variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance complexity complexity complexity variable variable assume assume assume assume assume assume assume classifier classifier classifier rules rules rules rules measure measure prior prior representations learned part center center previous previous cases cases good represent represent represent represent distributed expected equations region region errors errors errors errors errors errors errors errors minimum minimum tasks regression regression respect multi regions regions regions regions regions mapping mapping means optimization natural global knowledge knowledge knowledge em em em filter filter obtain obtain obtain obtain obtain obtain original original original vol vol samples samples represented represented true true true true provide location determined goal goal related related brain equal equal equal approaches approaches approaches approaches mit mit comparison larger train train dependent dependent dependent dependent modeling selection selection morgan morgan morgan department version individual individual individual individual individual individual advances advances advances exp bias bias bias bias environment hinton additional additional additional additional solutions estimates estimates estimates estimates estimates estimates estimates estimates estimates san san san efficient classifiers classifiers classifiers approximate statistics statistics vision estimated estimated give give derived derived derived derived derived weighted weighted randomly conditional clustering velocity constraint simply biological biological biological covariance normal describe tested limited close close inverse assumption corresponds corresponds corresponds predictions predictions amount amount assumed role main main eds eds eds adaptation adaptation easily easily noisy kaufmann kaufmann smaller underlying underlying underlying underlying underlying combination combination account unknown unknown unknown jordan mlp segmentation special squared squared international experts experts experts experts experts experts experts expert combined combined added improved discussed robust ensemble include identical identical identical identical sejnowski recently engineering compare compare calculated module module module module module module module module module module module module module module tions correspond achieve mixtures mixtures mixtures mixtures modified generalized generalized locally clusters setting conclusion assumptions conclusions depend depend central modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules learns mateo mateo mateo propose integration reduction proportional relationship introduce introduce manner groups groups acknowledgements digit digit digit digit ways ways ways estimating dept dept modeled recall missing missing missing missing missing missing missing explicitly averaging averaging averaging averaging averaging averaging averaging linearly electrical remaining easy slightly consisting gaussians expectation select select independently depending correlated correlated communication squares estimator estimator estimator estimator estimator estimator estimator estimator approximations centered decomposition decomposition decomposition decomposition soft approximated completely similarly reasonable dashed combining combining combining combining combining neighborhood assigned assigned david coupling coupling coupling coupling building handwritten handwritten handwritten handwritten thesis perceptrons weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting assignment candidate candidate coupled partially discussions gating gating gating simplicity reason closely divided divided driven included soc quickly superior superior superior superior notation michael modular modular providing giles giles leading consisted jacobs jacobs tesauro cowan cowan cowan simpler simpler simpler american american american american american american poor overfitting overfitting overfitting estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators hanson hanson hessian preliminary mappings mappings mappings mappings mappings combine relationships relationships reliable reliable func waibel waibel smallest act plausible subsets obvious improving simplest motivated phd integrate brown residual residual residual distinguish nowlan nowlan nowlan berkeley ring incorporate pool opt toronto res res author considerably evaluating evaluating cmu cmu bootstrap capability biologically maintain maintain extensions germany boston age unbiased unbiased unbiased don classifying tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp uncorrelated uncorrelated formally formally lagrange multiplier kaufman breiman breiman siemens siemens biased intuitively ylx alspector performances excellent excellent excellent corre patient appendix sides dependency bad sim sim designing valuable alternatively alternatively switches assigns unified unified unified unified unified summer ple ple ter ahmad ahmad ahmad ahmad ahmad ahmad forced tibshirani tibshirani retraining retraining obtains personal certainty certainty certainty stands stands stands reflected var var var var cohn preserved mathematically uncertain writer writer writer writer individually acquired flip gender disease disease meta discusses enforce tively inversely housing meir meir advantageous lation ping european european european european european european hat coin tors neuneier neuneier calculates concrete ning couplings reality faced appro appro catastrophic translates stacked fore technion decompose extrapolation extrapolation competence competence cient hampshire hampshire forgetting extremes volker volker volker volker volker volker acknowledged structuring duff miinchen gem 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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data function function function function figure figure figure figure time time time time time time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number system system system system system system system system system error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results units units units units units information information information information information information information information problem problem problem problem problem models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based based based based based based based space space space weights weights linear linear linear linear layer layer case case case case case case case vector vector vector vector vector vector order order order order order order order order order order order shown systems systems systems values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition approach approach approach approach pattern processing processing processing processing processing processing control large large large local local local analysis optimal optimal inputs inputs inputs inputs inputs form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms gaussian paper paper paper paper paper examples small size size feature net work work task task task task task methods methods methods step step step classification classification classification classification process process level current current current current current current current trained trained trained trained trained trained structure structure structure problems problems problems problems memory response similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation equation section fixed fixed rule vectors general general general generalization generalization generalization speech speech parameter parameter parameter real average states states states states states states states states states theory theory gradient gradient gradient gradient gradient obtained obtained obtained obtained term term term term term term note experiments experiments experiments experiments university variables variables variables variables variables variables variables computation computation computation computation solution solution research defined defined defined defined defined found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target dynamics dynamics initial initial table table table table estimate estimate standard standard standard standard standard standard standard connections connections science prediction prediction prediction presented presented map map present present present activation nodes temporal temporal temporal temporal temporal temporal temporal machine machine machine sets maximum maximum maximum maximum maximum maximum maximum maximum learn learn position outputs outputs outputs outputs outputs outputs outputs continuous continuous abstract find find convergence convergence convergence convergence convergence convergence density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic due ieee ieee ieee positive procedure procedure procedure procedure adaptive adaptive propagation propagation mixture mixture mixture context introduction introduction introduction complex complex estimation estimation estimation estimation behavior behavior statistical statistical dynamic generated generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change difference variable variable variable variable assume rules measure prior prior learned chosen chosen previous previous previous required binary long long long long long long bayesian bayesian bayesian bayesian bayesian expected expected equations equations equations markov markov markov markov markov markov markov markov markov fact proposed proposed proposed proposed proposed proposed proposed proposed proposed length length length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities forward forward finite finite finite finite finite finite resulting resulting resulting resulting ing tasks tasks tasks tasks tasks tasks tasks tasks tasks computed computed computed computed computed computed respect sum called called means means optimization optimization potential potential natural feedback global global applications knowledge knowledge knowledge em em em em em em em em em em em em em em obtain obtain artificial compared application application application application desired desired cross cross series define define define compute compute compute proc perform perform experimental experimental related related related constraints connected motor discrete discrete discrete discrete discrete discrete discrete discrete power approaches approaches steps accuracy comparison comparison connection update train train descent descent descent modeling modeling modeling morgan morgan morgan morgan report report report version version consists internal internal internal internal advances advances represents connectionist connectionist difficult difficult final final final final layers addition graph graph graph graph graph graph sequences sequences sequences sequences sequences considered considered framework computing computing hinton transition transition transition transition transition transition transition transition transition transition san top top determine requires statistics estimated pages pages increase validation validation con condition derived randomly conditional conditional conditional conditional criterion path actual actual provided finally finally selected backpropagation backpropagation backpropagation backpropagation iteration nature depends simply measured measured technical feedforward feedforward feedforward describe describe denote tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited assumption corresponds complete complete complete predictions amount amount short common effective assumed role main eds journal end easily kaufmann kaufmann kaufmann kaufmann probabilistic probabilistic probabilistic probabilistic probabilistic pairs underlying combination account account account account dynamical dynamical dynamical dynamical fully fully jordan interesting interesting interesting significantly significantly special trials trials trials trials trials trials principle principle language language squared numbers max bottom bottom experts experts experts supervised supervised supervised supervised supervised supervised supervised minimize description predict discussed improve property separate reported reported practical apply apply introduced include inference inference inference inference recently relevant compare previously unsupervised unsupervised observations works works smooth correspond differential trans trans mixtures mixtures chain chain observation generalized generalized lead extended trial trial trial alternative alternative correctly correctly hybrid hybrid touretzky column column setting minimal minimal reduce trajectories trajectories trajectories conclusions depend editors editors moody constrained mateo suggest propose taking presence external sigmoidal labeled min targets targets targets targets targets introduce introduce introduce introduce derivatives derivatives connectivity connectivity acoustic denoted denoted suppose suppose suppose appears relation derive produces sequential sequential transitions ann label dept modeled modeled implement missing multilayer mutual mutual minimization extraction expectation expectation expressed depending depending interpretation interpretation learner solved open updated updated fraction fraction lee soft static static static static static sizes sizes similarly similarly discrimination discrimination partial spaces fitting intervals intermediate string construction classified transactions activations perceptrons strings strings strings strings strings bell bell assignment assignment memories extension automatic maximize mozer mozer specifically grammar grammar grammar grammar gating gating successfully major simplicity columns regular regular regular straightforward hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms suitable modification effectively effectively effectively paths symbols wij successful successful successful miller essentially composed summary refer soc conf cun allowing moore link link interested interpreted interpreted interpreted interpreted interpreted criteria notation involved simplified play absence modular modular modular paradigm paradigm backward backward backward nips nips giles giles maximization extract jacobs jacobs jacobs deal deal tesauro cowan cowan unlike parametric transformed poor production production production difficulty put involving involving involving discriminant discriminant scalar fashion tech links mappings mappings investigated analytically dependencies dependencies dependencies dependencies dependencies dependencies structured structured root maximizing symbolic proved func fundamental fundamental neu induction induction induction hill plausible predicting predicts automata automata perfect perfect thought prototype aspect formal art store epoch simplest averages integrate languages asymptotically directed directed trivial guaranteed phenomena nowlan nowlan nowlan nowlan adapted capabilities capabilities baum lies comparisons processed processed producing strictly style style style ran worst worst bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio mation simard separately begin depicted depicted incomplete recognizing recognizing sun addressed researchers questions flexible generic generic capability introducing share adjustable remove slower rep maxima span controllers controllers rely summarized characterize differs extracting chen chen adjust focused viterbi converged credit credit softmax contextual analogue restriction restrict summing temporally conditioned homogeneous jth royal establish climbing extending air smith smith ranges difficulties adjusting accepted interpret exploit exploit removing ral bourlard effectiveness intuitively adequate corpus alphabet grammars grammars grammars grammars grammars grammars alspector representational iteratively decide dependency vertices evident consequences sim sim 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subnetwork subnetwork subnetwork subnetwork subnetwork propagates stan decompose noticed noticed wellekens wellekens subnetworks subnetworks subnetworks subnetworks subnetworks subnetworks subnetworks subnetworks subnetworks subnetworks stat hij hij hij hij accuracies collecting retrieve favorably italy weakness dealt dealt ito dard respects ply bernoulli mmi mmi supervision cent cent plants cog yoshua yoshua yoshua yoshua yoshua oij gem gem gem gem expressing eval contingencies renders resort synchronously accelerated succeeded quence ditional dsi designer subsequence rectly seeds siftcation requested decoupled intell successors successors inhomogeneous boutlard puting angluin angluin iro markovjan surveys recherche eee informatique levinson levinson levinson intermittent reestimation sondhi stoch dipartimento subproblem subproblem informatica montrdal universitd uated lul subproblems bengioy ult ult indefinite 
#@Bengio_Y,Frasconi_P,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm number error error error state state state state state state state state state state state state results results units units units units units units units units units units units units units units units units units units units units units units units information problem problem problem problem problem problem problem models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear case case case case case order order order order order order shown shown shown shown shown systems systems values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight functions functions unit unit unit unit unit unit distribution distribution distribution distribution recognition recognition method method method approach single single processing large rate matrix matrix matrix form form form shows shows shows shows signal simple simple simple simple paper feature feature feature feature feature feature feature net work work task methods step step step step step step step step step field field field field field features features features features features features features features features trained trained trained problems architecture show show show section section section section section section section section section rule rule rule rule rule rule rule rule rule rule rule general generalization speech speech speech parameter real states states states states states states states states states theory theory theory gradient gradient term term term term term note note note dimensional university solution solution research research log log log log log sequence sequence sequence sequence sequence initial estimate connections phase phase phase machine machine machine machine sets sets sets sets sets sets sets maximum maximum maximum range range range range press learn abstract find find find find computational properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic ieee procedure procedure procedure procedure procedure important important introduction complex hand estimation estimation estimation estimation estimation statistical statistical statistical statistical statistical statistical statistical statistical effect dynamic generated generated generated parallel parallel parallel parallel parallel parallel parallel parallel tion energy energy rules rules rules rules rules rules rules rules rules rules prior chosen higher center cases type required long long long long long long long long long represent represent equations markov markov markov markov markov markov markov markov markov markov markov markov make make fact correlation correlation correlation correlation correlation correlation length probabilities observed observed observed observed observed scale scale finite total human computed computed sum sum sum sum performed eq eq applications em em em em represented represented represented true compared cross cross series series series series series series series series series series series series provide compute compute compute compute proc proc perform goal related related constraints constraints constraints connected connected connected distributions gain gain discrete discrete discrete discrete discrete discrete discrete mit mit connection connection connection connection connection fields train descent nets modeling modeling modeling modeling modeling modeling modeling modeling institute technique technique internal represents represents bias bias addition sequences sequences sequences sequences ai ai ai framework framework framework framework framework framework cambridge cambridge cambridge equivalent directly directly hinton hinton hinton hinton hinton additional additional view curves design design transition transition determine full statistics statistics free validation con con derived derived levels types types product product product product provided finally processes nature biological arbitrary denote tested hmm hmm hmm hmm hmm hmm hmm hmm hmm fast limited inverse complete circuits common effective effective effective end future easily degree degree fit fit simulated probabilistic probabilistic probabilistic pairs pairs reduced reduced account account jordan jordan jordan jordan jordan jordan technology transfer programming ratio special special special special special leads leads call call call max making polynomial idea architectures architectures architectures architectures correlations correlations correlations exact exact exact pair separate separate takes typical subject machines machines machines machines machines machines machines trees trees trees sejnowski sejnowski varying varying works trans address address address address chain chain chain chain chain chain chain chain chain chain chain williams williams williams grant constructed lead studied occur wide loop boundary boundary starting designed clear constrained temperature suggest propose physics iii iii iii connectivity configuration configuration annealing acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann explicit suppose suppose monte carlo modeled pruning pruning pruning pruning implement slightly text spectral spectral scales scales scales scales scales scales scales interaction develop develop minimization expectation expectation versus versus versus versus family family review viewed interpretation influence codes codes operations approximated partition partition partition updates updates updates key slow spaces spaces combining fitting closed remains visible visible visible visible visible visible visible visible visible visible visible visible msec msec symbol degrees degrees degrees degrees coupling coupling coupling coupling avoid usa strings maximize maximize coupled coupled coupled holds characterized reason middle middle middle extra extra extra extra hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms computationally delta delta symbols symbols symbols successful efficiently mackay mackay mackay mackay comparing situation essentially capture summary soc quickly quickly procedures anderson anderson issue sci duration built built built comp comp vary vary michael michael michael michael michael maximization maximization maximization maximization disparity disparity neighboring modelling law powerful poor overfitting overfitting exhibit biases fewer school links rest analytically combine dependencies dependencies dependencies dependencies dependencies complicated complicated analogous naturally naturally transmission onset freedom freedom freedom freedom epoch epoch epoch epoch consist generates simplest submitted massachusetts spin spin inequality adjacent biology glass glass tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable benchmark baum baum baum baum organized arise laboratories acad pitch incomplete nsf mechanics mechanics mechanics integrating percent percent led amounts mod characterize parent enables electric redundancy expectations naive equivalence equivalence forming summing temporally nat flexibility caltech establish clamped clamped clamped chains chains chains chains chains chains chains chains chains chains chains chains chains chains chains chains chains chains occurred siemens replacing familiar loops loops loops exploit imply alphabet continue introduces saul saul saul saul saul saul connect connect connect regard ascent consequences sim belongs lawrence lawrence lawrence lawrence lawrence peterson peterson recog suggesting repeatedly ends roy eqs correcting correcting exploiting reverse jump designing statement dempster dempster baldi baldi vari mechanical mechanical emission emission emission emission street unified summer rubin rubin shorter alternating alternating nition welch welch amherst molecular stands assess chauvin chauvin toy carefully relate mediated conversely cartesian cartesian cartesian cartesian tied tied tied laird laird enforce funded resistors preprint knowing exhibited els things atr mann rabiner corporate solvable inequalities val ackley ackley ackley obey heterogeneous juang juang juang juang juang adjusts distorted sions prone statist counterpart cess tical artificially iterate capturing energies imum noticed elaborate ular fundamentally ables couple statis psyche psyche notably motivates aii aii aii aii aii aii aii aii cog kronecker ulation explosion shortcomings shortcomings shortcomings partic weaknesses trivially resort lend normalizes designer suc bij bij bij bij bij bij bij joining joining joining stolorz stolorz stolorz disparate disparate disparate disparate aaa cda discrim unfolded sider transi dation discus prosodic prosodic jpl cepstrum cepstrum mcclure mcclure shortcoming exert analogs hnction decimation decimation decimation decimation tln tln tln warrant oversampling ail strat countable technometrics putations egy 
#@Jordan_M,Saul_L,
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#*network network network network network network network network network learning learning learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure set set set set set networks networks networks networks networks training algorithm algorithm algorithm output output output number number number number number number number number error error error error error error error error error results results results results units units units units units information information information information information problem models models models models models models models models models hidden hidden hidden hidden hidden performance based based space space weights linear case case case vector vector vector order shown shown values values values values values parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach approach point point point point single control large local analysis analysis matrix optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows gaussian gaussian gaussian paper paper paper examples examples examples small small small small small size size work methods methods methods methods methods methods methods points points points points points process current current current current current current current current current current current current current current current current problems random random random random high high high high response similar architecture show show show equation section section section rule rule rule rule vectors generalization generalization parameter real real real approximation approximation approximation average average average average average theory obtained obtained term term experiments experiments experiments experiments experiments experiments experiments dimensional result result computation research independent independent independent independent defined defined defined found target target target target standard standard computer computer terms science science science prediction prediction prediction prediction prediction left left left phase low sets sets maximum maximum range press basis basis outputs sample sample sample sample sample abstract applied applied computational computational density density density references ieee procedure procedure procedure procedure procedure decision decision decision decision decision decision decision decision decision introduction action action action statistical statistical generated generated generated generated generated generated generated variance variance search search search tion tion tion difference difference difference complexity complexity complexity assume assume assume lower prior part part part part part center cases required represent distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected expected equations markov markov markov markov markov markov region proposed probabilities observed errors finite resulting resulting resulting regression respect performed performed regions regions mapping factor optimization optimization potential global global artificial specific samples true true true true true true true desired provide define compute perform perform active active determined experimental experimental posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints gain gain equal approaches approaches approaches approaches approaches steps steps steps steps steps steps larger larger larger contrast dependent selection selection selection selection selection selection selection selection selection morgan report report department loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss advances joint final final addition framework framework framework cambridge computing experiment experiment experiment experiment additional view estimates design design design design limit san effects capacity determine determine determine determine upper full full choice choice approximate approximate statistics estimated estimated increase increase con weighted weighted randomly randomly randomly randomly conditional conditional conditional criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion area entropy selected selected selected selected selected depends depends sampling sampling sampling sampling sampling normal technical feedforward increases arbitrary tested close actions predictions predictions assumed assumed assumed generate generate main eds eds eds eds square square square square square square square square square square square square square square future future future future future future future future future future future future future future future future future future kaufmann objective simulated probabilistic reduced reduced account account unknown unknown technology mlp mlp mlp ratio york york york uniform uniform uniform principle leads details details call numbers attention choose run added discussed improve recent exact takes typical typical strategy strategy side inference relevant sufficient compare previously observations observations observations observations observations observations observations observations observations observations observations observations observations calculated volume chain chain chain chain chain modified observation observation observation observation grid grid risk risk risk risk risk increased increased grant parts trial trial trial trial trial deviation deviation deviation predicted deterministic white white white white white white white white setting critical critical minimal minimal minimal minimal row row reduce reduce valued measures measures bayes bayes bayes numerical numerical mateo temperature reduction demonstrated intelligence regularization radial radial assuming averaged averaged averaged averaged areas suppose relation relation relation monte monte monte monte monte monte monte derive construct carlo carlo carlo carlo carlo carlo carlo factors sequential sequential sequential multilayer multilayer explicitly simultaneously averaging averaging physical develop develop integrated adding predictive predictive predictive springer expectation select decreases national review depending influence variation variation approximations approximated approximated performing measurements spaces reduces valid valid calculate sufficiently construction construction construction construction construction construction query query query query query query query query query query query query query query query query query query query query query query precision exploration exploration exploration exploration prove uncertainty uncertainty discuss candidate candidate candidate absolute discussions regular selecting importance importance importance society maximal mackay mackay mackay mackay situation situation situation verlag verlag repeated procedures procedures follow quantity sampled nips approximating neighboring receive oriented cowan situations situations wiley transformed create collection collection detail scalar tech project mappings decisions root root root proper func phases smallest gradients concepts necessarily queries queries queries quantities quantities versions perceptton extent arbitrarily defines seconds neal neal neal optimum integrate asymptotically theoretic theoretic theoretic theoretic trivial derivation analytic caused lin ring located mation acknowledgement universal calculations beginning gradually toronto addressed fluctuations reflects collected led led relevance consistency pseudo fed red effort effort marked marked employ dots dots variant variant rely summarized aim popular substantial germany yielding univ univ representative representative benefit redundant redundant perfectly approximates approximates grows grows royal systematic systematic ments chemical familiar mark exploit affected affected ylx ylx ylx ylx adequate nonparametric selects motivation infor published started started sion iteratively intended intended intended demonstration infinity captured facilitate approximators mlps mlps foundations clean informative concentration subsequently border severe reflex saad saad saad ties german german workstation var cohn distri gained uncertain concentrate concentrate maximally integrals hornik hornik hornik sollich sollich sollich sollich sollich sollich distinguished placing elsevier knowing drops experi mea conceptual sharply conflicting unreliable optima semiparametric sian gmd gmd gmd metropolis metropolis metropolis metropolis derives dence physica actively costly costly favors amsterdam derivations sparc infeasible tal crg rmse rmse rmse rmse proce berger berger berger berger berger alexander heidelberg hillclimbing concise fruitful walter walter walter plutowski plutowski plutowski asymptotics frank estima struction selec linden stinchcombe stinchcombe stinchcombe experimen ford ford ford ford dure weber advocated wld iip titterington pare neces surveys 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#@Kindermann_J,Paass_G,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function figure figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output number number number number system system system error error error error error results results results results results units units units units units units units units units units units units units units information information information information information information information information information information information problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based based based based based based weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case order order shown shown shown shown shown shown shown systems systems values values noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight neurons unit unit unit recognition recognition recognition method method method method method method method method method approach pattern pattern point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single single processing processing processing processing processing processing processing processing control control local local test test test test patterns analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form signal simple simple simple simple simple simple gaussian 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trained problems problems problems problems problems high high high high response similar similar similar similar similar representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture section line line line line line line line line line images images images images images general general general speech speech real real real real real theory note note experiments experiments experiments experiments experiments result result university university computation computation solution research research research research found sequence sequence target target target target target target target initial table table table table standard standard standard standard standard standard computer computer terms terms terms distance connections connections connections connections connections synaptic science science science science prediction prediction prediction prediction prediction prediction direction direction presented presented presented map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map present present present activation activation activation activation activation activation activation activation activation activation temporal machine object sets range learn learn learn components outputs outputs outputs outputs outputs outputs outputs sample abstract applied applied back back back back back back references component due due due important important important important important important important important important important important important important important important important important important important important important important important important adaptive propagation propagation mixture context hand estimation estimation stimulus effect parallel recurrent recurrent search tion tion change difference difference difference difference difference spatial spatial spatial spatial spatial spatial spatial spatial lower rules rules rules rules representations representations learned learned learned higher higher higher center center center center previous previous previous previous cases cases type required required required required multiple multiple multiple good represent represent distributed expected expected techniques correct errors errors errors errors forward forward ing ing ing ing ing ing tasks tasks tasks tasks tasks tasks tasks tasks tasks human human sum sum performed performed elements elements elements regions regions regions regions regions regions regions means means potential made made made feedback feedback feedback feedback feedback study study study study study knowledge knowledge knowledge filter filter artificial specific specific specific specific represented true compared application desired cross cross cross cross cross cross cross cross cross cross cross cross provide objects proc location location location perform perform perform perform perform perform perform perform perform perform active active active active determined determined determined determined experimental goal related related connected mit comparison larger connection support support morgan report institute implementation implementation implementation implementation implementation version technique technique technique technique internal internal internal internal code individual advances advances represents represents represents connectionist connectionist difficult difficult difficult difficult difficult difficult layers layers layers layers maps considered cambridge domain domain environment directly hinton transition transition transition transition top determine determine world world vision vision vision vision con con produce coding derived derived derived derived derived derived weighted randomly randomly randomly developed developed developed robot robot area area types types lines actual actual actual actual finally processes evidence backpropagation backpropagation backpropagation depends simply achieved achieved discussion technical tested tested tested predictions amount implemented supported require require require main eds eds journal pixel ability ability future future easily easily easily easily degree noisy including kaufmann smaller smaller needed combination account jordan jordan jordan jordan technology testing testing testing testing testing testing testing testing testing mechanism mechanism mechanism principal principal representing max pre direct making experts experts expert frame frame frame frame attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention produced run added added description description predict predict predict discussed improve directions directions directions exact exact property property separate element element element element typical typical typical similarity similarity reported reported introduced introduced pixels pixels trees relevant relevant relevant relevant relevant relevant relevant engineering interest interest interest interest interest approximately calculated works works tions tions solve mixtures positions positions locations locations grid grid grid grid channels gate entire increased increased constructed constructed constructed invariant scaling suggests extended extended predicted predicted predicted predicted predicted predicted alternative alternative alternative alternative alternative feed feed move move move move width greater conclusions conclusions differences sigmoid sigmoid sigmoid accurate retina retina retina retina designed designed designed peak learns constrained constrained encoding encoding strong hard hard hard mechanisms presence presence presence presence characteristics characteristics characteristics demonstrated demonstrated california selective selective selective selective selective selective selective manner manner manner scene scene scene scene scene scene scene scene scene scene identification program areas appears appears appears appears pro van construct edges edges edges perception perception perception perception optical ways factors sequential describes ann vertical changing explicitly simultaneously simultaneously involves transformations transformations slightly slightly slightly develop develop gaussians applying predictive predictive national national national independently focus focus focus focus focus focus focus focus focus expressed dependence reconstruction reconstruction influence influence influence influence influence influence transform restricted fraction frames frames frames understanding similarly discrimination sign key dashed additive additive additive performing tracking filtering filtering filtering construction foundation views handwritten activations activations activations activations activations activations priori retinal retinal retinal prove mozer mozer coupled absolute absolute partially gating gating gating aspects extra extra extra extra extra closely importance importance differ effectively effectively presentation identify identify comparing traditional traditional road road road road road road road road road road soc contained success anderson interpreted dis giles delayed denker automatically automatically automatically moves policies subsequent subsequent subsequent extract jacobs jacobs acknowledgments oriented cowan employed employed employed employed transformed create create difficulty environments strengths hanson fashion ideas school school rest detectors scaled scaled scaled scaled authors authors reliable comparable symbolic complicated complicated topographic matched saliency saliency saliency saliency 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track navigation navigation nowlan caused spatially spatially turns lin straight implementing tive tive sections shared style broad mation toronto patches depicted auto auto auto incomplete meaning mellon mellon fourth apparent improvements improvements carnegie carnegie elman cmu cmu tional conducted fed fed lack autonomous autonomous autonomous introducing adjustable passed incorrect rep reliability reliability psychological commands howard pittsburgh pittsburgh serve extensions expectations begins summed summed summed sharing sharing irrelevant trade contribute representative benefit benefit ear appearance appearance modify investigation driving driving narrow dynamically mobile reconstructed encoder lecun lecun suppression chance chance city multiplicative multiplicative vehicle vehicle vehicle vehicle contract contract contract serves serves occurring occurring analyzing fail cottrell effectiveness salient salient modifications intuitive presentations motivation infor performances document heavy ensures guarantees guarantees demonstration sim uni jackel captured propagated reproduce multiplied surprisingly eng ahead ahead ahead tracker tracker erlbaum impact explains propagate tures consecutive maintaining compressed anns ple unable users fellowship achieving kluwer deriving lane lane lane munro distinction distinction distinction boser connec hillsdale reconstruct alter alter cns attempted henderson cessing baluja baluja baluja baluja baluja baluja baluja goals graduate guidance pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau crosses crosses crosses efforts scope harder harder zip emphasized emphasized portions portions portions portions portions portions portions portions portions portions portions portions nonetheless nonetheless memo fea knowing knowing dramatic steering prevents travel treating signs experi helps architectural sessions appearing fortunately discontinuous suffers olshausen olshausen accomplish essen concrete incorporation markers resolved arpa decaying implied sions drastically creation creation feasibility vicinity addressing gathered focusing focusing tained ous dean dean dean dean dean ated actively rotational monitored monitored shares shares addi addi lights publishing clutter drawbacks crg tracked impor ogy respects posi versity tant translational tilt motivates army reconstructing highlight highlight tilted ghost confused extraneous extraneous ences premise safety hurt official cre psychol resentations government attend attend doubly photo overcomes dan simi interfere specially party suppressing masking signifi structed tered cluttered cluttered cluttered cluttered cocktail alteration vital vital weaken transforma intercept famous underway shumeet shumeet shumeet shumeet shumeet marking alleviate outdoor disappeared founda exten highway proceeded criticized daca dicted brighter brighter jor egg egg distracting distracting elim accomplishing ena choos phenom 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#@Baluja_S,Pomerleau_D,
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#*model model model model model model model neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure set set set set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number system system system error error state results results information information problem problem problem problem problem problem problem problem problem problem problem problem problem models models based space space space space space space space space space linear linear case case case case case case case vector order order shown shown systems values values values values values values values values values values values values values values values probability parameters parameters parameters parameters parameters parameters functions functions unit distribution distribution distribution distribution distribution recognition recognition method approach approach approach pattern pattern point point processing large local local analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal form form form form shows shows shows algorithms algorithms algorithms gaussian gaussian visual paper small small size work work methods methods fig fig fig step step step step step points points points points points points points field classification process process process process process process level structure structure structure structure structure structure problems problems problems random random random random random random random random random high high similar representation representation equation equation equation fixed rule general parameter real real approximation approximation approximation approximation approximation average theory term note dimensional dimensional dimensional dimensional dimensional dimensional result university variables variables variables variables variables variables variables computation solution solution solution solution solution solution solution solution independent log defined found sequence estimate estimate estimate estimate standard standard computer terms distance distance distance science presented low low maximum maximum maximum maximum maximum maximum maximum maximum maximum press basis basis nonlinear abstract applied find computational density density properties likelihood likelihood references component component stochastic ieee procedure procedure procedure important mixture introduction introduction hand estimation estimation estimation estimation statistical statistical statistical statistical statistical dynamic generated variance variance variance variance variance cost cost cost cost cost search tion tion energy energy energy energy energy energy complexity assume measure word center bound bound bound bound good good binary conditions conditions distributed expected expected expected expected expected equations equations equations equations equations equations equations make techniques proposed proposed probabilities probabilities finite minimum minimum minimum minimum resulting resulting total respect respect sum performed eq eq eq eq called means means means factor optimization optimization potential study em em original original original vol artificial specific samples true compared define location location active active active active active active active active active active active active determined determined determined determined experimental experimental posterior constraints distributions distributions distributions distributions connection fields fields support selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection morgan proceedings loss advances represents difficult final final final exp exp exp exp exp scheme scheme scheme sequences sequences sequences sequences framework framework framework equivalent experiment directly additional solutions estimates limit limit limit conference determine determine determine efficient efficient efficient upper upper upper upper requires requires approximate approximate statistics statistics statistics statistics free free free free free free free world estimated estimated estimated estimated pages pages condition condition derived derived derived derived derived derived derived derived derived randomly randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering levels criterion criterion criterion entropy entropy entropy entropy entropy entropy finally processes selected selected selected iteration iteration depends depends sampling constraint biological achieved covariance normal group group group inverse assumption assumption complete effective implemented assumed require require main square cluster cluster cluster cluster cluster cluster cluster cluster kaufmann simulated typically pairs pairs reduced account unknown unknown unknown unknown unknown unknown block programming significantly york consistent consistent structures empirical empirical empirical empirical empirical principle principle principle leads leads leads squared numbers international combined light denotes population discussed correlations exact robust robust takes similarity similarity similarity similarity similarity strategy strategy strategy side pixels pixels sense sense inference subset subset subset relevant dimensions dimensions dimensions dimensions calculated calculated calculated calculated calculated yields yields correspond correspond diagonal chain separation symmetric constructed expression expression expression scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling alternative deterministic clusters clusters clusters clusters clusters white half half conclusion minimal minimal assumptions assumptions reduce valued depend competitive central central interactions interactions measures temperature temperature suggest propose hard reduction reduction reduction minimizing minimizing minimizing min decrease iii averaged averaged introduce derivatives derivatives derivatives groups minima program program program annealing base question question denoted explicit explicit explicit derive solving solving factors estimating distinct metric metric metric metric metric missing explicitly explicitly coordinates coordinates coordinates coordinates simultaneously simultaneously physical dimensionality slightly minimization minimization shift quality quality blocks expectation boolean potentials potentials potentials potentials potentials letters yield yield family family family independently formation review stationary squares squares estimator estimator estimator solved densities evaluate restricted approximated approximated approximated completely partition partial partial calculation additive classical normalization convex purpose distances distances calculate calculate calculate calculate calculate calculate query query coupling avoid expect priori coordinate inter inter assignment assignment assignment assignment subspace sciences determines discuss absolute 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mechanics robustness explained questions reflects relevance dark dark amounts parameterized parameterized lack prototypes exhibits summarized extensions sums germany deviations simultaneous simultaneous wesley multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional yielding phenomenon acquisition acquisition uncorrelated uncorrelated saddle addison assign modify modify investigation restrict restrict circular addresses discover discover impossible grows arranged generality eliminated kullback ments replacing interpret scoring scoring tishby exploit belong belong krogh combinatorial combinatorial hertz hertz embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding respective displayed regarded guarantees uni facilitate 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#@Buhmann_J,Hofmann_T,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input input input input input input input input input input input input input input input input input input data function function function function function function function function function function function function function function figure figure time time set set set set networks networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output units units units units units units units units information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem problem based based weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer case case case case case case case case vector vector vector order order order order order order order order order order shown shown shown shown values values values probability probability probability noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions neurons neurons unit unit unit unit unit unit unit unit distribution distribution method approach approach approach approach approach approach point single single single processing processing processing processing local local neuron analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs form form form form form signal signal signal signal signal signal signal algorithms simple gaussian gaussian gaussian gaussian gaussian paper paper paper small small small size net net work work work methods fig fig fig fig fig fig points points process process process level structure structure problems random random random high similar similar representation representation representation architecture section rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors general general general general general speech speech speech speech parameter average average average theory theory gradient gradient gradient obtained term term term term term term term term dimensional result university threshold variables variables variables computation computation computation solution independent independent independent independent independent independent independent independent independent independent independent log log defined dynamics terms terms synaptic node node node node presented low nodes object maximum press press learn position components components components components components components components components components outputs outputs outputs outputs outputs outputs outputs outputs abstract computational convergence convergence convergence density density density density density density density references component component component component component stochastic stochastic stochastic adaptive propagation mixture introduction effect effect effect dynamic generated variance variance tion difference variable variable variable rules rules rules rules rules signals signals signals signals signals chosen chosen higher higher higher higher higher part part part previous bound cortex long conditions represent expected make make make fact fact fact techniques forward scale simulations minimum resulting resulting resulting multi performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq called times mapping mapping mapping mapping natural applications knowledge knowledge obtain original original vol artificial specific application cross cross series series provide rates proc proc goal distributions distributions distributions gain mit contrast descent dependent source source morgan institute department synapses code individual individual individual individual individual bias bias considered computing computing equivalent directly curve curve curves san stage effects capacity choice approximate statistics statistics con produce produce condition channel derived derived criterion entropy entropy entropy entropy entropy entropy entropy entropy entropy product provided finally processes depends depends achieved measured discussion discussion arbitrary tested transformation transformation transformation limited close inverse inverse finding common require require eds eds adaptation sensory sensory kaufmann objective objective pairs underlying hopfield combination unknown unknown coefficients coefficients transfer york increasing increasing structures matching matching leads representing making decay decay decay polynomial idea added sources sources sources sources sources sources sources sources sources sources sources sources sources denotes discussed separate separate separate takes identical sense sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski unsupervised unsupervised approximately calculated match studies converge converge achieve separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation bounded bounded lead lead concept occur suggests extended matrices feed deterministic occurs column column flow flow starting starting row row hebbian hebbian hebbian hebbian valued sigmoid sigmoid peak performs performs performs performs performs performs performs performs moody weak encoding propose reduction sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal california california turn assuming ica ica ica ica min derivatives manner minima acknowledgements pro pro written written perception laboratory dept changing segments linearly linearly linearly infinite involves unique mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual formed yield family focus expressed formation communication solved detailed detailed detailed evaluate forms forms static static completely suggested converges partial delays expansion expansion expansion roughly filtering filtering advantages recorded thesis priori priori usa bell bell bell bell bell bell bell blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind plotted illustrated discuss absolute tests determining capable capable wij wij wij wij wij wij successful situation situation online online ten road kind contained success success sci sci comp bar involved sampled write absence providing delayed highest highest maximization maximization maximization principles principles attempt illustrates mixing mixing mixing mixing decreasing receive diego transformed limitations issues rest project applicable tanh tanh tanh tanh tanh tanh statistically statistically statistically statistically hill perfect ensure singular olfactory logistic logistic taylor hebb ith multivariate mixed mixed mixed mixed mixed arbitrarily residual residual piecewise theoretic theoretic crucial derivation unstable unstable fairly slope slope slope biology independence sys satisfied shared forces consequence separately acad calculations toronto lowest linsker linsker fluctuations outer reflects people led amounts amounts orders passed passed passed music continuously rep anti anti anti anti anti anti anti anti popular extensions enables redundancy redundancy redundancy converged converged wesley univ lot don room addison ratios appropriately linearity linearity linearity linearity narrow recover concerned jth grows platt platt systematic dealing dealing khz adjusting proceeds odd familiar grow resulted hope removing removing neurobiology reasoning monotonically monotonically salk salk salk intuitively constructive natl moments moments moments substituting reliably interference separating recovered becker becker becker paul ascent tic multiplied permutation permutation permutation jolla jolla steepest messages statement hart inf balanced vari pdf pdf pdf pdf dividing speaking mind achieving basically deriving centre exception superimposed individuals affects causal decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation jacobian jacobian principled community insights cessing learnt deconvolution deconvolution terrence terrence terrence terrence terrence mediated picked concentrate altered covered barlow barlow barlow barlow barlow inverting det det durbin jutten jutten jutten jutten jutten unpublished unpublished manuscript coming sigmoids expansions fiat pdfs pdfs saturated photoreceptors transforming converging pouget viola reflecting determinant determinant supplied sharply sen atick atick partly dedicated anthony anthony anthony anthony anthony symmetrical tended degenerate degenerate transpose suffice inde edition mcgraw differentiate ance dent carrying indepen analyse noiseless maximisation maximisation maximisation maximisation maximisation adv schraudolph schraudolph schraudolph diverge linearities linearities linearities entropies unaffected pendent entering herault herault herault herault comon comon comon comon comon dominate entered forthcoming advice rigorously maximising maximising maximising maximising maximising maximising fac terry digitally wii noises stays positioned analogously maximise maximise maximise maximise maximise supplies stochas expands duce numerator generalised minimising minimising minimising yix yix presumed uninformative uninformative cumulants cumulants indebted didn lacks superpositions alterations minimally belew degeneracy degeneracy torrey pines criticism alexandre dition neut jacobjan transmitting transmitting tackled transmits transmits sory neuromimetic factorim factorim papoulis papoulis papoulis faggin faggin scrambled microphones tally incidentally ques suggestive redun cently calibrating tence caveat maximises ejnowski ecological dant vlx nici 
#@Bell_A,Sejnowski_T,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure time set set set set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output state results information information information information information information information information information information information information problem problem based space space space weights weights weights linear linear layer layer case case vector vector order systems systems values values values probability probability weight weight weight weight neurons neurons recognition approach approach approach approach image single processing control large local neuron patterns class matrix matrix form form form shows algorithms algorithms simple simple simple simple paper small size feature feature feature feature feature net net net net work task points features features features features features process random high high high architecture equation equation equation section rule rule rule images general approximation approximation average average average gradient note activity activity activity activity activity activity activity activity dimensional university computation computation solution log log found dynamics initial constant computer terms connections connections node node node node node node node node node node node node node science prediction prediction prediction left left present phase activation activation activation activation low low nodes nodes nodes nodes nodes nodes nodes nodes nodes sets learn learn nonlinear nonlinear nonlinear abstract applied computational computational references due ieee positive context context introduction action hand effect parallel search tion tion tion variable measure prior representations representations representations representations representations representations representations representations center bound multiple multiple cortex binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed equations equations equations fact region proposed scale ing computed sum regions regions means means factor factor optimization optimization optimization global knowledge obtain obtain original original specific active gain gain gain gain gain equal update support support morgan proceedings institute department version technique individual advances advances joint connectionist bias bias addition computing environment directly view san san san san bit conference upper significant approximate pages pages pages weighted lines lines entropy entropy entropy entropy entropy entropy entropy entropy entropy finally nature inhibitory inhibitory constraint biological biological achieved covariance covariance feedforward feedforward limited close close excitatory implemented require require adaptation adaptation adaptation journal ability ability kaufmann objective objective needed needed account account unknown fully fully fully significantly significantly mechanism mechanism mechanism empirical pre pre pre inhibition inhibition inhibition inhibition international magnitude architectures improved improved improve improve directions separate lateral lateral introduced identical quadratic quadratic sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive engineering unsupervised unsupervised unsupervised unsupervised volume volume volume studies achieve sparse sparse separation observation occur derivative derivative alternative clusters clusters clusters conclusion place hebbian competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive editors editors interactions numerical performs exponential faster practice mateo suggest strong strong mechanisms mechanisms mechanisms demonstrated california proportional proportional turn exist relationship relationship relationship acknowledgements digit written plot plot laboratory stability stability vertical mathematical distinct implement scales interaction interaction interaction adding minimization extraction extraction competition competition competition competition competition competition competition competition competition competition correlated correlated interpretation interpretation codes controlled labels approximated activities digits digits digits digits discrimination past remains intermediate advantages handwritten handwritten bell bell inter blind extension illustrated prove discuss discussions computationally computationally computationally identify detect efficiently schemes schemes schemes schemes comparing identity orthogonal excitation excitation cun prob interpreted neuroscience classify classify running content providing giles denker predictor predictor illustrates extend cowan diego diego diego hanson plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity maximizing trace implementations ensure logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic observe simplest simplest preference improves biology expensive expensive expensive reasons purposes forces gradually localized localized localized depicted amounts capability employ frequently ity maintain anti fall redundancy begins wesley classifying leen leen leen addison appropriately zemel discovery repre establish establish fails fails convenient simplify attractive grow neurobiology splitting splitting salk salk salk intuitive intuitive intuitive financial separating introduces equals paul ascent arrangement arrangement jolla rich informative storing valuable discovered fly lem informa discount guyon guyon gaps medium medium seek seek superimposed chapter letting clustered decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation constrain factorial schmidhuber schmidhuber gained gained interacting terrence terrence terrence terrence mediated mediated mediated mediated mediated mediated mediated mediated mediated mediated mediated mediated differentiation denver denver sized preserve barlow barlow inversely indication durbin stimulating saturated saturated saturated autocorrelation stochastically viola diffuse diffuse suppress evenly ally neurobiological complement factorization sis relaxed differentiate unusual scatter prominent discovers inappropriate maximisation objectives schraudolph schraudolph schraudolph schraudolph schraudolph schraudolph schraudolph plastic plastic subnetworks entropies pew sentations mediate nonlinearly terry conveys optimiza mitchison dreyfus differentiated interfering personnaz flanking itive unary interfere predictability questionable tives batches decorrelating decorrelating discriminants alterna resorting succeeds slowed factorize conventionally decorrelate miall nonmonotonic weigh decoupling competi nonadaptive nonadaptive ignorance compet nici 
#@Schraudolph_N,Sejnowski_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure 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optimal optimal inputs inputs inputs inputs form shows shows signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper paper examples size size net net net net net net work work work task task methods methods methods step step points points points points points field field field field field field field field field field process current current current trained trained trained trained trained trained trained trained trained structure structure problems problems problems problems problems similar similar architecture architecture show equation equation section fixed fixed fixed fixed fixed fixed line vectors general general real approximation approximation approximation average states states states gradient gradient gradient gradient gradient gradient gradient note experiments dimensional dimensional dimensional dimensional result university university variables computation computation computation computation solution solution solution solution solution defined defined target dynamics dynamics dynamics dynamics standard computer connections connections science prediction prediction prediction prediction prediction prediction prediction left direction direction presented phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation low frequency temporal temporal temporal temporal temporal temporal temporal sets learn learn learn learn learn position position continuous continuous sample abstract applied back back back computational convergence convergence analog analog properties references ieee ieee important propagation introduction complex complex complex hand hand behavior behavior generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion difference difference complexity signals signals learned learned learned higher higher higher part previous previous multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple good equations equations make fact techniques techniques techniques techniques forward forward forward forward simulations simulations resulting classes ing ing tasks tasks tasks tasks simulation computed respect regions mapping mapping mapping mapping means dimension dimension global applications filter represented desired desired desired desired desired desired series provide provide perform approaches steps steps comparison fields train train train train train descent dependent nets nets morgan proceedings institute institute technique consists advances difficult difficult layers layers layers delay delay delay delay scheme sequences considered framework framework framework framework framework directly curve curve curve additional view design limit limit limit limit limit limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san san san speed pages pages pages con produce developed criterion actual selected iteration iteration iteration simply normal feedforward feedforward feedforward feedforward feedforward feedforward feedforward arbitrary arbitrary arbitrary fast stable stable stable stable stable stable stable stable stable predictions predictions short short common supported journal journal easily makes kaufmann pairs pairs pairs underlying needed needed hopfield hopfield dynamical dynamical dynamical dynamical dynamical dynamical functional functional fully fully projection york head matching leads leads details iterations pre window window stored international magnitude idea produced pair pair separate typical movement practical apply moving moving moving include include side engineering dimensions teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher calculated volume volume volume works works solve converge converge differential definition williams williams storage grant amplitude parts feed feed locally locally move touretzky deterministic deterministic deterministic white half starting place trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories editors editors tangent clear moody practice learns learns mateo propose propose physics external reduction reduction cycle cycle cycle demonstrated california california california solid solid exist targets targets targets derivatives force force attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor explicit suppose appears van van van van longer ways generating generating plot plot stability stability stability stability stability dept multilayer explicitly explicitly explicitly coordinates linearly infinite physical physical transformations easy adding adding adding springer cycles cycles national independently review reconstruction reconstruction reconstruction reconstruction showed showed approximations approximations evolution forms understanding suggested partial dashed dashed dashed epochs delays purpose add closed closed valid intermediate initially visible visible visible visible visible visible visible visible visible visible visible visible construction avoid existing existing existing existing existing thesis combinations activations activations usa sciences determines coupled discussions determining straightforward capable differ successful successful oscillatory attractors attractors 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assumes store store store store simplest phd chaotic chaotic chaotic chaotic defines brown cos separable separable separable unstable unstable unstable unstable unstable unstable unstable waveform briefly reasons inside inside inside inside perspective straight tive choices mathematics acknowledgement universal universal circle circle demonstrates author addressed conjugate requiring behaviors offset embedded peter autonomous autonomous autonomous autonomous autonomous introducing detecting treated dots incorrect incorrect ity berlin differs popular comments baird traces shifted notes japan summing recover recover dynamically dynamically reconstructed discover turned spiral difficulties overcome fan abilities nearby fail methodology disjoint imply cottrell cottrell cottrell cottrell cottrell cottrell optimally embedding embedding embedding embedding embedding embedding excellent recovered periods washington den originally offers viewing viewing approximators approximators iterated 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#@Cottrell_G,Tsung_F,
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time set set set set set set set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training output output output output output output output output output output output number system system system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state results results results results results units units units units units units units units units units units units units units units information information information information information information information problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based space space weights weights weights weights weights weights weights weights linear linear linear linear layer layer layer layer layer layer case case case order systems systems values values values values values values probability probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method approach approach approach pattern pattern pattern point single single processing processing processing large large large large local local local local local local local local local local local local local local local local rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix optimal inputs inputs inputs inputs inputs inputs form form form form form simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples examples small small feature work task methods methods step step points points points points points points points level current trained trained high high high high high representation architecture architecture architecture architecture architecture equation line line line line rule generalization generalization generalization parameter parameter real approximation approximation approximation approximation approximation approximation states theory theory gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained term term term note note note note note dimensional result result result university university university variables solution research research log log target target target target target target target target target target target initial initial initial initial initial initial constant constant constant constant table table table table table table estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard standard computer computer computer computer computer terms terms terms connections connections science science science science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction left presented presented present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation activation activation low low low low low low low sets sets sets sets sets maximum maximum maximum maximum maximum press learn learn learn basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs abstract applied density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due ieee ieee ieee positive mixture mixture mixture mixture complex statistical effect effect effect generated generated generated generated generated variance variance variance variance variance variance variance variance variance variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost cost change difference complexity variable variable assume rules measure prior learned higher higher higher bound cases multiple multiple multiple represent represent represent distributed distributed distributed bayesian bayesian expected expected equations equations equations markov markov make techniques region region correlation correlation correlation observed observed observed errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors forward forward scale minimum minimum minimum minimum resulting resulting total regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect multi sum sum eq eq eq regions regions regions regions regions regions mapping factor made natural global applications obtain obtain negative negative vol artificial specific specific specific samples true true true true compared desired cross cross cross cross cross series series series series series series series series series compute location location related connected connected connected connected connected distributions equal accuracy contrast contrast update update update update update train train descent descent descent descent modeling morgan proceedings proceedings proceedings report institute institute department department department advances represents represents connectionist connectionist connectionist exp exp bias layers delay considered considered framework framework framework framework computing computing equivalent directly additional additional additional solutions estimates estimates estimates estimates estimates estimates estimates estimates estimates san top bit conference conference conference full full full full significant significant significant significant significant significant approximate approximate world estimated increase validation validation validation validation give give produce derived derived weighted weighted weighted weighted weighted weighted weighted randomly conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional levels actual provided provided finally finally backpropagation backpropagation backpropagation backpropagation sampling sampling simply simply simply discussion discussion covariance group limited limited corresponds corresponds complete complete complete predictions predictions predictions predictions predictions predictions finding finding effective effective assumed assumed assumed assumed shape shape generate generate supported require eds eds eds eds square end end end end future future future easily rumelhart rumelhart rumelhart rumelhart rumelhart noisy including kaufmann typically pairs smaller underlying underlying underlying underlying underlying underlying combination functional transfer significantly edge increasing uniform uniform uniform uniform uniform principle squared squared squared squared squared squared squared squared squared squared squared squared squared details details details direct making international international international bottom early minimize choose choose predict denotes architectures improved improved improved discussed correlations resolution exact exact exact robust separate separate separate separate takes typical apply apply apply apply apply cognitive cognitive highly highly varying volume volume tions smooth correspond evaluation evaluation evaluation evaluation evaluation evaluation evaluation chain generalized risk entire increased grant intensity intensity concept scaling suggests deviation predicted predicted predicted predicted predicted feed locally locally width pass demonstrate demonstrate demonstrate place place row row row row row row reduce reduce depend measures accurate bayes designed clear exponential exponential exponential constrained drawn drawn drawn demonstrated demonstrated solid solid regularization assuming assuming assuming start iii iii iii iii iii iii iii iii iii iii iii averaged averaged targets targets targets derivatives connectivity connectivity connectivity minima minima explicit monte derive construct carlo estimating vertical modeled confidence confidence confidence confidence pruning explicitly simultaneously averaging involves text adding gaussians applying applying formed quality quality quality quality competition competition competition national communication overlap viewed interpretation influence variation densities evaluate forms forms understanding understanding understanding approximated completely updates allowed past past past past reduces fitting intervals roughly roughly roughly add add add initially initially foundation david david david david david avoid existing figures coordinate extension illustrated maximize variations discussions characterized simplicity straightforward uniformly modification divided post post comparing reached receives summary traditional traditional prob interpreted interpreted interpreted stopping split split split lie sin sin sin manifold manifold manifold manifold manifold manifold manifold bar bar vary vary write usual nips nips quantization quantization quantization quantization quantization leading subsequent approximating approximating acknowledgments bars bars bars bars bars bars bars bars bars bars bars origin parametric parametric poor overfitting overfitting overfitting overfitting overfitting overfitting create access experience involving dotted dotted dataset dataset helpful scalar reducing ideal ideal scaled office root root maximizing tanh tanh tanh oscillation func phases phases phases phases phases momentum coefficient naturally predicting quantities assumes improving mixed mixed percentage residual residual residual indicating great rows rows defining improves nowlan independence starts shared easier filtered constructing incorporate incorporate bishop bishop bishop bishop bishop bishop potentially involve mechanics summation considerably composite composite evaluating bootstrap dark dark offset offset amounts parameterized parameterized parameterized parameterized introducing share employ employ frequently outliers http http passes anti characterize characterize weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend incoming deviations wesley wesley wesley summed extreme don www www addison addison addison conditioned resources concerned naval flexibility grey grey familiar moment abilities occurring obtaining obtaining obtaining definitions monotonically motivation inferior elimination analyses embedding embedding embedding financial introduces predictors forecasting forecasting forecasting forecasting colorado colorado colorado colorado colorado colorado lawrence iterated iterated francisco discounted arrive wolpert wolpert erlbaum eqs eqs eqs eqs pearlmutter santa santa std std std std lem leaving drop logarithm listed listed fellowship aston equivalently suboptimal feeding feeding feeding feeding residuals additionally ease personal avoided avoided demon auxiliary auxiliary auxiliary auxiliary auxiliary reflected pub pub ftp ftp ftp ftp chauvin chauvin impose graduate uncertain boulder boulder emphasize differentiation conversely enforce minor durbin mini stops picking chris attempting dropped dropped lists laser laser laser laser fft beneficial beneficial edited html html distorted suffice multimodal constraining constraining thing halves halves steve birmingham unimodal unimodal monitored mle bootstrapping meaningless mization pull fractional frozen tailored trick andreas andreas andreas andreas andreas andreas andreas extremes darker traditionally buntine buntine buntine ecs posterjori golden nix nix nix nix nix nix nix nix icnn emphasizes ixi ncrg poorer justifies dave dave freeze sudden anonymous gershenfeld gershenfeld gershenfeld gershenfeld predictability ume orlando strate barak heterogeneity ser 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#@Nix_D,Weigend_A,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure time time time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number system system error error error error error error error error error error results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information problem problem problem problem models models models models models hidden hidden performance performance performance based space weights linear linear linear layer layer case case case vector vector vector vector vector vector order shown shown shown systems systems values values values values values parameters parameters noise weight weight weight weight weight functions functions neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition point image single single processing processing local local neuron neuron neuron neuron neuron rate test test test test test analysis analysis analysis analysis class algorithms algorithms algorithms algorithms algorithms simple gaussian examples examples examples examples examples examples examples examples examples examples small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net work work work task step step step points points field field classification classification classification classification classification classification process current trained cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure structure structure structure structure structure structure structure structure structure response similar similar representation architecture section section fixed line line line rule rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors general approximation approximation approximation approximation approximation approximation obtained obtained term term note note note note note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university threshold variables computation independent independent defined defined found initial initial constant constant estimate standard computer computer computer distance distance distance distance connections connections connections connections connections connections connections connections connections synaptic synaptic node node science left left map map map map map map map activation activation machine maximum learn learn learn learn learn learn components basis basis basis abstract applied applied computational computational density references component component positive important decision propagation introduction introduction hand hand behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic tion tion tion change complexity complexity classifier measure measure prior learned learned learned learned type type good good good binary represent represent expected correlation correct errors forward simulations simulations simulations simulations resulting ing tasks simulation simulation simulation simulation simulation simulation respect respect multi sum sum sum performed eq eq eq times times regions regions regions reinforcement dimension natural study knowledge knowledge knowledge knowledge vol vol vol artificial artificial artificial samples represented compared compared compared application cross receptive receptive receptive receptive receptive receptive define proc proc proc location location active eye connected connected connected connected connected equal equal accuracy connection connection connection connection connection connection connection connection connection connection connection connection connection fields fields fields fields update train source source selection morgan morgan report report report report department version consists advances represents difficult scheme scheme graph ai maps maps maps maps maps maps maps maps cambridge cambridge additional additional additional san stimuli stimuli stimuli efficient upper upper choice choice choice statistics vision basic con weighted randomly criterion lines entropy actual actual provided provided finally finally simply simply associative achieved measured technical technical fast rbf rbf nearest nearest nearest nearest shape eds adaptation adaptation adaptation square square instance instance instance cluster cluster development including including including kaufmann mlp ratio structures structures structures structures structures structures structures structures structures structures structures structures matching matching matching matching matching principle principle principle leads leads principal squared squared squared squared representing representing representing representing details pre pre pre pre supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised idea idea idea idea choose run perceptron architectures improved discussed recent recent exact advantage advantage advantage reported reported lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral practical apply introduced introduced include hierarchical sejnowski sejnowski sejnowski cognitive recently dimensions conventional conventional unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised calculated calculated calculated yields yields speaker speaker sparse definition positions separation separation symmetric modified modified bounded improvement alternative correctly correctly locally loop loop loop loop loop loop loop clusters white conclusion hebbian hebbian hebbian hebbian hebbian neighbor neighbor neighbor neighbor neighbor competitive competitive competitive competitive competitive central measures measures peak moody moody mateo largest largest drawn drawn radial radial radial turn assuming start plane decrease targets manner program reference pro edges label tuned distinct missing linearly slightly consisting consisting adding applying competition family family squares labels organizing organizing forms margin updates calculation epochs epochs epochs epochs epochs epochs epochs epochs neighborhood neighborhood neighborhood interpolation interpolation distances calculate kohonen kohonen kohonen kohonen kohonen classified classified topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology avoid existing existing figures priori priori assignment assignment batch memories recognize black neighbors neighbors neighbors neighbors neighbors neighbors characterized compression identified closely delta delta delta build situation vowel reached refer verlag repeated repeated allowing heuristic heuristic success stopping stopping superior classify manifold manifold manifold manifold manifold manifold built quantization quantization quantization computes decreasing situations situations employed unlike layered collection updating updating replaced fewer fashion school school rest project topographic neu examined smallest circles circles math closest man perfect perfect perfect perfect perfect perfect perfect changed adjusted der som som taylor separated separated separated mapped hebb epoch consist submitted motivated serial serial serial attempts mentioned indicating growing growing growing growing growing growing answer cascade cascade benchmark benchmark benchmark handle starts starts berkeley sites incorporate worst depicted depicted radius mellon outer outer outer carnegie reflect relevance cmu cmu cmu cmu cmu cmu readily readily backprop backprop employ employ dots compares maintain robinson robinson robinson robinson rely pittsburgh resource resource resource resource resource resource resource resource resource resource resource resource resource resource serve serve serve qualitatively suited adjust adjust germany sophisticated sophisticated implements calls univ univ initialization restriction perfectly perfectly perfectly perfectly perfectly perfectly perfectly perfectly perfectly perfectly impossible connecting connecting spiral spiral spiral spiral kaufman ments darken promising proceeds proceeds check serves serves serves exploit exploit ral belong monotonically north responsible guide vowels holland conjunction lang lang lang lang vertices belongs uni thomas thomas thomas offers reader record ends inf fahlman fahlman fahlman fahlman fahlman fahlman accumulated accumulated accumulated accumulated dramatically spirals spirals spirals spirals spirals spirals spirals spirals spirals summer summer schulten anns rigorous outperform super employs preserving preserving preserving preserving preserving preserving preserving preserving preserving preserving incrementally pointed retraining centre centre utilize utilize utilize connec solely reports clas avoids avoids avoids pub exam num gas gas gas gas gas distant maximally kanerva overhead overhead insertion insertion insertion insertion insertion insertion insertion guided employing cij cij termed oculomotor sonar sonar sonar attached attached simplex simplex simplex article experi gorithm mea coordination utilizing served served deletion dim lation handling accordance wins wins aid attempting attempting conceptual conceptual imple establishes dropped dropped dropped reflecting reflecting dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs dcs sensorimotor ning concerns dissertation ples contributes preservation preservation preservation preservation preservation deals repository totally approaching adjusts informatik crl centres centres sis teaching teaching est enters inst emerged bidirectional tails insert martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz benchmarks benchmarks benchmarks amsterdam deleting lebiere lebiere predefined predefined inserted elegant approxima icann icann klaus forgetting jumps concurrently concurrently concurrently comprises burden ily ously draws fulfilled serving initializing mented beat continu isomorphic gerald gerald gerald gerald amples acti duce render oft emerging icsi correla encouraged witbrock vised publications restricts nicely christian guiding meets tionist postprocessing overlaid rock cated cording gorman gorman gorman gorman kiel kiel kiel kiel kiel adaption closes crn crn nection cnl submanifold continous str mine arti sticks sical ull inserts ancestor ancestor cept refered readable rnax promises zur overflow awj directory quest vated rial fect aleksander ficial iiv tro 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data function function function function function function figure figure figure time time time set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output number state results results results results results results results results units units units units units units units units units units units units units units units information information information information hidden hidden hidden performance based based based based based space space space space space space space space weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer vector vector vector vector vector order order order order shown shown systems systems systems systems values values values values values values values weight weight weight weight weight weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition method method method method approach approach approach approach point single single single single single single processing processing processing processing processing processing large patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class inputs form form form shows shows shows algorithms paper paper paper paper paper paper examples small small size size feature net net net net net work work methods fig fig fig fig fig fig classification process current trained trained structure problems problems problems problems random representation section section section fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general general general general general general general general general general general general general general generalization speech speech real real real real real real real average average obtained obtained experiments dimensional dimensional dimensional result university university university university university university threshold variables computation computation research research found found found found found found sequence target target target initial initial initial initial initial table table table table table table computer computer node node science science science presented presented presented present present phase phase phase phase activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation low low temporal machine machine machine machine sets sets sets sets maximum range press press position basis continuous abstract applied applied applied applied applied applied applied applied applied applied applied back find convergence convergence properties properties properties references due ieee ieee procedure procedure important decision decision decision propagation introduction complex hand hand behavior behavior effect generated generated generated generated generated generated generated parallel recurrent recurrent search search search difference difference variable assume assume assume lower lower lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules representations representations representations representations representations representations representations representations center bound type type type multiple multiple multiple multiple multiple multiple binary represent tree distributed distributed distributed distributed distributed distributed distributed distributed distributed equations make fact techniques techniques techniques techniques techniques techniques techniques techniques proposed proposed proposed correct correct correct observed observed observed errors errors forward forward forward resulting resulting resulting classes classes total total human human computed computed respect eq called regions regions mapping mapping optimization optimization optimization feedback applications knowledge knowledge knowledge knowledge knowledge original original original artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial specific specific specific specific specific specific specific specific specific specific specific specific true experimental experimental constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected connected connected connected discrete discrete approaches approaches approaches approaches approaches approaches approaches approaches steps comparison larger larger larger connection update morgan morgan morgan morgan morgan morgan proceedings proceedings proceedings report report report report words department loss loss loss version technique internal internal internal internal code individual individual advances advances advances advances joint joint joint joint joint difficult layers layers layers layers layers layers delay addition addition ai ai ai ai ai ai ai ai ai considered cambridge cambridge computing domain domain domain domain domain domain domain equivalent equivalent view view view view view view conference conference conference efficient efficient upper requires approximate world world speed vision produce condition derived randomly robot robot robot robot robot robot robot robot robot robot bounds bounds bounds bounds bounds bounds bounds area area area area backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature nature sampling simply achieved discussion technical technical technical technical describe describe describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote denote denote fast fast limited close close assumption corresponds short short short generate generate role instance instance future degree degree degree makes development including kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann probabilistic typically fully transfer transfer transfer programming programming programming programming programming programming programming programming programming character projection york mechanism mechanism mechanism mechanism mechanism consistent consistent empirical empirical language language numbers numbers max max international international international idea minimize added description description description denotes denotes architectures architectures directions recent separate reported practical strategy include side side side trees inference inference inference subset subset sejnowski recently highly previously volume volume works yields studies sparse positions generalized generalized interval interval interval interval interval interval interval interval interval interval arm arm arm arm arm arm arm arm arm arm arm arm arm arm constructed constructed exists exists studied scaling extended alternative alternative boundary boundary boundary generally generally runs half starting operator valued valued valued valued editors editors editors editors accurate numerical clear clear moody moody moody moody learns strong integration external turn variety variety variety variety start exist min min iii iii manner connectivity configuration configuration configuration configuration configuration configuration base denoted denoted denoted denoted denoted relation van written generating describes dept recall category coordinates simultaneously easy easy angle integrated extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extracted extracted extracted extracted extracted extracted extracted extracted extracted independently expressed expressed interpretation updated updated updated fraction forms forms completely key key key reasonable combining intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals generation remains initially assigned construction classified existing handwritten handwritten combinations activations activations activations activations activations activations instances subspace determines prove prove maximize mozer specifically candidate domains holds partially partially tests structural successfully successfully successfully successfully successfully successfully successfully major major simplicity computationally effectively presentation successful detect reached summary traditional compact compact compact notice notice notice notice notice notice graphs procedures success link showing interested interested interested interpreted lie lie list generalize generalize modular backward backward giles correspondence correspondence denker hypotheses hypotheses illustrates operating extract extract extract extract tesauro presents presents employed unlike powerful powerful american layered layered collection requirements detail detail replaced hanson hanson hanson hanson limitations accurately accurately accurately game issues lippmann lippmann lippmann lippmann biases applicable applicable symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic cover cover phases removed removed removed neu examined waibel induction induction concepts concepts editor configurations configurations configurations opposite created changed queries front front front obvious assumes fisher freedom mapped initialized art generates finds finds years years mentioned directed adjacent expensive benchmark tool tool inside perspective closer closer style style style style desirable consequence scientific scientific projected angles describing gradually gradually gradually members medical read depicted depicted author preceding mellon mellon argument considerably carnegie carnegie cmu cmu amounts amounts amounts generic generic generic autonomous detecting detecting employ frequently frequently frequently incorrect howard rely pittsburgh pittsburgh characterize extracting extracting extracting extracting extracting extracting extracting extracting extracting extracting monotonic proven proven proven prevent germany logical logical damage cumulative cumulative tresp tation appropriately linearity driving member connecting grey grey grey smolensky lecun robotics generality generality generality eliminated systematic air kaufman promising promising overcome mail simplify imposed vehicle analyzing analyzing operates ral methodology splitting disjoint monotonically canonical heuristics heuristics substituting substituting meaningful meaningful published slice falls falls representational zhang iteratively iteratively paul conjunction searching searching uni jackel propagated originally bases specialized specialized membership express cancer offer refers verification hypercube hypercube considerations dietterich fahlman shavlik shavlik shavlik shavlik shavlik default empty speaking verify verify land thrun thrun thrun thrun thrun thrun thrun thrun workspace workspace workspace workspace workspace constitute kinematics kinematics outperform validity validity validity validity validity validity validity validity validity validity validity validity validity validity validity validity incrementally propagating conjecture conjecture boser imagine auxiliary constrain argue verified verified verified henderson deep continues playing mitchell mitchell hubbard pomerleau careful considers projecting projecting increasingly represen spanned quinlan manipulator manipulator manipulator manipulator zip covered covered covered covered distinguished refinement refinement refinement enforce maintains suffer meet likewise admissible admissible admissible admissible simplex refined refined refined refined simplifies covers covers remarkable council consuming inconsistent inconsistent inconsistent inconsistent inconsistent institut tom tom sake attributed influenced rosenberg towell confirm hopkins december played suppress stay kinematic engine tip tip tip squashing squashing scenarios joints joints degenerate johns complement suffice safe safe safe safe safe safe informatik informatik nettalk physically bonn bonn bonn bonn bonn acyclic tenth mounted monk monk monk refine refine refine facilitates repetitive sebastian sebastian sebastian sebastian sebastian checked checked collision tighter excluded entities checks oil oil fiir slip excluding coverage coverage coverage confirms shrink structuring exhibiting draws craven craven craven craven proving neti neti neti neti neti neti neti henceforth inconsistency provably provably provably refining unstructured wishes shortcomings today acknowledgment tri tri tri iai trivially mooney bout keller invaluable seeds utgoff lacks diagnostics concludes asa recipes till questionable eleventh cheng intriguing lan negated aloud initializations pap propositional succeeding mcmillan deficiency inconsistencies inconsistencies overly michalski subsymbolic analyzes analyzes analyzes revise barely jhu eecs intersects intersects hollatz omlin comprehensibility comprehensibility mitsubishi rations universally managed managed violating finitely illus clayton jong refines ingly warrant marc breadth criticized erage ext trate preconditions preconditions preconditions jude configu ignorance attach prerequisite maxx enlarging enlarging appropriateness gratitude conjectures conjectures compilation 
#@Thrun_S,
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#*network network network network learning model input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function figure figure figure figure figure figure figure figure figure figure set output output output output output output output output output output output output output output output output output output output output number number number number number number number error error results results results results results results results results units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information information information information information information information information information information information models models performance performance performance performance weights weights weights weights case case case case case shown shown shown shown shown values probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern large large large rate rate patterns patterns patterns patterns patterns patterns patterns analysis analysis inputs inputs shows shows simple simple simple simple paper net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net methods points features level level level level level level level level level high high high high high memory memory memory memory memory memory memory response response response response response response response response similar show show section rule approximation theory theory theory theory theory theory obtained obtained obtained obtained obtained activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold research log log defined found table table table table standard computer terms terms synaptic science presented low low low low low low low low low low low low low maximum maximum maximum range range press press basis nonlinear abstract applied applied applied references due due positive introduction complex effect generated variance cost tion tion higher previous previous required required required good good binary binary binary binary binary conditions distributed probabilities probabilities probabilities errors errors simulations simulations simulations simulations minimum total respect sum sum sum sum sum sum sum sum called called times times times times times times times times study study negative relative relative relative compared compared rates perform active active active active active active active active active active active active active determined determined determined connected connected connected connected connected connected connected connected connected connected connected connected connected distributions distributions distributions distributions distributions distributions distributions distributions distributions brain brain brain brain brain brain brain brain brain brain comparison contrast connection connection connection connection connection connection support dependent nets loss loss version consists individual responses difficult equivalent bit bit bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine efficient efficient efficient efficient efficient efficient efficient efficient full full full full approximate free free free free basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic increase increase increase con con coding coding coding weighted levels levels levels levels levels actual selected nature associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative achieved achieved discussion transformation close corresponds finding amount amount generate theoretical theoretical theoretical theoretical easily makes makes noisy noisy noisy noisy noisy noisy noisy noisy including pairs pairs pairs reduced reduced fully fully ratio ratio ratio ratio ratio york operation numbers stored stored stored stored stored stored stored stored stored bits bits choose improved pair strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy include cognitive previously previously previously previously approximately calculated calculated calculated calculated calculated calculated works tions yields achieve trans trans sparse sparse sparse sparse sparse modified modified organization storage storage storage storage storage storage storage storage grant extended occurs setting setting setting setting setting conclusion place greater greater greater hebbian differences differences accurate numerical peak peak peak peak peak peak peak peak peak peak characteristics demonstrated start relationship manner connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity configuration acknowledgements distinct recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall applying formed versus versus versus fraction showed approximations partial partial partial partial measurements measurements reduces false false valid calculate calculate calculate calculate calculate dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic david david david david david david thesis thesis memories memories variations variations absolute absolute partially partially partially partially partially partially partially efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency presentation comparing situation soc contained interpreted strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies cue cue cue cue cue cue cue cue cue device cues cues cues cues cues cues cues notation highest highest thresholds simpler carried transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed rapidly behaviour biol analytically measurement measurement plausible configurations extremely expressions improving arbitrarily wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta optimum optimum indicating theoretic trivial agreement tractable purposes incorporate mation commonly commonly commonly calculations calculations medical greatly greatly pure incorporated calculating calculating calculating sums sums sums sums sums sums sums sums sums sums sums sums sums cumulative cybern oxford oxford extensive extending numerically iiii effectiveness spurious infor financial pat pat den den belongs uni chooses omitted theoretically theoretically roy storing fold thresholding thresholding thresholding thresholding usage usage usage usage usage usage usage usage usage usage usage usage usage usage listed email presenting willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw centre connec edinburgh edinburgh edinburgh edinburgh cns cns confirmed lond normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised normalised drops tin inactive capacities capacities capacities capacities ble council terns terns transforming transforming clarity identically marr marr ooo ooo deals retrieved approaching distorted edition tained recalled recalled greatest winners winners winners winners winners winners moderately moderately moderately moderately tivity holographic configured altering simula activa phil 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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number error error state results results results results results results results results results units units units units units units units units units units units information information information problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space space space weights weights weights weights weights linear layer layer layer layer layer case case vector shown shown shown systems systems values parameters parameters weight weight functions functions functions functions unit distribution recognition recognition recognition recognition recognition recognition recognition method method method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single processing processing processing processing large rate rate test patterns patterns patterns patterns analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class optimal inputs inputs shows shows shows shows shows signal signal algorithms gaussian gaussian gaussian gaussian paper paper paper feature net net net net work work task task task methods methods methods step points points classification classification process level level trained trained trained trained trained trained trained trained structure problems problems high memory response response similar similar architecture architecture architecture show equation fixed fixed fixed fixed generalization speech speech parameter theory gradient gradient gradient note note note experiments activity dimensional result university university threshold threshold threshold threshold threshold threshold variables computation independent independent independent log found constant standard standard standard node left left presented presented presented presented phase phase phase activation activation activation activation activation activation activation low nodes nodes nodes frequency sets sets range basis basis basis basis basis basis continuous abstract back back references ieee ieee ieee positive positive adaptive propagation propagation introduction dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic tion energy classifier signals chosen chosen higher higher part center center center center center cases cases type type required required required long long equations equations make proposed proposed proposed proposed proposed proposed correct correct correct forward resulting classes classes classes classes classes ing tasks simulation computed computed computed multi multi called called times means factor factor potential made global global global global negative negative vol specific samples compared proc proc proc proc perform perform determined determined approaches steps accuracy contrast contrast support train train descent descent descent dependent technique technique technique technique technique code individual advances connectionist final exp exp delay delay delay scheme addition addition addition addition ai ai cambridge hinton limit bit conference conference conference determine classifiers upper requires choice choice increase con coding derived derived clustering developed area area types backpropagation nature nature increases fast complete complete rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf nearest common role require adaptation ability probabilistic probabilistic probabilistic probabilistic probabilistic underlying combination coefficients mlp mlp mlp mlp testing testing matching database database database leads leads leads details details max max pre direct international international supervised supervised frame decay decay decay decay decay decay decay decay decay decay added perceptron perceptron denotes denotes correlations advantage reported introduced introduced introduced introduced introduced identical quadratic quadratic sejnowski sufficient compare compare previously unsupervised unsupervised works works solve solve speaker speaker trans positions locations locations locations modified modified generalized increased invariant deviation deviation correctly correctly correctly correctly correctly correctly locally locally locally hybrid white occurs pass demonstrate demonstrate critical conclusions moody moody moody faster faster practice propose radial radial radial radial radial radial radial radial selective targets introduce introduce acknowledgements areas areas areas areas areas construct construct construct stability stability tuned tuned tuned confidence confidence confidence recall implement category linearly dimensionality involves involves slightly slightly scales shift choosing extracted phoneme phoneme squares influence solved solved variation evaluate restricted centers frames epochs epochs epochs epochs epochs epochs normalization roughly add initially classified classified classified classified classified topology expect existing thesis activations activations priori priori usa recognize determines extension extension illustrated automatic major major straightforward straightforward suitable effectively build tdnn tdnn tdnn vowel quickly induced classify classify classify running hold hold michael michael michael michael michael play computes reach reach reach thresholds thresholds consisted consisted illustrates extract trains layered collection steady optimized optimized dataset fewer examine school project project biol boosting boosting boosting boosting analogous neu waibel waibel closest possibly created changed prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype noted noted algo separated epoch improving explain phd attempts mentioned indicating stop distinguish distinguish defining growing benchmark starts sys sections english cybernetics radius radius radius radius radius radius radius radius radius mellon fourth carnegie applies cmu cmu pseudo capability backprop prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes cal occurrence occurrence acoustics datasets adjust adjust adjust germany inherent picture college cooper cooper rithm ratios dynamically databases databases databases connecting inspired khz darken darken darken mark settings constructive vowels reset introduces introduces introduces ensures connect encountered overview lang lang advance tokens tokens modelled mlps theoretically properly ends dietterich santa fahlman discriminate spirals spirals spirals spirals spirals spirals spirals spirals summer converted corporation email email equivalently ease classic adjustment adjustment adjustment adjustment adjustment adjustment adjustment ftp tems disadvantage crosses individually individually rbfs rbfs rbfs rbfs rbfs rbfs covered sonar sonar sonar confusion nal gorithm gorithm gorithm recogni invertible grbf utilizes outperformed cylinder conversion distinguishing conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting partly consonants accumulate manually manually diamond diamond diamond diamond diamond acid informatik sis discriminating benchmarks particles particles resemble demanding shikano dilemma metal inability opportunity intel intel boost shrink reilly reilly tially lpc agation conflict conflict conflict british clus gorithms distinguishes distinguishes encounter neighbour rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce rce neighbours neighbours hanazawa braun prof prof mission karlsruhe witbrock und liapunov charges charged rock duplicate radii radii radii shrinks shrinks shrinks gorman tering eleven specht cylindrical jay jay jay jay jay commit commit commit declines rprop rprop rprop rprop rprop bench holler decline incrementing eri propriate electrostatic rll nput substan blvd dictive 
#@Berthold_M,Diamond_J,
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#*network network network network network network learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data data data data data data data data data function time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output number error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results units units units units units units units units units units units units units information information information information information information information information information information information information problem problem hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based based based based space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear vector vector vector vector vector vector order order order order order order order order order order shown shown shown shown shown systems systems systems systems systems systems systems systems values values probability noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions unit unit unit unit unit unit unit unit distribution distribution distribution distribution recognition method method method method method method method method method approach approach approach approach approach approach approach approach approach approach approach point single single processing processing processing processing processing processing processing processing large large large large rate rate test test test test test test class class matrix optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs shows shows algorithms algorithms simple simple simple gaussian gaussian gaussian examples examples examples examples examples examples examples examples small small small small small net net net net net net net task task task task task task methods methods methods methods step points points points points points points classification process trained high high high high high response similar similar similar architecture architecture architecture architecture architecture architecture show equation equation equation equation equation section section section section section section section fixed vectors vectors vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization approximation approximation approximation approximation approximation theory theory theory gradient gradient gradient obtained obtained obtained note experiments experiments experiments dimensional dimensional dimensional result university university university computation computation computation computation computation log log log log log log defined defined defined found target target initial constant constant constant table table standard standard terms terms distance distance distance connections synaptic science prediction prediction prediction prediction prediction left left direction present activation activation activation activation activation low low low low low low low low low machine sets maximum range learn components outputs outputs outputs outputs outputs abstract find find references component due due positive positive positive positive positive procedure important introduction complex complex generated generated variance parallel recurrent recurrent recurrent recurrent recurrent recurrent search search search search tion tion change difference difference difference difference complexity complexity complexity complexity complexity complexity complexity complexity complexity variable assume assume measure measure measure prior prior prior prior prior prior prior prior prior prior prior learned chosen center center previous previous cases required required required good good good good conditions conditions bayesian bayesian bayesian expected expected expected expected expected make region region region length length length errors forward finite minimum minimum minimum minimum minimum minimum minimum computed respect respect respect respect sum sum sum sum sum eq eq eq eq eq eq eq eq eq eq called called called called called regions regions regions regions regions regions regions regions regions made made applications obtain obtain obtain obtain negative vol artificial relative relative application application application provide define define compute compute active experimental experimental related posterior posterior posterior posterior posterior connected connected connected connected brain brain brain equal equal approaches approaches steps contrast descent nets nets nets nets nets nets nets nets nets nets nets nets nets selection morgan morgan morgan morgan morgan morgan morgan proceedings report report report report department department advances advances advances advances advances advances advances connectionist final exp delay maps framework cambridge computing computing equivalent experiment experiment experiment experiment experiment experiment experiment experiment environment environment hinton hinton hinton hinton hinton hinton hinton hinton additional additional additional solutions solutions trajectory san san san san san san conference efficient efficient requires requires requires choice significant significant significant approximate approximate basic pages pages pages pages pages pages pages pages pages increase validation give condition condition condition condition condition condition condition condition condition derived weighted weighted randomly lines product backpropagation inhibitory technical technical technical technical technical technical feedforward feedforward feedforward describe group tested tested fast close close assumption assumption assumption corresponds corresponds corresponds corresponds corresponds predictions finding finding finding finding effective theoretical theoretical theoretical require end rumelhart noisy noisy kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann smaller unknown fully mlp interesting character edge edge empirical principle leads leads leads squared squared details details details numbers numbers bits bits international early early decay decay decay decay decay idea minimize minimize minimize minimize choose added description description predict denotes denotes directions recent exact exact property property pair element reported practical cognitive engineering interest conventional conventional conventional conventional conventional conventional conventional approximately volume volume volume works axis axis axis axis tions solve correspond definition mixtures bounded bounded interval williams williams risk risk risk risk suggests derivative predicted predicted correctly feed touretzky touretzky setting half strength minimal minimal minimal row row assumptions assumptions assumptions assumptions assumptions assumptions assumptions reduce depend depend editors editors editors editors editors editors editors editors sigmoid sigmoid measures designed moody moody moody moody moody mateo mateo mateo mateo mateo mateo mateo mateo strong reduction reduction labeled decrease decrease decrease relationship introduce derivatives derivatives derivatives derivatives groups minima minima minima minima minima minima minima minima minima minima minima minima minima denoted denoted denoted denoted suppose relation relation relation relation relation van van van van van derive index index changing changing confidence confidence confidence confidence pruning pruning pruning sensitivity sensitivity sensitivity explicitly linearly remaining remaining adding adding minimization minimization springer implies implies expectation expectation select john choosing focus focus dependence influence solved fraction fraction soft approximated calculation epochs reduces fitting fitting fitting penalty remains valid initially norm classified degrees precision precision precision precision box box box box box box box box thesis activations activations priori coordinate sciences vapnik vapnik vapnik vapnik automatic priors priors absolute absolute holds structural structural simplicity simplicity maximal maximal maximal maximal divided divided effectively effectively effectively wij wij wij wij mackay mackay essentially interested stopping stopping stopping superior running strategies satisfy minimizes giles giles principles illustrates tesauro tesauro cowan cowan cowan cowan minimized minimized unlike unlike unlike layered wiley production overfitting overfitting overfitting overfitting overfitting overfitting exponentially put environments hanson hanson hanson hessian hessian hessian hessian hessian lippmann lippmann fewer school mse mse mse mse mse fault scaled stream func fundamental fundamental fundamental editor generalisation equally perfect thought obvious formal freedom store contributions phd finds finds defines defines rows directed variances variances defining defining nowlan nowlan multiplication comparisons obs purposes strictly forces immediately mation implicit implicit meaning relevance capability capability capability peaks backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop orders solla sharp sharp maxima ity ity outliers switch switch weigend gen germany inherent tolerance wang wang sharing initialization initialization pose ordinary pick pick kullback kullback murray stronger adjusting occurred satisfying simplify analogy replacing keeping intuitively intuitively exceeds intuitive carry alspector alspector elimination excellent ensures ensures ensures appendix appendix appendix appendix decide pruned conjunction forecasting searching entries entries laplace initialize advance matter wolpert wolpert pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter sons stopped influences market market market speaking boxes boxes outperforms outperforms outperforms leibler leibler guyon stork validity stock stock stock perturbed convenience boser causing causing acceptable acceptable acceptable acceptable acceptable mdl mdl mdl mdl mdl flat flat flat flat flat flat flat flat tendency tendency german german suppressed suppressed discovering discovering discovering discovering discovering discovering schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber ization searches simplifying simplifying simplifying simplifying simplifying switched statistic misclassified misclassified universit universit universit lippman mini mini continually mann fiat fiat fiat fiat fiat fiat fiat fiat fiat fiat fiat fiat hassibi sees corporate justified justified justified justified justification justification heavily conceptual supply broadly industrial kth suppress incorrectly bottou venkatesh subtracted subtracted huberman bond capital cardinality rating judd enhances denmark informatik informatik informatik informatik informatik sian thing gaus appro enforces enforces enforces surgeon surgeon surgeon indicators fixing ically ensuring ensuring ini awij awij awij awij insert terminology decompose amsterdam expresses technische technische technische kolmogorov kolmogorov markets mum mum conveyed utans monthly week week week week ess puter perturbing edwards posteriors ago regularisation ting structuring ously justify cent cent cent cent euclidian overfit overfit camp camp camp camp camp camp foreign industry embody rli awi awi hochreiter hochreiter hochreiter hochreiter hochreiter hochreiter business prefers pected owi decayed ume vances kauf raining closeness closeness pth enlarged rosenfeld mfinchen mfinchen mfinchen mfinchen sussex holden holden money quarterly stdev stdev pushing pur differenttable fki fki muenchen muenchen manufacturing violating jiirgen jiirgen jiirgen jiirgen pothesis simultane fakult fakult fakult competitor erate boa boa boa proximations wol wol brighton flit refenes confidently confidently feeling minimiza inpul flatten ifo weekly 
#@Hochreiter_S,Schmidhuber_J,
#t8
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data function function function function function function function function figure figure time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number number number number number number number number number system system system system error error error error error error error error error error results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden performance performance performance performance performance based space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer case case case order order order order order order order order order shown shown shown shown systems systems values values values values values values values probability probability parameters parameters weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution recognition recognition method method method method method method method method method method method method pattern pattern single single single single processing processing large local local local local local local local local local local local local local rate rate patterns optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian paper paper small small small small small small size size net work task task methods methods methods methods methods step step classification process process process process process level trained trained trained trained trained structure problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random random random random random random random random random random random random random random random high high high similar similar architecture architecture architecture architecture show section fixed fixed rule rule vectors vectors generalization speech average average average average average average obtained obtained obtained obtained result university university university threshold variables computation computation solution solution solution research research research research defined found found found found target target initial table table table table table table table table table standard standard standard standard standard standard standard standard computer computer terms terms terms terms terms node science science science science science prediction phase activation low low maximum maximum maximum range range range range range range learn learn learn position nonlinear abstract applied applied find find computational convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties references due ieee important introduction hand statistical effect dynamic dynamic dynamic search search search search search search search search search search search search search difference difference variable chosen chosen chosen chosen chosen higher higher higher higher higher higher higher higher higher previous cases cases cases type type required required required required required required required required required required required required required required required good long expected expected make fact fact fact fact proposed proposed correlation correlation correlation correlation correlation correlation correct correct correct correct simulations simulations simulations simulations simulations simulations simulations simulations simulations minimum resulting resulting total total total simulation simulation simulation performed performed performed performed performed performed mapping mapping mapping mapping mapping means factor optimization optimization optimization optimization optimization dimension global global global global global global global global global global global applications applications relative specific specific compared compared application desired desired provide provide compute rates perform perform power power comparison comparison comparison larger larger connection connection train train train train train morgan report report institute institute department department version version advances difficult addition graph domain domain equivalent equivalent equivalent experiment environment directly additional solutions san stage capacity capacity capacity capacity capacity capacity efficient requires choice choice approximate basic basic increase increase weighted randomly randomly bounds types types types types types types product product product product product product product product product product product product product product product product product product backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration simply simply discussion technical technical feedforward feedforward increases increases fast surface surface surface surface surface surface effective implemented implemented implemented implemented implemented implemented supported require main main main adaptation adaptation journal ability makes rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart rumelhart kaufmann simulated simulated smaller smaller smaller combination combination combination combination combination combination combination transfer transfer significantly significantly mechanism operation leads numbers iterations iterations iterations direct polynomial produced run added added architectures architectures discussed discussed discussed improve correlations advantage advantage separate typical reported reported reported reported practical introduced introduced include sense subset subset subset engineering sufficient compare previously previously approximately approximately volume works works solve solve smooth symmetric symmetric generalized bounded bounded increased increased increased invariant occur derivative derivative locally move hybrid hybrid touretzky white white runs runs conclusion minimal competitive competitive sigmoid sigmoid sigmoid sigmoid clear performs faster faster faster mateo physics sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal california california start start exist decrease derivatives manner manner minima minima minima minima minima minima minima minima minima annealing annealing question laboratory pruning implement implement implement implement electrical involves adding adding adding boolean boolean boolean competition choosing national solved evaluated evaluated evaluated evaluated evaluated evaluated restricted fraction showed lee lee lee lee lee centered margin sign earlier earlier earlier additive epochs epochs epochs epochs epochs epochs epochs epochs add add initially calculate sufficiently sufficiently construction construction transactions avoid expect existing existing figures combinations combinations combinations usa usa batch batch batch extension plotted illustrated candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate reason reason regular selecting selecting selecting aspects efficiency differ differ computationally delta delta delta included invariance online online ten reached procedures prob allowing sin criteria list bar absence giles giles giles giles giles giles giles giles automatically automatically processors attempt attempt preferred jacobs jacobs satisfies decreasing modelling layered xor experience rapidly rapidly replaced incremental mappings parity parity parity parity parity parity parity parity parity parity combine cover cover cover examined examined examined examined examined examined plausible possibly implementations versions noted noted algo assumes explored mapped logic logic logic logic initialized initialized epoch epoch epoch epoch epoch epoch epoch epoch generates electronic optimum integrate mentioned mentioned rows cos cos cos growing explanation cascade cascade cascade cascade cascade independence independence benchmark reasons reasons berkeley constructing constructing division worst mation pool pool computers bandwidth mellon summation summation summation summation carnegie reflect biologically partitioning limiting asymmetric enables logical logical logical logical logical logical logical sophisticated display converged converged displays initialization initialization initialization princeton princeton rithm rithm homogeneous homogeneous proceed accepted multiplicative los los resulted combinatorial constructive constructive constructive constructive constructive constructive constructive heuristics heuristics heuristics continue continue infor repeat separating representational irregular respective displayed sim sim sim sim sim sim sim competing competing initialize enable multiplied ends papers fahlman fahlman fahlman insensitive default assigning lem mind street geometrical slight outperform outperform solves sig ent benefits reports jabri jabri jabri jabri jabri australia australia remainder home home home home summarizes modifying rithms allocated disadvantage cosine cosine denver supports lapedes lapedes bill bill bill bill bill durbin durbin durbin durbin durbin durbin durbin gauss gorithm nec nec nec nec sigmoids functionality consuming accordance pitts decided satisfactory australian impractical firstly puts outperformed compo proposes kirkpatrick kirkpatrick optics fastest nontrivial inspection prone fair creation kowalczyk alamos alamos mul spec benchmarks lebiere lebiere lebiere predefined newly farber sydney proce examines imaginary ities arline enabled grown unlimited terminated nadal nadal nadal hypothesize hypothesize initializing nent retains horne horne wanted maxwell maxwell geometrically pitt explosion accelerate gation restarts restarts vecchi restricts combi comment pus pus pus pus pus pus pus pus pus pus pus pus pus pus pus pus pus pus relaxing public public dure differencing marwan marwan marwan marwan marwan marwan tiling tiling tiling tiling tiling tered nsw nsw zard reprinted tiple atypical atypical freezing freezing ash ash ash ful facilities advan automate suitability nonmonotonic sedal sedal downs termined conv conv conv ified initializes thirdly tages nations merical backpropa father interchangeably moid encoun exceedingly ucb csd 
#@Giles_C,Horne_B,Jabri_M,Leerink_L,
#t8
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#*learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time set set set set set set networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system results information information information problem problem problem problem problem problem models performance performance performance space space case case case vector vector shown shown shown systems values values probability distribution distribution distribution method approach approach approach pattern point point point point processing local local local local local local local local matrix form shows shows signal algorithms simple paper paper small work work step step step step step step step step step points points points points features process process process process current structure problems problems problems problems problems problems problems problems high equation section fixed fixed rule images general general generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter states theory theory obtained note note note note dimensional result computation computation computation solution independent independent log log log log log log log log log log defined defined found found sequence initial initial initial initial initial estimate estimate estimate science science direction presented presented present low machine machine maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum components basis sample sample sample abstract convergence convergence density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component stochastic stochastic ieee ieee ieee ieee positive procedure procedure important mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand estimation estimation estimation estimation estimation estimation statistical statistical statistical statistical statistical statistical effect effect generated cost cost cost cost cost search search tion change change energy energy energy energy energy energy energy complexity measure measure previous previous cases cases distributed expected proposed proposed proposed proposed total computed respect respect respect respect performed performed performed performed performed performed performed eq eq eq eq eq eq eq eq eq eq eq eq eq called called called optimization global global global global global global global study knowledge em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em obtain obtain obtain original original original original original samples samples compared define compute compute compute proc determined determined goal posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints distributions brain equal equal approaches mit steps steps steps contrast dependent morgan words words version technique advances joint joint exp exp exp exp exp exp addition computing hinton hinton hinton view view view estimates estimates choice statistics free free free free free free free free estimated estimated estimated increase increase give derived derived derived conditional conditional clustering clustering clustering criterion entropy entropy entropy entropy iteration iteration iteration depends depends depends discussion normal tested close close close assumption corresponds corresponds corresponds corresponds corresponds complete complete complete complete complete surface surface surface surface rbf rbf effective effective assumed role eds instance easily easily easily makes kaufmann objective simulated simulated jordan jordan programming interesting increasing increasing increasing special uniform principle principle principle principle experts experts choose added denotes denotes denotes practical apply machines hierarchical hierarchical cognitive recently recently recently highly unsupervised observations works tions converge trans trans trans mixtures mixtures generalized storage sensitive exists expression wide wide touretzky loop deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic occurs generally starting starting starting trajectories competitive central bayes practice practice temperature temperature temperature temperature temperature temperature taking taking hard hard physics physics largest variety minimizing min relationship introduce annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing boltzmann boltzmann suppose suppose pro derive derive dept missing explicitly equilibrium minimization minimization expectation expectation expectation expectation expectation expectation expectation competition competition competition letters independently communication interpretation interpretation influence soft soft soft completely converges converges converges converges converges partition partition partition sign earlier reduces reduces iterative iterative priori coordinate contour contour maximize successfully successfully plots plots soc procedures interpreted interpreted satisfy satisfy gibbs gibbs relaxation generalize minimizes quantization quantization observable observable maximization maximization maximization maximization maximization attempt jacobs employed employed unlike unlike unlike unlike replaced optimized optimized hessian ml ml successive incremental applicable reliable maximizing maximizing func analogous naturally integer der arbitrarily submitted neal neal neal mentioned indicating stop derivation track nowlan nowlan nowlan caused laboratories acknowledgement gradually gradually localized incomplete incomplete incomplete incomplete outer mechanics mechanics mechanics explained explained varies tional tional parameterized parameterized parameterized parameterized posed variant variant variant variant variant variant variant variant variant variant reliability maxima maxima maxima differs aim maximizes maximizes maximizes maximizes geman geman geman geman logp logp logp logp logp logp logp logp yuille begins eventually saddle saddle lagrange japan summing tem royal plays multiplier overcome analogy analogy attractive monotonically substituting repeat corre iteratively regarded regarded sides conjunction ascent demonstration theoretically eqs variants dempster dempster interestingly adopted escape mind logarithm vec rubin rubin equivalently alternating distinction adopt convenience ease ical superimposed hundred tor param grouped distribu thermodynamic thermodynamic thermodynamic labs simplifying noting noting buhmann buhmann worth laird laird anal anal preprint eigen eigen eigen tin rose rose gorithm rewritten parameterization nonnegative agrees grbf lated hoc finer identically condi proposes emerges fox maxi maxi statist cho wong wong iterate tit tit trapped trapped iir mization settles mum coincides utans utans ogy gun nakano nakano nakano nakano nakano nakano nakano nakano fil fil kyoto encouragement simu visualize ogp justifies eter sponds arrived suc soraku stolorz stolorz hue reformulated seika intell fined tth deterministically deterministically deterministically economy hikaridai biometrika gurewitz conven rior originates poste dye imizing rna petitive perature cessfully dial unobservable unobservable uration baysian config jacob 
#@Nakano_R,Ueda_N,
#t8
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural input input input input input input input data data data data data data function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output number number number number number number system system state state state state state state state state state state state state state state state state state state state state state state state state results results results information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models hidden hidden based space space linear case case case case case case case case case case vector order order order shown shown systems systems systems probability probability probability parameters parameters parameters unit distribution distribution distribution distribution approach approach approach approach approach processing processing local local local rate rate analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal form shows algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple paper paper paper paper paper paper size size work work work task step classification trained structure random similar architecture show equation equation section fixed rule vectors general parameter real average states states states states states states states states states states states states states states states theory gradient gradient term term term term term term term term term term term term term term term term term term term term term term term term term term experiments experiments experiments experiments experiments experiments experiments experiments result university variables variables variables solution solution research independent log log defined defined defined defined found found found found found sequence sequence initial initial initial initial initial initial initial initial constant constant constant constant standard standard standard terms terms terms distance distance connections left left left left left presented presented phase phase phase phase temporal sets maximum maximum learn learn learn learn learn learn learn learn learn learn outputs outputs continuous abstract find find convergence convergence convergence convergence properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee ieee positive positive positive positive positive positive positive positive positive important propagation context context introduction complex complex behavior generated generated recurrent recurrent recurrent recurrent recurrent recurrent tion lower rules rules measure measure prior prior part previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem cases cases type good good good good long long long long long long long long long long long long long long long long long long long long long long long long long conditions conditions conditions represent expected markov markov markov markov markov markov markov markov markov markov markov markov techniques proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed forward forward forward forward scale finite finite simulations simulations ing tasks tasks computed sum sum performed performed called called called called times times elements means optimization optimization study knowledge knowledge knowledge em em em em em em obtain obtain negative negative negative negative negative negative negative negative negative negative negative negative artificial artificial represented compared application series series define perform constraints constraints connected connected connected connected connected connected connected connected connected distributions discrete discrete discrete discrete equal equal equal approaches steps update support train train descent modeling morgan morgan report loss loss loss implementation version consists advances advances represents connectionist difficult difficult difficult difficult difficult final graph graph graph graph graph graph graph graph graph graph graph graph sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences considered equivalent directly solutions solutions transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition upper upper full requires requires requires condition condition randomly randomly conditional levels types path product product product product finally backpropagation depends simply achieved achieved achieved technical increases increases denote denote hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited close close corresponds corresponds corresponds proof short common effective assumed generate supported theoretical main eds eds square future makes makes kaufmann kaufmann underlying reduced account dynamical coefficients coefficients coefficients fully fully fully fully fully block block block block block block block block interesting interesting interesting interesting interesting significantly york increasing increasing special trials trials trials trials trials numbers stored choose run added improve improve exact advantage pair pair takes element apply period period period period period period period period period period period period period period identical identical hierarchical inference subset engineering sufficient varying volume module yields yields correspond studies studies converge converge trans trans diagonal diagonal diagonal definition definition definition definition definition definition chain chain chain chain chain chain chain chain generalized storage increased exists exists exists studied occur suggests suggests trial matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices loop loop loop deterministic deterministic deterministic generally column column column column half conclusion starting starting starting place row row row row row row greater numerical practice weak weak weak constrained taking taking taking hard integration largest external demonstrated exist introduce introduce groups connectivity connectivity explicit suppose suppose suppose suppose appears written longer index sequential generating generating generating generating transitions mathematical mathematical dept modeled easy slightly unique unique unique adding events events events springer implies blocks blocks blocks blocks cycles cycles cycles yield yield depending stationary influence influence influence influence lemma evaluate controlled controlled controlled evolution decomposition decomposition decomposition decomposition similarly converges converges allowed epochs symbol norm norm norm topology topology topology topology topology topology avoid avoid building bell eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues assignment illustrated discuss grammar reason columns extra hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms wij successful successful computations computations computations tend tend essentially identity identity characteristic composed traditional graphs kind strongly allowing allowing allowing issue hold gray backward backward backward eigenvalue eigenvalue eigenvalue ill acknowledgments deal cowan cowan presents explore parametric difficulty difficulty difficulty rapidly preliminary periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic investigated relationships dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies root proper proper eigenvectors eigenvectors symbolic complicated circles coefficient coefficient coefficient coefficient coefficient gradients necessarily integer integer analyze created equally rank rank rank algo epoch extent established percentage rows rows rows rows rows rows directed guaranteed diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion capabilities worse reasons ring strictly ran bengio bengio bengio bengio bengio bengio bengio bengio bengio products products products products products products products products products consequence consequence simard describing circle gradually gradually gradually gradually gradually gradually gradually depicted requiring geometric prop transient transient introducing ity span span span span span span span span operate gen suited replace kinds comments converged converged credit credit credit credit credit credit credit credit credit credit credit credit credit phenomenon phenomenon ordinary ordinary indices indices indices indices tation rithm arguments arguments conditioned branches ordering homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous homogeneous purely lost lost lost lost lost numerically stronger chains chains chains stated primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive loops occurring occurring occurring definitions canonical canonical canonical canonical canonical responsible corner exploring weakly weakly corollary studying injection lengths entries multiplied contraction contraction canada storing storing hypercube hypercube eigenvector eigenvector eigenvector propagate stopped appeared unified logarithm visually ties markovian markovian markovian markovian markovian markovian markovian legal emerge propagating propagating comparative aij aij aij aij aij aij aij aij algebraic equality distribu labs life considers represen cartesian alternatives retained drops exploited helps suggestions rewritten topologies mcculloch ergodic ergodic ergodic ergodic nonnegative corners corners influenced frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi confirm firstly stay bottou holmdel sym transpose triangular triangular zeros approached cyclic cyclic shortly stationarity greatest allowable allowable allowable allowable allowable allowable ini montreal replaces putting italy projective intervening fur absorbing retains roots roots canadian associating nserc yoshua yoshua yoshua yoshua yoshua wanted spans geometrically visualized quences multiples leak dsi ergodicity ergodicity ergodicity ergodicity ergodicity ergodicity proportionality proportionality incidence incidence incidence incidence incidence nxn sel itive constrains cies lai funding irreducible irreducible irreducible irreducible irreducible irreducible probabili jacobjan jacobjan iro zeroes zeroes limt limt limt limt preliminaries agencies soda incompatible thermore umontreal dipartimento erally gori informatica montrdal universitd axa axa inject bengioy frobenius frobenius bols dependen 
#@Bengio_Y,Frasconi_P,
#t8
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set set training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number error error error error error error results units units information problem problem problem problem problem problem problem problem problem models models models models models models models models models models models hidden space weights weights weights weights weights weights weights weights weights weights linear linear linear order order shown systems systems systems values values probability probability probability parameters parameters parameters parameters noise functions unit recognition approach approach approach approach pattern pattern point single single single processing local patterns patterns analysis analysis optimal optimal optimal optimal optimal shows shows shows signal algorithms algorithms algorithms algorithms simple simple simple simple simple paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work task task task task step points points features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features process process level structure structure structure structure structure structure structure structure structure structure structure structure problems problems problems problems problems problems random high high similar similar representation representation representation representation representation representation architecture architecture section section section section section line rule rule general general general real real states note computation computation independent independent independent independent log log log defined found found found found found dynamics constant constant constant table table table table standard terms terms science phase phase phase low low low low temporal object sets sets motion motion press learn learn learn position abstract find find find computational computational likelihood references component component positive procedure procedure mixture mixture mixture mixture mixture introduction complex complex complex hand hand hand hand hand behavior statistical statistical statistical effect generated generated generated generated generated variance cost cost cost search energy energy energy energy energy energy energy energy complexity complexity complexity variable spatial representations representations representations representations representations representations representations representations representations learned learned learned part part part part part part part part part part part part part part part part part part part part part part part part part part part part part previous multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple good good expected equations fact correlation correlation correlation correlation length correct observed observed observed scale simulations minimum resulting classes ing ing ing ing total total simulation human computed means factor factor potential natural natural em em em negative relative specific specific specific specific true true true true define objects objects determined determined goal goal related constraints constraints brain equal power approaches accuracy contrast update update morgan proceedings institute institute department individual individual advances joint difficult bias sequences maps maps framework cambridge directly directly hinton hinton hinton hinton hinton additional view limit san top conference determine full free free free free free free free world world world vision vision vision estimated give produce clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering entropy entropy actual actual actual actual iteration nature nature depends depends depends constraint constraint constraint constraint increases increases increases arbitrary arbitrary tested limited assumption complete stable stable predictions predictions predictions common common assumed generate require eds eds face cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster future easily easily makes makes makes fit fit kaufmann objective pairs underlying underlying underlying underlying underlying combination combination functional functional functional functional functional functional functional functional functional functional functional functional functional unknown unknown unknown fully technology significantly segmentation segmentation segmentation segmentation principal squared representing representing details call making normalized bottom minimize produced description directions recent correlations correlations robust robust separate takes takes typical movement apply include subject subject identical identical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical cognitive cognitive interest highly highly highly conventional unsupervised unsupervised unsupervised tions yields correspond correspond sparse positions positions positions separation generalized entire entire increased horizontal parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts suggests wide hybrid deterministic clusters clusters clusters clusters white setting demonstrate demonstrate strength starting hebbian conclusions valued competitive competitive accurate accurate weak weak mateo temperature propose strong strong strong strong minimizing minimizing minimizing decrease iii introduce derivatives annealing annealing acknowledgements appears pro factors factors factors factors factors factors primary generating generating generating generating transitions distinct distinct distinct distinct distinct distinct distinct distinct distinct category category category category category category category category category category category category category category category category explicitly simultaneously linearly physical slightly unique competition competition competition competition letters focus expressed review reconstruction reconstruction reconstruction reconstruction stages correlated correlated correlated correlated correlated viewed learner learner learner learner evaluate soft soft activities diagram diagram key normalization reduces boundaries remains intermediate visible advantages degrees degrees degrees degrees figures formulation assignment subspace subspace sciences extension plotted discuss specifically variations black black discussions characterized simplicity columns columns society differ differ efficiently plots traditional traditional notice notice kind kind kind split lie contribution generative generative generative generative generative generative generative generative categories categories categories categories categories categories categories categories categories categories categories categories categories gray usual dayan dayan dayan ill ill leading leading illustrates satisfies tesauro cowan situations simpler simpler simpler requirements rapidly accurately helpful fewer fewer fewer incremental authors hierarchy hierarchy hierarchy phases phases notion notion act naturally adapt configurations configurations configurations predicts facial ensure assumes freedom freedom freedom expressions hebb ith consist explain explain explain explain explain explain motivated motivated motivated finds finds neal massachusetts indicating indicating indicating distinguish variances independence tractable purposes sections controls medical depicted annual cybernetics mechanics mechanics mechanics explained explained varies flexible tional parameterized parameterized posed share dots templates howard anti limiting extracting extracting extracting extensions logp logp logp kinds specifies specifies specifies softmax primarily cooper assign forming member recover recover recover recover recover recover zemel zemel zemel zemel zemel zemel discover inspired ments familiar fail ral belong disjoint responsible spurious spurious composition composition alspector meaningful introduces belongs belongs lawrence competing competing dif claim claim multiplied advance recog membership membership membership membership gesture erlbaum variants captures explains explains explains discovered ignore balancing tures tures assigning assigning assigning limitation treat boxes helmholtz ent ent inferred ram opposed break emerge par weiss ideally tradeoff tradeoff ical hillsdale causal causal causal causal causal representa continuity continuity factorial factorial factorial factorial factorial factorial factorial factorial factorial factorial factorial factorial factorial magnitudes grouped grouped generators generators hughes challenging simplifying depicts increasingly harder distinguished diversity finger finger finger finger gilbert inverting fea fea holding eters rose rose strict moderate gestures gestures appearing stephen ongoing compete compete compete responsibility responsibility responsibility practically conflicting extracts fox fox ooo functionally functionally functionally joints joints occam tracks inde quick restrictive iterating seg derives derives capturing energies recovering addi ference configured configured expresses pendent relax mir tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum tracked observes decompositions recovers frozen invert tailored mentation perturbing psyche claims symmetries plain distinctive clus distinguishes articulated articulated articulated accord compose justifies fingers fingers fingers sume sume duce equiv formulating illustrative identities embody saund saund saund joshua joshua joshua joshua joshua ruth obser formalize decomposes coordinated richards favored prin pursuing ship cooperate cooperate cooperate autoencoders tering todorov todorov todorov todorov todorov inevitable gurewitz gurewitz facto ating biolog faithfully distributes proposals wjk tition tition imizing imizing imizing nts weigh vations subparts segregate hierar wik compe compe ently ener cooperating chical natu nem sixteenth rial emo inspect lil respon cipal constr dividual 
#@Tenenbaum_J,Todorov_E,
#t8
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#*network network network network network network network network network network network network network network learning learning learning learning neural neural neural neural neural input input input input input data function function function function function function function function function function function figure time time time time time set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number number number error error error error error error error results results results results results results results results results problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance based weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear vector vector vector vector vector vector vector vector order shown shown shown shown shown shown systems systems systems systems probability probability weight neurons neurons neurons neurons neurons neurons method method method method method method approach approach approach approach point point point point point point point point point point point point point point single processing control control control control large large local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate test analysis analysis matrix matrix matrix optimal optimal optimal inputs form shows shows algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper paper paper small small small small size size size size size size size size size work task methods methods methods methods methods methods methods methods fig step step step step step step step points points points points points points points points points current current current current problems problems problems problems problems problems response response similar show section section section fixed fixed line line vectors vectors vectors parameter parameter parameter parameter parameter parameter parameter real approximation approximation approximation average note note experiments result university university computation solution solution solution solution solution solution solution solution solution solution research research log log defined defined defined found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant computer distance science science science prediction prediction presented presented machine machine maximum basis basis basis nonlinear nonlinear outputs abstract applied computational computational computational computational computational computational computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density likelihood references component component stochastic stochastic due due ieee ieee procedure procedure procedure procedure procedure adaptive decision introduction estimation statistical effect cost cost cost cost cost cost search search difference difference complexity variable assume assume assume classifier classifier measure measure chosen chosen chosen chosen theorem theorem theorem bound bound bound type required represent fact techniques techniques techniques region region region region proposed proposed proposed proposed proposed proposed proposed length probabilities probabilities probabilities probabilities errors scale finite finite finite simulations minimum resulting resulting resulting resulting total total simulation computed respect respect respect respect respect respect respect respect called called mapping mapping means optimization optimization optimization optimization optimization optimization optimization optimization optimization dimension applications study em em em em original vol vol vol vol specific samples application desired series series provide provide define define rates rates rates rates related discrete mit mit steps steps steps steps steps accuracy connection update update update update update update update update update update update update update update update update update update update update update update update update update update update update descent morgan proceedings words consists advances advances advances exp computing hinton solutions solutions solutions solutions design san conference efficient full requires requires choice choice choice significant approximate con con condition derived randomly conditional conditional developed criterion criterion bounds bounds path path path path path path path path path path finally iteration iteration nature depends discussion discussion normal increases increases increases describe denote denote fast close close close assumption corresponds corresponds actions proof proof rbf rbf rbf theoretical theoretical eds square square square square square square future development kaufmann combination functional functional functional jordan jordan jordan programming programming programming increasing increasing principal numbers iterations iterations iterations iterations iterations iterations iterations max bits experts experts experts supervised expert combined minimize minimize minimize choose run run denotes architectures recent recent recent pair pair takes takes element introduced subject subject subject quadratic quadratic quadratic quadratic quadratic quadratic hierarchical cognitive cognitive recently engineering engineering conventional approximately approximately solve solve solve converge converge converge converge converge converge converge converge converge trans sparse mixtures mixtures mixtures modified modified observation scaling predicted predicted predicted hybrid hybrid hybrid reduce competitive competitive central central central central central central central central central central central central central central central learns constrained constrained mateo taking hard largest california solid radial radial radial assuming assuming minimizing minimizing minimizing minimizing exist min min manner manner manner manner identification identification denoted denoted areas boltzmann boltzmann produces produces produces longer solving solving solving solving solving stability stability distinct dept dept metric electrical electrical involves remaining scales scales minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization springer agent agent agent agent agent agent implies implies implies expectation expressed expressed review viewed viewed viewed viewed solved operations controlled approximations soft soft key convex neighborhood event boundaries generation remains valid valid valid weighting characterized characterized gating gating gating gating gating gating gating gating gating tests successfully efficiency efficiency efficiency efficiency closely modification modification modification modification efficiently computations receives characteristic verlag procedures prob allowing allowing stopping stopping lie lie lie contribution sin sin sin sin criteria notation michael michael michael michael michael minimizes computes computes ill ill maximization approximating jacobs jacobs decreasing decreasing receive extend presents minimized exhibit dual mass hall examine successive successive successive successive successive successive successive successive tech tech investigated referred referred referred hill concepts implementations implementations implementations implementations ensure ensure subsets rank rank noted algo finds established established years inequality publishers guaranteed guaranteed nowlan nowlan floating multiplication lies lies considerable forces choices arise mation controls controls inversion separately preceding preceding preceding preceding preceding addressed argument embedded parameterized peter peter peter peter peter rep rep exhibits proven extensions prevent decreased specifies simultaneous june proposition gap gap gap gap newton notes feasible guarantee guarantee guarantee rithm conditioned rotated controlling controlling controlling unity unity adds convenient logarithmic stated intelligent resulted infor repeat prentice introduces ranging programs ensures codebook viewing initialize reveals contraction augmented augmented augmented augmented steepest relies statement approximator approximator approximator adopted assigning vec ent break alternating alternating alternating alternating alternating alternating alternating alternating alternating alternating alternating dec july perturbed perturbed perturbed arg breaking leg leg arising preserved diag simplifying win barrier barrier barrier barrier maintains maintains preserve preserve siam normalizing tin lems lecture parameterization parameterization parameterization preserves interior interior interior interior interior interior interior interior jersey cliffs establishes tors kth concern proposes englewood triangle counterpart counterpart gence minimizer minimizer monotone 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#@Lemmon_M,Szymanski_P,
#t8
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#*network network network network network network learning learning learning learning neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data figure figure figure figure figure figure time time time time time set set set set set set set set networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm number number number number number number number number number number number number system units units units units units units units units units units units information information information problem models models based space space weights weights weights linear layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order systems systems values values values values values values noise weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition method approach approach approach pattern pattern pattern pattern pattern single single single single single processing processing processing processing large large large large large large local rate patterns patterns patterns patterns patterns patterns patterns inputs inputs inputs form form shows shows shows shows signal signal paper paper examples small small small small small small small small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature task task methods fig step classification classification level current current structure problems memory response response response similar 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sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial table table standard standard computer terms distance distance connections connections connections node node node node node node node node node node node node node node node node node node node science science science science map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map activation activation activation activation activation activation activation activation activation activation activation activation activation low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal sets sets sets sets maximum maximum position components continuous sample abstract applied find references component component ieee important important context context introduction complex complex behavior recurrent tion assume assume representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations word word word word word word word word word word word word part part part part center previous previous previous previous required multiple multiple multiple good good good binary binary represent represent represent represent represent represent represent represent represent represent represent represent represent represent distributed distributed distributed distributed distributed distributed distributed distributed proposed proposed proposed length length length length scale scale ing total simulation multi called called called times times mapping mapping mapping potential potential potential potential made natural applications applications applications applications vol artificial artificial specific samples represented represented represented represented represented represented represented represented represented represented series series active active active determined power approaches accuracy accuracy accuracy accuracy larger train dependent dependent proceedings proceedings proceedings proceedings report institute institute words words words words words words words words words words department loss consists consists consists internal internal individual joint difficult final layers sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences ai ai ai maps maps maps maps maps maps directly trajectory conference conference conference capacity determine efficient requires significant world world world world con derived types path selected selected iteration depends depends depends biological associative measured measured discussion arbitrary fast close complete finding finding short generate supported require main adaptation end future easily noisy including pairs needed needed reduced york york york database language representing representing numbers numbers numbers numbers iterations max max making making making international international international international international normalized decay decay decay run predict denotes architectures membrane recent recent exact exact advantage property separate similarity similarity lateral lateral lateral include sense subset subset cognitive cognitive cognitive cognitive recently highly conventional conventional calculated yields positions positions modified interval organization organization organization organization improvement entire entire grant occur loop occurs conclusion place differences designed clear exponential sound sound sound sound proportional turn turn turn exist manner denoted areas van van winner winner sequential sequential sequential sequential sequential sequential sequential sequential describes transitions implement category involves easy slightly unique unique unique unique consisting adding frequencies springer competition competition national formation phoneme phoneme phoneme phoneme phoneme phoneme labels organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing forms static static static sizes similarly past past epochs neighborhood neighborhood neighborhood neighborhood neighborhood string string foundation euclidean kohonen kohonen kohonen kohonen kohonen kohonen kohonen classified thesis retrieval inter sciences determines activated activated activated encoded encoded successful successful successful computations vowel vowel quickly allowing phonetic classify classify follow duration duration vary usual cat principles subsequent subsequent neighboring acknowledgments decreasing presents create updating accurately examine matches successive respond rest applicable variability proved encode neu smallest smallest trace trace trace trace plausible adapt extremely extremely changed changed front front taylor taylor mapped mapped mapped mapped mapped mapped mapped isolated isolated percentage percentage indicating indicating stop crucial track analyzed briefly tool starts processed sections potentially sounds gradually gradually gradually gradually english english incomplete recognizing recognizing radius researchers syllable spoken spoken experimentally ity berlin summarized ture differs fall occurrence proven proven ordered ordered phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes phonemes adjust display begins eventually initialization classifying classifying corrupted redundant sort assign forming modify resources repre establish lost inspired extending overcome serves reasoning ral north north integrator salient alphabet alphabet vowels repeat contexts representational james james james james james pat holland holland topological topological topological topological washington offers similarities similarities similarities winning winning winning winning winning recog layout master storing extends extends erlbaum consonant displacement displacement dense dense dense ure converted constitute forced tendency hillsdale remainder visited care decays allocated disadvantage challenging maximally maximally iri distinguished responding responding fea nal nil nil nil nil tail remarkable remarkable terns hilbert austin austin neighborhoods wins wins suffers focuses phonemic phonemic phonemic phonemic core consonants classi placement planck planck edition remained twelve format mis mis mis texas occurrences shares shares ira tory voiced voiced daniel daniel daniel daniel daniel winners winners winners winners mid amsterdam amsterdam activates sentations stand excluded decrement netherlands netherlands leaky strongest heidelberg miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen ames mild converting indistinguishable exclude densely buy expands shortcomings descriptive descriptive descriptive descriptive descriptive subsequence reuse strengthened subsequences phoneroes finland finland decayed decayed ffi memberships nijmegen wjk wjk wjk nized kangas kangas packed packed utexas pack pack pho textual reused mpi manages jon netic bitrary confusing fying 
#@James_D,Miikkulainen_R,
#t8
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural data data data function function function function function function function function function function function figure figure figure figure figure time set set set set set set set networks networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number error error error error error error error error error error error error error results results results results results information problem problem models models hidden hidden hidden hidden hidden hidden hidden based based based space space space weights case case case case case case case vector order shown shown shown systems values values values values values values values probability probability parameters parameters parameters noise noise functions functions functions functions unit distribution recognition method pattern pattern pattern pattern pattern pattern pattern point point point processing local local local local local local rate rate rate rate rate patterns patterns patterns patterns analysis analysis matrix matrix matrix matrix optimal optimal optimal optimal optimal inputs form shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper examples examples examples examples examples examples small small small task methods methods methods step step points points points points classification level current trained problems random memory similar similar similar similar show show show equation equation equation equation equation equation section section section section section fixed fixed fixed fixed general general parameter average average average average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term note experiments experiments experiments dimensional result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables variables computation solution research found sequence initial initial constant standard standard computer terms distance science presented presented presented present maximum range basis continuous abstract applied applied applied convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties properties properties properties properties properties properties properties likelihood likelihood likelihood references stochastic stochastic stochastic positive positive procedure procedure procedure mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction behavior behavior behavior statistical statistical effect variance variance cost cost cost cost cost cost cost cost cost change measure learned chosen previous previous previous previous bound bound type good long conditions expected markov markov make make region region proposed scale finite minimum minimum minimum minimum minimum ing computed respect sum sum sum elements means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means means optimization optimization optimization optimization optimization optimization potential applications knowledge em em em em em em em em em em em em em em em em em em em em em obtain negative negative vol artificial relative relative specific specific compared compared compared application compute compute rates rates rates rates rates rates rates rates determined experimental experimental related related discrete equal update update update update update descent descent descent descent descent descent descent descent descent descent dependent dependent morgan proceedings report institute department loss version version version consists consists consists advances final final final final framework framework framework computing equivalent equivalent equivalent directly curve curve curve additional conference requires choice choice significant statistics speed speed speed speed pages pages condition clustering clustering clustering finally iteration iteration iteration depends associative discussion technical arbitrary fast fast fast close close complete complete finding amount implemented theoretical theoretical adaptation journal square cluster cluster including including fit kaufmann probabilistic probabilistic probabilistic jordan jordan block interesting significantly ratio ratio ratio trials uniform principle leads representing iterations minimize minimize choose run run run run improve pair pair similarity apply subject quadratic quadratic recently unsupervised observations tions yields studies studies converge diagonal diagonal definition definition definition mixtures mixtures mixtures mixtures positions bounded bounded organization improvement improvement lead deviation derivative matrices matrices touretzky white white runs runs conclusion conclusions competitive editors differences measures performs moody moody moody faster faster practice practice hard hard hard hard hard hard hard radial exist exist min min averaged introduce introduce derivatives derivatives derivatives derivatives minima minima question explicit pro pro pro pro derive derive derive derive derive solving describes dept changing physical slightly gaussians gaussians gaussians applying minimization springer blocks blocks expectation versus versus decreases depending communication squares squares squares squares squares squares variation open open fraction soft soft soft soft soft completely converges converges updates partial earlier epochs epochs epochs epochs epochs epochs epochs measurements fitting neighborhood neighborhood valid initially assigned assigned assigned kohonen kohonen avoid thesis thesis thesis bell assignment assignment assignment batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch prove prove prove prove discuss maximize variations variations variations black black black black black black black holds reason reason selecting society computationally presentation presentation presentation literature comparing essentially online online online online online online online online online online online online online online online online online online online online online online identity identity identity composed traditional notice verlag induced superior running running write usual minimizes minimizes minimizes quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization computes maximization maximization preferred decreasing extend remain unlike unlike schedule carried wiley poor exhibit updating hessian hessian hessian recursive giving school analytically scaled proper proper proper variability scores understand circles circles circles circles circles circles gradients closest closest closest prototype prototype prototype prototype prototype prototype versions der algo fisher multivariate multivariate epoch epoch epoch epoch epoch arbitrarily motivated phd phd phd averages optimum residual residual slowly cos inequality inequality formula derivation derivation derivation derivation derivation improves nowlan nowlan expensive caused baum lies starts berkeley ring ring easier style style style style style bengio bengio bengio bengio bengio bengio bengio mathematics mathematics mathematics mathematics angles definite recording demonstrates incomplete mellon researchers argument carnegie limits applies empirically cmu cohen cohen share remove prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes switch berlin pittsburgh characterize reaches fall popular semi semi semi display display redundancy conditioning viterbi viterbi converged differentiable differentiable synchronization displays initialization initialization initialization newton newton newton newton newton newton newton newton newton newton newton newton benefit proofs proofs proofs proofs writing restrict arguments linearity linearity optimizing count unity royal extending chains darken darken ranges satisfying replacing replacing mark mark symposium intuitive loo displayed schedules similarities suggesting repeatedly canada canada extends dempster dempster dempster counts empty empty empty empty outperforms outperforms logarithm logarithm rubin rubin rubin benefits benefits presenting presenting welch theorems theorems par decomposed assignments assignments assignments auxiliary stands var 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#@Bengio_Y,Bottou_L,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure set set set networks networks networks training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number number number number number number number number error error error error error error error error error error results results results results results results results results information information problem problem models models performance performance performance performance based based based space space space space space space linear linear case case case case case case case case case case order order order order values values values probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions functions functions functions functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach point point point point point point point point point point point point point point single local rate rate rate rate test test test analysis class class class class class class class class matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple gaussian gaussian gaussian gaussian paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small work work work task task task task task methods methods step step step step points points points points points points points points points points points level random random random random random high similar similar show show show show show equation equation equation equation section section section section fixed fixed general general general general general general general general generalization generalization parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average theory theory obtained obtained obtained note result university computation solution solution independent log target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target estimate estimate estimate estimate estimate estimate estimate estimate standard computer terms terms science science left present maximum maximum maximum maximum maximum maximum maximum press learn learn learn components components basis basis sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract find likelihood likelihood references procedure procedure procedure procedure procedure procedure procedure important adaptive adaptive introduction behavior statistical generated generated variance variance variance variance cost cost cost cost cost search search tion difference difference difference difference difference difference difference complexity complexity complexity assume assume assume lower lower lower lower measure measure measure measure prior prior prior prior prior prior prior prior prior higher previous previous theorem theorem cases cases binary binary distributed distributed bayesian bayesian bayesian bayesian bayesian expected expected expected expected expected expected expected techniques techniques techniques observed observed simulations simulations simulations simulations resulting classes classes ing tasks total total total total total total total total total simulation regression respect respect performed performed regions means means potential potential natural obtain obtain obtain obtain obtain obtain obtain obtain artificial artificial specific specific samples samples true true application provide provide compute compute compute compute rates rates rates rates rates proc proc location location location location location location location location location location location location active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active goal goal goal goal goal mit mit mit steps steps steps steps contrast source selection morgan report report institute institute consists represents connectionist bias bias graph graph ai ai ai ai ai ai ai framework framework framework framework framework framework framework cambridge cambridge domain domain domain domain experiment experiment experiment solutions curves curves estimates design design design design design design design san san stage determine determine efficient requires requires approximate approximate approximate conditional developed developed developed levels levels levels criterion criterion criterion entropy actual finally depends sampling sampling sampling sampling sampling sampling sampling simply normal normal increases assumption finding rbf common assumed generate theoretical require require require face square square cluster easily degree degree degree degree degree degree degree degree degree noisy fit fit kaufmann objective objective typically account unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown coefficients technology technology technology technology interesting york special consistent uniform uniform uniform uniform uniform leads squared squared squared squared squared squared squared details numbers pre pre supervised polynomial polynomial polynomial polynomial polynomial polynomial polynomial attention choose choose predict improved exact exact advantage takes takes takes element strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy moving include sense sense recently engineering varying compare compare axis axis axis axis axis achieve diagonal address address locations locations locations grid sensitive horizontal parts expression concept concept concept concept concept concept deviation touretzky clusters white demonstrate strength assumptions assumptions conclusions depend differences bayes bayes bayes numerical clear faster mateo suggest propose propose taking taking presence physics california intelligence intelligence regularization regularization radial turn assuming assuming minimizing minimizing start averaged targets introduce question question suppose suppose suppose suppose derive derive derive derive derive derive generating plot describes describes laboratory laboratory mathematical dept multilayer averaging averaging physical easy slightly text text develop integrated integrated integrated integrated integrated integrated integrated applying applying minimization quality versus select select select choosing choosing focus review learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner detailed detailed centers centers sizes completely similarly key earlier earlier earlier earlier dashed dashed reduces reduces reduces remains construction query query thesis priori priori priori formulation formulation prove uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty 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sections organized style precisely incorporate circle robustness varies evaluating evaluating evaluating collected empirically conducted parameterized lack completion formulated incorrect polynomials polynomials polynomials polynomials polynomials polynomials polynomials differs aim incorporating lab pac optimality optimality optimality extensive fix girosi girosi optimizing approximates stated optimally optimally preparation carry selects motivation passive passive passive passive passive passive passive passive passive passive passive passive recovered corre chooses deg express express express indicator theoretically belonging summarize std std vari outlined learnable posteriori posteriori pressure outperforms outperforms summer incorporates encouraging ease ical valiant valiant options principled principled cohn cohn trends distri distri learnt ization maximally investigating sollich sollich sollich paradigms paradigms treating mini experi gauss develops helps bution bution opti 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#@Niyogi_P,Sung_K,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output output output number number number error error error results results results results results results results results results results results results units units units units units units units units units units units units units units units units units units information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based based space space space space space space space weights weights weights weights weights weights weights weights weights weights linear linear linear layer layer layer case case order order order shown shown systems systems values values values values values values values values values values values parameters weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit pattern pattern pattern pattern point point point point image image single single single processing processing processing processing large test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs shows shows algorithms small small feature feature net net net net net net net net net net net net net net net work work work work work work task points points points points points points points features process level current current trained trained trained trained problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems high high similar similar similar similar similar architecture line line generalization generalization real obtained obtained experiments dimensional dimensional dimensional dimensional dimensional result university university variables variables variables solution solution solution research research research research research research defined defined found target target target target target target target standard standard standard standard terms connections connections connections connections science science science direction presented present present present phase activation activation activation activation activation sets range press press press learn components components components components components components components components components components components components components components components components components components components components components components components components components outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous abstract abstract applied properties references component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component positive positive positive positive positive positive positive positive positive important context introduction introduction complex effect generated generated variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance parallel parallel representations representations representations representations representations representations representations representations representations representations representations representations representations learned learned learned learned previous previous type type required required multiple binary binary represent represent represent represent represent distributed distributed distributed expected make make fact fact fact techniques techniques techniques correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correct correct correct correct correct forward forward simulations total human multi multi multi sum performed performed times regions means means natural natural natural study study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge negative negative negative negative negative negative negative negative negative negative original vol relative specific represented represented represented represented true application application application cross cross cross cross cross cross cross cross cross cross cross goal goal constraints connected connected connected connected connected connected connected connected equal equal equal equal equal equal approaches steps comparison comparison comparison comparison comparison comparison comparison comparison contrast contrast contrast connection connection connection connection connection connection connection connection connection nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets modeling modeling modeling morgan morgan morgan proceedings proceedings report department version technique technique technique technique technique individual advances advances connectionist connectionist connectionist difficult difficult difficult difficult layers addition addition addition addition addition addition addition addition addition addition hinton additional view view solutions solutions san top determine determine determine determine efficient efficient requires requires world speed increase produce produce produce produce randomly randomly randomly types types types product product finally selected selected selected nature nature discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance limited limited close supported supported role role role role role main eds eds eds square end end end end end end end end end end end end ability cluster cluster makes development development including fit kaufmann kaufmann kaufmann typically typically pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs account account account account account coefficients structures operation operation principal principal principal representing representing numbers direct bits bottom combined combined produced produced produced added light predict predict perceptron improve recent separate apply apply include include subject identical sense sejnowski array array cognitive cognitive cognitive cognitive engineering interest dimensions dimensions dimensions dimensions dimensions sufficient sufficient highly previously previously previously subjects subjects yields yields pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca achieve diagonal diagonal diagonal diagonal diagonal separation separation separation generalized sensitive sensitive constructed parts scaling scaling deviation deviation matrices matrices matrices rotation correctly feed feed touretzky touretzky white white white white white white white starting starting place greater greater greater greater greater greater greater reduce reduce reduce conclusions valued differences sigmoid sigmoid sigmoid accurate designed clear clear clear clear clear constrained taking taking taking largest external external drawn demonstrated labeled labeled variety start targets targets targets targets targets targets manner identification explicit relation ways factors plot recall sensitivity explicitly explicitly coordinates coordinates dimensionality transformations transformations unique adding applying applying applying applying springer implies yield focus squares squares squares squares squares overlap viewed variation variation variation variation variation variation variation variation variation variation variation variation variation variation operations operations restricted showed approximations decomposition static understanding understanding understanding understanding sizes similarly discrimination sign sign sign partial earlier earlier additive epochs epochs epochs classical combining valid valid valid valid sufficiently advantages advantages existing activations activations activations activations activations sciences plotted plotted plotted black black black black black black black black black black major middle identified encoded encoded encoded effectively effectively paths mcclelland mcclelland identify identify identify identify score plots plots plots essentially essentially identity verlag strongly showing issue symmetry contribution contribution contribution contribution contribution contribution contribution contribution contribution classify generative vary play realistic acknowledgments tesauro cowan employed employed origin transformed xor xor xor xor xor xor xor xor xor essential relations involving association school behavioral scaled scaled scaled scaled scaled comparable scores scores scores scores scores scores scores scores scores scores scores scores scores scores understand cognition examined circles circles circles circles integer integer integer opposite psychology psychology equally noted separated separated separated shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes shapes multivariate multivariate multivariate contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions contributions isolated indicating developing distinguish distinguish variances variances phenomena coded coded coded coded coded coded answer answer cascade cascade cascade cascade cascade cascade cascade cascade cascade cascade multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication correction worse comparisons comparisons considerable rapid easier producing located ran products potentially circle fourth elman elman elman elman elman elman elman elman simulate marked psychological psychological psychological berlin characterize characterize inherent conclude focused begins tile progress progress displays extreme extreme arithmetic arithmetic arithmetic arithmetic arithmetic picture picture picture picture intractable oxford restriction extensive perfectly rotated rotated rotated rotated rotated rotated rotated rotated rotated theories eliminated spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral systematic multiplicative analyzing analyzing analyzing neurobiology roles roles sanger sanger sanger sanger sanger sanger sanger sanger implications implications enhanced alspector analyses analyses analyses excellent contexts separating ensures respective respective lang lang evident facilitate lawrence thomas thomas thomas thomas thomas claim approximators multiplied francisco master informative canada canada erlbaum erlbaum partitioned valuable summarize fahlman fahlman fahlman receiving integers integers integers integers integers integers default dividing dividing assigning dense spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals multiplying yielded yielded yielded yielded yielded yielded summer job revealed revealed revealed failed pieces distinction distinction distinction utilize 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#@Oshima-Takane_Y,Shultz_T,Takane_Y,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model neural neural neural neural neural neural neural neural neural input input input input data data data data data function function function function function function function function figure set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm output output output output output output output number number number number number number number error error error error error error results results results results results results results results results results results results results results units units units units information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based based based based based based based based based based based space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear case vector vector vector shown shown shown systems systems systems systems systems systems systems values values values values values values values values values values values parameters parameters parameters noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition method method method method method approach approach approach approach approach pattern pattern pattern pattern point single single single processing processing processing large large test test test patterns patterns patterns patterns patterns patterns class class optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple simple simple simple simple simple simple simple paper paper examples small small size size work task task task task methods methods methods step field classification process process process level level level trained trained trained trained trained trained problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems similar representation representation representation representation show show show section section section section fixed fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors general general general general generalization generalization generalization generalization generalization parameter real theory term term term term note university university university university university variables research research defined defined found target target initial initial table table table table table table table table standard computer computer computer computer terms distance distance distance distance connections science science science science science present activation activation activation activation machine machine press components basis basis outputs outputs outputs continuous abstract abstract applied back computational references due due positive positive procedure decision propagation propagation introduction complex behavior behavior behavior behavior behavior behavior behavior effect generated generated parallel cost search search search tion tion difference complexity complexity complexity variable assume rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure representations part part cases type type required required required multiple good good long represent represent distributed expected expected fact techniques region correct simulations simulations classes ing tasks tasks total total simulation simulation simulation simulation simulation human performed regions mapping applications knowledge knowledge knowledge knowledge artificial artificial specific specific represented true true true true compared compared application desired cross cross provide define define compute compute compute perform goal related discrete equal approaches mit steps comparison contrast train nets modeling selection morgan report institute department department department department version version version consists advances represents represents represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult final bias bias bias bias bias addition cambridge domain domain equivalent equivalent hinton additional additional solutions san determine efficient requires choice choice choice significant significant world basic basic basic basic pages pages validation give produce coding clustering developed levels types entropy product actual actual actual actual actual actual actual actual finally finally selected evidence evidence nature achieved achieved normal normal normal technical describe describe describe arbitrary group group group group tested tested tested limited limited assumption complete finding finding nearest nearest nearest nearest nearest shape shape shape shape shape generate main eds easily makes makes rumelhart rumelhart fit kaufmann typically typically transfer programming interesting interesting testing projection head head special mode language details direct making decay decay decay polynomial polynomial idea produced choose added description description description description description light predict recent resolution robust robust takes typical reported reported apply identical cognitive compare conventional approximately approximately calculated volume match background symmetric williams expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression lead lead concept studied wide alternative alternative setting demonstrate demonstrate conclusion place minimal minimal greater valued differences sigmoid sigmoid accurate accurate numerical clear moody exponential learns learns mateo sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal california labeled assuming variety variety variety exist groups groups appears appears 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template template template template template template template template template template thesis thesis activations color color inter batch mozer mozer mozer mozer mozer candidate candidate domains domains domains absolute tests simplicity reason reason identified efficiency included included mcclelland literature efficiently efficiently efficiently reached summary summary summary summary summary procedures procedures prob interested interested issue follow list michael michael michael michael michael generalize generalize paradigm providing minimizes highest principles attempt subsequent extract extract extend minimized body body explore simpler powerful layered xor xor xor xor xor xor xor xor xor access requirements put involving detail hanson recursive recursive recursive lippmann examine history authors comparable symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic symbolic 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extracting extracting extracting extracting extensions logical conclude returns diagnosis diagnosis cumulative cor cor cor don sort sort databases databases purely addresses eliminate nonzero extending fits murphy convenient promising stated check check effectiveness canonical continue colorado colorado colorado den captured scan facilitate offers offers initialize treatment foundations express cancer cancer cancer cancer cancer cancer augmented augmented augmented augmented relies valuable stopped fold shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik explorations lem uci uci uci uci verify dna microstructure thrun corporation minus validity validity benefits encouraging propagating instantiation exception exception exception additionally additionally additionally lit descriptions descriptions letting molecular remainder clas principled summarizes care pdp convert boulder boulder boulder nuclei nuclei categorization voting siam holding holding bill bill bill bill bill 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#@Alexander_J,Mozer_M,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set set set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number number number system system system system system error error error error error state state state results results results results results results results units units units units units units units units units units units units units units information information problem problem problem problem problem problem problem problem problem problem models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based space weights weights weights weights weights weights linear linear linear case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown systems values probability probability probability probability parameters parameters parameters weight weight weight weight weight weight weight weight functions unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution method method method approach approach approach pattern pattern point point single single processing processing large large patterns patterns patterns analysis analysis matrix matrix matrix matrix matrix form shows algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian paper paper paper paper small size methods methods step step step step step step step step step step step step step step step step step step field field field field field field field field field field field field field field field field field field field field field field field field features features process process process process process current current structure problems problems problems problems problems problems random random response representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture equation equation equation section section section fixed fixed line line line line vectors vectors vectors vectors vectors images images images images images images general speech real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states theory gradient obtained obtained obtained term term term term term result university variables variables computation computation computation computation solution research research independent independent independent independent independent log log log log log log found constant constant constant constant constant standard computer terms terms terms distance science science science presented presented presented phase machine machine machine machine machine maximum position components basis outputs outputs sample sample abstract find computational density density density properties likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic due due due due ieee important important mixture mixture mixture mixture mixture introduction statistical statistical statistical statistical statistical statistical generated generated generated generated generated generated parallel cost cost cost cost cost cost cost cost cost cost cost cost tion energy energy energy difference difference complexity complexity complexity signals prior representations higher part bound bound bound bound bound required required multiple multiple multiple multiple multiple good represent distributed bayesian expected expected expected equations equations equations markov markov markov fact fact proposed length length length length probabilities observed minimum minimum minimum resulting ing simulation human computed respect sum sum called means factor natural em em em em em em em em em em em em em em em em em em em obtain obtain obtain obtain obtain obtain obtain negative negative original artificial samples samples samples samples samples samples samples samples samples samples represented true cross series series provide compute compute objects perform perform goal goal goal related related distributions discrete brain equal mit mit steps steps steps steps accuracy comparison descent dependent morgan institute department loss technique consists consists consists consists code code connectionist exp exp exp framework framework framework framework cambridge computing computing computing computing hinton hinton hinton hinton curve curve solutions curves estimates estimates estimates estimates estimates san top determine efficient upper upper upper upper upper upper full requires approximate statistics statistics free free free world world estimated estimated derived derived derived conditional conditional clustering bounds lines lines lines lines lines lines entropy actual provided iteration iteration nature nature sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling discussion normal describe describe denote tested hmm assumption complete assumed supported require square instance easily noisy probabilistic underlying underlying needed combination combination combination dynamical jordan jordan jordan technology projection mechanism special special empirical empirical empirical empirical empirical principle principal squared squared iterations iterations normalized bottom experts experts supervised minimize sources sources description description description description light denotes denotes architectures recent exact exact exact exact exact exact exact exact property typical machines machines machines machines quadratic quadratic quadratic hierarchical sejnowski cognitive cognitive cognitive sufficient varying varying unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised calculated solve converge converge achieve diagonal diagonal mixtures mixtures background evaluation locations locations generalized generalized bounded grant grant grant grant horizontal horizontal extended matrices matrices matrices predicted alternative generally generally generally setting setting setting setting runs starting reduce valued competitive competitive editors differences accurate performs exponential exponential physics physics solid intelligence intelligence turn assuming minimizing minimizing averaged derivatives configuration question acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann pro pro monte derive derive carlo factors factors factors factors factors factors estimating vertical vertical mathematical dept modeled consisting interaction interaction interaction integrated equilibrium expectation expectation expectation expectation expectation expectation expectation select independently focus reconstruction stages communication squares squares interpretation solved solved evaluated updated updated forms soft approximated completely similarly partition partition partition partition partition key calculation calculation slow dashed expansion combining generation generation generation foundation advantages transactions expect fire thesis formulation sciences determines priors priors discussions characterized straightforward efficiency hmms hmms hmms hmms society computationally computationally composed composed traditional compact repeated allowing showing dis dis notation gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs sampled write michael relaxation quantization observable observable observable observable observable observable observable observable observable observable observable observable maximization maximization maximization maximization extract approximating approximating jacobs jacobs tesauro cowan minimized minimized bars explore unlike unlike difficulty divergence hall project mse mse office maximizing maximizing notion act gradients naturally configurations configurations thought shapes shapes multivariate neal neal massachusetts pairwise publishers guaranteed defining tractable tractable benchmark baum baum london inside formalism organized producing desirable arise mation laboratories consequence scientific describing calculations calculations toronto toronto arises arises author incomplete integrating questions reflect collected lack passes characterize fall monotonic geman geman geman geman replace logp logp logp expectations expectations expectations expectations differentiable softmax softmax softmax wesley ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani intractable intractable intractable sleep addison forming formally guarantee summing summing zemel zemel zemel zemel zemel zemel zemel reconstructed repre discover discover naval royal proceed clamped clamped clamped clamped clamped kullback chains promising promising promising siemens city resulted occurring scoring exploit operates adequate intuitive generalizes substituting date alspector lip saul corre iteratively guarantees den lawrence reproduce francisco surprisingly creating canada relies ignore dempster dempster dempster empty approx corporation rubin helmholtz annals leibler inferred cooperative cooperative cooperative cooperative presenting formulate expanding poses weiss mdl mdl multinomial discovering causal assess remainder factorial factorial factorial factorial factorial factorial factorial factorial factorial factorial factorial visited mutually exclusive chapman approxi gener crosses noting laird barlow barlow suffer atr ward simplifies observables observables 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#@Ghahramani_Z,
#t8
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data function function figure figure figure time time set set set set set set set networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number error error error error error error error error error results results results results units units units units units units units units units units units units units units units units units units units units units units information information information information problem models models models models models performance performance performance based space space space space space space space space space space space space linear linear case vector vector vector vector vector vector shown shown shown shown shown shown systems systems probability probability probability parameters parameters parameters parameters parameters parameters unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method approach approach approach approach single processing processing large large large local local local local local neuron shows signal signal signal signal signal signal signal signal simple paper paper small small small small size size size feature feature feature feature feature net work fig fig fig fig fig step step points points points points points points process process process current cell cell cell cell cell structure structure random high high similar similar similar fixed rule rule vectors vectors vectors general general general general parameter parameter states obtained term note activity dimensional dimensional dimensional dimensional dimensional result variables variables research defined target target initial initial initial initial constant constant constant constant constant table distance distance distance distance distance distance connections connections connections direction presented map map present present low nodes motion range learn position basis abstract applied find find density density references component component component due procedure important important decision introduction hand behavior statistical generated generated generated generated generated tion tion tion change complexity variable variable variable variable lower measure signals signals signals signals signals signals signals signals chosen part center center center previous previous previous previous required multiple make make make techniques region proposed proposed proposed correct simulations resulting ing total total simulation simulation simulation computed respect respect performed called called regions regions mapping mapping means applications applications applications original original original original artificial artificial application desired define perform determined goal connected connected approaches steps steps steps steps larger contrast contrast contrast connection morgan morgan advances advances final final final final scheme scheme graph graph maps maps directly directly san san top conference determine determine requires requires pages pages pages pages give weighted randomly clustering clustering criterion criterion criterion criterion lines lines lines finally nature depends biological achieved measured discussion arbitrary fast limited complete finding rbf nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest common effective generate generate generate main main adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation journal makes makes kaufmann kaufmann objective objective pairs smaller combination combination combination unknown significantly character projection edge edge edge edge edge edge edge structures structures structures structures structures structures structures structures structures principle principle principle leads leads principal principal squared squared representing call numbers pre direct direct direct international bottom supervised supervised supervised supervised early decay decay idea combined choose run denotes advantage property property movement movement practical apply introduced moving include sense recently unsupervised unsupervised unsupervised tions definition positions positions lead locally move clusters clusters setting demonstrate demonstrate strength row row row hebbian hebbian hebbian hebbian hebbian reduce neighbor competitive competitive competitive competitive competitive editors editors differences measures learns learns learns learns learns learns mateo mateo propose propose propose largest reduction drawn radial user start exist exist exist decrease decrease introduce areas areas areas areas areas reference reference reference explicit relation pro construct construct edges edges edges edges edges edges edges edges edges edges edges edges edges edges edges longer ways mathematical implement infinite dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality consisting consisting develop adding springer letters formation depending depending stages stages stages correlated influence influence organizing fraction centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers forms completely earlier spaces reduces neighborhood purpose purpose purpose purpose add add interpolation interpolation interpolation intermediate intermediate intermediate initially distances euclidean euclidean kohonen kohonen kohonen kohonen kohonen advantages advantages topology topology topology topology topology topology topology topology topology topology topology existing priori priori discuss partially neighbors neighbors neighbors closely closely suitable differ identify identify schemes situation quickly kind kind induced induced induced induced induced induced induced prob stopping dis sampled vary simplified quantization quantization quantization quantization moves illustrates neighboring neighboring tesauro decreasing cowan situations schedule create essential relations relations relations incremental incremental incremental incremental incremental incremental mappings possibility proper complicated phases closest possibly editor adapt adapt necessarily integer noted assumes hebb generates mentioned mentioned slowly crucial growth growth publishers track defining growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing biology adapted adapted briefly lies organized author cybernetics reflects evaluating evaluating flexible remove remove remove rely differs germany inherent decreased age age age age initialization ear optimality forming perfectly discover connecting outcome lost oja oja promising promising satisfying grow removing sanger sanger settings north optimally continue continue alspector connect corre iteratively respective decide holland regarded moved topological topological topological topological topological topological topological topological topological topological counter offers arrangement initialize advance advance thin border accumulated lem informa multiplying multiplying schulten schulten schulten schulten schulten schulten schulten schulten schulten schulten schulten schulten basically removal removal opposed preserving incrementally connec realize clustered shaded increment cessing thick thick distribu gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas met met insertion insertion insertion insertion insertion investigating anal preserve universit subspaces subspaces voronoi voronoi helps topologies topologies topologies topologies accumulation sponding institut continued continued heavily reversible reversible eliminates connects obey lying lying successively successively triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation poly decaying spirit dimen adapts vicinity gathered insert insert insert insert martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz martinetz ysis amsterdam amsterdam inserted simula elegant neigh amax amax dead insertions mar impor icann ogy ogy ogy concurrently tant topologically fur scratch fulfilled analyzer ending delaunay delaunay delaunay delaunay delaunay delaunay delaunay delaunay delaunay delaunay useless occuring rid pervised sole indefinitely overcomes aging aging masking zky touret invalid prin subgraph subgraph closeness unsu dimensionalities dimensionalities fractions sionality kangas optional adapta submanifold underlies halfway inserts gies neuroinformatik nay tribute ciple emanating emanating ruhr adaptations adaptations bors 
#@Fritzke_B,
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input data data function function function function function function function function figure figure set set set networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number results results results results problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models performance performance based based linear linear linear linear linear linear linear case case case case case case case case case case case case vector vector order shown shown shown probability parameters parameters parameters parameters parameters functions functions functions functions recognition method method method method method approach approach approach approach pattern single single single single single single single single single large local rate rate form form form form form form shows algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper net net net net net net net net net net net net methods methods methods fig fig step step step step step step classification classification classification process process current trained trained trained structure problems problems problems random random representation representation architecture architecture architecture architecture architecture architecture show show show show equation equation section section section section section line line rule general general general parameter approximation approximation approximation approximation approximation approximation approximation approximation gradient gradient obtained obtained note experiments experiments experiments result university university computation computation computation computation computation solution log log log log defined found found found table table estimate estimate estimate estimate estimate estimate estimate computer computer terms science science presented presented phase maximum maximum press press press learn basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs abstract find find find find convergence convergence convergence convergence convergence convergence convergence convergence density density density density density density properties properties likelihood likelihood likelihood likelihood references due ieee ieee adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation estimation tion tion variable variable classifier prior prior prior prior learned chosen chosen higher cases cases required multiple multiple multiple multiple multiple multiple multiple multiple long equations make fact proposed proposed proposed proposed proposed proposed correct finite classes ing total simulation simulation simulation simulation regression regression respect respect respect respect performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq called mapping mapping optimization optimization optimization applications applications em em em em em em em em em em em em em em em em em em em em em em em em em em em em em original original vol vol vol samples samples compute compute rates proc perform perform perform perform posterior brain equal mit steps comparison comparison update nets nets nets nets nets nets nets nets morgan morgan proceedings report report words technique consists consists consists individual advances advances joint joint joint difficult exp exp exp considered cambridge equivalent directly directly hinton hinton hinton hinton hinton hinton hinton curves limit san san determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full requires requires statistics world estimated estimated estimated increase give produce weighted conditional developed lines iteration iteration iteration iteration simply simply associative feedforward common theoretical require eds eds makes fit kaufmann kaufmann objective needed combination combination jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan testing testing significantly character special special special special special uniform uniform iterations iterations iterations iterations iterations iterations max max max direct experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert expert expert polynomial polynomial polynomial polynomial polynomial combined architectures improved improve pair takes takes apply apply apply identical hierarchical hierarchical cognitive recently sufficient compare previously previously conventional works solve solve solve smooth yields yields yields yields converge converge trans trans mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures modified modified modified generalized generalized improvement entire parts suggests extended extended alternative alternative alternative alternative alternative alternative loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop generally bayes exponential exponential faster faster mateo mateo propose propose propose external solid assuming variety manner derive written solving solving solving dept dept dept metric implement multilayer explicitly gaussians select family family family family squares squares solved solved solved solved showed approximations evolution evolution suggested suggested converges partition earlier earlier combining combining combining combining combining combining iterative iterative assigned avoid avoid handwritten includes sciences extension priors domains gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating extra computations comparing notation michael michael michael michael michael modular nips nips maximization maximization maximization maximization maximization maximization jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs jacobs tesauro tesauro cowan cowan parametric difficulty difficulty difficulty updating issues dotted ml ml ml ml scalar int analytically analytically analytically analytically analytically analytically combine combine referred ensure fisher simplest submitted piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise cos distinguish improves nowlan nowlan caused nonlinearity nonlinearity sections mation toronto toronto outer outer requiring requiring considerably considerably applies applies applies double double double switch semi implements implements softmax softmax softmax softmax softmax ghahramani ghahramani ghahramani tresp tresp guarantee appropriately linearity fits fits scoring canonical ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx alspector alspector analyses iteratively iteratively encountered regarded ascent ascent den facilitate canada eqs eqs implicitly speeds divide email ahmad pieces possibilities adjustment param geoffrey geoffrey geoffrey geoffrey geoffrey ijcnn approxi carefully speedup emphasized esti matlab rewrite eters mix handled utilizing argmax argmax remarks solvable neuneier cally seattle ally sity lnp lnp lnp smc smc sis corn corn corn corn corn corn denominator routine decompose diverge hood stepsize stepsize stepsize stepsize kong kong save inserting hong hong saved llx favorable optimiza xlo gem numerator chinese likeli gat portland ilx ilx trigonometric trigonometric congress para asymmetrical asymmetrical mations prespecified prespecified ylz flops flops flops specht specht deficient xla parameterizations xio influencing lei lei lei lei lei usu clouds clouds suen suen alx ofthe blending reweighted rescale mains guar analyti deserve xlt bypassing 
#@Hinton_G,Jordan_M,Xu_L,
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#*network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure set set set set set set set networks networks networks training training training algorithm output output output output output number number number error error results results results results results results information information problem problem problem problem problem problem models performance based based based based based based based space space space space space space space space weights weights weights weights weights linear layer case vector vector vector vector vector vector vector vector vector vector order order shown shown systems values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method approach approach approach approach approach approach approach approach approach approach point single single processing processing large local test analysis form form form form form form form shows shows shows shows simple gaussian gaussian gaussian paper paper paper work methods methods points field level trained problems similar similar representation representation representation section section section section section section section section fixed fixed fixed fixed fixed fixed fixed vectors vectors general general general parameter parameter parameter parameter real real approximation average obtained obtained obtained obtained obtained term university university university variables variables variables variables variables variables variables variables variables variables variables variables computation research research independent log defined target target target target standard computer computer terms terms science science prediction left left direction direction direction direction direction direction direction presented presented presented present activation activation low maximum range range range range press components components basis basis basis outputs outputs outputs outputs outputs outputs abstract applied applied applied applied back find density density density density density density density density density density density density density density density density density density density density density density density density density density properties likelihood likelihood likelihood likelihood likelihood references adaptive adaptive adaptive propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical variance tion variable variable variable variable variable variable variable variable variable variable variable variable rules measure signals signals signals chosen chosen chosen center cases cases cases good conditions techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques length forward forward forward finite minimum resulting ing total regression regression computed respect respect multi multi sum performed called called mapping mapping means optimization potential applications applications applications negative original artificial relative relative true true application application provide location perform determined determined determined determined related power approaches train selection morgan report report department department implementation technique technique code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances represents represents represents final exp exp exp ai ai ai ai considered considered considered framework computing computing domain domain equivalent directly directly hinton curve curve additional san stage determine statistics speed give give give con conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional velocity provided depends simply achieved normal normal normal normal normal normal normal technical group group transformation transformation transformation transformation transformation transformation inverse inverse complete complete complete complete surface finding common common effective ability easily degree typically typically underlying coefficients coefficients coefficients jordan technology leads leads principal making making normalized normalized experts experts minimize description predict discussed directions directions directions directions directions directions robust takes practical practical apply introduced introduced introduced side dimensions compare conventional conventional conventional conventional conventional axis axis tions smooth mixtures mixtures locations modified modified interval expression extended extended extended wide predicted alternative feed feed feed width width width white white occurs valued central central numerical clear california solid turn exist plane targets introduce introduce introduce derivatives derivatives construct written primary primary estimating estimating estimating estimating estimating estimating estimating estimating plot plot plot involves angle angle angle angle angle scales consisting gaussians gaussians gaussians extraction expressed squares squares overlap interpretation densities densities densities densities densities densities densities densities evaluated forms dashed measurements measurements normalization sec intervals valid valid construction euclidean euclidean euclidean euclidean euclidean avoid existing kernels kernels kernels kernels kernels kernels kernels kernels discussions major determining extra kind prob allowing showing lie lie sin quantity write write mixing mixing mixing mixing extract extract extract jacobs jacobs satisfies modelling modelling employed diego parametric investigate exponentially exponentially involving involving involving strengths preliminary biases periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic existence rise authors office office office maximizing maximizing func analogous coefficient extremely equally ensure ensure quantities academic synthetic synthetic averages cos cos cos band developing derivation track track defining nowlan lies london inside formalism directional bishop bishop bishop bishop bishop bishop bishop bishop probable mathematics acknowledgement involve angles arises arises summation summation summation summation summation tional formulated frequently schematic requirement passes mod mod aim extracting wind wind wind wind wind wind wind wind wind wind wind wind extensions softmax softmax newton secondary sensing sensing sensing restrict fix conditioned conditioned conditioned approximates circular circular circular circular circular circular reconstructed reconstructed unity convenient difficulties grow fail governed governed periods periods widths regarded von intended den spherical modelled radar radar radar radar radar radar radar radar logarithm ter aston aston aston ber quasi seek spaced remote remote remote illustration principled arising care num relating relating cartesian drawback grateful mimic els mann chris chris chris chris chris beam beam beam beam european european european water ers ers ers ers ers dropped periodicity condi agency agency labelling governing tended decaying weather triangular dimen centres gathered ensuring birmingham inappropriate satellite satellite satellite satellite satellite satellite satellite satellite satellite fore polar polar polar tails stan spanning spanning mid dard kirk calculus initializing live ncrg motivate equipped tlx peri ditional collaboration incidence unconditional unconditional cients replicating variate kauf exponentials positivity ian aea motivations coeffi assembled sionality bfgs lui lui lives rrr bessel erate antennae oix xix tackling sino zeroth odic 
#@Bishop_C,Legleye_C,
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training output output output output number error error error error error error error error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results information information information problem models models models models models models models models models models hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance space space space weights weights weights weights weights weights weights weights weights weights linear layer case case case order order order order order order order order order order order order order order order order shown shown shown systems systems values values values values values parameters noise noise noise noise noise noise 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step step step step step step step step step step step step step step step step step step step step step step step step step step step step process current trained problems problems random high similar similar representation show show show section section section rule rule rule generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter states states states states states states obtained term term term term term term experiments experiments experiments result university university computation computation computation research research independent defined defined sequence sequence target initial table table table table standard computer terms terms terms terms terms terms terms terms terms terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node prediction left left direction direction presented presented phase nodes nodes nodes nodes nodes nodes temporal temporal temporal range range range range learn learn learn sample abstract applied applied convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic stochastic due ieee positive important important introduction effect effect effect variance cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion lower lower lower lower lower lower lower representations representations learned higher higher previous cases good binary represent expected make region region length observed observed forward finite simulations simulations simulations resulting simulation simulation computed multi sum performed performed called regions regions regions regions means made study em negative negative artificial rates proc perform approaches steps steps update dependent dependent nets nets morgan morgan report institute institute words version version consists consists consists internal advances advances layers addition sequences sequences ai considered equivalent equivalent equivalent directly curve solutions curves san san effects effects effects effects effects effects effects effects effects effects effects effects effects upper free free free pages pages pages increase derived randomly developed levels area product achieved discussion discussion technical feedforward increases increases tested complete predictions predictions predictions predictions predictions amount amount common end end noisy noisy kaufmann kaufmann simulated simulated typically mlp mlp mlp testing increasing increasing operation representing pre decay decay decay decay decay decay decay choose added predict predict perceptron improved discussed improve improve improve improve improve improve improve improve improve improve improve exact practical include identical subset relevant previously volume works solve yields match correspond studies converge achieve achieve trans chain improvement sensitive entire occur occur derivative derivative derivative alternative correctly move white demonstrate demonstrate runs place reduce conclusions editors editors sigmoid sigmoid sigmoid sigmoid measures faster mateo mateo taking presence demonstrated demonstrated demonstrated regularization regularization regularization assuming minimizing min relationship introduce introduce derivatives carlo ways confidence multilayer simultaneously simultaneously consisting adding applying applying applying applying quality quality john yield yield stages stages stages codes codes controlled showed lee lee lee lee lee lee suggested updates sign sign sign sign sign partial partial partial partial reasonable additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive epochs epochs expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion event add valid string string string string string string string string string string string string string advantages classified combinations perceptrons strings strings strings strings strings strings strings strings plotted grammar straightforward closely closely capable encoded encoded effectively driven driven delta delta literature plots miller fine refer list absence absence absence giles giles giles giles giles giles giles giles giles giles giles giles attempt illustrates illustrates operating extend cowan layered updating rapidly rapidly hanson hanson hanson hanson hanson lippmann dual dual dual dual discriminant discriminant parity parity parity parity fault fault fault fault working working working proved momentum analogous removed coarse adapt analyze automata automata automata automata illustrate taylor taylor initialized consist improving advanced publishers publishers analyzed majority independence easier worst worst bishop bishop bishop products products beginning gradually begin sun raw raw raw raw improvements improvements limits peter introducing operate summarized mod perturbations extracting chen chen achieves achieves achieves tolerance tolerance tolerance tolerance tolerance tolerance implements focused 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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural input data data data data data data data data data data data data data function function figure figure time time time time time time time time time time time time time set set set set set set networks networks training training training training training training training training training training training training training training training training training training training output system error error error error error error results results results results results results units units units units units units information information information information information information information information information information information information information problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance space space weights weights layer layer layer layer layer layer layer layer layer layer case case case systems systems noise noise noise noise noise weight weight functions functions functions recognition recognition approach pattern pattern image image image image single single single single single single single single control rate rate test test test test test test test test patterns patterns patterns analysis class optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form shows shows shows signal signal signal signal simple simple gaussian small small size size size size size size size size size size feature 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real average theory gradient gradient gradient obtained note note experiments experiments experiments experiments experiments experiments experiments experiments university university computation research research independent independent independent independent independent defined sequence initial table table table table computer terms terms connections connections science science left left left left left direction present present machine object object learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn outputs outputs outputs outputs outputs outputs outputs outputs sample sample sample sample sample sample sample abstract find find find find find references stochastic due due due due positive procedure procedure important important important important important important important important introduction complex complex statistical statistical effect parallel search search search search tion difference difference difference difference complexity complexity complexity signals signals signals signals signals representations representations representations representations representations representations representations representations representations representations representations learned learned learned learned learned learned learned learned learned learned part center center center center cases type type multiple multiple multiple multiple multiple multiple good long represent represent distributed expected make techniques techniques techniques region region proposed scale finite ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks sum regions mapping potential dimension dimension made made made natural study original original original artificial artificial specific specific true compared compared provide provide provide compute rates rates rates location location location location location location location location location location location location location perform perform perform goal goal related related related related related related related related related related related related related related related related related related related related related equal larger larger connection train nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets selection selection selection selection selection selection proceedings proceedings proceedings proceedings proceedings connectionist difficult difficult difficult bias bias bias bias bias bias bias layers computing domain domain domain domain domain domain domain domain domain domain domain domain domain domain experiment experiment experiment experiment directly hinton hinton curve additional additional additional curves curves curves trajectory effects effects effects conference conference conference capacity capacity capacity capacity capacity determine determine efficient efficient efficient requires significant world world speed speed increase give con con channel channel derived developed robot robot types types finally selected selected evidence evidence backpropagation backpropagation backpropagation backpropagation backpropagation measured discussion tested tested tested limited surface common common common common effective effective effective shape generate main main main journal journal pixel pixel pixel ability hypothesis future future future makes makes sensory simulated smaller underlying underlying underlying needed needed transfer transfer transfer testing testing testing edge edge edge edge edge edge edge mechanism trials database empirical empirical empirical principle squared max pre pre direct international international international combined run run run added predict predict predict predict predict improved improved improved improve improve improve improve improve improve improve directions separate separate similarity reported subject identical pixels pixels pixels sejnowski cognitive relevant relevant relevant interest sufficient compare previously yields correspond studies modified grant exists horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal intensity intensity intensity wide wide touretzky width width width occurs occurs occurs occurs occurs column demonstrate runs runs runs runs half place depend interactions accurate peak performs learns learns learns learns learns learns suggest strong hard hard hard hard mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms intelligence intelligence regularization regularization pulse relationship relationship minima minima minima minima minima minima minima minima force acknowledgements suppose suppose suppose appears derive derive perception ways ways ways ways ways describes vertical explicitly simultaneously simultaneously averaging infinite physical easy easy easy text mutual applying predictive select john yield national independently phoneme phoneme overlap controlled restricted key smoothing performing epochs add initially advantages david recognize automatic specifically domains domains domains domains tests tests tests tests tests columns identified identified extra extra extra extra extra society computationally identify detect capture summary road road road road road road road road road road road road procedures moore showing showing showing running duration satisfy sampled simplified generalize realistic providing providing providing attempt extend camera presents simpler experience difficulty difficulty optimized biases fewer reducing ideas school school rest parity combine root working maximizing comparable symbolic affect attributes act gradients concepts created created created created equally equally thought versions initialized simplest simplest serial serial serial finds mentioned advanced preference preference preference stop developing growing improves improves expensive expensive briefly worse starts stress stress stress processed easier easier easier day day ran arise consequence english attribute attribute attribute attribute attribute medical read mellon mellon requiring percent percent carnegie carnegie double double collected cmu cmu peaks peaks backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop share share share share share share treated frequently compares commands pittsburgh fall fall monotonic phonemes prevent prevent curvature green substantial simulator kinds age begins begins calls hints hints hints hints hints hints hints sharing sharing irrelevant irrelevant lab corrupted benefit benefit benefit benefit benefit benefit benefit benefit benefit accomplished restriction restrict summing controlling mobile lost stronger difficulties grow balance biased biased biased exploit responsible generalizes generalizes generalizes falls falls falls falls programs patient mental lang enhance enhance demonstration scan schedules entries entries surprisingly rich rich rich rich rich extends inductive inductive projects dietterich dietterich valuable ignore balancing balancing balancing intersection intersection intersection intersection intersection fahlman treat learnable learnable learnable learnable andrew verify rms informa pressure abu abu abu abu outperforms yielded yielded summer blood unable mostafa mostafa mostafa thrun users exhaustive lane lane creates benefits diverse forced expanding conjecture comparative regularity regularity regularity blue affects examining formance blocking guidance mitchell mitchell pomerleau pomerleau pomerleau carefully relate individually conversely discusses amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification steering steering steering things things things things things aaai helps helps helps helps suggestions demonstrating rarely rarely rarely laws differently regularities regularities tom tom prefer prefer prefer prefer rosenberg locate overtraining overtraining interpreting hopkins stripes flows distinguishing agency manually beneficial pratt concert admission admission admission restricting restricting recognizes recognizes recognizes exploits arpa evolving predictable multimodal nettalk nettalk nettalk nettalk nettalk nettalk nettalk teaching scott computable comprised dent catastrophic mul blocked blocked blocked dean ming mounted simon aggregate sebastian pull caruana caruana caruana caruana caruana caruana caruana fight entered apparatus respects week helped multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask roads roads hild stripe experimentation outlines retains snapshots emphasizes plex nectionist cap cheap crafted dave gation cre sev snapshot door door door door door door door door door door door told chunks synthesizer synthesizer seeds badly percentages portant kamm doors doors doors doors doors doors doors doors doors discussing aloud alters bakiri ken incre precludes precludes tiple ating easiest helping noteworthy loc jhu eecs holden tick severity severity 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#@Camana_R,
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#*network network network network network network network network learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural input data data data data function function figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number system system system system system error error state results results results results information information information information problem problem problem problem models performance performance based based based based based based based based based based based space space space space space space space space space space space space space space space space space linear case case order order shown shown shown shown shown shown shown systems systems values parameters recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method method method method method method method method method approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point image image single single single single processing processing processing processing large large large test test test test test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class optimal optimal optimal optimal optimal optimal shows shows shows algorithms simple gaussian gaussian examples small feature feature work work work work work task task methods methods methods methods methods methods methods methods methods step step points classification classification classification classification classification classification classification classification classification classification classification current current current current current trained trained structure structure structure structure structure problems problems high high similar architecture section line line line line rule vectors vectors images general real real approximation average average average theory gradient note note note note note dimensional dimensional computation computation computation computation research research independent found found found found found found found found found found found initial standard distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance node node present low low nodes machine sets sets sets range range press basis basis basis basis continuous continuous continuous abstract applied applied back find find find find computational computational computational computational computational computational computational computational computational computational properties references due ieee adaptive propagation introduction complex statistical parallel parallel search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search tion difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity spatial classifier lower learned chosen center required required binary represent tree fact correct errors scale simulations minimum minimum minimum minimum computed means factor dimension natural global applications vol represented represented compared compared compute compute compute compute proc perform determined determined goal related constraints connected equal steps steps steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison contrast descent morgan morgan morgan report implementation technique kernel advances advances advances joint represents scheme scheme scheme graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph considered computing computing equivalent top efficient efficient upper full full full requires requires requires choice choice significant world world speed speed basic increase increase validation clustering criterion criterion criterion criterion criterion criterion criterion lines lines lines lines finally finally selected backpropagation depends depends depends achieved achieved normal arbitrary arbitrary arbitrary arbitrary group denote transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation fast corresponds surface surface nearest nearest nearest nearest nearest nearest nearest nearest eds eds eds end pixel instance instance instance instance future kaufmann kaufmann kaufmann smaller smaller underlying needed reduced reduced significantly significantly significantly significantly character projection increasing matching matching database database representing details pre stored stored stored normalized magnitude frame attention choose added architectures architectures improved improved improve directions directions directions directions recent recent recent resolution resolution resolution advantage separate takes takes typical reported introduced include include include pixels hierarchical hierarchical trees sense sense sense recently recently relevant interest interest interest highly calculated calculated tions address symmetric grid improvement improvement storage increased increased constructed invariant invariant invariant invariant invariant scaling scaling scaling suggests extended wide rotation rotation rotation rotation rotation correctly hybrid hybrid width loop loop hardware demonstrate half half flow starting starting reduce reduce conclusions neighbor neighbor valued central tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent accurate accurate accurate moody faster faster faster faster faster practice demonstrated california solid start averaged derivatives derivatives characters acknowledgements appears digit digit perception ways primary label label tuned recall recall metric metric metric metric category category category category category category category category category category category transformations transformations transformations transformations transformations transformations transformations slightly slightly text angle angle scales consisting formed formed formed shift decreases variation showed translation translation digits digits dashed performing normalization remains distances distances filtering construction construction construction euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean classified classified classified classified classified david david david david david handwritten handwritten handwritten handwritten handwritten includes combinations usa inter subspace subspace candidate candidate candidate candidate candidate candidate candidate candidate domains neighbors neighbors neighbors neighbors neighbors neighbors regular middle efficiency included efficiently computations projections projections projections comparing invariance invariance orthogonal ten road notice graphs cun cun cun cun success superior superior issue return categories categories quantity list list list list backward giles denker denker denker denker received attempt consisted illustrates illustrates illustrates tesauro cowan cowan simpler requirements rapidly put relations humans hanson hanson optimized limitations accurately accurately lippmann fewer reducing matches applicable relationships relationships understand hill smallest naturally closest closest closest closest possibly implementations adjusted adjusted prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype versions versions obvious portion formal noted explored art store finds isolated isolated optimum optimum years asymptotically percentage percentage cos cos crucial crucial crucial convolution fairly coded failure majority capabilities capabilities spatially rapid rapid rapid rapid arc closer closer organized preprocessing preprocessing constructing directional broad worst products simard simard simard simard simard simard simard simard simard simard simard simard simard simard simard simard calculations calculations calculations begin geometry geometry explained geometric prop reflect led relevance poorly marked marked employ employ incorporated incorporated requirement prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes popular incorporating incorporating coherent yielding distortion distortion irrelevant classifying sort pick pick databases rotated labelled labelled labelled minutes handwriting mark guide alspector meaningful analyses heavy connect corre negligible pat pruned overview searching counter initialize initialize april april thin theoretically properly ends storing park speeds insensitive empty metrics metrics multiply linked arcs arcs unified geometrical guyon guyon guyon stork stork stork stork stork stork seek solely imagine clustered jacobian visited visited visited shaded shaded arising invariances invariances invariances invariances summarizes hastie hastie hastie insights approxi dominated permits hubbard searches searches careful guided categorization categorization constructs spanned cation importantly failures helps architectural sponding nist sorting sorting sorting sorting sorting sorting ble assistance transforming transforming orthonormal orthonormal orthonormal concern visit sided successively inefficient colleagues senses vicinity ated tan insert tern applica sparc elegant accuracies pointers clockwise entities italy sought classifica begun mate seeking menlo complexities insure ism mere ricoh ricoh ricoh skew owing classifi progression albrecht snowbird snowbird grayscale downward accumulates associ guiding admit admit possessing 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output number error error error error error error error error error error error error state state results results results units units units units units units units units units units units units units units information information problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based based space space space space space space space space weights weights linear linear linear linear layer layer layer case case case case vector vector vector vector vector vector order order order order order order order order order order order order order order shown shown shown systems systems values parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition approach approach processing processing local test test test test test test test test test matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs form simple simple small small small size net net net net net net net net net net net net net net net work work methods methods methods step features process current trained trained trained structure problems problems problems high memory memory memory memory memory memory memory memory response response architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show equation fixed fixed line line line rule general general generalization generalization generalization generalization generalization parameter real real approximation approximation average gradient gradient term term term term term note note note note experiments activity result result result university threshold computation computation research research research research defined defined defined sequence estimate estimate estimate standard standard standard science prediction prediction prediction prediction prediction prediction prediction prediction left left left left left presented presented presented presented present activation activation machine range basis outputs outputs outputs outputs outputs outputs abstract back find computational computational computational convergence convergence properties properties properties properties properties properties properties properties properties references ieee ieee ieee ieee important important estimation estimation estimation cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion tion complexity complexity complexity chosen chosen higher center previous cases long represent fact fact fact correlation length errors errors errors computed sum sum times elements dimension natural feedback feedback feedback feedback applications obtain artificial application series series series series series series series series compute compute connected connected brain brain brain brain brain brain steps update update train train descent descent nets nets nets nets morgan proceedings proceedings institute institute technique internal internal internal internal internal internal internal internal internal advances connectionist final delay delay scheme scheme scheme scheme scheme scheme addition computing estimates design san san conference conference conference determine efficient efficient efficient full full full significant significant significant estimated estimated estimated produce area provided technical technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward increases arbitrary denote denote complete predictions implemented supported role role main eds eds eds eds future future future rumelhart development reduced dynamical functional fully fully fully fully fully fully interesting interesting significantly ratio ratio ratio ratio special special special structures mode squared squared international international international magnitude magnitude decay decay decay decay decay decay decay decay decay decay decay decay decay decay description predict denotes denotes denotes denotes denotes denotes architectures architectures improved improved improve robust reported apply include period period highly conventional conventional conventional conventional observations observations approximately calculated calculated diagonal definition evaluation generalized williams williams williams williams williams williams williams improvement increased expression expression studied studied studied derivative derivative derivative derivative derivative derivative derivative derivative derivative pass conclusion starting starting reduce largest largest largest largest external external external external demonstrated demonstrated regularization regularization start derivatives derivatives minima construct index ann pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning slightly springer select family family dependence solved detailed detailed controlled updated updated approximations lee understanding suggested suggested suggested past calculation slow slow fitting roughly visible construction transactions avoid recorded discuss discuss importance modification delta schemes ten traditional cun heuristic showing running quantity providing giles giles giles giles delayed eigenvalue eigenvalue eigenvalue eigenvalue denker ill thresholds predictor acknowledgments remain layered layered layered layered layered layered layered poor access essential investigate difficulty updating varied involving hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian recursive recursive preliminary investigated investigated int possibility func func analogous saliency circles analyze predicting predicts illustrate impulse impulse impulse panel panel panel panel panel panel panel panel panel panel panel panel observe optimum growth distinguish distinguish improves adapted adapted cascade benchmark benchmark benchmark benchmark obs obs obs obs obs obs obs tive purposes incorporate greatly fed lack introducing marked solla solla remove operate rely ture weigend weigend weigend weigend weigend popular incorporating prevent comments decreased damage damage wesley yielding newton newton newton newton indices indices indices indices addison investigation conditioned controlling unity connecting connecting lecun lecun lecun plays lost eliminated eliminated clamped inspired extending systematic significance difficulties simplify city analyzing modifications obd obd slice connect connect pruned pruned forecasting forecasting forecasting forecasting evident den originally francisco francisco ahead extends valuable lag lag lag lag lag lag lag zipser zipser zipser zipser zipser zipser appeared numerous session session stork retraining retraining convenience solely solely demon adapting magnitudes decays decays simplifying topic constructs hansen hansen hansen hansen hansen hansen hansen hansen electronics preprint preprint gauss gauss continually mann manuscript shallow nec demonstrating sessions hassibi hassibi hassibi hassibi hassibi sees justified builds nested firstly doesn recursion devised huberman architec slices autoregressive rtrl rtrl rtrl rtrl rtrl denmark denmark experienced remained est concatenated surgeon surgeon surgeon surgeon akaike akaike akaike akaike wolff 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#*network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure time set set set set set set set set set set set set set set set set set set set set set set training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number error results results results results results problem problem problem problem models models models models models models models models models models models hidden hidden hidden performance performance performance performance performance performance performance based based based based based based based based based based based based based based space space space linear linear layer layer layer vector vector vector vector vector vector vector vector shown values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise functions functions functions recognition recognition method approach approach pattern point processing large rate test test test test patterns patterns patterns patterns analysis analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class class class matrix matrix matrix optimal inputs shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples small small small small size feature feature feature feature feature feature feature feature feature feature feature work work work task task task task fig cells cells points points points classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification cell cell memory similar show show section section section section section section rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors generalization speech speech speech speech speech speech speech speech speech speech approximation obtained obtained obtained obtained term term note note experiments dimensional dimensional university research research research log found table table table table estimate computer computer terms terms terms terms distance distance distance distance science science science prediction presented presented present nodes nodes nodes sets sets maximum maximum maximum maximum components components components components components components components abstract density density density density density density likelihood likelihood likelihood likelihood references component component component component component component component component component component due procedure decision decision mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction estimation estimation statistical statistical tion assume assume assume assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier measure measure center cases represent bayesian bayesian bayesian techniques techniques proposed classes classes classes classes classes classes tasks tasks tasks respect multi regions means means means means means means means means means potential em em em em em obtain vol cross series compute compute perform perform experimental equal equal equal power mit accuracy accuracy accuracy accuracy train train selection selection proceedings proceedings institute institute department version consists consists code represents represents exp exp exp exp considered considered equivalent directly conference determine determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full full full full choice approximate free free estimated validation validation validation validation validation validation validation derived derived conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional clustering clustering clustering clustering finally selected selected associative discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance denote denote close corresponds effective effective assumed assumed generate supported main main adaptation cluster cluster cluster makes underlying reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced coefficients coefficients technology mlp mlp mlp mlp mlp mlp interesting database database language squared call call international choose discussed improve improve directions directions directions directions directions directions directions directions separate separate separate separate apply include identical identical identical identical engineering compare compare works axis axis diagonal diagonal mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures observation observation organization sensitive horizontal lead suggests matrices matrices matrices locally clusters clusters clusters clusters generally assumptions assumptions assumptions assumptions competitive central bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes sutton learns constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained propose propose propose propose propose taking taking hard largest largest drawn proportional proportional min min relationship relationship averaged scene force denoted relation relation relation derive derive derive derive derive derive derive derive derive written winner winner winner winner winner generating vertical modeled metric implement implement explicitly dimensionality dimensionality gaussians gaussians gaussians gaussians gaussians gaussians gaussians applying applying predictive springer john phoneme densities densities densities densities densities densities densities densities densities densities densities densities approximations approximations approximations approximations approximations approximations soft understanding partition partition reduces reduces fitting fitting fitting fitting boundaries distances assigned euclidean kohonen kohonen box perceptual perceptual thesis eigenvalues eigenvalues eigenvalues automatic priors priors discussions society build projections vowel vowel vowel composed summary soc notice verlag contained showing classify classify classify providing providing minimizes highest leading leading mixing mixing acknowledgments wiley poor collection accurately discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant ideas school office office maximizing maximizing eigenvectors eigenvectors eigenvectors rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank prototype noted algo algo algo fisher fisher phd wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta variances nowlan nowlan nowlan nowlan nowlan nowlan sections potentially scientific implicit implicit lowest incomplete preceding mellon summation summation greatly carnegie reflect cmu spoken poorly berlin partitioning ordered acoustics electric utterances lot classifying classifying classifying classifying classifying classifying ghahramani leen leen leen leen leen lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq approximates approximates jth naval royal air disjoint corpus days vowels vowels vowels surprising darpa darpa modelled draw sons partitioned hart grants dempster dempster assigns assigning ure specification listed rubin outperform employs axe axe axe par big rain param duda duda rithms rithms rithms graduate dominated dominated regularized relating relating cole cole surrounding unconstrained unconstrained unconstrained win laird hansen eigen eigen eigen eigen eigen eigen matlab rewrite eters oregon status voronoi voronoi acoust insufficient builds todd todd todd todd todd orthonormal orthonormal responsibility proportions proportions compo quantizer quantizer quantizer quantizer quantizer sym zoubin colleagues ignores alto constraining constraining constraining edition shop inaccurate experimented palo percep retaining timit timit timit timit accuracies accuracies accuracies erroneous ogi ogi ogi ogi utans week fanty plp plp ponent nent retains cse cse beat explosion explosion susceptible portland discarding discarding dft assump regularizing regularizing regularizing logs logs joachim hermansky hermansky thereof mahalanobis mahalanobis mahalanobis mahalanobis kambhatla kambhatla kambhatla kambhatla spherically trailing trailing trailing trailing tron aji ixt segregate segregate discriminatory sulting postulates census census census census jtn determinants 
#@Kambhatla_N,Leen_T,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure time set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output number number number number number number number number results results results results results results results results results information information information information information problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance based based based based based space weights weights weights weights layer layer case case case case vector shown shown systems systems systems systems systems noise noise weight weight weight functions functions functions functions distribution recognition method method method method approach approach approach pattern pattern pattern pattern pattern point point processing processing processing large large large test patterns patterns patterns analysis class class class class optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows shows shows shows shows signal algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples small feature feature feature feature net task task task methods methods methods methods methods methods step step step points points points points features features features features features classification classification classification process trained trained trained trained trained structure similar similar architecture architecture show equation equation equation equation equation equation equation equation equation equation equation section section line line line line line vectors vectors general general general generalization generalization real approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory gradient gradient obtained obtained obtained obtained obtained note note note note variables computation solution solution solution solution solution solution solution solution solution solution solution solution research research research research research independent independent independent log log log log defined found target constant estimate estimate estimate standard standard distance prediction prediction prediction prediction prediction prediction prediction present machine object maximum maximum components components components components components components components basis basis basis basis continuous continuous continuous sample sample sample abstract back find computational computational computational density likelihood likelihood likelihood likelihood references due important propagation introduction complex hand hand hand variance parallel complexity complexity complexity complexity complexity variable variable variable assume assume classifier rules prior chosen center center center good good tree bayesian equations equations fact techniques proposed proposed correct correct probabilities regression multi multi sum dimension applications applications applications knowledge em obtain obtain obtain obtain obtain obtain obtain obtain obtain vol relative specific samples samples samples samples application perform determined experimental experimental experimental experimental experimental related mit mit comparison contrast update morgan morgan morgan consists consists consists consists advances advances advances exp ai computing experiment environment additional view solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions san san san efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient approximate approximate approximate approximate vision increase derived derived weighted randomly clustering lines finally backpropagation backpropagation backpropagation backpropagation simply simply biological biological biological biological feedforward feedforward feedforward feedforward feedforward describe arbitrary tested tested complete complete complete complete complete complete complete complete complete complete predictions finding rbf amount nearest nearest nearest nearest theoretical theoretical main eds eds eds cluster easily easily noisy noisy including kaufmann probabilistic probabilistic unknown unknown unknown unknown unknown unknown unknown jordan jordan interesting testing character projection york increasing representing call normalized normalized normalized normalized normalized normalized normalized normalized normalized supervised supervised supervised supervised supervised choose choose sources description predict predict predict perceptron perceptron denotes advantage robust practical practical strategy interest interest dimensions dimensions sufficient compare compare compare compare compare approximately calculated works axis axis axis axis mixtures positions generalized generalized interval horizontal horizontal lead deviation width setting conclusions neighbor central central numerical exponential mateo mateo mateo integration assuming exist exist averaged scene pro written ways ways vertical pruning recall recall recall recall recall recall recall missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing coordinates remaining easy slightly gaussians gaussians gaussians gaussians gaussians quality expectation select select select select select john influence densities densities restricted approximations centers centers centered centered approximated approximated similarly earlier reasonable dashed dashed neighborhood closed closed closed classified expect recognize maximize neighbors neighbors discussions major sensor sensor included included poggio poggio poggio efficiently score contained dis write michael giles leading predictor approximating deal cowan cowan cowan wiley production exponentially exponentially hanson integral integral dotted dotted mass applicable scaled circles closest plausible extremely thought consist arbitrarily great great stop sensors derivation variances biology benchmark ring ring worst commonly commonly probable probable projected acknowledgement author incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete leave remove continuously biologically calculating price price weigend weigend sums germany germany boston boston windows windows windows windows windows multidimensional extreme ghahramani ghahramani ghahramani tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp tresp appropriately grows grows fails kaufman kaufman dealing dealing dealing dealing dealing dealing dealing numerically accepted siemens siemens siemens removing fail affected ylx ylx ylx ylx heuristics continue alspector alspector excellent appendix appendix widths pruned forecasting properly gesture gesture gesture sons implicitly valuable papers hart hart interestingly verify leaving summer corporation ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad ahmad poses restrictions verified publication exponent distri duda duda parzen parzen parzen parzen parzen uncertain uncertain rbfs rbfs integrals integrals finger page treating housing housing housing housing bution neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier tribution tip substitute substitute mill deals substitution zoubin economic alto appro mis mis problematic polar palo costly ted meaningless cient approxima substituted substituted substituted substituted substituted buntine buntine volker volker volker volker volker volker acknowledged sing sing miinchen miinchen dash zimmermann ralph ralph ralph ralph ralph otto otto publications dan visiting ijcai hans tomaso hahn hahn elliptical react hollatz hollatz zfe elaborated unavailable georg retrain maih substitutes subutai subutai subutai brunelli brunelli researcher jor ormation ormation ormation defi 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data function function function function figure figure figure figure figure figure time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number number number number number number number system system system system system system system error error error error error error error error state state state state state state state state state state state state state state state state state state results results results results results results results results problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case order order order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown shown systems systems systems values values values values values values noise noise recognition point single single single single single single processing control control control large large local local local local local local local local local local neuron rate rate test test class class class class class inputs inputs inputs inputs inputs form form shows signal signal algorithms algorithms algorithms simple simple simple simple simple paper paper paper paper small small small size net net net work step step classification current trained structure structure structure problems problems problems problems problems problems problems problems problems problems problems random random random random random random high high high high high high high high high high high high high memory memory memory memory memory memory memory response similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture fixed fixed fixed fixed fixed fixed fixed line line general general generalization generalization generalization generalization generalization speech speech states states states states states states states states states states states states states states states states theory theory gradient gradient gradient obtained obtained term note experiments experiments experiments experiments experiments experiments experiments result result result university variables variables computation computation computation solution research research found found sequence sequence target target dynamics dynamics dynamics dynamics initial initial constant constant table table table table table table terms terms terms terms terms terms terms node node node node node node node node node node node node science prediction presented nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency temporal machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine range range range range range press learn learn nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs abstract back back back find find find find references due ieee ieee ieee important important adaptive adaptive propagation propagation introduction estimation dynamic dynamic dynamic dynamic dynamic generated generated generated generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change measure signals word learned chosen previous previous previous previous cases cases good conditions represent distributed distributed distributed equations make make make fact fact proposed proposed proposed proposed proposed proposed proposed correlation length length forward finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite simulations classes classes simulation computed sum performed performed performed performed performed performed performed performed called feedback feedback feedback feedback feedback filter filter filter relative samples true compared application series provide compute proc proc perform perform perform perform determined experimental experimental experimental experimental experimental experimental related connected discrete discrete discrete equal equal comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison train train descent descent modeling institute implementation synapses individual represents represents represents bias bias layers delay delay delay sequences equivalent experiment experiment experiment experiment experiment experiment directly hinton solutions solutions solutions solutions determine significant statistics speed pages pages pages pages increase coding weighted weighted weighted randomly randomly randomly randomly randomly levels types provided finally depends simply feedforward feedforward tested limited close complete finding ability ability including typically dynamical dynamical mlp mlp mlp mlp interesting interesting interesting testing testing testing testing testing testing significantly significantly special trials uniform leads squared squared representing numbers filters filters filters window window normalized normalized run run added perceptron architectures architectures architectures architectures architectures architectures architectures architectures architectures improve property apply include machines quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic inference inference inference cognitive relevant sufficient compare compare observations observations approximately approximately approximately match achieve achieve trans observation extended alternative feed locally locally locally locally locally locally locally runs runs runs minimal conclusions conclusions conclusions designed designed clear clear constrained encoding encoding sigmoidal averaged groups identification identification identification identification identification denoted acknowledgements van sequential stability stability distinct multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer averaging consisting consisting adding yield review depending variation restricted lee lee lee lee lee static static past past past reasonable epochs epochs delays roughly string avoid strings strings strings strings specifically coupled domains characterized gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma extra extra capable capable uniformly uniformly uniformly included successful identify tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn miller prob vary generalize providing nips wave giles giles giles giles giles giles giles observable observable extend unlike unlike varied put involving replaced issues existence giving statistically fundamental matched neu waibel induction hill necessarily automata automata automata perfect changed thought explored logic initialized initialized initialized ith switching consist arbitrarily isolated years percentage percentage guaranteed fairly adapted independence caused worse comparisons widely products products begin elman elman elman elman elman elman elman elman elman fed experimentally quantitative poorly effort frequently robinson robinson summarized extracting popular popular ordered suited gave gave gave gave chose windows benefit benefit college princeton resources perfectly jth impossible fits held intelligent ral methodology methodology adequate adequate heuristics heuristics tap started surprising lang den claim initialize infer surprisingly surprisingly indicator suggesting offer grammatical grammatical grammatical draw draw park partitioned tures tures stopped std std std std adopted divide divide appeared sine sig uniquely recurrence recurrence sinusoidal principe home home home home summarizes favor argued fir holding bill bill bill bill bill rnn nec nec lems differently frasconi virtually hid broadly dropped connects cally bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear ning substitute architec architec inferring archi archi archi complement watrous cascaded fair mcgraw fsm fsm fsm fsm zeros handbook fication meant reviewed aip maryland emerged tsoi kuhn unexpected hot hot iir fundamentally vries fallside fallside accessible tecture tecture narendra narendra narendra narendra narendra narendra narendra narendra narendra narendra seemingly distinguishes taps taps taps taps taps 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#@Giles_C,Horne_B,
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results results information information information information information problem problem problem problem problem problem models models models models models models models based based based based based based based linear case vector shown shown systems systems systems systems systems probability noise weight weight functions functions distribution distribution distribution distribution approach approach approach approach approach point point processing processing processing processing processing control local local matrix optimal optimal optimal optimal optimal optimal inputs form form form algorithms algorithms gaussian gaussian gaussian gaussian paper paper paper paper paper paper paper examples examples examples examples examples examples examples examples work work points points points points current trained trained problems problems problems random random random memory show equation section general parameter parameter approximation approximation average average theory note experiments experiments experiments experiments university computation research found initial constant estimate estimate estimate estimate estimate estimate standard computer terms science left present low machine sets sets maximum press press basis continuous continuous continuous abstract applied applied find find find likelihood likelihood references ieee ieee adaptive mixture mixture mixture mixture mixture mixture mixture action behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance tion tion tion tion tion change change change change change change change change change change assume lower measure measure prior representations good expected expected expected expected expected expected techniques techniques techniques techniques techniques correlation correct scale scale minimum resulting resulting resulting simulation human regression regression regression regression regression regression regression regression regression regression regression regression regression computed computed computed computed computed sum sum performed mapping means means reinforcement potential em em em original compared series provide define define compute compute compute proc perform perform active active active active active active active active active active active active active active active experimental goal related brain power power power mit contrast support support selection selection selection selection selection morgan morgan report institute department kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances advances advances joint connectionist exp bias bias bias bias cambridge computing computing experiment experiment curves design design design efficient efficient efficient efficient upper requires requires requires approximate approximate statistics estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated produce derived weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted conditional conditional conditional conditional conditional robot criterion criterion criterion criterion criterion types actual actual actual actual actual actual actual selected selected selected sampling feedforward describe denote denote denote tested predictions common shape require eds eds eds journal ability easily noisy noisy including fit fit kaufmann kaufmann objective jordan jordan technology significantly york empirical squared squared details supervised minimize minimize minimize minimize minimize minimize produced choose added added added predict architectures architectures architectures discussed takes practical cognitive interest previously approximately volume rl trans mixtures mixtures mixtures mixtures mixtures mixtures background improvement sensitive grant arm arm arm predicted predicted predicted predicted predicted predicted predicted predicted alternative alternative locally locally locally locally locally locally locally locally touretzky white white setting demonstrate runs assumptions assumptions competitive editors accurate accurate performs moody practice constrained strong drawn solid minimizing minimizing minimizing minimizing selective decrease manner question denoted explicit explicit explicit relation monte carlo written written primary sequential plot plot confidence sensitivity sensitivity explicitly integrated integrated gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians predictive predictive predictive minimization expectation expectation expectation expectation select select select select select select select select choosing choosing choosing expressed review review review learner learner learner learner learner learner learner learner learner learner learner learner learner learner influence approximations centered centered forms soft allowed calculation smoothing spaces fitting fitting closed closed filtering assigned construction foundation query query query query advantages transactions david david david david david expect existing exploration sciences plotted plotted plotted uncertainty discuss candidate domains discussions successfully simplicity straightforward selecting selecting selecting selecting society computationally driven delta efficiently mackay mackay mackay mackay summary conf criteria criteria criteria hold sampled write michael michael michael michael michael wave computes principles extend cowan minimized environments environments integral helpful school tech mse mse mse applicable int combine statistically statistically statistically statistically 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cohn cohn cohn cohn cohn cohn cohn cohn cohn intuition schmidhuber schmidhuber laird funded places port atr exploited demonstrating learners learners learners learners corporate identifies mcdonnell responsibility contrasts schaal zoubin zoubin zoubin zoubin zoubin zoubin reflection magazine cleveland cleveland actively lwr lwr atlas ming ming ming pew technische elegant competence fractional disadvantages nondeterministic fiir opportunity psyche psyche hillclimbing concise miinchen univariate plutowski plutowski brevity stefan tha normality linden linden implementa simplifications regres iwl iwl lea lea lea timal cda deterministically weber weber grounded juggling specht specht commit gaining kindermann prac popularity sumptions fedorov fedorov aca ool queried queried econometrics xli sed cheaply las mic cobh ero ada demic 
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noise noise noise noise noise noise noise noise noise noise noise noise functions unit distribution distribution distribution recognition method pattern point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point image image image image image single large local matrix matrix matrix form form form form form algorithms algorithms algorithms algorithms algorithms gaussian visual visual visual examples size feature work methods points points points points points points points points points points points points points points points points points features features features features level level level level structure structure structure problems problems random similar similar similar similar similar similar representation architecture fixed fixed fixed line images images images general parameter term term note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional university university variables variables variables variables variables variables variables variables variables computation computation computation log log log log log log log log log log log defined defined dynamics dynamics initial initial initial standard standard standard standard standard standard standard computer computer terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance connections node science science science phase phase low nodes nodes object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object sets sets sets sets sets sets sets sets sets sets sets sets sets sets press learn learn learn position components abstract applied find find find find find find find find find find find convergence references introduction complex complex estimation statistical statistical statistical effect generated generated generated generated generated generated generated variance variance cost recurrent search lower measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure prior prior prior learned learned learned higher previous bound type long bayesian expected techniques techniques techniques proposed scale scale scale scale scale scale scale scale resulting total human computed computed respect respect multi times times mapping optimization optimization optimization optimization optimization orientation applications knowledge knowledge em em original original original artificial specific specific represented represented represented represented series series series series define objects objects objects objects objects objects objects objects objects objects objects objects objects determined experimental experimental experimental constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected power mit comparison larger descent descent descent descent descent morgan morgan morgan department department consists internal represents bias bias bias graph graph graph graph graph graph graph graph graph graph ai ai ai maps maps framework cambridge domain domain domain domain domain domain domain domain equivalent equivalent experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment curve solutions san san san stage conference efficient requires vision vision increase derived weighted weighted weighted weighted weighted weighted weighted weighted randomly randomly randomly randomly randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering levels levels levels bounds bounds finally selected selected nature constraint constraint achieved increases increases increases transformation transformation transformation transformation transformation fast close finding assumed generate eds eds eds eds journal square end end ability instance instance instance cluster cluster cluster cluster cluster cluster cluster cluster cluster future degree degree noisy noisy noisy kaufmann kaufmann kaufmann objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective probabilistic typically needed combination combination fully jordan jordan significantly edge matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform uniform uniform uniform call call numbers international experts supervised idea minimize minimize minimize minimize minimize minimize run run run run run run added added added added added description architectures directions pair takes introduced hierarchical inference subset recently engineering varying unsupervised unsupervised calculated tions match match converge address mixtures bounded williams williams increased constructed parts invariant invariant invariant invariant invariant invariant invariant scaling scaling deviation deviation deviation deviation deviation deviation matrices rotation rotation rotation rotation rotation rotation loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop deterministic deterministic deterministic clusters clusters clusters clusters occurs column column place row row conclusions tangent measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures designed mateo physics california intelligence regularization min introduce manner manner minima annealing annealing annealing annealing acknowledgements pro construct construct generating vertical dept dept dept missing missing missing transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations consisting consisting develop minimization minimization formed formed decreases solved transform transform transform evaluated evaluate centers centers centers centers decomposition translation translation translation translation translation translation reduces combining add iterative iterative tracking generation remains distances distances distances distances distances calculate figures coordinate coordinate coordinate coordinate coordinate instances instances instances instances instances instances instances instances instances instances instances assignment plotted plotted mozer domains domains domains absolute grammar columns selecting efficiency importance differ efficiently projections comparing identity graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs repeated contained contained cun link link dis hold bar generalize nips nips nips correspondence correspondence correspondence correspondence denker jacobs jacobs tesauro extend cowan minimized minimized minimized minimized explore diego create create essential varied varied replaced replaced hanson biases matches matches matches fashion fashion fashion tech links links incremental analytically scaled scaled scaled authors cognition phases created created created adjusted prototype prototype rows rows inequality trivial analytic london straight tive incorporate incorporate ran simard simard separately universal begin begin toronto outer outer outer outer outer outer outer researchers fourth greatly fuzzy fuzzy affine affine affine affine affine affine affine affine affine experimentally employ formulated formulated formulated formulated rep operate prototypes prototypes prototypes geman geman inherent inherent yuille yuille deviations converged softmax softmax univ univ univ displays consistently pose pose saddle saddle saddle lagrange lagrange tation optimizing zemel rotated rotated rotated null rigid generality multipliers multipliers minutes tools mail mail held imposed loops loops viewpoint serves occurring operates operates unlabeled unlabeled enhanced grammars hours spurious spurious spurious spurious spurious spurious spurious recovered mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness iteratively respective mental ascent ascent peterson peterson darpa initialize initialize treatment francisco permutation permutation jolla cpu speeds onr mind mind yale yale yale yale yale approx approx gold gold gold gold gold gold gold gold gold gold gold shepard shepard incorporates maximized expanding decomposed decomposed england workstation avoided clustered clustered clustered eric eric eric eric eric algebraic algebraic translated translated translated community ocr bounding carefully afosr individually argued argued projecting scope deleted deleted deleted deleted deleted deleted million million million barrier enforce enforce amplification compu aaai mea challenge helps ucsd ucsd appearing regularities bienenstock attributed transforming hundreds hypothesized steven steven steven steven steven dcs dcs compo incorporation rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan functionally meth tance spie distorted ods vertically relational connectionism bradford promise slack objectives objectives objectives objectives objectives objectives mai mai mai mai mai haven gij permutations permutations permutations permutations nents dilemma enforced enforced shear shear shear shear shear shear enhancing saved llx projective projective excluding clocked clocked begun begun permuted permuted permuted permuted permuted dissimilarity dissimilarity dissimilarity asso brains workstations prototypical prototypical today nadel ences rni rni organize quantifies quantifies signif mia mia doubt kosowsky kosowsky tives doursat oblique irrespective memberships memberships memberships objec objec transforma oper speeding ciated sgi adjacency anand anand anand anand mutations rnj yaleu yaleu routinely fuzziness ates graduated ami beled biologists icantly perceptions flattened convincingly distort isodata tabula rasa 
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output number number number system error error error error error error error error error error error error error error error error error error state results results results results results units units units units units units units units units units units units units units units units units units units information problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based weights weights weights weights weights weights weights linear linear layer layer case case case case case case case case case case vector order order shown shown shown systems systems values values values values values values values values values values values values parameters noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight unit unit distribution approach approach single single single single single single single single single processing large large large local rate rate test test test analysis analysis optimal inputs form form form form shows shows shows shows signal algorithms algorithms algorithms algorithms algorithms paper paper paper paper paper paper paper paper small task task task task task task task task task task task task task methods step step step step step step step step step step step step step step step step step step step step step step step step step points points points trained trained trained trained trained trained structure structure problems problems high response similar similar representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show equation equation section section section section section line rule rule rule vectors general general general real real real real average gradient gradient gradient gradient obtained note note note experiments experiments experiments experiments result university university research sequence target target target target target dynamics initial initial table table standard standard standard standard standard computer computer science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left present present present present present activation low low low low low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine machine sets sets sets range nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs sample abstract abstract applied applied find find analog references due context introduction hand hand behavior behavior statistical effect generated generated variance cost cost search tion change difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference rules learned learned chosen chosen higher part multiple good expected expected fact fact fact fact techniques observed observed observed observed observed errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors finite tasks tasks tasks tasks tasks regression regression respect respect respect multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi sum sum called em vol specific specific samples compared compared application application application cross cross series series series series series series series series series series series series series series series series series series series series series series series series series series series rates rates rates determined steps steps steps steps comparison comparison comparison comparison larger larger larger contrast update update update support train descent source modeling morgan proceedings institute department department implementation consists consists internal individual individual individual individual advances connectionist connectionist connectionist connectionist delay considered considered framework computing equivalent equivalent equivalent equivalent directly directly curve additional additional additional curves curves curves curves curves curves curves san bit choice significant significant significant significant world world increase validation validation levels actual actual actual actual actual actual actual actual actual actual backpropagation backpropagation depends depends depends simply simply simply limited predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions amount amount main eds square square end future future future rumelhart rumelhart noisy noisy noisy noisy kaufmann smaller smaller dynamical testing uniform empirical squared squared squared direct direct direct direct direct direct direct direct direct normalized normalized normalized supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised early idea minimize predict predict predict denotes architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures advantage pair pair pair separate separate separate separate separate separate separate separate separate separate takes typical practical side side side cognitive engineering sufficient compare compare compare compare compare calculated volume correspond chain observation observation observation observation grant exists intensity expression lead lead lead digital deviation predicted predicted predicted predicted predicted touretzky deterministic deterministic deterministic column pass runs runs row conclusions valued valued depend differences differences differences differences accurate sutton sutton sutton sutton sutton sutton drawn start exist exist decrease averaged question denoted appears longer plot plot describes metric multilayer electrical involves applying versus versus versus versus versus versus competition competition competition competition competition decreases national focus viewed influence forms understanding updates past past past past past past past key earlier earlier epochs epochs epochs epochs measurements reduces remains intermediate calculate calculate foundation views expect expect expect color color color weighting weighting batch mozer discussions structural reason driven driven successful comparing comparing comparing comparing plots essentially summary summary traditional vary vary vary paradigm paradigm nips nips minimizes quantization observable hypotheses principles overlapping subsequent neighboring acknowledgments tesauro tesauro situations situations presents bars overfitting overfitting investigate exhibit exhibit varied game game issues dataset rise examine successive successive successive successive giving school tanh gradients gradients gradients reading analyze predicting predicting predicting predicting equally implementations friedman friedman impulse algo explored ith ith arbitrarily finds chaotic chaotic chaotic slope adjacent adjacent adjacent adjacent briefly perspective shared shared shared shared shared shared shared shared shared shared organized ran ran arise projected begin begin percent elman peter peter peter peter peter poorly http http weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend weigend fall ordered richard chose begins wesley wesley sharing trade trade lab www addison addison forming resources concerned eliminate smolensky adds dealing significance breiman breiman ranges city stated monotonically games analyses performances performances predictors forecasting forecasting forecasting forecasting colorado colorado colorado colorado francisco april ahead ahead ahead ahead ahead ahead ahead erlbaum variants santa santa santa summarize outperforms summer basically leaming opposed opposed revealed propagating conjecture hillsdale pub home summarizes ftp ftp ftp ftp rithms continues allocated boulder boulder relating individually depicts associates paradigms paradigms paradigms paradigms paradigms exchange exchange continually challenge suggestions focuses converter outperformed kth cast pronounced pronounced diagnostic contrasts huberman huberman laser laser laser laser beneficial edited edited edited adjusts longest colors teaching differentiate acknowledges linking noiseless upward predic plotting plotting caruana andreas andreas andreas andreas andreas andreas andreas ecs begun multitask exhibiting explores signaling wanted nix nix mon accelerate hurt snowbird anonymous redwood gershenfeld gershenfeld gershenfeld depart eubank casdagli investigates ume currency forecast forecast initiation crucially ser sar sunspots offs recency recency recency recency recency discrepancies backpropagate incidentally ria reviewing descriptors nearer characterizations noisier 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data data data function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output number number number number system system system system system system system system system system system system error error results results results information information problem problem problem hidden performance performance performance performance performance performance performance performance performance performance performance based based weights weights weights weights linear linear layer layer layer case case case case order order shown shown shown systems systems systems values values values noise noise weight weight weight weight weight weight weight weight weight weight neurons neurons neurons neurons neurons method approach approach approach point single processing processing control control control large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate test test patterns analysis analysis class class class class inputs shows signal signal signal signal signal signal signal signal signal signal algorithms simple simple paper paper paper paper examples small small net net net work work work task cells points classification classification classification classification classification classification classification classification classification classification classification classification classification level current current current current current current trained trained trained trained cell cell cell cell problems problems random high high similar architecture architecture architecture architecture architecture architecture architecture architecture show section section section section section real real real average average obtained note note note experiments university university university university computation independent independent target target initial table table table table table standard terms node presented present present phase phase low low low low sets sets range range outputs outputs continuous sample abstract back references due due due due positive positive procedure introduction complex complex complex complex complex complex hand circuit circuit circuit circuit circuit circuit circuit circuit effect generated tion change energy energy energy energy assume classifier classifier classifier classifier classifier classifier lower learned chosen part required required required required required chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make techniques correlation length correct correct correct correct forward resulting ing ing ing tasks simulation respect multi multi multi sum sum performed performed called times elements factor factor feedback feedback study negative negative vol samples true true compared compared provide provide define perform gain gain gain gain gain gain gain gain gain equal power power power power power power power power power power power power power approaches approaches voltage voltage voltage larger larger larger connection train train train dependent source source source source morgan morgan department department implementation implementation synapses synapses synapses technique consists difficult difficult bias bias bias bias bias bias scheme scheme scheme ai considered considered domain domain environment additional design design design top stage effects bit bit detection detection detection detection efficient efficient choice statistics world increase increase increase condition derived weighted weighted weighted developed area area area area path path provided provided selected achieved achieved discussion technical increases increases describe denote tested circuits circuits circuits common common common common common common common common common common effective implemented synapse synapse synapse synapse synapse synapse synapse synapse vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi future typically needed functional technology block transfer testing testing testing testing ratio special matching mode mode mode mode mode mode mode mode mode mode leads iterations iterations max bits run run run run run run run run added perceptron perceptron discussed directions pair pair robust separate takes introduced quadratic array array engineering engineering engineering varying varying previously previously conventional approximately differential differential differential sparse separation improvement storage storage increased increased grant lead lead lead lead studied studied occur digital digital digital digital digital digital deviation correctly feed feed width loop loop occurs column setting demonstrate runs runs conclusion starting place place greater reduce reduce designed performs performs integration cycle demonstrated targets targets introduce identification base base denoted acknowledgements appears winner winner winner factors describes describes laboratory segments multilayer linearly electrical electrical remaining integrated formed shift blocks letters influence controlled controlled labels fraction showed margin margin updates sign diagram slow reduces false false penalty initially advantages classified classified classified classified recorded building template thesis combinations currents currents currents currents currents illustrated variations columns extra importance included presentation successful successful detect detect schemes online ten success split classify running running timing timing timing device device device device device device hold providing nips nips cmos leading chips attempt overlapping software perturbation perturbation requirements requirements requirements requirements requirements environments helpful tech possibility muscle transistor authors gates stream variability proved possibly generalisation generalisation generalisation generalisation generalisation generalisation generalisation adjusted detector academic store store detected mixed serial phd attempts attempts wta charge charge charge years distinguish agreement publishers publishers waveform multiplication multiplication briefly lin lin lin straight implementing easier transistors potentially separately arises researchers collected generic peter resistive resistive maintain limiting limiting incoming plan plan richard richard richard richard richard inherent implements patients patients patients patients patients patients patients patients patients patients patients patients converged converged converged converged summed summed distortion lab lab analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue drift linearity plays fan fan fan fan fan fan fan resistance resistance operates fail capacitor arrays clock corner patient patient patient patient patient patient patient patient patient patient patient appendix encountered heart heart heart heart heart heart heart sim facilitate winning repeatedly card card impact papers convergent thresholding switches acknowledge divide informa usage blood largely largely email kluwer bus bus ram ram classifications classifications classifications acceptable drain hundred jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri jabri rhythm australia australia options remainder modifying conduction conduction conduction mhz interacting considers switched distinguished distinguished distinguished distinguished discusses meet meet meet flower flower flower flower flower flower flower flower commercial commercial commercial commercial margins margins margins transients intensive september september strict strict november suggestions diagrams diagrams clinical clinical stephen stephen stephen stephen stephen january australian quadrant trainable settling designs hundreds firstly suite suffers supply suffices mirror morphology morphology morphology morphology morphology morphology morphology morphology morphology morphology morphology morphology morphology played converter fre conversion conversion floor floor meeting gram subtracted ally automation offsets offsets ref interpolating inspection consumption consumption consumption consumption consumption safe safe implying accommodate electrophysiological meant nominal jitter jitter tim detections detections detections detections costly imum jenkins converts cancel rhythms rhythms rhythms rhythms rhythms rhythms sydney sydney sydney sydney minimise minute minute quency advice package clarify missed corresponded cardiac cardiac niques ulation cancellation cancellation cancellation cancellation charac leong leong leong leong leong leong leong leong exercise beats beats electro buffers buffers predominantly suc ventricular ventricular ventricular ventricular ventricular bucket bucket bucket bucket bucket bucket bucket bucket publications optimise freeze clocks clocks clocks plete morphological disabled referring cycling cycling funding tam marwan marwan marwan marwan marwan ven mirrors mirrors mirrors polysilicon urn brigade brigade brigade brigade brigade brigade brigade brigade electrophysiology electrophysiology slowest dangerous dangerous dangerous pipelined orm tachycardia tachycardia tachycardia tachycardia netw injury subsections isscc photomicrograph photomicrograph effi prohibitive phi phi sedal sedal reduc duty duty deficits cancelling transferring buffered unused pacing pacing pacing batteries suffering cessfully morphologies morphologies complexes complexes born barry barry barry barry barry digest interfacing ciency matic castro castro alleviated consumes kauffmann kauffmann occasion facility bustness logged ergy lue pumping writes bypassing dissipates turbation 
#@Flower_B,Jabri_M,Pickard_S,
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#*learning model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set output output output output output output output output number number number system system state units information information information information based based based space space space linear layer case case case order order order order shown shown systems systems systems systems values values point single single processing large neuron neuron rate rate rate inputs shows shows shows shows shows shows signal signal signal signal simple simple simple simple simple simple simple simple simple visual visual paper paper small small small small work work features features process process process level level level current current current current current current cell cell cell random high high similar similar equation section section section line line line line line average note note note threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation research research independent dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial standard standard standard distance node node node node node science left left left left left left presented presented presented presented present present present activation low low low low low low low low low low low nodes nodes nodes nodes motion motion range position position position abstract applied applied applied back back back computational analog references component ieee positive positive positive positive positive positive positive positive important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction action action action action action action action action action action circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior effect effect effect tion change energy difference difference difference difference difference difference assume lower lower lower lower signals signals signals part bound bound required multiple multiple long long long conditions conditions conditions chip chip chip chip chip make region length scale scale resulting times potential potential potential potential potential potential potential made made natural feedback feedback feedback feedback feedback feedback feedback feedback feedback obtain negative negative negative negative negative negative negative negative relative relative application series provide provide rates perform determined experimental related related related equal power power power power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger support source morgan proceedings institute loss implementation consists consists advances represents represents final final bias bias bias bias bias bias bias bias bias bias bias bias delay delay delay delay addition graph graph graph graph graph considered curve curve curve curve additional additional view view design limit limit san stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage detection determine upper full speed increase increase con condition condition channel channel velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines finally processes nature biological biological biological biological biological biological increases denote limited assumption stable circuits circuits short shape shape supported journal end vlsi sensory including including including including kaufmann auditory auditory auditory simulated underlying underlying technology block block character edge increasing uniform uniform uniform uniform operation operation operation making early magnitude magnitude magnitude sources description description membrane membrane membrane membrane membrane membrane population population discussed takes typical period period period period period rl rl chain channels channels channels channels channels channels gate gate gate gate interval interval increased amplitude amplitude amplitude parts studied occur occur digital feed width width width width width width width width width width width width width width width width width width width width width width width width width width width width width width loop setting greater conclusions peak faster mateo mechanisms physics cycle california pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse turn denoted acknowledgements longer plot laboratory linearly linearly electrical scales scales applying events events formed implies potentials potentials potentials national depending stages stages stages stages stages stages solved detailed detailed detailed evolution static understanding completely completely sign slow event event event roughly roughly boundaries boundaries distances sufficiently foundation euclidean koch expect building building figures silicon silicon silicon silicon silicon silicon silicon silicon silicon currents currents currents determines coupled encoded computations computations reached excitation excitation excitation compact compact allowing moore split timing timing timing timing duration quantity localization cmos cmos cmos leading attempt neighboring body remain exponentially exponentially exponentially mead mead mead mead mead mead mead mead mead rapidly rapidly rapidly rapidly relations involving successive successive ideal transistor transistor transistor transistor transistor transistor office working matched matched patch patch reading voltages voltages voltages voltages voltages precise nerve logic nervous switching electronic electronic synthetic charge charge charge charge charge charge costs publishers fairly slope explanation cascade cascade briefly rapid rapid perspective perspective sys sections sections sections precisely precisely transistors transistors transistors transistors mation pulses pulses pulses ion ion ion axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon axon begin begin axons axons axons axons axons axons axons depicted depicted depicted geometry geometry geometry explained prop populations understood pseudo pseudo pseudo fed fed quantitative quantitative orders orders completion resistive release reaches pasadena semi decreased cochlea wesley cor picture physiology accomplished addison fabricated fabricated fabricated fabricated refractory refractory refractory refractory narrow narrow narrow velocities naval caltech lost systematic systematic saturation saturation saturation accepted mos held held held held held held grow grow grow grow grow serves operates operates affected capacitor capacitor capacitor exceeds infor service governed paul paul paul paul paul paul propagated propagated darpa diameter diameter specialized lazzaro lazzaro lazzaro ends ends propagate propagate propagate tures avoiding material speaking discharge discharge discharge crossing fellowship preserving additionally causing causing causing scenario preserved conduction subthreshold subthreshold biophysical tems continues continues graduate potassium potassium potassium crosses douglas douglas simplifying emphasize depicts overhead tied nonetheless maintains preserve pop happen fea behave reciprocal behaves wider wider hodgkin hodgkin hodgkin tau tau tau tau tau tau circumstances circumstances chris chris chris chris chris chris copies restoration restoration restoration restoration restoration restoration excess saturated twenty marks marks huxley huxley huxley mahowald mahowald capacitors capacitors lyon lyon inverter inverter inverter inverter inverter replicated neglect disturbances offsets attained interpolate company mosis mosis mosis mosis lewis lewis counterpart counterpart counterpart enforces promise promise ized wires shares shares shares propagates propagates propagates propagates propagates propagates publishing initiated initiated carver carver carver carver carver carver horiuchi horiuchi operated preventing pull pull pull pull pull pull orbit putting sodium sodium sodium sodium sodium quiescent shrink shrink shrink shrink shrink exceeded clipped disappear disappear beckman ramp ramp released ions ions ions bradley bradley bradley bradley bradley idealized passage inactivation inactivation opens opens ulation smear altogether rail rail rail rail rail rail rail rail rail rail rail rail rail travelling narrower bigger trivially unrealistic restored restored restored restored restored stant giant minch minch minch minch minch depict hasler hasler hasler hasler hasler refractoriness refractoriness tunable tunable charges impulsive charged terminating initiation comple nand nand nand nand polysilicon discharges discharges transmitting restore correlating dation nmos nmos nmos diorio diorio diorio diorio diorio cease universally influx instantaneously foun cancelling seminal cascading xxx xxx 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#@Coggins_R,Diorio_C,Hasler_P,Mead_C,Minch_B,
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#*network network network network network network network network network network network network learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time set set set set set set networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number number number number error error state results results results results results results results units units units units units units units units units units units units units units information information problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance space space space space space space space space space weights weights weights layer layer layer layer layer layer layer layer case case vector vector vector vector vector order order order shown shown shown shown systems systems systems values probability parameters weight weight weight weight functions neurons neurons unit unit unit distribution recognition recognition recognition recognition method method approach pattern pattern point point image image single processing processing large large large large neuron neuron neuron test analysis analysis class class class inputs form form shows algorithms algorithms algorithms algorithms algorithms paper paper size size net net work methods points points points points points points points points classification classification current trained problems random high high high high high high high high high high high high memory similar representation architecture architecture architecture show show equation equation equation equation equation equation section section section section section section fixed fixed fixed fixed fixed rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general speech speech real real real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average gradient gradient term note note note note note experiments activity activity activity activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university computation research independent independent defined defined initial constant table table table table table standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard terms distance distance distance prediction presented present phase phase phase phase phase low low low maximum range press basis basis basis basis abstract applied find computational computational density references stochastic stochastic due propagation propagation context estimation effect generated variance variance variance variance variance variance parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel search tion change complexity lower lower lower measure measure chosen chosen center bound bound bound bound cases required required required multiple good good good good good binary distributed distributed chip chip chip chip chip fact fact fact region correlation length length length length length length length length length length length length length length length length length length length length length length correct correct correct forward scale scale scale simulations simulations simulations resulting tasks total human human regression regression performed performed performed regions means factor optimization dimension dimension dimension dimension dimension original artificial artificial relative true cross rates rates perform perform perform perform perform experimental experimental distributions brain brain equal equal equal mit accuracy accuracy accuracy accuracy comparison comparison descent nets institute institute institute words version version final layers addition addition equivalent additional limit approximate approximate approximate approximate approximate approximate world world world speed speed vision increase give randomly randomly product product product product product product product product product product product product product product product backpropagation backpropagation backpropagation backpropagation constraint biological achieved discussion feedforward increases increases increases increases describe group fast corresponds corresponds implemented generate face face square square square square square square vlsi vlsi vlsi vlsi vlsi rumelhart rumelhart rumelhart fit simulated typically typically needed reduced functional functional mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp block block block block block block block block block block block block block block block block block block block block block block block block block block block block block block block block block block block significantly ratio ratio ratio ratio ratio ratio character increasing special uniform database database squared representing numbers numbers making making stored stored normalized choose population improve resolution exact advantage advantage advantage advantage property ensemble ensemble ensemble ensemble identical machines dimensions dimensions dimensions varying compare approximately approximately calculated calculated calculated calculated calculated volume works axis tions correspond achieve address bounded storage entire entire exists suggests suggests digital deviation deviation derivative derivative alternative generally column column demonstrate minimal greater valued central tangent tangent tangent tangent accurate accurate accurate accurate designed clear performs practice practice learns constrained constrained constrained suggest propose physics largest reduction characteristics radial radial radial radial assuming minimizing exist program question monte derive carlo optical plot describes describes label implement implement implement multilayer multilayer multilayer multilayer multilayer category averaging averaging averaging averaging averaging averaging averaging averaging dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality easy slightly depending interpretation interpretation approximated approximated approximated activities reasonable reasonable reasonable calculation calculation calculation calculation slow slow spaces spaces spaces spaces spaces combining add generation valid distances calculate calculate calculate calculate norm norm norm norm norm norm norm norm euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean faces avoid avoid avoid expect handwritten box thesis thesis thesis perceptrons perceptrons perceptrons perceptrons sciences holds major uniformly mcclelland efficiently showing anderson lie contribution running hold sampled michael michael michael michael michael dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot absence backward backward highest extend presents explore american accurately hall examine behavioral mse mse mse mse mse working comparable fundamental math editor editor configurations extremely illustrate equally implementations thought portion noted perceptton art ith ith ith improving improving motivated motivated serial serial serial phd phd asymptotically brown brown brown site great formula improves improves majority majority majority cascade multiplication implementing implementing implementing implementing arc incorporate commonly products products products products products products circle circle circle circle calculations calculations calculations ridge cybernetics outer outer outer explained axes adjustable incorrect release calculating calculating passes price suited enables inherent phenomenon cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper tation approximates connecting connecting flexibility grows tools city city city city city city city city city city city city city city city city city city city city city city city city city city city city city city city city city city city intuitive corner performances introduces corre dependency lengths lengths lengths lengths lengths histograms thomas darpa mlps mlps mlps mlps mlps foundations draw hypercube hypercube maintaining corporation ter minus minus listed utilize classifications classifications classifications ideally beta tight cns ibm werbos werbos werbos pdp chapman ocr rejected overhead minor thousands nil nil nil nil nil nil nil nil nil nil nil nil nil nil nil nil nil nil nil drops drops compu ward cube cube nist nist simplification lation thousand fill harvard calculates val station norms fin quick bottleneck bottleneck feb lar unrestricted watson tens enabling ues behaving spent sparc altering tighter heights pay classifica intel intel intel intel intel disagree reilly reilly reilly reilly hypersphere hypersphere rce simu providence behav expands periments news pertone pertone pertone pertone pertone pertone pertone pertone pertone pertone pertone accelerate attain deliver sponds perrone perrone perrone perrone perrone grayscale gions leon leon leon leon leon leon scofield scofield scofield simi degeneracy signifi yorktown shrinks slows sullivan sullivan sullivan companies ior supervisor tii validating rrr chap cantly halted iiz uct prod mount calcula provement uppercase uppercase dicate 
#@Cooper_L,Perrone_M,
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#*network learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data time time time time time time time time time time time set set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output system system system system system error error state state state state state results results results results information problem performance performance based based based based based weights weights weights weights weights weights weights layer layer layer layer case case vector shown shown shown shown shown shown shown systems systems values values parameters weight weight neurons neurons recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern point point image single single processing processing control control large test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns inputs shows shows shows shows shows paper paper paper paper size task fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig classification process process process process current current current current current current current current current current current current current current current current current current current current current current current current current current current structure high high high high memory memory response response architecture architecture architecture architecture architecture architecture architecture architecture section section section vectors parameter real real real real real real obtained obtained obtained obtained term term note note sequence sequence sequence constant standard standard standard computer connections connections connections synaptic presented low low low nodes nodes nodes nodes nodes machine machine machine learn nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs continuous abstract computational computational computational computational analog analog analog analog analog analog properties properties properties properties references ieee introduction action complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior parallel parallel parallel cost cost cost search change change complexity assume signals signals signals learned learned learned center previous type type type type type type binary binary binary binary binary binary binary long tree tree tree expected equations equations equations equations equations equations equations equations equations equations equations equations equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip proposed proposed resulting performed performed performed performed means means means global filter original original original original original original original original vol vol vol vol vol artificial true true application provide provide provide proc proc perform experimental experimental experimental experimental gain gain gain power power voltage connection connection connection update dependent source morgan implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation version version synapses synapses synapses synapses synapses synapses technique consists consists internal advances represents represents final final bias delay delay delay scheme scheme computing domain domain domain equivalent equivalent additional view view design conference full requires requires world speed speed vision clustering clustering clustering clustering clustering levels area area area area provided finally nature nature achieved measured measured measured measured discussion feedforward feedforward describe describe arbitrary fast fast fast stable circuits circuits circuits amount short implemented implemented implemented synapse synapse synapse synapse synapse generate journal journal journal square square square vlsi vlsi vlsi vlsi cluster cluster kaufmann needed significantly mechanism matching mode mode mode mode numbers iterations bits added sources sources sources sources sources sources description resolution robust typical typical reported reported introduced introduced pixels pixels pixels pixels array array array array conventional unsupervised tuning match differential differential differential differential differential differential achieve modified modified modified modified modified modified modified occur extended digital digital digital digital digital digital digital digital digital digital digital digital digital touretzky column hardware hardware hardware flow flow starting row row row row row row conclusions valued valued valued designed faster external solid solid configuration reference winner winner winner sequential describes vertical dept category easy easy unique events events versus versus competition letters national squares codes detailed controlled controlled organizing organizing updates updates updates diagram diagram diagram diagram reasonable measurements valid precision precision precision template currents currents currents currents currents currents currents currents extension extra extra capable suitable suitable modification computationally detect fine fine receives refer content categories categories built satisfy bar modular cmos cmos cmos cmos cmos cmos cmos cmos reach chips chips chips extract software software circuitry circuitry updating mead steady steady steady int gates proper matched reading voltages voltages voltages voltages implementations implementations implementations prototype prototype art art art art art art art art art art art art art art art art art art art art consist generates generates generates arbitrarily submitted submitted wta wta wta wta wta wta seconds asynchronous expensive expensive cascade handle inside transistors transistors grossberg implicit depicted double double experimentally experimentally adjustable adjustable adjustable compares templates templates templates switch spread phone implements implements summed yielding realized acquisition accomplished fabricated fabricated interface resources unity overcome mail mos mos programmable los operates presentations reset reset governed initialize enable modelled lazzaro lazzaro switches switches die die die massively massively clustered adjustment algebraic algebraic algebraic algebraic algebraic mismatch mismatch publication publication preserved graphics flip transconductance categorization ltm ltm ltm ltm ltm ltm ltm distinguished geiger preserve preserve electronics meet tune october oregon syn simplification european mahowald mirror mirror mirror mirror mirror mirror realizations engine 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#@Huertas_J,Linares-Barranco_B,Serrano-Gotarredona_T,
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#*network neural neural neural neural neural input input input input function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set networks networks networks networks networks networks output number system system state state state state state state state state state state state results results results based based weights weights weights linear layer layer layer layer order order shown shown shown shown shown shown systems values weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons neurons neurons single single single single large large local local local neuron neuron test test test test test test test test test test test test test test test test test test inputs form shows shows shows signal signal signal simple simple simple simple paper paper small cells process process process process level current current current current current current current cell high memory memory memory memory memory memory memory memory memory memory memory memory memory fixed states states obtained experiments activity activity university university threshold threshold threshold threshold research research research target standard synaptic synaptic synaptic synaptic presented present present activation activation low machine maximum maximum range range range range outputs outputs abstract applied applied applied applied applied references references ieee positive positive context introduction action circuit circuit circuit circuit dynamic dynamic parallel cost change complexity signals signals signals signals binary chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip techniques resulting resulting performed times times elements means means means applications negative original original application desired desired series series provide provide proc proc connected power power power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage steps accuracy contrast proceedings department implementation synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses technique difficult difficult layers equivalent experiment design design limit top conference conference approximate increase increase give give con produce channel channel levels levels area area constraint achieved measured normal normal normal describe tested fast circuits circuits circuits implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse generate generate main main journal vlsi vlsi easily easily easily noisy including typically fully fully technology technology technology programming programming programming programming programming programming programming programming increasing increasing mechanism mechanism mode operation details pre direct making making inhibition stored stored stored produced discussed separate takes typical apply include period period array recently engineering engineering compare previously conventional gate gate gate gate storage storage storage storage storage storage storage storage storage storage storage storage storage storage entire amplitude constructed constructed digital correctly occurs generally hardware demonstrate place place conclusions designed clear faster mechanisms mechanisms mechanisms integration integration integration integration physics physics cycle cycle demonstrated demonstrated pulse decrease program acknowledgements reference produces longer index ann ann ann ann ann stability stability stability stability vertical dept implement physical physical electrical consisting consisting integrated integrated implies blocks blocks letters yield variation controlled understanding earlier slow add closed construction transactions silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon currents sciences memories memories memories memories memories partially straightforward suitable included included characteristic characteristic excitation summary compact compact compact compact conf procedures procedures contained allowing sin device device device device device device device device device device device device device device device device device device hold write write board board board board board board cmos cmos cmos cmos cmos cmos cmos chips chips chips received operating load decreasing simpler remain remain carried carried circuitry circuitry issues terminal terminal int ideal referred stream removed neu neu neu neu measurement implementations ensure store improving improving electronic electronic isolated established established charge charge devices devices devices devices devices devices devices devices devices devices asynchronous floating floating floating floating implementing sections widely day day day transistors pulses pulses pulses pulses pulses pulses cut attribute read read understood embedded capability lack incorporated sharp exhibits adjust focused summed arithmetic arithmetic analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue sv interface interface forming narrow dynamically proceed multiplier saturation smith adds murray murray murray murray murray replacing imposed programmable programmable programmable resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance resistance operates ral capacitor capacitor capacitor capacitor capacitor capacitor capacitor capacitor date buffer sim thin thin contact waveforms storing route card considerations switches usage anns drop ple creates medium medium medium causing edinburgh edinburgh massively remote arising conduction resistor resistor resistor resistor thick epsilon epsilon epsilon epsilon epsilon hubbard electrodes electrodes electrodes scope retain meta monitoring drawback funded electronics electronics resistors suffer programmed programmed programmed programmed differing rose rose rose rose rose completed technologies syn syn syn replacement tail stores functionality council demand monitor trainable designs jointly hundreds firstly capacitors supply supply mirror hamilton graf fabrication fabrication fabrication fabrication subtracted ham comprising trol inspection tance comparator ings aip aip eeprom eeprom eeprom eeprom refresh operated months pointers metal accu capacitive tran holmes holmes holmes holmes holmes volatile volatile volatile volatile volatile volatile volatile volatile volatile volatile volatile volatile comprises electrically ramp ration supplies closing epsrc rail exercise conducting conducting micron plied amorphous amorphous amorphous amorphous amorphous amorphous amorphous amorphous 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#@Churcher_S,Hajto_J,Holmes_A,Murray_A,Rose_M,
#t8
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data function function function function figure figure figure figure figure figure set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number error error error error error error error error error error error error error error error error error error error error error error error error error state state state state results results results results results results results results information information problem problem models performance based based based based space weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer order order shown shown systems systems values parameters weight weight weight weight weight weight weight weight weight functions functions neurons neurons neurons neurons distribution distribution distribution distribution distribution recognition method method method pattern pattern single processing processing processing processing processing neuron rate test test test inputs inputs inputs inputs form form form form shows shows shows signal signal signal signal signal signal signal signal signal simple simple gaussian gaussian paper small small work work field field field field field classification classification classification classification classification classification level trained trained trained trained trained trained problems similar architecture equation equation rule rule generalization average average gradient gradient gradient gradient gradient gradient gradient term term term university university university university defined found found table table table standard computer distance connections connections connections direction direction presented presented presented present phase phase frequency sets sets range press position position position position position position basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous abstract applied applied applied applied applied applied applied applied applied applied applied applied applied applied applied back back back back back back back back back back back back back back references ieee ieee propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation complex effect effect effect effect effect recurrent recurrent change change change change difference variable spatial spatial spatial spatial signals signals signals higher higher type type type type type type type type type type type binary distributed distributed distributed distributed distributed equations equations equations equations equations equations techniques techniques region region region region region length correct correct correct correct errors forward forward forward forward forward forward forward forward simulations simulations simulation respect respect respect performed called regions regions regions regions regions means means factor made study vol artificial specific desired provide objects location location location perform perform experimental experimental experimental distributions discrete discrete power power power accuracy comparison connection connection fields fields update update update update train descent descent descent descent morgan morgan proceedings proceedings department technique internal internal individual advances connectionist final final final exp layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers addition considered framework experiment experiment experiment additional san conference requires approximate free increase produce produce produce produce derived weighted weighted weighted developed types path backpropagation backpropagation backpropagation backpropagation backpropagation nature depends constraint achieved measured feedforward tested tested proof amount amount amount common effective implemented implemented theoretical ability easily kaufmann pairs pairs pairs transfer increasing increasing uniform uniform leads squared details normalized normalized normalized minimize minimize light light light light light light light light light light light light light light light light light light discussed discussed discussed improve resolution advantage separate separate lateral lateral lateral subject pixels array engineering engineering engineering varying varying varying conventional conventional calculated calculated modified gate gate storage storage storage entire constructed intensity intensity intensity intensity intensity intensity concept scaling extended wide wide correctly feed feed feed width width width half half flow greater conclusions interactions weak constrained constrained mateo temperature taking taking physics sigmoidal minimizing start start start exist plane plane plane plane groups appears construct produces index index index index index index index index optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical describes laboratory recall implement physical physical physical electrical electrical minimization minimization choosing review variation controlled controlled updated constants allowed discrimination calculation expansion classified classified formulation formulation formulation formulation formulation formulation formulation weighting weighting weighting weighting weighting weighting weighting weighting assignment recognize illustrated prove divided effectively successful comparing composed composed composed composed traditional repeated cun moore classify device device device categories vary backward backward backward minimizes wave wave wave consisted satisfies simpler powerful updating preliminary fourier giving giving school root comparable gates coefficient coefficient gradients gradients transmission created thought separated separated logic logic logic logic logic logic logic logic logic glass glass benchmark spatially spatially spatially processed straight producing controls potentially calculations calculations beginning geometry conjugate requiring applies profile profile profile dark amounts capability posed calculating calculating pittsburgh serve electric progress realized accomplished assign lagrange lagrange lagrange modify dynamically bin multipliers multiplier imaging serves transforms integrator planar cone james respective demonstration sphere propagated propagated propagated propagated interconnections waves thin thin thin thin probe probe passing propagate material material material material material material material material material material material material mechanical summer basically alternating propagating propagating utilize medium medium medium profiles amplitudes reflected remainder perpendicular thick thick thick thick echo mask sonar steering steering steering ignoring echoes pineda pineda november species species beam beam beam beam beam beam beam beam beam lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian discretized thermal thermal diffuse loosely dropped steven eliminates wavelength thickness thickness striking laser optics tube era physically cruz feasibility materials materials materials materials materials materials materials carrying focusing focusing promise backwards propagates entering tutorial iris iris bright lens lens lens lens yann heat steep crystals rect steer micron microns microns microns microns microns pertinent clicks pump rewarded rio reversing wash modulator click optically optically optically optically optically optically backpropagate probed finish finish finish beams beams professional kaufinann 
#@Behrman_E,Cmz-Cabrara_A,Skinner_S,Steck_J,
#t8
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#*network network network neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set networks networks networks output output output output output output output output output output output output output output output output output output output output output output output output output output number number number system system system system error state results information models performance based based based based based based based based based linear linear linear linear linear linear linear case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown shown systems systems systems values values values recognition recognition approach pattern pattern pattern pattern image single single single single single single single single single processing processing large rate rate test test test test test inputs inputs inputs inputs inputs inputs form form shows signal signal signal signal signal simple feature net cells cells cells cells cells cells field features features features features level level level current current current current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure high memory response response response similar architecture architecture architecture architecture line line line line line line vectors vectors vectors vectors vectors vectors vectors vectors vectors speech real real obtained obtained obtained obtained obtained obtained term university threshold threshold computation independent independent log sequence sequence sequence dynamics constant table table estimate standard computer distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance presented presented presented presented presented presented map present present present phase phase low low motion maximum maximum maximum maximum range range range range range range range range range range range range range press press components components components components components components outputs outputs outputs outputs outputs outputs abstract back analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references component component component component component due due ieee ieee ieee ieee ieee positive positive positive positive positive positive positive positive positive positive positive introduction circuit circuit circuit circuit circuit circuit circuit estimation estimation estimation estimation estimation estimation estimation estimation effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic parallel parallel parallel parallel parallel parallel parallel parallel parallel search search tion energy difference difference difference difference difference difference difference difference difference complexity complexity measure measure word center previous binary binary tree expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip region region proposed correct observed minimum minimum minimum minimum resulting resulting ing total performed times regions means means feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback global global global global global global applications negative vol vol vol vol vol relative relative desired active determined experimental related connected connected equal power power power power power power power approaches approaches voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage accuracy larger larger source source source source source source source selection selection selection selection morgan proceedings institute department department implementation implementation implementation implementation implementation implementation implementation implementation implementation technique consists code advances represents bias bias bias bias bias bias bias bias bias scheme ai domain directly directly directly additional additional additional view view san top top stage stage bit bit bit bit conference classifiers requires significant significant speed speed vision estimated basic con levels levels levels levels levels area lines lines provided provided nature sampling associative achieved measured technical fast fast fast fast fast fast limited limited limited corresponds complete circuits amount common common effective implemented adaptation square vlsi vlsi vlsi vlsi vlsi vlsi degree including including typically smaller needed needed functional fully fully technology technology consistent structures matching uniform mode mode operation operation operation operation operation max pre pre pre stored stored stored bottom pair separate element typical typical lateral lateral lateral include period identical array array array array array highly approximately works tuning tuning tions differential differential address address address address locations gate storage entire entire parts digital digital wide wide wide wide correctly correctly locally locally width hardware demonstrate conclusion row row measures measures weak weak mateo encoding encoding encoding encoding strong largest largest cycle cycle cycle cycle cycle cycle characteristics characteristics characteristics demonstrated demonstrated california pulse turn exist min plane reference construct written written index index winner winner winner winner winner winner winner winner winner winner winner winner plot plot plot tuned distinct distinct metric metric metric metric metric metric metric implement involves remaining equilibrium springer shift cycles competition competition competition depending correlated communication variation evaluate evaluate operations fraction fraction fraction lee sign smoothing smoothing smoothing sec roughly roughly purpose initially distances kohonen kohonen kohonen topology transactions transactions transactions coupling coupling coupling coupling recorded template template template template template template template template template template template template template template template template template template template formulation illustrated activated coupled coupled absolute absolute absolute absolute absolute absolute absolute absolute absolute absolute absolute holds discussions tests structural major columns columns compression compression compression closely uniformly uniformly society encoded modification divided driven included presentation computations receives receives characteristic summary compact notice notice verlag decoding video conductance symmetry gray write write modular quantization quantization quantization cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos computes highest highest illustrates subsequent operating acknowledgments origin origin origin origin requirements requirements circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry circuitry mead mead periodic matches mse mse mse terminal transistor transistor transistor authors comparable fundamental smallest coefficient trace reading voltages voltages implementations implementations logic wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta charge charge charge charge charge charge charge charge charge rows rows rows rows rows fairly fairly fairly slope floating caused worse implementing tive producing constructing division transistors transistors transistors transistors consequence inversion inversion inversion beginning beginning geometry nsf argument applies double double double profile conducted readily frequently rep schematic schematic schematic schematic templates templates templates templates templates templates operate berlin mod characterize popular pasadena decoder implements eventually wesley displays realized indices addison dynamically dynamically dynamically rotated interconnected reaching caltech kaufman mail logarithmic mos mos mos mos mos balance serves observing wire settings synchronous synchronous synchronous capacitor capacitor selects selects service combines governed connect expanded buffer buffer competing offers offers darpa winning winning winning winning winning winning winning layout lazzaro waveforms waveforms extends speeds tures receiving adopted limitation accumulated metrics kluwer focal alternating additionally aij aij amplitudes flat flat capacitance subthreshold subthreshold searches inverted inverted scope scope scope complementary setup interconnect likewise fea increments inactive accumulation stimulating functionality reversed thermal marks settling settling settling settling settling losing mahowald supply supply supply supply hopkins converter fabrication replicated condi practically andreou core triangle quantizer quantizer quantizer quantizer quantizer quantizer ray resolved poly poly johns enhances consumption triangular triangular triangular comm comm comm comm comm mosis mosis accommodate cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs charles baltimore vanishing dissipation dissipation dissipation dissipation pact refresh dist modularity jenkins configured quantified plexity ece virtue cient organisation activating activating activating activating activating 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#@Cauwenberghs_G,Pedroni_V,
#t8
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#*network network network model model model model model model neural neural neural neural neural neural input input input input data function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time output output output output output output output output output output output output output output output output output output output system system system system system system system system system system system system system system system system system system system system results units units units units units units units units units units units units units units units units units information information information information information information information information models models models performance based based based based based based based based based based based space space space space space space linear linear case order order shown shown systems systems systems systems neurons recognition approach approach pattern single single processing processing large large local inputs inputs inputs shows shows signal signal signal signal signal visual visual visual visual paper small fig step points current current current current current response response similar similar similar architecture architecture line line line real theory note note activity dimensional dimensional dimensional threshold computation computation computation research research target estimate distance left left left map map map present phase phase phase phase activation low low frequency frequency frequency frequency motion position position position position position position position position position position position position position position position position components basis basis outputs outputs outputs continuous abstract back analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties references component component due positive important propagation introduction circuit circuit circuit circuit circuit behavior stimulus generated generated tion difference difference difference spatial spatial signals signals signals signals signals chosen chosen chosen center center center required represent represent chip chip chip chip chip chip chip chip chip chip proposed proposed proposed proposed correlation correlation correlation computed sum sum regions regions orientation applications applications study filter filter filter relative relative relative specific represented represented cross receptive receptive provide provide define compute location location location location active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye related posterior motor discrete discrete cortical cortical cortical power power approaches voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage accuracy comparison larger fields fields support source source source source source morgan institute institute implementation implementation implementation implementation implementation technique technique consists consists consists consists consists consists advances represents represents responses final layers layers delay delay delay delay delay scheme addition maps computing computing domain environment san top stage stage stage stage stimuli stimuli detection efficient full full vision basic channel developed lines lines lines lines lines actual nature nature biological biological describe transformation transformation transformation transformation transformation fast limited circuits circuits circuits supported role end end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi ability development sensory sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory technology technology technology block interesting projection projection projection head head head head head head head head head head structures operation operation operation representing bottom early frame denotes architectures population directions resolution movement movement movement include subset subset array array array array compare speaker positions locations locations interval entire grant constructed constructed constructed horizontal studied occur extended digital digital digital digital digital digital wide spikes spikes derivative rotation critical place conclusions clear peak mateo sound sound sound sound sound sound sound sound sound sound external external california california california pulse pulse pulse pulse pulse turn variety exist plane program acoustic acoustic acoustic acknowledgements areas reference van van perception laboratory laboratory laboratory mathematical coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates angle integrated events shift shift shift viewed transform transform transform transform transform transform transform transform centers centered centered forms suggested diagram diagram roughly valid intermediate intermediate intermediate filtering filtering koch koch koch koch degrees degrees degrees degrees degrees silicon thesis thesis coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate currents inter inter retinal retinal retinal retinal retinal plotted activated major closely differ driven invariance plots plots plots compact compact contained superior superior running timing cue cues comp localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization transformed transformed circuitry mead mead mead humans detail respond project project biol office comparable understand voltages thought front front noted separated mapped logic academic switching indicating sensors sensors slope spatially drive filtered filtered constructing pulses pulses pulses pulses potentially axon axon axon axon sounds angles angles pitch author author author double understood effort passed switch measuring pasadena logical physiol owl owl owl owl owl owl wesley cybern addison generator fabricated saccadic saccadic saccadic saccadic animals animals mobile naval arrival arrival arrival arrival robotics caltech plays kaufman khz khz khz khz primate primate primate primate moment obtaining operates shifts settings inferior exploring intended intended dendrite centroid centroid centroid parietal april neuromorphic lazzaro lazzaro lazzaro colliculus colliculus colliculus colliculus colliculus park extensively propagate acknowledge ball zipser crossing crossing crossing neurophysiology ent creates sinusoidal barn barn barn barn barn cns cns deep distant expand thresholded thresholded retinotopic retinotopic retinotopic bump bump ultimately oculomotor finger finger finger finger crossings electronics electronics meet meet investigations programmed nal mcculloch mcculloch transduction discretized pitts pitts justification synthesized assistance transforming micro somatosensory sensorimotor believed wavelength konishi konishi modalities zipset arriving bandpass bandpass bandpass andersen andersen multimodal fin deweerth subsystem carrying microphone microphone ears christof propagates carver cats horiuchi horiuchi horiuchi horiuchi horiuchi horiuchi horiuchi horiuchi entering converts activates biophysics primates primates primates deeper deeper simulates accepts menlo ages cent preset delbriick delbriick chord azimuth azimuth azimuth azimuth brooks birds mammals delivered volt prof prof psychol originated asymptote topographically opposing portable timothy timothy timothy timothy timothy orient prey sparks sparks sparks sparks triggering transforma audition bulletin centrally 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#@Horiuchi_T,
#t8
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#*network network network network network network network network network network network network network network network network network network network network network network model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data function function figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set training algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state results results results results results units units information information problem problem problem problem problem problem problem problem problem models hidden based space weights linear linear linear linear linear linear linear linear linear linear linear layer case case case case case case case case vector vector vector vector vector shown shown shown shown shown systems systems systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method approach approach approach approach approach approach point point point point point point point point point point point point point image single single single processing processing control large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test test test matrix matrix matrix matrix form form form form form form shows signal simple simple simple simple simple simple simple paper paper paper examples small small size size work work task step points points points points points points points points features features features features features features process process process process current current current current current current current structure structure structure problems high similar similar similar similar show show show equation equation equation equation section section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line vectors vectors vectors vectors images general parameter parameter parameter theory obtained obtained term note note dimensional dimensional result result university university computation computation computation solution solution solution solution solution solution independent log sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics computer terms terms connections connections science left left present present object maximum range position components components components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied find find computational convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties references component ieee positive positive positive positive positive procedure context context introduction hand hand hand circuit circuit circuit circuit circuit behavior generated recurrent recurrent change complexity complexity complexity assume previous theorem cases cases required conditions represent represent equations equations equations equations equations equations equations equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip markov make make make fact errors scale scale scale simulations simulations total total total respect performed performed times elements elements made natural applications applications obtain negative negative specific true application desired desired desired desired desired compute perform perform active active determined determined determined determined experimental experimental constraints connected gain gain gain power voltage voltage voltage voltage voltage larger connection connection nets nets proceedings institute implementation synapses consists code code represents represents final final final exp exp exp exp exp exp exp exp exp exp exp bias bias bias bias ai ai ai ai ai ai ai considered computing computing directly curve curve curve curve curve additional solutions solutions solutions design design design design san top top top bit requires choice choice approximate free basic produce condition condition coding coding coding coding coding coding coding coding coding coding criterion actual actual actual provided finally finally iteration iteration inhibitory simply discussion increases describe describe describe transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation inverse inverse corresponds corresponds stable stable stable stable stable stable stable stable proof circuits finding amount amount implemented shape generate generate eds journal vlsi vlsi vlsi vlsi easily needed needed needed needed account dynamical dynamical dynamical dynamical dynamical functional coefficients coefficients technology technology block block block block block block block block block block block block block block transfer transfer transfer programming programming york special special special structures mode mode operation call max making bits bits bottom bottom bottom idea choose run description takes element identical side quadratic sense engineering engineering interest sufficient sufficient highly highly highly highly conventional approximately solve solve yields converge converge converge sparse sparse sparse address observation channels channels gate gate entire grant horizontal expression expression expression expression concept occur digital digital loop loop loop loop loop half half depend depend depend depend differences exponential exponential temperature encoding encoding physics physics external external external external characteristics characteristics labeled turn derivatives derivatives groups connectivity connectivity program program acknowledgements appears derive construct construct produces produces solving solving solving laboratory label label stability stability dept implement physical physical physical physical physical electrical transformations easy unique unique adding applying implies blocks letters choosing choosing national expressed squares squares codes codes solved operations controlled completely similarly similarly similarly converges converges converges converges converges converges constants partial partial partial measurements measurements add remains calculate foundation topology topology topology expect currents currents currents eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues determines prove compression aspects differ included essentially receives receives characteristic characteristic composed road decoding satisfy sampled relaxation relaxation eigenvalue cmos cmos cmos cmos cmos chips operating satisfies receive receive law simpler diego transformed transformed transformed create investigate mead mead steady steady steady steady accurately preliminary behaviour rise ideas authors working complicated presynaptic hill necessarily configurations analyze voltages voltages voltages voltages voltages voltages voltages voltages prototype explored mapped mapped expressions switching simplest regime regime charge devices asymptotically trivial unstable unstable coded coded coded expensive briefly nonlinearity nonlinearity implementing sections sections forces operators transistors transistors immediately immediately ion scientific arises qualitative addressed affine affine affine affine affine affine affine amounts parameterized parameterized experimentally quantitative effort share share requirement passes exhibits exhibits characterize qualitatively qualitatively conductances conclude wesley globally room addison fabricated fabricated fabricated fabricated fabricated arranged inspired inspired inspired inspired multiplier adds odd odd loops hope operates receiver receiver salient capacitor selects spurious spurious spurious iteratively paul paul iterated iterated iterated iterated layout layout reader considerations summarize summarize robert unable constitute recursively copy copy medium chapter examining jacobian jacobian verified capacitance capacitance subthreshold subthreshold subthreshold subthreshold subthreshold subthreshold subthreshold subthreshold toy werbos individually intensities intensities sketch associates funded electronics happen vanishes det eters pineda pineda pineda pineda pineda pineda pineda suggestions factored topologies scanned uniqueness fractal fractal fractal fractal fractal fractal fractal fractal fractal fractal fractal fractal fractal fractal fractal thermal monitor oscillate hopkins hopkins suffices calculates concrete conversion subtracting dissertation andreou andreou andreou andreou andreou andreou andreou andreou johns johns johns volts volts volts volts volts volts suffice amplified mosis physically physically physically ionic essence addressing halves halves charles transmit transmit transmit transmit transmit transmit transmit baltimore decoded blocked dissipation jenkins operated richer converts converts settles generations coincides hirsch hirsch fet fet fet vdd vdd vdd excitable andreas andreas andreas andreas andreas schematically subsampling conversations tiny subsampled subsampled 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#@Andreou_A,Pineda_F,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data function function function time time time time time time time time time time time time time time time time time networks networks networks networks networks networks algorithm output output number number number number number error error error error error error error error error error results results results results results results results results results results results information information information information information problem problem problem problem problem problem problem based space space space space space space weights weights weights case case case case case case vector vector vector vector vector vector order order order order order order order order order order order order order order order order order order shown shown systems systems systems systems systems values parameters noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions recognition method method pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point single single single single processing processing processing processing processing control large local local local local local rate rate rate rate rate rate rate patterns patterns analysis analysis optimal shows shows shows shows algorithms algorithms algorithms small small small size work work work methods methods methods classification problems problems problems random random random random random similar architecture show equation section section section section fixed rule rule vectors general general approximation approximation approximation approximation average average average theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term term term term term term term term term term term term term term term term note note experiments experiments result result university computation found found initial initial initial initial initial constant constant constant constant table table table table estimate estimate computer terms terms terms terms terms terms distance direction direction direction presented presented presented present present press press learn learn learn abstract back computational convergence convergence analog analog analog analog analog analog analog analog references component stochastic stochastic stochastic stochastic due ieee ieee positive positive positive positive important important important propagation introduction hand hand estimation statistical statistical effect generated variance variance parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel recurrent tion change change change change change difference assume assume lower representations word word learned learned chosen chosen chosen chosen higher previous previous previous bound cases cases cases cases required required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple binary binary long long conditions conditions represent distributed distributed expected make make make fact fact simulations simulations simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum simulation respect sum performed times times times times times times factor optimization optimization natural study study study study study knowledge obtain negative negative negative relative relative relative true true application rates rates rates perform related related related related constraints constraints discrete equal mit mit mit larger larger fields update update update update update descent descent descent descent descent descent descent descent descent descent descent morgan morgan morgan morgan institute institute words loss implementation implementation implementation implementation implementation technique technique technique technique internal code code advances advances advances advances cambridge cambridge environment hinton san san san san bit bit efficient efficient full requires choice free speed pages pages pages pages pages condition condition randomly randomly randomly developed provided discussion discussion feedforward arbitrary tested tested tested fast limited limited limited limited close close close close close assumption assumption assumption complete surface circuits nearest generate theoretical vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi degree makes makes rumelhart rumelhart rumelhart rumelhart noisy kaufmann kaufmann kaufmann kaufmann smaller reduced technology york empirical leads numbers numbers making supervised magnitude magnitude magnitude run sources light discussed improve directions property takes takes takes quadratic quadratic sense sense recently relevant relevant sufficient compare address background williams improvement entire studied occur occur derivative occurs generally hardware hardware hardware runs conclusion reduce neighbor editors editors editors editors measures accurate faster faster practice asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic constrained mateo mateo mateo mateo taking presence california california california california california proportional labeled exist decrease averaged minima longer generating distinct dept multilayer simultaneously simultaneously averaging infinite physical physical springer implies expectation expectation expectation independently stationary stationary stationary squares detailed showed showed sign sign earlier performing performing convex combining penalty penalty calculate sufficiently transactions transactions precision precision precision precision precision expect thesis thesis specifically specifically tests successfully reason reason reason columns efficiency efficiency closely closely importance uniformly mcclelland presentation presentation presentation situation ten verlag quickly induced superior superior superior superior issue running running running follow follow realistic giles giles giles giles reach reach reach reach chips cowan cowan cowan cowan perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation experience hanson hanson hanson hanson limitations hessian issues preliminary helpful mse investigated investigated investigated investigated ideal proper func cognition neu math measurement measurement gradients possibly predicting implementations thought adjusted adjusted assumes multivariate arbitrarily motivated phd averages massachusetts mentioned asymptotically asymptotically brown brown brown trivial publishers publishers publishers publishers explanation answer briefly correction turns drive drive sys strictly strictly day desirable calculations begin definite explained argument argument argument argument empirically empirically relevance pseudo autonomous adjustable slower frequently summarized perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations perturbations measuring prevent curvature hamming hamming semi semi chose simultaneous summed generator guarantee oxford tation tation acts reaching reaching reaching significance difficulties held multiplicative imposed removing implications presentations presentations alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector alspector james surprising pat sim tic surprisingly shortest shortest shortest shortest master repeatedly theoretically theoretically hypercube implicitly valuable papers vari speaking mind mind multiplying microstructure basically tables presenting failed expanding jabri jabri jabri jabri jabri remainder summarizes concentrated tems met considers unconstrained apparently flower flower flower flower flower flower page indication rewrite ignoring ignoring signs gorithm strict strict continued impractical imple dominates dominates dominates tors outperformed ron calculates clark clark clark explanations concave fastest fastest sions cascaded ance bottleneck cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs faced unusual focusing parker tern noticed ted preferable preferable preferable preferable retaining repeating cient dominate perturbative perturbative perturbative perturbative perturbative perturbative perturbative ogy imation tran mentation perturbing perturbing superiority waiting kirk kirk kirk helped workers disappear cent behaved behaved reproducing bellcore stochas acknowledgment yuhas hurt kushner kushner kushner awi awi indexes seeds seeds jayakumar gert quadratically kerns recalling implemen implemen raising fleischer morristown eft consid thakoor insightful quicker proposing discus chu eecs bart ulations obt technol fixes pertur biggs biggs biggs edi ezplorations stray sheds gannett haber pert mysterious italics turbation 
#@Alspector_J,Lippe_D,
#t8
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#*network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data function function time training training output output output output output output number system system system error results results results units units units units hidden hidden hidden hidden performance performance performance performance based linear linear linear linear linear linear linear linear linear layer layer layer layer layer case case case case shown noise weight weight weight weight weight weight weight weight neurons neurons unit recognition recognition recognition recognition recognition recognition recognition method single single control control control control control large neuron neuron neuron neuron neuron test test test inputs simple paper paper size size size size size size size size size feature features features level current current current current trained cell cell cell problems high high similar general general general general general speech speech real real states dimensional result result computation computation computation research independent independent independent independent independent independent table table table table table computer connections connections connections connections connections connections connections connections connections synaptic synaptic phase phase low abstract applied back analog analog analog analog analog analog analog analog analog analog analog analog analog references propagation introduction circuit circuit circuit effect cost representations word previous firing type required binary conditions expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip fact proposed forward simulations total simulation simulation simulation multi multi multi multi multi times times means factor applications applications filter obtain artificial artificial samples samples samples samples samples application application application connected connected discrete power voltage voltage accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy connection connection train source source source words implementation implementation implementation implementation implementation implementation synapses synapses equivalent environment additional bit bit bit bit bit bit bit capacity full full world world speed speed speed speed speed speed basic condition channel channel levels levels area selected selected biological measured tested tested fast limited limited limited limited circuits short effective implemented synapse synapse synapse synapse synapse adaptation vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi makes development noisy including smaller reduced reduced reduced reduced reduced fully fully technology technology technology technology technology ratio mode mode operation operation operation numbers direct window frame minimize added perceptron perceptron perceptron improved improved improved practical array conventional conventional conventional conventional conventional works module module module module module module module module module module yields yields speaker speaker improvement extended extended digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware conclusion critical designed designed designed external external external reduction characteristics pulse variety configuration digit digit describes dept dept changing recall implement electrical electrical angle integrated select independently independently controlled controlled controlled controlled lee lee lee suggested digits digits digits past expansion expansion purpose purpose precision precision retrieval recognize successfully selecting suitable suitable suitable computations comparing comparing characteristic characteristic compact timing sampled sampled modular nips cmos cmos cmos chips chips chips chips chips chips chips preferred software extend transistor transistor comparable proved proved proved prototype prototype switching mixed mixed mixed mixed mixed mixed mixed mixed electronic band asynchronous multiplication snr snr implementing preprocessing ran ran laboratories pulses improvements double double substantially flexible flexible flexible flexible spoken spoken spoken spoken lack switch switch summarized summarized song song song song hamming inherent inherent decoder neuro realized fabricated fabricated interface interface bipolar bipolar bipolar flexibility flexibility flexibility enhancement murray khz interconnection resistance resistance affected synchronous modelled clean considerations limitation limitation limitation bank die realize degraded million placing loading info info hundreds hundreds hamilton industrial attained attained poly poly comm comm huge modularity modularity modularity custom custom configured operated operated operated severely severely metal metal men men men respects kim kim kim electrically wired wired insects experimentation hwang hwang hwang han han han han dong tarassenko emulation persons persons persons byte byte byte mosfet mosfet servo servo servo korea korea korea korea telecom adaptability reekie suffered precisions universally universally clocking soo soo soo extendable women women women 
#@Han_I,Kim_K,Lee_H,
#t8
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural input input input input input input input input input input input input input input input input data data data data function function function function function figure figure figure figure figure figure figure figure figure figure time time set networks algorithm output output output output output number number error error state results results results results results weights shown shown shown shown shown values values values values values values values values values parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions method method single single single single single single single single single single single single single single single single single single single single single single large large rate inputs inputs inputs form form shows shows shows shows shows shows signal signal signal signal signal algorithms visual small size size work fig fig fig step step field field field field field process process process process process process process level level current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current high high high high high high high memory memory similar representation section section section section section section section fixed fixed line line line line line rule rule rule rule speech parameter parameter parameter parameter average average theory term term term activity result threshold threshold threshold threshold computation research research independent defined table table standard standard distance synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic direction direction direction present low low low maximum range range range range range range range range range learn learn position position abstract back back analog analog references positive procedure introduction circuit circuit circuit effect effect effect change change change change change change change change change change energy energy energy rules measure measure measure signals higher higher higher higher higher higher part previous type required good long long long fact region region region finite resulting resulting resulting ing ing potential potential negative vol artificial cross cross cross provide compute compute compute compute compute rates rates perform perform perform goal related related connected connected gain equal power power power power power power approaches approaches voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger larger connection fields update update update update update update update dependent dependent source source source source source source source source source source source source source source source source source source source source source source source source source source modeling modeling report institute synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses joint bias bias addition ai considered computing experiment experiment additional additional design design top effects conference approximate approximate increase increase give channel channel channel channel developed developed area area lines lines product product product product product product product product finally finally finally selected backpropagation backpropagation backpropagation backpropagation iteration nature nature depends achieved achieved measured measured measured normal normal feedforward feedforward feedforward increases describe describe stable surface effective synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse supported require vlsi instance easily auditory typically typically typically smaller underlying combination combination reduced functional functional technology ratio edge edge increasing increasing increasing operation operation operation operation operation operation operation stored stored bits supervised magnitude magnitude produced resolution advantage separate typical typical typical typical typical array array array array array array array array array array array array array array array array sufficient varying previously approximately approximately correspond achieve achieve background background background gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate storage storage storage storage increased increased wide occurs column column column strength minimal row row row row row row row row hebbian reduce designed exponential weak constrained physics physics characteristics california proportional proportional proportional selective decrease pro pro modeled modeled simultaneously simultaneously simultaneously applying applying formed formed quality quality cycles cycles decreases decreases decreases yield dependence dependence depending operations operations operations operations operations controlled approximated updates past diagram diagram earlier measurements roughly add add boundaries foundation coupling expect silicon silicon silicon silicon currents currents coupled phys characterized successfully efficiency capable capable efficiently computations computations ten showing criteria device device device device satisfy satisfy quantity involved absence providing computes chips neighboring acknowledgments decreasing selectivity selectivity selectivity selectivity selectivity poor requirements requirements requirements experience experience circuitry circuitry mead mead mead mead mead mead steady examine examine tech terminal transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor office gates gates proper proper matched coefficient coefficient adapt rev voltages voltages voltages voltages voltages voltages voltages voltages store extent extent charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge charge years years devices devices devices advanced rows stop slowly developing analytic floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating multiplication starts drive implementing sections shared shared controls pulses ion arises fourth percent double profile substantially fed orders orders passed remove operate characterize modulated 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decrement decrement grown retention retention volatile collect electrically beckman ana surrounded oxide oxide oxide oxide oxide oxide oxide oxide oxide oxide oxide oxide bradley bradley bradley bradley bradley incremented preferentially preferentially minch minch minch minch minch minch hasler hasler hasler hasler hasler hasler hasler electrons electrons electrons electrons electrons electrons electrons electrons electrons electrons electrons electrons electrons electrons electrons transport dates neurm tam pulsed pulsed pulsed raising injecting couples efficiencies efficiencies pute polysilicon polysilicon permanently depletion benson diorio diorio diorio diorio diorio diorio electronically ify decremented swept incrementing tun trapping trapping fects repeatable opment castro upto capacitively capacitively boltzman inject transis float thinner penetrate 
#@Hasler_P,
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#*model model model model model model model model model model model model model model model neural neural neural neural input input input input data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number system system system system system system system system system error error error error error error state state state results results results results results results results results results results results information information information information information information information information information information information information information information information information information information information problem problem problem problem models models models performance based based space linear linear linear linear case case order shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown systems values values noise noise weight method approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern point single single single processing processing processing processing processing control large rate rate test analysis analysis form form form form shows shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms simple simple simple simple simple visual visual paper paper paper paper paper paper paper paper paper paper paper paper examples work work work work work work work work work task methods methods fig process process process process process process process process process level level level level level problems problems problems high response response similar similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show section section section section section section section section fixed line speech speech speech speech speech speech speech speech real theory note result result result result result result result result result university research research research research defined found found initial initial initial initial initial table estimate estimate estimate estimate estimate estimate computer computer science left left left left left left left presented phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low low frequency frequency frequency temporal temporal sets press position basis basis basis outputs outputs abstract back back back back back back back find computational computational computational computational references due due due due due ieee ieee ieee ieee ieee positive positive positive procedure procedure procedure procedure important important important introduction estimation effect cost tion tion tion tion tion change change change change change energy energy lower signals signals signals representations representations representations representations representations word word word word word part center center cases firing multiple good represent make make make make fact fact techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques correlation correlation correlation correlation correct correct correct errors forward scale resulting resulting tasks total human human human human human sum performed performed performed performed performed performed called filter filter filter filter filter filter filter filter filter filter filter filter negative original original original original original original original original original original original original original original original vol samples true cross cross cross proc proc proc proc determined related related related gain gain gain cortical power power power power power power power approaches steps steps steps steps train train train modeling proceedings report report loss implementation consists consists individual represents difficult difficult difficult final delay delay delay delay maps domain domain equivalent equivalent directly view estimates estimates san san top top stage stage stage bit bit bit bit detection detection efficient efficient efficient efficient efficient efficient efficient upper basic basic con con con con produce channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel lines lines path provided finally finally finally finally iteration iteration iteration iteration nature constraint simply measured normal technical fast fast limited limited inverse complete circuits circuits amount amount short short short short short implemented generate main eds eds adaptation square square ability easily makes noisy including fit fit auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory needed combination block interesting interesting projection projection projection projection projection special special consistent consistent consistent consistent database language squared details iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations filters filters filters filters filters filters bottom bottom early magnitude magnitude magnitude magnitude frame frame combined combined minimize choose run run added added predict improved improve separate separate apply identical identical identical sense sense relevant engineering interest highly compare conventional conventional calculated calculated volume tions speaker speaker match trans trans trans trans trans trans definition background separation separation separation separation separation separation separation separation modified modified channels channels channels channels channels interval interval interval improvement sensitive increased amplitude amplitude amplitude horizontal horizontal scaling rotation rotation column pass half half half half half half starting critical row row row row reduce reduce segment segment segment segment conclusions measures measures accurate numerical designed clear peak sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound demonstrated assuming minimizing scene acoustic acoustic relation pro produces produces produces perception perception perception perception ways ways factors describes describes describes mathematical mathematical segments segments segments segments missing missing missing sensitivity electrical involves unique spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral adding frequencies quality quality choosing reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction stages stages stages detailed detailed transform transform evaluate evaluate controlled evolution evolution understanding spectrum spectrum spectrum spectrum spectrum diagram diagram partial partial calculation calculation calculation calculation performing measurements convex convex convex convex combining combining combining roughly add iterative tracking intermediate filtering existing existing figures includes perceptual perceptual perceptual inter automatic maximize maximize variations domains absolute successfully compression compression compression middle aspects efficiency importance divided computations projections projections comparing ten fine fine capture road soc quickly graphs success interested issue running content timing localization simplified simplified backward wavelet wave wave wave delayed received overlapping acknowledgments minimized employed powerful wiley wiley transformed investigate difficulty steady accurately reducing reducing reducing fourier fourier fourier fourier history history ideas detectors ideal decisions proper plausible created equally perfect perfect perfect implementations impulse impulse impulse impulse impulse impulse impulse versions portion portion portion algo assumes detector explored separated separated speakers baseline detected motivated ment band trivial track slope waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform adjacent cascade multiplication correction nonlinearity comparisons implementing sys arc closer broad broad pulses inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion sounds sounds sounds sounds sounds pitch pitch pitch bandwidth annual addressed addressed addressed fourth fourth apparent improvements syllable profile profile cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear understood consistency consistency readily cal curvature suited acoustics acoustics adjust richard richard kinds neuro windows windows owl lim wang cochlea cochlea cochlea cochlea summed displays instantaneous cor cor picture spectra ear cooper cooper cooper summing summing rithm pick narrow recover recover recover recover recover recover rotated controlling reconstructed repre enhancement lost lost lost lost communications convenient imaging adjusting multiplicative determination bands bands utterance salient vowels vowels tap tap tap tap tap tap tap tap tap tap recovered recovered recovered sion corre uni yang yang initialize initialize waves arrive rich waveforms waveforms waveforms waveforms waveforms arrows extends correcting correcting sons sons splits alternatively interestingly dividing mechanical lag informa multiplying ure converted converted converted converted converted converted corporation outline piece sig dec july bank bank bank bank icassp icassp icassp icassp copy tor england england guess guess imagine reconstruct options summarizes preserved preserved duda mathematically convert convert convert convert neurophysiological neurophysiological inverted inverted inverted inverted synchronized noting noting noting noting worth worth portions portions preserve esti grateful grateful inverting inverting inverting inverting inverting page retained tune tune round ward correlate correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram fortunately acoust reversed reversed autocorrelation autocorrelation autocorrelation autocorrelation tial doesn lyon lyon lyon lyon lyon lyon stripes char conversion conversion 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#@Slaney_M,
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problem problem problem problem problem problem problem problem problem models models models models models models hidden hidden performance performance performance performance based based space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown shown systems systems values values values values probability parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise distribution distribution method method method method method method method approach approach approach single single single single single single processing processing processing large large local local local local local local rate rate test test test test test matrix matrix inputs form form form form form shows signal signal signal signal simple simple simple gaussian paper paper paper paper paper paper examples small size work work work methods step step step points points points classification classification level level level current trained trained trained trained structure structure problems problems problems problems random architecture architecture show show fixed fixed line line line line vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real obtained experiments experiments experiments activity activity university university threshold threshold computation computation solution research research log log defined target initial initial initial constant constant table table table table estimate estimate standard standard standard computer computer terms distance node node science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction activation activation activation activation activation frequency frequency maximum press nonlinear outputs outputs outputs abstract find density likelihood likelihood likelihood likelihood likelihood likelihood references due due ieee ieee ieee ieee ieee procedure adaptive mixture mixture mixture mixture mixture mixture mixture context context introduction estimation statistical statistical statistical statistical generated generated generated variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance recurrent tion tion energy energy variable assume lower lower measure prior prior part part previous previous multiple multiple good binary binary tree distributed distributed distributed distributed expected expected region probabilities probabilities probabilities probabilities errors errors forward scale scale simulations classes ing ing tasks total regression regression regression regression regression regression computed multi sum performed performed optimization applications applications em em samples true true application cross cross series series series series series series series series series series series series series series provide provide rates rates rates perform perform posterior posterior posterior distributions gain gain gain power accuracy comparison train train proceedings proceedings report institute department department loss consists consists consists consists joint represents connectionist connectionist connectionist connectionist exp scheme scheme scheme scheme scheme addition addition addition framework framework cambridge cambridge limit top bit bit bit bit conference efficient efficient full approximate world estimated validation validation give give con produce coding coding coding coding coding coding coding coding coding coding coding coding derived weighted conditional conditional conditional levels actual actual finally finally nature achieved discussion covariance covariance covariance covariance covariance covariance covariance normal technical describe describe describe describe describe describe assumption assumption predictions predictions predictions short generate supported supported journal journal future future future future future degree rumelhart rumelhart pairs pairs smaller underlying underlying underlying underlying underlying underlying account dynamical jordan jordan jordan jordan jordan mlp mlp mlp mlp mlp mlp ratio ratio principle principle operation operation squared squared direct direct 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solid solid assuming relationship acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic denoted acknowledgements construct produces solving plot plot vertical segments confidence confidence multilayer involves spectral spectral spectral consisting gaussians predictive predictive cycles select yield choosing review stages squares viewed codes evaluated updated frames frames frames decomposition understanding past spectrum earlier dashed dashed additive performing combining intervals calculate euclidean transactions transactions expect perceptual inter extension uncertainty specifically priors gating gating gating gating gating gating gating structural society efficiently plots traditional traditional notice sin sin sin follow follow duration gray gray quantity quantization quantization quantization predictor predictor predictor predictor predictor mixing mixing jacobs jacobs jacobs jacobs jacobs receive modelling modelling 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#@Robinson_A,Waterhouse_S,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output output output number system system system system system system system system system error error error results results units units units units units units units units units units units units units hidden hidden hidden hidden hidden performance performance based based based based based based based based space space weights weights weights order systems systems values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise weight weight functions functions unit unit unit unit unit unit unit unit single single single control control control control control control control control control control control control test test test test test test test test test test patterns analysis analysis inputs inputs inputs form form paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples size size feature net net net net work work task task points points features current current trained trained trained trained trained trained trained trained trained trained trained trained trained trained high high similar similar fixed fixed fixed fixed fixed fixed fixed fixed line general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter real real gradient obtained obtained note result university university university university research research research research independent defined defined defined defined defined target target target dynamics initial initial initial initial initial table table table computer computer computer terms science science science left left map frequency frequency frequency frequency frequency frequency machine sets sets sets motion range range range learn learn learn learn learn position position position position position position position basis basis basis outputs outputs outputs continuous abstract back back references procedure procedure important important adaptive adaptive adaptive adaptive adaptive decision decision decision mixture mixture introduction hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand generated generated generated generated variance parallel parallel parallel parallel parallel parallel search change change difference word learned required required good good long represent represent distributed expected expected expected expected correct errors errors errors errors forward forward forward forward ing tasks total called times times times mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping made made natural natural natural study original artificial artificial artificial relative determined determined determined related related steps contrast contrast descent report report report institute institute institute words words words department department implementation version consists consists internal individual joint difficult difficult difficult difficult scheme scheme addition ai ai hinton hinton hinton hinton hinton hinton hinton hinton additional transition requires choice significant approximate world pages con produce produce produce produce produce produce produce produce produce produce produce developed provided finally finally nature depends measured measured measured measured normal normal technical technical technical group fast corresponds corresponds corresponds corresponds complete rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount implemented shape shape require face adaptation adaptation journal square square square end degree rumelhart including smaller needed reduced functional block interesting interesting testing significantly york uniform uniform leads squared squared representing representing direct making making making stored bits normalized normalized normalized normalized normalized expert produced produced produced produced produced produced produced produced produced produced produced added added added added description improved typical typical movement reported include include subject subject subject subject subject subject identical approximately volume volume volume volume works works smooth speaker correspond correspond positions positions positions gate interval interval williams improvement sensitive entire amplitude amplitude amplitude amplitude horizontal horizontal intensity suggests rotation feed feed feed feed move move boundary critical place trajectories sigmoid sigmoid sigmoid sigmoid performs performs practice practice learns sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound hard reduction demonstrated labeled radial radial turn user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user start movements movements movements plane plane relationship averaged targets targets manner configuration configuration configuration configuration configuration configuration configuration acknowledgements produces index index index index transitions transitions transitions dept implement explicitly coordinates coordinates coordinates coordinates coordinates linearly text text text text text text text text angle angle interaction adding formed formed quality quality phoneme phoneme phoneme phoneme interpretation interpretation open open controlled controlled centered forms forms forms static static static static understanding activities allowed spectrum spectrum diagram key slow additive additive additive performing normalization normalization roughly interpolation interpolation remains initially msec msec degrees building includes perceptual activations priori bell contour inter variations gating gating reason middle middle middle middle extra closely uniformly differ divided driven schemes vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel ten summary quickly quickly link phonetic timing timing duration list dayan providing correspondence moves illustrates extract software origin poor production production create collection difficulty varied accurately pursuit respond fashion history mse mappings mappings muscle scaled scaled scaled scaled proved fundamental fundamental fundamental fundamental phases act closest adapt reading configurations configurations configurations configurations configurations configurations configurations created created created der mapped mapped mapped generates contributions finds attempts defines synthetic devices devices devices advanced stop stop stop stop stop stop slowly variances variances fairly fairly improves adapted drive rapid perspective closer ring ring ring producing producing division controls controls watkins sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds angles angles angles pitch pitch pitch pitch beginning begin toronto toronto toronto toronto toronto toronto toronto recording recording bandwidth bandwidth qualitative qualitative conjugate summation requiring fourth greatly syllable collected collected collected collected collected collected collected collected quantitative quantitative red peter poorly slower music continuously sharp vocabulary vocabulary vocabulary vocabulary phonemes phonemes phonemes adjust green green substantial decreased implements implements implements begins utterances june notes accomplished generator generator generator appearance interface interface interface interface forming controlling repre repre robotics plays spontaneous ranges adjusting held intelligent height height height intuitively hours hours hours hours vowels vowels vowels vowels vowels vowels vowels vowels vowels decide von overview overview moved bad chooses reveals tracker late contact contact contact gesture gesture gesture gesture gesture gesture gesture gesture motions motions extensively formant formant formant formant formant formant formant formant formant formant formant formant formant formant formant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant consonant switches switches dividing speaking speaking speaking speaking speaking speaking slight depression ent propagating centre year ideally spaced suppressed auxiliary param quantized musical musical formance articulator geoffrey geoffrey geoffrey geoffrey geoffrey geoffrey file dominated generators altered rbfs funded finger finger finger finger turning likewise articulatory articulatory articulatory articulatory articulatory tract tract tract tract tract eters ritter november sessions stops syn syn gestures gestures gestures gestures gestures gestures gestures drives lowe decided identifies played loosely eral fre floor consonants consonants consonants consonants consonants consonants consonants consonants consonants consonants consonants joints vocal vocal vocal vocal vocal vocal bandpass predictable reality tube robotic lewis fair centres centres centres centres quick articulation deter skill unusual translates talk revow predefined converts sentations mir crg manager save tongue tongue tongue tongue quency subtasks holmes decides mike collect thumb thumb thumb thumb thumb thumb thumb unlimited unlimited retrained puted translating manipulating formants formants spontaneously overshoot wji wji analysed converting centred canadian nserc tar mined voicing voicing voicing voicing multivariable closing fellow fingers fingers fingers granularity granularity granularity granularity contin qualities broomhead foot foot foot foot foot foot foot foot suit wild perceptually simplistic pilot sev instruments nasal roll synthesizer synthesizer synthesizer synthesizer synthesizer synthesizer synthesizer synthesizer synthesizer synthesizer synthesizer speak speak speak speak speak speak speak speak jaw actuators interfaces ject initiate verbal divisions oper malvern unscaled wolfgang wolfgang listening franklin netw spelling designate pronounce ang versatile nasals nasals nasals 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#@Fels_S,Hinton_G,
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#*network network network network network network network network network learning learning model model model neural neural neural input input function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time set set networks networks networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm output number number number number number number number number system system system system error state state state state state state state state state state results results results results results results results information information information information information information information information information information information models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space space space space linear shown shown shown shown systems systems systems systems values values probability probability parameters parameters parameters noise noise noise distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach pattern point point image image image image image image image image image image image image image image processing processing processing processing large large large local rate rate analysis matrix matrix matrix shows shows shows shows shows shows shows shows signal signal signal signal simple simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper small small small work work work work work work task task task task task field features features features features level level level current trained trained trained trained cell cell problems problems problems high response show show equation images images images images images images images images images images images images images images images images images images images images images images images images images images images images general generalization generalization generalization generalization generalization generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average average average average average average average states states states states states states states states states obtained obtained obtained obtained obtained term experiments activity university solution research research research research independent independent independent independent independent dynamics initial constant constant constant table table table table table table standard standard standard standard standard standard standard terms science science science left left presented presented present low low temporal temporal temporal temporal maximum position components basis outputs continuous sample sample sample sample sample abstract applied back find likelihood likelihood references component stochastic stochastic stochastic stochastic stochastic due due ieee ieee positive procedure procedure procedure important important important mixture mixture mixture mixture mixture introduction hand hand hand hand hand effect effect effect effect effect effect dynamic dynamic variance variance variance lower signals signals representations representations representations word word learned learned learned learned center previous previous cases cases cases good long conditions markov markov markov markov markov markov markov fact fact techniques techniques techniques techniques correlation correct correct correct correct probabilities probabilities scale simulations resulting human human human human human human performed performed times times means means means means potential potential potential potential potential dimension applications applications study filter original artificial artificial artificial artificial represented compared proc perform eye eye goal distributions distributions distributions distributions equal approaches support source morgan proceedings proceedings department department loss technique technique individual individual advances responses bias sequences sequences computing domain domain equivalent estimates estimates transition san san stimuli effects effects statistics statistics estimated conditional clustering developed levels levels area area nature achieved normal normal describe tested tested tested tested tested tested limited limited limited limited limited stable role role main main face face journal journal end pixel pixel pixel pixel pixel pixel pixel cluster easily development sensory sensory kaufmann auditory auditory auditory typically underlying underlying combination reduced reduced reduced coefficients transfer testing testing significantly ratio segmentation trials language principal principal filters filters filters filters bits early frame frame idea combined architectures architectures architectures architectures architectures architectures improved improved improve recent advantage robust practical subject subject subject side pixels pixels pixels sejnowski sejnowski cognitive cognitive cognitive cognitive relevant relevant relevant relevant interest dimensions highly varying varying compare compare observations approximately subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects calculated axis speaker speaker speaker studies studies mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation entire entire entire entire scaling suggests deviation deviation deviation deviation wide wide matrices matrices feed move width column pass pass half half starting starting starting row conclusions differences numerical numerical numerical peak mateo integration integration integration reduction characteristics california assuming variety minima acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic digit digit perception perception perception perception perception perception perception perception perception perception laboratory laboratory vertical modeled modeled sensitivity category averaging physical electrical dimensionality dimensionality develop gaussians events events independently independently independently focus stages solved densities evaluated centered frames frames frames frames understanding understanding digits digits digits digits digits digits digits allowed past reasonable reasonable reduces roughly roughly purpose initially filtering assigned assigned advantages exploration recognize recognize automatic variations tests successfully successfully reason sensor compression selecting aspects extra society delta delta delta delta delta delta delta delta delta delta delta literature literature build vowel vowel identity refer refer repeated repeated video video video video symmetry symmetry symmetry symmetry categories gray gray gray play thresholds automatically received consisted consisted extract tesauro camera cowan presents explore diego powerful poor create experience rapidly humans humans humans humans humans humans humans hall reducing matches dependencies variability variability understand understand phases waibel waibel waibel reading reading reading reading reading reading reading psychology psychology psychology illustrate front logistic logistic logistic speakers synthetic synthetic sentences sentences isolated integrate integrate integrate years years years percentage histogram histogram track track majority london processed preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing filtered filtered located immediately controls potentially recognized sounds beginning english english english english read exemplars exemplars exemplars raw raw robustness robustness robustness integrating composite fed fed car car poorly cohen gains vocabulary vocabulary vocabulary measuring measuring phone phone sophisticated display display segmented age age windows lot initialization consistently room benefit ear investigation acm approximates discover enhancement plays lost lost numerically simplify height biased belong illumination alspector lip lip lip lip lip lip lip lip prentice representational representational representational encountered enhance captured jolla papers avoiding thresholding thresholding thresholding thresholding severe audio audio audio audio audio compressed unified leaving leaving tables stork stork stork stork asked asked asked benefits bank preserving feeding convenience convenience sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma sigma regularity tendency letting preserved disadvantage thresholded efforts efforts efforts efforts emphasize differentiation portions accounted confusion confusion confusion confusion psychophysics students ucsd ucsd rabiner rabiner expense regularities monitor correspondences builds builds ongoing hearing hearing hearing hearing hearing hearing hearing savings jersey movellan movellan movellan movellan pictures played engine acoustical month bregler bregler bregler digitized digitized digitized colleagues tracks tracks america drastically prone multimodal constraining articulation articulation cauchy cauchy cauchy wolff wolff wolff wolff wolff translates translates percept capturing talk subtle trapped favors jenkins jenkins campbell discrepancy blurred blurred blurred equalization equalization centroids centroids centroids subsampling goldstein goldstein subsampled lips lips lips lips lips retention jackknife untrained untrained ames chi hild hild hild movie british initializing rationale trimming bimodal bimodal explores explores hwang hwang mined blurring blurring conveniently icnn emphasizes lipreading lipreading jackson jackson compensatory contingencies crafted crafted emerging yuhas yuhas blend confusions modulates males infant tolerate infants lea compressing fundamentals adults hear sharpening females instabilities vital cvpr impaired impaired impaired movies profound midline pulling illusions reception javier javier javier javier javier enforcement enforcement enforcement supplemented equidistant hinder sharpness recommendations preprocess intelligibility sharpened infancy unprocessed unprocessed psychologists voices unaware 
#@Movellan_J,
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#*network network network network network network network network model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data data data data data data data function function function function function function function time set set set set set set set set set set set networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error state state state state state state state state state state state results results results results information problem problem problem problem models models models models models models models hidden performance performance performance performance performance based based based based based space space space weights weights weights layer layer layer layer vector vector shown shown systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters weight weight functions distribution recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method approach approach approach approach point single single single processing processing processing large large large large large large large local local local local local rate rate rate test test test test class class class class class class class class matrix matrix inputs shows simple simple gaussian paper paper small small feature net net net net net net net work work work work work work work work task task step step step step step step step classification classification classification classification level level level level level current trained structure structure problems problems problems problems similar similar similar equation equation equation equation fixed speech speech speech speech speech speech speech speech parameter obtained obtained term result result computation computation computation solution research research independent independent independent independent independent independent independent independent independent log log log log found sequence initial initial table table table table table table table estimate estimate estimate estimate left left left present machine maximum press outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied applied applied back density density density density density density density density density density density density properties likelihood likelihood likelihood references due positive positive procedure important important decision decision decision decision decision decision decision decision decision decision decision decision decision mixture mixture mixture mixture mixture mixture mixture mixture context context context context context context context context context context context context context context context context context context context context context context context context context context context introduction estimation estimation estimation estimation estimation statistical effect variance parallel difference classifier classifier prior prior prior word word word word word word word word word word word word word word word word previous previous bound type multiple multiple good tree tree tree tree tree region region region region region region region probabilities probabilities probabilities probabilities scale scale resulting classes total computed multi multi multi sum sum regions regions regions regions regions regions regions means means means made made made em em em em em em obtain obtain negative negative specific samples compared application cross define compute compute rates rates rates rates proc perform perform perform perform experimental experimental posterior posterior posterior posterior approaches mit steps larger contrast train train dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent nets nets nets modeling modeling morgan morgan morgan morgan report report department implementation technique technique consists advances advances represents represents cambridge cambridge computing domain experiment experiment additional estimates estimates requires estimated weighted developed developed developed criterion criterion entropy actual iteration iteration iteration technical feedforward describe denote tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm complete amount amount common implemented implemented eds eds journal journal makes rumelhart development development development kaufmann kaufmann objective typically smaller needed jordan jordan jordan jordan technology increasing consistent structures principle language language language details max max direct experts experts experts experts experts experts experts experts experts experts supervised expert expert expert expert expert frame idea idea combined combined improved improve recent advantage pair separate separate reported apply identical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees trees trees trees recently solve smooth smooth converge sparse mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures modified modified modified generalized generalized generalized generalized generalized generalized generalized generalized generalized improvement improvement improvement improvement parts expression alternative hybrid hybrid hybrid pass segment segment conclusions differences performs performs constrained hard hard hard reduction reduction sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal demonstrated labeled labeled turn min iii manner program acoustic suppose relation label multilayer explicitly explicitly simultaneously simultaneously involves easy gaussians implies expectation expectation john john john john formation phoneme phoneme phoneme phoneme squares squares viewed viewed solved densities showed showed soft soft soft soft soft similarly reasonable combining fitting fitting fitting fitting fitting iterative iterative boundaries boundaries interpolation advantages avoid building priori weighting specifically priors priors priors priors priors priors grammar grammar grammar grammar gating gating tests major regular hmms modification computationally divided divided divided divided divided divided divided divided effectively efficiently composed prob phonetic phonetic phonetic phonetic phonetic lie built built satisfy list michael paradigm paradigm giles giles computes maximization maximization maximization maximization automatically automatically automatically acknowledgments cowan cowan explore simpler unlike hanson hanson comparable workshop man thought adjusted fisher art art art baseline baseline baseline baseline utility advanced publishers publishers publishers improves expensive benchmark organized division incorporate inversion recognized universal reflects hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme 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#*network network network network network network network network network network network learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data data data data data data function function function function function figure figure figure figure time time time time time time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output number system system system system system system system system system system system system system system system system error error error state state results results results results results results units units units units units units units information problem problem problem models models hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based space space space linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer case vector vector vector vector vector vector vector vector vector vector vector order order order order systems systems systems systems systems systems values probability parameters parameters parameters parameters parameters functions functions unit unit unit unit unit unit distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method single single processing large local local local rate rate rate test test test test test test test analysis analysis class class class class matrix matrix matrix optimal inputs form shows shows signal signal signal signal signal gaussian gaussian gaussian gaussian paper paper paper feature feature feature feature feature feature feature feature net work work methods methods methods methods features features trained trained trained trained trained trained trained structure structure representation architecture show section section section section section line line line vectors vectors general general general general general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter real approximation states theory theory gradient obtained obtained obtained obtained obtained obtained obtained obtained term term term term term term term experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional university university computation research independent independent independent independent independent log log log log defined sequence sequence sequence sequence target target target table table table table table table table estimate estimate estimate standard terms terms terms terms terms science left left presented presented sets sets maximum press components basis basis nonlinear outputs continuous continuous continuous continuous continuous continuous abstract applied applied applied applied applied applied convergence convergence references component ieee ieee ieee procedure procedure procedure procedure important context introduction hand estimation estimation statistical effect dynamic dynamic dynamic dynamic generated tion tion tion energy energy energy energy difference measure representations word higher higher part previous type type required required good long conditions markov techniques techniques proposed correct correct correct correct probabilities probabilities forward resulting total total total regression regression regression regression regression regression computed computed computed respect respect multi multi performed performed performed performed called called mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping optimization optimization optimization optimization optimization optimization made global global global applications applications study filter filter obtain original artificial specific compared compared application desired desired desired rates rates rates rates proc proc proc proc proc proc perform determined goal approaches mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy train descent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent words technique technique consists consists consists code individual kernel kernel kernel kernel kernel kernel kernel kernel advances connectionist connectionist connectionist connectionist sequences considered considered considered considered considered considered considered cambridge computing experiment experiment experiment view estimates estimates determine efficient efficient efficient significant significant statistics estimated estimated estimated pages pages pages pages pages pages validation con con con channel weighted weighted developed entropy constraint achieved achieved achieved discussion covariance covariance feedforward arbitrary tested hmm hmm hmm hmm transformation transformation transformation transformation fast limited close rbf rbf amount amount amount short short implemented implemented require main adaptation adaptation adaptation adaptation adaptation adaptation end end end development fit fit pairs pairs pairs pairs pairs pairs pairs reduced reduced account account functional coefficients coefficients coefficients coefficients transfer programming ratio ratio ratio york segmentation mechanism database mode principal principal pre window normalized normalized supervised supervised supervised supervised frame frame combined minimize sources perceptron discussed pair reported reported reported reported apply include subset dimensions compare compare previously unsupervised subjects volume module module tions speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker pca pca pca pca pca achieve trans diagonal diagonal mixtures locations locations generalized generalized generalized generalized generalized generalized generalized improvement improvement improvement grant extended matrices alternative alternative feed generally generally column column row reduce conclusions editors differences differences differences differences modules modules modules modules modules numerical designed designed performs constrained constrained constrained sound characteristics characteristics user derivatives derivatives acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic base reference reference reference reference reference reference reference reference reference reference reference estimating transitions segments segments segments modeled modeled implement averaging averaging transformations transformations transformations transformations transformations remaining text text spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral integrated applying formed formed extraction expressed depending variation variation detailed densities labels labels decomposition decomposition forms suggested translation diagram diagram epochs expansion spaces spaces spaces spaces spaces normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization sec fitting interpolation assigned norm norm expect includes kernels kernels kernels kernels kernels kernels kernels inter inter inter recognize automatic automatic automatic automatic variations variations hmms suitable society paths included included included poggio poggio poggio identify summary repeated heuristic heuristic interested phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic notation usual minimizes automatically consisted consisted deal presents simpler selectivity diego diego diego diego diego parametric transformed optimized recursive recursive recursive preliminary rest mse mappings scaled authors proper variability proved neu coefficient automata recognizer singular front front front versions portion portion art multivariate multivariate multivariate multivariate speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers baseline baseline baseline baseline sentences sentences piecewise crucial defining phenomena worse comparisons processed rapid lin lin lin purposes sections satisfied shared acknowledgement sounds sounds describing alignment percent percent percent percent applies affine flexible offset offset spoken generic introducing gen resource resource resource resource resource resource phonemes phone phone phone phone phone phone phone phone phone phone gave hamming decreased age utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances sentence sentence multidimensional yielding spectra interface ratios ratios girosi girosi girosi approximates concerned tem eliminate platt platt platt allocation allocation allocation convenient utterance utterance utterance ral corpus corpus corpus corpus corpus corpus corpus corpus corpus phrase phrase phrase phrase nonparametric days composition mance contexts introduces corre corre perfor male male male male male regarded regarded overview realization mel mel dif dif tic entries entries barron barron barron barron rich material material material material material material adopted metrics metrics dramatically leaving ple vec recursively ties bank tween icassp icassp icassp icassp icassp comparative residuals acceptable female female female female female female tor warping warping warping reflected exam allocated allocated relate differentiation acquired insertion statistic gender gender gender portions memo minor exploited september deletion ergodic sponding sponding consuming invertible transforming phrases phrases phrases orthonormal orthonormal orthonormal routines realizations subtracting subtracting mori huang huang huang normalize watrous watrous assp sis indicators ically allocating allocating allocating allocating allocating allocating watson ized indi spec spec lexical cepstral schema schema unifying collecting dtw dtw dtw dtw shikano shikano shikano cient favorably favorably insertions italy italy italy accu tailored llx syrup outlines poral pronunciation novelty ministry bandwidths bandwidths transcription transcription transcription deletions aver nectionist del del del cate pervised marcel dekker indexes males males males males males zation silence pauses unmodified requested superpositions sidered sidered elliptical elliptical elliptical pseudoinverse females females females females ject evidenced racy couples couples couples substitutions unacceptable uttered uttered uttered uttered uttered uttered troller acous ins ins adaptability adaptability adaptability adaptability adaptability ass tral tral coeffi decorrelate analy plication verse adapta monographs recipe recurslye sondhi sondhi anisotropy accents apex aat aat diff transac irdle irdle irdle italian italian italian pause erally bootstrapped bian bian hardy hardy llw commutative valida ferences 
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training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number system system system system system system error error error state results results information information information information information information problem problem models models models hidden performance performance performance performance performance performance performance performance performance performance performance based linear linear linear linear linear linear shown shown shown shown systems systems systems systems values values parameters functions recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach pattern pattern point point point processing processing processing processing processing processing processing processing large large rate rate rate rate rate rate rate rate rate test test test test test test test patterns analysis analysis analysis analysis analysis class signal signal signal signal signal simple paper paper examples small small small small work work task task points points points points points points features process process trained trained trained trained trained trained random random high high high high high high high high similar similar similar similar equation fixed line images images images general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real average average average average average average average obtained term experiments experiments university threshold threshold computation solution solution solution research research research independent defined found sequence target target target standard standard distance low low low frequency frequency frequency frequency temporal sets range position basis outputs continuous continuous continuous sample sample sample abstract applied applied back due ieee ieee propagation introduction estimation generated generated generated generated search variable classifier lower rules measure word word word word word word word word word word word word word word word word word word word word word word word word higher part previous good good long long represent distributed markov make make techniques techniques techniques techniques techniques length length length length length length correct errors scale scale scale scale scale scale resulting resulting classes classes ing ing ing ing ing human performed performed performed performed times times times natural natural natural applications policy obtain original original original original original original original original original vol vol vol vol vol relative represented application series series provide provide rates rates perform equal approaches mit mit mit accuracy accuracy comparison larger train train train source morgan morgan proceedings proceedings proceedings proceedings implementation technique technique technique technique individual individual individual individual represents difficult difficult difficult difficult difficult difficult difficult delay domain domain directly curve curve additional additional additional additional san san detection detection detection detection detection detection detection conference conference conference classifiers estimated increase increase produce coding randomly developed levels types provided provided processes iteration constraint achieved normal normal normal normal normal normal normal increases increases increases group tested hmm transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation rbf amount amount amount implemented shape generate generate generate generate generate generate generate eds eds adaptation adaptation adaptation adaptation square end including including kaufmann kaufmann typically fully block testing testing testing testing testing testing testing testing testing significantly ratio ratio ratio ratio ratio ratio ratio ratio ratio character character character increasing matching database database iterations filters filters pre window international international normalized frame improve improve improve separate takes reported period dimensions dimensions approximately approximately calculated calculated calculated axis axis speaker speaker speaker match trans trans trans trans background background evaluation separation modified improvement improvement risk increased invariant invariant scaling scaling deviation wide alternative hybrid differences faster mateo mateo sound sound california radial variety identification identification program program acoustic acoustic base base areas digit digit index index index index optical optical generating plot laboratory segments averaging linearly linearly linearly transformations transformations transformations transformations transformations transformations transformations spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral scales frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies applying formed formed versus versus versus extracted extracted expressed transform transform transform transform transform transform transform transform evaluated showed frames frames partition allowed past spectrum spectrum diagram performing performing epochs epochs epochs epochs epochs epochs epochs normalization false false false filtering calculate views existing existing includes thesis usa determines illustrated successfully identified differ modification comparing score vowel plots ten characteristic excitation excitation summary phonetic duration vary simplified providing giles ill ill thresholds attempt software tesauro cowan presents transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed poor poor create create create create create rapidly varied varied varied put hanson lippmann lippmann lippmann lippmann lippmann lippmann lippmann lippmann preliminary matches boosting scaled authors variability scores scores scores adapt onset recognizer explored explored explored explored art epoch epoch epoch epoch speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers speakers baseline generates improving attempts isolated averages years percentage percentage percentage percentage percentage percentage percentage advanced ment piecewise analyzed waveform waveform improves expensive expensive processed rapid style style mation simard acknowledgement separately pitch pitch pitch pitch pitch demonstrates researchers varies varies percent reflect profile profile embedded embedded conducted lack lack cohen introducing synthesis gen incorporating acoustics acoustics acoustics acoustics richard richard richard richard richard age viterbi utterances sentence credit credit credit initialization spectra spectra accomplished accomplished interface ratios ratios ratios lost spontaneous spontaneous ranges ranges adjusting resulted hope obtaining transforms observing corpus symposium vowels alspector ranging ranging schapire loo loo male male male male male male male male expanded expanded expanded expanded expanded expanded expanded mel mel mel mel artifacts modelled modelled creating card card card formant formant formant formant formant formant formant formant formant formant formant formant broken projects linguistic linguistic verify metrics dramatically ter users users users users users users accept presenting expanding tween discriminative spaced spaced female female female female female female female female female warping warping warping warping warping workstation sinusoidal sinusoidal eric eric eric eric eric alter modifying exam formance magnitudes magnitudes continues file file ocr compatible expand cosine alarm alarm tract tract tract tract tract tract tract tract recognizers recognizers recognizers recognizers syn nist nist lation tom synthesized insufficient transforming transforming transforming phrases phrases jointly envelope envelope envelope envelope envelope envelope 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#*network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input function function figure figure figure time time time time time time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm output output output output output number system system system system system system system system system system system system system system system system system system system system error error error error error results results results results results results results results results results information information information problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models performance performance performance performance performance performance performance performance performance performance based based based based based space weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case case vector vector vector vector vector vector vector order order order order order order order shown shown systems systems systems systems systems systems systems values values values parameters parameters parameters parameters parameters noise noise noise noise neurons unit unit unit unit method method method approach approach pattern single single processing processing processing processing processing processing processing processing processing processing processing processing processing control control control control control control control control local neuron rate rate test patterns analysis class class matrix matrix matrix matrix matrix inputs form form form signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms visual paper examples examples examples examples examples net work work work task methods methods methods points current structure structure problems problems problems problems problems problems problems problems problems problems high high memory similar architecture show line vectors general generalization speech speech speech parameter parameter parameter parameter parameter real average average average theory theory theory gradient gradient obtained obtained obtained note experiments experiments university university computation research research log defined defined defined defined defined defined defined defined defined found found found sequence initial constant table table table table computer terms terms synaptic node science prediction prediction prediction prediction presented presented presented presented present present low low low low nodes frequency frequency frequency temporal range press press press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied applied back back back back back back convergence convergence convergence convergence convergence convergence convergence convergence properties references stochastic due due ieee ieee ieee ieee ieee ieee ieee ieee procedure important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision context context context introduction complex complex complex complex complex complex complex estimation estimation estimation estimation estimation variance parallel difference signals word chosen higher part previous previous type required good represent proposed proposed proposed length observed observed observed observed forward forward finite tasks tasks simulation simulation simulation regression performed performed performed elements mapping means means potential made made feedback applications filter filter filter filter filter obtain obtain vol vol vol vol vol vol vol vol vol vol samples samples represented compared desired series provide provide provide provide provide define define define compute proc proc proc proc proc proc perform perform experimental gain discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete mit comparison comparison comparison comparison comparison comparison connection update update update support support descent modeling report department department consists advances advances joint joint represents represents bias layers layers delay considered considered considered considered considered framework equivalent experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment view design stage stage bit determine efficient approximate estimated estimated basic give derived derived criterion criterion provided provided provided processes selected sampling sampling technical feedforward increases tested tested transformation transformation fast fast stable stable surface circuits common eds eds square instance future typically smaller smaller reduced unknown coefficients coefficients coefficients coefficients coefficients mlp mlp mlp mlp mlp mlp ratio mechanism structures structures structures trials uniform details filters filters filters filters filters direct direct direct attention produced run perceptron perceptron denotes denotes advantage robust element typical reported reported introduced introduced moving moving identical recently recently engineering engineering engineering varying compare previously axis trans trans trans trans generalized interval improvement constructed extended digital digital digital digital digital digital wide alternative alternative alternative feed feed white setting setting pass runs runs conclusions operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator differences sigmoid practice mechanisms characteristics variety plane iii introduce manner manner identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification question acknowledgements appears appears monte carlo stability stability stability stability stability recall sensitivity sensitivity sensitivity sensitivity multilayer multilayer multilayer multilayer electrical electrical slightly shift shift shift shift shift shift shift shift shift shift shift shift expectation squares estimator lemma lemma variation evaluated restricted showed decomposition understanding updates partial performing delays reduces reduces filtering filtering advantages advantages degrees recorded recorded perceptrons perceptrons weighting extension tests tests gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma determining extra capable capable differ delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta identity conf conf conf conf procedures procedures allowing interested notation sampled usual usual usual providing attempt consisted modelling modelling modelling simpler powerful powerful layered updating updating kalman replaced hessian recursive recursive recursive recursive lippmann preliminary hall hall hall fewer successive giving applicable int int int authors tanh analogous act coefficient coefficient coefficient ensure ensure ensure freedom observe ith ith massachusetts developing derivation defining defining capabilities correction london comparisons comparisons snr snr snr snr snr purposes purposes operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators mathematics potentially potentially inversion inversion circle author author robustness requiring improvements improvements conducted conducted readily poorly introducing adjustable adjustable frequently mod popular gave gave gave replace replace focused instantaneous pole newton newton newton feasible primarily investigation restriction jth jth unity difficulties difficulties adjusting overcome mail fan biased occurring occurring occurring generalizes generalizes generalizes generalizes substituting prentice prentice prentice financial studying encountered refers interestingly cam treat andrew andrew andrew andrew andrew maintaining dec employs australia principe principe principe principe principe principe principe principe principe principe realize adjustment arising maintained uncertain echo noting termed termed suffer knowing indication indication williamson williamson round gauss gauss gauss wider replacement differently bridge acoust acoust acoust expense council council instability instability instability instability australian australian invertible cliffs cliffs clarity realizations bilinear bilinear bilinear seattle englewood englewood substitute juang raises lowpass transpose assp factorization multimodal poles poles poles poles elec acknowledges acknowledges assessed tsoi tsoi tsoi tsoi tsoi analyse retaining cations appli derivations iir iir unifying omit vries vries vries vries vries vries vries vries vries avg avg damped brevity cancellation kung kung kuo queensland omitting subscripts backpropagated adaline overcoming ljung decoupled kamm fundamentals viii silva instabilities stably cas chung chung chung chung chung shah goodwin backpropagating suffered piscataway complicate lucia lightly feldkamp puskorius qld cholesky melbourne disrupting 
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model neural input input input input function function function function figure figure figure figure figure figure figure time time set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number number number number number number number number system system error error error error results results results results results units units units problem based space space space space space space space linear layer layer layer case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order order shown shown systems systems values values values values noise functions functions functions neurons neurons unit distribution distribution recognition recognition method approach approach pattern pattern pattern point point point point point point point point point point point point point point point point point point point point point point point point point image image image image image image image image image image image image image image image image image image image image image image image image image single single processing processing large large large local local rate patterns analysis analysis class inputs form form form form form form shows signal signal signal simple simple gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small size work work task methods step step step points points points points points points points points points points points field field field process level current current current current current current cell structure random random random random random high high high high high high memory memory memory memory memory response response response response response response response response response response response response response response response response response response similar similar representation representation representation representation representation representation representation representation representation representation representation architecture show show section section section section line rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images general theory obtained obtained obtained obtained term dimensional dimensional dimensional dimensional dimensional dimensional result university university university threshold computation research research research log log log log log defined found found sequence target target initial constant constant computer computer computer computer computer computer distance distance distance distance distance science science science science science left direction presented presented map map map map map map map map map map map map map map activation activation low low machine object object object object object motion maximum maximum maximum range position components basis basis basis basis basis basis sample abstract back find find computational computational convergence convergence density density properties references stochastic due ieee ieee positive adaptive adaptive context context introduction introduction complex stimulus dynamic search search spatial spatial spatial spatial spatial spatial spatial spatial spatial representations representations representations chosen center center center center previous previous cases required required required required required multiple multiple multiple good represent distributed distributed distributed distributed distributed distributed distributed expected make region region region region region region region region region region proposed proposed observed scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale finite minimum tasks tasks simulation human human human computed computed computed computed sum called regions regions regions regions reinforcement reinforcement natural natural natural natural feedback knowledge knowledge filter filter filter filter filter filter filter filter obtain negative original original original original original original original original original original represented compared compared desired desired receptive receptive provide provide location location location location location location location location location location location location location location location location location active active active active active eye eye eye eye eye eye eye eye eye goal goal gain gain motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor discrete cortical cortical brain accuracy accuracy larger larger update report report report department department department department implementation implementation implementation represents responses responses responses responses responses responses responses responses responses responses responses layers layers layers layers addition addition addition graph graph maps maps maps maps framework framework framework cambridge directly view view design limit top top stimuli detection conference determine determine determine determine upper upper speed vision vision vision vision vision vision vision vision vision pages pages pages increase coding coding randomly area area evidence iteration simply achieved achieved achieved discussion normal technical technical technical increases describe describe describe arbitrary denote fast limited corresponds effective implemented generate supported role square end end instance instance instance makes makes development sensory sensory sensory sensory sensory sensory sensory fit simulated simulated typically smaller underlying needed transfer increasing segmentation segmentation mechanism structures matching matching matching uniform principal principal squared representing details details details iterations iterations iterations iterations max max max max max filters filters filters filters filters filters filters filters filters filters filters filters filters pre direct stored stored stored stored bottom frame run run run light denotes denotes denotes recent recent recent resolution resolution resolution resolution resolution exact property property property takes takes takes takes similarity movement movement movement strategy strategy strategy strategy strategy strategy strategy strategy recently recently interest interest interest compare previously previously previously previously previously previously observations approximately approximately calculated axis axis axis match match match match studies studies achieve sparse sparse sparse sparse sparse address evaluation positions symmetric modified organization improvement sensitive entire increased grant grant grant intensity invariant occur suggests wide derivative derivative derivative derivative derivative move move generally pass demonstrate runs starting minimal greater editors differences accurate accurate accurate accurate retina retina suggest encoding mechanisms mechanisms integration largest reduction characteristics proportional proportional intelligence radial variety variety exist movements movements movements movements movements movements movements movements movements movements movements plane decrease iii derivatives derivatives derivatives scene scene scene scene scene scene scene scene scene program relation derive perception perception optical optical optical primary changing metric coordinates slightly unique scales scales scales scales scales scales scales scales scales scales scales scales gaussians formed formed agent yield formation formation review variation variation detailed organizing centered centered understanding suggested updates allowed discrimination processor spaces combining neighborhood neighborhood neighborhood tracking generation initially distances euclidean kohonen kohonen transactions david avoid figures includes kernels color inter weighting retinal retinal retinal retinal retinal assignment extension plotted illustrated coupled variations characterized successfully texture texture sensor sensor sensor sensor sensor sensor sensor aspects suitable effectively literature comparing invariance invariance excitation excitation refer graphs video showing showing interested neuroscience superior superior superior superior superior issue return return return lie physiological strategies strategies strategies strategies quantity vary localization localization localization localization localization localization localization localization localization play nips ill automatically moves moves subsequent acknowledgments decreasing decreasing oriented camera bars bars command command command create humans humans optimized helpful existence existence fewer successive muscle reliable eigenvectors complicated cognition smallest patch patch patch closest editor adapt reading eyes versions portion precise separated nerve store detected simplest motivated finds seconds scenes directed crucial sensors sensors sensors sensors sensors sensors orientations orientations orientations orientations track analytic explanation adapted caused caused caused lies london considerable rapid closer organized organized filtered directional located desirable describing circle beginning gradually gradually nsf addressed alignment outer requiring fourth greatly behaviors behaviors freeman amounts peter autonomous psychophysical marked marked completion slower rep variant variant variant differs popular richard comments decreased age begins eventually june wesley pyramid uncorrelated aligned sensing accomplished addison saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic velocities approximates rotations receptors establish inspired inspired smith convenient accepted primate primate primate logarithmic neurobiology fail implications salient spot spot optic degradation muscles muscles falls ranging james corre conjunction uni lawrence thomas similarities initialize initialize initialize advance advance young young ballard ballard ballard ballard ballard ballard ballard ballard reader gaze gaze gaze gaze gaze saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades colliculus colliculus colliculus colliculus ends passing erlbaum exploiting subsequently insensitive executed executed executed assigns assigns assigning assigning outlined schulten outline bank bank employs rao rao rao rao rao rao rao rao rao smoothly year year profiles profiles stem descriptions descriptions hillsdale realize peripheral peripheral peripheral publication shifting shifting shifting shifting deep deep signatures continues graphics execute execute execute execute guidance guidance neurophysiological neurophysiological retinotopic retinotopic books kanerva kanerva adelson depicts depicts fixation fixation acquired multiscale multiscale multiscale multiscale multiscale multiscale multiscale employing cartesian drawback indexed associates oculomotor minor rochester rochester rochester rochester rochester rochester modality elsevier gordon exploited september supporting ritter scanning circumstances argmax dim consuming lation lation january january distortions synthesized calibration calibration interpolated adaptively supply hancock compo month month striking interpolating goldberg corrective corrective corrective corrective corrective corrective corrective corrective corrective comprising periphery periphery periphery interpolate william spirit bradford comprised comprised nih motors fovea fovea fovea fovea fovea ous clues carpenter manual actively allowable shares indexing indexing indexing polar polar polar polar polar martinetz dispersion dispersion gradual gradual gradual amsterdam facilitates infeasible months months upward transferred primates align locating locating locating nents deeper suitably resentation klaus apparatus albeit scribed lens versity convolving topologically favorable dana dana dana dana dana dana dana dana dana foveated foveated foveated foveated foveated foveated foveated foveated foveated exceeded exhibiting temporary foveal foveal foveal foveal foveal foveal radially vectorial malik surrounded signaling birth salience visualized weeks bears acuity acuity acuity confused steerable wurtz occuring octave deliver pipeline pipeline foveation foveation foveation depict targeting targeting ballistic rectly edward infant tolerate fixations outward downward infants infants infants infants infants multilayered convolutions adults adults cda enlarged illuminated necessitates precludes sparks perona weakening roger saccarles engaged centering universally lus circularly ils dxdy frontiers interpo iil baddeley popu mll imaged simultane leslie ablex brightest brightest brightest retinotopically rnin domi accrue rro phs infancy upto scal ery viously roland geared scrutiny norwood polation subserving nant helge delivering 
#@Ballard_D,Rao_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data figure figure figure figure figure time time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training output output output output output output output output output output system system system system system system system system system system system system system system system system system system system system system system system error error error error information information information information information information information information problem problem problem hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance based based based linear layer layer layer layer layer layer layer layer layer layer layer layer layer case order shown systems systems systems systems unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern image image image image image image image image image image image image image image image image single single single single single processing processing processing processing processing large large rate rate rate rate test test test test test test test test test test test test test test class class class class class class signal simple simple visual paper examples examples examples examples examples examples size size work work task fig fig fig fig fig fig fig fig fig fig step classification classification classification classification classification current current current current current current trained trained trained trained structure structure structure problems problems problems problems problems problems high high high high response response response similar similar similar architecture architecture architecture architecture architecture section rule images images images images images images images images images general generalization real real real average average average average average obtained obtained obtained dimensional result threshold threshold threshold threshold threshold threshold research independent independent sequence sequence sequence sequence sequence sequence table table table distance distance left left direction phase low machine machine machine object object object object motion motion range position position position position position position position position position position position position position position position position outputs continuous sample sample abstract applied back back find find find references due due ieee procedure procedure propagation propagation introduction complex complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference complexity variable spatial classifier lower signals signals representations chosen part part previous previous previous previous previous previous previous previous cases cases required good good conditions conditions chip fact correct correct errors errors errors errors errors errors simulations minimum classes classes classes tasks human computed computed performed performed means made made made made natural natural original original original original original original original original relative application cross cross cross provide provide provide objects objects objects rates rates location location location location location location location location location location location location location location location location location location location location perform perform active active connected gain gain accuracy larger contrast dependent dependent source morgan morgan morgan morgan implementation individual individual advances advances advances advances represents represents responses responses responses difficult difficult difficult difficult final layers scheme scheme scheme scheme scheme addition addition addition addition sequences sequences sequences environment trajectory trajectory trajectory trajectory san san san san san san conference determine classifiers upper upper full full full requires speed speed estimated estimated validation validation con produce developed area velocity finally achieved discussion discussion increases describe describe corresponds predictions predictions predictions predictions predictions predictions predictions nearest nearest common eds eds eds face pixel pixel pixel pixel pixel ability ability degree makes makes rumelhart kaufmann kaufmann kaufmann kaufmann account fully fully technology block block testing testing character head segmentation segmentation segmentation segmentation segmentation segmentation matching database database database database database operation details window window window window window stored frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame combined combined combined choose sources predict predict architectures improved discussed directions resolution resolution resolution resolution resolution resolution resolution advantage separate separate takes takes takes takes moving moving moving moving moving moving subject subject subject identical pixels pixels pixels pixels pixels pixels pixels pixels approximately subjects subjects subjects subjects solve achieve trans address address background background background background background background evaluation evaluation locations entire grant arm parts intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity scaling occur extended predicted predicted correctly correctly correctly correctly move move touretzky touretzky white white hardware hardware hardware hardware conclusions neighbor neighbor designed designed moody moody mateo mateo mateo mateo encoding strong strong presence presence largest largest largest demonstrated demonstrated variety user user manner manner characters characters scene identification acknowledgements digit construct factors primary metric simultaneously averaging averaging averaging remaining remaining remaining integrated integrated quality versus versus john john john john john independently correlated solved variation open open open open open open open open open open open open open open open open open open open open evaluate operations operations restricted centered centered centered centered centered frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames translation translation digits reasonable smoothing combining tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking closed closed closed closed closed closed closed closed closed closed closed closed closed closed closed closed closed closed closed remains filtering euclidean euclidean classified existing existing existing template handwritten handwritten box box color blind blind blind instances recognize recognize recognize determines determines determines illustrated black successfully texture determining capable maximal identify invariance invariance tend online summary compact compact contained cun cun allowing video video video video video video video video video video video video video video video video video video video video video video video video video video success issue sampled simplified generalize denker hypotheses thresholds overlapping deal tesauro camera camera cowan situations explore carried requirements difficulty varied environments environments environments detail hanson lippmann lippmann combine combine office office structured variability complicated pathway pathway pathway pathway pathway pathway coarse naturally plausible possibly portion seconds averages advanced scenes orientations track track track track track fairly nowlan nowlan nowlan nowlan nowlan nowlan caused purposes separately involve recognizing recognizing alignment alignment alignment greatly considerably percent limits empirically conducted capability lack operate operate operate howard windows tolerance extreme representative lab room room martin martin perfectly naval printed printed printed printed printed lecun eliminated platt platt platt platt platt platt platt platt platt platt dealing dealing held contract adequate motivation alspector weakly weakly combines moved jackel jackel captured captured candidates dif dif recog suggesting tracker tracker tracker tracker clean gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture observer davis onr dramatically maintaining rigorous users outperform piece convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional nition smoothly boser boser ease individuals examining henderson summarizes dominated ocr ocr ocr hubbard bounding bounding challenging individually investigating million portions voting voting voting voting voting indication dramatic suggestions stops circumstances gestures gestures lighting lighting identifies identifies crude ferent ave shot shot locate locate locate locate attempting steven steven steven steven steven keeler keeler char subtracted anna recognizes digitized totally inde positional positional gathered subsystem subsystem subsystem subsystem subsystem subsystem subsystem subsystem subsystem subsystem subsystem subsystem segmenting segmenting freely jose jose postal ference clutter clutter clutter pendent tracked broader ness examines hands hands hands hands hands dealt trick subsampling subsampling subsampling subsampling subsampled subsampled subsampled subsampled usps strongest ages disappear thirty arms subtraction subsample closing subsystems subsystems opening numerals aligning aligning aligning confusions indoor indoor wolf wolf requested rooms ickinger ickinger differencing synaptics synaptics synaptics synaptics reversing raining print print backgrounds gathering bromley tains locates locates subsections leow subtracts parkway parkway extendable reserved torso verifies orchard orchard accom blended joel acteristic flames plished 
#@Nowlan_S,Platt_J,
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#*network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input data data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm system system system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state results units units units units information problem problem problem models models models models models models models models models models models models models models performance performance performance based based based based based based based based based based based based based based based based based based based based based based based weights linear linear case case case case case case vector vector vector vector order order shown shown shown shown shown systems systems systems systems systems values values values values values values values parameters parameters parameters parameters parameters parameters functions unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method method approach approach approach approach approach pattern pattern point image image image image image image image image image image image image image single single processing processing processing processing control control control control control control control control control control control control control local analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis form shows shows shows signal simple simple simple paper examples examples examples small size feature feature feature work task task task task task methods methods methods methods methods methods methods methods methods methods methods points field field features classification level level level current trained structure structure structure structure problems high high response response response response similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show line images images images images images images images images general real real real real real real real real real real real real real real real real real real approximation states states states states states states states states states states theory dimensional dimensional dimensional threshold threshold computation solution independent independent independent independent defined defined defined found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics initial estimate computer computer computer computer computer computer computer computer terms connections prediction left presented presented presented present phase activation activation activation low object object object object object object object object object object motion range range position components basis basis basis basis basis abstract applied applied applied applied find find computational references due ieee ieee important introduction action action action complex complex complex hand hand hand hand hand estimation effect dynamic dynamic dynamic generated search tion tion lower center previous type type required multiple good good long represent distributed distributed distributed distributed distributed distributed make make make fact techniques techniques techniques techniques region region correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed observed forward scale finite resulting resulting resulting resulting tasks tasks tasks computed computed computed computed computed multi multi sum performed performed performed regions regions regions regions regions regions regions mapping mapping potential natural applications applications applications obtain artificial represented represented represented application desired provide define define compute compute compute objects objects proc proc location perform eye eye eye eye eye determined constraints constraints constraints constraints constraints gain motor motor motor motor motor motor motor motor motor motor motor motor motor motor power mit mit mit mit mit connection modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling proceedings proceedings implementation implementation technique technique consists difficult difficult difficult scheme addition graph sequences sequences sequences ai ai ai maps framework framework framework framework computing domain domain domain domain domain domain equivalent view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view estimates top stage stage conference efficient full full full full full full full full full requires requires significant statistics speed vision vision vision vision estimated pages give derived derived weighted clustering clustering developed developed developed developed developed developed levels levels levels levels area provided finally finally finally selected selected nature sampling sampling simply achieved describe describe group transformation transformation transformation fast fast fast fast fast fast fast close inverse rbf rbf rbf rbf rbf rbf rbf rbf rbf implemented shape shape generate generate generate face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face journal degree makes makes including simulated typically pairs pairs needed fully character character increasing special special matching leads direct making window window stored stored stored normalized normalized normalized normalized frame frame frame frame frame combined run added advantage advantage advantage robust robust robust robust robust separate ensemble ensemble ensemble ensemble element similarity practical apply apply include sense sense subset recently recently interest dimensions dimensions previously conventional conventional conventional conventional solve yields match match match match match correspond achieve trans locations williams williams entire entire constructed constructed intensity expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression invariant occur occur extended extended rotation hybrid setting runs half flow flow flow flow flow flow conclusion critical greater faster practice strong mechanisms mechanisms physics reduction demonstrated labeled radial radial radial radial radial radial user user user user user user user user user user user user user user user scene force explicit explicit derive derive construct construct perception perception perception optical optical optical ways estimating distinct distinct modeled physical physical dimensionality dimensionality transformations consisting consisting consisting develop integrated yield choosing focus interpretation detailed open evaluate controlled updated centered centered frames frames approximated completely similarly translation allowed allowed performing measurements measurements measurements tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking closed closed closed interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation generation intermediate intermediate initially faces faces faces faces faces faces faces faces faces faces faces views views views views views views views views views views views views views transactions coupling coupling coupling recorded template template figures perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual thesis activations activations activations activations activations priori contour coupled domains successfully major sensor capable maximal driven driven driven driven driven driven driven driven poggio poggio poggio poggio poggio successful successful detect invariance score traditional conf quickly quickly contained allowing video video video video video video video video video issue criteria criteria criteria strategies strategies strategies timing sci involved paradigm paradigm paradigm paradigm paradigm paradigm realistic realistic nips board correspondence illustrates extract extend camera camera camera trains simpler powerful humans matches matches fashion investigated applicable muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle combine reliable proved proved scores scores scores scores scores scores scores scores matched measurement closest plausible plausible facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial created eyes eyes eyes eyes eyes eyes eyes implementations aspect aspect aspect explored explored expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions attempts mentioned track track lies processed processed drive straight sections forces located desirable desirable immediately controls describing exemplars integrating geometric geometric pseudo generic capability share share reliability templates span synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis rely mod characterize extracting serve serve focused june multidimensional pose pose picture picture person lab lab lab lab lab appearance interface tation acm acm girosi impossible impossible connecting rotations rotations rigid rigid establish inspired inspired platt platt platt anatomical anatomical imposed interpret observing settings settings canonical canonical optic optic enhanced reliably passive passive representational connect connect connect sion sion overview offers reproduce augmented gesture motions captures limitation outlined ence ence unable users users users users users exhaustive ber asked opposed pentland pentland pentland pentland pentland pentland pentland pentland pentland poses spaced warping workstation pami num graphics graphics graphics graphics graphics mouth mouth mouth rectangle paired wise interactive interactive interactive interactive interactive interactive interactive interactive interactive topic attached thousands tissue tissue tissue compu gestures gestures gestures gestures drives scanned lation marks impractical skin skin skin skin suite interpolated interpolated interpolated interpolated shot shot alex alex alex alex alex drawing drawing replicated replicated replicated rare evenly core manually dedicated interpolating characterizes characterizes colleagues interpolate interpolate implied neutral neutral neutral physically physically physically physically physically restrictive media media media indirectly surprise surprise surprise promise tim mesh mesh mesh plastic extrapolation infeasible tracked tracked literal sensed sends deformations deformations deformations deformations conveyed hands relying animation animation animation animation animation animation animation animation darrell darrell darrell darrell darrell darrell topologically neurally neurally neurally neurally rosen ramp rendered rendered rendered rendered rendered accelerator rendering rendering polyhedral wishes geometrically cameras closing closing endpoints anatomically anatomically anatomically exercise render qualities trevor trevor trevor trevor trevor correla confer interpolator interpolator interpolator decoupled actuators interfaces terzopoulos terzopoulos mimics mimics surgery blink programmer shashua react overly eling marking ieice sgi ultra dozen siggraph siggraph siggraph afforded reduc decouple interpo acquiring constituted mase mase cartoon cartoon emotional brunelli brunelli beymer beymer beymer assessments creative alized arts 
#@Darrell_T,Essa_I,Pentland_A,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural input input input input data data data data data function function figure figure figure time time time time set set set networks training training training training training algorithm output number number system error results results results results results results results units units units units units units units information information information models models models models models models models models models models models models models models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based space weights weights weights case case vector vector vector vector vector shown shown shown shown systems systems values parameters noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight functions functions neurons neurons neurons neurons neurons unit unit unit unit unit recognition approach approach approach pattern point point processing large large local local rate rate rate rate test patterns patterns inputs inputs inputs form shows signal signal signal gaussian gaussian visual visual visual visual visual visual visual visual visual paper examples small small work task task task task task task task fig fig fig fig fig fig cells points field field field level level current current current current current current trained trained structure structure random random random random random high response response similar similar similar similar similar similar similar representation representation representation representation representation architecture show show show show section line line line rule rule rule rule rule vectors vectors general parameter approximation theory theory obtained obtained experiments experiments experiments experiments experiments experiments experiments university university threshold threshold computation computation research research research research research research research research research defined found found found dynamics estimate estimate estimate standard standard science science science science left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented presented phase phase frequency frequency temporal temporal temporal motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion press press learn learn learn abstract find computational computational properties properties references component stochastic stochastic stochastic due positive procedure decision decision decision introduction complex complex hand stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect dynamic parallel tion tion tion difference spatial spatial spatial spatial spatial rules measure signals signals learned learned learned chosen part part center center center center center center center required required required cortex cortex cortex cortex make make proposed proposed proposed correlation correlation correct correct observed scale scale simulations simulations simulations simulations classes ing tasks tasks tasks tasks simulation simulation human human human human computed computed made natural feedback feedback orientation orientation orientation orientation orientation orientation global global global global global global global global global global global global global global global global global global global global global global global study study study study specific specific specific specific specific represented series receptive receptive provide provide objects proc location perform experimental experimental cortical brain brain brain equal approaches approaches contrast contrast fields support support dependent modeling modeling modeling words consists internal individual responses responses responses responses responses responses final scheme ai considered framework environment directly curve additional additional view curves curves curves stimuli stimuli stimuli stimuli stimuli effects effects effects determine determine efficient choice choice significant speed speed vision vision vision vision pages increase weighted weighted weighted randomly randomly clustering clustering clustering clustering levels area area product provided evidence nature nature nature nature nature nature measured discussion tested fast fast fast fast fast fast fast fast fast stable stable stable stable amount amount short supported supported ability ability hypothesis cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster makes noisy underlying underlying combination combination reduced account account functional block block block transfer transfer testing testing significantly significantly increasing mechanism mechanism mechanism special consistent consistent trials trials trials trials trials trials trials trials details pre supervised supervised supervised supervised supervised early early magnitude frame idea neuronal neuronal neuronal neuronal neuronal architectures improved improved discussed improve directions directions directions directions directions directions directions recent takes takes typical reported reported moving period period subject cognitive engineering engineering engineering observations subjects subjects subjects calculated calculated tuning tuning tuning axis solve studies studies studies studies studies studies studies studies rl address separation interval williams improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement increased horizontal horizontal studied occur occur suggests trial trial trial deviation alternative correctly move move move occurs occurs occurs occurs demonstrate runs runs critical hebbian differences modules designed moody exponential faster practice practice practice practice practice practice practice practice practice learns learns learns learns learns learns learns suggest propose strong mechanisms mechanisms integration integration integration presence characteristics demonstrated proportional proportional selective selective averaged targets question relation van van index perception perception perception perception perception perception perception perception winner winner primary primary laboratory laboratory laboratory tuned tuned tuned tuned tuned vertical sensitivity averaging averaging averaging averaging involves angle gaussians blocks extraction national focus review correlated correlated correlated open controlled fraction fraction fraction fraction showed showed showed centers centers frames understanding similarly allowed discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination slow slow slow performing msec classified existing fire exploration perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual coordinate coordinate usa inter assignment illustrated specifically characterized tests successfully texture major reason middle middle closely uniformly differ differ computationally poggio poggio poggio poggio poggio poggio poggio poggio poggio identify computations computations ten ten reached repeated contained interested contribution sci involved dot dot dot paradigm paradigm paradigm paradigm paradigm correspondence computes reach consisted consisted consisted moves subsequent subsequent preferred preferred preferred acknowledgments deal deal decreasing receive situations explore selectivity carried collection investigate circuitry rapidly humans humans rest plasticity plasticity plasticity plasticity office comparable func understand attributes examined circles circles closest possibly opposite opposite extremely psychology perfect changed ith improving grouping motivated motivated integrate mentioned indicating fairly navigation biology explanation considerable spatially day day precisely directional monkey controls controls angles angles acad localized improvements improvements limits limits limits limits understood conducted quantitative quantitative psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical slower dots dots dots dots biologically biologically biologically schematic schematic schematic maintain operate exhibits aim qualitatively coherent boston boston boston boston display focused progress progress june displays cor consistently college college college analogue forming modify summing angular girosi jth jth naval connecting reaching lost cellular chance darken occurred proceeds attractive intelligent intelligent hyper keeping hope mark belong imply enhanced days days days days filled natl eqn exploring financial started edelman edelman studying decide moved monkeys monkeys monkeys uni exposure exposure exposure winning specificity harris grants alternatively ignore ignore ignore ignore ignore ignore ignore interestingly adopted acknowledge ball ball dividing consecutive mind discriminate discriminate street neurophysiology leaving fellowship session session session session wiesel wiesel july revealed forced lesions weiss weiss weiss preserved formance maintained retinotopic march mediated fixation fixation cosine macaque termed paradigms paradigms gilbert gilbert memo page retained retained dramatic compu psychophysics psychophysics psychophysics psychophysics psychophysics ward september examination sessions gratefully instability decided satisfactory thousand spring spring observers observers observers observers exper exper adult adult dropped essen essen physiologically exposed progressively judged judged beneficial colleagues colleagues suffice suffice safe rel accommodate accommodate accommodate accommodate accommodate accommodate cold cold gaus addressing ings correlates correlates substrate dence dean dean health tan discriminating newsome newsome newsome newsome newsome newsome newsome newsome newsome percep favors movshon directionally directionally directionally imaginary synthesize inte ogy grzywacz thorpe versity retention retention rightward rightward gibson gibson ative justify foveal psy psy tational perceive incremented namic weeks acuity acuity fund encourages pervised stereopsis discriminability maunsell maunsell originated compatibility hyperacuity hyperacuity hyperacuity hyperacuity hyperacuity hyperacuity stabilizes masking postdoctoral harmonics oblique tual orban orban unsu dominating sagi impaired judgement sts behaviorally bulletin harbor harbor judgements judgements judgements iments westheimer westheimer westheimer westheimer coherently ramachandran ramachandran evi ception underlies chophysical sians supplement lucia lucia lucia lucia lucia lucia progressive imental lasted disabling advocate britten britten dispersed tute investigative gether gration oscillated accommodates nore collaborators 
#@Sundareswaran_V,Vaina_L,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data function figure figure figure figure figure figure figure figure figure figure time time time time time time set set networks networks networks networks networks networks networks networks networks output output output output system system system system system system system error error state state state results results information information information information information based space linear linear linear linear case order order order order order order shown shown shown shown systems systems systems systems neurons neurons neurons neurons neurons neurons neurons approach pattern pattern point single processing processing processing processing control control large neuron neuron neuron neuron neuron neuron neuron neuron test test test test patterns analysis class class class matrix matrix optimal optimal optimal inputs inputs form form shows signal signal gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper small small work work methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field cell cell cell cell cell structure structure high memory memory response response similar representation architecture architecture show show equation equation equation equation equation equation equation section section line line line line line rule rule vectors general parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation average average theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained term term term experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments activity activity activity activity university university university variables variables variables variables computation research research independent independent dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant constant constant constant distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic prediction left left left left left left left left left left direction presented present sets maximum maximum maximum maximum maximum maximum range range range range press position position outputs outputs continuous abstract applied back computational properties properties properties likelihood likelihood references due positive important adaptive introduction estimation behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect dynamic dynamic dynamic dynamic generated tion tion change change change change change change change energy energy energy energy difference variable assume lower lower lower signals chosen part center center type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good good good long represent represent equations equations equations fact proposed proposed correlation correlation correlation correlation correlation length observed errors forward ing total human human human human human called called optimization feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation negative specific represented represented application receptive receptive receptive proc proc proc determined experimental experimental experimental experimental experimental experimental experimental gain gain cortical cortical brain brain mit comparison contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast connection connection connection fields support support modeling modeling morgan report department synapses synapses synapses synapses synapses advances joint represents difficult difficult considered framework framework cambridge computing experiment experiment environment environment directly curve curve curve curve curve additional view curves san top top stimuli stimuli stimuli effects effects effects effects effects effects effects effects conference upper upper requires significant significant statistics world vision vision vision estimated basic basic increase give give give derived derived derived developed developed developed developed developed lines lines lines lines lines lines lines lines lines lines actual finally inhibitory inhibitory depends associative associative associative associative associative associative associative associative associative associative associative associative associative associative measured discussion technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward complete stable stable stable stable stable actions predictions predictions predictions predictions predictions predictions predictions short effective effective assumed assumed shape supported role role theoretical theoretical theoretical theoretical theoretical theoretical theoretical theoretical eds eds adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation hypothesis future degree degree degree makes development development development development development development development development development development development fit fit fit simulated hopfield hopfield account dynamical dynamical functional functional interesting interesting york york mechanism principle principle leads leads call max inhibition inhibition international bottom bottom early decay idea idea neuronal neuronal neuronal neuronal neuronal neuronal denotes population population recent recent correlations ensemble ensemble lateral apply period side side highly compare observations works tuning tuning tuning tuning tuning tuning tuning tions studies achieve address bounded channels channels organization organization horizontal horizontal matrices predicted predicted feed touretzky width width width width width white white strength strength strength strength strength strength strength strength hebbian hebbian hebbian hebbian hebbian hebbian interactions interactions peak peak peak mateo physics physics drawn demonstrated california solid solid assuming exist selective selective selective selective selective selective selective selective selective selective relationship acknowledgements suppose appears appears van derive derive derive derive index perception perception primary primary primary primary primary describes describes laboratory laboratory ann tuned tuned tuned tuned tuned vertical vertical recall angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle develop develop develop applying focus formation depending correlated influence influence showed evolution understanding activities activities activities activities activities activities activities constants sign earlier earlier earlier reasonable measurements reduces roughly koch koch thesis usa color color color inter illustrated black partially columns columns columns columns aspects post receives characteristic refer notice kind symmetry symmetry symmetry sci satisfy involved surround surround surround surround surround wave cat cat cat cat cat cat cat neurosci principles illustrates satisfies neighboring intrinsic intrinsic receive oriented oriented bars selectivity selectivity selectivity selectivity experience circuitry put environments environments optimized dotted examine examine respond fashion relationships office office comparable lgn lgn lgn affect understand circles circles adapt necessarily predicts opposite opposite changed changed ensure quantities nerve nerve seconds preference agreement orientations orientations orientations orientations orientations orientations orientations phenomena explanation explanation adapted london london comparisons comparisons straight tive berkeley berkeley berkeley sections organized organized organized immediately afferent angles acad describing circle res res res res res res res linsker linsker meaning apparent people pathways tional quantitative quantitative quantitative quantitative quantitative quantitative quantitative psychophysical psychophysical psychophysical psychophysical psychophysical detecting ity anti anti cal qualitatively singer kinds physiol physiol simultaneous wesley contextual addison sv appearance appearance tation tation extensive dynamically rotated plays binocular kaufman convenient striate striate striate contract nearby implications optimally optimally natl substituting lyapunov ensures dominant accounts uni lawrence lawrence arrangement ensembles offer specificity agree explains outlined ics unchanged land unified wiesel wiesel wiesel maximized break revealed revealed isotropic connec arbor perceived perceived perceived perceived perceived perceived big hubel breaking breaking decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation adapting adapting mammalian mammalian neurophysiological neurophysiological rectangle rectangle rectangle careful emphasize confirmed surrounding surrounding surrounding surrounding surrounding selectively emphasized barlow reveal tij tij gilbert gilbert durbin emphasis reversed lation attributed attributed attributed agrees vis vis vis vis vis observers observers lated bold orthonormal connects essen seattle atick atick intracortical intracortical intracortical intracortical intracortical intracortical intracortical intracortical intracortical intracortical intracortical preservation preservation colors inducing inducing faced fovea carpenter actively imum campbell columnar columnar columnar columnar avenue redlich adap tilt tilt tilt tilt tilt nuclear nuclear gibson segev pri thompson outlines dynam noises mitchison psy psy mary dong dong dong dong dong dong dong dong dong dong tilted tilted tilted tilted implication ences interna portland strip strip strip illusion orienta orienta selectivities decorrelated decorrelated decorrelated congress hue orien ezp ezp iit opportunities originates decorrelate rhs miall westheimer illusions illusions illusions illusions illusions illusions illusions illusions fied chophysical agreements agreements fresh volves evidences etal gles director fluence 
#@Dong_D,
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural input input input input input data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time set set set set set networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number error results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information problem problem problem problem problem problem models hidden hidden hidden hidden hidden performance performance based based based based space space space space weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case order order order shown shown shown shown shown shown shown shown shown systems systems probability probability probability probability probability probability probability probability weight weight functions functions functions unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method method method method approach approach pattern pattern image image image image image image single single single single single processing processing local local local local test test patterns patterns patterns patterns patterns patterns patterns patterns patterns class class class matrix matrix matrix matrix optimal optimal optimal inputs inputs inputs inputs inputs inputs algorithms simple visual visual small small small feature feature feature feature net net work work task methods step features features features features features features features classification classification classification classification classification classification classification classification level level level trained trained trained trained structure structure random random random high response response response similar similar similar similar similar similar similar representation representation architecture equation rule rule rule images images images images images images real approximation approximation approximation theory gradient gradient note note experiments experiments result result university computation solution log log log log found found initial terms present low low low frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object object object object object object object object object object object object object object object object object sets sets range learn learn learn learn learn position outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous abstract applied applied applied applied applied back back density density density density density references positive procedure procedure procedure propagation propagation cost cost cost cost cost cost cost cost cost cost cost tion change complexity variable lower rules rules measure measure signals signals prior prior prior prior prior prior prior prior prior prior prior prior representations learned learned learned learned learned learned learned learned higher higher higher previous cases cases type required multiple multiple multiple multiple multiple multiple represent represent distributed bayesian expected equations proposed proposed proposed proposed correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed simulations classes classes classes classes respect respect multi multi multi made natural obtain obtain negative specific specific desired desired receptive compute objects objects objects objects objects objects objects objects objects objects objects objects objects location location location perform active goal goal related constraints constraints connected distributions distributions discrete brain steps fields update train train train descent nets morgan morgan proceedings report department advances advances joint joint joint joint joint joint joint joint joint joint joint connectionist responses responses final exp layers layers layers layers scheme sequences sequences computing equivalent equivalent hinton hinton hinton hinton hinton view solutions solutions top top efficient choice statistics vision pages pages pages increase con produce weighted randomly randomly randomly randomly types types lines actual actual actual finally selected selected nature depends constraint constraint constraint simply simply achieved achieved discussion covariance technical arbitrary group group group group group group transformation limited close common shape shape shape shape pixel ability future sensory sensory sensory sensory sensory sensory fit kaufmann kaufmann pairs smaller block block block block block block block block block block block block block edge special consistent uniform principle principle principle leads leads representing iterations iterations iterations supervised frame frame idea idea minimize minimize produced produced produced run run added added sources predict correlations exact robust ensemble ensemble typical lateral lateral moving moving moving moving moving subject pixels pixels subset varying varying varying previously unsupervised unsupervised unsupervised observations approximately works works module solve converge achieve achieve diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal mixtures positions positions locations locations grid williams organization organization horizontal parts parts parts parts invariant invariant invariant scaling extended derivative derivative derivative rotation predicted alternative alternative white white runs runs runs starting assumptions hebbian hebbian trajectories trajectories valued central modules modules accurate accurate retina retina practice learns encoding taking turn minimizing iii iii iii iii iii averaged averaged derivatives groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups scene configuration configuration configuration acknowledgements suppose derive derive derive edges laboratory vertical involves transformations transformations transformations consisting mutual mutual applying blocks blocks blocks blocks blocks extraction extraction versus stages squares squares organizing organizing centered centered frames frames frames suggested translation discrimination reasonable delays fitting fitting roughly intermediate views views views expect perceptual combinations formulation instances instances instances recognize maximize maximize specifically priors priors priors black black partially major sensor closely successful detect detect invariance invariance ten capture capture capture refer procedures prob success success success dis hold quantity usual dot dayan dayan minimizes subsequent extract receive receive receive oriented oriented powerful powerful powerful varied varied varied divergence preliminary helpful fewer successive successive successive respond school links detectors investigated applicable applicable maximizing momentum surfaces removed circles circles circles patch analyze extremely psychology equally equally equally perfect perfect perfect versions versions algo observe observe separated shapes shapes shapes ith detected mixed explain rows agreement agreement agreement agreement orientations fairly handle spatially preprocessing forces desirable optimize patches patches raw geometric geometric geometric considerably considerably populations populations items substantially flexible peter peter differs maximizes coherent coherent coherent comments coherence coherence coherence coherence coherence coherence coherence coherence coherence focused yuille yuille yuille converged softmax softmax yielding classifying sort tation temporally temporally rithm jth discover discover discover discover tem robotics kullback wrong dealing promising promising iiii iiii overcome moment moment viewpoint viewpoint viewpoint keeping nearby nearby nearby nearby observing adequate overlaps becker becker becker becker becker becker becker becker becker becker becker becker becker becker becker becker becker edelman edelman predictors displayed dominant sim lawrence competing entries laplace laplace recog permutation steepest agree agree observer erlbaum ignore interestingly receiving limitation counts treat discriminate multiply summer maximized encodes employs nition tween classifications classifications classifications classifications classifications classifications preferences covariances covariances multinomial associate associate remainder continuity translated pij pij pij pij pij pij pij pij pij distribu mammalian plate proach ambiguous ambiguous represen associates rotating modality modality challenge covers chris gratefully corners prefer crude puts hamilton harvard evenly optima optima optima 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#@Becker_S,
#t8
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number number number number error error error error error error error error error results results results results results results results results results results results results results results results results results results results results results units units units units units units units units units units units units units information information information information models hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer case case case case case case vector vector vector order shown shown shown shown parameters weight weight functions functions functions unit unit unit distribution recognition recognition method method method method method method approach approach pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single processing processing local local local patterns analysis analysis analysis analysis analysis optimal shows shows shows shows shows signal algorithms algorithms algorithms visual paper paper paper paper paper examples small size size feature feature feature feature net net work work work work methods methods methods cells cells cells cells step step step step points features level level level level level level level level level level level level level level level level level level level level trained trained trained trained trained cell cell cell structure structure structure structure structure structure structure similar similar similar similar similar representation representation representation architecture show section fixed fixed rule rule images images images images images images images images images images general general general real average average average theory theory gradient gradient gradient obtained note experiments experiments experiments experiments dimensional dimensional dimensional result university research independent table table table table standard science left left direction presented present present present present present low machine learn components abstract applied back back back back convergence convergence convergence properties references component component due ieee ieee ieee ieee adaptive adaptive propagation propagation propagation propagation introduction variance cost difference difference lower measure representations chosen higher part previous previous type good long long fact fact techniques techniques errors errors errors forward scale minimum resulting performed called called factor obtain original original original original original vol vol artificial desired provide provide provide perform determined determined experimental experimental goal goal constraints connected connected equal mit steps steps steps steps larger train train train descent descent words department loss loss consists internal code scheme scheme maps maps framework directly directly additional top bit bit bit bit bit bit conference upper free basic pages pages pages give levels levels levels levels levels levels levels levels levels levels levels levels levels finally finally finally finally sampling biological achieved achieved achieved achieved achieved measured discussion technical describe denote transformation stable amount amount amount supported pixel pixel pixel objective typically typically typically typically combination fully programming ratio ratio ratio ratio ratio increasing structures uniform uniform operation leads leads principal principal principal squared squared squared squared squared squared representing call window bits bits bits bits bits bits bits bits bits normalized bottom idea idea combined minimize minimize minimize minimize choose improved improved recent property reported reported reported reported reported apply apply introduced introduced include include identical identical pixels pixels quadratic hierarchical hierarchical cognitive interest compare compare conventional unsupervised volume works works yields pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca achieve achieve trans sparse improvement grant constructed intensity expression studied feed setting half half conclusions conclusions operator neighbor editors editors clear propose integration reduction reduction reduction reduction reduction reduction reduction demonstrated intelligence start start min introduce introduce connectivity minima minima program base relation sequential describes dept changing multilayer integrated springer shift shift shift extraction decreases yield national extracted reconstruction overlap transform transform controlled organizing centered centered decomposition decomposition completely completely similarly similarly similarly past expansion expansion reduces intervals remains remains filtering construction kohonen kohonen kohonen topology topology transactions transactions transactions expect thesis perceptrons extension extension discuss discuss neighbors successfully regular regular compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression suitable suitable society divided divided included literature literature situation compact verlag content usual usual modular wavelet wavelet wavelet quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization ill automatically presents minimized employed employed employed simpler relations relations relations replaced association scalar scalar fewer successive project mse analytically combine combine combine comparable proper cover patch naturally transmission adapt analyze analyze singular der der noted store store pyramidal simplest regime phd years histogram histogram histogram analyzed adjacent reasons reasons constructing desirable separately universal gradually depicted auto annual cybernetics conjugate improvements considerably considerably understood experimentally peaks treated characterize gave conclude shaped implements converged yielding pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid 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compressed compressed compressed outline visually munro retraining restrictions perceived letting hillsdale avoided laplacian laplacian laplacian laplacian laplacian constrain quantized quantized gained pami considers adelson adelson depicts lookup hornik hornik hornik hornik hornik hornik hornik hornik hornik hornik hornik hornik hornik hornik spanned alternatives preserve universit son son gorithm neumann restoration survey institut multiresolution house house kth burr cally cally ning automation quantizer quantizer quantizer wavelets autoassociative autoassociative autoassociative autoassociative autoassociative autoassociative multimodal informatik cascaded cascaded counterpart thing thing inst subnetwork subnetworks nice nice elaborate technische simula borders favorably favorably fiir compress compress compress pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids pyramids ninth kurt kurt kurt kurt kurt kurt unix analogously notations mat nmse nmse nmse nmse nmse nmse nmse und austria austria austrian vienna vienna vienna vienna batches quan burt burt quantize quantize pression equiva trm wien kangas kamp kamp kamp kamp correspon confine retrain quantizers hierar progressive progressive apex mallat mallat father father extensional ding compres fonds zur lloyd quant quant chical arielson lently 
#@Bischof_H,Hornik_K,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number system system error error error error error error error state results results results results results results results units units units units units units units units units units units units units units units information information information information information information information problem problem models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based based based based based based space space space space linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case vector vector shown shown systems systems systems values values values values values values parameters parameters parameters functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition method method method method method pattern point image image single single single single processing processing processing processing local test test analysis analysis class inputs inputs inputs shows shows shows signal simple visual paper paper paper paper paper examples examples examples small feature feature net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net net methods methods methods methods fig fig fig fig fig fig fig fig fig fig fig fig fig points features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level trained similar similar similar representation representation representation representation representation representation representation architecture architecture architecture architecture architecture show show show show show section section section section section section section section section section section images images images images images images images general generalization generalization generalization parameter real gradient obtained obtained obtained obtained note dimensional dimensional dimensional dimensional result computation research defined defined found constant constant computer science direction direction direction direction direction direction direction direction direction direction presented presented present low machine object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object range range range range range range range range range range range range range range range learn learn learn position position basis nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous abstract computational references component stochastic adaptive adaptive mixture mixture mixture mixture introduction hand hand variance difference difference assume classifier classifier classifier classifier classifier classifier representations representations representations representations previous previous type multiple good expected fact region region proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed correct errors simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations minimum minimum classes simulation simulation simulation human human multi sum mapping means dimension dimension dimension negative original original artificial provide objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects perform equal equal equal equal equal train nets nets nets nets nets nets nets nets nets selection morgan morgan morgan version consists consists consists internal internal internal advances advances advances difficult final exp layers layers layers layers scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme equivalent directly directly hinton additional additional additional view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view san san san determine efficient full full full full requires requires vision increase condition weighted randomly randomly randomly randomly clustering types provided finally selected selected selected selected selected nature associative associative associative associative associative associative associative associative associative associative associative feedforward denote tested transformation limited limited limited rbf implemented assumed require eds eds eds eds ability ability degree degree degree degree fit kaufmann kaufmann kaufmann objective objective objective objective objective jordan jordan jordan mlp interesting significantly significantly significantly principle principal squared squared squared call call direct experts experts supervised frame frame frame frame frame frame frame frame frame perceptron perceptron perceptron denotes denotes directions directions directions recent separate strategy period conventional unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised teacher solve converge achieve sparse mixtures modified williams williams entire entire entire entire increased lead studied invariant invariant rotation correctly touretzky clusters demonstrate demonstrate segment conclusions valued moody learns learns mateo mateo mateo suggest encoding encoding propose propose propose mechanisms mechanisms mechanisms reduction reduction demonstrated radial plane scene identification identification identification identification explicit produces describes describes describes describes describes coordinates linearly linearly dimensionality dimensionality transformations extraction select john yield extracted variation evaluate restricted organizing translation classical initially initially kohonen classified views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views expect existing figures figures figures retinal recognize recognize recognize determines plotted plotted plotted plotted plotted plotted illustrated maximize maximize mozer specifically partially discussions discussions successfully compression selecting selecting aspects identified encoded effectively effectively effectively poggio poggio poggio poggio poggio efficiently schemes invariance essentially identity showing interpreted classify classify classify categories gray vary modular modular modular modular giles quantization correspondence correspondence correspondence illustrates illustrates illustrates jacobs jacobs jacobs jacobs jacobs acknowledgments cowan presents presents wiley exhibit detail hanson hanson lippmann helpful existence examine examine examine examine examine matches matches matches rest mappings maximizing maximizing maximizing encode encode examined perfect freedom freedom freedom freedom explored finds established indicating separable publishers publishers publishers publishers analyzed nowlan organized forces forces forces forces laboratories projected projected projected projected gradually auto auto auto auto auto auto auto auto auto auto auto conjugate fourth fourth affine capability employ employ exhibits partitioning spread fall replace comments redundancy eventually softmax softmax classifying classifying identifying identifying analogue japan extensive recover zemel approximates rigid rigid rigid rigid fits oja oja ranges viewpoint viewpoint kawato wire wire wire wire wire wire wire wire wire splitting splitting splitting north cottrell cottrell effectiveness symposium selects selects selects recovered recovered recovered recovered recovered recovered recovered recovered recovered combines edelman edelman edelman edelman edelman holland ascent vertices vertices sphere sphere belongs recovery suggesting steepest sons hart hart encodes uniquely uniquely employs employs utilize solely spaced classifies classifies classifies classifies classifies classifies classifies hierarchies reconstruct duda duda eliminating rectangle rectangle acquired projecting investigating covered discusses inversely grateful elsevier atr atr atr aaai cube covers twenty satisfactory satisfactory satisfactory identifies identifies identifies evenly tells exploits exploits exploits arriving cho bottleneck discovers suzuki suzuki suzuki suzuki suzuki decode hip hip recovers weinshall weinshall compress compress nonlinearly nonlinearly demers demers ily ative gun surrounded 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#@Ando_H,Suzuki_S,
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#*learning model model model model model neural neural neural data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure time set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number error error error error error error results results results results results results results results information information problem problem problem problem problem problem problem problem problem based space weights linear case order systems values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise unit unit unit distribution distribution distribution recognition recognition recognition method method method approach point point point point point point point point point point point point point point point point point point point point point point point image image image image image image image image image image image image processing processing large rate test test test patterns matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs form algorithms algorithms algorithms algorithms algorithms gaussian gaussian examples small small size feature feature feature work step points points points points points points points points points points points points points points points field field features features features level current problems problems problems problems random random similar similar representation show section fixed fixed images images images parameter parameter average average average theory theory term term term term note experiments experiments experiments experiments university university variables variables variables computation research independent log log found found found dynamics dynamics standard standard standard standard standard standard computer computer computer computer computer terms distance distance science science science left present phase phase phase phase phase phase phase phase machine object sets sets sets sets sets sets sets sets sets range press components abstract applied applied find find find find find properties references component procedure context introduction estimation estimation estimation statistical generated generated generated generated generated generated generated generated generated tion tion measure measure measure measure measure measure representations representations representations word chosen higher center required multiple good good good long tree expected make techniques techniques techniques scale scale scale scale scale scale scale scale scale minimum ing computed respect respect multi sum mapping factor optimization optimization global em em original original specific represented application provide provide compute location experimental experimental related related constraints constraints constraints constraints constraints constraints constraints constraints approaches approaches mit accuracy accuracy update update descent descent descent descent dependent morgan words department department technique technique individual individual represents exp addition maps considered considered cambridge domain experiment experiment directly san determine full significant speed vision vision con derived derived derived weighted randomly randomly randomly randomly randomly randomly randomly clustering developed developed criterion area types actual finally finally selected selected evidence constraint constraint constraint constraint increases describe transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation corresponds corresponds common shape generate generate supported theoretical eds square instance instance easily easily degree noisy noisy noisy including kaufmann objective objective objective objective objective objective objective objective objective objective objective objective objective objective reduced unknown programming character character character matching matching matching matching matching matching matching matching matching matching matching matching matching uniform uniform uniform empirical max pre pre normalized normalized minimize minimize minimize added added added added improve robust similarity reported reported include engineering varying works works works solve match trans trans address modified generalized grid bounded increased increased grant grant invariant scaling scaling extended trial trial deviation deviation deviation deviation matrices rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation correctly correctly correctly width loop loop column column column setting conclusion critical row row segment hard physics drawn drawn regularization regularization minimizing plane introduce derivatives identification program annealing digit digit digit written solving winner generating generating generating estimating vertical vertical pruning missing missing missing coordinates involves transformations transformations transformations transformations transformations transformations transformations transformations transformations adding applying minimization letters letters letters independently focus expressed formation formation squares solved solved variation variation transform transform transform transform open updated updated updated updated fraction fraction decomposition decomposition decomposition forms understanding sizes translation translation translation translation translation translation translation translation translation translation translation translation translation digits digits digits converges allowed processor partial partial partial partial add iterative iterative closed handwritten handwritten handwritten figures figures silicon combinations coordinate coordinate coordinate coordinate instances assignment variations columns determining identified identified identified extra uniformly uniformly differ stopping hold dot nips correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence cat cat cowan minimized minimized minimized diego transformed essential replaced issues dual dual biases matches matches matches matches matches matches fashion int analytically authors root fundamental phases phases analogous contours created ensure singular precise initialized synthetic synthetic synthetic seconds seconds rows inequality inequality tool spatially spatially sys closer easier easier located acknowledgement separately angles describing beginning localized fuzzy fuzzy fuzzy fuzzy fuzzy affine affine affine affine affine affine affine affine affine affine axes introducing employ formulated summarized incorporating song song enables kinds neuro windows yuille yuille softmax pose pose pose pose pose pose pose newton saddle saddle writing interface forming lagrange lagrange lagrange lagrange recover recover recover null rigid rigid rigid rigid multipliers multipliers ranges mail proceeds held determination handwriting serves transforms unlabeled monotonically degradation spurious spurious spurious spurious mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mouse iteratively iteratively peterson peterson darpa treatment permutation creating jolla draw dividing dividing onr yale yale yale specification gold gold gold gold gold gold solves maximized poses additionally decomposed workstation eric eric eric eric eric equality graphics permits bounding afosr deleted barrier barrier enforce enforce enforce esti son likewise ucsd ucsd rewritten cube deletion drives discretized cursive ping ping ping ping ping correspondences correspondences correspondences correspondences steven steven steven steven steven inclusion drawing incorrectly calculates calculates calculates returned rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan screen rameters distorted hough slack slack slack imum deleting preferable enforcing haven enforced shear shear shear shear shear shear shear repeats repeats walker walker walker traditionally arline arline projective projective clocked clocked mate implementable implementable nation ordinate initializing unequal unequal pal pad differentiated formulating handles combi kosowsky kosowsky absorbed varia raising oblique oblique ject regu tackled combina grimson cosh cosh anand anand anand anand anand regularize wid permissible rnj rnj rnj rnj verge sinh sinh fuzziness llxi llw jittered larization bust drew yan 
#@Gold_S,Lu_C,Mjolsness_E,Pappu_S,Rangarajan_A,
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#*network network network network network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data data data data data data function function figure figure figure figure time time time time time set set set set set set set set set set set set networks networks networks networks networks networks networks training training training algorithm algorithm algorithm output output output output output output output output output output number number number number number number number number number error error error results results results units units units units units units units units units information information information information problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based space space space space space space space space space space space space space space space space weights weights linear layer layer case order order shown shown shown shown systems systems values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise weight weight functions functions unit unit unit unit distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method approach approach approach approach approach approach approach approach pattern pattern point point point point point point point image image image image image image image image image image image image image image image image image image image image image image image image image image image image processing processing processing control control control control control control control control control control control control control large large local local local rate test test test test test test test test test patterns analysis class class matrix inputs inputs form form shows shows signal simple simple simple gaussian gaussian paper examples examples small feature feature net net net net net net net net net net net net net net net net net net net net net net net net net work work work work work task task task task task task methods methods cells step points points points points points points points points points points points field field features features features features features features features process process process current trained trained problems problems problems high high high high similar similar similar similar similar architecture architecture architecture show equation equation equation section section section section fixed vectors images images images images images images images images images images images general general parameter parameter parameter parameter parameter parameter parameter approximation approximation average average states states theory gradient obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained term term term experiments experiments activity activity university university university university computation computation computation solution research research research log log found found found initial initial table table table standard computer computer computer computer computer computer terms terms terms distance science science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction map machine machine object object object object object object sets sets sets maximum press position position position position position position basis outputs outputs abstract applied find find find find density likelihood references due due procedure procedure procedure procedure important important adaptive adaptive mixture mixture mixture mixture mixture context complex complex hand hand hand hand statistical dynamic generated generated variance variance variance variance search search search search search search search search search search search search search search search search search search search search tion tion tion tion change energy energy energy energy energy complexity assume lower measure measure measure prior prior prior learned part part previous previous previous cases required required required required multiple good good good binary binary represent tree bayesian make make techniques techniques techniques techniques length correct correct correct probabilities errors errors errors errors errors scale minimum minimum classes total sum sum times times means factor factor factor factor dimension made made natural global global study knowledge em obtain obtain negative artificial relative relative provide provide define compute objects objects objects location determined determined determined determined posterior posterior connected mit mit steps comparison comparison comparison comparison train train train train nets nets nets morgan morgan proceedings institute department department consists internal advances advances difficult final final scheme ai ai ai ai maps framework cambridge computing directly directly directly directly hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton additional solutions top bit detection detection determine efficient full full full full full significant vision vision estimated basic pages pages validation validation validation give con weighted weighted developed area lines product evidence evidence backpropagation iteration iteration iteration depends depends depends simply biological achieved achieved measured discussion covariance feedforward arbitrary arbitrary arbitrary transformation transformation close assumption assumption predictions predictions predictions predictions finding amount amount amount short common common implemented shape shape shape generate require face pixel pixel pixel ability easily easily easily including fit fit kaufmann smaller combination combination reduced reduced reduced account jordan technology technology programming significantly significantly character character character character york increasing head trials uniform uniform database squared squared iterations max window international normalized normalized normalized normalized normalized bottom experts experts frame frame frame frame frame idea idea minimize minimize produced produced run added predict predict predict predict predict improved improve improve separate identical pixels pixels pixels pixels array recently dimensions dimensions sufficient sufficient highly compare volume volume volume tions smooth match achieve trans address mixtures mixtures background background evaluation positions positions locations locations locations locations locations locations generalized williams williams williams williams williams williams williams williams williams williams williams williams williams williams increased constructed lead invariant invariant occur suggests extended extended rotation rotation rotation predicted predicted alternative touretzky white demonstrate runs starting starting starting row row reduce reduce editors editors measures designed designed peak peak moody moody faster learns constrained taking hard drawn sigmoidal demonstrated proportional relationship iii targets targets characters characters minima annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing acknowledgements reference digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit van construct longer ways factors laboratory dept confidence infinite transformations remaining slightly scales gaussians gaussians springer quality expectation decreases independently stages viewed viewed interpretation codes transform transform transform transform transform evaluated evaluate approximated activities translation digits digits digits digits digits slow epochs normalization combining fitting fitting fitting fitting fitting fitting iterative penalty penalty interpolation interpolation sufficiently classified handwritten handwritten box box thesis usa contour weighting variations black discussions major identified uniformly computationally computationally divided poggio identify detect detect schemes mackay mackay tend essentially ten ten capture notice verlag strongly cun interested interpreted lie lie contribution running strategies timing hold vary michael michael michael michael michael dayan providing correspondence correspondence correspondence correspondence computes highest attempt consisted extract approximating jacobs jacobs deal decreasing presents schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule carried overfitting collection involving strengths hanson optimized integral hessian lippmann preliminary biases biases biases dataset helpful matches matches matches giving giving applicable ideal relationships authors office variability workshop cover editor predicting predicts spline spline spline spline spline spline taylor taylor shapes shapes shapes shapes improving phd isolated advanced advanced theoretic trivial trivial trivial trivial trivial trivial publishers publishers defining fairly nowlan adapted nonlinearity starts starts considerable straight sections closer broad broad mathematics pool ridge gradually toronto toronto toronto toronto recognizing recognizing recognizing conjugate geometric greatly limits affine affine affine affine affine conducted conducted fed readily lack peter peaks splines compares ity synthesis characterize aim aim aim adjust gave richard simulator chose segmented segmented tolerance softmax cor initialization initialization consistently pose forming formally formally investigation summing appropriately conditioned zemel bin printed printed printed printed rotations rotations rigid rigid fits imaging imaging imaging imaging imaging attractive handwriting viewpoint transforms affected carry service corre corre decide overview guarantees originally schedules schedules schedules schedules schedules elastic elastic elastic treatment modelled specialized ballard ballard rich canada agree explains generalizing displacement default default severe outlined verify logarithm aston expanding encouraging tibshirani smoothly discriminative perturbed centre instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation instantiation discovering guess stands reject param principled home home home trends distri community gained geoffrey geoffrey geoffrey geoffrey geoffrey geoffrey geoffrey graphics generators generators generators generators generators plate speedup unconstrained translations zip funded responding inverting memo cubic elsevier intensive intensive durbin mann bution consuming recogni twenty christopher christopher christopher christopher christopher impractical attributed crude correspondences correspondences settling settling settling spacing compete puts tors determinant settle peaked vote vote lying trol characterizes acid distorted multimodal hough hough hough hough hough hough hough deformation deformation deformation deformation deformation penalizes penalizes penalizes birmingham probabil revow revow revow revow revow revow revow revow revow revow revow revow predetermined spanning postal preferable assessing collecting shear shear deformations deformations hands ontario ontario posi arline perturbing dilation decides yann notably experimentation deformed deformed continuation hypothesize feeds canadian deformable deformable deformable deformable deformable deformable deformable deformable deformable deformable deformable positioned camp fellow tony cities skew instantiations eter extraneous iai official integrand integrand integrand chow rameter settled backpropagated votes rectly instantiated instantiated instantiated apple ink ink ink ink ink postprocessing postprocessing elongation elongation detectable danger logs shashua rob hunt hunt grimson grimson greyscale correspon imization mensional weightings weightings buffalo frontiers srihari regularize judging accumulator sharpness edi iiz iiz iim iim jepson lipp guesses xerion recalculated noranda cedar nearer fuller scalings evalua instantiate instantiate instantiate kauffmann alphabetic allan drew deserve aleksander binned 
#@Hinton_G,Revow_M,Williams_C,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural input input input input input data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm number system system system system system error error state results results results results information information information information information problem problem problem problem problem problem models models performance performance performance performance performance based based based based based based space space space space space space space space space space space space space space space weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case shown shown shown shown systems systems systems weight weight weight functions recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern point point point point point point point point point point point point point point point point point point point point image image image image image image image image image image image image image image image image image image image image single processing processing processing processing large large local local local local local local local local local local local local local local local local test test test analysis analysis form shows shows shows shows shows shows shows shows signal algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian visual visual visual visual paper paper examples examples examples examples examples small feature feature work task task task task task task task methods fig fig step points points points points points points points points points points points points points process level current structure high high high high high memory similar representation representation architecture show section section line line line line line vectors images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general general speech speech speech speech parameter real real average average average theory gradient obtained experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result university computation computation solution solution research research independent defined defined defined found sequence sequence sequence sequence target target target initial initial estimate computer computer distance science science science science direction presented present present low low temporal position components components basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract abstract abstract abstract applied find find computational computational references component ieee procedure procedure important adaptive mixture mixture mixture introduction complex complex hand effect generated generated energy energy lower lower lower lower lower measure chosen higher center center cases good represent distributed distributed techniques techniques proposed proposed length minimum minimum sum sum sum means dimension natural natural natural natural applications knowledge em em em vol vol artificial artificial relative specific desired desired define define define compute compute objects proc proc location perform experimental related related related related related constraints equal approaches approaches approaches approaches approaches mit steps contrast descent morgan morgan morgan institute institute implementation technique technique consists consists consists individual kernel advances advances advances represents represents represents final sequences sequences domain domain domain domain directly directly directly hinton curve curve curve curve curve limit trajectory trajectory trajectory top top efficient upper upper free free world world speed vision vision vision con produce produce weighted weighted clustering developed product actual finally constraint constraint simply simply discussion normal describe describe arbitrary fast close surface surface surface surface short nearest nearest generate generate require require face journal pixel pixel pixel pixel pixel pixel cluster development development sensory fit fit kaufmann kaufmann auditory smaller underlying jordan jordan projection database principal squared squared call iterations iterations stored bottom bottom experts expert early combined combined produced predict discussed robust robust apply moving period subject hierarchical hierarchical cognitive relevant dimensions dimensions dimensions compare compare subjects volume works works tuning axis tions smooth smooth smooth smooth speaker speaker speaker studies trans address positions locations grid sensitive constructed parts studied studied digital alternative move generally half half row row row row central central accurate constrained constrained reduction california radial configuration configuration acoustic perception ways estimating describes linearly linearly linearly dimensionality easy easy angle angle consisting consisting expectation formation viewed influence influence influence influence open centers frames frames frames frames frames approximated approximated partition partition earlier combining neighborhood closed closed interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation intermediate distances query query query faces recorded recorded recorded kernels perceptual subspace subspace subspace subspace subspace subspace subspace domains domains gating gating gating middle aspects aspects closely closely computationally computationally divided poggio projections projections projections projections comparing fine reached conf quickly kind kind induced induced induced induced induced induced induced contained issue lie lie lie lie manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold satisfy michael dot realistic correspondence denker maximization automatically moves moves illustrates illustrates jacobs jacobs camera camera camera bars bars bars bars bars accurately project project project mappings int int func patch patch patch patch patch patch patch closest closest necessarily reading reading reading reading configurations man spline thought thought queries singular algo consist simplest arbitrarily synthetic synthetic sentences averages developing smoothness nowlan answer independence lies nonlinearity lin lin straight straight straight straight berkeley berkeley berkeley sections arc closer closer preprocessing preprocessing division worst leaves immediately projected projected projected projected projected projected circle begin patches patches patches patches patches patches patches patches patches patches amounts embedded embedded embedded embedded embedded cohen compares synthesis perturbations ture fall acoustics neuro windows returns begins sentence globally lab ear leen princeton rithm optimizing optimizing resources databases rotated rotated purely repre unity unity connecting kaufman dealing numerically ments occurred iiii lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip lip excellent combines introduces iteratively induce moved washington lengths sphere modelled shortest shortest omohundro omohundro omohundro omohundro omohundro omohundro accumulated street largely presenting legal pentland die brightness constrain manifolds distant mouth mouth march memo fea milliseconds eigen experi aaai nec nec ucsd walk walk walk walk walk walk walk circumstances dim stephen stephen stephen stephen stephen quantify builds suite hypothesized interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated dominates pictures pictures evenly bregler bregler bregler bregler bregler bregler bregler bregler interpolating interpolating lying fair inducing enters sur experimented fore snake snake snake snake snake snake snake sented violate sensed nov relying lips lips lips nonlinearly iter iter iter iter iter movie proving cad positioned konig interpolant interpolant interpolant geometrically quences preferentially turk proj inexpensive joining joining neurm arose arose embed trast teeth teeth kambhatla graylevel graylevel graylevel graylevel graylevel graylevel submanifold halfway adelaide interpolates christoph christoph christoph christoph christoph ded quires unnatural impoverished curt 
#@Bregler_C,Omohundro_S,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data function figure figure figure figure figure figure figure figure time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm output output output output output output number number number number system system system system system system system system system system system system system error error results results units units units units units units units units units information information information information information information information information information information information information information information information information information information information information problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance based weights linear linear layer case case order order order shown shown systems systems systems systems systems systems systems systems values probability probability probability probability probability weight functions unit unit unit recognition recognition recognition recognition method approach approach pattern pattern point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single processing processing processing control large large rate rate rate rate rate rate rate test patterns optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows signal algorithms algorithms simple simple simple simple simple simple gaussian gaussian gaussian gaussian paper paper examples examples examples examples small small small small small size size size size size size size size feature feature feature feature net net net net work work work methods fig features features features features features features features features features features features features features features features features features features features process process process process level level level level level level level level level trained trained trained trained trained trained trained trained trained trained trained trained trained problems problems high high high high memory similar representation representation representation show show show section images images images images images images images images images images images images images images general parameter parameter real average obtained term term dimensional threshold threshold threshold threshold found found sequence sequence sequence target constant table table table table estimate estimate standard terms distance distance prediction presented presented map map map map map map map map low low low low low low low low low low low low low low low frequency frequency frequency frequency frequency machine object object object object object object motion learn learn learn learn learn learn learn learn learn learn components outputs outputs outputs outputs outputs outputs outputs sample abstract applied find references ieee ieee ieee ieee ieee ieee positive positive positive positive positive positive positive positive positive positive positive procedure procedure procedure context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context introduction complex hand hand effect dynamic search search search search search search search search search search search search search search search search search search search search search search search search search search search search search tion tion change energy energy energy energy energy energy spatial spatial lower lower lower lower lower lower lower lower lower lower lower lower lower lower measure measure measure signals representations learned learned learned chosen chosen higher higher higher higher higher higher higher higher part part center cases type multiple binary binary binary binary long techniques techniques techniques techniques techniques region region region region length forward scale scale scale scale scale scale scale scale scale scale scale scale scale simulations resulting ing total human multi multi multi sum performed regions regions regions regions means potential potential potential dimension made made made natural orientation applications applications applications negative original original original original original original original vol vol represented true true true true true application desired cross provide provide provide provide define compute objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects rates rates rates rates location location location perform constraints accuracy comparison comparison connection train train train train train train source nets nets nets nets nets selection selection selection proceedings proceedings proceedings proceedings proceedings proceedings version version technique code responses difficult difficult maps maps maps maps maps maps maps maps maps maps considered directly additional curves curves curves curves estimates design limit detection detection detection detection detection detection detection detection detection conference conference conference efficient efficient efficient statistics world vision vision vision validation give give con derived derived developed levels levels levels levels levels levels area area area entropy actual provided provided provided provided provided provided provided selected sampling sampling sampling simply simply simply achieved measured discussion limited proof finding finding finding finding amount nearest eds pixel pixel pixel pixel pixel ability ability cluster cluster cluster cluster cluster cluster makes objective typically typically smaller reduced reduced reduced account york operation details call filters filters filters direct window window international decay idea attention attention choose choose added description improved improved improve improve improve resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution advantage takes typical strategy moving include identical pixels pixels pixels pixels quadratic hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical relevant relevant interest interest interest interest sufficient compare trans definition entire increased constructed constructed constructed constructed constructed concept studied invariant extended extended extended feed feed hybrid hybrid width width clusters clusters clusters clusters clusters pass demonstrate demonstrate demonstrate demonstrate demonstrate half starting starting starting sigmoid measures faster suggest taking mechanisms characteristics sigmoidal regularization regularization regularization regularization user user iii targets manner force explicit explicit explicit explicit explicit construct longer ways laboratory laboratory tuned implement explicitly explicitly explicitly explicitly explicitly explicitly explicitly simultaneously linearly scales scales scales scales scales integrated implies john john john john john john national national extracted extracted extracted extracted dependence lee decomposition spectrum key performing performing combining false false false false false false false false tracking visible visible transactions precision building building building building building building building building building box figures automatic mozer mozer neighbors simplicity identified extra efficiency efficiency efficiency efficiency capable differ computationally divided detect detect computations tend fine fine fine fine fine fine fine fine fine receives road road road road road road road road road road road road road road road road road road road road road road compact quickly repeated repeated repeated interpreted dis sci usual usual realistic providing highest highest received received received received received extract extract acknowledgments oriented oriented oriented oriented oriented camera parametric poor varied put put put strengths helpful helpful existence existence fewer reducing reducing giving ideas ideas ideas tech investigated combine authors working workshop coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse concepts man changed adjusted versions versions versions versions versions versions algo detected detected detected improving extent attempts mentioned band band band distinguish orientations capabilities expensive expensive expensive processed purposes purposes constructing constructing res res lowest lowest lowest arises qualitative integrating greatly greatly reflect freeman freeman relevance peter effort passed passed music music music music frequently compares span ture ture suited gave chose sophisticated display display begins pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid don person classifying ordinary ordinary benefit benefit benefit benefit redundant sensing appearance appearance appearance appearance appearance princeton rithm narrow repre discover rotations exemplar exemplar exemplar fits primitive height contract bands bands exploit adequate adequate adequate carry composition composition exploring meaningful mance combines loo loo paul surprising perfor pruned expanded expanded expanded searching searching searching searching april suggesting ballard ballard draw proximity exploiting mind ence roc roc roc indirect tables inferred lane lane benefits benefits expanding expanding utilize discovering certainty certainty examining demon laplacian laplacian laplacian laplacian representa musical pami compensate expand adelson adelson adelson adelson adelson adelson multiscale complementary rough worth funded preserve things struc ward computa demonstrating demonstrating scanned textures doesn spacing finer pearson pearson pearson pearson pearson pearson pearson eral eral burr burr burr cally usefulness distinguishing distinguishing distinguishing subtracting ters resolutions resolutions resolutions resolutions resolutions resolutions resolutions resolutions resolutions resolutions resolutions resolutions architec bergen bergen bergen bergen bergen bergen successively positives positives exploits digitized digitized arpa sions irvine ben approached shop ically energies energies energies energies eighth kuhn fore sorted sorted detections began refine searched searched searched searched richer miyata miyata miyata leung blurred blurred blurred ohio spence spence spence spence spence spence pyramids pyramids pyramids roads roads roads roads roads clus missed thirty aware anandan blur blur blur correspondingly blurring niques taught enormous kung charac greenspan extraneous jim jim jim jim jim steerable steerable steerable weaknesses roi octave unoriented sev coarser coarser government yoon didn clay clay clay clay clay kamm sajda ended aerial aerial aerial aerial strate smart chellappa registered photographs photographs photographs photographs lution burt burt burt burt burt burt burt burt 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#@Bergen_J,Pearson_J,Spence_C,
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data function function figure figure figure figure figure figure figure figure time time time time set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output number number number number system system system system system system error error error error error error error error error state state results results results results results results results results results results results units information problem problem problem problem problem problem problem models models models hidden hidden hidden hidden hidden performance based based based space space space weights weights weights weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer case case case case case case vector vector vector vector vector vector vector vector vector vector vector order order order order order systems values values functions functions distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach approach approach pattern pattern pattern pattern point point single single single single single single single processing large large large local local rate rate rate rate test test test test test test test patterns patterns analysis class class class class class class class class class class class class class matrix matrix matrix matrix optimal optimal inputs inputs inputs shows shows algorithms simple simple simple simple gaussian gaussian paper paper examples examples examples examples examples examples examples examples examples small small small size size size feature feature net net net net net net net net net net net net work methods fig fig points classification classification classification classification classification classification classification classification classification classification process level trained trained trained trained high high memory memory memory memory memory memory representation architecture architecture architecture architecture architecture line line rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images general general general generalization generalization parameter parameter real approximation gradient gradient gradient obtained obtained obtained obtained obtained term note note note dimensional dimensional computation solution table standard distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance left presented presented present activation low low low low low low low learn learn learn learn learn nonlinear nonlinear outputs outputs outputs outputs outputs abstract applied find find computational convergence properties references references component stochastic due important important adaptive decision decision propagation context complex hand hand hand hand behavior behavior behavior parallel tion change difference complexity complexity complexity assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower measure measure measure measure learned learned chosen cases good good binary long long expected equations equations techniques proposed proposed proposed simulations minimum minimum resulting resulting resulting computed respect respect respect respect respect performed called called mapping factor optimization dimension made global applications knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge original original vol artificial artificial represented compared application application application desired desired desired desired desired desired desired desired cross cross cross define define define rates rates rates rates perform experimental related connected connected distributions approaches approaches approaches approaches approaches comparison comparison comparison comparison train descent nets morgan morgan morgan morgan morgan morgan institute implementation implementation version version version difficult layers layers graph domain domain directly directly hinton hinton additional additional conference conference efficient efficient efficient efficient efficient efficient classifiers classifiers classifiers upper upper upper upper full choice speed speed basic basic basic validation validation validation give give condition condition developed developed provided finally selected backpropagation backpropagation constraint achieved achieved achieved achieved discussion arbitrary transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation limited corresponds corresponds corresponds short nearest nearest nearest common supported main main eds eds eds eds eds eds journal pixel pixel instance easily kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann objective typically pairs underlying underlying unknown fully fully technology interesting ratio character character character character character character character character character character increasing mechanism special database database database database database database principle principal details iterations stored international normalized supervised supervised magnitude idea perceptron perceptron architectures improved improved discussed discussed improve advantage advantage ensemble takes typical typical reported reported practical identical side side side pixels pixels hierarchical hierarchical sense interest highly highly calculated calculated calculated module module module axis pca pca studies rl diagonal definition mixtures chain generalized storage increased grant horizontal horizontal invariant invariant invariant invariant invariant invariant invariant invariant invariant scaling rotation rotation rotation correctly correctly correctly locally touretzky touretzky touretzky column setting hardware hardware place minimal minimal reduce operator neighbor neighbor tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent measures measures numerical moody learns learns encoding propose hard reduction sigmoidal intelligence regularization minimizing min min introduce derivatives derivatives derivatives characters characters characters characters acknowledgements reference reference reference reference reference reference explicit explicit written longer optical optical solving ways multilayer multilayer multilayer transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations easy easy adding springer extraction letters letters letters letters letters national family expressed reconstruction reconstruction communication interpretation solved evaluate operations operations centered translation translation translation digits digits digits allowed partial calculation calculation performing classical classical normalization add iterative remains distances distances distances distances distances distances distances distances filtering calculate calculate calculate visible sufficiently euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean classified classified handwritten handwritten handwritten handwritten handwritten handwritten recognize recognize extension discuss structural major middle middle computationally divided build invariance invariance invariance invariance score score score orthogonal ten summary verlag decoding interested interpreted classify classify bar dayan dayan generalize modular nips nips nips nips nips nips nips giles denker denker denker denker denker chips consisted illustrates illustrates extract tesauro tesauro tesauro tesauro cowan cowan powerful powerful transformed transformed transformed transformed transformed transformed requirements investigate put hanson hanson lippmann graphical graphical discriminant detectors boosting boosting boosting possibility combine authors structured comparable comparable complicated complicated smallest analyze subsets prototype aspect versions algo expressions academic art art years costs convolution convolution derivation analytical adapted expensive expensive briefly rapid formalism shared shared shared preprocessing preprocessing incorporate hyperplane hyperplane mation simard simard simard simard simard simard simard simard simard simard simard simard separately separately author recognizing raw improvements prop prop prop prop evaluating double double double double double double double double double orders price rely summarized ture aim reaches achieves simulator sophisticated segmented lot trade representative leen leen leen optimality optimality extensive rithm databases databases hyperplanes reconstructed reconstructed lecun lecun lecun lecun lecun multipliers numerically promising mail odd optimally optimally optimally optimally moments service alspector published performances performances schapire schapire schapire counter offers indicator shortest propagate stopped metrics dramatically usage usage numerous indirect corporation stork stork presenting rejection year personal german big big workstation imagine invariances invariances hastie hastie ocr ocr ocr depicts paris spanned spanned worth associates france sized universit exchange applicability round computa tour nist nist nist nist preserves transforming heavily doesn focuses autoencoder char incorporation incorporation incorporation incorporation incorporation incorporation incorporation sided sided sided sided sided sided sided sided sided sided sided sided sided sided sided sided sided sided thickness architec screen convolved autoassociative autoassociative drastically demands unusual deformation deformation revow revow drucker drucker drucker drucker percep preprocessed multiplications multiplications favorable deduce deformed pierre transfor cedex victorri victorri realizing standards stance standardized schwenk schwenk schwenk schwenk schwenk schwenk schwenk schwenk ode ickinger ickinger speedups autoassociation autoassociation autoassociation autoassociation acter barely supervisor lnt interprets trons seldom precomputed reconstructs supposedly refs compilation parc hopes curie necess 
#@Milgram_M,Schwenk_H,
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#*learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data function figure figure figure figure set set set set set set set set set set set set set set set set set set networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number error error results results results results information information information problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models performance performance performance performance performance based space space space space case case vector vector vector vector vector shown shown systems systems systems values parameters recognition recognition recognition approach pattern pattern pattern pattern point point point point point image image image image image image image image image image image image image image single single single processing processing large large large large large large local local local rate test test test test test test test analysis class class class class class class class class class class class class class class class class class class matrix matrix matrix shows shows algorithms algorithms algorithms simple simple simple paper paper paper examples examples examples examples examples small small small work work step step step step points points points points points points points points points features classification classification classification classification level current current current current memory memory memory memory response similar similar similar similar show section line line line line line rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images images images images parameter parameter approximation average average average average note note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university computation computation solution solution solution research defined found found found found found found sequence initial table table table distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance left left present low sets sets sets maximum range components components components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear abstract find find convergence convergence references due due positive positive procedure context context introduction behavior cost recurrent tion tion tion assume assume classifier classifier measure prior learned learned learned learned learned chosen chosen chosen higher part cases cases make correlation errors errors scale scale resulting resulting total regression computed sum performed performed called called means means means means means means means optimization optimization potential dimension natural relative specific specific specific specific specific specific true true true true true true true true true true true true true true define define compute compute compute compute compute compute rates location location location perform goal morgan morgan report department advances advances represents difficult difficult scheme addition computing computing computing domain domain curve additional view san san top top efficient requires statistics statistics speed basic basic give derived derived clustering clustering clustering clustering criterion criterion criterion lines lines associative achieved discussion covariance technical arbitrary group denote transformation limited inverse corresponds corresponds corresponds complete finding finding finding amount amount nearest nearest effective effective generate theoretical main journal square end instance cluster cluster easily fit fit underlying underlying account account functional block interesting interesting ratio character character character character character projection projection projection matching matching operation principal principal squared squared squared representing representing representing details iterations iterations stored stored bottom bottom idea idea idea minimize produced description improved improved directions advantage property separate include pixels sense subset recently dimensions dimensions dimensions dimensions sufficient smooth correspond correspond achieve trans diagonal address definition organization horizontal concept invariant matrices rotation rotation rotation rotation locally loop generally column column setting conclusion row reduce reduce neighbor neighbor depend tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent measures modules mateo mateo suggest taking hard largest variety variety min min min min min min plane characters base appears digit digit digit digit digit digit digit produces solving ways generating describes vertical metric metric metric metric transformations transformations transformations transformations remaining slightly slightly angle unique develop springer blocks blocks versus versus decreases family family independently review stationary correlated squares squares squares squares solved showed centers decomposition decomposition approximated similarly digits digits digits digits converges converges converges converges partition partition reasonable slow slow reduces fitting fitting roughly iterative iterative valid distances norm norm norm euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean kohonen kohonen classified expect building building building handwritten handwritten handwritten handwritten bell bell bell bell subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace extension extension automatic columns columns middle computations schemes invariance invariance invariance invariance invariance invariance road road refer compact verlag success showing classify manifold manifold manifold generalize minimizes minimizes denker denker leading leading decreasing situations minimized explore experience experience rapidly hall ideas project root eigenvectors hill closest closest closest closest closest closest closest closest closest thought thought subsets subsets subsets rank rank rank prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype singular singular singular singular singular obvious obvious precise simplest finds residual rows rows trivial fairly expensive briefly nonlinearity comparisons drive stanford stanford incorporate hyperplane laboratories laboratories laboratories laboratories simard simard simard simard simard simard simard simard simard simard circle implicit affine affine tional red compares prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes berlin measuring spread incorporating incorporating replace replace kinds traces extreme don picture classifying ordinary indices identifying restrict lvq lvq lvq member rotated hyperplanes impossible rotations grey lecun lecun fails kaufman kaufman fits murray oja oja loops keeping shifts settings corner corner corner composition meaningful combines mjolsness mjolsness predictors corre iteratively entry displayed overview conjunction conjunction conjunction accounts accounts accounts elastic centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid initialize initialize winning rich rich rich variants generalizing insensitive metrics dramatically drop drop slight gold gold outperform solves solves email email email removal convenience convenience residuals arg big classifies guess invariances invariances summarizes hastie hastie hastie hastie hastie hastie permits permits flip rough drawback misclassified accounted accounted parametrized intensive intensive ignoring subspaces subspaces subspaces fortunately expense dim dim dim dim dim distortions recogni recogni impractical families orthonormal orthonormal holmdel holmdel svd svd svd svd svd svd svd svd svd svd svd thickness thickness rangarajan rangarajan attained interpretations seed seed att att digitized dimen accounting edition prominent minimizer iterate iterate iterate iterate rotate preferable neigh shear superscript usps prohibitively prohibitively classifica shrink ages functionals divides iix iix jim jim trevor trevor trevor trevor trevor trevor trevor patrice patrice patrice patrice patrice patrice interna compactly official proj proj proj proj proj proj proj proj proj proj proj proj 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#@Hastie_T,Sackinger_E,Simard_P,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm output output output output output number number number number number system system system error error error error error error error error error results results results results results results results results results results units units units units units units units units information information problem problem hidden hidden hidden hidden hidden hidden performance performance performance based based based based based weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer vector vector order order order order shown shown shown shown systems values values values values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions method method approach approach approach approach approach approach approach approach single single single control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large local test test test test test analysis class matrix optimal optimal optimal optimal inputs form form shows shows shows shows shows shows shows signal signal signal simple simple paper paper examples small net work methods points points points field field field current current trained structure structure high high high representation representation representation architecture architecture show equation equation equation equation equation equation equation section section section section section general real real real real real real real real real real real real real real real real real approximation obtained obtained obtained obtained obtained obtained note note experiments experiments university solution solution solution solution research research independent defined found found initial initial initial constant standard computer terms terms terms distance distance synaptic synaptic science presented map present activation frequency range range range learn position position position position position position position position position outputs abstract back find properties references due due due important important important context introduction generated parallel parallel tion energy energy energy variable measure measure signals signals signals signals signals signals signals signals prior chosen chosen chosen part center center required good long long conditions represent represent chip fact errors forward scale simulations ing total simulation respect sum sum called called regions mapping mapping mapping mapping mapping mapping mapping mapping mapping factor factor optimization potential feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications knowledge compared application application application desired desired cross cross cross cross cross cross cross cross series series provide provide location active determined determined experimental distributions power approaches steps accuracy accuracy accuracy comparison comparison larger larger fields fields fields source source source selection proceedings proceedings department department implementation implementation implementation implementation implementation implementation implementation implementation technique technique consists code code code represents represents represents difficult final graph computing equivalent experiment experiment experiment curve curve curve curve solutions design bit full requires requires significant free speed basic give give produce produce produce channel developed developed types nature achieved measured measured normal technical feedforward group denote denote transformation transformation transformation fast fast fast fast limited limited close close complete surface predictions predictions implemented shape shape shape shape shape shape shape shape shape shape shape shape generate generate generate supported typically smaller combination fully fully fully technology technology technology technology block block transfer transfer testing significantly significantly significantly database database database database database database database database principal making stored stored bits normalized early combined produced perceptron perceptron perceptron architectures improved improved improved discussed discussed recent exact advantage pair pair separate takes typical typical practical subset interest highly highly highly conventional works module axis axis differential channels improvement constructed suggests digital digital wide predicted hybrid loop loop loop boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware sigmoid accurate accurate numerical numerical designed clear exponential temperature temperature temperature temperature temperature temperature strong strong strong physics external external reduction sigmoidal sigmoidal demonstrated solid solid proportional radial radial radial pulse pulse variety plane configuration configuration force force base ways sequential generating plot laboratory laboratory stability vertical vertical vertical vertical changing sensitivity multilayer multilayer multilayer simultaneously electrical involves involves remaining remaining angle develop equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium predictive minimization springer extraction versus versus versus extracted reconstruction reconstruction squares squares solved controlled controlled restricted evolution evolution diagram diagram key partial earlier earlier dashed measurements normalization sec sec purpose iterative closed generation construction topology topology david precision figures includes currents currents currents currents currents bell plotted illustrated partially discussions major major simplicity straightforward suitable computationally paths build post post post post invariance plots plots plots plots characteristic characteristic verlag strongly prob allowing showing contribution sin follow device device quantity modular surround minimizes illustrates extract software software software intrinsic modelling presents explore unlike circuitry detail association optimized optimized accurately dataset dataset mappings possibility transistor scaled scaled tanh tanh proved analogous smallest circles gradients configurations voltages ensure adjusted front portion panel taylor shapes shapes shapes shapes contributions residual residual residual ment agreement analytic multiplication rapid purposes sections sections sections sections day located bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop transistors transistors transistors transistors transistors acknowledgement circle calculations arises bandwidth geometry radius radius sun addressed outer conjugate substantially understood offset tional capability peter incorporated schematic measuring adjust gave shaped shaped diagnosis trade acquisition analogue analogue analogue analogue analogue analogue appearance extensive linearity linearity pick pick labelled circular circular circular circular circular reconstructed repre flexibility multiplier smith smith smith smith smith smith smith khz ments minutes promising balance integrator modifications symposium symposium excellent governed corre paul regarded buffer enhance interconnections offers contact draw card exploiting davis dividing fusion fusion fusion fusion fusion fusion fusion lem fitted temperatures temperatures pressure pressure pressure unchanged multiplying geometrical geometrical aston aston magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic magnetic corrected acceptable ease tor workstation alter shaded shaded care evolve approxi ization challenging nuclei million minor loading intensive chris sponding parameterization thermal thermal thermal tom quadrant todd todd todd todd todd todd todd hundreds shot shot shot shot shot shot tors powers diagnostic practically normalize digitized cur compensated confined confined rel presently signed plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma plasma denominator tens tens birmingham monitored equilibria equilibria equilibria cope sented addi stan spanning cox cox custom configured configured elegant italy italy dard schematically reconstructions mike nuclear heat nation vme vme digitally digitally converters permitted ration successes chamber industry uncertainties cards multiplexed gation ordinates tailed tailed flowing torus torus torus diagnostics collectively collectively conduc attainable attainable 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#@Bishop_C,Haynes_P,Smith_M,Todd_T,Trotman_D,Windsor_C,
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#*network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data data data data data figure figure figure figure figure time set set set set set set set set set set networks training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number number number number number number number system system system system error error error error error error error error error error error error error results results results results results units information information information information information information information information information information models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden performance performance performance based based based based space space space space weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case vector vector vector shown shown systems systems systems systems systems values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern point image image image image image single single processing processing processing processing large large local local local local local local local local local local rate rate test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal inputs shows simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples examples examples examples examples examples examples examples examples examples examples examples small small small net methods methods methods step step step step step step step points points points points classification classification classification classification process level trained high high high memory memory similar similar architecture section section line vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images images images parameter parameter real approximation approximation states theory theory obtained term term dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university computation computation research research research research independent log log log log log log log log defined found initial table table table table table estimate computer computer computer terms terms distance distance distance distance distance distance distance distance science science left phase machine machine machine machine machine object sets sets maximum maximum press components components components components components components components components components components components components components sample sample abstract applied back computational convergence density density likelihood likelihood likelihood likelihood likelihood references component component ieee procedure procedure important important adaptive mixture mixture mixture mixture introduction introduction estimation statistical effect effect variance variance variance cost cost cost cost cost cost search tion tion tion change energy assume lower lower lower prior prior prior part previous bound cases required good binary binary represent distributed expected length length length length length length length probabilities errors errors errors forward minimum minimum minimum minimum resulting resulting classes classes classes classes classes classes classes classes classes classes classes classes ing ing sum performed performed performed means means means means means factor factor dimension knowledge em em em em filter filter negative original relative relative represented represented compared application cross define define define define perform perform perform perform determined related equal steps train train train morgan morgan morgan morgan proceedings institute department version version version version version version technique technique internal code code code code code code code code advances advances advances advances final scheme scheme scheme framework equivalent equivalent equivalent equivalent hinton hinton hinton hinton hinton hinton hinton hinton hinton curve view san san san san capacity efficient efficient upper upper full full full requires requires requires requires choice significant free free free free free free free vision basic basic validation validation validation validation validation validation validation give give produce coding derived weighted weighted weighted clustering clustering clustering clustering clustering clustering clustering criterion lines selected iteration constraint constraint constraint measured measured measured discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance describe tested transformation transformation transformation transformation fast fast limited limited limited close corresponds surface amount nearest nearest effective assumed generate pixel pixel pixel pixel cluster cluster noisy including fit fit kaufmann kaufmann kaufmann kaufmann typically typically underlying combination account account technology interesting testing testing character character edge database database database principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal squared squared squared squared details numbers numbers pre pre making stored bits bits idea idea idea choose choose added description description description description light improved improved improved population population directions directions directions directions directions directions directions directions directions directions directions correlations advantage separate takes reported apply subject subject pixels pixels hierarchical relevant dimensions dimensions dimensions dimensions sufficient highly highly unsupervised unsupervised calculated volume volume volume smooth pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca trans diagonal diagonal diagonal diagonal mixtures mixtures mixtures mixtures mixtures mixtures mixtures separation grid williams williams storage entire invariant invariant scaling matrices rotation alternative alternative locally locally locally clusters column pass reduce conclusions valued editors editors editors editors tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent clear moody mateo mateo mateo mateo suggest hard reduction proportional proportional intelligence assuming assuming plane plane relationship averaged derivatives characters digit digit digit digit digit digit digit digit digit digit digit digit construct construct factors factors segments metric metric metric metric multilayer explicitly coordinates dimensionality dimensionality transformations transformations transformations transformations transformations remaining easy easy slightly slightly text text adding adding adding adding adding gaussians gaussians gaussians quality implies expectation choosing review reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction correlated viewed viewed variation evaluated evaluate labels decomposition soft soft sizes similarly translation digits digits digits digits digits digits digits digits digits digits digits digits digits digits allowed allowed allowed allowed reasonable spaces reduces fitting fitting add add iterative interpolation distances assigned assigned euclidean euclidean euclidean classified transactions degrees degrees degrees handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten priori perceptrons subspace subspace subspace subspace subspace mozer variations variations variations absolute discussions major reason determining straightforward compression compression extra closely society differ computationally computationally computationally divided effectively included successful build post identity orthogonal orthogonal orthogonal orthogonal orthogonal ten capture capture capture cun cun dis return contribution classify generative generative generative generative generative vary usual michael michael michael michael michael dayan dayan dayan dayan dayan dayan dayan giles quantization denker denker leading illustrates preferred extract approximating tesauro tesauro cowan cowan cowan situations unlike powerful transformed poor poor collection requirements requirements investigate hanson hanson association lippmann helpful rise investigated biol ideal possibility scaled office coarse equally equally changed prototype singular versions versions versions assumes freedom freedom freedom explored generates submitted explain motivated phd neal neal averages great advanced stop formula costs variances variances variances variances variances variances defining defining defining improves briefly worse straight formalism incorporate incorporate choices leaves mation simard simard simard simard projected separately toronto toronto toronto auto auto auto auto cybernetics incomplete recognizing recognizing recognizing recognizing raw raw raw requiring requiring requiring prop prop prop prop prop prop evaluating amounts amounts amounts peter peter peter peter peter incorporated formulated formulated incorrect fall incorporating incorporating incorporating incorporating extensions segmented age distortion picture leen proportion sleep writing writing writing assign formally appropriately zemel zemel zemel zemel approximates encoder eliminate rotations rotations grey royal lecun turned turned convenient mail simplify replacing splitting settings bourlard responsible symposium infor reliably alspector alspector heavy heavy heavy heavy counting counting surprisingly creating smoothed properly canada canada storing likelihoods variants variants designing implicitly omohundro ignore dempster dividing assigns assigning informa dramatically yielded yielded leaving rubin helmholtz helmholtz helmholtz diverse isotropic isotropic isotropic isotropic pieces tibshirani pointed discriminative perturbed perturbed centre assignments descriptions imagine imagine examining wake reconstruct reject options invariances publication care hastie thick geoffrey geoffrey geoffrey geoffrey geoffrey geoffrey picked retain intensities ambiguous laird discusses funded places frey retained subspaces subspaces aaai develops emphasis chris styles styles styles styles styles bility distortions recogni decided insufficient heavily stochastically losing generafive err autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder responsibility hull tribution compo dissertation bregler ultimate constraining assessed assessed united undergo rec col revow revow revow revow revow dist infeasible severely altering minimise deformations deformations deformations substituted ther ontario ontario encourage reconstructions yann fur ages tums nent responsibilities reconstructing canadian nserc neighbour neighbour ponents lations encoders encoders encoders neighbouring fellow generatire qualities patrice official official official embody embody pervised victorri cheaper genera schwenk akin autoassociation autoencoders autoencoders unsu cloud cloud wished kambhatla deficient rejections rejections rejections rob barely generalise plication kamp weightings weightings weightings weightings marginally misfit iiz reconstructs reconstructs tangents tangents tangents recognise lection noranda cedar handful stor iie unfortunate ameliorate recognising generalising flatten summarise 
#@Dayan_P,Hinton_G,Revow_M,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning model model neural neural input input input input input data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set set set set set set set set networks training training training training algorithm algorithm output output output output output number number number number number system system system system system error error error results units information information information problem problem problem models models hidden performance performance based based space space space linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case vector vector vector order order order order order order shown shown shown values values values distribution approach pattern point point point point point single processing processing processing control control control control control control large large large rate test test analysis class class class matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs shows shows shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms simple visual paper paper examples examples examples small small small small task cells points points points points field field field current random representation representation representation representation fixed vectors vectors general general theory theory theory note note note experiments dimensional dimensional dimensional dimensional dimensional result variables variables variables variables variables variables computation solution solution defined found sequence sequence constant terms science left map map map map map map present sets motion motion range range range press press position position position position position components components components components nonlinear nonlinear nonlinear nonlinear outputs outputs outputs abstract applied references component ieee important adaptive adaptive adaptive introduction statistical variance search tion assume assume lower lower representations representations representations word word word learned learned chosen chosen theorem theorem cases cases good long represent make correct observed observed observed finite finite finite minimum resulting resulting resulting resulting resulting classes total total simulation simulation human human human human human human sum called elements mapping mapping mapping mapping mapping mapping made feedback feedback feedback applications original samples samples samples represented represented compared desired desired desired receptive receptive receptive provide define define perform goal constraints motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor discrete equal mit larger fields fields fields train morgan consists consists internal internal internal internal internal internal internal internal internal advances sequences sequences sequences sequences ai maps maps considered computing equivalent directly trajectory trajectory trajectory san full full choice significant significant significant approximate statistics statistics give con produce produce produce weighted randomly developed developed controller types biological biological biological achieved measured discussion discussion complete stable predictions predictions generate generate hypothesis hypothesis sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory kaufmann pairs smaller underlying reduced reduced reduced reduced account unknown unknown coefficients coefficients coefficients coefficients interesting ratio character projection projection increasing increasing special trials squared representing numbers numbers direct window window bottom combined combined minimize produced produced produced choose description takes takes takes movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement apply apply varying compare previously previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised approximately smooth smooth smooth smooth converge converge trans diagonal diagonal positions positions generalized exists horizontal horizontal horizontal horizontal concept concept concept concept extended wide alternative move touretzky loop loop demonstrate flow conclusion hebbian trajectories trajectories trajectories trajectories trajectories trajectories segment operator depend accurate designed designed practice constrained mateo propose propose taking strong reduction reduction variety exist exist movements movements movements movements movements movements movements movements movements configuration force force force pro derive produces produces produces written written sequential laboratory vertical vertical vertical segments linearly infinite infinite infinite dimensionality involves slightly equilibrium equilibrium equilibrium formed blocks letters letters letters stationary overlap interpretation detailed decomposition decomposition decomposition decomposition decomposition allowed diagram combining iterative iterative closed generation generation generation intermediate intermediate intermediate intermediate intermediate handwritten combinations combinations combinations inter extension prove compression compression compression letter encoded paths modes computations identity identity identity orthogonal orthogonal orthogonal neuroscience sampled sampled sampled write computes principles principles consisted extend extend minimized minimized minimized stimulation stimulation stimulation command command command command investigate examine successive giving possibility variability encode illustrate singular singular singular singular singular singular mapped shapes shapes consist explain attempts plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant interneurons considerable drive perspective producing forces projected projected demonstrates raw argument behaviors reflect double recordings ity commands commands commands synthesis pasadena asymmetric chose deviations instantaneous person accomplished discovery encoder discover discover primitive primitive handwriting handwriting handwriting handwriting transforms sanger sanger sanger sanger sanger sanger sanger sanger sanger sanger guide optimally alphabet planar corre pat intended intended multiplied modelled discovered pen pen pen pen pen pen pen mind compressed workspace workspace suboptimal theorems theorems spinal spinal spinal spinal spinal illustration leg leg leg community interneuron goals neurophysiological neurophysiological neurophysiological cartesian spanned investigations nal mini tonic covers dim dim primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives autocorrelation autocorrelation jet invertible terns adaptively accomplish drawing cord cord cord cord propulsion strokes strokes linearized resultant electrophysiological meant correlates eigenfunctions eigenfunctions frog frog frog frog frog frog frog frog aimed mussa ivaldi endpoint ily converting psy grove reproduction behav descriptive linearization linearization debate bizzi bizzi plete tives oak assures troller yll ior mized phi duction linearizing chophysical rti rts unexplained terence terence terence terence terence spond recombined 
#@Sanger_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output system system system system system system system system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state state state state state state state state state state state state state state results results results information information information problem problem problem problem problem problem problem models models based based weights linear linear linear case case case case vector order shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems parameters parameters noise noise noise noise weight weight functions functions functions functions functions approach approach approach approach approach pattern pattern pattern pattern control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control patterns patterns class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal simple simple paper paper work methods field features process process process trained trained trained trained trained trained trained trained problems problems problems problems high memory response similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show equation equation equation equation section section section section section fixed fixed fixed fixed fixed fixed fixed fixed line line line line line line line line line line line line line line line line line parameter real real states states states states theory theory theory theory theory gradient gradient gradient obtained obtained obtained obtained obtained activity result result result result result result result result result computation computation defined dynamics constant terms node node direction presented presented presented present present phase nodes sets learn components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample abstract applied applied applied back back back back back back back references due due ieee procedure important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive context introduction introduction dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference difference variable center previous good good good long equations equations make region proposed errors errors errors errors forward forward forward forward forward forward forward forward forward 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samples samples compared compared compared desired desired series provide proc perform gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain discrete update train words internal internal individual represents represents bias bias bias delay delay delay scheme addition considered computing equivalent equivalent additional additional san stage stage conference significant approximate approximate approximate approximate give con produce derived randomly controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller backpropagation backpropagation backpropagation backpropagation associative achieved achieved increases describe arbitrary arbitrary denote tested inverse assumption surface surface surface surface surface surface surface surface surface surface surface surface surface generate role theoretical main adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation ability ability ability ability ability ability degree makes smaller needed needed combination combination dynamical coefficients testing testing significantly significantly structures principle leads details international combined combined combined combined added added added architectures architectures architectures recent apply introduced include engineering varying compare compare compare conventional conventional conventional axis axis axis smooth studies achieve trans exists expression alternative alternative feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed demonstrate reduce accurate accurate accurate designed clear sutton learns presence physics external external external external external external external external external external external characteristics solid solid solid solid solid plane identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification denoted denoted reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference plot describes describes laboratory stability integrated integrated integrated integrated integrated integrated integrated integrated integrated integrated integrated integrated adding shift john national extracted expressed depending viewed controlled controlled updated completely calculation dashed dashed expansion reduces neighborhood add tracking tracking tracking tracking tracking tracking tracking tracking tracking advantages avoid includes illustrated illustrated uncertainty uncertainty discussions reason reason extra extra capable importance driven driven driven driven included included literature literature build miller receives excitation kind kind procedures link link link link link sin sin sin sin sin follow follow follow ill illustrates illustrates operating operating approximating law law employed employed unlike diego poor experience updating updating updating updating updating replaced rise rise combine referred complicated phases surfaces surfaces adapt adapt adapt adapt adapt taylor generates simplest plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant plant established established established crucial track unstable slope improves analytical correction correction nonlinearity nonlinearity sections producing division applies generic capability fed fed fed lack lack variant calculating gains gains gains gains gains controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers differs richard richard substantial kinds kinds kinds implements implements shifted shifted shifted flexibility establish plays fails consideration los los occurring krogh hertz combines paul induce scheduling thomas offers offers reveals avoiding robert robert robert robert robert unchanged liu liu liu liu liu slight largely creates rejection chapter chapter examining realize realize community compensate werbos mathematically scope noting worth emphasized slopes behaves persistent emphasis styles palmer functionality survey instability instability instability builds adaptively establishes disturbances disturbances disturbances settle ref edited edited disturbance alamos inaccurate unnecessary configured rises graphically mar psaltis psaltis traditionally accepts scheduled scheduled scheduled scheduled scheduled narendra narendra overshoot overshoot dash dash dash plants plants supplies uncertainties lacks originate subsection referring hypersurface hypersurface jacobjan parthasarathy andy hunt hunt brian brian brian brian brian anders backpropagating backpropagating backpropagating subsections ork imbedded imbedded complemented unresolved disturbed degenerates 
#@Ke_L,McVey_B,Tokar_R,
#t8
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data function function figure figure figure figure figure figure figure figure figure time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm output output output output output output output output output output output output output output number number number number number number system system system system system system system system system system system system error error error results results results results results units units units units units units units units units units units units units units units units units units units units units units units information information models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based based weights weights layer layer layer layer layer order order shown shown shown systems systems systems systems systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability unit unit unit unit recognition recognition recognition recognition approach approach pattern pattern pattern pattern pattern pattern pattern point single single single single single single single single single single single single single single single single single processing processing large large test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns inputs form form shows signal paper paper paper paper paper paper paper small small work task task task task task task methods classification level level current current current current trained trained trained trained trained trained structure random high high high high response similar representation representation architecture architecture architecture architecture architecture architecture section fixed line line line line line general speech speech speech speech real average average note note experiments experiments experiments experiments experiments university university threshold computation defined target target target target target initial constant table table table table table estimate estimate estimate estimate estimate estimate standard standard standard standard computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer connections connections connections science science prediction prediction prediction prediction prediction prediction prediction left phase activation activation activation activation activation activation frequency frequency frequency frequency frequency frequency maximum range learn learn abstract applied find likelihood likelihood references due due mixture context introduction introduction effect generated change difference variable variable measure word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word chosen chosen higher part part part previous type type type type type type type type type type type type type required required required good binary binary long represent represent tree expected expected markov make make fact techniques techniques length length length correct correct correct correct correct correct correct correct correct correct correct correct correct probabilities probabilities errors minimum resulting tasks total human human human multi multi multi performed called called called called times times times mapping potential potential potential potential potential potential potential knowledge artificial artificial artificial relative relative relative relative represented represented represented application application application application cross compute location perform perform goal goal goal goal goal connected connected distributions accuracy accuracy accuracy accuracy larger larger larger support support train train morgan proceedings report words words words words words words technique technique technique technique technique technique code code code code code individual individual individual individual advances represents connectionist connectionist connectionist connectionist connectionist connectionist final addition addition considered experiment environment directly hinton additional additional san determine determine determine efficient requires requires choice significant significant approximate speed speed speed speed speed speed speed speed speed increase increase validation produce produce produce developed developed criterion types types types types types types lines actual actual actual actual actual actual actual selected backpropagation backpropagation simply achieved achieved measured technical technical technical feedforward increases group tested tested tested tested predictions predictions predictions amount amount amount amount common common require require end ability ability ability instance future development development including including including kaufmann typically typically typically smaller smaller reduced fully fully programming significantly significantly significantly significantly ratio ratio character character york york increasing mechanism special special special trials trials trials trials database language language language squared squared representing call making making making window expert produced produced produced description description description predict predict perceptron perceptron perceptron perceptron perceptron perceptron perceptron architectures architectures architectures architectures architectures architectures architectures architectures architectures improved improved improved improve improve improve advantage separate takes takes reported reported subject subject subject trees subset recently recently recently recently sufficient highly highly compare compare previously previously previously previously subjects subjects subjects subjects subjects calculated calculated calculated match match achieve achieve sparse improvement entire entire occur suggests trial predicted predicted predicted predicted predicted predicted predicted alternative alternative alternative alternative alternative alternative correctly move half half half row reduce accurate designed faster learns mateo suggest suggest suggest suggest characteristics characteristics demonstrated solid labeled user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user decrease manner characters characters characters characters characters characters configuration question acknowledgements appears pro longer longer ways primary primary generating describes describes recall metric metric category category category category category category category remaining remaining remaining easy text text text text text text text text text text text text text text text unique integrated cycles cycles cycles letters phoneme communication communication communication evaluated evaluate activities activities suggested past key reduces tracking tracking classified classified classified david handwritten handwritten figures activations activations activations perceptrons instances illustrated automatic candidate candidate candidate candidate candidate candidate candidate candidate candidate variations variations absolute absolute tests tests determining middle efficiency efficiency efficiency efficiency computationally effectively included identify identify identify identify identify build score characteristic conf repeated repeated contained allowing heuristic device categories categories list list list involved usual generalize generalize denker thresholds automatically subsequent subsequent subsequent software situations employed employed employed collection exhibit rapidly put accurately accurately accurately accurately preliminary preliminary helpful helpful fewer fewer fewer matches matches matches matches school school rest rest mse mse mse investigated investigated investigated int ideal scaled office decisions decisions understand attributes attributes attributes attributes attributes attributes attributes attributes waibel waibel waibel adapt predicting predicting predicts front front improving years percentage percentage indicating publishers answer expensive caused stress stress purposes closer easier probable potentially english english english english english english english english attribute attribute depicted depicted author mellon mellon exemplars requiring improvements improvements improvements improvements improvements people people people people people greatly percent percent percent percent carnegie carnegie reflect collected collected collected cmu cmu spoken conducted conducted conducted conducted quantitative autonomous effort completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion frequently incorrect incorrect requirement calculating howard gains pittsburgh characterize characterize characterize extensions acoustics substantial substantial substantial sophisticated display display display display display age age age age redundancy deviations sentence displays displays naive person classifying benefit benefit identifying writing writing interface impossible lecun lecun lecun chance chance chance accepted intelligent intelligent serves exploit exploit exploit disjoint days hours hours hours hours hours continue meaningful programs programs programs programs programs displayed displayed displayed lang heart jackel propagated facilitate candidates arrangement layout layout suggesting suggesting gaze gaze informative parse parse impact papers speeds severe verify metrics usage usage usage usage parsing users listed listed accept accept accept email benefits employs encouraging year year year year utilize boser ideally possibilities possibilities letting conservative acting henderson home cessing baluja baluja baluja hubbard pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau efforts depicts names names speedup speedup speedup monitoring zip alternatives alternatives maintains suffer dictionary dictionary commercial thousands dramatic travel technologies suggestions identifies savings savings savings savings savings hundreds outperformed outperformed jain jain jain mistakes concrete rare core manually manually repetition inefficient modalities quantitatively quantitatively predictable frequent prone noun adapts twelve twelve twelve twelve twelve translates magic dean dean dean dean dean brought monitored huge huge verb simon moderately drawbacks drawbacks shikano save save entered couple week week saved package suggestion disappear prefix prefix prefix prefix prefix prefix prefix hanazawa descriptive today today fingers fingers accelerated accelerated accelerated accelerated encourages cursor apple spend spend wasted composing programmer programmer skip skip skip facto tremendous severity injury monitors suffered spelling subjectively skilled skilled strike aids rea conceivably displaying textual textual textual textual textual spending sonable sitting keys keys keys entirety entirety entirety waits adjective editing infancy aut momentarily 
#@Pomerleau_D,
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#*network network network network learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data function time time time time time time time set set set set set set set set networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number system error results results results results units units units units units units information information information information information information information information information information hidden hidden hidden performance performance performance performance based based based based based based based based based based based weights weights weights weights weights case case vector vector vector vector probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability functions unit unit unit distribution distribution distribution method method method method method method method method method method approach approach approach approach processing processing processing large local local rate test test test analysis optimal optimal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper small small small small size size size net net net net methods methods methods methods methods current current current trained trained high high high high representation representation representation representation representation show show section section fixed fixed line line line line line line line line line line line line line line line line line line vectors general general general general generalization real average average average average average theory theory obtained obtained term note note note dimensional dimensional dimensional university research research defined defined defined initial constant table table table table table table table estimate standard standard standard standard standard standard node node node node node prediction prediction left presented presented phase phase activation low low low low nodes nodes nodes nodes press learn position outputs outputs abstract applied applied back computational references component component due ieee ieee ieee procedure procedure procedure procedure procedure procedure propagation propagation introduction generated generated generated generated parallel recurrent search complexity complexity assume lower lower measure higher part center previous previous previous previous previous previous bound required good good binary binary binary binary binary long long long long long tree tree distributed expected expected expected make make make techniques techniques techniques techniques length correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed forward finite simulations ing ing regression respect sum called called factor potential potential made made applications obtain original original original relative specific true true compared application define compute proc perform experimental experimental distributions equal mit mit larger larger contrast nets nets nets nets proceedings report loss loss implementation version technique technique internal code code code code code code code code code code code code code code addition computing equivalent environment hinton additional upper requires requires free speed basic basic basic basic pages pages increase con con coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding conditional conditional conditional conditional conditional conditional conditional conditional developed path provided provided nature depends discussion technical technical tested fast limited close inverse inverse short short short short short implemented generate generate require main instance makes makes rumelhart including typically smaller account account account unknown unknown unknown unknown ratio ratio ratio ratio ratio ratio ratio ratio character character character character character character character character character character character character character character york special special special special details numbers window window bits bits magnitude idea idea attention minimize sources denotes improved improved improve directions exact strategy machines sense sufficient highly highly varying compare previously previously conventional conventional conventional conventional volume works works tions match achieve achieve achieve modified interval interval interval interval interval interval interval williams storage expression lead predicted predicted predicted alternative correctly hardware hardware hardware starting starting starting minimal minimal operator encoding encoding demonstrated labeled labeled turn turn assuming start characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters base acknowledgements construct produces written sequential sequential slightly text text text text text text text predictive predictive predictive predictive predictive predictive predictive quality implies expectation letters letters depending codes codes codes codes approximations sizes digits updates earlier slow normalization normalization boundaries boundaries boundaries remains sufficiently transactions transactions transactions david expect thesis combinations combinations sciences reason compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression encoded encoded encoded encoded encoded symbols mackay essentially receives decoding decoding dis content content content sci built built comp predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor chips attempt consisted consisted consisted operating software employed wiley essential limitations fashion ideas behavioral incremental terminal terminal terminal terminal terminal terminal root comparable encode adapt necessarily integer extremely created changed obvious precise precise logic message message message message message phd electronic neal theoretic theoretic guaranteed worse straight tive purposes widely mation universal beginning beginning optimize lowest addressed greatly capability fed fed orders slower variant variant variant variant variant rely branch branch achieves germany kinds inherent sophisticated sophisticated windows windows windows arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic lot lot benefit proportion proportion proportion modify extensive martin acm ratios ratios ratios ratios ratios ratios pick approximates repre grows grows lecun children communications dealing ments promising promising promising accepted tools tools proceeds held receiver receiver receiver receiver alphabet alphabet infor repeat evaluations excellent excellent excellent excellent sion sion predictors predictors equals guarantees lengths infinity entries specialized sons sons sons considerations messages variants variants variants variants variants variants statement alternatively alternatively default default default default limitation sequentially sequentially outperforms compressed compressed compressed compressed compressed outperform ties ties encodes encodes uniquely incrementally feeding feeding retraining copy weiss german german german german german reconstruct unseen unseen publication care schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber gained management werbos continues file file file file file file file file file file file disadvantage disadvantage paris harder universit son son sweeps commercial coming copies sees sees consuming ongoing ongoing powers powers lists outperformed char harvard tribution inefficient receivers informatik protocol protocol remained files files files files files files files files parker insert decode decode decode technische inserted simula elegant newly sentations predic excluded frozen fiir compress compress compress compress compress compress compress compress strongest retrained begun occupied miinchen unix unix unix unix unix unix unix unix unix functioning prefix bytes economics nected stefan stefan stefan stefan stefan exceeding comparatively comparatively comparatively comparatively articles articles articles articles articles articles articles articles articles concatenation proximate dure paragraph sender sender sender sender probabili probabili recommended restore cod cod pression installed unpredictable gerhard emits emits taining pack pack pack pack jiirgen jiirgen jiirgen outlook fakult competitor erage newspaper newspaper newspaper newspaper newspaper une promises binations acters conveying apprentissage compres compres decodes asym prohibits cognitiva decod 
#@Heil_S,Schmidhuber_J,
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#*network network network network network network network network learning model neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training output output output output output output output output output number number number number number number number number system error error hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based weights weights weights linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector order shown shown shown shown values values probability probability probability probability probability parameters weight functions unit unit distribution approach approach approach approach approach approach pattern pattern pattern pattern single single single single single single single large large test test test patterns analysis inputs inputs inputs inputs inputs shows shows shows shows shows shows algorithms simple simple simple paper small small small size feature feature feature feature feature net work work cells step points points points points points features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification classification current trained trained trained trained trained trained trained trained trained random random high high high similar similar similar similar architecture show average average average average average average states states gradient gradient obtained obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments experiments experiments threshold research independent found initial initial table estimate estimate estimate standard node prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left low nodes nodes nodes nodes nodes nodes nodes nodes nodes machine sets sets sets sets sets sets sets maximum maximum range range position outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous abstract applied applied likelihood likelihood component component stochastic stochastic due due important important important important decision introduction introduction complex statistical statistical statistical effect generated generated variance cost cost cost cost cost classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower lower lower lower lower lower lower lower lower measure higher previous previous type type required good good good good good binary binary represent represent represent bayesian bayesian expected probabilities forward forward ing total regression regression regression regression regression regression regression regression regression regression regression performed performed performed performed performed times mapping potential made study study policy original vol vol vol vol vol samples samples true true true true true desired cross cross cross provide provide provide provide related posterior equal approaches approaches approaches mit steps accuracy accuracy accuracy accuracy larger train train descent descent modeling selection department implementation individual individual individual individual individual difficult difficult computing equivalent curve curves curves curves curves curves estimates limit limit top stage stage stage determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper upper upper upper upper upper upper significant significant approximate statistics estimated increase increase increase developed developed levels levels criterion bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds area area area area types entropy entropy entropy actual actual provided provided provided provided provided provided provided provided provided selected selected selected selected selected selected sampling sampling sampling sampling sampling measured increases limited limited close close predictions predictions predictions predictions predictions predictions amount common implemented implemented generate journal square square future makes makes smaller smaller reduced mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp block block york database operation operation operation squared squared numbers pre pre pre normalized early early early decay produced produced produced added added predict predict predict predict predict predict perceptron improved improved improved improved improved recent recent apply identical side side subset subset interest interest varying varying compare conventional conventional subjects calculated studies separation interval risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk deviation predicted feed feed occurs column column column column half half starting critical valued interactions differences differences sigmoid sigmoid measures measures accurate accurate accurate characteristics sigmoidal demonstrated regularization regularization regularization force base base denoted areas areas areas areas areas areas areas areas pro pro produces produces factors generating generating estimating describes laboratory laboratory laboratory mathematical confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence implement missing missing missing missing missing sensitivity multilayer multilayer multilayer averaging averaging slightly slightly slightly interaction predictive predictive quality versus select select national expressed expressed stages stages stages stages stages squares squares squares squares evaluated evaluated evaluated evaluated evaluated evaluated evaluated open open operations operations operations operations operations operations operations operations organizing fraction fraction lee understanding diagram diagram epochs epochs epochs epochs fitting intervals intervals intervals intervals intervals intervals intervals intervals intervals roughly roughly add false false iterative assigned query advantages views david david david david david batch sciences tests tests determining selecting middle extra extra society society computationally divided included committee committee committee committee detect post post post post post comparing characteristic summary refer graphs procedures procedures procedures allowing allowing stopping stopping stopping stopping stopping stopping issue classify categories categories simplified simplified highest highest highest predictor received operating software software presents bars bars explore explore simpler create experience experience varied varied replaced accurately accurately lippmann lippmann lippmann lippmann lippmann lippmann hall history history history history history history history history history tech authors variability variability variability affect statistically momentum neu predicting predicting predicting predicting predicting predicting predicting predicting created created created created adjusted assumes logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic multivariate percentage percentage percentage percentage percentage percentage ment developing failure failure failure failure failure failure failure expensive nonlinearity comparisons obs preprocessing division immediately immediately medical medical medical medical medical medical lowest raw raw varies varies populations reflect substantially led led bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap fed fed fed maintain singer richard richard richard richard richard replace age age patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients median cumulative irrelevant count bin bin bin bin bin bin bin flexibility outcome air resulted keeping obtaining ral settings settings settings receiver guide exploring analyses weakly loo loo loo sion patient patient patient patient patient patient patient patient patient patient patient patient patient patient patient patient patient patient iteratively male schwartz reproduce reproduce reproduce dif mlps mlps mlps mlps mlps mem bins bins record specificity automated robert street ence roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc blood drop annals annals accept incrementally tween tibshirani female auxiliary auxiliary assess assess clas clas care stroke stroke stroke stroke stroke stroke stroke chapman proach pos pos disease outcomes sam placing nal treating status replacement sorting tom assistance ferent lists resampling seattle assessment alarms alarms offsets ray ray clark positives strokes evolving fol binomial binomial experienced experienced est ranged ranged fication categorical categorical categorical categorical outlier united united ated indi health replicate replicate hits explaining replaces amer sponsored stepsize stepsize progresses cations assessing lincoln lincoln lincoln omit omit omit marshall marshall plotting plans complications complications complications complications complications complications complications complications complications complications complications complications complications complications complications complications complications complications ver edwards sible billion chi chi lowing cardiac cardiac univariate sults bradley plex bypass bypass bypass bypass bypass bypass bypass bypass bypass bypass bypass bypass bypass jour fifty acknowledgment efron efron efron govern proaches nique official cate ations cre complication complication complication complication complication complication complication complication ventricular wood death death higgins higgins structurally siftcation replications percentages percentages percentages pling pump bers mono suspect lexington surgery surgery surgery surgery surgery surgery surgery surgery bibliography perfusion perfusion ern rior ass poste logit validating packed hospital hospital bot alp sifters chronic risks vided vided contingency spending wards ren reweighted devi procedural operative operative ican 
#@Kukolich_L,Lippmann_R,Shahian_D,
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#*network network network network network network network network network network network learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data function time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training number system system system system system system system system system error results results information information information models models models models models models models models models models models models models models models models models models models models models based based based based based linear linear linear linear linear linear linear linear order probability approach approach point image image processing test patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class paper paper paper paper paper size size size net work methods features classification classification classification classification classification problems response response show approximation states gradient gradient gradient gradient university variables variables variables variables variables research research independent table table computer terms terms node node science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction nodes nodes nodes nodes nodes maximum components components components continuous continuous sample abstract computational analog likelihood references component component due adaptive introduction action complex complex statistical statistical statistical statistical statistical variance variable variable measure measure cases cases cases cases cases required good binary binary spike tree tree tree expected correlation correlation correlation regression regression regression regression regression regression regression regression regression regression performed performed means potential artificial artificial artificial artificial artificial artificial artificial artificial relative specific specific specific true true compared compared cross provide perform accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy descent descent descent descent department department department technique individual joint addition graph computing curve curve curve curve curve stage stage stage stage stage detection determine determine significant increase validation randomly area area area area area area area types types types selected selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration iteration discussion tested tested fast close stable predictions effective square end future development including including objective objective objective probabilistic probabilistic probabilistic probabilistic probabilistic interesting testing testing testing significantly york york york mechanism language principal principal principal principal pre early added predict perceptron improved improve improve reported practical apply include trees trees trees compare compare previously conventional studies rl evaluation generalized generalized improvement storage lead scaling scaling extended predicted predicted generally demonstrate demonstrate critical assumptions reduce interactions interactions interactions measures accurate accurate accurate accurate accurate reduction intelligence assuming manner connectivity areas areas factors factors factors factors factors factors factors factors factors factors factors ann ann ann ann ann ann modeled missing multilayer multilayer interaction predictive predictive predictive predictive springer stages interpretation restricted fraction lee discrimination discrimination eeg david david david avoid combinations priori perceptrons dominance sciences phys reason determining identified computationally divided included included committee literature comparing comparing characteristic characteristic characteristic characteristic characteristic characteristic traditional traditional verlag lie follow follow follow criteria hold minimizes predictor predictor predictor attempt operating operating operating operating operating operating powerful american american collection requirements school relationships math predicting predicting predicting spline subsets friedman der logistic logistic logistic logistic logistic logistic logistic logistic art integrate years years cart cart cart cart cascade cascade cascade tive mation grossberg medical medical medical bandwidth meaning conjugate conjugate conjugate fuzzy fuzzy fuzzy fuzzy collected collected splines splines employ rely measuring chose age age patients patients patients patients diagnosis diagnosis diagnosis college college college gabor gabor linearity discovery outcome outcome outcome outcome breiman breiman stated intelligent receiver receiver receiver receiver receiver receiver enhanced nonparametric date infor published analyses analyses analyses becker sion predictors patient patient patient patient patient patient patient pruned pruned pruned cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer refers specificity relies relies fold automated vari vari resonance neurophysiology roc anns anns outperform outperform goodman goodman goodman asked asked employs pointed year year year year year year year comparative hundred jabri jabri assess representa summarizes care faults distant disadvantage cole categorization disease outcomes outcomes confusion meet cubic cubic cubic intensive october examination clinical clinical clinical clinical breast breast breast breast breast breast breast breast breast breast breast breast breast breast breast breast agents medicine medicine medicine medicine medicine seattle contrasts alarms goldberg goldberg orr goodness differentiate modern request carpenter carpenter united manual manual putative putative tory simon drawbacks drug survival survival survival survival survival survival survival survival accuracies ables ables putting assoc psych neurology philadelphia clin rosen rosen rosen rosen thirty specifications med pal brooks grove condensation olshen leong leong wadsworth articles stepwise stepwise regres diction death kohn prog requested survive iia kennedy crease harry harry harry assisted radiology radiology radiology specht specht acute ordinal pacific tachycardia ultra philip philip philip nonmonotonic pace tumor tumor tumor tumor termined hospital princi coleman proliferation psychiatry accom matic labora curate commission nail trapezoidal institution 
#@Burke_H,Goodman_P,Rosen_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time set set set networks networks networks networks training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output number number number number number number system system state results results results results results units units units units units units information information information information information information problem problem problem models hidden hidden hidden hidden performance performance performance performance based based based based based based based based based based based based based based based based based based weights linear case case vector order order order order systems systems systems systems values values values values values values values values values values values values values values probability parameters parameters weight weight weight functions functions functions functions functions functions functions functions functions functions method approach approach approach approach approach approach approach approach approach approach approach processing processing processing processing control large large large large local rate rate patterns optimal shows shows algorithms paper paper paper paper paper examples examples examples examples small small feature feature feature feature feature feature net work methods methods methods methods methods methods methods fig fig fig step points points features features features features features features features features process process process level level level level level level level current current current trained trained trained trained trained trained trained trained problems random random high high similar representation representation representation architecture architecture architecture show equation equation equation section section rule rule rule rule generalization generalization parameter parameter parameter approximation approximation approximation approximation obtained obtained term experiments dimensional result university university university university research research found found found sequence target target target target target target target target target target target target initial constant constant constant table table table table estimate computer computer computer computer terms terms science science science prediction left presented present present temporal temporal temporal temporal temporal temporal temporal machine machine machine machine machine machine machine machine press learn learn learn learn learn learn position position position abstract applied applied applied applied back back back back back find references component due positive procedure important important important important adaptive propagation propagation propagation propagation propagation context context context introduction complex complex complex hand hand hand statistical statistical effect dynamic generated cost search search search search search search search search search search search search search search difference difference difference difference difference variable assume rules prior prior representations representations representations learned learned learned learned learned learned chosen center center center center bound cases good good good good good expected expected techniques correlation simulations total human performed eq eq eq eq eq eq eq eq eq eq called called called called times reinforcement factor factor factor potential study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge original artificial artificial artificial artificial artificial relative specific specific specific represented represented represented represented application provide compute determined goal related related constraints power approaches approaches approaches approaches approaches approaches approaches approaches approaches mit steps comparison comparison update morgan morgan morgan morgan morgan morgan proceedings proceedings proceedings report report department loss loss loss loss implementation version version version version version technique individual advances advances advances advances connectionist final final final final final final final final final final final final final final final final bias addition addition ai maps maps considered considered computing computing domain domain domain domain domain domain domain domain domain domain domain domain view view design design san san san san san san conference determine requires choice basic pages pages pages pages produce produce robot criterion criterion actual provided finally processes selected nature sampling sampling sampling sampling sampling sampling sampling discussion technical technical arbitrary arbitrary denote fast limited close complete complete amount short short short common shape generate generate generate require require main journal end end end vlsi hypothesis development fit fit kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann needed unknown technology programming interesting testing mechanism mechanism database database database database database leads leads representing numbers max stored international international depth depth depth depth expert expert expert expert expert expert early early magnitude minimize produced description predict predict recent recent correlations advantage advantage separate takes takes typical reported reported practical practical strategy strategy side side sejnowski recently relevant previously previously approximately approximately approximately works works tuning smooth studies definition evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation chain bounded entire entire increased increased constructed expression extended derivative predicted alternative move move move move move move move move move touretzky touretzky white white white white white generally setting half half critical editors editors editors editors central tangent tangent differences measures designed designed sutton moody practice weak weak weak learns learns learns learns learns learns learns mateo mateo mateo mateo mateo mechanisms california intelligence intelligence selective min iii targets derivatives program program program denoted suppose relation derive longer sequential describes simultaneously simultaneously infinite easy develop develop quality versus john family learner learner learner influence open open evaluate evaluate evaluate updated forms approximated completely completely reasonable fitting fitting intervals event intermediate sufficiently faces building thesis thesis combinations assignment automatic discuss mozer specifically black black black black partially successfully successfully successfully major major planning planning reason regular determining middle importance importance importance successful successful situation notice notice success success interested interpreted dis list sampled michael play play play play play play play play play play play play play play play play play play play play play play play play dayan generalize generalize board board board board board board board board board board board board board board board board board board board board board board board board giles delayed denker moves moves moves moves moves moves moves moves moves illustrates illustrates illustrates illustrates illustrates approximating software tesauro tesauro tesauro tesauro tesauro cowan presents presents presents presents employed employed employed employed employed unlike diego poor poor poor poor essential experience exponentially strengths strengths strengths hanson hanson optimized accurately accurately accurately game game game game game game game game game game game game game game game game game game game game issues issues issues issues issues lippmann biases school school links ideal analytically dependencies symbolic symbolic workshop fundamental editor predicts illustrate illustrate versions obvious mapped expressions utility phd phd attempts ment smoothness track slope slope slope slope explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation explanation majority briefly benchmark tool worse reasons perspective formalism ring cut simard recognized describing beginning depicted depicted depicted author incomplete mellon sun raw apparent prop prop evaluating carnegie items empirically pure elman relevance relevance cmu amounts experimentally poorly orders employ employ frequently frequently frequently frequently variant variant compares rely rely measuring pittsburgh weigend extracting extensions prevent richard sums germany differentiable trade trade trade contribute bellman bellman bellman bellman leen assign princeton princeton acts dynamically purely purely discover smolensky lecun outcome outcome outcome outcome outcome outcome outcome outcome outcome establish plays plays plays plays generality fails fits adds murray promising overcome mail keeping transforms analyzing analyzing observing fail settings canonical responsible days games games games games games games games games games games games games games games games games games games games games games games games games evaluations excellent excellent programs programs programs programs paul schwartz uni thomas offers reproduce winning winning winning master master master master augmented late rich draw draw horizon relies erlbaum eqs inductive inductive inductive inductive inductive captures captures generalizing generalizing material material material material material adopted skills speaking summer sch sch thrun thrun thrun thrun thrun thrun thrun listed basically discount discount discount recursively recursively job presenting employs failed discriminative solely solely reports german descriptions experiences workstation hillsdale chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess chess backgammon backgammon invariances care ibm decays guidance playing playing playing mitchell mitchell mitchell mitchell carefully carefully challenging terrence careful differentiation player win win harder constructs constructs selectively importantly importantly associates refinement outcomes outcomes universit suffer exchange gordon slopes slopes slopes slopes slopes slopes slopes intensive rewritten learners gratefully reinforce expense tom tom tom tom heavily ongoing hundreds firstly wins king king king king opponent opponent loosely integrates integrates rare engine engine boyan assessment detects ultimate exploits suffice drastically safe amplified informatik goodness goodness experienced players players players server server acknowledges gammon gammon gammon bonn bonn bonn inaccurate surprise tenth excessive huge decades propagates explaining favors schraudolph searched sparc campbell unifying sebastian sebastian sebastian sebastian sebastian sebastian sebastian sebastian erroneous save sixth won availability ele pay quiescent evaluates comprises yann vast biasing mate rightmost suggestion unclear samuel samuel knight knight knight knight knight knight knight boards boards boards boards boards boards boards boards boards boards boards boards boards boards boards boards earliest workstations workstations workstations workstations completes correspondingly beat prototypical enormous gerald gerald shortcomings embodied weeks today acknowledgment ranks opening raymond chine weaknesses weaknesses attack mooney safely patrice hurt asynchronously buffers keller victorri disappears loses queen queen queen queen queen queen queen queen queen queen queen queen queen karlsruhe restarts utgoff guiding coordinated hardness loose hans hans lambda invest differencing grand grand grand grand ala discounting discounting discounting discounting danger carl testbed sacrifice violates analyzes 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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure time time time time set set set set set set set set set networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number system system system system system system system system system system system system system results results units information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models performance based based based based based based based space linear case case case case case case case case case vector order shown systems systems systems systems systems systems systems systems systems systems values values values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters functions functions functions unit unit distribution distribution distribution distribution distribution distribution method method approach approach approach point point point point point processing processing processing large large local rate rate test test patterns analysis analysis matrix matrix optimal inputs form form form form form form form algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples size feature work work work work work methods methods methods step step step step step step step step step step step step points field classification classification classification classification classification process process process current current trained problems similar equation equation fixed line line rule rule vectors general general parameter parameter theory theory theory gradient obtained obtained obtained dimensional result university university university university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation solution solution solution research independent independent log log log log defined found found found found sequence initial table table estimate estimate standard standard computer computer node science science presented present phase phase phase phase machine machine machine machine machine machine machine machine machine maximum maximum maximum maximum maximum maximum maximum press components components components components components components basis basis basis continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract find find computational convergence convergence convergence density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component due important important important important important decision decision decision decision decision decision decision decision mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction complex hand estimation estimation estimation behavior statistical statistical generated generated generated generated generated generated generated generated variance variance variance variance variance parallel cost cost cost search tion change variable variable variable variable rules measure prior learned chosen part previous cases cases type type good good good binary tree tree distributed bayesian expected expected expected expected expected expected expected equations equations make make make correct correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed observed errors errors resulting total total human regression regression regression regression computed computed computed sum sum performed performed performed means means reinforcement factor made applications applications applications knowledge knowledge knowledge em em em em em em em em em em em em obtain vol vol vol artificial artificial relative specific compared series compute active determined determined determined determined determined experimental goal goal distributions distributions approaches steps steps steps steps steps comparison update update support descent morgan morgan morgan morgan institute institute version internal internal advances advances advances joint joint joint joint difficult exp exp addition domain domain domain directly additional additional solutions estimates estimates san san san san san determine full statistics vision estimated estimated estimated estimated derived conditional conditional conditional conditional clustering developed types types types types entropy entropy entropy entropy entropy entropy entropy entropy provided selected iteration biological achieved covariance covariance normal feedforward tested tested fast corresponds complete complete common assumed assumed generate main adaptation journal journal future future kaufmann kaufmann kaufmann kaufmann probabilistic probabilistic probabilistic probabilistic typically underlying needed needed reduced unknown unknown unknown unknown jordan jordan jordan jordan jordan interesting york database database database database database database database principle principle principle details numbers numbers iterations max making experts supervised expert expert expert expert expert early early idea idea combined minimize choose choose added description description description exact pair reported introduced subject machines side trees trees inference inference inference sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski engineering dimensions dimensions varying varying previously observations observations observations observations approximately axis tions tions solve solve solve studies diagonal diagonal diagonal mixtures mixtures mixtures mixtures mixtures chain symmetric observation observation interval interval sensitive increased exists lead concept occur deviation alternative alternative correctly generally generally conclusion conclusion starting starting minimal assumptions assumptions segment conclusions conclusions valued competitive bayes peak exponential practice practice constrained mateo mateo mateo mateo strong strong hard hard hard presence largest california california intelligence radial radial radial radial user user exist decrease introduce question question question question question denoted denoted acknowledgements written ways sequential laboratory modeled missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing multilayer remaining easy easy gaussians quality expectation expectation expectation expectation expectation expectation select decreases independently formation dependence squares evaluated evaluate evaluate evaluate approximations soft completely suggested suggested earlier fitting fitting add iterative closed initially initially initially calculate construction foundation query avoid existing thesis priori perceptrons batch maximize maximize tests tests tests tests major reason society build miller miller traditional road repeated repeated induced induced interpreted classify built built built involved involved simplified simplified dayan absence absence reach maximization minimized remain diego parametric powerful experience exponentially exponentially helpful fewer history school tech rest rest project incremental investigated fault ideal analytically dependencies complicated phases induction plausible man changed aspect fisher shapes utility utility utility utility utility utility utility utility phd finds attempts years stop guaranteed growing fairly slope slope coded coded coded coded coded analytic explanation nowlan nowlan nowlan answer answer answer expensive independence independence tractable handle handle handle handle considerable choices desirable arise medical medical medical medical medical medical computers incomplete incomplete mellon questions questions questions questions carnegie tional peter effort introducing formulated formulated formulated formulated rep prototypes pittsburgh spread maximizes proven comments age age age shaped patients deviations diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis irrelevant realized naive initialization ghahramani ghahramani ghahramani ghahramani ghahramani tresp tresp tresp benefit identifying intractable intractable princeton princeton conditioned conditioned databases databases databases databases grows royal outcome outcome outcome intelligent neurobiology reasoning reasoning salk salk north adequate continue games male von von heart heart heart heart heart heart heart heart heart heart heart bases bases iterated foundations occlusion surprisingly indicator indicator ahead ahead record jolla dempster dempster dempster dempster dempster dempster influences automated automated pressure unchanged blood blood logarithm rubin piece misclassification solves session ahmad ahmad ahmad maximized asked incrementally pointed multinomial flat female resting resting possibilities possibilities england certainty avoided avoided adjustment principled principled cohn cohn gained num distribu terrence terrence terrence terrence terrence acquired pearl pearl disease disease disease disease disease disease disease disease disease disease disease disease quinlan quinlan laird outcomes outcomes outcomes outcomes tij refined intensive signs examination clinical handled picking rarely simplification simplification simplification consuming consuming reversible fill fill incorrectly medicine medicine medicine medicine condi diagnostic manipulated manually economic explanations repository presently binomial irvine irvine nominal nominal benign request assessed assessed clues cleveland cleveland cleveland manual sex sex col unnecessary refine unobserved derivations disorder newly utilities utilities utilities disorders disorders disorders disorders disorders disorders disorders disorders disorders disorders entered biomedical acceptance helped acknowledged myers heckerman heckerman heckerman radially zij zij vation exercise exercise exercise differentiated accompanying attain pain pain diseases diseases diseases dsi specialize complication marcel dekker traversing unconditional obser formalize lengthy observa investigators torrey pines labor leftmost symptoms symptoms symptoms defect recommended inconsistencies factoring inevitable acute dangerous originates prospects motivations mclachlan mclachlan alleviate automate automate diagnoses diagnoses decisive bination maker basford basford thirteen thirteen oval cholesterol magnus magnus magnus magnus magnus magnus reused annotated iwi procedural assessments oix recommend calcula conclusive erry inconclusive 
#@Sejnowski_T,Stensmo_M,
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#*learning learning learning learning learning learning learning model model model model model model model model model model data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure time time time set set set set set set set set set training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number system error results results results results problem problem problem problem problem problem problem problem problem problem problem models models models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance space space case order order order shown shown shown shown shown shown systems values values values probability probability probability probability probability probability probability probability probability probability parameters parameters parameters noise noise weight recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image single processing large large local local local rate rate rate rate test patterns patterns analysis analysis analysis analysis analysis analysis class class shows shows algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian visual paper paper paper paper paper examples examples small small small small small size feature work work work work work task task methods step step step field features features classification process current high show equation equation section line rule images images images images images images images images images images images images images general parameter average theory research research defined initial constant table table table table table table estimate estimate standard standard standard computer computer computer computer terms terms terms terms terms terms terms terms science science present present low machine object maximum maximum maximum maximum press press press basis abstract abstract applied back find computational convergence likelihood likelihood likelihood likelihood likelihood references references due ieee ieee procedure procedure procedure procedure procedure procedure procedure procedure mixture context introduction estimation estimation statistical variable variable variable spatial spatial assume classifier part previous previous type type type type type type type type type type type type type type type type type type type type type type type type type type type type multiple multiple multiple binary bayesian bayesian expected equations fact region proposed correlation correlation probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed observed scale total total total human human human human human human times times elements regions regions regions made natural applications applications knowledge knowledge em em em em em em em em em em obtain original vol vol vol vol relative relative relative specific true true true true true compared application application application application cross provide provide objects rates rates location experimental related posterior posterior posterior posterior posterior posterior posterior distributions mit mit steps accuracy train train modeling proceedings proceedings institute institute department technique consists individual individual advances represents bias scheme maps cambridge experiment curve curve estimates estimates estimates estimates estimates detection detection detection detection detection detection detection detection detection detection detection conference conference full full significant significant significant significant significant significant statistics statistics vision vision estimated estimated estimated estimated validation produce produce produce derived derived derived weighted weighted conditional conditional clustering developed types types types types provided provided provided provided evidence nature simply describe group denote limited assumption complete surface surface surface amount supported theoretical require eds eds eds journal square square square pixel pixel ability easily noisy noisy noisy objective probabilistic probabilistic probabilistic probabilistic probabilistic typically underlying account technology technology technology special database database empirical mode leads details details normalized experts experts experts experts experts experts supervised expert expert expert combined combined choose discussed recent resolution pair takes typical typical practical apply apply apply introduced machines engineering engineering interest interest interest interest teacher axis axis axis correspond correspond correspond correspond correspond studies diagonal address background background evaluation evaluation modified sensitive grant exists lead matrices matrices generally conclusion critical place greater assumptions central bayes suggest taking presence characteristics characteristics california california turn assuming assuming assuming manner acknowledgements reference reference reference perception ways estimating laboratory laboratory label label label label label label label label label label label label label label label label label label label label label label label confidence averaging electrical consisting expectation expectation expectation versus national independently independently focus focus expressed expressed depending interpretation evaluated evaluate operations labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels normalization combining combining event purpose false false false false false false false remains remains filtering calculate visible visible visible visible visible visible assigned extension extension uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty discuss discuss discuss maximize absolute phys discussions simplicity straightforward straightforward identified society differ latent latent detect literature projections comparing comparing comparing plots characteristic prob issue issue issue contribution follow criteria categories list list involved michael michael michael michael michael absence realistic maximization maximization operating modelling situations presents body carried carried carried carried collection experience humans humans estimators hanson accurately issues graphical examine examine fashion detectors detectors biol reliable working variability scores topographic fundamental notion matched patch man man analyze equally aspect front obvious noted algo synthetic years advanced ground ground ground ground ground ground ground ground ground ground ground trivial agreement publishers slope biology majority capabilities capabilities independence considerable considerable drive drive rapid perspective strictly division located scientific medical medical medical medical patches argument apparent collected collected items dark lack quantitative poorly detecting reliability reliability ity requirement characterize pasadena pasadena pasadena marginal age diagnosis diagnosis sensing sensing sensing primarily databases databases labelled labelled labelled labelled labelled circular discovery discovery caltech caltech caltech smith dealing imaging minutes determination los contract abilities abilities resulted resulted viewpoint viewpoint scoring methodology receiver north modifications carry hours repeat ambiguity mouse loo loo holland belongs counting originally diameter treatment april infer infer infer infer insight bins bins kearns observer concentration baldi baldi baldi baldi automated automated outlined treat radar radar radar radar appeared roc roc roc roc roc outline visually visually inferred opposed transmitted ical conservative conservative remote remote remote quantized intuition gener proba smyth smyth smyth smyth smyth smyth smyth smyth smyth investigating topic worth voting alarm alarm alarm alarm truth truth truth truth truth truth truth truth truth truth truth truth truth elsevier knowing indication nil ignoring aaai challenge november factored survey algorithmic algorithmic handling ate bility jet jet jet subjective subjective subjective subjective subjective subjective subjective subjective subjective subjective subjective subjective subjective subjective subjective subjective austin locate lists lists hour svd svd svd svd unreliable alarms alarms alarms vote automation manually labelling labelling labelling labelling labelling labelling labelling labelling labelling labelling labelling labelling labelling inferring inferring inferring inferring inferring inferring inferring propulsion propulsion propulsion ref positives rating screen arpa ignores rivest statist accounting accounting accounting gathered aperture modern inaccurate counted scattered manual tory probabil opinion detections detections amer degrades clutter severely collecting locating bright assoc buntine tll tll supervision ages sky consensus consensus scored scored aware cent aggressive elicited imagery med med ratings pierre pierre pierre pierre pierre grove grove wishes french french eval spacecraft earth earth administration uncertainties roi roi roi roi roi roi roi shapiro probabilistically quantifying flamework scientists scientists scientists scientists scientists scientists scientists scientists oak oak signifi alamitos twofold twofold kin pit pit optimistic optimistic photographs sar sar sar cvpr scientist scientist scientist scientist scientist scientist scientist scientist scientist scientist scientist fayyad fayyad fayyad fayyad fayyad fayyad fayyad fayyad fayyad perona perona perona perona perona perona perona perona erence hunt llt llt llt llt llt llt distinguishable diagnoses depicting appropri origins aero moon lugosi lugosi bernardo calibrating ett padhraic padhraic padhraic padhraic padhraic dawid dawid labora uated opinions opinions nit nit investigative telligence vll 
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#*network network network network network network network network network network model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data data data data figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set set set networks networks networks training training training training training training training training training training training training algorithm output output output output system system system system system system system system system system system system system system system system system system system system system state state state state state state state state state results results results results results results units units units units units information information information information information information information information information information information information information problem models models models hidden hidden hidden hidden performance based space space space linear linear layer layer layer layer layer layer layer case case case case vector vector vector vector order order order shown shown shown shown shown shown systems systems probability probability probability probability probability parameters parameters noise unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach pattern pattern pattern pattern pattern point point point point single single single single single single processing processing large large large local local local local local local local rate rate test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns inputs signal paper paper paper paper small small small size size size size size feature feature feature feature feature feature feature feature feature feature work task task task methods fig step step points features features features features features features features features features process process current trained trained high high high similar representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture section section section section section section fixed fixed line line line line line line line line line rule vectors vectors vectors vectors vectors general speech speech speech speech speech speech speech speech real real approximation average states states states states states states states experiments experiments experiments dimensional dimensional dimensional dimensional university university university independent independent independent independent independent independent independent independent independent independent independent independent independent log defined defined defined defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target initial table table table estimate estimate standard computer computer science science direction direction direction direction direction presented presented present present phase low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal sets maximum maximum maximum maximum range range range position continuous continuous abstract applied applied find find likelihood likelihood likelihood references component ieee procedure procedure important mixture mixture context context context context context context context introduction hand hand hand hand hand dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic tion tion prior representations word word word word word word word word word word word word word word word word word word word word word word word word word word chosen center long long markov markov make region proposed proposed proposed probabilities probabilities probabilities probabilities probabilities observed observed tasks tasks tasks tasks tasks tasks tasks tasks computed respect respect multi multi multi multi multi multi multi sum performed performed called called called called means means natural global applications em original original original original relative relative represented compared define rates rates rates rates rates rates determined goal goal goal posterior posterior connected approaches steps accuracy accuracy comparison larger larger dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent modeling modeling modeling morgan proceedings proceedings proceedings proceedings proceedings proceedings words words words words words words words words words words words words words words department implementation consists consists consists advances represents connectionist connectionist connectionist final final final final final final exp exp layers delay delay delay delay delay delay delay addition sequences sequences sequences sequences sequences framework framework directly hinton additional estimates design transition transition trajectory trajectory trajectory trajectory trajectory trajectory top effects conference determine determine world estimated basic give derived derived weighted randomly developed provided provided provided provided sampling sampling achieved achieved describe describe tested tested tested limited finding main journal future typically unknown character character character character character character character character character segmentation segmentation segmentation database database database language language language representing window window normalized normalized normalized normalized bottom frame frame idea idea combined description description resolution advantage advantage robust robust robust typical movement moving sense subset varying approximately approximately achieve achieve evaluation evaluation parts invariant invariant scaling scaling rotation loop minimal assumptions trajectories conclusions conclusions valued bayes designed labeled labeled variety characters characters written written written optical label explicitly coordinates coordinates text consisting consisting shift extraction phoneme evaluate labels sizes sizes sizes sizes completely translation past delays normalization normalization normalization combining boundaries boundaries boundaries visible assigned transactions recorded recorded recorded handwritten handwritten coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate plotted maximize characterized middle middle letter hmms encoded computationally paths included tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn kind kind cun interpreted sampled write michael michael michael michael michael simplified nips denker maximization automatically consisted approximating transformed school terminal combine combine dependencies variability proved scores waibel waibel waibel waibel waibel waibel waibel waibel waibel recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer baseline baseline improving isolated isolated integrate years capabilities capabilities processed preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing strictly strictly strictly strictly strictly style bengio consequence recognized english mellon alignment alignment alignment raw integrating carnegie collected collected cmu bootstrap remove remove rep rep calculating vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary pittsburgh ture maximizes maximizes ordered serve curvature curvature curvature curvature curvature curvature suited suited suited acoustics adjust logp logp logp germany germany windows viterbi viterbi viterbi softmax yielding cor feasible sort writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing writing tation printed printed lecun spontaneous kaufman promising simplify handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting handwriting transforms unlabeled observing generalizes evaluations combines combines combines combines combines ranging ranging ranging ranging lang originally originally originally originally originally recog recog modelled modelled april april april april smoothed refers proximity proximity proximity likelihoods likelihoods speeds instructions pen posteriori posteriori approx ure street constitute basically guyon guyon asked nition nition icassp icassp icassp icassp additionally german descriptions warping henderson preserved stroke wall compensate ocr ocr hubbard march writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer preserve dictionary dictionary fea normalizing october october corrections modal served info scanned styles styles styles argmax preserves preserves handling handling handling recogni recogni cursive cursive cursive cursive cursive cursive cursive cursive virtually alex alex alex alex alex integrates integrates bregler manually neighbourhood neighbourhood strokes arpa synergy sliding frequent distorted supposed ira ira fore rec jerusalem jerusalem expresses touch inte resentation resentation imation registration retrained puted writers writers writers writers writers writers nation hild posterjori resampled resampled ordinate inadequate lipreading hanazawa ogp ogp quences contin stefan stefan stefan stefan stefan aligning quence karlsruhe karlsruhe karlsruhe native uous albrecht rectly wsj wsj wsj wsj wsj finke finke finke finke finke finke schenkel script raining vocabularies vocabularies vocabularies vocabularies bitmaps bitmaps bitmaps bitmaps bitmaps bitmaps cid bitmap bitmap bitmap bitmap minneapolis wil rection crt crt adelaide adelaide adelaide segmen equidistant equidistant uka uka undesired rescale restoring wla icpr icpr 
#@Finke_M,Manke_S,Waibel_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data function function function function figure figure figure figure figure figure time set networks networks training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number number number system system error error error error error error error error error error error error error error error error state results information information information information information problem models models hidden performance performance performance performance performance performance performance performance based space weights linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown systems systems systems systems values parameters parameters parameters weight weight recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method approach pattern pattern pattern pattern pattern pattern pattern point image image image image image processing processing processing large large local local local rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns optimal optimal optimal inputs shows simple simple simple simple gaussian paper paper paper small small small small feature feature net net net net net work methods fig fig fig cells field field field field field field field field field field field field field field field field field field field field field field features classification classification classification classification classification classification classification classification classification classification classification process process process process process process level level current trained trained trained trained trained trained cell cell cell cell cell cell cell cell problems high high high similar show section section images images speech speech approximation states gradient gradient gradient obtained experiments result threshold threshold threshold threshold computation computation research defined defined defined defined defined defined defined defined sequence initial constant constant constant constant distance distance distance distance connections left direction direction direction presented activation activation activation activation low low object maximum maximum position abstract applied applied applied back back convergence convergence convergence convergence likelihood references ieee positive positive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision propagation propagation introduction hand hand hand estimation parallel parallel parallel parallel search search search tion tion classifier lower lower lower measure chosen chosen chosen chosen chosen chosen chosen chosen chosen previous bound bound bound type type long long conditions techniques correct correct correct correct correct correct scale scale minimum minimum minimum tasks tasks total total computed computed computed computed respect respect sum sum sum sum sum sum performed eq eq called called elements elements applications study obtain negative original original original original original vol vol vol vol vol vol vol vol vol vol relative relative samples compared compared compared desired rates rates rates location location location location location location location location location perform determined determined determined determined constraints gain equal equal dependent source source nets selection proceedings proceedings proceedings proceedings kernel advances advances advances advances final final addition computing experiment directly directly hinton hinton hinton hinton hinton additional san top top top top determine determine efficient requires speed estimated con coding derived criterion criterion processes selected iteration nature sampling constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint discussion tested tested inverse corresponds corresponds amount require adaptation pixel smaller reduced account fully character character character segmentation mechanism matching empirical squared squared details details numbers iterations iterations iterations pre pre pre pre pre pre pre bottom bottom bottom bottom combined combined combined combined combined minimize minimize choose added improved improved improved discussed improve element element moving machines machines quadratic sufficient highly calculated calculated calculated tions solve smooth yields yields yields converge trans address address address address locations locations locations grid improvement improvement improvement improvement improvement improvement intensity intensity intensity derivative derivative derivative derivative derivative rotation rotation correctly correctly correctly move greater reduce tangent numerical hard decrease decrease decrease iii derivatives derivatives configuration force force force force force force force force force force force force force force force force force force pro edges produces produces written sequential recall multilayer category category category category category category category category category category category category category category integrated equilibrium applying applying shift shift decreases decreases decreases independently evaluated centered approximated translation translation translation translation translation translation translation translation translation translation translation allowed key key partial partial partial partial partial partial reasonable epochs reduces reduces iterative boundaries interpolation initially calculate calculate classified avoid template template handwritten includes includes includes maximize structural simplicity driven delta delta delta delta delta delta delta delta delta delta delta comparing invariance score score score score score score repeated repeated induced link categories categories gray receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor satisfy satisfy highest moves overlapping satisfies satisfies presents presents simpler diego layered layered divergence existence scalar links applicable applicable applicable authors proved proved proved scores scores neu neu smallest smallest measurement naturally plausible plausible plausible adapt adjacent caused processed perspective sections sections satisfied satisfied formalism forces forces forces located mation mation laboratories simard simard simard simard simard simard simard simard circle lowest recognizing prop affine affine affine affine affine affine cmu offset capability lattice lattice lattice lattice lattice lattice lattice templates requirement calculating calculating june converged differentiable yielding cor shifted analogue lagrange japan martin martin martin appropriately appropriately appropriately rotated rotated printed printed receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors ral ral monotonically monotonically monotonically monotonically modifications lyapunov lyapunov lyapunov performances utilized utilized utilized utilized utilized mance falls iteratively induce perfor pat pat regarded moved moved moved washington infinity den searching originally originally elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic elastic diameter recog eqs papers fahlman fahlman fahlman executed discriminate misclassification misclassification misclassification achieving achieving rejection rejection rejection rejection nition par hundred hundred classifies letting certainty certainty certainty guess guess guess guess guess invariances modifying modifying modifying modifying shifting cessing compensate compensate ijcnn ijcnn ijcnn approxi rejected rejected rejected relates translations translations translations misclassified misclassified misclassified misclassified misclassified misclassified attached attached attached durbin durbin durbin november nec moderate ble handling handling traveling tom terns terns hundreds utilizes hid accomplish char connects seattle practically settle ters grids exploits totally salesman thresh deformation deformation deformation deformation transmit mis prominent violated rec repetitions applica ted altering schema blurred yamada yamada yamada deformations deformations deformations deformations deformations deformations deformations deformations deformations modifies orig forgetting equalization arline arline named proving resampled deformed deformed noises violation violation violation violation violation violation violation violation singapore blank enormous charac transfor barnard barnard barnard categorized categorized numerals numerals numerals numerals temporarily dsi presumed 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#*network network network network network network network network network network network network network network network network network network network network learning model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data function function function function function figure figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number number number number system system system system error error results results results results results results results results units units units units information problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden performance performance based based based based linear linear linear layer layer layer case case case case case case case vector order order order order order order order shown shown shown systems values values probability probability probability probability probability probability probability functions neurons unit unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single single single single single single processing processing processing neuron neuron neuron neuron rate rate test test test test test test analysis analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class optimal inputs inputs form shows shows algorithms algorithms algorithms algorithms gaussian gaussian gaussian paper paper paper examples examples examples small small small small small small size feature net net task task methods step step features classification classification classification classification classification classification classification classification classification classification classification level level trained trained trained trained trained trained problems problems problems problems problems problems problems problems problems problems representation representation representation architecture show show show show show show equation section section line rule rule rule rule rule images general speech speech real real real real real real average average obtained obtained note note note note result found found found table table table estimate terms terms terms terms distance distance presented present present present machine sets sets maximum position position position position position position position position position outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied applied applied applied computational computational density density density references references stochastic due ieee ieee ieee procedure procedure procedure procedure important decision context context context context context introduction hand estimation estimation estimation statistical dynamic generated cost cost cost cost assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower lower lower measure prior prior prior prior prior prior prior representations representations word word word word word word word word word word word word chosen higher part part part part previous previous long distributed distributed markov markov markov markov fact probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities minimum minimum resulting resulting resulting resulting classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes tasks total human computed multi multi sum performed performed performed performed times means made applications applications applications applications obtain obtain obtain obtain obtain obtain original original vol vol vol vol vol vol artificial represented true true true true true true compared application application series series compute compute compute compute compute goal posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions equal equal equal equal equal approaches approaches steps morgan morgan morgan proceedings words words words words words words words words words consists advances connectionist difficult difficult final exp layers considered computing view estimates estimates estimates estimates design limit limit conference classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper choice approximate world world world world world estimated estimated estimated validation validation validation validation derived weighted conditional conditional levels levels lines lines entropy backpropagation backpropagation depends depends covariance feedforward feedforward feedforward increases denote tested transformation limited assumption complete complete finding amount common assumed theoretical require main eds eds eds square pixel pixel hypothesis instance instance instance instance easily fit probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic pairs pairs unknown mlp mlp mlp mlp mlp mlp transfer transfer programming character character character character character character segmentation segmentation segmentation leads numbers pre pre pre pre pre pre normalized magnitude combined combined architectures architectures discussed discussed pair pair practical practical include subject subset relevant compare compare approximately yields definition chain chain generalized parts parts parts expression expression matrices matrices matrices touretzky generally generally column conclusion segment central bayes bayes bayes bayes moody faster practice practice reduction sigmoidal sigmoidal intelligence assuming iii characters characters characters characters characters scene base base base reference reference relation digit generating changing confidence multilayer multilayer dimensionality easy adding events minimization minimization minimization minimization springer springer quality quality quality letters letters letters letters letters letters letters letters letters letters letters letters letters letters phoneme interpretation interpretation solved solved transform densities densities densities soft digits partition performing normalization combining combining purpose closed intermediate string string transactions transactions david david david david david avoid building existing handwritten handwritten handwritten combinations priori priori priori priori priori perceptrons perceptrons sciences recognize discussions divided delta included efficiently efficiently efficiently strongly heuristic classify strategies gray gray list list list vary denker denker hypotheses acknowledgments powerful wiley transformed overfitting involving involving involving humans limitations lippmann links mse mse mse mse int combine relationships authors decisions decisions scores removed concepts necessarily reading reading reading recognizer recognizer recognizer recognizer recognizer fisher academic detected simplest isolated isolated mentioned percentage indicating pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise publishers correction tool tool reasons sections widely preprocessing probable potentially potentially recognized recognized recognized read recognizing amounts amounts amounts amounts amounts passed price price price price price vocabulary vocabulary partitioning ordered ordered ordered segmented segmented segmented segmented segmented softmax softmax softmax writing extensive printed lecun lecun establish kaufman dealing chance proceeds attractive check check check check check handwriting handwriting handwriting handwriting handwriting operates bourlard bourlard bourlard bourlard performances performances performances separating bad intended belongs originally bases bases mlps mlps mlps mlps mlps express insight insight reader informative informative informative designing subsequently valuable hart hart stopped stopped divide posteriori posteriori posteriori fitted incorporates kluwer graded uniquely retraining obtains associate modifying pij duda duda paris paris paris paris ambiguous importantly france france france france descending likewise union union bridle bridle bridle styles stimulating cursive cursive cursive cursive cursive vii vii vii vii transforming designs hid hid suffices contributes ultimate spirit simon simon simon simon simon simon costly wagner wagner postal postal postal postal postal wellekens wellekens neurones neurones drawbacks resemble literal literal literal literal herault herault checks checks checks checks checks checks checks checks favorably des viable fogelman fogelman originating french french french french live cleaning extractor vij vij vij vij vij vij vij vij vij vij vij vij vij vij dreyfus dreyfus dreyfus dreyfus dreyfus dreyfus dreyfus dreyfus critically nato nato extraneous interpretable rue rue rue cedex stefan stefan stefan stefan stefan personnaz personnaz personnaz personnaz personnaz personnaz personnaz multiclass stepwise neurocomputing neurocomputing hen mij mij mij mij estimations bahl soulie soulie conquer asi asi experimenting edit edit laboratoire revisited cnrs coping lion annotated numeral tol 
#@Dreyfus_G,Knerr_S,Personnaz_L,Price_D,
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input data function function figure figure figure figure figure figure time time time set set set set set networks networks training training training training training training training training training training training training training algorithm output output output output output output output number number number number number system system system system system system system system system system system system error error error state results results results information models models models models models models performance performance performance performance performance performance performance performance performance performance performance performance based based space weights weights weights case case vector vector vector order order order order shown shown shown shown shown shown shown shown shown systems weight functions functions functions functions functions functions recognition method approach pattern point point point point point point control control control control control control control large large large test test test patterns patterns matrix matrix inputs inputs form gaussian gaussian visual examples work work task task task task task task task task task task task task task task task fig fig fig fig fig fig fig fig fig fig fig cells cells field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field process process trained trained trained trained problems memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response similar similar similar representation representation representation show show show section line line line line line approximation states theory theory theory term term term term term term term experiments experiments activity activity activity activity result solution solution found found found found found found sequence sequence target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial initial estimate estimate estimate estimate standard standard standard computer terms terms distance synaptic synaptic synaptic science science science prediction direction direction presented presented presented presented map map map map map map map present present present activation low temporal temporal press press learn learn learn learn learn learn learn learn learn learn learn learn learn learn position position components basis outputs abstract computational computational computational computational computational convergence properties properties properties references due due adaptive adaptive introduction hand hand hand hand hand hand hand hand hand hand hand hand behavior stimulus stimulus stimulus dynamic dynamic change change change change change change change change change change change difference difference assume lower lower lower measure measure representations representations learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned previous previous previous previous firing cortex cortex cortex cortex long long long long long long conditions distributed equations make make correlation correlation observed observed observed errors errors resulting ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks human human human human human respect respect sum performed performed performed performed eq eq eq called called called called called called called called elements elements elements elements elements mapping mapping mapping mapping mapping mapping mapping feedback study study study study em negative vol artificial specific specific specific specific represented represented compared desired desired series series series proc proc eye eye determined experimental goal motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor discrete brain brain brain mit connection fields fields fields fields fields fields descent dependent words words words loss technique internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal joint joint connectionist responses difficult exp exp exp sequences ai maps maps maps framework cambridge experiment experiment environment environment environment environment environment environment environment environment environment estimates trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory stage effects determine determine upper upper requires significant significant significant approximate estimated con produce produce condition developed robot robot robot robot robot robot robot robot robot robot robot robot robot levels velocity velocity velocity velocity controller controller controller controller controller controller path path path actual provided evidence backpropagation nature simply associative measured measured measured measured increases arbitrary group group group group group denote tested tested tested transformation transformation inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse assumption amount short short short effective implemented adaptation end end ability ability degree degree makes typically typically reduced dynamical functional functional jordan transfer transfer transfer testing significantly significantly significantly significantly mechanism leads leads representing call call pre pre inhibition produced produced predict exact property separate element element typical typical similarity movement movement movement movement movement movement movement movement movement movement movement movement movement movement reported reported reported introduced introduced introduced strategy moving period period period period period period period period subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject sense cognitive cognitive cognitive cognitive recently sufficient subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects calculated volume smooth studies converge differential differential positions improvement storage increased increased arm arm arm arm arm arm arm arm arm arm arm lead suggests matrices rotation predicted move move demonstrate half half flow place hebbian trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories measures designed designed sutton sutton performs practice practice practice practice practice practice practice practice practice practice practice practice practice practice learns suggest suggest mechanisms presence largest largest reduction radial variety movements movements movements movements movements movements movements movements movements movements targets targets targets targets targets targets targets force force force force force force force force force force force force force force force force force force force force force force force force force force question areas reference reference reference reference sequential sequential sequential ann ann mathematical dept dept dept dept recall coordinates coordinates coordinates physical interaction interaction interaction formed decreases formation formation formation formation formation correlated correlated correlated correlated correlated correlated viewed influence showed showed understanding approximated suggested suggested suggested suggested intervals purpose remains initially initially initially initially msec expect recorded includes coordinate bell inter sciences coupled coupled coupled effectively literature literature post composed soc soc soc procedures strongly link interested neuroscience issue return return follow timing timing timing timing sci gray quantity list involved involved write paradigm reach reach reach neurosci neurosci neurosci attempt attempt consisted moves subsequent approximating neighboring intrinsic explore environments environments environments environments involving involving involving humans humans humans humans humans limitations fashion fashion behavioral mappings plasticity muscle proper proper encode act coefficient trace trace trace trace adapt opposite psychology perfect changed noted nervous nervous store baseline baseline baseline baseline explain phd attempts attempts seconds crucial explanation tool tool tool tool tool tool tool tool worse handle handle straight straight straight straight straight sys sys producing day day day day day day day forces forces forces forces forces forces forces immediately monkey projected describing begin res res read virtual profile profile led dark fed poorly psychological measuring anti anti anti anti anti semi display decreased shaped returns begins deviations eventually univ univ univ naive naive naive naive naive naive naive consistently phenomenon phenomenon acquisition acquisition lab ghahramani uncorrelated analogue physiology proportion null null null null null null reconstructed tem turned reaching reaching reaching reaching reaching wrong imaging minutes minutes minutes cerebellum cerebellum imposed imposed contract biased kawato affected preparation planar muscles muscles hours hours hours hours hours hours interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference interference periods respective encountered displayed enhance exposure israel israel cerebral eng master environmental storing steepest extensively wolpert wolpert interestingly mechanical mechanical mechanical blood sch session session asked break torque torque torque torque magnetic perturbed arbor causing causing tor chicago pairing jacobian manipulation acting attempted alternate interact compensate compensate interacting learnability altered books acquired termed setup breaks finger reveal confusion syllables indication programmed retained retained retained retained port develops sessions transducer transducer emphasis acquire reversed tom tom tom tom tom quantify hundreds interpolated interpolated puts hopkins purkinje purkinje returned anatomy conflicting dissertation impedance impedance impedance impedance impedance successively isolation joints joints johns lewis lewis schmidt schmidt magazine skill unusual motors motors motors motors motors baltimore catastrophic catastrophic catastrophic parker shortly shortly inform syst adv lights amer amer ference resemble transferred stand inability dominate regional visuomotor hands biomedical forgetting forgetting mussa mussa mussa mussa mussa mussa mussa mussa mussa opportunity decrement decrement decrement decrement retention ross ross untrained ivaldi ivaldi ivaldi ivaldi ivaldi ivaldi effector bruce bruce endpoint conflict temporary dynam med abs michigan succession psy hogan hogan kinetics french nectionist shoulder facing champaign subscripts instructed psychol psychol psychol psychol elbow adams bizzi badly quantifying grasp stiffness planned planned inertial recruited recruited accomplishes gomi deviate evidenced mri verbal sullivan impedances todorov friction wished jhu cont tangential northwestern perturb resist unpredictable constituted trajec trajec extrinsic bme physio evidences signifying overt 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#@Brashers-Krug_T,Mussa-lvaldi_F,Shadmehr_R,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural input input input input input input data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set networks networks networks training training output output output output output output system system system system system system system system results results results results results units units units units units information information information information information problem problem problem models models models performance performance performance based based based space space space space space linear vector order shown shown shown shown shown shown shown systems systems systems systems systems systems functions functions approach approach pattern pattern pattern pattern pattern pattern point point point point point point point point point point point point point point point point point point point point point point image image image image single single single single single processing processing processing control control control control control control control control control large large large local local local local local local local local test test patterns patterns patterns patterns patterns analysis inputs inputs inputs inputs inputs form form shows shows gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper examples work points points points points points points points points points points points field trained trained structure structure structure structure structure structure response similar similar representation representation representation representation representation representation representation representation representation architecture show show line line line rule vectors images general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization approximation approximation approximation approximation theory theory theory theory obtained note note variables variables computation computation research research independent found found target target target target target target target target target target target target target computer terms distance distance distance left left left direction direction direction direction direction direction direction map map map map map map map map map map map map map map map map map map map map map map phase phase phase phase object object object learn learn position position position position position position position position position position position position position position position position position position position basis basis basis basis outputs outputs outputs abstract computational computational computational computational computational computational properties properties properties references positive adaptive adaptive mixture mixture context context context context context context context context context context context context context context context context context context context context context introduction action behavior behavior stimulus effect dynamic tion tion tion change change change change change change change change change change variable variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial measure signals representations learned learned learned learned learned learned chosen chosen part previous required multiple multiple multiple cortex cortex distributed expected make proposed observed resulting ing total simulation human human human human human human multi regions mapping mapping mapping mapping dimension made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation global global global global global study study study study study study study study study study study study study negative negative relative specific represented represented represented represented desired receptive receptive receptive location location location location location eye experimental experimental experimental experimental goal goal goal related constraints constraints constraints constraints gain motor motor motor motor motor motor brain mit mit mit mit contrast fields fields fields fields dependent dependent dependent dependent dependent dependent dependent dependent dependent morgan proceedings institute department internal internal internal kernel advances joint ai maps maps maps maps maps maps framework cambridge experiment experiment environment hinton view effects determine significant significant significant significant significant world vision vision vision pages pages pages produce condition coding derived conditional area controller path path path actual actual actual actual actual actual constraint constraint biological measured measured discussion group group group group group group group transformation transformation transformation transformation fast limited corresponds stable generate supported adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation ability ability ability development sensory sensory kaufmann auditory auditory pairs pairs pairs pairs pairs functional jordan jordan jordan jordan jordan jordan jordan jordan technology projection projection projection york york york york york head head consistent consistent matching representing representing pre pre pre experts experts attention combined run predict predict property separate separate separate movement movement movement movement movement movement movement introduced introduced subject subject subject sejnowski sejnowski cognitive cognitive dimensions dimensions highly varying previously previously previously subjects subjects subjects subjects subjects subjects subjects subjects subjects volume volume volume module correspond studies studies studies studies studies achieve address positions positions locations locations locations locations grid grid grant grant grant grant arm arm studied studied occur wide rotation rotation locally touretzky occurs column column column demonstrate conclusion conclusion starting starting starting starting starting starting place place greater conclusions editors editors editors central central central central modules modules modules designed moody moody moody constrained suggest suggest suggest strong presence demonstrated solid radial radial assuming variety start start start start start start start start start start start movements movements movements movements plane relationship relationship relationship targets targets introduce groups groups groups groups groups groups groups groups groups groups configuration configuration question question question question explicit appears perception perception perception perception perception perception perception optical optical factors tuned tuned confidence coordinates coordinates coordinates coordinates coordinates coordinates linearly transformations transformations transformations transformations consisting shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift decreases focus review review review depending depending depending depending depending viewed transform open open open controlled restricted showed forms smoothing initially foundation perceptual perceptual perceptual perceptual coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate contour retinal retinal sciences sciences sciences sciences plotted gating society poggio poggio literature post post post plots plots fine receives composed repeated induced induced induced induced link showing showing interpreted neuroscience sin physiological physiological michael michael michael michael michael michael generalize generalize generalize paradigm correspondence ill reach reach reach consisted subsequent subsequent subsequent mixing extract jacobs jacobs intrinsic tesauro body body explore parametric parametric wiley wiley perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation varied varied varied varied varied accurately dotted examine examine examine project mappings plasticity plasticity possibility office func fundamental phases phases phases neu examined examined measurement editor adapt predicts opposite opposite psychology psychology explored explored mapped mapped mapped mapped nervous nervous switching extent massachusetts smoothness nowlan perspective mation controls laboratories inversion projected acknowledgement angles angles gradually localized localized localized arises depicted nsf virtual reflects reflects reflect led cohen posed share psychological psychological schematic schematic robinson howard howard perturbations perturbations perturbations perturbations perturbations modulated neuro conditioning displays lab ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani contextual contextual contextual contextual contextual proportion restrict conditioned conditioned conditioned pick pick girosi girosi controlling naval reaching reaching systematic kaufman darken darken darken siemens balance transforms ral spot spot spot spot planar infor alspector started ranging representational tone tone induce induce induce displayed displayed displayed displayed displayed cmac regarded regarded von topological lawrence thomas parietal parietal exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure exposure approximators young infer suggesting suggesting gaze gaze record repeatedly repeatedly wolpert wolpert wolpert wolpert wolpert wolpert wolpert erlbaum harris harris intersection displacement displacement displacement displacement displacement displacement displacement reflex appeared neurophysiology converted corporation workspace workspace shading visually visually visually visually visually visually helmholtz helmholtz annals pointing pointing pointing pointing pointing pointing pointing pointing pointing session tables emerge pointed pointed welch welch welch welch welch welch smoothly discriminative perturbed perceived perceived perceived tor england hillsdale examining gene reflected assess representa cns shaded gated gated gener ization inverted relating 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visuomotor visuomotor visuomotor visuomotor visuomotor visuomotor visuomotor visuomotor visuomotor visuomotor internally psyche psyche psyche rightward displaced displaced displaced prism prism sual sual feel tar presidential psy psy perceive georgopoulos georgopoulos cursor cursor cursor cursor leftward remap depended traced lighter lighter hen disparate ger ger gle alterations alterations crossed crossed austrian displacements displacements relearning rear rear tude coordi sensations ellipses crn prisms prisms contingent confine mentally decremented str priate suggestive exten visuo ned schematics interscience unaltered sively retinotopically sequently digitizing digitizing prerequisite coor nate chichester felt disrupted shades shades vestibuloocular tradition iment 
#@Ghahramani_Z,Jordan_M,Wolpert_D,
#t8
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data function function function function time set set set set set set set networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system system system error error results results results results results results results information problem problem problem problem problem models models models models models models models models models models models models models hidden hidden hidden hidden hidden performance performance based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear case case case order order systems probability probability probability probability probability parameters parameters parameters noise noise noise weight weight weight weight weight weight distribution method approach approach approach approach point single processing large large large local local analysis class class class class class class class class class matrix matrix matrix matrix matrix optimal form shows signal algorithms algorithms simple simple gaussian gaussian paper paper examples examples small small small small small size work work work work methods methods methods step step step step step step step step points field features features features features features features features features features features process level level level current current current current structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems problems random random high high high similar similar similar representation representation show section section line general general general general general generalization parameter parameter real average theory theory theory obtained obtained note note dimensional dimensional variables variables variables computation computation solution solution solution solution solution solution solution solution solution solution independent log defined found target target constant constant constant constant table table table table standard standard computer terms terms terms distance science science science science science presented presented present phase low object sets sets sets sets sets maximum maximum maximum press press basis abstract abstract applied back find computational computational convergence properties properties properties likelihood likelihood likelihood likelihood references procedure mixture introduction complex estimation estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical generated variance variance variance variance variance variance variance variance variance variance variance variance tion energy energy energy energy energy energy energy difference variable spatial spatial measure measure prior representations representations chosen higher higher previous previous previous previous required required multiple multiple multiple multiple multiple multiple multiple multiple multiple good binary binary long conditions conditions represent represent tree expected expected expected markov fact techniques techniques techniques techniques techniques correlation correct correct correct observed observed observed observed observed observed observed scale classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes ing ing ing respect respect sum sum sum times optimization dimension natural natural natural natural natural natural natural natural study em em em em em em em em em em em em em em obtain obtain original original original original original original vol artificial artificial artificial relative samples represented true true compared application desired provide experimental discrete discrete discrete discrete brain brain equal power approaches approaches approaches approaches approaches mit larger contrast modeling modeling modeling report report report report institute institute department technique internal advances represents connectionist difficult final final exp exp bias scheme considered considered considered framework cambridge cambridge computing domain equivalent equivalent equivalent hinton hinton estimates estimates estimates estimates limit top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli capacity efficient requires significant significant approximate approximate statistics statistics free free world speed basic basic basic basic give produce weighted weighted weighted weighted randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering types finally finally processes iteration iteration iteration depends sampling sampling sampling sampling sampling discussion technical increases increases limited close close complete complete finding finding finding amount common common common common common common effective assumed assumed assumed role theoretical eds cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster makes makes makes including including fit fit fit fit simulated probabilistic probabilistic probabilistic typically typically typically smaller underlying underlying underlying unknown technology programming significantly significantly york structures structures structures structures structures trials trials uniform principle squared squared numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers iterations iterations iterations iterations iterations making making magnitude magnitude magnitude minimize minimize run run run run run added recent property typical typical typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity reported practical practical strategy strategy quadratic hierarchical hierarchical hierarchical hierarchical hierarchical inference inference subset cognitive cognitive cognitive cognitive cognitive cognitive relevant dimensions varying compare compare conventional conventional conventional unsupervised unsupervised unsupervised subjects subjects subjects calculated tions solve solve yields correspond correspond correspond correspond correspond converge chain interval improvement increased exists concept scaling deviation touretzky clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters generally generally runs runs runs conclusion starting place greater greater central accurate numerical numerical numerical practice weak constrained temperature temperature propose propose taking decrease decrease averaged configuration configuration configuration configuration configuration configuration annealing annealing monte monte carlo carlo written written longer perception solving solving transitions mathematical distinct dept modeled metric physical remaining easy belief interaction interaction equilibrium equilibrium quality expectation cycles cycles cycles letters yield choosing independently focus dependence review review review phoneme communication squares squares squares viewed interpretation interpretation variation approximations earlier earlier earlier earlier additive additive additive additive additive additive additive additive additive additive additive additive additive additive additive reduces fitting fitting fitting fitting roughly initially calculate euclidean avoid expect recorded recorded recorded perceptual perceptual perceptual combinations priori formulation formulation color sciences maximize specifically priors priors domains domains holds neighbors discussions structural successfully major major simplicity reason middle efficiency efficiency efficiency uniformly divided effectively included included presentation miller miller miller essentially capture traditional soc soc procedures heuristic interpreted criteria generative generative generative gibbs gibbs gibbs gibbs gibbs involved play dayan dayan dayan absence realistic realistic highest maximization consisted consisted overlapping overlapping overlapping overlapping overlapping overlapping illustrates illustrates neighboring tesauro decreasing presents carried preliminary helpful fewer examine examine successive comparable hierarchy statistically surfaces measurement concepts concepts configurations configurations configurations configurations configurations configurations configurations psychology thought ensure subsets subsets subsets subsets subsets subsets subsets subsets rank rank front front precise observe academic generates improving simplest utility contributions arbitrarily arbitrarily arbitrarily explain motivated attempts neal neal neal neal neal neal neal massachusetts residual developing theoretic theoretic theoretic theoretic crucial analyzed guaranteed defining fairly lies satisfied leaves acknowledgement calculations members members begin english english toronto medical author incomplete mechanics robustness collected collected understood led amounts employ treated treated dots maxima maxima psychological psychological howard gains ture limiting spread incorporating phonemes phonemes phonemes extensions achieves marginal sums logp logp kinds kinds chose sophisticated expectations progress calls multidimensional multidimensional multidimensional arithmetic arithmetic arithmetic contribute ghahramani ghahramani ghahramani ghahramani identifying leen intractable proportion sleep recover perfectly homogeneous reconstructed discovery discover discover discover flexibility inspired inspired convenient odd odd odd familiar familiar serves hope star fail belong disjoint disjoint disjoint salient salient salient combinatorial meaningful published recovered recovered recovered recovered recovered recovered recovered recovered recovered equals induce accounts belongs belongs dif similarities similarities similarities similarities similarities recog insight insight indicator properly properly properly roy consonant consonant consonant captures dempster dempster integers integers integers integers vari assigning speaking speaking consecutive verify mind yielded rigorous rigorous shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard shepard ter rubin emerge nition perturbed instantiation obtains weiss seek arg personal classic classic descriptions discovering discovering wake factorial concentrated favor annealed annealed hughes challenging efforts argued categorization importantly laird paradigms accounted accounted accounted gilbert applicability frey ignoring treating treating rose rose tel gorithm unpublished strict stops stops stops served ble nonnegative generarive generarive satisfactory tial families subjective subjective ferent conceptual conceptual hoc tors powers appealing consonants judged judged contributes contributes fox interpretations sij sij sij phonology phonology complement spirit spirit pooling accounting accounting accounting ance iterating handbook compromise bear promise brought putation unexpected voiced voiced voiced unobserved unobserved unobserved unobserved configured configured configured configured elaborate mir judge judge tenenbaum tenenbaum tenenbaum tenenbaum crg competence recovers orig treats ities stim rigorously parsimonious scribed psyche phonological fac judgments judgments anneal anneal distinctive differed concise clus clus sults optimiza ponents lowering salience salience french underlie fellow embodied multiples multiples formulating alternately omitting omitting omitting confusions confusions bernstein saund saund joshua inspiration appeal revealing probabilistically nicely nicely nicely requested assump supplying lihood intell richards suspect pursuing verbal memberships memberships memberships memberships memberships tering unvoiced unvoiced unvoiced unvoiced grounds reprinted gurewitz violates intent roger inclusive inclusive inclusive judgment mathe compiled rations mensional ception eff cult grossly nasals nasals nasals matical assert accomodate accomodate ned inal psychologically psychologically bottlenecks artif nations configu promises promises awe numeral uli fricatives loglikelihood scal fio absorb exceedingly substan accommodates constr predoctoral 
#@Tenenbaum_J,
#t9
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#*network network network network network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model neural input input data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set set set output output output output number number number number results results results results results results results results results units units units units units information models performance performance performance performance performance performance performance performance performance performance performance performance performance based space space space space space weights linear linear layer layer layer layer layer case case order shown shown shown shown shown systems values values probability functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit pattern pattern pattern pattern pattern pattern pattern point point single single processing processing processing control control control control control control large test test test test patterns patterns analysis inputs inputs inputs inputs inputs shows simple gaussian visual visual visual visual visual visual visual visual task task task task task task task fig cells cells cells step step field process level level current cell high response response response response response response similar similar similar similar similar similar similar representation representation representation representation architecture architecture architecture show show line line line line line line line line approximation approximation theory theory theory theory theory theory gradient gradient obtained obtained experiments experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result university research independent independent defined defined found found found found found found found found found found target target target target target target target target target target target prediction left left left left left left left left left left left left left left left presented presented presented presented map map map map map map map map map map map map map map map map object object object object object object object object object range press press position position position position position position position position position position position position position position position position position position position position position position position position basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear abstract computational computational computational analog properties properties properties references due procedure important mixture introduction hand hand hand behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect generated spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial signals signals representations representations representations representations representations representations representations representations representations representations representations representations representations higher higher previous bound cases type type type type required required multiple multiple multiple multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long long conditions conditions conditions conditions conditions conditions conditions conditions conditions expected expected fact techniques correct resulting resulting ing ing human human human human regression computed respect respect respect respect performed performed called times times times factor orientation orientation orientation study relative relative represented cross cross receptive receptive provide provide objects objects objects objects location location location location location location location location perform perform active active active active eye eye eye eye eye eye eye eye eye eye eye eye eye experimental experimental related related constraints motor brain brain brain mit steps larger larger fields support support support dependent selection selection selection selection selection selection selection selection institute institute internal advances represents bias bias bias delay delay addition addition maps maps maps maps maps framework cambridge computing computing experiment experiment experiment experiment environment additional view stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects detection determine determine determine pages con con condition condition condition condition condition condition condition condition condition developed developed developed developed area area area area lines lines lines lines lines lines lines lines lines lines selected selected selected selected selected selected evidence evidence simply discussion increases increases tested tested tested transformation transformation amount short common implemented assumed assumed generate face adaptation adaptation journal ability hypothesis hypothesis hypothesis instance instance sensory sensory sensory sensory sensory auditory simulated simulated simulated reduced account account account account account functional functional fully fully interesting york head head head head head head head head head head head head head head head head head head head head head mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism consistent consistent consistent leads inhibition early frame frame frame frame predict neuronal improved improve exact takes typical typical reported reported reported lateral introduced moving identical side side side sejnowski sejnowski sejnowski sejnowski sejnowski recently recently dimensions compare previously subjects subjects subjects subjects volume module tions tions tions match studies studies studies trans positions positions positions organization parts lead lead suggests suggests wide touretzky half strength strength place row editors sigmoid modules retina designed clear peak faster faster suggest encoding solid solid proportional proportional proportional proportional movements movements movements movements decrease iii identification identification reference reference reference reference reference reference reference reference reference reference reference reference reference appears appears winner factors factors tuned tuned distinct dept segments modeled coordinates coordinates coordinates coordinates simultaneously simultaneously simultaneously simultaneously simultaneously involves transformations transformations transformations transformations transformations select competition decreases independently stages evaluated centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered frames frames frames frames frames frames frames frames frames frames forms activities allowed performing spaces intermediate intermediate intermediate intermediate sufficiently degrees degrees degrees combinations combinations retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal illustrated absolute absolute absolute phys characterized characterized selecting selecting aspects aspects uniformly encoded presentation identify projections refer notice strongly strongly strongly showing superior superior return follow involved vary modular modular computes computes highest hypotheses reach principles illustrates tesauro body body essential dotted dotted biases biases existence project project muscle encode func mixed attempts slowly distinguish processed straight straight shared shared organized precisely precisely located located ran nucleus consequence medical integrating integrating behaviors percent evaluating items profile simulate simulate lack lack item item item item share howard exhibits spread differs modulated modulated monotonic inherent display display patients patients patients patients patients patients patients patients patients patients patients simultaneous leen forming oxford recover rotated rotated rotated rotated purely purely theories turned turned turned turned reaching reaching los biased neurobiology operates operates affected affected salk salk salk inferior lip ensures patient patient induce displayed accounts originally competing reproduce reproduce parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal parietal multiplied recovery ahead ahead jolla matter saccade properly colliculus colliculus captures explains explains explains explains interestingly ure crossing appeared appeared ence equivalently covering asked asked asked opposed reaction reaction reaction reaction reaction reaction reaction reaction encodes revealed failed comparative connec lesions lesions lesions lesions lesions lesions ical solely affects affects affects affects simulating simulating simulating lesion lesion lesion lesion lesion lesion lesion lesion lesion trends favor favor neurophysiological crosses hughes retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic retinotopic terrence fixation frontal win cartesian cartesian cartesian cartesian cartesian weaker emphasized page induces coordination demonstrating clinical clinical syn resp resp appearing pouget pouget pouget pouget pouget contralateral contralateral contralateral contralateral contralateral tors alex eral sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor sensorimotor condi neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect physiologically ventral ventral manipulated ooo andersen distractors distractors distractors distractors distractors trend watson shares replicate preventing disorders thalamus ther angeles stim rightward rightward reproduces sought fur neurology plain terry rightmost deficit deficit deficit deficit deficit deficit deficit deficit deficit nation asso testable sual behaved neck cancellation cancellation cancellation cancellation cancellation anatomically vibration havior siegel selectivities selectivities gravity combi syndrome syndrome schenkel consis posture posture mimics sidered spe ucla tent alexandre dition retinotopy leftmost ciated midline ret taneously prisms neuropsychology sac hemispheres determin premotor premotor premotor simul deficits bisection wearing edi multaneously uli formations subdivisions hills hills fischer corticocortical anchor inconclusive 
#@Pouget_A,Sejnowski_T,
#t9
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input input input input input input input input input input input input function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output number number number number number number number number number system system system system system error results results results results results results information information information hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based based weights weights weights layer layer layer layer layer layer layer case case case case case case case case case case vector systems systems systems systems systems systems probability weight weight functions recognition recognition recognition recognition approach image single single single single single single single processing processing control control control control control control control large large local local local local local local local test test test test test test test test patterns patterns patterns optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs visual visual visual visual paper paper size size size size size size size size size size size feature feature feature feature feature feature net net net field field features features features features classification classification classification classification classification classification classification classification classification classification level level level trained trained trained trained trained trained trained problems problems problems problems problems problems problems random random random random high high high high high high high high high high high high high high high similar architecture architecture architecture line line line line rule images images images images generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization average average dimensional dimensional result result threshold computation computation found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant estimate distance distance node left left left left present present low low low low low low low low low nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency frequency frequency frequency frequency frequency frequency sets sets sets sets press learn learn learn learn learn learn learn learn position position position position outputs sample abstract references due due due due propagation hand effect effect effect generated variance variance variance variance variance variance parallel parallel parallel parallel parallel search search difference difference difference variable spatial lower lower measure representations representations word word word word word word word word word word word word word word word word word word word word word word word learned center previous cases cases type required cortex good long conditions conditions conditions conditions conditions conditions conditions distributed make fact fact region simulations simulations simulations total human human human human human human human human human human human human human human human respect called mapping made global obtain relative relative samples samples compared compared compared compared compared compared cross cross receptive receptive receptive receptive proc eye eye eye eye eye eye eye eye eye eye related connected brain equal equal mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy fields fields fields support train nets nets nets nets nets morgan words words words words words words words words words words words words words words words words words words words words words words words words words version internal represents bias bias sequences sequences domain domain equivalent experiment experiment experiment experiment experiment experiment experiment experiment hinton hinton effects capacity capacity capacity capacity capacity capacity capacity efficient upper free vision pages pages validation validation validation condition condition condition condition condition condition condition condition levels levels levels area lines backpropagation backpropagation backpropagation simply achieved achieved increases increases increases group group tested tested tested tested corresponds amount amount shape shape shape role role eds journal end rumelhart rumelhart rumelhart kaufmann simulated underlying hopfield combination reduced reduced transfer interesting interesting testing testing testing character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character edge edge increasing increasing consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent representing representing making making window window window window window window window window window window window window window normalized depth idea minimize run architectures improved improve advantage advantage movement reported pixels pixels cognitive works tions studies positions positions positions positions positions positions positions positions locations locations locations williams williams sensitive increased increased exists occur suggests suggests suggests extended touretzky width width width generally demonstrate starting greater reduce reduce reduce reduce accurate accurate accurate accurate accurate designed exponential asymptotic asymptotic suggest suggest mechanisms largest drawn drawn labeled movements movements selective plane characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters groups groups identification digit perception perception optical optical factors generating distinct sensitivity sensitivity category category category dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality slightly slightly text text text text text text text implies extraction versus letters extracted influence operations updated showed centered sizes digits allowed epochs reduces roughly remains valid string string string advantages classified classified classified classified handwritten perceptual perceptual perceptual strings strings strings strings strings extension automatic determining determining middle letter letter letter letter letter importance divided mcclelland mcclelland mcclelland detect detect build contained superior classify classify classify classify classify classify content duration list list list list involved involved vary dot generalize denker denker denker highest hypotheses reach reach thresholds consisted jacobs jacobs receive oriented minimized employed poor poor overfitting overfitting create difficulty difficulty difficulty limitations limitations preliminary hall biases periodic reducing reducing reducing detectors detectors detectors detectors detectors detectors variability variability cover examined reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading psychology created precise initialized consist consist consist consist consist consist consist baseline detected mixed great great great great great great baum sys shared shared arise arise potentially opt opt opt opt beginning beginning read read depicted recognizing recognizing preceding questions people people people share solla frequently maintain span howard howard exhibits ordered geman geman expectations attentional globally classifying classifying classifying classifying accomplished martin martin martin martin martin martin narrow optimizing printed lecun lecun murphy difficulties difficulties difficulties difficulties occurred occurred height check child prentice irregular surprising expanded evident schwartz jackel jackel viewing recog recog creating creating creating impact impact impact inf ignore material usage planes wiesel wiesel alternating alternating emerge failed expanding nition nition boser reports classifies hubel hubel clas constrain avoids manipulation henderson henderson mammalian ocr ocr ocr ocr ocr ocr ocr guidance hubbard fixation fixation fixation fixation fixation fixation fixation fixation fixation fixation scope represen mix scanning cube cube capacities opti dim dim regularities regularities regularities regularities regularities regularities bienenstock bienenstock font font font font impractical insufficient curse curse curse curse curse austin played determinant char fre fre horizontally horizontally ters ters carries successively reproduced dimen tations materials materials positioning positioning positioning positioning positioning positioning positioning positioning spa generaliza adv amer dilemma disorders won accu quency quency lowered lowered psych psych psych psych psych psych psych parame posi manipulations stim superiority lived lived lived lived lived lived lived lived lived coverage nth paid tially ages utilization frank spans highlight perf perf perf live readers jour jour jour jour jour jour recep charac unfamiliar story occupy raise reductions told replications replications fixations fixations asymptote asymptote mcc mcc pittman pittman doursat doursat forty fonts fonts racy ezp ezp ezp ezp ezp ezp ezp complez trl ulus wittner sionality effi infrequently ola skilled dorothy dorothy dorothy dorothy dorothy dorothy dorothy dorothy dorothy illus decline progressive regan regan ciency trainin alleviated stu gale 
#@Martin_G,
#t9
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data function function function function set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system system system system system system results results results results results units units information information information information information problem problem problem models hidden hidden hidden performance based based based based based based based based space space layer case case order order order order shown shown shown systems systems systems systems systems systems systems systems systems values values values values values values values probability probability parameters parameters parameters unit unit distribution method method method method method approach approach single single single single processing processing processing processing processing control large large large large large test test test test test test test test analysis class class class class class class shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples size size size size feature feature feature feature feature feature feature feature feature net net net work work work task task task task methods methods features features features features features features features features features features features features features features classification classification process process process process process process process level level level level current trained trained trained trained trained trained trained trained trained trained trained trained trained trained problems problems problems problems problems random high high high high high high similar similar section rule rule rule rule rule rule rule rule rule rule general general general general generalization parameter parameter parameter real real experiments experiments experiments experiments experiments experiments dimensional dimensional university threshold threshold threshold threshold research defined defined defined target target constant table table table table table table table table table computer computer terms node node node node node node node node node node node node node node node node presented presented present present present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency machine machine machine machine machine machine sets sets sets sets sets sets maximum range press press press press press press press learn learn continuous continuous abstract applied find density density references ieee ieee ieee ieee ieee procedure important important important important important decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision introduction complex complex complex complex estimation estimation statistical generated generated search search search search search complexity complexity complexity complexity complexity complexity assume rules rules rules rules rules rules rules rules measure measure measure measure measure representations representations representations representations representations representations representations learned learned learned chosen chosen previous previous previous previous cases type binary binary binary binary binary binary binary conditions conditions tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed bayesian make make make make make fact fact classes tasks tasks human human human regression respect regions potential made made knowledge artificial artificial artificial artificial specific represented represented represented represented desired cross cross cross cross cross provide provide proc proc proc proc proc proc proc proc proc proc goal constraints constraints constraints constraints constraints constraints distributions gain gain discrete discrete mit mit mit mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison contrast contrast contrast nets selection selection morgan morgan morgan morgan morgan morgan morgan department internal internal internal internal internal internal internal internal internal kernel advances advances advances advances joint represents connectionist connectionist difficult difficult difficult sequences considered framework domain domain domain domain domain equivalent directly additional solutions solutions limit limit san san conference conference conference conference conference conference conference determine determine determine determine classifiers classifiers significant significant significant significant statistics world world estimated estimated increase increase validation validation validation validation validation validation con produce produce produce produce produce produce coding coding coding coding randomly developed developed levels levels criterion criterion area area types types path path path selected selected sampling constraint simply simply discussion describe describe close complete complete complete amount nearest common common generate supported role role role require require end instance instance instance easily kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann kaufmann typically needed interesting ratio ratio head special consistent database empirical stored stored international international international international international international international bottom depth depth depth expert expert expert produced produced produced produced run description description description description predict discussed advantage advantage advantage separate takes trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees inference dimensions highly previously previously conventional conventional conventional conventional conventional volume volume volume volume works solve address evaluation evaluation separation interval grant expression expression expression expression concept concept concept concept concept concept concept concept concept concept concept concept predicted correctly touretzky touretzky touretzky demonstrate runs runs strength place conclusions neighbor valued valued editors editors editors editors differences differences differences accurate accurate accurate accurate accurate moody moody learns mateo characteristics demonstrated intelligence intelligence iii manner manner acknowledgements suppose produces ways describes ann label label confidence confidence pruning pruning recall involves scales scales integrated predictive formed formed extraction extraction extraction extraction extraction extraction extraction extraction boolean boolean boolean select select select select decreases national extracted extracted extracted extracted extracted extracted extracted extracted extracted extracted review learner evaluated evaluate evaluate evaluate evaluate evaluate evaluate labels organizing fraction approximations frames forms understanding understanding understanding approximated partition partition measurements measurements expansion expansion spaces spaces spaces add add symbol symbol query classified views existing template box color color instances instances instances instances instances instances instances instances instances instances instances sciences sciences recognize determines mozer mozer mozer specifically candidate candidate domains domains domains domains domains domains domains black phys partially selecting selecting selecting selecting aspects importance encoded symbols symbols symbols build procedures induced induced prob heuristic interested stopping stopping split split split split split split split split split split split split split split split split split return lie lie criteria criteria criteria hold satisfy list play generalize reach reach reach reach thresholds extract extract extract extract extract extract tesauro tesauro remain unlike unlike unlike unlike unlike unlike diego create requirements put put humans humans detail detail hanson accurately lippmann lippmann hall fewer school relationships decisions decisions structured structured structured structured root root root comparable symbolic symbolic symbolic symbolic symbolic symbolic workshop statistically statistically understand notion induction induction induction induction hill concepts integer reading queries queries queries queries queries queries queries queries queries friedman greedy algo algo algo expressions generates integrate percentage percentage cart stop stop growing adapted answer answer answer reasons purposes satisfied satisfied satisfied strictly protein protein protein protein precisely operators scientific recognized members medical medical evaluating fuzzy substantially understood red poorly passed remove remove rep maintain maintain ture extracting extracting extracting extracting extracting extracting extracting extracting extracting extracting extracting fall popular serve marginal begins lim specifies leaf leaf leaf leaf leaf calls calls representative ordinary ordinary leen leen proportion proportion restriction rithm rithm approximates approximates count count jth discovery repre repre discover grows smolensky outcome outcome children climbing generality murphy murphy murphy murphy consideration breiman breiman breiman promising grow interpret serves mark methodology salient symposium child constructive ranging programs respective respective induce induce decide decide pruned heart heart heart searching searching chooses initialize advance canada erlbaum inductive inductive splits splits splits splits splits splits splits splits splits splits splits splits splits splits splits splits splits splits fold fold shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik automated stone limitation limitation counts onr empty verify liu liu summer dna dna numerous thrun thrun users sig opposed arbor additionally blue amherst classifies descriptions descriptions descriptions descriptions demon argue queue queue queue queue queue queue increment rithms pdp chapman expand expand paired disease represen quinlan quinlan quinlan quinlan quinlan quinlan voting voting voting voting west fea applicability applicability refined aaai covers covers agrees towell towell lists calculates diagnostic diagnostic separates sym seed seed archi arrives syntactic syntactic amenable amenable wisconsin counterpart irvine irvine fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity fidelity tations problematic ensuring cleveland greatest allowable deciding tan tan montreal sorted saito saito gallant gallant sentations sentations accu madison madison respects saved accepts sible accessible alexander alexander silverman silverman nakano nakano concise craven craven craven craven craven craven craven craven craven craven craven confident brooks oracle oracle oracle oracle oracle oracle oracle oracle oracle oracle oracle oracle oracle oracle olshen tailed wadsworth resentations promoter promoter chitecture opaque constrains conjunctive strate racy loth tectures mcmillan mcmillan wisc wisc promoters promoters subsymbolic hawaii logically disjunctive scalability brunswick brunswick designers bolic comprehensibility comprehensibility comprehensibility coli queried queried superset hogg hogg macmillan conduct sibility sibility jude ited struct comprehension evanston dayton monterey 
#@Craven_M,Shavlik_J,
#t9
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#*network network network network network network network network network network network network network network network network network network network network network network network network model neural neural neural input function function function function function function function function function function function function function function function function figure figure figure figure figure time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm system system system system system system system system system system system system state state state state state results information problem models models models space space case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown shown shown systems systems systems values values weight weight weight weight weight weight weight weight weight weight functions functions point point single processing processing local local local analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix shows shows shows shows shows algorithms simple simple gaussian gaussian paper paper paper paper net work work work work work work work work work fig points points points points points process process level level level structure structure structure structure structure representation representation representation representation representation representation representation representation show show show equation equation equation equation section section section section section line line rule vectors vectors vectors vectors vectors real real theory theory theory theory theory theory theory gradient term term dimensional dimensional dimensional university university university university computation computation solution solution solution defined defined found initial initial table table table table computer node node node science science science left left left left left left direction activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation nodes maximum maximum press press components components outputs abstract find find find properties references positive positive positive positive positive positive positive positive context context context context context context hand effect dynamic tion tion change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy variable variable assume lower rules rules rules rules rules rules representations representations representations representations representations higher higher type binary binary conditions represent represent represent represent represent represent 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final final maps maps cambridge computing san conference conference determine determine determine free free free free free free increase con con product product product product nature technical describe stable stable stable stable stable stable stable stable stable stable stable stable stable stable surface surface shape role theoretical eds eds journal easily makes including including edge mechanism special structures structures structures language language language numbers polynomial minimize added added added description pair element include include include include side side trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees sense cognitive dimensions axis axis axis tions rl rl sensitive constructed occurs column column column conclusion critical critical greater depend mateo integration intelligence intelligence intelligence minimizing start plane plane plane plane decrease iii derivatives derivatives minima minima minima minima question acknowledgements suppose appears appears pro pro pro construct construct construct construct construct edges describes describes vertical vertical vertical mathematical mathematical easy integrated adding adding equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium implies implies yield yield national depending operations labels centered similarly similarly suggested classical add add add add add valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid string symbol symbol symbol construction construction construction construction construction box thesis activations strings eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues inter illustrated maximize domains grammar grammar grammar grammar grammar grammar grammar grammar grammar grammar major reason reason columns determining determining determining determining determining straightforward symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols situation essentially characteristic refer interpreted built satisfy satisfy satisfy giles eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue computes binding reach principles moves illustrates satisfies satisfies cowan minimized origin origin origin origin origin origin origin origin origin origin origin production production production production detail hanson recursive recursive recursive recursive recursive school rest root root eigenvectors eigenvectors symbolic symbolic symbolic symbolic complicated cognition notion psychology ensure formal formal noted academic consist contributions contributions languages formula distinguish analyzed implementing strictly products products author explained integrating posed passes reaches reaches maximizes parent boston comments yielding labelled labelled labelled labelled labelled tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor tensor harmonic harmonic impossible smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky smolensky reaching generality interpret serves harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony roles roles preparation grammars child child child child lyapunov lyapunov elimination elimination heavy heavy falls paul surprising guarantees vertices colorado lawrence claim multiplied master canada canada parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse agree erlbaum eigenvector eigenvector eigenvector implicitly intersection robert linguistic ure drop vec equivalently connec seek seek principled compatible spreading constructs constructs apparently happen det det det drops differing strict strict strict emphasis copies lation tors coincide concave fol connectionism cess concatenated concatenated legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre legendre unrestricted undergo equilibria equilibria equilibria equilibria unexpected simon simon simon amsterdam subtree subtree subtree miyata miyata miyata miyata miyata miyata miyata miyata miyata miyata miyata miyata miyata miyata inte gupta lowing golden golden roots aii ponents formedness formedness nectionist nectionist subtrees admits admits kauffman invaluable twelfth negation negation negation draft contradiction tionist invalid invalid admit calcu oxi oot oot oot oot oot oot intersects intersects ata founda convolve recurslye fraser fraser fraser ren produc sii succinctly yoshiro contend 
#@Gourley_R,
#t9
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#*network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural input input input input input input input input input input input input input input figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set set set set set networks networks networks networks networks output output number number system system system system system system system system system system system state state state state state state units units units units units units units units information information performance performance performance performance performance performance performance performance performance performance performance performance performance space space linear linear linear layer layer layer layer layer layer case case case case case case vector order order order shown shown shown shown systems systems systems systems probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight unit unit unit unit unit unit unit unit pattern point point point point point point point point point point point point point point single processing processing processing large test test matrix matrix matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs shows shows simple simple gaussian visual visual visual visual visual visual paper paper examples examples size task task step step points points points field process level level structure random random random memory memory memory response response show show equation section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed general general parameter parameter parameter parameter parameter parameter parameter average average average obtained obtained term term term term term term note note result result university computation research found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial table table table distance distance distance connections connections connections node node node node node node node node node node node node node node node node node node node science left left left left left left left left left left direction activation activation temporal press nonlinear nonlinear abstract back convergence convergence convergence convergence convergence density density properties references stochastic important introduction hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior effect generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change change change difference lower lower measure signals chosen higher higher higher higher center center previous bound cases cases cases multiple cortex long long long long long long long long expected equations markov markov markov markov fact forward simulations simulations simulations tasks tasks simulation simulation simulation human human sum mapping means means means potential made obtain cross determined experimental goal goal goal connected motor motor motor motor motor motor motor equal mit steps comparison connection connection connection connection connection connection connection fields support selection selection report institute implementation responses final exp exp bias bias bias bias bias layers addition graph graph graph graph domain equivalent environment environment environment curve curve curve curve curve view view view view transition transition transition transition transition transition transition transition transition transition transition san top top top stimuli detection determine upper upper world world world world world world world increase give con condition coding randomly randomly area area area achieved achieved measured discussion feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward denote tested tested stable stable stable actions amount amount nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest assumed assumed main journal ability hypothesis sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory simulated simulated dynamical dynamical dynamical dynamical dynamical dynamical functional programming programming programming programming interesting interesting mechanism mechanism mechanism mechanism mechanism attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention produced run population population discussed property pair pair robust typical reported reported lateral lateral lateral period identical cognitive cognitive studies studies achieve grid suggests matrices predicted move move occurs occurs setting setting pass critical place tangent sigmoid propose external external external external characteristics characteristics sigmoidal sigmoidal sigmoidal pulse turn turn turn turn selective reference appears appears longer longer factors factors plot dept changing changing sensitivity simultaneously agent implies john stationary stationary stationary stationary stationary stationary influence solved densities evolution evolution evolution evolution constants past past past diagram diagram diagram purpose generation generation generation remains visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible koch koch david david degrees degrees plotted plotted plotted activated candidate characterized simplicity reason reason importance miller reached composed quickly quickly quickly quickly contained oscillations strategies cue cues satisfy satisfies acknowledgments receive receive body diego essential requirements requirements investigate circuitry environments environments environments helpful fashion history investigated referred working proper cover phases removed adapt analyze psychology perfect bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation noted algo detected regime regime regime regime regime animal animal histogram directed directed crucial distinguish unstable phenomena slope inside inside inside inside shared laboratories potentially optimize optimize cybernetics qualitative qualitative qualitative behaviors items item item item item item commands commands commands commands measuring characterize reaches incoming parent cal enables comments returns focused converged converged shifted shifted saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle appearance japan japan optimizing food food food food food food food food food food food food food food food food food food food food food food food food food food consideration promising satisfying satisfying scoring scoring scoring neurobiology shifts performances performances regard enable jolla matter theoretically properly ends ure appeared ber emerge emerge convenience copy causing ical param argue formance rithms maintained ullman noting cij cij cij memoryless turning grateful atr atr manuscript ucsd diagrams walk walk emphasis advantageous copies ate doya doya doya doya doya twenty twenty traveling sake stochastically evolved suppress stay usefulness horizontally distinguishing emerges emerges beneficial lying tokyo tokyo tokyo evolving invisible invisible invisible invisible invisible invisible invisible falling evolutionary evolutionary evolutionary evolutionary demands demands demands demands quick quick quick quick quick quick format unexpected hip behaving survival survival survival survival generations generations generations generations broader broader fluctuation sition advice tran bistable bistable bistable jumps lived helped remember disappear hypothesize symmetrically rogers stays stays snyder percepts kyoto rising behav charac sector sector eter looked posner posner disappears disappears disappears torus soraku autonomously desimone desimone neurosciences survive seika maintenance maintenance maintenance maintenance opposing hikaridai suddenly biolog adaptability ior eat eat eat ect disappeared fki kenji nance cogsci creatures creatures creatures creatures guckenheimer guckenheimer ime ime generous remembering remembering lexp teristics itly offspring 
#@Doya_K,Nakahara_H,
#t9
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data figure time time set set set set set set set networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number number number number number number number system error results results results results results units information information information information information information information problem problem problem problem problem problem models models models models hidden based based based based based based based space space space space space linear layer shown systems systems systems systems values values probability functions unit distribution recognition recognition recognition method method pattern pattern pattern pattern single processing large large large test test test test analysis class class class shows shows shows shows algorithms algorithms simple simple simple simple simple simple simple paper paper paper paper examples examples examples examples examples feature feature feature feature feature feature feature feature net work work work methods methods methods fig fig fig fig step step step step step step points features features features features features features features features features features features features features features features features features features features features features features features features features features features classification trained problems problems problems problems random random random random random high high high high similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show show fixed fixed images generalization generalization generalization real real real real average average average average average average theory note experiments experiments experiments experiments experiments university research found initial initial constant constant constant table table table table table table table estimate estimate estimate standard standard computer computer computer computer computer science left left left present present low low low machine machine machine machine machine machine press press press press press press learn abstract back find find computational computational computational density density density references component component ieee ieee ieee ieee ieee important decision decision decision decision decision decision decision decision decision propagation introduction estimation estimation estimation estimation parallel parallel cost search search tion tion tion difference complexity complexity complexity complexity complexity complexity complexity lower lower measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations chosen higher higher cases good good good tree tree tree tree tree tree tree tree tree tree tree tree tree expected make fact correlation correlation correlation correlation correlation correlation correlation correlation correct correct forward minimum resulting classes classes classes ing ing tasks respect performed called called times factor factor factor factor dimension made natural applications applications obtain vol vol artificial artificial artificial artificial artificial artificial relative specific true true true compared compared cross cross cross cross cross cross define compute compute proc proc proc proc proc proc proc proc constraints gain gain gain equal power mit mit mit mit steps accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison train train train selection selection selection selection selection selection morgan morgan morgan morgan morgan report report department individual advances joint connectionist connectionist difficult difficult difficult exp exp exp addition sequences framework cambridge cambridge computing domain equivalent experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment additional additional estimates estimates design san san top effects efficient full requires choice world world world world vision validation validation validation validation validation con produce produce randomly randomly developed types finally finally selected depends sampling sampling sampling simply tested fast fast fast fast fast assumption assumption assumption predictions finding effective supported require eds eds face ability ability ability kaufmann kaufmann kaufmann kaufmann kaufmann typically pairs pairs pairs pairs smaller smaller needed needed transfer transfer transfer testing significantly uniform empirical call call numbers numbers numbers making supervised supervised magnitude added predict improved correlations correlations correlations advantage pair robust separate separate separate separate apply introduced subject identical identical trees trees trees trees trees trees trees trees trees trees trees trees subset engineering highly varying previously axis axis tions yields trans sparse address address entire increased grant grant constructed constructed exists concept concept concept concept concept concept concept concept predicted predicted predicted predicted predicted alternative correctly correctly correctly correctly correctly feed generally demonstrate runs conclusion conclusion greater conclusions depend depend depend depend depend depend depend depend interactions measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures measures accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate sutton sutton faster strong presence largest reduction demonstrated intelligence intelligence labeled user exist min min min min min min min min min min min introduce introduce construct produces ways factors estimating estimating ann ann ann ann ann ann ann ann ann ann ann ann confidence confidence recall explicitly text develop mutual adding predictive predictive predictive quality quality quality quality quality quality quality quality quality quality quality quality quality quality quality quality boolean boolean john john john choosing focus evaluate evaluate evaluate evaluate frames completely digits partition key reasonable roughly generation construction transactions transactions expect building building handwritten instances instances sciences candidate holds tests tests selecting selecting selecting extra extra extra society society society computationally successful comparing score online ten ten summary traditional conf conf conf conf conf conf conf conf quickly quickly strongly contained allowing classify content follow built list sampled vary vary generalize generalize thresholds predictor acknowledgments bars simpler collection rapidly hanson accurately dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset giving working proper symbolic symbolic workshop scores affect notion induction induction coefficient coefficient coefficient concepts concepts concepts concepts concepts concepts concepts concepts plausible integer reading reading predicting predicts created created created perfect perfect subsets rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank greedy assumes observe improving finds finds seconds percentage pairwise ground ground ground ground ground ground ground ground ground ground ground ground expensive expensive independence rapid rapid rapid rapid sys easier choices ran leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves pool pool pool recognized attribute attribute attribute demonstrates demonstrates recognizing nsf sun reflects varies evaluating evaluating reflect tional backprop backprop backprop orders orders introducing detecting incorrect gains summarized measuring measuring ture achieves datasets datasets datasets datasets datasets datasets datasets datasets datasets sophisticated deviations leaf irrelevant irrelevant consistently classifying redundant redundant redundant redundant redundant leen leen notes tation extensive fix count repre repre flexibility chance significance held held held held multiplicative intelligent scoring imply imply salient natl natl published introduces representational representational representational representational representational representational representational representational predictors counting branching ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking francisco surprisingly rich cpu cpu canada impact inductive inductive dietterich dietterich fold shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik counts onr radar dna dna dna dna dna dna dna dna dna dna dna anns anns anns anns anns anns anns anns anns minus outperform outperform fellowship graded diverse ease ease amherst classifies demon massively rain rain gene assess transparent representa representa representa met smyth statistic speedup constructs represen represen represen quinlan quinlan quinlan quinlan quinlan france paradigms intl intl intl intl intl nasa pools truth truth truth truth truth truth truth truth truth truth truth truth ignoring aaai aaai mea demonstrating info expense functionality nist nist nist nist nist nist nist nist nist nist attributed transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency transparency exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper exper seattle seattle believed successively rivest implying wisconsin tations tations terminates ings ings sentation generaliza fore montreal addi costly costly jose deleting pendent preventing accuracies avg avg avg avg avg avg avg avg avg avg avg avg scans caruana examines accu impor madison madison grown tant damaged ranked intel intel intel intel desire craven craven numbered complexities sorts blurring blurring blurring blurring blurring blurring blurring blurring blurring blurring blurring blurring blurring blurring cap ranks cheap selector chine qualities qualities rankings rankings rankings rankings validate heuristically quantifying sufficiency sufficiency sufficiency sufficiency sufficiency sufficiency sufficiency sufficiency sufficiency sufficiency sufficiency negation ric whitehead whitehead ijcai notable sparcstation cda kevin lets lets economy economy economy economy economy economy economy racy loth loth wisc fayyad fayyad fayyad perona kambhatla kambhatla profound hunt hawaii prospects brunswick brunswick folds afforded joined validating coli superset redun suits battiti battiti jude abundant verifies verifies motivating prevalence cepts kohavi strates overlooked dayton flames dant 
#@Cherkauer_K,Shavlik_J,
#t9
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input input input input input input input input input input input data function function function function figure figure figure figure figure figure time time time time time time time time time time time set set networks networks networks networks networks output output output output output output output number number number number number system system system system system state results results results results results results results results problem problem problem models models performance performance performance based space weights weights case order order order order shown shown shown systems systems systems values values probability probability probability probability probability parameters functions neurons neurons approach pattern pattern pattern point single single single processing processing processing processing processing processing processing processing processing processing processing local local neuron rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis inputs inputs inputs inputs inputs form form form form signal signal signal signal signal signal signal signal simple gaussian paper size feature net net work work task features process process process process process current current current current current high memory memory response response response response response response response response similar similar similar speech speech parameter parameter parameter theory experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result university university computation solution research research research research found found found sequence sequence sequence initial initial computer terms presented presented map map map activation activation low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal maximum maximum range range press press position position position position position position position position components basis basis basis abstract computational computational properties references stochastic due due important important important context introduction complex complex complex complex stimulus stimulus stimulus stimulus stimulus stimulus effect effect dynamic difference difference difference difference difference difference difference difference difference variable assume assume lower measure measure signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals higher higher part part previous previous previous firing firing type required required required required required multiple good distributed distributed distributed expected region proposed proposed proposed proposed proposed scale simulations resulting human human human sum means made made feedback feedback feedback global artificial represented represented compared compared application series rates perform determined determined related related related cortical brain equal equal equal mit mit source source source institute consists responses responses responses difficult addition addition maps considered considered computing experiment experiment experiment experiment experiment environment directly view trajectory stimuli stimuli stimuli stimuli detection determine significant significant world basic channel weighted developed developed processes nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory sampling simply simply discussion group group close inverse inverse excitatory excitatory excitatory common common assumed assumed end ability ability ability degree degree degree degree degree degree degree development development sensory sensory sensory sensory sensory sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory account account interesting significantly increasing increasing increasing segmentation segmentation segmentation segmentation segmentation mechanism language principal principal representing max pre direct making window window inhibition inhibition early decay decay idea attention attention produced produced produced run run added predict improve pair pair robust robust separate takes similarity include array array cognitive recently interest interest interest subjects subjects subjects subjects subjects subjects subjects calculated axis axis rl rl background background background background background background background background background background background background background channels channels channels channels channels interval interval interval improvement parts suggests extended wide alternative occurs occurs generally generally pass demonstrate strength strength strength strength starting starting trajectories depend competitive competitive competitive interactions interactions interactions interactions interactions interactions sound sound sound sound integration external characteristics relationship relationship relationship relationship relationship relationship relationship relationship groups scene scene scene connectivity acoustic acoustic appears van longer longer perception perception perception perception sequential sequential sequential tuned implement sensitivity easy interaction extraction extraction focus focus focus focus focus formation formation formation formation formation depending stages overlap interpretation influence influence restricted restricted restricted showed forms activities similarly constants constants constants sec sec sec iterative filtering coupling box weighting determines determines determines illustrated coupled successfully aspects aspects extra closely effectively effectively effectively driven included included included presentation presentation presentation presentation presentation presentation projections projections essentially receives characteristic characteristic allowing moore interpreted interpreted neuroscience neuroscience contribution michael simplified processors received principles subsequent subsequent essential investigate investigate experience oscillators oscillators limitations behaviour behaviour existence successive school fault relationships stream stream stream stream stream stream stream stream stream stream stream stream stream stream variability complicated workshop analogous act act concepts plausible onset onset man thought subsets aspect nerve grouping grouping grouping submitted seconds brown brown brown brown indicating distinguish agreement capabilities lies comparisons processed processed processed rapid easier arise separately sounds sounds sounds sounds sounds sounds sounds sounds involve pitch pitch pitch gradually arises summation reflects reflects limits reflect substantially cochlear pure simulate simulate psychophysical psychophysical psychophysical psychophysical psychophysical continuously frequently exhibits spread spread incoming incoming incoming incoming coherent coherent coherent coherent coherent expectations expectations coherence coherence coherence coherence coherence coherence coherence coherence returns eventually wang wang progress traces simultaneous simultaneous spectra discontinuities physiology primarily sv modify extensive temporally acts partitions significance ranges overcome simplify intelligent intelligent moment serves belong affected integrator synchronous arrays arrays enhanced exploring published tone tone tone tone tone tone ensures bad facilitate facilitate reproduce enable modelled modelled occlusion omitted belonging proximity proximity proximity proximity associations associations graded graded creates alternating alternating poses causing perceived reports tendency affects associate streams streams streams streams streams alter peripheral peripheral interact interact degraded interacting maximally argued investigating nuclei oscillating distinguished refinement refinement inversely tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones vanishes vice demonstrating resp resp resp resp resp appearing versa hearing hearing spacing developmental reflecting reflecting periodicity dissertation manipulated systematically neighbourhood isolation attended priming priming handbook foreground foreground foreground foreground foreground foreground foreground foreground foreground foreground foreground foreground foreground foreground foreground foreground fore enabling enabling cope replicate replicate linking bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman distractor distractor distractor distractor schema intrinsically judge judge attentive attentive organisation organisation organisation organisation modifies psych psych psych neurodynamics leaky reproduces remember continuation comprise centred centred exclude cooke cooke cooke alertness multichannel behavioural behavioural originating spans organism organism organism embodied confused extraneous doctoral groupings unrelated interrupted interrupted complication focussed gestalt emitted discriminated decomposes ijcai sheffield exemplified fused breakdown masking sharpening strengthening strengthening weaken perceiving judgement judgement judgement judgement judgement judgement interplay quicker pare judgements preattentive preattentive multistage declines fibre coincidences recognise distracting distracting manages eindhoven perceptions perceptions perceptions creative creative accidental bols summarise 
#@Denham_M,McCabe_S,
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#*learning learning learning learning model model model model model model model model model model model model model neural neural input input input input input input data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set training training training training number number system system system system system system system system system system system system system system system system system system system state results results results results results units units units units units information information information models models based space case case vector order shown shown systems systems systems systems systems systems values values probability functions neurons neurons unit point point point point point point point point point point point point point point point point single single single single single control control local local local local local local local local local local local local local local test analysis analysis inputs form form shows gaussian visual visual visual visual visual visual visual visual paper work task task cells cells cells cells cells cells cells cells cells cells cells points field field field field field field field field field field field field field field field field field field field process process process current current current current current current trained trained cell cell cell cell cell cell structure random high memory representation representation representation representation parameter theory theory term term note note experiments experiments experiments activity activity result result result university university university variables variables variables variables solution independent found sequence initial initial initial initial initial initial constant estimate estimate estimate estimate computer computer computer distance distance distance science science prediction left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction present present low low motion press press press learn position basis basis abstract computational computational properties references due behavior change change change change variable variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume measure representations representations representations representations representations representations representations representations representations higher higher part center center center center center cases firing firing type type type multiple multiple multiple multiple multiple cortex long fact fact fact correlation observed observed observed simulations simulations resulting resulting tasks simulation computed orientation orientation orientation original represented represented true define location location location location location determined determined experimental goal goal related motor cortical brain equal comparison fields fields fields fields fields fields fields fields fields fields fields fields modeling modeling modeling modeling proceedings proceedings report department internal code code code individual connectionist responses computing computing equivalent equivalent experiment experiment experiment experiment experiment experiment environment environment environment environment environment environment environment environment environment environment environment view view view view view view view view view view view view view view estimates effects conference choice choice estimated pages pages pages give produce derived derived randomly developed path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path product product product finally processes discussion discussion normal normal tested tested tested tested stable surface surface predictions finding amount supported role theoretical journal journal journal journal journal journal sensory sensory including including simulated pairs pairs reduced account unknown significantly york head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head mechanism consistent consistent consistent consistent consistent trials trials trials representing representing representing produced choose choose added sources description predict predict discussed directions recent pair pair separate reported introduced introduced moving moving moving moving identical identical cognitive compare observations module module module module module tuning tuning match match match address positions locations locations locations locations organization entire occur occur suggests trial rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation predicted touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky touretzky white critical place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place place greater segment segment editors editors interactions interactions interactions interactions interactions interactions integration integration integration integration demonstrated radial turn variety variety variety relationship relationship relationship relationship question denoted edges stability stability tuned tuned tuned tuned metric coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates simultaneously simultaneously angle angle angle angle angle angle angle angle angle angle angle interaction adding gaussians shift implies formation formation review viewed codes codes open open controlled controlled controlled showed showed completely completely key partial earlier earlier initially distances distances david david degrees recorded recorded recorded fire figures includes includes includes combinations combinations retinal memories activated activated mozer coupled variations black society maximal driven driven notice strongly showing showing neuroscience neuroscience neuroscience cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cues highest hypotheses attempt preferred preferred preferred rat rat rat rat rat rat rat rat rat modelling experience environments association association existence school behavioral behavioral behavioral reliable symbolic cognition examined editor predicts predicts opposite changed changed changed changed panel panel panel panel panel panel panel panel observe observe explored mapped detected contributions animal animal animal animal animal animal animal animal animal animal animal animal animal animal navigation navigation navigation navigation navigation navigation navigation navigation adjacent adjacent adjacent biology handle arc leaves hippocampal hippocampal hippocampal hippocampal hippocampal angles recording recording recording annual mellon alignment alignment researchers explained fourth fourth geometric carnegie double double substantially empirically elman consistency consistency consistency consistency consistency dark dark quantitative sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp maintain pittsburgh weigend synchrony cal green enables conclude conclude eventually consistently aligned aligned physiology oxford oxford drift drift animals animals animals animals rotated rotated rotated ordering purely reconstructed food smolensky outcome outcome outcome outcome outcome outcome outcome outcome outcome outcome outcome outcome outcome outcome outcome establish smith ranges familiar familiar familiar serves integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator integrator spot corner corner corner corner reliably reset reset reset reset reset reset reset reset reset reset reset entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry entry mental lawrence lawrence reproduce cerebral record matter probe probe probe agree card card card card card card card card card card card card card card card card card card card card card alternatively ignore unchanged unchanged associations arcs summer converted visually visually session nition comparative copy corrected perceived chapter hillsdale hillsdale manipulation thick wall wall wall wall wall neurophysiological denoting compatible compatible retain flip nuclei nuclei ambiguous associates associates maintains maintains outcomes outcomes outcomes outcomes outcomes west west retained priority priority priority priority priority priority sessions sessions sessions rats rats rats rats rats rats heading continued east east diffuse establishes floor anterior anterior mcnaughton mcnaughton mcnaughton symmetrical safe presently drifting comer comer comer comer comer comer comer comer correlates enters doubling scattered substrate freely freely freely landmark landmark landmark landmark landmark landmark landmark landmark rotate rotate rotate spent tightly wan wan wan wan entering entering entering discrepancy entered entered localize localize manipulations reproduces viable viable anticipate panels bearing bearing thalamic thalamic faculty cog persistence landmarks landmarks landmarks landmarks landmarks landmarks landmarks landmarks landmarks cards cards cards cards cards cards cards cards cards cards cards cards triples muller muller muller muller loses knierim knierim barnes internet pairings cheng cheng evidenced viability remembered flipped flipped cylindrical faulty redish redish redish redish redish redish redish redish navigating navigating resetting resetting leonard analogs analogs visuo mediates efference experimenter manipulates 
#@Rexlish_A,Touretzky_D,
#t9
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#*neural neural input input input input input data data data data figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time set set number number number results information performance performance order order order order shown shown shown shown shown shown shown shown shown systems probability noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons point single single single large large local neuron neuron neuron rate rate patterns analysis analysis form shows shows shows gaussian visual visual visual visual small small size work fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells points level level current cell cell cell cell cell cell structure structure response response response response response response response response response response response similar representation show show show show show section section average average average average average average average average average average term term term term term term term term term term note university computation research research independent defined found estimate standard standard standard synaptic science prediction prediction left left left left direction direction direction direction direction direction frequency temporal temporal temporal motion motion motion motion motion motion motion motion motion range components basis abstract references component component component due due due due procedure important introduction action action stimulus stimulus variance variance change difference lower lower lower measure measure higher center previous previous previous previous cases cases firing firing firing firing firing cortex cortex cortex good good spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long long long long long long long long long long long long long long represent expected expected region correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed observed observed errors scale scale scale scale scale scale scale scale scale scale scale resulting ing computed computed computed times times factor study study study relative cross cross cross cross cross cross cross cross rates rates experimental related cortical cortical equal comparison train train train train train train train train train train train train train train source institute institute institute represents responses responses final addition experiment additional limit limit stimuli effects upper significant vision estimated estimated weighted area area area area area area area area area area area area area lines lines processes nature biological measured measured measured discussion normal assumption excitatory amount short short short short short short short short short short short short common common common common common common common common supported adaptation hypothesis degree noisy noisy including typically pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs technology significantly significantly york consistent consistent consistent trials trials trials trials trials trials trials trials trials trials database principle call window window window inhibition inhibition inhibition inhibition inhibition inhibition normalized predict neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal pair pair pair pair pair reported reported identical previously axis yields studies definition interval interval interval interval interval interval exists occur occur occur trial trial trial trial trial trial trial trial trial trial trial trial trial trial deviation deviation wide wide spikes spikes alternative width width occurs half half conclusion assumptions central central central accurate peak peak peak peak peak peak peak peak peak peak peak peak taking strong strong mechanisms mechanisms mechanisms mechanisms presence california min min relationship relationship iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii iii averaged force base acknowledgements areas areas relation construct longer plot dept sensitivity simultaneously text text scales scales scales scales scales shift shift potentials potentials correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated transform fraction centered slow sec sec intervals intervals intervals intervals intervals intervals intervals intervals intervals roughly msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec msec foundation koch koch koch koch recorded recorded recorded recorded recorded thesis currents inter inter sciences determines plotted variations post ten excitation strongly strongly induced interpreted contribution duration duration michael play absence providing ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill ill predictor predictor neurosci neurosci preferred preferred preferred preferred preferred preferred intrinsic intrinsic trains trains trains trains trains trains trains trains trains trains trains origin stimulation carried circuitry steady hanson helpful fashion office office scores neu measurement coefficient coefficient coefficient coefficient coefficient onset panel panel precise pyramidal seconds histogram indicating distinguish derivation analyzed analyzed adjacent processed monkey arise pool scientific res medical medical raw fourth populations pathways transient lack psychophysical psychophysical peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks peaks operate howard howard poisson poisson occurrence occurrence serve pasadena substantial coherent coherent coherent conclude conclude attentional traces traces simultaneous simultaneous cor contribute room saccadic drift animals null null null count count count count count count count count count count count count count count count unity naval caltech arranged suppression suppression suppression suppression suppression air adds occurred occurred iiii iiii iiii iiii iiii iiii iiii iiii iiii iiii iiii iiii iiii height height analyzing neurobiology roles implications responsible responsible responsible responsible corner eqn inferior periods periods mouse widths washington injection monkeys monkeys israel ensembles thin bursts bursts bursts bursts stimulated creating creating omitted saccades broken broken messages alternatively avoiding lag lag lag lag lag lag lag lag lag lag lag lag counts counts counts counts counts discharge converted minus ram gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps gaps tween causing suppressed suppressed electrode electrode assess argue iff thick life potassium hughes hughes individually fixation surrounding surrounding macaque increasingly funded accounted milliseconds milliseconds milliseconds nil removes served correlogram autocorrelation hypothesized opponent pearson neocortical usefulness subtracted contrasts contributes anthony symmetrical william establishing inset longest longest pooling priming inst prominent counted tens christof newsome newsome newsome jerusalem movshon movshon hebrew broader examines dominate extracellular iiiii iiiii iiiii iiiii iiiii coincidence bair bair bair bair bair bair pushed scored scored excitability emphasizes behav occasional indicative interrupted sug doubt cients isolate connors connors llll llll llll iiiiii iiiiii iiiiii iiiiii iiiiii iiiiii iiiiii blink blink shadlen shadlen shadlen richmond richmond kenneth illl illl illl illl illl illl illl illl illl illl rst rst rst rst rst rst rst rst correlograms correlograms correlograms correlograms coeffi lll thalamocortical iiiiiiii iiiiiiii iiiiiiii iiiiiiii autocorrelations nyu illill illill illill illill excessively excessively lift complicates rosci multaneously iill iill kindly britten britten britten gested lllll lllll barrel consume wyeth respon 
#@Bair_W,Koch_C,Zohary_E,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input data function function function function function function figure figure time time time time time time time time time set set output output output number number error results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem models based based linear case case case case case case order order shown systems systems systems probability probability probability probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method approach approach point point point point point point point single processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate class optimal optimal inputs inputs inputs inputs inputs inputs inputs shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple gaussian gaussian gaussian size size size work methods methods methods fig fig fig cells process process current current random random high high high high high high high response response response response representation representation representation show equation equation line line line line line line line line line general parameter real average obtained obtained obtained term term term term note note note note note note experiments experiments experiments experiments experiments threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables solution independent independent independent independent independent independent independent independent independent independent independent independent independent log log log log log defined sequence sequence target target dynamics initial initial constant constant constant constant estimate estimate estimate estimate terms terms terms terms synaptic synaptic synaptic synaptic science present present present low low low low low temporal temporal temporal temporal temporal temporal temporal temporal temporal maximum maximum maximum maximum maximum maximum maximum maximum press press outputs abstract applied applied applied properties references component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic important introduction estimation estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus generated variance variance variance variance tion difference assume assume lower lower lower lower lower lower signals signals signals signals representations higher higher previous bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing required spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike conditions conditions conditions conditions conditions finite finite finite resulting total total computed sum sum eq eq eq eq eq eq eq eq eq called times times times times times times factor optimization potential potential potential potential potential natural natural applications applications knowledge filter obtain vol represented compared series series provide provide rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates determined experimental distributions discrete discrete cortical cortical cortical equal equal mit mit voltage voltage contrast train train train train train train train train train train train train train train train train train train train train train train train train train train train train train institute code code code code individual individual advances joint joint joint exp scheme considered considered considered cambridge cambridge equivalent equivalent equivalent directly curve curve view view solutions estimates limit limit limit limit limit limit limit limit top stimuli stimuli bit bit bit bit bit capacity capacity determine determine upper upper upper upper upper upper upper full requires choice statistics estimated estimated increase give produce produce produce condition condition coding derived conditional conditional conditional conditional conditional conditional conditional developed developed developed entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy actual provided provided provided processes inhibitory inhibitory depends depends depends simply simply measured discussion increases increases increases increases arbitrary fast close inverse assumption corresponds excitatory excitatory amount assumed theoretical ability hypothesis hypothesis noisy sensory smaller functional functional functional significantly increasing mechanism mechanism mechanism mechanism mechanism mechanism special empirical language bits bits bits bits bits bits bits bits bottom idea added added added added neuronal neuronal neuronal neuronal membrane membrane membrane membrane membrane recent correlations correlations correlations correlations correlations resolution resolution resolution resolution exact exact exact exact exact advantage advantage property property ensemble ensemble ensemble ensemble ensemble ensemble typical typical apply identical relevant interest interest highly highly compare compare compare calculated tions yields symmetric bounded interval interval interval interval entire increased expression expression expression expression occur occur occur occur trial trial wide spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes derivative alternative width deterministic deterministic deterministic white white white white occurs occurs generally generally pass greater greater greater greater reduce clear clear clear exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential exponential asymptotic suggest encoding integration integration presence presence characteristics drawn solid solid solid solid turn assuming assuming decrease question explicit suppose suppose relation pro van van longer generating generating generating estimating estimating describes mathematical changing infinite infinite infinite develop mutual mutual mutual mutual mutual mutual mutual mutual decreases decreases expressed expressed reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction correlated interpretation variation evaluated evaluate fraction completely completely calculation dashed dashed dashed dashed dashed dashed expansion expansion sec sec sec reduces intervals add generation generation remains msec msec msec msec msec msec msec msec msec construction construction construction koch koch precision precision precision precision precision precision fire fire formulation uncertainty uncertainty uncertainty specifically simplicity extra maximal encoded encoded encoded encoded effectively spiking spiking spiking spiking situation receives repeated repeated induced induced contained contained prob moore interested neuroscience content content timing timing list usual absence absence absence absence absence highest principles operating decreasing trains trains trains trains trains trains trains trains trains carried carried production varied varied involving preliminary preliminary variability variability variability variability encode encode neu hill coefficient possibly editor reading thought thought precise precise precise message multivariate detected regime regime regime regime regime integrate integrate theoretic distinguish agreement waveform improves correction turns filtered broad arise arise mation hippocampal hippocampal describing arises fluctuations double substantially substantially understood experimentally passed reliability reliability reliability reliability reliability limiting limiting differs reaches achieves instantaneous instantaneous uncorrelated generator guarantee temporally appropriately bin bin bin unity arrival eliminated occurred height grow balance balance balance balance balance balance balance obtaining neurobiology neurobiology observing monotonically monotonically salk salk intuitively intuitively infor analyses slice slice reset loo irregular bialek bialek bialek bialek bialek bialek bialek bialek injection injection somatic somatic hasselmo specialized bins bins jolla late theoretically border fold fold receiving adopted crossing usage minus transmitted encodes encodes convenience par tight tight tight assess iff subthreshold subthreshold subthreshold subthreshold subthreshold distri intuition gained mathematically permits bounding neurophysiological crosses regimes regimes complementary isi isi isi isi isi isi isi isi isi isi isi isi isi isi isi isi isi isi isi crossings crossings esti behave nil interspike interspike unpublished strict bution served transduction inconsistent attributed rons condi condi anthony resolved resolved resolved resolved stevens stevens stevens stevens stevens zador zador zador zador zador zador colleagues colleagues colleagues convolved communicate edition mcgraw restrictive charles approached approached transmit transmit steveninck steveninck ruyter ruyter noiseless quantified obeys rieke rieke rieke ness saturates saturates minute leaky leaky leaky mate ting epsps conveys univariate indistinguishable lose neglecting conveniently softky softky passage brevity ticular recon recon struction struction colored pilot pilot warland warland quantifying deterministically implausible transmitting resets resets asymp ses ses vides papoulis papoulis agreed agreed hnear formu emits seminal inpu uhlenbeck verge underestimate underestimate underestimate ornstein discretize telling underestimates underestimates totic perkel impinging biosciences vols suprathreshold 
#@Stevens_C,Zador_A,
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#*network network network network network network network learning learning learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time networks networks training training training training training training training training training training training training training training training training training training output system system system state state state state state state state results results results results results results results information problem weights weights linear linear case case case case case case order order order order systems probability probability probability probability probability probability probability probability weight weight weight weight weight weight weight weight functions functions functions functions neurons neurons neurons neurons unit point point point point point single processing local neuron neuron neuron neuron neuron rate test analysis analysis analysis analysis analysis analysis analysis form form form simple small small small small small small size size size size size size size size size size size size size size size size size net net net net work work work task points field field field field field field field field field field field features process trained representation show equation fixed general general general general approximation approximation approximation average theory theory theory obtained term term note activity activity activity activity activity activity activity dimensional result result threshold threshold threshold threshold threshold solution solution solution research independent defined defined defined found dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant constant constant computer computer computer terms terms terms terms distance connections synaptic synaptic synaptic prediction prediction prediction presented map map map frequency frequency maximum range range position position position position position continuous abstract density density references due due due due due due due due positive positive positive positive positive positive important adaptive adaptive adaptive adaptive introduction hand stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect tion change change change change change change change change change change change change difference difference difference assume assume representations part part previous firing firing firing type type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex binary long long conditions conditions conditions conditions conditions represent equations equations equations make make fact region region region region region region region correlation probabilities scale total simulation simulation simulation human sum sum regions regions regions mapping means means factor factor factor potential potential potential potential made obtain negative relative relative specific represented series receptive receptive receptive define proc proc location location active active determined experimental goal connected cortical cortical cortical cortical brain brain larger larger fields dependent synapses synapses consists advances joint maps maps considered framework framework directly solutions solutions transition stimuli stimuli stimuli effects effects effects conference basic increase increase increase con condition derived derived area area area area area area processes processes nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory simply discussion increases increases describe limited inverse inverse assumption excitatory excitatory stable surface surface predictions short assumed assumed assumed theoretical face face adaptation adaptation adaptation ability ability makes sensory sensory sensory sensory sensory underlying underlying account account dynamical functional fully fully fully fully mechanism consistent consistent consistent uniform uniform uniform uniform uniform uniform empirical details inhibition attention light light denotes denotes membrane membrane membrane membrane membrane membrane membrane discussed recent pair reported lateral lateral lateral lateral lateral apply sense array array cognitive recently engineering sufficient sufficient highly works tions definition definition symmetric locally touretzky width width occurs boundary boundary boundary conclusion assumptions hebbian hebbian hebbian hebbian operator competitive competitive interactions hard sigmoidal demonstrated selective selective decrease decrease relationship averaged manner manner denoted denoted acknowledgements areas areas suppose appears digit digit digit longer primary primary primary transitions stability changing coordinates linearly physical slightly equilibrium equilibrium equilibrium potentials competition john decreases decreases expressed expressed viewed showed showed sizes constants past reasonable classical roughly boundaries distances foundation expect usa inter sciences illustrated effectively build post fine soc prob prob success contribution physiological sci comp involved usual nips observable neurosci received decreasing modelling body body stimulation stimulation stimulation stimulation stimulation stimulation perturbation perturbation perturbation perturbation perturbation perturbation perturbation steady steady steady steady steady steady steady detail behaviour periodic periodic school biol biol biol proved topographic topographic topographic neu neu math math adapt adapt quantities der der der portion taylor taylor taylor taylor separated mapped expressions nerve amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari explain smoothness biology adapted caused caused caused london london london tive tive desirable monkey monkey arise afferent afferent afferent afferent afferent afferent acad beginning auto considerably empirically experimentally recordings ity maintain perturbations spread cal ordered prevent suited geman geman neuro physiol damage owl owl eventually phenomenon cybern cybern cybern college college formally narrow neurophysiol discover receptors proceed arranged extending fits fits convenient primate imposed reasoning natl edelman von von von monkeys uni modelled modelled modelled express cerebral stimulated stimulated surprisingly mem environmental contact border border border papers limitation schulten schulten largely minus nelson nelson nelson expanding willshaw willshaw willshaw willshaw tween perturbed perturbed centre centre ease malsburg malsburg malsburg resting peripheral gained wall wall mammalian life interacting hughes spreading spreading lond sketch conversely finger finger inversely siam grateful rotating travel signs simplifies completed ritter ritter vice correlate scanning sessions versa fortunately const justified crude rfs rfs skin skin king king puts somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory somatosensory adult adult pearson pearson val cally cally possess equa partly neurol tactile tactile tactile tactile tactile tactile tactile tactile tactile measurable colleagues merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich sis demands demands demands attended deter neglected neglected greatest sur sur probabil limb col analyse plastic jenkins jenkins jenkins jenkins jenkins jenkins jenkins jenkins jenkins stryker magnification magnification activates primates borders borders borders borders borders organisation touch touch superscript apparatus posi grossman perturbing enabled uniformity leaky blob blob blob seeking participate exciting disk disk bull theor mag analysed laterally centred centred centred finkel behavioural behavioural behavioural behavioural mined touching brings explosion mammals periments sponse blobs sketched electro psychol app pling neurosciences opaque brane strand graphic vital cou localised evidently creases reorganization reorganization reorganization tips tips tips tips analy petersen petersen petersen petersen kaas kaas kaas kaas phantom nick adaptivity competi cynader topo cept corti llin sation protocols tonically evokes haber haber roscience roscience territory territory gion dicate 
#@Peterson_R,Taylor_J,
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#*learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data figure figure figure figure figure time time time time time time time time time time time set set networks output output output output number system system system system system system system system system error results results results results information information information information information performance based based linear linear linear case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown shown shown shown shown systems systems values values parameters parameters parameters parameters neurons neurons neurons neurons neurons neurons unit unit unit image image single single processing processing control control neuron rate rate test analysis class inputs inputs inputs inputs inputs inputs inputs inputs inputs signal signal signal signal paper small fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells process level cell structure response response response response response response response representation representation representation representation representation architecture show show equation equation equation equation equation equation equation section fixed fixed rule vectors vectors vectors vectors vectors images images images general real average average obtained term term term term experiments activity activity activity activity activity university variables variables research research research target target target target target target target target target constant constant constant constant terms distance distance distance distance distance distance distance distance distance distance distance distance distance connections connections connections connections science prediction left left left left left left left left direction direction presented present phase activation object object object object motion motion range press position position position position position position position position position position position position position position position position position position position position position position position position position position position components components components nonlinear abstract find computational convergence references component component important important context context context context context context context context context context context introduction action complex hand hand behavior effect effect effect generated tion tion tion tion tion tion change change assume assume signals signals signals signals signals signals signals representations learned center firing firing required required required multiple multiple multiple good represent represent equations observed observed forward scale finite simulations resulting human computed performed called reinforcement orientation orientation study obtain obtain negative negative relative relative relative specific cross location location location location location location location location location perform perform eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye experimental related related posterior constraints connected gain gain gain gain gain gain gain motor brain brain brain brain brain brain equal mit comparison comparison connection source selection report report report report institute institute loss advances responses responses responses responses responses difficult considered cambridge directly view view san top determine determine speed speed basic increase produce derived derived velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines product product finally evidence inhibitory depends depends biological achieved measured measured measured measured discussion describe describe describe tested transformation transformation transformation close close assumption complete predictions predictions assumed assumed assumed supported theoretical require require main adaptation adaptation journal journal journal journal journal journal journal journal journal journal hypothesis hypothesis hypothesis makes sensory sensory sensory sensory fit typically smaller underlying needed combination account account dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical ratio head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head special special special consistent consistent details details direct magnitude combined combined combined sources exact movement movement movement movement movement reported identical identical side side side side side sejnowski sejnowski sejnowski sejnowski relevant dimensions compare calculated axis axis axis axis axis axis axis axis axis axis axis tions studies definition definition positions locations locations amplitude amplitude constructed horizontal horizontal horizontal horizontal horizontal horizontal horizontal expression studied studied studied studied suggests suggests wide wide derivative rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation correctly touretzky generally conclusion operator editors central retina retina retina retina peak peak learns learns propose taking mechanisms integration physics characteristics california solid proportional proportional variety exist exist movements movements plane plane plane plane decrease manner force question appears appears written written written laboratory ann vertical vertical vertical vertical modeled implement coordinates coordinates coordinates coordinates linearly transformations transformations angle angle angle angle angle angle formation depending stationary detailed transform open controlled ocular ocular ocular ocular ocular ocular ocular ocular ocular modulation modulation modulation translation translation translation translation translation translation translation translation translation translation translation constants allowed diagram calculation performing delays sec sec combining combining fitting generation remains remains distances distances symbol recorded coordinate mozer coupled discussions major encoded included literature computations computations computations computations computations road showing issue contribution contribution sin sin sin sin running oscillations oscillations oscillations physiological notation involved vary dot correspondence neurosci attempt acknowledgments law origin command diego experience varied varied humans replaced accurately divergence dotted helpful ideal ideal ideal combine combine dependencies dependencies dependencies dependencies working working proper proper pathway encode func understand closest possibly rev eyes eyes eyes eyes adjusted front front nervous fibers contributions contributions seconds site vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor cos agreement multiplication lies tool comparisons inside drive rapid rapid straight filtered precisely forces located nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus monkey monkey monkey monkey products angles angles angles calculations calculations calculations calculations medical author geometry fluctuations integrating requiring varies limits reflect pathways pathways pure transient dark axes axes recordings recordings robinson robinson robinson robinson robinson howard modulated modulated semi conclude focused instantaneous instantaneous shifted representative ear writing tation saccadic angular angular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular vestibular rotations rotations rotations rotations rotations rotations turned climbing fits consideration anatomical anatomical primate simplify cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum imposed neurobiology observing implications salk salk north integrator integrator integrator integrator integrator integrator integrator integrator integrator preparation motivation cerebellar paul overview infinity monkeys monkeys monkeys hasselmo reproduce dif viewing viewing viewing viewing laplace laplace ahead gaze gaze gaze gaze gaze gaze gaze gaze gaze jolla jolla waveforms arrows motions motions extensively relies captures severe boxes boxes informa informa reflex reflex reflex reflex reflex reflex reflex reflex reflex reflex reflex reflex neurophysiology neurophysiology neurophysiology neurophysiology neurophysiology neurophysiology neurophysiology neurophysiology neurophysiology neurophysiology kinematics kinematics kinematics fellowship sig diverse lesions amplitudes solely stem stem stem stem stem acceleration acceleration resting reflected ary verified perpendicular perpendicular insights mathematically graduate distant compatible hughes terrence mediated mediated mediated concentrate individually fixation noting nuclei nuclei nuclei nuclei nuclei translations translations translations flash flash oculomotor oculomotor oculomotor oculomotor oculomotor oculomotor afferents afferents knowing reciprocal corrections corrections unpublished correlate tonic tonic locomotion vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo mcdonnell ferent viola king king king king king puts purkinje purkinje affecting kinematic kinematic kinematic kinematic physiologically physiologically anterior settle intact sions reproduced compensated dimen brackets meant correlates stabilize carrying rotational rotational rotational tan stabilization mid decompose replicates modulate modulate pew vergence vergence vergence vergence vergence vergence vergence vergence vergence vergence judge judge walking sensed sensed sensed sensed inte tran hypothetical grossman grossman leaky anticipate canal canal canal canal canal bruce terry listing snyder snyder snyder snyder snyder reticular millisecond motoneuron multiplies compensatory compensatory useless rectly gravity sudden focussed departments canals canals canals canals canals canals canals canals stabilizes stabilizes ford nals inertial inertial torrey pines antagonistic posture phasic midbrain midbrain negatively semicircular semicircular semicircular semicircular semicircular semicircular ven necessitates latest integrators organs organs crawford duces clarke clarke sustain cajal cajal ents bracket integra hess hess olivier modula vestibuloocular vestibuloocular vestibuloocular sus affer 
#@Coenen_O,Sejnowski_T,
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#*model model model model model model model model model model model model model model model model model neural neural neural neural neural data function figure figure figure figure time time networks networks number number number number number number number system system system system system state state state results units units models models models models based case case systems systems systems probability neurons neurons neurons unit recognition single single single single single control neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate analysis analysis shows shows simple paper small small small size size size size size size size size work work work work work methods cells step process process level level level cell cell cell cell cell memory similar show equation equation equation equation equation section fixed real real average states term term term note experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result university university independent independent independent independent independent found dynamics initial initial terms terms terms terms connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science presented present present present activation activation motion range range components basis abstract computational references component due important important important introduction complex complex complex effect tion tion change change energy spatial assume bound bound bound bound bound required required required long long long equations equations make forward forward forward forward forward forward simulation simulation simulation simulation multi performed called regions made made made made feedback negative original original artificial artificial specific specific specific provide provide proc proc proc active active active active active active experimental experimental experimental experimental experimental related related related motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor comparison larger larger larger connection support dependent dependent dependent dependent loss loss version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses individual individual difficult final exp considered experiment directly transition effects effects effects effects effects free free free free increase give give con area area types types provided processes selected evidence nature nature nature constraint constraint constraint constraint constraint discussion normal normal normal normal limited stable stable surface surface surface surface predictions amount amount amount amount amount amount assumed synapse synapse synapse synapse synapse supported role role role role role role role theoretical journal journal journal end end hypothesis hypothesis development development development development fit fit account ratio mechanism mechanism mechanism mechanism leads direct direct idea produced membrane recent recent exact advantage advantage advantage advantage takes takes lateral lateral lateral lateral lateral lateral lateral cognitive cognitive compare volume volume volume volume match achieve entire increased parts expression studied suggests extended extended extended extended extended extended extended wide loop demonstrate demonstrate flow flow critical critical critical place place place place greater hebbian competitive competitive competitive competitive clear performs taking strong strong mechanisms mechanisms mechanisms mechanisms mechanisms presence presence largest largest demonstrated demonstrated proportional proportional proportional proportional proportional proportional proportional proportional proportional proportional exist selective selective selective decrease relationship iii identification acknowledgements areas appears relation produces factors mathematical physical electrical electrical electrical remaining interaction develop formed implies blocks versus competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition expressed formation dependence viewed showed understanding understanding suggested constants allowed allowed combining initially construction advantages david david includes includes usa dominance dominance dominance dominance activated activated candidate phys partially successfully identified efficiency efficiency divided situation tend identity reached capture soc soc kind kind strongly induced induced induced induced allowing allowing neuroscience sci receptor receptor receptor receptor receptor michael play play play absence binding binding principles subsequent subsequent rat rat rat rat rat remain stimulation perturbation perturbation create essential difficulty steady dual dual dual dual dual behaviour existence existence postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic ideas applicable terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal biol biol biol biol plasticity possibility muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle affect presynaptic presynaptic presynaptic presynaptic presynaptic neu patch patch naturally plausible plausible reading thought aspect nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nervous nervous nervous fibers extent extent mentioned percentage histogram histogram indicating ment developing developing developing developing growth distinguish biology sites protein protein protein constructing axon axon axon axon axon acad axons axons axons axons axons patches robinson robinson robinson release cal resource resource resource resource resource resource resource resource extensions achieves electric physiol findings findings findings cybern physiology sort sort proportion proportion ratios labelled connecting royal royal receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors suppression suppression eliminated extending extending cellular fits fits smith chemical efficacy efficacy interpret nearby roles illumination synchronous responsible days muscles natl elimination elimination elimination elimination elimination elimination mouse induce dependency demonstration histograms captured originally competing diameter diameter diameter hippocampus suggesting belonging extensively considerations cam convergent influences outlined mind converted achieving email email validity removal removal focal focal focal reaction reaction reaction reaction reaction reaction reaction reaction reaction reaction willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw tween distinction distinction distinction distinction terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals terminals centre centre junction junction junction junction junction junction junction individuals affects simulating simulating edinburgh edinburgh edinburgh edinburgh molecular molecular alter cns cns trends insights insights insights mammalian potentiation regulation neurophysiological expand plate lond lond pos employing distinguished sam inversely grateful gordon gordon gordon molecules molecules molecules inactive inactive inactive inactive inactive inactive manuscript suggestions resolve resolve justified junctions spring reversible reversible attempting compete compete compete compete diffuse diffuse developmental developmental adult transmitter ron suppress appealing affecting distinguishing conflicting evenly rasmussen rasmussen rasmussen accumulate resolved aggregation aggregation molecule molecule molecule molecule molecule cold subscript vicinity vicinity vicinity ben enters plasma substrate shares tory stabilization acetylcholine acetylcholine acetylcholine acetylcholine acetylcholine explaining aggregate trapped bodies survival survival survival simula joseph joseph joseph joseph joseph disadvantages dilemma plausibility examines apparatus apparatus apparatus tentative concurrently bind damaged displaced bruce justify justify samuel volumes syrup vitro poo poo membranes laterally laterally devise lose stays birth birth webb accumulating dbn underlie supplies neighbours intersecting graham resolving organ bigger bennett subscripts skeletal skeletal death transport transport establishment biochemical dan interacts muscular diameters subjected funding maintenance nals innervate conservation ship fibres fibres fibres fibres fibres crucially trophic trophic conformation plates cyb binds binds innervation innervation innervation innervation innervation innervation innervation innervation organising acta suppressive paradox paradox innervated innervated innervated innervated chances surviving influx ascertain ruled wallace wallace wallace phenomenological adhesion fibre fibre fibre coexist coexist lective implicated favour tempting achievement attract outset cle barry barry changeux fects postnatal ology lating speculative posit aggregates aggregates ronal physi quant protect uncovered nerves nerves biochemistry regenerative regenerative yao substance mus explana 
#@Joseph_S,Willshaw_D,
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input function function function function function function function function function function function function function function function figure time time time time time time time time time time time time time time time time time time time time time time output output output output output output output output output error state results information information models models models space case order systems values values probability probability probability probability probability probability probability probability probability probability parameters noise noise noise noise noise noise noise noise noise noise neurons neurons unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution point point point point point point point point point point point single single single single processing processing large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate inputs inputs inputs inputs shows signal signal signal signal signal signal signal simple simple simple gaussian gaussian gaussian paper small small net work fig cells step features process process process process process process process level current random random response show show show equation general parameter parameter parameter real real approximation approximation average theory obtained obtained note note result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation solution solution independent independent independent dynamics dynamics dynamics initial initial initial initial initial constant constant constant constant constant terms left left left low low low low temporal motion press press abstract references stochastic stochastic stochastic stochastic stochastic positive introduction introduction behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus generated variance variance variance variance variance variance variance variance variance tion difference assume lower lower signals prior chosen part part cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing good spike spike spike spike spike spike spike spike spike spike spike conditions conditions make make fact sum eq eq eq times times times means optimization optimization potential potential potential potential potential dimension study filter filter negative vol compared rates rates rates determined determined determined determined determined related distributions distributions gain cortical cortical mit voltage voltage voltage voltage voltage voltage voltage voltage contrast contrast contrast contrast train train train train train dependent institute institute code code advances exp exp addition addition graph cambridge cambridge curve curve view curves limit limit limit limit limit limit top top efficient free free produce condition derived derived derived conditional levels levels processes depends depends depends achieved discussion describe assumption short short short short short assumed shape shape theoretical main degree noisy noisy sensory sensory smaller functional transfer transfer transfer transfer increasing trials making inhibition bottom bottom early neuronal neuronal denotes membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane ensemble ensemble period period period highly varying varying varying solve yields studies studies modified modified modified modified interval interval interval interval interval organization expression expression spikes deterministic deterministic deterministic deterministic deterministic deterministic deterministic white white white boundary boundary boundary setting pass pass starting starting starting greater assumptions sigmoid sigmoid clear exponential exponential exponential exponential exponential exponential asymptotic asymptotic asymptotic asymptotic hard integration physics drawn sigmoidal solid assuming assuming attractor explicit suppose suppose relation relation derive derive produces produces dept slightly slightly integrated integrated events springer versus codes codes codes fraction evolution understanding understanding completely converges sign key key slow dashed expansion normalization intervals intervals add valid msec msec msec msec msec msec msec koch koch fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire thesis determines determines specifically phys characterized tests simplicity simplicity reason paths spiking miller miller reached excitation verlag link showing neuroscience list principles principles trains steady issues rise rise giving links links editor rev voltages thought formal observe regime phd integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate great great slowly distinguish convolution slope biology widely widely filtered filtered immediately immediately arise begin qualitative qualitative experimentally quantitative passed passed poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson modulated modulated modulated reaches reaches reaches neuro instantaneous instantaneous instantaneous instantaneous instantaneous instantaneous instantaneous instantaneous instantaneous equivalence equivalence princeton refractory refractory recover recover purely purely purely purely reaching balance balance balance balance balance obtaining obtaining obtaining neurobiology neurobiology neurobiology shifts salk salk salk salk exceeds started reset reset reset reset irregular dominant dominant infinity infinity hasselmo express insight offer jolla jolla extends pearlmutter pearlmutter jump captures captures tures thresholding treat crossing minus validity subthreshold subthreshold deep biophysical biophysical distribu expand thresholded thresholded isi isi isi isi isi isi isi isi isi crossings son fea interspike neumann inconsistent err ally anthony attained stevens stevens stevens stevens zador zador zador zador zador zador zador vivo vivo vivo vivo planck edition remained deter electrophysiological electrophysiological charles neglected substrate opinion opinion opinion newsome newsome newsome newsome instant instant obeys yon tsodyks tsodyks leaky leaky epsps amit amit vitro vitro absorbing fokker snyder snyder neglecting mined softky softky softky softky passage passage agnostic fpe fpe integrand leak rameter retrieving farther brownian probabilistically comment asymptote erf crossed eigenfunction deterministically jumping shadlen shadlen shadlen resets resets stimu expo lus ouput ouput til emits usu steeper uhlenbeck uhlenbeck uhlenbeck ornstein ornstein ornstein isl ise erfc erfc erfc erfc taneous intentionally instan zxt vols nential 
#@Stevens_C,Zador_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input data figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set networks training training training training training training training training training training training training output output output number number system system system system system system system system error error error results results results units information performance based based based based based space weights weights weights weights weights weights weights layer layer layer layer layer layer layer vector order shown shown shown systems values parameters parameters parameters noise weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method pattern point single processing control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate analysis inputs shows shows shows shows shows shows signal signal signal signal gaussian gaussian small feature net work work work work work work work task cells step step step step step step points points field field process current trained trained trained trained structure structure structure random random high memory memory response response response response response similar similar similar similar similar representation show equation equation section rule vectors real average average gradient note experiments university threshold threshold computation defined found sequence sequence target target initial initial estimate distance distance science left left presented presented map present phase phase phase phase phase phase phase phase activation low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal maximum range range range range range range press press learn learn learn learn components sample abstract back computational computational computational computational computational properties references component procedure propagation introduction behavior behavior stimulus generated generated tion prior representations representations representations learned learned chosen part center previous previous previous type type type long long long make length minimum resulting ing times mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made made natural feedback feedback feedback feedback feedback feedback study vol specific specific compared experimental related motor motor motor motor motor motor motor brain brain brain brain brain power power power power power power power mit steps steps steps steps accuracy accuracy contrast connection train train train train train train dependent dependent department individual advances responses responses responses responses responses responses responses delay considered cambridge experiment experiment san top stimuli effects effects produce produce randomly developed area area types types path path selected associative discussion normal normal fast stable short short assumed generate generate generate generate role require main main main eds journal journal hypothesis hypothesis hypothesis future degree auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory combination reduced segmentation structures trials making window stored stored stored bottom early early combined produced produced produced produced produced produced produced produced produced produced added predict membrane membrane robust typical lateral lateral side side sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive relevant unsupervised unsupervised unsupervised teacher approximately approximately approximately match studies evaluation bounded organization organization organization sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive amplitude amplitude amplitude lead predicted touretzky white white white white white half row greater assumptions competitive competitive competitive competitive editors interactions interactions peak learns sound sound sound encoding mechanisms external characteristics california solid groups acknowledgements areas construct perception perception perception perception perception perception perception perception ways ways plot vertical sensitivity sensitivity sensitivity sensitivity involves angle unique develop frequencies frequencies frequencies frequencies frequencies frequencies frequencies springer formation transform controlled controlled organizing organizing showed evolution modulation completely spectrum spectrum spectrum spectrum spectrum smoothing sec euclidean kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen recorded template template template template template template template template template template template template template template template template perceptual perceptual perceptual perceptual perceptual perceptual perceptual combinations plotted candidate black major identified encoded encoded divided divided wij presentation presentation identify computations ten receives verlag neuroscience neuroscience duration duration duration bar sampled simplified paradigm paradigm providing principles overlapping tesauro modelling presents trains diego american production production production production production production production production production production production production production production production production production production production create updating helpful fourier respond respond respond mappings pathway pathway pathway pathway affect cognition fundamental phases phases neu plausible illustrate thought aspect separated mapped nerve ith seconds animal indicating rows preference cos cos band crucial crucial crucial crucial distinguish waveform coded coded coded biology explanation explanation worst nucleus nucleus nucleus nucleus nucleus nucleus arise arise sounds sounds sounds sounds calculations localized demonstrates recognizing summation fourth questions limits syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable pathways pathways elman recordings passed frequently biologically berlin modulated cal acoustics song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song song green comments decreased segmented implements gap gap identifying identifying leen notes notes notes physiology accomplished assign temporally bin bin harmonic harmonic harmonic harmonic harmonic tem tem connecting turned air khz khz khz khz khz occurred neurobiology settings guide selects days days exploring governed periods lawrence reproduce winning winning winning modelled modelled waves young mem mem bins bins bins jolla sustained passing extends extends erlbaum broken projects explains fired fired mind converted sine achieving emerge uniquely responds responds copy copy lesions lesions profiles preferences preferences perceived examining shaded modifying life degraded degraded plate maximally cosine cosine categorization categorization sketch associates pools memo syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables syllables normalizing tin tin develops ucsd species species species tension tension doya doya doya doya doya doya doya doya doya christopher phrases phrases phrases played dropped caudal flows rons concrete proposal spectrogram spectrogram anterior anterior konishi konishi konishi konishi konishi konishi konishi konishi fft discarded governing isolation isolation vocal vocal sliding reproduced raised memorized memorized ically tim tim tim tory replicate mid mid mid mid gradual replicates sung sung spectrograms won thalamus mar advice apparatus bird bird bird bird bird bird bird wait ascending fur sing sing sing sing picks initializing poral birth birth refining han passage birds birds birds categorize categorize categorize categorize repertoire govern organ segregated reinforced wild silence sponses replicating memorization regulate innate innate innate innate innate wash fills fills underly evoke msecs msecs typ songs songs songs songs songs songs guides guides guides guides alike alike magnocellular cogsci trai refines lasts reused netj netj disrupt musculature ejnowski roedial modula ler neurobiologists brad audi institution 
#@Fry_C,
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#*neural set set set set networks system system system system error based based based space space space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear case case vector vector vector vector vector vector vector vector vector vector vector order order order order order order order shown systems systems systems systems systems systems unit unit unit unit unit unit unit point point point point point point point point point point single single single single single single single single control control local local analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form form shows visual work work step points field level level current structure structure structure structure structure structure structure structure representation representation representation representation equation equation equation equation section section section section fixed fixed line line vectors vectors vectors vectors vectors vectors general general parameter parameter parameter real approximation states theory theory theory obtained obtained obtained obtained term term experiments dimensional dimensional dimensional dimensional result result variables computation research research research log defined target target table table table standard computer terms terms terms science science left direction direction direction direction direction direction direction direction direction direction direction direction presented present object object sets motion range position position position position position position position position position position position basis basis basis basis basis continuous continuous abstract applied references component component component positive context introduction introduction hand hand generated generated generated parallel parallel tion representations representations representations chosen chosen part part part center center previous type type type required represent expected fact fact fact fact fact observed total computed multi multi sum performed performed called called called called called called called elements elements elements elements elements elements elements elements elements elements elements mapping means means factor natural natural natural orientation orientation orientation orientation orientation orientation global applications study study obtain obtain represented represented cross series series series define define define objects eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined related related related connected brain contrast contrast connection connection connection institute words department joint difficult exp exp exp exp exp exp exp exp exp exp exp exp exp exp exp exp addition addition addition addition considered considered framework domain equivalent equivalent equivalent additional view view curves trajectory upper full requires choice vision vision basic basic basic condition velocity velocity lines product product product product product product actual finally finally simply simply simply biological biological biological biological achieved achieved achieved normal normal describe describe describe describe group group group group group group group group group group group group group group group group group group group group group group group group group group group group group denote transformation fast corresponds corresponds short journal degree sensory smaller underlying underlying needed combination unknown projection projection increasing head head head special special operation operation operation operation operation principal principal principal principal principal representing numbers direct direct direct improve directions directions directions exact property property takes element element element movement lateral apply moving include side subset subset subset recently interest dimensions dimensions approximately calculated axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis tions tions correspond differential differential background positions positions positions positions positions positions arm constructed constructed horizontal expression expression invariant extended extended extended matrices matrices matrices matrices matrices matrices rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation locally move column setting demonstrate demonstrate runs conclusion conclusion depend depend central tangent tangent clear taking physics turn movements movements movements plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane plane manner groups denoted reference explicit relation van van van van van van van van van van van van written written written written optical primary primary primary primary primary primary primary vertical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical recall metric transformations transformations transformations transformations angle angle angle angle angle angle angle angle angle unique implies implies implies expressed expressed detailed restricted restricted approximations decomposition decomposition understanding allowed allowed allowed allowed sign sign calculation expansion expansion expansion expansion spaces spaces closed closed closed closed degrees combinations coordinate subspace subspace subspace determines discuss phys discussions closely suitable society differ divided identify literature projections comparing identity identity orthogonal reached reached summary notice kind kind kind kind repeated contained showing issue lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie lie sin sin sin sin sin sin sin sin sin manifold manifold usual usual correspondence correspondence modelling law law law law law law law law law law law law law law law law law law law law law law law law law law wiley collection essential investigate relations hall scalar scalar history notion math front taylor taylor freedom precise generates generates mentioned cos cos cos cos cos cos cos cos cos cos cos cos cos formula formula formula formula formula orientations orientations orientations answer multiplication caused briefly briefly lies lies lies tool straight leaves commonly mathematics projected projected acknowledgement involve angles angles angles angles angles angles angles angles angles angles angles angles geometry geometry geometry geometry geometry geometry geometry geometry geometry radius explained virtual double double understood led affine axes axes axes axes axes axes axes embedded embedded parameterized parameterized leave ity span span span span span reaches popular serve serve enables enables fiber equivalence formally tation angular angular rotated eliminate rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations consideration numerically convenient analogy obtaining north canonical canonical canonical canonical canonical intuitive analyses prentice studying holland sides topological den den den sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere israel treatment treatment ahead gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze gaze arrive saccade saccades saccades saccades intersection displacement dividing consecutive multiply neurophysiology specification constitute minus helmholtz helmholtz helmholtz helmholtz helmholtz piece covering validity validity uniquely uniquely pieces convenience constitutes constitutes constitutes constitutes stands stands stands stands summarizes perpendicular perpendicular exponent exponent mathematically mathematically generators generators manifolds denoting eliminating emphasize fixation employing cartesian spanned flash flash flash flash oculomotor oculomotor oculomotor oculomotor distinguished algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra algebra subspaces infinitely advantageous advantageous appearing parameterization parameterization stephen accordance orthonormal orthonormal bilinear bilinear equa functionally comprising joints america reality lar tan limb polar analyse analyse analyse addi stan mid initiated repeating vergence campbell campbell unifying unifying notions notions notions stand exponents exponents impor mention rescaling conversations conversations tant infinitesimal calculus fulfilled ordinate ordinate ordinate ordinate ordinate ordinate fruitful analysed listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing listing ending geometrically visualize closing anatomically particu equiv unitary ordinates ordinates ordinates ordinates ordinates ordinates ordinates ordinates ordinates ordinates ori amir baker baker restricts traced exponentiation parameterize bundle quotient quotient quotient quotient quotient quotient quotient bringing degeneracy hemisphere commun upwards weizmann weizmann weizmann parameterizations parameterizations parameterizations alent instructive rota westheimer westheimer saccarles saccarles saccarles saccarles algebraically submanifold submanifold equating customary berg berg berg gielen rehovot gisbergen gisbergen disregard entation antisymmetric bracket bracket bracket bracket bracket parameterizes sino sino algebras algebras obeyed charts wisdom 
#@Flash_T,Handzel_A,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input input input input input input input data function function function function time time time time time time time time time time time time time time time time time time time time time time time time set set output output output output output output output output number number number number number number number system state state results results units based based based based weights order shown shown values probability noise noise weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit distribution distribution distribution distribution distribution distribution single single processing processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate inputs inputs inputs inputs inputs inputs inputs shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal examples small small feature fig fig fig fig fig fig fig fig fig fig fig fig step process current current structure structure structure structure problems high high high architecture show show section line line rule rule rule average average average note note note note note experiments activity activity result threshold found dynamics initial constant constant constant constant constant constant constant constant standard connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic left left left present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal maximum range range range range range range range range range range position abstract applied find density references due due due due positive positive important context introduction stimulus stimulus stimulus generated generated difference difference spatial spatial assume assume assume assume assume assume assume signals signals signals signals signals signals signals firing firing firing firing firing firing required multiple spike spike spike spike spike spike spike spike spike spike spike spike spike fact fact correlation length length length total total total total simulation sum sum called factor potential potential potential potential potential potential potential study negative relative compared compared active active experimental related brain brain equal comparison larger train department department department synapses synapses synapses synapses consists consists consists individual final exp exp delay delay delay delay delay delay delay delay directly directly directly curves curves curves trajectory top stage effects detection detection requires requires requires significant estimated basic increase increase increase channel channel coding coding coding coding coding coding coding coding coding coding developed types depends achieved achieved achieved achieved achieved discussion arbitrary fast fast fast fast corresponds corresponds corresponds finding amount effective effective effective synapse synapse supported degree makes auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory combination reduced fully ratio mechanism consistent leads leads leads leads leads leads pre window window window window window bottom early magnitude magnitude combined light neuronal neuronal neuronal neuronal neuronal membrane membrane membrane membrane membrane improved resolution resolution resolution resolution pair takes typical typical period period period period period period period period subject highly unsupervised unsupervised approximately approximately approximately tuning tuning tuning tuning tuning tuning tuning axis smooth converge converge channels channels channels increased grant concept occur occur occur occur occur spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes width occurs runs half strength strength place hebbian hebbian hebbian hebbian measures clear peak weak suggest sound sound sound sound sound sound encoding strong strong external external external external reduction characteristics demonstrated solid solid solid pulse pulse pulse decrease decrease acoustic areas areas relation pro van van van van longer longer longer plot plot describes simultaneously averaging remaining remaining slightly slightly slightly angle frequencies formed shift extraction cycles cycles cycles depending stages variation constants constants allowed sign slow slow dashed dashed delays delays delays delays delays delays normalization sec precision precision precision precision precision precision precision precision precision precision precision precision precision precision coupling coupling coupling fire fire fire fire instances specifically holds simplicity aspects differ oscillatory fine fine fine fine fine receives receives receives receives duration comp comp vary localization localization localization realistic wave wave leading leading neurosci neurosci neurosci principles principles operating preferred acknowledgments trains remain remain remain essential exponentially periodic periodic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic rise rise rise rise fashion project oscillation pathway pathway pathway pathway pathway pathway pathway pathway pathway presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic phases phases phases phases phases phases phases transmission transmission transmission transmission transmission transmission possibly changed changed der der der precise precise nerve fibers fibers fibers generates defines integrate integrate integrate histogram histogram improves adapted precisely broad located located located nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus nucleus arise axon sounds beginning axons axons fluctuations fluctuations varies varies orders variant maxima operate exhibits richard germany germany germany germany decreased decreased physiol owl owl owl owl owl simultaneous uncorrelated ear ear narrow narrow khz khz khz khz anatomical simplify shifts belong fires reset equals soma soma soma soma soma branching dif diameter axonal axonal axonal arrive arrive arrive locked locked locked locked locked locked locked late late contact contact stopped severe depression shorter email transmitted responds poses hundred hundred evoked evoked scenario barn barn barn barn barn barn trends cessing magnitudes decays decays potentiation potentiation crosses concentrate pos refinement locking milliseconds refined supporting remarkable institut institut institut institut sake locate locate developmental developmental interaural interaural carrier hemmen hemmen hemmen hemmen periodicity sharply peaked konishi konishi konishi neurol coincide gerstner gerstner gerstner gerstner contacts contacts contacts contacts contacts contacts contacts contacts contacts contacts contacts contacts compartment cur arriving inset inset jitter shortly rent wagner wagner wagner wagner ference fiir fiir fiir coincidence coincidence sible ascending disappear miinchen miinchen miinchen miinchen miinchen retains rising spans spans millisecond millisecond millisecond millisecond physik physik physik physik physik physik physik regularly binaural fellow multiples modulo kempter kempter kempter kempter kempter psychol shed und ond prefactor strengthening dfg dfg sullivan leo mfinchen mfinchen scholarship deutsche balances occured coherently disappeared muenchen magnocellular magnocellular magnocellular magnocellular magnocellular magnocellular theoretische theoretische theoretische ffir ffir carr carr fakult incoherent forschungsgemeinschaft hermann lular 
#@Gerstner_W,Kempter_R,Wagner_H,vanHemmen_J,
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input data data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time set networks networks networks networks networks training output output output output output output output output output output output output output number number number system error error results units units units units units units units units units units units units units units units units units information problem problem problem problem problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden based based based based weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown shown shown shown systems values values parameters weight functions neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit recognition pattern pattern pattern pattern pattern pattern pattern pattern single control control control local local local local neuron neuron rate patterns patterns patterns patterns patterns patterns patterns analysis matrix matrix matrix matrix inputs form form form form form form shows shows visual feature feature feature feature cells cells cells step classification trained problems problems problems problems random memory memory memory memory memory memory memory memory memory memory memory response response response response response response response similar representation show show show show show equation rule rule rule real states states states states obtained obtained term term note experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university threshold computation computation computation defined dynamics initial computer connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science left left presented presented presented presented presented presented presented present activation activation activation activation machine range press learn learn components basis abstract applied applied back back back computational computational computational convergence convergence properties properties properties references component due ieee positive positive introduction complex effect tion change change difference rules rules rules rules representations representations representations learned learned previous type multiple cortex cortex cortex cortex cortex cortex cortex long long long distributed fact techniques region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region region proposed proposed correct forward forward scale simulations ing ing total total total simulation simulation simulation sum regions regions regions regions regions regions regions regions mapping feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation relative specific specific specific represented represented represented represented compared desired desired desired desired desired location active determined experimental experimental experimental cortical cortical cortical cortical cortical cortical brain brain brain brain brain equal steps larger modeling modeling department synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses individual represents represents represents represents represents final layers layers layers layers layers addition ai ai ai ai ai cambridge experiment hinton top top stage stimuli stimuli stimuli capacity basic con con con con con condition developed developed evidence inhibitory inhibitory depends depends constraint associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward tested inverse complete excitatory excitatory supported supported sensory sensory sensory underlying combination functional functional testing testing testing mechanism special structures structures pre pre inhibition inhibition normalized normalized bottom supervised combined combined neuronal architectures separate separate separate separate takes takes cognitive previously previously tions tions converge trans organization organization organization organization organization organization organization organization organization organization organization organization storage storage sensitive entire horizontal feed feed feed white column strength hebbian depend mechanisms mechanisms presence characteristics characteristics selective selective selective selective selective selective selective iii iii connectivity connectivity connectivity connectivity connectivity program van van van solving primary recall recall recall recall recall recall recall recall recall recall missing simultaneously simultaneously linearly linearly develop potentials potentials potentials cycles review depending stages influence influence solved organizing organizing organizing organizing organizing organizing ocular modulation modulation modulation modulation normalization combining combining valid recorded recorded recorded recorded figures perceptual dominance activated modification modification modification modification wij wij wij wij wij schemes post post post post post post post comparing miller miller soc procedures link showing anderson anderson anderson symmetry physiological sci michael dayan dayan dayan providing neurosci neurosci neurosci neurosci neurosci neurosci subsequent rat rat rat rat rat intrinsic stimulation selectivity xor xor xor xor xor xor xor xor xor xor xor investigate rapidly involving association ml respond giving project project detectors mappings combine proper tanh removed removed removed transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission transmission plausible man psychology olfactory olfactory der der hebb store consist consist generates neal rows ment separable separable defining caused interneurons starts organized organized organized afferent afferent afferent afferent afferent afferent afferent afferent cut hippocampal hippocampal grossberg gradually gradually gradually gradually res recording recording recording linsker demonstrates auto lack detecting slower incorrect psychological ity ity mod measuring spread cal prevent logical logical fiber neuro simultaneous cor cybern physiology physiology physiology physiology primarily primarily primarily appearance resources zemel neurophysiol neurophysiol encoder enhancement suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression cellular bower bower bower bower anatomical stronger stronger replacing height preparation utilized slice slice slice slice pat von von hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hasselmo hippocampus hippocampus stimulated mem matter tures influences influences associations maintaining cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic helmholtz responds connec connec connec malsburg malsburg suppressed suppressed imagine streams arising trends trends trends trends deep activate activate degraded degraded potentiation potentiation mediated electrodes ultimately selectively selectively selectively figs afferents responding responding modifiable modifiable modifiable modifiable struc ward ward ward ward ward syn syn syn syn stimulating influenced influenced imple termination somatosensory somatosensory somatosensory somatosensory morris reflecting harvard harvard neocortical essen essen essen slices neocortex neocortex neocortex neocortex neocortex neocortex neocortex neocortex neocortex successively mcnaughton mcnaughton optics ory transpose transpose smc nonstationary ically ensuring carpenter carpenter carpenter denominator undergo ini awij awij acetylcholine acetylcholine acetylcholine acetylcholine tern tivity ard progresses progresses vergence stryker activates settles settles erroneous coincides thalamus nections nections nections stim designated tially abstr vitro oooo mented elicited poten piriform suppresses prevented prevented behav laminar categorized rect alternately keller mediating superficial settled predominantly predominantly predominantly predominantly predominantly predominantly maunsell maunsell maunsell sug spreads spreads folded zation feedfor feedfor feedfor feedfor feedfor neurosciences cai agonist hecht hecht connors connors connors terminating wash perfusion perfusion biolog activ preparations synaptically influencing includ organi gustafsson gustafsson leam nielsen nielsen simulta neously neuromodulator uli lllll reynolds dal provid designates pyrami 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input input input input input input data function function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set networks training training training output output output number number system system system system system system system system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state results units units units information information information information information information problem models models models based based weights weights linear linear linear case order shown shown shown shown shown systems systems systems values parameters parameters weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution approach approach pattern pattern pattern point point point point point single processing control control control control control control control control control control control control control control control control control control control control control control control control control control large local neuron rate patterns patterns patterns patterns patterns optimal optimal inputs inputs form form form form shows shows shows shows shows signal signal signal simple simple gaussian gaussian paper small small feature work work task methods fig fig fig fig fig fig fig fig fig fig step step step step step step step step step step step level current current trained trained cell cell problems high high high high high high high high high high high high high high memory memory response response similar similar similar similar representation representation architecture show show fixed line line line rule rule rule rule states states states states states states states states states theory theory theory term term note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university university threshold threshold variables target target target target target target target target target target target target target target initial initial initial initial initial initial initial standard computer terms synaptic synaptic synaptic science prediction prediction presented present present present present present phase phase phase phase phase phase phase phase phase activation activation low low low low low low low low low low low frequency temporal object sets sets sets motion range range range range press press press learn learn learn learn learn learn position position position position position position position position position position position position position position position position position position position position position position components basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract back properties properties properties references due due positive important important adaptive adaptive adaptive adaptive introduction action complex complex hand behavior behavior behavior behavior behavior effect dynamic dynamic generated generated generated parallel parallel parallel tion tion tion assume signals signals signals prior representations learned learned learned learned learned type multiple multiple cortex binary binary spike long long conditions represent represent represent distributed distributed distributed fact length correct correct observed observed forward forward forward forward simulations simulations minimum ing ing ing ing total simulation human human human sum performed performed eq potential potential made feedback feedback feedback feedback feedback feedback feedback feedback feedback represented represented desired desired series provide define define active active related related related distributions motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor brain equal equal power mit train source proceedings words department department version version version version synapses consists code advances represents responses responses difficult final delay delay delay delay delay delay graph cambridge directly directly curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve additional additional view curves curves trajectory trajectory trajectory trajectory trajectory trajectory top top effects full full significant significant significant significant significant world con produce produce derived weighted randomly randomly developed velocity velocity velocity velocity controller lines actual actual selected evidence depends simply discussion discussion increases increases denote transformation fast fast corresponds corresponds actions predictions circuits circuits rbf rbf rbf short implemented assumed synapse synapse synapse synapse synapse synapse supported eds eds journal journal end end hypothesis hypothesis future future easily degree makes makes makes sensory sensory sensory objective pairs smaller needed needed combination dynamical jordan significantly york york increasing mechanism mechanism mechanism principle representing representing representing call direct bottom early early idea idea combined produced description light predict denotes denotes discussed discussed discussed movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement include period cognitive relevant relevant relevant works module studies studies sparse sparse positions positions positions positions positions interval arm lead lead occur occur suggests trial trial deviation correctly move move move move move move touretzky loop loop setting setting starting critical critical trajectories modules practice suggest encoding encoding encoding propose mechanisms mechanisms presence presence intelligence labeled labeled radial pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse movements movements movements movements movements movements movements plane plane plane decrease denoted denoted denoted van van produces mathematical involves involves involves text equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium predictive predictive predictive predictive predictive predictive predictive springer decreases decreases stages labels centers understanding similarly suggested past earlier barto barto barto barto barto barto barto barto dashed dashed delays delays delays delays delays delays delays delays delays delays delays sec sec sec remains remains intermediate intermediate filtering msec msec msec msec dendritic fire includes sciences determines determines absolute determining straightforward middle closely closely uniformly modification detect plots plots plots plots miller reached refer verlag neuroscience issue lie sin sin physiological physiological duration duration duration duration comp vary usual simplified simplified simplified simplified simplified simplified realistic realistic realistic delayed delayed delayed delayed reach thresholds predictor cat principles principles consisted tesauro decreasing extend situations law explore explore simpler command command command command command command command command command command command command command singh optimized preliminary mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass mass hall existence fashion school behavioral muscle muscle oscillation oscillation pathway presynaptic presynaptic coefficient trace trace trace onset predicting extremely illustrate illustrate aspect panel panel panel panel panel panel panel panel panel precise switching switching switching switching switching switching switching switching switching switching switching switching switching switching switching switching fibers fibers fibers generates plant plant plant plant massachusetts ment ment slowly explanation capabilities london considerable rapid easier producing strictly precisely monkey monkey afferent afferent acknowledgement beginning medical researchers virtual pathways pathways pathways pathways pathways led psychophysical marked marked adjustable adjustable commands commands commands maintain passes passes operate switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch switch controllers reaches reaches qualitatively collective adjust fiber fiber fiber fiber physiol implements eventually eventually traces traces pose gap ghahramani sensing leen physiology physiology physiology generator modify animals velocities reaching climbing climbing cellular cellular smith ments difficulties occurred occurred occurred occurred cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum height height moment moment moment moment serves mark roles implications arrays fires fires inferior prentice cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar cerebellar reset falls programs cone sion james cmac washington consequences consequences nonlinearities young ltp ltp late late ends ends ends extensively agree wolpert wolpert wolpert influences switches switches switches switches switches switches switches switches switches switches andrew discharge reflex truncated ple ter sig axe copy copy amherst superimposed resting tor chicago chicago suppressed spinal arising decays generators potentiation crosses crosses switched switched represen weaker eligibility eligibility eligibility eligibility eligibility eligibility attached tively places behave bring ward ward corrections completed triggered circumstances bridge sees sees justification spring spring spring spring spring spring spring spring spring spring spring spring spring spring spring spring spring spring spring spring spring spring cliffs ave east aid bold bold albus albus albus albus somatosensory keeler keeler accomplish accomplish purkinje purkinje illinois sensorimotor cally anatomy 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#@Barto_A,Buckingham_J,Houk_J,
#t9
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#*network learning learning learning model neural input data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure time time time time time time time time time time set networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number number number number number system system error state state state state state state state results results results results information information information information information problem problem problem problem problem problem performance performance performance performance based based weights weights weights linear linear linear case case vector vector vector order order order order shown shown shown systems systems probability noise noise noise noise noise noise weight weight weight weight weight method approach approach point point point processing processing large local rate rate rate rate rate patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix form form form shows signal signal signal signal simple paper small small task task task methods level current trained trained trained structure problems problems random random random random high high response response response response response response response response similar show fixed line line vectors speech speech speech states theory theory gradient gradient gradient obtained note experiments activity activity activity activity activity activity activity dimensional threshold threshold computation solution solution solution solution research research research research research independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent defined found target target target target dynamics dynamics dynamics dynamics dynamics initial initial initial distance left left left left presented presented present frequency frequency range position components components components components components components components nonlinear outputs continuous continuous continuous abstract applied computational computational computational convergence density density analog references component component component component component component component component stochastic procedure important propagation introduction complex stimulus stimulus statistical dynamic generated generated generated tion tion tion tion change complexity variable spatial spatial spatial assume rules measure measure signals signals signals signals signals signals signals signals signals prior higher higher part part center center center good conditions represent represent represent distributed distributed distributed expected fact techniques techniques techniques proposed correlation correlation correlation correlation correlation resulting ing ing human human human computed performed elements elements means potential dimension applications policy application series series rates proc location eye eye eye experimental related related related brain brain brain brain brain brain brain brain brain brain brain brain brain power steps larger contrast train train source source source source source source source source source source source source source source source source source modeling report report institute institute institute institute institute department department technique technique joint responses responses difficult final san san san san detection detection determine upper significant statistics statistics statistics speed give con channel channel channel channel channel derived levels criterion area entropy processes selected evidence depends sampling increases fast limited close close close assumption assumption assumption assumption stable surface finding finding amount amount amount short common effective supported supported sensory including auditory auditory auditory auditory pairs pairs account unknown principal call pre window window international produced produced produced sources sources sources sources sources sources sources sources sources sources sources sources correlations correlations separate separate separate separate takes movement practical period period subject subject sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive highly previously subjects subjects volume volume yields pca diagonal mixtures mixtures background background separation separation separation channels channels channels channels channels channels channels channels channels channels channels channels channels channels 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delays delays sec sec intervals intervals event event event closed closed filtering filtering filtering eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg views recorded recorded recorded box box box box includes bell bell bell bell bell bell bell bell bell blind blind blind blind maximize tests determining determining identified capable suitable differ effectively presentation identify oscillatory ten verlag verlag strongly induced dis physiological sampled localization localization localization localization localization relaxation wave maximization neurosci attempt overlapping overlapping overlapping mixing satisfies acknowledgments minimized unlike stimulation diego diego diego diego transformed transformed collection steady steady steady steady behavioral muscle authors office office referred maximizing proper statistically statistically statistically statistically topographic matched trace trace trace trace trace plausible eyes eyes ensure ensure obvious obvious portion portion portion portion panel panel panel panel panel logistic logistic logistic separated multivariate epoch detected detected detected detected detected mixed submitted seconds isolated residual residual advanced separable sensors sensors phenomena correction tool spatially spatially spatially satisfied sites widely widely filtered filtered filtered operators located involve medical medical meaning fluctuations raw reflect reflect collected collected collected collected transient conducted orders recordings recordings employ remove continuously howard howard berlin berlin perturbations characterize spread cal incorporating suited display coherence focused progress traces traces traces traces traces multidimensional synchronization instantaneous cumulative irrelevant lab lab lab identifying identifying identifying bipolar temporally pick naval naval naval naval naval chance significance stronger minutes promising promising adjusting alpha alpha hit hit transforms removing neurobiology neurobiology neurobiology observing observing salk salk salk salk salk salk muscles reliably meaningful separating separating separating periods sion negligible regard ascent dominant artifacts bursts bursts bursts bursts suggesting suggesting record probe sustained sustained eqs eqs grants stopped stopped insensitive influences dividing onr informa ent session session session session session session session session session focal dec rejection par medium ideally lit ical superimposed evoked evoked decorrelation decorrelation avoids publication shifting conduction conduction segregation segregation mathematically generators generators generators annealed hughes hughes deconvolution efforts terrence electrodes electrodes frontal erp erp erp erp erp erp speedup conversely portions apparently tively tones sta tissue article microscopic sessions sessions sessions sessions uniqueness scalp scalp scalp scalp scalp scalp ping bold interpreting dominates adult hour hour separates anthony artifact ignores factorization gence scott scott carrying defense derives sep stationarity health health health responded responded modest hits imposes contributing tracked checked decompositions broader comon makeig makeig makeig makeig makeig makeig makeig makeig jung jung jung jung jung jung eog eog eog quiescent conver convolving pushed permuted perspectives clin syrup poten tar alertness alertness alertness alertness concurrent sereno behav tony vij vij whitened chamber unitary official decomposing theta theta instructed sug government seeds assump bullock button dur questionable alert alert alert alert isolate locus decorrelating situated crease dale objec electrophysiology ses subcortical navy navy click click factorizes interspersed interspersed mil electroencephalographic electroencephalographic electroencephalographic electroencephalographic electroencephalographic segregate underdetermined thirteen irregularly verges smearing dynami tential objectively objectively aration nonstationarity las uncovered mains warm detectability twin nolta tials corticocortical isolating appreciably neurobiologically erry mak 
#@Bell_A,Jung_T,Makeig_S,Sejnowski_T,
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#*network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time networks number system system system state results results results results results information information models based space weights linear layer layer layer layer case vector shown systems systems neurons neurons neurons neurons neurons neurons neurons pattern single processing neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate analysis analysis analysis analysis form form form form 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direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented presented presented present present present present present present activation low temporal motion motion range press press press press press press learn position position position position basis abstract back computational computational properties properties properties properties properties properties references component positive important propagation propagation action action circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior tion tion tion tion spatial spatial spatial spatial spatial spatial spatial spatial lower higher higher higher higher center center previous cases firing firing firing firing firing firing firing firing firing firing firing firing multiple multiple cortex cortex cortex cortex cortex cortex cortex good equations region region proposed proposed observed observed simulations ing simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation regression respect respect respect performed performed eq called elements elements regions regions mapping feedback orientation negative specific specific represented represented compared desired compute compute compute rates location active active active active active experimental experimental experimental experimental experimental experimental connected motor cortical brain brain brain brain brain mit mit comparison comparison comparison modeling department implementation version code individual advances exp layers delay delay delay delay delay cambridge computing computing computing computing computing environment environment environment directly curve curve curve curves trajectory significant speed speed speed speed speed speed basic basic increase con con con condition developed velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types path actual actual actual evidence evidence evidence inhibitory inhibitory inhibitory inhibitory associative measured discussion fast fast fast fast fast limited close inverse corresponds excitatory excitatory excitatory predictions implemented implemented assumed assumed assumed supported supported role theoretical theoretical eds journal journal journal journal journal journal journal hypothesis hypothesis hypothesis future future future future future future future future future future degree degree degree degree makes sensory including simulated simulated simulated simulated simulated simulated functional projection head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head head representing inhibition inhibition magnitude frame idea description denotes denotes denotes population directions directions directions recent ensemble element reported lateral lateral lateral moving moving moving side side side sense sense cognitive cognitive recently recently compare tuning tuning tuning tuning tuning tions separation separation separation separation separation separation organization organization entire amplitude horizontal studied suggests suggests suggests suggests touretzky touretzky touretzky touretzky touretzky occurs occurs demonstrate starting place greater conclusions peak faster encoding encoding integration integration integration characteristics characteristics demonstrated proportional proportional turn turn variety plane iii averaged program areas areas reference reference pro pro van van ways describes tuned shift shift shift potentials potentials formation stationary showed forms static suggested constants slow slow slow slow delays sec sec calculate msec msec msec msec msec msec msec msec degrees degrees degrees degrees degrees degrees degrees degrees recorded recorded recorded recorded recorded fire fire fire fire fire fire fire fire fire fire includes illustrated neighbors neighbors neighbors neighbors neighbors society society society society differ projections plots receives receives receives excitation excitation summary quickly quickly strongly allowing allowing neuroscience neuroscience neuroscience neuroscience neuroscience neuroscience neuroscience neuroscience neuroscience michael play illustrates illustrates preferred preferred preferred preferred preferred acknowledgments rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat intrinsic tesauro presents presents presents body body remain exhibit exhibit rapidly steady limitations limitations accurately examine behavioral encode encode encode encode encode encode encode func topographic topographic cognition neu examined act transmission predicts predicts predicts predicts psychology illustrate portion noted panel panel assumes fisher nerve academic submitted submitted phd phd phd phd phd phd phd phd phd phd phd phd phd phd animal animal animal animal animal brown brown advanced preference preference preference preference ment stop agreement track navigation navigation navigation interneurons turns turns turns turns turns turns turns turns turns turns turns turns directional directional directional directional directional directional directional directional directional directional directional directional directional directional incorporate incorporate nucleus nucleus nucleus hippocampal hippocampal hippocampal begin begin addressed integrating integrating integrating fourth tional tional quantitative posed incorrect sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp sharp compares rely summarized spread spread modulated modulated modulated cal chen chen chen conductances green green green simulator simulator simulator neuro returns findings findings begins begins leen proportion temporally angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular angular velocities theories arrival arrival turned turned anatomical anatomical anatomical alpha occurring north exceeds wilson wilson fires fires fires fires fires fires fires fires continue weakly ranging governed zhang zhang zhang accounts accounts spherical diameter hippocampus foundations cerebral omitted sustained park projects projects projects projects discovered propagate characterization lag yale yale yale yale yale yielded incorporates fellowship fellowship kluwer comparative comparative comparative comparative causing reports acceleration acceleration imagine wake pub summarizes deep biophysical biophysical biophysical neurophysiological maximally surrounding spreading nuclei nuclei nuclei dorsal afferents turning turning turning turning turning turning turning turning turning turning turning turning turning turning turning turning behave refined unpublished unpublished manuscript triggered stops rats rats rats rats rats rats syn heading heading heading heading heading heading heading influenced influenced influenced influenced assistance send send maze water inhibit inhibit suffers exper morris clarity ron injected anterior anterior anterior anterior anterior anterior anterior anterior anterior anterior anterior anterior anterior mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton mcnaughton systematically approaching approaching presently presently steve lar lar indirectly propagates freely freely freely landmark bodies bodies wan wan haven haven ular direc direc direc direc direc clockwise clockwise clockwise clockwise clockwise clockwise clockwise clockwise clockwise clockwise clockwise excite dead dead rostral thalamus thalamus thalamus thalamus thalamus thalamus thalamus thalamus thalamus thalamus thalamus thalamus reproduces reproduces anticipate anticipate anticipate anticipate anticipate anticipate neurology neurology neurology neurology exciting tums tums tums tums tums tums testable inhibits thalamic thalamic thalamic formalized reticular reticular reticular altogether sector narrower shi particu abstracts abstracts abstracts abstracts facing facing facing facing facing facing facing facing nected tha rect burgess burgess cis muller muller muller muller keefe keefe leftward knierim knierim knierim barnes spreads slowing transport neurosciences counterclockwise counterclockwise counterclockwise counterclockwise counterclockwise counterclockwise counterclockwise mecha nimh hines hines hines hines markus markus momentary injecting script initiate iiiiii inhibiting inhibiting inhibiting inhibiting pute anticipatory anticipatory anticipatory anticipatory anticipatory anticipatory anticipatory anticipatory anticipatory anticipatory anticipatory anticipatory subcortical proposing targeted redish redish redish redish norwell thalamocortical thalamocortical thalamocortical thalamocortical thalamocortical thalamocortical thalamocortical thalamocortical reside reside leonard reckoning reckoning shut lishers thai nisms aptic navigates neuroengineering neuroengineering sists limita 
#@Blair_H,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data data function function function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time set set networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number system system error error error error state state state results results results results results units units units units units units units units units units units units units information problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance space space space space weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case case order shown shown shown shown shown systems systems systems systems systems systems systems systems systems values values parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight functions neurons neurons unit unit unit unit unit unit unit unit unit unit distribution distribution distribution recognition method method approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single processing processing processing processing control large large large large neuron neuron neuron neuron test test patterns patterns analysis optimal inputs inputs shows shows shows shows shows signal signal signal signal signal signal signal signal signal algorithms gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper small small size work methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells step step step points field field field field field field field field field process process level level level level level trained trained trained trained cell cell cell cell cell cell structure structure random random random high memory response response response response response response response response response response response similar similar similar architecture section images parameter parameter real real real real real real states states theory theory theory obtained obtained activity activity dimensional result result result result result university solution research independent initial initial constant constant standard standard connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic left presented presented map present present present present present present present present present phase activation low low low low low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine maximum position position position basis sample sample sample sample abstract applied applied find convergence properties properties properties properties references component due due ieee positive mixture introduction complex hand stimulus effect parallel change change difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower measure signals signals signals signals prior part part part part part center center center center center center center center center center center center center center center center type cortex good long long conditions conditions conditions conditions represent distributed make observed scale respect respect respect elements means means optimization potential potential made made made made made made made made natural study study study filter filter obtain negative negative original artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial true compared application series series series series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive proc proc eye eye eye eye connected gain discrete discrete brain brain connection fields fields fields fields fields fields fields fields update dependent dependent dependent dependent dependent dependent dependent dependent institute institute words words consists consists internal represents represents represents represents responses responses responses responses final final layers layers scheme addition considered domain domain experiment experiment experiment environment environment environment environment top top stage stimuli effects detection detection detection detection detection detection detection requires requires choice choice statistics world vision basic basic increase con condition coding randomly randomly randomly developed developed levels area types lines provided backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature nature nature biological biological biological measured discussion feedforward increases describe arbitrary group close corresponds complete short common common shape shape shape shape role eds adaptation adaptation adaptation square square end future development development sensory simulated functional technology technology ratio york edge edge edge edge edge edge edge edge mechanism mechanism mechanism mechanism matching iterations iterations inhibition bottom supervised early minimize produced added sources light light light light light light light light light light light light light light light neuronal neuronal neuronal architectures membrane membrane discussed property takes typical lateral moving include subject machines side sejnowski sejnowski relevant relevant unsupervised observations teacher tions correspond correspond trans background background background background background background background background background background positions positions positions locations observation interval organization organization improvement increased increased amplitude constructed intensity intensity occur occur wide wide wide wide derivative white generally place place operator central central differences retina retina retina retina retina retina retina retina retina retina retina retina learns learns mechanisms integration presence presence regularization regularization variety variety exist decrease decrease iii manner identification question question question reference appears edges edges edges produces longer longer ways factors laboratory ann ann ann ann ann ann ann ann ann ann ann averaging averaging physical consisting develop springer formed formed formed formed versus versus depending viewed open operations updated lee lee centered activities processor past earlier smoothing smoothing smoothing sec event remains filtering filtering filtering filtering filtering filtering filtering calculate msec sufficiently recorded priori usa retinal retinal plotted plotted illustrated illustrated structural major efficiency differ poggio presentation detect detect detect detect composed traditional conf conf kind kind showing interested sci duration receptor receptor comp absence paradigm paradigm surround surround surround surround surround surround surround surround principles illustrates deal software decreasing presents law carried create investigate varied steady optimized dotted preliminary hall hall respond respond respond respond fashion biol plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity possibility possibility referred proper pathway func phases notion analogous analogous analogous analogous contours contours examined examined examined examined patch measurement trace plausible necessarily opposite opposite changed changed impulse portion noted logic nervous hebb finds finds synthetic isolated optimum indicating scenes scenes band band theoretic waveform waveform waveform adapted adapted adapted adapted adapted adapted adapted adapted answer glass interneurons inside snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr tive sys ring sites broad broad ion acad arises arises recording recording linsker linsker meaning explained apparent fuzzy double profile profile profile dark dark dark dark dark dark dark dark dark tional tional experimentally share recordings recordings remove continuously sharp biologically release berlin kinds decreased decreased physiol findings corrupted corrupted corrupted corrupted cybern bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar japan japan japan japan japan narrow narrow narrow acts enhancement enhancement spontaneous anatomical occurred height spot filled natl dependency dominant washington photoreceptor enhance emergence emergence emergence insight reveals record stopped interestingly material fly fly fly fly speaking anns anns anns anns shading session session session stork stork ties opposed spatio spatio connec obtains profiles profiles profiles profiles profiles laplacian brightness brightness peripheral peripheral peripheral pami interneuron tems learnt gas maintained wise wise wise differentiation differentiation spreading records records represen flash flash flash flash flash flash flash flash anal paradigms figs figs intracellular intracellular intracellular differentiating differentiating wider answers shallow shallow species remarks dim reversed demand accordance trainable trainable locate opponent opponent opponent opponent opponent opponent opponent opponent morphology transmitter drawing wiring polarity tip possess possess atick atick emerges emerges marr luminance luminance slices chan deals rameters vertebrate vertebrate vertebrate vertebrate vertebrate vertebrate evolutionary evolves remained comprised compromise compromise compromise mach mach emerged hyperpolarization mounted depolarization saito saito saito saito spario putational prolonged plotting yamada yamada yamada yamada broader broader localize localize localize localize ther ther mention nections projective ago convolving terminated heidelberg intel vertebrates manipulating rightmost ordinate imagery torre 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#@Furukawa_T,Yasui_S,
#t9
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural input input input input input input input input input input data data function function function function function function function figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error state results results results results information information information problem problem problem problem problem hidden hidden performance based based space space space space space space space space space space space space space space space space space space space space weights weights weights weights case case case case case case case vector shown shown shown shown shown values probability probability probability probability weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution recognition recognition method image single single single single single single single single single processing large large large large analysis analysis analysis analysis inputs inputs inputs inputs inputs inputs form shows shows simple paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small net work task task task task task task task task task task task task task task task task task task task methods methods process trained trained problems problems problems problems problems random random high high similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show equation equation section section section fixed fixed vectors vectors general general general generalization average average average theory theory theory theory theory note note note note note result result university university threshold independent independent defined defined found found found found sequence constant constant computer node node node node science presented map present nodes nodes nodes machine sets sets sets sets sets sets sets sets sets sets sets press learn learn learn learn learn learn learn learn learn learn learn outputs sample sample sample sample abstract computational references procedure decision introduction statistical generated generated generated generated variance tion complexity rules measure measure representations 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proceedings report words department loss loss internal internal internal internal internal individual individual individual advances represents represents represents bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias layers layers addition addition framework domain domain domain domain experiment experiment experiment experiment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment solutions stage conference capacity capacity determine determine upper full requires statistics give give give con bounds bounds bounds bounds types actual backpropagation depends sampling sampling sampling sampling sampling sampling achieved measured technical denote tested tested limited amount common common common common assumed generate generate generate theoretical theoretical theoretical require main journal ability ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis noisy typically pairs reduced unknown character character character increasing empirical empirical empirical empirical empirical empirical empirical leads squared squared squared details details numbers expert expert idea idea idea improved improved improved exact advantage pair separate reported reported introduced introduced include include sufficient highly tions solve smooth definition definition definition definition symmetric symmetric symmetric bounded bounded bounded bounded entire constructed exists invariant generally conclusion minimal minimal reduce conclusions depend central sigmoid measures practice strong reduction drawn drawn california assuming minimizing minimizing minimizing characters characters suppose suppose ways metric category simultaneously scales develop formed formed boolean boolean boolean boolean decreases choosing choosing choosing choosing national extracted extracted extracted family family family family independently independently independently independently depending viewed learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner restricted lee sizes similarly updates spaces convex sufficiently sufficiently sufficiently sufficiently sufficiently symbol faces faces expect handwritten thesis thesis thesis formulation inter inter plotted domains domains extra uniformly suitable effectively situation plots receives capture kind prob showing symmetry notation providing providing leading automatically automatically attempt consisted satisfies environments biases biases behaviour reducing rest investigated parity authors cover surfaces smallest smallest possibly generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation perfect ensure ensure ensure ensure ensure formal assumes separated generates extent submitted phd mentioned ment formula theoretic trivial trivial distinguish london tive preprocessing preprocessing worst worst mathematics addressed argument argument greatly greatly prop empirically led cmu cmu pseudo experimentally introducing calculating measuring measuring spread geman kinds decreased hints hints extreme lot ordinary college acm perfectly perfectly labelled royal hope definitions monotonically preparation intuitive intuitive heuristics substituting bartlett corollary ranging ranging respective chooses santa inf inf fold outlined abu mostafa equivalently opposed restrictions copy copy chapter forcing australia stands scenario verified pub learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt gener mitchell bounding searches searches proba argued translations placing nal williamson differing 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#@Baxter_J,
#t9
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural input input input input data data function function function function function figure figure figure time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error results results units information information problem models hidden hidden hidden hidden performance performance performance performance performance based weights linear layer layer layer layer layer case case case case case case vector vector vector vector order order order order order order shown shown shown systems probability probability probability probability probability probability parameters parameters parameters parameters parameters unit unit distribution distribution distribution distribution distribution distribution point point point point point point point point point point point point point point point large large large large large large large large large large large large large large large local rate test test test test test patterns patterns patterns analysis analysis analysis analysis analysis class class class matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs shows shows shows shows shows paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small size size size size size net work fig fig fig fig step field process trained trained trained problems random representation show show section line line line rule rule rule general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter average average average average average theory theory theory theory theory theory theory theory theory theory theory theory gradient obtained note note note activity activity result university university computation computation independent independent independent independent log log log defined found sequence initial initial initial constant estimate estimate estimate standard computer computer terms connections science left direction present present present machine sets sets sets sets sets maximum range range range range range range range range press press press nonlinear outputs continuous abstract applied find density density likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic due due ieee ieee positive introduction hand hand behavior behavior behavior statistical statistical statistical statistical statistical statistical effect effect generated variance parallel search complexity variable assume classifier classifier classifier higher higher center theorem theorem theorem theorem good good distributed region region region proposed proposed proposed proposed probabilities observed forward forward forward scale scale simulations simulations simulations simulations simulations simulations simulations simulations minimum minimum classes ing ing respect respect respect sum performed eq eq eq eq eq eq called means means potential applications applications study obtain obtain obtain obtain obtain obtain negative vol artificial true true compared compared cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross proc perform perform perform connected distributions gain gain gain gain gain gain brain approaches approaches mit mit train descent report report loss loss loss loss loss version consists connectionist exp exp exp exp considered computing computing equivalent hinton curve curves limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory top top top determine determine determine approximate statistics statistics estimated validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation give give con randomly conditional conditional area entropy provided iteration measured covariance normal feedforward feedforward increases increases increases limited limited inverse corresponds proof proof proof short common effective effective effective effective effective effective effective supported eds ability ability ability ability future easily rumelhart rumelhart including smaller smaller testing testing testing testing testing testing testing testing testing testing testing testing testing testing testing ratio ratio trials uniform empirical empirical empirical details direct early early early early early early early early early early early early early early early early produced description denotes denotes denotes denotes improve improve ensemble takes practical practical practical strategy period period subject subject side side side side side side side side recently recently engineering dimensions compare teacher teacher teacher calculated smooth studies trans trans address modified williams risk risk risk risk risk increased constructed exists exists exists studied extended matrices feed feed feed touretzky deterministic deterministic occurs occurs occurs occurs setting conclusion starting starting starting sigmoid moody moody asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic physics demonstrated regularization minimizing minimizing question question denoted denoted acknowledgements relation ann mathematical dept student multilayer multilayer linearly physical slightly angle angle expectation expectation expectation expectation decreases decreases decreases decreases decreases decreases national independently review depending lemma lemma codes detailed detailed evaluated evaluate controlled controlled labels showed centered sizes completely converges converges converges partition normalization neighborhood neighborhood intermediate intermediate intermediate intermediate calculate calculate calculate sufficiently avoid expect figures includes batch batch extension mozer phys discussions determining divided divided included included poggio poggio comparing situation orthogonal receives strongly showing stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping sin sin sin sin nips nips nips nips minimizes minimizes minimizes minimizes minimizes denker decreasing extend overfitting access access divergence divergence biases school tech tech proved fundamental math closest generalisation analyze analyze predicts opposite opposite opposite opposite rev der fisher fisher observe observe consist generates amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari extent submitted optimum optimum asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically percentage stop stop stop stop stop stop agreement improves analytic analytical answer answer answer lies correction worse purposes producing producing division ran cut opt opt definite conjugate summation virtual elman quantitative solla solla solla passes berlin weigend reaches reaches gen maximizes logp logp logp logp germany germany attraction findings damage wang wang wang softmax softmax wesley univ univ picture lab addison japan japan extensive girosi girosi impossible smolensky lecun lecun lecun kullback kullback kullback kullback fits mail settings disjoint monotonically ylx ylx optimally adequate expanded vertices enhance sphere sphere sphere sphere sphere sphere sphere yang yang yang yang yang diameter diameter diameter arrive theoretically passing seung valuable inf inf alternatively intersection intersection intersection stopped stopped acknowledge divide divide posteriori geometrical saad schulten schulten schulten fellowship leibler leibler leibler leibler equivalently basin exhaustive exhaustive exhaustive ical hillsdale param argue modifying pdp realizable realizable realizable ization ization expand confirmed associates modifiable modifiable modifiable eters corrections mini helps advantageous saturated ping ping stochastically hop firstly overtraining overtraining overtraining overtraining overtraining overtraining overtraining overtraining overtraining overtraining drawing dom illinois stay rissanen venkatesh bss triangle ray ray ray ray ray ray ray ray ray attained tokyo tokyo tokyo tokyo squashing judd ory degenerate proves approaching approaching approaching statist permanent gmd gmd enters bonn inst inst health validated validated validated validated validated validated regularizers urbana urbana murata murata murata murata murata murata murata murata murata murata nice heskes heskes intersect klaus treats treats treats mal enabled eralization nth beckman barkai barkai compose compose ogp yoshizawa chine nected riken revised omitting kappen karlsruhe karlsruhe neurocomputing nns fundamentals finke finke finke finke finke finke finke finke hecht hecht surely mfiller mfiller mfiller mfiller mfiller numer mized institutes saitama phe emits rudower mer chaussee milllet milllet nielsen nielsen paral moller lel hospitality rro elucidate nomena warm bunkyo timator 
#@Amari_S,Finke_M,Mueller_K,Murata_N,Yang_H,
#t9
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#*learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural input input input input input input input input input input input input input data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output number number number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models hidden hidden performance performance performance performance performance performance based space space space space space weights weights weights weights linear linear layer case case case case case case case order shown shown shown values values values values values values values values values probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise functions functions functions unit distribution distribution distribution distribution method method method approach approach approach point point point single single large large large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test test test test analysis analysis analysis analysis analysis analysis class class class class class class class class class optimal optimal optimal optimal optimal optimal optimal inputs form form shows simple simple simple paper paper paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small small small size size size size size size size size size size size size work work work work work methods methods step step step step classification classification process process structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems problems problems problems problems problems random random random random random high high high high response similar architecture show show show equation section section fixed fixed fixed fixed fixed fixed fixed fixed general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained obtained obtained term term term term term note note note note experiments experiments experiments experiments dimensional result result research independent log log log log log log log log log log log log log sequence sequence target target target target target target target target target target target target target target target target target target target target target constant estimate terms terms terms terms terms terms prediction left presented present phase range range range range range range range range range learn nonlinear sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract computational convergence convergence convergence density density density density density properties properties properties properties properties properties references due due ieee ieee positive important important important important important important important important context context introduction complex complex complex complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical statistical statistical statistical effect effect effect generated cost complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume assume assume assume assume assume measure measure measure measure measure measure chosen chosen part part part part theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases cases good good long expected make make make fact length correct probabilities errors finite finite minimum minimum resulting resulting resulting classes classes classes ing computed respect respect respect respect respect respect respect respect called elements mapping means means factor factor factor optimization potential dimension dimension dimension dimension made natural natural natural natural natural natural applications study study knowledge obtain obtain negative relative relative relative relative relative specific samples samples true compared compared compared compared cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross define define define rates rates rates rates perform determined experimental experimental experimental experimental experimental goal goal gain equal equal equal equal equal power power power power power power power power power steps steps comparison larger train source selection selection selection selection selection selection selection selection selection selection selection selection proceedings version version consists consists represents represents represents difficult final delay addition addition curve curve additional curves top top top bit determine determine efficient full full choice choice choice choice choice choice choice choice choice significant significant approximate statistics free pages validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation give give give give give give condition derived derived randomly bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds actual provided provided selected selected backpropagation backpropagation depends depends depends simply simply simply simply achieved achieved increases increases increases describe arbitrary denote close assumption assumption assumption assumption assumption predictions predictions proof amount effective theoretical require main main hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance instance easily degree including fit typically smaller smaller smaller underlying underlying account unknown interesting interesting interesting interesting interesting interesting interesting testing testing testing ratio york increasing increasing increasing trials uniform uniform uniform uniform uniform empirical principle principle squared squared representing details details call bottom bottom bottom decay decay decay decay polynomial polynomial idea idea minimize choose choose choose added sources description perceptron perceptron perceptron discussed recent exact exact property property property apply introduced introduced approximately works tuning tuning axis axis axis yields symmetric modified interval interval sensitive entire entire entire increased expression expression expression expression expression expression invariant invariant invariant deviation deviation wide wide wide wide wide wide wide wide wide wide predicted predicted predicted predicted predicted predicted predicted predicted width width width occurs generally setting setting assumptions assumptions assumptions conclusions valued depend depend central differences differences accurate performs practice practice practice asymptotic weak propose physics drawn regularization labeled labeled labeled assuming variety minimizing minimizing minimizing exist min min min min min averaged introduce identification program acknowledgements suppose suppose suppose appears appears relation relation index index plot plot plot plot plot plot plot plot plot plot plot plot plot plot plot label label label label changing segments segments segments recall missing sensitivity sensitivity multilayer remaining slightly consisting consisting consisting frequencies events minimization minimization minimization minimization springer implies boolean boolean select decreases decreases yield yield choosing choosing choosing choosing choosing choosing choosing independently depending interpretation interpretation transform labels labels fraction fraction fraction fraction fraction fraction fraction approximations forms approximated suggested constants constants constants reasonable reasonable reasonable calculation performing performing epochs classical reduces fitting fitting fitting fitting fitting fitting fitting intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals initially sufficiently sufficiently transactions transactions expect expect expect expect expect figures figures perceptrons recognize determines vapnik vapnik vapnik vapnik holds holds simplicity determining straightforward straightforward straightforward importance uniformly computationally identify literature score situation plots plots plots plots plots plots plots plots plots essentially essentially summary refer notice verlag strongly split split notation quantity list involved usual michael realistic minimizes hypotheses leading approximating decreasing decreasing situations law law law law law law law carried parametric powerful powerful powerful investigate investigate exhibit accurately reducing fourier examine giving combine complicated cover cover cover cover notion analogous examined coarse plausible possibly necessarily analyze analyze predicts predicts extremely aspect obvious obvious formal formal precise precise precise precise observe extent extent extent simplest arbitrarily indicating cos phenomena phenomena independence lies worse sections formalism precisely precisely division worst arise potentially universal universal universal universal universal universal begin optimize annual qualitative qualitative qualitative qualitative qualitative qualitative researchers mechanics mechanics apparent greatly behaviors behaviors behaviors considerably applies consistency experimentally quantitative quantitative quantitative haussler remove exhibits rely replace sophisticated deviations deviations deviations yielding irrelevant realized phenomenon corrupted corrupted corrupted corrupted intractable primarily fix acm arguments perfectly partitions discover nonzero nonzero nonzero inspired adds consideration convenient significance accepted tools satisfying simplify held stated stated tishby tishby definitions settings settings disjoint implications optimally optimally optimally heuristics heuristics analyses sompolinsky mance slice representational representational perfor consequences chooses barron barron barron barron barron barron omitted kearns kearns kearns kearns considerations seung seung variants variants reverse captures insensitive insensitive ball assigns andrew andrew verify usage largely largely rigorous chervonenkis chervonenkis alternating alternating emerge suboptimal suboptimal adopt smoothly acceptable tradeoff generalizations generalizations generalizations mdl examining argue verified verified toy realizable bounding bounding bounding concentrate increasingly rough weaker knowing indication behaves coming fiat replacement dim accordance nested confirm ron pronounced pronounced pronounced progressively tells nontrivial nontrivial differentiate differentiate minimizer shortly shortly capturing occurrences occurrences violated violated refine replaces nice proximation meaningless obeys obeys omit plexity dependences conversations superiority mansour claims dana remember conflict complexities mild subsample subsample subsample idealized emphasizes seventh intersecting intersecting tri story conducting omitting saving appeal superpositions als labor nonincreasing deviates documented arl refinements insensitivity cid spherically borne bowl reside complements origins grossly shorthand interpolates keams eel disagrees sigrnoidal backpropogation warm cay 
#@Kearns_M,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state results results models models performance performance performance performance performance performance performance performance performance performance weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case vector vector vector vector vector order shown shown shown shown shown values parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight distribution distribution distribution distribution method pattern image single single single single single single single single single single processing large large large large large large large large large large large large large test test test test analysis analysis analysis matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs shows shows shows shows shows shows simple simple gaussian paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples small small small size size size size size size feature task task methods features process process process process level level trained trained trained trained trained trained trained trained trained trained trained trained trained random high response response equation equation section section line line line line vectors vectors general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech parameter parameter parameter parameter parameter parameter parameter parameter real average average average average average average average average average gradient obtained obtained obtained term term term term term term dimensional result result result result result university variables solution solution independent defined found found found target target target target target target target target target target constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate terms left left left presented present sets sets sets sets sets sets sets sets sets sets sets sets range range range press press learn basis basis basis nonlinear outputs outputs outputs sample abstract find find references stochastic stochastic due ieee positive important context introduction effect effect effect generated generated variance variance variance tion assume assume assume lower chosen chosen chosen chosen chosen chosen part cases fact length errors errors errors errors errors finite finite finite minimum minimum minimum minimum minimum minimum minimum resulting resulting resulting ing total total total total sum sum performed elements mapping factor optimization optimization optimization optimization potential global applications study study study knowledge obtain samples true cross provide define perform perform perform experimental approaches mit mit larger descent dependent selection department individual individual individual individual individual individual individual individual individual individual individual final exp exp bias curve additional curves limit limit limit limit limit limit top effects effects full significant statistics estimated estimated estimated estimated increase increase increase increase validation con weighted weighted weighted weighted randomly randomly randomly levels levels types lines lines provided depends simply simply simply corresponds corresponds predictions predictions amount amount amount common assumed main main adaptation journal instance easily makes noisy noisy fit smaller smaller smaller smaller smaller combination unknown unknown testing testing testing significantly increasing special uniform uniform uniform uniform details numbers making normalized bottom decay decay decay decay decay idea combined minimize minimize minimize added added perceptron perceptron perceptron denotes improve improve correlations advantage advantage robust ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble typical practical introduced identical identical identical identical identical identical identical identical inference sufficient approximately calculated calculated axis axis yields correspond achieve trans diagonal address improvement improvement improvement risk exists exists lead studied scaling occur occur wide wide white generally generally generally minimal minimal minimal conclusions conclusions measures performs practice temperature presence physics characteristics drawn solid solid regularization regularization regularization start averaged groups denoted denoted denoted relation construct written solving plot plot plot student student student student student student student student student student student student student student student student student student student student student averaging averaging averaging infinite easy slightly belief minimization yield yield choosing choosing choosing choosing independently independently focus dependence review communication squares overlap fraction fraction fraction approximated sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes similarly suggested updates dashed dashed additive additive reduces combining fitting fitting fitting purpose valid intermediate expect expect expect combinations determines discuss maximize phys phys phys simplicity simplicity simplicity reason differ differ effectively delta plots reached refer refer refer kind strongly strongly superior follow bar sampled realistic realistic realistic realistic nips nips nips predictor predictor overlapping overlapping overlapping overlapping approximating tesauro tesauro decreasing explore remain parametric overfitting overfitting overfitting collection optimized dotted dotted hall behaviour reducing tech investigated investigated analytically analytically referred cover adapt equally thought subsets quantities contributions submitted averages mentioned stop adapted caused briefly worse sections gradually optimize arises fluctuations explained improvements substantially offset parameterized peter marked remove treated rep limiting monotonic qualitatively prevent inherent conclude unbiased findings implements yielding yielding sharing globally globally globally globally corrupted uncorrelated cooper optimizing member nonzero nonzero nonzero nonzero stronger logarithmic held biased biased removing unlabeled unlabeled star sanger sanger monotonically krogh krogh krogh krogh krogh krogh krogh krogh intuitively optimally optimally optimally preparation carry hertz hertz overlaps ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity predictors predictors predictors predictors predictors predictors predictors predictors predictors forecasting consequences ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles surprisingly reader rich extensively agree wolpert implicitly insensitive treat temperatures ent benefits diverse tween pointed centre convenience obtains personal spaced suppressed suppressed edinburgh scenario constrain arising penalized publication intuition community insights gained decays decays decays decays chapman thermodynamic thermodynamic gener denoting regularized regularized regularized regularized regularized regularized regularized regularized regularized concentrate sollich sollich sollich sollich sollich sollich anal hansen diversity diversity holding mini students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students students demonstrating stops meir advantageous achievable solvable dropped kth compo ally separates systematically vanish convention transpose implying denmark correlates pin tical mach fixing indi generaliza unnecessary unnecessary analyse ambiguities ambiguities ambiguities tutorial nents dominate forthcoming alization confirms ily stars noises noises noises noises suppresses kronecker expects copenhagen perrone iden granger subjected exemplified intell timal timal fused discussing ject blegdamsvej acquires vedelsby kom mammone anders persists mized wasteful vidual salamon nordita thorbergsson tempting actu semble stu stu sembles 
#@Krogh_A,Sollich_P,
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number number results results results results information problem problem problem problem problem performance based based based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case case vector vector vector order order order values values probability parameters parameters parameters parameters weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions neurons neurons distribution recognition method method approach pattern pattern point point point large large large large class class class class class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form shows algorithms simple paper paper paper paper paper paper examples examples small small size size size size size net net net net net net net net net net net net work work points points points classification classification classification current current problems high memory memory similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show section section fixed fixed fixed general general generalization generalization real real real theory theory theory theory theory theory gradient obtained obtained obtained obtained obtained term term note note note note note note dimensional result result result result result result result result result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables computation computation computation computation computation computation computation computation research log log log log log log defined defined defined defined sequence constant constant constant constant estimate estimate standard computer distance node node node science direction activation activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine range press learn outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous sample sample sample abstract computational computational computational analog references references due due important context context introduction introduction complex estimation search tion complexity complexity assume assume assume assume assume assume assume assume assume lower lower lower rules chosen higher part theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound cases cases required required binary binary binary binary binary long conditions expected fact fact correct correct finite finite finite finite classes tasks total total total simulation computed computed computed multi sum called called called called called called elements means means means potential dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made made made made made made applications applications study original artificial samples samples samples samples compared desired provide define define compute compute compute compute compute proc proc related connected equal equal power power contrast contrast descent nets nets nets nets nets nets nets nets nets nets nets nets nets institute words department version version consists consists advances responses bias graph ai ai maps maps considered framework cambridge computing computing domain equivalent directly san bit capacity capacity upper upper upper upper upper full choice choice choice statistics basic con condition levels bounds bounds bounds bounds types types provided finally backpropagation discussion feedforward feedforward arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary transformation assumption corresponds proof proof proof proof proof proof proof amount common assumed assumed assumed shape supported supported theoretical theoretical main main main square hypothesis future fit fit kaufmann objective simulated typically smaller needed needed needed needed interesting special special matching empirical details call call numbers numbers numbers numbers numbers depth polynomial polynomial polynomial idea added added architectures architectures architectures discussed discussed recent property takes element practical machines machines quadratic quadratic quadratic quadratic quadratic quadratic sense subset subset subset subset subset subset recently relevant interest interest dimensions previously approximately rl definition definition definition definition bounded gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate interval grant constructed exists exists exists concept concept derivative derivative derivative correctly feed generally assumptions editors central central sigmoid accurate weak mateo taking hard hard hard sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal proportional proportional proportional proportional labeled labeled assuming exist exist derivatives force force question question question question reference estimating distinct changing coordinates linearly remaining unique unique unique unique consisting adding springer implies blocks boolean boolean boolean boolean boolean boolean open open open open showed showed showed showed showed sizes sizes sizes partition constants allowed sign sign sign fitting fitting intervals roughly roughly interpolation remains valid valid assigned assigned construction construction includes activations activations activations activations activations activations usa formulation assignment vapnik vapnik vapnik vapnik vapnik vapnik specifically variations simplicity uniformly uniformly maximal included essentially identity identity showing issue classify running sci hold built satisfy comp quantity sampled write write paradigm computes thresholds thresholds thresholds approximating approximating satisfies extend employed transformed transformed involving replaced recursive scalar scalar fashion dependencies reliable gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates gates cover cover notion neu induction induction possibly integer integer extremely aspect obvious assumes contributions motivated motivated established established mentioned piecewise piecewise piecewise piecewise piecewise piecewise distinguish smoothness answer baum baum starts lin purposes shared strictly products mathematics universal preceding limits limits limits applies affine tional fed fed lack effort haussler haussler haussler continuously rep ity berlin rely ture ture gen ordered boston lim lim lim lim proposition proposition proposition differentiable differentiable multidimensional realized consistently gap lab pac pac pac pac ear writing formally guarantee acm acm acm acm ordering ordering purely purely nonzero proceed establish maass maass maass maass maass maass maass air dealing dealing satisfying fan fan fan fan held replacing ral definitions definitions implications implications symposium combinatorial reliably lip excellent programs studying surprising infinity originally multiplied advance warmuth rich passing relies implicitly papers tures integers default assigning learnable speaking speaking listed fellowship sig kluwer graded recursively chervonenkis chervonenkis chervonenkis sontag sontag sontag sontag sontag sontag sontag sontag pointed theorems associate guess valiant valiant valiant tight tight continuity unseen pub bounding learnability learnability afosr picked fir france book parametrized ignoring computa sigmoids sigmoids remarks survey survey satisfactory hilbert blum blum lyon lyon lyon concern exclusively architec architec architec anthony anthony goldberg goldberg goldberg goldberg siu cardinality cardinality characterizes artifact shattered shattered shattered shattered shattered shattered sending comm reviewed acyclic syst completeness predetermined terminology terminology putational omit settles save blumer blumer resentation dealt eralization thompson perspectives standing ana ana koiran koiran koiran koiran koiran koiran listing vation rutgers rutgers acti oft oft cedex brute interna rrt settled ehrenfeucht ams quantifying speak formalize heaviside heaviside heaviside heaviside ifp textbook symp memorize shatter shatter shatter shatter shatter shatter weakening weakening bulletin informatique quoted moidal agreed brunswick lyl conceivable wlog lui lui cknowle dgement karpinski karpinski crt pletely lime ecole biggs biggs cnrs pacity eduardo eduardo macintyre lishers nonempty exceptional normale formalization formalization lap affirmative rected predecessor 
#@Koiran_P,Sontag_E,
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data function function function function function function function function function function function function function function function function function time time time time time time time time time time time set set set set set set set set set set set set set set networks networks networks output output number number number number system system system system error error state state results results results results results results results information information information information information problem problem problem problem problem problem problem models models models models based based based based space space space space space space space space weights linear linear linear linear linear linear linear linear linear case case case case case vector vector vector vector vector order order order order order order systems systems systems systems systems systems systems systems values values probability parameters parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit pattern pattern processing processing processing processing control control control control control control control large large rate patterns analysis class class class class class class class class class class class class class class class class class class class class inputs inputs inputs inputs inputs inputs inputs form form form form signal signal signal paper paper paper paper small size size work work classification classification classification level current current structure structure problems high response response response representation representation show equation section section section section section section fixed fixed rule vectors vectors general general general speech parameter parameter real real real real real real real real real real theory theory theory theory theory theory theory obtained obtained obtained obtained note note dimensional dimensional result result result result result result result result result university university variables computation computation computation computation computation computation computation computation research research log log log log log defined defined defined sequence sequence sequence dynamics constant estimate estimate estimate standard computer terms terms terms science prediction left presented presented map map map machine sets sets sets sets sets sets learn components nonlinear outputs sample sample sample sample sample sample sample sample abstract abstract abstract back back back back back find computational computational computational computational references references due due due due due ieee ieee positive positive adaptive decision decision decision decision context context context context introduction hand estimation estimation statistical cost cost cost cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search tion change complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume assume assume assume assume classifier classifier classifier lower lower lower signals prior higher part previous theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound cases required binary conditions represent fact fact fact fact fact techniques length length length finite finite classes classes classes classes respect respect called called called called called elements means optimization dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension feedback applications applications applications applications study study filter filter obtain obtain samples samples samples samples application application application desired desired series provide define define define compute compute proc proc eye experimental related related connected discrete approaches comparison comparison connection fields source nets nets modeling modeling morgan morgan report department department loss loss loss synapses advances advances advances advances represents difficult addition sequences sequences ai ai ai maps framework computing additional estimates estimates estimates san efficient classifiers classifiers basic channel channel bounds bounds bounds bounds bounds entropy product product product product finally selected depends discussion arbitrary complete complete proof proof proof proof finding finding supported theoretical theoretical main main main main eds eds eds hypothesis hypothesis hypothesis hypothesis instance instance future degree degree noisy kaufmann kaufmann typically underlying needed needed needed needed account dynamical dynamical dynamical dynamical dynamical interesting york special special special consistent empirical principle details call numbers numbers numbers numbers numbers numbers max max bits polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial choose perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron discussed discussed discussed recent correlations correlations advantage apply introduced introduced identical sense sense inference subset subset subset subset subset subset interest interest sufficient observations axis axis axis axis axis axis axis rl rl rl definition bounded channels organization grant exists concept concept concept digital digital digital correctly touretzky generally generally operator valued valued valued mateo encoding taking proportional labeled turn turn exist exist min min relationship introduce introduce scene identification identification force base denoted reference suppose suppose pro written index solving estimating stability changing confidence recall metric metric coordinates infinite infinite dimensionality unique consisting develop applying springer boolean boolean boolean select letters dependence lemma lemma lemma solved variation open operations lee decomposition forms sign sign sign sign sign sign sign sign sign sign measurements classical classical classical spaces spaces fitting roughly roughly closed filtering classified classified includes coordinate usa perceptrons perceptrons perceptrons vapnik vapnik vapnik vapnik vapnik prove prove prove prove discuss specifically characterized aspects suitable literature literature efficiently conf conf induced showing anderson interested interested issue classify classify involved usual generalize nips giles giles hypotheses wiley exhibit involving involving limitations limitations limitations limitations accurately recursive recursive recursive recursive recursive recursive recursive recursive recursive dual dual existence ideas rest mappings mappings mappings mappings applicable int dependencies authors authors referred referred proved proved notion concepts possibly integer automata subsets impulse impulse impulse assumes assumes precise observe separated perceptton simplest electronic languages formula theoretic separable publishers convolution defining defining fairly briefly briefly reasons filtered arise mathematics consequence acknowledgement toronto meaning meaning meaning sun reflects understood understood relevance consistency consistency consistency pseudo pseudo pseudo pseudo pseudo parameterized haussler haussler haussler haussler haussler berlin ture extracting popular chen chen acoustics semi boston boston boston arithmetic classifying classifying classifying classifying classifying pac proofs guarantee tation restriction restriction restriction acm acm angular pick pick pick maass maass maass air dealing dealing dealing mail logarithmic logarithmic check serves operates unlabeled definitions disjoint disjoint disjoint reliably meaningful excellent separating percepttons sim membership omitted reader reader record warmuth canada canada grammatical hart hart integers integers integers integers johnson learnable learnable learnable speaking logarithm kluwer kluwer equivalently chervonenkis chervonenkis chervonenkis chervonenkis opposed opposed dec sontag sontag sontag sontag sontag sontag sontag obtains generalizations generalizations classifies valiant tight tight algebraic algebraic quantized quantized unseen rectangular rectangular cessing duda duda bounding learnability learnability learnability learnability learnability afosr fir topic iri iri sketch represen siam son dichotomies dichotomies struc signs signs lecture survey nonnegative ate inequalities appealing dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy interpolating goldberg goldberg goldberg siu siu cardinality cardinality cardinality deals deals archi shattered shattered shattered shattered shattered comm poles signed mach fixing statements rem tsoi tsoi tsoi tsoi tsoi rent addi iir iir omit omit omit turing topics recovers blumer theo equalization dependences ontario roychowdhury roychowdhury thinking perspectives perspectives clarify recur subclass rutgers rutgers rect sharper ehrenfeucht publications formalize pollard pollard pollard kennedy dasgupta dasgupta dasgupta dasgupta dasgupta logs ingredients discriminants transmitting succeeds surveys brunswick warren supremum assured waterloo waterloo appropri nlog nlog nlog permissible eduardo imax cix emulating brighton nonempty birkhauser tur rationals narrowing pings ilarity logq ale 
#@DasGupta_B,Sontag_E,
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#*network network model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input data function function function function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks output output number number number number number number number results results results results results results results information information problem problem models models models weights weights layer layer layer case order shown systems systems systems systems values values probability probability probability probability probability probability parameters noise noise noise noise noise weight functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution point single single single processing processing large large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns analysis class shows shows shows shows small small small small small size size size size net net work work task step points features level random high high high high high response response response response response response response response response response representation show show section section section section fixed fixed fixed fixed parameter parameter real real average average term note activity activity activity activity activity university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation computation computation computation research independent independent defined constant constant constant constant constant computer computer computer terms synaptic science science science left left activation low temporal press press press press press outputs continuous continuous abstract abstract abstract computational computational computational computational computational computational computational computational computational computational computational computational computational analog properties references stochastic stochastic stochastic stochastic positive positive positive introduction complex complex circuit circuit circuit circuit circuit circuit circuit effect parallel tion difference difference complexity complexity complexity complexity complexity assume assume assume assume assume assume assume assume assume assume assume assume lower lower chosen chosen higher part part previous theorem theorem theorem theorem bound bound bound firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type type type cortex spike spike spike long conditions tree tree tree tree make make fact fact length length length length forward finite finite finite simulations classes simulation simulation computed multi called times times times times potential potential potential potential potential potential potential made negative negative vol vol vol artificial represented represented represented represented provide provide provide define rates location experimental experimental constraints distributions brain brain equal power power power power power power power mit mit mit larger contrast contrast source nets morgan proceedings report institute implementation version synapses synapses synapses synapses synapses synapses synapses synapses advances advances represents layers layers layers layers layers layers layers delay scheme addition addition sequences ai framework cambridge computing environment view bit bit bit bit bit efficient upper upper choice speed basic con coding coding coding coding coding coding coding coding coding coding coding coding randomly randomly bounds types processes processes evidence inhibitory inhibitory depends biological biological biological biological biological biological describe arbitrary arbitrary fast fast close close close assumption assumption assumption assumption excitatory excitatory excitatory excitatory proof proof proof circuits circuits circuits circuits circuits circuits circuits short short short common common common common assumed assumed assumed shape shape shape synapse synapse synapse synapse synapse role role theoretical theoretical theoretical require journal noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy kaufmann simulated unknown unknown mechanism mechanism mechanism mechanism special consistent principle principle principle details call pre inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition bits bits bits bits bits bits bits polynomial polynomial idea idea idea combined choose choose run light perceptron perceptron neuronal denotes exact exact property takes reported apply period period sense subset sejnowski sejnowski sejnowski relevant previously approximately module module module tions yields achieve achieve address background background chain gate gate gate gate gate gate gate gate gate gate interval interval interval interval interval interval interval interval organization constructed exists exists exists parts studied occur occur occur occur extended extended digital digital digital spikes deterministic deterministic pass conclusion assumptions assumptions assumptions assumptions assumptions assumptions assumptions segment depend modules weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak strong strong sigmoidal proportional exist exist introduce manner manner manner van van van van van construct label label label multilayer simultaneously simultaneously simultaneously linearly linearly easy easy consisting blocks boolean boolean boolean boolean boolean boolean boolean choosing choosing communication detailed transform completely allowed additive delays delays purpose remains intermediate msec msec msec msec msec msec msec msec sufficiently sufficiently sufficiently assigned construction construction construction construction dendritic dendritic dendritic dendritic building fire fire fire fire perceptrons prove activated absolute holds simplicity regular straightforward suitable encoded spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking computations computations computations computations computations computations computations situation receives refer refer refer contribution timing duration satisfy satisfy involved write realistic realistic realistic realistic realistic realistic nips hypotheses hypotheses subsequent satisfies satisfies deal decreasing decreasing receive presents employed powerful exhibit exhibit behaviour behaviour fashion reliable reliable reliable reliable reliable gates gates gates gates gates gates gates gates affect understand neu transmission integer automata automata der formal algo assumes precise consist arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily arbitrarily submitted years percentage formula caused turns turns turns straight closer precisely precisely arise pool pool pool pool pool pool pool pool pool pool pool explained argument double substantially simulate simulate simulate simulate simulate simulate simulate simulate simulate simulate employ frequently frequently biologically biologically biologically biologically reliability reaches lim shifted proofs sv oxford arguments appropriately refractory impossible impossible maass maass maass maass maass maass maass maass maass maass systematic chance chains difficulties fan fan fan automaton interpret exploit fail roles roles imply carry carry carry carry fires fires fires fires weakly corollary realization uni cerebral surprisingly surprisingly arrive arrive arrive record epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp epsp impact johnson fired land rigorous rigorous basically shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting shunting encodes encodes encodes encodes employs trigger trigger trigger trigger trigger acceptable simulating realize remote publication rithms impose distal assemblies apparently pools pools pools induces intensive travel article article article article article article failures spite persistent mcculloch survey pitts pitts unbounded sake abeles abeles abeles abeles suffices hemmen hemmen hemmen rons concrete concrete concrete unreliable unreliable contributes contributes correctness correctness correctness carries gerstner gerstner gerstner inspection remained computable handbook ically putation repetitions zone zone zone zone zone firings firings firings subtree subtree relax technische simulates delete ample forthcoming availability constructions constructions constructions constructions constructions constructions constructions constructions synchronize versity psp froin spontaneously throw seemingly shepherd shepherd shepherd inhibits rising lira lira lira mere tain iai fimction quantifies giant ipsp ipsp ipsp ipsp ipsp veto graz graz graz graz governs biochemical negation austria cated structed ciently 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#@Maass_W,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural input input function function function function function function function function function function function function function function function function function function function function function figure figure figure figure set set networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output output output output output output output number number number number number number number system system error error error error error error error error error error error error error error error error error error error error error results results results results units units units information problem problem problem hidden hidden weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear layer layer layer layer case case case case case vector order order order order order order order order order order order order order order order shown shown shown shown shown values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise weight weight functions functions unit method method method method method approach approach point point large large local local local local local local local local local local patterns patterns optimal optimal optimal optimal inputs inputs inputs shows shows shows simple gaussian gaussian paper paper examples examples examples examples examples examples examples examples examples small small small small small small size net net net work task task task task task task task task task task task task task task task task fig fig fig fig fig fig fig fig fig fig fig step process process process process process process process process process process process process process process level level level trained trained problems random high high high similar representation architecture show equation equation equation fixed line line line line line line line line line line vectors generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter real real real approximation approximation approximation theory theory gradient note note dimensional computation computation solution solution independent independent defined defined defined defined found found standard presented presented sets sets press learn learn nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous continuous continuous abstract references positive procedure important important introduction behavior statistical statistical statistical statistical parallel parallel cost difference difference difference variable variable lower lower lower lower lower lower rules measure measure measure chosen chosen higher higher bound bound cases good good good good distributed distributed correct correct correct observed observed errors forward scale scale finite finite finite finite finite finite finite finite simulations simulations simulations minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting ing tasks tasks tasks tasks tasks simulation simulation simulation simulation simulation sum sum called called mapping means means natural natural applications study study study knowledge vol artificial compared cross cross cross cross cross cross cross provide define determined related related gain gain gain gain gain gain gain gain gain gain gain steps steps steps comparison dependent dependent nets exp scheme directly curve curve curve curve curve curve curve curve curve curves curves curves curves curves curves curves curves curves curves curves limit limit limit limit limit effects conference capacity determine determine determine upper upper approximate approximate approximate validation validation validation validation validation validation give condition weighted weighted developed levels lines lines lines lines lines lines lines lines actual actual provided provided provided measured feedforward increases increases increases describe fast corresponds corresponds corresponds assumed role theoretical theoretical theoretical ability ability makes development noisy smaller interesting ratio increasing trials principle leads leads squared details international normalized supervised early early early early early early early early early minimize choose description description description description description perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron architectures exact property practical practical strategy strategy strategy identical identical identical highly compare compare teacher teacher teacher teacher teacher teacher teacher achieve definition definition evaluation observation storage expression expression lead lead lead concept deviation feed occurs runs starting critical critical critical minimal sigmoid sigmoid measures numerical learns learns learns learns learns learns temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature solid solid solid solid solid solid solid solid min min min min min min min decrease averaged averaged averaged minima minima minima explicit pro ways plot describes laboratory student student student student student student student student student student student student multilayer multilayer multilayer multilayer multilayer infinite develop develop quality implies implies dependence overlap interpretation interpretation updated fraction evolution evolution understanding approximated sizes completely completely earlier earlier reasonable calculation calculation dashed dashed dashed reduces reduces iterative remains intermediate calculate norm norm norm avoid avoid avoid avoid perceptrons perceptrons perceptrons contour contour contour determines determines absolute absolute absolute absolute phys discussions tests major reason reason suitable suitable presentation reached reached summary strongly interpreted stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping strategies built minimizes minimizes minimizes illustrates acknowledgments decreasing decreasing trains trains parametric parametric parametric parametric parametric parametric overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting difficulty optimized optimized optimized optimized optimized optimized dotted dotted dotted dotted dotted preliminary helpful existence examine possibility tanh tanh tanh tanh tanh tanh tanh tanh understand possibly reading rev illustrate quantities perceptton perceptton perceptton perceptton perceptton amari amari simplest arbitrarily finds established optimum indicating slowly slope slope explanation nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity starts straight straight purposes commonly calculations mechanics mechanics mechanics explained applies applies double double lack adjustable exhibits exhibits exhibits exhibits exhibits gains cal qualitatively wesley hints realized naive addison japan plays replica replica imply krogh hertz hertz hertz loo surprising realization percepttons infinity chooses approximators emergence emergence express ends ends hypercube considerations stopped avoiding temperatures schulten email exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive exhaustive emerge opper opper guess param transparent transparent avoids learnt learnt realizable realizable realizable realizable realizable realizable realizable realizable realizable realizable realizable thermodynamic thermodynamic concentrate guided guided tune eters simplifies stops palmer stimulating monitor marks marks realizations bss bss bss bss bss interpretations adjusts adjusts pin validated murata permutations teachers accepts aware dash dash abs abs abs miiller miiller fulfill amples shi riken riken concentrates absolutely unrealizable identi finke kinzel conventionally descend saitama wako clearer zoo outlook complicate vided herrmann 
#@Boes_S,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural input data data function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time set set set set set set networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number system error error error error error error error error error error error error error error error error error error error error results information problem problem problem problem problem problem models hidden performance performance performance performance performance performance performance performance based based weights weights weights weights case case case case case vector vector vector vector order order order shown shown systems systems systems values values values values values values values values values parameters parameters parameters parameters parameters noise weight weight weight weight weight weight method method method method method approach point processing control large large local rate rate rate rate rate rate rate rate rate rate rate rate rate test test analysis analysis class class class class class class matrix matrix matrix optimal form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper examples small size size net net net net work work work work methods methods methods methods methods methods step step step step step step points process problems problems problems problems problems problems problems random random random high similar show equation equation equation equation equation section section section section section section fixed fixed line line line rule rule rule rule vectors vectors vectors vectors vectors general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation approximation average average average states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term term term note note note note note note dimensional dimensional dimensional dimensional result result university solution found found found sequence sequence initial initial initial constant constant table table estimate direction direction direction direction direction direction direction direction direction direction direction presented presented present phase nodes sets press press press learn learn components abstract back back back back find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties references component due positive positive positive positive adaptive propagation propagation propagation context introduction complex estimation estimation estimation estimation behavior effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic parallel search search search change change change difference assume lower lower measure chosen chosen chosen theorem theorem theorem bound cases required good good good good good long long conditions represent expected expected expected expected make fact region proposed length length length length length probabilities finite minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting ing regression called elements regions optimization dimension made global artificial specific compared compared series rates rates rates location determined motor power power power power steps steps steps steps steps larger larger descent descent descent descent descent descent descent nets morgan morgan proceedings proceedings version advances connectionist sequences ai framework cambridge computing domain experiment experiment hinton additional design limit limit trajectory trajectory trajectory san san efficient upper requires requires choice significant significant speed speed pages pages increase produce derived criterion criterion criterion lines evidence backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation iteration iteration depends depends feedforward denote denote tested transformation fast close stable stable stable stable stable stable stable surface proof proof proof proof proof proof amount generate theoretical adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation square square square square square end end ability ability future sensory including kaufmann kaufmann simulated typically smaller smaller smaller needed needed needed interesting projection projection max international normalized normalized normalized normalized normalized decay decay decay minimize produced choose choose added improved improve improve directions directions directions directions directions directions exact property typical apply apply quadratic quadratic quadratic quadratic quadratic quadratic quadratic sense sejnowski compare works axis solve yields studies converge converge differential differential differential differential achieve diagonal diagonal symmetric modified bounded bounded gate improvement improvement increased exists exists studied studied occur trial locally touretzky touretzky loop boundary boundary setting setting setting minimal minimal conclusions editors numerical exponential asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic mateo mateo propose strong largest largest turn exist min min decrease derivatives minima minima minima minima minima minima annealing boltzmann explicit van produces solving estimating stability stability stability stability stability stability stability stability changing explicitly averaging infinite infinite adding minimization minimization quality quality decreases choosing dependence stages viewed solved evaluate evaluate restricted approximated completely converges constants updates sign slow epochs epochs epochs expansion construction norm kohonen includes thesis coordinate coordinate coordinate eigenvalues automatic prove holds holds reason reason regular regular straightforward straightforward identified extra uniformly uniformly differ successful genetic situation orthogonal reached reached refer quickly cun simplified eigenvalue eigenvalue reach jacobs deal decreasing schedule schedule parametric exhibit rapidly put put hessian hessian hessian recursive existence fewer school rest root root root notion notion momentum momentum smallest gradients editor necessarily extremely changed der greedy algo taylor taylor epoch epoch epoch improving phd finds asymptotically percentage great track unstable unstable unstable fairly lies comparisons implementing strictly incorporate leaves definite definite arises arises conjugate conjugate conjugate conjugate conjugate argument geometric improvements pure pure effort employ employ continuously dots berlin berlin berlin berlin occurrence germany decreased implements progress trade trade globally newton newton newton newton sort modify fix rithm drift tensor purely encoder encoder consideration consideration consideration numerically adjusting nearby exploit exploit exceeds symposium repeat reset becker regarded arrive matter statement implicitly fly escape outperforms leaving summer specification opposed opposed die quasi quasi obtains lit param pub perpendicular careful overhead overhead drawback covered weaker nonetheless universit algebra elsevier vanishes vanishes intensive october helps helps utilizing instability transforming virtually bold compete dominates powers powers powers calculates hemmen val proposes arrives proves proves informatik vanishing ensuring brought indi huge huge stabilization cope ues amsterdam investigator stabilizing stabilizing technische occasionally relying traditionally kramer convexity singularity singularity geometrically gra euler euler euler owing owing eter premise almeida stefan accelerated suit rid rid omitting havior rameter sug recipes eli teukolsky questionable estimations flannery rio expertise silva rit rit rit rit rit rit rit rit rit rit rit rit rit pit solver dii dii vetterling accelerating limt roger roger roger speeding vidual resetting virtues ive trap restarting lished owt vie battiti scent featuring gested leap overlooked confines surpasses 
#@Rueget_S,
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#*network network model neural neural neural input input input data data data data data data data data data data data function figure figure set set set set set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number error error error error error error error error state results results units information information problem problem problem problem problem problem problem problem problem problem problem performance performance based linear case case vector vector vector vector vector vector order order order order shown values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability recognition recognition recognition recognition method method method method method method method method method approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image image large large large large large rate rate test test test patterns patterns analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class optimal optimal optimal optimal paper examples small small size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work methods methods points field features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process cell cell problems problems problems problems problems problems problems problems problems problems problems problems problems random random high representation representation equation equation section section section section section fixed fixed vectors vectors vectors vectors vectors vectors vectors vectors average average theory theory theory theory obtained obtained obtained obtained term note note experiments experiments experiments experiments dimensional dimensional result university threshold independent independent log log defined sequence table table table table estimate estimate estimate estimate estimate estimate estimate computer science science science machine machine sets sets maximum range range press components components sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied applied applied find density properties properties references due ieee ieee ieee ieee ieee procedure procedure important important important mixture introduction estimation estimation estimation estimation estimation behavior behavior statistical statistical statistical generated generated variance cost search classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower prior prior chosen chosen chosen chosen chosen part required conditions represent distributed expected expected proposed correct probabilities probabilities errors errors scale finite finite finite finite finite finite finite finite finite finite finite finite finite finite resulting classes classes classes classes classes regression respect sum performed performed performed means potential dimension natural obtain obtain obtain obtain obtain obtain original vol vol vol vol vol vol vol vol vol artificial specific samples samples samples represented represented represented represented true true application series define rates determined determined experimental experimental posterior posterior distributions distributions distributions distributions distributions distributions distributions discrete equal support report department difficult sequences framework solutions estimates estimates estimates estimates estimates estimates estimates design design limit limit limit efficient classifiers classifiers classifiers classifiers classifiers upper statistics estimated estimated estimated estimated estimated estimated con weighted conditional conditional conditional bounds bounds types evidence nature nature depends achieved discussion normal describe describe denote denote stable nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest assumed assumed supported pixel pixel pixel pixel future degree development including fit fit fit fit fit typically smaller underlying underlying underlying coefficients coefficients coefficients coefficients coefficients interesting york york york york increasing consistent trials empirical empirical empirical squared representing minimize choose description denotes denotes denotes denotes denotes recent recent recent exact property property property property property ensemble ensemble ensemble reported practical practical pixels pixels pixels pixels subset engineering dimensions compare previously smooth smooth yields trans trans generalized bounded bounded risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk grant grant constructed expression trial correctly generally column setting conclusion minimal assumptions assumptions assumptions neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor depend accurate accurate bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak strong drawn intelligence intelligence labeled labeled assuming variety exist iii averaged derivatives manner scene force reference reference reference reference reference reference reference explicit appears construct construct construct construct construct estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating describes describes describes laboratory ann label label recall metric metric metric metric infinite infinite electrical dimensionality remaining spectral spectral implies implies select select john letters national extracted independently independently stationary squares densities densities densities evaluate evaluate approximations sizes sizes sizes converges converges constants discrimination discrimination partial slow expansion expansion expansion reduces sufficiently sufficiently sufficiently sufficiently foundation euclidean classified classified classified classified classified classified transactions transactions transactions precision plotted illustrated specifically neighbors neighbors neighbors columns columns selecting efficiency uniformly included repeated procedures procedures prob prob lie satisfy minimizes principles acknowledgments rat rat rat command parametric wiley overfitting estimators estimators estimators estimators integral accurately accurately examine school project applicable statistically cover cover cover cover cover understand examined smallest smallest math closest necessarily ensure academic submitted synthetic optimum inequality inequality inequality inequality band formula costs trivial publishers smoothness smoothness smoothness analytic briefly constructing constructing pool pool pool involve universal computers nsf robustness fourth fourth fourth fourth improvements evaluating empirically consistency consistency incorrect incorporating ordered enables begins progress representative classifying fix fix conditioned air fits allocation numerically numerically significance significance mail simplify abilities observing north nonparametric nonparametric nonparametric nonparametric eqn analyses equals equals displayed holland evident facilitate enable recog sons hart hart hart hart hart hart hart hart material robert assigns assigns assigns assigns assigns lem truncated truncated misclassification validity ties nition exception classifies descriptions evolve duda duda duda parzen emphasize reveal rod rod rod rod rod rod rod rod rod rod rod rod knowing served replacement replacement remarks resolve accordance identifies insufficient exper inequalities medicine rare venkatesh venkatesh venkatesh venkatesh venkatesh venkatesh frequent statist feasibility restrictive twelve mis texas inform inform satellite predetermined began favors nents psaltis psaltis psaltis tong evaluates bernoulli motivates lacking concluding oft multiclass multiclass multiclass rrt rrt rrt rrt unconditional nals extractors tractability devroye devroye devroye rests remedy deficiency fukunaga fukunaga fukunaga fukunaga landsat fdx risks rome discriminatory rosenreid erfc incur consulting imprecise 
#@Snapp_R,Xu_T,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number system system system system system system system system system system system error error state state state state state state results results results results results results information information information information information information information problem problem problem problem problem problem models models models models models models models models models models models models models based based based based based based based based based based based based based space space space space weights linear linear linear linear linear case case case vector order systems systems systems systems systems systems systems systems systems values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise weight functions functions distribution distribution distribution method single processing processing processing processing control local local local local local local test test test test test test test matrix optimal optimal optimal form form shows shows shows signal signal algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper work task process process current current similar architecture show equation equation section section fixed line line line line general general general general parameter parameter parameter parameter parameter parameter parameter approximation states states states obtained obtained term term term term term term term note note note note note result university university computation computation computation found dynamics initial table computer science prediction prediction prediction prediction prediction prediction presented press position position position basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied applied applied density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references ieee ieee positive procedure procedure adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated generated variance variance variance variance search tion variable variable variable variable prior prior prior prior prior prior chosen chosen chosen chosen part part part multiple multiple multiple multiple multiple multiple multiple represent represent bayesian bayesian bayesian expected expected equations equations equations equations markov probabilities probabilities probabilities probabilities probabilities probabilities errors errors errors errors resulting resulting resulting resulting ing computed computed multi multi elements mapping means means made made em filter filter filter filter filter filter filter filter filter specific true perform determined determined determined determined experimental experimental posterior posterior posterior posterior equal train selection selection selection selection selection selection selection morgan morgan proceedings proceedings report consists individual advances joint joint difficult exp exp exp exp exp exp scheme scheme scheme scheme scheme scheme considered experiment directly hinton estimates estimates estimates estimates estimates transition san san stage stage stage detection determine efficient requires choice approximate estimated estimated give weighted conditional developed developed developed developed developed developed developed robot criterion evidence evidence evidence evidence sampling simply simply achieved achieved covariance increases describe hmm hmm fast inverse inverse inverse inverse assumption predictions rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf assumed assumed eds eds adaptation adaptation adaptation end end end end end ability development development development fit kaufmann kaufmann underlying underlying underlying underlying underlying underlying underlying underlying underlying underlying underlying reduced account dynamical dynamical dynamical dynamical dynamical functional unknown unknown unknown unknown unknown coefficients jordan jordan block block block block block york increasing mode mode mode mode mode mode mode mode mode mode mode operation operation filters pre experts experts experts experts experts experts experts experts expert combined combined predict architectures discussed property property include include hierarchical sense inference recently sufficient varying varying varying varying observations observations observations observations observations observations observations mixtures mixtures mixtures observation observation observation observation observation observation observation observation observation grid arm arm arm studied studied extended extended predicted predicted predicted predicted predicted touretzky width width width demonstrate demonstrate place assumptions conclusions depend bayes bayes bayes bayes bayes mateo mateo taking hard hard hard hard hard hard hard hard hard radial radial exist relationship identification identification identification identification explicit relation relation relation generating generating transitions transitions transitions dept dept explicitly explicitly explicitly averaging slightly frequencies applying competition competition competition competition competition competition competition competition competition competition competition choosing choosing expressed expressed formation stages estimator viewed influence soft soft soft soft soft soft static approximated allowed past intervals iterative tracking interpolation assigned includes priori weighting weighting weighting extension extension automatic uncertainty priors priors gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating selecting identified closely uniformly modification modification modification modification modification effectively effectively modes modes modes modes modes modes successful identify schemes schemes schemes schemes schemes schemes mackay score capture procedures prob link dis sin sin bar vary modular modular modular modular modular modular modular modular highest highest highest preferred jacobs jacobs tesauro tesauro modelling cowan law law law law law unlike carried carried kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman involving involving association recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive scalar scalar scalar scalar relationships lgn workshop workshop affect measurement naturally predicting expressions expressions academic switching switching detected arbitrarily attempts cos developing developing growth derivation nowlan nowlan adapted adapted adapted adapted briefly correction bishop bengio mation mation probable probable probable separately angles angles definite demonstrates researchers apparent varies applies experimentally detecting controllers controllers mod progress ear leen assign turned rigid extending satisfying observing infor alspector combines widths expanded dependency dominant lengths eng indicator indicator indicator indicator jump alternatively outlined outlined kinematics kinematics kinematics kinematics aston recursively recursively recursively opposed centre centre centre arg ical adapting approxi rbfs cartesian manipulator esti differing modal modal modal modal frasconi grbf attempting tribution excited multimodal multimodal centres centres centres dent capturing undergo unimodal shares hood instant instant instant ular rmse rmse rmse devel undergoes sought nth nth nth nth nth nth mate effector effector effector effector effector ously previ continuation dynam plants prevented nonlin ncrg depen estima likeli invoked ordinates innovation decomposes sheffield sheffield sheffield vances oped increas kom methodologies shalom veloped tio decouple recurslye 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#@Kadirkamanathan_M,Kadirkamanathan_V,
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#*network network learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data function function function function function function function function function function function function function function function function function function function function function function function function function time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm output number number number number number number number number number number number number results results results results results problem models performance based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown shown systems systems values parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons unit recognition recognition method method approach pattern image single single single single processing processing neuron neuron class class class matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs form form shows paper paper paper paper paper small small small small small small size size size size size size size size size size size size size size size size size size size size size size size size size size work methods fig step field field field problems show show show show show section section section section section section section section fixed vectors vectors vectors vectors vectors vectors vectors vectors general general speech real states states theory note note note result result result result result result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables variables computation research research research research research research research independent independent log defined defined found constant estimate synaptic science present present present present present sets sets maximum press press abstract find computational computational computational computational properties references due ieee important introduction circuit behavior generated parallel search complexity complexity complexity assume lower measure measure part part center center center previous theorem theorem theorem theorem bound cases required multiple binary binary binary conditions distributed equations fact fact techniques minimum minimum minimum classes classes ing tasks tasks tasks total human sum sum called called called elements elements elements elements optimization made natural applications applications applications applications study study vol vol artificial artificial artificial artificial artificial relative application application application desired define define define define define define proc proc determined experimental constraints equal equal power power power mit larger larger report report institute loss technique technique technique technique technique technique technique consists code difficult difficult layers addition ai ai ai ai ai ai ai ai additional limit san determine determine determine requires basic basic basic pages increase increase weighted weighted developed developed bounds area finally finally finally depends constraint constraint biological technical technical feedforward arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary fast limited complete proof proof proof proof proof circuits circuits circuits circuits circuits circuits circuits finding finding finding implemented implemented implemented generate supported theoretical main main main main main main main future easily degree degree rumelhart rumelhart rumelhart including smaller smaller hopfield coefficients coefficients technology technology interesting numbers bits magnitude polynomial polynomial polynomial polynomial polynomial description light directions recent pair pair pair pair separate element element element element practical practical identical subset subset subset subset engineering engineering interest compare converge trans definition definition definition definition definition definition definition separation observation gate gate gate gate organization grant grant exists exists exists exists exists exists exists setting setting minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal row row conclusions exponential exponential practice constrained hard california california california turn start exist min program question question question acknowledgements suppose construct construct construct construct construct written written written written index solving mathematical mathematical implement implement implement coordinates coordinates physical involves easy unique develop develop implies implies blocks blocks blocks blocks versus boolean boolean national national lemma lemma lemma lemma lemma lemma detailed converges sign reasonable expansion spaces valid construction construction construction construction construction construction foundation foundation transactions building building building usa inter sciences prove prove prove prove absolute holds divided mcclelland literature build comparing orthogonal traditional notice interested interested superior contribution contribution built satisfy computes satisfies satisfies satisfies satisfies satisfies oriented presents presents wiley difficulty exponentially put relations limitations existence existence rest rest office root root root root root root root root root root root root root root root root gates gates gates gates proper cognition smallest smallest smallest math math naturally integer integer integer integer rank rank rank rank rank aspect taylor taylor taylor logic switching switching consist electronic electronic defines defines rows rows rows rows rows rows growth growth defining growing growing growing majority majority capabilities answer stanford stanford closer constructing constructing constructing division sgn sgn sgn sgn sgn sgn sgn sgn computers computers computers nsf limits orders slower requirement limiting gen pasadena achieves june extreme trade trade gap feasible generator generator generator generator generator acm caltech generality inspired smith smith smith dealing promising tools tools mail fan fan grow abilities analyzing settings motivation repeat introduces studying studying entries claim young neuromorphic reveals integers integers integers integers explorations switches empty verify ple microstructure outline fellowship opposed emergent july distinction aij big big simulating simulating ibm ibm magnitudes magnitudes mathematically mathematically academy indexed siam siam compu helps dim august august hop hop shawe shawe shawe focuses focuses puts fill powers loosely eral award agency anthony siu siu siu siu sloan inspection implying derives iterate bruck bruck bruck bruck bruck bruck col jose refine investigator boosted gij dealt tie proving oooo roots roots roots ire brains refining orthogonality tational implication subsystems multiples ein combi cients ffi calif admit subclasses muroga muroga muroga ccr coeffi sir sir offs wixi goldmann goldmann goldmann goldmann goldman goldman disc disc interconnecting karpinski stoc lective ecole strategic maih hastad hastad hastad hastad interscience almaden wards lausanne commerce 
#@Bohossian_V,Bruck_J,
#t9
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#*network network network model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural data function figure figure figure figure figure time time time time time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks number number system system state state state state state state results results results results results results information information models models models models models models models models models models models models models models models models space linear order order order order order order shown shown shown systems values probability probability probability parameters parameters parameters noise noise noise noise noise noise noise noise noise functions functions functions neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution approach pattern pattern pattern pattern pattern single local neuron neuron neuron neuron neuron patterns patterns patterns patterns analysis analysis form form shows signal simple simple simple simple simple simple simple simple simple simple simple simple gaussian gaussian gaussian paper paper paper small net work step level current current random random random random memory response show equation equation equation equation line line line line line line rule general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation states states states states states states states theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained obtained term term term note experiments result result university university variables variables variables variables independent found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial terms terms terms terms terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic prediction prediction present press press components components continuous abstract applied find find find properties references due introduction hand statistical statistical dynamic dynamic dynamic dynamic recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion energy energy lower center cases type type required good binary binary binary conditions distributed equations equations equations equations equations equations equations make make fact techniques techniques techniques techniques techniques techniques region region correlation forward scale finite finite finite simulations simulations simulations simulations simulations simulations simulations simulations simulations classes ing total simulation respect sum sum called called means potential made made natural applications applications applications specific provide provide rates location location connected distributions distributions approaches comparison contrast department version version version version version version synapses synapses consists consists kernel joint joint final final final exp ai ai ai ai ai ai ai ai ai ai directly view solutions solutions top upper upper upper full choice choice choice statistics statistics speed speed basic give derived derived lines lines lines lines lines processes nature depends depends discussion technical describe describe describe assumption stable stable theoretical theoretical theoretical main hypothesis instance degree degree including hopfield reduced account account dynamical dynamical dynamical functional functional fully leads leads leads details details details details stored choose choose description description recent recent correlations correlations exact exact exact exact exact exact ensemble takes typical strategy include subject identical sense relevant highly works works solve solve solve solve studies studies background background background symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric observation width deterministic boundary boundary generally flow flow assumptions assumptions hebbian trajectories trajectories interactions measures numerical clear constrained physics physics physics physics physics drawn solid solid solid solid solid solid turn plane plane plane averaged denoted attractor attractor attractor boltzmann written solving solving solving solving solving ways generating describes describes describes laboratory transitions transitions mathematical dept dept recall metric explicitly explicitly averaging averaging averaging physical physical involves involves remaining scales adding equilibrium equilibrium equilibrium equilibrium applying applying versus versus versus potentials potentials potentials potentials potentials potentials choosing national independently independently review depending correlated overlap overlap overlap solved solved restricted updated evolution evolution evolution evolution calculation calculation dashed dashed dashed dashed expansion closed closed remains advantages figures figures includes coupled coupled phys phys phys phys phys phys phys phys phys phys simplicity simplicity straightforward driven build schemes post post post post post post comparing essentially road refer graphs allowing link symmetry sin involved usual relaxation relaxation wave observable observable leading automatically subsequent simpler transformed relations oscillators integral accurately dotted dotted ideas reliable reliable working complicated complicated complicated tanh tanh tanh tanh tanh tanh tanh tanh tanh naturally generalisation predicts predicts extremely extremely extremely rev rev rev equally taylor store amari amari improving simplest simplest finds finds spin asymptotically advanced advanced advanced advanced advanced advanced ment cos trivial crucial agreement agreement unstable unstable analytic analytic analytic analytic analytical diffusion glass tool london london reasons formalism formalism sgn arise controls controls mathematics involve describing calculations calculations qualitative mechanics requiring limits applies leave autonomous introducing formulated dots dots price anti popular asymmetric conclude deviations lim lim progress cor college analogue analogue oxford oxford oxford arguments perfectly nat concerned theories theories theories outcome fails saturation saturation saturation saturation saturation saturation dealing numerically numerically tools familiar los los replica replica replica replica replica interference interference interference studying negligible pat spherical reproduce impact lett sequentially ter equivalently opposed employs expanding chaos concentrated community community evolve mathematically jij jij integrals minor elsevier macroscopic macroscopic macroscopic macroscopic macroscopic macroscopic transients transients transients transients transients transients transients drops microscopic microscopic microscopic microscopic modal observables observables observables observables observables coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen remarkable instability terns stochastically builds ongoing solvable king err err err sen partly retrieved nontrivial reality safe schmidt closure closure modern modern modern alamos alamos adequately recalled gardner amsterdam nice sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington sherrington elaborate quantified obeys ansatz complications complications ther scribed psp paid fur europhys yij yij xij mexico proaches lend resemblance kramers apr theme cumulants slowing slowing cumbersome strand deterministically modem modem realisation derrida derrida derrida fractions generalise diluted diluted diluted physicists pletely hitherto ural unexplained stoch ely overestimates overestimates suming ticity ener patt sociative convincingly nonsymmetric nonsymmetric nonsymmetric sitivity parisons 
#@Coolen_A,Laughton_S,Sherrington_D,
#t9
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number number number number system error error error error error error error error error error error error error error error error results results results results results results results results results results results results results information performance based space linear linear case case vector vector vector order order order order order order shown shown shown shown shown shown values values values values values values values values values values values values probability probability probability probability parameters parameters parameters parameters parameters noise functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach large large large large large large large large large large large large large large large large large rate test test test test test test test test test analysis class inputs inputs inputs form form simple paper examples examples small small small small size size feature work work work methods points points process process process level level level level level level level random random random random high high response response response response response response response representation representation representation show section section section section section section section section parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory theory theory theory theory term term term term term note note note note experiments experiments experiments experiments result result result result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables research log defined found found target target target target constant estimate estimate estimate standard computer computer terms node science science science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction present present present present low frequency frequency learn learn learn basis basis basis basis outputs outputs outputs sample sample abstract find computational computational computational properties likelihood references due procedure procedure procedure procedure procedure important important decision decision decision decision introduction statistical generated generated cost cost search search search search search search search search search search search tion tion assume learned learned chosen chosen chosen part bound bound cases cases cases cases tree expected expected expected expected make make make techniques correct correct correct correct correct observed errors errors errors errors classes ing total total total total total computed respect respect respect respect sum sum sum times times times times times means factor made made applications obtain obtain specific represented represented true true true true true compared series provide define define define define compute compute compute perform eye experimental equal accuracy accuracy accuracy larger connection connection implementation implementation implementation implementation implementation implementation technique technique technique technique technique consists advances represents addition graph computing computing experiment experiment curve curve curve additional curves curves detection detection determine determine determine determine efficient upper requires choice choice approximate approximate approximate approximate approximate basic pages pages pages pages increase increase condition randomly randomly randomly randomly randomly developed levels bounds bounds area area area product product actual selected evidence simply simply simply discussion increases increases describe describe close predictions circuits finding finding amount amount implemented implemented assumed shape generate generate supported supported role theoretical theoretical theoretical theoretical theoretical theoretical journal end hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis makes smaller combination coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients technology interesting interesting increasing increasing increasing mechanism special consistent trials uniform uniform uniform uniform uniform empirical squared details call making depth depth polynomial polynomial polynomial polynomial idea minimize choose choose choose choose choose choose run run run run run run run added predict improved discussed improve advantage element typical typical practical practical practical practical apply introduced include include include include trees trees trees interest interest compare previously approximately tions correspond achieve sparse sparse sparse grant exists occur extended trial deviation loop loop demonstrate demonstrate demonstrate demonstrate demonstrate runs strength minimal greater assumptions conclusions conclusions measures accurate accurate accurate performs largest labeled user introduce introduce force denoted factors describes dept confidence confidence confidence confidence confidence confidence confidence confidence recall spectral versus boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean decreases decreases decreases yield choosing expressed depending squares detailed detailed detailed transform transform transform transform transform transform transform transform transform transform evaluate fraction showed approximations approximations spectrum sign sign reasonable add calculate calculate string foundation norm query query query query query query query expect expect box figures includes includes priori bell instances determines black holds tests successfully major determining determining determining importance differ efficiently situation plots receives characteristic graphs graphs issue contribution contribution running running built list list michael play minimizes computes computes computes reach reach received approximating decreasing decreasing receive receive powerful powerful powerful powerful essential detail accurately accurately recursive recursive recursive recursive recursive recursive issues issues issues issues dotted ml rise fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier giving parity parity proved workshop workshop func coefficient coefficient coefficient coefficient coefficient coefficient coefficient coefficient coefficient naturally naturally naturally predicts predicts extremely extremely automata perfect ensure obvious logic academic detected finds finds finds defines established years great great crucial improves failure majority majority majority majority briefly briefly briefly correction tool tool tool tool tool implementing sections organized desirable acknowledgement depicted annual annual annual annual argument applies peaks peaks compares maintain operate aim aim aim parent extensions enables inherent conclude conclude shaped returns returns returns returns returns findings calls calls calls calls calls calls calls calls calls yielding yielding contribute contribute representative proofs redundant formally guarantee guarantee acm controlling grows outcome children children smith chance mail mail odd intelligent hope fail disjoint symposium symposium enhanced motivation weakly negligible guarantees originally israel israel israel membership indicator indicator indicator kearns papers discovered intersection fly fly empty dramatically maintaining usage kluwer super recursively benefits july uniquely corrected guess visited shaded shaded shaded pub pub translated iff deep deep goals distribu permits bounding bounding learnability learnability learnability learnability learnability academy names names names names drawback misclassified siam knowing tel tau tau survey survey characterizing algorithmic august virtually supply supply blum steven usefulness devised settle peaked ters beneficial edited correctness siu drastically implying zeros zeros reviewed inaccurate inaccurate fixing prominent derives aviv noticed noticed comprehensive severely incurred aims recovers intersect recursire recursire parame darker dnf dnf dnf dnf dnf dnf dnf dnf dnf dnf mansour mansour mansour mansour mansour mansour mansour mansour mansour mansour mansour sought solu proving missed seemingly lacking ministry prefix prefix prefix circumvent jackson jackson jackson ixi predicate predicate predicate calling rni rni subtrees subtrees brute mat additions pected pred cients proximate exemplified accessed jeffrey jeffrey instrumental remedy immune gaining faulty faulty runtime coeffi commu discrepancies constituting traversal traversal diminished uninteresting subroutine subroutine enhancements enhancements enhancements lightly portrayed portrayed indispensable indispensable signifying learnin singleton occasion israeli coincidental overwhelming 
#@Mansour_Y,Sahar_S,
#t9
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#*network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function function function function function function function function function function function function function function function function function function time time time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number system error error results results results results results results results results results results units units information information information information problem problem problem problem problem hidden based based based weights weights weights layer case case case vector vector vector order order order shown shown systems systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise weight weight weight weight weight weight functions functions functions functions functions functions functions neurons neurons neurons neurons unit unit distribution distribution distribution distribution distribution distribution distribution method approach approach single single single single processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate patterns analysis analysis analysis analysis class class class class class class class class class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form algorithms simple simple simple paper paper examples examples size size size size net work work step classification classification classification level trained problems problems random similar similar representation representation representation representation architecture show show section section section fixed fixed fixed fixed fixed fixed line vectors general general general general general general parameter parameter parameter parameter real real real real real real real real real real real real real real theory theory theory theory obtained obtained obtained obtained note note experiments result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation computation computation computation independent independent independent log log log defined defined defined defined found sequence sequence sequence sequence sequence sequence sequence sequence constant constant standard standard computer terms terms connections connections connections connections connections connections connections connections connections connections node node node node science science science present present activation activation nodes nodes nodes nodes nodes nodes nodes nodes sets range range basis outputs outputs outputs continuous continuous continuous continuous continuous sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract computational computational computational computational computational computational computational density properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee important adaptive introduction introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit generated generated generated generated generated cost tion difference complexity complexity complexity lower representations representations part previous previous previous theorem bound cases required required required required required required required required required multiple good binary binary binary binary binary binary expected chip fact fact techniques techniques techniques proposed correct correct probabilities simulations classes ing ing total total total simulation simulation computed computed computed computed computed computed respect multi sum performed performed performed performed performed dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made made made applications em vol vol artificial samples represented true compared series series series series provide compute compute compute perform perform perform determined determined related connected discrete brain equal equal equal power accuracy accuracy comparison larger connection support train proceedings proceedings report words implementation implementation implementation version version technique technique technique consists individual individual advances advances final final layers layers layers layers layers graph sequences sequences sequences sequences sequences sequences considered considered considered considered framework framework computing computing computing computing computing computing computing domain domain additional additional additional additional additional additional design bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit conference determine basic increase give give coding derived derived weighted randomly randomly developed bounds bounds bounds bounds lines product actual actual actual provided backpropagation backpropagation backpropagation depends achieved discussion technical feedforward describe group denote corresponds corresponds proof proof proof proof proof circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits finding theoretical theoretical main degree degree degree degree degree degree degree degree simulated simulated probabilistic smaller underlying underlying fully fully testing testing testing testing significantly significantly operation representing numbers numbers numbers numbers max bits bits bits bits bits bits bits bits bits bits bits bits bits international depth depth depth polynomial polynomial combined perceptron recent exact takes reported practical identical recently recently works tions solve smooth smooth correspond trans definition definition definition definition definition background bounded bounded gate gate gate gate gate gate gate gate gate gate gate gate digital derivative correctly correctly hardware hardware hardware hardware conclusion place valued valued valued valued interactions sigmoid sigmoid weak encoding encoding encoding propose taking taking hard presence cycle drawn drawn drawn drawn sigmoidal sigmoidal sigmoidal sigmoidal intelligence assuming introduce introduce derivatives manner question question denoted denoted denoted pro van derive derive construct construct construct construct generating generating generating dept confidence pruning pruning multilayer involves consisting consisting springer boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean john john family family independently independently independently independently expressed operations sizes sizes sizes sizes sizes sizes sizes sizes allowed sign sign performing classical classical combining assigned vapnik holds identified extra computations computations comparing comparing receives compact showing showing interpreted play nips computes computes computes create exponentially varied involving behaviour behaviour matches giving giving links applicable referred referred working gates gates gates gates gates stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream encode func func attributes neu naturally concepts integer generalisation generalisation generalisation generalisation generalisation generalisation extremely versions taylor taylor taylor taylor taylor taylor taylor taylor observe attempts formula directed adjacent adapted adapted benchmark london london perspective sys sys involve calculations attribute attribute attribute attribute attribute attribute arises addressed collected simulate peter cohen adjustable adjustable passed incorrect polynomials polynomials polynomials passes replace logical sophisticated progress proposition proposition proposition proposition proposition proposition proposition summed pac notes summing summing labelled tem royal royal fan fan programmable moment occurring definitions definitions corollary corollary corollary surprising interconnections claim extends statement subsequently receiving thresholding assigning assigning linked slight email stork stork chervonenkis tween feeding smoothly streams streams streams streams streams streams streams streams streams streams streams tems bounding termed attached sized happen mimic compu treating lecture replacement hassibi hassibi functionality functionality functionality functionality slots shawe shawe shawe shawe shawe shawe shawe shawe confirm interpreting blum dcs ron operational correctness lying carries polynomially tations signed carrying surgeon indepen acyclic unrestricted eighth monk monk monk monk monk monk monk monk monk monk monk monk monk monk analyse developments ceedings simula tal plexity suitably relying shortcut bernoulli bernoulli bernoulli bernoulli bernoulli bernoulli bernoulli bernoulli bernoulli colt switzerland motivates plp koiran completes pad delivered adaptable zhao zhao zhao zhao experimen focussed misclassifications timal holloway holloway xlx eft esprit stressed prospects neurocolt afforded dummy rhbnc karpinski karpinski eurocolt egham parametrised ferred probabihty probabihty probabihty macintyre macintyre corso surrey dently quote 
#@Shawe-Taylor_J,Zhao_J,
#t9
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error state state state state state state state state state state state state state state state state state results results results results results problem problem problem problem problem problem problem models models models models models models models models models based space space space space space space space space space space space space space linear linear case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values values values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions method approach approach point point point point point point point point point point point point point point point point point point single large local local local test test test class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs form form form form form form form form form form shows shows shows signal signal signal signal algorithms algorithms paper paper paper paper examples small work points points points points points points points points field field field field field field field field features process level level level level level level level level level level level level level level level level trained trained trained trained response response response response response response response similar similar equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation line line rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real real real real approximation states states states states states states theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained note note note note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university variables computation computation solution solution research independent independent independent defined defined defined defined defined defined defined defined sequence sequence target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial constant constant constant constant constant constant estimate estimate standard standard computer computer distance distance distance distance distance distance distance distance distance left presented presented presented presented presented present present present phase phase phase phase phase phase phase phase frequency frequency machine object sets motion motion range range press learn learn components components components components components components basis basis nonlinear nonlinear nonlinear nonlinear nonlinear continuous abstract applied applied applied applied applied find convergence convergence analog properties properties properties references component component component positive positive positive positive positive positive procedure adaptive introduction estimation behavior behavior behavior dynamic generated recurrent recurrent recurrent tion assume lower lower signals learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen chosen theorem theorem theorem theorem theorem theorem required conditions conditions conditions conditions equations equations equations equations equations equations equations equations equations equations equations fact proposed errors errors finite finite resulting total simulation computed respect sum called called called elements elements elements elements means potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential dimension dimension global knowledge negative negative relative relative specific specific specific samples represented true desired desired desired desired desired desired desired location location determined determined related steps fields fields descent descent selection selection department technique technique consists responses final ai considered framework equivalent curve curve curve curve curve curve curve curve solutions curves curves curves curves curves curves estimates estimates estimates design design design trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san stage effects determine determine statistics statistics statistics estimated estimated give produce path path path path product actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual actual depends achieved discussion normal normal normal normal normal normal normal normal normal normal arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary tested tested tested tested stable stable stable surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface proof finding assumed shape generate supported require journal instance instance makes pairs needed reduced dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical functional unknown unknown testing increasing operation choose denotes denotes discussed discussed pair element element element element sense engineering interest varying volume solve smooth smooth smooth converge converge converge converge differential differential differential achieve locations symmetric symmetric symmetric symmetric symmetric symmetric bounded bounded bounded interval grant constructed constructed constructed exists concept deviation deviation derivative derivative matrices matrices matrices matrices correctly locally move move move move half conclusion starting critical trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories valued valued valued depend depend depend tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent accurate designed designed designed designed designed suggest propose taking physics solid solid solid solid solid solid solid variety plane plane manner manner manner minima minima identification identification identification identification denoted attractor attractor appears appears construct solving plot plot mathematical mathematical changing recall explicitly linearly linearly linearly electrical involves easy unique frequencies equilibrium equilibrium equilibrium formed formed quality versus versus versus choosing choosing choosing stages estimator estimator estimator evaluate controlled controlled restricted decomposition decomposition similarly similarly suggested converges converges partition partition constants constants constants constants dashed dashed dashed dashed dashed combining neighborhood interpolation remains construction euclidean euclidean euclidean euclidean figures eigenvalues subspace subspace subspace subspace subspace determines plotted plotted plotted illustrated holds discussions straightforward selecting capable capable capable differ differ modification modes modes comparing situation plots orthogonal fine notice quickly showing contribution sin sin sin follow criteria moves satisfies satisfies acknowledgments extend remain remain remain remain diego estimators estimators estimators estimators dotted hall periodic periodic scalar possibility authors referred fundamental surfaces surfaces surfaces surfaces possibly portion portion academic ith mixed submitted defines isolated guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed starts considerable sys sys formalism constructing constructing choices located located mathematics definite definite definite definite cybernetics qualitative qualitative qualitative outer pure parameterized cohen cohen cohen treated continuously maxima maxima polynomials passes passes partitioning proven proven qualitatively qualitatively logical returns eventually differentiable ordinary ordinary saddle appropriately member jth height height height height contract effectiveness intuitively prentice james guarantees dif advance passing steepest steepest pearlmutter designing designing statement convergent convergent convergent ics speaking fitted saad ple vec axe axe axe axe axe pointed par par par solely decomposed decomposed decomposed constitutes tor tems tems mathematically altered integrals portions likewise algebra programmed vanishes vanishes vanishes vanishes bill eters subspaces suggestions stimulating reversed tom cliffs conceptual broadly kth cast flows excited judged hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian poly vanish vanish transpose dent approached approached approached equilibria equilibria equilibria equilibria equilibria terminology proximation hirsch bio conceptually emulate sato narendra dynam horne provably skew skew skew mexico eter depen albuquerque decomposing decomposing decomposing traversing services iia iia iia iia excites downhill downhill downhill downhill downhill downhill downhill ven hamiltonjan stably insightful complez obtainable limt noteworthy sociated emulates namical leaning slicing gregory sired 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#@Abdallah_C,Heileman_G,Howse_J,
#t9
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#*network model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data function function function function time time time time time time time time time time time set set set output output number number system system system system system results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information based based space linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case order order order order systems systems systems systems systems values probability probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions neurons neurons neurons neurons neurons neurons unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach point point point point processing neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis optimal optimal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple simple gaussian visual visual paper examples small small small small work work work work work cells step features features features features features process process process process process process process process process level current cell cell cell cell cell cell cell cell structure structure structure structure problems random high high high high high similar representation show show show section fixed fixed fixed fixed fixed general real real real real approximation average average average average average average average average average average average average theory term term term term term term term experiments experiments experiments experiments dimensional dimensional result university threshold threshold threshold threshold threshold threshold threshold threshold threshold variables computation solution independent independent log log defined defined defined defined defined dynamics dynamics dynamics constant estimate estimate terms terms terms terms terms terms terms distance prediction present present present present present low low low maximum maximum maximum maximum range range press press basis abstract back find find analog analog analog analog analog analog properties references due due due due ieee positive procedure procedure procedure important context context introduction action hand estimation statistical statistical statistical statistical search tion change difference assume assume lower lower lower rules measure measure measure measure measure signals signals signals signals signals signals chosen chosen chosen center previous previous previous bound bound firing firing firing firing firing firing required spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long represent represent equations fact fact proposed correlation correlation correlation correlation correct observed errors resulting resulting resulting total total total sum eq eq eq eq eq called called times times times times times times times means factor factor factor factor optimization optimization optimization optimization optimization optimization made natural filter filter negative negative vol specific specific specific true true provide provide rates rates rates rates rates rates proc experimental experimental experimental experimental experimental related constraints connected distributions discrete brain brain equal equal power power power mit mit train train train train train train train train train train train train train train train train train train train train train train train train train train train dependent dependent dependent dependent dependent selection proceedings proceedings institute words code code code code code code code code individual advances joint addition sequences equivalent view view limit limit limit limit limit conference full requires requires choice approximate approximate world world world give produce coding coding coding coding derived weighted conditional conditional conditional conditional conditional developed entropy entropy entropy entropy provided provided provided nature depends biological biological achieved discussion describe arbitrary assumption assumption stable finding amount amount amount amount common common assumed assumed shape theoretical require adaptation adaptation adaptation adaptation adaptation square hypothesis cluster cluster development sensory sensory sensory sensory pairs functional fully interesting significantly ratio ratio ratio ratio york consistent trials trials principle principle principle squared details call filters bits bits bits bits international minimize produced produced choose choose sources light denotes membrane membrane recent correlations correlations correlations correlations correlations correlations resolution exact exact exact movement reported apply introduced identical identical identical side recently recently recently relevant conventional observations observations approximately calculated volume tions yields correspond definition definition definition observation channels interval expression expression expression expression expression expression studied suggests wide wide spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes alternative generally setting half flow flow flow reduce conclusions retina exponential weak encoding encoding encoding taking integration integration integration presence presence physics drawn turn turn variety relationship targets explicit explicit appears relation van van van derive derive derive factors changing explicitly simultaneously averaging averaging linearly electrical slightly mutual mutual mutual mutual adding implies implies implies potentials choosing focus reconstruction reconstruction stationary stationary stationary correlated communication communication influence codes codes codes showed evolution evolution approximated completely similarly spectrum sign performing performing expansion expansion reduces event roughly roughly valid valid fire priori priori priori formulation formulation currents inter discuss discuss maximize maximize specifically coupled sensor aspects aspects efficiency encoded encoded encoded divided delta delta spiking build schemes comparing reached reached summary refer notice repeated decoding decoding decoding contained success dis strategies timing timing duration duration receptor notation quantity write write michael wave leading leading leading leading leading maximization principles principles principles principles principles principles principles trains trains trains trains trains unlike carried powerful production requirements put optimized integral preliminary existence history referred maximizing proper complicated affect encode understand understand notion naturally transmission transmission transmission transmission plausible adapt adapt man voltages ensure singular singular singular aspect front front expressions nerve nervous nervous explain averages averages averages averages optimum integrate histogram histogram histogram histogram band formula formula theoretic trivial crucial sensors variances variances biology biology biology answer briefly correction correction correction correction correction tool inside inside snr snr snr snr snr snr snr filtered filtered filtered filtered filtered filtered filtered filtered broad arise arise products products pulses pulses pulses ion potentially potentially universal universal universal describing axons bandwidth cybernetics robustness summation argument double led dark experimentally experimentally quantitative orders share remove calculating poisson poisson poisson poisson poisson poisson poisson poisson measuring measuring characterize modulated modulated modulated extracting prevent suited replace boston boston sentence hints spectra spectra uncorrelated uncorrelated redundant sort primarily summing fix ratios ratios narrow optimizing homogeneous bin discovery unity grows receptors arrival arrival arrival wrong analogy imposed imposed familiar height grow hope observing definitions salk salk carry bialek bialek bialek bialek bialek bialek bialek bialek studying realization evident consequences propagated counting hasselmo waves bins bins bins record jolla matter captures fly mechanical informa crossing crossing crossing appeared minus shorter ties transmitted transmitted transmitted transmitted transmitted transmitted emerge expanding expanding expanding expanding expanding smoothly personal suppressed molecular spinal cns arising peripheral care gained shannon shannon shannon distribu emphasize argued finger corrections hodgkin circumstances moderate moderate drives remarks resolve unbounded huxley lated powers powers appealing cord continuum dissertation offsets stevens stevens stevens zador zador tells sloan physically materials brackets compromise broadband jitter steveninck steveninck steveninck decoded vanishing ruyter ruyter ruyter physica emerged modest degrades frog noticed linearities nice converts quantified checked checked permutations cancel rieke rieke inserting touch formulations illustrating illustrating accessible tie seemingly reconstructing brains blowfly concluding salamander unrelated vibration berry warland warland warland warland checking checking cumbersome prin collects meister substitutions transmitting resets dirac crete sight meter adrian adrian adrian coincident sensation creatures shorthand asymptotes carlson ere renewal ciency discretizing accom norton ancestors 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#@Bialek_W,Deweese_M,
#t9
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural input input input input input input input input input input input input input function function function function function function function function function function function time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number error results results units information information problem weights weights weights weights weights weights weights weights weights case case vector order systems values probability probability probability probability probability probability parameters noise noise weight weight weight weight weight weight functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution method method single processing rate test test class class class class class class class class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form simple simple paper paper paper examples examples examples examples examples examples examples size size net net net net net methods step step points points classification classification level level level level level level level level level level level level level problems random random random random high high high similar similar fixed fixed fixed fixed fixed theory theory theory theory theory obtained university university university threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation independent independent independent independent defined defined defined defined defined defined defined defined defined found found target target target target target target target target target constant constant constant constant constant constant constant constant constant estimate estimate computer computer computer terms node node node node node node node node node node node node node science science left present present nodes nodes nodes machine machine press press press learn learn basis basis outputs sample sample sample abstract abstract abstract find find find find find find find find find find find find find find find find find find find computational computational properties references ieee positive positive positive positive positive positive positive important decision decision introduction action statistical statistical statistical statistical statistical statistical statistical generated tion difference variable variable variable variable variable variable variable variable variable variable variable assume assume chosen theorem multiple multiple make make fact fact fact fact proposed proposed proposed proposed proposed correct probabilities probabilities classes classes classes respect respect respect respect respect sum sum called called called negative original vol vol vol vol vol vol represented true define define compute proc perform perform goal constraints connected distributions distributions distributions distributions distributions distributions distributions distributions discrete nets nets morgan morgan proceedings proceedings department department loss version consists advances computing domain equivalent directly limit san san determine efficient efficient free free free estimated produce produce condition condition weighted weighted criterion criterion criterion bounds bounds bounds bounds types path path product product product product product product product product product nature simply normal technical arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote denote denote denote proof proof proof proof proof circuits finding finding short common common supported supported main ability hypothesis hypothesis hypothesis hypothesis easily including including probabilistic unknown unknown unknown testing york uniform uniform empirical operation call call making bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom depth depth depth depth depth depth depth depth depth depth depth depth depth polynomial polynomial idea idea idea perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes exact exact exact exact exact exact exact exact property property property property property pair introduced include include identical recently recently sufficient sufficient works works tions tions definition generalized gate grant occur feed loop loop loop setting runs valued learns learns learns learns mateo mateo propose strong strong strong strong strong strong strong physics physics labeled exist exist exist exist exist exist exist min min introduce manner manner manner connectivity connectivity connectivity identification denoted denoted denoted pro pro changing adding implies implies boolean boolean boolean boolean boolean boolean boolean boolean boolean family family family independently expressed learner learner learner learner learner influence influence influence lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma transform restricted updated key add remains valid valid query precision avoid perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons assignment assignment specifically discussions tests tests identified society differ identify identify identify identify identify build build strongly prob return contribution hold hold categories satisfy usual reach thresholds thresholds thresholds thresholds thresholds subsequent acknowledgments simpler create essential replaced replaced replaced referred root root root root gates gates gates gates proper ensure queries queries queries queries der der der perceptton perceptton perceptton perceptton perceptton perceptton perceptton generates generates explain finds formula theoretic trivial publishers majority majority tool perspective leaves read read read read read annual annual applies applies fed fed posed incoming incoming parent parent parent parent parent parent achieves sums sums replace replace replace replace comments gap gap pac pac pac proofs intractable formally oxford restriction restrict acm acm acm acm member member discover children children children children children children children children children children children children generality kaufman stronger tools loops los observing definitions definitions definitions belong symposium symposium symposium child child child child child child child child child child composition repeat repeat repeat repeat schapire schapire schapire percepttons enable membership membership membership membership foundations omitted omitted kearns kearns kearns canada canada parents learnable consecutive verify verify unchanged basically constitutes discovering valiant valiant valiant iff iff iff iff iff iff iff iff iff iff distri distribu distribu convert learnability learnability learnability simplifying guided sketch harder meta meta meta meta meta meta attached sta meet meet meet amplification computa bution remark tour info ble twenty tom tom identifies nested establishes establishes routines routines routines hancock hancock lists formulae conversion separates outgoing outgoing outgoing outgoing outgoing outgoing exploits exploits appl statist comm fin merged tags vanishing skeleton skeleton skeleton skeleton unimodal unimodal unimodal formulas formulas formulas formulas formulas simon percep routine routine amer ceedings triple tolerant assoc def def tll tll tll tll tll tll tll tll tll pushed theor lemmas lemmas feeds nserc subclass insure permitted pitt ogp possi sketched triples reductions appeal rooted tolerate nonoverlapping nonoverlapping nonoverlapping representable hans xlx xlx ont ont alamitos negated ottawa ottawa ottawa ottawa kin kin tistical tron goldman deepest deepest chernoff chernoff chernoff chernoff sequel mario bot bot ceptron ceptron pothesis eurocolt ancestor ancestor ancestor llxi ambitious ancestors kaufinann 
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function figure figure set set set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number system system system system system error error error error error error error error units units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based based based based based linear linear layer layer layer layer case case shown systems values values probability probability probability probability probability probability probability probability probability probability probability functions functions functions unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution method method method method method method method method approach point point processing local matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal shows shows shows shows simple paper paper paper small small small small methods methods fig fig step step step step points trained trained structure problems random random high high similar similar show show show show equation vectors generalization parameter parameter parameter approximation average average theory theory theory theory experiments experiments experiments computation independent independent defined defined target target initial initial estimate standard computer terms presented map map present machine machine sets maximum press basis continuous abstract applied applied find find likelihood references ieee positive positive positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important introduction estimation estimation estimation statistical statistical statistical statistical statistical statistical effect variable assume assume chosen part center theorem theorem theorem theorem required required conditions conditions conditions conditions expected make make make techniques techniques proposed proposed proposed errors errors forward simulations resulting ing regression computed computed sum sum eq eq eq eq eq times means made obtain obtain artificial samples samples samples samples samples true true true true true true true true compared define compute compute compute compute compute proc proc active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active active distributions distributions equal comparison train train descent dependent selection morgan technique technique advances joint graph maps experiment experiment environment environment environment environment directly curve curve curve curve curves design design san effects capacity determine determine requires increase increase increase condition condition condition condition criterion criterion criterion criterion actual actual actual actual normal normal normal denote denote inverse inverse inverse inverse inverse complete proof proof proof generate theoretical theoretical theoretical require ability easily easily makes kaufmann objective objective reduced reduced reduced reduced mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp leads squared squared squared numbers making minimize minimize minimize minimize choose choose choose added perceptron perceptron improved advantage advantage typical typical practical apply recently solve exists exists suggests deviation feed deterministic white white white occurs demonstrate demonstrate conclusion critical assumptions clear asymptotic asymptotic mateo propose propose propose propose propose taking reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction cycle sigmoidal sigmoidal variety exist exist iii averaged averaged introduce derivatives suppose suppose suppose relation derive changing changing multilayer multilayer multilayer multilayer multilayer multilayer linearly linearly applying expectation expectation cycles select select john choosing choosing family family focus review review review review review communication estimator evaluate evaluate approximated expansion reduces sufficiently existing existing exploration coordinate perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons discuss included included wij wij mackay mackay online conf conf comp write minimizes cowan trains law parametric layered wiley essential accurately mse mse applicable applicable applicable applicable applicable int int ideal proved statistically statistically changed singular singular singular singular singular singular singular der der taylor fisher fisher fisher fisher academic explain isolated developing crucial briefly perspective satisfied satisfied satisfied satisfied arise optimize robustness calculating characterize replace replace redundant redundant redundant redundant optimality japan tation fix arguments perfectly perfectly jth jth bin eliminate eliminate eliminate eliminated mail satisfying transforms observing methodology effectiveness effectiveness effectiveness selects elimination elimination elimination passive passive passive passive passive passive loo iteratively environmental environmental steepest sons regularity pairing verified verified cohn cohn approxi eliminating singularities singularities singularities rough rough sketch sketch union union holding resembles utilizing invertible utilizes eliminates devised coincide substitute chan seed fin lar watanabe mul aic actively actively mle mle mle mle percep degrades operated derivations arline tiny deduce nation necessity completes singularity singularity singularity singularity singularity ricoh ricoh periments periments sume nonsingular nonsingular nonsingular nonsingular nonsingular rli rameter jii bij bij looo erf erf erf sufficiency dur specially ciently ciently sive kom unavailable nction fedorov fedorov plication kenji passively passively obt yokohama yokohama trons dial expec prepare prepare shin toda tilayer 
#@Fukumizu_K,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural input input input input input input input input input input input input input input function function function function figure figure time time time time time time time set set set set networks networks networks networks networks networks networks training training output output output output output number number number number number number number number system system system error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results units units units units units units units units units units units units units units units units information information information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance space weights weights weights weights weights linear linear layer layer case case case case case case case case case case case case vector vector vector order order order order order order order order order order order order order order order shown shown shown shown shown shown shown shown shown systems values values values values values values values values values values probability parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit distribution distribution distribution pattern pattern point point point point point point point point point single control large large rate rate rate rate rate rate rate rate rate rate analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form form simple gaussian paper examples examples examples examples examples examples small small small small small small small small small size work task task task task fig fig fig fig fig fig fig fig fig fig fig step step classification process process process process process process process current trained trained trained structure random random random random similar similar similar similar similar similar similar architecture architecture show fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line line line line line line line rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter real average gradient gradient gradient gradient gradient gradient obtained obtained term term term note note note dimensional dimensional result university variables solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution independent independent independent defined defined defined defined defined sequence target target dynamics dynamics dynamics dynamics initial initial initial constant constant terms terms terms terms node node node node node node node node node node node node prediction map map map map phase phase phase phase activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine motion motion motion motion motion motion motion motion motion range learn components components continuous abstract find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references component positive positive adaptive adaptive behavior behavior behavior effect effect variance tion difference variable lower measure signals signals signals learned chosen chosen cases conditions conditions equations equations equations equations equations equations equations equations equations equations equations equations equations correlation length length observed observed finite resulting resulting resulting resulting resulting resulting resulting resulting ing tasks regression performed performed eq times elements made negative negative specific specific desired desired desired provide provide rates determined determined connected larger larger update train descent descent descent descent descent descent institute implementation internal internal maps maps equivalent curves limit limit limit limit full full requires requires significant significant increase increase increase increase con provided achieved discussion normal describe describe arbitrary arbitrary arbitrary fast close corresponds corresponds corresponds implemented supported role role ability easily degree degree degree typically needed dynamical dynamical dynamical dynamical unknown increasing mechanism uniform uniform mode mode mode mode mode mode leads numbers max max max pre normalized decay decay decay decay decay decay decay decay decay minimize description predict architectures architectures discussed correlations correlations correlations correlations correlations correlations correlations correlations correlations exact takes takes typical introduced identical quadratic relevant relevant teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher tions differential achieve diagonal diagonal symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric modified interval interval grant expression extended deviation derivative deterministic occurs occurs strength strength minimal depend differences differences numerical exponential exponential asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak constrained strong largest drawn proportional proportional proportional assuming decrease decrease decrease decrease averaged relation written written longer ways dept student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student implement multilayer multilayer multilayer multilayer explicitly coordinates involves remaining remaining remaining remaining unique unique applying formed decreases yield independently independently focus dependence dependence dependence dependence stages overlap overlap overlap overlap controlled controlled controlled controlled controlled evolution evolution evolution evolution evolution evolution evolution soft soft approximated converges slow expansion expansion expansion expansion expansion reduces closed remains remains initially initially sufficiently assigned norm david activations activations usa formulation bell eigenvalues eigenvalues eigenvalues eigenvalues subspace subspace subspace subspace subspace subspace subspace subspace illustrated illustrated specifically coupled phys phys characterized characterized characterized characterized characterized differ differ modification driven modes committee committee presentation presentation presentation identify orthogonal receives receives characteristic characteristic refer quickly success interpreted symmetry follow follow sci satisfy comp eigenvalue eigenvalue leading leading leading illustrates subsequent decreasing remain remain layered perturbation perturbation perturbation investigate investigate investigate investigate exhibit exhibit exhibit exponentially scalar examine investigated analytically analytically scaled fundamental math math onset onset analyze predicts rev perfect regime regime defines averages averages averages residual residual growth distinguish distinguish agreement agreement guaranteed unstable unstable analytic analytic tool straight leaves arise controls laboratories acknowledgement universal opt opt opt integrating reflects relevance quantitative leave solla solla solla solla solla exhibits characterize monotonic monotonic incoming ordered qualitatively begins begins begins deviations eventually eventually simultaneous initialization phenomenon gap picture shifted uncorrelated uncorrelated uncorrelated indices secondary secondary labeling arguments eliminate enhancement plays eliminated numerically height grow synchronous responsible exceeds overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps connect guarantees expanded dominant dominant schedules approximators emergence specialized specialized reveals refers agree implicitly explains explains escape escape escape escape unchanged geometrical saad saad saad saad saad saad truncated truncated aston aston graded isotropic isotropic suboptimal suboptimal suboptimal breaking scenario scenario mismatch evolve interneuron decays decays realizable realizable realizable realizable realizable realizable realizable realizable continues gener gener switched differentiation differentiation differentiation regimes increasingly spanned weaker inversely ation bring bring prevents tin examination students excess excess ate identifies ping orthonormal dominates holmdel equa couplings couplings couplings couplings contributes specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization plateau plateau plateau plateau plateau norms norms norms norms norms norms scenarios linearized fastest fastest curved denmark evolves evolves confined confined trend neglected ized birmingham monitored sented asymmetry intrinsically alization alization uniformity accessible schwarze dissimilarity biehl neglecting cybenko copenhagen emerging rin rin bohr proportionality weakened jii linearization app imitate imitate imitate shrinking erf erf erf 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#@Saad_D,Solla_S,
#t9
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time set set networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number number number number error state results results results results information information problem problem performance performance performance performance based based based based based based space weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order systems systems values values noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit approach approach approach single single single single single single single single single single single single single single processing large large large large large large large local local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate analysis analysis class class class class class class matrix inputs inputs inputs inputs inputs form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples net net work work work work methods step current structure problems problems problems random high high similar similar show section fixed fixed fixed fixed line line line line line line line line rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general generalization parameter parameter parameter parameter real real theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term term note note note note experiments experiments dimensional dimensional dimensional university university university threshold variables variables variables research research research defined defined defined defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial constant constant standard standard computer computer computer computer computer terms terms terms terms terms distance distance distance distance distance science science science prediction prediction prediction prediction prediction left presented activation low low low low machine maximum maximum maximum learn learn components components components components components components components components basis basis basis nonlinear nonlinear outputs outputs abstract abstract abstract applied back back back find computational convergence convergence references component component ieee positive positive important propagation propagation propagation introduction complex hand hand hand hand behavior behavior behavior cost tion tion variable assume assume assume assume prior chosen chosen chosen previous bound bound bound bound bound bound bound bound bound bound bound bound long long distributed distributed make make make make make length length observed errors classes total total total total total regression regression regression respect sum called called called mapping mapping mapping mapping mapping factor factor factor factor dimension study obtain obtain obtain original artificial artificial relative relative relative relative relative represented desired provide define define rates proc perform perform experimental goal related constraints comparison comparison comparison comparison comparison comparison comparison larger larger contrast update update update update update descent descent descent descent descent descent descent descent descent descent morgan report report report department department department loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss version advances difficult difficult addition ai additional additional san top upper upper upper upper upper upper upper upper upper upper full full choice choice significant free basic basic pages give give con produce derived bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds area area entropy path finally evidence depends simply achieved achieved achieved measured technical technical technical feedforward feedforward describe arbitrary arbitrary arbitrary transformation close actions require require main main main square square square square square square square square square end hypothesis instance instance future easily easily makes makes kaufmann typically needed unknown coefficients transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer programming interesting increasing increasing increasing increasing special trials matching matching matching matching matching matching matching matching matching uniform uniform empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical leads leads leads squared details details call call call numbers numbers direct normalized produced choose predict predict recent advantage pair takes element quadratic sense compare compare works trans sparse sparse sparse sparse modified generalized generalized bounded bounded bounded sensitive entire lead invariant invariant invariant scaling scaling scaling scaling extended extended trial trial trial trial setting setting setting setting assumptions segment valued valued depend depend depend sigmoid measures performs mateo suggest strong presence california california start start start min plane relationship introduce manner minima minima minima minima minima minima minima appears appears derive produces produces produces produces produces written describes recall recall multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer slightly applying applying implies versus formation dependence influence open forms similarly constants updates past key reasonable additive performing convex convex norm norm norm norm norm norm norm euclidean euclidean euclidean david avoid expect expect box includes combinations usa usa instances instances instances instances instances batch batch batch batch prove prove prove prove candidate absolute absolute holds closely uniformly comparing situation essentially identity identity identity identity identity identity identity notice kind contained hold hold satisfy satisfy write generalize generalize minimizes computes satisfies situations remain layered transformed create exponentially hessian divergence scalar matches root complicated func notion attributes attributes possibly reading analyze analyze formal noted algo algo algo logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic arbitrarily finds rows crucial growth slope reasons purposes closer strictly worst worst worst worst worst worst worst worst worst worst worst worst worst worst desirable immediately commonly definite annual behaviors embedded introducing solla solla measuring achieves begins begins differentiable differentiable differentiable differentiable wesley univ univ cumulative cumulative irrelevant irrelevant irrelevant irrelevant lab lab proofs indices feasible addison formally restrict summing rithm rithm impossible nonzero nonzero grows grows outcome outcome kullback adds convenient logarithmic multiplicative los los settings imply preparation spurious spurious meaningful performances combines introduces predictors studying nonlinearities treatment insight warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth santa santa santa santa santa santa interestingly interestingly receiving dense dense appeared appeared ple entropic entropic entropic entropic entropic entropic leibler session generalizations realize tight tight tight remainder unseen exponent exam intuition levin gained rithms life thresholded carefully relate emphasize exceed adversary maintains outcomes sized places prevents treating gorithm achievable achievable nonnegative discontinuous unbounded wins wins concern supplied evenly norms norms norms norms norms littlestone littlestone littlestone littlestone littlestone exploits convention losses losses losses losses losses distorted fin crl crl cruz cruz cruz cruz cruz cruz kivinen kivinen kivinen kivinen kivinen kivinen kivinen kivinen kivinen kivinen kivinen kivinen shop indi thc stan incurred meaningless tracked predic suitably impor dard ucsc ucsc colt manfred exponentiated exponentiated exponentiated exponentiated feel helsinki multiplies helmbold helmbold helmbold helmbold helmbold helmbold helmbold accelerated normalizes preceded logarithmically straints finland owi opened charged tth tth tth tth calif calif logarithms auer auer auer xixj ima wll famous merits fleisher sumptions bianchi 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#*learning neural neural neural neural neural neural neural neural neural input input input data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training output output output output number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results information information problem problem problem hidden based based based space weights case case case case vector vector vector vector vector vector vector order systems systems systems systems systems systems values probability weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons pattern pattern pattern pattern single single single single single single single single single single single single processing processing large large large large local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate analysis inputs algorithms simple paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small work work methods classification show show show show show show show show show show show show show show equation section section section section section section line general general approximation states gradient gradient gradient note dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result computation research log log defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant constant computer computer science phase machine sets sets sets sets sets sets sets sets sets range range range range outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract back back find references due ieee ieee positive positive positive propagation propagation introduction complex complex complex generated parallel variable assume assume assume assume part previous previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem multiple multiple multiple conditions conditions fact observed finite finite minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum tasks respect respect respect respect sum called called regions regions regions optimization dimension dimension dimension dimension dimension natural global global obtain artificial artificial relative desired desired desired desired goal constraints connected distributions equal approaches comparison contrast contrast update support descent report words department loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss consists bias bias bias bias layers sequences domain additional additional full requires pages pages give give produce condition area area area entropy finally finally backpropagation backpropagation simply simply discussion technical limited surface proof proof proof proof proof proof circuits common common supported square square square square square square square square square square square square square square square easily easily makes transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer york york york increasing increasing increasing increasing increasing matching matching matching matching matching squared supervised magnitude combined combined combined produced produced produced added denotes discussed property property property separate moving sense sufficient sufficient definition symmetric observation bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded interval grant grant exists exists exists lead occur occur derivative derivative occurs boundary generally setting setting place minimal minimal minimal assumptions assumptions segment tangent practice practice hard hard physics physics sigmoidal california intelligence minimizing minimizing exist introduce derivatives minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima minima areas distinct distinct distinct distinct distinct dimensionality easy easy consisting consisting adding boolean lemma lemma lemma lemma lemma lemma lemma open open similarly similarly suggested updates additive convex convex add calculate visible sufficiently sufficiently foundation transactions perceptrons perceptrons prove prove absolute holds holds holds holds discussions literature essentially identity identity anderson anderson strategies satisfy satisfy satisfy satisfy notation notation generalize denker satisfies acknowledgments remain remain american american layered layered xor exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially hessian hessian rise notion induction gradients editor editor formal logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic observe arbitrarily arbitrarily mentioned defining baum turns turns turns satisfied immediately optimize definite definite depicted nsf peter peter solla fall occurrence semi semi lim lim lim lim lim lim lim lim lim differentiable differentiable differentiable differentiable summed univ phenomenon phenomenon lab proofs proofs proofs proofs grows generality clamped clamped fails saturation saturation saturation saturation grow grow grow mark mark mark disjoint disjoint disjoint disjoint disjoint disjoint spurious composition composition composition respective demonstration counting omitted omitted warmuth warmuth warmuth warmuth warmuth warmuth santa santa valuable papers outlined andrew metrics entropic entropic entropic entropic entropic leaming leaming sontag sontag sontag flat flat flat flat flat flat flat flat pairing levin magnitudes realizable realizable realizable realizable realizable realizable realizable paired paired iri discusses sized likewise infinitely remark gratefully saturated hyperbolic hyperbolic unbounded unbounded curse blum suffices separates losses proves watrous crl teaching cruz essence acknowledges transaction statements monotone monotone monotone moderately comprehensive extrema mike ucsc ucsc manfred manfred manfred analogously succeed accelerated mat gin gin austria recalling calif auer auer auer auer auer auer haykin preliminaries preliminaries fleisher wittner brady wilczek finitely cfi macmillan lob eduardo fort fort fort gori undo 
#@Auer_P,Herbster_M,Warmuth_M,
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural input input data function function function function function function function function figure figure time time time time time time time time time time time time time set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number system system error error error error error error error error error error error error error error error error error error error error results results units units units units units units units units units units units units units units units units hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based space space weights weights weights linear linear linear linear linear linear layer layer layer layer case case case vector order order order order order order order order order order order order order order order shown systems values values values values parameters parameters parameters parameters parameters parameters parameters weight weight weight weight unit unit unit unit unit unit unit method point point point point point point point single control large large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis analysis analysis analysis matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs form form form form algorithms algorithms algorithms algorithms gaussian paper paper examples examples examples examples examples small small small small small small small small small size work work task fig fig fig fig fig fig fig fig fig fig classification process process trained trained trained trained trained random random similar similar similar architecture architecture architecture show show show show section fixed fixed fixed fixed fixed fixed fixed fixed line line line line line line line line line rule vectors vectors vectors vectors vectors vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter approximation average average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term term dimensional dimensional university university variables variables solution solution solution solution research research research research independent independent independent independent defined defined defined defined defined defined defined defined defined found dynamics dynamics dynamics dynamics dynamics initial initial initial constant standard standard terms terms terms distance node node node node node node presented presented map map map present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine motion motion motion motion motion motion motion maximum range range range learn learn learn learn components outputs continuous abstract back back back back back back back back back back back back back back back back back back back back back back find find find find find find find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references due due due positive positive positive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction statistical statistical effect effect effect variance difference difference variable lower measure measure measure signals learned higher cases good long conditions conditions equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations fact fact fact proposed length length length finite minimum minimum resulting resulting resulting resulting ing ing regression respect respect respect respect respect respect respect eq eq eq elements elements mapping factor applications study negative negative negative negative compared compared compared compared compared compared desired rates rates rates rates rates rates rates rates determined determined connected connected distributions comparison larger larger contrast update update update update descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent department difficult final ai maps framework framework computing equivalent limit limit full full choice choice significant significant increase increase increase condition condition achieved measured discussion discussion normal feedforward feedforward feedforward increases arbitrary arbitrary arbitrary group fast fast fast close inverse inverse inverse inverse inverse inverse inverse inverse stable implemented role theoretical main ability ability easily easily degree degree simulated smaller dynamical dynamical dynamical dynamical dynamical dynamical transfer transfer significantly significantly significantly significantly significantly significantly character increasing uniform mode mode squared max max max normalized normalized early magnitude decay decay decay decay decay decay choose predict improve recent exact typical typical typical typical typical typical introduced identical identical quadratic relevant relevant relevant highly varying compare compare teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher calculated tions yields yields studies studies studies converge converge differential differential differential rl rl diagonal diagonal symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric interval improvement improvement exists studied occur deviation derivative matrices matrices generally setting strength minimal reduce differences differences differences numerical numerical numerical numerical designed exponential faster faster faster faster faster asymptotic asymptotic temperature temperature temperature temperature temperature temperature integration physics reduction drawn drawn drawn sigmoidal sigmoidal proportional proportional proportional proportional proportional minimizing minimizing user user exist decrease decrease introduce derivatives question pro changing student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student multilayer multilayer multilayer multilayer multilayer multilayer explicitly averaging text scales scales scales consisting integrated minimization choosing independently focus expressed depending stages overlap overlap influence open evolution evolution evolution evolution soft soft converges converges earlier calculation calculation slow david activations activations activations perceptrons dominance eigenvalues eigenvalues eigenvalues instances batch activated coupled coupled phys phys characterized characterized characterized characterized efficiency efficiency efficiency suitable maximal maximal modes modes modes modes modes modes committee committee presentation presentation identify identify efficiently efficiently schemes summary quickly quickly success interested dis symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry sin follow providing providing eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue perturbation perturbation investigate exponentially optimized optimized optimized optimized behaviour behaviour examine ideas investigated analytically scaled eigenvectors eigenvectors complicated complicated math onset onset onset onset rev illustrate perfect adjusted regime regime regime regime motivated motivated defines growth distinguish distinguish derivation defining unstable unstable improves drive closer widely controls describing opt opt opt opt opt opt opt opt opt opt opt optimize optimize optimize mechanics mechanics explained integrating improvements varies considerably pure parameterized readily solla adjustable adjustable exhibits perturbations measuring deviations eventually eventually contribute initialization uncorrelated labeling approximates bin tem grows plays eliminated systematic numerically numerically numerically interpret hope preparation overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps negligible surprising den sim specialized mlps shortest motions eqs broken speeds alternatively escape escape saad saad saad saad saad saad truncated truncated truncated outline rigorous rigorous aston isotropic isotropic isotropic isotropic isotropic isotropic suboptimal suboptimal suboptimal suboptimal suboptimal tween acceptable breaking breaking breaking breaking edinburgh edinburgh scenario scenario remainder alter gained gained decays realizable realizable thermodynamic ization expand expand confirmed differentiation regimes investigating integrals harder emphasized breaks breaks breaks figs figs figs figs west west west west west inversely inversely rewrite achievable unbounded hid pronounced tribution optima equa couplings beneficial specialization specialization specialization specialization specialization specialization specialization specialization norms norms norms norms norms scenarios scenarios linearized fastest adjusts amplified randomness confined neglected neglected ized birmingham inappropriate rotational fore analyse ues trapped trapped decompose spent altering prolonged prolonged rela excluded saturates saturates teachers teachers teachers teachers enhancing rescaling schwarze qij qij qij qij qij qij diverges initializing rationale distinguishes analysed biehl oij gra sponse cybenko motivate rin rin rin specialize serially erf dient modulus slows neg inhibiting slowest effected linearize generically ilar qii qii qii scalars imitating pertur perature trapping trapping trapping 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#@Saad_D,West_A,
#t9
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#*network network neural neural input input input input input input input input input function function function function function figure figure figure figure set set networks training algorithm algorithm algorithm algorithm algorithm output output output output number system results problem problem problem models models models space space space space space space space space space space space space space space space space space space space space space space space space space space linear layer case case case case case case case order order shown shown shown values values values noise functions functions functions neurons unit distribution method approach approach approach approach approach approach approach approach pattern pattern point point point point single single large large local local local local local local local local local local local local local analysis analysis analysis class matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal inputs inputs form form form algorithms algorithms simple gaussian visual visual visual visual visual visual paper small small feature feature feature feature feature feature feature feature feature feature feature feature net net methods methods cells step points points points points points points points points points points points points points points points points points points points points points points points points points points points field features features features features features features features features features features features features features features process level current structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure high high high similar similar similar similar similar representation representation representation representation equation equation equation equation equation equation equation equation equation equation equation line line line line line images images general general general general general general theory activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university variables variables variables solution research defined defined defined defined defined target standard distance distance distance science left left direction direction direction presented map map map map map map map map map map map map map low sets sets maximum maximum maximum maximum maximum maximum maximum maximum range range range position position position abstract abstract abstract applied applied applied back find computational computational properties references ieee important important introduction complex complex behavior behavior statistical parallel cost cost cost cost cost cost cost difference spatial spatial assume assume assume assume measure measure measure measure word chosen higher cases cases cases type required cortex cortex cortex cortex cortex cortex cortex cortex cortex good good conditions represent techniques correlation correlation correct forward finite minimum minimum resulting ing simulation human sum mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means means optimization optimization optimization optimization optimization optimization dimension dimension dimension natural natural orientation orientation global global global global study obtain obtain specific represented true true true application application series define define eye goal related constraints cortical cortical cortical cortical cortical cortical cortical brain brain brain approaches larger larger larger report institute institute institute institute department consists represents difficult bias bias addition maps maps maps maps maps framework framework equivalent equivalent experiment experiment directly directly directly view solutions solutions transition limit san stimuli stimuli determine efficient statistics statistics world increase give give give con condition coding area lines path nature nature simply biological biological biological discussion discussion technical increases increases close inverse assumption finding assumed assumed end hypothesis instance instance instance degree degree degree degree degree degree development development sensory sensory sensory objective objective objective pairs account functional functional interesting interesting increasing increasing increasing special structures structures matching matching matching matching principle principle principle squared representing representing representing details call direct early idea idea population population discussed discussed recent correlations advantage pair separate separate separate ensemble similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity apply moving moving include sense sense sense sense sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski relevant interest interest interest dimensions dimensions highly varying compare previously match match studies trans positions symmetric generalized bounded organization exists occur wide wide matrices matrices predicted alternative alternative alternative locally width width width width column column setting half half half half half half place assumptions segment central measures measures measures retina suggest propose reduction california solid solid turn assuming exist exist question acknowledgements areas areas derive construct produces written longer ways ways primary primary label label vertical mathematical distinct segments explicitly physical quality implies implies blocks decreases decreases yield expressed formation formation formation correlated correlated correlated communication interpretation organizing organizing organizing organizing organizing ocular ocular ocular ocular ocular ocular ocular ocular ocular understanding understanding understanding understanding activities completely dashed spaces combining distances distances distances distances distances calculate sufficiently sufficiently euclidean euclidean euclidean euclidean euclidean kohonen usa usa usa dominance dominance dominance dominance dominance dominance dominance dominance dominance inter inter inter plotted discuss phys neighbors discussions simplicity columns columns regular straightforward extra extra closely projections tend tend miller capture capture road road refer interpreted dis strategies vary dayan cat principles principles principles principles preferred decreasing decreasing oriented explore origin unlike diego investigate rapidly put issues issues dual examine matches ideas tech detectors mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings investigated biol analytically analytically analytically relationships relationships relationships referred maximizing understand understand topographic topographic topographic topographic topographic topographic topographic topographic topographic notion matched attributes neu examined plausible analyze opposite opposite rev perfect eyes eyes obvious mapped mapped expressions consist simplest arbitrarily attempts attempts optimum optimum optimum optimum optimum great rows scenes slowly derivation biology answer tractable organized choices monkey potentially separately medical qualitative qualitative addressed geometric geometric geometric geometric apparent varies amounts peter frequently biologically maxima maxima maxima maxima maxima http howard measuring measuring characterize implements specifies multidimensional distortion globally globally globally indices indices cybern analogue optimizing optimizing optimizing optimizing optimizing ordering receptors receptors outcome arranged fits ranges ranges odd odd odd hope nearby nearby nearby nearby nearby ral shifts salk salk salk salk north north optic optimally intuitive intuitive edelman respective paul negligible regard consequences consequences captured captured elastic elastic similarities similarities similarities similarities jolla jolla jolla implicitly implicitly mechanical crossing crossing schulten outline outline constitute accept equivalently willshaw willshaw smoothly centre weiss additionally ease possibilities edinburgh edinburgh examining scenario mismatch argue pub trends ftp geoffrey impose impose distant distant distant intra disadvantage hughes terrence argued topic pos sheet sheet sheet sheet sheet sheet distinguished pop obermayer durbin durbin wider wider november topography topography helps coming stimulating preserves discontinuous unbounded invertible viola tectum developmental stripes stripes stripes stripes stripes stripes steven dcs wiring periodicity periodicity periodicity optima preservation tance implied reality salesman reviewed halves halves halves halves halves halves halves halves halves halves blocked blocked putation spec analyse correlational goodhill goodhill goodhill goodhill goodhill goodhill goodhill goodhill hood stryker ular deeper mason pursued jumps blasdel blasdel dissimilar topologically favorable occupied dissimilarity dissimilarity dissimilarity justify stripe vin mitchison neighbour conveniently analogously neighbouring neighbouring neighbouring neighbouring travelling keller geoff geoff traversing quantifying quantifying avail flamework gary neurosciences meets loose torrey torrey pines pines strained vout vout vout vout cnl intemal striped striped striped striped striped suggestive ified refered adoption prevalent chemically hav 
#@Finch_S,Goodhill_G,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input function function function function function function function function function function function function function function function function function function function figure figure figure time time time time time time time time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system state state results results results results results units problem models models linear layer layer layer layer layer layer layer layer layer layer layer vector order order order order shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems values parameters functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons unit method method pattern pattern pattern pattern pattern point point point point point point point point point point point point point control large neuron neuron neuron neuron neuron neuron neuron analysis analysis analysis analysis class class class class matrix matrix signal paper paper paper paper small small small net net points points points field classification process process level current problems memory memory memory memory response similar show show show equation equation equation equation equation section section section fixed fixed fixed rule rule vectors general parameter parameter parameter parameter approximation states states states states states states states theory theory theory theory obtained obtained term term term term term term activity activity activity activity activity university variables variables variables solution defined defined defined defined found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant constant constant standard connections synaptic synaptic synaptic synaptic synaptic synaptic presented present present activation temporal maximum nonlinear nonlinear nonlinear abstract find convergence convergence properties references ieee ieee ieee positive positive positive adaptive introduction complex complex estimation behavior behavior stimulus stimulus stimulus dynamic dynamic dynamic dynamic parallel recurrent variable assume assume lower rules part theorem bound cases type type type type type type type type type type type cortex long long conditions conditions expected equations equations equations equations techniques scale scale scale scale simulation sum sum sum sum sum called means global global global global study obtain obtain negative desired desired desired constraints cortical cortical cortical connection fields nets institute synapses technique represents layers layers ai ai maps maps considered considered considered design design design design stimuli stimuli determine determine determine upper give condition condition condition derived derived weighted weighted weighted levels levels criterion area types actual provided inhibitory inhibitory biological technical technical feedforward describe fast fast fast fast fast fast fast limited excitatory stable stable stable stable stable stable stable stable stable short short theoretical theoretical sensory reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced unknown unknown interesting increasing special inhibition inhibition inhibition normalized magnitude neuronal takes lateral lateral lateral lateral practical apply apply moving include include subject machines quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic sense works studies differential achieve symmetric modified organization organization organization organization storage concept concept extended wide deterministic boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary setting flow assumptions assumptions hebbian hebbian hebbian trajectories conclusions valued valued competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive asymptotic asymptotic asymptotic asymptotic constrained external external external external assuming assuming variety base suppose stability stability stability stability stability stability stability stability stability stability stability mathematical unique unique unique scales scales scales scales interaction equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium competition competition choosing communication restricted organizing evolution evolution centered understanding constants constants earlier earlier slow slow slow slow slow slow slow neighborhood closed msec msec msec sufficiently sufficiently symbol transactions transactions transactions illustrated automatic coupled variations absolute characterized aspects aspects maximal modification modification modification modification modes attractors attractors attractors reached composed capture traditional verlag interpreted contribution contribution contribution contribution hold hold relaxation reach modelling law origin origin origin origin wiley perturbation perturbation requirements exhibit put behaviour periodic scalar scalar root oscillation examined man extremely singular singular hebb store store amari amari amari amari defines established mentioned asymptotically asymptotically asymptotically asymptotically formula smoothness phenomena analytic tool tool nonlinearity mation universal grossberg grossberg grossberg grossberg describing recording cybernetics cybernetics mechanics cohen cohen posed treated perturbations aim extensions germany june phenomenon guarantee tation linearity jth receptors establish consideration stated stated primitive analyzing monotonically monotonically implications implications modifications lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov guarantees guarantees consequences sphere spatiotemporal storing considerations valuable rigorous basically shunting cooperative perturbed perturbed perturbed perturbed perturbed perturbed perturbed perturbed mutually modifying retinotopic ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm pools vanishes vanishes rewritten remarks characterizing nonnegative nonnegative inhibited inhibited inhibited inhibited inhibited interpreting interpreting inequalities inequalities pictures cooperation establishing smc smc deter stm stm stm stm stm stm stm stm stm dij dij dij equilibria histories histories puter exhibiting adopting mild laterally laterally laterally laterally laterally meyer meyer meyer meyer implication standpoint efficacies notations fluid und und namics mij investigates dii adiabatic stretching lyl lyl ministic decoupling permissible exci pertur pertur ama ama ise introductory informatics heb heb phenom rtl 
#@Meyer-Baese_A,Ohl_F,Scheich_H,
#t9
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural data data function figure figure figure figure figure figure set set set set set set set set networks networks networks networks networks networks networks training training training training number number error error error error error error error error error error error error error error error error results results results results results units models hidden based based based based based based based space space space space space space linear layer case case case case vector order order order order order order order order shown shown shown systems systems systems values values values values values values values probability probability probability probability probability parameters parameters parameters parameters functions functions functions functions distribution distribution distribution distribution distribution distribution distribution recognition pattern pattern point single large neuron neuron neuron neuron patterns patterns form simple simple simple simple paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples small size size fig fig random random show section line line line line line line line line line vectors general generalization generalization generalization generalization parameter parameter approximation approximation approximation average average theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained obtained note dimensional dimensional dimensional dimensional dimensional result result university university university university threshold computation computation computation research research research defined defined defined defined defined defined defined target target target target target dynamics initial constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate terms prediction direction present phase phase phase phase phase phase temporal machine range press press press learn continuous sample sample sample sample sample sample sample sample abstract find find find computational computational properties properties references ieee ieee ieee important introduction introduction complex estimation behavior statistical statistical statistical statistical statistical statistical statistical statistical complexity variable variable variable lower measure measure higher higher higher higher previous theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases binary long expected expected expected errors scale finite finite finite finite finite simulations resulting ing tasks tasks respect respect multi sum called called factor potential potential potential dimension dimension dimension dimension dimension dimension dimension dimension applications study knowledge relative specific specific specific samples samples true true true true true true true compared application series define proc proc proc proc approaches mit mit comparison contrast support dependent proceedings proceedings department version addition considered cambridge cambridge cambridge cambridge curve curve curve curve curve curve curve curve curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves estimates estimates estimates estimates estimates estimates limit top top top conference capacity efficient upper upper upper upper upper upper upper full significant approximate approximate basic basic basic basic pages pages pages pages give produce produce condition derived derived developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds types lines lines lines entropy selected discussion discussion feedforward arbitrary denote denote transformation limited close inverse assumption assumption predictions proof proof proof proof generate main main journal hypothesis hypothesis hypothesis hypothesis hypothesis degree including including coefficients projection consistent consistent consistent uniform empirical empirical empirical leads call max international bottom bottom decay polynomial perceptron perceptron perceptron perceptron perceptron improved discussed improve exact exact separate typical practical sense sense subset subset subset subset engineering interest interest dimensions dimensions compare calculated volume yields trans evaluation chain chain chain chain modified modified modified modified modified modified modified observation interval williams improvement storage exists exists parts expression expression lead lead generally conclusion conclusion starting minimal minimal minimal minimal conclusions conclusions central central central numerical numerical integration physics physics physics physics largest solid solid proportional turn assuming variety variety min decrease iii iii iii iii introduce introduce introduce question explicit explicit relation relation derive ways ways transitions transitions transitions transitions transitions transitions ann distinct distinct changing segments segments physical easy consisting springer implies implies national family family family family lemma lemma lemma lemma lemma solved evaluate restricted approximations sizes sizes sizes partition allowed slow classical combining figures subspace determines vapnik vapnik vapnik vapnik extension plotted plotted discuss holds holds determining maximal modification modification presentation plots composed road soc conf verlag cun split split split issue symmetry comp comp notation notation simplified nips nips hypotheses employed origin production difficulty relations dotted dotted dotted examine ideas affect cover cover fundamental fundamental analogous act possibly integer generalisation generalisation generalisation perfect perfect perfect obvious obvious obvious perceptton shapes shapes logic store amari amari inequality inequality band growth analyzed rapid formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism formalism style division laboratories laboratories acknowledgement universal arises arises qualitative mechanics mechanics improvements generic generic haussler haussler employ continuously measuring incorporating serve qualitatively wang june cumulative pac pac formally restriction fix acm acm homogeneous homogeneous homogeneous homogeneous partitions theories lost satisfying satisfying satisfying odd replacing bands tishby tishby shifts disjoint disjoint eqn eqn sompolinsky bartlett bartlett bartlett bartlett bartlett corollary corollary corollary corollary corollary corollary introduces ranging overview bad bad entries initialize suggesting warmuth kearns theoretically impact broken broken broken broken seung seung dramatically unified geometrical outline rigorous leaming leaming leaming leaming leaming leaming leaming leaming leaming leaming leaming leaming leaming chervonenkis chervonenkis additionally causal australia australia australia rain tight tight equality equality levin thermodynamic learnability oct refinement refinement union union drops williamson williamson williamson williamson williamson ignoring dichotomies manuscript gratefully council const const const const const australian australian crude crude inequalities substitute anthony cardinality cardinality governing proves implied era south elec acknowledges kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk allocating capturing rotational fore benchmarks adv adv murata tighter tighter tighter sydney sydney sydney sydney phil reviews blumer rom dependences jumps jumps uniformity uniformity uniformity uniformity uniformity uniformity uniformity uniformity uniformity uniformity uniformity acknowledged ting pared icnn permission ising sakurai muller loses ehrenfeucht innovation canberra sudden finke loose pattems pattems irl anu sacrifice trl void ifs ifs fujita ction ction publish determin fork inl clayton universality displaying itc biggs ise inspecting blackburn rnin shinomoto ding fuller iml ihl esis vic director itl itl 
#@Bartlett_P,Kowalczyk_A,Szymanski_J,Williamson_R,
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#*network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure time time time time time set set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number number number number number error error error results results units problem problem problem models models models models models models models models models models hidden hidden performance performance performance based based weights linear linear linear linear case case case case case case case vector vector vector vector order order order shown shown shown shown systems values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise weight functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method approach approach approach approach point single large large large local local test test test analysis matrix optimal optimal optimal optimal optimal form form shows simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples examples examples small small small net work work task task task task methods methods methods methods methods methods methods methods methods methods step step step step points points points classification process process process level level level level trained trained trained trained problems problems problems problems high similar similar architecture architecture architecture architecture architecture architecture equation fixed fixed vectors vectors vectors parameter parameter parameter parameter parameter approximation approximation obtained obtained obtained term term activity activity result university university variables variables variables computation computation computation computation solution solution independent log log log log log log found constant constant table table estimate standard terms terms prediction prediction prediction prediction prediction prediction prediction presented present low sets sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum range components basis outputs outputs outputs outputs outputs abstract applied find computational likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component stochastic due procedure procedure important important important adaptive mixture mixture mixture mixture mixture mixture mixture mixture introduction action complex hand estimation statistical effect effect effect generated generated variance variance variance variance variance variance variance variance variance variance tion energy energy energy energy energy energy variable variable assume assume assume assume assume measure prior prior prior prior prior prior prior prior prior prior chosen chosen previous previous cases cases type binary binary binary binary tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected markov make length observed observed simulations resulting regression regression computed sum times means made made em em em em em em em em em em em obtain negative artificial artificial artificial cross cross cross series series series series series series series provide perform posterior posterior posterior posterior posterior posterior distributions distributions distributions larger train train dependent selection selection selection proceedings department department consists consists consists consists consists consists joint connectionist connectionist exp exp exp exp exp exp exp exp exp bias bias scheme considered considered framework framework framework framework cambridge cambridge cambridge cambridge cambridge cambridge domain equivalent hinton hinton hinton hinton hinton hinton additional view solutions solutions solutions estimates classifiers approximate approximate free free free free free free validation validation validation give give conditional conditional conditional levels entropy entropy finally finally processes processes processes selected selected evidence evidence evidence discussion covariance covariance describe describe denote assumption assumption corresponds complete complete predictions predictions predictions predictions predictions finding finding common implemented assumed assumed journal journal future future rumelhart rumelhart objective simulated probabilistic typically underlying underlying account functional jordan jordan jordan jordan mlp mlp mlp significantly significantly ratio special principle squared making international experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert expert expert expert expert expert early decay combined description description predict denotes separate ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble typical quadratic hierarchical hierarchical hierarchical inference inference inference subset engineering engineering interest works works tions smooth smooth yields mixtures mixtures mixtures mixtures mixtures mixtures mixtures bounded gate gate gate gate gate gate gate gate gate entire increased constructed expression expression expression lead matrices alternative setting demonstrate demonstrate greater assumptions competitive bayes bayes bayes performs constrained constrained regularization variety min introduce manner minima van van van factors generating estimating laboratory missing belief gaussians predictive predictive quality expectation focus viewed evaluated approximations activities additive fitting fitting fitting fitting fitting fitting fitting fitting fitting fitting fitting interpolation david avoid expect expect includes includes priori extension uncertainty uncertainty uncertainty uncertainty priors priors priors priors priors priors simplicity gamma straightforward selecting selecting aspects society delta mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay tend tend traditional refer lie generative notation notation write computes approximating approximating jacobs jacobs jacobs jacobs modelling bars bars investigate experience divergence divergence ml ml ml ml ml ml ml ml ml ml ml ml ml scalar fashion fashion giving incremental variational variational variational possibility dependencies structured gates gates gates gates gates tanh func hierarchy analogous analogous naturally predicting portion portion noted consist submitted motivated neal neal neal years years stop piecewise separable separable separable separable smoothness smoothness smoothness products probable separately opt toronto incomplete hme hme hme hme hme hme hme hme hme hme hme hme hme tional robinson robinson robinson robinson weigend weigend weigend weigend hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters achieves geman geman logp inherent inherent simultaneous simultaneous softmax cor corrupted corrupted corrupted benefit www restrict fix branches approximates royal exemplar extending kullback hyper keeping responsible moments dominant eng eng indicator indicator indicator record augmented variants dempster dempster cam cam cam avoiding vari lag fitted outline rubin rubin leibler kluwer stock year ideally england england england param param constrain constrain avoids avoids avoids avoids avoids pub equality ftp ftp community deep deep deep deep distribu overhead noting laird laird isi normalised prevents eters eters tel tel tel coming advantageous bienenstock const const builds aid optimisation optimisation optimisation optimisation practically ters huberman huberman inferring inferring steve maximisation developments dilemma colt maximising regularisation regularisation regularisation pot rightmost wji wji confident overfit hyperparameter hyperparameter camp camp camp sunspot sunspot tony waterhouse waterhouse waterhouse waterhouse lend fii nmse nmse nmse optimise optimise readings radford optimising optimising optimising optimising optimising minimisation minimisation minimisation minimisation varia doursat doursat yearly leftmost documented biometrika sunspots sunspots url oid ola ola imizing arti minimises minimised encompasses underestimates ational maximises rupted dordrecht skilling isj cavendish ficial 
#@MacKay_D,Robinson_A,Waterhouse_S,
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#*network network network network learning learning learning model neural neural neural neural neural data data data function function function time set set set set set set set set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm system system system system system system state state state state state state state state state state results results results results results results results results results space space space weights linear linear case case case case case case case case case case case case case vector vector vector vector order order order order order shown values values values values values values probability probability probability probability probability probability probability probability probability parameters pattern point point point point single single single single single control large local local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form simple gaussian paper paper paper small small size size net work step step step step step step points field process process process process current random random random random random random random random random high memory memory memory memory memory memory memory show show show show show section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line rule rule vectors general general general general parameter parameter parameter parameter real approximation states states states obtained obtained term note note result result result result independent found found sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial computer terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic present sets maximum components abstract convergence convergence convergence convergence convergence convergence properties properties properties properties references stochastic positive positive positive positive procedure introduction hand hand statistical effect effect generated variance variance change energy energy energy energy energy energy energy theorem cases cases type type type good expected proposed correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities errors forward finite finite minimum minimum minimum minimum minimum minimum ing ing total total total total total simulation simulation simulation called means means factor dimension global knowledge obtain obtain relative specific true true true provide determined equal steps steps steps steps steps comparison fields fields update institute loss considered considered view view curves estimates limit limit trajectory stage capacity capacity statistics world estimated con condition condition condition condition condition condition condition conditional finally iteration iteration iteration iteration iteration iteration nature nature depends associative associative associative discussion increases increases increases arbitrary arbitrary arbitrary arbitrary denote close assumption proof proof proof proof assumed assumed main main eds hypothesis hypothesis instance underlying hopfield hopfield hopfield hopfield account technology interesting projection projection projection increasing increasing principle leads max max max max max making normalized normalized normalized denotes moving subset recently relevant interest interest sufficient unsupervised calculated calculated converge definition storage storage storage risk expression occur alternative alternative clusters generally setting pass pass pass strength strength strength conclusion starting place hebbian interactions interactions interactions numerical numerical asymptotic asymptotic temperature taking strong strong physics largest largest reduction turn assuming min min min min min min min decrease decrease iii iii averaged connectivity minima question explicit relation van van van written index sequential stability stability stability recall explicitly linearly remaining slightly scales consisting consisting springer implies implies choosing dependence dependence depending depending correlated correlated communication detailed detailed suggested past spectrum calculation iterative intermediate initially calculate calculate calculate formulation formulation retrieval retrieval retrieval eigenvalues subspace subspace subspace memories prove prove prove specifically absolute holds phys phys regular straightforward capable maximal maximal driven presentation schemes situation allowing contribution notation quantity involved vary write relaxation relaxation eigenvalue eigenvalue eigenvalue automatically subsequent situations explore carried exhibit exponentially put ml behaviour behaviour behaviour examine ideas rest possibility affect induction smallest concepts necessarily integer opposite rev obvious taylor hebb hebb isolated isolated years spin spin spin spin spin spin spin mentioned indicating inequality trivial derivation unstable slope analytical lies london stress satisfied satisfied sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn immediately hyperplane controls probable meaning researchers argument considerably relevance treated maintain calculating limiting limiting limiting limiting limiting limiting limiting limiting limiting differs reaches proven proven collective substantial conclude attraction unbiased unbiased unbiased unbiased unbiased unbiased proposition proposition summed sleep appearance appearance extensive summing summing summing pick unity unity impossible impossible nonzero turned consideration promising stated stated nearby reasoning sompolinsky sompolinsky sompolinsky studying sides realization realization evident infinity chooses advance iterated omitted contraction passing inductive statement statement statement statement statement fold convergent convergent convergent convergent convergent convergent convergent speaking verify temperatures multiplying slight rigorous presenting failed failed failed theorems theorems theorems theorems theorems obtains possibilities basins rain stands realize realize concentrated grouped jij jij proba met relate flip flip flip noting conversely spanned spanned worth france isi preprint bring eigen treating shallow walk walk palmer ble lation bility sake marks marks converging spins spins realizations hemmen hemmen hemmen proves transpose approaching permanent gence pin vanishing vanishing rem supposed metastable metastable metastable metastable metastable relax rises stabilizing elegant checked excluded superscript kanter kanter kanter aimed possesses excluding conver begun sing exhibiting surrounded asymptotics asymptotics asymptotics asymptotics flips flips flips rescaled simu supplies possi owing private realizing retrieving jii realizes lacks cumbersome pii pii sification flipping flipping breakdown breakdown arose mln decorrelating dition mech resides asymp contradicts indications barriers multiplicity multiplicity iil suggestive universality creasing slate moscow behaviours behaviours behaviours definiteness negligibly proximations restated feinstein steeply anisms tma enumerate elucidating designates thogonal 
#@Seinenov_S,Shuvalova_LB,
#t9
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#*learning learning learning model model model model model model neural neural neural neural input data data data data data data data data data data data data data data data data data figure figure figure time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm number number number number number number error error error error error error error error error error error error error error error error error error error results results results problem problem problem models models models space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector vector vector vector vector vector vector shown shown systems systems systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight distribution distribution distribution method method approach approach point point point point point point point point point large large large large local local local rate analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs inputs inputs inputs form form form form shows gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper size size methods points points points points points points process problems random random similar show fixed fixed fixed fixed fixed rule vectors vectors vectors vectors generalization generalization generalization generalization generalization generalization generalization parameter approximation approximation approximation approximation approximation approximation theory theory theory theory theory theory theory theory theory theory gradient gradient gradient gradient gradient term note note note experiments result result university variables computation solution research independent defined found dynamics initial initial initial initial initial initial constant estimate estimate standard standard standard computer terms terms science direction direction presented presented temporal temporal machine sets sets sets sets sets range press press learn position components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous continuous abstract applied applied find find properties properties properties references references component positive positive positive procedure procedure important important important important introduction hand estimation generated generated variance variance tion tion complexity bound bound good spike conditions distributed distributed distributed expected expected make fact correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length length length length length observed observed observed errors errors finite finite finite simulations simulations ing total regression regression regression regression regression regression respect sum sum eq eq eq eq eq eq eq eq eq eq eq eq eq eq made orientation true true true application define define determined goal connected equal equal mit steps descent descent descent nets selection morgan morgan morgan morgan morgan advances advances advances advances represents difficult exp exp exp considered cambridge equivalent equivalent solutions solutions solutions solutions estimates trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san san effects determine approximate statistics statistics world increase validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation con condition condition derived derived derived criterion criterion backpropagation backpropagation backpropagation depends depends simply covariance covariance covariance normal normal normal feedforward increases increases increases increases increases increases describe denote close inverse corresponds surface surface surface surface surface proof proof common effective assumed assumed shape supported role main eds eds eds end future easily rumelhart kaufmann kaufmann kaufmann pairs character york empirical squared direct early early early early early early early early early early early early early early early early early early early early early early early early early early early early early denotes denotes denotes population discussed recent exact typical apply apply apply apply moving moving include side side quadratic quadratic quadratic sense observations observations observations approximately approximately approximately approximately approximately approximately yields yields address definition chain symmetric observation grant constructed studied suggests extended matrices matrices move touretzky touretzky half starting starting segment peak peak peak peak peak asymptotic asymptotic mateo mateo largest reduction reduction sigmoidal proportional regularization assuming assuming assuming assuming start start plane plane plane plane plane plane plane plane plane plane plane plane plane decrease minima identification denoted suppose appears describes mathematical mathematical dept segments modeled modeled modeled recall infinite easy easy develop applying implies decreases squares squares squares squares squares squares squares squares squares squares squares squares squares squares squares evolution approximated converges converges additive additive sec sec neighborhood calculate foundation color mozer candidate candidate divided characteristic characteristic characteristic characteristic stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping split lie lie lie hold vary usual usual michael play nips nips nips nips giles correspondence acknowledgments deal tesauro tesauro extend cowan cowan employed origin carried access difficulty put hessian mass mass mass mass rise scalar ideas int smallest gradients gradients gradients concepts analyze analyze predicting der der formal noted academic extent regime asymptotically histogram histogram stop stop stop stop distinguish agreement publishers analyzed lies turns turns satisfied satisfied arc arc arc immediately immediately probable probable probable beginning beginning definite definite definite geometry geometry geometry geometry meaning nsf applies empirically offset backprop posed summarized weigend weigend fall gave gave gave replace wang wang wang wang progress proposition proposition proposition proposition proposition proposition phenomenon don don leen arguments pick pick purely outcome plays extending extending stated stated roles bourlard bourlard carry carry alspector james equals equals equals von von colorado histograms centroid 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define proc proc proc related related constraints constraints discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal equal equal equal equal equal approaches steps larger update update train train train train source version version represents bias graph ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai maps maps equivalent equivalent equivalent view solutions limit trajectory trajectory trajectory upper upper free free free free free free free free free free con condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition derived randomly criterion types product finally associative arbitrary denote complete stable stable proof proof proof proof proof proof theoretical including hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield 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information information information information information problem problem problem problem problem problem models models models models models models models models models models hidden hidden hidden based based based based based based based based based based based space layer case case case case case case shown systems systems systems systems systems values probability probability probability probability probability probability probability probability probability probability parameters unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach approach approach approach approach approach approach pattern point point point single single processing processing processing processing processing processing local local local local local local local local local local local local rate rate rate rate rate analysis optimal optimal inputs inputs inputs inputs inputs form form shows shows signal algorithms simple paper paper net net net work work work work step step step step step step step step step features features features features process current current trained trained trained problems similar architecture equation vectors vectors vectors general general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter approximation states states states theory theory theory theory theory gradient obtained obtained note note note experiments experiments experiments result result solution solution research log defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target dynamics initial initial initial initial table table estimate estimate estimate estimate estimate estimate standard standard standard computer computer terms terms science science left direction presented map map map low temporal maximum maximum maximum maximum maximum range press outputs outputs outputs continuous continuous continuous continuous abstract back back find find find convergence convergence convergence properties likelihood likelihood likelihood likelihood references due ieee ieee ieee procedure procedure procedure procedure procedure propagation context context introduction hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical statistical recurrent tion tion variable assume classifier word word word word word word word center center previous previous previous previous previous previous previous previous previous previous previous required required conditions conditions represent markov markov markov markov markov markov proposed length correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed forward forward forward minimum minimum ing computed computed computed multi sum mapping mapping optimization made global global global global global global global global global global applications em em em em em em original relative specific specific specific represented represented represented application application application desired cross cross series compute compute compute compute proc determined experimental goal related related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints connected gain equal approaches approaches approaches mit steps comparison support train nets nets nets nets modeling morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan morgan proceedings proceedings report institute institute institute words words consists consists advances advances represents represents represents connectionist connectionist connectionist connectionist difficult final scheme sequences sequences sequences sequences sequences sequences sequences framework cambridge equivalent additional estimates estimates estimates estimates estimates estimates estimates estimates transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition san conference conference conference determine determine efficient efficient full requires significant significant significant significant estimated estimated increase increase validation validation give condition derived conditional conditional conditional conditional conditional conditional conditional developed developed levels criterion lines entropy actual provided finally processes evidence evidence iteration iteration iteration iteration iteration iteration iteration nature sampling simply technical increases increases increases hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm corresponds corresponds corresponds complete finding generate journal instance instance kaufmann auditory probabilistic probabilistic typically pairs pairs pairs pairs combination account account fully mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp block testing testing testing testing database database database database database database principle language language language language details numbers numbers numbers iterations iterations pre pre making making window window international international frame combined minimize produced choose run sources light perceptron discussed recent recent reported side side sense recently sufficient volume tions smooth correspond correspond trans trans observation generalized generalized generalized improvement lead studied wide hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid touretzky touretzky boundary generally demonstrate row assumptions conclusions conclusions bayes practice mateo taking hard hard largest reduction labeled start decrease targets targets targets targets targets targets targets targets targets targets targets targets targets introduce introduce acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic index estimating transitions transitions transitions transitions transitions transitions ann ann multilayer involves remaining remaining easy consisting develop develop adding applying yield phoneme estimator estimator showed lee frames frames similarly suggested key earlier classical event boundaries valid sufficiently building perceptual combinations usa perceptrons formulation prove prove maximize maximize maximize gamma hmms hmms hmms hmms society computationally paths paths paths delta delta vowel composed composed summary prob follow duration duration duration list generalize realistic backward backward backward providing providing providing hypotheses maximization maximization maximization maximization maximization maximization maximization maximization maximization maximization maximization cat overlapping acknowledgments tesauro remain difficulty replaced accurately recursive recursive recursive recursive recursive recursive recursive discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant reducing links project int int office referred referred maximizing maximizing workshop naturally algo academic multivariate baseline baseline motivated sentences sentences sentences ment publishers guaranteed guaranteed capabilities glass glass baum perspective lin implementing berkeley berkeley berkeley purposes closer bengio bengio bengio bengio mation beginning incomplete alignment researchers double collected spoken spoken spoken spoken spoken lack rep requirement vocabulary summarized summarized phonemes acoustics acoustics acoustics chose windows viterbi viterbi utterances utterances leen feasible guarantee japan japan japan conditioned conditioned conditioned conditioned impossible impossible naval royal proceed rigid khz stated abilities utterance utterance belong bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard bourlard corpus corpus den chooses tic express insight refers likelihoods dempster dempster acknowledge posteriori posteriori posteriori posteriori posteriori posteriori posteriori posteriori posteriori street anns kluwer alternating legal nelson forced incrementally incrementally incrementally welch discriminative stands rithms num num num realizable graduate proba proba cole cole cole 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output output output number number number number number number system system system system error error error error error error error error error error results results results results results units units units units units units units units units units units units units units units units units units information information information information information information problem problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based based based based based weights weights weights weights layer layer layer layer layer layer layer layer case case case case case case case case case case case vector vector vector vector vector vector order order shown shown shown shown systems systems systems systems systems values values values values values values values values values values values values values values values values values values values values values values values values values values probability parameters parameters parameters parameters parameters parameters parameters weight unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition approach approach approach approach approach approach approach approach approach approach pattern pattern point point point processing processing processing processing processing large large neuron rate test test test test test test test patterns patterns patterns patterns analysis analysis class class class class class class class class matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples small feature feature net net net net net net net net work task step step step features features classification classification classification trained trained trained trained trained trained problems problems problems problems problems problems random random similar similar architecture architecture architecture architecture architecture architecture show show section section section section fixed fixed fixed fixed fixed fixed rule general general generalization parameter parameter parameter average average average gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained term note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments result result variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation computation computation computation found sequence sequence sequence sequence sequence sequence sequence sequence dynamics initial constant table table table estimate standard standard terms connections prediction left left left presented presented presented presented present phase low frequency machine machine machine machine sets sets maximum position components outputs outputs outputs outputs outputs outputs outputs abstract applied applied applied back back back back find find convergence density likelihood references component component due ieee ieee important adaptive propagation propagation propagation propagation propagation propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand hand hand hand behavior statistical effect generated cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change variable variable variable classifier prior prior word learned chosen chosen higher cases type required multiple multiple multiple represent expected expected expected proposed proposed proposed proposed length correct correct correct probabilities probabilities observed observed observed observed observed observed observed observed forward forward scale classes classes classes classes classes classes ing regression computed computed computed computed respect multi sum performed times times mapping means optimization made made feedback feedback feedback feedback feedback feedback feedback feedback em em em em obtain artificial specific represented compared compared compared desired desired provide compute perform experimental related connected discrete approaches approaches steps steps steps steps steps comparison morgan morgan morgan morgan morgan proceedings consists consists advances advances advances advances advances joint joint joint joint joint exp layers layers delay delay delay delay delay delay delay scheme scheme scheme scheme scheme scheme addition sequences sequences sequences maps considered framework computing experiment environment hinton hinton additional solutions solutions solutions trajectory san san san san san top conference full full full requires requires requires requires requires significant vision pages pages pages pages pages increase produce weighted randomly conditional conditional conditional clustering criterion criterion criterion types product finally depends covariance covariance feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward assumption complete complete stable stable stable finding implemented assumed generate generate require main main end end cluster kaufmann kaufmann kaufmann probabilistic typically account account dynamical jordan jordan jordan jordan jordan transfer significantly york special trials trials trials database database database squared squared numbers iterations international international bottom supervised supervised idea combined combined combined minimize minimize minimize run architectures architectures discussed advantage advantage advantage advantage advantage pair subset interest varying varying volume module module module module module module module yields converge generalized improvement occur extended deviation deviation matrices feed move hybrid hybrid hybrid touretzky loop loop half flow conclusion conclusion valued editors editors editors editors editors editors tangent tangent differences differences modules modules modules clear performs moody moody faster faster learns mateo mateo mateo mateo suggest propose propose propose taking taking taking taking largest assuming minimizing introduce groups boltzmann explicit produces sequential sequential sequential sequential sequential sequential sequential generating estimating estimating estimating estimating estimating stability dept dept changing modeled missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing averaging remaining scales scales scales develop frequencies frequencies frequencies frequencies gaussians gaussians gaussians gaussians implies expectation expectation yield squares evaluate updated evolution static static static static static static static static static static static static allowed slow delays delays delays normalization normalization normalization purpose purpose boundaries generation bell extension extension middle extra differ tdnn comparing essentially reached receives receives composed capture capture capture traditional traditional heuristic interested superior classify timing duration vary vary relaxation modular backward backward backward giles computes attempt preferred extract deal deal extend cowan cowan cowan bars simpler unlike diego transformed poor varied relations replaced replaced hanson hanson dotted preliminary discriminant discriminant discriminant periodic reducing reducing links links links links rest int dependencies dependencies dependencies dependencies scaled stream symbolic variability proved workshop removed attributes attributes waibel waibel gradients gradients gradients gradients possibly predicting predicting assumes precise initialized art epoch epoch epoch epoch simplest isolated percentage asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous publishers publishers coded coded handle reasons reasons inside producing preprocessing bengio bengio bengio bengio desirable simard simard recognized recognized gradually gradually attribute depicted depicted incomplete incomplete explained improvements amounts parameterized occurrence prevent specifies yielding ghahramani ghahramani ghahramani ghahramani ghahramani tresp tresp tresp tresp linearity optimizing databases databases lecun lecun exemplar exemplar clamped clamped kaufman kaufman replacing operates filled date alspector alspector performances financial financial financial periods encountered lang lang percepttons facilitate initialize initialize initialize initialize arrows reverse reverse explains explains ics uci uci yielded yielded numerous shorter ahmad ahmad ahmad ahmad super distinction propagating comparative comparative reports multinomial multinomial recurrence discovering avoids pub ftp labs rectangle statistic quinlan denver denver universit universit inverting page lippman bring tune normalizing pineda pineda completed lems fortunately handling handling tdnns tdnns hyperbolic hyperbolic decided ase firstly fill responsibility neuneier neuneier eral bottou bottou holmdel measurable cooperation economic daily frequent company periodically rectangles irvine zeros saturating capturing brought montreal montreal montreal montreal replaces degrade relax relax ular preprocessor miss graphically orig monthly wait subsampling encourage accepts collect collect supervision tot yoshua prototypical extractor partic almeida almeida concentrates sole sev unconditional unconditional unconditional relaxing relaxing relaxing 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algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number system system system system system system error results information information information information models models models models models models models models models models models models models models models models models models models models models hidden performance performance based based based space space space space space space space space space space space space space space space space space space space linear linear case vector shown systems systems systems systems systems systems systems values values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise functions functions unit unit distribution recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach approach approach approach approach approach approach approach approach approach point image image single single single single single single single single single single single processing processing local local local test test test test test test test analysis analysis analysis class class class class class class class form form shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian visual paper paper paper examples examples examples examples examples examples examples examples examples examples feature work task task task task task task task task task task methods methods methods points features classification classification classification classification classification classification classification classification classification classification classification process trained trained trained trained trained trained structure structure structure similar similar similar similar similar similar similar representation representation show show section section fixed fixed vectors images images general generalization speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation approximation average theory experiments experiments dimensional dimensional dimensional result university computation solution research research independent independent independent defined defined estimate computer terms distance distance presented presented map map map map map map present present present sets press press learn learn learn learn components components components components basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample abstract applied back back back back find computational density likelihood likelihood likelihood references stochastic stochastic stochastic stochastic propagation mixture mixture introduction complex hand estimation estimation estimation variance difference assume classifier classifier classifier classifier classifier classifier lower prior prior prior prior representations learned chosen chosen chosen chosen chosen higher center good represent represent represent represent bayesian bayesian markov techniques proposed correct correct correct errors scale ing ing tasks total total total human human regression respect performed performed mapping mapping mapping mapping mapping mapping mapping means means means means reinforcement optimization optimization dimension dimension dimension dimension dimension dimension dimension natural orientation global applications knowledge em em em em em samples samples samples represented true compared provide define define define objects perform determined determined determined posterior constraints distributions distributions approaches approaches approaches approaches approaches mit mit comparison comparison larger train train train train dependent morgan proceedings report report institute words words consists individual advances advances represents bias bias maps maps considered framework cambridge cambridge directly hinton san top top conference conference determine classifiers classifiers full full choice choice choice significant significant world vision estimated estimated estimated weighted conditional conditional clustering clustering clustering selected normal normal technical technical describe arbitrary group surface surface surface surface surface surface surface surface surface surface surface surface surface surface predictions predictions nearest assumed eds eds eds square square ability makes including fit fit fit fit fit fit fit fit fit fit fit kaufmann typically pairs underlying underlying underlying underlying combination account coefficients jordan jordan jordan jordan transfer transfer transfer significantly significantly character character projection projection projection projection projection projection projection projection projection projection operation principal principal principal principal principal principal representing representing call numbers international normalized experts experts supervised expert minimize choose improved improve improve pair separate separate separate separate separate takes similarity hierarchical dimensions dimensions sufficient compare compare teacher approximately approximately volume axis axis tions smooth speaker speaker speaker speaker speaker speaker speaker speaker speaker correspond sparse mixtures williams improvement entire rotation alternative alternative alternative alternative correctly touretzky loop loop boundary strength operator operator operator operator operator operator operator operator clear performs performs strong drawn drawn drawn drawn drawn radial plane manner manner acknowledgements explicit explicit explicit explicit digit monte construct carlo written winner primary label distinct recall implement explicitly physical text gaussians gaussians gaussians events expectation family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family family independently review overlap influence densities updated centers similarly converges partition discrimination additive convex fitting iterative boundaries interpolation classified avoid subspace subspace subspace subspace recognize recognize determines discuss maximize maximize maximize maximize priors coupled coupled coupled coupled neighbors neighbors discussions reason selecting selecting closely uniformly differ encoded identify detect literature projections mackay mackay vowel identity identity fine fine refer quickly kind repeated repeated induced classify sin sin manifold manifold manifold generative strategies sampled vary write paradigm paradigm highest maximization attempt consisted consisted approximating jacobs jacobs jacobs jacobs tesauro tesauro cowan situations simpler american collection exhibit exponentially hanson successive successive project applicable possibility root encode patch patch patch patch patch patch patch patch patch patch patch naturally naturally closest closest closest closest plausible equally recognizer thought algo initialized speakers speakers attempts defines percentage slowly cos cos distinguish publishers improves independence worse nonlinearity sections mation probable pitch toronto patches patches patches patches patches patches patches patches patches auto outer varies applies affine affine affine affine affine affine affine affine 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omohundro omohundro omohundro omohundro omohundro omohundro omohundro omohundro assigns smoothly comparative covariances classifies imagine examining param exam exam schmidhuber schmidhuber ocr searches interacting considers proach meta alternatives alternatives alternatives confusion tij tij tij universit mimic eters struc nec nec learners chris parameterization parameterization parameterization stephen font font font australian influenced trainable send families families ferent agents eliminates episodes episodes episodes episodes episodes episodes episodes episodes episodes episodes episodes episodes episodes episodes gram bregler bregler bregler bregler bregler bregler bregler ples ples pratt pratt lying baxter baxter baxter occam ignores ignores rivest unlabelled unlabelled unlabelled unlabelled informatik merged tical segmenting episode episode episode episode episode episode episode episode episode episode episode episode episode episode episode episode ensuring revow revow 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#*learning model neural data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set training training training training training training number number error error results results results results information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance based based based space space space space space space space space space space linear linear linear linear linear linear linear linear case case vector order values noise noise noise noise noise distribution recognition recognition method method method method approach approach approach approach approach approach approach pattern pattern pattern point point point point point point image image image image image local local local local local local local local local local local local local local local local local local local local local local rate rate test test test test analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix optimal optimal form form form shows shows shows shows shows shows simple simple simple gaussian gaussian examples examples examples small small small size fig points points points points points features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification high memory response similar show show show section section line line rule rule images images images images parameter parameter real real average average average average average average theory theory experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university variables variables research research defined found found found target target target constant constant constant estimate estimate estimate estimate estimate estimate standard distance distance distance distance left left left left left left direction direction direction map machine components components components abstract find find references component component ieee ieee ieee procedure procedure procedure procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision mixture mixture introduction action hand hand statistical statistical effect parallel parallel change variable classifier classifier lower lower lower lower lower rules measure measure prior cases long conditions techniques techniques techniques techniques techniques region region region proposed proposed correlation correct correct probabilities probabilities probabilities finite simulations resulting classes classes classes classes classes classes classes regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression computed computed respect multi sum sum sum sum called means means dimension dimension dimension dimension dimension dimension dimension global global global global global original artificial relative relative samples true true true true series compute rates proc proc perform perform perform determined determined determined goal goal goal posterior posterior distributions support source report department department department version version technique technique technique technique kernel kernel represents represents represents final bias bias addition addition computing computing computing equivalent curve curve limit top top determine determine statistics statistics statistics statistics free condition weighted weighted weighted weighted weighted weighted conditional conditional area types types lines lines actual provided discussion covariance covariance covariance covariance covariance covariance technical technical describe describe denote denote denote close close close close inverse inverse assumption corresponds surface short short short short short nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest common effective shape supported supported supported require eds journal pixel pixel pixel pixel instance future fit simulated simulated typically typically typically reduced projection edge principal principal principal details max making making polynomial idea produced produced produced predict denotes directions directions directions directions directions advantage robust strategy pixels pixels relevant interest dimensions dimensions dimensions dimensions observations observations observations approximately works tuning trans diagonal modified observation interval grant horizontal extended extended extended matrices matrices matrices predicted locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally boundary boundary boundary boundary boundary boundary setting segment neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor bayes designed asymptotic propose propose propose reduction reduction reduction reduction california solid solid intelligence variety reference appears longer winner ann label vertical vertical vertical distinct metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric coordinates averaging dimensionality dimensionality spectral spectral spectral spectral spectral spectral spectral gaussians national squares squares squares squares overlap centered decomposition decomposition suggested discrimination discrimination spectrum spectrum calculation smoothing dashed performing measurements neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood intervals boundaries boundaries boundaries distances distances distances visible query classified classified transactions avoid expect coordinate coordinate eigenvalues eigenvalues eigenvalues subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace candidate neighbors neighbors neighbors neighbors neighbors neighbors discussions middle middle middle extra society differ included situation situation situation plots orthogonal orthogonal conf procedures procedures procedures procedures prob link symmetry symmetry lie classify classify classify classify notation dot nips predictor predictor illustrates extract extract extend situations situations situations employed american detail recursive hall discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant giving project int authors authors eigenvectors cover cover surfaces closest adapt adapt illustrate rank friedman friedman friedman versions obvious panel panel panel panel panel panel panel panel panel panel panel panel taylor taylor separated consist consist arbitrarily cart band band band band convolution briefly lies correction tool worse inside stanford stanford stanford stanford sections style hyperplane acknowledgement recognized toronto toronto bandwidth demonstrates radius radius nsf apparent flexible flexible amounts amounts quantitative red red red red red frequently compares partitioning spread differs popular marginal green deviations deviations ordinary restrict narrow lvq recover null null null null circular grows grey grey grey wrong overcome abilities bands bands bands effectiveness combines sion predictors sphere sphere sphere sphere sphere sphere sphere sphere spherical spherical spherical spherical centroid centroid centroid centroid similarities entries iterated membership membership refers refers refers canada extends hart hart insensitive robert robert severe metrics outperforms ure land land land annals fellowship misclassification tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani generalizations rectangular concentrated hastie hastie hastie hastie hastie hastie hastie met argued projecting intensities spanned spanned sized lda lda lda lda lda lda lda lda eigen eigen port subspaces subspaces subspaces infinitely infinitely infinitely behaves council curse curse neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods suffers adaptively eral supplied appealing proportions proposal meeting proposes coincide classi classi lying tended complement complement frequent sions dimen dimen pooling fication fication appro scatter cleveland cleveland cleveland inform satellite satellite modest terminology routine severely neigh neigh neigh pooled pooled centroids centroids centroids centroids centroids centroids centroids centroids centroids claims favorable favorable shrink shrink iter deformed deformed panels panels panels ending unstructured neighbour neighbour cancellation expects beats trevor trevor trevor elongated resort concentrates hurt spheres spheres spheres illustrative compactly encouraged inn strip strip strip michie michie michie inspiration joining bor bor ric knowl spiegelhalter sphering shrinks crucially memberships pursue archive 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#*model model model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time set set set set algorithm algorithm algorithm number number number number number number number number system system system system system system system system state state results results results results information problem problem problem problem problem problem models based space space space case case vector order order order order order shown systems values values values values values probability probability probability probability probability probability parameters parameters distribution distribution recognition method method method method method method method method method method method method method method approach approach pattern point point point point point point point point point point point single large large large local local local local local local local local local local patterns analysis analysis shows shows algorithms algorithms small size size size size size size size size size work work work work methods methods methods methods methods methods methods fig fig step points points points points points points points points points points points points points points points points points points points points points points points points points points points points field field field features classification classification process structure structure structure problems problems high high high high high high high high high high similar similar similar show show equation line line line rule real average average average average average average average states states theory theory obtained obtained obtained obtained obtained obtained note note dimensional threshold threshold threshold threshold computation research independent independent log defined defined defined defined defined defined found dynamics initial initial initial estimate estimate estimate standard computer terms distance distance distance distance distance distance science science science presented presented presented present present present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low low frequency range range range range range range range range range range press sample abstract applied find density density density density density density density analog analog properties properties properties properties properties references due ieee ieee procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important complex hand hand behavior statistical statistical statistical statistical statistical statistical effect generated generated variance variance variance tion tion tion tion energy energy complexity variable variable assume assume lower measure measure chosen chosen higher center bound good long conditions conditions conditions distributed techniques region region proposed proposed proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length length correct probabilities observed observed scale scale finite simulations classes classes ing called called times regions regions regions regions regions regions regions regions regions regions optimization optimization optimization optimization made made natural natural natural global study knowledge obtain represented represented compared desired provide provide provide define perform determined determined goal related connected equal approaches approaches approaches steps steps steps larger larger larger contrast connection support institute department technique consists represents exp addition domain curve transition transition transition transition transition transition transition transition transition stage determine efficient efficient upper choice choice choice choice statistics estimated estimated randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering criterion criterion criterion path provided processes depends discussion discussion increases increases group group group denote close close close assumption stable stable short short nearest nearest common assumed supported supported main main main main cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster including pairs pairs pairs pairs smaller smaller smaller smaller smaller structures structures uniform max idea idea minimize choose choose denotes improved recent property typical typical similarity apply side hierarchical sense recently engineering interest previously calculated works solve correspond correspond converge trans trans sparse definition definition definition background background symmetric sensitive sensitive parts occur occur wide clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters occurs occurs occurs runs strength strength strength strength starting critical critical critical place place depend interactions interactions practice weak constrained temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature strong hard hard hard physics physics physics physics largest largest largest largest largest largest largest largest solid solid proportional variety min plane introduce groups groups groups groups minima configuration configuration denoted relation monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo index solving mathematical distinct metric simultaneously simultaneously averaging physical physical physical physical consisting consisting interaction interaction interaction interaction interaction interaction interaction interaction mutual mutual mutual equilibrium formed decreases yield choosing choosing national expressed correlated squares squares estimator overlap viewed influence sizes completely completely suggested partition partition diagram diagram diagram calculation slow dashed normalization neighborhood neighborhood neighborhood roughly intermediate intermediate distances calculate calculate assigned assigned foundation foundation classified inter inter determines discuss domains holds phys neighbors neighbors neighbors neighbors neighbors neighbors neighbors discussions reason identified identified identified efficiency closely uniformly suitable suitable maximal maximal divided divided divided divided identify identify identify identify identify identify identify build composed strongly strongly contained notation quantity relaxation relaxation quantization thresholds neighboring neighboring neighboring neighboring acknowledgments minimized parametric parametric parametric parametric parametric parametric powerful exhibit difficulty strengths existence rest func understand phases notion naturally configurations analyze analyze extremely rev quantities quantities quantities separated separated academic defines averages years spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin spin site site costs distinguish agreement agreement defining phenomena explanation adapted answer answer lies drive sites division division scientific fluctuations fluctuations fluctuations explained fourth pseudo tional peaks introducing marked marked incorporated formulated ity ity exhibits exhibits summarized mod ture spread aim ordered ordered serve collective collective enables germany chose chose chose conclude yuille yuille tile tile tile tile tile wang wang wang wang progress aligned aligned aligned aligned aligned aligned aligned identifying identifying assign assign formally ordering ordering ordering ordering ordering connecting connecting dealing convenient analogy analogy analogy analogy analogy analogy stated ral belong belong belong generalizes weakly governed ensures negligible decide pat regarded bad israel israel israel iterated belonging belonging belonging inf insensitive thresholding thresholding thresholding assigning dense temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures temperatures yielded appeared leaving super super super super super super super super super super super super super formulate magnetic decomposed affects associate stands stands reflected param rectangular rectangular distri pami thermodynamic thermodynamic thermodynamic life jij jij jij intra crosses rectangle careful flip deleted buhmann buhmann anal descending supports sweeps stuck vanishes vanishes vanishes dramatic exploratory rose rose vice bution utilizing advantageous versa opti thermal thermal autocorrelation identifies terns stochastically locate utilizes hoc spins spins spins spins spins spins spins spins spins spins spins spins spins spins spins spins spins drawing concrete triangles triangles bond fox fox hamiltonian hamiltonian hamiltonian rectangles rectangles rectangles terminates raised metropolis metropolis mach vanishing vanishing vanishing vanishing physica potts potts potts potts potts potts potts potts potts potts potts potts potts potts potts potts potts potts potts potts potts potts metastable metastable iris locating frozen frozen frozen delete kanter lowered lowered mal bonds bonds bonds bonds thumb intel deduce clus mag optimiza ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic accord flips idealized mere domany domany domany domany sharper suc manifest plied rooted walls freeze sudden interacts nij nij nij disordered flipping manifested eytan kosowsky kosowsky interac inhomogeneous crease propor transi tering derlying spectively fukunaga fukunaga fukunaga fukunaga gurewitz gurewitz weizmann biggest landsat imization disciplines ature ature rehovot pletely alg sharpness patt temper temper lexp natu pear tempera bsf ish tma shai 
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time set set set networks networks networks networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number error error error error error error error error error error error results results results results results results results results results results results results results results results information information problem problem problem problem problem problem models models models models performance based based based based based based based based based based based based based space linear linear linear linear linear layer case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown shown shown shown shown systems values values values values values weight recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method pattern pattern single processing large large local rate rate rate rate rate rate rate rate test test patterns analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class class optimal optimal shows shows shows shows shows shows shows shows algorithms algorithms algorithms simple simple paper paper small small feature work methods methods methods methods fig fig fig fig features classification classification classification high memory show show show section section line line line line line line rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors generalization generalization generalization parameter parameter states obtained obtained obtained obtained obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional result university research research defined defined defined defined defined defined defined initial initial initial initial initial constant table table distance distance distance distance distance distance low learn position position abstract applied back back convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references ieee ieee positive decision decision decision decision decision decision decision propagation propagation introduction cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost difference difference assume previous previous multiple good long represent proposed proposed proposed proposed minimum minimum classes classes classes ing total multi multi factor factor factor orientation study obtain obtain obtain obtain negative vol vol vol vol artificial relative compared compared compared compared rates rates proc proc proc proc proc location determined determined determined experimental experimental experimental experimental experimental experimental experimental experimental distributions distributions gain gain gain discrete update support support descent descent descent descent descent words words version version version joint difficult scheme sequences considered considered framework domain experiment design limit conference conference conference conference condition condition condition condition condition condition condition condition condition condition condition condition condition derived derived clustering criterion criterion criterion iteration iteration depends depends depends depends depends associative discussion discussion discussion discussion increases increases denote fast nearest nearest nearest nearest effective effective effective effective effective generate main ability ability ability ability ability ability ability ability ability ability ability simulated technology technology mlp programming ratio character character character character character character character character character character increasing increasing matching matching matching squared call call window window window window international international international international international supervised idea attention combined minimize minimize minimize minimize run perceptron improved improved improved improved improved discussed improve property property property recently conventional conventional conventional unsupervised converge converge converge converge trans trans definition definition definition definition definition modified generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized organization increased correctly width boundary boundary boundary boundary half half conclusion starting greater depend competitive sigmoid bayes bayes bayes peak peak propose propose propose minimizing minimizing minimizing min decrease decrease decrease decrease derivatives characters characters characters characters minima program annealing force force acknowledgements reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference reference digit written written laboratory simultaneously averaging linearly linearly equilibrium applying springer extraction focus review restricted updated updated updated updated updated updated updated organizing showed lee lee earlier earlier earlier calculation normalization boundaries boundaries boundaries boundaries remains remains remains remains distances assigned assigned assigned assigned assigned assigned kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen classified classified template template handwritten handwritten includes includes prove prove discuss discuss discuss refer verlag kind cun cun superior superior satisfy satisfy satisfy satisfy minimizes minimizes quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization denker approximating approximating satisfies satisfies satisfies law carried carried carried layered essential essential updating updating updating divergence divergence divergence preliminary preliminary preliminary helpful examine ideal ideal ideal ideal proved affect affect extremely ensure ensure quantities quantities noted noted algo improving improving improving improving improving mentioned separable separable defining correction satisfied forces forces forces forces forces commonly laboratories beginning gradually gradually meaning meaning requiring limits limits formulated formulated howard fall song song kinds decreased decreased owl owl lot shifted japan linearity linearity linearity linearity lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq lvq printed printed printed printed printed printed printed ranges mail attractive attractive attractive attractive attractive attractive belong belong belong belong monotonically 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#*learning learning neural input input input input input input data data data data function function function function function function function function function function function function time time time time time time time time time set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number number number number number number number state state state state state state state state state results results results results results results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance based based based based based based space space space space space space space case case case order order order systems systems probability probability probability functions functions functions distribution method method method method method method method approach approach approach approach approach point point single single single single processing processing processing large local local test test analysis analysis class class optimal optimal inputs inputs inputs inputs inputs inputs inputs form form form form form form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper paper paper paper paper paper small size size work task task task task task task task task task task methods methods step step process process current current current current current current structure structure structure structure structure problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random random random random random random random random random random random random random random random random random high high high high similar representation section section section fixed fixed fixed general general parameter average average average average average states obtained obtained obtained obtained term note experiments experiments experiments university university university variables variables solution solution solution research found found found found found found initial initial table table table table standard standard standard standard standard computer computer computer node node node node node node node node node node science left left direction presented presented presented presented present present phase phase low low low low nodes nodes machine machine machine machine machine machine machine sets maximum maximum range press position position position position position position position position position outputs abstract applied applied applied applied applied find find find computational references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic important adaptive introduction hand hand behavior dynamic generated variance search search search search change variable variable variable lower chosen chosen chosen chosen chosen chosen chosen higher part previous previous bound cases cases cases required required required required required required good good binary long tree tree tree tree tree tree tree expected make techniques proposed proposed proposed length length correct correct correct correct correct correct correct correct correct minimum minimum resulting tasks tasks tasks tasks total computed computed multi performed performed performed performed performed performed called means optimization optimization optimization optimization optimization optimization optimization natural natural study obtain obtain obtain specific specific specific specific true application application series rates perform determined experimental goal constraints discrete mit comparison comparison selection selection selection selection selection selection report words department department implementation version version version version technique individual advances connectionist difficult difficult bias scheme scheme graph ai ai ai ai ai ai considered cambridge computing equivalent experiment experiment additional view solutions solutions solutions solutions design design design transition transition top bit bit full full full full full choice approximate statistics world basic basic pages pages pages pages pages give give randomly developed provided provided selected selected iteration iteration iteration iteration nature depends biological achieved achieved achieved technical increases arbitrary group corresponds complete complete complete complete complete proof finding common generate generate generate supported role require require journal instance instance instance instance instance instance makes development including fit objective simulated simulated probabilistic pairs pairs programming programming programming interesting increasing structures structures trials operation operation operation operation details details details details details iterations iterations iterations pre direct making making bits bottom idea description light population population population population population population improve recent recent pair takes strategy moving moving subject identical identical machines machines hierarchical hierarchical interest highly compare compare compare compare conventional solve yields yields yields yields correspond correspond studies achieve achieve achieve address address address address address address address evaluation evaluation evaluation evaluation grant expression expression expression expression expression expression expression expression expression expression expression lead suggests deviation deviation wide move move generally demonstrate runs runs runs runs runs conclusion reduce operator operator operator operator operator operator operator neighbor neighbor neighbor depend competitive editors editors editors editors designed peak performs performs performs performs practice practice encoding encoding encoding encoding encoding hard hard characteristics drawn drawn california california user minima program program program program program program program annealing annealing appears construct construct index solving solving label label label label label mathematical distinct changing infinite involves involves involves involves easy easy slightly text unique consisting develop shift boolean boolean boolean boolean select john independently stages solved detailed evaluated open labels fraction fraction similarly similarly reduces neighborhood neighborhood purpose add generation string string string assigned box box includes includes thesis formulation formulation color color color color color instances instances assignment maximize black black neighbors simplicity selecting closely uniformly uniformly uniformly uniformly uniformly uniformly uniformly uniformly uniformly uniformly uniformly uniformly uniformly uniformly uniformly suitable differ encoded effectively literature schemes genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic refer kind repeated decoding prob prob prob success interpreted superior superior issue running sci list list involved usual play paradigm paradigm processors attempt attempt neighboring deal deal tesauro minimized employed simpler schedule schedule schedule schedule schedule schedule wiley create collection investigate investigate hall successive referred decisions root comparable symbolic encode encode phases removed hill hill hill hill math plausible plausible plausible editor adapt integer integer illustrate versions obvious portion observe observe observe expressions expressions expressions expressions expressions academic initialized initialized baseline baseline baseline baseline baseline baseline phd finds attempts chaotic defines optimum years years great great ment formula publishers adjacent explanation majority benchmark processed berkeley berkeley berkeley berkeley berkeley berkeley widely division operators operators operators operators operators operators operators operators operators operators operators leaves leaves mathematics pool cut potentially involve members read computers nsf addressed researchers improvements improvements improvements evaluating evaluating evaluating evaluating evaluating evaluating applies applies freeman substantially substantially understood tional employ remove formulated formulated treated variant compares execution execution http operate aim aim substantial replace replace chose chose sophisticated specifies wesley yielding shifted shifted www addison martin ordering ordering ordering circular children children climbing climbing climbing climbing climbing allocation promising mail mail imposed height hope obtaining mark imply effectiveness effectiveness effectiveness combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial wilson selects heuristics exploring alspector evaluations evaluations evaluations evaluations evaluations evaluations prentice document programs programs programs programs representational corre corre entry encountered holland regarded moved moved moved moved regard ascent scheduling scheduling scheduling scheduling scheduling counting offers chooses chooses treatment specialized permutation permutation permutation insight reader offer shortest fitness fitness fitness fitness fitness fitness fitness fitness fitness repeatedly vertex steepest sons davis papers inf material material material integers johnson lem lem constitute listed outperform kluwer ram randomized job job job job job job job job job job job job formulate employs comparative chapter constitutes constitutes constitutes stands gene modifying shifting shifting community community formance insights crossover crossover crossover crossover crossover crossover gas gas gas gas gas gas gas gas gas gas maintained execute elementary mitchell searches challenging landscape landscape increasingly records conversely tively investigations behave retained strict completed lems heading replacement replacement replacement replacement replacement replacement replacement sponding suite puts loosely industrial ackley partly goldberg goldberg markers markers markers markers markers markers markers markers symmetrical evolutionary evolutionary accommodate colors binomial remained shop shop shop tained mutation mutation mutation mutation mutation mutation enabling addi subtree subtree lisp lisp marker marker marker marker marker marker marker marker marker marker neigh neigh aims omit iris remarkably permutations undirected sition respects internally web comprises scheduled scheduled scheduled scheduled scheduled ross forrest forrest seeking thompson reilly occupied occupied hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing hillclimbing respec picks experimentation seeks earliest earliest michigan exposition xlo eval encouraged encouraged multiplexer multiplexer multiplexer multiplexer multiplexer multiplexer multiplexer sponds entails articles plications designer targeting subsequence operands operands operands operands operands operands 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#*network network learning learning neural neural neural input input input input input input data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure time time networks networks algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output results results results results results results units information information information information information information information information information information information information problem problem problem hidden hidden based space linear linear linear linear linear linear linear layer layer case case case case case case case case order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown values values values values probability probability parameters parameters parameters noise noise noise noise noise noise noise functions functions functions functions functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach point single single single single single single single single single large large analysis analysis analysis analysis analysis analysis analysis analysis analysis class class matrix form shows shows signal signal signal signal signal signal simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper small size work task task task task methods methods points points points points points features features features trained trained structure structure structure problems problems problems random representation representation representation representation representation show equation equation equation equation equation section fixed line line line line vectors general general general general general approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory gradient gradient obtained obtained note note note experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional result result variables computation research independent independent independent independent independent independent independent independent defined defined found constant table table estimate estimate estimate standard terms terms terms terms terms terms left left left left presented presented map map map map map map map map map map map present activation low basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous abstract applied find find computational computational computational computational references component component component component component component component component component component stochastic stochastic positive procedure important important introduction complex estimation estimation estimation statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical variance variance parallel parallel recurrent tion complexity complexity complexity complexity variable measure measure measure measure signals signals signals chosen higher higher higher higher higher higher higher higher higher higher higher higher higher center center center previous previous bound bound bound bound bound cases required multiple good represent represent distributed distributed distributed distributed equations fact fact fact techniques techniques proposed proposed proposed proposed proposed correlation correct correct correct observed observed forward forward minimum total computed computed respect multi multi multi multi eq elements optimization optimization optimization optimization orientation applications obtain obtain obtain negative vol specific represented compared compared compared series series provide define goal distributions distributions distributions distributions distributions distributions distributions distributions distributions update dependent dependent version technique technique technique individual individual represents maps maps maps maps maps considered equivalent experiment additional limit efficient upper upper upper upper upper statistics statistics statistics statistics statistics statistics statistics statistics free criterion criterion criterion criterion criterion criterion criterion criterion criterion lines lines entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy finally processes sampling measured measured measured measured covariance feedforward increases arbitrary arbitrary arbitrary transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation limited limited stable finding finding finding finding theoretical theoretical require square square including including coefficients interesting york uniform uniform uniform uniform uniform uniform uniform uniform principle principle leads leads leads leads leads principal squared squared squared numbers decay minimize minimize added perceptron directions directions directions correlations include quadratic unsupervised calculated volume volume volume volume volume volume volume volume volume volume volume volume match pca pca pca pca pca diagonal definition definition definition definition definition symmetric symmetric increased expression expression suggests rotation rotation correctly correctly feed feed width setting demonstrate minimal minimal row depend measures accurate exponential exponential exponential exponential exponential practice suggest suggest suggest suggest propose reduction reduction solid solid labeled turn minimizing ica introduce explicit explicit explicit explicit explicit explicit pro edges solving ways estimating estimating recall coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates linearly physical transformations transformations transformations transformations transformations transformations transformations transformations transformations text text angle mutual mutual mutual mutual mutual mutual mutual gaussians minimization minimization minimization minimization implies extraction select extracted expressed expressed expressed dependence review correlated transform restricted restricted approximations approximations evolution approximated approximated similarly partition partition key calculation dashed dashed additive additive additive measurements expansion expansion expansion expansion expansion expansion reduces intervals intervals purpose includes includes coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate holds capable divided detect computations tend road dis criteria sampled sampled sampled sampled sampled sampled usual relaxation leading extract transformed transformed transformed difficulty relations accurately scalar scalar scalar scalar scalar scalar reliable statistically hill measurement measurement measurement necessarily noted expressions generates arbitrarily submitted submitted finds finds defines averages advanced crucial variances variances improves analytic expensive independence independence independence correction correction london london turns lin strictly angles implicit implicit mechanics explained explained explained explained fourth fourth fourth varies considerably applies substantially substantially empirically axes parameterized polynomials measuring measuring measuring kinds redundancy deviations corrupted college ear accomplished summing princeton linearity linearity rotated rotated approximates partitions fails overcome siemens siemens multiplicative transforms fail moments moments moments guarantees dependency sim counting tic tic foundations matter papers alternatively limitation approx approx truncated logarithm logarithm logarithm solves basically validity preserving expanding avoided decorrelation decorrelation factorial factorial cessing distribu concentrate statistic statistic statistic discusses tively corrections simplifies simplifies gauss gauss expansions consuming const const corporate satisfactory east reversible orthonormal suffices reflecting reflecting unreliable proposes extracts repetition measurable restricting lnp triangular triangular triangular company company falling factorization factorization factorization factorization sian edition edition mcgraw gaus charles dent indepen fore tails addi noiseless hip hip hip publishing entropies entropies entropies entropies entropies entropies entropies entropies entropies inserted sixth comon comon comon comon comon comon comon parra parra parra parra parra parra parra parra parra parra parra imation ply tics statis cummings nonlinearly fac deco deco deco deco deco deco deco deco ordinate tributed conserving conserving conserving conserving conserving conserving conserving conserving conserving conserving conserving formalized stuart stuart cumulant abscissa expands rli factoffal factoffal realizing mat cumulants cumulants cumulants cumulants cumulants overcoming app variate accomplishes reads cutting conservation conservation tackled facto papoulis papoulis lln griffin truncating truncating lna unnikrishnan unnikrishnan lucas lucas equidistant kendall kendall benjamin rial abraham abraham scr mite 
#@Parra_L,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data data data data data data data data data data function figure set set set networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number results results results results results information information information information information information information information information information information information problem problem problem problem models models models models models models models models models models models models models models models models models models models models hidden based based space space space space linear case case case case case case case case case case case case case case case case case case vector order shown shown shown shown shown shown probability distribution recognition recognition pattern pattern pattern single single single single single single single single single single single single processing processing processing processing large local patterns analysis analysis form signal signal algorithms algorithms algorithms gaussian gaussian gaussian paper paper paper paper paper net net net net net net net net net net work work task task methods fig step step problems similar similar similar representation representation representation representation representation representation section section section fixed general general real real real theory theory theory obtained obtained note experiments university university computation computation computation computation independent log log log log log log defined defined defined initial table table table table table table table table table table table table table table table table table table table table table estimate estimate estimate estimate estimate estimate computer science science map present temporal temporal temporal machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum learn components components components basis abstract back back density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component ieee ieee ieee ieee procedure procedure procedure adaptive propagation mixture introduction cost cost tion signals representations representations representations representations representations representations representations representations representations representations representations part part part part part part part part previous cases cases cases cases cases type type type type good good binary binary binary bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov fact proposed proposed proposed proposed correct errors minimum minimum minimum minimum minimum minimum ing ing multi multi eq eq eq eq eq eq called called called called mapping potential dimension made made study em em em em em em em em em em em obtain obtain negative vol vol vol vol vol vol vol true cross provide provide proc proc proc proc proc proc proc proc related related steps comparison larger larger larger update update modeling modeling modeling modeling selection consists consists code code advances advances joint joint joint joint joint joint scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme addition considered framework framework equivalent equivalent equivalent equivalent equivalent hinton hinton hinton hinton hinton hinton hinton hinton hinton view capacity statistics free free free free free free free condition condition channel channel coding coding clustering clustering clustering clustering clustering developed developed criterion types types entropy entropy entropy entropy entropy entropy entropy finally finally finally iteration tested hmm inverse implemented implemented supported square square square cluster cluster including pairs pairs needed combination fully jordan special special special special special special consistent matching uniform uniform empirical leads call call max max max max max max max max max max max max max max max max max max max max window window bits bits bits supervised supervised supervised supervised supervised supervised description recent pair pair pair pair robust include sejnowski sejnowski sejnowski recently unsupervised unsupervised unsupervised unsupervised unsupervised approximately works tions smooth match pca pca pca studies converge trans mixtures mixtures entire grant parts parts lead lead studied extended alternative alternative clusters clusters competitive clear performs performs suggest turn min min min min min min min min min min min min min min min min min min min min iii denoted acknowledgements pro produces perception solving solving generating estimating describes mathematical dept changing implement implement develop mutual minimization minimization minimization minimization select letters national family family focus focus focus depending depending depending detailed densities open open organizing forms understanding similarly similarly suggested classical classical classical classical spaces reduces reduces reduces fitting fitting fitting fitting fitting purpose remains existing existing existing existing existing existing existing existing existing existing existing includes includes includes combinations combinations bell bell bell subspace automatic major major reason columns determining selecting selecting closely society literature conf conf conf criteria criteria dayan dayan dayan backward nips minimizes quantization correspondence maximization maximization attempt extend body body parametric parametric parametric parametric parametric parametric put replaced replaced divergence divergence divergence dual ml ml ml ml ml matches incremental relationships understand act transmission changed precise explored separated consist amari amari amari amari amari amari amari mixed mixed neal neal neal mentioned mentioned separable separable separable starts perspective lin lin sections producing producing producing day day choices choices choices choices desirable desirable desirable mathematics circle linsker linsker linsker auto auto geometry geometry geometry geometry geometry geometry argument fourth items experimentally effort summarized popular resource resource extensions replace replace logp age irrelevant gap lab equivalence fix fix fix fix fix fix fix fix fix fix fix fix acts zemel zemel zemel encoder encoder royal kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback fits replacing replacing shifts ylx ylx ylx ylx ylx ylx repeat repeat repeat repeat repeat repeat repeat repeat repeat repeat male male pat searching yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang yang counter bases bases eqs broken broken broken broken variants variants variants variants variants variants variants variants papers explains dempster dempster interestingly treat unified unified unified unified unified unified unified unified unified unified unified unified unified rubin helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz annals transmitted dec discriminative discriminative discriminative discriminative discriminative discriminative causing acceptable arg arg mdl mdl mdl female forcing stands stands stands stands stands representa summarizes summarizes concentrated concentrated deep parzen parzen oct oct argued guided laird inversely confusion confusion intl intl intl intl preprint xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly ation ation status status status status status status status status mix fortunately terns autoencoder formulae formulae atick atick preservation preservation preservation preservation ham seed seed siu complement complement complement complement gence shortly shortly inform inform talk talk decades kong unifying mum ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying ying nov nov hong redlich redlich counterparts counterparts ily missed sults icnn icnn equiv equiv chinese chinese useless useless estima conducting yix occupy occupy portland tab tab tab tab pervised heuristically hin hin hin hin philosophy discussing vances undefined maxa maxa maxa unsu ylz divergences factorim factorim mina mina mina dem dem alent invited invited invited invited ual ati ati lent submanifold submanifold lei dxdy escaping deeply transferring unused escapes escapes limn clarified probabihty aft iconip fies baysian baysian diver feat deserve sequent unifies 
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm output output output output output output output output number number number system system system system system system system system error error error error error error error error error state state results results results results units units units units units units units units units units units information problem problem problem problem problem problem problem problem problem hidden space space weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer case case case case case order order order order order order shown shown systems systems systems systems parameters parameters parameters parameters parameters parameters parameters parameters weight functions functions functions functions functions functions neurons neurons unit unit unit unit unit method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern point point point point point point single control control control control control control control control control control large large large local test matrix form form form form form form form shows simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple examples examples small small small small small small small size size net work task methods fig points points points points features classification process process process level level level level level level level level level level level trained structure structure problems problems random random high high high high high high high high similar similar similar representation representation representation representation representation architecture architecture architecture architecture show show show show show show section fixed fixed fixed fixed line general general general general general general generalization real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained note note activity activity dimensional result result result variables independent defined sequence sequence sequence target target target target target target dynamics dynamics initial initial initial constant constant terms terms distance connections connections connections connections connections synaptic synaptic present phase frequency frequency frequency frequency frequency range range learn learn learn components continuous continuous continuous continuous continuous continuous abstract applied applied back back find find find convergence properties properties properties properties references component component due ieee ieee propagation mixture mixture introduction introduction action complex complex complex complex complex complex complex complex circuit circuit circuit dynamic recurrent recurrent recurrent recurrent recurrent tion complexity assume measure measure measure measure learned higher higher part part previous previous theorem theorem theorem theorem cases type required multiple binary represent tree expected equations equations fact fact fact fact forward forward forward forward forward scale finite finite finite finite finite minimum classes ing tasks regression regression respect sum eq eq eq eq eq times times optimization made natural natural natural global applications artificial artificial specific specific represented represented true true compared desired series series provide rates gain gain gain gain gain gain motor equal equal equal equal equal approaches approaches approaches contrast support descent descent descent descent descent descent descent descent descent descent descent descent proceedings institute institute implementation consists internal joint connectionist difficult final final final layers layers considered curve curve curve additional design design limit limit limit limit limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory effects conference conference determine requires requires basic basic pages pages produce derived product provided finally iteration inhibitory biological biological biological feedforward arbitrary arbitrary arbitrary fast fast limited limited close inverse assumption assumption stable proof circuits circuits circuits short short common common implemented supported require square end instance instance instance instance instance instance instance instance instance instance easily degree fit needed needed combination combination dynamical dynamical dynamical dynamical dynamical dynamical coefficients coefficients coefficients coefficients fully fully fully technology technology transfer interesting uniform principle leads leads numbers numbers pre international international experts experts depth polynomial polynomial idea choose architectures architectures discussed exact pair typical typical strategy period period period period period period period period period period hierarchical hierarchical hierarchical hierarchical sense sense sense relevant varying calculated volume volume works module module module tions smooth smooth match converge differential achieve sparse sparse symmetric observation bounded bounded bounded bounded gate interval interval interval organization organization constructed constructed constructed lead occur extended extended extended trial derivative feed feed feed feed feed width loop white white generally generally hardware flow flow conclusion starting row greater greater reduce trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories central modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules clear clear suggest suggest suggest external cycle sigmoidal california california turn turn turn exist exist exist plane plane iii configuration explicit written solving ways ways ways laboratory stability distinct distinct multilayer infinite infinite remaining slightly slightly slightly slightly unique unique scales consisting consisting interaction frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies implies blocks cycles cycles cycles cycles yield independently review review depending overlap solved transform open open open fraction fraction approximations evolution decomposition decomposition soft approximated approximated approximated approximated activities completely suggested converges constants allowed allowed spectrum reasonable slow slow delays delays delays delays delays classical reduces combining combining neighborhood intervals remains calculate visible visible visible sufficiently norm transactions transactions precision building combinations combinations extension variations variations gating successfully capable capable capable uniformly uniformly suitable suitable successful successful oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory attractors literature comparing situation essentially fine notice notice notice issue sin oscillations oscillations oscillations duration satisfy satisfy vary write usual usual usual usual modular modular modular modular modular modular modular modular computes ill ill ill subsequent operating operating mixing approximating acknowledgments origin origin origin origin origin remain poor production essential essential rapidly varied oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators limitations recursive oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator existence fourier fourier fourier fourier fashion fashion ideas mappings investigated authors structured structured gates proper proper proper affect hierarchy hierarchy fundamental fundamental phases coefficient integer extremely adjusted adjusted bifurcation bifurcation obvious obvious portion portion logic switching consist regime regime arbitrarily arbitrarily arbitrarily band band band band biology analytic analytic analytic capabilities briefly briefly briefly worse reasons perspective ring easier producing producing producing constructing constructing constructing division leaves desirable immediately controls controls controls universal universal universal universal universal universal universal universal universal universal implicit begin arises argument questions fuzzy double double double double double understood relevance amounts fed readily adjustable adjustable adjustable schematic polynomials operate gains gains synthesis mod ture pasadena pyramid realized realized realized realized realized discontinuities proofs sort japan restrict fix fix fix pick impossible nonzero interconnected interconnected interconnected outcome robotics caltech arranged difficulties adjusting satisfying odd attractive attractive loops loops loops grow occurring transforms imply intuitively clock clock lip weakly combines governed periods periods encountered overview expanded washington lawrence approximators surprisingly matter ends relies eqs grants alternatively tures baldi baldi baldi baldi baldi baldi baldi onr speaking truncated ent july conjecture convenience tradeoff hillsdale continues execute generators afosr proach regimes regimes hornik hornik hornik hornik hornik hornik sketch superposition universit vanishes vanishes vanishes tune transients tin completed shallow accumulation accumulation fortunately uniqueness nonnegative january discontinuous synthesized jet losing oscillate loosely realizations identically identically architec architec propulsion spirit signed signed faced faced tra statements statements translate undergo allowable tory enabling ina cations rij rij triple relax technische occasionally cient approxima adjustments conceptually sparsity cir bifurcations bifurcations iterates challenges displaced kurt kurt kurt banks banks notational pierre pierre pierre pierre prevented maxwell millisecond namic rings rings rings charging amir amorphous amorphous amorphous stinchcombe stinchcombe abrupt abrupt abrupt coordinated cients cients obeying austria unwanted atiya rit advocated unsuccessful unsuccessful implausible tackle oscil perturb wien wien ify halbert coe coe coe gradi joined ixt ixt trajec conceivably flavor jectories organizational disrupted kit trajecto 
#@Baldi_P,Homik_K,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training output output output output output output output output output output number number number number system system error error error error error error error error error results results results units units units units units units units units units information information information information problem models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based based weights linear linear linear linear linear layer layer layer layer layer layer layer case case vector vector vector order order order shown shown systems systems values values probability parameters parameters parameters parameters parameters parameters noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions unit unit distribution approach point single processing processing processing control rate rate rate test test test test analysis analysis matrix inputs inputs inputs form form form form form form form shows simple paper paper paper small small small small small net net work work task task step process process current trained trained trained trained trained trained trained trained trained structure problems problems random random random high memory response section section section section general general general generalization parameter parameter parameter parameter approximation average average average theory obtained obtained obtained obtained obtained term term term term term term term term term term experiments activity result university variables variables computation computation computation computation computation computation computation independent independent independent defined defined found found found dynamics initial table table estimate standard standard standard standard standard standard standard standard standard computer computer connections connections connections science science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction present activation activation sets sets sets sets sets sets sets sets sets sets press press basis nonlinear nonlinear nonlinear outputs sample abstract applied applied applied back back back analog references due adaptive propagation propagation propagation introduction estimation behavior effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated variance parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion change change change variable assume assume prior prior previous previous previous cases cases cases cases required good good distributed distributed expected expected expected expected techniques proposed proposed length correct errors errors errors errors errors forward forward forward forward forward forward scale classes ing regression regression regression regression computed times elements elements factor feedback feedback applications knowledge knowledge obtain obtain obtain original original vol cross cross cross series series series series series series series determined determined goal goal related related connected distributions equal approaches approaches approaches mit larger nets nets nets nets modeling morgan morgan morgan proceedings proceedings report report institute institute technique consists consists internal internal advances advances represents connectionist connectionist layers delay delay delay delay cambridge equivalent directly directly hinton hinton hinton hinton hinton hinton hinton additional additional solutions limit san san san effects conference statistics statistics world validation validation validation validation validation validation con derived derived developed developed developed developed criterion criterion actual finally backpropagation depends depends covariance covariance covariance technical technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward tested predictions finding assumed assumed eds eds eds eds hypothesis instance easily easily degree degree rumelhart rumelhart rumelhart rumelhart rumelhart noisy noisy fit fit kaufmann kaufmann kaufmann objective simulated typically smaller smaller smaller dynamical dynamical dynamical functional unknown transfer transfer york york special special special special structures empirical squared squared call max max max pre normalized normalized supervised early decay decay decay decay decay decay decay decay decay decay decay attention minimize description predict denotes denotes architectures recent advantage separate reported reported include include subject quadratic quadratic quadratic sejnowski cognitive recently recently previously works works tions tions tions smooth smooth yields studies studies studies generalized interval williams williams risk constructed expression expression studied studied invariant extended extended trial feed feed feed feed feed feed touretzky touretzky white generally column critical minimal minimal assumptions valued measures measures performs moody moody moody moody moody moody moody moody moody moody moody moody moody moody moody constrained mateo sigmoidal demonstrated regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization radial assuming minimizing minimizing minimizing minimizing minimizing user min decrease iii iii targets derivatives derivatives appears van derive derive written index index index index index index index index index index index stability dept dept sensitivity simultaneously averaging develop formed formed john john decreases yield viewed detailed evaluate evaluate fraction fraction soft soft approximated translation partition past key earlier smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing additive additive fitting add closed closed norm euclidean recorded exploration discuss tests successfully selecting selecting maximal maximal maximal divided mcclelland modes poggio poggio committee committee committee committee committee committee committee committee committee oscillatory comparing refer heuristic interested issue return notation list delayed delayed ill ill leading leading automatically overlapping receive minimized minimized production production production production production production overfitting perturbation perturbation perturbation hall school tech dependencies referred tanh func cognition cognition neu coefficient editor integer predicting predicting predicting predicting spline spline spline changed subsets versions consist submitted established years inequality publishers publishers publishers derivation smoothness smoothness smoothness variances unstable nowlan nowlan nowlan nowlan capabilities lies starts widely bishop bishop mathematics mathematics ridge ridge ridge members nsf mellon exemplars robustness requiring requiring fourth varies prop carnegie elman elman cmu posed posed compares perturbations perturbations perturbations perturbations perturbations weigend weigend prevent simulator simulator conclude median median median simultaneous simultaneous simultaneous simultaneous sharing sharing ordinary uncorrelated leen leen girosi girosi jth partitions jones dealing determination intelligent biased ral implications exceeds nonparametric eqn eqn eqn eqn eqn eqn eqn eqn eqn eqn eqn eqn elimination elimination published predictors overview lengths francisco francisco emergence specialized papers tures stopped stopped std learnable outperforms summer microstructure dec tibshirani tibshirani tibshirani perturbed perturbed perturbed perturbed perturbed connec wahba wahba wahba solely chapter algebraic representa pub publication concentrated hastie hastie hastie levin levin chauvin werbos werbos chapman graduate graduate regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer regularizer simplifying option distinguished page knowing ward oregon oregon pineda pineda pineda completed housing covers covers remarks january january january overtraining supply december december december industrial industrial industrial industrial industrial month month month month huberman huberman marcus marcus disturbance economic evolves demands feldman handbook westervelt westervelt neglected indicators jan dence generaliza regularizers regularizers regularizers ference unobserved preventing optimizes regional monthly monthly damped netherlands agation wii wii vin exclude correspondingly niques insure eval cap calling waltz concluding economics plaut plaut plaut portland proj marcel dekker penalize feedfor readings eubank eubank eubank zky touret zee zee deduced tikhonov tikhonov tikhonov tikhonov tikhonov tikhonov observational grandmother uation onal corp confi wll money lagged lagged lagged lagged cbms eqns eqns monographs rehfuss rehfuss exogenous exogenous ablex pertur neurocontrol sofge technometrics regulariza winston reinhold nostrand 
#@Moody_J,Wu_L,
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#*network network network learning learning model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function figure figure figure figure figure figure figure time set set set set set networks networks networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number system error error error results results results results results information information problem problem problem problem problem problem problem problem models models models models models models models models models models models hidden hidden hidden hidden performance based based based based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case vector vector shown shown shown systems values values probability parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight weight functions functions functions functions functions functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition pattern point point point point point point point point point point single processing control large local analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form shows shows shows shows shows algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian paper paper small small small small work work methods methods step step step step step points points points points points current current trained structure problems random show fixed general general general general parameter approximation approximation approximation theory gradient obtained obtained obtained term term term note note note note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional university variables variables variables variables variables variables computation solution solution solution solution research research research log log target target initial constant standard standard terms terms terms left left map present present phase phase phase phase machine maximum maximum maximum maximum press components components components basis basis basis basis basis continuous continuous sample sample sample abstract find find find find computational convergence density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component procedure procedure important adaptive adaptive mixture mixture mixture mixture mixture context introduction hand estimation statistical generated generated generated variance variance energy energy complexity complexity complexity variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable assume lower prior prior prior chosen chosen part previous theorem binary represent represent distributed distributed bayesian bayesian bayesian equations equations markov fact fact techniques techniques techniques techniques techniques region correct probabilities observed minimum classes classes ing respect respect respect multi multi multi multi multi multi sum performed performed performed elements elements elements elements mapping mapping mapping mapping mapping mapping mapping factor factor factor optimization optimization optimization optimization dimension applications em em em em em em em em em em em em em em obtain obtain obtain negative negative compared application application desired define define determined posterior posterior posterior posterior posterior posterior distributions equal approaches approaches approaches steps steps comparison update train morgan version consists consists kernel advances represents represents exp maps maps maps computing computing computing hinton hinton hinton curve curves curves determine requires choice choice significant statistics statistics give give give give condition criterion provided finally iteration discussion covariance group group transformation transformation transformation corresponds corresponds finding finding common assumed supported eds square ability including typically typically typically underlying combination combination account functional interesting interesting character projection projection york special uniform uniform principle leads principal principal principal principal principal principal principal iterations iterations choose choose added denotes denotes discussed discussed discussed discussed apply apply include include machines quadratic interest interest dimensions dimensions dimensions conventional conventional unsupervised approximately calculated tions solve solve solve diagonal diagonal evaluation chain separation separation separation symmetric modified generalized generalized grid williams williams williams williams williams williams grant expression extended deviation locally width generally generally setting demonstrate flow flow bayes clear moody practice constrained integration integration integration presence presence physics physics drawn regularization regularization turn minimizing start decrease introduce introduce introduce introduce configuration configuration configuration configuration suppose pro monte monte monte monte monte carlo carlo carlo carlo carlo index generating generating generating plot plot label missing missing missing missing missing explicitly dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality involves unique consisting develop integrated springer expectation john focus expressed squares evaluated evaluate evaluate organizing fraction fraction decomposition soft similarly converges key key performing measurements measurements intermediate euclidean kohonen kohonen kohonen degrees subspace plotted illustrated illustrated partially simplicity gamma gamma gamma determining determining straightforward suitable suitable modification computationally included latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent mackay mackay mackay situation plots reached capture refer verlag kind kind repeated interested interested manifold notation write write write dayan dayan realistic ill leading leading deal intrinsic intrinsic wiley exponentially involving involving involving involving hanson accurately lippmann dual dual rise project project project analytically relationships maximizing maximizing func topographic phases phases act circles circles coefficient gradients configurations configurations predicting equally singular singular quantities formal freedom initialized consist mixed neal indicating inequality developing capabilities capabilities tractable reasons considerable considerable purposes precisely bishop bishop bishop bishop bishop bishop bishop bishop consequence consequence inversion projected projected acknowledgement universal arises conjugate conjugate summation apparent apparent considerably evaluating embedded embedded embedded readily effort introducing price berlin rely mod measuring gave replace conditioning redundant intractable oxford linearity zemel labelled approximates concerned homogeneous homogeneous discover discover printed extending convenient convenient ments grow viewpoint belong responsible filled exploring governed governed james james induce regarded demonstration spherical elastic similarities claim passing subsequently vari vari outlined geometrical geometrical drop unable rubin rubin helmholtz aston aston aston formulate tibshirani tibshirani convenience seek auxiliary visualization visualization visualization visualization arising arising acting toy toy toy gas gas gas regularizer crosses integrals integrals integrals constructs induces parametrized els intensive signs modal christopher christopher justification water water water responsibility flows flows flows cally diagnostic possess attenuation attenuation sity reality confined centres categorical appro carrying assessed shortly birmingham revow oil oil oil oil oil oil oil oil oil schematically paid nuclear nuclear jensen sults retains responsibilities responsibilities centred requests neglecting permitted visualize univer live visualized neighbouring eval epsrc tlx occuring pipeline pipeline instruments instruments integrations diagnostics superpositions tives markus markus tent photon cesses deriva annular annular spherically fractions fractions hnear subjectively svens svens svens svens staff priate lives pipelines revisited tlw hospitality beams wkj wkj kauffmann uated nately analyti synthetically xlt 
#@Bishop_C,Svensen_M,Williams_C,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural neural neural neural data data data data data data function function function function figure figure figure time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results units units information information information information information information information problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based based space space space weights weights linear vector vector vector vector vector vector vector vector vector vector vector vector vector order shown systems systems systems systems probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters unit unit distribution distribution distribution distribution distribution distribution method approach approach approach approach point point point single single single single single processing processing processing processing processing processing large test test test patterns class matrix matrix matrix matrix matrix matrix signal signal algorithms algorithms algorithms algorithms algorithms simple simple gaussian gaussian paper paper paper paper paper size size size net work task task methods step step step step step step step step step step step step step step step step step step step step step step field field field field field field field field field field field field field field field field features features features process process current current structure structure structure problems problems problems problems problems random random random similar representation representation representation representation representation architecture architecture architecture architecture show equation equation section fixed fixed vectors vectors vectors vectors generalization generalization speech speech speech parameter parameter parameter real real approximation approximation approximation approximation approximation approximation approximation approximation states states states states states states states states states states states states states states theory theory obtained term term term note note dimensional result result university variables variables variables solution research research independent independent log log log log log log log defined defined defined sequence sequence sequence sequence sequence sequence sequence dynamics initial constant constant constant table table table estimate estimate standard standard standard standard standard standard computer terms terms science presented presented presented presented present phase phase temporal machine machine machine sets maximum maximum press press press learn position components components basis outputs abstract applied applied find computational convergence convergence convergence convergence density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component due due due ieee procedure procedure procedure procedure procedure procedure mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction introduction hand estimation estimation estimation estimation statistical statistical generated generated generated generated generated generated generated cost tion tion change energy energy energy energy complexity complexity complexity variable assume rules rules prior representations representations representations representations representations representations representations representations part required multiple multiple binary represent distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed expected expected expected equations equations equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make fact proposed length length length probabilities probabilities probabilities probabilities forward forward forward forward minimum resulting resulting total total human computed respect respect respect sum sum made natural natural em em em em em obtain obtain artificial relative samples represented compared application cross cross series series series series series series compute compute compute proc related constraints constraints distributions discrete discrete discrete discrete discrete brain equal equal mit mit mit mit mit steps steps comparison comparison larger larger update train train modeling modeling modeling morgan morgan proceedings institute department department loss advances advances advances connectionist connectionist difficult exp exp sequences sequences sequences sequences ai ai ai framework framework cambridge cambridge cambridge computing computing hinton hinton hinton hinton hinton hinton hinton transition transition transition transition transition san capacity efficient efficient efficient efficient full requires approximate approximate statistics statistics statistics free speed speed estimated estimated estimated basic basic pages increase derived derived derived derived derived weighted randomly conditional product product product processes iteration nature nature depends sampling sampling sampling sampling sampling sampling sampling sampling constraint constraint biological discussion covariance covariance normal hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm limited inverse assumption corresponds corresponds finding common assumed assumed supported future makes kaufmann underlying underlying underlying underlying underlying underlying underlying needed combination combination combination jordan jordan jordan jordan jordan jordan jordan jordan jordan technology projection special special uniform empirical empirical iterations bits normalized normalized minimize run description denotes denotes denotes denotes denotes architectures architectures architectures exact exact exact exact exact exact exact exact exact exact exact exact exact property property separate introduced introduced introduced include subject machines quadratic sejnowski cognitive interest varying observations calculated works tions solve achieve chain chain observation observation williams williams williams williams grant grant grant grant deviation matrices matrices touretzky touretzky touretzky deterministic column column column setting setting setting setting setting pass runs conclusion reduce reduce reduce valued valued valued valued depend editors editors editors editors editors interactions sigmoid exponential exponential exponential faster practice mateo suggest encoding cycle cycle intelligence assuming minimizing introduce derivatives areas boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann monte carlo ways primary generating distinct modeled modeled belief belief interaction expectation expectation expectation expectation expectation cycles cycles independently formation solved solved densities densities operations updated updated completely similarly partition partition partition allowed processor slow spaces spaces roughly foundation advantages coupling silicon usa usa formulation strings sciences determines maximize maximize mozer priors priors simplicity columns columns straightforward efficiency closely hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms computationally included essentially capture traditional traditional traditional refer induced moore contribution running sci satisfy notation gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs michael backward backward backward backward observable observable observable observable observable observable observable maximization tesauro tesauro tesauro extend cowan simpler unlike overfitting overfitting divergence divergence successive history history school project analytically analytically combine dependencies dependencies office comparable fundamental analogous gradients naturally man extremely algo algo algo speakers contributions motivated neal neal neal massachusetts great growth publishers publishers defining defining biology capabilities expensive tractable tractable baum baum baum baum baum baum handle starts rapid formalism incorporate incorporate arise laboratories potentially acknowledgement acad toronto toronto summation integrating limits collected collected elman pseudo formulated rep mod limiting aim acoustics logp logp expectations expectations expectations simultaneous softmax ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani leen leen intractable 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observables observables observables factorized recogni tial mcdonnell vis stochastically suffers inherently ters couplings couplings quantizer quantizer quantizer juang juang juang zoubin zoubin transpose distorted magazine concatenated emerged monitored fore tit tit moderately substructures pew severely sentations approxima proce parame psyche psyche evaluates viable iterates fac widespread unclamped unclamped sit factoffal factoffal factoffal factoffal factoffal resentations penrose mij dure zky touret vances intractability autoencoders pute liebler pled sisj factorim factorim eling factorize factorize unavoidable ttt caution imations mcclure decouple quantizers alg diagnosed rive ooooo ooooo putationally exponen configura porally anew chosing obviates 
#@Ghahramani_Z,Jordan_M,
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural input data data data data data data data figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error state results results results results information information information problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance performance performance based based based based space space weights weights weights weights weights weights case case case vector vector vector vector order order shown shown systems values probability probability probability probability probability probability weight weight weight weight weight weight distribution distribution distribution distribution recognition recognition recognition recognition recognition approach pattern pattern pattern pattern single single single single single single large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class class class class class class class class inputs form form form form form shows shows algorithms algorithms visual examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small size size feature feature feature feature work methods methods methods step step step features features features features features features features features features classification classification classification classification classification process current trained trained trained trained trained trained trained trained problems problems problems high similar similar similar show show show show show line general general generalization generalization generalization average theory theory obtained experiments experiments experiments experiments dimensional university computation independent independent independent log log initial initial table table computer node node node node node node node node node node node node node node science science left nodes nodes nodes nodes nodes nodes machine machine machine sets sets range nonlinear nonlinear continuous abstract find computational computational references positive important decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision introduction hand hand statistical statistical generated change classifier classifier rules word learned chosen higher higher previous previous required required multiple multiple multiple multiple multiple good good tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree make make make fact techniques techniques techniques techniques correct probabilities errors errors errors errors total total regression performed called called called times times regions means potential made made applications applications applications applications study knowledge knowledge obtain original original original original original original original original original original original original original original original original vol vol artificial artificial samples samples application application series series series series series rates rates rates determined determined equal power approaches comparison comparison comparison train train morgan morgan proceedings report institute department department implementation implementation implementation implementation version technique technique technique technique technique technique consists consists internal individual individual difficult difficult difficult difficult difficult difficult final final final final graph domain curve curves curves design top conference conference statistics speed increase increase give give give give weighted weighted weighted weighted weighted randomly randomly randomly criterion criterion evidence depends depends technical increases increases amount shape main eds journal end pixel hypothesis hypothesis including kaufmann needed combination technology technology testing significantly ratio ratio character database database empirical call call international international bottom idea run run added improve separate ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble practical machines side trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees array compare compare previously approximately evaluation evaluation constructed constructed constructed constructed occur wide correctly correctly pass pass pass pass strength reduce conclusions accurate accurate accurate asymptotic weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak strong strong hard hard largest drawn california california proportional proportional intelligence intelligence decrease decrease configuration force appears digit construct construct written optical primary distinct pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning easy choosing national independently learner learner learner learner learner learner learner learner learner learner learner detailed evaluate fraction suggested suggested digits digits digits digits digits key reasonable penalty initially filtering calculate calculate calculate calculate calculate assigned assigned assigned assigned assigned assigned advantages classified classified expect building building handwritten box box bell bell weighting determines vapnik uncertainty discuss discuss black extra efficiency build ten superior superior issue classify classify built vary denker hypotheses reach reach poor create experience difficulty preliminary hall reducing examine terminal terminal terminal terminal terminal terminal terminal boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting combine root root root root workshop surfaces attributes attributes induction hill created equally subsets subsets subsets subsets subsets aspect friedman consist simplest cart theoretic distinguish publishers improves adaboost adaboost adaboost majority worse starts comparisons berkeley filtered filtered filtered filtered filtered filtered filtered filtered filtered filtered filtered filtered constructing constructing laboratories laboratories simard simard members attribute attribute arises recording substantially substantially poorly passed passed compares branch popular replace decreased attraction specifies specifies contribute pac feasible primarily pick pick pick pick member discovery discovery unity lecun lecun proceed murray breiman breiman breiman breiman imposed grow implications effectiveness programs schapire schapire schapire schapire schapire schapire schapire predictors iteratively respective pruned pruned pruned pruned jackel jackel competing claim claim claim initialize ensembles bagging bagging bagging passing splits harris stone divide sequentially converted users basically guyon validity recursively asked freund freund freund freund freund classifies remainder chapman ocr ocr ocr ocr ocr ocr ocr ocr ocr learnability picked picked picked picked altered interactive constructs termed termed termed termed quinlan quinlan quinlan quinlan misclassified elsevier holding september learners learners learners learners learners learners learners learners learners learners replacement replacement replacement appearing copies nist nist resolve justified prefer european jersey jersey overtraining supply mining mining incorrectly incorrectly appealing bottou bottou holmdel dissertation striking progressively progressively terminates prune prune prune prune proceeding cortes cortes cortes cortes cortes cortes drucker drucker drucker drucker drucker drucker drucker drucker jerusalem subtree subtree subtree subtree subtree severely accepting subsampled terminated resampled rationale wanted wanted trust olshen fifty doctoral muller kauffman standards guessing guessing inclusive interests buffalo pessimistic pessimistic traverses levitt attractions asymptotes asymptotes corinna kwok kwok distort emanating invariably pll 
#@Cones_C,Drucker_H,
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data function function function function function function function function function function function figure figure time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output system state state state state state state units units units units units units units units units units units units information problem models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden weights weights weights weights weights weights linear case case case case order order order order order order order order order order order order order order shown systems systems probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters distribution distribution distribution distribution distribution distribution distribution single processing large large form form form form form shows algorithms algorithms paper paper net methods methods methods step step step step field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field trained structure structure structure structure structure structure structure structure structure structure problems representation show show section section section section section fixed line vectors general general general generalization speech speech speech parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states states states states states states theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained obtained term term term note note note variables variables variables variables variables variables research research independent independent independent log found found sequence sequence estimate terms terms connections left left left left machine sets maximum range range range range range press learn outputs outputs continuous abstract applied applied applied applied find computational computational likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic procedure procedure important context context context context context context context context introduction complex hand hand estimation statistical statistical statistical tion tion energy energy energy energy energy energy energy energy difference assume assume lower lower lower lower lower rules signals prior chosen higher higher higher center previous bound bound bound bound bound bound cases type required required multiple multiple binary binary binary binary binary long long long long conditions represent represent distributed equations equations equations equations equations equations equations equations markov markov markov markov markov markov make fact techniques techniques techniques observed forward forward simulations resulting resulting ing computed computed respect respect sum eq eq eq eq eq eq eq eq eq eq eq eq times made applications applications knowledge em em em obtain obtain obtain obtain obtain obtain obtain obtain original artificial true true compared provide provide define define define compute compute compute compute proc proc related posterior posterior constraints connected discrete equal approaches mit steps steps update support support dependent modeling institute consists advances joint joint represents represents represents connectionist difficult exp exp addition framework framework framework cambridge cambridge computing computing equivalent directly hinton hinton additional transition effects effects effects effects efficient efficient efficient efficient requires requires approximate statistics statistics estimated basic basic basic developed iteration iteration biological describe denote tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm inverse assumption assumption complete nearest assumed assumed assumed role main eds probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic needed account account fully jordan jordan jordan jordan jordan jordan technology interesting interesting special consistent consistent consistent structures principle leads representing minimize choose architectures architectures exact exact exact exact exact exact typical apply side side quadratic trees trees inference inference approximately works module tions tions yields match sparse chain chain williams williams sensitive sensitive sensitive grant grant parts expression expression lead suggests touretzky clusters boundary setting pass conclusions neighbor valued depend depend interactions interactions interactions interactions interactions interactions interactions interactions modules modules modules modules modules modules accurate numerical weak weak weak temperature physics reduction assuming minimizing minimizing exist derivatives manner connectivity connectivity configuration boltzmann boltzmann boltzmann boltzmann suppose suppose longer index solving solving missing sensitivity averaging involves remaining scales develop develop develop yield choosing focus review phoneme correlated viewed viewed solved updated approximations approximations similarly similarly partition partition partition partition partial partial partial performing classical advantages degrees degrees degrees coupling avoid strings inter inter inter inter sciences extension uncertainty maximize coupled coupled coupled partially partially simplicity straightforward identified extra extra extra hmms hmms hmms hmms hmms hmms hmms hmms computationally wij wij wij efficiently computations soc conf quickly prob link anderson anderson comp gibbs sampled michael modular modular modular modular modular modular modular backward backward approximating load tesauro minimized simpler unlike relations relations recursive divergence divergence divergence existence ideas school links authors structured tanh tanh statistically analogous act gradients illustrate der algo freedom freedom freedom simplest motivated defines averages massachusetts inequality independence briefly tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable worse widely strictly incorporate mation laboratories acknowledgement calculations calculations calculations incomplete preceding nsf reflects reflects flexible flexible lattice introducing introducing introducing incorporated calculating cal cal incorporating serve serve extensions extensions marginal marginal sophisticated expectations expectations expectations expectations expectations expectations expectations wesley cor cor leen intractable intractable intractable intractable intractable intractable intractable intractable intractable intractable intractable feasible addison summing summing temporally royal plays kullback chains chains chains siemens replacing city abilities interpret exploit star definitions methodology substituting weakly heavy saul saul saul saul saul saul saul induce induce sides captured lawrence chooses peterson peterson augmented proteins roy eqs exploiting exploiting exploiting exploiting valuable dempster dempster acknowledge onr discriminate radar approx street unified summer corporation rubin rubin welch connec amherst decomposed scenario principled distri rithms interact distribu approxi jij denoting intra intra noting laird laird maintains reveal reveal intl supports behave behave parametrized refined atr treating corrections corrections corrections handled handled rabiner rabiner factorized factorized factorized factorized handling handling recogni couplings couplings couplings core core juang juang exploits exploits isolation distorted inducing semantics tical skeleton energies stationarity potts tivity elaborate triple triple substructures substructures substructures substructures substructures substructures substructures hij mir tighter lifetime couple psyche parisi parisi jensen ily sorts mented inferences kij kij kij rni backbone invoked subscripts correlator iden cumulants modulations stolorz stolorz establishment decoupled decoupled meets redwood cda interac tractability tractability unfolded butions manipulate liebler anticipatory sisj correlators hawaii factorize drastic coarticulation coarticulation coarticulation gradi decouple substructure superscripts factorizable ents mimicking technometrics lnz imp expecta 
#@Jordan_M,Saul_L,
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time 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information information information information information information information information information information information problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based based based space weights weights weights case case case order order order order shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems values probability parameters parameters parameters noise functions distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach pattern pattern point single single single single processing processing processing processing processing processing processing processing processing processing large local neuron patterns patterns analysis analysis analysis analysis analysis class class class matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs form form shows shows signal signal signal signal signal algorithms algorithms algorithms simple simple simple simple paper paper paper paper examples examples small small small small small net work work work work task step step step features features classification classification process level level level level level level current trained trained structure structure structure structure structure structure structure structure structure structure problems random random random high memory similar similar similar similar similar representation representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture show show equation equation section section section section section section section fixed general general general general general general speech speech speech speech speech speech speech speech speech speech speech speech average average average states theory theory gradient gradient term term term term term term term term term term term term term term term term term term term term term note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation solution research independent independent found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics initial initial initial standard computer terms terms connections left left presented presented presented presented presented presented map frequency frequency temporal temporal temporal temporal machine sets press press press press press press learn learn learn learn outputs abstract abstract applied applied back find density references ieee ieee ieee ieee ieee ieee ieee decision propagation propagation mixture context context context context context context context context context context context context context context context context context context context introduction introduction introduction complex hand statistical effect generated generated generated generated parallel parallel parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion change change energy energy energy energy variable variable variable variable variable variable variable variable variable variable variable variable variable variable spatial spatial spatial assume lower rules rules prior representations representations word word learned chosen chosen higher higher higher previous previous previous previous previous cases cases type required multiple multiple multiple multiple multiple good long long long long long long long long long long long long long long long long long long long long long long represent represent represent represent represent represent represent represent represent represent represent represent distributed distributed equations equations markov markov markov markov markov markov markov markov markov markov markov markov make fact techniques proposed proposed proposed proposed proposed proposed proposed proposed proposed length length length length probabilities probabilities probabilities probabilities probabilities probabilities observed forward forward scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale tasks regression regression multi multi multi multi multi multi sum sum performed performed performed performed times regions means reinforcement reinforcement reinforcement potential dimension made feedback applications applications knowledge knowledge knowledge knowledge obtain artificial artificial artificial artificial artificial specific specific represented represented represented represented represented compared compared compared compared application application application desired desired series series related connected distributions distributions discrete discrete discrete discrete equal approaches approaches approaches mit mit mit mit steps steps steps steps descent modeling morgan morgan morgan morgan proceedings report institute internal code advances advances advances advances advances advances represents represents represents difficult difficult difficult difficult difficult difficult final layers layers delay delay delay scheme scheme sequences sequences sequences sequences sequences sequences sequences considered considered considered cambridge cambridge cambridge domain hinton hinton hinton hinton hinton hinton hinton hinton solutions transition transition transition transition trajectory san san bit conference conference conference requires world basic pages pages pages pages pages pages pages pages pages give derived randomly randomly levels levels levels levels levels levels criterion types path product product product finally finally backpropagation nature depends constraint discussion technical technical increases increases increases hmm hmm hmm hmm hmm hmm hmm hmm fast close assumption assumption assumption assumption assumption assumption stable short short short common common generate generate journal journal end end easily easily rumelhart rumelhart rumelhart noisy noisy including kaufmann kaufmann kaufmann kaufmann objective probabilistic probabilistic probabilistic account dynamical dynamical fully jordan jordan interesting interesting significantly significantly york edge increasing increasing structures structures trials trials trials principle principle squared squared squared representing representing representing representing numbers stored international international polynomial idea idea idea idea minimize run added architectures architectures architectures architectures architectures architectures architectures architectures architectures architectures improved improve improve recent resolution resolution resolution resolution resolution advantage advantage robust reported side hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical inference recently engineering interest interest interest sufficient varying varying varying varying varying varying compare compare observations observations volume works module yields yields studies converge converge achieve achieve williams williams sensitive exists concept suggests extended deviation matrices matrices touretzky touretzky deterministic deterministic deterministic deterministic generally setting conclusion conclusion place assumptions assumptions reduce reduce depend editors editors editors editors editors editors editors editors differences sutton sutton moody faster faster practice practice constrained constrained mateo mateo propose propose propose taking taking taking hard integration presence intelligence intelligence intelligence intelligence assuming assuming introduce introduce introduce derivatives configuration force attractor boltzmann boltzmann explicit appears pro longer longer longer longer longer longer factors sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential dept dept changing modeled modeled implement implement involves transformations transformations transformations transformations scales scales scales scales scales scales scales scales scales scales scales scales scales scales scales adding events events events events implies implies cycles national family focus phoneme phoneme phoneme phoneme phoneme squares influence transform evaluate evaluate centered decomposition activities completely similarly converges allowed past past earlier earlier earlier slow slow performing delays delays delays normalization intervals intervals intervals advantages advantages advantages transactions transactions avoid expect expect building handwritten handwritten includes thesis priori priori priori priori priori priori priori priori usa bell bell eigenvalues eigenvalues assignment automatic discuss coupled variations grammar planning compression hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms uniformly differ effectively paths paths paths paths mcclelland detect literature tdnn identity traditional kind allowing phonetic contribution timing timing timing timing duration duration duration duration write localization dayan dayan backward backward wavelet wavelet giles giles giles giles eigenvalue denker highest attempt tesauro tesauro tesauro tesauro cowan cowan cowan bars bars simpler remain singh singh difficulty difficulty difficulty difficulty difficulty difficulty rapidly varied relations hanson hanson respond history ideas ideas links dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies structured working working proper variability tanh workshop hierarchy hierarchy hierarchy waibel waibel waibel waibel coarse coarse gradients recognizer rank obvious assumes precise precise precise precise initialized store simplest motivated motivated phd isolated advanced slowly slowly analyzed phenomena diffusion diffusion independence independence lies tool lin lin shared easier organized precisely incorporate bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio mation products products products simard simard simard simard simard simard simard simard simard involve pitch beginning meaning meaning meaning researchers researchers mechanics considerably pure amounts introducing introducing slower rep span span span span operate operate operate howard synthesis summarized gen extracting ordered acoustics credit credit credit credit credit credit differentiable sharing globally spectra identifying leen conditioned perfectly homogeneous lecun lecun lecun lecun lecun lecun proceed clamped inspired chains chains chains chains promising transforms synchronous guide intuitive carry reliably alspector alspector analyses analyses analyses financial saul saul studying encountered lang lang lang lang forecasting lengths lengths den jackel propagated shortest master master theoretically draw draw reverse reverse papers papers propagate summarize insensitive vari vari displacement consecutive unified numerous ent basically basically convolutional markovian markovian boser chapter classifies remote remainder jacobian representa continuity attempted henderson henderson henderson schmidhuber schmidhuber dominated labs hubbard oct oct relate concentrate confirmed harder cartesian zip alternatives france denver universit universit universit esti simplifies aaai helps factored factored factored rabiner rabiner rabiner rabiner rabiner tdnns tdnns tdnns tdnns tdnns decided tial frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi frasconi confirm puts hid phonemic holmdel resolutions proposes juang juang juang conditionally economic daily assp articulation magazine ben ings transaction artificially montreal montreal montreal spanning spanning ceedings segmental segmental ables fallside inserting sition monthly tran imposing subsampling helped classifica supervision justify justify narx horne yoshua spans kung successes periments proportionally quence hierarchically hierarchically validate suc farther feudal kamm knowl xlx injecting slave slave unfolded loth lxt lxt eration iro markovjan alt recherche recherche prosodic informatique informatique levinson levinson proposals omlin omlin ixt soda sondhi sondhi decimation umontreal oversampling erate homogeneity eve gori montrdal sequen ifil geared lipmann quential weekly 
#@Bengio_Y,Hihi_S,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm output output output number number number number number number number number state state information information information problem problem models models models models models models models models models models models models models models models models models models models models models models models performance based based based based based based based space space linear linear linear linear case case case case case case order order systems systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise weight distribution distribution distribution distribution distribution distribution approach approach single single large large large local local local local local local local local local local local local rate rate test test test test test test test test test optimal inputs inputs inputs form form form form form form form form form shows shows signal signal simple simple simple simple gaussian gaussian gaussian paper paper paper small small net work work step features process process trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems random representation representation equation equation equation equation equation section section line rule rule general general parameter parameter real average average states states states note note note note note experiments experiments experiments result result variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation research research research research independent independent independent independent independent independent log log log log log log log log log log log log defined defined defined initial initial initial initial estimate estimate standard terms terms distance node left left left left left direction direction direction direction direction direction present present present low nodes sets range nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample sample sample abstract find computational computational density density density density density density density density density density density density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due procedure procedure important important mixture context introduction introduction complex complex statistical effect generated variance variance variance variance search search search change change change difference difference variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable lower rules rules rules prior prior prior prior prior learned center previous good bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected equations markov markov markov markov markov markov markov make fact techniques techniques probabilities probabilities probabilities probabilities probabilities resulting ing computed respect respect respect elements means means optimization optimization dimension natural global global applications applications study knowledge knowledge knowledge knowledge knowledge obtain original artificial artificial specific samples samples samples samples samples samples samples samples represented represented represented true cross cross cross cross provide define location location determined goal goal goal related connected connected discrete discrete discrete discrete discrete discrete discrete approaches comparison update update update update update update update update train train train dependent modeling selection selection selection morgan words consists consists joint joint joint joint joint joint final final final bias bias bias addition addition addition addition addition ai ai considered framework framework framework computing domain domain domain experiment experiment experiment experiment experiment additional curves san efficient efficient full requires requires statistics estimated increase increase validation validation validation validation con produce produce produce condition weighted conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional developed types finally sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply normal feedforward increases describe arbitrary fast corresponds complete complete complete complete complete complete complete common common journal easily kaufmann probabilistic probabilistic typically typically typically smaller combination unknown unknown unknown unknown unknown unknown unknown unknown fully fully fully fully interesting interesting ratio mechanism consistent structures structures structures structures structures structures structures structures structures structures structures structures structures principle operation leads representing iterations normalized experts experts experts expert magnitude idea choose choose run added description predict predict improved population directions pair introduced strategy strategy include identical sense inference subset recently recently interest compare unsupervised unsupervised teacher correspond mixtures mixtures chain concept concept deviation deviation predicted alternative locally width generally demonstrate demonstrate runs runs runs conclusions central measures modules clear mateo hard hard drawn demonstrated intelligence radial assuming assuming introduce introduce annealing question denoted explicit factors modeled pruning pruning missing missing missing explicitly explicitly remaining remaining remaining remaining easy belief belief belief belief unique mutual gaussians gaussians gaussians gaussians gaussians gaussians applying formed extraction extraction decreases decreases extracted extracted extracted independently communication estimator influence influence solved densities densities densities open evaluate evaluate operations evolution centered centered centered partial dashed dashed neighborhood roughly penalty penalty penalty closed calculate calculate construction advantages combinations determines uncertainty priors black determining straightforward aspects closely closely importance computationally included comparing score score score score score score score score score score score compact quickly graphs allowing allowing heuristic interested interpreted superior follow criteria strategies strategies built notation notation gibbs gibbs gibbs gibbs gibbs quantity involved usual modular backward powerful powerful access relations estimators estimators estimators estimators estimators estimators optimized optimized optimized issues dotted examine ideas applicable fault relationships dependencies dependencies dependencies dependencies referred scores statistically notion removed removed smallest smallest predicting predicting predicting changed quantities greedy freedom defines averages great directed directed directed directed variances improves independence independence independence independence independence worse handle starts arc arc arc arc arc arc arc arc arc arc arc arc ring organized organized organized precisely located commonly commonly commonly members medical medical depicted depicted incomplete addressed conjugate apparent percent percent percent percent percent evaluating reflect understood consistency generic leave leave leave introducing remove treated treated maintain execution calculating price price price price price mod parent parent serve logp germany boston boston boston windows windows windows unbiased focused focused median diagnosis multidimensional irrelevant irrelevant pose tresp tresp tresp tresp tresp ordinary equivalence fix pick ordering partitions discovery discovery repre impossible nonzero children children children convenient significance promising accepted siemens siemens siemens intelligent loops loops loops loops scoring removing removing reasoning affected modifications child child child recovered loo studying widths induce pruned dependency den competing repeatedly concentration concentration likelihoods likelihoods exploiting reverse alternatively influences vari vari parents parents parents parents parents parents parents treat land arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs indirect accept basically removal removal removal removal legal rejection uniquely tween propagating par decomposed covariances discovering discovering discovering discovering causal causal certainty avoided concentrated community impose impose maintained parzen parzen parzen parzen parzen parzen picked rejected argued pearl pearl pearl pearl disease sam stuck els hofmann hofmann hofmann hofmann hofmann differing status housing housing housing housing housing housing housing factored stops emphasis learners reversal sees handling monitor loosely val rare ples inefficient sity reality charles faced indepen acyclic tained statements denominator indi indi ues decompose microsoft elegant tutorial ables dilemma miss undirected undirected undirected beliefs buntine buntine parsimonious volker volker strongest biasing thinking heckerman heckerman heckerman heckerman heckerman heckerman heckerman heckerman univariate ana exclude oxide oxide conveniently periments discard sume independencies independencies depen render renders otto depict pupil penalize business additions decomposes rooms causality causality hahn mfinchen ful zfe zfe vidual xil xil xil sinall tax lots displaying river reserved msr cates rele supposedly rri convincingly ticularly vant 
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#*network learning learning neural input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure time time time set set set set set set set set set set set set set set set set training training training training training training training training training training training training training training training training training training training training training training output number number number number number number number error error error error error error error results results results information information hidden performance performance performance performance performance performance space space space space space space space weights linear linear linear linear linear linear linear case order order systems values values values values values values values values probability probability unit distribution distribution recognition recognition method method method method method method method method method method method method method method method method method method method method method approach point point point point point single control large large large large large large large large local rate rate rate rate rate test test test test test test test test test class class class class class inputs inputs inputs form simple examples examples small small small small small small small small small small small small size size size size size size work task task methods methods methods methods methods methods methods methods points points points points points points points points points points points points points points points points points points points points points points points classification classification classification classification classification classification level trained trained high show fixed fixed line line line line line vectors vectors vectors images general general general general general general general general parameter average obtained obtained experiments dimensional dimensional dimensional dimensional dimensional dimensional university university university university university threshold threshold threshold threshold threshold research research independent log log log log defined defined defined defined defined defined found found sequence sequence sequence sequence sequence constant table table table table table table table estimate standard standard standard computer computer node node node node node node node science science left direction direction direction direction direction direction nodes nodes nodes nodes nodes nodes nodes nodes machine sets sets sets sets sets position continuous continuous continuous continuous abstract applied back back computational properties references decision decision decision decision decision decision decision decision decision decision introduction statistical variance cost search search search difference difference complexity complexity assume lower measure measure measure measure cases cases required required good binary binary binary tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree length minimum resulting resulting classes classes classes classes classes classes tasks tasks tasks total regression performed means factor factor factor factor factor natural natural study relative true compared compared application cross cross provide define define define define define define define compute compute compute rates rates rates rates perform perform perform determined gain equal comparison larger train train institute institute department department internal code code sequences sequences considered considered considered computing hinton hinton hinton hinton hinton hinton top top top stage stage stage effects determine determine efficient full requires choice significant approximate free estimated validation validation validation validation give give con types selected selected selected selected simply achieved achieved discussion increases increases group tested tested predictions amount effective effective main main main main main end makes pairs pairs pairs pairs pairs pairs pairs pairs fully interesting testing testing significantly significantly significantly ratio projection projection projection projection projection projection projection projection database database database database database database leads call call making bits bits bits bits bits bits international bottom supervised idea combined minimize choose added description description directions directions directions directions directions correlations advantage pair pair pair pair pair pair pair pair pair pair separate takes takes takes takes takes strategy side side side side pixels trees trees trees trees trees trees trees trees trees subset subset compare compare conventional conventional approximately axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis axis correspond expression suggests alternative alternative occurs occurs occurs occurs boundary column column minimal row row greater reduce interactions clear performs strong strong largest demonstrated california california assuming minimizing decrease minima identification identification program pro index index generating generating generating generating estimating distinct pruning pruning pruning missing missing involves remaining slightly angle applying versus yield choosing expressed expressed expressed depending depending stages operations operations sizes discrimination sign boundaries intermediate distances distances distances distances distances advantages avoid expect building building building building existing instances candidate candidate candidate candidate candidate major reason determining selecting selecting identified letter modification divided projections projections projections projections projections projections projections projections projections comparing vowel orthogonal summary quickly allowing link split split split split split split split split split superior issue hold list usual michael ill ill thresholds thresholds thresholds thresholds acknowledgments simpler wiley transformed overfitting overfitting overfitting overfitting overfitting limitations dataset dataset dataset dataset dataset scalar terminal terminal terminal terminal terminal terminal terminal scaled removed attributes attributes attributes plausible plausible plausible ensure subsets aspect versions noted baseline baseline simplest simplest plant defines defines defines synthetic synthetic mentioned percentage percentage advanced rows cart cart cart cart cart cart cart pairwise pairwise trivial trivial orientations waveform majority expensive glass glass glass lies lies lies worse processed producing division division hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane commonly pool pool toronto toronto toronto toronto toronto toronto attribute arises argument greatly pure pure pure pure pure axes axes axes axes variant rely limiting differs maximizes datasets datasets datasets datasets datasets datasets datasets datasets datasets datasets datasets datasets datasets datasets datasets chose june pole pole pole pole pole pole pole pole pole pole pole pole pole pole lot aligned aligned aligned aligned aligned aligned aligned aligned aligned aligned aligned aligned aligned feasible restriction restrict pick perfectly databases hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes robotics eliminated fits convenient breiman breiman breiman breiman overcome overcome attractive intelligent vehicle splitting splitting belong disjoint receiver receiver planar appendix appendix decide decide decide pruned pruned dominant searching searching candidates candidates candidates candidates candidates dif waves membership cancer repeatedly canada canada splits splits splits splits splits splits splits splits splits splits splits splits splits splits splits splits splits ignore summarize summarize fold thresholding stone default planes planes planes maximized randomized regularity mdl possibilities possibilities care geoffrey allocated regularized projecting intensities sonar funded sized ignoring compu computa mini picking preserves vii vii savings ferent breast suite outperformed supplied proportions resolved johns ignores communicate wisconsin edition irvine poles poles poles poles poles poles restrictive tained unrestricted unrestricted unrestricted unrestricted allowable modest modest tit tit revow revow revow revow revow trapped subtree subtree iris save save save disorders delete weakness pooled pooled ontario ontario burden designated belmont canadian nserc overfit neighbouring fellow olshen liver subtrees subtrees subtrees subtrees diabetes communicated tailed tailed rocks wadsworth signif pima twelfth flamework joining joining leo leo resorting guessing eleven divisions divisions divisions onal faithfully unscaled mized usable icant tionally loga ionosphere halfway distinctly disregard wine reserved mines kindly kindly cheaply weakest orthog recommend jections thyroid exercised indians tationally midway float 
#@Hinton_G,Revow_M,
#t9
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#*network network learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure time time time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm output number number number number number number number number number system system system system error error error error error state results results results results results results results results results units units units units information information problem problem problem problem problem models models models models models models models hidden hidden hidden hidden performance performance space space space space space space weights weights weights linear linear linear case case case case case case case case case vector order order shown shown shown shown systems systems values values values values values values values values values values probability probability parameters noise noise noise noise noise noise noise noise noise weight weight weight functions functions functions functions functions functions functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method approach approach approach approach point point point point processing processing control large large local local neuron rate rate rate test test test test test test test test test test analysis analysis class class matrix matrix matrix matrix matrix matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples small small small small size size size net net work work task task methods methods methods methods methods methods methods step step step step points points points points points field classification classification process process process process process process process process process process process process process process process process process process level level trained problems problems problems problems problems random random random random random response similar similar similar similar show show show equation equation equation equation section section section section section section fixed line line rule general general real real real real real approximation approximation approximation theory theory gradient gradient obtained obtained obtained obtained obtained obtained obtained obtained term term term term term experiments experiments experiments dimensional dimensional dimensional result university university university variables variables variables variables variables variables variables variables variables computation computation solution research independent log log log log log log log defined found target dynamics dynamics dynamics initial table table estimate standard standard standard standard standard computer terms terms distance connections science science prediction prediction prediction prediction prediction prediction prediction prediction prediction left presented present present phase low low machine sets sets sets maximum maximum maximum maximum range press position outputs outputs outputs outputs outputs outputs sample sample abstract applied find convergence likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references references stochastic stochastic stochastic stochastic ieee positive procedure procedure important mixture introduction complex complex hand hand statistical effect effect generated variance variance variance variance variance search search change change energy energy energy energy energy energy energy energy energy complexity variable spatial measure prior prior prior prior prior prior prior prior prior chosen previous previous cases cases cases required required good bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations equations markov make make make fact techniques proposed length observed observed scale scale scale scale finite finite finite simulations minimum ing total regression regression regression regression regression regression regression regression regression regression regression computed respect sum sum sum sum performed times times means optimization optimization potential potential potential dimension dimension dimension made obtain negative vol samples true compared compared application desired cross cross series series define experimental related posterior posterior posterior posterior posterior posterior discrete equal approaches mit steps larger larger nets nets morgan proceedings report report department loss implementation version version version consists code advances joint joint joint joint joint joint represents difficult final exp exp exp bias framework framework framework framework framework computing equivalent view view limit limit san conference full choice statistics world world world world world estimated pages increase validation validation give give give give produce weighted robot robot robot robot robot robot lines processes processes processes processes processes processes processes processes processes processes processes processes processes processes evidence evidence backpropagation backpropagation sampling sampling sampling sampling sampling sampling sampling simply achieved discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance group tested limited close close predictions predictions predictions predictions finding amount generate supported role theoretical require main future kaufmann pairs needed combination dynamical dynamical dynamical functional fully interesting increasing consistent leads squared squared squared details details call iterations max max bottom early decay idea idea combined produced produced run run run run run added added predict architectures directions correlations advantage takes reported practical practical practical apply introduced include identical subset sufficient highly approximately volume works works correspond correspond converge differential positions chain modified modified modified observation generalized williams williams williams williams williams grant arm arm arm arm arm arm constructed parts deviation deviation deviation derivative derivative derivative predicted predicted hybrid hybrid hybrid hybrid hybrid hybrid touretzky width runs starting reduce editors editors editors performs mateo integration integration physics largest regularization regularization start relationship iii targets targets targets targets derivatives derivatives manner minima denoted monte monte monte monte monte monte monte monte monte van carlo carlo carlo carlo carlo carlo carlo carlo carlo plot plot plot dept changing changing infinite integrated integrated gaussians gaussians predictive predictive predictive predictive predictive springer implies implies letters yield depending stationary correlated operations operations operations updated approximations approximations approximated similarly suggested allowed partial earlier earlier reasonable reasonable smoothing additive spaces purpose iterative iterative valid valid david exploration thesis formulation contour recognize illustrated automatic automatic uncertainty discuss mozer specifically priors priors priors partially discussions reason closely closely uniformly uniformly uniformly society poggio poggio poggio poggio poggio literature mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay plots quickly prob prob allowing sin gibbs gibbs gibbs gibbs quantity dayan giles highest highest modelling cowan employed carried carried wiley collection investigate put involving involving hanson limitations dotted behaviour rise scalar scalar giving giving rest mappings analytically working momentum momentum momentum momentum momentum surfaces smallest adapt necessarily spline spline implementations rank initialized multivariate detected contributions contributions phd neal neal neal neal neal neal neal neal neal neal neal neal neal neal integrate slowly slowly slowly cos derivation smoothness adapted adapted formalism broad choices bishop mathematics mathematics inversion inversion acknowledgement separately separately toronto toronto toronto toronto definite lowest computers nsf conjugate conjugate evaluating relevance relevance axes conducted conducted peter splines splines http hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters marginal datasets adjust gave comments conditioning conditioning specifies irrelevant irrelevant irrelevant irrelevant corrupted corrupted corrupted feasible feasible www assign formally investigation girosi girosi girosi girosi ordering concerned controlling jones jones plays significance minutes promising accepted determination determination check keeping hope nearby nearby observing excellent predictors regarded intended accounts infinity sim hasselmo initialize treatment treatment ensembles creating canada ignore avoiding schulten ple ple aston aston rejection rejection wahba wahba wahba hundred covariances covariances simulating mars workstation avoided illustration concentrated exam regularizer challenging emphasize rejected argued integrals indexed anal discretization induces permit ignoring walk lems lems picking picking chris copies twenty christopher suite hamilton industrial hour hemmen rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen discarded hamiltonian hamiltonian meth deals tells rameters html ods implying dimen ranged enter kinetic metropolis energies birmingham ysis imum ard ard expresses assessing unifying superscript regional zhu puter inertia inertia inertia shrink iter machinery initialised hyperparameter persistence persistence persistence arma susceptible epsrc domany kij equi saving ations plied ruth edward nicely technically radford radford aging kennedy augmenting ont leapfrog walks carl carl observational cbms oid oid imize delve delve duane duane drafts fictitious ellipse thirds momenta momenta momenta utoronto parametrically librium rescale advisable parameterizing burn pendleton provid 
#@Williams_C,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data function function function function function function function function figure figure figure figure figure figure time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training output output output output number number number number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results units units units information problem problem models models hidden hidden hidden hidden performance performance performance performance based based based based based based based based based based based based based based based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear case case case case case case case case vector vector vector order order order shown shown systems systems systems parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit distribution recognition method approach approach approach point point single processing processing processing control large local test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal inputs form form shows signal signal algorithms simple examples examples examples examples examples examples small small size size feature net methods methods fig step level level trained problems similar architecture architecture architecture show show show show equation line line general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real approximation approximation approximation approximation approximation approximation average average average average theory term term note note note note dimensional result university university variables variables computation computation research research independent independent defined defined found target dynamics initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard terms terms terms science prediction prediction prediction prediction prediction prediction left left left left presented sets learn nonlinear abstract applied find find find find computational computational computational references due due ieee ieee ieee ieee ieee ieee positive positive positive procedure important important important important statistical statistical effect generated variance cost cost cost cost tion change change change change change change difference complexity complexity complexity complexity complexity assume measure center center center cases type distributed make fact fact proposed proposed correlation errors errors errors errors errors errors errors errors errors errors errors forward forward forward finite finite minimum resulting resulting resulting resulting resulting ing total regression computed respect sum called elements mapping means means means means optimization optimization optimization optimization optimization natural applications obtain obtain artificial samples true application series series series series series series determined constraints connected connected connected brain brain brain brain brain equal equal larger support train train train train train train train train source nets nets selection selection morgan proceedings proceedings proceedings proceedings proceedings institute institute implementation implementation implementation implementation individual advances final layers delay scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme considered computing equivalent experiment view estimates estimates estimates estimates design design san san effects effects conference conference conference full full full requires significant significant approximate statistics estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated basic basic increase increase validation validation give derived derived criterion criterion actual actual actual actual actual actual actual actual actual actual provided provided provided provided selected selected sampling measured discussion technical technical technical inverse amount amount effective effective effective main main eds eds eds eds eds ability future rumelhart noisy noisy including objective needed reduced reduced reduced account account unknown fully fully fully significantly ratio consistent mode operation squared squared details filters pre direct international international international magnitude decay decay decay decay decay idea idea improve improve ensemble takes practical period quadratic quadratic quadratic quadratic quadratic quadratic interest highly teacher approximately tuning axis differential diagonal diagonal diagonal diagonal diagonal diagonal background evaluation modified improvement improvement storage storage storage expression expression expression expression scaling derivative derivative derivative matrices matrices alternative feed feed feed white white generally conclusion minimal minimal reduce reduce reduce sigmoid numerical clear moody moody moody practice asymptotic suggest taking integration largest solid proportional regularization regularization regularization decrease averaged derivatives configuration force acknowledgements written estimating plot plot ann stability vertical modeled pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning implement linearly infinite remaining scales scales applying versus family estimator estimator interpretation lemma detailed evaluate controlled showed evolution similarly suggested suggested digits constants calculation additive epochs fitting fitting fitting purpose iterative iterative iterative foundation degrees handwritten includes thesis batch plotted prove uncertainty candidate discussions successfully major columns columns columns straightforward computationally computationally wij presentation literature schemes schemes schemes schemes situation fine cun cun cun contribution quantity quantity involved involved involved denker thresholds thresholds situations explore carried poor overfitting overfitting detail estimators estimators hessian hessian hessian hessian hessian hessian hessian scalar scalar mappings int working comparable tanh workshop workshop affect saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency predicting illustrate illustrate illustrate implementations implementations ensure aspect obvious panel panel panel panel panel panel panel freedom contributions chaotic chaotic established asymptotically rows rows rows stop stop growth capabilities expensive cascade glass glass tool obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs perspective widely inversion inversion circle circle members definite definite depicted considerably reflect offset offset pseudo pseudo tional generic peter solla remove price operate weigend weigend aim curvature simulator simulator semi unbiased implements damage damage calls newton newton newton newton corrupted ear modify count lecun proceed extending extending kaufman consideration occurred attractive removing obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd spurious service service financial connect connect connect pruned pruned pruned pruned facilitate ranking ranking ranking ranking ranking ranking ranking francisco francisco ahead partitioned valuable acknowledge fitted outline accept stork expanding retraining retraining retraining retraining retraining retraining retraining retraining retraining retraining retraining retraining connec mackey mackey decays gener degraded denoting regularized regularized regularized regularized regularized regularized regularized regularized eliminating eliminating careful careful emphasize argued overhead deleted hansen hansen hansen hansen hansen hansen hansen hansen hansen hansen electronics electronics induces computa gauss gauss gauss gauss deletion hassibi hassibi hassibi hassibi handling influenced arrow arrow identically huberman ally beneficial juang autoregressive archi parti scenarios rameters denmark denmark denmark inducing surgeon surgeon surgeon akaike akaike akaike akaike akaike akaike wolff inst jan putation deleting stat recovers approxima save invert inserting delete delete italy icann jumps comprises paid tecture resampled rationale prefix augment tapped nonlin kung ghost superfluous assist fpe fpe fpe fpe fpe fpe fpe fpe mat sug larsen larsen larsen larsen larsen larsen larsen larsen larsen diction nuisance nuisance nuisance nuisance sudden kamm depart tionist saliencies saliencies saliencies saliencies saliencies saliencies saliencies saliencies prefactor prefactor prefactor reads danger kai neff neff neff neff neff neff neff neff neff neff neff danish ported viability viability viability inconsistencies atypical pression notoriously appreciated petersen gracefully morasso pioneered piscataway gest magnus lyngby lars reused ofa elaboration underestimates rearranging councils submatrix cular 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural input data function function function function function function function function function function function function figure figure figure figure set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number error error error error units units units information information information information information problem problem problem problem problem problem problem problem problem problem models models hidden hidden hidden hidden hidden hidden hidden weights weights weights weights weights shown systems systems systems probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters unit distribution distribution distribution distribution distribution approach pattern processing processing large local test test test test patterns class inputs inputs inputs inputs form form form form form algorithms simple simple gaussian gaussian gaussian gaussian paper paper examples small size net net net work methods step step points field field field field classification problems problems similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show equation equation equation section fixed line general parameter parameter approximation approximation approximation approximation theory theory obtained obtained obtained obtained experiments threshold threshold variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation research research independent log log log log log log log log log log log log log log log log defined found table estimate estimate standard standard terms terms terms science science prediction present present activation activation activation activation activation machine machine sets maximum maximum press learn components basis outputs continuous continuous continuous continuous continuous continuous abstract applied back find computational density density density density density density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic due procedure procedure important important propagation introduction hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior tion variable variable lower lower lower lower lower lower prior representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations learned chosen chosen chosen chosen part bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases cases cases type type type type type good good good binary binary binary binary binary binary binary binary binary binary binary long represent bayesian bayesian expected make make make make fact techniques proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed forward forward forward forward resulting resulting ing human respect respect sum eq means means optimization optimization made natural knowledge knowledge em em em obtain obtain obtain obtain negative original original original artificial samples application provide compute compute compute compute rates rates determined goal posterior posterior posterior posterior posterior constraints distributions distributions motor motor motor motor motor motor motor brain mit mit mit mit accuracy accuracy dependent modeling morgan report institute words department technique code advances joint joint connectionist bias addition addition ai considered framework framework cambridge computing computing computing computing computing computing domain domain domain domain domain equivalent equivalent equivalent directly directly hinton hinton hinton curves design san determine efficient efficient efficient full choice approximate estimated give con condition condition coding derived derived derived conditional conditional conditional conditional conditional conditional conditional developed bounds bounds bounds bounds bounds bounds bounds bounds lines product finally depends depends sampling sampling achieved measured measured technical denote denote transformation transformation transformation fast fast fast fast fast complete complete finding assumed assumed supported role ability kaufmann probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic needed reduced jordan jordan jordan jordan jordan jordan jordan technology special special structures structures principle principle operation leads squared representing numbers making making expert expert idea idea added architectures exact exact exact property introduced introduced introduced moving machines machines quadratic quadratic quadratic quadratic quadratic trees trees trees sense sense sense inference inference cognitive cognitive recently relevant highly varying unsupervised unsupervised works works works tions yields yields match sparse improvement grant grant grant grant grant exists parts lead suggests extended extended extended extended extended extended extended extended extended extended alternative alternative alternative alternative alternative alternative feed feed feed move conclusions central interactions interactions sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid accurate numerical clear exponential exponential practice practice mateo sound propose propose taking integration integration presence sigmoidal solid intelligence variety relationship introduce introduce configuration configuration boltzmann explicit explicit explicit derive derive written tuned missing involves remaining easy belief belief belief belief belief belief belief belief belief belief belief belief belief gaussians gaussians quality implies implies cycles select choosing family dependence depending squares viewed interpretation interpretation influence transform showed showed activities activities partial reasonable dashed performing performing performing classical convex visible visible construction foundation advantages avoid sciences uncertainty discuss maximize domains domains domains domains holds holds partially extra efficiency closely suitable included wij computations soc soc compact compact procedures contained issue generative notation gibbs michael michael dayan dayan dayan dayan dayan realistic consisted operating acknowledgments intrinsic layered layered difficulty hanson optimized integral divergence divergence graphical helpful existence ideas project fault fault fault relationships dependencies dependencies authors office working working comparable proper induction configurations illustrate perfect logistic logistic expressions store defines neal neal neal neal neal averages averages averages massachusetts inequality inequality theoretic growth distinguish derivation derivation defining fairly failure analytical tractable satisfied satisfied formalism precisely division directional choices laboratories inversion calculations optimize incomplete preceding nsf nsf integrating flexible peter detecting adjustable parent marginal marginal logp logp logp logp logp electric comments jaakkola jaakkola jaakkola jaakkola jaakkola cumulative spectra spectra intractable intractable intractable feasible sleep sleep writing writing summing fix zemel ordering approximates naval clamped kullback chains chains chains darken siemens intelligent resulted exploit reasoning substituting motivation recovered representational representational representational saul saul saul saul saul saul dependency propagated lawrence nonlinearities nonlinearities young refers properly informative roy roy relies relies likelihoods likelihoods likelihoods likelihoods likelihoods likelihoods likelihoods likelihoods likelihoods likelihoods implicitly dempster influences parents parents parents approx corporation rigorous rubin helmholtz helmholtz leibler equivalently deriving deriving super tables tables ties preserving poses adopt convenience assignments affects avoided wake wake tight assess avoids avoids ary summarizes equality ization permits bounding bounding bounding bounding bounding bounding inverted inverted inverted proba complementary complementary complementary complementary complementary complementary complementary complementary complementary complementary pearl pearl pos harder harder represen laird emphasized enforce frey atr failures observables appearing factorized mcdonnell heavily hat cast appealing incorporation fft fft petsche petsche petsche interpretations conditionally loads statist statist ready feasibility tations essence legendre dent fixing derives derives kuhn investigator proximation infeasible pew inserting imation formulations psyche psyche psyche jensen fac fac fac respec justify lacking tommi tommi subclass notational presidential altogether instantiations instantiations accompanying renders resort compactly manageable bilities vised appeal probabilistically hen instantiated instantiated instantiated instantiated quadratically ended cda spiegelhalter spiegelhalter admit admit probabili ffts ffts intractability lows urn lauritzen lauritzen lauritzen ins ins combina advan unavoidable directionality marginalization ils weigh marginally marginalizing conform tages pertain ely 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#@Jaakkola_T,Jordan_M,Saul_L,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input function function function function function function function function function function function figure figure figure figure time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number error error error error error error error error error error error error results results results results results results results results results results results results results information problem problem models hidden hidden hidden performance based based based based based based space space space space weights weights weights weights linear layer layer layer case case shown shown shown shown shown shown systems values parameters weight weight weight weight method method method approach approach pattern pattern pattern single single single single processing large large large rate rate test test test test analysis optimal shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper examples examples examples examples examples examples examples examples examples small small size size net net net net work work work work work work work work task task classification process level current current current current current current current current trained trained trained trained trained trained trained trained trained trained trained problems problems similar show show show show show equation equation equation equation equation equation equation equation rule generalization generalization generalization generalization average average theory term term term term term term term term term term experiments experiments experiments experiments experiments experiments result result result university university university university computation solution research independent target initial initial initial initial initial initial initial initial constant table table table table table table table table table table table table table table table standard standard standard standard computer computer computer terms science prediction present present activation nodes nodes machine machine machine machine range press outputs outputs abstract back find references ieee ieee ieee important important important adaptive propagation introduction generated generated variance cost cost cost cost search search search search search search search search change change rules rules rules rules rules rules rules measure measure measure prior prior prior part part previous previous previous type multiple multiple multiple multiple good good good good good good represent tree expected make make make make fact fact techniques techniques techniques techniques proposed correct correct correct correct correct correct errors errors errors errors resulting ing tasks human respect respect multi sum sum called called mapping study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge vol vol artificial artificial artificial artificial specific specific specific specific specific specific specific specific cross cross define define active determined experimental goal power power approaches approaches mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy train train dependent morgan morgan proceedings proceedings proceedings proceedings proceedings proceedings report report department department department department technique technique consists consists individual individual individual individual individual individual advances joint joint represents connectionist final final sequences considered considered considered framework cambridge computing domain domain domain domain domain domain domain domain domain directly directly directly additional san top conference conference conference conference conference conference classifiers classifiers classifiers significant statistics basic pages pages pages pages increase validation validation validation validation validation validation validation validation produce produce weighted weighted randomly randomly randomly randomly randomly randomly randomly randomly developed criterion types finally backpropagation backpropagation backpropagation backpropagation simply simply simply simply simply measured technical close close predictions predictions predictions predictions predictions predictions effective effective effective effective generate generate generate generate generate generate generate generate generate generate supported theoretical main journal ability instance instance easily fit fit kaufmann kaufmann objective objective objective combination reduced account significantly ratio edge increasing increasing empirical details max max max direct making making international international international international international international bottom idea combined combined combined combined combined combined combined combined choose run population population population population population population population population population population population population population population population population population population population population population improve improve improve ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble takes takes reported reported include subset highly highly highly highly highly highly highly highly varying previously approximately works works trans address address background background improvement grant parts parts extended predicted predicted alternative correctly correctly touretzky setting demonstrate demonstrate demonstrate place minimal row row row row row row row assumptions conclusions competitive competitive editors measures measures accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate accurate clear practice propose taking demonstrated demonstrated california intelligence intelligence intelligence start decrease decrease derivatives acknowledgements produces ways generating generating generating generating generating generating generating distinct confidence explicitly averaging text consisting quality quality quality quality quality cycles national focus focus review overlap showed showed soft partition partition partition key combining combining combining combining combining combining combining combining combining add add add add add calculate calculate topology topology transactions david expect existing existing thesis combinations inter instances sciences sciences vapnik coupled domains domains domains domains tests importance importance importance uniformly differ effectively effectively effectively effectively successful successful schemes genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic comparing comparing ten reached summary traditional refer notice notice quickly stopping classify running running running running hold usual usual generalize minimizes binding automatically illustrates tesauro decreasing decreasing decreasing presents trains trains trains production create create create create create create rapidly giving project boosting combine combine combine office referred referred decisions structured proved proved scores scores scores statistically possibly algo algo initialized consist consist generates generates phd defines defines defines ment ment pairwise growing unstable explanation starts reasons tive berkeley sites producing producing operators operators operators operators incorporate incorporate incorporate ran commonly separately separately describing members members members members members members members members recognizing meaning addressed researchers researchers explained improvements composite populations bootstrap frequently calculating differs differs datasets datasets adjust replace leen primarily rithm pick member member naval lecun fits adds breiman breiman breiman breiman proceeds keeping splitting settings settings settings settings knn krogh krogh krogh krogh krogh krogh effectiveness effectiveness generalizes heuristics heuristics started ambiguity predictors overview forecasting infinity jackel candidates initialize ensembles ensembles ensembles ensembles ensembles creating creating creating creating creating creating fitness fitness fitness fitness fitness fitness bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging cpu canada wolpert wolpert inductive fold fold shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik shavlik multiplying dna dna dna achieving ent tables creates diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse encouraging utilize utilize utilize junction junction junction tradeoff individuals individuals individuals classifies demon summarizes exponent care genes rithms crossover crossover emphasized emphasized portions hansen hansen hansen hansen misclassified diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity diversity refinement pop happen port things normalizing continually continually continually helps topologies topologies topologies topologies topologies topologies learners learners learners rarely lation tial junctions towell towell towell aid drawing eral mistakes mistakes normalize normalize normalize splice splice splice splice correctness correctness classi classi wisconsin wisconsin baltimore indirectly inaccurate stacked prune united mutation mutation actively actively actively ini montreal cortes drucker drucker refine collecting locating erroneous erroneous erroneous repeats madison madison disagree disagree disagree disagree disagreement disagreement motivates henceforth refining lowering kbann kbann ulation mon genome emphasizing emphasizing emphasizing emphasizing periments pertone tailed sev accompanied perrone signif reg focussed knowl eleventh eleventh effec orlando vedelsby vedelsby vedelsby vedelsby vedelsby vedelsby propositional bibliography wisc promoters promoters promoters minnesota fourteenth brunswick brunswick salamon salamon salamon icant forecasts maker popu ork refines genetically gent erage gies jude annotated awe mani mani prunes mains lates hind strates hopes tiers umn 
#@Opitz_D,Shavlik_J,
#t9
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#*network network network network network network network network network learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number error results results results results results results results results results results results results results results results units information information information problem problem problem problem problem problem problem problem problem problem problem problem problem models models performance performance performance performance performance based based based based based based based based space space weights case case case case case case case case vector vector vector shown shown shown systems systems values values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters weight unit unit distribution distribution method method approach approach approach approach approach pattern image single processing processing processing large large local local local local local test test test test test test test test patterns class class class class class class class class matrix matrix matrix matrix optimal optimal optimal optimal optimal inputs form shows algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples small size net work task task task task task methods methods methods methods methods methods methods methods methods methods step step step step points points points points points points points features classification classification classification classification classification classification classification classification classification classification classification classification classification process current trained structure problems problems random random high high high high high architecture section section rule rule generalization generalization generalization generalization generalization speech parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real real average note note note experiments experiments experiments experiments dimensional dimensional dimensional dimensional result result university university solution research research log log log log log log log log defined found found found found table table table table estimate estimate estimate estimate estimate estimate estimate standard standard computer terms terms terms terms terms terms terms terms terms terms science prediction prediction prediction prediction prediction prediction left map map map low sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum basis outputs continuous continuous sample abstract applied applied applied find find density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due due due procedure procedure procedure important decision mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex hand hand estimation estimation estimation estimation estimation estimation statistical statistical effect generated tion assume assume classifier classifier lower rules rules rules measure prior prior prior prior prior prior prior prior prior prior chosen chosen chosen center theorem bound cases required good distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected equations fact proposed proposed correct probabilities resulting resulting resulting classes ing ing tasks tasks tasks tasks regression regression computed computed respect respect sum elements knowledge knowledge em em em em em em em em em em em obtain obtain obtain original original artificial artificial samples samples samples true true true compared compared compared compared application application active determined goal posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions approaches approaches approaches approaches steps accuracy accuracy accuracy accuracy accuracy comparison larger contrast connection update update update train train train train source morgan morgan report report report report report institute version version consists consists consists consists consists individual advances advances final exp bias environment additional solutions solutions solutions estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates determine classifiers classifiers choice choice choice approximate approximate world world world estimated estimated estimated increase validation validation produce produce derived conditional product product actual constraint achieved achieved measured normal normal normal denote fast limited corresponds complete stable predictions predictions finding effective implemented implemented require journal degree degree typically typically underlying reduced technology leads leads leads numbers max max decay idea attention choose denotes denotes denotes denotes improved improved improved improved improved improved discussed discussed advantage separate ensemble ensemble typical practical apply apply apply introduced include identical identical sense subset subset recently recently recently recently compare compare previously yields correspond achieve diagonal mixtures mixtures mixtures mixtures mixtures mixtures mixtures improvement improvement improvement improvement improvement sensitive lead wide wide correctly hybrid deterministic clusters occurs column demonstrate conclusion starting starting greater competitive central bayes bayes numerical propose demonstrated intelligence regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization labeled radial averaged denoted relation derive derive derive construct written estimating label stability confidence missing category averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging infinite gaussians applying predictive springer expectation expectation expectation select yield yield yield choosing family family focus densities densities densities densities densities densities densities operations approximations soft constants reasonable spaces spaces spaces sec fitting intervals roughly iterative penalty penalty penalty penalty penalty penalty penalty penalty penalty generation advantages expect includes thesis thesis thesis priori bell recognize illustrated prove discuss maximize priors priors tests reason selecting society computationally detect efficiently computations mackay verlag prob dis superior superior notation maximization maximization maximization maximization predictor modelling overfitting overfitting overfitting essential estimators estimators mass hall discriminant scalar scalar school tech proper proved proved analogous possibly predicting extremely subsets multivariate multivariate simplest phd phd percentage rows trivial agreement variances variances unstable unstable analytic nowlan capabilities capabilities berkeley sections arise arise separately begin toronto medical incomplete mellon conjugate conjugate conjugate conjugate conjugate conjugate explained considerably considerably percent carnegie led led led peaks frequently maxima maxima compares pittsburgh ture pasadena suited suited germany germany chose patients deviations classifying tresp tresp tresp tresp tresp tresp benefit leen notes cooper optimality optimality partitions unity royal arranged kaufman kaufman numerically ments breiman breiman breiman breiman siemens siemens determination determination hyper responsible inferior performances performances performances introduces predictors predictors den belongs ensembles ensembles contraction master bagging bagging bagging bagging bagging bagging bagging bagging variants inf alternatively dempster interestingly robert severe severe severe lem posteriori discriminate dramatically multiplying yielded yielded blood ter rubin outperform ahmad formulate tibshirani restrictions reflected assess clas summarizes hastie community toy toy toy toy toy toy toy toy chapman labs regularized regularized concentrate singularities singularities proach dirichlet laird enforce universit applicability normalizing ward experi infinitely mix replacement replacement replacement replacement advantageous institut agrees outperformed realizations resampling resampling resampling resampling resampling ning possess coincide daily sity consumption consumption informatik iti iti iti iti iti iti iti neutral brackets artificially excessive generaliza proceeding favors disorder disorder technische technische prime accuracies attracted coincides fiir disorders parame llx llx llx llx buntine volker volker viable structuring disagree disagreement disagreement impressive impressive resampled resampled miinchen miinchen miinchen mac mac xlo pertone proaches liver liver liver tha tha subdivided subdivided appeal nical pling ond ala sive regu mfinchen iin kambhatla orm orm rob rob hollatz zfe adaption muenchen weightings resample lei lei regularize xll xll xll xll ofx impression straightfor xli xli xli larization aset baysian 
#@Ormoneit_D,Tresp_V,
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural input input input input input input input function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time set set set networks networks networks networks networks algorithm output output number number number number state results results results results results results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units information models performance space space weights weights weights linear linear linear linear linear case case order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order values values values probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions neurons unit unit approach point rate patterns analysis analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows algorithms simple simple gaussian gaussian paper small net work work work methods cells cells cells cells cells cells cells cells cells cells cells cells cells points features features features features process level level level current trained cell structure structure structure random random random random high high high high similar similar architecture architecture architecture show section general general parameter parameter parameter parameter average gradient gradient obtained obtained activity activity activity result result result university threshold research found found initial initial initial initial table table table table table estimate standard standard distance distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic science science science science science left left present present low low sets sets sets press press press press learn learn learn learn abstract abstract find density density density density density references due positive positive important introduction complex complex complex stimulus stimulus effect effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic change complexity complexity complexity complexity complexity complexity complexity complexity spatial spatial spatial spatial spatial spatial lower rules measure measure learned chosen higher part part center center center center center cortex conditions distributed region scale simulations resulting ing ing total total total total total simulation sum regions regions regions regions mapping means means reinforcement reinforcement reinforcement factor factor factor factor factor factor factor factor factor factor made made natural orientation orientation orientation orientation orientation orientation orientation orientation orientation study study study study study negative relative specific true series receptive provide determined determined related related connected motor cortical cortical cortical cortical brain brain contrast connection connection connection connection connection fields support source nets nets nets modeling selection selection proceedings proceedings institute department department internal internal internal internal internal layers scheme scheme scheme graph graph graph cambridge computing curve curve additional top effects effects effects effects significant speed basic basic basic basic increase increase increase increase produce levels area area finally inhibitory inhibitory inhibitory inhibitory biological fast inverse excitatory excitatory excitatory excitatory finding amount common shape shape synapse supported eds journal hypothesis degree development development development development sensory account dynamical functional mechanism pre direct inhibition normalized bottom bottom early early early early produced choose run run sources description identical identical machines cognitive cognitive interest highly varying approximately axis axis axis yields sparse sparse grid organization organization sensitive sensitive lead studied studied studied scaling scaling occur suggests suggests suggests suggests extended deviation move width width width width width width width width clusters column column column runs runs runs half strength conclusion hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian depend depend competitive numerical peak suggest encoding strong selective selective decrease decrease manner manner groups connectivity base base question areas explicit factors primary primary transitions pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning simultaneously simultaneously averaging linearly linearly linearly linearly linearly formed blocks blocks blocks cycles competition competition national national national focus correlated correlated influence influence influence influence influence influence influence variation restricted showed constants allowed slow false generation distances classified exploration figures figures usa usa usa assignment columns columns columns columns columns columns columns columns columns columns columns columns columns columns columns columns regular maximal modification presentation genetic genetic genetic tend miller miller miller composed excitation neuroscience classify follow gray surround wave wave wave wave wave wave wave wave wave wave wave wave wave wave highest reach received principles principles principles consisted overlapping extract deal decreasing presents presents presents presents explore simpler xor xor xor xor xor create difficulty varied varied varied humans strengths dual mass successive giving plasticity plasticity plasticity office working maximizing plausible man man created aspect aspect der der explored explored art grouping regime motivated great stop band separable separable separable separable separable growth growth growth growth growth analyzed slope slope slope slope slope slope slope slope slope slope slope slope slope cascade implementing tive organized ran scientific acknowledgement beginning patches patches patches linsker linsker linsker linsker bandwidth bandwidth bandwidth bandwidth author double led elman elman elman elman elman amounts embedded experimentally peaks orders orders orders orders share passed sharp reliability anti extracting extracting synchrony cal ordered gave logical logical logical logical logical logical kinds shaped windows findings findings findings deviations simultaneous wesley extreme cor uncorrelated addison generator appearance appearance appearance appearance appearance appearance appearance appearance appearance discover naval grows stronger analogy striate contract contract occurring mark settings affected motivation von accounts monkeys thomas arrangement parietal emergence emergence emergence emergence emergence waves waves waves spatiotemporal suggesting jolla jolla late late santa santa summarize cam explorations explorations explorations explorations pdf default default johnson johnson johnson johnson johnson johnson johnson johnson johnson johnson emergent emerge die decomposed forcing conservative verified inverted proba surrounding academy academy academy increasingly frontal apparently investigations slopes slopes slopes slopes slopes slopes travel increments wider ucsd ucsd ucsd ucsd appearing appearing remarkable bridge hyperbolic heavily jointly confirm firstly opponent diffuse developmental developmental stripes determinant exclusively manipulated manually goldberg goldberg sym sym sym sym sym sym sym sym sym sym sym seed systematically systematically symmetrical cooperation tended compensated gence essence format format stabilize neglected spa ini ini ini ini ini ini stabilization gradual tivity yon plexity plausibility organisation ascending structuring rightmost rightmost rightmost surrounded bandwidths ans justifies selec selec pointwise manifest lesser death death seeds seeds depended wrap recipes favored favored jeffrey undefined probabili probabili pursuing trophic trophic trophic trophic trophic trophic trophic trophic trophic trophic nand julesz sparser jeff ual confirmation cogsci cogsci swept ceiling ceiling disappearance changeux changeux immature emer dehaene dehaene netxvork congruence petition prun neuroreport 
#@Elman_J,Rebotier_T,
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#*network network network network network network network network network network network network learning learning neural neural neural neural input input input input input function function function figure figure figure figure figure figure figure figure figure figure set set set set networks networks networks networks training output number number number number number number number number number number number results units units units units units units information information problem hidden hidden hidden space space space space space weights linear linear linear linear linear linear case case case case case case case shown systems values values values values values values values values values values values values values values values values probability functions functions functions functions functions functions recognition pattern pattern pattern pattern point point point point point single single single single processing large large large local rate patterns patterns patterns patterns class class inputs inputs form form form form form form shows signal algorithms simple simple simple simple simple simple simple simple simple simple simple gaussian gaussian gaussian paper paper paper paper small small small small size net work work step points points points points points points points points points points points points classification classification classification current structure problems problems problems similar similar similar representation representation representation representation show show show equation equation equation equation equation equation equation equation equation equation section section section line rule rule general general general generalization real real approximation theory term term term note note result result result university university computation research defined defined found constant constant estimate estimate computer terms terms node science left left left left left activation activation activation activation activation activation sets maximum learn basis basis abstract find convergence convergence properties references ieee positive adaptive introduction hand statistical parallel recurrent difference difference difference difference difference difference difference theorem theorem theorem theorem theorem theorem theorem cases cases cases cases type good represent represent equations equations fact fact fact techniques probabilities finite classes classes total times times dimension dimension dimension dimension dimension global applications applications negative negative relative represented true compared compared experimental equal equal equal equal equal power power power power approaches approaches approaches approaches approaches approaches approaches approaches approaches mit comparison comparison comparison connection train report institute department version difficult layers ai equivalent equivalent curve curve curves curves transition limit limit limit limit limit limit limit limit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity full full significant free world increase give give finally finally finally evidence nature technical increases increases increases increases denote denote complete complete proof proof proof proof proof proof short short short short require end future typically smaller combination combination reduced interesting interesting interesting interesting interesting ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio york consistent consistent uniform making making normalized perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron architectures exact advantage advantage separate typical reported include identical identical identical identical machines side side side recently dimensions dimensions compare approximately works yields studies address generalized storage increased expression expression expression expression occurs conclusion place greater greater greater conclusions differences differences sigmoid accurate faster practice practice constrained suggest taking taking taking taking sigmoidal sigmoidal regularization radial radial exist relationship relationship relationship relationship relationship relationship relationship base denoted suppose appears derive derive derive plot plot laboratory distinct multilayer multilayer multilayer explicitly slightly consisting consisting consisting adding frequencies applying events versus versus versus versus versus versus letters decreases decreases independently expressed expressed stages lemma lemma lemma lemma constants constants diagram diagram diagram diagram additive combining closed valid valid advantages transactions expect figures thesis perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons vapnik plotted illustrated illustrated prove priors extra differ divided delta included poggio comparing comparing plots traditional road notice interested interpreted symmetry usual usual processors xor limitations issues fewer giving rest mappings mappings cover cover cover cover hill integer predicting illustrate perceptton perceptton store explain phd electronic asymptotically formula growth agreement derivation derivation fairly comparisons considerable sys sections easier widely choices sgn hyperplane consequence ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge computers meaning researchers researchers summation summation greatly splines passes passes fall monotonic lim lim lim lim lim lim lim lim lim lim lim lim lim lim yielding classifying proofs proofs college college college princeton pick girosi hyperplanes hyperplanes tensor concerned concerned count jones grows siemens siemens simplify multiplicative hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper exceeds substituting corollary corollary corollary respective equals percepttons infinity infinity infinity infinity infinity infinity infinity approximators advance mlps mlps foundations reader reader offer offer park park considerations partitioned dividing empty empty mind geometrical leaving email chervonenkis encouraging encouraging par additionally additionally recurrence recurrence recurrence recurrence recurrence modifying intuition tems crosses expand expand expand bump bump bump bump bump bump bump considers considers noting rbfs rbfs suffer memo vanishes dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies dichotomies coming factored capacities capacities capacities capacities capacities capacities capacities capacities capacities interior corporate trainable trainable east establishes inequalities december loosely keeler dichotomy dichotomy normalize proves william mcgraw thing computable compromise denominator maryland maryland subtle gardner gardner gardner gardner quantified obeys excluded plotting invert dominate rigorously rigorously sults indistinguishable conveniently lira story trivially resort rid identities noticeable gary ofp ofp ofp misleading representable nilsson nilsson nilsson nilsson ridges ridges ridges ridges ridges ridges ridges ridges ridges ridges ridges inclusive hartman nonmonotonic forp forp forp forp forp forp forp forp disregard consult consult consult superficially europhysics curious curious wouldn recompute scr lunch 
#@Flake_G,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data function function function function function function function function figure figure figure time time time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results units units information information information information information information information problem problem hidden hidden hidden performance performance performance performance performance based based based based space space weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer case vector vector vector vector order order order order order order order order shown shown systems values values parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions method method method approach approach approach approach pattern single single single processing processing control large large local local local local local local local local local local local local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate matrix optimal optimal inputs inputs inputs inputs inputs signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple examples size size size size size size size size net net work work work work task task task methods methods methods methods step step step step step step process process structure structure random random response architecture architecture architecture architecture show equation fixed rule general generalization parameter parameter parameter parameter approximation approximation average average average theory gradient gradient gradient gradient note note note note note note experiments experiments experiments experiments experiments activity activity activity activity activity activity university variables variables computation computation independent independent independent found sequence target target initial initial table table table table table standard standard computer distance connections node node node node node node node node science science left presented present activation activation activation activation activation activation activation low nodes nodes nodes nodes nodes nodes sets maximum maximum maximum maximum range range press learn learn learn nonlinear sample abstract back back back find computational computational convergence convergence convergence properties references component component component stochastic due due adaptive adaptive adaptive propagation introduction hand hand hand hand hand statistical effect effect effect cost cost cost recurrent tion tion change change change assume lower rules signals signals signals signals signals signals signals signals prior representations chosen chosen part center bound bound bound bound bound bound required required required required long conditions conditions represent tree distributed make fact techniques techniques techniques observed errors errors scale scale scale scale scale scale scale resulting ing ing total respect multi multi sum performed times regions optimization optimization optimization optimization made global global global global global global global global global global global knowledge obtain obtain samples samples cross rates rates rates rates rates rates rates rates rates rates perform active active active experimental experimental goal posterior gain gain brain equal equal equal equal equal power power approaches approaches mit comparison update update update update update update update update support descent descent descent descent dependent source modeling morgan morgan proceedings report institute department consists internal code individual advances advances bias bias bias bias bias layers layers layers ai ai ai framework cambridge computing equivalent directly directly directly hinton hinton hinton hinton hinton hinton additional view design san san san san conference conference efficient efficient efficient efficient efficient upper upper upper upper upper upper upper upper requires speed speed speed speed pages pages pages pages condition condition condition weighted criterion bounds bounds bounds entropy provided finally finally evidence backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation sampling simply measured discussion technical feedforward increases tested tested fast limited close close inverse assumption assumption effective effective shape adaptation instance makes makes fit kaufmann kaufmann objective typically typically typically typically account account transfer york special special uniform empirical empirical leads squared squared call max max pre magnitude magnitude magnitude frame decay combined combined produced run description predict denotes denotes denotes architectures improved improve improve improve correlations correlations typical reported include side side side quadratic inference sejnowski sejnowski sejnowski sejnowski cognitive cognitive recently highly compare conventional conventional conventional conventional volume volume yields studies achieve diagonal generalized improvement increased invariant invariant invariant invariant invariant invariant suggests suggests suggests deviation deviation predicted touretzky touretzky setting demonstrate editors central tangent differences sigmoid moody faster practice mateo mateo suggest encoding encoding taking largest external external proportional turn assuming assuming assuming variety decrease relationship relationship averaged targets targets introduce introduce acknowledgements explicit relation digit pro derive derive derive derive derive produces factors stability implement implement averaging unique equilibrium family family family family family family family family communication variation variation variation variation variation controlled centered centered sizes sizes activities activities updates updates key calculation epochs epochs epochs epochs measurements reduces roughly purpose remains remains calculate calculate foundation advantages expect expect expect existing priori priori usa inter batch batch batch batch batch batch batch batch batch batch batch batch activated specifically holds discussions structural structural structural reason society maximal maximal computationally effectively driven delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta wij wij schemes schemes online online online online online ten characteristic characteristic graphs allowing allowing heuristic neuroscience satisfy satisfy bar bar bar bar bar bar bar bar bar bar bar simplified dayan nips eigenvalue reach received subsequent jacobs jacobs deal extend minimized body explore unlike diego diego layered put relations relations relations relations association optimized optimized optimized optimized limitations hessian issues lippmann fashion giving ideas applicable applicable biol reliable reliable structured comparable proper proper tanh tanh affect notion momentum momentum momentum momentum momentum momentum surfaces matched act coefficient coefficient concepts plausible editor editor adapt illustrate created created created created created changed implementations implementations ensure quantities logistic logistic observe explored epoch epoch amari amari attempts residual residual residual residual residual indicating advanced derivation slope slope slope adjacent nowlan independence independence independence benchmark benchmark considerable considerable rapid sys sections strictly forces incorporate immediately separately members toronto definite annual radius preceding mellon conjugate prop carnegie collected empirically empirically empirically cmu amounts fed peter leave solla treated biologically reliability measuring pittsburgh proven sums germany simulator simulator simulator inherent redundancy yielding person person lab room newton redundant proportion proportion writing formally arguments member recover zemel approximates discover lecun lecun lecun lecun clamped ments ments fan fan fan fan held replacing replacing familiar serves hope removing neurobiology settings imply salk salk krogh krogh effectiveness synchronous canonical hertz financial respective sides propagated lawrence advance treatment rich steepest erlbaum impact valuable robert dramatically multiply approx largely deriving deriving shunting shunting shunting shunting shunting shunting benefits job isotropic isotropic isotropic feeding residuals residuals residuals residuals residuals acceptable amherst personal reports hillsdale forcing guess remainder pub increment favor deep deep deep interact tems file permits terrence relating relating retain statistic exceed exceed proach importantly option setup denver denver denver inversely book page knowing applicability struc experi simplifies utilizing remarkable expense expense handling hyperbolic prefer mcdonnell hoc hoc establishes exper inequalities lists incorporation subtracting ally discarded discarded archi restricting raises orr squashing squashing outgoing fastest contrary attenuation attenuation attenuation attenuation attenuation attenuation attenuation relational iti iti iti resultant successor clues translate eighth brought awij opinion imum schraudolph schraudolph schraudolph schraudolph schraudolph comprehensive comprehensive pew tutorial stand virtue kanter relying shortcut offered decrement rigorously topologically helped confirms tecture reilly reilly terry unequal surrounded trust lations continu cheap erties assist arbib plaut plaut plaut discarding saving geoff arrived backpropagated backpropagated backpropagated restarts backpropaga invaluable anonymous ficient suspect collapse dition textbook instrumental eft speedups haykin haykin refinements underly skip informational iments popularity duces propaga centering centering thorbergsson facilitating decouple linearizing coef macmillan equate permissible hitherto cision imately bottlenecks ooooooo ooooo battiti uts xerion xerion xerion recalculated customized posit ihl propriate tural directory sped fischer prescribe reap nici attenuate 
#@Schraudolph_N,Sejnowski_T,
#t9
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data data data function function function function figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output number number number number number number number number number system system system system system system system system system system system system system system system system error error error error state state results units information information problem problem models models performance based based space space space space space space space linear case case case vector vector vector vector vector vector vector systems systems values values values values parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions approach approach approach approach approach approach approach point point point point point point image image image single single single single single processing control large local local local matrix matrix matrix inputs inputs inputs form shows shows shows algorithms simple simple visual paper examples examples examples examples examples examples examples examples examples small small small small small size work work task task task task task task task task methods methods methods fig fig fig fig fig fig fig points points points points points points points features classification process level level level level level level level current current trained trained trained trained structure structure structure structure structure random high memory similar similar similar architecture section section fixed fixed line vectors vectors vectors vectors vectors images general parameter parameter parameter parameter parameter parameter parameter approximation approximation gradient obtained obtained dimensional dimensional dimensional dimensional dimensional dimensional dimensional university variables variables variables computation computation computation solution solution solution solution solution initial constant table table table standard standard computer distance distance distance distance science left left left left direction direction direction presented map map map map map map map map map map map present present present phase phase phase phase phase phase phase phase phase phase sets sets sets sets sets sets sets range range range range range range press press learn learn learn position position position position position position position basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs outputs continuous continuous continuous sample abstract applied computational analog references procedure procedure important important context context context context context context context context context context context context context context context introduction hand tion change change measure prior learned learned learned learned learned learned learned learned learned chosen chosen chosen higher part part part center center type required required required good good good distributed make length correct correct resulting ing ing tasks tasks total total respect respect performed eq mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping potential potential potential made made applications applications applications relative specific represented application desired desired desired provide compute proc location location location location determined determined experimental goal motor motor motor motor motor discrete discrete discrete discrete steps accuracy accuracy accuracy comparison larger contrast descent dependent dependent dependent source morgan proceedings department consists internal internal individual kernel joint joint joint joint joint final final scheme addition sequences ai maps maps maps maps maps maps maps maps maps maps considered domain domain domain domain domain domain domain environment environment environment environment environment environment environment environment environment directly directly additional solutions stage stage stage stage stage efficient efficient efficient efficient full full requires requires significant significant significant free free world world world vision pages pages pages pages give give con produce condition robot robot robot robot robot robot robot robot robot robot robot robot robot types provided constraint associative associative associative associative associative associative achieved achieved achieved achieved achieved achieved discussion normal denote denote transformation transformation transformation transformation fast fast fast limited inverse surface finding amount short require require require require adaptation adaptation square square square end end end end end pixel pixel pixel pixel pixel pixel ability degree makes underlying underlying combination dynamical unknown unknown fully projection projection projection special structures mode principle leads pre pre pre pre pre pre pre pre direct direct direct direct window normalized frame idea idea idea light improve directions advantage property property pair pair separate separate takes introduced introduced introduced side side hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical recently recently previously previously observations volume smooth match match match match correspond achieve achieve achieve diagonal positions positions positions positions positions positions positions locations observation observation observation observation observation observation observation observation observation observation observation observation grid grid grid grid grid organization entire entire constructed constructed constructed constructed constructed constructed constructed parts parts suggests deviation locally white pass demonstrate demonstrate demonstrate strength conclusion place reduce depend depend editors retina retina moody learns propose propose strong demonstrated demonstrated demonstrated intelligence radial minimizing minimizing user iii averaged scene identification identification identification question denoted attractor attractor attractor attractor attractor reference reference appears construct construct construct longer longer ways tuned tuned changing changing changing implement coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates angle angle angle integrated springer springer select independently independently independently review stages stages squares viewed learner learner learner solved transform restricted organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing lee partition partition earlier slow spaces spaces iterative iterative interpolation interpolation interpolation interpolation interpolation interpolation interpolation intermediate visible sufficiently assigned construction construction construction construction euclidean kohonen topology topology topology precision includes coordinate subspace subspace subspace determines variations domains characterized sensor extra efficiency capable suitable suitable suitable encoded encoded poggio situation orthogonal orthogonal fine characteristic capture capture summary verlag split split split split dis issue return contribution manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold notation involved vary simplified backward nips attempt subsequent disparity approximating camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera situations presents employed remain carried requirements rapidly put detail association rise fashion project mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings biol possibility possibility reliable structured structured root cover analogous matched hill extremely extremely extremely ensure prototype prototype som freedom improving motivated defines ment ment crucial crucial publishers growing lies tool rapid rapid rapid rapid rapid rapid rapid rapid rapid rapid rapid located leaves mation products angles angles angles demonstrates improvements embedded capability capability parameterized parameterized parameterized lattice lattice effort effort effort share marked completion completion completion completion completion employ compares polynomials passes passes berlin resource ordered enables germany kinds progress wesley sharing realized benefit cybern sensing feasible assign assign lagrange oxford girosi concerned unity robotics robotics robotics platt kaufman darken attractive attractive height hyper hyper hyper serves serves serves mark exploit responsible meaningful embedding interference contexts contexts contexts cone mouse displayed dependency demonstration stereo uni arrangement arrangement arrangement arrangement viewing specialized specialized specialized environmental belonging projects reverse implicitly subsequently omohundro alternatively generalizing generalizing automated skills skills skills skills land schulten drop ple kinematics kinematics pointing solves email covering focal benefits encodes preserving auxiliary constrain visited rectangular rectangular manifolds depicts proach increasingly paris win meta meta meta meta meta meta meta meta meta meta meta meta meta meta meta meta meta meta cartesian cartesian cartesian cartesian manipulator manipulator sam suffer places vanishes parametrized parametrized parametrized exploited ward october ritter ritter ritter ritter ritter ritter ritter coordination appearing factorized demand demand monitor monitor monitor transforming builds jointly calibration concrete condi tip practically tuple ref ref specialization specialization specialization specialization interpolating grids interpolate factorization rel rel mcgraw feasibility skill skill skill investment investment investment investment investment investment investment investment investment investment investment ically allocating freely freely dof dof dof martinetz costly dist dist dist dist dist dist dist dist gradual amsterdam resemble imposes ace elevation obeys argmin attracted attracted icann icann traversed extremes tiny retinas topologically heidelberg effector effector effector effector structuring structuring structuring structuring motivates knots walter walter walter walter walter walter walter positioned azimuth prototypical prototypical prototypical prototypical prototypical multivariable fragment visualized cameras cameras cameras cameras cameras cameras transfor calling equipped ordinates bumptrees manageable manageable hierarchically kappen specialize reuse powell technically visiting visiting invest invest situated tuples crease acquires clarendon 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#@Ritter_H,Walter_J,
#t9
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data function function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm output output output output output output output output output output output output output output number number number system system system system system system system system system system error error state state state state results results results results results results results results information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem models models models models hidden hidden hidden performance based based based based space weights weights weights weights weights linear linear linear layer layer case vector order order order order order order shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems values values parameters noise noise noise noise noise noise noise noise noise weight weight weight neurons unit unit unit distribution approach approach approach approach pattern point point point single single single control control control control large neuron rate rate rate rate rate test class class class class class class class class class class inputs inputs inputs inputs inputs inputs form shows shows shows algorithms algorithms simple simple simple simple paper paper paper paper paper small net work work work task task task methods methods methods methods fig step points points points points features classification classification classification structure structure problems problems problems problems problems problems problems problems problems problems memory similar architecture architecture show show show show show show show section fixed fixed fixed fixed fixed fixed fixed fixed average states states states states states states theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term note experiments dimensional university university university computation computation solution research research research independent found found sequence sequence target target target target target initial initial computer computer terms connections node node science science presented presented presented presented present temporal temporal maximum range range range learn learn learn learn nonlinear nonlinear nonlinear nonlinear nonlinear outputs abstract applied back back find computational computational computational references component due due due due due ieee ieee ieee ieee positive important introduction complex behavior behavior effect generated generated generated parallel cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion assume chosen chosen chosen chosen higher part part center previous previous multiple multiple long long long long long long long long long long long long long long long long long long long long long long long long long long long long long long represent represent distributed make length length length length observed finite simulations simulations resulting ing tasks total total total simulation simulation simulation simulation simulation respect respect respect respect sum called called called called times times times times times elements optimization feedback feedback feedback feedback global global applications knowledge filter samples samples compared desired desired series provide proc proc perform perform perform experimental experimental experimental experimental goal discrete discrete equal equal power approaches approaches steps steps steps comparison larger descent descent descent descent descent descent descent modeling proceedings proceedings report report report institute institute institute department synapses joint represents connectionist difficult difficult difficult difficult difficult difficult difficult difficult difficult final delay delay delay sequences sequences sequences sequences considered computing equivalent equivalent curves conference pages pages pages pages pages give give con randomly path actual finally processes backpropagation backpropagation backpropagation depends technical technical technical technical increases describe arbitrary stable stable stable surface predictions short short short short effective effective effective require journal journal journal end end end ability easily makes including typically reduced reduced reduced reduced dynamical dynamical dynamical ratio ratio trials uniform principle representing international international international run run added description description denotes architectures architectures architectures architectures architectures improved improve robust reported reported practical period identical machines machines hierarchical sense inference inference recently recently recently recently engineering engineering previously conventional conventional calculated volume works tions solve solve converge converge trans trans trans trans modified sensitive sensitive increased grant occur extended extended extended alternative correctly deterministic demonstrate runs conclusion place minimal greater editors designed clear moody faster propose integration presence external drawn demonstrated proportional assuming user relationship minima identification identification identification identification attractor attractor attractor acknowledgements explicit explicit derive written plot ann dept sensitivity multilayer electrical involves scales consisting equilibrium implies implies focus depending evaluate restricted fraction fraction showed showed lee approximated suggested suggested updates past past past past partial partial earlier epochs epochs epochs delays delays delays delays delays delays delays delays delays combining roughly remains valid sufficiently string string string symbol expect strings strings strings strings strings strings strings eigenvalues eigenvalues mozer specifically successfully simplicity reason reason reason regular compression capable uniformly uniformly encoded modification computationally effectively successful successful plots plots plots plots plots plots plots plots plots reached conf quickly quickly contained contained prob contribution classify classify follow sci generalize modular nips nips nips nips giles giles giles giles giles giles giles illustrates operating deal deal deal decreasing explore parametric powerful powerful powerful essential difficulty difficulty exponentially varied varied kalman relations involving involving involving hanson lippmann hall reducing giving history ideas investigated parity parity analytically possibility dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies comparable tanh tanh phases induction gradients gradients gradients gradients gradients necessarily man equally portion portion algo algo explored explored perceptton store arbitrarily defines percentage percentage percentage percentage unstable failure explanation analytical analytical capabilities capabilities independence independence inside lin lin lin lin ran bengio bengio bengio bengio simard involve circle circle res cybernetics robustness explained greatly pathways pathways capability readily peter autonomous autonomous autonomous poorly poorly orders adjustable passed perturbations chen chose chose lim lim converged univ consistently phenomenon indices college ear accomplished accomplished guarantee modify princeton princeton princeton princeton rithm linearity resources discover dealing accepted odd chemical operates fail reasoning intuitively intuitive intuitive grammars prentice mance representational perfor expanded realization lengths scheduling april eng eng ahead ahead ahead grammatical park inductive jump jump jump lem appeared unified slight ple shorter sontag sontag july propagating connec descriptions discovering alter jacobian jacobian musical argue argue favor exam schmidhuber schmidhuber schmidhuber toy rithms werbos march fir retain multiscale increasingly universit suffer drops bill increments rnn nec nec nec suggestions architectural architectural emphasis hyperbolic hyperbolic attributed attributed frasconi frasconi trainable heavily stay sym autoregressive vanish spie vicinity robustly robustly robustly robustly robustly vanishing vanishing vanishing capturing maryland maryland tsoi searched technische iir turing impor tant suggestion exceeded narendra hypothesize miinchen narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx narx bptt bptt bptt horne horne horne horne horne horne horne latch latch latch formalized tapped circumvent circumvent siegelmann siegelmann nonlin rutgers unambiguous farther hochreiter ljung attracting attracting latched decoupled insignificant orlando detectable unfolded unfolded unfolded pth sive jacobjan jacobjan florida parthasarathy rnns rnns rnns rnns speculate backpropagating unfolding dozen fki ruled ventional latches soda 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probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise method method approach point processing processing processing processing large large local local local local patterns analysis class class class class class matrix matrix optimal form form form form form shows shows signal algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple paper paper paper small small small small small work task task task methods methods classification classification classification classification classification classification classification classification process process process process trained trained trained trained trained structure structure structure structure random random high high similar architecture architecture architecture architecture show fixed fixed fixed fixed fixed fixed fixed fixed fixed rule general generalization parameter parameter parameter approximation obtained obtained university university threshold threshold threshold threshold computation computation computation solution solution solution independent log log log log log log log log log log log log defined standard standard standard standard standard computer node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node science presented present present activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes maximum press components nonlinear outputs outputs outputs outputs outputs outputs outputs abstract applied find computational likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due ieee decision mixture mixture mixture mixture mixture mixture introduction statistical statistical statistical effect tion tion variable rules measure chosen multiple good binary binary binary binary long tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree bayesian bayesian make make make techniques techniques techniques techniques correlation correlation correct correct probabilities probabilities simulations simulations classes ing ing ing regression regression regression computed computed multi multi sum times made made made made em em em em em em original original compared application application application desired cross series series define perform perform posterior brain brain power mit train train train train morgan report report institute department version technique consists advances advances advances final final final exp exp exp exp scheme scheme scheme scheme scheme scheme addition addition addition cambridge cambridge equivalent additional estimates san bit bit bit bit efficient efficient efficient classifiers classifiers significant statistics statistics speed increase increase increase increase validation conditional conditional conditional criterion criterion entropy path path path path path path path path path path path path path product processes selected constraint constraint achieved technical technical increases effective effective shape eds eds journal instance kaufmann kaufmann probabilistic underlying jordan jordan jordan significantly significantly leads iterations max max max making experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts depth depth expert expert expert expert expert expert expert expert expert expert expert expert expert expert idea combined combined combined added added denotes denotes discussed improve pair pair takes element apply hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees trees trees engineering sufficient solve yields achieve mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation evaluation gate gate gate gate gate gate gate gate gate gate gate gate gate gate increased lead alternative touretzky touretzky setting pass demonstrate greater greater greater greater reduce conclusions clear clear moody moody moody faster mateo california regularization variety start start iii iii introduce manner explicit pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning involves involves involves involves consisting adding applying applying expectation cycles cycles select depending solved solved evaluated evaluate showed evolution evolution forms soft completely partition updates earlier fitting fitting add add generation generation generation generation generation assigned avoid expect figures extension candidate candidate candidate candidate partially partially straightforward straightforward selecting selecting efficiency society paths paths build mackay mackay tend reached cun cun showing split split split split split split split split split split split split split split split split split split split split split split issue symmetry criteria usual simplified simplified denker denker thresholds thresholds jacobs jacobs jacobs modelling remain xor xor requirements hanson lippmann ml fashion school rest investigated terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal parity parity parity parity reliable structured structured root root root root root root root gates gates gates workshop circles friedman friedman perceptton seconds seconds seconds seconds optimum cart cart cart cart cart cart growing growing growing growing growing growing growing growing growing growing growing growing growing growing fairly 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#@Robinson_A,Waterhouse_S,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural data data data data data data function function function function set set set set set set set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number system system error error error error error error error error error error error error state state results results results results results results units units information information information information information information information information information problem problem problem problem problem problem problem models performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based space weights vector vector vector vector vector shown shown values values probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters distribution distribution distribution distribution distribution distribution recognition method method method method method method method method method method method method method method method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach point point image image single processing processing processing large local local local local rate rate rate rate test test test test test class class class class class class optimal optimal optimal optimal form form form signal algorithms algorithms examples examples small small size size size feature feature feature work work work work work work task methods methods methods methods methods methods methods methods methods methods methods methods methods field classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process process process process process level level level level level level level level level structure structure structure structure structure structure structure structure structure problems problems problems problems problems problems random random random random random random random high high fixed rule rule rule rule rule rule rule vectors vectors images general general general generalization generalization speech speech parameter parameter parameter average average theory theory theory gradient obtained obtained obtained obtained obtained obtained obtained note note note note note note dimensional dimensional result university university university solution solution solution solution solution solution solution solution log found found found sequence sequence target target table table standard computer computer distance science phase phase low low machine sets sets maximum maximum learn basis basis basis outputs outputs outputs abstract back back back references ieee ieee ieee ieee ieee important decision propagation propagation mixture introduction complex complex estimation statistical statistical statistical statistical statistical statistical statistical statistical statistical variance parallel parallel cost cost cost cost cost cost cost cost cost cost cost cost cost cost tion tion energy energy energy complexity complexity complexity complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier measure measure chosen chosen chosen chosen chosen chosen part part cases multiple conditions expected expected expected expected expected expected fact techniques techniques techniques proposed proposed probabilities probabilities probabilities probabilities probabilities finite simulations minimum minimum minimum minimum minimum minimum minimum resulting classes classes ing ing ing regression regression performed times regions regions mapping means optimization optimization optimization optimization optimization optimization optimization potential potential global global global global applications obtain original specific represented represented compared compared compared compared application desired series receptive receptive receptive define define proc proc proc perform experimental goal related related constraints constraints distributions distributions distributions distributions equal power approaches approaches comparison comparison larger contrast fields fields fields fields train descent descent descent descent descent descent descent descent descent descent descent words department department loss technique individual considered considered framework framework framework computing equivalent equivalent equivalent equivalent equivalent directly directly directly directly directly directly directly directly directly view solutions estimates design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design limit limit limit limit limit determine determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers requires choice choice significant approximate approximate approximate approximate statistics free free free vision estimated basic increase increase give con con derived derived clustering clustering clustering clustering clustering clustering clustering developed developed entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy constraint constraint constraint constraint constraint constraint constraint constraint simply achieved achieved achieved achieved achieved achieved measured measured group fast close surface surface finding rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf effective assumed supported end future future makes makes noisy noisy objective objective objective objective objective objective simulated probabilistic probabilistic probabilistic typically typically smaller fully technology mlp mlp significantly increasing increasing increasing consistent consistent consistent consistent structures structures structures structures structures structures matching uniform uniform uniform database empirical principle principle squared details max direct direct international normalized supervised supervised supervised minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize produced choose choose run description improve advantage pair reported reported subject subject trees sense sense sense sense sense recently engineering engineering interest interest highly conventional conventional unsupervised unsupervised yields converge achieve achieve achieve trans trans trans trans generalized risk increased grant lead extended alternative alternative locally deterministic deterministic deterministic deterministic deterministic deterministic occurs demonstrate demonstrate demonstrate starting critical critical greater greater reduce depend bayes bayes bayes bayes designed moody moody moody moody faster practice constrained constrained constrained temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature suggest suggest suggest propose hard hard hard hard hard hard hard hard hard hard hard hard hard hard physics physics physics demonstrated demonstrated demonstrated california california radial radial radial variety variety minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing start min min min min targets introduce introduce minima program annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing suppose pro derive produces index winner ways primary primary transitions label label tuned explicitly simultaneously physical physical electrical electrical involves involves develop minimization minimization minimization minimization choosing choosing national focus formation formation dependence reconstruction interpretation controlled controlled fraction fraction fraction similarly partition partition partition partition partition partition partition partition partition partition spectrum tracking assigned foundation david avoid formulation formulation formulation formulation determines determines extension extension uncertainty specifically phys structural structural structural structural structural structural structural determining effectively miller miller miller miller miller miller miller miller ten summary procedures procedures procedures allowing interested split dis dis superior comp comp notation gibbs write simplified minimizes minimizes quantization quantization ill maximization maximization attempt approximating satisfies decreasing modelling minimized employed poor overfitting investigate exponentially association association optimized accurately discriminant discriminant fashion ideas ideas tech applicable applicable referred decisions structured structured maximizing maximizing maximizing comparable comparable comparable comparable workshop matched naturally necessarily rev prototype quantities friedman submitted serial great theoretic theoretic theoretic theoretic theoretic theoretic theoretic derivation derivation waveform waveform benchmark comparisons tive purposes incorporate incorporate gradually gradually gradually mechanics greatly substantially experimentally poorly introducing posed formulated gains gains partitioning partitioning gen maximizes achieves substantial yuille yuille specifies realized initialization initialization college optimality formally lagrange lagrange lagrange restriction girosi girosi resources recover labelled partitions lost multiplier multiplier multiplier darken darken darken darken breiman breiman breiman satisfying satisfying intuitive combinatorial degradation motivation mance combines ensures sion respective perfor infinity tic claim smoothed reader offer steepest steepest steepest designing captures statement santa lett tures avoiding avoiding avoiding stone assigns assigns severe posteriori verify outperforms ure associations maintaining corporation corporation ter helmholtz helmholtz outperform outperform misclassification misclassification misclassification misclassification misclassification sig sig randomized randomized axe rao rao rao rao rao rao discriminative discriminative classifications seek seek assignments assignments publication shannon shannon shannon distribu labs emphasize echo ultimately noting topic unconstrained unconstrained associates emphasized anal anal misclassified geiger geiger enforce induces applicability dsp parametrized struc rose rose rose rose rose rose rose rose rose rose rose rose strict strict strict shallow satisfaction lagrangian lagrangian lagrangian opti allen identifies vis builds designs designs eral cast optima optima optima optima quantizer chan fox fox fox juang juang juang meth ultimate restricting repository sending sending ods constraining randomness randomness randomness randomness randomness randomness randomness randomness randomness irvine relaxed enforces enforces enforces enforces enforces enforces mis mach mach translate texas inform prescribed modest objectives objectives moderately degrade retaining retaining enforcing enforcing enforcing occasionally quantified mization continuing optimizes optimizes mrfs classifica belmont pot anneal concise justify distinguishes ire deformable neglecting niques tarassenko tarassenko shortcomings susceptible gression olshen recep sume tributions tributions pervised sole sole pennsylvania instruments wadsworth specialize gersho gersho gersho gersho gersho gersho iee deci sification sification bet intell intell roberts roberts analogies akin strained strained initializations increas objec unsu remedy barbara kenneth semiconductor gurewitz gurewitz gurewitz corp requisite requisite sociated 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#@Gersho_A,Miller_O,Rao_A,Rose_K,
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data function function function function figure time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output number number number number number number number number number number system system system system error error error error error error error error error state state state results results results results results units units units units units units units units units units units units information information information models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based based based based space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear layer layer layer layer layer layer case case case order order shown systems values values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method method method method approach approach approach approach single single single single single single control large large large large large large large rate rate rate test test test test test test test test test inputs inputs inputs inputs inputs inputs form form form form form algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples examples examples examples small small small small size size size size size size size size net task task task methods methods methods methods methods methods methods methods fig fig step step step step points process process process level level level level trained trained trained trained trained trained structure problems problems random random random random random high similar architecture architecture architecture rule rule general parameter parameter parameter parameter parameter parameter parameter real real real real real approximation approximation approximation approximation approximation average average average average average states gradient gradient gradient obtained obtained note note note dimensional university university variables variables variables variables variables computation research independent log log defined found dynamics dynamics dynamics initial initial constant table estimate computer computer computer terms terms terms connections connections connections connections science science prediction prediction prediction prediction prediction prediction prediction prediction left presented presented present phase phase low low object sets sets sets sets sets sets sets sets sets sets maximum maximum position components components basis outputs outputs sample sample abstract applied computational computational density references due due procedure adaptive adaptive decision introduction behavior generated variance variance variance variance variance variance search search tion change energy energy energy energy energy energy energy energy energy difference complexity lower measure prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior previous previous cases cases cases cases cases type required multiple good binary long long bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected equations make make region errors errors errors forward forward simulations simulations resulting tasks tasks tasks tasks tasks total total simulation regression regression regression regression computed computed computed computed computed computed respect sum sum performed performed performed eq times times regions means means potential potential potential made made made made knowledge original vol vol compared compared application desired cross cross cross series proc determined posterior posterior posterior posterior posterior posterior posterior posterior connected connected distributions gain discrete discrete equal equal steps steps steps accuracy larger larger larger dependent dependent source nets nets nets nets nets nets nets nets nets nets nets nets nets nets morgan institute department implementation implementation implementation implementation implementation implementation implementation implementation version version version version consists consists individual individual individual joint joint represents final final final final exp exp exp bias bias bias layers scheme scheme ai considered framework domain domain domain domain domain hinton limit san top top top top efficient full full full full choice significant statistics world world estimated increase validation validation validation validation validation give give give give weighted conditional conditional levels processes selected selected selected evidence evidence evidence evidence evidence backpropagation backpropagation iteration sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply achieved discussion group limited limited limited limited predictions predictions predictions predictions finding amount amount common common common common shape shape shape role face square instance including kaufmann dynamical dynamical dynamical fully fully testing increasing increasing increasing mode squared squared iterations iterations max max max pre direct direct direct direct making window window normalized magnitude decay decay decay decay idea minimize run run run run run description predict discussed advantage separate ensemble ensemble ensemble ensemble ensemble takes reported reported reported reported reported practical practical practical practical practical practical practical practical identical identical hierarchical sufficient previously conventional volume axis tions differential positions modified modified grid williams williams grant lead studied derivative feed feed locally hybrid hybrid hybrid hybrid touretzky generally runs runs half reduce conclusions valued valued editors interactions interactions bayes mateo physics largest largest assuming user user exist derivatives manner manner groups acknowledgements monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo written dept changing changing involves gaussians gaussians letters depending overlap evaluated evaluated evaluated updated updated updated updated updated approximations forms approximated sizes sizes sizes sizes partition constants updates updates updates updates updates updates allowed processor reasonable slow additive epochs combining intervals roughly purpose precision precision avoid exploration exploration exploration box thesis thesis batch automatic mozer specifically priors priors priors domains domains domains domains domains black tests simplicity gamma gamma gamma gamma gamma gamma gamma gamma gamma closely uniformly divided effectively included included modes modes efficiently mackay mackay mackay mackay comparing capture repeated allowing allowing allowing allowing allowing heuristic interpreted split dis gibbs gibbs gibbs gibbs gibbs gibbs bar sampled sampled vary nips highest highest reach attempt software bars bars bars employed explore poor overfitting essential experience experience updating rapidly integral hessian biases biases biases biases biases biases ml behaviour scalar analytically scaled scaled scaled root complicated complicated tanh statistically momentum momentum momentum momentum momentum attributes smallest smallest adapt adapt necessarily thought subsets subsets friedman friedman der art art multivariate multivariate improving phd neal neal neal neal neal neal mentioned slowly pairwise pairwise tool reasons producing worst mation cut toronto toronto toronto toronto toronto auto auto auto conjugate geometric geometric geometric geometric relevance relevance cmu amounts backprop splines splines http price price price price hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters marginal kinds sophisticated trade extensive appropriately partitions partitions robotics accepted determination intelligent check hyper grow grow keeping hope star adequate hours hours heuristics evaluations performances excellent combines combines introduces governed iteratively dependency insight cpu cpu cpu cpu cpu canada considerations std std std std avoiding default outlined outperforms approx truncated specification specification unable incorporates annals shorter rejection rejection rejection tradeoff big simulating mars mars mars mars mars mars mars mars mars forcing avoided avoided options remainder avoids unseen pub ftp ftp distri intuition mhz toy interact distribu approxi generators playing march eliminating picked individually rejected pos pos unconstrained termed quinlan quinlan funded sized grateful ignoring eters helps coming walk walk bution house house interpreting hamilton hour hour integrates rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen discarded hamiltonian hamiltonian vanish enter kinetic indirectly metropolis metropolis energies eighth monitored huge ard ard minute accu lowered saved ontario inertia inertia inertia inertia quarter symmetries stays dev dev dev neglecting unimportant hyperparameter hyperparameter hyperparameter persistence persistence persistence invoked mips sug subdivided edward utgoff initialisation initialisation quired collectively lihood radford radford questionable kennedy augmenting leapfrog leapfrog walks vastly vastly carl carl racy servo servo servo servo tedious lib crete obtainable rior terior terior poste compensating dictions namical duane duane pioneered fictitious companion gest parametrised competitors unexplained unexplained momenta momenta momenta caught normalising evidences oix mpg mpg underfitting pendleton tually 
#@Rasmussen_C,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function figure 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linear linear linear linear linear linear linear linear layer layer case case vector vector vector vector vector order order order order order order order order order order order shown shown shown shown shown systems systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions unit unit unit unit distribution distribution distribution distribution distribution method method method method method method approach approach approach approach point point point image single single processing processing control control control control large large large large large large large local local local local local local local local local local local local local local local local local local local local local local local local local rate test test test test matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs inputs inputs inputs form form form shows shows shows simple simple simple simple simple gaussian gaussian gaussian paper paper paper examples small small small size size size size size size size size feature feature feature feature work work work task task task task task task task methods methods methods points points points points field field field field field field field field field field field field field field field field features process process current current trained trained trained trained problems problems problems problems problems high memory similar similar equation equation equation section section section section section section fixed rule rule parameter real real real real real real approximation approximation approximation average average states theory gradient gradient gradient gradient gradient term term term term term term term term term note note result result result result result result result threshold variables computation computation independent found target target dynamics dynamics dynamics initial constant constant constant constant estimate standard standard standard terms terms terms terms distance distance distance distance distance distance distance distance distance distance prediction prediction prediction prediction prediction prediction prediction map activation activation activation activation low sets sets sets press learn learn learn learn learn learn basis nonlinear continuous continuous sample sample abstract applied applied back find computational density properties properties properties properties properties properties references component due due due due positive procedure important important important adaptive adaptive mixture mixture mixture introduction estimation effect generated generated generated generated parallel cost cost cost cost tion tion tion change change change change complexity complexity spatial assume classifier lower measure measure measure prior prior prior learned learned learned learned chosen higher higher higher higher higher part part part part part part center center center center theorem required required good represent distributed bayesian equations make techniques region region region region region region region correct correct probabilities forward simulations simulations minimum resulting ing ing tasks tasks tasks total total total simulation human regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect respect sum sum performed performed elements elements regions mapping means means means factor factor factor optimization potential dimension dimension orientation global global global global global knowledge em em filter obtain obtain original original artificial samples desired cross cross cross cross cross cross series series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive proc location location location location determined distributions distributions gain motor approaches approaches approaches approaches mit accuracy comparison comparison contrast contrast contrast contrast connection fields fields fields fields update update update update update update update update update descent descent descent descent descent modeling selection selection selection selection selection morgan report loss consists consists consists code individual individual individual advances joint final exp exp exp bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias scheme addition cambridge computing domain domain domain experiment experiment experiment hinton hinton additional view view view view view view estimates estimates trajectory trajectory detection detection detection detection detection detection determine determine upper upper upper upper full requires statistics statistics world speed speed speed validation validation validation validation validation con con weighted weighted weighted weighted weighted weighted weighted robot robot robot robot robot robot controller controller controller controller lines lines lines lines actual finally finally finally finally backpropagation achieved achieved discussion technical denote denote fast fast inverse inverse inverse inverse inverse inverse corresponds corresponds stable predictions predictions predictions predictions amount amount assumed assumed shape shape shape shape shape role require require eds eds adaptation square square end end end end end instance future easily easily makes noisy noisy fit kaufmann simulated probabilistic smaller needed reduced functional coefficients jordan jordan jordan jordan york york york york increasing increasing empirical mode squared squared squared squared squared squared squared max making bottom bottom bottom experts experts experts experts experts experts 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exists lead deviation wide derivative derivative derivative predicted alternative alternative alternative alternative correctly feed locally locally locally locally locally locally locally locally locally locally locally locally locally move move pass demonstrate demonstrate demonstrate place place assumptions assumptions trajectories competitive measures sutton sutton performs asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic suggest reduction reduction characteristics drawn drawn drawn sigmoidal demonstrated solid proportional variety variety minimizing minimizing minimizing movements relationship introduce introduce derivatives derivatives derivatives derivatives minima identification denoted explicit derive derive written primary generating estimating changing modeled modeled confidence confidence confidence confidence pruning pruning metric metric metric metric metric metric metric metric metric metric sensitivity averaging dimensionality dimensionality text scales springer quality competition independently independently review reconstruction reconstruction correlated squares squares overlap overlap overlap overlap overlap influence solved updated updated fraction centers centered forms sign smoothing smoothing smoothing additive epochs epochs epochs epochs epochs epochs classical expansion expansion sec fitting fitting fitting add iterative iterative penalty penalty penalty penalty penalty penalty valid valid calculate calculate query query avoid bell eigenvalues eigenvalues eigenvalues contour batch batch batch recognize determines determines determines determines activated activated priors domains domains domains domains domains gating major reason extra importance maximal computationally delta detect computations essentially identity prob moore moore interpreted dis duration received overlapping illustrates subsequent approximating jacobs jacobs jacobs jacobs deal receive oriented oriented oriented cowan minimized employed origin origin parametric parametric american wiley wiley create create investigate experience put strengths association limitations hessian recursive recursive hall giving tech mse mse mse incremental incremental incremental incremental incremental incremental incremental incremental incremental analytically combine scaled root root complicated workshop func act act act circles coefficient spline created equally implementations implementations adjusted rank rank quantities quantities obvious greedy noted taylor taylor logic initialized initialized switching multivariate baseline detected extent submitted submitted isolated isolated isolated mentioned asymptotically site great slowly piecewise derivation analyzed analyzed analyzed nowlan nowlan analytical london drive tive tive tive precisely incorporate sgn immediately arise recognized involve implicit ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge definite arises depicted explained explained reflects profile pseudo effort atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson marked marked adjustable splines employ incorporated sharp commands http http differs popular cal cal cal curvature curvature suited plan enables shaped wesley distortion irrelevant irrelevant globally newton newton newton college identifying accomplished www www addison assign temporally appropriately narrow acts rotated purely reconstructed repre plays generality dealing ments ments minutes adjusting adjusting occurred los affected guide constructive nonparametric nonparametric hours reliably alspector evaluations interference interference interference interference interference interference interference interference interference excellent mance introduces introduces introduces connect negligible perfor decide mental mental intended histograms uni facilitate offers initialize augmented draw draw wolpert wolpert partitioned subsequently tures avoiding avoiding default default accumulated yale maintaining ter ter basically leaming validity removal benefits incrementally incrementally incrementally tibshirani tibshirani convenience corrected additionally additionally ideally experiences assess verified penalized penalized perpendicular hastie hastie formance compensate decays chapman annealed eliminating bump iso iso acquired topic integrals rhythmic employing constructs accounted happen minor stuck avoidance avoidance prevents atr compu mix moderate moderate chris algorithmic acquire acquire ate christopher transforming subnet subnet subnet subnet subnet subnet subnet focuses focuses orthonormal compete compete compete imple err err err stripes cally cally devised schaal schaal schaal schaal schaal schaal schaal schaal accumulate placement cooperation cooperation cooperation cooperation rameters isolation isolation isolation isolation explanations tance sions triangular appl dimen experienced experienced remained cho counterpart creation scott scott thresh alamos catastrophic outlier outlier outlier vanishing stacked cleveland cleveland ated putation fore cope cope sented dof costly favors noticed stat assessing sparc sparc haven omit predic inserting minute forgetting forgetting ther possesses pursued ele multiplications ting shrink shrink fac fac gun scratch asso cen cen theor ana penalizing penalizing exclude kyoto tational fulfill fulfill expects gression gression recep recep recep sume faithful beats sketched stefan stefan quantifies recognizable rin cre marcel dekker realizes orienta gravity soraku structurally ljung ljung shrinking diagnostics atlanta eubank casdagli entity consis kuh kuh accomplishes expertise expertise expertise expertise expertise expertise expertise tent cooperate cooperate danger georgia gatech gatech gatech gatech incre incre ingredient hikaridai forget distributing dation deficient ciated parameterizations prac mclachlan mclachlan verse mensional cga casting competi basford basford influential permissible weighed 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set networks networks networks networks networks networks networks networks training output output output output output output output output number number number number number number system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results units units units units units units units units units units units units units units units units units units units information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based weights weights weights weights weights weights layer case case case case case order order systems values values values weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit approach approach approach point point point point single processing large rate rate rate rate analysis analysis class class class class class class class inputs inputs inputs form form form form form signal signal signal signal signal signal signal signal signal signal signal signal signal simple paper paper paper paper paper paper work work work step current current current memory response response response response response architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture equation equation equation section section section section section section section section section section section section section section section fixed fixed fixed fixed line rule rule rule general general states states states states states theory theory note note note result result result result university computation computation computation computation computation computation solution defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial initial constant constant constant constant constant terms connections node node node node node node node node science presented presented presented presented present activation activation activation activation activation activation activation activation activation activation activation nodes nodes nodes nodes machine machine machine range range range range range learn learn learn components outputs outputs abstract applied computational computational computational computational computational computational computational computational computational computational computational references ieee ieee ieee important introduction introduction hand recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent assume lower lower signals signals signals signals learned previous previous previous previous previous previous previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound cases cases type represent represent represent represent represent represent represent represent represent represent represent expected fact fact fact proposed correlation correlation correlation correlation correlation correlation correlation correlation length length length length length length length length finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite minimum minimum classes classes classes simulation computed sum sum sum performed mapping means natural original original specific specific specific represented represented represented define compute compute compute perform constraints connected connected power power power power power power power power approaches steps steps steps steps larger connection connection connection nets nets morgan proceedings words words words department version consists internal internal advances represents represents represents represents represents final scheme addition ai ai ai considered computing computing computing computing equivalent equivalent transition transition transition transition san efficient upper requires world world weighted weighted developed types types finally finally selected nature nature depends depends describe assumption assumption complete proof proof proof proof proof proof proof proof proof proof implemented implemented implemented implemented role theoretical require eds journal future fit kaufmann account unknown interesting york increasing increasing increasing special special empirical operation representing attention combined description architectures architectures discussed discussed apply apply apply period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period period machines machines interest rl definition definition definition observation entire constructed touretzky starting greater greater greater greater greater conclusions conclusions central sigmoid clear performs moody mateo cycle cycle cycle cycle cycle cycle cycle turn turn turn assuming start start start start start start relationship relationship connectivity connectivity question question suppose derive construct describes describes describes describes transitions transitions transitions confidence implement implement implement implement infinite infinite infinite remaining consisting applying applying implies implies implies implies implies implies implies implies implies cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles cycles depending viewed viewed interpretation lemma lemma lemma lemma detailed evaluate updated lee similarly similarly diagram remains valid string string string symbol symbol symbol symbol symbol topology topology topology transactions transactions transactions figures includes activations activations activations activations activations formulation strings illustrated prove prove prove prove prove specifically specifically holds discussions discussions reason identified identified importance symbols symbols symbols symbols identify computations comparing situation situation repeated repeated repeated repeated issue issue oscillations follow follow device hold play giles giles giles giles giles giles giles giles giles giles giles giles giles giles computes computes computes subsequent decreasing presents presents presents simpler unlike detail replaced replaced association limitations limitations recursive recursive lippmann existence examine relationships authors authors authors authors referred complicated proved proved oscillation oscillation oscillation oscillation oscillation workshop examined induction circles circles naturally possibly reading automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata automata formal formal formal noted noted noted noted logistic initialized initialized initialized extent languages formula formula guaranteed defining answer cascade cascade cascade cascade cascade cascade cascade cascade implementing organized style precisely products describing describing depicted depicted sun addressed requiring fourth fourth evaluating double elman mod mod modulated proven proven proven chen chen chen conclude implements wesley realized realized proofs proofs proofs sort accomplished addison equivalence formally formally investigation investigation summing fix acm acm member labelled labelled labelled adds 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remarks identifies oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate oscillate arrow mirror powers powers concern concern concerns concerns concerns concerns evenly evenly exclusively tuple fij substitution squashing proves proves proves proves proves proves implying cascaded oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates oscillates shortly allowable violate violate unifying accepting accepting turing reviews lowered def def def mal mal machinery numbered numbered numbered lemmas lemmas lemmas med med med divides divides originating siegelmann siegelmann concluded concluded expands expands concluding stefan ofp unrealizable unrealizable unrealizable ifp ifp ifp ifp ifp ifp ifp ifp contradiction representable 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#@Kremer_S,
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#*network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data function function function function function function function figure figure figure figure time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm output output output output output output output output number number number number number system system system system system system system system system system system system system system system system system system system system system error error results results results results results units units units units units units units units units units units units units hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based space weights weights weights linear linear linear linear layer layer layer layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown systems systems systems systems systems systems systems systems systems values values values values parameters weight weight weight functions functions unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition pattern pattern point point point point point point point point point point point point point point point point single single single single single single single single single single single single processing processing processing processing control control large large large large large large large rate rate rate rate rate class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix shows signal signal signal algorithms algorithms simple simple paper paper small small small small size size size size net net net net net net net net net work work work work work task task task features process process level level level current current current problems problems problems problems high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar representation architecture architecture architecture architecture architecture architecture architecture show section section section section section fixed fixed fixed fixed fixed fixed fixed fixed line vectors general general general general general speech speech speech speech speech speech approximation approximation approximation obtained result result university computation computation computation solution research research independent table table table table table standard standard standard standard computer computer science map present present activation activation activation activation activation activation low machine sets range range range components components continuous abstract back back back computational references ieee ieee ieee ieee ieee ieee important adaptive adaptive propagation propagation propagation propagation propagation introduction complex hand hand circuit parallel parallel cost cost cost cost cost change change change rules higher center previous type required required required multiple good distributed chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make length forward forward forward forward forward resulting resulting ing total human multi multi performed times times elements elements elements mapping optimization made applications applications applications applications applications applications obtain original artificial artificial compared application application application application application provide provide provide provide provide provide provide compute compute compute proc proc perform perform perform perform experimental goal related related connected connected connected gain gain larger contrast contrast update support support support support support morgan morgan morgan morgan morgan morgan morgan report institute department implementation implementation version version technique internal internal code code code code code individual kernel joint layers layers layers considered computing environment environment environment environment environment environment environment directly additional solutions solutions design design design design design design design design design design design design design design design bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit full requires significant significant significant significant significant pages increase produce developed area area area controller product provided provided finally selected backpropagation backpropagation backpropagation backpropagation backpropagation discussion discussion fast fast fast fast limited limited complete complete effective implemented implemented synapse synapse synapse supported require require require require main main main main main main main journal square end vlsi vlsi future makes makes development development development development including including including typically smaller needed needed reduced functional functional functional functional functional fully fully fully mlp mlp mlp block transfer increasing special operation language details call numbers max max max bits bits bits international run run run run added perceptron architectures improve improve advantage advantage advantage takes element element typical include include machines machines array array engineering sufficient compare compare conventional conventional works tions speaker studies achieve address evaluation evaluation evaluation modified organization grant constructed parts parts scaling extended digital digital digital wide wide wide wide wide matrices matrices feed move move loop hardware hardware hardware hardware hardware pass pass runs runs greater greater sigmoid sigmoid sigmoid measures designed peak peak performs performs external external external external external cycle cycle cycle cycle cycle cycle cycle california proportional manner manner program program base areas pro pro written written written index primary primary primary ann ann implement simultaneously electrical remaining integrated shift versus cycles cycles cycles cycles cycles john john john focus phoneme operations operations operations operations operations operations operations operations operations operations operations operations operations operations operations operations operations updated soft soft sizes sizes similarly processor processor processor processor processor processor processor earlier calculation reduces roughly purpose purpose purpose add add add interpolation interpolation generation intermediate initially advantages david degrees precision precision precision precision precision precision precision precision precision avoid building building existing existing includes sciences discuss maximize regular extra presentation presentation efficiently computations computations composed conf conf issue contribution running running running device write usual providing board board board board board board cmos cmos chips chips chips processors processors operating extract software software software software software software software software load load load presents schedule access access access access access requirements requirements requirements requirements exhibit circuitry optimized optimized optimized optimized hall scalar scalar scalar scalar scaled working symbolic understand math integer extremely equally implementations ensure portion observe academic store store utility serial devices devices piecewise developing developing floating floating floating floating floating floating floating floating majority expensive comparisons considerable considerable berkeley berkeley berkeley berkeley berkeley sections easier producing producing incorporate transistors potentially acknowledgement bandwidth bandwidth bandwidth bandwidth bandwidth demonstrates demonstrates demonstrates nsf sun outer double flexible flexible readily backprop employ employ execution operate operate instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction serve enables logical chose neuro neuro synchronization arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic trade representative representative fabricated interface interface interface interface interface interface tation extensive extensive optimizing acts multipliers multipliers adds tools tools siemens simplify determination programmable programmable loops contract clock enhanced evaluations prentice mance mance slice programs james perfor perfor scheduling scheduling assembly counter competing offers specialized mlps lazzaro offer cpu cpu extensively extensively card designing designing instructions instructions instructions balanced johnson johnson johnson johnson onr multiply multiply multiply multiply multiply multiply street leaving accept achieving kluwer bus nelson nelson die abstraction exception exception ease ease simd simd simd workstation workstation workstation workstation workstation workstation workstation workstation workstation workstation workstation workstation streams ibm ibm ibm mhz mhz mhz mhz formance management blocking gas file execute execute execute execute permits convert compatible compatible compatible compatible oct carefully overhead parallelism parallelism parallelism host host host host host host lookup investigating library library library library library library library library library library indexed indexed indexed attached attached register register register discusses intl intl supports algebra commercial commercial commercial commercial commercial commercial commercial port port holding intensive compu challenge accumulation functionality handling handling slot slot suite routines routines routines routines routines routines routines routines routines routines integrates integrates conversion conversion conversion station core core slices specialization correctness loads archi arpa server server server feldman saturating format modern trend focusing promise ized manual registers registers registers registers undergo linking saturate insert stan routine routine routine routine mid imum custom progresses sparc sparc pes pes pes utilities metal dominate inte dard advice package accessible notably tecture munich accelerator requests banks workstations workstations workstations workstations workstations multiplies multiplies multiplies throughput industry handles neurocomputer icsi icsi wawrzynek wawrzynek wawrzynek wawrzynek wawrzynek wawrzynek accelerated emulation pipeline pipeline pipeline pipeline pipeline mips mips mips mips mips mips mips microprocessor microprocessor microprocessor microprocessor microprocessor microprocessor microprocessor microprocessor microprocessor microprocessor microprocessor microprocessor operands operands inexpensive compatibility hen portant services services scalable microelectronics gee beck beck beck beck beck sparcstation sparcstation signifi compiler hammerstrom hammerstrom cache cache cache cache cache cache tiling ported speedups libraries vide aged brian packard invoking dram dram dram tains offs mcps sram sram sram sustain sustain striped interleaved hewlett bed pack pipelines pipelines pipelines operand expose accumulator ttm interfacing mflops mflops accesses accesses accesses jerry provement multimedia timer executable executable compilation uri rearranged unrolling formats 
#@Asanovic_K,Beck_J,Johnson_D,Kingsbury_B,Morgan_N,Wawrzynek_J,
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#*network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input function function function function function function function figure figure figure figure figure figure time time time set set set set set set set networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number results results results results results results results results results information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance case case case vector order order order order systems systems systems values values parameters parameters parameters parameters functions functions functions unit unit method method method method method approach pattern pattern point point point point processing processing processing large local local analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper paper feature net net net methods methods methods methods points points points process current problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems similar architecture show show fixed approximation obtained obtained term term term term term term term note note note note note experiments experiments experiments experiments experiments experiments experiments experiments result university university university computation computation log defined defined defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics computer terms terms terms terms terms terms terms terms terms distance distance distance node node node node science left left present present low nodes nodes machine press press press press continuous abstract applied applied find find analog references stochastic stochastic stochastic stochastic stochastic ieee ieee positive positive positive context introduction hand estimation statistical statistical statistical statistical statistical statistical statistical generated generated generated parallel recurrent recurrent tion tion tion energy energy energy energy energy energy energy difference difference spatial assume measure previous cases type required required required multiple multiple multiple represent represent distributed distributed expected techniques techniques techniques techniques techniques length minimum minimum resulting resulting ing ing ing ing respect respect times times times times elements elements elements elements mapping means optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization em em em original original specific compared compared series series series provide experimental goal constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints equal equal equal power mit mit accuracy accuracy accuracy comparison contrast update update update update update update update morgan department implementation implementation version version version version version version technique technique technique technique technique technique technique technique technique advances advances represents difficult exp graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph ai ai considered considered considered framework framework framework framework framework cambridge cambridge domain additional solutions san requires choice choice free speed speed speed pages pages con produce derived weighted randomly clustering clustering evidence evidence iteration iteration constraint constraint constraint constraint constraint constraint constraint constraint constraint simply biological arbitrary inverse common main square square square rumelhart rumelhart rumelhart including kaufmann objective objective objective objective objective objective objective hopfield hopfield hopfield hopfield hopfield hopfield special special matching matching matching matching matching matching details normalized early minimize run run run reported apply introduced include include subject subject quadratic quadratic recently recently compare previously previously conventional conventional volume works solve solve match converge converge trans modified generalized generalized generalized interval interval increased increased derivative matrices matrices matrices touretzky deterministic deterministic column setting demonstrate demonstrate conclusion critical row editors editors editors measures clear clear performs asymptotic temperature temperature hard hard physics physics physics physics physics physics physics intelligence minimizing minimizing min relationship iii iii iii introduce connectivity minima van van van derive solving solving winner winner winner winner ways ann stability dept implement implement quality versus versus versus versus john solved solved soft soft partition allowed sign partial expansion normalization roughly add add iterative penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty valid distances assigned assigned euclidean euclidean euclidean euclidean advantages advantages advantages advantages transactions avoid thesis formulation assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment specifically structural simplicity simplicity simplicity columns columns columns columns columns columns middle middle closely uniformly mcclelland mcclelland mcclelland miller miller miller reached graphs graphs superior notation paradigm correspondence tesauro tesauro cowan minimized minimized minimized employed simpler simpler remain parametric wiley essential updating updating fewer fewer decisions maximizing math integer equally thought ensure versions versions noted noted algo taylor serial serial serial serial serial serial serial serial serial phd finds wta wta wta wta wta wta wta wta rows rows rows rows rows ment ment glass glass glass glass glass glass glass glass glass glass glass glass glass satisfied widely strictly day day day day ran ran ran ran ran involve gradually members cybernetics preceding researchers evaluating conducted poorly employ slower slower slower slower compares partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning ture fall proven tank tank tank tank tank tank returns yuille yuille yuille yuille yuille yuille yuille calls softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax pose leen saddle saddle saddle assign assign assign lagrange lagrange lagrange extensive optimizing member bin bin bin repre multipliers multipliers city city city city city city city synchronous synchronous synchronous synchronous synchronous synchronous synchronous combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial spurious mjolsness mjolsness mjolsness dominant lengths den den den originally elastic elastic reproduce peterson peterson peterson peterson peterson peterson peterson peterson iterated treatment francisco membership membership membership membership membership membership permutation permutation permutation permutation permutation permutation permutation bins bins bins bins bins bins bins late sons partitioned partitioned partitioned papers alternatively adopted yale yale yale gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold gold employs restrictions par classic classic classic massively massively massively visited visited visited attempted annealed depicts parallelism employing employing employing termed termed emphasized barrier enforce enforce sized sized intl fea tune tune nal normalizing normalizing travel computa worked tour tour tour satisfaction traveling traveling traveling traveling tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp tsp steven eliminates returned diagnostic rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan salesman salesman salesman salesman salesman salesman invisible statist enforces enforces tained emerged emerged emerged massive potts potts potts potts potts potts potts potts potts potts potts potts potts modest benchmarks benchmarks benchmarks benchmarks benchmarks benchmarks benchmarks mid mai mai mai mai resemble enforcing enforcing haven haven gij sentations enforced lowered mal anneal optimiza tours jour cities cities cities cities cities modulo bout bout bout subscripts loses doubly doubly doubly doubly doubly lai kosowsky kosowsky kosowsky kosowsky kosowsky kosowsky kosowsky straint positivity radiology ima armed eling rior eee cit adjacency intention anand older timization enforcement kan graduated rithmic chichester sitivity lvi partitionings ploy eyi 
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#*network model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data function function function function function function function function figure figure figure time time set networks networks networks networks networks networks networks networks networks networks algorithm algorithm number number number number number number number system system state results results information problem problem problem problem problem problem based based based space layer layer layer layer case case vector order order order order shown systems functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons recognition recognition method method method method method method method method method method method method method method method approach approach pattern pattern pattern pattern point point point image image image image single control large large large large large large large local local local local neuron neuron neuron analysis class matrix matrix optimal form form shows algorithms simple visual visual visual paper examples small small size size size size net net net work work work work task task task methods methods methods methods methods methods methods fig fig fig step step step step points field level level level level current current problems problems problems problems problems problems problems problems problems problems problems similar representation representation representation representation representation section section section section section section line rule vectors general general general general parameter real approximation average average theory gradient gradient gradient gradient obtained experiments activity activity result result result result result university university variables variables variables variables variables variables variables computation computation computation computation solution solution solution solution solution defined found found dynamics dynamics dynamics estimate computer computer terms terms terms terms connections science left left direction direction presented present present present phase phase phase phase phase activation low temporal nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous abstract applied applied applied applied applied computational computational computational computational computational convergence convergence convergence convergence analog references component due ieee ieee positive important introduction behavior statistical effect effect effect effect effect dynamic cost cost cost cost cost tion tion difference variable spatial spatial spatial spatial measure measure measure measure representations chosen chosen chosen chosen part center good binary distributed make make techniques techniques techniques techniques techniques techniques region region region region region region region region region region region proposed proposed proposed observed scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale finite minimum minimum resulting resulting ing total total human computed performed eq eq eq eq eq eq eq times means means means optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization dimension dimension dimension made global global global global study obtain negative original original original original relative represented application series define compute proc active active active active determined determined determined experimental constraints discrete discrete discrete power approaches approaches steps accuracy comparison connection update support descent descent nets nets nets nets nets nets nets nets nets implementation difficult final scheme framework framework framework framework framework framework framework framework framework framework framework framework framework framework framework framework computing curves curves san detection determine efficient efficient efficient choice significant approximate speed speed vision vision vision vision increase con derived levels criterion actual finally processes processes selected nature discussion increases tested limited inverse corresponds complete surface common effective assumed supported theoretical theoretical theoretical adaptation journal end ability hypothesis instance makes fit objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective simulated smaller underlying underlying needed hopfield hopfield hopfield hopfield combination reduced reduced account block block block block block block transfer ratio increasing segmentation segmentation segmentation mechanism mechanism mechanism mechanism consistent consistent structures leads principal numbers early early idea attention attention attention attention attention attention attention combined combined combined combined combined minimize run neuronal neuronal directions property takes practical practical practical practical introduced introduced include quadratic quadratic quadratic sense subset recently engineering engineering sufficient highly highly axis tions tions solve solve solve smooth smooth correspond trans trans diagonal sparse sparse sparse modified modified intensity invariant scaling occur matrices predicted predicted alternative move loop deterministic deterministic deterministic generally conclusion starting reduce trajectories valued valued valued sigmoid measures measures constrained temperature propose propose mechanisms largest reduction reduction reduction reduction california regularization labeled minimizing exist selective min min introduce introduce introduce introduce introduce derivatives connectivity minima minima minima minima configuration annealing annealing annealing annealing annealing areas areas van solving solving winner describes dept dept simultaneously infinite electrical scales scales scales scales scales scales scales scales scales scales applying blocks national focus focus focus focus focus focus focus solved solved approximations static approximated sizes sizes partition partition partition updates past earlier expansion convex convex convex convex convex neighborhood valid sufficiently norm norm norm norm koch koch koch koch koch usa inter instances instances subspace subspace sciences discuss discuss specifically domains absolute absolute neighbors neighbors successfully reason determining determining efficiency computationally effectively delta included included presentation successful identify efficiently projections characteristic kind procedures allowing allowing success anderson neuroscience neuroscience dis notation notation quantity list relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation minimizes predictor routing law carried diego poor requirements requirements requirements requirements investigate investigate circuitry rapidly involving involving hessian hessian biol decisions structured func func func phases phases analogous neu saliency saliency saliency saliency saliency coarse coarse coarse necessarily created aspect versions obvious greedy noted assumes taylor taylor switching mixed established optimum indicating indicating costs agreement smoothness track handle nonlinearity spatially rapid closer incorporate acknowledgement grossberg implicit gradually optimize definite lowest depicted radius outer researchers mechanics conjugate reflects apparent reflect readily maintain price summarized tank tank tank curvature curvature curvature expectations focused yuille attentional attentional attentional attentional attentional attentional attentional attentional progress cumulative cumulative cumulative globally globally discontinuities discontinuities newton newton newton newton newton benefit analogue primarily linearity pick resources resources resources partitions unity tem robotics clamped accepted overcome loops neurobiology shifts adequate clock combinatorial spurious lip mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness governed corre pat guarantees dominant searching elastic jolla refers steepest steepest designing papers interestingly avoiding avoiding convergent convergent accumulated informa yale yale yale yale truncated entropic ent equivalently validity opposed alternating dec willshaw willshaw comparative quasi quasi medium seek eric arising pub rectangular summarizes iff evolve alternate pami wall maintained file discontinuity afosr ullman ullman ullman argued spreading multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale multiscale academy intensities indexed barrier sized siam thousands thousands intensive durbin durbin compu ucsd ucsd ucsd picking moderate beam opti sponding resolve agrees thousand nested hundreds suffers locate adaptively adaptively olshausen olshausen tsp conceptual termination fill finer inclusion accomplish essen usefulness devised partly coincide fij restricting exploits neurobiological syntactic periodically gence indirectly prominent tens tern objectives objectives objectives objectives objectives objectives objectives trapped instant preferable retaining haven mization prime putational optimizes borders inability extrema extrema formulations formulations reminiscent schematically sparsity pay tie conver clocked clocked numbered numbered justify tinuous responsive cse functionals functionals analogously trust trust trust trust trust trust spotlight assist coarser coarser marroquin decade mecha terzopoulos terzopoulos tives elliptical objec garrett notoriously preferably marquardt url barriers reduc multigrid nism timization levenberg yaleu perature lagrangians hessians hessians summand jective inexact subproblem subproblem tationally ingful conforms 
#@Mjolsness_E,Tsioutsias_O,
#t9
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function figure figure time time set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number error error results results results results results results results results units information information information information information information information problem problem based based based based based based based based based based based based based based based based based based based based based based space space space space space weights vector order order shown shown shown systems systems systems systems systems values values values probability probability noise weight functions functions functions functions functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method approach approach approach approach approach approach approach pattern pattern pattern pattern point image image single single single single single single single processing processing processing control control large test test patterns patterns patterns patterns patterns patterns patterns class class class shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple visual paper paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size size task task task task task task methods methods methods methods methods methods methods fig fig field features features level level current trained trained trained trained problems problems problems random memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar representation representation representation representation representation representation representation representation representation representation rule vectors images images images images images images images images images generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech approximation approximation theory theory gradient obtained obtained term experiments dimensional university university university computation research research independent independent found found target target target target target target target target target initial constant estimate estimate standard standard standard standard standard computer computer computer computer computer distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance science science science science science science prediction presented present machine machine machine object object object object object object sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets press press press learn learn learn learn learn learn learn position outputs abstract applied applied applied applied back back back back back back back back back computational references references due ieee positive positive positive positive important important important important important adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation context context context context context introduction complex complex parallel tion change energy complexity assume prior prior representations representations representations representations learned learned learned learned learned learned learned learned learned learned previous previous previous type type required multiple multiple multiple good good good distributed make fact fact techniques techniques proposed proposed proposed ing ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks human human regression called reinforcement reinforcement factor factor potential potential made natural study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge negative vol artificial artificial artificial artificial represented represented compared compared application desired desired cross series provide provide provide provide provide objects objects objects objects objects objects location perform determined experimental experimental goal related related related related related motor approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches mit mit accuracy accuracy accuracy accuracy accuracy accuracy comparison support support support support support support support support support support support support support support support support support support support support train source morgan morgan morgan proceedings proceedings proceedings proceedings report report report institute institute department department department implementation implementation version technique internal internal internal internal internal advances advances bias addition addition maps maps framework framework framework framework domain domain domain experiment directly directly hinton additional additional additional additional additional view view curves estimates san san san conference conference conference conference choice significant significant world vision estimated basic pages pages pages pages pages derived derived weighted clustering robot robot robot robot robot provided selected evidence evidence depends simply measured discussion technical technical technical increases describe describe group group tested tested inverse assumption assumption complete finding amount nearest nearest nearest nearest common assumed shape role role main face face face face journal journal pixel pixel ability rumelhart rumelhart fit fit kaufmann kaufmann kaufmann pairs pairs underlying account unknown unknown transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer testing testing significantly increasing consistent database database database empirical language numbers international international international international supervised supervised supervised combined minimize minimize choose description improve improve improve property property typical reported include include side previously conventional observations approximately approximately volume yields correspond studies studies studies achieve generalized williams entire entire entire expression concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept studied studied invariant scaling wide rotation alternative correctly correctly correctly locally setting demonstrate neighbor neighbor editors editors editors editors editors tangent tangent tangent differences differences differences differences accurate bayes moody learns mateo mateo mateo suggest propose mechanisms drawn assuming variety selective iii averaged force denoted denoted denoted denoted denoted denoted denoted suppose suppose suppose perception perception describes distinct confidence confidence metric metric metric sensitivity explicitly simultaneously involves involves yield national family learner learner learner learner learner learner learner learner learner influence detailed evaluated labels labels forms translation past key key interpolation query query query faces faces faces faces faces formulation color color color recognize specifically specifically specifically domains domains domains domains neighbors determining aspects aspects capable importance modification mcclelland poggio comparing traditional notice notice notice notice notice contained contained moore showing interested interpreted interpreted hold categories sampled play generalize generalize generalize generalize generalize generalize generalize generalize generalize board giles denker hypotheses approximating software extend camera cowan situations situations trains bars employed transformed collection essential essential experience humans humans humans humans hanson hanson hanson accurately accurately accurately accurately accurately accurately lippmann helpful school stream stream symbolic symbolic statistically notion hill concepts editor editor traffic facial illustrate illustrate illustrate eyes ensure obvious academic academic defines averages years preference inequality developing costs costs distinguish publishers publishers slope slope slope slope explanation explanation explanation explanation explanation explanation explanation majority briefly london drive formalism easier easier easier easier easier widely forces division incorporate commonly mathematics mathematics simard members author recognizing mellon mellon people prop prop prop prop prop carnegie carnegie cmu cmu embedded embedded lack autonomous car atkeson employ employ psychological psychological http rely pittsburgh pittsburgh characterize characterize differs extensions suited germany logical boston boston shaped returns differentiable yielding hints hints hints hints hints hints realized consistently consistently consistently person person sort www oxford investigation acm appropriately member member member concerned mobile addresses printed lecun robotics rigid plays communications systematic fits saturation wrong adjusting stated exploit exploit exploit reasoning reasoning knn knn knn knn illumination hint carry generalizes generalizes inferior service edelman edelman displayed dominant originally originally viewing approximators israel israel april indicator indicator indicator extends extensively relies inductive exploiting generalizing generalizing johnson skills abu unable unable mostafa thrun thrun thrun thrun thrun thrun thrun thrun thrun shepard shepard shepard shepard shepard shepard shepard users sig kluwer kluwer presenting employs conjecture exception personal spaced stem hundred classifies experiences chess scenario brightness invariances invariances invariances exam robots grouped mitchell mitchell searches inverted considers ullman investigating sketch constructs book book tune slopes slopes slopes port prevents gorithm november lighting january font institut hat hat virtually bold establishes december mining outperformed exclusively exclusively ples triangle automation petsche scenarios arrives judd baxter synergy interpolate distorted informatik upright experienced thing thing thing thing thing gathered faced faced bonn tenth generaliza accuracies sebastian collecting transferred transferred lifetime lifetime lifetime lifetime caruana fiir opportunity opportunity accepts web subsampled boost boost vast lay plain multitask encounter euclidian seventh enormous opens waltz facing brute victorri votes utgoff avail transfers persons misleading investigates intriguing rests testbed sullivan sullivan guessing dominating memorize weizmann weizmann holden scarce scarce scarce scarce precede dejong transferring transferring transferring iig rehovot rehovot irregularly beymer nificantly tangents stemming trix repr repr dordrecht counterexamples counterexample counterexample bottle bottle smoothers ack 
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number error results results results results results results results results results results results results results results results results results units units units units information information information information information information information information information information information information information information information information information information problem problem problem problem problem models models hidden hidden hidden hidden performance based based space space space space space space space weights weights layer case case shown shown shown systems systems systems systems systems systems systems noise noise noise noise noise weight distribution distribution distribution distribution recognition recognition method method method approach approach approach point point single single single single processing processing processing processing large local local local local local local local local local rate test test analysis class class class class class class class class class inputs inputs inputs inputs simple simple gaussian gaussian gaussian paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small size size size size size size size size work work work work work task task methods methods points points points points classification classification classification classification classification classification classification classification classification classification classification process process process level level level current current trained trained trained trained trained trained trained trained problems problems problems problems problems problems problems problems problems problems problems random random random random high memory response response response response similar show show show show section section section section section section section line line line line line line line rule vectors vectors vectors vectors general generalization generalization generalization generalization parameter real average experiments experiments experiments experiments experiments experiments experiments experiments experiments result result university research independent defined sequence sequence sequence sequence sequence target table table table table table estimate standard standard standard standard standard standard standard distance prediction presented machine machine sets sets sets sets maximum range learn learn learn position position position position sample abstract back computational properties references stochastic ieee procedure procedure procedure procedure procedure propagation context introduction behavior behavior statistical effect effect variance variance variance variance cost cost search difference classifier classifier prior word word word word part part bound bound type type type multiple multiple conditions conditions conditions distributed expected expected make techniques techniques forward times times potential dimension global global knowledge knowledge knowledge em em em em em em em em em artificial artificial relative specific samples samples samples samples cross provide perform goal goal related gain equal equal accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger contrast contrast train source nets selection proceedings report words words department implementation implementation implementation version technique technique advances advances advances advances bias addition addition addition addition addition framework curves curves curves estimates effects conference conference determine determine determine classifiers upper upper full requires requires requires requires requires significant significant significant significant statistics free free increase increase validation randomly robot criterion criterion criterion criterion criterion criterion path provided finally sampling simply achieved discussion technical increases tested amount nearest nearest nearest nearest effective effective effective effective generate generate generate supported theoretical require main main main main hypothesis instance instance smaller unknown jordan jordan jordan significantly significantly significantly significantly significantly significantly significantly significantly significantly structures empirical principle call max max bits international international supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised early idea predict improved improved improve improve improve improve improve advantage advantage property property takes similarity reported reported reported side sense sense sense highly previously observations works modified improvement improvement improvement improvement improvement parts parts occur suggests suggests suggests correctly correctly correctly correctly pass starting conclusions neighbor neighbor accurate asymptotic asymptotic asymptotic suggest encoding encoding encoding encoding largest largest largest characteristics intelligence regularization labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled turn start min min scene areas construct written perception ways describes label label label label label label label label label label label confidence missing missing missing missing missing missing missing remaining remaining slightly text adding decreases focus focus formation learner learner learner codes labels labels labels labels labels labels labels labels sizes reasonable neighborhood neighborhood roughly roughly add add boundaries generation generation generation generation query classified classified classified transactions recorded building box plotted uncertainty specifically domains neighbors neighbors tests tests major sensor sensor middle aspects uniformly effectively delta committee detect genetic essentially reached reached capture road graphs graphs repeated procedures contained link link link stopping stopping stopping stopping split superior superior return return classify criteria hold sampled attempt mixing neighboring neighboring explore explore unlike overfitting create collection exponentially replaced hanson hanson hanson hanson hanson hanson association dataset dataset dataset dataset investigated referred variability workshop encode statistically statistically statistically statistically cover cover cover smallest closest closest closest integer man created equally subsets explored initialized ith epoch epoch consist finds synthetic synthetic synthetic synthetic synthetic synthetic stop stop stop trivial distinguish improves improves failure biology biology majority expensive briefly worse turns stanford mation commonly controls controls cybernetics incomplete meaning greatly percent percent percent percent percent percent percent collected car marked incorrect incorrect rep variant synthesis synthesis occurrence serve serve serve prevent datasets datasets datasets datasets datasets datasets datasets datasets boston conclude returns patients begins sentence initialization consistently consistently consistently consistently consistently consistently consistently consistently consistently acquisition room room ghahramani ghahramani ghahramani college contextual labeling labeling princeton mobile turned reaching consideration siemens determination vehicle efficacy obtaining tishby unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled methodology methodology shifts hours inferior inferior inferior exploring infor tap repeat combines iteratively pat guarantees expanded intended intended intended intended injection counting centroid centroid specialized specialized record correcting inductive seung valuable summarize shavlik shavlik shavlik shavlik shavlik shavlik interestingly pen pen dna dna dna largely kluwer munro munro ties instantiation copy junction junction junction junction junction junction junction freund freund affects molecular molecular alter mismatch exam exam geoffrey gener gener guidance pomerleau pomerleau paired union indication prevents replacement expense achievable corporate synthesized junctions builds towell towell towell towell towell towell towell towell hundreds east fill inclusion suppress unreliable subtracted contrasts ples ples extracts substitute splice splice splice splice heterogeneous seed seed seed seed modalities judd judd noun lewis lewis senses senses senses filling filling encodings deter locality deformation request physica huge verb costly lexical tern refine replaces replaces retaining assessing occasionally neigh borders sition weakness synthesize synthesize synthesize synthesize synthesize synthesize synthesize synthesize accu alization alization reminiscent reminiscent scribed copied linguistics augment endpoints instantiations beats tailed disambiguation nucleotides nucleotides resentations subdivided reachable promoter promoter promoter downward bor subsection supplying eleventh eleventh criticism collects collects racy eleven promoters topical topical topical topical topical topical topical inclusive disjunctive matsuoka matsuoka matsuoka mine uncommon guesses beled squeeze unclassified centtold nucleotide 
#@Towell_G,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural input input input input input input input input input input input data data data data data data function function function function function function function function function function function function function function function function function figure figure time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number number number system error results results results results results results results results units information information problem problem problem problem hidden performance performance performance performance performance performance performance based based based based based based based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear layer layer layer layer layer layer case vector vector order order order order order order order order order order order order order shown shown shown shown systems values values probability probability probability probability probability probability probability probability probability probability parameters parameters noise noise weight weight functions functions functions functions functions functions functions functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method approach approach point point single processing processing large large test test test test test test analysis analysis class class class class class class class optimal optimal inputs inputs inputs algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper examples examples examples examples examples examples small size size size size size size size size size size feature feature feature feature feature feature feature feature work work work work work task task task methods features features features features features features features features features features features features features features features features features features features features features features features features classification classification process level level current trained trained trained trained structure problems problems problems problems problems random random random high high high high similar similar representation representation representation representation representation representation show show show show section section fixed line general general general generalization generalization generalization generalization generalization generalization generalization parameter real real real real real real real real real real approximation average theory theory theory theory theory note note experiments experiments experiments experiments experiments result result university university university threshold threshold threshold threshold research log log log defined found sequence sequence target target target target target constant table table table table computer computer computer terms science science map present present present present present machine machine machine sets sets range press press learn learn learn learn learn basis outputs sample abstract find find find computational references ieee positive positive positive positive decision decision decision decision propagation introduction complex statistical statistical generated parallel search search tion complexity complexity complexity representations representations representations learned learned chosen higher previous cases good good good represent represent represent represent distributed make fact fact fact fact correlation correlation correlation length finite finite resulting ing ing tasks tasks tasks tasks respect respect respect respect multi multi multi multi multi sum performed called called times regions regions potential made made made natural applications applications study knowledge knowledge artificial artificial specific specific represented represented true true application application cross cross cross cross define define compute compute compute proc proc proc proc proc discrete discrete discrete brain brain mit accuracy accuracy accuracy accuracy fields train train modeling morgan words words implementation version version consists internal advances joint represents represents represents difficult difficult difficult final final final bias sequences sequences ai domain domain domain domain domain domain domain domain domain domain hinton view limit stage stage stage stage stage stage determine classifiers classifiers choice choice significant approximate world world world world world world basic validation validation validation validation validation validation con produce produce produce coding coding coding coding coding coding weighted weighted weighted weighted weighted randomly developed developed bounds bounds evidence backpropagation backpropagation biological describe denote limited limited inverse predictions proof finding finding supported supported theoretical theoretical journal end ability ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis future future rumelhart rumelhart rumelhart rumelhart development noisy noisy noisy kaufmann simulated needed mlp mlp mlp mlp mlp mlp interesting interesting interesting significantly significantly consistent consistent consistent consistent database empirical empirical empirical details call call call call numbers international international polynomial polynomial polynomial polynomial polynomial produced produced produced produced run run run perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes recent recent advantage pair takes element practical practical practical practical apply apply include include trees trees trees sense sense relevant interest sufficient compare volume volume works works works tions match sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse address definition definition evaluation bounded williams grant grant concept occur suggests touretzky occurs runs minimal valued valued valued editors editors differences accurate accurate designed practice practice practice practice weak weak weak weak weak weak weak weak weak weak weak weak weak learns taking strong strong largest characteristics drawn california intelligence intelligence turn turn relationship introduce question question denoted acknowledgements areas appears produces produces produces produces produces produces factors factors describes ann dept dept confidence pruning pruning pruning recall recall explicitly explicitly involves easy consisting develop develop implies boolean boolean boolean select select select stages stages stages stages stages learner learner learner lemma lemma lemma lemma lemma open evaluate approximated sizes sizes sign sign sign sign earlier earlier reasonable reasonable initially filtering sufficiently symbol query advantages expect includes thesis perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons instances sciences recognize prove specifically specifically domains domains domains domains domains domains domains partially partially straightforward selecting efficiency included included mcclelland literature efficiently efficiently conf conf conf conf strongly induced cun cun interested interested stopping criteria criteria criteria denker hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses automatically overlapping operating preferred unlike powerful create collection investigate investigate exhibit exhibit exponentially humans humans humans limitations discriminant discriminant fewer boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting comparable comparable gates gates symbolic symbolic encode understand understand understand cognition notion induction smallest concepts editor integer integer integer integer analyze ensure noted algo algo precise perceptton ith generates explain phd finds stop stop pairwise developing theoretic crucial guaranteed defining biology adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost majority reasons tive widely producing protein protein protein protein protein choices choices choices bishop commonly mathematics mathematics potentially scientific involve involve implicit begin annual annual annual nsf outer explained explained explained explained consistency consistency consistency consistency consistency readily backprop solla haussler haussler remove frequently frequently variant calculating exhibits pittsburgh plan plan conclude conclude returns damage damage representative ordinary ordinary ordinary ordinary ordinary ordinary ordinary ordinary pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac identifying guarantee guarantee modify summing acm rithm rithm approximates approximates discovery harmonic nonzero nonzero nonzero adds convenient significance significance serves mark mark definitions methodology symposium constructive obd obd obd obd date meaningful weakly weakly programs schapire schapire schapire schapire decide decide pruned pruned pruned pruned pruned guarantees guarantees conjunction conjunction conjunction conjunction conjunction regard percepttons percepttons percepttons percepttons percepttons facilitate chooses bases bases bases bases bases claim foundations express suggesting offer proteins draw agree inductive considerations implicitly santa generalizing approximator approximator approximator approximator approximator fold fold shavlik shavlik shavlik interestingly explorations onr learnable learnable learnable learnable learnable learnable learnable learnable consecutive multiply approx maintaining dna dna dna microstructure ter exhaustive exhaustive creates utilize arbor additionally solely solely solely reports reports freund freund freund freund freund freund freund freund descriptions molecular valiant valiant valiant formance convert met paired constructs quinlan quinlan quinlan importantly france voting voting voting voting sized west siam ignoring ignoring mea challenge marks european ave termination loosely concern identically medicine returned believed proves polynomially acid communicate comm wisconsin cruz irvine irvine categorical nominal nominal sparseness sparseness sparseness iterate prune bruck bruck generaliza deciding percep percep terminology assessing tolerant terminate imation madison madison boost counterparts craven craven craven craven craven craven craven craven craven retains subclass salience jackson jackson jackson jackson jackson jackson periments oracle oracle oracle succeed tailed specialize conjunctions conjunctions conjunctions conjunctions conjunctions conjunctions quantifying freeze promoter promoter conjunctive representable consis consis charged negated jeffrey undefined exhaustively irl wisc promoters succeeds ccr triplets notoriously jeff ariaboost ariaboost hal hal lyl goldmann goldmann goldmann comprehensibility invoke informally queried superset trons consecutively hastad hastad conduct reviewing cept fee physician pends contend contend tency tency forbes understandable curate dayton basing 
#@Craven_M,Jackson_J,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number state results results results results results results units units units units units units units units units units units units information problem problem models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based weights weights weights weights weights weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer case case case case vector vector vector vector vector vector order order order order order order order shown values probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters weight weight neurons unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method method method method method method approach single single single single single large rate rate rate rate rate rate rate rate rate rate test test test test test test test test test test test test test test test patterns analysis optimal optimal form form shows algorithms simple simple simple paper paper paper examples small small size net net net net task task methods methods methods methods methods methods methods methods points field field field field field field field field field field field field field process trained structure structure structure random random high high high representation architecture architecture equation equation equation fixed line line rule rule vectors vectors vectors vectors images images images real real real approximation average states states theory gradient experiments activity dimensional dimensional university university variables computation research research independent independent log log log log log log log log log defined defined defined found found initial table table table table table table estimate estimate computer connections connections connections connections science science presented present low machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets sets sets sets sets sets sets sets sets sets sets sets maximum range range learn components components components components components sample sample sample sample abstract applied find find density density density density density density density density density likelihood likelihood likelihood likelihood likelihood references component component component component component component component component stochastic stochastic stochastic stochastic stochastic due procedure mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand estimation estimation estimation estimation estimation statistical generated generated generated generated generated variance variance variance cost cost cost cost cost cost cost cost cost tion tion energy energy energy assume lower lower lower lower lower representations representations chosen higher part previous bound bound bound bound bound cases cases type required required required good good good good good good binary binary binary binary binary binary binary binary binary binary represent expected expected markov make make make length length length correct probabilities observed ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total total total simulation computed computed computed respect respect respect respect respect multi performed performed performed performed called called called times times means means made made em obtain obtain negative negative artificial artificial relative relative compared compared compared compared series provide provide compute compute compute rates rates rates rates rates rates rates rates rates rates rates perform active active posterior posterior posterior posterior posterior posterior connected brain equal mit fields fields support train selection institute department department implementation implementation version version technique consists consists code connectionist difficult final layers layers layers layers layers addition ai cambridge computing hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton additional estimates top top top top top top top top efficient efficient upper upper full full requires approximate approximate approximate free free free world increase validation validation validation validation validation validation validation validation validation validation validation validation validation give con con con produce produce produce produce produce produce produce produce produce produce produce coding coding coding weighted randomly conditional conditional bounds lines entropy entropy entropy product provided finally selected selected depends sampling sampling sampling simply simply measured group fast fast close amount nearest effective assumed generate generate require require journal ability future easily makes fit pairs pairs pairs needed account unknown fully fully fully fully fully fully fully jordan jordan technology technology testing testing significantly significantly significantly special representing representing representing details call bits bits bits bits bits bits bits normalized bottom bottom bottom bottom bottom bottom bottom bottom early magnitude magnitude minimize produced produced produced produced run run architectures architectures architectures improve recent exact exact advantage separate separate practical subject machines hierarchical subset subset cognitive highly compare compare compare compare unsupervised unsupervised works works works tions yields match correspond constructed parts wide derivative deterministic clusters clusters clusters clusters generally pass runs runs starting greater reduce segment conclusions neighbor sigmoid performs performs performs faster faster faster faster temperature temperature temperature temperature taking hard largest sigmoidal intelligence intelligence variety variety minimizing minimizing min min derivatives groups connectivity program configuration base base base base base base base base base base base base base base base base base base base digit digit digit digit digit digit digit digit monte monte carlo carlo ways sequential estimating distinct segments segments segments multilayer multilayer belief belief belief belief belief belief belief belief belief equilibrium expectation overlap viewed transform restricted updated approximated approximated sizes activities activities activities activities activities digits digits digits digits past reasonable slow slow performing epochs fitting fitting fitting fitting fitting roughly roughly purpose visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible sufficiently avoid avoid avoid avoid handwritten usa sciences extension maximize maximize compression compression compression extra extra extra uniformly society computationally delta delta included efficiently ten ten ten composed prob interested dis oscillations follow generative generative generative generative generative generative generative timing gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs quantity sampled sampled sampled sampled sampled dayan dayan dayan dayan dayan dayan dayan dayan dayan dayan realistic minimizes maximization extract approximating acknowledgments software trains minimized body explore simpler unlike powerful overfitting overfitting overfitting estimators estimators estimators estimators replaced divergence biases biases biases helpful successive office complicated matched configurations implementations adjusted adjusted subsets subsets subsets versions versions obvious algo logistic logistic consist consist submitted synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic neal neal neal neal neal neal neal neal optimum massachusetts devices advanced costs coded independence tractable worse worse easier desirable members toronto toronto toronto greatly parameterized peter leave poorly poorly effort orders orders ity summarized mod ture ture gen gen prevent prevent asymmetric logp logp logp logp logp logp chose expectations unbiased jaakkola jaakkola jaakkola simultaneous softmax extreme arithmetic gap intractable intractable sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep restrict summing rithm perfectly zemel zemel unity connecting royal proceed proceed arranged keeping serves obtaining obtaining disjoint receiver imply exceeds filled service meaningful performances performances performances financial mance saul saul saul saul loo sion sion respective appendix appendix appendix perfor buffer sim lawrence multiplied matter canada partitioned partitioned likelihoods likelihoods dempster dempster default mind compressed compressed ple listed vec rubin rubin helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz tables tables tables asked ties break encodes employs connec tor avoided avoided avoided beta beta wake wake wake wake wake wake wake wake wake wake assess quantized visualization increment increment favor formance geoffrey distribu approxi annealed annealed annealed worth option laird laird sam sweeps sweeps frey frey frey frey frey frey frey frey els mini mix generarive tom mrf mrf mrf mrf mrf mrf mrf generafive generafive generafive generafive generafive generafive generafive generafive generafive tors accomplish connects wiring tribution subtracting ters ters judged architec archi communicate communicate rel fair est concatenated sweep transmit pointer bidirectional correlational postal entropies entropies prolonged iris cient broader fight codewords compress advice parame terminated 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#@Dayan_P,Frey_B,Hinton_G,
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#*model input input input input input input data function figure figure figure figure figure set set output output output output output output output output output output output output output output output output number number number number error state state state results results problem problem problem models models models models models models performance performance based linear linear linear linear linear linear linear layer order order order order order order order order order shown shown shown shown shown shown shown shown shown shown systems values parameters parameters functions single single single processing control control control control control control control large large large large large large local rate test test test analysis shows shows shows signal signal signal paper small small small small small small small size fig fig fig fig fig fig fig fig fig fig fig fig fig current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current structure structure high high high response similar show section section section section section section section section section section section section section line line line line line line line line line line line line line line line line line line line line line line line speech speech parameter parameter obtained obtained obtained obtained obtained obtained obtained threshold threshold threshold threshold threshold threshold threshold threshold threshold solution independent independent independent independent independent independent independent log left left presented presented presented present low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency maximum range range range range range range press position outputs abstract applied analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due due due ieee ieee ieee ieee important important introduction circuit circuit effect effect dynamic generated variance variance difference difference difference difference signals signals higher center previous good good distributed distributed chip chip chip chip chip chip chip chip techniques proposed proposed proposed length correct forward scale minimum minimum simulation respect times factor factor factor factor factor factor factor factor made natural natural feedback orientation filter filter filter filter filter filter filter negative original original vol vol vol vol specific true compared application cross proc proc active connected connected connected gain gain gain gain gain gain gain gain gain gain gain equal equal equal equal equal mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger larger larger larger larger larger source source source source source source source source morgan institute institute implementation implementation implementation version advances represents responses bias bias bias bias bias bias bias bias bias bias bias bias scheme domain equivalent directly additional curves design design design design design design design design san stage stage stage stage stage basic basic give channel area area velocity velocity velocity lines lines lines path actual actual actual finally depends depends depends depends depends biological biological biological measured measured normal close close surface circuits circuits circuits circuits common common common implemented implemented implemented main main end end end vlsi vlsi vlsi vlsi instance easily easily kaufmann auditory auditory typically typically smaller combination technology technology technology technology technology technology block structures structures matching matching mode mode mode mode operation operation operation language details filters filters filters filters filters filters filters filters filters filters filters filters filters filters pre normalized early combined sources sources sources sources sources sources sources sources sources sources sources sources membrane membrane membrane membrane improved improved improved improved improved improved improved improved improved improved improved improved improved discussed discussed discussed discussed improve lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral apply introduced introduced identical identical identical identical identical identical sufficient varying yields trans gate gate gate gate gate gate improvement improvement improvement amplitude amplitude digital wide wide alternative width generally pass pass flow flow critical critical place reduce conclusions depend depend differences exponential weak weak weak weak weak weak weak mateo temperature temperature temperature temperature temperature temperature temperature temperature largest drawn drawn california solid solid proportional proportional proportional proportional proportional decrease introduce base base base base base base base base base base van van van van generating stability vertical sensitivity linearly remaining remaining easy integrated integrated integrated frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies applying quality quality quality quality quality quality quality versus versus decreases decreases decreases yield stages stages stages influence variation variation variation controlled controlled showed approximated sizes completely measurements normalization purpose penalty intermediate visible symbol avoid avoid building silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon thesis currents currents currents currents currents currents variations variations variations variations variations major major identified identified identified extra extra efficiency effectively capture traditional conf allowing split device device device device cmos cmos cmos cmos cmos cmos cmos cmos cmos chips chips chips operating acknowledgments load decreasing decreasing decreasing decreasing decreasing remain create create create create create create exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially exponentially mead mead mead detail detail integral issues biases transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor scaled scaled scaled scaled scaled authors gates workshop matched matched matched measurement measurement created created changed voltages voltages voltages voltages voltages voltages implementations electronic electronic electronic electronic electronic electronic electronic electronic electronic devices devices devices devices derivation slope improves cascade cascade cascade cascade cascade cascade cascade independence briefly correction inside straight sections sections transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors transistors cut cut cut cut cut cut cut cut cut cut cut cut cut cut cut cut cut cut cut cut cut inversion inversion inversion inversion inversion inversion inversion beginning beginning beginning beginning res geometry addressed mechanics improvements improvements improvements cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear readily resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive span rely prevent pasadena substantial june june cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea yielding yielding room fabricated bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar bipolar amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier controlling controlling controlling purely eliminate connecting khz mos mos mos mos mos mos mos mos mos mos mos mos mos resistance resistance biased biased biased biased biased capacitor capacitor tap tap tap introduces negligible dependency buffer injection darpa creating layout layout layout layout ends ends ends ends ends santa border insensitive displacement displacement verify rms liu drop drop email ram july die terminals copy corrected regularity regularity regularity regularity regularity acceptable drain drain drain drain drain drain drain drain drain junction ideally amplitudes hundred hundred suppressed eric eric mismatch mismatch mismatch mismatch mismatch mismatch mismatch mismatch mismatch capacitance publication disadvantage disadvantage compatible compatible compatible compatible compatible compatible compatible compatible compatible compatible differentiation differentiation differentiation transconductance transconductance transconductance transconductance transconductance transconductance transconductance transconductance transconductance transconductance transconductance france placing amplifiers amplifiers amplifiers amplifiers amplifiers normalizing differentiating wider spite accumulation copies acoust saturated saturated thermal thermal instability doesn doesn spacing lyon lyon lyon lyon mirror mirror mirror clarity carrier flows flows periphery poly cruz pin fixing substrate substrate substrate substrate devoted decades preferable operated operated operated capacitive tilt tilt tilt notably biasing biasing biasing watts watts watts stabilized basilar basilar basilar basilar taps taps surrounded tilted tilted tilted differentiated charging buffers vittoz vittoz vittoz vittoz vittoz vittoz noticeable emitter emitter emitter emitter emitter emitter emitter emitter electrons indebted badly schaik schaik schaik schaik swiss federal pins pins mirrors carriers carriers carriers polysilicon polysilicon vout vout neuromimetic concentric compactness andr buffered 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#@Fragniere_E,Vittoz_E,vanSchaik_A,
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#*network network network network network network model model model model neural neural input input input data function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time output output output output output output output output output output output output output system system state results results results models space layer layer layer layer layer layer layer layer layer layer layer shown shown shown shown shown shown shown shown systems systems systems functions neurons point point image single processing processing processing processing processing large large local local class shows shows shows shows shows shows shows shows shows signal signal signal signal simple paper paper small small small small small small size fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field process level level level level level level level level level level level level level current current current current current current current current current current current current current current current high high high high high response response response response response response response response response response response response response response response response response response response response similar similar similar similar similar show show show show show show show section section section section obtained obtained obtained note experiments experiments dimensional dimensional computation independent log log log log initial initial initial constant constant node node science low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal range range outputs abstract back analog analog properties properties properties properties properties properties properties properties properties references adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus tion change change difference spatial spatial center center center center center center center center center center center center center center center center center chip chip chip chip chip chip chip region region observed observed performed called called means potential potential feedback feedback obtain receptive receptive receptive receptive receptive receptive receptive provide perform eye eye gain gain gain gain gain gain voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger contrast contrast contrast contrast contrast contrast contrast contrast fields fields support morgan institute institute institute version version synapses consists consists consists consists consists advances responses responses responses responses responses responses bias layers equivalent equivalent curve curve curve curve curves curves curves curves curves design design san stage stimuli speed speed speed vision increase increase increase increase coding levels provided measured measured increases increases corresponds corresponds circuits supported supported eds adaptation adaptation adaptation adaptation adaptation square vlsi pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel kaufmann smaller needed technology technology technology technology technology transfer testing ratio increasing increasing mode mode details details numbers direct direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition light light light light light light light light recent property property property property element element lateral lateral lateral moving moving moving moving moving moving moving moving moving moving pixels pixels pixels pixels pixels pixels pixels pixels pixels sense sense array array recently interest interest interest highly varying varying previously previously works background background background background background background background background background background background background background background background background background channels gate sensitive horizontal horizontal horizontal parts intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity wide wide touretzky white flow conclusion place row row retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina peak exponential faster faster mateo drawn california california california proportional proportional turn acknowledgements edges produces produces longer longer sensitivity sensitivity physical electrical spectral springer versus potentials formation influence variation variation open controlled modulation completely constants discrimination past past past past past past slow measurements sec sec sec sec filtering coupling figures figures figures silicon silicon silicon silicon silicon silicon silicon retinal retinal plotted coupled coupled absolute middle efficiency differ divided receives excitation excitation compact compact gray gray gray receptor receptor receptor surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround wave computes chips moves moves subsequent operating operating operating extract bars exponentially mead steady steady respond respond project transistor transistor transistor transistor transistor transistor proper measurement measurement adapt rev illustrate created voltages voltages eyes eyes eyes impulse impulse impulse explored electronic slope preceding preceding outer outer outer outer outer outer outer varies varies greatly understood led led led led transient transient transient transient dark dark dark dark dark offset red remove maintain passes exhibits berlin ture incoming incoming pasadena pasadena pasadena comments redundancy june sensing sensing primarily fabricated bipolar bipolar amplifier amplifier amplifier circular grows grey receptors receptors receptors receptors receptors receptors receptors receptors receptors receptors caltech caltech analogy analogy logarithmic logarithmic resistance biased serves operates illumination illumination illumination illumination illumination illumination capacitor symposium photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor april spatiotemporal draw reverse speeds speeds speeds speeds speeds speeds speeds speeds fly fly informa liu liu liu liu liu ure maintaining sine piece fellowship fellowship graded ties alternating die spatio spatio cns cns cns capacitance capacitance subthreshold subthreshold maintained activate surrounding lond intensities intensities intensities resistors memo memo rotating ignoring reciprocal differing drives drives thermal hyperbolic photoreceptors photoreceptors photoreceptors photoreceptors photoreceptors inhibit inhibit inhibited mahowald mahowald capacitors capacitors fabrication supplied excited excited excited excited possess wavelength contrasts contrasts contrasts andreou functionally cones cones cones vertebrate vertebrate vertebrate vertebrate vertebrate vertebrate vertebrate vertebrate vertebrate vertebrate sloan spie sity mosis adapts saturating decades decades decades decades mounted mounted carver spario spario spario spario spario spario transferred sensed sensed cient ver ver incident incident mediate retinas retinas displaced vertebrates insects insects boahen boahen boahen boahen boahen boahen boahen boahen boahen rendered analysed delbriick delbriick delbriick invertebrate invertebrate invertebrate invertebrate invertebrate invertebrate invertebrate oxide encouragement bradley supplies laminar laminar compound compound anatomically wheel minch strip strip strip strip strip inspiration incor invertebrates invertebrates charged antagonistic nimh orlando pulled sink depletion iin pulls shaw laughlin divider vet subtracts barriers continous instantaneously rrr illus rods lamina lamina strips transmembrane trate ciency phototransduction phototransduction inten tensity ick sus mathematica discern tracting facets tobias 
#@Boahen_K,Liu_S,
#t9
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#*neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time networks networks output output output output output number number number number number number number number number number number number number system state state results results results results results results results results results results information information information performance based based vector vector order order order order order shown shown shown shown shown systems systems systems systems systems systems image processing processing processing processing processing processing processing processing processing processing processing processing processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate test test test test test test test test test test inputs shows shows signal signal signal signal signal algorithms algorithms algorithms algorithms paper examples small small small size size work work work work fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells process process process process level level current current current current current current current current cell problems high high high high memory memory memory memory response response response architecture architecture fixed rule general real real obtained obtained term note result result result result university university threshold threshold threshold threshold computation computation research research standard computer node node node node science left presented presented present present low temporal temporal temporal temporal temporal temporal maximum maximum range press components basis outputs continuous continuous continuous continuous continuous continuous continuous abstract find analog analog analog analog analog analog analog references due due ieee ieee ieee positive important important introduction action action action circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit effect parallel parallel parallel parallel parallel parallel cost search search search search search search search search search search tion tion tion tion tion tion difference complexity variable rules rules rules rules rules rules signals signals signals signals signals part part part required multiple multiple binary binary binary long chip chip techniques region proposed correct correct scale minimum minimum minimum minimum minimum minimum ing total simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation sum sum sum called called means means potential potential potential potential made made feedback feedback feedback global applications vol vol vol application proc location perform determined determined determined gain discrete power power power power power power mit voltage voltage voltage voltage voltage voltage voltage voltage voltage accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison contrast source morgan morgan institute department implementation version technique code code advances advances advances represents delay delay delay delay delay delay delay delay delay scheme scheme addition maps cambridge computing design design design design transition transition san san top top stage stage stage stage stage bit bit bit detection detection detection detection speed speed increase increase increase increase increase increase increase give con produce weighted weighted developed developed levels nature associative associative associative measured measured measured technical increases increases fast fast stable actions circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits finding short common common common implemented implemented supported role role role vlsi instance future including including including kaufmann kaufmann simulated smaller reduced functional functional functional fully fully fully fully fully fully technology significantly significantly york mode mode mode mode mode mode mode mode mode mode operation operation operation operation operation operation operation operation operation numbers filters direct direct bits idea idea ensemble ensemble element element typical practical introduced engineering volume achieve trans trans gate gate gate gate gate gate gate gate gate gate gate gate organization increased increased increased grant concept digital digital digital loop loop loop loop loop occurs occurs hardware hardware hardware hardware hardware hardware conclusions competitive designed designed designed designed designed mateo strong strong mechanisms integration largest largest largest largest largest largest demonstrated demonstrated demonstrated solid turn turn turn turn assuming decrease manner manner configuration configuration acknowledgements appears relation relation pro winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner winner sequential laboratory electrical unique unique integrated integrated springer formed stages stages communication communication evaluated operations organizing organizing forms forms forms forms discrimination diagram diagram diagram diagram diagram key slow slow delays purpose tracking filtering kohonen kohonen precision coupling coupling coupling silicon combinations combinations retrieval memories plotted activated coupled partially successfully selecting identified identified build schemes composed composed composed verlag superior running device device play board board wave wave wave wave quantization cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos leading operating preferred software load load carried carried carried essential essential essential investigate circuitry circuitry circuitry mead put oscillators oscillator reducing tech int ideal transistor transistor transistor oscillation oscillation oscillation oscillation workshop func smallest measurement measurement equally equally voltages voltages implementations front noted detector detector detector logic logic store regime regime electronic electronic electronic wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta charge charge devices devices indicating ground floating floating floating floating floating floating floating floating floating floating caused turns turns turns turns turns turns turns ring ring ring ring ring forces transistors transistors controls scientific inversion inversion computers depicted demonstrates auto summation summation summation requiring double double double double flexible flexible conducted conducted conducted capability capability fed experimentally reliability reliability schematic operate kinds begins median yielding univ room accomplished accomplished fabricated fabricated fabricated fabricated fabricated japan japan optimizing plays plays odd mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos mos intelligent intelligent intelligent intelligent resistance moment biased biased serves removing capacitor capacitor carry utilized utilized utilized utilized reset respective moved buffer buffer enhance scan scan scan scan scan scan scan scan counting counter counter counter counter counter counter counter counter francisco lazzaro clean waveforms concentration papers papers receiving receiving receiving receiving receiving counts counts consecutive achieving super ber presenting uniquely axe axe axe axe axe axe terminals terminals terminals ical adjustment verified capacitance capacitance capacitance capacitance capacitance capacitance subthreshold subthreshold magnitudes num oct simplifying altered flip employing oscillating oscillating oscillating oscillating oscillating oscillating oscillating oscillating oscillating oscillating oscillating inverting loading completed technologies elemental elemental electron electron functionality sorting sorting sorting sorting sorting sorting sorting sorting sorting sorting sorting sorting sorting sorting sorting sorting sorting consuming mahowald aid imple capacitors supply inverter inverter inverter inverter inverter inverter inverter inverter inverter inverter inverter inverter inverter inverter inverter inverter 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#@Kaihara_R,Morimoto_T,Nakai_T,Ohmi_T,Shibata_T,Yamashita_T,
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#*network model model model neural neural neural input input input input input input input input input data data data data data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time set networks output output output output output output output output output output output output output output output output output output output output output output number number number number system system system system state results results units units models based space linear linear linear linear linear linear order order order order order order order order shown shown shown shown shown shown shown systems systems systems systems systems values parameters functions point point point point point point single single single single single single single processing processing control large large large large rate rate test test test test test test test test test test test test patterns analysis analysis optimal form form shows shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian small size methods methods points points points points features classification process high high high high high high response response response response response response response response response response representation representation architecture architecture architecture architecture architecture architecture section section section fixed line line speech speech speech speech speech parameter parameter parameter real real approximation obtained dimensional result result result university defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant constant constant standard computer present present present present phase phase phase phase phase phase phase phase phase low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal sets sets range range range range position components components components components components components components components components basis continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample abstract applied analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references component component component due ieee ieee ieee ieee ieee ieee adaptive introduction complex complex complex complex circuit circuit dynamic dynamic parallel parallel complexity lower signals signals signals signals signals representations representations chosen center center center center center center cases required required required multiple good binary binary binary binary binary binary binary binary binary expected expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip techniques techniques region length length length length scale scale resulting total simulation simulation mapping potential made made made applications applications filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter original vol vol vol vol vol vol vol relative relative relative samples compared compared application desired desired desired rates proc perform experimental related constraints constraints discrete power power power accuracy accuracy support department implementation implementation implementation implementation implementation implementation version consists code individual kernel kernel kernel responses exp exp exp scheme scheme scheme addition addition domain directly additional additional curves curves design top top stage stage effects bit bit full full requires approximate approximate approximate free vision con produce produce channel channel channel channel channel channel channel channel channel channel channel channel channel channel derived developed area actual provided sampling achieved measured measured measured measured measured measured measured measured increases group tested tested tested close inverse inverse assumption circuits circuits circuits circuits circuits amount effective effective implemented implemented implemented implemented implemented implemented implemented shape generate theoretical theoretical journal end vlsi vlsi vlsi vlsi vlsi fit fit auditory auditory auditory simulated simulated probabilistic smaller smaller needed account account technology block block transfer transfer ratio ratio ratio ratio ratio ratio uniform mode principle operation operation representing representing representing filters filters filters filters filters filters filters filters filters filters bits normalized bottom bottom magnitude added improved resolution exact advantage separate takes takes typical lateral include engineering engineering interest approximately approximately approximately approximately match achieve achieve trans trans trans address channels channels channels increased amplitude exists parts extended digital wide wide wide width conclusions accurate designed performs performs performs performs external demonstrated solid solid labeled iii base base reference reference reference produces optical primary mathematical electrical spectral scales integrated integrated frequencies frequencies frequencies frequencies applying applying springer quality select letters yield choosing choosing independently reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction stages transform transform transform transform transform transform transform transform transform transform transform operations controlled controlled controlled fraction modulation modulation modulation modulation modulation modulation modulation modulation modulation decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition understanding approximated processor processor processor processor processor processor processor processor processor processor diagram diagram key performing performing measurements delays fitting purpose purpose filtering filtering filtering filtering filtering advantages precision avoid silicon silicon silicon illustrated domains reason straightforward middle middle closely suitable suitable encoded divided effectively driven identity characteristic characteristic compact conf verlag allowing showing hold gray simplified wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wave wave wave wave wave wave wave wave wave wave wave wave wave wave wave cmos highest processors principles subsequent minimized requirements circuitry mead involving replaced optimized accurately accurately dotted oscillator periodic successive int ideal ideal ideal maximizing proper proper proper cover removed removed naturally trace trace trace trace reading created voltages implementations ensure adjusted front front precise precise logic generates mixed mixed electronic residual band agreement improves cascade multiplication multiplication correction tool lin lin implementing implementing implementing implementing implementing implementing sections sections sections sections sections sections producing producing filtered filtered filtered filtered filtered filtered filtered precisely located inversion separately bandwidth bandwidth bandwidth bandwidth demonstrates cochlear adjustable passed passed remove rep requirement passes measuring characterize differs modulated acoustics inherent decoder boston shaped shaped implements cochlea cochlea cochlea synchronization distortion distortion distortion distortion pole pole generator arguments narrow narrow approximates harmonic harmonic harmonic harmonic harmonic unity addresses addresses multiplier multiplier multiplier multiplier multiplier multiplier multiplier khz khz khz khz khz khz khz khz khz khz khz simplify logarithmic logarithmic bands transforms transforms transforms transforms north capacitor capacitor capacitor capacitor capacitor capacitor capacitor capacitor guide optimally clock clock clock clock clock clock clock combinatorial loo regard counter arrangement laplace multiplied bins offer properly subsequently multiplying liu liu approx audio maintaining street sine sine sine sine sine sine sine sine sine sine sine sine sine sine sine sine sine covering creates presenting july die spaced sinusoidal sinusoidal sinusoidal remainder alter mhz inverted inverted inverted switched switched switched fir ultimately scope cosine cosine cosine overhead increasingly oscillating electronics placing inverting tune september september removes reversal functionality lation justified attributed multiresolution multiresolution multiresolution orthonormal capacitors hopkins lyon lyon lyon inverter formulae andreou fft wavelets wavelets wavelets wavelets periphery periphery lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass johns implied consumption consumption bach accommodate cutoff cutoff cutoff zeros cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs charles baltimore ous tim dissipation tory voiced configured configured prime ece decompositions plotting imaginary resentation goldstein edwards edwards edwards edwards edwards edwards edwards illustrating prohibitively clocked clocked clocked clocked controllable watts translating multiplexing multiplexing multiplexing multiplexing taps parasitic bandwidths circumvent widespread idealized continu expands multiplexed multiplexed multiplexed multiplexer multiplexer multiplexer multiplexer multiplexer multiplexer multiplexer multiplexer multiplexer roll pertinent capacitances gert gert alternates kerns roberts shamma oak oak harmonics harmonics reversing timothy dig 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#@Cauwenberghs_G,Edwards_R,
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#*model model input input input input input input input input input input input input input input input input data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time set set set set output output output output output output output output output output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system information information information information information information information models models models models models models models models models models performance based based space space linear linear linear vector shown systems systems systems systems systems values values parameters parameters parameters functions functions unit method method method approach approach pattern point image single single single processing processing processing processing processing processing processing processing processing processing processing processing control control control control control control control control control analysis analysis analysis analysis analysis analysis analysis analysis analysis form shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms visual paper paper small small size feature feature work step features process process process current structure high response response response response response response response response similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture show fixed fixed fixed general speech speech speech speech speech speech parameter parameter parameter parameter real real real real experiments activity activity activity activity result computation computation research research research research research research research research independent log log initial constant standard present low low low low low low frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal motion range components components components abstract computational computational computational density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties references component ieee ieee introduction circuit circuit circuit behavior dynamic generated parallel parallel cost tion difference difference signals signals signals representations representations representations representations representations representations representations representations representations word word type multiple multiple multiple multiple chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip correlation computed multi multi multi multi multi multi multi multi multi multi multi performed times times elements dimension orientation applications applications applications applications applications applications applications filter vol compute compute compute compute compute rates determined connected connected equal power power power power power power approaches voltage voltage comparison support dependent words code represents responses final final final experiment environment environment environment directly additional additional solutions design design design design design design design design design top top bit conference efficient produce produce produce produce channel channel channel coding coding area lines product processes simply biological limited complete circuits circuits circuits circuits circuits short implemented implemented shape shape shape shape eds adaptation adaptation adaptation adaptation adaptation vlsi easily easily sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory needed needed functional fully block block block block block block block block block block block special special special mode language details pre pre bottom bottom bottom early recent recent recent resolution robust takes practical include include include array array array array engineering approximately tuning axis speaker trans address address address address address channels channels channels channels storage storage sensitive digital digital digital digital spikes width width hardware hardware hardware pass pass half designed clear peak peak sound sound sound sound sound sound sound strong integration external external cycle cycle cycle cycle characteristics pulse pulse pulse pulse pulse pulse variety start groups scene scene scene scene scene scene scene scene scene ways describes describes tuned vertical vertical implement linearly involves spectral spectral spectral spectral spectral spectral spectral spectral spectral formed blocks blocks john john codes codes controlled processor processor processor diagram diagram diagram diagram smoothing event event purpose purpose purpose boundaries tracking generation generation filtering advantages transactions includes includes includes silicon silicon silicon silicon silicon silicon retinal extension plotted plotted activated activated black characterized successfully texture major major compression middle middle extra extra successful efficiently post vowel receives summary summary summary summary summary summary summary decoding contained link showing phonetic running running follow criteria device dot wavelet board board wave computes computes chips chips disparity software software presents transformed essential essential mead mead mead periodic periodic transistor office decisions working working working measurement integer onset onset onset onset onset onset onset onset onset illustrate voltages mapped logic logic logic store electronic burst brown brown indicating advanced band developing developing asynchronous asynchronous asynchronous asynchronous waveform waveform waveform waveform multiplication processed implementing berkeley berkeley berkeley berkeley filtered division products products pulses acknowledgement sounds sounds pitch pitch bandwidth demonstrates auto auto qualitative sun sun sun raw raw summation reflects cochlear cochlear cochlear pure transient peter peaks share marked marked music sharp prototypes vocabulary suited richard implements cochlea cochlea summed merging sharing sharing sharing sharing secondary fabricated interface acts acts repre naval lost spontaneous adds khz khz khz khz khz khz logarithmic height serves transforms operates receiver vowels tone tone tone tone lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro arrows formant limitation audio audio audio audio audio audio audio audio audio compressed bus bus bus bus bus bus bus bus bus bus bus bus bus bus bus bus latency ties break ease acceleration workstation workstation workstation sinusoidal musical visualization preserved preserved generators host rectified funded tively supports likewise commercial programmed tunneling tunneling technologies architectural architectural copies copies copies acoust recogni transduction autocorrelation autocorrelation autocorrelation autocorrelation autocorrelation autocorrelation telephone supply micro lyon lyon lyon lyon converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter converter lists connects periodicity periodicity periodicity periodicity periodicity conversion conversion gram dedicated carries carries screen screen sions vertically amplified communicate mosis protocol creation cutoff brainstem brainstem sweep sweep sweep broadband pin transaction transaction transaction transaction sentation microphone microphone putation voiced voiced repetitive operated battery orbit sensed sends plausibility vdd vdd vdd corr corr puter kramer volatile viable burden controllable digitally unix trimming subtraction onsets onsets cooke cooke converters converters converters converters converters converters converters millisecond ishii binaural binaural emphasizing sponse acti arbitration arbitration resonant resonant wawrzynek wawrzynek wawrzynek wawrzynek wawrzynek wawrzynek wawrzynek stereopsis trim tunable plete sparcstation sender sender pulsed pins pins initiation alteration alterna aro sinusoid sinusoid sinusoid unvoiced accelerating buses buses buses buses audition discus referenced instrument 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#@Lazzaro_J,Wawrzynek_J,
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#*network model model model model model model model model model model model model model model model model neural input data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set networks output output output output output output system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error state results results units information information models models models performance performance performance performance based based based based based based based space space linear layer shown shown systems systems systems systems systems systems values noise noise noise method approach image image single single single single single single processing control control control control local local local test analysis optimal shows shows shows shows shows shows shows shows shows shows signal signal simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual paper small size size work cells cells cells cells field process process current current current current current current current structure high memory memory memory memory memory response response response response response similar similar similar similar similar representation representation representation architecture architecture show equation equation equation equation line real average obtained dimensional dimensional dimensional dimensional dimensional university university research research defined found target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target constant terms left left left left left left direction direction direction direction direction direction direction presented presented presented presented presented phase low temporal temporal temporal temporal machine machine object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum maximum maximum range range range range range range position components components outputs sample sample sample abstract back back back back back computational computational computational computational computational computational computational computational analog analog analog analog properties references component due ieee positive positive positive positive positive positive positive positive positive positive positive introduction hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit effect dynamic dynamic dynamic dynamic difference chosen previous cases required cortex cortex equations equations equations equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip region proposed correlation correlation correlation correlation correct observed finite minimum minimum human computed computed computed multi performed performed performed performed times elements elements factor factor feedback feedback feedback feedback feedback feedback feedback feedback global obtain negative negative negative negative negative negative negative negative vol vol vol vol vol vol vol vol relative relative represented compute objects location active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined gain gain gain gain motor motor motor motor discrete approaches voltage voltage voltage voltage voltage larger contrast contrast contrast contrast update dependent dependent source proceedings department implementation implementation implementation implementation implementation version technique technique technique internal internal internal represents represents final layers layers delay scheme scheme scheme scheme scheme sequences framework domain additional design design limit stimuli detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection efficient world speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed vision vision vision vision increase produce condition derived criterion velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity product provided sampling simply biological biological biological biological biological measured measured measured measured measured measured measured measured measured measured measured measured measured measured normal increases tested tested fast fast limited complete complete complete complete stable circuits circuits circuits implemented implemented implemented implemented implemented implemented role eds journal journal square vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel ability future future future sensory sensory combination reduced account block block transfer transfer york york edge edge edge edge edge edge edge increasing mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism matching matching matching matching mode principle operation operation direct stored stored stored stored stored magnitude magnitude magnitude magnitude magnitude magnitude magnitude added added light light light light predict predict discussed discussed improve improve improve directions directions directions element movement movement movement movement movement movement movement movement reported moving include pixels pixels array engineering engineering varying smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth match match match correspond achieve rl evaluation observation gate organization storage storage entire horizontal intensity intensity intensity suggests deviation deviation wide derivative derivative derivative feed feed feed feed move width width loop loop hardware hardware flow conclusion reduce segment central measures accurate accurate retina retina retina retina retina retina retina retina retina practice integration proportional proportional proportional pulse pulse pulse pulse pulse pulse pulse pulse exist movements selective min plane plane plane plane plane relationship targets targets targets areas areas van van van van van edges optical plot plot stability stability stability stability stability tuned mathematical sensitivity sensitivity sensitivity electrical electrical slightly integrated integrated integrated integrated integrated integrated predictive blocks blocks blocks versus letters expressed depending communication communication influence variation variation variation controlled showed showed forms forms converges updates updates updates diagram diagram slow additive measurements tracking tracking tracking tracking tracking tracking tracking tracking initially transactions recorded perceptual silicon silicon silicon thesis retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal prove gating successfully compression successful composed capture soc moore dis strategies hold hold hold wave wave delayed cmos cmos cmos correspondence predictor chips chips overlapping neighboring neighboring neighboring neighboring trains bars powerful layered wiley xor xor xor steady replaced pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit reducing school project detectors detectors ideal transistor root gates proved matched measurement measurement measurement measurement opposite opposite perfect implementations implementations implementations impulse der der der der der detector nervous detected detected grouping attempts attempts attempts electronic isolated indicating scenes track analyzed unstable capabilities caused caused london drive preprocessing directional choices transistors pulses pulses inversion projected projected projected opt bandwidth geometry apparent led psychophysical orders orders orders orders orders orders adjustable incorporated slower resistive schematic schematic schematic schematic robinson robinson robinson robinson robinson robinson robinson span calculating passes exhibits gains limiting limiting differs prevent asymmetric findings summed acquisition physiology physiology appearance appearance bipolar bipolar saccadic linearity perfectly imaging ranges primate primate primate primate primate primate primate primate primate primate primate logarithmic logarithmic mos mos city determination integrator integrator integrator integrator integrator integrator integrator muscles passive combines ranging widths paul photoreceptor consequences april gaze saccades partitioned davis subsequently subsequently subsequently explains alternatively market switches fly accumulated fitted discharge crossing crossing crossing compressed focal focal focal focal focal benefits perceived laplacian realize increment gated care grouped continues degraded oculomotor crossings barlow barlow inversely inversely amplifiers exhibited prevents reciprocal reciprocal reciprocal increments increments increments increments increments diagrams resembles architectural rarely lighting lighting lighting lighting stores accumulation accumulation accumulation accumulation accumulation restoration restoration dim dim handling autocorrelation photoreceptors photoreceptors illinois polarity polarity polarity believed believed accumulate seed swing cones tracks spie leakage amplified amplified amplified amplified falling lags lags aperture stabilize fovea mis mis jan palo unaffected stabilizing primates bright bright slip compress recursire damped cummings cummings cummings cummings cummings cummings cummings cummings cummings cummings cummings rightward retinas retinas retinas philadelphia philadelphia disappear foveal parasitic driver driver driver reichardt reichardt camp etienne etienne etienne etienne etienne etienne etienne etienne etienne etienne etienne ralph critically rabbit rabbit qualities southern restored charging buffers disappears disappears mueller mueller mueller mueller pennsylvania leftward realizes indoor wyatt wyatt wyatt wyatt wyatt wyatt wyatt mimics orlando pursuing detectable neg vital ambient ambient ambient ambient spiegel spiegel spiegel spiegel spiegel finely levick levick profound diverging cease disappeared assured str conserve buffalo rods latches disappearance phototransduction rer ght ght untilled zeroed coincidental 
#@Etienne-Cummings_R,VanderSpiegel_J,
#t9
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#*learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure time time time time time time time time time time time time set set set set set set set set set set set set set algorithm output number number number number number number number number system system results results information problem models models models models models models models models models models models models models models models models models models models models models models models hidden performance performance performance performance case case vector vector vector order shown systems systems systems systems systems values values values values probability probability probability probability probability probability probability distribution recognition recognition point point image image image single single single single single processing processing processing processing processing processing processing control control large large large large large large local local local local local local local local local local local local local local local local local local local local local local analysis analysis class class matrix matrix optimal form form shows shows shows shows signal signal simple simple simple simple visual examples small small small small small small small small size size size size size size size feature feature feature feature task step step points points points features features features features features features features features classification classification classification process process process process level level level level current current current current structure problems high high high high memory memory memory memory memory memory memory memory memory memory architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation equation equation equation general general general speech speech note variables computation computation computation computation computation computation independent independent independent independent log log log target initial initial computer computer computer computer node node node node node science science left presented low nodes nodes machine machine machine machine machine machine machine machine object object object range press components components components abstract applied applied applied find computational references references references due due ieee procedure procedure important decision introduction complex complex estimation effect effect effect parallel parallel parallel parallel parallel parallel cost cost cost cost cost search search search search search search tion complexity complexity complexity complexity complexity variable assume classifier word word word cases type type multiple multiple multiple multiple multiple multiple multiple multiple good binary tree tree tree tree tree distributed distributed distributed expected expected expected expected chip chip chip chip chip chip chip chip make fact fact techniques region probabilities simulations simulations ing tasks tasks total total simulation performed performed times elements elements elements elements elements elements elements elements factor factor factor factor optimization optimization potential potential made made natural natural global global global global applications knowledge knowledge knowledge knowledge knowledge knowledge relative compared compared compared perform determined constraints constraints constraints power power power mit larger larger support support support dependent dependent dependent dependent proceedings institute department implementation implementation version technique technique technique consists code code code code code code code code code code code code code code code code individual addition addition addition graph graph sequences computing computing equivalent equivalent environment directly view view solutions stage stage stage stage stage stage bit determine determine requires requires significant speed vision vision vision basic increase increase increase increase increase increase con con conditional conditional conditional conditional conditional conditional area area area area controller controller path path product iteration iteration depends simply achieved normal arbitrary group group group group group group group group group limited limited limited corresponds corresponds corresponds complete amount amount amount common common common common common common role require end vlsi hypothesis hypothesis hypothesis easily degree degree makes makes sensory sensory sensory sensory sensory sensory sensory including typically typically typically technology technology block block block block block block block block block programming programming programming programming programming programming programming programming programming testing ratio character edge matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform mode mode mode mode language language leads call numbers numbers max pre stored depth depth magnitude frame combined combined produced added added added added added added description architectures architectures architectures takes takes takes element practical introduced introduced include identical identical sense array engineering highly observations works match match match match sparse sparse address address background locations observation observation improvement improvement improvement improvement improvement improvement improvement improvement improvement entire increased exists expression matrices matrices locally loop loop loop loop loop loop generally hardware hardware hardware hardware hardware flow flow conclusion starting row row row greater segment clear faster faster taking largest external variety variety variety variety user user start introduce introduce characters groups groups program program program force acknowledgements explicit explicit suppose pro construct construct edges produces written index index ways ways implement implement explicitly simultaneously remaining consisting consisting adding adding adding adding adding adding applying applying implies decreases decreases decreases independently independently independently independently focus review phoneme phoneme stages stages stages stages communication communication communication communication interpretation evaluated evaluate evaluate evaluate restricted fraction evolution completely partition partition allowed processor processor processor processor processor processor processor processor processor processor processor processor processor reasonable performing performing sec purpose purpose boundaries string string existing existing existing existing existing box silicon priori priori usa inter inter inter inter assignment memories memories recognize extension tests straightforward hmms hmms suitable suitable suitable differ encoded driven post plots essentially essentially refer quickly procedures decoding heuristic heuristic success success interested stopping issue lie strategies usual realistic realistic realistic providing correspondence correspondence correspondence computes hypotheses hypotheses chips chips chips processors processors processors processors processors processors processors processors attempt attempt neighboring access access essential involving hanson hanson examine examine examine examine giving incremental incremental incremental stream stream stream stream complicated matched matched matched matched matched matched matched possibly panel panel panel panel logic consist utility regime rows rows rows rows rows rows rows floating expensive multiplication processed easier style forces choices products implicit implicit attribute recording author alignment outer geometric geometric varies greatly evaluating evaluating consistency consistency consistency consistency embedded slower frequently frequently frequently execution execution execution execution execution execution execution execution execution execution execution execution execution execution stack ture branch branch branch branch branch branch branch branch branch instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction phonemes viterbi leaf leaf leaf leaf leaf leaf leaf synchronization synchronization synchronization synchronization synchronization synchronization pose picture writing assign restrict branches branches branches count count count bin flexibility flexibility flexibility flexibility flexibility nonzero nonzero loops loops loops loops check clock child child encountered expanded buffer buffer assembly counter branching branching branching extends partitioned partitioned implicitly implicitly grants instructions instructions instructions instructions instructions tures executed executed executed assigning onr dense sequentially sequentially sequentially usage outline piece piece expanding pieces pieces exception obtains reports simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd simd pairing clustered trends cessing diag ijcnn graduate execute execute execute execute execute execute execute searches searches met argued scope scope scope synchronized synchronized parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism parallelism speedup speedup speedup conversely conversely constructs nonetheless barrier barrier register tij tij tij tij tij tij dramatic ignoring differing differing differing struc oregon behaves expansions syn gratefully expense expense functionality functionality functionality functionality functionality functionality functionality functionality functionality functionality sorting algorithmic handling recogni designs nested nested nested nested nested micro executing executing architec inefficient resolved deals trol tells tells arpa establishing essence delivery addressing addressing addressing addressing acknowledges steve unusual pin corn indexing indexing indexing decode bodies collections altering pes pes pes pes pes pes pes pes pes pes pes pes pes pes pes pes pes broadcast broadcast ample ogi traversed sparsity hypothetical sorts distinguishes executes cse communicating pad granularity chine succeed emulation portland pipeline indexes cheaper straints restricts checking distribute distribute distribute distribute traversing didn packing packing manage dan ond asymmetrical knowl unary pairings entity entity byte compiler hammerstrom hammerstrom hammerstrom hammerstrom hammerstrom hammerstrom programmer programmer programmer speedups synchronizing distributing onal surveys grimson grimson grimson asi asi runtime scalability semantically inp rehfuss rehfuss rehfuss rehfuss sired subroutine recursions conditionals synchronizes synchronizes synchronizes enclosing emit inefficiencies cached managing cheaply idle idle debugging debugging equiprobable parallelization quire fio aligns bulk alluded dress chronization 
#@Hammerstrom_D,Rehfuss_S,
#t9
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#*network network neural input data data data data data data data data function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time set networks algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output number number system results results units units problem problem problem performance performance based based linear linear layer layer layer layer layer case case vector order shown shown shown shown systems systems systems values values values values values values noise noise noise unit unit unit unit approach approach point point point point point image image image image image image image processing processing processing processing control large test test test analysis analysis shows shows shows shows signal signal signal signal simple size size size work fig fig fig fig fig fig fig step field field field field field field field field features process process level current current current current current current current current current current current current high high high high architecture architecture architecture architecture architecture equation fixed line line vectors vectors vectors vectors vectors images images speech average average average obtained obtained obtained obtained obtained obtained obtained obtained dimensional result threshold computation computation computation computation computation computation computation computation computation research research defined constant estimate estimate computer distance left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction present present low temporal temporal temporal object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum maximum maximum maximum position position components components components components sample abstract applied computational computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties properties properties properties properties properties properties references component component component due due due due due due due ieee positive positive positive positive positive positive important introduction circuit circuit circuit circuit circuit circuit circuit circuit stimulus stimulus stimulus stimulus stimulus effect parallel parallel parallel parallel parallel parallel tion tion change change difference difference complexity complexity spatial spatial assume lower lower measure signals higher part part previous theorem theorem theorem theorem cases spike spike spike distributed distributed expected chip chip chip chip chip chip chip chip chip fact techniques proposed correct correct observed observed errors errors errors errors simulations simulations simulations simulations simulations simulations resulting resulting ing ing total computed computed computed computed computed respect respect sum sum performed performed elements elements elements elements elements elements elements natural applications negative negative negative negative negative negative artificial relative application application proc proc location location location location location perform experimental equal mit voltage voltage voltage voltage voltage voltage voltage voltage voltage contrast contrast contrast contrast contrast contrast fields fields fields update update descent dependent selection selection proceedings report institute implementation implementation synapses internal individual represents represents layers layers delay sequences considered considered considered computing domain view view design top top stage stage stimuli stimuli stimuli stimuli detection detection detection detection conference determine determine requires vision vision estimated pages pages developed developed developed velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types types types types lines finally selected selected selected selected nature sampling measured normal technical describe inverse inverse inverse surface circuits circuits circuits circuits circuits circuits circuits short implemented implemented implemented implemented implemented implemented implemented implemented supported theoretical theoretical main journal vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel degree including fit fit fit simulated simulated simulated functional functional technology technology technology block block block significantly edge edge edge edge mode operation operation international bottom decay denotes architectures architectures architectures architectures architectures architectures architectures architectures architectures directions advantage property robust separate element element element element element typical similarity lateral moving moving side array array array array array array interest highly previously previously previously approximately calculated axis axis smooth match correspond achieve achieve trans sparse evaluation locations locations modified modified sensitive horizontal horizontal horizontal horizontal intensity invariant deviation wide predicted white boundary boundary generally setting flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow assumptions reduce conclusions measures measures measures accurate retina retina designed designed designed performs encoding taking taking presence presence california proportional proportional radial radial pulse pulse variety plane plane plane relationship relationship averaged edges edges perception optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical winner winner winner distinct implement implement integrated integrated shift blocks blocks versus independently focus focus focus focus stages densities evaluate restricted centered centered approximated sign diagram diagram diagram reasonable smoothing smoothing smoothing slow performing measurements measurements measurements expansion expansion expansion expansion expansion expansion neighborhood koch koch koch koch koch koch precision precision silicon silicon priori coordinate coordinate currents currents currents currents currents currents currents currents currents currents currents plotted maximize specifically specifically black absolute determining sensor sensor sensor sensor sensor sensor sensor aspects encoded modification paths poggio poggio poggio comparing comparing excitation excitation road soc compact induced prob interested device device built sampled sampled nips quantization cmos computes chips chips preferred neighboring acknowledgments software software software software intrinsic camera camera unlike carried mead mead mead integral integral divergence divergence divergence rise successive int transistor transistor hill circles circles patch patch closest closest closest possibly reading onset analyze predicts opposite voltages voltages voltages voltages implementations precise detector serial integrate integrate integrate devices advanced scenes slowly slowly slowly sensors sensors sensors sensors sensors sensors sensors sensors sensors analyzed navigation navigation adjacent adjacent adjacent biology considerable rapid rapid implementing division directional directional operators operators operators operators transistors desirable arise mation pulses projected circle circle circle demonstrates qualitative qualitative qualitative qualitative qualitative qualitative qualitative qualitative radius integrating fourth greatly pure dark offset simulate lack detecting employ sharp sharp sharp ity rely qualitatively pasadena green substantial implements implements june wesley shifted lab room room room room sensing sensing sensing sensing sensing sensing addison fabricated assign amplifier velocities velocities controlling null eliminate eliminate printed rigid caltech caltech caltech arranged arranged spiral spiral systematic consideration imaging imaging ranges ranges promising simplify logarithmic vehicle vehicle vehicle vehicle exploit illumination illumination illumination illumination north arrays arrays arrays arrays wilson selects continue infor service barron barron barron smoothed smoothed layout contraction contraction contact contact contact contact contact contact contact contact contact contact contact contact contact contact contact contact exploiting exploiting grants tures thresholding thresholding onr lem dense crossing crossing crossing crossing crossing crossing crossing crossing crossing crossing converted corporation pointing pointing validity validity focal encodes encodes expanding expanding smoothly smoothly theorems reflected brightness mismatch subthreshold formance decays ijcnn elementary elementary elementary elementary march bump confirmed lond transconductance selectively nonetheless crossings crossings crossings memo rotating rotating ation reciprocal travel differing exploited gauss gauss helps heading heading heading heading heading heading heading heading heading heading heading heading heading heading heading heading functionality sees satisfactory photoreceptors calibration spacing capacitors mirror mirror morris morris morris fabrication seattle sen andreou andreou andreou luminance separates detects architec offsets decaying decaying decaying constancy inspection approaching approaching mosis gence deweerth signed signed twelve aperture robustly mis rotational christof converts newly phil bright aliasing kramer kramer kramer kramer kramer kramer kramer kramer lens translational confirms confirms dissimilarity syrup disk boahen boahen boahen radially steepness steepness steepness steepness steepness steepness steepness feeds delbriick parasitic torre torre prevented tilted abscissa abscissa bypass diode gation leak correlator collaboration logarithmically logarithmically capacitances outward photo photo detec truck shadow radii klab klab klab precedes contracting contracting assures concentric inaccuracies delbrfick delbrfick carolina mathur manufacturing unambiguously evalu integrative imaged courtesy schematics schematics chapel aggregating ttm ttm ding iscas diodes tensity sors microscope diver proximately veloc navi 
#@Indiveri_G,Koch_C,Kramer_J,
#t9
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#*network network network network network network network network network network network model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data figure figure figure figure time time time time time time time set set set set set networks output output output output output number system system system system system system system system system system system system system results results units information information information information information models models models models models models hidden based based based based based based based based based based based based weights linear systems systems systems systems systems systems systems systems systems systems systems systems systems values parameters noise noise noise noise noise weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit recognition approach pattern single single single single processing processing processing processing processing processing processing processing processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns analysis analysis analysis analysis analysis form shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple visual feature work work work work work fig fig cells cells cells cells cells step features classification process cell cell cell high response similar similar representation representation fixed images speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real theory theory obtained term activity activity result university university university threshold threshold research research research log found found initial constant computer computer computer connections science science presented presented map map map map present activation activation frequency frequency frequency frequency temporal temporal temporal press continuous continuous abstract applied applied applied applied applied applied back find computational computational analog analog analog references due due due ieee ieee positive positive positive positive positive positive introduction introduction effect effect effect effect effect effect change energy energy energy difference lower signals signals signals signals signals signals representations part part part part center firing firing firing firing spike spike markov techniques techniques techniques techniques length length correct minimum simulation performed called times means means feedback feedback study filter filter filter filter filter filter filter filter negative negative negative original vol application proc proc perform active related motor equal power mit train source morgan proceedings report report department department implementation version technique technique technique technique technique technique technique technique technique internal internal internal internal internal advances responses responses exp maps maps considered computing directly directly directly stage stage stage stage effects effects detection detection detection determine efficient world increase produce produce channel channel channel channel channel coding coding coding weighted weighted clustering types types types types lines lines nature inhibitory biological biological biological biological biological achieved achieved achieved discussion technical increases excitatory excitatory excitatory finding short short effective effective effective effective implemented theoretical eds eds end end cluster kaufmann auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory dynamical technology edge increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation language call call filters making window early early early early produced produced produced produced run membrane membrane population population discussed discussed directions recent recent recent recent recent resolution element movement lateral period period period period period period period period period subset cognitive interest studies trans trans trans background background channels channels channels channels channels channels channels channels channels channels channels channels channels sensitive sensitive sensitive arm amplitude parts intensity intensity occur occur occur suggests spikes spikes spikes move white white boundary boundary generally generally pass pass place reduce segment segment segment segment conclusions operator depend clear clear peak sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound propose mechanisms integration presence external external demonstrated pulse pulse start scene acoustic acknowledgements areas appears pro pro pro van van edges perception perception perception describes vertical segments segments segments segments segments implement physical text text consisting consisting integrated gaussians gaussians applying events predictive springer formed implies implies implies stages interpretation interpretation interpretation interpretation interpretation lee modulation forms similarly suggested allowed spectrum spectrum calculation combining event intermediate initially filtering filtering filtering filtering visible fire fire fire fire fire fire fire fire fire perceptual silicon silicon silicon silicon silicon usa inter weighting coupled black black neighbors straightforward middle society differ divided driven driven driven tend excitation traditional soc soc verlag strongly allowing allowing moore moore showing phonetic phonetic superior contribution follow timing sci duration providing wave giles computes processors received extract extract neighboring decreasing modelling modelling modelling modelling modelling modelling extend cowan exponentially mead mead mead rapidly oscillators hanson limitations rise fourier fourier fourier math onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset onset psychology perfect ensure adjusted front front front nerve nerve nerve nerve nerve nerve nerve nerve nerve academic detected detected extent simplest grouping averages averages averages integrate integrate integrate integrate integrate integrate animal burst brown brown brown stop slowly slowly slowly band band band band band band convolution coded adjacent adjacent adjacent adjacent adjacent adjacent biology biology starts london ganglion inside inside inside processed tive producing producing filtered nucleus nucleus nucleus nucleus nucleus nucleus nucleus immediately pulses pulses mathematics sounds sounds sounds sounds acad pitch pitch members recording bandwidth author outer cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear pure led offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset spoken spoken fed car marked passed passed music sharp sharp biologically calculating mod spread aim aim reaches fall incoming phonemes acoustics segmented neuro cochlea cochlea cochlea cochlea synchronization sharing ear notes notes notes physiology temporally refractory refractory refractory refractory refractory refractory driving royal turned spiral smith smith smith smith smith smith smith smith smith smith smith smith adds khz khz stronger interconnection interconnection intelligent bands bands bands bands transforms transforms mark mark utterance utterance effectiveness natl fires fires inferior reliably reset falls tone moved enhance schwartz histograms mel modelled modelled specialized lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro arrive clean colliculus ends ends canada broken receiving insensitive divide pressure liu liu audio neurophysiology neurophysiology compressed compressed compressed hair hair hair hair piece shorter bank die die smoothly centre centre regularity aij england clustered musical musical cessing cessing mammalian maintained inverted crosses march cole cole paris rectified nuclei nuclei breaks tones siam articulatory echoes challenge emphasis emphasis accumulation acoust acoust transduction autocorrelation autocorrelation justification multiresolution hearing hearing impulses envelope envelope virtually mahowald interpreting pronounced integrates formulae medicine physiologically andreou marr marr offsets offsets offsets offsets offsets offsets chan carries digitized arriving arriving bandpass america appl rel edition brainstem broadband modern bear segmenting segmenting inst dissipation ears silent experimented voiced medial gradual publishing nice cats rises plausibility chang ther rectification goldstein leaky concurrently convolving convolving switzerland canal sing kim kim basilar onsets onsets onsets onsets onsets onsets onsets onsets onsets onsets onsets onsets onsets cooke bandwidths meyer meyer meyer meyer olive ences organ sivilotti wawrzynek occasional vibration vibration vibration vibration unambiguous instruments resemblance logarithmically schaik schaik sudden accumulates apple apple compressing sheffield effec patterson patterson patterson patterson patterson patterson innervate hear alters fibres fibres fibres hildreth hildreth nels envelopes eventual insensitivity scotland suddenly suddenly immune marking trm patent patent subtracts sensation ceases emits gillespie oval leslie cha peripherals atively confuse corti demanded blackburn blackburn lausanne wideband everyday ecological ecological lul mainstream syste eurospeech filed lncs mam 
#@Smith_L,
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#*network network network network network network network network network network learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data function figure figure figure figure figure figure figure time time time time time set set set set set set set networks networks networks networks training training training training training training training training training training training training training algorithm algorithm output output output output output output output system system system system system system system system system results results results results results results units units units units units units units units information information information problem performance performance performance based based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case vector shown shown shown shown systems systems systems systems systems systems systems systems systems values noise weight weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern pattern pattern pattern pattern pattern pattern pattern point point image image single processing processing processing processing processing control large large local local rate rate rate rate rate test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis inputs form form form form shows simple visual visual paper paper examples examples small size size feature feature net net net net work step step features features classification process process process trained trained trained trained trained trained trained problems random random high high response similar similar representation representation representation representation representation representation architecture architecture architecture architecture show rule rule rule generalization generalization generalization speech real real approximation average average average note experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity university university research target target initial initial initial initial initial constant constant table table standard standard standard computer computer computer connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections science science left direction presented presented map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map activation activation activation activation activation activation activation activation activation activation low sets sets sets sets range press press learn learn learn abstract back references important propagation introduction hand hand hand hand hand effect generated generated variance tion tion difference difference difference lower rules representations representations representations representations representations representations representations learned learned higher higher part part center center previous cortex cortex good represent represent equations make region proposed length correct correct forward simulations simulations resulting ing sum sum performed performed performed times applications obtain relative represented application receptive connected connected cortical equal approaches mit accuracy comparison comparison comparison comparison larger connection connection fields support train train morgan morgan morgan morgan institute department consists consists internal internal internal internal internal internal internal internal internal code advances advances advances advances advances represents difficult difficult final final final final final final final final final maps maps maps maps maps maps maps maps maps maps maps cambridge experiment directly directly additional view curves curves san san san san effects determine full full significant significant significant world world increase validation validation con weighted types actual provided backpropagation backpropagation inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends biological achieved measured measured measured discussion complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable short effective supported main adaptation adaptation adaptation square square end end end end end end hypothesis hypothesis future easily degree noisy including including kaufmann kaufmann kaufmann kaufmann account fully fully technology interesting testing testing significantly significantly character character character special database database database database representing direct making making inhibition inhibition inhibition inhibition normalized normalized normalized added perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron architectures architectures correlations separate reported lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral practical apply subset subset recently highly varying calculated tions modified modified organization sensitive sensitive sensitive grant grant scaling digital correctly feed touretzky touretzky touretzky touretzky touretzky clusters white strength conclusion starting starting starting hebbian hebbian hebbian hebbian editors differences differences differences differences differences sigmoid clear clear performs performs weak learns learns learns mateo mateo mateo mateo suggest suggest suggest proportional selective averaged averaged force acknowledgements areas areas digit digit digit digit digit digit digit digit digit digit digit digit digit digit written written written written primary primary distinct distinct distinct segments category dimensionality remaining remaining easy interaction formed formed formed formed letters letters decreases decreases national national focus squares codes organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing ocular showed forms forms forms forms forms digits digits digits digits digits constants epochs epochs epochs epochs epochs neighborhood neighborhood neighborhood roughly generation generation remains initially initially initially foundation building handwritten handwritten handwritten handwritten handwritten handwritten figures activations perceptrons dominance sciences recognize recognize recognize recognize recognize activated activated activated black neighbors regular delta delta wij wij successful identify excitation excitation excitation excitation repeated strongly cun cun denker denker denker overlapping tesauro decreasing receive employed powerful rapidly replaced preliminary reducing statistically cover topographic neu coarse closest editor editor editor editor recognizer front front front front front front versions som som som som som som som som som som som som som som som perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton hebb simplest motivated percentage indicating advanced stop piecewise separable crucial crucial adapted tive easier easier easier easier easier organized organized organized organized producing mation afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent afferent projected recognized beginning gradually gradually gradually patches recognizing recognizing recognizing radius radius radius radius radius radius raw raw raw raw raw raw raw raw varies collected bootstrap dark howard howard pittsburgh serve kinds decreased baird lot identifying leen forming martin martin databases databases connecting connecting printed interconnected interconnected interconnected interconnected interconnected interconnected lost promising handwriting ral north corner infor loo pat holland topological topological percepttons percepttons percepttons percepttons percepttons percepttons percepttons percepttons jackel jackel counting recog recog reveals splits splits splits grants johnson dramatically shading guyon cooperative diverse nition boser medium causing stem wake wake decorrelation decorrelation representa shaded pub pub henderson henderson concentrated ftp thick hubbard hubbard iri iri iri categorization represen zip zip elsevier rnn functionality nist nist nist nist nist recogni vii terns settling settling ferent austin austin austin graf eral practically dedicated tations texas texas emerged gardner fore propagates neocognitron neocognitron retaining richer gij joseph settles ample modifies fukushima fukushima nections patterned patterned anticipate miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen miikkulainen yij laterally laterally laterally laterally laterally laterally categorize vij iij settled settled settled settled settled decorrelated zation lat standards eij gov chitecture pittman pittman lij lij lij insignificant inh decorrelating bitmaps bitmaps bitmaps bitmaps bitmaps crucially lends confusable sparser memorize memorize realisation bitmap bitmap bitmap organising diminishes decorrelate decorrelate decorrelate decorrelate associator elevated nized yer inp inp inp inp evi adapta clearer alphanumeric organi utexas magnified moon lightly exc redun wet grad supercomputing lishers dant ually 
#@Cboe_Y,Miikkulainen_R,Sirosh_J,
#t9
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number system system system system system system system system system error error error error error error error error error error error error error error error error state state state state state state state state state state state state state state results results results results results results results units units units units units units units units units units units information information information information problem models models models models models hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based based based weights weights weights weights layer layer layer shown shown shown shown systems values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters functions unit unit unit distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method approach approach image image single single single single single single single processing processing processing processing rate rate rate test test patterns class class class class class class class class class inputs inputs inputs inputs inputs form shows shows shows shows shows shows simple simple simple paper paper paper paper paper task task methods methods methods methods methods fig points field features features classification classification process process process trained trained trained trained trained trained trained trained trained trained trained trained trained trained random random high high representation representation representation architecture section section section section section section section section section fixed fixed fixed line line line line line line line line rule rule speech speech speech speech speech approximation approximation states obtained obtained obtained experiments experiments experiments experiments result university university solution research independent found found found found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target target target target initial initial initial initial table table table table estimate estimate estimate estimate standard standard left presented presented presented presented presented presented map activation activation machine maximum nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs sample abstract applied applied applied applied back back find convergence convergence likelihood references due ieee ieee ieee procedure procedure procedure propagation propagation propagation propagation propagation context context introduction introduction estimation estimation estimation estimation estimation statistical dynamic generated parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search tion tion tion tion change lower prior prior prior prior representations word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word chosen part part part center previous previous previous required good good conditions represent represent represent represent represent represent distributed markov markov markov markov markov markov markov markov make length length length length length correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed errors forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward scale resulting classes classes classes classes ing multi multi performed potential made feedback feedback feedback feedback knowledge obtain relative relative represented represented represented true true application desired series series series series provide rates rates rates rates rates rates rates rates determined experimental goal posterior posterior posterior posterior posterior posterior posterior connected connected distributions distributions distributions distributions distributions distributions distributions equal equal equal steps accuracy accuracy contrast train train train train train train train nets morgan morgan proceedings words words words department department consists internal internal internal represents represents represents represents represents connectionist final final bias layers layers delay delay scheme sequences ai ai ai considered considered framework cambridge cambridge cambridge equivalent hinton estimates stage determine classifiers requires approximate approximate approximate speed estimated estimated estimated estimated estimated estimated estimated estimated give give give give con produce derived developed entropy actual provided provided finally backpropagation backpropagation iteration iteration iteration simply normal arbitrary tested hmm limited finding assumed assumed shape end end rumelhart rumelhart rumelhart rumelhart including objective objective probabilistic typically reduced account fully programming significantly character character character character character character segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation uniform database language squared representing representing representing stored normalized supervised frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame frame combined combined description perceptron improved improved improved improved discussed improve improve improve robust separate takes takes engineering engineering previously previously calculated calculated calculated calculated calculated volume match background generalized williams improvement improvement constructed parts parts invariant rotation hybrid occurs boundary generally half half place conclusions conclusions central sigmoid accurate bayes clear peak performs faster encoding taking hard external cycle cycle assuming variety start targets targets targets targets targets targets targets targets targets targets targets targets targets targets targets manner characters characters denoted denoted denoted pro derive written written longer estimating estimating describes describes describes describes transitions transitions label label label label label student remaining remaining adding letters letters letters letters letters letters letters letters letters letters letters letters estimator estimator overlap detailed detailed evaluated labels labels frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames frames soft soft allowed reasonable normalization calculate calculate transactions degrees degrees handwritten handwritten handwritten handwritten thesis thesis activations priori usa weighting blind recognize automatic automatic uncertainty uncertainty uncertainty priors variations variations successfully middle letter letter letter letter letter letter letter letter letter letter letter letter letter letter letter extra suitable divided delta mcclelland literature comparing identity identity identity compact repeated repeated prob duration usual backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward correspondence leading automatically subsequent receive modelling presents poor put put detail detail accurately successive giving links links scaled scaled scaled authors referred stream affect encode func cognition reading reading created recognizer algo freedom freedom mapped shapes initialized indicating ment distinguish slope improves adjacent adjacent caused processed purposes sections sections sections organized style broad probable probable recognized recognized definite definite read read read lowest alignment alignment alignment alignment alignment raw improvements bootstrap bootstrap conducted lack passed treated treated incorrect schematic robinson robinson robinson robinson robinson robinson robinson robinson vocabulary vocabulary summarized spread suited phone segmented segmented begins viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi viterbi softmax sharing naive naive appearance forming tation rithm narrow labelled labelled repre repre rigid significance adjusting analogy height handwriting handwriting handwriting handwriting handwriting handwriting handwriting abilities occurring transforms observing belong belong bourlard salient canonical date document document document regard lengths lengths percepttons propagated eng eng reader belonging likelihoods explains cam cam avoiding adopted explorations assigns assigns assigns empty andrew consecutive sequentially ure emission emission street slight specification microstructure shorter accept kluwer deriving deriving latency latency latency latency maximized recursively forced retraining retraining retraining retraining retraining retraining retraining retraining personal reports chapter england examining representa avoids pub pub pub publication ftp ftp ibm cessing stroke werbos distribu gener maintained ization writer books termed termed esti son page parametrized recognizers scanning removes rabiner rabiner rabiner scanned sorting satisfactory assistance lated clarity reflecting char thickness ally svr svr manually discarded juang juang juang falling assp magazine bradford signed reviewed tical inaccurate segmenting allocating durations durations watson brought rent addi postal asymmetry converts discrepancy heights sixth shear dealt ver albeit posteriors posteriors copied mike untrained untrained untrained untrained untrained outlines necessity tar tar historical recur transcription segmentations segmentations segmentations segmentations segmentations segmentations segmentations segmentations tony acknowledgment del del lexicon nected hochberg identities arrived strip mates calcu boutlard yorktown deviate initializations slant acter quicker url butler butler butler butler ceases reinforcing malized instants tivation sto segmen preparing alignments alignments alignments alignments wards tabulated senting aix boot 
#@Robinson_A,Senior_A,
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#*network network network network network network network network network network network network network network network model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data function figure figure time time time time time time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error state state state state state state state state state state state state state results results information problem models models models models hidden hidden based based based based based space weights layer layer layer case vector vector vector vector vector vector vector order order shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters functions distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach approach approach approach approach approach approach approach single single processing processing large large large rate rate test test test test test test test class class class class class class class class class class class form shows signal signal paper paper paper paper small small net work work work work work work task task methods process process process process level current current trained trained trained trained trained trained trained structure problems high similar similar similar similar representation architecture architecture architecture show vectors vectors vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech speech approximation average average states obtained term term experiments dimensional dimensional result result university university computation computation independent independent independent independent independent independent independent independent log log found sequence sequence constant table table table table table table table table estimate estimate estimate estimate estimate standard standard terms left left left presented presented machine sets sets sets sets maximum outputs outputs outputs outputs continuous continuous abstract applied applied back density density likelihood likelihood likelihood references due due ieee ieee procedure decision decision propagation mixture mixture mixture mixture mixture mixture context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context introduction introduction hand estimation estimation estimation statistical generated generated generated parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search difference word word word word word word word word word word word chosen required multiple good good represent tree tree tree tree tree markov probabilities probabilities probabilities observed forward forward classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes tasks tasks tasks tasks tasks tasks tasks total multi multi performed performed times means made em obtain vol vol compared compared compared application cross cross compute posterior posterior posterior posterior posterior posterior posterior posterior posterior accuracy comparison comparison comparison larger connection dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent nets modeling selection morgan morgan morgan morgan morgan morgan morgan department department version represents connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult layers scheme framework framework framework cambridge cambridge cambridge equivalent equivalent equivalent estimates estimates estimates estimates stage effects efficient full requires speed speed speed speed speed speed estimated estimated basic increase increase increase validation con conditional clustering clustering levels criterion finally evidence evidence achieved normal hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm fast fast fast fast fast assumption predictions finding short implemented generate cluster future rumelhart rumelhart development development development development needed combination reduced reduced reduced jordan jordan jordan technology technology mlp mlp significantly segmentation segmentation segmentation segmentation language language language language language language details making experts experts experts experts experts experts experts experts experts expert expert expert expert magnitude frame frame frame frame frame frame frame combined description description perceptron perceptron improved improved discussed improve recent separate separate takes typical reported include side hierarchical hierarchical trees subset subset engineering engineering conventional conventional observations approximately calculated module mixtures mixtures evaluation evaluation evaluation evaluation evaluation evaluation modified parts occur extended feed hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid conclusions modules modules modules modules modules modules performs sound reduction relationship manner acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic pro produces generating changing pruning implies expressed influence detailed lee lee frames frames frames soft discrimination past smoothing roughly sufficiently transactions transactions building building building building existing figures usa automatic priors gating gating tests tests tests hmms computationally divided included successful vowel ten compact compact compact decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic split classify classify running built built built built built vary modular modular modular providing nips nips overlapping jacobs jacobs jacobs modelling modelling modelling modelling modelling modelling presents american american american requirements fewer fashion fashion scaled workshop workshop analogous extremely assumes mapped mapped baseline baseline improving established ment publishers publishers improves expensive expensive tive purposes purposes sys broad english english english english english english english english english english english lowest integrating tional spoken spoken embedded red red red cohen cohen cohen posed treated robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson robinson requirement vocabulary vocabulary resource incorporating incorporating suited phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone phone decoder decoder decoder viterbi viterbi viterbi viterbi discontinuities contextual aligned aligned tem exemplar communications attractive keeping operates utterance utterance utterance utterance utterance utterance methodology bourlard bourlard bourlard bourlard responsible corpus corpus selects hours hours hours substituting evaluations contexts contexts contexts contexts decide overview guarantees schwartz schwartz similarities entries darpa multiplied modelled mlps mlps young young creating eng storing park likelihoods cam avoiding adopted posteriori discriminate discriminate discriminate street street email kluwer kluwer icassp england workstation workstation workstation clustered gained wall management proba speedup million nal drops drops differing rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn tel tel factored handled bility european powers appealing arpa arpa arpa arpa fol articulation meant format format format faced merged merged merged backwards rent validated decode decode decode renals renals renals renals renals renals phones phones phones phones phones phones phones phones whilst whilst avenue internally internally mike mike coverage menlo british british british lowing pronunciation augment augment augment augment dev dev recur eval tony jour lexicon numerator hochberg hochberg hochberg hochberg hochberg hochberg hochberg hochberg hochberg hochberg hochberg hochberg hochberg franco franco concentrates duced ist official makhoul makhoul sharper tying nasal overcoming flamework fax dan intro cook cook cook cook mono boutlard vastly factoring abrash abrash conven infeng bigram rprop timation trigram trigram discrimina texts acoustically delaying curacy augments 
#@Hochberg_M,Kershaw_D,Robinson_A,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural data function function function function function function function function function function function function function function function function figure figure networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number results information information information information information problem problem problem performance performance performance performance performance performance performance based based based based space linear case case vector order order order order shown systems values values values probability probability noise functions functions functions functions functions functions functions neurons neurons distribution distribution method approach approach approach point processing processing processing processing rate rate rate analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form shows signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian paper paper paper work methods random random random random random random random similar representation representation architecture show equation equation equation equation section line line line line line line line line line general general general general speech approximation approximation average average theory theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term note note note result university variables variables computation solution independent independent independent independent log log log log log log log log log defined defined defined found computer computer computer science left direction present activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation range components components nonlinear outputs outputs outputs outputs outputs outputs outputs abstract find find find find density density properties references component stochastic due ieee positive adaptive adaptive adaptive adaptive introduction estimation statistical statistical recurrent recurrent variable variable assume assume signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals chosen part previous cases cases cases represent represent distributed proposed proposed proposed proposed proposed simulations simulations simulations simulation simulation sum performed elements natural natural natural natural natural natural applications obtain obtain obtain obtain obtain obtain obtain obtain original original artificial compute determined determined goal distributions distributions distributions distributions brain update update descent descent descent descent descent descent descent descent descent descent dependent source source source source source source source source source source source source selection selection selection proceedings implementation joint difficult exp framework view design limit approximate approximate approximate statistics statistics statistics basic pages pages give derived randomly developed 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scalar scalar working affect coarse reading singular singular formal formal separated expressions amari amari amari amari amari amari amari mixed mixed mixed mixed mixed explain finds synthetic advanced cos cos trivial derivation answer independence perspective calculations definite medical arises geometry fourth questions evaluating evaluating evaluating evaluating simulate formulated polynomials monotonic monotonic monotonic monotonic monotonic marginal marginal marginal marginal marginal marginal replace logp logp instantaneous instantaneous lab lab lab indices notes japan japan japan japan extensive recover impossible nonzero rational rational kullback kullback kullback kullback kullback difficulties simplify odd replacing replacing check moment affected symposium moments moments moments substituting separating expanded dependency dependency dependency dependency dependency yang yang yang yang yang recog permutation permutation relies explains pdf pdf pdf pdf pdf geometrical 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#@Amari_S,Cichocki_A,Yang_H,
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#*network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input data data function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm output output output output output number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error state state state state state state state results results results results results information problem problem models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based based weights weights linear linear linear layer layer layer layer layer layer case case case vector vector order order shown shown shown systems systems systems systems systems systems systems values values values probability probability probability probability probability probability probability parameters parameters parameters parameters weight functions functions functions functions unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach pattern pattern point image image image image image image image image image image image image processing processing processing local rate rate rate rate test test test test analysis analysis analysis analysis analysis class class matrix optimal optimal inputs form form form form form form form shows shows signal signal gaussian gaussian gaussian paper paper examples examples examples examples examples examples size feature feature net net net task task methods methods methods cells cells points points points features features classification level level level current current current current trained trained trained trained trained cell architecture architecture architecture architecture architecture architecture architecture architecture section section section section section section line line line line line rule rule rule vectors vectors vectors images images images images images images images speech speech speech speech speech speech speech real real real approximation states states states states states states states states states theory theory theory theory gradient term term term note experiments experiments experiments experiments experiments result computation solution independent found sequence sequence sequence sequence sequence sequence sequence sequence initial table table table table estimate estimate estimate estimate estimate estimate estimate standard computer terms terms terms terms terms terms terms terms terms distance distance connections left presented presented present machine machine maximum maximum maximum position basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs outputs outputs outputs outputs outputs continuous abstract applied applied applied applied likelihood likelihood likelihood likelihood likelihood references stochastic due ieee ieee ieee ieee procedure procedure context context context context context context context context context context context context context context context context context context context context context context introduction hand hand estimation estimation estimation estimation estimation estimation estimation estimation statistical dynamic generated generated tion tion tion tion tion change difference difference assume assume assume classifier lower lower word word word word word word word word word word word word word word word word word word word word word word word word word word word chosen part part part part previous previous previous previous previous previous previous previous previous type bayesian markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make make fact fact proposed proposed length length correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed errors errors errors finite minimum resulting ing ing ing computed computed computed respect sum sum regions regions potential made made made applications applications vol vol vol relative represented represented represented represented true compared application desired rates rates rates proc proc proc proc proc proc proc connected connected distributions discrete discrete discrete equal approaches approaches accuracy train descent morgan morgan words words words words words words words words words words implementation connectionist difficult bias bias layers sequences sequences considered considered framework experiment directly directly solutions estimates estimates estimates estimates transition transition effects efficient classifiers classifiers full full requires choice significant approximate approximate vision estimated estimated estimated estimated con derived weighted developed criterion criterion criterion criterion types lines path path path path product product provided finally covariance covariance tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm close close assumption assumption stable rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount amount common assumed assumed assumed assumed square square pixel ability ability hypothesis future easily makes pairs underlying combination combination combination reduced account account account unknown transfer significantly ratio ratio segmentation special empirical idea produced improve directions resolution exact advantage separate takes element reported reported reported practical apply introduced pixels sense sense interest compare works module module tions tions smooth studies rl trans trans diagonal sparse sparse mixtures chain organization risk parts parts parts parts parts expression matrices hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid white generally generally demonstrate half conclusion reduce reduce segment segment segment segment segment segment segment segment segment segment segment depend depend depend accurate bayes bayes bayes bayes bayes bayes bayes bayes bayes numerical designed designed designed practice practice propose propose taking taking demonstrated demonstrated intelligence intelligence regularization radial radial radial radial radial radial radial radial radial radial radial radial radial radial exist exist derivatives base base explicit digit written written longer longer solving estimating estimating estimating describes describes transitions label segments segments segments segments segments segments segments segments segments segments segments segments segments segments unique consisting mutual gaussians gaussians applying applying applying events events quality select letters letters letters letters letters family independently correlated correlated labels labels showed decomposition decomposition decomposition approximated completely completely digits discrimination discrimination processor processor reasonable remains remains assigned assigned classified classified classified transactions handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten figures priori priori priori recognize automatic black straightforward identified letter letter letter letter letter letter letter letter letter letter letter letter hmms hmms hmms importance paths paths poggio poggio poggio poggio post post post post post tend ten reached characteristic conf conf conf conf conf conf prob interpreted issue strategies strategies write write absence paradigm situations parametric transformed poor relations replaced optimized lippmann lippmann biases discriminant discriminant mse mse mse mse mse applicable int int int int int combine relationships symbolic scores scores scores encode analogous act naturally recognizer recognizer separated multivariate generates mixed explain isolated optimum optimum charge brown formula formula analytical adapted tractable baum lies sys sys closer commonly products recognized recognized recognized depicted annual preceding alignment explained fourth evaluating amounts amounts conducted fed passed variant vocabulary vocabulary cal proven proven chen chen chen acoustics acoustics singer singer singer richard richard replace segmented segmented segmented segmented segmented segmented realized contribute consistently uncorrelated benefit contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual proportion investigation conditioned girosi girosi girosi girosi acts acts count tem inspired inspired ments accepted handwriting handwriting abilities exploit bourlard bourlard responsible enhanced performances contexts document document document sion respective overview overview conjunction bases recog recog extensively likelihoods likelihoods border papers interestingly consecutive posteriori informa unchanged outperforms emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission appeared outline outperform misclassification ties encodes markovian bank bank revealed nition welch icassp par connec regularity reports decomposed avoids publication tems proba simplifying simplifying rbfs france france france reveal confusion confusion confusion confusion lippman lippman lippman nec remark appearing differently differently recogni recogni recogni recogni font cursive justification eral meeting proposes manually contributes sym sym predictable transpose prone centres centres centres centres remained cess gaus halves halves halves halves stabilize seg seg bear tained assessed assessed ous formulas mle mle probabil rec rec postal postal ular plexity align sixth sixth proce ample forthcoming forthcoming mentation ities scribed writers mercer mercer previ centred zhou french french neighbours mere partic chine looked rue rue rue cedex cedex cedex hurt duced cri sev confusions confusions bilities badly assump ofp pred intro estimations probabili tual script bitmaps bitmaps bitmaps bitmaps bitmaps bitmaps loci loci bahl bahl bahl bahl statisti bitmap bitmap bitmap eee poste poste poste poste poste poste bernard bolic sumptions timation michel sti deeply iil jelinek weighed weighed sians textual terion isl dures gal ile ile ile introduc ognition ognition nizing assembling bols 
#@Gilloux_M,Lemarie_B,Leroux_M,
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#*network network network network network learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input function figure time time time time time time time time time time time time time time time time time time set set networks networks training training training algorithm output output output output output number number number number number number number number number system system system system system system system system system system system results results results results results results results units units units units units units units units units units units units units units information information information information information information information information information problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based based space weights linear layer layer layer vector shown systems systems systems systems values values parameters parameters parameters weight weight unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach approach approach approach approach pattern pattern point point image image image image image image image image image image image image image image image image image image image processing processing processing processing processing large large large local local test class class class class class class class class class inputs inputs form form form simple simple visual visual visual visual visual visual paper small small small small size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work work work work task task task fig step step step features features features features features features features features features features features features features classification classification classification level level level level level level level level level level level level level level level level level level level level level current current current trained structure problems high high memory representation images speech parameter real real average theory gradient term note note note note dimensional university university threshold threshold computation computation research independent log found sequence sequence sequence sequence initial table table table table standard computer computer connections connections connections connections science direction map map map map map map map map map map map map map map low low low low low low temporal temporal temporal temporal temporal temporal machine object object object object object object maximum press press position position position position position position position position position position position outputs sample sample abstract applied back back computational computational references stochastic ieee ieee propagation context introduction hand hand statistical effect effect generated generated parallel parallel parallel parallel parallel parallel parallel parallel parallel recurrent recurrent recurrent recurrent recurrent tion tion change complexity complexity complexity complexity complexity complexity complexity assume measure measure measure measure measure measure learned chosen chosen higher part part part part part center previous type type required required good good binary equations markov markov make make make region region proposed probabilities probabilities finite simulations classes human computed multi times regions regions factor factor made made made feedback orientation filter filter original artificial samples samples represented cross cross series define compute objects location location active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye connected motor motor brain brain approaches accuracy larger larger larger update train train dependent dependent modeling morgan morgan department kernel advances advances exp sequences sequences additional additional san san top top requires free free free world world vision basic increase validation give con condition criterion criterion criterion types entropy provided provided provided finally backpropagation nature associative associative associative associative associative associative associative associative associative discussion covariance normal normal feedforward feedforward denote complete complete complete finding amount amount short implemented implemented generate generate generate generate supported require require main eds eds kaufmann kaufmann probabilistic probabilistic typically typically smaller smaller combination reduced fully mlp block interesting interesting interesting interesting testing testing testing character increasing segmentation segmentation database operation pre pre pre pre pre pre pre making bottom bottom bottom supervised supervised idea attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention minimize minimize minimize minimize perceptron denotes architectures discussed resolution resolution advantage robust separate takes takes typical movement pixels pixels pixels engineering engineering sufficient sufficient compare previously tions positions positions locations locations williams williams grant exists parts parts parts invariant deviation wide alternative touretzky pass pass pass runs half place place row row sigmoid measures measures designed moody mateo mateo encoding propose integration reduction regularization movements movements movements selective selective selective selective selective selective selective selective selective selective decrease decrease decrease derivatives characters connectivity explicit digit digit digit digit digit digit digit digit van edges written longer perception perception winner winner sequential sequential sequential laboratory ann dimensionality text text integrated integrated integrated springer implies extraction extraction extraction decreases decreases extracted extracted extracted extracted extracted extracted extracted dependence interpretation detailed operations operations updated fraction completely completely similarly similarly translation digits digits digits updates diagram partial epochs epochs combining roughly initially sufficiently handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten activations usa color recognize partially partially neighbors literature computations computations invariance invariance conf cun cun cun success success success success success anderson neuroscience classify running content content sci cues relaxation highest binding neurosci extract decreasing decreasing minimized simpler carried carried carried american detail detail detail hanson behaviour behaviour fewer successive giving int possibility relationships complicated analogous examined examined saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency coarse plausible analyze automata psychology rev recognizer noted simplest defines mentioned brown brown brown rows rows convolution defining expensive processed processed ring organized filtered controls scientific acknowledgement preceding explained fed fed fed fed fed introducing passed passed slower commands berlin mod gen phone phone phone chose comments softmax softmax summed univ trade don feasible count caltech fails analyzing settings salient salient salient salient carry combinatorial programs moved ascent peterson augmented saccade saccades saccades draw propagate counts accumulated sequentially zipser zipser achieving ahmad ahmad emergent encouraging tween discriminative discriminative simd certainty brightness cns evolve gained discontinuity ocr met fixation fixation fixation fixation fixation fixation fixation fixation surrounding surrounding scope scope selectively translations memo rochester lippman ignoring bridle bridle continually scanning coming rarely info info stores expense expense nist nist nist ble corners allen heavily inhibit smoother focuses olshausen olshausen compete essen visit seattle extracts accumulate archi strokes implying smc goodness goodness attended compromise concatenated fovea fovea fovea fovea fovea fovea fovea fovea fovea fovea fovea fovea fovea allocating rem experimented experimented noticed attentive attentive attentive attentive attentive attentive attentive attentive attentive attentive attentive reviews fukushima fukushima psych puter internally eralization convolving quarter tecture symmetrically blur blur blur fogelman suppresses accumulating subsample subsample explosion possi posner posner foveation prepared attend treisman treisman associa fixations fixations fixations fixations fixations fixations fixations fixations fixations fixations fixations button conjunctive convolutions till rault extractors extractors funds unfolded ezp puting suf remembered cvpr arch bitmap stressed abstracted abstracted quarterly petersen skilled argm tax stark stark stark bivariate mxm advocate overt pxp behar exchanging atten advocates 
#@Alpaydin_E,
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#*network network network network network network network network network network network network network network learning model neural neural neural neural neural neural neural neural neural neural input input input input data data data figure figure figure figure time time set set set set set set networks networks networks networks training training training algorithm algorithm algorithm algorithm output output output output output output output output output output system system system system system system system system system system system system system system system system system units units information information information information information information problem problem models hidden hidden hidden hidden hidden hidden hidden based space weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer case order order systems systems systems systems values values noise recognition recognition recognition recognition recognition approach approach approach pattern image image image image single single single single single single processing processing processing processing processing processing processing processing control control control control control control control local local local rate rate rate rate rate rate test test test test patterns patterns patterns form form signal algorithms algorithms gaussian paper paper paper size size size feature feature net net work step step step field field field field field field field field field field field field field field field field field field field field field field field classification classification classification classification classification classification classification classification classification classification process process process level level level level level level current trained trained trained trained trained trained trained structure problems high high representation architecture section fixed line rule images images average dimensional dimensional dimensional result threshold threshold found target target distance node node node node node left left present activation activation activation activation low low low nodes nodes nodes nodes nodes sets position position position position position basis outputs outputs abstract back find find find references procedure procedure important propagation introduction estimation generated parallel tion difference spatial classifier classifier lower word higher center center center center previous required good good good long markov markov make make make fact correct errors resulting classes computed performed eq times regions factor dimension knowledge knowledge original original artificial specific compared compared application application application application receptive receptive provide provide rates rates perform determined constraints connected connected connected approaches approaches approaches accuracy fields fields fields fields fields fields fields fields fields morgan morgan morgan proceedings implementation version technique individual individual individual individual individual advances advances advances difficult final final final final exp scheme scheme addition addition additional additional additional additional san san san top top conference classifiers choice significant speed speed produce provided finally achieved achieved describe tested finding nearest common effective implemented role main main eds eds eds journal pixel pixel pixel pixel pixel pixel ability rumelhart fit kaufmann combination fully fully fully testing testing testing testing significantly character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character character projection projection projection projection segmentation segmentation segmentation segmentation segmentation segmentation special special special special database mode window window window window window window window window window window window window window window window international bottom combined combined combined run added improved improve directions recent separate separate moving moving identical pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels array array array array array array array array recently approximately works works module module module module module module module module module module module module module module module module module module module match match definition positions positions chain sensitive wide wide wide predicted predicted predicted alternative width width width generally generally hardware hardware pass place greater assumptions conclusions operator modules designed designed performs performs moody mateo drawn intelligence averaged introduce characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters characters question question index ways describes label confidence confidence confidence confidence confidence confidence involves remaining integrated integrated quality extraction competition letters extracted overlap variation transform labels labels organizing centers centered centered centered centered centered centered forms forms forms sizes allowed allowed allowed allowed allowed earlier normalization false valid valid string string string string string string symbol assigned precision precision precision expect handwritten handwritten box box combinations combinations activations activations activations activations strings strings strings subspace recognize recognize recognize discuss candidate candidate candidate candidate middle middle middle closely computationally divided included post post post projections projections projections ten ten contained success success success success interpreted providing board wave giles moves preferred tesauro cowan cowan difficulty replaced hanson lippmann mass successive rest rest scaled scaled complicated act integer man analyze recognizer portion art generates detected mentioned mentioned mentioned indicating rows ment distinguish publishers publishers publishers analyzed waveform adjacent expensive lies inside processed processed purposes sys shared organized organized organized organized preprocessing division lowest robustness robustness robustness fourth fourth percent collected lack autonomous remove variant variant rely serve achieves substantial chose windows implements wang irrelevant trade globally gabor gabor gabor gabor gabor gabor gabor martin martin recover purely tem impossible imaging stronger difficulties simplify alpha alpha resistance height height height vehicle vehicle vehicle moment mark mark shifts shifts shifts shifts reliably alspector started separating corre corre decide decide intended heart heart heart candidates competing arrangement specialized layout saccade saccades saccades ends ends thresholding displacement consecutive liu ence outline constitute minus sine ent session gaps gaps job rejection pieces guess guess stands beta henderson publication shifting chapman ocr ocr ocr ocr ocr ocr ocr ocr challenging plate individually rejected rejected rejected cosine paris unconstrained ambiguous weaker rochester things round october wider mea resembles replacement copies sponding decided decided christopher trainable ers virtually keeler keeler industrial agency agency alarms normalize wavelets corrective capital norms totally sliding company positioning positioning positioning positioning positioning positioning positioning positioning appro appro appro contents replication united united occasionally meaningless preprocessed miss putting touch icann tran posi registration alexander gupta gupta missed corresponded consensus confident positioned positioned driver driver touching touching touching blank blank disconnected charac ences numerals numerals assist disambiguation disambiguation theme tolerate business survive kingdom kingdom aaa postprocessing postprocessing postprocessing postprocessing postprocessing postprocessing postprocessing postprocessing postprocessing lly duplicated duplicated duplicate tered tered plates envelopes orm deficiencies serf numeric monitors rejects rejects rejects rejects alphanumeric alphanumeric alphanumeric alphanumeric alphanumeric alphanumeric alphanumeric ols dose individ subimages subimages subimages conv conv conform organizes practitioners immunity competitor fool ition ition multitude ely ely ely complicates 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results results results results results results results results results information information problem problem problem problem models models models models models models models hidden hidden performance performance performance performance performance based weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case order order order order shown shown shown shown shown shown shown shown shown systems values parameters weight functions functions neurons neurons neurons unit recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern processing processing processing processing processing control control large local local local local local local neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate test test test test test test test test test analysis analysis analysis analysis class inputs form form signal signal signal signal signal algorithms algorithms simple simple work task task task features classification classification current current current trained trained problems random high memory memory memory memory memory response response response response similar architecture architecture architecture architecture architecture show show fixed general generalization speech speech speech speech speech speech speech speech speech speech parameter parameter parameter approximation approximation approximation approximation approximation average gradient gradient gradient gradient gradient gradient obtained term term term term term term term note note note experiments result result university computation research research defined defined defined defined found sequence sequence target target target target target dynamics initial initial initial constant table table table table standard standard standard standard standard standard standard standard standard computer terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left presented present present present activation low low nodes temporal outputs outputs outputs abstract back back back back back back back back back back back back back back back back back back back find find find convergence convergence references stochastic stochastic stochastic due ieee important adaptive adaptive context introduction complex estimation statistical dynamic recurrent tion tion tion complexity lower word chosen higher part previous cases required required multiple long conditions equations equations equations fact region proposed proposed length length observed observed finite simulations simulations simulations minimum minimum resulting ing total computed multi multi multi performed performed performed called times times dimension global global global filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter obtain obtain negative negative artificial true true compared compared application series series provide define rates determined experimental related related gain gain gain gain gain gain gain gain discrete power power steps comparison update update update update update update update descent descent descent descent descent descent morgan proceedings department synapses synapses synapses synapses consists individual represents difficult difficult final bias bias layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers delay delay scheme graph sequences considered considered hinton additional additional additional view top conference determine requires significant significant vision pages pages pages validation derived criterion lines provided provided backpropagation nature nature nature increases arbitrary tested limited surface surface surface surface surface surface surface surface surface short synapse synapse synapse synapse synapse supported main end hypothesis hypothesis degree kaufmann account account coefficients mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp transfer significantly significantly increasing special special database database operation details filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters pre direct window window window window international bottom depth depth depth depth frame frame frame frame perceptron perceptron architectures architectures architectures architectures discussed improve advantage separate reported practical apply apply introduced engineering compare volume module correspond definition positions positions improvement increased deviation deviation deviation locally move deterministic column pass pass greater greater conclusions sigmoid modules accurate designed performs performs moody moody reduction pulse variety decrease relationship relationship manner minima minima question appears pro derive derive construct index stability stability stability confidence infinite electrical dimensionality dimensionality dimensionality adding adding versus extracted extracted extracted phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme controlled controlled frames frames frames frames frames frames static static past epochs epochs delays convex roughly false false false false false valid filtering filtering filtering classified degrees expect partially neighbors tests gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma society identify tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn comparing situation vowel refer procedures contained contained contained interpreted superior usual providing board acknowledgments software modelling modelling bars schedule schedule powerful poor poor create exhibit experience difficulty difficulty difficulty difficulty varied replaced history investigated scaled variability tanh proved func func analogous waibel act act closest possibly editor created impulse impulse impulse obvious freedom perceptton epoch epoch speakers speakers speakers isolated optimum optimum percentage percentage percentage distinguish distinguish smoothness smoothness guaranteed improves adapted worse nonlinearity reasons considerable inside processed perspective berkeley purposes widely organized located commonly recognized describing circle preceding raw considerably affine amounts poorly orders posed http gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains gains phonemes phonemes phonemes phonemes phonemes phonemes substantial softmax pole pole optimizing optimizing labelled connecting saturation consideration darken darken intuitive motivation motivation overlaps contexts appendix appendix encountered lang lang lawrence lawrence lawrence lawrence lawrence schedules candidates dif theoretically belonging statement default andrew unable minus listed listed basically classifications chaos recurrence australia principe principe principe principe principe principe options remainder pub ftp ftp surrounding fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir fir retain increasingly accounted electronics stuck nec coming heading council instability australian australian impractical attributed vii ferent curse smoother smoother suffers locate reflecting inclusion inclusion inclusion inclusion 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functions unit unit recognition recognition recognition recognition recognition recognition method method method pattern pattern pattern point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point image image image image image image image image image single single processing large large local local local local local analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix form form form simple simple gaussian examples small small small small feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work points points points points points points points points points points points points points points points points points points points points points points points points features features features features features features features features features features features features features features features features features features features features features classification random random random similar similar similar representation representation representation representation fixed fixed fixed fixed line images parameter parameter parameter parameter parameter real approximation term term term term term note note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional university variables variables variables variables variables variables computation solution solution independent independent log found initial initial initial constant standard standard standard standard computer terms terms science present present present present machine machine object object object object object object object object object object object object object sets sets sets sets sets sets sets sets sets range range position basis abstract applied find references component component due ieee ieee procedure introduction hand hand hand estimation estimation statistical statistical generated generated generated generated generated generated generated search tion tion change change energy complexity complexity complexity variable variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial measure measure chosen chosen chosen part part part center previous type multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple binary represent tree expected make region region region region length length correct correct correct ing ing human human computed respect performed eq eq called times elements elements elements regions regions regions regions regions mapping factor factor optimization optimization optimization optimization dimension dimension dimension original true true application application define location location location eye experimental related constraints constraints constraints constraints constraints constraints constraints constraints constraints equal equal approaches approaches accuracy accuracy update update update update update update modeling morgan technique technique technique technique individual advances represents represents represents final final exp exp scheme scheme addition maps maps considered considered framework framework framework framework framework framework framework equivalent curve limit san determine requires world speed basic basic randomly randomly randomly randomly developed developed criterion criterion types types types types provided finally constraint constraint constraint increases denote transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation limited assumption finding assumed shape generate theoretical require face face face face face square easily easily development sensory kaufmann objective objective objective objective fully interesting projection head head matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform details iterations added added added denotes improved improved improve robust element similarity similarity movement movement introduced identical subset subset subset subset recently recently sufficient sufficient approximately approximately approximately volume works module module module solve match match match match match match match match match match match trans trans address positions modified interval interval interval interval interval organization arm parts parts parts parts parts parts parts parts parts invariant invariant invariant invariant invariant deviation deviation deviation deviation rotation move touretzky loop column demonstrate runs runs runs conclusion starting row segment operator editors exponential weak integration presence presence physics physics characteristics drawn drawn drawn drawn intelligence intelligence turn turn min plane acknowledgements solving solving solving generating distinct changing explicitly explicitly explicitly coordinates physical transformations transformations transformations transformations transformations transformations remaining extracted expressed expressed expressed solved solved solved solved solved variation updated centered centered decomposition forms approximated translation updates updates updates updates processor partial normalization reduces penalty penalty closed closed closed remains remains valid handwritten perceptual formulation color contour assignment assignment assignment assignment assignment specifically holds partially texture determining extra uniformly uniformly divided identity reached capture repeated neuroscience stopping stopping return satisfy generalize minimizes correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence overlapping tesauro minimized schedule transformed matches matches fashion fashion rest applicable authors working analogous contours contours trace equally algo initialized synthetic synthetic synthetic synthetic synthetic synthetic seconds integrate indicating indicating indicating formula publishers tractable tractable lies handle perspective satisfied widely mation mation implicit members begin depicted geometric affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine amounts 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image image image image image image image image image image image image single processing processing processing processing control control control control control control control control control large neuron neuron rate analysis inputs form form shows shows signal signal simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual size feature feature feature feature feature feature feature feature feature feature feature feature feature work work work task task task task task task methods fig cells cells cells cells cells cells points field field field field field field field field field field field features features features features features features process level level level level current structure structure structure structure structure problems high similar similar show show section section section fixed line vectors images real average average average obtained obtained obtained obtained obtained obtained note activity dimensional result result result university computation computation computation computation research research research research sequence sequence sequence dynamics dynamics initial constant science science presented presented presented map map map map map map map map map map map map map map map map map map map map present present present present present present present present phase temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine machine object object object object motion motion maximum maximum maximum press components components basis abstract abstract applied applied applied find computational properties references positive context introduction action complex complex hand behavior behavior stimulus stimulus stimulus parallel parallel parallel change change change difference difference difference difference spatial spatial spatial spatial signals signals higher higher higher higher part part part part center center center center center center center center center center center center previous firing type required cortex cortex spike spike spike spike expected fact region region correlation correlation correlation observed human computed computed computed computed computed computed sum sum sum called called called times elements means optimization feedback feedback feedback orientation orientation orientation global global applications study filter vol relative relative application receptive receptive provide provide compute compute compute objects objects objects objects objects proc location location location location location location location location eye determined experimental experimental posterior brain equal mit larger contrast fields update train dependent modeling modeling modeling modeling selection selection selection selection selection report report institute institute institute department implementation implementation version consists internal advances represents responses exp maps maps maps maps maps maps maps maps maps maps maps framework cambridge additional additional view trajectory trajectory trajectory top top top stimuli stimuli stimuli stimuli stimuli stimuli determine world vision vision vision vision vision vision vision vision vision vision vision vision increase increase con weighted developed levels area area area area path product provided finally processes selected selected selected evidence inhibitory inhibitory simply biological biological biological achieved normal technical close close corresponds corresponds corresponds excitatory short short common implemented implemented implemented implemented implemented assumed generate supported require eds face face journal pixel pixel pixel pixel pixel pixel instance instance future degree sensory sensory including simulated underlying underlying combination account account functional functional technology 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mechanisms integration california california california selective selective selective selective selective selective selective selective scene scene scene minima program force question acknowledgements areas construct edges longer perception winner winner winner winner winner winner primary sequential sequential ann changing changing implement scales scales scales integrated integrated integrated adding adding gaussians potentials select select yield national national focus focus focus focus focus focus focus focus focus influence influence codes detailed detailed detailed detailed operations operations modulation modulation static understanding understanding activities activities suggested suggested suggested processor spaces combining roughly generation generation intermediate intermediate filtering foundation foundation faces koch koch koch koch koch koch koch koch koch koch koch koch degrees avoid building building fire fire fire color activated activated mozer black absolute characterized major major reason reason straightforward importance paths driven presentation computations essentially fine capture capture capture capture conf showing anderson anderson neuroscience return strategies sci quantity quantity quantity relaxation generalize surround surround surround surround surround surround surround surround subsequent decreasing decreasing decreasing receive oriented camera trains trains powerful essential circuitry limitations periodic existence postsynaptic scalar scalar scalar respond respond rest project plasticity office office office oscillation pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway topographic saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency saliency patch plausible plausible plausible necessarily opposite prototype obvious generates simplest wta wta integrate integrate 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units units units units units units units units units units units units units units units units information problem models models models models models models hidden performance based based space space layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector order order shown shown shown parameters noise noise unit unit unit unit unit unit unit unit recognition recognition method method approach pattern pattern pattern pattern point point point single single single single single processing large large local local local local local rate test test patterns patterns patterns patterns inputs inputs inputs inputs inputs inputs inputs inputs inputs signal signal signal signal signal signal signal signal signal simple simple visual visual visual visual visual visual small small fig fig fig fig fig cells cells cells features features features process level level level current cell cell cell cell cell cell structure structure problems problems high memory similar similar show fixed rule general general real real average theory activity activity activity activity activity activity activity activity activity dimensional dimensional result threshold threshold computation computation research independent independent found sequence target terms connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction direction presented present present present temporal temporal temporal temporal temporal temporal temporal temporal motion motion motion motion motion motion press press learn nonlinear abstract properties references due due positive positive important propagation context introduction hand circuit stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus dynamic dynamic generated generated tion difference spatial spatial spatial spatial rules rules rules signals signals signals signals signals signals signals learned higher center bound firing firing firing type type type type type type required cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good good good good good binary binary spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long conditions expected expected markov make make make correlation correlation forward forward forward forward scale scale resulting resulting classes ing ing sum times times means means natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation filter filter relative specific specific specific specific specific specific specific specific represented compared compared cross series series receptive receptive receptive compute objects rates location location active active determined experimental experimental goal cortical cortical cortical cortical cortical cortical brain brain mit mit voltage voltage voltage voltage accuracy larger fields fields fields train train train train synapses synapses synapses synapses synapses synapses synapses synapses internal internal individual individual responses responses responses bias bias bias bias layers delay delay scheme sequences environment directly hinton curve design top top top top top top top top stimuli detection detection detection detection detection detection determine efficient efficient upper requires requires requires requires requires significant world world pages pages con produce produce produce coding levels types types product actual actual actual nature discussion tested assumption excitatory excitatory excitatory predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions proof proof synapse synapse generate require face end end pixel pixel pixel pixel pixel pixel pixel pixel pixel hypothesis instance instance future future future future future future future future future noisy noisy noisy sensory sensory fit objective typically typically special consistent consistent principle operation making making inhibition inhibition inhibition normalized bottom bottom decay light predict predict predict predict predict predict predict predict predict predict neuronal architectures improve improve directions directions recent resolution resolution resolution exact advantage lateral lateral practical practical moving moving moving 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adding events predictive predictive predictive predictive predictive expectation expressed formation stages codes codes restricted fraction static completely earlier earlier smoothing slow slow slow delays classical event purpose purpose closed sufficiently advantages advantages faces koch koch precision avoid avoid avoid existing fire perceptual contour contour contour contour contour contour contour retinal determines activated specifically neighbors tests middle middle middle closely computationally driven driven driven driven driven spiking spiking spiking spiking spiking successful identify detect computations computations comparing comparing essentially fine characteristic excitation excitation excitation soc strongly contained stopping criteria timing timing bar bar bar bar bar dayan dayan providing quantization delayed delayed delayed delayed delayed highest binding binding leading neurosci neurosci principles moves subsequent trains body layered kalman environments issues 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time time time time time time time time set set networks networks networks networks networks networks networks training training training training training training output number system system system system system system system system system system system system results results results results results results results information information information information information information information information problem models models models based space weights layer layer layer layer layer layer layer layer layer layer layer layer order shown shown shown shown shown shown systems systems systems functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit recognition recognition method method pattern pattern pattern point image image image image single single single single single single single processing processing processing processing processing processing processing processing processing control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test analysis analysis analysis analysis analysis analysis inputs form form form shows signal signal signal signal simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper paper paper paper feature feature net work work task task methods methods methods methods cells field field features features features features features process level trained trained cell structure structure structure structure structure response response response response representation representation representation representation representation representation representation representation representation architecture fixed rule rule rule rule rule rule general general real theory activity activity activity dimensional dimensional university university solution research research research sequence sequence target initial initial initial constant standard computer computer computer computer terms connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections science science science science prediction prediction prediction prediction prediction prediction left left direction direction presented presented present activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation machine object object object object object object object object object object object object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range learn learn learn learn learn position position position position position position nonlinear continuous abstract properties references stochastic stochastic due adaptive adaptive propagation context introduction stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect dynamic generated parallel parallel parallel parallel parallel tion complexity spatial spatial spatial spatial lower rules rules rules signals signals signals signals signals signals representations representations representations representations representations representations representations representations representations representations learned learned learned chosen part bound type type type multiple multiple multiple cortex cortex cortex good long conditions represent represent represent represent represent represent region observed scale scale ing total simulation simulation simulation simulation simulation simulation simulation simulation simulation human made relative relative relative relative relative relative specific specific specific represented represented represented receptive objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects location active active active active active active determined related posterior posterior constraints connection connection support dependent source source morgan proceedings proceedings proceedings proceedings proceedings proceedings report institute department department version advances joint joint represents responses responses final layers delay scheme scheme sequences sequences sequences sequences sequences sequences sequences computing directly additional trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san san san top stage stage stage stimuli stimuli stimuli stimuli stimuli stimuli conference conference determine determine upper full world speed vision vision vision vision vision vision basic produce channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel derived randomly velocity actual actual actual actual actual evidence evidence evidence evidence evidence evidence nature nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends biological associative discussion technical feedforward describe limited corresponds complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable predictions predictions predictions predictions predictions predictions amount amount implemented generate generate supported role eds eds eds journal end future development including kaufmann simulated simulated simulated simulated simulated reduced functional york edge edge segmentation mechanism consistent principle principle principle operation operation operation leads representing representing representing representing representing representing representing pre direct inhibition international international bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom depth depth depth depth depth depth depth depth depth depth depth depth depth depth early early early frame combined combined predict predict predict predict predict predict predict predict predict predict predict neuronal architectures directions recent advantage pair separate separate separate lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral moving moving moving moving moving moving moving period period period cognitive recently highly highly previously previously previously unsupervised unsupervised approximately works positions positions positions chain chain chain chain chain chain chain chain chain chain chain chain chain channels channels channels channels channels channels channels channels channels organization organization organization storage sensitive sensitive horizontal horizontal parts studied occur suggests suggests extended extended predicted alternative pass flow starting row row row greater trajectories trajectories trajectories conclusions competitive retina faster learns learns learns learns mateo strong strong strong strong strong strong strong strong strong strong mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms presence presence presence presence presence solid solid solid solid variety selective iii manner scene question acknowledgements relation pro van edges produces perception perception perception perception perception perception perception perception perception perception perception optical winner factors describes describes describes describes describes stability stability tuned distinct distinct explicitly involves develop develop events events events events events events events events events events events events events events events events events events events events events events events predictive predictive formed implies formation correlated correlated viewed viewed restricted organizing organizing organizing organizing organizing organizing organizing showed activities similarly allowed discrimination partial sec event event roughly initially visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible sufficiently construction koch david includes perceptual perceptual activations activations activations retinal retinal uncertainty maximize activated activated activated activated specifically discussions texture major major major determining closely closely detect detect schemes post reached receives receives receives receives receives receives composed excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation strongly strongly induced allowing split dis duration duration gray gray gray involved vary simplified simplified absence giles delayed delayed delayed delayed reach cat consisted intrinsic receive oriented cowan presents remain carried carried carried diego diego diego powerful american varied relations relations relations replaced hanson limitations issues issues dotted dotted preliminary hall hall successive successive successive respond respond respond respond respond respond links detectors relationships cognition fundamental notion analogous surfaces contours contours matched removed neu neu neu neu hill hill circles transmission possibly predicts predicts psychology bifurcation bifurcation bifurcation detector hebb hebb hebb consist extent grouping grouping grouping regime animal indicating ment developing ground distinguish publishers phenomena phenomena failure failure handle handle handle handle ganglion ganglion sys sys organized organized organized preprocessing monkey monkey arise afferent consequence ridge gradually gradually addressed virtual virtual virtual fourth apparent behaviors limits understood capability poorly psychophysical cohen cohen detecting detecting variant ity maintain maintain maintain maintain operate anti reaches fall prevent chen chen richard enables boston display display expectations implements simultaneous univ cor contribute phenomenon contextual appearance equivalence investigation tation restriction martin martin martin martin homogeneous homogeneous discovery discovery repre repre repre enhancement reaching arranged establish extending fails stronger chains chains chains chains chains chains occurred moment los operates operates ral north north optic symposium presentations presentations child moments continue dendrites sion washington parietal parietal parietal exposure exposure exposure occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion occlusion infer indicator indicator indicator gaze contact arrows arrows arrows arrows arrows arrows motions motions extensively broken projects valuable speeds propagate propagate receiving robert onr linked associations associations neurophysiology constitute constitute shading shading shading latency inferred inferred inferred inferred inferred inferred revealed responds responds responds responds trigger lit constitutes constitutes letting examining mismatch verified acting favor robots interact grouped tems tems activate activate hubbard hubbard hubbard hubbard hubbard hubbard neurophysiological mediated paired books macaque macaque macaque pos conversely represen represen represen selectively selectively selectively responding pools pools likewise elsevier steering things reciprocal reciprocal psychophysics psychophysics psychophysics psychophysics inactive inactive answers modal develops helps persistent persistent remarkable stephen ble ble builds losing subjective subjective inhibit transparency opponent opponent opponent opponent opponent opponent developmental award award burr burr essen rons rons rons emerges chan carries carries carries successively successively meth restricting exploits spie spie spie reality invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible invisible ods tations tations priming correlates correlates occluded occluded occluded occluded occluded occluded occluded occluded charles aperture kinetic kinetic kinetic kinetic transmit sentation sentation sentation merit responded christof tory illusory illusory unexpected stabilization subnetwork completeness percep amsterdam occasionally activates marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall marshall excite excite activating mar mar mar mar ther possesses devel stim stim sequencing rightward rightward rightward postulated named challenges fac silverman silverman silverman silverman silverman silverman thompson thompson ily jonathan wired gupta disappear disappear asso multiplexing inadequate lose lose lose faculty accumulating george prevented mere smear sponse possi govern govern organize organize emerging reinforced triggers temporarily temporarily disappears disappears visibility visibility visibility visibility visibility visibility visibility visibility visibility visibility visibility visibility maunsell maunsell maunsell maunsell maunsell farther diction mingolla postulate indefinitely fax gestalt asymptote asymptote occluding ond decayed aaa regulated nel oak kevin lets lets differencing differencing nakayama nakayama nakayama nakayama nakayama nakayama nakayama nakayama amplify tual excites grounded grounded mech cesses miles increas supercomputer weaken perceiving facto hibitory subcortical noteworthy terior minnesota minnesota carolina carolina ulus ulus stimu kaplan kaplan excita distinguishable schmitt ramachandran ramachandran ciative disappeared disappeared disappeared lus strengthen multiplicity parallax exert tivation tivation lective organizes aries chapel 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#@Alley_R,Hubbard_R,Marshall_J,
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#*network network network network network network network network network network network model neural neural neural neural neural neural neural input input input input input input data data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set networks networks training training training training training output output output number number system system system system system system system system system system system system system system system error results results results units units units units information information information information information information information information information information problem problem hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based layer layer vector order systems systems systems systems systems values values values values parameters recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach approach pattern pattern point point image image image image image image image image image image image image image image image image image image image image image image image image single single processing processing control large large large large local local local local test test test patterns patterns patterns analysis analysis analysis analysis analysis analysis shows shows shows signal simple paper examples small small small size feature feature feature feature feature feature feature feature feature feature net net work work work work methods methods methods methods points points field field field field field features features features features features classification classification process level level trained trained trained trained structure high high architecture architecture equation line line line images images images images images images images images images images images images images images images images images images images images images images images images generalization generalization generalization generalization generalization real approximation states gradient gradient obtained obtained obtained obtained obtained obtained obtained obtained activity activity activity dimensional university university university university university computation research research research research research research research research independent independent independent defined defined defined defined sequence initial initial estimate estimate standard computer computer computer terms terms science science left left direction presented present low low temporal motion motion motion motion motion motion press position components components components components components components components abstract back back references component component due due procedure procedure important important propagation propagation introduction action action action action action action action action action action action action action action action action action action action complex dynamic generated tion difference difference difference difference difference difference difference spatial spatial spatial spatial classifier classifier classifier classifier lower lower measure measure measure measure measure signals prior representations representations representations center center previous previous cases required required multiple good represent make make make techniques region correct correct correct errors errors errors forward forward forward forward forward scale resulting ing total human human human human human human sum regions regions means means made applications applications study study obtain vol relative specific specific specific compared provide compute location location perform active eye eye determined determined experimental goal connected approaches approaches approaches approaches accuracy accuracy accuracy fields fields fields fields train descent source morgan morgan proceedings proceedings proceedings report report institute institute institute institute institute technique individual individual individual individual individual individual individual individual individual individual individual advances advances difficult final sequences sequences sequences sequences sequences directly estimates san san san san san classifiers classifiers classifiers classifiers upper upper upper upper full full requires significant speed estimated increase give give produce coding coding coding coding coding weighted developed developed area velocity product constraint measured measured measured discussion technical increases increases group surface actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions supported require face face face face face face face face face face face face face journal pixel pixel pixel ability objective pairs smaller underlying underlying fully transfer testing matching matching database database database database database principal principal principal principal principal principal principal squared international international normalized normalized experts experts combined combined combined combined combined combined combined combined sources sources improved population correlations takes similarity movement lateral apply include subject subject subject subject subject sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive compare compare subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects axis correspond address positions locations locations improvement improvement grant horizontal intensity intensity intensity intensity intensity expression expression expression expression expression expression expression expression expression expression expression expression deviation derivative alternative correctly feed feed feed feed feed touretzky touretzky white flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow critical critical reduce segment segment segment tangent interactions differences differences differences measures measures measures measures measures accurate performs mateo mateo suggest taking taking taking presence demonstrated labeled labeled labeled user reference explicit explicit produces optical winner ways primary laboratory laboratory vertical distinct distinct distinct distinct distinct explicitly physical consisting national extracted extracted extracted extracted extracted depending correlated evaluated evaluated static static understanding completely partial partial performing performing performing performing performing measurements combining visible foundation advantages classified classified faces faces transactions template template template template template template template includes combinations combinations inter plotted illustrated illustrated automatic automatic variations black structural successfully major major planning identified differ included detect detect detect detect projections projections projections score tend ten ten characteristic repeated video video video interested superior classify classify classify classify classify cue categories categories categories cues cues list involved dot cat automatically attempt attempt attempt subsequent acknowledgments bars body remain collection essential humans estimators estimators dataset dataset dataset dataset dataset examine matches matches giving behavioral behavioral behavioral muscle muscle muscle muscle muscle scaled reliable variability variability tanh workshop workshop workshop statistically removed neu measurement measurement measurement measurement measurement measurement coefficient gradients psychology facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial perfect eyes eyes eyes eyes aspect mapped expressions expressions expressions expressions expressions expressions expressions expressions expressions shapes consist baseline attempts wta seconds agreement tool tool comparisons considerable implementing sections widely located located laboratories projected beginning medical medical annual recognizing nsf nsf outer researchers conjugate questions people collected axes leave marked detecting detecting frequently compares templates templates templates howard howard measuring measuring differs achieves gave gave gave asymmetric age focused displays distortion classifying classifying classifying classifying classifying classifying classifying classifying classifying lab benefit redundant appearance appearance appearance investigation velocities velocities rotated branches turned kaufman kaufman promising tools city occurring scoring scoring obtaining salk salk cottrell cottrell cottrell cottrell cottrell salient optic optic symposium muscles muscles muscles exploring reliably reliably performances bartlett bartlett bartlett bartlett paul paul evident lawrence lawrence lawrence dif francisco francisco francisco smoothed contraction contraction jolla jolla gesture gesture gesture davis davis davis dietterich automated automated limitation verify visually benefits july pentland pentland pentland pentland pentland feeding medium classifies constitutes brightness clas attempted ibm mhz mhz gener intra hughes hughes terrence relate relating paired retain intensities intensities gender gender commercial thousands thousands expense distortions distortions distortions hyperbolic tom identifies emotion emotion emotion emotion emotion emotion emotion viola viola viola viola viola observers skin arrow reflecting compo subtracting devised assessment luminance automation manually manually huang huang contributes beneficial rating alto denmark neutral neutral neutral ready closure comprised jan manual maryland subtle subtle sur sex discriminating eigenfaces palo joseph iris stand lid lid nents favorably alization friesen friesen friesen friesen distinctions registration accessible jackknife subtract neurology terry scored comprise comprise lose ending pared pad altogether opening proaches adaptable copenhagen relied metcalfe metcalfe metcalfe ucsf ucsf omitting turk turk intend bohr larsen larsen larsen larsen emotions doubled muscular muscular muscular muscular lengthy holons interfaces scientists tape golomb golomb golomb golomb golomb golomb corp livermore voluntary referenced graylevel graylevel ieice eigenface zurich zurich automate bined utah mase mase mase consumer sitions emotional happy happy technological niels stewart pentium pentium reserved signify contractions contractions binations widening lake blended surprised musculature friendly tensity provement multimedia multimedia roscience consulting psychologists emo ficult connectionists exaggerated 
#@Bartlett_M,Ekman_P,Hager_J,Larsen_J,Sejnowski_T,Viola_P,
#t9
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#*network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure time time time set set set set algorithm algorithm algorithm number number system system system error results results results results results information information information information information information information information problem problem problem models models performance based based based space case case case case case vector vector vector vector order order order order shown shown shown shown shown shown shown shown systems systems probability noise functions functions functions distribution distribution recognition recognition method method approach pattern pattern pattern point point point point point image image image image image image image image image image image image image single single single single processing processing processing control large large local rate rate rate patterns analysis analysis analysis analysis shows shows simple gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper small small small size size feature feature work work work task task task task task task task task methods cells step points points points field field field features features process process process process process current current current current current current current current cell structure high high high high high high memory memory memory response response response response similar representation representation representation architecture show show section section fixed line vectors vectors vectors vectors vectors vectors vectors vectors images general general general parameter theory obtained obtained obtained experiments experiments experiments experiments dimensional dimensional result university university university university university university computation computation solution solution research research research research independent target target target target target target target target target target target dynamics initial constant table table table table table estimate computer computer computer computer terms terms distance science science science science science science science left map activation frequency object object object object object object object object sets motion maximum maximum press press position components basis basis basis basis basis continuous abstract applied find computational computational properties properties properties likelihood likelihood references component due ieee procedure important important decision decision introduction action behavior behavior effect dynamic dynamic generated search search search search search search search search search search search search search search search search search search search search search search search search complexity spatial spatial spatial spatial spatial spatial signals prior prior prior representations representations representations representations representations representations representations representations word chosen center center previous multiple multiple multiple multiple multiple multiple multiple multiple multiple cortex cortex cortex good long make make fact region proposed proposed correlation observed observed observed observed errors errors scale scale scale scale scale scale scale scale scale scale scale scale scale scale tasks tasks human human human human human human human human human human human human human human human human human computed computed times times made made made natural natural natural natural natural natural natural natural feedback orientation global study study filter filter filter filter filter filter artificial artificial represented represented represented compared compared application receptive receptive compute compute objects objects objects objects objects objects objects proc proc location location location location location location location location location active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined experimental experimental goal related distributions motor cortical cortical cortical brain brain mit mit mit comparison larger larger larger source source modeling modeling modeling modeling modeling modeling modeling modeling morgan report report report words department department implementation advances advances connectionist connectionist responses responses responses difficult difficult final scheme scheme sequences cambridge computing additional additional additional view estimates design trajectory top detection conference determine efficient choice significant approximate approximate world vision vision vision vision vision vision vision vision vision pages pages pages pages pages derived derived weighted weighted levels velocity actual actual processes processes processes selected evidence depends achieved discussion technical technical technical increases describe arbitrary group tested close amount implemented assumed generate supported role role role require main face face ability ability development fit kaufmann objective block programming programming testing york increasing mechanism mechanism special trials trials trials matching language language principal principal details details details max max max filters filters filters filters filters filters filters filters filters filters making making window window window window stored bottom bottom early frame attention attention minimize denotes denotes denotes denotes denotes population population recent recent correlations resolution resolution resolution resolution resolution resolution resolution resolution resolution exact property robust typical typical typical movement movement movement movement movement movement strategy strategy strategy strategy moving subject subject pixels pixels trees cognitive cognitive cognitive cognitive cognitive interest interest interest compare previously previously previously observations approximately subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects volume axis solve match match achieve locations locations locations channels improvement invariant scaling derivative predicted predicted predicted predicted move move move touretzky setting greater greater greater greater competitive editors central retina retina retina peak suggest suggest mechanisms mechanisms integration largest largest largest intelligence intelligence movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements selective plane plane averaged targets targets targets targets derivatives manner scene scene scene scene scene scene scene scene identification question question denoted perception perception perception solving solving sequential generating laboratory laboratory vertical dept category coordinates averaging averaging dimensionality remaining text scales scales scales scales scales scales scales scales scales scales scales scales formed formed select national national focus stages interpretation interpretation codes variation variation variation centered centered centered soft suggested suggested processor key spaces sec combining purpose purpose interpolation remains intermediate distances distances distances koch views david expect recorded recorded thesis color weighting retinal retinal illustrated mozer candidate coupled variations middle aspects aspects society society paths paths paths driven comparing invariance situation tend orthogonal ten fine fine fine fine fine fine composed summary refer conf graphs contained interested issue running criteria strategies strategies sci michael play board board correspondence computes computes illustrates subsequent subsequent subsequent preferred acknowledgments tesauro decreasing oriented oriented oriented oriented bars employed employed employed involving involving issues dotted dual preliminary preliminary existence existence matches successive fashion history muscle eigenvectors pathway pathway topographic cognition cognition analogous matched saliency saliency saliency saliency smallest patch patch patch coarse coarse coarse coarse coarse coarse closest possibly editor reading reading analyze predicts psychology psychology eyes eyes eyes adjusted prototype prototype assumes separated explain phd scenes scenes scenes scenes scenes crucial crucial crucial agreement agreement nowlan considerable rapid rapid closer located depicted annual annual recognizing nsf questions reflects reflects behaviors reflect freeman empirically understood spoken spoken peter peaks frequently compares execution limiting fall instruction incoming resource resource achieves substantial inherent chose decreased focused sentence instantaneous pyramid uncorrelated benefit identifying leen saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic purely addresses rotations rotations reaching smith primate proceeds proceeds proceeds attractive resulted serves cottrell mance falls sion perfor moved conjunction dominant histograms searching scan scan scan originally viewing initialize young suggesting ballard ballard ballard ballard ballard ballard ballard ballard ballard reader shortest refers saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades saccades arrows storing extensively relies relies exploiting omohundro grants grants cam consecutive sequentially linguistic approx parsing ter ahmad rao rao rao rao rao rao rao rao rao profiles profiles chicago possibilities chess chess assess illustration publication pami chapman elementary distant adelson depicts fixation fixation fixation multiscale multiscale multiscale iri iri speedup oculomotor oculomotor oculomotor supports rochester rochester rochester rochester rochester rochester rochester rochester rochester rochester rochester rochester rochester elsevier flight dramatic priority september november handled bridge stephen january resolve adaptively routines steven hancock inclusion purkinje appealing exclusively proposes periphery william experienced ready resultant nih motors fovea fovea fovea fovea fovea memorized memorized iterate inappropriate proceeding christof simon routine routine routine routine resemble spent tightly remarkably remarkably locating yamada inte pyramids accepts niebur convolving dana dana dana dana dana dana dana foveated foveated foveated lay thinking endpoint endpoint endpoint cortico machinery machinery distinctive foveal elicited elicited executes mary mary mary fell underlie acuity owing critically steerable relied forest rid octave pipeline sharper instructed sole targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting targeting ballistic ballistic edward fixations fixations fixations decomposes deci convolutions convolutions ade momentary crucially prespecified orient orient answered remembered burt garrison ineffective sri accessing popularity fork fork bench precedence gregory baddeley stark ernst leslie hori imately greg regan subutai skipping chase cvs cvs comprehension enjoyed maa embodiment phs exhausted foveate roland zontal advent prelim zeroth icpr rently inary 
#@Ballard_D,Hayhoe_M,Rao_R,Zelinsky_G,
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input input input input input input figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time networks system state results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units models based space weights weights weights weights weights weights vector vector vector order shown shown shown shown shown shown shown shown noise weight weight neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution method point single single single single single single single processing large local neuron rate test test test shows signal signal signal signal signal signal algorithms visual visual visual visual visual size work cells field field field process level level level memory response response similar similar similar similar similar similar architecture show equation average average average average term activity activity activity activity activity result result result result research research research research research defined found estimate left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented presented present present present present present phase phase activation activation activation activation motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion abstract applied references stochastic due due due important introduction hand behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference spatial signals signals cases cases multiple multiple equations simulations simulations simulations resulting simulation simulation simulation simulation simulation simulation human human human sum called called called elements means means feedback feedback feedback feedback global study study study study compared objects location location location active active active active active active active active active active active active experimental support proceedings report consists code code code kernel responses equivalent stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stimuli effects effects detection capacity vision vision vision vision con coding coding coding coding coding coding coding coding coding randomly randomly robot robot robot area area velocity velocity velocity velocity inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory discussion feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward denote denote close close corresponds corresponds corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory amount short assumed adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation journal journal journal ability ability simulated pairs reduced reduced ratio ratio ratio mechanism mechanism leads leads leads leads leads max max inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition decay light neuronal denotes denotes population population population population population population directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions recent movement movement movement movement movement moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving recently recently interest highly previously previously previously previously previously previously subjects subjects tuning correspond studies differential address williams williams williams williams grant lead lead studied studied suggests correctly width strength strength strength central interactions interactions interactions interactions interactions weak strong strong mechanisms presence turn assuming selective selective selective selective selective decrease decrease areas appears van van longer perception perception perception perception tuned tuned tuned tuned tuned tuned tuned tuned distinct distinct modeled modeled simultaneously averaging slightly slightly unique interaction interaction shift shift shift decreases national stages stages stages stages stages stages stages stages influence influence activities activities activities activities activities activities activities activities activities activities activities activities activities similarly similarly key remains sufficiently assigned degrees degrees recorded recorded fire kernels kernels kernels kernels kernels kernels kernels kernels kernels usa contour sciences illustrated activated activated activated activated activated black differ differ differ maximal maximal maximal detect detect situation receives receives receives excitation excitation excitation excitation excitation traditional strongly allowing neuroscience issue absence overlapping subsequent preferred preferred preferred acknowledgments receive receive receive receive receive receive receive explore selectivity selectivity carried detectors detectors applicable possibility phases act act act act act act adapt adapt adapt opposite opposite opposite opposite opposite opposite opposite opposite opposite opposite opposite psychology psychology equally precise baseline baseline baseline generates generates band convolution explanation adapted adapted independence caused perspective directional directional broad monkey products products mathematics consequence grossberg grossberg bandwidth explained explained integrating fourth apparent populations populations populations populations populations populations populations populations offset offset offset offset offset offset psychophysical psychophysical dots dots dots dots dots dots dots dots dots dots dots dots dots dots sharp occurrence pasadena enables germany coherent display display display decreased displays lot contribute primarily tation dynamically enhancement grey grey caltech stronger mail nearby affected weakly falls governed demonstration accounts viewing exposure exposure exposure recovery properly arrows arrows motions explains explains outline pointing transmitted failed perceived perceived perceived perceived perceived perceived perceived perceived adapting adapting transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent interact activate maximally maximally maximally macaque academy pop develops heading institut inhibit inhibited blake blake observers spacing broadly broadly broadly sen governing andersen andersen planck sheets counted percept percept percept percept percept percept registers registers unimodal unimodal unimodal unimodal unimodal illusory illusory illusory stepsize prolonged prolonged prolonged sends directionally excite broader fiir traditionally alexander dissimilar convolving adap differed british vectorial bimodal bimodal inhibits widespread perceive perceive raymond raymond rni rni rni rni unitary unitary unitary imbalance imbalance mediating interacts kybernetik unidirectional unidirectional unidirectional opposing excites excites excites registered registered runge barely quarterly tains treue treue ensured ction rection ensuing ulations ceases halfway kutta tivation sutherland sutherland parallels supplement sharpens reverberating sharpened sharpened enjoyed provision narrowly constancies hfsp lii 
#@Grunewald_A,
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#*network network network network network network network network network network model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data figure figure figure figure figure figure figure figure figure figure time output output output system system system system system system system system system system results results results results results results information information information information problem models space space case order shown shown values values values values values values values weight weight functions neurons pattern pattern pattern image image image processing control large local local local inputs form shows shows shows shows simple gaussian visual visual visual visual visual visual visual visual visual paper paper paper small feature feature work fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells step field field field features process process process process level current current current cell similar similar similar equation equation equation line general states states theory theory theory theory theory obtained obtained obtained note experiments experiments activity result result result result university computation research research research research research research independent dynamics dynamics dynamics initial initial initial constant constant computer terms terms terms science left presented presented presented map map map map map map map map map map map map map map map map map present activation activation object object press components abstract computational references due important introduction complex stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect effect effect variable spatial spatial spatial lower measure signals signals higher higher higher higher part part part previous bound bound cortex fact fact region region proposed proposed proposed length simulations simulations simulations simulations simulations simulations simulations resulting total total simulation sum called called regions regions regions regions regions dimension study study em cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross cross receptive provide provide define objects objects location perform active determined determined determined determined determined experimental experimental constraints gain discrete brain power larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields fields support words implementation implementation implementation code code code code code code responses responses final final scheme maps considered considered domain domain equivalent experiment top top stage stage stage stage stage stage stage stage stage stage stage stage stage stimuli effects effects effects detection detection full requires vision vision vision vision vision con produce weighted developed levels types nature inhibitory inhibitory depends sampling denote complete excitatory surface surface surface surface supported supported supported supported role eds adaptation journal hypothesis hypothesis hypothesis hypothesis hypothesis easily including including smaller reduced account account account account account functional ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio segmentation mechanism consistent uniform principle principle details direct inhibition inhibition inhibition inhibition inhibition bottom depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth depth early early early early idea light predict discussed recent movement reported lateral lateral lateral lateral lateral lateral side side side subjects correspond studies address address background background background background background background background background background background background background background background background positions separation symmetric organization sensitive increased intensity intensity correctly white white white white white white white white white white white white white white white boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary demonstrate strength strength strength greater conclusions central interactions measures measures measures measures measures measures suggest encoding propose propose strong strong mechanisms mechanisms mechanisms mechanisms reduction scene connectivity configuration configuration configuration force acknowledgements appears appears relation relation relation relation construct perception perception perception perception perception perception perception perception perception perception perception perception perception perception perception perception perception perception perception perception perception perception optical factors describes tuned implement develop quality quality formation review stages stages stages interpretation codes variation showed showed modulation activities activities activities activities activities constants allowed partial partial classical boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries remains initially filtering figures includes kernels activations activations color color color color color color color contour contour contour contour contour weighting retinal retinal retinal retinal retinal retinal retinal determines determines extension plotted specifically specifically variations domains black black black black black black black absolute partially partially partially straightforward middle middle middle society maximal modification driven detect detect comparing excitation lie lie follow gray gray gray gray gray gray gray gray gray gray gray gray gray gray gray cues cues involved paradigm providing disparity disparity receive oriented oriented extend experience relations matches relationships relationships authors office office gates pathway encode fundamental notion analogous surfaces surfaces surfaces surfaces matched patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch patch measurement measurement plausible necessarily configurations man predicts opposite psychology equally eyes noted extent explain percentage indicating ment cos ground orientations orientations phenomena phenomena phenomena adjacent adjacent adjacent explanation diffusion diffusion diffusion diffusion ganglion sys mation controls consequence scientific grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg localized patches patches patches patches patches patches patches patches patches patches addressed addressed reflect profile psychophysical psychophysical cohen cohen cohen completion psychological modulated modulated modulated modulated cal occurrence achieves boston boston display specifies specifies progress simultaneous simultaneous simultaneous simultaneous univ displays displays accomplished appearance appearance appearance forming formally oxford ratios ratios ratios ratios recover addresses tem naval theories outcome binocular binocular air consideration stronger proceeds odd determination determination determination resistance illumination illumination illumination illumination filled filled filled filled filled filled filled filled composition infor contexts respective respective respective conjunction arrangement arrangement dif recovery layout layout refers displacement onr fusion resonance land land neurophysiology unified usage largely minus minus employs junction junction junction perceived perceived perceived perceived reflected brightness brightness brightness brightness brightness brightness brightness brightness monocular monocular ary ary cns argue preserved gated maintained reflectance retinotopic afosr challenging surrounding spreading spreading multiscale discusses preserve preserve nal bill psychophysics psychophysics psychophysics psychophysics increments increments increments suggestions lighting neumann neumann insufficient junctions junctions builds diffuse stripes stripes stripes stripes stripes stripes accomplish 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yij neurally depths depths stripe disk disk specifications violation percepts zij isomorphic sponse jour iij leak predominantly modulates illusion illusion illusion illusion illusion annulus annulus mingolla mingolla mingolla mingolla lighter lighter lighter lighter lighter lighter jects instantiated gions sufficiency negation negation negation negation convolutions federal negated negated negated rio rio attenuated alters backgrounds backgrounds backgrounds leftmost leftmost trast fred shapley shapley whittle whittle whittle whittle arrange adjacency pergamon trough ception explanatory lowed featural dyi sharpened flashes convincingly everyday darkened diffused hnc tradition ployed 
#@Pessoa_L,Ross_W,
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#*network network learning learning learning learning learning learning learning model model model neural neural neural neural data data data data data data data data data data data function function function function function function function function function function function function figure figure figure figure set networks algorithm number number number results information information information information information information information information information information information information information problem problem problem models models based based space space space space vector vector vector vector vector vector vector order order order values values values parameters parameters parameters parameters parameters noise noise functions functions functions unit distribution distribution recognition recognition approach approach approach pattern pattern point image image image image single single processing processing processing processing processing processing processing processing neuron neuron rate rate patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis class optimal optimal form form form form form shows shows signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual paper small size size work step points points points points points points field field field field field field field classification process process current problems problems problems problems problems problems problems problems problems random random random random random random random random random random random random random high show show equation section line rule rule rule rule rule rule rule rule images images images images images images general parameter parameter parameter real real real real average theory theory theory obtained obtained term dimensional dimensional result result variables research log estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate computer computer computer computer computer distance connections left left left direction presented low low low low frequency object maximum maximum maximum maximum maximum press components components components components components sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied find find find find find computational density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood references component component component component component component stochastic stochastic ieee ieee ieee procedure procedure procedure procedure procedure important mixture context introduction complex estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior statistical statistical variance variance variance variance variance variance variance variance cost cost cost search search difference difference difference complexity variable variable variable variable variable variable variable variable variable spatial assume assume assume assume lower lower signals signals signals signals signals prior center type type cortex cortex cortex good binary conditions conditions fact fact techniques techniques proposed proposed correct finite finite simulations minimum minimum minimum resulting resulting resulting classes classes classes ing ing computed computed computed respect multi multi sum called times optimization orientation applications applications original original specific samples samples samples samples true true application cross receptive provide define compute compute related gain gain cortical mit mit contrast contrast fields update support morgan proceedings proceedings institute institute institute words implementation technique technique technique technique technique kernel advances advances joint difficult difficult difficult bias bias bias bias bias bias addition addition ai cambridge cambridge cambridge equivalent directly directly hinton hinton hinton estimates san top conference determine efficient efficient classifiers requires choice significant significant world world world world vision vision vision estimated pages pages pages pages validation produce derived clustering area entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy actual provided finally finally selected selected nature nature nature nature sampling constraint biological discussion discussion covariance covariance covariance covariance limited assumption assumption assumption assumption finding amount common common assumed shape role role journal journal square end pixel pixel pixel pixel pixel cluster cluster cluster easily easily degree makes makes makes development development development including kaufmann objective typically typically pairs pairs smaller functional unknown coefficients technology technology significantly projection projection projection projection projection projection projection projection projection york increasing increasing head head segmentation trials uniform empirical empirical empirical empirical empirical empirical empirical principle principal principal principal principal principal principal principal principal squared squared squared call call max max max max max window window window window window international bottom polynomial polynomial minimize minimize run description discussed robust robust takes element practical identical pixels quadratic quadratic sense sense subset subset sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently sufficient unsupervised unsupervised unsupervised calculated volume volume volume axis axis axis axis axis axis axis axis axis solve smooth match correspond pca pca pca pca pca pca pca pca pca studies differential diagonal address evaluation separation separation separation organization sensitive constructed constructed horizontal horizontal parts parts intensity concept wide derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative matrices matrices touretzky clusters white white generally half conclusion critical assumptions assumptions assumptions reduce editors editors accurate peak practice practice practice mateo strong largest reduction drawn drawn demonstrated proportional variety minimizing minimizing min min min min iii iii iii iii scene acknowledgements derive derive derive derive derive derive construct estimating estimating estimating laboratory laboratory stability vertical vertical vertical mathematical distinct changing recall simultaneously physical text interaction mutual mutual mutual adding expectation expectation letters expressed estimator densities densities densities densities densities densities evaluated evaluated evaluated organizing soft approximated converges discrimination calculation advantages existing perceptual thesis formulation bell bell bell weighting weighting blind automatic maximize variations successfully simplicity simplicity efficiency importance society computationally effectively effectively detect projections projections road conf procedures video interpreted neuroscience follow follow simplified play dot absence minimizes minimizes giles correspondence highest highest maximization maximization maximization maximization maximization maximization maximization tesauro decreasing cowan body body body selectivity parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric powerful wiley hanson integral integral issues matches applicable plasticity working maximizing maximizing comparable analogous surfaces act equally adjusted adjusted adjusted adjusted assumes assumes explain phd finds finds finds finds seconds massachusetts histogram histogram histogram great slowly derivation derivation smoothness biology correction correction correction correction correction correction reasons inside purposes closer widely precisely constructing constructing arise mation probable involve begin medical medical medical medical arises linsker linsker linsker author addressed alignment alignment summation requiring varies evaluating evaluating double understood flexible offset axes axes axes leave incorrect outliers outliers howard maximizes maximizes proven proven logp logp displays cor corrupted corrupted leen cooper cooper cooper cooper arguments acts impossible flexibility theories grey grey robotics binocular oja oja oja oja oja imaging simplify simplify multiplicative nearby neurobiology operates salk salk north infor published slice becker becker becker ranging paul overview demonstration accounts scan scan scan scan scan scan scan scan scan scan originally indicator jolla matter matter matter specificity informative projects speeds hart hart interestingly vari limitation resonance resonance resonance emission ple pointing maximized munro munro forced magnetic magnetic magnetic magnetic kurtosis kurtosis corrected corrected corrected corrected intrator intrator decomposed stands clustered clustered clustered var var var var manipulation manipulation manipulation manipulation manipulation manipulation manipulation manipulation manipulation manipulation exam intuition duda duda diag parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen playing searches hughes terrence argued scope records conversely anal distinguished register denver denver intl thousands tissue tissue tissue tissue tissue ignoring differing mini modal fat bienenstock bienenstock water savings hundreds viola viola viola viola viola viola viola viola viola viola viola lated interpreting kth bcm bcm bcm bcm bcm bcm integrates seattle sen manipulated modalities orr ory maxi contrary reality cho restrictive ance cauchy prominent discovers discovers violated subtle sur maximisation imum schraudolph schraudolph schraudolph schraudolph schraudolph schraudolph tightly elegant mization mization attracted align tighter scans optimizes stereograms registration manipulating ponent analyzer bimodal bimodal eval motivate quadratically imal party torrey pines prin wells wells wells wells wells wells akin akin oblique surgery bone cocktail mri mri mri mri mri mri mri mri mri mri mri mri wash assisted tropy corruption corruption grimson tackle unavoidable tissues differenttable ola formu shorthand uncorrected uncorrupted uncorrupted homogeneity brighter uated perturbs eld confounded inflexible cipal manipulates 
#@Schraudolph_N,Sejnowski_T,Viola_P,
#t9
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set set set set set set set set set set networks networks algorithm algorithm algorithm algorithm algorithm number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error state state state state state state state state state state state state state state state state state state state state state state state results results information information information information problem problem problem problem problem problem problem models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based based based based based based based based based based based based based based based based based based based based based based based based based space case vector vector order shown shown shown systems systems systems systems values values values values values values values values probability parameters weight unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method approach approach approach approach pattern point point point image image image single single single single single single single processing processing processing control control control control large rate rate patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis optimal optimal optimal shows signal simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual paper feature feature feature work task task task task task task task task task methods methods methods methods methods step step step step step field field field field field field field features features features features classification classification process process process level level current current current trained structure problems high high high high memory memory memory similar representation representation representation representation fixed fixed rule images images images images images images images general general real real real real real real real real approximation average states states states theory obtained obtained obtained obtained note experiments variables variables variables solution defined defined defined defined defined found sequence sequence sequence sequence target target target target target target target target target target table table computer left left left left left left direction presented presented map present present present low temporal temporal temporal machine machine object object object object object sets motion press press press press learn learn learn learn position position basis continuous abstract applied applied applied back find find find find computational computational convergence convergence likelihood references stochastic ieee ieee positive positive important important decision decision decision decision introduction action action action action action action action action action action action action action action action action action action action action action action action action action complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand behavior generated tion variable variable variable variable spatial assume assume assume assume signals prior representations learned learned learned learned chosen chosen part part part part type required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple represent represent represent distributed distributed distributed markov markov markov markov markov techniques correlation correlation correlation correlation correlation observed observed scale ing ing ing ing ing tasks tasks human computed computed computed performed performed performed performed performed performed performed reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made natural policy policy policy knowledge obtain negative original artificial artificial relative represented true provide provide provide provide define define define compute compute compute compute compute objects proc proc proc proc location location location location location perform perform perform active active active active active active active active active active active active active active active active active active active goal goal motor motor equal mit mit mit mit mit accuracy update update dependent selection selection selection selection selection selection morgan morgan morgan consists consists internal internal individual individual advances advances advances advances addition addition addition graph graph sequences ai considered considered cambridge computing equivalent environment environment environment environment environment environment directly view view view view view view view view view view view view view view view view view view view view view view detection determine determine determine full full full requires world world world vision vision vision vision vision vision vision vision vision pages produce developed provided provided provided finally processes processes selected simply simply describe group denote limited complete actions actions actions actions actions actions finding rbf nearest nearest nearest nearest effective implemented implemented implemented implemented implemented assumed require face face face face face face face face face instance instance instance instance instance easily makes kaufmann kaufmann pairs unknown jordan head head head head head head head head head head head segmentation mechanism mechanism special special trials trials matching operation operation language language language representing details details max pre direct stored bits normalized normalized magnitude attention attention attention attention attention attention attention attention attention attention attention combined produced added added description predict resolution resolution resolution advantage pair separate separate separate element similarity strategy include include period recently relevant interest sufficient sufficient sufficient highly previously previously observations observations observations module module solve match match match match converge address definition chain locations observation observation observation observation observation observation arm arm exists parts parts parts parts intensity expression expression expression expression expression expression expression extended extended extended wide wide wide wide wide move deterministic setting pass runs place place valued depend depend reward reward reward reward reward reward reward reward reward reward reward reward differences sutton performs practice practice learns propose taking largest external labeled radial assuming user user user user user user user user user user user user user user user user user user user user user user user user user user user user user exist plane plane iii targets targets targets targets targets scene identification configuration base index index perception perception generating confidence implement explicitly infinite angle angle consisting interaction interaction applying agent agent agent agent boolean boolean communication communication solved variation detailed evaluated operations static similarly earlier reasonable reasonable performing performing performing tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking interpolation interpolation interpolation faces faces faces faces existing exploration exploration exploration perceptual perceptual perceptual priori priori formulation color recognize plotted plotted automatic discuss maximize coupled coupled domains domains domains absolute partially partially partially partially partially neighbors neighbors neighbors successfully sensor sensor selecting driven poggio successful identify build essentially identity traditional soc video video video video video follow criteria criteria strategies comp comp list list simplified dayan paradigm paradigm wavelet observable observable observable observable observable highest attempt camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera camera body body body body body body body body body body body body body body employed unlike command schedule access access access singh environments humans graphical history history history history history history history combine office office workshop workshop scores coarse integer configurations analyze facial facial facial facial facial facial facial facial front explored expressions expressions expressions expressions expressions expressions expressions utility band developing directed costs ground ground ground track track track track track track track track track navigation briefly considerable considerable drive lin tive formalism shared ran ran controls watkins projected recognized geometry exemplars virtual virtual virtual people people behaviors considerably evaluating evaluating share rewards commands templates execution synthesis display implements jaakkola summed yielding pose pose pose pose person person person person person person person lab lab lab room room room room contextual formally narrow narrow narrow narrow narrow girosi resources perfectly inspired imaging primitive intelligent los pomdp pomdp pomdp abilities interpret illumination salient salient guide optimally optimally selects meaningful combines sion respective decide overview centroid discounted gaze tracker tracker gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture horizon motions eqs avoiding adopted executed discriminate discriminate informa maintaining street numerous users users annals pointing accept accept accept accept accept accept accept pentland pentland pentland pentland pentland pentland pentland pentland pentland poses spatio spatio arg arg workstation acting interact wall wall graphics execute life life expand maximally guided interactive interactive interactive interactive interactive unconstrained unconstrained selectively anal anal maintains intl modality aaai aaai walk walk littman utilizing gestures gestures gestures gestures gestures gestures gestures gestures drives survey algorithmic sees savings agents agents agents agents pan mirror routines routines routines routines routines routines routines routines routines alex usefulness executing tuple tuple ples screen degenerate tracks interpolate kaelbling neutral neutral neutral rel subscript distractors media media media surprise maxq maxq magic unexpected replaces ysis ysis distractor distractor distractor distractor operated mir superscript hands hands hands hands hands hands conceptually offered mediate animation darrell darrell darrell darrell darrell darrell darrell darrell darrell switzerland tilt foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated foveated ames neurally ponent organisms parentheses standing sondik rendered imagery imagery augment rendering driver cameras cameras oracle comput trevor trevor mccallum mccallum foveation foveation foveation foveation foveation foveation kauffman votes farther edward autonomously rooms cassandra deterministically alamitos envi rewriting walks undefined situated dition tuples unreasonable acquires remedy react loci calibrated obtainable expres aea aea aea ifs zurich sumptions ronment pressed athe creatures creatures perspec iil andj sitting signifies dicted evant inforcement surprised metaphor grab mains foveate foveate servation overlooked maes enumerate predators andi 
#@Darrell_T,Pentland_A,
#t9
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#*network network network network learning model neural neural input input data figure figure figure time time time time time time set set set set set set set set set set set set set networks training training training training training training training output output output number number system system system system error results results results results information problem problem performance performance performance performance performance performance performance performance performance based based based based based based based based based based based space space space space space vector vector order order order order shown shown shown shown shown shown shown values values values parameters noise functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach pattern image image image image image image image image image image single single processing processing processing processing large large large large large large local rate test test test test test test test test test test test test test test test test patterns form simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small small small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work fig fig fig field field field field features features features features features features features features classification classification classification level cell structure structure structure random random random high high high memory memory response response similar similar similar similar similar similar similar similar representation representation representation representation representation representation architecture architecture line images images images images images images images images images images general generalization generalization generalization generalization generalization real obtained obtained obtained dimensional dimensional dimensional university solution research independent log sequence sequence sequence constant estimate computer computer terms distance distance distance distance science left left left presented presented present present low low frequency object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object range range press press press position position position nonlinear outputs outputs outputs abstract applied properties references ieee ieee ieee positive introduction action complex complex complex complex behavior statistical statistical dynamic variance energy energy energy complexity spatial spatial classifier prior chosen chosen chosen higher part part cases cases cases required required multiple multiple multiple cortex cortex conditions represent tree distributed distributed fact correct correct errors scale scale scale scale scale scale classes total total human computed computed called means means dimension natural natural natural natural natural orientation orientation orientation orientation orientation orientation orientation global global global global global global applications filter filter filter artificial relative represented series series series series series receptive provide define objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc perform goal goal related related related related related related related related related related brain approaches mit mit support words department consists consists internal internal internal code individual individual responses difficult cambridge curve view view view view view view view view view view view view view view view view view view view view view curves design design significant statistics statistics statistics world world vision vision vision vision basic channel channel channel channel channel channel channel channel channel coding derived levels levels levels types achieved discussion normal feedforward feedforward feedforward fast assumption assumption stable surface surface nearest nearest nearest nearest nearest nearest common common common shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape main main main face cluster cluster easily degree rumelhart rumelhart rumelhart development development including including typically underlying block character increasing head segmentation mechanism trials matching matching database database database database database database pre bottom bottom depth depth depth depth discussed advantage robust separate similarity similarity similarity similarity similarity reported period subset subset engineering dimensions dimensions dimensions dimensions highly highly varying approximately smooth smooth smooth match match trans trans sparse sparse sparse definition background chain chain observation channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels storage sensitive sensitive sensitive sensitive sensitive sensitive entire entire parts intensity intensity intensity studied invariant invariant trial trial wide wide wide rotation rotation rotation correctly correctly correctly locally locally locally half minimal row row neighbor neighbor neighbor neighbor differences measures retina numerical practice mechanisms presence drawn california exist plane plane plane plane plane groups groups groups identification configuration base acknowledgements explicit longer optical segments modeled modeled metric implement multilayer category explicitly involves remaining angle angle angle angle scales scales consisting consisting quality potentials yield independently viewed detailed transform transform open open operations operations operations forms forms understanding allowed partial partial normalization combining intervals roughly roughly closed filtering filtering construction foundation advantages classified classified koch views views views views views views views views views views views views views views degrees degrees handwritten box figures includes includes combinations color color color color color color color color color color color color contour contour contour instances specifically neighbors discussions texture texture texture simplicity straightforward identified closely encoded included mcclelland mcclelland mcclelland identify identify computations projections invariance invariance identity identity identity conf kind strongly induced cun cun cun video video video sin cue categories categories categories categories categories cues cues vary vary providing board wave denker binding binding binding consisted consisted subsequent decreasing oriented oriented explore remain carried exhibit experience relations involving humans replaced replaced rise matches giving links project int int scaled office reliable structured working complicated proved notion contours contours contours matched coarse man extremely aspect noted freedom freedom shapes ith contributions arbitrarily arbitrarily explain seconds isolated massachusetts residual histogram rows rows scenes scenes scenes scenes scenes scenes cos orientations orientations caused lies lies spatially rapid perspective straight sys closer monkey recognized recognized angles angles res patches depicted cybernetics recognizing qualitative radius exemplars apparent apparent limits empirically led dark parameterized parameterized parameterized parameterized share howard ture fall fall ordered phonemes prevent segmented baird leaf multidimensional distortion phenomenon indices proportion extensive gabor gabor gabor gabor gabor summing ratios animals circular neurophysiol neurophysiol naval rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid rigid caltech inspired saturation chance chance minutes primate city familiar los interpret viewpoint viewpoint viewpoint canonical corner contexts bartlett heavy edelman edelman ambiguity surprising mental enhance histograms mel mel mel mel mel sphere jackel viewing viewing emergence emergence occlusion reveals ballard ballard ballard informative observer broken cam integers insensitive insensitive slight logarithm logarithm workspace visually achieving focal emerge responds poses poses perturbed par par boser quasi quasi medium profiles mismatch henderson rectangular rectangular preserved preserved formance pami hubbard simplifying relating emphasize individually books kanerva kanerva kanerva macaque guided relates distal records tied zip nonetheless distinguished funded accounted book book book fea permit round round elemental elemental elemental shallow shallow shallow emphasis bridge corners corners crude mcdonnell hat telephone telephone telephone telephone lated tanaka tanaka tanaka tanaka loosely cylinder cord cord cord cord striking judged chan intact quantitatively smc spirit colors colors scott ance locality ranged faced deformation bear segmenting convey devoted undergo christof indexing indexing indexing rec discriminating saito initiated clutter sparc pew remarkably remarkably continuing bright deformations deformations biomedical ito fukushima fukushima fukushima angeles subsampling excluding distinctions bind blob blob neurally articulated bag embodied blobs blobs blobs elongated elongated southern octave recognizable unrelated ations ations havior conjunctions warped presumed indoor hue jects jects dan chitecture rooms contradiction viii invalid oblique pursuing matan loth photographs photographs photographs photographs nels miyake mol inferotemporal inferotemporal helping outdoor situ interests allel allel grossly taining imbedded pendence swain swain swain digitizing chair usc patt shelf tensity leap sony methodological compressive bulk 
#@Mel_B,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number number number number number number number number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error state results results results results results results results units units units units units problem hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based based based based based based space space weights layer layer layer case order order shown shown shown shown shown shown systems systems values values noise noise unit unit recognition recognition recognition recognition recognition recognition method method method method pattern pattern pattern point image image image image image image image image image image image image image image image image image image image image image image single single single single single single single control large large large large large rate rate rate rate rate rate rate rate rate rate test test test test test test test test test test test test test test test test test test test analysis analysis analysis analysis analysis class inputs shows shows shows shows shows algorithms algorithms simple visual visual visual visual visual visual paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small size size size size size size work work task task task methods methods methods step step step step points points points features trained trained trained trained problems random random random random random random response similar similar similar similar similar architecture show show section section section section section section images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general speech speech real obtained obtained note note note note experiments dimensional university university threshold threshold computation research research research research initial initial table table table table table table standard computer terms distance distance distance distance distance distance connections connections connections science science left presented presented presented presented presented present present present present present activation low temporal object sets sets sets sets sets motion range position position position position position position position components outputs outputs outputs sample sample abstract applied applied applied applied applied applied applied find references component due due positive positive positive positive positive positive positive important decision introduction hand behavior effect generated assume measure measure signals chosen higher higher part cases type type multiple multiple multiple multiple multiple multiple multiple multiple conditions distributed make techniques techniques region region correct errors errors errors errors forward scale scale scale scale scale scale classes classes tasks total human human human human human human multi sum sum performed performed made made made orientation applications filter filter filter filter filter filter filter filter filter filter filter negative negative negative negative negative original artificial specific represented receptive receptive rates rates rates rates rates rates rates location location location location location location eye connected mit mit mit steps steps accuracy accuracy accuracy accuracy comparison comparison comparison larger fields fields train train selection department version consists consists consists consists consists code individual represents difficult difficult difficult final delay sequences computing hinton view design stage stage stage detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection determine upper significant world world basic pages give produce produce randomly clustering clustering developed types actual actual provided provided describe describe tested tested close close amount supported supported require main face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face square pixel pixel pixel pixel pixel cluster future future smaller needed needed combination reduced account testing testing significantly ratio character projection head database empirical principal squared squared representing representing numbers filters filters window window window window window window window window window supervised frame frame attention attention combined produced produced run run description perceptron architectures improved improve improve directions separate typical reported apply apply strategy varying approximately approximately axis tions correspond pca achieve positions positions positions locations locations locations entire entire grant grant exists horizontal parts intensity scaling occur wide wide correctly correctly clusters clusters clusters pass half reduce reduce conclusions conclusions conclusions differences measures measures accurate constrained strong presence drawn turn variety plane manner manner manner scene acknowledgements metric metric sensitivity sensitivity easy slightly slightly angle scales scales scales scales adding adding applying select decreases national extracted extracted focus focus expressed depending phoneme overlap overlap detailed evaluate showed sizes partial earlier normalization reduces combining neighborhood add false false false false false false false false false false false false false false false false false false false false false tracking distances filtering foundation euclidean classified faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces views views views avoid recorded handwritten box figures usa retinal subspace recognize determines determines illustrated illustrated partially partially major selecting identified divided poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio presentation detect detect detect detect detect detect detect detect detect detect detect detect schemes invariance invariance invariance plots receives quickly contained cun cun cun heuristic interpreted classify strategies gray michael absence providing denker thresholds predictor overlapping overlapping overlapping policies camera simpler unlike create difficulty biases fewer school ideal combine combine scaled scaled authors authors office referred working eigenvectors removed examined examined waibel waibel waibel necessarily analyze extremely created eyes eyes eyes eyes prototype portion detector perceptton art generates detected detected detected detected submitted histogram histogram histogram scenes scenes scenes scenes scenes orientations orientations correction correction worse comparisons spatially preprocessing preprocessing preprocessing preprocessing precisely located located commonly mellon mellon carnegie carnegie collected collected collected collected collected collected collected collected cmu cmu cmu cmu cmu cmu cmu cmu bootstrap bootstrap amounts compares span http passes howard rely pittsburgh serve gave sophisticated comments windows windows windows windows coherence wang merging merging merging merging merging pyramid pyramid pyramid pyramid representative representative representative notes www databases labelled labelled eliminate eliminate printed rotations lost eliminated fails smith adds siemens replacing check grow nearby selects heuristics heuristics heuristics heuristics heuristics heuristics elimination lip started document ranging ranging ensures decide lang jackel scan yang centroid centroid occlusion repeatedly merge merge merge merge merge merge merge merge merge merge ccd boxes boxes mind metrics listed fellowship ties randomized encouraging restrictions boser acceptable acceptable reports descriptions descriptions conservative henderson translated baluja baluja baluja baluja baluja baluja baluja baluja baluja geoffrey graduate pomerleau pomerleau pomerleau disadvantage mouth mouth challenging eliminating frontal intensities intensities intensities harder selectively translations zip portions portions portions memo rotating indication november rarely lighting lighting lighting scanned scanned scanned scanned characterizing corporate identifies heavily hat pictures pictures december alex incorrectly eliminates harvard harvard replicated detects detects detects detects manually manually normalize positives positives positives digitized html implied occluded occluded occluded gathered wong counted dean huge bootstrapping bootstrapping detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections detections progresses progresses sung sung sung sung sung sung sung sung sung sung sung sung sung sung sung sung sung preprocessed preprocessed collecting collecting permutations shikano miss miss examines equalization equalization equalization subsampling pyramids web web decides collect collect translating chi army army ages missed missed missed rowley rowley rowley rowley rowley rowley rowley rowley prototypical expands hanazawa nose kanade kanade kanade kanade kanade fingers kay kay arbitration arbitration arbitration arbitration arbitration arbitration arbitration arbitration arbitration arbitration official detec discriminated discriminated readings tomaso tomaso kevin photographs photographs photographs overlapped collapsed shumeet shumeet shumeet shumeet agencies collapsing henry henry illus drafts reliance subimages subimages subimages subimages television mirrored newspaper signifying subregion daah backpropogation hub har takeo takeo tput cbcl 
#@Baluja_S,Kanade_T,Rowley_H,
#t9
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#*network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output number number number number number number number system error error error error error error error error error error error error error error error error error error error error error results results results results units units units units information information problem problem problem problem hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based space space weights weights linear vector order values values values values values probability probability noise noise noise functions distribution method method method approach approach single large rate test test test test test test class class class class optimal optimal shows algorithms algorithms simple simple gaussian gaussian examples small small small small small small size size size size size size size size net net net task task task task task task task task task task methods methods methods methods methods methods methods fig fig fig classification classification classification classification classification classification classification current trained trained cell problems random high similar similar similar architecture architecture show show equation line rule rule general general general generalization generalization real real average obtained obtained experiments result university university university university university variables variables variables variables variables variables variables variables variables computation research initial table table table standard science science prediction presented low low low low machine machine machine machine sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets continuous sample sample sample abstract find references due due due due due due due positive positive positive procedure procedure procedure procedure procedure procedure important important decision introduction hand hand hand estimation estimation estimation effect effect effect effect variance variance variance variance variance parallel difference classifier lower lower lower lower lower lower measure chosen higher part part type good good good good binary binary expected expected expected make make techniques techniques techniques techniques techniques proposed proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation errors errors errors errors errors errors errors forward simulations minimum minimum classes classes tasks tasks tasks total total regression regression regression regression regression regression regression respect called times times means optimization potential made study study negative negative negative original original original original original original original original original original original original original artificial artificial relative samples represented compared compared cross cross cross cross rates perform determined goal gain approaches larger train train train train train train train nets nets proceedings institute institute department department department consists consists individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual difficult bias bias considered framework framework experiment experiment experiment experiment environment curve san top top top detection detection detection detection detection classifiers upper requires significant significant significant significant statistics statistics statistics free world world world basic validation validation validation validation validation validation randomly types depends depends depends depends sampling sampling measured increases increases denote denote tested limited assumption complete complete finding shape generate generate generate generate supported degree degree smaller smaller smaller smaller smaller smaller combination reduced interesting significantly significantly special making making stored bottom bottom bottom bottom early early early early idea idea idea idea produced improved improved population population population population population improve improve improve improve correlations correlations advantage pair ensemble reported introduced include include trees subset compare calculated calculated studies achieve trans background evaluation evaluation separation grid improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement entire entire grant constructed constructed studied occur boundary half half reduce reduce central central presence presence physics reduction reduction reduction reduction characteristics drawn proportional decrease relationship relation construct construct construct produces produces factors estimating distinct dept dept missing missing missing missing missing averaging averaging averaging averaging remaining national independently correlated correlated overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap evaluate fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction calculation calculation measurements roughly david existing thesis thesis combinations determines middle middle divided committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee detect build build situation tend tend summary notice repeated procedures contained stopping stopping stopping stopping split issue sin sin sin criteria criteria absence providing predictor predictor decreasing carried diego access put hall reducing giving giving giving rest rest project investigated investigated possibility combine removed removed removed removed removed necessarily analyze equally perfect perfect initialized consist baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline baseline improving improving improving improving improving improving extent phd phd synthetic established asymptotically brown developing caused worse worse berkeley berkeley constructing acknowledgement members members percent items items items items items items items items items items items items bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap conducted conducted leave effort item item item item share rep howard pittsburgh pittsburgh pittsburgh pittsburgh pittsburgh pittsburgh pittsburgh collective geman geman marginal logical patients patients june diagnosis diagnosis diagnosis diagnosis cor trade trade consistently consistently primarily databases databases partitions murphy murphy imaging chance breiman breiman breiman ranges removing intuitively degradation performances performances performances performances performances mance predictors predictors predictors predictors patient paul perfor originally treatment cancer cancer cancer cancer cancer cancer clean clean bagging bagging wolpert wolpert generalizing fold adopted divide ics uci uci dramatically maintaining blood slight slight misclassification misclassification achieving achieving exhaustive munro munro munro munro munro munro tibshirani tibshirani recurrence remainder mutually pub ftp exclusive chapman rectangle mimic places resembles clinical replacement replacement differently bienenstock twenty breast breast breast ave drawing appealing resampling resampling resampling resampling resampling resampling thickness coincide coincide coincide beneficial beneficial ultimate repository contrary compensated wisconsin 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural input input input input input data data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output number number number number number system system system system system system system system system system system system system system system system system system error error results results results results units information information information information information information information information hidden hidden hidden hidden hidden hidden hidden hidden hidden space weights weights weights layer layer layer layer layer layer layer layer vector vector vector vector vector order order shown shown shown shown shown shown shown shown systems systems values values probability probability probability parameters parameters noise weight weight neurons neurons neurons neurons neurons neurons neurons unit distribution recognition recognition recognition recognition method method point processing control control control control control control large large large local local local local neuron neuron neuron neuron rate rate rate rate rate rate rate rate test test patterns class class class class optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form signal visual visual paper paper paper paper paper small small small size size size net net task methods step step features process process process process level level level current trained trained trained trained trained trained trained trained trained trained trained trained trained structure random high similar generalization real average average average theory theory experiments experiments result result university solution research research found found found initial initial initial constant constant constant constant constant constant constant constant constant computer synaptic synaptic synaptic left left direction direction nodes object object object object object object object object object object object maximum maximum press press press learn position components nonlinear nonlinear nonlinear outputs outputs abstract applied back back back back back back find find references stochastic stochastic due due ieee adaptive propagation propagation introduction action action action action action action action action action action action action action action action action complex hand hand hand hand hand hand hand hand hand behavior parallel tion change difference complexity variable classifier signals signals learned chosen chosen higher cases multiple multiple multiple good long long long proposed errors scale minimum minimum ing human sum sum reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement potential made feedback feedback feedback vol artificial artificial desired desired desired desired desired objects objects objects objects objects objects objects objects rates perform determined experimental gain motor motor motor motor discrete equal mit mit mit steps train train dependent institute implementation internal connectionist connectionist connectionist layers layers layers layers considered cambridge cambridge cambridge cambridge cambridge experiment experiment experiment environment environment environment additional design top stage stage stage stage bit bit bit detection detection detection detection detection conference conference requires requires significant significant world speed speed con con developed robot robot levels levels controller controller lines finally backpropagation iteration feedforward feedforward tested tested limited close close close surface surface actions actions actions actions finding amount short short implemented implemented synapse square end end end makes makes makes development development noisy sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory needed reduced unknown fully fully block testing testing consistent trials operation operation operation squared numbers numbers numbers iterations direct international idea added light advantage separate takes takes takes takes strategy strategy strategy period period cognitive previously works works converge converge converge achieve achieve positions positions williams williams williams williams increased constructed constructed constructed constructed constructed horizontal occur suggests digital digital digital digital correctly feed locally move loop loop loop loop occurs hardware conclusion competitive competitive competitive competitive competitive central modules clear sutton sutton sutton sutton faster faster faster practice taking taking physics external solid intelligence start exist decrease minima minima force force force force ways ways laboratory laboratory changing changing category category physical physical integrated integrated integrated integrated adding blocks extracted expressed expressed depending depending open open operations controlled controlled converges converges converges constants processor diagram calculation calculation barto epochs epochs roughly purpose initially classified classified classified classified classified classified recorded recorded building existing existing includes thesis thesis recognize plotted coupled sensor sensor middle middle society driven detect detect miller miller miller orthogonal quickly graphs kind procedures strongly contained strategies hold duration categories categories categories simplified play generalize delayed moves oriented situations minimized body simpler unlike stimulation american varied existence existence reducing respond ideas project possibility muscle muscle cover neu plausible adapt adapt reading reading reading reading reading man perfect eyes assumes assumes observe nerve nerve nerve nerve detected detected detected simplest seconds seconds seconds seconds seconds massachusetts rows slowly ground sensors sensors sensors sensors sensors sensors analyzed correction lin lin straight implementing implementing sections precisely afferent watkins watkins cut separately beginning cybernetics meaning mellon varies carnegie tional conducted conducted capability fed simulate rewards pittsburgh adjust richard richard chose boston consistently college controlling controlling jth connecting imposed primitive primitive primitive primitive primitive primitive primitive intelligent vehicle ral intuitively optimally optimally optimally exceeds child hertz selects continue falls loo paul propagated propagated thomas contact contact fold convergent default robert assigns andrew dramatically pressure converted converted session diverse diverse propagating propagating retraining chicago letting spinal clustered adjustment manipulation manipulation manipulation manipulation manipulation manipulation manipulation manipulation perpendicular perpendicular robots werbos investigating setup funded finger finger finger finger finger finger finger finger finger finger nasa memo stuck port exploratory exploratory completed stops handling cable satisfactory send converging reversible king tors tors connects affecting sensorimotor inherently unreliable joints arpa fastest sending connectionism connectionism connectionism connectionism connectionism connectionism quick motors motors motors merit ears rotational rec damping damping damping damping wiener wiener wiener wiener bodies newly shear shear shear shear shear shear shear shear shear shear shear minute touch slip slip slip slip slip slip slip slip slip pay thumb scratch palm palm palm ronald ronald asso conserving explores brains constantly brooks brooks brooks communicating fell categorize categorize plex grasping grasping grasping grasping grasping grasping grasping grasping grasping grasping grasping embodied fingers fingers fingers fingers fingers fingers fingers stein stein stein selector selector selector categorized grasped grasped adaptable reinforced reinforced reinforced reinforced multiplexed ditional microprocessor rodney infant infants infants hardness hardness hardness hardness hardness hardness hardness hardness hardness hardness hardness hardness dur actuators readings readings readings readings actuator opposing detectable structed stably gan efferent efferent efferent ied pres conven ciative unpredictable monographs matsuoka matsuoka matsuoka matsuoka cknowle dgement retrain imbedded motorola motorola signifies preprocess firmly submodules telligence slipping 
#@Matsuoka_Y,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural input input data function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time set set set set set set training training training training training training training training training training training training training training training training training training training training algorithm number number number system system system system state results results results results results results results results results results results results results results results results results results results results units information information information problem models models models performance performance performance based based based based based based based based based based based based based based based space linear case case order order shown shown shown systems systems systems systems systems systems values values values values values values values values values values values values probability probability probability probability noise noise functions functions functions functions functions functions functions functions method method method method method approach approach point point single single processing processing processing processing control control control control control large large large rate rate rate rate rate rate rate test optimal optimal optimal optimal shows algorithms algorithms simple paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples small small size size size size size size size size work work work work work work work task task methods methods points field features current current trained trained trained trained trained problems random random random random high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar representation show show section section fixed fixed fixed rule generalization generalization generalization generalization real real real real real real approximation theory term experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments result result university university university university university university research research research research research defined defined found found target initial initial initial initial initial initial initial initial initial initial constant constant constant constant constant estimate computer computer computer computer terms terms distance distance science science science present low machine machine machine motion motion motion motion range range range range range range learn learn learn learn learn learn position position position position position position position position position position position position position position position basis continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract computational density likelihood references due ieee positive positive positive positive positive positive positive positive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision context introduction action action action action action action action action action action action action action hand behavior behavior behavior behavior effect effect dynamic dynamic dynamic cost tion tion assume lower lower representations learned learned learned chosen center previous previous bound bound bound bound required multiple multiple multiple good binary conditions make fact techniques techniques probabilities forward scale resulting ing ing tasks tasks tasks total total total total regression regression regression performed made study study knowledge artificial specific specific specific specific represented represented represented compared location perform experimental experimental goal goal goal goal goal goal goal goal goal goal goal goal goal related related discrete discrete comparison train selection morgan morgan morgan morgan proceedings proceedings report report department department department department technique technique technique technique technique individual individual kernel kernel kernel advances advances advances represents represents represents represents represents responses bias graph ai considered domain domain equivalent environment environment environment directly directly view view san conference conference conference conference conference capacity full full statistics world world world speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed vision pages pages pages pages pages pages pages pages con randomly randomly randomly randomly randomly developed area selected measured discussion technical technical tested fast actions actions finding amount short short nearest nearest nearest nearest nearest nearest nearest effective effective effective supported theoretical theoretical require ability instance future degree development development kaufmann testing testing testing york trials trials trials trials trials trials empirical leads representing representing details call stored international international supervised supervised early frame choose choose choose run advantage robust strategy moving moving moving moving moving array relevant varying varying varying varying varying works achieve achieve achieve address positions positions positions locations locations locations locations locations generalized generalized storage storage storage storage grant concept concept scaling extended trial trial trial locally move move deterministic white setting pass pass pass pass pass pass pass pass pass pass pass conclusion starting starting starting starting starting starting starting critical place conclusions neighbor neighbor valued valued editors editors differences designed designed clear sutton sutton sutton performs performs performs learns mateo presence presence demonstrated demonstrated solid intelligence intelligence intelligence force question question question acknowledgements reference longer describes describes laboratory laboratory laboratory changing recall simultaneously physical physical angle angle consisting develop applying applying agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent versus select choosing choosing national national focus expressed stationary stationary stages controlled approximations approximations approximations completely past roughly tracking remains initially initially views david existing includes includes thesis retrieval weighting instances memories memories memories variations variations variations variations domains black neighbors simplicity planning planning reason closely closely differ effectively successful successful score situation situation situation essentially online online notice notice notice verlag graphs graphs contained success success success success success success success success moore moore moore interested interpreted issue sin running strategies sci involved michael michael generalize generalize board board attempt attempt attempt moves moves policies deal deal tesauro cowan situations situations explore explore simpler command investigate experience experience experience experience varied environments environments involving game game behaviour helpful reducing incremental incremental incremental scaled scaled scaled authors decisions scores scores affect momentum closest closest concepts concepts concepts concepts concepts concepts possibly possibly necessarily man ensure front front explored initialized store store store optimum optimum percentage indicating advanced theoretic perspective straight broad broad ran ran immediately probable angles circle circle circle circle circle calculations begin attribute arises computers demonstrates cybernetics mellon mellon mellon mellon varies evaluating carnegie carnegie carnegie carnegie applies applies empirically led cmu cmu conducted conducted peter peter peter car car passes pittsburgh pittsburgh fall fall fall adjust gave richard enables sums simulator simulator simulator simulator simulator simulator simulator conclude begins begins simultaneous investigation extensive drift narrow acts controlling partitions repre air kaufman kaufman kaufman intelligent intelligent intelligent intelligent scoring fail reasoning knn knn knn effectiveness effectiveness effectiveness optimally symposium intuitive generalizes exploring alspector started started document decide decide thomas enable specialized mem mem mem mem mem mem mem mem mem mem mem mem suggesting master passing passing passing passing storing storing storing storing projects dietterich dietterich dietterich subsequently speeds speeds speeds interestingly influences vari stone stone stone stone stone stone stone stone stone stone stone stone ball ball ball ball ball dividing empty empty empty mind unchanged ence cooperative cooperative incrementally exception reports spaced affects experiences examining stands acting acting acting acting increment care robots robots magnitudes goals graphics playing playing playing eliminating rectangle guided relates investigating adversary adversary setup setup rod placing places round simplifies aaai november suggestions acquire slot august slots agents agents agents agents agents agents agents suffers shot shot attempting compete opponent opponent fill fill december december steven steven outperformed dom affecting continuum episodes conflicting evenly evenly agency boyan petsche alan alan inefficient ultimate raises retrieved arpa convention implied rivest robotic robotic robotic robotic robotic signed tenth tenth deciding deciding indexing fore sented began sponsored facilitates cars cars entering omit continuing observes retrieve miss nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic nondeterministic graphically reactive forgetting wright wright designated intel remember scratch scratch philadelphia british british mere mere mere facing succeed succeed succeed illustrative official ations retrieving retrieving retrieving retrieving snapshot signif government granger granger granger twelfth doubt anonymous whitehead whitehead whitehead graphic kuh kuh kuh aha aha aha testbed propor precludes permanently invariants friction situ unambiguously justin cheeseman conduct achievement achievement coping coping stewart columbia columbia cept kanazawa kanazawa kanazawa discretize practiced catch icantly beating beating reviewers aeronautical tabula tabula rasa rasa 
#@Stone_P,Veloso_M,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data function time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm output output output output number number number number system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error results results results results results information information information information information information information information information information problem problem problem performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based space space space case vector vector vector vector vector shown systems systems systems systems systems systems systems systems systems systems systems systems probability functions functions functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method approach approach approach approach approach approach point point point point point point point point image image image image image image image image image image image image image image image image image single single single single single single processing processing processing processing processing processing processing processing processing processing processing control control control control control large local local local rate test test test test test test test analysis optimal form form shows shows signal algorithms visual visual visual visual visual paper examples examples examples examples small small small feature feature net net net net work work work work work work work task task task task task task task task methods methods fig fig fig fig fig fig fig fig fig fig step step points points points points features features features classification classification process level level current current current current trained trained trained trained structure high high high similar similar representation architecture architecture architecture show show section vectors images images images images images images images images images images images images images real real real real real average obtained obtained obtained obtained experiments activity dimensional computation computation defined defined found target target target target target target target target target target target target target target target target target target target target target target target target constant table table table table table table table table estimate computer computer computer distance distance distance science left left left direction direction direction direction direction direction direction direction map map map map present low nodes nodes nodes nodes nodes machine object object object object object object object object object object object object object object range range range press position position position position position position position position position position components basis basis basis basis basis abstract computational properties properties properties properties references due due due procedure procedure procedure procedure important important important important important important important important important important adaptive adaptive context introduction complex complex complex complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand estimation estimation estimation statistical statistical generated search complexity lower measure chosen chosen chosen chosen part part center center center center center center center center center center center previous type required multiple good long long represent chip make region region errors scale tasks tasks tasks tasks tasks human human human human human human human human human human human human human human computed performed elements mapping factor orientation study study study em em filter filter original artificial artificial application define define define objects objects objects objects objects objects objects proc proc location location location location location location location location location location location location location location location location perform perform determined goal goal goal related related gain discrete approaches steps steps steps steps steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison larger larger larger fields train train train train nets morgan morgan proceedings report report implementation implementation consists consists consists responses graph maps maps maps computing experiment environment environment environment environment directly hinton additional view view view view solutions solutions solutions curves curves curves design stage detection determine determine determine requires significant world world world world world world world world world world world world world vision vision vision vision vision vision vision vision vision estimated estimated estimated pages pages pages pages pages pages pages con randomly developed robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels area area types lines lines actual actual finally depends sampling constraint biological biological biological achieved achieved achieved discussion increases transformation fast limited limited limited inverse surface surface actions actions finding shape supported theoretical require pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel development development development development pairs reduced functional functional functional unknown jordan jordan technology technology transfer significantly york york segmentation segmentation segmentation segmentation special details details experts experts experts supervised attention attention attention run sources description neuronal neuronal architectures architectures improved discussed directions resolution resolution takes element typical reported lateral practical apply apply strategy strategy strategy side side pixels pixels pixels pixels hierarchical hierarchical engineering sufficient sufficient previously previously previously calculated calculated calculated calculated calculated volume volume works works module module module solve yields yields studies achieve mixtures mixtures mixtures background evaluation evaluation positions positions locations locations symmetric grid grid grid grid grid grid grid grid grid grid grid grid improvement sensitive sensitive entire grant arm arm parts studied scaling occur deviation deviation deviation wide wide feed hybrid generally hardware flow place place place place place place place operator operator operator operator editors editors editors differences differences modules modules modules modules modules modules designed designed practice integration demonstrated targets scene configuration acknowledgements appears appears relation perception ways ways laboratory laboratory confidence sensitivity coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates transformations consisting interaction develop integrated integrated springer springer springer springer shift blocks extraction john letters yield yield yield extracted focus focus focus stages stages stages interpretation influence influence influence solved detailed detailed evaluate evaluate restricted restricted organizing organizing organizing centers centers centers centered centered centered centered centered completely discrimination earlier earlier slow sec calculate calculate visible construction euclidean euclidean views building exploration kernels coordinate coordinate color color color color color color color color color color black absolute successfully major major determining suitable driven identify build build build post comparing fine fine refer refer verlag verlag verlag video issue issue issue issue contribution contribution follow strategies strategies device device device device localization localization localization localization localization modular modular modular modular modular modular modular modular realistic realistic automatically moves moves moves subsequent subsequent extract extract extract jacobs jacobs software software tesauro camera camera camera camera camera camera camera camera cowan powerful powerful powerful overfitting create essential investigate experience experience rapidly put put environments environments dotted mass mass fashion fashion investigated applicable reliable reliable variability understand measurement naturally editor editor man extremely created equally precise mapped mapped academic arbitrarily submitted submitted devices great great advanced developing developing costs trivial publishers nowlan nowlan cascade lies processed processed processed rapid shared widely preprocessing strictly filtered precisely located desirable separately angles angles angles gradually begin recognizing recognizing radius robustness robustness robustness robustness virtual virtual virtual considerably considerably considerably led axes generic capability capability quantitative car effort reliability compares berlin berlin measuring serve suited conclude segmented segmented segmented segmented neuro focused focused deviations specifies progress semantic univ person person person person person person person person person acquisition acquisition acquisition classifying benefit notes interface interface interface interface extensive gabor gabor gabor restrict pick pick pick pick branches approximates reconstructed jones robotics arranged platt systematic kaufman kaufman dealing chance analogy serves transforms belong settings guide guide intuitive intuitive continue exploring exploring alspector evaluations negligible sides intended intended realization stereo stereo stereo uni uni offers ranking insight ahead tracker gesture gesture gesture gesture gesture gesture gesture gesture gesture gesture extends davis valuable workspace workspace workspace workspace workspace workspace pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing pointing achieving achieving convolutional focal focal pentland incrementally abstraction possibilities principled distri evolve cessing gained robots compensate ijcnn guidance guidance guidance guidance guidance guidance carefully carefully challenging frontal unconstrained cartesian cartesian cartesian cartesian cartesian cartesian cartesian cartesian manipulator manipulator manipulator universit suffer minor parametrized parametrized parametrized tune challenge ritter ritter ritter ritter ritter ritter ritter ritter ritter ritter lecture gestures gestures gestures gestures gestures gestures gestures gestures gestures functionality functionality heavily calibration lated evolved evolved aid responsibility steven inclusion drawing tip practically practically practically resolutions ally manually dedicated modalities cooperation recognizes cur reality reality safe vertically informatik informatik baltimore seg seg seg indirectly problematic syst manual rent mounted tit freely yellow predefined searched searched exploitation upward virtue excluded dealt icann mentation mentation mentation evaluates heidelberg heidelberg heidelberg ting challenges chi munich missed boards walter walter euclidian positioned positioned masks masks masks cameras cameras cameras cameras cameras cameras plex zimmermann prof told guiding persons persons persons interfaces interfaces frg frg arose posture wit cutting admit situated cooperate crucially prey prey bielefeld bielefeld bielefeld shah loc intersects referenced referenced arbi assembled hnear ction bryson bot wear releases sea flies centralized fakult spending inen eccv prerequisite zed neuroinformatik neuroinformatik quires grab grab buted assembling tackling helge 
#@Drees_A,Littmann_E,Ritter_H,
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#*network network network network network network learning learning neural neural neural neural neural neural neural neural input input input input data data data data data data figure figure figure figure figure figure time time time time time set set set set networks networks training training training training training training training training algorithm output output output output output number number system system system system system system system system system system system system system system system error state state results results results results results results results results information information information information information information information problem performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based linear layer case order shown shown shown systems systems systems systems values weight neurons recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach approach pattern pattern pattern pattern pattern pattern pattern point single processing processing local rate rate test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis inputs inputs inputs inputs form shows shows shows signal signal signal signal signal signal signal simple paper paper feature net task task methods methods methods methods features features features features features process process process process level level level trained trained trained high high high high high high high similar representation architecture architecture architecture show show show show show show line rule speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average average obtained experiments experiments result university university research found found table table table table table table presented present present present phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency machine sets sets sets sets range components components basis basis basis outputs abstract back back properties references component due important important important important propagation introduction introduction complex tion tion energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy classifier classifier classifier classifier classifier classifier signals signals signals center bound required good good long conditions represent make techniques techniques region proposed proposed proposed proposed proposed minimum classes total total total simulation simulation simulation human multi multi multi multi multi multi multi multi multi multi sum performed called called mapping means made natural global filter filter artificial artificial compared compared application desired desired desired provide provide compute perform perform experimental brain brain comparison train source selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection words department technique technique technique technique consists consists consists difficult environment directly design bit conference estimated produce produce produce channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel developed developed levels levels levels levels provided selected selected selected selected selected selected selected selected achieved normal increases group tested tested transformation fast limited corresponds amount short short common implemented implemented implemented shape generate require ability makes including auditory auditory auditory typically typically typically typically pairs needed reduced coefficients coefficients fully fully mlp mlp mlp testing testing testing testing testing significantly significantly significantly head database database mode leads squared call numbers filters filters pre direct window window international experts supervised frame frame frame decay produced separate practical strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy array array array engineering engineering compare compare teacher module module tions smooth speaker speaker speaker speaker speaker match channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels interval entire entire amplitude amplitude amplitude constructed constructed lead generally column conclusion row peak performs performs sound sound sound sound sound sound largest pulse relationship acoustic acoustic acoustic base base produces produces produces perception factors generating laboratory ann ann label label electrical electrical electrical electrical electrical transformations spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral frequencies frequencies quality versus select select yield extracted depending depending phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme communication overlap interpretation codes transform evaluated processor processor processor processor processor processor processor processor spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum diagram diagram epochs precision existing perceptrons selecting capable importance maximal divided divided divided divided effectively post score score score reached receives receives soc soc phonetic strategies device sampled simplified simplified play play highest leading leading processors processors processors extract stimulation stimulation stimulation limitations fourier successive matched matched matched matched matched matched matched matched matched matched matched singular fisher fisher separated nerve nerve academic art art speakers speakers speakers sentences sentences sentences sentences sentences mentioned residual residual cos developing distinguish publishers publishers improves coded tool directional directional broad nucleus commonly consequence sounds sounds sounds sounds sounds sounds read read recording reflects people applies cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear spoken spoken spoken fed share maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima maxima schematic schematic phonemes phonemes phonemes phonemes phonemes phonemes hamming hamming windows wang wang wang wang june sentence cochlea displays spectra indices indices ear bipolar restrict labelled labelled labelled labelled labelled lost khz khz bands bands bands bands ral receiver receiver receiver corpus symposium selects selects vowels vowels vowels ranging patient mel darpa stimulated creating refers relies tures stone discriminate discriminate informa listed kluwer asked bank bank centre amplitudes amplitudes jabri jabri jabri jabri jabri jabri electrode electrode electrode electrode australia peripheral graphics activate allocated allocated allocated picked considers electrodes electrodes electrodes cosine weaker turning fea commercial commercial commercial commercial commercial commercial commercial milliseconds tract october stops emphasis acoust acoust influenced synthesized synthesized synthesized heavily hearing hearing impulses skin imple exper morphology morphology morphology morphology morphology transmitter transmitter believed meeting consonants automation fft fft labelling labelling labelling edited edited clark clark decaying vocal bandpass bandpass amplified cascaded nonstationary raised unrestricted energies microphone microphone microphone ears spec publishing timit apical sydney orig tong strongest strongest allocate coil confused selector raymond selec confusions confusions confusions bernstein plied synthesizer speak morphological morphological morphological decayed specially living envi tape marwan marwan skrzypek delivers spe portable smart smart fibres stimulate patrick lows nsw electrophysiology highlighted proposing iments listeners sensations mor amplifies agreed selections selections sixteen sixteen quantised quantised quantised sifier sedal sensation sensation nasals founda inal morphologies cla menting entirety mcdermott mcdermott mcdermott fricatives melbourne 
#@Jabri_M,Wang_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data function function function function function function function function function function function function function function function function function function function function function figure figure figure time time set set set set set set set set set set networks networks training training training training training training training algorithm algorithm output output output output output output output output number number number number number number number system system state state results results results results results results units units units units units units units units information information problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden performance based based based based based weights weights weights weights weights linear linear layer layer layer layer layer vector vector order shown shown shown shown shown shown shown shown shown systems values values parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight unit method method method method method method method method approach approach approach pattern point image image single single processing local local local local local local local local local local local local local local analysis optimal inputs inputs form form shows shows paper examples examples examples small small size net work work work work work work work work methods methods methods methods methods methods fig fig fig fig fig fig fig step step field process current current trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems random random random similar show parameter real average theory gradient gradient obtained obtained obtained term term term experiments experiments result result result result result university university variables variables variables variables variables computation computation solution independent independent log log found sequence sequence sequence sequence sequence sequence target initial initial initial computer computer terms terms terms terms science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left present activation machine maximum maximum press press learn position position position basis abstract applied back find find density properties likelihood likelihood references ieee positive positive positive positive positive procedure procedure procedure procedure important important important important introduction introduction introduction estimation estimation estimation dynamic dynamic dynamic generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel cost change change change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference difference difference variable assume lower lower representations learned part cases good binary binary binary long long long represent represent bayesian fact correlation length length correct correct correct correct correct probabilities probabilities scale scale minimum minimum minimum minimum minimum resulting total total total total total called called called called called called called elements elements means made global global global global global study negative negative negative negative negative represented represented represented represented represented represented compared compared cross define define proc related constraints constraints constraints connected connected connected connected gain equal equal accuracy accuracy accuracy accuracy accuracy accuracy descent descent dependent dependent institute version consists consists represents final final scheme sequences sequences sequences ai ai ai cambridge cambridge hinton view limit san bit determine efficient upper full significant free free free estimated estimated increase validation give give give give coding coding developed types lines lines entropy provided selected selected iteration iteration depends constraint technical describe limited close assumption assumption corresponds corresponds predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions amount nearest supported theoretical journal square instance future future kaufmann simulated simulated simulated simulated simulated simulated pairs pairs pairs coefficients fully fully fully interesting york edge structures structures structures structures structures principle principle numbers numbers numbers pre window window window window window window window window window window window window window window window window window window combined combined minimize added predict predict predict improve improve improve directions directions directions correlations correlations correlations correlations correlations correlations correlations pair pair pair pair pair typical introduced introduced introduced introduced include include identical identical machines side side side side side sejnowski sejnowski sejnowski cognitive highly varying previously approximately works works yields yields correspond diagonal diagonal sparse definition positions positions chain chain chain chain chain chain chain bounded improvement grant exists extended matrices predicted touretzky white occurs generally generally conclusion minimal reduce neighbor central central interactions interactions interactions weak weak weak constrained constrained mateo temperature encoding encoding encoding encoding largest external labeled assuming minimizing minimizing min decrease introduce configuration configuration annealing annealing annealing annealing annealing annealing annealing boltzmann boltzmann boltzmann boltzmann construct written ways ways primary primary stability vertical explicitly linearly consisting consisting minimization minimization minimization formed letters letters expressed formation dependence correlated correlated interpretation solved fraction showed showed centered centered similarly sec combining add false false false string assigned assigned foundation avoid building assignment assignment prove black black regular straightforward middle identified letter successful mackay situation capture capture soc notice repeated repeated contained cun showing interpreted symmetry symmetry running categories gray gray comp involved minimizes board neighboring acknowledgments minimized minimized carried varied preliminary rise ideas rest applicable applicable biol biol biol combine combine predicting predicting predicting predicting predicts predicts predicts predicts opposite opposite perfect greedy fisher separated separated separated submitted explain attempts spin indicating trivial crucial fairly fairly improves biology biology glass reasons turns shared widely widely widely widely strictly protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein protein incorporate leaves gradually peter adjustable adjustable formulated calculating anti anti anti anti anti anti anti anti anti anti anti anti ture aim aim gave richard richard chose comments display display windows windows windows windows windows windows windows windows windows windows softmax wesley sharing sharing lot globally representative uncorrelated secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary addison forming interconnected proceed clamped inspired convenient chains chains chains chains chains analogy city chemical balance interpret sanger sanger belong krogh krogh krogh krogh krogh krogh krogh responsible hertz hertz weakly started mance contexts introduces introduces ensures displayed surprising perfor overview sides moved bad surprisingly proteins proteins proteins proteins proteins proteins proteins proteins proteins proteins balancing fold severe usage logarithm logarithm email email kluwer presenting bank employs encouraging encouraging centre imagine molecular molecular stands beta beta beta beta perpendicular alternate hubbard hubbard pos library amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino amino sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet sheet distinguished distinguished electronics preprint durbin struc bridle palmer sees water firstly spins periodicity rare believed couplings couplings triangle triangle edited edited edited inefficient positives acid acid acid acid acid acid acid acid acid acid acid implying denmark denmark constraining 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#@Krogh_A,Riis_S,
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#*network network network network network network network network network network network network network network network learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time set set set set set set set networks training training training training training training training algorithm algorithm output output output output output system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error results results results results results results results results units units units units units units information information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based based based based based based based based based based based based layer layer layer layer layer layer case case case case vector vector vector vector order order shown systems systems systems systems systems systems systems systems values probability probability probability probability weight neurons unit distribution approach approach approach approach single single single single single single single single processing processing control control control control neuron neuron rate rate rate test test test test test test test analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows signal signal signal algorithms simple simple examples examples small size size feature feature work work work work work work work task task points field features features features classification process process current current current current current current current current current current trained trained trained trained trained trained trained trained trained problems problems random random similar similar similar representation representation architecture architecture show line line line line line vectors vectors vectors average average average theory theory obtained obtained obtained obtained obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments threshold threshold threshold threshold threshold threshold threshold threshold solution research independent found initial constant constant table table table table table table table estimate standard standard standard computer prediction prediction prediction prediction present present phase phase phase low frequency frequency frequency machine sets press components components components components components outputs outputs continuous continuous continuous abstract applied applied applied analog references component ieee decision propagation introduction stimulus statistical statistical effect generated parallel cost cost cost tion change energy assume classifier classifier classifier classifier classifier lower lower measure signals representations chosen chosen higher part center center cases type type good good good conditions conditions conditions conditions conditions conditions distributed fact techniques techniques techniques proposed proposed observed errors tasks human human human human computed computed computed sum called times factor made made made filter filter filter artificial relative series series provide provide provide provide provide rates rates perform determined experimental goal related connected connected connected motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor power mit larger contrast connection support proceedings proceedings institute loss loss loss technique internal individual individual joint layers addition addition graph computing experiment experiment experiment hinton hinton curve curve curve curves curves design design design limit stimuli stimuli bit detection detection detection detection detection detection detection detection detection detection detection detection detection conference determine determine determine determine determine determine determine determine classifiers classifiers full full full full full full full full significant basic basic increase produce produce produce produce condition condition condition derived developed developed product actual finally selected selected selected selected backpropagation depends depends sampling constraint measured normal normal normal normal normal feedforward feedforward arbitrary arbitrary tested tested tested tested tested tested limited assumption assumption complete effective implemented generate generate require require require require eds adaptation end future future rumelhart rumelhart rumelhart typically typically typically typically combination reduced functional functional coefficients coefficients fully fully technology block interesting testing testing significantly increasing operation leads squared international expert expert expert expert expert expert early magnitude magnitude magnitude magnitude magnitude idea minimize produced produced run run run run description improve typical similarity reported reported introduced include subject subset subset interest sufficient compare tuning background locations observation interval williams williams improvement increased lead lead digital digital deviation predicted predicted alternative alternative correctly correctly correctly move occurs hardware demonstrate half half half critical minimal greater reduce reduce operator operator designed designed designed designed designed designed designed presence physics external cycle cycle demonstrated intelligence labeled turn variety averaged averaged averaged averaged averaged averaged averaged longer primary laboratory laboratory distinct distinct changing metric metric metric metric metric metric metric averaging linearly electrical consisting consisting frequencies blocks independently reconstruction operations centers completely spectrum spectrum spectrum spectrum measurements measurements measurements measurements measurements measurements classical false false construction recorded recorded recorded recorded building existing existing existing fire blind determines determines illustrated illustrated automatic specifically tests tests successfully identified included mcclelland wij successful identify identify detect detect detect build build ten ten ten ten receives road notice contained success running built built built bar bar involved absence computes thresholds automatically attempt attempt consisted overlapping overlapping illustrates illustrates illustrates operating operating operating operating operating load load load load load load load load load load load decreasing production production production collection collection requirements experience replaced hanson hanson hanson hanson accurately issues project detectors fault fault fault fault fault fault fault fault fault fault fault fault fault scaled scaled office oscillation oscillation oscillation oscillation notion induction induction induction induction induction induction act adapt necessarily illustrate illustrate changed changed prototype prototype obvious detector detector detector detector detector switching switching detected simplest advanced developing developing costs costs distinguish distinguish distinguish distinguish distinguish failure failure failure failure failure failure failure failure failure expensive expensive expensive expensive starts processed sites preprocessing filtered filtered operators sounds sounds hippocampal hippocampal recording annual outer outer improvements behaviors collected collected collected led axes recordings recordings continuously frequently frequently compares rely rely replace electric electric electric display damage conditioning deviations deviations progress diagnosis spectra spectra spectra spectra college feasible sort primarily princeton driving driving driving animals encoder eliminate eliminate fails chance minutes darken darken darken darken darken occurred occurred siemens siemens siemens siemens hope fail effectiveness responsible capacitor motivation date date financial induce bad bad bad bad bad thomas hippocampus hippocampus master record properly card broken broken broken broken balanced balanced balanced balanced balanced balanced balanced automated dividing mechanical mechanical mechanical mechanical mechanical mechanical mechanical consecutive audio listed listed session asked year year reports tor sinusoidal sinusoidal sinusoidal sinusoidal reconstruct reconstruct clas translated life crosses thresholded switched gluck gluck gluck gluck gluck records monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring alarm alarm supports rotating rotating rotating flight commercial tune failures failures failures failures replacement stephen excess thermal twenty corporate monitor monitor monitor monitor monitor monitor water east supply industrial converter wiring meeting core automation detects fft fft fft fft fft fft petsche petsche petsche petsche petsche loads loads loads loads loads loads loads resolved daily approaching amplified amplified presently periodically adapts feasibility motors motors motors motors motors motors motors motors motors motors motors motors manual kuhn kuhn kuhn kuhn wires monitored health unexpected mounted jose degrades anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly custom hole hole preprocessed collecting miss miss oil minute compress conceptually rated rated rated rated rated rated rated damaged damaged myers myers myers myers experimentation sorts radially novelty novelty novelty novelty novelty novelty bearing bearing bearing bearing bearing functioning contiguous exclude concluded iix equipment healthy healthy healthy healthy healthy healthy healthy healthy healthy healthy healthy healthy healthy cards cards multiplexed vibration vibration vibration vibration vibration vibration vibration signif inexpensive ein christian gary survive pump pump race race breakdown 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#@Darken_C,Hanson_S,Kuhn_G,Marcantonio_A,Petsehe_T,Santoso_I,
#t9
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#*network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm output number system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state results results results results results results results results results units units units units information information models hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance weights weights linear linear layer layer layer shown shown shown shown systems systems systems values noise noise noise distribution distribution method approach point single single processing processing processing large local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test test test test test test patterns analysis analysis analysis analysis analysis analysis analysis shows shows shows shows algorithms small small small size size work task task task task task task task task task task task methods methods fig fig fig fig cells cells level level level level level structure structure structure structure random random high response similar similar representation architecture show show generalization generalization parameter real real real real real real average average average average average average average gradient experiments activity activity activity activity activity activity activity result result threshold threshold research research research research defined found target target target dynamics dynamics initial table table estimate estimate estimate estimate estimate estimate estimate left presented presented present phase phase phase phase phase phase phase phase phase phase phase phase low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency sets maximum position components basis nonlinear continuous continuous abstract applied applied computational computational computational references procedure procedure propagation introduction complex complex complex complex complex estimation estimation estimation estimation estimation estimation stimulus generated parallel cost change variable variable lower lower lower lower lower measure measure measure signals signals signals signals chosen higher part center center center cases conditions distributed make correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation errors scale resulting ing tasks human human human human regression regression regression computed computed computed computed computed performed called times times means means potential potential applications policy knowledge cross cross series series series series series series series rates eye eye determined experimental related related related related cortical cortical brain brain brain brain brain brain power steps steps accuracy accuracy comparison larger train train descent nets morgan report report report institute institute institute department department loss internal individual domain domain domain equivalent equivalent hinton design san san san top top detection detection detection detection detection detection detection detection detection detection detection detection upper upper upper significant significant world estimated estimated estimated estimated estimated estimated increase increase validation give give give channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel derived randomly lines lines actual actual actual actual actual actual finally selected selected selected backpropagation sampling measured discussion normal feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward increases increases increases tested limited complete stable stable stable stable stable surface short supported role ability cluster cluster cluster degree degree rumelhart including auditory auditory auditory auditory auditory auditory auditory auditory simulated simulated pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs combination testing testing significantly increasing increasing principal squared squared window window window window window window window window window window normalized bottom minimize predict predict perceptron improved discussed correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations pair pair pair pair pair pair robust separate movement movement practical moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving moving subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject identical sejnowski sejnowski sejnowski sejnowski sejnowski cognitive cognitive recently highly previously previously subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects volume tions tions smooth smooth studies studies studies diagonal diagonal diagonal background background channels channels channels channels channels gate williams increased increased increased grant amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude intensity lead suggests clusters white half half strength operator operator central differences measures measures measures measures measures accurate exponential suggest strong characteristics solid selective min min decrease relationship relationship targets targets targets targets appears relation index estimating estimating transitions stability stability spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral frequencies frequencies frequencies frequencies frequencies frequencies frequencies blocks potentials letters expressed depending correlated correlated correlated ocular similarly spectrum spectrum spectrum spectrum spectrum spectrum sign smoothing smoothing dashed performing performing epochs fitting intervals intervals purpose closed eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg views recorded recorded recorded recorded recorded box box box perceptrons perceptrons bell bell maximize absolute absolute absolute identified differ differ included ten heuristic showing oscillations content vary subsequent acknowledgments origin diego diego diego environments humans biases reducing behavioral behavioral behavioral possibility relationships relationships relationships authors office referred root topographic topographic topographic topographic topographic topographic cognition removed neu trace trace trace onset eyes adjusted noted panel panel panel multivariate multivariate detected detected extent extent contributions submitted years site advanced pairwise band band band developing asynchronous analyzed waveform adjacent independence correction sites sites sites sites sites sites sites sites sites broad broad operators located medical fluctuations conjugate reflect reflect collected collected collected collected conducted poorly recordings passed continuously continuously continuously howard measuring gen synchrony synchrony synchrony monotonic cal prevent coherent semi decreased decreased shaped coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence traces traces traces traces simultaneous irrelevant cor contribute lab lab spectra spectra spectra spectra spectra sleep sleep sleep sleep sleep bipolar animals neurophysiol neurophysiol neurophysiol bin naval naval naval naval spontaneous chance significance significance significance minutes minutes hit bands bands bands bands mark neurobiology neurobiology observing bourlard salk salk enhanced sion corre studying conjunction conjunction enhance artifacts artifacts emergence bursts smoothed smoothed probe sustained sustained waveforms waveforms waveforms waveforms waveforms waveforms davis davis acknowledge lag lag lag lag lag onr rms rms rms rms rms rms rms rms rms rms rms rms rms rms rms dramatically multiplying linked linked appeared ence converted session session session session session session session session session session session session session session session session session session session session rejection failed tween tween profiles lit amplitudes amplitudes ical superimposed spaced causal electrode rain conservative wake rectangular publication conduction generators hughes terrence rejected electrodes projecting investigating frontal frontal frontal pos records records monitoring monitoring monitoring monitoring indexed portions figs tones esti article topography suggestions sessions sessions sessions sessions sessions sessions sessions sessions sessions sessions sessions sessions sessions sessions sessions sessions lation monitor monitor monitor monitor monitor monitor scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp ping developmental adult hour fft artifact artifact bandpass implying confined remained lags scott electrophysiological ranged ranged defense tical clues health health health responded replicate hits multilinear tivity postal collecting ness ness minute makeig makeig makeig makeig makeig makeig jung jung jung jung jung corr corr corr corr corr corr corr corr corr corr corr corr corr courses eog convolving pushed ative clin clin clin clin clin walter converting contiguous alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness alertness concurrent concurrent inactivation fell tony narrower healthy chamber correla correla official preferentially instructed pilot accompanied preceded government regres button mates interfaces alert alert adults insignificant graphic mln detectable neg subcortical subcortical adaptability steadily navy sumptions interspersed intimately thirteen irregularly neous chap nielsen appreciable objectively coordinating cept nonstationarity handed trainin participated wideband stood warm detectability advancing bustness practi fib moval vestigated 
#@Jung_T,Makeig_S,Sejnowski_T,
#t9
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#*network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output system system system system system system system information information problem problem problem problem problem hidden performance performance based space space space weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector vector vector order shown shown shown shown shown shown systems systems values values noise noise noise weight functions neurons neurons neurons neurons neurons recognition recognition recognition recognition method method method method method method method method method method method method approach point point image image image image image image image single processing processing processing control large neuron neuron neuron neuron neuron neuron rate rate test test test test test test test shows shows signal simple paper paper examples examples examples examples examples examples examples small net methods step step step step step step step step step field field field classification classification process level level current trained trained trained trained trained trained trained trained trained random response response similar similar architecture architecture architecture equation equation equation equation equation section section section section fixed line line vectors vectors vectors vectors images images speech parameter real real real real real real real real theory result result threshold threshold computation solution solution solution solution solution solution solution found found found constant standard standard standard left low low machine object press position position outputs outputs abstract applied applied applied back back back find analog analog analog analog analog references due ieee positive positive positive important propagation propagation propagation mixture action hand hand circuit estimation behavior behavior behavior change complexity spatial classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower center type type type equations equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make make make correct correct minimum classes ing ing computed computed multi sum sum optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization made negative negative vol application define active active active active active active active active active active active active active active active active active active active active active active active constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints gain accuracy accuracy contrast contrast train morgan morgan words implementation implementation code individual advances advances final bias delay addition addition equivalent equivalent equivalent equivalent directly hinton design design limit san san san top bit conference requires give con con con area area velocity types provided finally finally constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint simply simply simply describe tested tested corresponds amount effective implemented require eds square end vlsi vlsi vlsi pixel pixel pixel pixel hypothesis hypothesis easily makes makes kaufmann kaufmann combination combination coefficients technology programming programming character character character character character character character character character character character character character character character segmentation segmentation segmentation segmentation empirical principle principle principle principle principle details call call window bottom bottom bottom combined combined combined minimize minimize minimize choose choose choose added added sources light light light discussed takes takes takes practical side side side pixels pixels pixels pixels pixels pixels pixels pixels quadratic quadratic quadratic approximately approximately approximately works solve correspond correspond correspond background background positions positions locations entire entire constructed horizontal horizontal invariant move touretzky boundary column hardware hardware hardware hardware hardware hardware greater conclusions accurate retina retina retina retina retina retina retina retina retina designed peak peak performs 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straints pittman pittman ink parameterize synaptics synaptics synaptics synaptics reads reads straint timothy raining backgrounds resistant resistant resistant immune immune immune immune immune gill gill gill acous holes companies locates aca confidences confidences confidences sifier sifier sifier printing printing printing optically optically aids violating ime microseconds consult parkway lightly wik fourteen fourteen fourteen orchard staple obeyed 
#@Allen_T,Platt_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm state results results results results results results information information information problem problem problem problem performance performance performance performance based based based based based based based based space case case case order systems systems values values values values values values values values probability probability parameters unit distribution distribution approach approach pattern processing processing processing processing processing processing control control control control control control large local local rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows shows shows algorithms algorithms algorithms algorithms simple simple simple paper paper net net net net work work work work work fig fig fig step step step step step step step step step step process process process process level level level level level level level level level level level level level level current current current current current current current problems problems problems random random random high high high high high high high high high memory memory memory memory memory memory memory memory memory similar show general parameter parameter parameter average average average average average states note experiments experiments experiments result university university solution found initial initial initial initial initial initial initial table estimate computer terms terms terms node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node science science left left presented phase phase phase phase phase low low low low low low low low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency machine learn learn learn learn abstract applied find find computational references due due due positive important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision introduction hand estimation estimation behavior dynamic cost cost change change change change change difference difference difference assume lower prior learned learned learned chosen chosen higher higher part part part bound good good good good long conditions conditions conditions conditions distributed distributed distributed distributed expected make proposed proposed probabilities minimum minimum minimum minimum minimum ing ing simulation simulation simulation computed performed called called called called times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement feedback global global applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge negative original original original rates rates rates related power approaches steps steps steps steps steps accuracy larger larger update update source source source source source source source source source morgan morgan proceedings department version advances advances difficult difficult delay delay scheme scheme scheme addition environment environment environment estimates san san effects efficient efficient upper upper upper significant speed speed speed speed speed estimated estimated estimated estimated increase increase increase increase increase increase increase increase give con con randomly controller path path path path path path path path path path path path path path path path path path path path path path path path path path path path actual actual selected selected depends depends simply simply simply achieved increases increases increases stable stable stable stable actions actions finding short common common role eds adaptation end instance noisy including objective probabilistic needed needed technology programming york uniform empirical empirical leads max making international bottom bottom decay decay idea minimize minimize choose choose sources improve separate separate reported strategy strategy period period period period identical sense sufficient varying varying varying varying varying varying varying varying achieve rl rl rl address grid grid grid grid grid interval williams williams exists parts studied occur predicted deterministic white occurs generally generally demonstrate minimal greater depend clear performs performs performs performs performs faster faster practice mateo temperature propose taking california min decrease manner boltzmann longer longer longer longer longer longer solving generating changing changing changing changing changing slightly slightly slightly develop predictive predictive predictive predictive predictive predictive predictive predictive versus decreases decreases yield choosing stationary stationary communication communication controlled controlled updated activities activities updates allowed past past delays intervals remains topology topology topology avoid exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration thesis discussions major planning reason selecting middle middle middle extra closely computationally paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths successful detect situation tend tend fine fine refer notice notice prob moore moore moore link link superior issue oscillations oscillations gibbs realistic delayed leading automatically attempt policies policies policies policies policies subsequent subsequent operating operating neighboring neighboring neighboring neighboring deal routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing load load load load load load load load load load load load load load load load load load load load load load load load load load load load load load load load load load load load decreasing situations explore explore unlike unlike unlike essential involving periodic periodic periodic periodic periodic examine giving incremental possibility possibility decisions comparable complicated workshop phases transmission transmission possibly adapt traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic predicting predicting opposite extremely extremely adjusted noted algo generates simplest phd mentioned asynchronous crucial failure implementing tive strictly worst desirable watkins watkins gradually gradually gradually bandwidth researchers varies varies fuzzy reflect profile led pseudo simulate atkeson atkeson atkeson share continuously variant rewards requirement switch switch controllers controllers controllers controllers rely popular popular returns guarantee rithm recover acts dynamically dynamically controlling fails fails consideration proceeds imposed intelligent affected effectiveness effectiveness intuitively encountered sides candidates recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery mem shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest shortest passing hypercube subsequently dividing divide dramatically unchanged ure ure slight thrun thrun shorter tables dyna suboptimal convenience utilize utilize medium medium tradeoff solely affects experiences experiences experiences experiences england hillsdale reflected adapting adapting visited verified queue queue shifting packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets community alternate alternate continues continues overhead refinement sweeping sweeping packet packet packet packet packet packet packet packet tune tune mix littman littman littman littman littman littman topologies emphasis send send send send send send send water jersey suffers prioritized prioritized prioritized stay cally returned boyan boyan boyan boyan boyan boyan trol arrives ory degenerate contrary destination frequent reality sending sending randomness adapts gence bottleneck delivery delivery delivery delivery delivery delivery delivery delivery handbook oscillates trend trend putation bidirectional kong kong occasionally occasionally exploitation exploitation exploitation exploitation exploitation hysteresis hysteresis dilemma erroneous erroneous putting inability inability hong hong lowered conver samuel aggressive devise queueing telecommunications poorer selector selector selector occasional aperiodic aperiodic manageable depict probing probing probing probing probing slowing prefers yeung yeung yeung yeung cooperate ditions choi choi choi choi prespecified alterna infrequent adaptability probes probes probes alleviate multistage peng peng bay ceases ceases boy vantage glance dynami sofge ust continual continual dyn pends interleaving onwards onwards yan reinhold 
#@Choi_S,Yeung_D,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural neural input input data data data data data data function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time time time set set set set set set set set set networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output number number system system system system system state state state state state state state state state state state state state state state state state state state units problem problem problem problem problem problem problem problem problem problem hidden based based based based based based based based based space space space space linear case vector vector vector vector vector vector order order order shown systems values values values values values values values values values values values values probability weight functions functions functions neurons distribution method method approach approach approach point control control control large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form shows algorithms algorithms simple paper paper small small small feature work work task task task task methods fig fig fig fig step step step step points level level current current current problems problems problems problems random high high high high architecture equation equation equation equation section section section section fixed fixed fixed fixed line line line line generalization parameter real real real real average states states theory theory note note note experiments dimensional dimensional variables variables solution solution research research independent defined found found dynamics dynamics dynamics initial table table table table computer prediction prediction prediction prediction left left left present phase phase phase phase low low low low machine range learn learn position basis basis nonlinear nonlinear continuous abstract abstract applied back find convergence convergence density references stochastic stochastic positive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision context introduction action action action action action hand behavior behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance variance cost search tion change change change change change change change difference difference difference variable variable variable variable assume assume lower lower lower lower rules measure measure chosen chosen higher higher higher higher higher part part previous binary conditions expected expected expected expected expected expected expected fact fact techniques proposed probabilities probabilities probabilities finite finite resulting resulting resulting resulting resulting resulting total computed computed respect respect multi multi eq eq called elements elements elements means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor optimization optimization potential made made global applications applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy artificial artificial artificial relative series series series provide compute rates rates gain gain discrete equal steps steps steps comparison larger connection update modeling selection implementation consists consists consists represents difficult considered framework equivalent experiment experiment experiment experiment environment curve curve solutions estimates transition transition transition top top stage stage efficient upper upper significant approximate statistics statistics world world estimated increase increase derived weighted randomly randomly lines lines actual actual actual actual actual provided processes iteration iteration iteration depends depends sampling achieved technical describe describe describe denote tested tested tested fast complete actions actions actions amount short require journal end end end future future future future easily easily development development development development fit typically typically typically pairs needed combination combination reduced reduced reduced mlp mlp mlp mlp mlp mlp mlp block programming programming programming programming programming programming programming programming programming interesting interesting increasing increasing trials representing representing details iterations max max making making international bottom bottom magnitude combined description predict discussed recent recent apply apply strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy period identical interest interest sufficient conventional calculated volume works solve solve yields converge achieve achieve rl rl address risk risk risk risk risk risk risk constructed constructed horizontal scaling trial alternative setting demonstrate runs starting conclusions operator accurate sutton temperature proportional exist decrease relationship boltzmann pro longer index index sequential estimating confidence simultaneously infinite unique consisting applying shift extraction choosing expressed depending stationary influence influence solved evaluated evaluate understanding converges converges updates updates past sign barto barto barto epochs epochs epochs epochs classical spaces iterative transactions exploration plotted plotted plotted plotted prove maximize successfully successfully reason middle extra maximal divided included literature build situation plots prob heuristic success success success split superior return return return return return return return return return return return return return return follow follow strategies strategies relaxation dayan realistic principles moves moves policies satisfies decreasing remain wiley singh singh singh singh environments optimized optimized optimized optimized mdp mdp mdp mdp mdp mdp successive possibility scaled decisions decisions decisions decisions decisions decisions complicated cover phases hill changed changed changed assumes precise initialized initialized store store epoch explain years years asymptotically indicating great ment slowly developing costs costs costs costs costs costs costs costs costs growing benchmark benchmark benchmark benchmark straight closer ring day immediately watkins watkins probable probable recognized beginning beginning optimize demonstrates applies fuzzy fuzzy pure led amounts embedded simulate http aim aim germany neuro neuro returns returns returns extreme trade trade initialization bellman bellman shifted www extensive restrict allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation promising tools siemens siemens siemens proceeds attractive abilities mark exploit preparation selects days utilized financial financial decide bad realization realization chooses approximators approximators insight bins repeatedly horizon horizon extends exploiting market market market market market market trading trading accumulated outlined bertsekas bertsekas bertsekas bertsekas drop drop accept achieving achieving discount dec dec markovian markovian stock stock stock die german german german certainty certainty stands pij interact management management management management interacting oct carefully switched guided increasingly topic paris cation worth barrier exchange exchange exchange exchange exchange exchange exchange exchange exchange exchange exchange exchange exchange exchange exchange exchange admissible admissible applicability behaves portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio opti discretized corporate corporate justified quantify influenced imple neuneier neuneier neuneier neuneier neuneier neuneier sen proposes meth capital capital capital capital capital capital capital capital capital capital capital capital capital capital capital capital capital capital html ignores stocks stocks contrary daily daily coins ods asset asset asset asset asset asset asset asset asset asset asset asset asset cho mcgraw approached trend trend transaction transaction transaction transaction transaction transaction investment investment investment investment investment jan jan jan jan maxq ized expresses triple mir exploitation exploitation markets markets markets markets optimizes deeper deeper sition icann tran des investor investor investor investor investor investor investor investor investor investor investor investor investor investor pushed myers clarify clarify mented executes formalized wishes ration volatility compose foreign foreign ralph ralph beats gramming otto simplifications imitate nns nns nns obeying assets timal wealth wealth invest invest invest invest invest currency currency currency currency currency currency currency hahn delivers delivers opportunities liquid liquid markovjan markovjan revise dollars invested money finance finance finance zfe zfe mized explo influencing traded downs dollar ups tabulated professional exchanges advisable allo oscillated 
#@Neuneier_R,
#t9
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural neural input input data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time set set set set set set set set set set set set set set set set set set set set networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output number number error error error error error error error error error error error error error error error error error results results results results results results results units units units units information information information information problem problem problem problem problem problem problem problem models models models models models hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based space layer layer layer layer layer layer order order order order shown systems systems systems systems values values values values values values values values values values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability parameters functions functions distribution distribution method method method method approach approach approach approach pattern pattern pattern pattern pattern pattern single processing large large large rate rate rate rate rate rate rate test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis class class class class inputs inputs inputs inputs inputs inputs shows shows shows shows shows shows shows simple simple simple visual paper paper paper paper small size size feature net net net net net net net net net net net work work task methods methods methods methods methods methods methods methods methods methods features features features current trained trained trained trained trained cell problems problems problems problems problems problems high high similar similar similar similar similar representation section section section section general generalization generalization real real average average note experiments experiments experiments experiments university threshold threshold threshold threshold research found target target target target target target target target target target target target target target target target target target target target table table table table table table table table table estimate standard standard standard standard standard computer science prediction prediction prediction present present present present present low low low low low machine machine machine machine machine machine sets sets sets learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs sample sample abstract applied find find find find references ieee important important important decision decision decision action complex parallel cost search tion change change complexity lower lower measure prior prior representations representations learned learned learned higher higher higher part part cases cases cases cases cases cases cases long conditions make fact region probabilities observed observed errors errors forward scale scale scale scale resulting ing tasks tasks tasks tasks tasks sum sum sum performed made made made made applications policy knowledge filter original original original relative relative relative relative true application application application cross provide define objects rates rates rates rates rates rates location perform perform goal goal goal goal goal goal goal goal goal goal related related related approaches accuracy accuracy comparison comparison support support train train source nets nets nets nets nets nets nets proceedings proceedings proceedings proceedings proceedings code advances difficult bias bias bias bias bias addition ai maps considered considered domain domain domain directly directly additional conference conference conference conference conference determine determine determine significant significant world estimated basic basic basic basic validation randomly randomly robot robot criterion criterion entropy backpropagation backpropagation backpropagation backpropagation backpropagation achieved measured discussion discussion group predictions predictions predictions predictions predictions finding short nearest effective effective supported require require journal journal journal instance future future future future future future future future future future future future future makes makes fit typically combination testing testing consistent consistent trials trials trials database database database database database database database database database database database database database database database database details making making international international international international bottom bottom experts experts early early early idea idea attention combined run run run run run predict predict predict predict predict predict predict predict predict population population population population population population population improve improve advantage takes include include hierarchical sufficient sufficient works works works works smooth match studies converge converge achieve mixtures background evaluation evaluation evaluation evaluation evaluation evaluation evaluation improvement improvement improvement improvement risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk grant grant grant exists trial predicted move pass pass pass runs critical row row neighbor valued differences differences sigmoid bayes faster practice practice practice learns learns learns learns hard drawn drawn pulse user targets targets targets targets targets targets targets targets targets targets targets targets groups acknowledgements suppose index ways primary sequential student missing simultaneously simultaneously infinite infinite remaining easy predictive select yield squares squares squares learner evaluated evaluate fraction fraction fraction sizes key epochs measurements measurements measurements measurements measurements measurements measurements measurements filtering includes includes includes instances domains domains domains absolute tests tests tests tests tests tests tests determining straightforward sensor identified extra extra extra extra extra extra extra extra uniformly effectively identify identity ten ten ten ten fine fine capture summary traditional road road interested stopping stopping split sampled michael generalize generalize thresholds moves receive presents presents presents presents trains minimized employed simpler simpler simpler american overfitting accurately accurately accurately game preliminary history school applicable applicable applicable applicable scaled working comparable proper symbolic statistically statistically attributes closest man analyze predicting predicting predicts rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank mapped epoch detected submitted preference scenes developing developing navigation navigation improves improves improves expensive comparisons drive sections shared shared shared easier easier broad immediately pool separately members begin medical medical medical medical medical medical medical medical nsf nsf mellon requiring questions improvements carnegie collected cmu cmu pseudo tional quantitative autonomous autonomous autonomous car peaks backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop backprop detecting passed treated treated treated compares passes passes passes passes passes pittsburgh fall fall prevent singer adjust age patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients patients hints hints lab lab lab lab lab lab lab benefit benefit benefit secondary identifying identifying identifying identifying sort sort sort sort sort sort sort sort sort sort cooper cooper arguments driving driving recover databases count outcome outcome intelligent vehicle vehicle vehicle vehicle methodology reliably financial financial excellent patient patient patient patient patient patient patient patient patient patient patient entry entry lang competing ranking ranking ranking ranking ranking ranking ranking ranking treatment treatment treatment treatment ahead late rich inductive davis assigns counts fusion metrics pressure blood blood mostafa outperform outperform fellowship solves ties ties ties break break benefits legal diverse die die die die die die die poses year conjecture comparative ideally stands home care care care robots baluja baluja baluja baluja baluja baluja graduate labs labs mitchell mitchell mitchell mitchell mitchell challenging maximally acquired player records tied nonetheless mea rarely achievable sorting tom aid suffices stripes stripes broadly medicine medicine agency assessment assessment assessment assessment admission arpa quantitatively fair sis approached investment mul ically prescribed health health deciding sex walking markets caruana caruana caruana caruana caruana caruana caruana reviews opportunity visits simmons lived lived lived lived collect dissimilar offline multitask multitask multitask multitask multitask multitask multitask multitask multitask multitask aggressive sorts sorts sorts sorts insure brings pitt live live live news predicate ranks ranks ranks ranks ranks ranks ranks ranks ranks ranks ranks ranks ranks safely safely interna diseases sse sse sse sse sse sse sse sse sse sse sse sse sse backpropaga death death death utgoff discriminated alternates admit cording loth symptoms prespecified ern ern hsu smm died died died died died died died holden shumeet backpropagating duces outdoor elevated halt halt halt halt lives hospital hospital unused halting greg cha diagnosed surements keys acceptably performer lowers illness illness unusually admitted admitted diffi dies prescribes asks warranted excel unfor confound 
#@Baluja_S,Caruana_R,Mitchell_T,
#t9
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#*network network network network network network network network network network network learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data data function function function function function function function figure figure figure time time time time set set set set set set set set set set networks networks networks training training training algorithm output number number error state state results results results information information information information information information problem models models models models models models models models models models models models models models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case vector vector shown shown systems systems values values values values values values values values noise noise noise noise unit method approach processing control control large rate rate test test test test test analysis analysis analysis class form form form signal simple paper paper paper examples small feature net net net net net net work task task cells step classification process trained trained cell cell structure random similar similar show section section general generalization parameter real real approximation approximation average average average theory theory gradient term term result result variables computation research research defined defined table table table table table table estimate estimate estimate estimate standard prediction presented presented low range press learn components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample sample abstract back references component stochastic positive positive introduction introduction complex estimation estimation effect variance complexity assume measure signals representations higher bound good good long long long long long long long long long long long long represent tree expected expected expected expected expected expected expected expected correlation correlation correlation correlation errors resulting resulting resulting total total regression multi multi multi multi sum means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor natural natural global negative negative relative relative specific specific compared desired cross series active determined equal equal equal equal power power power approaches approaches mit larger larger larger train train descent source modeling modeling selection selection selection selection selection selection selection morgan report institute department implementation consists consists consists advances scheme ai ai ai framework cambridge hinton estimates san top full requires choice choice choice choice statistics free free world world world estimated estimated basic pages pages increase validation validation validation validation randomly developed finally finally selected selected backpropagation nature achieved achieved achieved measured technical technical technical feedforward feedforward feedforward feedforward increases group tested fast assumption assumption predictions predictions predictions predictions predictions amount short short short short short short short short short short short short assumed assumed assumed assumed role main journal journal journal ability ability ability future future future future future degree makes rumelhart rumelhart kaufmann objective objective simulated combination account unknown unknown fully fully interesting testing ratio ratio ratio increasing consistent mode leads principal principal numbers direct window bottom magnitude combined minimize minimize run added added sources sources predict predict predict predict predict predict denotes improved discussed directions correlations correlations movement reported practical practical strategy strategy strategy strategy strategy include period period side quadratic quadratic trees subset varying compare observations calculated volume volume works works works tuning studies positions positions positions generalized williams risk risk risk risk risk risk risk risk risk constructed constructed constructed derivative predicted predicted predicted predicted move white setting demonstrate editors editors performs moody propose largest reduction characteristics characteristics sigmoidal regularization regularization turn turn movements relationship relationship manner manner identification base denoted construct construct construct construct construct construct construct index index factors factors factors factors factors factors factors factors factors pruning pruning metric multilayer multilayer multilayer coordinates interaction adding events predictive predictive predictive predictive select john family family independently squares viewed controlled suggested translation past purpose construction construction construction construction recorded recorded figures sciences specifically specifically specifically black major reason regular aspects identified divided included literature build composed traditional anderson anderson stopping superior return return return return return return return return return return return return return return return return return return return strategies built built built simplified play extract jacobs jacobs tesauro cowan minimized employed powerful wiley put replaced replaced hall hall existence mappings referred referred comparable fundamental fundamental attributes predicting predicting equally friedman assumes consist explain attempts defines advanced costs costs costs costs improves capabilities benchmark benchmark benchmark tool tool starts berkeley forces constructing constructing commonly mathematics potentially separately universal universal beginning beginning beginning annual raw robustness explained evaluating limits substantially substantially substantially ity price price price price price spread spread proven incorporating returns returns returns returns returns returns returns returns returns returns returns returns returns returns returns returns returns wesley extreme extreme extreme cumulative realized realized realized consistently uncorrelated leen addison ratios controlling ments breiman breiman breiman tools overcome alpha attractive determination imposed grow krogh effectiveness hertz hertz alspector utilized utilized prentice financial mance ranging predictors sides bad enhance sim captured originally exposure exposure exposure exposure exposure exposure exposure exposure approximators francisco foundations insight record bagging impact captures santa ignore generalizing balanced insensitive insensitive insensitive insensitive stone market market market market market market market market market market market market market consecutive maintaining street appeared email stock stock stock stock stock stock stock stock stock stock stock propagating year utilize comparative ease affects options pub levin levin levin levin levin levin levin levin gained management management management chapman ization met eliminating records hornik hornik monitoring discusses book behave port bill bill bill round completed spite persistent portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio palmer opti sees interior excess excess monitor continued attempting imple hull hull outperformed realizations exposed month month month month month month month month month month sided capital capital losses stocks stocks stocks stocks stocks neutral neutral neutral neutral neutral neutral neutral permanent restrictive differentiate approached transaction transaction transaction transaction investment investment investment investment allocating capturing huge replicate rolling elaborate security security security security security security security security security security security security security security security security security security security levy levy levy accu monthly monthly monthly extremes extremes extremes extremes investor favorable quarter translating impressive consensus earning historical historical historical historical wishes french french live volatility shortcomings olshen charac cybenko cybenko premise informal neurocomputing neur stinchcombe superpositions optimizer optimizer till assets modem equity equity benchmarking reprinted intercept companies serf invested finance exposures exposures exposures exposures exposures exposures deemed loadings sophistication explanatory explanatory explanatory woo proxy rosenreid rosenreid unexplained ulated dat swings universe universe universe universe teristics ctive realistically ffl ucb trip fective 
#@Levin_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number system system error error state state state state state state state state state results results results results results results results results results results results units units units units units units units units information information problem problem problem problem problem problem problem problem hidden hidden hidden performance performance performance based based based weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case order order order order shown shown systems systems values values values values values values values functions unit method method method approach approach approach approach approach approach approach approach approach approach point point control control control control large test test test test test test test test optimal optimal optimal optimal inputs inputs inputs inputs shows shows shows signal algorithms algorithms paper paper paper paper paper paper paper paper examples small small size net net net work work work work task task task task task task task task methods methods fig fig fig fig fig features level current trained trained structure problems random random memory response architecture architecture architecture show section fixed line real real real real real real real real average average average average average average obtained obtained obtained obtained obtained note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments threshold threshold computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research research research research research research research research research independent found found found target initial initial table table table table standard standard computer computer terms connections synaptic synaptic left direction direction presented presented present low nodes maximum maximum maximum range press outputs outputs outputs outputs outputs outputs outputs abstract find references due ieee procedure decision introduction complex complex complex hand hand dynamic generated generated generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search difference difference difference lower chosen chosen higher previous previous cases cases cases cases cases cases type required required required required required required required required good good binary binary represent techniques proposed proposed errors errors tasks total total total total total total total simulation simulation simulation simulation simulation computed performed performed performed times times means factor factor factor optimization optimization optimization optimization optimization made global applications applications vol artificial relative specific samples compared compared application application application application application application application desired cross cross cross provide active active determined experimental goal constraints constraints constraints constraints connected approaches approaches approaches steps accuracy comparison comparison connection connection support support proceedings proceedings proceedings proceedings implementation implementation implementation implementation implementation individual represents connectionist connectionist final scheme scheme scheme ai considered computing equivalent experiment solutions solutions solutions solutions solutions solutions limit stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage conference conference capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine determine approximate approximate approximate approximate speed speed basic increase give give produce produce weighted clustering developed area controller controller path path path path path path path path path provided finally selected selected selected iteration depends constraint constraint constraint constraint constraint achieved achieved measured discussion feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward increases tested tested tested fast fast close complete amount amount nearest implemented generate require eds adaptation adaptation journal square ability instance instance future easily development development objective simulated hopfield hopfield combination technology technology programming programming programming programming programming programming programming interesting testing ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio mechanism consistent mode mode operation operation operation representing representing representing representing numbers iterations iterations iterations pre direct direct making making international international international idea combined combined combined combined combined minimize description perceptron perceptron perceptron perceptron denotes denotes architectures architectures architectures architectures pair typical reported reported reported practical practical introduced subject highly highly teacher teacher approximately calculated works module axis axis solve solve solve solve achieve improvement increased occur digital digital digital digital digital alternative move hardware starting reduce conclusions designed clear performs manner question question question optical optical optical describes label tuned changing implement physical physical physical transformations develop formed quality quality select solved evaluated operations operations fraction fraction completely completely suggested earlier reasonable calculation slow classical reduces generation valid initially initially assigned assigned topology transactions degrees inter inter instances instances instances maximize candidate partially partially major major efficiency efficiency paths paths paths paths paths paths paths paths paths road refer graphs heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic link link link link link link link link link link link link link link link link link link link link link link link link link link link link link link link satisfy satisfy vary dot providing leading thresholds thresholds thresholds automatically consisted consisted consisted moves satisfies acknowledgments software situations presents employed collection steady steady steady steady steady steady steady steady steady preliminary preliminary fashion giving links links links links links links links links project investigated investigated investigated gates gates stream stream workshop hierarchy hierarchy removed transmission transmission integer integer integer integer integer integer traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic extremely greedy explored perceptton perceptton perceptton perceptton switching extent arbitrarily arbitrarily serial seconds massachusetts percentage advanced developing crucial failure benchmark correction correction handle handle starts comparisons rapid sections sections closer closer producing precisely controls laboratories laboratories laboratories cut bandwidth bandwidth bandwidth bandwidth summation virtual virtual virtual virtual virtual virtual virtual improvements empirically generic simulate passed passed employ dots execution switch switch switch switch reaches serve qualitatively suited logical calls calls wesley initialization addison investigation connecting lost lost inspired communications allocation allocation allocation chance minutes adjusting occurred overcome overcome overcome city city check hit removing removing north synchronous synchronous synchronous responsible optimally degradation hours heuristics continue alspector utilized programs connect connect connect iteratively respective schwartz lawrence multiplied iterated storing erlbaum exploiting subsequently subsequently adopted switches switches switches switches mind usage achieving encouraging centre solely individuals individuals possibilities possibilities australia australia australia australia streams quantized toy management management management management blocking degraded degraded degraded degraded degraded degraded allocated allocated allocated allocated considers exceed mask mask mask mask mask mask mask mask drawback associates setup refinement simplex simplex thousands dsp amplification amplification amplification amplification corrections failures capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities capacities satisfaction satisfaction satisfaction satisfaction restoration achievable consuming demand demand demand demand demand decided continued australian australian impractical crude heavily heavily jersey firstly suffers attempting optimisation substitute substitute discarded seed periphery colleagues destination america denmark amplified teaching demands demands demands creation feasibility thing thing kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk bear inaccurate allocating allocating replicate gradual amsterdam predefined occasionally campbell campbell campbell campbell campbell campbell campbell campbell campbell transferred continuing tighter whilst repeats icann offered offered multiplications damaged acknowledged acknowledged kim initialised initialised initialised preset violation violation violation utilization taught highlight expands telecommunications telecommunications telecommunications telecommunications telecommunications reconfigurable reconfigurable throughput throughput throughput throughput throughput throughput throughput throughput throughput throughput throughput throughput permission permission copenhagen violations violations violations violations violations violations violations violations violations violations violations violations concentrates congress additions reformulated referring readings planned sparcstation sparcstation persist fibres dale dale dale dale dale trl trl trl trl rounded rounded deficiencies telecommunication virtues publish publish hungry clayton enforcement telephony itc managing managing blackburn brighton vic seminar director director europe 
#@Campbell_P,Dale_M,Ferra_H,Kowalczyk_A,
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#*network network network network network network network network network network network learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data function figure figure figure figure time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm output output output number number number number number number number number number number number system system system system system error results results results results results results results results units units units units information information information hidden hidden performance performance performance performance performance performance performance performance based based based based linear linear linear linear linear linear linear linear linear layer layer layer layer layer order order shown shown systems values probability probability neurons neurons unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image single single single single single single single single single single single single processing processing processing processing control large large local rate rate rate rate test patterns patterns analysis analysis class class class class class class class class class class class class class inputs inputs form signal algorithms algorithms paper small size size size size size size size size size work methods methods classification classification classification classification classification classification classification classification classification classification classification level current current trained trained high high high high high high high high high high similar similar similar architecture architecture architecture architecture line images images images images images images images images images images images images images images images parameter real real real real average average obtained obtained term experiments experiments experiments experiments experiments dimensional dimensional university university computation computation defined found found target target target initial table table table table computer distance node node node node node science science direction activation activation low nodes nodes nodes nodes nodes frequency sets maximum range press abstract applied back back computational computational references references references due due ieee positive important adaptive adaptive propagation propagation introduction hand effect parallel cost cost search difference variable spatial spatial spatial assume classifier classifier chosen higher higher higher part part part cases type required multiple multiple multiple multiple multiple multiple multiple good long conditions represent represent distributed distributed expected equations chip chip make techniques techniques length length forward scale minimum classes classes ing ing ing multi times times means orientation knowledge artificial artificial artificial artificial artificial artificial compared compared application rates rates rates rates rates rates rates rates rates rates location location location experimental connected distributions equal approaches approaches mit support train descent dependent nets morgan department implementation implementation implementation consists individual individual individual difficult addition considered domain equivalent curve design bit bit bit bit bit bit bit bit bit bit bit classifiers requires requires choice speed speed speed speed speed speed speed speed speed pages give randomly randomly clustering developed developed levels levels levels levels types types types selected selected nature nature achieved achieved increases arbitrary denote transformation fast limited amount short implemented shape shape shape shape shape shape journal journal square vlsi vlsi pixel pixel pixel pixel pixel pixel pixel pixel pixel cluster cluster rumelhart fully transfer significantly increasing structures matching matching matching matching matching matching matching matching matching matching matching matching matching mode operation bits bits frame description light light light light light denotes denotes resolution advantage takes reported reported introduced include pixels pixels pixels pixels pixels pixels engineering highly highly highly previously previously approximately approximately approximately volume volume achieve evaluation locations sensitive constructed intensity lead lead scaling wide feed clusters clusters column hardware hardware hardware hardware hardware hardware hardware conclusions valued valued reward faster faster faster constrained sigmoidal sigmoidal demonstrated proportional proportional variety variety min averaged averaged averaged averaged groups identification identification acknowledgements reference reference reference reference reference reference reference reference construct produces ann dept changing sensitivity averaging averaging electrical electrical develop formed extraction letters yield yield extracted correlated evaluate operations operations restricted approximations sizes processor processor reasonable combining penalty generation generation filtering construction construction construction advantages advantages transactions david recorded template template template template template template template template template template template template template template template template template template template template template template silicon thesis strings contour coupled determining efficiency capable capable capable society successful identify detect schemes plots procedures success classify classify device device highest leading attempt camera camera employed access hall behaviour rise reducing respond giving giving investigated investigated investigated investigated possibility authors reliable reliable structured root comparable comparable stream stream variability cognition closest implementations implementations taylor logic logic store phd electronic charge devices devices devices histogram site site site crucial benchmark sys easier producing preprocessing constructing angles lowest demonstrates apparent collected collected profile profile profile profile profile led passed templates templates templates templates templates templates templates templates templates templates passes hamming semi semi semi semi semi semi semi semi median univ univ univ univ univ trade addresses tem eliminate grey grey grey grey grey royal exemplar air air imaging north performances prentice financial heavy ranging paul paul paul holland uni spherical offers diameter eng offer offer offer refers environmental steepest extensively card considerations speeds speeds intersection avoiding explorations ccd multiply anns anns tables ram sigma sigma sigma profiles profiles profiles profiles acceptable reflected eric remainder gained thick grouped march overhead host exceed exceed termed cation monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring monitoring inversely electronics particle particle particle particle particle particle particle particle particle particle particle particle particle particle particle particle particle particle microscopic demonstrating cube beam beam beam beam stephen suffers micro powers powers optimisation resolutions resolutions laser laser laser laser laser laser judged accumulate accumulate neighbourhood optics drastically centres feasibility zeros scatter mul mul ensuring scattered scattered syst indexing particles particles particles particles particles particles particles custom intrinsically aims disadvantages plausibility minimise tailored theo multiplications registration versity notably implementable concentrations draws initialised volumes steepness centred banks accumulating enormous neighbouring epsrc crystals classifi chamber exceptions spheres cheaper cumbersome scalable scattering scattering scattering scattering scattering scattering scattering scattering scattering constrains subunits subunits kevin kevin photon fibres fibres quantisation quantisation tiple tiple immune offering realisation pipelined instrument instrument incurs brunel airborne airborne airborne airborne airborne airborne airborne airborne traverse quantised subunit subunit subunit utilised suppl inexact attributable alu edwin summarise 
#@Bolouri_H,Dixon_L,Ferguson_A,Kaye_P,Sabisch._T,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data function function function figure figure figure figure figure figure figure figure figure figure time time time time set networks training training training training training training training training training training output output output output number system system system system error error state state state state state state state state state state state state state state state state state state state state results results results units units units units units units information information information problem problem problem problem models hidden performance based based based based based based based based space space space space space space space space space space space space space space space space space space space space space case vector vector vector vector vector vector order order shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems values noise noise noise weight weight unit unit unit approach approach approach approach approach approach approach approach approach approach point point point point point image image image image image image single single control control control control control large local local local local local local test test test patterns patterns analysis matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs shows shows shows shows shows gaussian paper paper small feature task task task task task task task task task task task task task task task task task task task task task task task task task fig fig fig points points points points field field process level level level level level level level level level level level level current current trained structure structure structure structure structure problems problems problems problems memory memory representation representation representation representation representation architecture architecture architecture architecture section section fixed fixed images images real states states obtained obtained obtained obtained term experiments experiments experiments dimensional dimensional dimensional result independent found found sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial constant computer terms science science direction direction presented map map map map map map map map activation nodes temporal maximum maximum range range range range range range range range range range range range range range range range range range press learn learn position position position position outputs outputs continuous abstract applied applied back back find computational convergence convergence convergence references ieee ieee procedure important adaptive decision propagation propagation context context context context context context context context introduction action action action action action action action hand hand behavior behavior generated generated parallel recurrent recurrent recurrent tion spatial assume lower representations learned learned part required required binary long conditions represent distributed correct forward forward ing ing tasks tasks tasks tasks tasks total simulation multi called mapping mapping means reinforcement dimension global global global global global global global global study study knowledge filter obtain obtain original vol vol vol vol vol vol artificial specific represented true true desired desired desired desired desired desired desired desired desired desired provide define proc proc experimental goal goal goal goal goal motor motor motor motor motor motor motor motor motor mit modeling implementation technique consists internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal difficult scheme graph graph sequences sequences sequences sequences sequences sequences maps maps considered framework equivalent experiment experiment environment environment environment environment environment environment environment environment environment hinton view limit limit limit trajectory detection determine determine requires free world con condition developed robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels controller types types actual finally selected selected biological measured discussion describe describe describe arbitrary arbitrary stable finding effective assumed generate generate generate adaptation square degree rumelhart rumelhart rumelhart noisy noisy sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory objective objective objective objective dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical transfer interesting interesting mechanism special matching leads pre supervised idea denotes discussed directions robust robust takes typical strategy period sense sense cognitive highly observations solve smooth correspond converge converge trans trans address positions positions locations locations locations williams exists correctly feed loop loop loop loop loop loop loop loop loop white column setting flow starting starting assumptions trajectories trajectories trajectories trajectories trajectories peak peak learns learns mechanisms integration largest cycle cycle cycle intelligence labeled assuming attractor attractor attractor attractor attractor attractor explicit appears appears winner winner winner sequential laboratory stability coordinates physical unique consisting consisting consisting applying agent cycles focus focus formation depending depending communication detailed open organizing organizing fraction showed showed centered forms completely processor past past calculation smoothing purpose iterative initially sufficiently kohonen kohonen kohonen kohonen kohonen kohonen views coupling coupling coupling coupling coupling building exploration activations coordinate formulation formulation formulation inter inter memories determines discuss activated coupled black characterized structural determining sensor sensor sensor encoded encoded driven identify detect build schemes receives receives summary conf issue follow sampled minimizes quantization ill ill moves moves moves illustrates routing routing routing routing intrinsic situations bars employed employed employed remain command command command command command command command layered access environments examine investigated int workshop fundamental examined trace trace adapt man changed front bifurcation noted panel generates arbitrarily arbitrarily established rows ment directed directed directed trivial unstable navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation adapted perspective perspective lin lin lin lin sys arc organized organized organized arises cybernetics cybernetics qualitative behaviors composite profile profile profile profile profile profile profile profile elman elman elman embedded embedded embedded conducted fed leave lattice lattice lattice lattice autonomous autonomous autonomous autonomous autonomous completion employ formulated formulated formulated frequently commands commands perturbations branch branch branch branch reaches achieves achieves attraction coherence coherence coherence converged converged aligned sensing sort japan angular recover branches mobile mobile mobile mobile mobile tem robotics lost chance ranges proceeds moment moment mark fail reasoning adequate adequate adequate adequate exceeds obstacle obstacle repeat embedding embedding embedding embedding started contexts recovered representational ambiguity ambiguity encountered decide topological topological topological branching branching branching branching branching branching branching branching branching branching branching branching branching branching repeatedly environmental environmental environmental environmental receiving adopted adopted fusion ccd learnable learnable learnable learnable verify ure land compressed compressed compressed workspace workspace workspace workspace workspace achieving basin covering markovian emerge uniquely uniquely solely chicago adapting preserved evolve robots robots robots goals guidance mitchell mitchell mitchell mitchell surrounding discusses maintains responding sta macroscopic milliseconds nil nil nil travel exploratory rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn failures aaai stops utilizing emphasis ble acquire firstly focuses focuses suffices flows exposed automation laser laser laser tokyo vertically teaching resultant positioning skill routes routes routes robustly cyclic cyclic cyclic cyclic platform polar landmark landmark landmark tal collision erroneous internally decides accessible claims topologically supervision environ bptt associating taught cameras beer beer beer susceptible landmarks identifiable equipped attain havior finder structurally structurally pertinent depended autonomously experimen topographically cycling cycling cycling cycling readings readings analogical embed situated sider acquires navigational navigational navigational conventionally travels travels travels travels guides assured vironment conjectured rigidly grad staying directs expecting fluence spective sony arisen navigates navigates ually navi gular 
#@Fukumura_N,Tani_J,
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#*learning learning learning neural function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number system error error error error error error error state state state problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance performance based based based based based space space space space space linear linear linear linear case case vector vector vector vector vector order shown shown systems systems systems values parameters functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution method method method processing control control control control control control control control control control control control control local rate matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows shows shows simple paper paper paper paper work work methods cells step step step step step field field process current current cell cell cell problems equation line vectors parameter real approximation approximation approximation approximation approximation approximation approximation approximation average states states gradient gradient gradient gradient gradient gradient gradient gradient note note dimensional university university threshold variables variables computation computation solution solution solution solution solution independent independent log defined defined defined defined defined sequence initial initial initial initial initial initial initial initial estimate computer computer terms distance distance distance distance distance distance distance distance distance distance distance distance node node node node node node node science science left presented presented presented nodes nodes nodes nodes nodes motion motion motion motion motion motion motion motion motion range range nonlinear abstract convergence convergence convergence properties properties properties references component component component due ieee ieee ieee positive procedure procedure context introduction circuit circuit circuit circuit circuit circuit circuit circuit generated generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel search tion tion tion tion tion change change change energy complexity assume assume chosen chosen higher part theorem theorem represent represent represent equations fact fact proposed proposed proposed proposed proposed probabilities probabilities minimum resulting resulting resulting ing total computed respect respect sum elements elements elements elements reinforcement reinforcement optimization optimization optimization optimization optimization potential potential potential potential dimension dimension dimension dimension feedback applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy original artificial represented represented represented application series define define compute compute compute compute compute compute proc proc determined determined determined goal goal goal goal goal goal goal goal goal constraints constraints constraints constraints connected distributions discrete discrete voltage voltage voltage voltage voltage voltage voltage voltage steps steps steps steps fields update descent morgan report report department implementation implementation consists consists advances joint joint final final final final addition considered framework computing domain domain domain domain domain domain domain domain domain domain domain equivalent equivalent equivalent equivalent equivalent equivalent environment solutions san effects effects efficient requires world pages pages pages condition condition derived derived derived derived derived robot robot robot robot robot robot robot robot robot robot bounds velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller path path path iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration nature achieved measured discussion technical arbitrary fast assumption assumption assumption assumption assumption complete actions actions actions circuits implemented assumed assumed assumed assumed assumed supported require require adaptation journal instance kaufmann smaller smaller underlying technology york uniform iterations iterations iterations direct making decay idea combined minimize sources sources denotes architectures architectures architectures architectures architectures exact takes element element sense subset interest interest dimensions volume tuning tions tions solve smooth smooth smooth smooth smooth yields evaluation grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid improvement exists horizontal locally locally locally locally boundary boundary boundary conclusion reduce numerical propose demonstrated demonstrated proportional minimizing user user user user minima configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration question reference reference reference reference relation construct construct index index index index index index index factors primary sequential generating generating plot plot describes describes distinct distinct dept changing changing changing changing infinite dimensionality involves involves involves angle applying minimization minimization minimization agent implies potentials potentials potentials expressed expressed expressed detailed open evaluate evaluate key calculation calculation barto spaces sec combining combining neighborhood neighborhood neighborhood neighborhood closed intermediate initially initially initially construction existing exploration maximize specifically neighbors neighbors planning planning columns determining capable suitable suitable paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths driven efficiently situation essentially composed notice notice conf conf prob link interested conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance return criteria relaxation minimizes minimizes minimizes minimizes moves policies policies policies policies policies policies illustrates mixing approximating neighboring oriented minimized simpler command singh singh singh singh exponentially relations integral scalar scalar reducing tech incremental int int complicated affect affect removed hill coefficient configurations configurations illustrate equally adjusted versions versions formal generates defines defines seconds established established massachusetts massachusetts residual rows stop cos cos publishers derivation derivation derivation derivation derivation derivation derivation navigation navigation navigation strictly constructing mation depicted depicted nsf explained requiring lattice lattice lattice lattice lattice lattice lattice resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive controllers controllers controllers controllers controllers controllers controllers controllers synthesis synthesis synthesis measuring maximizes maximizes maximizes cal conductances conductances conductances conductances conductances conductances conductances conductances conductances conductances conductances conductances conductances conductances conductances adjust age shaped simultaneous cor globally indices indices primarily primarily optimality equivalence equivalence guarantee optimizing homogeneous homogeneous homogeneous harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic addresses robotics robotics robotics intelligent vehicle transforms affected affected responsible responsible obstacle obstacle obstacle obstacle obstacle obstacle mance negligible perfor guarantees advance francisco repeatedly grants characterization tures pen adopted adopted adopted lem informa leaving solves validity formulate obstacles axe axe incrementally tradeoff amherst simd simd affects breaking workstation conservative equality preserved preserved resistor realizable dominated proba simplifying depicts depicts ultimately cosine dirichlet iri iri manipulator meet admissible avoidance avoidance avoidance tune port travel travel travel travel travel travel travel travel travel travel travel travel computa simplifies behaves laws neumann simplification discretized tial neighborhoods imple establishes clarity affecting pronounced usefulness devised impedance architec normalize grids grids safe robotic constraining confined rel mcgraw south locality locality appro ensuring ized unnecessary completeness applica applica unaffected sparc incurred demanding intrinsically collision collision collision collision optimizes ogi ogi ogi modifies mentation topologically solu absorbing poten ire provably originating geometrically gra travelling del volt safety safety rect resembling havior resistances implementa bilities opera nical dient subjected rewarded collisions kuh displacements speedups ccr ili sociated fro tionally ruled din cknowle dgement chua chua chua chua laborious highway automat automat diate evant commanded vmues vmues posit kirchhoff bust interme approzimation warranted lfi promoted 
#@Coelho_J,Grupen_R,Sitaramen_R,
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#*learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input input input data data data data data data data data function function function figure figure figure time time time time time set set set set set set set set networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number number number number number system error error state state state state state state state state state state state state state state state state state results results information problem problem problem problem problem problem models models models models models models models hidden hidden hidden hidden hidden hidden performance performance space space space space space space space space space space space space space space space space space linear linear linear layer case case vector vector vector shown shown systems values values values values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise weight functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution method method method method approach approach approach approach point point point processing control control control large large local local local test test test class matrix matrix inputs form form form form form form form shows gaussian gaussian gaussian gaussian paper small small small small size feature feature task task methods fig fig step step step step step step points points points points features level level current current current trained trained random architecture architecture architecture architecture architecture architecture show show show section section section section section fixed line vectors vectors vectors general general general parameter parameter parameter parameter parameter real approximation average states states states states states states states states states states gradient gradient gradient obtained obtained obtained term dimensional variables computation solution solution independent log defined found found found sequence sequence dynamics initial initial initial initial constant constant table table estimate estimate estimate estimate estimate standard standard standard computer computer terms connections science prediction prediction prediction prediction prediction direction presented present present nodes temporal sets motion motion motion motion motion maximum range range press learn learn learn position position position position position position position position components components components components outputs continuous continuous continuous abstract find computational convergence convergence density properties properties properties likelihood likelihood likelihood likelihood references due ieee ieee positive positive important adaptive decision mixture mixture mixture introduction introduction estimation estimation estimation estimation statistical dynamic variance complexity complexity variable variable variable variable spatial assume assume measure prior prior prior chosen part previous cases cases required good represent represent represent expected markov markov markov markov markov markov markov markov markov markov length correct correct probabilities probabilities probabilities probabilities observed observed errors forward forward forward forward simulations simulations simulations resulting tasks tasks tasks tasks simulation simulation computed performed performed called called dimension dimension made made made applications knowledge knowledge knowledge knowledge em em em em em em em em em relative relative specific represented represented true true true compute objects objects objects objects objects objects objects determined goal goal goal goal posterior posterior constraints constraints connected discrete discrete brain equal approaches approaches mit mit mit mit accuracy accuracy update dependent report implementation version technique represents exp exp graph graph graph graph graph graph graph graph graph sequences ai maps considered cambridge cambridge cambridge cambridge domain domain domain equivalent equivalent environment environment environment hinton estimates estimates estimates estimates transition transition transition transition transition transition transition transition stage stage stage upper requires requires requires free free free free speed estimated estimated increase give produce produce produce weighted randomly conditional robot robot robot levels velocity velocity velocity velocity velocity actual selected iteration depends depends sampling achieved measured discussion technical denote tested hmm hmm hmm assumption complete surface surface surface common effective implemented shape role role main main eds face journal square future future easily noisy noisy noisy noisy simulated account unknown coefficients jordan jordan jordan jordan jordan jordan jordan jordan technology technology significantly increasing uniform uniform uniform uniform uniform uniform leads representing representing call direct experts experts experts experts experts experts experts experts experts idea combined run run added light predict predict improved discussed exact ensemble ensemble ensemble movement movement movement movement movement movement movement movement movement movement movement practical introduced cognitive cognitive relevant engineering highly observations observations observations solve correspond achieve trans mixtures mixtures mixtures mixtures mixtures mixtures positions positions positions chain symmetric generalized bounded arm arm scaling occur extended predicted predicted correctly move touretzky deterministic occurs generally setting starting starting reduce reduce trajectories trajectories trajectories depend taking hard presence assuming assuming relationship relationship connectivity configuration configuration configuration configuration force force appears derive solving sequential estimating transitions transitions transitions dept dept dept modeled implement implement explicitly explicitly explicitly physical physical physical physical physical physical physical physical electrical dimensionality easy unique consisting expectation versus decreases expressed dependence stages squares squares estimator estimator viewed viewed solved controlled controlled restricted updated evolution static partition partition additive performing measurements measurements measurements measurements measurements measurements measurements reduces combining purpose closed closed closed topology transactions degrees degrees thesis coordinate coordinate perceptrons batch sciences uncertainty uncertainty uncertainty coupled holds gating gating gating planning columns aspects aspects hmms society modification included successful efficiently fine fine fine fine fine graphs criteria sci involved michael play absence backward backward computes maximization maximization maximization maximization jacobs jacobs neighboring deal tesauro presents remain create difficulty difficulty recursive issues mse mse analytically root maximizing gates affect surfaces surfaces surfaces measurement measurement measurement integer configurations man predicting ensure quantities freedom freedom shapes initialized phd finds piecewise defining nowlan adapted comparisons sys bengio bengio consequence computers depicted geometry cybernetics incomplete meaning geometric composite applies variant maxima proven serve datasets replace softmax softmax softmax trade initialization consistently sensing leen restriction linearity velocities velocities velocities velocities velocities velocities velocities perfectly impossible grows royal robotics plays dealing significance imposed keeping affected corner generalizes planar moments introduces dependency ascent ascent ascent vertices propagated assembly assembly eng contact contact contact contact contact contact contact contact contact contact contact contact contact contact contact ends statement dempster dempster outperforms approx emission appeared arcs arcs geometrical geometrical geometrical rubin misclassification bank additionally aij aij aij aij ideally manipulation manipulation tems picked depicts surrounding complementary laird manipulator manipulator indexed associates discusses maintains discretization accounted happen admissible parametrized parametrized mea mea rarely rabiner rabiner argmax ble quadrant frasconi frasconi evolved juang juang exploits sliding implied assp confined confined rel fair magazine positioning locality elec nominal nominal nominal nominal nominal bear inaccurate neglected inst inst rotational linearities unobserved damping tolerant argmin entities proce sition subtasks imation tran mason mason ities rescaling psyche ily ulation grasping possi selector multiples unrealistic resort uncertainties decomposing lozano lozano checking jects lly dure relearning thereof friction friction meila meila meila meila meila perez perez pendence surements atively ere attach deprived neighbouts marina imprecise summa computability rected veloc surement 
#@Jordan_M,Meila_M,
#t9
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data function function function function function function function function function function function function function function function function function figure figure figure figure figure figure time time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error state state state state state state results results results results results results results results information information problem problem problem problem problem problem models models based based based based based based based based space space space space weights weights linear linear linear linear linear linear linear linear case case vector order order order order order shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values parameters parameters parameters parameters parameters functions unit method method method method method method method approach approach approach approach point point point point control control control control control control control control control control control control control control control control control control control control control control control control control control control control large patterns class class class class class class class matrix matrix inputs inputs form form form form form form form form shows algorithms gaussian gaussian gaussian paper paper paper paper small work work task methods methods step points points field field trained trained trained trained problems problems problems problems problems show show equation section section section section section section section section section section line line general general general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter gradient term result result result result result variables variables solution research defined initial initial initial initial initial constant estimate estimate estimate science science prediction presented present present phase sets sets sets nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous sample sample sample sample sample abstract find find find find find find find find find properties properties properties properties references due ieee ieee ieee ieee ieee positive positive positive positive positive positive procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic cost cost cost change difference complexity variable signals prior chosen chosen chosen chosen higher part part part part previous theorem theorem theorem theorem cases required conditions conditions conditions conditions conditions conditions conditions conditions equations make make techniques region proposed proposed proposed proposed proposed proposed proposed observed forward minimum resulting classes ing total total simulation simulation simulation simulation simulation eq eq eq eq eq eq eq eq eq eq elements elements optimization made made made feedback feedback filter filter obtain negative negative desired define determined determined determined goal goal goal goal goal constraints discrete equal power mit mit mit comparison train selection proceedings report report institute institute institute words words department department department represents responses responses difficult delay scheme addition considered cambridge cambridge equivalent environment solutions design design limit conference determine requires estimated estimated condition derived developed controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller types product actual achieved achieved achieved technical technical arbitrary denote denote tested assumption corresponds corresponds stable stable stable stable stable stable stable stable stable stable common assumed supported adaptation end rumelhart rumelhart objective simulated needed combination dynamical dynamical dynamical unknown unknown unknown unknown unknown jordan jordan technology technology programming testing testing significantly york mechanism structures operation leads leads max max max direct supervised idea minimize minimize choose choose choose choose denotes denotes denotes denotes denotes discussed discussed improve pair element typical apply introduced quadratic quadratic quadratic cognitive engineering engineering engineering engineering dimensions sufficient compare conventional teacher calculated yields converge converge differential address observation bounded bounded bounded grant constructed exists exists exists exists exists occur occur occur extended extended derivative derivative derivative matrices matrices loop loop loop loop loop loop loop loop loop loop loop loop occurs occurs generally assumptions assumptions assumptions assumptions assumptions trajectories trajectories depend propose presence presence external exist exist exist exist exist min min introduce derivatives identification identification denoted reference suppose suppose suppose relation construct written written index solving solving ways laboratory laboratory stability stability stability stability stability stability stability stability stability stability distinct linearly electrical springer formed implies decreases choosing choosing national focus focus expressed variation open open open open controlled centers centers completely completely converges converges past partial convex convex neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood penalty penalty tracking tracking closed closed closed closed closed closed closed closed closed closed closed closed closed valid filtering foundation classified transactions transactions transactions transactions figures figures includes includes plotted plotted discuss candidate determining closely composed composed refer compact compact compact compact compact verlag sin sin sin satisfy sampled minimizes leading predictor predictor operating satisfies acknowledgments origin origin origin origin origin origin origin origin origin origin origin origin origin remain parametric parametric requirements exhibit updating kalman kalman steady detail accurately hall hall scalar applicable applicable referred proper cover man illustrate ensure ensure adjusted quantities obvious arbitrarily submitted plant plant defines massachusetts massachusetts years asymptotically asymptotically asymptotically asymptotically inequality guaranteed unstable fairly analytical sections satisfied satisfied satisfied satisfied precisely choices scientific definite definite definite definite definite definite definite definite arises addressed limits posed continuously maintain controllers controllers controllers summarized adjust adjust differentiable differentiable differentiable lot realized newton guarantee approximates controlling establish establish establish ranges ranges adjusting contract monotonically imply adequate lyapunov lyapunov lyapunov lyapunov published prentice prentice loo respective respective surprising candidates ahead reader eqs statement tures mechanical mechanical mechanical bertsekas outline email email recursively ties levin levin realizable uncertain regulation march march confirmed scope scope distal unconstrained struc gauss completed november stops appearing interior interior ave ave ave ave ave neighborhoods cast disturbances possess measurable measurable meth scenarios linearized ods adapts vicinity stabilize stabilize stabilize stabilize carrying proceeding stabilization stabilization zone objectives objectives diverge stabilizing stabilizing stabilizing stabilizing stabilizing tracked dead nonlinearly nonlinearly nonlinearly ecs belmont narendra narendra narendra narendra narendra narendra stabilized stabilized stabilized thirty retains concluded expands compose tain resort uncertainties uncertainties uncertainties uncertainties uncertainties ner rameter linearization linearization pertinent pertinent athena regulated stably assures parthasarathy parthasarathy pertaining wished stringent bert goodwin goodwin goodwin 
#@Annaswamy_A,Yu_S,
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input input input data function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number system system system system system system system system system system system system system system system system system error state state state state state state state state state state state state state results results results results results results results results results results results results results results results results results units units units units units units units units units units units units information information information information information information information information problem problem problem problem problem problem problem problem problem models models hidden performance performance performance performance performance performance performance performance performance performance based space space space space space space linear case case order systems systems systems systems systems systems systems systems systems values values values values parameters unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution approach single processing control control control control control control control large large large large large rate rate rate rate patterns class class optimal optimal shows shows shows shows signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper small work methods level level level current current trained trained problems problems problems problems problems random random similar representation architecture architecture architecture show show parameter real real real real real real real real approximation average average average average average states states states states obtained obtained experiments university university university university university threshold computation computation computation computation research research research research independent defined defined defined defined found target dynamics constant table table table table table table table table estimate estimate estimate estimate computer computer computer science science left direction direction direction direction direction present present activation activation low low temporal temporal machine motion maximum range press learn learn learn learn learn components basis basis continuous continuous continuous continuous continuous continuous continuous abstract references stochastic due due due decision decision decision decision decision decision context introduction action action action action dynamic dynamic dynamic dynamic dynamic parallel parallel parallel parallel cost cost tion tion tion change difference difference variable variable variable variable assume measure prior learned part required required required required multiple good good binary binary long represent expected expected expected markov make techniques length scale scale finite simulations simulation human sum sum sum sum called times times times times times times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor factor optimization global global applications policy policy knowledge obtain artificial compared application application desired provide provide rates rates rates rates location perform constraints constraints discrete discrete discrete discrete discrete discrete discrete power approaches mit train proceedings report department department department version individual advances advances represents connectionist difficult difficult difficult bias addition addition cambridge domain domain domain environment directly additional additional estimates estimates top effects capacity determine efficient choice significant approximate approximate world speed speed estimated basic basic basic con produce randomly controller controller actual actual backpropagation nature depends depends depends constraint achieved measured technical feedforward describe group denote tested close complete actions actions actions actions actions actions actions actions amount amount amount amount amount amount nearest common assumed generate supported theoretical require require require eds eds future degree noisy including including including objective objective objective objective objective simulated simulated simulated simulated simulated needed needed combination unknown fully fully fully programming edge squared squared details call call stored bottom bottom experts experts decay minimize minimize minimize minimize minimize produced added added added architectures architectures architectures directions recent advantage typical practical practical moving moving moving include identical interest sufficient conventional conventional tions achieve achieve rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl positions observation interval interval grant parts parts occur occur move move move move touretzky touretzky occurs pass demonstrate trajectories conclusions conclusions valued valued sigmoid sutton peak peak peak peak peak peak peak peak peak exponential temperature suggest taking strong turn turn assuming min averaged program configuration force acknowledgements areas boltzmann explicit explicit appears longer ways ways ways describes describes changing modeled implement infinite infinite infinite events events events events events minimization agent agent agent select john yield solved open approximated approximated completely processor past barto barto barto barto classical spaces sec sec event event event penalty faces expect building building includes thesis thesis combinations combinations combinations activations inter inter mozer discussions gamma gamma computationally computationally effectively build situation online online online online receives traditional prob allowing allowing heuristic heuristic heuristic heuristic return vary play play generalize providing delayed observable observable highest highest highest highest cat attempt policies policies subsequent subsequent approximating load load load load load tesauro tesauro tesauro tesauro tesauro tesauro receive minimized employed explore unlike poor access investigate experience integral issues hall hall hall hall hall hall helpful examine school incremental possibility office encode naturally closest adapt traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic extremely extremely algo freedom improving improving improving improving utility utility phd phd attempts seconds seconds massachusetts massachusetts massachusetts massachusetts percentage stop stop stop stop stop stop tractable considerable considerable considerable sections day choices located controls watkins watkins scientific gradually incomplete varies people percent percent profile profile profile profile profile profile profile profile pure elman amounts car car car car car car car car car car car car car car car car car car car car car car car car share rewards maintain calculating operate controllers controllers controllers poisson poisson weigend suited achieves sums simulator simulator chose sophisticated expectations returns calls calls calls instantaneous person leen intractable pick acts controlling controlling homogeneous smolensky arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival air dealing difficulties primitive primitive responsible responsible generalizes days days hours hours hours continue continue date service entry negligible lengths branching discounted surprisingly master rich storing horizon horizon horizon erlbaum balancing balancing stopped stopped stopped stopped cam executed robert empty empty andrew informa appeared summer truncated ple ter discount discount discount tables encodes forced poses poses poses encouraging quasi profiles profiles amherst amherst amherst amherst assignments experiences workstation hillsdale forcing demon conservative avoids avoids backgammon backgammon backgammon visited visited queue queue queue queue queue queue queue queue exam rithms searches searches lookup integrals associates rod admissible bradtke bradtke bradtke priority priority intensive ignoring reciprocal travel travel mea spite spite bridge algorithmic sees ate prefer assistance agents agents agents agents agents agents agents agents agents agents agents hour floor floor floor floor floor floor floor floor floor floor floor floor floor floor floor floor floor floor floor push cooperation fastest arriving approaching elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator elevator longest longest longest lewis lewis fair teaching experienced enter sweep steve approached nonstationary nonstationary gammon gammon gammon indirectly focusing focusing promise objectives rein cars cars cars cars cars cars cars cars attracted upward upward lookahead ece teachers minute minute minute minute complications complications wait wait wait wait wait wait wait posi ele ele waiting waiting waiting waiting waiting waiting waiting waiting waiting waiting offiine pushed pushed vast challenges duff duff landing experimentation aware aware aware penalties penalties inadequate optimiza widespread namic sector sector sector sector sector accelerate story asynchronously dave reinforcements reinforcements reinforcements reinforcements arrivals arrivals arrivals arrivals arrivals mips mips specialize crites crites crites crites lesser probabilistically secs secs secs secs secs button button button button button knowl bet team team team team doors stochasticity kevin strate registered ered elapsed elapsed elapsed exhaustively sured dictates rounding obtainable victor subse exit pressed buildings communica complicates nonstationarity surpass surpass quent tes 
#@Barto_A,Crites_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number number number number number system system system system error error error state state state state state state state state state results results results results results results results results units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based based based based based based space space space space space space space space space weights weights weights weights layer layer layer layer shown values values parameters parameters parameters parameters parameters weight functions functions functions recognition recognition recognition recognition method method method method method approach approach approach approach approach point point single single single single single single single processing processing control test test test test test test test optimal optimal optimal form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian visual paper paper paper paper paper small feature feature feature net net net net work work work work work work task task task task task task task task task task task task task task task task task task task task task task task task methods methods methods methods methods methods methods methods step step features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features process process level level current current current current current current current current trained structure structure problems problems problems problems problems problems problems problems problems high high high high high representation representation architecture architecture architecture architecture architecture architecture architecture architecture show show show show show show show show show show fixed fixed fixed vectors speech speech speech average average average average average states states obtained obtained note experiments experiments result university computation solution solution solution solution solution solution research research research independent independent log defined defined found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial constant estimate estimate estimate standard standard computer terms terms distance science presented present low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine machine sets sets sets maximum learn learn learn learn learn learn learn learn learn position position position position position position abstract applied applied applied applied applied applied applied applied find find find find find find find references procedure important important introduction action action action action hand hand hand hand hand hand hand hand hand generated cost cost cost cost search search search search search search search tion change change change difference difference difference difference complexity classifier measure prior word learned learned learned learned higher center previous previous previous previous previous previous previous previous type type type type type required required required multiple good good good good good good make fact length length length length length forward scale scale minimum resulting resulting resulting resulting ing ing ing ing ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total total total total total total total total total computed computed computed sum performed performed performed performed called times times times times times times mapping means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor global global policy policy policy policy obtain negative negative artificial artificial true application application application provide define define define define define define compute compute compute compute perform perform perform perform perform perform determined goal goal goal goal constraints constraints constraints constraints connected connected equal approaches steps steps steps comparison comparison comparison update support support morgan report department technique consists code kernel kernel kernel final final final final final bias layers delay delay delay delay delay delay delay delay delay graph sequences domain domain directly directly hinton additional additional view view view solutions design capacity capacity capacity capacity capacity determine efficient efficient full requires requires free free estimated estimated estimated estimated pages pages validation validation validation validation validation give derived derived randomly developed developed path path path path provided backpropagation iteration constraint constraint simply increases describe group group complete complete actions actions finding finding amount amount amount short short effective effective generate main ability kaufmann simulated simulated simulated simulated simulated simulated simulated simulated typically combination fully block block block block block block block block block block block transfer testing testing testing significantly significantly significantly significantly details iterations max pre window attention combined combined minimize minimize minimize produced choose run run description predict improved discussed advantage advantage advantage separate ensemble practical apply apply apply apply apply engineering engineering engineering engineering works axis tions solve match match definition definition evaluation evaluation evaluation evaluation evaluation positions positions positions interval improvement entire grant constructed constructed constructed horizontal horizontal parts parts deviation deviation predicted predicted move move move move demonstrate runs starting starting starting critical critical critical critical place conclusions operator operator operator operator editors reward reward differences sutton sutton sutton sutton performs encoding taking sigmoidal turn start averaged program annealing annealing annealing annealing annealing annealing annealing denoted suppose monte construct produces produces index index index solving vertical confidence confidence averaging slightly slightly slightly develop applying applying quality quality quality quality quality blocks blocks blocks blocks blocks select select choosing extracted depending transform evaluate updated fraction showed showed key earlier calculation epochs spaces reduces reduces intervals iterative iterative iterative iterative iterative iterative iterative penalty existing handwritten figures figures kernels kernels kernels kernels inter assignment recognize plotted plotted discuss discuss partially discussions tests tests tests tests tests successfully major selecting importance maximal modification effectively included successful tdnn tdnn tdnn tdnn tdnn tdnn tdnn post score online quickly graphs success showing interested interested split superior running running follow duration duration duration duration satisfy satisfy list backward computes automatically attempt moves overlapping illustrates acknowledgments deal tesauro tesauro tesauro tesauro receive extend minimized bars bars bars bars schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule powerful create requirements requirements game issues biases helpful fewer fewer giving authors authors working proved waibel algo finds attempts isolated ment ment navigation adjacent starts inside inside inside inside processed sections satisfied satisfied satisfied operators pool pool pool pool pool pool pool pool pool pool beginning demonstrates nsf raw raw raw varies applies reflect autonomous adjustable employ formulated rep compares compares maintain requirement requirement requirement exhibits summarized maximizes cal resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource resource ordered achieves cumulative feasible formally summing resources resources resources count eliminate lecun lecun lecun eliminated ranges accepted accepted primitive primitive primitive primitive intelligent serves definitions carry days heuristics heuristics heuristics date date excellent combines irregular zhang zhang zhang zhang zhang zhang zhang zhang decide moved lang bad intended intended scan scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling thomas schedules schedules schedules schedules schedules schedules schedules schedules schedules dif dif creating record rich cpu cpu cpu cpu cpu cpu broken designing dietterich dietterich dietterich dietterich dietterich dietterich dietterich dietterich grants receiving acknowledge unchanged leaving ties job job job job job job job job job job job job year boser tradeoff chapter assignments assignments classifies breaking backgammon henderson rithms grouped continues allocated allocated allocated allocated convert pomerleau pomerleau pomerleau challenging ultimately iri cation zip distinguished distinguished nasa nasa nasa nasa nasa nasa nasa pools pools thousands retained retained permit nal computa oregon oregon challenge gratefully reinforce reinforce scanned scanned august prefer hundreds virtually industrial industrial fox tells sliding gammon gammon request shop shop shop shop shop shop shop shop shop shop counted translate slack slack violated monitored repetitions landmark terminology ference appli lookahead lookahead examines examines resentation saved dilation dilation encourage encourage convolving named designated ames seeking conflict impressive landing gorithms specifications utilization utilization utilization utilization utilization analogously formulating formulating violations violations violations violations mission reinforcements subdivided anova anova gin gin dates prefers spend ijcai cda duplicated walks conflicts conflicts conflicts ule opportunities opportunities opportunities wei attains dollars manufacturing bay shortcoming shortcoming reliance unused thirds perimental hori conduct sched halted idle scribe informed zontal configura ferences flames corvallis summa 
#@Dietterich_T,Zhang_W,
#t9
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#*network network network network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data function figure figure figure figure figure time time set networks networks networks networks networks networks networks networks networks networks training output output output output system system system system system system system system system system system system system system system system system system system system system state state state state results information information information information performance performance performance performance based based based based based based based based based space space weights weights weights layer case case shown shown shown shown systems systems systems systems systems systems systems systems systems systems noise noise weight weight weight functions functions functions functions approach processing processing processing processing processing processing processing processing control control control control control control control control control neuron neuron test matrix optimal inputs inputs inputs inputs form form shows shows signal signal signal signal signal signal signal simple simple simple paper paper paper small size size size size size feature work cells points points points field features features level level level level level problems problems random high architecture architecture architecture section section section fixed fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule real real real real real real real real real real real real states experiments activity activity result university university university university university computation solution solution solution research research defined table table table table table standard standard standard synaptic synaptic presented present present low low object motion motion motion range press press press press outputs outputs abstract applied applied applied back find find computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due due due ieee mixture mixture context introduction action action action action action action action complex complex dynamic dynamic generated generated cost cost cost search assume rules rules rules rules rules measure signals signals signals signals signals signals signals signals signals signals signals signals chosen chosen higher higher required multiple multiple multiple good binary conditions conditions distributed chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make techniques forward forward forward forward ing ing tasks tasks tasks total respect multi sum performed performed mapping mapping mapping means potential made applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications applications study study knowledge original original original artificial application application application application application application application application provide perform perform perform active constraints constraints gain motor motor motor motor motor motor motor equal power mit voltage voltage larger larger support support support support train train source proceedings department department implementation implementation synapses synapses advances represents represents bias scheme scheme addition cambridge computing environment environment environment directly directly directly directly directly additional view design design design design design san bit bit bit conference efficient efficient efficient requires requires free world world world world world world world basic basic pages increase give coding developed developed developed developed developed robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels levels area controller controller controller controller lines nature nature biological discussion increases tested tested tested fast limited actions actions actions amount amount effective effective implemented implemented implemented implemented generate vlsi vlsi vlsi vlsi vlsi vlsi ability future easily easily easily makes development development development development development development development development development noisy sensory sensory sensory including simulated simulated needed needed fully technology technology technology technology technology technology technology technology block transfer interesting significantly edge mechanism mode mode mode operation operation principal call pre direct direct direct direct direct direct direct stored early choose light light light improved improved improve resolution separate element practical introduced include side side engineering highly conventional conventional observations observations volume achieve evaluation storage sensitive constructed digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital digital alternative alternative alternative move move move width boundary column column hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware demonstrate strength conclusion place conclusions designed designed designed designed performs encoding characteristics intelligence pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse variety targets acknowledgements areas areas areas pro longer longer primary tuned physical electrical easy easy develop develop develop integrated implies decreases independently independently communication interpretation evaluated operations operations controlled controlled showed processor processor processor processor processor processor processor processor processor diagram key earlier slow epochs epochs roughly generation generation remains advantages box thesis priori inter determines specifically specifically discussions major reason sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor encoded encoded encoded encoded encoded encoded effectively paths driven included modes modes oscillatory situation tend compact compact strongly decoding allowing allowing link device device device device hold list nips board board board chips chips processors processors satisfies deal software software oriented oriented carried carried carried diego requirements requirements circuitry circuitry rapidly detail strengths strengths dotted behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour examine respond ideas investigated ideal working working comparable stream stream stream stream stream stream stream stream act naturally naturally adapt configurations extremely equally perfect implementations logic logic academic art phd established years devices indicating ment developing sensors sensors sensors sensors sensors sensors sensors majority multiplication comparisons drive drive drive rapid sys producing computers computers exemplars mechanics mechanics evaluating flexible flexible generic embedded embedded embedded readily lack autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous operate operate gains aim incorporating substantial substantial substantial replace inherent conditioning acquisition acquisition acquisition acquisition acquisition accomplished interface interface interface interface interface interface interface interface guarantee arguments resources mobile mobile mobile mobile mobile mobile mobile mobile mobile tem flexibility flexibility robotics robotics robotics murray murray murray murray murray murray murray murray analogy intelligent intelligent programmable programmable programmable programmable resulted occurring methodology implications affected optimally optimally corner corner carry carry obstacle obstacle obstacle obstacle continue periods periods surprising demonstration demonstration demonstration widrow widrow widrow somatic somatic somatic somatic soma chooses darpa darpa advance recovery recovery matter waveforms card card card card card card card card card card card card considerations fly mind leaving usage usage drop specification specification incorporates listed bus bus bus bus bus bus bus bus bus bus ram ram presenting emerge emerge diverse die medium obtains edinburgh edinburgh edinburgh edinburgh edinburgh edinburgh tight transparent transparent concentrated robots robots epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon epsilon goals wall wall continues intra overhead overhead overhead host host host host host host host breaks meet avoidance avoidance avoidance avoidance programmed bring dsp intensive differing inactive inactive suggestions served moderate tension tension tension tension tension tension stimulating functionality monitor monitor monitor monitor monitor designs firstly oscillate transparency aid hamilton hamilton accomplish converter conversion conversion conversion progressively progressively dedicated dedicated alan baxter fastest aggregation robotic robotic ance ance handbook violated modest modest mounted mounted refresh refresh refresh custom plastic preprocessed intrinsically prime competence competence competence competence competence competence competence competence competence continuing lifetime aimed undesirable undesirable internally concurrently strongest strongest exhibiting digitally initialised fuse fuse ramp ramp specifications specifications specifications specifications violation violation historical maximise highlight jackson jackson jackson jackson jackson jackson jackson regularly tarassenko successes reconfigurable attitude highlights selector industry handles cards cards cards geoff indefinitely actuators philosophy interfaces sic isolate embed dition pins dig predecessors pap vital scotland undertaken buses immune profound promote promote reekie navigational navigational navigational navigational ste ste gauge monitors engaged ternational facilitating facilitating strengthen compactness mother asymmetries butler versatile programmability buffered cascading conv conform technological utilised pertain summarised summarised interfacing interfacing interfacing loan adversely utilises iscas fusing import riding imperfections twin absorb lon mobility daughter prototyping 
#@Jackson_G,Murray_A,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural data data data function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number error state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results performance performance performance performance performance performance performance performance performance performance based based based based based space space space space space space space linear case order order shown shown shown systems systems systems values values values probability probability probability parameters parameters noise functions functions method method approach single control control control control control control control control control control control control large large large large large test test class optimal optimal optimal shows shows algorithms simple simple gaussian paper paper examples small small feature feature net work work task task task task task task task task task task task task task task methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step step points features features features current problems problems problems problems problems problems problems random random random random random random high memory memory similar similar representation show show fixed fixed line line line general general generalization generalization generalization generalization generalization real real approximation approximation approximation average states states states states states theory theory obtained note experiments experiments experiments experiments dimensional result university university university log defined found dynamics initial constant estimate standard distance distance left left left present present present temporal temporal temporal temporal temporal machine machine machine machine machine machine object sets sets motion motion press learn learn learn basis basis basis basis basis continuous continuous continuous continuous abstract applied applied applied convergence convergence convergence references ieee ieee ieee positive positive important important adaptive action action action action action action action action action action action action action hand behavior effect effect effect dynamic dynamic dynamic dynamic dynamic dynamic cost cost cost cost cost search tion tion difference difference lower representations learned learned learned learned learned learned learned chosen chosen part part center center cases multiple multiple good good good represent expected equations equations markov fact fact region scale scale finite finite ing tasks tasks tasks tasks tasks tasks tasks tasks total simulation sum times elements regions mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement dimension dimension dimension global study policy policy policy policy policy policy policy obtain negative negative negative negative artificial series series rates proc proc proc proc proc goal goal goal goal goal goal goal goal goal goal discrete brain equal approaches mit mit steps steps steps steps steps accuracy larger larger dependent morgan morgan morgan morgan proceedings report report report loss joint joint connectionist difficult difficult difficult final considered cambridge cambridge cambridge cambridge cambridge cambridge environment directly additional additional curves curves estimates estimates estimates estimates estimates estimates estimates estimates estimates san san effects conference efficient upper world world world world world world world world world estimated estimated pages pages pages produce coding randomly randomly randomly randomly randomly robot robot actual actual finally finally selected selected selected selected selected backpropagation associative technical complete stable stable actions actions actions actions actions actions actions actions predictions rbf amount nearest common effective theoretical theoretical future kaufmann kaufmann kaufmann objective pairs smaller needed combination reduced reduced programming programming programming programming significantly york edge consistent trials trials trials trials empirical squared details details details details call max combined choose run run run run run added predict predict improve directions resolution exact robust takes typical movement reported practical apply apply sense engineering dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions previously conventional works solve match studies achieve trans trans sparse sparse sparse chain increased studied studied scaling trial trial trial trial trial trial trial trial deviation alternative move loop runs runs starting starting place reward reward reward reward differences differences differences sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton exponential practice practice practice practice asymptotic asymptotic weak mateo taking strong largest largest intelligence radial turn start averaged averaged targets question question question pro pro monte monte monte van van carlo carlo carlo factors estimating plot dept dimensionality dimensionality dimensionality agent agent agent versus solved fraction fraction suggested constants updates key key earlier barto barto barto barto barto barto classical spaces intervals roughly penalty penalty initially advantages advantages avoid expect figures thesis thesis thesis usa variations variations major planning planning planning regular regular selecting uniformly uniformly differ computationally divided successful build plots miller miller online online online reached reached moore moore moore moore moore moore moore moore link anderson anderson bar bar usual dot dayan dayan dayan dayan modular nips nips delayed computes reach consisted consisted overlapping overlapping acknowledgments tesauro tesauro situations unlike american wiley poor singh singh singh singh singh singh singh singh requirements requirements requirements experience exponentially rapidly rapidly put issues divergence mass mass ml ml ml ml scalar links terminal terminal terminal analogous coarse coarse coarse thought greedy greedy greedy greedy panel panel observe improving improving mixed phd phd phd massachusetts massachusetts residual cart asynchronous costs critic unstable slope improves improves coded coded answer lin lin lin lin lin widely broad located worst watkins watkins watkins watkins involve author radius evaluating limits substantially empirically offset peter leave car car car car car car car car car car car rewards rewards gen proven richard replace replace replace replace replace conclude shaped returns returns returns tile baird baird traces traces traces traces traces credit univ univ pole pole picture velocities grows robotics systematic kaufman replacing intelligent resulted resulted moments inferior mance zhang zhang appendix appendix appendix encountered encountered cmac cmac cmac cmac cmac cmac perfor moved conjunction conjunction lengths lengths scheduling approximators approximators approximators approximators approximators approximators approximators francisco theoretically roy roy horizon broken tsitsiklis dietterich ignore summarize balancing approximator avoiding bertsekas bertsekas andrew boxes approx ent ties ties opposed torque torque torque torque torque job year ideally amherst amherst chapter england attempted attempted summarizes increment approxi inverted books eligibility eligibility eligibility outcomes outcomes bradtke bradtke gordon gordon gordon computa failures unpublished walk gratefully justification assistance jointly agents curse curse attempting albus albus engine returned tip tip concerns concerns boyan boyan boyan boyan boyan boyan boyan boyan meeting accumulate accumulate accumulate accumulate accumulate slices slices swing sarsa sarsa sarsa sarsa sarsa sarsa grids grids ultimate approaching smc elevator teaching demands niranjan niranjan resultant acknowledges robustly shop dean dean dean experimented mountain mountain mountain mountain mountain mountain mountain mountain mountain degrades incurred incurred putational continuing approxima reactive entered hands trick trick respects parame backups inertia offiine offiine satinder kim kim kim endpoint penalties penalties panels masses resolving poorer tain accelerate imperfect safely gramming gramming raise neuronlike crites crites depended depended depended depended app whitehead whitehead ijcai overlaid byte hashing hashing hashing tiles tiles tiles tiles tiles tiles tiling tiling tiling terminating swinging swinging ven argues argues oot mas ses feet infeng mately collapsing justin rum dejong dejong glanz exert ria hitherto lids vidyasagar vidyasagar kraft kraft counterexample approzimation backed narrowing tsitsildis imating 
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#*network network network network learning learning learning learning learning learning neural neural neural neural neural neural neural data function function function function function function function function time time time time set set set set networks networks networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number system error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results information information information information problem problem problem problem based space space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector systems systems systems values values probability probability parameters parameters parameters parameters parameters parameters weight functions functions functions functions functions functions functions functions functions distribution recognition method method approach pattern point point point processing control control control control control control control control control control control control control control control control large large large local local local class class class class class class class matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal form form form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper paper paper paper paper examples examples size size feature feature methods methods methods methods methods step step step step step field current current problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random high similar similar representation representation representation representation representation architecture architecture show show equation equation section section section fixed fixed fixed fixed vectors vectors vectors vectors vectors vectors vectors general generalization parameter parameter parameter parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states states states states states states states states theory gradient note note note dimensional dimensional result university variables solution solution research research research defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence target initial standard standard terms terms distance presented temporal temporal machine machine machine object maximum range range components components components basis sample sample abstract applied applied applied applied applied find convergence convergence convergence convergence convergence convergence convergence properties properties properties properties properties references component component component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due due important decision decision decision decision decision decision decision decision decision decision decision decision context context context introduction introduction action action action action complex complex hand behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost tion tion change difference variable assume lower prior representations representations representations representations representations representations representations representations representations chosen chosen previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound cases cases cases cases required long represent distributed expected markov markov markov markov markov markov markov markov markov markov fact fact length length length length scale finite finite finite finite classes classes computed respect respect respect respect called mapping mapping mapping mapping means reinforcement factor potential dimension made natural applications applications applications obtain relative samples samples samples represented represented desired desired provide provide define compute goal related related mit mit update descent descent morgan report report institute institute version version version individual advances represents scheme scheme scheme scheme scheme scheme framework cambridge computing computing transition stage full full full full full full requires choice approximate approximate approximate produce condition bounds bounds bounds bounds iteration iteration iteration iteration iteration technical technical describe describe arbitrary arbitrary denote limited close assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption complete stable stable stable stable stable actions proof proof proof common generate generate supported require main adaptation instance future makes kaufmann objective pairs combination technology technology programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming interesting projection projection projection special special uniform leads squared representing making stored attention minimize minimize choose choose choose predict denotes architectures architectures architectures architectures architectures improved discussed discussed discussed discussed discussed recent recent exact property pair pair takes takes practical practical practical practical practical practical apply identical recently interest interest interest works tuning tuning tuning tuning tions modified grid grant exists exists studied studied touretzky column column row row assumptions assumptions assumptions conclusions operator operator operator operator editors differences sutton sutton practice practice practice suggest variety start min min min configuration configuration question appears appears van van van van van index sequential generating laboratory laboratory transitions transitions transitions transitions transitions transitions stability stability infinite dimensionality involves easy easy unique unique unique develop applying extraction expectation expectation john viewed operations approximations approximations approximations approximations approximations approximations forms sizes converges converges converges converges converges reasonable classical classical spaces iterative generation remains norm norm norm norm norm norm norm euclidean euclidean euclidean euclidean euclidean euclidean topology expect expect subspace prove prove prove prove uncertainty discuss discuss candidate domains holds holds holds closely closely uniformly computationally successful identify literature efficiently schemes essentially traditional compact compact compact compact compact compact compact compact compact compact compact compact quickly heuristic success success moore moore lie criteria strategies sci hold hold hold notation involved minimizes ill approximating satisfies satisfies satisfies acknowledgments tesauro tesauro tesauro cowan situations employed employed access exponentially exponentially involving involving limitations issues fewer mappings possibility possibility decisions decisions naturally integer extremely thought thought rank rank formal ith ith generates established massachusetts massachusetts inequality guaranteed unstable unstable satisfied satisfied satisfied satisfied arise arise recording nsf mellon carnegie applies understood affine affine cmu tional parameterized parameterized parameterized poorly employ maintain rely rely rely differs proven sophisticated focused gap bellman intractable guarantee guarantee investigation restrict approximates concerned impossible grows grows establish establish establish systematic dealing dealing overcome mail replacing contract interpret operates methodology methodology intuitively guide meaningful sion overview overview conjunction schwartz captured offers tic approximators initialize discounted contraction contraction contraction contraction contraction contraction contraction roy roy roy roy roy roy roy roy horizon steepest extensively relies relies relies tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis vari limitation empty bertsekas bertsekas bertsekas solves discount uniquely uniquely employs pointed arg lit guess remainder backgammon visited visited queue queue queue queue pij player records associates happen applicability gordon gordon gordon tune tune rewrite gorithm served justified impractical vii curse hoc establishes eral exclusively boyan boyan grids characterizes characterizes rameters proves transpose totally establishing drastically spirit restrictive restrictive locality locality locality cauchy actively huge addi pact incurred ular approxima superscript forthcoming treats evaluates ecs notably belmont fil 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#@Roy_B,Tsitsiklis_J,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural function function function function function function function function function function function function function function function function function function function function function function function figure figure time time time time time set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number error error error error error state state state state state state state state state state state state state state state state state state state state state state state state results results results results results information information information information information problem problem problem problem problem problem problem problem problem problem based based based based space weights linear linear linear linear linear linear linear case case case case case case case vector vector vector systems systems systems systems values values values probability probability probability parameters weight functions functions functions functions distribution distribution distribution approach approach approach approach approach point point point point point point point point point point processing processing processing control control large large large rate rate rate class class matrix matrix matrix matrix matrix optimal optimal optimal form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper small small small small size feature work work work methods methods methods step step step step step step step points process problems problems problems problems problems problems problems problems problems problems random random similar similar similar equation section section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line rule vectors general generalization generalization real approximation approximation approximation approximation approximation approximation states states states states states states gradient gradient note result university variables computation computation research independent independent independent defined sequence sequence initial initial initial constant estimate standard standard standard computer distance science science science present frequency temporal machine machine machine machine machine machine range range range range range learn learn learn learn abstract applied applied back find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties references component stochastic stochastic stochastic positive positive decision decision decision decision introduction action action action action action action action action action action action action action hand hand hand behavior dynamic dynamic dynamic variance parallel cost cost cost cost cost cost cost cost cost cost cost cost tion tion change assume assume assume lower lower learned learned learned chosen chosen chosen chosen previous previous previous theorem theorem theorem theorem theorem bound bound bound good good long conditions conditions conditions represent represent represent represent distributed expected expected expected expected expected expected expected expected markov markov markov make fact region region errors errors scale finite finite finite finite resulting resulting classes ing sum called called called times elements mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor factor factor natural policy policy policy policy policy policy knowledge represented series define define define define compute compute compute compute compute rates rates perform determined goal goal goal related distributions steps steps steps steps larger larger update update update update update update update descent morgan morgan morgan morgan morgan proceedings proceedings proceedings proceedings proceedings report report department version version version advances advances scheme addition addition addition addition cambridge equivalent environment environment environment environment additional transition transition trajectory trajectory trajectory trajectory san san conference conference determine upper upper full requires requires choice approximate approximate approximate free estimated pages increase weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted types path path path path actual finally finally processes iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration depends depends simply discussion technical describe describe arbitrary arbitrary limited stable stable stable stable stable actions amount supported instance kaufmann kaufmann kaufmann kaufmann kaufmann pairs jordan jordan programming programming programming representing max max max max max max max max max max max max direct direct direct international international minimize minimize choose choose choose choose choose predict property pair element element element element apply apply identical quadratic quadratic quadratic volume volume volume solve converge converge converge converge converge converge converge converge diagonal diagonal diagonal diagonal background evaluation chain modified observation bounded bounded bounded bounded entire grant lead lead occur trial trial touretzky touretzky generally trajectories conclusions operator valued editors editors editors editors differences sutton sutton sutton sutton sutton sutton sutton performs practice constrained largest largest start start start decrease iii introduce program annealing acknowledgements suppose appears appears appears van van van longer solving laboratory transitions linearly involves slightly unique unique events agent agent agent agent agent agent agent agent agent choosing national national expressed solved restricted soft approximated completely converges converges converges updates updates allowed performing purpose iterative intermediate sufficiently foundation foundation norm norm norm norm norm norm norm norm norm norm norm norm views avoid exploration exploration exploration exploration box box thesis prove extra modification divided online online online online online online online online online online online online online online online repeated prob success moore moore moore dis follow follow satisfy satisfy notation write write dayan dayan giles delayed moves policies subsequent subsequent extract approximating tesauro tesauro tesauro tesauro cowan unlike singh singh singh singh singh singh difficulty difficulty difficulty rapidly put hanson accurately mdp mdp mdp mdp mdp mdp mdp mdp mdp hall fewer tech mappings mappings terminal terminal possibility decisions proved oscillation workshop cover smallest smallest act necessarily necessarily ensure versions algo observe mixed phd residual ment asynchronous costs distinguish guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed expensive handle sections sections satisfied arc arc arc worst mation watkins watkins watkins watkins author mellon researchers carnegie reflect cmu cmu frequently frequently rewards rely pittsburgh proven proven proven proven chose chose unbiased findings implements begins jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola baird baird baird traces bellman bellman proofs college concerned concerned discover proceed overcome replacing resulted observing optimally continue composition infor prentice periods guarantees approximators approximators approximators approximators francisco francisco discounted discounted discounted discounted discounted contraction contraction contraction contraction contraction contraction contraction contraction contraction contraction contraction contraction matter ends roy roy roy extends tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis summarize approximator convergent material mdps mdps mdps mdps mdps mdps bertsekas bertsekas lem fitted fitted fitted fitted fitted fitted fitted fitted fitted fitted fitted fitted fitted fitted fitted fitted fitted arcs arcs arcs indirect indirect fellowship discount discount discount randomized forced suboptimal theorems exception seek tradeoff ical experiences england imagine tight remainder backgammon visited visited acting publication perpendicular rithms geoffrey ijcnn approxi graduate regulation regulation interacting noting worth eligibility apparently minor bradtke bradtke gordon gordon gordon gordon gordon gordon gordon gordon gordon gordon gordon gordon infinitely reinforce heavily oscillate king accomplish visit boyan boyan boyan substitute sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa arpa arpa proves frequent aggregation aggregation aggregation aggregation aggregation oscillates benign united predetermined behaving proximation infeasible ton exploitation cient approxima approxima treats offline offline offline offline offline offline offline offline offline offline offline offline helped ponent gorithms provably prototypical nonsingular motivate safely comparatively cheaper government inexpensive twelfth twelfth comment lengthy mad lambda paragraph vances sut numer perceives absorption interleaved ine forever forever aggregated fluctuates recommendations unweighted unweighted unweighted unweighted unweighted boxed propriate opinions wouldn counterexample onwards backed 
#@Gordon_G,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time set set set networks networks networks networks system system system system system system error error error state state state state state state state state state state state state state state state state state information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem based based based based based based based based space space space weights weights linear linear linear linear linear linear linear linear linear case case case case case case case case case case case case case case case case case vector vector vector vector order shown shown systems values values values values values values parameters parameters parameters parameters parameters functions functions functions functions functions functions functions functions functions functions functions distribution method method method method method point point point point processing control control control control local local local local matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form form form shows shows shows algorithms paper paper paper small feature work task task methods methods methods methods methods step points points points points field field process process process process process current current structure problems problems problems problems problems problems problems problems problems representation show show show show equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation section line vectors general general general real approximation approximation approximation approximation states states theory theory gradient gradient gradient term term note note note dimensional dimensional dimensional result university university solution solution solution research defined defined dynamics dynamics dynamics initial constant constant constant constant standard standard standard standard terms terms distance science science direction direction direction temporal temporal machine object maximum range press press press press press learn learn learn learn learn components basis basis basis basis basis basis basis continuous continuous continuous continuous continuous sample abstract find computational references component component component stochastic stochastic adaptive adaptive decision decision decision mixture introduction action action action action action action action complex estimation dynamic dynamic dynamic dynamic dynamic dynamic dynamic cost cost cost cost tion tion change difference difference difference spatial spatial spatial spatial spatial spatial spatial spatial spatial assume prior learned chosen chosen center cases required good conditions conditions conditions represent represent represent markov markov markov make make length correct scale simulations ing total total total total total human respect respect multi sum sum performed called called means reinforcement reinforcement factor potential dimension global study policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge artificial relative relative samples samples samples true application provide define compute perform perform determined determined goal related related related constraints constraints constraints discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal mit mit mit mit connection fields fields fields descent report version version represents difficult scheme scheme scheme scheme graph ai cambridge cambridge cambridge cambridge cambridge cambridge equivalent equivalent equivalent equivalent equivalent environment directly directly additional additional transition transition trajectory determine determine determine requires requires approximate approximate free free world speed speed speed condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition weighted weighted weighted weighted randomly robot levels controller lines lines processes processes selected iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration constraint constraint biological discussion discussion technical arbitrary arbitrary tested limited close inverse surface actions actions actions actions actions actions actions actions actions effective generate supported require require require square square square square square square end instance degree makes including including including typically underlying needed combination combination functional jordan jordan technology programming programming programming programming programming programming programming programming programming character york york york call iterations making light predict improved discussed improve improve improve directions directions recent advantage advantage advantage advantage advantage advantage apply quadratic quadratic quadratic quadratic quadratic quadratic sufficient conventional conventional conventional conventional works solve smooth smooth smooth converge differential differential differential differential differential differential sparse evaluation evaluation locations symmetric improvement improvement improvement improvement lead lead alternative correctly move move deterministic deterministic generally setting starting starting reduce depend depend editors editors reward central differences measures clear sutton sutton sutton sutton taking integration integration cycle cycle cycle cycle cycle intelligence radial radial radial min min derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives force base question explicit edges written written longer longer solving ways sequential describes laboratory metric explicitly explicitly simultaneously linearly linearly infinite interaction agent agent agent agent agent agent agent implies cycles cycles choosing choosing solved solved evaluated evaluate updated showed showed forms forms completely similarly converges constants constants updates allowed key key barto barto barto barto performing performing performing penalty interpolation interpolation distances sufficiently advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages advantages existing existing thesis determines extension prove variations absolute absolute absolute major straightforward extra closely closely effectively poggio poggio tend miller essentially online fine characteristic graphs heuristic moore moore stopping symmetry return return return return lie satisfy satisfy satisfy satisfy satisfy satisfy satisfy satisfy vary michael simplified dayan dayan dayan dayan dayan generalize nips nips nips delayed leading moves policies policies policies policies policies policies policies policies approximating satisfies satisfies employed employed origin origin origin wiley essential singh singh singh singh singh updating integral issues dual terminal variational analytically analytically working working hill act circles possibly generalisation equally quantities obvious obvious academic improving improving improving improving utility utility regime phd optimum directed smoothness guaranteed improves explanation explanation starts turns turns turns turns tive easier easier precisely leaves mation mation watkins watkins watkins watkins watkins consequence involve cybernetics addressed apparent evaluating evaluating evaluating consistency consistency consistency consistency consistency consistency consistency consistency consistency consistency consistency flexible pseudo amounts peter atkeson atkeson share treated rewards maintain requirement howard howard rely measuring measuring measuring measuring sums chose comments neuro returns jaakkola baird baird baird baird baird baird baird calls extreme bellman bellman bellman bellman bellman bellman bellman discontinuities discontinuities newton analogue analogue analogue sort writing forming restriction princeton princeton girosi girosi controlling impossible proceed air siemens imposed nearby operates imply adequate infor started saul sion heart uni peterson peterson foundations discounted reader route grants alternatively approximator approximator approximator fly treat sequentially approx thrun thrun thrun corporation pointing piece discount equivalently centre solely solely tendency classic england conservative conservative conservative conservative representa continuity care magnitudes magnitudes impose werbos werbos werbos werbos werbos werbos werbos approxi distant mitchell mitchell mitchell regulation regulation challenging challenging books integrals enforce enforce apparently grateful knowing knowing bradtke permit normalised normalised normalised normalised atr worked circumstances lowe lowe acquire quantify insufficient designs maze interpreting hamilton optimisation optimisation cast concrete vanish confined centres centres mcgraw thing bradford addressing facts scattered scattered deciding noticed enforcing enforcing enforcing lqr lqr lqr lqr lqr lqr lqr ton mir rela undirected undirected enforced suitably minimise minimise conceptually mussa mussa respects encourage wright wright accessible mike maximising ivaldi ivaldi satinder notably calculus hjb inconsistency inconsistency inconsistency centred centred tommi nserc trouble multivariable namic neighbours dreyfus dreyfus jacobi modulo broomhead broomhead minimising encourages penrose optimise didn deci constrains consis patterson tives unreasonable payoffs deriva raphson sut inconsistencies inconsistencies intent andy gabriel mina differen merits merits merits merits incurs professor optimizers bowl bowl larry parameterised parameterised timization forever undiscounted imate cjch cjch differentiability tency compromised generalising vantages cbcl 
#@Dayan_P,Singh_S,
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#*network learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data data data function function function function function figure figure figure figure figure figure figure time time time time time time time set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number system system system system state results results units units information information information information information information problem problem problem problem problem models models models models models performance performance performance performance performance performance based based based based based based based based based based based based based based based based based space space space space space linear linear linear linear linear linear linear linear linear linear case case case case case vector vector order order order order order order order order systems systems systems systems systems systems values values probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise weight functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution method method approach approach approach point point point point point point point processing processing processing control control control control control control control control large large large large local local local local local local local local local local local local local local local local rate rate rate analysis analysis analysis matrix optimal optimal optimal optimal form shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian paper paper paper paper examples examples size size size size net task task task task methods methods methods methods methods methods methods methods methods methods methods methods methods fig step step step step step step step step step points points points points points classification process process process process process process level current current current current current problems problems problems random high high memory memory memory memory memory memory memory memory response response response response response similar similar similar show fixed fixed fixed fixed fixed general parameter parameter real real real real approximation approximation approximation approximation gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional university university threshold solution solution independent defined found initial initial estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate computer computer terms terms terms terms distance science science direction low machine machine range range range press learn learn components nonlinear outputs continuous continuous sample sample sample abstract applied back find find find find computational computational convergence convergence convergence convergence convergence convergence convergence properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic positive procedure important important adaptive adaptive adaptive decision decision decision context introduction estimation statistical statistical statistical generated generated generated generated variance variance variance cost search search search search tion change change change assume assume assume assume assume prior prior prior prior learned chosen chosen higher higher higher higher part center previous previous previous cases good conditions tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected markov make make techniques techniques region region observed observed observed forward simulations simulations ing total total total total human regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression multi performed performed means means reinforcement factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization dimension made made made feedback feedback global global global global global global global applications obtain artificial relative samples samples true true compared application desired provide compute location location location location perform active determined experimental experimental goal goal goal goal goal related posterior posterior posterior posterior distributions gain gain gain gain motor discrete discrete brain power mit mit steps steps steps steps steps steps steps steps steps contrast dependent selection morgan morgan morgan morgan proceedings proceedings proceedings proceedings report report report institute department version version version version technique consists kernel advances advances joint final final final exp delay delay addition domain experiment experiment experiment experiment experiment experiment environment directly directly estimates estimates estimates design design design design top effects conference conference conference conference full requires significant significant significant significant significant approximate statistics free free free speed estimated con con weighted weighted weighted weighted weighted weighted weighted weighted randomly randomly randomly developed controller controller controller controller controller controller controller path path path product product product product product product finally finally finally evidence discussion discussion covariance covariance technical technical technical feedforward describe tested tested fast assumption surface surface actions predictions predictions proof finding effective assumed generate require adaptation journal ability degree noisy noisy noisy noisy kaufmann kaufmann kaufmann kaufmann simulated simulated simulated simulated smaller needed needed needed reduced coefficients coefficients coefficients coefficients coefficients fully interesting interesting significantly head trials empirical operation leads principal squared squared numbers numbers international international international polynomial polynomial polynomial polynomial polynomial polynomial polynomial combined minimize produced run run added added added description recent recent robust typical movement apply quadratic quadratic quadratic cognitive recently interest dimensions sufficient highly highly varying varying compare compare conventional tuning converge converge achieve achieve achieve positions modified interval risk lead invariant deviation deviation deviation wide derivative predicted predicted locally locally locally locally locally locally width setting flow flow strength strength greater assumptions assumptions valued depend depend editors numerical moody practice practice weak temperature temperature temperature suggest strong presence characteristics drawn intelligence start start start start start min introduce base base base question areas reference pro monte monte derive carlo carlo solving solving tuned tuned mathematical dept confidence confidence confidence confidence confidence confidence confidence explicitly infinite infinite springer formed quality quality quality quality implies independently detailed restricted sizes partial slow performing performing performing performing spaces convex fitting intervals intervals intervals query query degrees avoid avoid building exploration exploration exploration exploration box box box figures thesis thesis thesis sciences determines determines extension prove uncertainty maximize maximize priors priors variations partially simplicity gamma sensor sensor sensor sensor aspects aspects identified extra importance suitable effectively identify identify literature literature build build efficiently comparing online verlag quickly quickly moore moore moore moore moore moore moore moore moore moore moore moore moore dis dis superior return content content content content content content criteria criteria vary delayed reach automatically moves moves operating operating decreasing extend explore explore simpler schedule american wiley poor varied hanson association association hessian fewer fewer examine examine respond school possibility reliable decisions decisions decisions decisions root affect surfaces examined hill hill coefficient gradients naturally necessarily queries rank versions versions greedy portion assumes freedom precise precise ith ith multivariate utility submitted phd phd plant plant plant plant plant plant plant plant established optimum optimum optimum optimum optimum optimum optimum optimum optimum optimum pairwise costs crucial sensors smoothness adapted adapted answer answer expensive expensive briefly briefly lies lies worse reasons reasons reasons comparisons considerable stanford broad broad immediately potentially beginning ridge optimize optimize lowest depicted depicted auto auto auto auto recognizing meaning mellon raw raw researchers questions questions apparent improvements considerably percent carnegie applies collected empirically cmu cmu embedded lack autonomous poorly poorly atkeson atkeson atkeson atkeson posed detecting detecting gains gains controllers rely pittsburgh popular proven extensions extensions suited marginal age june june summed corrupted benefit indices indices intractable saddle drift pick optimizing optimizing jth tem robotics climbing allocation chance minutes occurred proceeds replacing chemical chemical chemical chemical chemical chemical chemical chemical chemical chemical loops check methodology methodology affected composition composition date passive passive meaningful meaningful evaluations governed sion guarantees moved moved ascent ascent bad sim scheduling enable april reveals steepest steepest steepest steepest extends jump implicitly pdf andrew boxes mind ure annals solves sig ram reaction reaction pieces year exception causing classic conservative algebraic publication intuition deep diag diag continues permits careful considers fir proach investigating unconstrained importantly discusses tively places lippman permit permit permit september aaai answers continually november demonstrating stops argmax argmax externally acquire handling demand demand demand demand demand demand demand wins attempting supply december industrial concerns disturbances optima optima optima optima optima optima optima sen schaal discarded disturbance successively clark clark clark clark trol adjusts adjusts safe safe company kaelbling kaelbling kaelbling kaelbling kaelbling mcgraw contents contents indirectly indirectly problematic tenth february cleveland cleveland cleveland dence blocked manual unimodal deciding rec stan costly began unobserved unobserved cons incurred incurred incurred ton sensed manager ample repeats weakness hoeffding forgetting dard formulations schneider schneider schneider schneider jumps waiting anticipate remember tributed aggressive aggressive inadequate arms confident plants enormous periments xij justifies fifty fifty chamber chamber accelerate safety accelerated safely robbins robbins robbins roi roi roi roi kushner kushner kushner kushner wild wild encouraged prepared arrived matters monro monro monro regres incor badly badly mated investigates maron maron maron invalid collects regressions jumping danger danger strained thereof loth eration react accelerating forget forget dimensionalities crete confi armed armed jeff experimenting occured judgment unsatisfactory locates manufacturing manufacturing manufacturing diagnoses imize informally ques dejong greedily vantage timization timization risks perature formidable ulated hessians cautious cautious cautious cautious inefficiencies ely ely reals sixty beating beating nificant ile txt discards disastrous forgets conti confidently 
#@Moore_A,Schneider_J,
#t9
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural input input input input input input function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output system system system system system system system system error error error error error error error state state state state state state state state state state state state state results results results results information information information information information information problem problem models performance performance performance performance based based based space space space space space weights weights linear linear linear linear linear linear case case case case case vector order order shown shown systems systems parameters parameters noise noise noise weight weight functions functions functions functions neurons neurons approach processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control local optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows algorithms algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian paper small size task task task task methods methods step step field field problems problems problems problems problems random response equation equation equation fixed line line rule real real real real approximation approximation average gradient gradient gradient gradient note note note university solution research defined dynamics dynamics constant constant science prediction prediction prediction prediction prediction left temporal temporal temporal temporal temporal temporal temporal temporal machine press press position position position position basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied back find find computational convergence properties properties references stochastic stochastic stochastic ieee adaptive adaptive decision decision introduction action action action action dynamic dynamic dynamic cost cost cost cost search difference difference difference difference difference difference difference assume previous cases required good expected markov markov make proposed correct scale resulting tasks tasks simulation simulation human respect respect times elements reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor optimization optimization potential natural feedback feedback feedback feedback feedback feedback feedback policy policy knowledge artificial specific application define determined goal goal gain gain gain discrete discrete discrete discrete discrete discrete discrete discrete mit mit steps connection descent modeling modeling modeling proceedings report report version version version version internal advances difficult exp scheme cambridge equivalent equivalent curves limit trajectory approximate world basic pages pages condition condition condition derived derived derived derived weighted robot controller controller controller controller controller controller controller controller provided iteration constraint constraint biological technical technical arbitrary denote tested tested tested tested limited limited limited limited inverse rbf rbf rbf implemented implemented generate theoretical future future future easily degree smaller hopfield hopfield hopfield dynamical dynamical unknown programming programming programming york trials trials trials trials trials trials trials trials principle operation squared max max max max normalized early idea combined run added predict predict predict advantage advantage advantage period quadratic quadratic previously conventional conventional works works solve smooth smooth differential achieve evaluation bounded amplitude expression scaling scaling trial derivative derivative derivative predicted predicted predicted predicted touretzky conclusion valued valued editors editors sigmoid sigmoid accurate sutton sutton sutton sutton sutton taking intelligence radial radial variety decrease relationship relationship iii derivatives force base explicit derive derive derive laboratory unique equilibrium equilibrium applying national showed showed past past barto barto barto barto barto barto barto normalization convex convex convex sec neighborhood transactions degrees degrees avoid exploration exploration priori usa formulation weighting extension successfully differ maximal paths paths successful build ten anderson follow hold gray satisfy backward board delayed correspondence tesauro extend law law law law law law law law law law law command singh updating updating reliable phases momentum act trace trace man man perfect changed changed adjusted taylor freedom attempts plant seconds massachusetts cos formula critic critic critic critic critic critic critic critic critic trivial navigation satisfied laboratories actor actor actor actor actor actor actor cybernetics consistency variant maximizes maximizes monotonic collective semi baird baird specifies bellman leen modify japan appropriately air height substituting games started sion enhance facilitate discounted pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum davis implicitly alternatively boxes ence discount graded torque torque torque torque torque torque torque expanding amherst hundred modifying formance insights thick inverted differentiation differentiation differentiation differentiation noting academy eligibility eligibility enforce applicability bradtke bradtke bradtke bradtke bradtke bring atr atr differentiating doya doya doya doya doya discretized continued hamilton tip swing swing neurobiological falling smc upright upright upright upright upright upright edition cho houk houk houk ganglia ganglia tan publishing rein coincides ver formulations formulations ply wright wright duff duff gun hjb diverges basal basal wji inconsistency kyoto susceptible luo euler euler euler gullapalli gullapalli jacobi prepared ner forcement neuronlike soraku adams iwl bringing patterson hemisphere swinging swinging swinging ridges ovi ovi ovi ovi kenji bryson bryson bryson rts discretize scent ological unnatural zxt turbation 
#@Doya_K,
#t9
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input input input input input input input data function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time time set set networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number error error error results results results results results results results results results results units units units units units units units units units units information problem problem problem performance performance performance based based based space space space space space linear linear linear layer case case vector order shown shown shown shown shown shown shown shown systems values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters weight weight weight functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach point point point single single large large local local local local local local local local local matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal form form form form shows shows signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples examples examples small small small small small task task task step step step step step classification trained trained problems problems problems high high high high high high similar similar architecture architecture show equation equation equation equation section section line rule rule rule rule rule rule rule general parameter parameter parameter average average average average gradient gradient gradient gradient gradient gradient term term note note note note result result university computation solution solution log log log log defined found target target target target constant constant constant constant table table table table table table table estimate standard standard computer science science science direction direction presented presented presented present present present present present phase low low low temporal machine maximum maximum range range range learn learn outputs outputs outputs outputs outputs outputs abstract applied back find find convergence convergence convergence convergence convergence convergence convergence density density density density properties likelihood references stochastic due due procedure important adaptive mixture mixture mixture mixture mixture introduction action complex hand hand behavior behavior behavior statistical effect generated variance variance variance variance cost cost cost cost cost cost cost cost cost cost energy energy energy difference difference difference rules rules rules rules rules rules measure signals prior chosen chosen chosen chosen chosen chosen higher higher part previous cases good spike represent expected expected expected expected expected expected expected fact fact errors errors scale scale scale simulations simulations minimum minimum ing ing ing ing simulation simulation respect times times regions mapping means means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement optimization global applications negative original compared application desired cross series define define compute compute rates rates perform active determined determined goal posterior distributions distributions distributions brain equal equal equal equal steps steps steps steps steps comparison comparison comparison larger larger larger contrast connection update update update update update update update update update update update train descent descent dependent institute institute department version connectionist connectionist difficult final final final exp exp exp exp bias cambridge domain equivalent experiment environment environment environment environment environment environment environment environment environment environment directly hinton view limit free derived weighted conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional criterion criterion criterion criterion entropy entropy entropy entropy entropy entropy entropy entropy actual finally finally selected depends depends depends sampling sampling associative associative associative measured covariance covariance close inverse corresponds finding theoretical easily noisy typically typically typically pairs pairs pairs smaller jordan jordan jordan jordan jordan technology interesting trials trials trials trials trials matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform empirical mode leads representing details details details making making normalized experts experts experts experts experts experts experts experts experts experts experts experts experts experts supervised expert expert expert expert expert expert expert expert expert expert expert expert early early early idea idea minimize choose choose choose choose run added discussed advantage advantage typical typical reported apply apply identical identical cognitive engineering previously calculated match match match correspond converge converge converge mixtures mixtures mixtures mixtures mixtures mixtures generalized gate williams williams williams williams williams williams improvement improvement entire increased lead lead trial wide predicted predicted alternative locally move generally column runs runs runs runs half strength strength conclusion greater greater greater depend depend depend depend reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward differences differences differences differences designed sutton sutton peak peak peak faster faster faster practice learns temperature temperature temperature temperature reduction solid turn minimizing exist decrease manner minima minima force base boltzmann explicit derive construct plot describes dept dept electrical consisting gaussians applying implies select select choosing choosing choosing learner learner learner learner learner learner learner learner learner learner learner densities restricted updated soft converges converges converges past key calculation slow dashed normalization roughly purpose initially initially calculate advantages avoid existing existing existing exploration exploration exploration exploration figures figures figures thesis thesis assignment sciences determines maximize maximize priors priors absolute absolute absolute gating gating gating columns extra extra uniformly effectively effectively successful reached receives receives capture quickly interpreted dis issue running comp comp comp comp quantity quantity vary michael dot generalize minimizes highest highest ill maximization preferred jacobs jacobs jacobs jacobs decreasing receive employed employed explore explore explore exponentially updating updating put optimized divergence preliminary scalar scalar scalar rest ideal reliable analogous automata automata equally thought thought thought adjusted adjusted singular panel logistic baseline baseline arbitrarily phd phd averages massachusetts percentage preference ment agreement growing fairly improves nowlan starts reasons comparisons forces gradually begin begin optimize depicted qualitative qualitative conducted conducted conducted parameterized lack marked adjustable employ sharp maxima maxima maxima rewards rewards rewards rewards rewards rewards rewards rewards rewards maintain partitioning modulated maximizes maximizes suited logp converged converged converged converged converged converged credit softmax softmax representative optimality purely unity impossible proceed kullback adds chance alpha height balance balance keeping fail responsible ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx exploring reliably reliably ensures loo infinity chooses route balancing receiving temperatures temperatures converted logarithm employs suboptimal suboptimal connec amherst multinomial big forcing param attempted equality favor shifting distri realizable placing likewise places differentiating bution reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce reinforce advantageous stochastically smoother adaptively diffuse striking falling constraining sian sian gaus gaus translates energies energies probabil entropies mir mir exploitation exploitation broader rmse lowered ities psyche psyche burden favorable ily ily ily draws parentheses parentheses bimodal bimodal trouble lowering wtx susceptible highlights eter tributions encourages awi didn dur tionist lly cutting iip liebler mas notoriously peng peng philip sharpen sharpen stark sachusetts sectional bivariate flattened rai formalizing threefold 
#@Jordan_M,Sabes_P,
#t9
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning input data data data data function function function function function function function function figure figure time time set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number system system system system system system system system system error error results results results results results results results results results results information information information information information information information information information information information information models performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear case case case case vector vector vector systems systems systems systems systems systems systems values values values values values values values values parameters weight weight weight weight weight functions functions recognition method approach approach pattern point point point single single single processing processing processing large large neuron neuron neuron test test test test analysis analysis analysis analysis analysis analysis class optimal optimal form form shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms size work work work work work work work work work work task task methods methods methods step step classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process process process process process process process process process process process process process process current trained structure random random random similar similar representation representation representation show show show show section section rule rule rule rule rule vectors real real average average average gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term term term term term term term term term term term term term term term term term term experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments result result university threshold threshold threshold threshold threshold research research defined defined found found target target initial table table table table table table table table standard computer computer terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms distance distance distance science science presented presented presented presented presented presented presented present frequency frequency maximum press press learn learn learn learn learn learn abstract abstract applied applied find references component component component component component component due important important adaptive adaptive context introduction statistical statistical statistical statistical tion tion change change energy difference assume assume assume classifier classifier lower lower lower lower rules rules rules word previous previous bound bound bound bound type type type type multiple good good binary binary binary binary binary binary make make fact techniques techniques techniques length observed scale minimum resulting resulting tasks tasks total respect respect performed performed performed called called optimization optimization optimization potential natural natural natural natural natural natural natural natural feedback feedback feedback em filter original original original original original vol relative relative specific specific represented cross cross provide perform perform determined determined determined approaches approaches approaches accuracy accuracy accuracy accuracy accuracy fields update update update update update update update train descent descent descent descent descent descent descent dependent selection selection selection proceedings proceedings proceedings proceedings proceedings report words department department department loss loss loss loss loss implementation technique technique technique connectionist exp exp exp exp exp exp bias addition considered domain domain domain experiment environment additional limit san top top top top classifiers requires requires statistics statistics statistics increase con produce produce derived derived derived developed developed bounds area entropy actual actual finally processes processes evidence evidence evidence sampling sampling sampling sampling achieved achieved achieved normal increases increases increases describe tested tested transformation transformation inverse complete circuits finding common common effective assumed assumed assumed supported journal ability ability hypothesis hypothesis instance instance instance degree degree including including smaller smaller combination coefficients testing testing testing testing significantly significantly significantly significantly ratio york mechanism mechanism uniform uniform language language language language language language language squared squared numbers iterations iterations iterations stored stored stored international produced produced produced description improved improve improve improve recent recent advantage property pair pair pair element reported reported subset subset relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant sufficient previously previously approximately calculated calculated calculated calculated volume volume works works yields evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation modified observation generalized improvement improvement improvement improvement exists suggests correctly correctly occurs generally column conclusion row conclusions competitive central differences exponential suggest suggest presence assuming user user decrease program question appears produces index recall recall recall recall metric metric metric metric metric metric metric remaining text text text text text text text text text text text text text text unique unique quality implies implies versus select national focus expressed expressed evaluated evaluate evaluate updated static sign barto barto barto barto barto additive expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion sec purpose purpose purpose closed calculate assigned assigned assigned foundation euclidean query query query query query query query query query query query query 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follow follow strategies notation list list list list generalize nips minimizes denker leading leading thresholds operating operating operating satisfies layered transformed transformed collection collection collection collection collection collection collection collection collection collection collection collection collection collection collection collection collection humans association association hall hall rise rise tech tech combine stream func fundamental attributes attributes attributes attributes examined necessarily equally implementations subsets queries queries queries queries queries queries queries queries queries queries queries queries obvious algo assumes ith switching improving improving utility submitted sentences massachusetts ment stop agreement derivation derivation derivation caused sys widely producing cut cut cut optimize lowest author incomplete explained explained percent reflect empirically relevance relevance relevance relevance conducted conducted conducted 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document document document document document document document document document document document document document document document document document schapire predictors james corre entry expanded expanded expanded expanded expanded expanded expanded expanded expanded expanded expanded expanded expanded expanded expanded widrow originally originally ranking ranking ranking ranking ranking ranking ranking tokens record warmuth warmuth warmuth warmuth davis davis subsequently generalizing material material balanced default default counts trading trading andrew metrics metrics metrics metrics suffix street appeared roc roc roc roc roc roc parsing parsing slight incorporates listed listed accept maximized maximized cooperative legal employs axe axe axe expanding expanding connec classifications acceptable amherst rain formance rithms wall wall maintained inverted library register apparently commercial mini experi ucsd sponding sorting attributed thousand confirm cliffs cliffs suffers attempting hoc hancock ron supplied engine seattle englewood englewood judged judged judged judged manually contributes parti retrieved maxi maxi convention reality implying lewis crl teaching firm profit comprised kivinen kivinen kivinen kivinen kivinen semantics request request tical assessed ically ized hoff proceeding proceeding col discriminating sorted sorted sorted sorted jose publishing ference gallant collections collections triple incurred ular topics topics topics walker saved saved statis undergoes web ucsc ucsc judgments volumes volumes volumes volumes manfred sults inhibits exponentiated exponentiated exponentiated exponentiated exponentiated exponentiated exponentiated ire requests optimiza explores syntax syntax pared eval eval eval eval news news ranks partic nique invoked imbalance articles articles realizes congress morphological tionist attainable attainable investigates federal smart smart smart umass umass umass emd emd emd mas tropy lambert wittner trec trec trec trec trec trec trec trec wescon participating tioned sachusetts precomputed sigir sigir leaxning leaxning leaxning recommendations parsed stemming stemming stemming stemming rlt lection docu docu specif opinions doc allan commerce collec 
#@Barto_A,Callan_J,Papka_R,
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural input input input function function function figure figure figure figure figure time time time time set set set set set set networks networks networks networks networks networks networks training training training training training algorithm algorithm output number number number number number number system system system system system system system error state state state results results units units units units units information information problem problem problem problem problem models hidden hidden performance performance performance space space space space space weights weights weights weights weights weights weights weights weights weights order order order order systems systems systems systems systems probability probability probability probability probability parameters parameters noise noise weight weight unit unit distribution method method approach point point point point image single processing processing large test test patterns analysis shows shows shows algorithms algorithms algorithms simple simple simple gaussian paper small small small small small work work work work work work task task task methods methods step step points points field features features features features features level current current current trained trained trained structure problems problems random random random random random random random random random random similar similar similar similar similar show line general general general speech parameter average states term term note note dimensional result result result result result result university research research defined found found found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial standard computer computer computer distance distance distance distance science science direction frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal machine machine machine machine machine machine machine machine machine sets range press press press press learn learn position position basis continuous abstract applied back back back find find find find find find find find references due due positive procedure adaptive decision propagation propagation propagation context introduction complex complex complex complex complex hand behavior behavior statistical effect effect dynamic parallel parallel search search search change change difference difference difference difference difference difference lower rules measure representations chosen part part part part required required required good good good good good good long conditions conditions conditions represent expected expected expected make make make make make make fact fact region forward scale scale simulations ing ing ing ing ing tasks tasks tasks total total human human human respect respect called elements means reinforcement reinforcement reinforcement optimization feedback applications study knowledge knowledge artificial artificial artificial artificial artificial artificial relative relative relative true true cross perform goal goal goal connected connected power power approaches mit mit mit mit comparison comparison larger dependent dependent morgan morgan proceedings proceedings proceedings proceedings proceedings department technique internal internal advances advances connectionist bias bias bias layers addition graph ai ai cambridge cambridge domain domain domain domain domain environment environment environment curves san conference conference conference conference conference conference determine upper requires significant world world world pages pages pages pages pages pages derived randomly developed robot evidence sampling sampling constraint simply simply simply achieved achieved discussion feedforward increases increases tested close close assumption stable stable finding finding generate supported adaptation end end hypothesis hypothesis hypothesis instance makes development development including kaufmann simulated pairs pairs account fully jordan programming programming testing edge edge edge uniform language leads numbers iterations pre making making making international international international experts expert expert expert expert expert expert expert expert early idea combined run added added improved improved population population population improve advantage property practical apply introduced introduced strategy identical identical machines machines side teacher teacher teacher teacher approximately volume tuning tions tions match studies achieve evaluation evaluation organization improvement improvement increased increased increased grant lead lead lead studied trial feed touretzky deterministic deterministic deterministic occurs generally generally setting runs half starting critical critical minimal conclusions neighbor competitive competitive competitive competitive editors editors editors editors editors sigmoid clear weak learns mateo suggest taking strong strong hard hard start program program program annealing question areas boltzmann pro longer primary generating changing student student student student missing averaging easy slightly slightly develop mutual adding equilibrium equilibrium versus cycles select competition competition competition competition choosing national extracted family stages viewed viewed viewed interpretation learner learner learner organizing showed evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution understanding completely allowed epochs measurements neighborhood neighborhood add add tracking generation generation generation generation generation generation remains initially distances distances foundation euclidean avoid avoid expect exploration thesis inter prove domains domains neighbors major major middle capable capable suitable divided included successful successful successful computations genetic genetic genetic genetic comparing situation situation situation plots miller miller reached kind success success success success success success success success success success success success success interested dis strategies strategies strategies bar involved sampled sampled sampled play play play play play play play play play play play play play play play play play play play modular paradigm providing board board consisted moves moves moves moves moves moves moves moves subsequent operating acknowledgments tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro situations situations explore simpler simpler simpler unlike schedule powerful powerful essential rapidly environments involving humans humans game game game game game game game game game game game game game game game game game game game game game game issues helpful existence examine successive fashion parity decisions proper stream understand understand understand cognition neu hill hill hill hill hill concepts editor editor reading automata automata front taylor explored percentage percentage percentage great great advanced advanced ment stop developing improves improves improves floating answer benchmark benchmark starts purposes producing constructing choices arise ion scientific computers demonstrates sun mechanics explained questions questions improvements understood understood led led embedded simulate lack red poorly remove incorporated rewards http monotonic prevent substantial kinds inherent neuro begins eventually progress progress converged wesley trade phenomenon phenomenon acquisition sort www www addison forming forming formally acm drift drift pick narrow dynamically impossible impossible climbing climbing climbing climbing communications cellular spiral kaufman overcome overcome replacing replacing hit biased biased observing fail ral methodology modifications intuitive days games games games games games games games games games games games games games games games games games games games games games games games date exploring started falls programs programs loo loo surprising expanded accounts counter dif tic tic tic exposure claim enable winning winning winning iterated surprisingly surprisingly surprisingly suggesting pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack pollack master master fitness fitness fitness fitness repeatedly repeatedly contact draw draw draw broken reverse implicitly avoiding onr learnable escape rms rms rms rms dramatically spirals specification specification corporation ter piece fellowship leaming ber legal preserving responds poses suboptimal pieces pieces pieces pieces pointed chaos chaos chaos preferences preferences perceived reports letting forcing massively stands chess chess adjustment alter ary backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon home home ibm ibm evolve alternate num continues life life life life life playing playing playing playing uncertain mitchell mitchell mitchell convert learnability learnability douglas met player player player player player player player player player player player player player player player player player player player player win win win win win harder harder harder harder meta meta meta meta meta cation worth barrier setup setup setup refinement apparently denver sta page commercial programmed bring things answers mix challenge challenge technologies worked worked helps picking learners replacement survey sorting ble reversed decided european ers hundreds firstly observers neighborhoods wins wins coin evolved evolved evolved hoc opponent opponent morphology played played played played played played cast replicated replicated fre mistakes condi exposed boyan boyan rasmussen emerges judged seed alan cooperation cooperation losses losses losses losses evolving evolving evolving sity reality evolutionary evolutionary evolutionary evolutionary evolutionary evolutionary evolutionary evolutionary randomness randomness ready players players players players players players players players players players players players players cess gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon bear bear catastrophic actively putation unexpected replicate hits benchmarks schraudolph ference progresses jack rein rises neigh prime generations generations generations generations dilemma terminate ness won quency tag web rated burden untrained warp inertia challenges challenges forrest rolls rolls rolls rolls rolls rolls rolls hillclimbing hillclimbing hillclimbing solu draws draws impressive exciting samuel samuel samuel throw scored environ converting ending brooks brooks beat beat permitted univer gerald successes eval news equi weaknesses crafted succeed queen forcement michie michie michie suc suc millions roll sept business business genera replicating bet public race belew belew belew isolate pol postdoctoral mimics donald prey waltham vious dream leverage dangerous tremendous packard packard packard hillis hillis hillis counteract brandeis brandeis brandeis subse checkers pur calibrate origins sophistication cussed unlearnable pla expose kelso predator throwing lucky lucky genetically tac tac tac existent minority librium strat continual prevalent quent cooperating beating reynolds reynolds dozens checker abandoned competent nately degrading yardstick hopes tually maes maes hoods lular borhood capitalize 
#@Blair_A,Pollack_J,
#t10
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#*network network network learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input data data function figure figure figure figure figure figure set set set networks networks networks networks training algorithm algorithm algorithm algorithm algorithm output output system system system system system system system system system system system error results units units units units units units units units units units units information information information information information information information information information information information information information information information problem models models models models models models models models hidden hidden hidden hidden performance based based based based based based based based based based based based space weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case shown shown shown shown systems systems parameters parameters weight functions functions functions functions neurons neurons neurons neurons neurons unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image single single single processing processing processing processing processing processing processing processing processing processing control control control large local neuron neuron neuron analysis analysis analysis analysis analysis analysis matrix form form form form form shows shows shows shows shows signal signal signal simple simple simple gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual paper examples examples examples size size size feature feature net work task task methods methods cells cells cells cells cells cells cells field field process level level level current current trained trained structure structure structure structure random random random random memory memory memory memory memory memory response response similar representation representation representation representation representation representation representation show section fixed fixed rule rule rule rule images images images images images images images images images images images images images general general general real real real theory theory theory term note experiments activity activity activity activity activity activity activity activity activity activity activity activity activity solution solution solution target standard standard terms distance connections connections connections connections connections connections synaptic synaptic science science science left direction direction direction direction direction direction direction direction direction direction direction presented presented presented map map map present phase phase phase activation activation activation activation activation activation temporal machine machine object object object object object object object object object object object sets sets learn learn learn position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position basis basis basis basis abstract back computational computational computational references important propagation context context introduction stimulus statistical statistical effect dynamic generated parallel parallel tion tion spatial spatial spatial spatial spatial spatial lower lower lower lower lower representations representations representations representations learned chosen chosen chosen part part part part part part part part part part part part part part part part part center cases firing required required required required cortex cortex cortex cortex cortex cortex represent represent represent tree tree distributed distributed fact fact correct correct probabilities scale scale scale scale scale scale resulting resulting classes tasks human human performed mapping dimension natural study study knowledge knowledge artificial represented objects objects objects objects objects objects objects objects objects location location perform active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye related related connected motor brain brain brain mit fields fields support train train train selection morgan institute words department version version version version consists code advances connectionist connectionist responses responses difficult layers layers layers layers scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme ai ai cambridge cambridge equivalent equivalent hinton hinton hinton hinton view view view view view view curves curves san top top top top top top top top top top top top top top top top top top top top top top top stimuli stimuli stimuli stimuli stimuli effects capacity determine upper upper requires requires requires free vision vision produce coding coding randomly randomly developed levels levels levels levels levels area area area path actual provided finally selected selected evidence evidence nature nature associative associative associative discussion arbitrary arbitrary arbitrary inverse inverse inverse short effective effective implemented shape shape generate require require require require face face face face face face face face face face face face face face face face face face journal journal journal journal hypothesis instance instance instance makes sensory including including fit fit fit kaufmann probabilistic underlying account fully fully technology transfer interesting consistent empirical operation leads leads leads representing representing representing representing representing representing representing details iterations max direct window window window bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom early attention attention attention attention attention attention attention attention attention attention attention description neuronal neuronal neuronal neuronal neuronal neuronal population discussed directions directions recent advantage pair separate separate reported strategy subject hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees trees inference sejnowski sejnowski sejnowski cognitive cognitive relevant unsupervised unsupervised unsupervised tuning tuning tuning tuning solve positions positions positions positions locations observation sensitive sensitive entire exists exists parts parts parts parts parts parts parts invariant suggests matrices alternative correctly touretzky occurs column setting setting setting hardware hardware critical place depend editors editors sigmoid retina retina retina retina retina retina retina clear mateo encoding taking taking taking mechanisms mechanisms mechanisms intelligence turn turn movements selective selective selective selective relationship relationship relationship relationship manner scene scene scene connectivity force areas areas areas areas areas explicit appears van van van construct construct perception ways ways generating describes stability stability implement coordinates coordinates involves involves remaining interaction interaction interaction choosing focus focus focus focus dependence overlap viewed influence codes codes operations controlled restricted showed showed centers modulation modulation modulation modulation modulation modulation modulation modulation modulation centered frames activities activities key key performing expansion expansion generation generation generation generation generation intermediate intermediate assigned faces faces faces faces faces faces faces faces faces faces faces koch perceptual activations activations coordinate inter retinal retinal instances instances sciences sciences sciences recognize recognize recognize recognize determines extension illustrated automatic activated partially discussions characterized simplicity simplicity simplicity straightforward straightforward compression compression middle middle middle middle aspects aspects extra closely encoded delta delta delta delta poggio poggio poggio essentially identity fine graphs repeated allowing anderson anderson interested neuroscience neuroscience neuroscience neuroscience generative generative generative generative generative generative generative generative generative generative generative dayan dayan dayan dayan dayan dayan paradigm providing leading leading leading leading leading moves moves illustrates routing tesauro explore explore poor create experience circuitry accurately recursive ideas project behavioral behavioral mappings structured working lgn pathway pathway pathway pathway pathway pathway pathway pathway pathway hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy notion notion notion neu circles naturally plausible possibly possibly adapt analyze extremely illustrate created eyes eyes eyes eyes eyes implementations aspect der portion panel panel fisher consist generates synthetic synthetic synthetic neal established massachusetts defining coded biology caused lies inside processed perspective implementing implementing mation controls inversion recognized circle circle lowest depicted auto auto recognizing preceding addressed integrating reflects collected pathways pathways fed peter marked employ music variant requirement synthesis synthesis synthesis synthesis synthesis synthesis modulated cal ordered marginal substantial comments attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional specifies semantic naive room room aligned leen sort sleep sleep sleep sleep sleep sleep sleep forming saccadic appropriately addresses impossible turned binocular convenient imaging imaging primate primate multiplicative multiplicative intelligent viewpoint viewpoint analyzing neurobiology reasoning shifts shifts canonical inferior exploring infor heavy representational conjunction heart monkeys parietal parietal parietal parietal viewing multiplied offer pollack pollack pollack refers theoretically erlbaum variants reverse generalizing influences informa dramatically neurophysiology constitute visually helmholtz helmholtz creates revealed instantiation instantiation generalizations big hierarchies hierarchies hierarchies hierarchies hierarchies affects descriptions possibilities hillsdale stands reflected wake wake wake wake wake wake wake monocular manipulation activate mouth mouth mouth mouth mouth mouth mouth mouth mouth challenging investigating pearl pos conversely constructs superposition abbott abbott abbott placing memo frey dramatic handled stores accumulation reversed generarive generarive generarive generarive generarive generarive generarive rivalry influenced ping builds pouget pouget pouget pouget olshausen olshausen olshausen generafive generafive aid conceptual reflecting alex essen essen cally compo anterior anterior anterior peaked emerges accumulate lying explanations neurobiological suffice andersen connectionism attended feasibility feldman focusing decoded percept clues experimented gallant sung connor connor activates activating activating traversed modulating modulating thorpe illustrating mediate manipulating proving logothetis logothetis poral nent preset imagery feeds taught geometrically expressing nose nose nose nose renders geoff siegel depict shifter shifter inspiration ubiquitous traversing traversing fixations comment decoupled tomaso locus locus persist deviate thereof argues grounds inferotemporal terior elaborated inevitably requisite proposals ramachandran ramachandran tection traverse larry imbert traversal traversal intermittent intermittent cartoon cartoon cartoon recurslye drawings bruno stereoscopic impression exerts arranging sinha soundness elucidate blends modula roscience multiplicatively emilio neuroreport cbcl 
#@Dayan_P,Riesenhuber_M,
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#*network network model neural neural neural function function figure figure figure figure time time time time time time time set number system system system system system system system system system system system results results results information information information space linear case order order order order order order order order order order order order order shown shown shown shown values values probability probability probability noise noise noise noise neurons unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution point point point image processing processing processing processing processing processing control large large large large rate rate rate analysis analysis optimal inputs inputs form form form form form form form form form signal simple simple simple simple gaussian gaussian gaussian visual visual visual visual visual paper paper paper paper small work methods methods fig fig fig fig fig fig fig cells cells cells cells step step field field features process process process process process structure structure structure high response response response similar representation show section images images images images general speech speech speech speech speech speech speech speech speech parameter parameter average theory theory theory theory theory theory obtained obtained obtained obtained note note experiments university variables research independent log log log log log log log log log log log log log log defined found found found found found found found computer prediction direction direction phase phase phase phase phase phase phase phase low low low low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal range range range range range range press components sample abstract find properties properties properties properties properties properties references component stochastic procedure procedure procedure mixture mixture introduction introduction behavior behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical dynamic generated variance variance variance tion change change change change variable spatial lower lower signals signals higher part center center center center previous theorem cases cases type cortex cortex good good spike long long long long long represent distributed fact fact fact fact correlation correlation correlation observed scale scale scale scale scale scale scale scale scale finite finite finite ing computed respect sum performed performed called called times made natural natural natural natural natural natural natural natural natural natural study study knowledge filter filter filter filter filter filter filter obtain receptive provide rates determined determined related distributions distributions distributions gain cortical cortical cortical power power power power power power power power power power power power power power comparison comparison larger larger contrast fields fields dependent report code code individual joint responses responses responses difficult addition maps computing domain directly directly curves curves design limit limit san san san capacity requires choice choice statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics coding types types types provided finally processes nature sampling normal increases denote transformation fast fast corresponds complete supported supported theoretical theoretical square ability ability ability ability sensory including auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory functional functional interesting empirical principle details details filters filters making normalized early decay sources description neuronal neuronal membrane recent correlations correlations correlations correlations correlations correlations correlations resolution resolution resolution advantage property property robust ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble similarity similarity similarity similarity reported reported lateral identical identical identical identical identical recently relevant highly highly axis axis tions correspond correspond locations modified modified modified bounded increased increased grant amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude parts lead studied studied invariant scaling suggests wide predicted locally locally width conclusion segment central designed performs exponential exponential faster sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound encoding encoding presence presence characteristics california decrease averaged averaged averaged scene scene question acknowledgements relation pro van produces longer longer tuned segments segments consisting frequencies frequencies frequencies frequencies implies implies implies focus stationary stationary stationary stages stages interpretation transform transform transform restricted modulation modulation modulation modulation centered forms forms soft soft soft similarly suggested translation translation translation discrimination discrimination spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum normalization sec fitting roughly roughly remains valid valid valid filtering msec msec sufficiently foundation foundation recorded retinal retinal subspace maximize phys discussions suitable suitable suitable efficiently invariance invariance invariance miller essentially soc soc compact notice notice contained neuroscience lie lie content follow follow quantity quantity cat cat cat cat attempt overlapping intrinsic presents presents trains law law law law origin diego parametric parametric parametric parametric parametric investigate exponentially exponentially varied relations relations relations accurately accurately helpful fourier fourier examine examine successive office reliable lgn lgn statistically topographic phases analogous analogous examined examined transmission adapt analyze rev quantities quantities quantities impulse observe academic improving arbitrarily arbitrarily animal animal mentioned histogram indicating scenes scenes scenes scenes slowly cos cos band band band band band band defining adapted adapted ganglion organized organized broad nucleus laboratories sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds opt res bandwidth bandwidth bandwidth bandwidth bandwidth auto author prop limits reflect cochlear peaks recordings recordings passed formulated music music music music music music music exhibits incoming incoming song chose cochlea cochlea displays instantaneous cor spectra spectra spectra spectra spectra spectra spectra redundant physiology sv sv sv restrict narrow narrow naval reaching khz khz ments mail mail analogy logarithmic logarithmic keeping bands bands bands bands bands bands bands bands bands bands bands bands bands removing neurobiology neurobiology implications implications periods bialek bialek bialek studying guarantees enhance histograms histograms facilitate francisco francisco ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles suggesting suggesting suggesting environmental environmental environmental environmental probe lett characterization characterization fitted fitted discriminate audio slight ter shorter bank bank bank bank axe poses amplitudes amplitudes amplitudes spaced hundred hundred descriptions rain decorrelation decorrelation representa peripheral preserved perpendicular decays decays ization investigating locking sam pop sta sta sta sta sta sta sta sta sta sta sta sta sta investigations geniculate parametrized suggestions chris tail tail advantageous acoust preserves const hearing loaded hilbert virtually virtually cornput stripes carrier resolutions atick atick atick atick atick atick atick fft contributes beneficial periphery vanish sloan sloan sloan bandpass bandpass implying ruderman ruderman seg focusing experimented remarkably phy phy bird bird redlich redlich attias attias attias attias schreiner schreiner schreiner schreiner schreiner schreiner basal fil bandwidths bandwidths dong dong dong organism sponse erties progression occupy octave ucsf ucsf disappears logarithmically wolf unmodified traced pling cies manifested manifested consis woods hear tent loud xve manipulate modulator loca confirming keck lagged lagged songs manifestation clarke clarke attacked loga iog iog integrative occurence hagai redun frequen rithmic tence commercially ecological dant 
#@Attias_H,Schreiner_C,
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#*model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input data data data function function function function figure figure time time time time time time time time time time time set set set set output output system system error results results results units units units units units information information information information information information information information information models models based based based based linear linear linear linear linear linear linear linear case case shown shown shown shown shown shown values probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit distribution distribution distribution distribution approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point image image single single single single processing large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate test patterns patterns analysis analysis analysis analysis optimal optimal optimal optimal optimal inputs shows shows signal signal signal signal signal signal simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual small small size size size size size size size size size size work methods methods methods methods methods fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells points field cell cell structure random high high high high high response response response response response response response response similar similar similar show show fixed line line line line line line line line average average note note experiments experiments result university threshold computation log defined defined defined sequence sequence dynamics constant constant constant constant constant constant constant estimate estimate estimate estimate standard standard terms science science left left left left left left direction direction direction direction direction direction present low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum range position position abstract computational properties references references due due due positive adaptive introduction complex complex hand estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical dynamic dynamic generated generated tion tion change change change energy energy energy energy energy energy energy energy energy energy difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower lower lower lower lower lower lower lower lower lower signals signals signals signals signals chosen higher higher center bound bound bound bound bound bound cases cases firing type cortex cortex cortex binary binary binary binary binary binary binary spike spike spike spike spike spike spike spike spike spike spike spike spike spike long conditions represent distributed distributed expected expected fact correlation correlation correlation correlation correlation correlation correlation length probabilities forward scale minimum resulting resulting ing times made study filter filter filter filter filter negative negative negative relative relative relative relative relative compared cross cross cross receptive receptive receptive provide compute compute proc perform experimental discrete cortical equal power power power power larger contrast fields fields train train train train modeling modeling selection institute institute code individual responses responses responses responses responses responses responses responses responses sequences sequences computing experiment experiment directly curves estimates top top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli bit capacity upper significant significant statistics statistics statistics vision give con coding derived randomly developed area area area area area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity lines lines lines lines lines measured discussion discussion arbitrary tested tested tested tested tested tested limited limited finding effective implemented generate adaptation adaptation square square easily simulated simulated typically smaller smaller account functional ratio ratio york york segmentation consistent trials trials trials trials trials trials trials uniform uniform uniform details filters filters filters window window window bits bits bits bits bits bits bits bits bits normalized normalized bottom bottom bottom frame frame frame frame frame produced produced run sources neuronal neuronal neuronal neuronal neuronal neuronal neuronal typical movement movement reported introduced introduced moving moving moving period period period period period side side sejnowski sejnowski dimensions varying varying compare axis axis yields match match symmetric sensitive sensitive increased increased increased amplitude amplitude amplitude intensity studied scaling occur occur trial deviation wide spikes spikes spikes spikes move width width width width width width width deterministic white white white white white white white white pass pass half half half half half half half half half flow place greater peak peak peak peak peak faster mechanisms integration integration integration integration demonstrated selective decrease averaged manner acknowledgements appears appears van van perception perception vertical vertical slightly text integrated integrated frequencies frequencies frequencies frequencies shift extraction decreases reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction variation transform transform transform modulation modulation modulation modulation modulation frames frames approximated sizes sizes sizes spectrum spectrum spectrum spectrum intervals roughly visible construction koch koch koch koch koch koch koch koch david precision precision expect recorded fire combinations plotted tests effectively computations plots plots ten capture soc soc soc soc quickly induced video interpreted symmetry comp comp wave highest cat consisted consisted preferred preferred preferred preferred preferred preferred preferred software trains trains trains trains trains trains employed employed carried carried varied detail integral helpful rise rise rise rise fourier fourier fourier fourier examine respond detectors biol biol scaled scaled scaled reliable affect statistically matched neu transmission transmission transmission transmission transmission transmission possibly reading opposite panel panel panel panel precise seconds isolated integrate burst analyzed analyzed failure nowlan nowlan rapid snr snr snr snr snr snr snr snr snr snr snr filtered division directional monkey opt opt opt beginning res medical medical bandwidth auto preceding percent transient axes lack peaks peaks recordings slower slower dots dots dots dots dots dots dots dots howard howard summarized poisson poisson anti anti ture prevent display decreased yuille yuille yuille displays shifted shifted room cybern cybern aligned primarily investigation gabor gabor gabor gabor animals velocities null null null unity unity occurred held height height hope shifts eqn eqn analyses document ranging loo james bialek bialek bialek bialek bialek bialek induce moved moved moved washington monkeys lawrence thin thin thin thin thin thin bursts spatiotemporal broken reverse reverse reverse reverse jump jump jump jump jump jump jump jump jump jump jump jump fly fly fly fired informa yielded minus transmitted transmitted transmitted preferences big sinusoidal sinusoidal sinusoidal sinusoidal assess reconstruct transparent cns cns cns shifting thick thick thick thick thick thick thick thick lobe lobe lobe lobe dominated hughes hughes adelson adelson adelson adelson adelson macaque macaque macaque lond rectified ambiguous win funded reveal inversely wider unpublished spite opti tial assistance assistance opponent opponent opponent opponent opponent rons peaked heeger heeger heeger luminance architec anthony bergen bergen bergen bergen quantitatively convolved andersen adapts electrophysiological drifting drifting ranged aperture transmit gratings gratings gratings steveninck steveninck assessed ruyter ruyter ruyter spa putative responded christof dow behaving modulate modulate movshon movshon movshon movshon movshon operated occasionally quantified directionally rieke examines aliasing mal grzywacz grzywacz grzywacz jumps jumps jumps jumps bair bair bair bair bair puted reconstructing reconstructing reconstructing reconstructing panels panels panels blowfly tony narrower narrower neurophys stant correla octave keefe leftward leftward leftward preceded warland lacks octaves overcomes causality qian qian inhomogeneous unbalanced pute electrophysiology extrastriate trailing verse tection anesthetized interleaved interleaved nyu nyu nyu neurosc levitt levitt cha tun semble wyeth wyeth bait extracellularly narrowing narrowing thinner 
#@Bair_W,Cavanaugh_J,Movshon_J,
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#*network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set set training training training training training training training training training training training training output output output output output output output output number number system system system system results results results results units units units units units units units units units units units units units units units units information information information information information models models models performance based based based based based linear linear case case case vector vector vector vector vector vector vector order order shown shown shown shown shown shown systems values values values functions neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern pattern point image image image image image image image image image image image image image image image image image image image single single single single single processing large local local local local local local local local neuron rate rate patterns analysis class class inputs inputs form shows simple simple simple simple gaussian gaussian gaussian paper paper paper paper paper examples small small feature feature feature feature feature feature feature feature feature feature feature feature feature feature work task cells cells cells cells cells cells cells cells cells cells points features features features features features features features features features features features features features features features features classification classification process current current trained trained cell cell cell cell cell structure random memory response response response response response response response response response similar similar similar similar similar representation representation representation representation representation representation representation representation architecture architecture show show show vectors vectors vectors images images images general generalization generalization generalization average average theory obtained obtained obtained obtained experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional result threshold independent found found computer terms terms distance distance distance science science prediction left direction presented presented presented presented presented map phase phase phase phase temporal temporal machine object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object press learn learn position position position basis basis basis basis abstract properties properties properties properties properties references component ieee procedure introduction complex behavior behavior behavior stimulus effect effect effect spatial spatial representations representations representations learned learned learned learned learned learned chosen chosen chosen chosen chosen chosen chosen chosen chosen higher part center cases cases type cortex cortex cortex cortex cortex cortex cortex spike represent make region region region region proposed proposed proposed scale scale finite simulations simulations simulations classes tasks simulation simulation computed computed computed computed computed respect made natural natural orientation orientation filter filter original artificial relative specific specific specific specific specific specific specific specific specific specific specific represented represented represented represented receptive receptive define compute objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects location location location location location location location perform active cortical cortical cortical brain mit comparison comparison larger contrast fields fields support support support support support support support support dependent dependent dependent selection proceedings proceedings report report institute institute institute department version technique consists internal advances represents responses responses responses responses difficult graph ai considered cambridge cambridge cambridge cambridge additional additional additional view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view view curves design stage conference full full choice choice significant vision vision estimated pages weighted randomly levels provided provided provided selected nature depends depends simply discussion technical technical tested tested limited close predictions predictions predictions finding finding implemented shape shape main face journal pixel pixel instance instance easily makes simulated typically needed combination account technology testing significantly significantly mechanism mechanism consistent consistent matching mode leads representing filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters stored stored stored stored stored stored stored stored supervised depth choose description neuronal recent robust robust takes strategy sejnowski sejnowski array cognitive observations subjects subjects volume tuning tuning tuning correspond correspond positions locations locations locations locations locations locations locations locations locations locations locations locations locations symmetric organization sensitive constructed parts parts invariant invariant invariant invariant extended derivative rotation rotation rotation rotation predicted touretzky white critical critical place greater greater reduce conclusions operator operator valued depend editors designed clear performs practice learns suggest propose propose mechanisms mechanisms presence characteristics sigmoidal sigmoidal intelligence intelligence radial variety selective plane plane iii iii iii iii configuration configuration question suppose edges tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned segments explicitly coordinates linearly transformations angle angle national extracted dependence communication squares overlap influence open showed centered centered centered centered completely suggested translation translation key key reasonable performing combining purpose interpolation distances distances distances filtering filtering faces views views views views views views views views views views views views views transactions degrees avoid recorded figures usa bell sciences recognize recognize recognize recognize extension specifically black structural major selecting poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio poggio presentation invariance ten ten characteristic repeated contained sin physiological physiological physiological physiological physiological strategies gray generalize computes preferred preferred deal tesauro oriented oriented employed simpler origin selectivity selectivity humans issues existence matches successive detectors comparable variability affect circles closest closest plausible plausible configurations thought thought aspect versions precise precise precise detected massachusetts massachusetts massachusetts scenes orientations biology biology considerable filtered filtered filtered filtered directional monkey angles angles circle members qualitative geometric prop applies freeman freeman psychophysical psychophysical psychophysical recordings biologically biologically biologically biologically psychological schematic prototypes curvature kinds shaped attentional attentional consistently gap representative acquisition indices college leen linearity linearity labelled rotations grey imaging multiplicative attractive serves exploit wire salient intuitively preparation corner inferior interference edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman edelman regarded overview conjunction vertices vertices accounts monkeys monkeys monkeys monkeys monkeys monkeys searching chooses parietal parietal recog occlusion cerebral cerebral ballard ballard ballard relies alternatively interestingly discharge asked uniquely bank bank bank bank bank rao rao rao nition personal shaded verified care decays ization neurophysiological emphasize adelson adelson acquired macaque academy preserve memo memo investigations behave behave wider pouget pouget inhibited fill fill bcm affecting medicine concerns devised isolation drastically spirit presently electrophysiological occluded occluded occluded occluded occluded distractors distractors experimented ira moderately nice distractor distractor searched leung leung ular mir weakness exponents symmetries nth logothetis logothetis logothetis logothetis logothetis logothetis logothetis logothetis logothetis logothetis logothetis expects implication steerable steerable steerable steerable steerable partic sketched erties lend farther rotates occluding gle convolutions alert tomaso biilthoff biilthoff biilthoff biilthoff detectable ject ject cluttered implausible perona evoke highlighted inferotemporal inferotemporal underway pinker pinker baylor houston sinha sinha 
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#*network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input data data function figure figure figure figure figure figure figure figure figure time set networks networks networks networks algorithm system system results units units units units units units units units units units units units units units units units units units units units units units units units information information information models models models models models hidden based based based based weights layer layer layer layer layer layer layer layer case case case case case case order shown shown shown systems systems values probability parameters parameters neurons neurons neurons neurons neurons neurons unit unit distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition method method method method approach pattern pattern pattern pattern single single processing processing processing processing processing processing control control local rate rate test test test test test patterns patterns analysis class class class class class class optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form form shows shows shows shows shows signal simple simple visual visual visual visual visual visual visual visual visual visual paper net net work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field features process process process process process process process process process level level current trained cell cell random high response response similar similar representation representation architecture show show show images approximation approximation states theory theory theory gradient gradient gradient term note note note experiments activity activity activity activity activity activity dimensional result threshold computation computation research independent independent dynamics dynamics dynamics constant terms terms connections connections connections connections connections connections science science science left left left presented presented presented presented presented present present activation frequency frequency temporal machine machine machine machine machine sets range basis basis abstract find find find properties properties references component stochastic stochastic stochastic stochastic important important important adaptive introduction complex complex hand stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical effect effect dynamic generated cost tion tion change change complexity spatial rules signals prior prior learned higher higher higher part part type cortex cortex cortex cortex good represent represent represent represent expected expected equations equations markov fact correlation probabilities scale simulations resulting resulting respect sum times regions regions means made natural natural orientation study relative true provide perform active active active eye eye eye eye eye eye eye eye experimental experimental experimental experimental experimental related distributions gain cortical cortical cortical brain equal equal mit larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields descent descent descent descent modeling modeling modeling modeling modeling morgan report report institute department version version advances joint final layers layers addition cambridge equivalent equivalent hinton hinton hinton hinton solutions san top top top top top top top top top top top top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects effects effects effects effects detection efficient full full full significant vision vision vision produce levels levels levels levels lines provided provided processes evidence iteration nature nature nature nature depends sampling biological biological discussion normal normal normal feedforward increases increases fast inverse complete complete complete complete stable finding common implemented supported require require require adaptation adaptation journal hypothesis instance instance instance instance including kaufmann probabilistic account account account account account account account dynamical jordan technology significantly significantly increasing increasing increasing increasing increasing leads representing representing representing representing iterations direct direct direct direct inhibition bottom bottom bottom bottom early early early magnitude decay predict neuronal neuronal recent recent correlations exact advantage robust lateral period period period period period period subject hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical inference cognitive varying unsupervised observations observations calculated calculated works address chain modified organization sensitive constructed horizontal horizontal horizontal horizontal horizontal horizontal horizontal parts parts parts parts parts parts occur suggests alternative locally deterministic deterministic white generally generally demonstrate half half half half place greater reduce competitive sigmoid clear faster weak mateo suggest strong mechanisms mechanisms selective selective selective selective selective selective selective selective selective min decrease iii iii iii iii iii iii manner areas monte construct carlo longer perception perception perception perception perception perception perception perception solving generating vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical distinct changing changing explicitly explicitly physical slightly belief versus versus competition competition competition competition competition competition competition competition competition competition competition competition competition competition letters decreases decreases dependence dependence dependence review review review squares activities activities activities activities activities activities activities activities completely suggested suggested constants key earlier reasonable reasonable fitting generation sufficiently transactions david expect fire fire fire fire fire figures perceptual activations activations dominance dominance dominance dominance dominance color sciences activated activated activated activated black discussions extra capable society computationally driven miller characteristic compact graphs strongly heuristic anderson neuroscience physiological follow generative generative generative duration gibbs bar bar bar bar bar involved simplified dayan dayan dayan dayan dayan dayan dayan dayan paradigm reach thresholds thresholds consisted overlapping overlapping preferred preferred preferred preferred receive oriented extend bars bars bars bars bars explore origin stimulation stimulation exhibit rapidly varied involving humans strengths strengths dotted biases behaviour behaviour behaviour fewer examine successive giving complicated oscillation hierarchy hierarchy hierarchy hierarchy plausible psychology equally equally eyes eyes eyes eyes eyes eyes eyes eyes eyes obvious switching switching switching switching generates contributions explain explain neal neal integrate massachusetts residual residual residual residual residual residual residual residual scenes slowly phenomena phenomena explanation explanation explanation explanation explanation explanation explanation independence london division incorporate choices inversion grossberg grossberg read patches arises recording depicted cybernetics cybernetics incomplete summation explained apparent greatly reflect pathways peter psychophysical psychological psychological synthesis spread modulated modulated modulated modulated modulated modulated occurrence coherent coherent comments findings findings jaakkola jaakkola specifies specifies gap analogue sleep formally appropriately zemel zemel purely royal outcome arranged suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression suppression binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular numerically stronger primate simplify striate striate striate attractive intelligent check hope reasoning imply heuristics saul periods periods periods bialek bialek studying studying studying dominant dominant dominant bad accounts accounts monkeys monkeys monkeys monkeys monkeys monkeys competing competing competing competing competing viewing augmented late rich likelihoods ignore adopted adopted insensitive influences switches grating grating grating leaving helmholtz helmholtz helmholtz helmholtz helmholtz alternating alternating presenting emerge tween convenience suppressed suppressed suppressed suppressed suppressed suppressed suppressed suppressed suppressed reflected wake brightness alter adapting monocular monocular monocular monocular monocular argue increment alternate bounding neurophysiological neurophysiological neurophysiological argued switched spreading pearl paris ambiguous selectively accounted suffer grateful supports sta frey reciprocal differing psychophysics psychophysics behaves remarkable generarive generarive generarive accordance rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry quadrant settling subjective jointly blake blake blake blake blake suffers olshausen generafive broadly connects connects connects contrasts contrasts heeger fox fox fox fox fox successively grids explanations explanations explanations explanations explanations explanations explanations explanations explanations explanations explanations explanations explanations colleagues neurobiological randomness accounting electrophysiological meant correlates nih gratings percept percept percept percept percept percept percept putative silent explaining explaining percep goodhill unobserved modulate unaffected virtue plausibility whilst forthcoming modulating modulating ities projective projective bistable psyche rightmost wolfe participate participate logothetis logothetis logothetis logothetis logothetis earliest specifications tommi percepts percepts percepts percepts percepts percepts fatigue fatigue fatigue fatigue fatigue descriptive contingencies story preferentially preferentially geoff geoff stereopsis mueller mueller revealing revealing debate consequent montague genera alternation alternation stochasticity adam diffusive tistical argues carandini creases activ barely varieties elevated characterised bart matsuoka diagnose nance factorised drafts compelling lehky lehky lehky philosophical hitherto complicate unsuitable favour bruno fresh zhaoping herrmann behaviours domi nearer sinha introduc hague 
#@Dayan_P,
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#*network network network network network network network network network network network network network model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input data data data data data function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks algorithm algorithm algorithm number number system system system system system system system system system system state state results results results results results units information information problem problem models models models models models models models performance based based based based based based based based based space weights case vector vector order order order order order shown shown shown shown values weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach pattern point point point single single single single processing processing control control control control control control control local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns analysis analysis optimal inputs inputs form shows signal signal simple simple simple simple simple simple gaussian paper small small small net work work work work cells cells step field features features features process current cell cell cell cell structure problems response response response similar show section section section section fixed fixed fixed parameter real real real average theory theory gradient gradient gradient gradient gradient gradient obtained obtained term note note note note experiments experiments dimensional result result result university computation computation computation computation independent independent defined found found dynamics initial initial initial initial initial initial constant constant constant constant constant constant constant constant computer terms connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic direction direction presented presented temporal temporal sets sets sets sets sets motion range position position position nonlinear abstract find find convergence properties properties properties references stochastic due due positive positive positive procedure important important important adaptive adaptive propagation propagation introduction introduction action complex circuit circuit behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus recurrent tion difference variable spatial assume assume assume assume chosen higher higher center center center center center center previous previous multiple multiple long conditions conditions represent equations equations equations equations equations make make length length length length forward forward forward forward scale scale scale scale resulting ing total sum performed times means optimization optimization optimization optimization optimization potential potential potential made feedback orientation orientation orientation study study relative relative relative define compute compute compute compute proc location perform active experimental goal related posterior constraints constraints motor motor motor motor motor motor motor motor motor motor discrete voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage comparison train dependent dependent institute synapses synapses synapses internal individual individual represents represents responses difficult difficult exp bias delay addition computing equivalent equivalent environment environment environment environment directly additional view view solutions solutions solutions trajectory determine determine determine speed increase give con derived developed velocity velocity lines actual actual actual actual finally finally processes constraint simply simply biological biological biological biological biological measured measured measured measured discussion normal arbitrary surface finding short common effective effective effective effective assumed generate generate generate supported role require main main ability ability future future sensory simulated simulated simulated simulated simulated simulated simulated simulated simulated typically smaller smaller dynamical transfer transfer transfer transfer interesting head head head head head head head head head details direct direct making magnitude magnitude attention produced produced run run neuronal neuronal membrane membrane membrane membrane discussed discussed pair typical movement movement movement movement movement movement movement reported lateral lateral practical strategy strategy strategy moving include period side side sense relevant dimensions previously previously approximately volume differential trans trans observation improvement exists expression studied invariant suggests derivative derivative move move move move move move white white occurs boundary setting setting pass strength starting starting greater greater trajectories trajectories segment segment segment segment segment segment segment segment conclusions neighbor central suggest suggest mechanisms presence sigmoidal radial assuming assuming variety variety variety movements introduce program annealing force force acknowledgements relation derive derive derive produces produces longer generating laboratory laboratory label label stability distinct segments sensitivity sensitivity sensitivity coordinates coordinates coordinates averaging linearly linearly linearly physical electrical electrical slightly angle angle angle unique unique scales scales develop integrated equilibrium potentials choosing focus focus dependence viewed solved solved variation evaluated suggested constants constants constants allowed allowed earlier reasonable dashed performing delays classical combining roughly roughly distances sufficiently foundation avoid fire usa recognize determines discuss successfully successfully simplicity simplicity determining identified closely closely capable capable capable modification effectively effectively included wij score situation essentially reached receives soc soc compact showing showing neuroscience conductance dis sin physiological physiological physiological follow strategies strategies strategies strategies sci duration write realistic realistic backward wave wave computes leading neurosci moves moves moves moves intrinsic oriented presents presents body body body body body body body body body body body body body body body body body remain exhibit updating environments steady detail strengths strengths optimized optimized preliminary helpful existence existence existence existence postsynaptic successive respond rest behavioral behavioral behavioral behavioral possibility muscle muscle muscle muscle muscle muscle authors authors reliable reliable tanh tanh scores func understand presynaptic neu act math transmission transmission transmission transmission plausible necessarily rev equally voltages voltages algo assumes nerve nerve nervous nervous nervous nervous nervous nervous nervous nervous initialized generates improving established animal animal animal animal animal animal animal asymptotically indicating directed interneurons interneurons london comparisons considerable closer ring ring precisely forces incorporate potentially involve angles angles acad beginning optimize arises geometry radius nsf mechanics mechanics mechanics summation integrating requiring fourth geometric improvements behaviors embedded introducing recordings recordings recordings maxima commands commands commands maintain release release rely mod collective conductances conductances sums display decreased segmented shaped physiol instantaneous pose primarily generator assign modify rithm arguments nat controlling purely rotations anatomical anatomical anatomical anatomical numerically numerically numerically numerically minutes minutes simplify held chemical chemical chemical chemical chemical chemical chemical chemical chemical chemical chemical attractive biased observing imply intuitive muscles muscles muscles muscles published analyses analyses analyses expanded expanded sim somatic spherical thomas soma elastic reproduce tic tic diameter diameter diameter treatment contraction contraction contraction fitness fitness agree concentration concentration concentration concentration concentration davis davis captures onr pressure neurophysiology neurophysiology specification shorter sig graded graded graded graded graded goodman goodman goodman goodman ram responds flat resting sinusoidal sinusoidal sinusoidal sinusoidal sinusoidal sinusoidal sinusoidal constrain perpendicular searches emphasized dorsal dorsal dorsal dorsal dorsal turning knowing els intensive ward ward oregon oregon unpublished unpublished unpublished unpublished unpublished develops tonic tonic species locomotion locomotion locomotion locomotion locomotion locomotion locomotion tension tension tension differently cpg cpg cpg quantify quantify morphology morphology adult polarity tip tip tip tip believed believed anterior anterior ventral ventral ventral ventral ventral ally operational laser detects trol compartment tracks tracks sloan evolving rel senses sis relaxed electrophysiological electrophysiological ben sweep sweep sweep sweep corn putation freely freely depolarization initiated elegant orbit phil ito capacitive aimed albeit opportunity imposing ele ele ele ele ele ele ele ele ele ele tiny niebur niebur niebur niebur favorable thompson concentrations abstr overshoot compartmental comprise tar signaling ans ans ans ans ans ans neck neck 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#*network neural neural input data data data data function function function figure figure figure time time time time time time time time time time time set number system system system system system error results results information information information information information information information information information information performance performance performance performance space linear linear linear layer case vector vector vector vector vector vector vector vector vector order order order order order order order order order order shown shown systems probability probability probability probability probability probability probability probability probability probability parameters noise noise noise noise neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution recognition recognition method method method method approach pattern pattern image single single single single single single single processing processing processing processing processing large local local rate rate patterns patterns analysis analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal form shows shows shows signal signal signal signal signal signal signal signal signal signal signal small size size feature feature feature feature feature feature feature feature feature feature feature feature task task methods methods methods methods methods fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step field field field field field field field field field field field field field field field field field features features features features features features features features classification classification classification classification classification classification classification classification classification level level level cell cell cell cell cell random random random random random random random random random random high high high high response response response response response response response response response similar equation section section fixed line line line line line vectors vectors general obtained obtained obtained obtained obtained note experiments dimensional dimensional result threshold threshold threshold solution defined found found standard standard computer synaptic synaptic science left direction direction phase phase phase phase phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal maximum range press components sample sample abstract applied applied find properties references references component ieee procedure context introduction introduction introduction estimation estimation estimation estimation estimation behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical statistical generated generated variance difference difference variable variable variable variable lower lower signals signals signals prior chosen chosen higher higher higher part part center cases firing firing firing firing firing type type type type type type type type type type spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long expected expected region correlation length correct correct correct correct correct correct correct correct correct probabilities observed scale resulting resulting classes ing computed computed computed performed eq eq eq eq eq times regions means made made study filter filter filter filter obtain true compared compared cross objects objects location perform determined determined determined experimental experimental experimental posterior posterior distributions distributions distributions distributions distributions distributions motor equal power mit voltage voltage accuracy accuracy contrast fields support train train train train train train nets department department code code responses responses scheme maps cambridge domain experiment experiment experiment environment san stage stage stage stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects detection detection detection determine estimated estimated increase increase con con coding coding coding coding coding coding coding coding coding coding coding developed levels types finally sampling sampling discussion discussion covariance increases increases increases arbitrary close stable surface short short short eds square end ability ability easily sensory smaller underlying functional technology ratio ratio ratio projection york york york york york principal details details normalized minimize minimize sources neuronal neuronal resolution robust separate separate typical typical typical lateral lateral lateral lateral lateral moving identical sense sense engineering varying varying varying varying varying compare previously axis axis rl trans interval interval organization amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude horizontal horizontal studied studied deviation deviation spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes matrices white white white white occurs setting pass half conclusion place depend central central central differences encoding encoding encoding presence presence presence largest cycle california manner program pro van generating estimating ann vertical frequencies springer springer extraction extraction extraction extraction extraction decreases decreases independently formation communication communication communication squares squares squares squares squares solved solved detailed detailed detailed detailed detailed detailed transform transform open controlled fraction fraction fraction fraction fraction fraction fraction fraction modulation modulation modulation modulation modulation sizes activities similarly allowed discrimination discrimination discrimination spectrum spectrum dashed reduces false filtering koch koch koch koch koch koch koch koch dendritic recorded fire fire fire eigenvalues maximize specifically black black black characterized encoded encoded encoded encoded identify computations comparing plots verlag verlag strongly allowing anderson anderson anderson classify physiological categories receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor comp comp comp comp comp sampled wave wave wave leading neurosci subsequent subsequent subsequent acknowledgments receive trains trains trains trains trains trains trains trains trains trains body body carried diego wiley wiley wiley poor poor poor varied varied discriminant ml fourier fourier fourier respond investigated office reliable reliable maximizing pathway encode encode encode encode encode neu circles circles trace reading predicting rev fisher separated nerve nervous multivariate pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal generates extent isolated isolated isolated isolated isolated isolated isolated isolated established integrate burst burst burst burst burst burst burst burst burst burst burst burst burst site cos analyzed analyzed analyzed waveform waveform biology biology biology biology caused processed processed snr division division located located nucleus mation afferent afferent cut cut projected projected projected recording recording recording preceding preceding preceding preceding preceding preceding preceding preceding preceding preceding preceding preceding nsf nsf explained pathways poorly marked recordings recordings recordings dots schematic rely summarized characterize aim modulated extracting cal cal occurrence occurrence occurrence tank pasadena pasadena electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric electric physiol physiol summed yielding univ univ trade generator generator labeling labeling conditioned optimizing perfectly null neurophysiol bin bin bin bin bin bin receptors caltech caltech cellular chance occurred mail held resistance occurring occurring occurring occurring occurring occurring occurring occurring occurring carry carry filled infor reliably reliably reliably weakly weakly weakly weakly weakly weakly weakly mance bialek bialek perfor injection fish fish fish fish fish fish fish fish fish fish fish fish fish fish fish fish fish fish fish neuromorphic bursts bursts bursts bursts bursts bursts reveals bins bins locked locked jolla specificity belonging passing grants verify verify discharge multiplying crossing ple outperform encodes distinction quasi lesions reports covariances tor sinusoidal sinusoidal electrode adapting clas verified peripheral preserved exam lobe lobe lobe playing intra mouth relate individually electrodes electrodes electrodes differentiation anal alternatives distinguished distinguished afferents afferents afferents afferents afferents afferents afferents afferents afferents afferents afferents afferents afferents afferents intracellular intracellular intracellular intracellular intracellular alarm rod rod avoidance avoidance avoidance retained correlate ucsd fiat tail tail resp resp resp resp resp externally externally characterizing autocorrelation assistance locate hopkins hopkins cornput adult loosely carrier carrier jain jain drawing agency neurol neurol substitute substitute periphery raises convolved longest accounting cutoff positioning elec elec elec transmit transmit transmit mach steveninck assessed assessed ruyter syst dipole responded christof discriminating retaining wiener drug kolmogorov amax reviews extracellular pooled stim ell ell ell ell ell ell corresponded corresponded corresponded ordinate rogers walter beat clamp blank abscissa interfering organ organ proj raise warland torus heiligenberg heiligenberg heiligenberg heiligenberg heiligenberg modulations modulations modulations modulations modulations modulations bullock bullock bullock emitted sification intell tape tape tape raising midbrain attenuated klab klab neut neut sect sect sect sect sect sect sect sect sect trast electrophysiology electrophysiology sory amin faithfully faithfully terior ulus rectifying stations tio jolliffe jolliffe taining bessel strategic carr carr practitioners lined signaled recommendations rosci lowers pyra jections discharging nerves midal commerce exposing asterisk cytology binned 
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time output output output output output number system system system state models models performance performance performance based based space space space space space space space weights linear linear linear order shown shown shown noise noise weight neurons neurons neurons unit pattern image single processing control control control control control control control control control control local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns analysis analysis analysis optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs shows signal signal simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper small work fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field features features features features level cell cell cell cell cell cell response response response response response response response similar similar similar similar similar show equation equation line line line line line line line line line line line line line line line average average average theory note note note activity activity activity activity activity activity dimensional university university threshold threshold threshold research found target constant constant computer computer computer connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic science science prediction direction presented presented phase phase temporal object object motion maximum maximum range range press press press press basis outputs outputs outputs outputs abstract back back back find find computational computational properties references ieee introduction behavior dynamic cost recurrent spatial lower lower signals signals higher higher higher higher higher higher higher higher higher higher higher center center center cases firing cortex cortex cortex cortex long conditions represent distributed distributed expected correlation length length observed observed observed observed observed finite finite resulting ing ing ing human human times elements elements elements elements elements elements elements elements elements elements elements elements regions feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation orientation orientation orientation orientation orientation global global study receptive receptive receptive receptive receptive receptive provide objects objects objects rates proc proc location location location active active experimental experimental related connected connected gain discrete discrete discrete cortical cortical cortical cortical cortical brain brain equal approaches steps connection connection connection connection connection connection fields proceedings report institute loss internal individual individual responses responses responses difficult final addition addition graph ai curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curves curves curves curves curves curves curves curves curves top top top stimuli detection detection conference conference significant vision vision vision vision increase increase produce condition condition levels types inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological biological achieved discussion increases increases group group group corresponds complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory predictions circuits circuits finding finding effective supported role role require eds hypothesis easily sensory pairs smaller underlying underlying underlying needed needed jordan technology interesting testing ratio ratio york york edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge increasing increasing segmentation segmentation segmentation segmentation segmentation segmentation mechanism mechanism mechanism operation details numbers max inhibition inhibition international international bottom bottom bottom depth produced membrane membrane membrane recent correlations property property pair pair element element element element interest dimensions dimensions compare compare observations observations tuning tuning tions smooth smooth smooth smooth smooth achieve achieve achieve achieve background background background locations observation grid grid grid grid organization organization increased grant exists horizontal horizontal horizontal horizontal invariant occur suggests extended rotation predicted alternative feed white white white column column setting demonstrate strength row row row row row row segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment central central central central central central central interactions interactions interactions clear clear weak weak weak suggest mechanisms mechanisms mechanisms integration integration integration integration integration integration integration integration integration integration integration external reduction solid proportional proportional selective decrease decrease targets introduce introduce introduce scene denoted areas van van edges edges edges edges edges longer longer longer longer primary primary primary primary plot plot tuned tuned segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments sensitivity sensitivity sensitivity infinite potentials decreases decreases reconstruction influence open open open open operations centers centers centers centers centers centers centers centers centers centers centers modulation activities activities activities activities activities activities activities activities activities activities activities completely completely translation translation constants constants dashed delays roughly boundaries closed closed closed closed closed david existing existing existing existing figures usa usa color contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour black partially texture simplicity middle extra society effectively effectively identify post invariance plots receives receives receives composed composed excitation excitation excitation summary link link link showing dis symmetry oscillations oscillations physiological physiological sci sci hold gray play play dayan ill preferred extract neighboring neighboring neighboring oriented oriented oriented oriented explore essential exhibit put dotted helpful fewer rest applicable biol analytically analytically referred oscillation oscillation oscillation oscillation analogous contours contours contours contours contours saliency saliency naturally plausible plausible predicts predicts equally olfactory olfactory der assumes consist simplest grouping grouping grouping submitted explain isolated ment directed orientations smoothness smoothness phenomena phenomena analytical caused interneurons choices desirable desirable acad acad grossberg grossberg circle circle circle circle circle circle circle res res lowest cybernetics incomplete apparent applies empirically experimentally lack lack lack peter psychophysical psychophysical introducing treated biologically synchrony synchrony synchrony curvature curvature curvature curvature curvature singer germany boston comments decreased decreased findings contribute gap cybern aligned aligned aligned aligned aligned modify oxford gabor martin neurophysiol odor odor odor jones jones enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement enhancement generality saturation stronger stronger stronger primitive belong salient enhanced enhanced filled filled natl natl meaningful meaningful weakly introduces sion decide von moved enhance enhance enhance enhance enhance enhance enhance enhance accounts stereo bases infer cerebral locked ends belonging belonging route projects captures treat linked outline shorter shorter shorter gaps gaps employs axe axe axe connec preferences amplitudes amplitudes spaced malsburg publication 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#@Li_Z,
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#*learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure time time time time time time time set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm number results results results results units information information information information information information models models models models models models models models models models models performance based linear linear linear linear linear case case case case case case case case case vector order order order order order order order order order order order order order shown systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method approach approach approach approach approach approach approach approach pattern point point processing neuron neuron test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis matrix matrix inputs form form form form form form signal signal signal signal signal visual paper paper feature methods methods methods methods methods methods step trained cell cell cell cell structure structure structure structure structure structure structure structure structure structure structure structure structure structure high equation fixed general general general parameter parameter approximation states obtained obtained obtained obtained term term note experiments activity activity activity activity university university university university solution research research independent independent independent independent log log log log log log log defined found sequence sequence sequence sequence sequence target target table table estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard standard terms terms terms distance synaptic synaptic left presented presented presented map map present present present present activation activation activation nodes nodes frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal sets sets range range press press components abstract applied applied applied density references component component component stochastic due due due due positive procedure procedure adaptive introduction action behavior behavior statistical statistical statistical statistical effect search search spatial spatial assume assume assume assume lower lower prior prior prior prior prior prior prior prior higher higher higher previous cases cases firing firing firing firing firing firing firing firing firing firing type multiple cortex cortex cortex good binary binary binary binary represent represent represent represent distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected markov markov markov fact correlation correlation correlation correlation correlation correlation correlation correlation correlation probabilities probabilities observed resulting computed multi multi multi sum called called called called means means means potential made natural obtain obtain artificial specific specific specific specific specific represented compared define define active determined determined determined experimental posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions gain discrete brain brain equal equal mit larger larger connection update source morgan proceedings report institute institute code individual joint joint joint represents delay delay sequences ai framework cambridge cambridge cambridge computing equivalent experiment directly estimates transition san effects effects detection detection conference requires choice approximate estimated estimated estimated estimated estimated condition conditional conditional conditional conditional criterion criterion entropy entropy entropy provided provided selected evidence inhibitory depends achieved covariance normal technical group group group group group denote denote denote denote denote denote tested close close inverse excitatory circuits common common common assumed synapse journal journal journal hypothesis instance cluster cluster cluster cluster degree kaufmann simulated simulated simulated typically pairs interesting york consistent structures structures structures structures structures structures structures structures structures structures trials trials matching mode mode mode principle principle call max max max max max max pre magnitude light light light light light denotes discussed directions correlations correlations correlations correlations correlations correlations correlations correlations correlations exact pair include include period hierarchical subset subset subset subset subset subset engineering observations observations converge definition definition chain chain chain organization trial deviation deviation deviation deviation deviation predicted clusters demonstrate runs runs strength strength strength strength strength strength strength strength strength strength central central interactions interactions interactions interactions interactions interactions interactions interactions interactions accurate accurate bayes weak weak mateo propose presence presence external intelligence groups groups groups connectivity connectivity connectivity configuration relation monte monte construct carlo carlo written index index solving ways factors estimating estimating dept dept segments segments missing simultaneously simultaneously remaining unique interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction develop events events events events events events events events formed expectation expectation family family stationary stationary stationary interpretation influence densities evaluated approximations forms converges key key measurements expansion expansion expansion expansion intervals intervals intervals intervals intervals intervals event closed closed msec msec msec msec recorded recorded fire includes color illustrated uncertainty uncertainty discuss variations absolute characterized tests straightforward selecting capable capable encoded encoded spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking post verlag kind contained prob prob prob prob prob prob interpreted manifold physiological timing cue cue involved involved absence absence absence absence minimizes highest leading presents simpler carried american american wiley exhibit exhibit exhibit strengths strengths strengths association association integral mass existence existence school school biol dependencies dependencies dependencies proper proper proper proper proper proper cognition coefficient coefficient possibly possibly configurations configurations configurations configurations configurations configurations analyze changed subsets subsets subsets subsets subsets subsets subsets fisher observe hebb hebb hebb multivariate consist detected synthetic seconds established established piecewise pairwise theoretic analyzed analyzed analyzed phenomena independence shared ring strictly precisely constructing ran bishop bishop bishop bishop probable separately beginning medical medical author author author robustness summation explained integrating argument fourth fourth fourth fourth reflects reflects reflects double led parameterized red orders recordings recordings recordings recordings detecting detecting treated treated psychological release exhibits maximizes maximizes maximizes occurrence occurrence collective marginal marginal germany windows deviations specifies simultaneous simultaneous synchronization synchronization synchronization synchronization synchronization synchronization synchronization phenomenon shifted physiology mistake fix arguments refractory animals null turned extending kullback chance significance significance significance chains siemens siemens attractive check observing shifts synchronous synchronous adequate preparation carry moments fires composition composition holland regard dendrite monkeys monkeys monkeys monkeys monkeys monkeys assembly laplace laplace israel cerebral spatiotemporal indicator belonging assigns treat treat neurophysiology unified drop logarithm ent ent ent ent ent leibler spatio spatio spatio spatio spatio spatio conjecture quasi quasi quasi quasi seek leg visited magnitudes expand maximally statistic statistic frontal frontal distinguished assemblies assemblies assemblies supports preprint milliseconds milliseconds challenge challenge develops coming persistent rarely syn abeles abeles abeles abeles abeles drawing identically anatomy distinguishing conflicting offsets inferring characterizes complement establishing planck ready ready ready ready ready ready ready ready ready zeros capturing jerusalem jerusalem behaving behaving behaving spario spario spario spario marginals marginals marginals marginals marginals hebrew hebrew touch touch couple localize mason awake lasting exhibiting palm munich munich deco deco deco deco deco deco deco deco deco deco inferences george millisecond justifies unrealistic unitary unambiguous otto manifest silence vaadia vaadia vaadia vaadia vaadia xii bergman hahn twofold blink blink aertsen couples rhesus rhesus cyb 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#@Deco_G,Laskey_K,Martignon_L,Vaadia_E,
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#*network network network learning model model model model model neural neural neural input input input input input input input data function function figure figure figure figure figure figure set output number number number number number state results results results results results results results units units information information models hidden based based linear linear linear layer layer layer case order shown shown shown shown shown shown shown shown shown shown shown systems parameters parameters neurons neurons neurons neurons neurons method pattern pattern image image single single single single single single single processing processing processing processing processing processing control control large large large local local local local neuron neuron neuron neuron neuron neuron neuron neuron rate optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs form simple simple simple simple simple simple simple simple simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual small size size work work work methods fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field features level level cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random random random random random memory response response response response response response response similar architecture show section images images parameter average average experiments activity activity activity activity activity university university computation computation computation computation research independent independent sequence initial table table table estimate standard distance distance distance distance connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic science science left left presented presented presented presented present present phase low frequency frequency press position position position position basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs abstract properties properties properties references due due ieee introduction complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus generated recurrent tion change energy difference spatial spatial spatial spatial measure measure chosen chosen chosen center center center center center center center center center center center center center center center center center center center center center previous previous previous type type type type type type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike spike tree tree tree tree tree tree tree tree tree correlation correlation length errors simulations simulations classes ing total simulation simulation simulation sum mapping potential made natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study study negative vol series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide rates location location active active active active active active active active active active active determined experimental experimental distributions gain cortical cortical cortical cortical cortical cortical cortical cortical brain power voltage voltage comparison comparison larger larger larger larger larger contrast contrast contrast contrast fields fields fields fields dependent dependent dependent dependent modeling modeling modeling modeling morgan department implementation synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses advances responses responses responses responses responses responses responses responses responses responses responses responses layers addition environment directly curves curves curves curves san san top stimuli stimuli significant pages pages validation produce condition condition condition channel derived derived derived derived randomly clustering clustering levels area velocity velocity provided selected inhibitory inhibitory achieved achieved measured measured discussion normal group tested tested close excitatory excitatory excitatory excitatory excitatory excitatory excitatory synapse synapse synapse synapse synapse generate role pixel pixel hypothesis cluster development sensory including including including kaufmann pairs pairs pairs pairs pairs pairs pairs pairs unknown significantly significantly edge edge edge consistent structures uniform empirical principle principal details filters filters direct bottom depth polynomial run light light light light light light light light membrane membrane recent property property period pixels pixels pixels trees trees subset array array array array array engineering previously approximately tuning tuning tuning tuning tuning tuning tuning tuning tuning match studies studies trans background background positions positions modified channels channels channels exists invariant spikes width width width width width width width width width clusters white column column runs runs depend depend editors editors interactions retina peak moody mateo strong mechanisms integration california california turn turn variety variety selective averaged groups program suppose pro derive edges perception perception primary vertical vertical vertical vertical vertical vertical vertical vertical distinct modeled modeled modeled modeled modeled sensitivity sensitivity linearly involves consisting consisting interaction formed john choosing choosing national formation review depending correlated squares overlap detailed detailed lee centered activities suggested translation translation discrimination normalization sec neighborhood remains remains foundation dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic degrees degrees currents activated activated activated activated activated activated activated activated activated coupled coupled successfully columns columns columns aspects capable driven driven included included computations invariance receives traditional strongly contained moore showing interested neuroscience lie gray bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar michael absence surround surround surround surround surround surround surround cat cat cat cat cat cat automatically neurosci consisted disparity neighboring acknowledgments receive oriented oriented oriented oriented oriented oriented oriented oriented bars bars bars bars bars bars bars bars bars bars bars bars bars bars bars origin origin selectivity carried diego access exhibit put steady involving hanson lippmann rise rise respond respond giving detectors plasticity ideal scaled office referred lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn func hierarchy hierarchy phases neu circles circles circles onset man opposite implementations mapped mapped academic pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal explain established indicating site site preference slowly orientations orientations orientations orientations orientations guaranteed adjacent nonlinearity comparisons spatially inside drive drive sys sites filtered filtered products angles beginning res localized meaning summation explained virtual geometric apparent behaviors freeman freeman substantially pure led transient dark dark dark dark dark dark dark dark tional peaks frequently exhibits gen suited conductances conductances gave physiol physiol cybern ear physiology physiology feasible martin count neurophysiol neurophysiol naval outcome binocular striate striate striate resistance los los balance resulted nearby implications imply effectiveness salient optimally optimally optimally optimally optimally arrays arrays presentations wilson passive bartlett dendrites dendrites dendrites dendrites dendrites surprising mel mel mel mel mel mel mel mel sim somatic somatic somatic soma arrangement arrangement arrangement foundations thin thin thin stimulated layout epsp grants generalizing influences stone graded wiesel wiesel wiesel conjecture abstraction arbor arbor ideally big resting hubel hubel hubel clustered attempted conduction biophysical biophysical biophysical biophysical biophysical thick decays neurophysiological thresholded douglas relate lond rough selectively emphasized superposition funded afferents intracellular placing placing inactive inactive wider hodgkin crude huxley morphology ron neocortical horizontally physiologically sharply exclusively nmda nmda nmda nmda nmda heeger intracortical intracortical chan alan contacts establishing vertically absent pooling pooling remained remained ruderman ruderman ruderman ruderman ance thresh silent stabilization daniel initiated movshon cats elevation fundamentally excitable biomedical angeles angeles subsampling sodium restart mainen displaced displaced manipulating electrically cen monosynaptic thalamic violation originating nonlin southern southern asynchronously unoriented rodney subdivided subdivided ohzawa ohzawa originate ampa ampa conduc linkage minimally subunits kevin hines subregions subregions diamonds persist malpeli akin tered nels insensitivity intradendritic intradendritic intradendritic abstracted invari tances principally caution biophysically discrimina courtesy 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#@Archie_K,Mel_B,Ruderman_D,
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#*network network model model model model model model model model model model model input input input input input input input input input input input input input input input input input input input function function figure figure figure figure set set set set set set networks results results results results results results units models models models based based based space weights weights weights weights weights weights linear layer layer case shown shown shown parameters parameters noise noise neurons neurons neurons neurons neurons neurons unit unit unit pattern single single large large large large large local local local local local local local local neuron neuron neuron neuron neuron neuron rate rate rate rate rate patterns patterns patterns patterns patterns analysis optimal inputs form shows shows shows simple simple simple simple simple simple gaussian visual visual visual visual visual visual paper small small small work fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field features level level level level current cell structure structure structure response response response response response response response response response similar similar similar similar similar similar representation show show show fixed line parameter parameter parameter states term note experiments activity activity activity activity activity threshold research found target target target target dynamics dynamics dynamics constant connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic science science left presented map map map map map present phase activation activation activation activation activation activation activation activation activation activation range range range range range range range range range range range range range range range range range range position basis continuous abstract find find properties properties properties properties properties references due positive positive context introduction action complex circuit circuit circuit circuit behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect parallel change change spatial chosen chosen higher higher part part center center center center center center center center center center center center center center center center center center center center center center center previous previous firing firing type cortex cortex cortex cortex cortex cortex cortex long long long long long long long long long long long long long long long conditions represent observed observed observed observed simulations simulations simulations simulations simulations resulting ing sum performed times elements elements regions regions regions means potential feedback feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study knowledge specific specific specific cross cross cross receptive receptive receptive receptive receptive receptive receptive provide provide define proc gain gain gain cortical cortical cortical cortical cortical cortical cortical larger larger larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields fields fields dependent dependent modeling modeling modeling modeling words consists kernel responses responses responses responses exp exp exp maps curve curve additional additional additional additional curves curves curves stimuli stimuli stimuli stimuli effects effects determine full choice vision basic increase con derived levels levels lines evidence evidence nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends discussion denote excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory effective effective effective assumed assumed shape supported require main future dynamical mechanism consistent consistent leads leads representing inhibition inhibition inhibition added description light denotes denotes denotes population population population population population recent recent correlations property property element lateral lateral lateral lateral lateral lateral lateral identical quadratic sense array recently sufficient calculated tuning tuning tuning tuning tuning tions tions studies differential differential differential locations grid grid interval organization amplitude horizontal horizontal horizontal horizontal horizontal horizontal lead suggests wide width white column demonstrate demonstrate strength strength strength assumptions depend central central interactions interactions interactions interactions interactions interactions interactions interactions weak weak suggest suggest hard external external external external external external external demonstrated demonstrated assuming selective selective decrease averaged connectivity van primary primary primary tuned tuned tuned vertical modeled modeled sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity scales consisting interaction interaction interaction interaction implies independently focus dependence dependence depending depending depending stationary squares influence variation detailed restricted fraction fraction fraction centered sizes sign sign dashed dashed classical classical classical classical distances coupling coupling coupling coupling expect perceptual combinations combinations activated activated activated activated domains domains black discussions structural simplicity columns columns columns columns columns effectively driven driven driven wij wij wij wij wij wij wij presentation spiking post orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal receives excitation excitation excitation excitation summary strongly strongly strongly strongly strongly induced contribution physiological sci bar surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround leading neurosci neurosci neurosci neurosci preferred preferred preferred preferred preferred preferred preferred oriented oriented oriented oriented oriented oriented extend cowan cowan origin stimulation stimulation stimulation stimulation stimulation selectivity selectivity selectivity selectivity selectivity investigate exhibit exhibit circuitry circuitry dotted dotted postsynaptic postsynaptic matches respond respond respond biol analytically tanh encode act act patch patch patch patch patch patch patch patch patch possibly analyze equally perfect contributions isolated preference preference preference preference preference preference preference preference preference piecewise agreement orientations orientations orientations orientations convolution analyzed phenomena explanation independence lies inside turns turns sites arise arise arise afferent afferent afferent controls projected projected projected acknowledgement acad res localized patches demonstrates radius radius radius radius outer explained understood consistency consistency lack marked exhibits synchrony qualitatively singer substantial substantial germany shaped shaped findings implements displays cor phenomenon discontinuities tation tation driving recover nat bin bin jones enhancement enhancement enhancement grey grey grey interconnected arranged suppression anatomical balance analyzing analyzing enhanced wilson substituting sompolinsky weakly weakly recovered connect connect induce induce displayed surprising surprising uni emergence emergence stimulated stimulated stimulated stimulated stimulated stimulated stimulated stimulated stimulated specificity specificity partitioned davis captures interestingly influences acknowledge yielded incorporates email wiesel wiesel emergent emergent revealed nelson nelson rao isotropic tween abstraction chaos preferences spaced constitutes suppressed suppressed suppressed suppressed suppressed suppressed suppressed suppressed demon concentrated elementary distant distant distant regulation intra iso iso argued iri selectively selectively importantly figs figs responding universit gilbert gilbert gilbert pop preprint rotating exhibited exhibited exhibited tin tin tin utilizing stimulating lation institut hat hat inhibit virtually bold fill essen contrasts couplings intracortical intracortical intracortical intracortical presently ben nominal sur sur polar spanning depolarization modulate hirsch klaus klaus theo ities darker pursued niebur controllable kim blob exceeded sual usher pared physik blobs pawelzik pawelzik pawelzik pawelzik katz emerging nected neurophys strated preferentially rin normalizes normalizes ations mexican mexican rli ori ori cre cre knierim annulus amir selectivities pnas lat wolf wolf wolf wolf ubiquitous patchy modulations lighter gions summarizing reciprocally interac interac terminating orien orien sillito sillito sillito sillito sillito wei ain ain ain fred fred sagi todorov cyb interplay evoke deutsche ash centrally centrally balances ilar ilar radically theoretische continous sti yishai ffir ffir hypercolumns underlies popu tat tat tat ernst ernst ernst ernst regulates entation grinvald contrasting mpi forschungsgemeinschaft 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#@Fanst_U,Geisel_T,Pawelzik_K,Wolf_F,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model neural input input input input input input input input input input input input input input input input input input input input input input data data data data data data data function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set set networks networks networks networks networks output number number number number system system state results results results units units units units units units units units units units units units units units units units units units units problem problem performance performance performance based weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case vector vector vector order order order shown shown shown shown shown shown shown systems values values values probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit distribution distribution distribution distribution method method method method method method approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image image control large large large local neuron patterns patterns patterns analysis analysis analysis matrix optimal inputs form form form shows simple gaussian gaussian gaussian visual visual paper paper small small small small small feature work work work methods methods methods methods methods methods cells cells cells cells process process current cell problems random random response response response similar similar similar similar representation architecture show show show equation equation fixed fixed fixed line line line line line line theory obtained obtained term term term experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result variables variables variables variables variables variables solution log defined found found found dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard standard standard standard terms terms terms distance distance distance distance distance connections connections connections connections connections connections connections prediction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented present phase phase phase phase activation activation activation object motion motion motion motion maximum maximum maximum maximum maximum press position position position position position position position position components basis basis abstract find computational likelihood likelihood likelihood likelihood likelihood references component component component component component stochastic due ieee introduction complex complex estimation estimation estimation estimation estimation estimation generated variance variance variance variance variance variance variance recurrent recurrent recurrent recurrent tion difference difference difference difference variable variable variable variable variable lower measure prior prior representations chosen higher center center bound bound bound bound bound bound bound bound cases type cortex cortex good good distributed distributed bayesian expected expected expected equations equations make fact proposed simulations simulations simulations simulations minimum minimum minimum human computed respect respect called times mapping means factor factor orientation orientation orientation orientation orientation orientation global obtain obtain true true compared provide provide provide compute compute proc proc perform perform goal related connected connected motor motor motor cortical cortical cortical cortical brain brain equal comparison larger contrast contrast contrast dependent institute institute institute words words consists code code code code code code code code code responses responses responses responses responses final final final final final final final final exp exp bias bias ai ai ai ai ai ai ai ai equivalent equivalent equivalent equivalent equivalent directly curve curve curve curve curves curves curves curves curves estimates estimates limit limit determine determine efficient efficient efficient efficient efficient choice choice choice significant approximate free vision estimated coding conditional area types types product product product product actual provided iteration nature depends depends simply simply biological discussion normal normal normal arbitrary arbitrary denote tested close close assumption corresponds corresponds stable stable stable stable stable stable stable circuits finding common shape shape shape shape generate require adaptation square end end instance noisy noisy noisy sensory sensory sensory fit typically typically needed dynamical dynamical unknown fully fully fully york consistent trials squared squared representing iterations iterations iterations iterations iterations iterations iterations normalized minimize minimize choose neuronal neuronal neuronal architectures population population population population population directions directions directions exact property lateral lateral lateral lateral lateral lateral lateral practical moving moving moving array array cognitive relevant interest sufficient sufficient compare compare tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tions match match correspond converge differential trans definition background symmetric symmetric interval interval amplitude scaling scaling suggests extended extended trial trial deviation deviation deviation deviation deviation deviation deviation derivative derivative derivative derivative derivative boundary demonstrate critical place depend designed peak peak peak peak peak asymptotic characteristics demonstrated demonstrated solid solid radial turn minimizing minimizing start derivatives derivatives factors factors factors estimating estimating tuned tuned tuned tuned tuned vertical vertical vertical implement simultaneously involves slightly develop expectation decreases independently estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator overlap overlap codes codes codes codes transform showed showed understanding activities activities suggested discrimination discrimination slow performing classical classical classical expansion expansion fitting fitting fitting fitting purpose valid sufficiently advantages usa usa bell sciences determines plotted illustrated illustrated illustrated illustrated maximize neighbors characterized closely closely closely uniformly encoded encoded encoded computationally situation tend receives notice decoding showing interested sci comp comp comp comp comp comp comp comp comp comp comp bar bar involved vary write relaxation dot dot dot dot generalize minimizes reach reach attempt consisted disparity disparity preferred preferred preferred preferred preferred preferred preferred deal deal minimized minimized explore unlike unlike selectivity exhibit rapidly estimators estimators estimators estimators estimators dotted dotted dotted mass ml ml ml ml ml ml ml ml ml ml ml ml ml ml periodic periodic periodic periodic scalar scalar scalar fourier fourier fourier fourier fourier matches matches mappings investigated maximizing maximizing maximizing encode encode statistically statistically statistically statistically presynaptic hill hill hill hill hill hill hill hill hill hill hill hill hill hill smallest smallest coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse plausible reading predicts taylor taylor academic initialized simplest optimum optimum histogram stop cos orientations orientations variances unstable analytical adapted briefly widely broad consequence acad acad grossberg grossberg describing opt circle calculations medical read depicted populations profile profile profile profile profile profile profile profile understood transient transient transient readily psychophysical cohen cohen peaks recordings biologically howard poisson poisson poisson spread reaches maximizes shaped shaped shaped unbiased deviations deviations contribute contribute contribute corrupted uncorrelated uncorrelated primarily recover perfectly circular circular circular circular circular robotics reaching clamped clamped clamped spontaneous fits consideration consideration numerically interpret keeping keeping affected affected salk salk salk natl natl lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov performances sompolinsky sompolinsky sompolinsky governed governed zhang zhang zhang zhang zhang corre negligible negligible dominant washington initialize deg deg deg deg jolla relies relies seung seung subsequently valuable ignore vari vari consecutive consecutive outperform equivalently rao rao rao rao rao suboptimal suboptimal connec hundred suppressed guess adapting mathematically neurophysiological hughes retain cosine cosine cosine cosine cosine selectively voting funded preserve esti algebra simplifies develops resp resp sponding ble mcdonnell pouget pouget pouget suffers shot broadly alex disturbances believed settle sen vote inefficient inefficient symmetrical sity amplified thing ben ben compromise format format format format faced lar pew attracted contributing ables ables hirsch wait mate displaced neurally unclear euclidian dash suppresses originating univer cleaning cleaning possi looked depended discriminated simi liapunov suppressing estimations estimations estimations estimations alexandre cram implausible sory oll loc amplifies amplifies 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#@Pouget_A,Zhang_K,
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#*network network network model model model model model model model model model model model model model model model model neural neural neural neural neural input input input input data function function function function function function figure figure figure time time time time time time time time time time time networks error state results results results results results models models based space space space space space space space space space space space space linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer case case case case order order order values values values values values values parameters parameters parameters parameters functions functions neurons neurons neurons neurons distribution distribution approach point image image single processing processing processing large local neuron neuron test analysis analysis analysis class optimal optimal optimal optimal inputs simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple gaussian visual visual visual visual visual visual visual visual paper small size work work fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field field field field field field field field field field field features level cell cell cell cell cell cell cell cell structure structure structure structure structure structure structure high response response response response response representation show show fixed fixed general parameter approximation average average average theory theory theory obtained obtained obtained obtained obtained activity activity dimensional result result result result computation solution research research independent defined defined defined target target dynamics initial initial constant constant constant table table table table table terms distance connections connections connections connections synaptic synaptic synaptic synaptic direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented map present present phase phase low low low frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal motion motion motion motion motion motion maximum maximum maximum range range basis continuous continuous abstract computational computational properties properties properties references component due important context introduction introduction complex behavior behavior behavior stimulus stimulus dynamic tion energy variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume assume chosen higher center previous cases type cortex cortex cortex cortex cortex cortex cortex conditions represent represent distributed distributed distributed expected forward forward forward forward simulations simulations resulting resulting resulting ing human respect respect multi sum sum eq eq mapping mapping mapping feedback orientation study study study study filter specific specific specific compared receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive proc location determined related related cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain larger larger contrast fields fields fields fields fields fields fields modeling department synapses kernel kernel kernel kernel kernel kernel kernel kernel represents exp exp exp layers scheme scheme scheme considered considered considered considered considered framework domain domain domain domain domain domain domain equivalent equivalent directly directly curve view curves top stage effects effects upper vision vision basic basic give con produce derived levels area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types evidence inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological measured discussion group excitatory excitatory excitatory surface actions circuits circuits circuits amount effective shape supported role role theoretical end development including combination account account account dynamical functional functional functional functional block transfer transfer projection increasing mechanism mechanism mechanism mechanism uniform filters pre direct direct direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition bottom attention combined neuronal membrane population population population population recent reported lateral introduced moving engineering highly approximately tuning tuning tuning tuning tuning match organization organization organization improvement amplitude amplitude exists lead wide feed feed feed feed loop loop clusters clusters occurs pass pass pass strength conclusions central interactions interactions interactions interactions interactions interactions interactions propose mechanisms mechanisms mechanisms mechanisms integration characteristics characteristics characteristics assuming variety plane connectivity connectivity acknowledgements explicit pro derive produces index index plot describes ann stability tuned tuned tuned tuned mathematical modeled modeled modeled modeled modeled modeled metric explicitly explicitly mutual mutual mutual mutual mutual mutual mutual mutual gaussians blocks letters focus formation dependence review review influence influence suggested constants constants constants diagram diagram delays intermediate distances symbol koch dendritic coupling coupling building kernels kernels kernels inter inter extension variations domains partially neighbors characterized structural major simplicity reason driven driven included included schemes schemes post projections plots plots plots orthogonal orthogonal receives excitation soc soc soc induced interpreted interpreted issue localization wave correspondence cat cat cat cat cat neurosci preferred preferred preferred preferred preferred neighboring intrinsic oriented cowan origin remain selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity investigate circuitry varied varied put steady periodic existence rise fourier fourier biol combine reliable structured structured comparable pathway affect understand topographic transmission opposite rev adjusted observe observe separated nervous extent contributions contributions contributions contributions contributions electronic separable separable distinguish convolution analytic majority caused caused london spatially drive tive tive sites sites sites organized organized strictly directional monkey arise commonly consequence opt opt gradually res res res arises arises arises depicted reflects populations collected freeman offset offset offset quantitative posed marked marked formulated variant schematic schematic summarized spread spread cal collective asymmetric asymmetric asymmetric distortion sensing primarily extensive gabor restrict velocities homogeneous neurophysiol neurophysiol neurophysiol tem jones interconnected arranged systematic striate striate striate striate efficacy occurring occurring transforms operates wilson negligible von moved regard interconnections interconnections treatment deg deg deg deg deg deg deg deg deg deg deg deg axonal axonal spatiotemporal spatiotemporal spatiotemporal spatiotemporal relies eqs considerations influences discharge discharge grating geometrical numerous rigorous sine inferred inferred responds spatio spatio spatio spatio spatio spatio spatio tween pointed abstraction profiles profiles descriptions sinusoidal care biophysical biophysical neurophysiological neurophysiological intra interacting mediated mediated adelson worth superposition figs pools geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate tissue signs supporting examination topography architectural architectural architectural architectural architectural architectural architectural architectural architectural palmer tial sake lated bold bold albus hamilton concerns optima couplings intracortical intracortical intracortical intracortical intracortical intracortical intracortical intracortical intracortical intracortical intracortical bergen systematically enhances resultant drifting gaus faced deformation gratings watson spa spa ini analyse percep amer amer linearities asymmetry asymmetry spario spario spario assessing italy quadrature quadrature quadrature aimed strongest rap distinctive exhibiting separability palm parentheses tinuous symmetrically poral monosynaptic laterally laterally ies thalamic ponents tilted cancellation recep recep narrower primed dsi dsi dsi dsi dsi dsi dsi stud albrecht pling ohzawa originate originate namics nakayama differentially alteration evidenced evidenced esprit lution hildreth cou cou reid shapley anticipated lagged lagged equiva ceptive ceptive lent rection asymmetries asymmetries asymmetries asymmetries asymmetries asymmetries asymmetries sians appreciable corti evidences postnatal geniculo geniculo asym laying elicits geisler nput looms seelen asymmetrically 
#@Bisio_G,Sabatini_S,Solari_F,
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change change change change difference difference higher part previous previous firing firing firing firing firing firing firing firing firing multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long conditions conditions conditions conditions conditions conditions conditions expected make make fact techniques correlation observed observed observed observed observed observed observed observed forward simulations ing ing total simulation simulation simulation performed times potential potential potential made natural study study compared series determined determined experimental experimental experimental experimental experimental experimental experimental cortical cortical cortical cortical brain brain brain equal mit voltage train train train modeling report institute institute institute institute institute institute technique technique code code code code code code code code code individual individual individual individual difficult difficult scheme addition addition experiment environment environment additional additional additional view view view top top top top top effects effects effects effects effects effects effects effects effects determine upper statistics basic increase increase increase increase condition condition condition condition condition condition condition condition coding coding coding coding coding coding derived randomly levels levels levels levels types lines finally evidence nature depends sampling achieved achieved measured measured measured limited actions predictions finding nearest common supported role adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation square square square square square square square square square square hypothesis hypothesis sensory sensory fit simulated simulated underlying underlying reduced reduced reduced reduced reduced reduced block block block block significantly increasing increasing consistent trials trials trials trials trials leads details pre direct normalized bottom bottom bottom bottom produced neuronal neuronal neuronal membrane membrane membrane membrane membrane recent robust period period identical identical identical identical sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently relevant highly highly approximately approximately studies studies studies differential observation channels organization sensitive increased increased amplitude constructed constructed studied studied studied suggests trial spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes row row row greater conclusions interactions clear peak peak constrained encoding strong presence presence external reduction reduction reduction reduction reduction reduction characteristics pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse min derivatives program van van longer laboratory laboratory changing changing simultaneously involves belief events events events events implies blocks blocks versus potentials extracted reconstruction influence codes showed showed modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation completely suggested classical fitting intervals intervals intervals event event event event event remains koch koch koch david precision coupling recorded recorded existing inter inter inter plotted plotted discussions characterized characterized major major modification modification modification spiking detect literature projections plots contained conductance conductance conductance conductance conductance conductance contribution physiological physiological timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing duration absence absence absence realistic realistic cat neurosci neurosci neurosci acknowledgments rat rat intrinsic trains trains trains trains explore unlike stimulation stimulation stimulation stimulation helpful examine behavioral possibility possibility reliable reliable reliable comparable neu examined examined patch patch patch patch transmission plausible reading onset changed aspect obvious portion precise precise precise precise precise nervous pyramidal histogram histogram histogram histogram ment defining defining phenomena biology precisely monkey consequence ion res medical medical medical recording alignment alignment integrating apparent reflect led relevance experimentally experimentally experimentally lack lack peaks recordings reliability reliability maintain maintain howard howard howard serve serve serve conductances conductances conductances conductances conductances conductances conductances conductances conductances conductances display decreased lim traces calls instantaneous instantaneous phenomenon tation count neurophysiol grey receptors cellular occurred alpha resistance neurobiology neurobiology neurobiology ral implications affected salk salk days exploring slice bialek bialek bialek bialek bialek bialek encountered injection injection histograms monkeys captured somatic tic hippocampus cerebral cerebral spatiotemporal surprisingly smoothed smoothed jolla jolla horn pearlmutter epsp concentration concentration concentration generalizing generalizing displacement displacement displacement displacement displacement displacement displacement displacement displacement fly cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic cholinergic validity medium medium reports resting reflected capacitance preserved preserved preserved preserved preserved preserved preserved trends subthreshold blocking maintained potassium potassium potassium potassium potassium potassium inverted hughes hughes hughes terrence altered macaque insertion insertion frontal selectively cation importantly grateful milliseconds examination resembles rats rarely preserves preserves preserves house abeles abeles reflecting concern neocortical neocortical neocortical neocortical neocortical fre injected physiologically physiologically physiologically physiologically manipulated slices anthony preservation preservation preservation preservation preservation preservation stevens stevens stevens trol zador zador zador raises compartment vivo vivo vivo vivo vivo vivo vivo convolved william implied halves jitter jitter jitter jitter jitter steveninck tim blocked ruyter ruyter christof opinion acetylcholine newsome newsome frog behaving behaving appli quantified avg rieke rieke rieke rieke rieke fluctuation fluctuation fluctuation fluctuation fluctuation fluctuation fluctuation fluctuation fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating fluctuating thalamus quency andreas madison madison bair bair switzerland mainen mainen mainen mainen mainen adap nth manipulating concentrations concentrations concentrations concentrations concentrations concentrations concentrations conveys vitro vitro vitro environ excitability excitability excitability excitability elicited compartmental compartmental neuromodulation neuromodulation widespread reproducing clamp clamp clamp clamp reproduction delivered delivered vation neurotransmitter qualities unrealistic tang tang tang tang leak prepared accompanied ipsp axial warland warland prog debate sponses vaadia obser replicating neuromodulators neuromodulators agonist agonist bergman injecting ferster ferster initiation alters barak shadlen shadlen resistant resistant perfusion perfusion perfusion perfusion perfusion neuromodulatory neuromodulatory preclude extrastriate shortening shortening shortening lancaster profound tude chuck popularity evans ampli ach caution raster pharmacological mccormick mccormick jnowski ritz simulta contrasting challenged ited repeatable neously neuromodulator neuromodulator neuromodulator ological physi modifica ejnowski sult norepinephrine neuroscientists 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#@Bartels_A,Sejnowski_T,Tang_A,
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#*network model model model model model model model model model model model model model model model model model model model model model model model model input input input input input input input input input input input input input input function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set output number number state results results results results results problem models models space space space space space space space space weights linear linear linear linear case case order shown shown values probability probability parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach pattern single single single processing processing local local local local neuron rate analysis analysis inputs inputs inputs inputs shows shows simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual examples size feature feature feature feature net cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field features level current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell high high high high high response response response response response response response response response response response response response response response response response response response response response response response response response response similar similar similar similar show show general general parameter parameter average average theory obtained obtained note note note note note experiments experiments activity threshold threshold threshold threshold computation computation solution solution log log log log log log log log log defined defined found found found initial constant constant estimate distance connections connections connections connections synaptic synaptic synaptic science science direction presented presented presented present low range range range range nonlinear nonlinear nonlinear nonlinear sample abstract abstract find properties properties properties properties references due due behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect generated variance recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent difference spatial spatial spatial spatial assume assume chosen higher higher part center center center center center center center center center center center center center center center center center center center center center center center center cases cases firing firing firing firing firing firing type type required cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike long make make length observed observed observed observed observed observed observed observed simulations simulation computed computed times times elements regions regions potential potential dimension dimension made made orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation obtain specific compared receptive receptive receptive define compute compute rates rates rates rates rates proc location goal cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain mit mit voltage voltage larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast connection modeling modeling version synapses synapses synapses consists individual individual individual individual individual responses responses responses responses responses responses responses responses responses responses responses responses exp exp scheme ai framework framework cambridge computing experiment stimuli stimuli stimuli stimuli effects effects effects effects effects effects effects effects effects detection requires significant estimated increase increase con con developed levels levels levels levels levels types types product iteration nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory achieved feedforward feedforward increases increases describe limited limited complete excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory circuits amount assumed assumed shape role end end easily easily simulated smaller needed combination account account interesting interesting projection projection increasing increasing special consistent direct direct inhibition inhibition inhibition inhibition inhibition combined neuronal neuronal membrane membrane population population population population population population population population population recent property property property property property property reported reported reported lateral lateral introduced include cognitive recently recently dimensions dimensions sufficient observations observations observations approximately tuning tuning tuning tuning tuning tuning tuning tuning tuning achieve address locations modified grid entire increased amplitude horizontal studied invariant invariant invariant invariant wide wide width white setting half half strength conclusion valued central central interactions interactions interactions interactions interactions interactions interactions interactions interactions accurate clear clear peak peak peak exponential learns suggest propose strong mechanisms solid solid solid solid solid solid solid radial decrease iii connectivity connectivity connectivity connectivity areas van primary primary primary primary primary primary distinct dept changing modeled modeled modeled modeled modeled explicitly simultaneously simultaneously simultaneously linearly linearly infinite consisting interaction develop shift decreases independently centered completely smoothing dashed dashed dashed dashed dashed dashed classical classical classical classical classical classical roughly david recorded building kernels kernels currents currents sciences extension activated variations partially major simplicity straightforward uniformly maximal maximal projections projections projections orthogonal orthogonal orthogonal orthogonal orthogonal receives receives capture excitation excitation excitation soc soc strongly strongly strongly neuroscience conductance conductance stopping stopping symmetry physiological physiological physiological physiological sci bar vary dot realistic realistic surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround leading reach thresholds cat neurosci neurosci neurosci neurosci receive oriented origin selectivity varied varied varied steady strengths limitations accurately preliminary respond respond respond respond rest scaled lgn lgn lgn lgn lgn lgn lgn lgn lgn variability variability presynaptic presynaptic fundamental patch patch patch patch patch plausible necessarily analyze assumes detector extent explain isolated trivial orientations orientations convolution analyzed analyzed phenomena phenomena phenomena majority sys forces acad gradually res res outer outer researchers summation explained freeman substantially simulate passed exhibits poisson spread spread reaches incoming achieves achieves conductances sums boston neuro physiol contribute representative ear physiology tation martin martin arguments driving circular neurophysiol jones theories suppression cellular cellular cellular cellular air dealing anatomical ments held held resulted nearby analyzing definitions shifts settings optimally exceeds filled natl sompolinsky falls studying accounts accounts captured captured multiplied diameter diameter diameter diameter diameter diameter diameter diameter diameter deg deg deg deg deg ensembles cerebral surprisingly repeatedly rich contact relies davis border interestingly receiving receiving dense grating grating grating grating grating grating grating grating grating grating grating grating maintaining numerous ter achieving email shunting shunting wiesel revealed nelson isotropic responds pieces freund hubel suppressed suppressed suppressed suppressed guess param capacitance tems discontinuity activate intra douglas iso iso iso iso iso iso iso iso speedup weaker tively intracellular intracellular intracellular eters round ward experi sigmoids reversal prefer essen physiologically physiologically heeger heeger intracortical neocortex systematically compartment decaying ben saturating saturating saturating saturating ings gratings gratings massive sur sur shares analyse saturate saturate saturate facilitates neurones lund sat nov bonds nections projective niebur rightward rightward divisive disappear abstr wii cent cen dash thalamic usher suppresses nonlin anatomically sponse bigger ocularity sharper knierim feedfor somers somers somers somers somers somers somers outward downward originate conduc connors ferster kin orien sillito prince itera wei todorov todorov todorov todorov todorov carandini subpopulations subpopulation subpopulation arch annular upwards hibitory hibitory wee tances contradicts 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output output output system system system system error error error error information information information information information information information information problem problem based based based based space space space space space space space space space space space space space space space space space space space space weights weights weights case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown probability probability probability parameters noise noise weight weight weight weight weight unit unit distribution distribution distribution distribution method method method method method method pattern point processing processing large local rate matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal form form form form form form form form shows signal signal signal signal signal signal signal algorithms algorithms simple simple simple simple paper paper paper paper paper examples examples examples examples small small small small net work methods process current current current current current trained structure structure structure structure structure structure structure structure structure random random show show show equation equation fixed fixed line line line line line line line line line line line line line line line line rule rule rule rule rule rule rule general general general generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation average average theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient variables solution research independent independent independent independent log log log log defined defined defined defined target target target target target initial constant constant constant constant constant constant constant estimate terms distance synaptic synaptic direction direction direction direction direction direction direction present present present present maximum maximum press press continuous continuous abstract applied applied convergence density analog analog likelihood likelihood likelihood references component stochastic stochastic stochastic stochastic stochastic stochastic ieee ieee ieee positive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction estimation behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical generated parallel tion change variable assume assume measure measure signals signals prior theorem theorem theorem theorem bound cases good represent distributed expected expected proposed proposed proposed proposed length length observed observed respect respect eq called called natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural study em em obtain obtain obtain obtain original vol vol represented true desired define distributions mit mit connection connection descent descent descent descent descent descent descent descent descent source source proceedings loss loss loss loss loss loss loss loss loss loss version version version internal joint represents difficult exp exp exp scheme scheme scheme maps cambridge cambridge equivalent equivalent hinton view curves effects efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient classifiers choice choice choice statistics statistics estimated estimated give condition criterion finally finally processes depends constraint normal normal group denote close inverse inverse inverse inverse inverse effective effective effective role role theoretical eds ability rumelhart rumelhart noisy dynamical dynamical dynamical unknown unknown interesting consistent consistent structures operation squared squared squared squared call idea idea minimize choose choose sources sources perceptron denotes denotes denotes denotes pair pair pair takes typical introduced introduced introduced introduced subject subject quadratic sense conventional conventional conventional observations teacher teacher works works works studies studies studies studies differential rl trans trans trans mixtures separation separation separation separation separation separation separation modified modified observation williams exists exists studied invariant invariant suggests matrices matrices deterministic deterministic boundary column starting place tangent asymptotic propose physics minimizing averaged introduce manner program question question question attractor boltzmann explicit explicit written written metric metric metric metric metric metric metric metric metric multilayer multilayer multilayer multilayer explicitly physical springer expectation expectation review depending depending estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator lemma converges converges constants spaces spaces reduces calculate calculate norm norm euclidean euclidean euclidean euclidean euclidean euclidean coordinate coordinate coordinate perceptrons perceptrons perceptrons perceptrons perceptrons blind blind blind blind blind blind batch batch batch batch batch batch prove prove prove prove modification modification modification identity composed prob return lie manifold follow notation nips nips minimizes minimizes minimizes thresholds mixing satisfies extend simpler origin accurately mass scalar giving incremental applicable structured structured maximizing proved workshop cognition coefficient analyze analyze fisher fisher fisher fisher observe perceptton perceptton amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari simplest asymptotically asymptotically asymptotically asymptotically asymptotically slowly analyzed analyzed answer answer independence processed perspective located begin definite definite arises geometry geometry geometry geometry geometry mechanics treated popular logp attraction owl differentiable differentiable differentiable ordinary notes modify japan restriction recover tensor tensor tensor tensor connecting plays satisfying adequate sompolinsky sompolinsky sompolinsky sompolinsky excellent guarantees percepttons percepttons yang tic foundations surprisingly steepest steepest steepest steepest steepest seung treat speaking geometrical geometrical geometrical microstructure basin rao opper representa impose realizable gener convert met tively knowing modifiable modifiable dichotomies answers mix mea lecture remarkable fractal hyperbolic converging converging adaptively adaptively orthonormal orthonormal orthonormal orthonormal dichotomy proves proves implying shop cichocki ated riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian gij gij gij gij gij gij cardoso cardoso heskes heskes fluctuating adap tot tot barkai lira equivariant shi nonsingular riken riken riken kappen kappen ric jeffrey cram chines suddenly markovjan laheld ichi wako frontier awt emits zoo tured ologp ologp shun reused stoch fluctuates ymptotic rer covariant covariant 
#@Amari_S,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data function function function function function function function function function function function function function function function function function function function function set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output number number number number number number number number number number number number number number number system error error error error error error error error error error error error results results results results results results units units units units units units units information problem hidden hidden hidden hidden performance performance performance performance performance performance performance performance based space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer case case case case case case case case vector vector vector shown systems systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit distribution approach pattern pattern pattern single single processing large rate test test patterns patterns patterns patterns patterns analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class inputs shows shows shows shows shows algorithms algorithms paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small small small size size size size size size size size size size size size size size size size net net work points points classification classification classification classification classification classification classification classification structure problems problems problems random similar similar similar section section section section section section fixed fixed fixed fixed general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter real real real real real real real approximation approximation theory theory theory theory theory theory theory obtained obtained term term term result result result result result result result result result result result result university university university university threshold threshold computation computation research log log log log log log log log log log log log log log defined defined defined defined defined found sequence sequence sequence sequence sequence sequence sequence target constant constant constant constant constant constant estimate estimate estimate standard standard standard computer terms terms terms terms terms terms terms terms terms science map map frequency frequency sets range press press press press basis basis outputs sample sample sample sample sample sample sample sample sample abstract computational convergence properties references ieee ieee important important important decision introduction introduction estimation statistical tion complexity complexity complexity assume assume lower lower part part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound required binary long make fact techniques techniques proposed length correct correct correct correct errors errors forward forward forward scale scale scale scale finite finite resulting classes classes classes classes classes classes classes classes classes classes ing total total regression regression computed respect respect multi multi sum sum called called elements factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made applications applications applications em relative relative true true define define define define define define define define define define proc proc perform perform related related related constraints distributions brain mit accuracy contrast train dependent dependent nets proceedings report report report department department version version version version technique layers layers layers considered considered cambridge equivalent equivalent estimates conference conference upper upper full full full full pages give give give give give give give give give give give give give give give give con condition condition condition conditional developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds product provided provided finally depends depends constraint constraint technical technical technical feedforward arbitrary denote denote denote proof proof proof proof proof main end hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis makes including typically smaller smaller combination combination jordan york york york special uniform uniform uniform empirical squared squared squared squared squared squared numbers numbers max depth depth depth expert early early magnitude magnitude magnitude frame decay decay idea idea minimize minimize improved improved improved advantage property takes element element apply apply apply introduced subset relevant engineering engineering engineering compare observations tions tions definition observation bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded risk risk sensitive sensitive extended extended correctly feed feed feed valued valued valued valued valued valued valued sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid constrained taking largest largest radial minimizing minimizing start denoted suppose suppose derive derive construct solving solving factors factors factors factors infinite involves easy easy applying applying minimization springer implies implies implies implies expectation john national national national expressed review estimator lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma labels lee approximated similarly similarly sign convex convex roughly penalty valid valid norm norm classified david includes combinations combinations sciences determines vapnik vapnik vapnik vapnik vapnik vapnik vapnik prove holds discussions structural structural successfully simplicity determining extra closely comparing notice notice notice verlag quickly heuristic stopping stopping satisfy notation notation quantity quantity quantity usual computes hypotheses hypotheses attempt attempt approximating satisfies satisfies satisfies extend layered put involving recursive ml helpful scalar successive fashion school applicable func cover cover cover cover cover cover attributes neu neu neu examined smallest plausible editor changed versions taylor taylor taylor precise explain finds established mentioned piecewise inequality inequality inequality theoretic trivial crucial improves explanation baum baum turns sgn sgn sgn sgn sgn acknowledgement implicit sun argument argument reflects reflects considerably considerably applies double offset peter peter peter haussler haussler haussler haussler haussler incorrect passes aim gen popular comments comments comments wesley pac proofs proofs proofs proportion proportion proportion addison formally princeton acm acm acm labelled bin grows arranged maass satisfying satisfying satisfying satisfying satisfying imposed grow operates ral ral ral imply imply krogh symposium hertz heuristics bartlett bartlett bartlett bartlett bartlett bartlett bartlett bartlett corollary corollary corollary corollary corollary advance barron barron foundations permutation permutation warmuth informative relies statement ignore robert andrew maintaining misclassification misclassification misclassification misclassification misclassification misclassification misclassification misclassification misclassification misclassification misclassification covering covering covering covering covering ber chervonenkis chervonenkis chervonenkis chervonenkis encouraging classifications generalizations big classifies hierarchies australia quantized unseen pub iff exam ftp distri intuition magnitudes magnitudes num bounding learnability learnability thresholded erp erp erp sketch sketch indexed supports supports parametrized refined williamson williamson ignoring behaves bution fat fat fat fat fat fat fat fat fat fat fat fat fat fat fat fat fat palmer satisfactory australian australian australian shawe shawe shawe hilbert cally ples push anthony anthony squashing squashing baxter shattered shattered shattered shattered ben handbook closure kowalczyk corn inform skeleton generaliza indexing phil deeper lipschitz lipschitz hoeffding blumer dependences mike eralization shattering shattering shattering shattering shattering shattering shattering shattering shattering shattering shattering shattering shattering shattering shattering shattering jensen workers jonathan koiran koiran suppresses logn logn logn logn compose comput comput vcdim vcdim sketched arbib posner rrt ehrenfeucht canberra anonymous pollard mad loose minimisation adam compositions compositions nonincreasing anu annu annu fll wee sociated bianchi alon alon cesa distinctly distinctly verges eurocolt dlog dlog lugosi lugosi specifi ere aft mensions satis unnatural dln fying 
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results results results results results results results information problem models models space weights weights weights weights linear linear linear linear linear linear linear layer layer case case case case case case case order order order order order order shown shown shown values parameters parameters parameters parameters parameters parameters parameters noise weight weight weight functions unit distribution distribution method method method method approach approach approach approach approach approach approach point single large large large large local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs form shows shows simple gaussian gaussian gaussian paper paper paper examples examples examples examples examples examples small size size net net net work work work work task methods fig fig fig fig fig step process process process process process process process process process problems problems problems problems problems random random similar representation show section section section section line line line line line line rule general general generalization generalization generalization generalization generalization generalization generalization parameter real average average average average theory theory theory theory gradient term term term term term note note result result result result result result university solution independent independent defined found found found found dynamics dynamics dynamics dynamics dynamics dynamics initial terms presented presented presented components nonlinear outputs outputs abstract applied find find find find find convergence convergence convergence convergence convergence density density density analog properties references due introduction behavior behavior behavior behavior behavior behavior behavior behavior statistical statistical statistical variance assume lower lower chosen previous good good long conditions bayesian expected expected make fact region region correct errors errors finite simulations simulations minimum tasks simulation called called called called called means made study study vol artificial true cross cross series define related related distributions gain gain gain steps steps steps steps steps steps steps steps steps steps steps steps steps fields fields descent dependent dependent nets version directly directly directly directly directly curves limit limit limit limit limit conference capacity upper upper full statistics world increase increase increase validation developed lines actual actual actual actual provided finally technical describe describe inverse inverse inverse assumption corresponds proof role theoretical theoretical dynamical dynamical dynamical unknown interesting special consistent empirical empirical empirical principle details max max max max max max max max supervised early early early early early early early decay decay minimize minimize choose description description description description description description perceptron perceptron perceptron improved discussed discussed recent correlations exact exact typical introduced identical relevant compare teacher teacher teacher teacher teacher teacher calculated calculated calculated calculated calculated calculated solve yields rl diagonal diagonal storage risk risk risk risk risk risk expression expression extended extended occurs occurs minimal minimal minimal assumptions hebbian numerical faster asymptotic temperature integration integration physics solid solid turn assuming min min iii averaged averaged introduce introduce relation van describes describes student linearly infinite remaining minimization springer implies overlap restricted fraction static similarly similarly similarly calculation calculation dashed expansion add remains valid calculate calculate calculate calculate sufficiently combinations perceptrons eigenvalues eigenvalues eigenvalues eigenvalues batch batch illustrated discuss priors phys discussions major maximal maximal maximal maximal maximal maximal maximal maximal literature identity identity identity reached summary summary interested interested interested stopping stopping stopping stopping stopping stopping stopping stopping follow criteria criteria hold usual usual realistic nips eigenvalue eigenvalue correspondence reach reach reach overfitting overfitting overfitting overfitting perturbation hessian hessian dotted examine int analytically authors tanh tanh tanh proved examined trace reading illustrate assumes amari submitted submitted attempts defines defines averages averages averages asymptotically stop analytical briefly tractable starts perspective precisely opt read demonstrates addressed mechanics mechanics mechanics geometric varies pseudo lack adjustable reaches germany sophisticated conclude comments comments phenomenon lab japan restrict appropriately determination replica exploit implications krogh krogh moments started appendix appendix appendix appendix uni spherical multiplied eqs valuable lett stopped stopped stopped avoiding approx saad saad schulten slight basically email exhaustive opper opper opper opper opper opper opper opper opper opper guess param remainder thermodynamic thermodynamic thermodynamic thermodynamic playing guided relates integrals integrals integrals sollich sollich loading algebra algebra eters round round remarks dim monitor marks solvable realizations realizations realizations recursion recursion recursion hemmen neglect bss bss bss bss bss bss bss bss ref edited edited vanish scenarios scenarios brackets brackets enter validated terminate icann trick europhys diverges manfred novelty fulfill fulfill fulfill physik domany readers altogether acknowledgment shi riken riken attain identities identities replicas eps eps bij pected prefactor kinzel fulfills neces ichi cie sary saitama 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class class class class class class class class class class class class matrix matrix matrix matrix matrix inputs form form signal algorithms paper paper paper paper small net work work work step step step points points classification similar similar similar representation architecture architecture architecture architecture show show equation section section section section section line line general parameter real real real real real real approximation approximation theory obtained obtained obtained note note dimensional dimensional result result threshold threshold threshold threshold threshold variables variables computation solution solution research research research defined defined defined defined found found computer science direction direction nodes object sets continuous abstract applied references ieee ieee positive decision introduction complex complex complex hand hand parallel parallel search tion complexity complexity complexity assume assume assume measure higher higher higher part previous theorem theorem theorem theorem theorem theorem cases cases required multiple multiple multiple multiple multiple multiple multiple binary binary binary binary conditions conditions conditions equations equations fact fact region region region region region region region region region region region region region region length finite finite finite resulting classes classes classes respect respect respect respect respect multi called called called called regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions optimization dimension dimension dimension dimension dimension dimension dimension dimension global global study negative true define define define compute compute proc proc equal equal equal equal steps contrast nets report loss version consists difficult layers layers layers layers layers layers layers layers layers layers addition graph graph graph equivalent equivalent view transition transition full requires approximate pages pages give condition condition bounds bounds types lines lines feedforward feedforward feedforward arbitrary denote assumption complete proof proof proof proof proof proof proof proof finding finding finding finding finding finding supported journal journal instance easily easily makes pairs pairs pairs pairs reduced unknown fully edge edge edge edge edge principle early produced added description perceptron recent resolution exact exact property pair pair pair apply apply side side side side side side subset subset subset dimensions dimensions dimensions dimensions sufficient sufficient sufficient sufficient approximately volume volume works correspond correspond trans trans definition definition definition background exists exists horizontal extended extended locally locally white conclusion conclusion critical critical critical critical critical critical critical critical critical critical critical critical minimal minimal assumptions assumptions assumptions assumptions neighbor propose cycle cycle cycle cycle cycle cycle cycle cycle sigmoidal exist exist exist exist exist plane plane iii configuration configuration configuration configuration denoted digit digit written longer label label distinct distinct dept multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer linearly remaining adding adding adding springer springer springer implies implies implies implies implies implies implies boolean boolean boolean boolean boolean boolean boolean cycles cycles family family focus depending lemma lemma lemma lemma lemma lemma open open open labels labels labels labels understanding similarly similarly digits partition partial convex convex convex neighborhood neighborhood neighborhood intermediate intermediate existing thesis perceptrons perceptrons extension prove black holds holds characterized simplicity regular regular straightforward straightforward extra extra extra computations comparing situation situation situation situation situation situation situation situation situation composed compact compact verlag verlag verlag kind interested hold hold hold hold notation write write computes subsequent oriented explore layered xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor xor essential essential essential essential essential essential essential essential essential essential essential essential essential essential essential essential essential issues fewer successive project mappings authors func analogous neu math editor editor necessarily configurations configurations configurations configurations opposite opposite opposite opposite opposite opposite opposite opposite opposite ensure explored phd defines separable crucial adjacent adjacent capabilities baum london producing hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane mathematics acknowledgement involve universal universal meaning addressed argument geometric geometric geometric generic red red effort remove berlin ordered green green green focused progress realized realized realized realized realized realized realized realized realized realized restriction restriction restriction restriction restrict hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes labelled labelled jth jth impossible eliminate grey interconnected generality extending viewpoint ral definitions imply combinatorial combinatorial generalizes constructive lip lip separating heavy corre sides sides sides sides topological realization realization realization realization percepttons infinity infinity infinity infinity infinity infinity infinity infinity infinity infinity infinity infinity infinity interconnections counter approximators border intersection intersection intersection intersection intersection intersection intersection intersection intersection approximator street geometrical geometrical alternating emerge restrictions theorems conjecture conjecture realize realize algebraic equality equality iff iff iff iff iff iff ijcnn realizable realizable realizable realizable realizable distant challenging challenging complementary hornik france son union drops things subspaces dichotomies dichotomies dichotomies dichotomies dichotomies october rewritten rewritten resp sponding characterizing characterizing inconsistent inconsistent inconsistent unbounded unbounded unbounded unbounded sake quadrant european virtually inequalities inequalities inequalities inequalities inequalities blum lyon lyon lyon hull dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy dichotomy labelling huang huang totally implying colors computable computable computable closure closure closure closure subsystem neglected supposed simon simon hood neurones nice technische checked excluded excluded intersect intersect intersect dnf tie tie tie tie tie tie tie tie tie tie tie tie tie tie heidelberg gibson gibson gibson gibson gibson gibson gibson gibson gibson deduce exhibiting perspectives proving proving continuation inconsistency koiran koiran associating augment polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral intersecting cybenko cedex notations realizing realizing realizing realizing realizes stinchcombe superpositions reformulated ric contradiction contradiction intersections deduced esprit coo coo 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#@Brightwell_G,Kenyon_C,Paugam-Moisy_H,
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linear linear linear linear linear linear case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order values values values values parameters noise noise noise noise functions functions functions functions functions method method method point point point point point point point single large large local test test test test test test test test test test matrix matrix matrix matrix form signal simple examples examples examples examples examples examples examples examples examples examples small small size size size size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work points problems problems problems problems problems problems problems problems problems high high similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation vectors vectors vectors vectors vectors vectors general general generalization generalization real approximation approximation theory obtained obtained term term term term term term term experiments experiments experiments experiments dimensional university university variables defined constant constant constant constant constant constant constant constant table table table table table table table estimate standard standard terms terms terms prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction machine sets sets maximum press components components components components basis nonlinear nonlinear continuous sample abstract applied find find find find find find computational references due due positive procedure procedure procedure important important adaptive introduction introduction statistical generated difference difference variable variable variable lower measure cases cases cases type required good long represent represent represent expected make fact techniques observed observed observed observed observed observed forward minimum minimum regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect times elements means optimization applications obtain vol artificial artificial represented compared cross define define active determined determined constraints constraints constraints power power power power power power comparison comparison larger larger support support support support support support support support support support support support train dependent dependent dependent modeling modeling modeling modeling modeling selection selection report report department department loss loss loss loss loss loss loss loss loss version technique technique technique technique technique represents represents represents bias addition ai ai ai ai ai ai considered cambridge equivalent experiment experiment experiment upper choice choice choice choice statistics statistics free validation validation validation validation validation validation validation validation validation validation validation give randomly developed area product product nature technical supported square square square degree including objective objective objective objective objective objective pairs smaller unknown coefficients coefficients coefficients coefficients programming programming programming programming trials trials trials trials database database squared squared making magnitude polynomial polynomial polynomial polynomial minimize minimize choose discussed discussed typical introduced subject machines machines machines machines quadratic quadratic quadratic quadratic quadratic quadratic quadratic trees trees trees trees trees sense subset subset engineering varying varying compare observations observations calculated calculated solve solve diagonal definition observation expression concept matrices predicted predicted predicted predicted occurs column setting setting row conclusions depend depend clear clear presence presence california regularization regularization regularization regularization regularization labeled minimizing iii iii characters characters question acknowledgements suppose suppose suppose suppose relation construct winner explicitly simultaneously dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality remaining develop applying minimization springer versus family approximations constants expansion norm advantages advantages expect formulation bell bell instances vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik prove specifically columns committee comparing comparing miller miller essentially repeated repeated minimizes minimizes leading maximization predictor subsequent approximating approximating minimized poor requirements varied varied dual hall tech project working maximizing proper front friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman multivariate electronic defines optimum optimum optimum optimum optimum optimum site rows majority reasons inside berkeley berkeley worst mathematics ridge ridge ridge members radius fourth parameterized splines polynomials polynomials price branch boston boston boston boston boston boston boston median trade saddle lagrange ratios databases nonzero nonzero nonzero nonzero multipliers multiplier kaufman kaufman kaufman kaufman kaufman kaufman breiman breiman multiplicative contract obtaining obtaining observing north repeat combines predictors surprising holland sides bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging harris insensitive smola smola smola ics uci uci uci multiply unable creates reports burges burges burges attempted pub pub ftp ftp ftp ftp chapman labs labs labs life regularizer regularizer regularizer regularizer regularizer expand picked picked win termed termed termed termed termed west gilbert truth truth truth truth truth algebra algebra algebra elsevier matlab september tel differentiating housing housing housing housing housing housing housing emphasis emphasis chris lagrangian decided bold bold bold powers alex svr svr svr svr svr svr svr svr svr svr svr svr svr svr svr svr svr svr svr svr svr alan arpa transpose tube tube tube tube tube tube tube tube tube twelve raised counted prune greatest dij drucker drucker drucker drucker developments stat primal superscript package rationale 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#@Burges_C,Dmcker_H,Kaufman_L,Smola_A,Vapnik_V,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number results results results results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer layer case case case case case vector vector vector vector vector vector vector vector vector vector order systems systems systems parameters weight weight weight weight weight functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit approach approach approach approach approach approach approach point point point point point point image image single single single single single processing processing control control large local local local local patterns analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs shows signal simple gaussian paper examples examples examples examples examples examples examples size size size size size size size size size size size size size size feature net work work work points classification high similar similar architecture architecture architecture architecture show equation equation equation section fixed fixed fixed rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general general generalization real real real real real real real real real approximation approximation theory theory theory theory result result result result result result result result result result result threshold threshold computation computation computation independent independent independent independent independent defined defined defined found target target target target target presented present present activation sets learn learn learn learn learn position position position components outputs outputs outputs outputs outputs outputs outputs continuous continuous abstract applied find computational analog references component ieee context variance difference complexity complexity complexity variable assume lower lower lower lower representations part center theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound cases required multiple good binary represent finite finite ing ing called called dimension dimension dimension dimension dimension dimension dimension study knowledge samples represented desired define compute compute perform goal related related equal equal equal power steps nets report report consists internal represents bias considered computing computing computing computing view view view view solutions upper upper upper upper upper requires requires approximate pages pages con condition derived derived developed developed bounds bounds bounds bounds bounds lines product finally finally depends associative discussion technical feedforward feedforward feedforward feedforward arbitrary group close assumption assumption complete proof proof proof proof proof proof proof rbf assumed supported theoretical require hypothesis hypothesis degree development noisy including including smaller combination reduced reduced reduced block transfer transfer transfer transfer transfer transfer transfer database details pre direct early polynomial idea light discussed recent exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact property property practical practical practical apply quadratic subset subset dimensions dimensions sufficient sufficient sufficient sufficient sufficient varying varying compare previously works works works trans diagonal address definition definition definition positions increased exists exists exists expression expression expression scaling wide wide derivative matrices white column column column column column column conclusion starting row row assumptions reduce operator operator valued sigmoid sigmoid sigmoid propose sigmoidal exist exist iii derivatives derivatives derivatives derivatives denoted denoted suppose appears relation relation derive derive written index multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer linearly unique develop integrated implies blocks extraction extracted family family family squares detailed open open open similarly similarly spaces neighborhood neighborhood purpose interpolation valid valid construction topology figures includes priori perceptrons perceptrons perceptrons perceptrons retrieval subspace subspace extension prove prove prove prove discuss discuss discussions columns columns straightforward straightforward compression compression closely divided build projections identity orthogonal composed interested sci comp notation usual nips computes hypotheses extend extend presents unlike overfitting essential dataset existence scalar project mappings working fundamental fundamental math concepts rows rows formula analytic analytic analytic analytic analytic analytic capabilities baum baum baum baum baum baum perspective sections strictly commonly consequence inversion projected projected acknowledgement universal universal calculations auto auto geometry addressed addressed limits haussler haussler span differs conclude redundancy lim lot realized representative pac proofs maass saturation saturation saturation stated stated stated grow transforms symposium symposium constructive lip lip mental realization consequences consequences arrangement approximators approximators express considerations ball ball verify associations geometrical geometrical sig recursively sontag sontag sontag sontag sontag july tween decomposed realize jacobian jacobian jacobian jacobian jacobian jacobian equality iff cole hornik sketch france france indication dichotomies dichotomies dichotomies dichotomies october article sigmoids rewritten 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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm output output output number number number system error error error error error error error error error error results results results results results results information information information problem problem problem problem problem based based based based space linear linear linear linear linear linear linear linear case case case case case case case case case case vector vector vector order order order order order order order order order order order order order order shown values noise weight distribution distribution distribution distribution method method method method method single control large large large large large large large large test test analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal inputs form form shows simple simple simple simple simple simple simple simple gaussian gaussian paper examples examples examples size work work step step points points field classification classification classification trained random random response response response response response response response response response response response response representation representation equation equation equation equation section section section section section section vectors general general general general generalization generalization generalization parameter parameter parameter parameter real approximation average average average average gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained term term term term term term note note note dimensional result result result university variables variables variables variables variables variables variables variables variables variables solution research independent independent defined found found dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant constant constant table table estimate standard terms phase sets learn components continuous continuous continuous continuous continuous sample sample abstract back back computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties properties properties properties properties properties properties properties references component component due positive positive important important important introduction effect effect effect effect effect effect generated variance variable variable variable variable variable variable assume learned chosen part part part part center center previous previous required required required required good good equations make fact fact techniques proposed correlation correlation correlation observed forward finite finite simulations minimum minimum resulting resulting ing performed eq called times times times means means means means means factor dimension natural obtain original original original compared application series define determined goal equal equal equal equal equal steps descent descent descent descent descent descent descent institute consists exp bias ai ai ai ai considered directly additional limit limit effects requires requires requires choice choice choice world speed speed speed speed increase give derived discussion discussion covariance covariance covariance technical arbitrary arbitrary denote denote denote tested transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation fast surface finding finding amount effective supported theoretical theoretical main end end pairs significantly significantly ratio ratio increasing mechanism mechanism special empirical leads principal squared call iterations iterations iterations max max making added added perceptron perceptron denotes denotes correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations exact property pair pair practical apply identical quadratic quadratic relevant previously previously calculated calculated calculated calculated calculated tions solve solve solve solve pca pca pca pca pca pca pca pca pca pca diagonal diagonal observation observation observation observation interval expression expression suggests matrices predicted correctly feed column setting setting setting conclusion row numerical numerical numerical numerical exponential propose propose physics largest drawn sigmoidal proportional turn minimizing user decrease averaged averaged averaged areas derive derive written written transitions coordinates averaging transformations transformations transformations transformations transformations transformations easy john national independently correlated correlated correlated correlated correlated influence solved solved solved solved transform transform transform controlled fraction centered suggested allowed spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum earlier calculation slow slow slow add valid valid calculate calculate thesis coordinate perceptrons perceptrons eigenvalues eigenvalues eigenvalues eigenvalues sciences phys phys phys phys discussions characterized columns columns columns extra importance importance differ fine fine fine cun cun cun success showing superior quantity write write usual usual usual providing nips nips eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue leading leading leading consisted acknowledgments extend carried wiley transformed transformed transformed transformed transformed create hessian hessian recursive ml ml behaviour rise scalar reducing fashion giving analytically root eigenvectors eigenvectors tanh affect understand surfaces neu examined smallest smallest trace rev illustrate ensure singular singular perceptton perceptton perceptton perceptton improving improving improving explain motivated motivated defines indicating indicating trivial agreement agreement agreement agreement variances turns straight purposes sections immediately products inversion implicit implicit definite res medical medical medical read raw raw raw summation double readily introducing solla solla remove remove remove mod spread popular semi conclude conclude comments findings findings patients patients patients patients lim extreme cor contribute newton uncorrelated notes numerically numerically check biased replica keeping removing ral krogh krogh krogh guide combinatorial hertz hertz connect connect percepttons cerebral master sons valuable explains explains stopped unchanged geometrical entropic entropic ent deriving validity recursively removal obtains opper var var care diag thermodynamic thermodynamic win cij spanned sollich sollich sollich sollich hansen exchange investigations investigations parametrized corrections article removes dim doesn powers concerns fij contributes positives ultimate vanish implying denmark poles poles carrying wong expresses severely collecting amax amax amax inserting imaginary imaginary imaginary kanter kanter regional rescaling rescaling superiority infinitesimal cent cent cent cent unequal winther winther winther winther unimportant rescaled rescaled rescaled french zij zij jackson jackson rni copenhagen copenhagen hoped bohr stud rectly decoupled dan aaa aaa aaa aaa brody brody pairings grand kai blegdamsvej danish raphson kinzel itera xixj legend ied dirac slowest slowest negatives trl sara amin ole centering thorbergsson diagnose diagnose inl inl inl multiplicity uninteresting lars niels ren erations exchanging councils ish metabolism moval ido 
#@Halkjaer_S,Winther_O,
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#*network network network network network network network network network network network network network network learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output number number number number error error error error error error error error error error error results units information problem problem problem models hidden hidden performance based based based based based based based based based based based space space space weights linear linear case vector vector order order order order order shown probability probability probability probability probability probability probability probability probability parameters noise noise noise noise noise noise weight functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method pattern pattern pattern pattern pattern pattern pattern pattern point point single large large large test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix inputs inputs inputs inputs shows gaussian gaussian gaussian paper paper paper examples examples small task task methods methods methods methods methods fig step points points points points points points points points points level level level level level trained trained trained problems random similar similar similar similar similar section section line line line line line line line line line line line line line line line line line line line line line general generalization real average average average average obtained obtained obtained result university university variables variables computation computation computation computation computation independent independent found found found target target target target target target target target target target target constant table table estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard terms terms prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left presented low low machine sets sets sets press components outputs outputs outputs sample sample sample abstract applied find find density density density density density references component component component component stochastic due due ieee positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important context introduction complex estimation statistical statistical effect generated generated variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance difference assume assume assume measure chosen part part part part part good bayesian bayesian bayesian techniques techniques region region proposed proposed correct correct correct correct correct observed finite finite resulting tasks regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect sum called called called regions regions factor natural applications applications applications obtain original samples true true true true true true desired desired desired cross provide define compute compute compute compute compute compute perform equal accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison larger train train train dependent proceedings proceedings proceedings exp exp bias bias bias bias framework cambridge computing directly estimates estimates estimates estimates effects detection world estimated estimated estimated estimated pages increase validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation give derived randomly levels levels actual actual backpropagation depends simply discussion discussion feedforward feedforward limited limited limited limited close close inverse assumption assumption assumption predictions predictions amount amount amount amount assumed generate require main ability hypothesis makes noisy including including fit pairs underlying account account account unknown transfer transfer interesting empirical empirical empirical empirical squared max direct making early early early decay idea combined minimize choose run run predict denotes discussed separate ensemble ensemble ensemble ensemble ensemble practical practical practical practical practical practical introduced strategy strategy include include compare yields yields yields yields definition symmetric interval interval interval interval interval interval interval interval interval interval interval interval interval interval improvement improvement risk occur deviation wide alternative alternative alternative width width width width width width width deterministic boundary demonstrate runs runs runs runs conclusion place assumptions depend depend peak exponential weak suggest propose propose propose taking drawn drawn drawn solid solid solid solid solid solid solid solid regularization assuming exist targets targets targets targets targets targets targets suppose written factors estimating estimating laboratory mathematical mathematical confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence student student averaging remaining remaining slightly consisting minimization yield estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator viewed variation centered completely dashed dashed dashed dashed dashed dashed dashed dashed intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals interpolation interpolation sufficiently foundation advantages degrees expect existing existing inter illustrated uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty straightforward middle aspects delta symbols mackay tend prob interested interested interpreted stopping stopping sin sin content quantity quantity write minimizes deal deal bars bars simpler simpler simpler simpler simpler simpler origin overfitting overfitting overfitting collection estimators hessian dotted dotted dotted dotted hall reliable working proper variability tanh tanh circles circles possibly necessarily ensure adjusted aspect obvious freedom precise extent finds defines synthetic synthetic synthetic asymptotically percentage residual advanced advanced advanced advanced advanced advanced advanced advanced stop stop cos distinguish improves lies correction handle starts london reasons purposes closer incorporate incorporate bishop ion qualitative explained bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap peaks dots sharp compares ity outliers price weigend popular incorporating prevent prevent inherent unbiased unbiased naive naive initialization corrupted impossible adds breiman biased reasoning nonparametric introduces ensures predictors displayed negligible pat regard regard realization offers claim treatment modelled arrive arrive arrive arrive arrive arrive snn snn bagging bagging correcting exploiting explains balancing balancing stopped stopped fold treat ure leaving leaving usage incorporates minus minus tibshirani tibshirani residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals residuals tendency tendency tendency affects conservative conservative illustration ijcnn chapman crosses crosses crosses crosses bump considers regimes regimes alternatives alternatives sam truth truth knowing wider wider strict replacement tom tom quantify quantify ping terns suffices drawing resampling resampling incorporation unreliable partly inaccurate statements putation probabil bootstrapping bootstrapping bootstrapping bootstrapping bootstrapping bootstrapping replicates replicates replicates extrapolation severely heskes heskes heskes heskes heskes subsampling netherlands pay coverage ixl dash dash dash dash overfit overfit nix efron visualizing pling overestimate summarizing invalid corrects deficiency prescription prescription nijmegen nijmegen tremendous cially validating waste waste underestimate enclosed inaccuracy inaccuracy irdle straightforwardly straightforwardly espe ambitious kun loglikelihood crux subdivisions desirability mbfys polation geert grooteplein disregards 
#@Heskes_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural input input input input input input input input input function function function function function function function function function function function figure figure time set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm output output number number system system system system error error error results models performance performance performance performance space space space space space space space space space space weights weights weights weights linear linear linear layer layer case vector vector order order order order order order order order order order order shown shown values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight weight weight distribution distribution approach approach point point point point point point point image large local local local shows shows shows algorithms examples examples examples examples examples examples examples examples examples examples examples examples work work work methods fig fig fig step points points level level level level level level level level level level level level level level trained structure random high similar architecture architecture architecture architecture line line line line rule vectors vectors generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech parameter parameter parameter approximation approximation average average average theory note dimensional result university computation computation research log log defined defined science science science present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase machine maximum learn learn learn learn nonlinear outputs outputs outputs continuous continuous continuous continuous continuous abstract find find find find find find properties likelihood references positive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical generated generated generated tion energy energy energy assume lower lower lower lower lower rules rules rules rules rules higher multiple multiple multiple multiple good good binary binary long tree tree tree tree tree tree tree techniques correct observed observed errors scale scale finite ing respect respect multi multi sum eq means means factor dimension applications study study study study study em original provide related related related related related related approaches approaches approaches institute department individual represents exp considered hinton curve curve curve curve curve curve curve curve curve transition transition transition transition transition transition transition transition transition transition transition transition transition transition limit limit san top top top top free free basic basic increase increase weighted levels levels provided constraint measured feedforward feedforward group group group group close close predictions amount implemented supported role role makes makes including smaller smaller smaller fully jordan jordan jordan technology transfer interesting interesting ratio increasing mechanism special matching principle leads leads making experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert decay perceptron denotes denotes architectures exact advantage property pair pair typical strategy hierarchical hierarchical hierarchical recently interest highly teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher volume axis symmetric symmetric symmetric symmetric generalized parts boundary boundary conclusion critical critical critical designed asymptotic learns learns temperature temperature physics physics largest largest drawn solid turn variety minimizing groups minima program pro produces produces written written written plot plot transitions transitions transitions distinct distinct student student student student student student multilayer versus versus versus versus yield overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap overlap evaluate evaluate fraction soft partition partition partition partition partition calculation dashed dashed assigned expect formulation formulation weighting subspace phys phys phys partially partially discussions gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating simplicity letter closely divided divided divided effectively effectively driven driven committee literature plots plots orthogonal interpreted interpreted symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry gibbs gibbs modular consisted consisted jacobs jacobs neighboring poor dotted existence proper hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hill smallest rev rev rev perceptton ith generates defines integrate advanced cos cos slope analytic answer baum london considerable turns perspective easier division leaves leaves desirable sgn sgn probable mechanics mechanics mechanics mechanics mechanics mechanics mechanics hme capability capability haussler sharp partitioning partitioning branch branch qualitatively collective comments implements focused begins begins softmax phenomenon intractable cooper accomplished assign branches branches branches jth partitions partitions wrong mail replica keeping tishby belong overlaps overlaps overlaps sompolinsky sompolinsky saul infinity originally spherical branching branching specialized theoretically properly properly park park wolpert seung seung assigns assigning divide divide divide crossing crossing ical big breaking breaking breaking 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#@Kang_K,Oh_J,
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural input input input input input input input input data function function function function function function function function function function function function figure figure set networks networks networks networks networks networks training training training training training training number number number number number number number number number number number system system system system error error error error error error error error error error error error error error error error error error error error results results results results results results results results units units units units units units units information models hidden hidden hidden hidden hidden hidden hidden hidden based based based based based based based based space space space space space space space space weights weights linear linear linear linear layer layer layer layer layer layer layer layer case case case case case case case case case case case case case case case case vector shown shown shown shown shown shown systems systems systems systems systems values values probability probability probability probability probability probability probability probability probability probability probability parameters functions functions functions functions neurons unit distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition approach pattern pattern pattern pattern pattern pattern control large patterns patterns patterns analysis class class class class class class class form form form form form form paper paper paper paper examples examples examples small size size size size size size step points points points features random random similar show show show section section section fixed vectors vectors general general general general generalization real average average theory theory theory theory obtained note note note note dimensional result result result result result threshold threshold threshold threshold computation computation research research independent independent log log log log defined defined defined defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target target target target target constant constant constant constant constant constant constant constant constant estimate estimate estimate estimate terms connections connections presented presented low machine sets press press press learn learn position position position continuous continuous continuous continuous sample sample sample sample sample sample sample sample sample abstract computational density density density properties properties properties references ieee ieee positive introduction estimation behavior statistical statistical statistical tion difference complexity complexity variable assume assume assume lower lower lower measure prior part center theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound binary binary binary binary bayesian techniques finite resulting ing ing ing ing total respect respect respect respect multi multi sum called elements mapping mapping factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made applications study study specific specific samples samples samples samples samples samples samples true true true true desired objects proc proc proc proc proc proc proc proc determined determined related connected distributions distributions distributions distributions distributions equal equal mit mit mit steps comparison contrast support nets selection morgan report loss version version advances layers ai ai considered cambridge cambridge cambridge directly curve curve curve curve curve curve curve curve curve curve curve additional curves curves curves curves curves curves curves curves curves curves estimates estimates estimates estimates limit limit limit limit limit limit limit limit limit limit limit limit capacity upper upper upper upper upper upper requires world basic pages pages pages pages pages con derived derived derived derived randomly bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds types entropy entropy entropy entropy entropy entropy entropy entropy selected nature depends feedforward feedforward denote denote denote close assumption proof proof finding finding effective effective theoretical main main main journal hypothesis hypothesis hypothesis hypothesis instance easily degree account functional fully mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp significantly significantly significantly significantly increasing consistent consistent uniform empirical details call max max max max idea perceptron perceptron perceptron perceptron denotes denotes denotes denotes discussed discussed recent property element element element practical quadratic recently interest dimensions previously trans modified modified modified modified observation interval improvement storage exists exists exists exists expression concept concept scaling scaling scaling scaling scaling scaling scaling scaling segment central asymptotic asymptotic hard hard hard hard largest largest drawn sigmoidal sigmoidal sigmoidal start start min min min min min targets targets introduce introduce explicit plot mathematical recall implement multilayer multilayer multilayer multilayer multilayer multilayer coordinates linearly springer springer implies implies implies expectation interpretation lemma lemma lemma densities forms similarly partition sufficiently activations perceptrons perceptrons perceptrons perceptrons vapnik vapnik vapnik extension plotted holds holds straightforward differ maximal modification situation situation plots plots essentially essentially composed composed composed capture road soc verlag verlag link link hold comp usual generalize generalize generalize nips nips nips nips hypotheses hypotheses extend presents essential essential essential replaced existence giving applicable applicable possibility scaled scaled cover understand naturally integer generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation thought der der der der der obvious formal formal observe observe perceptton logic logic established piecewise piecewise trivial trivial trivial trivial trivial trivial publishers derivation defining improves analytic capabilities capabilities answer independence briefly turns formalism formalism formalism formalism formalism formalism formalism formalism formalism division worst worst worst immediately immediately laboratories laboratories acknowledgement mechanics argument generic marked haussler haussler polynomials ture differs monotonic monotonic extensions lim lim discontinuities discontinuities discontinuities ordinary proofs proofs acm partitions generality kaufman simplify replacing hope tishby fail splitting modifications combinatorial constructive bartlett corollary corollary equals equals overview percepttons counting counting counting counting counting counting entries claim claim claim claim claim claim claim claim claim claim claim claim refers warmuth kearns kearns extends seung splits integers geometrical logarithm outline rigorous rigorous accept chervonenkis sontag sontag par additionally lit associate australia auxiliary rain concentrated thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic thermodynamic mathematically ization discontinuity learnability oct regimes win win win preprint applicability det williamson williamson dichotomies simplifies behaves mcculloch mcculloch gratefully pitts pitts const virtually imple inequalities determinant char sided tuple ooo cardinality shattered shattered shattered implied establishing falling niranjan subscript closure elec kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk kowalczyk shortly cations appli ular ular tighter phil blumer dependences claims colt shattering acknowledged tinuous mented koiran earning provably provably provably provably shell shell shell icnn ism ticular cap proportionally rutgers permission partic partic sakurai ehrenfeucht ein innovation congress subsection heaviside heaviside loose lan optimistic coo remedy underly 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#@Ferni_H,Kowalczyk_A,
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#*network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training algorithm output output number number number error error error error error error error error error error error error results results results results units information information problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden based based based space space weights weights weights layer layer layer layer layer case case case case case case case vector vector shown shown shown values probability probability probability probability probability parameters parameters parameters parameters parameters weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution method approach approach approach approach approach single single large large large large rate rate rate rate rate rate rate class class class class class class class class class class class class class class class class class optimal optimal optimal optimal form form shows gaussian gaussian gaussian paper paper paper paper paper examples small small size size net work work task task points classification classification trained random random random random random random representation section section fixed general general general generalization speech real real real real real real approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory theory obtained obtained obtained obtained obtained note result result result result result result result result university university variables computation computation solution independent log log defined defined defined defined defined defined found target target constant constant constant estimate estimate estimate estimate estimate estimate estimate estimate standard computer terms science presented activation activation activation nodes nodes nodes machine basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear continuous sample sample abstract applied computational convergence convergence convergence convergence convergence convergence convergence convergence convergence references references ieee ieee ieee introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation tion difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable variable assume assume assume assume assume assume assume measure measure measure measure chosen part previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound type required good expected expected expected expected make errors errors finite finite resulting resulting classes classes total total total regression regression regression regression regression regression called called means means factor dimension dimension obtain obtain obtain obtain artificial artificial artificial artificial artificial artificial samples samples application series define define define define rates rates rates rates proc determined goal related constraints constraints accuracy nets nets nets nets nets nets selection morgan words words department loss loss loss loss loss loss loss loss loss loss loss loss loss loss version consists kernel kernel kernel kernel kernel difficult scheme ai maps considered considered determine efficient upper upper upper upper choice choice vision pages pages pages give condition condition derived developed bounds bounds bounds bounds lines entropy provided finally constraint measured technical feedforward describe arbitrary denote close proof proof proof proof rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf effective assumed assumed supported square hypothesis noisy including probabilistic smaller functional unknown unknown fully york special special uniform uniform uniform empirical empirical empirical empirical empirical empirical empirical empirical principle squared squared squared squared squared squared squared squared numbers numbers numbers numbers numbers max making window idea attention combined choose choose choose description predict denotes denotes denotes improved improve recent recent advantage robust robust apply apply introduced sense subset recently previously observations definition observation bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded risk risk risk risk risk risk risk risk risk grant grant grant exists exists exists concept studied studied matrices matrices matrices column minimal valued depend drawn sigmoidal sigmoidal regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization radial radial radial radial radial radial radial radial radial radial radial radial assuming minimizing minimizing minimizing minimizing minimizing exist min min min min relationship acknowledgements suppose suppose suppose dept metric metric metric linearly easy easy slightly unique minimization minimization springer choosing national family family family dependence review learner learner lemma lemma lemma variation variation variation variation variation variation variation detailed restricted lee lee centers approximated approximated constants constants allowed spaces convex convex convex convex convex penalty penalty penalty penalty closed valid norm norm transactions transactions transactions expect kernels combinations activations formulation formulation vapnik vapnik prove prove candidate candidate candidate candidate candidate characterized characterized closely importance uniformly uniformly poggio schemes schemes schemes verlag induced contained allowing sci hold satisfy satisfy satisfy satisfy comp notation minimizes ill ill ill ill predictor predictor predictor automatically received satisfies satisfies satisfies satisfies decreasing integral hall mappings investigated dependencies root comparable proved workshop cover math editor editor adapt integer precise academic arbitrarily motivated years great inequality publishers smoothness london considerable choices consequence universal members definite definite annual varies varies considerably formulated operate differs differs proven achieves enables yielding discontinuities pac extensive girosi girosi girosi girosi girosi girosi girosi girosi girosi member member member jones generality generality eliminated fits darken darken satisfying satisfying satisfying satisfying logarithmic fan imposed check nonparametric nonparametric published bartlett corollary barron barron barron barron barron barron canada extends extends extensively jump inf inf inf inf inf inf inf inf characterization balancing approx kluwer covering covering covering covering inferred sontag tradeoff rain rain arising penalized penalized favor chapman realizable realizable elementary regularized regularized march weaker discretization union williamson copies nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative families families hull kth kth archi transpose closure closure closure closure signed translates monotone penalizes ira ira montreal freely collections argmin argmin argmin topics activa broader optimizes lipschitz sixth dealt imation picks wii canadian functionals nserc emphasizing ogp viewpoints nato agnostic yix rid kauffman bernstein balls adam surely nonincreasing tectures mammone tropy asi elf supremum 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#@Krzyzak_A,Linder_T,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model data data data data data data data data data data function figure figure figure time time time time time time set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number state state state state state state results information information information performance performance performance performance performance based based based based space space space space space space linear linear linear linear linear linear linear linear linear case case case case shown values probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution point single single single single rate analysis analysis analysis analysis analysis analysis analysis analysis class class class class class optimal optimal optimal optimal optimal form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper small size work task task methods step points points classification classification classification process current current current current current similar similar similar similar show show show section section section section section section section section line line line line line line line line line general general parameter parameter parameter average theory theory theory theory theory theory gradient obtained obtained obtained note note note note experiments experiments experiments experiments experiments experiments experiments threshold threshold threshold threshold threshold computation research research research research independent log log log log sequence sequence sequence target target target target initial standard standard prediction prediction prediction prediction prediction prediction prediction prediction left present present present machine machine learn sample abstract abstract abstract applied applied computational computational computational density density density density references stochastic procedure procedure procedure important introduction introduction hand hand hand hand behavior behavior generated generated generated generated assume assume classifier prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen chosen chosen chosen previous previous previous theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound cases binary binary conditions conditions conditions represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected make make make make fact techniques techniques techniques techniques techniques techniques correct correct correct correct probabilities probabilities observed observed observed errors finite simulations simulations simulations resulting classes classes classes classes classes classes ing tasks tasks tasks tasks simulation simulation simulation simulation simulation simulation respect called times times elements factor potential made made made made made made made study study obtain obtain obtain negative original original original original original original original original original original relative relative relative relative relative relative relative application application proc proc perform experimental related related related posterior posterior posterior posterior posterior distributions distributions distributions equal comparison comparison comparison update update update morgan proceedings proceedings proceedings proceedings report institute institute loss version version technique internal addition graph considered considered computing san top bit conference conference conference choice choice world world pages pages pages pages pages pages condition condition condition condition condition condition derived derived derived derived weighted weighted weighted weighted weighted randomly conditional bounds bounds bounds bounds bounds bounds bounds bounds lines lines entropy entropy entropy actual depends depends depends depends technical describe describe close assumption assumption predictions predictions predictions predictions implemented generate end end instance instance instance instance instance instance instance instance instance makes makes makes makes makes makes noisy including including kaufmann probabilistic probabilistic typically typically pairs pairs pairs consistent trials trials trials trials trials trials trials trials trials trials trials matching uniform leads details details details call call call call call making attention attention choose choose run run run run description predict perceptron correlations advantage advantage advantage pair typical typical apply apply side side quadratic sense relevant relevant relevant relevant relevant relevant relevant relevant relevant interest interest interest compare observations tions match match definition background symmetric symmetric observation bounded bounded risk entire exists lead lead studied studied trial trial trial trial trial trial trial trial trial trial alternative deterministic setting runs runs conclusion conclusion greater assumptions assumptions assumptions assumptions assumptions depend depend depend depend bayes bayes bayes bayes bayes bayes clear performs asymptotic learns learns mateo suggest suggest suggest presence labeled labeled labeled labeled labeled variety variety start start start exist exist exist manner suppose suppose suppose appears appears appears appears derive derive derive construct construct construct generating plot plot plot label label label label label label label label label label label label label label label category linearly linearly linearly linearly versus boolean boolean decreases yield family family family family family family family family family family family interpretation learner learner learner learner learner learner learner learner learner evaluated labels labels labels labels labels labels fraction forms understanding similarly updates updates updates past earlier additive roughly purpose generation initially classified david expect expect expect recorded existing thesis instances instances instances instances instances discuss discuss priors holds discussions successfully extra extra extra suitable computationally divided driven driven driven driven driven driven driven driven driven driven driven driven driven literature comparing comparing comparing plots composed quickly success success showing interested interpreted symmetry symmetry symmetry symmetry symmetry symmetry strategies hold satisfy absence minimizes leading predictor acknowledgments situations situations put involving involving replaced preliminary matches matches giving tech dependencies authors comparable workshop workshop affect attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes closest predicting perfect perfect changed assumes assumes ith ith ith phd separable separable separable separable separable separable derivation track track track analyzed improves analytic majority majority majority majority capabilities capabilities expensive independence independence worse handle handle handle handle handle handle handle handle starts inside turns turns turns lin satisfied style style style choices worst leaves separately beginning members attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute annual annual reflects led tional tional treated variant variant variant variant variant variant variant variant variant variant variant variant progress progress univ cumulative irrelevant irrelevant irrelevant naive naive naive initialization gap gap picture ordinary redundant redundant ear mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake restriction restrict princeton princeton princeton acm conditioned perfectly perfectly count count jth fails wrong wrong ments stronger proceeds proceeds proceeds logarithmic imposed familiar biased keeping analyzing analyzing analyzing analyzing analyzing settings optimally exploring analyses separating equals guarantees bad intended intended ahead arrive record record warmuth warmuth theoretically santa counts unchanged maintaining unable deriving presenting classifications classifications lit lit lit lit lit lit lit lit lit lit lit lit lit lit freund stands winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow conservative impose impose distribu relating scope voting voting voting voting maintains applicability computa nec nec nec served chris styles stochastically coin attempting calculates fre fre mistakes mistakes mistakes mistakes mistakes conversion correctness conditionally littlestone littlestone littlestone littlestone littlestone littlestone littlestone littlestone littlestone littlestone crl cruz kivinen corn linking observes observes forgetting ther ele ucsc bernoulli intervening ninth ninth fur separability unclear converting exponentiated ies grove superfluous embodied embodied helmbold helmbold looked interna omitting told speak concentrating parameterize xii linkage linkage 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#@Littlestone_N,Mesterharm_C,
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#*network network network network network network network network network network network network model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input function function function function function function function function function function function function function function function figure time time time time time time time time time time time time time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks networks output output output output number number number number number number number system system state state state state results results results results results results units units units units information information information models hidden hidden hidden hidden hidden performance based based based weights weights weights weights weights weights linear linear linear layer layer case case order shown shown systems systems systems systems values values values probability probability probability parameters parameters parameters parameters parameters parameters noise noise noise noise noise weight functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition method method pattern pattern pattern pattern point point point single single single single single processing large large large large large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form shows shows visual visual visual small size size size size net net net net net net net net net net net net net work fig points classification current current high high response response response response response response response response similar equation equation section fixed rule general general general parameter real approximation average term note note result result result result result result result threshold threshold threshold threshold variables variables variables variables variables computation computation computation computation computation computation computation computation independent defined defined defined found initial initial constant constant constant constant constant constant estimate computer computer terms distance distance distance synaptic synaptic synaptic science phase phase activation activation activation activation activation activation activation nodes frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal sets range range range press position basis outputs outputs continuous continuous continuous continuous continuous abstract computational computational computational computational computational computational computational computational convergence analog analog analog analog analog analog analog analog analog analog references due due due ieee context introduction action action action hand hand circuit stimulus stimulus stimulus tion difference complexity complexity variable variable variable variable variable variable assume assume assume assume assume assume assume lower lower lower lower lower representations chosen chosen theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type type cortex binary spike spike spike spike spike represent make fact fact fact fact length finite simulations minimum resulting ing simulation simulation simulation multi sum sum sum times times times times times times times times factor potential potential potential dimension dimension dimension dimension made knowledge vol vol vol vol vol vol vol artificial represented application provide provide compute compute compute compute compute compute compute rates rates proc proc determined determined determined experimental experimental related related related related constraints connected power power power power power power power power approaches mit larger contrast nets nets nets nets nets nets nets nets nets nets institute synapses synapses synapses consists advances connectionist layers delay scheme scheme scheme scheme addition ai ai considered considered considered considered cambridge directly additional additional view bit conference determine approximate free free free speed produce coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding weighted weighted weighted bounds types actual provided finally finally evidence nature inhibitory depends depends biological biological biological biological biological biological biological biological biological biological biological feedforward feedforward feedforward feedforward describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary transformation fast fast assumption corresponds excitatory stable stable proof proof proof common common assumed shape role theoretical theoretical eds noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy smaller needed hopfield hopfield hopfield hopfield hopfield hopfield coefficients technology mechanism mechanism mechanism consistent uniform empirical principle details details numbers numbers numbers max window window window normalized directions recent recent advantage property element typical movement apply period sense subset subset relevant interest interest previously previously previously works works tions yields yields trans bounded gate gate gate gate interval interval sensitive exists exists digital occurs assumptions assumptions conclusions differences modules modules modules retina encoding encoding largest largest sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal demonstrated demonstrated variety manner appears appears van van van derive edges edges multilayer linearly linearly linearly involves shift implies implies implies potentials potentials focus stages stages interpretation interpretation variation constants allowed sign sign key reasonable additive delays normalization intervals intervals generation generation valid sufficiently sufficiently sufficiently sufficiently assigned construction construction construction norm koch koch koch david precision avoid fire fire fire automatic automatic prove absolute holds holds holds simplicity extra closely closely uniformly suitable differ differ maximal maximal maximal encoded encoded encoded encoded encoded spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking computations computations computations computations computations computations computations computations schemes schemes schemes tend receives refer refer refer refer neuroscience follow timing timing hold involved play realistic computes computes computes thresholds automatically subsequent satisfies modelling situations trains trains trains explore carried exhibit humans strengths replaced replaced behaviour helpful postsynaptic postsynaptic rise fashion links reliable gates gates gates gates gates gates gates complicated oscillation encode encode presynaptic presynaptic neu neu math onset ensure formal formal assumes assumes shapes simplest arbitrarily arbitrarily arbitrarily integrate years mentioned piecewise pairwise pairwise pairwise fairly perspective lin closer strictly precisely monkey acknowledgement universal preceding explained substantially simulate simulate simulate simulate simulate simulate haussler employ employ employ employ continuously biologically reliability reliability reliability http differs reaches fall focused extreme proofs www grows maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass generality generality communications systematic striate programmable programmable programmable interpret operates definitions imply north carry fires fires fires fires irregular bialek bialek bialek bialek bialek bialek surprising decide pat holland regard multiplied reveals arrive locked snn snn snn snn snn roy epsp epsp epsp epsp epsp epsp epsp epsp epsp inf accumulated hair sig basically basically graded equivalently encodes sontag sontag sontag sontag sontag sontag sontag employs employs theorems par trigger trigger resting simulating simulating avoided auxiliary auxiliary adjustment alter pub trends ftp ftp ftp ftp ftp goals lobe approxi approxi considers considers macaque host host isi elsevier flight interspike interspike tin article article article spite saturated saturated suffices rons concrete returned convention inspection shattered shattered connectionism steveninck steveninck steveninck shortly ruyter ruyter ruyter tern zone behaving technische direc sends rieke rieke rieke ohio ohio rigorously bair bair thorpe thorpe thorpe constructions constructions leaky mate ting ously previ poten koiran koiran koiran koiran koiran fogelman rising blowfly blowfly ticular expands compose compose rutgers mission cis cis ipsp ipsp ipsp ipsp ipsp ipsp ipsp ipsp native sse graz heaviside mated torques ciently leo vout archive archive archive fimctions fimctions ass moidal abbreviated igi wolfgang sistent yer ify ify imbert imbert imbert steels naptic suffi tential eduardo pfeifer neuroprose maa cry quires pear stereotyped scal restilts schreter bait tials 
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#*network network network network network network network network network network network model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number system system system system system system system system system system system system system system system system system system system system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results units units units units units units information problem models models models models models models models models models hidden space space space space layer layer case case case case case case case case case case case case case case case case case case vector order systems systems systems systems values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution method point point single single control large large large large large large neuron neuron neuron neuron analysis analysis analysis analysis analysis analysis class class optimal inputs inputs inputs inputs inputs inputs shows shows gaussian gaussian gaussian gaussian gaussian examples examples small small small small size net net net net net net net net work methods methods methods step step step step step step step step step features process process process process process process process level current current current structure structure structure random random high show show section fixed general general general general general general general parameter real real real real real real real average average states states states states states states states states states states states states states states states theory theory obtained obtained term note result university university university university computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation independent independent defined defined defined defined sequence dynamics dynamics dynamics dynamics initial initial constant constant computer computer terms terms distance distance distance science science direction activation machine machine machine sets sets range press press components components components components nonlinear outputs outputs outputs continuous continuous continuous continuous continuous abstract applied applied find computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational density density density density density density density density density density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references component stochastic stochastic stochastic stochastic due important important important important introduction complex complex complex effect effect effect effect effect effect effect effect effect effect effect parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent complexity assume assume assume assume assume assume assume lower measure chosen part previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound cases cases cases cases cases cases cases firing firing firing firing firing type type type type type type type required binary binary long conditions conditions conditions distributed expected expected markov make fact length length correct correct finite finite finite finite finite finite finite finite resulting total computed computed respect respect performed called times times dimension dimension dimension dimension dimension dimension dimension global applications original specific specific application provide provide provide provide define proc perform determined goal related distributions distributions distributions distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete brain power power power power power power power power power approaches steps steps steps steps steps larger larger contrast contrast nets nets nets nets nets nets nets nets nets nets nets nets nets institute words department loss version version internal internal internal internal internal internal internal internal kernel kernel kernel kernel difficult difficult addition addition sequences considered considered framework framework framework framework framework framework framework framework framework computing domain domain domain domain view view transition effects determine upper upper upper upper upper upper upper upper upper free free free world basic basic con produce produce condition condition condition derived bounds bounds bounds bounds bounds bounds types types types types types actual actual actual finally processes processes processes depends biological biological achieved feedforward feedforward feedforward arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote fast close assumption assumption assumption proof proof proof proof proof proof proof proof proof circuits common implemented assumed assumed theoretical require require require require require main eds journal instance noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy probabilistic probabilistic probabilistic probabilistic typically smaller needed dynamical programming york special special special special special special special special special language language leads leads leads details call numbers window international idea attention combined produced choose property property robust robust robust robust robust element practical introduced introduced moving identical machines sense subset subset previously axis tions tions studies studies rl address definition definition generalized generalized generalized bounded bounded bounded bounded bounded bounded bounded gate gate gate gate interval interval interval exists exists exists exists exists occur occur digital digital digital digital digital digital digital move move move hybrid occurs generally starting starting conclusions valued valued valued valued valued depend depend depend measures measures strong presence presence presence presence presence sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal exist introduce introduce introduce manner manner question denoted explicit explicit appears produces mathematical mathematical mathematical mathematical mathematical modeled events springer implies implies implies implies extraction boolean boolean select letters independently focus operations operations restricted completely completely completely similarly partition allowed reasonable reduces neighborhood neighborhood neighborhood intervals intervals valid intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate distances sufficiently sufficiently string norm avoid expect box box subspace batch batch batch batch recognize prove prove prove regular regular regular regular straightforward aspects uniformly uniformly uniformly uniformly uniformly uniformly differ spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations computations invariance online online traditional traditional refer refer soc compact compact verlag strongly strongly induced contained issue issue sin satisfy notation vary write moves moves moves moves satisfies satisfies cowan cowan cowan cowan access access investigate helpful reducing history dependencies dependencies reliable reliable reliable reliable reliable reliable gates gates gates gates func func cover cover notion math math math math analyze analyze analyze automata automata automata automata automata automata automata illustrate perfect perfect perfect perfect perfect perfect perfect perfect perfect perfect subsets formal formal academic arbitrarily submitted languages languages piecewise piecewise piecewise piecewise piecewise trivial briefly starts starts processed turns turns satisfied probable probable mathematics mathematics consequence recognized universal beginning read author preceding preceding preceding preceding preceding preceding argument argument considerably substantially pure pure pure flexible flexible amounts peter employ reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability requirement http berlin synthesis synthesis rely rely perturbations perturbations suited windows specifies extreme proofs proofs proofs proofs notes www investigation investigation investigation investigation investigation investigation restriction restriction restrict princeton princeton arguments refractory perfectly perfectly concerned null partitions addresses nonzero maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass maass generality wrong wrong consideration tools tools mail mail automaton automaton programmable analyzing analyzing definitions disjoint disjoint disjoint affected affected adequate adequate adequate fires continue composition corollary corollary corollary corollary surprising von von von von moved intended consequences captured claim diameter relies relies relies impact papers thresholding thresholding fired drop rigorous annals recursively ram sontag sontag sontag sontag tween theorems theorems par continuity continuity continuity continuity pub publication exam ftp ftp intuition shannon impose impose convert considers host topic setup distinguished distinguished distinguished register apparently universit universit happen minor union drops subspaces article article simplifies infinitely failures failures failures spite spite remark covers covers lecture neumann neumann neumann neumann remarks characterizing interior insufficient stochastically blum blum blum cornput suffices affecting fre concrete concrete concrete concrete practically unreliable unreliable ters tuple ally bss measurable measurable measurable measurable measurable measurable recognizes recognizes nontrivial nontrivial appl fin enters mach replication wires wires wires unnecessary amer initiated technische technische occasionally tolerant accepting turing ohio simulates adjustments assoc recursire parame possesses visits accepts accepts accepts conversations constructions unlimited lay claimed organisms tinuous mild mild noises siegelmann siegelmann siegelmann siegelmann siegelmann siegelmann siegelmann helsinki pad contin fimction temporarily occuring ist cis articles graz graz graz graz casey casey casey casey casey casey casey casey casey casey uous absolutely finland borel borel borel borel borel intro austria finished ered deviates auer detrimental archive bulletin fll fll preliminaries faulty igi wolfgang rejects harmful harmful terministic ined stark actu awe neuroprose radon nonempty exhausted counterexample titions dal computability 
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#*network network network network network network network network network network learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data data function function function function function function figure figure time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number number number number number number number number number system error error error error error error error error results results results units problem problem problem problem based based based based based space weights weights weights weights weights weights weights weights weights weights linear layer layer layer case case case case case vector vector order systems systems systems values probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method approach approach approach approach point single single control large large large large large large large rate test analysis analysis class optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs form shows shows shows simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples examples small small small work work methods methods points field field field field field field field field field field field field field field field field field field field field field field field field classification classification classification process random random random architecture show show show equation section section section section section section fixed fixed line line line rule vectors general general general general general generalization generalization generalization generalization parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average average average average average average average states theory theory theory gradient obtained obtained obtained note dimensional result result result result result threshold solution research research independent defined estimate estimate estimate estimate terms terms terms prediction prediction prediction presented presented present present machine components outputs outputs abstract find computational computational density likelihood likelihood references component procedure important important decision introduction statistical statistical statistical statistical statistical statistical statistical statistical generated generated variance variance variance variance energy variable variable variable variable assume assume assume lower prior prior prior prior prior prior prior prior part center theorem theorem cases cases type binary conditions tree distributed bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected expected equations equations equations equations equations equations equations equations equations equations make make make make fact techniques forward forward forward simulations simulations resulting simulation respect respect multi sum sum performed performed eq eq called called called called called means means made natural knowledge obtain obtain obtain obtain specific true compared cross posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior connected distributions discrete approaches steps larger fields fields selection morgan institute internal internal internal internal internal internal framework framework framework directly curve curve additional estimates estimates limit limit limit limit limit upper full full full choice approximate approximate statistics free free free world world basic basic increase validation give give give derived derived randomly randomly conditional conditional developed lines finally finally evidence evidence evidence backpropagation iteration depends depends depends depends discussion normal technical describe arbitrary arbitrary denote assumption assumption assumption assumption assumption assumption assumption predictions predictions predictions predictions predictions predictions effective assumed supported theoretical theoretical theoretical require main ability easily easily easily kaufmann pairs needed reduced reduced reduced reduced reduced reduced unknown unknown unknown fully interesting testing york mechanism consistent pre normalized produced perceptron perceptron perceptron perceptron denotes denotes denotes architectures discussed exact exact exact exact exact ensemble practical apply moving include subject inference teacher calculated calculated calculated calculated works tions entire parts parts alternative feed feed feed occurs runs conclusion assumptions central interactions bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes numerical asymptotic taking integration physics largest drawn drawn regularization variety start averaged averaged averaged denoted relation monte derive carlo written solving generating label label implement remaining slightly angle consisting develop applying predictive predictive springer expectation expectation independently independently expressed correlated correlated correlated correlated estimator estimator solved densities open evaluate labels approximations approximations understanding sizes partition partition sign sign reasonable reasonable reasonable calculation calculation dashed reduces valid calculate sufficiently expect combinations sciences extension uncertainty priors priors phys phys phys simplicity suitable encoded committee mackay mackay mackay situation verlag procedures anderson split contribution sin sin comp generalize realistic acknowledgments extend situations 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#@Opper_M,Winther_O,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural input input input input input input input input input data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm number number number number number number number number number error error error error error error error error error error state results results results results information information problem problem space case case case case vector shown systems systems noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions distribution method method method approach approach approach point processing large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis matrix optimal optimal optimal inputs inputs inputs inputs inputs signal algorithms simple gaussian gaussian paper paper paper paper examples examples examples examples small small size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size size current current current random similar show show show equation equation equation equation equation equation equation equation equation equation section fixed fixed fixed fixed fixed fixed line line line line line line line line line generalization real average average average average average average states theory theory theory theory gradient obtained term term term term note note note note note result university university solution solution log log target dynamics initial constant constant constant standard computer terms terms terms terms terms science presented presented present present phase phase sets sets sets components continuous sample abstract find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction complex behavior behavior behavior behavior generated search search search search search change change difference assume assume lower chosen chosen chosen theorem cases multiple multiple multiple good good long expected expected expected equations equations equations equations equations make scale finite simulations simulations simulations simulations simulations simulations simulations simulations simulations total total simulation simulation simulation simulation simulation computed respect sum times times times times times times times times times optimization dimension dimension filter obtain obtain obtain obtain vol samples compute compute compute compute rates active equal comparison comparison update update update update descent selection report institute department advances ai equivalent equivalent curve curve curve curves transition determine determine determine choice speed increase increase give give give randomly iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration simply simply technical increases denote denote complete predictions amount nearest theoretical theoretical journal square square square square simulated smaller needed needed block increasing increasing increasing special mode mode squared squared squared squared squared squared squared iterations international supervised early idea choose choose choose choose added denotes denotes directions directions advantage takes practical apply side subset subset interest dimensions dimensions varying compare approximately smooth yields address symmetric symmetric symmetric entire expression expression suggests predicted predicted alternative alternative alternative alternative move white occurs occurs occurs setting starting place reduce reduce reduce reduce exponential faster taking drawn drawn drawn drawn california solid solid proportional proportional proportional proportional assuming min decrease relationship targets annealing annealing annealing annealing annealing annealing annealing annealing annealing derive derive derive written solving solving solving ways ways plot dept unique unique equilibrium equilibrium gaussians decreases decreases decreases decreases choosing choosing solved solved evaluated sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes converges constants updates updates updates slow slow dashed dashed dashed reduces combining roughly iterative remains remains norm transactions thesis batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch batch plotted plotted characterized selecting presentation presentation online identity reached issue symmetry vary vary write simplified reach satisfies explore simpler schedule schedule schedule schedule investigate exponentially exponentially exponentially exponentially updating rapidly put detail hessian hall reducing reducing examine examine scaled authors momentum smallest trace trace integer analyze analyze illustrate subsets quantities greedy assumes regime phd averages asymptotically slowly slowly slowly slowly agreement defining slope starts perspective straight tive mathematics conjugate argument pure pure pure pure tional tional lms lms lms lms lms lms lms lms lms lms remove slower compares compares compares compares switch reaches reaches conclude decreased decreased tile tile tile tile tile tile displays displays redundant redundant redundant leen optimality martin summing arguments conditioned conditioned proceed logarithmic moment obtaining mark removing removing removing removing presentations presentations presentations presentations presentations presentations meaningful prentice loo appendix appendix appendix counting express refers clean late late late late late late late theoretically treat street graduate annealed annealed annealed annealed disadvantage expand confirmed sized prevents oregon oregon differentiating rewritten replacement replacement impractical todd jersey proposes fox fox fox ooo orr orr orr orr orr orr orr orr fastest gence gence approached greatest simon noiseless demanding putting putting dominate rom goldstein conver conver froin concise concise plutowski dash sume southern robbins subscripts monro looo dropping xlx compar rewriting batches rit incre propor propor xve haykin factoring rounds rounding proposing spherically spherically spherically ool halbert sumed obt larry ison genevieve genevieve genevieve owt gaussi gaussi moller moller suming zxt drb flatten 
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#*network network network network network network network network network network network network network network network network network network network network network model neural neural neural neural neural neural neural function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm number number number number state state state state state state state state state state state state state state state state results results results results results results results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem based based weights case case shown shown shown systems systems systems systems pattern image single single processing local local local local local patterns class class shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple paper paper size methods step field field field level problems problems problems problems problems high similar show show show section section section section images states states states states states states states theory theory theory theory theory theory theory theory term result result university threshold threshold computation computation computation research research research defined defined found found standard computer computer computer computer computer computer computer node science science science left left present nodes nodes nodes nodes nodes nodes nodes sets maximum press press press components components abstract computational computational computational computational computational convergence properties properties properties references references ieee ieee ieee positive positive positive important important important introduction introduction complex complex circuit parallel parallel parallel parallel parallel parallel parallel cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search tion change energy energy energy complexity complexity complexity complexity complexity complexity measure representations part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem type binary binary long make fact fact techniques techniques minimum classes classes classes classes computed called called called mapping mapping means optimization optimization natural global em proc active determined connected connected connected connected connected connected connected connected connected discrete discrete mit contrast contrast descent morgan proceedings department implementation technique consists internal difficult difficult difficult graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph computing computing computing computing computing bit bit determine requires pages pages give weighted developed developed levels path path path path path path evidence evidence depends increases arbitrary arbitrary arbitrary arbitrary arbitrary denote fast fast fast complete complete complete complete complete complete complete complete complete complete complete complete complete stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable proof proof proof proof proof proof proof proof proof finding finding finding finding finding finding finding finding common supported theoretical require main journal journal journal square easily easily degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree including including including including kaufmann hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield edge edge edge edge edge edge edge edge edge special consistent call numbers max max max bottom magnitude polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial combined architectures architectures property property property takes trees sense sense recently previously conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional tions solve solve solve converge converge converge converge converge converge diagonal definition background background background separation separation symmetric symmetric generalized grid grid bounded grant grant exists exists exists exists move runs conclusion row neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor measures measures exponential exponential exponential exponential exponential exponential exponential exponential faster faster faster faster faster faster faster faster faster strong strong hard drawn demonstrated labeled exist exist plane configuration configuration force force question question suppose suppose suppose relation edges edges edges edges edges edges edges edges edges edges edges written sequential describes distinct metric physical easy consisting consisting cycles cycles cycles cycles cycles cycles cycles select decreases national national viewed lemma lemma lemma lemma lemma lemma lemma solved solved solved restricted labels lee lee forms processor processor processor remains remains euclidean transactions transactions box sciences sciences prove prove prove prove major straightforward straightforward capable society differ differ maximal divided divided paths paths paths paths included literature essentially excitation excitation graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs induced prob interested running device hold board board computes processors command difficulty difficulty exponentially exponentially updating dual dual dual dual dual office complicated proved proved proved notion removed reading perfect consist finds defines devices theoretic crucial answer answer benchmark benchmark london sections style worst consequence cut cut cut cut cut cut cut cut cut cut cut scientific universal computers computers computers computers computers computers computers computers computers computers demonstrates demonstrates annual annual transient embedded embedded embedded embedded embedded embedded share slower polynomials http measuring popular collective substantial replace conclude realized proofs proofs notes assign assign assign assign acm acm acm acm member member member labelled discover connecting communications air air interconnection interconnection interconnection interconnection interconnection interconnection stated stated abilities removing definitions disjoint north synchronous exceeds arrays symposium symposium planar planar planar planar planar planar planar planar planar planar planar planar planar planar planar meaningful embedding embedding embedding embedding embedding embedding corollary respective vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices april foundations permutation permutation permutation omitted rich vertex vertex vertex vertex vertex vertex vertex vertex steepest hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube hypercube stone stone johnson johnson consecutive crossing sch sch sch sch sch shading ent goodman goodman break emergent connec superimposed simulating adapting iff landscape host host host academy sketch sketch sketch sketch sketch sketch apparently exchange exchange exchange exchange siam induces induces induces inactive manuscript lems cube cube cube cube cube tour tour tour algorithmic january twenty identifies tial rosenberg rosenberg hop hop hop suffices suffices suffices suffices suffices sym characterizes cur fastest texas mesh mesh mesh mesh mesh mesh mesh mesh bruck bruck linking completeness completeness completeness completeness completeness completeness completeness completeness completeness completeness completeness completeness completeness publishing hong hong incident incident puter knight knight knight knight knight knight knight knight knight knight knight knight knight knight knight provably optimiza permitted disconnected neurocomputing neurocomputing neurocomputing imitate collectively technically embed subgraph tradeoffs ian ian ian dation ccr ifs stating scalability scalability subsections bipartite bipartite bipartite url nection foun imitation imitation cknowle dgement versatile nar imitating imitating xxx xxx intercon attach scribe exponen pitman succinctly skipped transitive rently 
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function function function function function function figure figure time set set networks networks networks networks networks networks training output output output output number system system system system results results results results results results results results information information information information information information information information information information information information information information information information information information information information based based based based weights weights weights weights weights weights linear linear linear case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order systems systems systems values values values probability probability weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit distribution point point point point point point point point point point point point point point point point point point point point point single control large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate test patterns analysis class matrix matrix matrix matrix matrix form form shows shows signal signal signal simple paper paper paper paper paper paper paper paper examples size feature feature feature work methods fig fig fig cells step step points points points points points points points points points points points points points points points points points features features features features features features features features features process process process trained trained random random random high high high high high similar similar show show equation equation equation section section section section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line line line line rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors parameter parameter parameter approximation average theory theory gradient term term experiments experiments activity dimensional result computation solution solution solution research research research defined defined sequence dynamics dynamics dynamics initial constant constant constant constant constant constant constant constant constant computer distance connections connections synaptic synaptic synaptic synaptic synaptic synaptic direction presented present low low low low low low low maximum range learn learn components components components nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous continuous continuous continuous continuous abstract applied find find convergence convergence convergence density density references component component component component component component component component component component component stochastic stochastic stochastic stochastic ieee ieee ieee positive positive positive positive positive positive positive important introduction effect variance variance variance variance variance tion energy energy difference difference assume assume rules measure measure signals signals learned learned part part bound bound bound cases multiple cortex conditions conditions conditions conditions conditions conditions conditions distributed distributed make length length length length length length length length length length length length finite finite finite finite simulations simulations simulations simulations ing total respect sum called times elements dimension orientation obtain obtain obtain negative negative vol vol vol vol vol vol vol vol artificial artificial samples proc proc proc perform related related constraints constraints connected distributions distributions distributions distributions support descent proceedings institute individual bias ai considered experiment experiment experiment curve solutions solutions solutions limit limit upper upper choice choice speed condition condition derived weighted types provided iteration inhibitory inhibitory inhibitory inhibitory depends associative measured measured measured discussion discussion covariance covariance covariance covariance increases increases increases increases arbitrary tested fast corresponds corresponds stable stable stable stable stable proof proof amount assumed assumed assumed shape shape role theoretical main journal degree development typically typically smaller reduced reduced coefficients coefficients technology technology projection projection york mechanism principal principal principal principal principal principal squared iterations iterations iterations iterations iterations pre expert decay combined discussed directions apply apply identical unsupervised unsupervised tions smooth smooth smooth smooth match match match correspond pca studies converge differential differential trans symmetric symmetric bounded bounded bounded bounded bounded bounded bounded interval organization organization sensitive exists expression studied suggests suggests extended matrices predicted move move white occurs pass strength strength conclusion conclusion critical hebbian reduce sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid learns constrained hard mechanisms integration presence largest characteristics sigmoidal sigmoidal sigmoidal averaged averaged averaged averaged averaged averaged averaged base base base base base base base attractor relation relation relation produces written describes laboratory laboratory stability stability stability stability stability mathematical mathematical dept changing changing confidence confidence averaging infinite consisting mutual springer shift implies implies implies expectation decreases decreases yield expressed depending stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary correlated lemma lemma lemma lemma detailed evaluate understanding suggested converges converges converges converges converges sign sign remains remains valid calculate sufficiently sufficiently sufficiently avoid perceptual perceptrons eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues sciences memories determines determines prove holds discussions straightforward closely uniformly maximal computationally build post mackay miller orthogonal orthogonal orthogonal conf conf verlag induced interpreted content content content content content content content content content content content content content content content content comp comp simplified providing nips eigenvalue automatically extract extract satisfies satisfies satisfies acknowledgments decreasing decreasing situations law minimized origin origin origin origin origin origin poor investigate investigate detail optimized hessian hessian hessian hessian helpful giving giving project int int int int referred eigenvectors eigenvectors stream tanh tanh math coefficient coefficient coefficient adjusted der assumes precise hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb multivariate consist amari amari advanced cos directed growth growth growth variances defining unstable slope biology caused nonlinearity nonlinearity satisfied satisfied easier forces mathematics potentially gradually begin definite definite definite linsker argument detecting slower biologically characterize proven achieves geman expectations lim lim lim lim lim differentiable cor initialization japan japan japan japan japan resources acts nonzero nonzero nonzero nonzero nonzero nonzero nonzero grows suppression suppression climbing communications communications saturation oja striate check grow grow grow keeping monotonically implications exceeds carry carry financial corollary corollary combines equals equals von lengths enable emergence foundations insight eng rich eigenvector intersection intersection informa maximized dec employs employs convenience malsburg suppressed forcing avoided australia iff iff gener mathematically dominated oct oct ultimately ultimately increasingly unconstrained sketch responding siam prevents behaves sigmoids sigmoids characterizing characterizing council discontinuous accordance accordance accordance unbounded unbounded unbounded unbounded confirm confirm adaptively compo compo equa lying clark implying implying appl appl appl crl crl crl periodically cho cho ated preventing nov nov forgetting enabled enabled syrup syrup analyzer analyzer steepness steepness steepness steepness steepness steepness steepness nent nent ana ministry suppresses encouragement icnn steep implication cov cov telecommunications prof kushner electro exceeding neurocomputing unspecified constrains intersections investigates quotient suppressing suppressing suppressing kybernetik absorbed extractors rewriting strengthening ciently implausible implausible nondecreasing hibitory intersects traverse xxt xxt xxt pace conserve frontier munications violating collinear collinear collinear collinear integrable finish suffi sawai boundedness boundedness kobe nolta nolta disrupting 
#@Noda_H,Peper_F,
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#*network network network network learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set networks networks networks networks training training training training training training training algorithm output output output output output output system error error error error results results results information information problem problem problem problem models models models models models performance performance performance performance based space space space space space linear linear linear layer case vector vector order order shown shown shown systems values values parameters parameters parameters parameters noise noise noise noise weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method approach pattern point point point single test test test patterns analysis class class class matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal inputs inputs inputs inputs inputs form form form form form shows shows shows shows algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper size feature feature feature feature feature feature feature work work methods methods methods points points features features process process current current trained trained trained cell high high memory response similar similar similar equation section section section line line line line line line line line line line generalization real real average average average theory obtained obtained note note experiments dimensional dimensional dimensional dimensional dimensional dimensional result university university variables variables computation solution solution research research research research independent defined defined defined defined table table estimate estimate standard standard standard standard standard standard computer terms terms science prediction direction presented present present sets sets sets maximum range range range position position basis basis outputs outputs outputs sample abstract applied applied computational properties likelihood likelihood references component introduction generated generated generated generated generated generated variance variance variance variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search variable assume classifier lower lower prior prior prior prior prior higher required good good binary bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected expected expected expected expected markov techniques techniques correlation length scale scale finite finite regression regression regression regression regression regression computed computed computed multi performed eq eq elements elements elements means dimension dimension made applications samples samples true true true true true true application provide define define compute determined determined determined experimental posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions accuracy comparison train dependent dependent technique technique consists code kernel kernel joint difficult exp framework framework framework computing computing computing computing directly curve limit limit effects determine determine upper upper choice approximate speed randomly actual provided finally processes selected covariance covariance covariance covariance covariance covariance covariance normal increases arbitrary group group fast fast fast fast shape generate role theoretical theoretical main future easily noisy including account functional functional unknown interesting interesting uniform uniform mode leads principal details numbers bits bits bits bits bits produced added predict predict directions reported include inference interest previously volume differential diagonal chain williams constructed expression lead invariant invariant deviation deviation deviation deviation deviation wide matrices predicted setting pass pass demonstrate strength minimal conclusions operator operator valued valued valued competitive numerical numerical taking physics solid solid solid radial denoted acknowledgements appears appears monte carlo factors generating estimating mathematical dept explicitly infinite infinite remaining develop develop adding applying formed expectation boolean select select focus dependence variation variation evaluated evaluated controlled restricted translation reasonable calculation smoothing dashed dashed dashed dashed expansion expansion spaces combining interpolation assigned david avoid perceptrons strings subspace plotted plotted plotted discuss priors priors priors priors phys discussions straightforward straightforward straightforward uniformly suitable projections essentially essentially ten compact issue sin follow bar write play dot providing leading illustrates software bars bars carried difficulty rapidly replaced replaced replaced integral integral limitations dotted dotted helpful scalar tech applicable analytically analytically smallest circles plausible possibly generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation predicting illustrate subsets formal expressions defines defines defines neal neal neal neal optimum integrate histogram costs costs costs agreement agreement coded turns implementing sections formalism formalism formalism formalism formalism formalism producing producing precisely broad choices choices choices involve involve calculations toronto demonstrates applies understood readily readily quantitative peter slower calculating fall green richard sums sums semi conditioning benefit optimality investigation restriction fix fix fix resources numerically numerically numerically numerically promising familiar ylx ylx published excellent regarded overview evident treatment bins bins explains verify unchanged saad converted aston aston aston aston aston aston diverse suboptimal suboptimal suboptimal ical stands var illustration peripheral ftp thermodynamic denoting expand noting integrals integrals integrals integrals drawback sollich sollich det det det priority chris lated supply err err err err supplied ters tuple tuple tuple tuple tuple tuple triangle carries rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer rohwer quantitatively comprised unusual eigenfunctions birmingham analyse ted zhu zhu zhu zhu evaluates unlimited fil fil analysed associating brings supplies minimising illustrative worthwhile quantifying reg optimising eigenfunction xlx xlx xlx xlx zlx calcu numer mor generalise ultra ultra ultra sac quantised athe dxdy illus judging rept tabulated plugging rion trate introductory sation cix intelligently crite dxp eyi 
#@Morciniec_M,Rohwer_R,
#t10
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input data function function function function figure figure figure figure figure figure figure figure time time time time time set set networks networks networks networks networks networks training training training training training training training training training training training output output output output output output output output output output output output output output output output output number number number number number number system system error error error error error error error error error error error error error error error error error error error error error error results results results results results results results units units units units units units units units units units units units information information hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based space space weights weights weights weights weights weights weights linear layer layer case case case case case case case case case case case case case vector vector vector vector vector vector vector order order order order order order order shown shown shown shown shown systems values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight functions functions functions unit unit unit unit unit unit unit distribution distribution recognition method pattern pattern pattern point point point point point point point point point point single control large large large rate rate rate rate rate rate analysis analysis analysis matrix matrix optimal optimal optimal inputs form form simple gaussian gaussian gaussian examples examples examples examples examples examples examples examples small small small small small small small small small small small size feature work work task task task methods step features process process process process process process process process level level level level trained structure random random random random random similar similar similar similar similar similar architecture architecture show show equation fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line line line line line line rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter real approximation approximation approximation approximation average gradient gradient gradient gradient obtained obtained obtained obtained obtained term term note note dimensional result result result result university university variables variables computation solution solution solution solution solution research research independent independent independent defined defined found found target dynamics dynamics initial initial initial terms terms terms node node left map map map phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation activation activation machine motion motion motion motion motion motion motion motion press position components basis continuous continuous continuous abstract convergence references due due due positive positive positive positive positive positive important adaptive introduction behavior behavior statistical effect effect effect effect effect effect generated variance variance variance variance variance tion tion tion difference difference difference difference variable measure signals signals signals learned learned chosen chosen higher previous cases type long long conditions conditions represent bayesian equations equations equations equations equations equations equations equations equations techniques techniques correlation correlation length length length length observed errors finite finite finite resulting resulting resulting resulting respect respect respect performed performed performed times elements elements made made study obtain negative negative specific specific application desired determined determined goal equal approaches larger larger larger larger update update support descent descent descent descent internal individual maps framework additional solutions transition limit limit effects effects effects determine full requires approximate world increase increase randomly developed levels levels types types types actual actual provided provided provided provided provided depends constraint measured covariance normal increases increases increases increases describe arbitrary arbitrary arbitrary close corresponds corresponds corresponds stable surface surface short effective implemented ability easily degree degree noisy noisy noisy noisy pairs dynamical dynamical dynamical dynamical dynamical dynamical unknown coefficients coefficients fully fully interesting increasing increasing increasing increasing consistent uniform uniform uniform leads leads numbers max max normalized decay decay decay decay decay decay decay decay decay decay polynomial minimize choose improved discussed recent takes takes typical reported reported introduced introduced introduced quadratic relevant interest interest previously observations teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher correspond differential achieve achieve rl diagonal diagonal symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric modified interval interval grant expression deviation matrices predicted strength strength starting depend differences numerical numerical numerical numerical numerical faster asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic suggest propose mechanisms integration presence presence presence presence physics drawn drawn proportional regularization regularization regularization regularization regularization regularization labeled decrease decrease averaged introduce question explicit written longer longer ways dept student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student implement sensitivity multilayer multilayer multilayer multilayer coordinates coordinates coordinates coordinates coordinates remaining unique unique integrated equilibrium decreases decreases independently independently focus focus focus expressed dependence dependence review stationary stages overlap overlap overlap overlap evaluate labels labels evolution evolution evolution evolution evolution evolution evolution evolution evolution soft calculation calculation additive additive additive additive additive expansion reduces remains remains remains valid norm norm david figures activations activations usa assignment batch illustrated phys phys phys phys characterized characterized characterized characterized characterized characterized modification modification modification driven committee presentation presentation identify tend receives receives characteristic compact induced interpreted symmetry sci comp absence realistic eigenvalue eigenvalue eigenvalue decreasing remain carried powerful powerful layered overfitting perturbation investigate exhibit put scalar examine examine tech investigated analytically analytically analytically analytically analytically analytically possibility scaled affect phases phases matched matched math math adapt necessarily onset onset rev rev equally changed observe observe observe expressions expressions switching generates amari regime regime regime regime regime regime defines averages averages averages asymptotically asymptotically asymptotically agreement analyzed unstable phenomena analytic tool bishop commonly controls consequence acknowledgement gradually arises qualitative qualitative qualitative fluctuations fluctuations alignment explained integrating fourth reflects transient generic generic experimentally lack lack lack lack quantitative solla solla solla solla solla solla solla incorporated formulated frequently frequently exhibits exhibits mod monotonic incoming redundancy begins begins deviations eventually differentiable initialization initialization gap gap picture shifted corrupted corrupted corrupted uncorrelated uncorrelated uncorrelated secondary secondary redundant identifying oxford investigation investigation bin enhancement rational rational numerically overcome proceeds grow grow analyzing monotonically monotonically monotonically monotonically responsible utilized overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps excellent mance recovered encountered perfor dominant sim dif reveals rich extensively implicitly speeds escape escape saad saad saad saad saad saad saad schulten rigorous basically aston aston revealed isotropic isotropic isotropic isotropic suboptimal breaking scenario scenario scenario scenario scenario evolve realizable labs crosses concentrate differentiation differentiation differentiation noting regimes regimes increasingly increasingly worth preprint investigations bring corrections corrections expansions remark acquire acquire reversed instability justification focuses powers affecting holmdel emerges specialization specialization specialization specialization ray plateau plateau plateau norms norms norms scenarios att decaying decaying fastest fastest proves suffice amenable acknowledges trend focusing tained ized birmingham generaliza noiseless noiseless noiseless noiseless noiseless noiseless noiseless regularizers regularizers regularizers regularizers regularizers regularizers trapped murata schwarze anisotropic biehl biehl biehl indistinguishable niques epsrc amples amples ore cybenko rin rin rin app imitate erf ford finke detectable acquires sara ilar qii qii qii rau ably linearizing milllet trapping rnax jin widening corrupt dri nonsymmetric presenta 
#@Saad_D,Solla_S,
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#*learning learning learning model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure time time time time time set set set set set set set networks networks algorithm algorithm algorithm number system state information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models based based based based based based based based based based based based based based based space space space space space weights linear linear linear linear linear linear linear case case case vector vector vector shown shown systems values probability probability probability probability probability parameters noise unit unit distribution distribution distribution distribution distribution distribution recognition approach point image image image single processing processing large rate rate rate analysis analysis class matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal form form form form form shows shows shows signal signal algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples examples examples small small work work work step points points points points points points points points points points points points points points features classification structure high high high high high high similar show equation equation section section section fixed fixed line line line line line line line line vectors vectors vectors vectors vectors images images generalization speech speech speech real approximation approximation approximation obtained note note note note note note dimensional dimensional result result result variables computation solution log defined found found found found initial constant constant constant constant terms terms terms terms terms distance distance present low low temporal sets sets motion motion motion maximum maximum press position components components components basis continuous abstract abstract abstract find find find find find find find find computational convergence density density density density density density density density density density density density density properties likelihood references ieee positive positive procedure important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation statistical statistical statistical effect generated cost cost cost cost cost tion tion change variable variable lower measure prior chosen higher center center previous previous conditions represent represent distributed equations equations equations equations fact proposed length length length probabilities probabilities probabilities scale finite resulting ing tasks regression computed computed computed respect multi sum eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq times elements elements elements regions regions regions regions means factor factor optimization dimension dimension natural natural natural global applications obtain obtain negative vol true application desired desired define define define define define define compute proc location location perform determined goal constraints distributions distributions discrete equal mit mit mit steps support modeling modeling institute words loss individual advances joint joint exp exp scheme addition ai framework cambridge cambridge solutions estimates limit limit limit determine efficient upper choice statistics derived derived conditional conditional developed velocity types types lines path path path path path path path path path path path path path path path path path path path path path path path path path path path path product product iteration depends constraint biological discussion covariance covariance covariance covariance describe describe denote denote denote denote denote inverse inverse short common implemented assumed role eds face end cluster cluster cluster cluster cluster cluster future degree combination combination functional functional functional functional functional functional functional functional functional functional functional functional functional functional functional coefficients jordan jordan jordan jordan technology ratio segmentation segmentation segmentation special consistent principle principle principle principle principle principle principle operation squared numbers iterations making minimize minimize description denotes denotes directions strategy include interest dimensions dimensions dimensions works works solve smooth smooth smooth studies differential differential address bounded interval interval entire exists invariant invariant matrices locally touretzky clusters clusters clusters clusters clusters clusters boundary boundary boundary boundary boundary boundary boundary pass assumptions segment segment segment depend tangent measures measures clear practice taking taking radial turn plane plane plane plane plane iii minima suppose suppose appears derive derive solving solving solving label segments segments modeled modeled modeled modeled modeled modeled metric metric metric metric metric metric metric metric metric metric missing simultaneously dimensionality unique develop develop gaussians gaussians gaussians select competition focus expressed expressed viewed densities densities operations converges classical normalization convex roughly purpose iterative iterative boundaries penalty interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation remains intermediate assigned faces avoid expect thesis coordinate formulation weighting instances determines discuss specifically coupled variations gamma closely divided paths paths paths paths paths paths paths paths paths latent poggio poggio identify efficiently efficiently situation identity refer refer quickly induced induced induced induced video interpreted contribution manifold manifold criteria quantity michael minimizes minimizes minimizes minimizes computes moves satisfies tesauro extend body origin origin unlike collection collection optimized hessian divergence divergence divergence ml examine ideas variational variational variational variational variational variational variational combine complicated func fundamental hill prototype prototype prototype prototype multivariate multivariate multivariate multivariate simplest contributions finds defines defines massachusetts piecewise crucial lies lies london reasons inside inside sections arc arc arc organized projected circle circle implicit begin begin optimize optimize definite lowest lowest arises arises bandwidth geometry qualitative mechanics geometric reflect tional parameterized introducing frequently prototypes synthesis synthesis limiting curvature suited suited enables wesley multidimensional multidimensional multidimensional multidimensional multidimensional leen addison assign assign assign lagrange lagrange lagrange lagrange arguments girosi recover unity generality multiplier multiplier kullback murray multiplicative moment balance balance nearby nearby operates intuitively adequate substituting substituting saul saul saul saul connect sides lengths lawrence competing competing competing competing treatment matter omohundro omohundro dividing assigns assigns assigning speaking speaking metrics multiplying street logarithm email leibler poses profiles seek amherst acceleration mismatch exponent exponent goals goals goals goals decays distribu labs concentrate dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet spanned enforce memo simplex simplex simplex simplex simplex simplex rewrite exploited mini tension tension tension tension tension tension lagrangian lagrangian lagrangian lagrangian parameterization parameterization parameterization handling influenced telephone ave fill suffices suffices played continuum bregler bregler concave interpolate interpolate interpolate interpolate interpolate multimodal multimodal confined counterpart twelve shortly excessive snake mountain favors favors favors obeys coincides deformations traversed traversed traversed traversed respects goldstein animation infinitesimal calculus interpolant interpolant interpolant interpolant interpolant interpolant interpolant interpolant interpolant endpoints euler euler euler vation cheap handles alternately integrand modulates revealing meets masked collapse deviate shashua remedy prescription cloud iiw iiw eecs extremal tensions tensions collapsing intermittent traverses woo woo dep xxx lagrangians asterisks solv moti llw dies bend bend mizes adjoining adjoining 
#@Jordan_M,Saul_L,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural input input input input input data data data function function function function figure figure figure figure time time time time time time time time time time time time time set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output number number number number number number number number system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results results results results results problem problem problem performance performance performance performance performance performance performance space weights weights weights weights weights weights weights linear linear linear linear case case case case case case case case case case case vector vector vector vector vector vector vector order order order order order order order order order order order order order order shown shown shown shown shown shown values values values values values values values values values parameters parameters parameters parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions distribution method method approach approach single large large large large large large large large large large large large large large large large large large large local local rate rate rate rate rate rate rate rate rate test analysis analysis matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs form form form form form shows shows shows shows shows signal simple simple simple paper paper examples examples examples examples examples examples examples examples examples examples small small small small small small small small small small small small small small small small small size size size size size size feature net work work methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig process random random similar fixed fixed fixed fixed fixed fixed fixed vectors general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter real real average average average theory gradient gradient gradient obtained obtained obtained obtained term dimensional result university university threshold solution solution research research independent independent defined found found found dynamics dynamics dynamics constant constant constant constant constant estimate standard terms terms terms terms left presented presented low machine sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets motion maximum range components nonlinear outputs abstract applied applied find computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references due due ieee important introduction hand hand hand hand statistical statistical statistical effect effect effect dynamic generated variance tion difference assume assume lower lower chosen chosen chosen chosen higher cases required required good good good expected expected expected equations equations equations make make make correlation length errors finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite simulations minimum minimum minimum minimum minimum resulting resulting resulting ing ing total total total total simulation respect sum called times times times mapping means factor factor optimization optimization potential potential made made study study study study study obtain relative relative rates rates rates rates rates rates rates determined determined determined determined distributions discrete approaches approaches steps comparison larger larger larger larger larger larger larger larger update update update update update update update train descent descent dependent dependent selection department department loss version individual final final final final final exp exp exp exp computing equivalent directly directly limit limit limit limit effects determine significant significant approximate speed speed speed speed speed speed speed speed speed increase increase increase increase condition condition derived derived randomly randomly lines lines lines lines provided finally finally finally depends discussion normal increases increases increases increases increases increases increases group limited limited corresponds surface amount common effective effective effective assumed assumed supported role theoretical require main main main main future future future easily makes noisy smaller smaller underlying needed combination reduced reduced functional functional significantly significantly significantly ratio increasing mode mode mode mode mode leads squared squared details normalized supervised decay decay decay decay decay decay decay decay decay decay decay decay decay decay attention minimize description denotes architectures architectures discussed directions directions exact advantage practical practical apply introduced recently interest interest compare compare compare teacher teacher teacher teacher calculated calculated calculated calculated works solve yields yields differential rl trans address generalized sensitive increased grant exists exists lead scaling occur extended predicted predicted occurs generally runs strength critical critical critical minimal minimal conclusions valued numerical numerical performs practice practice asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic physics solid turn turn minimizing minimizing min min averaged question question explicit relation generating generating student student student student student student averaging averaging averaging linearly linearly infinite infinite infinite infinite infinite scales decreases decreases decreases decreases choosing focus focus expressed expressed expressed dependence dependence dependence dependence dependence dependence squares detailed transform transform transform transform updated updated evolution evolution evolution evolution evolution soft sizes converges constants updates updates updates updates updates updates updates updates updates updates updates updates partial reasonable reasonable calculation calculation slow slow dashed additive expansion reduces closed closed initially symbol david determines extension extension discuss discuss holds phys phys phys phys phys phys phys phys simplicity simplicity society maximal effectively symbols included committee presentation comparing tend essentially essentially essentially essentially online online online online online online online online online online online online online online online online online online online online online online online online online online online online reached characteristic allowing interested contribution contribution contribution contribution quantity quantity sampled usual absence realistic nips nips reach illustrates illustrates extend optimized optimized optimized dotted dotted behaviour behaviour behaviour behaviour applicable analytically analytically complicated workshop hierarchy opposite rev rev rev rev changed ensure der observe perceptton baseline extent regime finds finds slowly crucial agreement fairly fairly fairly analytical analytical analytical analytical analytical diffusion commonly mathematics inversion involve opt opt calculations optimize read demonstrates addressed mechanics improvements varies relevance peter effort solla limiting limiting limiting aim serve conclude eventually lim progress yielding yielding picture appropriately optimizing optimizing acts perfectly nonzero nonzero nonzero nonzero grows royal plays fits hope definitions settings settings hint hint krogh krogh krogh presentations hertz hertz hertz repeat evaluations analyses respective negligible negligible surprising consequences laplace laplace laplace laplace thin steepest speeds lett interestingly mechanical accumulated fitted saad outline ter aston isotropic isotropic encouraging encouraging restrictions convenience tradeoff affects edinburgh edinburgh scenario scenario assess arising community formance formance gener dominated crosses oct eliminating conversely cation importantly sollich sollich sollich sollich sollich induces drops hodgkin shallow advantageous const barber barber barber barber bold dominates powers powers affecting vanish scenarios decaying decaying fastest fastest fastest transpose implied approached pin focusing birmingham cope analyse analyse repetitions developments diverge diverge expresses omit heskes heskes teachers impor alization lowered undesirable parame parisi tant offline offline infinitesimal infinitesimal infinitesimal offiine offiine offiine offiine offiine offiine offiine offiine offiine offiine offiine offiine offiine offiine schwarze confirms anisotropic europhys diverges overshoot overshoot hypersphere biehl biehl indistinguishable fellow wtx wtx luo epsrc ror useless kappen worthwhile parameterize rio raining slows modem coo coo coo coo neut neut diffusive deficiency wei asymp asymp divergences divergences invoking counteract netw thorbergsson dorothy weigh deteriorate rau vanishingly ere straightforwardly watkin treatments totic totic ymptotic cyclical 
#@Barber_D,Sollich_P,
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#*learning model input data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure set set set set set set set set training training number number number number number number number number results problem problem problem problem problem problem problem problem problem based based based space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case vector vector vector vector vector order order order order order shown shown shown values parameters parameters parameters parameters noise noise functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions recognition method method method method method method method method method method method method method method method method pattern image image processing large large optimal optimal form form signal signal paper small small feature feature feature feature feature feature feature work methods points points points problems problems problems problems problems problems problems problems high high similar similar representation representation representation representation representation representation representation show show equation equation equation section section section line line rule vectors vectors vectors vectors vectors images general generalization real real real real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory obtained obtained dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional solution solution solution solution solution solution solution research research independent defined defined defined sequence constant estimate left left left left map present nodes nodes nodes press basis basis basis basis basis basis nonlinear abstract applied applied find find find find references positive important decision decision decision introduction hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical tion tion complexity chosen part theorem type type required required required good conditions equations equations equations techniques proposed regression regression regression regression regression regression regression regression regression multi called called elements elements optimization optimization dimension applications applications applications original desired desired cross cross define define define define define perform constraints constraints equal accuracy accuracy accuracy accuracy support support support support support support report technique technique code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel ai ai ai ai ai ai ai ai ai ai ai ai maps considered equivalent equivalent additional approximate approximate approximate statistics free free levels levels lines product product product product product product product product product product nature depends arbitrary denote inverse finding supported role require require require pixel ability noisy fit fit objective functional functional functional coefficients coefficients coefficients coefficients uniform leads representing numbers max polynomial polynomial element element subject subject side quadratic quadratic subset recently sufficient observations observations observations tions solve solve solve solve solve definition separation separation symmetric grid entire grant grant constructed extended demonstrate demonstrate demonstrate conclusion operator operator operator operator valued depend designed solid regularization minimizing start min min min introduce construct construct solving solving solving solving solving solving solving solving solving generating generating generating generating generating generating generating estimating estimating describes infinite dimensionality dimensionality easy applying springer national reconstruction reconstruction evaluate suggested reasonable dashed measurements measurements classical expansion expansion expansion expansion expansion valid initially construction kernels kernels kernels kernels kernels priori bell bell vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik maximize maximize black discussions compression compression differ verlag sin sin sin sin sin michael play minimizes ill approximating approximating acknowledgments requirements ml reducing fourier fourier hill circles spline spline spline spline mapped expressions academic generates generates cos cos cos cos formula analytical tool tool constructing constructing hyperplane products products laboratories mathematics universal nsf led parameterized lattice posed splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines splines dots dots berlin replace multidimensional multidimensional yielding corrupted sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv guarantee guarantee fix kaufman kaufman murray check star corner selects corre scan smola smola smola smola smola smola emission emission sch piece german big param avoids burges labs expand wise dirichlet spanned book eters article technologies expansions expansions chris remarkable sponding kopf hilbert hilbert hilbert hilbert hilbert hilbert ave steven steven alex alex holmdel wavelets att att arpa gmd gmd svs svs svs svs svs svs svs svs svs svs svs svs svs svs mountain amer tutorial plexity phy approxima assoc impor opportunity tant mercer perspectives reconstructing optimiza opens rni subsequence bernhard lucent lastly lastly regressions opportunities xixj xixj scholarship vladimir vladimir creases dation arx foun crawfords rudower radon chui vlad presenta 
#@Golowich_S,Smola_A,Vapnik_V,
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data function function function function function function function figure figure time time time time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm output output output output output output output output output number number number number number number number number number number number number error error error error error error error error error error error error results results results units units units units units units units units units units units units units units models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear layer layer layer layer layer layer case case case case case case vector vector vector order order order order order order order order order order order order order shown shown shown shown shown shown values values values values values values values values values values parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions unit unit unit unit unit unit distribution single single large large large rate rate rate rate rate rate rate analysis analysis class class class class class optimal optimal optimal optimal inputs form form form form form simple simple gaussian paper paper paper paper paper examples examples examples small small small small small small size size size size size net work work work work task fig fig fig fig fig fig fig fig fig step points points points points points features features process process trained trained random random random random response similar similar similar similar architecture architecture show show show show show show fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line line line rule vectors vectors vectors vectors vectors vectors vectors vectors general generalization generalization generalization generalization generalization generalization generalization generalization real real real approximation average average gradient gradient note note dimensional dimensional dimensional result university university university variables variables variables variables computation solution research research independent log defined defined defined defined defined defined found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial terms terms connections node node left direction presented presented present present phase phase phase phase phase phase phase phase activation nodes nodes nodes nodes nodes machine machine machine machine machine machine machine motion range range range basis basis outputs outputs continuous continuous continuous continuous abstract back back back find find find find convergence convergence convergence convergence convergence convergence convergence properties properties references due due due due important important propagation propagation propagation introduction complex complex statistical statistical statistical effect effect effect effect effect dynamic tion change difference difference complexity variable variable assume measure learned learned chosen chosen previous theorem cases cases cases cases cases required good long conditions conditions conditions equations equations equations equations equations equations equations equations equations equations make fact fact length length scale finite finite simulations simulations simulations minimum resulting resulting resulting ing respect multi performed times mapping dimension dimension applications study study study knowledge knowledge original original compared cross rates rates rates rates rates rates rates rates determined related constraints connected connected distributions gain gain comparison larger larger larger larger larger update update update support dependent department loss loss consists consists internal joint bias bias bias bias bias bias bias bias layers scheme scheme framework framework framework computing domain domain domain domain domain domain transition limit limit limit limit effects effects effects effects conference conference world world speed pages pages randomly provided provided finally constraint constraint constraint discussion normal feedforward increases arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary group denote denote denote limited inverse surface predictions proof proof proof common implemented theoretical theoretical theoretical theoretical main main square makes including simulated typically pairs smaller smaller combination dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical transfer transfer significantly increasing uniform uniform leads squared squared squared representing international international normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized magnitude magnitude magnitude magnitude frame recent correlations exact typical typical typical reported identical identical machines recently relevant interest interest dimensions dimensions dimensions dimensions sufficient highly compare previously previously teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher tions studies studies studies converge differential differential rl symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric interval sensitive sensitive increased lead lead lead studied studied studied studied studied studied studied studied suggests suggests extended matrices white occurs runs runs strength critical critical minimal trajectories trajectories differences sigmoid numerical numerical numerical numerical numerical practice learns strong integration physics drawn drawn sigmoidal sigmoidal radial turn variety user exist exist decrease decrease iii iii configuration question denoted denoted distinct student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student averaging averaging averaging averaging linearly infinite infinite remaining decreases choosing expressed dependence correlated overlap influence influence influence solved controlled restricted updated evolution evolution evolution evolution evolution evolution forms soft soft soft soft soft soft soft sizes sizes suggested suggested converges converges updates updates sign calculation calculation slow spaces reduces intervals remains remains initially initially norm norm david avoid priori priori perceptrons instances determines illustrated coupled holds phys phys phys characterized characterized characterized characterized simplicity simplicity determining suitable maximal effectively committee committee committee committee committee committee committee committee presentation presentation presentation presentation summary compact compact quickly quickly strongly strongly prob allowing heuristic interested issue symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry follow hold realistic put accurately issues biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases biases behaviour behaviour behaviour ideas investigated scaled referred root complicated func phases removed removed possibly integer configurations opposite rev quantities quantities noted academic initialized initialized extent motivated finds inequality inequality agreement derivation variances ran immediately universal universal universal universal universal universal universal universal universal universal universal universal universal describing depicted addressed addressed mechanics mechanics mechanics integrating varies considerably lack solla solla solla solla solla adjustable adjustable adjustable adjustable adjustable adjustable adjustable adjustable adjustable adjustable adjustable continuously http exhibits exhibits measuring spread sums sums attraction findings eventually progress progress differentiable initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization shifted uncorrelated www labeling restriction extensive restrict arguments labelled generality generality rational fails stronger logarithmic attractive attractive attractive attractive interpret mark motivation overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps corollary loo appendix dominant widrow widrow widrow uni approximators approximators approximators initialize mlps permutation insight reveals suggesting suggesting rich park park extensively eqs broken approximator approximator approximator approximator approximator approximator severe lem dense dense saad saad saad saad saad saad saad saad saad saad saad outline aston aston aston aston graded graded graded break break randomized employs isotropic isotropic isotropic isotropic isotropic isotropic suboptimal suboptimal suboptimal suboptimal suboptimal suboptimal suboptimal suboptimal suboptimal suboptimal suboptimal convenience solely breaking breaking breaking basins edinburgh edinburgh scenario scenario scenario scenario concentrated grouped decays ijcnn realizable realizable realizable thermodynamic thermodynamic thermodynamic thermodynamic approxi gener dominated dominated ization relating concentrate confirmed scope spreading spreading proach investigating integrals hornik hornik sollich breaks figs west west west west west inversely preprint likewise stuck stuck stuck rewrite travel moderate remarkable sake influenced confirm confirm suffers virtually barber barber dom identically evenly evenly equa couplings manipulated triangle triangle norms norms norms poly scenarios scenarios scenarios scenarios scenarios scenarios scenarios degenerate degenerate degenerate randomness brackets enforces fixing birmingham ini analyse noiseless freely trapped drawbacks attracted attracted cancel excluded oil teachers teachers teachers encourage tll thumb schwarze schwarze symmetries symmetries notably qij qij qij qij qij qij qij kim kim europhys diverges symmetrically symmetrically initializing initializing distinguishes biehl biehl biehl biehl biehl biehl biehl indistinguishable indistinguishable neglecting oij steep ncrg rin rin rin rin rin rin rin rin rin sharper serially trigonometric stinchcombe integrations integrations imitate lacks decayed spe ast legend legend ian promote slowed qii qii alike disappeared eff imitating nguyen nguyen nguyen seminal practitioners existent reals judiciously judiciously dri rll rationals ality nomials 
#@Nabney_I,Saad_D,West_A,
#t10
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#*network network network network network network network network network network network network network network network network learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training output number number number number number number number number number number number number number error error results results results results units units units units units units units units units units units units units units units units units units units units information problem problem models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based space space space space space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer case case case case case case vector vector order shown shown shown shown systems values values values probability probability parameters parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method point point processing large large large large rate rate test test analysis analysis analysis analysis analysis class class class class matrix matrix inputs inputs inputs inputs form form form form form shows shows simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples small size net net net net work work work task methods methods methods methods methods points points points field field process process process process process process process process process process process process process process process process process process process process process process process process process process process process process process level problems random random random random high similar similar similar similar similar similar similar architecture architecture show show equation equation equation equation equation equation section fixed fixed fixed fixed general general general parameter parameter real real approximation approximation approximation states theory theory theory obtained obtained term term note note note note note experiments dimensional result result university variables variables variables computation solution research research research independent independent independent independent defined computer distance science prediction prediction prediction prediction prediction prediction prediction present frequency sets sets press press press basis basis basis basis basis outputs outputs sample abstract applied applied applied applied find find convergence convergence convergence convergence density density density properties likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee important important introduction complex complex effect effect generated generated generated variance variance variance variance variance variance variance variance variance variance variance tion complexity variable spatial spatial spatial assume prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen part theorem theorem theorem theorem theorem theorem theorem cases required required good good distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected equations markov markov markov make make make make fact techniques correlation length length observed observed scale scale scale finite finite finite finite finite finite finite finite finite simulations ing ing ing regression computed respect multi called called elements regions mapping mapping made made made made made made made obtain obtain obtain obtain obtain specific compared application series compute goal related related posterior posterior posterior posterior distributions distributions distributions distributions distributions power power power power power mit comparison larger nets nets proceedings department version code kernel kernel advances joint final exp exp exp exp exp exp exp exp exp exp exp exp exp exp bias bias bias graph considered considered framework framework computing computing computing computing computing equivalent view view view view view limit limit limit limit limit limit limit limit stage conference full choice approximate statistics statistics world speed give give give derived derived derived product finally processes processes processes processes processes processes processes processes processes backpropagation depends simply achieved achieved discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance increases describe group denote denote denote limited inverse corresponds predictions predictions predictions predictions predictions predictions predictions proof rbf amount amount common common supported require eds square square easily makes makes makes makes including pairs needed needed needed fully transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer interesting interesting testing significantly consistent details making decay decay idea added description discussed directions directions correlations exact advantage takes practical strategy hierarchical sense sense sense sense inference subset relevant interest sufficient compare compare calculated works works correspond converge converge achieve achieve trans diagonal diagonal chain chain chain modified generalized bounded bounded bounded williams williams williams williams williams williams williams increased grant parts scaling wide wide wide matrices predicted alternative hybrid touretzky width place assumptions depend central central central central sigmoid bayes bayes exponential practice integration integration integration largest drawn drawn drawn drawn drawn drawn sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal radial radial turn variety introduce manner manner groups question acknowledgements appears monte monte monte carlo carlo carlo written written written longer longer longer describes describes linearly infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite dimensionality slightly angle spectral spectral spectral spectral integrated frequencies equilibrium applying predictive predictive predictive springer independently independently dependence depending depending depending stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary correlated viewed densities evaluated evaluate approximations centered centered forms understanding spectrum spectrum spectrum smoothing smoothing reduces roughly roughly valid valid calculate david david david avoid expect expect expect expect kernels perceptrons recognize mozer priors priors priors priors priors priors priors priors priors priors priors partially reason gamma selecting extra closely society differ computationally poggio poggio poggio literature literature literature efficiently mackay mackay comparing comparing allowing showing symmetry lie lie sin sin hold usual dayan generalize reach preferred law bars employed carried carried carried wiley collection essential integral integral integral biases behaviour existence fourier fourier fashion giving analytically analytically analytically analytically analytically analytically scaled maximizing variability tanh naturally opposite spline spline observe academic multivariate multivariate defines neal neal neal neal neal neal neal neal integrate great formula agreement derivation analyzed improves analytic expensive tractable considerable sections easier widely day choices bishop immediately commonly commonly probable mathematics mathematics mathematics inversion universal arises radius radius nsf integrating integrating integrating argument reflects evaluating applies conducted peter poorly splines splines incorporated polynomials calculating poisson poisson anti characterize modulated hyperparameters hyperparameters hyperparameters hyperparameters prevent marginal kinds kinds comments comments expectations multidimensional multidimensional cumulative cor analogue notes appropriately appropriately girosi girosi girosi convenient height hyper keeping obtaining settings imply intuitively moments contexts combines introduces corre entry regarded infinity infinity hasselmo entries approximators treatment augmented speaking dramatically appeared saad saad sig aston isotropic isotropic convenience wahba wahba wahba letting diag parzen parzen regulation denoting argued integrals integrals hornik hornik indexed responding tively mcmc mcmc mcmc mcmc rewritten chris lecture advantageous expense sponding christopher shot barber mining industrial suppress identically identically concerns believed rasmussen rasmussen characterizes amenable differentiate eigenfunctions eigenfunctions eigenfunctions birmingham spec developments facilitates damping wiener wiener derivations kolmogorov lid regional zhu availability rescaling excluding translational respec machinery feel overfit hyperparameter epsrc tly tly tly gps integrand nicely speak draft radford eigenfunction inhomogeneous inhomogeneous exponentials observational ian completing holden moidal whittle whittle cbms dummy tio tlo tlo tlo tlo sired hyperprior hyperprior hyperprior ylo ylo ylo tlw tlw wlo wlo wlo wlo wlo bas universities ile utu 
#@Williams_C,
#t10
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input function function function function function function function function function function figure figure figure set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number system system system system system error error state state state state state state results results results results information information information information problem models hidden hidden hidden hidden space space space space space weights weights weights weights weights weights weights weights layer layer layer layer layer case case case vector order shown shown shown shown systems systems systems values parameters parameters weight weight weight functions functions neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method approach approach approach approach approach point single single single single single large local local local local local local local local local local local local local local local local local local local analysis analysis analysis analysis analysis optimal optimal inputs inputs form shows shows algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size size size work fig fig fig fig step step step step step field field field field field field field field field field field field field field field field field field field field process process process level problems random random high similar similar similar equation line line line rule general general general general general generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter real average states states states states states theory theory theory theory theory theory theory theory theory gradient gradient gradient obtained obtained obtained note note result result university variables solution solution solution solution solution solution solution solution defined defined defined dynamics dynamics initial initial estimate estimate synaptic node node node node science prediction direction present present present low nodes nodes nodes nodes nodes nodes machine sets learn learn learn outputs outputs abstract applied applied find find find find find density density properties properties properties properties properties properties properties properties references due due due due adaptive introduction action action action action action statistical statistical statistical change change change change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy assume assume assume prior learned higher higher higher higher previous binary conditions conditions tree tree tree tree tree tree tree tree tree equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations fact fact fact techniques correlation correlation correct correct correct scale scale simulations simulations simulations simulations minimum minimum minimum resulting classes ing ing simulation simulation respect called called called elements mapping means means factor made global global applications applications original original original provide define determined determined determined distributions fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields descent descent descent institute department version consists individual final final final exp exp exp exp scheme addition addition addition addition addition maps considered equivalent solutions design effects capacity capacity capacity determine free free free world world condition condition condition derived derived derived derived measured measured feedforward inverse assumption assumption assumption corresponds complete stable stable predictions predictions supported eds journal journal journal ability ability typically smaller underlying underlying account account account dynamical technology ratio york consistent consistent consistent consistent iterations normalized normalized minimize added added added perceptron perceptron perceptron perceptron perceptron discussed correlations advantage identical identical identical machines recently previously conventional conventional conventional conventional teacher smooth smooth smooth smooth smooth smooth smooth smooth smooth yields yields yields converge background background symmetric modified generalized storage storage storage storage storage exists expression expression expression lead predicted alternative correctly clusters occurs conclusion assumptions central central interactions clear exponential exponential learns learns physics physics physics physics physics solid turn minimizing exist averaged averaged averaged averaged introduce introduce groups minima minima minima minima minima minima minima minima minima minima minima minima minima minima configuration suppose suppose suppose relation van van derive longer longer solving solving describes describes stability stability stability stability stability stability stability stability stability stability stability stability stability mathematical mathematical mathematical student multilayer infinite physical physical physical physical physical physical slightly slightly adding implies versus versus letters letters yield review review review review depending squares interpretation influence completely similarly sign dashed dashed neighborhood closed remains valid avoid expect perceptrons perceptrons retrieval determines determines holds holds symbols committee committee committee committee committee committee committee committee committee successful comparing situation situation summary strongly induced success success success anderson anderson anderson symmetry symmetry symmetry symmetry symmetry hold satisfy satisfy satisfy quantity quantity quantity involved usual michael generalize absence minimizes highest bars experience replaced existence rest applicable applicable comparable hill circles algo regime regime regime regime regime regime regime spin spin spin spin agreement agreement majority glass glass lies lies turns perspective satisfied sgn sgn mathematics scientific scientific describing begin mechanics mechanics argument argument argument requiring consistency generic fed fed simulate schematic branch extensions adjust adjust median median yielding gap picture picture picture uncorrelated tation extensive extensive arguments labelled connecting theories proceed mail satisfying check moment replica replica replica replica replica replica replica replica replica replica replica replica replica shifts published started ambiguity iteratively iteratively induce regarded expanded den den enable iterated explains mechanical sequentially verify verify yielded land deriving reaction expanding generalizations hierarchies breaking breaking breaking breaking breaking possibilities adjustment adjustment illustration distri insights rithms interact discontinuity maximally confirmed confirmed landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape landscape noting noting rough rough rough rough rough rough rough rough rough rough rough rough rough rough rough rough sketch loading loading knowing macroscopic macroscopic macroscopic macroscopic compu microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity bution rarely palmer palmer palmer instability agrees water confirm solvable drawing obey obey obey adjusts absent cho mcgraw resultant resultant iterating iterating iterating iterating pin pin modern wong wong wong wong wong wong wong wong wong wong wong wong neglected violated potts kuhn gardner gardner gardner gardner landscapes landscapes landscapes landscapes landscapes landscapes landscapes metastable metastable kong kong kong derivations obeys ansatz macro adjustments adjustments hong hong hong reactive perturbative perturbative ogy schematically schematically parisi parisi parisi parisi controllable biehl biehl biehl biehl singapore singapore emphasizing glasses glasses almeida ising multiclass aligning aligning aligning aligning aligning aligning aligning aligning aligning aligning aligning aligning aligning concludes technically nonoverlapping disordered disordered nilsson nilsson vastly precludes thouless thouless thouless thouless virasoro virasoro virasoro virasoro telecom zard zard zard kwon tucker derrida derrida derrida subse valleys bay cknowle dgement rau rau philosophical nonlocal nonlocal nonlocal nonlocal hopping adatron adatron complicate sour reviewing ust watkin watkin europhysics europhysics quent nonvanishing axa agreeing scopic 
#@Wong_K,
#t10
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#*network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data function function function function function function function function function function function function function function function function function function figure figure time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks algorithm output output number number number number number number number number number number number error error error error error error error error error error state state state state state state state results results results results results results results results results results results results results units information information information problem problem problem problem models models models models models models models models models models models models models models models models models models models models models hidden performance performance based based based based based based space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case vector vector shown shown shown shown systems values values probability probability probability parameters parameters parameters parameters parameters parameters noise functions functions functions functions functions functions functions functions functions functions distribution point point point processing large large local local local rate analysis analysis class class class class class class class class class class class class class class class class matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal signal algorithms algorithms simple gaussian paper paper size size size size size net work work work work work work work work points process process process process process process process process process structure structure problems random memory similar similar architecture architecture architecture architecture architecture architecture architecture section section fixed vectors general general general generalization generalization parameter parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average obtained note note note note experiments result result result result university university threshold threshold threshold variables computation computation independent defined found found found found target target target constant constant standard standard standard prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented press learn learn basis basis nonlinear nonlinear nonlinear continuous continuous sample sample sample sample abstract find convergence convergence density density references stochastic stochastic stochastic stochastic stochastic stochastic stochastic due mixture mixture mixture mixture context context context context context introduction estimation estimation estimation estimation behavior statistical statistical variance variance tion complexity complexity complexity complexity complexity assume assume assume assume lower measure measure part previous previous theorem theorem theorem theorem theorem bound bound bound bound bound multiple good conditions represent expected markov markov fact fact fact finite finite finite finite ing ing regression regression regression respect respect mapping made made natural global global study study study em obtain vol vol vol samples true series series series series series series series series series series series series series series series define define define define define define rates related related related related constraints discrete power approaches approaches comparison fields dependent dependent dependent dependent dependent modeling selection department department department department department loss loss loss version version version technique exp exp bias addition framework domain equivalent equivalent equivalent view limit capacity efficient upper upper upper upper upper upper upper upper upper upper requires approximate approximate statistics statistics statistics world increase conditional conditional conditional bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds provided processes nature constraint simply simply discussion discussion discussion feedforward feedforward feedforward feedforward denote denote denote denote denote tested assumption assumption assumption assumption complete proof proof proof proof proof proof proof proof common effective assumed assumed role role theoretical theoretical theoretical theoretical main main main main journal future degree degree degree objective probabilistic probabilistic underlying underlying combination reduced functional functional functional functional unknown jordan jordan projection york york segmentation squared squared squared squared details details details details details details numbers pre pre making normalized experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert decay attention combined combined description denotes denotes architectures recent exact takes introduced introduced strategy moving hierarchical hierarchical sense sense sense subset subset recently recently recently relevant engineering engineering engineering engineering interest compare compare approximately tuning tions tions smooth smooth smooth mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures background background risk risk risk risk risk studied studied extended matrices predicted locally white setting setting demonstrate demonstrate strength assumptions central numerical numerical asymptotic asymptotic suggest sound taking taking integration integration sigmoidal sigmoidal demonstrated demonstrated demonstrated proportional assuming assuming assuming minimizing derivatives derivatives derivatives manner question question denoted suppose relation pro describes stability electrical electrical electrical slightly minimization springer springer blocks blocks expectation expectation family family expressed dependence dependence stationary stationary stationary stationary stationary squares estimator estimator estimator estimator estimator estimator estimator estimator estimator viewed detailed evaluated decomposition constants past past reasonable reasonable additive expansion purpose advantages precision expect building existing formulation extension extension holds gating gating gating gating aspects fine composed compact compact compact verlag strongly contained interested dis criteria hold notation notation notation usual modular predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor mixing mixing approximating approximating approximating jacobs jacobs extend extend law powerful exponentially estimators scalar scalar history mse mse mse mse applicable referred structured proved func hill closest closest obvious noted logistic taylor fisher precise academic art art submitted synthetic established asymptotically ground growth defining defining analytic answer tractable tractable tool london stanford stanford stanford implementing widely widely strictly precisely precisely precisely precisely universal universal universal universal universal arises argument substantially substantially conducted slower formulated compares maintain polynomials price mod substantial enables comments unbiased unbiased proposition proposition proposition proposition proposition proposition representative lab proofs equivalence restrict restrict restrict linearity partitions establish establish plays plays generality chains chains satisfying proceeds proceeds stated stated keeping hope exploit analyzing imply north intuitive encountered surprising realization evident belongs belongs approximators enable israel foundations express mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem mem reader rich rich passing variants statement statement generalizing tures approximator approximator approximator approximator approximator approximator approximator fold robert lag lag lag lag mind mind approx pointed conjecture regularity seek mdl classic classic constitutes letting letting associate stands pub pub publication mathematically relating relates relates sketch sketch termed alternatives knowing els mix meir meir meir meir meir meir meir characterizing sake families focuses aid establishes december loosely ron possess autoregressive autoregressive autoregressive autoregressive autoregressive comprising poly degenerate enhances establishing establishing spirit subscript restrictive cess meant elec facts aic merit technion technion technion technion enabling completeness objectives stat obeys argmin argmin predic favorably favorably ver imation possesses pursued pursued imposing tong tong tong superiority exhibiting tar tar tar tar tar arma arma gression economics economics emerging normality attain lend weakened penalize diction innovation observa fined haifa deviates tradeoffs pursue carolina erated zeevi zeevi zeevi zeevi zeevi zeevi zeevi customary nar nar intimately glance econometrics chapel endowed isl introductory ficiently paring blends nomials 
#@Adler_R,Meir_R,Zeevi_A,
#t10
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#*network network learning learning learning learning learning learning learning learning model model neural neural neural data function function function function function function function function function function function figure figure figure figure figure figure figure figure time set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number state results results results results results results results results results results results results results results results results results results results results results results results units information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models hidden performance performance performance based based based based based based based based space space space space space case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown shown shown shown shown systems systems values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight weight weight functions functions method method method method approach point point point point single single single single large large large large large large large large large large large large local rate rate rate rate test test analysis class inputs inputs inputs shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper paper paper examples small size size size size feature net net net net work work work work work methods methods methods points points points points points classification process process level level problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random random random random random random random high high high high high high high similar similar similar representation show show section section fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors real theory theory obtained obtained obtained obtained note note experiments experiments experiments university university university university variables variables variables solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research research research independent independent independent independent independent log defined found found found found found found found found found found found initial table table table table standard standard standard standard standard standard standard standard standard computer computer computer terms node node node science science science direction presented presented presented nodes nodes frequency machine object object object object sets range press position position position sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied find find convergence convergence references stochastic stochastic stochastic procedure procedure important important important adaptive adaptive hand behavior behavior generated generated generated generated generated generated generated parallel parallel parallel parallel parallel parallel parallel parallel parallel cost search search search search search search search search search search search search search search search search search search search search search search search search tion tion tion tion tion tion change difference variable rules measure measure prior chosen chosen chosen higher higher higher higher center previous previous previous theorem theorem multiple multiple multiple multiple multiple multiple multiple good good good binary binary binary binary binary represent represent represent distributed distributed make techniques region length length length length length length length length length length length length length probabilities probabilities probabilities probabilities probabilities probabilities observed errors errors scale scale scale scale scale scale finite finite finite classes ing ing total total total total performed performed times times times times elements elements elements elements elements elements elements elements elements regions regions regions regions regions regions means optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization potential potential natural applications study study study study study study study negative negative negative artificial relative relative relative specific specific specific samples samples samples samples samples samples samples samples represented represented represented represented compared cross cross cross cross perform perform perform determined connected connected equal equal equal equal power comparison comparison comparison comparison comparison comparison contrast update update update update selection selection selection selection selection selection selection proceedings report version code code code code code code code code code individual represents represents final final bias bias layers addition graph graph considered equivalent directly solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions design design bit bit bit bit bit bit bit bit bit bit bit bit bit bit conference conference conference determine determine full significant significant significant significant significant statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics con con con condition randomly randomly area provided selected selected nature depends sampling sampling sampling sampling achieved technical increases describe group tested tested fast close finding amount effective effective generate generate generate generate generate generate adaptation square square ability ability future future easily makes including objective simulated typically pairs pairs needed combination fully significantly special trials uniform uniform uniform uniform empirical empirical empirical empirical empirical empirical operation details details details iterations max max max max max pre pre bits bits bits bits bits bits international international international international early early early minimize minimize minimize minimize produced choose run run run run population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population directions directions exact exact advantage pair separate element element element element element reported reported reported introduced include recently recently engineering interest sufficient sufficient highly highly varying calculated works works tions tions tions yields yields studies studies studies converge converge converge converge converge evaluation evaluation evaluation evaluation evaluation evaluation positions positions positions positions positions positions locations improvement improvement sensitive entire occur predicted alternative alternative move move white occurs runs runs runs runs conclusion conclusions operator operator operator valued competitive numerical numerical numerical numerical numerical numerical designed designed encoding encoding encoding encoding encoding encoding encoding encoding mechanisms mechanisms mechanisms cycle drawn variety user selective selective averaged manner base base base explicit explicit explicit explicit explicit ways ways sequential sequential sequential generating generating generating generating generating generating ann tuned distinct dept explicitly explicitly explicitly explicitly simultaneously easy unique shift quality quality blocks blocks select yield yield yield yield yield independently depending correlated correlated squares viewed influence variation detailed open evaluate evaluate updated updated updated showed showed evolution evolution evolution evolution static static static static static sizes constants updates key spaces combining intervals iterative iterative generation generation generation generation generation generation generation generation generation generation generation intermediate initially string string string assigned assigned expect building building includes strings strings color color color color inter inter inter extension extension maximize maximize candidate domains black partially tests selecting selecting middle extra closely suitable differ differ encoded encoded encoded encoded encoded encoded encoded encoded effectively effectively identify literature literature literature genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic tend reached summary summary summary traditional conf conf quickly quickly graphs contained contained prob prob prob prob prob prob prob heuristic moore moore superior contribution gray gray gray gray gray gray gray gray list list list list sampled localization nips nips nips quantization highest maximization moves moves overlapping subsequent subsequent explore simpler simpler carried parametric create create collection environments preliminary examine successive school school rest incremental incremental incremental parity ideal combine combine combine fundamental analogous analogous neu examined examined examined examined examined examined hill necessarily created created equally subsets prototype versions versions obvious noted algo assumes explored explored explored initialized art baseline attempts crucial track adapted answer answer answer operators operators operators operators operators worst worst worst worst worst leaves commonly implicit implicit gradually mellon mellon integrating improvements evaluating carnegie carnegie populations populations populations populations populations populations cmu cmu cmu cmu cmu tional tional conducted conducted simulate introducing introducing incorporated incorporated incorrect maxima maintain maintain maintain maintain maintain maintain http summarized pittsburgh extracting extracting serve plan replace age begins specifies converged wesley sharing phenomenon benefit benefit benefit notes sort www addison martin drift lvq lvq optimizing member member member member hyperplanes approximates count bin bin bin bin bin bin bin bin bin bin bin bin bin bin bin bin grey lost climbing climbing chance significance promising promising promising city city city city city serves exploit removing settings effectiveness alphabet planar heuristics heuristics heuristics evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations evaluations reset falls combines representational respective decide holland holland holland holland regard sim scheduling scheduling competing entries initialize foundations foundations mem reveals bins bins bins bins bins bins bins bins bins bins bins bins fitness fitness fitness fitness extends merge merge variants variants variants variants davis davis implicitly implicitly avoiding parents parents empty lem lem lem informa pressure approx maintaining maintaining crossing ple vec outperform outperform outperform leaming creates opposed randomized job alternating alternating diverse diverse preserving preserving forced par par copy copy copy arbor causing ideally spaced individuals individuals individuals individuals individuals individuals covariances tor shaded attempted attempted exam exam community alternate baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja baluja rithms crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover crossover gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas continues permits mitchell intra proba wise ultimately parallelism employing termed termed portions alternatives nonetheless diversity diversity diversity diversity diversity diversity diversity maintains sam preserve preserve suffer placing behave behave infinitely answers mann lems lems tour tour copies copies copies copies bility continued tial ave suite focuses tsp tsp tsp tsp tsp termination micro outperformed returned floor dissertation subtracted accumulate preservation goldberg goldberg goldberg goldberg goldberg goldberg sity multimodal communicate robotic evolutionary colors creation encodings encodings encodings encodings encodings shop shop mach mul dence mutation mutation mutation mutation mutation mutation mutation ini simon simon addi spanning replaces custom progresses progresses tightly newly avg generations generations generations generations generations generations optimizes caruana caruana hoeffding hoeffding pooled tics statis ele copied dissimilar restart restart restart ross 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#@Baluja_S,
#t10
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#*learning model input data data data data data data data data data data data data data data data data data data data data data data function figure set set set set set set set set set set set training training training training training algorithm algorithm algorithm algorithm algorithm algorithm error error results results results results results results results information problem problem problem problem performance based space order shown shown shown systems values values values values values values probability probability functions unit unit method method method method method method approach approach point point point point point point point point point point point point point local local local local local local local local local local local local local local local local local local local local rate rate rate class class class class class class class class class class class class class class class class class class algorithms algorithms algorithms algorithms simple paper examples examples small size size size size size fig fig points points points points points points points points points points points points points points points points points points points points points points points points points points points points field classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification structure problems high memory memory representation show show show section rule rule real average average average average theory university research research log defined defined defined sequence sequence table computer terms distance distance distance distance distance distance science prediction prediction presented presented presented present machine object object sets sets sets sets sample sample abstract applied find references ieee positive procedure decision decision decision decision context introduction hand behavior behavior cost tion tion difference difference difference complexity complexity complexity complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower rules rules higher higher center center cases cases cases cases cases cases cases expected expected expected expected expected expected expected expected expected expected expected expected expected expected region proposed proposed proposed proposed proposed proposed proposed correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities errors finite minimum minimum minimum minimum resulting resulting classes classes classes classes classes classes ing respect respect respect respect respect respect respect respect respect respect respect respect performed called called called called called called regions regions dimension made made negative vol vol vol vol artificial true compared compared application application desired desired define define define define define define objects objects objects rates rates rates perform perform perform experimental gain brain report institute institute words department loss loss implementation consists code joint joint represents difficult considered domain domain domain domain domain domain domain solutions design detection classifiers classifiers classifiers classifiers classifiers classifiers classifiers choice free increase increase produce condition condition condition condition derived derived conditional clustering criterion criterion criterion bounds finally evidence simply achieved denote close close finding nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest supported supported supported require require ability degree including probabilistic smaller reduced reduced reduced reduced reduced technology technology testing ratio ratio consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent call call call call produced produced produced produced produced produced produced predict predict perceptron advantage separate introduced include trees subset subset subset subset subset subset subset subset volume volume volume yields correspond trans definition observation organization risk entire suggests correctly correctly correctly correctly correctly boundary boundary conclusion minimal greater neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor depend depend performs propose propose propose propose hard reduction reduction reduction demonstrated demonstrated proportional intelligence labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled decrease decrease derivatives question denoted denoted denoted denoted denoted denoted denoted denoted denoted areas areas suppose suppose derive produces written written multilayer remaining remaining slightly consisting applying events select national family family family family review open open evaluate fraction centered centered soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft soft sizes sizes similarly suggested digits sign convex assigned assigned assigned assigned construction classified includes perceptrons assignment assignment assignment assignment assignment maximize domains domains domains discussions closely maximal maximal maximal maximal maximal maximal maximal included ten kind kind kind kind prob allowing success success success success classify quantity providing ill preferred extend simpler involving replaced behaviour rest decisions func cover notion notion plausible predicting created subsets versions assumes utility utility utility utility utility motivated motivated defines percentage percentage costs analyzed failure capabilities baum satisfied satisfied satisfied closer producing day day day day day desirable mation members medical author geometry recognizing radius radius geometric percent amounts leave incorrect incorrect incorrect psychological price fall fall age diagnosis trade trade don benefit benefit benefit benefit benefit benefit benefit benefit labeling databases eliminate outcome outcome consideration numerically intelligent unlabeled unlabeled days infor repeat meaningful performances performances performances contexts ambiguity ambiguity ambiguity patient patient respective evident sphere sphere spherical spherical spherical spherical competing competing israel israel israel israel extends statement valuable hart hart hart hart hart intersection intersection assigning trading trading trading trading trading trading trading trading empty divide radar stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock classifies classifies classifies associate care denoting argued records employing employing employing employing cation option option zip covered covered covered misclassified tively nasa supports union union union rnn rnn rnn rnn rnn rnn strict satisfaction satisfaction council decided decided decided decided identically stay beneficial correctness classi economic economic occam occam occam stocks stocks stocks daily daily presently remained creation firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm firm profit profit profit profit profit investment translate technion technion technion technion predic couple couple separator separator separator separator separator separator separator separator separator separator separator separator separator separator separator separator separator separator separator excluding des decides ames claimed claimed respec conflict conflict rosenblatt complexities complexities complexities surrounded surrounded webb webb webb razor razor razor acknowledgment classifi healthy oft oft oft mission cis reductions reductions amir pected consis consis atiya conflicts tent tent haifa haifa condensed condensed cnn cnn cnn cnn cnn cnn yoram xls invested invested duction unambiguously traded traded hospital moffett disregard pays excludes firmly uncovered stor denser monly tiers bought 
#@Baram_Y,
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#*network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training algorithm algorithm algorithm output output output output output output output number number number number number number number number number number number number number number number number number number error error error error error error error error error error error error state results results results results results results results units units units units units units units units units units units units units units units units problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based based space space weights weights weights weights weights weights weights weights linear layer layer vector order order shown shown values values values values values values values values values values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise weight weight functions functions functions functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method approach approach approach approach approach approach approach approach single single single large large local local test test test test test test test test form form form form form form form form form shows shows shows shows simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small small small small size net work task methods methods points points points process level level current problems problems problems random high show show show fixed line vectors parameter parameter parameter parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory gradient obtained obtained obtained obtained obtained obtained term term note note note note dimensional dimensional result result result university university university variables variables computation solution research log log defined defined found found found found target constant standard standard standard computer terms terms terms science present motion maximum maximum maximum press learn basis outputs sample sample sample sample abstract applied back back find find computational computational likelihood likelihood likelihood likelihood references references important important propagation mixture complex complex complex estimation statistical statistical effect generated variance variance change complexity complexity prior prior prior prior prior prior prior prior prior prior prior chosen chosen chosen chosen chosen theorem theorem required required good good bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected equations markov markov markov make make fact fact techniques techniques techniques techniques techniques length length probabilities probabilities probabilities probabilities probabilities errors errors forward scale minimum minimum ing total total total regression regression computed multi sum called regions regions regions mapping optimization made knowledge knowledge original relative relative relative specific samples samples samples samples samples application application desired provide define compute location perform determined goal related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions distributions distributions approaches approaches comparison comparison comparison comparison comparison comparison comparison comparison comparison comparison larger larger contrast selection report department implementation implementation technique consists consists individual joint difficult difficult exp exp exp exp exp exp exp framework framework framework framework framework framework framework computing computing computing equivalent equivalent additional solutions solutions solutions estimates limit limit limit limit trajectory trajectory trajectory stage requires requires significant statistics free estimated estimated pages give give give give weighted developed robot robot robot robot criterion evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence sampling sampling sampling sampling discussion normal technical increases group group group limited limited close close close inverse assumption corresponds corresponds corresponds corresponds corresponds complete complete predictions predictions common effective effective effective effective effective shape generate supported theoretical end ability easily easily makes including probabilistic typically pairs pairs smaller account account unknown significantly ratio ratio ratio increasing consistent mode mode leads leads representing numbers numbers iterations making combined choose choose run denotes advantage pair separate takes takes takes practical apply introduced hierarchical inference inference inference compare compare conventional volume works axis correspond rl rl diagonal evaluation evaluation evaluation evaluation evaluation evaluation chain chain chain chain chain chain chain chain chain williams williams williams increased grant arm arm arm arm scaling extended deviation hybrid hybrid hybrid hybrid loop generally setting accurate accurate bayes bayes bayes numerical peak peak practice strong integration physics physics radial assuming assuming minimizing minimizing decrease decrease targets groups reference reference reference reference suppose relation monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo written factors plot plot plot plot vertical distinct distinct distinct explicitly infinite infinite infinite involves transformations integrated equilibrium springer expectation versus versus select select letters yield expressed expressed evaluated evaluated evaluated evaluated evaluated evaluated evaluate evaluate evaluate evaluate evaluate evaluate updated approximated similarly sign additive performing normalization normalization fitting fitting intermediate initially sufficiently david precision precision precision silicon priori perceptrons plotted discuss priors priors priors priors discussions reason reason gamma gamma gamma straightforward closely computationally divided modes modes modes modes committee detect mackay mackay mackay mackay mackay mackay characteristic characteristic success link dis symmetry contribution sin sin running follow gibbs write reach maximization attempt software modelling bars origin poor poor involving replaced limitations limitations hall biases biases biases biases successive successive successive links analytically analytically analytically analytically possibility maximizing tanh momentum hill hill coefficient trace extremely neal neal neal neal neal neal neal neal neal indicating great cos cos costs derivation fairly analytical expensive reasons perspective precisely broad broad bishop bishop bishop bishop bishop bishop probable acknowledgement beginning toronto lowest arises conjugate conjugate evaluating introducing marked slower partitioning kinds expectations converged corrupted uncorrelated notes oxford ratios ratios ratios ratios narrow grows convenient chance significance accepted determination check hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper viewpoint keeping settings hours evaluations governed governed governed initialize treatment treatment treatment omitted offer arrive augmented dense largely kinematics aston isotropic reports illustration principled arising arising exponent distri chapman graphics dominated challenging challenging argued flip increasingly integrals indication matlab challenge bution chris lecture accordance christopher barber barber barber barber barber kth formulae tribution hamiltonian occam occam degenerate interpolate interpolate lnp lnp reflection statist periodically periodically metropolis inaccurate neglected energies denominator ized birmingham degrade crg accu inte devel opportunity symmetries bruce missed devise correspondingly accord epsrc ncrg ror numerator chaining chaining chaining chaining chaining chaining chaining chaining chaining chaining chaining chaining chaining chaining chaining chaining governs richardson integrations overcomes optimizer kennedy leapfrog leapfrog spiegelhalter wld wld wld wld prescription ash ass scarce ola neglects gilks gilks duane duane fictitious lna decline weighed dia dia dia momenta interchange evidences evidences evidences evidences rately kass kass pendleton gration ilu inapplicable 
#@Barber_D,Bishop_C,
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#*network network network network network network network network network network network network network network learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data data data data data function function function function function function function function function function function function function function function function time time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm output output output output output number number number number number number number number number number number number number system system system system error error error error error state state results results results results results results results results results units units units units information problem problem problem problem problem problem problem problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden performance performance performance performance based based space space space space space space space space space weights weights weights linear linear linear linear case case case vector order order systems values values values values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters noise noise weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method method method method method method method method method method approach approach approach pattern point point point point processing large large large local local rate rate test test test test analysis class class class class class class class class matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples examples examples examples examples examples examples small small size size size net net work work work work task methods methods methods methods methods methods methods methods methods methods methods methods step step points points points points points points points classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process process process process trained trained structure problems problems problems problems problems problems problems problems problems problems random random high similar similar similar show show equation equation equation equation equation equation equation equation equation equation equation section section section section section fixed fixed fixed rule parameter real real real approximation approximation approximation approximation approximation approximation approximation approximation average states theory gradient gradient obtained obtained obtained obtained term experiments experiments dimensional dimensional university variables variables variables variables variables variables computation computation computation solution solution solution research research research log log log log log log log log log log log log log log log log log log log log log log defined found found found found found found found dynamics initial initial initial table table table table table table table estimate estimate standard standard standard standard computer computer terms connections science science prediction prediction prediction presented presented presented map map map present present phase activation activation activation activation low low low machine maximum maximum maximum maximum maximum maximum maximum maximum maximum press position position basis basis outputs sample sample sample abstract applied applied applied applied applied applied find find find find find likelihood likelihood likelihood likelihood references component stochastic stochastic stochastic due positive procedure important decision mixture mixture introduction hand hand statistical variance energy energy energy energy energy energy energy energy difference complexity variable prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen previous previous theorem required required required required multiple multiple good good tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations equations equations markov markov markov markov make make make make fact region proposed correlation length length length probabilities errors forward scale scale scale scale finite finite simulations simulations minimum classes tasks tasks total total simulation regression regression regression regression regression regression regression regression computed respect respect respect respect respect respect sum elements means means factor optimization potential potential dimension dimension made made obtain obtain obtain obtain obtain obtain negative relative cross cross cross provide define define compute perform perform perform related posterior posterior posterior posterior posterior posterior equal equal approaches mit steps steps nets selection report department implementation implementation code advances joint joint joint joint difficult final exp exp exp addition framework cambridge computing computing computing directly view design limit limit trajectory trajectory determine efficient full requires requires requires approximate approximate approximate statistics statistics world estimated validation validation validation give give give produce product actual processes processes processes processes processes processes processes processes processes processes processes iteration iteration iteration sampling sampling sampling sampling simply simply simply achieved achieved discussion discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance normal increases describe group denote denote denote denote denote tested fast close inverse complete predictions predictions predictions predictions predictions finding finding generate supported role require main eds eds future future easily degree degree including typically typically smaller needed account dynamical dynamical dynamical fully transfer transfer transfer transfer increasing leads leads details call call iterations iterations pre pre direct making making making making magnitude idea idea idea produced run run directions directions advantage reported strategy include identical identical side quadratic quadratic calculated calculated volume works works correspond converge differential achieve diagonal chain chain chain modified generalized generalized bounded williams williams williams williams williams williams williams williams williams williams grant expression studied extended deviation derivative matrices matrices matrices predicted alternative hybrid hybrid hybrid hybrid hybrid hybrid touretzky place place valued valued depend sigmoid sigmoid accurate accurate bayes performs faster practice practice asymptotic suggest integration integration integration physics demonstrated radial derivatives relation pro monte monte monte monte monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo longer changing infinite infinite infinite consisting integrated equilibrium applying predictive predictive predictive springer springer letters yield review depending correlated estimator transform transform densities evaluated approximations approximated similarly similarly reasonable smoothing slow purpose iterative calculate query advantages david avoid expect expect activations extension automatic priors priors priors priors priors priors partially characterized simplicity straightforward straightforward straightforward closely closely computations mackay ten split split dis classify gibbs usual maximization attempt approximating modelling employed carried transformed collection put involving integral integral hall discriminant discriminant dataset dataset behaviour rise rise scalar successive investigated analytically analytically analytically analytically analytically analytically combine dependencies maximizing maximizing maximizing maximizing comparable comparable comparable momentum momentum attributes attributes naturally necessarily predicting implementations implementations friedman logistic logistic logistic logistic fisher initialized art multivariate baseline neal neal neal neal integrate percentage derivation analytic adapted expensive glass glass glass glass briefly tractable tractable tractable worse comparisons broad choices mathematics inversion acknowledgement implicit ridge ridge definite localized arises conjugate conjugate argument improvements greatly relevance flexible readily readily adjustable adjustable employ employ slower http http calculating hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters marginal datasets datasets datasets green green gave gave logp findings specifies converged converged softmax cumulative irrelevant classifying newton newton notes www formally formally formally investigation optimizing labelled grows plays lost dealing anatomical accepted determination interpret keeping hope nearby scoring obtaining obtaining observing nonparametric hours hours regarded intended hasselmo laplace laplace laplace laplace laplace laplace creating record belonging extends partitioned ignore fold vari consecutive outline shorter aston aston job rejection rejection welch covariances simulating mars mars guess avoided stands jacobian pub distri diag chapman mitchell rejected integrals cation indexed discretization inverting mcmc mcmc mcmc mcmc mcmc induces matlab matlab normalizing ignoring differentiating challenge coming walk bution lecture twenty continued christopher prefer justification hundreds barber barber barber barber barber hamilton hamilton tribution rasmussen rasmussen rasmussen discarded meth rameters interpolate ods differentiate ance enters kinetic metropolis metropolis iterate iterate energies birmingham ini sex sex sex developments facilitates ard tightly fundamentally inability inte albeit beliefs beliefs iterates inertia pushed vat silverman silverman centred asymptotics exposition epsrc ncrg classifi ripley ripley ripley ripley ripley ripley ripley ripley ripley prof prof tly tly tly tly tly tly tly diabetes diabetes diabetes diabetes normality gps gps gps gps gps gps gps multiclass integrand pima pima pima pima pima diction integrations integrations erf kennedy augmenting leapfrog leapfrog ast ast hamiltonjan raphson raphson quan vide stats sgi parametrization dictions mensional marginalization marginalization marginalization duane duane tlo tlo fictitious hyperprior indian indian indian wechsler extendable momenta ptp mension elegance rescale parameterizing appended indians aset burn pendleton tities placements 
#@Barber_D,Williams_C,
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#*network network network network network learning model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function figure figure figure figure time time time set set set set networks networks networks networks networks networks networks networks training algorithm algorithm algorithm output output output output output number number error error error error results results results results results results information problem problem problem problem problem problem problem problem models models models models based based weights linear linear linear linear linear case case case vector vector vector vector vector vector vector order order shown systems systems values values values values probability parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight functions functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition approach approach approach approach approach pattern point point point point single single single processing large large large local local test analysis analysis analysis matrix matrix matrix matrix inputs form form shows shows shows algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small size work work work methods methods methods points points points level trained problems problems random show show show show show section fixed fixed fixed general generalization parameter approximation approximation average average gradient obtained obtained obtained term note result result result result result result university university variables variables variables variables computation computation solution research research independent log log log log log found found found found found target target target constant constant constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard computer terms terms science prediction left left sets sets sets sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press press basis basis basis nonlinear outputs sample abstract find find find density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due procedure procedure important important adaptive adaptive mixture mixture mixture context introduction hand hand hand hand effect effect effect generated generated variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance change variable variable variable variable variable variable assume prior prior chosen part cases required multiple represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov techniques proposed observed forward scale scale finite ing regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression computed respect sum performed optimization optimization optimization applications applications obtain obtain obtain negative negative artificial true true true true perform determined goal goal posterior posterior posterior distributions gain equal equal equal approaches approaches approaches mit larger contrast train train dependent dependent dependent dependent dependent dependent dependent dependent proceedings report report institute department technique consists code individual kernel kernel advances joint joint represents represents exp exp exp exp bias bias bias bias bias bias bias framework cambridge computing computing hinton curve curve curve curve curve curve stage conference requires requires choice choice approximate estimated estimated estimated estimated estimated estimated validation give give conditional conditional conditional conditional conditional finally evidence sampling discussion covariance normal technical technical arbitrary group group tested fast close inverse corresponds predictions finding finding finding assumed assumed generate supported eds eds easily easily noisy noisy probabilistic probabilistic smaller smaller reduced unknown unknown jordan technology interesting significantly special leads leads leads representing max pre experts frame idea minimize choose predict predict denotes denotes improved discussed takes takes introduced hierarchical hierarchical inference recently highly compare conventional volume yields mixtures chain chain williams williams grant expression expression lead invariant alternative feed touretzky width loop deterministic generally runs depend depend clear taking taking taking drawn drawn california solid turn assuming minimizing minimizing min averaged averaged averaged introduce derivatives denoted acknowledgements suppose relation monte monte carlo carlo plot plot averaging remaining consisting integrated minimization minimization expectation national dependence dependence squares solved densities suggested constants slow dashed dashed dashed additive fitting degrees combinations eigenvalues inter extension illustrated maximize priors priors simplicity straightforward mackay mackay mackay mackay mackay mackay plots plots summary contribution gibbs realistic realistic leading subsequent jacobs jacobs intrinsic tesauro modelling minimized bars bars bars simpler involving involving involving integral limitations limitations hessian rise analytically scaled scaled maximizing maximizing hierarchy hierarchy contours contours contours removed gradients extremely quantities freedom multivariate generates generates neal neal optimum defining nowlan bishop bishop bishop bishop bishop bishop bishop bishop probable probable probable probable probable begin toronto arises outer conjugate conjugate integrating integrating evaluating substantially treated http passes passes weigend weigend maximizes maximizes hyperparameters marginal marginal marginal marginal marginal substantial unbiased unbiased unbiased extreme extreme leen oxford fits numerically overcome hyper biased biased biased biased viewpoint intuitive exploring governed governed regarded infinity uni chooses treatment treatment treatment treatment treatment treatment treatment modelled modelled infer insight verification fitted aston aston aston aston aston isotropic isotropic adopt chapter sinusoidal illustration penalized toy proach paris coming fiat simplification christopher jointly spacing determinant val val meth systematically systematically maxi evolving sity ods centres shop shortly denominator denominator birmingham ues ues imum occasionally crg icann versity adopting fogelman nix nix interpolant univer gra eval epsrc ncrg ncrg iai omitting discarding integrations dropping dient nen logarithms gallinari ilwll wld pare equiva inevitably borne parametrization cie skewed imization mizing treatments treatments cry uated hav lently dictive 
#@Bishop_C,Qazaz_C,
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#*network network learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure time set set set set set set set set networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number results results problem problem problem problem problem problem models models models models hidden hidden based based space space space space space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear linear layer layer case vector vector probability probability probability probability parameters parameters noise weight weight functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition approach approach approach pattern point point point point point point point point point point point single large local analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form form form form form form shows shows shows shows algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples size feature feature feature net net net net work methods methods methods step step step step step step points points points points points points points process trained trained trained trained problems problems high similar representation representation representation equation section section fixed line line line vectors vectors vectors vectors vectors general general parameter approximation approximation approximation gradient obtained obtained term note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university variables variables variables variables variables computation computation solution research research research research independent log log defined defined defined standard standard standard terms terms terms terms terms node left left map map map map map map map map map present phase phase nodes nodes sets maximum maximum maximum components basis basis basis continuous continuous continuous continuous sample abstract applied applied find find find convergence convergence convergence convergence convergence density density density density density density density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood references procedure procedure procedure procedure procedure procedure procedure procedure procedure adaptive mixture mixture mixture mixture mixture mixture mixture mixture introduction hand statistical statistical statistical statistical effect generated variance variance variance tion energy energy difference variable variable variable variable variable spatial spatial lower prior prior prior chosen part theorem represent bayesian techniques techniques techniques region proposed correct probabilities probabilities probabilities classes ing computed respect respect multi multi multi multi sum performed times elements elements elements elements elements elements mapping mapping mapping mapping mapping mapping means optimization optimization dimension made applications applications em em em em em em em em em em em em em em obtain obtain compared application application provide define define define experimental goal goal goal goal related posterior posterior posterior posterior posterior posterior discrete discrete equal equal comparison contrast contrast dependent report version version version version consists consists code code represents represents maps maps maps maps maps considered computing computing computing directly curves curves top stage stage stage determine choice choice choice significant significant significant statistics con derived derived provided provided provided provided provided finally nature nature simply biological biological biological biological achieved achieved discussion technical arbitrary arbitrary group group group transformation limited close close inverse inverse corresponds complete proof finding nearest effective supported role require journal ability development development objective objective objective simulated typically typically smaller functional projection projection principle leads leads principal principal principal principal representing details call making making early early choose choose run discussed takes practical include include quadratic relevant dimensions compare compare unsupervised approximately smooth smooth correspond correspond converge diagonal locations generalized generalized grid grid williams williams williams williams williams williams williams organization grant studied suggests wide wide alternative alternative alternative alternative alternative move generally setting demonstrate runs flow flow flow flow flow conclusion place differences clear constrained constrained constrained integration integration physics physics characteristics drawn regularization variety variety exist introduce derivatives acknowledgements reference explicit relation monte carlo factors factors plot plot describes missing explicitly dimensionality dimensionality dimensionality transformations unique consisting develop gaussians springer expectation expectation cycles select choosing independently formation solved solved evaluated evaluated organizing organizing organizing organizing organizing organizing organizing organizing organizing forms forms similarly key smoothing measurements assigned euclidean kohonen kohonen kohonen kohonen kohonen advantages includes formulation formulation batch batch illustrated maximize tests major gamma regular regular straightforward society delta delta latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent mackay mackay situation plots refer verlag success success success interested interpreted lie manifold manifold manifold manifold manifold manifold criteria list play maximization maximization automatically automatically principles deal software intrinsic intrinsic modelling modelling modelling unlike updating involving optimized integral limitations limitations limitations dual existence ideas project project analytically possibility referred maximizing topographic topographic topographic topographic fundamental phases analogous removed circles gradients concepts necessarily configurations configurations implementations singular noted algo algo algo algo algo som som som som som som som som som som som som som som som som som som som som som som som som som som som som som mapped mapped consist submitted attempts attempts defines defines seconds years site great developing guaranteed guaranteed capabilities reasons considerable spatially perspective organized located bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop consequence inversion projected universal localized arises auto cybernetics cybernetics incomplete conjugate empirically embedded embedded introducing formulated compares ity http http passes berlin summarized spread gen proven neuro yuille differentiable lab newton rithm rithm rithm appropriately optimizing optimizing ordering ordering ordering homogeneous royal convenient overcome proceeds interpret belong preparation introduces governed james james codebook codebook induce spherical elastic elastic elastic elastic tic tic similarities arrive late cpu extensively papers dempster dempster geometrical schulten gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm rubin solves aston aston aston aston aston aston aston convolutional preserving tibshirani tibshirani centre centre quasi seek seek constitutes principled principled principled principled principled visualization arising formance diag rithms rithms distribu gas manifolds regularizer disadvantage crosses careful considers laird sheet superposition book book induces obermayer parametrized durbin durbin signs tail acquire generarive generarive generarive generarive satisfactory christopher christopher water hat suffers lated responsibility responsibility responsibility responsibility flows flows flows shrinkage compo diagnostic possess preservation neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood reality lnp salesman unlabelled spirit confined centres centres centres centres centres centres gaus reviewed indirectly files shortly tens birmingham birmingham probabil retaining magnification magnification neigh nents disadvantages oil oil oil oil oil oil oil oil web topologically nuclear nuclear shrink responsibilities responsibilities centred centred visualisation live visualized visualized successes epsrc ncrg ncrg ncrg travelling govern premise crafted tly tlx tlx robbins robbins invoked encouraged pipeline pervised instruments instruments monro monro mat bilities inspiration shrinking overcomes markus markus shrinks shrinks lxt lxt unsu trast dii annular highlighted stressed deficiencies deficiencies deficiencies fifteen svens svens svens svens staff pipelines revisited sians tlw tlw hospitality matic motivating metaphor trt doo xlt 
#@Bishop_C,Svensen_M,Williams_C,
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#*learning learning model model model model model model model model model model input data data data data function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number state state state state state state state state results problem problem problem models models models models models hidden based based based space weights weights weights weights weights weights weights weights linear case case case order shown values values probability probability probability probability probability probability probability probability parameters parameters noise noise weight weight weight distribution distribution distribution distribution recognition recognition approach approach approach approach approach approach approach pattern pattern pattern pattern point image image single single processing control local rate test analysis analysis matrix optimal form form shows simple gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual size work task methods methods methods methods methods step step step step step step step step step step step step step step step step field features features features process process process current problems problems random random random random random random random random high similar representation representation representation equation equation equation fixed rule rule images images images images general general general general speech real approximation states states theory obtained dimensional dimensional dimensional result result university independent independent independent sequence sequence sequence sequence sequence sequence target constant standard computer computer computer terms science prediction prediction presented low temporal temporal temporal machine machine object object object object object sets sets sets sets motion motion motion motion motion motion motion motion motion motion press press press position position position position position nonlinear nonlinear continuous continuous continuous sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied applied applied applied find find computational computational density density density density density density density density density density density density density density density density density density density references component stochastic stochastic stochastic stochastic stochastic stochastic ieee ieee procedure propagation propagation propagation propagation propagation propagation propagation introduction complex hand estimation estimation estimation statistical statistical effect dynamic generated generated cost complexity measure measure signals prior prior prior prior prior prior learned learned learned learned learned chosen chosen chosen chosen chosen previous multiple multiple multiple multiple multiple good binary represent distributed bayesian bayesian bayesian bayesian markov fact techniques forward multi multi multi performed times times elements elements elements elements means applications study knowledge filter filter obtain obtain samples samples samples represented represented objects proc proc proc proc posterior distributions distributions distributions discrete discrete power power mit steps steps fields support report department consists represents represents framework cambridge cambridge computing curve curve curve curves curves curves curves estimates top stage efficient statistics statistics free speed vision vision vision give weighted weighted weighted randomly conditional conditional conditional conditional conditional conditional conditional levels finally finally iteration iteration iteration sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply simply biological achieved achieved achieved measured measured increases limited finding effective effective effective effective effective effective shape shape shape shape shape shape shape generate generate generate generate theoretical journal journal hypothesis instance noisy noisy including simulated probabilistic typically needed dynamical dynamical dynamical functional york head structures principle operation operation representing representing details iterations filters filters direct frame choose run predict predict discussed robust robust separate element element moving identical identical engineering sufficient varying previously observations observations approximately tions differential differential trans trans trans background background background evaluation positions positions observation observation observation observation observation observation observation entire entire entire constructed extended alternative generally runs conclusions accurate bayes suggest hard drawn demonstrated demonstrated proportional intelligence intelligence plane targets configuration annealing denoted monte monte construct construct construct carlo carlo generating transitions missing develop applying applying predictive predictive springer select select choosing reconstruction estimator detailed densities densities densities densities evaluated evaluated evaluated static static sizes allowed allowed diagram intervals iterative iterative tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking closed filtering filtering sufficiently david template figures includes contour contour extension plotted illustrated discussions tests successfully capable hmms uniformly effectively effectively driven modes efficiently soc conf verlag contained prob prob allowing video video split running strategies gibbs bar bar sampled relaxation realistic observable hypotheses hypotheses leading leading deal modelling extend powerful essential kalman kalman kalman kalman kalman involving detail detail association accurately graphical hall hall rise reducing successive successive fashion int int possibility authors comparable stream proved proved contours contours contours smallest naturally editor configurations shapes academic store switching generates mixed mixed seconds seconds seconds seconds crucial derivation track track track guaranteed handle operators desirable 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raises multimodal multimodal fair centres gence foreground foreground iterate undergo unimodal recovering modest clutter clutter clutter clutter clutter clutter clutter clutter infeasible remarkably tracked tracked tracked tracked phil deformations hands hands hands ply undergoes web lips nth blob seeking experimentation temporary dynam hwang hwang epsrc quences condensation condensation condensation condensation condensation condensation condensation condensation condensation condensation condensation condensation condensation condensation condensation condensation altogether attitude ripley ripley occasional occasional occasional chow depict depict sug comment iee subjected fundamentals variate attainable isard isard isard isard isard isard isard zlx zlx zlx bush bush cluttered normalisation screening zisserman stringent roger papoulis papoulis terior sgi shalom shalom gelb gelb namical xlz xlz xlz cknowle dgement resent satisfactorily satisfactorily intelli sutherland sutherland 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#@Blake_A,Isard_M,
#t10
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#*learning learning learning learning learning learning learning learning learning model neural data data data function function function function function function function function function function figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number state results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance based based space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear vector vector vector order shown functions functions recognition recognition method method method approach approach approach pattern pattern pattern point point point point point point point point point point point point processing large local local test test test test analysis analysis class class class class matrix matrix matrix optimal form form form form form shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple paper paper paper examples size size size size size size methods methods points points points points points points points points points points points points points features classification process trained trained structure structure problems problems problems problems random random similar section section section fixed fixed vectors vectors general general real real real real real real real theory theory obtained obtained obtained obtained term note note note note note note dimensional dimensional result university university university variables variables variables variables variables solution solution solution solution solution research research initial constant table table computer computer computer distance distance distance distance distance distance node science science science present machine machine machine machine sets sets sets maximum maximum range range press components components nonlinear abstract applied applied applied applied find computational computational computational computational computational convergence convergence references due due ieee important important important introduction hand hand estimation statistical statistical statistical cost search difference variable variable variable lower measure word center center center center center center center center center center theorem theorem type type good expected expected make fact fact fact proposed proposed proposed proposed correct finite finite finite finite finite finite minimum minimum minimum minimum minimum minimum classes ing total sum sum sum sum sum sum sum sum sum elements means optimization optimization optimization optimization optimization dimension global global global global global global applications applications study knowledge knowledge knowledge obtain obtain original original original represented true compared compared desired compute determined constraints constraints approaches steps contrast contrast update department department department implementation difficult ai ai ai ai ai ai ai ai ai 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testing testing testing ratio database database database database database database database database database database database principle principle leads leads leads squared representing iterations max supervised supervised supervised supervised supervised supervised supervised idea minimize minimize minimize minimize choose description improved robust robust robust robust robust robust robust robust strategy strategy subject subject subject side side subset subset subset subset subset subset subset subset subset unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised solve solve solve separation observation generalized constructed matrices correctly clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters column runs conclusion starting starting row assumptions numerical propose hard hard california intelligence minimizing minimizing minimizing minimizing minimizing min min min min averaged averaged groups minima minima program program program program program program program program program program program program program program program program program denoted acknowledgements explicit solving solving solving solving ways label mathematical mathematical mathematical mathematical mathematical mathematical distinct distinct explicitly explicitly explicitly linearly consisting equilibrium minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization national national extracted stationary stationary stationary stationary squares squares squares influence lemma lemma lemma lemma solved solved labels centers centers centers centers centers centers centers centers sizes sizes suggested discrimination key partial convex convex convex intervals closed closed closed closed closed distances distances distances distances distances distances assigned assigned assigned foundation norm norm norm norm norm norm norm norm norm norm norm norm norm euclidean euclidean classified transactions coordinate formulation instances assignment assignment assignment sciences sciences specifically tests determining importance computationally computationally comparing essentially ten quickly prob prob heuristic split dis dis dis dis superior issue notation minimizes leading software minimized minimized minimized carried carried difficulty varied replaced dual dual hall ml successive incremental applicable comparable comparable closest closest necessarily integer ensure obvious fisher separated separated perceptton perceptton academic utility finds stop piecewise piecewise piecewise piecewise piecewise separable guaranteed guaranteed defining fairly majority majority lies tool handle starts turns precisely immediately immediately medical incomplete considerably percent axes axes leave poorly formulated formulated formulated outliers outliers differs patients patients median median median median median median median median median median median median median median median median median median median median median median median median median median median median proposition acquisition proofs www writing optimality optimality optimality optimality assign guarantee databases databases databases databases databases databases databases databases discovery communications murphy tools tools satisfying satisfying stated obtaining star star star carry nonparametric lip prentice corollary programs programs programs programs programs programs equals cancer cancer cancer cancer grants characterization characterization shavlik convergent automated vari assigning assigning lem lem ics uci uci street street street street street outline fellowship misclassification email email formulate formulate failed die additionally equality formance pami concentrate depicts depicts smyth harder west siam placing exhibited status gorithm remark remark remark remark appearing opti algorithmic decided breast breast breast breast cliffs solvable utilizes conceptual establishes mining mining outperformed jain proportions cally cally bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear diagnostic diagnostic ters englewood correctness correctness correctness correctness correctness correctness correctness correctness correctness correctness correctness correctness correctness correctness correctness norms html repository concave concave concave concave concave concave concave concave concave concave concave concave concave concave concave concave concave transpose wisconsin wisconsin wisconsin wisconsin wisconsin est irvine terminates terminates signed scatter contents inaccurate indicators cleveland health completeness costly preferable survival survival survival survival survival survival survival months vergence mization primal lid ness bright assoc ver madison tie tie philadelphia separability volumes gorithms cen converting functionals bradley bradley bradley bradley polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral polyhedral mangasarian mangasarian mangasarian mangasarian mangasarian mangasarian mangasarian mangasarian mangasarian mangasarian chine bennett bennett departure shapiro linearization linearization votes concludes quadratically reformulation reformulation obser ismail alternates discrim weber weber weber initiate aha wisc wisc fukunaga fayyad chung parison ccr institutes kaplan publicly locates locates surviving dummy tumor tumor ang galaxy galaxy termined vations duality kdd kdd jude subproblem subproblem signify llp ination dayton sus tracting nln theoreti 
#@Bradley_P,Mangasarian_O,Street_W,
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#*network network learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input data data data data data data data data data data data data data function function function function function function function time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system system system system system system system system system system system system system error error error error error error error error error error error error results results results results results results results results results results information information information problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance based based space space space space space weights weights case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown systems systems systems systems systems values parameters functions recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method method method approach approach approach approach approach pattern pattern pattern pattern pattern pattern point point processing processing processing rate rate test test test test test test test test test test test test test test test class class class class optimal optimal form signal algorithms simple paper paper examples examples examples examples small size size work task methods methods methods methods methods classification classification classification classification classification classification classification classification current trained trained trained trained trained problems problems problems high high high representation equation equation equation equation equation section section section section section section section fixed rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images general general general general generalization generalization generalization generalization generalization generalization generalization generalization approximation approximation approximation approximation average theory theory gradient gradient gradient gradient obtained note note note note note note experiments dimensional dimensional dimensional dimensional threshold threshold threshold threshold threshold threshold threshold threshold variables variables computation solution solution solution solution solution solution solution research defined defined found found constant table table table table table table terms terms distance present present phase phase phase phase machine machine machine machine machine machine machine machine machine machine machine machine machine object maximum maximum press abstract find computational properties properties references due positive positive positive procedure procedure important adaptive decision decision decision decision decision decision decision decision decision introduction complex hand estimation estimation estimation estimation statistical effect generated generated cost tion difference complexity assume classifier classifier lower rules measure part bound cases cases good good binary binary expected equations equations fact fact fact techniques errors errors errors errors resulting resulting classes ing regression regression regression computed computed computed computed computed computed sum called times times elements mapping mapping means factor factor factor factor factor factor factor made study study study knowledge knowledge knowledge knowledge knowledge knowledge negative original original original original original original original original artificial artificial artificial artificial artificial samples samples application desired provide compute compute determined experimental goal distributions discrete approaches accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison comparison support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support train train train descent descent morgan proceedings proceedings loss loss technique kernel kernel kernel kernel kernel advances advances final bias domain domain domain directly directly san effects conference conference conference conference classifiers classifiers classifiers classifiers requires speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed estimated basic increase increase increase validation give give give give produce types product finally finally selected nature simply achieved achieved measured discussion discussion discussion discussion normal describe describe close close surface surface finding finding finding implemented generate generate generate supported supported eds face end pixel instance easily kaufmann objective objective objective typically typically reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced reduced functional interesting significantly york york increasing increasing database empirical empirical leads details numbers numbers numbers max international international international international international normalized polynomial combined combined choose choose added improved improve improve directions correlations advantage apply apply introduced subject machines machines machines machines machines machines machines machines machines machines machines machines machines quadratic sense sense relevant varying varying observations approximately approximately approximately approximately approximately approximately yields achieve improvement improvement improvement improvement improvement increased lead suggests derivative boundary boundary greater reduce operator competitive tangent bayes bayes bayes bayes bayes bayes clear performs moody faster mateo solid minimizing start start plane groups force denoted digit digit digit digit digit digit digit ways estimating label stability explicitly infinite physical physical transformations transformations applying springer springer springer implies choosing choosing expressed expressed expressed dependence depending viewed interpretation solved restricted labels labels approximated margin margin margin margin translation digits digits digits sign key reasonable slow slow expansion sec combining roughly remains intermediate assigned euclidean views expect handwritten handwritten handwritten kernels kernels kernels bell bell vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik discussions columns columns importance computationally svm svm svm svm svm svm svm svm svm svm svm svm poggio poggio build efficiently invariance tend ten ten ten ten road verlag verlag verlag repeated cun cun allowing symmetry symmetry lie lie lie classify classify built built built satisfy bar simplified dot dot dot absence minimizes computes denker denker denker ill approximating satisfies decreasing unlike carried requirements exhibit replaced hanson lippmann fewer fewer reducing rest applicable applicable applicable applicable applicable analytically combine referred referred referred comparable workshop removed smallest possibly necessarily assumes explored improving improving improving improving improving improving improving improving improving improving improving improving submitted motivated separable separable trivial distinguish biology analytical expensive handle purposes formalism widely forces incorporate hyperplane hyperplane hyperplane mation products products laboratories simard simard simard simard simard acknowledgement separately english annual conjugate conjugate conjugate conjugate requiring virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual fourth prop collected substantially readily posed incorporated slower compares compares berlin pittsburgh characterize extracting incorporating incorporating incorporating incorporating achieves gave gave germany conclude progress cumulative shifted room sv sv investigation restriction summing acm discovery rotations lecun lecun lecun lecun lecun proceed adds adds adds adds adds adds dealing analogy held contract reasoning corner infor separating separating separating combines sion overview overview jackel jackel reader record refers park speeds stopped interestingly mechanical smola smola smola unchanged multiply multiply multiply multiply multiply multiply ence svms svms svms drop sch sch sch sch sch sch sch vec achieving guyon guyon guyon guyon convolutional maximized year boser boser acceptable constitutes burges burges burges burges burges burges burges burges burges burges burges burges burges burges burges burges invariances invariances invariances invariances invariances invariances invariances invariances invariances invariances summarizes equality perpendicular formance labs disadvantage noting speedup constructs constructs million sheet sheet tively aaai technologies chris nist cable kopf kopf kopf institut hilbert err tors mining bottou bottou holmdel holmdel thickness striking separates lying inefficient arpa cur planck ings translates slack sur cortes cortes cortes cortes cortes drucker drucker drucker jerusalem boosted boosted appli fiir orig orig orig orig orig orig orig orig icann dependences des retrained symmetries symmetries symmetries translating respec menlo parentheses fogelman miiller miiller brings periments fifty fifty fifty victorri comparatively schslkopf schslkopf schslkopf confer bernhard incor lucent ink summarizing compar kybernetik ickinger ickinger torques biilthoff biilthoff tual gallinari strained slows opportunities fayyad russian bilateral crawford advan lkopf lkopf lkopf ison moscow tages exerts mpg rently 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#@Burges_C,Scholkopf_B,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function figure figure figure figure figure figure figure networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number number number number results results results results results units units information information information problem problem problem problem models models models models models models models models models models models models models models models models models models models hidden performance performance based based based based based space space space space weights weights weights weights weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer case case case case vector vector order order order shown shown shown systems values values values parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions unit method method method method approach approach approach approach approach approach approach approach approach approach approach approach point point point point point single single single large large local analysis matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal form form form form form form shows simple paper paper examples small small small size work work methods methods methods step points points points points classification classification level current trained trained trained trained problems high high high response response response response response response response response response representation equation equation equation equation section section section section section section section fixed fixed fixed fixed real average note note note experiments dimensional result university variables variables computation solution solution research independent defined found found found target target target target target target initial table estimate standard standard standard standard terms terms science prediction presented presented presented maximum press basis basis basis basis basis basis nonlinear sample sample sample abstract applied applied applied find computational computational density references due positive procedure procedure important important important important adaptive adaptive decision introduction estimation statistical statistical statistical statistical statistical statistical effect effect effect effect effect variance variance cost change change change complexity measure measure learned chosen chosen higher previous previous multiple conditions bayesian bayesian expected expected fact techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques correlation correlation correlation correlation observed observed scale finite resulting classes classes classes classes classes simulation simulation regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression computed respect multi performed regions regions regions factor factor potential dimension natural obtain original original original vol vol artificial samples represented application cross provide provide define perform active experimental experimental experimental related related related equal power approaches approaches comparison larger connection train dependent selection morgan proceedings department technique individual kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel final bias bias layers framework framework framework cambridge equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent equivalent experiment additional curves estimates san effects effects conference capacity capacity significant approximate statistics estimated estimated estimated estimated estimated estimated estimated validation give derived weighted weighted developed area types selected nature simply discussion discussion discussion discussion describe describe describe describe arbitrary limited limited inverse inverse finding rbf amount nearest effective effective effective shape shape shape main main journal ability ability ability instance future degree degree including kaufmann simulated typically typically combination reduced account account functional transfer interesting testing significantly projection projection increasing details decay decay decay decay decay decay decay decay attention run added added discussed directions property ensemble ensemble takes similarity practical practical side quadratic trees trees dimensions observations observations match modified observation observation grid interval risk entire increased parts expression concept suggests suggests matrices correctly assumptions assumptions differences sigmoid sigmoid moody moody mateo suggest suggest propose propose propose taking taking sigmoidal regularization radial radial radial turn turn manner derive derive derive construct estimating estimating estimating estimating estimating estimating estimating estimating estimating changing sensitivity sensitivity transformations transformations slightly interaction interaction applying minimization versus expressed expressed expressed squares squares squares viewed viewed influence influence transform controlled controlled controlled understanding understanding approximated approximated approximated approximated calculation smoothing additive additive additive combining fitting fitting initially calculate calculate query degrees degrees degrees degrees degrees degrees degrees degrees degrees degrees degrees degrees expect existing existing kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels weighting uncertainty uncertainty regular closely closely capable society computationally literature mackay mackay comparing tend summary summary notice procedures allowing return running follow notation sampled sampled vary vary write providing providing nips nips wave wave leading automatically parametric parametric parametric parametric parametric parametric parametric parametric parametric powerful american transformed perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation perturbation investigate investigate investigate investigate estimators estimators association limitations limitations hall dataset pursuit pursuit fashion school possibility possibility combine combine understand notion notion coefficient coefficient trace generalisation spline spline illustrate friedman friedman friedman friedman friedman freedom freedom freedom freedom freedom freedom freedom freedom freedom freedom freedom freedom freedom multivariate motivated advanced analytic analytical lies tool london london london comparisons considerable perspective ring broad mathematics gradually definite fourth flexible pseudo pseudo effort backprop adjustable adjustable adjustable adjustable splines splines splines incorporated formulated compares outliers calculating price rely perturbations kinds conditioned narrow reconstructed reconstructed reconstructed reconstructed flexibility flexibility extending significance breiman breiman tools nearby definitions implications krogh krogh intuitive nonparametric periods dominant reproduce reproduce similarities treatment ensembles route relies stone limitation fitted approx indirect minus sine sine annals break tibshirani tibshirani tibshirani tibshirani tibshirani adopt retraining perturbed causing wahba wahba ease spaced possibilities rain concentrated modifying hastie hastie hastie hastie hastie community learnt chapman allocated inverted cole relates accounted turning drops intensive treating sigmoids expense lowe lowe quantify heavily smoother smoother smoother smoother smoother smoother smoother focuses diffuse err industrial evenly conditionally raises raises restrictive restrictive faced unifying battery battery whilst adjustments shortcut albeit albeit perturbing retrained regularisation regularisation regularisation philadelphia centred brooks visualisation opens olshen highlights adaptable generalised generalised fimction fimction fimction fimction fimction burgess burgess burgess burgess burgess pointwise wadsworth manifest business overcomes overcomes overcomes iee relaxing variate optimised optimised absorbed absorbed absorbed vedelsby vedelsby analysing viability observational facilitated stuetzle stuetzle fimctions fimctions fimctions accommodated accommodated needing converse nonlocal suffering parametrised unperturbed backpropogation hum lon monterey 
#@Burgess_A,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set networks networks training training training training training training training training training training training training training training output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number error error error error error error results results results results results results results results units units units units units information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance space linear layer layer layer layer layer case case shown shown shown shown systems systems systems systems values values values values values values values noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions unit unit unit unit distribution point single processing processing processing processing large large large large test test test test test test test test test test patterns patterns patterns patterns patterns class optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows shows shows shows shows shows signal simple simple simple gaussian gaussian gaussian paper paper paper paper paper paper examples small small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net net net net net net net net net net net net net net net net net net net net work task task task task task task task task task task task task points points features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification classification classification classification classification classification classification level trained problems problems problems problems problems random random random high high high high similar similar similar representation show section section section section section section section section section section section section line line line vectors real average average gradient note experiments experiments experiments dimensional result result university university university research independent defined target target table table table table standard standard standard standard terms prediction prediction prediction left left map present present low low low low sets sets sets sets sets sets sets sets sets sets range range learn learn learn learn learn learn learn learn learn learn learn learn learn learn learn nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous sample abstract back back find references due due adaptive introduction effect effect generated parallel tion tion tion change difference difference difference complexity measure measure signals representations representations learned learned higher part center center previous previous previous cases cases cases cases cases good binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary expected make make techniques correlation correlation correlation correlation correlation correlation correlation correlation correlation observed scale scale scale scale scale scale scale scale scale scale finite resulting classes tasks regression regions regions mapping mapping mapping mapping mapping mapping means dimension dimension dimension dimension made policy original original original artificial specific true cross cross provide compute perform perform perform goal goal related related connected connected connected distributions distributions accuracy larger larger larger larger descent nets nets nets nets nets morgan morgan morgan report version version code code code code code code code individual advances advances advances advances joint bias addition graph hinton curves san san bit bit conference capacity capacity choice free coding coding coding coding coding coding entropy provided provided finally selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation nature depends sampling simply measured discussion increases increases increases increases increases group predictions supported supported theoretical main main main main main main main main main main main journal ability future future makes noisy noisy noisy noisy noisy noisy noisy noisy noisy kaufmann kaufmann kaufmann typically reduced fully fully fully transfer transfer interesting interesting testing testing testing significantly significantly significantly trials trials trials trials trials squared squared direct supervised supervised supervised supervised early early early early early early attention minimize run added predict predict predict architectures improve correlations correlations similarity include previously unsupervised axis axis solve smooth yields modified interval improvement improvement risk risk sensitive sensitive increased grant grant grant constructed horizontal trial deviation predicted predicted boundary pass depend depend depend tangent tangent sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid clear clear practice learns learns mateo suggest encoding encoding drawn drawn california intelligence acknowledgements suppose longer ways simultaneously linearly linearly involves easy easy scales scales adding applying predictive decreases yield focus formation correlated correlated correlated correlated codes codes codes evaluated organizing showed similarly key reasonable measurements foundation avoid expect domains tests tests tests regular regular regular regular regular regular regular extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra extra uniformly uniformly encoded encoded situation plots identity graphs graphs graphs graphs strongly decoding contained cun allowing neuroscience stopping stopping stopping stopping gray gray gray gray gray gray sampled sampled sampled dot denker neighboring receive presents presents presents unlike poor poor poor poor poor poor access updating detail preliminary reducing examine mappings ideal root understand surfaces coefficient integer perfect noted mapped mapped epoch baseline extent simplest explain explain synthetic smoothness phenomena improves improves improves coded worse formalism shared ran simard toronto toronto demonstrates nsf mellon outer conjugate varies varies considerably prop prop carnegie cmu cmu amounts tional poorly backprop compares pittsburgh fall simulator simulator simulator findings patients deviations eventually hints hints extreme extreme lab lab room uncorrelated benefit benefit benefit benefit benefit benefit sort bin significance promising check biased biased neurobiology unlabeled definitions methodology embedding performances excellent separating combines becker surprising surprising expanded moved propagated francisco bins rich canada canada passing steepest ignore ignore tures std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std std integers integers integers informa abu mostafa thrun benefits benefits benefits expanding distinction distinction causing imagine arising invariances care formance baluja baluja mitchell mitchell bounding pomerleau expand carefully harder sized modality knowing behave mea worked worked vice correlate sigmoids cube moderate versa 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#@Caruana_R,de-Sa_V,
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#*network network network network network network network network network network network network network network network model model neural neural neural input input input input data data data data data data function function figure figure figure time time time time time time time set set set set networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output system error error error error results results results results units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden performance based based space weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case vector vector vector vector order order order order order values values values probability probability probability probability probability weight weight weight weight weight neurons neurons neurons unit recognition method method method method method approach approach approach approach approach approach pattern pattern point image image single single single processing processing processing processing control large large large neuron neuron neuron neuron rate rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal inputs inputs inputs form shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper small feature feature feature work methods methods points points points points points points points points points points classification classification classification classification classification classification process process process process current current trained trained trained trained problems problems problems problems problems random random random random high high similar representation show show equation equation equation equation equation equation section vectors vectors vectors vectors vectors vectors vectors vectors general real real real approximation approximation approximation approximation approximation approximation theory theory theory theory theory theory gradient gradient obtained obtained obtained obtained obtained obtained note experiments experiments dimensional dimensional computation solution solution solution solution found sequence sequence sequence standard terms distance distance connections direction direction present frequency sets press components basis basis nonlinear nonlinear outputs continuous continuous sample abstract computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due ieee ieee ieee positive positive positive positive procedure procedure procedure procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive mixture introduction introduction complex hand hand statistical statistical cost assume assume assume assume classifier lower measure chosen part part part previous previous theorem theorem theorem theorem bound required conditions represent represent correlation correlation correlation correlation observed forward forward forward forward finite classes classes classes classes total computed computed respect respect respect respect respect respect respect respect multi multi elements elements dimension dimension dimension made natural applications applications applications study study study study study obtain obtain obtain obtain obtain obtain obtain obtain obtain obtain obtain obtain vol vol vol samples samples samples samples samples samples samples samples true application application application desired desired desired desired desired desired desired provide compute compute determined experimental gain steps accuracy update update descent descent proceedings department loss consists internal code individual final final final addition sequences sequences sequences sequences sequences sequences sequences domain domain domain domain domain equivalent directly estimates estimates stage bit detection detection detection detection conference determine upper upper requires requires requires significant significant significant estimated estimated estimated estimated give give give derived derived derived derived developed criterion criterion criterion criterion associative associative associative associative associative associative associative associative associative discussion covariance describe arbitrary arbitrary arbitrary denote denote transformation close assumption assumption assumption stable stable stable stable stable stable stable proof proof proof proof proof proof proof proof finding amount common effective implemented assumed assumed theoretical require square including including unknown york special uniform principal principal principal principal principal principal principal principal squared details making bits perceptron advantage property sense subset subset subset subset engineering previously conventional conventional conventional conventional conventional observations observations works yields studies studies converge converge converge converge differential differential differential differential rl diagonal diagonal diagonal symmetric symmetric symmetric symmetric generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized bounded bounded organization organization risk constructed exists parts parts lead digital digital digital digital matrices matrices matrices matrices matrices matrices matrices matrices matrices feed feed feed feed locally clusters occurs column column row assumptions accurate bayes numerical numerical performs performs asymptotic constrained constrained constrained suggest suggest suggest largest largest largest demonstrated minimizing user user user user user user base base base explicit relation derive construct solving multilayer multilayer multilayer simultaneously simultaneously electrical involves develop equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium formed quality implies extraction extraction extraction yield yield yield stationary stationary stationary communication communication lemma lemma lemma lemma lemma lemma lemma transform transform transform transform transform transform transform organizing organizing organizing organizing organizing organizing organizing organizing organizing decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition slow slow performing performing performing performing tracking closed closed classified transactions transactions perceptrons perceptrons eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues weighting blind subspace batch automatic prove prove prove prove discuss discuss uniformly suitable divided schemes online online online online online online online online summary compact compact compact compact procedures strongly criteria criteria criteria hold hold hold hold hold hold duration satisfy satisfy generalize generalize generalize minimizes eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue received extract extract extract satisfies satisfies decreasing situations minimized explore updating relations relations relations association association association association recursive discriminant discriminant discriminant discriminant discriminant scalar scalar reducing fashion fashion mse mse mse mse mse int eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors naturally adapt separated academic contributions submitted established optimum optimum optimum optimum optimum asymptotically asymptotically asymptotically asymptotically derivation unstable unstable multiplication rapid commonly definite definite definite definite definite argument evaluating gains aim extracting attraction attraction attraction attraction lim lim lim converged converged instantaneous ordinary ordinary ordinary ordinary corrupted guarantee mobile mobile mobile mobile jth jth jth jth arranged generality communications communications communications significance imposed los belong belong receiver receiver receiver receiver substituting interference interference interference interference interference interference interference interference interference started washington belongs offers permutation permutation offer eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector std insensitive sequentially approx corporation rigorous rigorous rigorous constitute misclassification maximized transmitted transmitted formulate generalizations spaced constrain mhz mhz insights diag diag diag grouped dominated dominated denoting projecting cosine cosine lda lda lda lda lda lda lda lda lda lda lda lda lda lda lda lda lda lda lda det det det det eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen eigen infinitely infinitely infinitely infinitely differentiating differentiating demonstrating lowe lowe slot firstly orthonormal subtracting deals establishing triangular receivers demands edition counterpart irvine scatter scatter scatter scatter fore derivations aims collecting collecting avenue angeles visits visits visits roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury roychowdhury prohibitively separability separability lemmas fogelman webb webb cancellation cancellation cancellation cancellation equi nonsingular nonsingular nonsingular nonsingular nonsingular worthwhile nxn ljung ljung ljung ljung referring liapunov ode ode ode ode ode ode ode ode xlx optimised ucla gallinari gallinari hetero hetero hetero hetero hetero hetero hetero hetero hetero hetero hetero hetero hetero dii transmits transmits fukunaga fukunaga soulie equating limk limk limk limk limk limk multiplicity dio antennas alg alg unify unify lsb pxp lso 
#@Chatterjee_C,Roychowdhury_V,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output number number number number error error error error error error error error state state state state state state state state state state state state state results results results results units units units units units units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance weights weights weights weights weights weights weights layer layer layer layer layer case order order order order order order shown shown shown weight functions functions functions functions unit recognition recognition recognition method point single single processing large large large rate test test test test test test test analysis analysis class class class class inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows shows shows signal simple paper paper paper paper examples examples examples small small small size size size feature feature feature feature feature feature work work step step step features features classification current current current current current current trained trained trained problems problems problems problems problems problems problems problems problems problems memory memory memory similar similar similar representation representation representation representation architecture architecture architecture architecture show show show show show equation equation equation equation equation equation equation section section section section section section section section section section fixed line line general general general general general general generalization generalization generalization generalization speech speech states states theory term term term note note note university university university solution research research research research defined standard computer computer computer terms terms terms terms terms terms terms connections node node node node node node node node node node node node science science science prediction prediction prediction presented present present present activation activation nodes nodes machine machine machine machine machine sets sets learn learn learn position outputs outputs abstract applied back back back find find find references ieee propagation introduction introduction hand behavior behavior behavior behavior behavior behavior statistical effect effect effect generated generated change difference difference difference difference complexity variable word learned learned chosen previous previous required required required required required conditions represent represent represent represent represent represent fact fact techniques techniques length length length correct forward forward forward finite finite finite finite finite finite simulations simulations simulations simulations simulations simulations simulations minimum classes classes classes total total simulation simulation simulation simulation simulation computed performed mapping mapping mapping mapping means made knowledge original specific specific samples represented represented represented represented represented represented compared series series series define compute perform determined gain discrete steps steps steps steps connection report report institute institute consists internal internal internal internal internal internal internal internal represents represents represents represents connectionist difficult difficult difficult bias bias bias bias bias bias bias layers layers layers delay delay delay delay delay delay delay delay delay delay delay delay addition graph framework domain equivalent equivalent equivalent equivalent equivalent equivalent equivalent hinton hinton curve curve design transition transition transition transition transition transition san san san effects requires requires significant significant significant statistics speed randomly randomly lines path evidence simply technical limited close close close stable short short short theoretical theoretical theoretical require future including fit fit fit smaller interesting interesting significantly significantly york trials trials trials trials empirical empirical language language language language language language language language language representing representing representing call call making window window window description architectures architectures architectures improve recent recent recent recent reported include include include include identical identical identical machines machines machines machines machines side side engineering engineering engineering compare solve match match definition entire exists trial deviation wide wide wide wide wide wide wide feed feed feed width width width width width width generally demonstrate demonstrate demonstrate strength conclusion conclusion minimal minimal minimal row greater conclusions editors interactions performs performs strong demonstrated demonstrated california california california california labeled relationship construct construct longer solving factors factors factors factors factors describes mathematical dept dept dept implement remaining interaction shift versus versus boolean boolean phoneme updated showed lee understanding sizes completely updates past diagram diagram earlier earlier epochs epochs epochs delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays intervals string string string symbol construction transactions expect includes includes strings strings strings strings strings strings strings strings strings inter specifically absolute tests tests capable capable capable capable differ detect literature tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn plots plots online composed composed composed refer graphs kind kind repeated repeated repeated repeated repeated repeated repeated interpreted split follow notation giles giles giles giles giles giles delayed computes computes computes computes predictor subsequent presents bars diego diego diego poor create replaced biases biases biases helpful fewer fewer respond ideas ideas ideas detectors detectors detectors mappings mappings comparable momentum removed waibel waibel waibel waibel waibel induction induction induction induction induction induction induction hill concepts automata automata equally perfect changed subsets detector detector switching consist detected utility utility finds isolated languages languages languages languages languages languages languages languages languages languages languages percentage percentage percentage separable capabilities capabilities independence independence comparisons precisely constructing ran ran definite definite definite demonstrates demonstrates percent percent percent percent tional lack remove span summarized weigend incoming incoming suited acoustics kinds kinds windows wesley shifted shifted addison princeton princeton pick narrow narrow narrow narrow narrow narrow narrow narrow narrow perfectly perfectly perfectly repre repre stronger stronger familiar loops serves cottrell cottrell cottrell cottrell cottrell generalizes generalizes alphabet tap tap tap tap repeat repeat representational representational representational representational representational representational representational lang lang lang lang forecasting propagated reproduce insight jolla jolla repeatedly inductive inductive inductive inductive inductive inductive inductive inductive inductive stopped stopped discriminate ence unable outperform accept accept sig equivalently recursively ties uniquely regularity regularity reject reject representa home home concentrate careful individually cole register reveal reveal supports bill differing supporting wider nec nec nec nec helps ucsd ucsd diagrams diagrams copies tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns tdnns repetition repetition repetition repetition repetition repetition repetition functionally functionally functionally squashing sliding company longest confined edition mcgraw fsm fsm fsm fsm fsm fsm computable computable computable computable corn completeness daniel publishing wan wan wan wan wan wan accepting accepting shikano repeats lacking horne horne horne horne horne horne horne subclass subclass brooks reproduction hanazawa highlights rejecting rejecting bilities anova anova percentages negation lastly gershenfeld representable representable representable representable fsms investigates ended planned subclasses garrison confirming intuitions intuitions intuitions intuitions wid stretched ilk ilk ilk capa senting adverse rice rice rice nificant saves agreeing kohavi kohavi kohavi chitectures monterey 
#@Clouse_D,Cottrell_G,Giles_C,Horne_B,
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#*network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data function function figure figure figure figure figure time set set set set set set set networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number number number number number number number number number system system system system system system error error error error error error error error error error error error error error results results results results results problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden performance performance based based based based weights weights weights weights layer layer layer layer shown shown shown shown shown systems systems systems values values values values probability probability parameters weight weight functions functions method method method method method method method method method method method method method approach approach point point point point point single single single single control control large large large large large large large large large large large large local local neuron rate test test test test test test test analysis class class class class class optimal inputs inputs form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper small small small small small small net methods methods methods methods methods methods methods methods methods methods points points points points points points points points points points points points points points points points points points points points points points points points classification classification classification classification classification classification classification trained problems problems problems problems problems problems problems problems problems problems problems problems problems random high high equation equation vectors parameter theory theory gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained obtained obtained note dimensional dimensional university university university computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution research defined defined found found found found target target target target initial initial initial initial initial initial initial initial initial initial constant table table table table table standard standard standard computer terms node science present nodes nodes nodes nodes nodes sets sets sets sets nonlinear nonlinear nonlinear abstract find find convergence convergence convergence properties properties properties properties references due due due due ieee ieee introduction introduction statistical difference complexity lower measure measure chosen theorem theorem bound type type multiple multiple multiple multiple multiple represent equations equations equations equations equations equations equations equations equations equations equations make make fact fact forward simulations minimum minimum classes classes classes classes tasks total total total total total multi multi mapping optimization optimization global global vol compared desired desired provide proc perform power approaches approaches approaches approaches approaches accuracy contrast support descent descent nets department department final final final final final final considered considered considered solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions estimates estimates trajectory trajectory stage stage stage stage stage stage stage stage stage stage stage determine requires choice significant significant significant approximate basic con produce produce criterion types path path path path provided finally finally evidence backpropagation arbitrary close corresponds complete surface surface surface surface surface surface surface surface surface proof finding finding finding finding finding finding finding common theoretical main square degree degree makes objective simulated typically typically unknown mlp transfer interesting interesting significantly significantly significantly ratio ratio ratio increasing increasing trials trials empirical empirical squared numbers numbers numbers iterations polynomial produced light perceptron architectures recent typical typical reported introduced quadratic subset engineering engineering engineering interest varying tions solve studies converge converge evaluation bounded bounded interval grant constructed exists trial trial trial trial correctly correctly correctly feed move generally generally runs runs runs starting trajectories trajectories trajectories trajectories trajectories conclusions tangent accurate accurate numerical numerical numerical regularization regularization regularization exist exist exist exist exist min minima minima minima minima minima minima minima minima minima minima minima minima minima minima annealing acknowledgements appears appears appears produces solving solving solving sequential sequential plot stability mathematical mathematical distinct distinct distinct distinct distinct distinct distinct distinct explicitly electrical electrical yield choosing national stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary overlap solved solved evaluated open showed partial spaces foundation norm euclidean classified thesis characterized selecting aspects efficiency capable capable capable capable suitable suitable suitable society differ differ divided paths paths paths paths paths paths comparing ten summary compact compact compact repeated procedures procedures procedures allowing heuristic lie manifold manifold principles illustrates illustrates satisfies presents bars bars unlike american poor poor xor xor xor xor xor xor xor xor xor xor xor create accurately hessian divergence divergence existence existence mse mse mse referred proved surfaces surfaces smallest necessarily extremely extremely ensure subsets subsets subsets rank noted algo separated perceptton initialized consist extent phd finds synthetic established percentage trivial distinguish track guaranteed briefly benchmark perspective sections producing producing producing constructing constructing choices commonly mellon mellon mellon conjugate conjugate conjugate conjugate conjugate requiring requiring carnegie carnegie carnegie empirically empirically cmu cmu dark pseudo continuously maxima maxima maxima maxima exhibits pittsburgh pittsburgh pittsburgh characterize serve qualitatively conclude extreme extreme globally globally classifying classifying newton newton newton newton newton newton newton secondary intractable saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle equivalence equivalence equivalence equivalence equivalence equivalence equivalence fix princeton rithm conditioned numerically numerically numerically difficulties difficulties difficulties overcome overcome siemens attractive occurring fail disjoint canonical reliably reliably reliably excellent heavy connect topological infinity infinity sphere yang yang yang yang yang yang yang insight insight reader repeatedly repeatedly verification correcting discovered characterization convergent convergent sequentially crossing solves tables tables forced incrementally icassp auxiliary factorial regularized regularized cation reveal exhibited signs gorithm completed gratefully remarkable opti characterizing hyperbolic corporate quantify heavily establishes suffices connects believed inefficient arrives implied relaxed ensuring unexpected sorted diverge diverge damping vergence mization putational attracted fundamentally ece ece conceptually damped damped damped illustrating accessible bifurcations sought sought terminated symmetries acknowledged differed solu deformed rogers historical providence concluded disconnected disconnected jour weeks classifi useless meets negated llll contrasted tremendous deficient surveys diverging tracing unsolved virginia ensured monographs ception ably island econometrics interchange dle rhode detroit mip unaware 
#@Coetzee_F,Stonick_V,
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data data data data data data data function function function function function figure figure figure figure figure time time time time time set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output number number number number number system system error error error error error error error error error error error error error error error error error error results results results results results results results information information problem problem problem problem problem problem problem problem problem problem models models performance performance performance performance based based based based based based based based based based space linear case case case case case order order order shown systems systems systems systems systems systems systems values parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight functions functions distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method approach approach approach approach approach approach approach point point point point point point processing control large large local local local rate test test class optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form form shows simple simple simple gaussian gaussian gaussian paper paper paper paper paper paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples small size size work work work methods step step step points points points points points points points problems problems problems random random random random random random memory response response similar representation show equation equation equation section section section section section section section section rule parameter parameter parameter real approximation approximation average average average average average theory term term term term term note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional computation computation computation research research research research independent defined target target initial estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard terms terms terms prediction prediction prediction left low low machine machine machine machine sets sets sets sets sets press press learn position position components outputs sample sample sample abstract back references component component component due due ieee important adaptive introduction introduction estimation estimation estimation statistical statistical statistical statistical statistical statistical effect variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance cost cost search tion tion change change change change change change difference assume assume assume assume chosen chosen chosen higher higher higher center center previous previous previous cases cases cases type required required good good bayesian bayesian expected expected expected expected expected expected make techniques techniques region correlation correct errors resulting resulting resulting ing tasks tasks regression regression regression regression regression regression regression regression regression regression regression regression computed computed computed respect performed called times means means made applications applications filter original original original original artificial specific specific true compared compared cross cross cross cross cross cross cross cross cross cross cross series series series define define compute compute compute compute proc perform perform perform active active active active active active active mit accuracy source source selection selection selection selection selection selection selection proceedings implementation implementation technique technique technique kernel kernel kernel kernel advances joint joint joint joint difficult bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias considered considered cambridge cambridge computing computing computing domain equivalent equivalent experiment experiment additional additional estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates design design trajectory trajectory trajectory conference efficient requires choice significant statistics free free free free estimated validation validation validation validation validation validation validation give produce produce produce coding weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted randomly randomly robot robot robot criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion actual selected selected evidence sampling sampling sampling sampling simply discussion describe describe describe describe describe group denote denote tested assumption assumption assumption corresponds surface actions actions predictions predictions amount common common common effective effective assumed assumed shape theoretical eds eds eds journal journal future future makes noisy noisy noisy objective typically unknown unknown jordan significantly york york york empirical empirical empirical squared squared squared squared squared squared details international magnitude combined minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize minimize produced run added predict denotes denotes discussed discussed discussed discussed discussed discussed discussed directions recent correlations robust apply apply introduced strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy interest dimensions sufficient sufficient varying previously approximately approximately match converge achieve trans evaluation entire arm arm arm arm arm arm arm arm parts expression studied suggests locally locally locally locally locally locally locally locally locally deterministic deterministic deterministic deterministic white white generally demonstrate runs runs assumptions depend depend accurate accurate accurate accurate designed performs practice practice constrained constrained constrained suggest strong presence presence presence presence drawn drawn drawn demonstrated minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing averaged introduce force reference reference reference reference reference monte derive derive carlo produces produces ways estimating estimating estimating estimating estimating estimating describes describes describes describes distinct confidence explicitly simultaneously averaging predictive minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization expectation expectation expectation select select select select select select select decreases yield estimator estimator estimator learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner variation evaluated centered centered forms forms margin reasonable reasonable smoothing smoothing performing spaces spaces fitting fitting fitting purpose add add construction query query query query query query query query query query query query query transactions david expect expect building exploration exploration exploration exploration exploration box box box coordinate maximize maximize maximize candidate candidate candidate candidate candidate candidate priors domains domains domains straightforward selecting selecting selecting selecting selecting selecting selecting selecting selecting uniformly uniformly uniformly mackay mackay comparing procedures prob heuristic content criteria strategies strategies strategies write write write write predictor predictor predictor attempt tesauro situations minimized minimized wiley poor poor create estimators estimators optimized integral hall biases reducing mse mse int workshop surfaces neu smallest smallest perfect queries queries queries queries queries queries queries queries queries queries queries queries obvious greedy portion assumes assumes observe explored academic attempts synthetic seconds seconds seconds integrate years defining defining defining fairly analytic answer correction correction worse inside perspective purposes sections strictly strictly ran ran leaves commonly involve angles angles begin optimize addressed explained argument argument improvements composite composite empirically empirically bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap leave atkeson atkeson atkeson frequently operate measuring incorporating geman geman marginal unbiased unbiased unbiased unbiased unbiased unbiased unbiased differentiable globally consistently don representative pac benefit optimizing concerned adds promising moment biased biased observing ral ylx ylx ylx optimally planar planar planar selects days alspector passive conjunction facilitate lawrence candidates offer clean motions route erlbaum correcting inductive dietterich dietterich ignore default divide speaking speaking outperforms outperforms outperforms yielded drop drop slight kinematics outperform outperform outperform accept deriving break failed tibshirani tibshirani residuals residuals residuals residuals residuals corrected decomposed decomposed covariances covariances constitutes hillsdale rain remainder remainder cohn cohn cohn cohn cohn cohn cohn cohn cohn cohn cohn cohn intuition chapman concentrate argued complementary unconstrained unconstrained sta places thousands mini simplifies lems learners learners learners learners bienenstock justified savings clarity industrial dom russell appealing resampling val rare tip believed schaal schaal schaal tells restricting arrives contrary statist thing ance corn cleveland cleveland cleveland lwr lwr lwr lwr lwr lwr lwr lwr lwr validated validated validated bootstrapping amer kong kong sparc connor connor dilemma excluded simulates assoc notably concise univariate comprise plutowski plutowski enormous brevity explosion telecommunications periments efron efron efron efron shoulder shoulder temporarily selec theta disambiguation elbow elbow doursat corrects pursuing tistical juggling querying noteworthy dollars money gather kindermann fedorov fedorov queried mize soo uncorrected uncorrected uncorrected econometrics isn rion strat bootstrapped crite trainin trainin egy fewest minimiza rected 
#@Cohn_D,
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#*learning learning learning learning learning learning learning learning model model model neural input input input input input data data data data function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number results results results results results results information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance based based based based space space space space space case case case vector vector vector vector order order order shown shown shown systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach point point point point point single single single single single processing large large local local local rate class optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper examples small work work task task task points points points process process process process process process process current structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems problems problems problems random random random random random random high high similar similar representation representation representation show section line parameter parameter approximation approximation theory gradient obtained obtained obtained term term experiments experiments experiments dimensional result result university threshold variables variables solution solution solution solution solution solution research research research research independent log log defined defined defined initial initial estimate estimate estimate estimate standard standard standard standard standard science left map present present low nodes nodes machine press press components components sample sample sample abstract back find computational computational convergence density density density density density density references component important introduction action action complex complex circuit estimation behavior effect generated generated generated generated generated cost cost cost cost cost cost cost cost cost cost cost search search search search search search search search search search search search search search search search search measure signals learned learned learned chosen chosen chosen part previous bound cases required required required required required long conditions represent distributed expected expected fact proposed probabilities probabilities probabilities probabilities probabilities probabilities finite finite minimum minimum resulting total total respect performed called regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization natural global global global knowledge knowledge negative artificial artificial relative samples samples samples samples samples samples samples samples samples samples samples samples true true true true true true true true compared define define perform goal related related related related related distributions distributions distributions distributions distributions distributions equal approaches approaches mit steps steps larger contrast update descent dependent dependent report institute technique technique advances joint joint joint joint joint joint difficult difficult exp graph graph graph framework framework framework cambridge cambridge computing computing equivalent directly directly additional additional additional solutions effects bit conference conference determine efficient efficient choice significant statistics statistics statistics speed con derived randomly conditional conditional conditional conditional conditional conditional clustering bounds entropy entropy finally iteration iteration nature sampling sampling simply achieved measured technical describe group close close complete actions actions actions finding finding finding finding finding amount common effective generate generate generate generate supported main adaptation fit simulated simulated pairs underlying underlying underlying underlying unknown jordan jordan jordan jordan jordan technology york head head head head consistent trials matching uniform uniform empirical empirical empirical operation operation operation operation operation representing numbers numbers iterations max max max pre bits international early magnitude combined minimize choose choose choose description description improved population population population population population population improve advantage pair element element include include identical identical identical sense subset subset sufficient highly approximately approximately volume match match evaluation positions positions positions improvement grant constructed constructed parts parts occur suggests wide move touretzky clusters clusters clusters clusters runs half half critical assumptions conclusions depend editors reward peak peak peak performs performs performs performs faster temperature taking taking intelligence turn variety variety variety start exist groups groups groups minima minima program annealing annealing force denoted boltzmann pro derive construct construct produces ways ways generating generating generating generating generating generating estimating estimating estimating estimating laboratory distinct simultaneously mutual events formed boolean yield choosing extracted independently stages stages estimator estimator estimator estimator estimator learner learner learner variation densities densities densities densities evaluated approximated sizes sizes completely completely completely similarly converges classical spaces normalization generation initially string advantages david existing exploration color color color color determines plotted prove maximize maximize maximize candidate variations partially structural successfully determining straightforward straightforward middle middle efficiency closely closely closely closely capable uniformly uniformly genetic genetic genetic genetic genetic genetic genetic genetic fine capture capture capture capture capture capture capture graphs graphs repeated procedures procedures dis return running minimizes minimizes leading leading leading attempt subsequent approximating acknowledgments powerful access collection experience put association divergence divergence divergence divergence divergence reducing successive successive history incremental incremental combine relationships relationships office maximizing notion hill hill closest analyze created thought greedy algo explored explored extent attempts attempts attempts attempts established established optimum optimum optimum massachusetts pairwise pairwise pairwise pairwise pairwise directed agreement agreement adjacent adjacent benchmark baum baum worse comparisons closer strictly incorporate incorporate incorporate gradually optimize lowest mellon reflects improvements greatly carnegie tional poorly peaks peaks peaks peaks peaks peaks peaks peaks peaks employ maxima maxima maxima maxima maxima gains synthesis ture ture maximizes maximizes maximizes popular occurrence logp logp logp chose attraction begins median consistently consistently representative benefit benefit benefit assign pick optimizing ordering discover naval establish climbing kullback kullback proceeds replacing exploit removing splitting intuitively guide preparation intuitive inferior date reliably evaluations evaluations evaluations evaluations evaluations evaluations evaluations embedding paul paul holland holland lang lang searching uni captured candidates candidates permutation permutation permutation insight surprisingly fitness fitness propagate approximator interestingly temperatures temperatures approx land slight fellowship basin ties randomized randomized randomized randomized randomized encodes suboptimal pieces utilize exception obtains regularity arg tor imagine principled principled attempted attempted equality insights baluja baluja baluja rithms goals crossover crossover crossover crossover crossover crossover crossover crossover crossover gas gas gas gas gas labs landscape landscape landscape landscape retain increasingly importantly denver preserve preserve happen mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic mimic knowing thousands struc struc mini tail tail tail tail viola viola viola oscillate hoc mistakes condi tribution optima optima optima optima optima kirkpatrick kirkpatrick beneficial beneficial lying successively communicate colors computable charles charles faced tenth shortly mutation probabil ceedings diverge progresses pendent occasionally pull permutations permutations caruana caruana compress ities sible versity viable helped favorable nth machinery sorts ana michigan ponents iix ixi ixi beats brute colored sole ditional perrone preceded preceded millions millions vecchi vecchi structurally twelfth unconditional unconditional notable initiative accomplishes probabili unreasonable coloring coloring coloring coloring coloring programmer gelatt gelatt liebler liebler garrett garrett intent trailing trailing trailing ili cease randomization infrequently filnction interests ola inl contradictory diminished dod lxi lxi lxi lxi lxi greg conditionals uts jeremy jeremy granted firmly genetics enjoyed communicates dimensionm pitfalls multidisciplinary pll wla excel respon hindered offspring 
#@Isbell_C,Viola_P,de-Bonet_J,
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#*learning learning model model model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data data function figure figure figure set set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number error error error state state state state results results results results results results results results results results results units information models models models models models models models models hidden hidden hidden performance performance performance performance performance based based based space space space weights weights weights weights weights case vector vector vector vector order order order order order order order systems values values parameters parameters parameters parameters parameters parameters noise noise noise weight weight weight weight weight distribution method method method method method method method method method method method approach approach approach image image image single single processing processing processing large large analysis analysis analysis matrix matrix matrix matrix shows signal algorithms algorithms simple simple simple simple simple simple simple simple simple gaussian gaussian gaussian gaussian examples examples examples small small small small small small size size size size work methods methods methods methods methods step step step step step step step step step step field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field level level current structure structure structure structure structure structure structure structure random random random similar similar similar show show equation equation equation equation section section section section section vectors images images parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation average states theory theory theory theory theory obtained term dimensional university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation research research research independent log log sequence initial constant table table table estimate estimate estimate estimate estimate estimate standard standard terms terms science left presented presented presented sets maximum maximum press learn continuous sample sample abstract applied applied computational computational computational likelihood likelihood likelihood likelihood likelihood references component due due positive procedure procedure introduction complex complex hand estimation estimation estimation estimation estimation statistical statistical statistical effect effect generated generated generated generated variance variance difference difference complexity complexity complexity variable variable variable variable chosen higher part good binary binary markov markov markov make fact fact techniques correct correct correct correct correct probabilities observed errors scale simulations simulations simulations simulations simulation simulation computed respect sum performed called called called elements elements means means potential made study study study em em em em em em em em em em em em em em em em em em em em em em em em em em em em obtain artificial represented true true true true true compared compared compared series series provide connected distributions discrete mit mit steps steps steps steps steps comparison larger larger larger fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields selection report report report department version version version consists individual individual advances joint joint joint joint joint final final exp considered cambridge directly estimates estimates estimates estimates estimates estimates estimates estimates estimates stage efficient full statistics world estimated estimated estimated estimated estimated estimated give give produce conditional clustering lines product sampling simply discussion covariance covariance technical increases increases increases close close assumption complete assumed generate supported eds eds end instance cluster objective underlying needed unknown coefficients jordan jordan jordan jordan interesting significantly york uniform empirical squared squared squared iterations iterations iterations max combined added added denotes improve improve improve improve typical typical reported introduced cognitive recently engineering compare compare observations approximately approximately volume tions correspond correspond converge trans trans diagonal mixtures positions positions separation grant horizontal suggests suggests deviation deviation matrices matrices matrices matrices matrices matrices correctly touretzky conclusion place row greater reduce conclusions sigmoid accurate numerical performs performs performs performs exponential propose taking physics physics physics reduction intelligence averaged introduce annealing denoted acknowledgements explicit explicit longer longer longer ways estimating estimating vertical dept implement category physical involves remaining remaining easy easy belief quality expectation expectation expectation evaluated evaluated evaluate evaluate evaluate showed showed approximations approximations approximations sizes expansion purpose iterative avoid building figures blind sciences sciences extension illustrated successfully simplicity simplicity identified efficiency modification modification modification modification modification modification modification delta latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent modes situation situation identity soc procedures procedures success interpreted contribution hold notation notation gibbs involved realistic realistic ill leading approximating tesauro situations carried wiley essential investigate exponentially involving estimators estimators estimators dataset dataset behaviour fewer giving giving ideas tech tech reliable root complicated possibly predicting created equally quantities obvious taylor taylor taylor taylor taylor message multivariate consist simplest spin rows pairwise formula trivial crucial failure expensive glass correction correction correction straight straight closer producing producing products scientific read incomplete qualitative fluctuations evaluating double profile profile profile lack introducing frequently rep differs maximizes marginal datasets substantial expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations jaakkola jaakkola converged softmax wesley univ extreme cor naive naive naive naive naive naive naive naive naive naive naive representative ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani benefit leen notes feasible feasible addison summing summing conditioned jth connecting consideration numerically numerically simplify city check methodology adequate preparation tap started heavy saul saul zhang zhang zhang expanded expanded bad realization omitted omitted indicator statement explains dempster dempster johnson outlined rms rms rms rubin rubin benefits encouraging adopt pointed ease factorial factorial care care care bounding disadvantage employing harder buhmann buhmann laird laird west west west algebra indication refined dramatic hofmann hofmann corrections corrections corrections answers cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity spite expansions circumstances lecture observables observables observables observables observables observables remarks restoration council institut ers clarity realizations incorrectly appealing calculates alan scenarios ignores informatik statist statist zeros brackets meant categorical bonn energies indi replaces imum degrade degrade approxima fiir ample superscript mention parisi parisi parisi parisi parisi mike yij yij confident refining singapore pared kronecker brevity iai factoffal stud eij eij eij eij eij eij postulate redwood wit advocated analysing virasoro virasoro virasoro titterington titterington titterington titterington titterington titterington titterington titterington ied stats stats aea 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#*learning model model model model model model model model model model model model model neural neural neural data data data data data data data data data data function function function function function function function function function function function function function function function function function figure figure set set set set set set set set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm error error state state results information problem problem problem models models performance space linear linear linear linear linear linear linear linear linear linear case case order order shown shown shown probability probability probability probability probability probability probability probability probability probability noise noise distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition method method method approach pattern pattern pattern pattern point point image single control control large local patterns patterns analysis matrix optimal optimal optimal form form form form form form shows algorithms algorithms algorithms paper paper paper paper paper paper examples small size size size feature net net work work cells step step field field field features process process process process process process process process process process process process process process process process process level level current current cell structure structure random random random random random similar representation representation show show show show equation equation equation equation equation equation equation equation equation equation section section section section section rule images average average obtained term term term experiments result result university variables variables variables variables variables variables variables variables variables variables variables computation computation computation independent log defined defined defined dynamics initial initial constant constant constant standard standard standard standard standard computer computer computer computer terms distance distance distance distance distance distance distance distance distance distance distance distance distance node node node node science direction direction direction direction nodes nodes nodes nodes nodes nodes nodes nodes nodes maximum range position components continuous continuous continuous continuous continuous continuous continuous sample abstract applied find computational properties references component stochastic stochastic stochastic stochastic ieee ieee ieee ieee ieee important important mixture introduction complex hand estimation statistical statistical statistical statistical effect effect effect dynamic generated cost cost cost cost cost cost cost cost cost search search search tion tion energy energy energy energy energy energy energy energy energy difference measure measure measure measure measure measure measure measure measure measure measure binary binary binary represent represent bayesian bayesian bayesian bayesian bayesian equations equations equations fact fact fact fact techniques techniques techniques region proposed correct correct correct probabilities errors errors errors minimum resulting ing ing ing computed computed respect respect sum means means potential potential potential potential potential potential potential potential potential natural global global global global global global global study knowledge em em em samples represented represented represented compared cross cross series series series provide compute compute compute location determined experimental experimental experimental experimental goal goal goal related related distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal comparison comparison connection connection update update update update update update update update update update update update update update update update nets proceedings proceedings words words words department technique technique technique technique technique consists individual represents represents connectionist connectionist final exp exp exp exp exp exp exp exp exp exp graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph framework framework framework computing computing computing computing computing equivalent equivalent experiment curve curve curves effects conference vision vision vision basic basic basic basic con con weighted weighted weighted weighted clustering developed levels criterion provided provided provided finally simply denote complete common common effective effective effective effective effective effective effective assumed role main main main main main main square instance instance degree development simulated account interesting interesting significantly significantly york york mechanism consistent consistent structures matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching principal representing representing max max max pre international international frame idea idea idea idea idea added added description recent recent property pair similarity movement reported include subject identical quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic array recently recently interest interest compare compare conventional match match match match match match match match match match match match match match achieve rl evaluation locations modified constructed lead studied derivative derivative derivative matrices matrices matrices setting demonstrate demonstrate starting conclusions conclusions central differences differences measures exponential exponential constrained constrained temperature taking physics physics physics physics drawn solid proportional relationship averaged derivatives derivatives derivatives derivatives derivatives derivatives derivatives manner manner connectivity configuration annealing annealing annealing annealing explicit suppose suppose relation pro pro pro construct construct edges perception generating generating describes label label label mathematical involves involves develop develop mutual adding equilibrium applying applying applying quality potentials potentials potentials potentials potentials potentials potentials expressed review transform controlled controlled controlled fraction fraction fraction fraction fraction fraction fraction fraction soft soft soft suggested partition key partial partial reduces tracking distances distances assigned coupling coupling formulation inter assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment specifically tests structural structural structural structural structural structural successfully straightforward importance uniformly suitable society modification successful literature literature efficiently genetic genetic plots graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs induced induced prob prob dis dis superior issue symmetry lie contribution contribution notation gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs quantity simplified relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation dot dot providing modelling modelling modelling remain schedule updating updating updating relations relations relations detail issues issues dotted reducing matches matches matches matches matches matches investigated func analogous matched matched matched matched matched matched matched act naturally configurations thought ensure quantities versions consist contributions contributions synthetic synthetic ment briefly considerable stress leaves arise potentially res meaning addressed fluctuations consistency consistency consistency consistency consistency consistency consistency consistency consistency consistency amounts red dots ity maintain aim aim aim aim geman geman geman geman richard sums sums replace hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming hamming conclude display yuille contribute pose corrupted corrupted contextual contextual sort formally summing proceed plays logarithmic exploit exploit symposium intuitive wilson wilson wilson wilson wilson wilson wilson wilson wilson wilson substituting mjolsness regarded regard captured originally offers modelled insight stimulated reveals reveals arrive matter contact route extensively relies statement papers papers tures adopted andrew radar outperforms outperforms maintaining gold gold gold gold gold gold clique graded formulate descriptions associate mutually concentrated exclusive pami pami pami pami compensate scope relates relates topic deleted memoryless memoryless barrier confusion ation exploited struc bridle bridle bridle voronoi voronoi lems lems appearing appearing appearing restoration attributed firstly locate exper dominates optimisation optimisation optimisation optimisation optimisation optimisation optimisation optimisation optimisation optimisation optimisation hancock hancock hancock hancock hancock hancock hancock hancock hancock hancock hancock cast rangarajan rangarajan rangarajan rangarajan rangarajan corrective seed triangulation neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood tance smc relational relational relational relational relational relational relational relational relational relational relational relational relational relational relational relational amenable confined protocol counterpart cess cess convey potts probabil refine deleting predefined relax demanding neigh contributing ansatz ansatz mft fluctuation fluctuation fluctuation modifies apparatus apparatus rom rescaling draws novelty imagery deformable ism compound delaunay delaunay delaunay delaunay generalised simplistic shapiro optimise assump doubly comment optimising insignificant ingredients ingredients resides resides crete effected effected corruption corruption corruption corruption corruption corruption discus evans surviving surviving adjacency realised realised edit optim factorised initialise hitherto infra imental inexact inexact bracket graduated graduated graduated graduated uration eccv isation corrupt 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#*learning learning learning learning neural neural input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function time time time time time time time set set set set set set set set set set set set networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number number number number number number number number number number number number number number number number number number number number number system error error error error error error error error error error error error error results results results results results information problem problem performance performance space space space space space space space space space space case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown values functions unit recognition method approach approach approach approach pattern point image image processing large local analysis analysis analysis analysis analysis analysis analysis analysis analysis optimal form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple small feature work work work work methods step points points points points points points points points points points points classification classification classification classification level level level trained cell structure structure structure structure structure structure problems problems problems problems high high memory similar representation show show fixed fixed line line line vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general parameter parameter parameter approximation average average theory theory obtained obtained obtained note note note experiments experiments activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university variables variables research research research defined defined sequence initial table standard terms terms terms terms terms terms terms distance distance distance distance science map phase phase frequency sets sets sets sets sets sets sets sets sets press nonlinear abstract applied find find find convergence convergence convergence convergence density properties properties properties references component component component due ieee ieee procedure procedure introduction action statistical statistical effect effect effect generated generated variance variance variance cost tion tion energy energy difference variable variable variable spatial spatial lower lower measure measure measure measure measure measure word higher higher higher higher higher higher center type type type type multiple multiple multiple multiple good good expected expected make make fact fact techniques techniques techniques techniques techniques techniques proposed correlation correlation correlation correlation correlation correlation correct forward finite minimum minimum minimum minimum minimum resulting ing ing total total computed computed computed computed computed multi times times times mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means means means means means means means means means factor factor factor factor dimension dimension dimension dimension dimension dimension study study study study original vol vol vol vol vol vol artificial artificial artificial samples represented true true true compared series series define compute compute proc perform perform perform experimental related related related distributions distributions distributions distributions distributions discrete equal equal equal equal approaches mit steps steps comparison comparison comparison comparison comparison larger connection update update descent dependent dependent dependent dependent dependent institute institute department technique technique technique technique consists internal code code code code code code code code code code code code code code code code code code code code code code code code code code advances ai maps maps maps maps maps maps maps maps maps maps framework cambridge directly directly additional additional additional view solutions solutions design design design limit effects effects effects effects full significant significant significant statistics basic give con produce produce randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed actual constraint simply biological associative achieved measured discussion discussion discussion normal normal normal normal normal normal normal transformation transformation transformation limited proof finding finding amount amount common common shape supported theoretical theoretical theoretical main main eds end end ability ability cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster future degree degree degree including objective needed combination unknown technology significantly significantly significantly increasing empirical empirical empirical empirical empirical empirical empirical principal principal principal squared squared squared squared squared squared squared numbers numbers numbers numbers iterations direct normalized idea combined combined combined combined combined combined run light improved discussed recent recent recent exact property pair similarity reported apply introduced identical identical sense relevant interest dimensions dimensions dimensions dimensions dimensions dimensions compare compare unsupervised unsupervised observations volume volume volume match correspond pca studies achieve evaluation grid grid grid grid grid grid williams organization grant exists concept scaling scaling scaling scaling scaling scaling scaling scaling scaling alternative locally clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters setting runs conclusion starting minimal competitive differences differences measures accurate accurate designed designed clear performs performs practice strong external drawn intelligence intelligence minimizing minimizing user exist question acknowledgements produces index index index index index index index index factors factors metric coordinates coordinates dimensionality dimensionality dimensionality transformations remaining slightly consisting consisting consisting consisting applying minimization springer springer springer extraction letters decreases decreases yield yield expressed overlap restricted restricted restricted updated organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing showed forms completely partition partition partition partition updates updates allowed sign classical spaces iterative remains remains distances distances distances distances distances distances distances distances distances distances distances distances distances kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen topology topology topology topology topology transactions transactions existing includes coordinate sciences determining compression closely closely differ effectively literature literature projections comparing comparing online online online traditional traditional traditional traditional traditional traditional procedures procedures prob dis lie lie lie gray built comp quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization consisted tesauro decreasing remain rapidly detail replaced replaced limitations limitations limitations limitations limitations tech combine notion notion examined math psychology rank versions noted noted som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som precise mapped mapped mapped shapes multivariate multivariate multivariate multivariate detected established ment pairwise pairwise formula formula formula formula guaranteed defining capabilities caused tool tool tool worse worse worse worse reasons comparisons comparisons comparisons comparisons berkeley worst bishop bishop bishop bengio bengio bengio commonly separately author cybernetics radius radius argument questions improvements reflect berlin aim popular ordered marginal gave gave gave replace decreased age findings findings deviations multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional distortion distortion distortion distortion distortion distortion distortion distortion distortion distortion distortion initialization notes cooper cooper cooper cooper formally guarantee guarantee oxford restriction restriction restriction recover perfectly ordering ordering ordering ordering ordering partitions nonzero nonzero nonzero printed communications wrong abilities obtaining symposium alphabet alphabet planar planar planar planar planar planar planar planar planar performances performances started james iteratively codebook overview topological evident spherical counter similarities similarities properly steepest agree variants stopped assigns assigns counts outperforms yielded schulten numerous gtm shepard shepard shepard ter vec outperform ent preserving preserving preserving preserving preserving poses big tor reflected representa factorial factorial principled visualization visualization visualization academy employing anal misclassified discretization preserve preserve book book book book book book book book book book book book book book book book book book book book book book book book investigations obermayer things examination mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds preserves preserves preserves january ate crude crude european bold pearson pearson appealing inherently bottou bottou bottou ters quantizer quantizer quantizer quantizer preservation preservation preservation grids grids grids neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood neighbourhood isolation contrary iid dimen lewis ready mul denominator denominator brought recovering recovering sponsored ysis comprehensive comprehensive stat pull blurred pointers advice corr centroids centroids centroids centroids centroids centroids centroids centroids strongest fbr unclear clus clus gorithms ministry psy pared reproducing reproduction reproduction reproduction reproduction brevity helsinki aver implication lbg numerator numerator doctoral correla nique tributions entails heuristically transport speak orderings extremum nonoverlapping austria austria xii variate till masked austrian austrian austrian austrian federal compar vienna vienna vienna vague grand rand rand rand rand rand answered answered pled abbreviated sionality halt jolliffe jolliffe 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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural input input input data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training algorithm algorithm algorithm number number state state state state results units units units units units units units units units units units units units units units units units units units units units units information information information information information problem problem problem models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based space space space weights linear linear linear linear linear linear layer layer layer layer case case case case case case order shown shown shown shown shown shown shown shown systems systems systems systems values values values values values values values probability probability probability probability probability parameters parameters noise noise noise noise noise noise noise noise functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method approach point point single processing processing processing large local rate rate analysis analysis shows shows shows simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples examples small small net work work task task task task task methods methods methods methods step step step field process trained trained trained trained trained structure structure problems problems random random random random random random random random random random similar similar show show show 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continuous continuous sample sample sample sample abstract applied computational density density density density density density density density density density properties likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due procedure procedure procedure procedure procedure procedure procedure decision decision propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex behavior behavior behavior generated variance variance variance variance variance variance parallel tion variable variable assume assume lower higher part previous theorem cases cases cases cases cases type required binary binary binary binary binary binary binary binary binary long represent distributed distributed distributed bayesian bayesian bayesian equations equations markov markov markov markov markov markov markov make region proposed proposed proposed proposed proposed correct observed observed observed observed scale simulations classes ing total simulation computed computed computed multi sum performed performed performed called times times factor factor factor optimization feedback knowledge em obtain obtain negative original artificial artificial represented represented compared application application perform perform eye eye determined related posterior posterior posterior connected connected distributions distributions distributions distributions discrete discrete discrete discrete equal approaches approaches approaches mit mit mit mit steps comparison larger contrast fields morgan morgan proceedings department version consists advances advances advances joint joint joint joint connectionist connectionist connectionist difficult difficult difficult difficult difficult difficult exp exp exp exp exp bias layers graph sequences considered framework cambridge cambridge cambridge cambridge computing computing computing domain domain experiment experiment experiment directly hinton hinton hinton hinton hinton hinton hinton hinton curves transition san san top top top top top top top top top top effects conference determine determine efficient requires requires statistics give con produce produce derived randomly randomly randomly conditional conditional conditional conditional conditional conditional developed developed developed types types selected depends sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling discussion transformation fast complete short supported require require main easily easily easily rumelhart including including kaufmann kaufmann simulated probabilistic needed combination jordan significantly structures uniform uniform uniform uniform mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode operation operation principal representing representing making making making bits bits normalized experts expert expert expert expert expert added added description correlations element element moving moving include include machines machines quadratic hierarchical hierarchical hierarchical inference inference inference inference inference sejnowski cognitive dimensions highly highly unsupervised unsupervised approximately volume converge converge converge rl rl rl trans evaluation chain chain chain chain chain chain symmetric bounded interval interval interval interval interval williams increased horizontal scaling deviation deviation alternative touretzky touretzky touretzky deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic boundary pass pass demonstrate greater segment valued valued valued valued valued valued valued editors editors editors editors editors sigmoid bayes designed mateo propose integration physics drawn drawn drawn drawn drawn drawn sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal proportional intelligence intelligence variety variety variety iii force acknowledgements boltzmann boltzmann boltzmann explicit appears pro monte monte monte monte monte carlo carlo carlo carlo carlo produces produces ways generating changing changing segments segments segments implement implement implement multilayer multilayer multilayer multilayer linearly linearly remaining easy easy belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief applying formed expressed depending correlated viewed influence densities densities densities evaluate controlled labels labels activities activities activities activities activities activities activities activities activities activities activities suggested translation converges processor spectrum slow performing epochs spaces roughly boundaries interpolation visible visible visible foundation topology figures perceptrons perceptrons perceptrons perceptrons perceptrons uncertainty maximize mozer mozer mozer variations domains discussions determining selecting identified identified capable capable uniformly uniformly computationally included mcclelland mcclelland mcclelland latent latent latent latent modes modes modes modes modes modes modes modes modes mackay mackay mackay tend ten road quickly repeated procedures interested interpreted dis lie contribution categories categories categories gibbs dayan dayan dayan dayan consisted deal modelling essential exhibit updating integral integral integral divergence divergence dual graphical mass mass biases biases helpful successive mappings mappings reliable func cognition contours contours plausible plausible adapt extremely illustrate illustrate illustrate shapes initialized initialized consist neal neal neal neal neal neal neal histogram great ment slowly directed directed distinguish variances guaranteed guaranteed diffusion independence lies lies lies broad broad broad choices ran bishop bishop bishop ridge toronto toronto preceding behaviors behaviors behaviors peter effort peaks peaks peaks marked employ biologically maxima requirement span operate operate switch poisson extracting ordered windows jaakkola jaakkola jaakkola jaakkola extreme cumulative cumulative naive picture picture picture representative tresp indices college intractable sort sleep fix appropriately conditioned pick pick narrow narrow narrow zemel kullback kullback adds ments minutes accepted accepted accepted simplify proceeds imposed intelligent keeping obtaining obtaining reasoning guide preparation combinatorial combinatorial slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice ranging ranging saul 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information information models models models models models performance performance performance performance performance performance based based based based based based based based based space space space space weights weights linear linear linear layer case case case case case vector vector order systems systems systems systems values probability probability probability probability parameters parameters parameters parameters parameters parameters recognition recognition recognition recognition recognition recognition method method approach approach approach single processing processing processing control large large large large large local local local rate rate rate rate rate rate test patterns class class class class class class optimal optimal shows shows shows shows shows shows signal algorithms simple gaussian gaussian paper paper small small small small small size size size size feature feature feature feature work work task task task methods fig fig fig fig fig fig fig fig fig step step step features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification current current current current current trained trained trained problems random random high similar representation architecture architecture architecture architecture architecture architecture show fixed fixed fixed fixed vectors vectors vectors vectors general generalization generalization speech speech speech speech speech speech speech speech speech speech parameter parameter average average gradient obtained note note experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional university threshold threshold computation computation computation computation independent independent independent log log log log log log log log sequence target initial standard standard standard standard standard standard standard standard standard standard standard standard standard standard terms terms terms node node node node node node node node node left presented presented activation activation activation activation activation activation activation low nodes nodes nodes nodes nodes nodes nodes sets maximum maximum maximum range range press press basis outputs outputs outputs outputs continuous continuous continuous abstract applied applied find find convergence density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component ieee procedure adaptive adaptive decision decision decision decision mixture mixture mixture context context context context context context context context introduction effect generated tion difference complexity classifier lower lower measure measure prior prior representations word word chosen chosen higher higher binary tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree expected equations equations region region proposed proposed correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed errors forward minimum minimum classes ing tasks tasks tasks tasks tasks regression regression regression computed multi sum sum performed times times regions regions regions factor factor factor factor potential potential made applications study em em em em em artificial samples represented compared application desired cross define compute proc determined determined determined posterior posterior posterior distributions equal mit mit accuracy larger contrast update train train train dependent dependent dependent dependent dependent modeling modeling selection selection morgan proceedings proceedings implementation version version technique technique technique internal internal advances advances final final considered considered directly directly hinton additional additional additional curves estimates san bit determine determine efficient upper full full requires requires requires choice statistics statistics speed increase validation produce weighted clustering developed levels levels criterion path path path path path path path product actual provided achieved hmm hmm hmm hmm hmm fast implemented eds journal journal degree kaufmann auditory probabilistic probabilistic probabilistic probabilistic smaller needed account unknown fully jordan jordan jordan jordan testing significantly york mechanism special consistent database database leads leads numbers iterations max pre pre pre making normalized experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts depth depth depth expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert magnitude combined perceptron architectures improve separate introduced hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees trees trees subset subset subset recently compare compare volume speaker correspond mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation evaluation evaluation generalized generalized gate gate alternative hybrid hybrid hybrid white pass half reduce conclusions performs performs moody faster mateo propose strong turn plane plane targets pro generating estimating plot label pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning slightly consisting consisting consisting consisting consisting frequencies gaussians formed formed expectation select yield squares squares overlap interpretation solved solved evaluated evaluate restricted restricted restricted showed soft static understanding partition partition partition updates measurements expansion false boundaries boundaries boundaries generation generation remains visible topology existing perceptual activations activations determines automatic black black absolute gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating structural society society computationally effectively driven presentation build efficiently score vowel vowel vowel vowel vowel plots plots tend reached traditional soc kind decoding showing interpreted phonetic phonetic split split generative gray michael providing computes automatically automatically overlapping jacobs jacobs jacobs jacobs receive receive carried powerful american estimators hanson recursive lippmann preliminary graphical hall tech investigated terminal terminal parity dependencies scaled scaled scaled scaled decisions decisions root root comparable comparable workshop workshop hierarchy hierarchy hierarchy phases neu waibel waibel waibel waibel waibel waibel adapt illustrate equally recognizer epoch speakers baseline improving histogram histogram indicating growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing growing improves nowlan expensive tool worst worst leaves leaves products laboratories english mellon alignment carnegie hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme understood cmu orders posed variant robinson robinson vocabulary perturbations pittsburgh aim 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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data data data data data data data data data function figure figure set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training algorithm output output output output number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results units units units information information information information problem problem problem problem problem problem problem hidden hidden hidden performance performance performance performance performance performance performance based based based based based weights layer vector vector order shown systems systems probability probability probability probability probability probability parameters weight weight functions distribution distribution distribution distribution distribution method pattern pattern pattern pattern pattern pattern single single processing processing large large large test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis matrix optimal inputs form form shows shows paper paper paper paper paper small small work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods points points trained trained trained trained trained structure structure problems problems random random high similar architecture show show section general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real real real average average average average average average average average average average average average theory obtained obtained obtained term term term term note result result result university university variables computation solution independent found initial initial initial table table table table estimate estimate estimate estimate estimate estimate standard standard prediction prediction prediction prediction prediction prediction prediction left left left present low low machine machine sets sets sets sets sets press components outputs outputs outputs outputs outputs outputs outputs sample sample sample sample abstract applied applied find find find references due ieee procedure procedure procedure context introduction hand statistical search tion variable chosen chosen chosen chosen part part part part part previous cases cases cases good conditions conditions expected expected expected make techniques proposed proposed correct observed errors errors errors errors errors errors simulations simulations ing regression regression regression sum called times times factor factor natural study em obtain obtain relative relative relative relative samples samples true true compared compared cross cross define define define perform active goal related constraints constraints constraints mit larger fields train morgan proceedings report report institute words department version consists individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual advances advances final bias bias ai ai ai ai considered cambridge computing view estimates estimates estimates estimates estimates estimates estimates san choice approximate world world world estimated pages pages increase validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation validation give give give con produce weighted randomly depends depends depends depends depends simply measured discussion technical technical feedforward describe tested assumption complete complete complete complete predictions predictions predictions predictions finding amount generate generate theoretical kaufmann combination combination combination combination account unknown unknown fully programming programming programming ratio ratio increasing database empirical empirical principle squared squared call call max max pre experts early early idea idea idea minimize choose run run run run run run predict discussed improve advantage ensemble ensemble ensemble ensemble takes reported practical apply introduced introduced strategy include subject identical quadratic quadratic quadratic inference inference recently highly compare compare calculated yields yields definition expression scaling occur occur deviation deviation touretzky touretzky column runs runs runs runs conclusion starting minimal editors editors accurate accurate clear practice practice mateo taking taking taking largest drawn solid solid intelligence min decrease decrease decrease decrease decrease averaged targets targets targets introduce configuration reference reference suppose written winner factors factors factors factors factors factors factors estimating laboratory confidence confidence averaging slightly minimization quality implies yield estimator variation variation completely completely suggested reasonable reasonable calculation dashed dashed combining combining combining combining combining combining fitting intervals intervals intermediate calculate foundation transactions figures figures figures figures combinations weighting weighting weighting weighting weighting weighting weighting weighting discuss mozer reason straightforward computationally delta included literature kind strongly interested stopping stopping stopping stopping stopping stopping stopping split content follow involved write maximization maximization maximization predictor predictor attempt jacobs tesauro receive overfitting overfitting collection estimators estimators estimators estimators estimators estimators estimators dotted hall ideas combine combine combine combine referred referred comparable proper tanh neu smallest smallest smallest smallest configurations perfect store store store store store store store store indicating stop track unstable unstable improves adapted expensive worse starts london day incorporate leaves circle circle toronto lowest lowest lowest meaning pure relevance bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap bootstrap peaks outliers price summarized gen gen gen popular proven incorporating serve prevent boston boston boston median yielding lot naive naive naive leen restrict breiman keeping keeping serves obtaining star star star star ral implications krogh krogh performances performances performances performances performances mance ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity ambiguity predictors negligible perfor decide realization hasselmo multiplied ensembles ensembles ensembles ensembles reveals reader arrive snn snn bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging wolpert implicitly santa santa balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing stopped stopped stopped stopped stopped fold outperforms constitute tibshirani tibshirani convenience residuals options chapman ization ization bump argued argued sollich alternatives hansen challenge housing housing housing housing replacement stores stores instability tom tom resampling resampling resampling val conflicting assessment economic arriving weather fair thing compromise compromise stacked bootstrapping bootstrapping bootstrapping bootstrapping bootstrapping bootstrapping favors favors replicates replicates replicates replicates replicates replicates replicates repetitive newly argmin heskes heskes heskes heskes heskes week coincidence subsampling netherlands netherlands eralization eralization eralization helped stacking deduce knight lose notational efron ror interpretable percentages reads vedelsby divisions inevitable nijmegen nijmegen sight dictions imizing resample imize imize bal aggregating subdivision subdivision subdivision subdivision erage cently ignorance kun bootstrapped bootstrapped pirical cates assessments crux advisable subdivisions 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#@Heskes_T,
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm 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hidden hidden hidden hidden hidden hidden hidden performance performance based based space space space weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer case case order order order order order systems systems systems systems systems systems systems values values values values values parameters parameters noise noise weight weight weight weight weight weight weight weight weight functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition method method method approach approach approach pattern processing processing processing processing processing processing rate test test test test test test test test test test test analysis analysis class class class class class matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs form signal algorithms algorithms algorithms algorithms simple simple simple gaussian examples examples examples size size size size net net net net net net net net net net net net net work work work work work work task task task task task task task task task methods methods methods methods methods methods cells cells cells cells cells cells cells cells cells cells cells cells cells step step classification classification classification classification current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random random random random random random random high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory architecture architecture architecture architecture architecture architecture show show show show section section fixed fixed fixed line line parameter real real real real real average average average average average average average average average states gradient gradient gradient gradient gradient term term term term term term note experiments experiments experiments university university computation computation computation computation computation solution solution independent defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target target target dynamics initial initial initial initial constant constant constant constant constant constant constant standard computer connections connections connections connections connections connections science activation activation activation activation activation activation activation temporal temporal temporal machine range press learn learn learn learn learn components components components components components outputs continuous continuous continuous continuous abstract back back back computational convergence references component component component component due ieee ieee important propagation propagation propagation complex complex effect dynamic dynamic dynamic generated generated generated variance recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search search search search search change change complexity complexity complexity signals signals signals signals signals representations representations representations representations chosen chosen chosen chosen higher previous previous previous previous previous cases cases cases required required required binary long long long long long long long long long long long long long long long long long long distributed distributed distributed fact proposed proposed correlation correlation length length length correct errors errors errors errors errors finite finite finite finite simulations resulting classes tasks tasks tasks tasks tasks tasks tasks computed computed respect multi sum sum called called called called called times elements elements elements means optimization global study em em em em artificial compared compared define perform experimental experimental connected connected connected connected discrete discrete discrete discrete equal approaches approaches approaches mit steps steps comparison comparison connection connection connection update update descent nets nets nets nets nets nets morgan morgan morgan morgan proceedings report report report institute department version consists internal internal internal internal advances advances advances advances advances advances difficult difficult difficult final final final final final final bias bias bias bias bias bias bias bias bias layers layers addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences cambridge cambridge experiment experiment experiment experiment additional additional solutions san san san san conference determine efficient efficient requires requires free free basic basic pages pages pages pages pages pages produce weighted randomly randomly randomly randomly randomly randomly randomly randomly randomly conditional criterion criterion types types types types finally depends technical technical technical tested tested tested hmm close close short short short short short effective generate supported theoretical require require main main journal journal end end end end end end instance instance instance instance noisy including including kaufmann kaufmann kaufmann kaufmann simulated simulated pairs pairs pairs pairs account dynamical fully fully fully block block testing special special structures trials trials trials trials trials trials trials trials trials trials trials trials principle leads details details details numbers stored stored international international denotes architectures architectures architectures recent recent recent recent recent recent recent pair pair pair takes element element reported reported identical hierarchical cognitive relevant relevant engineering highly compare conventional conventional conventional works works tuning tuning tuning solve solve solve solve solve solve solve solve solve studies achieve achieve achieve sparse definition definition definition definition positions grid gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate interval interval williams storage grant lead lead scaling extended trial alternative correctly correctly correctly correctly correctly touretzky touretzky deterministic runs flow flow flow flow flow flow flow flow flow conclusion minimal minimal minimal minimal minimal trajectories valued valued valued valued editors editors editors editors editors central sigmoid sigmoid sigmoid sigmoid sigmoid moody moody moody faster learns learns learns learns mateo mateo mateo mateo propose propose propose hard hard hard hard hard demonstrated intelligence user targets targets derivatives annealing annealing denoted denoted denoted reference solving sequential ann recall involves remaining scales scales consisting consisting adding quality blocks blocks versus versus select select focus formation formation review communication communication viewed solved solved solved solved solved solved solved solved solved open open updated evolution constants reasonable reasonable initially construction classified topology topology topology transactions transactions precision precision precision precision precision includes thesis activations activations assignment mozer mozer absolute absolute absolute compression suitable differ maximal driven successful tdnn tend miller essentially identity ten fine receives traditional refer quickly quickly quickly strongly stopping stopping classify classify classify built providing nips giles giles delayed extract acknowledgments deal deal deal tesauro tesauro receive cowan perturbation perturbation access access access investigate exponentially varied involving involving hanson hanson fewer fashion history ideas parity parity parity parity parity dependencies dependencies scaled authors authors authors authors gates gates gates induction induction induction hill integer automata automata automata automata ensure logistic logistic precise precise precise precise observe separated initialized initialized store store utility averages mentioned mentioned advanced stop directed trivial trivial trivial trivial trivial trivial trivial trivial trivial cascade cascade caused briefly benchmark benchmark benchmark benchmark benchmark worse worse comparisons processed processed processed processed lin widely widely widely located ran bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio controls controls simard calculations calculations beginning begin demonstrates annual exemplars summation fourth prop elman pseudo pseudo backprop backprop marked marked marked variant robinson release incoming serve serve germany expectations credit differentiable differentiable sharing irrelevant irrelevant initialization ordinary newton newton indices college leen www www www drift drift drift appropriately impossible smith significance odd odd multiplicative multiplicative biased biased mark mark fail presentations grammars grammars grammars grammars alspector repeat excellent excellent appendix decide overview lengths lengths propagated propagated facilitate facilitate initialize initialize mem mem pollack properly park pearlmutter variants papers papers papers fahlman stopped stopped lag lag lag lag lag lag lag outperforms outperforms truncated numerous outline shorter solves solves solves solves sig ent convenience sigma sigma arbor personal personal reports superimposed classifies remainder alter schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber altered confirmed multiscale proach represen alternatives universit universit universit minor likewise likewise lippman lippman recognizers mann survey sees sees institut frasconi frasconi frasconi frasconi frasconi incorrectly rare classi restricting vanish ory ory zipset arriving rtrl rtrl rtrl rtrl watrous informatik informatik informatik informatik informatik fin chunking tations lags lags lags lags lags inducing schreiber fication enforces enforces contents contents tomita tomita tomita tomita tomita tomita tomita tomita vanishing vanishing durations convey convey backwards maryland cleeremans kuhn trapped infeasible infeasible technische technische technische marker stand fallside fiir fiir fiir inability inability conveyed ther mention tiny superiority switzerland cued agation neti aware aware aware aware miinchen miinchen miinchen narx bptt bptt bptt horne latch latch latch latch yoshua yoshua densely depen prof revised quence exceeding matters matters native backpropagated flowing flowing hochreiter hochreiter hochreiter hochreiter hochreiter hochreiter hue nals paragraph undefined vastly dfg guessing mfinchen facilitated deutsche promote infeng artifi peng fki muenchen muenchen facilitating cially trap multigrid sea jiirgen aren fakult fakult competitors lipp tomira tomira tomira protect protect protect recommend corso 
#@Hochreiter_S,Schmidhuber_J,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data function function function function function function function function function function function function function function function figure time time time time set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number information information information information information problem problem problem problem models based based based based linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown shown shown shown shown values parameters noise noise noise noise weight weight weight weight functions neurons neurons unit unit unit unit unit unit unit unit unit unit unit method method approach approach approach approach approach point point point point point point point point point point point point point point point point point point image image image single single single processing processing processing processing processing large large local neuron neuron neuron neuron neuron neuron neuron rate rate rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs form form form form form shows signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small size feature feature feature feature work methods methods fig fig step step step points points features level current random random random random random random random random random similar architecture equation equation section section section section section section section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors images images images images images images general general generalization generalization approximation average gradient gradient gradient gradient gradient gradient gradient obtained term term term note note note note experiments dimensional university university university university variables variables variables variables variables variables variables computation computation solution independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent defined defined defined found found sequence sequence initial constant constant constant constant constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate computer computer computer computer science science science science left left direction present range press learn position components components components components components components components components components components components components components components components components components components components components nonlinear nonlinear sample sample sample sample abstract applied back find convergence convergence convergence convergence convergence convergence convergence convergence convergence properties references component component component component component component component component component component component component component component component component stochastic stochastic stochastic due ieee ieee positive positive positive positive positive positive positive positive positive important important adaptive adaptive adaptive mixture introduction hand estimation estimation estimation estimation statistical effect effect variance variance variance variance search variable variable assume assume assume assume assume rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules signals signals signals signals part part good make make fact fact fact fact fact correlation observed observed observed observed observed minimum resulting resulting multi sum eq eq eq eq eq eq eq called called called called called times times elements means means optimization dimension made made natural natural feedback feedback feedback applications filter obtain obtain negative negative negative negative negative negative negative negative negative original original original original represented compared application desired desired desired series define define define proc proc determined goal goal related discrete equal accuracy contrast descent descent descent source source source source source source source report report report implementation version version technique technique kernel final final scheme addition framework equivalent experiment environment directly solutions solutions solutions efficient efficient full choice choice significant approximate speed estimated estimated estimated estimated estimated basic basic basic basic basic condition developed criterion entropy provided finally iteration iteration iteration depends constraint constraint constraint discussion covariance technical technical technical arbitrary arbitrary arbitrary arbitrary transformation fast fast close assumption stable stable finding finding assumed require main adaptation journal pixel pixel makes makes makes objective objective objective needed needed needed needed combination combination combination combination reduced account unknown unknown unknown technology technology technology interesting interesting projection principal iterations iterations normalized polynomial polynomial polynomial minimize minimize choose run added added sources sources sources sources perceptron discussed advantage property separate separate separate separate separate separate separate introduced introduced introduced introduced introduced introduced side sense subset subset subset sejnowski sejnowski sejnowski sejnowski highly previously observations correspond pca trans trans mixtures mixtures mixtures mixtures separation separation separation separation separation separation separation separation symmetric generalized generalized bounded amplitude concept scaling scaling alternative loop column starting minimal hebbian hebbian hebbian hebbian hebbian hebbian faster faster practice learns learns constrained mechanisms presence ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica relationship introduce introduce introduce introduce minima explicit suppose construct edges ways estimating estimating laboratory laboratory laboratory laboratory mathematical mathematical mathematical explicitly simultaneously simultaneously linearly linearly dimensionality easy unique unique adding extraction extraction extraction expectation family expressed stationary approximations suggested converges constants constants constants allowed sign sign sign slow performing classical normalization combining roughly add add penalty penalty penalty penalty valid valid norm norm norm advantages combinations combinations bell bell bell bell blind blind blind blind blind blind blind blind blind maximize maximize holds holds simplicity simplicity columns columns closely suitable maximal maximal modification modification divided computations orthogonal interpreted criteria criteria categories gray satisfy simplified nips maximization mixing mixing mixing mixing mixing minimized simpler transformed transformed detail replaced replaced replaced scalar scalar scalar scalar scalar scalar reducing tech combine reliable reliable tanh statistically statistically fundamental neu illustrate ensure rank obvious observe observe academic mixed simplest simplest utility submitted finds mentioned rows rows scenes scenes convolution analyzed defining multiplication inside tive sections preprocessing preprocessing preprocessing forces choices ran begin depicted depicted raw robustness explained argument fourth considerably collected introducing adjustable maxima outliers anti anti proven proven proven enables germany wang irrelevant trade uncorrelated feasible accomplished accomplished optimality modify restriction restriction restriction linearity linearity recover recover unity oja oja oja oja oja oja oja oja oja oja oja oja oja oja oja oja oja oja numerically simplify replacing multiplicative moment ral modifications adequate meaningful separating recovered equals equals equals equals equals ascent ascent bad realization colorado tic enable express omitted properly speeds vari dividing divide ics ics ics ics ics ics ics ics ics ics ics ics ics ics ics ics ics ics multiplying visually email super maximized distinction kurtosis kurtosis kurtosis 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#@Hyvarinen_A,Oja_E,
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#*network network network network network network network network network network network learning learning learning model model model neural neural neural neural function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm number number results results results results information problem models models models models models models models models models weights weights weights case case case case case vector order order shown shown shown systems systems values probability probability parameters parameters parameters parameters parameters parameters weight functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach point single processing large large large class class matrix matrix form form form algorithms simple simple simple paper examples small small size size size size net methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods field field field field field field field field structure structure structure problems random random high representation show show line line line rule general parameter real real approximation approximation approximation approximation theory theory obtained note note note note note note note note result result university variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation computation computation solution log log log log log log defined defined defined found target initial initial initial standard terms terms terms node node node node presented presented nodes machine range press press learn basis abstract find properties likelihood likelihood references due due procedure important propagation context introduction hand estimation effect change change difference difference difference difference complexity variable variable variable variable variable variable variable variable assume lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower rules chosen chosen bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases cases cases type binary binary binary make fact fact techniques techniques techniques techniques techniques probabilities probabilities probabilities probabilities probabilities errors errors scale scale scale resulting resulting ing respect respect sum eq eq eq eq eq eq times means factor factor factor applications knowledge em em obtain obtain original artificial artificial relative relative relative relative true application application desired desired desired desired provide provide compute compute goal goal goal related posterior constraints connected connected connected connected distributions distributions distributions gain brain mit steps accuracy accuracy accuracy accuracy accuracy connection connection connection proceedings institute words department consists advances joint joint joint joint joint joint joint joint connectionist exp graph graph graph graph graph graph graph considered framework framework framework framework cambridge computing computing computing domain domain equivalent hinton additional solutions estimates estimates stage conference upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper approximate approximate free world world conditional conditional conditional conditional conditional conditional developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds entropy product provided finally simply achieved group denote tested fast limited inverse finding main main ability ability cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster objective probabilistic probabilistic probabilistic probabilistic needed combination combination reduced functional fully fully jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan technology special special special structures uniform operation iterations pre direct added architectures improved improve exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact exact introduced introduced introduced include include machines machines machines machines machines machines machines machines machines machines quadratic quadratic trees inference cognitive interest highly varying observations works yields match correspond address chain chain chain chain chain chain chain chain chain chain chain chain chain symmetric generalized bounded risk constructed expression studied studied suggests extended clusters clusters clusters generally conclusion assumptions tangent tangent tangent interactions interactions sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid accurate physics solid solid intelligence intelligence turn start start selective introduce manner boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann derive written index factors factors factors factors factors factors factors factors confidence linearly remaining remaining belief belief belief belief belief belief belief belief belief belief develop develop develop integrated integrated adding applying yield yield controlled controlled restricted restricted approximations approximations approximations approximations approximations approximations approximations forms forms forms forms partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partial earlier earlier earlier dashed dashed performing classical convex reduces combining combining remains remains calculate degrees existing inter sciences determines illustrated uncertainty uncertainty domains structural straightforward uniformly literature literature efficiently schemes plots refer graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs kind success anderson anderson quantity involved michael simplified simplified dayan dayan maximization illustrates subsequent approximating approximating approximating minimized remain carried powerful replaced recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive dotted dotted graphical graphical graphical graphical graphical graphical graphical graphical graphical biases biases biases biases biases biases biases rest applicable applicable applicable variational variational variational variational variational variational variational variational variational variational variational variational relationships structured structured proper proper removed quantities quantities quantities observe expressions expressions extent utility neal neal neal massachusetts inequality inequality developing formula directed directed crucial derivation derivation fairly adjacent adjacent independence tractable tractable tractable tractable tractable lies reasons comparisons considerable formalism formalism formalism formalism formalism formalism formalism formalism calculations calculations begin qualitative addressed integrating applies applies amounts amounts generic experimentally passed calculating calculating qualitatively marginal replace sophisticated jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola consistently consistently don ordinary intractable intractable intractable feasible feasible oxford oxford ratios ratios linearity zemel interconnected eliminated eliminated eliminated chains attractive serves obtaining removing methodology settings implications affected continue elimination elimination elimination elimination elimination elimination elimination elimination saul saul saul saul saul saul appendix appendix conjunction evident facilitate peterson peterson claim reveals reveals relies likelihoods exploiting vari mind approx approx leaving outline rigorous rigorous rigorous helmholtz deriving maximized ties benefits medium verified translated translated exponent exponent exponent goals goals permits bounding bounding jij jij jij jij jij jij jij denoting eliminating eliminating translations importantly importantly attached maintains preserve refined refined refined refined refined refined refined refined strict handled topologies factorized factorized factorized factorized factorized factorized transforming suffices routines recursion recursion recursion recursion recursion recursion recursion recursion recursion recursion recursion recursion recursion recursion medicine medicine sparsely attained concave concave creation feasibility carrying translates translates formulas formulas sented objectives imposes substructures substructures enforcing mir recovers undirected undirected undirected graphically imation relying recursire formulations rigorously rigorously rigorously psyche jensen jensen tommi inferences stays convexity convexity densely bears tain render emerging likeli normalizes mediating 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#@Jaakkola_T,Jordan_M,
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#*network network learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number system error error error error error error error error error error error results results results results results results results results results results results results results units information information problem problem problem problem problem problem problem problem problem problem problem hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based space space space space space linear linear linear linear layer vector vector vector order shown shown systems parameters parameters parameters parameters parameters weight weight distribution recognition recognition recognition recognition recognition recognition recognition method method method method method method method method pattern pattern pattern processing large large large large large large test test test test test test test patterns analysis analysis class class form shows algorithms algorithms algorithms simple simple simple simple examples examples small small size size feature feature feature feature feature feature work work work work work work methods methods methods methods classification classification classification classification classification process process trained trained trained trained trained trained trained trained trained problems problems problems problems problems problems random random random random show show show show line line line vectors vectors vectors vectors vectors generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real real real real real real real average average average average average average average theory gradient obtained obtained obtained experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional result result university threshold threshold threshold computation research independent independent found found found sequence table table table table table table table standard standard standard standard standard computer terms science prediction direction present present machine sets sets sets sets sets learn learn learn sample sample sample sample abstract applied applied find find find computational properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic due ieee positive important important decision introduction hand hand hand generated generated generated generated generated variance cost cost complexity variable assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier learned chosen chosen chosen chosen chosen chosen higher type required multiple good good good good good binary distributed distributed region region proposed proposed observed observed observed scale simulations classes classes classes total total simulation multi multi called called called times elements factor factor factor factor factor dimension dimension applications applications applications applications obtain obtain obtain obtain obtain obtain obtain obtain obtain original vol vol vol artificial samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples represented compared compared application application provide provide determined experimental experimental experimental experimental related distributions power steps comparison larger support train descent nets modeling proceedings report institute department department version consists consists individual individual individual difficult bias addition equivalent environment directly limit effects effects determine efficient efficient efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers choice statistics randomly randomly randomly randomly randomly developed developed provided finally selected selected selected backpropagation sampling sampling measured technical feedforward increases tested tested fast fast assumption amount nearest nearest nearest nearest nearest generate generate theoretical theoretical theoretical instance easily underlying needed needed needed combination combination testing testing testing testing character special uniform database database details making international supervised polynomial polynomial idea combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined combined choose run perceptron directions directions recent property property reported reported pixels engineering compare compare previously achieve achieve achieve achieve trans observation entire entire scaling scaling scaling suggests suggests extended extended deviation correctly correctly white pass pass runs runs runs runs strength strength neighbor neighbor neighbor neighbor bayes bayes bayes performs faster practice weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak propose propose sigmoidal demonstrated demonstrated intelligence variety base suppose digit digit digit digit written written written written index solving ann ann linearly linearly electrical dimensionality remaining slightly develop develop develop gaussians gaussians gaussians gaussians gaussians versus versus versus versus versus select national focus overlap fraction fraction fraction digits digits digits partition partition discrimination discrimination combining combining combining purpose assigned assigned foundation advantages advantages classified recorded existing existing existing existing handwritten figures combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations combinations priori plotted black discussions discussions characterized determining determining selecting efficiency efficiency efficiency efficiency efficiency computationally computationally computationally refer compact quickly quickly repeated repeated prob success issue classify follow providing overlapping overlapping overlapping carried collection investigate investigate helpful ideas rest rest rest rest investigated boosting boosting comparable comparable proper workshop integer ensure subsets observe improving motivated synthetic synthetic synthetic synthetic theoretic separable separable variances majority majority majority capabilities worse considerable berkeley berkeley easier hyperplane hyperplane hyperplane mathematics simard acknowledgement sun sun sun people http price partitioning partitioning characterize characterize gen gen deviations deviations credit don don don www extensive databases databases hyperplanes systematic breiman breiman breiman breiman handwriting knn knn utilized schapire schapire schapire schapire schapire sion percepttons percepttons bases april record cpu cpu cpu cpu properly card card partitioned papers lem dna ple users annals randomized randomized randomized forced acceptable freund freund letting workstation realize clas clas pub pub care ftp ftp ftp ftp formance continues proba learnability iri weaker misclassified suffer tin picking gratefully nist nist bility curse accomplish vote vote vote vote discarded sym poly att dimen trend jan deciding ira drucker benchmarks degrades nice nice stat sparc neigh newly newly weakness weakness weakness weakness weakness eralization ecs acknowledged boost boost paid ences discriminations discriminations discriminations diabetes diabetes ucl arcing cheaper nicely anonymous bor variate customer deviates guessing yoav cnn erating tackle bined discrepancies discrimi buffalo frontiers sifters uka peo tificial kan nations guesses career sifiers polytechnic rpi rpi 
#@Ji_C,Ma_S,
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#*learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input input data data data data data data data data function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output state state state state state state state state state results results results information information information models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space linear case case case case case vector vector shown shown shown shown systems systems systems values values values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters functions distribution distribution distribution distribution distribution distribution distribution recognition method approach approach point single single single single processing processing processing rate matrix matrix matrix matrix inputs form algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian paper paper paper paper paper size feature work methods methods step step step step step step step field field field field field field field features classification process level level level level level level level level level current current current current structure structure structure structure structure structure structure structure structure problems random random random random random random high similar architecture architecture architecture fixed vectors vectors vectors generalization generalization speech parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states theory obtained obtained obtained obtained note note note dimensional result university variables variables variables variables variables variables variables variables variables computation log log found found sequence sequence sequence sequence sequence sequence sequence dynamics constant constant table table standard computer terms terms terms terms node node node node node node node node node node node node node node node node science presented present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal temporal temporal temporal temporal machine press press press basis outputs abstract computational computational convergence convergence likelihood likelihood likelihood likelihood references ieee adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision mixture mixture context introduction complex estimation statistical statistical statistical statistical generated generated generated variance variance tion energy variable variable variable variable variable spatial assume assume lower lower higher center previous previous bound bound cases cases multiple multiple binary represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed equations equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make make proposed correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed forward scale scale scale scale scale scale resulting resulting total simulation simulation regression regression computed computed respect multi sum sum performed performed times regions regions factor dimension dimension dimension dimension made natural study em em em obtain obtain obtain obtain original artificial artificial artificial artificial represented application series series series series series series series provide provide provide provide determined determined determined goal posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions discrete mit mit mit steps steps fields fields support support support dependent dependent modeling modeling modeling modeling modeling modeling proceedings institute department consists advances advances advances represents bias bias layers graph graph graph graph graph graph cambridge cambridge cambridge cambridge domain directly view view view curves curves transition transition transition transition transition top efficient efficient choice approximate basic basic increase produce condition conditional conditional conditional levels levels levels levels lines lines entropy path path selected biological measured covariance describe describe arbitrary denote denote denote hmm hmm hmm hmm hmm hmm hmm hmm assumption assumption common implemented assumed eds eds eds development probabilistic probabilistic probabilistic probabilistic account account fully fully jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan technology significantly special special structures structures iterations max bottom bottom experts experts experts early idea idea minimize run run run architectures architectures resolution exact exact exact typical practical include include hierarchical hierarchical hierarchical trees trees trees trees trees trees trees trees trees trees trees trees trees trees subset interest interest varying varying yields correspond correspond rl mixtures evaluation chain chain chain chain chain horizontal horizontal horizontal horizontal expression scaling matrices matrices alternative touretzky touretzky touretzky runs runs runs runs runs starting conclusions depend interactions accurate physics turn start start reference appears ways ways factors factors vertical vertical vertical modeled modeled involves involves involves transformations scales scales scales scales scales scales scales scales develop events potentials extracted independently stages viewed viewed viewed viewed viewed viewed influence solved densities restricted approximations approximations approximations approximations approximations approximations decomposition decomposition soft approximated completely completely completely key key key key key key key earlier earlier calculation calculation calculation calculation calculation calculation calculation spaces reduces fitting fitting event event event sufficiently foundation classified coupling includes includes usa inter mozer mozer coupled coupled coupled coupled partially partially partially simplicity straightforward straightforward middle middle encoded paths presentation literature literature ten fine fine fine refer graphs graphs induced prob duration duration write write michael simplified simplified backward wavelet providing eigenvalue jacobs jacobs jacobs jacobs tesauro remain investigate exhibit exhibit recursive divergence graphical graphical graphical graphical graphical graphical dataset dataset dataset dataset existence links links links links links terminal variational variational variational variational variational variational variational variational variational possibility dependencies dependencies dependencies decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions root root hierarchy removed attributes attributes coarse coarse coarse coarse naturally configurations illustrate adjusted algo massachusetts percentage directed guaranteed defining defining tractable tractable tractable tractable tractable tractable tractable baum lin formalism formalism bengio bengio leaves probable separately calculations calculations calculations calculations calculations calculations calculations pitch pitch toronto toronto attribute preceding explained explained apparent percent pathways hme hme hme hme hme generic parameterized parameterized lattice lattice remove treated incorrect calculating calculating calculating calculating summarized ordered datasets kinds expectations expectations expectations conditioning viterbi viterbi viterbi viterbi viterbi viterbi viterbi leaf wesley synchronization ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani ear leen intractable intractable intractable intractable intractable addison tation restriction restrict restrict summing summing rithm pick signature signature ordering ordering concerned homogeneous theories children children clamped extending kullback chains chains chains chains chains chains proceeds replacing replacing city multiplicative moment moment abilities resulted shifts shifts shifts substituting analyses utilized combines saul saul saul saul saul saul saul loo iteratively guarantees den captured captured captured lawrence hasselmo hasselmo branching branching tic arrive canada exploiting alternatively parents assigns uci arcs arcs arcs drop super recursively markovian markovian spatio welch utilize utilize utilize par medium 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probabilistically downward decoupled decoupled dur redwood parameterize inhomogeneous lxt liebler erm rior terior poste imm rations neglects neglects ime subroutine recursions thirteen lime lime lime superscripts configu signifying vmues lxl secure arguably nomial ticularly 
#@Ghahramani_Z,Jordan_M,Saul_L,
#t10
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#*network network network network network network learning learning learning learning neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function figure figure figure figure figure figure time time set networks networks networks networks networks networks networks networks networks training training training output output output output output output number number number number number error error error state state results results results results units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information information 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patterns patterns patterns patterns patterns patterns patterns patterns optimal shows shows simple paper paper size feature net net methods methods methods methods methods methods methods methods methods methods methods level trained problems problems random random architecture equation section section section section rule general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter average theory obtained obtained obtained activity activity activity activity university computation computation log log log log log log log log defined defined defined defined defined defined defined initial initial initial initial initial initial table table table table table estimate standard standard terms terms terms terms connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections science science present activation activation maximum maximum maximum maximum maximum maximum range press outputs abstract applied applied applied applied applied properties references due important introduction hand generated cost tion tion tion tion variable rules rules rules rules prior prior representations representations representations previous previous cases cases firing firing firing firing firing multiple expected expected make correlation probabilities probabilities errors errors errors errors errors errors finite minimum ing total computed respect respect respect sum performed elements means means knowledge em negative negative negative negative vol vol vol artificial relative cross cross define define rates rates rates experimental experimental experimental goal related equal comparison larger larger larger connection connection connection connection connection update train selection implementation internal internal internal individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual individual exp bias bias bias bias bias bias bias addition addition addition addition addition considered considered framework framework directly view stage stage stage detection approximate speed increase increase increase give con con produce randomly randomly conditional conditional conditional conditional conditional conditional levels levels levels criterion controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller entropy entropy entropy actual actual discussion close close close corresponds generate theoretical significantly york segmentation segmentation mechanism principle language language representing max normalized supervised supervised magnitude decay decay decay decay minimize minimize minimize architectures improved improved discussed improve improve pair element apply engineering unsupervised approximately works observation concept concept concept concept concept wide strength minimal reduce reduce weak propose taking sigmoidal assuming assuming minimizing min decrease manner suppose suppose suppose produces ways laboratory multilayer explicitly explicitly explicitly explicitly simultaneously simultaneously simultaneously simultaneously mutual minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization competition john independently formation depending interpretation interpretation controlled controlled controlled updated reasonable reasonable purpose 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collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective collective logp logp logp logp logp logp kinds kinds eventually simultaneous proposition realized ordinary ordinary japan appropriately concerned jth jth jth jth jth jth jth jth jth jth jth discovery repre impossible impossible smolensky suppression overcome mail intelligent interpret interpret interpret interpret obtaining fires fires infor infor infor infor elimination elimination elimination elimination mance perfor dif infer infer sons std std std std vari verify rms rms rms informa informa ence maximized maximized maximized maximized maximized suppressed gener ization ization carefully confirmed confirmed confirmed acquired apparently syllables els inactive rewritten inhibited overtraining kth kth kth kth kth kth kth exclusively devised rameters differentiate minimizer minimizer minimizer tenth lsi supposed 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#@Kamimura_R,
#t10
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input data data data data data data data function function function function function figure figure figure figure figure figure figure figure figure figure time set set set set set set networks networks networks networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number error error error error error error error error error error error results results results results information information information information information information problem problem problem models models models models models models models models models models models models models models models models hidden hidden hidden performance performance performance based based based space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer vector vector vector vector vector vector vector vector order shown systems systems systems systems systems systems weight neurons neurons neurons neurons recognition recognition recognition recognition method method pattern pattern point point point point point point point point point point point point point image image image single single processing processing processing processing processing processing large large local local local neuron rate rate rate rate test test test test test patterns patterns analysis analysis class class class matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs shows shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper examples examples examples examples small small small size feature task methods methods points field field features features features features features classification trained cell structure problems memory similar similar similar similar representation representation representation representation representation fixed rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images images average gradient gradient obtained term term result result variables variables variables variables computation computation solution independent log log found found found found dynamics dynamics dynamics initial distance distance distance distance distance connections connections synaptic synaptic left machine sets sets range range range basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear continuous sample abstract applied applied back back find find find convergence analog properties likelihood references component component stochastic due due ieee ieee decision mixture introduction hand hand circuit circuit generated cost cost cost energy difference variable prior prior representations representations representations chosen chosen chosen part previous bound bound required multiple multiple good good good binary binary binary conditions represent represent represent represent distributed distributed make fact fact proposed proposed length errors errors errors errors errors simulations minimum minimum minimum minimum resulting resulting resulting classes ing sum performed performed eq eq eq eq eq eq eq eq eq called called elements elements means optimization optimization optimization optimization optimization made natural natural feedback feedback global knowledge knowledge em relative compared compared receptive related related constraints constraints constraints constraints constraints constraints constraints distributions distributions discrete equal equal equal steps larger larger contrast contrast connection connection update update support support support descent modeling modeling proceedings proceedings implementation implementation consists code code code individual individual advances advances advances advances advances advances represents represents difficult considered considered computing equivalent equivalent hinton hinton detection efficient efficient efficient upper approximate approximate free produce produce coding coding coding coding coding coding coding coding coding coding coding weighted product actual backpropagation nature nature inhibitory constraint constraint constraint constraint simply simply discussion covariance feedforward increases describe transformation transformation transformation limited complete excitatory finding finding nearest nearest nearest nearest nearest nearest nearest implemented implemented require main pixel instance cluster makes noisy fit probabilistic typically hopfield combination combination combination combination account coefficients coefficients coefficients programming programming programming segmentation structures database database operation leads principal principal max stored normalized normalized bottom polynomial minimize minimize minimize description discussed directions directions correlations separate ensemble ensemble introduced identical pixels quadratic quadratic quadratic hierarchical dimensions highly highly previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised solve correspond pca pca pca pca pca pca pca pca pca pca trans trans sparse sparse sparse grid improvement invariant scaling locally locally generally column hebbian neighbor neighbor neighbor neighbor tangent tangent performs weak constrained constrained constrained constrained constrained encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding taking largest drawn assuming exist exist exist min min decrease minima minima minima question explicit appears digit digit digit digit digit index solving ways ways distinct distinct multilayer linearly involves transformations unique adding minimization quality competition yield expressed reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction correlated squares viewed interpretation interpretation codes codes lee lee lee lee forms activities activities digits digits digits digits digits digits earlier convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex penalty penalty interpolation interpolation visible classified building handwritten handwritten handwritten handwritten combinations combinations combinations bell bell bell eigenvalues determines vapnik domains discussions columns importance encoded encoded modification computationally computationally computationally computationally schemes essentially capture conf cun cun allowing issue classify manifold dayan dayan providing quantization quantization denker illustrates deal remain put helpful rest project scaled working eigenvectors hill smallest math closest closest integer opposite implementations thought prototype prototype obvious noted submitted finds finds finds finds trivial capabilities tractable tractable tool worse nonlinearity widely laboratories laboratories simard simard projected separately involve localized arises depicted understood affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine haussler variant templates templates templates prototypes extracting tank prevent sums segmented summed classifying ghahramani accomplished zemel zemel discovery encoder encoder encoder unity unity lecun arranged extending kaufman fits fits murray promising occurring obtaining combinatorial saul cone displayed emergence extends seung seung seung seung seung omohundro alternatively acknowledge geometrical helmholtz alternating freund freund burges burges factorial invariances hastie labs manifolds intensities zip zip emphasized superposition intl siam grateful technologies develops nonnegative ate discontinuous heavily virtually olshausen orthonormal cornput cornput hull hull hull hull hull hull hull hull hull hull hull converter incorrectly eliminates stay bregler inefficient inefficient vanish vanish strokes degenerate fastest appl factorization encodings encodings encodings encodings encodings encodings encodings encodings zeros enforces corn adequately shortly syst watson discovers revow cortes violate demanding spots fundamentally blurred optimizes sparsity arline arline arline arline arline rectification wright reconstructions reconstructions reconstructions reconstructions usps usps subtract shrink gorithms reconstructing han geometrically encoders encoders encoders encoders encoders encoders encoders encoders encoders encoders encoders encoders encoders iix interpretable interpretable segregated discarding saund noticeable zation lucent degeneracy ickinger contrasted optimizations restarted tractability autoencoders pute cas scholkopf grandmother cod backer fixes substructure kdd leaxning erro 
#@Lee_D,Seung_H,
#t10
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data function function function function set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number error error error error error error error error error error error error information information information information information problem problem models hidden hidden performance performance performance performance performance performance based based based based space weights weights weights layer case vector order systems systems systems values probability probability probability probability noise noise noise noise weight unit distribution distribution distribution recognition method method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single processing processing rate test patterns patterns patterns patterns patterns patterns patterns class class class class class class class class class class class class matrix optimal optimal optimal inputs inputs inputs inputs inputs shows algorithms algorithms simple simple paper paper small size size size size size net task task methods methods points classification classification classification classification classification process process current current trained trained trained trained trained trained trained problems problems problems problems problems problems problems random random random random random random high high high high high high equation fixed line vectors generalization generalization generalization approximation average average term term note note note experiments experiments experiments dimensional dimensional dimensional dimensional university university university computation independent independent log target initial table table standard standard standard standard standard standard computer node node prediction presented low low low low low low nodes nodes nodes machine machine machine sets sets sets sets sets sets sets sets maximum press press press learn continuous sample abstract applied find find computational properties references component stochastic ieee ieee ieee procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision introduction introduction hand behavior statistical variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance cost change change difference variable variable classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower rules chosen part previous good tree tree fact techniques techniques techniques techniques techniques proposed proposed correct probabilities probabilities probabilities probabilities probabilities errors errors errors scale finite minimum minimum resulting classes classes classes classes classes classes classes classes tasks regression computed sum called called called called called times times mapping negative original original original vol vol vol artificial artificial artificial artificial artificial artificial artificial true compared compared application cross cross cross rates rates active active active posterior posterior posterior mit steps steps comparison comparison update train train dependent dependent nets nets nets selection selection selection morgan morgan proceedings proceedings department department loss loss loss loss loss version kernel advances advances joint bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias addition cambridge cambridge directly estimates effects bit conference conference classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers approximate statistics statistics statistics validation validation validation con coding coding weighted actual finally backpropagation depends sampling sampling sampling simply measured covariance normal normal denote denote denote denote denote effective theoretical main eds eds square makes noisy kaufmann kaufmann typically typically typically reduced unknown unknown mlp york uniform uniform empirical squared call international international expert idea combined combined combined combined denotes exact introduced introduced introduced trees recently compare compare works works solve yields improvement risk risk risk risk risk risk risk risk risk risk risk risk risk risk increased increased constructed constructed lead touretzky white demonstrate runs reduce measures measures bayes bayes bayes bayes bayes bayes bayes performs moody taking integration drawn california california california minimizing introduce introduce introduce suppose monte construct construct carlo ann ann ann ann ann ann ann ann ann ann averaging remaining independently review depending depending decomposition decomposition decomposition understanding completely combining roughly add boundaries valid advantages classified topology transactions transactions includes usa usa usa usa perceptrons bell mozer black gating importance importance importance uniformly society included included presentation build identity ten summary procedures paradigm simpler powerful xor xor xor xor create hanson issues lippmann hall reducing reducing tech tech tech investigated boosting boosting boosting boosting combine combine combine combine combine combine combine combine combine hill adapt initialized consist improving improving submitted indicating cart theoretic publishers unstable unstable majority majority majority benchmark benchmark benchmark benchmark starts berkeley berkeley arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc laboratories toronto bootstrap bootstrap bootstrap bootstrap bootstrap leave rep rep rep variant compares popular sophisticated unbiased unbiased unbiased initialization classifying classifying grey spiral spiral systematic systematic murray breiman breiman breiman breiman breiman breiman breiman breiman breiman breiman overcome los biased replica disjoint presentations repeat repeat utilized introduces schapire schapire schapire schapire predictors equals negligible realization realization den uni hasselmo approximators initialize initialize mlps repeatedly bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging canada wolpert correcting dietterich dietterich dietterich assigning assigning speaking spirals spirals spirals spirals anns anns anns anns anns slight misclassification misclassification misclassification ties ties ties ties opposed tibshirani tibshirani tibshirani tibshirani decomposed freund freund freund freund australia var var var var var adapting clas clas chapman hornik hornik hornik hornik hornik hornik harder quinlan quinlan misclassified misclassified misclassified voting voting voting voting voting voting voting voting universit vanishes helps replacement replacement replacement ble instability institut ave dominates hid jain jain jain resampling resampling resampling resampling resampling resampling resampling resampling resampling resampling resampling resampling resampling replicated vote contrary sity drastically creation jitter jitter jitter ically stacked replication cortes drucker mountain decompose kong kong kong technische decompositions decompositions sydney favorably fiir versity picks kurt kurt univer proportionally ripley efron efron bigger arcing arcing arcing arcing arcing arcing arcing arcing arcing arcing arcing arcing arcing votes votes replications replications und austria misclassifications alamitos wit probabili probabili probabili regressions corrects structed aps aps aps initializations miyake miyake typ wien wien monographs limk resample resample resample resample resample resample resample resample sifters aggregated aggregated aggregated friedrich friedrich sifter jittered kohavi 
#@Hornik_K,Leiseh_F,
#t10
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure time set set networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number state state state state state state state state state state state state state state state state results results results units units units units units units units units units units units units units units units units units units units units units units information information information problem problem problem problem problem problem problem problem problem problem problem models models performance performance based based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case vector order order order order order order order order order order order order order order order shown shown shown shown systems systems systems systems values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters weight weight weight weight weight weight unit unit unit unit recognition method approach pattern pattern pattern pattern pattern pattern pattern pattern single processing processing local local local local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns matrix optimal optimal inputs inputs form shows algorithms simple simple simple simple simple simple examples examples small size feature feature net work work methods methods methods methods field field features features features features process process process level level level level level level level level level level level structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems problems problems random random random random random high high high high representation representation representation representation representation show fixed fixed general general real average average average states states states states states states states states states states states states states theory obtained obtained obtained obtained obtained term term note note note note variables computation computation research independent log defined found initial initial terms terms terms terms science left left left direction direction direction direction present present present low low low low frequency machine machine maximum press learn outputs sample abstract find computational density density references stochastic stochastic procedure important adaptive context introduction complex complex statistical statistical statistical statistical statistical statistical generated generated generated parallel cost cost recurrent recurrent change change change complexity variable variable variable variable spatial assume assume lower lower lower lower lower lower prior prior prior prior representations representations representations representations representations representations representations representations representations representations learned learned learned learned higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher higher cases type required multiple good good good good binary long conditions conditions represent represent represent represent represent distributed bayesian bayesian bayesian bayesian bayesian bayesian equations make make fact proposed probabilities probabilities scale resulting tasks tasks computed computed computed sum sum sum sum performed times factor potential natural natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback global em em obtain obtain artificial artificial samples samples samples represented true application application series provide active active active active goal posterior connected connected distributions distributions equal mit larger larger modeling morgan morgan proceedings institute institute internal internal internal internal internal internal internal individual advances joint joint joint connectionist exp exp exp exp bias layers layers layers graph framework cambridge computing hinton hinton hinton hinton hinton hinton hinton hinton additional additional view solutions solutions estimates limit san san top top top bit conference determine determine determine determine efficient efficient efficient upper upper full statistics statistics world speed pages pages pages give produce produce derived derived weighted randomly conditional conditional levels levels levels levels levels levels levels levels types lines lines lines lines lines lines lines product product selected selected nature nature depends sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling discussion feedforward feedforward feedforward feedforward feedforward tested limited close finding finding common common effective require require main square ability makes makes rumelhart noisy noisy noisy fit kaufmann kaufmann objective objective objective probabilistic typically underlying underlying underlying fully jordan interesting ratio consistent structures structures representing bits bits bits bits international bottom expert combined architectures discussed correlations correlations exact property ensemble typical typical identical machines machines hierarchical hierarchical hierarchical hierarchical inference inference subset subset sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski interest highly unsupervised unsupervised unsupervised unsupervised unsupervised approximately volume volume volume works module achieve separation grid horizontal horizontal horizontal expression expression touretzky generally setting pass demonstrate runs runs runs row row assumptions editors editors sigmoid modules accurate accurate accurate exponential faster constrained mateo mateo strong strong proportional intelligence intelligence minima boltzmann solving generating stability vertical vertical vertical changing changing multilayer transformations remaining remaining remaining belief belief belief belief unique shift shift shift shift shift shift blocks blocks extraction select formation overlap interpretation influence influence controlled updated updated approximations approximated digits converges discrimination slow performing epochs epochs epochs add calculate handwritten illustrated mozer priors priors gamma determining straightforward selecting importance effectively effectively mcclelland wij wij wij detect detect efficiently computations capture capture capture capture capture capture soc prob allowing interpreted interpreted interpreted interpreted gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs sampled sampled michael dayan dayan dayan dayan dayan illustrates illustrates situations powerful powerful circuitry circuitry rapidly relations estimators graphical dataset dataset dataset ml rest relationships relationships complicated adapt adapt adapt adapt adapt changed epoch epoch grouping neal neal neal neal neal integrate rows formula costs ground crucial explanation explanation adapted adapted benchmark reasons turns easier desirable probable probable probable calculations medical medical lowest lowest integrating integrating fourth considerably parameterized posed remove variant reliability howard mod prevent datasets sophisticated redundancy jaakkola specifies specifies naive shifted representative lab contextual redundant intractable intractable feasible sleep sleep sleep zemel discover discover royal children children convenient proceeds intelligent mark neurobiology reasoning shifts shifts shifts salk salk salk reliably saul saul ambiguity ambiguity ambiguity ambiguity ambiguity periods iteratively displayed washington hasselmo arrive jolla informative arrows discovered stopped influences parents parents helmholtz helmholtz helmholtz axe axe axe axe axe chapter discovering discovering causal causal causal wake wake wake adapting adapting adapting adapting mutually acting exclusive approxi approxi mathematically proba proba hughes terrence increasingly pearl pearl pearl pos ambiguous ambiguous ambiguous ambiguous inversely placing sweeps frey frey frey els prevents topography ble inconsistent inherently fij fij fij fij inferring resolved resolved resolved sij explanations explanations lewicki lewicki lewicki lewicki lewicki computable sid ensuring discovers dominate parsimonious copied copied collect nth mate terry stabilized wji wji conveniently prevented bilities shifter shifter shifter shifter arrangements cleaned itive wrap mations torrey pines duplicated duplicated axi axi axi spiegelhalter spiegelhalter relearning symptoms lauritzen lauritzen overly overly bench nlog marginalizing keys caught leaxning methodological parameterizes wla 
#@Lewicki_M,Sejnowski_T,
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural input input input input input input input input function function function function figure figure figure figure time time algorithm algorithm algorithm algorithm algorithm algorithm output number number system system system state state state state state state state state state results units units units units units units units units units units units information based space linear linear linear linear linear linear linear linear linear case vector vector shown shown shown shown shown shown shown shown values probability probability unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution approach approach approach approach approach approach approach approach approach approach point processing processing processing processing processing control large local local local local local local local local local local rate matrix matrix optimal form form signal algorithms algorithms algorithms simple gaussian visual paper size feature net net net net net net work work work work task task fig fig fig fig fig fig fig fig fig step points points points points field field field field field field current cell cell cell cell cell cell cell structure structure structure high high high high high response response response representation representation representation representation representation representation representation architecture show equation line rule rule rule rule rule rule rule rule images general general general generalization speech speech approximation approximation approximation approximation theory theory obtained activity activity dimensional dimensional dimensional dimensional dimensional result result university university university computation computation computation solution independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent defined dynamics dynamics dynamics standard terms distance left left left map map map low low maximum components nonlinear abstract find find computational computational convergence density density density density density density density density density density density density density density density density density density density properties likelihood references component component component component component component component component component component component component adaptive mixture mixture mixture mixture mixture context introduction introduction action estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical dynamic parallel parallel tion tion change rules measure signals signals prior representations representations required required cortex distributed distributed equations make region region scale simulations resulting ing ing ing tasks simulation performed performed regions regions mapping factor potential dimension made natural natural obtain represented true desired desired desired desired desired cross receptive define define proc proc perform perform active goal goal constraints connected distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions discrete discrete discrete approaches approaches update source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source nets modeling modeling selection department department department code individual represents represents difficult addition maps maps maps maps maps directly top stimuli stimuli full full full give con con condition condition condition channel coding coding coding coding coding coding coding coding randomly developed lines lines lines product nature nature nature nature nature nature nature nature depends simply discussion normal arbitrary arbitrary arbitrary denote denote transformation transformation transformation nearest role require easily sensory sensory fit fit needed significantly uniform pre pre direct direct polynomial sources sources sources sources sources sources sources sources sources sources sources directions directions directions exact exact exact advantage property takes typical typical movement introduced quadratic sense sense sejnowski sejnowski sejnowski sejnowski recently dimensions highly correspond correspond correspond achieve achieve sparse sparse sparse definition mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures positions positions positions separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation modified modified grid williams sensitive invariant digital digital digital digital digital digital rotation alternative locally hybrid generally demonstrate place place assumptions conclusions neighbor clear performs learns taking physics physics reduction demonstrated proportional turn assuming ica ica ica ica ica ica ica exist introduce groups configuration configuration configuration configuration construct edges distinct dimensionality transformations transformations unique springer springer formed quality extracted extracted dependence stationary squares squares squares labels organizing organizing organizing organizing organizing organizing organizing organizing similarly partition partition partition partition partition partition partition partition partition partition partition updates sign sign dashed dashed neighborhood neighborhood generation remains remains valid initially norm kohonen kohonen kohonen kohonen topology topology topology david degrees coupling coupling coupling priori coordinate coordinate coordinate coordinate bell bell bell bell bell weighting blind blind blind blind blind blind compression importance modification modification tend essentially orthogonal composed verlag verlag quickly dis follow comp comp comp nips nips nips maximization mixing mixing mixing mixing mixing satisfies cowan cowan cowan cowan cowan cowan cowan cowan parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric exponentially rapidly steady steady steady steady steady steady steady steady limitations mass fewer matches biol proper statistically contours contours contours contours contours contours math coarse coarse possibly equally singular aspect bifurcation der som som som som som som som som som som som som som som som som som som som som freedom mixed mixed simplest attempts histogram histogram histogram histogram histogram scenes separable trivial trivial trivial trivial independence independence lin lin lin lin lin lin lin lin bishop bishop sgn sgn sgn sgn sgn sgn sgn geometry alignment percent pseudo pseudo axes axes axes axes axes dots dots berlin berlin partitioning branch branch branch branch extracting resource focused median wesley cybern aligned aligned aligned accomplished addison modify acts branches branches hyperplanes hyperplanes controlling controlling purely partitions partitions partitions partitions grows grows proceed generality fits allocation analogy city attractive primitive primitive primitive primitive krogh modifications modifications hertz eqn eqn separating sion sides vertices enhance den counting yang yang elastic claim winning winning winning winning winning emergence verification verification verification extensively hypercube eqs pearlmutter pearlmutter captures alternatively alternatively dividing linked audio appeared geometrical geometrical schulten schulten gtm rigorous seek amplitudes spaced chicago chicago chicago chicago chicago chicago representa principled rectangular modifying distri deconvolution wise wise singularities complementary ritter ritter voronoi voronoi voronoi voronoi voronoi voronoi palmer uniqueness uniqueness uniqueness suffers olshausen olshausen olshausen cornput suffices sharply sharply sharply sharply sharply sharply sharply peaked peaked peaked peaked peaked peaked peaked inspection sity curved dimen physically periodically quick fidelity sparseness bauer bauer cuts tained files sep noiseless constituent jack magnification magnification magnification intrinsically fundamentally align align inserting couple parra parra pursued prohibitively anisotropic anisotropic perspectives perspectives unmixing utilization tours karhunen hyperparameter equivariant equivariant equivariant equivariant equivariant equivariant whitened faithful faithful faithful equiv tributions aligning postulate joining quadratically redwood intersections modulus hyvarinen prin whitening contrasted structed butions ridges cod arbi decorrelate tition trary supplemented concen hinder herrmann herrmann herrmann stewart trate aration parametrically iconip separa ciple ejnowski 
#@Cowan_J,Grier_D,Lin_J,
#t10
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#*network network network network network network network network network network network network network network learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number system error error error information information problem models models models performance performance performance performance based based based based space space space space space space space space space space space space space space weights weights weights weights weights weights weights weights linear linear layer case case vector vector order order order order order shown values values values values parameters parameters weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution recognition method method method approach approach approach approach approach approach pattern pattern pattern point point point point point point point image control test test test test test test test test test test patterns analysis analysis analysis analysis analysis class class class matrix matrix matrix optimal form form shows simple gaussian paper paper small feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work work methods points points points points points points points points process process process process level trained trained trained trained trained trained trained structure structure structure structure problems problems architecture architecture architecture architecture show section fixed vectors general general general real theory gradient obtained term term term note note dimensional dimensional result university university research research independent found target target constant standard terms terms distance distance left low range range basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear abstract find properties references component ieee ieee procedure procedure important important context introduction complex statistical effect effect effect effect generated generated generated variance complexity complexity complexity complexity complexity spatial measure measure measure measure measure measure prior prior higher part previous previous good good good equations fact fact techniques observed observed observed observed observed errors errors errors errors forward forward forward forward forward minimum resulting total total respect sum sum mapping mapping mapping mapping mapping dimension dimension dimension dimension applications knowledge knowledge artificial artificial artificial relative relative relative relative relative relative specific specific samples compared provide provide determined determined determined determined determined related related related approaches approaches approaches contrast implementation technique kernel kernel kernel final final addition maps computing computing domain experiment additional solutions conference significant world give coding derived derived criterion provided provided evidence nature constraint achieved achieved arbitrary arbitrary group tested tested tested transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf effective effective supported theoretical theoretical theoretical theoretical hypothesis instance cluster fit fit objective typically account functional functional interesting interesting projection mechanism empirical empirical principle principle squared details details numbers iterations supervised supervised supervised supervised supervised supervised supervised supervised supervised magnitude decay decay decay added predict exact property property property pair pair separate element introduced introduced introduced quadratic subset recently recently relevant interest dimensions dimensions dimensions dimensions highly previously approximately approximately tions smooth smooth match correspond positions positions locations separation observation observation entire entire invariant scaling scaling scaling extended matrices predicted alternative feed feed feed feed feed locally clusters clusters clusters clusters occurs generally generally setting conclusion reduce reduce depend measures reduction reduction proportional radial radial radial radial radial radial variety variety iii targets derivatives configuration acknowledgements explicit explicit explicit derive longer factors factors factors metric explicitly explicitly coordinates transformations transformations transformations transformations implies extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction select decreases formation squares viewed viewed influence evaluated labels understanding partial smoothing smoothing smoothing smoothing smoothing spaces spaces reduces reduces combining iterative iterative distances distances distances distances distances distances distances norm euclidean euclidean kohonen kohonen advantages transactions transactions david thesis priori inter inter inter illustrated automatic coupled aspects extra closely closely suitable included projections projections situation identity traditional refer lie satisfy sampled usual michael absence ill automatically illustrates presents employed transformed production overfitting overfitting issues dataset behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour reducing reducing reducing reducing mappings mappings mappings mappings relationships func topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic fundamental necessarily generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation configurations ensure adjusted rank taylor multivariate epoch phd attempts synthetic optimum residual smoothness smoothness smoothness smoothness analytic explanation london stress stress stress stress stress stress stress stress stress stress stress stress stress purposes producing strictly incorporate located inversion universal implicit computers fourth geometric reflects apparent apparent applies empirically tional quantitative posed incorporated schematic requirement http http mod aim hyperparameters hyperparameters incorporating curvature curvature curvature curvature curvature curvature curvature curvature curvature curvature inherent inherent deviations multidimensional multidimensional multidimensional phenomenon www www arguments linearity acts flexibility rotations lost ranges adjusting imposed contract occurring nearby operates operates imply affected optimally intuitive intuitive enhanced performances excellent mance widths perfor demonstration spherical counter counter counter insight insight informative concentration implicitly implicitly implicitly insensitive insensitive displacement accumulated outlined outlined posteriori posteriori street largely aston aston aston aston aston aston diverse preserving seek acceptable ease preserved intuition intuition exclusive magnitudes gener permits maximally depicts monitoring alternatives apparently preserve retained els exploratory exploited differentiating expansions mds differently lowe lowe lowe lowe lowe lowe lowe lowe lowe lowe lowe justification justification transforming subjective firstly attempting broadly jain jain possess triangle preservation preservation neighbourhood vanish vanish contrary contrary inde rel centres centres centres goodness demands comprised tra trend indirectly fixing birmingham excessive predetermined developments tipping tipping tipping tipping tipping tipping tipping tipping tipping tipping tipping pendent iris iris iris iris ness minimise minimise minimise minimise regularisation regularisation lay counterparts ily ative supervision supervision supervision supervision complexities webb webb visualisation epsrc ncrg ncrg nose critically interna minimising embodies avail iee iee subsection optimising optimising philosophy minimisation deduced ast insensitivity neces effected effected organising ata parameterised equate peculiar minimises utilised deteriorates embodiment generalising generalising ditionally 
#@Lowe_D,Tipping_M,
#t10
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#*network network network network network network learning learning learning model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input data data data data data data data data data data data function function function function function figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training training training output output output output output number error results results information information information information problem problem problem problem problem models models models models models models models models models hidden hidden performance performance based based based based based based space space space weights weights weights linear linear linear linear layer layer layer case vector vector order order order order shown values values values values values values values values values values values values values values values probability probability probability probability probability probability probability parameters weight weight functions unit distribution distribution distribution recognition recognition method method approach approach approach approach approach pattern pattern pattern pattern single single single single single local test test test test test test test test test patterns patterns patterns patterns analysis class class class class class class class matrix optimal inputs inputs form form form shows shows algorithms algorithms gaussian gaussian gaussian examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples feature work task methods methods methods points points points points points points classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level problems random high high response response section section fixed line line line line line line line line rule rule general parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average average average average average theory note university university variables variables variables variables computation computation solution research independent independent independent independent independent independent log log log log log log log log log log found found found found table table table table table table table estimate estimate estimate estimate standard standard connections connections node node node node prediction prediction map low nodes nodes machine object sets sets maximum maximum maximum press learn learn learn position components continuous sample sample sample sample sample abstract convergence density likelihood likelihood likelihood likelihood likelihood likelihood likelihood references references component decision decision decision decision mixture mixture mixture estimation statistical statistical statistical statistical effect effect generated change change change variable variable variable assume assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier lower measure chosen higher bound cases required required good good good good conditions bayesian bayesian markov markov make make make fact techniques techniques region region proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed scale classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes tasks tasks tasks simulation simulation simulation regression regression regression regression regression respect sum times times times made natural natural natural applications obtain relative specific samples samples samples samples samples samples samples samples represented true cross cross cross series provide define define compute eye eye eye determined posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints constraints connected motor motor motor motor discrete discrete approaches approaches approaches support dependent report department loss loss loss loss loss loss loss loss loss individual bias scheme scheme framework cambridge cambridge equivalent estimates estimates estimates estimates effects classifiers classifiers upper full full full full full requires requires choice approximate approximate statistics statistics world basic validation validation validation give give give con conditional conditional conditional conditional conditional conditional conditional area actual provided selected selected depends sampling sampling sampling sampling sampling sampling sampling measured covariance increases denote denote close corresponds complete complete complete complete complete complete complete complete predictions predictions predictions finding common require require eds eds eds journal journal future future future degree objective account fully testing york york york increasing increasing head head head head head head head head mechanism special consistent empirical details making making making decay light predict predict predict predict denotes denotes improved improve separate separate takes element reported practical strategy engineering interest sufficient sufficient approximately axis definition definition mixtures chain chain improvement parts parts expression occur occur occur predicted predicted predicted predicted predicted alternative correctly feed occurs boundary generally starting row greater depend differences sigmoid bayes bayes bayes bayes bayes moody learns propose taking mechanisms integration characteristics solid proportional averaged averaged acknowledgements suppose suppose monte monte monte construct carlo carlo carlo plot distinct distinct distinct changing recall missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing averaging averaging averaging averaging averaging averaging gaussians applying predictive predictive predictive predictive predictive predictive predictive predictive predictive springer formed interpretation densities evaluated approximations approximated suggested converges converges past past earlier reasonable dashed dashed fitting fitting boundaries generation sufficiently classified avoid avoid avoid existing includes plotted illustrated uncertainty maximize maximize priors discussions successfully gamma importance society modification computationally wij build build score tend road verlag repeated repeated allowing return classify classify classify running strategies hold satisfy gibbs gibbs gibbs gibbs gibbs gibbs gibbs usual paradigm paradigm maximization software software software extend employed simpler unlike stimulation wiley essential varied put integral accurately hessian biases dataset dataset fewer reducing giving giving comparable cover predicting predicts equally ensure friedman logistic logistic taylor observe ith averages years adjacent expensive easier incorporate located located pool cut cut cut cut cut cut scientific separately universal circle author incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete incomplete geometric considerably dark flexible flexible pseudo pseudo completion completion incorrect maxima maxima maxima maxima maxima ity http exhibits mod ture ture weigend hyperparameters ordered ordered ordered ordered ordered ordered ordered ordered ordered ordered logp logp logp age age age age patients patients patients patients median median median median median median median softmax softmax arithmetic cumulative classifying classifying classifying proportion www assign oxford oxford extensive ordering ordering ordering ordering jth royal outcome outcome outcome allocation dealing murray convenient chains occurred mail check mark disjoint hours hours substituting motivation analyses patient bad belongs belongs tic laplace recovery recovery recovery recovery recovery modelled young belonging likelihoods variants approximator vari default assigning severe severe severe severe severe treat treat fitted fitted abu mostafa shading incorporates rubin rubin rubin randomized reaction centre classifies classifies letting avoided reflected impose rejected library funded accounted esti gordon completed completed completed rarely moderate ergodic parameterization crude calibration hoc val diagnostic diagnostic substitute architec beneficial attained rameters inde constraining pooling south categorical categorical nominal nominal nominal nominal dent mis investment indicators indicators shortly occurrences subtle decades putation ues unobserved pendent months months lid eta eta eta eta eta ables whilst dead dead putting inte imposing llx ago pri numbered adopting tinuous confident centred ies lose singapore epsrc justifies ore ripley ripley ripley ripley ripley ripley permission depen interpretable michie michie pupil app unconditional unconditional ofp sampler sampler optimizer reacting reacting ors spiegelhalter sumption plug plug verbal iip iip iip iip impaired neurological skip skip stats stats aining ordinal ordinal ordinal ordinal ordinal ordinal ordinal ordinal ordinal brian unavailable incurs incurs incurs injury injury injury injury injury injury injury mating suffered benefited url allel accommodated regularize dep ork wechsler conditionals conditionals conditionals conditionals ofthe ameters parametrically ellis limbs glasgow refenes curred unordered inflexible 
#@Mathieson_M,
#t10
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#*network learning learning model model model model data function function function function function function function function function function figure figure time set set set set set set set set set set set set networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number state state state state state state results results results results results results results results results results information problem problem problem problem problem problem problem problem models models performance based based space space space space space space space space space space weights weights linear linear shown values values values values values values values probability probability weight weight weight weight weight weight weight weight weight functions functions functions distribution distribution method method method method approach approach point point point point point point large large large large large large local test test analysis matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal form form shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper paper small small small size size size feature net net net net net work task task methods methods step step points field field field field process process level current structure similar similar representation show section section section section section section section section line line general parameter approximation average average average states states theory gradient obtained obtained obtained obtained obtained obtained obtained obtained term term result result result university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation independent log log defined defined sequence initial table standard standard computer terms terms terms terms node node node node science present present present present present low low nodes nodes nodes object object maximum maximum press position nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied computational convergence density references component stochastic stochastic stochastic stochastic procedure procedure procedure procedure procedure procedure procedure introduction hand cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search search search search search tion difference difference variable variable variable lower lower representations representations chosen center bound bound cases cases cases required required good good good good represent represent represent represent represent represent tree tree tree tree tree tree tree tree tree tree tree markov markov proposed length length correct probabilities probabilities finite simulations minimum minimum minimum minimum resulting resulting tasks total total computed computed respect respect respect sum sum sum called called called called called called called called called times times elements means means means optimization optimization optimization optimization optimization optimization optimization optimization potential dimension made natural applications study obtain obtain represented true true true compared compared define define compute compute compute objects perform perform experimental experimental connected connected distributions discrete discrete discrete discrete equal power mit larger proceedings report institute words words department version consists joint joint represents final addition graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph ai ai cambridge computing computing computing domain domain domain domain domain domain domain domain directly directly directly directly view limit stage stage upper upper upper approximate statistics statistics give condition conditional bounds path path path product product product biological technical describe denote fast close finding finding assumed supported journal ability makes makes makes including objective objective objective objective objective objective simulated simulated probabilistic probabilistic smaller combination reduced fully fully jordan jordan jordan jordan jordan jordan jordan technology ratio york edge edge edge edge edge edge edge trials trials empirical operation operation operation representing call call call max idea idea choose run run added exact advantage takes element reported introduced subject quadratic trees inference inference inference inference recently interest varying smooth smooth correspond converge converge evaluation interval increased constructed exists suggests wide matrices matrices matrices matrices deterministic column column demonstrate runs half conclusion conclusion critical place row row row depend bayes bayes clear performs performs hard hard hard hard largest cycle solid proportional minimizing exist min min relationship introduce introduce minima annealing annealing annealing denoted denoted acknowledgements reference reference explicit construct edges edges edges edges edges edges produces solving ways ways mathematical remaining belief belief belief belief applying applying minimization implies implies cycles select expressed dependence stages interpretation transform densities operations fraction approximations decomposition decomposition soft sizes sizes dashed additive spaces convex convex convex convex purpose add penalty penalty sufficiently expect expect formulation formulation assignment assignment discuss domains neighbors neighbors discussions tests tests reason straightforward aspects aspects differ maximal maximal maximal maximal maximal maximal computationally paths literature computations computations situation plots graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs contained contained heuristic heuristic heuristic heuristic heuristic heuristic heuristic satisfy notation notation michael highest reach reach operating extend presents presents minimized body schedule transformed graphical behaviour behaviour giving rest relationships dependencies authors comparable variability proved plausible possibly editor necessarily rev perfect subsets assumes academic optimum massachusetts piecewise directed directed directed agreement agreement defining defining defining answer tractable lies tool worse inside closer easier widely choices choices ran immediately mathematics mathematics consequence consequence lowest qualitative raw argument embedded embedded quantitative ity span rely aim proven marginal kinds kinds chose display jaakkola median extreme extreme contribute optimality formally conditioned optimizing acts ordering ordering ordering ordering eliminate connecting nonzero proceed eliminated eliminated extending dealing convenient significance stated hyper hope exploit intuitive filled heuristics date elimination elimination elimination elimination elimination elimination published embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding embedding introduces becker becker becker connect loo surprising vertices vertices vertices vertices vertices vertices vertices vertices searching searching nonlinearities treatment permutation permutation permutation permutation permutation permutation permutation permutation permutation permutation permutation express reveals indicator shortest vertex vertex vertex vertex vertex agree hypercube vari parents divide outperforms outperforms arcs clique clique clique clique clique clique clique clique clique clique clique recursively ease junction junction junction junction junction junction junction junction junction junction junction assignments assignments assess constrain iff iff iff gained convert picked emphasize scope investigating win cartesian discusses discusses geiger geiger geiger enforce siam siam siam grateful induces retained intensive rose rose rose rose rose rose factorized algorithmic algorithmic interior interior corners sake influenced confirm cornput fill fill hull eliminates cast cast stay progressively attained triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation cardinality cardinality nontrivial implying denmark factorization cliques cliques cliques cliques cliques cliques cliques cliques cliques amenable acyclic acyclic penalizes triple permutations permutations permutations permutations permutations permutations permutations permutations ables undirected undirected undirected undirected nondeterministic suitably suitably incident comprises scored henceforth tommi violation chord oij oij oij oij opens lations emphasizing poorer comput tri independencies independencies independencies succeeded invaluable doubly doubly doubly doubly concludes embed embed cording querying differen uai conquer oth attaining continous precedence precedence precedence precedence ivi organizes isn existent mazimum transitive marina aforementioned denser enumerate 
#@Jordan_M,Meila_M,
#t10
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#*network network network network network network network network learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data function function set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm number number number error error error error error error error error results results information information information information information information problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models performance performance performance based based based space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear case systems systems systems systems values values values weight weight weight weight weight weight weight functions functions functions functions method method method method method method method method method method method approach approach approach approach approach approach approach approach approach approach pattern image single processing processing processing processing processing test test test analysis analysis analysis matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal form form form form form form form shows algorithms algorithms paper paper paper small size size net work work task task methods methods methods methods methods methods methods methods methods step step classification classification classification classification high similar representation representation representation show equation equation section section section section general general generalization generalization speech approximation average average gradient gradient gradient obtained obtained term term note note note experiments result university university university threshold threshold variables solution research research independent independent defined found found initial constant constant constant table table estimate computer computer terms terms science science prediction prediction prediction prediction prediction prediction prediction prediction prediction map present present low low machine machine machine sets sets sets sets sets sets sets sets sets sets sets maximum range press press components components components components components components components components components components components components components components components components components components components components sample sample sample abstract applied find find properties references component component component component due ieee important decision propagation introduction complex statistical generated generated generated variance variance parallel search lower learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen chosen part required required good long tree distributed make fact fact proposed proposed proposed errors errors errors minimum resulting resulting resulting ing ing regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect respect performed elements elements elements means made obtain original original original original original original vol artificial true true cross cross provide provide active experimental goal goal goal goal goal related constraints constraints constraints equal approaches approaches approaches approaches mit mit larger larger train train descent descent descent source selection morgan morgan morgan morgan proceedings advances advances advances advances final bias bias scheme ai ai ai ai considered cambridge cambridge domain equivalent hinton estimates estimates estimates estimates estimates estimates estimates limit san san san san conference efficient statistics statistics statistics statistics estimated estimated basic basic basic validation validation give produce produce produce produce produce derived derived weighted randomly developed developed developed area provided provided finally finally selected constraint constraint covariance covariance covariance covariance describe denote inverse inverse predictions predictions finding finding amount main main eds eds square ability ability future degree rumelhart rumelhart rumelhart fit kaufmann kaufmann kaufmann kaufmann pairs combination combination combination combination account dynamical coefficients coefficients coefficients significantly york york increasing trials trials uniform uniform leads leads leads principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal making international idea minimize minimize produced produced choose choose run added predict architectures improved improved population discussed discussed improve improve improve advantage robust robust ensemble ensemble ensemble ensemble element reported include include subject subject identical trees subset subset relevant highly highly varying calculated solve pca pca address address evaluation evaluation symmetric generalized williams increased suggests trial predicted hybrid touretzky column demonstrate strength conclusion row assumptions conclusions accurate accurate accurate practice practice constrained constrained constrained constrained constrained constrained constrained mateo mateo mateo mateo propose taking taking taking demonstrated california intelligence regularization regularization turn turn exist suppose suppose pro derive written written written written ways generating estimating describes dept dept dept dept recall sensitivity category involves involves springer versus select select john choosing focus focus focus dependence dependence dependence dependence dependence depending correlated squares estimator estimator evaluated evaluated evaluated evaluate evaluate approximations sizes completely similarly spectrum earlier combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining purpose topology transactions transactions expect existing existing combinations weighting weighting weighting weighting mozer domains domains domains tests major columns extra closely uniformly computationally divided included included included build build build ten composed summary refer verlag procedures procedures strongly strongly allowing showing stopping stopping issue issue issue criteria criteria built satisfy michael predictor predictor automatically extract deal explore simpler wiley poor overfitting collection collection collection collection collection estimators estimators estimators estimators limitations limitations limitations limitations limitations mass hall dataset dataset ideal referred coefficient predicts friedman friedman friedman friedman fisher consist simplest utility arbitrarily finds finds finds attempts mentioned residual advanced rows agreement agreement unstable fairly fairly handle sections satisfied closer producing mation ridge ridge ridge ridge members members members members members members toronto lowest lowest mellon addressed robustness carnegie effort formulated variant rely summarized mod mod mod serve datasets datasets gave inherent redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy deviations progress extreme extreme extreme representative tresp tresp tresp cooper cooper cooper cooper cooper cooper cooper guarantee investigation member member member member approximates smith smith smith smith dealing breiman breiman breiman breiman breiman breiman breiman breiman adjusting biased observing krogh krogh krogh exceeds intuitive motivation date infor sion sion predictors decide decide demonstration widrow accounts uni hasselmo entries multiplied ensembles ensembles reveals reveals refers refers warmuth warmuth warmuth cpu cpu cpu cpu agree agree agree wolpert wolpert wolpert sons partitioned santa explains summarize fold shavlik shavlik shavlik vari stone limitation ics uci uci pointing pointing break diverse expanding tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani comparative examining demon demon constrain mutually verified trends cessing chapman disadvantage expand regularized regularized regularized regularized regularized eliminating simplifying paired unconstrained unconstrained unconstrained unconstrained meta cij cij library hansen hansen voting suffer esti meet els els els challenge housing housing housing handled handled meir meir meir meir uniqueness sees interior handling instability christopher justification agrees bold stay compo compo continuum continuum continuum continuum unreliable discarded chan chan chan edited meth meth tended tended repository ods ods constraining crl cruz irvine gence ance reviewed kivinen kivinen kivinen faced robustly stacked stacked ated cti cti sorted bootstrapping spanning terminology preferable retaining severely nents nents cient checks devel ucsc stacking ting shrink belmont disagree differed draws circumvent circumvent ponents gem gem gem gem gem gem gem gem gem olshen discard discard pertone pertone rni proaches motivate progression strated discarding tailed wadsworth perrone perrone manifest regres regres decorrelated decorrelated subsection mates regularizing merz merz merz merz merz oped vedelsby vedelsby vedelsby regu refinements intense mammone intercept coeffi hnear salamon salamon biggest elf misfit misfit misfit intelli unweighted underfitting backpropogation ley iie timator 
#@Merz_C,Pazzani_M,
#t10
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function figure figure figure set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output number state results results results results results results units units information information problem problem problem problem problem problem problem problem models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based case case case case vector vector vector vector order order shown shown shown shown systems systems systems values probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters functions functions recognition method method method method method approach approach approach approach approach approach pattern pattern point point image image image image image image image processing processing processing processing processing large local test test test test test test test test test class class class class class class class class class class class class class class class class class class class class class class class class class class matrix optimal form form form form form form shows shows signal algorithms algorithms algorithms algorithms gaussian gaussian gaussian small small small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work work work work work work work methods methods methods methods methods methods methods methods methods features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification trained trained structure structure structure structure random random random similar section fixed fixed fixed fixed rule rule rule vectors vectors vectors vectors images general generalization generalization speech parameter parameter approximation gradient obtained term term term term note note note note note note experiments experiments dimensional university university computation computation computation independent log log defined found found found found found target constant estimate estimate standard distance science sets sets sets sets maximum maximum maximum range range range range learn learn components components components components components components components components basis basis basis basis basis sample abstract applied applied applied applied back density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component due ieee ieee ieee important decision decision propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context context introduction estimation estimation estimation estimation estimation statistical statistical statistical statistical statistical statistical effect effect generated generated energy energy difference difference difference classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier measure prior prior learned chosen part part part previous previous previous cases type required required good good conditions equations equations make fact fact fact proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities resulting resulting classes classes total regression computed computed computed performed elements elements mapping optimization dimension made made global applications knowledge knowledge em em em em em em em em em em em em em em em em em em em em em obtain negative relative relative samples samples samples true compared application application application provide perform experimental related posterior posterior posterior equal approaches approaches approaches approaches accuracy larger update update descent selection department loss consists consists consists consists consists joint joint joint joint joint joint joint joint joint final scheme scheme scheme scheme scheme scheme scheme ai considered considered framework framework equivalent equivalent equivalent equivalent equivalent equivalent equivalent directly directly directly hinton additional additional curves estimates estimates design design design design design design design efficient classifiers classifiers choice choice choice choice significant significant estimated con condition conditional developed criterion criterion selected iteration simply simply covariance fast limited limited assumption complete complete complete complete rbf rbf rbf rbf rbf rbf rbf rbf amount amount common common effective assumed assumed assumed assumed assumed assumed assumed assumed supported role require journal future future noisy objective typically pairs pairs pairs jordan jordan jordan jordan segmentation segmentation segmentation segmentation segmentation special special structures database database database mode principle operation operation operation operation operation leads squared iterations iterations experts experts experts experts experts experts experts experts experts supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised expert combined combined combined combined combined combined combined minimize produced denotes improved advantage separate takes element practical practical practical introduced identical hierarchical subset subset subset subset subset engineering varying previously previously conventional conventional tions tions speaker achieve achieve achieve achieve address address mixtures mixtures mixtures modified modified observation observation generalized generalized improvement entire entire lead lead suggests suggests extended extended alternative alternative alternative locally deterministic generally generally generally setting setting setting demonstrate trajectories segment clear moody moody exponential practice suggest suggest suggest propose hard hard hard labeled radial radial radial variety exist averaged annealing suppose derive written written ways primary estimating label label label label label label label label label label label label tuned distinct distinct distinct distinct missing missing missing missing missing missing missing multilayer electrical involves develop minimization expectation letters national focus depending viewed viewed viewed viewed viewed viewed viewed densities updated labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels labels suggested suggested suggested updates key expansion roughly purpose foundation classified transactions transactions david existing includes formulation formulation batch batch batch batch batch determines prove maximize maximize variations gating reason selecting modification effectively effectively effectively identify build schemes situation miller miller miller miller miller miller miller miller miller miller miller miller miller miller essentially soc conf heuristic split dis superior contribution classify classify classify classify classify classify classify sci usual usual absence paradigm maximization maximization maximization maximization mixing extract jacobs situations situations minimized unlike unlike unlike parametric powerful powerful investigate investigate difficulty updating involving accurately accurately lippmann existence reducing fashion fashion fashion investigated comparable comparable cover cover phases notion analogous analogous neu naturally possibly adapt subsets subsets subsets quantities consist consist mixed mixed mixed mixed mixed submitted mentioned expensive expensive briefly briefly lies considerable sys formalism widely division incorporate arise commonly ion acknowledgement recognized separately medical medical arises incomplete incomplete incomplete incomplete incomplete qualitative preceding addressed greatly greatly items gains gains gains mod measuring ture differs extensions suited achieves substantial substantial chose segmented age implements initialization initialization phenomenon representative representative ghahramani ghahramani tresp tresp sensing sensing equivalence modify conditioned resources labelled labelled labelled labelled labelled labelled labelled labelled labelled labelled labelled labelled labelled tem tem dealing imaging significance significance darken darken analogy obtaining unlabeled star ral definitions affected adequate intuitive motivation contexts realization realization percepttons modelled surprisingly suggesting matter roy park partitioned partitioned partitioned partitioned partitioned implicitly dempster dempster interestingly insensitive dividing outlined divide posteriori ure rubin achieving basically ahmad dec forced rao suboptimal arg solely solely remote remote alter clas argue goals playing hughes scope rbfs rbfs iri pos laird differing struc rose mix mann info simplification ble justification inclusion neuneier realizations award incorporation conflicting discarded classi concert interpretations unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled unlabelled amenable amenable irvine irvine irvine deter magazine fication seg satellite mle mle objectives hood applica triple triple severely preprocessed fundamentally sat mentation respects formulations formulations formulations albeit postulated vast iter clarify posterjori parentheses fil imagery inadequate possi discard tri selector rni rni rue likeli hurt invoked pervised sole pennsylvania departure realizing native gersho incor hen hen quired lihood als expertise expertise akin optimistic meters unsu argues fulfills archive deficient deficient ministic sequel sifters communica clarified envision ere lipp career innovative sisting lutions porating 
#@Miller_D,Uyar_H,
#t10
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data function function time time time time time time time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number number number system state results results results results results results results results results results units information information hidden performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based space space space space space space weights case case order order order order order order shown shown systems systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method method method method method method method method method method method method method approach approach approach approach approach approach pattern single control local local local test test test analysis class class form form form form algorithms algorithms simple gaussian paper paper paper paper paper paper paper small size size size work work task task task task task task methods methods methods methods methods step points classification classification level level current structure structure structure structure structure structure structure structure structure structure structure structure problems problems random high high high high representation representation show show show equation equation equation equation equation section section section section section section section section rule general general generalization parameter parameter parameter parameter approximation approximation approximation approximation average theory theory gradient gradient term term term term term experiments experiments experiments experiments result result university university university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation computation computation computation computation solution research research independent independent independent defined defined defined defined defined constant constant table table table table estimate standard standard standard terms terms terms terms terms terms node node node science prediction presented present present present nodes nodes nodes nodes machine machine sets press press learn position continuous continuous continuous continuous continuous continuous continuous sample sample abstract applied applied applied applied find computational density properties references component ieee positive procedure procedure procedure introduction estimation statistical statistical statistical generated cost cost search search search search search search search search search search search tion difference difference difference difference difference difference difference difference difference difference difference variable variable variable variable variable variable variable assume assume assume assume assume assume assume assume measure measure prior prior prior prior prior prior prior prior learned chosen center previous previous cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases cases multiple represent distributed distributed distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov make fact fact fact techniques techniques proposed proposed proposed correct probabilities simulations simulations simulations simulations classes classes ing tasks simulation simulation simulation simulation computed respect respect sum performed performed performed performed times means potential potential made made made natural global global study knowledge knowledge obtain original artificial artificial artificial artificial artificial represented compared compared application application application application application application cross cross cross cross cross cross cross cross define compute proc perform experimental experimental experimental experimental connected distributions distributions distributions distributions distributions distributions discrete discrete discrete discrete discrete discrete discrete discrete approaches approaches mit accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison train train selection morgan proceedings proceedings report implementation technique technique advances joint joint joint joint joint joint scheme scheme scheme scheme scheme addition addition graph ai ai ai considered framework framework computing computing domain domain domain domain estimates san conference conference conference efficient requires choice significant significant significant significant significant significant significant significant approximate statistics estimated basic pages pages pages validation condition condition weighted randomly conditional conditional conditional conditional conditional conditional developed developed developed developed entropy entropy entropy entropy entropy entropy product finally finally nature nature measured measured technical increases describe describe arbitrary denote denote fast assumption assumption assumption assumption assumption assumption corresponds complete complete common generate theoretical require main main main main journal square easily makes simulated probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic needed needed needed needed needed needed account fully testing consistent structures structures structures structures structures structures structures structures structures structures structures structures structures structures structures uniform uniform uniform uniform uniform database database database database database database database database database empirical representing representing representing call call making making making making normalized supervised magnitude idea idea choose run added added added added added added added architectures discussed exact property property reported practical include identical inference recently relevant engineering interest compare compare compare yields yields correspond achieve definition definition mixtures background evaluation evaluation evaluation evaluation evaluation evaluation chain modified improvement sensitive sensitive grant occur deviation deviation column setting setting assumptions assumptions assumptions assumptions assumptions assumptions reduce conclusions valued differences measures measures measures measures clear clear exponential propose propose propose taking taking hard presence presence reduction drawn california solid regularization assuming introduce program question areas suppose edges written estimating ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann ann distinct metric metric metric metric metric metric metric metric metric metric metric metric missing missing sensitivity category explicitly involves slightly belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief implies national independently focus showed forms suggested suggested calculation sec purpose add closed calculate foundation foundation views transactions uncertainty uncertainty uncertainty maximize priors priors priors domains domains domains domains domains tests tests successfully simplicity planning selecting extra extra extra suitable society differ modification computationally computationally literature literature build schemes comparing comparing comparing invariance invariance score score refer notice heuristic showing interested contribution absence nips attempt subsequent acknowledgments carried powerful essential essential requirements requirements updating updating updating rapidly varied detail estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators estimators preliminary preliminary fewer fewer rest incremental applicable relationships relationships dependencies scaled comparable comparable comparable complicated workshop statistically statistically statistically statistically statistically statistically statistically statistically induction plausible integer changed rank greedy greedy noted algo assumes assumes explored art multivariate arbitrarily established established directed growing expensive independence independence independence independence briefly london formalism formalism arc arc arc organized ran ran ran bishop products optimize conjugate conjugate collected conducted lack effort share slower slower formulated maxima rely summarized summarized measuring measuring pittsburgh pittsburgh pittsburgh pittsburgh characterize differs cal conclude implements median median diagnosis softmax room tresp identifying cooper cooper cooper cooper cooper cooper cooper cooper oxford extensive ordering grows royal extending kaufman adds adds significance intelligent intelligent scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring reasoning settings intuitively guide heuristics date elimination recovered recovered induce regard counting originally francisco infer omitted omitted omitted omitted omitted omitted reader fitness informative inductive discovered fold avoiding avoiding adopted insensitive insensitive parents parents parents parents parents parents parents parents metrics metrics metrics metrics metrics multiply ence arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs arcs anns anns anns anns encouraging tween instantiation instantiation instantiation instantiation ideally ideally personal reports reports multinomial multinomial england discovering reflected assess remainder alter unseen increment simplifying increasingly iri pearl monitoring importantly drawback geiger geiger geiger funded alarm alarm alarm alarm alarm alarm alarm alarm sta likewise stuck suggestions opti suffices suffices tors inclusion concern medicine cardinality cardinality governing factorization factorization feasibility brackets semantics acyclic neglected replaces developments microsoft microsoft preferable entropies spent triple infeasible permutations cancel ample mal availability buntine heckerman univariate inferences augment circumvent pitt superfluous susceptible instantiations instantiations instantiations instantiations tri independencies govern oft estima asserts uninformative secs orderings instantiated reed reed reed misses cies surgery oped loth loth tistical iip lows bbn bbn bbn bbn bbn bbn revise experimenting parametrization parametrization xil gregory rea bination participating participating participating moller msr interchange concisely dawid dawid informatics wrongly wrongly pear forbes rll europe prelim redmond instan basics practi fori inary dependen 
#@Cooper_G,Monti_S,
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#*network network network network network network learning learning model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training algorithm output output output output output number error error error error results results results results results results units units units units units units units units units units units information problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden performance based space space space weights weights weights weights weights linear linear linear linear linear layer layer layer layer case case case case case case case vector vector vector vector order order order order order order order order shown shown systems values values values values values probability parameters parameters parameters noise weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit distribution distribution distribution distribution distribution method approach approach approach pattern single processing large large large large large large local local local local local local local local local local local patterns analysis analysis class class optimal inputs inputs form form form form form form form form form shows shows shows signal algorithms simple simple simple simple simple gaussian gaussian small small small net work work points points points points trained problems problems response similar similar architecture equation equation general general general general general general general generalization generalization generalization parameter parameter parameter real approximation approximation approximation approximation average average theory note experiments dimensional dimensional dimensional result university threshold variables variables computation computation computation research independent defined target target constant constant constant estimate standard standard standard computer computer terms terms science prediction prediction left left presented present low maximum press basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear abstract applied applied applied applied applied find density references ieee ieee important introduction hand effect variance variance variance cost cost difference difference assume lower prior prior representations learned higher bound bound bound bound bound bound bound cases cases cases required good good expected equations equations equations region region proposed proposed proposed proposed correlation errors errors finite classes classes classes classes ing simulation simulation regression regression regression regression computed eq regions factor factor global global global global global global global global global global global vol relative compared compared desired series compute compute determined constraints constraints equal equal approaches approaches approaches support morgan proceedings institute institute department technique technique internal internal internal internal advances exp bias bias bias bias bias graph graph ai directly solutions design limit limit san conference upper upper upper upper requires requires choice choice approximate approximate statistics world estimated estimated estimated give developed bounds bounds bounds bounds bounds bounds bounds area types discussion discussion feedforward arbitrary denote assumption rbf common effective require require require require require eds eds easily including fit fit kaufmann objective objective account functional functional functional transfer transfer transfer transfer significantly ratio projection projection projection projection special empirical empirical empirical empirical squared direct direct making decay decay decay decay decay decay decay decay decay decay denotes denotes denotes denotes denotes architectures advantage practical apply quadratic quadratic quadratic relevant engineering dimensions previously works smooth smooth smooth yields studies differential trans address generalized bounded risk grant grant parts expression expression studied studied suggests extended extended deviation wide wide derivative setting demonstrate demonstrate demonstrate assumptions assumptions operator operator operator interactions interactions interactions performs performs performs moody moody moody moody moody moody moody moody moody moody moody moody moody moody moody exponential practice mateo propose integration sigmoidal sigmoidal proportional regularization regularization regularization regularization regularization regularization radial radial radial radial radial variety relationship relationship averaged derivatives question acknowledgements reference explicit explicit monte monte monte monte derive derive derive derive construct carlo carlo carlo carlo carlo factors factors plot confidence dimensionality interaction quality implies select john john yield review depending approximations approximations approximations approximations forms forms forms activities converges key smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing additive reduces interpolation sufficiently norm norm euclidean box box weighting weighting weighting weighting weighting weighting sciences determines holds letter importance differ differ effectively driven poggio poggio poggio poggio comparing capture capture summary illustrates minimized bars simpler unlike poor rapidly replaced hanson integral integral integral integral lippmann hall biases biases pursuit pursuit reducing fourier applicable authors complicated tanh tanh workshop necessarily spline spline extremely friedman friedman simplest submitted inequality distinguish distinguish publishers derivation derivation smoothness smoothness smoothness smoothness smoothness improves expensive lin widely widely choices bishop bishop commonly controls controls mathematics implicit arises nsf nsf integrating requiring geometric limits applies flexible offset parameterized poorly poorly orders splines splines polynomials limiting monotonic curvature curvature curvature curvature curvature geman geman lim tresp ordinary uncorrelated uncorrelated uncorrelated uncorrelated oxford extensive extensive girosi girosi girosi girosi tensor unity jones jones connecting wrong multiplicative contract efficacy bands mark roles roles preparation nonparametric ensures sides regard enable matter extensively extensively balancing acknowledge onr drop outperform tibshirani tibshirani centre wahba wahba wahba stands tight algebraic options shaded favor hastie decays impose chapman graduate regularizer regularizer regularizer regularizer rbfs rbfs increasingly integrals option distinguished enforce september simplifies oregon strict strict manuscript sigmoids sigmoids covers gratefully stimulating bienenstock bienenstock council impractical smoother doesn hoc clarity bilinear arpa informatik subscript subscript subscript steve appro regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers regularizers amer sponsored cox stat imposes tightly intrinsically fundamentally tighter dilemma ness vdd ogi regional assoc mason projective projective projective projective projective projective projective projective volker desire penalizing penalizing penalizing cse functionals multivariable trivially quantifies portland marcel dekker ruth ruth integrations integrations lacks reg powell powell eubank eubank eubank cda absorbed rio parenthesis doursat doursat mth mth clarendon observational stuetzle stuetzle deutsche cbms parametrization algebraically algebraically monographs priate weigh rehfuss enforcement enforcement integrable rive bas smooths sweden 
#@Moody_J,Rognvaldsson_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output output number number error error error error error error error error error error error error error error error error error error error error error error error error results units units units units units units units units units units units units units units units units units information information information information information information problem hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance space space space space space space space weights weights weights weights weights linear layer vector shown systems systems systems systems parameters parameters noise weight weight weight weight weight functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method approach approach point single single processing processing processing processing processing processing local rate test patterns class optimal optimal optimal optimal form form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple examples feature task task task task task task task task task task task task task task task task methods methods methods classification classification classification classification classification process process level trained trained trained trained trained trained trained response response response response response response response response similar show general generalization generalization generalization generalization generalization generalization generalization generalization parameter average average average average average average states note note note note experiments experiments university university university university variables variables computation computation research defined defined defined found target target initial constant terms science prediction prediction left presented presented machine machine sets maximum range press press components outputs outputs outputs continuous abstract applied back back back properties references due procedure procedure procedure important important adaptive propagation propagation introduction hand estimation estimation stimulus stimulus stimulus stimulus stimulus effect dynamic variance variance variance variance variance variance variance parallel complexity variable classifier lower measure signals signals learned chosen binary distributed expected techniques region region correlation correlation correlation correlation correlation correlation correlation errors errors errors simulations simulations classes tasks tasks tasks tasks tasks tasks tasks tasks tasks regression computed computed computed respect respect sum sum regions factor factor factor optimization relative relative relative compared compared compute compute related related brain brain mit mit comparison train nets morgan morgan morgan morgan morgan morgan proceedings department department department technique technique individual individual individual individual individual individual individual individual advances advances advances advances advances responses responses responses responses responses bias bias bias cambridge cambridge directly hinton additional san san top detection determine classifiers classifiers classifiers significant significant statistics world estimated weighted types backpropagation backpropagation backpropagation depends depends depends depends discussion feedforward increases arbitrary assumption corresponds complete surface surface finding assumed generate eds eds easily degree rumelhart rumelhart rumelhart rumelhart kaufmann kaufmann kaufmann kaufmann combination combination reduced jordan significantly uniform operation leads principal direct bottom experts supervised early magnitude decay idea combined run added description predict architectures improved improve recent correlations correlations correlations typical introduced identical unsupervised studies converge definition mixtures separation modified improvement improvement improvement sensitive entire entire occur derivative hybrid touretzky touretzky touretzky touretzky generally reduce reduce reduce competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive central performs mateo mateo presence physics reduction reduction reduction regularization introduce manner minima minima base base denoted edges edges produces winner winner primary primary primary primary primary primary primary primary dept changing explicitly explicitly simultaneously simultaneously averaging averaging unique adding quality versus competition competition competition competition competition competition decreases decreases stationary correlated correlated squares viewed viewed influence static static partition dashed convex combining assigned thesis thesis combinations weighting extension mozer middle extra differ included included mcclelland committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee comparing plots plots tend receives receives receives induced cun cun success stopping gray gray sampled generalize wave denker highest predictor predictor predictor jacobs jacobs receive estimators reducing reducing reducing reducing reducing reducing respond cognition notion notion examined necessarily subsets panel separated baseline baseline baseline improving improving arbitrarily arbitrarily phd phd years brown rows pairwise improves improves improves improves improves nowlan comparisons drive drive berkeley constructing members percent dark fed red item item share solla variant variant pittsburgh pittsburgh pittsburgh cal geman geman geman geman adjust damage damage diagnosis univ picture ordinary corrupted secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary secondary primarily lagrange discovery multipliers consideration breiman breiman affected degradation degradation predictors predictors paul guarantees facilitate hasselmo multiplied ends arrows wolpert wolpert interestingly receiving receiving influences explorations zipser zipser zipser microstructure sine misclassification munro munro munro munro munro munro munro munro convenience tradeoff auxiliary auxiliary auxiliary decorrelation decorrelation decorrelation visualization mutually exclusive chauvin chauvin management compensate degraded thresholded projecting cation denver handled bienenstock bienenstock bienenstock bienenstock attempting resampling inherently ning tip vote vote systematically sis stacked stacked greatest excessive health constituent degrade modulate dilemma caruana caruana caruana fight respects reminiscent manipulations favorable disagree notational pitt pitt delivered telecommunications dam perrone perrone perrone perrone purdue granger granger congress interfere replicating misclassifications misclassifications merges committees doursat doursat doursat regressions negatively rests sinusoid quarterly forecasts lse ols participating touretsky iance supplementary attributable erro 
#@Munro_P,Parmanto_B,
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural input data data data data data function function function function function function function function figure figure figure time time time time time time time time time time time set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number system system error error error error error error error error results information information information information problem problem performance based space space space space case case vector vector vector vector order order order shown shown values parameters weight functions functions functions functions functions distribution approach approach point point single processing large large large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal form signal signal signal signal signal signal algorithms simple examples examples examples examples small small small small small small small net work work work task task fig fig fig fig points process current structure memory memory similar similar representation equation equation equation section section section section section section fixed line line line line line line line line line line line line line line line line line line line line rule rule rule rule rule rule rule rule rule rule rule rule vectors general general general general generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real average average average average average average gradient gradient gradient note note note note note dimensional dimensional solution research independent found sequence target dynamics dynamics initial initial constant constant constant estimate computer distance distance left direction direction direction low machine maximum range press press learn learn continuous continuous continuous continuous continuous continuous abstract applied find convergence convergence convergence convergence convergence references references stochastic ieee ieee positive positive positive important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive mixture introduction estimation behavior behavior statistical statistical effect generated tion change change change change variable assume assume assume rules rules signals signals signals signals signals learned chosen part previous previous good conditions expected expected expected expected equations make make proposed proposed proposed proposed proposed observed observed forward minimum minimum minimum minimum minimum minimum ing tasks simulation simulation simulation computed respect eq eq eq eq eq eq eq called times elements means means means natural applications applications applications obtain obtain negative negative original vol vol represented application application desired cross provide define define compute rates proc goal distributions distributions discrete equal equal approaches mit mit descent morgan loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss implementation technique difficult ai framework cambridge equivalent experiment experiment environment environment environment environment additional view solutions efficient choice approximate statistics world world estimated estimated estimated estimated estimated give lines sampling simply simply measured increases describe group fast fast fast fast limited limited limited close inverse corresponds corresponds short short effective assumed role eds adaptation adaptation adaptation end future easily rumelhart rumelhart kaufmann smaller underlying interesting projection projection head squared details details iterations iterations idea idea idea idea idea choose sources sources sources denotes denotes denotes discussed correlations correlations correlations pair takes typical practical practical apply apply strategy strategy sense sejnowski sejnowski sejnowski recently sufficient observations approximately approximately works tions yields speaker trans separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation generalized scaling wide matrices predicted correctly feed locally boundary setting setting pass flow flow flow flow flow flow flow flow flow flow conclusion starting depend depend depend accurate numerical sutton sutton moody moody practice asymptotic asymptotic asymptotic strong demonstrated assuming min averaged averaged averaged introduce annealing acoustic acoustic attractor explicit explicit explicit explicit explicit suppose pro longer estimating laboratory ann stability changing changing changing changing changing changing changing changing metric simultaneously infinite remaining easy depending stationary stationary stationary stationary estimator estimator learner learner evaluate controlled showed evolution approximated converges converges converges converges converges constants allowed past earlier sec sec purpose filtering calculate sufficiently norm existing bell bell bell blind blind blind blind blind blind blind blind blind blind blind blind batch batch batch determines extension prove holds holds holds holds phys phys simplicity efficiency maximal modification modification modification modification mcclelland comparing orthogonal receives capture conf follow follow follow follow comp paradigm nips nips nips eigenvalue eigenvalue automatically automatically moves mixing mixing mixing mixing mixing mixing extend employed origin powerful access investigate environments environments environments environments hessian hessian hessian hessian hessian hessian existence rise scalar scalar workshop workshop func math coefficient adapt adapt rev rev thought quantities quantities versions algo som observe observe observe amari amari amari amari amari amari amari amari amari amari mixed mixed mixed simplest motivated motivated finds seconds averages averages asymptotically slowly variances variances analyzed turns perspective straight controls cut scientific projected gradually definite sun fluctuations fluctuations mechanics mechanics applies pseudo amounts generic conducted simulate introducing solla solla incorporated music music http switch switch berlin rely suited gave germany inherent attraction utterances differentiable instantaneous instantaneous feasible japan rithm drift nat tensor plays extending extending fits khz darken darken tools satisfying proceeds imposed check moment reasoning intuitively intuitively adequate evaluations sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky excellent encountered intended omitted arrive theoretically theoretically storing extensively eigenvector eigenvector eigenvector eigenvector seung switches switches switches robert speaking audio saad saad aston basin failed adopt auxiliary var scenario scenario scenario intuition pdp pdp annealed annealed annealed annealed annealed expand emphasize switched noting noting page vanishes jutten jutten jutten dichotomies consuming fractal sake converging adaptively ning ning substitute html reproduced drastically alto statist sian experienced adapts gmd gmd server stabilize files facts neglected cichocki riemannian tit tit palo murata murata murata murata applica drawbacks infeasible schuster schuster schuster schuster aims omit heskes heskes herault herault herault fluctuating modifies klaus klaus andreas relying web accessible leaky leaky leaky leaky leaky confirms cooling ant singapore miiller miiller miiller barkai gra altogether shi accelerate riken riken robbins robbins robbins kappen kappen monro monro monro sudden assure dient accessed ingredients ven lution suddenly obtainable ichi drastic saitama wako caption clever rudower zoo trai chaussee milllet shun fluctuates rlt rlt rlt iscas import ded lear hes audible audible listener 
#@Amari_S,Milllet_K,Mumta_N,Ziehe_A,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural input input input input input data data data function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set networks networks networks networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number number error error error error error error error state results results results information information information information information information information information information information information information problem problem problem problem problem problem problem models hidden performance performance performance performance performance performance performance performance space weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear layer vector vector vector vector vector vector vector shown shown shown systems systems systems systems systems values probability parameters parameters noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight method pattern point point point point point image single single processing processing processing processing processing processing processing large large large large large large large large large large local local local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs form form shows shows shows shows signal signal algorithms algorithms algorithms algorithms simple simple gaussian gaussian paper examples small size net net work work work work work methods step classification classification classification classification classification classification current trained trained trained trained problems problems random similar architecture show show section section section section section line line line line rule rule vectors generalization speech speech parameter parameter parameter parameter parameter average average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term note result result result result university university university computation computation computation computation computation independent independent independent log log log log log found target dynamics dynamics dynamics dynamics constant constant constant constant constant constant constant constant constant constant constant constant constant constant constant estimate estimate estimate estimate estimate estimate estimate standard standard computer computer node node node science science science prediction prediction prediction presented present phase phase phase phase nodes nodes nodes nodes learn nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous abstract applied back back back back back find computational convergence convergence convergence convergence convergence convergence convergence convergence properties likelihood references references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation introduction estimation behavior behavior behavior behavior behavior behavior statistical cost cost search search search search search search search search search search search search change complexity assume prior prior part center previous cases cases cases required multiple multiple distributed expected expected make techniques proposed correct correct forward forward finite simulations classes ing ing total total computed respect performed called times times times times times times means optimization optimization optimization optimization optimization made knowledge knowledge vol vol vol artificial provide provide compute compute compute compute rates rates perform perform connected equal accuracy accuracy comparison comparison update update descent descent descent descent descent descent descent nets nets morgan morgan morgan morgan morgan report institute institute institute implementation implementation version technique consists consists code advances advances advances advances advances difficult bias scheme addition graph computing computing equivalent equivalent curve curve curve curves curves estimates estimates transition transition san san san san san top determine efficient full requires requires requires requires choice significant statistics con con con con condition condition developed developed product product finally depends sampling constraint constraint achieved achieved achieved technical feedforward increases increases arbitrary fast fast fast fast fast fast fast close close inverse inverse inverse inverse corresponds complete effective effective effective effective implemented supported theoretical theoretical require require require require journal square easily makes noisy kaufmann kaufmann kaufmann kaufmann kaufmann typically reduced coefficients fully fully technology block significantly ratio consistent database mode language squared squared squared squared call iterations bottom early decay combined combined combined choose run improved improve improve exact ensemble ensemble takes include subject pixels relevant engineering dimensions dimensions compare compare previously works smooth converge converge converge converge converge achieve achieve storage storage storage storage storage entire increased grant grant suggests correctly white pass demonstrate demonstrate runs reduce trajectories trajectories trajectories editors editors editors editors editors differences measures moody moody moody moody moody exponential faster constrained constrained mateo mateo mateo mateo propose propose taking physics largest largest california regularization turn start targets minima annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing explicit explicit appears written written primary plot mathematical dept dept dept averaging averaging averaging blocks versus john john phoneme phoneme phoneme phoneme phoneme densities approximations understanding completely suggested updates earlier earlier earlier calculation calculation dashed performing combining advantages classified transactions box includes thesis thesis eigenvalues eigenvalues batch batch batch batch batch extension extension automatic automatic discuss holds efficiency maximal modification efficiently essentially identity summary refer refer notice quickly heuristic heuristic showing return return lie satisfy dot backward giles giles giles eigenvalue eigenvalue eigenvalue maximization attempt subsequent acknowledgments intrinsic tesauro cowan cowan cowan cowan unlike schedule poor requirements detail hanson hanson hanson hanson hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian hessian dataset dataset helpful scalar scalar scalar scalar examine examine mse mse scaled authors comparable eigenvectors complicated momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum momentum neu smallest adapt predicts implementations store switching switching switching switching epoch epoch epoch improving phd phd attempts averages averages optimum optimum optimum optimum optimum optimum asymptotically costs publishers improves diffusion expensive expensive multiplication multiplication starts reasons perspective tive purposes leaves mathematics simard simard inversion inversion inversion opt opt opt opt begin optimize lowest lowest conjugate conjugate conjugate conjugate percent percent percent prop prop spoken lms lms lms lms lms lms readily backprop detecting adjustable incorporated treated compares passes switch switch switch incorporating incorporating phonemes curvature curvature curvature curvature curvature curvature achieves achieves acoustics datasets datasets adjust comments displays displays displays displays instantaneous leen leen leen leen leen leen optimality restriction optimizing tensor concerned lecun lecun lecun turned turned extending extending darken darken darken darken darken proceeds efficacy resulted ral optimally presentations presentations presentations presentations date date alspector started started ranging equals regarded enhance originally schedules tic francisco late late late cpu roy pearlmutter pearlmutter pearlmutter pearlmutter summarize yale street slight minus annals basin basin adopt obtains hundred param jacobian pub decays graduate graduate graduate annealed annealed annealed annealed annealed annealed annealed annealed annealed annealed annealed annealed afosr surrounding regimes rough indication transients eters oregon oregon oregon oregon behaves settling todd todd todd dominates accomplish eliminates identically calculates optima placement orr orr orr orr orr orr orr cur william cess trapped vergence amax amax continuing heskes invert ogi couple goldstein burden yann yann adap prohibitively agation anneal plp cse insure etienne timestep tain barnard southern robbins robbins 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#@Leen_T,Orr_G,
#t10
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#*network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input data data data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time set set set set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number number system information information information information information problem problem problem problem problem problem problem problem problem problem models models models models models models models models models performance performance performance based space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case vector vector vector vector order shown shown shown shown shown shown shown shown shown systems systems systems systems values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise weight functions functions distribution method approach approach approach point single processing processing processing processing processing test analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal form form form form form form form form shows signal signal signal signal signal algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian task task methods step classification process process process process process process process structure structure structure random random representation show equation fixed fixed vectors general generalization speech parameter real real approximation average theory gradient gradient gradient gradient gradient gradient gradient gradient term term term term term term term term term term note note note note note experiments experiments experiments dimensional result university computation computation solution solution research research independent independent independent independent independent independent log constant estimate estimate estimate standard computer terms terms terms terms science prediction left left left low low temporal temporal maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press press press press press press press position components components components nonlinear sample abstract applied find find computational convergence convergence density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component stochastic stochastic stochastic stochastic stochastic ieee ieee positive important important mixture mixture mixture mixture mixture mixture mixture mixture context estimation estimation estimation effect effect variance recurrent recurrent recurrent recurrent tion tion tion change complexity complexity variable spatial signals signals prior chosen higher center center required good bayesian equations make fact techniques correct probabilities forward scale simulations resulting resulting respect performed called elements elements elements means means made natural natural natural applications applications knowledge em em filter filter filter filter negative original original specific specific samples samples true true true define related related distributions distributions approaches mit mit accuracy accuracy update dependent dependent source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source proceedings institute version technique technique individual individual advances advances difficult exp bias maps framework framework framework equivalent experiment directly solutions stage conference conference full requires free speed vision estimated estimated estimated estimated estimated estimated estimated estimated estimated give give produce types product processes constraint measured discussion denote denote denote transformation transformation transformation fast inverse inverse inverse assumed theoretical require square square instance easily easily makes makes including probabilistic probabilistic underlying unknown unknown unknown coefficients coefficients coefficients technology ratio york special special special consistent uniform leads details call numbers filters filters filters filters filters stored international international normalized attention run added sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources denotes improve recent recent advantage separate separate element practical apply moving include sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski engineering interest interest sufficient highly varying conventional volume mixtures separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation generalized sensitive sensitive constructed expression expression expression expression scaling derivative derivative deterministic white white column row row assumptions assumptions assumptions operator clear exponential constrained sound strong presence presence sigmoidal intelligence assuming assuming assuming variety ica ica ica ica ica ica ica selective introduce derivatives explicit explicit explicit explicit pro derive produces dept changing changing explicitly coordinates linearly springer expectation potentials independently expressed expressed expressed stages communication influence densities densities restricted similarly similarly diagram reasonable performing reduces event closed closed filtering calculate calculate thesis bell bell bell bell bell bell bell bell bell bell bell blind blind blind blind blind blind blind blind blind blind blind blind blind blind plotted simplicity reason straightforward straightforward straightforward sensor sensor sensor sensor extra suitable suitable society computationally driven included post ten ten ten ten ten road refer refer verlag neuroscience dis manifold follow criteria generative generative generative cues notation quantity quantity delayed maximization maximization maximization maximization mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing situations transformed production production production production varied varied involving optimized dataset dataset fewer fashion history history history history history history tech combine complicated affect statistically reading equally perfect perfect singular logistic logistic logistic logistic logistic amari amari mixed mixed mixed arbitrarily submitted integrate residual scenes distinguish sensors sensors convolution convolution convolution derivation derivation nonlinearity processed purposes purposes producing filtered filtered inversion implicit definite axes conducted parameterized posed incorporated frequently rep http maximizes logical inherent begins differentiable instantaneous ordinary college contextual contextual contextual contextual sort www guarantee japan princeton driving driving recover jth fits convenient siemens siemens simplify city intelligent efficacy serves salk symposium financial separating recovered recovered recovered recovered recovered recovered recovered introduces ambiguity appendix forecasting forecasting histograms histograms yang yang nonlinearities israel permutation permutation express express surprisingly pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter generalizing assigns assigning trading infomax infomax infomax multiply audio truncated slight indirect constitute convolutional kurtosis convenience residuals aij aij aij aij personal causal pub ftp ftp toy searches expand deconvolution deconvolution fir fir inverting inverting algebra modifiable parametrized jutten jutten simplifies diagrams parameterization parameterization corporate invertible european east clarity dropped eliminates cast cast bss 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#@Parra_L,Pearlmutter_B,
#t10
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#*network neural neural neural neural neural neural neural function function function function function function function function function function function function function function figure figure figure set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number state information problem based based based based based based linear linear linear case vector vector vector vector vector order shown shown shown systems values values parameters parameters parameters parameters parameters functions unit recognition pattern pattern point single processing control rate analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form form form form form form form shows shows algorithms simple small small step step step step step step step step step step points process problems problems problems problems random high high show show show show equation equation equation section section fixed fixed general general general parameter parameter parameter parameter parameter term term term note note dimensional result university variables variables computation computation log log log log log initial terms terms terms terms distance distance distance node left left left machine sets press abstract convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due due ieee positive positive positive positive positive procedure procedure procedure introduction action statistical change change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference difference difference difference difference difference variable variable measure measure measure chosen chosen chosen part part theorem theorem theorem cases cases required good conditions make make simulations simulations minimum minimum ing sum elements optimization optimization optimization optimization optimization dimension applications applications obtain obtain negative negative negative negative negative negative negative negative negative negative negative original original original specific true application desired desired provide define compute eye experimental constraints constraints constraints constraints constraints constraints constraints mit steps update update institute words department technique advances final exp graph graph graph graph graph graph graph graph graph graph ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai equivalent equivalent san san efficient choice choice free pages con con derived derived randomly developed criterion criterion criterion criterion lines product product provided iteration iteration constraint constraint achieved increases increases increases arbitrary transformation transformation close assumption assumption proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof proof effective require require require require require require main end end end end makes objective objective objective objective objective objective objective objective combination projection projection increasing matching matching matching matching matching matching matching matching matching operation operation operation operation operation leads squared numbers iterations iterations iterations making property property property property strategy quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic recently recently dimensions calculated tions yields yields converge converge converge converge achieve achieve bounded increased matrices matrices deterministic deterministic deterministic deterministic column column column column column column column column column setting setting setting conclusion row row row row row row row row valued depend depend central central central designed constrained constrained temperature temperature temperature presence physics largest largest largest largest largest demonstrated demonstrated california intelligence variety minimizing min decrease manner annealing annealing annealing annealing explicit derive written written written solving plot plot plot dept recall metric involves transformations transformations adding implies implies versus decreases decreases decreases decreases decreases independently transform reasonable calculation roughly add remains symbol euclidean euclidean transactions coordinate eigenvalues eigenvalues eigenvalues eigenvalues inter assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment subspace subspace subspace subspace subspace extension columns columns columns columns extra delta identify efficiently identity graphs prob heuristic success return return return sci hold comp quantity relaxation relaxation providing eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue satisfies decreasing extend diego transformed transformed involving involving school proper cover trace trace possibly analyze ensure algo initialized established rows rows rows crucial guaranteed defining handle style operators ran immediately separately begin begin begin begin definite definite preceding summation considerably readily requirement requirement requirement partitioning partitioning fall sums sums sums returns yuille yuille yuille yuille yuille yuille softmax univ benefit benefit benefit benefit formally lagrange lagrange lagrange lagrange lagrange lagrange restriction summing summing rithm appropriately optimizing unity turned eliminated kullback kullback kullback smith mail simplify city imposed effectiveness effectiveness salient combinatorial mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness ensures ensures entry guarantees guarantees ascent tic initialize francisco specialized permutation permutation permutation permutation permutation jolla augmented statement summarize convergent yale yale yale unchanged street street gold gold gold gold gold gold gold corporation vec vec leibler leibler leibler break alternating aij eric algebraic algebraic algebraic algebraic algebraic picked fir projecting spanned spanned spanned barrier thousands thousands bring amplification amplification normalizing normalizing simplifies gorithm ucsd ucsd lems demonstrating demonstrating satisfaction satisfaction satisfaction fortunately justified east tsp tsp tsp tsp tsp tsp tsp tsp steven steven char stay medicine diagnostic rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan rangarajan alan archi transpose essence zeros slack slack emerged emerged dij benchmarks objectives mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai mai haven vergence prime collecting argmin def def apparatus manipulations constituents excluding excluding tecture preset executes kronecker kronecker stochas cap cities cities modulo manageable compatibility combi doubly doubly doubly doubly doubly doubly doubly doubly doubly doubly doubly reed cai cai cai cai cai cai cai cai cai cai obeying referring kosowsky positivity radiology garrett concatenating adjacency negativity negativity negativity anand anand recipe verge maih maih maih definiteness graduated graduated 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#@Gold_S,Mjolsness_E,Rangarajan_A,Yuille_A,
#t10
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural input input input input input function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number error error error error error error error error error error error results results results results units units units units units units units units units problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based weights weights weights weights layer layer layer layer layer case vector vector vector vector vector vector order order order order order order order order order order order order order order order order order order order order order order order order systems values values values values values parameters parameters noise noise weight weight weight weight weight weight weight weight unit unit unit unit unit distribution recognition recognition method method method pattern point processing processing processing processing processing processing processing processing processing processing large large large local rate rate test test form form form form shows shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple gaussian gaussian paper paper paper paper examples examples examples examples examples examples examples examples examples small feature methods step step step step level problems problems problems similar similar section section fixed rule general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization approximation average average average average average average average average average gradient gradient gradient gradient obtained term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term term note note note note experiments experiments experiments experiments experiments dimensional result result computation computation computation computation defined defined found target target initial initial initial standard standard standard terms terms terms terms terms terms terms terms terms terms terms terms terms science science direction present activation range press press learn learn learn basis basis abstract applied back find computational convergence convergence convergence convergence convergence convergence convergence references due positive procedure procedure procedure important important propagation introduction effect effect effect effect generated generated parallel parallel tion difference complexity prior higher required required conditions bayesian bayesian bayesian proposed length length length length scale scale ing ing total total regression regression regression regression respect respect performed performed performed called times times times times means factor factor factor factor factor factor factor factor factor factor factor factor dimension made made negative negative true true cross cross cross cross cross cross cross cross cross rates experimental experimental comparison comparison comparison larger larger larger update update update descent descent morgan proceedings consists advances represents difficult exp bias bias bias layers addition maps framework framework experiment directly hinton hinton hinton san effects conference efficient significant validation validation validation validation validation validation validation validation validation con randomly criterion criterion backpropagation iteration simply normal increases fast limited amount implemented assumed assumed shape main eds adaptation square future easily degree kaufmann objective objective objective objective combination combination increasing trials trials trials squared squared squared squared squared squared squared squared squared squared squared squared squared squared squared iterations making making normalized normalized normalized normalized normalized normalized supervised supervised supervised early decay minimize predict denotes denotes denotes architectures improved improved improved practical quadratic calculated calculated calculated calculated calculated calculated volume works converge converge evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation williams williams williams improvement entire lead invariant deviation deviation deviation touretzky generally setting conclusion starting minimal minimal trajectories trajectories depend accurate designed mateo sigmoidal regularization regularization regularization minimizing derivatives minima pruning pruning multilayer involves consisting adding adding adding adding adding springer decreases independently expressed review communication evaluated evaluated evaluated operations showed showed showed translation partial partial calculation smoothing sec sec sec purpose add penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty interpolation initially sufficiently includes includes combinations contour priors absolute absolute absolute absolute structural determining efficiency efficiency efficiency efficiency computationally poggio poggio efficiently efficiently efficiently efficiently efficiently mackay mackay mackay comparing verlag link stopping decreasing minimized origin experience hanson hanson hanson graphical graphical graphical biases examine successive tech investigated applicable scaled referred root func contours contours contours naturally changed adjusted consist seconds seconds languages advanced unstable improves improves improves reasons bishop bishop bishop desirable laboratories computers computers sun conjugate improvements empirically leave adjustable employ employ frequently rep compares compares compares compares compares compares berlin gen plan decreased age arithmetic lab newton newton corrupted japan japan girosi girosi adds city determination keeping north adequate adequate adequate adequate evaluations evaluations displayed holland laplace advance cpu cpu cpu cpu cpu steepest explains adopted adopted stone stone fitted multiplying ence basically utilize par comparative quasi tendency tor massively ization discontinuity pos stuck signs worked worked worked lation tial oscillate lated pratt pratt pratt drastically drastically drastically statist cho adequately adequately amsterdam saito saito saito saito saito saito saito saito demanding newly rmse rmse rmse rmse rmse rmse graphically forgetting undesirable tics statis sible evaluates eralization conver terminated gun nakano nakano nakano nakano nakano nakano nakano nakano exceeded differed kyoto aver viewpoints equiv almeida almeida almeida estima valley struction sit soraku seika ade bringing silva silva silva silva calcu calcu clarendon stably hikaridai recommended transposed eckmiller ating speeding knew alent conceivable effi bfgs bfgs bfgs evalu bination incidentally incidentally pessimistic woo woo perimental invented wlx battiti battiti oss oss binations tsukuba ciency europe halved ovals 
#@Nakano_R,Saito_K,
#t10
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure time set set set set set set networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training output output output output output output output number number number number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results results results units units units information information information information information problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based space weights weights linear linear linear linear linear linear linear linear linear layer layer layer layer layer case case case case vector vector vector order shown shown shown systems values values probability probability probability probability parameters noise weight weight functions functions distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method method method method method method method pattern pattern point single single rate rate rate test test test test test test test test test test test test test class class matrix form shows simple gaussian gaussian paper paper examples examples examples examples feature net net net net net net work work task task task task task methods methods methods methods features features features features features features features classification classification classification classification classification process level current trained trained trained trained problems problems problems problems problems problems random high high similar architecture architecture show section section section section section vectors vectors general general generalization real real real real real approximation approximation approximation approximation approximation states obtained obtained obtained term term term note experiments experiments experiments experiments experiments experiments experiments result result variables variables variables variables variables computation computation log log log log log log log log defined defined defined defined target target target target target target target target constant constant table table table distance connections connections low frequency machine machine machine nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous abstract density likelihood likelihood likelihood likelihood references due due positive positive procedure adaptive introduction introduction estimation effect generated generated variance variance variance difference difference complexity complexity variable variable variable variable variable variable assume assume classifier classifier lower measure measure measure measure prior prior prior prior prior learned learned chosen chosen chosen chosen higher previous theorem cases cases good represent represent bayesian bayesian bayesian bayesian make make make techniques correlation observed observed resulting resulting classes classes tasks total regression regression respect performed performed means means factor optimization dimension natural applications applications applications applications applications negative specific application application application define define define determined determined experimental experimental related constraints constraints equal equal contrast contrast train report institute institute technique joint represents represents final bias scheme addition considered framework curves capacity determine efficient significant significant significant significant approximate statistics world world world world world estimated basic increase increase validation validation validation derived randomly randomly conditional area finally backpropagation iteration iteration iteration simply simply simply measured covariance tested tested tested transformation limited common theoretical journal ability ability instance future future easily degree makes noisy noisy noisy fit fit objective objective objective objective objective objective objective objective objective pairs pairs pairs pairs technology technology significantly significantly character increasing increasing increasing consistent uniform database database mode principle leads leads squared representing details call iterations direct direct normalized early early early idea choose predict predict improved improve improve improve directions directions directions advantage advantage pair pair pair similarity reported practical introduced include side sense highly approximately smooth observation observation improvement improvement improvement sensitive entire increased exists occur suggests deviation half conclusion assumptions assumptions bayes performs constrained strong strong strong drawn drawn demonstrated california california minimizing exist decrease decrease iii averaged program denoted index ways describes describes label implement implement implement missing simultaneously belief consisting expectation decreases decreases depending stages interpretation approximated similarly allowed normalization fitting roughly penalty visible assigned degrees avoid expect thesis priori priori batch maximize specifically candidate candidate candidate holds discussions tests tests tests reason middle middle divided stopping stopping stopping split split nips denker principles principles decreasing decreasing decreasing powerful wiley overfitting overfitting overfitting overfitting perturbation exponentially scalar reducing authors maximizing maximizing statistically statistically statistically statistically necessarily predicting thought thought quantities freedom freedom perceptton perceptton extent arbitrarily averages established years indicating ground trivial benchmark worse nonlinearity london reasons lin purposes easier day incorporate sgn sgn arise probable cut simard acknowledgement describing optimize medical medical medical lowest meaning researchers explained greatly collected flexible leave frequently monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic proven incorporating song substantial substantial decreased credit credit credit credit credit credit credit credit credit credit credit credit credit credit credit diagnosis diagnosis diagnosis hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints hints ear conditioned pick databases databases concerned partitions lecun caltech caltech eliminated occurred familiar resulted interpret interpret occurring observing reasoning monotonically monotonically monotonically imply imply hint hint hint hint hint hint hint hint hint motivation financial financial patient patient patient forecasting nonlinearities multiplied modelled modelled omitted omitted draw draw card card card card considerations partitioned splits statement vari market market default default default default ics uci abu abu abu abu abu abu abu yielded leaving blood blood blood mostafa mostafa mostafa mostafa mostafa mostafa mostafa vec piece piece email email equivalently tables maximized maximized job bank monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity eric constrain attempted pub invariances ftp ftp distri intuition formance maintained ization ultimately discusses investigations bution justification lated tors reflecting val obey obey beneficial beneficial capital tracks repository daily irvine profit meant neglected derives translate excessive excessive excessive monitored monitored modest unnecessary histories histories histories enforcing enforcing quantified obeys joseph markets abnormal abnormal disorders disorders extremes imposing symmetries implementable desire meanings meanings malik penalizing violation violation liver liver liver liver liver liver liver liver liver liver liver rect indicative occupy cre worthwhile subdivided penalize joe ismail obeying assets compar sill sill sill sill yaser yaser calcu crease irrespective screening screening dictates dation analyzes sacrificing magdon enforcement cancelled mildly consumes directory 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#@Abu-Mostafa_Y,Sill_J,
#t10
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure figure time time time time time set set set set set set set set set set set set set set set training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number number number number number number number number number number number number number number number state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results information problem problem models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based based based based based based based based based space space weights weights weights weights linear case case case case case vector vector vector vector order order order order order shown shown systems values values values values probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions distribution distribution distribution approach point single processing large local local local local rate rate rate rate rate rate rate rate test test test test test analysis class class class class class matrix matrix matrix matrix algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian paper paper paper paper examples small small work methods methods step step step step step step step step current current current current current current current problems random random random similar similar similar similar similar show show show equation section fixed line line line line line line rule speech speech speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation approximation approximation average average average states states states states states states states theory gradient gradient gradient gradient obtained obtained obtained obtained note note note experiments experiments experiments experiments result university computation computation computation computation research research log log log log log log log log log log log log log log sequence sequence sequence sequence sequence sequence sequence initial initial initial initial initial table table computer distance distance distance distance distance distance distance distance distance distance distance distance distance distance science left presented present maximum maximum maximum maximum maximum maximum continuous sample sample sample sample sample abstract find computational computational convergence convergence convergence convergence convergence convergence convergence properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic due due mixture mixture mixture mixture context introduction hand hand estimation estimation estimation estimation estimation estimation statistical statistical dynamic generated generated generated generated complexity assume assume assume prior word word word word word chosen chosen higher part previous previous bound bound bound bound cases good conditions conditions bayesian expected expected expected equations markov markov markov markov markov markov markov markov proposed proposed length length length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities forward finite finite finite resulting resulting resulting classes ing total total sum sum sum sum sum sum times times times times times elements mapping means factor factor dimension dimension dimension natural natural natural natural natural study knowledge knowledge em em em em em em em em em em em obtain obtain obtain negative negative original artificial relative relative relative relative relative relative relative relative represented compared compared provide compute compute compute rates rates proc perform perform constraints connected discrete mit steps comparison comparison comparison comparison comparison larger contrast contrast update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update update train descent descent dependent morgan words words words department version version version individual advances joint joint difficult difficult difficult final final final final exp sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences ai framework framework framework framework framework additional additional additional view curves curves estimates transition transition transition transition transition transition upper full full requires requires requires choice approximate approximate approximate approximate approximate speed estimated pages give give produce derived derived derived derived randomly randomly entropy entropy entropy entropy entropy entropy entropy entropy entropy path path path actual actual finally iteration iteration iteration iteration iteration depends simply achieved achieved discussion arbitrary denote denote denote denote denote tested tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm fast limited close close close corresponds proof common generate generate require journal future future easily kaufmann probabilistic probabilistic probabilistic probabilistic typically typically typically typically pairs needed needed coefficients fully jordan programming interesting significantly special special database database leads leads call call numbers numbers iterations iterations iterations iterations iterations iterations iterations iterations iterations max supervised denotes discussed improve exact takes moving side side inference relevant sufficient compare compare compare previously observations observations observations observations observations observations observations calculated volume solve solve smooth yields converge converge converge converge achieve rl sparse sparse sparse sparse sparse sparse sparse definition mixtures evaluation evaluation observation observation observation observation observation observation observation observation observation observation observation observation generalized improvement exists horizontal lead studied occur derivative matrices matrices matrices alternative alternative alternative alternative alternative setting setting setting setting starting starting place row row row row row greater trajectories conclusions depend depend depend depend differences measures accurate clear clear exponential exponential faster faster faster practice practice suggest suggest suggest hard demonstrated california minimizing averaged derivatives derivatives acoustic acoustic denoted denoted denoted denoted relation derive derive derive construct construct generating generating estimating mathematical recall averaging remaining slightly slightly expectation expectation expectation expectation expectation expectation versus family viewed lemma lemma evaluated evaluated evaluate evaluate updated labels labels showed showed approximations soft approximated approximated approximated approximated approximated approximated approximated approximated approximated approximated approximated approximated approximated converges partition updates updates updates updates updates updates updates updates updates updates updates updates updates updates updates updates updates updates updates updates updates updates past partial reasonable calculation expansion normalization convex reduces purpose purpose add iterative iterative iterative distances calculate calculate calculate symbol symbol avoid building batch discuss maximize maximize maximize discussions reason reason hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms society paths paths symbols symbols symbols presentation efficiently comparing reached composed capture showing interpreted phonetic phonetic phonetic follow built notation notation involved backward correspondence highest ill maximization maximization maximization approximating acknowledgments deal wiley divergence dataset fewer maximizing maximizing variability proved workshop workshop cover induction hill naturally necessarily automata automata created equally ensure versions versions taylor initialized initialized ith speakers generates synthetic synthetic synthetic rows inequality formula derivation derivation guaranteed baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum baum starts starts processed sections filtered commonly laboratories potentially calculations annual annual incomplete summation evaluating evaluating led generic parameterized experimentally readily lack leave employ slower slower calculating calculating calculating calculating anti maximizes maximizes phonemes achieves singer singer singer singer singer singer singer phone replace replace expectations expectations expectations expectations expectations expectations expectations expectations expectations returns converged merging merging irrelevant trade initialization indices aligned generator lagrange summing summing fix temporally royal reaching clamped clamped clamped multipliers murray ranges difficulties simplify simplify replacing biased occurring tishby belong settings krogh alphabet motivation inferior date started started schapire ensures predictors iteratively iteratively induce belongs thomas entries reveals omitted omitted contraction arrive warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth ends waveforms partitioned partitioned partitioned omohundro santa valuable dempster baldi dense dense multiply approx approx appeared usage entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic constitute incorporates rubin annals outperform ent equivalently benefits job legal legal welch welch welch welch welch welch welch welch welch welch welch welch welch welch welch welch welch welch welch welch comparative seek adapting visited visited chauvin alternate goals learnability carefully laird tune rewrite treating mea rewritten emphasis rabiner ergodic differently differently parameterization parameterization sake attempting clarity ron stay stay pronounced val practically juang att arriving lnp longest fair sis cruz magazine kivinen kivinen kivinen acyclic texas eighth eighth occurrences occurrences tens subtle predetermined ues mountain replaces dist dist timit phones omit avenue def ucsc infinitesimal ixl ixl ixl manfred manfred absorbing absorbing absorbing absorbing theor theor pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation exponentiated cse convexity ending subclass transcription transcription brevity xlo gem helmbold equiv instruments fii fii checking fernando unspecified lets initializations meters uttered yoram preliminaries anders stolcke slx slx compensates 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#@Singer_Y,Warmuth_M,
#t10
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#*learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure time time set set set set set set set set set set set networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number error state state state state state state state results results results results results results results results information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based based based based based space space space space space space space weights linear linear linear case case shown shown shown shown shown shown shown shown values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters weight distribution distribution distribution distribution recognition method method method method method method method method approach approach approach approach approach approach approach image single single large large large test test test test test test test test test test test test matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal form form shows simple gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper paper small size size feature feature feature feature feature feature work work methods methods methods methods methods methods step step step step points structure structure structure structure random random similar equation equation equation fixed rule vectors vectors general general general general generalization speech speech parameter parameter parameter parameter parameter approximation approximation average average states states states states theory term note note note dimensional university computation solution solution solution solution log log log log log log log log log log log log log log log log log log defined found found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics initial initial initial initial initial initial table table estimate estimate standard standard standard standard standard standard standard computer terms terms terms distance distance distance distance distance distance distance distance distance distance distance science prediction prediction prediction prediction presented present temporal sets sets sets sets sets sets maximum maximum press press learn components components components components components components components sample sample sample sample sample sample sample sample abstract applied computational computational computational density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component component component component component component due ieee procedure procedure procedure procedure procedure important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context context context context context introduction estimation estimation behavior effect dynamic generated generated generated generated difference complexity complexity complexity assume assume assume lower lower measure measure measure prior prior word chosen chosen part conditions represent bayesian bayesian bayesian bayesian markov markov markov markov markov markov markov markov markov markov markov fact fact techniques techniques techniques proposed proposed length length correct correct probabilities probabilities probabilities probabilities probabilities observed forward forward scale finite ing total total computed performed times times times means means means means means potential natural natural natural natural applications applications knowledge knowledge em vol relative relative samples true true true true true true true true compared cross cross cross cross cross cross cross cross cross cross cross cross cross cross series series define define proc proc experimental experimental goal posterior posterior posterior posterior posterior posterior posterior connected discrete approaches comparison larger contrast train train modeling modeling modeling selection selection proceedings technique consists consists individual individual difficult difficult final final scheme sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences ai directly directly view estimates estimates transition transition transition transition transition transition top top conference upper full full requires requires approximate statistics estimated estimated estimated basic validation validation validation validation validation validation validation validation validation validation con randomly randomly randomly randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering provided sampling technical increases group group tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm complete stable surface amount assumed assumed assumed generate generate journal hypothesis cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster easily fit fit fit fit fit fit simulated simulated simulated probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically underlying unknown unknown fully block block block block block block block block block testing uniform uniform uniform uniform details details numbers making international experts produced run run run denotes architectures discussed robust robust reported reported strategy hierarchical hierarchical hierarchical hierarchical calculated volume diagonal diagonal diagonal diagonal diagonal diagonal address mixtures mixtures mixtures background evaluation evaluation observation observation deviation matrices matrices matrices matrices alternative alternative hybrid clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters generally runs conclusion greater reduce neighbor depend differences bayes clear clear clear peak performs practice practice practice practice california assuming assuming variety variety variety min manner manner groups groups groups groups appears monte monte monte monte carlo carlo carlo carlo produces primary generating metric metric metric metric simultaneously consisting predictive quality quality quality quality choosing choosing estimator estimator viewed evaluated evaluated evaluated evaluate evaluate fraction fraction approximations lee approximated converges partition earlier reasonable fitting fitting fitting initially distances distances distances calculate assigned building priori priori priori extension maximize priors priors reason determining determining determining selecting hmms hmms hmms hmms hmms hmms hmms uniformly uniformly uniformly effectively detect comparing tend composed refer compact conf repeated procedures prob heuristic generative usual backward observable maximization automatically subsequent modelling explore simpler unlike difficulty varied issues graphical fashion rest investigated int ideal maximizing variability variability variability removed hill closest necessarily equally changed obvious obvious obvious observe initialized multivariate multivariate multivariate grouping contributions mentioned pairwise trivial trivial adjacent biology analytic answer baum baum baum purposes purposes closer protein protein protein immediately potentially potentially separately qualitative addressed addressed integrating fourth apparent composite composite composite composite composite composite composite composite reflect substantially empirically empirically offset axes lack poorly detecting slower slower switch mod ture gen popular ordered marginal gave unbiased deviations merging initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization initialization consistently room modify appropriately jth jth jth jth partitions discovery discovery grey climbing kullback proceeds grow viewpoint keeping star belong disjoint krogh krogh intuitively intuitively modifications motivation inferior inferior meaningful governed loo surprising mental lengths den initialize initialize initialize park partitioned partitioned likelihoods likelihoods likelihoods likelihoods subsequently fold baldi default default lem ics uci fitted yielded sig leibler welch welch welch comparative seek tradeoff covariances covariances affects discovering imagine clustered penalized penalized penalized intuition chauvin toy crossover gener individually smyth smyth smyth smyth smyth smyth pos cation alternatives discusses fea refined experi aaai worked handled meir meir rabiner rabiner rabiner rabiner rabiner impractical stay peaked separates obey inferring juang juang juang juang autoregressive seed irvine semantics february inappropriate validated validated validated validated lid lid bio assoc dealt pooled pursued encourage dissimilarity motivates menlo clus initializing initializing subtraction unstructured unstructured unstructured unstructured descriptive descriptive descriptive poorer confused critically suit worthwhile revealing seeds seeds ink lihood alphabets tering mol eling terior erated zeevi zeevi bic slo reserve initializes initializes ition padhraic imi framed alized spective noisier identifi 
#@Smyth_P,
#t10
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network neural neural input input input input input input input input input input data data data figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time set set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number number number number number number number number number number number error error error error error error error error error results results results results units units units units units units units units units units units units units units units units units units units units information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden performance based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights case case case case vector order order order shown shown systems values weight weight weight weight weight weight weight weight weight weight weight weight weight neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method method method pattern single processing rate test test test analysis analysis class matrix matrix matrix matrix matrix matrix matrix optimal optimal inputs shows shows shows shows shows algorithms algorithms small small small small size feature feature feature net net net net net net net net net work work task task fig fig fig fig fig fig step step step features features classification classification classification process structure problems problems problems high high section section section rule rule rule general average average average obtained obtained term term term result result university computation computation solution solution solution solution found found found found found found found found found found target initial initial table table table table table table table connections connections connections connections connections connections connections connections connections maximum maximum maximum range abstract applied applied find find find find find references ieee important important introduction tion tion complexity complexity rules signals higher type good good binary long expected fact fact simulations minimum minimum minimum minimum total simulation respect eq eq eq eq eq eq eq eq eq eq called called called called called times means factor factor optimization global original compared compared application compute compute goal connected brain brain brain equal steps steps accuracy comparison update train train nets nets nets nets nets nets selection morgan report report institute words consists consists consists advances framework equivalent conference determine speed basic basic basic pages pages increase increase increase increase increase increase increase condition condition condition condition developed developed finally finally backpropagation measured technical technical feedforward describe group group fast fast fast fast fast fast fast inverse inverse inverse inverse complete amount main main main main main ability makes makes kaufmann smaller smaller smaller underlying underlying underlying underlying needed combination combination combination reduced unknown unknown fully interesting special special special special leads leads leads leads leads leads international idea idea idea idea idea minimize denotes improved improved exact advantage advantage advantage advantage advantage takes takes takes element apply introduced side side side subset subset subset compare calculated calculated volume generalized generalized generalized generalized generalized generalized improvement exists lead conclusion minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal row row reduce reduce reduce faster physics min min min derivatives groups solving solving describes describes changing pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning multilayer transformations easy slightly slightly applying applying extraction extraction extraction extraction choosing choosing choosing expressed influence solved operations restricted showed showed showed showed understanding understanding reasonable reasonable calculation calculation calculation calculation calculation slow reduces reduces reduces initially calculate calculate calculate calculate calculate advantages advantages topology topology expect combinations combinations combinations combinations combinations combinations perceptrons formulation candidate absolute major selecting comparing reached summary refer prob classify criteria categories comp layered replaced optimized hessian hessian hessian hessian hessian helpful helpful reducing removed removed removed removed removed removed removed removed removed removed neu smallest act algo algo finds indicating adapted multiplication benchmark benchmark benchmark lies lies obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs obs sections attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute medical considerably remove remove remove remove remove remove remove remove remove remove remove remove remove remove remove calculating calculating aim germany logical logical logical focused patients contribute indices indices lagrange martin rithm rithm eliminate wrong minutes overcome overcome exploit removing removing hours repeat pruned pruned pruned pruned pruned pruned pruned evident evident uni originally originally facilitate insight cpu cpu cpu lem informa email stork stork stork stork stork stork stork break additionally big big big big big big big workstation algebraic disadvantage disadvantage disadvantage eliminating considers considers speedup speedup speedup speedup speedup speedup speedup deleted deleted deleted universit knowing mini article article article article hassibi hassibi hassibi hassibi hassibi hassibi hassibi hassibi consuming institut institut dominates rons neglect outgoing outgoing outgoing outgoing outgoing outgoing outgoing outgoing outgoing outgoing drastically drastically surgeon surgeon surgeon wolff wolff wolff wolff wolff wolff wolff prune prune prune prune prune prune ira ira monk monk monk monk monk monk monk monk monk monk deleting deleting deleting sparc mum fiir fiir delete delete delete shortcut solu unimportant unimportant unimportant perf perf perf bigger karlsruhe karlsruhe karlsruhe und und und extremum extremum referring referring timal mth urn urn speeding runtime runtime anymore vantage rna 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#@Riedmiller_M,Stahlberger_A,
#t10
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#*learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure time set set set set set set set set networks networks training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm number number number number error error error results results information information problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models hidden performance performance performance performance performance based based based weights linear linear linear linear linear linear linear linear layer vector vector vector vector vector vector vector vector vector order order shown shown shown shown shown shown systems systems systems values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions recognition recognition recognition recognition method approach approach approach approach approach pattern pattern point image image single single control test test test test test test test test test analysis class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form shows shows shows algorithms algorithms algorithms simple gaussian gaussian visual paper small small size work work work work work task task task methods fig fig fig fig fig fig fig fig fig fig fig fig fig step step step step classification classification classification classification classification classification classification classification classification classification classification classification classification current current trained trained structure structure problems problems problems problems problems similar representation representation representation section section fixed rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images general generalization generalization speech speech speech speech parameter parameter real real approximation obtained obtained obtained obtained obtained note dimensional dimensional dimensional dimensional result university independent independent independent independent independent independent independent independent found found initial constant constant constant estimate estimate standard standard terms prediction left left presented present phase phase phase phase low low temporal motion range press learn learn components basis basis basis basis basis basis basis basis basis basis basis abstract applied find computational properties references ieee ieee procedure procedure procedure important adaptive adaptive adaptive adaptive propagation mixture mixture mixture mixture introduction complex estimation dynamic generated generated generated generated generated variance variance change energy complexity complexity assume assume assume classifier prior prior representations learned learned learned learned chosen multiple good good good conditions conditions conditions conditions represent represent represent equations techniques techniques length correct correct correct correct correct observed observed observed observed observed observed observed observed observed errors scale minimum resulting classes classes classes classes classes classes classes classes classes tasks tasks tasks tasks tasks tasks tasks tasks total human computed multi sum sum eq eq eq eq eq eq called elements elements elements mapping factor factor factor factor factor factor factor natural applications applications em em em em em em obtain vol specific specific specific specific samples samples represented represented compared compared application application desired desired provide define compute proc proc proc proc proc related related brain equal equal equal update update modeling institute institute words consists represents connectionist connectionist connectionist difficult final final exp framework framework framework cambridge cambridge cambridge cambridge computing hinton additional estimates estimates estimates efficient choice significant significant statistics free world world vision estimated basic pages pages pages con con product actual finally finally backpropagation constraint simply describe describe arbitrary denote tested tested complete surface nearest nearest nearest common common common common assumed shape shape shape shape shape face face adaptation easily easily makes makes fit fit fit fit fit fit fit fit probabilistic typically typically pairs underlying underlying combination combination functional unknown coefficients coefficients coefficients coefficients technology transfer testing testing testing testing testing testing testing testing testing character head head head head head head matching database empirical squared squared call call numbers supervised attention combined minimize description perceptron discussed improve separate separate practical pixels subset cognitive recently engineering varying varying varying varying varying compare compare unsupervised observations observations observations observations observations observations observations observations observations observations observations observations observations observations subjects subjects volume volume volume solve solve solve solve yields speaker speaker speaker speaker differential achieve symmetric symmetric symmetric symmetric symmetric observation observation observation improvement exists matrices matrices column column column setting setting setting demonstrate row row row row conclusions neighbor neighbor neighbor depend depend depend interactions propose labeled assuming averaged derivatives acknowledgements reference explicit van index ways factors factors factors factors factors factors factors factors estimating stability dept dept metric missing missing missing missing explicitly explicitly simultaneously simultaneously dimensionality dimensionality dimensionality dimensionality remaining easy easy unique interaction interaction interaction interaction predictive expectation letters letters letters letters letters letters letters letters letters letters letters yield family family independently independently focus squares solved controlled controlled labels labels labels labels labels labels centered decomposition soft similarly translation translation translation translation translation translation allowed spectrum earlier reasonable measurements combining combining fitting fitting fitting fitting fitting roughly closed closed sufficiently classified faces faces faces faces faces faces david degrees thesis priori color color sciences illustrated prove prove uncertainty uncertainty discuss maximize specifically priors black holds partially discussions columns columns columns straightforward letter efficiency computationally wij identify vowel vowel vowel vowel identity identity identity soc compact kind procedures procedures prob allowing success classify classify content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content comp comp notation involved vary write play modular maximization neurosci received illustrates illustrates mixing deal extend powerful wiley production overfitting discriminant discriminant dataset helpful analogous naturally concepts possibly adapt adapt adapt adapt analyze ensure singular singular observe explored speakers speakers speakers speakers consist mixed grouping explain phd finds massachusetts indicating rows rows rows separable separable separable separable crucial tractable benchmark benchmark baum sys style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style style desirable involve describing opt english res medical incomplete incomplete raw requiring people people collected collected freeman freeman freeman freeman freeman freeman substantially cmu flexible flexible generic frequently robinson robinson robinson howard stack synthesis characterize ture extracting maximizes phonemes gave asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric sums logp logp electric decreased pose pose pose pose pose pose pose pose pose pose pose gap person person person person classifying lab spectra ghahramani identifying writing sv summing zemel labelled tensor discovery fits held handwriting unlabeled roles settings illumination illumination illumination generalizes vowels vowels separating separating separating separating separating combines ensures male male pat originally facilitate spherical initialize offer augmented extends considerations implicitly omohundro alternatively summarize treat dramatically helmholtz stork break benefits pentland poses poses poses poses tibshirani tibshirani weiss seek seek lit assignments assignments assignments female female letting streams adapting adapting continuity factorial factorial factorial unseen unseen unseen unseen hastie hastie formance interacting interacting hughes books depicts proach categorization anal anal figs figs intl intl esti struc simplifies mea lems topologies lighting lighting lighting info info info info styles styles styles styles styles styles styles styles styles styles styles styles styles styles styles styles styles styles font font font synthesized synthesized synthesized vis vis subjective calibration focuses accomplish bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear bilinear svd svd svd svd ning thickness restricting raises digitized william factorization spirit iterating iterating compromise corn doom mach translate translate translate translate translate stacked subtle eigenfaces eigenfaces multilinear adv adv adv adv particles ysis stepsize unobserved unobserved unobserved modulate modulate extrapolation extrapolation extrapolation extrapolation extrapolation extrapolation extrapolation extrapolation extrapolation mir tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum pointers caruana treats treats schematically psyche reproduces calculus clamping british symmetrically rendered overfit rendering cog reproduction categorize fellow kanade govern render turk factoffal coarser bernstein joshua joshua fluid extrapolate extrapolate extrapolate extrapolate avail reflections ric alternates parameterize intell favoring richards embed embed analogies tent tent fonts fonts fonts fonts fonts koenderink autoencoders manipulate uttered cvpr sured smm smm smm smm smm smm smm smm smm smm smm smm dimensionalities dimensionalities archive ash generically eigenface mating mitsubishi bench bic specular broadway broadway merl merl accomodate magnus accents econometrics ficiently boa beled loglikelihood creative ofy yls extrapolating predoctoral 
#@Freeman_W,Tenenbaum_J,
#t10
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#*network network network network network network network network network network network learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training algorithm output output output output number number number error error error error error results results results results units information information information information hidden performance performance performance performance performance performance performance performance based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights vector vector order order shown systems systems systems parameters parameters noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit distribution method method method approach pattern pattern pattern pattern point point point point point processing processing processing large large local local local local local rate test test test test test test optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form shows shows gaussian paper paper paper small small small small small work methods methods methods current current trained random response show show show show equation equation equation equation fixed fixed fixed general parameter approximation approximation approximation approximation approximation approximation approximation approximation states theory theory theory gradient gradient obtained term term term note note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments result variables variables variables independent defined initial table table estimate estimate estimate estimate estimate estimate terms terms prediction direction machine sets sets sets sets sample sample abstract applied convergence convergence convergence references component due procedure introduction complex hand variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost tion tion tion tion difference variable assume assume cases cases cases required good binary binary distributed expected make fact correct minimum minimum minimum regression performed performed times means means potential obtain vol relative samples samples samples samples true compared provide perform active experimental experimental brain brain brain brain brain brain brain brain brain brain brain brain brain brain update train train descent dependent selection morgan morgan morgan report words advances advances advances bias bias ai ai ai ai ai ai ai considered experiment estimates estimates estimates estimates estimates san san san approximate statistics free estimated estimated estimated increase increase increase increase increase increase increase increase increase increase increase validation validation validation validation con criterion finally achieved achieved increases close inverse assumption assumption assumption eds eds easily easily typically typically typically typically needed reduced mlp interesting significantly principle leads call call early early early early early early early early early early early early early early early early early early early early early early early decay idea idea improved element practical apply apply apply introduced introduced quadratic quadratic quadratic quadratic quadratic quadratic quadratic sense relevant calculated tions rl rl diagonal diagonal diagonal diagonal diagonal diagonal diagonal improvement improvement studied extended extended locally touretzky demonstrate demonstrate row row assumptions assumptions assumptions assumptions assumptions reduce conclusions practice practice practice mateo mateo mateo characteristics drawn demonstrated regularization assuming decrease derivatives denoted explicit pro written pruning pruning pruning pruning pruning pruning consisting showed approximations updates reasonable additive neighborhood valid calculate absolute divided comparing online reached repeated cun cun interested stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping quantity quantity giles denker illustrates preferred tesauro cowan cowan minimized employed hanson accurately hessian hessian reducing reducing mse dependencies reliable removed removed saliency saliency saliency saliency onset thought quantities obvious assumes consist improving simplest averages optimum optimum residual residual rows explanation starts starts starts comparisons obs obs obs obs obs obs obs closer ring strictly desirable potentially ridge meaning fluctuations requiring improvements considerably solla price extensions extensions sums germany boston boston boston boston boston damage damage damage damage damage damage damage damage damage owl converged displays tresp tresp tresp tresp tresp uncorrelated databases approximates cellular kaufman kaufman kaufman siemens siemens biased intuitive obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd obd motivation alspector pruned pruned pruned pruned pruned realization candidates candidates candidates ranking cancer cancer cancer cancer cancer draw ics uci uci ber ber removal removal removal benefits benefits retraining retraining connec connec demon stands var var var var var var var pub translated ftp num num ization simplifying dramatic technologies housing housing housing housing housing advantageous hassibi hassibi hassibi hassibi corporate heavily breast breast breast breast breast neuneier neuneier neuneier neuneier neuneier incorrectly calculates calculates calculates usefulness beneficial tells occam explanations repository cess benign surgeon surgeon surgeon surgeon surgeon wolff violated violated violated violated terminate enforced volker volker evaluates terminated retrained retrained retrained miinchen malignant analogously analogously razor zimmermann zimmermann zimmermann zimmermann zimmermann ralph ralph diabetes diabetes diabetes diabetes strated rankings otto awi awi validate finnoff finnoff assump assump reg owi owi loose questionable hans hahn invalid renormalization pursue divisions nonconvergent dation mchp tains publicly publicly harrison georg georg wold fluctuate ihi fluence vali 
#@Neuneier_R,Tresp_V,Zimmermann_H,
#t10
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#*model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input function function function function function function function function figure figure figure figure figure time set set set set set algorithm output number number system system system system system results results units units units units units units information information information information information information information information information information information information models models models models models models based based based space space space space linear linear linear linear linear case case shown values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters noise noise noise noise weight functions functions functions functions functions functions functions functions functions functions neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method pattern point single single single single single single single single single single single single single single single processing processing processing processing control large analysis form form form form form form shows shows simple gaussian gaussian gaussian gaussian gaussian visual paper paper examples work work work work work task methods methods methods methods methods methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step level current cell cell cell cell structure structure random random high equation equation equation equation equation fixed general general real approximation approximation approximation approximation note note experiments activity activity activity activity activity activity university university variables variables variables computation computation research research independent independent log log log log log log log constant constant constant constant table table estimate standard standard standard standard standard standard terms terms terms distance science science left direction direction direction direction present low motion motion motion motion motion maximum maximum maximum maximum range range press learn position position components basis basis outputs abstract computational computational computational density properties likelihood likelihood likelihood likelihood likelihood references ieee positive important mixture mixture mixture introduction complex behavior stimulus stimulus stimulus stimulus statistical statistical variance variance variable variable variable variable spatial assume lower lower measure prior prior part part part bound cases firing firing firing required multiple multiple multiple good good represent represent represent represent bayesian bayesian bayesian make fact correlation observed scale resulting classes ing tasks total total computed respect respect sum performed made natural natural study knowledge em em em em em represented represented represented represented true compared provide provide objects rates rates location perform perform perform determined distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions cortical brain brain power approaches mit steps comparison modeling modeling proceedings proceedings report loss loss loss implementation version version version version synapses consists code code code code code code code code code individual kernel kernel kernel kernel kernel joint represents difficult final ai maps framework framework framework framework framework framework framework framework cambridge experiment experiment environment environment directly directly hinton hinton hinton hinton hinton top top stage stage upper full requires requires choice approximate approximate statistics statistics statistics statistics statistics world world world world increase give con con coding coding coding coding derived weighted weighted conditional area provided provided evidence nature depends biological biological measured measured measured discussion describe limited close inverse inverse assumption assumption assumption complete finding nearest common generate generate role theoretical main journal journal square instance instance instance instance degree makes makes noisy noisy sensory including fit fit probabilistic probabilistic probabilistic probabilistic probabilistic typically underlying underlying underlying underlying underlying underlying underlying underlying underlying underlying underlying combination combination combination projection projection projection projection york special empirical operation operation operation operation representing representing representing representing representing representing representing call iterations making international normalized magnitude idea idea combined added population population population population population population population population population population population population population population population population population population population population population population directions robust takes takes typical practical moving moving moving moving include identical calculated works tuning tuning tuning tuning tuning tuning tuning tuning tions tions definition locations generalized interval sensitive entire scaling extended extended extended extended extended spikes alternative width deterministic generally generally starting starting place place place place place row row greater greater operator depend clear suggest suggest encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding taking physics intelligence relationship targets groups explicit explicit van longer ways tuned averaging electrical frequencies frequencies gaussians gaussians gaussians gaussians extraction expectation national extracted formation dependence stages stages overlap interpretation interpretation interpretation interpretation interpretation interpretation interpretation codes codes codes codes codes codes codes codes codes codes codes evaluate evaluate operations operations operations operations operations operations showed forms activities activities activities activities activities activities activities activities activities activities activities activities activities activities activities activities activities activities suggested discrimination key key spaces combining remains filtering sufficiently recorded existing existing existing fire fire usa sciences extension uncertainty maximize activated absolute characterized determining middle extra society encoded encoded delta delta delta comparing capture capture summary decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding showing anderson anderson anderson anderson interested neuroscience issue issue built built quantity quantity quantity quantity quantity quantity quantity quantity quantity quantity quantity quantity dot dayan dayan dayan dayan dayan leading maximization attempt illustrates subsequent mixing preferred extract extract extract extract neighboring rat rat rat rat extend stimulation american collection difficulty difficulty difficulty rapidly integral accurately divergence existence existence successive respond referred maximizing variability encode encode encode encode understand understand notion examined naturally plausible plausible possibly integer onset analyze illustrate ensure obvious noted simplest integrate animal histogram histogram ground distinguish smoothness worse precisely broad broad broad broad commonly products scientific implicit implicit implicit arises cybernetics integrating evaluating populations substantially tional quantitative peter detecting treated dots dots dots rep biologically poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson poisson characterize characterize aim gen extracting richard substantial sums coherent decoder display specifies specifies simultaneous irrelevant animals narrow narrow member zemel zemel zemel zemel zemel zemel zemel royal plays systematic kullback attractive interpret transforms salk generalizes elimination sompolinsky corollary studying washington schwartz consequences monkeys offers reproduce hippocampus treatment motions relies seung characterization characterization summarize dempster baldi receiving posteriori rubin piece piece leibler encodes axe adopt instantiation exception spaced certainty certainty summarizes preserved distribu distribu life uncertain uncertain uncertain afosr picked wise wise argued relates academy conversely laird apparently funded abbott pop familiarity son places places knowing treating treating computa rats rats characterizing lation discretized crude insufficient mcdonnell stochastically pouget pouget pouget pouget shot puts alex char concern cast proportions essen evenly extracts fij interpretations carries periphery governing implying multimodal presently creation hough fidelity fidelity thing nih modern decoded capturing unimodal unimodal supposed freely newsome newsome movshon pew severely discrepancy mir complications ities complexities seemingly inadequate inadequate bimodal bimodal provably underlie georgopoulos faithful motivate rings attack recon neurophys keefe proportionality ubiquitous heiligenberg stochasticity stochasticity regularizing funds alexandre rounding behaviorally arizona arizona fruit stressed completing activ snippe xlw xlw inevitably proposals reporting mensional ulations emits bination georgetown resent informally waste nar nar imitating popu criticized erate xlc photons reconstructs britten decodes handful rla rla rla wouldn tucson kettner ifo subtleties 
#@Dayan_P,Pouget_A,Zemel_R,
#t10
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#*network network network network network network network network network network model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time set networks networks networks networks output output output output output output output output output output output output number number number system system system system system system system results results results results units problem models models models models models models performance performance performance based based based based based based space space space weights weights linear layer layer vector vector vector shown shown shown shown shown shown shown shown values values functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution recognition recognition method method approach point point point point point point point point point point point point point point point point point image image image image image image image image image image image image image processing processing processing large large large neuron neuron neuron analysis matrix inputs inputs inputs shows shows shows shows shows shows shows simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper examples feature feature feature feature feature feature feature feature feature task cells field field field features features problems response response response response response response similar similar architecture architecture architecture show show show equation equation equation line line line line line line images images general general general general general general general general general general general general speech speech real real real average average obtained obtained activity dimensional result result university university university threshold threshold threshold threshold threshold computation constant constant constant constant table table computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer synaptic synaptic synaptic synaptic synaptic synaptic synaptic science left left direction direction direction direction presented presented phase phase phase frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal sets motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range range range components outputs outputs outputs continuous continuous continuous abstract computational computational computational computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties references due due due positive positive introduction estimation estimation estimation estimation estimation estimation estimation behavior stimulus stimulus parallel parallel parallel parallel parallel parallel energy energy complexity complexity complexity variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial measure measure measure signals chosen chosen higher part required required multiple cortex cortex cortex binary distributed chip make proposed proposed proposed observed scale scale minimum ing ing total total total computed sum sum sum performed elements dimension dimension orientation orientation orientation orientation orientation orientation orientation orientation applications applications applications filter filter filter filter filter filter filter filter filter filter filter filter obtain negative original vol vol vol vol vol relative represented desired cross cross receptive receptive receptive receptive compute proc proc perform determined discrete discrete cortical cortical cortical cortical cortical cortical cortical cortical brain contrast fields implementation implementation implementation implementation implementation implementation implementation implementation implementation synapses synapses synapses synapses synapses synapses synapses technique technique technique consists responses responses difficult difficult exp computing domain domain domain domain domain additional curves curves curves curves curves stimuli stimuli stimuli effects bit bit bit detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection efficient full requires speed speed speed speed speed channel weighted weighted weighted area area area area velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity types actual sampling sampling biological biological biological biological transformation fast circuits circuits circuits circuits circuits circuits implemented implemented implemented implemented implemented implemented implemented implemented implemented implemented implemented synapse require main end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pairs pairs pairs pairs pairs functional functional functional coefficients fully technology transfer programming edge special mode numbers filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters direct inhibition inhibition normalized early combined combined architectures population discussed recent resolution lateral lateral introduced moving moving moving moving moving quadratic quadratic quadratic engineering engineering engineering works tuning tuning tuning tuning tuning yields yields modified observation channels interval sensitive constructed constructed intensity extended digital wide wide correctly move hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware pass runs runs flow conclusion starting minimal reduce modules modules modules retina retina retina retina retina retina retina retina peak california proportional user selective selective selective selective plane plane plane plane relationship derivatives van van van van van van van van edges edges longer perception optical optical estimating plot plot tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned mathematical distinct dept modeled implement implement implement implement implement implement sensitivity electrical electrical electrical unique unique unique scales interaction frequencies frequencies extraction extraction extraction extraction extraction extraction extraction national independently variation transform centered centered constants constants constants constants constants constants constants diagram smoothing normalization normalization reduces purpose purpose purpose purpose purpose purpose purpose david david degrees recorded silicon silicon silicon silicon silicon silicon silicon thesis contour contour variations variations middle aspects importance society society wij computations orthogonal orthogonal composed capture moore moore sci gray comp modular delayed cat chips chips moves moves subsequent extract extract software load oriented oriented oriented oriented oriented oriented oriented oriented oriented oriented employed selectivity selectivity create create circuitry estimators estimators estimators graphical reducing fourier fashion school school ideal complicated affect cover cover cover fundamental circles circles measurement opposite opposite opposite opposite front impulse der der der der der der freedom freedom nervous electronic cos cos band slope slope coded capabilities capabilities capabilities implementing constructing constructing division monkey axon axon axon axon substantially detecting schematic requirement span switch exhibits measuring pasadena display shaped traces traces summed summed univ realized realized realized physiology interface modify amplifier summing summing linearity linearity velocities flexibility eliminated binocular ranges tools logarithmic odd odd odd odd odd odd odd odd odd interconnection replacing programmable programmable programmable programmable programmable resistance balance transforms operates operates modifications modifications constructive interference dendrites dendrites dendrites dendrites paul intended realization monkeys offers offers cerebral spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal master implicitly subsequently subsequently market switches neurophysiology leaving piece planes planes planes wiesel wiesel wiesel focal feeding decomposed hubel hubel hubel realize realize realize attempted perpendicular mhz magnitudes toy toy realizable adelson adelson adelson adelson adelson adelson adelson adelson wise macaque macaque host host academy investigating rectified transconductance placing minor places programmed info agrees loaded hopkins illinois essen essen executing heeger heeger heeger heeger heeger heeger heeger bergen bergen bergen bergen bergen bergen bergen bergen america america drastically compensated physically inst jan tim emerged simoncelli replaces cox linearities movshon ton cancel quadrature quadrature avenue aliasing aliasing reminiscent rectification cummings cummings cummings cummings cummings counterparts philadelphia philadelphia philadelphia philadelphia tot tot tot tot tot tot tot mosaic circumvent quadrants spans etienne etienne etienne etienne etienne extractor ralph neurocomputer southern mueller mueller mueller mueller mueller mueller pennsylvania pennsylvania pennsylvania noticeable maunsell maunsell realizes torus chitecture decomposes extractors extractors locus differencing differencing symp spiegel spiegel spiegel spiegel spiegel spiegel oot takahashi takahashi takahashi takahashi lobes str allel analogs buffered configure capitalize prototyping 
#@Apsel_A,Etienne-Cummings_R,Mueller_P,Takahashi_N,VanderSpiegel_J,
#t10
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural input input input input input input input input input input input input input function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time set set networks networks networks networks networks output output output output output output output output output output output output output output output system state state units information information information problem models performance based based based based based weights weights weights weights vector vector vector vector vector vector vector vector order shown systems systems systems systems parameters parameters parameters weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight neurons neurons neurons neurons single single large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate inputs inputs inputs inputs inputs signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple small process current current current current cell cell cell memory representation representation architecture show show equation equation equation section fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule parameter real approximation approximation approximation average average average average average note activity result threshold threshold threshold threshold threshold threshold variables research independent independent constant constant computer terms terms connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left frequency temporal temporal temporal temporal temporal temporal press outputs outputs outputs abstract back analog analog analog analog analog analog analog analog analog analog analog references ieee ieee important adaptive propagation introduction introduction action action action action action action action action action circuit circuit behavior behavior effect tion change variable assume lower lower rules rules rules signals signals signals signals signals signals representations part part previous firing multiple binary spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike represent distributed distributed chip chip make correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length correct observed simulation simulation times means means potential potential potential potential potential potential applications artificial artificial relative relative compared provide perform active active active determined cortical brain equal voltage voltage voltage voltage voltage support train dependent report institute institute implementation implementation implementation implementation synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses represents design design san top upper upper approximate approximate approximate speed basic pages coding product finally processes processes nature nature nature inhibitory biological biological associative discussion fast limited assumption assumption implemented implemented synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse generate vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi ability instance future auditory simulated smaller combination reduced reduced functional increasing mechanism mechanism mechanism mechanism max pre pre making bottom magnitude magnitude magnitude decay decay decay decay description neuronal neuronal correlations correlations correlations correlations correlations exact advantage property property property pair pair pair period sense recently relevant sufficient highly solve differential differential differential achieve achieve trans address address modified modified interval organization storage storage storage increased amplitude digital digital spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes width occurs occurs occurs demonstrate assumptions assumptions assumptions assumptions hebbian hebbian differences accurate designed encoding mechanisms integration exist connectivity produces written longer longer slightly develop frequencies frequencies equilibrium equilibrium equilibrium equilibrium events springer formed potentials potentials potentials competition independently correlated communication fraction evolution translation updates updates earlier delays normalization normalization normalization normalization normalization normalization intervals event event event event add valid foundation kohonen kohonen kohonen dendritic fire fire fire silicon usa currents inter absolute holds holds holds middle middle closely encoded modification spiking detect detect refer timing timing involved simplified simplified cmos cmos chips processors illustrates acknowledgments intrinsic receive trains trains trains trains trains trains trains carried limitations preliminary postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic fewer matches history transistor transistor transistor combine relationships office gates complicated encode presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic removed trace trace trace trace analyze changed implementations nervous academic pyramidal pyramidal electronic synthetic seconds integrate integrate integrate percentage slowly ground floating starts reasons drive shared easier division division division division immediately controls implicit depicted integrating percent formulated biologically operate operate berlin poisson poisson poisson poisson differs popular incoming occurrence occurrence plan instantaneous realized fabricated naval eliminate stronger stronger stronger mail mail mail efficacy capacitor capacitor capacitor capacitor capacitor capacitor capacitor fires fires reset dendrites dendrites somatic somatic somatic soma soma soma tic express neuromorphic neuromorphic mem lazzaro davis santa discovered propagate switches executed fired fired fired dramatically incorporates bus removal centre additionally affects increment increment increment gated decays approxi inverted crosses met simplifying simplifying records weaker weaker meet normalizing tin tin increments tel tel tel tonic tonic tonic triggered stores preserves ongoing suite mahowald mahowald mahowald mahowald mahowald compete neocortical neocortical believed core leakage communicate thresh ous ated violated insert rises pull tailored capacitive corr decrement decrement tsodyks des leaky volatile strongest switzerland switzerland subtract puted watts watts watts watts gatsby suppresses stuart markram opens incremented continu subsystems fifty bigger sivilotti wawrzynek correla normalizes vittoz matters weakened snapshot snapshot restarts strengthened debate synap swiss brane decayed pulled mckenna react fulfills ses pulls mately influencing redistribution coincident coincident gillespie naptic revision conform mirrored mirrored mirrored spines neuroinformatics neuroinformatics incrementing peripherals organizations neuroinformatik lloyd lloyd sakmann lau citatory misha misha strengthens rns charitable conforms 
#@Hiffiiger_P,Mahowald_M,Watts_L,
#t10
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#*network neural neural neural neural neural input input input input input input input input input input input input data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time networks training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number system system system system system system system system system system system results results results results information information information problem problem problem linear linear linear linear case case order order shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems values values values parameters parameters parameters method method point point point single single single processing processing large inputs inputs form shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple visual visual visual paper paper paper examples small methods points process level current current current current current response show show equation equation equation equation equation equation section fixed fixed fixed line line line images images images parameter real real real approximation approximation average average average average average average average average average average average average average theory term term note experiments experiments university threshold solution research research independent initial constant constant constant constant constant constant constant constant constant estimate estimate standard standard computer terms left left direction direction direction present present low low low low low low low low low low frequency frequency temporal object motion motion motion motion motion components nonlinear continuous continuous continuous continuous continuous continuous continuous abstract back computational convergence analog analog analog analog analog analog analog analog properties references component ieee ieee procedure adaptive adaptive adaptive adaptive adaptive introduction complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation stimulus statistical effect effect effect variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance change change difference difference variable variable measure signals higher higher required multiple multiple long long long long long long long long long long conditions represent equations chip chip chip chip chip chip chip chip chip techniques region region region correct ing human computed called called factor natural natural applications knowledge filter filter filter filter obtain obtain obtain original vol true objects proc proc proc constraints constraints constraints constraints constraints constraints gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain power power voltage contrast dependent morgan report department implementation implementation implementation version version technique difficult exp exp bias experiment environment curve additional additional additional design san top top conference full requires statistics statistics statistics statistics statistics statistics world world world vision pages pages pages pages con area area velocity types lines constraint constraint constraint constraint constraint constraint constraint simply biological biological achieved measured measured measured measured measured measured measured normal tested limited assumption assumption assumption complete circuits amount short implemented adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation square vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel ability future easily easily sensory kaufmann typically account unknown technology technology technology technology technology block block block testing increasing mechanism special mode operation operation leads filters window international bottom bottom produced produced added light advantage takes apply moving moving identical identical machines pixels pixels array array array engineering engineering varying subjects subjects subjects calculated tuning converge achieve achieve definition definition definition definition definition background gate sensitive amplitude amplitude amplitude amplitude amplitude parts intensity studied studied invariant occur digital deviation deviation derivative derivative derivative derivative touretzky hardware hardware hardware pass pass pass pass pass pass demonstrate reduce conclusions editors measures retina retina retina retina designed designed clear peak peak peak peak temperature suggest mechanisms integration presence external characteristics characteristics characteristics characteristics demonstrated demonstrated demonstrated proportional proportional proportional plane plane plane decrease decrease relationship averaged averaged scene scene appears pro derive written longer perception perception describes laboratory changing averaging infinite electrical slightly scales integrated integrated integrated frequencies shift blocks john extracted family expressed stationary stages squares variation transform densities static similarly converges constants constants constants constants past diagram diagram additive additive additive additive normalization normalization normalization sec purpose norm expect building building includes includes silicon silicon color color color illustrated variations variations variations variations variations variations variations variations variations variations variations variations variations absolute absolute absolute holds successfully major simplicity sensor sensor sensor sensor sensor sensor sensor sensor sensor middle middle suitable symbols build build invariance tend essentially ten fine reached soc procedures procedures gray built vary vary usual board wave wave wave wave wave cmos cmos cmos cmos ill chips operating operating operating operating acknowledgments software software camera camera situations circuitry circuitry exponentially mead mead mead mead varied humans dual history tech rest ideal transistor transistor scaled authors office gates fundamental editor adapt adapt necessarily opposite opposite extremely equally quantities assumes detector detector mapped academic arbitrarily electronic integrate mentioned slowly formula sensors sensors sensors sensors sensors sensors sensors sensors publishers variances floating floating correction correction correction straight straight implementing preprocessing filtered desirable desirable immediately immediately potentially potentially nsf addressed researchers robustness varies varies offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset embedded fed red psychophysical posed posed adjustable continuously schematic schematic outliers gains rely curvature curvature achieves replace chose neuro shaped eventually eventually wesley benefit sensing addison fabricated fabricated amplifier drift recover unity unity impossible naval theories multiplier khz imaging minutes minutes simplify mos mos multiplicative height contract hope fail capacitor capacitor arrays arrays arrays arrays symposium hours photoreceptor laplace advance francisco april layout jump harris harris harris harris harris acknowledge severe maintaining constitute sine sine sine sine kluwer focal focal focal focal preserving forced acceptable perceived perceived adjustment brightness subthreshold subthreshold subthreshold challenging ullman ullman surrounding lond transconductance transconductance transconductance intensities enforce amplifiers amplifiers thousands thousands challenge sees saturated calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration calibration opponent capacitors capacitors fabrication award possess triangle offsets offsets offsets neurobiological spie frequent consumption consumption curved curved curved alto colors colors colors periodically periodically adapts sweep feb clues ming col palo violate cancel inability gibson delbriick roots canceling graham chiang chiang chiang chiang loses psychol psychol pathological straints avail hue ismail pected infrared technically ume orlando smart florida cancels calibrated tremendous hunt aerospace bert apriori unavoidable divider divider divider divider divider divider divider divider ultra ultra calibrate calibrate calibrate calibrate infra mismatches factory carlson plementation calibrating calibrating gainesville nology career fluctuate ceived transduced fier 
#@Chiang_Y,Harris_J,
#t10
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#*model model model model model model neural neural neural neural neural neural neural input input input input data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set networks output output output output output output output system system system system system system system system system system system system system system system system system results information information information information information information performance based based based based based based based based based based case case shown shown shown shown shown systems systems systems systems systems systems systems neurons distribution pattern point image single processing processing processing processing processing control control local test inputs form form shows shows shows shows shows shows signal signal signal signal signal simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper feature feature feature feature feature work work task task task step field field features level level current current current current current current current high architecture show show fixed line line line line line line line activity activity activity activity dimensional dimensional dimensional dimensional threshold threshold computation computation computation computation computation computation computation research research research research target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target constant computer computer computer node left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction map map map map map map map map temporal temporal temporal temporal temporal temporal temporal temporal temporal object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum press press position position position position position position position position position position position position position position position position outputs abstract computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog references ieee adaptive adaptive decision introduction action circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior stimulus stimulus stimulus stimulus parallel tion change change spatial spatial spatial spatial spatial spatial spatial lower measure signals center center center center previous previous distributed distributed distributed chip chip chip chip chip chip chip chip techniques proposed ing simulation human human human human computed computed computed computed made vol vol vol specific compared compute compute compute proc location location location location location location location location active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye goal motor motor power mit voltage voltage voltage voltage voltage voltage voltage accuracy comparison comparison contrast support selection selection selection selection morgan institute institute institute institute institute institute implementation advances advances difficult exp delay addition maps maps maps experiment experiment view top top top determine speed speed vision vision vision weighted weighted area velocity velocity velocity product selected selected selected selected selected describe close circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits common common common common common implemented generate generate supported supported role role vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel sensory sensory including kaufmann typically technology technology technology technology technology block block programming interesting edge edge mechanism mechanism mechanism mechanism mode operation representing max window window window inhibition inhibition normalized bottom bottom attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention added description light directions recent movement movement movement movement reported moving moving moving moving moving include subject pixels pixels pixels pixels pixels array array array array array array array array array array recently engineering engineering engineering varying smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth match match correspond studies studies background locations locations locations locations grant occur derivative derivative derivative derivative derivative derivative derivative derivative derivative derivative move move move move loop occurs occurs hardware hardware hardware demonstrate demonstrate demonstrate editors editors performs encoding strong integration integration external characteristics california california exist movements movements movements movements movements movements movements selective selective selective selective plane targets targets targets targets derivatives derivatives derivatives manner program van edges perception perception perception winner winner winner winner winner winner winner winner ann modeled electrical electrical adding formed shift extraction cycles select letters formation stationary stages centered centered centered diagram diagram performing sec sec reduces combining tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking closed generation msec msec koch koch koch koch koch koch koch koch thesis currents retinal retinal retinal absolute absolute absolute neighbors society driven mcclelland conf anderson comp bar localization delayed cmos highest neurosci neurosci moves extract neighboring cowan essential circuitry pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit ideas tech links detectors office oscillation topographic saliency saliency saliency saliency saliency saliency saliency saliency saliency measurement trace trace trace opposite rev equally voltages voltages front der motivated finds finds attempts wta wta wta wta wta wta wta wta seconds seconds seconds years ment ground track track track spatially drive drive drive drive drive drive shared located leaves monkey monkey mation nsf varies fuzzy profile tional passed incorporated switch extracting incoming cal pasadena pasadena shaped physiol begins attentional attentional attentional attentional attentional attentional attentional traces traces summed sensing summing saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic driving tem naval enhancement caltech caltech ments ments primate primate los neurobiology shifts shifts shifts salient preparation clock selects continue infor combines photoreceptor photoreceptor centroid winning winning winning winning winning neuromorphic neuromorphic neuromorphic neuromorphic creating saccade saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades saccades saccades motions speeds speeds speeds mechanical incorporates latency latency focal reaction revealed expanding trigger suppressed acting shifting mathematically elementary emphasize ullman ullman ullman fixation fixation exceed pos oculomotor oculomotor oscillating oscillating electronics intl intl steering steering psychophysics psychophysics status status scanning triggered triggered triggered triggered drives drives fiat externally stephen photoreceptors photoreceptors send vis tanaka supply puts morris morris morris morris morris morris morris integrates believed believed coincide tracks volts volts consumption lisberger lisberger lisberger attended deweerth deweerth deweerth deweerth deweerth deweerth deweerth signed feb christof mounted mounted freely percep mid imum horiuchi horiuchi horiuchi horiuchi horiuchi primates tracked tracked hysteresis hysteresis hysteresis hysteresis hysteresis tran apparatus psych jumps cummings switzerland nation ously facilitation ramp poral inhibits sual requests passage etienne continu perf spotlight preferentially preferentially mueller ger atlanta atlanta microelectronics tam alamitos timothy differentially swinging swinging cluttered backgrounds klab georgia georgia georgia gatech derlying spiegel triggering voluntary delbrfick saccarles centering centering discrimi bishofberger ition overt dle disrupt atten lausanne pads foveate hum ality hikosaka califor volved nia 
#@DeWeerth_S,Horiuchi_T,Koch_C,Morris_T,
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#*network network network network network network model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time networks networks networks networks networks networks networks output output output output output output output output output output output output output number state state results results results information information problem problem problem problem performance based based linear layer layer layer layer order shown shown shown shown systems parameters functions distribution distribution method processing processing processing processing processing processing processing control control control control control large neuron neuron test analysis inputs inputs inputs inputs shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal paper paper paper examples examples small small work process process process process level level level current current cell cell cell cell high high high high similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show show fixed fixed fixed fixed line approximation term experiments result result result result result threshold threshold research research defined dynamics constant constant constant table table estimate node node node node node node presented phase low low low low low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency frequency frequency frequency frequency frequency frequency frequency temporal maximum maximum press components outputs outputs abstract applied applied applied applied applied applied back analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references component component component due due ieee ieee adaptive adaptive introduction hand circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior effect dynamic dynamic dynamic parallel change change difference difference difference difference complexity complexity spatial signals signals signals signals signals part multiple long expected equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make make fact techniques region proposed proposed forward scale scale scale means factor feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications applications filter filter filter negative vol vol vol relative relative relative application application desired active experimental experimental experimental experimental experimental gain gain gain gain equal equal power power power mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage accuracy larger larger support implementation implementation implementation synapses synapses advances advances represents difficult considered considered cambridge view design requires vision basic channel channel channel derived weighted weighted levels levels levels area controller controller controller controller path path processes inhibitory inhibitory biological biological biological measured measured measured measured measured corresponds stable circuits circuits circuits circuits circuits circuits role theoretical main eds adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation vlsi vlsi vlsi vlsi ability smaller smaller smaller smaller needed dynamical dynamical technology technology block mechanism mode operation operation operation filters filters filters making making stored resolution resolution resolution takes practical practical introduced period period engineering varying calculated achieve trans background background background background background background channels amplitude amplitude amplitude digital digital feed touretzky loop pass pass pass pass pass pass conclusion place greater greater assumptions competitive competitive competitive faster strong mechanisms largest characteristics characteristics characteristics characteristics characteristics solid pulse pulse pulse pulse pulse pulse pulse pulse turn reference construct winner winner winner winner winner winner winner winner winner winner winner winner primary describes changing physical scales consisting interaction frequencies applying implies implies competition focus controlled organizing approximated completely completely constants diagram diagram key reasonable slow precision building figures silicon silicon color successfully successfully major major reason sensor extra closely divided divided modes characteristic characteristic characteristic allowing conductance device device device device device device device delayed cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos automatically chips chips chips chips overlapping carried carried poor mead rapidly existence investigated transistor authors working affect removed measurement adapt adapt adapt voltages voltages voltages voltages voltages voltages voltages consist wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta charge devices devices devices slowly band band band sensors agreement unstable unstable waveform explanation explanation floating implementing division laboratories pulses lowest lowest fluctuations researchers greatly double offset offset offset offset offset offset offset offset offset offset offset offset offset offset offset fed fed sharp schematic schematic incoming incoming incoming prevent electric inherent inherent inherent neuro neuro neuro neuro neuro lot fabricated fabricated fabricated fabricated fabricated fabricated fabricated guarantee guarantee japan dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically clamped inspired consideration mos mos mos mos balance bands bands affected illumination effectiveness capacitor capacitor clock excellent enhance originally winning waves lazzaro lazzaro waveforms waveforms waveforms waveforms lett explains yielded specification break die drain experiences massively realize compensate compensate compensate compensate transconductance rough steering port spite diagrams electron laws settling ave mahowald utilizes utilizes compete supply supply mirror suppress fabrication proposes proposes obey compensated compensated compensated adapts remained counterpart cutoff comparator comparator foreground foreground foreground foreground foreground modern devoted syst dissipation competence hysteresis metal fluctuation fluctuation fluctuation fluctuation fluctuation fluctuating fluctuating fluctuating fluctuating vdd vdd quiescent quiescent retinas vin vin vin vin vin vin specifications specifications prevented prevented compose acknowledgment adaptable adaptable adaptable adaptable adaptable adaptable adaptable adaptable equipped ist resistances inn follower photo photo twofold attenuated enlarged choi optimistic vth vth vth vth vout vss adaptability adaptability eee overlapped conquer compensates manufacturing manufacturing duty deteriorate shut historically osaka 
#@Iizuka_K,Matsui_H,Miyamoto_M,
#t10
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#*network network network learning learning model model model neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set networks output output output output output output output output output output output output number number system state state state state state state state state state state state state state state results results results based based linear linear case case case vector order order shown values noise noise noise noise noise pattern point point point single single single large large analysis analysis analysis analysis analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows shows shows shows shows simple simple paper paper paper small small small small small small feature feature fig fig fig cells cells cells step step step step step step step step step step step classification process process process level level current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current cell cell cell cell cell cell cell cell high high high response response response response similar similar show equation equation equation equation fixed fixed fixed fixed line general general general general parameter states states term note note note note result independent dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial constant constant standard terms node node node node node map present present present frequency maximum press nonlinear outputs outputs abstract applied back analog references due due due due due due due procedure procedure important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior change change change change change change change change change change change change change change change change change change change change change energy energy difference difference difference complexity assume assume assume assume assume lower measure signals higher higher part previous previous multiple multiple multiple conditions conditions equations equations equations equations equations equations equations equations make make region region region region total mapping factor factor potential potential potential dimension natural feedback feedback global negative vol vol true cross cross location determined experimental related connected gain gain equal equal equal equal equal equal equal mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage steps steps steps steps larger larger source source source source source source source source source source nets selection morgan institute loss synapses synapses difficult final exp exp exp exp exp bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias maps experiment directly directly additional solutions san stage full approximate increase increase increase increase increase channel channel channel channel channel channel channel coding levels levels finally processes biological measured measured measured measured measured measured discussion increases describe describe arbitrary tested fast fast fast fast corresponds surface surface surface circuits amount common common synapse main adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation ability easily development kaufmann smaller technology technology technology technology technology ratio ratio edge increasing increasing increasing operation operation operation operation operation call making inhibition inhibition idea attention added added advantage advantage property pair identical identical identical identical sufficient approximately solve differential differential differential differential differential differential modified gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate expression lead concept derivative move occurs half half starting starting minimal greater greater greater competitive differences designed exponential exponential exponential weak mateo mechanisms largest largest drawn california proportional proportional proportional assuming assuming start start decrease decrease relationship iii iii introduce derive derive solving winner winner winner winner winner winner recall explicitly linearly linearly slightly slightly slightly develop develop adding frequencies frequencies equilibrium equilibrium equilibrium equilibrium equilibrium implies versus decreases dependence review overlap variation diagram diagram diagram earlier measurements classical roughly roughly roughly add sufficiently sufficiently sufficiently koch koch koch koch coupling coupling silicon currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents coupled phys characterized middle efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency importance maximal characteristic excitation notice allowing return return device write write simplified simplified nips nips quantization cmos reach moves moves illustrates operating operating decreasing decreasing law perturbation difficulty mead mead mead steady steady steady steady steady steady steady steady steady steady steady steady steady steady rest detectors terminal transistor transistor transistor transistor transistor transistor gates gates saliency saliency saliency adapt adapt adapt adapt necessarily rev rev voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages freedom observe extent regime wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta established charge slowly slowly band band publishers floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating floating transistors transistors transistors transistors transistors immediately involve universal grossberg begin lowest percent employ http http mod pasadena begins traces traces traces traces traces picture secondary www www writing fabricated fabricated amplifier amplifier amplifier amplifier amplifier amplifier acts null enhancement reaching caltech caltech caltech generality held operates salient exceeds continue motivation governed governed governed sion respective equals equals equals equals paul paul paul intended injection injection injection injection injection injection injection injection injection injection injection injection injection injection injection injection injection injection injection injection injection winning winning winning winning winning winning lazzaro lazzaro lazzaro impact impact impact propagate rms rms rms drop drop slight outline creates encodes responds par drain drain drain drain drain drain junction junction classic classic classic classic classic classic classic classic classic classic classic classic classic affects tor reflected illustration capacitance capacitance modifying subthreshold subthreshold subthreshold intuition intuition crossover crosses crosses relate iso iso iso relates win win win indexed barrier travel tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling tunneling electron electron electron electron electron electron electron electron electron electron electron electron electron restoration losing losing losing losing losing losing losing losing inhibit doesn mahowald reflecting accomplish accomplish supplied injected neglect devised settle settle swing swing swing substitution cur amplified amplified amplified amplified amplified amplified appl adapts christof shares hot hot hot hot hot hot hot hot hot hole hole hole tal elegant snow obeys excite vdd capacitive capacitive ther wait jumps pay grown favorable favorable ages exciting inhibits oxide bradley lowering fatigue ryckebusch stretch proportionally volt cyber safely minch minch minch minch minch minch designer nmse lesser hasler hasler hasler hasler hasler hasler electrons electrons kcl kcl kcl kcl kcl experimen atlanta supplying manifested manifested pfet pfet pfet pfet pfet pfet pfet pfet pfet pfet pfet pfet pfet klab dii depletion depletion quicker evoke returning gaining diorio diorio recoding ify equating allel sio extendable mally netics iscas kirchhoff transis 
#@Hasler_P,Koch_C,Kruger_W,Minch_B,
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#*model model model input input input input input input input input input input input input input input input input input input input input input input input data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set training algorithm algorithm output output output output output number system system system system system system system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information information problem problem problem models hidden hidden linear linear linear shown shown shown shown shown shown shown shown shown shown shown shown systems systems systems values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters noise functions recognition recognition recognition recognition recognition recognition recognition recognition method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single processing processing control control control control control large large large large local local rate rate test test test test test test test test patterns patterns patterns patterns patterns inputs form form form shows shows shows shows shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple simple paper paper small small small small feature feature work work process process current current current current current current current current current cell high response response response similar architecture show show equation equation equation equation equation equation equation equation equation equation equation equation equation equation section section section fixed rule speech speech speech speech speech speech speech speech speech speech speech speech parameter real average states states states states states states states states states states term term term term term note experiments experiments experiments experiments experiments dimensional result threshold variables variables variables research research log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log constant constant constant constant constant estimate estimate left presented presented present temporal temporal machine machine machine machine machine machine sets range range range range range range range range range range range range outputs continuous continuous continuous continuous continuous continuous abstract back analog analog analog analog analog analog analog analog analog analog likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component positive positive positive procedure propagation introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior behavior dynamic recurrent tion tion change change change difference difference measure measure signals signals signals word word word word word word word word word word word word word word word word word word word word word word word word word word type type type required required multiple binary binary long long long expected chip chip chip chip chip chip chip chip chip chip chip chip chip markov markov make techniques length length correct probabilities probabilities observed scale minimum ing simulation computed computed called called times applications negative negative vol desired series define define perform experimental goal goal related discrete discrete discrete discrete discrete discrete equal power power power power power mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage accuracy larger connection update support support morgan proceedings words words words department implementation implementation implementation implementation implementation implementation version version version technique consists consists internal responses final delay delay delay delay delay delay delay delay delay addition sequences experiment experiment experiment experiment estimates design design design design design limit limit top detection detection detection detection detection conference full full significant significant increase produce area types types path measured measured measured normal normal increases describe describe tested hmm hmm hmm hmm hmm hmm hmm hmm hmm corresponds corresponds corresponds corresponds complete complete complete complete complete circuits circuits circuits circuits circuits short short short common common supported require end end end end end end end end end end end end end vlsi vlsi vlsi vlsi simulated simulated probabilistic functional fully block block block block block block block block block ratio edge edge edge mode mode mode operation operation operation operation operation numbers window international frame frame frame frame frame frame frame frame frame produced produced choose added added improve takes element element element element apply period period period period array array array sufficient varying varying correspond differential entire expression scaling wide correctly loop loop generally conclusions valued accurate accurate peak weak weak weak encoding encoding presence largest largest labeled labeled labeled labeled labeled labeled configuration force pro plot plot plot describes describes laboratory transitions transitions segments implement involves involves consisting blocks cycles john john decreases review solved restricted updated static static updates diagram key performing generation generation generation advantages topology topology recorded includes currents currents currents currents currents currents determines extension plotted plotted partially partially neighbors grammar grammar grammar hmms modes modes successful detect detect detect detect detect detect plots online ten ten decoding decoding decoding decoding decoding decoding decoding decoding allowing showing contribution device duration sampled sampled wave computes overlapping operating operating operating acknowledgments unlike create exhibit varied varied detail lippmann lippmann lippmann lippmann lippmann lippmann fashion transistor transistor transistor transistor transistor scaled scaled office understand removed circles trace necessarily equally aspect observe switching detected detected regime regime regime integrate devices advanced smoothness defining waveform waveform waveform waveform waveform waveform floating floating lin berkeley berkeley berkeley berkeley sections sections producing division transistors transistors transistors probable inversion inversion inversion involve circle qualitative led formulated requirement operate characterize reaches occurrence qualitatively acoustics richard enables semi decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder comments returns implements implements implements arithmetic room benefit feasible fabricated fabricated extensive amplifier amplifier acts approximates naval connecting eliminated air adds mos mos fan fan replacing analyzing bourlard integrator exceeds clock clock clock clock enhanced combinatorial filled falls falls ensures connect expanded intended captured creating layout lazzaro lazzaro lazzaro lazzaro lazzaro projects likelihoods likelihoods likelihoods likelihoods likelihoods likelihoods likelihoods dense street truncated truncated specification specification presenting presenting presenting nelson incrementally convenience trigger hundred examining rectangular magnitudes playing altered transconductance transconductance unconstrained likewise behave triggered drives algorithmic recogni settling confirm spacing filler filler filler filler filler fabrication flows excited excited subtracting agency settle settle subtracted operational interpretations repetition repetition plateau alan systematically volts consumption consumption consumption mosis est voice cess nominal defense durations durations durations durations united backwards merit dissipation cope decode decode sponsored lincoln entering spotting fundamentally orbit chang kramer clocked numbered numbered specifications notational wawrzynek wawrzynek wawrzynek wawrzynek follower follower wood flowing manage anonymous dan plete alternates interfaces lets unidirectional unidirectional unidirectional hammerstrom portable lexington grounded renormalization renormalization renormalization renormalization renormalization renormalization renormalization cancels brian incom tracing plateaus keywords keywords exit plementation recommendations flag decodes reviewers conversational attributable opinions pll uri stereotypical 
#@Lazzaro_J,Lippmann_R,Wawrzynek_J,
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#*network network network network network neural neural neural neural input input input input input input data data function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output number number state information information information information information information information problem problem problem problem models performance performance performance performance performance performance performance performance performance performance performance performance based based based space layer layer layer layer layer layer vector vector vector vector vector vector vector vector vector vector vector vector vector order systems values values noise noise noise weight unit unit recognition recognition approach approach approach approach pattern single single single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing neuron neuron rate rate rate analysis analysis analysis class class class class class class class class class class class class form form form shows shows signal signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple paper paper small feature feature feature feature feature feature feature feature feature feature feature feature feature work work work step step step step step step step step features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level level level level level current current structure problems random high high high high high memory memory memory memory memory similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show section section vectors vectors vectors vectors vectors speech speech speech speech speech speech real real real real real real average term note experiments experiments experiments experiments experiments dimensional result result result university university threshold threshold threshold threshold threshold threshold computation solution solution solution solution research research independent log found sequence initial initial constant estimate estimate computer connections left presented present present present low low low low low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency outputs outputs sample sample sample sample sample abstract applied applied find analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references references component component component stochastic ieee ieee ieee positive positive positive important introduction complex complex complex hand hand circuit effect effect effect generated cost change energy energy energy energy energy difference difference complexity complexity signals signals signals signals signals signals representations representations representations representations word higher center center center previous required binary binary binary binary binary binary binary binary long conditions distributed expected chip chip make make fact fact proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length length correct correct forward scale scale scale scale simulations simulations simulations resulting resulting resulting classes total human respect performed performed performed performed performed elements elements means factor factor factor potential natural applications filter filter filter filter samples true compared desired cross provide compute rates rates proc perform perform perform determined determined goal related connected equal power power power voltage steps dependent morgan morgan report report report loss implementation implementation implementation implementation consists consists internal represents represents represents difficult scheme addition domain domain environment design stage stage stage bit bit bit bit bit bit bit bit bit conference conference determine efficient requires requires requires significant significant significant world world world speed validation produce produce channel channel channel channel channel channel channel channel channel channel area lines lines lines path provided finally finally nature simply simply discussion denote transformation corresponds complete circuits circuits implemented generate supported supported role require require require vlsi vlsi vlsi vlsi vlsi vlsi future development noisy noisy auditory needed hopfield hopfield reduced reduced programming increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation matching operation principal max filters filters window window stored stored stored bits normalized normalized normalized normalized normalized normalized normalized normalized normalized produced produced description correlations advantage robust typical typical reported practical practical include identical machines machines side engineering engineering highly highly approximately approximately approximately approximately yields speaker correspond correspond achieve trans address channels channels channels channels channels channels channels channels channels gate gate gate storage storage storage storage storage storage storage storage entire grant horizontal intensity intensity suggests digital derivative derivative derivative derivative derivative derivative generally hardware hardware pass pass pass pass demonstrate half conclusions competitive accurate clear performs practice propose propose physics physics largest characteristics drawn turn minimizing acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic question appears digit winner winner winner factors laboratory laboratory tuned tuned vertical dept changing changing implement implement implement averaging electrical remaining easy easy develop integrated frequencies events shift shift shift stages stages correlated influence solved detailed operations evolution soft understanding completely digits spectrum spectrum sign sign sign sign diagram key calculation calculation smoothing smoothing smoothing slow performing performing normalization normalization normalization normalization normalization normalization normalization normalization normalization reduces purpose initially filtering filtering calculate sufficiently norm norm advantages transactions precision expect expect recorded building template template template template template template template template template template template template template template template template template template template perceptual currents currents determines maximize absolute holds compression extra uniformly modification modification computationally effectively receives composed compact showing content device device duration duration quantity absence wavelet delayed delayed highest thresholds thresholds automatically processors processors illustrates satisfies software decreasing remain create requirements requirements preliminary preliminary school incremental office office reliable variability encode statistically fundamental plausible onset prototype quantities observe explored store store consist baseline baseline baseline baseline baseline baseline baseline baseline baseline detected motivated electronic electronic isolated isolated years devices devices devices devices burst burst advanced developing analyzed analyzed floating floating floating multiplication multiplication multiplication multiplication multiplication handle nonlinearity considerable straight preprocessing choices consequence cut calculations calculations lowest exemplars raw raw raw collected collected cochlear cochlear empirically empirically transient transient transient transient transient transient transient transient transient transient transient transient fed leave adjustable passed employ employ continuously biologically biologically schematic schematic templates templates templates templates templates templates templates price rely spread incoming tank tank serve phonemes qualitatively qualitatively prevent acoustics replace sophisticated sophisticated segmented segmented wang wang wang progress cochlea instantaneous instantaneous instantaneous pole shifted ear ear fabricated bipolar bipolar forming forming bin bin bin bin nonzero multipliers systematic multiplier khz khz simplify attractive serves exploit bourlard salient modifications corpus symposium degradation hours intended washington evident yang yang yang neuromorphic neuromorphic smoothed smoothed smoothed bins clean clean rich properly properly impact subsequently summarize interestingly assigns dramatically multiply multiply multiply multiply maintaining crossing crossing compressed compressed compressed drop largely creates emerge bank bank bank poses seek arg spaced descriptions workstation mismatch concentrated mammalian thresholded differentiation exceed exceed rectified rectified rectified rectified misclassified register register register crossings intl minor mimic transients transients transients transients transients transients transients transients transients transients transients transients transients transients transients transients transients transients transients transients drops examination differentiating recognizers recognizers pineda pineda pineda pineda pineda pineda pineda architectural removes picking achievable algorithmic algorithmic quadrant quadrant quadrant quadrant quadrant quadrant envelope hopkins hopkins hopkins hopkins fill played fabrication excited subtracted andreou andreou offsets measurable comprising lowpass digitized johns johns quantitatively bach aggregation aggregation differentiate cauwenberghs cauwenberghs cauwenberghs cauwenberghs concatenated charles baltimore baltimore tim durations denominator maryland maryland degrades elegant ece align abnormal rectification goldstein goldstein edwards edwards edwards edwards challenges counterparts insects missed disk multiplexing multiplexing flips birds iix mammals mammals multiplies differentiated differentiated aligning correlator correlator correlator correlator correlator correlator correlator bucket fernando fernando gert gert clicks clicks accumulates shamma shamma shamma segmenter segmenter segmenter segmenter segmenter tape timothy hermansky hermansky evidenced ambient undertaken brigade correlating distributes correlators jhu jhu electronically unsatisfactory ultra trail diagnose wear wear mirrored unnikrishnan unnikrishnan dat dissipated dissipated amplifying budget catch pops apl uncontrolled detroit consume judicious throws ordinarily pings collaborative laurel 
#@Cauwenberghs_G,Edwards_R,Pineda_F,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input input input input input input input input data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set networks output output output output output output output output output system results units information information models based based linear case case vector vector order order order shown shown shown shown shown systems systems systems parameters parameters noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition point point single single single single single processing processing control control neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate test test inputs inputs form form shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal paper small small fig fig fig fig fig fig fig cells cells cells cells cells step step process current current current current current current current current current current current current current current current cell cell cell cell cell cell cell cell cell cell cell high high high high high high response response response similar similar similar similar similar similar similar similar representation show section section section section section line line speech parameter parameter real average gradient experiments activity result threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold independent found constant estimate computer computer node presented presented present present present low low low low low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal maximum maximum range range press press press outputs abstract analog references component component positive positive important important introduction action complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit estimation estimation estimation estimation estimation stimulus stimulus effect effect effect effect effect generated difference lower lower lower signals signals higher higher higher higher part part part part center firing firing good spike spike spike spike spike long expected expected chip chip chip chip chip chip chip chip chip fact fact scale total total multi called elements factor potential potential potential potential potential potential potential potential feedback feedback filter filter filter filter filter filter negative negative negative original artificial relative application series rates proc connected gain brain brain equal power voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage larger institute implementation consists internal individual advances represents responses bias bias considered cambridge experiment additional stage stimuli stimuli bit bit detection detection detection detection detection detection detection free speed basic increase increase increase give give developed developed velocity velocity actual actual processes simply simply biological biological measured increases increases increases group group group group group group group group group group group close complete excitatory stable circuits circuits circuits circuits short implemented adaptation vlsi vlsi easily easily easily makes auditory auditory auditory auditory typically smaller smaller technology transfer york increasing increasing mechanism mechanism details filters filters filters filters filters depth depth combined membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane improved discussed pair element typical lateral lateral practical introduced period period period period period period period period period period period period period period period period yields yields differential background observation observation gate increased amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude exists parts intensity intensity intensity intensity spikes spikes spikes spikes spikes spikes width width setting pass pass pass pass pass pass half conclusions peak exponential weak sound sound sound sound sound sound mechanisms presence drawn proportional turn decrease groups acoustic acoustic acoustic base relation relation van van van van van van van van modeled modeled modeled sensitivity sensitivity sensitivity slightly integrated integrated integrated frequencies frequencies frequencies quality blocks blocks blocks decreases yield yield depending stages influence influence variation controlled controlled controlled controlled controlled modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation understanding completely allowed allowed diagram diagram performing measurements add generation generation building building building fire fire silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon currents characterized tests major simplicity capable society driven driven spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking build build post situation situation reached receives soc soc conf repeated repeated allowing conductance conductance physiological physiological duration absence nips wave delayed extract load intrinsic intrinsic decreasing receive presents stimulation stimulation stimulation stimulation stimulation create create humans detail detail helpful rise matches project project detectors int pathway pathway understand fundamental fundamental plausible recognizer voltages ensure detected electronic electronic charge years burst histogram histogram slowly band band band band band unstable cascade cascade caused briefly division transistors transistors nucleus nucleus nucleus nucleus nucleus cut cut cut cut sounds pitch pitch pitch pitch pitch pitch pitch fuzzy double cochlear cochlear cochlear cochlear cochlear cochlear cochlear pure pure lms fed detecting detecting detecting detecting resistive resistive biologically operate modulated modulated modulated modulated incoming neuro cochlea cochlea cochlea cochlea cochlea cochlea synchronization instantaneous ear bipolar bipolar amplifier refractory refractory refractory refractory refractory refractory refractory linearity driving harmonic impossible khz khz khz khz khz odd odd determination handwriting los biased biased keeping neurobiology reasoning ral exceeds fires inferior inferior inferior inferior date tone tone tone periods periods loo loo originally similarities insight stimulated colliculus colliculus colliculus valuable explains influences influences displacement discharge discharge hair hair hair hair hair hair email creates creates resting resting eric eric mismatch capacitance capacitance capacitance capacitance conduction insights mammalian mammalian potassium compatible compatible synchronized transconductance intensities intensities intensities win drops normalizing article article rarely acoust acoust resolve envelope envelope envelope envelope envelope envelope envelope envelope envelope envelope doesn supply carrier carrier carrier inverter inverter inverter inverter periodicity injected impedance coincide leakage leakage leakage leakage falling brainstem brainstem stabilize stabilize stabilize pin explaining completeness plenum ina ina rises stabilizing pull lowered corr wait coincidence coincidence coincidence coincidence coincidence coincidence coincidence coincidence coincidence coincidence synchronize synchronize synchronize synchronize synchronize synchronize waiting waiting controllable exceeded exceeded basilar basilar basilar stays psth psth psth psth psth rising rising rising rising rising nato valley rid charging vittoz vittoz vittoz vittoz schaik schaik schaik schaik schaik schaik schaik schaik swiss microelectronics stimulations charged charged federal alamitos harmonics cutting stimulate vth vth carriers carriers sinusoid neuromimetic nmos nmos asi valleys psycho psycho obt andr lime conv itseft synchronizes synchronizes synchronizes nnmber nnmber lausanne compressive mitter anew 
#@Fragniere_E,Vittoz_E,van-Schaik_A,
#t10
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#*network learning learning model model model model neural neural neural input input input input input input input input input input input input input input figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set set networks networks networks training training algorithm algorithm output output output state state state state state state state state state results results results results results results results results results results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information models models models models models models models hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space linear vector vector order shown shown shown systems systems systems values values probability parameters parameters parameters parameters recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach image image image image image image image image image image image image image image image image image image image processing processing processing processing processing processing processing processing processing processing local local local test analysis analysis analysis inputs inputs shows shows shows shows shows signal signal signal signal gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small small small size feature net work work work work work task task task task task task methods methods step points field features features features features features features features features features level level level current trained trained trained trained similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture equation images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general general generalization speech speech speech speech speech speech speech speech speech speech real average states states states states obtained obtained activity activity dimensional dimensional university university computation computation research research research defined found found found found found initial table table standard computer science science science left left left left left left left left left direction present present present present low low low low low low low low low low low low low low low low low low low low low low low low temporal temporal temporal machine motion motion motion range range range range range press position position position position components components components components components sample sample sample abstract back find computational references component stochastic due due due ieee ieee ieee ieee important mixture mixture introduction hand hand dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated variance variance tion tion tion tion change difference difference difference difference difference difference difference signals signals signals representations representations representations representations representations representations representations representations representations representations word learned learned learned learned learned higher part center center cortex represent expected markov markov markov markov techniques techniques techniques techniques techniques region correct probabilities probabilities probabilities scale scale scale scale scale scale scale scale scale scale scale scale simulations resulting resulting computed computed performed performed means means factor made made global global applications em em obtain original original relative represented compared compared compared provide active distributions equal approaches approaches approaches mit steps steps comparison comparison comparison comparison comparison contrast modeling morgan proceedings proceedings proceedings report institute institute words words kernel advances advances represents final delay addition addition considered cambridge estimates transition san san san san san san top top top conference upper full pages pages pages pages give give con derived clustering clustering levels area area area provided finally finally nature nature sampling constraint discussion normal normal normal technical feedforward tested tested tested hmm hmm hmm hmm hmm hmm amount shape shape shape shape supported main face face end pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel noisy noisy sensory sensory sensory fit kaufmann auditory pairs reduced account coefficients coefficients projection segmentation mechanism matching database database database database language leads principal principal principal principal principal principal numbers numbers bits normalized normalized normalized normalized normalized normalized normalized normalized normalized bottom bottom bottom frame frame frame combined combined combined combined combined architectures architectures improved improved improved resolution resolution resolution advantage robust separate movement reported reported moving subject side pixels pixels pixels pixels pixels pixels pixels sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive cognitive cognitive relevant relevant engineering interest compare compare approximately subjects subjects volume volume volume speaker correspond pca pca pca pca pca pca sparse mixtures mixtures mixtures mixtures positions locations locations symmetric symmetric symmetric increased parts intensity intensity intensity intensity intensity lead occur wide wide rotation rotation rotation feed touretzky column column column column column column column column column pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass half half half flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow starting critical editors editors differences differences designed integration integration integration reduction california variety variety variety variety derivatives acoustic acoustic acoustic acoustic acoustic acoustic acknowledgements digit digit digit digit digit digit edges edges perception optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical vertical dept modeled category explicitly averaging averaging electrical dimensionality remaining gaussians formed formed extraction yield influence variation showed showed centered frames frames frames frames frames frames frames frames frames static translation translation translation digits digits discrimination processor normalization normalization normalization combining roughly purpose purpose purpose filtering filtering filtering filtering filtering exploration template box contour contour recognize recognize illustrated illustrated illustrated automatic automatic automatic variations variations absolute reason compression compression selecting middle middle closely hmms hmms delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta delta tdnn tdnn tdnn projections projections projections vowel vowel contained contained video video video video video video video video video video video neuroscience lie gray gray gray gray gray gray gray gray gray gray gray gray gray gray gray michael michael reach consisted consisted subsequent subsequent subsequent tesauro tesauro camera cowan diego diego diego diego diego powerful poor rapidly environments humans humans humans optimized dataset dataset dataset dataset reducing successive successive investigated investigated investigated combine combine combine notion analogous matched matched neu neu examined examined reading reading reading front algo panel panel panel panel panel panel explored explored explored explored shapes initialized improving motivated sentences crucial distinguish track biology explanation lies sys sys preprocessing filtered filtered filtered filtered filtered filtered filtered directional located mation separately beginning english english medical computers raw raw raw raw raw raw raw improvements substantially understood led tional spoken spoken spoken spoken effort howard acoustics datasets datasets gave gave gave gave substantial substantial kinds kinds kinds kinds sophisticated display display segmented windows lab room leen forming japan tation reconstructed eliminate eliminate eliminate lost eliminated systematic systematic systematic systematic significance primate alpha stated neurobiology ral ral salk canonical optic intuitive carry planar planar hours vowels motivation infor alspector utilized lip lip lip lip lip lip lip lip lip lip lip lip excellent mance perfor washington captured francisco surprisingly jolla consonant captures valuable valuable thresholding thresholding informa informa dramatically yielded yielded yielded yielded yielded land email stork stork asked asked dec pentland icassp ical individuals australia brightness mhz formance insights rithms tems ization ization hughes mouth mouth mouth mouth challenging terrence careful wise retain intensities represen accounted worked students ucsd monitor mcdonnell hearing movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan engine engine believed bregler bregler bregler bregler contributes carries tended explanations digitized digitized digitized tracks approached wolff wolff tical capturing generaliza proceeding talk sur jenkins jenkins pew centroids centroids goldstein goldstein lips lips lips lips lips lips sought movie lowing sual subtraction konig konig konig konig conveniently prototypical george lipreading lipreading lipreading lipreading yuhas yuhas interna suc males hen departments muscular atlanta markedly females dig strained initializations movies garcia garcia downsampled downsampled downsampled midline prasad prasad javier mase mase adelaide inquiry psychophys succinctly partment multiplicatively voices 
#@Gray_M,Movellan_J,Sejnowski_T,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural data data function function function function figure figure figure time time time time time time time time time time set set networks networks networks networks algorithm algorithm algorithm algorithm output system system system system system system system system system system system system system system results results results results results information information information information information information problem problem problem problem problem problem problem problem problem based based based weights weights weights weights weights weights linear linear case vector vector order shown shown shown systems systems systems systems systems systems probability weight functions functions functions unit unit unit unit distribution recognition recognition approach approach approach approach approach point point single processing processing processing processing local rate rate rate test test matrix matrix matrix matrix matrix matrix matrix optimal shows shows shows shows shows signal signal signal signal signal algorithms algorithms size net work work fig fig fig fig fig fig fig points process process problems random response similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show section section rule rule rule rule rule rule rule rule rule rule rule speech speech speech speech speech real real real real real real real real real real theory gradient gradient gradient gradient gradient gradient gradient gradient note note experiments experiments university university university computation solution research independent terms terms terms distance phase phase phase phase phase phase phase phase phase phase phase phase phase frequency frequency frequency frequency frequency frequency temporal maximum press nonlinear abstract applied back back computational convergence density references references due due ieee ieee ieee important adaptive adaptive mixture complex hand generated recurrent energy rules rules rules rules rules rules rules rules signals signals signals signals signals signals signals signals signals signals signals signals signals learned chosen higher cases multiple multiple long equations techniques observed minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum minimum resulting ing tasks simulation simulation multi performed performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq mapping natural natural natural natural natural natural natural natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications applications knowledge filter filter filter filter filter filter filter filter original original original true application application cross proc proc proc proc proc perform mit source source source source source source source source morgan institute department advances advances joint joint represents difficult exp exp delay delay delay delay delay delay delay delay ai domain domain domain domain domain domain domain domain equivalent experiment top full world world give con derived types entropy entropy entropy entropy entropy finally nature depends sampling sampling feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward group limited inverse inverse inverse assumption assumption assumption assumption assumption corresponds complete stable stable stable stable stable assumed supported main eds square fit fit kaufmann simulated coefficients transfer transfer transfer transfer special principle leads max filters filters filters filters filters filters filters filters filters filters filters filters bottom bottom bottom polynomial sources sources sources sources sources sources sources sources sources sources sources sources sources denotes denotes architectures separate separate reported reported subject sense sejnowski sejnowski array engineering engineering approximately solve solve solve speaker achieve trans address mixtures mixtures mixtures mixtures background background background separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation bounded increased grant amplitude amplitude exists extended derivative white white occurs occurs occurs demonstrate demonstrate half starting row row row assumptions conclusions sigmoid moody propose presence california california exist minima derive derive solving solving dept missing electrical electrical involves slightly develop shift blocks independently formation transform transform evaluated showed lee lee lee lee lee static static approximated completely suggested digits digits earlier reasonable performing delays delays delays delays delays expansion roughly recorded recorded recorded recorded box thesis usa usa usa usa bell bell bell bell bell blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind illustrated discuss maximize discussions sensor sensor society delta wij wij successful successful post identity ten ten ten characteristic road prob success follow follow notation delayed delayed delayed delayed delayed delayed delayed delayed delayed leading leading mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing acknowledgments requirements involving detail periodic combine dependencies dependencies dependencies office working workshop statistically waibel recognizer recognizer obvious algo logistic logistic separated ith speakers speakers amari amari amari amari mixed mixed mixed mixed phd sentences sentences rows ground sensors nonlinearity inside inside inside filtered filtered involve circle circle circle circle circle meaning mellon addressed conjugate people people considerably considerably carnegie collected led cmu spoken fed recordings recordings recordings remove remove music music music music music music music passes pittsburgh monotonic acoustics germany chose comments simultaneous converged sharing person person room room room room room room room spectra appearance japan japan rithm linearity linearity linearity recover jth naval arranged plays platt platt spontaneous air khz khz adjusting transforms neurobiology operates fail fail fail reasoning reasoning salk salk substituting interference interference separating separating separating sides lengths yang yang competing reproduce entries jolla clean implicitly speeds pdf infomax infomax infomax infomax infomax lem speaking speaking speaking unable fellowship sig transmitted dec formulate kurtosis centre icassp convenience convenience medium causing aij superimposed causal causal causal causal causal demon laplacian adjustment learnt learnt learnt inverted deconvolution deconvolution deconvolution deconvolution altered differentiation fir fir fir fir fir fir fir interactive grateful inverting inverting inverting inverting inverting algebra algebra rewrite simplifies status worked served invertible firstly lated alex russell compensation compensation fft anthony archi symmetrical transpose convolved convolved convolved convolved convolved convolved convolved planck south poles poles zeros zeros zeros artificially cichocki cichocki cichocki cichocki dij dij dij dij dij recovering maximisation maximisation maximisation maximisation iir iir iir iir iir iir iir iir iir elegant cardoso plotting invert invert won superscript rescaling rated maximising tecture terry picks proving neti conveys ordinate unmixing unmixing unmixing unmixing unmixing taps roots multichannel icnn maximise gra equivariant tony generalised strated southern freq sept rooms rooms dient atlanta causality quotient nals torrey pines separations hermitian symp lution loud loud restore coordi lambert lambert lambert lambert lambert lambert lambert lambert laheld faggin faggin listening lyl sepa microphones microphones microphones formu autocorrelations intern houston uncorrupted usc existed nate oyi supposedly blindly audible nolta califor nia 
#@Bell_A,Lambert_R,Lee_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data function function function function function function function function function function function figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number system system system system system system system error error error error error error error error error error error error error error error results results results results units units units units units problem problem problem problem problem hidden performance performance based layer layer layer layer case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown shown shown systems values noise functions functions functions functions functions functions functions functions functions functions neurons unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach pattern pattern pattern pattern pattern single processing processing processing processing neuron rate rate rate rate rate rate test test test test test test test test test test test test class class class optimal optimal inputs inputs shows algorithms algorithms paper paper paper examples examples examples examples examples small size size work work work work work work work work step step step features trained trained trained high memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response similar similar architecture show section section fixed line line line line line rule vectors vectors vectors vectors general generalization speech parameter approximation average average obtained experiments experiments experiments experiments experiments threshold computation computation computation computation solution independent independent independent independent independent independent independent independent defined target target target target table table table estimate estimate standard standard computer distance distance distance distance distance distance presented present maximum range range press press learn basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs outputs outputs outputs abstract applied applied applied back properties properties references ieee adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation introduction hand hand hand estimation statistical statistical statistical classifier classifier classifier classifier classifier lower lower word word word word word word word word word word word word word word word learned learned chosen center previous previous previous previous previous required required multiple multiple correct correct correct correct correct correct correct probabilities probabilities errors errors errors errors errors errors errors errors forward ing total human regression regression computed computed performed performed performed eq made specific specific specific represented true compared application desired desired provide provide rates rates rates rates goal related related connected gain accuracy accuracy accuracy accuracy contrast dependent dependent words words words words words version code difficult difficult difficult difficult delay ai ai ai ai maps maps considered considered curve additional additional additional additional additional san top top upper full requires statistics statistics statistics statistics speed speed speed estimated increase actual actual simply tested tested fast limited corresponds rbf rbf rbf rbf rbf rbf rbf rbf amount amount amount amount nearest nearest nearest nearest nearest shape require adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation end development development needed combination character character character character character character character character character character character character consistent consistent consistent consistent consistent call call call max pre pre stored stored stored stored stored polynomial combined combined combined run improve takes takes element typical typical typical pixels subset sufficient module module module module module module module storage entire entire extended correctly feed width place place greater reduce conclusions neighbor neighbor editors designed learns taking radial radial radial radial radial radial radial user user user user user user user user user user user user user user user user user exist min decrease relationship iii characters characters characters characters characters characters characters characters acknowledgements digit construct produces produces produces produces written written index ways sequential describes describes label label label stability tuned confidence confidence metric metric multilayer linearly linearly linearly scales adding john decreases review depending updated labels showed static partition updates reduces add add interpolation interpolation euclidean handwritten memories memories memories memories memories memories recognize recognize recognize recognize determines vapnik plotted tests major columns suitable suitable society effectively tdnn tdnn tdnn tdnn post post post post tend tend characteristic characteristic characteristic quickly cun list write simplified simplified simplified denker denker highest highest decreasing decreasing employed poor create create create create requirements difficulty put detail replaced replaced replaced helpful reducing applicable ideal affect editor adapt adapt adapt recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer recognizer subsets multivariate consist baseline baseline finds fairly slope slope improves improves nowlan adapted adapted correction correction correction correction correction starts processed purposes closer widely style style style constructing ran ran ran ran hyperplane hyperplane controls controls recognized people substantially substantially consistency pseudo lms quantitative quantitative incorrect incorrect incorrect incorrect incorrect incorrect variant resource resource resource prevent decreased instantaneous cumulative cumulative contextual contextual writing writing writing oxford member count jth jth jth partitions addresses printed printed grows grows inspired platt platt platt platt platt platt platt adds ments difficulties handwriting handwriting handwriting handwriting handwriting handwriting handwriting exploit exploit disjoint effectiveness constructive constructive constructive constructive degradation spurious started recog creating creating creating creating cpu wolpert papers treat boxes dramatically users guyon guyon guyon failed retraining corrected corrected arg reflected adapting henderson allocated allocated allocated carefully writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer writer constructs cij misclassified discusses dictionary elsevier retained bring prevents corrections mini mini experi recognizers recognizers recognizers recognizers suggestions styles simplification simplification decided tom tom affecting proposes tokyo recognizes recognizes drastically inde adapts niranjan creation steve stacked allocating allocating allocating allocating experimented putation rec modest jose amsterdam cox noticed progresses nice unaffected pendent sentations entered mason stacking stacking retrained writers writers writers writers writers writers writers writers writers posterjori perplexity allocate allocate unambiguous instructed albrecht joe tunable powell interfaces synaptics synaptics synaptics corrects corrects clarendon cid atypical atypical atypical atypical atypical atypical atypical sacrifice confi confidences confidences confidences confidences ifx allocates phantom interactively parkway dial ofa orchard curacy abc abc rag neatly augments 
#@Matic_N,Platt_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data function function function function function function function time time time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output output output output output output output output system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error results results results results units information information information information information information information information information information information information information information information information information information information information information information problem models models hidden hidden performance performance performance performance based based based based based based based based based weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters weight neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern single processing processing large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate test test patterns patterns patterns class class class class class class optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper paper paper small size feature feature feature feature feature feature feature feature feature feature net net work task task task task task task methods methods features features features features features level trained trained trained trained trained trained trained trained trained trained trained structure structure high equation equation equation section fixed vectors vectors vectors vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter parameter real average theory theory theory theory theory theory theory gradient gradient obtained obtained obtained term experiments university university variables independent independent independent independent log log log log log log log log defined found sequence sequence sequence sequence initial initial table table standard standard computer terms terms distance synaptic synaptic science left presented presented presented presented presented presented presented presented presented presented presented presented presented presented presented presented present low maximum maximum maximum maximum maximum maximum maximum maximum maximum components continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract back likelihood likelihood likelihood likelihood references component component component component component component component ieee ieee ieee procedure procedure decision propagation mixture context context context context context context context context introduction behavior behavior behavior behavior behavior dynamic generated recurrent search search complexity complexity assume word word word word chosen higher higher previous cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing required multiple good good binary represent expected markov markov markov markov markov fact fact fact fact fact fact fact length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed resulting resulting resulting resulting resulting resulting resulting resulting resulting resulting resulting classes classes classes classes classes computed computed computed respect sum eq means means means made vol artificial represented compared rates rates proc proc active goal posterior posterior distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal approaches accuracy comparison larger dependent dependent dependent dependent dependent dependent dependent dependent dependent modeling modeling selection morgan report words words department implementation implementation technique internal joint connectionist connectionist difficult final considered considered considered considered directly additional transition stage efficient full basic give con derived derived derived clustering developed developed criterion criterion criterion criterion criterion criterion area provided iteration depends increases arbitrary arbitrary tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm assumption proof finding finding effective implemented assumed assumed generate generate theoretical theoretical main journal end instance future easily easily development including including probabilistic probabilistic probabilistic probabilistic typically combination combination combination combination reduced technology special special special special special database principle 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superior issue issue built generalize paradigm paradigm leading leading maximization processors principles principles principles deal presents law law minimized powerful powerful involving detail estimators issues ml ml ml ml possibility maximizing stream stream stream stream stream stream stream stream front obvious obvious noted academic baseline baseline baseline generates mentioned mentioned mentioned mentioned great advanced formula formula theoretic publishers capabilities capabilities capabilities capabilities briefly briefly processed sections constructing desirable describing explained improvements improvements improvements substantially pure fed introducing formulated formulated compares compares robinson http gains vocabulary vocabulary rely summarized characterize popular popular resource resource serve phonemes achieves germany semi sophisticated expectations lim softmax yielding yielding realized realized www modify arguments member approximates approximates consideration chance logarithmic abilities serves belong bourlard bourlard affected optimally presentations fires fires fires continue codebook dependency dependency realization belongs uni foundations express extensively pdf outlined audio emission emission emission emission street unified unified unified kluwer maximized maximized discriminative icassp icassp obtains arg arg arg arg warping realize realize wall management management oct paradigms distinguished ation exploited info characterizing jointly incorporation quantizer quantizer quantizer quantizer quantizer quantizer quantizer quantizer quantizer correctness characterizes html quick feb feb carrying facts sep recalled replaces renals entropies demanding exploitation favorably substituted mmi mmi mmi mmi mmi mmi mmi mmi challenges perplexity faculty faculty prevented ogp crisp hochberg hochberg neurocomputing concludes wsj wsj atlanta recalling cook csr profound bigram descend triphone trigram gerhard gerhard quantizers triphones triphones 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vector shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise functions functions unit method method method method method method method approach approach approach approach single processing processing processing control control control control control control control control control control control control control control control control control control control control control large large large rate test test analysis inputs form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal gaussian gaussian examples examples small small small small small small net net net net work work work task task fig fig fig fig step step features level trained trained trained trained trained structure structure problems problems problems problems high high high similar architecture show section fixed vectors vectors vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech parameter approximation approximation approximation approximation gradient obtained obtained obtained experiments dimensional dimensional dimensional dimensional dimensional dimensional university computation computation computation research found found sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant standard standard standard computer prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented present present present phase phase activation frequency basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous sample sample abstract applied computational density properties properties properties references due due due ieee ieee procedure context context context introduction introduction estimation estimation estimation estimation behavior statistical effect effect dynamic parallel search tion difference assume assume lower measure signals signals signals signals signals signals signals signals signals signals signals signals signals signals word word word word word word word word word learned higher previous theorem theorem cases good good long long represent techniques proposed proposed observed forward finite resulting resulting resulting resulting ing respect eq eq mapping means factor optimization optimization dimension dimension dimension dimension dimension dimension applications applications applications obtain obtain negative original original original original original original original vol artificial artificial samples samples samples represented compared compared application application application series series series series series series series series series series series series series series series series series series series series series series series series series power power power power train modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling proceedings proceedings proceedings version consists consists represents represents difficult exp delay delay delay sequences domain equivalent directly directly directly additional conference requires approximate approximate free basic pages pages increase give give produce derived actual actual actual finally selected iteration iteration sampling normal technical increases describe arbitrary arbitrary denote fast close close complete stable stable stable rbf rbf rbf rbf rbf rbf rbf amount short short theoretical theoretical require main eds journal future smaller smaller underlying underlying needed combination dynamical dynamical dynamical dynamical dynamical dynamical interesting interesting increasing increasing consistent leads call pre pre normalized decay predict directions property practical practical practical practical practical apply apply apply apply introduced subject identical varying varying varying varying varying volume volume works works works tuning smooth yields yields yields yields speaker achieve interval improvement improvement increased increased increased exists exists scaling scaling extended deviation deviation predicted locally touretzky demonstrate demonstrate minimal assumptions valued valued valued editors sigmoid clear moody weak sound sound sound sound physics characteristics demonstrated solid regularization regularization radial radial decrease derivatives acoustic question attractor attractor attractor attractor attractor attractor attractor attractor attractor longer estimating describes transitions transitions transitions stability stability stability stability tuned develop adding minimization springer shift quality quality select choosing review reconstruction reconstruction reconstruction reconstruction variation controlled evolution evolution centers forms understanding past spectrum spectrum spectrum earlier dashed measurements normalization neighborhood neighborhood purpose interpolation interpolation remains remains valid foundation transactions building building activations coordinate coordinate coordinate formulation extension discuss discuss major major major straightforward closely closely capable successful identify attractors attractors attractors attractors build build situation ten characteristic capture summary success follow duration duration duration comp sampled nips quantization delayed delayed predictor approximating tesauro modelling modelling extend extend extend employed employed investigate investigate investigate investigate varied optimized optimized ideas mappings investigated possibility possibility possibility possibility workshop understand onset predicting predicting consist explain chaotic chaotic slowly unstable unstable capabilities handle considerable turns straight producing bishop hyperplane hyperplane mathematics universal universal describing pitch explained considerably considerably considerably fuzzy tional tional spoken leave posed detecting music music music music music music music berlin berlin berlin berlin synthesis synthesis synthesis mod ture weigend incorporating phonemes plan enables germany chose neuro wesley leen notes addison investigation arguments concerned impossible khz khz ments darken stated methodology symposium lyapunov lyapunov infor embedding embedding embedding embedding embedding tone tone tone tone tone tone ensures loo sion respective regarded intended forecasting uni reproduce reproduce initialize initialize iterated iterated foundations young ahead ahead park extensively impact speaking consecutive rms outline incorporates email uniquely 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cost search difference difference complexity complexity complexity complexity complexity measure measure learned chosen binary binary equations equations equations fact proposed proposed proposed proposed observed observed finite classes total total computed computed computed computed computed computed computed computed respect respect respect performed performed means dimension dimension dimension dimension dimension negative original relative desired define define compute determined determined equal accuracy accuracy accuracy comparison descent version version version technique technique consists considered considered computing curve bit efficient increase give randomly developed developed developed developed developed criterion types depends achieved normal normal normal tested tested transformation transformation transformation nearest generate require main square easily easily underlying reduced account character projection increasing increasing special operation leads representing representing representing numbers pre normalized normalized idea idea run added added added denotes improved improved improved typical reported introduced subset relevant relevant calculated solve converge converge rl definition observation improvement increased studied invariant invariant suggests trial rotation rotation rotation rotation rotation locally conclusion starting reduce reduce operator neighbor tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent clear peak faster faster faster propose min introduce denoted reference digit written sequential generating label metric multilayer multilayer transformations transformations transformations transformations transformations transformations transformations transformations transformations remaining remaining remaining angle adding adding versus versus family reconstruction squares interpretation controlled fraction decomposition approximated suggested digits digits digits digits digits converges converges key generation distances norm norm euclidean euclidean euclidean advantages advantages building building building perceptrons subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace holds characterized importance efficiently comparing invariance tend dis manifold hold notation modular minimizes computes computes computes reach automatically automatically automatically automatically consisted approximating presents remain diego transformed requirements requirements requirements discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant dataset fewer fewer reducing combine authors closest changed subsets subsets subsets prototype prototype prototype singular algo algo observe art epoch epoch isolated trivial adapted capabilities capabilities capabilities capabilities capabilities capabilities capabilities expensive drive style controls simard simard simard researchers geometric parameterized slower sharp prototypes prototypes prototypes mod measuring gave display implements irrelevant irrelevant cor cor rithm rithm grey fails adds dealing ments stated constructive constructive constructive constructive constructive constructive constructive constructive constructive constructive constructive constructive degradation degradation performances combines iteratively pat percepttons sim counting centroid centroid 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processing processing control control control large test test test test test test test matrix matrix matrix matrix optimal optimal optimal inputs inputs form form form form form form form form form signal signal signal signal signal signal signal algorithms algorithms algorithms gaussian gaussian gaussian paper paper paper paper work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step step step points points process process process process process current current trained trained problems problems memory memory show equation equation equation equation fixed fixed fixed line line line general general speech speech speech speech speech speech speech speech speech parameter approximation approximation approximation average states states states states states note note note note note note experiments experiments university variables log log found initial table table table table estimate estimate estimate estimate estimate estimate estimate standard standard standard computer prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction present temporal maximum maximum maximum maximum maximum maximum maximum nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample sample abstract applied applied find computational computational convergence convergence convergence likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic due due ieee ieee ieee ieee procedure important adaptive context introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior dynamic generated variance variance variance variance variance parallel parallel cost cost cost cost cost cost recurrent recurrent recurrent tion tion tion assume prior prior part type required conditions equations equations techniques proposed proposed correlation errors errors errors errors errors forward forward forward forward forward forward forward forward forward simulations minimum minimum minimum minimum resulting resulting ing tasks regression regression computed computed computed computed performed optimization optimization optimization optimization optimization optimization optimization optimization optimization made made applications study knowledge knowledge filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter vol samples samples samples samples true compared cross cross series series series series series series series series series series series series series series series series series series provide perform perform perform determined constraints approaches approaches approaches comparison comparison comparison update train train train train train proceedings report institute words department joint joint represents final bias addition framework framework framework framework framework equivalent equivalent equivalent experiment directly directly directly additional estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates transition limit stage efficient efficient requires requires requires requires requires requires requires significant approximate statistics statistics statistics statistics free estimated estimated estimated estimated estimated validation produce produce weighted conditional developed developed developed product provided provided provided finally backpropagation iteration nature simply simply simply achieved achieved technical feedforward tested fast inverse assumption corresponds predictions short common generate generate generate role require square square square ability future future makes development noisy noisy noisy noisy noisy noisy noisy noisy noisy including fit simulated typically underlying underlying needed account account account unknown unknown unknown unknown unknown unknown unknown unknown unknown testing testing testing significantly york leads filters filters filters filters filters filters filters window normalized bottom combined run improved improved discussed improve improve exact pair robust separate separate takes takes practical include include engineering varying varying compare compare observations observations observations observations observations observations solve smooth smooth match achieve diagonal address 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recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method approach approach approach pattern point point point image single single single single single single single single processing processing processing large large large large local rate rate rate rate test test test test test test test test test test patterns analysis analysis optimal inputs form form algorithms simple simple simple simple simple simple simple simple simple simple simple simple simple paper paper paper paper small small size feature feature work work work work task task task task methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods classification classification classification classification classification classification classification classification level level level current current trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained problems random show section section section section fixed vectors generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average average average average average average average states obtained term experiments experiments experiments experiments result result result university university computation log found found sequence target initial initial table table table table table standard standard standard standard standard standard terms left presented presented presented map present machine machine sets sets sets maximum outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous abstract properties references due ieee procedure procedure procedure procedure adaptive mixture mixture mixture mixture mixture context context context introduction dynamic recurrent recurrent tion tion energy lower prior prior word word word word word word word chosen chosen chosen chosen center previous previous previous previous previous bound bound cases cases cases type binary expected markov techniques techniques techniques techniques correct correct probabilities probabilities probabilities probabilities probabilities ing ing ing ing tasks total human computed multi multi multi multi performed regions made natural knowledge knowledge filter filter compared application cross cross cross series provide provide rates rates proc determined posterior posterior posterior posterior distributions comparison contrast train train train train train selection selection morgan morgan words department department consists consists consists consists consists code advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist scheme scheme scheme scheme addition addition addition considered considered framework framework framework cambridge cambridge cambridge hinton hinton additional estimates design conference significant significant estimated basic increase validation validation validation give con con produce produce channel weighted randomly randomly randomly randomly clustering clustering types types selected selected selected nature sampling feedforward hmm hmm hmm hmm hmm hmm complete short common effective eds journal journal journal journal journal journal hypothesis development typically typically typically smaller combination combination combination combination combination combination combination combination combination combination combination combination account dynamical coefficients coefficients jordan jordan technology technology mlp mlp mlp mlp mlp mlp mlp character consistent consistent database database database database database database database principle language language language language language language language details window international experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts supervised expert expert expert expert expert expert expert expert frame frame frame combined combined combined combined combined produced choose description architectures improved improved improved improved improve improve improve directions advantage separate separate separate ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble reported reported reported practical machines subset engineering engineering interest previously previously previously unsupervised approximately works solve speaker achieve mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation evaluation evaluation observation gate gate gate gate gate gate gate gate gate gate gate gate gate improvement improvement improvement correctly correctly hybrid hybrid hybrid pass conclusion starting designed learns learns hard hard hard reduction intelligence turn start targets targets targets program acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic question question digit optical winner generating describes describes label averaging averaging averaging remaining remaining consisting consisting expectation select select select extracted phoneme phoneme phoneme phoneme phoneme phoneme phoneme overlap codes evaluated evaluated evaluated evaluated evaluated showed frames frames frames frames frames frames frames soft soft soft static digits digits digits digits digits digits digits digits additive performing combining combining add closed closed transactions david recorded recorded recorded perceptrons perceptrons weighting gating gating gating tests tests tests tests tests selecting differ divided divided delta included phonetic superior criteria providing providing giles jacobs jacobs jacobs cowan trains layered hanson hall rest boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting combine combine combine combine combine authors gates workshop workshop matched ensure subsets subsets fisher fisher speakers speakers speakers speakers speakers speakers speakers speakers speakers consist baseline improving improving mixed mixed mixed mixed mixed mixed mixed simplest simplest wta wta sentences isolated isolated isolated isolated publishers nowlan nowlan answer answer benchmark benchmark considerable easier filtered filtered simard simard acknowledgement members members members members members members members members members improvements improvements spoken spoken spoken recordings robinson robinson robinson robinson robinson vocabulary vocabulary vocabulary vocabulary vocabulary vocabulary aim phonemes phone phone phone phone phone datasets decoder focused utterances utterances softmax softmax cor naive cooper cooper tation pick member member member member member databases databases labelled labelled partitions addresses addresses inspired kaufman khz proceeds resulted obtaining utterance utterance synchronous corpus corpus corpus corpus corpus enhanced service schapire schapire paul paul entries darpa ensembles ensembles ensembles ensembles ensembles eng eng mem record merge agree broken cam cam johnson outlined divide sequentially street street street street street street email retraining additionally classifies england clas principled principled principled unseen unseen gated gated gated gated gated gated gated gated gated wall wall wall wall wall wall 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output output output output output output output output output output output output output output output output number number number number number number number number system system system system system system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error state results results results units units units units units units information information information information problem models models models performance performance performance performance based based based based linear layer layer vector order shown systems systems systems values values values probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach approach approach approach pattern pattern pattern pattern pattern single single processing processing processing processing processing processing processing control control large large large large local local rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class class class class class class class class optimal form shows signal signal signal simple simple visual paper paper examples small small small small net net net net net net net net net net net net net net net net net net net net net work work work work methods methods points features classification classification classification classification process process process process process process process level level level level level level level current trained trained trained trained random random random high high representation architecture fixed line line line line line vectors vectors vectors general general general general general generalization speech speech speech speech speech speech parameter parameter real average average theory obtained note note experiments computation computation computation research independent defined defined defined found found sequence target target target target target target target target target target target target target target target target initial constant estimate estimate estimate estimate standard standard computer computer computer computer computer computer terms distance science present phase activation low low low low low low low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency maximum maximum range range press learn learn learn nonlinear nonlinear continuous sample sample abstract applied applied back back back find find likelihood likelihood references component stochastic due due ieee ieee ieee ieee ieee positive positive adaptive adaptive adaptive propagation propagation propagation context context context context introduction introduction hand hand hand estimation estimation effect effect effect effect effect dynamic search search search search search search change assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower measure prior prior prior prior prior prior representations word word word word word word word word word word word word word word word word word word word chosen higher higher part multiple good good represent represent represent represent bayesian bayesian markov techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques correct correct correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities forward scale scale minimum resulting classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes ing total total total computed multi multi multi multi elements factor factor factor factor factor natural natural applications applications knowledge obtain obtain negative negative negative negative negative negative negative negative negative negative negative negative original original vol vol vol vol vol vol artificial artificial relative relative relative relative relative relative samples samples samples samples represented represented represented represented represented represented represented represented cross provide provide provide provide provide define compute compute rates rates rates rates proc proc eye related related related related related related related posterior posterior constraints equal equal equal mit steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger train train train train train morgan morgan morgan morgan morgan morgan morgan morgan institute words words version technique technique technique technique technique technique consists consists individual individual advances advances advances connectionist connectionist connectionist connectionist difficult bias bias bias bias bias bias bias scheme scheme scheme addition graph sequences framework domain experiment directly hinton curve additional view estimates estimates san top stage stage stage stage bit determine efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers full full choice choice choice choice choice choice significant significant significant significant statistics increase increase increase validation give produce produce derived derived randomly levels levels types selected selected simply discussion normal normal hmm hmm hmm hmm transformation transformation inverse amount amount common effective effective effective effective implemented theoretical eds eds eds eds end ability ability future future easily degree degree noisy including including including fit kaufmann kaufmann simulated probabilistic probabilistic typically typically typically pairs needed needed combination reduced reduced account jordan technology block significantly significantly significantly ratio character character character character character character character character character character character character character character character character character character character character character character character character character character character segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation consistent uniform empirical empirical language squared squared squared representing representing international normalized normalized bottom experts early decay decay attention combined combined combined minimize run perceptron discussed discussed discussed directions robust typical typical typical apply apply pixels quadratic quadratic subset previously tuning yields yields converge achieve trans trans address mixtures background modified increased exists lead rotation rotation correctly correctly correctly correctly correctly correctly hybrid hybrid loop setting pass pass half starting reduce reduce segment tangent tangent tangent clear moody suggest taking reduction reduction reduction assuming variety minimizing user user user user start start decrease iii introduce characters characters characters characters characters characters minima annealing annealing annealing acknowledgements explicit explicit produces produces written longer ways primary transitions ann ann ann ann ann distinct segments segments segments segments segments segments implement multilayer explicitly infinite infinite transformations transformations transformations transformations text consisting integrated integrated integrated frequencies applying springer versus versus yield yield focus formation depending stages stages interpretation variation detailed controlled restricted forms static converges diagram reasonable performing epochs normalization normalization normalization normalization normalization normalization reduces reduces reduces reduces combining combining combining event valid valid valid classified classified classified activations priori priori priori coordinate coordinate determines specifically priors priors priors priors priors variations variations variations absolute absolute partially discussions tests modification driven driven driven presentation presentation invariance conf conf verlag repeated repeated repeated prob prob classify classify classify strategies strategies simplified backward providing denker denker denker hypotheses hypotheses hypotheses attempt jacobs tesauro decreasing body remain schedule schedule poor create exhibit replaced hanson accurately lippmann lippmann lippmann lippmann lippmann lippmann lippmann biases biases biases biases fewer reducing reducing reducing reducing reducing reducing reducing giving ideas links phases examined examined necessarily necessarily recognizer recognizer recognizer recognizer adjusted aspect friedman obvious art epoch optimum percentage histogram slowly defining fairly fairly improves nowlan tractable formalism easier forces bengio bengio products controls actor actor actor simard potentially implicit english english questions improvements prop prop applies amounts capability readily cohen share treated operate berlin acoustics acoustics richard richard richard inherent inherent segmented segmented viterbi yielding lot consistently representative newton newton benefit benefit writing writing writing writing writing arguments optimizing resources resources printed printed lecun lecun lecun lecun fails chance ranges handwriting handwriting handwriting balance biased bourlard bourlard bourlard exploring repeat repeat weakly ranging ambiguity overview heart percepttons histograms scheduling francisco rich properly impact impact impact variants valuable discovered balancing balancing balancing balancing balancing pen pen pen dividing escape divide posteriori posteriori posteriori posteriori verify dramatically pressure pressure pressure pressure unchanged anns anns anns anns anns drop numerous minus equivalently guyon guyon opposed benefits job job presenting legal uniquely year utilize acceptable classic classifies experiences warping warping warping warping letting forcing forcing burges argue verified henderson invariances favor favor stroke stroke stroke stroke stroke stroke stroke stroke stroke alternate pami pami convert eliminating writer writer writer individually retain ambiguous misclassified intl intl elsevier induces applicability permit prevents prevents prevents bill normalizing normalizing failures unpublished technologies worked helps helps emphasis emphasis emphasis emphasis emphasis emphasis moderate styles styles styles styles styles survey distortions primitives vii trainable builds families phrases coin conceptual lyon lyon lyon lyon lyon lyon incorrectly eliminates ning emerges beneficial repetition repetition repetition raises strokes strokes strokes colleagues frequent frequent voice voice unusual unusual raised seg penalizes replication modest talkers predetermined renals renals renals dist comprehensive ambiguities ambiguities wellekens wellekens modulate repeating repeating repeating spotting unifying stand nents chang chang conceptually modulating modulating offered tentative tentative tentative decides writers controllable biasing biasing unclear participate scored serving mag converting webb webb webb webb webb allocate allocate skew foreign dam franco albuquerque conducting groupings normalizes victorri cited warped collaboration modulates modulates theme theme theme albrecht indebted probabilistically para apple apple apple apple apple apple apple apple concentrating lets invalid invalid invalid invalid invalid invalid corrects les print print gish gish renormalization nohl vital recommended refinements skip skip overly speculate speculate legitimate duces usable patent nmnber printing larry island lots decipher pending wechsler precomputed equency suen alx finish delineated subproblem skipping skipping skipping skipping stylistic unusually scalings lear wholly tbr erratic skipped specifics ctive innovations paying ibr exaggerated 
#@Lyon_R,Webb_B,Yaeger_L,
#t10
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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set set set set set set set set set set set set networks training algorithm algorithm algorithm algorithm output output output output output output output output number number number number number number system system system system system system system system error state state results results results results units units units units units units units information information information information information information information information problem models performance performance performance performance performance performance performance performance performance performance performance based based based based based weights linear linear layer layer layer layer vector vector order order order order order order order shown shown systems systems systems weight weight weight weight weight weight neurons unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image processing processing processing processing processing local local neuron neuron rate test test test test test patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs form signal simple visual visual visual visual visual visual visual visual examples feature net work task task cells cells cells cells cells step step classification classification classification process current trained trained structure random high high high memory memory similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture show equation equation equation section section rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images images generalization generalization generalization average states obtained obtained obtained obtained term term term activity activity activity activity activity activity dimensional university university university threshold research independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent defined found sequence table table table table computer computer terms distance connections connections connections connections connections science left left left presented presented present activation activation activation temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object object object object object object object press press press learn position components components components components components components components components components basis basis basis basis basis nonlinear nonlinear outputs outputs outputs outputs outputs abstract applied computational computational references component component component component component component component component component component component component ieee ieee important important mixture complex complex complex complex variance tion tion tion change change energy energy spatial spatial spatial measure signals signals representations representations representations representations representations representations learned learned higher part center previous cases cortex cortex cortex long correlation correct correct correct simulations simulations ing total simulation simulation sum sum performed performed natural natural natural natural filter filter filter filter filter filter filter original original original compared compared compared compared desired provide objects rates determined experimental goal related related related brain approaches mit steps accuracy contrast update update update train source source source source source proceedings report institute institute institute department individual advances advances advances responses responses responses responses responses responses responses sequences cambridge equivalent san san san san san top stage stimuli conference statistics statistics statistics statistics vision basic basic basic increase produce channel channel weighted randomly developed developed provided inhibitory depends biological technical feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward increases transformation transformation close amount nearest nearest supported eds face face face face face face face face face face face face face face face face face face face face face face face face face face face face face rumelhart rumelhart development auditory pairs combination combination unknown unknown unknown coefficients testing significantly ratio ratio edge leads principal principal principal principal principal principal principal principal squared filters filters filters filters bottom magnitude magnitude combined produced added sources sources sources improve correlations correlations correlations correlations correlations advantage reported lateral lateral lateral lateral lateral lateral include subject subset subset sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive cognitive recently varying unsupervised unsupervised unsupervised unsupervised subjects calculated volume tuning pca pca pca pca pca pca pca pca pca pca locations organization concept invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant extended touretzky row greater hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian neighbor competitive competitive competitive competitive competitive constrained mateo encoding mechanisms largest demonstrated california california ica ica ica ica ica ica ica ica ica ica ica ica ica selective attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor produces winner winner winner winner sequential laboratory label averaging angle scales consisting consisting mutual mutual mutual national independently communication transform open open open showed centered centered centered forms activities activities activities activities activities intermediate intermediate sufficiently eeg euclidean faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces views views views bell bell bell bell bell bell eigenvalues blind blind memories selecting society encoded wij wij successful attractors invariance invariance invariance invariance invariance tend capture soc soc contained contained contained neuroscience neuroscience superior superior running comp comp comp highest maximization cat automatically neurosci neurosci consisted mixing mixing extract acknowledgments employed explore diego diego diego diego powerful powerful create experience experience experience experience experience association association association respond project int relationships relationships relationships structured statistically statistically statistically trace trace trace trace trace trace trace man psychology rev changed explored separated hebb hebb hebb academic mixed serial animal rows rows rows scenes scenes agreement orientations spatially spatially sys filtered monkey projected recognized begin begin medical recognizing recognizing recognizing recognizing requiring percent passed passed incorporated rep howard synthesis maximizes proven ordered gave gave substantial attraction attraction attraction attraction attraction summed pose pose pose pose pose pose pose pose pose pose pose pose pose pose pose pose oxford gabor temporally temporally temporally ratios discovery repre addresses tem tem tem bower ranges primate replacing los viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint salk salk salk salk cottrell cottrell optimally moments moments substituting inferior bartlett bartlett bartlett bartlett bartlett bartlett separating recovered representational mental lawrence hasselmo hasselmo interconnections interconnections viewing winning jolla jolla sustained proximity calcium assigning sequentially multiplying zipser largely largely converted ter sine sine basin axe axe axe axe pentland pentland pentland poses poses poses personal individuals descriptions basins basins basins basins associate associate associate representa continuity manipulation grouped lobe hughes deconvolution terrence paired considers acquired acquired projecting cosine cosine gender represen associates associates associates associates anal tively pools modifiable modifiable experi acquire recogni twenty mcdonnell emotion lated cornput conversion compo nmda nmda heeger heeger successively lowpass lowpass lowpass lowpass lowpass lowpass lowpass lowpass zipset tations comprised sentation capturing responded awij eigenfaces eigenfaces eigenfaces ysis facilitates movshon pew comon comon makeig makeig jung tsodyks tsodyks tsodyks proximal proximal proximal proximal comprises comprises rolls rolls rolls rolls terry amit amit amit fil poral poral nent comprise cog tony metcalfe metcalfe alternately selec turk turk turk resentations decorrelated decorrelated dropping sponses holons party vances kauf cocktail livermore accessing graylevel graylevel graylevel eigenface influx electroencephalographic landy suppl beymer stewart stewart viewer bian abst separa heb navigates broadened manipulates 
#@Bartlett_M,Sejnowski_T,
#t10
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training algorithm output output number number number number system system system error state state results results units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information information hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based based based space weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector vector vector vector order order shown shown shown shown shown shown shown systems systems probability parameters weight weight weight weight unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition pattern pattern image image image image single processing processing processing processing processing processing processing large local local rate rate test test test test patterns patterns patterns patterns class class matrix inputs inputs inputs inputs form form form signal signal signal signal signal signal signal signal simple simple simple gaussian gaussian gaussian visual visual visual visual visual visual visual paper examples small small size feature feature feature feature feature net net work work work cells cells cells cells cells step field features features features features features features features features features features classification classification level level level level current current current current trained trained trained cell structure structure high similar similar architecture architecture architecture architecture architecture show show show equation equation section section fixed fixed fixed fixed rule rule rule rule rule rule images images general general generalization generalization speech speech parameter parameter real real states theory gradient term term experiments activity activity result result university computation computation research research research independent independent log log found sequence constant table table table standard distance connections connections connections connections synaptic science presented present present activation activation low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object object sets maximum maximum maximum maximum range press learn learn learn basis outputs outputs outputs outputs continuous continuous abstract abstract applied applied back back back back back properties properties likelihood likelihood likelihood likelihood likelihood references due positive important important important adaptive propagation propagation propagation propagation propagation mixture mixture context context context context context context context context context context context context context context context context context context context context context context context context context action complex behavior stimulus stimulus statistical effect effect variance variance cost cost cost cost cost cost cost recurrent recurrent tion tion spatial classifier classifier classifier classifier lower lower rules signals signals signals representations representations representations representations representations representations word word learned learned higher higher part required multiple cortex cortex cortex cortex cortex long long represent represent distributed expected expected markov fact fact techniques proposed proposed proposed length length correct correct correct probabilities observed simulations simulations simulations simulations simulations classes simulation computed computed multi multi multi sum performed means factor natural natural feedback global applications em em filter filter vol artificial relative specific samples samples compared series receptive receptive receptive receptive objects objects objects perform active active related constraints motor cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain equal equal mit steps larger larger contrast contrast contrast fields fields fields update update update source source source source morgan morgan proceedings words words words department implementation version individual individual advances responses responses responses layers layers layers delay delay delay sequences sequences sequences sequences sequences considered framework cambridge equivalent hinton hinton hinton hinton hinton curves curves san san top top top top stage effects effects effects bit classifiers basic basic channel weighted clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed levels lines lines lines provided finally finally processes evidence nature constraint constraint constraint simply achieved achieved discussion discussion discussion covariance feedforward feedforward feedforward arbitrary group group group tested tested transformation close assumption assumption predictions predictions common common implemented implemented supported role role eds eds face face face face face face face journal end end pixel pixel ability ability ability cluster easily easily rumelhart rumelhart development development noisy sensory sensory sensory sensory sensory kaufmann kaufmann smaller smaller account account account functional functional coefficients jordan programming edge edge consistent structures language call iterations max filters pre inhibition inhibition stored international normalized bottom bottom bottom experts experts experts experts experts supervised supervised supervised supervised supervised supervised supervised supervised early decay combined added sources sources sources predict neuronal neuronal improved improved correlations advantage advantage separate separate reported reported reported reported reported reported lateral apply moving identical identical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical cognitive cognitive engineering dimensions varying unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised module module module module tuning achieve achieve mixtures organization organization organization organization storage entire increased increased grant grant lead lead invariant invariant scaling scaling wide predicted predicted predicted alternative correctly correctly touretzky clusters clusters clusters demonstrate runs runs runs hebbian hebbian hebbian depend competitive competitive competitive competitive competitive interactions sigmoid modules modules weak constrained mateo mateo propose taking strong demonstrated intelligence selective averaged averaged averaged averaged groups acknowledgements areas pro pro perception perception winner ways ways primary primary tuned explicitly infinite transformations slightly interaction develop mutual mutual gaussians shift extraction letters independently review review review stages communication overlap overlap overlap viewed viewed influence influence influence codes labels modulation modulation modulation modulation modulation modulation centered forms understanding activities activities margin completely allowed reasonable reasonable classical normalization fitting fitting fitting intervals interpolation generation sufficiently assigned euclidean classified faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces views views views views views views views views views views views views views views views box box box perceptual activations activations activations weighting instances batch sciences memories recognize extension candidate domains discussions gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating gating major simplicity reason reason reason columns columns columns sensor compression middle middle letter closely hmms importance society modification divided included mcclelland mcclelland efficiently post comparing invariance tend essentially online identity identity identity ten ten capture refer compact compact quickly procedures procedures strongly allowing success neuroscience stopping classify cues built involved sampled generalize absence modular realistic surround providing providing giles leading processors received mixing mixing preferred jacobs jacobs software receive receive receive modelling modelling extend cowan explore powerful powerful powerful layered poor difficulty circuitry rapidly humans accurately successive successive respond history history history detectors dependencies comparable stream stream stream stream stream lgn lgn pathway hierarchy analogous contours contours removed removed attributes reading psychology illustrate equally thought der der obvious obvious ith epoch epoch baseline detected simplest simplest arbitrarily explain motivated motivated integrate integrate mentioned mentioned smoothness smoothness smoothness adjacent adjacent adjacent nowlan nowlan nowlan nowlan nowlan majority worse considerable considerable spatially shared widely recognized recognized gradually gradually gradually gradually lowest arises explained people people considerably considerably percent poorly posed posed remove incorporated slower continuously frequently biologically psychological span summarized modulated modulated modulated maximizes maximizes incoming incorporating incorporating substantial replace coherent coherent coherent expectations coherence findings findings wang utterances softmax semantic semantic summed distortion contribute phenomenon classifying classifying lab contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual secondary secondary intractable accomplished temporally temporally temporally temporally temporally temporally temporally temporally temporally conditioned partitions discovery discover discover discover discover discover discover connecting connecting theories royal children murphy murphy odd odd multiplicative multiplicative abilities viewpoint viewpoint viewpoint viewpoint nearby fail fail salient canonical contexts becker becker becker becker becker becker becker becker becker predictors induce von ascent sim lawrence competing competing competing hippocampus modelled young spatiotemporal suggesting canada extends agree erlbaum valuable generalizing dempster dempster stopped stopped receiving insensitive influences stone stone limitation fusion infomax treat unable incorporates rubin pointing achieving shunting maximized benefits benefits alternating forced pointed centre additionally personal hillsdale discovering clustered clustered streams continuity mutually exam insights segregation alternate guidance argued smyth interactive laird associates sheet assemblies son rotating rotating rotating modality modality computa gorithm mea persistent persistent persistent persistent persistent fortunately council mcdonnell assistance virtually lated evolved overtraining puts hamilton loosely outperformed ron identically neocortical proportions proportions ning incorporation believed ples progressively neocortex ooo ooo modalities digitized iid constraining priming handbook meant appro assessed assessed counted generaliza illusory illusory fore unexpected phillips phillips favors modularity stems modulate pew preprocessed yon contributing won thalamus ther ply encourage humphreys package analyzers fur shrink cortico yij yij yij numbered numbered scored cen retains centred thalamic laminar cleaning categorize persistence quences kay organize arbib compactly encouraged perceptually geoff geoff geoff pervised disappears disambiguation superficial superficial superficial preceded incentive ubiquitous disparate plete markedly mates roberts ont fid sumption tual tered sillito sillito ken eleven subcortical incom exposures larry clude pervasive xerion succinctly flattened imizes mounting 
#@Becker_S,
#t10
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#*network network network network network network network learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural input data data data data data data data data data data function function function function function function function function figure figure figure figure set set set training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number system system system results results results results results information information information information information information information information information information information information problem models based weights weights weights linear linear linear linear linear linear linear linear linear case case case vector vector vector vector vector vector vector order order order order order order order order order order order order shown shown shown shown shown systems systems values probability noise noise weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons approach approach point point image image image image image image image image image image image image image processing local local local local local local local local local rate patterns patterns analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form shows signal signal signal simple simple gaussian gaussian gaussian visual visual visual visual visual visual small feature feature feature feature feature feature net work work work methods methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells field field field field field field field field field field field field features process process trained trained trained high similar similar similar representation architecture show show show show show show show section fixed line rule rule rule rule rule vectors vectors images images images images images images images images images images images general speech theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient obtained experiments experiments result result result result variables computation computation computation computation computation solution solution solution solution solution solution solution solution solution solution solution solution independent independent independent independent independent independent independent independent independent independent independent independent independent log found found constant computer left left left present phase phase phase phase phase phase phase activation low frequency frequency frequency frequency frequency machine sets range press components components components components components components components components components components components components components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs outputs outputs outputs abstract applied applied find find computational convergence convergence density density properties references references references component component stochastic stochastic due ieee important adaptive introduction generated variance difference spatial spatial spatial spatial spatial spatial lower lower measure signals higher higher higher part cases cases type type type type type required required required multiple cortex cortex cortex cortex long conditions conditions distributed distributed expected make fact techniques techniques proposed correlation length observed simulations minimum resulting resulting resulting ing ing ing ing performed eq eq eq eq eq eq eq eq eq elements means natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural orientation global global global global knowledge filter filter filter filter filter filter filter filter filter filter filter filter original original original relative specific samples represented compared compared series receptive receptive receptive receptive receptive receptive provide define proc perform perform goal goal related related constraints distributions distributions cortical equal approaches mit comparison larger fields fields fields fields fields dependent source institute institute version version code code code advances joint joint represents connectionist responses difficult bias addition framework equivalent view solutions solutions limit top top top detection determine efficient full full full approximate statistics statistics statistics statistics statistics vision basic con produce produce condition coding coding coding coding randomly developed developed developed levels criterion criterion entropy entropy entropy entropy product selected achieved achieved covariance covariance describe transformation inverse inverse finding supported eds square square end end pixel pixel makes rumelhart development sensory sensory sensory objective typically underlying underlying underlying underlying underlying combination combination functional transfer interesting edge edge edge increasing leads principal principal principal max filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters pre direct bottom magnitude magnitude produced produced produced produced choose predict denotes resolution ensemble ensemble trees sejnowski sejnowski sejnowski sejnowski sejnowski compare unsupervised unsupervised approximately calculated calculated calculated calculated calculated calculated calculated calculated calculated calculated pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca studies converge trans diagonal diagonal diagonal sparse sparse sparse address separation separation separation separation organization sensitive sensitive amplitude amplitude exists exists horizontal horizontal concept scaling scaling scaling suggests extended wide matrices matrices rotation rotation predicted locally generally column column pass conclusion starting starting row row greater greater hebbian hebbian depend differences exponential taking reduction reduction characteristics drawn sigmoidal demonstrated california variety ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica exist exist scene question acknowledgements relation pro pro edges edges edges edges edges produces produces produces produces longer longer longer longer ways primary laboratory vertical vertical averaging linearly linearly involves slightly mutual frequencies formed extracted formation detailed transform transform transform open updated approximations understanding suggested translation spectrum spectrum spectrum spectrum reasonable roughly roughly advantages david avoid perceptual perceptual perceptual bell bell bell bell bell eigenvalues weighting blind blind blind blind activated absolute absolute absolute discussions columns columns columns columns importance modification wij invariance miller identity orthogonal orthogonal orthogonal road quickly repeated induced showing showing neuroscience dis running satisfy involved simplified surround surround maximization principles subsequent satisfies oriented oriented oriented oriented oriented oriented oriented oriented oriented unlike transformed transformed transformed involving involving behaviour fourier fourier giving detectors detectors detectors analytically dependencies scaled root eigenvectors tanh statistically cover patch naturally possibly opposite extremely ensure versions algo logistic logistic logistic logistic observe detector detector consist amari amari explain attempts histogram rows rows preference scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes theoretic theoretic theoretic theoretic theoretic answer nonlinearity spatially spatially closer preprocessing broad ran monkey potentially separately medical patches patches linsker meaning meaning raw raw explained argument requiring varies double amounts orders orders orders slower howard synthesis anti ordered ordered ordered ordered ordered qualitatively semi semi display redundancy redundancy physiol displays cumulative shifted writing appearance gabor gabor gabor rithm arguments appropriately linearity linearity linearity pick nat ordering circular minutes satisfying striate transforms transforms transforms neurobiology fail reasoning affected salk salk salk optimally presentations hours paul displayed displayed displayed ascent lengths histograms histograms histograms monkeys yang yang nonlinearities arrangement entries entries jolla repeatedly late theoretically erlbaum pearlmutter reverse reverse avoiding convergent infomax infomax infomax infomax infomax infomax verify multiplying multiplying yielded yielded converted wiesel wiesel super dec emerge preserving kurtosis kurtosis kurtosis kurtosis centre centre classic hubel hubel reflected decorrelation decorrelation jacobian constrain factorial factorial factorial invariances shifting cessing learnt learnt learnt hughes deconvolution terrence altered argued gluck spreading multiscale multiscale speedup rough barlow barlow barlow barlow barlow barlow grateful sweeps sweeps sweeps det matlab supporting removes rarely lighting info tail tail tail stimulating ble sake viola olshausen olshausen olshausen olshausen olshausen olshausen olshausen olshausen olshausen orthonormal determinant eral condi exposed subtracting peaked ters ters ters atick atick atick sparsely sparsely anthony wavelets symmetrical symmetrical lowpass sian senses thing locality gaus sweep sparseness sparseness sparseness sparseness tical cichocki cichocki sep backwards emerged supposed awij decades polar maximisation maximisation resemble cats sparc preprocessed cardoso cardoso recovers redlich redlich devel nadal nadal permuted terry implementable initialised initialised ordinate thirty tributed serving fil fil fil rescaled maximise equivariant tony whitened whitened whitened whitened tailed sev proportionality iden selectivities parga parga notable torrey pines cedure batches whitening whitening whitening whitening decorrelating decorrelating decorrelating decorrelating decorrelating decorrelating decorrelating decorrelating sphering barak localised localised localised localised localised localised localised localised localised localised helping laheld laheld greyscale stimu descend xxt xxt includ factorised minimises coincidences coincidences ural bruno wtw wtw wtw sphered departs phrased aration utilises recognise lating opment fuller oyi oyi oyi cyclical maximises maximises succinctly kurtotic scal attributable ecological twin 
#@Bell_A,Sejnowski_T,
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#*network learning model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural data function function function function function function function function time set set set set set networks networks networks algorithm algorithm number number number number number number system system error results information models models performance case case case case case case order order order order order order systems systems systems systems values probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters functions neurons distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach approach approach pattern point image image image image image image image image image image image image large large patterns patterns patterns analysis optimal form form form form simple simple visual visual visual paper examples examples examples small feature task step step level level level level level level level cell structure structure problems problems random high high high high high high representation architecture line rule rule rule rule rule rule images images images images general general general general speech parameter parameter parameter parameter average theory theory theory theory theory obtained note note experiments activity activity dimensional result result university university university university computation computation solution research research research independent independent independent log log log log log log log log log log log log log log log log log defined defined defined defined defined defined defined found found constant table table table table table table table table table table terms synaptic synaptic synaptic science present present present present present low temporal machine object object object object object object object object object object object object object object object object sets press press position position position position position position basis basis abstract applied applied applied applied applied computational likelihood references stochastic due important decision decision decision context complex hand estimation statistical effect effect effect effect dynamic cost cost cost cost cost cost cost search tion energy energy energy energy energy energy energy energy energy energy energy complexity complexity lower lower rules rules rules rules rules rules rules rules measure signals prior prior prior representations word word word word chosen higher previous bound bound cases cases firing firing type type type multiple cortex cortex good binary binary binary binary binary binary binary binary binary binary binary long long conditions represent tree tree tree tree tree distributed bayesian bayesian bayesian bayesian make proposed correlation length length length length length probabilities probabilities probabilities observed finite finite minimum minimum total total total total sum sum performed times elements elements potential made natural natural feedback global applications define define define define define objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects gain gain brain brain brain brain support support support institute words words implementation consists consists consists internal code code code code final addition framework cambridge equivalent directly curve curve curve curve curve view curves top bit determine efficient efficient free free free world world vision vision increase con channel derived conditional conditional levels levels levels levels lines lines product product product provided finally finally evidence nature sampling simply biological technical describe arbitrary arbitrary fast inverse assumption circuits finding amount short supported require eds eds eds pixel pixel instance instance easily easily including including including including including fit typically typically smaller smaller combination account account account account functional interesting ratio york york edge segmentation mechanism consistent structures principle principle principle principle principle principle operation language language language language language leads details call max bits bits bits bottom bottom description description description neuronal denotes advantage pair practical include subject subject identical pixels pixels pixels pixels hierarchical sense array array array cognitive interest highly approximately approximately yields studies definition definition definition positions positions positions locations symmetric observation observation organization horizontal horizontal horizontal occur extended alternative generally column setting pass half critical valued central measures measures accurate weak sound encoding encoding encoding encoding encoding propose propose demonstrated demonstrated labeled labeled assuming variety introduce characters characters scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene configuration force denoted denoted acknowledgements explicit appears construct construct ways describes label label label label label label label label label label label label label label label vertical mathematical mathematical dept recall unique consisting mutual select john letters letters letters letters letters letters yield yield national family family independently communication overlap viewed viewed viewed interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation codes codes detailed detailed evaluate operations labels labels labels labels labels labels labels labels labels labels evolution activities translation allowed reasonable add boundaries string string string string string construction foundation advantages expect handwritten thesis combinations combinations usa formulation formulation formulation formulation strings strings strings illustrated specifically priors priors priors priors coupled black black black regular regular regular regular straightforward letter letter extra capable uniformly spiking efficiently projections fine composed composed composed composed refer quickly induced induced interested interpreted interpreted phonetic superior issue symmetry symmetry physiological strategies satisfy list list write wave observable observable highest binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding principles operating neighboring neighboring employed remain wiley wiley collection collection collection collection collection collection collection collection exhibit oscillators association recursive recursive dual mass mass periodic rise fashion giving giving links rest plasticity plasticity office office structured structured structured maximizing workshop encode encode hierarchy cover cover cover cover cognition cognition cognition cognition fundamental phases notion surfaces neu plausible necessarily necessarily illustrate equally equally thought ensure adjusted aspect der der der der greedy nervous generates arbitrarily motivated phd brown brown brown brown brown brown scenes scenes formula formula costs trivial trivial trivial trivial trivial trivial growth adjacent adjacent reasons straight formalism shared shared precisely precisely division division division leaves leaves arise probable probable mathematics mathematics mathematics scientific angles angles implicit argument composite composite composite composite composite composite composite composite empirically tional tional leave formulated frequently frequently biologically ity templates requirement requirement measuring occurrence suited geman geman geman geman geman geman geman geman geman geman geman adjust germany logical redundancy redundancy leaf synchronization synchronization displays realized person contextual redundant redundant intractable notes assign formally dynamically purely naval jones proceed arranged arranged arranged chance chance chance chance chance chance chains chains occurred analogy analogy city attractive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive check balance resulted interpret occurring observing implications preparation carry combinatorial alphabet alphabet selects filled composition composition composition composition composition composition composition composition composition composition composition composition composition composition composition composition service performances ambiguity ambiguity ambiguity ambiguity ambiguity pat von von von von mental propagated propagated assembly thomas thomas competing arrangement arrangement arrangement arrangement arrangement arrangement arrangement arrangement bases laplace laplace laplace laplace laplace laplace laplace laplace laplace laplace laplace laplace occlusion cerebral reader reader shortest locked refers refers rich vertex correcting sons sons statement interestingly linguistic linked largely outline users accept equivalently equivalently recursively recursively creates encodes uniquely axe encouraging restrictions restrictions regularity seek mdl mdl mdl mdl mdl mdl mdl mdl mdl ical ical chapter malsburg malsburg malsburg malsburg constitutes molecular realize ary lesion deep biophysical shannon elementary elementary denoting scope names unconstrained ambiguous ambiguous constructs covered west crossings turning happen supports truth elsevier union port port normalizing intensive spite spite covers covers observables advantageous advantageous remarks regularities regularities bienenstock bienenstock bienenstock bienenstock bienenstock bienenstock bienenstock bienenstock bienenstock bienenstock compositional compositional compositional compositional compositional compositional primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives primitives impractical terns junctions junctions hypothesized reversible abeles abeles fill broadly inclusion rissanen rissanen affecting rare horizontally proposal codeword evenly devised konishi partly couplings couplings ally ally neocortex interpretations interpretations interpretations interpretations interpretations carries carries resolved resolved intact convention convention syntactic syntactic syntactic triangular triangular curved planck fin connectionism bradford handbook addressing ings transmit carrying sparseness problematic sur putation probabil col noiseless daniel lexical lexical constituent cons operated incurred notions judge observes sixth codewords relying constituents constituents constituents constituents coincidence synchronize bind named rightmost chi suggestion army rationale articulated sults thalamic brains singapore stuart analogously providence blank opens mere intersecting intersecting shortcomings lock compose today braitenberg dam dam concluding govern crafted renders arbib groupings admits saving unambiguous hierarchically chemistry arrangements arrangements arrangements debate jects reformulation decade tives favored suspect compositions compositions compositions compositions essay les fodor fodor mech evidenced sillito aertsen sil puting exhaustively argues argues distributing biolog ses infrequent iio compositionality compositionality compositionality compositionality compositionality compositionality compositionality compositionality compositionality relay drastic veloped daal pylyshyn pylyshyn dms rea nlog lowed realm engage gerstein sonable inquiry gies pervasive changeux judiciously anism ener stricted arguably corticonics arisen inclined inclined mans affords assemble gsttingen lapping probabilit 
#@Bienenstock_E,Geman_S,Potter_D,
#t10
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#*network learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural input data data data function function figure figure figure figure figure figure figure figure figure figure time set set set set set set set set set networks training training training training training training training training training training training training algorithm algorithm output output number number number number number number system error error error error error results units information information information information information information problem models models models models models models models models models performance performance based based based based based based based based based based based based based based based based based based based based based based space space space space linear linear linear linear linear linear layer case vector vector vector vector vector order order order shown systems values parameters parameters functions functions functions functions distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach approach point point point image image image image image image image image image image image image image image image image image image image image image image single single processing processing large large local local local local local local local local local local local local local local local local local local local local local local local local rate rate rate rate rate test test test test test test analysis analysis analysis analysis analysis analysis analysis class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix form shows shows shows shows simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual paper paper examples examples examples examples small size size size size size feature feature feature feature feature feature feature feature feature feature task points points field field features features features features features features features features features features features features classification classification classification classification classification classification classification classification classification classification process level level current trained trained cell structure problems high high high response response response response representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture show show section fixed line vectors vectors images images images images images images images images images images images images images images images images images images images general general general generalization average theory gradient note experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional university computation computation computation research research independent independent estimate estimate computer computer computer computer computer computer computer science left present low low object object object object object object object object object object object object object object object object sets motion motion motion range components components basis basis basis nonlinear nonlinear nonlinear abstract applied applied applied applied applied applied applied back back back back back back back find computational references component component due ieee important important decision decision decision decision propagation mixture mixture introduction complex hand hand statistical effect dynamic generated tion energy complexity spatial spatial spatial spatial spatial spatial classifier classifier lower representations representations representations representations representations representations representations representations learned part part part part part part part part part multiple multiple multiple represent represent make fact techniques techniques techniques techniques techniques techniques techniques techniques region region region region proposed errors scale scale scale scale scale scale scale scale scale scale scale classes classes tasks tasks human human human computed computed sum sum sum performed called times regions regions regions regions regions regions dimension dimension made made made natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global global global global global global global study knowledge em em filter filter filter filter filter filter filter filter filter filter filter filter filter obtain artificial specific specific specific represented represented represented represented compared application desired receptive receptive provide compute compute compute objects objects objects objects proc goal goal related gain power approaches larger train report report version version technique technique technique technique technique technique technique technique consists consists code code individual kernel kernel represents responses responses responses responses responses responses responses responses difficult considered framework computing domain domain domain domain domain domain domain domain experiment experiment view view view detection conference classifiers classifiers full choice significant significant significant significant statistics vision vision vision vision vision vision vision vision vision vision vision vision estimated estimated pages give give produce coding derived weighted weighted weighted randomly area types types lines selected selected sampling biological achieved achieved covariance covariance covariance covariance covariance normal technical technical corresponds surface finding nearest nearest nearest nearest nearest nearest common shape shape shape face face face face face face face pixel pixel pixel pixel pixel degree makes makes noisy objective account jordan jordan jordan jordan interesting ratio edge special consistent database database database database database database principal principal principal principal principal representing representing details call filters filters filters filters filters filters filters filters direct window window window window international normalized experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert early early early early magnitude idea choose choose run description directions directions resolution advantage robust robust takes typical apply moving pixels hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical cognitive recently interest volume volume axis axis axis axis mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures positions locations generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized grid grid grid grid grid grid grid grid improvement storage horizontal parts parts parts parts parts parts parts parts parts parts parts intensity invariant invariant invariant derivative derivative matrices rotation alternative boundary flow conclusion reduce segment segment segment neighbor neighbor peak propose propose hard hard hard mechanisms demonstrated california radial start selective selective relationship relationship averaged derivatives derivatives derivatives derivatives scene question appears relation digit van van van van van edges edges produces optical describes vertical explicitly averaging dimensionality remaining scales scales scales scales scales scales consisting consisting develop applying shift shift letters extracted family family reconstruction stages correlated variation variation variation detailed restricted labels approximations centered decomposition decomposition decomposition decomposition decomposition decomposition soft soft soft soft understanding understanding sizes discrimination discrimination reduces reduces combining neighborhood neighborhood neighborhood neighborhood roughly iterative boundaries tracking interpolation intermediate calculate advantages faces transactions degrees avoid handwritten handwritten kernels kernels kernels kernels combinations weighting weighting subspace subspace subspace automatic variations variations domains domains domains black neighbors neighbors neighbors neighbors discussions gating gating structural structural successfully successfully texture texture texture texture texture texture texture texture texture texture texture planning reason determining straightforward poggio successful schemes invariance characteristic characteristic characteristic composed capture capture capture capture traditional soc kind strongly induced cun link neuroscience superior issue classify classify content sci categories categories categories categories categories categories categories categories categories cues cues comp sampled vary michael paradigm providing nips correspondence denker thresholds thresholds automatically overlapping overlapping extract extract jacobs jacobs jacobs neighboring acknowledgments deal oriented oriented oriented camera camera essential requirements investigate detail discriminant helpful fewer examine detectors biol int int int relationships scaled scaled decisions workshop phases notion surfaces surfaces patch patch patch patch patch patch patch coarse coarse measurement gradients gradients gradients naturally trace traffic man eyes eyes eyes aspect der precise shapes utility motivated motivated years percentage histogram scenes separable orientations orientations orientations analytical adapted worse nonlinearity considerable considerable considerable berkeley berkeley berkeley berkeley berkeley division operators choices choices ran potentially potentially projected projected recognized angles opt computers robustness robustness greatly greatly freeman hme hme hme hme hme hme pure generic embedded car car car car car car car car peaks peaks peaks solla maxima maxima http howard partitioning synthesis rely characterize popular enables chose redundancy windows tile tile tile distortion don don cybern www appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance pick databases databases circular reconstructed impossible jones lost inspired ments ments significance breiman occurred primate attractive height vehicle vehicle vehicle vehicle vehicle moment moment moment moment moment moment moment moment moment moment viewpoint reasoning illumination responsible moments moments moments moments moments moments moments moments moments moments moments composition saul corre induce histograms histograms stereo jackel lawrence thomas offers bases bases occlusion occlusion young spatiotemporal reader rich gesture gesture captures implicitly interestingly dividing discriminate leaving outline misclassification misclassification misclassification misclassification misclassification email covering convolutional bank pentland poses poses poses pointed boser profiles ease decomposed decomposed decomposed malsburg classifies descriptions stands stands stands reconstruct brightness care baluja reflectance disadvantage disadvantage mouth mouth march rectangle rectangle plate plate multiscale buhmann misclassified assemblies confusion confusion memo eigen eigen eigen eigen eigen subspaces exploited exploited experi lighting tail advantageous bridge january decided european junctions junctions nested families doesn shot hoc tanaka loosely russell bilinear heeger bregler bregler bregler bregler bregler bregler bregler operational classi html feldman fication motors mis february capturing energies experimented experimented mounted discriminating eigenfaces lights decompose decompose lange nice collections cars cars leung yon mir broader nov weakness compress ago convolving unclear outlines malik malik malik malik malik malik malik malik malik banks banks rowley wanted subsample textured stuart koller roth nose nose kanade granularity granularity shi steerable elongated elongated elongated elongated vehicles vehicles lend turk sponds stereopsis stereopsis door conical orienta restricts decoupled compressing scalable doors doors doors doors doors tiles tiles tiles weber koenderink wash modem rear leo shashua plates perona graylevel preattentive surveillance lades zipcode windowed windowed lime dep richness christoph beymer viewer ology textural jerry mainstream ucb csd collaborators doug 
#@Bregler_C,Malik_J,
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#*network network network network network network network network learning learning model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data function function function function function function function figure figure figure time set set set set set set set set networks algorithm output output output output output system system system system system system system system system system system system system system system system system system system state results results results results results results results results results units units units units units units units units units units units units units information information information information information information problem problem models based based based based space weights weights linear linear linear linear linear linear layer layer layer layer layer layer layer vector vector order order order shown shown shown shown systems systems systems systems systems probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise unit unit unit unit unit unit unit method approach point point single single single processing processing processing processing processing large large large large large large local local local local local local local local local local local local local local local local local local local local analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal inputs inputs form form form shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper small work work work task fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points field field field field field field field field field features process process level level level cell cell cell cell cell cell cell cell structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure random high high high response response similar similar similar similar similar similar representation representation architecture show equation section section line images images images images images images images images general general parameter parameter real average average states theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained note note experiments activity activity activity result result result university university threshold variables computation computation computation computation computation solution solution solution solution research research independent independent independent independent defined dynamics dynamics terms distance distance connections connections connections left direction direction direction direction direction direction direction direction direction direction direction direction presented present low low low low low frequency sets range press position position components outputs outputs abstract applied find find properties properties properties properties properties properties properties properties properties references component due due procedure introduction complex stimulus stimulus statistical statistical statistical statistical statistical generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change spatial spatial spatial spatial spatial spatial spatial assume assume assume assume measure measure signals signals signals chosen higher higher part center center previous previous previous previous cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good good long represent expected expected fact fact correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correct forward forward forward forward forward forward forward forward forward tasks respect regions optimization natural natural natural natural natural natural natural natural natural natural natural feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study study knowledge filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter obtain obtain obtain obtain relative relative specific samples represented represented true application application series receptive define define define compute compute perform perform experimental experimental experimental related connected connected distributions cortical cortical cortical cortical cortical cortical power power mit comparison connection morgan department department individual kernel kernel kernel advances advances represents ai equivalent equivalent environment directly additional solutions curves design san effects effects statistics statistics statistics vision vision basic give give produce produce produce coding derived levels area finally processes processes nature depends depends depends biological biological associative achieved achieved discussion describe describe arbitrary arbitrary transformation transformation close assumption assumption assumption assumption assumption complete complete stable effective assumed assumed supported require require require eds square square hypothesis easily sensory sensory fit fit fit fit fit fit auditory underlying underlying account account dynamical block transfer ratio projection edge edge edge edge edge special structures structures uniform operation filters early early magnitude magnitude magnitude magnitude idea idea light neuronal recent correlations correlations correlations correlations correlations ensemble lateral lateral lateral lateral lateral lateral lateral apply include include sejnowski sejnowski recently dimensions sufficient compare compare unsupervised approximately calculated calculated volume volume tuning axis axis solve studies achieve achieve diagonal bounded organization sensitive sensitive grant constructed exists horizontal horizontal expression studied invariant invariant invariant scaling suggests suggests suggests derivative derivative derivative rotation feed feed feed feed feed feed feed feed feed locally pass pass strength assumptions conclusions central central retina weak mateo propose mechanisms presence presence presence reduction reduction reduction solid proportional proportional assuming assuming minimizing minimizing selective selective selective selective selective selective selective selective averaged derivatives connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity denoted relation derive edges edges edges edges edges perception plot describes describes tuned tuned tuned tuned tuned mathematical distinct distinct explicitly averaging averaging angle angle angle angle angle angle unique unique develop mutual applying applying minimization springer implies select decreases review correlated correlated interpretation codes variation operations ocular forms similarly suggested translation translation translation spectrum spectrum calculation calculation calculation measurements measurements sec calculate calculate calculate foundation degrees degrees expect expect expect building figures kernels dominance bell bell eigenvalues retinal retinal plotted partially compression compression selecting aspects differ receives receives soc verlag heuristic interpreted interpreted neuroscience classify classify physiological physiological physiological physiological bar realistic realistic minimizes correspondence preferred preferred preferred preferred preferred preferred preferred preferred neighboring neighboring intrinsic tesauro receive cowan cowan cowan cowan cowan cowan cowan cowan selectivity relations environments steady integral fourier fourier matches ideas ideas rest rest detectors detectors detectors detectors detectors detectors analytically possibility possibility possibility lgn pathway pathway pathway pathway statistically topographic act circles gradients thought singular obvious observe detector detector detector simplest submitted averages established years mentioned scenes scenes scenes scenes scenes cos cos cos cos theoretic separable agreement unstable improves adjacent caused correction handle reasons comparisons spatially spatially processed lin lin sys directional directional directional monkey mathematics mathematics inversion projected angles opt calculations patches patches arises integrating argument requiring reflects reflects populations profile profile pathways pathways dark readily quantitative psychophysical introducing recordings sharp sharp gains berlin aim reaches incoming qualitatively redundancy redundancy redundancy redundancy redundancy specifies picture picture benefit benefit appearance equivalence modify pick acts tem lost lost kaufman anatomical imaging promising primate overcome striate striate striate abilities bands implications implications salient alspector james bialek bialek respective captured suggesting specificity agree considerations captures receiving convergent numerous sig creates formulate isotropic ical chicago chicago chicago chicago decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation factorial manipulation perpendicular perpendicular concentrated discontinuity denoting relating cosine topic indexed preserve barlow barlow barlow accounted turning inverting geniculate knowing amplification nal nil nil differing helps suggestions factored utilizing autocorrelation autocorrelation autocorrelation attributed textures insufficient mcdonnell hat pictures pictures broadly physiologically atick atick atick atick atick atick atick atick atick functionally attenuation inde ruderman ruderman hypercolumn hypercolumn jack rij rij rij rij optimizes redlich redlich redlich redlich redlich awake thorpe thorpe alexander anticipate anisotropic complexities laterally encounter necessity asymptotics enormous dong dong proportionally faithful duce equiv unitary unitary mexican intend ori mat strengthened structurally pertinent eigenfunction intriguing woods envi analogies analogies amplify decorrelating decorrelating orban orban orban orban strengthening recurrently informational retino alent decorrelate decorrelate compiled discrepancies ronment imbert cknowle dgement hypercolumns princi pendence entation sibility broadening homogeneity cortices pie lates umn tremendously 
#@Cowan_J,Dimitrov_A,
#t10
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#*network network model neural neural input input data data data data data function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time system system system system system system information information information information based based based based based space space space space space space space linear case case shown shown shown shown shown shown shown shown shown shown shown systems systems noise noise noise noise noise noise noise noise noise distribution distribution distribution distribution distribution point point point image image processing processing matrix matrix matrix optimal optimal optimal inputs form shows signal signal signal signal signal simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small work methods cells cells cells points points field structure structure high high high response response response similar similar similar similar representation show show fixed fixed line line line images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general real approximation theory theory theory theory experiments experiments result threshold computation computation independent independent log log log log constant constant constant constant constant constant prediction prediction prediction prediction left low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal motion motion motion motion range abstract applied back find find find find properties properties properties properties references references component component due important introduction statistical statistical effect dynamic dynamic tion change change spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume signals higher previous type good good good expected make fact fact fact proposed correlation correlation correlation correlation correct observed scale human human human human human human human human human human human human human times means made natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural study knowledge filter filter filter filter filter filter relative compared compared objects objects eye eye eye experimental cortical power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power approaches contrast contrast contrast contrast contrast contrast contrast contrast contrast institute loss code responses responses directly curve curve curve curve curve curve curve curve curve curves curves curves curves curves curves curves curves curves curves top significant significant significant statistics statistics statistics statistics world world vision vision vision vision vision vision increase con coding coding derived derived derived velocity velocity velocity velocity velocity velocity velocity types lines actual finally depends simply simply simply measured measured measured measured measured measured measured measured measured measured measured covariance technical technical tested limited limited assumption assumption assumption surface predictions amount amount shape shape theoretical theoretical theoretical journal end hypothesis hypothesis easily degree degree degree degree degree degree degree degree degree degree degree fit fit underlying underlying needed technology interesting interesting interesting significantly ratio ratio ratio ratio ratio york increasing empirical empirical bits bottom early early light light light light predict advantage typical lateral moving moving moving pixels pixels interest highly highly highly varying varying varying varying varying varying varying varying varying varying varying previously previously works studies positions symmetric channels entire exists horizontal parts parts scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling predicted predicted predicted white white white white pass pass pass segment conclusions conclusions central retina designed clear asymptotic strong presence presence cycle cycle cycle cycle cycle drawn california solid solid solid solid solid solid proportional movements decrease relationship relationship relationship iii scene scene scene scene scene scene question question acknowledgements reference reference relation relation relation van derive perception optical optical plot plot vertical segments segments segments segments segments sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity averaging easy develop frequencies frequencies frequencies frequencies frequencies shift quality decreases independently expressed correlated correlated overlap overlap overlap transform transform modulation frames frames frames frames frames static static static static spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum earlier earlier reasonable smoothing measurements measurements measurements measurements fitting coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling silicon color bell plotted plotted plotted plotted plotted plotted plotted plotted coupled coupled coupled coupled phys discussions discussions summary refer soc soc kind kind strongly video video video showing sci board cat moves illustrates law body explore american collection rapidly relations detail optimized optimized behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour existence fourier fourier fourier respond ideas analytically scaled scaled scaled scaled scaled scaled scaled scaled scaled scaled authors lgn func statistically measurement measurement measurement predicts rev obvious portion separated separated regime regime regime regime regime ment scenes scenes band separable separable separable trivial agreement agreement analyzed analyzed answer multiplication turns ran nucleus immediately universal opt opt res author pure pure quantitative psychophysical psychophysical exhibits exhibits exhibits modulated modulated fall pasadena achieves irrelevant shifted shifted shifted shifted shifted spectra spectra spectra spectra primarily ratios ratios ratios ratios ratios ratios appropriately velocities concerned repre caltech lost systematic fits ments mail city hope settings days elimination loo loo bialek dominant photoreceptor viewing spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal spatiotemporal park summarize interestingly vari default consecutive approx grating ence compressed equivalently ram break obstacles revealed revealed poses pointed regularity decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation intuition graphics dominated confirmed intensities intensities accounted accounted reveal supports geniculate milliseconds treating gratefully regularities thousand shot flows horizontally horizontally atick atick atick systematically optics digitized digitized quantitatively ruderman acknowledges format transmit seg translates translate repetitive spario campbell sentations joseph phy plotting compress imation movie stabilized thirty snapshots snapshots sual suppresses psy dong dong dong dong dong dong sensitivities sensitivities sensitivities sensitivities dates intriguing woods tape whitening movies rgb greyscale greyscale lagged decorrelate kelly domly iol chophysical decoupling decoupling snap television television factory baylor asymptotes uncommon hateren entific chosing 
#@Dong_D,
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#*network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input input input input input input input input input input input input data data data data function function function figure figure figure figure figure figure figure figure figure figure time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm output output output output output output output output output output output output output output output output output output output system results results results results units units units units units units units units units units units units units units units units units units information information information information information information information problem problem problem models performance performance performance based based based space space space space space space space space space space space space space weights weights weights weights layer layer case shown shown values values values noise noise noise neurons neurons neurons neurons neurons unit unit unit unit unit distribution approach approach pattern pattern image image image image image image image image single single single single single single single processing processing local local local local local local local local local local local local local local local local local local local local local local local local local test test patterns analysis analysis analysis form form shows signal signal algorithms gaussian gaussian visual visual visual visual visual visual visual visual visual paper cells cells points field field process level trained random random random random random random random high high high high response response response response similar similar representation architecture architecture section fixed line images images images images images images images general real real real real average theory theory obtained note experiments activity activity activity dimensional university university threshold threshold threshold threshold threshold threshold computation computation found found found found found found found table table estimate estimate estimate estimate estimate estimate estimate standard standard science science left left left left left left left left presented presented map map map present present phase phase activation activation activation activation activation low low frequency frequency frequency machine machine object object object object object object object sets motion motion motion motion motion motion motion motion motion maximum maximum learn nonlinear outputs outputs outputs sample sample sample abstract back back back computational properties references ieee adaptive propagation propagation propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus generated generated tion change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference difference difference spatial spatial spatial spatial spatial representations learned learned learned part part part part type type multiple multiple cortex cortex cortex binary long conditions represent techniques techniques region region correlation correlation correlation correlation correlation correlation correlation length forward scale scale minimum minimum ing ing ing human computed computed multi multi sum sum performed performed regions regions regions regions regions regions regions mapping factor factor global filter filter filter filter filter filter obtain relative specific represented compared compared compared compared desired desired cross cross cross cross cross receptive receptive provide provide provide compute compute objects objects objects objects objects location location location location location location location active active eye eye eye eye goal gain cortical power approaches approaches comparison contrast contrast contrast support support support nets nets selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection report institute institute institute words implementation represents represents represents layers layers addition addition maps framework computing computing domain domain domain domain directly directly hinton hinton estimates estimates estimates san san top top top top top stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects detection detection detection determine determine upper significant world world world vision estimated con weighted developed developed area area area velocity path product actual actual actual finally evidence backpropagation measured discussion technical describe tested tested corresponds role role journal journal pixel pixel pixel pixel pixel ability noisy sensory fit fit objective pairs combination functional jordan jordan york york edge edge segmentation segmentation mechanism mechanism mechanism mechanism mechanism consistent consistent principle operation operation leads numbers max max max filters filters filters filters filters filters filters normalized normalized bottom bottom bottom bottom experts experts experts experts experts experts experts experts experts experts experts experts experts depth depth depth depth depth depth early combined description directions recent recent recent resolution property robust separate separate separate identical pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive sufficient highly compare yields studies sparse sparse mixtures background locations locations locations locations locations locations locations locations locations locations grid sensitive increased lead correctly feed move white pass pass row row row row row segment differences differences measures accurate retina retina propose strong integration integration integration integration integration integration california california proportional intelligence variety variety selective selective selective selective selective selective targets introduce scene scene appears appears edges edges edges edges optical optical primary primary primary estimating estimating tuned tuned tuned changing sensitivity sensitivity averaging remaining remaining develop develop integrated frequencies gaussians gaussians competition competition john focus formation stages stages squares interpretation interpretation open soft soft soft similarly partial combining fitting boundaries filtering filtering filtering filtering construction transactions recorded box activations activations retinal retinal discuss activated specifically domains black partially tests major straightforward middle middle society society poggio poggio poggio detect summary traditional refer soc compact kind strongly strongly contained contained dis superior physiological gray gray gray gray gray gray gray gray cues cues cues cues michael michael play dot dot dot dot dot dot realistic hypotheses thresholds thresholds thresholds thresholds thresholds thresholds neurosci received received received received consisted consisted consisted overlapping overlapping overlapping disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity jacobs jacobs neighboring receive situations diego diego diego layered wiley poor difficulty difficulty detail optimized accurately accurately accurately dual scalar matches respond fashion rest detectors detectors applicable parity reliable reliable reliable reliable reliable reliable reliable pathway pathway pathway pathway pathway analogous surfaces surfaces hill measurement plausible plausible configurations eyes friedman friedman friedman der der der detector explored mapped extent integrate rows biology nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan nowlan adapted caused nonlinearity spatially spatially shared shared organized organized organized filtered division pool pool separately optimize medical qualitative questions double freeman freeman profile substantially pathways pathways pathways pathways pathways pathways readily quantitative psychophysical psychophysical biologically reliability ity ity howard suited datasets datasets datasets datasets datasets green green richard neuro findings summed summed lab discontinuities tation gabor zemel zemel zemel zemel zemel zemel zemel binocular promising occurred occurred neurobiology affected salk salk salient corner utilized displayed von von von moved stereo stereo stereo monkeys uni captured viewing occlusion occlusion insight layout layout indicator jolla rich sons valuable discriminate email creates cooperative pentland pentland medium ideally transparent transparent transparent monocular insights searches neurophysiological neurophysiological neurophysiological hughes challenging terrence individually selectively selectively responding knowing psychophysics rose rose rose circumstances tial tial pouget pouget pouget pouget pouget pouget transparency transparency steven alex jain jain conflicting unreliable devised america america demands mcgraw essence thresh convey spa spa responded responded responded behaving clutter quantified neigh stereograms stereograms stereograms stereograms stereograms ities devel awake darrell darrell terry exhibiting corresponded depths banks signaling pared zhou zhou zhou disparities disparities disparities disparities disparities disparities disparities disparities disparities poorer bears acuity stereopsis stereopsis stereopsis stereopsis hyperacuity occluding topographically ohzawa ohzawa departments alexandre oped behaviorally collapsed westheimer sistent tition discrimina segmen stereoscopic stereoscopic olds swets swets compe adversely ener neurophysiologically gion boring neurobiologically 
#@Gray_M,Nowlan_S,Pouget_A,Sejnowski_T,Zemel_R,
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#*network network network network network network network network network network network network learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data function function figure figure figure figure figure figure figure figure time set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training algorithm output output output output output output output output output number number number number system system system system system system system system system system system system system system system system system state results results results results results results results results results results results information problem problem performance performance based based based based based space space space vector vector order shown shown systems systems values values probability probability probability probability probability probability probability probability parameters noise unit distribution recognition image image image image image image image image image image image image image image image image image image image image single single processing processing large local local local local local rate rate analysis class class class class inputs form algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual examples examples small size feature feature feature feature feature feature feature feature feature feature feature net net task task task step field features features features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process level level level current problems problems high high similar representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture equation equation equation equation rule vectors vectors vectors vectors images images images images images images images images images images images images parameter real real average average obtained obtained obtained obtained obtained obtained obtained obtained obtained term note note dimensional dimensional dimensional result result result university university threshold research research research research defined defined defined defined dynamics dynamics dynamics dynamics estimate standard standard standard node node science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left left left left left left presented map activation activation activation activation nodes maximum range learn learn learn sample sample abstract applied applied computational properties properties references ieee procedure adaptive mixture context introduction complex hand hand effect variance variance search search tion tion energy variable variable spatial spatial spatial spatial spatial spatial classifier classifier rules rules measure measure measure learned chosen chosen chosen chosen chosen chosen chosen chosen chosen center center center center bound bound multiple multiple multiple multiple conditions represent tree distributed equations equations make region region region region region region region region region region correct correct correct correct correct correct correct correct probabilities probabilities probabilities probabilities probabilities errors scale scale scale scale scale scale scale scale scale scale resulting classes ing ing simulation human multi sum called regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions mapping mapping mapping mapping means dimension dimension dimension made made made natural natural natural natural natural natural natural orientation orientation study study filter obtain relative compared receptive define compute rates location determined determined determined determined distributions steps accuracy contrast contrast contrast contrast contrast contrast contrast contrast report department consists internal kernel represents represents represents responses responses difficult difficult final final exp exp exp addition addition addition maps maps additional estimates estimates estimates top stage stage stage stage stage full requires statistics world world vision clustering developed levels criterion criterion actual finally evidence biological technical group fast fast close surface surface surface surface surface surface amount amount common common effective generate supported supported main pixel pixel pixel pixel pixel pixel pixel noisy noisy noisy including fully ratio york segmentation structures matching representing filters filters pre normalized bottom bottom bottom bottom bottom early magnitude decay produced produced added predict improved improve recent recent resolution resolution advantage property separate ensemble ensemble ensemble ensemble ensemble ensemble ensemble trees array cognitive interest sufficient varying unsupervised smooth smooth yields yields match match match match match match trans improvement improvement horizontal intensity intensity invariant deviation deviation deviation predicted correctly hybrid hybrid hybrid hybrid hybrid hybrid clusters boundary boundary boundary half strength row row row differences differences differences measures measures accurate learns learns learns learns learns taking cycle labeled labeled minimizing selective force acknowledgements produces produces perception perception perception perception perception perception perception label label label vertical vertical vertical sensitivity category category category category category category category category category category category category category category remaining scales scales develop frequencies applying extraction versus competition yield yield yield national review stages evaluated evaluated evaluated operations operations updated updated labels organizing organizing organizing organizing organizing organizing organizing static discrimination smoothing smoothing epochs epochs classical combining boundaries boundaries boundaries boundaries boundaries boundaries boundaries tracking filtering filtering foundation classified classified figures includes perceptual activations color contour contour batch determines plotted plotted automatic automatic maximize activated activated structural texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture middle middle middle middle middle middle middle closely effectively presentation ten composed summary road road road road road soc soc soc soc soc quickly anderson anderson sin categories categories categories categories categories categories categories categories categories categories categories categories categories categories surround surround surround wave computes automatically illustrates extract satisfies deal oriented oriented oriented oriented oriented oriented oriented oriented transformed exhibit accurately scalar fewer reducing incremental incremental mappings mappings mappings mappings office office office reliable structured maximizing comparable comparable variability variability created subsets versions initialized initialized art epoch utility motivated synthetic synthetic great advanced scenes orientations orientations orientations phenomena improves improves diffusion diffusion diffusion diffusion spatially spatially organized preprocessing preprocessing operators scientific grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg grossberg demonstrates meaning nsf nsf raw greatly tional lack cohen cohen share marked detecting completion slower sharp rep rep biologically variant psychological mod ture extracting popular achieves achieves achieves boston boston boston boston begins credit credit multidimensional multidimensional cumulative pyramid pyramid pyramid classifying classifying classifying classifying classifying classifying classifying classifying classifying appearance gabor gabor gabor rotated rotated ordering repre naval naval air height analyzing belong belong belong illumination illumination canonical carry carry constructive filled filled filled filled filled filled filled filled filled reliably reset reset reset reset loo james james pat enable thin thin thin informative projects variants onr onr onr onr onr radar radar radar radar outperforms outperforms resonance maintaining maintaining street unified achieving goodman goodman shunting shunting creates emergent bank employs incrementally obtains obtains arg arg brightness brightness brightness brightness brightness brightness brightness brightness brightness brightness brightness brightness brightness representa constrain ary ary cns cns summarizes shifting segregation pami continues afosr afosr wise spreading proach iri iri intensities intensities intensities library cation indexed misclassified maintains sized son parametrized williamson williamson williamson williamson williamson williamson williamson williamson williamson williamson normalizing psychophysics psychophysics supporting resembles remarkable stephen stephen textures textures textures textures textures textures textures textures textures textures multiresolution utilizes fill agency contrasts classi bergen bergen cooperation bandpass bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs permanent permanent fair pooling pooling filling filling filling filling fication signed signed steve aperture aperture aperture aperture raised raised seg sentation segmenting illusory discriminating addi tern linearities tal preprocessor ness bright resentation convolving notably roads roads separability initializing mented mosaic mosaic unstructured blurring blurring blurring segmentations vigilance incremented greenspan greenspan greenspan greenspan greenspan invoked iij iij normalizes resentations mingolla mingolla mingolla mingolla mingolla sponses tex decomposes shadow shadow shadow postprocessing raining chellappa chellappa sar sar sar sar sar sar sar sar sar cas sand sand grass grass shadows sociated compensates compensating dictions rectifying caption optional taining macmillan timate organizes aries decimation decimation regan committed calibrating textural psi fer jtn localizes 
#@Grossberg_S,Williamson_J,
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#*model model model model model model model model model model model model model model neural data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number error information information information problem problem problem problem problem performance based based based based based based based based space space weights linear linear case vector vector vector vector vector vector order order shown shown shown shown shown probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions distribution distribution distribution recognition recognition approach approach pattern pattern point image image image image image image image image image image image image image image image processing control control local local local local local local local local local local local analysis matrix matrix matrix matrix form shows shows shows shows algorithms simple gaussian gaussian gaussian gaussian visual paper paper paper paper paper feature feature feature feature feature work methods step step step points features features features features process process process process process process process process process process process level level level current structure structure structure structure structure structure structure structure structure structure problems response representation representation equation equation equation line line line line line line line line images images images parameter parameter parameter parameter parameter parameter approximation obtained experiments result university computation computation log log log defined found dynamics dynamics initial initial initial initial initial initial estimate estimate estimate computer computer computer computer terms terms terms terms terms terms distance science prediction map map map map map phase phase low low low object maximum maximum maximum position position components components components components components components components abstract find computational convergence density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references ieee ieee ieee ieee ieee ieee procedure procedure mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand hand hand estimation estimation estimation statistical statistical statistical statistical effect effect variance variance parallel parallel parallel tion tion tion variable variable variable variable spatial assume prior required required good good represent represent represent bayesian expected equations equations equations make fact fact fact region probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed scale regression computed computed computed respect multi multi elements elements means reinforcement reinforcement potential potential potential natural orientation orientation global global global global global global applications applications study study knowledge em em em em em em em em em em em em em em em em em em em em em filter filter filter original original original original artificial represented represented represented application cross series receptive provide compute compute goal distributions comparison fields support proceedings words words words department technique represents responses final final exp exp ai framework framework framework framework computing computing equivalent equivalent directly curve curve curve curve curve curve curve curve curve curve curve solutions solutions solutions curves estimates estimates detection detection detection conference determine upper full world vision vision vision vision vision basic basic give condition condition channel weighted weighted weighted weighted weighted weighted weighted weighted conditional conditional conditional conditional conditional developed developed criterion product processes evidence iteration iteration measured covariance describe denote limited limited limited limited inverse inverse corresponds surface surface finding finding common role require require journal journal journal pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel instance makes development fit fit fit fit fit probabilistic probabilistic probabilistic underlying underlying underlying underlying combination account account coefficients jordan york york edge consistent consistent structures structures structures leads squared representing details details max filters window window international international international experts early idea idea idea attention attention attention description description pair robust robust element reported reported practical practical practical practical introduced pixels pixels pixels recently recently recently highly observations tions solve differential achieve mixtures mixtures locations sensitive horizontal intensity wide predicted move width column row conclusions operator operator operator operator operator central tangent bayes clear demonstrated intelligence turn turn iii scene connectivity denoted explicit suppose index solving estimating estimating describes vertical segments physical involves develop applying quality expectation expectation expectation expectation expectation expectation expectation expectation expectation letters expressed review reconstruction squares squares squares estimator viewed viewed densities densities densities evaluated evaluated evaluate operations updated updated evolution evolution evolution allowed key measurements classical classical combining combining fitting fitting fitting fitting fitting fitting fitting fitting iterative iterative iterative iterative iterative iterative iterative iterative intermediate initially initially initially distances assigned transactions david contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour weighting illustrated gating successfully determining modes successful successful literature essentially fine fine fine fine fine fine reached road road road road road soc notice notice prob prob showing interested interested contribution satisfy quantity write write relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation providing computes attempt subsequent mixing mixing mixing mixing jacobs modelling employed poor essential exhibit updating involving limitations ideas comparable proved proved statistically cover contours coarse measurement measurement measurement measurement plausible spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline spline ith detected extent residual great developing formula theoretic theoretic orientations adjacent perspective perspective operators operators operators cut scientific optimize patches incomplete incomplete incomplete incomplete raw raw raw evaluating understood readily red red red posed splines splines splines splines splines splines splines splines splines splines biologically biologically biologically passes aim branch branch branch sophisticated progress converged picture picture discontinuities indices formally jth jth purely reconstructed connecting enhancement enhancement enhancement royal proceed arranged inspired inspired significance overcome overcome abilities roles moments moments motivation meaningful iteratively widths originally arrangement recovery surprisingly omitted draw draw extensively exploiting dempster dempster dempster dempster dempster displacement displacement divide posteriori posteriori posteriori posteriori rubin rubin rubin rubin bank distinction convenience residuals residuals residuals quasi arg junction junction junction junction junction assignments associate associate adjustment reject remainder clas arising perpendicular evolve pami pami pami uncertain expand retain ambiguous ambiguous sketch laird laird laird laird indexed indexed indexed indexed indexed indexed refinement refinement descending descending suffer dictionary dictionary dictionary dictionary dictionary dictionary dictionary meet cubic cubic cubic cubic article gorithm gorithm lems bridge inconsistent junctions compete hoc clarity optimisation hancock hancock hancock hancock hancock hancock hancock hancock hancock hancock hancock drawing appealing proportions proportions proportions proportions labelling labelling labelling labelling labelling labelling inferring edited substitution neighbourhood neighbourhood neighbourhood adjusts smc smc smc spirit sian sian essence positioning gaus gaus ings outlier ically iterate putative putative snake snake maximisation maximisation maximisation maximisation maximisation maximisation maximisation maximisation newly battery aims fractional align locating virtue recovers organisation organisation organisation organisation organisation organisation organisation organisation organisation organisation minimise forthcoming aimed recursire offered reminiscent mediate sought iterates iterates maximising maximising maximising regularisation puted displaced kim draws outlines centred centred multichannel refining notational datum datum conveniently maximise mon neighbouring neighbouring shortcomings delivered delivered organ motivate ordinates manifest opera compatibility compatibility zucker zucker zucker zucker zucker zucker zucker zucker flamework flamework flamework flamework initialisation lihood philosophy viii terzopoulos fined aerial aerial aerial rio ors delivers delivers cording regulate ridges couples ken documented rosenfeld rosenfeld rosenfeld derlying iip methodologies highlighted originates tection realised realised confine characterised initialise hummel hummel hummel hummel seminal enforcement shorthand infra infra infra recomputed rosenreid rosenreid rosenreid sical erage contrasting subregion subregion isation jen elusive residing hancement methodological methodological laxation dobbins 
#@Hancock_E,Leite_J,
#t10
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#*network network model model model model model model model model model model model model model model model model model model model model model model model model input input input input input input input input input input input input data data function figure figure figure figure figure figure figure figure figure networks networks networks system system system state state state state results results results units information information information problem problem models based space space space space weights linear linear case order order shown shown shown shown shown neurons neurons neurons neurons neurons neurons neurons neurons pattern pattern point single processing processing processing control control control control large large local local local local local local local local local local local local local local local local local local local local local neuron rate test test test test test patterns patterns analysis analysis analysis analysis analysis inputs inputs form form simple simple simple simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper examples examples small small small small size size work work work work work work cells cells cells cells cells points field field field field field field field field field features features features level cell cell cell high response response response response response response response response response response response response similar similar similar similar architecture show show show show show show fixed line line line line line general obtained obtained note experiments experiments experiments activity activity dimensional result result university university university computation defined defined found found dynamics constant constant connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic science science present low frequency temporal object range range range range range range range range components basis abstract properties references component component due positive important context context introduction action complex complex circuit circuit circuit stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect parallel recurrent recurrent recurrent tion tion tion spatial higher part part center center center center center center center center center center center center center center center center center center firing firing firing type multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good long long long long long long conditions represent tree tree equations fact fact region region observed scale simulations simulations simulations simulations resulting ing ing total total human respect respect elements potential potential potential dimension dimension dimension dimension natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global study study filter negative original relative specific specific compared cross cross cross receptive receptive receptive receptive receptive receptive receptive receptive provide rates rates determined determined experimental experimental experimental experimental gain gain gain gain cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain voltage voltage contrast contrast connection connection connection connection fields dependent dependent dependent dependent dependent department department kernel kernel kernel responses responses exp considered domain equivalent experiment curve view view stage stimuli stimuli effects effects effects effects effects detection detection choice vision vision basic basic basic give condition area lines lines lines processes evidence nature nature nature inhibitory inhibitory inhibitory inhibitory inhibitory depends constraint discussion increases excitatory excitatory excitatory excitatory excitatory excitatory excitatory circuits circuits circuits finding finding finding common effective effective effective supported role theoretical degree development including typically smaller smaller account account account account account account functional interesting edge edge edge edge edge increasing increasing segmentation mechanism mechanism consistent consistent uniform mode principle principle operation leads max pre direct direct direct direct direct direct direct inhibition inhibition inhibition inhibition inhibition inhibition early magnitude added neuronal neuronal neuronal membrane membrane membrane population population population population population discussed recent recent recent separate typical typical lateral lateral lateral lateral lateral lateral apply introduced include sejnowski sejnowski recently recently relevant dimensions dimensions dimensions conventional observations tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning axis axis axis axis correspond studies differential differential differential differential separation symmetric channels channels channels organization organization organization organization sensitive increased increased grant amplitude amplitude amplitude amplitude amplitude horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal parts lead studied wide wide clusters clusters occurs occurs generally generally setting setting pass demonstrate strength strength critical critical critical reduce interactions interactions interactions interactions interactions interactions interactions peak weak suggest encoding strong strong strong mechanisms reduction characteristics solid variety variety averaged manner manner connectivity connectivity connectivity acknowledgements appears appears appears appears edges perception primary plot tuned tuned tuned mathematical modeled implement sensitivity explicitly explicitly coordinates simultaneously linearly involves angle angle angle angle angle interaction interaction equilibrium equilibrium versus potentials potentials dependence dependence communication detailed detailed open centers forms sign key earlier dashed classical classical classical reduces distances filtering foundation coupling expect kernels kernels kernels priori formulation color currents currents currents inter determines coupled absolute absolute characterized successfully simplicity columns uniformly maximal modes spiking orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal characteristic characteristic excitation excitation excitation excitation summary refer refer soc dis physiological bar simplified surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround providing cat cat cat neurosci neurosci principles operating operating preferred preferred preferred oriented cowan cowan cowan cowan cowan cowan stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation selectivity selectivity circuitry circuitry circuitry circuitry circuitry involving involving strengths biases rise detectors detectors detectors detectors detectors detectors detectors structured lgn fundamental neu act circles circles math math naturally man opposite opposite bifurcation detector separated switching baseline regime explain preference preference preference preference preference preference cos cos cos cos band distinguish orientations orientations orientations phenomena phenomena phenomena phenomena fairly explanation rapid ring nucleus immediately monkey arise mathematics mathematics consequence cut ion separately involve angles res res res localized localized patches patches patches arises fluctuations populations populations populations populations populations populations populations populations double freeman understood lattice psychophysical psychophysical psychophysical detecting treated cal cal decreased findings focused cor discontinuities physiology physiology physiology primarily tation neurophysiol neurophysiol jones connecting enhancement enhancement enhancement plays suppression suppression suppression suppression suppression suppression suppression primate striate striate balance balance balance biased keeping operates wilson filled sompolinsky sompolinsky sompolinsky weakly weakly falls irregular james corre negligible reproduce reproduce reproduce viewing deg modelled cerebral stimulated stimulated stimulated extensively considerations davis balanced balanced outlined grating grating grating grating grating grating grating grating grating grating grating slight indirect indirect indirect indirect indirect indirect indirect ter wiesel focal emergent nelson nelson adopt chaos preferences preferences preferences ideally personal hubel chicago chicago chicago chicago chicago chicago continuity exam insights distribu distant neurophysiological neurophysiological iso iso iso iso iso confirmed depicts depicts surrounding macaque macaque assemblies assemblies assemblies afferents gilbert gilbert pop pop pop geniculate tissue psychophysics examination simplifies simplifies mea correlate stimulating sponding lation mcdonnell converging hundreds broadly suppress eral continuum sharply believed emerges comprising quantitatively quantitatively vivo reproduced inducing inducing inducing tical gratings modulatory carpenter carpenter sur sur hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn neurones jack proximation tal attracted hirsch hirsch formulations tsodyks tsodyks stim rigorously sodium sodium sodium sodium sodium blasdel blasdel blasdel mediate bifurcations niebur niebur alexander reproduces comprises postulated tilt tilt tilt tilt tilt tilt tilt tilt tilt tilt designated neurology neurology pri conflict volumes cen radially usher usher suppresses mary brevity katz trevor invoked mediating mediating sev ner illusion illusion illusion illusion somers somers experimen ohzawa departments referring markedly attenuated mech orien sillito sillito johnstone johnstone johnstone hibitory pression tude suppressive suppressive originates originates victor victor illusions illusions illusions ceptive ampli ampli skewed thalamocortical reduc hypercolumns hypercolumns satisfactorily compelling ined popu exci ferred surements summarised corti fects fects rosci inves uli tatory inhi redrawn realistically anisms prelim bition ceptual bridging augments inary preferring attenuates 
#@Cowan_J,Dimitrov_A,Mundel_T,
#t10
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#*network network network network network network network network network network network network network learning model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data data data data data function figure figure figure figure set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training output output output output number number number number number number number number number system system system system system error error error error error results results results results results results information information information information information information problem models hidden hidden hidden performance performance performance performance performance based based based based based based based based based based space space space space space space space space space space space space space weights weights weights linear layer layer case vector vector order shown shown shown systems systems values values values values noise noise noise noise recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single single single single single processing processing processing large local local local local rate rate rate rate rate rate rate rate test test test patterns patterns patterns analysis analysis class inputs form shows signal signal signal signal simple simple visual visual examples small small size size size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work work work work work work work work task task fig fig fig fig fig fig points points features features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification trained trained trained trained trained trained structure problems random random random random random random random random random random random random random random random random random random response response response similar similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture show show fixed fixed vectors images images images images images images images images images images images images images images images images images images images images images images images images images images general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization average average average average average average obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained university university research research independent found found found found found sequence sequence initial standard computer computer computer distance distance connections science science science left presented presented activation nodes machine machine machine object object object sets sets sets sets sets range range range range press learn components components components basis abstract back references component component due due due ieee ieee ieee procedure procedure important propagation introduction action action action complex hand generated generated variance variance variance tion tion tion difference classifier classifier classifier classifier classifier classifier lower representations representations representations representations representations representations representations representations representations representations representations representations representations representations higher higher part part previous previous previous previous type required required long expected expected expected make make make make techniques techniques techniques techniques techniques techniques region observed observed forward scale ing ing tasks total total total human human human human human human human human respect respect respect sum performed regions regions regions regions regions regions mapping potential made made made natural natural natural study em original original represented compared cross provide provide provide provide objects objects rates rates rates rates eye eye eye eye eye eye determined goal related connected approaches mit morgan proceedings department department technique technique technique technique technique consists individual individual individual individual individual individual individual individual individual advances advances represents responses responses difficult difficult final final scheme scheme sequences sequences sequences considered cambridge directly curve curve view curves design design san san san san top top bit conference conference determine determine determine classifiers classifiers classifiers full full full full full requires significant significant significant vision vision pages increase increase validation give give produce produce coding coding derived derived derived derived weighted weighted randomly developed area area path finally selected nature simply achieved achieved achieved achieved discussion increases tested limited predictions finding amount amount nearest generate generate generate face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face ability ability instance future makes kaufmann typically typically combination fully block block block block block block block block block block block block block block testing testing testing significantly significantly ratio projection projection projection projection edge increasing increasing head trials database database database database database database database principal principal principal principal principal representing representing representing representing making making making normalized normalized normalized normalized normalized normalized early combined combined minimize ensemble takes typical typical strategy strategy pixels pixels sejnowski cognitive relevant relevant interest interest dimensions varying compare compare observations approximately subjects subjects calculated calculated calculated works tions tions pca pca pca studies achieve trans locations improvement entire entire entire increased constructed expression expression expression expression expression expression trial deviation deviation wide alternative correctly feed touretzky touretzky generally demonstrate flow flow conclusion reduce reduce neighbor valued editors editors differences differences differences differences differences sigmoid moody constrained mateo reduction characteristics drawn drawn demonstrated california california intelligence labeled labeled turn identification identification areas areas areas areas areas pro pro construct construct perception perception perception optical optical winner factors generating vertical distinct distinct distinct confidence sensitivity linearly remaining develop develop formed quality blocks blocks blocks blocks blocks blocks versus choosing extracted extracted independently expressed depending variation variation evaluated open open evaluate evaluate evaluate evaluate fraction static static static sizes discrimination discrimination reasonable reasonable performing spaces spaces normalization combining initially faces faces faces faces faces faces faces faces faces faces views transactions transactions expect template mozer variations variations variations variations variations tests structural major determining determining aspects efficiency capable suitable suitable differ divided effectively effectively poggio poggio poggio successful identify identify schemes schemes schemes projections projections projections projections projections projections projections projections projections comparing invariance score essentially orthogonal fine compact repeated success superior classify content strategies strategies strategies hold hold involved generalize modular highest highest highest highest leading attempt consisted consisted overlapping extract bars employed diego diego diego poor poor exhibit varied dataset dataset dataset examine examine possibility possibility scaled eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors proved scores scores affect affect encode statistically examined measurement plausible editor facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial eyes eyes eyes eyes eyes eyes eyes eyes aspect portion expressions expressions expressions expressions averages indicating developing agreement agreement explanation explanation reasons snr purposes purposes shared located located actor actor potentially projected projected localized localized patches patches patches patches demonstrates demonstrates annual recognizing researchers varies evaluating reflect substantially rep rep rep biologically compares psychological templates templates span exhibits rely perturbations differs achieves substantial substantial age windows irrelevant cor consistently consistently phenomenon pose classifying classifying classifying classifying aligned identifying tation ratios eliminate rigid minutes minutes promising familiar resulted imply cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell guide muscles reliably bartlett bartlett bartlett representational representational representational representational representational sion respective respective respective respective respective displayed male overview bad captured facilitate hasselmo ensembles express jolla jolla impact impact impact davis davis davis valuable tures asked benefits pentland pentland pentland pentland pentland pentland encouraging exception seek seek generalizations generalizations individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals female constitutes suppressed examining reflected clas clas clas representa representa representa preserved preserved care gained permits mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth mouth depicts projecting scope gender employing mask represen anal anal portions voting indication lippman eigen normalizing students covers lighting uniqueness attributed heavily emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion emotion viola attempting imple tors pictures accomplish normalize archi digitized enhances alto neutral neutral neutral neutral accommodate resultant categorical faced prominent surprise devoted sex validated eigenfaces eigenfaces eigenfaces eigenfaces palo stems collecting broader favorably inability resentation resentation ver localize mentation acceptance friesen friesen friesen friesen friesen friesen friesen friesen friesen distinctions superiority untrained tecture disagreement inadequate subtraction pal prototypical aver duce relied relied metcalfe metcalfe metcalfe metcalfe metcalfe metcalfe metcalfe metcalfe metcalfe metcalfe metcalfe conducting suit cited grained iden larsen emotions emotions emotions emotions emotions emotions emotions emotions incor pertinent percentages cial jects para concentrating holons intell sparcstation uncover garrison vides expres greyscale ieice assembled eigenface eigenface suitability suitability ascertain mase mase mase stretched emotional happy sifters tically princi brunelli brunelli brunelli suits suits porated propriate jections sifter consulting psychologists cropped tity emo emo ployed 
#@Cottrell_G,Padgett_C,
#t10
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#*network network network model neural neural neural neural neural neural input input input input data function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set networks networks output output number number number number number number number system system system system system system system system system system system results results results results results results units units units units units units units information information information information information information information information information models models models based based space space layer layer layer layer layer layer layer layer layer layer layer layer layer case order order order order order order order order order shown systems values values parameters weight neurons neurons neurons unit recognition recognition pattern pattern pattern pattern point image image image image image image image image image image single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing large large large large large local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate test test inputs inputs inputs inputs inputs form shows shows shows simple simple simple simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small feature net net net fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step step step points field field features process process process process process process level level level level level level cell cell cell cell structure problems high high high response response response response similar similar similar representation representation architecture architecture architecture fixed fixed images images note note note note note experiments activity activity activity activity activity activity activity activity result result result threshold threshold threshold threshold threshold computation computation computation sequence target target dynamics initial initial initial initial initial constant estimate connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic science presented presented presented map map map map present present present activation activation activation activation activation activation activation activation low frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal machine press press position components basis continuous abstract computational analog analog analog analog analog analog properties references important propagation propagation propagation propagation propagation propagation propagation introduction action complex complex complex complex stimulus stimulus stimulus effect effect effect generated generated parallel parallel parallel variable spatial spatial spatial spatial spatial spatial spatial center center center center center center center center previous previous firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type type cortex cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike conditions conditions make make fact fact region observed scale scale simulations simulations simulations simulations simulations simulations simulations resulting total simulation human human performed times elements regions regions means potential made natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation original application receptive receptive provide rates proc location constraints constraints constraints cortical cortical cortical steps contrast contrast dependent version version code code code code code code connectionist responses difficult final layers layers layers layers layers layers delay delay delay scheme maps maps maps maps maps equivalent equivalent additional view limit top stage stimuli determine efficient choice approximate world speed speed basic basic produce produce coding coding coding coding coding coding coding weighted developed developed developed developed levels levels levels area area area area finally nature nature nature nature nature depends depends biological achieved achieved achieved achieved measured normal increases increases fast limited limited limited corresponds corresponds complete excitatory amount amount amount short short short synapse generate generate generate main eds eds eds face journal end pixel instance cluster development simulated simulated needed hopfield hopfield account transfer head mechanism special details numbers numbers filters filters window early frame decay idea produced run neuronal architectures membrane population takes include pixels pixels sejnowski sejnowski recently recently recently highly previously previously conventional conventional correspond correspond correspond studies organization sensitive horizontal intensity intensity intensity spikes spikes spikes spikes spikes spikes spikes spikes alternative white occurs pass demonstrate strength conclusion starting row row row conclusions differences retina retina retina exponential faster demonstrated start targets appears digit tuned tuned tuned modeled sensitivity involves scales frequencies decreases stages stages stages stages stages stages overlap codes understanding processor key slow delays intervals event event roughly roughly roughly roughly roughly roughly add add generation remains calculate calculate calculate msec advantages faces views fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire retinal retinal retinal retinal retinal retinal activated activated activated activated activated specifically major middle efficiency efficiency capable maximal encoded effectively effectively driven driven spiking spiking schemes post post post post plots tend essentially ten soc quickly kind strongly strongly neuroscience timing timing timing sci gray list list involved involved vary absence realistic reach reach reach illustrates preferred intrinsic receive oriented oriented unlike selectivity put matches respond respond investigated biol possibility possibility lgn cognition contours contours onset onset onset onset onset onset onset onset extremely precise separated pyramidal grouping seconds integrate integrate integrate percentage great preference asynchronous orientations biology majority expensive ganglion ganglion turns rapid rapid rapid rapid rapid perspective filtered operators afferent scientific involve axons lowest virtual reflects profile profile transient simulate simulate experimentally orders reliability poisson differs aim suited simulator simulator simulator sophisticated sophisticated instantaneous phenomenon pose redundant sort proportion proportion extensive velocities arrival reaching systematic chance promising primate primate primate primate striate efficacy occurring implications affected north optimally exceeds fires fires reset surprising holland cerebral surprisingly shortest specificity informative speeds interestingly severe treat treat escape fired fired fired fired fired fired grating neurophysiology neurophysiology depression depression email latency latency latency latency transmitted encouraging centre centre medium classic affects forcing unseen shifting conduction mhz lobe lobe argued lond selectively million nonetheless france elsevier elsevier places milliseconds inactive remarkable send hat neocortical neocortical excited physiologically subtracting striking progressively progressively progressively functionally arriving connectionism unusual huge simon discriminating amsterdam hypercolumn plenum initiated neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones neurones spots primates plausibility bright activating tsodyks tsodyks awake awake thorpe thorpe thorpe thorpe thorpe thorpe thorpe thorpe thorpe thorpe thorpe thorpe thorpe thorpe convolving mainen mainen vast rolls rolls latencies latencies latencies latencies latencies sorts outlines earliest earliest earliest earliest fogelman converters converters converters converters workstations markram markram millisecond asynchronously unambiguous mexican conical wasted gutfreund masking peters pit eckmiller reprinted extrastriate recherche kaas hartman ruled redistribution imbert imbert imbert imbert imbert steels ups recalculated pfeifer jacques invariably schreter 
#@Gautrals_J,Thorpe_S,
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#*network network network network network network model model data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time networks training algorithm algorithm algorithm algorithm algorithm algorithm number error state state results results results units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information problem problem problem problem problem problem problem models models models hidden hidden performance performance performance performance performance based based based based based based based linear linear linear case case vector shown shown shown systems systems values probability probability probability probability probability probability parameters parameters unit unit unit unit unit unit unit unit recognition method method approach approach approach approach approach approach point point point image image image image image image image image single processing local local local local local local local local local local local local local local local local local local local local local local local local local optimal optimal optimal optimal optimal optimal optimal form form form shows shows shows shows shows shows shows shows shows shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple gaussian gaussian visual visual visual paper examples small net work work task task methods methods methods methods methods methods step points points points points points points points points points points field field field field field field field process process process level current problems problems problems problems problems problems random random similar representation architecture architecture architecture architecture show show show show equation equation equation equation section section rule rule rule images images images images images general general speech real states theory gradient gradient gradient gradient gradient gradient gradient note activity activity activity activity activity activity activity activity activity activity activity activity threshold computation solution research defined defined defined sequence sequence sequence constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard computer terms terms distance distance distance left left left left direction direction direction temporal motion motion motion motion motion motion motion press press continuous continuous abstract applied applied find computational convergence convergence convergence convergence convergence convergence convergence properties properties references due due ieee ieee important propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation context introduction hand hand hand hand hand hand estimation estimation estimation estimation variance parallel parallel cost cost cost cost cost tion difference difference spatial rules rules rules rules rules rules rules rules representations previous cases type required long represent represent represent represent represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations equations equations equations equations equations markov markov markov markov fact fact techniques region length correct correct correct correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities forward minimum minimum minimum minimum multi multi sum sum sum sum eq times regions factor made global global global filter original original samples represented represented represented true application define location location location location location location determined posterior posterior posterior posterior posterior posterior posterior posterior connected discrete discrete brain mit mit comparison update update update update update update update update update update update update update descent descent descent descent descent descent nets nets modeling morgan institute represents represents scheme scheme addition addition sequences ai considered cambridge cambridge equivalent estimates estimates estimates estimates limit determine efficient requires choice choice choice significant significant vision vision vision vision give derived conditional conditional bounds velocity velocity types types finally iteration iteration iteration iteration discussion discussion denote denote denote denote denote fast assumption corresponds corresponds corresponds stable surface supported role journal makes noisy kaufmann probabilistic typically needed needed hopfield hopfield reduced account functional functional functional functional functional functional jordan technology ratio iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations filters normalized magnitude magnitude frame frame minimize minimize produced produced light light denotes denotes denotes architectures architectures discussed improve resolution resolution advantage property takes typical identical side side quadratic hierarchical sense inference array array array cognitive cognitive recently sufficient compare yields yields yields correspond converge converge converge converge rl sparse symmetric symmetric grid interval interval improvement grant lead suggests correctly locally demonstrate flow minimal central differences faster faster faster constrained integration assuming minimizing minimizing minimizing exist derivatives scene scene minima derive derive derive derive written written perception optical solving generating generating plot label label mathematical dept recall slightly slightly belief belief belief angle angle springer versus extracted extracted extracted review depending depending depending stages interpretation interpretation operations updated labels approximated activities activities similarly similarly suggested suggested converges converges converges converges converges converges updates updates updates updates updates updates updates updates updates updates calculation slow performing measurements measurements combining iterative interpolation interpolation intermediate transactions transactions existing usa contour contour contour contour contour contour contour contour contour contour contour contour sciences specifically neighbors neighbors discussions regular hmms hmms differ differ differ differ maximal efficiently schemes schemes schemes schemes schemes plots reached reached traditional traditional traditional traditional traditional traditional traditional traditional traditional traditional verlag interested neuroscience generative generative generative cue cue cue sampled relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation dayan backward minimizes minimizes ill ill reach reach reach reach subsequent neighboring neighboring neighboring neighboring neighboring neighboring neighboring neighboring acknowledgments updating updating kalman kalman replaced integral issues preliminary hall rise successive combine combine authors reliable maximizing analogous analogous analogous contours measurement plausible editor man illustrate equally quantities obvious expressions pyramidal massachusetts slowly ground derivation guaranteed guaranteed arise mathematics ion calculations cybernetics qualitative improvements freeman dark orders orders orders introducing posed posed variant calculating proven extensions enables comments globally sort labeling labeling labeling labeling labeling labeling labeling labeling guarantee guarantee guarantee unity plays wrong wrong significance overcome overcome intelligent mark reasoning prentice ambiguity ambiguity ambiguity guarantees evident propagated propagated propagated propagated lawrence refers refers refers messages propagate propagate summarize dense dense dense markovian encouraging distinction propagating propagating propagating propagating propagating weiss weiss weiss weiss solely streams avoids translated translated ization bounding denoting interacting adelson multiscale pearl pearl pearl distinguished gilbert minor likewise ation ation normalizing normalizing rewrite mini gauss manuscript rabiner stimulating lation prefer mrf insufficient hop hop hop hop interpolated interpolated interpreting interpreting interpreting interpreting marr juang interpolating colleagues inspection sions communicate rel rel essence aperture transmit transmit propagates dof dof dof dof dof dof dof dof refine refine relax tenenbaum mum ver alization mrfs beliefs beliefs beliefs beliefs beliefs beliefs psyche posteriors calculus calculus calculus calculus finkel convexity convexity hwang constantly notational prototypical prototypical mart mart mart identities arrived arrived arrived arrived theme zucker dates formalize sajda sor sor sor sor sor sor sor owi fundamentals timal propagations hildreth hildreth rosenfeld rosenfeld rosenfeld acute tude differen gelb willsky willsky interpo vanishingly hummel revision pays construc seidel luettgen allan arthur unfor iiv tunately magni 
#@Weiss_Y,
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#*network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set networks output output output output number number number number system system results results results results results results results results results results results results results results performance performance performance performance performance performance performance performance performance based based based based based based based weights weights linear shown shown shown shown shown systems parameters noise noise weight neurons pattern pattern pattern pattern pattern pattern pattern point point point point image image image image image image image processing processing processing processing local local local neuron neuron test patterns analysis analysis analysis form form shows shows simple simple simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual feature methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field process process cell cell cell cell cell cell cell cell cell cell cell random high high response response response similar similar similar architecture architecture show show show show line rule images images images images images images parameter real real real real real average experiments experiments experiments experiments experiments experiments activity result university threshold threshold threshold threshold variables computation computation research research research research research defined defined defined defined defined found found found target dynamics dynamics initial terms terms distance distance distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic science science presented presented presented present phase phase phase phase low frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal machine machine sets maximum maximum maximum maximum maximum maximum range range range range range position basis abstract applied properties references ieee ieee ieee context introduction hand behavior stimulus stimulus stimulus stimulus stimulus effect effect parallel parallel change change energy difference spatial spatial spatial spatial spatial spatial spatial chosen higher higher part multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good long long long long long long tree tree make fact region proposed correlation length length correct observed observed scale simulations simulations simulations simulations simulations tasks simulation simulation human human human computed respect respect sum elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements regions regions means made made made orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation applications applications applications study filter filter filter filter original relative represented compared application series receptive active active determined experimental experimental related related constraints cortical cortical brain power steps comparison contrast contrast connection connection connection fields support dependent proceedings proceedings institute department represents represents represents represents represents represents represents represents represents responses responses responses addition addition maps computing computing computing directly curve curve curve additional additional additional additional additional design stimuli stimuli stimuli stimuli effects effects detection detection detection detection efficient approximate speed vision vision vision vision increase increase condition randomly randomly randomly randomly developed levels area path path path evidence evidence nature depends constraint constraint biological measured measured increases increases group tested tested tested tested fast limited limited assumption excitatory actions circuits finding short common common assumed shape supported role role role role eds journal journal journal journal ability ability hypothesis degree fit pairs smaller account functional functional functional functional ratio ratio ratio york increasing increasing segmentation consistent consistent trials trials mode mode filters filters filters filters filters filters filters pre pre inhibition inhibition inhibition magnitude combined run added added added added added added added neuronal improved population recent property separate element element element element element element typical reported reported lateral lateral apply inference array cognitive recently compare subjects subjects calculated axis axis axis axis axis axis axis smooth studies studies studies trans trans trans background background background background positions positions chain chain chain chain chain chain chain chain chain chain separation separation separation separation separation separation separation separation separation channels organization improvement increased horizontal horizontal horizontal occur deviation deviation deviation derivative locally boundary strength strength conclusion interactions interactions interactions differences propose propose strong strong strong mechanisms integration integration integration characteristics intelligence intelligence plane decrease decrease relationship scene connectivity connectivity connectivity connectivity identification program acknowledgements appears edges perception primary plot mathematical modeled missing sensitivity sensitivity averaging angle angle angle angle angle angle angle angle adding frequencies extraction extraction extraction extraction extraction extraction extraction national national extracted expressed review transform open open open open open open open open open open open open open open showed modulation modulation activities suggested allowed discrimination spectrum reduces closed closed closed closed closed closed closed closed closed closed closed closed closed closed closed closed generation initially foundation koch transactions transactions transactions coupling coupling kernels perceptual perceptual perceptual perceptual usa usa contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour contour inter inter sciences sciences sciences determines plotted automatic coupled coupled coupled coupled coupled coupled coupled coupled coupled coupled successfully texture columns columns computationally included wij identify oscillatory post post post orthogonal orthogonal orthogonal orthogonal orthogonal excitation showing neuroscience neuroscience neuroscience symmetry lie oscillations oscillations oscillations physiological physiological physiological physiological physiological physiological physiological hold gray gray gray gray play highest highest binding binding binding binding binding binding thresholds cat attempt consisted consisted illustrates preferred extract extract extract extract neighboring intrinsic intrinsic oriented oriented oriented oriented oriented oriented oriented remain remain oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators association association oscillator oscillator oscillator existence existence office fundamental phases contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours examined examined saliency saliency saliency saliency trace thought shapes pyramidal detected percentage ground agreement agreement orientations biology capabilities rapid immediately monkey mathematics gradually patches patches annual cybernetics incomplete qualitative qualitative fourth freeman freeman freeman freeman pathways pure consistency offset embedded conducted lattice psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical share recordings detecting ture modulated modulated extracting synchrony parent parent qualitatively curvature curvature singer singer coherence findings findings findings deviations wang wang synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization globally aligned aligned aligned aligned aligned aligned aligned aligned identifying gabor gabor angular angular angular narrow narrow circular circular homogeneous naval jones interconnected suppression extending communications cellular anatomical anatomical significance stronger chains chains chains primate fan striate striate striate striate striate striate monotonically monotonically affected salient salient salient salient salient salient salient salient salient salient salient salient salient salient salient salient salient salient synchronous responsible arrays arrays enhanced weakly iteratively accounts monkeys facilitate reproduce deg deg deg deg cerebral cerebral stimulated passing passing ignore interestingly baldi baldi receiving automated ics consecutive discharge dramatically neurophysiology ent ent emergent revealed nelson nelson nelson comparative spaced spaced simulating evoked insights intra adelson adelson synchronized synchronized synchronized synchronized synchronized synchronized synchronized academy academy responding gilbert gilbert gilbert pop pop places reciprocal meir meir bursting bursting bursting bursting bursting ase mcdonnell families hilbert inhibit observers spacing horizontally intracortical intracortical lying governing confined confined closure closure closure closure enter enter promise zones satellite tan tan newsome zone behaving plenum das lund lund lund lund pew contributing nents attentive quadrature ito ito ele bair pyramids synchronize synchronize synchronize synchronize synchronize synchronize mediate postulated neurology picks philadelphia epsps wii facilitation facilitation earliest finkel finkel finkel salience salience salience salience salience salience salience salience salience salience salience salience salience salience laminar steerable steerable steerable steerable steerable steerable steerable katz rings perceptually perceptually pennsylvania superficial axial axial axial axial axial axial zucker zucker somers somers somers grayscale cheng breakdown alert masking viii peters ermentrout ermentrout ermentrout ermentrout ermentrout kopell kopell kopell kopell kopell kopell sagi sagi sagi sagi neurological julesz julesz julesz julesz julesz julesz julesz julesz julesz facilitated suddenly stringent rockland rockland whitaker preattentive preattentive westheimer 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space space weights weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case order order shown shown shown shown values values values values values values values values values parameters parameters parameters parameters parameters noise noise noise noise noise neurons neurons neurons neurons neurons neurons unit distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition method method method method method method method method method method method approach approach pattern pattern pattern pattern pattern pattern pattern single processing processing large large large large large local local neuron neuron neuron test test test test test patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis class inputs inputs algorithms algorithms simple simple simple simple visual visual visual visual visual visual examples examples examples small small small size size feature feature net net work task task task methods methods methods fig fig fig cells cells cells cells field field field field field field features features classification classification classification level level level trained cell cell cell cell cell cell cell structure problems problems high high high high high high high response similar similar similar representation representation representation architecture architecture architecture architecture show fixed fixed fixed fixed fixed line line line line generalization generalization parameter average obtained obtained obtained obtained note experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university threshold computation computation independent defined defined defined found found dynamics constant standard computer connections synaptic science left left left left presented presented present present present present activation activation activation low low nodes maximum range components outputs sample sample sample sample sample sample sample sample sample sample abstract applied applied back back find find find find computational analog properties properties references due due due procedure procedure important decision decision decision propagation introduction complex hand generated parallel parallel search energy energy difference difference complexity complexity spatial lower signals signals signals higher higher part part part part center previous cases cortex cortex good long conditions distributed distributed expected expected expected make make fact fact fact region region region correlation correlation correlation correlation correlation correct observed forward forward ing total multi multi multi performed performed performed elements elements elements elements elements means means means dimension orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global global study study filter obtain obtain obtain obtain obtain obtain negative samples represented represented compared application application cross receptive receptive receptive receptive receptive define define define define location location location location location location perform active determined determined goal distributions discrete discrete discrete larger fields train train selection selection selection selection selection selection report implementation consists consists consists consists consists consists difficult layers layers layers design stage stage effects full full significant free free free speed vision vision vision basic produce developed levels criterion criterion criterion types types lines lines lines lines lines lines path path provided selected inhibitory depends achieved group fast fast limited limited close complete excitatory amount supported require main pixel pixel pixel pixel pixel pixel pixel including typically typically account account interesting testing projection projection operation language leads details expert early magnitude description neuronal improved discussed resolution resolution advantage advantage advantage takes takes typical typical apply side pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels array relevant sufficient varying compare conventional conventional conventional conventional approximately volume tuning correspond correspond definition locations separation modified modified grid grid grid grid grid grid grant constructed lead concept concept concept concept feed feed clusters clusters clusters white hardware hardware pass segment interactions interactions clear performs performs constrained taking presence presence physics physics physics physics physics physics largest largest largest characteristics start selective selective selective selective selective selective selective selective selective selective selective selective selective iii iii iii connectivity connectivity identification identification denoted denoted areas areas construct winner tuned angle adding applying events events events events events events events events events events events events events events events events events events events events events events events events events events events events events events events events events events events quality quality choosing depending depending stages squares transform transform transform transform transform transform open operations labels fraction centered centered sizes allowed allowed dashed reduces event event event event event roughly purpose calculate assigned assigned foundation david existing recognize determines determines automatic automatic activated activated activated activated activated candidate holds phys phys phys characterized major selecting middle identified efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency maximal identify identify post post post tend characteristic characteristic composed summary strongly allowing allowing lie highest highest leading leading thresholds consisted neighboring neighboring receive remain selectivity selectivity layered layered requirements circuitry limitations fashion ideas school rest detectors detectors detectors naturally naturally equally thought noted detector detector detector detector detector detector detector detector separated extent wta wta wta defines devices ment developing distinguish orientations orientations orientations orientations orientations orientations convolution fairly adjacent majority tool straight straight straight straight straight straight constructing choices mation cut acknowledgement describing calculations res depicted fluctuations fourth percent percent evaluating collected led dark fed leave leave lattice lattice lattice lattice lattice lattice lattice lattice orders detecting passed employ employ employ incorporated dots reliability semi inherent conclude conclude segmented physiol implements implements cor contribute aligned identifying identifying identifying identifying identifying identifying proportion labeling acm acts bin bin grey proceed eliminated dealing iiii tools replacing check transforms neurobiology neurobiology responsible carry generalizes infor reset corre studying encountered regard realization lengths belongs scan scan scan scan israel israel ballard horn horn horn horn horn properly draw extends hart lett lett empty consecutive basically wiesel isotropic quasi trigger chapter chapter hubel auxiliary auxiliary auxiliary auxiliary reflected shaded shaded duda dominated elementary picked pos refinement responding 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error results results results results results results results results results results results information information problem problem problem problem problem problem problem problem problem models models performance performance based based based based based based based based based based linear linear linear case case case case vector vector vector order shown shown shown shown shown shown systems systems probability parameters weight weight weight distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method approach pattern point point single single single single single control control control control control control control control control control control control control control control large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test test analysis analysis class optimal form form shows shows simple simple simple paper paper paper paper paper paper paper paper small small small small small small small small small small size size size size size size size size size feature feature feature feature feature feature net work task methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods classification classification classification classification classification classification classification classification classification process level level level level level level problems random high high memory memory memory similar similar similar similar similar similar show section section fixed fixed fixed vectors general general real real real real average average average average average average average average average experiments experiments experiments experiments result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold solution solution independent independent independent independent independent independent independent independent independent independent log log found found target constant table table table table table table table table table table table table estimate computer computer computer terms terms terms distance connections present low sets sets maximum maximum range range range range range sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied applied applied applied applied applied applied applied applied applied applied find computational properties references due due due due ieee ieee ieee ieee procedure adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision introduction statistical dynamic generated generated generated variance tion change variable variable variable assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier chosen chosen chosen chosen higher higher higher previous bound required multiple multiple good good good long conditions conditions conditions conditions conditions expected expected expected markov techniques techniques techniques techniques proposed length correct probabilities observed errors simulations resulting resulting ing total total total simulation computed sum sum sum called times times regions regions factor factor factor factor factor factor factor potential dimension made applications original vol vol vol relative relative relative relative specific samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples true true compared application desired desired desired desired desired provide provide rates rates rates rates rates rates rates rates proc proc determined goal goal goal goal related constraints constraints discrete discrete approaches approaches approaches comparison comparison larger larger larger larger larger connection connection train train source source source source source source source source source source source selection loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss technique technique consists individual individual individual represents difficult difficult difficult difficult bias bias bias bias bias bias bias bias bias bias bias bias delay delay delay scheme scheme scheme scheme considered equivalent experiment experiment experiment directly directly directly directly solutions estimates estimates estimates estimates estimates estimates design transition effects bit capacity determine full full requires requires requires requires requires choice significant significant significant significant significant world world speed increase con con produce produce produce derived derived derived weighted weighted controller controller types types nature nature depends sampling simply simply simply measured normal normal normal normal normal normal normal normal group group stable proof short short nearest nearest nearest generate end fit typically smaller smaller smaller smaller combination combination combination combination combination combination account testing increasing increasing mechanism trials trials trials trials trials trials trials trials trials uniform uniform uniform uniform uniform uniform leads squared representing call call call pre direct making normalized normalized normalized magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude combined produced produced produced choose choose choose choose choose added added added added sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources predict advantage takes typical typical typical typical practical apply apply introduced period period period engineering sufficient sufficient sufficient previously previously conventional works tions solve trans sparse sparse interval increased increased exists exists lead occur occur suggests trial wide alternative alternative alternative correctly width boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary column setting conclusion starting starting critical critical critical critical critical greater greater greater greater neighbor neighbor depend depend measures accurate accurate accurate accurate accurate accurate peak peak peak peak labeled turn start exist targets targets groups denoted appears pro produces solving solving generating plot describes transitions distinct dept modeled modeled confidence confidence confidence confidence confidence confidence metric metric implement averaging averaging infinite electrical easy consisting applying applying events events quality quality quality quality quality implies choosing choosing correlated correlated communication variation detailed showed sizes sizes sizes partial earlier earlier reduces neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood event roughly boundaries boundaries boundaries boundaries closed calculate sufficiently sufficiently euclidean classified classified degrees combinations combinations combinations combinations combinations combinations combinations combinations inter weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting plotted 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analyze analyze extremely obvious assumes freedom freedom precise mapped ith ith store consist consist consist arbitrarily submitted chaotic synthetic years brown brown brown brown brown indicating indicating indicating indicating band analyzed analytic analytic analytic analytic analytic tractable processed processed tive closer preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing day ran immediately beginning recording bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth meaning raw empirically pseudo pseudo effort orders orders orders orders orders orders orders orders orders orders orders detecting remove remove treated calculating exhibits monotonic resource incorporating unbiased unbiased unbiased unbiased unbiased specifies traces traces traces calls calls cor classifying uncorrelated uncorrelated identifying assign dynamically dynamically dynamically dynamically eliminate arrival arrival arrival arrival arrival arrival arrival lost lost lost lost lost lost lost lost lost communications allocation allocation significance minutes ranges accepted accepted occurred biased biased observing carry wilson days hours hours moments service service service service service service service service meaningful heavy introduces ranging periods equals negligible decide decide guarantees guarantees dependency buffer buffer buffer buffer buffer buffer buffer colorado colorado chooses dif dif dif tic deg april creating arrive interestingly interestingly assigns empty dense dramatically outperforms logarithm users users users users solves solves accept accept accept accept accept accept accept accept sig ent ber diverse utilize par acceptable acceptable acceptable decomposed classifies conservative conservative conservative conservative reject ary queue queue queue summarizes packets packets packets packets packets packets packets packets packets packets packets packets packets 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#*learning learning learning learning input input input input input input input input data data data data data data data data data function function function function time time time time time time time time time set set set set set set set set set set set training training training training training training training training training training training training training training training training algorithm algorithm algorithm number number number number number number number number number number system system system system error error error state state state state state results results results results results results results results results results results results results information information information information problem problem performance performance performance performance performance performance performance performance performance performance performance based based space space space space space space space case case case vector shown systems systems systems values probability parameters functions method method method method approach approach approach approach approach single single single single large large large large large large large large large rate test test test test test test test test inputs inputs inputs inputs inputs inputs inputs form form algorithms algorithms simple simple simple simple paper paper paper paper examples examples examples examples small small small small size size size size feature feature feature feature feature feature work work work work task task methods field features features features features features features features classification process trained trained trained random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar show show section section section section section section section section fixed general general general general general generalization generalization term term term note experiments experiments experiments experiments experiments experiments experiments experiments university computation research research defined defined found found target target target target table table table table table table table standard computer computer computer computer computer computer terms terms terms science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented machine machine machine machine machine machine object sets basis abstract back properties references positive positive procedure procedure procedure adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision hand behavior effect effect effect effect dynamic dynamic dynamic parallel parallel cost cost cost tion change difference complexity lower rules measure learned learned learned learned part previous cases cases cases required required required good long long long long long tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree make make make errors errors classes regression sum sum times times times times optimization made made made applications applications applications applications applications applications study negative negative negative original artificial specific specific specific specific specific application application application application application application provide compute compute objects objects objects objects objects objects objects rates proc determined experimental experimental related equal equal accuracy accuracy comparison comparison comparison comparison selection report report words words words words words department loss loss loss loss implementation implementation final final scheme addition addition graph graph graph graph graph considered domain domain equivalent directly design top top conference determine efficient efficient efficient requires significant significant approximate statistics free free speed speed con clustering levels criterion criterion criterion area types types finally depends depends measured measured measured discussion normal technical group group tested tested predictions predictions predictions predictions predictions predictions predictions predictions predictions short short short short short short short short short short short short short short short short short short short short short short short journal end end ability instance future future future including including typically typically needed technology mlp block block block block block block block block block block block programming testing significantly significantly significantly special special special special empirical language language language squared details call call call call call call call call numbers pre making international depth frame combined produced choose run run run run predict predict predict predict predict predict improved discussed improve improve improve improve improve improve directions recent exact advantage advantage typical typical typical reported reported strategy subject trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees subset relevant relevant relevant relevant varying approximately tuning axis axis match match address address modified improvement improvement storage storage entire entire lead studied studied predicted predicted predicted predicted predicted predicted correctly hybrid loop loop runs runs runs runs runs critical critical place greater greater segment central accurate accurate accurate designed clear faster faster suggest largest demonstrated demonstrated intelligence labeled variety decrease manner identification program program program program program program program program program program program program program program program program program program program program program program program program program program program program force question explicit appears pro pro derive produces longer describes tuned tuned distinct dept pruning pruning explicitly explicitly applying events predictive predictive predictive predictive predictive predictive springer blocks blocks blocks extraction cycles focus review detailed fraction showed sizes sizes allowed spaces purpose purpose purpose purpose purpose purpose false false false false false false false false false false false construction advantages advantages david degrees recorded existing existing includes thesis inter discuss discuss specifically holds tests straightforward efficiency efficiency efficiency computationally computationally included included identify literature build efficiently characteristic traditional traditional verlag heuristic success split return running running criteria list write minimizes predictor automatically automatically automatically subsequent operating operating extract software software software simpler create collection singh singh singh singh varied put detail limitations accurately examine examine examine examine combine combine decisions comparable workshop statistically statistically examined examined examined induction smallest act trace trace analyze predicting predicting predicting predicting predicting predicting equally friedman noted logic store store mixed mixed mixed mixed arbitrarily arbitrarily seconds averages site site site site site site site site site site great ment distinguish distinguish distinguish track improves benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark purposes sites sites sites sites producing forces division incorporate incorporate leaves leaves mation commonly pool pool pool pool pool potentially potentially separately optimize computers raw reflect led relevance conducted incorporated 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informa linked maintaining usage usage usage truncated truncated largely unable shorter pieces encouraging exception classifications profiles ideally tradeoff forcing examining attempted attempted pub cohn cohn cohn cohn cohn summarizes ftp ftp ftp formance management management management management management management file file file file file file file file file allocated allocated allocated allocated allocated allocated allocated allocated allocated allocated allocated boulder concentrate argued argued noting pos pos pos cation worth drawback misclassified discusses discusses bring intensive handled handled handled survey characterizing tom synthesized ongoing nested savings savings savings hundreds puts routines routines routines dropped incorrectly fre returned concerns exclusively inefficient positives ory ory ignores company permanent permanent permanent permanent permanent permanent permanent permanent permanent permanent permanent permanent quick est locality gathered 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#*network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data function function function function figure figure figure time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output number number error error error results results results results results results results results results results results results results results results units units units information information information information information information problem models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based based based based space space weights weights weights weights weights weights weights weights weights weights weights linear linear layer layer layer layer layer layer layer layer vector order order systems systems systems systems values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions distribution distribution distribution method method approach approach approach point processing processing processing large large large test test test test test test test inputs inputs inputs form form simple paper paper paper paper paper paper examples examples examples examples small small small size size net net work work work work task task task task task task task task task task task task task task task task task task task task task methods methods methods step step features current current current current trained trained trained trained trained random similar representation representation architecture architecture architecture architecture architecture architecture architecture show section section section section generalization generalization generalization parameter parameter parameter parameter average average average theory theory gradient obtained obtained obtained obtained obtained obtained term experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional variables variables variables variables variables variables variables variables variables variables variables research independent defined defined defined found found found sequence sequence sequence initial initial initial initial table table table table estimate standard standard standard standard standard terms science prediction prediction prediction prediction prediction presented presented present present present low sets sets sets maximum maximum maximum maximum maximum press press press learn learn learn learn learn position outputs outputs outputs outputs abstract computational likelihood references due due due due due procedure decision introduction hand hand variance variance variance parallel tion tion tion change difference difference measure measure measure measure measure prior representations learned learned chosen chosen chosen part previous previous previous previous previous previous cases type multiple multiple good long conditions represent expected expected expected make make resulting resulting ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total total regression regression computed computed respect respect respect respect multi multi multi multi multi multi multi multi multi multi multi multi sum performed performed performed performed performed performed performed performed called times made applications study knowledge knowledge knowledge knowledge obtain obtain obtain obtain negative artificial relative specific specific specific specific represented compared compared compared compared application application desired desired desired series series series series series series rates experimental experimental related related related related related mit mit comparison larger connection modeling selection selection selection selection selection selection selection selection morgan proceedings proceedings report internal internal internal advances advances advances advances represents represents represents bias bias layers layers layers layers layers layers layers layers considered cambridge experiment directly curve curves san top conference choice significant statistics free free free free free free free world world world speed basic pages pages pages pages increase give give derived derived criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion types types types types types types types types provided selected depends simply measured covariance technical technical technical describe close actions short common shape main main journal journal hypothesis future future future future future future future future future including kaufmann objective combination account account unknown transfer transfer interesting interesting testing significantly significantly ratio ratio ratio special consistent consistent uniform squared squared representing max making bottom idea minimize sources predict predict predict architectures architectures improve improve directions advantage pair separate apply include period period period period period period relevant interest sufficient volume volume volume module module module module module tions yields yields yields evaluation risk risk risk risk risk risk risk risk risk risk risk risk studied deviation deviation deviation deviation feed touretzky touretzky conclusion conclusion conclusion place assumptions depend editors editors editors reward reward reward differences measures moody moody faster constrained mateo suggest propose taking strong cycle cycle california variety question question pro construct index index index index ann dept dept dept remaining remaining text text belief mutual mutual equilibrium yield yield yield choosing choosing national family family family family review depending viewed viewed learner learner learner learner influence influence influence controlled evolution suggested past partial partial additive performing epochs fitting interpolation sufficiently faces transactions inter extension maximize maximize mozer variations absolute partially suitable suitable build build refer allowing allowing superior issue return return return return return return return return return return return return return return return return return return return return return return return lie lie manifold manifold manifold manifold manifold manifold hold hold hold hold hold hold hold hold hold hold built generalize backward giles computes hypotheses hypotheses hypotheses automatically automatically tesauro extend cowan situations minimized explore explore production hanson biases giving ideas ideas mse mse mse decisions maximizing comparable comparable variability variability variability gradients gradients predicting spline ensure adjusted adjusted adjusted adjusted subsets freedom ith defines years years years years costs costs benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark benchmark comparisons shared shared shared shared shared shared shared shared shared shared shared shared shared shared shared forces incorporate bengio bengio bengio bengio bengio bengio bengio bengio separately optimize toronto toronto medical depicted annual annual addressed addressed affine embedded parameterized parameterized parameterized share share share share share share share share share share share share share incorrect price price price price price summarized summarized serve conclude windows returns returns returns returns returns returns returns returns deviations differentiable sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing sharing realized leen sort tation restrict acm ratios concerned discovery discovery systematic alpha alpha alpha alpha alpha alpha alpha alpha days repeat financial financial financial financial financial financial financial financial financial edelman edelman periods washington belongs theoretically inductive omohundro omohundro omohundro santa cam vari market market market market market market market trading trading trading trading trading treat verify yielded anns anns anns anns anns anns tables tables tables presenting stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock diverse year year comparative comparative comparative intrator intrator beta beta beta beta beta beta beta levin levin cessing baluja baluja management management labs ization mitchell mitchell rejected acquired acquired statistic statistic relates represen worth worth worth worth worth worth worth worth worth worth alternatives nonetheless setup universit universit exchange exchange book port learners portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio bridge ble excess excess excess excess january january firstly micro micro micro micro industrial holmdel month pratt pratt pratt capital capital capital economic economic economic economic economic economic economic economic economic economic economic baxter baxter baxter stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks company company company company asset asset asset asset asset cruz thing thing profit concatenated transaction transaction transaction statements february february eighth stationarity montreal montreal montreal montreal montreal benchmarks benchmarks benchmarks linearities preferable preferable extrapolation months months months transferred ables markets macro macro macro macro macro graphically caruana caruana caruana caruana caruana caruana monthly monthly monthly monthly monthly monthly bonds prices retention multitask multitask mercer mercer mercer impressive justify canadian canadian canadian optimiza yoshua buy buy buy buy buy buy buy buy buy buy buy buy spans compound pertone fund discriminability backpropaga restricts distribute seeds congress business business business dates dates parameterize public assets assets assets assets assets assets assets signifi yearly yearly yearly yearly yearly yearly yearly yearly yearly iro iro recherche recherche recherche companies finance informatique informatique informatique quarterly inns backpropagate ques rehfuss rehfuss explanatory explanatory explanatory consumer cantly risks risks risks pending lucky umontreal umontreal deterioration pricing universe sell sell bengioy refenes refenes tabula rasa 
#@Bengio_Y,Ghosn_J,
#t10
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#*network network network network network network network network network network network network network network network model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm output output number system system system system error error state state state state state state state state state results results results units units problem problem problem problem problem models models models hidden performance performance performance based based based based space layer order systems systems systems systems systems values values probability probability unit distribution method approach approach approach pattern pattern single single control control control control control control control control control control control control control control control control control control control control control control control control control control control control control local test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs shows shows shows shows simple simple simple simple paper net net net work work work work work work work work work work task task task task methods step step step process level current current current current current current trained trained structure structure structure structure structure problems high response response architecture architecture show fixed fixed fixed fixed parameter real real real real real real approximation average average states obtained term term term term experiments experiments result result result university university variables research research research independent independent found sequence sequence sequence sequence sequence sequence sequence sequence initial constant constant constant constant constant constant constant constant table table table table table table table table table table table table table estimate estimate standard computer computer science prediction prediction prediction prediction prediction left present present sets sets sets motion motion range range components components components continuous abstract back back find properties likelihood references component due ieee adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision propagation context statistical statistical effect dynamic generated generated cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search search tion energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference variable variable assume assume lower rules measure measure chosen chosen part part part part previous required multiple binary expected expected expected make region proposed errors scale simulations resulting ing ing total total total total simulation simulation simulation simulation human computed computed performed performed performed called times times means means factor factor made natural natural global applications policy policy policy policy policy policy policy artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial relative relative relative relative true compared desired cross compute perform perform determined determined determined goal goal constraints discrete discrete steps comparison update support proceedings report report department loss loss loss loss loss loss internal individual individual individual final exp exp addition sequences sequences sequences sequences sequences sequences considered considered framework framework domain environment environment environment environment environment environment curve additional determine efficient full requires significant approximate estimated basic basic basic validation con con con con produce condition weighted weighted weighted weighted conditional levels velocity controller controller controller controller controller controller controller controller controller controller controller controller actual actual actual actual actual depends depends depends simply achieved measured discussion describe describe arbitrary denote finding short common common effective assumed generate require main eds future future future future degree development noisy including objective objective objective simulated simulated combination combination combination combination combination unknown programming testing significantly york uniform operation operation squared normalized normalized frame combined minimize run description light predict predict predict population recent robust robust reported introduced period period period engineering sufficient highly highly conventional studies converge generalized interval interval interval interval interval interval storage storage entire entire increased grant deviation wide predicted alternative alternative hybrid loop deterministic deterministic half half conclusion central accurate clear learns temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature suggest sound propose turn assuming variety minimizing iii averaged manner identification program program denoted denoted pro produces produces produces produces produces index index index index index index index index index index index index index factors transitions scales consisting interaction interaction integrated integrated predictive predictive predictive predictive predictive predictive predictive formed expectation focus expressed evaluated evaluated evaluate fraction margin past past earlier earlier reasonable measurements normalization intervals intervals roughly purpose add closed transactions transactions transactions transactions avoid expect building building building includes weighting mozer mozer mozer mozer mozer mozer simplicity planning planning planning planning planning planning planning aspects efficiency included mcclelland literature build schemes tend miller miller miller essentially ten capture repeated strongly contained video anderson anderson anderson interested return return return return contribution contribution running physiological follow follow follow follow follow duration involved michael minimizes minimizes minimizes minimizes delayed delayed predictor predictor predictor predictor predictor automatically consisted policies policies policies policies policies policies operating operating software remain remain schedule schedule schedule schedule schedule schedule american varied varied varied mass periodic periodic existence rise reducing examine history project project project mse mse mse scaled decisions decisions decisions decisions decisions maximizing variability variability variability variability variability variability variability variability variability variability variability variability variability encode encode encode encode neu examined hill predicting predicting predicts equally quantities formal panel panel panel assumes assumes detector switching submitted explain devices residual residual indicating indicating ment ment directed costs costs costs costs costs costs costs costs costs costs costs costs costs costs costs costs costs sensors tractable inside inside inside inside perspective tive day day day day day day day day day day day day day worst acknowledgement res nsf fourth collected collected empirically tional conducted parameterized readily detecting execution switch controllers controllers controllers measuring ture monotonic achieves plan damage begins lim cor don sort proportion proportion investigation concerned homogeneous lost air air air air air air air air air minutes minutes minutes minutes minutes minutes minutes minutes adjusting resistance resistance interpret observing observing methodology settings intuitive selects days days days days hours hours reliably combines irregular predictors predictors iteratively paul overview colorado colorado heart stereo consequences bulb bulb schedules schedules bins rich environmental environmental environmental horizon horizon horizon horizon horizon horizon horizon erlbaum considerations splits dividing robert empty empty empty boxes outperforms outperforms maintaining unified unable incorporates outperform exhaustive reaction regularity regularity acceptable preferences preferences preferences ideally hillsdale alter quantized capacitance capacitance home home home home home home home home home home home home home home home publication trends hastie formance wall wall wall gas life regulation regulation regulation regulation regulation searches searches boulder considers considers switched lookup lookup iri indexed responding tively likewise commercial commercial drops exploited september mini status status status status technologies students suggestions triggered triggered triggered architectural architectural lighting 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#@Dodier_R,Mozer_M,Vidmar_L,
#t10
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#*network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure time time time time time time time time time time time time time time time time set set set set set set networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number system system system system system system system system system system system error error error error state state state state state state state state results information information information problem problem problem problem models models models performance performance based based based based based based space space linear vector vector vector vector vector vector vector vector vector order order shown shown systems systems values parameters parameters noise noise noise noise noise noise weight functions functions functions functions unit approach approach approach approach approach approach approach approach approach approach point processing processing rate rate rate rate test analysis matrix matrix matrix matrix matrix matrix matrix optimal inputs form shows shows shows signal signal signal algorithms simple paper paper paper paper paper paper paper small small work task methods fig fig process process process process trained random random random architecture show show equation equation equation equation section fixed vectors speech speech parameter approximation approximation states term term experiments experiments dimensional dimensional university computation solution target dynamics dynamics initial table table table table estimate estimate terms terms terms prediction direction presented presented presented present phase phase components basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied applied back convergence references ieee positive introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation variance recurrent difference complexity assume assume assume measure measure prior part required multiple good represent equations equations equations equations equations equations correct correct observed observed observed observed observed observed errors errors errors errors simulations simulations simulations computed respect called elements elements means dimension natural natural study knowledge filter filter filter filter filter filter vol artificial true true application desired series series define compute rates rates posterior gain approaches approaches approaches comparison train selection proceedings proceedings department consists consists difficult addition considered considered considered considered framework framework framework cambridge cambridge computing computing equivalent environment directly additional estimates estimates estimates estimates estimates trajectory trajectory conference conference conference determine full approximate approximate free free estimated estimated estimated estimated estimated give processes discussion covariance covariance normal inverse rbf rbf rbf rbf rbf rbf rbf implemented assumed assumed including pairs pairs pairs pairs pairs underlying underlying underlying underlying underlying underlying underlying combination account dynamical dynamical unknown coefficients interesting interesting testing york leads squared call call call call call call call call call call call call making window window window international denotes denotes discussed pair reported apply moving moving moving period period identical recently recently relevant engineering interest interest interest interest interest interest highly highly varying conventional observations observations observations observations diagonal diagonal diagonal evaluation positions modified risk risk risk risk lead studied extended extended extended trial trial derivative derivative derivative matrices matrices setting flow assumptions trajectories differences practice radial radial radial derivatives derivatives derivatives manner manner identification force denoted denoted index index sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential generating simultaneously linearly easy consisting consisting consisting applying select squares variation past expansion tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking filtering filtering transactions formulation formulation inter weighting weighting weighting batch batch discuss black black black black black black black black black black reason straightforward identified extra suitable driven driven delta delta poggio identify build essentially prob allowing bar bar simplified principles consisted software modelling modelling presents simpler parametric updating kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman put put put put put put put put put put environments involving hessian recursive recursive recursive hall behaviour behaviour behaviour tech hill measurement trace subsets quantities algo taylor freedom freedom expressions explain formula formula trivial derivation correction london closer widely style day day definite addressed pseudo incorporated calculating price price price price price price price price price price price price price price price price price price price popular acoustics credit instantaneous instantaneous instantaneous cumulative picture picture ear fix rithm systematic implications optimally nonparametric days days days date published prentice financial financial financial financial financial financial financial forecasting viewing eng cam trading trading sequentially sequentially sequentially truncated recursively propagating icassp ekf ekf ekf ekf ekf ekf ekf ekf england options options options options options options options options options options options jacobian jacobian publication community community community ocr option option option option option option option option option option option option option option option option option option option option option esti normalised normalised coming walk walk lems portfolio portfolio lowe european house december december hull hull hull bond rating arrives economic implied implied implied asset asset asset asset asset neutral niranjan niranjan niranjan niranjan niranjan niranjan niranjan niranjan niranjan niranjan est mcgraw nonstationary nonstationary february cox tracked eta rela markets markets markets markets markets markets lifetime macro prices prices prices prices prices prices prices prices prices prices prices formants yij univariate niques trust nonlin volatility volatility volatility volatility volatility volatility readers unfamiliar innovation contracts contracts contracts contracts contracts contracts contracts flamework cial iee iee mates minimisation currency react finance finance finance shalom shalom thrown facilitating strike strike strike strike strike strike strike traded lln lln lln ature nonlocal adelaide reestimate neurocontrol hessians feldkamp feldkamp pricing pricing pricing pricing pricing puskorius puskorius upto ality wisdom 
#@Niranjan_M,
#t10
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#*network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training output number number number number number number number number number error error error error results results results results units units units units units units units units information information information information information information problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based weights weights weights linear linear linear linear linear linear linear layer case order order order order order shown systems systems systems values probability parameters parameters parameters parameters parameters parameters parameters weight functions distribution method method single single single processing processing control control control control control control control control control control control control test test test test test test test test test test test test patterns analysis analysis analysis analysis analysis optimal shows shows simple simple simple simple simple simple simple simple paper paper paper examples examples small small size size net work task task methods methods methods methods methods methods methods step step step step step step step step step step step step step step step step step step step step step step step step step step points features features features classification classification classification classification level trained trained trained cell random random random similar line general generalization generalization parameter parameter parameter parameter parameter real real real average average average theory gradient term term note experiments university university threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation research log log standard terms terms prediction prediction frequency machine machine sets sets sets maximum maximum press press continuous sample abstract applied applied properties references due due positive positive positive procedure procedure procedure procedure procedure important important introduction complex complex complex complex complex complex complex complex complex complex complex complex complex statistical statistical statistical statistical statistical statistical statistical statistical statistical effect effect effect effect difference complexity complexity variable measure chosen chosen chosen cases cases cases multiple good good good good binary binary binary binary binary binary binary tree tree tree tree tree tree tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian make fact techniques techniques techniques techniques techniques scale scale minimum ing ing ing tasks total total regression regression regression regression regression regression regression regression regression regression regression regression regression regression sum sum performed performed times times factor potential potential made applications applications study study study study negative original artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial artificial samples true true true true true true compared compared application cross cross cross cross series provide perform related related related related equal power mit mit accuracy comparison comparison comparison comparison fields modeling modeling modeling modeling modeling selection report implementation version version technique technique individual individual individual individual advances advances difficult final bias bias considered framework framework cambridge cambridge curve effects effects effects effects full full full full full full full full full full full full full full full full full choice pages pages validation validation validation validation validation give con derived derived derived weighted randomly levels criterion criterion area types selected selected selected selected selected evidence evidence evidence evidence achieved achieved achieved discussion fast complete complete complete predictions predictions predictions predictions predictions predictions predictions predictions predictions common common effective effective effective effective effective main main ability ability ability degree degree including including including fit fit underlying reduced interesting testing consistent consistent squared numbers pre supervised early early early early early improved improved population recent correlations separate reported reported practical practical introduced subject subject subject subject subject subject quadratic trees trees trees trees trees trees trees engineering engineering interest sufficient compare subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects works smooth studies studies studies evaluation generalized generalized generalized improvement improvement improvement risk risk risk entire increased horizontal suggests touretzky touretzky column column demonstrate demonstrate half starting starting reduce conclusions conclusions editors editors interactions interactions interactions interactions interactions interactions differences differences measures bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes designed practice weak suggest strong strong strong reduction reduction reduction regularization regularization regularization regularization regularization regularization relationship identification question question ways mathematical dept dept modeled modeled pruning missing missing missing remaining slightly interaction predictive predictive quality select select select select john choosing independently independently review detailed evaluated operations restricted labels lee lee completely partition partial smoothing smoothing additive additive additive additive fitting fitting fitting penalty penalty penalty penalty penalty calculate avoid expect figures priori inter inter inter inter illustrated automatic prove partially tests major simplicity selecting identified letter included included included included included committee successful mackay mackay mackay mackay mackay comparing fine repeated contained contained interpreted stopping stopping stopping superior superior comp providing board predictor predictor predictor automatically consisted acknowledgments software tesauro tesauro body poor poor overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting essential essential difficulty varied lippmann lippmann dotted preliminary hall giving giving history applicable relationships relationships relationships relationships relationships relationships relationships relationships relationships relationships reliable complicated tanh naturally plausible predicting predicting spline spline spline equally perfect rank rank friedman logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic logistic taylor taylor nervous mixed utility years years years years percentage indicating site site site site site site site site site stop pairwise band band band band analyzed unstable answer worse worse worse worse starts london reasons comparisons comparisons comparisons purposes purposes sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites sites day day constructing division division ran controls controls controls controls controls controls probable ridge ridge ridge ridge ridge ridge ridge optimize lowest conjugate explained apparent considerably percent percent percent relevance bootstrap bootstrap bootstrap bootstrap flexible flexible flexible flexible flexible flexible flexible flexible flexible flexible flexible conducted lack detecting frequently gen prevent prevent age age age age age age age age age age age age age age age age age age unbiased findings patients median median diagnosis diagnosis contribute consistently ordinary ordinary identifying leen leen controlling controlling controlling null null null null null null null null null null discover discover discover discover discover outcome outcome reaching eliminated fits dealing chance breiman breiman breiman breiman breiman held chemical chemical determination resulted transforms transforms transforms methodology guide optimally date tap analyses started mance predictors predictors predictors perfor decide pruned pruned infinity mel mel mel dif omitted omitted indicator indicator cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer bagging bagging bagging bagging bagging bagging bagging canada canada canada canada grants stopped stopped stopped fold fold balanced vari stone fitted fitted fitted fitted fitted appeared leaving roc usage slight goodman goodman goodman revealed revealed tibshirani tibshirani comparative personal reports possibilities hastie hastie chapman life carefully met plate plate plate plate individually retain statistic records records records records funded outcomes outcomes outcomes outcomes tively west west minor examination hodgkin cavity worked clinical justified impractical breast ave ave skin puts eral dom shrinkage affecting affecting affecting medicine rare rare rare rare rare rare seattle compensation agency agency agency agency agency frequent consumption consumption consumption spirit binomial firm ranged categorical trend tical indicators tenth penalizes replication replication replication aic aic ated aggregate aggregate aggregate hood linearities linearities linearities linearities linearities ard ard ard survival preventing collecting iris rela avg avg virtue lifetime sixth biomedical biomedical complications week traditionally traditionally devel statis package superiority ranked ting shrink belmont workers british british british complexities resampled rosen rosen rosen lacking nserc overfit overfit pierre beat beat bag unimportant bypass beer tony olshen likeli cre wadsworth freq freq freq freq articles coarser michie michie grained males males stepwise stepwise stepwise stepwise stepwise stepwise stepwise stepwise checking replications replications replications replications reg dates wyatt wyatt markedly signifi spiegelhalter spiegelhalter regressions regressions terminating ported possessing guessing odds odds intent bert bert bert bert reporting reporting timation grace grace grace grace includ oral oral lucas alc alc columbia columbia columbia wine vancouver vancouver vancouver vancouver ological ellis joel pendleton drew inadequacy parisons ascertained 
#@Band_P,Bert_J,Grace_J,Plate_T,
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input input data function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks training training training training training algorithm number number number number number number number number number number number system system system system system system system system system system error error state state state state state state state results results results results results results information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance based based based based based based weights linear linear linear linear linear linear linear case case case shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems values values values probability probability probability parameters parameters distribution method method pattern pattern pattern pattern pattern point point processing processing control control control control control control control control large large large large local local rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns optimal optimal optimal optimal optimal optimal optimal form form algorithms algorithms paper paper paper examples small feature feature feature feature feature feature feature feature feature work methods methods methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells features features features features features process current current current trained trained trained cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell problems problems random random random random high high similar representation representation representation show show show show equation equation fixed fixed fixed line general real approximation average average average states states theory gradient gradient obtained term note note note experiments university solution solution solution solution independent independent found found computer distance distance distance science left left presented presented present present low low frequency temporal temporal temporal machine machine sets sets learn components basis sample sample abstract applied back find find find likelihood references component stochastic stochastic due ieee ieee ieee important important decision decision decision action action action action action action complex effect effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic cost tion tion difference difference difference difference assume learned learned chosen chosen previous cases multiple good long represent expected make make fact techniques probabilities probabilities scale simulations simulations minimum minimum minimum resulting total simulation called times means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor made policy policy policy policy policy policy policy policy policy policy knowledge original vol artificial relative relative compared compute rates rates rates rates rates rates rates perform related mit mit comparison larger update update descent descent department technique consists advances advances graph considered framework cambridge equivalent environment curve curve additional solutions solutions solutions curves curves curves estimates estimates estimates estimates transition transition limit efficient requires choice choice approximate approximate approximate free free free free free free free free free free free free free free free free free free free estimated estimated con channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel weighted randomly developed area area area area provided provided provided processes processes nature depends depends constraint constraint constraint constraint constraint constraint constraint constraint simply actions actions finding amount short effective effective effective future future future future makes including objective objective objective simulated smaller hopfield technology technology block programming programming programming programming programming programming programming programming programming programming programming uniform uniform uniform uniform empirical empirical empirical empirical empirical leads leads squared squared call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call numbers max max pre making early minimize minimize minimize choose choose predict improve recent recent recent advantage advantage pair pair separate separate takes reported reported practical practical introduced strategy strategy array array array array array array highly compare compare approximately approximately solve solve studies rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl trans address separation channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels sensitive sensitive increased exists occur wide move deterministic occurs generally generally conclusion operator depend depend differences sutton sutton sutton exponential exponential asymptotic asymptotic learns learns learns learns largest largest demonstrated demonstrated intelligence labeled assuming variety variety minimizing start start introduce program configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration base suppose suppose longer transitions modeled modeled sensitivity simultaneously simultaneously simultaneously infinite infinite expectation decreases depending communication communication viewed solved evaluated evaluate updated showed approximations approximations approximations approximations centered forms forms static similarly diagram barto barto barto barto spaces event event event event event event event event event event roughly roughly purpose boundaries sufficiently symbol assigned assigned assigned assigned assigned assigned assigned assigned assigned assigned transactions transactions existing existing figures figures formulation assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment sciences maximize variations importance computationally divided divided divided divided literature literature literature plots plots compact compact notice graphs graphs heuristic heuristic heuristic heuristic superior strategies duration duration list bar bar highest highest ill ill policies policies policies policies policies policies policies policies tesauro tesauro presents presents presents minimized explore unlike powerful create singh singh singh singh singh singh varied varied game issues possibility decisions decisions decisions maximizing smallest smallest smallest act naturally naturally adapt traffic traffic traffic traffic traffic configurations configurations configurations illustrate ensure separated mapped improving arbitrarily percentage trivial comparisons spatially rapid rapid directional directional broad worst commonly scientific scientific separately bandwidth bandwidth bandwidth qualitative radius fluctuations explained apparent reflect leave formulated formulated rep http partitioning poisson poisson aim resource resource phone chose sophisticated neuro neuro simultaneous simultaneous simultaneous calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls cumulative cumulative consistently bellman lab ear www optimality assign assign assign restrict restrict appropriately ordering mobile mobile mobile partitions partitions arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arrival arranged cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular cellular allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation ments minutes minutes minutes minutes serves nearby exploit exploit methodology disjoint responsible arrays service service service service service interference interference interference combines zhang zhang zhang zhang zhang zhang entry regarded colorado colorado colorado demonstration scheduling scheduling scheduling approximators discounted creating creating arrive horizon partitioned partitioned tsitsiklis tsitsiklis dietterich dietterich valuable approximator approximator approximator approximator approximator market market executed assigns assigns bertsekas bertsekas bertsekas bertsekas bertsekas bertsekas bertsekas bertsekas bertsekas bertsekas speaking sequentially usage usage outperform discount discount discount discount job job formulate formulate medium ical big big tor backgammon mutually blocking blocking blocking blocking blocking blocking blocking blocking approxi crosses boulder careful win win locking happen minor sta bradtke bradtke bill bill intensive info stores payoff payoff payoff demand demand continued impractical stochastically ongoing ongoing ongoing ongoing ongoing ongoing ongoing ongoing telephone telephone telephone termination termination dropped dropped cally returned returned returned trol admission admission arrives arrives arrives arrives screen html elevator elevator accounting adapts profit profit terminates terminates terminates nominal nominal nominal nominal nominal nominal nominal nominal tra shop shop jan durations durations inform blocked blocked blocked blocked blocked blocked blocked violated ming objectives mai violate infeasible notions accepting accepting whilst resentation availability availability availability albeit undesirable uniformity uniformity superiority favorable favorable terminated satinder mate fur belmont belmont occupied ously numbered numbered numbered numbered numbered numbered numbered previ temporary serving serving serving requests neighbour wishes disconnected allocate allocate allocate nonlin extractor successes del triggers arrivals mceliece mceliece ditional departure departure departure departure departure departure crites crites reuse reuse reuse reuse reuse reuse reuse reuse reuse reuse packing packing packing packing packing dropping dropping athena athena borrowed borrowed borrowed borrowed borrowed borrowed borrowed borrowed borrowed borrowed borrowed customers insignificant lambda discounting textbook textbook crease elapsed permanently eat numeric hnear commu rations caption imize imize busy munication lots unused centralized lids competitors competitors dynami probabihty fic configu handed handed freed freed baveja uncontrollable exercised vols tsitsildis nore 
#@Bertsekas_D,Singh_S,
#t10
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#*network network network network network network network network network neural neural neural neural neural neural neural neural input data data data data data data function function function function function figure figure figure figure figure time time time time set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system system error error state results results results results results results results results results results results results results results results results information information problem problem performance performance based based based based based based based based based based based based based space weights linear case case order order order order order order order order shown shown values values values method pattern pattern single processing processing processing processing large large large test test test test test test patterns patterns analysis analysis analysis analysis analysis class class class class class shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms small methods methods methods methods methods cells step step step step step step step step step step step step step step step step step step step step step step step step step step step step features classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process process process level current current current current trained trained high high high high high similar section section section section section fixed fixed generalization real real average average average average obtained obtained obtained obtained obtained obtained note dimensional result university university university university research table table table table table table table table table standard standard standard computer computer science prediction presented low machine sets sets range press components basis basis basis basis basis outputs outputs outputs sample sample abstract references component component component component due ieee procedure procedure procedure procedure procedure important decision decision decision decision decision introduction statistical statistical statistical statistical statistical statistical statistical statistical cost cost cost cost cost cost cost cost cost cost classifier classifier classifier measure higher higher part previous cases cases type multiple represent techniques techniques correlation correct correct observed errors forward scale total human human human multi multi multi multi performed called times times times times means means means potential dimension made study obtain obtain relative samples samples samples samples samples samples samples samples samples compared compared compared compared application provide provide provide provide provide perform experimental goal related related steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison connection selection selection proceedings implementation implementation implementation version technique technique technique consists consists kernel kernel difficult final addition addition considered solutions solutions estimates stage detection detection detection detection detection detection detection detection detection detection detection detection detection determine classifiers requires requires choice significant significant significant significant statistics statistics statistics world estimated pages increase increase validation validation channel clustering developed developed developed developed types types provided finally selected nature depends sampling achieved achieved achieved achieved measured measured discussion discussion normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal describe fast rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf amount common effective effective effective implemented implemented supported journal journal development development development development development pairs pairs smaller reduced reduced mlp significantly significantly leads principal principal principal principal pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre pre direct making making making making experts experts experts experts expert expert expert expert expert early run run improved improved improve improve pair separate ensemble ensemble ensemble ensemble typical typical reported reported introduced array recently relevant relevant engineering engineering highly calculated pca achieve achieve definition evaluation evaluation evaluation locations locations locations separation improvement improvement improvement entire increased grant intensity lead lead concept scaling occur occur deviation wide demonstrate demonstrate runs runs half half minimal greater reduce reduce accurate accurate designed designed performs presence reduction reduction intelligence radial radial radial radial radial program program acknowledgements reference pro optical mathematical dept dept changing sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity category averaging electrical electrical involves slightly spectral spectral consisting develop applying correlated variation evaluated controlled soft discrimination discrimination discrimination discrimination spectrum normalization combining penalty initially classified kernels kernels kernels kernels kernels kernels kernels perceptrons inter discuss specifically coupled variations tests selecting selecting identified effectively included literature reached excitation excitation excitation excitation excitation excitation excitation excitation quickly quickly repeated repeated induced success interpreted stopping superior board wave consisted illustrates software presents presents american american layered collection collection association ideal reliable reliable maximizing variability variability reading reading adjusted adjusted adjusted algo algo panel logistic logistic explored initialized initialized initialized multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate detected improving established established percentage percentage indicating site analyzed processed processed sections sites sites forces potentially medical medical qualitative nsf addressed varies greatly evaluating substantially substantially capability readily frequently reliability reliability reliability compares maintain logical fiber decreased deviations median median median converged diagnosis diagnosis diagnosis diagnosis diagnosis trade initialization representative spectra spectra spectra spectra spectra spectra spectra spectra spectra spectra labeling labeling extensive rithm imaging difficulties mail simplify simplify simplify simplify contract fail optic spurious utilized patient patient patient patient patient patient patient washington lengths consequences belongs dif treatment ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles ensembles mlps mlps cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer cancer probe probe probe specificity specificity specificity specificity specificity specificity specificity specificity specificity specificity specificity specificity specificity specificity wolpert wolpert subsequently adopted automated automated automated limitation outlined sequentially discriminate discriminate discriminate emission emission emission drop unable unable gold outperform misclassification misclassification failed corrected clas lesion care rithms management management mitchell intra afosr acquired acquired disease meta cation hansen hansen misclassified misclassified misclassified misclassified applicability tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue tissue intensive article examination differentiating differentiating differentiating demonstrating clinical clinical clinical clinical clinical moderate satisfactory satisfactory ferent breast austin austin austin austin ave ave ave ave ave calibration calibration focuses concern val diagnostic diagnostic wavelength wavelength laser laser modalities modalities ultimate screen cur quantitatively quantitatively vivo vivo vivo vivo vivo pooling pooling cess compromise lar stacked texas texas texas texas ini rent enabling enabling enabling col col routine constituent constituent constituent constituent constituent constituent constituent constituent appli discrepancy ece ece columnar columnar columnar columnar columnar columnar abnormal abnormal hands hands hands hands hands biomedical biomedical pooled ther wright concurrently concurrently ecs fur missed analyzer consensus initializing comprise med med med med med smear smear smear smear smear smear smear smear smear smear highlights healthy healthy agnostic duced diode articles spreads spreads spreads turner turner turner turner turner ware congress biochemical biochemical quired morphological simi ade richards richards richards richards richards grade grade portable pap pap pap pap pap pap pap pap pap pap pap pap pap pap labor bethesda sil sil sil sil sil sil sil sil sil bibliography screening screening screening screening screening screening screening screening screening wavelengths wavelengths wavelengths smeared probes mahadevan alleviate salamon salamon discriminates dye tissues tissues tissues tissues tissues tissues inns ascertain ascertain loadings utexas utexas utexas utexas sifters engr engr erroneously women multitude guidelines invasive discards disastrous speci speci speci misclassifying misclassifying clinically clinically cytology mous 
#@Ghosh_J,Ramanujam_N,Richards-Kortum_R,Tumer_K,
#t10
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function figure 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space space space space space space space weights linear linear case case vector vector shown shown shown shown shown probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight functions functions unit unit unit unit unit method method method method method approach approach approach approach approach approach approach single single large local local local local local local local local local local local local local local local local local local local local local local local local analysis analysis class matrix matrix matrix matrix matrix optimal form form shows shows shows shows gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper small small small size methods step step points points points points points points field level current trained random random high similar similar architecture architecture architecture architecture show show section fixed general generalization generalization generalization generalization generalization generalization parameter parameter parameter real real approximation theory obtained experiments result variables variables computation computation computation computation computation log log log defined initial table table table table estimate distance distance distance science science science science science science science science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction direction direction map map map present low sets sets sets sets sets maximum maximum learn learn learn learn learn learn learn learn basis basis basis basis basis basis outputs sample sample sample sample abstract computational likelihood references due due due ieee adaptive adaptive adaptive adaptive adaptive adaptive adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation estimation statistical statistical generated generated generated generated variance variance variance cost spatial spatial spatial spatial spatial spatial spatial assume measure prior prior prior prior prior learned learned learned learned learned learned learned previous cases required good bayesian expected fact region region region region region region region proposed correlation observed simulations simulation respect sum regions regions regions regions regions regions regions regions regions regions mapping mapping mapping mapping mapping means made made natural global global global global global global global global applications applications applications em em obtain obtain negative original samples true true true true true true true true true cross compute compute location location perform perform posterior posterior approaches accuracy accuracy accuracy accuracy accuracy comparison larger support train train selection proceedings proceedings consists joint joint joint difficult exp exp exp exp ai computing equivalent equivalent equivalent hinton estimates estimates estimates design conference upper significant significant statistics world estimated estimated validation validation validation validation give derived weighted randomly conditional conditional levels levels levels levels lines lines evidence constraint achieved discussion discussion covariance transformation close close assumption assumption assumption assumption assumption complete complete surface predictions rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf nearest nearest nearest common effective assumed generate generate including objective simulated simulated simulated simulated simulated simulated simulated simulated simulated smaller needed account account unknown unknown jordan jordan jordan jordan jordan technology significantly york consistent structures leads squared squared squared squared squared squared max making normalized normalized normalized normalized bottom experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert expert expert expert expert expert decay combined discussed improve improve improve improve resolution advantage separate separate introduced identical identical identical identical hierarchical hierarchical hierarchical hierarchical sense subset subset subset interest varying conventional approximately approximately match achieve sparse sparse sparse address mixtures mixtures mixtures mixtures mixtures mixtures locations locations generalized generalized generalized improvement improvement entire entire parts lead locally width width width width width setting demonstrate critical reduce conclusions neighbor neighbor accurate clear performs exponential exponential practice practice learns learns learns sound hard solid solid proportional regularization regularization regularization regularization regularization radial radial radial radial radial radial assuming assuming assuming minimizing minimizing relationship relationship reference written estimating laboratory label distinct distinct missing physical physical physical involves remaining applying expectation competition focus dependence dependence stationary stationary stationary stationary correlated correlated correlated correlated correlated correlated squares viewed interpretation interpretation evaluated showed showed centers decomposition soft soft soft soft partition partition partition partition allowed normalization fitting fitting boundaries boundaries interpolation interpolation interpolation interpolation interpolation valid valid valid construction norm norm norm norm kohonen box coordinate coordinate formulation weighting weighting weighting weighting sciences plotted automatic discuss priors priors priors priors priors priors priors priors priors priors neighbors gating gating gating gating gating gating gating gating gating gating gating structural structural simplicity selecting closely divided divided paths poggio poggio mackay mackay capture capture traditional refer compact interpreted quantity absence modular minimizes observable maximization predictor predictor predictor predictor attempt overlapping overlapping jacobs jacobs jacobs jacobs jacobs jacobs modelling extend wiley accurately dotted dotted ml ml ml scalar reducing matches rest rest maximizing maximizing maximizing proved statistically statistically statistically statistically statistically statistically contours contours act formal improving extent motivated separable smoothness smoothness smoothness smoothness smoothness improves improves nowlan comparisons considerable spatially spatially straight widely widely producing precisely precisely division directional located worst commonly ridge localized apparent apparent collected profile profile profile hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme hme affine conducted poorly effort share share partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning summarized hyperparameters prevent achieves unbiased implements softmax softmax globally globally don ordinary ordinary ordinary assign restrict girosi girosi partitions partitions partitions fits convenient adjusting simplify observing fail north north north north effectiveness ylx ylx ylx adequate planar combines ensures loo loo widths evident evident captured spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical thin thin smoothed indicator indicator augmented partitioned alternatively listed listed maximized employs isotropic isotropic isotropic isotropic isotropic isotropic magnetic magnetic magnetic magnetic magnetic magnetic magnetic pointed exception arg flat australia summarizes discontinuity expand plate plate spanned west west west west flight helps resembles rewritten expense australian quadrant grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf east east east east interpolated compete manually interpolating interpolating interpolating interpolating restricting orr orr interpolate lnp lnp lnp lnp lnp lnp south south ance sparseness focusing prominent stationarity stationarity stationarity stationarity stationarity stationarity stationarity formulas spanning extrapolation cons wan wan wan wan wan wan wan locating oil oil 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#@Bone_D,Wan_E,
#t10
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#*network network network learning model model model model neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure time time time time time time time set networks networks networks training training algorithm algorithm algorithm output number number number number number number number number system system system system state state results results results results results units information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem models hidden based based based based space space linear linear layer case case order order order order order order order order shown systems systems systems systems systems systems values values probability probability parameters noise noise noise noise noise noise functions functions functions functions distribution approach approach approach approach approach processing processing processing processing processing processing control local local analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs signal signal signal signal signal gaussian paper paper net net work task task task task process process process current random high high high high high high high high high high high high high memory similar architecture architecture show show show show equation section section section section line general general generalization average average average theory theory theory obtained obtained obtained term term term term term term term term term note university variables variables computation independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent log table table table estimate estimate estimate estimate standard standard computer terms terms science prediction left left left presented presented frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency sets sets motion motion maximum maximum press press press components components components components components components components components components components components components components components components components components nonlinear nonlinear nonlinear outputs outputs outputs abstract find find density properties properties properties likelihood references component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component component stochastic due due due due due due due due ieee ieee ieee positive procedure adaptive adaptive mixture mixture context context introduction hand hand estimation behavior behavior statistical statistical effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect recurrent tion change energy assume lower lower lower signals higher higher higher part part cases cases cases multiple long long long long represent expected make make techniques techniques proposed correlation correlation observed observed observed observed observed scale scale scale scale tasks multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi sum mapping means means factor potential potential applications applications applications em obtain negative negative original original original original original original original original vol artificial artificial true true true true true compared application desired cross cross cross cross cross series series series series series series series provide compute rates rates rates rates rates rates rates perform eye goal distributions distributions brain equal equal equal approaches approaches approaches approaches mit mit mit comparison larger source source source source source source source modeling modeling modeling modeling modeling modeling modeling modeling selection morgan proceedings proceedings report report institute institute department technique individual advances advances advances joint connectionist difficult difficult framework cambridge cambridge cambridge cambridge curve curve additional additional estimates san effects effects detection conference conference upper upper upper upper requires choice significant vision estimated coding developed criterion lines entropy product evidence nature simply discussion normal technical technical describe describe denote transformation stable stable short short short short short short implemented assumed generate eds eds eds journal journal noisy noisy noisy sensory sensory including kaufmann pairs underlying needed unknown coefficients coefficients jordan jordan jordan technology transfer transfer transfer ratio ratio empirical empirical empirical empirical empirical principle leads international international normalized experts experts minimize choose run sources sources sources sources sources sources predict architectures correlations correlations property property property property separate separate element practical apply moving moving include include subject side side sejnowski sejnowski cognitive works tions correspond studies rl separation separation separation separation separation separation separation separation separation separation separation williams williams sensitive sensitive horizontal expression concept studied studied occur suggests alternative touretzky touretzky column column conclusion row greater reduce segment segment segment depend moody moody moody moody moody moody moody moody moody moody moody exponential faster weak propose propose taking strong presence presence reduction demonstrated demonstrated solid assuming ica ica ica ica ica ica ica ica ica ica ica movements movements movements movements groups reference reference reference reference reference reference reference reference reference appears van van longer longer index index generating dept segments segments modeled confidence confidence slightly scales scales scales scales mutual springer competition john extracted dependence review review correlated correlated communication viewed variation transform densities decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition constants diagram diagram barto barto smoothing smoothing smoothing additive measurements expansion expansion expansion intervals filtering filtering filtering transactions transactions box box perceptrons bell bell blind blind blind blind blind blind blind blind sciences discuss maximize mozer mozer absolute absolute characterized major planning regular regular regular regular regular regular regular regular regular regular regular regular regular sensor divided divided divided identify literature orthogonal orthogonal characteristic characteristic traditional verlag interested oscillations oscillations sampled modular wavelet wavelet wavelet ill maximization maximization principles principles overlapping jacobs jacobs intrinsic intrinsic modelling presents optimized dotted dotted preliminary existence existence successive referred referred referred reliable affect statistically fundamental coefficient adapt analyze extremely panel panel panel panel panel panel panel panel taylor observe separated amari amari amari motivated massachusetts residual indicating band band sensors sensors sensors sensors publishers navigation analytic diffusion independence caused briefly comparisons purposes satisfied widely widely products linsker reflects pure embedded orders compares compares price price price price price price price price price price price price price price price price price price price price price price price price price price price price price price price price price price price price price characterize occurrence marginal marginal conclude display redundancy returns returns returns deviations deviations median progress identifying identifying ratios conditioned pick minutes minutes los removing disjoint moments moments eqn eqn performances financial financial financial financial financial financial financial recovered periods equals sides forecasting forecasting forecasting forecasting widrow widrow originally hasselmo yang yang francisco pearlmutter pearlmutter messages splits subsequently market market fitted informa liu liu microstructure outline listed shorter basically basically equivalently axe axe axe smoothly spaced decomposed decomposed decomposed decomposed flat factorial mutually mutually mutually mutually trends trends trends trends trends trends decays graduate dominated intra deconvolution individually depicts associates superposition barlow barlow reveal exchange exchange exchange exchange exchange exchange exchange exchange exchange siam nal jutten jutten september september september september september oregon survey fractal autocorrelation autocorrelation autocorrelation autocorrelation autocorrelation ongoing impulses king usefulness station gram petsche preservation chan wavelets measurable economic totally daily coins iid lags lags dent trend trend indepen facts facts outlier surprise surprise surprise surprise surprise surprise surprise surprise surprise surprise surprise surprise surprise surprise surprise surprise cichocki cichocki sep tens terminology mid decompose applica kong leung transferred fractional fractional fractional decompositions decompositions decompositions decompositions decompositions decompositions decompositions decompositions herault herault markets markets markets markets markets ness ness comon comon comon hong sition parra parra bird prices prices prices prices prices prices prices lasting volatile volatile volatile switzerland switzerland switzerland confirms temporary panels turbulence turbulence canceling singapore zhou zhou dong dong regularly volatility jour news news news foreign foreign foreign foreign foreign foreign foreign foreign foreign foreign economics useless dave dave portland portland decomposing decomposing muller muller comparatively cumulants cumulants cumulants cumulants cumulants cumulants brownian brownian business business borrowed chou chou walks regu arch neuromimetic finance finance finance dem dem dem dem dem tick tick tick tick zurich zurich zurich supervisor unnormalized autocorrelations autocorrelations autocorrelations autocorrelations cancelling redundancies blackwell econometrics catch catch speculative erratic decompo arate microscope fect lax mislead 
#@Moody_J,Wu_L,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system system system system error state state state state state state state state state state state state state state state state state state results results results results results results results results results results results results results results information information information problem problem models performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based space space space space space space space space space space weights linear linear case case case case case case order shown shown shown systems systems systems systems systems values values values values values values values values values functions functions functions functions functions functions functions functions unit unit method method approach point point point point point point point point point single processing processing processing control control control control control local test optimal optimal optimal shows shows shows shows algorithms algorithms algorithms simple paper paper examples small size size size size net task task methods methods methods methods methods methods step step points points points points points points points points points points process level current cell cell random random high high high memory similar show equation line rule generalization generalization real approximation approximation average average average average average average average average average states states states states states states gradient term note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university computation computation solution solution solution research research research research log initial constant computer distance science science left left map low temporal temporal machine machine machine maximum maximum range press learn position position continuous continuous continuous continuous continuous abstract applied back computational convergence convergence convergence convergence references stochastic important decision decision introduction action action action action action hand hand hand behavior effect dynamic dynamic dynamic dynamic dynamic generated cost cost tion tion tion difference variable variable variable assume assume assume learned learned learned learned higher higher part center previous previous cases cases cases cases required required multiple long represent expected markov techniques techniques region region scale resulting resulting resulting tasks computed sum sum performed performed performed performed performed performed elements means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement dimension global applications study policy policy policy policy em negative true provide perform determined goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal discrete discrete discrete steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps steps larger update update nets nets morgan proceedings report department implementation implementation joint joint final final final scheme maps cambridge domain domain domain domain experiment directly solutions curves transition transition transition trajectory top top top top effects conference efficient significant significant speed speed increase produce coding derived weighted weighted weighted weighted randomly robot levels velocity controller controller provided provided provided processes iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration simply achieved achieved achieved increases describe arbitrary tested fast close close corresponds complete complete stable surface surface surface actions actions actions actions common common assumed generate require square future kaufmann typically pairs needed combination unknown coefficients programming programming programming interesting significantly significantly significantly ratio york trials trials trials trials trials trials trials trials trials empirical empirical mode mode details making stored international bottom bottom early run predict perceptron improved improved discussed improve improve resolution resolution resolution resolution resolution takes element practical practical identical array relevant relevant dimensions dimensions dimensions dimensions dimensions sufficient previously conventional axis axis axis axis axis studies converge achieve sparse positions locations locations grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid improvement improvement entire entire entire parts lead lead studied studied trial trial trial trial trial trial trial touretzky touretzky boundary demonstrate half starting place place conclusions editors editors reward reward reward reward differences accurate clear sutton sutton sutton sutton sutton sutton faster weak taking taking taking taking taking taking taking variety start start start start plane iii iii averaged manner manner pro derive transitions vertical changing explicitly coordinates averaging linearly involves applying applying cycles cycles cycles select national stationary learner learner learner learner learner learner learner learner learner learner learner learner learner restricted updated centers approximated sizes sizes completely completely suggested updates allowed barto barto barto performing performing spaces spaces spaces spaces convex sec sec sec sec sec sec roughly 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faces faces recorded exploration exploration exploration box box box box box box box box box thesis thesis coordinate coordinate formulation formulation weighting mozer mozer domains tests regular regular computationally successful literature schemes schemes online online online online online online fine fine fine fine fine reached quickly graphs strongly moore moore moore moore moore moore moore moore moore moore moore moore moore link link split usual paradigm quantization quantization quantization quantization delayed highest reach reach policies approximating neighboring tesauro tesauro tesauro decreasing explore poor rapidly recursive game issues mdp mdp mdp mdp matches tech project int func hill hill hill hill hill coarse coarse coarse coarse coarse gradients adapt opposite opposite extremely rank academic generates improving phd phd attempts stop piecewise unstable fairly expensive expensive expensive expensive expensive worse worse worse inside straight ran immediately commonly watkins watkins watkins watkins potentially projected calculations calculations calculations mellon improvements improvements varies carnegie cmu car car car car atkeson atkeson atkeson atkeson atkeson atkeson formulated frequently rewards rewards rewards execution passes controllers controllers rely pittsburgh proven extensions kinds age eventually eventually june converged multidimensional multidimensional extreme cumulative cumulative cor consistently college appropriately angular angular pick narrow velocities velocities robotics reaching fits dealing ments promising satisfying attractive intelligent height implications guide adequate corner corner corner corner planar date mance ensures cmac perfor guarantees conjunction hasselmo hasselmo chooses approximators approximators approximators approximators permutation express surprisingly arrive park hypercube hypercube broken approximator approximator escape andrew boxes boxes boxes boxes fellowship failed continuity continuity acting ibm mhz interact graduate concentrate books harder option paradigms paradigms sweeping sweeping sweeping sweeping funded discretization discretization responding simplex simplex simplex simplex simplex simplex simplex simplex simplex simplex simplex simplex simplex simplex gordon gordon gordon gordon dramatic learners learners learners learners learners learners learners learners rarely sorting sorting consuming lation corners corners corners corners corners discontinuous satisfactory satisfactory smoother ave interpolated interpolated interpolated interpolated interpolated interpolated lated albus albus albus prioritized prioritized prioritized prioritized king routines award boyan boyan boyan resolutions resolutions triangles beneficial interpolating triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation triangulation parti grids grids grids grids grids grids tells interpolate interpolate interpolate compensated elevator mcgraw scott scott enter successor problematic translate watson backwards mesh mesh kuhn kuhn kuhn kuhn multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear multilinear began datapoints datapoints datapoints datapoints datapoints datapoints datapoints rein sparc occasionally reminiscent encourage encourage offline offline offline offline offline backups backups backups backups backups backups backups backups backups backups backups ross ross ross offiine prohibitively vast absorbing initializing initializing associating brains driver niques steep aver travelling cheap shoulder safely raise forcement trim elbow elbow crites crites crites gravity davies davies davies davies davies didn cornell actuator torques byte occupies situated discounting cording initiation assures itera eration inaccuracies gather quantizing knew datapoint thrust thrust interpo interpo greedily forwards vided dlog ooooo spell omission earn hes fare forbes shallower diagonally 
#@Davies_S,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural neural input input input data data function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time set networks networks networks training training training algorithm output output output output output output output output output output output output system system system system system system system system system system system system system error error error error error error state state state state state state state state state state state state state information information information information problem problem problem problem models models performance performance performance performance performance performance based based based based based based based based based space space space space space space space space space space space weights linear linear linear linear linear linear linear case case case case vector order order shown shown systems systems systems systems systems parameters parameters functions functions functions point processing processing processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control local local local local local local matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows algorithms algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian examples size work task task task task task task task task task task task task task task task task task task methods fig fig points field current current current trained trained trained trained problems high memory memory architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show equation equation equation equation fixed line general generalization real real real real theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term note experiments experiments activity dimensional dimensional result computation computation computation computation computation solution solution research independent target target target dynamics dynamics dynamics dynamics constant estimate prediction prediction prediction direction direction activation temporal temporal temporal machine motion motion range press press press learn learn position position basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied find references stochastic ieee important adaptive introduction action action dynamic dynamic dynamic parallel cost cost cost cost cost search tion tion tion difference difference difference difference variable signals learned learned learned higher higher center center required good long expected expected proposed proposed proposed length simulations ing tasks tasks tasks tasks simulation simulation simulation human respect multi performed times elements reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor potential dimension dimension made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback global study study policy policy represented desired desired provide define goal related related constraints motor motor motor motor motor discrete discrete brain brain brain brain mit mit mit connection train implementation implementation implementation version version internal advances advances represents difficult difficult exp scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme framework framework cambridge view curves curves estimates trajectory efficient efficient efficient efficient requires requires world basic pages pages pages pages con con condition condition derived controller controller controller controller controller controller controller controller controller controller controller controller controller controller provided selected constraint biological discussion arbitrary tested tested limited limited limited short effective implemented assumed generate square end makes reduced dynamical functional functional functional unknown programming york mechanism trials trials trials trials principle call numbers max max max max max max max direct direct direct direct direct direct direct direct making bottom experts supervised supervised early minimize minimize predict predict recent movement lateral subject quadratic hierarchical sense cognitive relevant highly teacher solve match differential achieve address symmetric grid grid amplitude amplitude constructed parts parts trial alternative hybrid touretzky touretzky boundary editors editors editors editors sigmoid sigmoid sutton sutton sutton faster faster practice learns propose integration integration demonstrated plane force force attractor areas areas perception solving sequential generating plot explicitly simultaneously physical dimensionality transformations angle integrated applying stages estimator solved updated centers soft soft soft soft sizes diagram partial calculation barto barto barto barto barto slow convex reduces closed intermediate transactions figures figures usa weighting determines automatic mozer mozer phys successfully successfully society society maximal paths successful build schemes schemes anderson neuroscience neuroscience neuroscience follow backward correspondence maximization load law law law law law law law law command command command command command transformed preliminary ml project comparable comparable cover momentum trace man adjusted art generates motivated cart cart cart cart cart cart cos critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic derivation track track track improves cascade multiplication laboratories actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor involve cybernetics cybernetics behaviors consistency transient flexible capability atkeson atkeson schematic ture maximizes monotonic adjust enables enables replace chose pole pole pole pole pole pole pole bellman room oxford japan japan dealing mail cerebellum cerebellum cerebellum cerebellum cerebellum imposed height balance kawato kawato kawato kawato transforms roles slice monkeys facilitate hasselmo hasselmo cerebral pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum davis summarize balancing balancing cam avoiding mechanical ics ure ure accept discount latency torque torque torque torque tor verified verified eligibility esti bring atr atr computa differentiating resembles bridge doya doya doya doya doya doya doya doya doya doya doya doya doya doya stochastically emotion curse hamilton tip practically schaal schaal architec swing swing swing swing swing swing swing swing swing swing swing swing swing trol mcnaughton cooperation isolation predictable transpose drastically upright upright upright iti evolves crl crl crl quick edition cho cho appro houk houk houk ganglia ganglia ganglia ganglia ganglia ganglia ganglia suzuki generaliza medial publishing demanding collision virtue repeats visuomotor albeit confirms mate rolls chi gun gun hjb basal basal basal basal basal basal basal dynam inconsistency kyoto kyoto abstracts abstracts jacobi neuronlike soraku soraku adams iwl doubled assure seika seika hemisphere swinging mri ridges rand hikaridai hikaridai voluntary biggest monitors pergamon kenji allocates bryson bryson ventional frontiers furukawa procedural prepare lexp correc hikosaka hikosaka mator pioneering 
#@Doya_K,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set training algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models performance performance based space space space space space space space space case case case shown shown systems systems values values values values probability probability probability probability parameters parameters parameters parameters functions unit distribution distribution distribution method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern point point control control control control control control control control control control control control control control large large local local local local local local local local local local local local local local local local local class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows algorithms algorithms algorithms simple simple paper paper paper paper paper paper size feature feature feature work task methods methods step step step step features process process process process process process process process process process process process process process process process process process process process process process process process process process process process process process process process level current current structure structure problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random random response similar equation equation section section fixed general general general general general general generalization parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states states states states states states states theory obtained obtained note experiments result result result result university variables computation computation computation computation computation computation solution solution solution research research research independent defined defined defined defined defined defined sequence sequence dynamics dynamics initial computer computer terms terms terms terms node node science science science presented presented map phase phase phase phase machine machine machine press press learn position components basis abstract applied computational computational computational convergence references component component component component component component ieee ieee positive important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision introduction action action action action action action action action action action action action action action action action action action action action action action action action dynamic dynamic dynamic dynamic dynamic dynamic dynamic search search difference variable prior prior prior learned higher part part part center theorem required good conditions tree tree tree bayesian bayesian bayesian bayesian expected expected expected expected expected equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make make fact proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed forward scale scale scale finite resulting ing ing simulation computed computed computed computed respect respect multi multi multi multi multi sum called times times means means reinforcement reinforcement optimization potential dimension policy policy policy policy policy policy policy policy policy policy policy policy original represented true true compared provide compute compute compute compute proc perform perform perform goal goal goal distributions distributions distributions distributions gain gain gain gain gain gain discrete power approaches approaches mit steps steps steps contrast update update update support modeling selection report report department version version individual represents scheme graph considered considered computing computing domain equivalent view view solutions estimates design transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition effects effects conference efficient approximate approximate approximate approximate approximate approximate approximate approximate statistics statistics statistics free basic basic give con con derived levels controller lines path path processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes evidence sampling sampling simply simply achieved discussion discussion discussion discussion discussion discussion technical denote actions actions actions actions actions actions actions actions proof amount short supported theoretical require require makes makes makes makes typically pairs pairs pairs underlying needed account functional unknown unknown unknown unknown programming programming programming programming programming mechanism special special special special special special special empirical principle principle leads details details details direct window international early idea choose choose denotes pair practical strategy strategy include quadratic sense sense sense sense sejnowski sejnowski recently sufficient sufficient sufficient sufficient compare previously approximately approximately approximately approximately approximately approximately yields trans trans trans chain chain chain chain modified grid entire grant constructed exists exists lead concept suggests suggests wide loop starting starting greater greater trajectories depend reward reward reward reward reward reward reward reward reward reward reward reward reward bayes bayes bayes bayes clear performs learns constrained taking taking taking taking largest largest largest largest demonstrated labeled turn exist manner identification denoted acknowledgements explicit suppose suppose suppose suppose suppose appears appears pro pro construct written index index index index index index index index index index index solving transitions transitions ann label pruning explicitly explicitly explicitly infinite infinite interaction shift versus versus yield yield choosing national family expressed stages stages learner learner operations restricted approximations suggested suggested suggested suggested suggested suggested suggested suggested suggested past diagram key reasonable reasonable barto barto barto performing false closed remains calculate foundation exploration exploration exploration exploration exploration figures thesis priori formulation recognize uncertainty uncertainty uncertainty maximize maximize activated determining determining aspects maximal modification computationally effectively paths literature efficiently efficiently schemes schemes miller online summary refer soc soc conf procedures procedures procedures heuristic heuristic heuristic interested stopping stopping superior issue return criteria strategies strategies strategies bar bar michael dayan dayan backward delayed highest highest attempt policies policies policies policies policies policies approximating presents remain experience exponentially issues dual dual dual dual dual mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp rise reducing history ideas school tech terminal terminal decisions root root statistically examined circles math math thought thought ensure subsets aspect quantities obvious greedy noted observe observe academic consist motivated defines massachusetts years asymptotically great turns perspective perspective strictly precisely forces mation controls watkins watkins watkins watkins ion recognized recognized calculations gradually depicted auto auto preceding conjugate evaluating applies led led amounts rewards rewards rewards rewards rewards rewards controllers limiting gen ordered extensions substantial semi semi semi semi semi semi begins calls univ realized trade trade pose bellman bellman bellman bellman bellman indices indices indices indices indices indices indices indices indices indices intractable sort sort optimality assign equivalence equivalence equivalence equivalence equivalence optimizing concerned jones jones jones grows grows proceed proceed proceed extending allocation allocation wrong consideration consideration chains chains proceeds proceeds proceeds replacing determination imposed moment balance biased biased hope removing imply salient salient modifications selects inferior infor elimination repeat repeat sion sion regarded regarded regard bad consequences uni captured captured originally viewing viewing discounted discounted discounted discounted discounted repeatedly horizon horizon horizon horizon horizon horizon horizon horizon route tsitsiklis tsitsiklis captures ignore avoiding avoiding acknowledge andrew andrew arcs arcs constitute shorter achieving asked dec expanding adopt seek amherst amherst perceived recurrence certainty certainty certainty certainty certainty certainty imagine beta beta beta beta beta beta streams summarizes activate uncertain uncertain uncertain uncertain proba flip flip relates increasingly cartesian anal turning happen happen admissible things intensive examination infinitely resolve ate bility twenty locate coin coin coin coin coin concern eral identically settle striking proposes splice resolved trol trol degenerate coins coins invisible appl statist evolves computable ings enters acknowledges sweep nominal nominal tical prominent metastable initiated occasionally notions collecting exploitation exploitation exploitation observes observes topics frozen activating jumps versity bernoulli bernoulli bernoulli ago ecs duff duff duff duff duff duff duff duff duff duff ire stays subclass subclass flips flips heads heads heads heads unrealistic lend sole manageable rameter probing twelfth comment deci forty umass tered deviate cesses pute defects mas flipped flipped returning armed armed armed armed armed armed armed underway prac shalom shalom deemed multistage caution scalars adopts maker maker maker maker maker maker sachusetts macqueen macqueen flavor itseft breadth enjoy truncate sem decom signifying concisely elegance staying entail quest encoun 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model data function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure time time time time time time set set set set set set set set set set set algorithm algorithm algorithm algorithm number number number number number number number system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden hidden hidden based based space space space case case case case case shown shown shown values values values values values values probability probability probability probability probability probability probability probability probability functions point single single single processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large rate rate class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form shows algorithms simple simple paper paper paper size net work work work work work work task step step step step classification process process process current current current current current current cell cell cell problems problems problems problems problems high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar show show show show rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general generalization parameter real states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states theory theory term note note note result result result result result university university university threshold solution defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence table computer computer node science science science science left left direction direction direction direction direction present present low nodes machine machine press press learn learn learn abstract find find find computational convergence convergence convergence convergence references stochastic stochastic procedure adaptive decision decision decision decision decision introduction action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action hand behavior effect effect effect dynamic dynamic cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search change assume assume assume assume assume assume measure representations learned learned learned learned learned learned learned learned learned learned part part previous theorem theorem theorem bound bound bound bound bound bound bound bound bound bound conditions represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree expected expected expected expected expected markov markov markov markov markov make make fact length length length length length probabilities probabilities probabilities observed observed observed observed finite finite finite finite finite finite finite resulting resulting ing ing total total computed means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor feedback feedback feedback policy policy policy policy policy policy policy policy original original original artificial artificial artificial artificial represented represented true application desired provide provide define define proc proc location location goal goal goal goal goal goal related discrete equal equal equal mit contrast support dependent selection morgan report department consists consists consists consists represents represents addition sequences sequences sequences sequences sequences sequences ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai cambridge additional estimates estimates estimates transition transition transition transition transition transition transition transition upper upper significant significant significant free world estimated estimated developed robot robot robot robot robot robot robot robot levels controller controller controller controller controller controller controller path path path path path path path path provided processes processes processes technical technical increases describe describe denote denote denote denote denote denote denote denote fast limited limited limited assumption assumption assumption corresponds corresponds complete stable actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions proof proof proof proof proof short effective effective assumed require main hypothesis hypothesis instance easily makes makes makes sensory sensory sensory sensory including including including kaufmann pairs pairs underlying underlying underlying underlying underlying programming programming interesting significantly special special special mode mode principle call call max direct making depth depth idea combined improved improved improved improved improved improve pair pair pair pair takes movement apply strategy moving include side side sense sense sense subset subset sufficient sufficient sufficient works works yields converge converge rl rl rl rl rl rl rl rl rl address address definition definition observation observation generalized grid grid grid grid interval interval improvement improvement improvement sensitive increased grant constructed studied extended move move move move move loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop loop deterministic deterministic conclusion greater greater reward reward reward reward reward reward reward reward reward reward reward reward accurate learns learns learns taking taking taking taking taking taking taking intelligence intelligence intelligence assuming minimizing start relationship relationship introduce manner identification question reference suppose suppose longer solving laboratory modeled pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning agent agent national focus stationary open open open open open open open open open open open open open open open open open open open open open open open controlled controlled restricted updated fraction fraction similarly similarly converges converges converges converges converges converges converges converges converges partial barto barto barto barto barto barto barto performing expansion intervals closed closed closed closed closed closed closed closed closed closed closed closed closed remains foundation degrees degrees exploration exploration exploration exploration exploration exploration exploration includes includes thesis extension extension prove prove prove uncertainty partially partially partially partially partially partially sensor closely receives receives receives refer conf conf heuristic showing notation notation dayan dayan dayan delayed observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable reach moves moves subsequent subsequent receive explore explore singh singh exponentially environments mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mass history int possibility combine combine reliable root root root root proved analogous induction act illustrate perfect perfect perfect perfect perfect perfect perfect ensure der explored explored explored explored explored explored mixed mixed mixed mixed mixed mixed extent attempts massachusetts massachusetts stop inequality costs costs costs costs costs distinguish sensors sensors sensors sensors track lin lin widely immediately watkins watkins watkins watkins watkins acknowledgement optimize optimize optimize incomplete addressed addressed limits rewards limiting limiting limiting limiting branch reaches prevent kinds decreased focused focused progress converged converged converged converged converged cumulative sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing sensing acts nat impossible grows reaching reaching convenient convenient obtaining observing observing north optimally optimally optimally optimally corner combinatorial combinatorial continue exploring exploring exploring exploring exploring exploring separating appendix appendix encountered pruned pruned pruned pruned pruned pruned pruned pruned pruned pruned regarded regarded regard intended discounted discounted discounted discounted insight reveals arrive ends relies relies relies inductive inductive statement grants receiving mdps mdps mdps andrew indirect minus shorter discount recursively pointed tradeoff amherst amherst england imagine eric constrain visited visited acting intuition exclusive formance management continues execute execute uncertain uncertain uncertain expand carefully emphasize statistic lookup iri million hansen hansen hansen hansen hansen hansen hansen west knowing bradtke bradtke prevents aaai behaves stops stops simplification survey east identically core core core raises south feasibility deciding tan tan cope behaving observes deeper opportunity distinctions intervening 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#*learning learning learning learning learning learning learning learning learning learning learning learning model model model model data data data data data function function function function function function function function function function figure figure time time time time time time time time time time time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number system system error state state state state state state state results results information information information information problem problem problem problem problem problem problem performance based space space space space space space case case case vector order order order shown systems systems values values parameters parameters functions functions functions method approach point point point point control control control control control control control control control control control control control control control local local local rate rate test analysis matrix matrix optimal optimal optimal optimal optimal optimal form form form shows algorithms algorithms algorithms simple work methods methods methods methods methods methods methods methods methods methods methods cells cells cells cells cells process process process process process process process process process process process process current cell cell cell cell cell cell cell cell cell cell problems problems problems problems high similar show equation equation equation equation equation equation equation equation equation equation section section section section section section fixed parameter real real obtained note computation computation solution solution independent defined defined defined initial constant terms low maximum maximum basis nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous sample abstract applied applied applied applied applied find computational convergence properties properties properties references stochastic stochastic stochastic stochastic due adaptive decision decision introduction hand dynamic dynamic variance variance variance variance cost cost cost cost cost cost cost tion theorem theorem theorem theorem theorem cases type type conditions conditions equations markov markov markov markov make fact techniques techniques techniques proposed correct probabilities probabilities probabilities probabilities probabilities observed observed observed observed observed observed observed observed observed observed finite minimum total simulation simulation multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi called times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor feedback applications policy obtain obtain represented application application application application define define discrete discrete discrete discrete discrete comparison larger modeling sequences ai ai computing domain transition transition transition transition transition transition transition transition determine determine full choice give con produce condition condition condition weighted levels levels levels levels area controller controller path product actual processes processes processes processes processes processes processes processes processes processes processes processes processes processes iteration iteration iteration sampling sampling sampling discussion denote denote close close assumption assumed assumed main journal objective objective typically needed needed reduced fully programming special special consistent consistent empirical empirical empirical empirical empirical empirical empirical details numbers iterations pre early early attention minimize choose choose choose choose choose added denotes recent separate takes takes apply introduced introduced include subset sufficient observations calculated calculated converge converge converge differential differential diagonal sparse definition definition chain observation observation observation observation observation observation observation generalized grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid bounded matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices predicted locally locally locally locally boundary generally starting assumptions assumptions assumptions operator reward numerical numerical numerical numerical numerical reduction cycle demonstrated demonstrated minimizing min min relationship identification identification relation pro produces transitions transitions transitions transitions transitions mathematical interaction applying applying springer springer implies expectation expectation expectation expectation expectation extracted expressed stages stages controlled controlled controlled controlled controlled controlled controlled controlled controlled centers centered centered centered sizes suggested converges calculation calculation calculation barto smoothing reduces reduces boundaries penalty interpolation interpolation calculate calculate calculate box kernels kernels thesis contour holds differ plots plots verlag verlag kind prob prob prob heuristic dis hold minimizes neighboring load load decreasing receive presents law law law remain carried singh working stream act coarse coarse possibly ensure der der assumes art switching phd great formula directed directed costs crucial smoothness diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion correction inside arise controls separately angles radius radius reflects consistency consistency consistency calculating differs germany semi shaped converged converged bellman bellman bellman bellman picture guarantee restriction restriction restriction homogeneous homogeneous theories analogy stated grow star repeat repeat respective respective decide von sides uni counting initialize discounted arrive route subsequently inf boxes verify verify approx truncated truncated truncated rigorous discount discount ties formulate axe tween aij streams penalized rejected depicts anal refinement discretization discretization discretization discretization discretization discretization discretization universit bradtke refined holding atr ward corrections gauss lems fat ate discretized discretized ongoing smoother hamilton hamilton finer finer reflecting stay bilinear agency attained trol grids grids grids grids grids grids att att att att att att evolves server server server server server server counted tory sung hysteresis tran posi pay hjb hjb hjb stars stars stars constantly vation tri accelerate jacobi jacobi rtdp 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#@Pareigis_S,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set networks networks training training training training system system system system system system system system system system error state state state state state state state state state state state state state state state state state state state state state state state results results results results information information information information information information information problem problem problem problem problem problem models models performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based based based based space space space space space linear linear linear linear linear linear linear linear linear linear case case case vector vector vector order order order order order shown shown shown shown systems systems systems systems systems systems systems systems functions method method method method method approach approach approach approach approach pattern point single single single processing processing processing processing processing processing processing processing control control control control control control control control large large local analysis matrix matrix optimal optimal optimal optimal optimal optimal shows shows shows shows signal signal algorithms algorithms visual visual visual visual paper paper paper work task task task task task task task task task task task task task task task task task task task task task task task task methods methods methods methods methods step step step step field process process process process process level current current current current structure problems problems problems problems problems problems problems problems problems high high response similar similar equation equation equation equation equation equation section section section section section section section section section section section line vectors vectors general real real real real real real real real approximation average average average states states states theory theory term term note note dimensional dimensional result result university university variables variables variables variables variables computation computation research research research log defined defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial initial initial estimate estimate estimate computer terms science science left presented temporal temporal machine machine press press press press press press learn learn learn learn learn learn learn learn learn learn learn learn position position position position position components basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous abstract applied applied applied find find find find find find convergence references due due ieee procedure procedure important adaptive adaptive context context context context context context introduction action action action action action action action action action action complex complex complex hand hand hand behavior behavior effect dynamic dynamic dynamic dynamic search tion tion tion tion difference difference difference complexity complexity spatial assume measure prior prior prior learned learned learned learned learned learned previous previous previous required required good good good good long long long long long conditions conditions conditions conditions conditions conditions equations make make make fact observed observed observed observed observed forward simulations simulations simulations simulations simulations ing ing ing ing ing ing ing ing tasks tasks tasks tasks tasks tasks simulation human human human human human human human human regression regression regression regression elements mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement optimization optimization optimization feedback global policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge knowledge knowledge knowledge filter obtain artificial artificial artificial represented represented compared application series series proc proc proc proc goal goal goal goal gain discrete discrete discrete approaches approaches mit mit mit mit steps accuracy comparison larger contrast contrast contrast update support morgan morgan morgan proceedings proceedings implementation implementation implementation implementation implementation implementation version version consists internal internal internal advances advances advances advances difficult delay delay graph graph framework cambridge cambridge cambridge computing environment curve additional curves curves curves trajectory trajectory conference conference conference efficient requires requires requires significant significant significant significant significant world world world world speed speed speed speed speed speed vision vision con con condition weighted robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot criterion controller controller actual actual actual actual provided provided provided processes iteration iteration nature depends constraint biological increases arbitrary arbitrary denote tested tested fast limited limited limited close close inverse inverse stable actions actions actions amount amount amount implemented supported require require main eds eds eds eds eds eds ability easily easily noisy kaufmann kaufmann kaufmann needed combination dynamical dynamical unknown transfer programming programming programming programming programming programming significantly significantly significantly special special trials trials trials trials trials trials trials principle principle direct international experts supervised supervised supervised expert expert idea attention run architectures discussed recent advantage robust takes typical typical strategy include quadratic quadratic quadratic quadratic previously teacher teacher teacher approximately approximately approximately subjects tions solve trans observation interval entire entire entire arm arm arm arm arm arm arm arm arm arm studied trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial matrices alternative alternative correctly touretzky touretzky generally setting demonstrate conclusion starting starting critical reward reward reward reward reward differences differences sutton sutton sutton sutton sutton sutton performs moody moody faster learns learns demonstrated intelligence turn variety minimizing exist exist min areas pro pro pro longer index index ways laboratory laboratory linearly infinite involves text text interaction interaction integrated applying predictive predictive predictive predictive extracted extracted extracted extracted extracted focus focus formation squares squares learner learner evaluate controlled controlled restricted fraction forms understanding approximated approximated similarly suggested suggested suggested suggested past past barto barto barto performing delays spaces spaces iterative foundation transactions expect building exploration includes includes thesis formulation color assignment sciences extension illustrated automatic automatic automatic mozer mozer partially characterized planning planning planning planning maximal driven driven included successful successful successful literature comparing situation reached quickly video moore moore showing showing showing showing anderson anderson issue sin running strategies timing comp involved realistic minimizes minimizes giles delayed delayed delayed delayed delayed observable received received subsequent extract extract extract extract approximating approximating acknowledgments cowan employed explore command command command command command command command command powerful singh singh investigate kalman humans humans humans humans hanson hanson association optimized recursive recursive issues lippmann lippmann biases biases ml scalar school tech investigated relationships stream symbolic symbolic complicated complicated complicated momentum man equally ensure singular front explored explored academic message submitted seconds seconds seconds animal years great cart cart cart cart cart cart cart cart stop cos crucial guaranteed explanation lies worse drive tive sys sys easier widely forces directional mation watkins watkins watkins actor actor actor actor actor actor actor ion scientific arises demonstrates cybernetics mellon alignment robustness robustness questions people greatly evaluating carnegie empirically consistency consistency amounts tional tional autonomous car atkeson atkeson atkeson atkeson atkeson item marked formulated reliability commands commands commands execution http calculating pittsburgh extracting extracting extracting extracting extracting cal serve qualitatively qualitatively suited suited achieves plan replace kinds segmented traces traces credit credit pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole acquisition acquisition benefit college analogue accomplished www equivalence japan investigation optimizing turned robotics robotics smith smith dealing numerically accepted overcome analogy city primitive balance balance interpret viewpoint kawato kawato kawato observing reasoning symposium infor reliably reliably started started corre paul surprising surprising overview overview mental mental mental mental mental washington demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration widrow widrow stereo assembly assembly assembly hasselmo hasselmo candidates candidates nonlinearities offers offers offers chooses dif approximators discounted smoothed smoothed smoothed augmented theoretically theoretically properly horizon pendulum pendulum pendulum pendulum pendulum pendulum impact inductive inductive inductive considerations projects subsequently inf inf inf instructions balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing balancing approximator interestingly johnson executed assigns divide skills ics kinematics basically validity benefits torque torque dyna dyna dyna dyna incrementally pointed arg ideally lit perceived solely german german acceleration acceleration classic possibilities certainty demon demon demon assess argue manipulation formance diag tems approxi execute dominated labs elementary regulation regulation host sketch conversely manipulator manipulator covered eligibility finger sam son investigations applicability bradtke bradtke bradtke bradtke refined prevents atr atr differing gorithm picking rarely rarely sponding achievable consuming consuming lation doya doya doya doya doya doya tial ferent ers shot shot shot imple clarity dropped dropped accomplish accomplish accomplish hour kinematic kinematic usefulness neglect incorporation ally schaal schaal schaal schaal schaal schaal schaal schaal schaal extracts substitute automation beneficial concert swing swing swing swing swing swing swing swing swing swing swing cooperation isolation totally coins smc robotic sian upright upright upright upright physically teaching teaching teaching experienced cho poles profit profit profit profit profit profit priming priming priming priming priming priming skill nonstationary focusing manual ini dyer dyer dyer dyer dyer adv mountain replaces replaces spent rein rein rein stabilizing stabilizing stabilizing stabilizing lqr lqr lqr lqr lqr lqr lqr lqr lqr prime prime omit argmin tracked minute italy icann mason ess pursued alexander prohibitively claimed fac gun nakano scratch scratch scratch scratch scratch scratch scratch scratch scratch scratch scratch scratch scratch complexities fulfilled syrup tinuous tinuous overshoot standing mented dynam indistinguishable kyoto densely han opens cameras recep blobs facing equipped stefan stefan interna interna gramming gramming gramming succeeded cate lozano lozano lozano primed primed primed primed primed primed primed primed primed primed steer forcement forcement forcement iden nxn nxn neuronlike gravity soraku downward reformulated quired pump atlanta lastly mated proximate observa reacting investigates pol pol accomplishes gomi gomi strate contaminated georgia gatech gatech hikaridai gan eration pled fulfills scholarship spartan dangerous inaccuracies cer knew dem dem dem demonstrations demonstrations demonstrations quently mcreynolds mcreynolds mcreynolds mcreynolds perez perez brady brady tally anymore conse formu imitation imitation bal sophistication usu dejong dejong bot 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function figure figure figure time time time time time time time time set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number system system system system system system system system system system system system system system system system system system system system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results information information information information information information problem problem problem problem problem models models models models models models models models performance performance performance performance performance performance performance performance performance based based based based based based space space space space space linear linear linear linear linear linear case case case case case case case vector vector order order shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems probability probability probability probability probability parameters noise noise noise weight weight weight distribution distribution distribution distribution method method method approach point point point point single processing processing processing processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control local local local local local local test analysis optimal optimal optimal optimal optimal optimal form form form form algorithms algorithms simple gaussian gaussian paper paper paper small small small size task task task task task methods methods methods methods methods methods fig fig fig fig fig step step step step step step step points points points points points process process process process process level problems problems problems problems random high high memory response similar architecture show equation equation section fixed fixed fixed line line line line vectors real real real real real approximation states states theory theory obtained term term term term term note note experiments dimensional dimensional result result university variables variables computation computation independent defined found found target dynamics dynamics dynamics initial initial initial initial table table estimate standard terms distance distance distance prediction prediction presented presented low low machine machine range range press press learn learn learn learn learn learn learn position position position components basis nonlinear nonlinear nonlinear continuous continuous continuous continuous abstract applied applied computational convergence density density properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee important important adaptive adaptive adaptive adaptive decision introduction action action action action action action action action statistical statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated cost cost cost cost cost cost cost cost cost cost cost search tion variable assume assume assume assume measure prior learned learned learned learned cases long long long represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected equations make fact techniques techniques techniques region region region region region length correct correct correct correct observed forward finite resulting resulting ing ing total total simulation regression regression regression regression regression regression regression regression regression regression computed computed computed computed computed computed respect sum sum eq eq called times elements regions regions regions mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement optimization optimization potential dimension dimension made global global global applications policy policy policy policy policy policy policy policy obtain obtain original true compared application desired desired provide compute compute compute perform active active determined experimental goal goal goal goal goal goal goal goal related discrete approaches steps steps steps steps steps steps update update update update update modeling modeling modeling institute loss kernel kernel advances advances advances advances advances represents represents difficult difficult difficult exp addition maps considered considered additional additional estimates estimates estimates estimates estimates transition transition trajectory trajectory top top top conference significant significant significant significant speed pages con con produce weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted randomly levels levels criterion bounds bounds velocity velocity velocity velocity velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller path product finally iteration iteration discussion covariance normal normal describe fast inverse assumption assumption assumption assumption stable amount amount common common effective assumed generate generate theoretical journal end easily including fit fit simulated simulated functional coefficients programming programming programming programming programming programming programming programming programming programming programming programming programming programming significantly trials trials trials operation operation operation operation operation leads representing details call iterations making stored stored stored stored international bottom early combined minimize minimize run added added improve recent advantage advantage robust takes takes typical movement reported moving subject quadratic recently highly solve smooth smooth yields yields achieve positions grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid improvement improvement risk risk constructed lead concept concept studied occur trial trial trial trial trial trial trial deviation wide predicted locally locally locally locally locally locally locally locally move move move move width width deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic occurs demonstrate runs minimal minimal assumptions assumptions valued valued valued accurate designed sutton sutton sutton sutton faster weak learns sound propose propose taking strong strong assuming assuming minimizing start program force denoted pro construct construct stability mathematical changing changing modeled confidence confidence confidence confidence explicitly physical physical easy easy angle angle angle angle adding applying applying quality choosing depending stages correlated controlled suggested converges updates updates updates allowed barto barto barto spaces spaces fitting intervals penalty penalty interpolation interpolation interpolation interpolation remains foundation query transactions avoid building existing exploration exploration exploration exploration exploration illustrated illustrated uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty planning planning gamma efficiency literature literature literature build build build build situation situation plots reached receives summary summary quickly quickly quickly repeated repeated prob moore moore moore moore moore moore moore moore moore moore anderson interested issue running hold hold bar bar bar absence nips nips nips reach operating operating mixing software presents simpler origin origin origin parametric parametric american production production updating environments association dual dual dual dual dual dual mass mass respond rest rest applicable scaled scaled decisions hill hill trace trace trace concepts man predicts extremely perfect assumes assumes assumes observe explored academic academic improving simplest attempts defines seconds seconds seconds cart cart cart cart cart cart cart cart cart slowly slowly costs trivial crucial derivation failure failure failure failure adapted independence independence worse sys mation controls controls implicit optimize cybernetics mellon considerably considerably carnegie applies cmu atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson treated treated execution execution passes operate controllers controllers summarized pittsburgh fall prevent kinds traces pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole pole naive globally benefit identifying angular angular angular narrow addresses addresses tem flexibility robotics ranges familiar balance viewpoint symposium symposium date infor repeat repeat started started started started started combines sion iteratively moved vertices chooses chooses chooses approximators record record rich ends pendulum exploiting exploiting exploiting exploiting approximator approximator approximator pdf pdf executed lem mind informa maintaining drop outperform benefits dyna suboptimal causing avoided conservative scenario scenario illustration illustration argue management uncertain degraded inverted considers ultimately increasingly increasingly names harder sweeping sweeps gordon gordon gordon bring exploited increments increments september failures aaai aaai wider coming covers covers moderate acquire acquire pdfs discretized discretized discretized stochastically spring inhibited spacing prioritized pictures dropped industrial industrial disturbances devised schaal schaal schaal trol economic safe safe safe safe quick mcgraw mcgraw ready positional restrictive stabilize stabilize stabilize inaccurate catastrophic catastrophic catastrophic cleveland cleveland cleveland lwr lwr huge talk ming dyer dyer dyer multilinear multilinear operated operated assessing incurred lqr lqr lqr lqr exploitation graphically schneider schneider schneider schneider schneider schneider schneider schneider encourage collect cooling experimentation overshoot aggressive aggressive aggressive aggressive aggressive penalties confident completes prevented namic namic narrower safely safely discarding encouraged probing probing probing probing neuronlike regres davies davies davies davies didn dropping dropping abrupt stabilizes setpoints setpoints dur reacting cache cache stably stably eventual radians vide balances jeff invited incurs shalom shalom shalom mcreynolds mcreynolds mcreynolds verse unpredictable caution optimizers inl acquiring interpolates xtx vanilla discretize cached cached ignorance choos disappointing utu incurring 
#@Schneider_J,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number error error error error error error error error state state state state state state state state state state state state state state state state state state state results results results results results results results results results results results problem problem problem problem problem problem problem problem based based based based space weights case case case case vector vector vector shown shown values values values values values values values values values values values values values values probability parameters parameters parameters parameters parameters parameters weight functions distribution distribution distribution distribution distribution method method method point point single single single control control control control large large large rate rate rate rate rate rate analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal form form form shows shows shows shows shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper small small small size size size size size size size size work task methods methods methods step step step step step step step step step step step step step step step step step step step points process structure problems problems random random random random random random random random random high high high high high high memory show show equation equation fixed fixed fixed fixed fixed fixed fixed rule vectors general general general general general general general parameter parameter real states states states states states theory theory gradient obtained obtained obtained obtained obtained term term note note note note result result result result university university computation computation defined found sequence sequence initial initial initial initial initial initial initial initial constant constant constant constant table estimate estimate estimate estimate estimate estimate estimate standard standard computer computer terms science prediction prediction presented presented present present present low low low low frequency temporal temporal temporal temporal temporal machine machine machine range range range range components sample abstract applied find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic introduction complex hand estimation behavior behavior behavior behavior behavior behavior effect effect effect effect effect effect effect effect effect effect effect dynamic variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance change change change change difference difference difference difference lower lower representations chosen chosen chosen higher higher higher part part previous cases cases cases cases good good good long long long long expected expected expected expected equations equations equations equations equations equations equations equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov make make fact correlation length observed observed observed errors forward finite finite finite finite simulations minimum minimum minimum resulting resulting classes classes simulation simulation simulation simulation computed called called called times reinforcement reinforcement reinforcement reinforcement applications knowledge em specific specific specific specific true true true desired provide define compute compute rates rates rates rates rates rates determined brain mit mit steps accuracy accuracy larger larger larger larger larger larger larger larger larger larger larger larger larger update update update update update update update update update support department version technique final bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias bias cambridge cambridge computing computing computing directly curve curve curve curve curve curve curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves estimates estimates estimates estimates transition effects determine determine determine determine determine choice choice choice choice significant approximate speed speed estimated estimated estimated estimated estimated estimated increase produce produce produce weighted weighted weighted weighted lines provided provided provided provided provided evidence evidence evidence nature nature depends depends depends covariance covariance covariance covariance covariance covariance covariance increases describe close close complete stable stable predictions amount short effective effective theoretical main main main square square square square end end hypothesis smaller smaller smaller fully programming programming interesting interesting ratio increasing increasing consistent trials trials trials trials empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical language leads leads leads squared squared details call call numbers iterations making early magnitude combined minimize produced choose choose run predict predict discussed exact exact exact advantage apply apply quadratic cognitive interest interest highly highly calculated calculated axis match studies converge converge converge converge rl rl rl address chain chain chain chain chain symmetric bounded sensitive arm exists lead lead lead lead trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial deviation hybrid generally setting setting runs runs runs runs starting place minimal greater greater greater greater assumptions assumptions conclusions conclusions conclusions conclusions depend depend clear sutton sutton sutton sutton sutton sutton sutton sutton sutton faster faster faster asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic suggest hard largest largest largest largest largest largest largest reduction reduction reduction reduction drawn start min decrease decrease averaged averaged manner denoted digit monte monte monte monte monte derive carlo carlo carlo carlo carlo produces plot plot transitions stability segments segments averaging linearly linearly linearly develop versus decreases yield yield choosing choosing choosing choosing depending updated showed approximations lee forms understanding sizes similarly suggested converges converges converges updates updates updates allowed key reasonable reasonable barto barto slow combining iterative remains remains calculate calculate calculate sufficiently expect thesis eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues sciences determines black straightforward extra differ differ maximal maximal maximal maximal maximal maximal computationally divided delta comparing quickly graphs interested contribution contribution hold quantity quantity dayan dayan dayan dayan dayan dayan dayan realistic providing nips delayed eigenvalue eigenvalue eigenvalue eigenvalue computes hypotheses subsequent software software software schedule singh singh singh singh singh singh singh singh singh exponentially detail estimators preliminary biases scalar successive mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse mse investigated applicable applicable terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal analytically analytically trace trace trace trace trace opposite illustrate greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy assumes precise expressions expressions expressions expressions expressions submitted phd indicating ment developing trivial crucial agreement guaranteed phenomena coded analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical analytical tool tool worse comparisons rapid rapid straight strictly choices choices choices ran desirable controls watkins watkins potentially inversion optimize definite lowest lowest fourth questions questions apparent substantially empirically pure amounts peter rewards calculating calculating calculating popular substantial replace kinds shaped shaped returns returns focused traces trade consistently feasible feasible extensive controlling bin fails stronger minutes chains chains chains chains chains chains chains chains chains chains chains chains replacing nearby nearby intuitive intuitive days analyses combines loo studying surprising ascent evident colorado colorado colorado consequences counter schedules schedules surprisingly repeatedly agree agree agree explains ball bertsekas ence unable outline users deriving tables conjecture causing england var param visited ftp ftp decays boulder challenging eliminating lookup lookup harder conversely eligibility eligibility eligibility eligibility eligibility million million million million apparently reveal places eigen holding holding eters answers gorithm walk walk walk reversal payoff payoff payoff payoff payoff instability converging impulses err accumulate accumulate beneficial fastest inset inset cyclic cyclic ically excessive excessive tails tails tails tails diverge unaffected derivations whilst whilst minimise minimise tailored visits offline intervening intervening terminated offiine satinder confirms confirms duff duff absorbing absorbing absorbing analysed analysed analysed analysed lose tar highlight endpoints minimising lend revealing optimise optimise comment asymptote anonymous modulus modulus graphic amplify shrinks payoffs payoffs trl offs confirmation greedily minimises bsc lids unexplained sively msr answering vmues vmues vmues initiates vmue cheaply caveats caveats runaway baveja illustrations trades conjectures determinants periment ause 
#@Dayan_P,Singh_S,
#t10
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural input data data data data data data data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set networks networks training algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number system system system system system system system system system system system error state state state state results results results results results results results results results results units units information information information information information information information problem problem problem problem problem models models models models models models models models models performance based based based based based weights linear linear linear linear linear linear case case case case case case vector vector order order shown shown shown shown systems systems systems systems values values values values values values values values values values values values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability functions functions functions unit unit method method method method method method method method method approach approach processing rate rate rate rate rate rate test test test test matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal form form signal signal signal signal simple simple simple paper paper paper paper paper paper examples net net work work methods methods methods step step classification process process level current current trained problems problems random random high similar show show equation section fixed parameter parameter parameter real real real real approximation approximation approximation approximation approximation approximation average average average average average states states states theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained note note note result result result university university university variables variables variables variables variables variables variables variables variables variables variables solution research defined found found found sequence sequence sequence sequence sequence initial initial standard standard standard computer terms science science left left left left presented low low low temporal temporal temporal temporal machine machine machine machine sets maximum maximum maximum maximum maximum maximum maximum maximum press press press learn learn learn learn learn continuous continuous continuous continuous continuous continuous abstract applied find find find convergence likelihood references ieee positive positive procedure procedure important important important adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision mixture mixture mixture mixture mixture mixture context introduction introduction complex complex behavior statistical cost cost cost cost cost cost search search tion tion difference difference variable variable variable variable variable representations learned learned learned chosen chosen chosen part part part previous cases cases cases cases cases cases type type good good binary binary represent tree expected expected expected expected expected expected expected expected expected expected expected expected equations equations make make make correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed errors errors errors errors errors forward minimum resulting ing total computed called means means means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor made natural applications em em em negative original vol relative represented compared compared compared compared application series determined distributions power mit steps steps accuracy accuracy update update support modeling institute institute institute loss loss loss loss version consists code advances joint joint joint final final considered considered considered cambridge directly directly additional additional determine efficient full full significant world world world increase give con randomly randomly conditional clustering levels levels types types types types actual provided provided selected iteration iteration iteration simply achieved achieved discussion normal normal complete actions actions predictions effective effective require journal future future future future including objective objective probabilistic needed needed combination interesting york york database database database database database database database database database principle principle operation representing iterations iterations iterations pre making making making making experts expert magnitude run description description description description description predict predict predict predict predict directions pair separate element reported apply subject subject inference sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski previously observations observations observations observations subjects calculated works tions achieve modified observation observation observation observation observation observation observation observation observation improvement risk risk risk risk increased occur occur extended deviation deviation deviation matrices predicted alternative alternative correctly touretzky column column demonstrate half half starting place row row reduce segment valued editors editors differences differences differences accurate sutton sutton sutton sutton peak learns cycle california california question question question acknowledgements longer sequential sequential sequential sequential sequential modeled modeled missing missing missing missing linearly linearly text applying expectation expectation interpretation evaluate updated past reduces penalty penalty calculate assigned assigned assigned foundation advantages classified transactions recorded recorded recorded includes thesis prove uncertainty maximize maximize specifically specifically discussions tests tests tests tests major reason reason efficiency capable society presentation efficiently situation situation situation situation summary road graphs kind repeated repeated induced induced interpreted notation notation dayan dayan absence highest hypotheses leading maximization received tesauro experience experience exponentially varied detail tech rest project investigated fault decisions decisions decisions complicated act adapt predicts perfect improving utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility arbitrarily phd finds years preference preference stop theoretic theoretic theoretic theoretic theoretic theoretic theoretic costs costs trivial trivial slope slope coded coded adapted adapted answer answer processed lin straight berkeley berkeley purposes division choices watkins watkins probable mathematics medical medical medical medical medical arises computers demonstrates cybernetics incomplete robustness questions questions questions questions questions questions questions questions questions questions questions questions questions questions improvements people people empirically orders price howard howard howard howard howard howard howard summarized decreased age age differentiable differentiable diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis diagnosis cor lot benefit ear leen princeton princeton databases concerned unity tem grows royal royal outcome outcome outcome outcome rational chance chance chance adjusting los salk salk north intuitively optimally presentations games date financial sion patient patient male von von bad bad heart heart heart heart heart heart heart heart heart claim foundations ahead jolla matter dempster dempster automated automated automated automated pressure multiplying yielded blood blood depression specification converted converted minus listed rubin misclassification misclassification misclassification accept discount discount discount asked asked suboptimal preferences preferences preferences preferences preferences perceived perceived ical female resting resting compensate compensate life convert convert intra hughes terrence maximally maximally maximally maximally confirmed disease disease disease disease disease disease disease disease disease disease disease disease laird outcomes outcomes outcomes outcomes outcomes outcomes outcomes outcomes outcomes outcomes behave increments answers answers completed worked vice helps handled fiat versa neumann neumann savings subjective subjective reversible supply russell usefulness medicine diagnostic devised subtracted assessment manually tells economic repository contrary reality safe safe company est irvine categorical nominal benign cleveland cleveland cleveland cleveland maxq maxq maxq manual sex sex plenum instant instant instant instant unobserved disorder disorder disorder eta eta utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities biomedical scribed scribed scribed paid paid terry tot tot heckerman heckerman heckerman poral med formalized dev stuart french french quences exercise exercise exercise estima colored pain diseases diseases diseases marcel dekker rectly diction death death death death plete deci timal consis fined torrey pines prin tent defect answered answered answered quicker incom dollars dollars originates mclachlan mclachlan publicly uij awt awt rea mine mine acquiring ques dollar basford basford founda cholesterol magnus magnus creased fourteen nology ellis chichester sweden ciple sult observ hum rag sists mak 
#@Sejnowski_T,Stensmo_M,
#t10
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural input input input input data data data data data data function function function function function function time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system error error error error error error error state state state state state state state state state results results results results results results results results results results results results results results units units units units units units units information information information information hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance based based based based space space space space space weights linear linear linear layer layer layer layer layer layer layer layer layer layer case case order order order order order order order order order shown systems systems systems values values values values values probability noise noise unit approach point point single single single single single single processing processing processing control control control control large large large large large large rate test test test test test test test test optimal optimal optimal optimal shows shows shows shows algorithms simple simple simple simple small net net net work task methods methods step step step step step step step step step points points features features features process level level level level level level level current trained trained trained structure problems random random random random random random random random random high high similar similar representation section fixed line line line line line line line line line line line line line real real real real real real real real real average average average average average states states states obtained obtained term term term term note note note experiments result computation research defined defined defined defined found target initial initial initial initial initial initial initial initial initial initial initial table table table table table table table table table table table table estimate estimate estimate estimate estimate estimate standard computer computer terms terms node node node presented present nodes nodes nodes temporal temporal temporal machine machine machine machine machine range range press press position position position position position position position position position position nonlinear nonlinear abstract applied back back find convergence convergence convergence properties references due due due positive positive procedure procedure procedure adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision propagation introduction action action action action action hand hand statistical statistical dynamic dynamic dynamic generated generated variance variance variance parallel parallel parallel parallel parallel cost search search search search search search search search search search search search search search search difference difference difference measure measure measure representations learned chosen chosen center previous bound cases cases required required required good long long long long represent expected expected expected expected expected expected expected expected expected markov markov make make make make make make make make make make fact fact fact techniques proposed observed simulations simulations resulting resulting resulting resulting resulting ing ing ing tasks tasks tasks total total simulation simulation simulation simulation simulation simulation human human human human human human computed computed computed computed respect multi multi multi multi multi multi performed performed called called times times times times times mapping reinforcement reinforcement reinforcement reinforcement factor factor factor factor factor factor made made applications applications applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy obtain negative original relative relative true compared application application application provide compute location perform related equal equal power approaches mit mit mit steps steps steps steps steps steps steps steps comparison comparison contrast contrast contrast support train nets morgan loss loss loss loss loss loss loss loss loss loss loss loss loss loss implementation implementation implementation technique technique technique technique technique technique consists individual advances advances advances represents connectionist difficult final final delay sequences sequences ai considered cambridge computing domain equivalent equivalent equivalent environment environment additional estimates estimates trajectory efficient full full full full full full full full full requires requires choice significant world world speed speed estimated estimated estimated estimated basic increase give give give give con derived developed levels controller controller controller controller controller controller controller actual actual actual finally selected iteration iteration iteration iteration iteration iteration nature depends sampling sampling sampling achieved measured measured measured measured measured discussion normal normal increases increases arbitrary fast fast close close actions actions actions actions amount amount common effective implemented implemented main main eds eds square end ability ability ability future easily easily easily kaufmann simulated simulated typically typically smaller smaller smaller needed needed needed needed needed reduced technology programming programming programming programming interesting testing significantly significantly significantly ratio ratio ratio ratio ratio head trials trials trials trials trials trials trials trials trials trials trials trials trials trials operation numbers making making making making making depth depth expert expert expert magnitude magnitude magnitude idea produced produced run added added description predict improved improved improved improved improved improved discussed improve improve improve recent robust typical typical typical typical reported reported reported practical side side side recently highly varying previously previously tions yields yields studies converge achieve achieve achieve rl address evaluation positions positions improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement increased grant studied trial trial trial trial trial wide wide alternative alternative alternative move move move move move move move move move move move move move move move move move move move move move move move move move touretzky width deterministic deterministic white runs strength strength strength starting starting trajectories trajectories trajectories trajectories valued reward reward reward reward reward reward differences accurate accurate sutton sutton performs faster faster weak encoding propose propose taking strong strong strong reduction reduction reduction reduction reduction reduction reduction variety variety user start program program program base base base base base base base base base base base base base base base base base base base base base base base base base base base base appears appears appears monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo produces produces solving ways factors factors estimating confidence pruning pruning averaging averaging involves slightly scales applying quality quality quality quality expectation national national independently depending depending depending communication communication reasonable barto barto barto slow slow slow performing performing sec sec sec sec sec sec sec combining intermediate intermediate initially msec sufficiently sufficiently expect expect expect expect recorded recorded box prove candidate candidate candidate candidate candidate candidate domains black middle efficiency capable differ differ effectively effectively successful efficiently score reached heuristic success running running involved play play play play play play play play play providing board board board board reach processors moves moves policies policies policies policies acknowledgments tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro tesauro trains access collection requirements requirements exponentially optimized game game game game game game game issues fewer giving investigated investigated combine authors decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions decisions maximizing comparable scores scores func statistically examined possibly integer configurations extremely perfect perfect greedy noted algo algo improving seconds seconds great advanced advanced ment guaranteed fairly fairly floating capabilities expensive tractable benchmark benchmark worse worse rapid lin lin lin lin lin lin lin lin lin lin lin lin lin lin lin sections closer closer closer widely widely laboratories laboratories cut potentially potentially potentially potentially potentially potentially scientific raw raw raw reflects reflect substantially substantially substantially substantially amounts amounts capability simulate simulate completion completion completion completion completion slower slower slower frequently requirement price summarized plan substantial substantial substantial sophisticated decreased implements yielding lab feasible extensive extensive extensive extensive extensive acm rithm rithm ratios ratios purely outcome outcome outcome outcome outcome plays plays plays eliminated stronger stronger stronger promising hit abilities biased operates methodology methodology exceeds degradation hours games games games games games meaningful ranging zhang zhang displayed surprising regarded guarantees sides conjunction bad sim scheduling scheduling candidates candidates competing offers offers branching approximators approximators approximators offer repeatedly rich theoretically cpu cpu cpu cpu cpu cpu cpu cpu cpu cpu cpu cpu cpu cpu cpu cpu extensively extensively extensively dietterich dietterich dietterich subsequently std std onr accumulated bertsekas bertsekas multiplying truncated truncated truncated truncated truncated truncated truncated truncated truncated basically basically job job legal legal employs conjecture additionally acceptable acceptable preferences chess chess backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon backgammon care ibm ibm ibm ibm deep shannon shannon shannon playing playing playing playing playing playing playing playing playing playing playing searches parallelism lookup player player player player player player player player player player player player player player player player player player player player player player player player player player player player player player player proach investigating speedup rough win drawback million sweeps sta thousands thousands dramatic intensive exploited continually gorithm strict argmax resolve monitor tial thousand savings hundreds doesn wins wins suite opponent opponent played executing trol fastest comm spirit compensated elevator elevator encodings tations players players players players players players players players players players players players players players players players players players players players players players iterating signed acknowledges sweep gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon gammon doubling trend shop shop successor prune watson watson tens huge rolling benchmarks heights albeit ply ply ply ply ply ply ply ply ply ply ply ply burden favorable terminated belmont exhibiting absorbing aggressive mag poten augment dev dev ulation gerald crafted crafted alternately reductions signif crites crites crites overcoming pected athena grade grade yorktown optimistic optimistic efficiencies equity equity equity equity equity equity equity equity equity equity benchmarking tradeoffs weaken stats stats navy borne checkers checkers checkers icant gregory gregory deliberately philosophical simulators supercomputers supercomputers mflops weakest checker choos hav por superlinear 
#@Galperin_G,Tesauro_G,
#t10
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system system system error error error error error error error state state state state state state state state state state state state state state state state state state state state results results results results results results results results results information information problem based based based based based space space weights linear linear linear linear linear case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order systems values values values values probability probability probability probability probability functions functions functions functions distribution distribution distribution distribution method method method approach point point single control control control control rate rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix optimal optimal form form form shows shows shows algorithms algorithms algorithms simple paper paper examples examples examples examples examples examples net work step step field process process process level level current current current structure random similar show show equation section section section section section section fixed fixed fixed line line line line line line line line line line line vectors vectors general general general generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average states states states states states states states states term term term term term term term note note note note note result result result result university computation solution research research independent defined defined defined found found found sequence sequence sequence sequence sequence dynamics dynamics table standard terms distance distance distance prediction prediction direction presented presented presented presented presented present present present present temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine machine machine basis basis basis nonlinear nonlinear continuous sample abstract applied applied back back back back convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic stochastic stochastic ieee positive important adaptive decision decision context context context introduction hand behavior dynamic dynamic dynamic dynamic dynamic generated generated generated generated cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference assume assume prior representations higher part part previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound required required multiple long long long long long long conditions expected expected expected markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make make make make fact fact proposed probabilities probabilities observed observed finite finite finite resulting resulting resulting ing respect respect sum sum called mapping mapping reinforcement reinforcement factor factor dimension study original original original vol vol application application series series provide define define define define define define define define experimental goal related distributions mit mit larger morgan proceedings proceedings report institute final addition addition cambridge computing view view view view view curves transition transition transition transition transition transition limit limit limit limit limit limit limit limit trajectory trajectory trajectory san stage stage stage conference conference efficient full full significant approximate con con produce weighted weighted bounds bounds bounds provided provided provided iteration nature depends sampling sampling sampling sampling measured discussion discussion discussion technical technical technical arbitrary arbitrary denote denote denote complete predictions predictions predictions proof proof proof proof generate supported main main main eds eds ability future future future future future future future makes including fit fit objective simulated smaller combination technology programming programming programming programming interesting interesting projection projection consistent leads leads leads squared details making making international attention predict predict improved improved discussed improve property property property takes apply include sense sense sense subset relevant dimensions previously previously works tions tions converge diagonal diagonal definition chain chain chain chain chain chain chain chain chain chain chain chain observation bounded grant grant constructed exists exists exists exists expression lead invariant suggests alternative deterministic deterministic deterministic deterministic deterministic generally column column setting setting demonstrate conclusion row assumptions assumptions assumptions assumptions assumptions trajectories operator operator operator reward central differences accurate sutton sutton sutton sutton sutton sutton sutton performs suggest presence min relationship introduce introduce manner question question denoted denoted suppose van van van van van van van van van van van van van van van construct construct factors estimating laboratory transitions transitions implement sensitivity linearly linearly linearly linearly infinite physical involves involves involves involves remaining easy easy easy unique unique springer expectation expectation john independently communication communication viewed viewed interpretation interpretation evaluated open operations updated updated approximations approximations approximations approximations evolution centers understanding understanding approximated sizes sizes suggested converges converges updates allowed past spaces spaces spaces remains norm norm norm norm transactions combinations automatic prove prove discuss discuss regular closely refer refer verlag repeated strongly moore sci hold satisfy notation sampled sampled sampled dayan dayan providing attempt moves subsequent approximating approximating satisfies satisfies acknowledgments carried singh singh requirements requirements updating updating updating updating steady steady steady steady steady steady involving recursive scalar project applicable referred workshop func fundamental analyze predicting adjusted rank formal formal formal algo observe initialized initialized ith massachusetts residual inequality developing costs costs publishers track defining fairly turns satisfied satisfied precisely desirable commonly commonly scientific begin nsf mellon addressed addressed carnegie relevance relevance cmu tional parameterized parameterized parameterized parameterized parameterized introducing variant variant maintain span gains berlin pittsburgh reaches enables neuro baird baird differentiable proofs formally formally modify restrict rithm arguments kaufman convenient significance stronger stronger chains chains chains mail replacing interpret reasoning reasoning reasoning implications implications implications intuitively intuitively guide intuitive composition composition composition meaningful entry overview conjunction originally originally counter counter counter counter counter counter counter counter counter counter counter entries ranking approximators approximators approximators approximators approximators approximators approximators francisco discounted discounted discounted insight contraction contraction contraction contraction rich properly roy roy roy roy roy roy roy roy roy roy roy roy roy roy roy horizon correcting tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis statement characterization approximator approximator approximator adopted influences bertsekas bertsekas bertsekas bertsekas bertsekas bertsekas truncated truncated truncated corporation rigorous constitute pointing discount recursively july arg lit lit lit personal personal reports examining param remainder visited intuition intuition intuition pij distribu indexed eligibility eligibility eligibility eligibility discusses inversely preprint margins rewrite infinitely behaves gorithm simplification unbounded converging establishes establishes flows russell continuum boyan interpretations trol characterizes characterizes raises cur establishing amplified spirit counterpart gence successor statements convey dij dij rent predetermined terminology diverge diverge proximation vergence incurred incurred lid lid nonlinearly nonlinearly conver deduce deduce belmont belmont concise clarify clarify diverges aware adopting absorbing tain eter aperiodic aperiodic omitting iij iij informal informal plied originated twelfth formalize athena athena tives irreducible irreducible instrumental ffts closeness nonincreasing deriva propor aro iit erence erence erence arbi virtues daal trary benveniste benveniste benveniste cash undiscounted ame benjamin manifests illuminating entific endless 
#@Tsitsiklis_J,van-Roy_B,
#t10
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number error error error state state state state state state state state state state state state state state state state state state state results information information information information information problem problem problem based based space space space space space space space weights weights weights linear linear linear linear linear linear linear case case case case vector vector vector vector vector systems systems systems systems values probability probability probability parameters parameters parameters weight functions functions functions functions functions functions functions functions functions functions functions distribution method method approach point point point single processing processing control control large large large local analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form form form algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper paper feature work methods methods methods methods step step field process process current current problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems similar show show equation equation fixed fixed fixed fixed fixed fixed line vectors general parameter parameter parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states obtained term note result result result university university computation solution solution solution research independent defined defined defined defined found sequence dynamics constant table presented presented presented present temporal temporal temporal machine machine machine machine press basis basis basis basis basis basis continuous continuous abstract back computational convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic due due due adaptive decision decision decision decision decision decision decision decision introduction hand dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic difference difference variable assume prior representations theorem theorem theorem theorem theorem theorem theorem bound type good long conditions expected expected expected markov markov markov markov markov markov markov markov markov make fact fact proposed proposed proposed length length probabilities probabilities scale finite finite resulting classes classes simulation respect respect respect respect mapping reinforcement reinforcement factor potential dimension applications policy policy policy policy policy obtain original vol vol vol vol desired provide provide provide provide define define define define define define compute related discrete equal equal approaches mit mit mit steps support morgan report report institute institute advances advances difficult scheme scheme addition cambridge cambridge cambridge computing computing computing computing solutions solutions solutions solutions solutions solutions transition limit trajectory trajectory trajectory trajectory full full full full requires choice significant approximate approximate approximate approximate approximate approximate approximate approximate approximate statistics con produce weighted weighted bounds processes processes technical technical arbitrary arbitrary denote denote limited limited stable stable proof proof proof proof common effective effective shape generate supported theoretical theoretical theoretical ability future future easily development fit fit fit kaufmann objective simulated typically underlying underlying underlying combination combination jordan jordan jordan jordan technology technology programming programming programming programming programming programming programming programming programming programming projection projection projection projection projection projection max max max max max making making making idea combined minimize choose choose choose predict denotes denotes discussed directions property element typical practical practical practical apply side tuning solve diagonal diagonal chain chain chain chain chain chain chain chain grant grant studied invariant touretzky deterministic deterministic column column setting conclusion starting starting starting row operator operator valued editors editors reward reward reward reward reward central differences sutton sutton sound sound propose propose propose propose propose min introduce denoted van van van van van van van van van van written solving solving sequential sequential sequential sequential laboratory laboratory transitions metric linearly infinite infinite dimensionality dimensionality involves involves easy easy unique unique unique springer expectation expectation john focus stationary viewed viewed viewed updated updated updated approximations approximations approximations approximated sizes converges converges classical classical spaces spaces spaces spaces spaces purpose iterative iterative iterative foundation norm norm euclidean combinations subspace determines uncertainty maximize mozer partially literature verlag contained prob prob allowing stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping sci hold satisfy notation notation dayan dayan providing delayed observable maximization approximating approximating approximating satisfies satisfies satisfies satisfies acknowledgments tesauro extend cowan presents employed singh singh singh experience steady steady steady steady involving limitations limitations issues dual scalar scalar ideas mappings terminal possibility decisions decisions coefficient naturally analyze analyze analyze predicting extremely rank rank formal initialized ith store motivated established massachusetts massachusetts stop stop stop piecewise inequality inequality asynchronous tractable tool arise watkins watkins watkins watkins watkins watkins watkins involve begin nsf mellon summation prop carnegie cmu variant rewards berlin serve extensions jaakkola jaakkola jaakkola jaakkola bellman intractable intractable intractable approximates approximates addresses establish establish establish convenient difficulties tools mail serves analyzing methodology methodology generalizes continue continue continue composition analyses analyses analyses financial contexts ensures iteratively overview overview overview conjunction conjunction conjunction schwartz consequences sim hasselmo entries approximators approximators approximators approximators approximators approximators discounted discounted discounted contraction contraction contraction contraction contraction roy roy roy roy roy roy roy roy roy roy storing storing horizon horizon extends tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis variants variants inf approximator approximator stopped stopped stopped bertsekas bertsekas rigorous discount exhaustive markovian uniquely uniquely incrementally arg letting options equality rough isi suffer algebra induces gordon gordon tune lems served nonnegative unbounded unbounded curse curse focuses establishes interpreting dissertation establishing establishing iid iid iid iid iid iid iid iid restrictive addressing cauchy united predetermined stepsize severely amax lid lid lid lid lid broader terminate terminate forthcoming forthcoming evaluates jensen belmont concise gorithms serving exposition ulation lira doctoral aperiodic iij theme traced athena kingdom zky touret irreducible irreducible deduced nonincreasing aro dii stating daal benveniste benveniste lids erty preconditions componentwise binations soundness soundness soundness benjamin iif iif iif traction tabular entific dressed endless 
#@Tsitsiklis_J,van-Roy_B,
#t10
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#*network network network network network network network learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input data data function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set networks output output output number system system system system system system system system system system system state state results results units units units units units units units units units information information information information information problem problem models models models models models models hidden hidden performance performance performance based based weights weights weights weights weights weights weights weights linear case case order order order order order order order order order order order order order order order order order order order order order shown shown shown shown shown shown shown shown systems systems values noise noise weight weight weight weight unit unit unit unit unit recognition recognition approach pattern pattern pattern point single single single processing processing processing processing processing processing processing control control control control control control control control control control control large local rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis inputs inputs inputs inputs inputs form form shows shows visual visual paper small feature net work work work work work work task task task task step step points points points field features features features features features process process level level level level level structure structure structure structure structure structure problems random random high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory response similar similar similar representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show show show rule rule rule generalization speech speech speech speech speech states theory theory theory theory theory theory theory term term term experiments experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result computation computation independent found found found found found sequence sequence sequence sequence sequence sequence target target target target target target target target target target target target target target target target target target target target target target dynamics constant standard distance distance distance distance connections connections connections connections synaptic left left presented presented present present present present present phase phase phase phase phase activation activation low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object object motion motion range range range press press learn basis outputs outputs sample abstract back back computational analog references references component due due important important important adaptive context context introduction action action action complex hand hand behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect dynamic dynamic dynamic dynamic tion tion difference difference difference spatial spatial spatial spatial assume lower lower lower lower signals signals learned learned learned higher higher higher higher higher higher higher higher higher higher higher higher higher higher part bound bound required required required required multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex binary expected expected expected expected expected expected expected equations region proposed correlation correlation correct observed errors scale scale scale ing ing tasks tasks tasks simulation simulation simulation simulation human human human human called called factor factor factor potential dimension made natural feedback relative relative relative relative specific specific compared cross series series provide provide compute objects rates rates rates proc location location location location active active determined experimental experimental experimental related connected gain motor motor motor motor motor motor motor motor motor motor motor motor motor motor discrete cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain brain brain mit steps steps larger connection support source source source morgan loss internal internal internal code advances responses layers layers addition sequences sequences sequences cambridge experiment experiment experiment experiment experiment experiment experiment experiment experiment directly additional view transition transition top top top top stimuli stimuli stimuli stimuli stimuli determine determine upper full full full choice approximate speed vision vision basic pages produce condition condition channel channel coding coding derived derived derived developed developed levels levels levels levels area lines actual actual finally processes selected evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence depends associative associative associative associative associative normal increases fast fast fast fast fast fast close close close assumption complete short common common generate generate generate journal ability hypothesis makes sensory sensory sensory sensory sensory sensory sensory sensory sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory underlying account dynamical functional increasing mechanism mechanism mechanism mechanism mechanism special consistent trials principle operation filters filters filters filters pre pre direct direct window window window early frame frame frame decay attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention added added added recent pair separate separate separate separate ensemble ensemble takes takes element movement reported lateral lateral lateral moving period period period period subject identical identical identical hierarchical inference inference cognitive cognitive cognitive cognitive relevant sufficient sufficient sufficient observations subjects subjects subjects works works module module module tions solve solve match match match match match match studies trans sparse background background background background background background background background locations locations grid channels channels channels channels channels channels entire increased amplitude amplitude amplitude amplitude amplitude constructed parts parts occur suggests suggests suggests suggests trial trial deviation locally occurs occurs column setting flow flow minimal greater greater hebbian hebbian editors reward modules modules modules modules modules modules modules modules modules modules modules modules retina peak faster sound sound sound sound sound sound sound sound strong mechanisms mechanisms mechanisms mechanisms largest external external external reduction reduction cycle cycle cycle cycle cycle cycle cycle cycle demonstrated turn selective selective selective selective plane targets targets targets targets targets targets targets manner scene scene scene scene scene scene program base base base base base base base base base base base base base attractor attractor attractor attractor attractor attractor attractor attractor attractor areas areas areas areas areas areas areas areas areas areas areas areas areas areas appears appears appears appears van produces longer longer perception perception perception perception perception perception primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary sequential sequential sequential transitions transitions transitions vertical distinct dept segments modeled modeled recall implement missing sensitivity coordinates coordinates simultaneously slightly interaction interaction develop frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies events events events events events formed shift quality implies expectation expectation expectation expectation expectation potentials potentials potentials cycles cycles cycles cycles select yield focus formation formation formation formation formation formation formation formation communication communication communication transform labels labels centered centered suggested suggested discrimination slow slow dashed expansion sec reduces intervals event intermediate intermediate msec msec msec msec msec msec msec eeg eeg eeg coupling coupling coupling coupling coupling box includes perceptual perceptual perceptual perceptual perceptual coordinate coordinate usa memories recognize recognize activated activated coupled partially columns gamma gamma gamma gamma gamma gamma gamma gamma regular determining aspects uniformly effectively driven driven driven included presentation presentation presentation oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory attractors attractors attractors attractors attractors attractors attractors detect composed capture capture capture capture capture capture quickly kind strongly showing phonetic dis oscillations oscillations content physiological timing timing timing timing timing timing timing timing timing timing sci vary vary absence absence absence absence absence absence absence giles binding binding binding binding reach automatically principles attempt overlapping overlapping illustrates intrinsic intrinsic cowan body body body body stimulation stimulation stimulation poor create create exhibit exhibit rapidly put put oscillators oscillators oscillators humans hanson dotted oscillator oscillator oscillator oscillator oscillator periodic periodic rise rise fourier successive respond rest incremental investigated reliable proper stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream oscillation oscillation oscillation oscillation oscillation oscillation workshop affect fundamental notion matched act act act math reading reading onset onset onset onset onset man psychology created equally equally thought thought adjusted subsets olfactory noted assumes nerve switching switching consist extent grouping explain seconds seconds seconds seconds seconds seconds seconds seconds established integrate brown brown brown brown brown brown brown brown brown band band band band band band ground guaranteed phenomena explanation explanation adapted caused worse drive drive berkeley berkeley berkeley sites organized mathematics mathematics cut ion acad pitch begin localized read read demonstrates cochlear cochlear elman elman elman elman offset simulate simulate simulate simulate psychophysical peaks employ music rep psychological psychological ity switch spread spread fall synchrony synchrony synchrony synchrony synchrony synchrony synchrony incoming incoming incoming cal cal serve phonemes qualitatively logical coherent coherent coherent coherent expectations implements focused attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional deviations deviations wang wang wang wang baird baird baird baird baird baird baird baird baird traces synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization irrelevant trade shifted lab ear appearance appearance forming tation extensive pick driving acts tem jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones jones theories theories arrival arrival arrival children establish establish lost lost cellular kaufman fits overcome overcome satisfying held determination determination determination moment moment serves occurring nearby nearby fail fail shifts shifts clock clock clock clock clock clock clock clock clock clock clock clock clock clock natl continue spurious reliably tap reset reset tone tone tone tone tone tone tone tone tone tone tone tone tone tone periods moved dominant accounts monkeys monkeys captured captured facilitate counter claim advance hippocampus fish recovery recovery treatment ensembles ensembles specialized bursts indicator indicator arrive locked repeatedly environmental environmental probe gesture erlbaum impact impact captures explains explains convergent default default default learnable divide sequentially sequentially sequentially appeared appeared appeared leaving unable unable ter sig sig basin alternating alternating tween distinction distinction par connec causing causing personal individuals classic tor recurrence rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm rhythm evoked evoked evoked streams streams streams streams streams streams streams streams streams streams streams streams streams streams streams streams decorrelation alter alter ary ary mismatch mismatch mismatch mismatch mismatch mismatch mismatch mismatch mismatch mismatch mismatch shifting evolve segregation segregation segregation segregation segregation grouped decays decays activate intra altered synchronized synchronized synchronized synchronized synchronized synchronized multiscale multiscale multiscale rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic rhythmic erp erp selectively selectively oscillating register sweeping pop pop pop pop tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones tones supports sweeps meet tune refined eigen nal port bill tissue tissue radio continually coordination utilizing rats served syn bridge accordance insufficient insufficient send send vis oscillate oscillate fill somatosensory somatosensory contralateral caudal caudal eral eral eral neocortical wiring sensorimotor periodicity replicated fre fre fre horizontally nmda nmda core dedicated repetition functionally characterizes ory vertebrate arriving arriving bandpass enhances evolving sliding sending communicate communicate emg absent experienced attended attended attended attended attended voice brainstem distractors distractors foreground seg mis ous ous brought violated talk tan tory repetitions eeckman tivity tivity plenum bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman bregman boosted boosted configured cations cats cats repetitive prime contributing broadcast broadcast broadcast primates pointers rhythms rhythms rhythms rhythms rhythms rhythms rhythms rhythms activa recovers excite excite rostral thalamus quency quency quency mentation stim perturbing synchronize synchronize synchronize synchronize synchronize pay clocked clocked biasing nuclear schreiner thinking tially wired insects previ hypothesize hypothesize hypothesize excitability temporary temporary fil poten inhibits thalamic thalamic thalamic thalamic onsets onsets onsets onsets counters counters counters counters cooke cooke cooke cooke cooke cooke cooke cooke constantly mined reticular simu birds perceive interfering resonant resonant resonant resonant resonant resonant segregated segregated nected occuring perceptually quence asserts asserts instructed arrived ner suc told resentations spreads flanking flanking flanking flanking flanking flanking flanking flanking flanking flanking flanking flanking flanking flanking decorrelated decorrelated lat lat depended gestalt infants clocks clocks chitecture chitecture discriminated stabilizes cycling cycling ijcai cies identi mecha party nals separations hemisphere accomplishes prefrontal film delivers pulled decorrelating crosstalk crosstalk finished initiate cocktail ven verbal verbal orient recurrently binds binds synchronizing synchronizing expressive vious quantize assisted dream audition audition voluntary promote listeners dem ulus preattentive preattentive hawkins stories unavoidable taneously engaged nized negativity negativity negativity negativity negativity negativity negativity declines nism pacemakers segregate accents neurotransmitters pays lasts equency equency synchronizes psychologically gent intercon ents physio associational telling expec taneous spon frequen nate zed regenerate exchanging passband passband quant directs obscured nizing nonspecific ind nize listener diver rag tials nant anchor audi itly ause 
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#*network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time set set set set set set set set set set set set set set set set set set set networks training training training training algorithm algorithm output output output number number number number number number system system system system system system system system system results results results units information information information information information information information information information information information information models models performance performance performance performance performance based based space space space linear linear linear layer layer layer layer layer case order order shown shown systems systems systems values values values values values values noise neurons neurons unit recognition approach single processing processing processing processing processing processing processing processing processing processing processing processing processing local local analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis optimal inputs inputs shows simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper paper examples examples small size size size size size size size feature feature feature feature feature feature feature feature feature work work task task task task task task task task task task task task task task task task task task fig fig points field field features features features features features features features features process process process level level level level trained trained trained trained high response response response similar similar similar similar representation architecture show line line line line line vectors vectors vectors vectors vectors vectors images general general general general generalization generalization theory theory obtained obtained note experiments experiments experiments experiments result result result university university independent found found sequence target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target constant constant standard standard standard standard standard computer terms terms terms connections science presented presented presented presented presented map map present present phase phase phase low low low learn learn learn components outputs outputs abstract applied applied back find computational computational computational computational computational computational references component component component component due propagation mixture mixture introduction complex hand hand stimulus statistical generated variance variance variance variance variance variance variance variance variance variance parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel search search search search search search search search search search search search search search search search search search search search search tion difference difference difference difference difference difference complexity measure signals representations representations representations representations representations representations representations representations type type required cortex long conditions conditions conditions conditions conditions conditions conditions proposed forward simulations resulting resulting resulting tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total simulation human human respect performed performed performed performed performed times mapping dimension dimension dimension dimension orientation orientation orientation orientation orientation global global global global global study study study study study study true compared objects rates perform perform perform experimental experimental experimental experimental experimental experimental goal related connected distributions cortical cortical brain source source source modeling modeling proceedings department loss internal connectionist layers maps maps environment additional view stage stage stimuli detection detection detection detection detection capacity full full requires choice world speed vision vision basic pages con condition condition condition condition condition condition condition randomly criterion criterion criterion types types lines lines actual actual processes processes evidence biological achieved measured measured describe group group group group denote denote fast fast fast fast fast limited limited close assumption surface surface surface surface surface surface surface finding finding short shape shape supported role role require main main main face face journal journal journal ability ability ability hypothesis hypothesis sensory fit fit fit fit simulated smaller combination reduced transfer interesting interesting significantly significantly principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal representing pre pre pre pre pre pre pre pre supervised early early attention attention attention attention attention attention attention attention attention produced produced produced description description description predict recent separate separate takes similarity similarity similarity similarity similarity similarity similarity similarity similarity movement array array array cognitive cognitive cognitive cognitive dimensions previously unsupervised subjects calculated module module module module module module module module module module module module axis axis axis axis axis axis axis axis tions yields pca pca pca pca pca pca pca pca pca pca pca pca pca pca background background background background background locations locations separation separation separation separation observation generalized constructed studied suggests suggests deviation deviation matrices matrices matrices feed white demonstrate minimal hebbian tangent differences differences measures modules numerical numerical learns propose taking integration integration reduction demonstrated exist averaged targets targets targets targets targets manner manner groups groups groups groups groups groups groups groups scene scene identification explicit perception perception perception perception factors primary describes vertical vertical vertical vertical vertical mathematical physical involves remaining formed versus versus versus versus versus versus versus choosing focus dependence review review interpretation detailed updated sizes sizes sizes sizes sizes discrimination spectrum spectrum slow performing epochs classical classical intermediate intermediate msec msec faces degrees degrees degrees degrees degrees exploration formulation color color eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues sciences sciences illustrated illustrated black holds successfully determining compression compression compression compression compression efficiency capable capable uniformly differ maximal identify detect detect detect detect detect projections projections projections projections projections projections projections identity composed composed composed summary dis dis hold gray involved involved play paradigm paradigm providing providing providing eigenvalue eigenvalue eigenvalue correspondence subsequent presents presents presents powerful transformed essential exhibit replaced issues mass existence existence existence examine school behavioral detectors detectors investigated pathway pathway fundamental fundamental phases notion examined examined examined hill circles circles math naturally analyze psychology psychology psychology psychology psychology psychology friedman detector detector detector detector detector detector detector separated perceptton detected detected serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial serial indicating indicating distinguish orientations orientations orientations orientations orientations orientations variances variances analyzed slope coded explanation processed processed processed processed processed processed sys producing incorporate mation separately arises depicted demonstrates qualitative preceding explained explained apparent varies considerably items items items items items items items items items pathways tional axes axes axes axes axes axes axes axes axes axes axes axes axes axes experimentally experimentally quantitative cohen cohen cohen cohen cohen item item item detecting detecting slower formulated continuously sharp psychological span mod extracting ordered ordered qualitatively logical inherent inherent inherent display display display display display display display display display display display conditioning attentional attentional attentional attentional attentional deviations deviations yielding displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays displays spectra physiology physiology primarily ratios homogeneous homogeneous homogeneous tem impossible grows outcome reaching replacing keeping analyzing analyzing operates sanger sanger cottrell cottrell intuitive intuitive equals realization realization realization evident evident sim scan similarities similarities similarities claim claim claim enable israel israel insight suggesting offer belonging designing explains interestingly interestingly vari assigning compressed compressed compressed compressed compressed summer asked reaction reaction diverse distinction distinction distinction distinction distinction par ical representa mismatch argue trends concentrated gained magnitudes compatible compatible gender gender employing employing categorization mask spanned spanned emphasized retained eigen slopes slopes slopes slopes slopes ward signs signs computa tel tel tel tel answers vice tau tau info beam beam versa scanned scanned scanned characterizing hyperbolic accordance accordance transforming emotion emotion ruppin ruppin ruppin ruppin ruppin exper exper supply anatomy practically dedicated heterogeneous explanations explanations quantitatively confined ance schreiber distractors distractors distractors distractors distractors distractors distractors distractors distractors distractors distractors distractors sparseness aviv aviv aviv aviv servan enabling stems distractor distractor distractor richer fundamentally attentive attentive availability humphreys humphreys humphreys humphreys humphreys humphreys humphreys viable workers wolfe wolfe wolfe wolfe wolfe wolfe wolfe wolfe wolfe wolfe tributed mag specifications sual snyder pared perceive underlie tilted tilted organism posner posner succeeded comparatively serially serially serially flanking flanking treisman treisman treisman treisman feedfor departments compressing holons duncan duncan duncan duncan duncan duncan duncan manifested manifested eytan discrim ule irrespective irrespective prescription devil reprinted succeeds iments manifestation proposals psycho surviving depicting allel obscure connell asterisks stewart nitude ination distin metaphor mensions rial rial ceptual metaphors 
#@Cohen_E,Ruppin_E,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural neural neural neural neural neural input input input input data data data data figure figure figure figure figure time set set set set set set set set set set set networks networks training training training training training training training training training training output output output output system system system error error error error error error error results results results results results results results results results results results units units units units information information information information information information information information information information information information information information information information information information information information information information models hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based based space weights weights weights linear layer layer layer layer vector vector vector vector vector vector shown systems values weight weight weight weight unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image processing processing processing processing processing processing processing processing processing control control control control control control large large local local rate test patterns patterns patterns patterns patterns analysis analysis analysis class class class class matrix inputs inputs inputs form form form shows shows shows shows shows simple simple simple simple simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual paper examples small small size size size net work work work task task task task task task task task task task task task task task task task task task task task methods field field field features features features features classification classification classification classification classification classification classification classification classification process process process current current current trained trained trained trained cell random random high high high high high high high high high high high high high high high high high high high high high high high memory representation representation representation architecture architecture architecture architecture show show show section section vectors vectors images images images images images images images images images images images images images images images images images images images general generalization generalization average average experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result threshold threshold threshold computation research independent found initial initial constant estimate standard computer distance connections connections connections connections connections connections science science science presented presented presented present present low low low low low low low low low low low low low low low low low low low low low low low low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency object object object object object object object object object object object object object object object object object object object object object object sets maximum range range press press learn position components components basis basis outputs outputs outputs outputs abstract find computational computational likelihood references component component due procedure important important important adaptive mixture mixture mixture mixture complex complex hand estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect tion tion tion spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower lower rules representations representations learned learned higher previous cases type type type type type type required multiple multiple multiple multiple cortex cortex cortex good conditions conditions proposed proposed correct observed observed forward forward forward scale scale scale scale scale resulting resulting resulting classes classes classes ing ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks human human human human computed performed performed performed performed elements elements elements elements factor feedback feedback orientation orientation study study study study knowledge filter filter filter filter filter filter filter filter filter filter filter filter filter compared receptive receptive receptive receptive receptive provide provide provide provide objects objects objects objects objects objects rates perform eye determined experimental experimental constraints constraints brain brain brain brain brain brain brain brain accuracy accuracy fields fields support proceedings proceedings department individual individual individual individual advances joint responses responses responses layers layers layers layers graph graph equivalent experiment experiment environment hinton hinton san stimuli stimuli stimuli effects effects effects effects effects effects effects conference conference full full choice significant vision basic pages pages increase give developed types types types types provided evidence evidence evidence evidence evidence evidence backpropagation backpropagation simply simply simply simply associative discussion covariance normal normal describe denote tested tested stable amount shape role role role face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face journal journal ability ability hypothesis instance degree development development development development including pairs combination reduced reduced account account functional coefficients jordan jordan jordan mechanism mechanism mechanism special special special matching database principal principal squared numbers max filters international experts experts experts experts experts experts expert expert early frame idea combined choose predict recent separate separate separate element element reported reported reported moving pixels hierarchical cognitive cognitive cognitive cognitive cognitive relevant relevant relevant engineering highly subjects subjects subjects module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module pca studies differential mixtures background evaluation grid gate gate gate gate entire parts expression expression lead occur suggests feed feed feed hybrid touretzky occurs pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass pass runs runs critical reduce reduce competitive competitive competitive competitive competitive competitive editors modules modules modules modules modules modules modules modules modules moody learns suggest suggest suggest encoding strong strong strong strong mechanisms largest exist decrease averaged identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification configuration force areas perception perception winner factors primary tuned sensitivity sensitivity category dimensionality dimensionality scales scales scales scales scales scales consisting interaction develop frequencies frequencies frequencies expectation competition extracted extracted review overlap controlled controlled restricted showed showed showed soft sizes similarly allowed discrimination discrimination discrimination earlier performing performing measurements remains initially filtering filtering filtering filtering filtering filtering assigned faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces recorded perceptual recognize recognize discuss variations partially gating gating gating gating gating gating gating gating determining middle middle middle suitable society differ driven identify identify identify situation plots identity fine reached receives receives receives receives receives receives receives composed composed quickly contained contained video neuroscience split split split split split classify cue cue hold cues play modular modular modular wavelet wavelet cat cat received received received received received received illustrates jacobs jacobs jacobs jacobs jacobs receive camera bars diego requirements difficulty relations humans limitations biases mse mse mse investigated investigated investigated combine scaled referred referred eigenvectors eigenvectors cognition momentum smallest coarse plausible opposite extremely psychology facial facial equally thought thought adjusted der der submitted explain preference stop slowly developing distinguish orientations orientations track nowlan nowlan briefly london stanford organized preprocessing preprocessing filtered filtered filtered filtered filtered filtered division division mation mation controls projected separately describing describing members begin localized arises annual recognizing raw apparent considerably double double empirically empirically biologically psychological rewards mod occurrence resource gave kinds chose implements implements damage damage patients begins softmax softmax displays distortion cor consistently consistently consistently pose person classifying classifying classifying identifying primarily gabor gabor gabor gabor gabor gabor gabor gabor resources resources homogeneous homogeneous homogeneous repre jones jones inspired allocation held striate multiplicative abilities biased resulted resulted resulted occurring splitting implications implications affected cottrell cottrell cottrell cottrell cottrell cottrell cottrell cottrell adequate degradation exploring infor infor von captured captured captured lawrence competing claim recog specialized specialized specialized jolla relies erlbaum broken summarize receiving assigns ccd informa dramatically grating maintaining visually ent asked nition responds malsburg malsburg individuals individuals tendency sinusoidal scenario ary publication preserved gated formance ijcnn ization convert hughes hughes books books books books books books books books books acquired complementary gender buhmann buhmann responding book book book book book book lippman retained drops drops drops port psychophysics mix develops ucsd resembles served served rarely lighting lighting palmer palmer jet jet jet jet jet heavily emotion wins overtraining overtraining compete tanaka tanaka fre fre tip distinguishing settle beneficial specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization specialization isolation maxi convolved fication stabilize clues parker parker parker parker allocating subtle unnecessary degrades gradual tal mization preprocessed sentations yon remarkably quency quency availability availability subsampled damaged damaged damaged damaged pri deficit deficit deficit exhibiting ant birth pared nose acuity acuity metcalfe metcalfe neurophys preferentially cate freq freq freq freq freq freq specialize sug infant infant infant infant grayscale grayscale grayscale bor bor holons identi mecha mecha 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#@Cottrell_G,Dailey_M,
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#*network network network network network network network network network network network network network network network model model model model model model model neural neural neural neural neural neural neural input input data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set networks algorithm output system results units units units units units units units units units information models models performance based space space space space layer case case case case case shown shown shown shown weight functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit recognition approach pattern point image image single single single single processing neuron neuron neuron neuron patterns inputs shows shows shows simple simple gaussian visual visual visual visual visual visual visual visual paper paper paper small size size feature task task task task task task task task cells cells cells cells cells cells cells cells step field field field field field field field field field field field field field features trained cell cell cell cell cell cell cell cell cell cell structure structure response response response response response response response response similar similar similar similar representation representation representation representation representation representation representation representation architecture architecture show show show show show show fixed general generalization generalization real theory gradient gradient obtained term note note note experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional result result university variables defined defined defined defined defined defined defined defined found found found found sequence constant constant table connections connections science prediction prediction left left left left left left left left left left left left left left left left left left left left left left left left left left left left direction direction direction direction direction direction direction presented presented map map map map map map map map map map map map present temporal object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object position position position position position position position position components basis basis basis basis basis basis basis basis sample abstract find find computational properties properties properties properties references due positive complex generated tion tion tion difference difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume lower signals signals signals prior representations representations representations representations representations representations representations representations representations representations part part part part part center previous cases type cortex cortex cortex cortex cortex cortex cortex cortex binary conditions conditions conditions conditions conditions make observed observed observed observed observed simulations resulting ing tasks simulation computed respect respect respect respect respect performed performed mapping mapping orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation represented represented compared cross receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide provide objects objects objects objects objects objects location location location location perform perform perform perform perform perform perform active active eye eye eye eye eye eye eye experimental experimental experimental experimental related related gain gain gain gain gain gain gain gain gain gain motor motor motor motor motor cortical equal steps fields fields fields fields fields fields fields fields fields institute consists code represents connectionist responses responses responses difficult delay scheme scheme scheme maps maps maps maps maps maps maps maps maps maps maps maps maps maps maps considered experiment experiment experiment experiment experiment directly directly hinton curve curve curve curves curves limit top top top top stage stage stimuli determine upper upper upper requires basic condition condition condition condition condition condition condition coding area types lines lines product provided provided provided finally evidence evidence simply simply achieved discussion describe group group group tested tested transformation corresponds corresponds predictions predictions implemented assumed assumed generate generate generate journal hypothesis instance instance future future future makes sensory sensory sensory simulated typically combination account account account account account edge edge edge edge edge edge edge edge edge edge head mechanism consistent consistent consistent consistent empirical leads leads leads call making bottom bottom frame frame attention light predict predict directions recent property movement period subject side side side side side side side side side side side side side side side side side side side side side side side side side side side side side side side side side side sense subset subset sejnowski cognitive cognitive recently recently recently sufficient sufficient compare previously subjects volume tuning tuning tuning tuning tuning axis correspond positions locations locations observation amplitude amplitude horizontal horizontal horizontal horizontal parts parts lead lead invariant invariant occur trial trial boundary boundary column column column column greater operator retina performs suggest encoding encoding propose propose demonstrated intelligence radial exist movements movements movements movements selective selective selective selective selective selective selective groups groups areas reference reference reference explicit explicit explicit explicit appears appears appears edges longer plot plot vertical vertical vertical changing modeled modeled recall coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates transformations transformations applying independently independently communication communication showed modulation modulation modulation modulation modulation modulation modulation centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered centered frames frames activities performing performing performing add closed remains intermediate intermediate expect recorded combinations bell inter retinal retinal retinal retinal retinal sciences plotted partially partially partially columns columns columns columns selecting middle letter suitable society encoded computationally computationally divided detect detect situation situation plots plots composed kind decoding allowing showing neuroscience neuroscience superior issue cue cue cue cue cue cue bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar dot dot absence paradigm consisted preferred oriented body selectivity selectivity selectivity selectivity command command command command command command command command command command command command command command command command command command command command collection investigate difficulty involving involving dotted dotted preliminary mass existence respond respond respond respond respond possibility authors func analogous neu neu saliency gradients opposite thought friedman der observe shapes explain indicating indicating indicating indicating preference directed directed directed directed directed directed directed directed directed directed ground orientations adapted briefly worse tive tive easier broad broad located monkey monkey monkey monkey projected involve beginning read arises depicted demonstrates meaning fourth fourth varies applies recordings commands schematic schematic modulated modulated modulated modulated modulated modulated modulated instruction instruction instruction segmented shaped patients patients patients patients patients summed irrelevant irrelevant gap gap gap gap gap gap representative summing saccadic rotated rotated repre consideration simplify held ral representational representational von sides sides intended intended washington sim belongs belongs reproduce parietal parietal parietal parietal parietal parietal suggesting saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades saccades saccades saccades colliculus belonging discovered ignore interestingly receiving multiplying unified outline basically asked opposed failed responds responds responds responds lesions perceived perceived personal personal hierarchies lesion lesion lesion lesion lesion lesion argue inverted inverted compatible compatible compatible compatible retinotopic retinotopic maximally wise argued fixation fixation ultimately macaque frontal frontal represen oculomotor responding responding responding son supports page ation behave vice vice demonstrating appearing versa versa send pouget pouget pouget pouget contralateral contralateral alex rons neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect neglect triangle triangle triangle triangle ref inefficient screen screen screen upright wong carpenter allocating responded responded polar modulate sentations upward upward upward clockwise clockwise clockwise modulating cued deficit formalized driver driver driver driver driver driver zhou zhou oij oij seventh tilted recep recep particu abstracts sit orienta modulations cial syndrome syndrome syndrome counterclockwise counterclockwise counterclockwise hemisphere hemisphere hemisphere hemisphere alexandre inhibiting neurological uation erence coordi invoking artifi situ recoding sac sac wallace georgetown georgetown georgetown underlies compelling subparts larly nates viewer flashed tative reconcile supplementary supplementary supplementary unilateral upside polation 
#@Deneve_S,Pouget_A,
#t11
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input input input input input input data data data data data data function function figure figure figure figure figure time time time time time time set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output number number system system system results results results results results results results results units units units units units units units units information information information information problem models models models models models based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case vector order order shown shown shown shown shown shown shown systems systems values values values values parameters weight weight weight weight neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern point point image large rate rate rate rate test test patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis inputs inputs shows signal signal signal simple simple simple simple simple simple visual visual visual visual visual paper examples small feature feature feature feature feature feature feature feature feature net work work fig fig fig fig fig fig process process process level current current trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained random random random random random random random random random high high memory memory memory similar similar architecture architecture architecture show show fixed fixed fixed fixed fixed fixed rule rule rule rule rule rule vectors vectors vectors general general real real real real real average theory term term term term experiments university computation found found found target target initial initial initial initial constant constant terms connections connections connections connections connections connections connections node science science direction direction presented presented phase phase activation activation activation activation activation low temporal temporal object object object object object object object object object object object object object object object object object object object sets motion press learn learn learn position basis basis outputs outputs outputs outputs abstract computational computational likelihood references positive positive positive important important important important action complex hand hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus effect effect effect tion change change change change change change change difference difference lower lower measure representations representations representations representations learned learned learned learned learned learned learned higher higher previous previous previous cases firing firing required binary binary long long conditions conditions conditions conditions conditions conditions conditions represent fact simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations ing ing simulation simulation simulation simulation human human means factor obtain negative relative relative relative relative relative specific represented compared provide objects objects objects objects objects objects objects location experimental related brain approaches comparison larger larger fields modeling modeling modeling department consists consists responses responses bias bias layers layers addition considered directly san stimuli stimuli efficient requires approximate basic increase increase produce condition developed levels levels levels processes processes processes processes processes nature simply simply measured discussion discussion discussion feedforward increases increases increases increases describe group tested tested limited finding short implemented assumed assumed supported require require face journal pixel future future easily degree development development development development including including underlying needed account account account unknown unknown fully interesting interesting testing testing testing significantly increasing increasing head head head head head head head head head head consistent consistent iterations iterations iterations iterations stored decay decay decay decay decay produced produced choose improve takes takes apply moving include period period period period identical pixels cognitive recently recently relevant relevant relevant relevant interest interest interest interest sufficient highly previously previously calculated calculated works solve correspond studies address address background positions modified modified sensitive sensitive sensitive sensitive sensitive sensitive increased increased suggests trial generally column setting strength strength strength strength conclusion critical place place place minimal assumptions hebbian hebbian conclusions valued valued depend central tangent interactions interactions interactions interactions differences measures retina clear clear learns learns suggest suggest hard hard mechanisms mechanisms mechanisms presence california turn decrease decrease groups groups acknowledgements appears produces winner winner winner factors primary describes modeled modeled missing physical involves slightly interaction interaction interaction interaction interaction interaction develop develop develop develop develop develop cycles decreases decreases decreases national formation review correlated influence influence open ocular understanding similarly allowed allowed allowed allowed slow intermediate intermediate faces exploration box box box box box box box box box box box box box box box box box box activations dominance retinal retinal sciences recognize recognize aspects aspects build genetic comparing score score score score score score score score score miller miller receives capture summary summary quickly kind allowing allowing allowing success success issue running built vary received received preferred preferred preferred preferred preferred bars bars bars diego experience experience experience experience experience experience humans detail issues behaviour behaviour rise rise rest rest project project project behavioral investigated investigated scaled complicated scores scores scores scores naturally plausible onset analyze psychology psychology psychology changed detector detector detector detector detector detector explored hebb hebb hebb hebb baseline extent extent motivated animal animal animal animal mentioned percentage preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference slowly slowly slowly developing analyzed phenomena fairly fairly fairly failure biology biology floating adapted handle starts rapid rapid purposes leaves involve beginning beginning implicit lowest qualitative qualitative researchers behaviors behaviors behaviors behaviors substantially understood understood dark dark dark tional red red backprop detecting incorporated treated sharp compares psychological exhibits exhibits rely rely measuring ture parent qualitatively prevent replace kinds shaped begins displays displays irrelevant naive naive naive naive naive naive naive naive naive picture picture picture picture picture picture picture picture picture picture picture ordinary sort oxford tation appropriately animals acts interconnected outcome lost fails saturation hyper moment biased biased serves hope neurobiology operates fail affected days days hours hours meaningful analyses periods periods periods periods periods periods pat moved intended accounts facilitate facilitate similarities entries exposure winning winning jolla horn horn horn horn horn horn horn horn horn horn horn horn horn horn horn horn horn horn horn horn horn draw discovered interestingly johnson johnson johnson johnson johnson johnson johnson johnson johnson johnson johnson johnson boxes unable incorporates fellowship reaction blue blue preferences preferences preferences preferences preferences preferences preferences preferences preferences ideally tendency tor simulating clustered assess lesion home exam interact interact interact goals life life activate activate interacting altered maximally acquired proach proach portions turning programmed programmed modifiable dsp prevents compu ward computa develops develops develops ucsd removes species stores handling prefer prefer crude terns inhibit developmental pictures pictures pictures pictures pictures pictures pictures cylinder cylinder cylinder cylinder cylinder cylinder cylinder cylinder cylinder cylinder affecting exposed exposed sen subtracted architec seed intact intact isolation colleagues approaching neutral accounting correlates gathered plasma plasma replicate medial replicates cats stryker preprocessed activates hysteresis excite excite excite excite preprocessor frozen chang weakness bird bird devel postulated untrained untrained untrained untrained untrained counterparts reilly reilly reilly neurally clarify pattem fil bateson bateson bateson bateson bateson preset birds birds birds birds birds neck neck neck neck neck neck neck neck neck neck underlie heads heads heads heads heads heads heads heads unfamiliar unfamiliar wheel organize sketched keller loses stud strengthened infant davies davies hen hen focussed infants detec prefers interacts successors mimics implemen danger alters innate innate ven clarendon neurological neurological ied ifi bolic nary striped domestic domestic domestic domestic domestic ine cogsci lesioning subparts exogenous ial inquiry reared premature covariant psychobiology nately tationally exposing 
#@Hadden_L,
#t11
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#*figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set set training training training training training training training training training training training training training training training output number system system system system results results results results results results results results units units performance space case shown shown shown shown shown values noise noise noise method point point image processing control control control control control control control control control control control control control control control control large large large test analysis analysis analysis shows shows shows shows shows shows shows shows shows shows shows shows shows shows shows shows signal signal visual visual examples examples task methods methods field features features features features process process structure response response representation representation show show show show show show show show show line line line generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real real experiments experiments independent independent defined found target target target target target target estimate standard terms distance direction phase phase phase phase phase phase phase phase phase phase sets sets maximum maximum press learn position position abstract back back analog references important context context context context context context introduction action action estimation behavior effect effect effect effect variance variance tion change change change measure measure measure measure measure measure signals representations representations word word word word word word word word word center type make make observed observed observed observed scale human human respect called called called called called made made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback study study study study study study study study study vol represented provide motor motor motor motor motor motor motor brain mit mit mit comparison words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words individual responses responses delay addition cambridge cambridge cambridge experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment directly san effects bit significant significant significant significant estimated lines path path path path path path path path path path path path path path path path path actual finally finally selected evidence evidence evidence measured measured measured measured measured discussion discussion transformation transformation transformation transformation transformation transformation transformation transformation corresponds nearest common common common theoretical eds adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation end end end sensory auditory auditory smaller smaller jordan jordan jordan jordan testing testing testing testing testing testing testing testing testing testing significantly ratio projection projection projection projection projection york empirical magnitude magnitude idea minimize produced produced produced produced produced produced produced run added reported subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject hierarchical hierarchical cognitive relevant subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects calculated calculated tions trans interval interval interval organization organization sensitive constructed studied studied digital deviation feed generally half half half strength conclusions measures designed clear learns sound sound sound sound sound sound sound drawn solid solid solid solid labeled relationship averaged targets targets targets groups acoustic question suppose perception optical plot plot vertical dept transformations transformations transformations transformations transformations remaining remaining slightly slightly slightly spectral frequencies frequencies frequencies frequencies shift shift shift shift shift shift john john phoneme detailed transform transform transform open lee lee past spectrum spectrum spectrum epochs epochs intervals purpose generation initially distances expect box plotted specifically variations discussions aspects divided divided divided symbols symbols post projections projections projections vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel vowel plots plots plots plots plots plots identity ten reached composed composed summary soc soc soc soc induced video video interested phonetic phonetic physiological sci device duration built notation michael absence absence board board correspondence reach consisted acknowledgments extend presents carried american wiley transformed production production production production production production production production production production production production production production production production production access exhibit exhibit varied varied humans limitations accurately accurately dotted dotted dotted helpful examine examine examine respond investigated cognition phases removed examined circles circles adapt adapt illustrate changed eyes subsets front epoch epoch epoch speakers speakers baseline baseline baseline adapted adapted caused drive shared producing sounds sounds sounds english addressed spoken remove exhibits synthesis reaches reaches reaches gen gen phonemes prevent adjust focused deviations naive shifted shifted shifted shifted ear feasible accomplished controlling controlling theories theories reaching reaching kaufman occurred held hit north generalizes filled hours vowels vowels vowels vowels vowels vowels vowels contexts contexts male facilitate thomas exposure exposure exposure exposure exposure francisco eng suggesting ends arrows formant formant formant formant formant formant formant sons consonant consonant consonant consonant speaking linked linked visually helmholtz creates preserving welch perceived amplitudes alter alter alter alter adapting arising shifting shifting shifting shifting conduction alternate compensate compensate compensate altered altered altered altered altered altered altered altered altered altered altered altered altered maximally maximally increasingly setup pop pop pop rochester retained retained retained retained retained retained exhibited dsp supporting supporting students acoust acoust acoust font monitor monitor hearing hat adaptively arrow arrow arrow dropped hour sensorimotor sensorimotor sensorimotor compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation compensation exposed exposed exposed exposed dissertation subtracted subtracted stevens optics phonology america compensated compensated rel voice articulation handbook blocked blocked microphone microphone microphone brought tal mir phy minute minute minute minute apparatus apparatus psyche postulated formants formants formants formants formants formants formants formants formants formants formants ramp ramp overshoot mild prism prism prism retains inferences meyer glasses glasses glasses glasses endpoints periments doctoral gat ucsf ucsf normalizes native synthesizer heard heard heard heard heard heard heard heard heard experimen jects misses alterations alterations masked masking signifi hear collects aloud bone pap pap alteration alteration observational oot transforma parison keck century compensates intention phonetics prompted prompted appreciable lasted vie wearing wearing existent signify sation evant produc mount participated phonetically phonetically sits conclusive seat adaptations weren 
#@Houde_J,Jordan_M,
#t11
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#*network network learning learning learning learning learning learning learning learning learning model model model model model neural neural neural input input data data data data data data data data data function time time set set set set set training training training training training training training output output number number number number number system error error error error error state state results results results results units information information information information information information information problem problem hidden hidden performance performance performance performance based based based based based based based based space space space weights linear linear linear linear layer layer case case case case vector vector vector vector vector vector vector order order order order order order shown values values probability probability probability weight functions method method method method method method approach approach point single single single single single processing large large large large large large large large large large large large local local local rate test test test test test test test test test test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class matrix matrix matrix matrix optimal optimal form algorithms simple examples examples examples examples net net work work methods methods cells features classification process process process process process process level level trained trained trained trained trained cell structure structure structure high high high memory memory similar similar similar similar similar similar similar representation representation representation representation representation representation representation representation representation show section vectors vectors vectors vectors vectors vectors vectors general speech approximation average average average average average average average theory experiments experiments dimensional dimensional dimensional result result result result result university university university university university solution research research research research independent found found target target target estimate standard computer terms connections science science science science science present activation nodes frequency object object sets press press press press press press press press press press press press learn learn components components components basis continuous continuous sample sample sample sample abstract applied applied applied applied computational computational computational analog properties likelihood likelihood references component component due due important important context context introduction hand hand estimation behavior behavior statistical statistical difference lower lower lower measure measure measure representations representations representations word word word word word word word word word word word word word word word word word word word word word word word word learned cases cases cases cases multiple multiple multiple multiple multiple good good good long represent represent represent represent markov make make techniques techniques correlation correlation correlation correlation length length length length correct probabilities probabilities probabilities errors scale scale scale scale finite resulting classes classes classes total total simulation simulation human human human human human human human human human human human human human human human human human human human human human human human regression computed computed respect called called times elements means means potential dimension dimension dimension made made made natural natural natural natural natural natural global applications applications applications applications applications knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge original original specific specific represented represented represented represented true compared compared desired cross provide determined experimental related related related constraints constraints constraints gain discrete brain brain equal approaches steps accuracy accuracy comparison larger larger source proceedings proceedings proceedings report report report report institute institute words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words department department technique technique technique individual individual individual joint represents difficult ai considered cambridge cambridge computing computing domain domain domain domain equivalent equivalent experiment additional additional additional view estimates estimates design transition transition limit conference conference full choice choice choice choice choice choice significant approximate statistics basic basic con produce coding coding derived derived weighted types product finally finally processes processes processes processes evidence evidence depends depends constraint constraint simply associative measured measured measured technical describe group tested tested tested limited close complete complete amount amount short short short generate theoretical eds journal journal ability ability hypothesis easily degree including including objective objective simulated typically pairs pairs underlying combination combination fully technology testing testing testing significantly york mechanism special structures structures structures matching principle language language language language language language language principal representing numbers numbers max pre direct international experts experts expert expert expert expert early combined combined produced choose choose added sources sources sources sources sources description description predict predict improve pair separate typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity reported reported practical identical identical machines machines inference inference subset subset cognitive cognitive cognitive cognitive recently relevant relevant engineering dimensions dimensions dimensions sufficient sufficient highly varying previously previously previously unsupervised observations approximately subjects match studies differential diagonal increased constructed constructed parts concept concept matrices predicted alternative alternative correctly move occurs half place greater valued differences measures measures measures measures accurate faster strong mechanisms largest largest external reduction demonstrated intelligence variety variety variety manner manner question question explicit relation produces produces written ways ways ways ways ways ways student student student student student student student student student student student category simultaneously dimensionality dimensionality easy slightly text text text text text text text text text text text text text text text text text text text text text text text text text text text angle angle angle consisting mutual mutual adding frequencies frequencies events quality quality quality quality quality implies versus boolean choosing national extracted extracted independently expressed expressed review review correlated squares viewed solved evaluate evaluate showed decomposition decomposition decomposition decomposition decomposition decomposition decomposition discrimination past earlier spaces string assigned assigned assigned strings retrieval retrieval retrieval retrieval retrieval inter subspace illustrated automatic automatic prove uncertainty uncertainty candidate tests tests tests tests tests tests tests tests tests tests tests structural successfully columns columns identified identified letter capable society society society included latent latent latent latent latent latent latent latent latent latent latent successful computations score score score score score score tend ten ten ten characteristic capture summary traditional kind kind kind kind strongly induced contained contained contained allowing success showing content content content content categories categories categories quantity quantity quantity list sampled sampled write write michael correspondence correspondence automatically preferred extract extract extract acknowledgments body american access experience experience relations relations relations relations relations relations relations relations relations relations relations relations relations humans humans humans humans humans humans humans humans humans humans association limitations accurately accurately issues biases biases successive successive history ideas ideas school relationships relationships comparable comparable symbolic symbolic scores scores statistically cover cognition cognition cognition fundamental analogous induction induction induction possibly predicts psychology psychology psychology psychology psychology perfect queries queries singular singular singular singular singular singular singular singular singular singular aspect quantities explored expressions expressions logic improving utility utility sentences sentences sentences sentences sentences sentences sentences averages averages established languages indicating rows cos cos cos growth phenomena coded answer answer answer multiplication briefly starts reasons purposes satisfied producing style choices commonly potentially scientific implicit implicit members members english english english read read computers annual qualitative meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning meaning fourth questions questions questions people people people people people behaviors reflect items items amounts simulate lack lack peter documents documents posed treated frequently frequently psychological psychological psychological passes vocabulary vocabulary vocabulary rely rely rely differs reaches extracting popular occurrence occurrence serve prevent gave logical logical inherent sophisticated sophisticated tolerance coherence coherence damage utterances progress progress progress progress sentence semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic representative representative person person acquisition acquisition contextual aligned redundant sort sort primarily accomplished accomplished assign oxford restriction member member concerned children children lost smith smith occurred moment interpret scoring scoring reasoning reasoning preparation corpus corpus intuitive phrase phrase heuristics heuristics service service meaningful evaluations analyses embedding contexts contexts contexts document representational representational induce induce decide conjunction conjunction conjunction conjunction dominant intended colorado colorado colorado heart heart thomas offers similarities similarities similarities similarities similarities similarities similarities similarities entries young express express express reader offer grammatical passing considerations statement valuable material acknowledge assigning assigning limitation speaking linguistic users listed deriving inferred validity asked asked asked bank bank revealed forced centre centre acceptable constitutes descriptions descriptions simulating simulating associate causal reflected reflected reflected reflected assess assess assess assess publication preserved translated exam insights boulder boulder carefully picked paired argued cosine cosine cosine cosine cosine cosine cosine topic topic topic categorization represen worth associates million alternatives diversity apparently sized dictionary dictionary simplex induces retained retained things unpublished manuscript students students students students students students students littman littman satisfaction satisfaction nist acquire acquire insufficient spring phrases phrases jointly hypothesized hypothesized calibration orthonormal conceptual conceptual conceptual adult adult accomplish replicated anatomy svd svd svd svd striking extracts judged judged preservation alan admission rating artifact exploits america syntactic factorization crl presently edition resultant priming correlates facts statements convey convey discovers occurrences occurrences lsi indexing indexing indexing sorted constituent bodies newly fundamentally stand topics sixth simulates inability conveyed conveyed conveyed advice psych ontario traditionally mike rated rated rated comprises darrell unlimited canal vast schreiner schreiner schreiner schreiner judgments judgments judgments judgments judgments myers myers exceeded positively perspectives wolfe wolfe wolfe wolfe meanings scored standing sorts walter inferences ratings syntax syntax syntax bag masses passage passage passage passage passage underlie bellcore mere readers readers readers readers readers readers foreign mexico relied interpretable unitary emulation unrelated instruments freq corpora corpora articles landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer landauer berry berry told collaboration standards subjected till till discourse discourse discourse discourse adults adults reciprocally essay essay essay essay essay essay essay essay essay essay essay essay essay essay essay essay textbook verbal mirrors efficiencies social guessing deficiency supercomputer calibrated wished confirming triplets abstracted abstracted participants judgment judgment judgment judgment unfolding comprehensibility trec subjectively bob waterloo deeply underlies acquiring superset superset chomsky supplemented aries textual texts texts texts unconscious paragraphs paragraphs paragraphs multitude objectively resembled deerwester introductory introductory educational educational educational occupation leamed etal professional extensional affairs las adequacy agreeing commutative seminar protection encyclopedia encyclopedia objection accommodates 
#@Foltz_P,Laham_D,Landauer_T,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model neural input input input input input input input input input input input input data data data data function function function function function function function function figure figure figure figure figure figure figure set set set networks networks networks networks output number number system error state state state results results results results results models performance performance performance performance linear linear linear linear linear linear case case case case order shown shown shown shown shown probability parameters parameters parameters functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit pattern point point point single single single single single processing processing processing processing large local local neuron neuron neuron neuron neuron neuron neuron neuron rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis inputs inputs inputs shows visual paper small net fig step field field field field field features features features features features level level level level cell cell cell cell structure structure structure structure structure structure problems high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response similar show show show section section section fixed fixed fixed line line rule rule rule rule parameter obtained obtained obtained activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result university university threshold threshold threshold computation solution defined defined defined found dynamics initial standard standard standard computer connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science left left presented presented low low low sets range learn components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract abstract find computational computational computational computational properties references component stochastic important introduction behavior difference variable variable assume signals chosen chosen chosen cortex cortex cortex cortex cortex cortex binary binary conditions distributed distributed equations equations equations equations make fact fact proposed correct observed observed observed simulations simulations resulting resulting ing ing ing total total total total simulation simulation multi multi multi multi multi multi multi multi multi multi multi multi potential potential global study study study negative relative specific specific specific specific compared compared active active active active active cortical cortical cortical cortical brain larger larger proceedings words version synapses synapses consists internal internal code represents represents represents framework experiment hinton curve curve view view view curves effects capacity capacity capacity capacity capacity full choice give condition coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding derived randomly developed levels levels levels levels levels levels levels levels levels levels levels types types processes inhibitory inhibitory associative associative associative associative associative associative associative associative associative associative associative associative achieved measured describe tested limited limited assumption assumption corresponds corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable stable stable stable stable stable effective role theoretical main ability ability smaller account account account consistent consistent consistent consistent trials language leads pre inhibition inhibition inhibition stored stored run light membrane membrane population population robust trees cognitive cognitive cognitive cognitive recently highly compare conventional conventional works module module module module module module module module module module module module module module correspond correspond rl rl sparse sparse sparse sparse organization storage storage constructed lead studied trial trial setting critical critical critical critical critical place hebbian hebbian hebbian hebbian hebbian hebbian sigmoid sigmoid sigmoid sigmoid modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules integration physics physics external external external characteristics characteristics sigmoidal sigmoidal sigmoidal solid solid proportional proportional proportional assuming start manner manner connectivity denoted attractor areas distinct category category category category electrical adding quality quality implies versus letters review review overlap overlap overlap overlap overlap overlap overlap interpretation codes fraction completely completely similarly converges allowed partial partial partial partial advantages advantages dendritic dendritic dendritic dendritic dendritic david coupling includes includes includes retrieval retrieval retrieval retrieval retrieval retrieval retrieval inter inter inter inter inter inter inter inter inter inter memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories memories plotted successfully differ encoded post post plots ten ten composed capture summary conductance cue cues cues cues dot modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular modular body investigate updating updating association association postsynaptic school rest complicated presynaptic presynaptic cognition naturally transmission transmission necessarily perfect freedom hebb ith ith ith ith store store store store store store fibers contributions contributions motivated motivated motivated mentioned distinguish unstable unstable coded analytical inside turns perspective choices afferent afferent axons considerably populations populations populations dark treated psychological span span price mod tank conductances conductances conclude findings findings damage damage damage damage damage damage semantic semantic semantic semantic phenomenon corrupted physiology forming narrow homogeneous homogeneous homogeneous homogeneous homogeneous jth jth repre jones interconnected rational fails chance chemical check hit hit hit efficacy efficacy operates imply symposium connect dendrites sion regard evident evident assembly nonlinearities dif enable israel israel rich horn horn horn horn partitioned shading shading validity tween ease simulating verified deep segregation segregation mammalian mammalian elementary jij intra intra intra intra intra intra acquired assemblies assemblies memo memo investigations ignoring treating tel tel tel tel develops capacities capacities capacities stores stores nested nested nested ferent ruppin ruppin ruppin ruppin somatosensory kth concrete couplings couplings couplings retrieved enhances accommodate accommodate modern problematic aviv aviv aviv aviv decades tivity levy levy levy levy ular columnar retrieve enhancing tsodyks proximal ago consciousness adopting cen comprise necessity dash functioning zij zij susceptible repertoire embody shapiro conscious departments obser alterations eytan mimics mimics situated situated impairment impairment impairment impairment odds coexistence nand virasoro pertaining pertaining subcortical sustain sustain sents lesioning marginally vations cajal tins realm astronomy pays cortices nir supposedly codings codings citatory stor igh sus homogeneously 
#@Horn_D,Levy_N,Ruppin_E,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model model model model model model model model model model model model model model model model model model model input input data data data data data data data data data data data data data data function function figure figure figure figure figure time time set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training training output output output output number number number number number number system error results results results results results results results results results results results results results results units information models models models models models models models models models models models models performance performance based based based based based based based linear linear layer layer layer case case vector order order order order shown shown shown shown shown systems values noise weight recognition method single single single single single single single single single single single single single single single single single processing processing processing control control control control control control control control control control control rate rate rate test test test test test test test analysis analysis analysis analysis shows shows shows shows simple paper paper paper size size size net net work work work work task task task task methods fig process process process level trained trained trained structure memory response similar representation architecture show show show show show rule general real obtained obtained note note experiments experiments result result university university university research independent log defined defined defined defined defined found found found target target target target initial table table table table table standard standard computer computer terms terms distance node science science prediction left left left left left direction presented presented presented presented present present activation activation activation activation activation activation low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency sets range range press position position position position position position position position position position position position position position position position position position position position position position outputs abstract computational computational computational references component due due context context context introduction hand hand statistical statistical statistical statistical statistical statistical effect effect effect effect effect effect effect effect effect generated parallel parallel parallel parallel recurrent recurrent search tion change difference difference difference difference difference difference difference variable rules rules rules rules rules rules measure measure measure word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word learned learned chosen higher higher part previous previous previous cases required distributed distributed expected fact length correct correct correct correct correct correct correct correct correct errors errors errors forward forward forward forward forward forward simulations simulations simulations resulting resulting ing tasks total human human human human computed multi performed times mapping mapping mapping mapping mapping mapping study obtain represented compared compared compared compared compared desired desired desired desired cross provide define location active related related equal approaches comparison contrast support support support dependent modeling words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words technique connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult final final delay delay scheme addition considered considered considered experiment san san stimuli effects effects effects effects statistics statistics statistics basic validation produce produce produce condition weighted randomly developed developed criterion criterion entropy provided provided finally selected selected selected evidence evidence evidence nature inhibitory simply simply achieved achieved normal normal increases group tested complete finding amount common implemented implemented role require journal journal journal end hypothesis hypothesis instance cluster cluster cluster easily rumelhart rumelhart development noisy objective pairs account account account account account account account fully testing ratio ratio ratio mechanism database database database database language language numbers making early decay attention predict recent recent exact robust separate similarity include subject subject identical identical identical sense relevant engineering engineering compare approximately approximately approximately subjects subjects subjects calculated calculated calculated calculated works works studies address definition definition definition definition definition definition background evaluation positions locations modified improvement increased exists occur extended wide feed feed feed feed feed feed clusters clusters occurs occurs starting row greater greater neighbor interactions interactions differences differences differences measures clear performs faster learns sound largest california california assuming decrease averaged averaged appears appears written longer longer perception perception sequential recall simultaneously averaging averaging unique consisting consisting interaction interaction interaction interaction develop letters review review review review phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme understanding earlier earlier slow epochs epochs epochs epochs neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood false calculate string expect expect weighting batch activated activated activated specifically domains neighbors neighbors neighbors neighbors neighbors major regular regular regular regular regular regular regular middle identified letter letter letter letter letter letter differ differ delta delta mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland successful literature vowel vowel vowel vowel vowel tend tend online capture summary quickly criteria criteria bar play providing correspondence correspondence correspondence leading principles extract decreasing decreasing body explore origin diego diego collection exhibit difficulty limitations dual dual dual dual dual dual dual dual dataset dataset rise fewer respond fashion links project mse mse mse mse mse mse mse working proper notion momentum momentum matched matched examined editor reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading onset onset onset onset onset psychology psychology created rank rank rank formal explored explored message consist consist grouping grouping explain explain serial serial serial serial serial serial electronic defines brown slowly agreement phenomena phenomena phenomena phenomena explanation explanation explanation majority majority adapted cascade lies processed strictly day precisely controls controls controls controls separately separately beginning beginning beginning beginning members begin english english english english english english english medical read exemplars raw explained explained explained varies reflect syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable syllable items pathways cmu cmu fed simulate slower incorrect psychological psychological psychological psychological differs cal phonemes phonemes phonemes phonemes phonemes phonemes logical findings begins cor phenomenon gap representative representative proportion investigation ratios databases ordering ordering ordering concerned eliminate printed resulted fail monotonically affected affected hint cottrell corpus corpus date irregular irregular irregular irregular irregular irregular irregular irregular displayed displayed accounts captured counting ranking ranking ranking exposure claim claim claim claim claim claim claim claim jolla jolla late late late late informative route route route route route route route route route route route route route route route route route route route route relies agree agree erlbaum consonant consonant consonant consonant consonant explains alternatively automated counts counts counts outlined outlined ure land ter ter shorter latency latency latency latency latency latency latency latency latency latency latency latency latency latency reaction presenting connec quasi exception exception exception exception exception exception exception exception exception exception exception exception exception exception exception exception regularity regularity regularity regularity regularity regularity regularity regularity regularity causing hillsdale adjustment ftp ftp alternate alternate interact activate activate activate disadvantage considers confirmed insertion interactive interactive ambiguous accounted dictionary syllables examination challenge deletion regularities council decided european neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods neighborhoods hypothesized fill developmental filler phonemic phonemic drawing affecting pronounced distinguishing exposed conflicting meeting settle vote consonants consonants substitution phonology phonology phonology contrary frequent falling amenable experienced addressing format gathered routes routes approached appro trend trend trend counted prune dence supposed validated lexical lexical lexical lexical lexical lexical amer violate ular neigh avg scribed phonological collect claims claims claims latencies latencies latencies latencies latencies latencies perspectives clus consensus asso standing pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation pronunciation conveniently psy providence trust trust intersecting cap foreign lexicon lexicon lexicon lexicon lexicon ences accompanying exceptions exceptions plaut plaut plaut plaut sug spreads slowing nouns doubled interacts xii tionist patterson favored aerial aloud aloud aloud aloud aloud aloud orthographic orthographic orthographic orthographic odds impaired inconsistencies undertaken garrison helping agreed engines pronunciations pronunciations pronunciations pronunciations pronunciations pronunciations pronunciations pronunciations pronunciations spelling ciative edit correspon universally duplicates oral gest convincing irregularities irregularities irregularities irregularities irregularities tured psychologically psychologically diff modelers annotated ena neighbouts phenom ican advocates chology duplicating identifica 
#@Cottrell_G,Milostan_J,
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#*network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model input input input input input input input input input input input input input input input input input input input input input input input input input input data data function function function function function figure figure figure figure figure figure figure time time time time time time time time time time time networks networks networks networks training training training algorithm output output output output output output output output output output output output output output output output number system system system system error error error error error error error error error error error error error error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state results results results results units units units units units units units units units units units hidden performance performance performance performance performance performance performance performance space space space space space linear layer layer layer layer case case vector vector systems systems systems systems systems probability probability noise unit unit unit unit unit unit unit distribution distribution distribution distribution distribution recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point single single processing processing processing processing processing processing large rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class inputs inputs shows shows visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual examples small small feature net net net net net net net net net task task task task task task task task task task task task task task process process process process level current trained trained structure random random high memory response response response response response response response response response response response response similar similar similar representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show equation rule parameter parameter parameter average average theory theory theory theory theory theory theory term term activity activity activity activity activity dimensional result university university university threshold computation research found dynamics dynamics dynamics initial table table standard standard standard computer computer terms terms distance distance connections connections connections science science science science science prediction left presented presented presented presented presented presented presented presented presented map map present present activation object object object object object object range range press basis outputs abstract back computational computational convergence convergence references component component component due due due positive procedure important important important propagation introduction complex complex complex hand behavior effect effect effect effect generated generated recurrent recurrent tion tion tion change difference lower rules word chosen chosen chosen chosen chosen higher higher type type required required required required required required multiple multiple multiple multiple cortex cortex binary distributed fact fact region proposed proposed proposed correlation correct correct correct correct correct correct correct correct correct correct correct correct correct correct observed observed errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors simulations resulting ing ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total simulation simulation human computed respect multi sum performed times times elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means means made made made made made made made made study relative relative specific specific specific represented provide objects objects objects objects objects objects objects objects objects rates rates rates rates location determined experimental related related posterior constraints cortical brain brain brain equal equal power approaches mit accuracy accuracy update train nets nets modeling proceedings proceedings report report report consists internal represents connectionist connectionist connectionist connectionist connectionist responses responses responses responses responses responses responses difficult exp bias layers addition ai ai maps maps framework cambridge domain domain directly design transition stage stage stage stage stimuli stimuli effects effects effects effects effects conference conference capacity capacity requires requires significant significant significant speed speed speed speed vision basic give produce produce produce weighted weighted randomly randomly levels bounds types types path path actual processes processes selected nature depends constraint associative discussion normal normal normal feedforward feedforward feedforward feedforward feedforward feedforward arbitrary denote denote denote denote tested tested close close close close close close assumption assumption assumption assumption assumption assumption corresponds predictions predictions rbf rbf rbf amount amount amount supported require require require require journal hypothesis cluster cluster degree makes makes makes noisy noisy noisy noisy including including fit auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory simulated simulated simulated smaller account account account account account account functional functional functional fully increasing mechanism mechanism mechanism mechanism trials leads leads details making early idea combined produced produced produced produced produced description architectures property property element typical similarity similarity similarity similarity similarity strategy period subject subject cognitive cognitive cognitive recently recently sufficient sufficient sufficient sufficient highly highly previously subjects works tions tions smooth correspond correspond converge definition definition symmetric increased grant constructed exists concept occur occur occur occur wide alternative correctly clusters clusters generally generally demonstrate strength strength strength critical valued interactions interactions measures designed weak strong strong strong mechanisms presence external external characteristics radial assuming variety program attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor appears pro produces perception ways primary generating distinct distinct dept dept dept changing implement averaging involves slightly interaction interaction interaction interaction interaction formed formed shift independently focus review interpretation interpretation influence transform updated fraction fraction activities activities activities activities suggested suggested converges allowed past sign partial partial partial partial partial partial partial earlier additive spaces spaces spaces spaces spaces spaces roughly iterative generation intermediate initially sufficiently euclidean classified avoid box determines mozer mozer mozer mozer mozer mozer mozer mozer mozer mozer black partially simplicity reason determining society society included mcclelland mcclelland attractors attractors attractors literature kind repeated contained neuroscience dis categories cues cues built involved michael absence modular subsequent subsequent acknowledgments deal receive presents presents bars bars explore explore unlike carried perturbation perturbation difficulty rapidly varied relations involving involving involving involving strengths rise rest rest rest rest mappings referred proper pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway pathway understand cognition removed examined act circles psychology perfect ensure aspect mapped mapped mapped initialized ith ith ith arbitrarily submitted explain explain established asymptotically trivial unstable phenomena phenomena phenomena explanation explanation explanation explanation cascade cascade straight tive tive tive purposes producing producing forces forces immediately arise consequence sounds annual annual incomplete qualitative preceding meaning meaning explained requiring apparent considerably items pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways pathways amounts fed share marked slower incorrect psychological operate proven gave conclude age neuro damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage damage patients patients patients patients patients patients patients patients begins attentional median eventually eventually semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic semantic yielding irrelevant irrelevant cor trade trade trade phenomenon corrupted corrupted corrupted proportion proportion summing acts acts zemel concerned eliminate eliminate connecting grey eliminated wrong wrong chance chance chance chance chance chance chance chance mark removing wire methodology shifts imply cottrell optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic responsible modifications modifications corpus reliably mance mance mance becker becker representational representational representational representational governed patient patient perfor perfor perfor conjunction mental colorado colorado accounts accounts accounts searching dif surprisingly creating suggesting clean clean clean clean clean clean clean clean clean clean clean clean clean clean clean clean properly arrows arrows gesture gesture gesture gesture erlbaum erlbaum partitioned explains explains explains influences severe severe severe sequentially boxes yielded associations land visually visually visually visually visually visually visually visually basin asked forced feeding feeding adopt perturbed lesions lesions lesions tendency tendency hillsdale hillsdale guess representa visited mutually argue arising home publication exclusive interact compensate impose denoting boulder boulder paired books nonetheless tively accounted turning minor minor refined compu experi examination continually continually manuscript coming architectural demonstrating sorting ping mcdonnell correspondences vis ferent shot arrow diffuse interpreting interpreting proportions tribution sharply floor believed contrasts interpretations explanations explanations explanations frequent compensated experienced quick quick bradford priming priming priming priming priming meant semantics semantics semantics semantics semantics semantics semantics semantics semantics inaccurate ated ini subtle tory propagates explaining facilitates elaborate localist relax relax disorder disorder disorder pew occasionally quantified pull rela turing virtue plausibility entities erroneous erroneous disorders disorders disorders disorders accu lowered offered availability tics parsimonious constructions copied damaged damaged damaged damaged damaged damaged damaged damaged damaged damaged damaged damaged damaged damaged damaged damaged damaged lesioned tially deficit deficit deficit deficit deficit deficit serving testable feeds responsive responsive responsive tational mon anatomically dam dam dam duce succeed plaut plaut plaut embody quence pennsylvania implementa modulates sug strengthened cleaned cleaned conscious associ simi manifested manifested consis interac tent strengthening racy verbal verbal alterna impairment impairment impairment impairment impairment impairment neurological eventual loci weaken inevitable benson benson corruption corruption proposing aged aged aged slowed arbi fifteenth semantically neuropsychology mentally behrmann behrmann conse mathis mathis mathis lesioning trary deficits exert cascading cascading unconscious sem occipital ceiling posit posit finishing gested larity disrupted unilateral audi questioned 
#@Farah_M,Mozer_M,Sitton_M,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input input input input input input input input input input data data data data data data data data function function function function function function function function figure figure figure time time time time set set set training output output output output number number number number system system system system system system state results results results units units units units units units units units units units units information information information problem problem models models models models models models models models models models models models models models models performance based based based based weights weights weights weights weights layer vector shown systems values probability probability weight unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point single single single single local neuron rate test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis inputs inputs inputs inputs form shows shows shows shows signal signal signal signal signal signal signal simple simple simple simple simple paper small size feature feature feature feature feature feature feature work fig fig cells cells features features features features features features features features features features features features process process process level current current structure random random high high high high high high high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response similar similar similar similar similar similar representation representation representation architecture rule rule rule general average obtained obtained term term term note note activity activity activity activity activity activity activity activity activity activity activity activity result result university university university university threshold threshold threshold threshold threshold threshold solution solution defined found dynamics dynamics initial constant standard terms connections synaptic science presented present present present phase activation activation activation activation activation activation activation low low frequency temporal range learn learn components components components components components components basis continuous abstract back back back back back computational computational references component component component due due due due positive important important context context introduction circuit behavior statistical parallel cost recurrent recurrent tion tion tion tion tion tion tion change variable spatial assume assume assume signals prior representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations word word word word word word word part part center bound required required multiple multiple cortex cortex cortex cortex good binary spike long long long expected fact fact length length length length length length length correct correct resulting resulting resulting resulting resulting ing simulation simulation human respect performed elements regions regions regions mapping means means potential potential feedback feedback global global global global global study study study study study study study study study study study study knowledge original original original relative relative specific specific represented application series provide provide compute active active active active active experimental experimental related cortical cortical cortical cortical cortical cortical cortical cortical approaches contrast update source source source department department department version version consists individual individual individual individual represents responses layers layers scheme cambridge computing computing equivalent experiment environment directly directly additional additional top stimuli effects effects effects effects upper approximate approximate free basic basic increase increase increase increase increase coding weighted randomly developed levels levels levels levels levels area area area types processes evidence evidence evidence evidence nature nature nature inhibitory inhibitory depends depends simply simply biological associative associative associative achieved achieved discussion normal increases describe arbitrary corresponds corresponds complete complete excitatory excitatory excitatory finding finding short short effective implemented implemented implemented generate generate role role eds journal journal journal journal ability ability easily makes noisy including typically pairs pairs pairs pairs pairs pairs pairs underlying needed combination reduced reduced reduced account account account account fully fully interesting testing significantly character character increasing increasing increasing increasing increasing increasing increasing increasing increasing mechanism mechanism consistent consistent consistent consistent consistent structures matching matching matching language language leads principal representing representing representing details details details call numbers window window inhibition stored stored stored normalized idea combined combined minimize predict predict predict predict neuronal membrane membrane discussed recent recent recent pair pair pair pair pair pair robust robust separate similarity similarity similarity similarity similarity similarity similarity similarity similarity sense sense subset cognitive relevant dimensions highly previously subjects subjects works match match correspond sparse sparse sparse sparse sparse sparse mixtures separation separation separation separation separation channels organization storage storage sensitive entire entire constructed constructed constructed exists exists exists lead lead studied studied studied studied studied studied studied studied studied studied studied studied studied studied studied studied studied studied studied studied studied occur occur wide loop loop occurs occurs occurs column column demonstrate place greater hebbian hebbian valued competitive interactions measures weak learns encoding encoding propose strong mechanisms presence characteristics labeled labeled labeled assuming assuming relationship connectivity connectivity question areas areas areas areas areas areas areas areas explicit relation relation pro produces produces primary primary primary mathematical mathematical distinct distinct distinct confidence recall recall recall recall recall recall recall recall sensitivity sensitivity involves slightly text consisting consisting gaussians events events formed quality quality quality quality quality quality quality decreases formation review review review review correlated overlap overlap detailed controlled updated forms understanding suggested translation past diagram key partial partial expansion roughly false false false false valid intermediate intermediate topology existing existing box thesis combinations combinations usa color retrieval retrieval inter memories memories automatic tests tests reason reason columns columns columns columns selecting capable capable driven driven driven mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland wij presentation presentation successful successful projections projections comparing miller miller essentially receives receives summary strongly allowing showing showing showing showing neuroscience issue issue contribution contribution contribution contribution contribution physiological cue cues list list list list list list providing correspondence highest hypotheses thresholds cat attempt overlapping operating body essential experience rapidly involving issues dual dual rise fashion reliable pathway pathway affect cognition cognition cognition trace predicts psychology psychology psychology psychology psychology psychology psychology thought assumes precise separated separated pyramidal extent extent extent extent extent extent extent extent contributions arbitrarily explain phd years slowly separable distinguish phenomena independence caused rapid rapid rapid tive producing producing producing division mation controls scientific hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal arises auto mellon mellon researchers explained reflects composite carnegie items items items items items items items items items items items items items items items items substantially cmu bootstrap amounts tional car cohen item item item item item item item item item item item item item item item completion completion treated frequently incorrect rep psychological psychological psychological psychological rely rely mod pittsburgh pittsburgh differs fall cal occurrence occurrence gave decreased decreased decreased findings findings focused eventually semantic cor cor contextual secondary physiology proportion extensive appropriately plays suppression fails systematic anatomical anatomical stronger stronger occurred occurred occurred familiar loops abilities serves fail receiver receiver combinatorial infor interference interference interference interference interference interference interference interference interference interference interference interference interference interference james encountered conjunction evident colorado colorado histograms accounts accounts lawrence reproduce reproduce claim claim claim hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus treatment recog recog rich rich rich rich rich rich rich rich rich probe probe probe probe probe probe probe probe projects projects projects explains avoiding influences informa linked linked linked ure ure street appeared largely corporation leaming creates opposed opposed failed forced expanding nition nition nition convenience lesions trigger trigger trigger trigger trigger trigger tradeoff ical big experiences recurrence rhythm hillsdale assess reject reject mismatch publication preserved deep formance insights boulder boulder thresholded mediated paired paired paired paired paired increasingly complementary frontal rough represen importantly associates nonetheless apparently responding responding turning familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity els ward failures vice coming rarely drives reversal stores stores versa preserves slot slot resolve font accordance autocorrelation slots slots slots slots slots slots reversible reversible reflecting eliminates harvard harvard neocortical replicated rare condi anatomy compo distinguishing episodes alarms fox neocortex neocortex neocortex repetition functionally functionally mcnaughton mcnaughton mcnaughton raises raises compartment sending encodings tations comer compromise sparseness sparseness tical catastrophic episode problematic adequately occurrences recalled silent responded awij explaining degrades constituent tivity plenum publishing preventing predic nents virtue activa activa erroneous ness dealt psych manipulations stim humphreys humphreys scribed registration dissimilar consciousness remember cued cued judgments reilly reilly reilly reilly reilly reilly reilly reilly reilly reilly reilly reilly translating distinctive experimentation oooo walter walter associating cog successes cap critically critically critically critically acti unitary efficacies communicated leak prepared theta sole blend accompanied cited superficial conjunctions conjunctions conjunctions conjunctions stud resentations conical feedfor conscious lacks desimone flamework unspecified tex cai lastly conjunctive conjunctive conjunctive conjunctive mecha aging aging aging aging aging recalling pairings adults adults signifi labor comple odds impaired impaired sparser sparser facilitated facilitated entorhinal ied kenneth hibitory probes probes participants participants participants elaborated elaborated shaw shaw richly dentate facilitating discrimi concomitant perspec contradictory nism integrative occurence lective campus amnesia cantly suffering creased consult unconscious tured episodic retrieves complemented nate uli inhi sits vated contradict randall desireone lect eco eco bition confidently istics confound 
#@McClelland_J,Norman_K,O'Reilly_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time set set set networks training training training training training training training training training training training algorithm algorithm algorithm output system system system error error error error error state state state state state state state state state state state state state state state state state state state state state state results results results results results results results information information problem models based based based based based based weights weights linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case vector vector vector vector vector vector order order shown shown shown systems systems values probability probability noise noise weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern image image image image image image image image image image image image image image image image image image image single processing processing processing processing processing control control control large rate rate matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal inputs inputs inputs inputs inputs form form shows simple gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper examples examples size size size net net work step step points field field field field field field process process process process process process process process process level current current current current current current current trained trained trained trained random high high response response response similar similar show show show show equation equation equation equation equation equation equation equation equation equation equation line rule rule images images images images images images images parameter theory obtained obtained obtained obtained note note note note note note result university university threshold threshold threshold threshold threshold threshold threshold computation research research log log defined sequence sequence sequence sequence sequence sequence dynamics dynamics initial initial initial initial constant constant constant constant constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard computer computer synaptic science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction activation activation temporal object object object object object object object object object object object object object object motion maximum press press learn learn components components basis outputs outputs abstract applied back convergence properties likelihood likelihood references stochastic due important context introduction hand estimation estimation estimation behavior behavior behavior stimulus statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic recurrent recurrent recurrent search tion tion difference lower signals signals signals signals prior higher part cases multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex binary binary distributed distributed expected markov make region proposed proposed observed observed observed observed observed observed errors errors errors errors minimum resulting ing simulation simulation simulation human computed sum sum regions regions optimization optimization optimization optimization natural natural natural feedback feedback feedback feedback study knowledge em em em filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter negative negative artificial represented represented series receptive receptive provide compute objects objects objects objects objects objects objects objects objects objects objects objects objects objects perform active experimental experimental goal goal related related posterior gain gain gain cortical cortical brain equal mit mit larger contrast fields train train modeling modeling report institute words department implementation implementation internal internal internal internal internal internal advances advances represents responses responses final sequences sequences sequences cambridge cambridge equivalent directly view estimates estimates estimates transition transition top top top top top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects effects determine requires choice choice statistics statistics free basic pages pages con produce derived weighted weighted criterion criterion area path actual provided evidence iteration nature nature depends simply covariance covariance covariance covariance covariance technical feedforward feedforward feedforward increases describe denote tested predictions predictions common implemented implemented implemented assumed generate supported journal square end pixel pixel ability ability ability future future sensory sensory sensory sensory sensory sensory simulated simulated account dynamical functional jordan interesting significantly york york segmentation segmentation mechanism special squared squared squared squared filters making inhibition bottom bottom bottom decay decay decay attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention neuronal denotes denotes denotes denotes denotes property property pair robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust introduced moving moving moving moving pixels pixels hierarchical hierarchical hierarchical subset relevant interest interest highly varying varying previously previously previously previously previously previously previously observations works tuning tions yields yields correspond trans diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal address background background background locations locations entire grant horizontal horizontal horizontal horizontal invariant suggests suggests suggests matrices matrices predicted predicted predicted predicted touretzky white white white generally setting demonstrate demonstrate demonstrate row row conclusions operator editors editors accurate designed taking taking taking mechanisms mechanisms presence presence characteristics intelligence turn minimizing minimizing minimizing selective selective selective selective min scene scene question areas explicit explicit pro van derive solving ways primary generating laboratory vertical vertical vertical vertical vertical modeled pruning explicitly explicitly simultaneously involves remaining remaining easy interaction interaction minimization expectation expectation cycles john john national focus focus focus review reconstruction reconstruction depending depending squares squares squares squares squares viewed viewed viewed interpretation influence updated modulation modulation modulation forms forms forms forms forms static static static static static suggested converges classical normalization normalization reduces reduces filtering filtering filtering filtering koch degrees degrees recorded figures recognize recognize recognize determines determines determines extension mozer mozer discussions gating gating gating gating gating gating gating middle extra society computationally effectively effectively successful miller essentially identity identity identity identity road procedures showing anderson interpreted interpreted interpreted interpreted neuroscience neuroscience stopping issue lie lie generative generative bar bar bar bar bar bar bar dayan minimizes observable maximization predictor attempt routing extend minimized bars wiley wiley essential circuitry updating rapidly kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman integral ml scalar rest maximizing gates proved encode understand analogous measurement measurement measurement measurement measurement measurement necessarily predicts predicts assumes assumes initialized ith ith ith ith ith switching explain serial attempts residual residual residual residual residual residual residual residual residual residual residual ment ground derivation biology answer expensive handle handle implementing implementing arise mation recognized recognized gradually gradually depicted author annual incomplete recognizing fourth prop simulate simulate treated treated outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers switch modulated extracting popular incoming resource display decreased expectations expectations attentional attentional attentional attentional attentional attentional deviations deviations converged don temporally linearity recover royal suppression primate mail replacing familiar salk exceeds substituting inferior infor equals regarded dominant dominant hasselmo viewing entries entries exposure artifacts occlusion occlusion occlusion discounted eng smoothed smoothed suggesting ballard ballard ballard jolla davis subsequently subsequently ignore ignore dempster interestingly automated specification numerous rubin sig emergent emergent rao rao rao rao rao rao rao tween residuals residuals obtains corrected corrected demon shifting alternate neurophysiological neurophysiological mediated switched depicts mask mask ambiguous ambiguous selectively laird maintains tively grateful minor mimic rochester rochester rochester rochester ignoring treating september gauss suggestions gestures gestures remarkable differently resolve bility generarive recogni rivalry crude mst olshausen generafive generafive pan arrow exper essen conflicting possess petsche interpretations measurable measurable comprising cooperation recognizes tended neurobiological transpose complement complement attended attended resultant zeros priming priming cess comprised correlates correlates correlates correlates correlates correlates occluded nih distractors robustly foreground cyclic outlier outlier outlier outlier enabling rec unnecessary newsome explaining refine instant instant instant clutter clutter clutter clutter clutter clutter clutter clutter clutter repeating repeating preventing huber gross inability reviews possesses accessible niebur dana genesis suggestion itd panels sual fatigue susceptible sponse quences highlights rejecting generatire extraneous spotlight spotlight spotlight spotlight spotlight preferentially maunsell attend attend attend attend consequent consequent grayscale desimone desimone occluding occlusions occlusions occlusions occlusions occlusions duncan duncan depart lai nals effec torrey pines corrects deviate possessing asme anu tackled spectively extrastriate collapsed treue nary cnl depicting bryson influencing phe ques interprets interprets instants verges tln erty capa imental gent summand summand uts fects mediates unresolved emer attending metaphor phs matfix nomena modula moran prescribes strates desireone bulk petition paying occupying inconclusive 
#@Rao_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input data function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training output output output output output output output output output output output number number number number number system system system system system system system system system system system system system system system system system system system system system system system error error error error state state state state state state state state state state state state state state results results units units units information information information information information information information information models hidden hidden hidden hidden space space space space space space space space space space space weights linear linear linear linear linear layer layer layer case vector vector vector vector vector vector vector vector vector shown systems systems systems systems systems systems values values values values values values values values values values values values noise weight weight functions functions functions functions unit recognition point point point point point point point point point point point point point point point point point point point point point processing processing processing processing processing processing processing processing local rate rate test analysis analysis analysis analysis analysis analysis analysis analysis matrix shows shows shows shows shows simple simple simple simple simple simple simple simple simple simple simple paper work work work work task task task task task task fig step step step step step step step step points points points points points points field field process process process process process current trained trained structure high high similar similar similar similar show show show show show show fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line line line line line line line line parameter real real real real states theory theory theory note note note activity activity dimensional dimensional dimensional dimensional dimensional university university university variables variables variables computation computation computation computation computation computation computation solution solution solution solution solution solution research research research independent found sequence sequence sequence sequence dynamics dynamics dynamics dynamics initial initial constant constant constant distance distance connections connections node node node node node node node science science science prediction prediction prediction prediction prediction left left direction presented present phase phase phase phase phase phase activation activation low machine machine learn learn learn learn learn learn learn learn components components abstract back computational analog analog analog analog analog analog analog analog analog references important decision decision decision decision propagation context context context introduction hand hand effect recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion tion change complexity variable variable variable variable learned learned center previous previous cases distributed equations equations equations make fact region region region region region length length length correct errors errors finite finite simulations simulations ing ing total total total total total performed times regions regions regions means dimension dimension dimension dimension dimension dimension dimension made made global study relative application provide provide rates location determined discrete discrete discrete discrete discrete discrete power steps steps steps steps steps contrast train proceedings words department department implementation version version version consists consists consists consists consists bias graph graph graph sequences maps considered equivalent directly solutions solutions transition transition transition transition transition transition transition transition transition transition trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san conference requires free free estimated basic condition condition derived derived developed criterion processes nature simply close complete complete stable predictions predictions predictions predictions predictions predictions finding short end end end end end end end end end end end hypothesis easily easily makes makes makes needed dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical functional fully technology character projection projection increasing increasing head mechanism mechanism mechanism consistent empirical empirical principle principle language language language language language language language language language language language language language details pre making stored early added sources predict predict predict takes takes element include side side subset cognitive cognitive cognitive recently recently relevant dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions dimensions axis tions match evaluation evaluation generalized sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive grant grant correctly correctly correctly clusters clusters clusters occurs setting half half half half half flow flow conclusion conclusion starting starting place place trajectories trajectories trajectories valued valued encoding strong mechanisms mechanisms california solid solid proportional proportional proportional turn plane characters base base question acknowledgements pro produces produces longer longer longer longer longer plot plot describes transitions transitions recall implement implement implement implement explicitly explicitly linearly linearly easy develop develop extraction boolean boolean focus evaluate evaluate restricted updated organizing organizing showed showed margin similarly similarly updates dashed dashed performing expansion expansion expansion expansion add string string string string string string string string string string string symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol precision precision precision expect includes activations coordinate strings strings strings strings strings strings strings strings strings strings strings strings strings eigenvalues eigenvalues subspace subspace holds regular symbols symbols symbols symbols symbols symbols symbols build computations plots composed refer notice kind kind kind moore moore moore moore moore moore running manifold manifold hold backward eigenvalue extend situations diego investigate put issues graphical graphical graphical behaviour periodic periodic periodic periodic matches school investigated proper proper eigenvectors affect encode encode understand matched matched removed induction man predicts predicts predicts predicts psychology recognizer recognizer implementations aspect aspect der formal store store store store store store store store isolated languages languages languages mentioned piecewise separable separable unstable unstable unstable coded coded processed processed processed sys organized arise ion projected projected projected projected separately demonstrates demonstrates annual researchers researchers questions composite composite elman elman elman elman embedded embedded embedded autonomous maintain stack stack exhibits rely cal enables hamming picture saddle saddle saddle saddle saddle saddle saddle saddle assign resources perfectly count count count count count count count count count count count repre discover tem turned maass maass maass wrong occurred occurred serves salient generalizes alphabet published embedding reset paul expanded dominant dominant counting counting counting counting counting counting counting counting counting counting counting counting counting counting counting counting lawrence counter counter counter counter counter counter counter multiplied foundations contraction contraction contraction contraction pollack pollack jolla properly ends reverse implicitly implicitly santa dividing dividing dividing dividing dividing dividing dividing dividing counts counts counts counts informa ure piece accept accept planes expanding copy copy copy copy copy affects hillsdale australia clustered reject jacobian representa crosses investigating harder harder harder importantly associates oscillating funded inversely inversely inversely pop sweeps sweeps likewise tune tune tune tune tune eigen treating rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn recognizers recognizers mix helps ucsd ucsd transducer transducer moderate stores stores copies copies council acquire ate ate recogni australian jersey oscillate arrow mirror realizations recursion visit visit injected dissertation ally push sym sym maxi predictable inspection inspection inspection longest longest ranged cess ings oscillates robustly contents counted ous prescribed wiles wiles wiles wiles wiles wiles wiles tory hot accepting cancel graphically proce ample trick devel des copied copied ting fur solu tums latch counters counters counters divides mined siegelmann siegelmann siegelmann siegelmann ons ons continu expands expands expands quences queensland queensland rutgers occuring embody matters subsequence subsequence subsequence casey casey casey concatenation contracts contracts attracting attracting attracting attracting subsequences subsequences oped rodriguez rodriguez rodriguez rodriguez rodriguez lution precedes transi contracting contracting vious rnns rnns rnns rnns rnns informational ash brunswick subse namical ouput haft haft haft haft haft haft cogsci bed superset trajec janet janet disregard interpolates colinear dynami ofa ofa nnmber dle drs bol rele seventeenth subsumes mite bols substring vant 
#@Rodriguez_P,Wiles_J,
#t11
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#*network network network network network network network network network model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time set set set set set set networks networks networks training training training training algorithm algorithm algorithm algorithm system system system system system system system system system system system system system error error error error error error error error error error error error error error error error error error error error state results results results results results information information information information information information problem models models models hidden hidden performance performance performance performance performance based based space space space weights layer case case case case case case vector order shown systems probability probability parameters recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach pattern image image processing large local rate rate rate rate rate rate rate rate rate rate test test test test analysis class class class optimal shows shows shows shows algorithms simple visual examples examples small size size feature task task task step step step step step process process level level level level level level level current structure high high high high high similar similar architecture architecture show fixed images images images images general speech speech real average average average note note experiments result university university university university university threshold threshold threshold solution research research independent found found found found found sequence sequence target initial initial initial table table standard computer computer distance distance distance distance distance distance connections connections presented presented presented presented map map present low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets sets sets sets range position basis outputs abstract computational references ieee context context context context context context context context introduction hand behavior stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect generated generated generated generated parallel cost cost cost cost search difference difference difference difference difference difference difference difference difference complexity lower lower prior prior word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word word higher higher higher higher higher higher higher higher higher cases type good good good binary expected expected expected markov markov markov fact region proposed proposed proposed proposed length length length length length length length length correct correct probabilities probabilities probabilities probabilities probabilities probabilities observed forward classes classes ing ing tasks total total human human human human human human human human human human human human human human human human human human human respect respect multi multi sum times times times times times times times times means made made natural study study study study knowledge knowledge knowledge knowledge knowledge original original original original artificial relative specific compared compared series compute rates rates rates rates rates rates rates rates rates rates rates rates perform goal constraints gain steps comparison comparison comparison comparison comparison comparison comparison morgan proceedings report words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words technique consists advances represents layers layers delay delay addition graph sequences sequences equivalent experiment experiment experiment directly hinton estimates design limit stage stimuli stimuli effects effects effects effects significant significant significant significant statistics world speed speed basic pages con produce produce produce derived randomly randomly randomly developed levels levels levels levels levels levels levels lines path actual simply achieved discussion technical describe hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm fast fast corresponds corresponds complete finding finding amount short short short implemented shape shape generate supported main main pixel pixel ability ability ability ability noisy including fit kaufmann smaller smaller combination combination combination account interesting testing significantly character character character character character character character character character character character character character character character character character character character character character character character character character character character character increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation database database mode mode mode mode leads call direct window window window window window window window normalized produced produced run description light resolution takes reported reported reported introduced subset interest compare compare compare compare compare approximately calculated calculated calculated match increased grant grant lead deviation wide predicted feed generally generally pass half half greater greater segment depend differences accurate performs performs performs moody faster taking strong hard physics characters characters characters characters characters characters characters characters characters groups groups groups force base base appears digit longer longer longer longer longer optical ways ways label dept dept dept metric simultaneously electrical electrical slightly slightly angle unique interaction interaction interaction interaction integrated frequencies frequencies frequencies quality quality quality quality quality quality extraction select depending viewed viewed influence influence codes detailed evaluate operations restricted discrimination earlier calculation calculation slow additive calculate string string string string string string string string string string transactions expect recorded recorded includes coordinate strings strings strings strings strings recognize recognize recognize recognize recognize determines specifically tests successfully determining selecting middle capable divided presentation build efficiently score tend composed refer cun cun return return timing timing timing timing duration list list list list list list list list list list involved involved denker denker highest consisted acknowledgments humans humans humans humans humans humans humans humans humans humans humans humans detail optimized behaviour matches terminal possibility decisions scores scores scores scores scores scores scores scores scores smallest smallest smallest possibly editor reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading reading extremely psychology created recognizer recognizer thought obvious speakers mixed indicating costs costs costs costs capabilities tractable correction worse worse worse processed shared preprocessing incorporate leaves leaves probable probable recognized recognized english english read computers mellon alignment questions reflects reflects reflects improvements varies considerably considerably evaluating evaluating carnegie limits collected substantially empirically pure pure cmu dark documents documents documents documents documents documents documents calculating calculating pittsburgh occurrence chose chose segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented implements viterbi semantic semantic semantic hints hints gap contextual sort tation restrict pick pick concerned printed printed printed grey systematic chains difficulties replacing multiplicative height handwriting abilities keeping preparation alphabet degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation selects service mance document document document entry entry entry entry displayed perfor lang bad bad viewing eng eng reader verification merge correcting interestingly interestingly influences displacement divide posteriori unchanged geometrical geometrical converted visually visually basically session guyon convolutional convolutional convolutional asked asked asked asked creates break break randomized legal legal legal legal legal legal axe pieces medium medium exception causing jabri jabri jabri jabri jabri big australia australia australia reflected assess burges factorial care ocr degraded degraded degraded degraded hubbard convert picked picked emphasize argued confirmed depicts insertion million sweeping denver dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary dictionary behaves status students scanning picking deletion differently council font decided monitor australian heavily doesn tanaka lists lists char hour returned resolutions striking normalize repetition successively substitution screen inspection sliding sliding sliding sliding frequent reproduced consumption priming dent indepen surprise counted durations eighth lexical lexical lexical lexical lexical lexical stems ted segmental align topics sydney sydney sydney sydney sydney sydney sydney sydney insertions touch excluding tentative prohibitively paid blur explores syntax deletions closing neighbouring readers readers skew instructed native albrecht nicely decade schenkel schenkel schenkel schenkel schenkel schenkel recruited marwan reversals matan print print ported analysing illegal illegal illegal illegal illegal illegal illegal illegal illegal cnn memorize nsw nsw nsw aged barely participants participants participants participants participants participants participants participants participants benefited edit edit edit edit edit edit declines sedal sedal sedal trigram staff grams ably deficits taining reliance uncorrected segmen morning dations acters workings informed doc instructing melbourne looses 
#@Jabd_M,Latimer_C,Schenkel_M,
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#*network network neural neural neural neural neural neural neural neural neural neural input data data function function function figure figure figure figure time time set set set set set set set number number system system system system system system system error results results units units units units information information information information information information information information information information information information information information information information information based based based based based based linear linear linear case order order shown shown shown shown shown shown systems probability noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach approach point point point single processing processing processing processing processing processing processing processing processing large large neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate test analysis optimal optimal optimal optimal inputs inputs inputs inputs form form shows shows signal signal signal signal signal signal signal signal signal signal simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual paper paper paper examples work work work methods fig fig fig fig fig fig fig fig fig fig cells step points points field field field random high response response response response response response response similar similar similar show show section line line line line line line line line line line line line line line line line line line line images images images speech speech speech real theory theory theory theory theory theory obtained obtained obtained note result university variables research research independent log log log log log log log log log found found found found estimate estimate estimate estimate estimate terms science left left left left left left present present present phase phase low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal object sets sets sets range press press press components components abstract applied find properties properties properties properties properties properties properties references procedure important introduction complex complex complex estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical variance variance variance variance variance variance tion complexity spatial lower lower lower measure signals signals signals chosen chosen higher higher higher higher center center center previous previous bound bound bound firing firing spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long long make fact correlation observed observed resulting resulting computed computed computed performed called times made made natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural study study study study filter filter filter filter filter filter filter obtain obtain true compared compared receptive provide define compute rates proc location experimental goal distributions distributions distributions distributions gain cortical power power power mit mit comparison comparison support train train train train train train train train train dependent consists consists code code code code code code kernel kernel advances joint responses responses responses responses responses responses difficult exp scheme cambridge computing computing experiment curve curves design san san san stage stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects bit bit bit bit bit bit capacity efficient efficient efficient requires statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics vision vision estimated increase give coding coding coding coding coding coding coding coding coding coding coding conditional conditional conditional conditional lines entropy entropy depends sampling measured measured describe arbitrary transformation limited limited inverse assumption corresponds corresponds predictions short supported theoretical main adaptation ability hypothesis hypothesis future makes sensory including auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory transfer interesting significantly significantly significantly ratio ratio ratio ratio consistent uniform uniform uniform uniform database leads call window normalized normalized normalized normalized normalized early early decay minimize produced discussed robust robust reported lateral identical compare conventional approximately calculated correspond studies background background locations modified modified organization amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude constructed parts expression studied scaling scaling occur occur suggests spikes spikes width width white generally generally conclusion starting segment exponential exponential exponential exponential exponential exponential sound sound sound sound sound sound sound sound encoding encoding encoding hard characteristics characteristics characteristics characteristics characteristics characteristics characteristics drawn drawn drawn demonstrated california solid solid solid solid solid solid solid min iii averaged manner scene scene scene identification program question acknowledgements relation van van construct construct primary primary changing segments segments segments segments segments averaging averaging averaging slightly consisting mutual mutual mutual mutual frequencies frequencies frequencies frequencies gaussians choosing extracted independently reconstruction reconstruction stages stages estimator estimator estimator codes codes transform transform controlled restricted modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation understanding approximated completely similarly constants discrimination discrimination spectrum spectrum spectrum spectrum spectrum spectrum calculation calculation dashed dashed dashed dashed dashed dashed dashed dashed dashed normalization sec sec sec sec msec foundation foundation advantages recorded coordinate retinal plotted plotted plotted phys straightforward efficiency efficiency differ effectively comparing miller miller soc soc notice neuroscience dis issue duration sampled cat cat preferred neighboring extend trains trains trains trains explore explore simpler unlike carried diego investigate relations humans dotted dotted dotted dotted dotted hall fourier fourier examine respond fashion ideas office complicated understand topographic matched neu transmission concepts reading rev adjusted impulse observe nervous academic extent animal animal indicating scenes scenes scenes scenes scenes scenes scenes cos cos band band band band band analyzed adapted processed snr snr snr snr snr snr snr snr snr snr closer constructing incorporate nucleus sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds opt read auto author addressed reflects pure pure amounts capability capability recordings detecting slower music music music measuring measuring modulated modulated extracting incoming incorporating enables chose shaped findings instantaneous spectra physiology physiology conditioned narrow narrow narrow naval systematic khz khz khz khz mail mail simplify analogy familiar abilities bands exploit neurobiology ral affected optimally carry inferior inferior inferior exploring prentice bialek bialek bialek bialek bialek bialek bialek bialek bialek bialek displayed displayed enhance laplace enable francisco francisco insight creating mem suggesting theoretically colliculus colliculus colliculus lett fitted discriminate discriminate informa transmitted responds corrected amplitudes evoked evoked evoked electrode decorrelation assess reconstruct musical equality distri distri distri gener mathematically fir lond investigating selectively importantly distinguished figs tones tones syllables geniculate milliseconds bution bution bution chris const quantify hearing hearing jersey focuses finer played carrier fre atick atick atick atick atick atick ally fft successively comprising systematically exploits exploits sloan sloan quantitatively enhances sliding sions cutoff cutoff ruderman ruderman ruderman focusing steveninck steveninck translates ruyter ruyter tens frog frog cats wiener wiener wiener wiener assessing quantified quantified phy phy rieke rieke rieke rieke rieke rieke rieke imaginary quency bird redlich redlich stim attias attias attias attias attias attias attias schreiner schreiner schreiner schreiner schreiner schreiner schreiner differed differed basal hypothesize elicited elicited thalamic banks accord dong dong sponse comput kay kay unfamiliar discriminations ucsf ucsf instruments indexes warland warland discriminated brane fundamentals elicit woods midbrain midbrain midbrain midbrain carriers pursue evoke discus keck lagged lagged songs laughlin laughlin anesthetized iiiiiiii iiiiiiii integrative hagai uli natu hancement ecological 
#@Attias_H,Schreiner_C,
#t11
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#*model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input data data data data data data data function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time set set set output number number number number number number number number number number number system error error error results results results results units models models models based layer case order order order order shown shown shown shown shown shown values values values probability probability probability probability noise weight weight weight weight neurons neurons distribution distribution distribution distribution distribution distribution method single large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test patterns patterns analysis shows algorithms gaussian visual small small methods fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells features process process level cell cell cell cell cell cell cell cell cell cell cell cell structure random random random random random random random high response response response response response response response response response response response similar similar similar equation rule general parameter parameter real real real real real real real real real average average average average average average average average obtained experiments experiments university solution defined defined found found found found sequence constant constant table table estimate standard standard standard standard standard computer science science low temporal temporal temporal temporal temporal temporal temporal sets sets maximum maximum range range range press press abstract computational references due due procedure important introduction action action action action behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect generated generated generated variance variance variance variance variance variance lower lower measure signals signals higher bound cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike conditions expected fact fact correct observed observed observed scale scale finite resulting ing total multi multi sum performed performed times times times times times times times times factor factor factor potential potential made relative relative relative relative relative relative relative relative compared provide rates rates eye eye determined related discrete discrete equal equal equal mit larger larger contrast contrast support support train train train train train institute department code individual responses responses responses addition cambridge cambridge computing curve curve stimuli stimuli effects statistics statistics statistics statistics free free free free free free free free free free free free free vision estimated estimated give produce randomly types product actual finally depends depends measured measured measured limited close close assumption complete nearest generate generate generate role role end noisy including fit fit auditory auditory probabilistic probabilistic probabilistic probabilistic typically typically account significantly consistent trials trials trials trials trials trials trials trials trials trials uniform squared numbers added description light light light light neuronal population recent include period period period period period period period period period period period period period period period period period period period period period period period period period identical array varying compare approximately calculated calculated calculated calculated calculated match match sparse definition modified bounded interval interval interval interval interval entire constructed exists intensity intensity intensity extended trial trial trial trial deviation deviation deviation deviation deviation spikes spikes spikes spikes spikes spikes spikes spikes predicted white occurs generally greater greater segment segment segment segment segment retina retina retina retina peak exponential taking strong largest solid solid start relationship relationship averaged averaged minima van van produces written solving generating describes transitions confidence linearly events events events events events events events events events events events versus potentials potentials decreases choosing national national expressed viewed restricted fraction completely similarly calculation smoothing dashed measurements sec intervals intervals intervals event event event event event event event event event event roughly add boundaries boundaries generation assigned foundation advantages precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision precision recorded fire usa inter inter inter inter inter inter retinal retinal retinal retinal retinal retinal plotted prove uncertainty absolute absolute absolute absolute absolute absolute absolute absolute characterized determining selecting identified closely maximal divided divided included spiking spiking spiking spiking spiking spiking spiking spiking plots miller miller summary soc soc notice notice repeated repeated repeated repeated repeated repeated repeated contained contribution timing timing timing timing quantity quantity michael play absence realistic neurosci neurosci illustrates neighboring acknowledgments trains trains trains trains trains trains trains trains trains trains trains trains bars stimulation stimulation stimulation difficulty exponentially dotted dotted matches matches matches investigated comparable variability variability variability matched circles circles transmission necessarily integer panel nerve nerve simplest isolated histogram histogram inequality distinguish agreement agreement agreement biology ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion ganglion spatially constructing projected recognized beginning beginning recording qualitative addressed raw recordings continuously sharp reliability maxima compares compares summarized poisson poisson poisson poisson poisson poisson reaches fiber median distortion instantaneous instantaneous acquisition generator generator generator generator formally restriction extensive refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory refractory count count count count bin bin bin bin bin unity enhancement cellular numerically occurred determination imposed removing affected enhanced continue exploring repeat combines periods periods periods periods periods periods periods bialek bialek conjunction photoreceptor counting counting recovery recovery recovery recovery recovery recovery recovery thin bursts bins extends std johnson johnson fly dividing counts accumulated discharge discharge dramatically yielded drop unable shorter asked obtains spaced electrode molecular illustration thick interneuron argued covered exhibited milliseconds drops rose acoust acoust monitor smoother harvard episodes triangles triangles ref vertebrate reproduced acknowledges acknowledges approached jitter jitter jitter jitter jitter steveninck steveninck assessed ruyter ruyter ruyter silent saturate rises rises quantified quantified intrinsically obeys remarkably recovers rieke rieke repeats excluding conversations mike reproduces corresponded contiguous exclude dev psth psth psth prevented regularly narrower rabbit identifiable salamander salamander salamander salamander peri peri berry berry berry berry berry berry berry berry berry berry berry berry berry berry warland warland pnas silence silence refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness refractoriness heaviside elicit diamonds diamonds diamonds markus markus inhomogeneous sharpening meister meister meister meister meister meister meister meister lasts lasts baylor reviewing ooooo parsed steeply drew extracellularly 
#@Berry_M,Meister_M,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural data data data function figure figure figure time time time time time set set set set set set set set set set set set set set training algorithm number system system system system system error error error error error error results results results information information models models models models models models models models models models models models models models models models models models models models models based based based based based based based based based based case case systems systems systems values probability probability parameters noise noise weight distribution distribution method point single processing processing processing control large large large large rate test test class class class form form form form form shows shows signal algorithms simple simple paper paper small small small small small net net net net net net work cells cells level current trained problems high similar similar representation show show show show show equation equation equation equation equation equation equation equation equation section rule rule rule rule rule rule theory theory theory theory theory theory theory theory term note note experiments experiments experiments experiments experiments experiments experiments activity activity university university university computation research research found dynamics table table table table standard standard standard computer terms terms synaptic science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented presented phase phase temporal temporal sets sets maximum press press press press learn learn learn basis basis basis basis basis abstract abstract computational convergence likelihood references due ieee positive positive positive positive positive important important important important mixture mixture mixture mixture mixture mixture mixture mixture introduction behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical effect effect variance variance tion tion change change difference difference variable rules rules rules rules rules rules prior previous cases cases multiple multiple binary long long long long long long represent expected expected expected equations make make fact fact correct ing ing tasks tasks sum called called called called called means means means means means reinforcement factor potential potential potential made made made natural applications study study em negative negative samples true provide compute rates rates perform perform perform experimental experimental experimental related posterior constraints constraints brain brain brain mit mit steps comparison support support selection proceedings report report department implementation individual joint represents represents final delay cambridge cambridge directly hinton stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects capacity capacity world world world world vision con condition condition derived area types actual finally processes evidence evidence nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory biological associative discussion discussion normal normal describe tested limited limited close inverse complete actions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions short short generate face adaptation journal journal journal end end instance instance makes makes makes makes makes makes makes makes makes makes makes probabilistic combination account account jordan jordan block interesting character york york consistent consistent consistent trials trials trials trials trials trials trials trials trials trials pre pre pre direct making making making bottom experts experts experts experts experts experts expert attention added light light light light light light light light light predict predict predict predict predict predict discussed advantage separate reported apply introduced side sense inference inference sejnowski cognitive cognitive recently calculated tions rl rl rl rl mixtures background background studied suggests suggests trial trial trial trial trial alternative alternative demonstrate strength greater competitive competitive competitive competitive competitive competitive editors editors editors reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward interactions sutton sutton sutton sutton sutton sutton practice suggest sound sound sound sound sound sound sound sound sound sound presence presence presence presence presence presence presence turn start exist relationship reference construct construct index perception ways ways describes changing changing modeled simultaneously easy easy interaction integrated gaussians events events predictive expectation expectation competition competition competition competition competition competition competition independently review review review review review review depending communication detailed forms soft similarly similarly similarly suggested processor key key key key key key key partial partial barto barto barto barto barto barto barto additive additive additive classical classical fitting remains sufficiently foundation foundation transactions expect expect existing existing existing figures thesis priori formulation sciences uncertainty discuss candidate candidate black texture reason reason aspects importance society society computationally computationally divided delta delta delta delta symbols included presentation successful successful miller miller essentially online reached characteristic capture capture traditional allowing moore moore moore anderson anderson neuroscience neuroscience generative satisfy notation involved involved dayan dayan dayan dayan dayan dayan absence absence absence absence absence absence paradigm paradigm leading mixing extract jacobs jacobs jacobs jacobs body unlike stimulation collection difficulty updating association association association association hall hall hall hall ml ml behaviour fashion history behavioral behavioral terminal terminal terminal complicated complicated affect statistically statistically presynaptic notion removed removed act possibly man predicts extremely psychology equally aspect obvious separated separated explain phd seconds established established animal animal animal animal animal animal variances variances variances variances explanation explanation nowlan nowlan nowlan handle handle london reasons implementing shared producing forces controls consequence consequence involve grossberg grossberg grossberg grossberg grossberg cybernetics incomplete qualitative mellon carnegie freeman substantially tional experimentally peter share share slower slower incorrect psychological psychological psychological psychological psychological psychological psychological rewards rewards rewards rewards fall collective substantial sophisticated findings conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning attentional attentional irrelevant cor corrupted proportion oxford oxford conditioned conditioned conditioned conditioned animals animals animals animals animals animals animals food theories theories theories theories theories theories royal outcome extending fails fails neurobiology implications affected affected responsible presentations combines tone tone tone tone tone tone tone tone tone tone predictors predictors predictors predictors studying surprising holland holland holland holland conjunction accounts consequences uni lawrence similarities hippocampus insight insight probe probe properly erlbaum considerations variants captures captures captures explains dempster dempster cam cam informa associations drop incorporates listed rubin discount cooperative reaction emerge distinction adopt pointed lesions chicago chicago england hillsdale causal forcing assess argue distri blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking blocking dominated considers gluck gluck proach constructs laird weaker paradigms paradigms paradigms paradigms funded tones dramatic computa status challenge suggestions suggestions bution stops circumstances circumstances bridge bridge expense continued justification ers wins hoc opponent opponent dropped proportions tip conflicting partly ventral operational marr marr neurobiological implied dopamine implying essence delivery delivery delivery delivery delivery comparator comparator inaccurate surprise substrate capturing unexpected explaining wagner wagner wagner wagner lights rein ton prolonged predic reviews versity confirms paid vertebrates thompson thompson translating justify disappear seeks asso responsibilities trouble trouble maximise prevented expects delivered klein bears owing diseases forcement embodies rectly diction pnas stance montague montague montague montague wealth separations separations discounting instrumental acquires crucially sink upwards upwards upwards upwards gabriel gabriel gabriel anticipated century reporting css serotonin dictions pergamon rescorla rescorla rescorla rescorla contingent phe interleaved pharmacological awt pavlovian pavlovian pavlovian pavlovian parameterised integrative philosophical flaw variabilities variabilities contingency substitutes awl awl schultz schultz involvement founded founded orienting dickinson dickinson dickinson wards challenged ctl omission treatments nomena shock appleton crofts minded abandon prokasy 
#@Dayan_P,Long_T,
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#*learning learning neural data data function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set number number number number system system state results results units models based based based space space space linear case case order shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown shown systems values values values values parameters noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit distribution method method method method method pattern pattern pattern single single single single processing processing large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns analysis analysis class class class optimal optimal optimal optimal optimal optimal form shows shows shows shows signal simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual feature feature feature feature feature feature task methods methods methods methods cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field field field field field field field field field features process cell cell cell cell cell structure structure structure structure structure structure structure structure random random high high high high response response response response response response response response similar similar similar representation representation representation representation show show show show show show show show images average average average average average average average dimensional dimensional dimensional university independent independent found found found dynamics standard standard connections science prediction left left left direction presented presented presented presented phase frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal sets motion motion range range range range press components components components continuous abstract find density density analog properties properties references component component component component component component component procedure procedure context introduction action action action complex complex complex complex complex stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus dynamic dynamic dynamic search change change energy energy variable spatial spatial lower signals signals signals prior learned chosen center center previous firing firing firing firing firing firing firing firing firing firing firing type type type type type type type multiple multiple multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good spike spike spike spike spike long make region region correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed forward scale scale resulting classes tasks computed computed performed times times regions regions regions regions regions optimization potential potential made orientation study knowledge filter negative relative specific specific specific receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive compute rates rates rates rates rates related cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain steps steps comparison fields fields fields fields fields fields fields fields fields fields fields fields fields fields dependent technique individual individual individual responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses addition addition environment directly directly curves san top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects efficient full significant estimated increase increase give produce randomly randomly randomly developed velocity provided selected selected selected nature nature nature nature nature inhibitory inhibitory inhibitory sampling sampling sampling arbitrary corresponds corresponds corresponds corresponds complete excitatory excitatory surface finding finding short short common common common effective effective role role future including including including fit auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory typically typically typically typically typically smaller underlying underlying functional functional functional functional york edge mechanism special structures structures trials numbers inhibition inhibition inhibition inhibition inhibition bottom magnitude attention combined light neuronal neuronal neuronal neuronal neuronal improved lateral lateral moving moving moving moving identical identical array cognitive recently recently highly previously observations approximately approximately tuning tuning tuning axis axis axis axis correspond correspond correspond locations interval organization sensitive sensitive increased increased increased amplitude amplitude amplitude amplitude horizontal horizontal intensity intensity intensity studied studied extended wide spikes spikes spikes spikes clusters white pass pass greater segment conclusions central interactions designed designed designed clear sound sound strong mechanisms characteristics characteristics characteristics california turn selective selective selective decrease decrease acoustic edges edges edges longer perception primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary primary transitions tuned tuned vertical vertical changing changing sensitivity simultaneously simultaneously linearly spectral interaction develop integrated frequencies frequencies frequencies frequencies versus potentials decreases decreases yield correlated open showed showed modulation decomposition soft understanding understanding suggested suggested discrimination spectrum earlier performing sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec add initially msec msec msec msec msec recorded recorded figures combinations activated determining selecting aspects driven presentation detect detect efficiently ten fine characteristic characteristic composed excitation excitation excitation traditional soc compact strongly showing interested neuroscience content timing timing categories receptor sampled michael computes hypotheses cat cat cat cat cat cat cat cat cat cat preferred preferred preferred preferred extend trains bars bars bars explore selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity parametric parametric wiley involving detail ml respond respond respond fashion giving behavioral detectors detectors referred analogous analogous analogous analogous analogous analogous analogous analogous analogous neu onset onset onset onset onset created created thought portion portion panel panel detector detector nervous consist consist detected animal animal animal animal animal histogram histogram indicating indicating preference asynchronous caused considerable considerable considerable drive tive sites producing filtered directional leaves monkey monkey commonly probable probable recognized sounds sounds sounds sounds opt res res res res res res read read recording recording geometry preceding preceding addressed questions populations reflect collected substantially pure transient dark quantitative recordings recordings continuously variant ity rewards schematic span span span characterize characterize characterize modulated modulated serve suited decreased decreased shaped physiol unbiased owl wang wang wang cochlea cor spectra spectra spectra spectra linearity narrow neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol neurophysiol tem jones jones jones jones binocular khz khz khz minutes primate primate primate analogy striate striate hope nearby nearby shifts shifts preparation composition tone tone tone edelman pat pat lengths enhance monkeys monkeys enable francisco spatiotemporal spatiotemporal insight suggesting repeatedly repeatedly specificity sustained sustained sustained sustained extensively reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse reverse characterization characterization characterization receiving unchanged grating grating audio shading shading deriving wiesel wiesel wiesel ber ideally hubel hubel hubel brightness brightness oct oct oct oct oct oct oct oct oct oct oct oct oct oct oct oct oct oct relate echo individually individually individually electrodes adelson adelson confirmed cosine macaque tones tones tones tones tones milliseconds transients transients manuscript topography topography triggered triggered coordination coordination species species species correlogram palmer palmer palmer palmer characterizing characterizing characterizing characterizing reversed twenty christopher prefer quantify terns stochastically spacing abeles somatosensory adult neocortical rons tip tip tip diagnostic spectrogram acoustical sharply evenly impedance impedance progressively progressively tactile edited lying bergen bergen isolation isolation digitized merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich bandpass multimodal drifting drifting drifting drifting drifting drifting drifting twelve gathered sweep gratings gratings ically actively silent sorted phillips phillips tern spanning ripple ripple neurones jenkins sat locating phy phy spectrograms spectrograms thalamus extracellular awake awake awake awake awake awake awake awake awake sought mate schreiner schreiner schreiner schreiner schreiner schreiner schreiner schreiner schreiner pri latencies disk poral knight elicited monosynaptic chord chord chord surrounded oxide roth namic recep tonal tonal tonal tonal occasional indicative indicative indicative octave octave octave octave octave ucsf ucsf microns conjunctions farther selectivities percentages quantifying modulations octaves octaves octaves vaadia prefers plete tex masking shamma shamma shamma shamma hear hear hear hear hear midbrain merz aertsen loud evoke reid reid reid reid reid reid reid reid shapley shapley typ keck tips ret ceptive ultra verse intention passively anesthetized cynader cynader chronic brosch brosch newman newman organizational lasted rnsec rnsec rnsec minority discernible fer microelectrodes outstanding 
#@Merzenich_M,deCharms_R,
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#*network network network network learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time set set set set networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number state state results results results results units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance weights weights weights weights weights weights weights weights layer layer layer case vector order order order shown shown shown shown shown systems systems systems systems values values probability probability probability probability probability noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution recognition recognition recognition recognition method method method method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single processing processing processing processing processing large large large large large large large large large local neuron rate rate rate rate test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns optimal optimal optimal form form shows shows simple simple visual paper examples small small size size work task methods cells step current trained cell structure structure structure structure structure random random random high high response similar representation show show fixed real real real real approximation average states states states states gradient obtained obtained note activity activity activity activity activity activity university variables variables variables computation independent independent log log log log log log dynamics terms connections connections connections connections connections connections science science science prediction left left left left left present present present activation activation low frequency frequency frequency frequency frequency temporal temporal temporal machine machine machine press press sample sample sample abstract applied applied applied back back density properties properties likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due procedure important introduction action action stimulus stimulus statistical effect generated parallel cost cost cost search search search search tion tion complexity variable spatial lower lower lower lower lower lower measure measure learned chosen chosen higher higher higher part center center previous bound bound bound bound bound bound cases firing firing firing firing firing firing firing firing firing firing firing firing type type type multiple cortex cortex cortex cortex cortex cortex good binary binary binary binary binary spike spike spike spike spike spike spike spike spike spike spike spike spike spike conditions conditions represent represent represent distributed expected expected expected expected fact correlation length observed observed observed observed observed observed observed observed observed observed forward forward finite resulting resulting ing total total multi multi multi multi multi multi multi multi sum times means optimization potential dimension made global study negative artificial compared series compute rates rates experimental goal discrete discrete cortical cortical cortical cortical cortical brain mit mit larger larger support descent modeling morgan proceedings version consists code code code code individual individual individual advances advances advances represents responses responses responses bias bias bias addition addition ai considered considered directly hinton hinton hinton hinton hinton hinton hinton hinton hinton additional additional san top top top stimuli stimuli detection full full significant approximate approximate pages pages pages increase validation validation give produce channel channel channel channel channel channel channel channel channel channel channel channel channel channel coding coding coding coding coding derived derived actual actual actual nature nature nature nature constraint biological associative discussion describe tested limited close predictions circuits finding finding finding finding common theoretical require journal journal ability instance instance makes sensory including fit kaufmann objective auditory auditory typically account jordan transfer transfer mechanism trials trials numbers numbers numbers numbers window window window normalized early early produced produced added added added added added added added added added added added predict neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal correlations correlations correlations correlations exact ensemble ensemble ensemble takes typical reported apply apply introduced strategy include identical machines machines machines machines machines machines array unsupervised calculated calculated calculated volume volume tions match match match match correspond studies studies background background background modified modified constructed constructed occur occur trial spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes correctly touretzky clusters column column column column editors editors editors interactions interactions interactions interactions exponential exponential presence presence reduction reduction reduction reduction reduction reduction drawn demonstrated california assuming identification question question acknowledgements relation pro construct produces primary primary modeled modeled missing simultaneously simultaneously averaging involves remaining slightly adding adding applying events events events events springer quality extraction potentials national extracted family stationary stages correlated squares codes controlled centered centered centered understanding understanding understanding understanding activities earlier performing reduces false msec foundation david recorded recorded existing template template template inter retinal instances instances plotted prove activated activated activated mozer mozer absolute characterized encoded computationally spiking oscillatory detect efficiently mackay situation verlag graphs showing showing neuroscience issue physiological generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative gray gray gray involved michael dayan dayan dayan dayan dayan giles observable observable cat extract extract approximating deal decreasing cowan trains trains trains trains trains simpler carried carried create exhibit difficulty varied involving strengths estimators hanson dataset dataset dataset dataset dataset helpful matches matches maximizing maximizing variability statistically statistically understand smallest analyze analyze analyze analyze predicts extremely adjusted greedy greedy detected detected simplest attempts attempts attempts seconds neal neal isolated animal percentage great pairwise pairwise theoretic ground ground crucial crucial fairly analytical tractable tractable benchmark ganglion sys ran monkey monkey monkey monkey monkey probable sounds recording addressed reflects populations populations populations populations reflect collected generic embedded introducing recordings recordings recordings recordings recordings recordings recordings recordings detecting passed rep reliability templates templates templates calculating poisson modulated extracting occurrence occurrence prevent singer datasets comments redundancy redundancy redundancy redundancy neuro windows windows windows windows owl summed synchronization synchronization globally shifted shifted representative feasible sleep sleep temporally pick zemel bin bin bin bin bin bin bin bin bin discovery repre discover promising primate nearby tishby tishby tishby tishby neurobiology observing observing imply combinatorial exploring meaningful financial ranging corre pat monkeys monkeys searching searching searching propagated hasselmo dif francisco ensembles ensembles ensembles spatiotemporal bins bins bins bins bins theoretically reverse jump automated acknowledge neurophysiology neurophysiology largely helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz helmholtz incrementally incrementally incrementally incrementally propagating connec quasi quasi trigger trigger trigger trigger trigger electrode electrode wake wake acting tems challenging ultimately academy frontal importantly assemblies alarm frey frey frey frey milliseconds treating treating challenge manuscript suggestions coordination sponding characterizing recogni christopher generafive overtraining abeles abeles abeles abeles abeles abeles abeles abeles abeles abeles abeles abeles abeles interpreting adult adult played calculates partly petsche sloan sloan merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich merzenich sliding cascaded cascaded cascaded cascaded cascaded cascaded permanent accounting electrophysiological elec assessed promise february tim spa occurrences occurrences occurrences occurrences tens hits tern spanning behaving behaving spario contributing columnar phy phy phy mar awake awake excluding ascending challenges pri deco missed pattem pattem temporary historical surrounded signaling behavioural behavioural konig flips mary engel meilijson duce partic gat gat gat gat ucsf ucsf ucsf geoff grayscale vaadia vaadia vaadia technically mad bergman bergman bergman suspect merz meister meister meister meister meister meister aertsen correlating stepping eee keck virginia artifi invoke cially sents resent greedily integrative cascading chronic chronic decipher decipher decipher equency baylor gerstein gerstein gerstein redun redun sulting brightest arisen microelectrodes gether ish reproducible reproducible ingful ficult darkest lular margalit binned 
#@Merzenich_M,de-Sa_V,deCharms_R,
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural input data data data data figure figure figure figure time time time time time time time time time set output system system system system results results results results results problem models based linear linear order order shown shown shown shown shown values values parameters functions neurons neurons neurons neurons unit pattern pattern image single single control control control control rate rate rate rate analysis analysis form shows shows shows shows visual visual feature work work work methods fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells process cell response response response response response response response response response response show equation parameter result result result result university university university threshold threshold threshold initial initial initial initial initial constant constant constant constant connections synaptic science direction direction direction direction phase phase phase phase phase phase phase phase low low low low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency press press press press press press position position continuous continuous abstract computational computational references due due due due ieee ieee positive adaptive introduction complex hand hand behavior effect effect parallel parallel parallel parallel parallel search tion tion tion variable lower lower lower lower lower lower signals higher higher higher part center center center previous firing firing firing firing firing multiple multiple multiple represent distributed distributed distributed distributed expected proposed observed observed observed observed observed scale simulations resulting simulation multi sum called times times times elements natural natural natural feedback negative negative specific specific provide provide compute rates eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined determined experimental experimental experimental related gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain brain brain brain brain brain equal support institute institute department technique consists represents final exp exp addition limit limit limit stimuli upper increase increase increase increase increase increase increase increase con con produce produce produce levels velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity evidence inhibitory inhibitory inhibitory measured discussion discussion normal normal normal technical increases increases increases describe fast fast fast limited complete stable stable stable circuits common supported adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation ability hypothesis makes sensory including simulated simulated simulated typically reduced reduced reduced york increasing head head head head head head head head mechanism consistent matching details pre making making inhibition inhibition inhibition decay idea combined combined produced produced produced produced added element movement movement movement movement movement movement reported lateral period period period varying previously previously previously previously subjects subjects calculated tions tions smooth trans trans storage storage storage storage storage storage storage storage storage storage increased increased grant amplitude amplitude amplitude constructed horizontal parts lead studied occur occur occur occur suggests suggests rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation move loop loop loop loop loop loop loop loop loop loop loop loop loop half conclusion greater central central central central central central central peak suggest propose strong reduction cycle cycle cycle cycle start movements movements min decrease decrease decrease decrease decrease decrease decrease decrease decrease decrease decrease decrease decrease decrease decrease decrease decrease groups produces produces longer longer perception ann ann stability modeled simultaneously simultaneously physical involves interaction frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies cycles cycles decreases decreases national independently influence ocular centered static completely suggested constants slow slow slow slow slow slow slow sec roughly roughly roughly valid recorded retinal illustrated absolute characterized characterized effectively included showing oscillations oscillations sci comp comp realistic neurosci moves operating neighboring neighboring acknowledgments decreasing stimulation stimulation circuitry circuitry varied humans humans periodic periodic periodic periodic periodic periodic periodic biol plasticity oscillation oscillation oscillation oscillation pathway pathway pathway pathway phases phases removed removed trace trace onset opposite opposite opposite rev adjusted explored simplest vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor vor directed analyzed unstable unstable unstable unstable unstable unstable unstable phenomena biology biology caused caused nonlinearity starts rapid tive sys sys producing nucleus nucleus nucleus immediately ion gradually res res recording limits pathways pathways pathways pathways pathways pathways pathways dark dark simulate simulate experimentally cohen peaks adjustable continuously biologically ity robinson robinson robinson robinson robinson robinson robinson robinson tank tank semi decreased decreased decreased decreased neuro neuro neuro damage damage naive naive naive naive lab cybern physiology physiology oxford oxford tation velocities vestibular vestibular vestibular vestibular vestibular vestibular vestibular rotated rotated tem tem tem jones jones jones eliminate enhancement enhancement enhancement rotations rotations rotations rotations rotations rotations rotations rotations suppression saturation saturation cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum cerebellum check check occurring nearby wilson wilson wilson cerebellar cerebellar cerebellar cerebellar cerebellar reset reset thomas nonlinearities laplace fish fish deg eng eng vari vari divide resonance resonance resonance resonance resonance reflex slight slight gold gold alternating alternating alternating alternating alternating alternating alternating responds magnetic lesions lesions lesions superimposed superimposed sinusoidal demon molecular alter alter shifting wall compensate mammalian mediated mediated acquired nuclei nuclei nuclei conversely oculomotor maintains tively rotating differing circumstances circumstances species bility instability vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo vestibulo continued assistance ongoing oscillate oscillate pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan pan termination purkinje purkinje purkinje purkinje purkinje purkinje purkinje suppress illinois illinois pronounced inherently fre cally horizontally equa trol ultimate intact intact digitized colleagues enhances reproduced permanent fol est ous platform durations brought rotational rotational health col zone dow dow dow dow dow dow dow dow dow dow dow dow dow dow dow dow dow dow dow dow dow dow urbana urbana urbana urbana plenum modulate disorder severely biophysics biophysics prolonged prolonged prolonged prolonged prolonged prolonged prolonged anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio anastasio dead bio posi posi cir canal canal canal controllable tially tially respec ously digitally spontaneously stabilized previ beckman beckman temporary temporary temporary temporary shepherd symmetrically poten inhibits concurrent inactivation fell coil sponse subsystems differentiated permission resonant resonant resonant strated temporarily resembling resembling champaign champaign interrupted lumped lumped mat sug asymmetrical canals alternates markedly nystagmus nystagmus nystagmus nystagmus nystagmus nystagmus nystagmus nystagmus nystagmus zee zee semicircular darkness darkness darkness darkness instabilities creases acta acta organiza bilateral institutes rota bined hartman cuits abruptly abruptly rection lowed ernst creased suppl sulting llin singleton singleton integra continual continual gested hess hess hancement rad uncontrollable sinusoidally unilateral unilateral quencies substan neuroreport neuroreport curred abil dress 
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set set networks networks networks training training training training training training training algorithm algorithm algorithm output system system system system system system system system system system system system system system system error error error error state state results results results information information information information problem problem problem models models models models hidden performance performance performance performance performance performance performance performance performance based based based based based based based space space space space weights weights weights weights weights weights weights case case case case case vector vector vector shown shown shown shown systems systems systems systems probability weight functions functions functions single single single single control class form shows shows shows shows shows gaussian paper size work task task task task task task task task task task task task task task task task task task task methods methods fig cells cells cells cells cells cells cells cells cells cells cells cells cells points field field field field field current current current cell cell cell cell cell problems problems problems problems random memory memory memory memory similar similar representation representation representation show show show show equation fixed fixed rule rule general general general real real real term term note experiments experiments university university computation computation solution independent independent defined defined constant estimate estimate estimate standard standard distance synaptic synaptic science science prediction prediction prediction direction direction direction direction direction direction direction map map temporal temporal temporal machine motion motion motion learn learn learn learn learn learn learn position position position position position position position position position position position position position position position components basis basis basis basis outputs abstract abstract abstract abstract abstract abstract applied find computational convergence properties references stochastic ieee procedure procedure important important important decision decision context introduction action action action action action action action action action action complex behavior behavior behavior difference difference difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial measure prior prior learned learned learned chosen previous firing firing required required required long long represent expected markov fact fact correct probabilities simulations ing ing tasks tasks tasks tasks tasks total simulation simulation simulation regions mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor natural policy policy policy policy knowledge knowledge knowledge knowledge original relative specific specific samples represented provide provide provide provide provide proc location location location location location location perform perform goal goal goal goal goal goal goal goal related brain mit steps comparison larger contrast contrast contrast fields fields fields update support dependent dependent report report version connectionist exp exp exp exp exp cambridge cambridge environment environment environment environment environment curves estimates estimates effects full full full full requires choice choice significant increase con area path path path evidence evidence evidence nature nature depends achieved discussion normal arbitrary arbitrary arbitrary fast fast fast fast limited stable surface actions finding short short short assumed shape generate role require main eds adaptation end future future development simulated simulated simulated needed account block transfer testing head head mechanism mechanism mechanism consistent consistent consistent consistent consistent trials trials trials trials trials trials empirical empirical principal max max pre pre direct stored early early early frame run run predict predict improve recent recent recent property separate separate typical moving previously approximately solve solve solve match match match rl trans positions positions positions locations locations grant parts parts trial trial trial trial trial trial trial trial trial trial trial trial trial trial move touretzky boundary setting runs starting critical place place place place place place place place place place place place place place place place place place place place reward reward reward reward differences accurate designed clear sutton sutton sutton sutton faster asymptotic learns learns learns taking integration integration integration demonstrated relationship relationship targets manner manner manner reference reference reference explicit explicit van longer factors stability tuned tuned distinct modeled coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates simultaneously easy slightly interaction integrated integrated competition choosing depending solved detailed open open open restricted evolution understanding activities completely suggested converges past diagram key barto barto barto slow remains remains calculate foundation david exploration figures figures figures thesis coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate specifically closely importance modification computationally paths paths paths build schemes receives receives quickly decoding showing anderson neuroscience neuroscience issue contribution contribution contribution built dayan dayan dayan dayan dayan dayan absence nips delayed delayed neurosci neurosci moves overlapping policies preferred rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat rat extend situations presents origin origin remain remain unlike powerful singh exhibit exhibit rapidly put environments involving involving lippmann mass respond ideas school tech tech behavioral biol biol plasticity plasticity plasticity ideal complicated complicated hierarchy phases phases matched measurement possibly man extremely changed adjusted extent phd established established integrate animal animal asymptotically brown slowly slowly critic critic critic critic critic critic critic critic critic critic critic fairly navigation navigation navigation navigation improves analytical spatially spatially day day day day day day day watkins watkins actor actor actor actor actor actor actor actor actor pool hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal hippocampal implicit gradually res demonstrates demonstrates demonstrates demonstrates cybernetics incomplete nsf integrating apparent apparent substantially substantially consistency peter sharp rewards requirement requirement aim reaches plan richard credit univ univ acquisition acquisition acquisition ordinary sort guarantee extensive drift drift drift drift angular animals perfectly controlling circular jth addresses generality generality attractive imposed abilities abilities abilities abilities fail preparation wilson days days days days days excellent governed periods guarantees moved moved regard lengths lawrence tic diameter hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus hippocampus treatment modelled modelled offer late late roy proximity proximity extensively erlbaum tsitsiklis speeds interestingly escape escape street summer slight email discount leaming markovian centre centre centre lesions amherst edinburgh edinburgh edinburgh lesion mutually goals blocking challenging challenging acquired importantly barrier funded abbott abbott placing placing refined supporting demonstrating rats rats rats rats rats rats rats rats rats rats rats rats rats rats heading heading reinforce simplification acquire swimming swimming mcdonnell stochastically maze maze maze maze maze maze water water water water shot shot shot conceptual blum morris morris morris morris morris morris gerstner placement mcnaughton mcnaughton evolving cold shaping adequately ensuring platform platform platform platform platform platform platform platform platform platform platform platform platform platform platform platform platform platform substrate replication united cope gradual gradual enforcing pew wan fundamentally rela whilst psych internally comprises vertebrates latencies latencies latencies tums absorbing centred provably behavioural behavioural expressing expressing reinforced cyber burgess embody simplistic keefe keefe indexes indexes bucket foster foster foster foster establishment establishment establishment montague lengthy kingdom alteration remembered remembered scholarship extinction coordi redish thrown neurobiol barriers influencing expe constituted parameterised parameterised sutherland mazes awl schultz refines lids cjch cjch rim coor nate tionship instantiate competent disrupts placements 
#@Dayan_P,Foster_D,Morris_R,
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#*model model model model model neural neural neural neural neural data data data data function figure figure figure figure figure figure figure set set set set set set set set set set set system system system system system system system information information problem problem problem models models models models models models models models models models models models models based based linear linear linear linear linear case case case case case case case case shown shown shown shown values point point point point point point point point local local local local local patterns analysis analysis analysis class optimal form form shows signal signal signal signal signal signal visual visual paper paper paper paper work current cell cell cell cell cell cell high high equation equation line line rule rule rule rule rule rule rule rule rule general gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient activity activity university university computation research research independent found initial initial initial constant constant constant terms terms distance distance distance connections connections science left map map map map map map map present low low low temporal temporal temporal temporal temporal sets maximum maximum press position position position position position position abstract computational computational positive introduction action action action action action tion assume assume assume rules rules center center type type required required required required required multiple long long conditions fact proposed proposed minimum ing performed performed called mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping obtain negative relative specific specific true true application proc proc proc proc location experimental experimental experimental experimental experimental experimental experimental related related posterior posterior distributions brain brain brain institute technique advances addition addition maps maps maps limit effects effects requires requires requires con produce produce produce derived developed levels actual evidence evidence depends discussion discussion normal tested assumption surface predictions predictions shape shape shape shape shape role role role role theoretical theoretical theoretical require require end ability instance instance instance instance makes development development development development development development development pairs interesting projection projection projection increasing increasing increasing increasing mechanism special special consistent consistent structures matching matching direct direct early idea idea produced light predict membrane membrane membrane recent recent correlations reported lateral introduced cognitive cognitive recently relevant relevant dimensions sufficient previously works axis axis axis axis axis axis axis axis axis axis axis smooth smooth studies trans positions horizontal horizontal expression expression expression expression occurs generally column column half conclusion depend interactions interactions interactions retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina retina encoding largest proportional groups groups groups pro derive longer generating ann vertical vertical mathematical mathematical distinct distinct interaction interaction interaction formed competition competition family family family independently expressed expressed expressed expressed expressed expressed expressed expressed expressed expressed expressed formation formation formation formation ocular constants constants constants sign combinations combinations combinations combinations combinations usa dominance retinal retinal retinal retinal retinal retinal sciences discuss black major simplicity uniformly differ committee committee literature literature projections reached road refer soc soc soc soc allowing anderson dis sci sci sci hold cues cues receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor satisfy notation play absence paradigm binding binding neurosci neurosci modelling cowan cowan law law unlike unlike strengths mass mass mass mass mass existence existence mappings investigated plasticity relationships referred referred complicated topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic neu induction gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients rev thought friedman friedman friedman friedman friedman friedman versions der der precise precise separated nerve shapes shapes shapes shapes shapes shapes shapes shapes shapes optimum optimum optimum optimum stop stop developing developing developing developing growth growth growth analyzed growing biology biology majority capabilities ganglion producing protein protein directional directional axon axon axon axon axon axon axon axon axon axon acad acad beginning members members members axons axons axons axons axons axons medical arises led experimentally quantitative quantitative requirement rely branch reaches ordered ordered fiber attraction wang www optimality forming member nat nat unity receptors receptors receptors receptors receptors receptors receptors establish occurred attractive attractive attractive grow optic guide cone cone zhang decide von von conjunction regard regard regard washington consequences infinity infinity uni originally enable hippocampus hippocampus fish specificity proteins roy roy concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration discovered ence unified ent ent graded goodman goodman goodman goodman validity reaction diverse willshaw willshaw willshaw willshaw personal malsburg malsburg flat flat tor possibilities molecular molecular care genes geoffrey guidance guidance guidance guidance guidance regulation lond lond proach names hansen discusses dorsal dorsal dorsal tively inversely round topography topography topography resembles rats tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum tectum developmental tors caudal caudal caudal caudal anterior anterior ventral ventral ventral tells vivo vivo establishing fol restrictive reviewed shortly emerged medial spanning hip goodhill goodhill goodhill goodhill goodhill goodhill goodhill goodhill developments tectal tectal tal marker quantified phil rostral rostral rostral rostral rostral reviews reviews ther nections bind respec lowing exciting vitro vitro standing testable lacking formalized originating zhou zhou supplies gra quences recep recep dreyfus kij abstracts duced geoff proportionality nasal nasal nasal nasal nasal yoon shed establishment topographically guiding kinase kinase dient intro standardized cheng cheng cheng cheng retinotectal retinotectal retinotectal retinotectal retinotectal retinotectal retinotectal retinotectal retinotectal retinotectal retinotectal retinotectal comple increas bibliography binds binds defects sussex stretching analyzes repulsive repulsive repulsive repulsive elf elf elf situ dozen orderly neurobiol conse gradi georgetown georgetown georgetown cussed lamina communica perimental implicated refines signaled rosci ology jection nomenclature nomenclature nomenclature mentary polarized reservoir anchor 
#@Goodhill_G,
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#*model model model model model model model data data data function function function figure figure time time time time time time time time time time number number system system system system system error results results results problem space order order order order order shown shown shown shown shown systems systems systems systems values values values values values values parameters parameters parameters noise noise noise neurons distribution point control large large large large large large large large large rate rate rate rate rate analysis optimal optimal signal paper paper small small small small size cells cells cells process process cell cell cell cell cell cell high high high high response response show equation fixed fixed fixed line line line general parameter parameter gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained experiments experiments activity activity dimensional dimensional university solution solution solution independent independent log found found target target target target target target target target target target target target target target dynamics constant constant constant constant constant constant constant constant constant constant constant constant constant estimate estimate estimate terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance science science science science prediction prediction left left left low low low low low low low maximum maximum maximum maximum maximum maximum maximum maximum range range range range range range range range press position position abstract computational component stochastic stochastic due due important important important important introduction introduction hand statistical effect effect effect effect effect tion tion tion tion change change change change change change change assume assume lower higher higher center bound bound cases cases cases cases required distributed expected expected equations fact observed observed observed scale minimum minimum minimum minimum minimum ing performed times times times times times times times times times times regions means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor orientation relative specific provide provide provide proc active active experimental experimental related related constraints constraints constraints constraints constraints constraints constraints constraints constraints brain equal comparison larger larger larger contrast dependent source source source source source source source source source institute graph graph considered considered considered domain directly curve curve curves estimates limit limit limit limit limit limit limit limit limit limit limit limit limit top detection detection detection detection detection upper upper estimated estimated estimated estimated increase con con con derived derived derived derived bounds lines lines evidence nature nature nature nature nature depends constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint biological discussion discussion increases increases increases increases increases increases increases tested limited limited inverse corresponds amount effective effective effective assumed assumed assumed shape role role theoretical main journal end instance makes sensory sensory smaller needed significantly increasing mechanism uniform empirical max direct bottom early magnitude decay neuronal membrane membrane population population discussed discussed exact robust movement moving identical sense cognitive recently relevant dimensions approximately calculated calculated volume axis yields yields studies studies background symmetric observation exists studied scaling occur occur occur suggests extended width width width width occurs occurs occurs occurs generally generally column column critical row row greater greater central central numerical clear peak asymptotic asymptotic constrained suggest suggest taking taking hard mechanisms physics largest characteristics characteristics solid assuming assuming start start start start start targets targets targets appears longer longer longer factors factors factors factors factors factors factors plot ann vertical mathematical mathematical mathematical mathematical mathematical mathematical sensitivity sensitivity linearly infinite physical scales decreases decreases decreases decreases family focus stages variation modulation modulation suggested earlier reasonable reasonable calculation dashed sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec reduces reduces fitting roughly roughly roughly remains initially initially distances distances distances distances distances distances sufficiently usa retinal sciences extension plotted plotted absolute identified detect literature road quickly quickly graphs induced showing dis dis dis follow cue sci receptor receptor receptor receptor receptor receptor receptor satisfy involved play play providing binding binding reach reach neurosci neurosci neurosci neurosci neurosci moves body production production production production production production investigate rapidly rapidly rapidly varied optimized limitations dotted mass mass mass mass mass reducing reducing investigated biol biol biol root root affect math gradients gradients gradients gradients gradients predicts rev ensure taylor nerve nerve nerve nerve nervous nervous nervous nervous mentioned mentioned percentage percentage slowly slowly developing developing developing developing developing formula directed growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth growth analyzed growing growing biology explanation diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion starts starts starts ganglion spatially purposes satisfied satisfied satisfied closer easier protein protein day day day day directional immediately immediately mathematics mathematics axon axon axon axon axon axon axon axon axon axon acad axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons axons definite medical radius fluctuations explained apparent limits limits limits limits limits embedded readily lack release summarized limiting branch reaches gen fall monotonic prevent prevent asymmetric attraction contribute benefit sensing sensing oxford animals nat branches receptors receptors receptors receptors reaching fits fits ranges overcome proceeds determination determination nearby exploit exceeds days days filled hours hours hours hours substituting falls falls cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone cone mouse surprising dominant dominant washington consequences dif diameter diameter diameter diameter diameter diameter axonal spatiotemporal insight creating cancer cancer concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration concentration considerations subsequently characterization yielded piece piece goodman goodman encodes smoothly hundred constitutes molecular molecular spinal spinal spinal arising peripheral trends trends trends evolve gained biophysical geoffrey impose mammalian mammalian mammalian mammalian mammalian guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance guidance plate considers guided guided guided guided complementary deleted deleted weaker dorsal tively inversely turning induces molecules molecules molecules tissue tissue tissue tissue tract mea cube saturated thermal firstly pictures pictures eral hour cord cord evenly possess floor equa chan maxi ignores evolving evolving vivo vivo vivo vivo vivo establishing molecule molecule molecule molecule molecule molecule molecule molecule edition restrictive vicinity ance reviewed appro substrate subtle limb limb limb goodhill goodhill goodhill goodhill goodhill goodhill goodhill imum fractional fractional mum extracellular apparatus devel lasting bind respec concentrations concentrations concentrations concentrations concentrations concentrations stabilized stabilized vitro vitro vitro vitro vitro tributed tributed symmetrically poo radially basilar earliest torre ies crick crick camp camp steep steep stant microns microns microns microns ner stud sug davies davies davies davies asymptote dan detec interacts guiding commissural commissural kennedy kennedy varia raising detectable fibres clarendon bibliography interplay tances conceivable tum crn tissues nonmonotonic forp forp priate coincident rum rum rum rum rum berg berg georgetown georgetown gest hitherto stants concen concen transmembrane asymptotes asymptotes releasing releasing erfc erfc erally produc rim eur chemically rele peptide steeply firsfly reservoir tration tration vant 
#@Goodhill_G,
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#*network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set networks output output output number number system system system system system system system system system system system system system system system system results results results units units information information information information information information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem based based space space weights weights weights case case case case vector vector vector vector vector vector vector vector vector shown shown shown shown systems systems systems parameters noise noise noise weight weight weight weight neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single single single single single single single processing processing processing processing large large local neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns inputs inputs inputs inputs inputs inputs inputs shows shows signal signal signal signal simple simple simple examples examples examples examples small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net work task cells cells cells cells cells cells step step features features features features features features features features features features process level current cell cell cell cell cell cell cell cell problems problems problems problems random high response response similar similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation architecture show fixed line line line vectors general general speech speech speech speech speech speech speech speech speech speech speech real real average average term term term activity activity activity result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables computation computation computation computation computation computation computation computation computation computation computation computation solution solution solution solution research research research independent independent independent log log log log log log log found sequence target target target target target target target target initial computer computer distance connections connections connections synaptic science left left left presented map present present present present present phase phase phase phase frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal maximum maximum maximum maximum range position components components components components components components components basis basis basis outputs outputs continuous sample sample abstract computational computational computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog references component component component due due due ieee propagation propagation action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action complex complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior stimulus stimulus stimulus stimulus stimulus effect generated generated generated variance tion tion change change change change change difference difference variable signals word word word word word word word chosen chosen higher higher part part center center previous previous previous bound firing firing firing type type required cortex spike spike spike spike spike spike long represent represent represent represent represent represent fact fact region region region length length correct errors scale scale scale scale scale scale resulting classes ing ing ing total computed computed computed respect respect respect sum called times times times times times times times times times factor factor factor potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential dimension natural natural natural relative relative relative relative relative represented represented represented represented represented compared desired receptive provide define compute compute rates active active eye determined connected connected connected connected connected connected connected brain equal power power accuracy contrast connection connection fields train dependent dependent source modeling proceedings institute words words words words words words words words internal internal code individual represents final delay delay delay delay delay delay delay delay delay delay delay scheme computing computing computing computing computing computing computing equivalent equivalent equivalent environment additional additional view view design top stage requires requires requires requires requires speed vision basic increase produce channel channel channel criterion area types types lines lines lines lines product product product actual actual finally processes nature simply biological normal increases describe describe describe describe fast corresponds surface amount short short short short short short common common effective effective effective effective effective shape generate supported supported adaptation adaptation end end end degree makes sensory sensory sensory fit fit underlying underlying underlying underlying hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield unknown technology block block significantly ratio matching uniform uniform uniform uniform uniform uniform mode principle operation operation representing representing call filters pre normalized normalized bottom magnitude decay idea combined minimize produced produced produced sources population recent resolution advantage separate typical subset relevant relevant engineering engineering engineering engineering engineering engineering engineering engineering conventional conventional conventional solve solve solve solve speaker speaker speaker match match match match match match match match match match match match match converge mixtures channels channels channels channels interval interval grant parts intensity intensity intensity intensity intensity concept invariant spikes occurs setting hardware hardware hardware hardware hardware pass pass strength strength strength critical place competitive central differences faster faster weak suggest encoding encoding encoding taking strong strong hard presence cycle cycle cycle cycle cycle california pulse pulse pulse pulse start start relationship averaged scene identification identification program base question acknowledgements suppose appears digit digit digit pro solving factors factors generating generating describes describes describes describes ann vertical dept changing changing missing missing simultaneously physical easy adding frequencies events events events shift quality quality quality potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials cycles john decreases national national national independently viewed viewed viewed codes solved solved variation frames activities similarly digits digits allowed diagram diagram diagram reasonable calculation slow slow slow delays delays delays delays delays delays delays normalization normalization normalization sec event roughly roughly boundaries distances foundation euclidean euclidean transactions precision template template template template instances sciences sciences sciences recognize recognize recognize recognize recognize recognize recognize recognize determines illustrated illustrated illustrated illustrated discussions characterized major identified identified identified importance importance importance importance maximal encoded encoded effectively effectively driven driven driven identify oscillatory efficiently efficiently computations computations schemes post projections excitation traditional refer notice strongly strongly decoding contained showing interpreted timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing duration duration duration receptor quantity sampled dot dot delayed delayed thresholds thresholds illustrates intrinsic intrinsic employed poor requirements investigate difficulty difficulty difficulty mead steady preliminary rise fashion giving ideas project detectors ideal possibility scaled authors reliable comparable oscillation oscillation oscillation oscillation oscillation oscillation pathway encode hierarchy fundamental fundamental phases matched removed neu analyze recognizer changed implementations prototype olfactory olfactory olfactory olfactory olfactory olfactory olfactory algo detector detector detector detector detector nerve nerve shapes consist generates generates detected simplest utility burst great stop slowly slowly band band band band band trivial sensors coded biology biology biology biology biology biology caused starts considerable processed satisfied producing style forces nucleus pulses pulses recognized recognized recognized recognized recognized recognized recognized separately sounds describing calculations beginning implicit gradually axons axons axons recognizing recognizing recognizing recognizing recognizing recognizing meaning exemplars greatly limits cochlear tional spoken spoken spoken capability readily peaks passed sharp sharp rep rep biologically vocabulary occurrence resource tank tank tank tank tank substantial sums comments shaped utterances utterances utterances cochlea displays picture shifted indices redundant generator generator generator generator princeton princeton driving animals animals circular repre encoder encoder odor odor odor odor odor odor odor odor odor odor odor odor unity receptors rigid rigid inspired wrong convenient adjusting occurred overcome analogy multiplicative determination bands analyzing neurobiology star utterance ral monotonically hint salient clock clock clock clock clock clock composition reset conjunction dominant sphere propagated multiplied neuromorphic creating smoothed arrive arrive arrive properly canada draw arrows broken discovered interestingly insensitive vari thresholding dividing accumulated sequentially discriminate informa crossing crossing converted logarithm logarithm piece ram encodes bank responds propagating feeding ideally hierarchies breaking rhythm rhythm rhythm rhythm rhythm rhythm imagine molecular molecular molecular molecular molecular adapting attempted attempted rithms decays generators elementary elementary elementary elementary playing mouth thresholded eliminating insertion noting academy academy pos sonar sonar apparently sam syllables stuck investigations indication retained molecules molecules inactive answers manuscript stops circumstances species species species species council transforming spacing conceptual conceptual dominates loosely broadly carrier eral cast award distinguishing spectrogram excited contrasts normalize hopf bat bat bat bat odors odors odors odors vertebrate arriving sliding sending falling communicate periodically thresh thresh inaccurate monotone ized propagates discriminating ceedings carver spotting activates biophysics upward ables dilemma spectrograms spectrograms examines dominate weakness iiiii wait leaky retention warp warp warp warp warp warp warp warp warp warp warp warp warp warp pushed remember thinking concentrations concentrations movie movie epsps epsps pattem ramp ramp ramp ramp ramp ramp converting responsive responsive responsive panels ies nserc tapped mined mined lowering lowering stretch isomorphic mammals nose resolving rejecting contin weaknesses relied sketched resembling cate aligning sev stud uous lacks downward roweis roweis roweis roweis roweis concentrating coordinated brody brody brody brody logarithms logarithms initiation surely necessitates increas derlying grandmother grandmother grandmother grandmother scientist pres creases conven integrators deficiencies ineffective oscil sents resent participating grossly grossly unnikrishnan unnikrishnan unnikrishnan unnikrishnan unnikrishnan ands ands ands timescale equency sibility disabling superficially imax stereotyped contend eld facility hav interleave confounded regenerative erik carlos neurobiologists stimulates 
#@Brody_C,Hopfield_J,Roweis_S,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set algorithm output number number number number number system system system error error error error error results units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information information information information information information models models models models models models performance performance performance performance performance performance based based based based space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case order order order order shown systems systems probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise functions neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit method pattern pattern pattern point point point single processing processing processing processing processing processing processing processing processing processing processing control large large large large test test test test test patterns patterns patterns optimal optimal optimal optimal signal signal simple gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small small small size work work task task task task task task task task fig features level level problems random random high high high high response response response response response response response response similar similar similar section fixed fixed fixed general general general parameter parameter parameter parameter average theory theory obtained term term note experiments experiments activity activity activity activity dimensional result university threshold threshold threshold threshold threshold threshold computation computation research independent independent independent independent independent independent log defined found initial constant constant constant constant constant estimate estimate standard node science prediction presented phase frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency maximum maximum maximum maximum range range range range range range press press press learn position components components abstract find computational computational density properties properties properties properties likelihood references stochastic due ieee procedure procedure important decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision introduction complex complex complex estimation estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical variance variance variance variance variance variance tion tion energy energy energy difference variable variable variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume assume assume assume assume assume assume assume lower chosen center center theorem bound firing represent represent distributed distributed fact techniques region proposed correlation correct observed observed observed scale minimum tasks tasks tasks tasks total human human human human human human human human human computed computed computed computed computed respect respect sum sum eq means orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study study filter obtain relative specific true cross receptive compute compute rates proc proc proc location perform determined determined determined constraints constraints gain cortical brain brain power mit comparison larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields dependent source institute implementation consists represents represents represents represents responses responses responses responses responses responses responses responses responses responses responses responses considered framework framework cambridge experiment experiment curve curve additional additional additional curves curves curves curves curves curves limit limit limit stage stage stage stage stage stimuli stimuli stimuli detection determine determine efficient efficient efficient efficient full full choice significant free speed vision vision vision vision vision estimated increase derived weighted developed developed criterion area types types lines lines provided finally evidence nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends constraint constraint biological achieved measured measured measured measured discussion covariance normal increases arbitrary limited close close close assumption assumption assumption assumption excitatory excitatory excitatory predictions predictions circuits assumed assumed assumed shape shape generate supported theoretical theoretical require main main main square square instance easily degree degree noisy fit fit fit simulated simulated simulated pairs underlying account account account account account account account account technology interesting ratio consistent trials trials filters filters filters filters filters filters filters filters filters filters filters filters making inhibition inhibition inhibition early early early early early early early minimize produced added added predict neuronal neuronal neuronal population population population population population population population population population population population resolution property apply introduced introduced strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy period period engineering interest dimensions sufficient varying varying observations observations observations observations tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning yields sparse background background background locations generalized entire entire entire expression expression expression extended trial trial trial trial wide wide wide wide wide derivative predicted predicted alternative correctly correctly correctly correctly width width width deterministic deterministic half conclusion conclusion minimal assumptions assumptions assumptions depend central central central interactions interactions interactions interactions interactions differences differences constrained suggest propose propose propose presence presence presence presence characteristics characteristics sigmoidal california solid assuming assuming variety targets derivatives manner groups annealing appears appears derive derive derive derive derive laboratory tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned vertical mathematical sensitivity infinite remaining slightly scales gaussians predictive cycles cycles yield dependence stages stages estimator estimator overlap detailed fraction lee lee lee lee centered approximated sizes completely similarly similarly similarly similarly discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination partial partial dashed normalization normalization fitting fitting remains koch koch koch koch koch koch existing existing usa inter inter weighting automatic automatic uncertainty absolute absolute importance differ differ presentation detect post composed excitation excitation excitation excitation soc soc soc contained success dis issue physiological physiological sci bar vary play absence thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds cat automatically neurosci consisted overlapping subsequent acknowledgments oriented oriented oriented extend situations situations situations situations situations law law minimized carried wiley wiley investigate circuitry humans estimators behavioral behavioral behavioral behavioral behavioral behavioral biol biol biol ideal ideal possibility possibility combine complicated cover notion act naturally predicts equally adjusted adjusted assumes fisher fisher fisher fisher fisher fisher fisher fisher extent extent contributions attempts asymptotically separable separable agreement agreement agreement orientations orientations orientations orientations orientations variances slope slope slope independence independence tive strictly ran desirable commonly pool pool pool pool pool pool pool pool potentially acad opt opt attribute res res res res res demonstrates qualitative qualitative nsf addressed questions reflects reflects varies varies greatly populations reflect readily quantitative psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical posed exhibits exhibits poisson poisson poisson poisson cal cal qualitatively pasadena achieves green shaped unbiased implements converged multidimensional contribute contribute consistently cybern cybern investigation gabor linearity linearity purely unity unity inspired fits fits saturation numerically tools tools simplify odd striate familiar hope neurobiology optimally optimally optimally presentations wilson wilson wilson wilson natl motivation sompolinsky interference periods periods loo loo corre respective studying accounts accounts uni thomas reproduce reproduce dif deg deg deg deg deg deg deg eng suggesting arrows extends observer observer observer sons sons seung seung adopted onr informa ure unified unified ties opposed uniquely nelson forced rao adopt ical var continuity increment interact num oct relate simplifying relating overhead statistic statistic statistic statistic relates pos mask mask mask mask mask mask mask mask mask mask mask mask mask accounted reveal reveal pop simplex psychophysics psychophysics wider correlate transducer transducer transducer transducer transducer transducer transducer info sponding vis vis vis vis vis vis vis ferent observers observers calibration calibration calibration hoc cornput appealing pronounced evenly unreliable contrasts contrasts contrasts contrasts contrasts contrasts heeger heeger heeger heeger heeger extracts bergen sloan quantitatively quantitatively bandpass inde pooling pooling pooling pooling pooling pooling pooling pooling pooling pooling pooling pooling pooling pooling electrophysiological thresh carrying ically translates putative sur christof rec discriminating addi phillips developments ference pendent elevation elevation elevation remarkably primates sixth quadrature exponents theo pooled pooled pooled pooled pooled pooled pooled pooled pooled pooled pooled sible unlimited ross prohibitively vat divisive divisive divisive divisive participate participate articulated earliest med malik psy psy bradley idealized masks sponse braun braun braun braun braun render numerator discriminations discriminations neurophys sharper siegel ori freq flanking sept erf erf erf discriminated teukolsky favoring masking nimh discrim ors ors oblique cram weber ferster koenderink sillito klab dale sagi calibrated calibrated calibrated accelerating subpopulation electrophysiology perona chung statisti behaviorally snippe arbi neuroanatomical domly calibrate unambiguously trary chophysical chophysical sharpens entation swets psychophys psychophys psychophys ination ech compressive detectability nator gree strengthens controversy obviates 
#@Braun_J,Itti_L,Koch_C,Lee_D,
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#*model model model model model neural neural input input function function function function function function function function function function function figure figure figure figure figure figure time time time time time time time set output number number system system system system system system system system system system system system system system error results results results units units units units units units units units information information information problem models based based linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear order order order order order order shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values parameters noise noise noise noise noise noise noise noise neurons neurons unit unit unit unit unit unit unit unit unit unit method method method approach approach approach approach point point point point point point single single single single single large large large neuron rate rate rate analysis analysis analysis analysis analysis analysis form shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal visual paper paper small small small small small small small small size size size size size work work work work methods methods cells step points points points points points level level random random high memory memory response response response response response response response response response response response response response response response response response response response response response response response response response response show equation equation section section speech real approximation average average term term term term note note note experiments result result university research research found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence estimate estimate estimate estimate standard computer terms terms terms terms terms terms connections presented presented presented presented present present phase frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal range press press press components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied applied back back find find properties properties properties properties properties references component stochastic procedure procedure important adaptive adaptive context introduction action hand circuit circuit behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical effect dynamic generated tion change assume assume higher center previous theorem bound firing firing firing type good good binary binary spike spike spike spike spike long make fact fact correlation correlation correlation correlation length length length length errors scale finite simulations sum sum sum sum sum sum sum performed eq eq eq eq eq eq eq eq elements factor feedback applications study study study study study study filter original original vol application cross cross cross cross cross series series series receptive compute compute compute compute rates rates rates rates determined determined discrete discrete approaches steps larger fields dependent modeling proceedings kernel kernel kernel kernel kernel kernel kernel kernel represents responses responses responses responses responses responses responses responses delay graph graph graph sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences domain equivalent experiment experiment experiment curve estimates limit san san top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects determine full full full significant statistics vision pages increase give con coding derived derived derived selected evidence biological discussion arbitrary group close assumption stable amount effective effective effective effective assumed supported theoretical main adaptation adaptation journal instance instance fit auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory typically smaller underlying combination functional functional functional unknown coefficients transfer transfer transfer transfer transfer transfer transfer ratio york increasing trials trials trials matching matching operation operation stored bits bottom depth depth depth depth depth depth depth depth depth magnitude polynomial polynomial combined combined added added description neuronal discussed exact advantage ensemble ensemble takes element practical introduced side sense engineering engineering highly highly calculated tuning axis axis axis yields yields achieve grant amplitude amplitude amplitude amplitude scaling deviation wide wide white white half central central central accurate accurate practice sound taking mechanisms presence presence presence physics cycle california california turn exist manner identification identification identification identification identification identification identification base derive derive construct written solving primary plot plot tuned tuned changing physical scales shift shift implies implies potentials cycles cycles yield depending correlated communication squares organizing lee lee modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation static approximated sizes constants expansion sec sec sec add add calculate calculate calculate sufficiently foundation recorded recorded box kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels combinations sciences discuss characterized structural determining determining middle extra efficiency suitable society orthogonal characteristic characteristic characteristic characteristic sin physiological physiological hold duration sampled usual simplified simplified simplified wave wave wave cat cat cat cat operating operating operating operating operating operating operating operating operating rat perturbation perturbation perturbation perturbation perturbation perturbation scalar history statistically measurement measurement transmission editor integer thought impulse impulse impulse impulse assumes taylor nerve asymptotically indicating advanced piecewise inequality inequality formula convolution derivation analyzed unstable cascade tool nonlinearity london purposes sys closer widely nucleus sounds bandwidth incomplete limits double double pure pure pure pseudo effort detecting passed calculating calculating mod measuring characterize characterize limiting modulated modulated popular resource tank logical neuro trade contribute ordinary uncorrelated uncorrelated uncorrelated uncorrelated identifying physiology physiology primarily accomplished arguments linearity linearity purely bin nonzero royal cellular systematic systematic fits khz numerically convenient difficulties multiplicative resistance hit hit los mark neurobiology inferior inferior inferior inferior inferior inferior inferior analyses recovered ranging bialek studying conjunction sim uni nonlinearities nonlinearities nonlinearities nonlinearities francisco francisco ensembles creating matter colliculus colliculus colliculus colliculus colliculus colliculus colliculus park implicitly alternatively robert onr yielded neurophysiology sine sine email deriving perturbed tradeoff ical sinusoidal sinusoidal sinusoidal sinusoidal sinusoidal sinusoidal demon conservative tems depicts register register superposition afferents tively commercial milliseconds milliseconds drops rewrite simplifies expansions chris handling autocorrelation autocorrelation autocorrelation hearing hearing envelope ave inequalities powers carrier carrier carrier carrier periodicity inherently floor floor fft vanish sloan sloan amplified subtle indexing plenum wiener collecting phy phy rieke rieke rieke putting perturbative perturbative perturbative perturbative perturbative perturbative perturbative perturbative perturbative perturbative 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#@Kvale_M,Schreiner_C,
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inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual feature feature feature work fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells features level cell cell cell cell cell cell cell cell cell cell cell cell cell random response response response similar similar similar similar similar representation architecture architecture show line line line line rule images images images general average theory theory note experiments activity activity activity activity activity activity activity activity activity activity activity activity activity result university independent defined found target dynamics dynamics dynamics dynamics standard connections connections connections synaptic synaptic synaptic synaptic synaptic science left left left left left left left left left left presented presented presented presented present present present phase phase activation activation temporal temporal temporal temporal temporal temporal temporal temporal motion range basis nonlinear outputs abstract find properties properties references introduction action action complex complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus recurrent recurrent recurrent tion tion difference lower lower lower lower lower lower signals signals representations higher higher higher higher higher higher higher part center previous firing firing firing firing firing firing firing firing firing firing firing multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike spike spike long long conditions conditions conditions represent distributed distributed distributed correlation probabilities observed forward forward simulations simulations simulations simulations simulations ing ing ing called called regions feedback feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global study relative relative relative relative relative relative relative specific specific specific compared cross series receptive provide rates rates rates rates rates rates eye eye eye eye eye eye eye eye eye experimental related related gain motor cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain equal contrast contrast contrast contrast contrast connection fields support modeling report report institute institute department version consists consists consists internal responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses addition addition estimates stage stage stage stage stage stage stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects effects effects effects effects effects effects upper upper upper upper vision vision vision vision vision basic give con con produce produce levels levels area area area area area area area lines lines lines lines lines path finally evidence nature nature nature nature nature inhibitory inhibitory inhibitory inhibitory achieved normal normal feedforward increases describe group group group group group excitatory excitatory excitatory stable circuits circuits circuits circuits circuits circuits shape supported role role face square degree degree degree degree including simulated pairs underlying reduced reduced reduced account account functional functional significantly mechanism consistent consistent empirical principle max max inhibition inhibition inhibition early early early early early early attention combined description light predict neuronal neuronal neuronal neuronal neuronal neuronal recent recent property separate similarity similarity similarity reported lateral lateral cognitive recently sufficient previously observations calculated studies differential differential differential differential differential modified channels organization horizontal suggests alternative occurs demonstrate demonstrate strength conclusion competitive competitive competitive interactions interactions interactions differences retina clear suggest propose strong mechanisms mechanisms mechanisms integration integration integration integration integration turn selective selective selective selective selective selective iii averaged groups groups groups groups groups groups groups groups groups groups groups groups groups connectivity connectivity acknowledgements areas areas areas areas areas areas areas appears van van index index index perception perception perception perception perception perception primary primary primary plot plot plot sensitivity involves develop mutual mutual applying events events shift potentials competition competition competition competition competition competition competition competition competition competition extracted independently depending stages stages stages stages stages correlated interpretation interpretation influence detailed restricted fraction ocular understanding activities activities suggested earlier earlier delays delays remains visible koch david fire perceptual perceptual perceptual perceptual perceptual perceptual dominance dominance dominance inter discuss activated activated coupled absolute discussions structural selecting middle differ divided driven driven oscillatory oscillatory oscillatory projections projections plots orthogonal orthogonal orthogonal excitation excitation soc induced interpreted physiological timing timing timing timing timing timing timing timing timing timing gray gray simplified simplified backward highest leading predictor cat cat cat cat cat neurosci neurosci neurosci neurosci neurosci overlapping operating receive receive remain remain stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation stimulation selectivity selectivity selectivity selectivity selectivity selectivity exhibit exhibit exhibit circuitry involving strengths helpful rise examine respond respond combine comparable lgn lgn lgn lgn lgn lgn lgn pathway pathway pathway pathway hierarchy fundamental matched neu patch naturally naturally transmission transmission onset onset onset configurations rev rev rev eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes thought der der mapped epoch epoch regime established integrate preference orientations orientations orientations phenomena phenomena london london spatially drive organized incorporate nucleus nucleus monkey mation involve arises demonstrates fluctuations reflects reflects varies populations populations populations reflect pathways pathways pathways quantitative quantitative psychophysical incorporated incorporated rep maintain span switch exhibits exhibits exhibits mod modulated synchrony serve singer singer singer singer singer singer singer coherent comments physiol coherence findings tile yielding synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization synchronization instantaneous instantaneous instantaneous phenomenon phenomenon uncorrelated uncorrelated indices college secondary secondary secondary martin jones interconnected outcome outcome establish establish lost suppression suppression suppression binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular anatomical primate primate striate striate striate moment belong implications synchronous synchronous synchronous canonical responsible enhanced infor ranging von overview conjunction dominant dominant monkeys monkeys competing tic viewing emergence insight stimulated suggesting locked convergent convergent influences influences lag boxes discharge informa linked grating grating grating fellowship ent discount cooperative emergent emerge revealed nelson forced responds tween terminals trigger perceived malsburg malsburg affects suppressed suppressed reflected remainder monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular monocular mutually exclusive biophysical grouped grouped mammalian mammalian maintained neurophysiological interacting douglas douglas paired altered fir fir scope synchronized ambiguous ambiguous importantly weaker weaker distinguished west crossings crossings crossings reveal universit gilbert gilbert geniculate geniculate prevents round manuscript correlate topography coordination coordination coordination coordination coordination coordination coordination syn remarkable rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry rivalry blake blake mahowald contralateral neocortical stay pronounced essen essen conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting conflicting assessment contrasts emerges chan interpretations comprising colleagues vivo planck inducing correlates correlates bear percept putative ipsilateral sur explaining gallant gallant cats cats ular yon columnar inability inte mason awake stim synchronize registration dissimilar bind confirms neurology neurology dissimilarity manipulating unclear unclear unclear abstr logothetis logothetis logothetis logothetis logothetis logothetis elicited earliest responsive sual sual subtraction thalamic percepts concurrent ulation tilted tilted tilted tilted tilted tilted stochas sponse engel engel engel tonal sector sector psychol psychol comparatively queen chemistry selectivities selectivities straints somers somers ficient visiting alternation alternation alternation inh inh inh inh admit sillito sillito registered stimulate nels suf discharges discharges discharges annu extrastriate extrastriate extrastriate patterning patterning patterning patterning patterning resented ulus relay relay professor elevated elevated desynchronization ksnig ensuing sustain plaid plaid plaid ception lehky lehky lamina lamina desynchronized probed brussels gerstein hospitality grated suarez rival integra thomson eur eur exchanges wcin erik gree determinants gsttingen hibition 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#@Lumer_E,
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probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit recognition approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point single single single single processing processing control control large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis form form form form form form form shows shows shows simple simple simple visual paper examples small task task task task task fig fig fig fig fig fig fig points features process process process current current structure structure high response response response response response response response similar similar representation representation show show show show show show equation section section fixed fixed fixed fixed general general parameter parameter parameter parameter parameter parameter parameter average average states term term term term term note note activity activity result result result result variables variables computation computation computation computation computation computation computation computation independent sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant standard standard computer computer terms terms connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science left left presented map activation low low temporal temporal temporal temporal temporal sets range range range range range range position outputs abstract abstract abstract find computational computational computational computational computational computational computational computational computational computational references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due positive positive positive context action complex hand hand hand circuit stimulus effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic parallel change change difference assume assume assume assume assume assume assume assume signals signals signals chosen higher higher previous theorem theorem theorem theorem theorem firing firing firing firing firing firing firing firing type multiple multiple multiple cortex binary spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike conditions represent represent expected make make make fact fact proposed length length length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities scale simulations resulting resulting ing tasks total computed sum eq eq eq eq times times potential potential potential potential study artificial artificial artificial artificial specific represented compared rates rates proc experimental related constraints connected gain gain motor cortical power power power larger larger larger connection support train train train train train train train train train train train train train train train train descent dependent dependent dependent institute institute version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists internal internal internal internal internal internal code individual responses delay delay sequences ai considered considered framework computing limit top detection detection detection full significant basic increase give give con produce produce produce condition coding coding coding coding coding coding area processes processes backpropagation nature nature inhibitory inhibitory depends depends simply biological biological biological biological biological discussion increases describe describe describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary tested fast close assumption excitatory excitatory excitatory circuits circuits circuits short short short short short common assumed assumed assumed assumed assumed synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse role role theoretical theoretical main main easily pairs smaller underlying hopfield hopfield hopfield interesting significantly york increasing mechanism mechanism leads details numbers numbers making window window stored bottom supervised magnitude decay decay decay choose choose description neuronal population population population population population pair side side sense subset recently highly varying varying varying unsupervised solve solve achieve positions interval interval interval interval interval interval interval interval interval interval sensitive entire occur wide wide spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes move move setting strength greater depend editors central central central exponential exponential exponential exponential exponential propose strong mechanisms turn variety start decrease groups longer longer primary changing implement scales scales consisting interaction integrated focus dependence dependence dependence depending depending correlated correlated viewed showed static static static static completely similarly slow delays intervals intervals intervals intervals intervals intervals intervals intervals intervals purpose boundaries visible advantages fire fire figures usa assignment assignment suitable differ maximal encoded encoded computationally spiking spiking spiking spiking computations computations reached reached summary traditional refer refer strongly prob timing sci vary neurosci moves illustrates rat cowan trains trains trains trains trains trains trains trains trains trains trains trains employed wiley investigate steady dotted postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic rise scalar examine respond respond history terminal terminal terminal plasticity plasticity plasticity plasticity plasticity plasticity reliable complicated presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic analogous analogous transmission transmission transmission analyze formal formal formal formal freedom detector explored expressions pyramidal pyramidal consist arbitrarily arbitrarily integrate burst burst burst site site site fairly failure turns sites sites sites widely strictly precisely choices arise commonly pool pool pool acad preceding preceding fourth apparent varies populations substantially substantially readily readily quantitative detecting formulated treated reliability release 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incorporates email nelson tween distinction par trigger resting stands emphasize emphasize considers considers investigating associates abbott abbott abbott abbott universit interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike interspike differently differently sees agrees dominates neocortical neocortical inherently val unreliable sen sen anthony carries stevens stevens stevens stevens stevens stevens stevens zador zador zador zador zador zador zador zador zador zador zador html sloan arriving nontrivial translate tim zones probabil validated zone initiated plastic technische fundamentally ities tics berger berger berger tsodyks tsodyks tsodyks tsodyks tsodyks tsodyks tsodyks gibson translating translating positively positively facilitation facilitation facilitation facilitation facilitation facilitation facilitation facilitation facilitation released released released stays analogously markram markram markram markram markram markram markram gra ticular neurotransmitter neurotransmitter neurotransmitter triggers triggers triples ipsp ipsp graz graz graz publications dient austria attainable heterogeneity depletion depletion depletion depletion depletion ifi igi wolfgang conventionally redistribution releases releases releases releases tins rive emaih cept maa ynaptic multiplica focussing taxget rmeters gall cay 
#@Maass_W,Zador_A,
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#*model model model model model model model neural neural neural neural neural neural input input input input data function function figure figure figure time time time set set set output output number number number number number number system system system system system system system system system system error error error error error error error error error error error results results units information information information information information information information information information information information information information information information models models models performance performance performance performance performance performance performance performance performance performance performance performance based linear linear linear linear linear linear linear linear case case case case case case case case shown shown shown shown shown shown shown shown systems systems systems systems values values values values values values values values values values values probability probability probability probability probability probability probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons unit distribution distribution distribution distribution approach approach single single single single single single single single single single processing processing processing processing large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate test analysis analysis analysis analysis analysis analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple simple gaussian gaussian gaussian gaussian gaussian small small small small size size size work fig fig fig fig fig fig fig fig fig fig fig process process process process process current structure random random random random random random random high high response response response similar similar similar rule general general parameter parameter parameter parameter parameter average theory theory theory obtained obtained obtained note dimensional result result threshold threshold variables variables variables computation computation research independent independent independent independent log log log log defined defined found found constant constant estimate standard standard terms terms terms distance synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science presented present present low low low low low low low low low frequency press press components basis nonlinear outputs continuous continuous abstract applied find find find density density density density density density density density properties likelihood likelihood likelihood references component stochastic due due due due procedure important decision decision decision decision decision decision introduction action estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation stimulus stimulus stimulus stimulus statistical generated variance variance variance variance variance parallel parallel parallel tion tion tion energy variable variable variable variable variable assume assume assume assume assume assume assume lower lower lower lower lower lower lower lower measure signals signals prior chosen chosen chosen chosen chosen chosen part center theorem bound bound bound bound bound bound cases firing firing firing firing firing firing firing firing firing firing multiple binary binary binary binary binary binary binary binary binary binary binary binary binary spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike make fact correlation correlation probabilities probabilities probabilities observed errors errors scale finite minimum minimum tasks computed computed respect sum called elements factor potential made study knowledge filter filter filter filter filter filter filter filter filter filter filter filter obtain specific samples compared cross cross cross define compute compute rates rates rates proc active goal related posterior cortical cortical cortical cortical cortical brain power power power power power power power approaches mit mit voltage voltage voltage voltage voltage voltage voltage support train train train train dependent source source institute synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses code code individual individual individual considered considered cambridge cambridge domain estimates limit limit san stage effects detection detection detection detection detection detection detection detection detection detection detection detection detection capacity capacity capacity capacity capacity capacity choice choice significant increase increase increase channel channel channel channel channel channel channel channel channel channel channel channel coding coding criterion bounds entropy path nature nature nature depends achieved achieved measured measured increases increases increases increases denote denote denote denote denote denote fast limited limited assumption assumption corresponds corresponds amount amount effective effective effective effective effective effective effective effective effective effective effective effective assumed assumed assumed assumed synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse supported role role theoretical eds square square square square square square easily sensory objective objective probabilistic probabilistic technology block transfer ratio ratio ratio ratio ratio york increasing mechanism consistent numbers making bits bits normalized normalized combined choose added sources light neuronal neuronal neuronal denotes denotes denotes denotes membrane membrane exact robust ensemble takes identical identical identical identical sense sense recently highly conventional correspond correspond studies generalized interval improvement improvement amplitude amplitude expression expression expression expression expression expression digital trial trial deviation deviation spikes spikes deterministic white white white white occurs occurs occurs generally pass place conclusions depend central central encoding presence california pulse pulse decrease relationship program denoted denoted denoted acknowledgements explicit pro pro van van derive derive longer longer distinct modeled modeled modeled modeled linearly linearly linearly spectral spectral spectral spectral spectral spectral mutual mutual mutual events quality versus versus focus expressed expressed reconstruction reconstruction reconstruction reconstruction reconstruction stages communication communication estimator estimator estimator estimator estimator estimator estimator transform evaluated similarly constants spectrum diagram additive additive measurements sec sec reduces reduces false closed closed closed msec msec msec msec koch koch koch koch koch koch koch dendritic box priori usa black absolute discussions characterized characterized gamma encoded encoded encoded driven svm spiking identify post post post post post post post post plots plots plots characteristic notice notice prob follow sci device device write absence paradigm paradigm paradigm paradigm paradigm minimizes neurosci operating decreasing minimized origin carried wiley poor preliminary graphical fourier history terminal ideal reliable variability variability variability variability cover cover presynaptic presynaptic presynaptic presynaptic matched matched transmission transmission transmission transmission transmission transmission transmission plausible possibly reading analyze analyze perfect observe observe detector detector detector detector detector expressions expressions expressions pyramidal detected detected simplest regime regime regime site inequality band formula theoretic theoretic theoretic theoretic theoretic convolution variances variances failure failure analytical considerable perspective perspective perspective perspective perspective snr snr snr snr snr snr snr snr snr snr snr snr snr filtered ran commonly separately hippocampal hippocampal involve acad bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth nsf researchers profile empirically empirically empirically tional generic poorly treated treated treated schematic release release release release release release release release release release release poisson poisson poisson poisson poisson poisson poisson measuring monotonic cal occurrence occurrence pasadena substantial sophisticated redundancy redundancy redundancy redundancy redundancy neuro progress arithmetic consistently phenomenon uncorrelated primarily sv optimality optimality restrict member bin bin bin harmonic theories caltech caltech communications communications spontaneous spontaneous fails systematic numerically occurred occurred occurred tools simplify efficacy efficacy efficacy biased neurobiology observing optimally preparation exceeds generalizes natl exploring bialek bialek bialek negligible decide regarded accounts thomas insight suggesting ahead snn epsp epsp epsp epsp epsp calcium davis inf inf std insensitive informa roc rigorous email opposed transmitted presenting employs amplitudes tor conservative representa cns argue argue peripheral gated trends intuition formance gained biophysical denoting relating paired integrals records employing covered paradigms paradigms alarm thousands det psychophysics quantify quantify hundreds shot shot shot dom sided slices normalize chan chan chan stevens stevens stevens vertebrate sloan ignores convention inset compensated cascaded sian absent gaus format transmit transmit steveninck steveninck deciding christof tan zone ina wiener expresses quantified quantified rieke rieke rieke miss inability tsodyks tsodyks unclear deco amit vitro facilitation released invertebrate noises noises noises markram markram standpoint faithful oft estima quantifies quantifies appeal warland warland doubly erf detec ric ampa nel nimh tractability neff klab klab ezp meters kom tedious spectively depletion ineffective nary skewed buffering phenomenological eff biophysically 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#@Koch_C,Manwani_A,
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#*network learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input data data function figure figure time set set algorithm output number number state results results results results results results results units information information models models models based based based linear linear linear linear linear case case order order order shown shown shown shown shown shown shown shown shown shown systems systems values values parameters parameters parameters parameters parameters neurons neurons neurons neurons distribution distribution pattern pattern point single single single single single single single single single processing processing processing processing local local local neuron neuron neuron neuron rate optimal optimal inputs inputs inputs inputs inputs inputs inputs form shows shows simple simple simple simple simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual size size feature work work work work work work methods fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field field field features process current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure random random high response response response response response similar similar similar similar architecture show rule general parameter real average average average average average average experiments activity dimensional result university university computation computation computation computation computation computation computation computation research research independent independent defined initial constant constant table table standard terms terms terms terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science left left left left left left left left left left left direction presented presented presented present present present present present phase phase activation activation frequency frequency motion range range range range press press position position position position position position basis nonlinear nonlinear nonlinear abstract applied density density references ieee important important propagation propagation introduction action complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex stimulus stimulus stimulus stimulus stimulus stimulus generated generated tion energy energy energy energy energy energy energy energy energy energy energy difference complexity spatial spatial spatial spatial spatial spatial spatial spatial lower chosen chosen chosen higher center center center previous previous cases type type type type type type type type type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good spike spike represent tree tree tree tree tree tree equations equations fact proposed proposed correlation scale simulations simulations ing ing ing total simulation simulation simulation computed computed respect sum sum factor factor factor factor potential orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global filter negative original vol vol relative relative relative relative specific cross cross cross receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide provide location location active eye eye eye eye eye eye eye experimental cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain power mit mit voltage voltage voltage comparison comparison larger contrast contrast contrast contrast contrast connection fields fields fields fields fields fields fields support dependent dependent modeling modeling morgan proceedings institute department implementation synapses synapses synapses synapses individual individual individual advances advances responses responses responses responses responses responses responses responses responses responses responses responses exp exp exp exp exp scheme considered considered cambridge cambridge curve curve curves curves curves curves curves san stage stage stimuli determine full free vision vision basic produce produce produce channel channel channel derived derived randomly randomly randomly randomly randomly evidence nature inhibitory measured measured discussion normal arbitrary complete excitatory excitatory excitatory short role eds eds eds eds including kaufmann pairs pairs pairs smaller smaller needed account account account account account account account account jordan ratio projection york york edge uniform uniform uniform principle operation leads squared representing details details details max max filters filters inhibition international depth depth depth depth depth early early frame frame frame frame frame frame combined light light light light light light light light light light light light light light neuronal membrane membrane population correlations correlations resolution property pair ensemble ensemble similarity reported reported lateral moving period identical pixels pixels quadratic hierarchical recently recently relevant engineering interest dimensions highly highly previously previously approximately approximately tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning studies trans diagonal address positions positions positions positions symmetric channels channels channels organization horizontal horizontal horizontal invariant invariant wide predicted width width width column half half half assumptions hebbian depend interactions interactions interactions interactions peak peak peak peak moody mateo suggest suggest suggest encoding strong strong strong integration drawn california california labeled variety groups program program acknowledgements relation derive produces perception perception primary plot tuned tuned tuned vertical vertical modeled modeled modeled modeled sensitivity sensitivity simultaneously consisting consisting interaction mutual springer shift shift potentials yield national formation dependence correlated detailed operations fraction showed centers centers centered similarly suggested translation constants discrimination discrimination past earlier earlier roughly roughly assigned assigned assigned assigned foundation foundation koch koch koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic degrees degrees recorded building determines illustrated mozer specifically absolute absolute importance importance driven driven driven driven driven included poggio poggio poggio poggio computations computations invariance plots miller essentially excitation road verlag kind contained showing neuroscience conductance conductance symmetry lie sin sin cue bar bar play play surround surround surround thresholds cat cat cat cat cat cat cat cat cat cat cat cat consisted overlapping overlapping disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity preferred receive oriented oriented oriented oriented cowan bars bars bars bars bars bars bars bars bars body body selectivity carried carried powerful wiley essential put steady hanson lippmann helpful rise rise rise respond giving giving ideas detectors int scaled authors office proper lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn func phases matched matched matched matched neu trace man man eyes eyes eyes eyes eyes nerve hebb pyramidal pyramidal pyramidal pyramidal pyramidal pyramidal isolated isolated isolated site site site site site site preference slowly cos cos pairwise crucial crucial agreement analytical adapted adapted spatially spatially sys sites bishop bishop arise controls pool involve opt res localized qualitative virtual reflects freeman freeman freeman freeman pure transient dark dark dark dark dark dark dark dark dark tional ity summarized fall ordered ordered suited suited conductances conductances conductances substantial sums comments shaped physiol physiol june cor cor shifted cybern aligned primarily interface gabor martin branches neurophysiol neurophysiol naval outcome robotics robotics eliminated binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular binocular minutes held held striate striate multiplicative multiplicative resistance resistance los los roles salk salk arrays symposium fires passive published bartlett edelman dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites paul displayed surprising mental injection stereo mel mel mel mel mel mel mel mel mel mel mel mel mel mel den somatic somatic somatic soma branching arrangement arrangement arrangement arrangement spatiotemporal mem jolla extends epsp fold unchanged neurophysiology leaving largely numerous numerous fellowship wiesel wiesel wiesel abstraction par quasi arbor ideally reports superimposed hubel hubel hubel demon monocular monocular monocular monocular monocular monocular monocular monocular biophysical biophysical biophysical biophysical potassium neurophysiological douglas douglas mediated emphasize maximally adelson adelson fixation distal rectified nonetheless funded inversely exhibited hodgkin demonstrating syn syn copies excess huxley hypothesized bold bold conceptual puts cornput developmental finer finer finer morphology ron neocortical fre polarity polarity polarity exclusively exclusively subtracted subtracted nmda nmda nmda nmda nmda petsche bergen bergen systematically contacts contacts contacts contacts sloan tance tance tance reproduced vertically falling ruderman ruderman ruderman ruderman ruderman ruderman ruderman kinetic robustly enforces tical mul prominent excessive responded decades decades christof stabilization correlational daniel amer configured movshon movshon ular biophysics literal mft mft mft quency excitable excitable biomedical ogy formulations angeles angeles excluding sodium subsampled compartments thompson thompson conflict membranes monosynaptic compartmental formalized signaling pared subsample stuart stuart kinetics inactivation fell underlie underlie ticular disparities disparities render organize southern southern rin rin ori ori unoriented unoriented unoriented unoriented implementa simplifications rodney rodney bernander ohzawa ohzawa ohzawa ohzawa ohzawa ohzawa ohzawa ohzawa ohzawa ohzawa ohzawa tex brane diameters ampa ampa ampa ampa conduc subunits subunits subunits torrey pines antagonistic kevin hines hines subregions orban orban axo ered ken geometries sive tiple incapable confirming intradendritic intradendritic intradendritic intradendritic occured tips scrambled scrambled scrambled scrambled paradox taneously ceptive finest brady simul coexist subunit subunit subunit subunit subunit courtesy stereoscopic tun tential challenged usc usc subfields existed pyra biotaed geniculo acted sakmann sakmann ght exhausted specifics allan pas midal dobbins gall 
#@Archie_K,Mel_B,Ruderman_D,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input input input data data function function function figure figure figure figure figure figure figure set set set set set set set set set set set set training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm system system system system system state results results results units information information information problem problem models models models models performance performance performance based based based based based based based space weights linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case shown shown shown shown shown shown shown values values neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method pattern pattern pattern point image image image image image image image single processing processing processing large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test test class inputs form form shows shows shows shows shows shows shows simple simple simple simple simple gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small small size size size size size size size size size size size size size size size size size feature feature feature feature work task task task fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step field field field field field field field field field field field field field field features features features features features features features features features features classification process level level level level level current current trained cell cell cell cell cell cell cell cell cell cell random high memory response response response response response response response response response response response response response response response similar similar similar representation representation representation representation representation show show show show show show show show show section section section section images images images images images general real real average average average average average average average theory obtained experiments experiments experiments experiments experiments experiments activity dimensional result result computation found found found found estimate connections connections connections left left direction presented frequency frequency temporal temporal object object object object object object object object object object object object object object object object object maximum maximum maximum maximum maximum range range range range press press press position position position nonlinear sample abstract abstract applied find computational computational computational properties properties properties properties properties properties properties properties properties properties properties references component due due procedure mixture context context introduction complex complex complex complex complex complex complex complex complex hand stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus dynamic generated generated variance variance parallel recurrent change change complexity spatial spatial spatial spatial measure representations learned learned learned chosen chosen higher higher higher part center center center previous previous previous previous previous previous type type type type required multiple cortex cortex cortex cortex cortex good represent proposed observed observed observed observed scale scale scale scale scale scale scale scale scale scale scale simulations simulations simulations classes total respect sum times elements orientation orientation orientation em em filter original relative specific specific specific specific represented compared compared receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc location location location perform determined experimental related related posterior posterior cortical brain equal approaches mit mit mit mit steps contrast contrast connection fields fields fields fields support dependent report report institute department individual advances advances responses responses responses responses responses responses responses difficult difficult difficult exp layers layers scheme scheme addition sequences ai ai cambridge experiment experiment experiment curve curve curve curve additional additional view view view view view view view view view view view view view view view view view view view view view view view view view top top top top top top top top top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects requires requires significant world vision vision give randomly randomly area area area product selected nature biological biological biological achieved discussion discussion feedforward tested tested tested tested transformation limited limited close corresponds complete stable proof amount common assumed assumed shape shape square square hypothesis instance instance instance instance future degree degree degree underlying underlying account technology interesting significantly increasing mechanism mechanism mechanism mechanism mechanism mechanism matching operation operation operation leads iterations max max filters filters pre direct inhibition normalized normalized bottom depth depth depth depth depth depth depth depth attention attention attention neuronal neuronal population improve improve recent recent robust separate element pixels pixels pixels pixels pixels pixels cognitive engineering previously unsupervised unsupervised unsupervised tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning correspond studies studies achieve parts studied invariant invariant invariant suggests wide derivative rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation feed feed clusters demonstrate competitive interactions interactions retina clear learns taking strong mechanisms mechanisms presence labeled turn variety selective decrease derivatives question areas areas areas appears appears van derive construct produces winner primary plot plot plot plot plot label label tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned distinct changing modeled sensitivity transformations transformations transformations transformations transformations transformations transformations text angle angle angle angle angle angle angle scales scales gaussians gaussians shift extracted independently focus focus review stationary communication detailed detailed detailed controlled organizing showed centered centered centered sizes activities completely completely translation translation translation translation translation translation translation translation translation translation translation allowed key key partial normalization combining intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate intermediate filtering faces faces faces views views views views views views views views views views views views views views views views views views dendritic degrees degrees expect usa retinal retinal instances instances sciences recognize activated discussions simplicity middle middle aspects closely closely capable differ included poggio poggio poggio poggio poggio poggio poggio poggio computations schemes comparing comparing invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance tend reached receives excitation excitation excitation excitation soc compact strongly strongly contained allowing showing showing anderson physiological physiological physiological physiological physiological physiological physiological sci dot dayan dayan dayan paradigm realistic received subsequent preferred preferred preferred preferred preferred preferred neighboring neighboring routing bars body employed stimulation selectivity selectivity transformed transformed transformed essential investigate investigate exhibit experience experience experience involving strengths respond respond respond respond behavioral detectors detectors detectors investigated scaled scaled comparable stream pathway pathway hierarchy hierarchy cognition neu patch plausible plausible plausible plausible perfect implementations implementations versions versions explored mapped mapped shapes shapes initialized explain attempts isolated massachusetts mentioned crucial agreement orientations orientations convolution variances defining biology explanation caused implementing producing broad broad located monkey monkey monkey monkey afferent afferent afferent afferent afferent afferent pool recognized recognized acad beginning cybernetics addressed researchers summation explained collected pathways led simulate experimentally experimentally peter psychophysical psychophysical incorporated biologically biologically biologically ity exhibits exhibits aim plan chose chose comments tolerance findings yielding physiology optimizing nat rotated rotated rotated connecting rotations rotations establish stronger ranges familiar familiar viewpoint viewpoint illumination adequate preparation preparation corner inferior falls ranging edelman edelman edelman demonstration monkeys monkeys monkeys monkeys mel candidates recog cerebral considerations explains explains interestingly dramatically yielded neurophysiology numerous solves covering covering opposed feeding profiles personal reports tendency hierarchies imagine unseen invariances invariances invariances invariances invariances translated crosses compatible ullman macaque macaque macaque macaque macaque macaque macaque increasingly investigating selectively translations translations afferents afferents afferents afferents afferents accounted exhibited manuscript resp lation corners corners synthesized olshausen tanaka tanaka cornput essen excited exposed anterior ventral ventral progressively marcus neurobiological spirit feasibility ruderman distractors distractors distractors distractors gratings gratings brought explaining neocognitron neocognitron spanning clutter neurones distractor distractor distractor distractor distractor distractor unaffected tightly plausibility plausibility phy borders ito fukushima fukushima undergoes reilly picks jonathan abstr logothetis logothetis logothetis logothetis logothetis logothetis logothetis logothetis densely viewpoints confused organize neurophys neurophys neurophys octave resembling cri comparatively shifter selectivities foster desimone desimone octaves octaves octaves octaves octaves octaves octaves occlusions tomaso akin mech irrespective exhaustively inferotemporal inferotemporal inferotemporal inferotemporal inferotemporal inferotemporal inferotemporal intradendritic abstracted terior fujita interpo cartoon cartoon neurosc prompted shimon rosci clip clip clip reynolds subordinate anisms nize spond sensibly 
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#*learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data data data data figure figure figure figure figure figure time time time time time time time time time time time time set algorithm number number number state state state state information problem problem problem problem problem models models models models models models models models models models models models models models models models models models hidden performance performance based space space layer case case case case vector shown systems systems systems systems values values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach approach approach approach single single single single single single single single single single processing control large large neuron patterns matrix signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples work work cells cells cells cells cells cells cells cells cells cells cells cells cells step step step step step points process process process process process process process level current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure random high similar similar representation show section section section section section section fixed fixed line rule vectors vectors general general general general general general general approximation approximation obtained term note activity dimensional threshold threshold threshold threshold threshold threshold variables variables variables variables computation solution solution research research independent independent log defined found constant constant constant estimate estimate standard standard terms terms connections phase low low low nodes machine object sets sets range press position components components components components components components components sample abstract applied find find find computational computational properties likelihood likelihood likelihood references component component component stochastic stochastic due due due due due due due due positive procedure procedure procedure important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction action action hand statistical statistical statistical effect effect effect dynamic generated cost tion variable variable variable assume signals signals signals signals signals prior prior chosen chosen chosen higher center center previous bound firing firing firing firing firing firing firing firing firing firing firing multiple cortex good spike spike spike spike spike spike spike spike spike spike spike spike spike represent represent represent expected markov markov make make make make fact techniques region proposed length observed errors errors errors forward forward scale sum performed called called times times times times times times times times times means potential potential potential potential potential study em em em filter filter obtain obtain obtain negative original specific specific specific specific true true cross cross provide rates location determined experimental posterior posterior distributions distributions discrete brain power approaches approaches steps connection selection selection selection morgan institute version advances represents difficult final scheme scheme graph graph framework framework framework framework equivalent additional additional view solutions solutions estimates estimates transition san san stage detection detection upper choice choice choice estimated basic basic basic validation con channel channel weighted weighted conditional clustering developed lines path actual provided provided finally finally processes selected evidence iteration depends measured measured measured covariance covariance covariance covariance covariance describe describe describe arbitrary hmm hmm close close close assumption assumption assumption complete proof proof finding short common common effective implemented shape shape shape shape shape shape supported theoretical square easily makes fit fit fit fit fit fit kaufmann probabilistic probabilistic hopfield reduced account account account dynamical dynamical functional jordan jordan technology special special empirical leads principal principal details details filters making making minimize produced sources description description discussed discussed directions recent recent recent advantage property robust robust separate ensemble ensemble takes apply introduced period period subject identical hierarchical hierarchical hierarchical inference inference inference inference inference inference inference inference inference engineering varying varying compare previously calculated calculated rl sparse background background background background background background background background separation separation separation separation modified observation channels amplitude amplitude digital spikes spikes spikes spikes spikes spikes alternative correctly touretzky deterministic clusters pass pass assumptions assumptions segment segment segment valued depend depend depend interactions differences differences measures clear peak peak mateo external drawn drawn drawn california introduce introduce manner acknowledgements areas reference explicit explicit pro pro construct construct edges edges longer index index transitions distinct distinct segments segments segments segments segments segments sensitivity explicitly simultaneously electrical remaining remaining easy gaussians gaussians events events events events events events events expectation potentials john john national extracted extracted extracted extracted independently focus focus dependence stages stages stages correlated squares overlap overlap overlap influence operations fraction forms static understanding similarly suggested earlier earlier reasonable additive additive epochs measurements event event event false false filtering filtering visible construction foundation foundation avoid avoid recorded recorded recorded recorded recorded recorded recorded recorded fire includes usa currents prove discuss discuss discuss coupled partially discussions tests straightforward selecting identified identified identified identified identified hmms maximal modification latent latent identify projections soc allowing neuroscience neuroscience dis lie lie sin generative generative generative gray comp sampled write write write write backward providing wave maximization attempt subsequent subsequent extract neighboring neighboring neighboring neighboring intrinsic remain diego powerful collection collection collection rise giving history history dependencies dependencies root stream stream variability variability variability variability variability neu circles measurement trace plausible thought formal shapes academic multivariate simplest utility motivated isolated burst band directed derivation derivation waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform nowlan nowlan adapted briefly tractable considerable stress filtered filtered broad commonly pulses probable probable probable cut projected describing recording recording recording recording recording requiring reflects considerably double collected empirically transient axes lms introducing recordings passed incorrect ity schematic outliers calculating operate mod fall prevent pasadena marginal richard replace comments shaped pole aligned identifying intractable sort conditioned refractory refractory refractory refractory purely repre repre royal caltech caltech caltech caltech caltech caltech adds khz khz khz bower bower stated attractive nearby nearby nearby wire preparation preparation heuristics fires fires fires fires fires motivation overlaps overlaps overlaps separating falls bialek histograms histograms den arrangement parietal diameter infer neuromorphic indicator arrive matter probe probe ends waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms waveforms arrows davis statement summarize dempster dempster avoiding influences counts consecutive fired fired rms rms mind unchanged unchanged crossing crossing ence drop slight specification rubin benefits isotropic kurtosis par exception trigger electrode electrode electrode electrode electrode adapting penalized trends trends biophysical biophysical distribu permits eliminating altered individually ultimately laird indexed sam electronics els bill normalizing rewrite eters exploited technologies manuscript handled handled fiat remarks sorting sorting sorting excess excess consuming vis suffers hoc diffuse hid clarity adult converter incorrectly tribution tip tip tip exposed exposed peaked inferring autoregressive isolation digitized sloan convolved convolved implying andersen andersen andersen andersen andersen andersen andersen amplified lewicki lewicki lewicki gathered foreground foreground foreground foreground foreground foreground foreground foreground media acyclic tenth excessive wires health col spanning objectives custom bodies rises derivations omit men extracellular extracellular extracellular extracellular extracellular aliasing advice sodium nth exhibiting digitally membranes lacking responsibilities responsibilities responsibilities responsibilities functioning multichannel ponents inactivation accompanying sketched sketched neurophys duced linden factoffal presumed ruth ruth ruth ruth ruth invaluable heuristically dag roweis mad bundle funding unreasonable tiling emd emd rhesus tucker keck institutes borne benefited philip deflection sophistication sophistication modulators irregularly reestimate flaw bessel tat catalog founded inserts ameters vmues lection fee fee marginalized mgorithm roscience arisen kleinreid 
#@Andersen_R,Pezaris_J,Sahani_M,
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#*network learning model model neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data function figure figure figure figure time time time time time time time time time set set networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number results results results results information information information problem problem problem problem problem based based based based based linear vector vector vector vector vector vector vector vector vector order order order order order order order order shown shown shown shown systems systems noise unit unit unit distribution distribution method method method method method method method method approach approach approach pattern point point processing processing processing processing processing large local local local local patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix shows shows shows shows signal signal signal signal signal signal signal simple gaussian paper paper paper methods methods methods methods fig step step step field field field features process process random high high architecture fixed fixed line line vectors vectors vectors vectors theory gradient gradient obtained activity activity activity activity activity activity dimensional university university computation solution solution solution solution research research independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent defined defined defined found found found found found found found target initial initial constant constant estimate estimate estimate standard computer science left left presented presented presented present present low low frequency frequency temporal sets maximum press press position components components components components components components components components components components components basis basis sample abstract applied back back find find references component component component component component component component component component component component component component component component component due due due ieee adaptive context context introduction introduction stimulus stimulus statistical statistical statistical statistical statistical statistical generated generated variance tion assume rules measure signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals higher higher higher part cases required multiple good long expected make make length ing ing total human regression respect respect sum sum performed eq eq times elements factor potential dimension made made orientation global applications applications study study study study original artificial relative samples application proc proc perform eye eye eye eye eye eye eye eye experimental related related related distributions discrete discrete brain brain brain brain brain brain brain brain brain mit mit descent source source source source source source source source source technique technique joint represents computing equivalent solutions solutions stimuli efficient full statistics estimated estimated basic basic give produce produce produce channel derived weighted weighted developed product finally processes processes simply achieved discussion discussion covariance fast close close close assumption assumption complete finding common assumed shape supported eds face journal needed combination unknown unknown unknown coefficients coefficients fully technology technology projection projection head head principle principal principal squared making produced produced produced run sources sources sources sources denotes discussed directions directions directions separate separate typical similarity movement introduced include period subject subject subject subject side subset sejnowski recently varying subjects calculated calculated correspond pca pca pca pca pca studies studies studies studies achieve trans diagonal definition mixtures mixtures mixtures mixtures positions locations separation separation separation separation separation separation channels williams entire increased amplitude amplitude amplitude horizontal horizontal horizontal expression concept studied extended digital digital digital spikes loop column pass pass demonstrate starting differences temperature presence presence physics largest cycle ica ica ica ica ica ica ica ica ica movements movements min min identification identification identification identification identification identification identification identification areas reference relation relation relation relation plot vertical mathematical changing category simultaneously electrical electrical dimensionality remaining remaining remaining remaining extraction expectation expectation extracted expressed dependence controlled ocular ocular ocular lee similarly spectrum slow measurements event visible eeg eeg norm norm norm euclidean views avoid avoid expect expect recorded recorded recorded recorded recorded box box eigenvalues blind blind blind extension plotted activated columns sensor included presentation identify identify tend orthogonal orthogonal orthogonal strongly strongly contained showing showing physiological device list nips nips nips mixing mixing mixing mixing satisfies presents employed stimulation access essential dotted tech authors root working eigenvectors eigenvectors affect affect measurement measurement measurement illustrate created changed eyes noted noted algo ith consist simplest seconds years rows slowly band sensors sensors sensors agreement guaranteed independence independence independence independence independence correction correction tool tool inside sections producing strictly filtered filtered filtered broad located nucleus commonly beginning lowest recording recording recording author geometry fourth fourth double capability recordings recordings recordings recordings recordings remove http extracting suited neuro patients eventually wang lab lab room room room uncorrelated accomplished www restriction restrict fix saccadic rithm pick neurophysiol neurophysiol spontaneous dealing dealing oja oja oja oja oja oja oja oja oja oja oja minutes los occurring belong effectiveness effectiveness guide muscles separating separating introduces introduces ranging heart captured multiplied artifacts artifacts artifacts artifacts artifacts artifacts artifacts 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constancy bandpass inde fin fin cutoff cutoff feasibility reviewed ings modern baltimore facts investigator resemble resemble relax demanding lqr tutorial rhythms herault herault herault metal comon comon comon minute reviews makeig couple jung jung eog eog ago army digitally clin clin kurt kurt cardiac cardiac cardiac cardiac nent nent canceling cumulant karhunen karhunen karhunen helsinki helsinki regularly anatomically acknowledgment ecg ecg ecg nique electro electro discarding hyv hyv hyv hyv hyv plications pathological hut hut hut hut hut internet originated originated fluid finland finland finland muscular muscular conduc questionable nals isolate isolate collects silva whitening whitening sphering blink ilwll teeth neurological eventual neuromimetic infrequent iiw downsampled meter infrequently electroenceph electroenceph xxt flux flux haft haft electroencephalographic origins berg berg erkki erkki arti irregularly princi mckeown pendence inen sphered sphered communities 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#@Hamalainen_M,Hari_R,Jousmaki_V,Oja_E,Vigario_R,
#t11
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time set set set set algorithm output output output output results results results results results results information models models models models models models models models space space space space space space space linear linear case case case values values values values values values probability parameters parameters parameters parameters parameters parameters noise neurons neurons unit approach image image image image image image image image image image image image image image image image image single control control control control control control control control control control control control control local local rate test test test patterns patterns patterns optimal form form form form shows shows gaussian gaussian gaussian visual visual visual visual visual visual paper paper small small size size size size size task methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field field field field field field field field field features features level cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure high response response response response response response response response response response response similar similar show equation equation equation equation equation equation images images images general parameter parameter parameter parameter real real approximation approximation average average average average gradient obtained obtained obtained obtained obtained obtained term term term term term activity dimensional dimensional dimensional result university university university university research sequence sequence dynamics dynamics constant constant constant table table table table table terms direction presented presented presented present present phase phase phase frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal sets motion motion press position position position position basis nonlinear continuous sample abstract find find properties references due due positive procedure introduction complex complex complex complex complex complex complex stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy difference complexity variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial part center center cases multiple cortex cortex cortex cortex spike techniques region region region region correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation scale ing ing total total human computed respect performed performed times times regions made made made natural natural natural natural natural natural natural natural natural natural natural natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study study study negative original relative relative compared series receptive receptive receptive receptive receptive receptive receptive provide location eye eye eye eye determined gain gain gain gain gain gain gain gain gain gain gain gain gain discrete cortical power power power power power power power comparison contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields fields support dependent dependent modeling modeling modeling modeling modeling report report department department consists consists responses responses responses responses responses responses responses responses responses responses delay delay scheme equivalent curve curves estimates stimuli stimuli effects effects effects effects effects effects effects detection choice significant significant approximate free free free free free free free vision vision vision vision vision estimated increase validation weighted area area area area area area area area product finally discussion assumption adaptation journal journal journal journal hypothesis future future development including fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit simulated combination functional interesting york mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism consistent consistent consistent leads leads leads max max filters frame frame frame frame attention combined neuronal improved improved improve recent correlations correlations correlations correlations correlations resolution apply apply include pixels sejnowski relevant highly highly compare tuning tuning match match match match match modified observation improvement improvement sensitive entire invariant invariant suggests width width white generally generally setting half half half half greater greater central interactions strong mechanisms mechanisms mechanisms california california variety movements selective selective selective selective selective selective scene identification acknowledgements areas areas van van van van van produces optical primary tuned vertical modeled modeled confidence sensitivity explicitly averaging averaging slightly unique adding applying formed versus versus versus versus versus competition extracted independently independently independently independently review review review review review review review review review review review review review review review review correlated overlap evaluated controlled showed showed centered frames forms static static static static static approximated completely discrimination earlier classical classical classical classical classical normalization normalization normalization fitting fitting fitting fitting fitting intervals roughly roughly foundation david recorded dominance color color color color color weighting weighting subspace black characterized tests texture texture texture texture texture texture texture texture texture texture extra closely society divided divided delta delta included included successful score receives composed composed strongly contained neuroscience neuroscience neuroscience neuroscience physiological gray gray gray cues realistic surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround minimizes wave wave delayed delayed delayed delayed delayed delayed computes highest cat oriented oriented oriented oriented situations stimulation stimulation stimulation selectivity selectivity selectivity selectivity selectivity parametric poor collection collection collection detail accurately preliminary fourier fourier fourier matches matches matches maximizing examined examined examined patch patch coefficient predicting psychology perfect implementations defines seconds seconds seconds animal animal animal histogram great scenes separable separable convolution improves improves biology nonlinearity spatially drive drive drive berkeley berkeley berkeley berkeley berkeley berkeley division directional directional directional directional incorporate incorporate monkey monkey monkey separately separately describing beginning localized lowest patches patches arises recording recording improvements greatly reflect collected collected collected collected empirically consistency offset continuously maxima compares compares limiting asymmetric sums sophisticated display median tile oxford gabor gabor gabor saccadic drift linearity approximates reaching cellular khz significance occurred striate striate striate neurobiology affected wilson wilson wilson excellent ensures pat ascent accounts monkeys reproduce viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing viewing diameter permutation spatiotemporal suggesting saccade sustained characterization influences automated outlined dense dramatically grating grating grating grating neurophysiology unable corporation incorporates incorporates latency latency latency latency failed responds spatio sinusoidal sinusoidal molecular reflected attempted modifying degraded mediated simplifying considers adelson adelson fixation fixation fixation fixation fixation surrounding surrounding macaque macaque macaque statistic statistic rectified rectified dramatic scanned remarkable discretized discretized monitor assistance terns envelope envelope envelope envelope envelope inhibited doesn played pearson inclusion inclusion lists eliminates essen essen essen essen essen striking heeger heeger heeger heeger heeger luminance luminance manually bergen bergen isolation america william prone cascaded protocol accounting enter correlates charles enters nih broadband gratings gratings assessed promise manual modest modest freely behaving replicates jack gallant gallant gallant gallant gallant gallant gallant gallant gallant cats connor connor connor connor preprocessed discrepancy joseph primates directionally directionally directionally directionally simulates proce awake awake rectification rectification divisive divisive divisive picks suggestion movie movie movie movie movie movie movie movie movie movie movie movie movie movie movie rogers converting suppresses suppresses surrounded psth psth psth psth psth psth psth psth psth psth brings highlights imperfect peri knierim knierim albrecht albrecht desimone photo misses mecha alert subunits subunits dure phasic phasic phasic phasic tiling mech squaring squaring annular extrastriate movies movies movies movies movies movies movies movies movies movies movies movies balances suppressive suppressive suppressive suppressive suppressive suppressive suppressive barely hnear contamination contamination compensates ceptive ception lehky lehky explanatory subunit mismatches tun objectively flashed flashed anism controt controt nisms geisler geisler neuroreport abstracting 
#@Gallant_J,Vinje_W,
#t11
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input data data data data data data data data function function function function function function function function figure figure time set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training number number number number number number system error error error error error error error error error error error state state results results results results results results results results information information information hidden space space space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear layer case case case case case case vector vector vector vector shown shown shown systems values weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution recognition recognition method method point image image single large large test test test test test test test test class class class class class class matrix optimal optimal optimal optimal optimal optimal optimal inputs form form shows shows paper paper examples examples examples examples examples examples examples examples examples examples examples examples small small small small small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature points features features features features features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification trained problems random show show show show equation equation section section section section section section section section section section fixed fixed fixed fixed fixed vectors vectors images images general general speech speech real real real approximation approximation approximation average theory theory gradient experiments result university university university variables independent log log log defined defined estimate estimate estimate estimate estimate distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance presented presented presented presented presented presented present present present low machine machine machine sets range press learn learn learn learn learn learn sample sample sample abstract find computational convergence references ieee positive procedure introduction hand tion tion tion tion change change change complexity complexity complexity complexity variable variable assume classifier classifier classifier classifier classifier measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure representations chosen part theorem theorem theorem theorem theorem theorem theorem bound bound bound cases cases required required good good good good conditions expected expected make techniques resulting classes classes classes total computed computed respect sum sum sum performed called mapping means optimization original original original samples samples samples represented true compared application provide define compute experimental experimental experimental experimental goal related related comparison support train descent proceedings proceedings report report department loss loss loss loss loss version technique technique technique consists internal individual difficult final final exp exp exp bias bias scheme sequences ai ai ai ai maps domain domain experiment experiment experiment experiment experiment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment directly directly directly conference conference efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers approximate world estimated estimated pages give give conditional bounds bounds bounds provided provided selected sampling simply achieved achieved achieved measured technical technical feedforward group group denote transformation assumption stable proof nearest nearest nearest nearest nearest nearest nearest nearest nearest common common common common common effective assumed generate generate generate supported theoretical main face hypothesis pairs pairs combination combination combination unknown unknown unknown technology testing testing testing testing significantly character character character character character character character character york uniform database empirical empirical empirical empirical squared squared squared squared squared squared squared squared squared squared squared making stored international international combined minimize sources denotes property pair pair pair pair similarity introduced subject sense sense subset engineering calculated tions symmetric bounded improvement entire constructed exists exists alternative occurs setting conclusion conclusion row row valued valued valued depend accurate practice strong strong minimizing minimizing minimizing exist characters characters characters characters characters characters characters characters characters characters characters characters characters characters suppose suppose suppose label label stability stability distinct recall recall metric category explicitly explicitly averaging involves remaining quality expectation choosing national expressed expressed expressed expressed expressed overlap learner learner learner lemma lemma lemma lemma approximations lee understanding reduces reduces reduces purpose purpose initially distances sufficiently sufficiently sufficiently assigned norm euclidean euclidean euclidean euclidean euclidean euclidean euclidean transactions handwritten combinations combinations prove specifically reason extra essentially heuristic showing showing split dis hold satisfy notation sampled sampled sampled quantization quantization quantization consisted minimized investigate environments environments environments environments environments proved proved func func cover cover smallest reading generalisation generalisation generalisation ensure mapped mapped utility ment inequality trivial distinguish explanation tool london perspective producing ion separately english english author qualitative raw argument double peter treated compares http perturbations measuring aim proven segmented distortion distortion distortion distortion distortion distortion distortion distortion distortion distortion distortion distortion representative pac pac pac college primarily www optimality optimality acm databases impossible printed printed royal turned simplify fan definitions canonical canonical canonical canonical canonical canonical canonical canonical canonical canonical symposium bartlett bartlett bartlett bartlett bartlett bartlett document ensures encountered surprisingly clean broken statement statement implicitly grants outlined treat verify misclassification misclassification misclassification misclassification equivalently asked july july restrictions australia clas clas pij toy toy learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt learnt maintained maintained ocr ocr ocr ocr ocr ocr ocr ocr ocr degraded carefully investigating erp cation cation nonetheless distinguished page union indication williamson supporting remark scanned remarks recogni recogni sake australian subjective exper err err err japanese japanese japanese japanese japanese japanese japanese japanese japanese assessment triangle baxter baxter baxter baxter baxter baxter baxter tance est ranged benign eighth routine constituent gij neigh remarkably hong tailored hoeffding trick ily jonathan jonathan jonathan jonathan environ analysed neighbour neighbour neighbour neighbour neighbour neighbour neighbours neighbours neighbours epsrc classifi classifi shi agnostic 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#@Bartlett_P,Baxter_J,
#t11
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#*learning model neural neural neural neural neural neural neural neural neural neural neural neural input input input input function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure set set networks networks networks networks networks number number number number number number number number number system results results results information information information models based based weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer case order order order shown shown shown systems systems systems systems weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons recognition approach pattern image single single single single single single single single single single single single single single single processing processing processing neuron neuron neuron analysis analysis analysis class class optimal inputs inputs inputs inputs inputs inputs inputs shows shows simple paper paper paper paper paper paper examples examples small small size size size size work work methods field field classification classification classification classification process problems problems problems representation show show show show show show section section section fixed general generalization speech theory note note result result result threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold research research log defined defined defined defined found found computer computer computer terms science science direction machine press press press outputs outputs outputs outputs outputs outputs outputs outputs abstract applied computational computational computational computational analog properties references ieee ieee ieee ieee important introduction hand circuit circuit circuit circuit circuit circuit circuit circuit estimation estimation behavior parallel complexity lower part part theorem theorem multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple binary binary distributed chip techniques resulting classes classes ing simulation human computed multi sum sum sum sum sum sum sum sum sum sum called called times elements elements elements elements elements elements elements elements elements elements optimization natural applications applications study study study study study original vol vol vol vol vol vol vol vol artificial artificial relative relative relative true define compute compute compute compute compute compute compute compute proc proc goal related related related related related equal power power power power power mit mit mit comparison comparison comparison proceedings report institute implementation implementation implementation implementation implementation implementation version version version synapses consists consists consists code advances advances layers addition addition addition addition addition addition addition addition addition cambridge cambridge computing computing computing computing computing computing computing computing domain san bit bit bit bit bit bit bit bit bit bit bit conference conference capacity efficient efficient efficient efficient efficient efficient requires requires significant basic pages con weighted weighted weighted weighted bounds area area area area area area area product product product product product product product product product product product product provided provided evidence depends constraint constraint constraint simply biological technical describe arbitrary arbitrary arbitrary arbitrary arbitrary limited limited corresponds complete complete proof proof proof proof proof proof proof proof circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits implemented supported theoretical theoretical theoretical main main main main journal vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi future future rumelhart rumelhart rumelhart including including hopfield hopfield reduced reduced technology technology interesting principle call call bits bits international depth depth depth depth depth depth depth magnitude polynomial polynomial polynomial polynomial polynomial polynomial polynomial idea idea choose directions recent element element element element element element element element element element element element apply include include subset interest compare trans definition definition definition definition definition symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric observation generalized generalized generalized bounded gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate organization exists lead demonstrate demonstrate conclusion minimal greater reduce conclusions performs performs exponential exponential strong hard california intelligence relationship iii introduce introduce program denoted relation derive construct written solving transitions transitions transitions transitions transitions transitions transitions transitions transitions implement implement implement implement implement physical spectral consisting consisting blocks versus boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean national communication showed sign sign sign add add add add add add false remains transactions transactions silicon thesis usa sciences sciences illustrated prove prove prove partially characterized capable mcclelland build efficiently traditional traditional notice superior sin follow hold built comp comp comp comp comp computes computes computes computes computes computes thresholds thresholds acknowledgments powerful powerful powerful wiley xor xor xor xor xor exhibit mead relations relations limitations limitations issues issues ideas parity parity parity transistor transistor gates gates gates gates gates gates proper proved understand cognition neu math math math math integer implementations formal logic logic logic logic logic logic logic logic logic store contributions contributions motivated phd electronic growing floating floating majority capabilities capabilities multiplication lin implementing implementing organized division division sgn members computers computers annual nsf argument requiring prop orders introducing slower schematic requirement http mod characterize pasadena returns june proposition univ realized realized picture picture redundant redundant ear fabricated investigation restrict acm harmonic caltech caltech establish maass inspired fits mail analogy odd fan programmable programmable abilities ral definitions definitions corollary introduces belongs claim claim claim claim claim april young layout layout layout layout characterization characterization integers integers integers integers integers integers integers integers integers integers integers integers integers explorations abu unable microstructure mostafa outline fellowship deriving emergent conjecture conjecture chicago simulating stands stands stands algebraic iff march depicts academy ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm ltm siam siam siam siam october tunneling copies august unbounded unbounded unbounded designs designs designs hat hop december inclusion award sym sym siu siu siu siu siu siu siu siu siu poly html sloan amenable creation subscript thresh february bruck bruck bruck bruck bruck bruck bruck bruck bruck bruck bruck bruck bruck col hip kailath investigator boosted scans cir roychowdhury constructions undergoes claims lay brains ixi ixi ixi erties struction minch hasler hasler hasler hasler electrons combi cial separations separations separations injecting muroga muroga muroga ccr diorio wixi goldmann artifi cuits goldman goldman goldman disc disc disc disc xiy interconnecting karpinski stoc lective dep lxi maih hastad hastad interscience multilevel hajnal hajnal boo innovative wix szegedy szegedy szegedy laying layouts pudlak turan 
#@Bohossian_V,Bruck_J,
#t11
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#*network learning learning learning learning neural neural neural input input data data data data data data data data data data function function function function function function function function function function set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training number number number number number number number number number number number number number number number number number error error error error error error error error error error results results results results results results results results results results results results information information information performance space space weights weights layer layer case case case case case case case vector vector vector vector vector order order order order systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach pattern pattern pattern single single processing large large rate rate rate rate test patterns analysis analysis class class class class class class class class class class class class class class class class class optimal optimal form form form form form form form shows shows shows shows simple simple simple paper paper paper paper examples examples examples examples examples examples examples examples examples small small size size size size size size size size size size size size size size size size size work methods methods points classification classification classification classification classification classification classification classification problems problems random random high similar similar similar similar similar show show show show show show show section fixed fixed fixed fixed fixed generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter real real approximation average average average average theory theory obtained term term term term term term term term term term note result result result result result result result result result university university threshold threshold computation research research research log log log log log log log log log log log defined defined defined defined defined defined constant constant constant constant constant estimate estimate estimate standard standard terms terms terms terms terms terms terms terms terms terms terms terms terms distance node present nodes machine machine machine sets press sample sample sample sample abstract applied find find references positive positive positive positive procedure important decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision introduction complex generated tion complexity complexity complexity complexity complexity complexity complexity complexity complexity variable assume assume assume assume classifier classifier rules measure measure measure measure representations chosen chosen chosen chosen previous theorem theorem theorem theorem theorem theorem theorem theorem 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give give give give give con con bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds path actual evidence depends depends normal describe arbitrary arbitrary arbitrary denote denote denote denote denote denote denote denote denote proof proof proof proof proof proof amount effective effective effective effective effective effective effective effective effective effective implemented theoretical theoretical journal journal ability hypothesis hypothesis hypothesis hypothesis easily makes including kaufmann kaufmann smaller smaller smaller smaller smaller smaller smaller combination combination combination combination combination coefficients coefficients coefficients interesting york increasing consistent consistent consistent consistent consistent consistent uniform uniform uniform empirical empirical empirical representing international depth depth depth depth depth frame choose choose choose choose recent recent pair apply machines machines side quadratic trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees subset relevant engineering engineering engineering dimensions rl definition definition bounded risk expression suggests extended setting setting conclusions valued valued valued valued valued depend depend depend depend sigmoid measures measures accurate numerical numerical faster practice mateo suggest suggest taking intelligence intelligence labeled force base base base base base base base denoted acknowledgements derive written written written recall linearly electrical easy slightly applying implies implies implies expectation expectation expectation expectation boolean boolean boolean boolean boolean boolean boolean boolean decreases yield yield choosing choosing national independently fraction fraction fraction fraction fraction lee lee lee lee lee approximated margin margin margin margin margin similarly key convex convex convex convex convex convex convex convex convex convex convex convex convex event closed valid assigned combinations combinations combinations combinations sciences prove holds tests structural structural simplicity determining closely uniformly build notice notice notice induced induced induced prob lie follow satisfy satisfy satisfy quantity correspondence hypotheses hypotheses hypotheses hypotheses hypotheses reach attempt approximating satisfies satisfies satisfies satisfies satisfies extend extend extend simpler carried replaced optimized behaviour helpful school school applicable boosting boosting boosting root affect cover induction act act equally thought thought thought friedman der greedy taylor freedom precise ith utility inequality inequality inequality inequality formula formula formula growth growth defining explanation inside sections sections widely widely choices choices choices leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves 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australia australia remainder summarizes iff iff iff exam exam intuition intuition thresholded thresholded thresholded thresholded thresholded thresholded thresholded thresholded thresholded thresholded academy sketch sketch quinlan covered refinement voting likewise union williamson aaai mea covers ble inconsistent inconsistent australian australian quantify shawe hull lists formulae formulae formulae formulae formulae formulae ples ples anthony occam occam maxi maxi implied era thresh probabil probabil literal literal mason mason mason mason dnf dnf dnf dnf dnf dnf dnf dnf dnf dnf dnf dnf dnf dnf dnf dnf colt jensen belmont nation webb razor razor olshen possi vcdim vcdim vcdim vcdim vcdim vcdim vcdim vcdim oft forest stant wadsworth ehrenfeucht canberra canberra combi negation negation composing als minimisation neff neff neff neff yoav fayyad uncover rob combina disjunctive wee fourteenth monomials wlog wio wio enlarge disjunction eri ois ois pis pis defence orem moid uncovered 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#@Bartlett_P,Golea_M,Lee_W,Mason_L,
#t11
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#*network network network network network network learning learning model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data data data data function function set set set set set set set set set set networks networks networks networks networks networks networks networks training training algorithm output output output output number number number number error error error error error error error error error error error error error error state results results results units information information information problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models hidden space linear linear linear linear linear linear linear linear linear linear linear linear case case case order order order order shown systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters noise weight weight functions unit distribution distribution distribution distribution distribution method method method method single single processing processing processing processing local patterns analysis analysis analysis class class optimal optimal optimal optimal inputs inputs inputs form form form simple simple simple simple simple simple simple gaussian gaussian paper paper examples examples examples examples small small small net work methods methods methods methods classification classification classification classification classification process trained problems problems similar similar similar representation show show show equation section section section fixed fixed rule vectors general general parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation average average average average average average average average average theory obtained obtained obtained obtained term term term term term note dimensional result result university computation computation computation solution solution research log log log log log defined defined found target initial constant constant constant constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard terms terms terms terms distance science science prediction left machine range press press press nonlinear nonlinear outputs outputs outputs outputs continuous abstract applied find find density density density density references references references ieee procedure procedure procedure procedure introduction hand hand estimation estimation variance variance variance variance variance variance variance variance variance variance variance difference difference variable variable assume measure measure measure measure chosen part type good long bayesian bayesian bayesian make make fact fact proposed probabilities probabilities observed errors finite finite ing simulation regression regression regression regression regression regression regression regression regression regression sum sum sum sum sum sum sum sum sum sum called called elements made obtain obtain specific samples samples true true true cross cross cross cross define define compute compute active constraints constraints discrete discrete equal equal equal equal mit mit mit accuracy larger larger larger larger dependent dependent proceedings words version individual individual individual individual individual individual individual individual individual advances advances advances joint difficult difficult final exp exp bias bias bias bias bias bias bias cambridge cambridge cambridge equivalent equivalent equivalent directly estimates estimates estimates estimates estimates estimates choice choice statistics estimated pages pages pages validation derived derived weighted weighted conditional conditional entropy entropy depends depends constraint simply simply normal feedforward close inverse assumption assumption corresponds corresponds corresponds corresponds complete proof proof finding finding generate supported role main end easily makes makes objective objective probabilistic smaller smaller smaller combination combination combination combination unknown unknown jordan technology technology programming programming programming programming programming edge leads leads leads squared squared squared squared squared squared squared squared squared details normalized experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert magnitude minimize choose choose recent exact advantage property property property robust ensemble ensemble ensemble ensemble reported practical practical introduced side side quadratic quadratic quadratic quadratic quadratic quadratic quadratic interest unsupervised works solve yields yields yields yields yields correspond studies symmetric symmetric generalized williams constructed expression expression suggests deviation deviation touretzky starting depend editors editors editors differences bayes exponential exponential suggest suggest integration minimizing minimizing minima explicit suppose suppose pro van construct written written factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors estimating confidence explicitly averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging 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overfitting overfitting replaced replaced optimized optimized integral divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence helpful maximizing complicated tanh tanh func naturally naturally closest necessarily man obvious formal formal logistic expressions multivariate extent residual inequality formula theoretic variances unstable tractable handle stress sys easier easier easier strictly division immediately immediately arise pool pool pool pool pool pool pool pool pool pool pool pool pool pool pool pool pool pool pool pool pool pool acknowledgement optimize cybernetics applies bootstrap bootstrap bootstrap introducing remove treated reliability ity gen prevent asymmetric asymmetric replace conclude irrelevant benefit proofs leen writing writing formally lagrange tation optimizing optimizing nonzero outcome plays generality multiplier kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback kullback convenient convenient convenient ments breiman overcome logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic logarithmic multiplicative interpret interpret interpret belong settings krogh canonical canonical canonical ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx ylx heuristics heuristics ambiguity ambiguity ambiguity ambiguity predictors corre dependency realization claim ensembles suggesting arrive arrive matter bagging bagging bagging bagging properly ends belonging wolpert wolpert statement balancing balancing assigns assigns treat treat fitted fitted multiply logarithm minus minus minus minus accept leibler leibler leibler leibler leibler leibler leibler leibler leibler leibler leibler leibler leibler leibler leibler leibler leibler convenience residuals decomposed scenario manipulation management tems carefully smyth integrals rough sketch represen drawback drawback discusses pools pools pools pools pools pools pools pools stuck indication things mea helps suggestions suggestions suggestions rewritten cube replacement sponding externally tom tom puts outperformed realizations appealing neglect neglect incorporation settle proposes substitute petsche petsche beneficial economic statements statements statements statements stacked opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion opinion replicate dispersion dispersion replicates replicates derivations elegant argmin blurred decompositions heskes heskes heskes heskes heskes heskes relying netherlands jensen consensus ministry aver exercise numerator weaknesses story gramming kappen unconditional anonymous dan supplying lihood aging contrasted summations vedelsby ylz nijmegen nijmegen divergences divergences divergences divergences bert plateaus tionally logit tax aggregating programme swain jor kun affairs assessments assessments assessments supra supra dxp dxp lear loglikelihood loglikelihood loglikelihood loglikelihood crux mbfys prohibits rre vlx geert grooteplein 
#@Heskes_T,
#t11
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#*learning model neural data function function function function function function function function function function function function function figure figure figure set set set set set algorithm algorithm number number number number system system system results results results results information information information information information information information information information information information information information problem problem problem based based based based based based based based based based based based based based based based based space space linear linear case case case case case case case vector vector order order order order order order order shown shown values values values values values values probability weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution method method method method approach approach approach approach approach processing processing processing large analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix optimal optimal form form form form shows signal signal algorithms simple simple simple simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples examples examples examples examples small small methods methods fig features features structure random random random random random random random random random similar similar similar architecture show show section section section section section section section section section general general general parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory obtained term term term note note note note experiments dimensional university university university variables computation solution independent independent independent independent independent independent independent independent independent independent log log log log log log log log log log defined defined defined defined defined defined defined found found sequence constant constant constant constant estimate computer computer computer terms terms terms science science science left maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press components basis continuous continuous sample sample sample sample abstract find computational computational computational computational density density density density density density density density density density density density density density density density density density density density density density density density density density density density properties references component component component component component component component positive positive positive positive positive positive positive important important important important important adaptive mixture mixture context introduction hand hand estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical variance variance variance variance variance variance variance search search search tion tion variable variable variable variable variable variable variable variable assume measure measure measure prior chosen higher higher higher higher part part cases cases conditions conditions equations make make make make make fact proposed proposed proposed observed finite finite finite finite finite finite ing ing simulation performed eq called called elements means means means means means means dimension made natural applications applications applications applications knowledge obtain obtain negative negative negative true true true compared compared compared application provide define compute proc determined constraints constraints constraints constraints constraints constraints constraints distributions distributions distributions distributions distributions distributions approaches mit comparison comparison connection dependent source report report words version advances difficult difficult difficult difficult exp exp exp exp exp exp exp addition ai ai considered considered considered considered considered framework equivalent directly directly curve curve curve curve curve curve curve curve additional view solutions estimates limit effects determine efficient efficient requires choice choice choice choice approximate statistics statistics statistics estimated estimated estimated estimated basic basic basic pages con derived derived derived criterion criterion entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy finally finally constraint simply simply measured measured technical technical technical technical denote transformation fast assumption assumption assumption assumption assumption assumption corresponds finding theoretical main end degree typically smaller needed functional technology technology technology interesting projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection special special special consistent consistent leads leads making making early polynomial polynomial polynomial choose choose sources directions directions exact exact robust takes takes practical practical practical practical apply introduced introduced introduced identical side side sense highly observations solve yields correspond differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential trans sparse sparse definition separation symmetric symmetric symmetric interval sensitive sensitive exists lead concept touretzky conclusion critical place minimal assumptions depend depend editors central central measures measures measures measures accurate accurate accurate numerical clear exponential exponential exponential faster faster faster practice practice practice practice practice asymptotic asymptotic asymptotic asymptotic integration solid solid assuming assuming ica ica ica ica ica exist introduce areas derive derive derive derive construct construct index index index index index index laboratory laboratory laboratory metric linearly linearly infinite mutual mutual mutual mutual minimization minimization implies expectation john choosing family family family family family family family expressed formation dependence estimator detailed transform densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities evaluated restricted approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations decomposition completely constants constants constants constants dashed dashed dashed dashed measurements measurements measurements measurements classical classical expansion expansion expansion expansion normalization purpose purpose remains remains construction avoid box includes formulation blind blind plotted discuss mozer simplicity aspects society computationally computationally projections plots orthogonal capture heuristic sin sin follow criteria criteria criteria quantity dot dot nips approximating approximating approximating approximating satisfies minimized simpler unlike american wiley poor requirements exhibit put estimators dotted dotted graphical mass pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit pursuit scalar scalar authors reliable reliable statistically statistically cover possibly ensure friedman noted noted assumes taylor taylor shapes multivariate amari averages advanced theoretic growing expensive reasons reasons reasons reasons lin choices mation recognized opt calculations depicted depicted explained considerably double amounts poorly outliers outliers outliers outliers polynomials polynomials polynomials http measuring measuring measuring measuring reaches cal asymmetric enables enables expectations expectations ordinary www extensive purely jones grows royal consideration difficulties simplify logarithmic odd odd grow grow substituting infor meaningful heavy ranging encountered equals decide infinity hasselmo yang thomas dif laplace matter theoretically eqs concentration sons considerations cam convergent vari largely annals validity ties nition kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis centre obtains obtains obtains obtains obtains obtains regularity generalizations algebraic distribu distribu ization compatible compatible compatible met retain emphasized det parametrized parametrized jutten ignoring exploratory simplifies infinitely expansions expansions expansions expansions expansions expansions bridge justified justified invertible ferent firstly smoother orthonormal orthonormal orthonormal conceptual establishes accomplish compo compo practically gram gram gram gram gram gram gram company inde fin schmidt schmidt vicinity charles neglected cichocki sep tails tails tails entropies entropies entropies cations proximation proximation asymmetry asymmetry appli unaffected pendent hole derivations demanding dilemma herault erroneous huber comon offered manipulations sparsity sparsity ixl ixl ily calculus fulfilled asso henceforth nent nent orthogonality stuart cumulant cumulant cumulant cumulant cumulant cumulant cumulant cumulant cumulant cumulant cumulant helsinki helsinki helsinki fulfill useless cis hyv hyv indexes hut hut hut cumulants cumulants cumulants cumulants cumulants pertinent quadratically quadratically finland standardized standardized standardized standardized identi cook cook hyvarinen hyvarinen sidered thereof thereof attains fulfills skewness asymp grounds neuromimetic monomials ool griffin integrable kendall excludes emaih dations aration classically classically proximations proximations defi bust curate totically 
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural neural neural data function function function function function function function function function function function figure time time time networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number state state results results results results results results results units units units information problem problem problem problem problem problem problem problem models models hidden hidden hidden performance performance performance based based space weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear case case case case vector order order order order order order order order order order shown systems values values values values values values probability probability probability probability weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method method method method point point point point large local neuron neuron neuron rate patterns matrix matrix matrix matrix optimal gaussian paper small small small small small small net task task methods methods fig fig fig fig field field field field field field field field field field field field field field field field field field field field field field field field field field problems problems problems problems problems problems problems problems problems problems problems random response response response response response response response show show show equation equation equation fixed fixed fixed rule general parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average states states states states theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory gradient gradient gradient obtained obtained term term term note result university university variables variables variables variables variables computation computation computation computation computation computation solution solution solution solution solution solution solution solution solution research research independent independent log log log log log log defined target target target target dynamics dynamics dynamics standard standard standard terms terms connections science science presented presented present present present phase phase phase phase phase phase machine machine machine machine machine machine machine maximum maximum range press press abstract applied applied applied applied applied applied find computational convergence convergence properties references stochastic due due due important introduction complex statistical statistical statistical effect generated generated variance tion energy energy energy energy energy energy energy energy difference difference difference difference difference difference difference complexity complexity rules measure measure higher higher higher higher theorem firing firing multiple binary long equations equations equations equations fact fact fact proposed observed finite finite simulations minimum minimum resulting ing total computed computed computed computed computed computed respect multi sum sum eq eq eq eq eq eq eq eq eq eq eq times elements elements means study obtain obtain obtain obtain artificial compared define define compute rates rates perform constraints connected connected distributions distributions distributions equal accuracy comparison comparison comparison descent descent descent dependent department consists consists consists consists individual difficult exp exp exp addition cambridge cambridge cambridge directly directly directly hinton hinton solutions solutions efficient full requires requires requires significant approximate approximate approximate statistics statistics free free free free free free free free free condition derived randomly bounds sampling discussion arbitrary arbitrary denote transformation transformation transformation inverse supported journal journal instance unknown fully fully jordan technology interesting significantly significantly york increasing principle leads leads max making improved discussed improve correlations correlations correlations correlations correlations correlations correlations correlations correlations exact exact exact exact exact advantage practical introduced machines machines machines machines cognitive highly highly compare works works solve solve yields converge diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal symmetric improvement expression expression matrices alternative deterministic depend sigmoid sigmoid numerical numerical clear performs performs exponential exponential physics physics physics intelligence assuming minimizing min averaged introduce manner minima configuration boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann explicit derive plot plot mathematical infinite infinite physical involves belief belief interaction adding equilibrium equilibrium quality quality expectation expectation expectation expectation letters review depending stationary squares restricted updated approximations approximations approximations approximations approximated partition partition expansion expansion expansion expansion expansion expansion normalization convex foundation coupling coupling coupling expect instances instances instances instances instances recognize characterized reason closely importance suitable included wij wij wij wij wij refer refer anderson issue gibbs gibbs gibbs gibbs gibbs thresholds thresholds thresholds simpler wiley poor investigate exponentially involving involving hessian divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence graphical behaviour applicable applicable applicable tanh gradients configurations thought observe observe explored contributions regime spin spin spin spin spin spin spin spin spin spin spin spin spin spin inequality derivation derivation improves improves glass glass glass glass glass glass glass glass glass glass glass glass glass glass correction correction correction worse worse division inversion inversion acknowledgement separately fluctuations conjugate applies introducing variant ordered chose conclude conclude expectations jaakkola wesley displays naive consistently feasible addison approximates clamped clamped clamped systematic systematic kullback kullback kullback kullback numerically adjusting replacing imposed hope effectiveness intuitively tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap saul encountered peterson steepest eqs eqs eqs implicitly subsequently insensitive severe magnetic magnetic magnetic weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss weiss aij acceleration assess assess assess assess argue verified impose realizable jij jij expand challenging cij cij apparently isi suffer cubic matlab mini modal factorized factorized factorized factorized thermal invertible invertible solvable inclusion inclusion inclusion val kirkpatrick kirkpatrick economic ignores multimodal brackets legendre legendre legendre dent indepen potts unimodal unimodal awij awij awij fore ues sherrington sherrington biophysics mum parame netherlands parisi jensen wii wii ant ministry ferromagnetic concluded ore del rni ising ising ising normalizes unclamped kappen kappen kappen kappen kappen ein absolutely para para rodriguez rodriguez chines sisj sisj nijmegen nijmegen divergences tangential monographs ooi ooi frontiers programme deteriorates solv putationally affairs acldey spain correc geert grooteplein naively unordered 
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural input input input input input input input data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time set set set networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output system error results results results results results information information information information information problem problem problem problem problem problem models models hidden performance performance performance performance performance performance based based based based based weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector order shown shown systems systems values values probability probability probability parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions neurons neurons neurons method point single single single processing processing processing local local local rate rate rate rate rate analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper examples examples examples examples examples examples small feature work work work work methods methods methods classification current problems problems problems problems problems problems random random similar architecture show show show section section fixed fixed fixed fixed fixed fixed line line line line line line line line line line line line line line rule vectors vectors vectors vectors vectors vectors general general general general general general general general general general general generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real real states theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university threshold computation solution independent independent defined defined defined defined defined sequence sequence sequence sequence sequence initial initial initial constant standard computer computer terms terms terms terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance science science prediction prediction prediction prediction prediction prediction left presented present nodes nodes maximum range range range range press press press components nonlinear outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous abstract abstract applied find find convergence convergence properties properties references positive positive positive positive positive important context context context introduction statistical generated variance parallel tion tion tion variable variable assume assume assume assume assume measure measure chosen chosen previous previous previous bound bound bound bound bound cases cases multiple good good good long represent equations make make errors resulting tasks total regression regression regression regression regression regression regression regression regression regression regression regression regression respect sum called mapping mapping mapping means factor optimization potential potential potential potential potential potential potential potential potential potential made natural feedback study knowledge knowledge obtain obtain obtain obtain negative artificial relative relative relative relative relative relative relative relative relative relative relative relative relative relative specific application desired desired desired desired define define define define define proc proc proc proc proc determined goal goal goal goal related distributions discrete approaches mit mit mit steps comparison contrast connection update update update update update update update update update update descent descent descent descent descent descent department department loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss final exp exp exp ai maps framework framework framework cambridge cambridge cambridge directly additional additional view view view top conference full choice choice choice choice approximate approximate statistics statistics free basic basic basic pages pages pages pages give give give produce derived developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds lines entropy entropy entropy path path actual actual actual actual finally finally depends achieved measured discussion discussion discussion technical arbitrary arbitrary arbitrary denote denote transformation fast assumption predictions common supported supported require main square square square square square instance easily easily makes fit fit fit probabilistic probabilistic typically transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer interesting interesting interesting york increasing increasing increasing increasing increasing special special special trials matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching squared call max max max max max max making making stored polynomial idea minimize minimize choose added advantage property pair apply apply sense recently relevant compare previously previously previously previously approximately approximately tuning tions solve solve match match match differential differential achieve rl sparse definition observation generalized generalized generalized generalized generalized gate grant lead suggests suggests extended trial trial matrices move row row assumptions assumptions assumptions valued valued valued valued competitive exponential taking largest largest california intelligence assuming introduce manner minima minima minima pro produces recall minimization minimization springer implies implies versus versus family review evaluated evaluate evaluate updated updated updated updated soft completely completely completely similarly constants constants updates updates partial earlier earlier additive additive additive additive additive additive additive additive additive convex convex convex convex convex convex convex convex convex convex convex convex sec penalty distances norm norm norm euclidean david avoid box activations usa holds holds holds phys discussions straightforward identity identity identity notice notice notice conf conf verlag kind kind kind kind interpreted satisfy write write usual generalize generalize minimizes eigenvalue eigenvalue predictor predictor predictor predictor predictor satisfies acknowledgments receive receive situations parametric exponentially updating detail integral integral integral integral integral integral hessian divergence hall discriminant helpful project authors func func func notion math possibly possibly front noted algo logistic logistic logistic taylor perceptton amari amari explain motivated motivated asymptotically asymptotically inequality analyzed briefly tool worse processed turns purposes strictly strictly strictly strictly worst worst bishop immediately commonly mathematics definite definite definite nsf explained argument tional introducing berlin measuring gen popular cal prevent suited achieves progress differentiable softmax softmax softmax softmax softmax softmax softmax softmax softmax softmax multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional proofs proofs analogue notes restrict restrict fix acm acm jth jth connecting generality kullback convenient logarithmic analyzing analyzing analyzing roles definitions sion dependency advance omitted warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth santa santa alternatively fold unified geometrical converted annals basically leibler deriving adopt regularity guess realize jacobian gained rithms chapman bounding eliminating careful relates academy drawback alternatives discusses maintains outcomes discretization discretization algebra unpublished manuscript november november chris parameterization parameterization parameterization parameterization parameterization nonnegative january losing families puts cornput cornput triangle sym symmetrical symmetrical symmetrical littlestone littlestone rameters convention losses losses quantitatively fin goodness cruz cruz kivinen kivinen kivinen kivinen kivinen kivinen kivinen indi unnecessary incurred tighter ample men repeats complications tums manfred manfred exponentiated exponentiated exponentiated convexity grove grove analogously helsinki euler amples tri helmbold helmbold normalizes realizing stud theme nxn regres rectly foster foster dates finland finland tth sional cesses esprit auer lows annu annu ied tropy vovk vovk ccr ifs neurocolt oth drastic expo bianchi bianchi bianchi nick cesa cesa cesa tioned regulating schuurmans ama tradi investi semidefinite 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#@Kivinen_J,Warmuth_M,
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distribution distribution recognition recognition pattern pattern point point point point single processing large large large rate analysis matrix matrix optimal optimal optimal optimal optimal optimal signal simple simple paper paper examples small small size size size size task methods level structure random random random random random random high high high similar architecture show show equation section section section fixed fixed line line vectors vectors vectors general generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real approximation approximation approximation average average theory theory theory theory theory theory theory obtained obtained term term term term term dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university variables variables variables independent independent independent independent independent independent defined found sequence sequence constant constant constant constant estimate estimate terms terms prediction prediction left present press press press basis basis basis nonlinear nonlinear nonlinear sample sample sample sample sample sample sample sample sample sample sample abstract back density references ieee ieee positive positive positive positive introduction statistical statistical tion change variable assume assume assume assume chosen chosen chosen chosen chosen higher part previous previous previous previous previous theorem bound bound bound bound bound cases type required good conditions conditions distributed expected expected fact fact fact fact techniques techniques techniques finite finite minimum minimum minimum resulting regression regression regression regression regression regression regression regression regression regression regression respect sum called mapping means means means study study study negative negative cross series series define define proc determined determined gain equal contrast support support dependent institute department loss addition cambridge additional design design design upper upper upper choice choice statistics statistics statistics statistics estimated pages validation give give con condition criterion criterion bounds provided provided provided finally depends discussion covariance normal normal technical denote assumption assumption assumption assumption assumption assumption assumption corresponds proof proof proof proof amount amount common effective assumed assumed ability ability instance easily degree degree degree degree degree degree makes makes pairs pairs pairs needed needed coefficients technology edge uniform uniform leads squared details international magnitude magnitude polynomial polynomial polynomial polynomial polynomial polynomial idea predict improved improve pair pair pair takes introduced quadratic quadratic sense sufficient compare axis axis smooth yields converge converge symmetric generalized generalized bounded bounded improvement improvement improvement improvement risk risk risk risk exists exists horizontal studied derivative predicted correctly correctly correctly correctly deterministic deterministic deterministic setting greater assumptions assumptions assumptions depend depend depend depend depend editors editors asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic solid regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization turn assuming exist exist min introduce acknowledgements suppose suppose derive derive construct construct written describes vertical mathematical mathematical changing dimensionality easy unique unique consisting develop develop applying springer springer expectation versus john john independently independently review estimator lemma evaluated approximations approximations converges converges converges constants allowed allowed smoothing dashed expansion expansion expansion expansion expansion expansion expansion expansion expansion neighborhood penalty penalty valid sufficiently sufficiently sufficiently degrees degrees expect box sciences plotted holds holds holds discussions reason regular selecting uniformly divided situation situation refer compact notice notice notice verlag quickly interested interpreted lie hold hold satisfy notation notation quantity quantity quantity quantity quantity leading leading approximating deal wiley wiley perturbation perturbation collection rapidly rapidly detail existence scalar scalar scalar ideas ideas root workshop analyze analyze formal taylor taylor taylor taylor taylor taylor improving simplest regime regime residual ment inequality inequality inequality formula formula formula smoothness lies worse worse turns turns turns satisfied strictly bishop bishop desirable calculations ridge ridge ridge ridge ridge definite read author preceding integrating integrating effort orders popular proposition proposition proposition proposition proposition proposition proposition proposition proposition proposition arithmetic proofs oxford fix jth grows turned proceed arranged tools odd stated stated fail generalizes wilson moments moments moments meaningful financial mance equals perfor guarantees schwartz schwartz uni omitted properly concentration sons sons davis davis inf inf inf inf inf johnson dramatically outline annals deriving validity theorems convenience illustration illustration param concentrated distri gained ization carefully regularized academy sketch sketch worth hansen hansen setup setup setup refined article differentiating helps helps bution expansions expansions expansions expansions expansions expansions remark moderate survey nonnegative nonnegative quantify invertible heavily identically triangle markers degenerate fin cauchy cauchy catastrophic minimizer minimizer minimizer minimizer minimizer minimizer minimizer minimizer indi formulas formulas repetitions tics statis versity ixl roots asymptotics helsinki helsinki ripley ripley eter rni numerator prepared matters matters rameter specialize specialize larsen larsen roll quantifying finland finland lengthy cients referring visiting vienna cated cated admit ditions surely resides titterington titterington legend easiest coeffi supremum ensuing iyi committed emaih rewarding regulariza delicate textbooks xix encyclopedia noticing admitting 
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural input input input input function function function function figure time time time time time time set set set set set training training algorithm output output output number number number number number system system system system system system system system system system error error error error error error error error error error error error error error error error error error error error error results results results results results results results results results units units information information hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based space space space weights weights weights weights weights linear linear layer layer case case case case case vector order order order order order order order order order order order order order order order order order order order order order order order order shown systems systems systems values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight unit distribution distribution distribution approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach point processing processing rate rate rate rate rate rate rate rate rate rate analysis optimal optimal optimal optimal optimal optimal optimal inputs form form form form form form form signal algorithms algorithms gaussian gaussian gaussian paper paper small small small task task methods methods fig fig fig process process architecture architecture equation equation equation equation equation equation equation equation equation equation equation line line line line vectors vectors vectors general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation average obtained obtained obtained obtained obtained obtained term note university university variables variables solution solution solution research independent dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant constant standard terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms terms science science presented presented activation nodes nodes nodes nodes nodes machine motion motion motion motion maximum abstract find convergence convergence convergence convergence density density density density density properties properties properties references stochastic stochastic stochastic stochastic due positive adaptive adaptive context introduction behavior statistical generated variance variance variance variance cost cost search tion difference assume assume lower lower measure higher higher cases required multiple long conditions conditions expected expected expected expected equations equations equations equations equations equations equations equations equations make scale minimum minimum resulting ing human respect sum eq eq eq eq eq called called times factor factor dimension dimension study study study knowledge obtain obtain obtain series series provide provide compute related related distributions gain gain approaches approaches approaches approaches approaches approaches approaches approaches larger contrast contrast update support support descent descent descent dependent morgan morgan report report institute institute consists advances advances exp addition maps framework computing directly directly additional estimates limit limit limit trajectory trajectory san san upper full full requires choice choice choice choice significant condition condition condition derived derived derived bounds actual finally finally finally depends depends measured discussion discussion normal normal technical describe describe group close close complete easily easily kaufmann kaufmann typically smaller coefficients coefficients coefficients coefficients coefficients technology interesting special mode principal squared squared squared squared max international decay decay decay decay decay decay decay attention choose description description description light advantage takes identical side side side quadratic quadratic recently recently relevant relevant engineering interest dimensions sufficient sufficient teacher teacher teacher teacher solve studies differential differential differential differential rl symmetric studied scaling extended alternative deterministic deterministic deterministic deterministic deterministic deterministic strength starting critical critical critical critical critical critical reduce operator editors editors numerical numerical clear moody asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak mateo integration drawn california proportional assuming minimizing targets identification program annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing denoted acknowledgements explicit relation derive written primary primary describes ann dept dept dept sensitivity sensitivity multilayer explicitly averaging averaging infinite transformations remaining scales equilibrium equilibrium equilibrium choosing independently expressed dependence dependence dependence dependence dependence dependence review depending stages stages influence densities densities densities approximations evolution evolution evolution evolution soft converges partial partial earlier earlier calculation additive expansion expansion expansion expansion expansion expansion expansion closed closed david box includes thesis thesis formulation eigenvalues eigenvalues eigenvalues eigenvalues coupled holds phys phys phys phys phys characterized successfully simplicity identified included modes committee literature literature summary notice interested symmetry contribution contribution sci sci comp comp minimizes giles eigenvalue leading leading reach tesauro cowan cowan employed employed unlike schedule schedule schedule requirements rapidly relations replaced hanson helpful scalar examine examine examine investigated proper analogous examined math math analyze rev rev rev quantities quantities der taylor expressions expressions regime regime regime regime regime regime regime phd phd finds optimum asymptotically asymptotically publishers diffusion starts formalism precisely operators mation mathematics potentially describing opt implicit res nsf fluctuations fluctuations fluctuations researchers mechanics offset offset offset offset leave employ employ slower slower calculating calculating curvature curvature enables enables replace lim cor picture ordinary ordinary corrupted leen leen leen leen leen leen formally recover homogeneous extending convenient moments moments moments moments alspector overlaps overlaps dominant dominant schedules schedules schedules schedules dif tic francisco insight insight insight master master master master master master master jump jump jump lett ignore adopted rms saad saad saad saad saad ter minus minus aston aston equivalently ber validity emerge isotropic isotropic pieces pieces obtains examining exponent distri evolve num decays decays decays thermodynamic thermodynamic graduate graduate dominated annealed annealed ization met responding investigations macroscopic macroscopic macroscopic macroscopic october corrections oregon oregon oregon microscopic bution observables observables observables observables observables preserves achievable excess excess august accordance monitor influenced ferent todd focuses err powers cast calculates optima restricting restricting orr orr rameters decaying sity appl statist amenable accommodate absent gence vicinity appro dence birmingham generaliza tit tit jerusalem ted ted expresses hebrew heskes fluctuation dominate ogi entered perturbative goldstein conver prohibitively schwarze ecs unclear comprise biehl biehl cse rendering asymptotics insure passage trust univer barkai depen 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#*network learning learning learning model model model neural neural neural data data data data data data data data data function function function function function function function function function function function function function time time time time time time time time time time set number number number number number number number number number error error error error error error error error error error error error error error error error error error error error error results results results results results results results results results information problem problem problem problem problem problem problem problem problem models models hidden performance performance performance based based based based based space space space space space linear layer case case case case case case case case case case case vector vector vector vector order order order order order order order order order order order order order order shown shown values probability probability functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution method method approach approach approach approach approach approach point point point single control large large large large large large large large rate rate rate analysis class class class class class class class class class class class class class class class class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form simple simple paper paper paper paper size size size size size size size size size size size size net net work work work work work work work work work work step process process process process process process process process process process process process process structure random random random random memory memory memory memory equation section section section section section fixed fixed fixed line line general general generalization real approximation approximation approximation approximation approximation approximation approximation approximation average theory theory theory theory theory theory obtained obtained obtained term term term term term term term term term term term term note note note note note dimensional dimensional result result result result result variables variables variables variables variables computation solution solution independent independent independent independent independent independent independent independent independent independent independent log log defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence constant standard standard standard standard terms terms terms terms terms terms terms science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction present present present nodes temporal press components sample sample sample sample sample sample sample abstract computational convergence convergence convergence convergence convergence convergence convergence convergence properties references stochastic stochastic stochastic stochastic stochastic stochastic ieee positive positive procedure procedure procedure adaptive decision context context context context complex complex hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior effect generated tion tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable assume assume assume measure chosen chosen chosen theorem theorem theorem theorem theorem theorem theorem bound bound type type type conditions conditions distributed distributed expected expected markov make make fact fact proposed observed errors finite finite finite finite finite finite finite finite resulting classes classes classes classes regression regression respect respect respect respect respect respect called called called called called mapping mapping mapping dimension dimension made made made made applications study study knowledge em obtain obtain obtain obtain original original original original original original artificial specific specific true application application series series series series series series series series series series series series series provide define define define define define define define compute rates rates rates rates related related related related related related related related approaches approaches approaches larger dependent dependent selection selection department loss loss loss loss loss loss loss loss loss version exp exp sequences sequences considered considered framework framework framework computing domain domain curve additional limit upper upper upper upper upper upper upper upper upper full full full full choice choice choice free estimated basic basic basic basic basic pages increase con con condition condition derived conditional conditional developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds finally finally processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes selected nature depends depends achieved achieved technical feedforward denote denote denote denote denote transformation transformation close close assumption corresponds proof proof proof finding amount amount common assumed supported role require main main main main main face square hypothesis future easily makes development fit fit probabilistic probabilistic needed needed account functional functional functional functional functional functional unknown unknown unknown unknown coefficients block block block block block block block block block block york york york york increasing increasing uniform uniform uniform uniform uniform uniform uniform empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical principle principle leads details numbers numbers numbers numbers numbers numbers numbers numbers numbers max making idea idea minimize minimize added added added predict discussed discussed discussed recent recent recent robust takes practical strategy sense sense sense sense recently engineering dimensions sufficient sufficient observations calculated works yields yields converge converge converge achieve achieve achieve trans definition bounded bounded bounded bounded bounded bounded bounded bounded risk risk risk risk risk risk risk risk grant exists lead studied studied studied setting minimal assumptions assumptions valued valued measures clear clear exponential exponential practice practice asymptotic weak weak propose taking hard regularization regularization regularization turn assuming assuming minimizing minimizing minimizing minimizing exist exist exist min introduce denoted suppose appears pro pro derive construct longer index index generating recall metric infinite infinite infinite electrical involves easy easy slightly text events minimization minimization minimization minimization minimization minimization minimization minimization springer springer springer springer formed implies implies blocks blocks blocks blocks blocks blocks blocks expectation boolean select competition yield choosing choosing dependence dependence depending depending stationary stationary stationary stationary stationary estimator estimator lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma similarly similarly similarly converges constants constants constants past past past spaces event symbol construction construction construction foundation norm norm expect expect determines vapnik vapnik vapnik vapnik vapnik vapnik vapnik extension extension prove absolute holds characterized structural structural structural structural structural structural structural structural simplicity straightforward selecting selecting selecting extra situation compact compact verlag verlag verlag verlag showing split split issue issue follow follow notation notation notation quantity usual minimizes minimizes leading predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing deal situations presents law law minimized parametric transformed transformed poor requirements exponentially exponentially exponentially detail estimators scalar ideas proved proved hierarchy attributes coefficient coefficient coefficient editor thought subsets quantities der obvious freedom precise observe academic arbitrarily submitted established established established years years great inequality inequality inequality inequality theoretic costs crucial crucial briefly choices ran ran immediately immediately potentially potentially universal implicit implicit meaning empirically empirically consistency consistency consistency pseudo pseudo pseudo effort haussler haussler haussler incorporated incorporated requirement price cal extensions achieves inherent deviations deviations deviations lim trade pac proofs indices guarantee guarantee modify extensive restrict restrict appropriately conditioned concerned establish plays generality generality extending balance definitions definitions definitions intuitive combinatorial nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric motivation utilized weakly corollary corollary predictors guarantees demonstration sphere belongs tic israel israel advance barron late rich passing extensively extensively balancing balancing generalizing lag lag lag lag lag lag lag lag lag lag outlined divide mind ple annals annals kluwer deriving deriving covering covering covering covering covering covering covering covering covering covering covering covering chervonenkis chervonenkis chervonenkis distinction utilize sigma regularity regularity tradeoff generalizations algebraic algebraic remainder penalized modifying num decays approxi elementary relate relate relating ultimately pos termed termed memoryless memoryless memoryless sam tively knowing cube meir meir meir meir laws laws appearing appearing excess january accordance pan establishes inequalities ron char dom dom identically identically conflicting settle obey restricting decaying fastest demands cess dent dent indepen indepen minimizer devoted blocked merit merit fore technion technion retaining vergence incurred incurred incurred incurred srm srm srm srm srm srm settles predic topics dilemma dependences pursued statis sible adap biasing paid claimed complexities ell ell penalties penalizing utilization ans stochas ixi ixi sketched bernstein complication overcoming packing collectively pollard obeying simi timal haifa cesses possessing precludes pursue overly stringent borne mating randomization expo algebraically algebraically loga sequel termined pioneered adaptivity permissible pla larly vidyasagar lugosi lugosi broadening irdle phrased ited acterized mani pirical weakest algebras nite nential 
#@Meir_R,
#t11
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#*network network network network network network network network network network network network network network learning model model model model neural neural neural neural neural input input input function function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set networks networks networks networks networks networks networks networks networks networks networks networks output output output output output output output output number number number number number number number number number system system system system system state state state state state results results results results results results units units units units units units units problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear layer layer case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown systems systems values values unit unit unit unit unit unit unit recognition point point point point point point point point single single single single single single control large local analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix inputs inputs inputs inputs form form form form form form form form shows signal signal simple paper size size size work work step step field field current trained problems random random random random high high similar similar similar similar similar similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation section fixed fixed fixed fixed line line rule rule vectors vectors vectors general general general general general general general general generalization speech speech parameter parameter parameter real approximation approximation average average states theory obtained term term term term term term term term note note note note dimensional dimensional dimensional dimensional result result result result result university threshold variables variables variables variables variables variables variables variables solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research log defined defined found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial constant distance science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented map map map map present phase phase phase phase phase phase activation low frequency temporal maximum components components components components components components components components components components nonlinear abstract applied find find properties references references component component component component component component component component component component due ieee positive important decision context complex complex complex behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior dynamic dynamic dynamic dynamic dynamic generated generated generated generated generated recurrent tion change chosen higher higher higher center previous cases cases cases type type long long long long long long long long conditions equations equations equations equations equations equations make fact forward forward forward forward scale scale scale simulations simulations simulations classes total respect respect eq eq eq eq eq eq eq eq eq eq eq eq times times dimension dimension dimension dimension dimension dimension dimension made study study study study study knowledge original original vol samples represented represented represented application series series series series series series series series series series series provide define define define proc related gain gain gain power power power power power larger larger larger larger larger contrast fields support support dependent words department consists internal exp exp bias layers delay delay delay addition sequences sequences sequences sequences sequences sequences ai ai ai ai ai hinton curve solutions solutions transition transition limit limit limit trajectory stage choice approximate approximate free condition condition condition condition condition condition derived developed bounds area actual nature depends depends measured measured measured discussion increases arbitrary arbitrary arbitrary arbitrary denote denote limited close close stable stable predictions predictions predictions predictions predictions predictions short short short short common common generate generate supported role require main main ability ability future easily fit fit simulated typically typically typically smaller smaller smaller combination combination combination combination account unknown ratio special consistent consistent details details numbers max magnitude produced predict perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron architectures architectures architectures discussed discussed exact takes takes typical practical practical practical apply relevant relevant interest highly approximately trans address address observation observation generalized bounded amplitude amplitude scaling scaling scaling scaling feed feed feed feed feed locally loop loop loop flow flow flow flow flow flow flow flow flow flow conclusion conclusion conclusion starting minimal row greater trajectories measures numerical numerical clear clear clear asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic taking physics largest largest largest largest largest largest external cycle cycle assuming start start min question question attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor relation relation relation relation written written longer index ways generating generating describes multilayer multilayer multilayer multilayer coordinates linearly easy develop develop frequencies applying springer shift shift shift shift choosing independently focus focus reconstruction depending depending stationary stationary stationary stationary stationary stationary stationary stationary stationary phoneme open evolution decomposition understanding constants spectrum spectrum spectrum spectrum sign reasonable dashed dashed delays add closed generation valid valid valid foundation david expect includes perceptrons eigenvalues eigenvalues extension discuss mozer coupled coupled coupled coupled holds phys phys simplicity straightforward capable capable capable divided driven identify attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors literature tdnn tdnn characteristic characteristic characteristic composed verlag interpreted sin manifold manifold follow follow bar involved relaxation relaxation relaxation relaxation relaxation delayed delayed eigenvalue eigenvalue leading reach principles extract approximating acknowledgments law law origin remain estimators divergence preliminary periodic periodic periodic periodic periodic periodic periodic fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier fourier ideas rest mappings investigated analytically complicated complicated tanh tanh tanh tanh tanh tanh tanh proved phases phases removed neu waibel waibel hill smallest naturally trace possibly possibly integer integer reading onset onset onset rev ensure bifurcation bifurcation bifurcation bifurcation formal observe perceptton consist generates simplest regime regime regime regime chaotic chaotic chaotic chaotic chaotic chaotic defines cos cos cos cos cos growing slope analytical analytical analytical capabilities tool stress purposes widely incorporate ran ran probable potentially universal begin qualitative outer considerably generic generic generic generic embedded quantitative share detecting http exhibits aim incorporating prevent conclude conclude attraction eventually eventually wesley gap notes primarily addison restriction restrict restrict bin reconstructed harmonic plays rational numerically tools mail mail biased biased biased serves nearby operates operates star ral adequate embedding weakly started governed governed governed governed governed connect predictors lang dominant dominant dominant dominant tic approximators israel israel treatment reveals reveals reader arrive refers extensively eqs considerations lett characterization characterization treat equivalently basin preserving axe conjecture quasi quasi quasi quasi amplitudes hierarchies tor reconstruct carefully careful depicts exceed regimes regimes hornik hornik page indication corrections lecture acoust demand influenced ping focuses clarity dom flows flows flows flows possess hopf ory linearized linearized inspection evolves mcgraw vicinity vicinity vicinity ated stationarity analyse analyse analyse percep attracted orbit inserting kanter kanter kanter kanter kanter web bernoulli motivates oooo analysed turbulence faculty reproducing ponents hanazawa dictated takens takens quence cre ner strange probing speak decade interfere gershenfeld gershenfeld gershenfeld gershenfeld gershenfeld proximate predictability predictability predictability predictability casdagli casdagli manifested manifested prefactor mln mln mln harmonics harmonics gan kinzel transposed interplay interplay interplay interplay interplay linearize sauer sauer sauer tron mathe domly indications companion ceptron complicate sour sour sour sour attract attrac fic coor nay matics reformulating tractor investiga lays nev ido 
#@Kanter_I,Kessler_D,Priel_A,
#t11
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural input input input input input input input input input input input input data function function figure figure figure figure time time time time time time set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number number number number number number system error error error error error error error error error error error error error error error error error error error error error error error state results results results results units units units information information information information information problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance space weights weights weights weights layer layer case case order order order shown shown systems systems systems systems systems systems systems values values parameters parameters noise weight weight unit recognition method method method method method method method method approach approach approach approach pattern pattern pattern point single single processing processing processing large large large large local local rate rate rate rate patterns patterns patterns analysis matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form form form form form form form form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple gaussian examples examples examples examples examples small small net work work work work work work work task task task methods step step field field field process process process process process process structure problems random response similar show show show show fixed fixed fixed line line line line line line line line line line line line line line line rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors vectors general general general general general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter real real average average gradient gradient gradient gradient gradient gradient obtained note dimensional result result result university university variables computation solution solution solution solution log defined defined defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics computer terms terms terms node node node node node node node science left presented presented map present present present present phase activation activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes machine machine machine machine machine machine machine machine machine motion motion motion maximum press press press learn learn learn components basis continuous continuous continuous continuous continuous abstract applied find find find find find properties properties references stochastic stochastic procedure important important adaptive adaptive introduction complex statistical statistical statistical statistical statistical variance tion tion change change change change change change difference difference complexity complexity variable rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure measure previous previous bound bound cases cases required required required long long long conditions conditions distributed expected expected expected expected expected expected equations equations equations equations equations equations fact fact length forward forward resulting resulting ing total total total computed performed eq eq eq eq eq eq eq eq eq eq eq times times times times times mapping mapping mapping optimization optimization optimization dimension dimension natural global global global vol vol vol relative true desired provide provide provide define define rates perform determined determined determined determined determined determined determined related discrete discrete discrete discrete discrete equal approaches mit mit comparison comparison descent descent descent descent descent descent descent morgan department loss advances advances advances final exp considered considered considered framework framework framework framework cambridge computing solutions solutions estimates design limit limit limit limit trajectory san bit determine determine determine determine upper requires approximate statistics statistics statistics statistics estimated basic basic derived randomly randomly depends depends achieved measured discussion covariance technical describe describe arbitrary denote denote surface finding common effective supported role require require require main eds eds eds future easily typically functional functional functional unknown jordan jordan interesting significantly significantly ratio edge leads leads leads pre window decay decay decay minimize produced choose choose description description predict perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron discussed improve improve takes takes typical practical practical practical practical practical apply apply machines machines quadratic sense recently recently relevant compare observations teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher smooth differential symmetric symmetric generalized storage grant expression expression expression expression extended deviation derivative feed locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally deterministic boundary boundary boundary setting demonstrate conclusion critical greater greater hebbian hebbian reduce depend depend performs exponential faster asymptotic asymptotic learns learns constrained mateo propose taking taking taking reduction reduction reduction drawn sigmoidal solid minimizing minimizing minimizing exist configuration denoted denoted explicit written plot describes student student student student student student student student student student student student student student student student student student student student student student multilayer averaging averaging averaging linearly integrated applying boolean boolean yield independently independently dependence review correlated correlated variation evaluated evolution soft soft soft soft soft soft soft soft completely suggested dashed reduces closed closed closed closed calculate david degrees expect activations activations activations activations activations batch extension maximize maximize mozer mozer variations variations phys phys phys phys phys phys phys characterized characterized characterized determining determining determining straightforward straightforward uniformly modification committee committee committee committee committee committee committee committee committee presentation presentation successful literature refer compact heuristic heuristic showing issue criteria quantity involved write dot giles observable observable leading attempt cowan employed employed remain exhibit difficulty hanson optimized integral hessian scalar examine matches mappings variational affect func phases rev rev rev rev ensure quantities quantities quantities freedom expressions initialized multivariate amari motivated defines averages averages averages averages integrate integrate asymptotically asymptotically formula separable tractable tractable sys formalism bishop desirable sgn sgn commonly commonly mathematics consequence simard acknowledgement involve optimize mechanics mechanics mechanics mechanics applies transient lack poorly poorly solla employ slower frequently calculating exhibits rely measuring anti limiting aim modulated gen incorporating curvature gave returns differentiable differentiable multidimensional displays globally globally globally globally globally globally globally globally globally globally globally globally globally globally globally globally corrupted uncorrelated indices leen optimality lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange oxford oxford fix ratios arguments appropriately perfectly lecun plays generality multipliers multipliers multipliers multipliers multiplier multiplier multiplier multiplier kaufman numerically replacing fail ylx modifications carry heuristics heuristics substituting overlaps overlaps overlaps overlaps overlaps overlaps overlaps overlaps iteratively iteratively captured facilitate deg permutation late theoretically pearlmutter broken designing lett lett cam sequentially outperforms suffix saad saad saad saad saad outline outperform ent aston aston aston expanding tween pointed obtains scenario scenario scenario adapting principled principled unseen exam evolve tems realizable realizable realizable ization careful differentiation cation macroscopic macroscopic macroscopic eigen rewrite bridge invertible invertible supply dropped reflecting exclusively sen ally ples petsche petsche beneficial specialization plateau plateau orr scenarios scenarios scenarios retrieved cho brackets brackets gathered pin carrying ous backwards birmingham generaliza sented progresses appli stand retrieve ample aimed eralization sought schwarze symmetries symmetries disagreement justify biehl biehl continu epsrc vation acti trivially integrand arrived integrations erf knowl stochasticity contrasted deduced instrumental ule latest qii emulates gradi xiy complements complements terministic terministic termined magnus ances caught unobservable unobservable erfc covari dri dri quire idealization 
#@Rattray_M,Saad_D,
#t11
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#*network network network network network network network network network network network network network network network model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks system system system state state state state state results results results information problem space space space space space space space space linear linear linear linear case case case case case case vector vector vector vector vector vector shown systems systems parameters functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method pattern pattern point point point point point point point point point point point point single single single single processing local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate class class class form form form form shows simple paper paper paper paper paper paper net work task points points points points points points points points points points points points points points points points points points field field field memory response similar section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed vectors vectors vectors general general general general general generalization parameter parameter parameter parameter parameter theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term note activity activity activity result result result university university variables computation computation computation computation computation research defined defined defined defined defined defined defined defined defined found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant standard standard terms terms terms terms terms terms terms science left phase phase phase phase maximum range press components components nonlinear abstract applied applied back find computational convergence convergence convergence convergence convergence convergence convergence analog properties references component component component ieee positive positive positive important context context complex complex hand circuit behavior behavior behavior behavior behavior behavior behavior statistical effect effect parallel recurrent recurrent tion change energy energy energy energy energy energy energy energy energy energy assume lower lower lower previous previous type required multiple multiple long long conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions represent represent equations simulations minimum minimum resulting means optimization optimization optimization optimization optimization potential potential potential dimension made feedback feedback feedback global global global global global global global global global global global global global obtain obtain negative specific true define proc perform active active constraints cortical brain brain brain equal power power larger connection fields descent descent descent descent descent descent descent descent descent descent descent dependent dependent nets nets modeling words words version synapses consists bias delay delay ai framework computing additional additional limit limit limit limit limit limit limit limit limit requires choice choice choice speed pages con derived derived velocity velocity types types provided provided provided finally finally nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends depends constraint technical fast fast close inverse assumption assumption excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable proof proof circuits finding finding finding finding finding effective supported role instance makes makes including including objective objective objective objective hopfield hopfield hopfield hopfield hopfield hopfield dynamical dynamical dynamical functional programming interesting york york special special leads details max max inhibition inhibition inhibition inhibition inhibition inhibition inhibition minimize added sources population population population population pair similarity lateral include include identical identical sense sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient previously volume works smooth yields yields studies converge converge differential definition definition symmetric symmetric symmetric symmetric symmetric symmetric symmetric generalized bounded bounded bounded bounded bounded storage constructed constructed exists exists invariant invariant invariant invariant derivative derivative matrices locally generally setting pass half strength assumptions competitive competitive competitive competitive competitive interactions interactions interactions interactions interactions interactions interactions numerical clear asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak weak constrained strong hard physics largest largest external cycle cycle turn variety exist exist min relationship iii introduce derivatives derivatives minima attractor attractor attractor attractor suppose relation pro construct construct written written winner winner winner winner winner stability stability stability stability stability stability stability stability stability stability mathematical mathematical mathematical distinct dept dimensionality transformations easy unique unique scales interaction interaction interaction interaction adding applying applying potentials cycles cycles cycles cycles cycles cycles competition competition competition formation formation depending transform transform open restricted forms soft activities similarly similarly similarly converges converges converges converges constants sign partial calculation slow classical classical convex convex convex convex reduces reduces neighborhood roughly remains valid symbol symbol construction existing includes usa bell bell bell illustrated prove maximize absolute holds discussions reason straightforward straightforward extra extra extra divided oscillatory oscillatory oscillatory attractors attractors attractors attractors comparing situation identity receives receives summary contained anderson neuroscience symmetry oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations manifold manifold manifold manifold sci categories notation involved paradigm eigenvalue eigenvalue acknowledgments intrinsic cowan cowan situations origin american relations detail replaced existence scalar scalar scalar scalar rest rest applicable biol biol proved understand analogous hill editor editor versions olfactory noted assumes nervous nervous academic art amari amari regime regime regime regime chaotic chaotic established guaranteed defining defining unstable biology biology nonlinearity reasons stanford stanford choices arise laboratories mathematics acad grossberg opt calculations definite definite mechanics mechanics mechanics conjugate conjugate conjugate explained argument questions behaviors behaviors behaviors behaviors populations populations populations populations populations double understood affine affine effort cohen reliability exhibits monotonic monotonic occurrence tank collective asymmetric asymmetric asymmetric asymmetric display display yielding realized globally proofs proofs proofs cybern cybern saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle saddle writing guarantee princeton princeton ratios velocities purely purely nonzero establish establish generality platt murray convenient tools attractive imposed generalizes wilson natl lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov lyapunov contexts mjolsness mjolsness sides ascent ascent ascent ascent ascent ascent ascent ascent ascent bulb entries waves rich sustained sustained park park seung seung seung seung explains explains discovered alternatively speaking leaving incorporates graded revealed axe axe die tween theorems generalizations generalizations classic molecular eric algebraic verified equality labs labs labs relates regimes rough win son happen happen page vanishes vanishes vanishes vanishes tissue signs signs signs infinitely infinitely behaves technologies tonic demonstrating nonnegative traveling hop ave wins conceptual arrow establishes establishes inequalities inequalities unreliable contrasts contrasts hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian lying hopf cooperation concave neurobiological reality minimax minimax minimax minimax minimax minimax minimax minimax minimax confined restrictive vicinity closure legendre legendre kinetic kinetic kinetic kinetic kinetic kinetic kinetic energies dissipation violated violated proceeding asymmetry tal cient reviews ito damped rectification helped perspectives thalamic provably violation optimiza suppresses supplies repertoire inverses arbib manifest manifest ams richardson richardson richardson richardson lucent lengthy pump kybernetik structed ermentrout excites excites hamiltonjan hamiltonjan 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#@Hopfield_J,Lagarias_J,Richardson_T,Seung_H,
#t11
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#*network learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural input input input input input data data data data data data data data data data data data data data data data function function function function function function function function function function function function function set set set set set set set set set set set networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number system error error error error error error error error error error error error results results results problem performance based space space space space space space space linear linear linear case case vector vector order order order order order systems values values values values probability probability probability probability weight functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach approach approach approach approach point point point processing control large large large test test test test test test analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class optimal inputs inputs shows algorithms algorithms simple paper paper paper examples examples examples small small size size size net work task points points points classification classification classification classification classification classification process structure problems problems random high similar section vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization real real real real real real real theory obtained obtained obtained obtained obtained obtained obtained obtained note experiments experiments experiments experiments result result result result result university university university university threshold research log log log log log log log defined defined found sequence sequence table estimate standard standard standard standard computer computer computer computer computer terms terms terms terms terms terms terms node node node node node node node node node node node node node node node node node node science science science science prediction left left phase low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine machine machine machine sets sets sets sets range press learn position position continuous sample sample sample sample sample sample sample sample sample sample sample sample abstract abstract abstract applied find find computational convergence references due due ieee ieee positive positive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision introduction hand hand effect generated generated generated parallel parallel tion tion assume classifier classifier classifier classifier lower lower previous theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound cases binary binary binary long long tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree expected techniques techniques probabilities observed errors scale scale finite finite resulting classes classes total respect performed performed performed means means means dimension dimension dimension dimension dimension dimension dimension made natural study study em em em original original original artificial artificial relative samples represented cross cross perform determined experimental gain accuracy accuracy accuracy larger connection train dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent morgan proceedings proceedings proceedings report report department technique internal internal internal internal internal internal internal individual individual difficult maps experiment experiment experiment view top stage bit bit conference conference capacity determine efficient efficient classifiers choice free estimated pages pages validation validation give con condition condition bounds bounds bounds bounds bounds bounds path path path actual nature simply achieved normal technical technical feedforward arbitrary group denote denote tested tested fast proof proof proof finding common common implemented assumed generate theoretical main journal journal journal hypothesis hypothesis kaufmann simulated account unknown testing testing testing testing testing testing ratio york york edge increasing consistent structures structures uniform uniform uniform details details details call numbers numbers numbers numbers direct making international combined produced choose choose choose run perceptron perceptron perceptron perceptron perceptron architectures improved improved improve advantage element reported strategy strategy side side trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees sense sense subset relevant relevant engineering engineering dimensions dimensions dimensions dimensions axis axis tions tions definition definition definition definition evaluation generalized generalized generalized bounded bounded bounded bounded risk risk risk sensitive sensitive exists parts parts concept studied occur extended predicted alternative correctly correctly correctly correctly hybrid loop boundary boundary demonstrate half half half place minimal minimal greater greater greater greater assumptions valued valued valued depend differences sigmoid accurate performs performs performs taking largest external drawn california intelligence intelligence labeled labeled exist annealing suppose suppose pro produces generating dept dept confidence pruning pruning metric metric implement linearly unique predictive minimization springer springer formed expectation expectation boolean boolean boolean john john choosing national independently viewed learner lemma lemma lemma lemma lemma evaluated evaluate restricted fraction fraction sizes sizes margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin partition allowed classical classical classical classical interpolation remains sufficiently assigned advantages classified classified classified classified classified transactions david david combinations priori priori assignment sciences vapnik extension automatic structural structural structural reason importance society maximal maximal maximal maximal maximal divided divided post essentially reached traditional traditional verlag verlag verlag heuristic interested interpreted split split criteria categories categories notation notation quantity quantity involved write usual michael absence thresholds automatically principles subsequent satisfies satisfies decreasing origin transformed create investigate optimized ml ml behaviour authors root working cover cover cover attributes attributes neu induction induction concepts generalisation generalisation generalisation created ensure friedman taylor taylor taylor taylor taylor fisher perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton perceptton multivariate multivariate improving explain finds cart cart separable derivation growing adapted tool london stress turns implementing sys satisfied closer easier choices choices choices leaves hyperplane hyperplane hyperplane hyperplane mathematics ion begin optimize computers radius researchers researchers argument argument argument percent double double pseudo pseudo pseudo peter peter peter peter posed price berlin partitioning summarized measuring reaches popular replace boston leaf notes www guarantee martin martin fix fix perfectly databases databases hyperplanes hyperplanes hyperplanes hyperplanes labelled labelled tem royal turned reaching reaching reaching convenient breiman simplify simplify replacing stated hyper los los obtaining observing splitting imply symposium child performances performances bartlett bartlett bartlett bartlett corollary corollary programs schapire ensures sion paul regarded percepttons percepttons percepttons percepttons tic foundations foundations permutation omitted cancer kearns agree splits statement integers stone ball robert robert robert ics uci uci posteriori appeared achieving ent covering covering ber validity chervonenkis expanding feeding classifies classifies hierarchies representa pub num bounding bounding compatible proba learnability parallelism names indexed indexed misclassified placing preprint page ation ation union union margins margins margins margins margins margins margins margins margins williamson williamson housing november covers covers covers lecture fat fat fat fat fat fat fat fat fat fat fat fat fat fat fat fat fat differently ble const australian european shawe shawe shawe shawe shawe breast confirm confirm puts outperformed dcs incorrectly incorrectly inherently dichotomy executing anthony anthony classi repository repository shattered shattered irvine inducing ben benign freely vergence discrepancy discrepancy iris iris srm srm srm srm eta permutations permutations traditionally pursued shattering shattering shattering shattering shattering shattering shattering nadal belmont analysed associating subsample polyhedral gression olshen oft diabetes duced wadsworth bilities pima internet utgoff utgoff deci intro holloway minimisation mln delivers oblique oblique probabili packages tackled divisions mammone tackle neurocolt publicly distinguishable thi philip philip bianchi alon alon rhbnc rhbnc ces creasing eurocolt egham ike coor hem dra agreeing informations ech ofy indians satis surrey quote shai probabilit 
#@Cristianini_N,Shawe-Taylor_J,
#t11
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#*network network network learning learning learning learning input data data data data data data data function function function function function function function function function function function function function function function function function function function figure set networks networks networks networks training training algorithm algorithm number number results results results problem problem problem problem problem problem performance performance based space space space space space space space space space space space space space space space space space space space space space space linear linear case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order shown shown shown values values functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution recognition recognition recognition method method method pattern pattern pattern pattern point processing processing control control control large analysis class class class class class form form shows signal simple gaussian gaussian gaussian gaussian gaussian gaussian paper examples small feature feature feature feature feature feature feature work work task task methods methods methods methods fig points points points classification structure structure problems high high high high high high similar similar representation representation show show show show section section section section section section line line rule vectors general general general general generalization real approximation approximation approximation approximation approximation approximation theory theory theory theory theory gradient term term note note note dimensional dimensional dimensional dimensional dimensional dimensional result result result result computation solution solution defined defined defined defined found found target constant constant constant computer terms terms terms terms terms terms distance left map map map low frequency machine machine machine machine machine machine sets motion press press press components basis basis basis nonlinear continuous continuous abstract find find computational properties properties properties references ieee ieee positive positive positive positive positive positive context context introduction hand estimation estimation estimation statistical cost cost cost cost cost complexity complexity lower lower lower prior cases type good good good conditions bayesian equations fact fact proposed resulting regression regression regression regression mapping means means optimization applications knowledge negative negative original specific true provide define compute proc perform perform determined goal related connected mit mit connection connection connection support support support support support support support support support support support support support support support proceedings report kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel exp exp ai considered computing computing computing computing equivalent equivalent equivalent equivalent additional view san conference capacity capacity capacity efficient classifiers choice choice choice vision pages pages con condition condition condition condition condition condition condition bounds area types lines lines product product product product product product provided provided provided provided finally finally nature achieved discussion discussion discussion technical limited inverse corresponds corresponds corresponds proof proof proof finding rbf generate supported supported theoretical theoretical require main main ability hypothesis future degree degree degree typically reduced account functional functional functional functional unknown coefficients coefficients coefficients programming programming programming projection projection york york special empirical empirical leads leads details details max frame polynomial idea idea combined minimize minimize minimize minimize minimize minimize denotes denotes property property separate practical introduced introduced introduced include subject subject machines machines machines machines machines machines machines machines machines machines machines machines quadratic quadratic quadratic quadratic quadratic quadratic sense interest sufficient sufficient approximately tions tions yields correspond correspond correspond correspond differential trans diagonal sparse sparse sparse definition definition symmetric symmetric symmetric risk risk risk risk risk grant parts parts lead lead lead concept concept concept invariant matrices width setting setting strength assumptions operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator neighbor valued editors editors performs mateo propose strong solid regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization radial radial radial radial minimizing minimizing minimizing start start relationship relationship question acknowledgements pro van derive construct written written solving solving solving ways generating ann distinct metric explicitly dimensionality frequencies frequencies frequencies frequencies gaussians minimization springer blocks yield choosing choosing family expressed viewed interpretation solved detailed transform showed decomposition understanding understanding understanding completely completely completely translation translation spectrum sign dashed additive expansion expansion expansion spaces sec purpose interpolation interpolation interpolation interpolation interpolation interpolation symbol construction avoid building kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik prove discuss specifically specifically priors discussions structural simplicity simplicity regular determining uniformly suitable suitable society differ svm poggio poggio comparing invariance tend identity orthogonal compact verlag link link sin sin follow hold satisfy satisfy notation dot dot dot dot dot dot dot nips correspondence satisfies satisfies satisfies minimized overfitting overfitting exhibit exhibit strengths dual helpful fourier fourier fourier fourier fourier fourier fourier fourier authors func func math possibly necessarily obvious mapped academic multivariate generates defines established mentioned trivial convolution smoothness briefly tool tool worse worse turns tive easier constructing operators operators operators operators operators operators operators operators operators operators operators leaves desirable products products mathematics potentially inversion inversion calculations definite definite definite definite definite prop evaluating tional splines splines splines splines splines formulated polynomials polynomials polynomials http calculating berlin extracting monotonic serve serve green green green green green green green germany germany semi comments coherence yuille yuille deviations proposition proposition proposition trade sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv equivalence equivalence equivalence girosi girosi girosi girosi girosi girosi girosi girosi girosi girosi tensor null jones connecting satisfying odd multiplicative multiplicative hope exploit exploit analyzing reasoning implications constructive substituting mance introduces equals perfor regarded washington treatment foundations infer infer thin insight indicator park considerations exploiting statement papers explains insensitive robert smola smola smola smola smola smola smola smola smola smola verify unchanged sch sch sch sch sch sch sch sch sch nelson nelson nelson pointed pointed utilize stem tor remote burges burges burges penalized ization denoting denoting denoting regularized plate dirichlet dirichlet employing enforce preserve memo memo admissible admissible admissible admissible admissible admissible admissible amplification port ward aaai vice expansions expansions removes chris appearing versa bridge nonnegative kopf kopf kopf kopf kopf kopf kopf kopf institut sake sake transforming converging hilbert hilbert hilbert hilbert hilbert hilbert hilbert curse adjoint hemmen ally automation conditionally conditionally conditionally conditionally conditionally norms exploits html contrary attenuation planck gmd gmd gmd gmd counterpart schmidt schmidt schmidt schmidt schmidt zeros svs svs vanishing monotone scattered cti cti dij subtle hood preferable sung enforcing newly decompositions klaus grzywacz grzywacz posi sparsity multiplications llx llx llx llx des scribed sible alexander translational mercer mercer mercer mercer wolfe menlo seemingly formalized reproducing exposition kronecker gression confused erties interna gramming rrt rrt rrt rrt rrt rrt rrt ilx ilx bernhard opera concludes recalling kybernetik axi llll twofold dfg leo tikhonov regu scholkopf scholkopf tedious fayyad yll yll yll yll leverage vladimir gill fll fll stating sinc url lkopf dxdy berg scalars xll coef rudower chaussee reviewing llxi llxi tential kdd iill paring dyn dyn federico mtiller disregarded ficients mpg defi sisting larization kill chui nite 
#@Scholkopf_B,Smola_A,
#t11
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#*network learning learning learning learning learning model model neural neural neural neural neural data function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time set set set set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm number system system state state state state results problem problem models models models models models space linear linear linear case case case case case case vector vector shown shown shown shown shown shown shown shown shown systems values values probability probability noise weight functions functions functions functions functions functions neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point single single single single single single single large large large local local local patterns patterns analysis analysis class matrix matrix matrix matrix form form form shows algorithms algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual paper examples examples examples examples examples examples small size work work work methods methods methods methods fig fig fig step step features cell problems random similar similar representation representation representation line vectors vectors images images parameter real approximation approximation approximation states states states states states theory theory gradient gradient gradient gradient gradient gradient note activity activity activity activity activity dimensional dimensional variables variables variables variables variables variables variables variables variables variables variables variables variables solution solution defined defined defined defined found found dynamics dynamics dynamics dynamics dynamics initial constant standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard standard synaptic science science direction direction direction direction present low low machine machine machine machine object object object object press components components nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample sample sample sample sample sample abstract find find find find density likelihood references component component due due ieee positive positive positive procedure procedure important mixture mixture mixture mixture mixture introduction behavior behavior behavior generated generated generated change energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy energy complexity variable variable variable variable variable variable variable variable spatial representations chosen higher cases type multiple multiple multiple cortex cortex cortex cortex good good binary conditions conditions conditions represent represent distributed equations make make make make region finite finite finite minimum minimum minimum minimum minimum minimum minimum tasks multi eq regions factor potential orientation orientation global global global applications applications negative negative negative negative original specific samples samples samples samples define define define proc proc proc location constraints constraints constraints constraints distributions distributions distributions distributions distributions distributions distributions motor motor discrete discrete discrete brain equal equal equal power power power larger contrast update update update nets modeling modeling modeling modeling modeling words version version version difficult maps hinton hinton hinton hinton hinton limit limit limit determine efficient full requires approximate world basic basic pages give produce produce condition condition condition types types depends sampling sampling sampling sampling sampling sampling sampling constraint biological discussion covariance covariance covariance covariance covariance covariance normal increases transformation close inverse corresponds corresponds surface finding finding finding finding finding short generate supported cluster probabilistic probabilistic underlying reduced dynamical block programming programming programming programming programming programming interesting interesting ratio character york head head uniform empirical mode mode mode mode mode mode leads principal max pre bottom polynomial polynomial description discussed directions directions directions property property ensemble practical practical introduced subject machines quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic hierarchical sejnowski cognitive cognitive recently interest previously approximately tuning solve correspond converge converge trans trans sparse sparse mixtures locations separation symmetric increased increased increased lead studied studied invariant invariant suggests matrices matrices correctly boundary generally generally critical critical reduce valued depend competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive interactions interactions differences designed clear clear clear peak practice constrained constrained constrained constrained constrained temperature temperature temperature temperature temperature temperature temperature temperature strong presence drawn drawn drawn turn introduce minima minima minima minima minima minima minima minima minima minima minima minima minima configuration configuration configuration question boltzmann boltzmann boltzmann boltzmann boltzmann monte monte monte carlo carlo carlo winner winner winner winner generating modeled modeled simultaneously involves easy angle angle angle unique consisting interaction interaction gaussians gaussians gaussians gaussians gaussians gaussians competition competition decreases decreases depending stationary stationary stationary stationary stationary updated lee lee lee lee centered approximated approximated approximated approximated approximated approximated completely completely digits updates updates earlier reasonable reasonable calculation convex convex convex convex convex roughly remains calculate coupling expect handwritten figures usa usa bell bell bell eigenvalues illustrated discussions closely modification modification modification modes modes modes modes modes modes modes modes attractors capture soc strongly neuroscience dis superior manifold manifold manifold generative sci sci satisfy bar dayan leading neurosci acknowledgments intrinsic situations origin powerful integral accurately hessian graphical graphical helpful rest project investigated possibility eigenvectors variability topographic fundamental analogous analogous contours matched matched hill editor illustrate eyes thought prototype separated academic amari simplest spin spin cos directed ground ground ground ground ground guaranteed defining analytic explanation tractable tractable tractable ring ring ring ring ring ring ring ring ring ring easier laboratories laboratories consequence cut cut scientific projected acad acad definite definite definite arises demonstrates geometry reflect empirically axes peaks peaks peaks rep ity span price characterize aim curvature collective marginal shaped shaped deviations ghahramani ghahramani ghahramani corrupted sort saddle saddle saddle saddle saddle nat unity unity nonzero rotations arranged inspired murray numerically accepted tools tools imposed intuitive natl lyapunov sompolinsky sompolinsky representational representational saul zhang regarded sides regard infinity centroid tic augmented roy arrows relies seung seung seung seung seung seung vari bertsekas temperatures neurophysiology cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative cooperative axe aij aij aij spaced descriptions discovering invariances perpendicular distri distri intuition intuition labs manifolds manifolds manifolds rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified rectified translations translations importantly barrier mini technologies technologies bution bution info nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative interior interior const solvable spins concrete concrete tribution ackley vanish cooperation curved multimodal multimodal multimodal multimodal multimodal multimodal ben fication metropolis cyclic shortly syst probabil enabling revow stan adv permutations ables mum phil undirected undirected dard acceptance rectification accepts anisotropic belmont unclear diverges bimodal provably singularity singularity flips lowering brings georgopoulos viewpoints bears instantiations contin govern arbib concentrates normalizes sit depict resemblance uous lacks slowing lucent lucent athena representable prefactor deviates xixj tucker tucker negativity trough trough trough trough trough barriers bowl bowl yishai resent sitting wine singleton singleton singleton flattened specifics ergy bottle economical indefinite 
#@Lee_D,Seung_H,Socci_N,
#t11
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural input input input input input input input input data function function function figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output number number number system error error error error error error error error error error error error error error results results units units units units units information information problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear case case case case case case case case vector vector order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown shown systems values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight functions unit unit unit unit unit distribution method large large large large local local local rate rate rate rate rate test test analysis analysis analysis analysis analysis analysis analysis matrix matrix inputs inputs form form form shows shows gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples small small small small small size size size size size size net work work work step points random random similar architecture show show show show equation equation equation equation equation equation fixed line line line line line vectors vectors vectors vectors vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter average average average average average average average theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory gradient gradient note dimensional dimensional result result result result result university university variables variables variables variables variables variables variables solution research defined defined found found found found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial estimate standard standard standard standard standard terms left presented present present present activation activation activation activation machine machine machine sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets press press components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs continuous continuous abstract applied references component due due due due due introduction hand hand hand statistical statistical generated generated variance variance variance variance variance variance tion change difference variable variable assume chosen chosen previous required required multiple good distributed distributed expected equations equations equations equations equations equations equations equations equations equations equations equations fact fact correlation length errors errors finite finite finite finite finite finite finite finite finite finite finite finite simulations simulations simulations simulations simulations simulations simulations simulations simulations resulting resulting resulting resulting simulation sum eq times times mapping dimension dimension study study study study study obtain obtain relative compared compared application define define rates discrete equal equal equal mit mit accuracy comparison comparison comparison larger larger update update update update descent descent department department technique individual final addition framework directly curve curve transition limit limit limit limit limit top top effects effects effects choice significant significant approximate approximate approximate increase give derived developed developed levels lines selected evidence depends depends constraint achieved discussion technical describe close close assumption assumption complete surface surface predictions predictions predictions common common assumed theoretical theoretical require main main journal journal journal future makes makes makes including typically hopfield account dynamical dynamical dynamical dynamical dynamical dynamical significantly principle principle leads details bottom bottom bottom supervised decay decay choose choose added description description perceptron perceptron discussed directions correlations correlations correlations correlations exact exact exact exact pair include recently interest highly teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher calculated tions yields correspond studies differential improvement grant studied extended predicted correctly generally starting assumptions assumptions reduce central accurate accurate clear clear practice suggest suggest taking presence presence physics physics physics physics physics drawn drawn turn variety manner minima minima minima force denoted denoted explicit explicit appears longer primary student student student student student student student student student student student student student student student student student student student explicitly averaging averaging averaging averaging infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite physical physical develop integrated blocks letters expressed review review correlated correlated correlated overlap overlap overlap detailed updated updated evolution evolution evolution evolution forms forms soft soft soft similarly updates updates updates updates updates updates spectrum reasonable calculation calculation calculation dashed dashed additive closed closed intermediate initially sufficiently symbol symbol david includes combinations activations activations activations activations activations activations activations activations activations activations activations activations activations activations eigenvalues eigenvalues eigenvalues extension discuss holds holds discussions reason reason straightforward straightforward capable society effectively committee committee committee committee presentation comparing online online online online online online online online online online online orthogonal capture summary compact strongly contained split symmetry symmetry contribution write write realistic nips nips nips delayed delayed eigenvalue eigenvalue acknowledgments deal extend overfitting difficulty difficulty integral integral integral dotted preliminary behaviour helpful rise scalar successive successive giving history mappings workshop surfaces circles circles adapt predicting predicts perceptton finds defines averages averages averages mentioned asymptotically histogram great ment trivial agreement track variances unstable analytical caused comparisons considerable choices immediately products mathematics projected projected projected projected involve implicit implicit qualitative mechanics considerably limits quantitative peter marked solla remove incorrect calculating calculating limiting aim qualitatively qualitatively begins naive phenomenon ordinary uncorrelated uncorrelated saddle acts ordering repre royal extending fails difficulties difficulties tools overcome overcome replacing imposed replica transforms definitions intuitively intuitively carry presentations motivation overlaps introduces ensures encountered negligible dependency consequences sim originally originally laplace stimulated rich captures captures saad outline constitute aston aston break break restrictions convenience seek covariances breaking breaking edinburgh edinburgh representa distri goals thermodynamic compatible rough sketch sollich sollich sollich sollich sollich west tij happen hodgkin worked shallow bution replacement coolen coolen inhibited barber barber barber barber barber barber ning ning ning ning ning ples specialization ooo plateau scenarios governing quantitatively curved absent restrictive dent appro indepen rem birmingham violated violated cope unnecessary developments sherrington sherrington expresses histories discrepancy discrepancy omit heskes infinitesimal schwarze mate disagree diverges biehl functionals completes fellow epsrc cov cov sume unrealistic kappen specialize replicas erf cumbersome neurm mri ven chines aining eigenspace numeric conceivable leaning sumed str ulations dorothy ature underestimate gaussi gaussi ooooooo senting pie europhysics controt squ uated advancing investiga nite ove incurring 
#@Barber_D,Sollich_P,
#t11
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#*learning learning learning learning learning learning learning learning neural data data data data data data data data function function function function function set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number state results results results results results information problem problem problem problem problem performance performance performance performance performance performance performance weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case vector vector values values values values probability parameters parameters noise noise weight weight functions functions functions unit approach approach approach approach analysis analysis analysis analysis analysis analysis class class matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal form shows shows algorithms algorithms algorithms algorithms algorithms simple simple gaussian paper paper paper paper paper paper paper paper feature feature task problems problems problems random response response response response similar similar show section fixed fixed line line line line line line line line line line line line rule rule vectors general general general general general general average theory theory theory theory theory theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term term term term result result result university university variables variables computation computation computation log log found found sequence constant constant constant constant constant constant constant constant standard standard standard computer computer science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction nodes sets outputs abstract applied find computational computational computational computational computational properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee ieee ieee ieee positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure important important decision context introduction hand estimation statistical statistical generated tion tion difference complexity complexity complexity variable variable variable assume assume assume assume lower lower prior prior chosen part previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound cases cases cases type multiple good good binary binary long represent bayesian bayesian expected make make proposed length minimum total regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression performed performed called called times times mapping natural applications vol true compared proc goal goal equal equal comparison descent descent descent descent descent descent descent descent morgan proceedings proceedings proceedings report words words loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss implementation version version version technique consists consists consists difficult scheme scheme addition ai framework framework framework san conference conference efficient upper upper upper full give give give con weighted weighted weighted developed bounds bounds bounds bounds bounds bounds bounds bounds bounds nature nature nature nature nature nature nature nature nature depends depends measured covariance covariance technical close close close assumption corresponds predictions proof proof finding amount short short assumed require require main eds square square end end future degree degree kaufmann probabilistic typically typically interesting interesting york york york mechanism mechanism mechanism mechanism special trials trials trials trials empirical call call experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert idea idea idea description description description recent advantage takes typical apply apply introduced strategy strategy strategy strategy strategy strategy strategy strategy quadratic sense sense inference relevant compare bounded bounded bounded bounded bounded trial trial trial trial trial trial trial trial wide matrices column setting conclusion assumptions assumptions assumptions assumptions assumptions assumptions depend competitive competitive competitive competitive competitive competitive competitive competitive competitive performs exponential exponential weak mateo california start start start exist suppose suppose derive generating ann linearly linearly linearly transformations easy easy easy slightly interaction predictive predictive springer springer quality implies implies versus learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner operations operations constants reasonable additive closed norm norm norm norm norm expect priori vapnik vapnik extension prove specifically specifically holds partially gating simplicity identified efficiency modification computationally successful literature comparing situation situation soc compact compact notice notice kind strategies strategies strategies hold notation notation usual usual usual predictor predictor attempt moves extract acknowledgments situations situations situations put put replaced accurately recursive game game game game dual dual giving giving rest authors proved workshop func attributes attributes predicting predicting perfect assumes message generates submitted years ment inequality inequality inequality inequality inequality inequality inequality inequality inequality inequality theoretic trivial derivation analyzed guaranteed majority majority majority worse worse worse london comparisons turns closer worst worst worst pool pool pool pool universal describing ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge definite read read arises annual annual annual annual greatly items items items items haussler splines continuously variant span polynomials berlin differs gen proven expectations merging merging merging arithmetic arithmetic cumulative trade naive phenomenon corrupted ear notes fix fix acm acm member royal plays stronger accepted logarithmic replacing stated multiplicative grow los biased interpret occurring imply symposium analyses ensures ensures loo predictors predictors forecasting chooses chooses chooses dif warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth santa inf inf inf forced exception additionally generalizations lit freund freund freund big imagine remote tight intuition playing disadvantage considers player player topic indexed weaker weaker outcomes suffer suffer suffer pools det nil behaves gorithm resembles rewritten lecture gratefully differently unbounded influenced todd coin compete cornput suffices december reflecting dcs rissanen returned attained norms norms symmetrical littlestone littlestone transpose statist minimax dimen protocol protocol protocol crl cruz relaxed restrictive fication kivinen kivinen kivinen corn mach mach inform inform inform inform inform syst violated replaces noticed noticed ference assoc assoc advice advice advice puter tiny ucsc deduce deduce distinctive manfred exponentiated exponentiated exponentiated exponentiated exponentiated exponentiated ans iix cov cov comput comput revised stant ations asserts logarithmically foster foster foster foster foster foster iwl assump reg doubt spend holloway paragraph alamitos deduced ilwll lxt lxt attains violates vovk vovk vovk vovk vovk vovk vovk vovk oper parison erated appreciated manifestation lyl guaranteeing guaranteeing suffered philip sionality bianchi bianchi wallace foun lnt rhbnc cesa cesa lln xtx tln egham aggregating aggregating aggregating aggregating aggregating modi dations elaboration complemented dawid surrey nln wegman 
#@Vovk_V,
#t11
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#*network network network network network network network network learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number number number number error error error error error error error error error error error error error error error error results results results results results problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem space space space space weights linear layer layer case case case case case case case vector vector vector order order order order shown probability functions functions unit unit method method method point point analysis class class class class class class class class class class class class class class class optimal inputs inputs inputs form form form shows algorithms simple paper paper paper paper examples examples examples small small small small small small small small small small small small size size size size size size size size size net net net work work step step step step step step step points points points points points points points points points points points points process process problems problems problems random high high show show show show show show section section section section section section section fixed fixed rule vectors vectors vectors vectors general general general general parameter real real real approximation approximation approximation average theory note note result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold solution solution research independent independent independent found constant constant constant standard computer node node science left present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets sets sets maximum maximum maximum press outputs outputs outputs abstract find find find find find computational references due due positive positive positive positive positive positive positive positive positive important important important context introduction hand behavior statistical difference complexity variable assume assume assume assume assume lower chosen chosen center previous previous previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound cases cases cases required required conditions fact fact techniques techniques length correct correct errors errors errors errors classes classes classes classes classes classes computed respect called called times elements elements means means dimension dimension dimension dimension natural applications obtain negative negative negative original vol vol relative relative relative relative relative relative desired provide goal related mit steps connection train department consists layers ai ai ai considered considered considered computing view san san determine determine upper free give give con produce produce provided nature depends achieved technical describe describe arbitrary arbitrary denote denote denote denote close complete proof proof proof proof proof proof proof proof proof proof finding finding finding common main main main main journal square end degree degree degree degree makes fit fit probabilistic smaller interesting interesting ratio ratio ratio edge edge edge edge edge edge special special special special squared squared squared squared squared squared details details call call call numbers max max max max max bits magnitude magnitude polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial choose choose choose denotes denotes denotes recent sense sense compare works works works works solve yields achieve achieve achieve definition definition definition generalized constructed constructed extended extended occurs demonstrate half half depend sigmoid sigmoid clear weak hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard reduction reduction reduction sigmoidal california exist iii question question question question question question question question question question suppose appears appears van construct edges edges edges edges edges edges edges edges produces metric involves easy easy implies implies implies implies influence open open open showed lee similarly constants key earlier reduces combining roughly roughly purpose interpolation interpolation remains sufficiently sufficiently norm norm norm norm norm norm norm norm norm norm norm classified classified classified avoid avoid avoid color color color color assignment assignment assignment assignment prove prove prove discuss absolute absolute holds discussions reason closely importance computationally computationally symbols refer refer notice repeated prob follow follow satisfy notation notation write leading thresholds thresholds thresholds thresholds thresholds thresholds satisfies satisfies satisfies satisfies decreasing extend origin carried collection investigate investigate difficulty association existence existence ideas ideas tech tech authors authors authors referred proved proved examined smallest math integer integer perfect subsets algo logistic observe arbitrarily great inequality formula formula crucial crucial distinguish answer answer answer handle handle reasons tive satisfied organized mathematics acknowledgement involve computers argument argument questions freeman red red red red poorly posed haussler formulated rep rep ity ity conclude display pac proofs proofs proofs intractable investigation fix fix arguments perfectly jones jones jones grows inspired rational fits fits fits dealing convenient exploit guide clause clause clause combinatorial corollary loo loo vertices vertices vertices vertices vertices vertices claim claim advance advance barron francisco matter warmuth vertex vertex vertex properly properly hypercube statement statement santa generalizing johnson limitation limitation lem verify verify yale yale yale listed misclassification solves achieving achieving basically chervonenkis theorems theorems conjecture exception blue blue blue blue chapter associate argue modifying ibm rithms learnability misclassified book preprint preprint truth truth truth truth mea manuscript circumstances resp remarks remarks prefer prefer blum blum blum clauses clauses clauses clauses clauses clauses floor norms judd judd complement rivest rivest neutral neutral rel colors crl cruz thresh statements monotone unnecessary completeness jose terminology infeasible omit sat rela literal literal cient blumer trick mention mention ucsc claims ative separability completes polyhedral luo luo readers readers iai ehrenfeucht app hardness hardness ifp ifp coloring coloring coloring coloring coloring coloring coloring terminating sider intractability intractability comple comple fll garey cult mll almaden olds finish ceiling whe ciency seminar aix aix aix iei iei tity maz 
#@Vu_V,
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#*network network learning learning neural neural neural neural input input input input input input input function function set set networks networks networks networks output output output output number number number number number number number system system system results results results results units units units units units units units units units units units units units units units problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space space space space space space space space space space weights weights weights weights weights weights weights weights layer layer layer layer layer layer case case case case case case order order order order order order order order order order order order order shown parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit distribution method method method method method approach approach approach approach pattern point point single single single single large large large large large large large patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis form form paper small small small size size work work cells cells step step step step step step step step field field process structure structure structure structure structure structure structure structure structure similar similar similar representation representation representation architecture architecture architecture vectors vectors general generalization real approximation average average obtained obtained result result result result result result university solution solution solution solution solution research research research independent defined found found found found estimate standard standard node science science science present present phase phase phase phase phase phase phase phase phase nodes nodes machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine sets range press continuous continuous abstract applied applied references component introduction hand hand behavior behavior behavior statistical statistical statistical statistical energy energy energy energy energy energy difference representations representations representations representations representations representations representations bound bound bound bound bound bound bound bound bound good good tree equations equations fact region proposed correlation observed forward finite respect respect multi multi multi multi sum eq called called means factor applications applications study study study obtain obtain obtain negative negative negative vol compared receptive receptive receptive related related related related connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected connected discrete equal equal power approaches approaches larger larger contrast fields selection institute institute department department version internal internal internal internal internal internal internal internal internal internal internal internal difficult exp exp scheme scheme scheme maps curve solutions solutions transition transition transition transition limit limit limit limit limit limit limit san capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity upper free free free free free free world world basic basic condition condition derived derived derived derived derived developed lines entropy entropy entropy entropy finally finally constraint describe synapse synapse synapse supported supported role role eds makes smaller reduced reduced account fully fully fully fully fully fully fully fully fully fully fully fully fully fully fully fully fully fully technology interesting interesting interesting increasing special consistent consistent leads details perceptron perceptron denotes discussed recent recent correlations typical reported apply machines machines recently recently relevant interest compare previously conventional conventional conventional conventional conventional conventional conventional conventional conventional volume volume volume volume volume volume volume volume volume yields symmetric symmetric symmetric storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage storage grant grant expression studied studied studied studied scaling scaling scaling scaling derivative feed critical critical critical numerical clear asymptotic asymptotic physics physics physics proportional proportional introduce program acknowledgements explicit explicit relation written written mathematical mathematical scales implies decreases yield yield focus focus overlap detailed evaluated evaluated sizes similarly suggested suggested partition allowed calculation calculation calculation calculation calculation calculation calculation foundation perceptrons formulation bell bell discuss phys phys phys phys phys phys phys phys phys phys phys phys phys partially discussions successfully letter suitable divided effectively committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee fine fine notice showing interpreted symmetry symmetry symmetry symmetry symmetry symmetry usual leading leading overlapping overlapping overlapping satisfies satisfies satisfies satisfies unlike layered transformed relations relations association applicable parity parity parity parity parity parity complicated hill coefficient trace possibly integer analyze analyze rev rev rev rev rev rev rev perceptton ith store store explain attempts directed derivation briefly handle handle tive formalism formalism formalism formalism closer sgn sgn sgn laboratories scientific mechanics mechanics mechanics mechanics people posed frequently ity mod phenomenon picture picture indices indices indices cybern saddle saddle jth jth connecting connecting nonzero dealing murray consideration check replica replica replica replica replica replica replica replica replica replica analyzing enhanced hertz published overlaps overlaps overlaps overlaps overlaps overlaps sompolinsky sompolinsky introduces corre expanded den spherical specialized specialized permutation permutation permutation properly park subsequently lett lett lett lett lett summarize ics geometrical numerous numerous rigorous pointed opper breaking breaking breaking breaking breaking guess examining thermodynamic dominated labs elementary elementary elementary elementary elementary elementary elementary ization discontinuity efforts confirmed induces indication durbin durbin durbin durbin technologies sponding instability agrees agrees ave lated hid replicated believed ref ref attained sym enhances tance cho correlates legendre vanishing gardner gardner gardner gardner gardner gardner gardner gardner gardner gardner gardner gardner gardner gardner gardner gardner mountain noticed entropies entropies ansatz saturates kanter kanter impor trick europhys europhys europhys workers volumes volumes volumes volumes volumes volumes volumes wji ministry biehl mitchison mitchison mitchison mitchison singapore barkai barkai barkai barkai engel engel engel news fund partic chine almeida bennett accompanied replicas replicas replicas lucent originate heaviside aaa prefactor reads education thouless korea korea korea korea dominating violates violates violates kwon kwon kwon kwon kwon kwon kwon kwon derrida derrida perspec galaxy capac jong jong aft decom ymptotic ymptotic lnz overlooked ult plies pioneering collaborators 
#@Kwon_C,Oh_J,Xiong_Y,
#t11
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural input input input input input input input function function function function function function function function function function figure figure figure figure figure figure time networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number system error error results results information information information information information information information information information information information information information information problem hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based based based space space space space space space space space space linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer vector vector vector vector vector vector vector vector order shown shown shown shown systems systems probability probability parameters parameters parameters parameters parameters parameters noise noise noise weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons distribution method single single single single processing processing large large large large large local neuron neuron rate rate rate rate rate rate rate rate matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs form form form shows shows signal algorithms algorithms algorithms algorithms simple gaussian gaussian paper examples examples examples examples small methods points points level level structure structure structure structure random high architecture show equation section fixed line line line line line line line rule rule rule rule rule rule rule rule rule rule rule vectors vectors general parameter parameter parameter parameter parameter parameter parameter parameter gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained note dimensional dimensional dimensional dimensional dimensional computation independent independent independent log defined defined defined found initial initial constant estimate estimate estimate computer distance science science direction direction phase phase phase phase phase machine machine machine press abstract find find convergence density likelihood references component stochastic stochastic stochastic stochastic stochastic stochastic due ieee adaptive introduction statistical generated generated variance search search search search search change complexity complexity complexity complexity complexity variable assume assume assume assume assume assume lower lower lower chosen bound bound required represent represent represent equations make techniques proposed proposed length errors errors errors errors simulations simulations classes simulation simulation simulation simulation computed computed respect respect multi multi multi multi multi multi multi multi multi multi multi means dimension dimension dimension dimension dimension dimension natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural obtain obtain negative true true true define define compute compute compute compute compute compute rates brain brain mit larger larger larger larger train train train train descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent morgan institute institute department loss loss loss loss loss advances joint scheme scheme scheme scheme scheme scheme ai ai ai framework cambridge computing design design san efficient efficient efficient efficient efficient efficient efficient estimated pages pages give randomly levels levels selected iteration iteration depends depends simply measured describe denote denote denote fast fast fast close inverse inverse inverse inverse inverse inverse inverse role main main main eds square square square kaufmann needed combination combination reduced reduced unknown unknown coefficients jordan block block block consistent iterations iterations choose choose run run perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes advantage robust robust robust robust apply machines quadratic dimensions dimensions teacher teacher works converge converge converge converge converge differential rl interval studied trial matrices column column demonstrate runs runs critical conclusions depend designed moody moody moody faster asymptotic weak mateo taking drawn start min decrease decrease annealing estimating metric metric implement physical formed blocks decreases review stationary estimator estimator estimator estimator estimator forms soft partition spaces box includes combinations usa perceptrons perceptrons perceptrons perceptrons mozer efficiency efficiency efficiency efficiency efficiency divided driven driven committee committee committee efficiently symmetry sin sin dot thresholds satisfies law schedule schedule schedule schedule schedule difficulty difficulty difficulty difficulty updating detail hanson lippmann divergence divergence scalar structured root proved proved statistically statistically analyze algo algo fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher expressions expressions perceptton multivariate amari amari amari amari amari amari amari amari amari submitted inequality inequality analytic briefly lin implementing implementing optimize robustness robustness robustness robustness conducted item solla solla howard synthesis reaches gave logp logp logp unbiased unbiased differentiable lab ear japan rithm rithm tensor tensor plays kullback darken darken accepted overcome operates ral exploring lip encountered regarded regarded yang yang yang yang schedules schedules entries storing storing steepest discovered pdf multiplying saad saad converted leibler ber axe rao rao rao par aij aij verified num graduate confirmed confirmed fir fir integrals integrals integrals integrals win weaker breaks tively 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#@Amari_S,Yang_H,
#t11
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data function function function figure figure set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm output output output output output output output output number number number number system system error error error error error results results results units problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden performance performance based space space weights weights weights weights weights weights weights weights linear linear linear linear linear layer layer layer layer layer case vector vector vector vector systems values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight weight weight functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method method method method method method approach approach approach approach approach approach pattern single single single large local local local test test test test analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs form form form form form form form form form shows simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples examples small methods classification current trained problems high similar similar similar similar show show section fixed fixed vectors vectors general parameter average average average average average theory theory gradient obtained obtained term term term term term term term term term note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result university university university university variables computation computation research research research research independent independent independent defined target target initial constant constant table table table estimate estimate standard standard standard standard standard computer terms terms terms terms node science left left present activation maximum press components components components basis outputs abstract applied applied back find computational computational convergence likelihood likelihood likelihood references procedure procedure procedure procedure procedure adaptive adaptive propagation mixture introduction estimation estimation variance cost prior prior prior prior chosen theorem required required represent distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov make make fact techniques techniques techniques length forward simulations simulations minimum minimum minimum minimum minimum minimum ing regression regression regression regression respect respect respect multi multi multi multi multi multi performed called called elements regions factor factor optimization optimization made applications study obtain negative artificial samples true true true true compared compute compute posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions distributions distributions approaches comparison contrast dependent dependent proceedings proceedings proceedings report report institute department implementation version consists joint joint represents difficult exp exp exp exp exp exp exp exp addition ai framework framework framework framework cambridge computing computing computing directly hinton hinton hinton hinton view conference determine full full requires approximate approximate approximate statistics free give give give con derived weighted conditional criterion entropy product simply discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance technical technical group group denote limited assumption assumption predictions predictions predictions predictions finding implemented generate supported adaptation easily easily including fit fit fit fit fit probabilistic typically pairs reduced functional functional unknown mode mode mode mode squared representing representing pre supervised minimize choose choose choose description recent correlations correlations correlations ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble practical practical introduced include include subject quadratic quadratic calculated yields achieve diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal address address evaluation evaluation chain chain locations williams increased grant parts extended extended extended alternative feed locally deterministic occurs reduce depend depend sigmoid sigmoid accurate bayes numerical numerical constrained constrained strong integration integration integration integration integration sigmoidal proportional intelligence minimizing minimizing minimizing minimizing start plane introduce derivatives derivatives derivatives acknowledgements appears monte monte van van van van carlo carlo written longer changing involves remaining remaining text scales springer springer blocks expressed dependence dependence evaluated evaluated evaluated evaluate controlled showed approximations approximations forms similarly suggested partition constants calculation calculation additive performing normalization reduces fitting iterative calculate david degrees priori coordinate coordinate extension discussions successfully simplicity gamma gamma gamma straightforward suitable computationally computationally latent mackay mackay mackay mackay mackay mackay mackay mackay orthogonal capture capture lie follow notation write leading leading approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating deal modelling modelling extend extend simpler simpler unlike unlike parametric exponentially involving replaced integral integral integral limitations divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence preliminary graphical mass biases biases biases dataset helpful rise scalar scalar reducing mappings analytically analytically analytically analytically analytically scaled scaled complicated topographic coefficient plausible illustrate algo logistic freedom finds defines neal neal neal averages established optimum integrate integrate advanced derivation analytic analytic expensive tractable tractable tractable tractable tractable benchmark benchmark reasons formalism formalism preprocessing broad bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop leaves mation probable mathematics consequence involve optimize annual annual conjugate summation evaluating flexible lack treated http http http berlin summarized hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters curvature achieves boston expectations globally shifted notes www www www www writing oxford rithm appropriately narrow unity unity kullback kullback kullback kullback kullback kullback kullback fits simplify keeping symposium laplace laplace laplace laplace laplace laplace laplace laplace laplace advance treatment snn snn fitted ple unable aston aston aston aston email leibler leibler leibler leibler leibler leibler leibler isotropic isotropic encouraging diag toy approxi concentrate fir integrals integrals integrals integrals pos unconstrained spanned cation accounted suffer det det prevents normalizing eters eters september differentiating housing chris lecture const const const const const const const const christopher transforming house barber barber barber barber barber barber barber imple clarity industrial integrates coincide offsets quantitatively sity lnp lnp lnp lnp lnp deter ance enter corn corn neglected capturing birmingham birmingham ming ming developments developments microsoft microsoft richer vergence pull aims sixth proce quadrature quadrature dealt treats netherlands netherlands strongest fac desire initializing mented centred mined oij oij george hyperparameter camp camp camp camp univer epsrc ncrg nato relied alternately succeeded integrand plied integrations iwl unspecified quadratically lea lea optimizer dure tractability wld wld wld wld tackled archive nijmegen nijmegen nijmegen rior terior poste istic determin pressed delve delve wid wid hyperprior lna modifi sigrnoid lal fic recognise kun kun treatments underestimates lexp lwl lwl lwl ada mbfys mbfys wla geert grooteplein troduced basing 
#@Barber_D,Bishop_C,
#t11
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#*network network learning learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training output output output output output output number error error error error error error error error error error error error error error error error results units information information information information information information problem problem problem models models hidden hidden hidden hidden performance performance based based based based weights weights weights weights weights weights linear linear linear linear layer layer case case vector vector shown values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method approach approach approach approach approach approach approach approach point point point point single single single single single processing large local local local local test test test patterns matrix matrix optimal optimal optimal form form form simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples feature work methods methods methods methods points points points classification classification level trained trained problems high similar similar equation fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line generalization parameter parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation average average average average average average theory theory term note experiments dimensional dimensional dimensional university 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introduction complex complex estimation estimation estimation effect variance variance search lower lower prior prior prior prior prior prior learned chosen chosen chosen center center center center center center center center center bound bound bound type type bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov techniques techniques techniques techniques techniques length probabilities errors minimum resulting regression regression respect respect respect respect multi multi performed called optimization optimization em em artificial samples application cross cross cross cross cross cross cross cross cross compute compute compute compute perform determined determined determined posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions distributions approaches approaches approaches approaches approaches approaches approaches contrast contrast connection update support selection selection selection proceedings proceedings proceedings report report report department loss loss technique joint represents difficult exp exp exp exp exp exp exp exp ai ai ai ai framework framework framework framework computing computing computing computing computing hinton estimates choice approximate approximate statistics pages validation validation validation validation validation validation validation validation validation weighted conditional developed criterion lines lines evidence achieved covariance covariance covariance technical technical technical increases describe group group group denote fast fast inverse inverse inverse corresponds surface predictions predictions predictions predictions predictions rbf rbf rbf rbf rbf require adaptation easily easily noisy fit fit fit fit probabilistic typically pairs combination account account functional functional functional unknown coefficients fully york uniform mode mode mode mode mode mode principle principle leads pre supervised combined minimize choose choose choose description light denotes advantage ensemble ensemble takes apply include identical cognitive highly compare conventional unsupervised approximately calculated yields diagonal address positions chain williams deviation locally locally move width occurs generally setting setting setting minimal minimal greater greater conclusions peak peak moody hard integration integration solid intelligence regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization radial radial radial radial radial radial radial radial radial radial radial radial turn assuming minimizing minimizing minimizing averaged averaged targets manner acknowledgements relation monte van carlo produces estimating plot plot tuned averaging averaging averaging averaging remaining text gaussians minimization minimization springer springer yield choosing expressed viewed influence variation evaluated evaluated controlled updated centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers centers approximated completely completely constants constants constants constants constants constants constants constants constants constants constants constants constants constants constants dashed dashed additive additive additive fitting iterative iterative interpolation assigned david includes priori priori priori perceptrons plotted automatic uncertainty priors discussions successfully successfully gamma gamma gamma straightforward uniformly suitable computationally delta delta identify mackay mackay procedures procedures contained contained allowing showing dis issue quantity quantity bar sampled leading leading approximating approximating approximating approximating deal modelling bars bars bars bars simpler simpler parametric overfitting optimized hessian hessian divergence divergence divergence divergence divergence divergence divergence divergence divergence mass dataset rise examine examine giving giving ideal ideal analytically analytically combine workshop affect adapt extremely improving defines neal developing formula trivial analytic analytic analytic analytic analytical adapted adapted adapted expensive expensive lies formalism bishop bishop bishop bishop leaves mathematics potentially optimize annual annual fluctuations fluctuations integrating integrating requiring flexible incorporated incorporated dots http http popular hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters inherent chose specifies converged corrupted corrupted notes www assign assign fix fix optimizing optimizing labelled kullback kullback kullback kullback kullback fits fits fits fits darken tools keeping keeping symposium carry widths widths widths widths widths widths widths widths dependency demonstration demonstration percepttons viewing laplace laplace laplace laplace laplace laplace laplace laplace treatment treatment treatment treatment treatment suggesting snn snn draw broken subsequently assigning assigning outlined treat posteriori approx rigorous constitute aston aston aston aston aston email leibler leibler leibler leibler leibler tween centre regularity seek ideally edinburgh edinburgh principled principled principled principled penalized penalized exponent distri regularizer regularizer crosses regularized regularized rbfs rbfs rbfs algebra retained det eters compu september mini bution chris chris lecture advantageous fortunately achievable const const shot barber barber barber barber barber barber barber barber interpreting clarity optimisation industrial formulae formulae tribution ning assessment discarded discarded orr orr lnp era fixing fixing problematic iterate birmingham birmingham birmingham deciding fore developments cations appli proce beliefs beliefs beliefs llx llx llx netherlands netherlands tll colt cen centred penalizing seventh wishes hyperparameter camp trust ncrg gression adaptable adaptable quantifies omitting bernhard penalize reg collectively proximate dure regularizing regularizing cated contrasted tual ven wld puting regu nijmegen nijmegen returning wasteful wasteful hyperprior hyperprior mizing lna mll favour encompasses objectively wander normalising kun kun treatments larization lla lla mbfys tationally geert grooteplein discourage imating 
#@Barber_D,Schottky_B,
#t11
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#*learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data function function function function figure figure figure figure figure figure figure figure time set set set set set set set set networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number error state state state state state results results results information information problem models models models models models hidden hidden hidden based weights weights case order order order systems values values values probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition method single single single processing processing processing processing processing processing processing large large large large local local local local local local local local rate rate rate test test test analysis shows shows algorithms algorithms simple simple paper paper paper paper paper small size size size size size size size size work work task task task methods points classification classification process current trained structure structure structure memory memory memory memory similar similar similar similar similar representation fixed fixed line generalization generalization speech speech speech speech speech speech speech parameter parameter real obtained obtained obtained obtained obtained note note experiments experiments experiments result threshold threshold research independent log found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence computer computer node node node node node node node node node node node node node node node node node node node node node node node presented present phase nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes frequency maximum maximum maximum maximum maximum maximum maximum press press learn position continuous abstract references stochastic ieee ieee important adaptive decision mixture mixture context context context context context context context context context context context context context context context context context introduction statistical variable variable variable variable variable variable variable measure measure measure prior prior prior word part part type required multiple multiple multiple represent represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree markov markov markov markov make make make proposed proposed proposed proposed proposed proposed length length length length correct probabilities scale finite finite minimum ing human respect performed performed performed performed called called called called times elements mapping mapping made natural natural natural natural applications study em obtain obtain obtain obtain obtain relative relative represented represented represented represented represented represented represented compared compared application application series define define define define compute rates experimental experimental distributions distributions distributions distributions distributions distributions distributions gain gain gain discrete mit accuracy accuracy accuracy accuracy accuracy larger update update modeling modeling proceedings report loss version internal internal advances represents represents represents delay scheme graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph sequences sequences sequences sequences sequences sequences sequences considered cambridge equivalent experiment limit conference estimated pages con weighted weighted weighted weighted weighted conditional conditional conditional conditional conditional conditional clustering clustering path path path finally finally constraint simply technical technical increases tested tested end end instance probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic pairs smaller smaller smaller smaller interesting interesting york structures database database language language language language language language details max max international supervised depth depth depth depth depth depth depth depth predict pair pair pair element element element similarity similarity similarity reported introduced trees trees trees trees recently compare compare compare observations observations observations tions correspond mixtures mixtures background symmetric symmetric observation parts parts studied touretzky deterministic deterministic deterministic conclusion starting starting greater editors performs performs constrained propose propose labeled labeled labeled labeled min program pro written longer sequential label dept text text adding adding cycles cycles yield yield expressed evaluated labels labels labels labels labels labels labels understanding sizes updates past past combining intermediate string string assigned construction advantages transactions avoid building existing usa usa strings bell automatic mozer hmms maximal maximal maximal maximal maximal paths paths symbols identify build efficiently comparing tend reached reached graphs graphs graphs graphs graphs graphs graphs graphs showing interpreted delayed extend create create updating divergence divergence reducing links decisions root root root root root root root root workshop phases phases neu hill possibly editor automata illustrate recognizer algo algo algo observe academic art attempts asynchronous directed directed directed directed directed growth comparisons arc arc arc arc shared shared shared shared shared shared shared shared shared shared shared shared precisely bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio bengio leaves laboratories laboratories laboratories preceding requiring requiring flexible amounts tional parameterized experimentally share marked slower rep vocabulary vocabulary summarized limiting limiting parent prevent singer singer singer singer singer singer singer singer singer singer singer asymmetric chose chose yielding merging merging merging merging merging merging merging merging merging sharing fix fix rithm rithm resources purely proceed reaching children children rational kullback murray tools grow grow operates ral corpus phrase alphabet alphabet alphabet child child child child child child child child constructive constructive constructive constructive heuristics contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts induce decide lengths counting dif canada canada canada canada canada merge merge merge merge merge merge merge merge merge merge merge merge merge thresholding parents parents parents parents parents assigns mind suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix yielded arcs arcs arcs arcs shorter recursively bank comparative comparative obtains decomposed simulating associate forcing guess rain remote reject distri distri cessing rithms labs labs allocated searches picked regimes universit bution transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer transducer continued frasconi frasconi phrases ferent ers cast condi holmdel transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers transducers arpa noun noun noun constraining longest longest longest inducing ings concatenated merged merged merged tags tags tags acyclic acyclic acyclic acyclic acyclic acyclic shares verb montreal montreal montreal montreal pact favors applica kong predefined mum mum delete des des associating yoshua yoshua accord pertone compactly quence subsequence rooted rooted rooted rooted rooted rooted rooted rooted rooted rooted rooted ein ein ein baker baker merges merges merges ode subgraph ala ala butions pereira pereira pereira pereira liebler iro iro freezing yoram succeeds mina mina mina subse subsections loga anymore deepest deepest deepest deepest memorandum resent munication jelinek jelinek ancestor upenn jean jean freed ren ren rithmic ile ile adjective sla sla bengioy yla yla asymmetrically 
#@Bengio_S,Bengio_Y,Isabelle_J,Singer_Y,
#t11
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#*network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural function function function function function function figure figure figure figure figure figure time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number error error error results results results units units units units units units information information information information information information information problem problem problem problem problem problem models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based weights weights weights weights linear linear linear layer layer layer layer case order order shown shown systems values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach approach approach pattern pattern pattern image single single processing large patterns patterns patterns class class class class form form form form form form form form form form shows shows algorithms simple paper small small small size net net work methods methods step field field field field field field field field field field field field field field field field field field field field field classification trained trained trained trained trained random representation architecture show section images general general parameter parameter approximation approximation approximation approximation approximation states states theory theory theory theory theory theory theory theory theory theory gradient obtained term term term term term note note experiments result university variables variables variables variables variables variables computation solution research research independent log log log log log log log log log log log log log log log log log defined defined found constant constant standard standard standard standard computer terms terms science science left direction presented nodes maximum press learn components components components components components components components components components components components components components components components components components components components basis abstract applied applied find find computational convergence likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction introduction hand hand hand estimation estimation generated tion difference variable variable variable assume assume lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower representations representations chosen chosen chosen chosen center bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases good binary binary represent represent bayesian bayesian bayesian bayesian equations equations make make techniques correct forward scale scale ing total respect respect respect respect respect respect respect respect respect respect respect multi performed times optimization optimization optimization optimization em em obtain obtain obtain original artificial artificial relative true true true true true true true true true true true true true true compared application application posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints connected connected distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions gain equal equal mit mit steps larger proceedings institute individual individual advances represents connectionist final exp exp layers considered framework cambridge computing equivalent directly directly hinton hinton hinton hinton additional determine efficient full requires requires choice approximate give give con randomly randomly conditional criterion bounds entropy product product finally finally simply biological discussion increases arbitrary group denote assumption assumption common generate eds journal easily easily probabilistic combination coefficients coefficients coefficients fully jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan technology uniform uniform leads leads leads leads leads leads details numbers numbers making normalized normalized polynomial choose denotes denotes denotes improved improved improved discussed improve improve exact exact takes takes apply introduced introduced subject trees inference inference interest interest compare unsupervised volume works tions tions yields yields yields sparse mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation evaluation chain locations bounded improvement improvement improvement improvement improvement increased increased increased increased horizontal expression derivative alternative feed touretzky demonstrate demonstrate starting greater interactions interactions sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid practice weak taking strong largest intelligence intelligence turn introduce introduce introduce derivatives connectivity boltzmann digit derive written plot label label vertical dept involves involves remaining slightly belief belief belief belief belief belief belief belief belief belief belief belief belief belief mutual mutual mutual mutual mutual mutual applying quality quality expectation expectation versus versus family expressed review interpretation solved detailed evaluated evaluated evaluated evaluate forms completely diagram key smoothing smoothing smoothing smoothing smoothing smoothing convex remains visible visible visible sufficiently sufficiently expect thesis extension plotted prove maximize maximize maximize maximize maximize maximize mozer coupled simplicity computationally computationally computationally computationally computationally divided identify efficiently efficiently schemes plots reached summary follow bar write michael dayan mixing mixing mixing approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating deal modelling bars bars bars explore remain parametric layered investigate exponentially exponentially updating involving optimized optimized divergence graphical graphical biases biases variational variational variational variational variational analytically maximizing gradients gradients gradients adapt adapt configurations configurations configurations configurations configurations configurations illustrate logistic expressions extent neal neal neal massachusetts indicating ment inequality inequality developing formula separable improves briefly tractable tractable tractable tractable tractable tractable tractable tractable considerable considerable considerable tive tive satisfied formalism formalism bishop bishop bishop bishop mathematics optimize optimize summation summation argument requiring flexible ture aim sums replace jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola intractable intractable intractable intractable intractable sleep summing optimizing flexibility clamped systematic systematic systematic kullback convenient adjusting keeping presentations substituting saul saul saul saul saul saul saul saul iteratively equals regarded sides sides regard histograms histograms histograms histograms uni lawrence lawrence lawrence lawrence hasselmo omitted impact exploiting adopted parents treat street logarithm outline rigorous rigorous aston leibler kluwer presenting instantiation connec seek amherst stands wake illustration remainder adapting factorial factorial verified manipulation arising translated distri distribu distribu jij jij jij jij individually frey parametrized permit rewrite mix modal modal diagrams bution factorized factorized factorized simplification simplification const const christopher ters ally conditionally resolved governing feasibility restrictive birmingham unimodal ira ira ira ira tivity proximation substructures richer richer omit marginals marginals marginals marginals substituted parame posteriors bernoulli bernoulli puted occupied initialised tommi densely densely nato looo instantiated tti effec effec sider initializations summations summations stressed asi factorize sumed substructure lna lna lnz tightest 
#@Bishop_C,Jaakkola_T,Jordan_M,Lawrence_N,
#t11
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data function function function function function figure figure figure figure figure set set set networks algorithm algorithm algorithm algorithm algorithm output output output output output output output output results results information information information information problem based based based weights weights linear linear case case vector order order order order shown shown shown shown shown shown systems systems systems systems systems values functions functions functions neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach point point point point image image image single single single single single single single single single single processing processing processing large neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis matrix optimal inputs inputs form form form form form form form form form form form form form form form signal signal signal simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual examples small small feature feature feature work work work methods methods methods cells points field field field field field field field field field features current cell cell cell cell cell cell cell cell cell cell structure structure structure structure structure structure structure structure structure structure structure structure structure random high high high high high similar similar similar similar representation architecture architecture show show show section fixed fixed fixed fixed rule rule rule rule rule rule rule rule rule rule rule vectors vectors vectors vectors images images images images general theory theory theory gradient gradient gradient gradient gradient obtained note activity activity dimensional dimensional dimensional dimensional dimensional university university university university university university threshold variables variables computation computation computation research research independent independent independent independent independent independent independent independent independent independent independent independent independent log defined defined found found found found standard connections synaptic synaptic science left left left presented present phase low frequency frequency frequency maximum maximum press press press components components components components components nonlinear abstract find find find find find find computational properties properties properties properties properties references component component component component component stochastic positive positive procedure procedure important important mixture mixture introduction estimation statistical statistical statistical statistical statistical statistical statistical search change change difference difference difference difference difference difference spatial spatial spatial spatial lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure measure measure measure measure measure measure measure measure signals signals signals signals representations higher higher type required cortex conditions conditions equations make fact proposed proposed observed resulting resulting ing multi multi multi performed made natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural orientation orientation study study study study study study study filter filter obtain negative original specific application receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide define goal goal goal related related related distributions distributions distributions distributions distributions distributions distributions gain cortical brain brain approaches comparison comparison comparison comparison comparison contrast connection connection fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields dependent morgan proceedings proceedings report institute institute department department version technique code code code code advances represents difficult addition considered framework environment environment environment environment environment environment environment directly directly san top top effects conference determine upper upper requires requires significant statistics statistics statistics statistics vision pages produce produce produce coding coding coding coding coding coding coding derived developed developed developed entropy iteration iteration nature simply biological biological achieved achieved discussion discussion covariance technical denote transformation fast finding finding finding common assumed supported journal journal journal cluster degree development sensory including kaufmann objective objective underlying needed interesting interesting significantly projection projection projection projection projection projection projection york edge mechanism leads leads details details filters direct normalized normalized normalized normalized normalized bottom polynomial polynomial sources neuronal neuronal neuronal denotes discussed directions directions lateral include identical side quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently recently compare compare compare compare compare approximately calculated calculated volume volume smooth pca achieve sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse separation separation separation symmetric sensitive sensitive sensitive sensitive sensitive entire parts expression lead concept concept suggests suggests deviation deviation deviation deviation deviation derivative touretzky clusters clusters demonstrate half half depend depend depend editors differences sigmoid measures measures measures measures measures measures retina exponential learns mateo strong physics physics ica ica ica ica ica ica ica ica ica ica introduce introduce manner manner scene scene scene scene scene denoted edges edges produces index stability mathematical mathematical sensitivity sensitivity sensitivity involves angle interaction interaction develop mutual frequencies gaussians events formed implies extraction extraction extraction expectation national national formation formation formation formation formation dependence review codes lee lee allowed additive additive additive iterative visible foundation foundation norm formulation bell bell bell bell bell bell blind blind sciences sciences maximize straightforward modification modification modification modification included projections projections projections projections comparing tend tend orthogonal strongly contained neuroscience dis symmetry sci satisfy quantity sampled realistic maximization maximization maximization maximization maximization acknowledgments oriented oriented oriented oriented law law law simpler selectivity american investigate relations environments environments detail association pursuit pursuit pursuit pursuit pursuit pursuit examine successive fashion school int plasticity office maximizing maximizing maximizing lgn statistically statistically removed removed friedman friedman friedman versions versions versions portion portion precise mixed mixed mixed motivated attempts percentage percentage percentage brown brown brown brown advanced scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes cos orientations orientations derivation preprocessing preprocessing preprocessing projected projected patches annual qualitative requiring percent percent percent percent double quantitative biologically outliers outliers exhibits measuring measuring measuring monotonic qualitatively qualitatively enables deviations cor lab primarily cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper cooper appearance tation recover circular naval eliminate eliminate eliminated binocular systematic oja oja oja oja oja oja oja odd multiplicative multiplicative multiplicative moment moment neurobiology reasoning moments moments moments moments moments moments motivation motivation elimination iteratively studying ascent ascent searching israel emergence express insight surprisingly specificity relies explains inf lem slight corporation outline munro removal removal removal removal removal removal responds kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis intrator intrator intrator intrator intrator intrator intrator intrator intrator clustered alternate deconvolution eliminating concentrate academy rectified deleted portions outcomes sta modality modality compu compu exploratory exploratory exploratory tel behaves behaves mann deletion bienenstock bienenstock bienenstock rfs rfs rfs rfs rfs rfs coin olshausen olshausen olshausen bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm bcm eliminates rare tribution normalize dog vanish ory sparseness sparseness tenth aviv aviv stabilization stabilization stabilization tails tails maximisation plenum publishing publishing preprocessed plausibility comon comon conveyed extrema sparsity sparsity rectification dana claimed claimed seeking stuart stuart stuart providence providence providence helsinki emphasizing skew skew skew whitened whitened whitened whitened whitened whitened disappears leon hyvarinen hyvarinen hyvarinen lan discussing batches whitening sphering advocated skewness skewness skewness skewness skewness skewness skewness skewness skewness skewness skewness brian freedman rectifying clouds kendall kendall kendall iim diaconis lipp motivating sigrnoidal kurtotic kurtotic tationally 
#@Blais_B,Cooper_L,Intrator_N,Shouval_H,
#t11
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#*learning learning neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set networks training training algorithm algorithm algorithm algorithm algorithm algorithm number error error error error error results results results results results information problem problem problem problem problem performance performance performance performance based based space space space case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order values values values values probability probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions distribution distribution distribution distribution method approach approach point point point point point point image image image image image image image image image image image processing rate rate rate rate test test analysis analysis class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal form shows shows shows shows shows shows signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms gaussian size size size size size work fig step step step step step step points points process process level trained trained problems high high similar representation representation representation representation section fixed fixed fixed fixed line line vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images generalization speech parameter parameter parameter approximation approximation average average average average theory theory obtained obtained note note dimensional dimensional dimensional result university variables computation solution solution solution solution defined found estimate standard computer distance distance distance distance science left left presented map map map map map map map map map phase phase phase phase phase phase phase phase phase low low low low sets maximum maximum basis abstract applied applied applied applied find find find computational convergence likelihood references component stochastic due ieee ieee important introduction behavior behavior statistical variance cost cost cost cost cost cost cost cost tion tion tion change energy difference representations chosen center center center previous cases required good good good binary binary binary binary binary binary fact length probabilities probabilities probabilities probabilities probabilities minimum resulting ing ing ing total regression performed eq eq eq eq eq eq eq eq eq eq elements elements factor optimization optimization optimization dimension global study em obtain obtain original original vol vol vol vol vol vol vol artificial relative compared desired determined determined equal comparison contrast train source source source source source source source source source proceedings proceedings department version version code code code code code code code code code code code code code code code code code code code code code code code code code code code code represents exp exp exp exp scheme scheme scheme scheme scheme scheme maps maps transition transition transition transition transition limit top bit bit bit bit bit efficient upper free con channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel coding coding coding coding coding coding coding coding coding derived derived derived clustering clustering clustering lines lines entropy entropy finally iteration iteration constraint simply achieved measured covariance covariance covariance technical arbitrary arbitrary group denote tested inverse inverse inverse inverse inverse inverse inverse predictions predictions supported theoretical theoretical pixel pixel easily noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy fit objective probabilistic account account ratio ratio increasing special principle principle leads leads leads principal principal principal principal squared squared details call call max max max max bits bits idea idea combined minimize denotes exact robust robust robust apply introduced introduced compare axis axis axis axis axis tions yields yields achieve diagonal diagonal positions positions positions symmetric symmetric symmetric symmetric channels channels channels increased move deterministic deterministic deterministic deterministic deterministic occurs occurs demonstrate demonstrate conclusion starting starting starting critical critical critical critical critical critical critical competitive central numerical numerical performs performs performs performs exponential temperature temperature temperature temperature temperature temperature temperature temperature temperature encoding encoding encoding encoding encoding hard largest largest largest drawn demonstrated solid solid labeled assuming assuming start averaged annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing acknowledgements pro derive derive index solving plot plot transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions vertical modeled coordinates averaging infinite infinite physical physical slightly slightly text consisting develop develop applying springer formed expectation expectation letters family focus review review reconstruction reconstruction reconstruction communication labels organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing organizing approximations soft soft soft soft soft soft soft soft convex neighborhood neighborhood neighborhood neighborhood neighborhood purpose calculate assigned assigned euclidean euclidean kohonen kohonen kohonen kohonen kohonen kohonen transactions transactions existing coordinate eigenvalues eigenvalues assignment assignment assignment assignment assignment assignment determines determines determines determines plotted determining compression compression efficiency differ encoded computationally computationally computationally computationally computationally modes schemes tend miller miller traditional verlag induced interpreted split split split split split superior superior superior symmetry gray gray gibbs generalize quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization eigenvalue eigenvalue maximization maximization received received principles consisted moves minimized employed remain schedule schedule schedule relations replaced optimized optimized optimized optimized mass mass successive fashion giving eigenvectors encode func topographic topographic topographic topographic naturally naturally transmission transmission transmission transmission transmission opposite front versions versions som som som som som som som som grouping scenes costs trivial trivial agreement convolution derivation derivation unstable caused worse worse snr snr snr snr snr located bandwidth demonstrates mechanics robustness limits fuzzy generic dots dots dots variant http berlin berlin berlin berlin summarized cal suited enables germany hamming hamming decoder displays distortion distortion cor representative indices indices indices www optimizing reconstructed repre repre encoder communications multiplier splitting splitting nonparametric embedding recovered sion corre codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook regard washington offers permutation hypercube eqs eqs eqs eqs eqs eigenvector eigenvector eigenvector broken assigns assigning temperatures approx ure compressed usage usage drop incorporates ent ber ber ber ber ber ber ber ber ber transmitted transmitted transmitted legal expanding responds icassp convenience additionally solely assignments assignments simulating possibilities possibilities stands diag toy toy toy ijcnn annealed annealed annealed annealed crosses crosses crosses crosses buhmann buhmann obermayer obermayer obermayer obermayer obermayer applicability eigen hofmann rose rose rose rose rose gorithm lagrangian expense distortions accordance accordance jointly solvable condi quantizer fox tracks maxi inset inset era deter transmit decoded decoded analyse analyse ted vergence demanding demanding demanding demanding mir mir direc heskes heskes mum organisation sition icann klaus advice tran comprises cooling anneal munich asso analysed reconstructing opens opens expands charac lbg lbg lbg lbg lbg lbg lbg lbg lbg lbg lbg lbg story elongated sponds kappen hut dur bers bers nen oblique transi quantisation gurewitz pression pression chuck ciated vmax vmax istic determin ministic appropri sents terministic terministic quantizers quantizers quantizers quantizers quantizers cartoon munication bsc bsc fuzziness impression ama departs omission gles marginalized xix sult ici ately baysian oby 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural input input input input input input input data data data data data data data data function function function figure figure figure figure figure set set set set networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm output output number number number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results results results results information information problem models models based linear linear linear linear linear linear linear linear linear linear linear linear case case case case case vector shown shown shown systems systems systems systems probability noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition method method method method method method method method method method method method approach approach pattern pattern pattern image processing large large large large test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form shows shows signal signal simple simple paper examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small size work work methods methods step classification classification classification problems problems problems problems high similar show show show show equation equation equation equation section section section section section section general general parameter parameter parameter parameter parameter parameter parameter real approximation theory term term note experiments experiments result solution solution solution solution solution solution solution solution solution solution solution solution solution independent log found target target target target target target target target constant constant table table computer terms terms terms science prediction prediction machine sets press press press nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs sample sample abstract find find find find properties properties references ieee positive mixture mixture introduction behavior statistical effect variance variance variance variance assume assume assume classifier lower previous theorem theorem theorem theorem expected expected expected expected expected expected equations errors errors scale minimum minimum resulting ing regression computed computed computed respect respect respect respect elements dimension applications applications applications em obtain vol vol artificial specific specific samples samples compared provide experimental experimental goal equal mit train institute institute department department version consists advances bias bias addition addition cambridge directly additional solutions solutions solutions top approximate approximate approximate approximate estimated increase validation validation give give criterion depends covariance covariance increases increases increases increases increases group group group denote denote corresponds corresponds proof proof proof proof proof finding finding main eds square square hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis future noisy noisy noisy noisy noisy noisy noisy noisy including smaller smaller smaller unknown unknown technology technology ratio ratio consistent database squared call making international experts early early early minimize choose denotes takes include engineering approximately observation derivative derivative touretzky occurs occurs pass greater conclusions moody exponential propose propose drawn demonstrated california california labeled labeled labeled labeled minimizing minimizing minimizing minimizing minimizing minimizing minimizing minimizing targets targets targets introduce van written solving factors estimating averaging electrical dimensionality remaining spectral john john letters decreases focus depending squares squares squares squares estimator estimator estimator estimator estimator estimator estimator estimator sizes similarly similarly similarly transactions includes determines prove discussions extra extra extra computations miller miller composed stopping stopping stopping write providing minimizes minimizes hypotheses acknowledgments tesauro minimized minimized wiley access investigate investigate exponentially replaced hall existence existence scalar reducing reducing tech applicable analytically working cover cover trace possibly possibly necessarily necessarily necessarily art art art explain formula formula formula analytic analytical worse london snr snr snr sections day incorporate bishop definite medical medical radius cal incorporating incorporating incorporating incorporating incorporating incorporating incorporating incorporating incorporating extensions pasadena pasadena song replace age unbiased unbiased proposition proposition proposition credit credit consistently sensing leen oxford ratios databases nonzero caltech caltech consideration alpha biased unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled prentice financial appendix appendix realization realization uni augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented augmented extends extends sons valuable default default ics uci abu blood mostafa leaming ber expanding remote pub num num hughes regularized concentrate discusses knowing knowing ignoring ble overtraining overtraining overtraining hopkins powers bond bond bond bond bond rating johns baltimore jan experimented applica joseph disorders versity alexander mented malik multiplies liver liver liver liver prof discarding cre amir incor sept ismail ismail ismail ismail aaa sill atiya yaser aug clarendon magdon magdon magdon magdon magdon augmentation augmentation augmentation augmentation augmentation augmentation augmentation tending xxt rrr porated loan skipped rre rre onwards 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model data data data data data data data data data data data data data data function function set set set set set set set set set set set training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number system system error error error error error error error error error error error error error error error error error error error error error error error error error results results results results information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance based based based based based based based based based based case case case case case case case order shown shown systems systems values probability probability probability probability probability probability parameters parameters parameters distribution distribution distribution distribution distribution distribution distribution distribution method approach approach approach approach approach approach approach approach pattern point single single single processing control control large large test test analysis analysis analysis analysis class class form form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper paper paper examples examples examples examples small size size work work work level current problems problems problems problems problems problems problems problems problems problems problems problems random high show show equation equation equation equation equation equation equation equation real real real real real average average states theory theory theory theory note experiments result result variables computation computation solution solution independent independent independent defined defined defined defined defined initial table table table table estimate standard standard standard standard standard terms machine machine machine range press press press press basis sample sample sample sample sample abstract abstract computational references stochastic due due ieee ieee procedure adaptive decision decision decision decision decision decision decision decision decision decision decision introduction introduction action complex estimation behavior statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical generated variance variance variance parallel cost cost cost cost search search search change change difference difference complexity measure prior bound bound bound cases cases required required multiple multiple tree distributed distributed distributed distributed distributed bayesian bayesian expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected expected make make make techniques techniques techniques techniques techniques techniques proposed correct correct correct correct correct correct correct observed observed errors errors errors errors errors errors finite finite minimum ing ing total total human respect performed times times elements elements means means means reinforcement optimization optimization optimization optimization potential potential feedback applications applications applications applications policy knowledge knowledge knowledge samples samples samples samples samples samples true true compared compared compared application application application application desired desired desired cross provide define compute compute proc proc proc proc proc proc proc perform experimental experimental related related constraints distributions distributions distributions equal approaches approaches approaches approaches approaches approaches approaches mit mit comparison comparison comparison comparison comparison comparison selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection proceedings institute loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss implementation technique consists individual individual represents framework framework framework framework framework cambridge directly directly directly additional additional view view estimates estimates estimates estimates estimates design design design design san san conference determine efficient efficient efficient efficient efficient efficient significant statistics statistics world world world world world speed estimated estimated estimated estimated estimated estimated increase produce bounds actual actual actual provided finally finally selected selected sampling sampling sampling sampling sampling sampling achieved discussion discussion normal normal normal normal normal describe describe describe describe describe denote limited limited limited assumption common implemented assumed theoretical require require require eds ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance future future degree including probabilistic pairs pairs underlying underlying underlying underlying underlying combination account unknown unknown unknown unknown unknown technology block block significantly significantly trials empirical empirical empirical empirical leads details details details pre depth early produced description denotes improved improved population recent advantage pair reported inference inference relevant highly previously unsupervised observations observations observations approximately approximately approximately subjects studies differential differential rl trans address evaluation evaluation evaluation evaluation evaluation evaluation bounded interval entire trial trial trial deviation wide wide predicted predicted alternative alternative correctly correctly demonstrate conclusion conclusion assumptions assumptions assumptions reduce reduce reduce conclusions depend clear clear practice encoding taking strong strong hard drawn demonstrated california intelligence turn variety minimizing user exist averaged targets base areas areas longer solving solving solving factors sequential sequential estimating estimating laboratory mathematical dept confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence implement remaining review correlated viewed interpretation influence densities lee forms sizes key earlier reasonable additive combining add iterative valid valid assigned existing dominance formulation instances sciences sciences determines determines extension extension candidate candidate candidate candidate tests reason reason selecting selecting aspects divided effectively literature literature literature literature efficiently genetic online summary repeated procedures procedures heuristic heuristic heuristic heuristic moore moore moore moore issue content criteria criteria criteria criteria criteria criteria criteria criteria criteria sci hold satisfy satisfy satisfy comp sampled sampled hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses policies satisfies situations parametric american poor requirements requirements requirements investigate relations recursive recursive recursive recursive recursive recursive recursive recursive recursive ml ml fewer fewer examine successive tech tech investigated combine combine combine structured comparable comparable analogous removed attributes induction math necessarily configurations equally changed ensure rank rank rank rank rank rank freedom academic improving utility utility utility utility utility utility utility utility utility utility utility defines defines synthetic synthetic synthetic inequality pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise theoretic theoretic theoretic trivial orientations variances variances variances variances analyzed adjacent adjacent adjacent adjacent explanation expensive london comparisons comparisons comparisons comparisons comparisons comparisons comparisons considerable drive purposes broad worst pool separately medical demonstrates demonstrates incomplete robustness requiring requiring questions evaluating evaluating populations applies understood understood embedded frequently incorrect incorrect rep ity requirement requirement requirement requirement requirement http howard howard howard howard partitioning resource ordered extensions pasadena datasets datasets datasets datasets june june univ cumulative sharing cor pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac www www formally modify acm resources databases ordering establish generality communications rational allocation allocation allocation allocation chance serves analyzing observing reasoning definitions effectiveness effectiveness effectiveness adequate mance contexts combines respective perfor consequences candidates competing chooses ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking treatment extensively impact inductive pen default treat learnable divide divide rigorous annals achieving kluwer tables july july july july suboptimal weiss weiss weiss weiss valiant valiant valiant conservative options remainder favor community formance impose blocking blocking approxi bounding allocated disadvantage met met considers ultimately scope proach topic speedup speedup alternatives alternatives nasa nasa sta likewise applicability applicability aaai aaai aaai aaai answers demonstrating served beam expense algorithmic august inconsistent cursive jet designs designs designs families families dominates outperformed drawing dom recursion russell russell russell russell illinois inherently rare seattle ally propulsion goldberg goldberg goldberg interpretations interpretations seed scenarios html sloan establishing rivest rivest rivest kaelbling kaelbling kaelbling evolutionary voice thing thresh steve steve modern artificially allocating blocked blocked excessive formulas jose jose obeys utilities utilities utilities favorably formulations ply imposing visits perspectives experimentation gorithms unequal unequal unequal formalized correspondingly niques grove allocate eval spacecraft spacecraft spacecraft dictated normality normality rect rect rankings rankings marcel dekker serially subdivided incor requested requested fax gov gov asa lihood public oak signifi parenthesis restarted lends bibliography columbus columbus tistical preclude uation pare dation scarce jpl jpl jpl norwell mately unavailable brunswick subsections selections selections selections selections selections usable adjacency adjacency adjacency confidences unnecessarily allocates til craig vanishingly dejong dejong hogg hogg macmillan cantly assert restarting additively additively additively soil dicted esis esis esis hypoth hypoth hypoth vali algorithmically transitive inance pas presume penetrate parisons 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model input data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure time set set set set set set set set set set set set set set set set set set set set set set set set set set set set training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number system system system system system system system system system system system results results results results results results results results results results information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance based based based based based based space weights weights weights weights linear linear linear linear linear linear case case case case case case case vector vector vector vector vector vector vector vector order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown systems systems systems systems values values values values probability probability probability probability parameters weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions method method approach approach approach approach approach approach single single processing large test analysis class class optimal optimal optimal optimal optimal inputs form form form form form shows algorithms algorithms simple simple paper paper examples small size feature work work methods features classification classification classification classification process level current trained trained problems random similar similar show show show section section section line line line line line line rule general general general general generalization parameter approximation approximation approximation approximation approximation approximation average average average theory theory obtained obtained term note experiments experiments result university university university university threshold research defined defined defined defined defined defined defined sequence initial initial constant constant table table table table estimate estimate standard computer computer terms node node science prediction presented map present present present low nodes nodes machine machine machine maximum press learn learn learn position abstract applied find find find find references references positive decision decision decision context introduction hand hand effect search search search search search search search search search search search search search search search search search search search search search tion complexity complexity assume assume assume assume assume classifier classifier measure measure measure prior learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen chosen chosen chosen higher higher previous previous theorem theorem theorem theorem theorem theorem bound cases required good good good good good good good binary binary binary expected fact fact fact correct classes total total total total total total total total total total regression regression regression computed computed computed respect respect respect sum sum sum sum sum performed eq eq eq eq called times elements elements elements elements elements mapping means factor factor potential potential potential natural natural natural natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications applications knowledge filter obtain obtain specific specific specific specific specific application application application series provide define define define define compute compute location location experimental experimental experimental goal related related constraints constraints equal equal approaches comparison comparison fields update words words words words loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss consists individual difficult final graph graph graph considered framework domain domain domain domain domain domain domain domain domain domain domain domain domain domain domain equivalent environment directly directly directly directly additional top top top top top top top top top top top stage stage stage stage efficient efficient efficient efficient classifiers classifiers full choice estimated estimated pages pages pages give give give weighted weighted weighted weighted weighted weighted weighted weighted weighted randomly actual provided finally finally simply achieved achieved describe describe describe arbitrary close close assumption complete complete complete complete complete complete complete proof finding finding finding finding finding common effective implemented assumed theoretical require journal end hypothesis hypothesis hypothesis instance instance instance instance instance instance instance instance simulated simulated probabilistic typically pairs pairs pairs pairs pairs smaller smaller needed combination combination combination combination combination combination combination combination combination reduced fully interesting testing york edge special special special special consistent call iterations making making experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert expert expert expert expert combined combined combined minimize minimize produced choose advantage pair pair pair pair element similarity similarity strategy strategy side relevant relevant relevant relevant relevant interest sufficient conventional conventional approximately approximately approximately correspond constructed constructed constructed constructed constructed constructed concept studied predicted occurs generally setting setting demonstrate demonstrate place greater assumptions operator competitive interactions measures numerical numerical numerical performs performs practice practice learns propose strong hard hard hard hard reduction turn minimizing user user user user user exist exist decrease decrease introduce question question denoted suppose suppose appears construct edges edges edges produces ways ways ann distinct distinct infinite remaining remaining remaining slightly consisting formed implies boolean expressed viewed viewed interpretation learner learner evaluated evaluate evaluate evaluate operations restricted restricted updated updated updated labels similarly partial partial reasonable performing expansion expansion expansion normalization normalization combining combining purpose remains initially symbol assigned assigned query query query query query query query query query query query query query query query recorded recorded combinations retrieval retrieval instances instances instances instances instances instances instances instances instances instances instances instances instances sciences prove discuss maximize specifically specifically domains domains holds holds identified identified uniformly computationally effectively latent schemes comparing receives summary notice quickly kind kind repeated link link showing interested interested interpreted interpreted classify classify classify strategies sci comp list list list list list list usual illustrates subsequent preferred preferred preferred preferred preferred deal routing receive receive employed access collection investigate ml ml ml ml ml ml links applicable boosting combine combine combine combine combine maximizing scores scores encode func notion notion removed removed attributes possibly necessarily analyze predicts adjusted queries queries queries queries queries queries rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank rank greedy greedy greedy greedy greedy greedy greedy greedy noted noted message message message finds finds defines mentioned indicating preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference preference inequality pairwise directed theoretic agreement agreement agreement agreement guaranteed fairly fairly majority majority majority briefly tractable tractable easier easier producing producing desirable desirable immediately opt opt read computers preceding researchers researchers robustness argument collected freeman relevance relevance relevance simulate leave documents documents documents documents documents documents documents documents documents cohen cohen cohen cohen requirement exhibits anti maximizes maximizes ordered ordered ordered achieves singer singer singer singer singer chose chose returns median semantic univ univ univ univ cumulative irrelevant naive naive naive naive naive consistently person person person person ordinary sort www www www www www assign formally tation princeton princeton appropriately narrow ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering ordering generality rational allocation allocation convenient convenient mail multiplicative imposed primitive primitive interpret obtaining obtaining observing observing imply effectiveness guide document document document document document document document document document document document schapire schapire schapire schapire schapire schapire schapire schapire entry expanded expanded regard vertices vertices ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking ranking claim membership foundations infer surprisingly omitted ahead ahead ahead ahead ahead ahead warmuth vertex park park agree agree agree agree agree agree agree inductive messages messages messages summarize receiving johnson robert assigns assigning assigning fusion empty empty approx approx converted converted outline minus listed listed listed email email email randomized presenting presenting incrementally adopt exception preferences preferences preferences preferences ideally freund freund freund imagine winnow tight remainder home home home home summarizes iff iff concentrated management labs searches searches searches picked noting sketch deleted meta worth weaker weaker enforce maintains page induces priority things things things things compu round round strict appearing appearing fortunately fortunately opti argmax prefer quantify agrees agrees agrees agrees ave accomplish concrete engine engine engine engine returned returned returned progressively triangle retrieved outgoing att littlestone littlestone littlestone repository losses losses totally william company company fair restrictive cyclic cyclic artificially statements statements shortly occurrences indexing completeness publishing mization permutations save incident availability tie named ranked ranked ranked ranked ranked ranked ranked ranked ranked ranked ranked ranked ranked thinking judgments judgments judgments judgments disagree disagree disagree manipulating picks syrup theor rationale behaved listing allocate ranks chine rankings sole sole retrieving retrieving orderings orderings orderings orderings orderings orderings orderings orderings orderings orderings gary prefers social precedes irl rounds rounds yoram easiest gathering preliminaries merits unavailable engines engines engines trec trec click click click click click click url abound florham ivi precede agreements oss universities universities advisable hanks underscores facets promoted institution 
#@Cohen_W,Schapire_R,Singer_Y,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural input input data data data data data data data function function function function function function function function function function function function function function function function figure figure figure figure time time time time time time set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number number number system system system system system error error error error error error error state results results results information information information problem problem problem problem problem problem problem problem models hidden hidden performance performance performance based space space weights weights weights weights weights weights weights weights weights weights linear linear linear linear layer layer layer case case case case vector vector vector vector order order shown systems systems systems systems systems systems values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise functions functions neurons neurons distribution method method approach approach approach approach approach pattern point single single processing processing processing control control control control local rate rate rate analysis analysis matrix matrix matrix matrix matrix optimal optimal optimal optimal inputs shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper small net work work methods methods methods methods methods methods methods methods step step step step field process process process process level trained problems problems problems random random similar representation show equation equation section general general parameter parameter parameter parameter approximation approximation states states theory theory gradient obtained obtained obtained obtained obtained obtained obtained obtained obtained term experiments university university university university university university computation solution solution research research independent initial initial initial initial initial initial initial estimate estimate estimate estimate estimate estimate estimate terms terms terms terms prediction prediction prediction prediction prediction direction map map map map map machine machine maximum maximum maximum press press press press learn nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs abstract applied applied applied back back back back back back back back back back back back back computational computational computational density density density density density density density density density likelihood likelihood likelihood references stochastic stochastic stochastic stochastic due ieee ieee adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction introduction complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation dynamic generated variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance recurrent tion change difference complexity complexity complexity complexity variable variable prior prior prior representations chosen chosen chosen previous cases multiple multiple conditions conditions conditions conditions represent represent represent distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations equations equations equations equations equations make techniques techniques techniques techniques techniques proposed proposed proposed errors finite minimum minimum minimum minimum minimum minimum minimum minimum ing ing total computed computed computed respect multi multi multi called elements global applications filter filter filter filter obtain vol samples cross cross series series compute rates posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior gain gain gain discrete equal equal equal equal equal mit comparison update update update update descent selection proceedings report department department department implementation individual individual advances advances joint represents represents represents difficult difficult exp exp exp exp scheme addition sequences sequences ai framework framework framework framework framework framework framework framework framework framework framework framework framework framework cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge directly view solutions estimates estimates design san detection conference determine requires statistics statistics statistics statistics estimated validation con produce condition conditional conditional entropy entropy actual actual finally finally processes selected evidence evidence evidence evidence evidence backpropagation depends simply simply simply measured covariance covariance covariance covariance covariance covariance covariance covariance feedforward feedforward describe fast corresponds complete predictions predictions rbf effective effective assumed supported role theoretical theoretical eds adaptation future makes makes makes development noisy reduced dynamical functional mlp mlp mlp mlp increasing consistent mode filters international depth choose run predict denotes denotes improved separate reported practical practical engineering engineering engineering sufficient compare compare conventional conventional conventional conventional conventional conventional conventional conventional calculated works correspond achieve achieve diagonal diagonal diagonal background improvement extended extended extended extended extended extended trial trial matrices matrices matrices matrices matrices matrices matrices matrices touretzky touretzky white conclusions accurate sutton sutton sutton sutton peak mateo suggest propose propose external intelligence min acknowledgements areas pro ways sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential mathematical confidence confidence multilayer multilayer physical involves involves choosing choosing choosing choosing choosing independently expressed stationary stationary squares estimator estimator estimator estimator estimator estimator estimator variation operations controlled updated updated updated updated updated updated updated updated updated updated updated updated updated approximations lee lee lee lee evolution approximated sizes updates performing measurements measurements measurements expansion expansion combining combining intervals purpose tracking interpolation filtering filtering filtering filtering filtering filtering foundation transactions transactions building perceptrons perceptrons eigenvalues batch illustrated automatic discuss mozer efficiency uniformly uniformly suitable differ encoded committee committee schemes mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay comparing situation essentially online online identity identity identity identity heuristic link link issue contribution contribution sin sin criteria strategies quantity quantity bar bar bar bar bar modular automatically principles attempt attempt approximating approximating software modelling extend bars employed simpler layered essential difficulty updating kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman relations environments estimators estimators integral hessian hessian recursive scalar reducing ideas tech tech links links fault analytically authors referred reliable workshop affect measurement coefficient generalisation implementations algo taylor explored academic academic multivariate integrate track navigation considerable choices desirable mation describing describing author varies readily effort peaks http weigend weigend hyperparameters proven serve serve boston unbiased unbiased unbiased median college www extensive rithm approximates controlling controlling establish plays extending communications difficulties overcome hyper hyper hyper hyper enhance hasselmo centroid entries entries modelled mlps mlps mlps mlps mlps eng eng eng eng cam cam cam cam assigning andrew sequentially sequentially sequentially sequentially sequentially sequentially yale outperforms constitute propagating propagating comparative acceptable covariances covariances covariances covariances covariances ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf constitutes constitutes constitutes england england england guess scenario jacobian jacobian toy grouped eliminating eliminating scope integrals cation esti placing placing mea modal accordance attributed firstly house suffers seattle svr trol arrives governing degenerate fair niranjan niranjan niranjan niranjan niranjan niranjan south corn tical facts statements merit formulas bootstrapping percep percep ard expresses putational ample recursire statis multiplications buntine buntine burden maximising regularisation regularisation regularisation regularisation regularisation regularisation regularisation regularisation regularisation regularisation regularisation regularisation puted cued adopting freitas freitas freitas freitas freitas freitas freitas freitas rogers rogers analysed earliest circumvent datum datum niques seventh maximise expressing beats estima minimising validate embodies nical overcoming optimise integrations decoupled reformulated gee gee gee gee gee gee optimised singhal singhal singhal singhal committees vastly cesses scholarship wll shah shah surveillance shalom shalom shalom shalom shalom subsections tron gelb gelb gelb gelb initialise decoupling decoupling trons frameworks lal feldkamp feldkamp judiciously imax studentship puskorius puskorius provement termine occasions surement circumstance identifi 
#@Gee_A,Niranjan_M,de-Freitas_J,
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#*learning learning model model model model model model model model model model neural data data data data data function figure figure figure figure figure figure figure figure time set training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number error state results results information information information information information information information information problem problem problem problem problem problem based based based space case case case vector order order order order systems probability probability probability probability probability probability probability probability parameters noise noise distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method approach approach point large local test analysis analysis analysis matrix matrix matrix optimal optimal optimal optimal optimal algorithms algorithms algorithms algorithms algorithms simple paper work methods methods classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification problems random random random random similar similar similar similar similar show show equation section section real approximation approximation approximation average theory theory theory theory result result university threshold computation computation independent log log log defined defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence standard standard standard computer terms distance distance science left left left presented presented presented present low machine press continuous sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied applied density properties likelihood likelihood likelihood references component due due ieee ieee important important important mixture mixture mixture mixture mixture mixture introduction estimation estimation estimation estimation estimation statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical generated generated generated generated generated generated cost lower measure measure measure measure measure measure measure measure measure measure measure measure measure measure prior prior chosen higher part center theorem theorem theorem theorem bound good good spike represent tree tree bayesian markov markov markov markov markov make techniques techniques length length length finite finite finite finite finite finite minimum resulting resulting ing computed computed computed computed respect sum called elements means means natural natural applications applications applications applications applications applications applications knowledge obtain artificial relative relative specific specific samples samples samples samples samples samples samples samples true true true application application application application cross cross cross cross cross series provide objects proc distributions distributions distributions distributions distributions discrete discrete discrete power approaches comparison connection connection source source source source source source source source source source source source source source source source source source source source source source source source source source modeling institute code code individual individual individual joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences considered considered computing computing experiment experiment directly directly estimates design efficient statistics world estimated estimated estimated give give coding coding coding randomly randomly conditional clustering clustering clustering clustering clustering clustering clustering clustering levels types entropy entropy entropy entropy provided processes selected nature nature nature biological biological biological biological discussion arbitrary denote limited assumption assumption assumption complete complete short short short implemented require end easily needed testing ratio character character character character york york york head database empirical empirical empirical empirical empirical language representing details max max max pre direct bottom bottom bottom bottom supervised depth combined choose choose choose sources sources sources sources sources sources sources description denotes improved discussed robust typical typical typical typical typical typical typical typical typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity practical apply apply hierarchical hierarchical hierarchical trees sense sufficient highly unsupervised unsupervised unsupervised unsupervised unsupervised yields definition symmetric symmetric symmetric improvement exists suggests extended extended matrices loop generally place minimal minimal assumptions assumptions differences measures measures measures measures measures clear clear asymptotic suggest propose drawn proportional min min relationship iii introduce introduce characters annealing explicit explicit explicit explicit explicit construct construct generating estimating estimating estimating estimating estimating describes segments sensitivity category explicitly explicitly explicitly averaging text text text unique unique events blocks john john family family family independently independently focus approximated sizes completely key remains distances distances distances string string symbol symbol norm transactions transactions existing usa extension specifically candidate priors discussions compression compression compression compression compression compression compression compression compression differ maximal symbols identify identify efficiently fine fine fine fine fine notice notice success split dis dis dis symmetry sci gray generalize quantization hypotheses satisfies acknowledgments trains wiley wiley access integral limitations divergence divergence divergence divergence divergence divergence divergence helpful existence existence statistically cover fundamental notion naturally naturally naturally naturally illustrate illustrate illustrate illustrate thought greedy greedy greedy academic art generates generates detected grouping motivated synthetic established languages languages languages languages languages languages languages languages languages asymptotically asymptotically asymptotically asymptotically pairwise pairwise pairwise pairwise pairwise theoretic theoretic costs analytic turns lin lin lin lin tive closer widely protein protein protein protein protein protein precisely ran ran ran immediately mation potentially universal universal universal universal universal universal universal acad english english depicted depicted author meaning meaning alignment orders passed remove synthesis synthesis rely mod measuring measuring measuring chose comments lim merging merging merging merging merging merging merging merging merging merging initialization classifying arguments rational kullback smith smith smith smith accepted alpha alpha stated tishby tishby tishby tishby tishby tishby belong optimally alphabet alphabet alphabet natl repeat repeat sion encountered guarantees sides sim thomas centroid similarities similarities similarities similarities similarities similarities israel emergence express offer proteins proteins proteins proteins proteins proteins proteins sons sons discovered empty consecutive linguistic suffix suffix suffix compressed largely numerous leibler randomized randomized markovian markovian markovian markovian markovian markovian markovian markovian axe theorems german beta argue translated exponent exponent distri shannon shannon dominated books categorization memoryless amino amino esti unpublished manuscript bution ergodic appearing appearing appearing unbounded identifies justification agrees european european ongoing families families families families breast suffers utilizes king unreliable substitution tance acid fol ben acids merged vanishing capturing occurrences jerusalem drawbacks entropies entropies entropies entropies cations appli argmin hebrew touch darker traditionally lens bernoulli puted jensen ixl ixl clus lowing provably provably convexity transcription french french eval quences cities particu agnostic agnostic agnostic agnostic agnostic agnostic agnostic agnostic agnostic agnostic agnostic alternately quence integrand entails absolutely lacks kinase kinase kinase kinase imal als als als bachrach bone ingredients ingredients ingredients danish danish eft ingredient tering derlying uation asymp crete divergences succeeds markovjan feet eling lyl lyl tances ual bined preparations sixteen edit domly istic determin grace bachtach assertion individ larly huji naftali preparing invented eighteen eighteen iim iim inves italian italian 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#@El-Yaniv_R,Fine_S,Tishby_N,
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input function figure figure figure figure figure figure time time time set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number system system system error error error error state results results results results results results results results information hidden hidden hidden based based based space space space linear linear linear linear linear linear linear layer case case case order order shown systems probability probability probability probability probability noise noise weight neurons neurons neurons neurons neurons distribution distribution recognition approach point point point point point image image image image image image image image image processing processing large local local rate rate rate rate rate rate rate rate rate rate rate rate test test test test test test test test test analysis analysis analysis inputs shows visual examples examples examples examples examples examples examples examples examples examples examples small size size size size size task step process process process trained trained trained trained trained trained trained trained trained trained problems random similar similar similar architecture show show equation equation equation fixed line line images images images images general general general generalization real real real average average theory obtained obtained obtained obtained obtained term term term experiments threshold threshold threshold computation computation solution solution solution defined defined table table table table table table terms distance distance distance distance science left low sets sets motion maximum maximum range position position components components nonlinear outputs outputs abstract applied applied back find references component component important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture complex estimation statistical statistical variance variance variance variance cost variable assume lower prior chosen previous theorem binary conditions distributed distributed proposed proposed scale finite tasks total human human human human performed called times orientation orientation orientation orientation orientation orientation orientation orientation orientation knowledge obtain obtain obtain obtain original relative application perform goal goal goal related approaches approaches approaches comparison comparison comparison comparison connection train report technique individual difficult bias bias bias layers layers layers layers layers layers hinton curve view view view view view view view view view detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection conference approximate estimated conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional iteration nature depends discussion technical tested tested tested tested tested tested tested tested tested close close close close close corresponds nearest nearest effective face face face face face face face face face face face face face face face face face face face face 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generalized gate gate gate gate gate gate gate constructed reduce reduce reduce reduce bayes learns constrained constrained constrained reduction reduction reduction reduction solid regularization assuming decrease minima produces label label vertical vertical sensitivity dimensionality scales springer quality versus versus letters extracted extracted extracted extracted independently independently reconstruction reconstruction estimator estimator estimator evaluated evaluate evaluate evaluate evaluate evaluate approximated partition smoothing dashed reduces purpose false false false false false false false false false false false iterative tracking calculate faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces degrees combinations combinations color vapnik vapnik vapnik plotted automatic prove gating gating gating compression poggio poggio poggio detect detect detect detect detect detect ten composed composed verlag classify classify manifold manifold generative notation modular modular modular modular computes thresholds jacobs jacobs jacobs extend extend extend extend camera camera camera estimators estimators behaviour giving detectors detectors detectors combine combine subsets front front front front front front front front precise detector detector detector detector detector detector detector detector detector separated art consist histogram scenes orientations nowlan independence benchmark processed processed shared controls consequence separately limits collected collected collected cmu cmu cmu cmu cmu remove berlin geman geman geman phone adjust windows windows windows representative www fix fix databases databases databases reconstructed reconstructed impossible turned turned turned turned turned turned turned turned turned ylx ylx enhanced published performances equals equals belongs counter counter counter counter counter counter counter counter ensembles 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#@Bernier_O,Feraud_R,
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#*network network network network network network network network network network network network network network network learning model neural input input input figure figure figure figure time time time time set set set set set networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number system system system system error error error error error error error error state state state state state state state state state results information information information information information information information information information information information information information information information information information information information information information information information information information problem problem models models models hidden performance performance performance performance performance performance performance performance performance performance based space space linear linear linear linear case vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown shown shown shown shown shown systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise distribution distribution distribution distribution approach control large local rate rate rate rate rate rate rate matrix optimal optimal optimal inputs form shows shows shows shows shows shows algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian paper paper paper examples small size net net work work work work work methods methods fig fig fig fig fig fig fig fig fig fig level level level level level level current problems random memory similar show show fixed fixed general real real states states theory obtained obtained obtained experiments dimensional university university university threshold variables variables variables variables variables variables variables variables variables variables variables computation computation research research research independent independent found found sequence estimate estimate standard standard standard computer computer science science science presented presented present low low low low low low low low low low machine machine machine sets sets sets maximum press press outputs outputs outputs abstract back back back find find computational density density density density density density density density density density references due ieee procedure 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#@Frey_B,MacKay_D,
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input input data data data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure time set set set set networks networks networks networks training algorithm algorithm algorithm number number state state state state state state state state results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units 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probability probability probability probability probability parameters parameters parameters noise noise noise noise noise noise noise noise noise noise weight weight weight functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition method approach pattern point image image image image image image image image image large large large local local local local local local local local local neuron rate analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix inputs inputs inputs form simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian 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multiple multiple multiple spike spike long long conditions conditions represent represent distributed distributed distributed distributed distributed bayesian markov make make fact correct correct correct probabilities observed simulations ing total respect respect performed eq eq means factor factor factor factor factor factor factor factor factor factor factor factor factor natural natural natural natural global global em em filter negative negative negative specific samples samples represented true true application define compute compute compute compute objects objects perform perform perform perform perform eye eye eye determined posterior posterior posterior posterior posterior posterior posterior posterior constraints connected connected connected distributions discrete cortical equal equal equal equal approaches mit mit accuracy contrast connection connection nets report consists connectionist difficult difficult bias layers layers layers addition maps maps maps maps maps maps cambridge cambridge equivalent hinton hinton hinton hinton hinton hinton hinton hinton additional additional additional view view top top top top top top top top top top top top top top top effects effects effects determine full requires approximate speed vision con coding randomly developed area area product selected iteration iteration nature depends depends sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply simply achieved discussion technical describe describe corresponds corresponds surface surface predictions effective implemented implemented assumed role theoretical require main main eds square pixel pixel pixel easily makes makes makes including including probabilistic probabilistic typically pairs pairs combination combination combination account jordan edge consistent leads squared iterations filters direct inhibition bottom bottom bottom depth depth early decay idea combined produced run added added sources correlations correlations correlations advantage separate typical lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral introduced quadratic quadratic quadratic quadratic quadratic quadratic hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical sense inference inference inference inference inference inference inference inference inference subset subset sejnowski sejnowski array array unsupervised unsupervised calculated works module tions trans sparse sparse mixtures symmetric symmetric grid entire parts expression lead scaling deviation wide derivative correctly correctly locally locally locally white boundary column setting strength hebbian hebbian reduce segment valued valued valued depend interactions interactions interactions interactions interactions interactions sigmoid modules modules modules performs practice constrained solid turn turn turn assuming assuming derivatives derivatives manner manner acknowledgements boltzmann boltzmann suppose appears longer index ways factors factors factors factors factors factors generating vertical dept implement multilayer infinite involves involves involves belief belief belief belief belief belief belief consisting adding equilibrium equilibrium equilibrium equilibrium gaussians gaussians shift select formation formation formation formation formation correlated viewed codes controlled ocular lee lee activities similarly partition partition partition partition partition key slow dashed classical convex add penalty penalty intermediate visible visible visible kohonen kohonen perceptual perceptual perceptual perceptual perceptual perceptual perceptual activations priori dominance bell extension mozer variations black major major columns determining selecting selecting middle middle uniformly driven delta delta delta delta delta mackay online online identity orthogonal orthogonal excitation soc notice quickly showing contribution contribution follow generative generative generative generative generative generative generative hold comp gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs simplified simplified dot dot dayan nips nips reach reach attempt consisted overlapping disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity neighboring neighboring parametric powerful layered layered layered difficulty exponentially replaced divergence mass mass biases biases periodic rise giving detectors detectors detectors detectors detectors detectors detectors incremental proved affect func topographic topographic topographic topographic topographic topographic topographic phases plausible plausible generalisation generalisation eyes thought subsets aspect assumes assumes separated separated 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#@Ghahramani_Z,Hinton_G,
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#*network network model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data function function function function function function function function function function function function function figure figure figure figure figure set set set set set set set networks networks networks networks networks networks networks training training training algorithm algorithm output output output output output number error error error state state state state results results results information information information problem problem problem models models models models performance based space weights weights linear linear case case vector vector vector shown systems systems systems values values values values values values values values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method method method approach approach approach pattern point processing processing control large local rate rate rate rate rate rate rate test matrix matrix matrix matrix matrix inputs inputs form form form shows shows shows algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper small work work methods methods methods methods methods points points points points points classification classification process process process process process process process process process process process process process process process process process process process process process process process process process process process process process process level level level level level level level level level level current structure problems problems problems problems random similar similar similar similar similar show equation equation equation equation equation section section fixed fixed fixed fixed fixed line line vectors general general real approximation approximation average average average average states obtained obtained obtained obtained obtained obtained term term term term term note note note dimensional result university university university university university university variables variables variables research research research independent independent independent independent log log log log log log log log log log defined found standard standard standard standard standard standard standard standard standard standard computer computer terms science science prediction prediction prediction prediction left present maximum press press press press components components components components outputs sample sample sample sample sample sample sample sample sample sample sample sample abstract applied find find find convergence density likelihood likelihood likelihood references component component component stochastic stochastic stochastic mixture mixture mixture mixture statistical generated generated variance variance variance variance variance variance variance variance variance variance variance complexity variable variable assume prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen required good good distributed bayesian bayesian expected equations equations equations markov markov markov make make fact fact proposed length length correct observed scale scale finite finite simulations regression regression regression regression regression regression regression regression regression regression regression computed sum means dimension made made natural natural natural natural natural global global global obtain obtain obtain obtain obtain obtain obtain negative negative samples samples samples samples true true true provide define compute rates rates rates rates perform goal posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions power mit mit steps larger contrast dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent proceedings report report department department department implementation advances advances joint joint joint difficult difficult exp exp exp exp exp exp exp exp addition framework cambridge cambridge cambridge computing computing computing experiment curve curve efficient approximate approximate statistics statistics free free world validation give con conditional lines processes processes processes processes processes processes processes processes processes iteration depends depends sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply achieved covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance technical technical technical increases increases group group denote denote denote tested close inverse assumption assumption assumption corresponds predictions predictions predictions predictions predictions predictions predictions predictions predictions short effective implemented assumed assumed assumed eds eds square easily makes makes including probabilistic typically pairs needed functional unknown fully jordan ratio consistent leads representing representing iterations iterations iterations making making making making making stored international added discussed discussed discussed discussed advantage robust separate introduced moving hierarchical hierarchical sense inference subset varying approximately approximately tions smooth mixtures background evaluation chain chain chain interval williams williams williams williams williams williams grant deviation deviation deviation deviation deviation deviation deviation derivative matrices matrices alternative hybrid touretzky demonstrate place place place place reduce segment conclusions practice practice constrained taking demonstrated solid solid turn turn turn min introduce manner denoted acknowledgements pro monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo written longer confidence explicitly explicitly averaging linearly infinite remaining easy easy develop adding adding gaussians gaussians gaussians predictive predictive shift approximations centered updates updates updates updates dashed fitting fitting add add expect thesis coordinate plotted plotted illustrated uncertainty uncertainty discuss mozer mozer priors extra suitable literature efficiently mackay mackay plots notice allowing sin gibbs gibbs gibbs gibbs gibbs involved sampled sampled usual usual usual ill approximating satisfies bars bars bars carried parametric parametric parametric create collection replaced integral integral dotted graphical giving analytically matched removed neu examined predicting predicting quantities assumes art ith multivariate multivariate phd synthetic synthetic neal neal neal neal ment agreement multiplication tractable handle reasons considerable incorporate ran bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop immediately inversion separately english toronto toronto toronto localized explained offset offset incorporated http http hyperparameters hyperparameters prevent logp kinds sophisticated conditioning specifies representative feasible generator generator generator oxford conditioned conditioned approximates controlling accepted observing ral settings intuitively responsible carry motivation predictors studying paul uni hasselmo treatment treatment treatment treatment treatment treatment agree likelihoods papers street aston aston aston aston inferred alternating rejection rejection rejection rejection isotropic isotropic sinusoidal reject adapting adapting argue distri diag distribu regulation crosses challenging depicts paris cation indexed crossings book placing mcmc mcmc mcmc ignoring gorithm bution handled expense const christopher christopher house dcs identically val proposal proposal wavelength wavelength rasmussen rasmussen rasmussen petsche discarded ref goldberg goldberg 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#@Bishop_C,Goldberg_P,Williams_C,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure time time set set set set set set set set training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number error error error results results results results results results results results results results results results problem problem problem problem problem problem models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based space space weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case case vector vector vector shown values values values values values values values values values values values values values values values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight weight weight functions neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach approach approach approach approach approach point point single single single single control local local rate test test test test patterns patterns class class class class class optimal optimal optimal optimal optimal optimal form form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper examples examples examples examples examples small small small size size size feature work work task task task task task task methods points features features features classification classification classification classification classification classification process process current trained problems random random random random random random random response similar similar show show show show equation equation section section section section section fixed fixed fixed line rule rule rule rule general parameter parameter parameter parameter parameter parameter real real real real average average average average average theory theory note note note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional university university threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables variables research research independent independent independent independent independent found found found found target target constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard computer science prediction prediction prediction prediction prediction present phase phase phase machine machine machine sets maximum maximum maximum maximum range press press learn learn learn learn learn sample sample sample sample sample sample abstract find find find find find find find find find convergence convergence properties likelihood likelihood likelihood likelihood likelihood likelihood references due positive positive positive positive positive positive procedure procedure important important important important context context context context introduction complex hand statistical statistical effect generated generated generated variance search search search search search search search change difference difference variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable assume assume assume classifier classifier classifier classifier classifier measure measure word learned chosen chosen chosen chosen chosen cases type good good good good good good good good good good good binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary expected expected fact fact fact fact techniques techniques techniques region region correlation correct correct correct correct correct correct correct observed observed observed observed observed errors tasks tasks tasks total computed computed computed computed respect performed called times times means factor made made study study study study study study study knowledge em em em em em em em em em em em em em em negative negative relative specific specific specific specific specific samples samples samples samples true true true compared compute compute compute proc proc proc active active determined experimental experimental goal related distributions equal equal power power power approaches approaches approaches accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison comparison larger contrast update update support support selection selection morgan report report institute department loss version version version version technique technique individual individual difficult final bias scheme considered considered considered considered cambridge domain domain environment directly directly directly directly directly directly directly curves estimates estimates estimates estimates estimates limit san conference determine determine efficient classifiers classifiers classifiers full choice significant world world world basic basic basic basic pages pages pages produce weighted weighted weighted weighted randomly randomly conditional developed developed levels criterion actual finally finally iteration nature nature depends sampling simply simply simply simply simply simply simply achieved covariance covariance covariance increases increases denote denote denote denote denote denote denote fast limited assumption assumption assumption finding finding finding effective assumed assumed assumed assumed generate generate supported theoretical main main square ability hypothesis hypothesis hypothesis instance instance instance makes makes noisy noisy including including including fit fit fit kaufmann probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically typically pairs pairs smaller underlying unknown fully interesting interesting testing significantly significantly york york consistent trials trials empirical empirical empirical empirical empirical principle language leads details details call numbers iterations direct direct international normalized normalized idea idea idea choose choose choose choose choose choose choose run light predict predict predict predict perceptron denotes advantage robust robust separate takes takes practical practical apply strategy strategy quadratic sense sense sense dimensions varying compare compare compare compare previously unsupervised observations works works solve correspond correspond converge separation symmetric interval sensitive sensitive sensitive entire grant exists exists concept suggests deviation wide wide width generally generally generally setting setting conclusion assumptions reduce conclusions conclusions valued valued valued depend depend depend accurate designed clear faster faster faster practice practice practice practice practice mateo suggest taking strong hard hard characteristics drawn drawn proportional labeled assuming minima question question denoted suppose appears appears construct produces generating generating generating estimating estimating label label distinct modeled confidence linearly linearly remaining easy easy slightly slightly belief develop applying predictive expectation expectation expectation expectation versus select select select family family independently independently independently independently expressed correlated interpretation controlled restricted restricted understanding sizes margin similarly converges updates allowed past sign sign sign reduces fitting purpose iterative remains remains valid initially construction construction expect expect expect figures priori perceptrons instances determines discuss discuss specifically domains partially reason determining importance uniformly uniformly society differ divided successful efficiently reached traditional traditional quickly quickly quickly graphs induced heuristic success interested interested stopping superior issue issue contribution classify criteria notation involved involved vary write providing minimizes minimizes observable maximization maximization maximization maximization maximization predictor predictor received attempt illustrates bars simpler parametric parametric parametric parametric collection exhibit difficulty difficulty difficulty difficulty difficulty difficulty detail replaced issues ml fewer fashion giving rest analytically reliable root workshop workshop statistically understand understand understand fundamental notion attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes concepts concepts concepts concepts concepts plausible plausible plausible plausible plausible necessarily predicting predicting predicting predicting predicting predicting predicting predicts predicts predicts predicts extremely extremely extremely illustrate equally perfect perfect perfect thought obvious noted noted noted ith baseline detected attempts synthetic synthetic sentences averages optimum mentioned percentage pairwise separable separable trivial trivial trivial crucial distinguish derivation guaranteed phenomena phenomena fairly fairly majority independence briefly briefly correction reasons turns widely constructing located probable begin attribute attribute attribute attribute attribute read incomplete qualitative qualitative meaning robustness robustness robustness apparent empirically parameterized experimentally passed measuring measuring characterize maximizes occurrence qualitatively achieves inherent inherent display expectations deviations deviations deviations deviations deviations irrelevant representative representative uncorrelated redundant sort proportion proportion writing mistake mistake assign princeton acm perfectly perfectly controlling impossible grows royal chance significance significance adjusting simplify determination biased observing methodology methodology modifications modifications optimally exceeds nonparametric degradation substituting repeat performances ranging predictors studying equals surprising surprising surprising dominant searching scheduling chooses surprisingly omitted omitted repeatedly draw concentration valuable dempster onr ence rubin rejection conjecture tradeoff lit lit lit lit lit covariances covariances covariances covariances classic classic examining winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow conservative beta beta unseen iff concentrated concentrated intuition thick thick careful statistic statistic rough conversely laird voting tij indication dramatic drops rewrite differing signs signs supporting nec nec observables styles simplification parameterization parameterization const const const ave attempting attempting blum cornput cornput drawing concern harvard illinois unreliable partly separates conditionally conditionally conditionally conditionally restricting littlestone artifact nontrivial minsky fair fair relaxed indirectly iterate cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia cia experimented simon degrades degrades degrades urbana urbana degrade unobserved richer omit omit lid separator separator separator separator separator separator separator separator postulated thinking differed henceforth inferences subsample grove grove grove grove grove roth roth roth roth roth cov cov highlights indicative champaign restarts appeal postulate postulate postulate shed dan visiting depart attainable fined adam deviates deviates annu annu expressive expressive originates knew spelling spelling abound reestimate paperr postulates departs departs advocate ota desirability meaningfully imp calendar promoted characterizations nail surpasses 
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#*model model model model model model model model model model model model data data data data data function figure figure figure figure figure figure figure figure figure set set set set set set set set set training training training training training training algorithm algorithm algorithm algorithm algorithm number number error error error error error error error problem problem problem problem problem problem problem problem problem models models performance performance performance based based based based based space weights linear linear linear linear linear linear linear linear linear linear case case case case case vector vector vector vector vector shown shown shown probability probability probability probability probability probability probability parameters parameters parameters parameters functions functions unit distribution method method approach approach approach approach point point large large rate rate test test test test test test test test test test analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class matrix optimal form shows shows shows shows shows shows shows shows shows shows gaussian gaussian gaussian gaussian paper paper paper paper examples feature work work task methods methods methods step step points points classification classification classification classification classification classification classification classification classification classification classification classification classification problems problems problems problems random similar similar similar similar similar show show section section section section section section rule rule rule rule rule rule rule rule rule rule rule rule rule vectors general general generalization approximation average average average states gradient obtained note dimensional university university university university university threshold threshold threshold threshold threshold threshold variables solution solution solution research independent independent independent independent log log log log log log log log log defined table estimate estimate standard standard distance distance science left frequency maximum maximum press learn basis nonlinear sample abstract applied applied back find find find find find convergence convergence density density density likelihood references references due procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure decision decision decision decision decision decision decision decision decision decision mixture mixture mixture introduction action generated generated generated tion assume classifier classifier rules rules rules rules rules rules rules rules rules rules chosen part multiple long distributed expected equations equations equations region probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed errors scale simulations resulting resulting classes classes classes classes classes classes classes classes classes multi times regions optimization optimization optimization optimization optimization optimization optimization optimization natural natural study obtain relative provide define compute rates rates rates rates rates perform perform goal posterior constraints discrete approaches mit larger support support support report report department department department version joint final bias bias addition ai ai ai cambridge equivalent equivalent equivalent hinton additional estimates estimates estimates estimates estimates estimates estimates estimates estimates top top classifiers classifiers classifiers classifiers classifiers classifiers requires requires statistics statistics statistics free estimated estimated estimated give give give derived weighted conditional criterion criterion criterion area nature sampling discussion discussion covariance covariance technical technical increases close close nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest common common supported supported square makes fit fit simulated simulated simulated typically pairs combination block special consistent uniform uniform leads details numbers numbers max max max max max max max max max max bottom experts attention minimize description predict predict population discussed improve exact advantage pair pair apply apply apply strategy include include subject subject machines machines machines quadratic sense sense engineering dimensions sufficient compare observations observations observations observations works solve match observation observation bounded grant grant constructed constructed constructed scaling matrices boundary boundary boundary reduce neighbor neighbor neighbor bayes bayes bayes bayes clear performs california proportional minimizing start relationship areas suppose appears pro derive longer winner ways estimating ann involves gaussians events expectation national squares forms margin suggested converges updates discrimination key reasonable measurements combining event iterative iterative boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries boundaries distances foundation david coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling eigenvalues weighting sciences prove discuss discuss discuss specifically coupled coupled partially neighbors discussions efficiency closely uniformly score score plots tend orthogonal ten ten ten ten notice procedures procedures prob prob prob prob prob dis return classify satisfy sampled predictor predictor predictor acknowledgments situations simpler issues discriminant discriminant discriminant discriminant helpful examine examine matches fashion fashion giving giving history combine decisions eigenvectors math rank friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman friedman versions panel panel panel panel panel panel panel panel panel panel panel multivariate consist neal preference pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise answer briefly worse comparisons comparisons comparisons comparisons stanford stanford stanford stanford satisfied easier organized producing bishop bishop arise separately separately calculations optimize optimize optimize toronto toronto arises incomplete qualitative argument requiring fourth improvements substantially tional lack item share gains ture suited marginal datasets median progress sharing globally benefit proportion assign formally guarantee modify extending kullback kullback biased intuitive carry repeat evaluations predictors holland holland sphere entries treatment modelled modelled membership membership offer offer canada thresholding thresholding acknowledge robert drop achieving leibler leibler equivalently job tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani tibshirani pointed preferences covariances guess adjustment shaded mutually argue favor hastie hastie hastie hastie hastie hastie hastie hastie hastie pij pij compatible compatible thresholded paired paired paired paired win win isi confusion tij tij tij tij tij tij pop lda lda lda lda lda lda lda lda lda lda lda lda preprint council crude vii vii vii vii designs jointly wins wins wins wins wins wins medicine settle vote resolved scenarios approaching statist randomness accounting binomial binomial binomial compromise modern translates sep dij dij dij health applica nice rij rij rij rij rij rij rij rij rij rij rij rij rij gij gij neigh observes ample terry terry terry terry terry terry parentheses parentheses unequal panels roots neighbour neighbour neighbour bradley bradley bradley bradley bradley bradley ulation neighbours neighbours resolving beats looked trevor trevor roi geoff pling bor nij nij nij nij nij nij nij radford cedure closeness discriminants memberships cou rob ili neighbout institutes ida ida ida precisions caption ports logit logit dms rii ris putationally gausstans gausstans jerry jerry jerry hatched arate recompute burdensome tempt 
#@Hastie_T,Tibshitani_R,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure time time time time set set set set set training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number error results results information information information problem problem problem problem performance performance performance based based space space space space space space space space weights weights case vector order order order systems probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters unit unit distribution distribution recognition method method approach approach approach approach approach approach approach approach approach pattern point point point point image image image image processing control control rate rate rate test test test test test test test test test test test test test test analysis analysis analysis analysis analysis class matrix matrix matrix optimal shows simple paper paper paper small size work work fig step step points process structure structure structure structure structure structure structure structure structure structure random random random random equation section fixed fixed fixed line line line line line line line line line line line line line line rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors images images parameter parameter parameter parameter real approximation approximation average average theory theory gradient gradient obtained note experiments experiments experiments experiments dimensional dimensional dimensional dimensional variables computation research defined defined sequence constant estimate estimate distance distance distance distance distance node node node node node science science left phase phase phase nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets sets maximum maximum maximum press learn learn learn components components continuous sample sample abstract applied applied applied applied convergence convergence references stochastic due due ieee procedure adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision introduction hand hand hand hand dynamic generated variance variance cost search change energy energy difference difference complexity variable variable rules rules rules rules rules rules measure measure measure learned chosen higher good represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree expected expected expected expected fact proposed proposed probabilities probabilities probabilities probabilities probabilities probabilities observed errors errors scale scale scale scale minimum minimum minimum resulting ing sum sum performed elements means optimization optimization optimization dimension made obtain obtain original original specific samples samples samples samples samples samples represented cross cross cross cross rates active experimental related constraints distributions discrete mit accuracy update update source source source source source source source source source source source source selection version advances represents final exp exp exp exp exp exp exp exp exp exp scheme scheme addition maps experiment experiment experiment additional additional transition transition transition transition trajectory top stage determine determine requires choice free free world pages condition channel weighted clustering clustering clustering clustering clustering clustering developed criterion criterion criterion velocity velocity types entropy entropy entropy entropy entropy entropy entropy path actual measured measured discussion covariance increases complete stable nearest nearest supported require adaptation adaptation cluster future degree degree degree degree makes development development development fit probabilistic probabilistic probabilistic reduced account jordan technology significantly segmentation segmentation segmentation segmentation segmentation special structures structures empirical principle principle principle principle principle leads window idea minimize minimize run sources sources sources sources sources description denotes denotes denotes denotes denotes denotes resolution separate typical apply introduced introduced identical identical identical pixels hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees trees trees trees trees trees trees trees trees trees trees trees sense dimensions dimensions unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised yields yields match address positions positions channels channels grant exists expression suggests deterministic deterministic deterministic deterministic clusters clusters clusters setting demonstrate runs flow flow conclusion minimal minimal reduce trajectories neighbor editors differences differences measures measures learns encoding encoding propose largest characteristics demonstrated labeled start min min min min min iii introduce annealing annealing annealing annealing derive derive edges sequential describes transitions transitions transitions changing changing slightly gaussians gaussians minimization minimization minimization quality letters letters stationary stationary stationary stationary stationary stationary detailed detailed detailed densities labels evolution completely partition partition partition partition partition partition partition calculation expansion add tracking tracking tracking tracking distances distances assigned assigned foundation topology topology topology topology topology topology topology transactions priori color assignment determines uncertainty maximize mozer successfully simplicity efficiency capable differ encoded presentation detect miller miller miller orthogonal induced induced induced induced split split sin gray gibbs minimizes quantization eigenvalue highest neighboring deal deal receive extend presents origin carried wiley updating environments environments optimized optimized issues divergence divergence fashion ideal ideal ideal decisions decisions root root hierarchy hierarchy hierarchy cover cover analogous gradients gradients gradients naturally adapt necessarily prototype greedy observe switching switching switching amari simplest grouping grouping defines established established formula costs costs costs costs costs costs costs costs growing starts reasons sections preprocessing leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves leaves controls controls acknowledgement opt gradually depicted demonstrates demonstrates fluctuations robustness explained questions fuzzy empirically incorporated treated http calculating prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes switch partitioning partitioning summarized reaches extracting parent parent parent parent parent parent parent parent parent extensions germany inherent leaf leaf leaf leaf leaf yielding merging merging merging merging distortion distortion distortion distortion distortion distortion distortion distortion contribute www www assign lagrange lagrange lagrange restrict fix angular rotated partitions addresses multiplier multiplier multiplier kullback kullback ments overcome overcome held held held held held balance splitting splitting splitting generalizes performances combines introduces sphere belongs uni uni thomas centroid centroid centroid israel reveals augmented sons alternatively balanced parents parents assigning sequentially leibler equivalently recursively july employs arg tradeoff assignments assignments assignments assignments assignments assignments assignments assignments assignments german mismatch increment guided proach buhmann buhmann buhmann buhmann buhmann buhmann attached attached attached descending universit rotating refined september rose rose rose rose topologies topologies topologies resp resp dim dim dim institut nested confirm confirm solvable marcus petsche discarded fox informatik evolves drifting bonn bonn bonn mis february stationarity stationarity huge huge huge datapoints murata murata murata entropies predefined tracked optimizes optimizes treats leaky nth heat snapshots snapshots snapshots ministry indistinguishable accord rescaled tilted supplies iix shortcomings lbg accompanying duced hierarchically rotates mia mia crit federal fid education joachim mfiller mahalanobis unbalanced unbalanced unbalanced yll gurewitz unsatisfactory datapoint datapoint landsat landsat landsat landsat landsat timation imization lei ffir occurence realm fuzziness friedrich emaih restructuring proto accom mic unclassified aset artifical weighs ler similiar 
#@Buhmann_J,Held_M,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training algorithm algorithm output output output output number number number number number number state results results results information information information problem problem problem models models models models models models models models models models models models models models models models models hidden based based based based based based based space space space linear case case case case shown shown shown shown systems systems values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters weight functions functions functions functions functions functions functions distribution distribution method method method method method method method method approach approach approach approach approach approach approach approach approach approach approach pattern pattern point image processing processing large large rate rate rate rate test test test patterns analysis class matrix matrix matrix matrix optimal optimal inputs inputs shows algorithms simple gaussian gaussian gaussian paper paper paper small small small size size size net work work methods points process process current current trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems random high similar representation representation representation representation representation show show show show show equation equation equation equation section section section section images general general average average states gradient gradient term term note note note note note note note note experiments dimensional dimensional dimensional dimensional variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables research independent independent independent independent independent independent log log log log found found found constant estimate estimate terms distance connections node node left left map present present present phase low low low low low nodes nodes machine machine machine machine sets sets maximum maximum maximum press learn basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample abstract applied applied find find density density density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic ieee positive positive positive positive decision mixture mixture introduction introduction estimation estimation statistical statistical effect effect generated variance variance variance variance variance search tion tion complexity variable variable variable variable variable variable variable variable variable variable variable variable assume assume lower learned learned learned center previous theorem cases cases cases cases required required good conditions represent represent represent represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov fact fact correlation correct observed finite finite resulting resulting resulting resulting ing computed respect multi performed performed elements dimension dimension dimension made made natural study knowledge knowledge original original artificial relative relative specific samples represented true true true true cross cross cross cross provide define rates location location perform goal goal connected connected connected connected connected connected distributions distributions discrete discrete equal approaches mit comparison larger contrast connection connection fields update train train dependent dependent dependent selection morgan morgan morgan morgan report words words words consists consists code kernel joint joint joint joint joint joint joint joint joint joint joint difficult difficult final final exp addition graph graph graph graph graph graph graph graph graph graph graph graph graph domain experiment experiment experiment experiment directly view san full choice approximate statistics free estimated validation validation validation validation give give con weighted conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional levels types path path product product product product product product product sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling constraint simply simply achieved achieved achieved discussion covariance covariance technical technical describe arbitrary corresponds complete finding generate supported main end easily easily makes development including including kaufmann probabilistic typically typically typically smaller smaller smaller underlying underlying underlying reduced reduced functional unknown unknown unknown unknown fully fully fully fully fully technology interesting interesting significantly ratio ratio ratio projection edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge special structures structures structures structures structures structures structures structures structures leads numbers direct direct direct direct direct direct direct direct direct international normalized experts experts expert idea run description population population improve improve directions pair strategy pixels pixels inference inference inference inference inference inference inference interest dimensions dimensions sufficient sufficient compare teacher calculated works correspond trans diagonal diagonal sparse sparse address address exists lead lead concept wide locally loop boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary column demonstrate demonstrate strength row conclusions faster weak weak mateo suggest strong integration integration demonstrated intelligence radial variety user user start start exist exist decrease relationship relationship relationship relationship relationship introduce boltzmann reference explicit monte monte construct edges edges edges edges edges edges edges edges edges edges edges edges edges index index index index index index index describes mathematical modeled modeled recall metric missing missing explicitly explicitly explicitly remaining easy easy belief belief unique consisting consisting adding gaussians gaussians gaussians quality implies implies john decreases decreases decreases national extracted independently focus focus depending estimator viewed interpretation influence influence influence influence solved densities densities densities densities densities densities densities evaluated restricted showed centered centered centered decomposition understanding approximated approximated diagram normalization neighborhood purpose penalty penalty penalty penalty penalty penalty penalty penalty closed initially calculate calculate priori formulation discuss candidate candidate domains black absolute tests tests structural structural major reason determining middle identified identified identified suitable differ maximal score score score score score score score score score score plots interested interpreted return built notation gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs approximating neighboring wiley access estimators optimized graphical graphical graphical graphical graphical graphical graphical dataset existence examine rest relationships relationships relationships relationships relationships relationships relationships dependencies dependencies reliable maximizing scores scores scores removed removed removed smallest possibly equally obvious noted precise multivariate motivated motivated percentage pairwise pairwise directed adapted independence independence independence independence independence independence briefly arc arc shared easier strictly strictly day day day precisely located desirable describing describing addressed explained improvements improvements greatly composite composite composite composite composite composite percent percent percent percent percent evaluating collected pseudo quantitative leave leave remove remove rep price price price price price price price mod ture popular suited suited geman geman geman geman geman geman germany germany germany germany germany boston boston boston boston boston boston boston boston display display windows windows windows unbiased median multidimensional tresp tresp tresp tresp tresp cooper japan ordering jones connecting connecting grey communications air stronger difficulties siemens siemens siemens simplify familiar intelligent interpret hope scoring removing removing removing reasoning affected preparation intuitive reliably meaningful financial financial financial displayed displayed dependency dependency dependency dependency searching candidates tic express insight reveals repeatedly concentration sons exploiting tures market approx land indirect gold clique clique clique clique clique inferred inferred removal removal removal removal removal ties stock stock uniquely tween tween ideally ideally decomposed german causal causal certainty realize param representa principled penalized insights pami parzen parzen parzen parzen parzen individually topic pearl pearl pearl pearl pearl deleted weaker exchange exchange els hofmann hofmann hofmann hofmann hofmann hofmann hofmann eters struc struc status status status strict strict mann housing housing housing housing housing housing housing housing housing housing housing removes deletion deletion deletion deletion deletion factorized accordance const corporate prefer industrial cally cally unreliable emerges tells economic stocks stocks stocks stocks cliques cliques cliques sian gaus charles scatter indicators ically statements statements statements blocked denominator ated unnecessary unnecessary tern obeys judge excluded undirected undirected inte bonds pursued excluding volker volker earning earning oxide conveniently visualize readers independencies independencies independencies independencies independencies independencies independencies independencies independencies renders decomposing communicated encourages unclamped ditional embodies compatibility compatibility compatibility compatibility compatibility business business business business ofp decomposes rooms rooms rooms rooms owi cies als subgraph positivity positivity uation ful companies companies companies mchp mchp resented gaining gaining imm imm caution mensional tax retrain lots ork consult parems parems portrayed stoch river nctions nctions ently chapters supposedly clifford europe dependen 
#@Hofmann_R,Tresp_V,
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#*network network learning learning learning model model model model model model neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number system error state results results results information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem models performance performance based based based based based based based based based based based based space case case case case vector vector order order order order shown values values values values values probability parameters noise functions functions distribution distribution distribution distribution distribution distribution recognition recognition method method method method method method method method method method approach approach approach approach approach approach pattern pattern pattern pattern pattern point point point image image image image image single control large large large large large local local local local local local test test analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix optimal optimal optimal optimal shows shows algorithms algorithms algorithms simple gaussian visual paper size size size feature work work work task task methods methods methods methods fig fig fig step step step field features features process process process process structure structure structure structure problems random random random random random random random random random random random random high representation representation representation fixed fixed line rule vectors images images speech average average average average average theory theory theory obtained obtained term experiments experiments experiments dimensional result result result solution solution solution solution solution solution solution solution defined defined found target initial estimate estimate computer computer computer computer terms terms terms terms distance science science present phase low machine machine machine machine object object object object object sets sets sets motion press learn learn learn basis nonlinear sample sample sample sample sample sample sample abstract applied applied find computational computational computational convergence density references stochastic due ieee ieee ieee procedure procedure procedure important important decision decision decision decision decision decision decision decision decision decision decision mixture context introduction complex behavior behavior statistical statistical statistical statistical statistical generated generated generated variance variance variance cost tion tion tion energy complexity variable assume assume rules measure measure measure measure prior prior prior word higher center center bound bound cases type required required required good binary represent distributed distributed bayesian bayesian expected expected expected expected expected expected expected expected equations fact techniques techniques techniques proposed probabilities observed scale scale scale scale scale scale resulting resulting tasks total respect respect multi sum eq called regions means optimization optimization optimization optimization potential potential natural applications applications applications applications knowledge knowledge knowledge filter obtain obtain obtain vol artificial samples samples samples samples samples samples samples samples samples samples samples samples samples represented true compared application series provide define compute compute compute compute objects objects objects objects location perform active active active active active active active active active active active active active active active active active active active active active active active active determined experimental experimental experimental related distributions distributions distributions distributions gain gain gain mit mit mit comparison contrast fields update update selection selection selection selection selection selection selection selection proceedings loss technique technique technique difficult final exp exp scheme graph ai considered framework framework cambridge cambridge equivalent experiment experiment experiment experiment directly additional additional additional additional additional additional additional solutions solutions estimates estimates estimates design design design design design limit detection detection choice statistics statistics speed vision vision vision pages increase validation give weighted clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed developed criterion criterion criterion criterion criterion criterion finally selected evidence depends sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling biological achieved achieved achieved measured increases increases group group close corresponds corresponds corresponds complete complete short assumed supported require main main pixel pixel hypothesis cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster future makes objective simulated probabilistic pairs pairs pairs needed unknown significantly significantly segmentation segmentation segmentation segmentation segmentation segmentation database database database empirical empirical principle leads squared details call making making making making international depth combined run run light population population improve improve improve resolution resolution advantage robust robust typical typical typical similarity similarity similarity similarity similarity similarity apply apply apply introduced strategy strategy strategy strategy strategy strategy hierarchical subset subset relevant interest sufficient unsupervised unsupervised unsupervised unsupervised unsupervised tions tions solve speaker correspond achieve rl sparse sparse sparse address definition evaluation evaluation symmetric observation improvement risk risk risk grant concept concept concept concept scaling loop deterministic deterministic clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters white setting conclusion starting minimal row reduce trajectories segment segment depend measures performs performs faster asymptotic constrained sound propose external demonstrated intelligence intelligence turn assuming user exist iii introduce introduce groups minima minima program configuration annealing annealing annealing annealing annealing annealing base base denoted areas suppose relation pro monte van van van derive construct carlo index index index index index ways sequential sequential sequential sequential generating changing metric metric student student missing simultaneously averaging involves unique scales minimization quality quality quality quality implies boolean extracted depending stages estimator densities densities densities evaluated evaluated evaluate restricted fraction sizes processor calculation performing measurements measurements neighborhood neighborhood neighborhood event roughly generation generation generation intermediate intermediate calculate calculate foundation euclidean advantages transactions transactions degrees avoid usa color retrieval retrieval retrieval inter assignment assignment assignment assignment priors characterized texture texture texture texture texture major simplicity gamma straightforward selecting selecting efficiency suitable suitable suitable encoded computationally effectively successful detect efficiently comparing comparing invariance characteristic notice notice repeated prob video video link stopping dis follow criteria gray gray gray gray gibbs gibbs quantity sampled simplified relaxation realistic principles principles acknowledgments deal access put replaced association integral mass hall dataset dataset ideas incremental terminal terminal structured comparable proved proved workshop affect func func hierarchy fundamental fundamental measurement illustrate illustrate perfect quantities quantities quantities greedy freedom separated store utility grouping grouping contributions regime regime finds averages averages averages optimum inequality pairwise pairwise costs costs trivial crucial distinguish distinguish variances expensive tool london reasons comparisons shared sites sites choices ion depicted depicted incomplete incomplete raw robustness greatly populations populations fuzzy relevance dark dark amounts amounts documents documents documents posed posed variant ity partitioning rely summarized extracting cal occurrence serve suited geman geman geman geman geman geman geman geman geman geman marginal marginal datasets enables sums germany inherent boston unbiased unbiased consistently acquisition corrupted notes formally guarantee gabor linearity pick member databases homogeneous tem outcome fits wrong dealing chance significance promising overcome alpha replacing moment optimally optimally selects reliably meaningful meaningful utilized prentice document document document combines connect entry overview histograms uni thomas offers bases similarities claim advance membership membership infer indicator indicator matter belonging belonging belonging belonging proximity proximity proximity proximity proximity proximity proximity proximity papers automated assigning lem sequentially specification numerous deriving randomized revealed incrementally utilize medium chapter assignments assignments assignments assignments clustered assess algebraic avoids ary visualization arising distri file elementary intra cosine statistic buhmann buhmann buhmann buhmann buhmann buhmann buhmann buhmann drawback anal distinguished outcomes tively esti hofmann hofmann hofmann hofmann hofmann hofmann hofmann hofmann hofmann hofmann hofmann hofmann round exploratory spite bution electron lecture advantageous restoration preserves ate fractal institut decided decided textures textures textures cliffs neighborhoods utilizes hoc establishes suffices suffices mining mining mining jain jain jain drawing drawing possess englewood core triangle fij fij fij inferring deals systematically restricting concave frequent informatik deter profit bonn bonn bonn sparseness sparseness sparseness actively actively dij dij dij dij dist ysis violate mir mir mir argmin fundamentally remarkably entities entities entities entities entities entities entities entities entities entities inserting manipulations distributional tentative dissimilar structuring counterparts dissimilarity dissimilarity dissimilarity dissimilarity scratch motivates solu clus fulfilled vectorial vectorial ministry refining faculty textured textured continu expects rejecting fund abstracts accelerate motivate quantifies occuring pervised hierarchically snapshot snapshot informal uninformative nicely nuisance avail reformulation sampler cycling supplying proximate entity entity entity entity summarizing federal interac education joachim puzicha atom atom lution alterna unsu tering exhaustively subpopulation cloud distributing distributing unification topical topical rior rior poste poste spends anticipated advan unavoidable perturb prohibitive skewed ministic simul sequel ffir queried queried vided suffering perature additively disambiguate sical transac solv tage decom ener hierarchi jection incur imag imag expecting stead ifj interleave unfavorable partitionings ling interleaves 
#@Buhmann_J,Hofmann_T,
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#*network network network network learning learning learning neural input input input input input input input data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set set set set set set networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number number number number error error error error error error results results results information information problem problem problem problem problem problem problem problem problem problem models models hidden hidden hidden based based based space space space space linear linear linear linear linear linear linear linear linear linear linear layer layer layer case vector vector vector vector vector vector order order shown shown shown shown shown shown shown values parameters weight weight weight weight weight functions functions functions functions functions functions method approach approach approach large local local local local local test test test test class optimal optimal optimal optimal optimal optimal form form form form algorithms algorithms algorithms simple simple simple simple paper paper paper paper paper size size work work work work task methods methods step step step step step step step step step points points points classification current current current trained problems show show show show equation fixed vectors general general generalization approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average theory theory gradient note note note note dimensional result result result result university solution solution solution solution solution solution solution solution solution solution solution solution solution independent independent defined defined found found found found sequence initial initial initial initial initial estimate computer terms terms node node node node node node node node node node science present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes learn position position position basis basis basis basis nonlinear nonlinear continuous continuous sample sample abstract find convergence convergence properties properties references component ieee ieee positive procedure introduction introduction estimation estimation effect search search search search search search search change complexity complexity assume lower lower chosen chosen part part bound bound bound bound type required good good good good good conditions fact region finite finite finite finite finite finite finite minimum minimum minimum minimum ing total total total total regression regression computed sum times regions regions regions regions regions optimization optimization potential dimension dimension dimension dimension made made orientation global global em obtain samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples true compute compute rates active determined determined constraints constraints equal equal steps steps steps steps steps steps update update update update update train descent descent descent dependent implementation code code individual difficult final final final addition addition considered framework experiment additional solutions solutions solutions solutions curves curves curves design determine efficient upper upper upper full requires significant significant approximate approximate statistics world produce produce condition condition developed developed criterion criterion criterion criterion bounds backpropagation nature nature nature simply achieved achieved stable stable stable stable stable stable stable stable surface proof proof proof proof proof proof supported role role theoretical theoretical end end easily development development development development development fit fit fit fit typically reduced reduced reduced unknown programming programming programming programming programming projection projection special uniform empirical empirical empirical principle squared squared call call polynomial polynomial minimize produced produced run run run added property robust takes typical typical strategy moving include subject identical machines side side quadratic quadratic quadratic quadratic quadratic sense interest dimensions dimensions previously works solve solve correspond converge achieve background positions positions locations locations bounded risk risk entire grant constructed expression expression expression scaling derivative derivative move move move move deterministic deterministic boundary boundary boundary boundary generally pass pass runs runs starting critical differences sigmoid sigmoid numerical numerical designed designed performs exponential constrained constrained hard hard characteristics sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal minimizing minimizing minimizing user start start min min manner minima minima program question denoted denoted acknowledgements pro produces produces longer solving transitions tuned dept multilayer simultaneously infinite dimensionality easy unique unique unique scales develop adding springer formed formed formed blocks versus family focus dependence dependence depending lemma lemma lemma lemma lemma detailed approximations completely suggested partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition allowed allowed reasonable expansion convex convex fitting fitting fitting iterative iterative assigned norm advantages transactions transactions avoid avoid determining determining middle middle efficiency computationally computationally literature plots fine fine road refer compact verlag allowing allowing heuristic stopping return lie comp sampled vary play minimizes ill ill moves subsequent approximating satisfies employed poor varied pursuit pursuit referred referred referred referred comparable proper workshop necessarily opposite subsets subsets subsets rank rank aspect friedman friedman greedy portion logistic explored optimum residual residual residual residual stop piecewise piecewise inequality inequality pairwise crucial defining unstable unstable unstable adapted worse starts starts purposes widely scientific universal universal begin begin definite geometry outer conjugate substantially tional parameterized posed continuously continuously maintain fall popular extensions wesley initialization don feasible feasible addison modify tation restrict restrict ordering hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions jones jones proceed plays inspired fits breiman breiman breiman breiman breiman stated determination methodology methodology settings intuitive combinatorial combinatorial constructive constructive motivation started separating induce induce expanded arrangement dif bases bases approximators barron barron barron barron barron barron mlps omitted augmented ends ends reverse designing onr divide maintaining numerous minus minus annals sig exhaustive employs axe remainder pub challenging challenging simplifying scope scope retain flip flip flip translations importantly importantly sweeping sweeping sweeping sweeping placing inverting sweeps meet retained tune bill dichotomies dichotomies dichotomies gorithm walk walk preserves algorithmic algorithmic ping builds builds hilbert curse ples tells hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge hinge subscript schmidt iterating comprised comprised elec sweep sweep spec percep routine proximation snow terminate suitably impor traversed bird visits terminated prohibitively seeking seeking seeks horne horne horne horne positioned flips flips sume mexico albuquerque valley occupy admits admits gramming invoked omitting lozano lozano lozano lozano fernando superpositions tunable iia iia iia iia iia flipping fined implemen remedy flipped hinges hinges hinges hinges hinges hinges hinges moidal manifestation sociated descend descend descend descend tition tition luenberger luenberger luenberger monographs joined joined joined swept iil revisited trons ified unexplained une tradi accom bend quest provisions titions titions enumerate necess ize mechanically vll plished 
#@Horne_B,Hush_D,Lozano_F,
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#*learning learning learning learning data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure set set set set set set set set set set set training training training training training training training training training training training algorithm output output number number number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results results results results problem problem problem performance space linear case case case case case case case vector shown shown shown values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability distribution distribution distribution distribution method method method method method method method method method method method approach point point point point point point single large large large large large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test test test test test test class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal form form form shows shows shows paper paper paper small small small small small small size work work methods methods points points points points points points points classification classification classification classification classification classification classification classification classification process trained structure structure structure structure problems problems problems problems random random random random random random random similar similar similar similar similar show section section section fixed fixed fixed line vectors general general general general parameter parameter approximation average average average average states states states theory theory obtained term note note experiments result result result result university university variables research independent log log defined constant constant table estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard terms terms terms distance distance distance distance distance low low low low low machine machine machine sets sets maximum basis sample sample sample abstract back convergence convergence references component procedure procedure procedure introduction behavior statistical generated variance variance variance variance variance change change change change change difference variable classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower rules chosen previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound cases type binary binary binary conditions conditions conditions conditions tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed distributed make fact fact fact fact techniques correlation correlation correlation correct probabilities probabilities errors errors errors errors errors scale scale classes classes classes ing ing simulation performed means means potential original artificial true true provide rates rates rates posterior posterior posterior distributions distributions equal equal equal power approaches approaches accuracy train morgan proceedings report words department loss technique individual joint final final bias bias bias considered curve curve curves curves estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates limit conference classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper statistics statistics statistics estimated estimated give give give produce produce produce produce produce produce produce coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding derived randomly randomly randomly randomly randomly randomly randomly conditional conditional conditional conditional provided provided provided depends depends sampling sampling sampling sampling sampling sampling sampling simply simply covariance normal normal technical increases increases group group group group group group group group group group group group denote tested transformation assumption assumption assumption assumption assumption assumption corresponds common assumed assumed generate generate main journal journal ability hypothesis hypothesis degree fit fit fit fit fit kaufmann simulated simulated simulated smaller smaller uniform empirical empirical empirical empirical leads call call max max max max max max max max max max max max max max max max max max direct international idea choose choose sources sources light improve improve improve property property pair takes element apply moving identical identical identical identical trees trees trees trees trees sense recently observations calculated works match correspond converge achieve definition separation observation bounded improvement exists expression suggests correctly correctly deterministic deterministic column column column column conclusion minimal row row row greater assumptions reduce reduce depend central bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes designed designed designed clear clear exponential exponential exponential exponential suggest suggest strong largest reduction reduction reduction reduction reduction intelligence decrease relationship relationship averaged groups groups groups groups groups groups groups groups groups groups groups groups groups question suppose suppose suppose suppose pro solving solving estimating plot dept changing changing dimensionality remaining unique develop formed formed expectation decreases decreases choosing choosing viewed influence influence codes restricted completely suggested converges constants allowed past past past reasonable expansion calculate classified expect expect expect expect coordinate plotted plotted prove reason columns gamma regular uniformly differ literature essentially identity composed notice success success success interested interested lie classify classify classify follow quantity usual correspondence predictor predictor consisted illustrates law explore unlike american transformed create investigate exponentially rapidly association dotted fewer examine ideas variability variability variability variability proved affect examined necessarily necessarily predicts predicts thought quantities quantities friedman friedman noted taylor ith ith ith ith motivated great rows rows cart inequality inequality unstable fairly fairly explanation answer caused caused caused stanford stanford sections producing ran consequence lowest improvements improvements improvements substantially empirically empirically consistency effort gave sums hamming hamming hamming unbiased unbiased classifying classifying sort optimality optimality guarantee jth jth jth eliminated fits fits stated hope intuitive motivation motivation motivation repeat corollary corollary james james james bad bad infinity originally rich correcting correcting designing dietterich dietterich dietterich dietterich explains vari assigning outperform equivalently super super super super super super randomized randomized theorems theorems classifications classifications corrected corrected arg arg arg arg arg arg arg classifies rain rain clas clas attempted summarizes iff hastie hastie hastie hastie pij pij march simplifying exceed lda supports drops strict circumstances curse inequalities powers concern cally classi systematically substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution substitution tells tells tells tells tells repository randomness randomness irvine deter deter zeros devoted pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact pact kong hoeffding hoeffding corr vat zij zij zij zij dam classifi duce motivate motivate motivate trevor unrealistic unrelated multiclass shed siftcation siftcation shrinking tti standardized insignificant corrects plug plug plug plug plug bakiri bakiri bakiri tradeoffs lib wished easiest rob slowed adaption argmaxp argmaxp veloped ministic ministic ces bivariate fier unduly boot probabilit 
#@Hastie_T,James_G,
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#*network network network learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure figure time set set set set networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number error error error error error error error error error error error error error error error results results results units units units units units units units information information information information problem models space space space space space space space space space space space space space space space space space space space weights weights weights weights vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector systems systems values probability probability probability parameters noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution method approach approach approach point point point point point point image image single processing large neuron rate rate analysis analysis matrix matrix matrix form form form algorithms algorithms algorithms simple simple gaussian gaussian gaussian gaussian paper small step points process level trained trained trained problems random random random random random section section section line rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors parameter parameter parameter parameter parameter parameter parameter approximation gradient obtained obtained note note dimensional university university university solution research research log log defined defined defined defined found initial initial initial constant computer computer terms terms distance connections science science left left direction map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map present phase activation activation activation activation maximum press position basis basis basis basis basis basis basis basis basis basis basis nonlinear sample abstract computational convergence convergence density density density density density density density density properties likelihood likelihood references component ieee ieee ieee procedure procedure introduction hand hand statistical statistical generated generated generated variance variance parallel change difference difference assume lower rules rules rules rules prior prior center cases long bayesian expected proposed simulations simulations minimum minimum minimum resulting tasks simulation respect sum called mapping mapping mapping mapping mapping dimension dimension natural applications applications applications applications em em negative negative original vol vol vol vol vol vol vol artificial artificial specific series determined experimental posterior posterior connected equal equal mit steps connection connection update update update update update update descent proceedings proceedings implementation version version version code individual advances final exp exp exp exp exp scheme maps maps maps considered framework computing equivalent additional view view limit top top top top conference conference full full requires choice choice approximate basic increase increase product product product finally group tested inverse inverse complete generate theoretical theoretical eds journal square ability ability makes makes objective objective probabilistic probabilistic probabilistic probabilistic probabilistic needed functional fully fully jordan technology technology york increasing uniform principal details international international normalized normalized normalized bottom bottom bottom bottom early minimize minimize choose added discussed advantage practical introduced sense engineering tions tions tions solve yields rl rl locations modified williams organization organization organization organization organization organization sensitive increased increased wide wide wide alternative move width width strength hebbian hebbian conclusions suggest sound strong hard assuming assuming variety minimizing user start introduce configuration configuration configuration annealing question pro pro written written index winner winner winner winner winner ways plot laboratory laboratory mathematical changing metric metric metric metric metric slightly consisting springer springer potentials decreases decreases yield review review viewed interpretation open open updated updated organizing organizing organizing organizing organizing organizing organizing organizing centers forms updates key epochs combining neighborhood neighborhood neighborhood neighborhood purpose norm norm euclidean euclidean kohonen kohonen topology box box activations activations activations activations activations activations usa usa batch batch batch batch sciences plotted mozer specifically columns regular straightforward middle middle suitable society computationally delta delta latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent showing interpreted manifold manifold generative generative generative generative notation simplified simplified simplified simplified simplified dot dot dot minimizes minimizes reach principles moves moves neighboring decreasing unlike schedule updating involving strengths behaviour mappings mappings combine comparable func func topographic topographic topographic topographic topographic phases closest closest adapt analyze opposite adjusted singular algo som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som mapped initialized ith ith epoch epoch epoch epoch epoch consist generates generates slowly slowly formula guaranteed biology briefly lies starts tive organized strictly choices choices ran bishop bishop desirable arise qualitative questions questions pure capability capability lattice share employ variant http berlin popular proven june softmax softmax distortion trade contribute initialization initialization initialization initialization tation narrow nonzero royal turned rigid oja oja oja oja oja oja stronger stronger difficulties proceeds resulted interpret serves guide displayed regarded sim sphere offer record properly properly dempster gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm rubin aston aston axe axe tendency tendency adjustment illustration principled equality rithms realizable oct oct careful monitoring laird associates nal matlab matlab compu mea resembles resembles council satisfactory jersey jersey dom agency preservation html reproduced fin fin counterpart ready server appro defense facts ized ized birmingham experimented ceedings stems tivity hood applica searched simula neigh heskes tll tll tll heidelberg impressive analyzer accumulating icnn icnn helsinki helsinki emphasizing jour proportionally narrower organize organize organize organize resort likeli succeeded kappen apr spreads hut hut finland finland mates alterna iit iit recommended offering malvern organising experimenting unfolding kangas url leaning unnormalized svens svens memorandum erkki erkki piscataway shorthand recommendations interpretability pis manages equiprobable heavier heavier plicity cil borhood iiv 
#@Kiviluoto_K,Oja_E,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural input input data data data data data data data data data data data data data data data data data data data data function function function function function figure figure figure figure figure algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm error state state results results results information information information problem problem problem models based space space weights linear linear linear linear linear linear linear linear linear case case case case case case vector vector order order shown systems values probability probability probability probability probability probability noise noise noise noise noise noise noise noise noise noise unit distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach point point point point point single processing processing processing large large large analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix optimal optimal optimal inputs form form form shows shows shows shows shows signal signal signal algorithms algorithms simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples examples examples methods field field field features cell structure structure problems random random similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture show show show equation equation fixed rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images general general general generalization speech speech speech speech speech real approximation approximation approximation approximation approximation approximation states gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained obtained term term term term note result university variables variables computation computation solution solution independent independent independent log log log log log log log log log log log log log log log log defined found standard standard terms terms terms terms terms direction direction presented present present present low low low low frequency maximum range components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample sample sample sample abstract computational convergence density density density density properties properties likelihood references component component component component component component component due due due due positive positive positive positive positive adaptive statistical statistical statistical statistical effect generated change change change difference assume assume assume assume assume signals prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations learned learned learned learned learned learned higher cases required represent represent represent distributed distributed make make make fact observed minimum minimum resulting computed computed respect called elements elements elements elements mapping means optimization optimization made natural natural natural natural filter obtain obtain obtain obtain obtain obtain obtain obtain negative negative original samples true true true true true compared compared compared desired desired receptive provide posterior posterior posterior posterior posterior distributions equal power power larger source source morgan report institute institute technique internal internal internal internal code code advances exp graph cambridge equivalent equivalent view san efficient efficient efficient efficient full full approximate approximate estimated pages increase coding coding coding coding coding coding randomly levels nature simply simply simply simply discussion technical increases describe transformation limited limited inverse complete complete complete complete complete complete finding finding finding main square including fit fit fit kaufmann objective objective objective probabilistic probabilistic probabilistic probabilistic typically smaller underlying underlying reduced reduced reduced coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients programming programming programming significantly projection database operation operation leads leads principal iterations iterations iterations bits bits normalized magnitude minimize minimize run sources sources sources sources sources sources sources improved exact exact robust ensemble element identical sense sense inference subset sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently approximately approximately volume smooth yields yields yields speaker pca pca diagonal diagonal sparse sparse sparse sparse mixtures separation separation separation separation separation separation separation generalized channels channels entire expression expression expression lead derivative alternative alternative alternative width demonstrate row row greater greater assumptions assumptions segment segment valued valued exponential mateo encoding presence solid assuming assuming assuming variety ica ica ica ica min derivatives program explicit derive derive generating plot plot laboratory dept segments modeled dimensionality involves remaining spectral yield viewed viewed solved solved densities evaluated restricted decomposition approximated spectrum dashed additive additive combining fitting fitting fitting valid norm norm advantages degrees precision avoid bell bell blind blind blind blind blind blind subspace determines extension maximize maximize priors priors priors priors columns columns efficiency efficiency literature mackay mackay mackay essentially orthogonal orthogonal orthogonal ten capture summary traditional traditional graphs symmetry notation notation sampled michael wavelet maximization consisted unlike unlike involving integral integral hessian hessian hessian hessian hessian hessian dataset dataset dataset pursuit fewer fourier fourier fourier fourier fourier fourier analytically scaled scaled maximizing tanh matched removed removed removed possibly adapt necessarily rank rank initialized initialized amari amari mixed mixed utility defines defining adapted adapted handle rapid stanford stanford preprocessing precisely broad ran ran ran probable probable probable probable probable probable probable opt gradually definite medical arises conjugate requiring axes generic marked span howard chen chen chen achieves logp logp redundancy redundancy redundancy specifies specifies specifies specifies specifies yielding univ lab redundant tation optimizing approximates removing neurobiology salk salk salk selects selects induce induce yang offers bases bases bases bases bases bases bases bases bases bases bases bases viewing emergence specialized specialized jolla cam influences speaking multiplying deriving deriving deriving inferred ram tendency letting letting laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian pub rectangular ftp ftp ftp dominated disadvantage inverted hughes deconvolution terrence simplifying simplifying wise noting represen anal inverting vanishes det det jutten jutten jutten differentiating overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete removes preserves uniqueness interior interior interior lation const invertible invertible olshausen olshausen drawing sen inferring inferring multimodal inde lewicki lewicki lewicki lewicki lewicki broadband problematic cichocki ira routine ysis stepsize stepsize drawbacks stat pendent derivations stabilizing timit phy herault herault herault invert invert comon comon putting illustrating package tially terry poten singularity donoho lira ogp inverses relied loses plete breakdown torrey pines denoising rewriting criticism pseudoinverse solver derlying atomic neuromimetic msecs xla xla xla xla xla saunders slx ata ata publicly formu tax bra misfit maxp maxp marginalizing aat ologp objectively aft org covariant sla alleviated cavendish tences 
#@Lewicki_M,Sejnowski_T,
#t11
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#*neural neural neural input input function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure set set set set algorithm number number number number number number number number system system system system system system results information information information information information information information information information information information information problem space linear linear linear linear case case case case case order shown shown shown systems systems systems values values probability noise noise noise noise functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach point point processing processing local local local local local local local local local local analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form form shows signal gaussian gaussian gaussian gaussian paper small fig fig points points points points points points process current structure structure structure structure structure structure show equation equation general general generalization approximation obtained obtained obtained experiments experiments dimensional dimensional dimensional dimensional dimensional result university university threshold threshold variables computation solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent log log log defined defined defined found constant standard terms presented presented presented present present present low low frequency frequency temporal maximum maximum maximum range range press press position outputs sample abstract find find find find density references component component component component component component component component component component component component component component component component component component component due positive mixture mixture mixture mixture mixture context context complex estimation statistical effect effect generated generated tion spatial spatial assume lower lower measure chosen chosen higher previous distributed expected expected expected expected equations equations equations fact fact fact length scale finite simulations minimum minimum classes classes classes classes classes classes classes classes classes classes classes classes classes classes sum elements elements regions regions optimization made made natural natural natural orientation orientation orientation orientation orientation orientation negative samples represented application desired cross define define define perform determined goal constraints constraints constraints constraints constraints constraints constraints distributions distributions discrete mit mit mit mit contrast connection support dependent source source source source source source source source source source source words department loss consists consists advances advances joint joint joint joint joint joint joint joint joint joint joint joint addition ai considered framework cambridge cambridge cambridge equivalent curve solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions curves estimates determine upper full choice give give randomly conditional lines product product product product product product product product product product product actual actual finally nature nature sampling sampling sampling constraint constraint discussion arbitrary arbitrary arbitrary denote denote denote transformation transformation transformation assumption corresponds complete proof proof nearest square degree makes fit pairs pairs pairs pairs underlying underlying needed needed functional functional unknown coefficients jordan block block block block ratio increasing special special operation direct frame frame frame frame frame choose choose added sources sources sources sources sources sources directions directions directions introduced quadratic sejnowski relevant interest dimensions sufficient approximately tions tions tions tions solve smooth yields correspond correspond correspond differential diagonal diagonal diagonal diagonal diagonal address definition definition positions positions locations separation separation separation symmetric symmetric symmetric amplitude constructed exists exists concept spikes derivative derivative matrices locally locally touretzky width width width generally pass demonstrate demonstrate starting starting greater greater assumptions reduce operator operator valued accurate accurate accurate numerical numerical clear peak performs presence physics demonstrated ica ica plane derivatives identification denoted appears relation relation relation relation relation relation pro derive derive solving factors factors mathematical distinct sensitivity explicitly coordinates simultaneously linearly involves scales gaussians implies expectation decreases extracted extracted extracted formation solved open centers centers frames decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition forms understanding constants partial smoothing dashed additive performing normalization combining fitting roughly iterative iterative valid david degrees avoid figures thesis coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate formulation bell blind plotted plotted plotted uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty mozer mozer coupled discussions differ orthogonal characteristic repeated interpreted symmetry lie sin sin notation subsequent mixing mixing mixing mixing mixing satisfies cowan parametric transformed hessian hessian hessian hessian issues preliminary graphical graphical dataset rise scalar scalar giving giving investigated analytically root proper proper eigenvectors func understand phases notion notion integer rank singular noted noted algo freedom freedom multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate amari mixed mixed mixed simplest defines histogram histogram histogram histogram histogram histogram histogram pairwise separable orientations orientations orientations orientations orientations convolution defining analytic analytic analytic analytic analytic analytic analytic analytic independence independence multiplication perspective lin lin lin lin lin lin satisfied formalism formalism leaves products ion describing begin patches author preceding addressed summation summation geometric geometric geometric geometric reflects double simulate peaks peaks peaks peaks peaks formulated ity ordered logp logp decreased simultaneous proposition proposition differentiable differentiable irrelevant cor representative representative indices equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence tensor tensor tensor circular count count bin bin bin bin repre proceed generality generality multiplicative determination determination determination height obtaining transforms transforms intuitively preparation combinatorial generalizes moments widths widths widths counting counting counting hasselmo yang multiplied treatment waves smoothed reveals arrive rich extends pearlmutter eigenvector robert counts counts counts counts counts counts counts divide audio audio audio slight logarithm rigorous constitute vec email equivalently seek ease ideally amplitudes tor chicago chicago chicago letting letting reflected decorrelation decorrelation decorrelation decorrelation algebraic preserved modifying cessing rithms differentiation differentiation acquired mask mask superposition discretization responding confusion grateful strict removes rarely uniqueness justified invertible loosely concerns equa equa coincide petsche edited edited convention factorization factorization factorization factorization factorization factorization factorization factorization factorization factorization factorization factorization factorization factorization factorization factorization factorization scatter vanishing mul translates translates cichocki tan tan propagates noiseless noiseless datapoints datapoints decompose jack nice hij continuing topics undirected sition parra pursued imposing tie necessity roots stein transfor equiv attack indicative admits admits admits admits primed ein invaluable assump formalize mations irreducible irreducible irreducible irreducible wavelengths radians radians radians radians rounded factorizes aji aji representatives representatives representatives ial reinforces diagonalization diagonalization diagonalization nctions ciency differentiability accomplishing covariant decompo osi osi darkest unordered 
#@Lin_J,
#t11
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number state results results results information problem problem problem problem problem problem problem problem problem problem performance performance performance space space space space space space space space space weights weights weights weights case case vector vector vector order shown shown shown probability probability parameters noise noise noise noise distribution distribution distribution distribution approach approach point point point point point point point point point point point point point point point point point point point point image image image image image single single large local local test test test test test test test class shows shows shows shows shows algorithms algorithms algorithms simple simple simple simple simple paper paper paper examples examples examples examples examples examples examples examples examples examples small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work task points points points points points points points features features features features features features features classification classification problems problems problems high high high high high high high high high high high similar similar representation representation show show show show section section section section rule rule vectors images images images images images images images general general general general average average average average theory gradient gradient note note note note activity activity activity activity dimensional dimensional dimensional result threshold threshold threshold research independent target target target target target target target target target table terms distance distance distance distance distance distance prediction prediction prediction prediction low low low machine sets sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum range learn learn learn learn learn learn learn learn continuous sample sample abstract find find find find find find find computational density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density likelihood references positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive important important introduction hand statistical generated generated parallel parallel search energy energy assume assume assume measure measure measure measure prior prior learned learned chosen higher higher bound bound required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple long long long represent represent make fact correct ing computed computed respect respect respect multi called called means factor potential potential made natural natural global applications applications applications applications applications knowledge negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative artificial artificial artificial samples represented true compared application application application desired desired cross series series series series provide define define define location location location location location location location perform perform related distributions mit mit mit accuracy accuracy accuracy accuracy support modeling selection selection selection proceedings report technique individual individual individual represents represents difficult difficult difficult difficult exp addition ai ai ai ai framework framework framework framework framework framework framework framework framework cambridge cambridge domain domain domain domain equivalent equivalent directly additional top bit conference efficient efficient upper vision validation give weighted weighted weighted randomly randomly area area area area path product provided selected depends technical increases describe describe describe describe arbitrary arbitrary denote tested tested close close close assumption assumption assumption complete surface surface surface surface surface finding finding amount nearest common shape shape shape shape shape shape shape shape theoretical journal square square square square square hypothesis hypothesis hypothesis instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance degree degree noisy noisy noisy fit objective probabilistic typically typically smaller underlying needed testing ratio ratio head uniform database empirical principal numbers max max making bottom bottom supervised supervised supervised supervised polynomial idea run run description description description description description predict pair takes reported reported apply recently dimensions varying teacher teacher approximately approximately tuning axis axis axis correspond achieve definition evaluation locations grant parts lead lead lead concept concept concept concept concept concept concept concept concept concept concept concept scaling scaling scaling scaling occur wide wide correctly white runs runs half half conclusion starting starting starting place neighbor bayes bayes clear peak peak performs practice largest drawn drawn intelligence labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled assuming assuming variety variety start scene program acknowledgements suppose appears van derive produces solving solving solving ways plot plot label metric involves transformations remaining easy develop adding applying applying decreases choosing independently independently learner learner variation centers sizes key key roughly roughly sufficiently euclidean query exploration includes inter weighting weighting instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances illustrated maximize maximize maximize candidate candidate candidate candidate domains black discussions major regular regular determining middle middle middle middle uniformly differ divided paths paths paths included ten receives repeated strongly heuristic interested issue return return return return return return return contribution classify manifold manifold manifold manifold involved dayan highest binding predictor predictor predictor deal receive bars bars collection difficulty exponentially put optimized preliminary helpful fewer fewer investigated possibility maximizing maximizing maximizing maximizing maximizing comparable complicated fundamental fundamental fundamental notion momentum surfaces surfaces closest trace concepts created created assumes shapes shapes shapes shapes shapes shapes contributions arbitrarily submitted synthetic years answer tool reasons reasons drive shared shared protein protein protein protein protein protein products ion describing people flexible lack peter leave peaks peaks dots maxima maxima price parent returns irrelevant contribute person person person person person person person person person person person lab lab pac pac pac restriction restrict pick jth discovery discovery rigid rigid dealing consideration chance chance held intuitively performances falls ambiguity ambiguity paul induce expanded ascent ascent dominant bad den searching iterated iterated concentration dietterich dietterich dietterich dietterich dietterich dietterich papers ignore intersection intersection intersection intersection intersection intersection intersection receiving minus sine maximized stock stock stock stock stock stock stock diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse diverse adopt year arg descriptions causal molecular illustration remainder attempted manifolds manifolds manifolds afosr march landscape investigating disease harder likewise likewise likewise likewise union molecules molecules molecules molecules molecules molecules molecules molecules molecules molecules worked chris argmax twenty tom viola blum blum blum hancock lists returned month month month subtracting sided conditionally stocks stocks stocks stocks stocks stocks stocks sity fair colors molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule molecule rectangles rectangles rectangles restrictive approached ild adequately convey tan tan tan drawbacks drug drug drug drug drug drug drug drug retrieve intersect intersect weakness bind bind bind bind bind bind ranked begun positively positively missed formalized legs bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag bag fell intersecting lock motivate lozano lozano lozano lozano lozano apr apr apr apr apr apr apr apr uninformative ijk bij subsection maron maron maron maron maron maron maron discrim discrim closeness auer auer auer auer auer benchmarking cvpr negatives disjunctive neurocolt deemed subimages assert torso kindly rim scalings elim elim elim motivating instantiate climb 
#@Lozano-Perez_T,Maron_O,
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#*network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input data data data data data data data data data data data data data data data function function function function function figure figure figure figure figure figure set set set set networks networks networks algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number state state state state state state results results results results information information problem problem problem problem problem problem problem models models models models models models models models models models models models models models hidden based based space weights weights weights weights layer case case case case case case case case case vector vector order order order order order order shown shown shown shown probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach single processing large test analysis analysis analysis analysis class matrix form form form shows signal signal simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small small methods step step field current current problems problems random random random fixed fixed line line general parameter parameter parameter parameter theory obtained term dimensional dimensional dimensional result result variables variables variables computation research independent defined defined target initial estimate estimate estimate estimate estimate estimate standard distance map map map maximum range components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components basis basis basis basis continuous sample sample abstract find density density density density likelihood references component component component component component component component component component component component component component component component component component component component component component due due due due decision decision mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation estimation estimation estimation estimation estimation statistical generated generated generated variance search tion tion tion tion classifier prior prior prior prior prior prior prior prior chosen chosen higher type required multiple conditions represent represent represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov markov markov techniques proposed correct forward finite resulting resulting resulting resulting resulting multi means dimension applications applications study em negative original artificial samples samples samples samples samples application application desired desired series define define define define define posterior distributions distributions distributions distributions steps comparison comparison fields selection version technique technique technique technique technique joint joint joint joint joint final final exp scheme addition addition full full full full full full choice statistics estimated estimated estimated derived derived randomly conditional conditional conditional conditional criterion controller types lines iteration nature sampling sampling measured normal normal normal tested transformation transformation transformation limited common implemented generate main eds hypothesis simulated simulated simulated simulated simulated simulated pairs combination combination unknown unknown testing testing ratio leads principal principal representing numbers numbers numbers numbers making choose choose choose choose denotes pair pair takes apply introduced moving moving include hierarchical hierarchical hierarchical recently compare observations calculated correspond correspond diagonal diagonal mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation chain chain chain chain chain chain chain chain observation amplitude expression occur move move move move move move move move move move move move move move move conclusion editors bayes practice practice drawn drawn demonstrated demonstrated radial radial iii introduce question question denoted pro monte monte monte monte derive derive construct carlo carlo carlo carlo longer factors generating estimating label dept averaging involves transformations frequencies expectation choosing choosing choosing choosing choosing independently formation stationary detailed labels forms key key key spaces combining combining add degrees precision priors priors priors priors gamma extra capable capable literature comparing comparing vowel vowel vowel vowel vowel vowel soc prob split split split split split split follow criteria hold satisfy gibbs simplified hypotheses leading moves moves moves moves moves moves subsequent mixing extend extend carried wiley updating updating updating updating issues issues hall hall dataset dataset giving combine combine combine combine combine combine combine combine office complicated hierarchy thought noted freedom expressions ith multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate consist optimum optimum histogram histogram histogram variances diffusion lies straight purposes sections strictly projected conjugate leave orders frequently ity ture ture green green attraction utterances intractable extensive ratios labelled labelled repre smith smith allocation allocation allocation accepted simplify hyper hyper balance star roles splitting published widths spherical spherical spherical spherical spherical spherical spherical spherical spherical peterson peterson peterson enable extends formant jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump jump designing ignore yielded specification axe axe encouraging encouraging regularity ease rain rain rain rain beta beta assess jacobian arising arising care distri toy chapman chapman distribu mathematically allocated proba met dirichlet importantly anal sam mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc subspaces treating mix mix bution bility invertible nested nested firstly reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible determinant drawing compo compo ning proposal agency ples alan placement comprising sions centres centres centres signed tra metropolis allocating rem phillips ysis nents treats acceptance imposing ting desire nation british posterjori ponent univariate nent barney barney visualisation neighbours xlo regularly neighbouring rejecting eter independencies permission generalised estima conducting aperiodic richardson richardson richardson looo irreducible spiegelhalter spiegelhalter ven propor kom kom titterington malvern tio tio nts obt gilks gilks terministic timate equate bivariate outset copyright recognise defence boo dra jected propo 
#@Marts_A,
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#*network network network network learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input data data data data data data data data data data data data data function figure figure figure figure time set set set set set set set set set networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number results results results results results information information information information problem problem problem problem problem models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden performance performance based space space space space weights weights linear linear case case case case vector shown shown shown shown systems systems values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight weight weight distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach pattern point single single processing local rate rate test test patterns patterns class class class class class optimal optimal inputs form form form shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper paper paper size size feature net work work work task methods step step step step step step step step step step step points field classification classification classification current trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems random representation representation representation representation representation show section section section section section section section section section fixed vectors vectors images images general parameter parameter parameter real approximation theory theory obtained obtained obtained obtained term note note note experiments experiments dimensional dimensional result variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation research independent independent independent log log log log found found target initial constant table table estimate computer terms node science presented presented presented presented map map present present present present phase phase nodes machine machine machine sets sets maximum maximum maximum maximum press press components components continuous continuous continuous sample sample abstract find computational computational computational convergence density density density properties properties likelihood likelihood likelihood likelihood likelihood references component component component ieee procedure procedure procedure important important decision decision decision decision mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction introduction complex estimation statistical statistical tion tion tion difference complexity variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable classifier prior prior prior prior prior prior prior prior prior prior representations representations learned chosen center previous good good good binary conditions conditions represent represent represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree bayesian bayesian bayesian bayesian bayesian bayesian expected make length correct probabilities probabilities observed observed observed observed finite minimum minimum classes total simulation computed performed called called called called called means factor made knowledge knowledge em em em em em em obtain negative original artificial artificial artificial samples represented represented represented compared define compute compute compute compute rates rates rates proc perform related posterior posterior connected connected connected connected distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions discrete discrete discrete mit mit comparison comparison nets nets nets nets modeling morgan morgan proceedings report report report institute institute words department consists joint joint represents exp addition addition graph graph graph ai framework framework framework framework cambridge computing equivalent equivalent equivalent hinton view san conference conference efficient efficient efficient classifiers classifiers choice choice statistics free free world world estimated basic basic basic basic basic basic basic basic pages pages pages validation give give produce produce randomly randomly conditional conditional conditional conditional entropy actual sampling sampling biological technical technical technical arbitrary denote denote denote tested tested tested assumption assumption corresponds complete finding finding finding amount common common generate generate role journal ability ability instance degree including including fit fit fit kaufmann objective probabilistic pairs pairs pairs pairs combination account unknown fully jordan jordan jordan jordan jordan jordan technology technology testing testing edge edge edge edge edge edge edge edge edge special special special structures structures structures structures structures structures trials uniform uniform database empirical representing call call max direct bits bits experts choose added added description description denotes exact advantage pair pair similarity introduced include pixels quadratic trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees sense inference inference inference subset subset relevant interest dimensions observations achieve sparse sparse sparse definition mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures modified expression expression studied suggests extended trial trial correctly runs strength starting conclusions depend editors interactions bayes bayes bayes designed exponential mateo taking presence largest intelligence intelligence intelligence variety exist averaged introduce introduce base denoted denoted acknowledgements explicit digit digit digit digit digit digit digit edges edges edges index index winner ways factors generating generating estimating estimating estimating estimating estimating estimating laboratory changing pruning pruning pruning pruning easy belief belief belief belief belief mutual mutual mutual gaussians expectation cycles cycles choosing national family dependence dependence dependence depending depending estimator viewed viewed influence solved soft sizes digits digits digits digits digits digits digits digits digits digits allowed smoothing performing fitting fitting fitting fitting fitting penalty penalty visible visible advantages advantages topology topology transactions building handwritten handwritten includes includes instances assignment prove uncertainty maximize maximize mozer priors priors priors priors priors priors priors priors priors priors priors priors domains domains absolute successfully simplicity compression compression compression compression selecting importance society encoded encoded literature literature efficiently efficiently essentially capture contained contained contained superior running running satisfy notation notation sampled vary vary vary usual michael play dayan absence paradigm paradigm realistic providing maximization maximization automatically attempt approximating approximating modelling extend presents presents body body estimators estimators graphical graphical graphical graphical dataset dataset dataset dataset dataset ml ml ml ml ml rest rest investigated possibility relationships relationships dependencies dependencies dependencies dependencies dependencies dependencies root root root maximizing maximizing maximizing fundamental attributes plausible possibly friedman friedman versions ith optimum massachusetts massachusetts pairwise pairwise directed directed agreement publishers publishers independence independence independence perspective perspective precisely constructing constructing constructing broad commonly separately universal attribute medical recording incomplete exemplars conjugate double double relevance flexible flexible introducing http measuring differs aim parent marginal marginal datasets datasets replace logp logp logp logp logp age conditioning credit credit person www sleep sleep conditioned conditioned conditioned conditioned dynamically discover royal proceed proceed kaufman fits tools simplify attractive intelligent height balance obtaining exploit reasoning intuitively substituting overlaps excellent recovered introduces introduces patient patient iteratively iteratively studying dependency dependency dependency dependency dependency dependency dependency dependency dependency dependency bad vertices hasselmo approximators deg bins vertex properly informative park extensively likelihoods exploiting dempster dempster empty ics uci uci fitted liu liu liu liu ure ple unable rubin helmholtz helmholtz tables maximized recursively failed encouraging encouraging mdl mdl mdl multinomial multinomial imagine beta wake wake constrain avoids factorial factorial factorial factorial verified picked picked paired dirichlet dirichlet dirichlet dirichlet dirichlet pearl pearl disease worth laird discusses discusses geiger geiger geiger geiger geiger accounted confusion frey frey frey frey tin aaai wider develops handled info argmax argmax factorized factorized factorized factorized discretized australian australian insufficient families mst mst mst mst mst morris morris dropped appealing html repository maxi demands counterpart ings focusing tenth iterate penalizes spanning spanning spanning spanning datapoints imum microsoft unobserved marginals marginals retrieve retrieve cient mum undirected graphically inte incident sing menlo heckerman heckerman heckerman spans ons disconnected comput del independencies healthy forest forest ations chow chow chow chow factoffal cited retrieving penalize concludes instantiated ond compressing aaa sumption bitmaps uncover facto datapoint ual suffered abound obt obt obt ivi pioneered fictitious marginalizing mlearn enjoy enjoy dat signifies msr solv touretsky mlrepository brendan ivy imizes marina por cbcl 
#@Jordan_M,Meila_M,
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data function function set set set set set set set set set set set set set set networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number error error error error error error error error error error results results results results information information information information information information information problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models performance performance performance performance based based based space space space space space space space space space space space weights linear vector systems systems systems systems values values weight functions method method method method method method method method method method method method method method method method approach approach approach approach approach approach approach point point single single single single processing processing processing processing processing rate rate rate test test test test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper examples examples examples examples examples examples examples examples examples examples examples work work work work methods methods methods methods methods step points points features classification classification classification level trained problems similar similar similar representation representation representation representation representation representation representation representation representation representation representation section section section section section section general general general generalization real approximation average theory obtained result university computation research research defined found table table table table table computer terms science prediction prediction presented present phase phase machine machine machine machine machine machine machine machine machine sets sets sets sets sets sets sets sets sets sets press press press press press learn position components outputs outputs sample sample abstract applied applied applied find references component important decision decision decision decision propagation introduction introduction hand generated generated generated generated generated generated generated variance variance parallel cost cost cost search search search search search search search search tion tion tion difference representations representations learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned previous multiple multiple conditions tree bayesian make make make techniques techniques techniques techniques length length correct errors errors errors errors errors errors errors errors errors errors resulting resulting resulting classes classes ing ing ing total regression regression regression respect respect performed performed performed called called called made study obtain relative samples represented true true application application rates determined experimental experimental goal goal goal goal goal approaches approaches approaches mit mit mit mit comparison train source selection morgan morgan morgan proceedings proceedings report technique technique consists consists internal individual advances advances advances advances represents final bias bias bias scheme scheme scheme considered framework hinton estimates estimates san stage stage stage stage conference determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers significant significant significant significant world basic pages pages pages pages give give coding derived weighted weighted developed developed area actual provided finally finally backpropagation measured group group limited limited close close predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions predictions nearest nearest nearest nearest nearest nearest nearest nearest nearest effective effective effective generate generate generate main rumelhart rumelhart rumelhart rumelhart kaufmann kaufmann typically typically underlying combination jordan ratio ratio ratio ratio ratio ratio york database empirical empirical empirical principal principal pre direct making international description denotes architectures improve pair robust ensemble element reported reported apply introduced strategy include trees trees recently recently dimensions dimensions dimensions highly highly varying previously previously volume volume volume volume volume tions achieve diagonal diagonal diagonal diagonal definition definition evaluation williams improvement improvement sensitive parts lead occur matrices matrices touretzky touretzky column column column column column column column runs runs conclusion place row row row neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor editors editors editors editors editors accurate accurate bayes bayes bayes bayes bayes bayes bayes clear performs performs performs performs weak mateo taking reduction california labeled turn variety min relationship relationship relationship relationship suppose suppose derive derive solving ways generating generating describes describes describes describes label label label dept pruning sensitivity category coordinates coordinates coordinates coordinates coordinates coordinates slightly integrated focus depending stages correlated correlated correlated correlated squares codes detailed detailed evaluated evaluate labels labels labels decomposition approximated approximated approximated completely similarly partition partition partition partition sign combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining combining generation generation symbol assigned assigned assigned classified classified classified classified existing mozer mozer variations holds major reason columns columns columns columns columns columns capable mcclelland build summary heuristic dis issue return lie lie classify classify classify classify sin strategies strategies strategies strategies strategies strategies strategies vary wave wave correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence attempt approximating tesauro tesauro receive cowan explore unlike poor poor poor poor overfitting create create collection collection collection collection collection hall biases matches matches applicable boosting boosting ideal combine combine combine combine combine combine relationships scaled scaled scaled referred proper symbolic statistically statistically cognition neu induction induction induction closest closest predicting predicts singular versions versions noted explored mapped academic baseline improving improving improving submitted residual rows rows rows rows rows rows publishers fairly analytical majority glass glass multiplication lies london london sections closer closer preprocessing broad calculations calculations calculations members members members medical arises demonstrates fluctuations geometric percent percent percent percent profile bootstrap conducted effort frequently requirement stack partitioning rely credit naive naive consistently consistently uncorrelated uncorrelated uncorrelated leen ratios databases approximates homogeneous partitions murphy murphy murphy consideration breiman breiman breiman breiman breiman adjusting ral intuitively exceeds exceeds motivation alspector mance programs predictors entry perfor decide heart belongs hasselmo entries entries winning foundations reveals indicator indicator indicator matter repeatedly bagging bagging wolpert wolpert wolpert wolpert wolpert wolpert correcting correcting broken dietterich dietterich dietterich explains explains shavlik shavlik shavlik shavlik insensitive explorations divide ics uci uci uci appeared converted converted microstructure randomized presenting revealed diverse diverse tibshirani tibshirani tibshirani convenience par residuals exception reports assignments freund freund freund descriptions scenario unseen unseen unseen intuition pdp chapman gener gener regularized efforts relate records spanned quinlan quinlan quinlan sonar diversity voting voting voting likewise retained dramatic aaai aaai challenge mann spite emphasis meir meir meir meir meir learners learners handling christopher breast wins suite suite hypothesized hid fill clarity lists cast resampling svd svd ally vote vote petsche heterogeneous heterogeneous heterogeneous meth clark clark clark exploits repository repository losses losses losses proves prone ods irvine categorical nominal stacked stacked capturing capturing prescribed dence dence ated ated bootstrapping constituent constituent constituent constituent kong kong kong elaborate iris predic predic locating erroneous optimizes putting putting superscript scribed colt stacking stacking stacking stacking stacking stacking stacking stacking draws thirty tributed henceforth overfit masses masses masses masses geometrically geometrically amples instantiations pertone pertone efron efron premise chine liver tailed perrone perrone votes mij genera gle standardized standardized reacting insignificant insignificant grand merz merz merz oblique corrects kauf pres descrip advan numeric hal tition correspon correspon reside bay ionosphere neous committed redefine ise tage caveats ali appended ind ind unclassified unclassified aset 
#@Metz_C,
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural data function function function function function figure figure figure figure time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training algorithm algorithm algorithm algorithm output output output output system system error state state state state state results units units information information information problem problem problem problem problem models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based space space space space space weights linear linear linear case case case case case vector vector vector shown shown systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise functions unit distribution distribution distribution distribution distribution distribution distribution recognition recognition approach single processing processing control control large local local local rate rate rate matrix optimal optimal inputs inputs form form form shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple gaussian gaussian visual visual paper paper examples work work work task task points process process process process process process process structure problems problems problems problems problems problems problems random random random similar representation equation equation equation equation equation equation equation equation fixed fixed fixed fixed line line line rule general generalization speech speech parameter parameter parameter parameter parameter parameter real real average average average average average average states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained term term term note note note note dimensional dimensional dimensional university university university variables computation solution solution solution solution solution research independent independent independent independent log log log log log log log log log defined defined found found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial constant estimate computer connections connections synaptic synaptic science science science present activation activation nodes nodes nodes nodes temporal temporal object sets motion motion motion motion motion motion motion maximum maximum learn position components components components components outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied computational density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic procedure important important important decision decision propagation introduction introduction estimation estimation estimation estimation estimation estimation statistical dynamic generated generated generated generated variance parallel cost cost recurrent recurrent recurrent tion variable variable classifier measure measure measure signals signals prior part previous theorem theorem type required good conditions conditions conditions conditions tree tree distributed bayesian bayesian bayesian bayesian equations equations equations equations markov markov markov markov fact techniques techniques techniques techniques correct correct correct probabilities probabilities observed resulting tasks tasks total simulation respect respect respect respect respect respect respect respect respect performed called called optimization potential natural natural feedback applications em filter artificial samples samples represented application provide define proc related distributions distributions distributions distributions distributions discrete equal equal power contrast connection fields modeling morgan department department department advances advances represents represents exp exp exp exp bias addition sequences considered framework framework framework computing equivalent equivalent equivalent curve curve curve curve curve curve curve curve solutions solutions design design design limit limit limit san san san stimuli stimuli stimuli stimuli stimuli detection detection detection detection detection detection detection detection detection efficient efficient choice choice approximate approximate speed vision estimated estimated pages give condition derived weighted conditional levels path path path path path path path path path path path path path path processes processes processes processes processes processes backpropagation depends sampling constraint discussion discussion discussion tested close corresponds corresponds corresponds complete assumed shape generate supported supported role theoretical eds end pixel future makes noisy noisy fit fit kaufmann simulated probabilistic probabilistic probabilistic typically needed needed ratio trials language leads representing details direct idea improved machines sense inference cognitive cognitive cognitive engineering interest interest interest interest interest sufficient sufficient conventional conventional observations volume yields yields speaker differential differential address interval williams williams williams williams entire entire scaling trial trial wide derivative derivative derivative hybrid deterministic deterministic setting hardware hardware strength assumptions assumptions trajectories operator valued valued valued valued valued valued valued depend depend numerical numerical designed practice practice weak weak propose presence sigmoidal sigmoidal california california california solid variety variety identification identification denoted denoted denoted acknowledgements boltzmann reference reference reference reference reference reference explicit explicit explicit monte monte carlo carlo written sensitivity explicitly unique equilibrium applying springer springer implies focus communication viewed interpretation open evaluate approximated additive performing performing spaces spaces normalization reduces event false iterative tracking tracking tracking valid filtering filtering perceptual perceptual contour contour contour determines prove domains partially efficiency importance suitable suitable suitable paths paths paths paths paths paths paths paths wij detect literature computations characteristic characteristic conf verlag kind procedures induced prob allowing showing interpreted neuroscience neuroscience dis sin gray satisfy quantity usual realistic realistic observable observable observable observable observable observable observable observable observable observable observable observable observable correspondence maximization illustrates operating operating approximating satisfies satisfies tesauro cowan law law law employed simpler diego diego diego poor poor poor experience kalman environments involving involving involving optimized optimized integral integral recursive dotted hall helpful existence ideal combine scaled authors notion coefficient naturally thought ensure aspect obvious formal explored detected improving regime defines averages mentioned developing formula formula formula formula formula theoretic crucial growth publishers orientations defining adapted diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion purposes filtered desirable desirable mathematics potentially implicit members optimize optimize nsf nsf addressed conjugate integrating profile flexible formulated treated ity mod proven proven achieves marginal asymmetric expectations ordinary identifying identifying identifying identifying drift drift drift drift drift drift drift drift drift drift driving optimizing plays numerically numerically numerically hit hit receiver receiver intuitive alspector prentice paul paul mental den treatment jolla jolla jolla refers rich theoretically observer observer grants interestingly divide ure ure ure roc roc roc roc fellowship achieving markovian distinction quasi quasi sigma generalizations sinusoidal care graduate denoting denoting differentiation differentiation sweeping alarm algebra page page elsevier els ucsd ucsd ucsd lems rabiner rabiner observables observables observables observables laws opti uniqueness send european builds blake blake blake blake movellan movellan movellan movellan movellan movellan dominates concern dom tribution couplings obey contributes anthony juang juang measurable sity fin accommodate appro lar ized mle dispersion dispersion dispersion dispersion dispersion hood mization collision cient undesirable undesirable ily calculus environ henceforth functionals xlo expressing condensation contin particu formulating likeli succeeded integrand factoffal factoffal uous ruth brownian brownian brownian brownian brownian brownian brownian borel borel borel ger fundamentals mations intriguing isard isard isard isard rio rio coo sinusoid facto apriori apriori unfolding fro timation mensional dms cogsci cogsci javier seldom spect timescale timescale minority unperturbed radon radon radon odes sinusoids localizes bustness algebras veloc 
#@Mineiro_P,Movellan_J,Williams_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number system error error error error error error error error error error error error error error error error error error error problem models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based space space weights weights weights weights weights linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer case case vector vector vector shown shown shown shown shown shown values noise weight weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point image image image image single single processing processing control local neuron test test test test patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis class class class class matrix matrix matrix form form form shows shows shows signal signal signal signal signal signal signal signal signal signal algorithms algorithms gaussian visual visual visual examples examples examples examples examples work work methods step step step step step step step step step step step step step field features classification classification process process process process process process process level trained trained trained trained trained trained trained problems response similar architecture show fixed rule rule rule vectors vectors vectors vectors vectors vectors vectors images images images images images images images generalization generalization approximation average theory gradient gradient gradient gradient term note experiments experiments experiments dimensional dimensional dimensional dimensional dimensional variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation computation computation computation research found sequence target target target dynamics dynamics terms terms connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic science science science left present activation machine machine machine object object range learn learn learn learn components components components components components components components basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous abstract applied back back convergence properties references component component component component due due ieee positive procedure important adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation action hand statistical dynamic generated generated generated generated parallel cost cost cost cost cost recurrent recurrent tion difference prior representations learned learned cases multiple cortex good long represent equations techniques proposed correct errors classes classes ing respect respect respect respect performed performed performed called called called called times means optimization optimization optimization potential feedback feedback feedback feedback feedback feedback global global negative negative negative negative negative relative compared compared define define proc proc perform constraints constraints power accuracy comparison comparison comparison contrast update update descent descent descent descent descent modeling modeling modeling words consists internal bias layers layers maps computing equivalent equivalent experiment hinton hinton hinton hinton view solutions curves top top top top top top top top top top top top top top top top top top top top top top top top top determine world pages coding levels types types processes backpropagation backpropagation nature depends constraint discussion group tested transformation transformation fast close proof finding finding nearest shape generate generate generate generate generate generate generate generate generate generate supported supported theoretical pixel pixel ability ability ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis rumelhart sensory sensory sensory sensory sensory sensory sensory sensory sensory sensory fit probabilistic probabilistic probabilistic probabilistic needed fully fully jordan transfer programming programming testing testing testing testing consistent matching database database database operation operation operation language principal principal principal principal principal principal principal principal principal squared representing normalized bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom early produced added denotes improved improved discussed improve improve advantage separate separate separate ensemble subject subject inference sejnowski cognitive cognitive relevant relevant compare previously unsupervised unsupervised tions solve pca pca pca pca pca pca pca pca pca converge mixtures chain grid williams constructed matrices matrices locally locally loop loop loop loop deterministic generally pass pass pass pass pass demonstrate conclusion operator neighbor editors editors sigmoid performs performs learns encoding encoding encoding propose cycle radial min min averaged groups minima attractor attractor attractor boltzmann boltzmann explicit explicit explicit appears digit digit digit digit digit digit digit digit digit digit written written written longer perception perception sequential sequential distinct multilayer transformations belief belief belief interaction adding minimization minimization springer formed quality versus choosing review reconstruction reconstruction reconstruction reconstruction reconstruction depending interpretation interpretation variation approximations lee lee lee evolution evolution activities completely completely digits digits digits digits digits digits digits slow epochs epochs epochs convex reduces add iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative generation generation generation generation generation generation generation generation generation generation generation generation generation generation remains foundation classified existing handwritten handwritten handwritten handwritten handwritten handwritten activations activations bell bell bell inter batch batch recognize variations domains phys discussions tests columns compression aspects suitable driven attractors attractors online identity traditional compact verlag quickly interpreted superior symmetry manifold manifold manifold manifold manifold generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative notation vary dayan dayan minimizes minimizes minimizes hypotheses ill minimized layered varied dual helpful variability variability variability proved encode understand cognition hill closest editor predicts rev adjusted prototype logistic generates simplest neal derivation derivation multiplication briefly nonlinearity nonlinearity nonlinearity starts starts starts processed processed perspective perspective immediately laboratories scientific scientific inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion inversion implicit implicit res meaning mechanics argument geometric prop prop prop prop prop prop prop prop prop prop prop prop empirically embedded readily lack lack backprop backprop backprop continuously span operate synthesis reaches reaches gave expectations jaakkola converged converged globally sleep appearance lagrange lagrange acts repre lecun multipliers multipliers adds murray convenient balance resulted viewpoint cottrell enhanced saul iteratively iteratively regarded dominant den propagated propagated treatment recog permutation surprisingly surprisingly omitted ballard park seung seung seung seung seung seung seung variants propagate propagate alternatively summarize tures bertsekas indirect vec helmholtz helmholtz helmholtz munro rao nition encouraging propagating connec hundred auxiliary auxiliary rain wake mismatch deep interact labs labs manifolds manifolds manifolds manifolds inverted inverted argued intensities constructs represen suffer suffer grateful inverting inverting inverting inverting inverting inverting inverting inverting inverting inverting frey parametrized technologies spite spite utilizing info info generarive generarive generarive saturated tial thousand skin utilizes generafive generafive generafive generafive generafive generafive generafive generafive king cornput cornput autoencoder autoencoder hid tors outperformed ackley partly architec tended tended zipset inde confined cho wong inaccurate sentation problematic syst syst recovering revow adv adv stepsize stepsize stepsize richer activates sebastian lid lid invert invert inability deformations usps usps belmont disagreement singapore singapore tational ans gra generatire generatire generatire generatire generatire generatire generatire generatire generatire revised compactly resembling linden realizes incentive lucent dan dient athena intell yeung emd emd emd emd chines upwards kwon kwon revise revise deficiencies kindermann plateaus closes virtues awt terministic sharkey subimages jong ablex unconscious artif extensional mage perceptions sequen pretation multidisciplinary pendently norwood dressed professorship deforming 
#@Oh_J,Seung_H,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model input input input data data function function function figure figure time time time time time time time time time time set set set training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number error error error error error error results results results results results information problem problem problem problem problem performance based based based based based based based based based based based based space linear case vector vector vector vector vector vector vector vector vector vector vector vector vector order order values probability probability probability probability probability probability probability probability probability functions distribution distribution distribution distribution recognition recognition recognition recognition recognition approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern single large large rate test patterns patterns patterns analysis class class class class class class class class class class class class class class class class class optimal optimal optimal optimal form form shows algorithms algorithms simple simple paper examples examples examples examples examples examples examples examples examples examples examples examples small small size size size size size size size size size size size size size size size size size size size size cells cells step step classification classification classification classification process level current current current current current cell cell cell cell structure structure problems problems problems problems random random random random high section fixed fixed fixed fixed fixed line rule rule rule rule rule rule rule vectors general general general generalization generalization generalization generalization generalization average average theory theory theory theory gradient obtained experiments dimensional dimensional result university variables computation computation independent defined defined defined defined defined defined defined sequence sequence sequence sequence constant estimate computer computer terms direction present machine maximum maximum press learn learn components outputs outputs sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract computational computational density density density density references component component component ieee ieee positive positive positive positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important decision decision mixture introduction complex hand estimation estimation statistical generated generated change difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower rules chosen chosen part part bound represent expected make make make region correct correct probabilities probabilities probabilities probabilities minimum classes classes classes classes classes classes classes classes classes classes classes classes classes ing ing total total total respect respect respect respect multi multi multi multi multi multi multi multi multi multi dimension knowledge em em obtain vol vol specific specific samples represented represented true true compared compared series define define define active determined experimental experimental experimental related constraints distributions discrete equal equal accuracy accuracy contrast update descent descent selection morgan proceedings report report report institute loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss consists consists consists joint represents represents cambridge computing domain experiment directly solutions curves curves curves san stage effects efficient efficient efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers significant significant randomly randomly randomly conditional conditional conditional criterion criterion criterion criterion criterion criterion criterion criterion types path selected selected depends depends sampling sampling technical describe denote denote denote denote denote denote denote denote denote denote fast limited assumption amount nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest assumed assumed assumed assumed generate theoretical require main end end end end end ability hypothesis instance easily makes kaufmann probabilistic pairs pairs underlying underlying underlying reduced reduced unknown unknown unknown unknown unknown technology programming interesting character york increasing increasing uniform empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical principle call call call stored international minimize run run denotes denotes denotes denotes recent separate element element typical practical introduced array relevant engineering dimensions approximately calculated tuning trans trans definition definition background bounded bounded bounded improvement risk lead deviation boundary boundary setting runs runs minimal minimal minimal minimal minimal minimal minimal minimal reduce reduce reduce neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor depend bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes learns taking drawn drawn drawn drawn proportional regularization labeled labeled labeled labeled labeled user start selective min manner characters denoted produces written index label label distinct dept confidence implement category category category category category category category category coordinates infinite dimensionality dimensionality remaining consisting consisting consisting consisting minimization minimization minimization minimization minimization minimization springer springer implies expectation expectation versus boolean boolean boolean boolean boolean boolean boolean select select family expressed expressed review viewed learner labels labels forms sizes converges partition diagram false false boundaries boundaries boundaries penalty query query query query query handwritten handwritten priori priori priori priori batch batch batch batch batch batch batch batch batch batch recognize vapnik vapnik vapnik vapnik vapnik structural selecting uniformly refer refer refer verlag verlag procedures procedures procedures contained success showing interested return return contribution classify classify running satisfy write minimizes rat minimized powerful collection discriminant reducing ideas incremental incremental incremental incremental incremental incremental incremental incremental incremental referred referred gates gates workshop closest necessarily necessarily necessarily integer integer integer reading queries queries queries queries queries queries prototype prototype prototype prototype prototype greedy greedy algo freedom generates improving mentioned adjacent briefly closer style ran ran hyperplane commonly author geometry geometric questions improvements frequently http prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes berlin differs aim achieves inherent initialization picture representative pac www labeling fix fix fix rithm hyperplanes jth partitions jones jones connecting handwriting obtaining settings nonparametric selects passive sion corre displayed counting chooses initialize israel recog indicator draw draw draw hart hart integers limitation maintaining ple ple misclassification misclassification basically basically asked ram ram chervonenkis axe nition incrementally decomposed hundred constitutes letting letting reject reject pub pub cohn cohn cohn increment increment increment perpendicular exam ftp ftp learnt permits harder cation cation sam ignoring gorithm voronoi voronoi voronoi voronoi voronoi info info sponding ble const const nested families utilizes utilizes puts err outperformed proportions ples separates beneficial triangulation triangulation scenarios losses complement rivest inde comprised elec minimizer actively actively ira atlas atlas technion technion technion discriminating pendent argmin argmin argmin borders impor theo theo dependences puter tant silverman silverman separability participate henceforth henceforth henceforth subsample subsample subsample subsample subsample possi classifi classifi delaunay delaunay cri inn inn inn inn inn inn inn inn inn inn arrangements swiss dropping federal devroye devroye devroye condensed condensed resorting dictates querying querying querying querying querying querying querying expres ioo ioo occured occured url queried rnj ilk lugosi terion ail pie proto adverse beled pirical beating equiprobable 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#@Ratsaby_J,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model model neural neural neural neural input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time set networks networks networks networks networks networks networks networks networks training algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number number number number number number number number state state state state state state state state state state state state state state state state state state state state state state state state state results results units units units units units units units units units units units units units units units units units units units units units units units units information information information weights shown shown shown shown shown shown shown shown shown shown shown shown systems systems values values values values values values values values values values values values values values values values values values values values values values values values values functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit recognition pattern point point point single single single processing processing class inputs inputs inputs inputs form shows shows simple small small net step step step step step step step step step points current current current current current current structure structure structure structure structure structure structure structure structure problems similar architecture equation section section fixed fixed fixed generalization real states states states states states states states states states states states states states states states states states states states states states states states states states states states states result university threshold threshold threshold threshold threshold threshold threshold solution research sequence constant constant constant constant constant table computer computer connections node node left activation nodes temporal press press basis basis outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous abstract applied back computational computational computational computational references propagation introduction generated generated generated generated generated generated generated generated generated cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent lower lower higher higher center previous previous previous theorem bound type required long represent represent represent represent expected fact proposed proposed correlation correlation correlation correlation correlation finite finite finite finite finite finite finite finite finite finite finite finite mapping means means made specific represented represented represented compute compute compute compute compute determined connected connected discrete discrete discrete discrete discrete power power mit steps connection connection source modeling modeling modeling report words department department consists advances sequences considered transition transition transition transition transition transition limit san efficient upper pages pages increase con produce produce developed lines lines provided simply simply technical describe describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary fast limited limited limited assumption proof proof proof proof proof proof proof proof proof proof proof proof implemented implemented assumed generate generate generate generate theoretical theoretical future future development including including kaufmann pairs pairs fully technology transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer interesting principle principle representing details call call call making making bits produced produced discussed property pair practical apply period period period period period period period period interest converge rl generalized exists alternative touretzky touretzky demonstrate conclusion starting greater greater greater reduce editors editors sigmoid sigmoid sigmoid sigmoid sigmoid designed moody mateo hard hard hard hard hard hard sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal california labeled labeled radial radial assuming assuming exist exist manner manner produces factors factors generating generating laboratory transitions transitions transitions distinct distinct distinct distinct distinct distinct distinct distinct distinct modeled modeled modeled modeled category explicitly explicitly infinite remaining unique implies national expressed lemma lemma lemma lemma restricted labels labels showed lee dashed purpose remains sufficiently sufficiently foundation transactions existing existing includes thesis sciences mozer mozer mozer mozer mozer mozer specifically efficiency capable capable computationally receives receives composed composed link showing notation simplified modular giles giles giles giles giles giles giles giles computes overlapping receive exhibit detail limitations limitations limitations limitations limitations reducing reducing reducing links mappings investigated parity parity oscillation circles automata automata psychology generates massachusetts distinguish distinguish distinguish distinguish distinguish publishers capabilities capabilities cascade cascade cascade cascade processed ring ring ring ring ring ring producing circle toronto demonstrates meaning sun argument argument applies share share fall proven proven serve chen chen germany kinds sophisticated sophisticated sophisticated focused begins eventually lim arithmetic proofs proofs proofs proofs proofs feasible impossible arranged significance odd replacing automaton automaton automaton automaton serves mark mark exploit substituting continue reliably ambiguity intended uni suggesting offer master matter repeatedly repeatedly repeatedly repeatedly theoretically inductive inductive fahlman fahlman fahlman mind arcs arcs email distinction ease amherst german remainder fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa fsa names ambiguous minor places refined mann demonstrating functionality oscillate oscillate oscillate identically distinguishing discarded discarded restricting proves proves proves inspection gmd gmd gmd oscillates oscillates allocating crg accepting repeats versity mike proving lemmas exposition assist triples triples reachable reachable unspecified representable representable representable isolate paragraph bachrach bachrach bachrach gan cas incapable incapable incapable incapable incapable mor conceivable ifx ifx ifx ifx bachtach sophistication sophistication goudreau ces halting halting lipp augustin cyclical cyclical hopes liere 
#@Ring_M,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure time time time time set set set set set set training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number error error error error error error error state state state state state results information information information information information information problem problem problem problem problem problem models models models models models models hidden hidden hidden hidden hidden space space space space space space space space space space space linear linear linear linear linear linear linear linear linear case case case vector vector order shown shown shown shown systems systems values values values values values values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise functions unit distribution distribution distribution distribution distribution distribution distribution method method method approach point point point point point point point point point point point image single single single single single single processing large large large large local local local rate test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs inputs form form form form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples small small small small size work work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step step step step step step step step step step points points points points points points points points points points features level level current current current structure structure structure structure structure problems problems problems random high high high high high high similar similar representation show show show equation section fixed line vectors vectors vectors vectors vectors vectors general general general parameter real real real states states states states states states obtained note note note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university university university variables computation computation computation computation computation solution solution research research independent independent independent independent independent independent defined defined found found found found found dynamics initial constant constant estimate estimate estimate standard standard standard standard standard computer terms terms distance distance distance science left left left direction direction present present low sets maximum maximum maximum maximum maximum range press press components components components components components components components basis sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied find find find find find computational computational convergence convergence convergence convergence convergence convergence convergence density density density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references references component component component component component component component component component component component component component component positive procedure important important hand hand hand statistical effect generated variance variance cost cost energy complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable variable variable lower lower rules learned learned previous cases cases cases required required required required required multiple distributed distributed distributed expected expected expected make fact fact techniques techniques correct observed observed observed observed observed errors scale scale minimum resulting resulting ing regression computed computed computed computed sum performed performed called called times means factor factor dimension feedback orientation orientation orientation global global study em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em obtain original true true true compared series provide define define compute compute compute compute compute compute compute compute perform perform perform goal related related posterior posterior posterior equal equal power power power power approaches steps update update morgan report report report report report institute words words version technique consists individual advances joint represents difficult scheme computing computing computing computing computing computing computing computing computing equivalent equivalent directly directly directly hinton hinton curve estimates limit limit limit limit efficient efficient efficient full full full full significant free free free vision estimated pages give give produce condition derived derived developed criterion lines lines product product actual provided finally finally finally iteration iteration iteration depends constraint simply discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance normal normal technical technical technical technical group group denote transformation transformation limited limited limited limited limited complete complete complete stable finding finding finding finding assumed assumed shape generate generate generate require require require require journal easily easily easily makes fit kaufmann probabilistic probabilistic probabilistic probabilistic typically hopfield reduced unknown unknown unknown unknown jordan interesting ratio projection projection projection projection structures operation principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal squared squared squared squared squared call call numbers iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations direct direct making stored normalized supervised minimize minimize minimize produced choose choose choose choose run improved discussed directions directions directions directions directions pair reported apply identical inference inference inference inference inference interest dimensions dimensions dimensions dimensions dimensions dimensions varying observations volume axis axis pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca converge diagonal diagonal diagonal mixtures mixtures evaluation symmetric observation observation observation generalized generalized storage storage constructed lead scaling scaling deviation deviation matrices matrices correctly column column column setting runs critical critical greater reduce competitive editors central taking taking taking presence reduction drawn drawn drawn drawn california solid assuming assuming variety exist introduce introduce question denoted denoted acknowledgements explicit appears van written written solving estimating estimating dept recall missing missing missing missing missing missing missing missing missing missing missing explicitly explicitly explicitly explicitly explicitly explicitly explicitly explicitly coordinates linearly physical dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality easy unique scales expectation expectation john extracted family reconstruction reconstruction reconstruction reconstruction reconstruction squares squares squares viewed viewed lemma variation evaluated evaluate operations operations operations operations operations restricted restricted restricted restricted decomposition similarly converges key partial dashed dashed dashed additive performing reduces reduces roughly roughly iterative iterative interpolation remains symbol assigned construction norm advantages avoid recorded recorded recorded combinations combinations coordinate coordinate usa eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues contour subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace illustrated uncertainty maximize columns columns columns regular straightforward compression compression closely society modification computationally latent latent latent efficiently efficiently efficiently computations projections projections projections online identity identity orthogonal capture capture summary notice notice notice notice repeated showing interested running follow generative generative notation write usual michael michael michael dot generalize minimizes minimizes minimizes eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue highest leading leading leading leading leading leading leading leading leading reach maximization maximization deal software tesauro cowan bars origin unlike requirements investigate dataset dataset behaviour behaviour behaviour scalar fewer fashion ideas tech tech tech project project project investigated relationships working working proper proper proper proper eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors hill trace trace possibly extremely created rank rank rank singular front front obvious obvious portion algo panel panel panel panel panel multivariate contributions defines synthetic synthetic rows formula floating floating multiplication multiplication multiplication lies lies worse london widely ran bishop bishop bishop bishop arise products products mathematics ion inversion inversion inversion projected projected toronto incomplete incomplete incomplete incomplete outer requiring greatly pseudo amounts axes employ variant span release http limiting limiting cal ordered datasets datasets datasets coherent sophisticated comments lim lim progress june naive ghahramani ghahramani ghahramani proofs aligned aligned aligned identifying www assign forming oxford restriction restrict fix rithm ratios arguments pick controlling royal oja difficulties analogy replacing attractive attractive sanger guide ylx ylx hours motivation repeat excellent excellent iteratively lengths uni yang spherical spherical spherical properly informative eigenvector eigenvector eigenvector eigenvector eigenvector likelihoods implicitly lett lett dempster ics speaking multiplying multiply users rubin achieving aston aston lane benefits restrictions solely hundred england workstation guess guess guess guess guess guess imagine gene algebraic cns intuition intuition geoffrey chapman graduate dominated denoting careful projecting spanned laird nonetheless sam rod rod rod rod rod rod grateful stuck xly xly xly xly xly thousands thousands thousands permit eigen holding matlab matlab matlab september october unpublished completed manuscript students served chris fortunately christopher christopher invertible invertible invertible thousand spring hundreds suffers virtually shot shot shot attempting hoc hopkins determinant dom identically cally svd svd discarded zoubin zoubin johns transpose factorization constraining accommodate edition ance charles feb unusual baltimore subtle modest explaining costly costly datapoints datapoints datapoints datapoints datapoints datapoints datapoints datapoints rotate tipping tipping tipping tipping jack searched collections crg plexity plexity save save graphically trick trick multiplications mike infinitesimal analyzers puted remember numbered complexities complexities reconstructing ana turbulence trouble dong gerald fellow shortcomings ncrg ncrg altogether trivially nique geoff joshua plied roweis roweis roweis roweis anonymous ofp extremum compressing brody pursuing restarted pute crc crc eration flops 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#@Roweis_S,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time set set set networks networks training training algorithm algorithm algorithm output output output output output output output output output output output output output number number number number number number number number number number number system results results results results results results results results results results results results results results information information information information information problem problem problem problem models models models based based based based space space space space space space space space weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case vector vector vector vector vector vector vector order order order shown shown shown shown systems systems systems systems probability probability parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight functions functions functions functions unit unit unit unit distribution distribution distribution distribution method approach point point point point single single single processing processing processing processing processing control control control control control large local local local local local local local local local local local local local local local local local local local local local local local local local test test test test patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form signal signal algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper small size work methods methods methods methods methods methods methods methods step step step step points points points points process process process process process process level problems problems problems problems random high high high high high high high high high high high high high similar architecture show equation equation equation equation equation section section line real approximation average average average average average average obtained obtained obtained note experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university threshold variables variables variables variables variables computation computation research research research research independent log defined found found dynamics estimate estimate estimate estimate computer distance distance distance science science science science present low low low low low low low low low low sets sets sets sets sets maximum press press press press press press components components components nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs outputs continuous abstract find computational convergence density likelihood likelihood references component component component component component component component component component component due due positive important important mixture context context introduction hand estimation statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical effect dynamic generated generated generated variance variance variance variance variance variance variance tion tion tion variable variable variable assume measure prior chosen chosen chosen previous previous theorem cases cases cases good conditions conditions conditions conditions conditions conditions conditions conditions conditions distributed distributed distributed expected expected expected fact techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques correlation correlation length correct correct correct observed simulations ing ing ing tasks human human regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect respect sum performed called times elements mapping means factor factor factor factor factor factor factor factor factor factor factor factor made global global study knowledge em em em em em negative artificial artificial true true true application cross compute perform perform perform perform perform perform determined determined experimental distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions brain equal equal equal mit fields support modeling selection morgan institute institute department loss version technique technique technique technique technique kernel kernel kernel kernel kernel advances advances joint joint joint joint joint joint joint final bias bias considered framework cambridge cambridge computing hinton hinton hinton view view view conference efficient efficient requires choice significant statistics estimated increase validation con condition condition condition derived weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted randomly randomly conditional robot finally iteration iteration biological biological covariance covariance covariance covariance covariance normal normal normal feedforward arbitrary transformation fast inverse assumption complete common assumed assumed shape generate generate supported theoretical require require eds face journal instance easily makes including kaufmann probabilistic underlying reduced account functional coefficients coefficients coefficients coefficients coefficients coefficients coefficients jordan jordan jordan jordan technology technology significantly ratio projection york york special trials uniform uniform empirical principle principle principle principle principal principal principal principal principal principal principal principal principal iterations max max pre international experts experts magnitude magnitude produced choose added added added added added sources denotes denotes denotes improve robust robust robust robust robust element quadratic quadratic quadratic quadratic quadratic quadratic quadratic hierarchical dimensions dimensions dimensions dimensions varying varying compare calculated tions tions pca studies diagonal diagonal diagonal address evaluation increased grant arm exists parts lead lead lead wide alternative locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally locally touretzky touretzky conclusion row assumptions assumptions assumptions assumptions assumptions conclusions operator clear clear performs performs practice weak taking strong strong largest largest reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction reduction characteristics sigmoidal california intelligence assuming movements iii iii iii force question denoted areas relation pro monte monte monte monte monte derive derive derive derive carlo carlo carlo carlo carlo factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors generating generating generating estimating estimating plot ann dept confidence metric metric averaging dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality transformations easy slightly slightly text quality expectation expectation national independently focus focus focus review stages squares squares squares squares squares squares squares squares squares squares squares viewed evaluate evaluate evaluate evaluate evaluate controlled showed forms soft suggested partial partial partial partial partial partial partial partial partial additive additive reduces fitting neighborhood neighborhood neighborhood neighborhood purpose iterative iterative remains remains sufficiently foundation foundation query query advantages advantages avoid includes includes combinations coordinate weighting weighting weighting subspace illustrated candidate candidate candidate tests major simplicity determining closely closely closely uniformly computationally divided latent latent successful projections projections projections projections projections projections projections projections comparing essentially identity summary summary summary summary refer repeated strongly prob moore moore moore moore interested neuroscience superior issue contribution contribution follow device comp quantity involved computes maximization consisted jacobs jacobs acknowledgments tesauro origin parametric powerful american wiley wiley transformed investigate put put relations association association hall ml pursuit examine tech project incremental incremental authors office eigenvectors func statistically adapt equally equally equally equally perfect ensure ensure friedman friedman friedman friedman friedman versions noted assumes assumes assumes assumes precise nervous multivariate synthetic averages rows ment defining growing fairly expensive cascade cascade caused briefly worse worse london considerable spatially drive tive division ran ran worst worst laboratories scientific inversion inversion projected projected projected separately involve calculations definite localized localized robustness robustness robustness apparent empirically tional atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson employ formulated frequently incorrect incorrect ity ity http http http calculating summarized summarized spread extracting achieves geman semi kinds kinds kinds kinds shaped tolerance univ irrelevant globally globally globally ordinary ordinary college secondary leen primarily www www www forming perfectly perfectly perfectly perfectly dynamically outcome turned robotics generality air fits adds tools proceeds hyper hyper hyper los kawato bands obtaining exploit operates imply constructive evaluations interference bartlett sion equals surprising von uni spherical spherical spherical candidates offers chooses chooses dif bases initialize initialize recovery foundations young surprisingly omitted offer late theoretically horn horn hypercube papers tures fahlman fahlman interestingly balanced johnson johnson empty empty rubin rubin recursively july employs suboptimal residuals additionally german german descriptions guess guess summarizes translated translated translated magnitudes geoffrey chapman distribu activate degraded degraded projecting noting lookup increasingly spanned tively inversely grateful sta atr subspaces exploratory mix lems circumstances cube cube served chris observables observables advantageous bienenstock accordance christopher sake ferent curse neighborhoods suffers puts accomplish japanese award appealing appealing sensorimotor condi schaal schaal schaal schaal schaal schaal schaal schaal schaal schaal schaal automation manually manually interpolating tokyo tokyo explanations maxi prone inde dimen cho cutoff gence south scott scott deter locality acknowledges robustly mis translate lwr lwr putation addi degrades lebiere lebiere proximation pendent contributing dilemma dilemma approxima optimizes invert ness fight weakness ver angeles excluding alexander fac ily gun perspectives fulfilled fulfilled clipping serving fil unequal unequal unequal arms arms ministry indistinguishable mined kyoto presidential mary orthogonality frank frank frank frank frank mon gression gression proportionally ror violations violations stefan loses inexpensive soraku ubiquitous autonomously diagnostics originate ric cients seika atlanta investigators identi variate estimations kuh chart chart doursat regressions regressions regressions regressions education dition contaminated contaminated cording surely ported georgia gatech gatech guessing itera wei scholarship holes coeffi abbreviated sumptions ensured aca sionality domly duction anymore mensional outperforming outperforming violating cga founda influential intelli tically pending culture slab mally subdivision wold wold usc usc atlantic qua evalua jections ofy believes warranted telligence hopeless charts 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#@Atkeson_C,Schaal_S,Vijayahunar_S,
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#*network learning learning learning learning learning learning model neural neural neural neural input input input data data data data data data data data data function function function function function function function figure time time set set set set set set set networks networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm number system error error error error error error error error error results results results results results results results results results results results results information information information information problem problem problem problem problem problem problem problem performance performance performance performance performance based based based space space space space space space space weights linear linear linear linear linear linear layer case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown systems systems values values values weight weight functions functions functions functions functions functions functions functions recognition recognition recognition recognition recognition recognition recognition method method method method method approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image image image image image image image image image image processing processing control large local local local local local local local local local local local local local local local local local local local rate rate rate rate rate test test test test test patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal form form form form simple gaussian gaussian examples examples examples examples examples small feature feature work work task task task methods methods methods methods fig points field features features features features classification classification classification classification classification classification classification level trained structure random random random high memory similar similar show show section section rule vectors vectors vectors vectors images images images images images images images general general parameter parameter theory theory theory gradient obtained obtained obtained obtained obtained obtained obtained term term note note note experiments experiments experiments experiments dimensional result result variables computation solution research defined defined defined defined found found target initial constant constant constant table table table table table table estimate estimate standard standard standard standard standard standard computer computer terms terms distance distance science map present present present present machine machine machine machine machine machine object object maximum maximum range range range range press press press learn components components components nonlinear nonlinear nonlinear nonlinear continuous sample sample abstract applied applied back back computational references component component ieee positive positive positive important adaptive decision decision decision decision decision decision introduction introduction action hand statistical effect variance complexity classifier classifier prior prior prior prior prior prior prior prior prior chosen chosen higher part bound cases cases type required binary long long conditions conditions represent make fact fact techniques techniques techniques region proposed forward minimum resulting resulting resulting classes classes ing ing tasks tasks regression computed respect respect respect multi sum sum called elements elements regions regions factor optimization optimization optimization optimization dimension dimension natural global study study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge obtain obtain obtain obtain original vol relative relative specific specific compared desired series receptive receptive receptive provide define compute compute compute rates rates rates rates determined experimental experimental goal related constraints constraints equal power power accuracy comparison fields fields support support support support support support support support support support support support morgan morgan proceedings proceedings report report words technique technique code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances ai ai considered considered considered domain domain domain directly additional design san san conference determine efficient classifiers classifiers upper full speed speed pages pages pages pages pages condition condition condition derived types types types types types lines product product product product product product product product product product provided finally selected nature depends discussion discussion covariance covariance covariance covariance technical describe group group tested transformation transformation fast limited inverse inverse corresponds corresponds corresponds stable short nearest common assumed require main main face square square square end pixel instance instance future degree degree degree degree degree degree degree kaufmann kaufmann objective typically account account account account testing testing significantly york edge database principle operation operation leads leads leads leads leads principal principal principal principal call max max international polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial choose run run sources predict denotes improved improved directions directions directions directions correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations resolution resolution element include subject subject subject machines machines machines machines machines machines machines pixels pixels pixels pixels quadratic quadratic subset subset sufficient compare approximately tions solve yields yields pca pca pca pca pca diagonal diagonal diagonal background positions chain locations separation separation modified modified observation improvement increased horizontal parts lead invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant scaling scaling scaling suggests deviation derivative locally boundary generally reduce editors editors editors tangent tangent tangent tangent tangent tangent tangent performs moody practice mateo mateo taking hard reduction reduction turn turn assuming variety minimizing minimizing minimizing minimizing start exist min relationship derivatives characters groups base base question acknowledgements digit construct written written vertical dimensionality dimensionality dimensionality transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations text scales consisting consisting applying minimization springer springer implies choosing choosing choosing interpretation evaluated evaluated open controlled centered forms margin margin margin margin suggested translation translation translation translation digits sign smoothing smoothing slow slow expansion expansion expansion convex sec sec sec sec sec sec sec sec reduces combining purpose distances construction norm advantages degrees handwritten handwritten handwritten kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels usa formulation bell eigenvalues eigenvalues eigenvalues inter vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik maximize partially partially discussions importance society modification build invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance orthogonal orthogonal verlag verlag verlag symmetry lie lie hold hold dot dot dot dot dot dot dot dot giles eigenvalue denker denker denker leading leading leading automatically extract deal cowan presents explore carried carried transformed put put put hanson hanson lippmann dual helpful giving ideas detectors applicable applicable applicable applicable possibility relationships relationships scaled scaled reliable reliable reliable root maximizing comparable eigenvectors eigenvectors workshop affect editor thought ensure subsets der der pyramidal pyramidal defines rows fairly explanation worse drive satisfied formalism preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing preprocessing strictly constructing constructing constructing incorporate ran leaves desirable sgn sgn sgn sgn hyperplane hyperplane hyperplane hyperplane hyperplane mation products products simard simard simard simard simard simard simard simard circle beginning gradually definite definite definite localized annual argument argument requiring virtual virtual virtual virtual virtual virtual virtual improvements improvements improvements improvements improvements improvements improvements prop applies understood led led led affine consistency amounts red leave poorly introducing haussler incorporated incorporated variant compares requirement span berlin berlin berlin pittsburgh incorporating incorporating incorporating substantial substantial substantial germany germany differentiable differentiable pyramid trade notes sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv sv modify acm acm appropriately appropriately recover hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes labelled controlling homogeneous homogeneous homogeneous nonzero rotations lecun lecun lecun lecun lost dealing simplify exploit exploit carry generalizes heuristics substituting substituting substituting service separating separating separating introduces corre respective von von evident jackel dif entries entries diameter diameter membership express designing implicitly explains alternatively integers dividing assigning smola smola smola smola smola smola speaking unchanged yielded usage drop ple sch sch sch sch sch sch sch sch sch sch equivalently equivalently guyon guyon chervonenkis chervonenkis bank tween retraining boser reports malsburg german possibilities possibilities burges burges burges burges burges arising invariances invariances invariances 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#@Scholkopf_B,Simard_P,Smola_A,Vapnik_V,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks 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class class class class class class class class class class class class matrix optimal shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple simple visual paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small size feature net net net net work work work work task task task methods methods methods methods methods methods points points features features features features classification classification classification classification classification process trained trained trained trained trained trained trained trained structure problems random random random random high high high similar similar similar representation architecture architecture architecture architecture architecture show equation fixed fixed fixed line vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real approximation obtained obtained obtained obtained obtained obtained obtained note note note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments result result university university independent independent log log log defined defined sequence sequence sequence constant constant table table table table table table table computer terms distance distance distance distance distance distance distance distance distance science left left map low low low low machine machine machine machine machine machine machine machine sets sets sets sets sets press press learn learn learn learn learn sample sample sample abstract applied applied applied back find computational properties properties properties references references references due due due due due positive positive important important adaptive adaptive adaptive adaptive adaptive adaptive decision decision decision decision decision decision decision propagation introduction hand hand hand behavior behavior behavior effect effect generated generated variance variance variance variance variance cost cost cost cost cost cost cost cost cost tion change difference difference classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower measure measure measure chosen chosen chosen higher part part part previous previous previous previous theorem theorem bound bound bound cases multiple good good good distributed proposed correct correct correct probabilities observed errors errors resulting classes classes classes ing ing ing tasks computed respect respect respect respect multi multi multi multi multi multi multi multi performed performed performed performed performed called called called dimension dimension global applications knowledge knowledge obtain obtain original original artificial artificial artificial specific true compared application application application cross rates rates rates rates perform perform perform connected connected distributions distributions distributions approaches mit steps comparison update update train train train train train nets nets morgan proceedings proceedings proceedings report department loss version version version version version version version version version version version version version version individual individual individual individual difficult final final bias scheme sequences sequences domain directly directly directly view design top conference conference conference capacity efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers requires choice choice significant significant approximate statistics statistics statistics world basic basic basic basic pages pages pages pages pages pages pages validation give weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted clustering criterion bounds bounds actual selected selected selected evidence depends sampling sampling constraint associative associative achieved achieved achieved technical increases increases increases transformation transformation transformation fast finding rbf nearest effective role theoretical journal hypothesis hypothesis hypothesis hypothesis hypothesis instance instance instance makes kaufmann objective typically typically combination combination fully fully mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp interesting interesting interesting significantly character character character character character character character character increasing increasing database database database database squared squared squared details iterations pre pre international international international international normalized normalized bottom bottom early idea combined combined combined combined combined combined improved improved improve improve directions advantage takes typical reported machines machines machines machines machines machines machines machines trees trees trees trees trees array recently recently recently compare compare unsupervised observations calculated works works module yields yields yields converge improvement improvement improvement sensitive increased increased invariant invariant invariant invariant occur occur extended extended alternative correctly loop generally conclusion conclusions neighbor tangent tangent tangent tangent differences measures performs performs weak learns learns learns suggest reduction reduction demonstrated california intelligence intelligence labeled labeled decrease decrease characters characters characters base base base written written written written written written longer label dept dept confidence confidence averaging transformations transformations slightly spectral frequencies springer letters letters letters decreases choosing independently reconstruction labels labels labels labels fraction lee centered soft margin margin margin margin margin margin margin margin margin margin margin margin margin digits digits digits digits converges earlier performing epochs epochs epochs epochs epochs epochs epochs epochs epochs classical normalization normalization convex convex reduces combining fitting add calculate calculate calculate visible assigned classified handwritten handwritten handwritten handwritten handwritten coordinate coordinate perceptrons weighting weighting weighting assignment assignment recognize extension letter importance efficiently score score score tend online online online online online online online online online online online reached reached refer compact conf verlag induced success dis superior issue classify hold nips nips nips computes denker hypotheses hypotheses hypotheses hypotheses hypotheses automatically extract deal decreasing explore powerful poor exponentially rapidly hessian discriminant discriminant boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting combine authors authors maximizing workshop scores scores func statistically notion neu neu smallest extremely versions versions art epoch epoch epoch epoch generates improving simplest asymptotically great cart theoretic explanation adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost benchmark worse worse reasons berkeley satisfied easier style style incorporate bengio bengio bengio bengio laboratories simard auto auto explained fourth improvements varies considerably considerably composite composite composite collected pseudo lack poorly orders formulated continuously continuously reaches reaches proven suited suited achieves achieves gave conditioning eventually cor lot consistently don don ordinary writing writing writing writing writing assign reconstructed repre connecting printed printed plays wrong chance breiman breiman promising ral ral effectiveness responsible repeat repeat published performances bartlett falls combines schapire schapire schapire schapire schapire sion displayed displayed surprising dif dif advance mlps mlps mlps mlps mlps mlps mlps mlps reader bagging bagging bagging bagging bagging bagging bagging bagging bagging bagging canada explains ignore stopped fold sequentially uci uci uci uci uci uci uci yielded encodes ideally hundred freund freund freund freund freund big reconstruct summarizes summarizes summarizes stroke continues ocr bounding writer writer paris constructs quinlan importantly voting voting responding margins margins permit round emphasis emphasis tour replacement replacement styles styles styles styles argmax argmax continued continued continued satisfactory ferent ferent ers doesn doesn overtraining king autoencoder autoencoder autoencoder incorrectly resampling resampling resampling resampling resampling resampling resampling resampling manually occam tance distorted zeros zeros zeros approached raised sentation brought satellite satellite satellite satellite montreal cortes drucker hood boosted boosted boosted boosted boosted boosted boosted boosted boosted boosted expresses infeasible clockwise clockwise putting icann strongest offiine confirms writers writers writers boost boost iter plain disagree impressive resampled resampled resampled hypothesize unequal overfit subclass subclass subclass subclass yoshua brings razor emphasizing emphasizing emphasizing likeli arcing strange plied didn counterclockwise counterclockwise deci schwenk schwenk schwenk schwenk schwenk schwenk schwenk schwenk intriguing fonts autoassociation autoencoders autoencoders autoencoders guessing subclasses subclasses iro iro iro iro ariaboost ariaboost ariaboost preferably fourteenth selections randomization duction landsat init init abort sutherland aren umontreal umontreal encod montrdal montrdal universitd universitd thirteenth ada ada bengioy contradict alphabetical curt 
#@Bengio_Y,Schwenk_H,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input function function function figure figure figure figure figure figure figure figure 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neurons neurons recognition recognition recognition recognition recognition method method method method method method method method approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point image image image image image image single single single single single single processing large large large large local local local neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis class class matrix matrix matrix matrix matrix form algorithms algorithms algorithms simple simple simple visual visual visual visual paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size size size size feature feature feature feature feature net net work work work work work task task task task task task task task task task task methods methods step points points points points points points points points points points points points points field features features features features features classification process level trained trained trained trained trained trained trained cell structure problems random memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar representation representation architecture architecture architecture architecture architecture architecture architecture architecture fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line vectors vectors vectors vectors images images images images images images images images images real real real approximation average theory theory gradient gradient obtained term term term term term term term term experiments experiments activity activity activity dimensional dimensional variables variables computation computation solution found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial standard standard standard terms connections connections connections connections connections connections synaptic synaptic science science science direction direction direction map map map map map map map map map map present present phase machine object object object object object object object object object object object object sets press learn learn learn learn learn position components continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract back find convergence convergence convergence density density density density references component component component component stochastic ieee procedure important propagation propagation estimation estimation estimation estimation stimulus statistical statistical effect parallel parallel cost cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change energy difference difference difference spatial representations learned learned learned chosen chosen part part required multiple multiple cortex cortex long long conditions conditions represent represent represent represent represent represent equations make correct scale minimum resulting resulting classes regression regression regression regression performed optimization made made natural feedback feedback feedback orientation orientation orientation applications specific represented represented represented true true true true true desired receptive receptive receptive receptive objects objects objects objects proc proc proc proc proc location location perform perform eye goal goal related related constraints constraints constraints constraints connected connected connected motor discrete discrete discrete discrete discrete brain equal equal mit steps steps comparison larger fields fields fields fields fields update update train train train train descent descent descent version version consists internal final layers layers layers layers layers layers layers layers layers addition cambridge equivalent equivalent equivalent equivalent equivalent hinton hinton view top top top top top efficient efficient requires requires choice approximate approximate approximate world pages pages con con condition developed developed evidence backpropagation backpropagation backpropagation iteration iteration iteration iteration iteration iteration nature nature nature nature nature constraint biological associative associative associative discussion feedforward feedforward feedforward feedforward feedforward feedforward feedforward arbitrary fast fast fast limited close close complete complete complete complete complete complete short short short short short short short shape supported theoretical ability ability rumelhart rumelhart sensory sensory sensory sensory including smaller smaller hopfield hopfield hopfield combination combination dynamical dynamical dynamical dynamical functional programming projection head head special database empirical leads leads principal principal principal principal squared squared squared representing representing representing representing iterations iterations iterations iterations iterations max stored stored stored stored bottom bottom bottom bottom bottom idea idea idea idea architectures architectures discussed discussed discussed improve recent exact ensemble takes practical practical include machines pixels pixels sejnowski cognitive cognitive cognitive relevant unsupervised unsupervised volume works tuning correspond locations locations symmetric williams organization increased invariant invariant invariant suggests suggests matrices alternative alternative locally locally locally loop loop loop loop generally setting conclusion starting hebbian hebbian hebbian operator editors editors editors learns learns encoding encoding encoding drawn drawn demonstrated minimizing minimizing relationship averaged connectivity connectivity minima attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor boltzmann boltzmann digit digit digit digit edges ways estimating distinct recall missing missing missing missing missing coordinates physical dimensionality springer quality versus versus yield family family formation review solved restricted organizing fraction lee approximated completely digits converges converges converges updates earlier slow slow slow remains visible visible visible visible visible visible visible visible visible visible kohonen handwritten handwritten combinations usa usa usa formulation formulation formulation formulation formulation formulation retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval bell bell bell eigenvalues subspace subspace memories memories memories memories memories extension illustrated illustrated specifically partially discussions compression aspects suitable suitable modification mcclelland presentation attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors identity identity identity identity verlag repeated dis superior superior lie lie manifold manifold manifold manifold manifold manifold manifold manifold manifold sci sci sci gray bar involved relaxation relaxation relaxation paradigm automatically neurosci illustrates acknowledgments intrinsic minimized minimized simpler powerful biases biases helpful existence ideal proper variability topographic topographic topographic topographic topographic topographic topographic topographic cognition neu hill patch patch patch patch trace concepts editor analyze eyes rank aspect aspect quantities initialized initialized initialized consist motivated mentioned indicating indicating developing theoretic trivial trivial multiplication tractable lies nonlinearity spatially spatially inside perspective perspective perspective perspective forces forces laboratories scientific acad acad acad preceding addressed mechanics explained requiring understood understood embedded embedded conducted completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion slower vocabulary synthesis synthesis anti tank prevent collective collective gave substantial shaped attraction attraction attraction distortion naive phenomenon pose picture corrupted corrupted corrupted corrupted corrupted corrupted uncorrelated intractable sort drift drift drift acts acts perfectly nat nat repre unity lecun reaching clamped clamped murray convenient adjusting held attractive attractive attractive attractive abilities interpret viewpoint ral cottrell cottrell intuitive filled natl spurious spurious spurious spurious sompolinsky sompolinsky introduces ranging representational saul zhang surprising regarded regarded regarded dominant evident evident reader properly grammatical storing seung seung seung seung seung seung variants variants tures baldi limitation pressure associations neurophysiology slight largely basin basin munro randomized emergent employs instantiation trigger chapter classic basins suppressed forcing massively argue alternate labs labs manifolds manifolds manifolds disadvantage argued landscape depicts depicts retain retain retain retain retain retain retain retain retain hornik spanned drawback nonetheless sta ation parametrized technologies develops develops spite triggered removes info satisfaction palmer restoration king autoencoder autoencoder autoencoder autoencoder autoencoder autoencoder eliminates ackley architec retrieved zipset linearized neurobiological syntactic constraining evolves filling filling filling cho bottleneck bottleneck iterating ben wong sentation mul ous adv constituent stabilizing putational sebastian virtue plausibility men synthesize tailored trick dependences nections rectification projective projective retention retention usps iter perspectives tributed tinuous standing lacking contiguous suppresses singapore singapore georgopoulos viewpoints instantiations instantiations instantiations equiv restored suit unrelated retrieving linearization realizes vised appeal lucent coder composing suppressing yeung sharpening tistical restore restore kwon deficient alent unfolding trough trough enlarge yishai sharkey tioned equate depiction ablex reverberating mension extensional rupted feinstein idealization abandoned imperfections multidisciplinary unsuper norwood objection 
#@Seung_H,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data data data function function function function function function function function function function figure figure figure set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training algorithm output output output output output output output output output output output output output output output number number number number number number error error error error error error error error error error error error error error error error state results results results results results units units units units units units units units information information information information problem problem problem problem problem problem problem problem models models models models hidden hidden hidden hidden performance performance performance performance performance performance based based weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer vector vector order order shown shown shown shown shown shown systems systems systems parameters parameters functions functions functions unit unit unit unit method method method method method method approach approach approach point point point point point point point point point point point point single processing large rate rate rate test test test test test test class optimal inputs inputs form form shows shows algorithms examples examples examples examples examples examples examples examples examples examples small small size feature net net net net net net net net net work work task task task methods methods methods fig points points points features features classification classification level level trained trained trained trained trained trained problems random random architecture architecture architecture architecture show section section section section section section line rule general parameter real real real real real approximation average gradient gradient gradient gradient gradient obtained obtained obtained obtained term term term result variables variables computation computation computation computation research found target target target target target constant constant table table table table standard standard standard standard standard standard standard standard standard terms connections prediction prediction prediction presented presented presented presented present present machine machine machine maximum maximum maximum maximum maximum maximum maximum range outputs outputs outputs outputs continuous continuous continuous continuous continuous sample abstract applied find references positive positive positive procedure procedure procedure procedure adaptive adaptive adaptive adaptive adaptive decision context introduction hand variance variance variance tion change energy complexity variable assume lower measure measure prior prior prior prior higher higher theorem theorem theorem bound cases cases required required good good techniques minimum minimum minimum minimum minimum minimum regression respect called mapping means optimization optimization optimization optimization dimension dimension dimension made made made applications applications applications applications knowledge knowledge knowledge negative negative specific represented true compared application desired desired define define compute rates perform active active active active active active active active active active determined experimental constraints constraints constraints constraints connected connected approaches approaches accuracy accuracy update support descent descent institute implementation technique technique technique consists consists advances represents difficult final final final bias bias bias addition addition computing domain environment additional capacity determine determine choice choice significant approximate approximate approximate free world world world world world world increase validation validation developed types finally iteration constraint constraint constraint constraint constraint feedforward feedforward feedforward arbitrary arbitrary arbitrary group group group group group group group group group group group group group group group group group group group group group group group group group group group group tested tested tested transformation complete surface surface proof proof proof implemented implemented implemented implemented main eds journal ability hypothesis instance future future degree fit fit objective typically functional functional fully technology interesting increasing increasing increasing increasing mode mode operation squared squared call iterations iterations iterations direct direct direct early early magnitude predict improved directions directions recent robust takes apply apply sufficient highly compare approximately evaluation observation grid grid grid grid grid grid grid grid grid bounded bounded bounded bounded bounded bounded bounded risk risk exists exists exists lead derivative derivative setting demonstrate conclusion conclusion place greater greater assumptions segment moody exponential constrained constrained constrained suggest taking taking characteristics sigmoidal demonstrated california plane decrease iii targets derivatives derivatives derivatives derivatives groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups groups minima program areas areas appears ways describes implement unique consisting consisting adding adding adding john yield operations operations labels similarly similarly partial partial partial partial reasonable convex roughly sufficiently sufficiently construction degrees combinations priori priori priori priori coordinate instances batch batch determines discuss specifically holds discussions straightforward straightforward aspects capable importance uniformly uniformly computationally presentation refer stopping stopping split split split split issue issue issue follow hold usual usual usual usual computes computes satisfies acknowledgments software decreasing decreasing decreasing presents minimized wiley overfitting overfitting perturbation accurately accurately biases dataset func statistically understand fundamental momentum momentum surfaces naturally closest necessarily predicts equally equally quantities algo taylor freedom logic logic logic academic academic initialized initialized multivariate consist consist arbitrarily averages stop piecewise crucial agreement failure expensive worse london london reasons considerable considerable implementing implementing tive hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane commonly scientific universal universal lowest arises arises author meaning meaning addressed led capability experimentally lack leave treated measuring monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic monotonic proven pasadena geman geman geman song enables enables conclude comments implements differentiable differentiable hints hints hints hints hints consistently assign formally modify ratios ratios hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes hyperplanes caltech stronger determination observing guide intuitive financial financial financial financial ranging ensures intended facilitate thomas similarities approximators theoretically wolpert wolpert wolpert hypercube partitioned splits papers integers vari market default abu abu abu abu abu abu abu abu abu abu street converted mostafa mostafa mostafa mostafa mostafa mostafa mostafa mostafa mostafa mostafa outperform outperform piece email planes planes planes planes planes planes revealed monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity monotonicity tradeoff tradeoff chapter eric assess assess constrain formance rithms wall dominated guidance emphasized enforce grateful commercial signs signs signs rnn tonic tonic fiat bienenstock bienenstock bienenstock corporate corporate spacing dominates dominates dominates dominates dominates reflecting supplied concerns agency bond bond bond bond bond bond bond bond bond bond bond beneficial capital rating rating rating rating rating rating rating rating rating rating rating rating concave company constraining firm firm firm firm firm feasibility enforces excessive monitored health ira ira ming freely publishing enforcing obeys obeys joseph virtue virtue ables dilemma markets enforced enforced enforced enforced enforced dominate bonds package distinctions investor alexander rated anticipate pri meanings meanings malik convexity ratings ratings ratings keller asserts worthwhile amir joe avail ismail supplying proximate aaa mono mono sill sill sill sill sill sill ors atiya yaser reversing eration differen chu publicly agencies agencies ensured magdon kangas taining outset mains alleviates refenes netwo netwo lunch 
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#*network learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training algorithm algorithm number number number number system error error error error error results results results results results results information information information problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden performance performance performance performance performance based based based based based space weights weights weights weights weights weights linear case case case case case case case vector shown shown shown values values probability probability probability parameters parameters parameters parameters parameters weight weight weight weight weight weight weight functions distribution recognition method method method approach approach pattern point point point point single single single single single single single single single single single single single single single processing large test test test test test test test test test test test test test analysis analysis class class class class class class matrix matrix optimal optimal optimal inputs form shows simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper paper paper small size size size size size size work work work methods methods methods methods methods methods points points points points points points classification classification classification classification process trained trained trained trained structure structure structure structure structure structure random similar representation fixed fixed fixed fixed fixed rule rule vectors general generalization parameter real real real real real average average average average average note note experiments experiments dimensional university variables variables computation research research independent independent independent log log log log log log log log log log log log defined defined found found found table table table table table table estimate estimate estimate estimate standard computer terms science direction machine machine machine sets sets sets sets sets sets sets sets sets maximum press press press learn components components components components components components basis sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied find density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood 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techniques techniques techniques correct observed observed observed scale scale finite finite finite finite finite finite finite finite resulting resulting ing ing ing ing ing regression regression regression regression multi multi performed performed times times elements dimension dimension natural natural global global applications knowledge knowledge em em em relative relative relative relative represented true true true true true true true true true true true compared cross cross cross cross cross cross cross cross cross cross provide provide provide provide determined experimental experimental experimental related posterior posterior distributions mit accuracy accuracy accuracy support support modeling modeling selection selection selection proceedings institute institute technique technique technique consists individual kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances joint joint joint represents difficult scheme considered considered considered equivalent directly additional view estimates estimates estimates estimates estimates estimates conference determine efficient upper full full full choice choice significant world world estimated validation validation validation validation validation validation validation weighted randomly clustering clustering clustering types finally finally finally selected selected sampling measured discussion discussion discussion covariance increases denote predictions predictions predictions predictions finding common effective effective assumed shape shape shape supported role journal hypothesis easily degree fit fit fit fit simulated simulated simulated simulated simulated simulated probabilistic typically typically typically pairs smaller smaller underlying underlying needed combination combination combination combination combination functional coefficients coefficients jordan jordan technology technology testing significantly significantly special uniform uniform uniform uniform uniform uniform uniform uniform squared max pre window international experts experts supervised supervised supervised supervised supervised combined run improved improve improve robust similarity similarity reported introduced include side hierarchical hierarchical hierarchical inference dimensions dimensions dimensions highly previously unsupervised unsupervised observations studies mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures background background evaluation locations entire grant exists deviation width clusters clusters generally generally setting demonstrate runs place conclusions valued depend differences bayes bayes performs strong largest drawn california california california start min relationship relationship manner manner acknowledgements monte carlo ways generating plot laboratory laboratory distinct explicitly explicitly averaging infinite involves gaussians gaussians gaussians gaussians applying predictive predictive predictive formed shift quality expectation select john choosing choosing national independently estimator overlap viewed densities densities densities densities densities evaluated evaluate labels approximations approximations centered forms approximated sizes sizes sizes sizes partition partition partition partition partition partition partition allowed key reasonable performing normalization convex reduces combining combining combining combining combining combining combining combining combining roughly roughly penalty penalty valid david expect kernels kernels kernels kernels kernels kernels kernels kernels combinations combinations weighting weighting weighting weighting weighting weighting uncertainty uncertainty uncertainty uncertainty uncertainty maximize reason columns columns selecting selecting extra uniformly society driven driven driven driven symbols symbols included literature schemes schemes projections score situation vowel vowel vowel vowel vowel vowel tend soc repeated allowing split issue sin follow strategies quantity write play wavelet highest hypotheses maximization jacobs simpler parametric wiley investigate involving estimators estimators estimators estimators estimators estimators estimators graphical applicable possibility combine combine referred reliable scores fundamental removed necessarily opposite extremely thought rank portion fisher fisher fisher shapes shapes shapes ith multivariate multivariate consist improving averages worse worse closer strictly worst mation mation commonly sounds gradually bandwidth bandwidth bandwidth nsf reflects reflects composite applies empirically bootstrap flexible poorly poorly frequently frequently incorrect calculating stack summarized cal pasadena marginal contribute tresp tresp writing fix null partitions partitions discovery grows royal smith smith wrong consideration chance chance breiman breiman breiman breiman breiman breiman difficulties proceeds contract scoring scoring star star star star star star introduces representational representational loo predictors entry conjunction realization originally peterson bagging bagging roy park wolpert wolpert wolpert wolpert wolpert wolpert sons likelihoods likelihoods exploiting fold fold uci fitted outperforms outperforms ple specification specification diverse restrictions classic certainty reflected summarizes exam regularized rejected argued smyth smyth smyth smyth smyth smyth noting names topic iri worth nonetheless sam west west nasa nasa esti esti truth truth truth truth truth induces parametrized exploratory aaai modal jet jet clarity played outperformed outperformed cally subtracted assessment ples propulsion propulsion exploits occam inspection triangular triangular triangular triangular triangular spirit fin fin accounting irvine resultant scott signed cauchy mis mis mis stacked stacked stacked stacked stacked stacked stacked stacked stacked stacked stacked stacked stacked stacked stacked stacked stacked 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#@Smyth_P,Wolpert_D,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input data data data data data data data data function function function figure time set set networks networks networks networks networks networks networks output output output output output output output output output number number number system system system error error error error error error error error error error error error error error error results results results results results units units information information information information information information information information information information information information information information information information models models models models models models performance performance performance performance based space weights layer layer case order order order shown shown systems systems systems systems parameters parameters noise noise noise noise noise noise noise noise noise noise weight weight neurons recognition recognition method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image processing processing processing processing large local local local neuron neuron rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix optimal algorithms simple simple simple simple simple simple simple simple simple simple simple small size size feature feature feature feature work task fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells step step step step step step features features features features process process process level level cell cell random random random random random random high high high high high high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory show show show fixed fixed general general states theory gradient experiments experiments experiments experiments activity activity activity activity activity result result university threshold threshold threshold threshold threshold threshold threshold variables research independent defined dynamics initial initial initial initial initial initial initial initial estimate standard standard terms terms synaptic synaptic synaptic synaptic science left left left left left presented presented present present present activation low sets maximum range press components components components components abstract applied applied back find computational computational properties references component component due due due due ieee ieee important adaptive introduction complex complex statistical statistical statistical parallel parallel parallel recurrent search search search search search search search search tion tion tion energy energy difference variable lower lower lower rules representations word chosen higher bound bound bound bound cases cases required cortex cortex good binary binary binary binary distributed distributed equations techniques proposed proposed proposed proposed proposed proposed proposed correct probabilities observed errors errors errors errors errors errors errors errors errors errors finite finite finite simulations simulations simulations resulting classes tasks respect respect sum sum eq eq called called called mapping mapping mapping mapping factor potential global applications applications original original represented represented compared compared compared compared cross cross provide rates rates determined determined experimental experimental distributions cortical comparison descent proceedings proceedings department implementation synapses individual scheme maps considered directly curve view curves limit bit bit bit bit bit bit bit bit bit capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity efficient efficient efficient upper upper upper requires vision basic con con coding coding coding coding coding coding coding coding coding coding derived weighted randomly conditional types product provided provided processes evidence iteration iteration iteration nature depends simply simply biological biological associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative achieved technical technical denote tested close corresponds corresponds complete complete stable common synapse generate supported theoretical theoretical require end ability ability instance noisy typically pairs hopfield hopfield account functional significantly increasing increasing segmentation segmentation trials call stored stored stored stored stored early added denotes improved discussed improve improve property robust similarity practical practical apply cognitive cognitive conventional calculated works axis axis yields yields yields yields yields rl rl trans trans sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse address address address address address address address address address address address address address evaluation channels improvement storage storage increased increased grant parts parts lead occur column column column setting setting setting conclusion starting starting hebbian hebbian hebbian reduce editors faster asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic encoding propose reduction reduction cycle demonstrated demonstrated intelligence variety user min denoted stability recall recall recall simultaneously physical easy text text text applying events formed extraction extraction expectation versus boolean potentials national extracted independently overlap overlap evaluated evaluated evaluated showed forms sizes sizes sizes activities activities activities activities completely diagram diagram add add add add add add add add add iterative iterative iterative iterative iterative dendritic dendritic existing usa retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval sciences memories memories memories determines extension activated columns letter society modification modification efficiently efficiently schemes reached composed composed summary procedures procedures contained prob prob prob prob prob link link link neuroscience neuroscience dis contribution strategies strategies strategies strategies providing providing correspondence leading leading reach load load load load situations simpler transformed replaced biol fault fault fault fault fault authors working naturally closest plausible man analyze opposite psychology perfect adjusted quantities quantities assumes pyramidal improving submitted great publishers growing coded coded analytic explanation briefly london processed widely acknowledgement recognized computers cybernetics addressed robustness pathways tional axes completion completion completion completion completion completion completion completion biologically ity robinson calculating measuring anti anti characterize extracting collective sums germany sophisticated display expectations expectations tolerance tolerance tolerance tolerance damage wang yielding realized contribute person cybern cybern labeling labeling forming forming restriction conditioned conditioned conditioned addresses addresses addresses addresses addresses addresses addresses addresses theories royal adds held abilities exploit reasoning imply north optimally enhanced spurious entry pat pat holland uni assembly similarities entries iterated mem draw variants exploiting inf stopped thresholding emergent die willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw willshaw ical superimposed superimposed decomposed hillsdale arising acting trends magnitudes shannon signatures denoting proba individually academy cij cij distinguished superposition superposition assemblies elsevier places behave refined drops reciprocal rnn differentiating diagrams diagrams triggered capacities syn syn syn syn syn syn syn mcculloch deletion pitts terns terns hop hop returned sparsely sparsely chan heterogeneous successively optics raises retrieved retrieved retrieved autoassociative autoassociative distorted accounting binomial binomial cruz concatenated syst talk talk ira indexing gardner bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional bidirectional col noiseless plenum converts leung tolerant tolerant plausibility retrieve miss miss miss miss gibson cortico palm palm palm palm palm palm palm palm palm palm ant pal completes timestep graham encourages ations bilities fragments higgins assump associ namics heaviside lai accessed kybernetik enlarged autoassociation autoassociation sect eckmiller mas pare deutsche triplets ste ste ste ste ste invari lyl shaw augmentation ruled dummy uij uij capac renormalized nectivity friedrich sively forschungsgemeinschaft cepts similiar umn 
#@Palm_G,Sommex_F,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure time set set set set set set set set set set set networks networks networks networks networks networks algorithm algorithm output number number number number number system system system state results results results information problem problem problem problem problem problem models models models models models models performance based based based based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space weights linear linear linear linear linear linear linear linear linear vector order shown shown shown shown values parameters parameters parameters noise noise weight functions recognition approach point point image image image image image image image image image image single single large large local local local local local analysis analysis class class optimal form form shows shows shows algorithms algorithms algorithms algorithms simple gaussian visual visual visual visual paper paper examples examples examples examples examples small small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net work methods methods methods methods methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig step step step step step step points points points points points points points points points points points points points points points points points features features features features classification classification classification structure structure structure structure structure structure structure structure structure structure structure structure random high high high high high high memory similar similar similar representation representation representation representation representation representation representation representation representation show show section section section section fixed fixed line line line vectors vectors vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images general general parameter parameter approximation approximation approximation approximation approximation note note note activity dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional computation computation computation research research defined found found sequence constant standard standard computer terms terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance node node science presented presented presented map map map map map map map map map map map map map map map low low low low low low low low low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes object object object sets sets sets range range range range range press press press learn components basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied applied find find find computational computational density properties references component due due ieee procedure procedure procedure procedure procedure procedure procedure procedure important introduction complex complex complex complex statistical dynamic variance variance parallel search search assume assume lower measure measure measure prior representations learned learned chosen higher required good long conditions techniques techniques techniques techniques techniques correlation correlation length length scale scale scale resulting resulting ing tasks tasks human computed computed computed computed computed computed sum eq called mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping factor optimization dimension dimension dimension dimension made natural global global global global global global global global global applications knowledge knowledge obtain negative original original original original relative samples represented true true true compute compute compute compute proc perform determined goal related constraints connected discrete discrete discrete brain equal equal approaches approaches approaches mit mit mit steps steps contrast contrast contrast support support support support morgan institute institute department implementation version technique consists code difficult difficult graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph cambridge computing domain hinton view view solutions estimates estimates limit limit top top top stimuli efficient efficient efficient efficient choice significant significant free give produce randomly randomly clustering lines lines lines path path path path path actual actual actual provided finally measured measured measured measured discussion increases increases increases denote transformation transformation transformation transformation transformation transformation limited limited close inverse inverse corresponds complete surface finding rbf generate generate generate main face face face face face face face face face pixel pixel ability cluster future development noisy noisy sensory fit fit fit fit fit pairs pairs pairs underlying underlying combination combination reduced reduced unknown unknown jordan jordan technology programming significantly edge head special principle principal principal principal representing direct making bottom polynomial produced produced added description correlations resolution similarity similarity practical introduced pixels subset subset cognitive relevant dimensions dimensions dimensions dimensions dimensions dimensions sufficient sufficient highly highly highly varying previously conventional conventional conventional unsupervised observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations approximately tions smooth pca pca pca pca pca pca pca pca mixtures observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation generalized grid williams williams organization amplitude exists scaling scaling scaling deviation wide wide correctly locally locally locally generally demonstrate flow conclusions accurate accurate retina clear exponential practice practice learns constrained strong reduction reduction reduction reduction demonstrated demonstrated radial min min plane decrease decrease minima minima configuration force acknowledgements explicit explicit construct construct construct perception optical solving generating plot describes modeled metric metric metric metric metric missing sensitivity explicitly coordinates coordinates linearly infinite infinite physical dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality transformations transformations transformations transformations transformations remaining easy easy angle angle angle integrated adding applying springer versus select choosing focus learner detailed operations operations operations operations restricted organizing evolution centers centers completely digits converges classical spaces fitting purpose interpolation interpolation interpolation interpolation interpolation interpolation interpolation valid valid distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances sufficiently foundation euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean kohonen kohonen views views topology topology topology topology topology topology building handwritten perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual priori priori formulation formulation retinal subspace sciences discussions successfully texture selecting identified closely closely computationally paths paths paths paths paths paths paths paths poggio poggio poggio poggio poggio identify efficiently projections plots compact link link link dis lie lie sin sin sin sin sin sin sin sin manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold criteria generative simplified dayan dayan generalize absence realistic nips nips nips nips minimizes correspondence correspondence automatically illustrates illustrates subsequent intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic carried carried carried parametric poor create access exhibit hall helpful fashion links applicable variational scaled authors reliable topographic topographic topographic topographic analogous circles coarse closest extremely perfect thought rank obvious greedy greedy som som som som som som assumes precise initialized ith generates arbitrarily submitted submitted finds massachusetts mentioned indicating cos cos cos cos cos cos cos trivial guaranteed lies stress stress stress straight straight straight sections broad bishop consequence consequence consequence recognized angles implicit implicit medical depicted demonstrates author geometry geometry geometry recognizing raw raw raw freeman pure axes generic embedded embedded embedded embedded embedded embedded embedded embedded parameterized parameterized formulated sharp psychological howard berlin popular monotonic proven serve curvature curvature sophisticated sophisticated wesley multidimensional multidimensional multidimensional globally pose addison appearance appearance appearance assign guarantee arguments girosi girosi girosi recover ordering discovery discover discover discover discover connecting connecting grey fits analogy analogy analogy analogy familiar nearby nearby fail settings illumination cottrell cottrell canonical preparation arrays exploring reliably meaningful meaningful meaningful meaningful embedding embedding embedding embedding embedding recovered recovered programs saul saul topological viewing viewing viewing similarities initialize shortest shortest shortest shortest ends informative considerations designing captures omohundro omohundro omohundro generalizing tures fold insensitive severe schulten schulten schulten gtm gtm gtm gtm gtm gtm gtm visually leaming leaming preserving preserving preserving poses suboptimal smoothly weiss seek seek seek flat classic big descriptions discovering reconstruct visualization manipulation goals chapman manifolds manifolds manifolds manifolds manifolds manifolds manifolds manifolds reflectance hughes challenging acquired rbfs categorization figs figs discretization preserve preserve gilbert supports applicability matlab struc infinitely manuscript topologies moderate mds mds mds mds mds mds mds mds mds mds mds mds preserves preserves preserves satisfactory identifies impractical synthesized grbf grbf grbf virtually generafive orthonormal autoencoder bregler bregler bregler contributes triangulation characterizes maxi interpolate interpolate essence ensuring prescribed discovers recovering recovering revow revow martinetz martinetz martinetz trapped gradual cox cox cox cox comprehensive degrade extrapolation extrapolation extrapolation extrapolation predefined predefined intrinsically intrinsically elevation elevation ton tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum recovers save respects respects rescaling manipulations psyche nonlinearly nonlinearly nonlinearly nonlinearly nonlinearly demers demers ily rendered imagery azimuth azimuth azimuth fellow viewpoints ripley delaunay interpretable succeed perceptually perceptually perceptually kauffman bernstein joshua revealing folded extrapolate foster foster hin overestimate observa richards unfolded unfolded haykin haykin refinements holes ordinal ordinal ordinal ordinal brian tances carded gracefully optimizers specular macmillan synthesizing synthesizing beymer beymer granted proliferation iiz mani crux predoctoral 
#@Tenenbaum_J,
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#*model model model model model model model model model model model model neural neural data data data data data data data data function function function function figure figure figure figure figure figure figure figure set set set set set set set set set set set set networks networks number number number error error state results units units units information information information information information information information information information information information information problem models models models models hidden performance based based based space linear case case case case order order shown shown shown systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability functions unit distribution distribution distribution distribution method method method method method method approach approach approach point image image image image image image image single single single single single processing processing processing processing processing processing processing analysis optimal form shows shows algorithms simple simple paper paper paper examples size work work work task field features process process process process level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level current current structure structure structure structure structure structure structure problems problems random similar representation representation representation representation representation equation equation equation equation fixed line line line line line line line line line rule rule rule rule images images obtained obtained term term term term term note result result result university university computation independent independent defined constant estimate estimate computer distance node node node node node node science map map map map map map map map nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes object object object sets sets press components continuous abstract applied find density references ieee ieee ieee ieee ieee important decision introduction complex hand parallel cost cost tion difference assume lower measure prior previous previous theorem cases cases required required represent represent tree bayesian bayesian markov markov make techniques techniques techniques correct correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities errors errors errors errors errors errors resulting classes ing ing ing ing ing ing multi elements mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means means made global study study original relative represented application application application application compute objects objects determined determined experimental experimental goal goal constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints connected distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal comparison comparison fields update update support dependent source selection morgan words words words words words department technique technique technique consists individual individual individual individual joint joint joint joint represents represents connectionist exp exp scheme scheme scheme scheme scheme scheme scheme graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph framework computing equivalent directly additional view san top top significant significant vision vision give produce condition coding conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional developed developed levels levels levels levels levels levels levels levels levels levels levels levels criterion area types lines lines lines lines lines provided provided finally finally processes selected depends constraint constraint constraint constraint achieved technical group denote denote denote limited assumption assumption assumption effective shape require main ability instance easily development development development development development development sensory sensory kaufmann probabilistic probabilistic probabilistic fully jordan jordan york york consistent consistent consistent structures structures structures structures structures structures structures structures matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform bottom bottom bottom bottom idea idea idea attention denotes improve resolution property element element element element practical apply identical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical interest previously previously match match match match match match match match match match match match match match match match match match correspond evaluation chain intensity expression expression expression concept occur digital digital correctly correctly setting critical critical assumptions assumptions conclusions central measures measures bayes bayes clear exponential practice constrained constrained constrained propose drawn assuming manner manner manner scene scene configuration denoted denoted edges edges edges index sequential label label label label label vertical distinct segments segments segments segments segments segments segments segments segments segments segments averaging involves develop develop develop develop develop applying extracted extracted extracted focus focus communication viewed interpretation interpretation interpretation interpretation interpretation interpretation influence evaluate operations restricted labels labels labels constants allowed allowed allowed key key performing measurements boundaries remains assigned assigned assigned topology topology topology topology figures perceptual perceptual perceptual perceptual inter inter inter inter inter inter inter inter inter inter assignment specifically black structural structural structural structural structural structural successfully reason identified capable importance effectively effectively effectively effectively effectively effectively modes literature literature build schemes comparing comparing graphs graphs graphs graphs kind contained prob link dis follow notation quantity quantity quantity quantity write write write relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation relaxation highest operating extract satisfies deal modelling modelling extend explore powerful requirements difficulty updating relations relations relations detail graphical graphical graphical graphical graphical matches matches matches matches matches matches mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings mappings referred referred symbolic proved encode hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy analogous matched matched matched attributes attributes measurement measurement measurement naturally configurations illustrate quantities mapped mapped mapped expressions pyramidal pyramidal grouping residual developing directed coded adjacent independence independence independence tractable tractable straight widely immediately mation potentially lowest preceding raw raw explained evaluating limits items items freeman consistency consistency consistency consistency consistency consistency consistency tional cohen incorporated incorrect operate ture aim aim cal marginal richard hamming june indices intractable feasible cooper formally oxford conditioned member labelled concerned concerned concerned homogeneous repre unity grey proceed children children children children children children children eliminated dealing consideration consideration convenient overcome proceeds familiar intelligent loops exploit reasoning effectiveness corner corner child child child child child child wilson wilson wilson wilson wilson wilson infor elimination facilitate tokens francisco express sustained belonging draw impact impact davis propagate adopted parents parents counts severe outlined outlined radar radar radar radar clique clique clique clique clique clique clique super super super super super super super super super super ber markovian legal preserving preserving preserving preserving preserving propagating adopt adopt restrictions centre abstraction abstraction assignments hierarchies hierarchies descriptions possibilities causal henderson henderson pami pami pami pami pami num uncertain intra intra intra intra intra intra intra intra efforts relate landscape smyth noting pearl worth memoryless preserve reveal dictionary dictionary dictionary els exploited struc rarely moderate argmax resolve corners corners inconsistent inconsistent attributed quantify heavily firstly lated conceptual hancock hancock hancock hancock hancock hancock drawing concrete exclusively marr labelling labelling labelling labelling labelling labelling heterogeneous conditionally conditionally conditionally triangulation triangulation vertically cliques cliques cliques relational relational relational fidelity mis bear segmenting assessed prune merit brought lsi lsi subtle ambiguities clutter clutter clutter operated operated inserted inserted battery rela entities entities insertions conveyed tailored traditionally excluding topologically topologically topologically counterparts desire draws heckerman elicited centred centred violation mart sume delaunay groupings groupings groupings groupings decomposing decomposing raise simplifications compatibility optimise flamework flamework unary unary philosophy grade persist conflicts vances spiegelhalter contrasted sumption ridges renormalization ingredient normalisation sar resides lauritzen upwards upwards realisation corruption organising factorize legitimate meila assembled realised edit dummy dummy 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#@Hancock_E,Wilson_R,
#t11
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural data data function function function function function function function function function function function function function function function time algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system system system results information information information information information information information information information information information information information information information information information information problem based based based based based based based based based space space space space space space space space space space space space space space space space space linear vector vector vector order shown systems systems functions functions functions functions functions method method method method method method method method approach point processing processing processing processing processing processing large matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal form form form form form form form form form signal signal signal signal signal algorithms algorithms algorithms algorithms paper paper points structure problems problems high high show equation equation equation equation equation equation line rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general parameter parameter parameter parameter parameter parameter approximation average theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained computation computation solution solution independent log log log defined defined defined defined defined defined found initial initial estimate computer science left direction direction low maximum maximum maximum maximum maximum maximum maximum press press learn basis sample abstract computational likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due due due ieee ieee ieee positive important adaptive adaptive mixture context context introduction estimation estimation statistical statistical complexity complexity complexity assume assume prior prior theorem theorem theorem theorem theorem theorem type good fact fact proposed proposed minimum ing called called called mapping dimension natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural obtain obtain obtain obtain obtain obtain negative negative negative relative relative relative relative relative relative relative relative relative true true define define define define define compute mit mit descent descent descent descent descent descent descent source source source source source source source source institute department loss advances advances joint difficult ai ai ai ai ai ai ai ai ai ai ai ai ai ai framework framework cambridge cambridge computing computing design design choice pages pages condition derived entropy product product product depends depends depends constraint constraint denote denote denote denote denote inverse inverse inverse inverse inverse inverse inverse assumption proof proof eds needed unknown unknown unknown jordan special operation details idea idea choose sources sources sources sources denotes denotes property property property property property property property property property property property robust introduced introduced works yields yields match differential differential rl rl rl rl trans trans diagonal diagonal diagonal diagonal definition separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation extended matrices matrices matrices touretzky generally column conclusion row assumptions operator operator operator operator operator practice practice asymptotic asymptotic asymptotic asymptotic taking minimizing ica decrease relation derive written estimating metric metric metric metric metric metric metric implement easy mutual equilibrium equilibrium equilibrium equilibrium applying applying applying applying applying applying applying applying letters focus forms forms spaces calculate calculate euclidean david avoid box usa blind blind blind blind blind blind blind blind blind blind blind blind blind blind prove maximize maximize maximize mozer mozer absolute holds reason reason columns straightforward driven driven efficiently identity identity induced induced induced induced michael michael simplified simplified operating operating mixing satisfies minimized employed unlike updating updating updating updating updating updating updating updating updating updating replaced replaced replaced hessian hall structured maximizing proved proved singular singular singular singular fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher amari amari amari amari amari amari amari amari amari amari amari amari amari motivated serial multiplication meaning apparent calculating howard replace instantaneous ordinary ordinary ordinary ordinary ordinary writing tation tensor tensor tensor tensor tensor tensor accepted simplify replacing multiplicative multiplicative multiplicative multiplicative multiplicative multiplicative multiplicative multiplicative multiplicative multiplicative scoring scoring scoring scoring scoring scoring prentice sion appendix appendix appendix entry entry hasselmo yang yang yang yang yang yang entries entries entries enable april permutation steepest steepest steepest steepest steepest designing pdf infomax verify geometrical vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec vec mismatch mismatch cns increment increment increment increment diag diag diag diag diag diag impose graduate inverting rewrite rewrite rewrite compu oregon november factorized pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs invertible cliffs december englewood fij fij fij fij fij fij fij fij petsche cichocki sep riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian riemannian hij hij cardoso cardoso cardoso cardoso cardoso 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#@Yang_H,
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#*network network network network network network network network network network network network network network network network learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks output output output output output output output output output output output output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system state state state state information information information information problem performance performance performance performance based weights weights weights weights weights linear linear case case order order order order order order order order order shown shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems systems values values parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method single single single single single single single single processing processing processing processing processing processing control large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate inputs inputs inputs inputs inputs form shows shows shows signal signal signal signal signal signal simple paper small size work work fig fig fig fig fig fig fig fig fig step step step level cell cell cell cell cell cell cell cell cell structure problems problems problems response response response response response similar equation real states states states obtained obtained term university threshold computation dynamics constant constant constant constant constant constant constant table computer computer computer computer computer terms connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science present low frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal maximum range nonlinear outputs continuous continuous abstract back computational density density analog analog analog analog analog analog analog analog analog properties references stochastic positive positive positive positive important introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior generated generated generated generated parallel parallel parallel recurrent difference variable spatial measure signals signals signals part cases cases type binary equations chip chip chip chip chip chip chip chip chip chip chip chip chip scale scale scale total total total performed eq eq eq eq eq eq times factor factor factor factor factor made feedback feedback feedback feedback feedback feedback feedback filter filter filter negative negative negative represented compared proc proc proc proc gain train morgan morgan proceedings institute implementation version synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists consists consists internal internal internal individual individual advances joint responses responses responses responses responses responses responses responses addition directly design san san bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit bit conference efficient full speed speed speed speed speed increase increase produce developed developed levels lines path path inhibitory inhibitory inhibitory inhibitory inhibitory sampling sampling constraint constraint measured feedforward feedforward feedforward feedforward feedforward transformation fast fast limited inverse excitatory excitatory excitatory excitatory circuits circuits circuits circuits circuits circuits circuits circuits circuits implemented synapse synapse synapse synapse synapse synapse synapse supported main main eds eds eds end vlsi vlsi vlsi vlsi vlsi vlsi including including including kaufmann kaufmann probabilistic pairs hopfield dynamical fully fully fully fully fully technology testing increasing mode operation operation details iterations filters filters international international international magnitude magnitude magnitude attention run run run improved takes reported identical identical identical identical side array array solve solve converge differential differential gate gate gate increased scaling scaling digital digital digital digital digital digital digital digital feed occurs setting setting hardware pass pass strength strength strength strength place tangent performs faster mateo mateo hard integration integration external external proportional proportional pulse pulse pulse pulse pulse pulse pulse pulse variety manner program configuration acknowledgements van derive produces written winner winner winner winner winner winner describes laboratory changing physical physical physical physical physical text frequencies expressed squares solved open controlled controlled sizes constants constants sign sign sign diagram diagram diagram slow slow sec sec combining filtering filtering filtering msec msec sciences extension illustrated illustrated absolute differ driven driven driven wij literature tend ten characteristic characteristic conf conf content sci board giles cmos chips chips chips chips chips chips chips chips chips tesauro receive extend extend extend cowan cowan body body body body body body body body carried create mead put hanson oscillator oscillator hall fashion project gates gates gates stream stream transmission extremely illustrate created implementations implementations implementations adjusted adjusted prototype aspect der noted seconds seconds seconds massachusetts advanced band developing asynchronous asynchronous crucial publishers 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counter counter counter counter counter counter counter competing competing competing competing spatiotemporal spatiotemporal spatiotemporal arrows cam limitation appeared ence outline solves graded bus transmitted transmitted axe feeding feeding terminals personal personal workstation workstation realize realize pub mhz mhz epsilon ijcnn march synchronized host host host host host win million million million million million million electronics grateful grateful loading loading gordon milliseconds completed diagrams fiat saturated hyperbolic twenty thousand thousand thousand thousand thousand ers jersey micro hamilton industrial wiring wiring cally seattle station proposal resolved baxter physically cutoff cauwenberghs contents counted tim registers lsi mounted mounted mounted mid publishing instant bodies relax relax inserted mum sixth won won modulating modulating cir courses package unlimited billion billion paid kim counterparts chi wired oooo oooo oooo poral boards analysed narx counters brevity etienne euler faithful exceptions asynchronously integrand interrupted mueller collaboration collaboration internet looo looo emitted ond microelectronics identi nodal conflicts vances pins pins ven propor spiegel latest inevitable takahashi reekie chronous publish designate designate nar intern intern desynchronized xxx cuit ttm lsb fourteen tsukuba tsukuba tsukuba vmue shelf physi lishers asyn hitachi ibaraki propo toda bypassing 
#@Hirai_Y,
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#*model model neural input input input input input data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time set set output output output output output output output output output output number number system results layer layer layer layer layer layer case shown shown shown shown shown systems values values values values values parameters noise noise noise noise pattern image image image image image control control large large form form form shows shows shows shows shows shows signal signal signal signal signal visual paper small small small small work work work cells cells cells step step step step process level level current current current current current high high high high high high high high high response response response response response response response response response response response response response response show equation equation section section section fixed general average dimensional computation research log log log log constant constant constant constant constant constant constant constant constant constant constant constant constant constant node node node presented present present phase low low low low low low low frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal motion motion range range range nonlinear abstract back back back density density analog properties properties properties properties properties properties properties properties properties properties properties properties properties references due adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior stimulus stimulus stimulus stimulus stimulus effect generated tion tion change change change change change change change change change change change change change change spatial signals higher higher part center conditions conditions conditions conditions conditions equations equations chip chip chip chip chip chip observed observed resulting resulting factor potential feedback feedback filter filter filter filter filter filter filter filter obtain obtain define determined gain gain gain gain gain voltage voltage voltage voltage voltage voltage larger larger contrast contrast contrast contrast contrast contrast contrast dependent source source source source source source institute institute implementation consists consists responses responses responses responses responses responses responses responses bias bias bias bias bias bias bias bias layers layers layers domain domain experiment experiment curve curve curve curve curve curve curve curve curve additional curves curves curves curves curves design top significant basic increase increase give channel levels levels levels levels levels levels depends depends depends biological measured increases increases increases increases describe describe corresponds corresponds corresponds corresponds corresponds corresponds surface circuits circuits implemented synapse synapse supported adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation 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#@Liu_S,
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parameters parameters parameters functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons approach approach pattern pattern pattern pattern pattern pattern pattern point point single processing control control control control large large large large large large large large large large local local local local local local local local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis analysis inputs shows shows paper net work work work cells cells cells points points current current current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure high similar show equation fixed fixed rule rule general parameter parameter parameter parameter parameter parameter parameter real real average states theory gradient obtained obtained obtained note note experiments activity result threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables research research research independent independent constant constant constant computer computer terms distance distance connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science left left direction direction direction direction direction present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency sets motion motion motion maximum maximum maximum maximum maximum position position nonlinear abstract applied back back computational computational computational computational computational analog analog analog analog analog analog analog properties properties properties properties properties properties properties properties references due due due due due due due due due due due due due ieee positive positive positive positive positive important introduction complex complex complex circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior behavior behavior effect effect effect effect effect effect effect effect effect effect effect effect generated tion change difference complexity complexity variable variable spatial assume lower representations type type good long long conditions conditions conditions conditions expected equations make make fact fact region proposed proposed length length correct observed forward forward scale scale minimum minimum minimum minimum minimum resulting resulting resulting ing ing ing simulation respect respect performed factor factor potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential made made made feedback global study study study negative negative negative negative negative negative negative vol artificial represented application perform experimental experimental experimental connected connected connected connected connected gain motor motor motor motor motor motor motor motor motor motor equal equal power approaches approaches voltage voltage voltage connection dependent modeling modeling modeling modeling modeling modeling modeling proceedings institute version synapses consists consists individual individual represents exp exp exp exp exp exp exp bias addition addition addition experiment curves curves curves design design transition limit effects effects conference capacity determine free free free free free free free free free free free free increase increase validation give con con con produce produce produce produce produce produce produce condition developed levels levels provided provided nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends biological biological biological discussion increases increases increases increases tested tested fast fast limited close corresponds corresponds corresponds complete excitatory excitatory excitatory excitatory stable stable actions circuits circuits circuits circuits short short nearest nearest nearest nearest nearest nearest common common implemented implemented implemented implemented implemented implemented synapse supported role role role role role theoretical eds square square vlsi vlsi vlsi vlsi vlsi vlsi vlsi hypothesis future degree makes makes development sensory sensory including including smaller underlying underlying account account functional technology technology technology interesting interesting york york increasing increasing head head head head mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism mechanism structures uniform mode mode mode mode mode mode operation operation operation operation operation pre inhibition minimize produced produced neuronal neuronal neuronal neuronal architectures membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane improve directions directions recent robust typical lateral period period period period engineering sufficient varying previously tions tions tions tions correspond correspond correspond 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generation valid coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling expect building box silicon silicon silicon silicon silicon silicon silicon currents currents currents currents specifically coupled coupled coupled coupled coupled coupled coupled coupled variations variations variations absolute absolute neighbors characterized major regular importance society differ modes modes oscillatory oscillatory build ten repeated repeated neuroscience neuroscience conductance dis oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations device comp comp play modular backward backward backward backward delayed observable cmos ill neurosci principles principles illustrates illustrates operating neighboring neighboring acknowledgments software load intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic receive explore explore investigate investigate investigate exhibit circuitry varied environments oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators issues oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator existence postsynaptic rise school tech biol muscle transistor transistor transistor transistor referred proper variability oscillation oscillation oscillation oscillation affect func understand presynaptic presynaptic presynaptic phases neu math math gradients gradients gradients gradients gradients gradients gradients necessarily predicts opposite rev voltages adjusted adjusted explored nervous ith electronic established years devices brown great advanced unstable biology caused rapid rapid rapid perspective sys incorporate transistors immediately controls consequence cut inversion inversion geometry qualitative nsf behaviors behaviors percent understood understood understood understood lack quantitative cohen cohen cohen cohen cohen cohen sharp sharp sharp release release release release release release release release release release release release release exhibits anti spread spread reaches reaches cal incorporating collective inherent inherent fiber decreased decreased segmented segmented segmented segmented lim progress lot analogue generator generator amplifier dynamically count unity addresses connecting nonzero turned cellular cellular anatomical stronger stronger stronger stronger chains adjusting mos los exploit analyzing observing observing observing synchronous capacitor capacitor periods connect corre pat mental facilitate counter tic neuromorphic bursts insight insight creating mem locked rich waveforms designing insensitive default mechanical lag lag limitation escape escape escape escape escape escape escape escape maintaining ence ties emergent isotropic connec connec additionally additionally additionally tor spinal spinal mismatch mismatch shifting shifting formance biophysical biophysical goals tems compensate maintained maintained generators regulation crosses douglas douglas regimes complementary transconductance descending descending descending cubic behave travel increments ward supporting hodgkin students tonic tonic tonic tonic coordination coordination coordination coordination coordination coordination coordination coordination coordination coordination coordination leech leech leech locomotion locomotion locomotion syn tail tail sponding externally bursting bursting bursting stephen thermal thermal swimming swimming swimming swimming swimming swimming swimming swimming swimming swimming huxley inhibit inhibit envelope inhibited inhibited inhibited inhibited inhibited inhibited inhibited inhibited inhibited inhibited inhibited inhibited inhibited inhibited oscillate mahowald mahowald morris morris morris morris morris morris morris contralateral contralateral contralateral transmitter connects fre fre fre fre fre fre rons usefulness cord possess ples operational mill mill archi periphery raises ory volts volts volts volts volts volts volts volts constancy arriving neurobiological contrary sions establishing marder deweerth deweerth deweerth deweerth deweerth deweerth deweerth deweerth lags lags lags lags lags lags lags lags lags lags lags stomatogastric selverston selverston ipsilateral ipsilateral silent silent silent hyperpolarization saturate tern modularity depolarization facilitates facilitates configured operated disorder quantified discrepancy discrepancy neigh segmental segmental segmental activates continuing ece ece ece intersect vdd quency quency quency quency quency friesen friesen nections cir undergoes undergoes ascending ascending ascending ascending accessible viable anisotropic anisotropic anisotropic anisotropic counterparts biophys symmetrically retains lacking feel interconnectivity underlie underlie behav behav ishii lations lobster mere gra embodied charac swim swim giant emulation marcel marcel dekker dekker autonomously synap reg establishment iee bor asymmetrical asymmetrical asymmetrical asymmetrical coordinated coordinated vas brane brane scalable invertebrates atlanta elicit phasic funds reciprocally reciprocally reciprocally reciprocally reciprocally alamitos endogenous endogenous endogenous endogenous endogenous injecting ditions ermentrout ermentrout ermentrout kopell kopell kopell kopell georgia georgia illuminated vth vth rand gatech gatech gatech tectures eleven eleven oscilla oscilla ating oper discus trailing ior ior lecar lecar lecar lecar lecar lecar metrical oscil confirmation cuits synaptically facilitating escaping ceases mario biosci tins stants princi ohmic modelers ext jeremy jeremy lowers delaying ota mic asym teristics locomotor ame aptic tate observ mathemati igh quencies seventeenth ish neuroscientists abstracting approachable 
#@DeWeerth_S,Holleman_J,Patel_G,
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#*network network network network network network network network network network network model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input data data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time networks algorithm output output output output output output output output output output output output number number number number number system error error state results results results results results results information information models performance based based based based based based based based space shown shown shown shown shown shown shown shown shown systems systems values values parameters parameters noise noise functions functions neurons neurons distribution distribution point point image image image image image image image image image image image image image image image image image image image processing processing processing control control control neuron test test test test analysis analysis analysis analysis inputs inputs inputs inputs form shows shows shows shows signal signal signal algorithms algorithms algorithms gaussian gaussian gaussian visual paper small small small work work cells cells cells cells cells cells cells field features process process process current current current current current current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random response response response response response response response response response response similar similar similar similar architecture architecture architecture architecture architecture show show equation section fixed images images parameter parameter real real real real real real real theory theory theory obtained dimensional dimensional dimensional dimensional dimensional result result university threshold research research defined constant constant constant standard standard terms node science left phase phase phase phase phase phase phase phase phase phase phase phase low low nodes nodes frequency frequency frequency temporal machine machine machine machine machine machine motion motion motion motion range components nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous abstract applied applied back analog analog analog analog analog analog analog analog analog references due due due ieee ieee positive positive positive positive positive introduction complex complex complex complex complex complex complex hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit estimation estimation estimation effect effect parallel tion tion energy energy energy spatial spatial spatial assume lower measure measure chosen chosen chosen higher part part part center center type type type cortex good good represent distributed chip chip chip chip chip chip chip chip chip chip chip chip chip techniques region length correct errors finite ing tasks tasks computed respect called times times regions potential potential dimension orientation global applications filter filter filter filter filter filter filter negative negative negative negative negative negative vol vol vol vol vol relative receptive receptive define proc proc location active active determined related constraints cortical approaches voltage voltage voltage voltage voltage comparison larger larger larger larger larger larger fields source source proceedings department implementation implementation implementation consists internal kernel bias bias bias bias bias bias addition considered design design design design design effects conference upper requires speed vision vision vision vision vision vision vision vision vision vision increase increase con con con developed area area velocity lines lines lines lines lines provided selected biological measured measured increases increases describe denote tested corresponds corresponds circuits circuits circuits circuits circuits circuits common common common implemented implemented implemented assumed supported theoretical theoretical require eds square square vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel future fit technology ratio ratio ratio mode operation operation squared representing filters filters filters filters filters international normalized depth minimize sources pair robust takes reported pixels array array array array array array engineering sufficient approximately approximately correspond correspond differential diagonal gate gate gate gate gate sensitive grant parts parts parts parts deviation deviation predicted correctly feed width width width occurs setting setting flow flow conclusion place greater valued valued valued valued valued accurate designed designed designed clear peak exponential exponential exponential solid solid turn turn selective decrease decrease acknowledgements edges perception optical optical optical generating describes describes changing implement implement simultaneously physical electrical remaining remaining unique unique spectral integrated integrated frequencies equilibrium equilibrium springer shift shift implies blocks blocks blocks decreases reconstruction stages controlled controlled labels ocular static understanding understanding approximated constants constants smoothing smoothing dashed measurements measurements valid filtering filtering filtering filtering filtering filtering building building includes kernels kernels currents variations variations variations variations partially middle middle closely society divided invariance essentially road verlag interested conductance conductance conductance conductance conductance conductance dis lie follow follow wave cmos cmos cmos cmos cmos cmos cmos chips chips chips chips chips chips disparity disparity disparity satisfies requirements exhibit circuitry circuitry steady replaced limitations dotted dotted rise matches transistor transistor transistor authors maximizing gates matched neu smallest measurement transmission transmission voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages voltages implementations ensure adjusted prototype prototype prototype prototype prototype prototype impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse observe separated academic switching generates generates motivated electronic cos cos cos cos band ground ground publishers convolution convolution convolution analytical floating caused nonlinearity processed processed implementing preprocessing transistors transistors transistors transistors arise ion read read read read bandwidth robustness varies offset offset offset offset offset offset adjustable adjustable slower operate operate gains gains gains berlin spread modulated modulated conductances conductances gave enables boston findings implements implements implements realized globally primarily primarily generator fabricated fabricated gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor amplifier amplifier amplifier amplifier ratios angular linearity labelled controlling bin cellular cellular binocular binocular binocular saturation mos mos mos operates ral capacitor arrays symposium intuitive corre widths intended realization realization stereo stereo stereo stereo barron barron barron spatiotemporal grants propagate sine kluwer die spatio profiles corrected remainder conduction resistor resistor resistor resistor resistor resistor resistor evolve num adelson adelson cosine investigating transconductance transconductance transconductance transconductance transconductance transconductance transconductance attached west resistors resistors resistors resistors resistors resistors resistors amplifiers amplifiers amplifiers amplifiers amplifiers amplifiers amplifiers wider sponding externally externally achievable achievable council acquire settling settling settling water suite capacitors capacitors capacitors fabrication fabrication realizations flows flows supplied supplied subtracting impedance dedicated offsets offsets offsets offsets offsets offsets bergen trol america mosis ranged oscillates feb tan cox kong kong kong kong vergence vergence vergence vergence mir orbit nov nov hong hong hong hong imaginary imaginary imaginary imaginary imaginary cir cir pushed translating implementable implementable draws vin parasitic bandwidths bandwidths supplies neighbouring plex narrower shi shi shi shi shi shi nected estima champaign vittoz modulates farther opera edward capacitances microelectronics bers nodal ors grand grounded grounded prince mirrors cvpr cnn cnn cnn cnn cnn crete nmos pulls pacific pacific century pushing pushing sistent pulling bay chap cuit cuit 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#@Hui_K,Shi_B,
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#*network network network network network network network network network learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data function function figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number system system system system system system system system system error error state state state state state state state state state state state state state state state results units models models models models models hidden hidden hidden hidden hidden hidden hidden hidden performance based based based space linear linear linear layer case case case case case case vector vector order shown systems systems systems systems values probability probability probability probability parameters parameters noise weight functions distribution distribution distribution recognition recognition method method method method method method method method method method method method method method method method approach approach approach point point single single single single processing control large local rate rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix optimal shows signal signal gaussian gaussian paper size size net net net net net net net net net net net net net net net net net net work fig fig fig fig fig fig step step step step points classification process process trained trained trained trained cell structure structure high high equation fixed line rule rule rule general speech speech parameter parameter real approximation states states states states states states states states states states states theory gradient obtained obtained term term term note note dimensional computation computation computation log log log log log defined found found found found sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial standard computer computer science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented present low sets basis basis nonlinear outputs continuous abstract applied applied applied applied applied back back back computational density likelihood likelihood references references procedure important adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction generated generated generated generated change assume assume assume assume signals prior chosen type type multiple multiple good good represent represent equations markov markov markov markov markov markov markov markov fact correct probabilities observed errors resulting total human human respect respect multi performed performed performed performed eq eq eq eq elements potential dimension dimension natural applications knowledge knowledge filter relative specific represented represented application application application application series series series series series series series series series series series series series series series series series series series series series series provide experimental posterior gain discrete approaches steps steps steps steps steps steps steps comparison comparison fields support train nets nets nets nets nets nets nets nets nets nets nets nets nets modeling modeling modeling morgan consists represents represents represents final exp delay delay delay delay delay delay framework computing directly hinton transition transition transition transition san stage stage stage stage detection detection detection upper choice choice choice free world estimated increase increase give channel channel channel weighted levels finally processes selected depends simply achieved measured discussion describe describe hmm hmm hmm hmm fast fast fast assumption assumption predictions rbf rbf rbf short shape eds eds ability future future kaufmann objective underlying underlying account account dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical coefficients jordan significantly segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation special mode mode mode mode mode mode mode mode mode mode mode mode mode principle squared details pre pre experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert expert produced choose description description denotes improved resolution resolution resolution resolution pair robust separate ensemble ensemble ensemble ensemble ensemble takes takes introduced subset engineering sufficient previously unsupervised unsupervised unsupervised unsupervised unsupervised smooth smooth yields yields yields yields differential trans mixtures mixtures observation grant parts occur occur spikes derivative correctly locally loop loop deterministic setting pass runs segment bayes performs performs moody moody exponential mateo hard hard integration physics radial manner identification annealing acknowledgements appears pro plot transitions transitions tuned modeled coordinates coordinates coordinates remaining remaining text applying applying springer competition reconstruction stationary stationary stationary stationary detailed detailed detailed open restricted lee evolution evolution understanding completely allowed past measurements delays normalization combining closed intermediate construction eeg eeg eeg eeg eeg eeg eeg eeg expect recorded priori priori perceptrons weighting determines maximize phys discussions gating simplicity straightforward straightforward selecting middle hmms modes modes modes modes modes modes modes modes modes modes successful attractors detect detect summary refer interpreted physiological physiological physiological physiological physiological physiological physiological physiological physiological write paradigm predictor predictor predictor predictor predictor operating operating operating operating operating operating mixing mixing mixing extract jacobs extend essential relations detail dotted scalar scalar applicable root oscillation removed removed removed waibel coefficient onset onset equally equally equally subsets aspect art switching switching switching switching switching switching switching switching switching multivariate consist improving mixed chaotic established crucial analyzed defining biology nowlan glass glass glass glass baum handle starts starts tive commonly probable probable mathematics medical medical medical medical lowest recording recording recording depicted demonstrates demonstrates applies understood pure pure relevance recordings recordings detecting incorporated operate switch berlin berlin weigend gen germany germany germany kinds inherent viterbi viterbi viterbi diagnosis wesley indices notes feasible accomplished sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep addison drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift drift communications darken darken stated imposed hope operates fail modifications preparation symposium embedding embedding embedding predictors predictors predictors predictors predictors predictors predictors predictors predictors predictors predictors respective respective respective respective respective respective heart originally competing competing competing competing competing approximators treatment artifacts specialized young omitted offer repeatedly properly tures interestingly switches switches acknowledge pressure blood blood exhaustive removal alternating tween welch chaos wake wake wake wake wake wake wake wake wake wake wake wake mutually mackey mackey mackey mackey publication exclusive insights annealed distant regulation ultimately paris superposition apparently reveal electronics mix mea worked rabiner lecture remarkable algorithmic consuming accordance accordance tial assessment assessment dedicated successively falling appl sian gmd gmd feasibility drifting drifting drifting drifting drifting drifting drifting drifting drifting drifting brackets gaus nonstationary nonstationary manual manual manual manual manual manual manual manual fore comprehensive arousal tutorial cient rmse rmse rmse disorders sition forthcoming icann tran subsampling awake subsampled eog reproduces adap fruitful reconstructing turbulence turbulence miiller miiller miiller miiller miiller pawelzik pawelzik pawelzik pawelzik pawelzik pawelzik pawelzik healthy ecg takens exceeding strange plications subdivided diction autonomously nicely originate namics abrupt disabled fundamentals gershenfeld readings dfg rand analysing sured infrequent infrequent vides erated ieice cie ries prohibitive intention coe casting rudower rudower chaussee chaussee occipital occipital nonstationarity mpi resolves specializes prerequisite exponen dri dri nolta yls gsttingen 
#@Kohlmorgen_J,Muller_K,Pawelzik_K,
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#*network learning learning model model model model model neural neural neural neural neural neural neural neural input input data data data data data data data data data data function figure figure time time time time time time time time time set networks networks networks training training training training training algorithm algorithm algorithm output number system system system system system system system system system system system error error state state state state state results results results information information information information information information information problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based order systems systems systems systems systems systems systems systems systems systems systems systems probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise weight weight weight distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach approach approach approach approach approach approach image image processing processing processing processing processing processing processing processing processing local local local test test test analysis analysis matrix matrix optimal optimal optimal optimal form form shows shows signal signal signal signal signal signal signal signal simple simple gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper examples small feature work work work task task task cells features features features process process level current trained trained trained trained response architecture architecture show fixed fixed fixed line line line rule rule rule rule rule rule rule vectors images images images images generalization generalization generalization generalization generalization generalization speech speech speech speech speech speech speech parameter average states states states theory obtained obtained note university university university university variables computation solution solution solution solution independent independent independent independent independent log log log log defined defined found dynamics table table table standard standard standard standard standard standard terms terms science science science science left presented temporal machine maximum press press press press basis basis outputs sample sample sample sample abstract applied find properties properties likelihood likelihood references component stochastic stochastic ieee procedure procedure decision decision mixture mixture mixture mixture context context context context context context context context context context context context context context context context context context context context context context context context context introduction hand estimation statistical statistical statistical statistical dynamic variance variance variance variance variance tion energy difference difference difference variable assume rules signals signals signals signals signals signals signals signals prior prior word chosen previous previous cases good conditions conditions conditions represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected markov markov markov make make make make fact fact proposed proposed correct correct probabilities minimum total respect respect called times times times times regions factor orientation applications applications applications study knowledge em em em obtain specific samples compared application application desired provide rates proc proc perform determined experimental related connected equal power power power approaches approaches approaches approaches mit mit mit accuracy comparison dependent modeling modeling modeling morgan proceedings proceedings department department department implementation consists consists advances advances advances joint joint joint joint final exp ai framework cambridge cambridge cambridge experiment experiment experiment experiment environment environment environment additional view estimates estimates design design san san san bit conference significant significant statistics statistics statistics estimated pages pages pages pages pages pages increase give con channel channel channel channel channel channel conditional conditional conditional conditional conditional conditional conditional conditional conditional levels levels area area product provided provided provided provided sampling simply achieved achieved discussion covariance tested tested tested tested tested tested hmm hmm hmm hmm hmm assumption assumption assumption corresponds assumed eds eds eds eds eds eds end hypothesis hypothesis easily easily sensory sensory sensory sensory including including kaufmann auditory auditory auditory auditory auditory auditory typically typically typically typically typically smaller combination coefficients jordan testing testing testing testing significantly significantly significantly significantly york york trials database database database database database database database language representing call numbers iterations pre frame frame frame frame frame frame frame idea attention combined combined sources sources description architectures architectures robust ensemble ensemble ensemble takes typical subject subject subject machines machines pixels sense inference inference inference inference inference inference sejnowski sejnowski cognitive cognitive cognitive cognitive dimensions compare observations observations subjects subjects calculated volume volume volume volume volume module module module module module module axis pca differential address mixtures mixtures observation channels channels channels channels channels channels entire occur deviation wide wide wide matrices alternative alternative alternative correctly touretzky white white white white white strength strength assumptions assumptions assumptions assumptions assumptions competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive modules modules modules modules modules modules modules modules modules modules modules bayes bayes bayes bayes practice practice practice integration integration integration integration integration california california california assuming assuming variety variety variety variety digit digit produces produces produces perception perception perception factors label vertical explicitly simultaneously infinite dimensionality consisting integrated applying springer springer implies choosing stationary stationary stationary stationary stationary stationary communication interpretation interpretation interpretation influence influence influence influence densities evaluated open restricted restricted frames frames frames decomposition soft digits digits classical classical valid valid calculate msec norm expect box box box box box kernels perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual usa weighting recognize automatic automatic uncertainty discuss maximize mozer priors variations variations black partially characterized tests reason sensor letter extra closely society encoded effectively delta delta mcclelland successful identity road refer soc soc conf conf verlag verlag repeated video video video video video video video video video video video interpreted interpreted interpreted superior running gray gray notation sampled absence modular minimizes correspondence maximization maximization automatically automatically automatically overlapping operating tesauro tesauro receive camera cowan situations explore diego diego diego collection environments environments environments humans humans detail optimized scalar ideas ideas ideas ideas investigated int int reliable reliable working proper statistically statistically waibel waibel patch patch opposite front explored explored separated academic multivariate speakers improving explain finds advanced publishers track variances analyzed independence independence independence independence independence independence independence worse worse perspective perspective tive sections preprocessing products probable probable probable probable scientific implicit optimize arises annual incomplete addressed robustness explained explained reflects composite affine bootstrap spoken spoken simulate car car passed templates templates templates http operate operate vocabulary mod mod phone replace logp logp logp logp logp logp logp boston yuille yuille yuille yuille yuille yuille yuille yuille yuille deviations deviations deviations utterances calls calls naive phenomenon shifted contextual contextual leen gabor gabor ratios jth grey exemplar extending systematic adjusting adjusting occurred hope star star utterance cottrell optimally symposium date alspector mance contexts contexts contexts contexts contexts combines paul displayed perfor male bad centroid dif recog occlusion occlusion jolla jolla clean clean clean clean clean clean clean clean clean clean roy roy likelihoods implicitly assigns fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion boxes informa audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio leaving leaving rubin rubin outperform kluwer stork stork stork stork ties markovian nition ideally classic classic classic classic female forcing reflected factorial principled principled principled mouth thresholded synchronized laird laird siam esti meet modality page els drops radio radio radio behaves worked students modal ucsd ucsd ucsd acoust argmax argmax argmax argmax argmax argmax argmax argmax interior inconsistent justified jointly jointly jersey compete compete movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan movellan resampling engine engine station subtracting bregler bregler dedicated petsche interpretations interpretations conditionally clark clark clark clark clark clark clark contrary multimodal multimodal multimodal era senses creation occluded occluded robustly wolff wolff catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic catastrophic percept microphone unimodal talk talk linking stan modularity modularity ference replicates cepstral cepstral cepstral checks plans inte dard jackknife occupied lpc lpc philadelphia separability hild hild digitally fuse lipreading lipreading nato nato efron efron lexicon lexicon talker pennsylvania factoffal factoffal bernstein bernstein uninformative consequent percentages percentages nuisance lea mated aaa lai doors fused fused biilthoff contaminated contaminated contaminated contaminated mahalanobis packages friction contamination contamination contamination contamination sumptions factorizes minneapolis prasad prasad asr loadings cogsci cogsci cogsci retrain busy spectrally javier maxp telephony highway 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#@Mineiro_P,Movellan_J,
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#*network network model model model model model model model model model model model model model neural neural neural data data data data data data data data data data function figure figure figure figure time time time time time time time time time time set set set set networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number number number number number number number number number number number number number number number error error error error error error error error error state state state state results results results results results results information information problem models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based space space linear linear case vector vector vector vector shown systems systems probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise functions unit distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method pattern point processing processing large large large large local local test test test test test test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form form shows shows signal signal signal algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper small small small small size feature feature feature feature feature feature feature feature feature feature feature work methods methods methods step step points points features features features features features features features features features features classification process level trained trained problems random random random random random high high high high high memory memory memory memory similar show show section section section fixed fixed fixed vectors vectors vectors vectors vectors images speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter real average average average average average average states states states states states obtained obtained note experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university variables variables research research research independent independent log log log log log log log log log found found sequence initial initial table table table table table table estimate estimate standard computer terms terms distance distance left left left map present present low maximum maximum maximum maximum maximum press press press components components components components components components components components components components components components continuous continuous continuous continuous continuous sample abstract applied applied find find computational density density density density properties properties properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component due ieee ieee positive procedure procedure procedure procedure procedure procedure procedure important important important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context context introduction introduction hand hand estimation estimation statistical statistical statistical generated generated tion energy difference variable variable variable variable variable variable assume lower lower lower measure word word word word word word word word higher higher required represent represent distributed markov markov markov markov markov markov markov make make fact observed errors errors forward resulting tasks tasks total total respect respect sum eq eq eq eq eq eq times elements elements elements elements means means means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor dimension dimension em em em em em em em em em em represented compute compute rates rates rates rates rates rates rates determined goal goal posterior posterior posterior constraints connected discrete mit accuracy accuracy dependent dependent modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling proceedings report report version consists advances represents represents difficult graph graph framework cambridge cambridge cambridge computing computing directly hinton hinton hinton additional estimates estimates determine efficient full full full full full requires requires requires choice choice significant statistics free speed speed estimated increase derived weighted conditional types types types types lines lines lines finally finally depends sampling discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance technical increases describe describe arbitrary arbitrary denote denote denote denote denote hmm hmm hmm hmm transformation limited close complete amount amount short short short common eds end future makes makes makes including including objective typically smaller account coefficients coefficients interesting testing segmentation segmentation language leads principal details numbers making normalized frame frame idea idea idea combined combined combined combined denotes denotes improve correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations typical strategy include side side sense dimensions dimensions highly highly varying compare speaker speaker speaker correspond pca converge achieve diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal mixtures mixtures mixtures mixtures mixtures mixtures background observation observation organization lead lead studied matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices occurs conclusions competitive tangent differences accurate accurate numerical faster practice constrained reduction reduction reduction reduction reduction minimizing derivatives derivatives acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic explicit explicit suppose relation longer ways ways factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors factors estimating estimating plot plot plot plot modeled modeled modeled modeled modeled modeled explicitly explicitly dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality spectral mutual adding applying applying expectation expectation versus versus versus versus versus letters yield expressed expressed review depending stationary lemma variation densities densities densities densities evaluate decomposition forms digits digits digits digits digits updates updates updates updates calculation dashed dashed sec sec iterative iterative transactions transactions recorded building handwritten handwritten strings strings bell subspace subspace subspace subspace recognize recognize recognize recognize automatic automatic automatic maximize variations variations discussions grammar grammar gating simplicity columns columns columns straightforward straightforward aspects hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms importance divided divided divided delta latent latent efficiently plots tend essentially identity identity capture compact notice procedures procedures heuristic heuristic return strategies built vary vary dayan backward providing giles denker maximization maximization consisted extend cowan employed powerful poor investigate investigate hanson issues hall hall ml ml ideas maximizing variability variability variability variability scores scores scores scores scores notion circles circles naturally possibly necessarily extremely recognizer recognizer front art store baseline motivated motivated integrate brown derivation variances variances variances guaranteed expensive briefly london reasons comparisons tive ring choices ran arise arise mation simard scientific inversion acknowledgement involve implicit begin optimize toronto toronto definite integrating questions questions improvements considerably applies understood led embedded vocabulary rely rely ture occurrence acoustics marginal adjust substantial enables enables utterances utterances utterances utterances utterances extreme extreme sharing ghahramani ghahramani corrupted investigation conditioned conditioned purely lecun systematic consideration ments overcome alpha alpha alpha attractive monotonically intuitively infor reliably prentice heavy saul saul saul saul connect corre male den uni captured lawrence recog surprisingly reader cpu cpu cpu cpu cpu properly ends storing storing park park eqs likelihoods likelihoods variants captures implicitly implicitly subsequently summarize summarize summarize informa multiply vec rubin tables ties opposed nition discriminative icassp obtains additionally female imagine imagine summarizes iff diag chapman labs labs labs labs manifolds inverted challenging overhead insertion noting relates unconstrained spanned tied tied importantly worth worth grateful likewise likewise loading loading nal holding struc recognizers recognizers recognizers recognizers recognizers recognizers recognizers recognizers answers factored factored rarely rabiner deletion parameterization sees pdfs pdfs pdfs pdfs twenty twenty telephone cliffs ave imple tors appealing pronounced juang conditionally conditionally sian gaus compromise twelve sparseness translate revow drawbacks imposes cepstral cepstral accuracies crg invert examines tailored extremes versity analyzers analyzers prohibitively mercer throw thirty thirty mented stars stars allocate lations expects expects emphasizing multiplies multiplies reductions tying tying wood recipes fundamentals teukolsky zlx zlx flannery comple lxt pute answered tradeoffs tradeoffs confusable vetterling bahl sgi cepstrum cepstrum coarticulation coarticulation xlz xlz xlz alphanumeric alphanumeric reduc florham trices aat aat modi tages complicates componentwise investi incur mani mentary deserve engle 
#@Rahim_M,Saul_L,
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#*model model neural neural neural data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure time time time time time time networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number system results results information information information information information information information information information information information information information information information problem models models models performance performance based based based based space linear linear case case case case case case case case case case vector vector vector order shown systems values values probability parameters parameters noise weight weight weight functions functions functions unit unit unit unit unit distribution distribution distribution distribution method method method approach approach approach approach approach approach approach approach approach approach point single single single processing processing processing processing processing processing processing processing processing processing processing large rate rate rate rate rate rate test matrix matrix matrix matrix form form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms simple gaussian paper paper examples small small small small work work methods methods methods methods methods methods fig fig fig points points field process process current current current random show show show equation equation equation equation equation section line rule rule general generalization parameter parameter parameter parameter real real real real approximation approximation approximation average average gradient gradient gradient gradient gradient note note note note experiments result variables computation solution solution solution solution solution research independent independent constant constant constant constant constant constant direction direction direction direction phase phase phase phase phase phase phase phase phase phase phase frequency maximum maximum maximum maximum maximum maximum maximum press learn components components components components components components components components components basis nonlinear nonlinear nonlinear outputs outputs continuous sample sample sample sample sample sample sample sample sample abstract applied applied applied convergence convergence convergence density density density density density density density density density density properties properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component due due ieee ieee ieee ieee ieee important important adaptive context introduction complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex estimation estimation dynamic dynamic dynamic dynamic change change difference difference difference variable spatial spatial spatial assume assume signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals learned higher part part part cases multiple multiple multiple good good good binary conditions conditions conditions conditions conditions conditions conditions distributed distributed equations equations fact fact techniques techniques techniques techniques techniques proposed length correct correct observed observed forward finite simulations simulations simulations resulting resulting total respect sum sum sum called times elements made natural natural knowledge knowledge knowledge relative relative relative samples samples samples samples samples samples samples samples samples represented true true true compared application compute proc proc location determined related distributions distributions distributions distributions distributions discrete discrete equal equal approaches approaches approaches contrast connection update update source source source source source source source source source source source source source source source source source source source version version technique advances represents represents final delay graph graph graph graph computing environment transition limit limit top stage conference requires statistics speed speed pages pages give channel channel channel channel channel derived derived randomly developed finally nature discussion describe tested fast fast close close inverse inverse assumption corresponds corresponds corresponds amount short short nearest assumed theoretical require main main adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation end instance degree makes makes simulated simulated simulated typically typically smaller smaller needed needed account coefficients ratio increasing increasing special direct making making making making making window window window international bottom supervised combined added sources sources sources sources sources sources sources denotes denotes denotes directions exact robust separate separate takes reported reported practical practical apply apply apply moving include subject subject subject sejnowski sejnowski array array array array recently varying varying varying unsupervised calculated axis axis axis tions tions smooth smooth yields yields converge differential trans definition mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures locations separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation grid grid channels channels channels channels channels channels channels channels channels channels channels improvement sensitive amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude constructed constructed horizontal horizontal parts scaling scaling scaling digital digital digital deviation wide derivative derivative derivative matrices matrices move half assumptions assumptions assumptions assumptions operator operator valued valued valued valued valued valued valued depend tangent peak faster practice weak reduction characteristics demonstrated proportional radial radial radial radial assuming start ica plane plane plane plane plane plane explicit van derive construct construct estimating changing changing changing changing angle spectral springer shift shift shift expectation expectation letters communication squares densities densities densities evaluate evaluate updated modulation modulation modulation modulation modulation modulation centered forms static static static static static static sign sign purpose purpose add add remains valid valid visible symbol symbol symbol symbol symbol symbol transactions degrees combinations combinations coordinate usa bell bell blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind instances instances plotted discuss specifically reason regular straightforward straightforward uniformly encoded divided paths paths paths symbols symbols symbols symbols symbols symbols successful successful successful literature efficiently reached notice conf repeated dis lie contribution manifold sampled sampled vary generalize reach maximization maximization maximization maximization maximization maximization maximization maximization maximization received received received received received mixing mixing mixing mixing mixing mixing mixing mixing approximating extend employed access updating rapidly rapidly rapidly rapidly rapidly replaced ml ideal ideal ideal ideal ideal ideal ideal scaled tanh tanh tanh tanh tanh tanh tanh tanh tanh tanh tanh workshop workshop phases phases phases coarse gradients closest adapt adapt adapt equally singular der noted separated separated separated separated separated separated separated separated shapes amari mixed mixed seconds seconds integrate piecewise band derivation slope analytical independence independence nonlinearity processed purposes division operators incorporate incorporate choices worst commonly controls circle circle circle circle circle circle beginning beginning implicit implicit ridge attribute arises computers depicted depicted depicted integrating evaluating evaluating amounts axes lms lack leave variant ity rely rely rely spread aim incorporating coherence simultaneous simultaneous differentiable instantaneous instantaneous instantaneous instantaneous discontinuities aligned feasible japan linearity acts null circular circular circular circular mobile mobile mobile unity communications communications communications communications communications communications communications occurred multiplicative vehicle keeping receiver receiver receiver receiver receiver receiver receiver receiver receiver modifications arrays intuitive carry alphabet alphabet alphabet alphabet alphabet alphabet alphabet constructive continue repeat interference interference started separating equals lengths infinity yang nonlinearities modelled april april smoothed pearlmutter pearlmutter speeds pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf pdf infomax consecutive users email email covering transmitted transmitted pointed avoided reflected algebraic adapting ary concentrated deep mhz mhz labs inverted deconvolution deconvolution douglas depicts depicts depicts france parametrized radio radio radio radio radio radio radio radio radio radio radio radio ignoring september vice served versa simplification pdfs hyperbolic corporate quadrant utilizes december carrier carrier carrier carrier carrier transmitter transmitter transmitter transmitter wavelength bss bss bss bss fij fij accumulate sym squashing tracks maxi contrary transpose transpose sliding convolved suffice subscript restrictive differentiate essence bumps handbook approached nonstationary antenna antenna antenna cichocki durations denominator emerged stationarity maximisation insert predetermined dispersion kong inserted inserted occasionally cardoso cardoso cardoso tracked mum inserting hong imaginary quadrature quadrature parra parra equalization lasting seemingly unmixing cent steepness steepness steepness steepness devise stays bandwidths multichannel quadrants kyoto fragment mere plex equivariant differentiated wireless 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#@Torkkola_K,
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data function function function figure figure figure figure figure figure time time time set set set set networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm output output output output output output output number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error state state state state state results results results results results results results results units information information information information models models models hidden hidden hidden hidden hidden performance performance performance performance based based based based based based based based based based based space weights weights linear linear linear linear linear linear linear linear linear linear layer layer layer case case vector vector vector vector order order order order order order order order systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters weight functions functions distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach single processing processing large large rate rate rate rate test analysis analysis analysis class matrix matrix optimal shows gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net net net net net net net net net net net net net net net net net net net work work task task methods step features features features features features features features features features features features features features features features process process trained trained trained trained trained trained trained trained trained trained structure similar similar architecture architecture architecture architecture architecture architecture architecture architecture show equation section section section section section section section section section rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter real average states states states states states gradient gradient obtained term experiments experiments experiments experiments experiments university computation independent independent log defined found table table table table table estimate standard standard standard standard standard standard computer connections science presented presented presented presented presented present activation nodes nodes nodes nodes sets maximum range press components components components components basis basis nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied back computational density likelihood likelihood likelihood likelihood likelihood references component component component component component component component ieee ieee ieee ieee ieee positive procedure procedure procedure procedure procedure procedure important adaptive mixture mixture mixture mixture mixture mixture mixture mixture context context context context context context introduction hand hand estimation estimation estimation estimation estimation behavior generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion energy difference difference complexity prior word word word word word higher part part type multiple multiple multiple multiple multiple good good good good good tree markov markov markov fact fact fact fact proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed correlation correlation correlation classes ing ing ing total computed computed computed computed respect respect respect respect respect respect respect respect respect respect respect respect multi multi multi multi performed performed performed eq eq eq eq eq eq eq eq eq mapping mapping means means means optimization natural global original original original original original vol vol relative specific application provide compute rates rates rates proc proc proc proc proc perform perform perform experimental experimental related related posterior connected distributions discrete discrete discrete discrete power approaches approaches approaches accuracy accuracy accuracy accuracy accuracy train train train train train descent dependent dependent dependent dependent dependent dependent dependent source nets nets nets nets modeling modeling modeling modeling morgan report words department technique consists consists internal code advances connectionist connectionist connectionist delay addition considered considered framework equivalent directly directly additional additional additional additional additional additional additional additional additional additional additional additional additional estimates determine determine efficient free estimated estimated estimated basic basic increase give con con produce produce produce produce produce clustering criterion criterion criterion criterion criterion criterion types lines simply simply achieved achieved achieved achieved covariance increases increases increases arbitrary group hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm transformation transformation transformation transformation transformation transformation transformation transformation fast rbf rbf rbf rbf rbf common common main end instance future future future future easily easily including including objective objective objective probabilistic probabilistic underlying underlying account account account coefficients coefficients coefficients coefficients coefficients fully jordan jordan technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp transfer increasing increasing increasing increasing database database principle language language leads frame frame frame frame combined produced description perceptron denotes denotes improved improved improved improve improve improve improve improve improve correlations advantage advantage separate separate takes takes takes reported reported reported subset engineering highly observations observations calculated tions tions achieve trans trans trans diagonal mixtures mixtures chain separation observation observation observation observation generalized improvement extended extended derivative derivative derivative derivative derivative derivative matrices hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid conclusion reduce accurate faster practice weak weak propose taking reduction reduction radial radial manner acoustic acoustic acoustic acoustic acoustic denoted pro produces longer longer ways ann modeled modeled modeled modeled modeled pruning pruning pruning electrical dimensionality dimensionality dimensionality easy slightly slightly mutual mutual mutual adding gaussians gaussians gaussians applying extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extraction extracted independently independently independently formation dependence phoneme correlated interpretation detailed transform densities densities densities labels showed frames frames frames frames frames frames completely discrimination processor past past past past past past partial partial calculation calculation dashed purpose iterative assigned assigned advantages advantages avoid building assignment extension extension extension extension illustrated illustrated prove prove maximize maximize maximize grammar successfully major major major simplicity simplicity capable capable capable capable capable hmms hmms hmms hmms hmms hmms suitable divided divided delta delta delta delta delta kind procedures strongly strongly decoding decoding decoding prob phonetic dis dis nips nips quantization computes computes computes computes computes neighboring relations relations detail replaced replaced optimized discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant possibility possibility combine combine referred maximizing stream stream stream stream stream stream stream stream stream stream stream stream stream stream stream tanh workshop func extremely extremely extremely extremely som academic art art art baseline baseline baseline improving years fairly expensive independence straight sys sys closer division bengio commonly demonstrates alignment alignment explained explained improvements improvements substantially flexible spoken embedded fed formulated maintain robinson vocabulary ture ture proven resource achieves achieves achieves phone gave germany semi semi semi decoder chose chose viterbi viterbi differentiable don uncorrelated forming lvq unity unity tem impossible turned turned extending convenient stronger abilities abilities resulted keeping keeping exploit bourlard bourlard bourlard combines combines codebook displayed displayed regarded regard uni offers offers offers offers advance mlps mlps matter likelihoods lett tures pdf pdf outlined outperforms outperforms outperforms audio ure emission unified unified unified leaving slight incorporates vec outperform ent kluwer dec propagating pointed discriminative discriminative discriminative discriminative discriminative year icassp icassp icassp utilize connec arg warping recurrence reflected clustered streams streams streams streams streams streams streams streams streams streams streams streams management management tems distribu denoting oct lookup proach covered denver dictionary lda lda lda lda lda lda lda lda book fea fea ation ation retained retained experi mix resembles topologies topologies moderate remarkable remarkable recogni pdfs pdfs pdfs hyperbolic sake exper tors mining lists lists incorporation incorporation incorporation incorporation incorporation ally quantizer tended arpa contrary contrary totally sian experienced ance gaus feb feb ous ous jan sep daniel replaces renals inserted timit phones remarkably plexity cient preprocessor won modifies nections mmi mmi mmi mmi mmi mmi mmi mmi mmi mmi mmi mmi mmi mmi mmi mmi ative separability tinuous perplexity lose faculty neglecting transcription continu continu today ences hochberg hoped alternately tributions pipeline tying tying subdivided reuse unmodified para para xii cook quotient arose cedure discrim meters lows ney ney xlw xlw cepstrum cosh meter effi triphone triphone intention rprop gerhard gerhard outperforming outperforming usu cussed triphones triphones triphones subdivision subdivision tangents emitting oix oix oix pends lwl nax eurospeech 
#@Rigoll_G,Willett_D,
#t11
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#*learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input input input data data function function function function function figure figure figure figure figure figure figure figure figure set set set set networks algorithm number number number number error error error state results results results results results results results results information information information models models models models models performance performance based based based space space space linear linear case case case vector vector vector vector shown shown values values values values values probability probability noise noise noise noise noise noise noise noise noise noise functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition method method approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single processing processing processing processing large local local local local test test test analysis analysis analysis analysis analysis matrix matrix matrix form signal signal signal algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian visual paper examples small small feature feature feature work work methods points field features features features features classification classification classification classification classification process process process level level level level level current current trained trained trained structure structure structure structure structure problems random random random random random high high high similar similar similar similar similar similar representation show show fixed fixed vectors vectors vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images speech real average average average theory theory theory note experiments result result result result university university threshold variables computation computation computation research research research independent independent independent independent independent independent independent independent independent independent defined defined target constant estimate computer computer computer science presented presented present low low low low low low low frequency frequency frequency frequency frequency frequency machine machine machine machine sets maximum range range position basis basis sample sample abstract applied applied applied back find find density density density likelihood likelihood likelihood references stochastic stochastic due ieee ieee ieee ieee ieee procedure important important important introduction complex complex complex estimation statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical effect effect generated generated generated generated generated cost search tion tion energy difference complexity complexity variable spatial assume assume assume assume assume lower lower lower lower measure prior higher higher higher higher higher cases type multiple multiple long long long long long tree tree bayesian bayesian expected expected markov markov markov fact techniques techniques techniques proposed correct correct observed observed observed observed errors forward scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale classes classes tasks tasks human computed computed computed computed multi multi multi multi multi multi multi multi multi multi performed elements regions factor dimension made natural natural natural natural natural natural natural natural natural natural knowledge filter filter filter original original original original original original artificial specific specific samples samples compared compared cross cross series provide define define define compute perform related related related constraints distributions distributions distributions distributions distributions distributions distributions distributions distributions power power approaches approaches approaches approaches accuracy accuracy larger contrast contrast fields fields dependent modeling modeling modeling modeling modeling selection proceedings proceedings proceedings report report institute department implementation version technique technique technique technique technique joint joint joint difficult ai ai ai cambridge directly directly directly hinton hinton hinton additional view top top top top conference efficient efficient requires significant significant approximate statistics vision vision estimated estimated estimated estimated pages pages condition condition coding weighted weighted conditional conditional conditional conditional conditional conditional conditional conditional developed levels levels levels levels levels types types types entropy finally processes evidence iteration sampling sampling simply biological achieved achieved achieved achieved achieved achieved achieved measured technical describe group transformation limited inverse inverse inverse inverse assumption assumption complete effective effective assumed assumed assumed generate generate supported require main main adaptation journal square pixel pixel pixel future easily noisy noisy including probabilistic probabilistic probabilistic smaller underlying unknown coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients technology technology ratio edge edge consistent structures structures structures uniform empirical empirical mode operation filters filters filters filters direct window international bottom frame combined choose resolution similarity pixels pixels pixels pixels pixels pixels pixels hierarchical subset subset recently interest highly varying unsupervised observations observations volume smooth match achieve address chain chain chain chain chain observation grant constructed occur white white pass critical row conclusions depend interactions interactions measures accurate designed weak strong strong reduction reduction intelligence intelligence variety scene program areas appears monte construct carlo edges edges ways primary generating generating generating generating generating generating estimating laboratory modeled modeled modeled explicitly averaging easy slightly slightly slightly scales scales frequencies frequencies frequencies frequencies quality john choosing independently dependence overlap transform transform transform transform transform transform transform transform transform iterative generation generation generation generation generation generation generation transactions transactions transactions recognize discuss priors successfully texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture regular straightforward compression maximal driven modes build efficiently fine capture capture notice notice conf strongly success dis gibbs sampled relaxation dayan dayan dayan realistic wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet attempt overlapping neighboring neighboring acknowledgments deal deal parametric parametric parametric parametric parametric parametric wiley transformed collection involving humans humans limitations accurately accurately reducing reducing fashion tech int int combine dependencies scaled office structured statistically patch extremely created thought formal assumes explored art seconds neal neal massachusetts residual residual residual residual residual residual residual histogram great great convolution convolution convolution smoothness smoothness independence caused starts spatially spatially stanford snr snr snr shared arise localized cybernetics requiring prop freeman generic generic generic leave lattice share remove frequently sharp http synthesis synthesis synthesis synthesis synthesis synthesis measuring ture reaches gen parent parent parent parent parent parent occurrence geman geman geman acoustics substantial germany chose redundancy redundancy redundancy returns returns pyramid pyramid pyramid pyramid pyramid pyramid pyramid lot shifted corrupted uncorrelated redundant sleep appearance gabor gabor acm pick zemel discover naval convenient minutes chains chains hope nearby transforms transforms composition date published paul paul conjunction captured captured arrangement recog draw relies sons captures border hart hart discriminate unified unified unified geometrical ple incorporates vec helmholtz helmholtz helmholtz email removal bank nition smoothly icassp conjecture conjecture perceived workstation wake preserved exam insights duda duda alternate continues graphics graphics parzen careful adelson adelson adelson adelson adelson multiscale conversely termed drawback enforce frey exploited struc ergodic restoration restoration mrf mrf mrf mrf mrf mrf textures textures textures textures textures textures textures textures textures textures textures textures textures synthesized multiresolution multiresolution viola viola viola viola viola observers suite suite generafive generafive tors shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage resampling cally rare striking heeger heeger heeger heeger heeger heeger heeger wavelets wavelets wavelets wavelets wavelets bergen bergen bergen bergen bergen bergen contrary emerged unimodal putation freely simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli mid mir mir mir competence mumford mumford inability synthesize zhu zhu switzerland rightmost rightmost munich ages resampled hypothesize golden donoho donoho donoho donoho descriptive generatire generatire weaknesses interpretable erties proj ergodicity initiative chou prin tiles sharpening tiling chellappa chellappa sagi sagi tropy johnstone johnstone johnstone johnstone statisti downsampled ect siggraph willsky discriminator benveniste influential dod petitive 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#@Viola_P,de-Bonet_J,
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#*learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural data data data data data data data data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure set set set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number error error error error information problem problem problem problem performance based space space space space linear linear linear case vector vector vector order order order order order shown systems systems probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise distribution recognition recognition method method method method approach point point point point point point point point point point point point point point point point point image image image image image image image image control local rate test class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form shows shows algorithms gaussian paper paper paper paper paper feature feature feature feature feature feature feature work work task methods step step step step step points points points points points points points points points points field field features features features process process process process process process process process process process current current current structure structure structure structure structure structure problems problems problems random random representation architecture architecture show show equation line line rule rule vectors vectors images images images images images images parameter parameter parameter parameter parameter real approximation approximation average gradient experiments experiments university variables variables variables variables computation computation computation log log log found initial initial initial constant estimate estimate estimate computer computer computer computer computer terms terms terms terms distance distance distance distance node node node node science low nodes nodes nodes nodes object object object object sets sets sets sets sets sets sets sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum position components components abstract abstract density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references ieee ieee ieee ieee ieee important adaptive mixture mixture mixture mixture mixture mixture mixture mixture introduction complex estimation estimation estimation estimation estimation estimation estimation estimation statistical effect dynamic variance tion change difference assume assume assume lower theorem cases cases required multiple good good binary represent represent represent represent bayesian expected expected expected expected expected equations make make fact correct correct probabilities probabilities probabilities probabilities probabilities observed errors errors ing tasks computed computed computed respect elements means potential study knowledge em em em em em em em em em em em em em em em em em em em original artificial represented represented application cross cross cross cross provide provide provide compute objects objects goal related related constraints constraints constraints constraints constraints constraints distributions discrete steps comparison update update proceedings words words department technique technique final final final exp exp exp exp addition addition addition graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph framework framework framework computing domain estimates detection conference upper requires significant significant world world vision vision vision vision vision estimated estimated estimated basic basic basic basic con condition conditional conditional conditional conditional clustering developed bounds product processes processes selected iteration iteration constraint covariance covariance transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation close inverse predictions theoretical require main instance development development jordan jordan projection york york edge edge matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform operation leads squared representing representing representing pre international bottom experts experts idea idea idea denotes improve robust reported reported practical practical apply apply apply strategy hierarchical hierarchical recently compare conventional tions solve match match match match match match match match mixtures evaluation chain gate gate gate gate expression expression expression lead invariant scaling occur extended matrices rotation predicted correctly occurs column column column flow row row row conclusions measures bayes bayes exponential presence intelligence turn scene configuration configuration configuration configuration configuration configuration denoted denoted explicit appears relation relation index index index ways estimating estimating describes pruning sensitivity sensitivity involves develop develop applying formed quality expectation expectation reconstruction squares squares overlap viewed viewed densities densities densities updated updated updated understanding similarly translation key key reasonable iterative closed initially initially symbol euclidean euclidean advantages views coupling template weighting illustrated maximize specifically coupled gating gating structural structural structural structural structural structural structural structural structural structural structural structural structural columns capable importance effectively soc graphs graphs graphs graphs allowing link contribution contribution satisfy notation write write relaxation correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence correspondence ill attempt extract extract jacobs jacobs simpler poor involving association accurately hessian dual dual dual dual dual graphical graphical graphical graphical graphical matches matches matches matches matches matches matches matches matches matches matches matches matches matches matches matches matches matches matches matches matches ideas ideas gates fundamental matched matched matched measurement measurement measurement measurement measurement measurement measurement configurations configurations illustrate singular der algo multivariate generates contributions contributions contributions contributions optimum residual capabilities independence tractable stress perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective perspective constructing located ion computers geometry geometry geometry geometry geometry geometry geometry geometry incomplete incomplete preceding outer robustness fourth geometric reflect items bootstrap consistency consistency tional generic readily readily posed variant outliers outliers templates switch measuring ture aim aim aim aim aim extracting popular cal replace hamming hamming hamming converged distortion cor consistently pose pose pose pose pose pose pose pose pose pose pose identifying feasible saddle formally formally tation rithm conditioned recover recover concerned concerned concerned homogeneous homogeneous jth royal robotics proceed establish establish imaging overcome simplify imposed viewpoint exploit exploit exceeds wilson wilson wilson planar composition mjolsness corre von stereo offers offers recovery recovery modelled indicator indicator indicator indicator arrive augmented augmented steepest davis statement dempster dempster counts severe andrew speaking posteriori posteriori rms radar outperforms gold rubin rubin break benefits poses adopt residuals residuals residuals residuals arg ical illustration representa constrain constrain constrain gated gated pami pami pami pami goals impose proba expand challenging buhmann laird laird distinguished bring gorithm mea voronoi appearing appearing simplification lowe bility corners correspondences correspondences correspondences correspondences correspondences correspondences correspondences jointly locate optimisation optimisation broadly hancock hancock hancock hancock hancock hancock hancock hancock condi moss optima architec rangarajan triangulation triangulation triangulation neighbourhood neighbourhood neighbourhood ultimate optics degenerate lnp suffice era relational relational relational amenable counterpart compromise pin prune rem dence recovering recovering recovering recovering recovering maximisation maximisation maximisation maximisation refine imum hood lange kong drawbacks hole aims locating locating shear accu aimed apparatus offered arline projective registration registration registration maximising counterparts counterparts posterjori posterjori posterjori posterjori amit ordinate ordinate ordinate disk augment maximise delivered rejecting delaunay delaunay delaunay delaunay delaunay delaunay likeli wurtz tributions ordinates ordinates ordinates ordinates matters structurally checking exponentiation signifi delivers twofold documented ser observational invariants ita zisserman statisti unification invoking poste lades marquardt sgi argmaxp mcreynolds realised correspon wil constituting inch levenberg unify probabihty egg residing methodological alleviates configura recognising edwin effecting surement 
#@Cross_A,Hancock_E,
#t11
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#*learning learning model model model model model model model model model function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number system results results problem problem problem problem problem problem problem problem problem problem problem problem problem models models performance performance performance linear linear linear linear linear linear linear linear linear vector order order order order order order order order order order order shown shown systems values values probability probability probability probability probability probability parameters noise noise unit distribution approach approach approach approach approach pattern point point point point point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single processing large large local test test test test test test test test test optimal shows shows shows shows algorithms simple simple simple simple simple simple simple simple simple gaussian gaussian visual visual visual visual paper paper paper examples small small work work work work work task task methods step points field field field features level level level cell structure problems random random high high similar similar show line images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general approximation approximation average average average average average gradient gradient term note experiments experiments dimensional dimensional dimensional dimensional dimensional result computation solution solution solution solution log found found found constant constant computer computer computer left left left left direction direction direction direction map low low frequency machine object object object object sets range press press press outputs abstract applied applied find find computational computational computational computational properties properties properties likelihood references due ieee ieee ieee procedure procedure procedure procedure introduction behavior statistical statistical generated variance parallel search tion assume assume measure prior prior prior prior prior prior prior prior prior prior prior prior prior chosen higher cases required good good binary long conditions bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected make make make make correlation correlation correlation correlation correlation correlation correlation correlation correlation correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed scale scale scale scale total human human human human human computed multi eq eq regions optimization optimization optimization made made made made made made natural natural natural global applications study study filter filter filter filter artificial specific compared compared compared receptive receptive define compute objects objects proc proc location goal related constraints constraints distributions mit steps comparison descent descent source source source modeling modeling modeling modeling institute version code individual individual individual responses responses responses responses responses exp addition framework framework framework framework cambridge cambridge cambridge cambridge experiment directly directly effects effects determine full requires significant world world vision vision vision vision vision vision pages pages give give give condition randomly finally processes nature nature nature simply simply simply biological normal normal describe describe assumption assumption assumption surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface finding assumed assumed shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape generate pixel pixel pixel hypothesis hypothesis easily including account technology ratio ratio projection edge increasing consistent consistent uniform uniform uniform operation depth depth choose light light light light light light light improve recent recent correlations correlations correlations correlations correlations resolution resolution resolution resolution property property takes takes practical apply apply moving subject subject subject pixels subset subset sufficient highly varying compare compare subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects solve solve trans sparse channels horizontal intensity intensity intensity intensity derivative half starting starting assumptions measures numerical numerical numerical designed exponential constrained constrained constrained strong integration physics physics intelligence assuming relationship averaged scene appears index index perception perception perception perception perception perception perception vertical vertical simultaneously averaging physical dimensionality involves remaining unique formed choosing formation review reconstruction stages communication interpretation interpretation interpretation interpretation interpretation interpretation interpretation solved solved variation evaluated showed showed showed showed approximations approximations allowed reasonable calculation dashed classical normalization combining generation valid calculate visible assigned assigned degrees inter determines determines priors priors variations discussions texture simplicity middle computationally identify score score score score tend notice conf conf quickly kind prob showing hold comp comp involved vary wavelet ill illustrates decreasing decreasing decreasing bars bars body body employed simpler parametric create essential essential helpful proper proper proper complicated scores statistically examined examined patch patch patch coefficient coefficient naturally editor configurations illustrate created rank rank rank noted assumes explored shapes shapes shapes shapes shapes shapes shapes shapes nervous extent submitted explain explain explain attempts integrate massachusetts histogram histogram histogram ground ground trivial agreement fairly fairly fairly slope explanation explanation explanation explanation explanation explanation explanation answer answer caused worse london reasons filtered choices probable probable probable probable probable probable probable mathematics acknowledgement begin attribute res annual explained explained people people people people people people people freeman freeman freeman freeman freeman freeman dark dark generic generic generic psychophysical posed compares compares synthesis ordered gave logp logp electric univ naive naive picture picture lab lab aligned assign perfectly ordering arranged air imaging analogy interpret viewpoint mark fail illumination illumination combines ranging programs paul decide accounts scan arrangement chooses multiplied multiplied emergence april surprisingly surprisingly arrive arrive horn draw observer projects explains explains instructions tures interestingly material assigning treat neurophysiology shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading inferred inferred removal removal uniquely pentland pentland distinction adopt seek seek seek seek lit lit personal individuals individuals freund flat flat flat assess assess constrain shaded shaded shaded manipulation favor distri insights pami graphics distant reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance adelson adelson adelson adelson adelson adelson adelson depicts interactive rough indexed indexed maintains intl intl intl truth truth page bring slopes treating psychophysics psychophysics simplifies bution lighting lighting fiat fiat survey survey survey survey survey survey survey characterizing consuming marks marks vis vis viola viola observers observers interpolated virtually olshausen blum pictures concrete rare inferring interpretations interpretations interpretations interpretations markers plateau plateau rating rating rating rating rating rating rating explanations explanations bandpass william spirit icl est ranged raised corn shop assessed assessed recovering simoncelli sorted sorted sorted percep publishing ambiguities putational mir judge tenenbaum mumford ample zhu darker darker illustrating sought switzerland quarter consensus rendered rendered rendered penalties rendering rendering percepts ratings ratings ratings ratings ratings ratings ratings ratings ratings conveniently brooks psy prototypical concluded ogp formulating story rankings rankings rankings rankings rankings rankings rankings rankings rankings rankings penalize penalize badly knowl recipes teukolsky pairings terzopoulos flannery illuminated ridges orthographic manipulate vetterling confirming judgements judgements judgements judgements judgements judgements speculate greyscale mitsubishi raster photograph underdetermined broadway merl merl routinely alignments multilevel abilistic disambiguate impression brighter sinha sinha proximations editing kurtotic realistically wla arielson dth dressed coincidental exaggerated 
#@Freeman_W,Viola_P,
#t11
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#*network model model model model model model model model model model neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure set set set set set set set networks algorithm state state state state state results results information information information information information information information information information information information information information information information problem problem problem problem models models models based case case case case case case case vector vector vector vector vector vector vector vector vector order order order order shown values values values probability parameters parameters parameters parameters parameters noise noise noise noise noise noise distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method method method method method method method method method approach approach approach approach approach pattern point image image image image image image image image image image image image image image image image image image image image image image image image processing processing large large large large analysis analysis analysis matrix matrix matrix optimal form signal simple simple gaussian gaussian gaussian gaussian small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature methods methods methods methods step step step points features features features features features features features features features features features features features features features features features process process process process random random random random representation representation show rule vectors vectors vectors vectors images images images parameter parameter theory theory theory gradient obtained obtained obtained term term term term term note note note note dimensional dimensional dimensional dimensional dimensional dimensional result result result result result university university university variables variables computation computation solution log log log log defined defined defined defined constant constant constant constant estimate standard computer computer computer computer computer terms terms distance distance distance distance science science science science direction direction direction sets maximum continuous abstract applied applied find find find computational computational properties references stochastic ieee positive important important important important important important decision decision introduction estimation statistical generated variance variance variance variance variance variance variance variance tion change variable variable variable assume assume assume assume assume lower lower measure measure prior representations chosen center required good binary represent distributed distributed expected markov markov markov make make proposed proposed correlation minimum ing total computed respect respect respect elements optimization natural obtain obtain negative vol represented application define define define compute compute proc goal posterior posterior posterior distributions distributions power steps larger larger larger larger larger connection connection modeling proceedings institute institute department department version final graph ai considered framework computing computing computing equivalent environment environment directly hinton conference choice statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics vision vision estimated estimated estimated produce derived derived conditional conditional conditional entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy selected depends depends sampling simply increases increases increases group denote close close complete complete surface surface surface surface proof finding finding effective effective effective effective effective effective effective effective assumed supported supported pixel pixel pixel pixel pixel pixel pixel pixel pixel makes development typically smaller smaller smaller smaller smaller smaller smaller coefficients coefficients ratio ratio york york york york york edge edge edge edge edge edge edge increasing principle principle language representing direct direct direct direct direct direct international idea choose added added added denotes denotes denotes exact property apply apply apply apply pixels pixels quadratic sense sense sense sense sejnowski relevant sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient sufficient compare works works tions solve solve trans sparse sparse sparse sparse sparse definition definition chain organization grant grant horizontal intensity intensity intensity intensity intensity lead scaling occur deviation alternative deterministic occurs conclusion minimal neighbor depend depend depend bayes clear constrained taking largest assuming minimizing minimizing iii averaged introduce derivatives manner derive construct edges edges edges edges edges edges edges index estimating vertical develop mutual mutual mutual expectation expectation decreases choosing expressed formation formation reconstruction reconstruction reconstruction reconstruction communication suggested smoothing smoothing slow normalization normalization normalization convex convex fitting boundaries boundaries initially symbol perceptual formulation prove partially neighbors neighbors texture simplicity compression importance uniformly society driven delta computations computations conf kind repeated contained contained showing interested interested dis contribution contribution contribution criteria generative generative gibbs quantity vary vary write write usual maximization neurosci extract satisfies extend minimized carried wiley investigate investigate investigate hessian hessian hessian ideas maximizing maximizing maximizing cover topographic notion surfaces removed removed coefficient naturally plausible possibly opposite psychology portion precise multivariate detected averages averages averages mentioned site site inequality inequality theoretic variances variances failure baum drive straight precisely precisely precisely precisely precisely mation consequence calculations definite arises linsker nsf alignment varies amounts remove remove maintain marginal marginal marginal logp semi boston conclude conclude lot contribute ghahramani corrupted conditioned homogeneous royal kullback kullback chains simplify keeping affected infor decide moved mental realization thomas surprisingly environmental environmental environmental environmental environmental environmental captures grants grants summarize summarize tures adopted treat approx logarithm leibler leibler graded maximized recursively formulate formulate welch seek personal discovering principe var var var reconstruct constrain cns argue equality increment trends modifying afosr afosr march statistic statistic statistic ltm geiger geiger geiger inversely esti fea normalizing tel corners corners invertible junctions junctions junctions jointly jointly viola hoc concrete concrete concrete tribution archi minimax nih appro contents spent phil mumford won perturbative perturbative perturbative zhu ther manipulations berger decides puted fur fur continuation continuation continuation continuation continuation continuation environ seeks linguistics analogously enormous discard recon struction simplifications fii fii lesser lesser ficient ficient departments sufficiency sufficiency envi wells lattices florida fred dirac mating priate sequel nyu nyu nyu imately interscience thermore gainesville interchangeably projec osi ordinarily 
#@Geiger_D,Maloney_L,Rudra_A,
#t11
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#*model model model model model model model model model model model model model model model input input input input input input input input input input input input input input input input figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set system results models models models models based space space space space space space space space space space space space space space space linear linear linear order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown shown shown shown shown shown systems parameters parameters noise neurons neurons distribution approach pattern image image image image single processing processing local patterns matrix shows signal signal signal signal signal signal signal simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple visual visual visual visual visual visual size feature feature feature work work task task cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step cell cell cell cell cell cell cell cell cell random random response architecture show show show line general gradient obtained obtained experiments dimensional dimensional dimensional dimensional result result threshold research defined found found constant connections science science left left left left left direction direction direction direction direction direction direction presented present present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation activation temporal object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum position components basis abstract references due positive introduction complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus parallel tion energy energy energy energy energy energy energy energy energy energy energy difference spatial spatial signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals center type multiple cortex cortex cortex cortex cortex cortex cortex fact fact proposed correlation correlation simulations resulting ing simulation respect respect respect performed regions regions means means means means dimension dimension dimension dimension made feedback orientation orientation orientation orientation orientation orientation orientation study study filter filter filter filter filter obtain relative cross receptive receptive receptive receptive receptive provide objects objects location location location location active active cortical cortical cortical equal steps contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields fields fields fields fields support institute words code kernel kernel kernel kernel responses responses responses responses responses responses final equivalent environment directly additional transition stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stimuli stimuli stimuli stimuli detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection full requires con con developed area velocity velocity types types types lines actual provided finally evidence evidence inhibitory depends finding generate supported require ability easily makes development account account functional technology edge edge edge edge consistent filters filters filters filters direct direct direct inhibition inhibition inhibition added description light light light predict denotes denotes directions directions recent robust separate separate separate movement lateral moving moving moving moving moving moving moving side side cognitive subjects tuning tuning yields match correspond correspond correspond correspond differential background background locations sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive invariant occur suggests move move move white occurs half half conclusion place retina clear peak peak peak strong integration drawn california exist selective selective relationship introduce manner program relation pro van van edges longer perception perception perception plot plot plot transitions tuned sensitivity explicitly explicitly slightly interaction shift competition competition competition yield yield yield dependence reconstruction stages stages influence transform operations restricted showed similarly partial earlier remains faces avoid includes includes kernels kernels kernels kernels kernels extension illustrated black black absolute absolute reason straightforward middle poggio poggio identify detect detect detect detect detect detect detect mackay mackay plots essentially essentially essentially excitation soc soc built built built bar bar bar bar bar bar bar bar bar bar dot surround wave wave wave leading leading cat cat cat cat cat neurosci moves preferred preferred acknowledgments receive receive receive receive receive oriented oriented remain selectivity selectivity poor exhibit humans fourier fourier fourier fourier fourier fourier respond respond detectors detectors detectors detectors detectors detectors detectors detectors detectors detectors detectors investigated plasticity stream lgn lgn lgn lgn lgn lgn lgn lgn phases matched removed possibly predicts opposite opposite opposite opposite opposite der detector detector detector detector mapped detected detected detected detected detected detected simplest motivated preference preference preference biology nonlinearity spatially stress inside inside turns organized filtered division directional nucleus arise arise arise consequence separately opt opt opt res freeman dark dark dark dark offset psychophysical detecting ity schematic cal pasadena germany conclude neuro neuro physiol physiol findings identifying physiology physiology physiology physiology physiology physiology physiology drift linearity purely reconstructed reconstructed grey grey caltech binocular mail striate striate loops interpret wilson wilson analyses ensures ensures loo loo studying uni nonlinearities treatment spatiotemporal spatiotemporal spatiotemporal spatiotemporal stimulated suggesting suggesting considerations reverse ignore avoiding balanced insensitive insensitive insensitive insensitive insensitive insensitive insensitive insensitive insensitive insensitive insensitive insensitive pointing wiesel wiesel responds responds distinction hubel hubel increment cessing mammalian activate simplifying relating adelson adelson confirmed rectified rectified selectively universit pools geniculate psychophysics vice vice develops reversal reversal versa versa differently neumann neumann neumann justified mcdonnell vis vis vis inhibit opponent broadly alex polarity anatomy excited excited subtracted intracortical luminance luminance luminance luminance detects bergen bergen daily convolved convolved convolved convolved convolved informatik fol pooling pooling gaus adequately tivity pew bright bright bright pooled decrement rectification rectification alexander rightward suggestion encounter constantly accord zhou zhou reichardt reichardt reichardt reichardt elongated elongated synchronously neurophys neurophys unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented unoriented inspiration sug subdivided baker baker ohzawa sponses detec cies kybernetik persist analogies elongation reversals reversing trast insensitivity insensitivity concentric trailing ordinal polarities polarities polarities elaborated collapsed reverses reverses rectifying rection henry henry lives quenched lowed sians concen corti postnatal sensitiv neuroinformatik sensi curiously volved 
#@Grunewald_A,Neumann_H,
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#*network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data figure figure figure figure figure time time time time time time time time time time set set algorithm algorithm algorithm algorithm algorithm number number number system system error error results results results units units units units units units units units units units units units units units units information information information information problem problem problem problem problem problem problem models models models performance performance based based based based based based based based based based based based based based based based space space space space space space space space layer case order systems systems values values values unit unit unit unit unit approach approach approach approach approach pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image single single single single single single single processing processing processing processing processing processing large large local local test test patterns class class class class shows signal algorithms algorithms algorithms algorithms simple simple simple simple simple simple simple simple simple simple simple simple simple simple visual visual visual visual visual visual paper small small size feature feature feature feature feature feature feature feature feature task task task methods fig fig fig fig fig fig fig fig cells cells points points field field field field features features features features process current structure structure structure structure structure structure problems problems problems random random random random similar equation equation fixed fixed line images images images images images images images images general general real average theory theory theory obtained obtained obtained obtained obtained obtained activity activity dimensional dimensional university computation solution research defined defined found found estimate estimate estimate estimate standard standard left left left left left left left left left left left left left left left left left left left left direction direction direction direction direction direction direction direction presented presented map map map map map map map map present present present present phase phase phase phase phase phase low frequency frequency frequency object object object object sets motion motion motion range range range range range press position position position position basis abstract applied applied applied back computational computational computational references stochastic stochastic stochastic due ieee ieee context introduction introduction complex estimation estimation estimation estimation effect dynamic parallel parallel search search search search search search tion tion energy energy energy spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial measure measure measure measure prior chosen higher cases type type required required multiple cortex cortex cortex make fact fact techniques techniques techniques techniques techniques techniques techniques proposed correlation correct correct correct correct observed scale scale minimum minimum resulting classes classes human multi performed times regions regions regions knowledge obtain relative relative relative samples samples true true true compared define objects proc proc eye eye eye eye eye eye eye constraints constraints discrete discrete discrete discrete cortical approaches approaches approaches approaches approaches approaches approaches approaches mit institute institute implementation implementation implementation implementation implementation code responses difficult difficult layers layers scheme scheme scheme scheme scheme scheme addition maps maps maps maps maps maps maps maps considered cambridge directly additional additional additional view view view view view view view view view view view view view view view view view view view estimates estimates estimates estimates estimates estimates limit limit limit effects effects effects effects effects detection detection detection detection detection detection detection requires requires world speed vision vision vision estimated estimated estimated basic basic validation validation validation validation validation validation coding coding coding derived area area area area area velocity velocity types types lines lines lines lines lines provided processes processes processes nature sampling sampling sampling sampling simply simply biological increases group fast fast fast fast fast fast fast limited close complete stable stable stable surface common common common assumed assumed theoretical require eds eds cluster easily makes needed fully fully programming interesting ratio structures structures structures matching matching matching principal principal iterations max max direct direct international depth neuronal discussed discussed directions directions directions directions resolution property property robust apply moving include subject hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical cognitive sufficient compare calculated calculated calculated converge positions positions channels channels horizontal horizontal parts intensity intensity intensity intensity lead scaling suggests correctly locally locally generally half half half flow flow flow flow flow flow flow flow flow flow flow assumptions clear peak performs mechanisms integration physics largest largest cycle regularization turn turn turn assuming exist min min scene scene scene scene scene scene configuration acknowledgements areas areas areas relation edges edges optical optical optical optical optical optical solving primary sequential stability tuned implement missing missing missing easy slightly slightly angle angle scales scales scales scales scales scales springer shift shift shift extracted extracted independently independently expressed depending solved operations fraction static calculation calculation calculation calculation calculation smoothing smoothing smoothing slow classical classical classical reduces reduces false false iterative valid valid intermediate views precision recorded box combinations coordinate inter retinal retinal variations structural texture texture reason middle middle middle middle closely suitable maximal encoded computationally included poggio schemes schemes schemes schemes online fine fine summary soc kind split split dis running content physiological comp comp correspondence leading leading maximization overlapping disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity disparity neighboring neighboring receive extend camera minimized create essential experience circuitry circuitry humans estimators estimators estimators estimators estimators estimators estimators estimators issues fourier matches matches respond rest rest detectors int int parity combine reliable reliable working working working comparable proper complicated complicated complicated complicated matched patch patch patch coarse coarse coarse coarse plausible plausible plausible analyze extremely eyes eyes der der detected band band trivial analyzed analyzed analyzed guaranteed explanation expensive caused caused caused reasons turns turns turns located immediately cut potentially axon axon opt opt calculations calculations calculations calculations patches raw summation virtual collected freeman dark tional fed readily share sharp ity requirement http http calculating calculating operate stack stack stack stack stack stack stack stack stack stack stack extracting cal extensions coherent inherent comments display coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence coherence yuille yuille traces realized aligned aligned extensive restrict count impossible impossible robotics arranged binocular systematic wrong wrong wrong ranges ranges difficulties difficulties exploit analyzing splitting belong belong corner wilson reliably utilized ambiguity conjunction topological topological stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo stereo searching searching uni uni scan arrangement similarities barron barron specialized spatiotemporal reveals belonging ignore robert fusion dense dense dense dense linked slight converted solves equivalently maximized creates cooperative cooperative cooperative failed die exception additionally causing realize acting modifying shifting pami pami grouped denoting intra adelson adelson overhead lond intensities superposition superposition geiger responding psychophysics computa failures reversal algorithmic algorithmic handling primitives primitives marks vis vis blake blake transparency finer finer loosely wavelength wavelength marr marr marr slices bergen nontrivial inspection sions vertically prominent stacked aic spec applica movshon repeating repetitive vergence intrinsically ular collecting direc rela borders borders borders fight imaginary zhu aliasing aliasing aliasing aliasing aliasing aliasing des registration quarter heidelberg notably exceeded perspectives physik physik kanade disparities disparities disparities disparities disparities highlights modulo resort resembling internet traced und christian occlusions ohzawa pollard wrap fused fused fused qian qian displacements undefined registered registered stacks stacks stacks stacks stacks stacks stacks stacks kiel kiel kiel wavelengths movies discus sight famous sri coherently coherently coherently coherently usable ception landy cult tins needing complicate courtesy stereoscopic jepson everyday manifests bfilthoff diagonally hermann 
#@Henkel_R,
#t11
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural input input data data data data data data data data data data data data data data data data data data data data function function function function function figure figure figure figure figure algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm error state state results results results information information information problem problem problem models based space space weights linear linear linear linear linear linear linear linear linear case case case case case case vector vector order order shown systems values probability probability probability probability probability probability noise noise noise noise noise noise noise noise noise noise unit distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach point point point point point single processing processing processing large large large analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix optimal optimal optimal inputs form form form shows shows shows shows shows signal signal signal algorithms algorithms simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples examples examples methods field field field features cell structure structure problems random random similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture show show show equation equation fixed rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images general general general generalization speech speech speech speech speech real approximation approximation approximation approximation approximation approximation states gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained obtained term term term term note result university variables variables computation computation solution solution independent independent independent log log log log log log log log log log log log log log log log defined found standard standard terms terms terms terms terms direction direction presented present present present low low low low frequency maximum range components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample sample sample sample abstract computational convergence density density density density properties properties likelihood references component component component component component component component due due due due positive positive positive positive positive adaptive statistical statistical statistical statistical effect generated change change change difference assume assume assume assume assume signals prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations learned learned learned learned learned learned higher cases required represent represent represent distributed distributed make make make fact observed minimum minimum resulting computed computed respect called elements elements elements elements mapping means optimization optimization made natural natural natural natural filter obtain obtain obtain obtain obtain obtain obtain obtain negative negative original samples true true true true true compared compared compared desired desired receptive provide posterior posterior posterior posterior posterior distributions equal power power larger source source morgan report institute institute technique internal internal internal internal code code advances exp graph cambridge equivalent equivalent view san efficient efficient efficient efficient full full approximate approximate estimated pages increase coding coding coding coding coding coding randomly levels nature simply simply simply simply discussion technical increases describe transformation limited limited inverse complete complete complete complete complete complete finding finding finding main square including fit fit fit kaufmann objective objective objective probabilistic probabilistic probabilistic probabilistic typically smaller underlying underlying reduced reduced reduced coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients programming programming programming significantly projection database operation operation leads leads principal iterations iterations iterations bits bits normalized magnitude minimize minimize run sources sources sources sources sources sources sources improved exact exact robust ensemble element identical sense sense inference subset sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently approximately approximately volume smooth yields yields yields speaker pca pca diagonal diagonal sparse sparse sparse sparse mixtures separation separation separation separation separation separation separation generalized channels channels entire expression expression expression lead derivative alternative alternative alternative width demonstrate row row greater greater assumptions assumptions segment segment valued valued exponential mateo encoding presence solid assuming assuming assuming variety ica ica ica ica min derivatives program explicit derive derive generating plot plot laboratory dept segments modeled dimensionality involves remaining spectral yield viewed viewed solved solved densities evaluated restricted decomposition approximated spectrum dashed additive additive combining fitting fitting fitting valid norm norm advantages degrees precision avoid bell bell blind blind blind blind blind blind subspace determines extension maximize maximize priors priors priors priors columns columns efficiency efficiency literature mackay mackay mackay essentially orthogonal orthogonal orthogonal ten capture summary traditional traditional graphs symmetry notation notation sampled michael wavelet maximization consisted unlike unlike involving integral integral hessian hessian hessian hessian hessian hessian dataset dataset dataset pursuit fewer fourier fourier fourier fourier fourier fourier analytically scaled scaled maximizing tanh matched removed removed removed possibly adapt necessarily rank rank initialized initialized amari amari mixed mixed utility defines defining adapted adapted handle rapid stanford stanford preprocessing precisely broad ran ran ran probable probable probable probable probable probable probable opt gradually definite medical arises conjugate requiring axes generic marked span howard chen chen chen achieves logp logp redundancy redundancy redundancy specifies specifies specifies specifies specifies yielding univ lab redundant tation optimizing approximates removing neurobiology salk salk salk selects selects induce induce yang offers bases bases bases bases bases bases bases bases bases bases bases bases viewing emergence specialized specialized jolla cam influences speaking multiplying deriving deriving deriving inferred ram tendency letting letting laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian laplacian pub rectangular ftp ftp ftp dominated disadvantage inverted hughes deconvolution terrence simplifying simplifying wise noting represen anal inverting vanishes det det jutten jutten jutten differentiating overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete removes preserves uniqueness interior interior interior lation const invertible invertible olshausen olshausen drawing sen inferring inferring multimodal inde lewicki lewicki lewicki lewicki lewicki broadband problematic cichocki ira routine ysis stepsize stepsize drawbacks stat pendent derivations stabilizing timit phy herault herault herault invert invert comon comon putting illustrating package tially terry poten singularity donoho lira ogp inverses relied loses plete breakdown torrey pines denoising rewriting criticism pseudoinverse solver derlying atomic neuromimetic msecs xla xla xla xla xla saunders slx ata ata publicly formu tax bra misfit maxp maxp marginalizing aat ologp objectively aft org covariant sla alleviated cavendish tences 
#@Lewicki_M,Olshausen_B,
#t11
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#*model model model model model model model model model model model neural input input data data function figure figure figure figure time time time time time time output number system system system system system system system system system system system system system system system system system state results results results results results results information information information information problem problem problem problem models performance performance based case case case case case case case case order shown systems systems systems systems values noise noise functions recognition approach approach pattern pattern point point point point point image image image image image image single single single processing control control control control control control control control control large neuron test test test analysis analysis analysis analysis analysis analysis shows signal simple simple simple simple simple visual visual visual visual visual visual visual visual visual visual small small small small small feature work work work work fig fig fig points points field field field field field field field field field field field field field field field field field field process process process process level level level current high response response response response response response response response response similar similar similar equation equation section section section fixed line images real real real average average average experiments experiments result university threshold threshold threshold computation computation solution solution independent defined found found target target target target constant constant constant constant constant estimate computer computer terms terms distance distance distance distance distance distance distance distance prediction left left left left left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented presented presented map map phase activation activation activation low low frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal object object object object object object object object motion motion motion range range range position position position components continuous sample abstract find analog references ieee ieee adaptive introduction complex circuit estimation behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior effect effect effect dynamic dynamic parallel parallel change difference complexity spatial spatial spatial spatial assume assume assume assume assume lower lower lower measure chosen higher higher type good good distributed distributed chip chip make make make techniques techniques correlation length correct correct observed observed forward forward forward minimum minimum resulting ing tasks computed respect mapping factor factor factor made vol vol vol artificial relative relative relative relative cross cross objects objects proc proc proc active experimental experimental experimental experimental related constraints gain gain gain gain motor motor motor motor motor motor discrete equal power larger support support proceedings report institute implementation implementation implementation implementation implementation implementation implementation technique technique technique technique technique joint bias scheme scheme scheme addition addition addition addition maps maps computing computing equivalent experiment experiment environment environment environment environment curve curve view view top top stage detection detection detection conference requires requires requires significant world speed vision vision vision vision vision estimated basic basic basic basic give con channel derived robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot area velocity velocity velocity velocity velocity types path path finally finally finally finally finally finally finally evidence evidence evidence evidence depends depends sampling sampling sampling biological biological biological achieved measured discussion normal feedforward increases describe describe describe fast limited limited inverse corresponds surface circuits circuits implemented implemented require end pixel easily degree makes simulated typically account ratio ratio projection projection increasing increasing head head head head head head head head special uniform principle operation details call making making inhibition stored international bottom depth depth depth depth depth frame idea idea choose choose run added added description predict improved improve separate separate element element element element typical movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement lateral lateral lateral strategy strategy moving moving side side side pixels pixels array array array array array recently relevant sufficient varying varying module axis axis axis correspond differential trans trans modified sensitive sensitive grant grant horizontal horizontal wide derivative derivative derivative derivative derivative derivative derivative derivative derivative rotation rotation rotation rotation move move move move loop hardware half flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow place modules retina retina retina retina designed clear practice taking integration characteristics solid intelligence turn turn movements movements movements movements movements selective selective selective selective selective selective selective selective selective selective selective selective selective plane plane decrease derivatives scene scene base base base relation derive optical ways factors tuned distinct distinct changing modeled modeled implement implement averaging physical physical text angle unique integrated integrated john decreases focus focus communication interpretation interpretation open ocular centered frames frames suggested suggested suggested translation translation key reasonable reasonable smoothing smoothing slow expansion false false valid distances avoid avoid expect perceptual silicon silicon usa blind blind blind blind blind retinal retinal illustrated illustrated candidate black absolute absolute absolute absolute absolute tests tests simplicity reason determining sensor identified identified capable capable capable society maximal maximal maximal maximal modification computationally divided driven driven literature build composed soc soc compact conf success success success success success success success success neuroscience stopping stopping symmetry symmetry symmetry symmetry sin comp quantity chips chips chips received principles acknowledgments camera camera camera camera camera camera presents body body body body body body body body command mead mead involving replaced issues divergence divergence divergence divergence periodic periodic fashion fashion behavioral detectors detectors detectors detectors detectors biol int int authors pathway pathway pathway pathway pathway pathway scores understand understand patch patch patch patch closest plausible analyze extremely created eyes implementations front front front front front noted detector detector detector detector detector detector detector detector detector separated separated mapped mixed motivated defines animal animal animal ment ment ment vor ground sensors sensors analyzed navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation biology briefly spatially drive drive rapid rapid perspective directional directional immediately mation projected opt circle circle circle author author author radius nsf addressed requiring behaviors behaviors collected pathways pathways empirically pure capability readily autonomous autonomous car detecting detecting slower compares commands rely incoming replace conclude eventually progress summed cybern aligned accomplished fabricated angular narrow velocities velocities dynamically dynamically concerned mobile mobile inspired inspired inspired anatomical intelligent mark neurobiology reasoning implications implications spot spot spot spot spot optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic optic arrays arrays arrays obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle substituting substituting infor falls zhang zhang zhang photoreceptor stereo searching diameter neuromorphic neuromorphic thin thin eng ahead gaze gaze gaze gaze gaze saccade saccade horn horn contact observer observer observer observer observer insect insect insect insect insect papers hart stopped avoiding fly fly mechanical onr outlined empty dense dense dense dense fitted reflex numerous visually visually shunting focal break obstacles obstacles obstacles obstacles obstacles nelson nelson nelson convenience solely reports reports breaking breaking breaking workstation workstation alter monocular monocular peripheral peripheral perpendicular perpendicular trends robots robots robots toy toy toy wall compensate compensate elementary mediated concentrate plate surrounding lond guided guided exceed rectified rectified rectified deleted library translations translations translations anal barrier setup setup setup setup setup setup setup setup attached attached apparently voting tively likewise avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance flight bring det prevents reciprocal article failures failures failures failures failures failures failures failures differentiating stops circumstances heading heading heading heading heading crude crude crude agrees vis envelope imple hoc drawing drawing flows illinois illinois wiring striking vote vote anthony swing substitution spie spie era robotic robotic robotic robotic amenable lewis lewis lewis lewis senses periodically periodically quick comprised reviewed acknowledges acknowledges acknowledges stabilize motors motors motors mach platform rotational rotational rotational mounted mounted stabilization stabilization stabilization stabilization stabilization stabilization sorted bee bee bee urbana custom custom modulate stat hole competence remarkably rela sensed align collision phil dead favorably hong avenue lens translational intel vertebrates desire insects insects insects neurally neurally narendra environ seemingly seeks beckman serving serving mented laterally accord textured textured reproducing cameras blowfly blowfly lock lock lock lock resolving opening opening opening organ organ facing wheel votes votes votes grained inspiration inspiration cot avail neurosciences neurosciences mecha roberts roberts roberts nystagmus cda ucla jumping weber weber navigate cvpr adder eration divergent assisted organs gauge victor victor arrange reporting sgi compensates amp installed centering centering centering facilitating photograph clever parallax parallax parallax parallax parallax parallax parallax parallax imitating bot suggestive soda flies lucia throwing lightly lightly mally cle behaviours barry flying flying loan debugging restated nisms iei illustrations detectability refs confidently icpr naively mous 
#@Lewis_M,
#t11
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model input input input input input function function function figure figure figure set set training number number number number number system system results results results results results information information information information information information information information information information information information information information information information information information information information information information problem models models models models models models models models models models models models models models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance linear linear case case case shown shown shown probability probability probability probability probability probability parameters parameters parameters noise noise noise noise noise noise noise functions functions distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method approach pattern point point image image image image image image image image image image image image image image image image test test test test test test analysis analysis class class class class class class matrix optimal optimal optimal optimal optimal optimal optimal form shows shows gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual paper size task task task task task task task task task methods fig fig fig fig step classification level level level structure memory memory memory similar representation representation representation representation representation representation section line rule rule images images images images images images theory theory obtained obtained obtained note dimensional dimensional result result result result university threshold threshold threshold solution solution research research research independent independent independent independent independent independent independent independent independent independent defined defined defined defined found target target target constant constant standard standard standard standard standard standard standard terms terms distance distance presented present low object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object object sets range basis abstract applied find computational computational computational computational computational computational references component due due ieee procedure important important important adaptive decision decision introduction stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical statistical statistical generated generated variance variance variance parallel search search tion change difference difference assume assume assume assume measure prior prior prior learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned higher higher higher higher type type multiple long conditions conditions conditions represent bayesian bayesian bayesian bayesian bayesian make correct correct correct correct classes classes classes human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human human called called means feedback feedback study original original original original relative relative relative relative relative relative relative relative relative specific specific represented compared define define define compute objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc experimental constraints constraints constraints equal equal equal comparison comparison comparison comparison larger larger larger larger contrast support support dependent dependent dependent dependent institute words words implementation implementation represents represents difficult exp exp exp exp exp exp addition addition addition equivalent experiment experiment additional additional view view view view limit stimuli upper requires choice significant significant approximate free free free free vision vision vision con con produce derived derived randomly randomly criterion provided provided provided selected selected evidence nature nature depends depends depends depends measured increases denote tested tested transformation transformation transformation transformation transformation transformation transformation limited limited limited limited assumption assumption assumption nearest nearest nearest nearest implemented implemented assumed supported theoretical ability hypothesis hypothesis hypothesis hypothesis degree makes typically smaller smaller smaller account account account account account account account account projection projection projection increasing increasing increasing increasing trials trials matching matching matching matching matching principal stored stored stored normalized depth frame idea choose choose choose choose choose added added added predict recent property pair pair pair separate similarity similarity similarity reported strategy strategy strategy strategy strategy subject subject sense sufficient sufficient varying compare subjects subjects axis yields yields yields match achieve positions symmetric symmetric symmetric observation generalized increased invariant suggests suggests deviation deviation deviation deviation deviation deviation deviation rotation rotation rotation conclusion conclusion conclusion critical greater assumptions assumptions conclusions neighbor neighbor neighbor neighbor neighbor central central measures bayes learns constrained constrained constrained constrained suggest taking strong mechanisms integration radial assuming plane plane question question index perception modeled metric metric explicitly explicitly coordinates transformations transformations transformations transformations transformations transformations transformations transformations angle adding adding implies implies yield yield dependence dependence dependence dependence dependence dependence dependence review depending estimator viewed solved variation variation variation detailed operations operations operations restricted restricted restricted restricted showed showed decomposition completely constants allowed discrimination key partial reasonable closed interpolation interpolation intermediate distances calculate euclidean views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views views degrees template template template template template template template template template template template template template includes recognize recognize recognize structural structural structural structural structural structural structural structural reason straightforward aspects aspects efficiency efficiency efficiency efficiency efficiency efficiency efficiency efficiency poggio identity identity capture capture interested interested issue symmetry contribution classify strategies sci sampled sampled generalize minimizes correspondence computes access essential humans humans humans humans humans humans humans humans humans humans humans humans dotted rise rise fashion applicable ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal proved affect understand understand cognition smallest coefficient trace possibly necessarily man implementations implementations adjusted prototype singular aspect fisher precise explored extent pairwise theoretic crucial derivation track answer benchmark benchmark tool reasons closer acad lowest geometric evaluating led affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine affine psychophysical compares ity templates templates templates templates templates templates templates templates templates templates templates measuring characterize conclude age shaped shaped shaped shaped shaped shaped shaped shaped findings focused extreme extreme naive appearance equivalence appropriately rotated rotated flexibility rotations rotations rotations rotations rigid rigid rigid stronger familiar familiar resulted interpret viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint viewpoint serves fail wire optimally planar planar natl mance mance edelman edelman ambiguity irregular irregular irregular irregular irregular irregular displayed displayed perfor perfor vertices vertices viewing recog recog occlusion suggesting vertex extensively observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer observer implicitly assigns liu liu liu liu liu liu yielded ple shading shading outperform outperform inferred nition nition exception regularity regularity regularity regularity regularity lit descriptions tor conservative conservative reconstruct reconstruct representa pami familiarity mimic mimic likewise rotating det psychophysics nec factored stores stores copies copies copies crude insufficient converging designs grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf grbf observers observers observers observers observers observers observers observers observers observers observers observers observers observers observers observers observers observers observers observers lated mirror integrates normalize sym sym functionally recognizes distorted distorted reflection binomial est positional tations thresh counted watson putative probabil discriminating daniel distractor distractor distractor weinshall deformations psych psych arline arline arline arline arline arline arline arline arline arline arline workers exceeded provably simu embodied viewpoints viewpoints estima lend tributions cri debate debate reflections reflections occlusions mimics balls balls balls sider irrespective efficiencies efficiencies orthographic impaired pare oliver minnesota llt ttt ati rejects interleaved ils ine conceivably sio parallels spect perimental princi aft ois advocate firmly boyd quest bfilthoff 
#@Kersten_D,Liu_Z,
#t11
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#*network network model model model model model model model model data data data data function function figure figure figure figure figure set set set system error results results models models models models linear linear linear linear linear case shown shown shown shown shown probability probability probability probability functions functions unit distribution distribution distribution distribution distribution distribution point image image image image image processing processing large local local local local local local local local local test test test test analysis analysis analysis analysis analysis shows shows simple simple gaussian gaussian gaussian gaussian visual visual visual visual size size size work work work work work fig fig fig fig fig fig fig fig points field field field process process process structure structure structure structure random similar similar similar similar similar representation representation representation show show line images images images images images images images images images images images images images images images images images general general parameter parameter parameter parameter parameter average obtained obtained obtained obtained obtained obtained obtained dimensional dimensional result result variables variables research research independent log log log log defined defined defined found found found found constant constant terms terms terms terms terms science prediction prediction prediction direction direction direction direction direction direction direction direction direction direction present sets maximum maximum range range range range range press press press position abstract find properties properties properties properties properties properties properties properties properties properties properties properties properties references references component stochastic stochastic stochastic important important important context introduction hand estimation statistical statistical statistical variance variance variance variance energy energy energy energy difference variable variable variable variable variable variable variable variable variable variable variable variable variable variable lower chosen chosen type good fact fact fact correct correct observed observed observed observed scale scale scale scale scale scale scale scale scale scale scale scale scale finite finite resulting regression respect eq eq eq eq eq eq eq eq called called factor dimension dimension dimension natural natural natural natural natural natural natural natural natural study study study obtain obtain obtain original specific compared compared receptive define define determined related distributions gain power power power power larger contrast contrast contrast contrast contrast fields modeling consists consists kernel kernel kernel kernel kernel represents considered cambridge cambridge domain environment directly effects determine upper statistics statistics statistics statistics statistics vision vision estimated basic developed velocity actual provided processes processes processes nature depends discussion technical arbitrary tested corresponds corresponds surface predictions amount supported main adaptation square hypothesis hypothesis easily development development sensory fit fit fit fit pairs underlying fully interesting interesting edge edge edge edge edge edge edge edge edge structures structures details call direct normalized early choose description predict predict predict denotes directions directions directions recent resolution property property property property property ensemble takes similarity similarity similarity similarity similarity similarity similarity similarity similarity introduced pixels pixels pixels pixels sense sejnowski cognitive recently relevant dimensions approximately yields definition definition definition evaluation grant horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal lead scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling suggests extended extended derivative derivative derivative predicted predicted starting segment conclusions accurate numerical numerical asymptotic taking presence largest solid program base denoted acknowledgements appears appears relation relation relation relation van edges edges edges edges edges edges edges edges longer plot plot describes vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical vertical category scales scales scales develop expressed expressed expressed dependence dependence stages communication squares squares variation detailed detailed transform evaluated evaluated similarly partition spectrum spectrum valid box bell plotted illustrated holds holds holds holds holds holds holds phys phys phys phys phys phys phys discussions discussions aspects uniformly differ delta delta included invariance invariance identity reached composed refer refer refer soc notice graphs link interested manifold manifold manifold generative hold hold comp quantity generalize correspondence law law bars investigate put integral integral integral mass dataset behaviour behaviour behaviour existence existence existence giving authors statistically understand fundamental necessarily predicts rev rev rev rev rev rev rev singular singular singular singular singular singular singular noted ith simplest contributions explain defines established histogram great ment scenes scenes trivial variances variances variances analyzed cascade cascade inside choices cut opt qualitative addressed argument reflects understood relevance quantitative effort sharp sharp sharp maxima exhibits poisson poisson poisson poisson measuring marginal marginal univ naive representative physiology nat theories stronger mail mail mail analogy analogy multiplicative multiplicative multiplicative moment moment moment obtaining moments moments moments motivation composition bialek studying reproduce ensembles insight surprisingly rich verification lett lett lett lett lett lett acknowledge fitted logarithm validity german exponent exponent exponent exponent manifolds ocr ocr crosses singularities erp erp paris paris paris france france figs barlow universit grateful dramatic remark stimulating regularities characterizing sees justified prefer vii olshausen flows flows flows flows flows atick partly obey predictable ruderman ruderman ruderman ruderman ruderman legendre tical derives physica physica dissipation dissipation dissipation violated dispersion elaborate discrepancy kolmogorov kolmogorov kolmogorov nents borders exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents exponents inte ess ess ess ess ess ess ess ess ess ess ess ess ess ess ess ess ess ess statis infinitesimal nadal nadal nadal nadal nadal nadal fruitful turbulence turbulence turbulence turbulence pierre singularity singularity french rue cedex forest collaboration accumulates dan associ parga parga parga parga parga parga inertial diamonds reads reads pth pth illuminated patrick ating bernard offs laughlin brunel expo laboratoire laboratoire baddeley baddeley lna ecole maih ural phrased jean vmue controt hateren transverse transverse qth spain stor roland normale ish hor izontal antonio mong 
#@Mato_G,Nadal_J,Parga_N,Turiel_A,
#t11
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#*model neural input data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure set set set set set set set set set training training training algorithm number error error results results results results information information problem problem problem problem performance performance performance performance performance performance performance performance performance based based based space space space space space space linear linear linear linear linear linear linear linear layer layer case vector vector order order order order shown systems systems values values probability parameters parameters parameters functions recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method pattern pattern pattern pattern pattern pattern pattern pattern point point image image image image image image image image image image image image image single single single single processing large large local local local local rate test test test patterns patterns patterns patterns patterns patterns analysis class optimal signal algorithms algorithms simple gaussian examples small small small small small small work work work task task points points features features features classification classification classification classification classification classification classification classification classification process level level level current problems random high high high memory show show equation equation equation equation equation equation equation equation equation equation equation equation equation section line images images images images images images general general parameter parameter parameter parameter parameter real approximation approximation gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained term experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional threshold computation computation computation solution research defined defined sequence initial initial initial constant estimate estimate estimate estimate estimate standard terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance left left left left presented low low low motion range range range range range range range press nonlinear sample sample abstract applied find computational computational computational convergence convergence convergence convergence convergence convergence properties properties references due due due ieee procedure important introduction complex hand hand estimation estimation estimation generated generated cost cost tion tion spatial spatial spatial classifier classifier classifier classifier measure higher higher higher higher center required good conditions equations fact fact fact techniques region proposed correct errors errors errors errors errors scale scale minimum minimum minimum minimum minimum minimum minimum minimum minimum tasks tasks tasks regression computed computed computed computed respect respect respect respect respect respect performed performed performed optimization made global global global global study obtain vol artificial artificial specific represented true application application series series define compute compute proc proc proc experimental distributions mit mit accuracy accuracy accuracy accuracy accuracy accuracy update report version version version version version version version technique consists code difficult difficult final considered considered considered framework framework framework framework cambridge computing equivalent equivalent experiment experiment experiment experiment environment view view view top detection conference efficient efficient classifiers classifiers requires significant significant significant statistics statistics vision vision increase increase types finally finally selected iteration iteration iteration iteration iteration iteration nature achieved normal increases describe transformation transformation transformation transformation transformation transformation transformation close corresponds corresponds surface surface nearest common shape require require main face face face face face face face face face square ability easily easily easily easily degree degree typically typically smaller reduced functional programming significantly significantly significantly character character character character increasing increasing database database database database database database database leads leads leads leads squared iterations iterations iterations bottom magnitude idea attention combined combined combined minimize minimize minimize light improve resolution resolution resolution resolution resolution robust robust robust robust robust robust robust robust robust robust similarity reported introduced subject subject subject subject subject subject subject subject hierarchical sufficient approximately subjects tions smooth correspond achieve achieve trans improvement improvement sensitive sensitive entire amplitude expression lead invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant scaling scaling scaling scaling scaling scaling scaling occur extended extended deviation rotation rotation rotation rotation rotation setting setting starting starting greater conclusions neighbor editors tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent tangent designed designed designed taking drawn minimizing min min min plane derivatives derivatives derivatives minima minima minima reference solving laboratory metric metric metric missing coordinates involves transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations remaining remaining slightly scales scales applying minimization minimization minimization minimization minimization minimization minimization john john decreases choosing extracted squares estimator variation variation evaluate evaluate evaluate restricted approximations centered decomposition decomposition decomposition decomposition understanding approximated completely translation translation translation translation allowed key partial expansion reduces combining purpose purpose iterative iterative iterative valid distances euclidean euclidean euclidean euclidean classified faces faces faces faces faces views views degrees degrees avoid combinations usa formulation extension extension variations variations variations variations variations partially partially discussions major simplicity simplicity regular regular straightforward importance computationally literature literature invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance invariance identity identity composed composed composed compact notice notice repeated procedures procedures cun cun showing superior issue issue classify classify classify sin manifold manifold manifold manifold manifold manifold manifold hold simplified denker denker leading leading leading reach consisted approximating acknowledgments employed wiley wiley transformed transformed difficulty estimators estimators estimators estimators estimators limitations limitations hessian dataset dataset matches int variability variability variability workshop surfaces surfaces surfaces coarse necessarily analyze facial facial illustrate created created front portion taylor taylor expressions academic multivariate stop track guaranteed expensive caused tractable starts considerable easier easier laboratories simard simard simard scientific lowest robustness argument improvements led affine affine affine affine affine affine affine affine affine affine affine tional conducted effort passed incorporated outliers outliers templates prototypes exhibits exhibits exhibits rely rely summarized measuring characterize ordered datasets datasets datasets datasets datasets datasets hamming inherent age shaped median median pyramid pose newton newton newton newton newton newton newton newton newton narrow girosi ordering rotations extending communications imaging hyper fail roles degradation substituting substituting substituting inferior embedding lip iteratively bad stereo darpa israel relies limitation limitation bertsekas andrew metrics metrics metrics metrics metrics dramatically dramatically slight kluwer break break benefits tween chapter covariances flat warping guess guess avoided laplacian manifolds manifolds manifolds manifolds manifolds manifolds manifolds adelson depicts topic harder translations translations maintains denver applicability lippman lippman lippman drops increments increments computa moderate stimulating heavily multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution multiresolution suffers shot appealing sided thickness resolutions resolutions resolutions resolutions resolutions discarded bergen drastically amenable doubling media media outlier trapped jerusalem degrade drawbacks decompositions huber fight fight substituted extremes registration registration ames exhibiting impressive impressive throw anandan deformable originating glasses kanade blobs attain occlusions occlusions ink athena bringing embed screening burt leverage transforma cup stringent carded gracefully lucas graceful ptp ptp ptp undesired tangents federico uneven disregarded hardest hardest hardest weighs disregarding resolu 
#@Lippman_A,Vasconcelos_N,
#t11
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#*learning learning model model neural neural neural data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number number number number number number number number number number number number number system system system error results results results results results results information information information information problem problem problem problem models models models models models models models models models models models models models based based weights case case case case vector shown shown shown shown systems systems systems values values values values values values values parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight method approach approach pattern pattern point image image image image image single single single single single single single single processing processing large large local local local local analysis analysis analysis analysis analysis analysis analysis analysis matrix form form shows shows shows shows shows shows shows shows shows simple simple simple gaussian gaussian gaussian paper paper small small small net work task methods step points points points points field field field features level level level level level level current structure problems similar similar similar similar representation representation show show show show show equation equation equation equation section section fixed line line images general general parameter parameter parameter real real real average theory theory gradient gradient obtained obtained note result result variables computation computation solution solution solution solution solution solution solution log log log found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial constant standard computer computer prediction phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase temporal object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum range range press components components components abstract abstract find find likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component due ieee ieee ieee positive positive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context estimation estimation estimation estimation estimation estimation statistical generated generated generated generated generated generated generated variance variance complexity complexity spatial spatial assume required multiple multiple multiple multiple multiple multiple multiple multiple conditions conditions tree tree tree tree expected equations make fact techniques correct correct simulation times applications em em em em em negative negative application cross cross cross cross objects objects objects objects objects proc proc proc location brain brain equal equal approaches mit mit fields institute version technique advances difficult difficult layers sequences sequences sequences sequences framework framework framework framework framework cambridge directly hinton additional additional additional additional additional solutions estimates transition transition transition transition transition transition transition transition transition transition choice significant statistics vision vision vision vision vision estimated estimated pages pages pages pages increase validation validation give condition derived weighted weighted weighted clustering clustering clustering clustering levels velocity velocity velocity velocity lines lines lines lines finally achieved discussion arbitrary denote assumption assumption assumption assumption corresponds corresponds surface surface surface surface surface surface surface surface surface surface surface surface surface predictions finding assumed assumed assumed assumed assumed supported theoretical theoretical require require pixel easily easily makes noisy noisy noisy noisy noisy noisy fit fit fit probabilistic typically underlying needed technology projection york segmentation segmentation segmentation special consistent consistent squared squared squared representing direct making depth combined added description description predict exact advantage property robust typical moving moving moving identical identical identical identical identical identical pixels pixels pixels pixels sense cognitive sufficient varying calculated correspond correspond converge background background generalized organization organization organization organization organization grant horizontal horizontal horizontal intensity intensity lead wide matrices predicted move move move move touretzky generally runs flow flow flow critical critical critical critical assumptions segment editors clear faster faster practice practice weak encoding taking proportional assuming plane introduce derivatives scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene denoted explicit monte derive derive carlo longer optical optical optical solving estimating estimating estimating estimating estimating plot transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions distinct distinct distinct distinct distinct dept segments segments segments modeled modeled recall simultaneously physical involves easy unique unique unique adding expectation versus letters family dependence review depending depending interpretation evaluated restricted frames translation converges diagram diagram diagram reasonable calculation calculation additive performing measurements measurements fitting add remains valid assigned assigned assigned transactions avoid figures includes perceptual perceptual perceptual perceptual perceptual perceptual perceptual eigenvalues eigenvalues eigenvalues sciences automatic maximize priors black partially partially discussions reason compression maximal symbols comparing tend soc conf conf conf repeated prob video video video video video video video video video showing showing split issue notation simplified absence eigenvalue maximization subsequent subsequent mixing acknowledgments tesauro camera camera camera camera camera camera camera camera origin origin origin origin origin parametric layered overfitting overfitting difficulty varied varied varied varied varied hessian hessian hessian hessian hessian dataset ml ml rise rest rest int reliable maximizing maximizing surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces surfaces measurement editor necessarily analyze predicts predicts illustrate illustrate illustrate illustrate observe finds finds finds synthetic massachusetts residual residual residual residual residual scenes scenes costs derivation analytical analytical analytical answer closer closer closer commonly separately involve definite auto author incomplete mechanics understood affine affine parameterized posed maxima maxima maxima maxima http incorporating enables sums sums semi segmented segmented coherence yuille wang progress june lot consistently benefit leen www velocities velocities velocities branches branches branches rotations rigid imaging imaging promising determination balance intuitively intuitive exploring meaningful contexts slice slice iteratively captured captured elastic advance advance recog recog suggesting belonging motions motions motions splits implicitly dempster avoiding lem unified rubin maximized maximized residuals weiss weiss weiss weiss weiss tradeoff tradeoff mdl solely transparent intuition intuition grouped adelson adelson adelson depicts smyth proach topic ambiguous harder buhmann translations laird portions flower flower flower flower page durbin september rose stimulating prefer prefer prefer house house cornput cornput cornput mining horizontally horizontally conflicting fox interpretations maxi salesman statist bcs pooling pooling demands handbook fication translates shares hood hood repeating imposes tenenbaum tenenbaum undergoes undergoes undergoes web analyzers translating translating analyzer segmentations visualized visualized travelling undergoing segregated arbib likeli likeli perceptually factoffal danger todorov gurewitz mized timation matically parallax bed bed bed erroneously ofx founded straightforwardly kdd organizations organizations jepson scalings speci isting 
#@Weiss_Y,
#t11
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#*network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set set set set set networks networks networks training training training training training training training training training training training output output output output output number system system system system system system system system system system error error error error error error error state state state state results results results units units units units units units units units units units units information information information information information information information information problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based based based based weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer case vector order shown shown shown shown shown shown shown shown shown shown shown shown systems values values values probability parameters noise noise noise noise noise noise noise weight weight weight method method method method method method method method method approach approach point point point point point point image image image image image image image image image image image image image image image image image image image image single single processing processing processing processing processing processing processing processing processing control control control large large large rate rate rate rate rate rate rate rate rate rate rate rate test analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows shows signal simple simple simple simple gaussian gaussian visual visual visual visual visual paper paper paper paper paper paper examples examples examples small small small size feature feature net net work work work work task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task methods methods methods methods methods methods methods methods methods step step step step step step step step step step features features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification process process process process process current current current current current current current current current trained trained trained trained trained trained trained trained trained trained trained problems random random random high representation representation architecture architecture architecture architecture show section section section section rule rule images images images images images images images images images images images images images images images images images real real real real real real average note note note experiments experiments university research defined found found found found found found found found sequence sequence sequence target target target target target target initial table table estimate standard computer computer distance connections connections science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left left left left direction direction direction presented presented presented presented map map map map present phase activation activation activation activation temporal machine machine object object sets motion motion press press press learn learn learn learn learn position position position position position position position components outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs sample abstract find find references due procedure procedure important important important important important important important important important important context introduction complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand estimation effect dynamic dynamic tion difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference difference rules rules rules learned learned learned chosen chosen center previous previous previous previous previous previous previous previous previous previous cases required multiple multiple expected expected expected expected expected expected expected expected expected expected make techniques region region region region region correct correct forward forward classes ing tasks tasks tasks tasks tasks tasks tasks tasks total simulation human computed computed multi performed regions regions regions mapping means potential dimension made feedback feedback applications applications study study study study study knowledge knowledge knowledge knowledge knowledge knowledge filter obtain original original specific specific specific specific specific specific specific specific specific specific specific specific samples samples samples compared application application application desired desired cross cross cross define define objects objects objects rates location location location location perform perform active active determined goal goal related related constraints connected approaches approaches mit mit mit steps comparison larger contrast connectionist difficult difficult difficult difficult layers layers layers layers layers layers maps maps considered considered considered considered domain domain domain domain domain domain experiment directly transition transition limit top top top top detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection capacity determine determine determine full significant free world world world world world world vision vision vision vision vision vision vision vision estimated estimated estimated con produce weighted weighted developed developed robot robot types actual actual actual actual actual actual actual actual actual finally sampling sampling constraint achieved achieved measured tested fast limited limited close assumption predictions predictions amount amount assumed role role role require require main main face pixel pixel pixel pixel ability future future future future future easily easily easily makes fit kaufmann underlying underlying underlying underlying underlying needed account account account fully transfer testing edge principal details filters filters pre making bottom supervised magnitude frame frame idea attention attention attention attention attention attention attention attention attention attention produced light predict predict predict perceptron architectures architectures improved improved improved discussed improve separate separate typical similarity movement moving moving subject subject side side side pixels relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant interest interest interest previously approximately approximately module module solve solve solve solve solve correspond pca studies background background background background background locations locations locations locations locations modified modified modified improvement entire entire constructed horizontal horizontal parts intensity intensity extended predicted predicted correctly feed feed move runs half row row reduce reduce reduce reduce reduce reduce reduce reduce reduce reduce conclusions differences modules modules accurate retina retina encoding encoding strong mechanisms integration integration presence largest demonstrated turn variety selective selective manner manner scene scene scene scene scene scene appears appears appears pro construct edges edges perception solving ways transitions ann distinct changing changing explicitly explicitly explicitly slightly text develop integrated gaussians applying formed formed expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation expectation select focus focus focus reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction interpretation fraction centered centered centered frames frames understanding reduces purpose false false false false false tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking intermediate visible faces koch koch expect thesis activations activations activations activations activations activations activations activations activations priori priori priori priori priori inter black neighbors determining determining sensor compression middle middle identified extra closely importance suitable differ differ differ differ encoded encoded encoded encoded encoded driven poggio post summary summary summary road road road road road road road road road road road road road road road road road road quickly contained contained heuristic criteria sampled providing nips delayed automatically automatically attempt acknowledgments camera camera camera camera camera situations presents body body employed simpler unlike layered create create collection circuitry kalman kalman environments humans humans accurately accurately accurately accurately matches school school tech detectors fault fault fault fault fault fault scaled scaled variability encode encode notion matched removed removed examined examined saliency saliency saliency saliency saliency traffic created created created subsets portion explored academic detected detected detected detected detected attempts synthetic scenes scenes scenes developing directed track track navigation navigation waveform waveform waveform waveform waveform adjacent nowlan nowlan inside processed strictly filtered filtered filtered filtered precisely incorporate located potentially demonstrates demonstrates auto auto author mellon mellon addressed raw requiring improvements carnegie carnegie relevance relevance relevance cmu cmu cmu amounts conducted fed autonomous autonomous autonomous autonomous autonomous autonomous car car car car poorly posed marked marked detecting remove remove reliability commands schematic measuring measuring measuring pittsburgh pittsburgh extracting incorporating sums expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations expectations coherence coherence focused yuille yuille irrelevant irrelevant irrelevant irrelevant irrelevant shifted person person person proportion mistake appearance drift driving driving dynamically signature signature signature signature controlling circular mobile reconstructed reconstructed reconstructed reconstructed tem eliminate eliminate robotics platt platt allocation wrong ments promising city city vehicle vehicle vehicle vehicle vehicle interpret neurobiology fail shifts cottrell cottrell salient salient salient guide guide guide guide guide guide degradation heuristics heuristics heuristics heuristics obstacle obstacle spurious heavy connect corre moved den den den reproduce dif april creating creating creating indicator ahead ahead tracker tracker tracker tracker tracker passing passing exploiting tures discriminate yielded appeared appeared land ence ple unable unable visually kluwer convolutional convolutional lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane lane pointed classifications solely solely descriptions imagine avoided reconstruct reconstruct attempted exam robots alternate baluja baluja baluja baluja baluja baluja baluja baluja baluja faults faults faults faults faults faults faults faults guidance mitchell intra pomerleau pomerleau pomerleau pomerleau pomerleau pomerleau crosses eliminating emphasize emphasize emphasize ullman ullman noting translations drawback emphasized emphasized emphasized emphasized emphasized emphasized emphasized portions portions portions portions portions portions tively accounted inversely fea places avoidance avoidance steering steering travel october signs mea worked helps removes acquire tom continued trainable ferent blake blake puts hid hid hid fabrication fabrication fabrication fabrication wavelength sen ples manually clark clark periphery predictable predictable predictable predictable predictable rel accounting subscript gathered gathered shaping plasma plasma plasma plasma plasma plasma sep dean deciding fore unexpected unexpected unexpected mounted sented began anomaly anomaly cations distractor appli cars marker marker marker marker marker neigh fundamentally tracked tracked tracked attentive fight fight hands hands hands hands posi thorpe thorpe subsampled manipulating roads poral ana confident positioned driver niques pared emphasizes categorize emphasizing emphasizing wafer wafer wafer wafer wafer wafer wafer wafer wafer wafer wafer wafer wafer wafer wafer kanade tain landmarks confused confused extraneous extraneous extraneous extraneous ences ences chamber recon vehicles selec unrelated unrelated sponds anomalous attend freeze reflections nns nns emitted pected pected sor predictability tives tomaso envi cluttered cluttered cluttered gan sured semiconductor semiconductor semiconductor semiconductor parison mor gauge lll shumeet marking marking marking marking marking contamination outdoor unpredictable unpredictable ronment ascertain ascertain weightings allocates simulta uts brighter evant evant strat ier neously discernible attending attending distracting distracting incorpo gon arate egy triplet triplet igh takeo mous 
#@Baluja_S,
#t11
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#*network learning learning model model model neural input data figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set set set set set set set set networks algorithm algorithm algorithm algorithm output number number system system system system system system system system system system results results results information information problem performance performance performance performance performance performance performance based based based based based space space space space space space space weights linear linear linear linear layer layer case vector vector order order shown shown shown shown shown shown systems systems systems values values parameters weight neurons recognition recognition recognition recognition recognition approach approach approach pattern pattern pattern point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single processing large large large large large local local local local local patterns patterns analysis analysis analysis form form form shows algorithms algorithms simple visual visual visual visual visual visual visual visual visual visual visual examples examples size feature feature feature feature feature feature feature feature feature feature work methods methods methods methods cells cells points points features features features features features classification level current structure structure structure structure structure structure high memory response response response response similar similar similar similar similar similar representation representation show show images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general general real approximation obtained experiments experiments experiments experiments experiments experiments dimensional dimensional result result university computation defined defined found target target target target target target target target target target target target target target target target target target target target target target target standard standard terms distance distance distance distance science left presented presented presented presented present present low temporal object object object object object sets sets sets sets sets sets sets position basis basis outputs sample sample abstract find find properties properties properties properties references due procedure context introduction complex complex complex complex complex stimulus effect generated generated generated variance variance tion tion energy difference difference spatial lower measure measure measure measure measure measure measure part type type cortex conditions tree tree tree distributed distributed bayesian techniques techniques techniques techniques techniques techniques proposed scale scale scale scale resulting ing ing ing tasks total human human computed computed multi performed elements elements elements regions regions regions factor dimension dimension made made natural orientation global filter filter vol artificial relative relative specific compared compared provide compute compute objects objects rates rates location location perform perform perform perform determined related mit mit mit mit comparison contrast contrast contrast proceedings report report report institute technique technique technique consists responses responses responses difficult layers graph ai ai ai ai ai cambridge computing domain experiment experiment directly additional additional additional limit top top top top effects detection conference determine upper full full world world vision pages weighted developed criterion criterion criterion types types types path simply achieved measured discussion technical technical technical increases describe group group group group group inverse inverse assumption finding finding nearest shape shape generate journal square cluster cluster cluster cluster development including typically fully technology technology technology projection projection edge mechanism consistent consistent matching database database database database database database database database database database database database database database database operation filters filters international international normalized bottom bottom added light improved resolution resolution resolution property property pair element element element typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity practical moving include pixels sense relevant compare compare yields trans diagonal sparse definition channels channels organization storage sensitive constructed constructed exists exists horizontal wide rotation rotation hybrid boundary half half conclusion critical critical reduce neighbor interactions measures measures clear strong strong hard hard characteristics proportional intelligence labeled user user selective iii groups groups scene scene question edges edges edges produces index perception ways laboratory vertical vertical remaining formed extraction john decreases extracted variation variation variation variation variation variation operations soft translation measurements measurements measurements combining roughly false false initially filtering query query query query query query query query query query query query query perceptual color color color color color color color color color color retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval absolute structural structural successfully texture texture texture texture texture texture texture texture texture texture texture determining straightforward capable importance importance importance differ differ driven driven driven driven included successful literature schemes post projections projections projections projections comparing comparing ten ten characteristic characteristic characteristic characteristic characteristic characteristic characteristic characteristic characteristic characteristic characteristic characteristic characteristic characteristic capture repeated repeated strongly strongly strongly video neuroscience content content content content content content criteria vary paradigm computes highest approximating receive oriented camera camera situations bars wiley experience humans examine respond project project project relationships relationships cognition fundamental circles measurement necessarily created perfect perfect changed queries queries queries queries queries rank der der portion observe ith consist detected submitted electronic massachusetts percentage histogram convolution defining answer producing res depicted researchers people greatly axes axes lack share marked ity http http http http measuring characterize ture differs achieves sophisticated conclude windows windows deviations semantic summed cor contribute pose lab lab sort sort www www www interface formally gabor appropriately databases databases databases databases databases signature signature signature signature signature signature signature signature signature signature approximates homogeneous establish imaging reasoning salient symposium inferior paul von von histograms histograms histograms histograms histograms arrangement tic deg deg recog occlusion discounted ballard ballard bins specificity specificity sons projects captures hart hart tures automated dividing outperforms outperforms visually visually achieving email creates rao rao pentland pentland responds responds encouraging icassp par comparative perceived perceived perceived ical malsburg malsburg brightness manipulation attempted ibm ibm duda duda signatures signatures signatures signatures searches searches carefully met macaque rectified meta meta supports rochester fea indication thousands normalizing lation recogni textures textures textures textures textures textures textures viola viola viola viola viola viola viola observers barber loosely pearson jain jain resolutions alarms extracts extracts detects inferring positives retrieved quantitatively america convolved spie spie media eighth indexing discriminating distractor distractor repeating collections cars tightly mir mir retrieve retrieve gross rectification web web web quarter ranked bruce vat vat tially tot ages thirty sual ticular bears indicative correla rankings depict resemblance rectly nmse desimone photo tex ric convolutions compar vienna mahalanobis squaring highlighted rgb rgb querying downsampled downsampled preattentive albright shadows shadows shadows kelly kelly url photograph ature fibre conform alignments almaden asterisks searchers descriptors jeremy prevalent textural characteris supplementary prevalence handful multimedia nize desireone substan icpr manipu 
#@Viola_P,de-Bonet_J,
#t11
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#*neural data function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time networks algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output output output number system system results results results results results information problem performance space space space space linear linear linear case shown shown shown shown shown shown systems values values values values noise unit recognition recognition method approach approach approach approach pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control control control control control large rate rate rate inputs form form shows shows shows shows shows shows shows signal signal signal visual visual visual paper examples small small small small size size size size size size feature fig fig cells cells cells cells cells cells cells cells cells cells cells field field field field field field field field field field field features process current current current current current current current current current cell cell cell cell structure problems high high response response response response similar similar architecture architecture architecture architecture show equation equation equation equation fixed line line line line line line line line line line line images images images images images images general general general general general general general general general general average obtained obtained term university computation computation computation independent independent defined defined found found dynamics initial initial initial standard terms terms connections connections left direction direction direction direction presented presented presented presented presented low low temporal temporal temporal maximum maximum maximum press press outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous abstract computational density analog analog references positive positive positive positive introduction hand hand circuit circuit circuit circuit circuit circuit circuit circuit behavior parallel parallel parallel parallel parallel parallel parallel complexity spatial spatial spatial spatial measure signals signals chosen part center center center center center required required required required required multiple multiple conditions conditions conditions expected expected expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip observed observed scale tasks tasks computed computed performed performed performed factor made feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation obtain negative original original original vol represented compared application application application receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive location location location perform perform constraints connected connected discrete equal power power power steps contrast contrast contrast contrast contrast connection connection fields fields fields fields fields fields fields fields department implementation implementation implementation consists individual kernel kernel kernel kernel kernel kernel kernel kernel kernel responses addition addition addition addition considered experiment directly additional curves san top stage bit bit bit bit detection detection detection detection detection detection detection detection detection detection detection detection determine efficient speed speed vision vision vision vision vision vision increase increase levels area types lines provided provided selected biological biological biological achieved measured measured measured normal increases transformation transformation fast fast circuits circuits circuits circuits circuits circuits circuits implemented main eds eds end vlsi vlsi pixel pixel pixel pixel pixel pixel pixel pixel makes coefficients coefficients coefficients block block block block block transfer transfer character character character edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge increasing head mechanism structures numbers filters filters pre direct window window normalized bottom early early early magnitude frame frame light light light light light light discussed resolution advantage pair pair takes reported identical pixels pixels array array array array array array array array array engineering engineering varying approximately works axis smooth yields match background locations locations gate organization entire constructed horizontal horizontal horizontal parts intensity intensity intensity intensity intensity intensity intensity intensity intensity deviation width white white column column column column column column column column column column column column hardware pass demonstrate conclusion row row row row row row row row row row row row row row row row segment segment segment segment segment operator central central central central central retina retina performs labeled plane plane plane plane plane plane relationship relationship relationship relationship groups program configuration configuration van edges edges edges edges edges produces produces written perception perception optical plot vertical vertical vertical segments segments implement implement sensitivity sensitivity sensitivity sensitivity sensitivity simultaneously linearly electrical angle angle angle consisting develop shift shift shift shift blocks extraction extraction extraction select select decreases decreases expressed variation variation controlled controlled controlled restricted frames sizes processor past diagram smoothing smoothing smoothing performing performing performing measurements purpose purpose purpose purpose purpose purpose purpose purpose purpose visible visible figures figures includes kernels kernels kernels kernels silicon silicon silicon silicon silicon currents currents currents currents currents currents retinal retinal retinal retinal plotted illustrated black black successfully columns sensor selecting delta identify receives composed compact compact repeated gray surround cmos computes cat chips processors preferred extract extract extract load oriented oriented oriented presents origin origin origin selectivity diego layered transformed mead mead reducing ideas detectors detectors detectors detectors detectors detectors detectors detectors ideal ideal ideal transistor front versions versions der mapped academic academic detected mixed finds percentage rows ground ground ground sensors convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution convolution capabilities considerable processed processed processed processed processed turns straight shared constructing operators operators transistors transistors controls controls angles circle read read read read read outer raw raw raw raw raw raw virtual virtual virtual virtual evaluating evaluating limits applies collected dark orders detecting detecting detecting slower operate switch switch switch extracting fall maximizes begins summed summed summed displays realized acquisition room room accomplished generator generator bipolar gabor amplifier amplifier amplifier amplifier rotated rotated addresses lost eliminated inspired khz imaging imaging primate logarithmic logarithmic logarithmic logarithmic programmable programmable programmable programmable responsible exceeds arrays arrays clock substituting displayed overview overview photoreceptor photoreceptor scan specialized foundations neuromorphic spatiotemporal smoothed smoothed card card impact partitioned subsequently switches switches dividing compressed kluwer bus bus bus bus bus bus bus bus bus bus bus bus bus bus bus focal focal focal focal focal focal benefits uniquely die restrictions laplacian laplacian laplacian realize brightness capacitance peripheral peripheral peripheral peripheral peripheral peripheral mhz mhz realizable lobe generators neurophysiological thresholded scope mask mask mask mask mask covered register register register loading loading programmed normalizing round round round completed scanning scanning scanning scanning scanning scanning scanning scanning scanning scanning scanning scanning scanning scanning scanning scanning helps lighting lighting copies copies scanned scanned scanned saturated transduction discretized identifies send supply fill mirror illinois connects horizontally horizontally sharply subtracted subtracted periphery drastically consumption consumption vertically vertically amplified counterpart essence mis registers repeating survival survival converts converts sends clockwise bright bright activating incident cummings cummings cummings cummings collect engineers army army corresponded parasitic densely densely ism camp camp camp masks masks masks masks etienne etienne etienne etienne smear throughput highlights ralph southern diode realizing realizing realizing serially logarithmically indoor imitate photo photo photo ismail cai cai cai cai constrains actuators nodal occupies loth newell prey spiegel buses buses buses buses buses buses buses restore ima ima nmos nmos ior amplifies ice ice ice ice ual abruptly imitation packed packed programmability programmability programmability programmability imaged predator pentium departs lxl lxl lxl controt controt werner unprocessed capitalize 
#@Cai_D,Etienne-Cummings_R,
#t11
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#*model model model model model model model model model model model model model neural neural neural input input data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time set set set set algorithm output output output output output output output output system system system system error state state units units information information information information information models models models models performance performance based based based based order order shown shown shown shown shown systems systems systems systems neurons neurons neurons neurons neurons neurons neurons approach pattern pattern point single processing processing processing processing control control large large large large large local neuron neuron neuron neuron neuron neuron neuron rate test analysis shows shows shows shows shows signal signal algorithms simple visual visual visual visual visual visual visual visual visual visual visual visual paper small small small size work work work fig cells cells field field field field field field field process process level current current current current current current current current current current current current current cell high high high high high high high high high response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar representation representation architecture architecture show show equation equation equation equation equation fixed fixed real real real real theory theory theory theory theory theory theory note note experiments experiments result result result computation computation research independent log log log found found constant constant constant constant constant constant terms node node left left direction direction direction direction direction direction direction direction direction direction direction direction presented present phase phase phase phase low low low low low low low low low low low low nodes frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range components components outputs outputs outputs continuous continuous abstract computational analog analog analog analog analog analog analog analog analog analog analog properties properties references references references component component due due positive positive positive important adaptive adaptive introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit estimation behavior behavior behavior behavior stimulus stimulus stimulus effect dynamic parallel tion tion spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial higher part center center firing good long represent chip chip chip chip chip chip chip region region proposed correlation correlation correlation correlation length observed observed errors errors resulting tasks computed sum means feedback orientation applications applications study filter filter filter filter filter filter filter filter filter filter filter filter filter negative negative negative negative relative compared compared series objects determined determined related connected gain gain gain power power power power approaches voltage voltage voltage voltage voltage contrast contrast contrast contrast contrast contrast contrast contrast contrast dependent dependent source institute implementation version version version version synapses individual individual represents responses responses responses responses responses difficult final exp bias bias bias bias bias delay addition addition graph ai ai ai ai computing domain experiment experiment directly directly directly curve curves curves curves curves stage stage stage detection full full significant approximate world vision vision vision basic give con channel channel weighted developed developed developed velocity velocity actual evidence evidence nature biological measured measured measured arbitrary tested tested tested fast limited complete circuits circuits circuits circuits circuits circuits circuits circuits implemented implemented supported supported eds adaptation adaptation vlsi vlsi vlsi vlsi vlsi vlsi vlsi future future easily sensory sensory including fit fit fit typically needed combination account functional technology block block interesting matching mode mode mode mode mode mode mode mode operation numbers filters filters filters direct making normalized normalized normalized normalized magnitude magnitude added description light neuronal advantage robust separate separate separate separate takes movement movement movement movement practical moving include include array relevant engineering engineering engineering engineering engineering approximately works works tuning tuning axis studies rl background evaluation separation symmetric channels channels channels channels channels channels channels channels channels gate gate gate sensitive sensitive sensitive sensitive sensitive sensitive amplitude intensity studied deviation wide wide wide derivative derivative derivative derivative move loop loop hardware hardware pass pass pass pass pass pass pass pass pass pass pass pass pass pass conclusions designed peak peak peak peak peak exponential suggest integration integration integration integration integration cycle california proportional selective selective program program acknowledgements van van van van produces optical ways estimating implement sensitivity sensitivity linearly slightly integrated integrated frequencies frequencies frequencies springer cycles cycles cycles extracted family expressed formation communication evaluate showed forms processor past performing visible koch koch koch koch koch building building silicon silicon currents currents currents currents currents candidate holds phys discussions identified capable capable encoded presentation spiking soc notice verlag strongly neuroscience follow comp comp simplified simplified wave delayed cmos cmos neurosci attempt receive selectivity selectivity selectivity mead mead mead mead mead mead mead rapidly rapidly varied steady steady mass ml pursuit matches giving detectors detectors detectors detectors detectors detectors detectors biol biol int transistor scaled gates matched removed act trace trace trace trace reading opposite changed voltages voltages thought ensure versions der noted detector detector detector detector detector detector detector detector detector detector detector detector mixed charge charge integrate years devices indicating ment cos separable separable separable sensors adjacent adjacent floating floating floating floating floating multiplication multiplication multiplication comparisons filtered constructing constructing directional directional directional directional directional directional transistors transistors consequence consequence potentially opt res recording recording nsf integrating integrating greatly behaviors pure transient transient transient offset offset axes introducing detecting remove variant operate switch exhibits berlin rely qualitatively qualitatively pasadena inherent inherent physiol begins wesley summed summed distortion pole cybern cybern primarily accomplished addison forming amplifier angular angular mobile tem printed caltech caltech multipliers multipliers extending spontaneous multiplier multiplier saturation wrong convenient minutes logarithmic mos mos contract affected capacitor arrays muscles weakly introduces von dependency dominant photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor photoreceptor nonlinearities nonlinearities multiplied deg deg deg deg neuromorphic neuromorphic spatiotemporal spatiotemporal contact extensively relies insect insect insect insect insect insect insect insect insect insect fly fly fly fly fly fly fly fly fly fly fly fly fly fly fly fly lag onr onr discharge grating grating grating grating grating ure largely sine fellowship inferred creates ram focal responds die personal avoided sinusoidal sinusoidal sinusoidal sinusoidal sinusoidal mismatch mismatch mismatch mismatch capacitance subthreshold crossover elementary elementary elementary elementary elementary elementary elementary elementary convert retinotopic cosine cosine pos portions accounted accounted rotating flight milliseconds tin mea resembles removes laws stimulating thermal photoreceptors photoreceptors photoreceptors quadrant heavily spacing supply mirror tors supplied sensorimotor wavelength subtracted manually optics optics ory colleagues colleagues cur safe compensated cutoff drifting drifting drifting drifting drifting drifting ranged saturating saturating enforces gratings gratings steveninck steveninck ruyter ruyter decades christof ming mounted mounted stabilization resemble altering discrepancy directionally broader fet fet couple capacitive capacitive capacitive aliasing aliasing aliasing lowered sible lens lens ago machinery insects ponent landing landing pattem parasitic subtraction subtraction exponentiated ies bradley legs reichardt reichardt reichardt reichardt reichardt reichardt underlie blowfly blowfly blowfly blowfly blowfly blowfly diode minch minch minch minch minch follower stud cot hasler invaluable capacitances chitecture detec detec survive kybernetik unidirectional unidirectional pfet emd emd emd emd emd emd emd klab mirrors sured iin correlating reid reid delbrfick delbrfick correlators tangential diorio dram elaborated amplifies laughlin divider divider divider harrison harrison harrison harrison harrison harrison pioneered tins pho pho flies flies flies flies flies flies flies warrant orienting retinotopically phototransduction hateren hateren commercially flattened sult capacitively exposing facets attenuate attenuates 
#@Harrison_R,Koch_C,
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input figure figure figure figure figure figure figure figure figure time time time time time time time time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training algorithm algorithm number number number number number number number number system system system system system system system system system system system system system system results results results results results results results units units information information information information problem problem problem problem problem models models models performance performance based based based vector vector order order order order shown shown shown unit distribution distribution recognition recognition approach approach approach point processing local rate rate test patterns patterns class class class class class class class optimal form form shows algorithms simple simple paper examples examples examples examples examples small small small size size feature feature feature net task task task task task task task task step field field field field field field field field features features classification classification classification classification classification classification classification process process level level level current current trained trained trained trained cell structure structure structure structure structure structure structure structure high high similar similar similar similar similar representation representation representation representation representation representation representation representation section fixed fixed general real real note note note note note note note note note note note note note note note note note note note note dimensional result result research found sequence sequence sequence sequence sequence sequence initial initial table table table table computer computer computer distance science science science prediction prediction left direction direction presented presented map map map activation press learn learn learn learn learn learn learn position abstract abstract abstract applied applied find find find find references component ieee ieee procedure important important important important important context context context introduction complex complex hand hand behavior behavior effect generated tion tion complexity classifier classifier lower lower rules rules measure representations learned learned chosen higher higher higher higher higher part part part part type type multiple good long represent tree tree correct scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale simulations simulations resulting resulting classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes ing ing human human human multi multi multi multi multi performed performed performed performed called called called called elements elements regions factor global global knowledge obtain obtain vol artificial specific represented represented represented represented perform determined goal constraints discrete power approaches approaches steps update update dependent nets nets nets nets proceedings proceedings proceedings proceedings implementation individual advances connectionist final scheme sequences sequences sequences sequences sequences ai maps considered considered considered computing computing equivalent equivalent directly directly bit bit bit bit conference conference conference determine significant world validation validation validation validation produce coding coding coding coding coding coding clustering developed levels area area types provided depends achieved achieved achieved achieved feedforward tested corresponds corresponds complete surface common adaptation degree degree degree development fit smaller reduced reduced reduced account interesting testing mechanism special structures structures details window bits bits bits bits bits bits international international international experts idea idea idea idea produced produced produced choose added description predict improved improved improved discussed discussed directions element element similarity similarity introduced hierarchical hierarchical cognitive relevant relevant previously previously unsupervised unsupervised works works match correspond separation observation interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval interval organization lead lead correctly conclusion starting starting starting practice learns learns integration decrease relationship relationship groups groups groups question question reference reference pro produces written perception simultaneously scales scales scales scales consisting adding formed formed quality quality independently depending depending variation variation variation variation variation variation variation variation variation variation variation variation variation variation variation detailed evaluate organizing fraction evolution evolution decomposition earlier epochs classical combining intervals intervals intervals intervals intervals intervals intervals remains kohonen kohonen kohonen kohonen kohonen kohonen kohonen kohonen advantages classified fire includes contour contour recognize recognize determines determines determines activated mozer mozer mozer variations variations variations variations variations variations variations variations variations variations variations variations variations variations variations variations variations major major major simplicity reason straightforward middle suitable encoded committee committee invariance composed composed capture capture summary notice kind kind kind kind strongly contained success classify classify built built michael nips delayed automatically overlapping overlapping operating preferred neighboring presents presents unlike carried varied successive relationships relationships decisions working comparable symbolic encode cognition contours contours predicts predicts opposite shapes art seconds integrate mentioned great distinguish distinguish lies considerable easier easier producing producing style style style style style style style style style style style style style style style mathematics beginning preceding preceding fourth fourth improvements lack introducing passed music music music music music music music music music music music rely song gave germany kinds coherence coherence deviations displays realized shifted notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes investigation investigation rotated rotated harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic harmonic repre repre establish fits dealing consideration occurred overcome intelligent height occurring harmony harmony harmony harmony harmony harmony harmony star star star belong phrase phrase motivation composition composition composition meaningful mance corre displayed perfor regarded dominant topological thomas thomas arrangement reproduce reproduce reproduce dif recog mind unable solves solves recursively nition pieces pieces distinction abstraction connec personal descriptions imagine realize musical musical musical musical musical musical musical musical musical musical musical mutually interacting considers interactive complementary rhythmic rough tied alternatives responding descending suffer rotating helps tonic styles styles sponding institut prefer prefer heavily phrases confirm subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet subnet melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody lists concrete concrete concrete returned proposes coincide judged swing resolved bach bach bach bach era experienced experienced voice prominent capturing ira montreal sented kong prime prime sebastian aims contributing sixth sixth sixth hong subtasks subtasks puter puter illustrating ascending ninth ninth quarter quarter quarter classifica chorales chorales nation hild hild hild continuation chord chord chord melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic melodic seventh seventh seventh resolving organ organ bigger qualities duced octave octave octave octave octave ist karlsruhe karlsruhe combi und readings composing melodies melodies melodies melodies melodies melodies melodies bringing compositions cutting twofold western ered consid famous famous menzel folk listening rprop disciplines ffir conform thirds invented invented uka wolfram tage jos bel cooperating wrote codings sixteenth sixteenth sixteenth hermann tradition tradition voices excit predecessor 
#@Hornel_D,
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#*network learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time set set set set networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number system results results results results results information information information information information information problem problem models based based based based based based based linear linear linear linear case order order shown systems systems probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions neurons distribution distribution distribution method method method method method method method method method approach approach processing processing large large large large large large large rate rate rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix form form form shows shows shows shows signal signal signal simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian small small size work work methods methods methods methods methods methods methods fig fig fig fig fig level current structure problems response similar show show fixed line line line line line line line line line line line rule rule rule rule general real real approximation approximation approximation theory theory gradient obtained obtained obtained term term term activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university computation computation computation computation research research independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent initial computer distance left left left left left left left left left left left left left left left left left map map present present present activation activation activation activation low frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal sets position components components components components components components components components components components components components components components components components components components components components components nonlinear nonlinear abstract computational convergence density density density density properties references component component component component component component component component component component component component component component component component ieee propagation introduction stimulus effect generated variance variance tion difference variable spatial spatial spatial spatial spatial spatial signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals chosen higher part center center center previous previous multiple multiple multiple multiple multiple multiple multiple multiple good represent make techniques region proposed proposed proposed proposed length simulations minimum resulting ing ing ing regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect sum performed performed performed performed performed performed means natural orientation applications applications policy negative original original original original original relative series series series series series provide proc proc proc location eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye related related distributions distributions distributions distributions cortical brain equal power power comparison larger contrast contrast fields dependent source source source source report institute institute institute department department loss version advances advances joint joint joint represents maps maps maps domain domain domain domain domain domain domain domain domain san san san san effects effects conference determine determine efficient requires requires approximate statistics statistics free free free estimated give con con produce channel channel channel channel derived derived derived derived derived types types entropy entropy selected selected selected selected selected evidence sampling biological biological biological achieved discussion arbitrary fast limited limited close inverse assumption assumption assumption complete surface amount amount amount amount effective effective effective effective effective supported supported role require future simulated simulated simulated underlying underlying needed needed needed reduced account account transfer transfer transfer transfer transfer transfer projection uniform representing iterations international normalized minimize produced choose sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources separate separate separate movement movement movement movement movement movement movement movement movement movement movement movement movement sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski relevant relevant interest highly unsupervised volume pca mixtures mixtures mixtures separation separation separation separation separation generalized bounded channels channels channels channels channels channels channels channels channels channels channels channels channels channels grant horizontal occur extended extended extended extended extended extended wide wide wide wide move generally generally generally generally generally generally assumptions hebbian hebbian conclusions depend differences sigmoid numerical peak practice propose hard presence presence presence presence california variety variety variety variety ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica movements movements movements movements movements movements movements movements movements min groups groups reference reference reference reference reference appears derive segments segments simultaneously electrical involves remaining remaining spectral spectral mutual mutual gaussians gaussians gaussians gaussians applying implies potentials potentials potentials decreases decreases expressed overlap overlap interpretation variation evaluate ocular ocular lee lee lee lee lee decomposition activities processor processor sign sign sign earlier reasonable dashed performing performing epochs delays expansion sec sec sec sec sec sec sec sec sec sec event filtering filtering filtering foundation eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg advantages views recorded recorded recorded recorded box box activations activations priori bell bell bell bell blind blind blind blind batch maximize domains columns gamma middle middle middle middle middle middle middle aspects differ differ computationally effectively effectively effectively spiking identify detect comparing excitation strongly contained contained success conductance dis minimizes maximization mixing origin remain unlike diego diego diego diego essential essential rapidly strengths accurately dotted periodic periodic giving giving tech project applicable applicable applicable applicable ideal muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle authors office maximizing maximizing tanh tanh tanh statistically removed removed measurement psychology psychology eyes thought thought versions portion portion portion portion portion portion algo assumes taylor amari detected detected contributions contributions arbitrarily isolated isolated isolated rows rows rows slowly band sensors sensors sensors phenomena phenomena independence correction correction nonlinearity nonlinearity considerable spatially satisfied sites sites sites sites sites filtered arise arise commonly commonly gradually medical recording recording meaning raw raw raw raw requiring reflect reflect double collected tional tional share recordings recordings recordings recordings recordings recordings recordings recordings employ remove remove remove frequently rep reliability howard rely anti spread spread spread spread sums inherent traces simultaneous instantaneous lab spectra spectra appearance martin martin temporally temporally temporally temporally rithm approximates naval naval plays lost occurred alpha occurring removing removing removing removing removing removing removing removing removing removing removing neurobiology salk salk intuitively meaningful separating periods patient respective negligible lang heart heart heart yang artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts 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anal matlab article sessions removes removes removes removes clinical appearing differently characterizing scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp impractical impractical ping invertible subtracting separates separates separates chan squashing artifact artifact artifact artifact artifact artifact artifact artifact artifact artifact artifact artifact artifact artifact artifact bandpass inspection rel accounting sis materials scott scott thresh dent defense indepen facts cichocki dipole dipole dipole health ysis tivity elegant contributing favorably ness won sition weakness makeig makeig makeig makeig makeig makeig jung jung jung jung jung jung relying availability undesirable ontario courses courses courses courses courses eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog eog confirms clin clin clin clin syrup syrup ponent ponent tributed cardiac cardiac cardiac cardiac cardiac cen preset widespread ponents ponents rejecting rejecting duce concentrates interna official government neurosciences decomposes intro conduc alterations masked questionable peters butions blink blink blink blink blink blink blink unacceptable nels cancels navy tains inevitably analy contamination contamination contamination contamination contamination contingent electroencephalographic electroencephalographic electroencephalographic berg berg regressor technol arti intern complicate unsuitable mckeown mckeown mckeown mckeown mckeown girolami girolami ferred cancelled wtw wtw wtw olds atively multaneously psychophysiology distracting oyi elim chichester inversions blindly decompo obscured obscured nolta lue dth isolating placements erry moval 
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data data function function function function function figure figure figure figure figure figure time time time time time time set set set set networks networks training training training number system system system system error error error results results results results results results results results results results units units units units information information problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance based based based based weights weights weights weights weights weights weights layer layer layer layer layer layer layer case vector order order order shown shown shown values values values probability probability probability probability probability probability probability probability noise noise noise noise noise noise noise noise noise noise noise weight weight neurons neurons neurons neurons neurons neurons neurons neurons unit method method method method approach approach approach approach approach approach approach pattern pattern pattern pattern pattern single single single single single single single single large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis optimal inputs form shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms gaussian gaussian gaussian gaussian visual paper feature feature net net net net work task task methods fig fig fig fig fig fig features features classification classification classification classification classification classification classification classification classification classification classification classification classification process process process level level trained trained structure structure structure random random random high response response response response similar representation architecture architecture architecture rule rule rule vectors vectors vectors general general general general parameter real average average theory theory obtained term activity activity activity activity activity activity activity activity activity activity result research research research defined defined found sequence target target target target target target target target target target target target target table table standard standard connections synaptic synaptic synaptic synaptic node node science presented presented presented presented presented presented presented presented present low low low nodes nodes nodes frequency sets sets range press learn components sample sample sample sample sample abstract applied applied applied applied back back convergence convergence convergence convergence convergence convergence convergence properties references component component component due ieee ieee ieee ieee ieee positive positive procedure procedure important important decision decision introduction estimation estimation estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical effect effect variance variance tion change energy variable variable variable assume assume classifier classifier lower lower lower lower lower signals signals signals signals signals signals prior higher part previous cases type type type type type required binary binary conditions conditions distributed distributed expected make techniques techniques techniques proposed minimum resulting ing total simulation simulation simulation simulation simulation human potential potential potential potential potential applications study study study study study study study study study knowledge filter vol vol vol vol vol specific specific true true true compared series provide define active active active determined experimental experimental experimental experimental related related related related related related related related related related related related related related related related related related related connected discrete brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain brain voltage modeling modeling proceedings institute department department department loss consists consists consists internal individual represents represents responses responses responses responses responses bias bias scheme experiment experiment limit limit top top stimuli stimuli stimuli stimuli stimuli effects effects effects detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection conference requires choice choice approximate condition randomly levels levels types actual provided finally processes processes selected inhibitory inhibitory depends simply achieved measured discussion discussion denote tested assumption assumption assumption corresponds excitatory surface common common common common theoretical ability hypothesis hypothesis cluster cluster makes rumelhart rumelhart noisy simulated typically reduced unknown unknown unknown coefficients coefficients technology significantly ratio character increasing mechanism trials empirical representing iterations iterations max pre pre international normalized bottom bottom attention population population population recent property takes moving include subject subject subject subject subject trees trees trees subset cognitive cognitive cognitive cognitive cognitive relevant relevant engineering engineering engineering engineering interest varying conventional unsupervised unsupervised approximately yields converge converge converge trans trans trans background background background background background background evaluation interval amplitude amplitude studied trial trial trial alternative deterministic deterministic clusters white white occurs generally half half strength conclusion place row row row reduce competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive learns strong presence external characteristics demonstrated solid labeled assuming assuming assuming assuming assuming start selective selective selective selective relationship averaged averaged identification identification identification identification identification identification identification identification identification identification identification identification explicit appears digit pro pro van van van laboratory distinct modeled confidence confidence confidence confidence confidence category category averaging averaging averaging averaging averaging averaging electrical electrical electrical electrical electrical slightly spectral consisting consisting develop applying applying events events versus potentials potentials potentials potentials potentials potentials potentials potentials competition competition john extracted formation open evaluate modulation decomposition completely digits reasonable slow dashed additive additive additive additive additive measurements event event event event event event event event event event event purpose purpose false false false false filtering filtering filtering filtering foundation eeg eeg eeg eeg eeg eeg eeg eeg eeg classified classified recorded recorded recorded recorded recorded includes priori priori priori priori usa usa usa automatic characterized major simplicity middle identified identified identified society divided driven included presentation identify post post repeated repeated dis lie oscillations timing categories categories categories categories categories paradigm paradigm paradigm paradigm paradigm wave automatically received received received principles principles overlapping presents presents minimized explore carried powerful layered layered layered wiley rapidly dotted existence matches respond respond respond respond respond detectors applicable relationships referred working variability complicated statistically cognition matched matched matched matched matched matched neu math coefficient coefficient extremely equally equally perfect impulse noted assumes observe detector detector detector separated initialized epoch epoch simplest grouping grouping grouping indicating theoretic theoretic ground agreement agreement analyzed biology analytical capabilities perspective perspective snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr snr gradually members annual fluctuations raw raw raw robustness explained freeman freeman empirically relevance relevance transient generic generic generic generic generic generic embedded embedded embedded embedded recordings recordings continuously frequently dots reliability templates templates requirement requirement limiting branch fall suited segmented converged converged converged converged converged wesley yielding yielding shifted shifted classifying spectra corrupted college proportion addison appearance appearance concerned null discovery discovery discover connecting spontaneous chance significance mail mail mail mail odd odd odd odd odd analyzing operates operates ral salient salient optimally preparation filled motivation exploring meaningful meaningful meaningful embedding ranging decide pat regarded realization realization realization evident evident enhance competing enable israel israel israel israel israel winning winning winning winning winning ensembles eng eng eng locked locked locked sons statement subsequently ignore ball ball ball ball ball severe empty usage sig session session latency validity ram obstacles bank bank bank responds convenience regularity classic classic classic possibilities evoked evoked evoked evoked assess assess param adapting clas ary concentrated shifting magnitudes magnitudes goals maintained elementary eliminating electrodes acquired synchronized complementary rhythmic pos erp erp erp erp erp erp erp erp erp erp categorization categorization categorization categorization paradigms breaks sweeps sweeps sweeps nal eters october inactive inactive triggered appearing appearing appearing differently reversed scalp synthesized synthesized terns ongoing ongoing ongoing ongoing inhibit wins filler industrial inherently inherently medicine polarity practically sharply exposed exposed ters push pratt pratt pratt pratt pratt pratt autoregressive positives positives scenarios screen zipset zipset company company gence comprised akaike prominent capturing occurrences supposed technion technion technion technion technion technion technion mounted daniel mid amsterdam lange lange lange lange lange lange lange lange lange lange lange lange lange lange comprehensive publishing publishing dead coincides constituents constituents berger conver classifica adopting asso symmetrically siegelmann siegelmann siegelmann siegelmann aver categorized gramming colored instructed instructed hierarchically hierarchically specialize theme overcoming siftcation jaw button itive ger masked hans elicit whitening haifa haifa cording neg haykin haykin iit iit iit iit negatives negatives aged ciated referenced manifestation ries confidences confidences declines facilitating electromagnetic macmillan 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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input data function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set networks networks training training training training training training training training training output number number number system system system system system system system system system system system system system system system system system system system system system system system error error error results results units units units units information information information information information information information information information information information information information problem problem hidden hidden hidden hidden performance performance based based based based based based based based based based weights weights weights weights weights weights weights weights weights weights weights layer case order order order shown shown systems systems systems systems systems systems systems systems systems values probability recognition recognition recognition recognition method approach approach image image image image image image image image image image single single single processing processing processing processing processing processing processing processing processing processing control control control large large large large rate rate analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows shows shows shows signal signal signal signal signal algorithms algorithms simple simple simple simple visual visual visual visual visual visual visual visual visual paper paper examples examples small small small small small small feature feature task task task methods fig field field field features features random high similar representation representation architecture architecture architecture architecture architecture section fixed rule images images images images images images images images images images real real real real term variables solution found target computer computer terms direction map map present present phase low object object object object object object sets motion motion motion motion maximum range learn learn learn learn learn learn learn learn learn position position position position position components nonlinear abstract back find analog references component ieee ieee positive propagation introduction complex hand hand hand behavior generated cost cost search difference difference difference lower lower rules rules signals signals signals signals signals representations learned center center type multiple represent represent errors scale scale scale scale resulting resulting resulting ing human human human human computed computed sum times reinforcement reinforcement natural natural applications filter relative relative relative specific represented true application desired desired desired series provide objects objects objects objects objects objects objects rates proc proc proc proc location location location location location location location location location location active active eye eye eye eye eye determined determined accuracy update update support train train train train train modeling proceedings implementation version consists individual advances advances advances advances advances represents difficult final bias sequences environment environment environment curve view view view view bit detection detection detection detection determine determine world vision vision give give give coding velocity types actual actual finally selected biological discussion fast fast fast close circuits finding face face face face face face face face face adaptation adaptation adaptation adaptation adaptation vlsi pixel pixel ability ability future easily easily sensory including auditory auditory typically needed combination interesting character character head head head head head head head head head head head head head head head head head head head head head head head head head mode squared direct normalized early frame frame frame frame frame attention combined run sources sources light light denotes architectures architectures resolution resolution resolution resolution resolution robust robust separate separate typical typical similarity movement apply moving moving moving moving moving moving include pixels pixels calculated calculated smooth match correspond achieve background channels channels channels channels channels channels channels constructed constructed exists parts parts invariant wide rotation move loop occurs hardware hardware hardware competitive differences learns learns learns sound sound presence external characteristics characteristics sigmoidal proportional user user user user user user user user movements movements movements movements movements movements min manner manner manner denoted areas appears digit written winner describes changing implement scales yield focus depending stationary communication operations controlled updated lee lee lee lee frames understanding similarly constants past diagram sec sec combining tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking faces faces faces koch handwritten box includes kernels kernels kernels color color color color color bell bell bell weighting batch batch plotted automatic automatic automatic absolute discussions closely importance maximal poggio detect computations invariance invariance situation online online online online online online capture conf quickly quickly cun video video video video video video video video video video video video video video video video video video video showing follow follow cues cues built sampled board automatically automatically moves operating camera camera camera camera camera camera camera camera camera camera camera camera camera camera presents body difficulty difficulty rapidly rapidly rapidly rapidly environments environments detail graphical graphical graphical pursuit helpful scalar scalar fashion int authors office office office office reliable stream stream stream stream stream complicated tanh workshop workshop workshop neu neu waibel saliency saliency saliency saliency hill gradients necessarily facial eyes eyes implementations thought prototype portion detector detector detector detector shapes shapes initialized consist seconds integrate integrate years devices ment scenes distinguish track track track track track track track track track track track track fairly fairly nowlan considerable rapid preprocessing filtered filtered constructing directional located located desirable commonly laboratories laboratories potentially separately angles beginning res computers author author preceding raw integrating improvements behaviors dark generic readily marked reliability schematic schematic modulated adjust enables windows calls person person person room interface interface saccadic saccadic saccadic saccadic angular narrow labelled labelled platt murray khz ments ral ral salient salient salient salient salient salient muscles cone mouse mouse moved captured yang viewing deg ballard tracker tracker repeatedly arrows gesture eqs eqs seung seung seung seung seung speeds acknowledge ccd ccd ccd ccd discriminate discriminate slight converted pointing hair session convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional convolutional rao pentland corrected corrected auxiliary streams scenario peripheral concentrated baluja labs maximally maximally maximally maximally maximally oculomotor oculomotor attached attached commercial matlab matlab continually technologies technologies acquire telephone telephone ave skin skin locate locate locate evolved pan graf exclusively resolutions resolutions resolutions luminance luminance luminance luminance luminance labelling successively digitized tracks adjusts invisible colors quick ready enter robustly robustly robustly robustly motors motors motors transmit platform manual ears ears actively sur ira mounted mountain initiated custom microsoft jack sung resemble horiuchi attracted tracked minute pyramids subsampled subsampled lens animation retinas darrell burden named tilt heat ages fil rowley gra gra kanade renders occasional depict tying targeting backpropagated emitter iden inexpensive inexpensive grayscale hue lucent lucent infrared infrared infrared infrared infrared party situated tered cluttered marvin marvin marvin marvin marvin marvin marvin marvin marvin marvin marvin marvin marvin servo servo assisted rounding highlighted rgb rgb rgb smeared levinson microphones microphones aca sac sedal chromatic chromatic chromatic cartoon bishofberger needing oval accomodate surroundings proliferation watching fee multimedia mainstream maes equip 
#@Lee_D,Seung_H,
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model input data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm results results results results information problem models models models models models models models models models models models models models models models models models models models models performance performance performance performance based based based based based space order shown shown shown shown systems systems probability probability probability probability probability parameters noise functions functions functions distribution method method method approach approach approach point point single large large rate rate rate rate rate rate rate test analysis analysis analysis analysis analysis analysis analysis analysis form shows shows shows simple simple simple simple simple simple simple gaussian gaussian paper paper small size size work work work work work work work work task methods methods methods methods step step step step step process process process process process process process process process process level level level structure structure problems high high similar similar similar similar similar similar similar similar similar similar show show show section line line general general parameter parameter parameter real real average average theory theory obtained obtained obtained obtained obtained obtained result result university computation computation computation research log log log found found found estimate standard computer terms terms terms left temporal temporal machine maximum range range range range range range range range range range range range range range range basis sample sample sample sample sample sample sample sample sample sample sample abstract computational computational computational computational computational density density density density density density density density density density properties properties properties properties properties properties references references references references component due due due due ieee ieee ieee ieee ieee positive procedure important important mixture introduction complex complex complex complex estimation behavior behavior statistical statistical statistical statistical statistical statistical statistical statistical effect generated generated variance variance variance variance variance variance variance variance variance variance variance variance cost tion complexity complexity complexity complexity variable variable assume measure chosen previous previous previous previous theorem theorem theorem required good good good long long long long long long long long represent represent expected fact techniques correlation correlation correlation correlation correlation correlation correlation correlation length length length length observed observed observed scale scale scale scale scale scale scale scale resulting ing ing tasks simulation simulation multi multi multi called called made natural obtain obtain obtain obtain original vol vol vol represented application series series series series series series series series series series series series series series series provide compute perform perform determined experimental goal distributions discrete discrete equal approaches steps steps comparison dependent dependent dependent source source source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling proceedings proceedings report institute words department loss loss loss loss loss loss version difficult difficult considered domain domain domain domain domain domain domain domain domain domain domain domain curves design limit top bit bit capacity efficient efficient efficient efficient significant statistics statistics developed developed developed criterion area processes processes processes selected nature normal normal normal normal normal normal normal technical increases increases group transformation transformation transformation fast inverse inverse inverse inverse complete short short short short short short short short generate generate generate generate generate generate theoretical theoretical main main journal future makes needed needed account coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients consistent principle details details normalized frame frame choose sources sources sources sources sources sources sources correlations correlations property property takes takes similarity reported moving include include recently recently engineering engineering sufficient sufficient conventional volume axis axis match match evaluation storage horizontal suggests suggests extended deviation deviation deviation deterministic deterministic demonstrate demonstrate strength conclusions accurate accurate accurate accurate accurate faster demonstrated scene scene scene derive factors generating generating plot plot plot vertical modeled modeled modeled simultaneously electrical scales scales scales scales scales develop integrated integrated shift shift versus versus independently dependence dependence dependence dependence dependence dependence dependence stationary communication transform transform transform transform transform transform transform evaluate sizes similarly key generation generation transactions transactions transactions existing existing includes includes simplicity simplicity encoded computationally computationally computationally comparing plots plots plots plots ten capture capture capture video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video video wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet load exponentially rapidly existence existence rest rest complicated understand understand naturally trace trace integer integer traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic noted mixed motivated developing crucial variances variances variances variances analyzed coded tool london turns straight lowest lowest demonstrates auto auto auto auto auto auto auto auto behaviors empirically empirically tional rep rep synthesis summarized summarized characterize marginal marginal marginal marginal marginal marginal marginal marginal marginal traces traces feasible feasible acm acm acm resources encoder communications communications fails fits minutes mail held transforms transforms transforms mark analyzing star star star star star intuitively intuitively wilson regarded buffer buffer buffer buffer buffer buffer buffer buffer buffer buffer sim treatment theoretically theoretically cpu impact compressed compressed unified unified unified outperform ideally workstation streams expand challenging careful anal suffer siam fea loading page rose behaves syn tail lation slot demand autocorrelation autocorrelation synthesized synthesized synthesized synthesized synthesized synthesized synthesized water pictures hour possess ally huang wavelets wavelets wavelets wavelets wavelets wavelets attained ignores inde physically voice feasibility feasibility feasibility cess media media media tained neglected mul allowable ysis cations appli stand fractional fractional fractional saturates possesses sible philadelphia nent walter circumvent behav persistence interpretable attain havior suc resentations pertinent attainable differencing aug patrick garrett tiple ortho resented ilar ior tackle quantile quantile taneously simul neglects mother mother mother autocorrelations lectures cessfully fic regressive queuing queuing polytechnic heavier rpi rpi overflow overflow overflow tes tes tes pendently 
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural input input function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set networks networks networks networks training training training training training training training training training training training training training algorithm number number number number number system state state state state state state state state state state state state results results results results results units units units information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance based space linear case case case case vector vector vector vector order systems systems systems systems probability parameters functions unit unit unit method method approach approach approach approach approach approach approach single single processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control large large large large local local optimal optimal optimal optimal inputs form form form shows shows algorithms small small size size feature feature feature feature feature work methods methods methods methods methods methods cells step step features features current current current current problems problems random high high similar representation representation representation equation section rule rule rule rule parameter parameter parameter parameter parameter parameter approximation approximation approximation average average average average average average average average average average average average average average average states states obtained obtained obtained obtained term term term term note note solution solution solution independent found found table table estimate estimate estimate node node node node presented present phase phase phase phase phase nodes nodes nodes nodes nodes temporal temporal temporal machine machine press press press learn learn learn abstract applied applied find find convergence references due important important decision decision decision decision decision context introduction action action action action action action complex complex complex dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic difference difference assume assume measure chosen chosen higher higher higher type type type type type type type type type type type type type type good good good long long long long long distributed make observed scale scale classes classes ing total total total total respect respect sum performed called times times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor potential global policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy obtain obtain obtain obtain obtain compared compared application define rates rates experimental experimental related constraints equal equal mit mit mit mit mit mit mit steps steps steps comparison comparison comparison comparison connection connection connection update update update update update update support train source source source words implementation implementation consists consists advances advances final delay scheme addition cambridge cambridge cambridge cambridge cambridge environment view trajectory capacity capacity capacity capacity capacity significant approximate approximate speed give channel channel types types types types types types types path path path processes processes processes constraint constraint achieved achieved increases close close actions actions amount generate eds eds future makes makes objective objective combination technology programming programming programming programming programming programming programming programming significantly significantly leads call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call max max direct direct direct direct direct making making making combined combined choose choose choose choose choose predict architectures improved advantage advantage advantage pair pair pair separate takes takes practical apply quadratic quadratic compare compare approximately approximately solve studies rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl exists alternative alternative alternative alternative alternative alternative alternative touretzky touretzky deterministic occurs occurs conclusion operator reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward differences designed sutton sutton sutton sutton learns hard reduction solid program pro derive transitions modeled simultaneously easy consisting consisting consisting consisting consisting integrated integrated integrated integrated integrated integrated applying events events events expectation john expressed communication communication viewed solved solved open open evaluate approximations decomposition decomposition decomposition decomposition decomposition decomposition decomposition forms forms earlier barto barto dashed reduces reduces event event event event event event event event event event views exploration exploration exploration maximize mozer mozer characterized characterized computationally divided paths paths successful efficiently composed summary traditional compact compact compact compact heuristic heuristic heuristic heuristic heuristic heuristic link link link link link link link link link link link link link link link link link link link link link link link link interpreted duration list list list list list correspondence highest policies policies policies policies policies routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing tesauro tesauro singh singh exponentially game issues behaviour behaviour behaviour links links links links links links decisions decisions decisions maximizing naturally naturally configurations configurations store improving defines percentage percentage percentage indicating formula leaves commonly commonly commonly commonly potentially scientific arises bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth author addressed peter orders formulated formulated formulated rep compares rewards rewards rewards rewards rewards poisson maximizes gave germany germany chose windows calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls calls bellman pick resources resources resources arrival cellular allocation allocation accepted accepted accepted accepted accepted siemens siemens obtaining methodology optimally carry heuristics heuristics service service service service service service service service service service service service service service service service service service service service service service service service service mance zhang zhang perfor decide scheduling scheduling scheduling hasselmo hasselmo entries discounted thin shortest shortest arrows route route route route route route route route route route route route route route route route route route route route tsitsiklis tsitsiklis tsitsiklis dietterich dietterich valuable approximator approximator assigns bertsekas bertsekas bertsekas bertsekas outperforms outperform shorter shorter accept accept accept accept accept accept email email email discount maximized job formulate rejection rejection obtains arg reject reject reject reject avoids backgammon thick rejected rejected rejected exceed exceed proach universit holding holding holding holding holding supporting vice demand demand demand corporate ongoing hop hop hop ers telephone termination kth kth kth kth kth exclusively admission admission admission admission admission admission admission admission admission admission admission admission admission admission admission admission admission admission arrives destination destination destination elevator elevator fair demands routes routes routes routes routes routes routes routes routes request shop shop successor successor ming decompose violate violate predefined predefined infeasible technische accepting resentation albeit belmont munich munich requests requests requests extractor exercise exercise routed routed routed routed routed routed arrivals arrivals arrivals crites crites athena cies customers customers unidirectional unidirectional vances cording cesses consid ser pursue pursue oliver oliver mchp telecommunication telecommunication marbach marbach marbach marbach marbach appropri permissible icy lids lids incur nication natu sell ately config tsitsildis actly mak 
#@Marbach_P,Mihatsch_O,Schulte_M,Tsitsiklis_J,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural input input input data data data function function function function function function figure figure time time time time time time time time time time time time time time time set set set set set set set set networks training training training training algorithm algorithm algorithm algorithm number number number number number number number system error state state results results results results results results results results results results results results results results units units information problem problem problem problem problem problem problem hidden hidden performance performance performance performance performance performance performance performance based based based based based space space weights weights weights weights linear layer layer layer case vector vector vector vector vector order order order order order order order order shown shown shown systems values values values values values values values values values weight weight unit unit method method method method method method method approach approach approach point single single processing large large local local local test analysis class class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs form form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small size size size feature feature feature feature feature feature feature work work work work work work work task task task task task task task task task task methods methods methods cells points features features features features features features features features features features features features features features features features features features features features process process process process process level current current current current current trained trained cell cell cell cell random high high high memory memory representation representation representation representation representation architecture architecture architecture architecture architecture show show show line line line line line line vectors general general generalization real real real approximation average gradient obtained obtained term experiments experiments experiments experiments experiments experiments experiments result university university solution independent found sequence sequence sequence sequence sequence target table table table table table table table table table table table standard standard standard computer computer computer computer terms terms science presented presented map present low frequency temporal temporal machine machine machine machine sets maximum press press press learn learn learn learn nonlinear sample sample sample abstract back back find find find find find properties references references references positive procedure procedure important important important decision decision decision decision decision propagation propagation propagation context introduction complex complex hand hand hand hand hand hand hand hand parallel parallel cost cost cost cost cost search search search difference difference assume lower measure prior representations learned chosen higher previous bound multiple good good good good good good good good good long long conditions represent tree tree tree tree tree distributed expected expected make make make make techniques techniques techniques proposed proposed length correct correct observed forward simulations resulting resulting resulting resulting resulting resulting classes ing ing total total total total total computed respect respect sum performed called called called called times times times times times times times mapping mapping mapping means means reinforcement reinforcement reinforcement reinforcement factor optimization potential made made made made global negative artificial relative relative relative represented true true true application application cross provide provide define proc proc location location perform determined experimental experimental experimental experimental experimental goal related related related related mit steps larger larger support descent selection selection report report report department implementation implementation technique consists consists internal internal code code code code code code code code individual individual represents represents layers delay scheme scheme maps maps considered considered considered cambridge computing equivalent equivalent directly hinton hinton additional additional view design design determine efficient requires choice choice choice significant statistics speed speed speed basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic basic validation give produce produce produce produce produce condition weighted weighted weighted conditional path actual provided finally selected selected selected depends measured measured discussion technical technical tested fast close complete predictions predictions finding short effective generate require eds end end ability easily degree makes rumelhart rumelhart objective simulated simulated simulated pairs pairs pairs pairs pairs needed needed needed combination account functional functional coefficients block block block block block block block block block block block block block block block testing testing ratio ratio character york consistent consistent empirical empirical call call numbers max pre making making bits supervised supervised supervised supervised supervised produced produced produced produced choose description predict predict perceptron architectures architectures architectures improve improve improve property pair pair pair pair takes takes practical practical apply apply introduced include recently relevant relevant interest interest varying compare compare tuning tions achieve achieve address evaluation evaluation chain generalized williams williams sensitive entire constructed constructed expression expression expression studied digital digital digital digital digital predicted predicted predicted predicted predicted correctly feed generally setting setting hardware hardware demonstrate runs runs runs runs critical critical greater conclusions valued valued depend reward differences measures measures measures sutton performs faster hard cycle cycle cycle cycle characteristics labeled labeled labeled assuming assuming assuming variety variety exist targets program program program program program program program program program program program program program configuration question question reference appears appears appears appears appears relation relation relation relation relation relation relation relation relation relation relation relation relation relation relation relation relation relation construct edges produces produces produces written written written longer longer longer ways factors factors sequential distinct distinct dept confidence confidence linearly remaining easy applying applying predictive predictive quality quality quality blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks boolean boolean boolean boolean cycles cycles cycles cycles select john extracted extracted focus focus focus expressed dependence dependence dependence depending codes transform evaluated evaluate evaluate showed translation converges updates processor processor processor processor processor processor processor sign partial partial partial partial partial partial partial partial partial partial partial partial partial reduces combining intervals false remains calculate construction foundation advantages david expect building existing existing includes strings instances instances specifically candidate candidate candidate selecting selecting aspects efficiency efficiency closely suitable suitable divided paths mcclelland build efficiently genetic genetic comparing ten ten fine composed refer conf conf conf conf procedures heuristic heuristic heuristic heuristic heuristic heuristic heuristic success link interested issue issue issue issue issue issue issue running follow timing sci hold categories comp comp list vary vary highest automatically automatically processors processors policies preferred acknowledgments deal schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule production production production production create collection collection essential essential updating updating detail detail issues issues dual dual dual dual preliminary preliminary mass scalar scalar fewer int int int scaled authors decisions decisions decisions comparable complicated affect affect affect cognition notion momentum matched induction induction induction necessarily integer greedy greedy greedy algo mapped art utility submitted massachusetts mentioned preference preference preference preference preference preference preference preference preference pairwise pairwise costs costs floating answer answer answer expensive benchmark benchmark benchmark benchmark tool starts comparisons drive drive rapid perspective straight straight straight straight straight straight sites sites widely producing constructing choices choices choices choices ran commonly potentially calculations beginning begin computers meaning sun researchers conjugate fourth geometric geometric geometric questions questions apparent apparent apparent people considerably evaluating tional item employ employ treated frequently execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution measuring anti branch branch instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction simulator simulator simulator simulator simulator simulator logical chose conclude unbiased returns univ cor contribute accomplished equivalence modify acm ratios optimizing optimizing optimizing resources resources member member member member ordering concerned impossible proceed promising promising adjusting tools proceeds odd odd odd odd odd alpha alpha alpha height hit hit resulted keeping mark belong belong optimally adequate generalizes constructive selects heuristics heuristics heuristics date meaningful evaluations evaluations programs programs programs programs programs programs programs paul lang captured scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling counter counter counter counter counter counter counter counter counter schedules schedules schedules schedules schedules schedules schedules schedules schedules schedules candidates multiplied infer infer infer infer eng mem omitted offer offer offer matter repeatedly cpu impact impact hart summarize instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions generalizing approximator fold interestingly integers executed executed executed executed ence ple microstructure sch corporation corporation logarithm minus latency exhaustive inferred inferred inferred creates dec dec dec dec dec dec dec dec dec presenting suboptimal pieces preferences preferences amherst amherst examining massively realize publication translated intuition intuition rithms goals execute execute execute carefully acquired ultimately parallelism noting lookup lookup lookup lookup records harder constructs constructs tied worth indexed anal alternatives register register register sam investigations tune holding differing october signs vice correlate picking covers versa opti opti reversed consuming consuming discretized heavily suite suite suite cast cast cast supplied moss moss moss moss moss moss moss striking judged inferring raises isolation ory fastest reality safe safe iti iti longest fair demands edition elec categorical semantics semantics semantics semantics semantics request pointer bear focusing ous ous manual manual tens brought enabling spec spec spec benchmarks ysis comprehensive preferable nice triple triple triple triple triple triple triple pendent infeasible permutations precup precup precup precup precup precup precup broader adjustments suitably orig orig orig orig orig orig aimed apparatus mal dependences dependences offered wait manipulations evaluates dissimilar scheduled scheduled scheduled scheduled scheduled scheduled scheduled claims writers judgments previ previ earliest earliest earning standpoint equipment equipment today narrower crafted crafted crafted crafted rect buffers triples triples triples triples triples triples triples triples loses settled purdue microprocessor prog dag dag dag dag dag dag utgoff utgoff utgoff utgoff utgoff utgoff utgoff utgoff utgoff unconditional orderings sor timal attainable accessed suspect compiler compiler compiler compiler compiler compiler logarithms logarithms optimizations optimizations modem modem modem rand atom atom haykin preclude cloud corp packard explo publicly elf elf elf elf elf microsystems compiled compiled compiled rations patent patent patent patent semantically tending bench hewlett fortran lafayette busy taining pipelines pipelines macmillan equate outlook outlook aggregating mally warrant pertain pertain sched proces revising tradi restructuring granted answering accesses customized rumel doina disproportionately everyday instrumentation tricky writes writes filed curiously equip parisons 
#@Brodley_C,Cavazos_J,Moss_E,Precup_D,Scheeff_D,Stefanovic_D,Utgoff_P,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural input data data data data data data data function function function function function function function function function function function function figure figure figure time time time time time time time time time time time set set set set set set set networks networks networks training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number system system system error state state state state state state state state state state state state state state state results results information problem problem problem problem problem models performance based based based based space space space space space linear linear vector vector vector vector vector order order shown shown systems systems systems values values values values values values values values values values values values values probability weight functions functions functions functions neurons unit unit distribution approach approach single processing control control control large rate test test test test patterns patterns analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs signal paper small feature net work work work work task task methods methods fig fig fig fig step step step step step step step step step step step step step process level level level current trained problems problems problems problems random high equation equation equation section section section general generalization real real real real approximation approximation approximation approximation average states theory theory theory note note note experiments university variables solution solution research independent independent log defined sequence sequence dynamics dynamics initial table table prediction prediction prediction prediction prediction prediction prediction prediction left left phase phase phase temporal temporal temporal temporal machine sets position position position nonlinear continuous abstract applied applied find find convergence convergence convergence references stochastic stochastic stochastic stochastic due due positive positive procedure adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision decision decision introduction introduction introduction introduction introduction action action action action action action complex hand hand behavior dynamic dynamic dynamic dynamic dynamic dynamic generated variance variance variance variance variance variance search tion tion change change difference assume measure chosen chosen part part previous required conditions expected expected expected expected expected expected equations markov markov markov markov markov make techniques techniques techniques proposed proposed proposed proposed probabilities finite finite resulting resulting total computed multi multi multi sum sum eq called called called elements elements elements reinforcement reinforcement reinforcement reinforcement reinforcement optimization optimization policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy negative vol vol artificial artificial represented application application compute compute compute compute compute rates rates proc proc location constraints constraints constraints constraints discrete discrete steps steps comparison comparison comparison update update support dependent modeling selection consists consists difficult scheme considered considered framework framework framework computing equivalent curve additional estimates design design transition transition transition transition transition transition transition transition transition stage efficient approximate approximate free free free world world increase increase con randomly randomly randomly randomly developed processes processes iteration iteration iteration iteration iteration iteration iteration measured technical describe tested tested assumption assumption assumption actions actions actions actions actions amount implemented generate main journal end end future future future easily development including fit typically pairs combination reduced account technology programming programming programming programming programming interesting testing ratio ratio ratio ratio special leads leads leads max max max max max max pre pre frame combined predict improve advantage separate takes typical typical typical apply strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy period period relevant interest sufficient compare compare volume solve solve yields rl rl evaluation chain grid improvement risk risk risk risk risk risk risk risk risk risk risk risk constructed constructed lead lead derivative alternative loop deterministic deterministic deterministic deterministic conclusion minimal assumptions assumptions assumptions differences differences differences accurate moody moody faster suggest taking demonstrated start start min relationship program explicit construct construct written index index index describes changing explicitly simultaneously simultaneously infinite consisting integrated expectation john depending stationary stationary influence influence influence solved variation updated approximations approximated converges converges converges past sign epochs epochs epochs classical classical spaces iterative remains intermediate intermediate intermediate intermediate construction exploration exploration includes formulation formulation formulation maximize reason reason straightforward maximal maximal presentation successful situation fine heuristic heuristic success interested split issue return return return return return return return return return return strategies strategies strategies strategies strategies hold hold hold simplified dayan realistic maximization policies policies deal employed wiley singh requirements environments optimized optimized recursive mdp mdp mdp mdp rise project variational possibility possibility referred decisions decisions decisions decisions maximizing complicated phases naturally analyze changed adjusted adjusted obvious epoch epoch generates utility utility defines massachusetts percentage advanced advanced stop costs costs costs costs costs costs costs costs costs costs costs smoothness analyzed analyzed guaranteed defining defining defining expensive benchmark benchmark starts day day watkins scientific scientific scientific describing describing beginning reflects improvements people evaluating fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy pure parameterized switch gains rely weigend aim aim cal germany neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro returns returns returns returns returns converged extreme trade naive naive naive gap bellman bellman indices indices concerned concerned controlling controlling allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation allocation stronger promising siemens siemens siemens proceeds stated attractive observing responsible exceeds days days financial financial financial financial financial financial financial combines forecasting den advance discounted discounted matter matter draw draw horizon horizon sons tsitsiklis subsequently valuable explains approximator interestingly market market market market market market market market market market market market market market market market switches mdps mdps mdps mdps mdps limitation trading trading trading trading trading trading outlined bertsekas bertsekas approx incorporates email tables alternating alternating dec markovian stock stock stock stock stock arg arg preferences german german german german constitutes suppressed certainty avoids penalized community management management management management management carefully retain relates cation simplifies behaves november portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio portfolio resp bridge opti simplification achievable corporate european stochastically thousand hid neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier sen sen tuple classi meth capital capital capital capital capital capital capital capital capital capital capital capital capital losses stocks stocks stocks enhances daily ods asset asset asset asset asset asset asset asset asset asset asset asset asset asset asset asset constraining cho cho deter differentiate profit profit profit modern transaction transaction transaction transaction transaction transaction transaction transaction transaction investment investment investment investment jan jan penalizes penalizes ming benchmarks benchmarks benchmarks kong relax aims simulates fight hong forthcoming enhancing enhancing enhancing enhancing recursire recursire bonds prices investor investor investor investor investor investor investor investor investor investor investor investor investor investor investor controllable controllable paid clarify executes formalized formalized formalized historical historical buy buy buy wishes volatility cap zimmermann zimmermann foreign ralph ralph ralph fund beats beats quantifies tab reformulation reformulated obeying referring athena athena assets assets assets assets wealth planned invest invest invest invest vances aug maxa opportunities equity lows liquid revise mchp mchp invested invested money finance aea mized invited relaxes ministic ventional influencing cash stoc strategic revision realm tabulated tabulated fic dicted diate spon iconip manages exchanges trt dicting uncontrollable uncontrollable allo upside adaptations 
#@Neuneier_R,
#t11
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input data data data data data data data data data data data data data data data figure figure figure time time time time time time time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training output output output output output output output output output output number number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system state state results results results results results results results results results units units units units units units information information problem problem problem problem performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector order order order order order order order order shown systems systems systems systems systems systems systems systems systems systems values values values values unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach approach approach approach approach approach approach approach pattern pattern pattern pattern point large rate rate rate rate rate test test test test test patterns patterns patterns patterns patterns analysis analysis inputs form shows shows signal paper paper paper paper examples small small size size size size net work work work task task task task task methods methods step features features level current current current trained trained trained random random random high similar representation architecture architecture show section section line line line line line line line line line line line line rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general general general general general parameter real real real real real real average obtained experiments experiments activity activity activity activity activity activity dimensional dimensional university university university university university solution research research research research independent log sequence sequence table table standard standard computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer terms science left left direction presented activation activation activation activation low frequency frequency machine machine machine sets sets learn learn learn learn learn nonlinear continuous sample abstract back find references component component ieee ieee ieee ieee ieee positive important important important important important important adaptive introduction hand hand behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical generated generated recurrent tion tion change change lower measure measure prior learned chosen chosen chosen higher higher higher higher higher part part part previous cases cases cases type required good good good long long long represent represent expected make make fact techniques techniques proposed correct correct correct observed scale scale resulting resulting resulting tasks total total performed called called times times times times means made made feedback filter obtain artificial specific represented represented represented application application active experimental approaches approaches accuracy larger larger train train selection selection proceedings proceedings proceedings proceedings proceedings words department department department department department implementation implementation version version consists consists consists individual individual represents difficult difficult difficult difficult sequences sequences considered environment environment curve curve transition transition top detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection conference conference conference determine determine choice statistics statistics free world world world increase give give coding randomly randomly randomly randomly actual actual actual actual actual backpropagation backpropagation backpropagation sampling simply simply discussion normal normal normal normal normal describe describe group tested tested tested tested tested tested tested short common common effective effective implemented implemented generate supported require require require require end future future future future easily including account account unknown programming programming interesting testing special matching representing representing representing window window bottom magnitude idea idea idea run run run run description predict predict architectures improve recent recent correlations takes practical period period engineering engineering engineering engineering highly highly subjects works tions match match match achieve evaluation evaluation interval interval entire entire entire grant grant lead occur occur occur occur correctly correctly correctly correctly column runs conclusion place row accurate accurate accurate designed clear suggest hard drawn demonstrated intelligence user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user introduce identification identification identification identification identification program program question acknowledgements pro longer ways sequential modeled implement implement simultaneously linearly electrical electrical remaining remaining easy easy easy easy slightly develop applying events predictive versus cycles national national national depending squares overlap open updated activities updates past earlier epochs expansion intervals intervals intervals intervals intervals intervals false false false false false false false false false false false false generation classified transactions transactions avoid recorded recorded building activations inter sciences sciences recognize activated variations reason regular regular identified identified identified society differ computationally computationally divided included identify identify identify identify identify identify identify detect detect detect detect detect detect build build build schemes tend receives quickly kind allowing split issue issue categories built vary usual generalize realistic realistic board highest highest leading cat attempt attempt consisted operating software software receive presents command command command command command command command command command command command command command command command command command powerful exhibit detail issues issues matches giving ideas rest reliable reliable decisions proper affect phases possibly editor man predicting predicting extremely created noted detector detector mapped detected detected detected utility seconds years indicating great scenes crucial coded expensive tractable tool reasons rapid lin lin lin lin sections sections closer easier day day day day day day day day day constructing leaves cut optimize res nsf addressed varies people behaviors collected collected profile profile profile profile led fed experimentally effort effort posed share detecting detecting detecting detecting detecting detecting employ frequently commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands commands maintain ture differs differs chen gave simulator simulator kinds sophisticated lot lot picture identifying identifying identifying sort forming investigation fix arguments optimizing communications fits chance promising mail mail mail mail mail mail intelligent contract keeping serves exploit operates observing guide symposium symposium days days days days days days days days date becker programs programs displayed overview colorado histograms histograms accounts den record matter matter refers impact splits splits splits splits splits interestingly executed executed executed executed executed dramatically usage usage usage constitute users users users users users users users users users users users users users users users users users users users users users users users users users users listed accept accept session revealed poses retraining profiles profiles profiles profiles profiles spaced big constitutes constitutes constitutes certainty favor shifting pdp distribu boulder boulder rejected ultimately iri records monitoring monitoring monitoring monitoring option maintains alarm alarm alarm alarm fea programmed increments struc challenge sessions sessions utilizing picking fortunately characterizing decided tom identifies prefer ping send austin austin austin austin austin austin austin austin hundreds overtraining hid finer reflecting cally ning proposes alarms alarms alarms alarms fox fox positives positives arpa proves predictable daily daily daily fin neutral accounting periodically feasibility thing meant concatenated concatenated unusual unusual unusual unusual unusual modern trend counted counted counted platform platform texas texas texas texas texas violated generaliza rec anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly anomaly security security security security security security security miyata miyata elegant collecting collecting direc ece sends hands enabled scribed distinctions web mike collect anticipate anticipate burden offiine retrained miikkulainen miikkulainen miikkulainen miikkulainen suggestion suggestion suggestion suggestion motivates outlines outlines unix executes tar historical constantly frank frank superfluous vation granularity acti jim attack peri anomalous anomalous anomalous anomalous manageable raise strip inexpensive revealing reed services cies ryan ryan ryan ryan ryan collects education print print print print logs logs logs logs logs deviates sive quicker corp raven negatives infrequent legitimate legitimate legitimate legitimate legitimate legitimate legitimate legitimate legitimate legitimate scalability pur dozen infrequently edit ports trail utexas utexas utexas suggestive parses dod falsely levitt engage sibility diff lined coordinating attacks attacks attacks sed browsing spell cvs mand avenues frequen editing compromised forgets calendar tee compilation config tput happening accidentally 
#@Lin_M,Miikkulainen_R,Ryan_J,
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#*network network network learning learning neural neural neural neural input input data function function figure figure set algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number number number system system error results units units information information information information information information information information information information information information information information hidden performance based based based based based based based case case case case case case case vector vector vector order order shown systems systems systems systems systems systems values probability probability probability probability probability probability probability noise functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach pattern pattern pattern image image single single processing large large local rate rate patterns analysis class class class class class class class class class class class class class optimal inputs visual visual paper paper paper examples small size size size size size feature feature feature feature feature feature feature feature feature feature work work work task methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step step step features features features features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell high equation equation section section section section section section rule rule rule vectors vectors images images images images images images images images images images images images speech real average theory theory obtained dimensional result computation computation computation independent independent log log constant table table estimate estimate estimate standard standard standard standard standard standard standard computer computer terms distance science presented presented presented present present machine object object object object object object object object object object object object range press nonlinear outputs sample sample abstract applied applied applied find find find computational references due due due positive important important decision decision decision decision decision decision context context context context context context context context context context context context context context context context context context introduction statistical effect cost search tion change difference complexity assume prior word center center center cases cases cases cases cases conditions bayesian bayesian make fact proposed probabilities forward classes classes classes classes classes total total human potential potential made made made made made made applications applications study negative negative vol vol relative samples samples compared application application application application application application cross compute compute compute compute compute objects objects objects objects objects objects objects constraints distributions equal mit comparison larger dependent dependent institute institute institute words department implementation technique technique technique joint joint joint difficult final framework framework framework framework framework cambridge additional top stage stage efficient classifiers full requires vision estimated basic give developed developed robot area area types types types types types types types entropy provided finally simply achieved normal group denote tested assumption assumption assumption common shape shape role role eds eds pixel pixel instance makes typically typically technology technology technology transfer testing testing significantly significantly ratio character edge edge database database empirical empirical empirical leads call direct international experts choose description population takes typical introduced include pixels pixels pixels engineering engineering compare observations observations differential differential address background evaluation generalized intensity intensity occur deviation deviation deviation deviation deviation deviation deviation correctly feed white white white white white white white white white white white flow assumptions reduce conclusions conclusions sigmoid sigmoid bayes designed designed propose taking presence presence characteristics drawn demonstrated california california california assuming manner identification identification identification identification identification identification identification identification identification program suppose perception laboratory dept dept implement implement electrical electrical consisting springer springer extraction extracted extracted independently dependence interpretation labels labels showed sizes reasonable measurements reduces combining combining false false false false false false false valid calculate assigned classified precision fire includes priori color color color color discuss specifically specifically domains tests tests texture texture major major major identified extra importance differ identify detect efficiently post identity identity identity identity verlag verlag prob superior superior physiological hold quantity list relaxation correspondence automatically acknowledgments deal situations production essential lippmann mass helpful helpful authors referred decisions decisions utility percentage percentage fairly expensive independence comparisons comparisons rapid implementing satisfied preprocessing preprocessing precisely incorporate members medical medical medical demonstrates author sun varies greatly collected fed red red red red red red red red red red red red red red red passed variant maximizes incorporating incorporating incorporating incorporating incorporating incorporating pasadena pasadena pasadena marginal adjust song song song song green green green green green green green green green richard segmented segmented age patients median median median median median median diagnosis diagnosis diagnosis diagnosis contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual contextual proportion primarily addison pick ordering labelled concerned count count count impossible caltech caltech plays plays eliminated eliminated fits consideration consideration imaging imaging significance adjusting occurred simplify bands composition performances ambiguity equals mental belongs captured counting artifacts infer captures pen counts posteriori posteriori posteriori posteriori informa abu abu abu abu associations blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood mostafa mostafa mostafa mostafa ter exhaustive recursively classifications classifications blue blue blue blue blue blue blue blue blue blue blue decomposed hundred remote scenario relate individually relates regimes ambiguous descending alarm alarm alarm supports commercial commercial microscopic suggestions clinical clinical clinical clinical utilizing rewritten served info argmax argmax simplification interior interior interior interior ave virtually incorrectly proportions alarms labelling rating raises isolation company company differentiate unusual indepen indicators dence subtle unnecessary routine joseph iris iris abnormal abnormal abnormal abnormal abnormal abnormal disorders tailored advice puter alexander conveys analyzer malik surrounded pierre pierre mature mature categorize duce bigger accompanying accompanying normality identities identities identities unambiguous accompanied matters intervention shapiro simplifications chemistry pathological amir unsegmented joe pertinent ismail sill sill sill sill atiya yaser yaser ucla ucla screening harbor harbor instrument duces quantile quantile quantile quantile quantile magdon dye infrequently lives josef josef busy levitt ential confuse fourteen maturation immature immature immature flag incorpo intensively pert worry numbering 
#@Abu-Mostafa_Y,Kasdan_H,Sill_J,Song_X,
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#*network network network network network network learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set set networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number system system system system system system system system system system system results results results information information information information information information information information information information information problem problem problem problem performance performance performance performance performance based based based based based based based based based based based based based based based weights weights weights weights linear linear layer order order order order shown shown shown shown systems systems systems systems systems values values probability weight weight weight weight method method approach processing processing processing processing test analysis form form form algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper examples examples examples examples examples examples examples examples examples examples small small size size net methods step points classification process process process current current current current current current current current current current trained problems high similar representation representation representation representation section rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule real real real real real real real real real real real real real real average average average theory theory note note note note note note note note note note note note result result computation computation research independent independent independent log log defined table table table table computer terms left presented present low low sets learn continuous abstract applied references decision introduction hand hand estimation behavior effect generated generated generated generated generated recurrent complexity classifier lower lower lower rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure measure measure measure measure measure measure learned learned chosen chosen higher part previous cases cases required required multiple good good make techniques correct correct correct probabilities probabilities probabilities forward scale scale scale scale ing multi made knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge true desired provide provide provide perform determined experimental goal constraints constraints constraints constraints constraints discrete discrete steps steps steps accuracy accuracy accuracy comparison comparison dependent dependent dependent dependent nets morgan morgan institute loss loss version individual advances advances connectionist connectionist difficult final final delay addition graph ai considered considered domain additional additional additional additional san san determine determine determine determine determine determine determine determine determine determine requires choice significant significant approximate speed speed speed speed speed basic increase produce produce derived randomly types processes nature nature nature simply simply increases describe describe describe tested fast complete amount amount amount amount common common common effective generate generate generate generate generate generate supported journal end end ability ability ability future makes development development including including kaufmann kaufmann probabilistic needed reduced reduced account technology edge increasing segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation consistent leads combined produced produced added predict predict predict resolution advantage robust similarity apply identical side side hierarchical subset array sufficient compare previously yields match background modified modified improvement increased extended predicted correctly correctly feed demonstrate half greater greater greater segment segment segment bayes moody learns mateo mateo presence characteristics california proportional start start start program program base base acknowledgements pro produces primary primary primary generating generating transitions transitions segments segments pruning pruning applying focus expressed review evaluated evaluated allowed allowed allowed delays classical event generation generation initially advantages advantages faces avoid existing fire fire fire fire fire fire fire fire fire fire fire fire box box box box priori priori priori priori priori mozer mozer major major determining straightforward efficiency symbols build miller contained contained prob prob success return content duration duration list list play absence highest received subsequent extract deal decreasing presents simpler collection varied limitations lippmann hall reducing symbolic func func func func func removed removed predicts changed rank algo algo improving great theoretic analyzed briefly london easier preprocessing style style style desirable desirable desirable mation sounds pitch pitch attribute attribute attribute attribute attribute meaning nsf improvements greatly limits incorporated music music music music music music music music music music music music music music sharp gains gains incorporating prevent pasadena substantial conclude segmented segmented segmented segmented segmented segmented segmented segmented segmented segmented specifies summed secondary notes notes notes notes notes sort rithm rithm harmonic harmonic outcome outcome caltech caltech plays plays dealing chance accepted imposed abilities harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony harmony removing alphabet fires fires fires fires composition composition composition infor meaningful performances prentice governed ensures ensures surprising dependency dependency mel specialized infer infer insight insight impact valuable valuable generalizing accumulated accumulated sequentially fired fired fired fired converted unable piece piece fellowship goodman goodman goodman goodman goodman goodman inferred pieces classic affects rhythm examining examining reconstruct quantized musical musical musical musical musical translated gener elementary playing compatible challenging paired smyth lookup deleted worth maintains outcomes meet xly xly xly xly xly retained milliseconds priority priority tel gorithm stops picking rarely remarks functionality functionality algorithmic resolve twenty todd todd cliffs inhibited inhibited virtually melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody melody micro micro played played played played clauses inherently mistakes gram englewood bach bach bach bach bach bach bach bach bach bach bach bach bach bach bach bach alto alto alto alto alto alto alto voice voice voice ranged format format format segmenting segmenting ous tens voiced objectives imposes richer checked corr ranked chorales chorales chorales chorales conflict conflict hild hild previ lacking chord chord chord chord chord chord chord chord chord chord chord chord chord melodic refining grove lowering timestep timestep timestep live live eval tonal jim accompanying instruments noticeable rodney unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented unsegmented synthesizer higgins speak knowl meets spend composing melodies melodies milton ating timesteps timesteps timesteps menzel menzel hawkins hawkins hawkins hawkins hawkins instrument rhs rhs rhs rhs aids bal diminished happy happy attacks performer stylistic cix distracting nizing trades randall randall har meas 
#@Goodman_R,Hawkins_J,Spangler_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data data data data data data data function function function time set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number number number number number system system system error error error error results results results results results results results results results results results results results units units units units units units problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based space space space weights weights weights weights weights weights weights linear layer layer layer layer layer vector vector order shown systems systems values probability parameters parameters parameters parameters weight weight weight weight weight weight weight unit unit distribution distribution distribution distribution distribution distribution distribution recognition method method method method approach approach approach approach approach approach approach approach pattern pattern single large large large large large large large large rate test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis class class class inputs inputs inputs inputs inputs inputs inputs shows shows shows algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian paper paper paper examples small small small size size feature feature net work work work work work work task task methods methods methods methods methods methods methods methods field field field features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level level level level level level trained problems problems problems problems similar architecture architecture section section section section section fixed vectors general general general parameter parameter real real real real approximation approximation approximation approximation approximation approximation approximation average term note experiments experiments experiments experiments experiments result result university university university university variables computation computation solution solution solution solution solution solution solution solution solution solution solution research research independent defined found found found target table table table table table estimate estimate estimate standard computer computer node science science science direction map map map map map map activation activation activation activation activation activation frequency frequency maximum range press outputs outputs outputs outputs outputs outputs continuous sample abstract applied applied applied back density density density properties properties likelihood references due due ieee positive important decision propagation introduction action complex hand hand statistical effect effect effect effect effect effect variance variance variance variance variance search tion complexity assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower rules rules rules measure signals prior prior prior chosen higher part theorem cases cases cases required good good good binary tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian make make techniques techniques techniques techniques techniques techniques techniques region region proposed correlation correct correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed finite resulting resulting classes classes classes classes human human human regression respect multi sum performed performed performed called regions regions regions regions regions mapping mapping optimization made made made applications study artificial artificial artificial artificial samples samples samples represented represented compared compared compared compared compared application application application application application application application desired cross cross cross cross cross define perform perform eye eye eye posterior posterior posterior posterior posterior posterior posterior posterior distributions power approaches approaches approaches approaches larger larger larger selection report report report institute institute department implementation implementation implementation implementation technique technique represents exp exp scheme ai ai ai ai framework framework framework cambridge domain experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment environment additional solutions estimates estimates estimates estimates estimates limit stage effects detection detection conference conference conference classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper upper full full full significant statistics world world world world estimated pages pages validation validation validation validation give give give coding conditional levels levels entropy selected evidence evidence evidence evidence evidence depends sampling sampling biological achieved achieved technical transformation transformation transformation transformation transformation close inverse amount amount short nearest nearest nearest nearest nearest nearest nearest common main ability hypothesis instance easily degree including smaller needed interesting testing significantly significantly york increasing consistent database leads leads leads leads details details international international international normalized expert expert decay decay decay decay decay decay decay run description perceptron perceptron advantage advantage property separate takes movement movement movement movement movement movement movement reported reported reported practical apply include subject side side inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference sufficient sufficient compare approximately subjects subjects subjects calculated calculated calculated calculated calculated tuning tuning solve evaluation generalized williams williams horizontal expression expression lead lead lead studied studied deviation correctly move hybrid hybrid hybrid hybrid hybrid hybrid column conclusion critical neighbor neighbor neighbor neighbor neighbor neighbor neighbor differences differences sigmoid measures bayes bayes bayes bayes bayes bayes bayes clear exponential exponential practice integration proportional intelligence intelligence regularization regularization assuming assuming movements relationship relation monte monte monte monte monte monte derive carlo carlo carlo carlo carlo carlo longer label label vertical dept confidence confidence confidence implement remaining easy spectral applying predictive springer family expressed review stages stages stages stages influence influence solved solved densities evaluated restricted showed showed showed discrimination key reasonable calculation classical classical penalty penalty interpolation valid calculate calculate calculate calculate assigned eeg classified classified classified classified transactions activations activations automatic automatic automatic automatic discuss priors tests reason reason reason capable detect detect build build build mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay mackay comparing score procedures interested lie built bar sampled automatically consisted software bars simpler transformed integral integral examine project investigated analytically analytically muscle scaled scaled office reliable reliable reliable decisions comparable comparable encode removed neu coarse coefficient plausible extremely der algo motivated motivated neal neal neal neal neal neal analytical nonlinearity london rapid closer forces bishop bishop bishop bishop bishop probable probable probable pool consequence consequence acknowledgement recognized separately toronto medical computers recording cybernetics researchers robustness fourth percent evaluating relevance peter peter peter peter effort marked recordings recordings detecting reliability ity outliers outliers outliers outliers outliers rely limiting weigend weigend aim aim softmax softmax softmax softmax softmax softmax softmax softmax person college college sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep guarantee oxford investigation restriction rithm significance significance significance interpret scoring ral hours motivation periods periods periods periods conjunction conjunction washington express arrive clean clean clean impact inductive inductive designing fold fold fold std std std acknowledge posteriori neurophysiology ter incorporates inferred inferred inferred inferred validity rejection revealed suboptimal year comparative comparative reports experiences experiences experiences experiences possibilities possibilities guess assess reject summarizes publication publication formance distant uncertain careful careful rejected rejected electrodes electrodes electrodes million misclassified misclassified reveal examination examination january ate decided heavily european lated outperformed suppress illinois cally medicine manually ray ray ray inspection est nih outlier derives rem manual emerged terminology sponsored urbana spent activa biomedical zhu buntine buntine neurology scored ministry dev dev concluded perf perf perf tarassenko vation rejecting acti healthy ising embody champaign government transport doubt doubt doubt doubt doubt doubt doubt doubt doubt gions iee departments infrared standardized austria xii bet roberts roberts roberts austrian austrian federal vienna vienna vienna calcu clarendon tedious activ electronically wien wien printing bfgs marginalization marginalization marginalization marginalization marginalization georg georg josef josef algorit enhancements competitor cla blindly gratitude imperial commission schottengasse automati biomed 
#@Dorffner_G,Rappelsberger_P,Sykacek_P,Zeitlhofer_J,
#t11
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training algorithm output output output number system system system system system system system system system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state state state state state results results results results results results units information information problem models models models models models models models models models models models models models models models hidden performance performance performance performance performance based based based space space space weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case vector vector vector order order order order order order order order order shown shown systems systems systems systems systems systems systems systems values values values values values values probability parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise functions functions functions functions functions approach approach single control control test test test analysis matrix matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs form form form form form shows shows shows shows shows algorithms simple simple gaussian paper paper paper small small feature work work work step step step step step process level level level current trained trained trained trained trained trained trained trained trained cell response response response response response response response response response response response response response architecture show show equation equation equation equation equation equation section section section fixed line line line line rule rule rule rule rule rule vectors general general general parameter real real states states states theory theory note note note experiments experiments dimensional variables solution solution solution solution independent log log log log log log defined defined found target target target dynamics dynamics initial constant table table table estimate estimate estimate estimate estimate estimate estimate standard standard standard terms prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left left left left maximum maximum maximum maximum maximum press press learn nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous abstract applied applied find convergence density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic complex complex effect effect variance variance variance variance variance variance variance variance variance variance variance variance variance recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent variable variable variable assume assume rules rules rules rules part previous previous previous cases cases cases type multiple multiple long conditions conditions equations equations equations equations equations equations equations equations equations equations equations equations make proposed proposed proposed forward forward forward forward forward forward forward forward ing ing ing respect multi sum sum performed called times times times times times times times times means means means dimension dimension natural applications applications applications knowledge em em em em em em em em em em filter filter filter filter filter filter filter filter filter filter filter filter filter obtain obtain obtain artificial relative specific specific application application application application series series series series series series series define determined goal equal approaches mit steps comparison train dependent modeling report consists individual represents responses responses responses considered considered experiment experiment solutions design transition effects significant statistics free free free free free free free free free free estimated estimated estimated estimated give con conditional conditional conditional levels actual finally processes iteration constraint constraint achieved achieved achieved achieved measured measured measured measured measured covariance covariance covariance normal normal normal normal normal normal technical describe describe denote fast close corresponds complete predictions predictions common implemented implemented implemented assumed assumed eds adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation noisy noisy including typically typically typically typically combination combination combination combination combination combination dynamical dynamical dynamical functional functional unknown unknown unknown unknown technology testing significantly special special mode mode mode mode mode mode mode mode mode mode leads leads leads leads squared squared combined predict predict predict perceptron resolution advantage advantage advantage typical typical apply introduced introduced include include period period identical interest interest interest sufficient highly highly highly highly highly varying compare teacher teacher teacher teacher teacher teacher teacher teacher approximately tions solve observation improvement improvement improvement risk lead lead lead lead lead lead extended extended extended deviation deviation predicted alternative locally deterministic deterministic deterministic deterministic deterministic deterministic setting conclusions interactions interactions measures moody moody practice propose integration targets introduce appears pro monte derive carlo describes tuned modeled modeled modeled recall recall missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing text consisting develop develop predictive predictive predictive predictive predictive expectation expectation john yield solved solved controlled approximations approximated similarly converges updates past reasonable reasonable reasonable smoothing slow dashed dashed additive additive measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements delays intervals intervals intervals intervals intervals event intermediate filtering filtering calculate expect recorded recorded uncertainty maximize maximize major major reason regular suitable computationally capture capture traditional traditional interested running running running running running running running running running running physiological physiological physiological physiological involved backward backward backward backward backward backward backward backward delayed delayed deal powerful wiley transformed updating kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman hanson dotted dotted dotted mappings int int int int int int analytically authors maximizing proper stream circles measurement measurement measurement measurement measurement measurement measurement measurement measurement measurement measurement measurement measurement measurement adapt adapt adapt predicting predicts predicts impulse impulse academic baseline simplest explain explain integrate residual residual great derivation variances adapted adapted adapted diffusion expensive tractable tractable considerable sys sys ring day day day day day day day division leaves desirable desirable arise circle optimize explained explained explained explained explained explained considerably percent percent collected amounts employ calculating popular achieves gave germany logical expectations initialization person person person tresp tresp tresp tresp tresp tresp tresp uncorrelated uncorrelated uncorrelated intractable notes physiology purely food food food food food tem generality difficulties siemens siemens chemical responsible days days hours hours repeat irregular irregular irregular irregular irregular sion patient patient patient patient appendix appendix appendix appendix bad injection injection forecasting infinity den thomas thomas nonlinearities bases tic iterated iterated iterated iterated iterated iterated iterated treatment relies davis implicitly explains alternatively ignore interestingly limitation limitation lem lem lem lem lem lem lem lem lem lem lem lem lem approx blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood blood basically forced forced nition suboptimal suboptimal encouraging lit lit lit amplitudes covariances forcing forcing forcing forcing forcing forcing certainty realize beta regulation individually acquired integrals integrals integrals integrals tract treating treating exploited rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn rnn mea clinical corporate imple realizations realizations realizations recursion recursion injected substitute linearized ignores ignores rtrl rtrl rtrl rtrl daily sity protocol lewis lewis lewis fol problematic iterate iterate durations nice stabilizing months predic minute substituted substituted substituted undesirable volker volker compartments retrained retrained counterparts plain nation lowing basal miinchen mented sults recur completes stochas comput exercise exercise exercise exercise exercise diabetes otto unknowns avail avail combi dur deterministically hahn sidered spe cesses intense pursue latest rnns rnns rnns confirming dangerous dangerous mchp unsatisfactory ttt recursions injections substitutes surements recommendations physio cific jtn defi untilled summa metabolism metabolism rth rtl 
#@Briegel_T,Tresp_V,
#t11
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#*network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set networks networks training training training training training training training training training training training training training training training algorithm output output output output number number error error error state state results results results results results results information hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance based based based based space weights layer layer layer layer layer layer case case vector vector order order shown systems systems values values values values parameters parameters parameters neurons neurons distribution distribution recognition method method approach pattern single single single single processing large rate rate rate rate rate rate test test test test test test test analysis class class inputs inputs inputs inputs inputs form shows shows simple gaussian gaussian paper paper paper examples examples examples examples small small feature feature work work methods methods methods methods features features features features classification classification classification classification classification level level level level level level level trained trained trained random high high high response response similar architecture show show section section section section section section line line rule images parameter parameter parameter parameter parameter real states gradient gradient gradient obtained university university threshold threshold threshold threshold threshold threshold research research independent log defined found table table table table table table table table standard standard standard standard terms terms terms science science prediction prediction prediction prediction prediction prediction prediction prediction left left left present present present activation activation low low press press outputs continuous continuous continuous sample sample sample sample sample sample sample sample abstract back back references positive positive positive positive positive positive positive positive positive positive positive positive positive decision propagation introduction action generated cost cost cost cost cost cost cost tion change difference variable variable assume classifier classifier classifier classifier classifier classifier classifier classifier classifier measure measure measure measure representations chosen higher center cases cases cases cases cases cases cases cases cases cases type type binary binary binary binary distributed make make make make make make fact techniques techniques techniques techniques region correct errors forward scale resulting classes classes classes classes ing total total total total total total total total total total simulation human regression multi multi multi means optimization optimization optimization optimization optimization optimization optimization optimization optimization study obtain negative negative negative negative negative negative vol vol vol vol vol vol artificial relative relative relative relative samples samples samples true true true desired desired desired desired define power approaches accuracy accuracy accuracy update descent dependent selection internal bias bias graph considered considered hinton curve curve curve curve curve curve curve curve curve curve curve curve curves curves curves curves curves curves curves curves curves curves curves curves curves design limit limit classifiers classifiers classifiers validation give give give give give con derived derived weighted randomly randomly randomly levels criterion area area area area area area area area area area area area area actual selected selected selected nature simply measured group fast complete predictions predictions short role square easily rumelhart development development development objective objective objective objective objective simulated simulated simulated simulated simulated simulated simulated needed needed account fully technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp ratio york york york increasing structures squared squared squared squared numbers iterations supervised supervised combined combined description description predict predict predict predict perceptron perceptron perceptron architectures architectures population population population population population population population population discussed recent reported practical practical practical practical practical introduced introduced sense relevant engineering sufficient highly varying varying varying compare compare observations observations calculated calculated calculated calculated calculated calculated calculated calculated smooth smooth smooth studies observation interval williams risk risk entire horizontal horizontal expression trial trial trial deviation deviation deviation deviation predicted predicted feed flow flow conclusion valued valued valued valued valued measures accurate numerical numerical practice temperature temperature taking taking integration presence presence presence presence presence characteristics characteristics characteristics characteristics demonstrated solid solid solid labeled decrease relationship averaged averaged introduce introduce introduce annealing annealing annealing annealing annealing annealing annealing annealing annealing areas areas areas boltzmann van index plot plot plot plot laboratory dept dept sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity electrical remaining consisting adding predictive predictive predictive formed versus versus versus select john john john expressed detailed detailed showed allowed discrimination dashed epochs neighborhood false false false false false false false false false false false assigned classified color color color illustrated discuss discuss maximize tests columns efficiency uniformly included detect detect detect comparing comparing score characteristic characteristic characteristic characteristic characteristic refer interested split classify criteria sci device gray absence absence reach thresholds thresholds operating operating operating operating operating operating jacobs acknowledgments schedule carried wiley wiley collection investigate replaced accurately hessian dotted mass ml rise project project mse mse mse mse mse mse mse mse mse mse combine authors office referred reliable reliable reliable reliable decisions comparable comparable comparable tanh tanh tanh neu examined examined examined measurement concepts concepts concepts concepts concepts adjusted portion logistic initialized submitted motivated attempts preference improves explanation expensive lies tool tool considerable widely organized bishop scientific scientific acad medical depicted meaning meaning meaning parameterized measuring proven incorporating prevent gave gave gave enables chose age age age age age attraction patients patients patients patients patients patients patients patients deviations differentiable diagnosis diagnosis representative acquisition newton newton proportion proportion proportion proportion proportion proportion proportion proportion writing oxford outcome outcome outcome murray numerically numerically numerically imaging imaging accepted accepted ral receiver receiver receiver receiver receiver receiver receiver started started irregular patient sides counting express indicator indicator indicator indicator indicator cancer cancer reader specificity specificity specificity specificity specificity specificity specificity specificity specificity specificity steepest extensively concentration stopped stopped dividing consecutive unchanged ence roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc roc usage blood blood logarithm presenting propagating quasi quasi hundred associate conservative assess clas community wall wall wall management differentiation differentiation differentiation acquired scope relates spanned drawback misclassified outcomes tively refined tissue matlab status status status scanned consuming august august monitor marks vii heavily heavily subjective overtraining overtraining suffices responsibility lists lists diagnostic diagnostic subtracting coincide kirkpatrick markers deals positives positives ignores convention reality sions protocol goodness experienced experienced poles benign benign benign benign benign benign benign benign benign benign benign benign benign benign benign benign benign benign indicators indicators indicators indicators indicators indicators indicators discriminating discriminating tivity initiated drawbacks drawbacks drawbacks rises assessing campbell marker marker prime notions predic traditionally wright versity cooling cooling respec missed ant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant malignant med icnn rescaled masses masses spans spans spans spans spans visualize fund imperfect assist normality mips vecchi fluid fluid siftcation percentages walls walls walls standardized minimally situated surgery rests gelatt radiology gill ian malvern collins bilateral erating marquardt belgium belgium belgium tumor tumor tumor tumor bfgs levenberg frameworks yves irregularities culture superscripts programme thinks thirdly swets fletcher subregion subregion imag assessments textbooks cepts ery invasive universiteit universiteit sensi nant trapezoidal institution 
#@Moteau_Y,Timmerman_D,Vandewalle_J,Verrelst_H,
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#*network network network network network network network network network learning learning model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time networks networks networks networks output output output number number number number error error state results results results results results results results results units units units units information information information information problem problem problem models models models models models models hidden space weights weights linear linear layer case case order order order order order order shown shown systems systems systems systems values probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise weight functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach approach approach approach pattern pattern single single single processing processing processing large large local patterns patterns analysis analysis analysis analysis analysis analysis inputs inputs inputs inputs inputs form form shows shows shows shows shows shows shows algorithms simple paper paper feature features process process process process process process process process process process process current problems problems random random similar similar representation show equation equation line general general parameter parameter real average gradient term term term term term term note note note note note university university university variables variables variables variables variables computation computation computation research research independent log log log log found sequence sequence sequence sequence sequence sequence target initial initial initial constant constant constant standard standard standard left present present present present maximum maximum press press press press press learn components nonlinear outputs outputs outputs continuous continuous continuous abstract applied applied applied applied back density properties likelihood likelihood likelihood likelihood likelihood references references component component component component stochastic stochastic stochastic positive positive important important mixture mixture mixture mixture mixture mixture introduction estimation statistical statistical statistical statistical variance difference complexity variable variable assume assume lower prior prior prior chosen chosen higher higher part part previous previous previous required required long long bayesian bayesian bayesian expected expected expected markov markov markov markov markov make fact fact fact techniques techniques techniques length length probabilities probabilities probabilities probabilities observed scale minimum resulting resulting regression computed computed respect times means made made natural applications study em specific series series series series series series location perform determined connected distributions distributions distributions discrete discrete discrete discrete approaches approaches mit mit larger larger dependent dependent dependent dependent modeling morgan individual advances advances advances joint exp exp exp sequences considered considered cambridge computing computing additional view view estimates design effects effects effects efficient upper full full choice choice significant statistics estimated pages pages pages pages con conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional levels lines actual actual actual provided provided processes processes backpropagation nature depends depends simply achieved discussion discussion normal increases describe denote denote hmm assumption corresponds amount amount amount amount amount amount amount amount amount amount amount amount amount amount short assumed shape shape require require journal journal journal journal journal instance noisy fit smaller smaller smaller underlying needed account account fully jordan jordan significantly ratio increasing mode principle iterations supervised early architectures recent takes period period period side sense cognitive engineering interest sufficient compare compare observations observations approximately calculated axis tions smooth yields studies chain chain chain chain chain observation williams williams williams williams williams williams williams sensitive scaling suggests deviation deviation deviation hybrid touretzky touretzky generally assumptions conclusions conclusions depend depend depend editors editors editors editors central numerical clear exponential taking integration integration presence physics cycle drawn proportional regularization regularization assuming derivatives derivatives base question suppose pro monte written longer longer index estimating vertical mathematical pruning pruning integrated integrated integrated events events implies cycles cycles family expressed expressed dependence dependence depending stationary interpretation solved variation variation variation variation densities densities approximated activities past past past partial fitting fitting fitting event event event event event roughly roughly purpose purpose remains remains calculate transactions david avoid recorded combinations activations sciences sciences sciences determines determines specifically specifically variations variations domains holds discussions simplicity simplicity planning gamma gamma gamma gamma gamma gamma determining determining straightforward selecting suitable suitable suitable society prob sin sin sin sin content providing automatically extract extract deal software tesauro tesauro tesauro decreasing decreasing modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling modelling cowan presents bars overfitting overfitting experience rapidly rapidly rapidly replaced behaviour periodic fourier fourier fourier fourier successive school school links comparable gates proper adapt necessarily integer onset illustrate illustrate ensure aspect assumes multivariate optimum integrate years years indicating cos cos cos cos distinguish growing adapted considerable turns strictly protein day day day day day day day day day day day day day day day bishop bishop commonly commonly controls consequence acknowledgement universal implicit english annual annual incomplete incomplete preceding preceding summation summation integrating integrating empirically understood amounts amounts amounts amounts amounts amounts amounts peter peter adjustable frequently weigend weigend occurrence occurrence occurrence occurrence occurrence occurrence occurrence occurrence occurrence marginal marginal datasets expectations expectations conditioning progress traces ghahramani ghahramani leen leen acm resources resources royal stronger chains chains occurred occurred iiii balance abilities occurring occurring observing adequate days days days days days days days days days days days alspector displayed pat dependency dependency dependency evident approximators laplace modelled modelled modelled modelled modelled modelled indicator environmental valuable baldi baldi insensitive fitted summer summer email ber recursively ram ties year year year year year year year medium lit chapter england examining rain rain rain rain rain rain rain rain rain rain rain rain rain rain rain rain rain stands trends trends trends trends trends trends trends trends trends trends trends distri chauvin chauvin num decays distribu discontinuity distant regularizer regularizer regularizer relate concentrate relates relates relates complementary unconstrained worth covered distinguished september completed mann november ergodic sponding simplification terns stochastically stochastically water water jointly todd envelope envelope east adaptively adaptively puts recursion recursion station station extracts daily daily daily daily daily daily daily daily daily daily daily daily daily daily daily daily weather weather weather weather pooling edition south subscript lags lags cyclic cyclic stationarity ira jack extrapolation expresses putting minimise italy distributional distributional distributional tong winter winter winter quarter confirms historical succession nix nix supplies gerald gerald volatility quences weeks today katz katz katz katz earth assist indicative omitting peri chemistry joshua incidence edward indebted unconditional unconditional referring recipes lastly supplying investigators teukolsky recalling envi flannery persist harmonics harmonics portable vances kauf jumping lution analysing exponentials exponentials vetterling skewness sussex sussex parametrization professor dry ifx stations stations stations stations stations stations strike coe forecasts arnold fortran ison subroutine vided integrable wet verifying atmospheric suming kindly italian italian mount provision psi brighton underfitting ecological stood drew narrowing odic 
#@Williams_P,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function figure time time time time time time time time time time set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output number number system system error error error error error error error error error error error error error error error error error error information information models hidden performance performance performance performance performance performance performance based based space space space space weights weights weights weights weights weights weights weights weights weights linear layer case case case vector vector vector vector order shown systems values values values parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point control control control control control control local local local local local local local local local rate rate rate rate rate rate rate rate rate test test test test test test test patterns patterns patterns analysis analysis class optimal optimal optimal optimal inputs inputs inputs inputs inputs form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple gaussian gaussian gaussian paper paper paper examples small small small small small small size size work work work work task methods methods step step field process process process level level level trained trained structure structure structure structure structure structure structure structure structure structure structure structure random random high high high high high memory similar similar section section fixed rule vectors vectors vectors generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter real approximation approximation approximation average average theory gradient gradient gradient gradient term term term term term term term note experiments experiments result result variables variables computation solution research sequence target constant constant table estimate standard terms terms terms terms prediction present present phase low low low maximum maximum press learn learn basis basis nonlinear abstract applied back find convergence convergence convergence likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due due positive procedure procedure procedure important important important important adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation context introduction hand hand hand behavior variance variance cost search search search search search tion tion variable assume assume assume assume learned chosen higher part part part part part previous cases type good good distributed expected expected make proposed correct observed observed observed observed errors minimum minimum minimum minimum minimum resulting resulting ing tasks human human regression regression regression computed computed respect respect sum sum eq eq eq eq eq eq called elements elements elements means optimization optimization potential potential global applications applications knowledge knowledge knowledge artificial true compared application application series series series define proc perform related constraints constraints distributions brain brain brain approaches mit contrast update train train descent descent dependent dependent selection report version version version consists individual individual individual represents difficult final final scheme directly directly additional view solutions solutions limit effects effects effects bit approximate free free world estimated increase randomly levels levels levels levels actual depends depends achieved measured normal normal fast fast limited close assumption predictions effective adaptation hypothesis noisy noisy noisy noisy noisy fit fit typically typically typically underlying combination combination combination combination technology technology transfer testing ratio mechanism uniform uniform uniform uniform uniform uniform principle leads leads leads leads leads representing making early early combined minimize minimize produced description architectures improve improve exact separate separate takes element typical typical reported introduced relevant engineering compare observations solve smooth achieve rl rl rl rl diagonal diagonal definition evaluation separation symmetric symmetric observation observation observation observation observation observation observation improvement parts parts lead concept invariant invariant invariant invariant invariant trial deviation predicted correctly locally runs strength minimal row depend measures measures clear moody practice propose propose propose propose propose external drawn drawn drawn regularization turn assuming decrease derivatives manner minima minima minima minima annealing pro written ways stability mathematical changing changing pruning pruning pruning pruning pruning pruning pruning infinite easy interaction interaction applying minimization minimization springer expectation choosing independently depending viewed evaluated evaluate evaluate understanding approximated approximated updates updates sign smoothing slow classical expansion expansion combining fitting add add penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty penalty advantages topology building building exploration includes priori batch batch determines characterized reason aspects identified maximal divided driven presentation presentation successful build build situation fine reached characteristic verlag procedures cun interested interpreted dis superior return return return return return return return follow vary write usual simplified simplified nips nips nips computes denker operating preferred approximating receive overfitting overfitting overfitting create hessian hessian giving tech project possibility combine relationships complicated tanh proved analogous analogous possibly perfect perfect implementations adjusted quantities assumes taylor taylor separated separated separated initialized consist consist generates improving explain residual residual residual residual residual advanced formula smoothness variances variances failure correction correction correction turns sections preprocessing forces forces bishop consequence potentially implicit implicit implicit fluctuations fluctuations explained solla variant compares psychological psychological outliers outliers operate berlin weigend aim incoming proven curvature curvature curvature curvature achieves asymmetric asymmetric enables germany germany germany neuro neuro neuro neuro returns damage damage damage simultaneous cumulative realized realized trade phenomenon phenomenon tresp newton newton corrupted corrupted benefit indices indices drift optimizing acts acts connecting adds allocation siemens siemens siemens siemens siemens analogy held hit hit nearby analyzing obd obd obd motivation elimination financial financial financial financial financial introduces introduces iteratively pruned realization forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting heart searching searching counter candidates april clean clean draw observer observer observer observer observer observer observer implicitly implicitly summarize influences market counts trading trading accumulated empty fitted informa dramatically unified unified unified unified unified constitute constitute achieving basically creates pieces quasi corrected additionally reports flat flat flat flat tendency german german rain var var var var var var var var clas continuity increment favor community schmidhuber alternate ization searches disadvantage concentrate emphasize individually cation supports tune increments increments increments corrections covers covers covers covers laws portfolio characterizing corporate corporate christopher european smoother december inclusion neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier identically resampling mistakes tribution month bond bond bond bond correctness correctness disturbance implied implied asset asset experienced profit reviewed reviewed reviewed jan violated shares regularizers favors sponsored preferable unifying eta eta eta eta eta cancel dilemma dilemma dilemma dilemma dilemma dilemma dilemma dilemma markets markets icann advice acceptance pushed gorithms miinchen standing canceling taught unimportant buy cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning cleaning expands zimmermann zimmermann zimmermann zimmermann zimmermann zimmermann zimmermann zimmermann zimmermann zimmermann zimmermann ralph handles tang cited awi finnoff finnoff hochreiter cleaned cleaned cleaned cleaned cleaned cleaned doubled assure hans favoring suppressing estimations cedure favored interac batches batches forecast forecast yearly clarendon memorize defects nonconvergent easiest mchp mchp quently subse vet forecasts georg georg awt awt awt awt sical collapses tricks iconip advisable sell disastrous allo eco prun rmeters 
#@Neuneier_R,Zimmermann_H,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural data function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure time time time time time time time set set set set set set set set networks networks networks algorithm algorithm number number number number number number number number system system system error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information information information problem problem models performance performance based based based based based based based based based based based based based based space space space space space case case case case case case case case case case vector vector vector order shown shown shown systems systems values values values values values values values values probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions distribution distribution distribution distribution method method method method method method method method approach approach approach approach single single single processing large large large large large large large test test optimal optimal optimal optimal optimal form shows shows simple simple paper paper paper paper paper paper size size work work methods methods methods methods cells step step step step step step step step process current current cell cell cell cell structure structure structure problems random random random random random high memory similar similar similar similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation show show show equation equation equation equation equation equation section section section section rule vectors general general general general general general generalization generalization parameter real approximation approximation approximation approximation approximation approximation average average states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states gradient gradient gradient term note note note note note note note experiments university university variables variables variables variables variables variables computation computation computation computation research research research dynamics dynamics dynamics dynamics constant table table estimate estimate estimate estimate estimate estimate standard standard standard standard computer computer terms terms science science science left direction presented present frequency machine machine machine machine maximum maximum learn learn learn components components abstract abstract applied find computational computational convergence density references component due due due procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important decision propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction introduction action action action action action action action action action complex hand hand hand estimation effect dynamic dynamic dynamic dynamic dynamic cost tion change change change change change change change change change change change change change change change change change change change change difference difference difference variable variable variable assume assume assume assume assume assume measure prior prior prior representations representations representations representations representations representations representations part previous previous bound bound bound bound cases cases cases cases good good binary represent bayesian bayesian bayesian bayesian bayesian expected expected expected expected expected markov probabilities probabilities probabilities probabilities observed errors scale finite resulting resulting ing total computed computed sum times mapping means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor made policy policy policy policy policy knowledge knowledge knowledge original artificial specific represented represented application application define compute compute proc proc proc perform perform perform goal goal related constraints gain approaches steps steps steps steps larger contrast update update update update update update update update update update update update update update update update update update report report loss consists advances joint scheme scheme addition graph graph graph graph graph graph graph framework computing computing computing computing domain domain domain equivalent experiment experiment experiment experiment experiment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment curve additional estimates estimates estimates estimates transition transition transition transition transition transition transition transition transition transition determine efficient upper upper upper upper requires requires requires requires approximate approximate approximate free world world estimated basic basic increase conditional conditional conditional conditional conditional conditional conditional bounds bounds bounds types product finally finally processes selected iteration depends simply simply discussion discussion discussion technical technical describe describe describe describe denote tested limited complete stable actions actions actions actions actions finding finding finding supported supported require main journal end ability future easily easily objective underlying needed needed combination programming programming programming special consistent consistent consistent consistent principle principle principle principle principle principle principle call call numbers iterations iterations max max max max max max max max max max max making making experts magnitude attention combined choose added description description description description architectures discussed recent similarity apply apply apply apply introduced strategy strategy strategy strategy strategy side side sense subset recently engineering compare achieve achieve sparse sparse evaluation generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized generalized bounded williams improvement improvement grant expression lead scaling locally loop loop setting runs valued depend depend reward reward reward reward reward reward reward reward reward reward differences designed clear sutton performs performs performs faster faster faster faster practice propose propose propose presence largest largest california intelligence intelligence labeled labeled assuming start start start iii introduce introduce introduce manner manner groups program question question denoted denoted denoted denoted denoted explicit explicit explicit explicit explicit explicit explicit explicit derive generating estimating estimating describes transitions transitions transitions transitions modeled recall recall metric explicitly explicitly infinite involves involves easy easy easy easy easy slightly unique integrated integrated applying agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent choosing national focus focus focus focus stages learner evaluate evaluate updated updated updated similarly converges updates updates updates updates updates updates updates past spectrum partial earlier reasonable performing performing performing performing classical classical spaces roughly add interpolation initially assigned assigned david avoid expect existing exploration exploration assignment assignment assignment assignment assignment recognize recognize determines maximize priors priors domains discussions planning planning planning planning straightforward straightforward straightforward straightforward middle computationally identify efficiently situation essentially essentially orthogonal reached reached receives capture refer compact compact compact compact notice conf conf conf procedures procedures procedures procedures procedures procedures procedures heuristic heuristic moore moore showing issue issue return lie notation notation notation quantity ill reach reach received received attempt moves policies approximating approximating approximating approximating acknowledgments deal deal receive receive receive extend extend extend situations situations parametric experience updating updating updating updating game preliminary mdp mdp hall fewer examine int int int combine combine working affect understand notion concepts changed changed thought friedman friedman friedman friedman versions greedy formal noted precise store extent simplest utility attempts attempts formula directed ground trivial crucial briefly berkeley berkeley arc division choices worst worst leaves desirable immediately involve author summation summation explained improvements reflect empirically amounts tional conducted parameterized atkeson marked marked marked variant rewards rewards execution execution execution exhibits aim suited inherent comments implements eventually baird specifies converged differentiable multidimensional extreme bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman benefit primarily primarily assign assign assign assign forming formally formally summing resources resources nonzero reaching dealing murphy adjusting simplify simplify multiplicative familiar intelligent keeping reasoning settings affected carry generalizes motivation reset ensures ensures negligible vertices captured entries claim claim approximators approximators approximators multiplied discounted discounted discounted reader record vertex horizon extends agree agree exploiting captures captures explains explains balancing generalizing generalizing generalizing approximator approximator parents parents executed assigns assigns mdps mdps counts counts counts counts speaking verify minus fellowship discount tables benefits dyna propagating instantiation arg ideally ideally tradeoff generalizations assignments assignments multinomial multinomial classic classic classic classic classic classic tor tight assess assess reconstruct representa principled visited acting queue queue queue perpendicular graduate execute relate lookup topic dirichlet dirichlet sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping sweeping maintains maintains grateful happen minor gordon gordon retained priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority priority increments computa november littman factored factored factored factored factored factored fortunately survey inconsistent marks maze maze maze jointly locate utilizes prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized prioritized russell supplied visit val val val val val tuple beneficial triangulation raises arrives exploits exploits kaelbling factorization differentiate sweep enforces sparseness defense acyclic dean probabil costly pact microsoft tutorial aims observes parr parr parr parr parr examines ities pursued pay pri pri pri pri ronald heckerman roots pal pal pal pal pal pal pal pal pal pal stuart dbn dbn dbn dbn dbn dbn dbn dbn dbn dbn fragment persistence independencies independencies independencies independencies imperfect unrealistic resort succeed revised geoff reachable davies overestimate overestimate lea spend reacting kevin envi propagations propagations propagations maxa maxa maxa maxa aro resets northeastern anticipated discrepancies discrepancies ronment violating soda refines spending spending thirdly msr kanazawa afford nir nir flag flag daah boltzman recompute muri enumerate interleaves burdensome repaired 
#@Andre_D,Friedman_N,Parr_R,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input data data data data data data data data function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time set set set set set training training algorithm output output number system system system error error error error state state state state state information information information problem problem models models models models models models models models models models models models performance based based based based based based based based based based based based based based based based based based space linear order shown systems systems systems systems values values parameters noise noise functions functions method method method method method method approach approach approach approach approach point point point point point processing processing processing control control control control control control control control control control control control control control control large large local local local local local local local local local local local local local local local local local local local local local local local local local local local optimal optimal optimal optimal optimal form signal signal algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper small feature work work work work work work task task task task task task task task task task task methods methods fig cells step step step step points points points process process process process process level current current current current current cell cell structure structure problems problems high response architecture show equation equation section line general parameter real theory gradient term dimensional university solution solution solution research independent independent found found found dynamics dynamics dynamics dynamics dynamics initial initial constant constant estimate estimate computer computer terms terms terms distance prediction prediction phase phase machine machine motion motion motion motion press press press press learn learn learn learn learn position position position position position components basis nonlinear sample abstract applied find find find computational references ieee ieee adaptive introduction complex hand hand hand hand hand hand hand hand hand hand hand behavior behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic cost cost cost cost cost cost tion difference complexity signals learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen type type required required required represent represent represent make make make techniques observed observed errors errors errors forward forward ing ing ing human human human human human human human human regression eq reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement optimization optimization optimization optimization optimization made feedback global global study policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge original original artificial artificial artificial artificial represented represented true application cross cross provide perform goal goal approaches mit support modeling modeling modeling modeling modeling modeling modeling modeling morgan morgan morgan proceedings proceedings institute implementation version technique advances advances joint difficult difficult difficult bias graph cambridge cambridge computing estimates estimates trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory san san san conference efficient efficient full full requires free speed vision pages pages pages pages pages increase validation validation con produce produce produce produce produce condition weighted weighted weighted weighted weighted developed robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot criterion criterion criterion criterion velocity lines actual actual iteration constraint constraint discussion fast finding finding finding amount amount amount amount implemented assumed role require require journal end end future degree degree kaufmann kaufmann kaufmann simulated fully fully fully fully jordan technology programming programming programming programming programming programming programming programming programming programming programming programming programming programming york consistent consistent consistent consistent consistent consistent consistent consistent consistent trials trials trials trials database database mode representing direct direct direct direct stored international international international early early early magnitude minimize minimize predict architectures discussed exact advantage movement movement movement apply apply include quadratic quadratic hierarchical axis axis correspond differential differential differential differential differential differential grid williams entire arm arm arm arm arm constructed constructed constructed horizontal trial trial trial trial trial derivative locally locally locally locally locally locally locally move conclusion starting starting reduce trajectories trajectories trajectories trajectories trajectories trajectories editors editors reward reward reward interactions differences accurate numerical sutton sutton sutton sutton sutton sutton sutton practice mateo mateo mateo hard mechanisms integration integration demonstrated intelligence intelligence intelligence intelligence minimizing minimizing relationship introduce derivatives derivatives configuration explicit explicit derive longer index describes describes describes tuned vertical vertical changing segments segments modeled confidence confidence confidence confidence confidence explicitly easy angle unique interaction integrated integrated integrated adding applying focus review review stages stages stages learner controlled controlled soft reasonable barto barto barto dashed reduces reduces penalty initially calculate calculate query query avoid avoid exploration figures priori usa mozer holds neighbors neighbors structural successfully planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning reason effectively effectively successful build traditional traditional compact quickly strongly moore moore moore follow follow sampled vary backward automatically attempt attempt policies policies subsequent approximating neighboring neighboring tesauro cowan command parametric parametric parametric singh difficulty difficulty humans optimized optimized optimized optimized accurately hessian dotted ml reducing respond history history incremental maximizing maximizing workshop workshop affect fundamental act predicting spline spline changed obvious observe academic message generates generates extent attempts plant seconds integrate unstable answer reasons producing forces choices located separately separately separately angles optimize integrating integrating integrating integrating reflects reflects apparent people people people greatly collected collected consistency consistency consistency lack cohen cohen cohen cohen atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson atkeson splines splines splines compares http http http http price gains gains fall cal plan plan plan plan plan kinds deviations deviations pole globally bellman benefit college aligned notes www modify japan angular angular velocities repre establish fails convenient minutes tools attractive intelligent balance balance resulted symposium nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric exploring exploring alspector ranging demonstration demonstration demonstration demonstration demonstration demonstration demonstration demonstration stereo initialize pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum balancing balancing pen balanced balanced executed ics metrics liu liu ure indirect failed failed failed dyna alter mismatch favor continues graphics inverted lookup interactive meta enforce maintains son elsevier bradtke amplification amplification ignoring atr atr aaai worked littman chris opti opti opti survey inconsistent inconsistent inconsistent inconsistent christopher spring ers focuses played dom disturbances schaal schaal schaal schaal schaal schaal schaal petsche wavelets swing swing swing swing swing swing swing swing archi html html cur ignores kaelbling kaelbling upright hinge cho planner planner planner planner planner planner planner planner magazine magazine vicinity tra stabilize focusing inaccurate inaccurate penalizes eighth backwards rotational rent fore dyer dyer dyer aggregate cations enforcing mization mization mization obeys sentations ton ton plans plans plans availability tics animation terminated fac gun seeks inconsistency inconsistency inconsistency inconsistency knot knot knot kyoto idealized seventh namic fulfill fingers chine succeeded ner rotates publications publications publications soraku checking imitate powell obeying obeying recipes atlanta parameterize teukolsky reacting reacting insignificant planned actuator flannery amplify umass umass umass swinging georgia gatech gatech sut sut accelerations tectures hikaridai vetterling bulletin slowed ineffective demonstrations demonstrations amplifies mcreynolds mcreynolds mcreynolds sistent siggraph optimizers optimizers optimizers optimizers imitation imitation imitation rea halfway cga modifi sonable commanded multaneously swings repeatable characteris jectory curate oscillated 
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#*learning learning model model function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time time set set set set set set set set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information information information information information information information information information information information information information problem problem problem problem models models hidden performance performance performance performance performance based based based space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown shown systems values values probability probability probability probability probability parameters unit method approach approach point point point single single control control control control rate test optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows shows shows shows shows shows shows algorithms algorithms algorithms simple simple simple simple simple paper paper paper paper paper examples work work work step step step step step step step step step step step step step step step step step process process current problems problems high memory representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show show show show show show show show show equation equation equation section section section vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors generalization average states states states states states states states states states states states theory note dimensional dimensional dimensional result result university university university university research research research defined found found initial initial initial standard standard standard standard computer computer computer science science science science science left presented map low low machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine maximum range continuous continuous abstract applied back find find computational computational convergence convergence references stochastic important important decision decision decision decision decision decision decision decision decision introduction action action action action action action action action action action action action action action behavior dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated change change change complexity complexity complexity assume representations representations part theorem theorem theorem good long represent represent represent expected expected expected expected equations equations markov markov markov markov markov markov markov markov markov markov markov markov fact fact region region probabilities probabilities probabilities probabilities probabilities observed observed observed observed observed finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite total computed computed called times times times regions regions mapping mapping mapping reinforcement reinforcement factor factor factor potential made made policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy original represented represented represented represented represented represented represented represented represented represented compared compared define compute proc proc perform determined determined discrete equal equal equal comparison comparison update update update update update update update update update update update update support selection report department department department implementation version version version version represents represents represents difficult difficult difficult ai ai ai framework computing equivalent equivalent equivalent directly transition transition transition efficient efficient efficient choice choice choice choice con con con condition developed developed controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller product product product product product provided processes processes processes processes processes processes processes iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration simply simply measured discussion technical increases describe denote denote denote denote denote transformation transformation transformation transformation fast close corresponds corresponds corresponds corresponds corresponds actions actions actions actions actions proof proof proof finding generate easily makes makes makes makes makes makes makes objective needed jordan jordan programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming testing significantly representing iterations iterations iterations iterations making making polynomial combined run added added added denotes denotes denotes improved improved improved improved improved improved improved improved improved improved improved improved improved improved exact exact exact advantage advantage advantage reported practical strategy period recently engineering sufficient sufficient observations observations observations approximately calculated solve match match correspond converge trans background evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation observation observation observation observation improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement studied suggests deterministic deterministic boundary runs starting starting minimal greater reward reward reward reward bayes clear performs exponential faster faster faster faster practice demonstrated labeled labeled assuming relationship iii denoted acknowledgements appears appears index index solving solving solving solving describes ann pruning implement implement implement implement implement implement infinite infinite infinite infinite infinite infinite infinite electrical transformations easy easy easy easy agent agent select national national independently formation stationary stationary interpretation solved transform transform operations operations operations updated updated updated updated sizes completely completely completely converges converges updates updates updates key key earlier dashed dashed dashed dashed performing performing convex convex convex convex convex convex convex convex convex convex add calculate foundation includes thesis thesis uncertainty maximize domains partially partially partially partially partially partially partially partially partially partially partially partially partially partially partially discussions successfully planning straightforward straightforward straightforward straightforward straightforward closely computationally computationally detect efficiently ten ten receives conf conf interpreted interpreted interpreted interpreted stopping contribution michael simplified nips observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable computes policies illustrates subsequent satisfies simpler transformed transformed transformed transformed transformed create create singh singh experience preliminary mdp mdp helpful fewer history links links links links links links incremental complicated proved understand circles circles circles circles math necessarily extremely illustrate changed changed changed algo detected detected arbitrarily phd phd finds finds defines massachusetts massachusetts brown residual residual preference preference preference preference preference piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise inequality theoretic costs expensive expensive expensive briefly stanford easier organized choices worst mation recognized describing annual lack lack detecting compares controllers controllers rely summarized limiting substantial jaakkola jaakkola converged consistently consistently consistently bellman bellman feasible feasible optimality optimality optimality optimality optimality optimality optimality rithm linearity nat significance difficulties pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp transforms transforms star canonical canonical optimally combinatorial infor started sion zhang zhang pruned pruned chooses dif discounted discounted discounted theoretically horizon horizon horizon horizon horizon horizon horizon horizon horizon implicitly implicitly grants explains market market executed mdps mdps mdps mdps mdps unchanged unchanged pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps outperforms outperforms outperforms maintaining arcs discount discount suboptimal arg preferences preferences amherst amherst reports reports reports hundred avoided eric avoids acting summarizes pij management execute dominated scope statistic iri iri speedup speedup alternatives hansen hansen hansen hansen hansen hansen hansen hansen isi admissible simplex bring littman littman littman littman littman littman littman simplification survey preserves preserves impractical influenced suite termination inequalities dominates dominates dominates dominates dominates continuum exploits fastest company kaelbling kaelbling presently presently hinge gence profit ranged lar successor successor successor successor successor successor successor successor successor prune indi converts converts omit observes optimizes dominate reviews modifies conceptually conver translating sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik sondik ies convexity polyhedral geometrically bears particu iai imperfect imperfect invoked pointwise pointwise pointwise pointwise pointwise pointwise pointwise reachable reachable restricts concludes cassandra cassandra cassandra cassandra cassandra timal duplicate duplicate duplicate duplicate duplicate duplicate cated umass dominating troller troller neces discus exit fifteen clearer duplicates duplicates duplicates consumer consumer consumer verge blackwell blackwell blackwell ural revising mber recast 
#@Hansen_E,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model input function function function function function function function function function figure figure figure time time time time time time time time time time time time time time time set set set set training training training training training training training training training algorithm algorithm algorithm algorithm number number number system system system system system system system system system system system system system system system system system system system system system system system system system system error state state state state state state state state state state state state state state results results results results results results results results problem problem problem problem problem problem problem problem problem problem problem models performance performance performance weights weights weights weights weights weights linear linear linear linear case case vector vector vector vector systems values values values values parameters parameters parameters parameters functions functions point single single single control control control control control control control control control control control control control control control control control large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test analysis optimal optimal optimal optimal inputs inputs inputs inputs inputs form form form shows shows shows shows algorithms algorithms algorithms algorithms simple small feature feature work methods fig fig step step points features features features features process process process process level level level level level problems random random random high high high high response response response similar fixed rule general parameter real real approximation approximation approximation states states states states theory gradient gradient gradient gradient obtained obtained obtained term experiments experiments experiments experiments experiments experiments experiments result result result result university variables variables variables variables computation solution research defined found dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial initial constant standard computer computer terms science left present machine motion maximum maximum maximum maximum range range range range range range range learn learn position nonlinear nonlinear nonlinear nonlinear continuous abstract applied applied applied references component positive positive positive positive positive adaptive introduction action action action action action action action action action parallel tion learned learned learned learned learned learned learned chosen chosen chosen center previous theorem cases cases cases cases required required required conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions distributed techniques region region region region region region observed scale scale minimum minimum minimum minimum minimum ing total total total simulation simulation simulation simulation simulation simulation simulation multi multi performed eq eq called times times times times means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor made orientation orientation global policy policy policy policy policy policy policy policy policy policy policy policy policy policy negative negative original represented true application desired desired desired cross cross provide define determined goal goal goal goal goal goal goal goal goal goal goal constraints constraints constraints constraints constraints constraints constraints gain discrete discrete equal larger larger update update update descent descent dependent dependent morgan proceedings report report report department loss loss version responses responses responses difficult difficult final bias addition sequences maps considered considered domain domain domain experiment additional additional additional additional transition transition san effects conference requires choice significant approximate approximate approximate speed con con produce produce produce condition condition derived velocity controller controller controller controller controller selected selected selected constraint constraint achieved achieved achieved normal normal normal normal normal normal normal technical technical describe arbitrary arbitrary limited limited close complete stable actions actions short implemented implemented supported eds degree degree development including including kaufmann simulated simulated simulated simulated simulated simulated needed combination dynamical jordan jordan programming significantly york special consistent consistent mode details pre pre direct direct international normalized early magnitude magnitude attention combined run improved improved discussed improve advantage advantage advantage advantage advantage advantage advantage advantage robust reported lateral include quadratic relevant relevant interest sufficient highly previously previously previously approximately approximately approximately approximately approximately approximately axis axis axis axis axis axis axis axis axis axis axis axis tions tions correspond achieve rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl address definition evaluation symmetric modified generalized bounded sensitive increased amplitude concept trial alternative loop loop loop occurs boundary column pass demonstrate demonstrate conclusion place place designed designed sutton faster constrained constrained suggest presence cycle minimizing decrease relationship derivatives derivatives derivatives program force force longer longer solving laboratory transitions transitions stability stability stability vertical modeled modeled simultaneously physical slightly angle angle angle angle angle angle angle angle develop develop applying agent agent agent agent agent agent agent versus yield choosing extracted variation evaluated evaluated restricted restricted updated showed forms approximated updates calculation barto barto barto barto barto performing sec sec sec sec sec sec sec boundaries tracking tracking initially david coupling coupling avoid avoid building building exploration formulation formulation sciences extension candidate variations phys successfully successfully reason capable uniformly suitable effectively successful reached summary criteria strategies satisfy notation absence providing minimizes reach consisted consisted policies policies subsequent subsequent subsequent approximating acknowledgments software software software law body body body body body body body body employed command command wiley collection experience experience experience rapidly involving involving integral preliminary scalar tech authors authors proved opposite ensure noted freedom attempts massachusetts residual residual residual residual residual residual ment directed directed ground ground ground ground ground ground trivial distinguish orientations orientations orientations orientations majority caused straight straight straight straight straight sys satisfied satisfied closer division division incorporate worst controls controls controls controls controls mathematics angles pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch pitch outer outer robustness apparent greatly limits limits limits limits transient pseudo pseudo tional tional axes axes axes axes axes axes axes axes axes axes conducted readily formulated rep rewards commands commands commands commands requirement execution execution summarized mod perturbations limiting qualitatively substantial substantial asymmetric asymmetric kinds chose focused focused baird baird baird baird baird traces traces trade consistently consistently primarily accomplished extensive extensive extensive martin appropriately recover recover recover recover approximates purely tem naval air air convenient promising satisfying satisfying alpha imposed vehicle contract contract removing monotonically responsible hours hours meaningful started mance reset recovered governed encountered expanded expanded expanded conjunction enhance nonlinearities recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery barron barron barron barron francisco deg deg deg deg deg deg deg deg deg deg deg express express suggesting tracker augmented rich sons designing valuable tures avoiding automated automated automated automated automated automated automated vari executed executed outlined andrew maintaining maintaining appeared converted vec discount aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft formulate formulate restrictions medium medium exception causing acceptable acceptable amherst acceleration acceleration acceleration acceleration acceleration acceleration acceleration acceleration acceleration acceleration acceleration acceleration tor workstation workstation formance mathematically maintained execute inverted inverted afosr challenging efforts efforts exceed proach unconstrained unconstrained unconstrained unconstrained unconstrained associates associates associates nonetheless accounted fea admissible investigations flight flight flight flight flight flight flight flight flight flight flight flight flight flight modifiable bring bring ward ward ward ward ward ward worked vice reinforce versa demand monitor continued attributed water oscillate suite suite outperformed russell supplied condi condi station station station station station station incorporation episodes meeting contributes corrective corrective scenarios scenarios elevator counterpart feasibility fidelity fidelity fidelity fidelity resultant signed compromise stick stick stick stick stick stick stick stick stick stick stick mach successor platform ated rotational allowable allowable allowable deciding atlas ming col sented addi repeating imposes histories histories histories stabilizing stabilizing pull manager ables approxima bird availability sible wright nonlinearly translational translational effector effector effector effector effector effector ily ously corresponded corresponded penalties inadequate inadequate inadequate mature successes lock descriptive nose attitude attitude attitude owing owing qualities earth formulating attack attack attack emerging safety sensitivities conducting occasional buckingham attain attain theta pilot pilot pilot pilot pilot pilot pilot trim trim trim trim trim trim trim trim trim trim trim trim roll twelfth depended indefinitely indefinitely lea associ coordinated disabled bringing actuator actuator actuator actuator fined inertial inertial inertial pol jeffrey displacements ditions ditions umass longitudinal longitudinal longitudinal longitudinal longitudinal longitudinal longitudinal accelerations remedy remedy harmon harmon harmon harmon dictates wished severity descend injury drastic principally principally afforded strike strike expe interfaced sired vantage aero falsely hitting simultane actu icy marc collapses dimensionless flying fects commanded commanded chief unperturbed mand stricted tactical tolerances climb ator handful excursions rad gion aforementioned satis heed forgets adhere adhering excursion eled umn fying 
#@Barto_A,Monaco_J,Ward_D,
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#*learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model function function function function function function function figure figure figure time time time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system system error state state state state state state state state state state state state state state state state state state state state information problem problem models based based based based based based space space space space space case case case case case case order order order order probability probability method method method method approach point point point control control control control control control control control control control control control control control control control control control control large local class matrix matrix matrix optimal optimal optimal optimal optimal optimal signal algorithms paper paper work methods step step points process current current problems problems problems problems problems problems problems problems problems random equation equation equation equation equation equation equation equation equation section section fixed line line rule rule rule rule real approximation approximation approximation states states states states gradient gradient obtained obtained result university solution solution solution defined target dynamics dynamics dynamics dynamics dynamics initial initial initial constant constant motion motion motion learn basis nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract back back find convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due positive positive positive positive decision introduction estimation estimation dynamic dynamic dynamic difference difference difference difference difference difference difference assume assume assume assume assume assume lower part theorem theorem theorem theorem theorem theorem bound conditions conditions equations markov fact probabilities probabilities forward finite finite finite finite finite finite ing called called reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor optimization optimization dimension applications policy obtain obtain negative artificial artificial samples true compared series define define compute proc update update joint scheme scheme scheme scheme scheme scheme scheme scheme scheme scheme ai cambridge equivalent solutions solutions transition trajectory trajectory trajectory trajectory trajectory trajectory stage stage upper approximate free free con con con condition condition condition condition condition condition derived bounds processes processes processes processes iteration depends covariance denote denote proof square hypothesis future noisy including objective dynamical functional functional unknown unknown programming programming interesting york principle leads iterations max max international property property property property property strategy sense subset subset relevant sufficient sufficient differential differential differential rl rl rl rl rl rl rl rl rl definition bounded bounded exists exists exists exists exists exists parts wide feed feed deterministic deterministic boundary boundary boundary boundary boundary conclusion starting trajectories trajectories trajectories reward numerical learns propose propose propose intelligence intelligence variety min derivatives program suppose suppose suppose suppose appears appears solving generating estimating unique springer springer springer expectation influence open controlled controlled updated updated updated updated updated updated evolution approximated approximated approximated converges constants partial barto precision building exploration thesis prove prove prove holds holds uniformly uniformly maximal compact verlag verlag verlag running hold hold backward delayed ill satisfies satisfies presents law law singh updating updating updating hall successive successive successive proved act closest integer taylor generates motivated phd asynchronous adjacent diffusion diffusion diffusion diffusion reasons satisfied satisfied formalism mation watkins mathematics fluctuations prop peter dots lim differentiable cumulative bellman bellman bellman bellman drift linearity approximates approximates concerned overcome replacing replacing synchronous adequate inferior prentice appendix appendix paul infinity infinity diameter discounted thin contraction designing convergent convergent convergent convergent convergent integers bertsekas andrew discount discount ber markovian incrementally arg aij possibilities rain approxi france france discretization discretization siam knowing bradtke round gauss remark remark covers discretized christopher hamilton hamilton hamilton hamilton steven poly neighbourhood neighbourhood convention transpose hits ference neigh lipschitz satinder deduce deduce deduce hjb hjb tinuous tinuous stays aii regularly jacobi jacobi jacobi jacobi cedex cedex kushner kushner brownian brownian viscosity insures insures bet bers ffi deduced lattices viability kom sts occured hnear exit exit lent ction fied frontier frontier parabolic usu probab occurence ecole sto eel erty war merical learnin lake seidel satis satis parc 
#@Bourgine_P,Munos_R,
#t11
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural data data function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set algorithm algorithm algorithm number system system system system system system system system error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state results results information information information information problem problem problem problem problem models based space space space space space space space space space space space space space space space space space space linear linear case case vector order shown shown shown shown shown shown systems systems systems systems values values values values values values values functions functions functions functions method method method approach approach point point point point processing control control control control control control control control control large large large large large large large large large large local local local local local local local local local rate rate analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form shows shows algorithms algorithms simple simple examples small small size size size size work work work methods methods methods methods methods methods step step step step step step step points points points process current current current current current problems problems problems problems problems problems problems problems problems random high high high memory similar similar show equation equation equation equation equation equation equation equation equation fixed fixed fixed parameter approximation approximation approximation approximation approximation approximation approximation approximation states states theory result solution solution solution defined initial constant constant constant constant constant constant constant constant constant constant estimate estimate computer computer terms distance machine press learn continuous continuous continuous continuous sample abstract applied applied applied find convergence convergence references due due due procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction action estimation estimation cost cost cost cost cost cost cost cost tion tion tion variable assume assume assume chosen chosen higher cases conditions equations equations equations make make make region region observed finite simulations ing ing computed respect respect multi multi performed performed performed performed performed performed called elements regions regions regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor dimension made global knowledge obtain vol vol application series provide define define compute compute compute rates rates rates rates goal goal discrete discrete discrete discrete discrete discrete discrete mit steps accuracy accuracy accuracy accuracy update update update update update update update update update update update update update update update update update update dependent implementation advances difficult difficult scheme ai considered cambridge additional solutions solutions solutions estimates estimates estimates trajectory trajectory trajectory trajectory effects effects choice choice choice choice choice choice choice approximate approximate approximate approximate speed con con produce criterion criterion criterion criterion criterion bounds controller processes iteration iteration iteration depends depends depends sampling discussion fast close corresponds stable theoretical end future future future smaller needed needed combination functional functional functional fully fully fully fully fully ratio ratio ratio ratio ratio ratio mechanism mechanism consistent call max stored stored stored early polynomial combined minimize choose denotes resolution resolution takes apply apply period side side dimensions dimensions volume volume tuning yields differential differential differential differential achieve grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid grid bounded bounded bounded bounded interval storage constructed concept trial trial correctly locally locally locally locally locally locally locally locally locally touretzky loop deterministic deterministic boundary demonstrate demonstrate starting starting starting place conclusions depend editors numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical suggest propose propose turn minimizing minimizing start start start min min suppose relation produces ways infinite infinite implies depending depending stationary stationary solved open controlled showed approximations approximated approximated approximated sizes constants updates past reasonable reasonable performing spaces neighborhood neighborhood intermediate intermediate intermediate intermediate calculate sufficiently sufficiently norm degrees coupling thesis eigenvalues mozer holds regular middle middle middle schemes schemes schemes schemes schemes fine fine fine moore dis dis follow hold hold ill automatically subsequent subsequent receive experience updating involving integral game game investigated combine smallest smallest math coarse naturally closest adjusted der der obvious algo assumes taylor store store arbitrarily arbitrarily explain phd defines ment inequality crucial crucial distinguish improves adjacent adjacent adjacent diffusion diffusion reasons comparisons tive choices desirable arise controls controls ion ion calculations depicted depicted depicted argument varies considerably considerably considerably consistency consistency consistency atkeson proven proven serve prevent gave germany tolerance tolerance eventually eventually semantic multidimensional globally bellman bellman bellman bellman bellman bellman bellman bellman picture picture picture picture picture ordinary ordinary optimality equivalence rithm arguments resources rotated robotics difficulties vertices vertices vertices vertices vertices infinity uni hasselmo viewing waves waves discounted discounted insight indicator contraction vertex vertex vertex draw horizon horizon impact inf dense posteriori posteriori shorter opposed suboptimal suboptimal regularity regularity big big big big reflected rectangular dominated ization depicts ambiguous refinement refinement refinement refinement refinement refinement refinement refinement refinement discretization discretization discretization discretization discretization discretization discretization discretization discretization discretization discretization discretization discretization discretization discretization universit esti simplex simplex simplex simplex simplex simplex simplex simplex refined refined refined holding challenge worked lation handling handling resolve discontinuous discontinuous cornput hamilton hamilton pictures triangles triangles measurable triangulation triangulation triangulation triangulation trol grids ultimate ory appl sweep iterate iterate mesh unnecessary refine refine refine refine refine winners dist linearities drawbacks yon stand lipschitz lipschitz inserting conveyed visits jumps adap mate ages posterjori aware constantly constantly kronecker kronecker kronecker kronecker resolving bigger jacobi jacobi rtdp stant steer cre eps depended requested christian imal assets timal timal effec maxa kiel kiel kiel kiel refinements ain friction creases mina mina recherche coordi differen cer ries dry finest finest istic determin ime ime ime nates refines programme caught truncation uncontrolled righ advisable resolu tol hese stiff 
#@Pareigis_S,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural neural function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm number number number number system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results information information information information problem problem problem problem problem problem problem problem problem problem models models performance performance performance performance based based based based space space space space space space space linear order shown shown shown systems systems systems systems systems values probability functions method method method approach approach approach approach approach approach approach approach approach approach approach point point point point point point point point point single single processing processing processing control control control control control control control control control large rate analysis class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form shows shows signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper paper paper paper paper size size work work work task task methods methods methods methods methods methods methods methods methods points points points features process process process process process process process level level level level level level level level level level current current current structure structure structure structure problems problems problems problems high high high similar architecture architecture show section section section fixed general general general generalization generalization parameter parameter parameter real real real real approximation approximation average states states states states states states states states states states states states states states states states states states states states states states states states states states gradient note experiments activity university university university university computation computation solution solution solution solution solution solution research research research defined defined defined initial initial initial initial initial initial table standard standard standard standard computer computer computer computer science science science science left left left left direction direction direction direction direction direction direction direction presented present present present phase low temporal temporal temporal machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine range range press press press learn learn learn basis continuous sample sample abstract abstract abstract abstract abstract abstract abstract applied applied applied applied applied back back find find find find convergence convergence references component component component component component component stochastic stochastic stochastic stochastic ieee important decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision context introduction action action action action action action action action action complex complex hand behavior behavior behavior behavior dynamic parallel parallel cost search search tion change complexity complexity complexity complexity variable assume assume lower lower lower measure prior prior prior learned chosen higher part previous previous previous previous previous previous theorem theorem theorem theorem theorem theorem cases cases required required required good long tree distributed expected expected expected expected markov markov markov markov markov markov markov markov markov markov markov markov make make techniques techniques techniques proposed proposed probabilities probabilities observed forward finite finite finite resulting ing ing tasks total total human respect multi called called regions mapping mapping means means means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor made natural natural applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge knowledge knowledge knowledge knowledge obtain original original original original original original artificial artificial artificial specific represented true true application application desired cross provide provide objects rates proc proc proc proc proc determined experimental goal related related constraints constraints constraints constraints constraints constraints constraints constraints power approaches approaches approaches approaches approaches approaches approaches approaches approaches mit mit steps steps larger larger update update morgan morgan morgan morgan morgan proceedings report department department department loss version code advances joint represents represents difficult scheme scheme graph sequences sequences maps considered considered considered framework framework framework cambridge computing computing domain domain equivalent equivalent environment environment environment environment environment environment environment environment environment environment environment environment environment environment directly directly directly hinton hinton solutions solutions solutions solutions curves design transition transition transition transition transition transition transition transition transition san top top top effects conference conference conference conference conference determine efficient upper choice choice choice choice choice choice choice choice choice choice choice choice choice choice choice choice choice choice choice choice choice significant significant significant world world basic basic give produce produce robot levels levels levels criterion controller types lines product actual actual provided processes processes processes processes processes iteration iteration iteration iteration constraint achieved achieved achieved discussion technical transformation transformation transformation transformation close inverse assumption corresponds complete complete surface actions actions actions actions actions actions actions actions actions actions proof proof proof amount short generate supported require require journal end future including kaufmann kaufmann kaufmann kaufmann typically typically pairs pairs reduced reduced fully jordan jordan transfer programming mechanism consistent consistent consistent consistent consistent language language language language language leads call call call call iterations iterations iterations making making making making making making making international decay decay idea idea combined combined choose choose description description description description directions resolution advantage property property property pair robust takes element element typical typical movement apply apply apply apply apply introduced strategy moving moving subject machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical varying approximately volume axis tions solve yields converge achieve rl rl rl organization organization entire grant exists exists exists exists scaling extended extended extended extended move move move touretzky deterministic clusters generally demonstrate demonstrate runs runs greater greater reduce reduce reduce reduce reduce conclusions valued valued valued editors editors editors reward reward reward reward reward reward reward accurate numerical sutton sutton sutton sutton exponential faster faster faster faster learns learns constrained mateo temperature encoding hard hard reduction demonstrated california intelligence intelligence intelligence intelligence variety start start start relationship averaged introduce program program explicit appears construct produces produces solving solving solving sequential describes describes transitions transitions transitions distinct distinct explicitly infinite involves scales integrated applying applying applying events events springer agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent versus select yield yield choosing focus focus expressed review review squares lemma lemma lemma lemma variation open showed lee decomposition decomposition decomposition decomposition decomposition decomposition soft understanding activities activities activities activities completely converges partition updates partial partial partial partial partial performing classical reduces roughly add iterative intermediate initially assigned construction construction expect exploration exploration exploration thesis thesis priori coordinate blind determines determines determines prove coupled domains domains domains domains domains partially partially partially partially planning planning planning planning planning planning planning reason selecting selecting suitable effectively effectively effectively successful successful identify detect efficiently orthogonal reached reached verlag kind induced induced induced induced induced induced induced induced link showing showing return return follow follow follow strategies strategies satisfy simplified simplified dayan dayan generalize paradigm providing providing giles observable observable observable leading reach reach received attempt moves policies policies policies policies policies policies policies policies operating tesauro extend cowan unlike layered layered layered transformed transformed transformed access access singh singh singh singh singh environments detail replaced hanson divergence mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp hall pursuit reducing reducing behavioral investigated decisions complicated complicated oscillation hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy cover analogous removed naturally concepts created equally equally quantities formal assumes consist phd phd defines seconds seconds seconds massachusetts brown stop directed directed directed track defining navigation navigation navigation navigation adjacent lin lin lin lin lin berkeley berkeley purposes closer easier organized style division choices choices ran begin mellon requiring reflects improvements behaviors carnegie autonomous effort incorporated treated compares rewards execution execution controllers pittsburgh aim maximizes adjust plan plan plan logical semi conclude implements begins begins begins jaakkola specifies specifies traces calls calls leen intractable feasible appearance optimality formally oxford oxford temporally temporally circular mobile discover eliminate robotics reaching kaufman consideration simplify city familiar primitive primitive primitive primitive intelligent intelligent efficacy observing reasoning roles north north effectiveness symposium generalizes obstacle obstacle obstacle obstacle obstacle obstacle obstacle prentice contexts ranging programs programs guarantees guarantees intended colorado thomas enable discounted omitted reader repeatedly specificity ends canada passing horizon extends inductive tsitsiklis tsitsiklis exploiting dietterich dietterich intersection intersection avoiding convergent executed assigns mdps mdps mdps mdps mdps mdps accumulated bertsekas bertsekas treat divide divide speaking leaving specification constitute basically discount discount discount discount discount equivalently leaming leaming leaming leaming july july obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles obstacles suboptimal theorems abstraction flat hierarchies hierarchies hierarchies hierarchies hierarchies descriptions descriptions certainty principled acting perpendicular distri robots wall wall wall impose execute execute uncertain topic speedup speedup sketch sketch library indexed eligibility sonar sonar sonar enforce maintains denver preserve confusion thousands modifiable bradtke bradtke permit permit dramatic things october oregon oregon strict november elemental bution fortunately stephen handling august august corners decided thousand ongoing ongoing designs designs agents agents agents jersey cliffs virtually establishes december loosely russell russell russell russell russell concrete executing executing tuple proposes englewood automation detects detects ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham ham concave establishing aggregation aggregation aggregation aggregation constraining constraining amenable amenable amenable planner comer closure enters maxq dean dean dean tens tens montreal jose violate jack unifying unifying transferred precup nondeterministic nondeterministic macro parr parr parr parr parr hong reactive reactive treats respects albeit reminiscent ninth quarter duff duff wired ronald seemingly rendered provably brooks brooks brooks stuart permitted providence providence expressing embodied calling spheres illustrative invoked lend pennsylvania michie informal abstractions reachable reachable feudal feudal twelfth badly traversing walls traced manage decoupled disparate interacts constrains cies composing reacting intersections intersections nilsson nilsson pursuing tractability aro opportunities methodologies accelerating hsu hsu benson benson descrip succeeds conquer conquer carolina runtime abbreviated fourteenth navigating invoke caution traverse attacked grace matically unnecessarily lnt lnt lnt halt island island waste transferring encounters decoupling subroutine hitherto synthesizing furukawa women rhode rhode provision dra daah thirteenth tate hier boltzman subproblems dictate corvallis recombined muri 
#@Parr_R,Russell_S,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input data function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set networks algorithm algorithm algorithm system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models based based based based based based based space space weights weights weights weights weights linear case case case vector vector vector vector vector order order order order shown systems values values values values values values values probability probability probability weight weight weight functions functions functions functions functions functions functions unit distribution method approach approach approach point point single single processing control control control control control control control rate class matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal form form form form form form form shows paper paper paper paper paper paper paper work work work work work task task cells step step step step step step step step step step step step step step step step step step step step step step step step step process level level level level current current cell cell cell cell cell structure problems random random random random response show equation equation equation equation section section vectors vectors general general general general general general general general generalization parameter parameter parameter parameter real real average states states states states states states states states states states states states states states states states states states theory theory result result result university university variables variables variables computation solution research defined defined defined defined sequence sequence target target initial standard standard terms science prediction prediction prediction prediction left direction presented presented present temporal temporal temporal temporal temporal machine machine machine machine machine object press learn learn learn position components components basis basis abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract abstract applied properties properties references component component component stochastic stochastic due due positive adaptive decision decision decision propagation mixture mixture mixture mixture mixture mixture introduction action action action action action action action action action action action action action action action action action behavior behavior behavior effect parallel tion difference complexity variable assume measure prior prior prior learned learned chosen higher higher part previous previous required multiple multiple good long long long represent represent represent expected expected equations equations equations equations equations equations markov markov markov make make fact probabilities probabilities forward scale finite resulting classes ing tasks respect respect multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi performed called called called called times times elements mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor potential natural policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy obtain artificial represented true define define define define define define compute compute compute compute compute compute compute compute perform goal goal goal goal goal goal goal goal goal goal goal goal discrete discrete power power mit steps steps steps support modeling modeling modeling morgan morgan morgan morgan proceedings proceedings proceedings advances connectionist sequences ai framework framework framework cambridge cambridge experiment environment environment environment environment environment environment environment environment environment environment environment environment environment environment hinton hinton additional transition trajectory trajectory trajectory trajectory trajectory trajectory san san san san effects conference conference conference conference efficient efficient full full requires world world world speed speed basic produce condition weighted conditional levels levels area types path path processes processes iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration depends constraint achieved describe describe arbitrary arbitrary arbitrary denote denote assumption corresponds corresponds complete stable actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions predictions common common common generate supported role theoretical theoretical main end ability instance future future including including kaufmann kaufmann kaufmann kaufmann objective typically interesting significantly mechanism special consistent iterations iterations iterations max max max max direct making international international international frame decay combined combined choose choose added denotes denotes denotes directions resolution property separate takes element introduced moving include include include identical hierarchical hierarchical sense sense sense sense sense cognitive previously conventional volume solve correspond correspond correspond converge achieve diagonal address definition mixtures locations grid grid grid williams williams grant grant scaling matrices move move move loop column column setting half starting trajectories depend reward reward reward reward accurate accurate accurate numerical sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton exponential faster practice learns learns mateo mateo mateo mateo taking drawn proportional intelligence variety relationship iii averaged averaged introduce introduce question denoted suppose relation pro produces ways describes mathematical mathematical changing modeled coordinates coordinates averaging averaging averaging remaining scales scales scales scales adding agent agent agent agent agent agent agent agent agent agent agent agent agent agent implies expectation yield yield focus viewed viewed operations operations controlled showed completely similarly similarly suggested updates key barto barto barto barto performing penalty closed closed closed valid valid valid valid valid valid valid valid foundation advantages includes thesis combinations priori weighting weighting weighting weighting extension domains holds discussions characterized planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning regular importance suitable society successful efficiently online composed refer kind kind kind moore moore showing interested return return criteria built satisfy notation notation notation quantity write usual dayan dayan dayan dayan generalize delayed received moves policies policies illustrates neighboring acknowledgments receive situations singh singh experience rapidly put put environments environments preliminary mdp hall helpful ideas incremental authors comparable workshop fundamental notion notion predicting predicting predicting predicts illustrate illustrate illustrate greedy improving mixed simplest phd established massachusetts ment distinguish adjacent adjacent adjacent failure multiplication handle starts london inside straight purposes purposes producing operators watkins watkins circle lowest annual nsf integrating substantially led consistency consistency effort atkeson atkeson rewards rewards rewards maximizes proven serve plan richard richard richard enables enables comments lim cumulative bellman bellman bellman bellman bellman bellman bellman bellman bellman room room room room room room room room room room room room room proofs temporally temporally temporally temporally temporally temporally concerned homogeneous homogeneous repre tem outcome outcome outcome outcome outcome turned convenient primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive fail roles imply north generalizes composition composition ensures corre holland searching propagated propagated offers chooses advance discounted refers repeatedly rich ends extends reverse implicitly discovered alternatively summarize limitation andrew andrew truncated discount validity validity dyna convenience abstraction abstraction amherst imagine illustration visited visited visited acting acting summarizes summarizes intuition goals wall wall afosr afosr wise wise proach option laird laird sweeping denver happen elsevier permit travel experi walk differently sponding achievable traveling attributed attributed prioritized anatomy compo unreliable executing attained kaelbling kaelbling chunking ranged ranged closure acknowledges semantics lar sentation successor promise tenth ensuring capturing ceedings behaving publishing expresses richer notions contributing utilities virtue precup precup precup precup precup precup precup precup precup macro ness plans plans plans sition hypothetical hypothetical ninth ecs exceeded temporary cent stays seventh grasping particu signif feudal twelfth walls interacts rooms rooms icml icml icml icml discounting umass eft newell itera expressive expressive expressive expressive andy perceives suitability suitability peng peng icant limk interrelated flying inforcement equalities pitman doina doina ght gether porally lunch unifies 
#@Precup_D,Sutton_R,
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#*network learning learning learning learning learning learning learning learning model model data function function function function function function function function function figure figure figure time time time time time time time time time time time time set set set set set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state information problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance based based space space space space space space space space space case case case case case order systems systems values values values values values values values probability probability probability probability probability parameters functions functions functions approach approach approach approach single single control control large analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form shows simple simple simple paper paper paper size work task task task task task task task task task task step step step step step step step step step current trained trained problems problems random random high show equation equation equation section section section section fixed fixed rule general parameter real real real states states states states states states states states states states states states states states states states states states obtained note note note note result result result university university solution solution solution solution solution solution solution solution solution solution solution research independent defined defined defined defined defined defined found found initial initial initial initial initial initial initial initial initial initial standard computer computer science science science presented presented present machine maximum range press learn components components abstract find find find find computational convergence convergence references component component component component component component component component component component component component component component component component component component important adaptive decision decision decision decision decision decision decision decision decision decision decision action action action action action action action action action action action action action action action action action action action action action action action action estimation behavior effect effect dynamic dynamic dynamic dynamic dynamic dynamic parallel parallel parallel parallel difference assume assume assume lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower learned chosen chosen chosen previous bound bound bound bound bound bound bound bound bound bound type required multiple multiple multiple multiple multiple multiple multiple multiple good expected expected expected equations markov markov markov markov markov markov markov markov make probabilities resulting tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks respect sum sum sum sum called times times means means reinforcement reinforcement factor factor factor factor factor factor factor policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge negative negative artificial represented cross cross define define compute compute compute compute location perform perform perform perform constraints constraints constraints constraints constraints equal mit steps update update update update department department version version individual individual individual delay ai ai considered framework framework framework cambridge cambridge computing directly directly directly directly solutions solutions solutions solutions solutions solutions solutions curves transition transition transition transition transition determine efficient upper upper upper upper upper upper upper upper upper upper upper upper upper upper requires requires requires requires requires requires requires significant significant world randomly robot bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds lines path product product processes processes processes processes processes processes processes processes iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration iteration technical feedforward describe describe describe arbitrary group actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions finding finding short common supported theoretical ability future future easily makes makes makes objective typically needed account programming programming programming programming special max max max max max making making making making bottom attention attention combined choose advantage apply include identical machines subset cognitive engineering interest previously approximately solve solve correspond converge converge modified modified observation grid bounded bounded bounded bounded bounded interval storage entire grant lead studied studied occur matrices matrices move generally generally demonstrate conclusion starting starting critical trajectories competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive competitive clear performs practice sound sound taking presence largest characteristics intelligence start start start start start start start start start exist iii question denoted denoted acknowledgements longer solving solving solving transitions pruning pruning pruning simultaneously simultaneously simultaneously simultaneously simultaneously physical remaining easy easy consisting agent agent implies implies select choosing independently stationary learner operations updated updated updated updated converges converges converges converges converges converges updates updates calculation calculation barto barto additive performing spaces spaces spaces spaces roughly remains remains sufficiently assigned david avoid avoid avoid avoid existing thesis thesis combinations assignment illustrated illustrated maximize selecting aspects aspects encoded symbols efficiently efficiently efficiently online composed composed traditional refer refer quickly quickly quickly heuristic moore moore contribution running strategies hold delayed highest automatically automatically moves moves policies satisfies extend situations presents explore remain create singh singh singh singh singh singh singh singh updating updating environments mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp fewer successive fashion ideas terminal terminal combine proper proved notion act naturally analyze analyze illustrate illustrate aspect quantities quantities obvious obvious obvious greedy greedy greedy greedy portion assumes initialized submitted phd phd finds finds optimum rows distinguish guaranteed fairly fairly worse stanford stanford strictly strictly day incorporate desirable arise watkins watkins potentially scientific scientific opt opt opt depicted nsf people composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite substantially embedded atkeson atkeson frequently frequently compares rewards reaches maximizes resource resource resource semi neuro begins simultaneous simultaneous converged converged summed univ merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging merging irrelevant naive bellman bellman bellman benefit optimality assign formally pick pick narrow resources dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically dynamically mobile food food food food food food food food eliminate arrival proceed eliminated consideration chance mail mail optimally motivation falls zhang zhang decide pruned guarantees intended colorado colorado infinity scheduling scheduling scheduling scheduling scheduling scheduling advance treatment discounted discounted theoretically theoretically park merge merge merge merge merge tsitsiklis tsitsiklis tsitsiklis dietterich dietterich valuable avoiding avoiding assigns mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps mdps bertsekas bertsekas bertsekas bertsekas bertsekas piece discount discount job job job job job job job job job job job job formulate formulate formulate obstacles obstacles suboptimal suboptimal incrementally england guess guess avoids factorial factorial cohn cohn cohn cohn cohn dominated dominated boulder eliminating individually considers importantly million million sweeping sweeping maintains bradtke ignoring exploited infinitely status continually picking argmax argmax payoff payoff payoff payoff payoff payoff payoff payoff payoff ongoing ongoing savings focuses lated prioritized prioritized optima executing discarded discarded discarded inefficient arrives arrives exploits isolation isolation isolation isolation isolation maxi kaelbling kaelbling era sis terminates delivery faced nonstationary nonstationary shop shop shop shop shop shop shop shop successor iterate prune ference elaborate infeasible decompositions miss backups backups backups backups backups backups backups backups backups backups backups backups satinder satinder belmont belmont menlo ponent ponent allocate allocate namic discard discard safely rtdp occuring intend factoffal indexes reachable reachable reachable reachable reachable walls manage reformulated reformulated constrains athena athena augmenting charged lambda ffi payoffs payoffs payoffs payoffs payoffs payoffs payoffs payoffs jobs jobs jobs jobs sts sts eat eat eat eat bined argm formu accommodated termined nar petitive predator predator predator predator predator predator superscripts etal iis baveja ivy ator ffl backed backed tsitsildis predators 
#@Cohn_D,Singh_S,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural function time time time time time time time time training algorithm algorithm algorithm number state state state state state state state state state state state state state state results results results results information models based based based case case case systems values probability probability probability probability probability distribution distribution distribution distribution distribution distribution method method point single processing control control large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate optimal optimal optimal form form form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper paper paper paper task methods step step step step step step step step step step process process process process process process process process process process process process process process process process process process process process random random random random random random similar similar similar similar show show show equation equation equation fixed fixed fixed fixed line general real approximation approximation approximation approximation approximation approximation average average average average states states states theory theory obtained obtained term note note note note note note note experiments result result result university university variables variables computation research research independent independent independent defined defined defined found sequence sequence sequence constant constant table estimate estimate estimate estimate standard computer presented presented presented present present machine machine machine machine machine machine maximum maximum maximum press learn components abstract abstract applied find computational computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic due decision decision decision introduction action action action action action action action action action action action action action dynamic dynamic dynamic dynamic change difference difference difference assume assume assume assume lower signals signals theorem theorem theorem theorem theorem bound bound bound bound bound bound conditions conditions conditions markov markov markov markov techniques techniques probabilities probabilities finite minimum ing ing simulation computed multi called times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor optimization made applications applications study policy policy policy artificial artificial samples application application provide provide define rates rates rates proc related related discrete steps steps update support morgan morgan proceedings proceedings version scheme framework cambridge cambridge computing environment transition transition san san san conference conference upper upper upper upper requires choice statistics estimated pages pages con con con condition condition developed developed bounds bounds bounds lines actual provided provided provided provided finally processes processes processes processes processes processes processes iteration depends depends sampling sampling sampling sampling sampling simply associative discussion technical arbitrary group assumption assumption assumption assumption actions actions proof proof proof proof proof proof proof common common common assumed assumed assumed assumed supported main main main ability kaufmann pairs pairs pairs pairs underlying underlying underlying underlying underlying underlying underlying reduced jordan jordan programming programming programming programming programming ratio york mechanism special uniform empirical direct international international idea idea idea discussed discussed exact pair pair pair introduced include identical sense sufficient compare yields yields converge converge rl rl rl rl address definition modified generalized generalized interval grant grant parts extended deviation deviation conclusions operator reward reward reward faster faster faster asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic integration demonstrated california intelligence min min min denoted acknowledgements explicit pro longer ways missing explicitly explicitly slightly interaction frequencies frequencies applying agent agent agent john choosing stationary stationary stationary stationary stationary lemma lemma lemma lemma updated updated approximations forms soft similarly converges converges converges iterative iterative norm expect thesis extension absolute holds holds holds holds discussions major major identified identified suitable presentation literature comparing notice notice conf kind prob showing showing hold hold notation sampled michael relaxation delayed received satisfies satisfies satisfies decreasing decreasing extend extend extend law law law law employed simpler wiley perturbation essential essential singh singh singh singh singh singh relations replaced mdp mdp helpful history history investigated int proper complicated proved smallest act math analyze thought algo algo expressions ith generates phd averages devices asymptotically brown inequality inequality asynchronous asynchronous derivation guaranteed defining defining london reasons satisfied day immediately watkins watkins watkins consequence scientific separately calculations argument greatly effort effort effort introducing slower slower slower treated ity rewards rewards rewards http aim maximizes popular sums neuro jaakkola jaakkola jaakkola jaakkola jaakkola eventually simultaneous univ proofs proofs college appearance arguments harmonic stronger simplify contract obtaining optimally preparation preparation games games respective enable iterated iterated iterated francisco francisco francisco foundations discounted discounted discounted sons tsitsiklis tsitsiklis tsitsiklis tsitsiklis convergent mdps mdps bertsekas bertsekas bertsekas usage numerous logarithm logarithm logarithm outline annals discount discount discount discount markovian markovian markovian markovian markovian nition pieces perturbed perturbed monotonicity tradeoff stands stands var remote ary visited visited rithms rithms proba lookup integrals exploited exploited mini mini article simplifies infinitely strict strict littman littman littman littman littman littman littman littman littman littman littman littman littman littman fortunately bility heavily firstly king cally cally station executing automation html maxi aggregation relaxed restrictive iterating backwards imum rein vergence vergence vergence putting forthcoming relying ross ross belmont proving mild sults ministry exclude namic chine robbins rli forcement monro spend spend athena eleventh eleventh sic admit admit limt pression oll holden llt adaption mahadevan mahadevan mahadevan mahadevan xll aggregated aggregated educational occupation occupation atl orem budapest defi boundedness har lvi zxt zxt tsitsildis tro 
#@Szepesvfixi_C,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural input data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time set networks networks training training training algorithm output number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system error error error error error state state state state results results based linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case order order order shown shown shown systems systems systems systems values values values values values values values values values values values values values probability neurons approach single control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control neuron rate rate rate rate rate rate test inputs shows shows shows shows simple examples small small step step step step step step step step step step step step step step step step step step step step level trained trained trained trained trained trained trained trained trained trained trained trained trained structure problems problems problems problems problems problems similar architecture equation general generalization parameter real real real real real real real real real real real real real approximation average average average average states states states states obtained obtained obtained dimensional computation computation independent defined sequence initial initial initial initial initial initial initial constant constant constant constant synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic phase temporal machine object motion motion motion learn learn learn learn learn learn learn learn learn learn position position position position position outputs abstract applied applied applied back references ieee ieee ieee procedure procedure adaptive introduction action action hand behavior dynamic difference signals signals learned learned learned learned learned learned learned learned higher higher center type type type type type type type required required multiple conditions represent represent represent represent expected expected equations equations equations equations equations equations make proposed proposed proposed proposed ing tasks sum performed performed called reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor study study study study policy em negative negative negative negative vol vol vol vol vol vol vol vol application desired desired rates steps steps dependent dependent selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection proceedings loss advances difficult considered considered environment curve conference upper requires requires requires requires free free free free free free world world speed con con condition coding robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot velocity velocity velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller selected selected selected selected selected selected selected describe denote denote denote fast fast inverse actions actions actions shape ability easily development objective simulated smaller needed combination combination dynamical dynamical jordan technology ratio ratio ratio ratio special trials trials trials trials trials trials trials trials trials trials trials trials trials trials experts experts decay choose run denotes improve separate reported period period hierarchical hierarchical hierarchical dimensions approximately calculated calculated calculated calculated calculated calculated module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module axis axis axis axis solve solve differential differential trans sparse mixtures mixtures storage amplitude constructed trial trial derivative hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid runs runs strength strength strength strength conclusion interactions modules modules modules modules modules modules modules sutton sutton sutton learns propose propose reduction characteristics assuming program modeled angle angle select dependence dependence dependence open controlled controlled controlled controlled controlled controlled controlled controlled controlled updated approximated approximated barto intervals closed symbols symbols successful successful successful miller composed composed quickly quickly quickly quickly quickly quickly quickly quickly quickly quickly quickly anderson usual usual usual usual usual usual play modular modular modular nips consisted jacobs tesauro body singh strengths strengths strengths strengths applicable applicable applicable combine examined circles coarse measurement measurement man greedy indicating advanced ment ment ment sensors slope slope slope slope failure failure failure failure caused caused lin lin lin lin lin sys sys sys controls controls angles angles angles angles pitch pitch beginning beginning annual hme hme hme autonomous mod fall fall prevent achieves electric traces traces pole cybern japan angular angular angular repre tem tem robotics rigid ments replacing replacing height height height height balance cerebellar cerebellar falls respective cmac cmac cmac cmac cmac cmac master motions motions motions skills consecutive corporation discount failed profiles flat acceleration rhythm backgammon leg leg leg leg leg leg leg leg leg leg leg leg exceed manipulator manipulator eligibility eligibility exchange exchange exchange exchange supporting supporting walk rarely fiat fiat fiat fiat fiat fiat reinforce reinforce reinforce albus albus termination termination japanese tip tip tip tip floor floor floor floor floor floor floor floor floor floor floor floor floor floor sarsa trol falling smc crl teaching articulation articulation gammon gammon transaction transaction watanabe watanabe watanabe watanabe watanabe watanabe ira began bodies rein rein rein rein rein rein rein rein rein rein rein rein rein rein walking walking walking walking walking walking walking walking walking walking walking yamada yamada yamada yamada yamada yamada bio ele terminated exceeded stabilized legs gullapalli adaptable rect forcement forcement roll roll sel sel sel sel sel sel sel sel sel sel ended inertial torques ule stably stably succeeding asme asme franklin mitsubishi photograph sents acquiring irregularly magnified vided inforcement trolled weighs 
#@Nakashima_M,Watanabe_A,Yamaria_S,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural data data data data data function function figure figure figure figure time time time time time time time networks networks networks training number number system system system system system system system system system system system system system system system system system error error error error state state state state state state state state state state state state state results results results results results results models models models models models models models models performance performance performance based based based based based based based linear linear case shown systems systems parameters parameters parameters parameters parameters parameters parameters method method approach approach pattern pattern pattern point point point point point point point point control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large rate test patterns analysis matrix shows shows signal signal signal task task methods methods methods methods methods methods fig fig fig fig fig points points field field field field field field field field field field field field field field field field field field field field field field field field field field classification process process process current current current current trained trained trained trained memory similar similar representation architecture architecture architecture show show show show show equation line line real obtained term result university defined defined found found found target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial constant estimate estimate estimate estimate standard distance distance science left left direction direction direction direction presented activation activation activation range press learn position position position position position position basis nonlinear nonlinear nonlinear nonlinear abstract applied applied computational computational computational computational computational computational properties references due due adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction action hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand behavior behavior behavior behavior behavior behavior behavior behavior behavior effect dynamic dynamic generated change difference spatial measure signals learned learned learned type required long conditions conditions expected expected expected expected expected make fact proposed proposed length correct correct observed observed observed observed errors errors errors forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations minimum minimum simulation simulation human human human human human human human human human human human human human human human human human computed performed performed eq made made made feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback represented represented represented represented compared compared desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired provide provide experimental experimental experimental related gain motor motor motor motor motor motor motor motor motor motor brain equal comparison contrast fields fields fields fields train internal internal internal internal internal internal internal internal internal internal internal joint joint joint joint joint joint joint joint joint delay delay delay delay addition addition maps maps experiment environment environment additional curves estimates transition transition trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory effects speed speed speed estimated estimated estimated estimated estimated estimated produce developed velocity velocity velocity velocity velocity velocity velocity velocity controller controller controller controller controller controller controller controller path path path path path path path path path path path path path path actual actual actual evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence nature nature feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse complete stable stable stable stable finding assumed assumed generate theoretical adaptation adaptation adaptation adaptation adaptation adaptation adaptation journal journal rumelhart rumelhart sensory sensory sensory fit fit simulated pairs pairs combination combination combination combination dynamical dynamical functional jordan jordan jordan jordan segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation structures squared supervised idea produced predict predict architectures architectures architectures directions directions directions directions directions exact exact typical typical typical movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement period subject subject subject subject subject subject relevant relevant engineering varying teacher approximately subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects calculated solve match match correspond studies converge entire arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm concept concept occur occur deviation deviation derivative derivative matrices predicted move move loop loop occurs column column column column flow trajectories trajectories segment segment segment segment segment central central differences accurate clear performs faster practice practice external external external external external external external characteristics characteristics proportional assuming movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements targets identification force force force force force force force force force force force force force force force force force force force force force force written solving stability stability distinct dept segments segments modeled involves angle angle angle angle angle interaction integrated equilibrium formation formation formation formation stages transform transform controlled updated showed completely suggested constants constants key earlier reasonable delays delays sec sec sec sec purpose initially initially msec msec msec msec columns middle middle identified divided divided paths paths situation composed neuroscience issue physiological physiological duration vary absence delayed delayed computes reach neurosci principles principles command parametric rapidly rapidly environments existence examine examine behavioral biol possibility muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle muscle hill act predicting predicting predicts equally observe nervous plant plant plant plant plant plant ment directed unstable adapted adapted adapted rapid straight straight straight straight straight straight sys easier producing precisely mechanics behaviors evaluating simulate marked incorrect rep commands commands controllers controllers rely proven substantial segmented segmented deviations deviations deviations deviations deviations deviations converged cumulative cumulative cor ghahramani discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities cybern accomplished accomplished accomplished unity theories reaching reaching reaching eliminated fails ments imposed moment muscles muscles muscles muscles muscles muscles passive eng relies relies relies agree agree wolpert wolpert wolpert wolpert wolpert subsequently tures mechanical reflex reflex kinematics achieving email removal torque copy corrected corrected spaced acceleration acceleration acceleration acceleration acceleration acceleration simulating causal spinal spinal spinal spinal spinal spinal jacobian adapting adapting cns acting perpendicular compensate signatures continues altered altered switched distal termed covered flash attached descending descending descending behave holding corrections differently differently instability instability instability quantify utilizes hopkins incorrectly incorrectly sensorimotor kinematic kinematic kinematic kinematic architec push corrective corrective corrective corrective archi joints tracks tracks johns ignores reproduced comm baltimore seg seg seg seg inappropriate rotational huge progresses upward upward remarkably clockwise clockwise biomedical inte mussa mussa mussa inertia offiine pushed pushed ivaldi ivaldi ivaldi narendra narendra environ rationale arms cog cog charac shoulder accompanied elbow neur sudden sudden jects downward downward downward viscosity viscosity muscular stiffness mimics jerk jerk jerk jerk corrects tectures facilitated jhu jhu resented varieties miall miall miall sixteen bme bme cle initiates reflexes curious matics expecting expecting kine gration mus teristic rns 
#@Bhushan_N,Shadmehr_R,
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural input input function function figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks training training number number number system system system system system system system system system system system system system system state state state state state results results results results results results results results results results information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models performance performance performance based based based case case case order order order order order order order shown shown shown shown systems systems values values values values values values values parameters noise weight weight functions recognition method method method method method approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point image image image image image image image image image image single single single single single single single single control large local local local rate shows shows shows shows shows shows shows shows shows algorithms simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper size size size size feature net work work task task task fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig process process process process level level problems problems problems problems problems problems problems random random high high similar architecture architecture architecture show show show show show show show show show images images images images images images general general generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter states theory theory term note activity activity activity dimensional dimensional dimensional dimensional result result university university university threshold threshold computation computation computation solution solution solution solution solution solution solution defined defined defined defined sequence sequence sequence initial initial initial standard computer terms terms terms synaptic science science science left presented phase phase phase phase phase phase phase phase phase phase phase phase activation activation activation activation activation temporal temporal temporal temporal temporal machine object object object object object range range press press press press position position position basis basis abstract applied applied applied applied applied applied computational computational references due due due positive decision propagation introduction behavior behavior behavior behavior behavior behavior stimulus stimulus dynamic parallel parallel tion tion tion tion difference difference difference difference difference spatial measure measure measure measure measure measure chosen part part part center center previous bound cases cortex binary binary represent represent represent represent distributed equations make proposed proposed proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation simulations simulations simulations simulations simulations simulations simulations simulations resulting resulting simulation simulation simulation simulation human human human human computed called times elements regions regions regions means orientation orientation orientation orientation global global global global global study study specific specific specific specific specific specific objects objects objects objects active active active active active active active active active active active active active related connected connected connected connected connected connected brain brain mit mit mit mit contrast contrast contrast morgan report report report institute department version internal represents represents represents represents connectionist difficult exp delay delay delay delay delay delay delay delay delay scheme framework equivalent curve curve solutions solutions solutions solutions solutions solutions top stimuli effects effects determine determine determine determine vision con produce condition randomly area area area area area area area area area area area area provided provided processes nature inhibitory simply biological achieved achieved achieved achieved achieved achieved achieved achieved achieved achieved achieved achieved achieved achieved achieved discussion technical describe group group group group group group group denote denote denote limited limited limited limited corresponds corresponds corresponds corresponds corresponds corresponds excitatory nearest shape shape shape shape shape supported theoretical end pixel pixel pixel hypothesis degree makes kaufmann pairs underlying unknown significantly segmentation segmentation special special special consistent representing representing representing representing representing representing representing representing representing representing representing representing representing representing representing max max max max max max inhibition bottom attention combined combined perceptron neuronal neuronal denotes discussed exact takes typical reported reported reported introduced introduced period period period period period period subject side side pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels cognitive recently recently recently interest highly highly highly subjects works tions solve solve solve solve solve solve yields correspond correspond studies achieve trans definition background background background background background background separation separation entire entire entire entire grant grant amplitude concept concept studied occur suggests extended alternative alternative locally locally white white boundary generally conclusion starting trajectories trajectories depend interactions sigmoid constrained suggest suggest suggest integration external external turn min min min min min plane plane groups areas areas areas areas areas suppose appears relation relation perception perception perception perception perception perception perception perception perception perception perception perception solving sequential laboratory multilayer multilayer simultaneously simultaneously simultaneously simultaneously simultaneously involves consisting develop applying formed competition national formation formation formation formation formation formation formation formation formation formation formation formation formation formation review review squares overlap solved solved solved solved open showed showed forms sizes activities activities similarly suggested key earlier slow delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays delays purpose boundaries boundaries boundaries closed closed symbol construction coupling coupling coupling coupling coupling figures figures figures figures figures figures perceptual usa perceptrons perceptrons perceptrons perceptrons perceptrons contour recognize determines illustrated activated activated activated coupled black black black holds neighbors neighbors neighbors neighbors neighbors discussions identified identify oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory receives excitation refer kind prob neuroscience oscillations timing gray gray involved sampled sampled relaxation relaxation wave wave wave received illustrates neighboring neighboring neighboring acknowledgments explore unlike stimulation stimulation exhibit rapidly rapidly rapidly rapidly relations relations relations relations relations relations relations relations relations relations relations relations relations oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators steady humans humans limitations limitations limitations oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator periodic periodic examine respond school analytically authors oscillation affect cognition phases plausible plausible illustrate illustrate illustrate illustrate der portion portion portion observe observe observe observe initialized serial serial serial ground ground distinguish distinguish distinguish analyzed failure failure failure explanation adapted adapted adapted caused benchmark benchmark lies inside inside inside inside inside inside inside inside inside inside inside inside inside inside inside inside inside rapid perspective perspective broad broad controls involve grossberg grossberg annual qualitative nsf addressed fourth questions reflects varies people prop applies double double double double double double double double generic generic generic conducted readily readily detecting continuously biologically biologically psychological synchrony synchrony synchrony synchrony synchrony synchrony qualitatively chen chen chen chen chen chen chen chen chen chen singer singer sophisticated eventually wang wang wang wang wang wang wang wang wang wang wang wang wang wang wang wang wang wang wang wang synchronization cor globally identifying investigation discovery arranged arranged generality spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral spiral fails fails numerically mail interpret methodology belong belong synchronous synchronous synchronous intuitively reliably connect lang lang evident demonstration propagated counting diameter young stimulated stimulated stimulated stimulated refers theoretically belonging belonging propagate propagate limitation onr onr lem spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals spirals summer listed listed listed emergent distinction distinction pointed pointed conjecture malsburg malsburg tor examining realize attempted biophysical grouped bounding emphasize emphasize ullman ullman ullman ullman ullman ullman ullman iri importantly distinguished assemblies grateful book investigations behaves triggered lation traveling traveling traveling attributed routines routines routines routines routines tors pictures loosely award stay stay stay stay stay inherently inherently condi distinguishing cooperation minsky minsky minsky minsky minsky minsky minsky planck enter enters statements physica physica proceeding silent putation propagates propagates routine routine routine investigator campbell campbell campbell campbell campbell intrinsically ular yon sends ohio ohio ohio ample sition conceptually mention ities agation stabilized stabilized stabilized stabilized distinguishes steepness snapshots snapshots snapshots snapshots snapshots snapshots snapshots snapshots inhibits emphasizes simu perceive perceive disconnected disconnected disconnected disconnected standpoint papert papert papert papert papert papert papert duce partic segregated segregated nected nected mission correla duced cis cis havior snapshot snapshot chemistry spreads witbrock witbrock alternates intro intro mecha loose loose loose loose fined coloring columbus oscilla oscilla julesz julesz perceiving perceiving perceiving perceiving perceiving perceiving runge chronous inevitably inhibi discriminates invoke caption caption caption dxi nism ques kutta influential aries dyi synchronizes china gion forma abil dress chronization 
#@Chen_K,Wang_D,
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#*network network network network network network network network learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural input data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set networks networks networks training training training training training training training training training training training training training training training algorithm algorithm output output number number number number number error error error error error error error error error error error error error error error error error error state state results results results results results units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models hidden performance performance performance performance based based linear layer layer case case case vector vector vector shown systems probability parameters noise noise noise distribution distribution distribution distribution distribution distribution point point single single single processing processing rate rate test analysis analysis analysis analysis form form shows algorithms algorithms algorithms simple simple simple simple size size size size size size size size size feature net work work work work work work work work task methods step points features process process process process process current current current trained trained trained trained trained trained trained trained trained problems problems problems problems problems problems high memory memory response response response similar similar similar similar representation representation representation representation representation architecture architecture architecture architecture architecture section section line vectors vectors vectors general general general general parameter real theory theory obtained note activity activity dimensional dimensional result result result university university university computation research research defined constant constant constant table table table table table table table table table table table table table table table table table table table table table table table left presented presented presented presented map phase activation frequency frequency press press learn learn position basis basis abstract abstract back find computational computational references positive propagation introduction introduction introduction hand effect effect effect effect effect effect effect effect effect effect effect generated generated parallel assume assume assume rules rules representations representations representations representations representations learned chosen part previous cases type cortex represent distributed expected make make make fact fact fact proposed proposed length correct correct correct correct errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors forward forward simulations minimum tasks tasks human human human multi sum sum performed times times times times regions potential dimension made made made made made natural feedback study knowledge original vol specific samples represented provide rates rates perform perform experimental experimental experimental experimental experimental goal related distributions brain equal mit mit comparison comparison larger support support modeling modeling institute department department consists consists advances connectionist difficult final final addition addition addition addition considered cambridge cambridge design bit full requires approximate basic basic basic increase produce coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding levels levels types types types types provided evidence nature constraint simply biological associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative associative discussion normal normal normal normal normal normal normal increases increases close close close corresponds complete implemented generate generate generate eds eds eds journal journal journal journal journal journal end ability ability hypothesis hypothesis instance degree rumelhart rumelhart rumelhart noisy including fit fit fit simulated smaller technology interesting testing increasing mechanism mechanism trials trials operation operation operation operation operation operation operation operation operation operation details numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations direct bottom magnitude magnitude combined run description exact separate subject inference engineering varying compare studies address grid occur suggests suggests suggests suggests trial wide predicted feed feed generally column demonstrate flow greater greater conclusions competitive interactions numerical clear propose mechanisms presence characteristics drawn california intelligence variety groups force attractor acknowledgements explicit digit digit digit digit digit digit digit winner winner winner winner plot transitions distinct distinct category category text versus decreases independently expressed review overlap interpretation codes operations operations understanding understanding suggested suggested digits digits digits reasonable performing epochs reduces fitting remains remains remains classified expect box instances sciences plotted specifically aspects capable capable included mcclelland literature literature tend ten ten ten ten characteristic characteristic summary summary anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson anderson superior issue categories providing correspondence consisted preferred exhibit rapidly involving humans humans humans humans humans humans humans humans humans humans humans humans humans humans humans humans humans humans replaced replaced behaviour existence existence fashion ideas school possibility possibility symbolic symbolic symbolic symbolic proved cognition cognition cognition cognition cognition phases coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse concepts concepts concepts plausible psychology psychology psychology psychology psychology psychology psychology psychology perfect aspect noted noted noted logistic precise precise precise precise precise precise precise precise perceptton generates great defining phenomena phenomena phenomena slope improves coded coded coded answer answer answer answer answer answer multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication multiplication immediately demonstrates auto auto author author author addressed researchers questions apparent percent marked rep psychological schematic schematic switch instruction occurrence pasadena inherent comments display eventually arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic arithmetic concerned addresses caltech children lost fits wrong dealing dealing methodology cottrell cottrell guide financial financial excellent mance becker becker becker becker becker patient surprising perfor mental regard intended demonstration accounts monkeys counting lawrence surprisingly mem suggesting pollack canada canada park erlbaum explorations treat microstructure listed listed revealed individuals individuals hillsdale manipulation translated translated distri stroke pdp life bump bump conversely cation associates retained retained permit permit permit slopes matlab tin architectural bution species species copies council hamilton hamilton mistakes placement artifact ory convention contrary sliding reality accounting experienced bradford bradford acknowledges acknowledges trend facts facts facts problematic greatest putation publishing sung sung localist campbell campbell campbell prime miss miss save resentation sparsity coincidence multiplications claims translating encounter canadian concurrent blank highlight graham graham graham categorized conserved linden sole entails stud wood operands operands operands operands operands operands operands operands grasp recalling adults adults ont ont resorting documented ied incapable tude deficiencies judgment quarterly suffered pressed cult deliberately operand operand operand operand ablex creased superficially levine diffi codings appropriateness outstanding magni 
#@Becker_S,Christianson_G,
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#*learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure time set set set set set set set set set set set set set set set networks networks training number number error error results results results results results results results results results results results information information models models models models models models models models models models models models models models models models models models models models models performance based based based based based based based based based based space space space space space space space space space space space space space space space space space space space space space space space space space weights weights weights weights weights weights weights linear case case vector vector vector vector order shown probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters noise noise weight functions unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach pattern pattern point image image image image image image image image image image single single single processing processing processing processing processing processing processing large rate rate rate rate rate rate test test test test test test test test test test test test test test test analysis analysis analysis matrix matrix matrix form form form shows shows simple simple simple simple gaussian gaussian gaussian gaussian visual paper examples size size size work work work work task task task task task methods methods points points points features process level problems memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show section images images images images images images images images images images images general parameter parameter parameter parameter parameter average average obtained note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university threshold solution research research research target constant constant table table standard computer distance distance distance distance science science science prediction prediction prediction prediction left presented phase low object press press press press position components components basis basis basis abstract applied density density density density density density density density density density density density references component due due important important adaptive adaptive adaptive adaptive adaptive decision mixture mixture mixture mixture context context context context context estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect spatial assume assume measure measure measure measure prior prior prior representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations representations higher part previous good long represent make make make proposed proposed correlation correlation observed observed errors errors errors errors resulting resulting tasks human human human human human human human human human human human human human human human human human human human human human computed respect respect multi sum sum performed performed performed performed performed performed mapping means means factor factor made made natural global global global study study study study study study study study study study study study filter filter filter filter filter filter obtain negative original original samples true compared provide provide provide location determined experimental experimental experimental experimental related related comparison larger larger larger fields support modeling modeling proceedings proceedings report report department department version version version technique kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel joint responses responses responses responses responses responses bias graph framework framework experiment experiment experiment experiment experiment experiment directly directly additional limit san stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects conference conference determine requires significant significant free free free speed basic pages pages con produce derived derived weighted weighted weighted criterion types actual actual actual evidence sampling sampling sampling simply simply simply measured discussion discussion covariance covariance tested transformation assumption surface surface surface surface predictions predictions predictions finding nearest common effective supported theoretical theoretical require require require face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face journal journal journal journal journal square ability ability hypothesis hypothesis hypothesis future future easily easily degree noisy noisy including fit fit fit fit fit fit fit fit fit probabilistic typically pairs pairs pairs pairs pairs pairs pairs underlying underlying combination account account account account account account account account fully fully testing testing projection projection projection consistent consistent consistent consistent matching uniform database empirical principal principal principal squared squared representing details call filters stored international normalized normalized normalized idea attention combined minimize minimize choose predict predict predict predict predict improve improve pair pair robust takes typical typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity reported introduced include subject subject subject subject hierarchical cognitive cognitive recently engineering sufficient compare compare subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects volume tions sparse background background evaluation positions positions locations generalized generalized generalized grid grid increased grant constructed lead lead studied studied studied studied studied studied studied studied studied studied invariant scaling scaling scaling scaling deviation deviation predicted predicted predicted predicted predicted correctly correctly width width width boundary generally setting critical critical reduce depend propose mechanisms proportional proportional minimizing targets targets targets introduce identification attractor acknowledgements areas explicit relation derive perception recall recall category category category explicitly explicitly explicitly linearly dimensionality dimensionality scales frequencies applying quality quality formation review correlated overlap detailed evaluate centered completely constants constants constants allowed discrimination discrimination key earlier reasonable spaces normalization normalization fitting fitting fitting fitting intervals false false false boundaries distances distances euclidean euclidean faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces template kernels kernels kernels kernels combinations combinations retrieval priors priors priors priors domains neighbors neighbors society modification included projections projections projections projections tend tend essentially allowing allowing neuroscience dis criteria categories categories built built vary vary vary wavelet providing giles automatically principles attempt extend minimized diego poor create investigate varied humans limitations scaled scaled eigenvectors eigenvectors variability affect cognition cognition notion surfaces examined hill predicting predicting predicts predicts predicts predicts predicts predicts predicts psychology psychology psychology psychology psychology facial facial facial facial facial facial facial facial facial facial created eyes eyes rank prototype prototype aspect der der der store baseline baseline extent extent extent submitted submitted submitted submitted submitted orientations orientations phenomena fairly stress perspective purposes sys producing located worst bishop bishop bishop consequence potentially potentially inversion inversion inversion inversion inversion inversion inversion inversion inversion projected describing members annual exemplars exemplars exemplars exemplars exemplars exemplars exemplars researchers researchers evaluating evaluating empirically empirically pseudo quantitative quantitative psychological outliers outliers prototypes prototypes rely modulated parent parent parent parent parent parent parent parent parent parent achieves plan logical comments comments shaped attentional attentional multidimensional multidimensional multidimensional summed summed summed distortion cor globally contribute consistently aligned oxford oxford gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor narrow optimizing rotated ordering repre exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar exemplar climbing rational occurred held height height height height hit efficacy resulted resulted keeping nearby settings cottrell cottrell cottrell cottrell cottrell effectiveness intuitively adequate intuitive child child published representational studying widths widths widths widths encountered surprising von von von conjunction accounts accounts accounts thomas exposure mem mem jolla probe probe probe probe probe probe probe erlbaum implicitly ignore interestingly parents parents parents parents parents parents parents parents parents parents outperforms largely hair asked asked asked opposed job job encodes formulate pentland pentland responds responds tween ideally ical malsburg malsburg malsburg tendency tight representa translated insights tems ijcnn convert carefully categorization buhmann buhmann paradigms sam sam responding alarm alarm familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity places applicability wider ucsd chris lighting lighting mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds mds achievable prefer prefer jet tanaka tanaka dropped outperformed alarms ory ory digitized colleagues relaxed twelve distractors distractors sparseness mis rem indi responded responded experimented validated simon eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces stan degrade ted distractor searched sentations rela rmse rmse rmse rmse rmse rmse rmse ness men dard stim parsimonious dissimilar dissimilar dissimilar dissimilar dissimilar remember judgments judgments judgments distinctive distinctive distinctive distinctive distinctive british scored hypothesize standing banks ratings ratings ratings periments blobs unfamiliar turk turk blend pilot plied males probabilistically grayscale gary gary draft race race nimh sional unreasonable yll garrison evoke motivations ulus quarterly lades eigenface eigenface folds psycho sistent illusions indiana indiana influencing influencing aids matthew volves blending avenues tionship blended caveat caveat cropped mahwah bloomington multidimen disappointing 
#@Busey_T,Cottrell_G,Dailey_M,
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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set set set set networks networks networks networks networks networks networks algorithm output output output output number number number number number system system system system error error error error error error error error error state state state state state state state results information information information information information information problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden performance performance performance performance performance based based based based based based based based based based based based based based space space space space space space space space space weights weights weights weights weights linear linear linear layer order order shown shown shown shown values probability probability probability probability parameters parameters parameters weight weight weight weight weight weight recognition approach approach point single single single single processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large large large local matrix matrix matrix inputs inputs shows shows shows shows signal signal signal signal signal signal signal signal visual visual visual visual visual visual paper small small size size size size size size size task task task fig fig features classification classification process current current current current current trained trained trained problems problems problems high high similar similar architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation equation equation section fixed line rule vectors generalization generalization generalization parameter average states states note note experiments dimensional result result result computation computation research dynamics dynamics dynamics dynamics dynamics initial constant table table table synaptic science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left presented presented presented activation low object object object object object object object object object object object object object object object object motion learn learn learn learn learn learn outputs abstract properties likelihood likelihood references component ieee adaptive adaptive mixture mixture mixture context context context introduction action action action complex complex hand hand hand hand estimation behavior behavior behavior dynamic dynamic generated generated generated tion difference signals signals signals signals signals signals signals signals prior prior prior prior prior prior learned learned learned required multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple good binary conditions conditions bayesian equations markov make fact correct probabilities observed errors errors errors errors errors errors errors errors errors errors forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward simulations tasks tasks tasks total simulation simulation simulation human human human human human human human human human human computed computed sum times regions regions natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback knowledge em represented represented true compared compared compared desired desired desired desired desired series provide provide define objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects posterior posterior motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor brain brain brain brain equal contrast update selection selection selection selection selection selection selection selection institute words department internal internal represents represents difficult final final final final exp exp considered experiment environment hinton estimates estimates estimates estimates estimates estimates trajectory trajectory trajectory trajectory trajectory trajectory top top top top top determine determine approximate free estimated estimated basic basic pages pages produce produce produce derived derived weighted randomly randomly controller controller controller controller controller controller controller controller product actual actual actual actual finally processes processes selected selected selected selected evidence depends feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward describe arbitrary inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse predictions predictions implemented assumed shape shape generate supported role adaptation square end end end ability ability ability makes noisy sensory sensory simulated simulated probabilistic pairs pairs pairs pairs smaller needed needed combination combination jordan technology technology programming interesting segmentation mechanism mechanism special details numbers iterations max max max pre direct normalized bottom bottom bottom bottom bottom experts experts experts experts experts experts supervised supervised supervised expert expert expert idea combined produced light light light recent resolution pair takes movement movement movement movement movement movement movement movement movement movement apply introduced strategy strategy subset highly compare calculated calculated calculated calculated module module module module module module module module module module module solve locations gate gate gate grant arm arm arm arm arm arm arm scaling spikes predicted alternative generally demonstrate demonstrate conclusion place trajectories competitive competitive editors central modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules modules accurate accurate bayes exponential learns learns hard characteristics characteristics sigmoidal start exist movements movements movements movements averaged introduce manner manner manner force force force question appears relation produces produces ways generating describes distinct distinct simultaneously simultaneously simultaneously simultaneously physical text predictive select select competition competition estimator estimator solved densities evaluated open approximations evolution forms soft soft soft soft understanding allowed past diagram combining tracking tracking visible precision coupling existing formulation retinal retinal automatic coupled partially discussions gating gating gating gating gating gating gating gating planning selecting suitable computationally driven plots capture capture summary kind repeated induced induced contained showing superior lie contribution contribution strategies cues cues cues involved modular modular modular modular modular predictor predictor predictor predictor predictor predictor neurosci illustrates jacobs acknowledgments load intrinsic receive command command command command command command command command command command command transformed poor poor experience difficulty humans association mass helpful existence examine examine project combine cover notion act trace trace possibly editor adapt onset equally equally perfect changed thought impulse panel panel shapes shapes ith ith switching switching switching switching switching switching switching switching mixed extent contributions advanced track nowlan correction correction london closer forces division laboratories beginning beginning res res computers demonstrates demonstrates summation apparent transient psychophysical sharp ity commands schematic schematic execution execution execution switch switch switch controllers controllers controllers controllers controllers controllers rely mod mod ture qualitatively coherent traces traces converged converged wesley acquisition ghahramani contextual contextual contextual contextual contextual contextual contextual contextual addison japan japan appropriately perfectly jth jth addresses flexibility outcome reaching held kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato kawato transforms north responsible exceeds filled utilized started contexts contexts contexts contexts heavy heavy programs ensures ensures predictors corre holland regarded vertices vertices forecasting forecasting accounts consequences consequences reproduce properly contact arrows arrows wolpert wolpert wolpert wolpert wolpert splits splits approximator approximator interestingly receiving adopted influences dividing divide divide divide neurophysiology unable copy copy perceived solely decomposed acceleration acceleration illustration manipulation dominated annealed annealed activate uncertain relate paired paired paired paired paired paired paired paired paired switched switched switched switched acquired proach knowing gordon holding normalizing atr atr coordination picking remarkable sponding acquire spring somatosensory responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility responsibility japanese val cally agency manipulated manipulated manipulated manipulated manipulated loads zoubin scenarios spirit presently periodically experienced cho transaction mul united inappropriate thc daniel ues hip hip initiated replicates damping tightly erroneous simulates adjustments superiority comprises neurology manipulating manipulating gun narendra narendra responsibilities responsibilities responsibilities responsibilities responsibilities responsibilities responsibilities 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performance performance performance performance performance performance performance performance performance performance based based based based space space space layer shown shown systems systems values values noise functions neurons neurons unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution recognition approach approach approach approach approach approach approach approach approach approach approach pattern pattern point processing processing processing processing processing processing processing processing processing processing processing processing processing processing neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate test patterns patterns patterns patterns patterns patterns patterns form signal simple simple simple simple simple simple simple simple simple visual paper paper small size size size feature work work methods step step step step step step step step step process process process level level structure structure structure structure structure structure structure structure random memory memory memory memory similar similar representation representation representation representation architecture architecture architecture architecture architecture equation equation section section fixed rule rule general generalization parameter average states states states states theory theory theory term university university threshold threshold variables research research sequence dynamics dynamics constant constant standard connections connections connections connections connections science science prediction left present present phase phase phase activation activation low low temporal temporal temporal temporal press basis abstract computational analog references stochastic stochastic positive positive positive important decision decision introduction complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex behavior behavior stimulus effect effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic change difference complexity complexity complexity lower rules measure representations representations representations representations representations representations representations representations representations representations representations representations part part part previous bound bound cases firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type multiple multiple multiple cortex cortex cortex cortex good spike represent represent represent represent represent represent represent represent represent represent represent represent tree tree tree tree tree tree distributed distributed equations make fact proposed correlation correct correct errors finite simulations simulations simulations simulations simulations ing ing ing tasks human multi times elements elements elements elements elements factor factor dimension orientation knowledge negative negative negative artificial specific represented represented represented represented provide objects objects rates rates location perform active determined experimental discrete cortical brain brain brain brain power power steps steps steps steps steps accuracy connection connection connection connection connection connection connection connection connection connection support modeling morgan proceedings proceedings report department synapses internal code code code code code individual advances connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist connectionist difficult difficult addition graph sequences considered framework computing computing equivalent equivalent equivalent view view curves curves curves design san conference capacity determine requires requires choice significant free world speed speed speed pages give con 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structures structures structures structures structures structures structures structures structures structures structures structures trials trials uniform empirical operation representing representing representing representing representing call max making making window window window window depth depth depth depth depth depth depth depth early idea run added description neuronal neuronal neuronal recent recent advantage advantage advantage reported reported introduced period period identical hierarchical trees trees trees sense sejnowski cognitive cognitive recently relevant engineering sufficient varying varying smooth yields studies locations sensitive increased expression lead occur suggests suggests spikes spikes spikes predicted width occurs generally generally runs strength starting critical greater greater conclusions editors editors central differences clear mateo suggest suggest taking taking mechanisms mechanisms presence characteristics drawn intelligence decrease averaged manner program relation relation relation pro construct produces longer longer perception ways ways factors factors label mathematical sensitivity category explicitly simultaneously simultaneously simultaneously simultaneously linearly remaining slightly slightly events events events events john john john john choosing national national extracted independently formation formation formation review review viewed codes codes evaluate updated digits intervals false dendritic dendritic coupling fire fire fire fire fire fire fire fire fire fire fire usa sciences sciences candidate holds structural structural reason columns society computationally effectively effectively identify situation tend fine receives characteristic characteristic summary notice notice notice allowing allowing neuroscience neuroscience neuroscience issue oscillations timing timing timing timing timing timing timing gray built vary providing providing minimizes wave giles binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding binding hypotheses cat principles acknowledgments decreasing extend extend cowan remain schedule schedule requirements relations relations relations relations relations humans hanson limitations limitations recursive recursive recursive helpful postsynaptic fashion behavioral behavioral behavioral behavioral behavioral office structured complicated encode encode encode encode encode statistically cognition cognition neu examined act act act transmission psychology psychology psychology created ensure aspect der panel explored explored grouping grouping attempts chaotic established devices asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous asynchronous publishers defining diffusion spatially organized organized organized directional directional directional directional immediately monkey arise mation auto annual alignment researchers researchers researchers argument greatly behaviors percent evaluating hme hme embedded embedded lack lack posed share share marked marked marked rep rep biologically psychological ity calculating calculating stack mod reaches fall synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony singer sophisticated sophisticated comments findings findings findings findings sentence sentence semantic yielding feasible sort formally oxford refractory refractory refractory refractory refractory resources ordering ordering discovery naval arrival rigid lost lost inspired systematic systematic systematic kaufman chance primate analogy analogy proceeds hit hit hit interpret mark fail roles ral affected synchronous synchronous synchronous synchronous synchronous synchronous synchronous synchronous synchronous synchronous synchronous synchronous combinatorial fires fires fires fires fires fires fires fires fires fires spurious spurious composition infor analyses embedding combines representational representational representational representational von conjunction mental mental mental intended intended intended intended monkeys schedules branching branching branching branching branching branching branching branching spatiotemporal reveals offer pollack pollack matter repeatedly parse extends erlbaum epsp variants exploiting valuable alternatively fold interestingly interestingly accumulated fired fired fired fired fired fired fired fired associations neurophysiology neurophysiology fellowship creates opposed reaction encodes encodes encodes alternating distinction distinction distinction utilize utilize utilize utilize ideally malsburg affects discovering tight tight assess argue intuition community cessing biophysical graduate uncertain parallelism academy frontal represen locking page elsevier thousands els treating strict correlate walk utilizing utilizing utilizing utilizing utilizing utilizing syn bienenstock slot slot slot slot slot slot slot slot bility institut influenced slots slots slots builds builds telephone hundreds bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings bindings virtually utilizes abeles abeles establishes interpreting filler filler filler filler filler filler filler filler concern identically anatomy neglect believed believed believed partly couplings discarded ooo contrary frequent establishing establishing planck relational periodically periodically demands tations schmidt ings defense statements 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interrelated love love love love love struct historically evanston accrue ecological nomena construed commonalities commonalities alleviates mahwah pictorial uti gsttingen connectionists abil resents margalit 
#@Love_B,
#t12
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model input input input input function figure figure figure figure figure time time time time time time time time set set set set set set set set set training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output number number number number number number system system system system system system system system system system system system system system system system system error results results results results results results results results results results results results results results problem performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based space space space space vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown shown systems noise noise noise noise pattern single control control control control control control large large local rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis signal signal signal signal signal signal signal signal signal visual visual visual visual visual visual visual visual visual paper small small small size size task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task fig fig fig fig fig fig fig fig process process current current trained trained trained trained trained trained trained trained trained trained trained trained problems problems random random random random random high high high high high high high response similar similar similar similar show show show show show show section rule rule vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization average theory theory obtained obtained note experiments experiments experiments result university university variables independent found found found found found initial constant estimate standard standard computer terms science science prediction left left left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction presented low low frequency sets sets sets motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion learn components components components abstract find computational computational computational computational computational computational references component component component component component component due due important decision decision decision decision decision introduction hand hand behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect generated search search search search search search tion change change difference difference difference variable spatial assume assume assume assume assume assume measure measure measure signals signals signals signals signals signals signals signals signals signals prior learned chosen chosen chosen chosen chosen chosen previous previous previous cases cortex good long expected expected make make make correct observed observed ing tasks tasks simulation simulation human human computed made made feedback feedback orientation obtain original specific specific specific specific specific specific specific specific specific specific represented rates location determined goal cortical cortical cortical brain larger contrast contrast support train selection report words individual individual difficult difficult difficult difficult difficult difficult difficult difficult difficult difficult difficult exp exp exp scheme scheme scheme addition graph ai considered considered framework equivalent experiment experiment directly top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli detection detection capacity efficient significant significant significant significant significant significant significant significant significant speed speed speed speed speed speed speed increase increase increase increase give give con condition condition condition condition condition randomly randomly randomly randomly randomly randomly levels levels area provided finally processes evidence nature nature nature depends constraint simply biological measured measured measured measured measured normal normal denote fast fast limited limited limited limited limited limited assumption assumption assumption complete predictions amount effective assumed require end hypothesis makes simulated typically needed needed needed account transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer significantly significantly significantly increasing consistent trials trials trials mode language leads leads iterations direct direct direct direct making making early early magnitude combined combined added predict neuronal improved improved improved population population population population population population population improve directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions property takes reported moving moving moving include subject subject subject subject subject subject subject subject subject subject identical sense subset subset cognitive cognitive relevant sufficient varying varying previously previously subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects tions solve trans generalized generalized improvement improvement improvement improvement improvement improvement improvement sensitive sensitive entire increased increased occur occur trial trial trial trial trial trial trial trial trial trial deviation generally column column demonstrate demonstrate half half half place place row greater assumptions assumptions practice practice asymptotic learns taking mechanisms mechanisms mechanisms mechanisms labeled assuming exist identification denoted areas areas appears appears perception perception solving primary primary primary primary primary primary primary primary primary primary distinct sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity simultaneously remaining remaining remaining easy easy easy easy easy easy easy easy easy easy easy easy easy easy easy angle decreases viewed detailed operations forms discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination slow measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements measurements classical tracking remains remains intermediate sufficiently existing perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual contour inter retinal specifically candidate discussions characterized texture middle middle aspects identified importance maximal encoded divided modes modes poggio traditional traditional repeated dis dis vary vary vary dot generalize generalize paradigm highest highest highest operating difficulty difficulty replaced rise rise rise tech detectors plasticity comparable encode analogous attributes attributes measurement measurement measurement measurement measurement measurement measurement measurement measurement naturally possibly predicts perfect changed thought thought thought separated baseline generates improving great agreement phenomena phenomena phenomena phenomena biology starts processed easier directional directional directional directional directional directional directional worst consequence separately involve beginning gradually gradually localized localized demonstrates qualitative explained varies varies greatly percent profile profile generic generic readily quantitative psychophysical dots ity schematic resource qualitatively qualitatively substantial substantial findings median extreme instantaneous extensive extensive resources resources resources resources null null null null circular outcome proceed ments ments proceeds hyper interpret belong modifications modifications generalizes generalizes generalizes generalizes generalizes edelman displayed negligible decide moved accounts accounts searching searching searching counter exposure israel deg deg specificity specificity specificity specificity specificity specificity specificity informative informative informative informative informative informative informative informative informative informative informative informative extensively fold balanced ball skills consecutive discriminate discriminate discriminate discriminate discriminate discriminate unchanged liu liu liu liu liu liu rubin session session session session session session asked forced adopt exception exception causing acceleration acceleration acceleration classifies possibilities brightness argue verified searches searches emphasize fixation acquired employing importantly gilbert familiarity dramatic mini mea mea sessions sessions sessions sessions sees monitor identifies identifies hypothesized replicated concrete continuum dichotomy practically exposed judged trol rating ignores skill skill skill skill aperture surprise illusory spanning replaces searched searched searched direc hebrew weinshall weinshall weinshall weinshall extremes hypothetical evaluates scratch ously previ aii divides rutgers acuity sensitivities sensitivities sensitivities cri stereopsis uninformative uninformative uninformative embodies pnas pnas doubled abrupt abrupt stabilizes replicating als manifested manifested nals nakayama oblique ingredients sagi shapley sgi ramachandran interleaved interleaved discrimina supplement surements surements practiced sensitiv fer speci newark doubles periment broadened 
#@Liu_Z,Weinshall_D,
#t12
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm output output number system system state state state results results results units units units units units units units units units units units units units units units units information information information information information information problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based weights weights linear layer layer layer layer layer shown shown systems values values probability parameters parameters neurons unit unit unit unit unit unit unit unit unit unit approach pattern pattern pattern pattern pattern pattern pattern pattern point image image image image image single single processing processing processing control local local rate test patterns class class form form form form form shows simple simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper examples examples small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net net net net work work work work work work task task task task task task task fig step field field features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification process process level level level level level level level current current trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure random random memory memory response similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture architecture architecture architecture show fixed fixed fixed fixed fixed line line line line line line line line images images images generalization approximation average states theory theory note note experiments experiments activity activity activity activity dimensional university university research research target target target target target target target target target dynamics initial computer computer terms terms connections connections connections science science science science science science left left direction direction direction direction direction presented map map present present present present present present phase phase phase phase phase nodes nodes object object object object object object object object object object object object object maximum range range range range press learn learn learn position components components components outputs sample abstract abstract applied applied back back back find computational properties likelihood references component component stochastic positive positive procedure important propagation introduction complex complex complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical dynamic generated generated generated generated variance variance variance variance variance variance variance recurrent tion tion energy variable spatial spatial spatial assume measure measure measure measure prior representations representations learned higher higher part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part part center firing type type type multiple cortex cortex binary conditions represent tree tree tree tree tree tree tree tree tree tree distributed distributed make make fact proposed proposed proposed correlation scale simulations simulations resulting ing ing ing ing ing simulation simulation simulation simulation human human human human human respect respect performed elements elements regions means means factor made made made made made made orientation global knowledge knowledge knowledge artificial relative relative relative relative relative represented compared compared provide define define objects objects objects objects objects objects objects objects objects objects objects objects goal goal related related connected brain mit larger contrast contrast contrast support train nets nets nets nets modeling modeling proceedings proceedings proceedings proceedings report report institute department department version version consists internal internal individual advances advances represents connectionist responses scheme addition maps cambridge equivalent experiment experiment experiment experiment experiment experiment environment environment environment environment environment environment environment directly directly hinton hinton additional additional additional view limit top stimuli effects conference capacity determine requires requires requires requires requires statistics statistics increase con con con con condition randomly randomly clustering clustering clustering developed levels levels criterion lines lines lines lines lines lines lines lines product provided selected selected iteration iteration iteration iteration iteration nature nature nature inhibitory depends simply biological associative achieved technical describe describe arbitrary group group group tested tested corresponds complete stable finding common supported role require main eds eds cluster easily degree makes makes development objective objective pairs needed account account functional functional jordan interesting significantly head head head head mechanism special consistent consistent structures structures structures structures uniform uniform empirical principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle principle representing representing call call call iterations max supervised supervised depth magnitude idea combined combined combined combined run resolution property pair pair moving identical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical array array array array array cognitive cognitive cognitive cognitive cognitive dimensions dimensions sufficient sufficient highly compare compare unsupervised unsupervised unsupervised unsupervised unsupervised teacher teacher teacher teacher teacher subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects tuning yields studies converge achieve address address positions locations williams williams williams williams grant arm arm constructed horizontal horizontal horizontal parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts parts studied studied invariant rotation alternative alternative alternative correctly feed feed touretzky occurs strength segment segment segment conclusions depend central differences performs weak learns constrained suggest encoding propose propose propose taking strong external characteristics proportional intelligence labeled turn turn start min plane relationship groups groups scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene configuration configuration configuration configuration configuration configuration force force force base acknowledgements explicit explicit explicit relation pro written ways generating vertical vertical vertical distinct distinct distinct dept segments segments segments segments segments segments confidence implement category category category category category category category category category category category category category category category category category category physical involves integrated formed formed extraction select yield extracted extracted viewed interpretation transform centered decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition activities activities activities activities suggested suggested suggested suggested translation spectrum spectrum key partial partial earlier earlier earlier fitting initially sufficiently assigned assigned assigned avoid box box includes includes perceptual perceptual perceptual instances instances instances instances instances instances instances assignment recognize recognize discuss mozer mozer mozer mozer mozer mozer mozer mozer structural regular regular regular selecting identified extra uniformly society society society encoded encoded encoded divided divided oscillatory oscillatory detect invariance composed composed capture contained contained contained allowing neuroscience issue issue classify classify oscillations oscillations categories categories categories categories gray gray gray list vary michael relaxation paradigm paradigm paradigm providing binding binding cat cat received principles principles neighboring neighboring tesauro oriented oriented body body body explore remain powerful powerful exhibit experience difficulty relations relations relations relations relations environments recursive issues graphical scalar respond respond detectors combine combine relationships relationships relationships relationships relationships relationships relationships relationships relationships relationships relationships relationships root symbolic symbolic encode encode encode encode encode fundamental phases notion notion contours contours patch patch patch patch coarse coarse concepts possibly configurations configurations configurations configurations configurations configurations man man man man man man man man man illustrate illustrate eyes eyes eyes thought aspect versions der panel panel panel mapped nervous consist consist grouping grouping established indicating indicating scenes scenes scenes scenes scenes scenes scenes scenes distinguish variances guaranteed defining nowlan nowlan briefly handle london spatially spatially tive sys closer directional directional directional directional directional directional directional directional directional directional directional broad incorporate controls pool pool describing implicit implicit begin read patches depicted auto annual annual annual annual cybernetics nsf mellon alignment exemplars exemplars exemplars reflects carnegie limits applies applies cmu offset tional tional readily share incorporated ity ity requirement pittsburgh spread extracting incoming cal serve qualitatively suited singer coherent attentional specifies leaf leaf synchronization naive don leen sort sort sort primarily labeling assign assign tation angular angular narrow resources acts zemel zemel zemel zemel tensor homogeneous discovery discovery discovery discovery discovery discovery tem smolensky smolensky outcome turned rigid arranged establish establish plays clamped clamped murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy murphy convenient stronger stronger promising adjusting proceeds primitive primitive primitive primitive primitive interpret serves neurobiology observing belong belong salient arrays corner carry presentations continue composition becker becker representational irregular pat von von sides sides colorado accounts den den sphere branching arrangement arrangement arrangement reproduce dif bursts pollack pollack belonging belonging belonging belonging erlbaum erlbaum erlbaum erlbaum variants propagate tures tures tures tures vari informa informa dramatically yielded yielded yielded ure specification recursively recursively recursively asked asked ram encodes diverse distinction connec regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity regularity additionally junction decomposed decomposed malsburg flat flat hierarchies hierarchies hillsdale hillsdale hillsdale hillsdale examining clustered clustered tight leg leg gated biophysical grouped grouped grouped impose neurophysiological denoting mouth mouth mouth mouth boulder depicts depicts synchronized iri pos categorization categorization worth weaker nonetheless paradigms paradigms pools pools minor rotating fea fea fea fea indication permit struc status mann regularities regularities regularities regularities regularities regularities compositional continued mcdonnell junctions establishes autoencoder autoencoder autoencoder hid hid finer finer cast award compo concerns continuum continuum gram detects neocortex dog dog dog dog restricting outgoing screen screen reality planck spirit sian bumps bottleneck inducing twelve tags tags tags 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#@Mozer_M,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model neural neural data data data data data data data data data function function function function function function function function figure figure figure figure set set set networks networks networks algorithm algorithm number number number number number number number number number error state results results units units information information information problem problem problem problem problem problem models models models models models models performance based based based based based based based based based based space space space space space space space space space case order order order order order shown shown systems values values values values values values probability probability probability probability probability probability weight weight weight unit unit unit distribution approach approach approach approach approach point processing large rate patterns patterns analysis analysis analysis form form shows algorithms algorithms algorithms simple simple simple simple simple paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small size size size size size size size size size size size size size size size size size size size size size size feature feature work work work task task task task task task task task task task task task task task task fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig points points features classification classification process process level level level level structure random random random random response similar similar similar show show show show section section section section fixed line rule rule rule general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter real real approximation average average theory theory theory gradient note dimensional dimensional result threshold threshold variables variables solution solution independent independent independent independent independent independent independent log defined estimate standard computer computer distance distance science science science science left left present present machine machine machine machine machine machine machine machine machine object object maximum maximum maximum maximum range range range range range range range range learn learn learn learn components nonlinear sample sample abstract abstract applied applied computational computational density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive procedure important introduction complex complex behavior behavior behavior behavior behavior generated generated generated generated parallel parallel tion complexity complexity variable assume assume lower prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior word learned learned learned chosen higher part previous previous theorem cases type multiple good bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected expected expected expected expected make fact fact techniques techniques proposed correct correct probabilities probabilities observed observed observed observed observed observed scale scale scale minimum tasks tasks human human human human human human human human human human human human human human human human human human human computed sum eq eq eq eq factor factor dimension dimension dimension dimension dimension dimension dimension dimension natural natural natural natural natural applications study study study knowledge knowledge negative negative negative negative negative negative negative artificial specific true true true true true true true true application compute objects objects objects objects location location perform determined determined experimental related posterior posterior posterior constraints brain brain equal approaches approaches approaches approaches approaches approaches approaches mit larger larger larger contrast contrast contrast contrast contrast nets modeling modeling modeling modeling modeling proceedings institute institute words department department consists consists individual advances joint connectionist exp exp exp considered considered framework framework framework framework framework framework framework cambridge domain experiment experiment experiment curve view design detection detection conference requires choice choice free world estimated estimated increase give con weighted weighted weighted randomly randomly randomly randomly randomly randomly developed levels levels levels levels levels levels bounds bounds lines entropy provided evidence evidence evidence evidence evidence depends sampling simply increases increases increases increases increases increases describe arbitrary arbitrary group group fast limited limited limited limited limited limited close assumption assumption assumption assumption corresponds corresponds corresponds corresponds corresponds complete predictions predictions predictions predictions predictions predictions finding short short nearest nearest common assumed assumed theoretical theoretical theoretical theoretical require main ability ability ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance easily fit fit probabilistic probabilistic typically smaller smaller unknown fully jordan technology programming testing york consistent consistent consistent consistent consistent consistent consistent consistent consistent trials trials trials uniform empirical empirical empirical principle principle principle principle principle principle principle principle principle principle leads leads call numbers window window window international normalized magnitude attention produced choose description light denotes directions directions typical similarity similarity apply subject inference subset subset subset subset cognitive cognitive cognitive cognitive cognitive cognitive cognitive relevant relevant interest dimensions dimensions dimensions observations observations observations teacher subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects volume axis axis axis axis yields yields studies converge rl rl definition background horizontal horizontal horizontal concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept invariant extended trial trial wide wide predicted hybrid width boundary column setting demonstrate row row row row row row row greater greater greater greater conclusions neighbor valued central sigmoid bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes practice practice practice weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak suggest propose drawn drawn drawn intelligence intelligence labeled labeled assuming assuming assuming min min min min min min min min min min min plane averaged question denoted explicit suppose appears produces solving plot vertical vertical category category belief unique decreases independently independently independently independently independently focus focus dependence dependence depending depending learner learner understanding converges key key earlier earlier reasonable reasonable reasonable intervals intervals boundaries boundaries closed valid existing existing includes includes perceptual perceptual thesis priori formulation color instances instances instances instances sciences sciences plotted specifically priors holds discussions successfully reason determining selecting aspects capable importance differ computationally successful invariance capture capture interested neuroscience classify generative hold categories categories categories sampled sampled sampled sampled vary generalize generalize generalize generalize generalize generalize generalize generalize generalize generalize realistic realistic observable hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses automatically automatically principles principles illustrates acknowledgments receive presents law unlike powerful wiley essential experience exponentially exponentially exponentially rapidly rapidly varied humans humans mass helpful behavioral investigated applicable ideal analytically variability cover cognition contours hill smallest smallest smallest math gradients gradients naturally concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts predicts extremely psychology psychology rev illustrate illustrate equally ensure subsets aspect versions formal assumes assumes precise observe logic art extent extent extent simplest contributions submitted explain explain explain attempts massachusetts rows rows rows developing developing separable explanation tractable inside inside style precisely broad broad broad universal universal members members medical author qualitative qualitative meaning integrating integrating integrating integrating reflects apparent people people people applies applies freeman understood axes backprop orders detecting haussler haussler slower dots dots dots dots dots dots dots dots sharp sharp psychological howard fall qualitatively kinds kinds jaakkola jaakkola multidimensional gap pac aligned exemplar exemplar fits hope hope hope scoring scoring scoring belong settings monotonically responsible exceeds generalizes generalizes grammars excellent falls saul schapire mouse corre equals equals decide conjunction belongs chooses enable treatment infer infer mem extends inductive inductive likelihoods variants dietterich dietterich explains explains generalizing generalizing generalizing assigning treat linguistic discriminate appeared appeared rigorous shepard shepard shepard shepard leaming leaming job emerge emerge discriminative weiss generalizations generalizations solely spaced classic guess guess conservative principled principled principled mutually rectangular trends exam exclusive insights mitchell mitchell mitchell mitchell mitchell bounding hughes rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle rectangle considers ultimately gluck guided regimes pos spanned spanned spanned spanned spanned worth weaker figs figs supports preprint preprint challenge challenge completed completed capacities learners learners rarely rarely remarkable sponding prefer austin bold autoencoder loosely broadly incorrectly peaked core ples measurable systematically screen screen amenable mcgraw rectangles rectangles rectangles rectangles rectangles rectangles rectangles rectangles rectangles rectangles rectangles rectangles feldman feldman feldman discriminating entering tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum broader psych psych darker darker darker distributional psyche thinking myers perspectives meanings novelty novelty novelty inferences inferences refining blank fellow amples healthy healthy healthy healthy healthy healthy healthy story embody perceptually lozano told joshua inspiration uninformative uninformative uninformative uninformative uninformative uninformative embodies embodies distribute shed doubt detec itive misses guiding kruschke bers richards isolate embed textbook tered guessing offering confirming perez ruled rna deliberately frameworks interpolates cholesterol cholesterol cholesterol cholesterol sharpens keams routinely enclosing cept rnin leamed universe cix cix cix cix ihl ihl ihl tightest encoun puters feat impoverished bridging predoctoral quadruple 
#@Tenenbaum_J,
#t12
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set networks networks networks networks networks output output output output output output number state state state state state state state state state results results results results results results results units units units units information information information models models based based based weights order order order order shown shown values values probability probability probability probability probability noise weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution pattern pattern pattern pattern pattern pattern pattern point point single single processing local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate patterns patterns patterns patterns inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows shows shows shows signal simple simple size size size size net work cells cells cells cells cells features level level current current cell cell cell cell cell structure problems random random high high high response response response response response response show show show show show rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule real real average average average average average average average theory theory term term term term term term term note experiments activity activity activity activity activity activity result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables computation computation research research independent independent found sequence sequence constant constant constant constant standard distance connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science science science prediction left map low temporal temporal temporal temporal temporal temporal temporal temporal sets maximum range range press press learn continuous continuous abstract applied back find computational computational computational properties properties references due positive positive important important important context introduction introduction action action action action action action action action action action action action action action action action action action action action action action action action action action circuit behavior stimulus effect effect effect dynamic generated parallel tion tion tion change change change difference difference difference difference difference difference variable spatial assume lower lower lower lower lower rules rules rules signals learned higher part part center firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type type required multiple cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long long long long long long long long long distributed make fact fact fact fact proposed correlation scale scale resulting ing total total total multi times times means means potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential made global study study negative negative artificial relative relative relative relative relative represented application application cross cross rates rates rates rates rates rates rates rates active determined determined experimental experimental related gain motor motor cortical cortical cortical cortical cortical cortical cortical equal equal equal mit voltage steps comparison larger larger larger contrast connection support train train train dependent department synapses synapses synapses consists individual individual individual responses delay addition sequences sequences sequences maps cambridge curve curve curve curve curve curve curve curve curve curve curve curves transition transition transition transition transition stimuli detection detection upper upper upper world give give produce produce condition coding coding area area area area area lines lines provided provided finally nature nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends biological biological associative achieved discussion arbitrary arbitrary group group fast limited close close assumption assumption corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable actions circuits finding effective effective assumed assumed synapse synapse synapse generate generate generate supported supported role role theoretical journal journal ability rumelhart rumelhart pairs needed functional functional interesting interesting interesting york york york mechanism mechanism mechanism mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode operation operation operation operation operation leads leads leads pre pre pre pre pre pre pre pre pre pre pre direct making making window window window window window window inhibition normalized magnitude magnitude magnitude produced produced produced neuronal neuronal neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane discussed discussed recent recent recent recent correlations correlations correlations exact takes element apply side side side side side sejnowski sejnowski sejnowski recently relevant relevant relevant highly highly varying compare approximately approximately tions correspond studies studies separation modified interval organization organization sensitive sensitive sensitive grant amplitude lead studied occur suggests suggests trial wide wide spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes strength strength strength strength strength strength critical critical place greater greater hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian depend editors central differences exponential exponential weak strong strong strong strong mechanisms integration integration solid solid start relationship relationship introduce manner manner groups connectivity question suppose van van van van van van produces produces produces plot recall sensitivity involves slightly slightly slightly equilibrium equilibrium equilibrium equilibrium potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials competition yield national expressed formation dependence dependence depending codes variation variation controlled modulation forms sizes activities activities similarly past partial dashed dashed intervals intervals intervals generation generation generation generation generation initially sufficiently construction foundation foundation koch koch koch avoid existing fire fire fire fire fire figures figures bell bell bell illustrated illustrated activated regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular regular maximal modification modification modification modification modification modification modification modification modification modification mcclelland mcclelland modes modes modes modes spiking spiking spiking spiking situation miller miller miller miller miller essentially reached reached excitation induced neuroscience neuroscience neuroscience neuroscience conductance split physiological physiological follow follow timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing timing receptor comp comp comp involved vary vary vary absence realistic reach automatically automatically neurosci neurosci neurosci neurosci acknowledgments rat rat receive origin carried wiley transformed requirements circuitry steady strengths strengths strengths strengths strengths strengths postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic rise respond giving ideas behavioral plasticity plasticity plasticity structured variability variability variability variability variability variability variability presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic cognition matched matched induction induction coefficient coefficient trace illustrate changed adjusted der panel panel panel panel taylor precise separated separated separated hebb hebb hebb switching pyramidal generates submitted attempts chaotic charge integrate integrate integrate years histogram histogram histogram histogram histogram indicating indicating developing growth distinguish fairly navigation biology starts rapid rapid rapid closer producing pulses hippocampal hippocampal hippocampal hippocampal describing fluctuations fluctuations fluctuations fluctuations reflects apparent slower slower slower frequently frequently requirement operate operate howard summarized summarized summarized poisson reaches reaches fall fall synchrony synchrony synchrony song song song song asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric neuro neuro physiol windows conditioning wesley synchronization primarily primarily addison temporally temporally temporally temporally temporally temporally temporally temporally temporally temporally temporally driving narrow neurophysiol tem turned turned turned plays spontaneous chance chance significance stronger cerebellum imposed balance balance balance efficacy efficacy resulted occurring occurring neurobiology neurobiology shifts implications krogh integrator capacitor modifications hertz hertz fires analyses sompolinsky sompolinsky sompolinsky sompolinsky reset reset reset irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular irregular zhang zhang zhang zhang induce sides histograms interconnections hippocampus hippocampus hippocampus cerebral cerebral mem reveals ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp properly extensively impact jump statement harris receiving balanced balanced balanced balanced balanced vari fired fired discharge dramatically ple depression depression depression microstructure ter fellowship boser chaos solely covariances flat causal tight tight arising arising trends trends resistor community impose potentiation potentiation potentiation potentiation potentiation potentiation potentiation potentiation regulation hughes mediated paired paired synchronized topic isi abbott abbott abbott abbott abbott abbott abbott abbott abbott abbott abbott abbott abbott milliseconds dramatic drops interspike holding compu computa strict resembles palmer excess excess excess resolve discontinuous inconsistent monitor marks puts tectum blum blum blum blum blum blum neocortical hemmen hemmen integrates sen huang slices slices push gerstner gerstner gerstner gerstner gerstner gerstner gerstner sloan cur vivo vivo vivo reflection inducing enters robustly transmit adequately shortly shortly substrate prescribed blocked rent opinion spec newsome newsome newsome newsome wagner plenum ard asymmetry asymmetry imposes levy levy levy levy levy quantified plotting fluctuation fluctuation conveyed couple modifies schematically coincidence tsodyks tsodyks tsodyks synchronize lasting lasting leaky postulated thompson epsps epsps amit amit volumes cen poo poo poo poo poo panels panels panels softky softky softky han markram markram markram markram millisecond regularly alternately charging charging kempter kempter kempter quence pain plications preceded preceded preceded preceded amir strengthened congress unmodified assump looo abrupt abrupt brane conduc causality causality causality pairings pairings hyperpolarized arose strengthening aps retinotectal shadlen shadlen shadlen shadlen depolarizing contiguity transi eration waltham weakening weakening weakening pression correlograms keck navigational brandeis brandeis offs explo tances compensates brunel brunel brunel preparations rations inns unambiguously dms precede precede gustafsson gustafsson culture culture ified appreciable devia uncontrolled sakmann holt porally abraham curred hindered predoctoral dress 
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#*network network network learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input input data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time set set networks output output output output output output output number system state state results results results results units units information information information information information information information information based based weights order order order order shown systems values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters noise weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution distribution method method approach approach pattern pattern image image image single single single single single single single processing control large local neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test shows shows shows simple simple simple simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small small small feature fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells field current current current current current current cell cell cell cell cell cell cell structure random high high high high high high high high high high high high high high high response response response response response response response response response response response response response similar similar representation show show section line line rule rule rule rule rule rule general parameter average average average gradient obtained term term term term term term term experiments activity activity activity activity activity result result university threshold threshold independent log dynamics dynamics dynamics dynamics initial constant constant estimate standard standard standard standard standard computer connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science phase phase phase phase phase phase activation low low low low low low low frequency frequency frequency frequency temporal temporal temporal range range abstract applied back back find references component component component component component component component component component component component component component component component component component component component stochastic due introduction hand hand circuit estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect dynamic dynamic recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion change change change assume lower measure signals higher higher higher higher previous firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good spike spike spike spike long conditions distributed expected equations fact proposed simulations simulations resulting ing ing ing eq eq eq eq factor potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential feedback feedback feedback feedback orientation study study obtain relative specific samples represented compared application cross series series receptive receptive rates rates rates proc eye eye eye determined determined determined experimental experimental experimental experimental goal related related connected gain cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain power comparison larger larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields dependent source modeling selection synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses code individual advances exp exp exp delay delay addition computing domain equivalent experiment environment curve additional view curves design stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects capacity efficient requires approximate statistics statistics free world estimated increase increase increase con con con coding derived weighted developed levels levels area lines lines lines lines lines entropy processes depends depends measured technical feedforward feedforward increases increases increases fast fast fast fast fast fast fast fast limited close close corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory actions circuits amount amount short short short effective effective synapse synapse synapse synapse role role role role eds adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation hypothesis hypothesis degree including objective smaller underlying account functional fully transfer testing significantly increasing increasing increasing mechanism mechanism mechanism matching leads leads leads pre inhibition normalized light neuronal membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane recent reported lateral lateral lateral lateral lateral lateral lateral apply period period side sejnowski sejnowski approximately approximately calculated calculated calculated volume tions background background sensitive amplitude amplitude amplitude amplitude amplitude amplitude intensity expression deviation deviation deviation deviation deviation wide spikes spikes spikes spikes spikes locally occurs half strength strength strength strength hebbian hebbian hebbian peak peak weak constrained suggest suggest suggest propose propose strong strong strong largest largest characteristics drawn demonstrated solid solid solid solid proportional proportional proportional assuming assuming decrease averaged averaged averaged targets derivatives relation derive derive factors primary primary primary primary primary primary primary dept changing changing changing modeled modeled modeled involves slightly mutual mutual mutual mutual frequencies events shift shift shift decreases decreases decreases decreases decreases decreases decreases decreases dependence stationary evolution modulation modulation static converges key key earlier slow slow slow dashed dashed dashed dashed additive measurements normalization fitting intervals event foundation koch koch fire fire perceptual bell bell inter blind blind retinal plotted maximize activated absolute characterized major maximal maximal maximal driven presentation spiking spiking spiking oscillatory receives summary induced prob prob conductance conductance conductance conductance timing sci duration quantity play play nips observable binding binding maximization maximization cat cat cat cat cat neurosci neurosci neurosci neurosci neurosci principles subsequent operating acknowledgments decreasing trains trains explore stimulation circuitry exponentially steady steady integral postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic rise rise plasticity plasticity plasticity plasticity plasticity authors maximizing maximizing maximizing lgn affect encode func presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic neu circles circles transmission adapt adapt predicts predicts predicts portion portion pyramidal extent explain explain explain motivated integrate integrate agreement phenomena slope analytic caused ganglion rapid rapid nucleus mation consequence consequence acad axons res res summation explained integrating integrating evaluating freeman transient fed experimentally experimentally slower maintain release release release release release release release release release release release release release release release release release release release release release release release release release http berlin berlin berlin berlin mod poisson poisson anti anti modulated modulated modulated modulated resource resource resource resource resource singer germany physiol findings wesley phenomenon www addison martin refractory linearity neurophysiol harmonic receptors arrival saturation chance chance chance alpha striate interpret ral shifts shifts shifts integrator integrator responsible natl moments infor weakly reset reset saul saul ensures surprising mental ascent accounts advance recovery express cerebral cerebral suggesting saccade epsp epsp epsp explains fly infomax infomax infomax infomax grating depression depression depression depression depression depression depression depression depression depression basically maximized revealed revealed revealed nelson profiles profiles german affects resting evoked decorrelation scenario adapting adapting adapting adapting adapting subthreshold subthreshold subthreshold segregation segregation pij pij pij pij pij pij pij pij pij pij pij pij pij blocking mammalian proba deconvolution douglas mediated macaque intensities amino setup funded barlow barlow abbott intracellular intracellular esti grateful geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate geniculate obermayer obermayer obermayer obermayer molecules interspike tissue durbin experi tonic tonic covers palmer palmer bility accordance accordance justified tial vis vis hypothesized lated lated transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter transmitter neocortical affecting pronounced compo contrasts heeger ally luminance luminance slices successively resolved maxi acid sions inde spirit protocol protocol fol adapts drifting lar sentation fixing fixing substrate hyperpolarization rent plastic movshon movshon rij rij pendent altering simula gij gij prolonged prolonged sat sat hysteresis hysteresis saturates saturates saturates saturates klaus tsodyks tsodyks leaky leaky leaky mediate strongest epsps epsps justify lowing conveys ponent fruitful vitro ramp ramp nent poten sual stays signaling recur mitchison accord markram markram ulation steep mammals engel engel comput neurotransmitter modulates prog neur modulations christian ohzawa ohzawa simi mated calcu ferster ferster ferster ferster ferster ferster ferster ferster ferster rit alteration trast trast trast carandini carandini carandini carandini carandini carandini carandini carandini carandini carandini carandini carandini discus integrators shapley adaption ret paradox stimu kaplan kaplan laughlin laughlin miall trec caption adapta interleaved naptic mize steeper 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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural input input input input input data data data data figure figure figure figure time set networks networks algorithm output output output output output output output output number system error error error results results units units units information information information information information problem models models performance performance performance performance performance performance based space space space space space space space space space space space space weights weights linear layer layer layer layer layer layer layer layer layer case vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown systems parameters parameters parameters parameters weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution distribution distribution distribution point image image single single single processing large large local neuron neuron neuron neuron neuron neuron neuron matrix matrix matrix shows shows simple gaussian visual visual visual visual visual visual visual visual visual visual visual small feature work task task fig fig fig fig fig fig fig cells cells cells cells points points process trained cell cell cell structure structure random random random response similar similar representation representation representation architecture equation rule vectors vectors obtained experiments activity activity activity activity activity activity activity activity activity activity independent defined found found target target initial constant estimate connections connections science science left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction map activation object maximum range learn position position position position position position position position position position position position position abstract likelihood references due due important introduction action action action action action action action complex hand hand behavior behavior behavior stimulus effect effect effect dynamic generated generated difference difference difference difference signals chosen chosen part part part previous firing cortex cortex cortex cortex cortex cortex cortex good distributed distributed distributed distributed distributed distributed distributed distributed region proposed proposed length length length correct correct correct correct correct observed observed observed forward forward simulations regression computed multi regions regions regions mapping mapping mapping global obtain specific represented compared desired desired desired desired desired desired desired desired desired desired provide determined experimental constraints distributions motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor motor cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain equal steps internal internal code joint joint joint joint joint bias considered equivalent solutions curves trajectory trajectory effects choice give produce coding coding coding coding coding area velocity actual actual actual actual actual actual actual provided processes processes depends depends discussion describe describe tested transformation transformation transformation transformation limited close assumption complete effective effective assumed role easily degree sensory underlying combination transfer call making magnitude combined combined produced produced predict neuronal neuronal neuronal population population population population population population population population population population population population population population population population population directions directions directions directions directions directions directions directions exact pair movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement movement lateral lateral lateral sufficient approximately calculated tuning tuning tuning positions positions positions positions positions positions positions positions positions positions entire arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm parts correctly feed feed move move move move move move move move conclusion trajectories central interactions sigmoid accurate retina designed suggest encoding mechanisms cycle characteristics solid movements movements movements movements movements movements movements movements movements movements movements targets targets connectivity areas areas areas reference relation produces produces describes tuned tuned tuned tuned tuned tuned tuned tuned coordinates transformations transformations transformations transformations expressed expressed correlated estimator operations organizing organizing showed frames forms activities completely translation sign partial calculation calculation dashed epochs intermediate calculate norm degrees degrees coordinate coordinate plotted planning sensor identified closely closely uniformly uniformly uniformly uniformly uniformly uniformly maximal maximal modification paths delta link link contribution physiological involved vary vary play correspondence thresholds neurosci neurosci neurosci neurosci neurosci attempt preferred preferred preferred preferred preferred preferred preferred preferred receive presents command command command command powerful investigate humans accurately dotted biases biases existence matches successive ideal muscle muscle muscle muscle muscle fundamental neu act necessarily configurations configurations configurations perfect changed noted noted noted ment ment ment ment piecewise cos sensors sensors coded coded multiplication tool tool tool inside arc arc precisely directional directional directional directional directional broad consequence grossberg attribute attribute res res geometry geometry addressed questions questions varies populations populations populations populations populations reflect experimentally experimentally lack red psychophysical psychophysical marked marked adjustable continuously variant commands commands commands commands commands commands gen monotonic collective deviations deviations deviations deviations extreme extreme realized contribute representative aligned formally angular angular neurophysiol neurophysiol reaching reaching reaching reaching reaching reaching reaching reaching reaching reaching reaching reaching reaching inspired wrong ments ments ments primate analogy transforms fail fail planar muscles fires combines schwartz somatic somatic somatic somatic parietal parietal iterated cerebral cerebral cerebral cerebral stimulated contraction johnson johnson sequentially emission arcs ple workspace workspace workspace workspace workspace workspace workspace workspace visually visually pointing pointing asked sigma sigma tor spinal spinal jacobian trends modifying learnt mathematically guidance compatible cosine cosine guided guided exceed frontal frontal pos paris rough cartesian cartesian cartesian cartesian cartesian cartesian cartesian france attached abbott abbott abbott universit mimic behave gordon vanishes article answers bold arrow arrow broadly broadly broadly broadly broadly sensorimotor sensorimotor sensorimotor kinematic rons cord physiologically sharply coincide contributes repetition arrives synergy synergy sending positional scott scott scott tra unusual supposed linking analyse multilinear das das rotate resemble discrepancy directionally borders visuomotor visuomotor visuomotor visuomotor visuomotor visuomotor eralization anisotropic stabilized stars pierre pierre georgopoulos georgopoulos georgopoulos georgopoulos georgopoulos visualized regularly faithful faithful shoulder shoulder cedex proprioceptive proprioceptive proprioceptive rect otto accompanied raise antagonist antagonist elbow ubiquitous bullock bullock bullock muscular muscular coordinated coordinated agonist agonist posture posture pute finely finely concentric creases ccr elaborated bernard premotor yves anisotropy anisotropy anisotropy perimental jectories readable elaboration existed codings curie asymmetrically excursion 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#*network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model model model model model model model model model model input input input input input input input input input input input input input input input input input input input input input input input input input data function function function figure figure figure figure figure figure figure figure figure time time time time time time time time set number state results units information information models models models based layer case case case shown shown shown values values weight weight weight weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons pattern single processing processing processing control large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate analysis analysis matrix matrix matrix optimal inputs inputs inputs inputs inputs form form simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small size feature cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field field field field field features level current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure high high high high high high response response response response response response response response response response response response similar similar similar similar representation show show show equation equation equation equation parameter theory term term experiments experiments activity activity activity activity result result university solution solution research independent independent independent independent dynamics constant constant constant constant constant standard terms connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic science science science left direction direction presented presented phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal sets motion range range range range components basis abstract find properties properties properties properties properties references due important important mixture introduction complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex circuit behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change energy difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume assume representations representations chosen chosen center center previous previous previous previous firing type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike long represent represent distributed make fact proposed proposed proposed correlation correlation classes classes ing performed factor factor factor orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study filter specific cross receptive receptive receptive receptive receptive receptive receptive receptive receptive provide rates proc eye determined determined determined determined gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain equal contrast contrast connection connection connection fields fields fields support institute department synapses technique represents represents responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses exp exp exp exp layers ai curve curves curves curves top top stimuli stimuli stimuli stimuli stimuli stimuli effects capacity basic increase increase give con con produce randomly levels area area area velocity velocity velocity lines provided evidence evidence nature nature nature inhibitory depends depends depends depends discussion feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward increases increases close complete excitatory excitatory excitatory stable predictions circuits short synapse generate generate supported role role theoretical ability makes combination functional functional block block mechanism mechanism mechanism mode mode mode numbers direct direct direct inhibition inhibition inhibition bottom bottom bottom choose neuronal neuronal membrane movement reported lateral highly approximately tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning solve studies studies differential differential modified interval organization organization organization sensitive invariant invariant invariant invariant invariant suggests wide width column flow strength strength strength strength interactions differences weak weak propose propose strong strong mechanisms mechanisms mechanisms integration largest largest cycle cycle characteristics characteristics proportional proportional turn variety selective selective decrease manner connectivity connectivity acknowledgements derive produces produces produces produces produces produces perception primary primary primary primary primary primary generating generating describes describes tuned tuned tuned modeled interaction frequencies frequencies gaussians cycles national national dependence dependence influence lee suggested translation allowed allowed measurements measurements roughly remains intermediate intermediate initially foundation foundation foundation koch figures figures usa dominance eigenvalues eigenvalues determines coupled coupled partially characterized texture determining middle uniformly divided paths included wij wij wij computations mackay mackay mackay invariance invariance invariance receives excitation excitation refer soc soc strongly neuroscience contribution sci notation bar vary simplified play play absence realistic eigenvalue eigenvalue cat cat cat cat cat cat cat cat cat cat cat cat cat cat cat cat neurosci neurosci neurosci neurosci preferred preferred preferred receive receive selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity create exhibit exhibit exhibit circuitry circuitry steady replaced respond respond investigated eigenvectors lgn lgn pathway pathway phases attributes attributes attributes act act predicts equally noted panel panel extent regime submitted cos cos cos cos cos cos biology drive tive closer incorporate desirable nucleus monkey arise arise arise arise afferent consequence acad opt definite res res res arises arises bandwidth summation varies behaviors modulated modulated modulated singer singer sums physiol physiol physiol physiol physiol physiol traces traces displays phenomenon primarily primarily modify gabor gabor martin acts neurophysiol neurophysiol neurophysiol neurophysiol suppression binocular chance chance chance chance chance chance chance held held striate striate striate striate striate striate striate balance neurobiology neurobiology natl sompolinsky sompolinsky weakly loo loo moved mel mel mel sim reproduce deg deg deg deg deg express spatiotemporal suggesting eigenvector receiving insensitive insensitive insensitive insensitive stone stone grating grating grating grating grating grating grating grating grating grating grating grating maintaining ple depression depression wiesel wiesel wiesel wiesel emergent revealed nelson nelson nelson nelson nelson nelson responds responds preferences hubel hubel hubel hubel evoked sinusoidal representa arising arising conduction blocking douglas douglas douglas adelson adelson retain lond lond lond lond conversely selectively selectively afferents tively abbott abbott abbott abbott abbott intracellular geniculate tune amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification amplification supporting differently accordance twenty vis inhibit mahowald tanaka dominates char neocortical intracortical bergen bergen archi sloan sloan predictable sity amplified amplified amplified amplified ruderman drifting drifting drifting drifting drifting drifting drifting drifting drifting drifting ben ben ben oscillates doubling gratings gratings gratings gratings ous denominator sur rent opinion tivity neurones movshon movshon movshon movshon movshon movshon excite excite dominate enhancing manipulations manipulations rectification reproduces cooling tecture thompson thompson exhibiting electrically perspectives sky previ panels panels abs thalamic thalamic thalamic recur widespread univer plex narrower correla selec selec havior selectivities selectivities somers somers sponses tex masked duplicated malpeli malpeli malpeli malpeli malpeli malpeli amplify amplify ferster ferster ferster ferster ferster ferster sillito sillito efferent waltham silenced insensitivity insensitivity chung chung chung shapley shapley shapley intradendritic keck appreciated brandeis brandeis elevated elevated acteristics dms yishai yishai yishai sharpen coexist cynader tured alfred tun broadening suarez responsiveness ceils geniculo sisting sinusoidally broaden broaden maining broadened 
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning model model model model model model model model model neural neural neural neural input input input input function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time set set set set set networks networks networks networks networks networks networks number number number number system system state state state state state state state state results results results results results results results results results results results results results models models performance performance performance performance performance performance performance performance performance performance performance performance weights weights weights weights linear linear linear case vector shown shown shown shown values values values values values values values values values values values values values values probability probability parameters parameters parameters noise noise weight weight functions functions functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution method pattern pattern single control neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns analysis analysis analysis analysis matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows shows signal paper paper paper paper paper small small net net work work work work work step step field field field field field process process process process process level level level level structure random random random random random random high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar similar show show show show show show show show section section rule rule rule rule general general parameter parameter parameter average average obtained obtained obtained obtained term term activity activity activity activity activity activity activity result university university threshold variables computation computation research defined found sequence sequence sequence dynamics dynamics initial initial initial constant standard standard connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science activation low low low low low sets range range range range range press components continuous continuous abstract applied find computational computational computational computational references positive positive positive positive important important important introduction effect effect effect tion tion energy assume lower lower lower measure chosen previous previous bound bound bound bound bound cases firing firing required required long distributed proposed proposed correct correct correct observed observed observed observed simulations simulations resulting resulting ing total simulation simulation human human multi eq eq eq eq eq eq times factor optimization optimization potential potential dimension dimension dimension dimension dimension global study study study study obtain negative original original original original specific compared determined constraints constraints constraints connected cortical brain brain brain brain brain brain brain brain brain brain brain brain power steps steps steps steps comparison dependent dependent synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses addition addition maps framework transition limit limit effects effects capacity capacity capacity capacity capacity capacity capacity efficient efficient efficient efficient upper upper upper upper requires basic increase con coding derived derived randomly levels levels levels levels levels levels levels levels levels levels bounds bounds processes nature nature inhibitory inhibitory inhibitory inhibitory depends constraint constraint constraint biological associative associative associative associative associative measured discussion limited limited limited limited limited close excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable finding common assumed synapse synapse synapse synapse generate role role role role role role role require main main face hypothesis development development development development development development development probabilistic underlying account account functional interesting interesting ratio mechanism mechanism mechanism mechanism mechanism operation operation operation pre inhibition stored stored stored stored stored early neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal membrane membrane advantage typical similarity strategy strategy strategy strategy strategy subject recently recently compare previously calculated calculated works yields studies studies studies studies converge rl sparse modified modified observation organization organization organization storage amplitude lead lead lead studied studied studied studied scaling suggests wide correctly half half strength strength strength strength strength strength critical hebbian hebbian hebbian hebbian central sigmoid numerical performs performs weak weak weak weak sigmoidal sigmoidal turn selective manner manner manner manner manner manner connectivity connectivity connectivity question attractor areas derive derive primary describes mathematical mathematical modeled pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning implement explicitly explicitly linearly remaining remaining remaining remaining remaining develop adding expectation versus independently focus review correlated overlap evaluate evaluate restricted organizing fraction showed evolution soft understanding sign additive performing reduces reduces combining remains retrieval retrieval retrieval retrieval retrieval retrieval retrieval sciences sciences memories memories memories maximize structural structural major major identified identified efficiency maximal modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification modification computationally driven driven driven wij wij attractors efficiently post post plots plots plots identity strongly strongly showing showing lie strategies strategies strategies satisfy play play play leading neurosci moves operating operating satisfies law essential investigate updating put strengths integral reducing school rest rest behavioral muscle maximizing maximizing maximizing func func fundamental fundamental fundamental math math math closest plausible plausible plausible possibly man nervous nervous ith ith pyramidal baseline baseline defines animal animal percentage ment slope improves diffusion answer sys consequence axon arises cybernetics preceding reflect relevance tional conducted experimentally remove continuously biologically biologically biologically biologically maintain maintain maintain maintain maintain maintain requirement limiting reaches incoming incoming incorporating qualitatively neuro neuro implements implements implements implements implements implements traces sharing phenomenon feasible forming lagrange modify modify modify investigation resources resources resources jth tem fails significance satisfying alpha alpha alpha multiplicative efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy efficacy serves removing removing removing modifications optimally enhanced degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation degradation elimination mance mance studying studying studying negligible perfor perfor pruned pruned pruned pruned pruned dependency evident infinity israel israel mem suggesting theoretically theoretically horn properly storing eqs impact considerations davis implicitly lett maintaining deriving goodman maximized nelson preserving terminals comparative junction junction simulating letting peripheral trends modifying segregation segregation segregation compensate mammalian degraded degraded regulation regulation regulation regulation regulation regulation regulation regulation regulation regulation regulation regulation regulation deleted deleted deleted deleted meta meta weaker weaker weaker weaker memoryless paradigms maintains maintains son ation vanishes vanishes eigen tel tel tel tel mea tau tau tau removes served deletion deletion deletion deletion deletion deletion deletion deletion deletion deletion deletion deletion deletion deletion unbounded stochastically ongoing ruppin ruppin ruppin ruppin ruppin ruppin ruppin ruppin hypothesized developmental developmental adult reflecting determinant inherently medicine ning sparsely beneficial vanish ory degenerate evolving consumption dent lar wolff focusing ically prune aviv aviv aviv aviv recalled massive massive massive massive massive diverge metastable metastable metastable metastable metastable metastable searched levy modifies modifies modifies tsodyks undergoes undergoes waiting europhys ously wii seemingly fil fil sults ana continu mammals meilijson meilijson meilijson meilijson meilijson bears acuity acuity acuity dictated undergoing undergoing undergoing undergoing undergoing depen govern facing efficacies efficacies efficacies strengthened strengthened strengthened traced muscular muscular obeying simi alterations maintenance regulated regulated eytan strengthening strengthening strengthening strengthening strengthening strengthening regulate regulate dale sive viability hetero numer positivity positivity inevitable mas restore wasteful duces fro surviving effi concomitant strengthen taining nectivity vantage leslie regulates portrayed collapses isaac cently quantal judiciously rlt devi gal weakest weakest ynaptic infancy prunes dozens roland degenerates liss yardstick multiplicatively prun prun maining 
#@Chechik_G,Meilijson_I,Ruppin_E,
#t12
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model neural neural input input input input input input input input input input input input input input data function function function function function function function figure figure figure figure figure figure figure time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output number state state state results results results units units units units units units units units units information information models performance performance performance weights weights weights weights weights weights linear linear linear layer layer layer layer layer layer layer layer layer case case case case case vector vector vector vector vector order order order order order shown shown systems parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight neurons neurons neurons unit unit unit unit unit unit distribution distribution distribution method approach approach approach pattern point point point point point processing processing control control large large large large local local local local patterns analysis analysis analysis class class class matrix matrix optimal optimal optimal optimal optimal inputs inputs simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual paper paper small small small feature work work work work task cells step points features process cell high response response similar show show show show show show show equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation fixed fixed fixed fixed line line line line line line line line line line line line line line line general general general general general general generalization parameter parameter real approximation approximation average states theory obtained obtained term note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional dimensional dimensional result result result university threshold threshold threshold computation computation research independent independent independent found found found found sequence sequence initial initial initial initial initial initial constant constant constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate standard terms terms terms terms connections science low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency motion maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum position position basis basis nonlinear nonlinear nonlinear nonlinear continuous continuous abstract applied applied find find find computational properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due important context hand hand estimation estimation estimation estimation behavior stimulus statistical variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance variance recurrent variable variable spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial assume chosen higher part part bound bound bound bound bound bound bound bound cases type required cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex long long long conditions conditions conditions conditions conditions equations fact fact proposed finite simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations minimum tasks total simulation human human respect respect eq mapping mapping mapping mapping mapping means orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study filter filter filter true compared compared application compute compute perform determined distributions gain gain discrete cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical equal equal equal equal equal equal equal contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast morgan institute consists consists advances represents responses responses final addition considered considered considered framework computing equivalent experiment experiment directly directly curve curve curve curves curves curves curves curves curves curves curves san top effects determine determine efficient upper vision coding coding area types product actual finally finally iteration depends sampling achieved covariance covariance covariance arbitrary denote denote close close close close close close close close close close inverse inverse corresponds stable stable stable stable stable stable stable amount implemented assumed generate generate role role role theoretical theoretical require require square square ability ability easily noisy noisy noisy sensory sensory including kaufmann account mechanism consistent consistent leads leads squared call numbers numbers iterations iterations iterations iterations iterations filters direct inhibition inhibition bottom combined combined produced choose added neuronal neuronal denotes improved population population population population population population population population recent property property property takes lateral lateral apply identical quadratic quadratic quadratic array cognitive recently subjects volume tuning tuning tuning tuning tuning tuning tuning tuning smooth yields match match correspond achieve symmetric symmetric expression lead studied suggests suggests trial derivative predicted touretzky width width width generally pass pass demonstrate demonstrate demonstrate conclusion critical place conclusions editors interactions sigmoid peak peak moody asymptotic mateo propose propose taking hard presence proportional proportional turn turn assuming denoted denoted attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor areas areas edges written written primary mathematical distinct recall implement implement explicitly involves angle angle frequencies implies implies implies implies versus choosing focus dependence stages stages stages estimator estimator estimator estimator estimator estimator estimator estimator estimator codes evaluated evaluated controlled updated approximations activities activities activities discrimination reasonable dashed performing normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization combining filtering filtering filtering filtering filtering filtering filtering filtering filtering calculate sufficiently koch avoid sciences extension illustrated prove specifically variations simplicity straightforward straightforward closely closely differ encoded wij wij wij presentation presentation presentation attractors attractors attractors attractors efficiently efficiently orthogonal symmetry follow notation sampled simplified relaxation play dot realistic providing eigenvalue eigenvalue eigenvalue cat preferred preferred extract receive extend explore estimators hessian periodic existence ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal ideal analytically authors lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn lgn affect statistically hill hill hill hill hill hill integer thought adjusted quantities explored expressions consist isolated ment cos cos cos cos cos cos cos distinguish distinguish agreement orientations fairly nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity implementing satisfied satisfied closer filtered division nucleus mation commonly consequence circle read read read preceding preceding preceding requiring applies profile generic experimentally quantitative treated continuously chose conclude neuro unbiased unbiased unbiased eventually eventually lim lim converged multidimensional acts acts circular circular interconnected reaching reaching plays clamped spontaneous numerically striate multiplicative los keeping serves obtaining neurobiology infor sion zhang negligible washington infinity parietal express express clean extensively relies observer observer observer observer observer observer observer observer eigenvector rao rao rao rao expanding convenience aij aij aij aij aij spaced jacobian jacobian compensate expand expand expand frontal indexed geniculate behave lippman exhibited ward wider sigmoids inconsistent pouget pouget pouget pouget pouget observers observers observers observers observers bold adjoint contrasts heeger heeger heeger fij fij fij fij fij diamond colleagues transpose approaching confined pooling pooling pooling pooling pooling subscript iterating iterating iterating comprised simoncelli hypercolumn prime checked perturbative pooled pooled pooled angeles scribed divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive divisive lacking ana sual formalized subclass orthogonality oij oij oij braun tain looked handles admits admits admits matters decayed decayed ucla alexandre cram cram cram cram squaring squaring weaken barely circularly timation uij georgetown georgetown malized cortices straightfor widening idealization hills 
#@Deneve_S,Latham_P,Pouget_A,
#t12
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#*network network model model neural neural neural neural neural neural neural data data data data data data data data data function function function figure figure figure figure time time time time time time time set set set set set set networks networks training training training number state results results results units units units units information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem models models models models models models models models hidden hidden hidden hidden performance based case case case case case case case case case shown shown shown values values values values values probability probability probability neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution distribution distribution method method method approach single single single single single single single single processing neuron rate rate rate test patterns patterns analysis simple visual paper paper examples examples examples work task task task task task task task task methods methods cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells classification level level level level level current trained cell cell cell cell cell cell random random random high response similar representation show fixed generalization average average average average states states theory theory obtained obtained obtained note experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result university university university university university university variables variables variables variables variables variables variables variables variables variables variables computation computation computation computation computation research research research independent independent independent independent independent log log log defined found found table table table estimate estimate estimate estimate computer computer terms science science science science science prediction left direction present sets press press position sample abstract computational computational references due positive positive positive positive positive positive positive positive positive positive important important important context context introduction introduction hand estimation estimation behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical generated tion tion tion change change change change difference difference variable variable variable variable lower lower measure measure measure measure higher part part part center center previous previous bound bound bound cases cases firing multiple cortex cortex cortex cortex cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike spike represent expected expected expected expected markov markov markov markov fact techniques proposed correlation correct correct correct correct correct correct observed observed observed observed observed ing respect respect respect multi sum eq elements natural study study study negative negative negative negative negative negative negative relative specific samples represented true application cross cross cross cross provide provide provide provide provide provide define define compute location location perform active active active determined experimental experimental distributions motor cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain brain brain brain brain brain equal comparison larger larger support train train train dependent modeling modeling modeling institute institute institute institute words technique code joint joint joint responses delay delay delay considered considered considered cambridge cambridge experiment experiment directly curve detection detection detection detection detection detection detection detection detection detection full requires significant significant basic increase increase increase coding coding conditional conditional conditional conditional area types entropy entropy entropy product depends simply associative achieved measured measured normal technical hmm fast close close complete finding assumed supported theoretical theoretical theoretical theoretical ability hypothesis pairs underlying underlying underlying combination interesting interesting significantly special trials matching uniform mode mode mode mode mode mode mode mode mode mode details pre pre pre bits supervised idea choose light predict predict neuronal neuronal neuronal population population population population discussed improve correlations correlations pair pair robust movement reported apply include include period period recently compare works tuning yields correspond studies address address background chain symmetric entire grant expression expression expression suggests trial spikes correctly move column depend depend reward reward reward reward reward measures clear clear practice suggest strong mechanisms mechanisms demonstrated turn decrease relationship question question denoted areas van construct written ways estimating laboratory ann ann simultaneously simultaneously simultaneously simultaneously simultaneously simultaneously simultaneously mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual independently independently independently dependence dependence dependence dependence dependence depending depending correlated correlated evaluated evaluate evaluate fraction activities similarly reasonable calculation additive measurements sec remains foundation classified classified expect recorded recorded recorded recorded recorded recorded recorded recorded recorded recorded recorded fire combinations inter discuss determining modes modes modes modes modes modes modes modes attractors detect detect detect post post post post identity notice notice kind categories categories quantity paradigm delayed computes acknowledgments trains trains trains trains trains trains trains trains trains unlike wiley exhibit exhibit exhibit rapidly relations divergence respond respond school behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral behavioral plasticity complicated cover fundamental fundamental fundamental examined measurement analyze quantities observe nerve detected detected extent simplest animal animal percentage percentage histogram pairwise theoretic theoretic analyzed independence handle processed monkey monkey mation mation probable separately medical recording recording recording recording collected pure pure quantitative quantitative recordings recordings detecting measuring collective collective collective collective marginal redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy redundancy synchronization displays sharing globally redundant princeton conditioned conditioned conditioned conditioned animals animals neurophysiol nonzero nonzero nonzero chains familiar tishby tishby tishby tishby tishby tishby tishby affected ylx ylx preparation infor infor infor periods bialek bialek schwartz histograms monkeys monkeys monkeys monkeys monkeys monkeys monkeys monkeys thomas claim enable israel israel infer infer insight suggesting discriminate informa cholinergic drop session session cooperative alternating revealed comparative electrode conservative verified exam electrodes frontal frontal frontal pos paradigms xly macroscopic dramatic tissue computa challenge vice nec nec sessions sessions rewritten syn versa quantify quantify jointly jointly jointly impulses hypothesized abeles abeles abeles abeles micro incorrectly station believed conditionally cooperation synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy synergy william permanent indepen steveninck dence ruyter ganglia ganglia ganglia ganglia ganglia ganglia jerusalem jerusalem behaving behaving behaving behaving behaving behaving behaving entropies entropies inserted primates tighter tighter hebrew hebrew hebrew hebrew collect remember participate disappear amit basal basal basal basal basal psth psth encouragement touching georgopoulos bears depen yix gat gat gat gat gat gat shed vaadia vaadia detec itive dur mations rewarded signifi bergman bergman parenthesis prefrontal economy liebler strengthen raster participating ined hagai falsely falsely cantly huji naftali born tonically tonically caveat dkl cooperativity cooperativity corticonics bsf binational dently reproducible tractor moshe israeli kettner 
#@Gat_I,Tishby_N,
#t12
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#*network neural neural neural neural neural input data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set networks networks algorithm algorithm algorithm algorithm output output output results results results information information information information information information performance performance based linear linear linear vector order order order order order shown systems noise noise noise noise noise distribution distribution method method method approach point point point image image image image image image image single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single single processing processing processing patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix optimal form shows shows shows shows signal signal signal signal algorithms simple gaussian gaussian gaussian visual visual visual visual visual visual small small size feature feature feature task task methods methods fig fig fig fig fig points field features classification problems problems random response response response response response response response response response response response response response response response response response response response response response response response response response response show show fixed fixed fixed fixed line line line line images images images images average average average average average obtained note note note note note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity university computation computation research research research independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent target target target target target target target dynamics dynamics dynamics left left left left left left left left left left left left left left left presented presented presented presented presented presented present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation activation activation activation frequency temporal temporal temporal sets press press components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components sample abstract applied applied applied applied applied applied back back computational references component component component component component component component component component component component component component component component component component component component component due positive positive introduction complex complex hand behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus parallel tion spatial spatial spatial spatial spatial signals signals signals signals signals part center center center center multiple multiple make fact fact fact proposed proposed proposed ing multi sum sum sum times times potential potential made study study study filter filter original relative relative application cross provide proc location location location perform active eye eye eye eye eye eye eye eye experimental experimental experimental experimental related related related related related related related related related related related related related related related related related related related related related related related posterior distributions motor brain brain brain brain brain brain brain brain brain brain brain brain brain brain power voltage larger source source institute institute version technique individual advances joint represents responses responses responses responses responses responses responses responses responses responses experiment san san san top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli significant increase increase increase increase give channel channel channel channel derived derived derived developed types types types types lines entropy selected selected evidence normal normal normal normal normal normal normal normal normal normal inverse stable amount amount makes sensory simulated pairs underlying underlying underlying ratio ratio ratio ratio projection projection increasing increasing increasing trials trials trials trials trials trials trials trials trials trials trials trials trials representing details details details numbers filters window bottom bottom bottom bottom bottom bottom early early early early early early attention attention attention attention minimize sources sources sources sources sources separate separate separate movement movement movement introduced moving moving subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject identical sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects volume tions mixtures mixtures background background background background background background background background background locations locations locations locations locations locations locations locations locations separation separation separation separation separation generalized bounded channels entire entire entire amplitude horizontal horizontal scaling extended extended trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial demonstrate assumptions conclusions central central central central differences differences peak california solid solid proportional variety ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica movements movements movements selective averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged targets targets introduce identification annealing derive ways laboratory vertical vertical distinct distinct distinct distinct averaging remaining angle mutual events events events events events quality quality blocks blocks extraction expectation potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials extracted extracted squares showed lee lee lee decomposition activities activities activities processor smoothing performing epochs epochs epochs epochs epochs epochs epochs epochs epochs epochs epochs measurements delays sec sec sec sec event event event event event event event event event event event event event event event event event event event event event event event event visible msec msec msec msec msec msec msec msec msec msec msec msec msec msec eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg avoid recorded recorded recorded recorded recorded recorded recorded recorded recorded recorded box box activations activations activations usa usa bell bell bell blind blind blind blind blind blind plotted plotted plotted plotted variations variations black black successfully columns columns middle middle middle middle middle middle middle extra extra suitable effectively identify oscillatory oscillatory oscillatory projections projections projections projections projections plots plots plots plots plots tend notice link neuroscience physiological strategies timing sci vary vary paradigm minimizes quantization maximization overlapping overlapping overlapping extract minimized employed origin diego diego diego poor investigate varied relations relations relations relations relations strengths replaced successive respond project project applicable applicable muscle muscle muscle relationships maximizing variability variability variability removed circles trace trace plausible onset eyes adjusted panel panel panel panel panel panel panel panel panel panel panel panel panel panel separated separated mixed contributions contributions contributions isolated averages site site site site site site advanced rows rows rows band sensors sensors sensors analyzed phenomena phenomena phenomena analytic correction tool tool tool tool nonlinearity spatially spatially spatially spatially spatially spatially sites widely widely potentially separately involve angles acad circle medical fluctuations fluctuations fluctuations fluctuations raw populations populations applies poorly recordings detecting remove frequently ity maintain howard extracting occurrence ordered prevent sums coherent coherent display median median median median traces traces traces traces traces summed irrelevant globally aligned aligned aligned aligned aligned primarily forming temporally temporally temporally temporally drift naval children spontaneous spontaneous spontaneous systematic tools tools tools tools tools alpha alpha alpha alpha alpha alpha resulted occurring analyzing analyzing analyzing analyzing analyzing removing neurobiology shifts affected salk salk enhanced presentations presentations natl loo loo loo loo loo loo respective displayed captured counting counting deg deg artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts permutation smoothed reveals locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked locked record jolla augmented augmented late waveforms outlined infomax infomax infomax consecutive dramatically linked ter sig session session session super super latency latency asked removal removal removal reaction reaction reaction reaction reaction reaction reaction reaction reaction reaction reaction tween corrected corrected blue amplitudes amplitudes amplitudes ical spaced evoked evoked evoked electrode electrode eric tight visualization visualization visualization visualization visualization visualization visualization arising arising arising arising arising peripheral preserved conduction formance thick thick blocking ization hughes deconvolution terrence electrodes electrodes fixation fixation fixation fixation fixation projecting investigating frontal erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp erp records records records records records records records records records records records records records records records records records records records anal anal portions locking accounted accounted reveal nal increments topography topography removes clinical sorting continued scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp scalp identifies attributed ping invertible ongoing suffers exper adult broadly compo evenly subtracting proposes separates functionally artifact artifact artifact artifact artifact tended vertically longest colors absent accounting accounting accounting accounting attended attended attended attended attended attended materials scott scott concatenated focusing prominent blocked blocked blocked sep health sorted sorted sorted decompose decompose ysis arousal richer altering plotting save makeig makeig makeig makeig jung jung jung jung jung jung jung fukushima fukushima ther stim courses courses courses courses courses eog eog eog rightmost latencies latencies latencies clin clin clin lowing nent laterally panels onsets onsets onsets alertness multichannel multichannel multichannel multichannel multichannel multichannel fatigue ulation contributed visualizing visualizing visualizing visualizing visualizing aligning instructed instructed instructed instructed attend attend sponses button dur cies graphic endogenous endogenous sharpening contaminated blink blink blink blink leftmost documented highlighted aged activ alleviate mentally electroencephalographic smearing smearing smearing smearing mckeown girolami imental pervasive pervasive flashed sharpened separa participated blindly arate lapping disregards placements erry 
#@Courchesne_E,Jung_T,Makeig_S,Sejnowski_T,Townsend_J,Westerfield_M,
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks output output output output output output output output output output output output output output output output output output output output output output output number system system error results information models models based based based based based based based based based based based based based based based based based based based based based based based weights weights weights weights weights weights linear linear linear linear linear linear linear case order order shown systems values parameters parameters noise weight weight weight weight weight functions neurons neurons neurons neurons neurons distribution point point point point point processing local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis analysis optimal form simple simple paper fig fig cells points process process process level level cell structure structure structure structure high high response response similar show show equation equation equation equation equation equation equation equation equation fixed fixed fixed fixed line line line rule rule rule rule rule rule rule rule rule rule rule rule general general general real real average average average average theory theory term term term term term term term term term term term term term term term term term note note note note note experiments activity activity activity activity activity result independent independent independent defined defined found found found dynamics dynamics constant constant constant standard standard terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science left frequency frequency temporal temporal temporal temporal temporal range range press press continuous abstract applied find find properties references stochastic stochastic stochastic stochastic stochastic due due due positive positive positive positive positive positive positive positive positive positive positive positive important important important context introduction action hand hand hand behavior generated tion tion change change change change change change change change difference difference difference difference variable assume assume assume rules rules rules signals center previous firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long conditions expected expected expected expected expected expected make correlation correlation correlation correlation correlation correlation scale scale scale scale scale scale scale scale scale scale simulations total total sum eq times means means potential potential potential potential made study study study em obtain obtain negative negative negative negative negative negative specific compared compared compared compared compared compared compared series receptive define define define rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates proc experimental distributions cortical cortical mit comparison larger larger contrast contrast contrast fields train dependent dependent dependent institute loss synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists kernel delay addition ai cambridge equivalent additional effects effects effects detection determine full full requires significant approximate free increase condition coding coding coding derived derived product provided finally processes evidence nature nature depends depends depends simply discussion arbitrary denote fast assumption assumption assumption assumption assumption corresponds corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable amount amount amount short assumed assumed synapse synapse synapse synapse synapse synapse synapse synapse generate role role role theoretical require main main square square square hypothesis development noisy auditory auditory auditory auditory account functional technology interesting york york mechanism special consistent principle details pre pre pre window window window window window window window window window window decay idea run run description description description neuronal neuronal neuronal membrane membrane discussed discussed recent correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations property takes typical include subject identical side side side sense previously calculated volume tions differential differential achieve definition definition definition chain separation interval interval interval organization amplitude parts intensity suggests extended spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes width width width setting starting starting place hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian reduce conclusions valued depend depend depend editors editors central differences numerical exponential faster weak strong strong integration proportional pulse turn turn assuming exist exist iii iii averaged averaged averaged introduce acoustic denoted suppose relation relation van van van van derive index describes stability stability mathematical changing changing recall recall averaging averaging averaging averaging linearly slightly scales scales scales scales adding events springer implies implies implies expectation expectation expectation potentials formation formation dependence interpretation interpretation interpretation interpretation interpretation influence evaluated restricted approximations evolution modulation activities similarly constants sign sign reasonable slow slow slow slow dashed normalization normalization reduces reduces intervals intervals event generation generation sufficiently sufficiently sufficiently sufficiently expect existing existing usa formulation formulation formulation phys driven driven spiking spiking spiking identify identify oscillatory mackay mackay mackay tend tend miller miller miller receives receives strongly induced contained interested interpreted contribution contribution contribution timing sci hold notation notation quantity vary vary usual play play play nips neurosci principles operating intrinsic intrinsic intrinsic trains trains wiley rapidly integral integral integral integral dotted existence existence existence postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic rise biol referred variability statistically presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic possibly necessarily predicts rev rev changed precise precise separated nerve hebb hebb hebb hebb hebb hebb hebb hebb hebb hebb pyramidal contributions contributions contributions regime regime motivated years cart cart cart cart slowly slowly growth convolution derivation analyzed analyzed reasons inside inside bishop separately acad describing linsker linsker linsker linsker linsker linsker linsker linsker author argument relevance introducing formulated formulated formulated operate rely poisson poisson poisson poisson poisson anti modulated richard asymmetric sums germany germany decreased owl univ instantaneous instantaneous instantaneous cybern formally formally summing temporally temporally temporally angular pick driving impossible arrival arrival arrival arrival proceed maass generality spontaneous spontaneous consideration consideration khz simplify chemical efficacy efficacy efficacy efficacy interpret enhanced natl tone zhang zhang zhang bialek bialek corre corre sides accounts reader epsp statement accumulated divide specification shorter graded formulate hundred resting causal causal barn argue equality equality toy impose mathematically mathematically mathematically intensities win win win distinguished superposition enforce abbott preprint induces vanishes vanishes milliseconds milliseconds interspike interspike bution rewritten remark lation accordance institut institut insufficient stochastically stochastically abeles abeles puts reflecting eliminates stay stay hemmen hemmen hemmen hemmen contributes carries gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner gerstner arriving arriving arriving convolved convolved convolved brackets brackets brackets brackets enter enter stabilize stabilize pin pin talk dow tivity technische technische literal ansatz fiir inserting coincidence switzerland psp qij qij qij qij qij claimed aii markram markram markram markram highlight millisecond millisecond millisecond millisecond millisecond lations physik physik physik domany comput contributed triggers efficacies efficacies efficacies correla kempter kempter kempter kempter kempter kempter kempter kempter kempter proportionality noticeable fii refractoriness swiss federal pulsed inhomogeneous inhomogeneous inhomogeneous mth leo precedes precedes precedes precedes precedes precedes mfinchen mfinchen annu iin iin iin iin neuromimetic invited muenchen theoretische theoretische neglects aji aji aji ffir naptic naptic coincidences sour emaih evokes malization nay lausanne resolu 
#@Gerstner_W,Kempter_R,vanHemmen_J,
#t12
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#*network network model model model model neural neural neural input input input input input input input function function function function function function function function function function figure figure figure figure figure figure figure figure time time time time set networks output output output number number number system system system error error error error state state state state state state state results results units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information information information performance performance performance linear linear linear linear linear linear linear linear linear linear case case case order shown shown shown shown systems systems values values values values probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions neurons neurons neurons unit unit unit unit unit unit unit approach approach single single single single single single processing processing processing neuron rate matrix optimal optimal form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal gaussian gaussian paper small small small small task task task methods cells process process current current current current current current current current current current current current current current current cell random random random random random random response response equation equation equation equation section general general parameter real states states states theory theory obtained activity activity dimensional dimensional dimensional dimensional dimensional university threshold threshold variables variables variables computation computation research independent independent independent independent initial constant constant constant constant terms terms terms distance distance distance distance synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science present activation frequency maximum maximum press press press press press press basis basis abstract find find find density density density density density density density density properties references stochastic stochastic stochastic stochastic stochastic due due due due due due due due due due due due due decision decision introduction introduction action circuit estimation effect parallel tion tion change change change variable assume assume assume assume lower signals prior prior center theorem theorem firing binary binary binary spike spike spike spike spike spike spike spike conditions conditions represent tree distributed distributed distributed correlation length length length length length length length length probabilities total computed sum eq eq eq eq eq elements means potential potential potential potential potential potential potential potential study study study filter obtain relative specific specific series compute location location location location active active active active active active active active active active goal related related power power power power power power power power power power power mit mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage comparison comparison comparison larger train train dependent dependent source source source source source source modeling modeling institute loss loss loss synapses synapses synapses consists advances represents represents addition framework cambridge cambridge cambridge computing equivalent equivalent solutions limit limit limit limit detection detection detection detection detection detection detection detection detection detection detection capacity choice con con con channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel randomly conditional types entropy processes processes nature nature nature depends denote denote denote denote denote denote denote fast fast limited limited close close assumption short effective effective supported role role theoretical theoretical main eds eds end ability noisy noisy noisy noisy noisy noisy objective objective objective functional jordan technology transfer transfer transfer ratio york york york york structures uniform details details pre stored bits attention combined choose sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources neuronal neuronal neuronal neuronal neuronal neuronal neuronal denotes denotes denotes denotes membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane recent apply strategy include identical identical identical identical sense sejnowski sejnowski sejnowski sejnowski interest compare differential differential differential trans address background background locations locations channels channels channels channels channels channels channels channels channels channels channels studied suggests extended wide white occurs boundary hardware conclusions central measures clear peak peak weak temperature integration integration integration presence presence presence presence presence california decrease program denoted denoted denoted denoted denoted denoted acknowledgements boltzmann pro derive derive modeled modeled modeled modeled linearly infinite infinite infinite infinite infinite infinite infinite infinite electrical electrical spectral spectral spectral spectral spectral spectral spectral interaction mutual mutual potentials expressed stationary stages influence transform transform transform densities densities open open open open open open open open open open open similarly spectrum spectrum spectrum spectrum spectrum diagram diagram classical reduces reduces event false closed closed closed closed distances distances distances msec koch koch koch koch koch koch koch koch koch koch koch koch koch koch koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic currents inter discuss absolute discussions characterized detect detect detect literature post post plots summary refer refer soc prob link conductance conductance conductance conductance conductance conductance conductance conductance contribution sin notation simplified simplified simplified relaxation relaxation absence absence paradigm paradigm paradigm minimizes hypotheses hypotheses neurosci attempt satisfies satisfies wiley investigate steady steady postsynaptic fourier fourier fourier fourier tech rest investigated biol analytically cover cover understand presynaptic presynaptic presynaptic presynaptic fundamental matched hill smallest measurement measurement measurement measurement transmission transmission man perfect quantities detector expressions nerve nerve nerve ith pyramidal pyramidal pyramidal detected charge asymptotically theoretic theoretic variances waveform waveform analytical analytical capabilities london rapid perspective lin satisfied satisfied formalism formalism filtered ran commonly probable probable patches arises arises nsf sun sun fluctuations fluctuations fluctuations fluctuations questions limits double consistency embedded experimentally quantitative solla schematic schematic summarized poisson poisson characterize characterize cal tank tank pasadena conductances conductances conductances conductances conductances conductances green green green green neuro deviations spectra spectra spectra spectra spectra corrupted cybern ear sv sv oxford restrict restrict receptors clamped spontaneous spontaneous systematic saturation convenient significance simplify alpha familiar resistance resistance resistance resistance abilities efficacy efficacy transforms neurobiology synchronous optimally optimally substituting substituting reliably reliably passive weakly weakly weakly weakly weakly weakly weakly excellent dendrites dendrites dendrites dendrites dendrites dendrites decide regard dominant dominant lengths dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite dendrite thomas thomas tic treatment express express express mem mem mem reader reader kearns considerations considerations propagate adopted influences verify informa informa equivalently validity transmitted transmitted resting resting resting resting resting resting certainty scenario assess assess assess verified arising arising gated gated gated gated gated gated gated resistor resistor magnitudes biophysical mammalian activate efforts ultimately alarm drops microscopic hodgkin hodgkin syn reversal reversal reversal reversal reversal reversal resp resp resp thermal thermal thermal thermal thermal thermal cable cable cable cable cable cable cable cable cable cable cable cable cable cable cable cable cable cable sake quantify quantify huxley huxley eral dom neocortical neocortical sided sloan ignores convention sity mcgraw fidelity ionic ionic ionic ionic assessed christof tan propagates propagates propagates noiseless noiseless degrades plenum campbell apical biophysics miss sodium nonlinearly convolving mainen mainen mainen mainen segev segev segev amit abstr continuation membranes membranes membranes mild noises ions inactivation brevity univer equi equi unitary leak leak sev quantifying synap brane brane brane ampa ampa charges gpe timal stochasticity nimh longitudinal ported klab vth ezp geometries transmitting ses invoking papoulis papoulis moo moo moo century engaged verse rig cajal biophysically naptic lna dia ttm ttm yarom dimensionless erfc transverse rele ductance ductance boo boo ynaptic distort steeply illuminating detectability timely vant rth 
#@Koch_C,Manwani_A,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set networks networks networks output output output output output output output output output output output output output output output system system system system system system state state state state state state results results results models models models models models models models models models models models models models models based based based weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer case case case case vector vector order order order order order order order order order order shown values values values values probability parameters noise noise noise weight weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point large large large local local local local local local neuron neuron neuron neuron neuron neuron neuron rate rate patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis matrix matrix matrix inputs form shows shows shows shows shows shows shows simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual small small small small size feature feature feature work cells cells step step step step points points points field field field features features features features features process process cell structure structure random high response response response response response response similar similar show show show show equation equation equation equation equation equation equation equation equation equation equation equation section section rule rule rule rule rule rule rule rule rule rule rule general parameter parameter parameter real average states gradient term note note activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity dimensional dimensional dimensional result result university computation log log log found dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant constant constant constant standard computer terms terms connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science prediction prediction prediction prediction left left left left map map map map map map map map map map map map map map map map map map map map map map map map map map map map map phase activation low sets maximum maximum range range position nonlinear nonlinear nonlinear nonlinear outputs outputs abstract applied find find find find properties properties likelihood references stochastic positive positive positive positive important important important important introduction complex hand hand hand hand hand stimulus stimulus stimulus stimulus stimulus stimulus effect effect variance variance variance variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost tion tion tion tion tion change difference difference variable spatial assume lower signals higher higher higher higher higher higher previous bound cases cases type type type cortex cortex binary binary long conditions conditions conditions distributed expected equations make make proposed proposed correlation correlation correlation correlation correlation length length simulations simulations simulations simulations simulations simulations simulations simulations minimum minimum minimum minimum minimum minimum resulting classes ing simulation simulation simulation respect respect sum sum sum times times mapping dimension orientation orientation orientation orientation global global global study study study obtain obtain series series receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive rates rates rates proc location location active active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye determined constraints cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical equal approaches approaches larger larger connection fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields descent dependent individual joint represents represents connectionist responses exp exp exp exp exp exp exp exp exp exp layers layers layers scheme addition maps maps maps maps maps maps maps maps framework directly additional additional additional curves curves transition transition transition transition transition limit limit limit limit limit limit limit limit limit limit limit limit limit stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli determine determine requires requires choice choice significant approximate statistics statistics statistics statistics statistics statistics statistics basic con types finally finally depends depends constraint constraint covariance technical assumption assumption stable stable stable stable stable stable circuits common effective implemented shape shape shape shape shape supported role role role role role role require square ability degree degree degree degree degree degree degree degree degree degree degree degree degree degree development development development development development development development development development development development development development development development development development development development development development development development development development development development noisy fit objective simulated smaller smaller underlying interesting projection projection projection projection projection increasing increasing increasing increasing mechanism uniform principle leads leads leads leads inhibition inhibition minimize predict correlations correlations correlations correlations correlations correlations advantage advantage lateral lateral lateral lateral lateral lateral lateral lateral lateral lateral introduced subject subject identical identical identical identical relevant varying calculated module smooth yields yields yields yields yields match locations locations symmetric generalized generalized grid grid grid grid sensitive grant amplitude lead lead lead suggests deviation predicted boundary column half strength strength critical critical critical critical critical critical critical critical assumptions hebbian hebbian hebbian hebbian hebbian hebbian conclusions neighbor depend depend competitive interactions interactions interactions interactions interactions interactions interactions interactions interactions weak weak weak weak weak weak weak weak strong strong strong strong strong hard hard mechanisms largest largest reduction labeled labeled labeled averaged introduce connectivity annealing annealing attractor acknowledgements boltzmann relation derive derive produces index winner winner winner winner winner winner transitions transitions stability dept interaction interaction develop develop develop develop develop develop develop expectation competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition decreases yield yield formation formation formation depending correlated correlated correlated correlated correlated correlated correlated influence transform organizing organizing organizing organizing organizing ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular ocular lee centered soft sizes activities activities completely past additive additive expansion expansion sec sec remains remains intermediate intermediate intermediate intermediate initially initially degrees degrees figures includes usa dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance dominance eigenvalues plotted plotted discuss uniformly modification presentation plots plots miller excitation prob interpreted contribution contribution sci comp vary realistic minimizes eigenvalue eigenvalue eigenvalue eigenvalue cat neurosci preferred decreasing remain selectivity selectivity perturbation investigate exhibit put put strengths strengths periodic periodic fourier matches biol biol analytically analytically scaled structured structured structured lgn lgn lgn lgn lgn lgn affect func cover cover understand understand topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic analogous neu neu eyes eyes eyes eyes eyes eyes eyes eyes eyes som som som som som som som som taylor taylor fibers consist amari regime regime regime regime explain explain ment slowly slowly distinguish unstable unstable analytic analytic analytic analytic inside drive drive drive tive satisfied forces nucleus mation afferent acad begin optimize localized localized localized localized localized localized qualitative percent percent limits poorly continuously sharp biologically biologically maxima http berlin berlin berlin berlin anti anti anti anti anti characterize spread qualitatively germany shaped implements yuille cor uncorrelated uncorrelated www linearity recover nat binocular binocular binocular binocular binocular stronger stronger stronger stronger imposed interpret analyzing affected exceeds presentations moments moments moments mental dominant dif initialize emergence emergence emergence emergence emergence stimulated influences schulten ent basically basin emergent emerge emerge emerge emerge nelson profiles profiles arbor arbor additionally suppressed avoided beta monocular monocular ary intuition interact intra regimes weaker enforce sam sam sam sam sam responding responding pop amplifiers geniculate obermayer obermayer obermayer obermayer obermayer obermayer permit ritter ritter topography topography topography develops argmax const marks ferent ers compete stripes stripes stripes stripes stripes stripes stripes dom rons rons intracortical emerges emerges emerges emerges grids systematically amplified gence enforces bauer tical sur ues tivity hood relax stryker ular ansatz impor klaus localize rescaling stim tant exceeded wired unstructured unstructured unstructured rescaled analogously ons blobs critically emerging ocularity ocularity keller neur neur somers assump christian originate ond ond effec paragraph innervate lets sharpening sider dfg renormalization cyb cyb defects suddenly coarsely ulus inhibi oth sociated netw tition ceptive leaning istic sharpen sharpen competi competi petitive abe interpolates spect sharpens rii lished diagonalized outset 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#@Obermayer_K,Piepenbrock_C,
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#*network model model model neural neural neural neural neural neural input input data data data data data data data data data data data function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time set algorithm algorithm output output system system system system system system system system system system results results units information information information information problem problem based linear linear linear linear linear linear order shown shown shown shown shown shown shown systems systems systems probability noise noise noise noise noise noise noise functions functions functions functions functions neurons neurons neurons neurons unit unit unit method method method approach approach approach approach approach single single single single single processing processing large neuron neuron neuron neuron neuron test test patterns patterns signal signal signal signal simple simple gaussian gaussian paper examples small methods methods methods cells cells cells step current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random high high response response response response similar similar similar similar similar representation representation fixed fixed fixed real real real average note note experiments experiments experiments activity activity activity activity university university variables research research independent independent independent independent independent independent defined found found found constant standard computer science science left left direction direction direction direction presented presented phase phase phase phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal sets range press position components components components basis abstract applied find find properties properties properties references component stochastic important introduction action action action complex complex complex complex complex complex complex complex complex complex stimulus stimulus stimulus statistical effect generated generated generated variance variance variance variance parallel tion change change energy energy measure measure signals signals signals part center previous previous firing type multiple multiple multiple multiple spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long represent techniques techniques techniques proposed resulting total respect multi multi multi multi multi multi called called called potential potential potential made made relative relative relative relative specific represented provide objects determined posterior connected brain equal equal approaches voltage steps steps institute institute technique technique technique code code individual individual individual represents responses difficult difficult addition addition considered cambridge cambridge experiment experiment additional detection detection detection detection detection detection detection determine full full full statistics statistics statistics basic condition coding clustering clustering clustering clustering clustering clustering clustering clustering clustering types types types types provided processes processes sampling simply measured measured measured tested assumption assumption stable stable short assumed assumed shape shape shape shape shape shape shape generate main journal journal journal journal journal journal end cluster cluster cluster cluster cluster cluster cluster easily noisy typically transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer significantly ratio ratio ratio york window window frame frame idea idea idea idea combined produced sources neuronal population directions advantage pair separate separate typical movement side sufficient approximately calculated correspond converge address amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude parts studied invariant invariant spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes clusters clusters clusters clusters column conclusion depend central central differences differences differences differences presence proportional movements plane denoted denoted appears relation edges plot simultaneously electrical potentials extracted review depending stationary stages stages overlap overlap overlap transform centers frames frames frames frames frames frames similarly spectrum spectrum spectrum spectrum spectrum delays remains classified degrees recorded currents determines automatic prove activated candidate candidate variations discussions characterized characterized columns importance society differ differ build invariance fine kind neuroscience neuroscience neuroscience contribution running timing categories cues built vary vary paradigm attempt acknowledgments deal body remain remain carried american collection detail behaviour fourier tech links rest variability proved statistically hill circles separated separated nerve nerve nerve nerve shapes shapes shapes nervous detected detected detected detected detected animal great slowly variances waveform coded independence tool tool interneurons interneurons starts ganglion ganglion directional located leaves mation describing axons axons recording recording recording geometry fluctuations raw varies varies greatly collected pure axes recordings detecting detecting schematic templates wind wind cal suited shaped simultaneous simultaneous contribute shifted spectra spectra spectra spectra uncorrelated uncorrelated physiology physiology physiology sort primarily princeton ratios ratios ratios ratios ratios ratios ratios ratios ratios driving velocities flexibility air dealing dealing stated chemical tishby tishby tishby tishby tishby tishby wire carry hours infor overlaps overlaps overlaps bialek male expanded evident assembly arrangement israel treatment clean clean waveforms extensively insect insect broken insensitive escape escape escape escape dense fired neurophysiology neurophysiology numerous pointed comparative comparative comparative medium hundred electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode electrode clas grouped expand relating electrodes electrodes electrodes electrodes electrodes electrodes electrodes electrodes electrodes electrodes electrodes electrodes electrodes surrounding records cartesian translations emphasized dorsal preserve 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#@Davidowitz_H,Rinberg_D,Tishby_N,
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#*network network learning model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure time set set set number number number number system error state state results models models models models models based based based based based weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear layer order order order order order order order order shown shown shown shown shown systems systems systems values values parameters parameters parameters functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons method image image image image image image image image image image image image image image single single processing processing processing processing processing processing control control large large large neuron neuron neuron rate rate analysis analysis analysis analysis analysis optimal optimal form form shows shows shows signal signal signal signal simple simple simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper examples feature fig fig cells cells cells cells field field field field field field field field field process process level cell cell cell cell cell cell response response response response response response response response response response response similar similar similar similar show show show show section fixed fixed fixed images images images images images images images images images images images images images images images parameter approximation approximation states theory obtained experiments university university university computation computation research research research research independent independent independent independent independent independent independent independent independent independent independent independent log dynamics constant constant connections science science science science science prediction left left direction direction presented presented presented presented presented presented presented presented frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal range press position position components components components components components components components components basis basis basis basis basis basis basis basis nonlinear outputs abstract find find properties properties properties properties properties properties references component component component component ieee positive procedure important mixture context context behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical effect effect effect effect effect variance parallel parallel parallel tion tion spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial signals signals signals representations chosen chosen higher higher higher center center center center center center center center center center center firing firing firing type required cortex cortex cortex cortex cortex cortex cortex expected expected make region proposed observed observed observed scale scale scale scale scale minimum resulting resulting resulting resulting ing human computed respect multi multi sum sum eq means means natural natural natural natural natural natural natural natural natural natural natural natural natural natural feedback feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation applications filter negative vol relative relative relative relative relative relative specific receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive provide provide rates proc determined determined determined determined goal constraints gain gain gain cortical cortical cortical cortical cortical cortical cortical cortical mit comparison larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast fields fields fields fields fields fields fields source modeling modeling modeling institute implementation implementation code joint joint joint joint joint responses responses responses responses responses responses responses responses addition sequences sequences computing experiment curve curve additional curves stimuli stimuli stimuli effects effects efficient full full choice statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics vision vision vision vision vision pages pages pages pages pages coding coding derived derived derived derived derived weighted weighted weighted weighted weighted weighted conditional conditional levels area area entropy finally processes evidence inhibitory normal feedforward increases increases describe transformation close corresponds predictions common supported role theoretical theoretical adaptation square pixel ability ability hypothesis hypothesis sensory sensory sensory sensory fit typically typically pairs pairs underlying combination combination combination reduced account account account coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients interesting significantly significantly projection york york edge increasing mechanism special consistent matching principal principal principal principal squared squared squared squared squared squared filters filters direct inhibition inhibition normalized normalized normalized normalized normalized normalized early early early magnitude magnitude minimize description neuronal discussed recent recent pair typical movement lateral include include pixels pixels sejnowski recently highly highly highly highly varying varying previously unsupervised observations approximately volume volume tions tions achieve diagonal diagonal positions positions positions positions separation symmetric modified entire constructed horizontal intensity intensity concept scaling occur occur wide wide generally column setting demonstrate half conclusions mechanisms presence presence largest demonstrated assuming variety variety selective min introduce scene question explicit relation pro pro derive produces produces perception primary primary primary vertical vertical mathematical mathematical modeled missing explicitly simultaneously text unique scales scales scales scales scales develop shift john letters independently dependence correlated correlated communication influence decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition static discrimination reasonable measurements measurements measurements measurements classical classical classical classical classical classical normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization neighborhood roughly thesis bell weighting weighting sciences specifically absolute phys neighbors tests compression compression aspects uniformly divided divided poggio successful computations computations tend tend essentially soc conf neuroscience neuroscience neuroscience dis issue symmetry lie physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological physiological simplified realistic surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround surround wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet providing delayed highest cat cat neurosci principles preferred approximating neighboring neighboring neighboring neighboring selectivity selectivity selectivity essential exhibit relations steady steady optimized optimized issues preliminary preliminary examine examine examine examine biol plasticity plasticity relationships relationships dependencies dependencies dependencies scaled authors authors authors comparable proper proper func statistically statistically statistically statistically statistically statistically statistically fundamental phases notion matched coefficient coefficient coefficient coefficient concepts concepts editor editor necessarily rev rev noted panel panel academic extent explain attempts attempts histogram histogram histogram histogram indicating scenes scenes pairwise ground separable publishers orientations orientations orientations orientations orientations orientations derivation adjacent adjacent biology independence nonlinearity comparisons comparisons purposes division operators monkey commonly consequence acknowledgement involve opt localized localized researchers researchers researchers summation integrating behaviors behaviors behaviors led recordings rep http synthesis characterize popular cal occurrence qualitatively qualitatively marginal age simultaneous instantaneous pyramid cor globally uncorrelated cybern redundant www linearity approximates purely purely repre suppression suppression suppression suppression suppression suppression eliminated eliminated eliminated oja primate striate striate striate bands transforms transforms removing neurobiology sanger splitting splitting shifts moments loo loo james james bialek bialek corre pat moved dependency dependency evident schwartz schwartz schwartz schwartz schwartz chooses bases diameter diameter diameter diameter augmented proximity messages characterization cam fly dividing dividing divide grating grating neurophysiology specification sine fellowship kluwer deriving shunting recursively ties july uniquely spatio icassp utilize additionally ical decomposed chapter sinusoidal sinusoidal decorrelation illustration representa constrain cns cns summarizes perpendicular perpendicular exponent exam cessing labs ization disadvantage adelson surrounding macaque macaque macaque rectified rectified rectified rectified rectified rectified importantly anal figs barlow pop mimic rochester page page investigations round september unpublished november syn remarkable bridge justification justification multiresolution hypothesized olshausen orthonormal orthonormal orthonormal fill mirror hancock eral recursion eliminates appealing physiologically physiologically practically exposed meeting heeger heeger heeger heeger heeger wavelets resolved dog substitution isolation lowpass lowpass digitized html sloan sloan spie comm cascaded electrophysiological ruderman ruderman locality drifting drifting saturating gathered sentation mach adequately ated ated stationarity sur simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli movshon movshon ular neigh cardoso decompositions examines quadrature resentation bonds psych bair switzerland divisive divisive divisive divisive rightmost ously ages ordinate ordinate analyzer previ cent imagery roots miiller miiller grove rescaled ulation steep abscissa abscissa sponse instantiations duce partic abstracts indicative sponds sev annulus annulus cot albrecht decorrelated decorrelated decorrelated decorrelated eps publications sponses obser associ associ diameters cients intell denoising ume woods woods suspect surrounds ridges documented carandini carandini annular informational loca statisti suppressive suppressive suppressive pacific norwell rectifying anesthetized nyu nyu nyu nyu vations coef ined supplement asilomar alfred mallat ficients lausanne kurtotic geisler investigative puters boring 
#@Schwartz_O,Simoncelli_E,
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input function function function figure figure figure time time time time time time time set set set set set set networks networks networks output output output number number system state state state results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem models models case case order shown systems systems systems systems systems values values values values probability probability probability probability probability probability parameters parameters parameters parameters noise noise functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach single single single single single single single single single processing large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs simple simple simple simple gaussian gaussian visual visual task fig fig fig cells cells features features level level level level level current current current current current current trained cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure random response response response response response response response representation representation representation representation representation fixed fixed line line rule rule rule rule rule rule parameter parameter parameter approximation approximation average average average average states states theory term term activity activity university variables variables computation dynamics initial constant constant constant constant constant constant standard standard standard terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science direction presented presented activation activation activation activation activation low frequency sets sets maximum maximum maximum range range range range range range range range press press learn basis nonlinear nonlinear continuous continuous abstract applied properties properties properties references stochastic stochastic stochastic positive complex behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical dynamic dynamic generated variance variance variance tion change change change change energy variable spatial assume lower rules rules learned learned higher bound firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing type required required multiple spike long long conditions conditions represent distributed equations proposed probabilities probabilities scale finite minimum minimum ing ing ing tasks eq eq eq eq times means factor potential potential natural natural feedback global negative negative negative original specific define rates rates rates rates rates rates rates rates rates rates rates proc experimental constraints gain brain equal equal equal equal equal voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage train dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent source consists code code represents responses difficult exp addition sequences maps maps cambridge equivalent environment directly curve additional limit limit stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli efficient efficient choice statistics statistics statistics free world vision estimated increase increase con con con con con channel channel derived randomly randomly randomly finally selected nature nature nature constraint constraint constraint constraint simply simply feedforward increases increases tested transformation limited limited limited limited corresponds excitatory effective effective theoretical adaptation adaptation adaptation adaptation instance instance development sensory simulated dynamical transfer transfer transfer york mechanism mechanism matching matching uniform principle principle representing details details pre bits predict neuronal neuronal neuronal denotes membrane membrane membrane membrane membrane membrane property element typical typical period sense sejnowski sejnowski recently recently unsupervised definition chain separation modified generalized channels channels channels channels channels channels channels organization increased amplitude amplitude constructed intensity expression occur occur occur occur occur deviation spikes derivative predicted alternative loop occurs flow hebbian depend depend competitive central central retina peak peak peak peak peak exponential learns sound sound presence largest cycle drawn drawn proportional proportional turn decrease relationship averaged program question question denoted boltzmann boltzmann transitions ann distinct distinct changing changing changing changing changing changing modeled physical transformations scales consisting consisting mutual mutual mutual mutual mutual adding frequencies implies potentials focus depending correlated interpretation detailed densities open open constants dashed additive sec sec neighborhood closed closed msec msec msec msec koch koch koch koch koch dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic coupling bell bell bell blind illustrated automatic maximize maximize coupled coupled simplicity compression spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking invariance ten soc allowing conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance conductance dis duration satisfy comp comp simplified dot delayed ill maximization maximization maximization maximization maximization maximization maximization neurosci neurosci illustrates body explore wiley exhibit experience steady steady optimized dotted periodic periodic existence postsynaptic postsynaptic fewer matches maximizing maximizing maximizing maximizing maximizing proper proper affect analogous matched naturally naturally transmission transmission possibly adapt adapt adapt adapt adapt necessarily predicts rev equally equally equally equally voltages voltages voltages voltages nerve nerve nervous hebb hebb academic switching arbitrarily charge charge asymptotically growth orientations slope slope slope waveform waveform adapted answer perspective strictly protein commonly commonly consequence ion ion ion ion ion potentially linsker reflects behaviors transient transient experimentally adjustable adjustable ity http http 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insert initiated tightly connor connor remarkably settles electrotonic compress extracellular sodium nonlinearly compartments compartments adap respec biophys biophys biophys ages steepness walter kinetics inactivation inactivation continu aver regularly regularly blowfly stein dictated govern volt equi silence governs postulate modulations guiding conduc decayed wealth charged subunits subunits rio conservation conservation straint midpoint midpoint midpoint relearning alters klab klab klab klab transmitting correlating balances aged johnston advan tances laughlin laughlin interspersed din messenger rectifier baddeley zoo hitting regulating photons tage librium continual posit ductance ductance ductance ihi ihi sakmann encountering impinging cascades suprathreshold 
#@Koch_C,Stemmler_M,
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#*network network model model model neural neural neural function function function function figure figure figure figure figure number number number number number number number number number system system system system results results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information models models performance case case case case case case case case case case case case case case order order order order order order order order order order shown shown shown shown shown shown shown shown systems systems systems values values values values parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution point single single single processing processing large large large large large large large large large large neuron neuron neuron rate analysis matrix matrix matrix inputs form form shows shows shows shows signal signal simple simple gaussian gaussian gaussian gaussian gaussian visual visual visual paper paper small small small small size size size size fig fig fig fig fig fig fig fig cells cells features structure response similar similar show show show show equation fixed general general general general parameter parameter real states theory theory obtained note note note note activity activity activity activity activity dimensional result result result university computation research research independent independent independent independent independent defined defined defined found constant constant estimate synaptic science science direction present maximum maximum range range range range range range press press outputs abstract find references component stochastic positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive important introduction hand hand estimation estimation behavior behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect effect effect effect effect effect effect variance variance tion difference difference difference variable spatial assume assume assume lower lower measure measure center bound bound bound bound cases cases cases cortex cortex cortex cortex cortex long long represent distributed distributed expected fact correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length length length length length observed observed observed observed observed scale scale scale scale scale finite finite finite finite finite finite finite total respect eq eq eq eq eq eq eq eq eq eq eq means means means means dimension made made orientation orientation study study negative negative negative negative negative negative relative relative relative true true cross cross proc motor motor motor motor motor cortical cortical equal accuracy accuracy accuracy accuracy accuracy comparison larger larger larger larger contrast institute code code code code represents responses exp exp exp exp scheme scheme considered considered curve curve curve curve curve curve curve curve curves curves curves curves limit limit limit limit limit top top top effects effects capacity capacity capacity capacity capacity capacity capacity upper upper choice basic increase increase con channel coding coding coding coding coding coding coding coding nature depends depends depends discussion covariance covariance increases increases increases increases increases close inverse amount amount short assumed assumed assumed assumed shape supported main eds sensory sensory sensory pairs smaller smaller smaller york increasing increasing special consistent uniform uniform uniform mode representing details normalized normalized normalized bottom bottom bottom bottom bottom magnitude magnitude neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population discussed discussed improve correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations pair pair ensemble typical movement identical recently relevant relevant relevant varying varying conventional volume tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning studies rl evaluation entire entire grant arm amplitude amplitude amplitude studied scaling width width width width demonstrate half half strength strength strength reduce reduce conclusions valued depend interactions numerical peak weak weak weak weak strong strong strong strong strong strong physics reduction reduction characteristics proportional assuming min min plane decrease decrease decrease decrease decrease manner areas areas areas areas areas derive primary tuned tuned modeled linearly linearly linearly text angle angle angle angle angle scales scales scales implies implies implies implies decreases extracted formation formation depending correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated correlated codes codes codes codes codes detailed detailed transform evaluate fraction fraction fraction fraction fraction lee lee lee understanding discrimination sign sign sign reasonable reasonable calculation normalization remains remains remains remains valid valid degrees degrees degrees degrees usa eigenvalues discuss holds partially neighbors discussions characterized efficiency importance uniformly essentially characteristic characteristic capture decoding running comp vary dayan dayan dayan dayan dayan leading thresholds neurosci preferred preferred preferred preferred preferred acknowledgments intrinsic situations remain investigate exponentially exponentially rapidly estimators helpful fourier respond rest biol biol biol analytically variability variability variability variability variability affect statistically coefficient integer integer reading opposite opposite extremely perfect fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher freedom freedom freedom multivariate multivariate extent utility utility contributions regime regime regime regime regime regime regime regime indicating great cos cos cos pairwise pairwise orientations guaranteed coded coded analytical correction strictly broad broad commonly pool pool pool angles angles angles acad definite localized fluctuations explained behaviors limits limits profile profile substantially led generic capability capability lattice psychophysical peaks frequently biologically biologically biologically biologically ity calculating incorporating substantial substantial substantial substantial substantial conclude decreased redundancy unbiased tile tile tile specifies traces traces extreme extreme extreme extreme phenomenon uncorrelated uncorrelated uncorrelated cybern cybern cybern formally tation restrict angular angular angular angular circular jones enhancement grows grows saturation saturation saturation smith smith convenient primate overcome odd odd odd striate stated height keeping keeping analyzing implications enhanced natl sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky sompolinsky pat intended enhance uni parietal israel israel israel ensembles cerebral impact seung seung seung seung discharge discharge rao smoothly smoothly utilize argue decays crossover gener concentrate regimes academy cij cij indexed apparently abbott abbott abbott abbott abbott abbott preprint likewise likewise port port port reversed lation lation spacing broadly broadly believed peaked ally exploits decaying decaying proves inspection receivers compensated rel acknowledges trend prominent tim united denominator denominator newsome newsome jerusalem jerusalem plenum activates sebastian hebrew columnar saturates saturates saturates extremes claims claims subtract claimed dissimilarity fbr retains lacking subtraction spans spans enormous georgopoulos georgopoulos georgopoulos implication fund bigger presumed bij bij bij bij yoon yoon yoon yoon yoon yoon peters cram koenderink koenderink koenderink koenderink koenderink koenderink shadlen shadlen crucially detrimental suppressive snippe snippe snippe snippe snippe snippe kruse kruse kruse universally larry capac founda popu popu variabilities huji huji cha fmax fmax evant haim haim expec racah bsf binational ahnost fiz israeli ibr wisdom 
#@Sompolinsky_H,Yoon_H,
#t12
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input data data data data data data data data function function function figure figure figure figure figure figure figure figure figure set set set output output output number number number number system error error error units units units information information information information information information information information information information problem models models models models models models models performance performance performance performance performance performance based layer case case case shown systems values values values values values values values probability probability probability probability probability parameters noise noise noise noise functions functions neurons unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method approach approach approach pattern pattern point single single single single single single single single single single single single single single single single single processing processing processing processing large test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis optimal inputs form form form shows shows simple gaussian visual visual visual visual paper examples small small work work methods methods fig cells cells cells cells cells points field current current cell cell cell cell cell cell cell random random random response response response response response response response response response response response response response response response response similar show show equation equation equation equation fixed fixed line general general general general average average average average average average average theory obtained obtained term experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity university threshold variables computation computation research research log log log log log log log log log defined defined target target estimate estimate estimate estimate standard standard standard standard standard standard standard standard standard standard standard standard connections left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction temporal motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum range press components components abstract applied applied applied computational computational density density density likelihood references component due due important decision mixture mixture complex behavior stimulus stimulus stimulus stimulus stimulus statistical statistical statistical effect generated generated variance variance variance parallel tion tion tion tion tion tion tion difference difference variable variable variable variable variable measure prior prior prior prior prior prior prior prior part part cases multiple multiple multiple multiple multiple multiple multiple multiple multiple multiple cortex cortex distributed bayesian bayesian bayesian bayesian bayesian bayesian expected make fact proposed proposed correct correct correct correct observed observed observed observed simulations ing ing tasks tasks human human human called elements knowledge relative relative relative true true receptive provide objects rates rates perform determined determined determined experimental experimental experimental distributions distributions motor motor discrete discrete equal approaches approaches mit comparison support dependent report report loss loss version consists code code code code code individual individual kernel kernel kernel advances represents responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses exp ai considered framework framework framework framework framework framework cambridge domain directly hinton curve additional additional view view curves design transition top stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli detection determine determine approximate vision vision con produce coding coding coding coding coding coding coding coding coding coding coding weighted weighted area types actual actual finally sampling measured feedforward describe describe assumption assumption finding finding role theoretical theoretical theoretical eds journal journal journal journal journal hypothesis degree makes noisy noisy noisy noisy noisy noisy including including including fit fit simulated simulated simulated probabilistic underlying underlying underlying underlying account mechanism consistent consistent consistent trials matching uniform empirical principle operation operation representing pre international idea produced produced light predict neuronal neuronal neuronal neuronal neuronal neuronal population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions pair separate takes takes element movement movement reported reported lateral moving moving moving moving moving moving moving moving identical inference compare subjects subjects subjects subjects subjects subjects subjects subjects subjects tuning tuning axis tions tions correspond studies studies address address positions separation williams williams williams sensitive entire grant amplitude lead trial trial spikes alternative alternative width deterministic starting critical greater greater conclusions depend central differences accurate clear clear clear performs encoding encoding encoding encoding encoding encoding encoding encoding encoding taking mechanisms mechanisms selective selective relationship relationship iii acknowledgements van van van produces produces produces longer longer perception perception perception factors generating plot plot plot plot distinct involves angle angle unique consisting consisting gaussians applying quality quality versus decreases extracted extracted extracted reconstruction reconstruction communication communication communication viewed interpretation interpretation codes codes codes codes codes codes codes codes codes codes codes evaluate operations modulation forms activities activities activities activities activities activities activities activities activities activities suggested additive normalization sec fitting roughly remains foundation foundation existing includes kernels uncertainty uncertainty uncertainty uncertainty mozer discussions discussions successfully simplicity determining straightforward extra extra closely society society encoded encoded encoded encoded encoded delta delta modes modes modes modes presentation comparing plots essentially composed composed kind decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding showing anderson anderson anderson anderson neuroscience neuroscience neuroscience neuroscience neuroscience neuroscience dis superior superior issue satisfy quantity quantity quantity play dot dot dayan dayan dayan dayan dayan dayan dayan paradigm providing thresholds cat attempt preferred preferred preferred extract extract body explore unlike unlike create investigate involving involving accurately helpful existence matches matches matches matches behavioral behavioral behavioral behavioral ideal ideal possibility decisions decisions stream complicated workshop encode encode encode func understand understand surfaces neu examined naturally possibly psychology equally adjusted assumes precise baseline baseline generates explain finds optimum animal band band distinguish distinguish convolution smoothness smoothness smoothness coded coded explanation answer answer starts tive directional directional directional directional directional broad monkey arise consequence ion involve angles angles begin apparent reflect double collected profile profile profile profile profile peter poorly psychophysical psychophysical psychophysical psychophysical peaks recordings treated dots dots sharp sharp requirement poisson poisson reaches gen maximizes qualitatively richard logical logical expectations begins consistently ghahramani proportion proportion tation recover recover acts zemel zemel zemel zemel zemel zemel zemel zemel zemel reconstructed reconstructed reconstructed theories fails fails fails fits ranges multiplicative multiplicative intuitively selects reliably recovered ambiguity intended monkeys uni hasselmo deg deg deg deg deg young surprisingly matter colliculus informative motions motions motions motions motions motions motions motions motions motions motions motions extends considerations captures grants explains onr treat fitted ure neurophysiology unable equivalently asked break responds tween profiles profiles profiles ical personal personal personal reports superimposed flat transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent transparent distri distribu distribu uncertain regularizer neurophysiological depicts investigating represen apparently funded reveal pop pop things wider challenge modal handled preserves lation tom pouget pouget pouget transparency transparency transparency suffers mst interpreting char award appealing proportions tribution physiologically evenly peaked zoubin colleagues sliding rel pooling deter lar decoded decoded mul mul adequately convey unimodal unimodal unimodal unimodal unimodal unimodal unimodal recovering newsome newsome decode decode investigator movshon movshon unifying judge recovers erroneous broader chang conveyed conveyed darker pursued distributional distributional distributional distributional distributional distributional distributional distributional distributional distributional distributional stim scribed conversations judgments judgments judgments judgments ative perspectives vectorial reconstructing bimodal bimodal bimodal bimodal bimodal bimodal gatsby gatsby percepts percepts mined perceive ulation ulation sponse bears particu abstracts abstracts stefan gat wurtz wurtz wurtz cri cri unambiguous geoff ucl opera ond plete collectively investigators zky touret nimh detectable shrinks butions condensed shadlen shadlen shadlen quan alterna tiple tiple acute pression arizona arizona combina snippe snippe erating ulus quarterly treue treue treue treue treue treue treue treue treue treue tending nonmonotonic bot popu popula schwarz psychophys encod britten britten inefficiency equivalents acterized fare xix viously tity neuroreport decod charitable mml 
#@Dayan_P,Zemel_R,
#t12
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#*network network network network network network learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural data data function function function function function function figure figure figure time time time set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm number number number number error error results results results units units units information information problem problem problem problem models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden performance based based weights weights weights linear linear case case case vector order order order order systems systems systems systems values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method approach approach approach approach point point single processing large large local test class class class class class class class class class matrix matrix matrix matrix optimal optimal form form form form form form form shows algorithms simple simple paper paper small size size size size size size size net work methods methods methods methods methods methods methods methods fig fig fig fig fig fig fig step field field field field field field field field field process current structure structure structure structure structure structure structure structure problems problems problems similar show equation section section section section section section fixed fixed fixed fixed fixed fixed fixed line rule general general general general speech parameter parameter parameter real approximation approximation approximation approximation approximation approximation average states theory theory theory gradient gradient obtained obtained term term term term term term term note note note university variables variables variables variables variables variables computation computation computation solution research research log log defined defined found constant constant standard standard standard standard standard terms terms connections node node node node node node node node node node node node left present present nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine maximum maximum press press press press learn components abstract applied applied computational convergence likelihood likelihood likelihood likelihood likelihood references component component procedure adaptive adaptive propagation mixture mixture context introduction complex hand hand estimation statistical generated tion change energy energy energy energy energy complexity variable variable assume assume assume lower lower lower rules rules rules learned higher higher bound bound bound bound bound bound bound bound bound bound bound bound bound required binary tree tree equations equations equations markov markov techniques techniques probabilities observed scale scale scale classes classes classes classes ing total simulation computed respect respect respect respect respect respect respect respect sum sum performed called potential made knowledge obtain obtain obtain original original original original original artificial artificial artificial artificial relative relative true true true compared application application application application desired provide provide define define compute compute posterior connected connected distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions equal power approaches approaches mit mit mit mit steps larger larger contrast connection connection connection institute consists consists advances joint represents connectionist final final final final exp exp exp exp exp exp exp exp bias bias bias bias graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph considered considered considered framework computing computing computing computing computing directly effects upper requires significant approximate approximate approximate statistics statistics world pages give con randomly conditional conditional conditional conditional conditional developed bounds bounds entropy entropy entropy product product product provided provided provided provided provided depends simply discussion describe describe assumption finding theoretical journal journal instance future probabilistic probabilistic probabilistic typically typically underlying needed reduced reduced functional fully fully fully jordan jordan jordan jordan jordan technology interesting ratio increasing structures structures structures structures structures structures structures structures uniform max max max max expert polynomial denotes denotes denotes improved improve directions advantage reported introduced introduced include include machines machines machines machines machines machines side trees inference inference inference subset recently interest previously works yields yields definition mixtures mixtures mixtures evaluation chain chain improvement improvement improvement improvement horizontal expression lead lead lead lead scaling suggests derivative touretzky deterministic deterministic clusters clusters clusters setting demonstrate conclusion greater greater depend editors sigmoid sigmoid sigmoid sigmoid sigmoid accurate accurate exponential exponential exponential suggest suggest physics reduction drawn solid solid intelligence intelligence intelligence intelligence relationship averaged introduce derivatives boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann explicit relation monte van carlo generating metric linearly involves remaining text belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief applying springer overlap overlap overlap variation variation variation evaluated open restricted approximations approximations approximations approximations approximations approximations approximations approximations approximations forms similarly similarly partition partition partition partition allowed normalization normalization reduces iterative remains visible visible visible visible foundation david coupling expect includes thesis priori plotted discuss black holds successfully simplicity identified extra efficiency suitable maximal computationally wij wij wij identify literature literature efficiently efficiently plots procedures anderson dis dis issue quantity vary write providing nips nips nips nips approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating approximating tesauro minimized remain powerful powerful transformed limitations recursive divergence divergence divergence graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical biases biases biases dataset existence scalar variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational analogous removed removed removed removed gradients quantities quantities quantities obvious fisher message explain phd neal averages averages massachusetts site site site directed directed directed directed directed directed trivial crucial briefly tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable tractable benchmark considerable considerable considerable producing broad bishop mation mation products potentially describing optimize optimize optimize optimize medical read qualitative improvements considerably understood parameterized readily lack quantitative effort remove compares partitioning partitioning ture popular jaakkola jaakkola jaakkola jaakkola diagnosis naive shifted shifted shifted leen intractable intractable intractable intractable intractable intractable intractable feasible guarantee recover partitions partitions partitions eliminated eliminated extending kullback numerically chains accepted mark carry elimination elimination elimination elimination elimination saul saul saul saul histograms belongs facilitate lawrence chooses peterson enable snn refers repeatedly partitioned partitioned exploiting exploiting speeds vari parents approx entropic rigorous clique clique clique clique clique clique leibler benefits convenience par junction community gained toy toy compensate distribu approxi approxi jij jij concentrate termed termed weaker reveal suffer normalizing differentiating mix expansions factorized factorized factorized factorized factorized factorized factorized factorized factorized factorized factorized factorized factorized factorized factorized barber barber barber barber barber barber clarity clarity ters substitute fij fij sym restricting vanish lnp lnp lnp lnp lnp lnp lnp lnp lnp compensated sis sis computable iterating iterate probabil fore entropies substructures richer richer marginals marginals tighter undirected 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#@Barber_D,Wiegerinck_W,
#t12
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input data data function function function function function function function function function function function function function function function function function function function function function function function function function function set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output output output output output output output output output output output output output output output number number number number number number number number number number number number number number number number number number number number system system system error error error results units units units units units units units units units units units units units units units units units units units units units information problem hidden based weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case case vector vector vector order shown systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution approach point point point single single processing class class class class class class class class inputs inputs inputs inputs inputs inputs inputs inputs inputs form form shows shows shows paper paper small size size size size net net net net net net work work work points points points points points points points points points points random response response response response response response response similar similar similar representation representation architecture show show show show show show show show show show section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed vectors generalization parameter parameter parameter parameter parameter parameter parameter parameter real real real real real real real real real real approximation approximation approximation average theory obtained obtained obtained term note note result result result result result result result result result university university threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation log log log log log log log defined initial constant constant constant computer node science present activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation activation machine sets sets press press learn components outputs outputs continuous sample abstract computational computational computational computational computational computational properties properties references stochastic due positive positive procedure important estimation behavior generated variance tion tion complexity assume lower lower lower lower lower lower lower lower lower lower lower lower lower measure chosen previous theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound required required binary binary binary binary binary conditions fact fact fact region resulting classes classes total total computed computed computed computed computed multi multi sum sum called called called called called regions regions dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made applications em obtain obtain obtain specific true application define compute compute compute compute compute rates determined related equal equal mit accuracy larger nets nets department department department loss loss advances represents final bias layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers layers graph ai ai ai ai ai ai ai ai ai ai considered considered cambridge computing computing computing domain domain additional bit bit bit determine upper upper upper upper upper upper upper upper upper full choice world pages derived bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds provided finally simply achieved discussion technical feedforward feedforward feedforward feedforward feedforward arbitrary denote denote denote denote corresponds proof proof proof proof proof proof proof proof amount theoretical main main main journal ability degree degree degree degree degree degree degree degree degree degree degree pairs unknown york york edge edge edge edge empirical details numbers max making bits bits polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial idea choose choose choose improved practical quadratic quadratic quadratic subset recently engineering engineering varying varying volume volume works smooth definition bounded improvement constructed constructed exists exists lead concept derivative setting valued valued valued valued sigmoid measures largest largest largest largest drawn sigmoidal demonstrated exist base base question denoted suppose suppose suppose suppose suppose derive construct construct edges edges factors distinct distinct recall recall electrical involves involves remaining easy easy easy springer springer implies implies boolean national independently independently depending stages lemma lemma lemma lemma lemma lemma approximated similarly partition partition partition partition partition partition partition partition constants constants constants constants allowed sign sign sign sign combining combining neighborhood add remains construction vapnik vapnik prove holds selecting extra closely identify identity identity identity notice verlag verlag induced split dis superior contribution follow hold notation vary realistic minimizes leading extract layered replaced replaced replaced replaced accurately biases fewer giving ideas scaled scaled func act integer integer subsets subsets precise arbitrarily submitted established piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise directed track briefly sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn mathematics describing describing begin argument considerably limits affine pseudo pseudo pseudo parameterized peter peter haussler polynomials polynomials polynomials polynomials extracting conclude conclude conclude conclude lim differentiable yielding pac optimality fix fix acm approximates grows grows grows arranged arranged establish establish maass maass adds convenient ranges logarithmic grow definitions imply intuitively generalizes motivation bartlett bartlett bartlett bartlett bartlett bartlett recovered infinity israel israel foundations indicator warmuth erlbaum lett inf integers integers multiplying slight outline recursively chervonenkis break break break sontag sontag presenting solely chapter assignments assignments assignments hillsdale australia stands scenario tight tight param publication iff approxi bounding refinement parametrized eters dichotomies behaves behaves 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#@Bartlett_P,Maiorov_V,Meir_R,
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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input data function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training number number number number number number number number number number number system system error error error error results results results results results results problem problem problem hidden performance weights weights linear linear linear layer layer case case case case case vector vector vector vector order order order order order order order order order order order order order shown systems systems values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight weight weight weight weight weight functions functions neurons distribution distribution distribution distribution distribution approach point point point point point point single single large large local local local local rate test analysis inputs inputs inputs form shows shows shows shows simple simple gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples examples examples examples examples examples examples size size size size size size size net work task step step field field field field field field field process process process trained random random similar show show show show equation equation equation equation equation equation equation equation equation equation fixed fixed line line line line line line line line line line line line line line line rule rule rule vectors general general general general generalization generalization parameter parameter approximation approximation approximation average average average average theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory obtained note result result university solution solution solution solution solution solution solution solution research independent defined defined defined defined found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics standard standard terms terms terms terms terms prediction left left presented map present present present present sets sets sets sets sets sets sets sets sets sets sets range learn outputs abstract density references references stochastic procedure procedure introduction statistical statistical dynamic dynamic dynamic generated complexity assume lower rules rules learned chosen previous theorem type type good binary equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations make observed observed observed observed errors errors errors errors finite finite finite finite finite finite finite finite finite simulations simulations simulations simulations simulations simulations simulations resulting classes ing tasks simulation simulation simulation simulation respect respect called times times made made natural applications study study study study study specific perform perform distributions distributions distributions distributions distributions distributions distributions distributions comparison comparison larger fields fields fields fields fields fields fields fields dependent proceedings joint represents represents final addition computing computing experiment experiment solutions curves curves curves limit limit limit limit limit limit determine upper full full requires choice choice choice approximate approximate approximate approximate statistics statistics free world derived randomly randomly conditional conditional developed lines lines lines lines lines finally depends measured discussion technical group close predictions predictions predictions predictions predictions predictions finding short generate theoretical theoretical theoretical theoretical main main main noisy including including underlying dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical functional functional fully fully fully special special leads leads pre making making making supervised supervised supervised supervised supervised supervised supervised choose predict predict predict predict perceptron perceptron recent correlations correlations exact exact exact exact exact exact exact exact exact exact strategy identical machines relevant relevant compare compare compare conventional teacher teacher teacher teacher teacher teacher calculated calculated calculated works tions solve rl rl rl symmetric symmetric expression predicted alternative correctly deterministic deterministic deterministic flow critical assumptions assumptions hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian depend central measures measures numerical numerical numerical numerical numerical drawn solid proportional turn turn iii averaged question denoted explicit derive longer longer longer solving solving generating dept student student student student student student student student student student student student explicitly explicitly simultaneously averaging averaging averaging linearly infinite infinite infinite infinite infinite physical involves involves text text text unique scales develop mutual implies versus extracted expressed review solved solved evaluated evaluated restricted restricted restricted restricted restricted restricted restricted restricted evolution evolution evolution evolution evolution evolution soft updates updates key key dashed dashed expansion reduces reduces reduces closed closed closed closed closed closed remains intermediate calculate sufficiently construction expect activations batch batch batch batch batch batch batch batch batch extension specifically variations phys phys phys phys phys phys characterized characterized tests successfully simplicity simplicity middle effectively committee successful build identity composed sin follow built write simplified observable leading carried layered layered layered layered existence scalar circles math math generalisation analyze rev rev expressions expressions simplest regime motivated finds finds finds averages spin agreement agreement agreement analytical diffusion diffusion diffusion diffusion glass benchmark benchmark london london turns satisfied formalism formalism formalism formalism formalism formalism formalism formalism formalism incorporate sgn sgn sgn sgn sgn sgn sgn mathematics scientific describing describing fluctuations fluctuations mechanics consistency introducing introducing posed solla dots execution execution gen gen proven incorporating incorporating extensions green enables progress cumulative irrelevant don college saddle saddle saddle saddle saddle saddle restrict arguments recover recover theories familiar familiar replica replica replica replica replica replica replica replica replica replica replica replica operates operates guide preparation moments overlaps excellent excellent excellent excellent ensures iteratively realization realization histograms infinity draw impact implicitly lett lett lett mechanical saad 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#@Coolen_A,Saad_D,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural data data data data data data data data data function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number system system system system system system system system error error error error error error error error error error error error error error error error error error state state state results results results results results information problem problem problem models performance performance space space space space space space space space linear vector vector vector vector vector vector vector vector vector vector vector order order order order systems systems values values values values parameters parameters parameters parameters functions functions recognition recognition recognition method method approach approach pattern pattern pattern point point control control test patterns patterns matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal form shows shows algorithms simple gaussian gaussian gaussian gaussian gaussian paper examples small small small small small small feature feature feature feature feature feature feature methods methods fig fig fig step step points points points points points classification classification classification process process structure high high similar show equation equation section section section fixed general general general general generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real states theory theory theory theory theory theory theory gradient obtained dimensional dimensional result university university solution solution solution found found found found found found found constant estimate estimate estimate standard standard computer terms terms distance science left presented presented map present present phase phase machine machine range press position position nonlinear continuous continuous continuous continuous continuous continuous sample sample abstract back back find find computational computational computational computational computational computational convergence properties references procedure procedure procedure procedure procedure procedure procedure procedure important decision decision introduction hand statistical cost cost cost cost cost tion complexity complexity complexity complexity complexity complexity assume chosen previous theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound good good good fact proposed correct observed simulations simulations minimum minimum resulting computed respect performed performed performed called elements mapping means means means means optimization potential made study knowledge artificial compared provide define compute compute perform determined experimental experimental experimental experimental constraints constraints mit accuracy comparison comparison support support support support support support support support support support train dependent dependent selection selection selection selection selection selection selection selection selection selection morgan proceedings proceedings report words kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances scheme maps cambridge computing curve curve additional additional additional additional curves curves curves san top conference conference conference capacity determine determine efficient efficient classifiers upper upper upper upper upper upper upper upper upper upper full full choice choice choice significant increase validation validation validation validation validation validation validation validation give produce derived developed criterion bounds bounds provided provided nature depends constraint simply technical tested fast close close close complete surface proof amount implemented theoretical theoretical theoretical theoretical eds ability hypothesis instance easily makes noisy needed functional programming testing iterations iterations iterations max international international international choose architectures advantage separate separate takes takes strategy strategy subject subject subject machines machines machines machines machines machines machines machines machines machines machines machines machines quadratic quadratic quadratic trees sense sense subset sejnowski sejnowski recently engineering engineering sufficient approximately tuning tuning axis axis smooth smooth achieve definition risk risk increased exists suggests move generally generally conclusion starting starting starting place depend numerical designed practice learns propose reduction solid solid minimizing min plane averaged derivatives derivatives derivatives program digit written plot plot dept dept dept pruning implement explicitly dimensionality angle unique equilibrium gaussians minimization minimization springer shift john expressed centered soft margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin digits digits digits partial partial partial reasonable dashed convex add remains norm handwritten handwritten handwritten figures kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels usa instances vapnik vapnik illustrated automatic prove prove maximize variations variations structural structural determining suitable maximal maximal maximal maximal maximal maximal maximal maximal computationally efficiently situation situation plots reached verlag showing showing quantity quantity dot denker reach reach automatically automatically automatically satisfies explore origin origin poor overfitting overfitting investigate updating rapidly dotted dataset dataset dataset dataset dataset tech investigated authors smallest generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation changed adjusted rank rank singular singular singular aspect algo taylor taylor taylor taylor taylor taylor observe separated defines optimum mentioned advanced stop stop publishers expensive rapid choices hyperplane hyperplane hyperplane products mathematics mathematics simard beginning implicit implicit implicit implicit gradually medical lowest radius radius radius radius radius amounts tional experimentally effort continuously continuously continuously gen maximizes proven proven datasets datasets datasets datasets datasets display differentiable differentiable diagnosis trade trade indices indices indices college sv sv sv sv sv sv sv lagrange lagrange fix rithm dynamically dynamically dynamically dynamically dynamically hyperplanes labelled controlling discovery royal lecun multipliers adjusting satisfying satisfying hyper service repeat bartlett bartlett corollary corollary sion james regarded ascent sphere jackel initialize francisco foundations cancer cancer rich implicitly implicitly shavlik ball ball ball robert smola outlined svms svms svms svms svms svms unable sch guyon maximized validity smoothly smoothly smoothly solely reports hierarchies remote adapting adapting adapting adapting burges burges pub iff ftp ftp life life noting noting rough conversely indexed indexed sonar sonar sonar bring port williamson exploited increments mini mann remarkable lagrangian lagrangian lagrangian survey kopf christopher shawe shawe shawe shawe breast breast mirror routines mining dcs dcs bottou anthony sym sij neighbourhood degenerate adjusts wisconsin wisconsin ance faced doubling united brought actively generaliza kuhn ming addi cortes drucker predetermined routine mid postal campbell campbell campbell campbell campbell campbell gij tutorial srm srm srm mum coincides alexander eralization usps maximising maximising maximising maximising belmont calculus positively overfit fogelman incremented cheap chine alternately muller wadsworth rameter bernhard traversing tunable tunable imal holloway calif kauf negatively gallinari gorman gorman confirming proposing expres 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#*network network network network network model model model model model model model model model model model neural neural neural neural neural neural neural neural data function figure time time time time time time time time time time time time set set networks networks networks networks networks networks number number number number system system system system system system system error state state state state state state results results results results problem problem models models models models linear case case order order order order order order systems systems systems systems values values values probability probability probability probability probability probability probability parameters parameters parameters noise functions functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons unit method method pattern pattern pattern pattern point point point single single single single single single single single single single single large large local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix form form form form simple simple paper paper paper size size size size net task methods methods methods methods methods methods step step step step points field field process process level current memory memory response response response response show line line general general parameter real average average average average states theory obtained obtained obtained term term note note note result result result university university variables variables variables solution solution solution independent found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial constant constant standard standard standard computer computer terms terms prediction presented present present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase activation temporal temporal components abstract applied find find find find find references due due due important introduction introduction introduction introduction hand statistical statistical statistical effect effect dynamic parallel parallel cost change change change variable measure measure measure measure measure measure measure measure chosen chosen higher higher bound type represent represent represent represent equations equations equations equations equations equations equations equations equations equations markov markov make make fact proposed proposed correlation correlation correlation probabilities probabilities scale finite finite simulations simulations simulations simulations simulations simulations simulation respect eq called times potential study knowledge original specific compared compared perform related gain discrete steps fields fields fields fields fields fields represents ai ai ai directly curve additional additional additional solutions solutions solutions transition transition transition limit limit limit limit stage effects capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity upper upper full choice approximate give give con weighted developed area area types path path path path path path product product provided evidence iteration depends simply measured discussion tested limited close close inverse stable finding short effective assumed assumed assumed supported role theoretical theoretical theoretical makes hopfield hopfield hopfield hopfield hopfield hopfield hopfield hopfield reduced account dynamical dynamical dynamical dynamical functional functional interesting interesting interesting significantly uniform mode operation leads leads leads details stored bits combined exact exact exact separate apply apply introduced sense sense tions solve solve symmetric symmetric symmetric symmetric symmetric gate storage storage storage storage storage storage storage storage storage storage storage increased exists parts expression lead invariant scaling scaling scaling suggests boundary depend interactions interactions numerical numerical numerical numerical designed temperature physics physics physics physics external cycle solid turn turn exist plane averaged averaged introduce identification explicit van van derive index sequential sequential sequential generating generating describes describes dept dept dept confidence recall recall recall recall recall recall recall recall recall infinite infinite physical physical involves unique interaction interaction interaction interaction interaction interaction interaction equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium springer shift cycles review depending stationary stationary stationary overlap overlap influence solved solved detailed detailed evaluate evolution static translation translation constants updates updates past diagram diagram diagram diagram diagram diagram diagram diagram diagram performing performing roughly closed closed closed calculate precision activations activations activations inter coupled coupled phys phys phys phys phys characterized characterized simplicity build schemes invariance notice induced allowing interested interested interpreted interpreted contribution hold notation quantity play absence absence absence absence delayed overlapping bars origin unlike powerful essential difficulty difficulty relations involving involving strengths association integral integral integral behaviour behaviour behaviour applicable reliable complicated tanh tanh tanh tanh tanh tanh func presynaptic phases phases notion removed math math rev rev rev versions formal expressions expressions store store amari amari finds finds spin spin spin mentioned site site site agreement agreement agreement agreement derivation analytic explanation glass starts london turns formalism mathematics describing calculations meaning explained reflects reflects understood tional introducing introducing introducing employ frequently compares berlin reaches gen gen occurrence ordered asymmetric eventually lim lim lim lim uncorrelated indices college saddle saddle saddle oxford oxford oxford oxford oxford oxford extensive acm acm arguments proceed saturation saturation numerically numerically simplify stated balance balance replica occurring occurring transforms definitions overlaps sompolinsky excellent excellent excellent separating separating corre sim originally express arrive theoretically properly storing storing storing storing lett lett mechanical mechanical mechanical schulten rigorous reflected assess transparent arising exponent exponent exponent thermodynamic thermodynamic dominated jij jij compatible concentrate concentrate scope integrals integrals macroscopic macroscopic macroscopic macroscopic macroscopic normalised transients transients prevents rewrite microscopic microscopic microscopic microscopic removes persistent persistent observables observables observables observables observables observables observables coolen coolen coolen coolen coolen appearing lation discontinuous confirm king hemmen hemmen possess ters equa kirkpatrick markers vanish governing prescribed united united united sherrington sherrington sherrington sherrington sherrington sherrington sherrington asymmetry disorder disorder disorder ansatz ansatz ansatz fluctuating parame sible heidelberg meanings symmetrically sults violation pared flips lations lira glasses domany quences confused accompanying modulo quence amir kcl jects decade collectively gutfreund kingdom kingdom kingdom causality isolate rewriting film calcu enlarged mth condensed condensed acquires normalisation normalisation trast realisation died cosh cosh cosh ruled ulations 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#*learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural neural data data data data data data data data data data data data function function function function function function function function function function figure figure figure figure set set set set set set networks networks networks networks networks training training algorithm number number error error error error error error error error error error results results results information problem problem models models models models models models models models performance performance performance based space space space linear linear linear linear linear linear case case case vector order order order shown shown shown systems values probability probability noise functions functions functions functions distribution recognition method method method approach approach pattern point point point point large large class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper small size size size size size size size work work task methods methods methods step points points points points process process process process process process structure problems problems problems random random random show show show show show show equation equation equation section section fixed general generalization generalization generalization generalization generalization generalization generalization approximation approximation approximation approximation approximation approximation approximation approximation average average average average obtained obtained term note note note note note experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result university university university university variables computation computation research independent defined found constant computer science prediction prediction prediction prediction prediction prediction prediction low frequency sets sets sets press press basis basis basis abstract applied applied back find computational computational computational computational computational density references due due ieee introduction hand hand estimation effect variance variance variance variance cost cost difference difference complexity complexity complexity complexity complexity complexity assume lower measure prior prior prior prior prior prior prior prior prior higher theorem theorem theorem bound bound bound bound bound bound bound cases required bayesian bayesian bayesian bayesian bayesian expected expected make fact fact fact fact finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite finite minimum minimum classes regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression computed computed computed performed means means means factor dimension applications knowledge obtain obtain artificial relative samples samples samples samples series provide provide define compute perform determined determined experimental experimental goal posterior posterior posterior posterior comparison dependent department implementation kernel joint difficult scheme ai ai ai ai ai ai cambridge computing computing computing equivalent equivalent experiment experiment curve view view view curves curves curves design design limit limit determine upper upper upper upper upper upper choice choice approximate approximate approximate approximate estimated controller product processes processes processes processes processes processes processes depends depends simply simply simply simply achieved discussion covariance covariance covariance covariance covariance increases group corresponds predictions proof proof proof amount assumed theoretical theoretical main main eds square noisy including reduced reduced account dynamical unknown coefficients jordan interesting interesting interesting projection increasing consistent empirical leads squared call call call filters idea minimize minimize improved improved practical apply side inference engineering interest compare observations observations calculated tions tions studies diagonal diagonal definition definition definition definition locations modified observation williams williams williams williams williams williams increased expression expression lead scaling scaling suggests suggests matrices matrices alternative width setting setting minimal minimal differences measures bayes bayes bayes numerical clear practice practice asymptotic taking hard drawn drawn solid intelligence regularization assuming assuming minimizing start start start introduce identification identification question acknowledgements explicit explicit suppose pro derive derive estimating estimating laboratory averaging linearly scales scales scales applying applying minimization springer choosing family independently stationary stationary estimator estimator estimator lemma lemma lemma lemma lemma lemma lemma calculation calculation calculation dashed expansion expansion spaces add intermediate calculate calculate expect thesis eigenvalues eigenvalues eigenvalues plotted plotted plotted plotted priors priors holds holds holds determining straightforward aspects suitable society computationally computationally delta mackay mackay mackay notice conf conf verlag showing interested superior issue gibbs gibbs dot providing predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor approximating approximating decreasing carried wiley estimators integral dotted preliminary graphical dataset tech investigated int analytically proved hill coefficient naturally possibly editor spline academic ith motivated motivated phd electronic asymptotically asymptotically asymptotically asymptotically asymptotically stop formula formula formula growing expensive lies perspective easier division choices mathematics mathematics inversion inversion projected projected projected describing calculations calculations english arises arises demonstrates nsf considerably consistency generic conducted poorly orders orders rep span http calculating ordered differentiable naive corrupted intractable optimality optimality guarantee dealing stated obtaining obtaining definitions effectiveness inferior evaluations predictors predictors predictors predictors belongs uni approximators approximators belonging extensively sons statement inf characterization approximator approximator approximator approximator approximator approximator cam outperforms aston aston aston aston kluwer obtains wahba opper opper opper opper opper opper edinburgh edinburgh remainder mutually regulation paired noting conversely compu manuscript remark christopher hilbert hilbert suffers pictures industrial accomplish shrinkage practically coincide lying rohwer rohwer sij html enters wong mis derives eigenfunctions eigenfunctions eigenfunctions eigenfunctions eigenfunctions eigenfunctions eigenfunctions birmingham birmingham birmingham ira datapoints noticed ted proximation plexity tighter phy cient italy regional forthcoming zhu zhu zhu zhu superiority shrink forrest ously motivates mercer mercer proving manfred lemmas narx dash orthogonality kronecker tational ncrg ripley 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning neural input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number error results results problem problem problem problem problem problem problem problem problem based based based based based space weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case vector vector vector vector vector vector vector vector vector order shown values probability probability weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions neurons neurons method method method point point single single large neuron neuron neuron neuron neuron neuron neuron rate rate rate analysis analysis class class form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper examples examples examples examples examples examples work classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process current current current structure problems problems problems problems representation show show show show equation equation section section section section fixed line line line line rule rule rule vectors general general general general parameter parameter average average average average average average average average average average average average average average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term note note note note note university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables solution defined defined defined defined defined defined defined sequence table standard computer terms terms science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction direction activation activation activation activation activation machine sets press press outputs outputs continuous abstract applied back computational convergence convergence convergence convergence properties references due positive positive positive positive context introduction introduction introduction introduction hand hand tion difference assume assume assume classifier classifier classifier classifier chosen previous theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound cases cases type good binary binary binary make fact region correct correct errors finite minimum resulting classes ing ing total total total regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression sum performed called optimization potential potential potential potential potential natural study obtain artificial relative relative relative relative relative relative relative relative relative relative relative compared application desired define determined goal related related related related distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete mit mit comparison connection update update update update update update update update update update update update update update update update descent morgan department loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss version version version version version version version consists exp considered framework framework framework domain domain domain domain domain domain domain domain equivalent equivalent view view view limit full increase give con derived derived bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds entropy entropy entropy finally depends discussion discussion technical describe arbitrary denote inverse predictions proof proof finding short common supported require square square end hypothesis instance instance instance instance instance instance instance instance easily easily makes noisy fit kaufmann needed needed transfer transfer transfer transfer transfer transfer transfer transfer programming increasing increasing special consistent consistent trials trials trials trials trials trials matching matching matching matching matching matching matching matching matching matching matching matching matching details call call call pre making normalized normalized normalized normalized choose predict predict perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron denotes discussed discussed discussed property property property apply apply introduced introduced sense relevant previously approximately approximately works tuning solve solve smooth smooth correspond rl rl definition increased grant parts trial trial deviation occurs occurs occurs boundary generally setting setting conclusions valued performs exponential taking strong hard hard physics california california intelligence regularization variety minimizing introduce question appears derive solving ways factors factors label label label label label label label changing linearly infinite infinite infinite remaining easy unique equilibrium minimization minimization minimization versus family focus dependence lemma lemma lemma lemma labels labels understanding margin margin margin margin margin margin margin margin margin margin margin margin margin margin similarly converges updates updates updates updates updates updates updates sign key key additive additive additive additive additive additive classical classical expansion convex convex convex convex convex convex purpose add add norm views views includes thesis usa instances prove prove prove holds holds modification essentially identity receives receives link link link link link link link link link return lie lie lie follow notation involved usual relaxation nips nips predictor subsequent extend minimized employed unlike carried replaced limitations divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence graphical discriminant ml ml ml ml ml ml matches giving rest int int int int int int int int int working tanh tanh tanh tanh tanh func notion notion attributes attributes predicts predicts predicts predicts predicts changed subsets versions versions versions versions algo algo logistic logistic logistic logistic taylor observe observe perceptton perceptton motivated motivated phd established mentioned mentioned inequality inequality slope slope slope slope slope lies tool stress purposes purposes sections strictly strictly strictly strictly worst immediately commonly mathematics beginning attribute attribute definite definite meaning nsf parameterized passed measuring limiting limiting limiting gen gen proven proven serve achieves achieves sums replace differentiable differentiable differentiable multidimensional irrelevant redundant mistake mistake mistake mistake mistake mistake mistake mistake summing acm acm rithm arguments arguments tem impossible generality adds wrong ranges logarithmic logarithmic multiplicative grow interpret interpret viewpoint keeping keeping definitions affected hint mance schapire equals equals perfor widrow viewing reveals omitted warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth santa santa speaking speaking multiply slight converted converted logarithm logarithm 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#@Gentile_C,Warmuth_M,
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#*learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data figure figure figure figure set networks number system results results results results results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem performance performance performance based based based space space linear linear linear linear linear linear case case case case case vector vector vector order order shown shown shown shown shown values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution pattern processing large large large large patterns patterns patterns patterns patterns matrix matrix matrix optimal optimal optimal form signal simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian small small size work task task task task fig fig fig fig fig cells features features structure structure show show show show section line line line parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter average average average average average average average theory theory theory obtained result computation solution independent defined found estimate standard direction direction direction direction direction direction presented phase phase range abstract find find computational properties references due ieee ieee positive positive introduction estimation estimation estimation estimation stimulus statistical statistical statistical generated variance variance variance variance variance tion energy energy energy energy energy energy assume lower lower lower lower lower prior prior chosen part center bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound distributed bayesian fact observed scale finite resulting tasks computed computed performed dimension dimension dimension orientation obtain specific related related related related related related equal equal equal equal equal proceedings technique technique technique technique technique technique consists consists represents exp exp exp graph framework framework cambridge directly curve curve curve view solutions solutions curves curves limit limit limit limit upper upper upper upper upper upper choice free free free free free free basic pages pages give coding coding coding coding coding derived conditional conditional clustering clustering clustering clustering bounds bounds bounds bounds bounds bounds entropy entropy entropy product finally sampling discussion covariance stable amount amount amount common assumed supported unknown interesting york special uniform uniform uniform making supervised supervised supervised supervised denotes directions recent recent correlations exact exact exact exact exact property typical recently relevant interest interest compare compare unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised observations observations observations observations calculated works tions correspond converge differential trans trans observation observation expression studied studied studied clusters half conclusion editors bayes bayes bayes bayes faster asymptotic asymptotic asymptotic asymptotic asymptotic taking physics physics physics demonstrated solid solid assuming decrease relationship acknowledgements van van van van van van van derive derive derive derive written written estimating laboratory ann averaging linearly mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual springer implies expressed review depending estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator overlap overlap overlap overlap interpretation detailed centered activities suggested calculation calculation calculation calculation calculation dashed false remains valid valid calculate visible instances extension discuss specifically phys phys phys phys phys discussions straightforward straightforward maximal literature symmetry symmetry symmetry symmetry contribution gibbs gibbs gibbs gibbs gibbs gibbs quantity quantity bar reach put relations relations relations estimators estimators estimators replaced mass behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour behaviour scalar possibility possibility workshop workshop analogous math analyze rev rev rev rev quantities noted fisher fisher regime regime inequality inequality inequality agreement smoothness tool tool leaves probable universal universal calculations calculations calculations calculations calculations mechanics mechanics limits introducing haussler haussler haussler haussler haussler haussler formulated http branch branch branch branch gen qualitatively wesley www addison acm purely eliminate logarithmic check grow contract replica replica replica replica replica replica replica replica replica replica replica replica replica replica replica replica replica replica performances dependency den den den den den den sphere reproduce barron barron barron barron extensively santa lett posteriori posteriori schulten logarithm deriving rao rao rao rao acceptable opper opper opper opper opper opper 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#@Herschkowitz_D,Nadal_J,
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#*learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input data data data data data data data data function function function function function function function function figure figure figure time time set set set networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number results results results results results information information information information models models models models hidden based weights linear linear linear linear case case vector vector vector order shown probability probability probability parameters parameters noise noise noise distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition point point point point single single single analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix inputs shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple small net work work work work work methods step step step step step step step step step step step similar show show show show show show show show show show show equation section section section rule rule general general general general general real average average gradient gradient gradient gradient gradient term dimensional result result result variables computation computation log log log log log log defined defined defined defined defined defined defined constant estimate terms terms science science science phase phase phase phase phase phase phase phase phase machine machine machine maximum maximum learn nonlinear continuous abstract applied applied applied find find find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density density likelihood likelihood references stochastic due positive positive positive procedure introduction hand hand behavior statistical difference difference difference difference difference difference chosen conditions ing respect respect respect respect respect respect eq eq eq eq eq called called means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor em em em em em em em em em em em em em em em em em em em em series series define define define define brain brain brain brain brain steps steps steps steps steps contrast update update update update update institute institute version version version version consists consists consists exp exp equivalent equivalent equivalent equivalent equivalent equivalent hinton hinton statistics statistics statistics give give condition condition randomly conditional finally iteration discussion discussion covariance describe describe describe corresponds proof finding generate generate easily projection projection special empirical leads leads choose denotes denotes property property property property similarity similarity similarity include include side side sense unsupervised volume works works works works converge converge converge converge converge differential rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl diagonal generalized studied derivative flow flow flow flow flow hebbian valued clear clear taking minimizing minimizing minimizing decrease decrease decrease derivatives derivatives derivatives derivatives suppose averaging slightly springer expectation john independently densities updated updated showed showed understanding converges converges visible prove prove prove prove holds holds discussions reason reason reason society differ delta projections verlag manifold manifold manifold follow generative generative generative generative generative generative generative generative generative generative satisfy dayan dayan dayan dayan maximization satisfies satisfies deal minimized minimized minimized wiley wiley essential essential essential updating detail divergence divergence divergence divergence divergence proved proved proved phases phases amari amari amari amari amari amari amari neal neal neal neal averages mentioned mentioned guaranteed satisfied arc arc definite geometry incomplete peter peter berlin rely logp logp logp logp conclude converged lot notes sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep modify japan japan kullback ylx ylx ylx ylx ylx ylx substituting theoretically theoretically theoretically sons dempster ence geometrical geometrical geometrical geometrical geometrical rubin helmholtz helmholtz helmholtz helmholtz leibler wake wake wake wake wake wake wake wake wake wake wake wake wake wake diag diag diag diag diag diag diag geoffrey geoffrey realizable realizable realizable realizable realizable manifolds manifolds laird apparently frey rewrite atr article article article article rewritten lecture argmax generarive tial doesn flows flows essen sions invisible era era era era era era era era era iterating mle mle mle mle mle mle murata argmin argmin won schematically standing stays gem gem acknowledgment chine riken riken riken riken riken alternately accompanied ofp 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#@Amari_S,Ikeda_S,Nakahara_H,
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#*network learning model neural data figure figure set set set set set set set set set set set set set set set networks networks number system system system system system system error error error error error error error state state state state results results results results results results results results results results results results results results information problem problem problem models models models performance performance based based based weights layer case case case case case case case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems values values values values values values values values values values values values values values probability probability probability probability probability probability noise noise noise weight weight weight unit method method method method method method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern large rate rate rate rate rate rate rate rate patterns patterns patterns patterns patterns patterns patterns patterns analysis matrix optimal optimal optimal optimal optimal form form form form form form shows paper paper paper small size work work task methods methods methods methods methods methods methods methods methods methods fig fig points field field field field field field field field process current current random random random high high similar similar similar similar similar similar similar show show show show equation equation section section section section section fixed line line line rule general general general general approximation approximation states theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained term term term note note dimensional dimensional university variables variables variables variables variables variables variables variables variables variables solution solution solution solution research initial initial initial initial standard standard standard standard terms terms terms left left presented presented presented presented presented presented phase low low machine press press components components components abstract applied applied convergence likelihood references due due important propagation propagation propagation propagation propagation context context context introduction behavior statistical statistical statistical statistical statistical statistical statistical generated recurrent tion energy energy variable variable assume rules prior prior prior prior prior prior prior representations word word theorem cases cases cases cases cases cases type required multiple good good good good binary binary conditions conditions conditions conditions conditions conditions conditions represent represent tree bayesian bayesian expected expected equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations make fact fact fact correct probabilities probabilities probabilities probabilities probabilities probabilities observed errors finite finite finite resulting resulting resulting resulting ing respect respect respect eq eq eq eq eq eq eq eq elements elements elements elements elements elements elements elements elements mapping means factor factor potential knowledge obtain obtain obtain obtain obtain obtain obtain original original original original original original original specific specific specific specific represented represented true compared compared compared provide provide provide rates proc goal related related related posterior posterior posterior posterior posterior posterior connected connected connected connected connected connected distributions approaches approaches mit mit steps comparison fields fields fields fields source source morgan institute words loss code code code code code code code code code code code code individual individual joint joint represents represents represents difficult bias bias layers scheme scheme graph graph graph framework framework framework framework computing equivalent directly directly solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions bit bit bit bit bit bit determine choice choice choice choice significant free estimated basic con con channel channel coding coding derived derived derived derived derived randomly conditional conditional product product provided selected iteration nature discussion normal describe arbitrary group limited close inverse assumption corresponds stable effective effective effective supported theoretical theoretical theoretical theoretical theoretical theoretical theoretical require easily makes makes noisy kaufmann probabilistic probabilistic smaller dynamical dynamical dynamical dynamical dynamical coefficients fully fully technology significantly significantly ratio ratio mechanism special special consistent direct making making bits bits bits bits normalized frame run description improved exact element element element element element typical similarity similarity practical practical practical introduced subject inference recently recently recently recently interest highly highly highly compare previously previously calculated calculated tions correspond correspond converge converge trans sparse sparse sparse sparse sparse improvement sensitive sensitive grant expression expression expression lead digital deviation deviation deviation deviation generally generally runs runs runs runs runs runs runs conclusion starting critical row assumptions assumptions conclusions interactions differences differences bayes bayes bayes numerical numerical numerical numerical clear temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature encoding encoding taking external solid variety variety introduce manner program question boltzmann boltzmann boltzmann boltzmann explicit explicit explicit explicit relation relation derive index index index index index index factors mathematical dept infinite slightly belief belief belief belief belief belief belief belief belief belief belief belief belief belief expectation cycles dependence dependence review communication codes codes codes codes codes codes codes solved solved solved open restricted showed approximations understanding approximated partial calculation dashed dashed additive expansion normalization normalization iterative iterative iterative iterative remains calculate calculate symbol david expect formulation formulation determines discuss coupled coupled coupled phys phys phys phys phys phys partially straightforward identified identified differ encoded encoded encoded encoded encoded encoded encoded encoded symbols included successful successful schemes mackay mackay tend summary soc soc decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding link showing showing anderson anderson sci notation write received received attempt preferred employed employed explore unlike perturbation updating replaced limitations accurately recursive graphical graphical biases biases behaviour examine examine examine dependencies dependencies proper tanh tanh tanh tanh removed examined examined naturally transmission plausible predicting rev rev rev equally assumes expressions art art art message message message message message message message message message message message message message message message message message message message neal neal spin site site ground ground ground agreement agreement agreement agreement analyzed analyzed defining phenomena explanation analytical answer tool sites sites sites sites forces desirable products calculations implicit alignment raw mechanics mechanics mechanics mechanics mechanics mechanics explained pseudo lattice marked employ calculating enables conclude unbiased unbiased unbiased unbiased unbiased unbiased converged multidimensional cor representative corrupted corrupted corrupted corrupted corrupted corrupted corrupted corrupted indices indices assign japan japan drift tensor tensor tensor tensor tensor discover connecting arranged generality convenient replacing intelligent efficacy efficacy efficacy efficacy biased biased biased biased biased biased biased biased biased biased biased replica replica replica replica obtaining obtaining reasoning implications affected optimally adequate exploring tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap tap corre iteratively iteratively iteratively iteratively dependency realization vertices vertices similarities enable refers draw 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#@Kabashima_Y,Saad_D,
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#*network learning learning learning learning learning learning learning neural neural input data data function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number error error error error error results results results results results units problem performance performance performance performance performance performance performance performance performance performance performance performance space weights linear linear linear case case case case case case case case vector vector order shown shown values values values values values values values values probability probability probability probability probability probability probability probability probability probability weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution approach approach approach point point point image large large test test test test test analysis analysis class class class class class class shows shows algorithms algorithms algorithms paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples size points points points points points points points points classification classification classification classification classification classification classification classification classification current current current random random section section section vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter real real real real real real real real average average average theory theory theory obtained obtained term note note note experiments experiments experiments experiments experiments experiments result result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold solution independent log log log log log log log defined defined defined defined found found initial initial initial initial table table table estimate standard standard standard standard standard standard computer computer terms terms terms terms terms distance science science machine machine machine machine machine machine sets sets sets sets maximum range outputs continuous continuous sample sample sample abstract applied applied applied find find computational computational references ieee positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive procedure decision introduction effect effect effect parallel parallel parallel change assume assume classifier measure chosen higher higher previous theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound required binary binary binary expected expected proposed correct correct correct probabilities observed finite minimum minimum classes classes total respect respect sum times mapping factor factor dimension dimension dimension dimension dimension dimension dimension made natural natural global em em em negative negative negative negative negative negative negative negative negative negative negative negative true true provide define compute compute compute goal constraints discrete equal equal approaches approaches approaches approaches accuracy accuracy contrast update support support train proceedings proceedings proceedings proceedings report words department loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss final final exp exp exp exp exp exp exp addition addition addition maps considered framework framework experiment estimates conference conference conference classifiers choice choice choice choice choice choice choice significant significant basic pages pages pages validation con randomly criterion criterion iteration iteration simply simply discussion group denote denote tested assumption corresponds corresponds complete proof theoretical theoretical hypothesis hypothesis hypothesis hypothesis typically account programming consistent consistent consistent consistent uniform empirical empirical empirical empirical numbers numbers max making international polynomial polynomial idea minimize minimize minimize produced choose choose choose improve recent property property reported apply side side pixels quadratic recently compare solve rl trans definition definition definition definition definition background bounded bounded bounded bounded improvement risk expression expression expression suggests suggests extended derivative predicted alternative correctly correctly correctly move boundary setting setting place greater greater valued valued valued valued valued valued differences measures clear performs weak weak weak weak weak taking taking taking largest largest largest drawn drawn demonstrated assuming assuming assuming minimizing movements iii introduce introduce force force suppose suppose suppose longer solving ways factors confidence recall recall unique develop applying implies john john john choosing national learner learner evaluate lee margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin suggested constants classical normalization reduces combining purpose false false false false closed closed distances classified classified precision precision includes perceptrons inter vapnik specifically candidate holds holds holds reason importance maximal maximal maximal maximal maximal maximal presentation situation capture summary heuristic showing built satisfy notation notation usual michael generalize hypotheses hypotheses thresholds extend difficulty dataset dataset dataset dataset dataset dataset examine giving investigated boosting boosting boosting boosting boosting root gates attributes smallest smallest coefficient closest adapt ensure adjusted front der taylor taylor taylor taylor taylor taylor taylor expressions distinguish analytic adaboost adaboost adaboost adaboost adaboost adaboost adaboost tool london tive sections closer closer choices sgn sgn 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classifications classifications seek freund freund england letting beta searches thresholded simplifying picked concentrate investigating erp erp erp erp erp indexed indexed weaker misclassified misclassified misclassified misclassified voting williamson gorithm develops learners learners fat fat fat fat fat fat fat fat fat fat fat fat algorithmic sake shawe shawe shawe shawe shawe shawe shawe dcs dichotomy anthony beneficial classi positives positives positives positives positives positives html repository repository losses losses shattered shattered subscript fication formulas formulas formulas explaining cortes boosted retaining minimise devel colt shattering shattering shattering shattering shattering shattering shattering shattering ranked boost unequal unequal unequal unequal unequal unequal unequal unequal unequal confident canadian maximise bigger minimising ist theta theta optimising eleventh suppressing holloway optimised icml icml yif yif yif oped yoav ern yoram vladimir keywords equating bay rhbnc stants mlearn egham dlog corinna emaih emaih investi reals prevalent prevalent mlrepository incur uneven nega dln dln imperial emo commerce quote misclassifying 
#@Karakoulas_G,Shawe-Taylor_J,
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#*network network network network network network network network network network network learning learning model model neural neural neural neural input input data function function function function function set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm output output number number number number number number number results results results information information problem problem problem models models models models models models models models based space weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case case order order order order shown systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions unit distribution distribution distribution distribution point point point point point single processing processing large large large large large large large large large large large large large large large large large large large large large large large large large large local local local rate patterns optimal optimal optimal inputs inputs form form algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian paper paper paper examples small small size net work work methods methods methods methods methods methods methods field random random random random random show show show show equation equation equation equation equation equation equation equation equation equation equation section section section fixed fixed fixed rule generalization generalization parameter parameter real approximation approximation states states theory theory theory gradient gradient obtained term term term term note result variables variables variables variables variables variables variables variables computation computation computation research research independent independent independent defined defined constant constant estimate standard terms terms terms node node node node node node node node node node node science nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets maximum components outputs outputs outputs sample abstract find find find computational computational convergence convergence convergence convergence properties references due important important introduction introduction introduction hand hand hand behavior behavior statistical tion energy difference difference complexity variable assume lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower previous previous theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases multiple binary binary binary binary binary binary binary conditions conditions conditions represent represent bayesian bayesian bayesian bayesian bayesian bayesian expected equations make make make make fact fact probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities minimum resulting ing computed sum sum sum sum sum sum sum called called times times elements elements mapping means means means means means means means factor made natural natural natural applications study study knowledge obtain original artificial artificial artificial specific represented represented represented compared application provide provide provide provide provide define define compute compute compute compute compute compute rates rates rates rates perform perform goal distributions power larger larger larger larger larger descent morgan proceedings words loss individual joint joint joint connectionist bias layers layers layers layers layers ai considered considered computing computing computing directly directly hinton hinton limit limit limit limit san conference capacity efficient upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper upper choice choice choice choice approximate approximate approximate approximate give give give weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted weighted conditional conditional conditional conditional conditional conditional conditional conditional bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds types entropy evidence evidence evidence evidence evidence depends constraint simply simply simply arbitrary denote denote assumption assumption complete proof common common effective effective require main face instance future easily noisy sensory kaufmann probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically smaller smaller smaller hopfield reduced jordan jordan jordan transfer transfer transfer transfer transfer transfer transfer transfer transfer transfer interesting interesting significantly special leads representing details numbers magnitude decay choose choose run exact exact exact exact exact pair takes typical practical apply apply strategy include machines side side side side inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference subset interest interest interest interest interest compare unsupervised observations works yields studies converge converge definition definition definition symmetric symmetric symmetric observation observation bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded interval interval interval interval lead studied studied studied studied scaling occur suggests deviation deviation deviation deviation deviation deviation deviation deviation deviation deviation deviation deviation deviation generally generally setting setting demonstrate minimal differences sigmoid bayes numerical clear exponential constrained mateo largest largest cycle intelligence intelligence intelligence min decrease manner boltzmann suppose suppose suppose suppose suppose derive derive derive factors factors estimating laboratory recall multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer multilayer averaging averaging averaging involves belief belief scales events competition independently independently dependence depending detailed approximations centered soft allowed partial earlier earlier additive combining combining intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals intervals event roughly valid valid valid valid valid valid sufficiently expect expect prove prove uncertainty variations simplicity maximal computationally efficiently essentially refer notice graphs graphs interested interpreted lie satisfy quantity michael dayan generalize leading satisfies satisfies situations unlike layered layered layered exhibit exponentially exponentially exponentially involving involving involving involving graphical graphical graphical biases examine ideas links rest variational dependencies fundamental examined induction induction gradients possibly necessarily analyze ensure queries freedom precise observe academic art ith defines neal neal neal directed directed directed trivial trivial crucial guaranteed guaranteed defining phenomena phenomena phenomena slope slope slope adjacent independence briefly lies lies lies tool inside organized precisely choices choices choices choices desirable commonly products probable involve optimize annual mechanics tional frequently requirement rely fall incoming incoming incoming incoming cal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal sums sums sums sums sums sums sums sums sums conclude deviations deviations deviations deviations jaakkola differentiable wesley summed cumulative trade trade trade trade gap gap ghahramani intractable cooper cooper sleep addison guarantee fix fix arguments conditioned conditioned conditioned generality extending convenient city intelligent abilities occurring occurring exploit exploit exploit exploit reasoning reasoning definitions definitions definitions settings krogh generalizes child hertz hertz hertz analyses governed governed saul saul saul saul saul saul saul saul encountered guarantees guarantees regard ascent lawrence tic multiplied omitted reader kearns kearns kearns kearns kearns kearns kearns park park extensively inductive considerations exploiting exploiting thresholding parents parents parents speaking maintaining maintaining rigorous rigorous kluwer deriving tables tables ties adopt causal wake illustration translated decays shannon thermodynamic dominated labs denoting proba proba proba challenging flip noting pearl pearl conversely weaker sam meet places union union union union union union union frey vanishes treating ward computa behaves palmer tom crude builds appealing val diagnostic floor obey tells explanations establishing falling inde computable semantics semantics acyclic acyclic promise translate ted damping pendent entering entering entering quantified obeys marginals tighter undirected enforced avenue reminiscent sible rightmost motivates motivates throw throw throw feeds oij oij oij wishes quences generatire resort uncertainties uncertainties uncertainties uncertainties told tti tti tti formalize redwood parameterize composing varia probabili deviate intractability intractability leftmost nondecreasing preclude preclude violates violates violates violates balances incom preliminaries invited assured xil conse lui lui lui lui lui lui florham violating bilistic bilistic bilistic companion straightfor encompass hierarchi lth arguably informed inductively inductively inductively whichever dth disposal 
#@Kearns_M,Saul_L,
#t12
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#*network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data function function function function function time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks training training training output output number system system system system state state state results results results results results units units information problem models models models models models models models models models models models hidden hidden hidden hidden hidden performance space space space weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer case case case case case case case vector vector vector vector vector order order order order order order order order order order order order order order shown shown shown shown shown systems probability probability probability probability probability probability probability noise noise noise noise noise noise noise weight weight weight weight functions functions distribution distribution distribution distribution distribution distribution method approach point point point point point single single single rate test analysis analysis analysis analysis class class inputs inputs form simple paper paper paper paper net work methods points features features process process process process process process process process process process process process process process process process process trained trained structure random random random memory memory memory similar similar similar similar show equation equation section section section section fixed fixed fixed fixed line vectors vectors general generalization parameter parameter real average average theory theory theory theory theory theory gradient obtained obtained term term term note dimensional dimensional dimensional result university computation research independent defined defined defined defined defined defined defined defined defined defined defined defined defined constant constant constant constant estimate estimate estimate standard standard standard standard standard standard standard standard standard standard standard terms connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections science science prediction prediction prediction prediction present sets sets range range range press basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs continuous continuous sample sample abstract applied density properties properties properties references stochastic stochastic stochastic stochastic due due ieee ieee positive positive positive positive positive positive positive positive important important important important important important important adaptive introduction introduction estimation behavior behavior behavior behavior generated variance variance variance tion change difference difference difference assume measure measure part part part part center theorem theorem theorem type long long long long long conditions conditions conditions conditions equations equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov techniques observed finite finite total multi called called called called called mapping means means natural applications knowledge negative artificial artificial true true true series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series series define distributions discrete steps steps larger support train train train nets nets modeling modeling modeling proceedings version advances final exp ai considered equivalent additional estimates estimates trajectory determine determine approximate statistics estimated give con condition conditional conditional conditional criterion finally processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes nature covariance normal feedforward denote denote denote transformation fast close assumption complete complete stable stable predictions proof proof short short implemented generate generate supported square easily easily including probabilistic hopfield reduced dynamical unknown mlp mlp mlp mlp interesting york york special uniform operation details details call call call magnitude polynomial polynomial perceptron denotes architectures architectures directions property similarity practical apply introduced moving moving sense recently interest interest sufficient converge chain chain chain chain chain chain chain chain chain chain chain chain bounded bounded bounded bounded bounded interval grant exists exists parts extended deterministic starting starting trajectories operator operator depend depend central differences differences sigmoid exponential asymptotic asymptotic asymptotic asymptotic weak taking taking strong strong integration integration integration integration integration integration integration integration integration radial radial radial exist relationship relationship question question pro pro stability stability stability stability stability mathematical modeled recall averaging averaging integrated integrated integrated integrated integrated integrated integrated integrated adding equilibrium springer springer implies expectation cycles choosing review depending stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary stationary lemma lemma lemma variation transform transform transform densities forms converges allowed additive additive additive expansion reduces intervals remains foundation transactions transactions usa usa perceptrons perceptrons tests society driven driven included literature invariance essentially reached reached reached characteristic characteristic characteristic capture summary compact compact compact verlag kind kind repeated interested notation write write usual usual usual mixing satisfies software extend law origin origin remain transformed transformed transformed transformed poor exhibit exhibit exponentially ml scalar scalar giving rest working tanh concepts possibly integer integer traffic traffic man analyze predicting aspect quantities quantities taylor taylor multivariate years asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically guaranteed defining growing growing london lin organized strictly strictly strictly controls acknowledgement beginning fluctuations questions applies limiting popular popular popular popular extensions chen expectations lim wang wang displays proofs proofs ear generator oxford acm null null homogeneous homogeneous unity jones royal establish stronger chains chains chains overcome wilson moments lyapunov financial weakly started started started started combines appendix appendix equals guarantees uni mlps mlps surprisingly motions hypercube davis davis davis implicitly pdf pdf pdf pdf pdf speaking ure truncated ple piece basically basically additionally decomposed covariances classic classic remainder remainder ary care gained rbfs rbfs rbfs pos hornik hornik hornik hornik sam preserve universit exchange siam happen sta sta mimic vanishes infinitely walk walk ergodic ergodic ergodic ergodic ergodic fractal institut institut unbounded unbounded loosely flows inherently station equa chan chan chan chan autoregressive autoregressive autoregressive autoregressive autoregressive autoregressive autoregressive autoregressive autoregressive autoregressive autoregressive autoregressive autoregressive iid iid cess cess tra nonstationary cuts stationarity stationarity stationarity stationarity stationarity stationarity stationarity stationarity stationarity stationarity stationarity stationarity stationarity stationarity comprehensive technische fractional fractional fractional fractional fractional fractional checked ness ness fiir fiir examines inte shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut shortcut tong tong tong tong tong tong tong kurt tinuous roots roots noises geometrically geometrically geometrically geometrically geometrically arma arma cov rail foreign economics aperiodic aperiodic ergodicity rameter rameter incor nns nns nns eet borel borel austria austria variate austrian differencing differencing differencing differencing differencing irreducible irreducible irreducible irrespective packages fulfills wien wien wien wien wien shortcuts shortcuts shortcuts shortcuts shortcuts shortcuts shortcuts adrian adrian lnt autocorrelations friedrich river porated grated ier atl jectory recommend textbooks aix sfb 
#@Homik_K,Leisch_F,Trapletti_A,
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#*network network network network network network network network network network network network network network network network network network model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output output output system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system results results results results units units units units units units models models models models models models performance performance based space space weights weights weights weights linear linear linear linear linear case case case case case case case case case case case case case shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values parameters parameters parameters parameters noise weight neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit pattern pattern pattern point point point point point point point point point point point point point point point point point point point point single large large large local local rate analysis analysis analysis class class matrix matrix inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form shows shows shows shows shows simple simple simple simple gaussian gaussian gaussian visual visual visual visual visual paper paper small small feature net net work work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells points points points points points points points points points points points points points points points points points points field field level cell cell cell high response response response response response response response response response response response response response response response response response response response response response response similar similar similar similar show show show show show show show equation equation fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line parameter real real average theory theory theory term note note activity activity activity activity activity result result threshold threshold threshold computation computation computation computation research log defined defined found found dynamics constant constant connections connections connections connections connections connections connections node science direction direction phase phase phase phase activation frequency frequency motion motion motion motion motion range range range range press position nonlinear nonlinear outputs outputs outputs outputs abstract abstract computational computational computational computational computational computational computational computational computational computational computational computational convergence references component ieee positive positive context introduction complex complex behavior behavior behavior behavior behavior behavior behavior dynamic dynamic dynamic recurrent recurrent recurrent recurrent recurrent tion energy energy difference difference difference spatial spatial measure measure higher part part part bound cases cases multiple cortex cortex cortex cortex cortex good spike long long represent represent equations make fact fact region region scale scale finite ing ing simulation times elements elements regions means means factor factor factor dimension made orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation global global global applications study study vol relative relative specific true true compared compared compared define define define location location perform eye constraints connected motor cortical brain power mit larger connection connection modeling represents responses responses cambridge computing equivalent experiment directly additional design design limit limit limit limit limit limit trajectory trajectory trajectory trajectory trajectory effects capacity upper full significant vision con condition levels levels lines selected selected nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends biological biological group group fast limited close assumption assumption corresponds excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory stable stable stable stable stable stable stable stable stable stable proof short short effective generate generate supported theoretical require eds adaptation journal journal journal journal journal square instance instance degree noisy sensory including including including including pairs pairs pairs underlying hopfield hopfield dynamical dynamical dynamical dynamical fully significantly significantly ratio ratio ratio ratio ratio ratio ratio head segmentation consistent mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode leads leads principal representing details details call pre inhibition inhibition inhibition depth idea idea population discussed recent exact advantage separate apply period subject sejnowski recently recently works tuning tuning tuning tuning tions smooth smooth smooth studies converge rl diagonal locations separation separation symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric parts studied studied studied studied invariant invariant invariant invariant occur extended extended deviation deviation wide wide matrices matrices matrices locally setting critical greater conclusions depend editors interactions differences differences differences differences differences differences differences differences designed designed clear peak performs faster suggest mechanisms external external cycle cycle cycle cycle demonstrated solid solid solid variety selective selective selective selective selective selective selective selective selective selective relationship groups question question van solving ways ways factors primary primary primary primary stability stability stability stability tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned mathematical sensitivity easy scales scales interaction develop equilibrium equilibrium springer springer quality cycles cycles family showed evolution evolution evolution evolution activities completely suggested suggested translation translation translation translation constants constants key reasonable dashed dashed combining purpose false generation koch koch transactions degrees avoid expect expect expect eigenvalues contour contour contour contour contour activated texture texture simplicity simplicity reason straightforward aspects aspects aspects extra extra extra closely society driven wij wij wij wij wij wij modes modes modes modes oscillatory oscillatory oscillatory oscillatory oscillatory literature computations computations projections tend identity characteristic excitation excitation excitation verlag strongly strongly strongly induced showing interested neuroscience neuroscience neuroscience neuroscience neuroscience symmetry symmetry symmetry symmetry symmetry symmetry symmetry symmetry oscillations oscillations oscillations oscillations oscillations oscillations oscillations gray bar bar dayan dayan dayan dayan dayan dayan dayan nips correspondence binding thresholds cat preferred preferred receive oriented oriented cowan bars selectivity selectivity selectivity powerful powerful poor perturbation essential put put involving dotted dotted dotted existence fourier investigated relationships scaled complicated oscillation oscillation oscillation phases contours smallest smallest man extremely illustrate created quantities olfactory der freedom regime regime regime isolated isolated great ment crucial growth growth orientations orientations unstable unstable unstable unstable unstable unstable unstable unstable unstable unstable unstable unstable unstable biology explanation analytical analytical answer interneurons london perspective perspective lin lin straight sys sys cut involve grossberg grossberg grossberg demonstrates cybernetics cybernetics cybernetics qualitative fluctuations fluctuations greatly behaviors evaluating substantially understood relevance peter poorly cohen peaks posed biologically biologically compares maintain maintain calculating differs popular cal cal qualitatively qualitatively singer asymmetric asymmetric asymmetric deviations wang simultaneous synchronization irrelevant cor trade ear ear tation amplifier amplifier appropriately angular linearity acts dynamically dynamically homogeneous homogeneous homogeneous homogeneous discovery repre tem enhancement enhancement enhancement enhancement inspired significance significance stronger logarithmic grow keeping transforms intuitively guide enhanced enhanced enhanced lyapunov lyapunov spurious meaningful published sompolinsky sompolinsky weakly governed governed governed zhang zhang von guarantees evident originally hippocampus suggesting suggesting sustained ends seung seung dramatically dramatically neurophysiology leaving leaving equivalently break break break preserving responds perturbed convenience ical malsburg breaking breaking england suppressed suppressed suppressed suppressed suppressed pairing subthreshold segregation interact tems dominated permits jij jij jij jij jij douglas bump simplifying landscape scope host exceed regimes regimes ambiguous selectively selectively breaks breaks responding amplifiers amplification amplification amplification amplification amplification amplification amplification differing exploited infinitely answers vice fiat versa expense simplification instability textures builds hop hop pouget king dominates dominates dominates broadly suppress hemmen replicated polarity judged mcnaughton symmetrical symmetrical symmetrical symmetrical symmetrical symmetrical quantitatively amplified amplified falling inset inset inducing ben fication enters oscillates oscillates robustly wong ous unimodal linking analyse linearities kong boosted schuster magnification ular whilst broader attentive hong thalamus ther albeit superiority fur counterparts counterparts eckhorn spontaneously diverges sorts symmetrically wji gatsby behaved konig konig rising zij zij engel braun braun stein partic abstracts resort deliver comparatively comparatively comparatively ucl ucl queen pnas pnas pnas pnas pnas roll pertinent asymmetrical asymmetrical asymmetrical asymmetrical asymmetrical invertebrates constrains cies questionable yeung rio interac amplify ermentrout orien instabilities stably stably golomb golomb answered carandini dictates coarsely biolog faithfully ioo amplifies amplifies amplifies metrical proposals kleinfeld ampli intuitions pressed pressed sents yishai termined tivation mccormick 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#@Dayan_P,Li_Z,
#t12
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#*network network network network network model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input function function function function function function function function function function function function function time time time time set set set set set set set set set set set set set set set networks networks networks networks networks networks output output output number number number number system system system system system system state state state state state state state state state state state state results units units units units units units information information models space space space weights layer case case case case case case case case case case case vector vector vector vector order shown shown shown shown systems systems systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method method method method method point single single single processing control large large large large large large large large large analysis class class class matrix matrix inputs inputs inputs form form form form form simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small small small small size net net net net net net net net net net net net net net net net net net work step step step step step level random similar similar architecture show show show show show show equation section section section section section section section section fixed fixed fixed fixed fixed line line vectors vectors vectors general general general general states states states states states states states states theory theory note result result result result result result result result result result result university threshold threshold threshold threshold threshold threshold computation computation computation computation computation computation computation computation computation computation computation computation log log defined defined defined sequence sequence sequence sequence sequence sequence dynamics initial initial constant constant constant constant constant constant constant computer computer science science presented presented map map present present activation activation activation activation activation machine sets press components outputs abstract applied applied find computational computational computational computational computational computational computational computational computational computational computational density density density density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties references references component stochastic stochastic stochastic stochastic stochastic due ieee ieee positive positive positive positive introduction hand hand circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit effect effect recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion difference complexity variable assume assume assume assume assume assume assume assume measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure word part part part part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound type type type type type type type type type required binary binary represent distributed equations fact fact techniques length length length finite finite finite finite finite finite finite finite finite finite resulting resulting resulting total means factor negative negative negative negative vol vol vol vol vol application desired define define compute proc determined related related constraints distributions distributions distributions discrete discrete discrete discrete power steps steps steps comparison larger support support nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets nets words words version version technique consists internal kernel kernel advances final layers delay delay sequences considered considered considered considered view full give give give condition condition condition condition condition condition types types types types finally finally nature constraint biological feedforward feedforward feedforward feedforward feedforward feedforward feedforward feedforward arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote proof proof proof proof proof proof proof circuits circuits common common common common common implemented supported theoretical theoretical main main main main journal end end end easily easily makes noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy probabilistic probabilistic combination york special special special language language language language language language language language language language language language language language language language language making making making making idea choose choose choose choose denotes exact robust robust robust robust robust robust robust robust apply apply introduced subject subject subset subset previously previously previously yields studies studies achieve definition definition definition definition definition definition definition bounded gate gate gate gate exists exists occur wide matrices move deterministic conclusions valued differences measures measures measures measures measures asymptotic presence drawn sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal min introduce introduce manner characters construct longer transitions mathematical recall missing infinite physical consisting consisting consisting applying applying implies implies implies extraction boolean boolean boolean boolean boolean independently focus lemma lemma lemma lemma lemma variation transform evolution completely allowed event distances string symbol symbol construction construction kernels usa strings strings strings strings batch recognize recognize recognize recognize recognize recognize recognize prove prove prove discuss absolute holds holds holds partially regular regular regular regular regular regular regular regular regular regular regular regular maximal maximal encoded symbols included literature computations computations computations invariance essentially identity receives receives receives soc compact compact prob prob prob prob sci hold notation involved write realistic giles giles giles giles computes thresholds satisfies satisfies satisfies satisfies satisfies deal extend employed exhibit difficulty project applicable referred reliable gates gates gates gates gates gates proved fundamental fundamental math math necessarily integer integer reading reading automata automata automata illustrate perfect subsets subsets subsets subsets der formal assumes precise precise precise precise precise precise observe arbitrarily arbitrarily languages languages languages languages languages languages languages languages languages languages languages languages languages languages inequality fairly multiplication turns sys sections satisfied strictly strictly precisely precisely constructing constructing operators immediately mathematics mathematics mathematics recognized recognized recognized recognized recognized recognized recognized recognized definite recognizing preceding preceding preceding argument pure readily employ employ reliability reliability reliability reliability reliability reliability reliability ity exhibits synthesis differs conclude conclude begins begins begins begins formally formally investigation fix acm arguments pick pick pick pick impossible nonzero nonzero nonzero maass maass maass maass maass maass maass maass maass maass generality tools analogy fan replacing definitions disjoint disjoint adequate carry alphabet alphabet alphabet alphabet composition corollary corollary corollary introduces decide decide regard regard regard realization belongs claim recog ends extends statement characterization characterization characterization assigning limitation limitation severe accept basically email email recursively sontag sontag sontag sontag restrictions par lit lit possibilities letting reflected concentrated tems distribu complementary universit son supports union exhibited compu article article article article article mea completed spite replacement copies nonnegative nonnegative decided agrees hilbert virtually conceptual suffices concrete unreliable unreliable edited measurable measurable measurable measurable measurable measurable measurable measurable measurable measurable sym recognizes recognizes recognizes america complement signed signed signed signed signed signed benign mach inst devoted sur probabil rec noiseless noiseless terminology developments decompose decompose cox cox instant technische accepting accepting accepting accepting accepting simulates assoc assoc tag accepts constructions ily rosenblatt proving organisms bull encounter ana tapped tapped completes completes tational blank ticular quences comput rutgers rutgers notations designer designer graz graz graz casey casey casey nxn zation concatenation heaviside borel borel borel borel borel borel technically austria fined reads batches contrasted iit iit stats fll folk igi wolfgang brunswick omlin omlin omlin omlin nized ruled conse foun mll dep technological cha dations inspecting inspecting eduardo fonds bol zur maa padded vestigated 
#@Maass_W,Sontag_E,
#t12
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#*network network network network learning learning learning learning learning learning neural neural neural data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set networks training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output number error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error results results results results information problem problem models performance performance performance performance performance performance weights weights weights weights weights weights linear linear linear linear linear linear case case case vector vector vector vector vector vector vector order order shown shown shown systems values values values values values values values values values values values probability probability probability probability weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach pattern pattern point single large large large large large local test test test test test test test test test test test test test test test analysis class class class class class class class class class class optimal optimal optimal optimal optimal form form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper examples examples examples examples examples examples small small small small size size size size size size size methods step step step points points points classification classification problems problems problems random random random random high high similar similar show show show show show show show show section section section section section fixed fixed line vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter real real average average average average average average average theory theory gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term term term term term note experiments experiments experiments experiments result result result result university university university threshold solution solution solution research research independent independent log log defined found sequence sequence initial constant constant constant constant constant terms terms node prediction left direction direction direction direction presented low low machine sets sets sets sets sets range sample sample sample sample sample sample sample abstract back find find references ieee procedure procedure important important important decision introduction complex effect generated generated cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search tion tion tion difference difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower lower learned chosen chosen chosen chosen chosen chosen chosen chosen chosen chosen chosen higher part previous previous theorem theorem theorem theorem theorem theorem theorem bound bound bound cases cases cases cases good good conditions conditions conditions make make fact length errors errors errors errors errors finite finite minimum minimum minimum minimum minimum classes ing multi multi sum performed called times regions mapping optimization optimization optimization optimization optimization optimization optimization optimization made made obtain negative artificial relative compared application application application cross cross cross cross cross provide define distributions distributions distributions discrete equal approaches steps comparison comparison larger larger larger update train descent descent descent proceedings report report department department department version version technique code final exp considered experiment directly curve curve curve curve curve estimates estimates limit conference classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper full full choice significant significant statistics statistics estimated pages validation validation validation validation validation validation validation validation validation give give con con con con con produce produce condition randomly randomly bounds bounds bounds bounds bounds bounds lines provided provided provided provided selected selected iteration nature constraint constraint simply measured technical technical tested corresponds stable surface surface proof proof proof proof proof amount short effective effective generate supported supported supported role face hypothesis hypothesis hypothesis instance makes probabilistic smaller combination combination combination combination combination reduced reduced reduced account coefficients coefficients coefficients database database operation squared details numbers iterations direct direct direct direct direct direct combined combined combined combined minimize minimize minimize minimize produced produced produced produced choose run run added light light denotes denotes improved improved improved improved directions directions directions recent advantage pair takes takes practical subset recently relevant engineering engineering axis axis axis solve yields correspond correspond correspond address definition definition definition definition definition modified interval interval improvement improvement improvement grant constructed horizontal expression lead alternative move generally setting pass conclusion reduce valued valued valued valued central sigmoid measures taking hard reduction reduction california intelligence regularization regularization regularization minimizing minimizing minimizing decrease averaged minima base base base base base base base base question question explicit suppose derive solving plot plot label vertical vertical involves involves scales adding expectation expectation versus select national national national family family family family family family family family family family independently approximations lee lee margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin similarly convex convex convex convex convex convex convex convex convex convex convex convex intervals penalty penalty penalty transactions avoid combinations combinations combinations combinations combinations subspace plotted maximize simplicity reason closely uniformly suitable suitable suitable successful plots plots plots orthogonal fine notice graphs repeated prob heuristic success dis dis lie lie satisfy quantity bar bar hypotheses hypotheses hypotheses consisted moves illustrates illustrates satisfies satisfies acknowledgments remain overfitting investigate investigate involving involving helpful existence reducing reducing examine boosting boosting boosting boosting boosting maximizing proved examined smallest act integer ensure ensure ensure ensure algo observe separated extent explain great piecewise piecewise piecewise piecewise piecewise inequality inequality inequality fairly improves improves improves improves explanation adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost glass caused lies lies worse worse berkeley sys closer closer ran sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn sgn projected optimize optimize sun addressed reflects dark dark pseudo peter marked http http aim aim reaches achieves achieves datasets datasets datasets datasets datasets datasets adjust chose chose comments progress progress credit credit credit credit cumulative cumulative cumulative discontinuities discontinuities proportion www restriction summing fix fix rithm optimizing optimizing optimizing databases labelled labelled approximates plays breiman difficulties adjusting adjusting satisfying satisfying replacing hyper balance settings effectiveness generalizes heuristics games bartlett bartlett bartlett bartlett bartlett bartlett bartlett bartlett reset schapire schapire schapire ensures heart tic ensembles cancer cancer cancer impact implicitly ignore adopted ball ball ball ball ball ball ball ics dense uci uci annals fellowship misclassification basically planes failed freund freund german australia remainder exam gained magnitudes tems discontinuity crosses relate projecting disease conversely indexed sonar sonar sonar sonar voting admissible admissible admissible admissible admissible union margins margins margins margins margins margins margins margins margins margins margins exhibited parametrized parametrized gorithm suggestions lems fiat fortunately council council sake australian australian australian australian australian marks agrees families families breast breast breast blake king king concern award devised baxter baxter baxter baxter baxter baxter html repository implied implied wisconsin wisconsin irvine irvine irvine terminates doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom monotone monotone cleveland generaliza hits explaining moderately applica plexity suitably mar hoeffding complications mason mason mason mason mason mason distinctions jonathan jonathan draws completes correspondingly 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#@Bartlett_P,Baxter_J,Mason_L,
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data function function function function function function function function function function function function function function function function time time set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number error error error error error error error error error error error error error state results results results results results results results results results results results results results results units units information problem problem problem problem problem hidden hidden hidden hidden performance performance performance performance based based space space space space space space weights weights linear linear linear linear linear layer layer layer case case case case case case case case case case case case case case case case case order order order shown shown shown shown shown shown shown systems systems values values probability parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons unit unit unit unit method approach approach approach approach point point single single single single processing processing control large local rate rate rate analysis class class class class class class class class class class class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper paper examples small small size size size net work work work work work work work work work work work work task step step process structure problems problems problems random random random high representation representation architecture architecture show show show show show section section section section fixed fixed fixed general general general general general general general general general general parameter real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average theory theory obtained obtained obtained obtained obtained obtained obtained obtained note note note note dimensional dimensional result result result result result result result result variables variables variables variables defined defined defined defined found found sequence sequence sequence constant constant standard standard standard standard standard terms terms node node science science science left presented present activation activation sets sets press press continuous abstract applied back convergence convergence convergence convergence convergence convergence convergence convergence density references stochastic due ieee ieee ieee positive positive procedure procedure procedure important context introduction estimation estimation estimation estimation estimation statistical statistical generated tion tion complexity variable assume assume assume lower lower lower lower chosen chosen part part center previous previous previous theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound cases type type required required good good long long conditions conditions conditions conditions represent expected make make fact fact fact fact techniques region finite resulting classes classes classes ing ing regression respect respect respect respect respect respect multi multi sum sum performed performed factor optimization optimization optimization optimization made made study obtain obtain obtain compared application desired desired define rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates perform equal approaches mit mit accuracy contrast morgan proceedings report report department department version advances advances advances difficult scheme scheme addition sequences ai ai ai considered considered considered computing domain equivalent view design stage stage stage stage stage stage stage efficient upper upper upper upper upper upper upper full full full requires approximate approximate approximate statistics world speed basic basic pages pages pages give con con con con condition condition condition condition derived developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds types lines product product product provided provided finally nature depends achieved achieved measured discussion technical technical feedforward feedforward arbitrary denote denote corresponds complete complete proof proof proof proof proof proof proof proof proof proof proof generate supported supported theoretical theoretical theoretical theoretical main main main main main degree makes kaufmann needed functional functional coefficients projection special empirical leads details details details max max making early polynomial idea idea combined denotes architectures recent recent property reported introduced identical sense subset recently recently relevant engineering engineering interest sufficient highly observations volume tions tions solve smooth smooth yields yields achieve achieve trans trans definition background bounded bounded bounded bounded bounded grant grant exists exists exists extended extended extended derivative locally move touretzky pass demonstrate operator operator valued editors measures numerical clear clear practice strong sigmoidal sigmoidal regularization assuming exist minima denoted explicit explicit longer factors factors estimating ann multilayer multilayer infinite electrical electrical remaining remaining minimization minimization minimization implies implies blocks expectation select letters letters yield independently focus expressed expressed formation lemma lemma detailed detailed open open restricted approximations approximations approximations lee lee lee approximated approximated similarly sign partial performing spaces spaces spaces spaces spaces spaces spaces convex convex convex convex convex convex convex convex convex convex convex event event purpose add iterative interpolation distances construction foundation norm norm norm norm norm norm norm norm norm norm norm norm building usa mozer holds partially characterized characterized major simplicity determining straightforward extra computationally presentation schemes comparing essentially compact compact compact procedures allowing heuristic showing dis contribution contribution follow follow hold satisfy notation notation bar write usual wavelet wavelet ill ill approximating approximating approximating approximating approximating extend extend simpler parametric powerful powerful essential exponentially optimized integral limitations issues pursuit existence fourier fourier ideas incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental incremental authors authors comparable func attributes neu editor editor spline spline spline subsets der der der obvious greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy algo freedom observe consist submitted submitted established established established established established established advanced ment inequality inequality inequality inequality crucial crucial growth smoothness smoothness guaranteed tool turns lin lin lin lin lin lin lin lin constructing worst worst mathematics mathematics universal universal ridge begin optimize demonstrates author geometry preceding greatly splines span span price characterize popular extensions achieves sums sums inherent boston conclude don proofs optimality optimality optimality optimality optimality optimality optimality interface guarantee restriction restriction restriction fix fix appropriately concerned jones jones jones establish establish establish generality extending extending dealing darken proceeds logarithmic logarithmic logarithmic fan stated attractive moment obtaining transforms transforms ral definitions definitions belong symposium constructive nonparametric date embedding embedding embedding bartlett corollary guarantees washington realization demonstration belongs belongs hasselmo counter claim israel israel israel israel advance advance barron barron barron barron barron barron barron barron warmuth belonging belonging belonging belonging belonging belonging belonging relies statement papers inf inf inf inf inf pdf pdf pdf pdf mind unchanged approx approx opposed sontag incrementally distinction pointed restrictions quasi regularity solely pub publication ftp formance rithms relate wise argued increasingly sketch sketch sketch sketch weaker williamson compu exploited october gorithm completed november demonstrating meir meir meir meir meir meir meir opti simplification survey heavily hilbert hilbert hilbert hilbert establishes blum hull hull hull ron possess triangle triangle obey wavelets attained norms norms norms judd establishing establishing establishing suffice rivest implying gence closure closure closure transaction focusing slack unrestricted technion technion technion technion technion technion dist dist amer facilitates incurred incurred incurred demanding demanding mization unifying direc approxima approxima lipschitz assoc statis statis conver draws impressive clarify aware theor theor henceforth ministry convexity historical tational expressing implication agnostic rid rid superpositions comment comment proximate variate depart recalling zky touret haifa haifa intractability auer tedious lib lib iin stringent absorption absorption arx sequel benveniste greedily timization conform integrable putationally ila netxvork radon concreteness birkhauser nomenclature nalysis concomitantly uppercase surge ditionally wegman 
#@Maiorov_V,Meir_R,
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#*learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural input input input input input input input input input input input data data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training error error error error error error error error error error error error error error error error error error error error results results results results results information information information information information problem models models models models performance based based based based based based space space space space space linear case case case case case case vector order order order order order shown shown systems systems systems values values probability noise noise noise noise noise weight weight functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach approach point point single single processing processing processing large large large matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs form form shows shows shows simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small small work work methods methods points points points field classification classification classification process process process process level level level level problems problems random random random random random random random random similar show show show show equation equation fixed fixed fixed fixed fixed line line line general general general general generalization generalization generalization generalization generalization generalization real real approximation average average average average average average average average obtained obtained obtained obtained obtained experiments experiments experiments dimensional dimensional dimensional dimensional result result university university university university university variables variables computation research independent independent log log defined defined found target target estimate computer computer science science prediction prediction prediction prediction prediction prediction direction direction presented sets press press press abstract applied density properties properties likelihood likelihood references stochastic introduction statistical effect generated variance variance energy variable assume assume assume assume assume assume assume lower lower lower lower prior prior prior chosen chosen higher higher part bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound type type distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected fact fact fact fact region correlation probabilities observed errors errors errors errors errors errors finite simulations simulations simulations simulations classes ing regression regression regression regression regression regression regression regression regression respect respect respect sum performed performed performed performed factor factor dimension dimension made knowledge obtain obtain vol relative relative true compared compared application define define goal posterior posterior posterior distributions distributions equal mit mit mit report report implementation kernel kernel kernel exp exp considered cambridge computing computing curve curves curves curves curves curves curves curves curves curves curves curves stage bit determine classifiers upper upper upper statistics statistics statistics free estimated basic give con derived weighted bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds types lines lines entropy entropy entropy product processes processes processes processes processes processes processes processes processes processes processes processes depends sampling simply simply discussion covariance covariance covariance covariance covariance covariance technical technical group denote complete complete proof proof rbf rbf supported eds eds eds square easily reduced unknown unknown coefficients jordan jordan special empirical squared direct direct making improved exact exact exact reported identical engineering dimensions observations yields correspond symmetric modified interval interval williams williams williams williams williams williams risk expression hybrid touretzky deterministic minimal assumptions bayes bayes bayes bayes bayes numerical numerical clear exponential drawn drawn drawn drawn drawn drawn drawn drawn solid solid explicit relation pro monte monte monte carlo carlo carlo written written generating dept dept confidence confidence metric infinite infinite infinite develop mutual integrated predictive predictive springer expectation independently overlap learner lemma lemma lemma lemma lemma detailed evaluated spectrum calculation expansion spaces convex generation expect figures figures figures kernels priori coordinate coordinate eigenvalues eigenvalues eigenvalues weighting vapnik mozer mozer mozer priors phys discussions differ included mackay mackay mackay compact graphs graphs graphs graphs contained showing interested hold satisfy gibbs sampled nips eigenvalue eigenvalue eigenvalue bars bars bars simpler carried requirements integral integral dotted dotted dotted dotted dataset behaviour variational maximizing eigenvectors proved proved understand neu generalisation generalisation rev observe expressions expressions explain motivated finds electronic neal neal asymptotically asymptotically asymptotically asymptotically inequality inequality inequality inequality developing analytical lies precisely immediately immediately products probable acknowledgement describing begin toronto mechanics integrating evaluating understood peter haussler formulated http popular qualitatively marginal marginal datasets datasets datasets expectations differentiable yielding cumulative cumulative cumulative lot corrupted notes summing kullback ral intuitively ylx nonparametric overlaps loo appendix appendix equals regard realization lengths hasselmo specialized arrive cam sequentially entropic entropic entropic entropic entropic annals ent aston aston aston leibler chervonenkis conjecture opper opper opper opper opper covariances scenario tight pub equality equality distri community learnt expand noting increasingly sollich grateful preprint preprint bution lecture replacement nonnegative smoother barber barber orthonormal orthonormal inequalities rasmussen petsche petsche rohwer concave losses nontrivial inde gence signed signed fixing united eigenfunctions eigenfunctions birmingham completeness completeness datapoints tutorial crg tighter tighter tighter phy coincides italy zhu zhu jensen jensen rightmost british manfred dash dash convexity convexity ncrg gression quantum looo kingdom ast cesses hadamard iip stretching aerospace sir combinatorics bessel pendence yil studentship marina diver 
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#*network network network learning learning learning learning learning model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data function function function function function function function set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output number number number system error error error error error results results results results results units units information information information information problem problem problem problem problem problem problem problem problem models models models models models models models hidden hidden hidden hidden based based based space space linear layer layer layer case case case case case case order order order order order shown shown shown systems systems systems systems systems systems systems values values values probability probability probability probability noise noise noise weight weight functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method approach approach approach approach approach approach approach approach approach point point point single single single single processing processing processing large large large test test test test test test analysis analysis class matrix optimal inputs inputs inputs inputs form form form algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples examples small small feature work work methods methods methods methods methods methods step points points field field field field field field field field field field field field field field field field field field field field field field field field field field field field classification classification classification classification classification classification classification classification classification process process process trained problems random random random random high show show equation equation fixed generalization generalization real approximation approximation theory theory theory theory theory obtained obtained term term term note dimensional result result result result result university university university university university variables variables variables variables variables variables computation computation solution solution solution solution research research research research independent defined defined found found found found target initial table table table estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard computer computer terms terms science science prediction prediction prediction present sets maximum range press press press press nonlinear abstract applied applied applied back back find computational convergence convergence likelihood likelihood likelihood likelihood references due positive positive positive important propagation complex complex statistical statistical statistical statistical statistical statistical variance variance energy energy difference variable variable assume assume classifier measure measure prior prior prior prior prior chosen chosen chosen center previous previous cases type type binary binary binary conditions bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations equations equations equations equations equations equations equations equations make make make fact fact fact length errors forward forward simulations simulation simulation simulation regression regression regression regression respect respect respect respect respect called optimization dimension made made natural applications study knowledge obtain obtain negative negative original specific true true compared application application desired provide define define goal posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions equal equal approaches mit mit mit mit contrast contrast fields fields fields fields fields nets modeling modeling modeling report institute implementation final exp scheme framework framework framework framework cambridge computing computing computing equivalent directly additional additional limit limit limit limit classifiers full choice choice choice choice approximate approximate approximate statistics statistics free free world basic give give condition conditional bounds bounds product finally processes processes processes processes processes processes processes processes processes evidence iteration sampling discussion covariance covariance covariance technical technical technical group denote corresponds complete predictions assumed supported theoretical eds eds eds eds needed reduced reduced dynamical functional jordan jordan jordan interesting interesting interesting testing special leads leads details pre direct magnitude minimize added added description perceptron perceptron denotes discussed correlations exact exact exact exact exact exact exact exact robust ensemble practical apply introduced introduced introduced introduced introduced introduced machines sejnowski sejnowski sejnowski recently relevant engineering interest approximately calculated calculated calculated axis axis converge achieve diagonal definition symmetric generalized williams williams williams williams williams williams matrices predicted feed feed hybrid touretzky setting setting starting assumptions reduce depend interactions interactions interactions interactions interactions interactions interactions bayes bayes bayes bayes bayes practice suggest hard hard integration integration physics physics physics physics physics external external targets introduce derivatives derivatives boltzmann pro monte monte monte derive carlo carlo carlo written solving solving ways ways estimating label label label label stability dept changing multilayer infinite infinite infinite remaining easy easy belief unique interaction integrated minimization springer expectation versus yield expressed estimator estimator solved transform transform approximations approximated partition partition sign sign calculation calculation expansion spaces add foundation expect expect expect priori perceptrons formulation inter sciences discuss mozer mozer mozer mozer priors priors phys phys phys phys successfully major simplicity determining determining straightforward straightforward presentation mackay mackay mackay mackay mackay mackay comparing essentially orthogonal anderson anderson split contribution contribution contribution contribution classify running built satisfy gibbs gibbs gibbs nips automatically received acknowledgments simpler simpler simpler simpler unlike parametric layered layered perturbation difficulty replaced helpful rest applicable ideal variational variational variational math rev der formal simplest motivated electronic neal neal neal neal averages averages averages averages averages averages spin spin spin spin spin spin ment agreement smoothness glass glass glass glass correction tool comparisons processed turns tive division probable scientific toronto lowest raw mechanics mechanics prop leave leave leave leave orders treated http gen hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters expectations expectations expectations converged naive naive naive naive naive naive naive naive corrupted corrupted notes notes forming purely nonzero theories turned turned eliminated eliminated numerically promising tools determination replica keeping preparation combinatorial tap tap tap tap tap tap tap tap tap tap tap published introduces connect connect bad hasselmo dif laplace laplace route eqs likelihoods likelihoods lett lett cam vari treat logarithm aston deriving validity reaction failed opper opper opper opper opper opper opper opper opper ideally covariances guess auxiliary pub community cessing thermodynamic thermodynamic cij cij cation drawback sonar sonar sonar sonar particle preprint normalizing corrections infinitely infinitely microscopic microscopic cavity lecture lecture replacement palmer palmer sake ferent solvable barber barber spins conversion rasmussen rasmussen coincide petsche petsche petsche rameters nontrivial drastically denmark brackets legendre legendre wong wong birmingham gardner lund lund nice nice derivations haven crg predic ables phy phil mft mft mft mft mft mft mft imaginary imaginary imaginary fluctuating dealt rescaling parisi parisi parisi parisi subtract europhys manfred mag circumvent winther winther winther winther winther winther winther winther concluded classifi proaches copenhagen copenhagen ising ising rid bohr rocks specialize integrations integrations lengthy disordered disordered blegdamsvej danish danish ast gorman gorman gorman thouless thouless virasoro virasoro zard zard zard zard flipped rior ioo ioo poste ole truncating strategic niels factorizable mines wol sweden councils esting 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural input input input input input input input input figure figure figure figure time time time time time time time time time time set set set set set set set set set set set set set networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output output output output output output number number number number number number number system system error error error error error error error error error error results results results results results results results results information problem models models models models models based weights case case case vector vector vector vector vector vector vector vector order order order systems systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution processing large large large large large large local local local local local rate rate test test class class inputs inputs inputs form form shows shows shows simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples small size size size size size work task methods step field field field field field field field field field process process process process process process current structure random random random random random random memory response show equation equation equation fixed line line line line line line rule rule vectors vectors vectors general general general general general general general parameter average average average average average theory theory theory theory theory theory theory note note note note note note experiments variables variables computation solution solution solution solution solution independent independent independent independent defined found found dynamics dynamics dynamics dynamics dynamics initial initial initial terms terms terms prediction prediction left left left present sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets basis sample sample abstract find find find find find find density density density density density properties references stochastic due due important introduction introduction complex variance variance difference variable assume assume assume assume assume lower lower lower rules rules rules chosen part theorem cases cases type conditions conditions conditions equations equations fact correct observed observed errors errors errors finite simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulation simulation respect respect called times times made study study negative relative specific true true true true compared compared application provide define rates rates perform related distributions distributions equal mit comparison larger larger larger fields fields fields fields fields support dependent dependent department version advances joint joint joint joint represents difficult difficult difficult cambridge computing directly solutions limit limit stage stage effects upper upper upper choice significant statistics statistics give condition randomly conditional developed lines lines lines lines path path product actual finally iteration simply measured discussion increases arbitrary tested tested assumption predictions predictions predictions predictions amount short effective effective generate role theoretical theoretical theoretical eds ability instance makes noisy noisy noisy noisy including combination account dynamical dynamical jordan special consistent leads details making supervised decay decay decay decay choose sources description predict perceptron perceptron perceptron discussed recent recent correlations exact exact exact exact exact exact exact property reported identical sense sense interest highly teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher calculated calculated tions solve achieve rl expression expression scaling extended extended wide starting starting starting hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian reduce depend central central measures numerical numerical numerical numerical numerical numerical numerical numerical clear clear clear clear peak asymptotic drawn drawn solid min minima question question question denoted explicit explicit suppose longer solving student student student student student student student student explicitly averaging linearly linearly remaining scales scales consisting develop independently independently dependence dependence review solved restricted restricted restricted restricted restricted restricted restricted restricted restricted restricted restricted restricted evolution evolution understanding updates past reasonable calculation calculation calculation remains perceptrons perceptrons perceptrons prove holds phys phys phys straightforward straightforward literature graphs graphs repeated contained dis quantity vary write write observable carried carried layered overfitting involving scalar scalar analytically authors statistically fundamental circles math generalisation generalisation generalisation generalisation generalisation generalisation generalisation extremely assumes observe expressions expressions regime averages averages averages averages averages advanced agreement agreement agreement benchmark benchmark london london london considerable satisfied formalism precisely choices choices choices sgn sgn sgn sgn sgn sgn sgn sgn sgn immediately controls mathematics calculations calculations calculations arises fluctuations fluctuations mechanics questions questions questions reflects double led consistency amounts solla incorrect compares calculating rely gen replace sophisticated sophisticated lim lim lim progress consistently representative college college accomplished writing writing restrict unity theories theories theories theories theories theories dealing attractive replica definitions krogh preparation hertz selects composition excellent excellent respective negligible negligible histograms sim kearns valuable lett unchanged saad saad presenting solely associate auxiliary concentrated execute picked careful ultimately integrals sollich sollich sollich sollich sollich sollich minor preprint sta macroscopic infinitely microscopic microscopic microscopic students develops circumstances circumstances observables observables observables observables observables coolen coolen coolen coolen coolen coolen coolen preserves satisfactory satisfactory barber barber king king err err err err err played char pronounced tribution striking obey markers vanish vanish scenarios evolving inspection randomness randomness randomness randomness randomness randomness iterating noiseless progresses nice assessing teachers teachers albeit enabled regularisation europhys lira lira expressing tain generalised kcl kcl kcl kcl integrations strand diamonds logs mth mth mth ingredient acter tistical exponentials irl tedious realisation confirmation characterised arccos convincing limn demanded normalise yardstick yardstick reproducible 
#@Coolen_A,Rae_H,Sollich_P,
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#*network network network network network network network network network network network network network network network network network network network network network learning learning learning neural neural neural neural neural neural neural input input input input input input input input input input input input input function function function function function function function function function function function function function function function function function function function figure figure figure set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks output output output output output output output number number number number number number number number number number number number number number number number number number number number number number number number results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based space weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer case case case case case case case case case case case case case case case case case case vector vector order order values values values values values values parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit unit unit unit large large large inputs inputs inputs inputs inputs inputs form form form form algorithms simple simple paper paper small points points points points points points classification similar similar similar architecture architecture show show show show show section fixed fixed real real real real real approximation theory theory theory obtained obtained obtained obtained obtained obtained term note note note note note note note result result result result threshold threshold threshold threshold threshold threshold variables variables variables variables independent independent independent independent log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log defined defined found sequence sequence sequence sequence sequence sequence sequence sequence constant constant constant computer terms science science science science left left present activation activation activation activation activation activation activation activation activation activation activation activation activation activation sets sets maximum maximum maximum maximum maximum range components components nonlinear outputs outputs abstract computational computational analog references positive introduction tion difference complexity complexity variable lower lower lower lower lower lower lower lower lower lower lower prior higher part part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases cases cases cases cases type binary binary binary binary binary binary binary binary fact fact fact fact region length length length length length classes total total total sum sum sum called elements elements elements means dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension applications knowledge obtain obtain represented series proc proc proc proc proc proc proc perform perform constraints connected connected equal power power power power power connection nets nets proceedings institute words version consists consists code code exp layers layers layers layers layers layers scheme computing computing bit conference upper upper upper upper upper upper upper upper upper upper upper upper give give weighted weighted developed bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds types types types path path path product backpropagation depends depends technical denote inverse inverse proof proof proof proof proof proof proof proof proof proof proof circuits role role role theoretical main ability easily easily easily degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree including underlying needed combination technology technology special matching numbers numbers bits bits bits bits bits 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lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma codes solved open restricted showed allowed calculation combining roughly roughly calculate calculate sufficiently combinations assignment vapnik specifically specifically holds holds simplicity simplicity importance suitable encoded encoded composed composed composed refer decoding follow sci satisfy comp notation usual exhibit replaced school complicated proved func func surfaces induction integer logistic logistic asymptotically advanced piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise piecewise fairly multiplication multiplication multiplication multiplication satisfied precisely precisely precisely precisely constructing annual annual argument composite parameterized orders posed adjustable polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials proven proven replace replace decoder decoder decoder 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#*learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural input input data data data data data data data data data data data data function function function function function function function function function function function figure figure figure figure figure figure time time time set set set set set set set set set set networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system system error error state results results results information problem problem problem problem problem problem problem problem problem problem models models models performance performance based based space space space linear linear case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown shown systems values values values probability probability parameters parameters parameters noise noise noise noise noise noise noise functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution recognition recognition recognition method approach approach pattern pattern pattern pattern point point processing processing control control control control large local test test patterns patterns patterns analysis class class class class optimal optimal optimal form form form shows shows shows algorithms algorithms gaussian gaussian examples examples examples examples examples examples examples small size size feature feature work task task methods methods fig fig step points points points points points points points points points points level level structure structure random similar similar representation show section vectors vectors vectors vectors general general generalization generalization generalization generalization parameter parameter parameter parameter parameter approximation average theory theory theory theory theory obtained obtained term term term term term term term term term term note note note note note note note experiments experiments experiments dimensional university variables variables variables variables variables variables variables variables computation solution solution solution solution solution target constant constant constant constant constant constant table table table estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard terms left left map present present low object range press press press press press basis nonlinear continuous continuous sample abstract computational convergence properties references due due due due due ieee positive decision decision introduction hand statistical statistical statistical statistical generated generated variance tion change change change difference complexity complexity complexity assume assume assume lower lower lower prior prior prior prior chosen chosen chosen bound bound bound bound cases cases cases cases cases long long conditions conditions represent make make fact fact fact techniques proposed errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors ing regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression computed computed respect sum performed called called optimization optimization optimization optimization optimization applications knowledge knowledge knowledge knowledge obtain original artificial artificial relative compared desired desired experimental experimental related related constraints equal approaches mit mit mit accuracy accuracy accuracy accuracy larger larger support support support support support support support support support support support support support support support support support support train train dependent proceedings proceedings proceedings loss loss loss loss loss loss loss loss version consists kernel kernel kernel kernel kernel kernel advances advances advances exp addition addition cambridge cambridge cambridge computing computing equivalent directly directly additional view estimates top top top top top top top top conference conference conference capacity capacity determine classifiers classifiers upper upper upper choice choice choice free speed estimated estimated pages pages pages pages pages pages increase increase increase validation give give give give con condition randomly developed bounds product product finally nature constraint constraint constraint constraint constraint constraint simply achieved discussion discussion denote denote close close assumption corresponds corresponds surface proof proof proof proof rbf shape shape supported role theoretical theoretical face instance instance makes makes makes noisy including objective objective typically smaller needed reduced account functional jordan ratio york edge edge edge increasing consistent trials uniform uniform empirical empirical empirical leads leads leads leads squared call numbers max direct international international international bottom bottom bottom bottom bottom bottom bottom idea minimize minimize minimize minimize run advantage advantage property robust robust robust reported subject subject subject subject machines machines machines machines quadratic quadratic quadratic quadratic trees sense sense subset recently interest match correspond studies trans sparse symmetric modified observation generalized bounded risk risk wide predicted width width width occurs boundary setting pass runs starting starting minimal editors editors editors editors editors editors accurate asymptotic constrained suggest taking taking largest external drawn drawn proportional proportional regularization regularization radial minimizing minimizing movements min decrease iii iii program program program question suppose suppose pro edges edges edges solving changing changing metric category linearly linearly dimensionality remaining remaining springer springer springer implies implies implies select letters national dependence depending estimator influence evaluated open fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction decomposition soft margin margin sign calculation additive expansion sec sec sec sec sec includes kernels kernels kernels kernels kernels priori priori priori priori priori priori priori priori formulation vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik automatic automatic discuss maximize maximize holds determining straightforward compression selecting middle closely uniformly maximal modification divided poggio essentially refer verlag verlag verlag induced interested interested split lie lie lie sin sin sin hold simplified dot dot minimizes leading leading automatically automatically automatically automatically automatically decreasing parametric parametric parametric parametric parametric estimators dotted dual dual dual dual dual dual dual dual dual graphical graphical helpful reducing giving mse mse mse mse ideal referred maximizing proper workshop understand analogous smallest closest plausible editor adjusted shapes art motivated optimum asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically crucial briefly benchmark benchmark lies handle arc widely precisely desirable hyperplane controls watkins simard acknowledgement separately definite annual radius radius robustness argument argument questions double understood understood understood flexible fed experimentally peter peter leave introducing solla haussler outliers http http berlin berlin berlin pittsburgh extracting proven incorporating sums germany boston boston conclude conclude findings deviations eventually proposition proposition proposition proposition proposition proposition proposition proposition proposition proposition proposition trade contribute www sv sv sv sv sv sv sv sv sv sv sv sv lagrange fix princeton acm acm girosi girosi girosi perfectly approximates homogeneous discovery nonzero proceed multipliers convenient significance adjusting satisfying grow biased imply ylx ylx carry generalizes performances performances excellent bartlett bartlett bartlett bartlett bartlett bartlett bartlett recovered respective equals negligible sides captured originally multiplied recog kearns bagging theoretically theoretically park agree statement std std std interestingly 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#@Bartlett_P,Scholkopf_B,Smola_A,Williamson_R,
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#*network network network learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time set set networks networks networks networks networks networks networks networks system system system state state state state state state results information problem models models models models models models models models models models models models models models models models models based based space space case case case case order order order order order order order order systems systems systems systems values values values values parameters parameters parameters parameters noise noise neurons neurons neurons neurons neurons neurons neurons neurons recognition method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point point image single single processing processing processing large large large large neuron neuron neuron analysis analysis class class matrix matrix matrix matrix matrix form form form form form shows shows simple simple simple simple paper paper size net net methods step points points points points field field field field field field field features process structure structure random random random memory response similar similar representation show show show equation equation equation fixed fixed fixed line line line line line line line parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter average average average states states states states states states states states states states states states states states states states states gradient obtained obtained obtained obtained note note note note activity dimensional dimensional dimensional dimensional result result result variables variables solution solution solution solution solution solution solution research independent log log log log log log log log found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial terms distance synaptic synaptic synaptic synaptic synaptic synaptic science left left left left left presented map present present present present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low range range range range range range range range range range range range range range range range range range range range range range range range range press components basis continuous continuous continuous continuous abstract find find properties properties references stochastic due due due due positive important introduction complex statistical statistical effect generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent tion tion energy difference complexity spatial spatial spatial lower lower representations bound cases firing type type type multiple binary binary spike long long long long long long long long long long long long long long conditions represent equations equations equations equations equations equations make fact techniques techniques techniques techniques region region region region region region region region region region region probabilities finite minimum minimum resulting respect called called regions regions regions regions regions made study study study obtain negative negative specific true cross perform determined determined approaches mit contrast contrast descent dependent modeling modeling synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses technique advances difficult exp exp exp addition addition addition addition addition graph ai ai ai ai ai ai ai ai ai maps solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions transition transition transition transition transition transition transition transition transition transition transition transition transition limit limit stage determine determine upper full full choice choice choice free increase give con condition types types types types types types lines lines lines lines lines lines lines lines lines lines lines provided finally nature inhibitory inhibitory inhibitory biological associative discussion technical describe describe arbitrary transformation transformation transformation close close corresponds excitatory amount short short short short short short short short short short short short short short short nearest nearest nearest nearest nearest nearest nearest synapse generate role theoretical main eds eds instance instance combination combination combination combination combination combination combination reduced reduced dynamical fully transfer transfer transfer transfer interesting interesting significantly increasing mechanism special uniform operation language leads details inhibition stored early early magnitude magnitude neuronal neuronal exact exact exact exact exact pair pair separate takes strategy identical array array interest calculated works works correspond correspond studies converge rl trans trans diagonal symmetric exists expression expression occur occur occur occur occur matrices predicted alternative touretzky deterministic deterministic occurs strength strength strength critical place place place place hebbian hebbian hebbian hebbian hebbian hebbian hebbian interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions measures taking strong presence largest cycle drawn drawn solid turn turn turn turn exist plane plane plane plane plane iii iii iii iii derivatives identification areas boltzmann van derive produces written longer solving solving solving solving ways sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential generating describes describes transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions mathematical dept recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall recall physical physical physical transformations unique interaction equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium springer quality quality implies expectation 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periodic existence existence fashion giving biol analytically structured tanh tanh tanh tanh tanh tanh tanh tanh tanh tanh phases editor generalisation generalisation opposite opposite rev rev created created thought quantities bifurcation bifurcation bifurcation taylor expressions expressions pyramidal finds finds finds finds finds finds finds trivial trivial trivial trivial trivial trivial publishers defining unstable unstable phenomena phenomena analytical analytical analytical analytical analytical starts london london london spatially turns precisely precisely controls mathematics potentially mechanics mechanics limits understood treated biologically execution execution calculating mod anti anti occurrence qualitatively qualitatively curvature substantial enables lim lim lim lim lim lim lim lim picture picture picture picture picture cybern college college redundant notes saddle saddle saddle saddle saddle saddle formally oxford tation restrict acts purely purely eliminate nonzero turned arranged saturation ranges mail familiar transforms definitions preparation corner eqn elimination published sompolinsky sompolinsky ensures ensures corre induce induce evident hasselmo arrive arrive storing jump subsequently papers lett material vari crossing schulten ter pointing inferred covariances covariances auxiliary illustration transparent translated exponent exponent exponent evolve evolve interact dominated discontinuity discontinuity differentiation differentiation scope insertion regimes regimes regimes regimes anal sta elsevier induces macroscopic els infinitely microscopic behaves status diagrams lecture observables coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen advantageous differently sponding discontinuous discontinuous discontinuous discontinuous discontinuous discontinuous discontinuous discontinuous discontinuous discontinuous discontinuous discontinuous solvable compete king king hemmen exploits inspection reality est sid translates 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#@Beckmann_C,Coolen_A,Skantzos_N,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural input input input input input input input input input input input input input input input input input input data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function figure figure set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training output output output output output output number number number error error error error error error error error error error error error error error error error error error results results results results results results results results results information information problem problem problem problem models performance performance performance based space space space space weights linear linear linear linear linear linear case case case case case case case case case case case case vector order order shown systems values values values values values values values values noise noise noise noise noise noise noise noise weight functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach point point large large large large large large large test test test matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs form form form form shows simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples examples examples examples examples examples examples examples small small small small small small small small size size work work work work methods fig fig step points process process process process process level level problems random similar similar representation representation show show equation equation equation equation fixed line vectors vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter real real 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difference variable assume assume lower lower lower lower lower lower lower lower lower lower lower lower lower measure prior prior prior prior prior prior prior prior prior prior representations learned learned learned chosen previous previous theorem bound bound bound bound bound bound bound bound bound bound cases type required good good good long conditions bayesian expected expected expected expected expected expected fact fact fact fact fact fact techniques region correlation length length length length length correct correct errors scale scale scale scale scale scale finite finite simulations simulations minimum resulting resulting resulting simulation simulation simulation regression regression regression regression regression regression eq eq called called elements elements dimension dimension dimension made made applications applications true true true true true true provide provide perform perform determined determined posterior posterior posterior posterior posterior 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inference relevant varying compare compare compare compare observations observations observations teacher teacher teacher works solve smooth smooth yields yields yields converge differential differential achieve diagonal diagonal address definition symmetric modified generalized generalized williams williams williams williams williams williams williams williams williams expression expression lead studied occur suggests suggests deviation deviation wide derivative alternative correctly boundary generally setting starting starting starting starting assumptions assumptions valued valued editors numerical clear clear exponential exponential practice practice asymptotic asymptotic asymptotic asymptotic suggest taking taking taking integration physics physics largest characteristics solid solid start introduce derivatives question acknowledgements pro monte derive derive derive derive carlo produces written winner implement explicitly averaging averaging averaging easy easy scales consisting 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#@Sollich_P,
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#*network learning learning learning learning learning learning learning model model model model model model model neural neural neural neural neural neural neural neural data function function figure figure set networks networks networks networks networks networks algorithm algorithm algorithm system system system system system system error state state state state results information information information information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models based based linear linear linear linear linear linear linear linear linear linear case vector order order order order order order order order order order order order order order order order order order order order order order order order order order order order shown systems systems probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions unit distribution distribution distribution distribution recognition method approach approach approach pattern point point point single processing large large matrix form form algorithms algorithms algorithms paper paper small fig fig field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field process structure problems random random response response response response response response response response response response architecture equation equation equation equation equation equation fixed fixed general general approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states theory theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained term term note note university variables variables computation solution solution solution solution solution solution independent log log log defined defined defined defined defined defined found target estimate computer terms terms terms distance science left presented presented present present present present present present present present machine machine machine machine machine machine machine machine machine machine press basis basis abstract applied find convergence convergence references ieee ieee context introduction complex estimation estimation behavior statistical statistical statistical statistical statistical statistical statistical statistical change energy energy energy energy energy energy energy variable assume assume assume measure higher higher higher higher higher part part part theorem theorem theorem theorem theorem theorem theorem theorem theorem good binary represent expected expected fact proposed correct simulations classes ing ing computed respect respect respect respect respect respect respect respect respect eq eq eq eq eq called called called called called called called called called means means potential vol represented true true application desired proc determined determined equal mit support department advances represents represents difficult framework framework framework framework framework framework equivalent equivalent directly hinton view view view conference efficient approximate approximate approximate approximate statistics statistics free free free free free free give give condition condition condition condition condition condition clustering depends discussion inverse inverse inverse inverse surface finding common common theoretical eds eds including including fit pairs pairs coefficients coefficients coefficients coefficients coefficients coefficients fully jordan consistent consistent consistent principle squared call international denotes correlations correlations exact exact property pair pair pair takes element practical machines machines machines machines machines machines machines machines machines subset sejnowski cognitive relevant engineering approximately calculated works tions solve differential trans trans observation expression expression expression alternative deterministic deterministic place depend measures clear exponential exponential exponential exponential exponential hard physics physics physics reduction minimizing iii introduce introduce derivatives derivatives derivatives annealing boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann 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#@Tanaka_T,
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#*network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure set set set set networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number number state state state state state results units units units units units units units units information information information information information problem problem problem problem problem models models models models models models models hidden hidden hidden hidden hidden hidden performance based based based linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case case vector vector vector vector vector systems systems systems systems systems values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise functions functions functions functions unit unit unit unit recognition approach approach approach approach approach approach approach approach point single single single processing processing processing processing processing processing large analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix optimal optimal form form form form form form form form signal signal algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper small size net work task methods fig fig fig step step step step step points field field features classification level level current trained structure structure representation representation representation representation architecture fixed fixed fixed line general general general general generalization generalization speech speech real real real real real real real approximation approximation approximation approximation approximation states states states theory gradient gradient gradient gradient gradient obtained obtained obtained term term term term note university university variables variables variables variables variables variables variables variables computation computation computation computation research research independent independent independent independent independent independent independent independent independent independent independent independent log log log log log defined estimate estimate terms terms presented presented presented map map map present object object maximum maximum maximum maximum maximum range range range press press press press press press press learn components nonlinear outputs outputs continuous continuous continuous abstract computational density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component due due ieee procedure important adaptive adaptive adaptive adaptive propagation mixture mixture mixture context context introduction complex complex estimation estimation dynamic generated tion tion variable assume lower lower lower lower lower signals signals prior prior representations learned learned learned chosen center previous previous previous bound bound bound bound bound bound bound bound bound cases cases required required required multiple binary binary binary binary binary represent represent distributed distributed equations equations equations markov make proposed proposed proposed observed observed observed observed observed observed resulting resulting resulting resulting resulting tasks tasks tasks means means means factor factor factor factor factor factor factor factor made knowledge knowledge em em em em em em em em em obtain artificial true true true application desired determined related posterior posterior posterior posterior posterior posterior posterior posterior posterior connected connected gain discrete brain equal power mit mit mit mit dependent dependent source source source source source source source source source source source source source source source source source source source morgan technique technique technique consists consists individual advances advances advances advances joint joint represents difficult exp exp exp exp exp exp exp layers layers layers layers layers layers addition graph ai ai ai maps framework computing hinton hinton hinton additional additional view san san san top stage determine efficient full full significant approximate free produce produce coding derived conditional types lines product product provided provided finally finally iteration iteration depends depends sampling simply discussion covariance covariance covariance increases arbitrary arbitrary arbitrary transformation limited close assumption corresponds complete implemented assumed assumed supported theoretical journal square square ability hypothesis makes makes noisy noisy noisy noisy sensory including including probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic underlying functional functional jordan jordan jordan jordan interesting interesting special matching mode principle leads numbers numbers making making idea produced produced choose sources sources sources sources sources sources sources sources sources description description denotes recent correlations exact exact exact exact separate introduced hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical inference inference inference inference sejnowski sejnowski recently highly highly highly highly highly compare unsupervised calculated calculated axis tions sparse address chain separation separation separation separation separation modified sensitive exists concept extended wide alternative deterministic deterministic occurs setting setting valued valued valued valued valued depend depend depend depend sigmoid accurate accurate learns learns learns mateo integration sigmoidal california intelligence labeled ica ica ica ica ica ica ica ica ica ica ica ica introduce introduce derivatives manner acknowledgements suppose relation relation relation relation pro monte carlo longer solving describes segments multilayer multilayer multilayer multilayer averaging averaging linearly involves easy slightly belief belief belief belief belief belief belief belief belief belief belief belief develop develop develop gaussians gaussians blocks blocks blocks expectation letters extracted extracted focus dependence dependence dependence estimator estimator viewed solved solved densities densities densities densities restricted labels approximations approximations forms completely similarly allowed sign slow slow sec closed calculate foundation degrees box includes bell blind blind blind blind blind blind batch extension mozer mozer specifically holds holds discussions modification latent latent latent latent latent latent latent latent composed composed composed notice notice notice notice notice repeated strongly allowing neuroscience generative generative generative generative generative providing maximization maximization maximization operating mixing mixing mixing mixing mixing mixing mixing mixing extract oriented simpler unlike parametric create create difficulty exponentially exponentially optimized optimized integral limitations graphical graphical graphical ml ml helpful examine incremental variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational analytically office maximizing statistically statistically topographic possibly configurations adjusted assumes academic ith ith mixed explain explain neal inequality directed crucial variances variances guaranteed adapted adapted adapted tractable handle handle london lin potentially describing begin begin optimize integrating tional readily introducing introducing treated treated requirement maximizes maximizes incoming collective replace logp logp semi begins jaakkola softmax softmax softmax softmax softmax summed don ghahramani indices college intractable intractable intractable intractable summing fix conditioned linearity linearity naval eliminate ranges adjusting analogy proceeds intelligent keeping neurobiology reasoning belong slice slice recovered saul ascent ascent ascent ascent bad realization den advance francisco francisco recog insight creating omitted omitted arrive pearlmutter variants alternatively infomax divide informa multiply maintaining drop logarithm kluwer employs failed nition smoothly covariances constitutes laplacian param mutually mutually dominated bounding deconvolution pearl constructs sam placing frey frey bring parametrized parametrized parametrized parametrized eters mann overcomplete factorized factorized generarive generarive jointly hid dom proportions proportions horizontally ters 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#*learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output error error error error results results results results results results results results results results results results information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance based based based based based weights weights linear linear linear linear linear linear linear case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown shown systems values probability weight functions functions functions distribution recognition recognition recognition method method method method method approach approach approach approach approach approach approach approach pattern pattern pattern pattern point point point point point point point point point point point image control control large large large rate rate rate class class class class class class class class class optimal optimal optimal optimal optimal optimal form form shows shows algorithms algorithms algorithms algorithms simple paper examples small small small size size size size feature feature work work work task methods methods methods methods points points points points points points points points points points points classification classification classification classification classification classification classification classification classification classification problems problems problems problems problems problems problems problems problems high show show show show section section section section fixed fixed fixed fixed vectors general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter real real approximation theory theory theory theory theory theory obtained term note note dimensional university university university university university solution solution solution solution solution solution solution research research research found found found found found found found constant estimate estimate estimate estimate standard standard standard standard computer computer distance distance science left left direction presented machine machine machine machine machine machine machine machine machine machine sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets nonlinear nonlinear nonlinear sample abstract applied computational computational computational computational computational properties references due due decision decision decision decision mixture introduction estimation estimation statistical statistical statistical statistical statistical generated parallel search tion tion tion tion difference difference difference difference difference variable variable classifier chosen chosen cases required good errors minimum resulting resulting classes classes classes classes classes ing total regression performed performed performed performed called called means means optimization optimization optimization optimization optimization potential applications applications applications knowledge em obtain artificial relative compared compared application cross define determined determined constraints constraints approaches approaches approaches larger larger support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support modeling modeling selection report report report report report report report report report report institute institute institute institute department department department version code code kernel final final ai equivalent solutions estimates estimates limit conference capacity capacity capacity capacity capacity capacity capacity significant significant significant significant significant significant world world basic basic basic increase validation con produce randomly clustering clustering clustering clustering bounds lines provided provided nature depends constraint constraint achieved discussion discussion technical technical technical technical technical technical technical tested fast corresponds corresponds theoretical theoretical theoretical journal objective objective underlying technology programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming programming significantly significantly significantly york york segmentation special database empirical empirical empirical empirical empirical empirical principle principle language language supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised supervised magnitude idea combined minimize minimize minimize added added added improved improved improved population improve improve recent advantage robust robust robust practical introduced subject subject subject identical identical machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines quadratic trees trees engineering engineering sufficient sufficient compare unsupervised volume solve solve solve solve solve solve achieve rl separation separation separation separation separation separation separation generalized improvement improvement improvement improvement risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk entire arm arm arm arm constructed constructed constructed constructed lead extended extended extended trial deviation deviation alternative correctly occurs conclusion minimal depend editors clear propose propose reduction reduction characteristics california california labeled labeled minimizing start exist min min min min min min plane plane plane decrease introduce program program program program pro solving solving estimating mathematical mathematical mathematical mathematical mathematical mathematical linearly linearly dimensionality minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization minimization springer springer yield yield extracted focus review viewed codes solved solved variation open labels showed showed margin margin margin margin margin margin margin margin margin translation discrimination discrimination discrimination past measurements spaces purpose purpose add add penalty penalty sufficiently norm norm norm norm norm norm norm norm norm euclidean expect expect expect expect priori priori formulation formulation formulation sciences sciences vapnik vapnik vapnik vapnik vapnik vapnik vapnik discuss maximize specifically partially structural structural structural structural structural structural structural successfully major computationally svm svm svm svm svm svm svm svm svm svm svm svm successful identify ten ten ten ten ten traditional verlag success showing classify usual usual nips minimizes minimizes hypotheses maximization principles illustrates software remain overfitting association hall hall scalar dependencies working working working working working working working working working working working working working working working working working working working working working working working working working working working working working working working working maximizing maximizing workshop func func induction induction smallest circles math math closest integer integer integer integer integer integer integer integer integer integer integer explored mixed mixed mixed mixed mixed submitted massachusetts great formula formula separable separable improves improves briefly worse handle lin lin forces constructing incorporate incorporate located potentially english attribute geometry geometry questions questions improvements fuzzy empirically posed posed posed incorporated incorporated maximizes incorporating incorporating incorporating extensions prevent semi semi semi semi semi semi semi semi semi semi semi semi semi semi semi semi conclude globally globally picture picture benefit benefit benefit ear ear feasible assign investigation girosi resources databases discovery tem platt murphy promising unlabeled unlabeled unlabeled unlabeled star intuitively adequate filled separating washington heart infinity branching express cancer cancer theoretically inductive hart fold automated empty empty uci converted misclassification misclassification misclassification misclassification misclassification misclassification misclassification misclassification equivalently planes planes chervonenkis formulate failed chapter freund constitutes transparent burges unseen publication distri gener file proach constructs constructs library misclassified sonar sized memo likewise commercial margins mini supporting worked housing dim dim dim transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction insufficient mining calculates calculates calculates practically contrasts triangles norms repository concave america wisconsin wisconsin wisconsin irvine seg slack massive excessive generaliza cortes phillips moderately degrade microsoft nice mization tutorial srm srm srm srm srm cient bright bright alization madison madison madison mentation formulations humphreys parsimonious helped deduce thirty sults meyer pared bradley bradley geometrically mangasarian mangasarian mangasarian mangasarian hurt bennett bennett bennett bennett bennett bennett bennett bennett gramming pima sheffield compar discrim icml butions aha mri ilwll ilwll ilwll ilwll solver xve 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#@Bennett_K,Demiriz_A,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural data data data data data function function function function function function function function function time time time time time set set set set set set set set set set networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number error error error error error error error error error error error error error error error error error state state state results results results results results results results information information information problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models performance performance based based based based based based based based based space space space weights weights linear linear linear linear linear linear linear linear linear linear linear case case case case vector vector vector vector order values parameters parameters weight weight weight weight weight distribution distribution method method method method method method method method method method method method approach approach approach approach approach approach point point point point point point point point point point point point point control control large local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local test test analysis class matrix matrix matrix matrix matrix matrix matrix matrix optimal paper paper paper paper examples examples examples examples examples examples examples examples examples examples size size work work work work work work methods methods methods methods methods methods methods step points classification classification level random memory similar show section fixed line rule rule vectors vectors generalization generalization speech parameter parameter parameter parameter parameter approximation approximation approximation approximation average average average average obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained term experiments university variables computation computation solution solution defined defined defined defined sequence sequence constant constant constant constant constant constant constant constant constant table table table table table table table table estimate estimate standard distance distance distance distance prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented presented present present present machine machine machine press press press press basis basis basis basis basis abstract computational properties references references procedure procedure procedure context context introduction hand hand hand hand hand hand estimation estimation variance variance variance search variable assume measure measure chosen higher cases cases cases cases required conditions fact fact region proposed proposed proposed proposed errors errors errors errors errors errors errors errors scale regression regression regression regression regression regression regression regression regression regression regression performed performed performed eq eq eq eq eq eq eq eq called mapping means optimization optimization optimization optimization optimization made natural global global global global global global global applications obtain artificial artificial artificial relative relative relative relative specific specific compared compared compared compared compared compared cross cross cross cross cross cross cross cross cross define experimental experimental experimental experimental discrete equal approaches approaches approaches approaches comparison comparison comparison larger update modeling modeling modeling selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection morgan proceedings words technique consists consists consists final final final final ai considered considered considered considered considered considered considered directly directly directly estimates design conference efficient efficient requires choice significant significant statistics vision pages pages validation validation validation validation validation validation validation validation validation validation validation validation validation con derived weighted weighted weighted weighted randomly developed developed criterion criterion criterion criterion criterion criterion provided finally finally selected selected selected simply simply tested tested inverse inverse assumption assumption corresponds predictions predictions nearest nearest nearest nearest effective implemented assumed supported supported require main main main adaptation journal square square square square square square square ability hypothesis instance future future degree degree including including kaufmann combination combination combination combination combination combination combination combination combination reduced reduced unknown testing significantly significantly significantly significantly significantly significantly significantly york special database principle details pre international international normalized polynomial polynomial polynomial polynomial attention combined improve advantage ensemble ensemble takes takes takes takes takes element element element introduced introduced strategy strategy strategy strategy relevant relevant relevant interest calculated diagonal diagonal diagonal evaluation evaluation generalized sensitive grant alternative correctly locally locally locally locally hybrid conclusion row row reduce neighbor neighbor neighbor competitive performs performs performs propose propose propose characteristics characteristics characteristics intelligence intelligence turn assuming exist min averaged introduce groups groups groups identification identification identification identification identification identification identification program explicit suppose index solving winner winner winner winner winner ways ways sequential generating generating estimating modeled metric metric metric metric metric metric metric metric metric metric explicitly involves remaining text implies select family family focus focus review review squares squares squares squares squares squares squares squares squares squares squares influence evaluate evaluate updated showed centered centered partial performing classical classical combining combining neighborhood neighborhood neighborhood calculate assigned euclidean query query query query query query query query query query query query query query query query query query query query query query query query query query query query combinations priori priori formulation extension absolute absolute neighbors neighbors neighbors neighbors neighbors neighbors neighbors structural structural major simplicity reason straightforward straightforward selecting identified identified identified divided driven driven driven identify comparing identity composed summary summary notice repeated moore issue contribution contribution strategies strategies notation paradigm paradigm providing minimizes received extract extract neighboring neighboring acknowledgments software extend explore parametric parametric updating estimators estimators estimators estimators optimized optimized recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive recursive hall dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset tech mse mse mse incremental incremental incremental incremental investigated combine authors reliable comparable removed queries singular friedman friedman assumes explored explored academic art art art ith ith mentioned ment piecewise piecewise trivial growing tool tool worse handle perspective stanford involve members bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth reflects relevance flexible generic experimentally leave leave leave leave leave leave leave atkeson atkeson atkeson atkeson atkeson frequently reliability http extracting ordered datasets datasets datasets datasets datasets datasets datasets boston sophisticated returns returns globally globally globally initialization initialization picture identifying identifying cooper cooper www linearity databases databases concerned concerned concerned jth jth jth murphy murphy consideration consideration significance significance breiman breiman promising accepted stated stated moment settings effectiveness ylx constructive selects conjunction belongs approximators approximators approximators approximators approximators creating indicator cpu cpu cpu wolpert wolpert wolpert exploiting approximator approximator approximator approximator fold fold adopted adopted adopted adopted adopted integers acknowledge uci uci discount deriving recursively recursively cooperative adopt obtains unseen unseen unseen unseen publication favor exam chapman paired statistic statistic statistic statistic quinlan quinlan quinlan quinlan quinlan worth alternatives paradigms tively universit union things housing housing housing gratefully opti sake european hat confirm compete appealing returned returned concerns ples schaal schaal schaal extracts interpolating interpolating repository repository factorization ance modern request request corn assessed tenth stacked validated comprehensive mization intrinsically tutorial argmin tailored prices prices prices ross ross counterparts disagree myers myers myers fulfilled wii adopting confident conveniently conveniently pertone unitary tailed perrone validate iden penalize inexpensive diction meets meets meets meets depart effec merz merz cording aha aha mth ered consid leo leo servo servo servo mammone pertaining belgium belgium bined overload overload imizing validating rept regressors regressors adoption adoption adoption covari mpg mpg mpg lected appended ceived gion noticing deserve 
#@Bersini_H,Birattari_M,Bontempi_G,
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks training training training training algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number results results results results results results problem problem models models models models models models models models models models hidden performance performance based space space space space space space space space space space space linear linear linear linear case case case vector vector vector vector vector vector order order order shown shown shown shown shown shown shown shown shown shown systems values values values values values values values values values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition approach approach approach approach pattern image single single large large large local test test test test test analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal form form form form shows shows gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper small small small methods step step step step points points points points points points points points points points process structure problems random high representation representation show section fixed vectors vectors vectors vectors vectors images generalization generalization parameter parameter approximation approximation average average average obtained obtained obtained obtained obtained obtained obtained obtained experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional result result university variables variables variables computation solution solution solution solution solution solution research independent independent independent independent independent log log log log log log log defined defined defined defined found found found found estimate standard standard standard standard standard left direction presented sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum range range press components components components components components components components components components components components basis continuous continuous sample sample sample abstract applied computational convergence density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component component component component component component component component procedure important mixture mixture mixture mixture mixture mixture mixture mixture context context context introduction complex hand estimation estimation estimation estimation statistical generated generated variance variance variance variance variance variance variance cost cost search search tion complexity complexity complexity variable variable variable variable variable variable prior prior prior prior prior prior prior chosen part part theorem type type distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected markov make make techniques probabilities observed observed observed observed observed scale finite resulting ing total respect respect sum elements optimization optimization optimization dimension dimension natural em em artificial specific specific specific specific application cross cross cross define define location determined determined determined determined determined posterior posterior posterior posterior posterior posterior posterior posterior discrete approaches comparison larger support train dependent selection selection proceedings technique technique represents represents represents exp ai ai ai framework framework framework framework cambridge cambridge computing equivalent equivalent hinton curve curve additional limit limit conference determine determine determine determine determine full choice choice choice choice significant significant significant statistics estimated validation validation validation validation validation give weighted randomly conditional developed criterion finally evidence sampling achieved achieved achieved covariance covariance covariance covariance covariance covariance describe transformation close inverse assumption corresponds corresponds corresponds predictions effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective journal easily easily easily easily degree including fit probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic reduced reduced significantly projection projection mechanism database mode mode operation leads leads principal principal principal principal principal principal principal principal principal principal principal principal principal principal principal numbers international supervised choose denotes denotes discussed directions directions directions directions directions directions directions directions advantage property practical practical introduced identical quadratic hierarchical hierarchical inference inference inference recently recently recently dimensions dimensions dimensions dimensions dimensions dimensions dimensions sufficient sufficient compare compare conventional conventional conventional conventional conventional conventional observations tions correspond correspond pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca diagonal address mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures evaluation evaluation chain extended deviation deviation deviation matrices alternative alternative alternative clusters central bayes practice constrained constrained largest largest drawn solid iii averaged averaged introduce introduce derivatives appears monte construct carlo written plot plot plot plot plot implement dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality involves involves remaining remaining remaining remaining consisting develop integrated gaussians predictive versus versus focus expressed review reconstruction stationary squares interpretation evaluated showed showed completely digits digits key dashed additive spaces reduces fitting purpose visible degrees degrees degrees avoid avoid avoid expect box combinations formulation formulation formulation formulation eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues weighting subspace subspace plotted illustrated automatic automatic priors successfully columns columns columns columns determining straightforward compression suitable suitable society computationally computationally effectively driven latent latent latent latent latent latent latent latent latent latent latent latent latent efficiently mackay mackay mackay mackay tend quickly quickly quickly allowing showing showing showing dis dis dis issue issue issue generative generative gray satisfy satisfy gibbs paradigm highest automatically automatically automatically automatically modelling modelling minimized explore explore explore remain updating involving involving detail hessian hessian issues graphical helpful variational analytically scaled maximizing maximizing eigenvectors eigenvectors eigenvectors eigenvectors naturally trace plausible der freedom freedom freedom freedom motivated neal ment formula convolution tractable widely choices bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop bishop controls controls probable consequence potentially circle relevance capability introducing introducing mod ture cal extensions marginal marginal deviations deviations intractable intractable intractable intractable saddle oxford controlling controlling discover royal lost accepted replacing determination hyper hyper hyper hyper hyper hyper recovered governed governed governed displayed displayed offers offers offers treatment treatment treatment smoothed eigenvector partitioned likelihoods limitation treat treat multiplying street logarithm equivalently exhaustive exhaustive july seek ideally suppressed illustration illustration illustration avoids avoids principled visualization shaded verified publication concentrated distri distri diag gener permits plate switched switched singularities singularities superposition accounted retained retained retained retained retained normalizing mix diagrams bution bution handled moderate advantageous factorized simplification const christopher impractical insufficient insufficient house lated tribution extracts discarded comprising comprising lnp ically problematic discovers ated cti hood microsoft microsoft tipping tipping tipping tipping tipping tipping ard proximation omit direc graphically alization comprises analyzers analyzers george tri tlx tlx likeli iee reformulation reformulation reformulation associ unwanted suppressing suppressing wld wld dimensionalities dimensionalities dimensionalities crete 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#@Bishop_C,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural data data function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set set set set set set set set set set set set training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system system system state state state state state state state state state state state state state state state state state state state state state units information problem problem problem problem problem models models models models models models models models models models hidden hidden based based space weights linear linear linear linear case case vector vector vector vector vector order order order order order order order order order shown systems systems values values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise distribution distribution recognition recognition approach approach pattern pattern point image single control analysis analysis analysis class class class class class class class class class class class class class class class class matrix matrix matrix optimal form form form signal algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian visual visual paper paper examples small size methods step step classification classification classification classification process process process process process process process process process process current current current structure structure random random random memory response representation show show section section fixed rule general general general speech speech parameter real states states states states states states states theory theory theory obtained note note experiments experiments experiments experiments experiments dimensional dimensional dimensional university variables computation independent independent independent independent log log defined defined found sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial estimate standard standard standard computer computer terms science frequency temporal machine object sets sets sets sets sets motion motion motion motion motion motion motion motion motion motion maximum maximum maximum press press learn learn position nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample sample sample sample sample sample sample sample abstract applied back back computational computational density density density density properties properties properties likelihood likelihood likelihood likelihood references component component component component component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic important propagation propagation propagation propagation introduction introduction complex complex complex hand hand estimation estimation estimation estimation estimation estimation estimation generated complexity complexity signals signals signals prior prior learned learned learned learned learned learned higher part part previous required required multiple multiple good represent represent bayesian expected expected expected expected markov markov markov markov make techniques techniques observed observed observed forward forward forward finite resulting classes classes classes classes ing human computed respect respect multi multi multi multi multi multi multi multi multi multi multi multi multi multi performed times means applications applications em em em em em em em em em filter filter relative samples represented represented series series series compute compute proc proc proc goal related posterior discrete discrete discrete discrete discrete discrete mit mit steps steps steps update support department version advances joint represents represents represents represents final addition graph sequences framework framework cambridge computing computing experiment directly directly directly estimates transition transition transition transition limit determine requires choice statistics statistics vision vision vision estimated pages pages channel coding conditional conditional actual processes processes sampling sampling sampling simply simply achieved achieved normal arbitrary arbitrary hmm complete short assumed assumed shape shape journal instance degree probabilistic needed dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical special representing representing iterations filters filters filters direct stored combined choose choose choose added light predict denotes discussed correlations exact exact exact exact property property property property pair reported practical practical include include quadratic engineering engineering varying varying observations observations observations observations observations observations observations observations observations observations observations observations approximately correspond converge chain chain separation observation observation observation observation entire entire entire entire entire constructed invariant extended extended extended alternative deterministic generally starting place trajectories valued measures clear physics drawn drawn turn assuming user identification acoustic question acknowledgements pro monte construct carlo longer longer perception perception transitions transitions label dimensionality spectral frequencies frequencies frequencies predictive springer expectation expectation expectation independently review solved densities evaluated restricted labels approximations lee suggested translation allowed allowed allowed smoothing smoothing smoothing sec combining tracking filtering filtering eeg eeg topology topology coupling uncertainty sensor selecting hmms hmms importance suitable effectively literature tend soc conf conf verlag quickly procedures prob allowing video built notation backward backward backward backward observable observable modelling modelling presents parametric essential essential kalman kalman kalman involving accurately graphical graphical graphical hall hall successive history history rest int variability plausible plausible editor integer thought thought ensure aspect consist mixed mixed mixed mixed mixed mixed mixed formula directed crucial sensors fairly briefly baum baum lies handle starts processed drive purposes widely medical auto auto auto auto incomplete prop understood bootstrap dark offset offset offset amounts formulated incorrect http cal inherent expectations expectations expectations specifies instantaneous college sensing www oxford oxford oxford oxford fix conditioned conditioned conditioned member acts approximates purely grey grey grey generality multipliers smith north north north north north north carry carry carry carry moments moments prentice prentice weakly governed forecasting forecasting forecasting modelled augmented roy motions davis davis dempster dempster automated visually rubin opposed emerge welch welch convenience lit acceleration acceleration streams mutually cessing robots stroke dominated life harder laird maintains particle grateful gordon gordon normalised treating ward rabiner rabiner rabiner replacement expense ble autocorrelation stochastically smoother blake blake blake blake blake blake blake blake clarity drawing formulae continuum continuum bregler bregler emerges classi carries proves suffice dimen longest neutral fication iterate mle mle mle mle mle mle tit maximisation maximisation maximisation mid walker walker respects web comprises lpc agation initialised throw throw throw throw hwang hwang hwang tarassenko epsrc periments condensation condensation condensation condensation condensation condensation condensation altogether healthy chaining chaining chaining chaining generalised emerging electro omitting ballistic ballistic ballistic ballistic ballistic ljung ljung ljung iee fundamentals roberts isard isard isard isard isard isard sional accelerations lauritzen lauritzen juggling juggling juggling juggling juggling arbi fro gelb gelb gelb gelb gelb engaged namical namical autocorrelations autocorrelations trary ixt tat superscripts dynami dynami encompass regressive regressive regressive sation catch catch catch catch accom restoring kit multiplicatively recognising plished 
#@Blake_A,Isard_M,North_B,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model data data data data data data data data data function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time set set set networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system system error error error error error error error error error error error error state state state state state state state state state state state state state state state state state state state results results results results results results results results results results results information information problem problem problem problem models models models models models models models models models models models models models models models models models models models hidden hidden hidden performance based based based based based based space linear linear case case case case case case vector vector vector order shown shown shown shown shown systems systems systems systems systems systems probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters distribution distribution distribution distribution recognition approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach point single processing large large large large local local local rate test test analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple paper paper paper paper small small small small small small small small small size size size size size work work task task task task task task task task task step step step step step step step step step points process process process process process process process process process process process current current current current structure structure structure structure structure structure structure problems problems problems problems random random random high response response representation representation representation representation representation representation representation show show show show show show show show fixed fixed vectors vectors generalization generalization speech speech parameter parameter parameter parameter parameter parameter parameter real real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average states states states theory obtained obtained note note note note experiments experiments experiments experiments experiments result result result result variables variables variables variables variables variables variables variables variables variables variables variables computation solution research independent log log defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics initial table estimate standard standard standard computer computer terms terms distance distance distance distance science science prediction direction presented present present present phase phase phase phase temporal temporal temporal temporal temporal temporal maximum maximum maximum maximum learn learn learn abstract applied applied back computational computational computational computational convergence properties likelihood likelihood likelihood likelihood likelihood likelihood references component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due positive procedure procedure important important propagation propagation propagation propagation propagation propagation propagation context introduction introduction complex complex complex complex complex behavior statistical effect effect effect effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated cost cost cost cost difference difference difference difference variable variable assume assume assume lower lower prior prior representations learned learned theorem bound bound cases cases type multiple good good good long long long long tree tree tree tree tree bayesian bayesian bayesian bayesian bayesian expected expected expected expected expected markov markov markov techniques techniques proposed correct correct probabilities observed observed observed observed errors errors forward forward forward forward forward forward forward forward forward forward forward forward forward resulting resulting resulting resulting resulting resulting human computed computed computed computed computed called times times elements factor dimension natural applications knowledge knowledge em em em em em em em em em em em em em em em em em em em em em em em em relative relative relative relative represented represented compared application application provide provide provide define define compute compute compute compute compute compute rates proc proc proc proc experimental goal related connected distributions distributions distributions steps accuracy accuracy accuracy accuracy accuracy accuracy comparison larger contrast update update update update update loss implementation technique consists joint joint joint represents bias scheme graph sequences considered computing domain domain directly hinton view view view transition transition transition transition transition transition stage effects efficient upper full full requires significant approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate statistics statistics statistics statistics statistics statistics statistics estimated basic pages pages pages condition condition conditional clustering clustering clustering bounds bounds bounds bounds bounds bounds types entropy entropy entropy product product finally finally processes processes processes processes processes processes processes processes processes evidence evidence evidence evidence evidence iteration iteration iteration iteration depends simply simply simply discussion discussion describe describe describe denote denote tested limited limited limited close close assumption short short short effective implemented generate supported role theoretical require require main journal ability hypothesis hypothesis hypothesis hypothesis hypothesis cluster future future future future future future future easily makes fit fit fit probabilistic smaller jordan jordan significantly projection increasing structures structures uniform empirical empirical leads filters direct making window window window window window window window window window window window window window expert expert decay decay idea idea idea attention combined minimize recent exact exact exact exact exact exact exact exact exact separate practical practical apply apply apply apply apply include inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference subset recently relevant relevant relevant engineering sufficient sufficient sufficient sufficient sufficient sufficient sufficient highly compare observations observations observations observations observations observations observations observations tions converge achieve sparse address address definition observation observation observation observation bounded improvement entire entire entire entire entire entire entire entire lead concept suggests matrices alternative alternative clusters clusters column setting setting setting setting setting runs conclusion starting starting depend accurate accurate accurate peak exponential exponential exponential exponential faster faster faster practice weak weak learns suggest integration largest largest reduction proportional min min min min iii introduce introduce program acknowledgements reference explicit construct longer distinct dept dept metric implement missing explicitly belief belief belief belief belief belief belief belief integrated quality quality quality quality quality quality quality quality expectation expectation focus correlated lemma lemma evaluated evaluated updated updated updated showed showed approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations static static static static static static static static static static static approximated completely completely similarly suggested converges converges converges updates updates updates past key spaces sec iterative remains filtering advantages advantages batch batch batch batch batch batch extension extension extension extension prove prove prove partially discussions tests structural structural structural structural structural structural structural simplicity reason reason straightforward straightforward straightforward closely closely hmms hmms hmms hmms hmms society encoded computationally computationally efficiently computations schemes essentially online online online online online online online online online online online online online ten reached soc compact compact compact repeated repeated induced allowing allowing showing showing showing stopping running running follow comp realistic backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward backward providing nips observable observable computes reach maximization extend situations simpler remain wiley access exponentially exponentially exponentially updating rapidly kalman kalman divergence divergence graphical ideas incremental applicable applicable int variational variational analytically combine structured structured structured structured structured structured structured comparable proved cover phases notion notion smallest coefficient closest closest editor reading traffic analyze equally changed subsets friedman friedman obvious obvious message message message message message message message message message improving neal crucial track guaranteed fairly answer expensive expensive caused caused tractable tractable worse worse starts turns rapid stanford stanford stanford stanford closer easier easier precisely incorporate incorporate incorporate incorporate ran mation consequence read incomplete qualitative sun fluctuations outer applies empirically empirically conducted conducted leave passed frequently maintain 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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural neural neural neural input data data data data data data data function figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm system system system system error error error error error error error error state state state state state state state state state state state state state state results results results results results results results results results results results results units information information information information information information problem problem problem models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based based based based based based based based based based based space space space space space space space space weights weights weights linear linear linear linear layer case case case case vector vector order shown shown shown systems systems values probability probability probability parameters parameters parameters parameters parameters parameters noise noise noise noise weight weight weight distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach point point point point point point point single single single single single single single single single single single processing processing control local local test test matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal inputs inputs form form form shows shows shows shows shows signal algorithms algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper paper paper net work work work task methods methods step step step step step step step step step step step step step step step step step step step step step step process level level level level level current current current trained trained trained problems random show show show show show show show show equation equation equation section section section section section section section section section fixed fixed line vectors vectors vectors general general general general real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average states states states states states theory gradient gradient gradient obtained obtained obtained obtained obtained obtained obtained note note note note experiments experiments experiments experiments experiments result variables variables variables variables variables variables variables variables solution solution solution solution independent independent independent log log log log log log log log found found sequence dynamics initial initial initial initial estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard prediction left left left left left presented presented presented presented presented presented present present present present maximum maximum press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous sample sample sample abstract back computational computational convergence convergence density density density density density likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic due ieee ieee positive procedure important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex complex estimation estimation estimation estimation estimation estimation dynamic generated generated generated generated recurrent tion difference variable variable assume rules measure prior center center center previous previous cases cases conditions conditions distributed expected expected expected expected expected expected expected equations equations equations equations equations markov fact fact region region proposed correct correct observed observed forward forward forward forward forward forward forward forward resulting ing ing tasks regression computed respect respect respect multi sum sum sum sum sum sum performed means means means dimension applications em em em em em filter filter filter filter filter filter obtain obtain obtain obtain obtain obtain obtain samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples true true true true true true compared compared application application series series series series series series series series series series compute compute perform experimental related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions approaches approaches approaches approaches approaches approaches approaches approaches mit steps steps update update update update modeling report words implementation version consists individual individual individual individual individual advances joint difficult difficult sequences considered considered considered considered considered framework cambridge computing equivalent experiment experiment experiment experiment experiment additional solutions solutions estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates determine efficient efficient significant approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate statistics estimated produce condition derived derived derived derived derived derived derived derived weighted weighted weighted weighted conditional backpropagation sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply simply achieved covariance covariance covariance covariance covariance covariance covariance covariance technical fast close inverse complete finding finding rbf amount implemented implemented implemented implemented assumed assumed generate generate generate generate generate generate generate adaptation future noisy kaufmann kaufmann kaufmann simulated typically typically dynamical unknown unknown unknown unknown coefficients technology block significantly significantly significantly significantly significantly significantly significantly significantly significantly significantly significantly significantly significantly significantly york special special mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode leads leads leads squared squared squared squared squared representing frame idea idea idea idea perceptron denotes denotes exact exact exact apply apply moving include sense inference inference inference inference inference inference inference inference inference inference inference inference inference inference sufficient sufficient highly highly observations calculated calculated tions smooth converge chain observation generalized generalized generalized generalized generalized improvement extended extended extended extended extended extended extended deviation alternative correctly deterministic pass starting starting assumptions assumptions conclusions conclusions performs exponential propose hard integration largest external assuming exist introduce monte monte monte monte monte monte monte monte derive derive carlo carlo carlo carlo carlo carlo carlo carlo solving ways generating dept missing missing explicitly easy easy gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians expectation family independently focus stationary correlated estimator estimator estimator estimator estimator viewed solved densities evaluated updated showed approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations approximations decomposition past smoothing smoothing smoothing dashed measurements measurements measurements measurements expansion iterative closed closed filtering filtering filtering filtering calculate transactions weighting weighting reason suitable computationally modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes successful score online soc repeated prob moore moore moore anderson anderson anderson dis superior lie lie gibbs gibbs write backward backward backward backward backward backward backward backward subsequent approximating approximating approximating approximating approximating approximating approximating load bars bars bars bars bars bars kalman kalman kalman kalman kalman kalman kalman kalman kalman integral accurately dotted dotted hall mse mappings authors maximizing proper proper hill gradients gradients adapt adapt algo taylor fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher multivariate multivariate finds finds cos analytical tractable lies worse worse nonlinearity turns sections ring division definite auto requiring amounts solla treated rep maxima passes ture hyperparameters gave gave germany chose multidimensional multidimensional multidimensional irrelevant initialization initialization ghahramani ghahramani tresp tresp tresp tresp tresp tresp tresp newton uncorrelated uncorrelated intractable rithm arguments conditioned extending communications communications ments ments significance significance significance significance significance difficulties difficulties tools siemens siemens scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring prentice appendix appendix appendix conjunction forecasting den thomas thomas nonlinearities dif iterated smoothed smoothed draw draw davis avoiding lag treat mind sig equivalently recursively recursively rejection rejection suboptimal convenience obtains covariances covariances covariances covariances ekf stands illustration adapting cohn translated approxi approxi gener mathematically paired proach integrals integrals sam sta holding hofmann hofmann gauss mix gorithm lems corporate crude crude jersey smoother smoother exper hid tors substitute discarded discarded multimodal multimodal multimodal multimodal multimodal sian mcgraw thing thing ance gaus nonstationary mul ized mle linearities stepsize stepsize applica unobserved heights heights inserting inserting ample pursued volker volker offline mate challenges fac munich sults bimodal dash notational ogp tributions otto validate badly pling und roweis roweis dropping subsection subsection hahn ain forget linearize mchp llt llt ttt mating trices recursions recursions timate exogenous keams ologp neurocontrol feldkamp feldkamp interrelated regressive ofw ofw 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output output number state state state state information information information information information problem models models models models models models models models hidden hidden hidden performance performance based space space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear layer layer case shown shown shown shown shown systems systems values values values probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise distribution distribution method approach approach approach approach point processing processing local local neuron neuron test test test matrix matrix matrix matrix inputs inputs form signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples size net task methods methods step step step process process process process process process process process level level trained trained trained structure problems high representation show equation equation equation equation fixed line parameter parameter approximation approximation approximation gradient university university university university university university university university threshold variables solution research research research dynamics initial initial initial estimate estimate estimate estimate estimate estimate prediction prediction prediction left presented phase phase phase phase low sets press learn nonlinear nonlinear nonlinear nonlinear outputs sample sample abstract applied computational computational density density density density density density density density density density density density density references component stochastic important important mixture introduction estimation estimation effect generated generated generated variance variance search tion tion tion assume assume measure measure signals chosen previous multiple conditions represent bayesian bayesian bayesian bayesian equations markov make techniques techniques proposed errors resulting simulation simulation respect multi multi multi multi performed mapping made global global global global global global applications applications applications filter filter filter obtain original original vol vol samples samples samples samples samples samples samples samples samples samples true compared perform posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions gain discrete mit steps update train report report report report report department department department department department department implementation consists code advances advances represents represents difficult addition addition sequences framework framework framework cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge computing equivalent directly view estimates design transition transition san stage stage stage efficient full requires choice approximate statistics statistics estimated pages increase derived levels levels levels sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling covariance covariance covariance technical technical technical increases describe describe complete complete complete predictions predictions predictions assumed assumed assumed assumed supported eds ability easily easily makes development including including typically unknown unknown jordan mlp mlp details filters filters choose predict denotes denotes denotes improved recent strategy strategy strategy strategy include engineering engineering engineering engineering interest interest varying works tuning storage scaling scaling extended extended extended hybrid touretzky setting trajectories trajectories trajectories trajectories conclusions depend accurate performs mateo propose external drawn assuming user start derivatives relation monte monte monte monte derive derive carlo carlo carlo carlo index index sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential sequential plot describes describes confidence multilayer linearly physical involves expectation stationary stationary transform densities densities evaluate operations evolution evolution evolution soft approximated approximated allowed past past measurements measurements measurements intervals tracking tracking filtering filtering filtering filtering filtering foundation figures formulation uncertainty discuss specifically efficiency importance importance importance importance importance importance importance importance importance suitable delta latent modes identity interpreted sin list involved vary leading approximating deal deal software modelling modelling employed employed powerful requirements updating kalman kalman kalman involving involving detail recursive history tech tech authors authors measurement generalisation logistic logistic perceptton improving site track track track nonlinearity london turns strictly author explained pseudo fed solla http http http http http http suited chose expectations expectations converged corrupted corrupted uncorrelated uncorrelated college college www www www www www oxford ratios ratios ratios ratios addresses eliminate arrival smith smith ments ments roles loo studying percepttons histograms uni eng eng eng eng eng eng eng ahead kearns draw draw subsequently papers cam cam cam cam cam cam cam adopted displacement displacement andrew speaking sequentially multiply session adopt adopt covariances ekf ekf ekf constitutes england england england england england england auxiliary assess assess param adapting evolve distribu distant represen particle particle particle modality mcmc induces gordon gordon normalised eters modal simplification tial tial optimisation optimisation optimisation optimisation optimisation optimisation optimisation drawing award resampling resampling resampling resampling inherently proposal proposal svr svr svr html html niranjan niranjan niranjan niranjan niranjan niranjan niranjan niranjan niranjan niranjan south carpenter carpenter merit stationarity ard marginals gross recursire parsimonious web versity regularisation regularisation cued cued cued freitas freitas freitas freitas freitas freitas freitas freitas freitas freitas freitas fil pitt pitt pitt economics estima nical nical avail iee loose gee gee gee gee gee gee gee gee gee gee gee singhal singhal ors neff jacobjan tering scholarship dirac stats stats infeng infeng infeng imm lent resample tative studentship avenues 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parameters parameters parameters parameters parameters parameters weight weight distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method method method method method method method method method method method approach approach approach approach approach single control large large large large large large large large large large large test test test optimal form form form form shows shows signal paper paper examples examples examples small small small small size size size size size size size net work work work work task methods features classification problems random random random high similar representation show show show equation section fixed rule rule parameter parameter parameter parameter parameter approximation approximation average average states states theory theory theory term term term term note note note experiments result university variables solution independent independent log defined defined sequence initial initial table table table estimate estimate estimate estimate standard standard terms terms prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left left presented present low frequency machine machine sets sets sets sets sets sets sets sets sets sets sets sets abstract back find find properties properties properties properties references references stochastic due due ieee ieee ieee positive procedure important adaptive adaptive context context context context context context context context introduction introduction introduction complex complex hand hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior behavior statistical statistical statistical statistical 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relative specific specific true compared compared compared application desired define define define define define compute compute compute perform perform perform perform related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions discrete discrete discrete discrete discrete discrete discrete approaches approaches approaches larger larger source modeling report words words words loss loss loss consists individual represents represents exp scheme addition sequences ai computing domain directly estimates estimates estimates estimates limit efficient efficient efficient efficient efficient choice choice choice significant statistics basic basic derived derived types actual finally depends depends depends sampling simply simply discussion discussion describe denote denote denote denote tested close close assumption assumption corresponds predictions predictions predictions predictions predictions predictions predictions proof proof common supported theoretical main main square hypothesis instance instance probabilistic probabilistic probabilistic smaller smaller combination dynamical unknown unknown testing significantly ratio character character character character character character character character special consistent consistent trials empirical empirical language language language language language leads details polynomial combined predict denotes population population exact exact advantage takes apply apply side side side hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees trees inference inference inference inference inference inference inference inference subset subset subset subset subset interest interest compare previously previously observations studies achieve trans trans sparse sparse sparse sparse sparse sparse sparse definition mixtures evaluation evaluation risk grant grant exists exists lead scaling suggests trial assumptions assumptions assumptions depend depend depend competitive differences accurate accurate bayes bayes bayes exponential exponential practice largest external drawn intelligence start manner characters characters characters characters characters explicit suppose appears construct construct optical estimating estimating estimating estimating describes confidence explicitly infinite involves easy easy text text text develop frequencies frequencies events events events events events events events events springer implies blocks family family expressed evaluate fraction fraction approximated approximated sizes sizes converges past key reduces closed sufficiently symbol symbol symbol symbol assigned assigned assigned expect building bell weighting uncertainty candidate priors priors priors priors priors priors priors priors priors priors priors priors priors priors domains domains domains domains domains discussions characterized simplicity planning gamma compression compression identified suitable symbols symbols symbols symbols included identify efficiently efficiently efficiently mackay mackay score tend tend online online reached receives capture notice verlag showing showing symmetry sin follow follow comp quantity quantity write hypotheses hypotheses reach consisted acknowledgments deal decreasing decreasing situations law law law simpler exponentially exponentially exponentially exponentially rapidly put estimators mass mass mass mass mass hall dataset examine examine examine examine successive history tech referred decisions structured comparable statistically induction hill naturally closest possibly analyze predicting predicting predicting extremely ensure subsets subsets queries friedman friedman friedman friedman friedman noted assumes art averages asymptotically great analytic correction perspective berkeley choices immediately involve english lowest conjugate conjugate summation summation summation summation substantially frequently price hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters singer singer singer singer singer conclude lim lim proposition proposition proposition proposition univ contribute indices feasible feasible feasible feasible cooper assign assign assign formally princeton flexibility grows outcome outcome generality simplify stated hyper occurring methodology corpus phrase alphabet alphabet alphabet alphabet alphabet alphabet alphabet contexts programs moved dependency intended laplace laplace laplace advance advance advance barron treatment eng omitted characterization ignore material insensitive counts onr divide verify multiplying suffix numerous logarithm entropic constitute constitute incorporates multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial classic examining illustration illustration unseen unseen 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#*model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number results results results information information problem problem problem problem problem problem problem problem problem performance based based based space space weights weights weights weights weights case case 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methods methods methods methods methods step step points points points points points points points points points points points classification process process level level level level level level level current structure problems random random random random high high memory similar similar similar similar similar representation representation representation representation representation representation representation representation representation show section section section section section section fixed fixed line rule rule generalization generalization generalization parameter parameter parameter real average average theory theory obtained obtained obtained obtained dimensional university university threshold threshold threshold threshold threshold threshold computation solution log defined found found found sequence constant constant estimate estimate estimate estimate estimate computer terms terms distance node science left present low low low low low low nodes nodes nodes nodes nodes nodes sets sets range components components components components components components components components components components components components components components continuous sample sample abstract find find density references component component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due positive procedure procedure procedure procedure introduction hand estimation estimation effect generated change complexity assume lower measure higher part center bound cases cases cases good good binary binary long long represent distributed expected expected make techniques proposed correlation scale minimum computed computed computed multi sum sum sum sum called called times times means means optimization made made applications represented represented true application cross provide compute proc related related connected connected connected connected connected connected distributions distributions discrete steps steps larger contrast connection selection selection selection selection report institute implementation version version technique represents difficult difficult exp exp scheme scheme graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph framework framework equivalent estimates stage capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity determine efficient estimated estimated condition weighted clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering levels selected selected iteration iteration nature nature sampling sampling sampling sampling simply achieved achieved measured technical describe denote transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation fast corresponds complete complete finding amount nearest nearest nearest common common implemented implemented assumed shape role require main journal ability ability cluster cluster cluster cluster cluster cluster cluster cluster cluster makes noisy including including probabilistic probabilistic probabilistic probabilistic typically typically pairs needed interesting york edge edge edge edge edge edge edge edge edge edge increasing increasing segmentation segmentation special representing numbers iterations direct direct direct normalized normalized normalized normalized decay decay decay polynomial polynomial choose correlations resolution exact exact advantage advantage property pair pair pair robust robust robust separate typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity apply strategy strategy strategy include identical identical identical side side side hierarchical hierarchical hierarchical sense recently interest sufficient sufficient compare works correspond rl sparse sparse address background chain separation generalized constructed constructed exists exists parts parts parts parts parts scaling suggests deterministic deterministic deterministic deterministic deterministic clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters demonstrate demonstrate half flow flow starting minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal neighbor neighbor neighbor depend measures measures performs performs constrained temperature temperature temperature strong hard hard hard presence largest largest proportional proportional start min min min plane iii scene annealing annealing annealing boltzmann explicit explicit pro edges edges edges edges edges edges edges edges edges edges index ways describes category averaging physical physical transformations transformations easy easy slightly text unique mutual mutual events formed formed select select decreases choosing family stages estimator viewed variation variation variation variation variation variation approximations soft understanding partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition reasonable reasonable reduces neighborhood neighborhood iterative remains remains valid intermediate distances distances distances distances distances distances assigned assigned construction construction euclidean euclidean existing existing figures figures figures includes assignment specifically specifically variations selecting closely importance differ maximal maximal maximal divided effectively driven wij wij wij wij wij wij wij wij wij wij successful identify composed capture refer notice graphs graphs graphs strongly induced induced prob prob showing categories categories michael relaxation absence eigenvalue highest subsequent subsequent subsequent subsequent subsequent subsequent subsequent satisfies satisfies satisfies satisfies satisfies employed remain remain remain parametric parametric parametric parametric wiley transformed essential exponentially relations relations relations replaced replaced replaced association association hall rest rest combine proper notion closest integer integer configurations greedy algo algo generates simplest motivated motivated defines defines isolated isolated spin spin spin great inequality pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise theoretic 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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural input input input input data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure time time time time time time time time time set set set set set set networks networks networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state results results units information information problem problem problem models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based space space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear case case case vector vector vector vector vector shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method approach approach approach approach approach approach approach approach point point point single single single processing control control control large local analysis analysis analysis matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form form shows shows shows algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper paper methods methods methods methods methods step step step step step step step step step step step step step step step step step step step points points current trained trained trained high response similar show show show show equation equation equation section section section section section section fixed line line line line line line line vectors vectors general general general general generalization parameter parameter real real states states states states states states states theory gradient obtained note experiments dimensional university variables variables variables variables computation solution log log dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant estimate estimate estimate estimate estimate estimate estimate prediction left left left left presented presented present present present low machine sets maximum maximum maximum range press press learn components basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs outputs sample sample abstract applied applied computational density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic due ieee procedure important important important propagation mixture mixture mixture mixture mixture mixture mixture mixture introduction complex complex estimation estimation estimation estimation statistical effect tion tion change variable variable variable assume prior learned learned learned part part part center center type required required required multiple equations equations equations equations markov markov markov fact fact observed observed forward forward ing regression computed computed computed computed respect mapping means factor factor optimization potential dimension applications knowledge knowledge em em em em em em em em em em em em em em em em em em em em em em em em em filter filter samples samples represented represented represented represented series series series series define define compute compute compute perform determined goal related related distributions distributions discrete discrete approaches mit mit steps steps steps contrast support support report words technique consists kernel kernel difficult exp exp exp bias framework framework cambridge computing computing directly curve solutions estimates estimates estimates estimates determine full full full requires requires requires approximate approximate approximate approximate statistics estimated estimated basic basic derived conditional conditional conditional conditional conditional conditional conditional conditional conditional lines actual finally evidence evidence evidence backpropagation sampling sampling sampling simply discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance technical describe describe arbitrary denote denote tested fast assumption stable rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf assumed assumed generate supported theoretical journal instance makes including fit fit fit fit fit fit fit fit fit fit fit fit fit fit objective probabilistic probabilistic pairs dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical coefficients fully jordan mlp mlp testing special special iterations iterations pre takes practical strategy side quadratic inference inference inference inference inference inference inference recently recently engineering engineering engineering engineering engineering dimensions volume volume tions solve address chain chain observation extended extended extended extended extended extended extended extended extended extended extended wide matrices matrices matrices locally width white occurs generally setting half starting valued valued valued depend sigmoid sigmoid clear moody practice learns taking solid solid solid radial radial radial radial radial radial radial turn turn minimizing exist min min derivatives derivatives characters characters identification identification identification acknowledgements relation pro monte monte derive carlo carlo written stability tuned missing missing multilayer multilayer linearly easy slightly belief belief belief consisting integrated gaussians gaussians gaussians gaussians expectation expectation expectation choosing focus stationary stationary solved solved solved densities densities densities evaluate approximations evolution forms understanding similarly partial partial smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing slow dashed dashed dashed additive classical classical classical spaces normalization fitting fitting fitting iterative filtering filtering advantages transactions kernels kernels kernels combinations perceptrons formulation batch illustrated automatic prove uncertainty discuss maximize domains regular straightforward middle middle extra capable uniformly society computationally driven modes literature situation plots essentially online kind kind neuroscience notation quantity usual backward maximization maximization maximization maximization maximization automatically attempt consisted illustrates employed exponentially kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman limitations recursive dotted graphical graphical examine examine history history rest variational variational variational analytically analytically analytically analytically analytically authors tanh func analogous examined gradients analyze der panel panel panel panel panel assumes fisher observe observe observe initialized initialized initialized initialized neal integrate trivial derivation defining analytic analytic tractable handle nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity starts london london sys sections easier arise incomplete nsf conjugate integrating integrating applies applies tional readily lack poorly dots variant variant http expectations expectations expectations expectations expectations expectations expectations jaakkola differentiable initialization initialization initialization representative ghahramani ghahramani ghahramani ghahramani ghahramani tresp tresp tresp indices college feasible www modify tation acts royal darken scoring observing generalizes heuristics lyapunov exploring saul appendix widths widths guarantees forecasting heart sim nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities approximators infer infer infer neuromorphic augmented ends canada draw observer captures discovered dempster vari acknowledge multiplying multiply multiply rubin inferred formulate exception generalizations ical spaced covariances classic classic pairing alter principled intuition gained tems dominated permits uncertain uncertain uncertain uncertain paired proach rbfs rbfs rbfs rbfs rbfs rbfs integrals cij laird sam tij fea rewrite const nested smoother attempting char award inherently ters ters inferring inefficient sij zoubin vanish linearized linearized linearized linearized evolves filling centres centres centres restrictive brackets brackets addressing nonstationary modern ini decades col crg ables approxima complications complications treats recursire acceptance parame parame ontario sible posteriors notably aware dynam gatsby gatsby panels noises devise nserc inferences brings nonlin bypass fund resort gat ucl complication complication fii ljung roweis roweis roweis lengthy 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#@Ghahramani_Z,Roweis_S,
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#*learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure time time time set set set set set set set set set set set set set set training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number error results results results results information information information information information information problem problem problem problem problem problem problem problem problem problem models performance based based based space space space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order systems values values values values values values values values weight weight weight functions functions recognition recognition recognition recognition recognition method approach approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern image image processing processing large large large test test test analysis analysis analysis analysis analysis class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal form form form form form form shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple gaussian visual examples examples examples small small size feature feature feature feature feature feature feature feature feature work task task task methods fig fig fig points points features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification structure structure problems problems problems problems representation representation representation show show equation section section section section line line vectors vectors vectors vectors vectors vectors vectors vectors vectors general general general general generalization generalization generalization real real real theory theory obtained obtained obtained note note note note experiments dimensional result result university university threshold threshold threshold threshold threshold computation computation solution solution research independent defined defined defined found found target target table table table estimate standard computer terms terms terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance connections science presented map present phase machine machine sets maximum press learn learn basis continuous sample abstract applied applied applied find find computational references stochastic due ieee positive positive positive positive positive positive positive procedure procedure procedure decision decision decision decision decision decision decision introduction behavior behavior behavior statistical tion tion tion tion energy difference assume lower measure measure measure measure prior prior prior representations chosen chosen part center previous previous cortex cortex cortex cortex cortex cortex cortex conditions represent make length observed scale resulting classes classes ing human regression sum called called called elements elements regions regions means means means natural applications knowledge knowledge obtain obtain negative negative negative negative negative negative negative negative negative vol represented represented represented true compared cross cross cross series provide objects objects objects objects perform perform active constraints constraints cortical approaches comparison larger contrast connection connection connection connection connection connection support support support selection proceedings implementation consists consists advances sequences framework domain equivalent equivalent equivalent equivalent directly directly determine classifiers full full choice choice choice statistics statistics world world world vision pages pages pages validation validation validation con con clustering clustering developed lines product product product product product product product finally finally finally processes nature nature nature nature simply achieved covariance normal technical technical group group corresponds corresponds nearest nearest nearest nearest common effective assumed journal square future auditory needed combination functional unknown unknown coefficients fully block block programming york increasing increasing empirical principle numbers max pre making magnitude idea combined choose light directions pair takes takes similarity similarity practical apply apply introduced introduced quadratic recently dimensions previously unsupervised calculated calculated volume volume volume axis axis axis axis axis axis axis tions diagonal diagonal definition symmetric symmetric risk risk lead concept scaling scaling scaling scaling scaling occur alternative deterministic deterministic setting demonstrate conclusion minimal assumptions neighbor neighbor neighbor neighbor editors differences differences measures measures measures measures modules bayes numerical clear performs practice weak suggest suggest strong physics largest intelligence turn assuming minimizing plane plane iii iii introduce connectivity areas areas areas explicit explicit perception ways plot plot metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric missing linearly dimensionality easy slightly text unique unique spectral scales consisting minimization minimization springer springer springer springer expressed solved evaluated labels organizing decomposition margin margin suggested suggested spectrum spectrum sign sign sign sign diagram dashed performing performing classical spaces spaces spaces intermediate distances distances calculate calculate assigned assigned assigned assigned assigned construction norm euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean classified transactions expect figures kernels dominance formulation eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues sciences vapnik vapnik illustrated absolute absolute absolute discussions characterized characterized structural structural structural structural successfully major reason columns columns columns determining importance suitable maximal encoded literature literature schemes comparing identity fine refer verlag verlag verlag graphs kind kind procedures procedures contained interpreted neuroscience symmetry contribution follow hold satisfy usual providing providing eigenvalue correspondence cat cat cat cat cat cat cat cat jacobs acknowledgments decreasing powerful wiley investigate strengths replaced replaced replaced replaced optimized optimized hessian hessian hessian dual dual dual mass dataset examine examine rest project investigated analytically referred referred maximizing eigenvectors workshop analogous necessarily necessarily psychology rank rank formal assumes rows pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise separable publishers analytical majority turns protein protein protein protein protein hyperplane hyperplane hyperplane products products cut cut cut inversion angles definite definite definite definite definite demonstrates annual explained considerably evaluating collected items items items items items items items items items pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo pseudo amounts axes axes axes embedded embedded embedded peter leave leave item item item item item item item item item item incorporated formulated frequently ity ity calculating operate berlin berlin berlin berlin berlin berlin ture fall incorporating serve serve germany germany semi semi semi kinds focused focused progress multidimensional multidimensional multidimensional multidimensional extreme lot consistently sv assign restriction signature signature signature signature proceed generality consideration anatomical convenient accepted tools proceeds city city serves serves imply optimally embedding embedding embedding embedding embedding embedding embedding embedding embedding ensures cone sion guarantees offers young cerebral cerebral refers refers proteins proteins proteins proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity proximity considerations subsequently characterization fold fold influences severe dense discriminate metrics metrics metrics metrics metrics metrics incorporates sig guyon preserving boser obtains additionally chapter reconstruct reconstruct representa visualization publication gained pij pij pij diag diag diag diag toy thick gener flip noting buhmann buhmann voting funded elsevier obermayer obermayer obermayer obermayer obermayer det hofmann hofmann psychophysics struc mini tension fiat bridge preserves characterizing prefer bold interpreting somatosensory mirror mirror hancock determinant cast calculates bilinear bilinear bilinear meth ods evolutionary absent faced tained vanishing indi generaliza generaliza cope sorted imum mization weinshall alization klaus ities heidelberg heidelberg solu wolfe wolfe wolfe participate fruitful vin aware neglecting flips visualize economics prof equipped cate indebted quadratically pii flipping minkowski minkowski minkowski minkowski minkowski minkowski minkowski ume embed embed sidered sional sect parison discus popularity apriori xtx xtx realm tured circled neuroanatomy projec biochemistry biochemistry multidimen 
#@Bollmann-Sdorra_P,Graepel_T,Herbrich_R,Obermayer_K,
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#*network learning learning learning learning learning learning model model model model model model model model model neural neural neural neural neural neural neural input input input input data data data data data function function figure figure figure time time time set set set set set set set networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number system problem problem models models models models models models models hidden based based based based weights weights weights weights weights weights weights linear linear linear linear linear linear linear layer layer case case vector vector vector shown shown shown shown shown shown shown values values values values probability parameters parameters parameters parameters parameters parameters parameters noise weight weight weight functions functions functions functions functions unit unit unit unit distribution distribution distribution distribution distribution distribution point point single control control control local test matrix matrix matrix matrix matrix optimal optimal inputs form form form algorithms simple gaussian gaussian examples examples small small size feature net net methods fig fig fig step step step step points features current problems random high response response response representation show section section section section section fixed fixed vectors general generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation average average average obtained obtained note result university variables variables variables variables variables computation computation solution solution solution solution solution log defined defined defined defined defined defined defined defined initial estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard node node prediction prediction prediction prediction prediction prediction prediction left presented present machine maximum maximum press basis basis sample sample sample sample sample abstract applied applied applied applied applied applied applied applied applied find find convergence convergence convergence likelihood likelihood likelihood references due positive positive procedure procedure procedure important adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive mixture introduction complex hand estimation estimation estimation statistical effect variance variance cost cost cost cost search tion difference complexity complexity complexity complexity complexity complexity variable variable variable variable variable variable variable lower prior prior prior prior prior prior higher higher part previous bound required conditions conditions conditions conditions bayesian bayesian expected equations techniques techniques proposed proposed proposed proposed scale minimum classes ing ing ing regression regression regression regression regression regression regression regression regression regression regression regression computed computed computed respect multi performed times times mapping mapping means optimization optimization optimization dimension natural natural global global applications negative negative negative samples samples represented represented true compared compared cross cross series series provide define compute compute compute goal goal posterior constraints constraints distributions equal approaches approaches accuracy accuracy accuracy accuracy connection support support support dependent modeling modeling modeling modeling modeling modeling selection selection selection selection selection selection report loss loss loss loss loss version individual individual kernel kernel kernel kernel kernel kernel kernel responses final final ai ai framework cambridge cambridge computing equivalent equivalent equivalent equivalent equivalent equivalent experiment experiment hinton solutions curves estimates estimates estimates design determine determine efficient choice choice choice choice choice significant statistics statistics statistics estimated estimated estimated pages validation validation give con con produce produce produce produce types finally finally depends constraint constraint constraint constraint constraint constraint constraint measured normal normal technical increases denote fast stable amount amount effective effective generate require main main square cluster future easily easily easily easily easily fit fit fit simulated simulated pairs smaller underlying reduced functional coefficients coefficients coefficients coefficients coefficients coefficients coefficients mlp mlp programming interesting york york york special uniform empirical pre supervised decay minimize minimize improve practical include subject subject machines quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic sense sense sense subset relevant relevant relevant highly observations volume volume volume tuning tuning tuning tuning tuning tuning tuning solve solve smooth converge achieve diagonal sparse sparse sparse definition mixtures evaluation modified observation generalized exists parts parts lead invariant suggests extended trial deviation wide derivative alternative clusters setting operator operator operator depend editors accurate bayes bayes numerical clear faster suggest propose drawn drawn solid proportional proportional proportional turn variety minimizing user exist groups groups configuration pro derive index laboratory ann pruning explicitly remaining easy gaussians applying minimization minimization springer springer select select decreases yield independently independently dependence squares squares viewed interpretation solved evaluated showed centered centered centered soft soft soft soft soft similarly updates partial smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing additive additive additive additive additive additive additive additive additive performing classical fitting fitting fitting fitting avoid kernels kernels priori coordinate perceptrons extension plotted illustrated automatic automatic candidate priors absolute absolute absolute absolute absolute absolute absolute absolute absolute absolute holds society society modification computationally effectively included svm svm svm computations mackay tend tend identity ten capture graphs procedures procedures induced link interpreted usual simplified wavelet wavelet predictor predictor predictor automatically automatically automatically operating presents minimized minimized parametric layered replaced optimized issues dotted hall dataset dependencies variability proved affect understand coefficient coefficient coefficient configurations spline spline spline spline spline spline equally obvious noted initialized detected motivated neal cos cos formula smoothness smoothness variances unstable nowlan expensive stress sections sections easier choices consequence opt ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge lowest lowest preceding explained explained relevance relevance relevance relevance bootstrap bootstrap fed leave backprop splines prototypes rely spread maximizes maximizes incoming extensions sums simultaneous multidimensional sharing phenomenon benefit notes optimality equivalence equivalence equivalence equivalence equivalence equivalence equivalence equivalence lagrange conditioned girosi girosi jth royal eliminated multiplier breiman breiman analogy analogy determination hyper hyper hyper hyper hyper hyper hyper hyper balance balance balance imply modifications nonparametric heuristics predictors corre encountered dependency dependency infinity exposure advance refers extensively statement statement alternatively summarize balancing fold avoiding thresholding thresholding thresholding thresholding posteriori fitted rigorous annals achieving achieving tibshirani tibshirani tibshirani tibshirani par residuals corrected generalizations penalized penalized penalized penalized trends modifying distri hastie diag diag diag chapman distribu simplifying unconstrained unconstrained harder france outcomes universit cubic cubic cubic eters signs lecture lagrangian lagrangian differently sponding parameterization ble algorithmic instability quantify heavily heavily smoother clarity concern identically shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage formulae practically ooo interpolating economic proves statist minimax pooling comer cess trend mul ensuring penalizes putation stabilization replicates predefined vergence argmin argmin icann pooled pooled pooled pooled treats ess encourage adap shrink asso univariate univariate univariate univariate accord hyperparameter donoho gression xij possi ror interpretable cedex penalization penalization penalization penalization penalization penalization penalization penalization penalization penalization penalization penalization penalization penalization penalization plied badly unspecified cients mono planned tives nodal fid regressions butions divergent tiple johnstone incom gather monographs cially coe perspec regressor ols ols ols ols ols ols ols individ malized yves yves algorit algorit mer ates cnrs tun irdle regressors 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#@Canu_S,Grandvalet_Y,
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#*learning learning model model model model model model model model model model model model model model model model model neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure set set set set algorithm algorithm algorithm algorithm algorithm number number results results results information information information information information problem models models based based based based space space space space space case case vector vector order systems probability probability probability probability parameters parameters parameters parameters distribution distribution distribution distribution distribution recognition method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern point image image image image image image image image image image processing large large large large large large analysis analysis analysis analysis analysis optimal algorithms simple simple gaussian gaussian gaussian gaussian visual visual small feature feature feature work methods methods methods fig fig fig fig step points points points points points points points features features features features features process process process structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure random high high high high similar similar similar equation fixed rule images images images images images images images parameter parameter gradient gradient obtained obtained obtained note note note note experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result university variables variables variables computation solution solution solution solution solution solution solution research research research log log defined estimate estimate computer science science science left presented present present low low low low low low low low low low frequency machine object object object object object object object object object object object sets maximum maximum maximum maximum range range range press position position components sample sample abstract abstract abstract abstract applied applied applied computational density density likelihood likelihood likelihood likelihood likelihood likelihood references stochastic due ieee procedure procedure mixture mixture mixture mixture mixture mixture mixture mixture context introduction complex hand statistical statistical statistical generated generated cost tion tion change variable assume assume measure chosen chosen higher type distributed make fact region proposed proposed proposed proposed proposed proposed correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed observed scale scale resulting resulting resulting classes tasks computed mapping mapping mapping natural natural global applications applications knowledge em em original original artificial artificial artificial artificial relative true true true compared application provide define objects objects objects objects objects objects objects objects objects perform distributions distributions power approaches approaches mit mit comparison contrast descent descent report words technique technique consists consists advances difficult exp exp exp exp scheme scheme addition framework framework framework computing experiment additional view solutions solutions solutions estimates estimates efficient upper choice choice statistics statistics estimated estimated estimated estimated estimated pages channel channel coding derived conditional conditional clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed area area types types types lines evidence measured measured measured technical group group group group group group group group group group group group group group group group group group group group group group denote close complete complete amount common common common assumed assumed generate supported supported role theoretical journal cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster easily makes development probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically underlying underlying coefficients jordan technology projection york structures database database database database database database database empirical empirical principle principle leads representing representing details filters making idea idea choose choose description description description description description description description recent exact similarity similarity similarity similarity identical hierarchical hierarchical hierarchical sense inference inference inference interest dimensions dimensions unsupervised unsupervised observations approximately volume yields yields positions positions observation channels williams grant grant exists exists invariant scaling scaling scaling extended deviation matrices rotation alternative locally deterministic deterministic deterministic clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters demonstrate conclusion valued valued hard demonstrated intelligence assuming variety variety minimizing user user user user iii iii iii introduce groups groups groups annealing annealing annealing areas explicit relation pro produces plot plot dept modeled missing scales develop frequencies minimization boolean select letters yield extracted focus squares overlap interpretation interpretation interpretation interpretation detailed lee completely completely suggested translation partition key key key key key spaces spaces spaces fitting iterative generation distances distances distances distances visible foundation foundation foundation euclidean euclidean euclidean euclidean transactions avoid color retrieval retrieval retrieval contour inter inter inter inter assignment assignment assignment assignment assignment assignment assignment assignment extension plotted discuss texture texture texture simplicity identified efficiency uniformly uniformly uniformly latent latent schemes schemes plots capture refer heuristic interpreted interpreted issue contribution contribution generative generative providing ill principles extract extract approximating deal essential exhibit relations humans association issues divergence divergence divergence divergence divergence hall pursuit applicable applicable reliable structured maximizing encode hierarchy topographic fundamental fundamental contours circles gradients naturally plausible rank separated separated grouping grouping grouping grouping grouping histogram histogram histogram histogram histogram histogram histogram pairwise formula theoretic orientations phenomena london reasons purposes protein broad broad broad bishop bishop mathematics consequence english depicted annual cybernetics explained apparent fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy empirically understood generic generic generic embedded embedded detecting treated http prototypes prototypes prototypes prototypes prototypes prototypes prototypes prototypes partitioning mod ture aim aim occurrence occurrence occurrence substantial substantial germany inherent expectations simultaneous multidimensional multidimensional multidimensional distortion feasible www www generator generator assign gabor gabor acm acm databases databases databases databases databases rotated homogeneous partitions partitions generality kullback fits ments held held held held held interpret interpret viewpoint occurring tishby exploit effectiveness adequate embedding embedding embedding embedding embedding embedding document recovered recovered ranging decide conjunction histograms histograms histograms belongs uni uni centroid enable israel membership infer insight insight bins proximity proximity proximity proximity partitioned implicitly explains explains summarize vari assigning ple gtm gtm rigorous ent ent aston email leibler inferred inferred inferred validity creates bank preserving par seek assignments assignments assignments assignments assignments assignments hundred german german descriptions forcing scenario principled visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization preserved preserved preserved translated care pami chapman dominated annealed ization ization denoting crosses iso emphasize maximally maximally maximally differentiation interactive buhmann buhmann buhmann buhmann buhmann worth worth sam preserve fea els hofmann hofmann exploratory exploratory struc september examination rose mix mann mds mds mds generarive discretized institut satisfactory textures textures textures interpreting dropped mining mining meeting marcus extracts fox heterogeneous inspection inspection inspection inspection inspection informatik inde spirit colors fol concatenated bonn bonn bonn tical tical jan ira enabling mid cox cox unobserved 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#@Buhmann_J,Held_M,Puzicha_J,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data data data data data data data data data function function function figure time set set set set set set set set networks networks networks networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output number number number number number number number number error error error error error error error error results results results results units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information problem models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based space space space weights weights weights weights weights weights weights linear layer layer layer layer case vector vector vector order order shown shown systems systems systems systems systems systems probability probability parameters noise noise weight weight weight weight weight weight weight weight weight functions functions functions functions unit unit unit unit unit unit unit recognition method method method method approach approach pattern pattern point image image image image image image single single processing processing processing processing processing processing processing large large large local test test test test test test patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis class class optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs signal algorithms algorithms simple simple simple simple simple simple gaussian gaussian visual visual paper small size size feature feature feature net net net work work task task task methods methods cells step field field field field field field features features features features features features features features classification process process level trained cell cell cell cell cell cell random high high high memory response similar similar similar similar show show images images images images images images general general general generalization generalization real real real real average average theory gradient gradient term term term term term term experiments experiments computation computation computation computation computation computation research independent independent independent independent independent independent independent log found constant constant table table estimate standard standard computer terms science left left activation activation activation activation activation activation low low low low low low low low low sets sets press press press press components components components components components components components basis basis basis nonlinear outputs outputs abstract computational properties properties properties properties references component component component component component component component stochastic due due ieee ieee ieee positive important important introduction statistical variance parallel cost cost search search search tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity measure signals signals representations representations chosen center previous previous previous type type required required required required multiple cortex good represent represent distributed distributed distributed distributed make make region region proposed length length probabilities observed errors minimum minimum minimum minimum minimum minimum resulting resulting tasks human computed respect respect respect sum eq eq called called called regions mapping natural applications obtain negative original receptive receptive provide determined experimental goal discrete discrete discrete discrete brain mit mit mit mit steps contrast connection connection connection fields fields train descent source source source source source nets morgan morgan proceedings proceedings report report report version consists code code code code code code code code code code code code code code code code code code code code code code code code code code advances advances advances advances advances joint difficult final exp framework cambridge cambridge cambridge experiment hinton hinton hinton additional view san san conference determine efficient efficient choice free world world world pages pages pages pages pages pages pages pages coding coding coding coding coding coding coding coding coding coding coding coding coding coding randomly levels entropy product product product product product product nature sampling associative measured technical technical describe describe describe describe denote corresponds finding finding finding common implemented assumed generate supported theoretical theoretical require journal pixel pixel pixel pixel pixel pixel pixel pixel makes makes rumelhart noisy noisy sensory sensory sensory kaufmann kaufmann objective objective objective objective typically typically underlying needed needed reduced jordan interesting york principle principal principal squared details pre making bits bits bits bits bits bits bits bits international supervised sources sources sources sources sources sources description description denotes denotes denotes population recent correlations robust separate separate apply pixels pixels sense sejnowski recently relevant compare compare compare previously previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised volume works tions pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse positions separation separation separation separation separation separation separation separation grid interval organization organization sensitive grant grant horizontal scaling matrices touretzky touretzky touretzky conclusion minimal minimal reduce reduce reduce valued competitive competitive editors editors editors editors editors measures moody mateo mateo suggest taking reduction regularization regularization regularization regularization regularization regularization regularization regularization assuming assuming assuming minimizing minimizing minimizing minimizing minimizing start ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica decrease minima minima minima force force denoted explicit appears monte carlo index generating tuned vertical pruning implement sensitivity sensitivity explicitly simultaneously transformations remaining minimization springer shift quality extraction extraction competition letters yield choosing choosing focus focus focus review reconstruction reconstruction viewed influence codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes detailed evaluate sizes reduces reduces reduces intervals intervals add iterative generation generation generation intermediate kohonen transactions david precision precision precision expect figures perceptual activations activations activations activations priori priori bell inter blind blind blind blind recognize activated mozer mozer phys tests simplicity reason columns regular determining determining determining compression efficiency efficiency efficiency society divided efficiently efficiently efficiently tend ten summary traditional refer compact decoding decoding decoding decoding contribution generative gray comp notation bar bar bar vary michael michael dayan dayan realistic surround delayed maximization automatically automatically subsequent subsequent mixing preferred extract acknowledgments tesauro tesauro oriented cowan minimized bars bars bars bars bars bars bars bars bars bars unlike unlike exhibit limitations limitations lippmann fewer tech mse detectors mappings mappings mappings scaled func neu plausible editor versions observe separated separated separated generates amari finds finds finds attempts attempts neal massachusetts developing theoretic theoretic theoretic costs costs costs costs defining coded adapted expensive independence benchmark producing producing constructing broad broad desirable linsker annual exemplars capability capability backprop backprop solla biologically ture resource germany redundancy redundancy focused realized contribute contribute representative representative ghahramani redundant redundant leen www www sleep forming pick zemel zemel discovery royal oja ments primate siemens fail ral responsible alspector separating pruned overview hasselmo yang advance emergence specialized young express reveals reveals kearns impact partitioned partitioned inf mechanical dense dense dense dense dense dense dense dense dense dense dense zipser outperforms piece piece piece piece piece piece forced encouraging tween adopt mdl mdl stem flat flat flat flat flat flat discovering discovering discovering wake reconstruct factorial factorial factorial favor favor schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber schmidhuber diag goals goals num shannon ization regularizer regularizer deconvolution simplifying intensities harder anal barlow frey things prevents subspaces mini experi overcomplete fiat heavily shot olshausen olshausen cally neglect conflicting extracts extracts inferring meth informatik informatik inde spirit lewicki handbook compromise appro sparseness sparseness watanabe decoded cichocki prune convey denominator discovers rec regularizers regularizers regularizers terminology objectives favors favors ysis enforcing technische technische schuster cardoso cardoso tolerant conveyed reviews parra encourage switzerland deco mitchison correspondingly owij owij cumulant superfluous numerator arbib revised embody wood wood hochreiter hochreiter hochreiter hochreiter hochreiter hochreiter hochreiter postulate iee collectively genera predictability aerial whitening logarithms dfg dfg mirrors mfinchen mfinchen mfinchen finely deutsche unification loc loc loc loc loc barrow zfe scarce subsections subsections fki muenchen striped priate ffir ffir philosophical jiirgen cision tured pendence mally wards redun redun forschungsgemeinschaft prunes fluence corso automati nore 
#@Hochreiter_S,Schmidhuber_J,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure time set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number error state results results results results results results results information information information information information problem problem problem models models models models models models models models models models models models models models models hidden performance performance performance performance based based based based based based based space space space space space weights case case case case order order order shown shown shown systems values values probability probability parameters parameters parameters parameters weight distribution recognition method method approach approach pattern pattern pattern pattern image image image image processing processing processing control control local neuron rate test test analysis analysis analysis class class class class class class class class class class class class class matrix optimal shows shows simple simple visual paper paper feature feature feature net methods fig fig fig fig fig step step step step step step step field field field process process cell structure structure structure structure structure structure problems problems similar similar representation representation representation equation equation section line rule rule rule vectors images general generalization generalization generalization parameter real approximation approximation approximation obtained obtained term experiments result variables variables variables computation solution solution independent independent independent independent independent log log defined defined defined found sequence target table table standard standard standard standard standard standard computer computer terms node node node node presented map present present phase phase nodes nodes nodes machine machine object sets sets sets sets sets sets motion maximum maximum maximum learn learn learn learn learn learn learn sample abstract abstract applied find computational computational computational likelihood likelihood likelihood likelihood likelihood likelihood references ieee procedure important important important mixture mixture mixture mixture mixture mixture mixture mixture mixture context context introduction circuit estimation estimation behavior statistical statistical statistical statistical statistical effect generated search energy difference complexity variable variable variable variable classifier prior representations word word word word word center cases type type multiple binary spike spike represent represent represent tree tree tree distributed equations equations equations equations equations markov markov make fact fact techniques region proposed proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed scale finite resulting classes classes ing ing ing ing tasks computed multi sum called called called mapping mapping mapping optimization made made made made natural applications em em em em em em em em em em em em em filter obtain obtain negative original specific specific represented compared compared application application cross cross provide provide define define objects objects objects location perform perform active posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions power mit update update train train modeling modeling modeling modeling modeling proceedings proceedings words words words words version version technique consists advances advances joint represents exp ai framework framework framework cambridge computing domain domain domain domain equivalent additional curves curves design limit top top stimuli determine approximate statistics free world vision estimated pages validation validation con weighted conditional conditional conditional conditional conditional conditional conditional clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering levels levels levels criterion criterion types entropy path path constraint simply biological achieved discussion technical technical inverse assumption assumption assumption corresponds corresponds complete complete complete complete complete common assumed shape role role journal cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster fit fit probabilistic probabilistic probabilistic probabilistic typically pairs underlying jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan significantly increasing segmentation segmentation segmentation segmentation segmentation empirical empirical language language language language details details details pre direct international experts experts early idea idea architectures architectures discussed improve resolution advantage element typical apply introduced hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical sense subset highly compare unsupervised unsupervised unsupervised unsupervised observations observations observations observations observations observations observations observations yields correspond correspond studies mixtures mixtures mixtures locations observation observation observation organization organization improvement exists horizontal parts alternative deterministic deterministic clusters clusters clusters clusters clusters clusters clusters clusters setting strength conclusion conclusions differences differences bayes bayes bayes performs performs temperature propose propose propose taking intelligence intelligence turn variety variety iii iii iii iii averaged introduce introduce annealing annealing annealing areas relation derive derive written ways ways estimating laboratory transitions transitions vertical missing explicitly infinite physical remaining slightly text unique scales mutual applying expectation expectation boolean letters independently focus review detailed transform evaluated restricted lee forms updates past key key spaces reduces reduces fitting filtering visible construction euclidean topology transactions degrees formulation retrieval retrieval retrieval retrieval uncertainty maximize coupled coupled coupled domains domains characterized successfully texture straightforward straightforward aspects aspects aspects aspects aspects aspects identified modification effectively effectively latent latent latent latent latent latent latent latent latent latent latent latent latent post post post soc notice notice induced prob heuristic stopping dis symmetry contribution usual michael play maximization maximization subsequent subsequent mixing jacobs jacobs jacobs decreasing overfitting collection collection collection collection involving association association optimized scalar tech project terminal terminal terminal possibility referred referred hierarchy hierarchy understand fundamental notion analogous naturally predicting predicting aspect aspect aspect aspect aspect aspect aspect aspect aspect aspect aspect aspect aspect aspect aspect aspect aspect formal algo freedom art art mixed simplest contributions defines averages established years burst preference preference preference crucial orientations defining answer independence comparisons shared broad probable probable english arises depicted author incomplete preceding mechanics empirically red documents documents share maxima ity partitioning partitioning mod cal occurrence occurrence occurrence marginal substantial substantial replace germany progress yielding naive identifying identifying tation gabor summing rithm conditioned partitions discovery discovery theories royal systematic imposed abilities interpret tishby intuitively intuitively corpus corpus corpus days reliably meaningful utilized utilized utilized document document document document ranging saul saul saul dependency dependency topological uni thomas offer refers refers 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counted jan jan inform inform occurrences occurrences occurrences occurrences occurrences brought col aggregate aggregate favors stems unobserved unobserved subtree subtree unifying forthcoming distributional distributional distributional grown anneal clus linguistics linguistics dynam perplexity perplexity perplexity perplexity perplexity textured prototypical continu visualized abstracts tab disambiguation confer heuristically compatibility jects nouns octaves associ decade lihood dyadic dyadic dyadic dyadic dyadic dyadic dyadic dyadic dyadic dyadic dyadic ade alternation aerial aerial aerial aerial tractability puzicha puzicha puzicha puzicha puzicha puzicha puzicha puzicha puzicha puzicha pereira pereira pereira orient tering weaken ima gurewitz ifi activ meila meila meila bigram equiva oscil keywords plication disciplines ffir tioned lob lob lob conditionals conditionals alc rept tential descriptors organizations browsing skipping skipping dyn hierarchi imag sensitiv cry adjective 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#@Hofmann_T,Jordan_M,Puzicha_J,
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#*network learning model model model model model model model model model model model neural neural neural input data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure time set set set set set set set set set set training training algorithm algorithm number number number error results results results information information information information information information information information information problem problem problem models models models performance based based based based based based space linear linear linear linear linear linear linear case case case case vector vector vector vector vector shown shown values values values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions unit unit unit distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method method method method method method method method method approach point point point point image image image image image image image image image image image image image image image image image image processing processing processing processing large large local local test test analysis analysis analysis analysis analysis analysis analysis class class matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal form form form shows shows shows shows shows signal signal signal signal algorithms algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper examples examples small small small feature methods methods methods methods methods methods methods methods fig fig fig fig fig step step field field features features cell structure structure random random random random random high similar similar representation representation representation representation representation representation representation show show show show section section section fixed fixed fixed fixed line line line line line line line line line line images images images images images images images images images general general speech real theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained note experiments experiments experiments experiments experiments dimensional result result university university university variables variables variables variables variables computation research independent independent independent independent independent independent independent independent log defined constant estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard computer computer computer science science science left left left low low sets maximum maximum maximum maximum maximum maximum maximum maximum maximum press press components components components components components components components components components components components components components components components components components components components components components components components basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear abstract applied back find find find computational density density density density density density density density density density density density density density density density density density density density properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component component component component component component ieee procedure procedure important important important adaptive context introduction hand hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical statistical effect generated variance variance variance variance variance variance variance variance variance tion energy difference variable variable variable assume assume assume assume assume measure representations theorem theorem cases fact fact fact fact fact proposed observed observed observed observed scale scale minimum minimum resulting resulting performed performed called means means means made made natural natural natural applications applications obtain obtain negative original original original original application series series receptive compute proc proc active active determined experimental goal related related related connected connected distributions distributions distributions distributions brain mit mit comparison comparison comparison contrast modeling report report version version code code code code code code code code code code code code code code code code code code code advances exp scheme addition considered framework cambridge equivalent equivalent experiment environment directly estimates limit efficient efficient choice statistics free free free free free free estimated estimated estimated pages pages give coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding coding derived derived weighted randomly developed nature nature depends simply simply technical technical describe denote denote denote transformation transformation transformation transformation transformation transformation transformation fast assumption assumption finding finding amount assumed main journal square square makes noisy noisy noisy noisy noisy noisy noisy sensory underlying reduced coefficients technology technology technology significantly significantly significantly projection consistent principle principle principle principle principle operation details max max filters making window normalized normalized normalized minimize choose choose neuronal advantage property takes takes typical typical typical typical reported practical practical apply apply apply introduced pixels sense sense dimensions correspond sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse symmetric observation observation concept invariant scaling deviation matrices alternative white pass pass conclusion starting minimal assumptions assumptions reduce reduce reduce reduce reduce operator operator editors differences measures measures peak exponential practice constrained strong hard reduction reduction solid solid assuming minimizing ica ica ica ica ica ica ica introduce relation relation edges index estimating estimating estimating estimating estimating estimating plot describes laboratory laboratory linearly transformations transformations easy scales applying applying extraction yield choosing choosing choosing choosing family family estimator estimator estimator estimator viewed codes solved transform transform transform transform transform densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities showed showed forms soft activities activities sign sign earlier dashed dashed additive classical classical spaces convex reduces filtering filtering advantages koch degrees avoid box absolute absolute absolute phys determining determining determining determining closely closely closely closely closely suitable suitable suitable society computationally divided effectively plots plots essentially orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal conf strongly strongly criteria wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet nips ill attempt consisted consisted minimized explore parametric transformed transformed access relations detail accurately dotted dotted dotted dotted ml ml ml ml ml pursuit mse mse mse mse int analytically root maximizing fundamental contours removed adapt analyze fisher fisher fisher fisher observe observe observe shapes multivariate simplest utility utility motivated rows scenes developing derivation variances tractable nonlinearity nonlinearity turns purposes purposes preprocessing strictly operators inversion begin depicted depicted meaning argument double amounts leave remove treated treated sharp sharp http acoustics logp germany inherent inherent age age windows windows deviations median differentiable irrelevant lab ordinary ordinary corrupted corrupted corrupted corrupted benefit www optimality restriction restriction restriction restrict arguments linearity purely theories royal oja oja oja oja oja oja attractive belong imply intuitively moments analyses heavy encountered equals equals realization nonlinearities nonlinearities nonlinearities nonlinearities nonlinearities bases laplace laplace laplace laplace laplace laplace laplace laplace enable emergence modelled rich davis summarize vari thresholding thresholding thresholding rigorous annals equivalently super icassp lit illustration adapting representa constrain principled concentrated life neurophysiological denoting denoting wise projecting barlow overcomplete rarely parameterization sees justified families olshausen olshausen appealing shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage shrinkage inferring neocortex intact implied minimax fin lewicki relaxed relaxed ance sparseness artificially artificially tails freely predetermined percep moderately retaining argmin dilemma plausibility invert huber comon imaginary equalization equalization sparsity shrink munich dash dash blurring ponents donoho donoho donoho donoho helsinki helsinki helsinki fulfill viewpoints transfor conserved unrealistic cis hyv hyv hyv hyv hyv hyv proj hut hut hut hut hut shrinking shrinking finland mations fined denoising denoising denoising denoising denoising denoising denoising denoising denoising denoising denoising denoising denoising denoising denoising denoising nen cancels sparser sparser sparser johnstone parameterizations parameterizations parameterizations veloped erkki erkki flavor inen rescale lul lul ects tually oratory 
#@Hoyer_P,Hyvarinen_A,Oja_E,
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#*learning learning learning model model model model model model neural neural data data data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number system system system system error results results results results results results results results information information information information information information information information information problem problem problem problem hidden performance performance performance performance performance performance performance based space space space space space space space space space space space linear linear linear linear linear linear case vector vector vector vector vector order shown systems values values values values values values probability noise weight distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method method method approach approach approach approach approach approach approach approach approach approach approach pattern single single processing processing large large large large large large local test analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple visual small small small size size work task task task methods features features process structure structure structure structure structure problems problems random high high high high high similar similar similar similar similar similar show show section section section section line vectors vectors general general general general general generalization average average note experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional result result result university university variables computation computation solution research independent independent independent independent independent independent independent independent independent defined found found found found standard standard computer computer terms terms distance science presented present present low frequency machine object sets sets sets press press press components components components components abstract find find find find find find find computational computational computational properties properties properties properties properties likelihood references component component due ieee positive important important mixture context context introduction hand generated generated search tion lower lower measure measure measure measure measure measure measure representations representations word word word word word word word word word word word word higher previous type multiple spike spike represent represent represent represent make fact fact fact techniques techniques techniques techniques techniques techniques proposed observed resulting total total computed called times elements elements elements elements elements means means potential dimension dimension made made made natural natural natural feedback global policy knowledge negative negative original original artificial specific specific specific represented represented represented represented represented compared define compute compute objects perform perform perform active goal goal related related related related related related related related related distributions distributions approaches approaches steps comparison comparison comparison larger larger contrast source source source proceedings proceedings proceedings report institute words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words words version technique technique technique technique technique individual individual individual advances represents represents difficult final scheme scheme graph cambridge computing equivalent directly directly additional view curves transition top conference conference conference conference determine determine efficient efficient efficient efficient full full choice significant vision vision pages pages pages give give con derived weighted clustering clustering clustering clustering clustering clustering clustering area area product product product product product finally finally finally evidence nature measured discussion discussion discussion normal describe describe describe group group group group transformation transformation close assumption finding finding amount short common common effective effective effective effective assumed assumed assumed require face journal journal journal journal square cluster cluster makes makes development including including smaller smaller smaller smaller underlying underlying underlying underlying underlying combination unknown unknown technology interesting significantly character projection projection projection projection structures language language principal squared details max international international supervised supervised magnitude choose predict denotes improve improve advantage robust robust typical typical similarity similarity similarity apply apply include subject subset subset subset sejnowski sejnowski sejnowski recently relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant sufficient highly highly highly highly compare compare unsupervised unsupervised unsupervised axis axis axis axis axis axis smooth yields pca achieve diagonal diagonal sparse sparse sparse sparse sparse sparse sparse separation separation symmetric symmetric modified modified constructed concept concept occur occur suggests alternative move clusters clusters clusters clusters white white white occurs column minimal assumptions assumptions assumptions operator editors central designed clear clear performs performs practice practice practice weak suggest suggest suggest propose propose strong presence presence largest largest largest reduction reduction reduction reduction proportional intelligence minimizing user user ica ica ica ica ica ica ica ica ica ica exist relationship iii groups groups groups question appears pro derive construct construct produces written generating laboratory mathematical distinct distinct recall recall recall recall recall linearly dimensionality dimensionality dimensionality dimensionality text text text text text text text text text text text belief consisting interaction applying select national expressed expressed variation variation transform lee centered centered decomposition understanding completely completely similarly earlier reasonable reduces fitting false false generation generation generation norm query query query query query query query query query query query advantages advantages advantages precision precision precision combinations retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval bell bell bell eigenvalues eigenvalues weighting blind blind blind automatic domains domains domains simplicity straightforward closely society encoded latent latent latent latent latent latent computations projections projections projections projections tend tend identity orthogonal orthogonal capture refer refer notice success success return dot absence absence minimizes minimizes hypotheses attempt illustrates illustrates subsequent extract deal routing routing intrinsic unlike collection collection collection collection collection collection collection collection collection collection collection collection collection difficulty difficulty updating involving hall hall rise rise tech project project project project referred eigenvectors eigenvectors eigenvectors fundamental removed naturally naturally editor necessarily subsets queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries queries rank singular singular singular singular obvious algo observe explored separated store baseline baseline baseline amari amari improving simplest finds finds attempts massachusetts percentage percentage histogram great distinguish distinguish improves improves improves improves expensive briefly worse drive shared shared operators operators incorporate leaves desirable mation projected projected projected projected projected projected projected begin meaning robustness relevance relevance relevance relevance relevance relevance relevance amounts axes axes axes axes axes axes axes axes axes axes axes axes axes axes axes simulate documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents car poorly characterize extracting cal occurrence occurrence extensions semantic semantic semantic semantic semantic semantic irrelevant representative room college guarantee tation restrict acm acm acts count discovery discover proceed ranges tools overcome hope operates intuitively selects selects selects infor meaningful prentice prentice weakly weakly document document document document document document document document document document document document document document document document document document respective equals paul searching searching yang yang centroid centroid entries refers refers park park assigning counts counts counts divide maintaining street street street ence leaving inferred asked removal pentland pentland kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis adopt tradeoff discovering imagine demon param formance gained rithms wall wall wall management labs searches deconvolution projecting topic topic topic topic topic topic topic topic topic topic topic topic constructs represen represen nonetheless induces induces thousands thousands eters removes removes insufficient losing hundreds hundreds viola house house house hoc hopkins hull hull hull returned returned svd svd svd svd distinguishing proposal continuum thickness sparsely separates lying conditionally positives ultimate johns convention company south south tations addressing ings charles dent request request indepen indicators outlier cichocki cichocki ized occurrences tens lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi lsi shares indexing indexing indexing indexing indexing indexing indexing discriminating eigenfaces sorted zone rij collections collections collections collections collections plexity decompositions topics topics topics topics topics topics topics topics topics avenue manipulating supervision motivates retains roots provably unimportant fifty hoped nique decomposing turk turk confer saund landauer told embodies apple singhal singhal smart negatives fruit sacrificing popularity tains ola ola ola abound florham releases disambiguate sigir sigir deerwester deerwester deerwester restructuring restructuring restructuring restructuring loan loan classically kwok suffixes jected kurtotic doc enjoys sheer frobenius anc characterizations 
#@Isbell_C,Viola_P,
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#*learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure set set set set set set training training training training training training training training training number number number state state results results information information information information problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance based based space space space space space space space space space space weights linear linear linear linear linear case case vector vector vector vector vector vector vector vector order order values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions distribution recognition recognition recognition recognition recognition method method method method method point control large local local local rate rate test test analysis analysis analysis class class class class class class class matrix matrix matrix matrix matrix matrix form form form form form form shows shows simple simple simple simple simple gaussian gaussian gaussian gaussian paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature net work methods methods methods methods methods methods methods methods methods methods methods methods methods features features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process current current structure structure structure problems problems problems problems similar representation show show section section section section fixed line line line line rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors general general general speech parameter parameter parameter parameter parameter theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained term note note note note experiments result university university computation solution solution solution log log log log log log log log log log log log defined defined defined defined defined defined found sequence sequence sequence constant constant constant estimate estimate estimate computer terms terms distance distance distance science left left left direction direction presented map map low maximum maximum maximum press position position components abstract applied back find find computational properties likelihood likelihood likelihood likelihood likelihood likelihood references positive procedure procedure important decision decision decision mixture mixture mixture context context context context introduction introduction introduction hand statistical statistical cost search tion tion complexity variable variable variable variable variable variable assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier measure prior prior prior prior chosen higher previous previous theorem theorem theorem cases binary long long markov markov markov proposed length length length length length errors errors errors errors forward minimum resulting resulting resulting ing regression regression regression regression regression regression respect respect sum sum called regions regions mapping mapping mapping mapping mapping optimization optimization optimization natural natural natural natural natural natural natural natural natural obtain negative original original artificial relative specific true true true true application cross cross series provide provide define define define objects rates experimental experimental related posterior distributions power approaches approaches mit mit comparison comparison comparison comparison comparison comparison larger connection support support support support report words department loss loss version version version consists kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel difficult difficult bias bias addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences ai maps cambridge cambridge equivalent experiment directly directly directly directly directly additional solutions curves curves curves conference determine classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers full requires choice significant statistics free vision basic validation validation derived derived derived derived derived conditional clustering developed types types product product product product product product product finally processes nature depends depends simply biological discussion covariance covariance hmm hmm hmm transformation transformation corresponds finding finding common role role role theoretical main square easily degree development development objective probabilistic underlying underlying combination coefficients coefficients coefficients coefficients coefficients technology transfer testing mechanism uniform database details call call call idea idea combined combined combined combined combined combined combined combined combined choose sources recent similarity machines machines machines machines quadratic quadratic hierarchical relevant relevant sufficient compare works solve yields achieve definition definition generalized generalized generalized generalized improvement improvement parts invariant occur extended predicted feed generally generally setting setting setting setting demonstrate place assumptions assumptions assumptions depend bayes bayes bayes exponential propose propose taking california solid solid intelligence turn assuming start plane averaged areas suppose pro derive derive construct written written written longer longer ways generating describes label label label label label label label label label metric metric metric metric metric metric metric metric metric metric metric metric missing missing linearly remaining text unique develop develop springer quality implies expectation family family family independently expressed expressed dependence dependence depending labels labels labels sign sign key dashed dashed normalization roughly purpose purpose false false false false false false boundaries boundaries boundaries interpolation generation valid valid valid intermediate distances sufficiently euclidean euclidean classified david includes kernels weighting recognize vapnik discuss specifically variations structural structural structural major simplicity regular regular straightforward middle hmms hmms importance suitable included included latent efficiently mackay score score score score identity capture verlag induced prob superior superior superior issue manifold manifold manifold manifold manifold generative generative generative generative generative generative generative generative generative generative generative generative generative generative notation vary maximization automatically attempt consisted consisted extract deal employed simpler parametric transformed poor poor put relations relations relations relations relations detail replaced divergence dual discriminant ideas ideas applicable applicable applicable ideal combine maximizing scores scores fundamental fundamental coefficient gradients naturally naturally naturally naturally possibly spline extremely logistic logistic logistic logistic logistic logistic logistic fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher art amari extent defines defines defines defines averages asymptotically asymptotically site pairwise separable derivation guaranteed defining defining defining handle considerable tive tive sites sites protein protein protein style immediately arise mathematics begin definite arises author recognizing nsf argument applies flexible pseudo amounts generic generic generic adjustable haussler haussler haussler haussler haussler http http summarized summarized mod mod extracting maximizes proven incorporating incorporating suited suited substantial substantial semi chose jaakkola jaakkola jaakkola jaakkola jaakkola tile tile tile tile tile tile specifies differentiable naive naive consistently ordinary proofs identifying www assign approximates plays systematic systematic dealing stated hyper nearby obtaining exploit krogh effectiveness guide arrays alphabet inferior separating sion sion ascent demonstration tic similarities enable arrive refers proteins proteins proteins steepest exploiting exploiting exploiting exploiting exploiting santa summarize fold fold fold fold cam assigns speaking posteriori roc dna dna dna dna dna slight listed achieving equivalently equivalently deriving deriving deriving benefits encodes discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative discriminative theorems par wahba suppressed suppressed gene var remote illustration clas principled argue penalized penalized penalized formance hubbard challenging met picked emphasize noting relates complementary topic topic pos employing els els things durbin treating advantageous appearing parameterization preserves generarive generarive generarive generarive generarive generarive generarive generarive generarive generarive generarive generarive justification invertible transforming thousand families families families establishes played substitute contributes splice splice splice concave concave distorted evolutionary cruz ready meant reviewed legendre pin jan tim tim riemannian riemannian primal accepting phy plotting inserting suitably suitably suitably ample regional orig ver enhancing ily nation motivates mercer perspectives tommi tommi rendering mitchison refining fragment emphasizing ticular owing fimction revised admits embodies regres fragments traversing para itive deci compar xve xve xve xve xve observational ied vide fimctions combina slx cbms nction discrimi xio xio ison informally nar discrimina discrimina discrimina shorthand inal 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#@Haussler_D,Jaakkola_T,
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#*learning model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number results results results results results results results results units information information models models models models models models models models models models models models models models models hidden hidden hidden space linear linear linear case case case case order order shown shown shown shown shown systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters functions distribution recognition method approach approach pattern point point point point point point point single single processing local local test test class matrix optimal form form form form algorithms simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian feature feature work methods methods step step step step step step step step step step step step step step step step step classification process current current trained problems problems high similar representation architecture equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation fixed fixed fixed rule general parameter parameter average gradient gradient obtained term term note note note note result variables computation computation computation computation computation solution solution independent log log log log log log log log log log log log log log log log log log log initial table table table estimate standard terms terms map present maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press components components continuous continuous abstract applied applied applied applied computational convergence convergence convergence density density density density density density density density density density density density density density density density properties properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component due important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex complex estimation estimation estimation estimation statistical tion difference assume assume lower lower lower lower lower lower rules higher part previous previous previous previous previous bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound good markov techniques techniques techniques techniques techniques proposed correlation forward scale tasks regression regression regression regression regression computed computed respect respect respect respect respect respect sum sum sum sum sum sum sum performed performed called elements means means means means means means optimization optimization applications applications em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em obtain negative true true true application desired provide compute compute location constraints discrete equal approaches mit mit steps accuracy comparison comparison update update update update update update update update update update update update train descent modeling modeling selection report loss implementation joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint difficult final exp ai ai framework framework cambridge computing computing computing directly directly hinton solutions solutions efficient upper upper requires statistics vision estimated increase con con derived derived weighted conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional clustering bounds bounds bounds bounds bounds iteration iteration nature simply discussion covariance covariance covariance covariance covariance covariance technical limited limited corresponds complete finding role require journal cluster makes makes including fit fit probabilistic typically combination unknown jordan jordan jordan jordan ratio ratio ratio ratio empirical call max max direct stored experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert attention practical apply quadratic quadratic quadratic quadratic quadratic quadratic quadratic hierarchical interest dimensions yields yields yields yields yields yields converge mixtures mixtures mixtures mixtures evaluation generalized bounded bounded gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate gate increased parts expression studied extended alternative width deterministic clusters clusters occurs setting critical minimal minimal reduce peak taking strong demonstrated demonstrated turn targets introduce introduce derivatives derivatives derivatives derivatives derivatives derivatives annealing acknowledgements derive derive produces solving estimating estimating describes laboratory laboratory label modeled missing missing missing missing transformations gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians expectation expectation expectation independently squares estimator solved solved solved transform densities densities densities evaluated evolution forms similarly updates updates earlier reduces reduces reduces purpose remains advantages thesis extension plotted maximize specifically specifically priors holds discussions straightforward straightforward straightforward efficiency society effectively efficiently identity identity capture superior superior superior superior follow hold vary write usual michael simplified simplified absence maximization maximization maximization maximization maximization maximization maximization maximization maximization maximization maximization maximization maximization operating mixing mixing mixing jacobs satisfies extend simpler remain poor optimized hessian dual discriminant rest incremental incremental incremental variational variational analytically maximizing maximizing maximizing maximizing comparable gates gates gates gates gates gates gates gates notion necessarily explored amari amari motivated phd finds integrate inequality inequality inequality inequality inequality growth growth derivation derivation answer cascade caused tractable straight purposes formalism bishop desirable immediately calculations calculations optimize optimize geometry incomplete summation summation summation summation tional formulated variant variant http http exhibits maximizes maximizes monotonic monotonic monotonic monotonic resource marginal marginal logp logp conditioning conditioning conditioning summed lot www www oxford appropriately appropriately conditioned conditioned conditioned conditioned conditioned resources databases royal generality allocation numerically numerically promising overcome held serves obtaining operates wire monotonically monotonically monotonically ylx ylx ylx ylx ylx substituting substituting spurious utilized iteratively ascent originally facilitate counter offers centroid dif omitted offer contact contact contact contact broken subsequently subsequently dempster ics uci uci maintaining logarithm logarithm logarithm logarithm logarithm logarithm logarithm rubin rubin solves deriving pentland pentland pentland pentland obtains obtains covariances covariances covariances covariances tight visualization visualization gated bounding bounding bounding bounding bounding bounding bounding individually depicts ultimately lookup laird maintains inverting exhibited exhibited 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#@Jebara_T,Pentland_A,
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#*learning learning learning learning learning learning model model model model model model model model neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number error error error results results results results information problem performance performance performance performance performance performance based based based based based based space linear linear case case case vector shown shown values values values probability probability parameters parameters parameters parameters noise noise noise noise noise noise noise unit distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method approach approach point point point large large local local local local local rate rate analysis analysis analysis matrix optimal optimal algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian paper paper paper examples examples small small small size size size size size size work work work task methods step step step step step step step step step step step points points points points points points points points points points points points points points field process random high similar show show section section fixed fixed fixed line line line line line line line line line line line line line line line line line line line line line line line line line line images images general general general parameter parameter parameter parameter average average average average average average average average average average theory theory theory gradient note note note experiments dimensional dimensional dimensional university university university university threshold computation computation solution independent independent log defined defined defined found found found constant constant estimate computer computer terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance connections science science presented low sets sets sets sets sets sets sets position position components components basis nonlinear continuous sample sample sample sample abstract applied find computational computational computational computational convergence convergence convergence density references component component due important introduction introduction complex estimation estimation behavior statistical statistical statistical statistical generated generated generated generated generated variance variance variance variance cost tion difference complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity measure measure measure measure measure chosen chosen chosen part previous previous previous previous cases cases required long long distributed expected expected expected make make proposed proposed proposed length length length length length length length length length observed errors finite finite minimum resulting resulting simulation simulation simulation sum called called regions regions means factor factor factor optimization optimization optimization optimization made made natural global knowledge knowledge em obtain obtain original original original vol vol vol vol true application define perform perform determined determined experimental distributions distributions distributions equal steps accuracy descent descent descent dependent dependent proceedings department loss loss implementation implementation consists kernel difficult difficult bias bias bias bias maps maps considered considered directly curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curve curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves san determine determine choice significant approximate approximate statistics statistics basic increase increase give give produce condition condition condition condition randomly randomly clustering clustering developed developed criterion criterion criterion criterion criterion bounds selected iteration iteration nature constraint achieved normal denote denote denote denote denote tested transformation close finding amount common shape shape supported theoretical theoretical theoretical theoretical theoretical theoretical theoretical theoretical theoretical journal journal square end makes makes fit fit fit objective reduced coefficients fully projection projection projection projection projection york increasing special consistent consistent empirical 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calculated works works smooth smooth smooth smooth achieve achieve trans definition definition definition definition definition definition definition definition definition definition definition positions generalized bounded organization sensitive sensitive grant grant exists exists invariant scaling loop loop loop setting pass demonstrate demonstrate half half half half half flow conclusion starting greater reduce segment segment segment segment segment segment segment segment segment practice propose propose taking hard largest drawn california proportional proportional minimizing minimizing start start start decrease manner identification question areas suppose produces produces generating generating generating generating generating generating generating generating generating generating generating generating generating generating generating generating generating estimating mathematical dept dept dept segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments coordinates linearly electrical slightly angle angle consisting develop adding adding adding adding adding springer formed national national family independently dependence open updated organizing organizing approximations centers sizes similarly converges partition partition reasonable smoothing smoothing smoothing smoothing smoothing smoothing additive additive additive normalization convex add iterative iterative penalty penalty penalty penalty penalty penalty closed closed closed closed closed construction foundation kohonen expect expect expect thesis priori formulation vapnik plotted illustrated automatic variations neighbors reason regular middle closely closely closely closely uniformly suitable computationally computationally identify schemes plots plots refer verlag induced heuristic heuristic stopping stopping stopping stopping stopping dis issue follow usual absence minimizes minimizes minimizes minimizes attempt subsequent acknowledgments oriented situations situations minimized remain diego american american transformed replaced replaced association optimized hall existence giving giving tech tech project project project project int comparable comparable comparable proved notion surfaces circles coefficient coefficient necessarily analyze spline spline aspect der der der algo shapes shapes motivated phd site piecewise defining defining fairly stanford stanford straight constructing constructing constructing constructing constructing constructing constructing commonly mathematics projected angles angles angles angles circle circle circle circle circle circle circle radius radius robustness prop substantially empirically led consistency consistency parameterized sharp sharp sharp rep rep compares span http http http exhibits exhibits curvature curvature curvature curvature curvature chose decreased shaped initialization uncorrelated identifying www www www www generator generator formally 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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure set set set set set set set set networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number system system results results results information information information problem problem models models models models models models models models models performance based based weights linear linear linear linear case case case case vector vector vector vector vector vector order shown shown systems systems systems probability probability probability probability parameters parameters parameters noise noise noise noise weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution method method method method method method method method approach approach approach approach approach approach approach approach approach pattern pattern pattern point point image image image image image image image image image image image image image image image processing processing processing test test test test test analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class matrix matrix matrix matrix matrix inputs form form shows shows shows shows shows signal signal algorithms simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples small size task methods methods methods methods points points field field field field field classification classification classification classification classification classification classification classification classification process process trained trained trained trained trained trained trained trained trained cell structure structure structure structure structure structure structure structure structure problems problems problems problems high high high similar similar similar similar representation show show show show show rule rule rule rule rule vectors vectors vectors vectors images images images images images images images images images images images images images images images images images speech real approximation approximation gradient gradient gradient gradient gradient obtained obtained term term note note experiments dimensional dimensional variables variables variables variables variables computation computation computation computation research independent independent independent independent independent independent independent independent independent independent independent independent log log log log log log found table table estimate standard standard standard computer terms terms terms left presented presented presented present present present present present frequency sets sets sets sets sets sets sets maximum maximum press press press learn learn learn components components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear abstract applied find computational density density density density density density density density density likelihood likelihood likelihood likelihood references component component component component component component due ieee adaptive adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction estimation estimation generated generated generated generated generated generated generated generated tion difference difference assume assume assume lower signals prior prior representations learned learned learned learned learned higher higher theorem bound type required required multiple good represent represent distributed distributed distributed distributed bayesian bayesian bayesian proposed proposed proposed proposed probabilities observed observed errors classes classes classes classes classes classes classes classes classes classes classes classes classes ing total computed performed eq eq eq eq called called called called called elements factor potential potential potential natural natural natural natural natural natural natural natural natural natural natural applications applications applications applications em em em filter obtain compared compared compared receptive receptive provide compute compute rates perform determined goal distributions distributions distributions equal power approaches approaches steps steps fields update source source source source source source source source source source modeling modeling modeling modeling proceedings report institute institute technique technique code individual individual advances advances connectionist exp exp bias bias bias bias bias framework framework view top detection determine efficient efficient efficient efficient efficient efficient full choice significant statistics vision pages pages pages coding coding coding coding coding coding coding coding coding coding derived derived derived randomly randomly randomly conditional criterion types types types types types types entropy selected nature nature nature nature nature nature nature nature nature nature nature simply achieved discussion technical arbitrary inverse assumption assumption assumption assumption complete complete finding finding implemented assumed main journal pixel pixel pixel degree noisy including including underlying account unknown coefficients york edge uniform uniform principal representing iterations iterations filters bits bits bits bits bits international international bottom sources sources sources sources sources sources sources sources sources sources sources sources improved improved directions advantage separate ensemble reported apply introduced include pixels sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently recently sufficient previously unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised yields pca pca pca pca pca pca trans diagonal sparse sparse sparse mixtures mixtures mixtures mixtures separation separation separation separation separation improvement improvement improvement amplitude extended extended extended extended deviation matrices alternative column column demonstrate greater greater greater greater differences clear peak encoding encoding encoding encoding encoding encoding encoding encoding demonstrated demonstrated demonstrated california ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica scene scene scene index solving laboratory stability changing modeled modeled modeled missing linearly dimensionality text text text text text text text text text text text text text text text text text text applying expectation expectation yield expressed stages stages codes codes codes codes codes codes codes transform densities densities densities densities densities densities updated showed showed lee lee lee lee lee lee lee lee lee lee lee lee lee lee approximated approximated approximated sign sign reasonable additive additive reduces eeg classified precision precision expect priori coordinate coordinate usa bell bell bell bell bell bell bell blind blind blind blind blind automatic automatic prove priors priors priors holds simplicity compression compression efficiency efficiency efficiency efficiency efficiency efficiency identify comparing comparing orthogonal capture traditional road graphs sampled michael generalize computes maximization maximization maximization automatically automatically consisted illustrates mixing mixing mixing mixing oriented situations bars wiley transformed exhibit environments environments dataset scalar school dependencies comparable tanh tanh workshop encode encode statistically patch math adapt rank assumes academic initialized switching multivariate mixed mixed finds scenes scenes scenes scenes scenes scenes publishers adapted independence independence independence benchmark tool perspective bishop bishop medical medical localized patches patches patches patches patches patches prop applies axes sharp compares howard switch switch modulated proven suited logp logp logp logp logp logp converged summed classifying ghahramani ghahramani sleep purely flexibility flexibility neurobiology unlabeled observing salk salk generalizes heavy widths ascent ascent lengths emergence membership jolla extends hart hart hart limitation infomax infomax infomax infomax yielded summer kluwer super super super super super super super removal utilize laplacian laplacian laplacian laplacian clas mutually mutually mutually mutually exclusive exclusive exclusive duda duda duda shannon hughes deconvolution terrence regimes represen det simplifies overcomplete overcomplete overcomplete overcomplete tail scanned ate crude olshausen olshausen olshausen olshausen olshausen olshausen olshausen rare compo bss inferring inset inde lewicki lewicki lewicki lewicki lewicki lewicki lewicki lewicki lewicki lewicki lewicki lewicki filling nonstationary sparseness mul promise tails stepsize resemble pendent unifying cardoso cardoso cardoso won attias attias classifica terry nent bimodal ncrg telecommunications equivariant categorized categorized erties ations articles siftcation relaxing relaxing torrey pines laheld laheld laheld cosh xio nlog cheeseman cheeseman girolami girolami girolami girolami girolami xlc isl isl newspaper heavier ematical blindly hancement 
#@Lee_T,Lewicki_M,Sejnowski_T,
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#*network network network learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set networks training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output number number number number number number number number number number number number number state state state results results units units units units units units information information information models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based space space space space space space space space weights weights weights weights weights weights linear linear linear linear linear linear case case vector vector vector vector order order shown shown shown shown shown shown systems systems systems systems values values values values probability probability parameters weight unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition approach pattern image image single processing processing processing large large large analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form shows shows shows simple simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples examples examples examples small small small small small small small small feature cells cells field process process process process process process cell structure structure structure structure structure structure structure high high similar similar equation equation equation equation equation equation equation equation section fixed fixed rule images images images images images images images images images images images general real real real approximation states states states states states states theory obtained dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation log defined defined found found standard computer distance science science left present phase low low low low low low machine machine maximum range learn learn learn components components components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied find computational density properties properties likelihood references component ieee ieee positive positive positive positive positive positive positive positive procedure introduction complex statistical statistical statistical generated generated generated generated generated variance tion change variable variable variable variable lower measure learned learned chosen center binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary spike spike conditions represent fact techniques region correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation observed scale resulting resulting resulting resulting resulting ing ing total computed computed computed multi sum sum mapping mapping means means means means factor factor factor global applications applications negative negative negative original original original original relative samples represented location determined determined determined determined related related related related related related related related related constraints connected connected discrete equal comparison contrast contrast support train modeling proceedings institute technique code individual advances advances advances exp exp exp exp directly directly directly directly directly directly directly hinton hinton curves top bit determine efficient efficient significant approximate statistics world lines entropy entropy entropy entropy entropy backpropagation sampling constraint constraint normal feedforward feedforward feedforward arbitrary arbitrary transformation transformation transformation inverse assumption common assumed assumed journal pixel pixel pixel easily makes fit probabilistic typically smaller underlying underlying underlying needed combination account york database empirical empirical principle principle principal principal principal principal principal numbers bottom combined directions correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations correlations pair machines side side sejnowski cognitive dimensions conventional conventional conventional conventional conventional approximately calculated calculated calculated calculated match correspond pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca trans mixtures modified bounded constructed constructed expression invariant invariant invariant invariant scaling occur suggests matrices white white boundary half half valued valued valued depend clear temperature presence physics largest largest largest reduction reduction drawn sigmoidal proportional plane relationship relationship relationship boltzmann boltzmann boltzmann relation digit digit van longer longer longer generating generating linearly dimensionality dimensionality involves easy slightly slightly belief unique adding applying springer yield yield yield yield yield independently overlap solved approximations lee lee lee lee digits digits digits partition spectrum spectrum spectrum spectrum spectrum spectrum spectrum sign sign diagram reasonable dashed normalization interpolation interpolation intermediate intermediate distances visible visible visible construction foundation advantages topology transactions handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten activations perceptrons bell bell bell eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues instances plotted plotted illustrated illustrated illustrated illustrated illustrated black black discussions columns determining compression closely importance computationally latent wij modes modes post characteristic capture capture verlag induced induced success lie sin sin sin manifold manifold manifold manifold manifold manifold generative generative generative generative generative generative generative generative generative generative generative generative generative generative dayan wave eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue observable observable leading illustrates neighboring modelling trains american transformed exhibit exhibit association integral integral biases biases biases biases periodic helpful scalar fourier rest detectors investigated analytically relationships office working proper eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors variability variability cover understand analogous analogous hill configurations configurations configurations configurations configurations configurations configurations man extremely illustrate rank rank rank rank rank rank rank rank rank obvious assumes mapped utility utility utility electronic defines spin spin spin spin spin spin spin spin spin spin spin spin spin rows directed variances nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity london widely incorporate sgn sgn sgn sgn sgn hyperplane hyperplane hyperplane commonly commonly laboratories laboratories definite definite depicted argument reflects understood embedded rep variant ity schematic span differs differs gen qualitatively qualitatively hamming display lim cor representative spectra indices ear intractable accomplished guarantee hyperplanes hyperplanes hyperplanes unity impossible nonzero rotations lecun arranged murray numerically convenient hyper cottrell preparation utilized sompolinsky sompolinsky sompolinsky sompolinsky corre den captured israel israel recog surprisingly seung omohundro alternatively thresholding acknowledge dividing dividing unchanged geometrical drop unable incorporates incorporates sine sine nition tween par streams illustration alter hastie labs manifolds bump bump cosine integrals integrals zip induces eigen technologies technologies ate ate generarive distortions impractical generafive generafive abeles inequalities cornput hid spins spins spins char cally ackley continuum bregler triangle ooo inset inset elec charles denominator revow sorted daniel jerusalem tipping hebrew demers clipped clipped clipped clipped clipping clipping clipping clipping clipping clipping clipping distinguishes flips flips visualisation lations nonlin particu renders lucent lucent compressing manifested autoencoders sisj sisj underly flipped stuetzle transforma wll stretching pression generically css css css translationally translationally translationally translationally translationally appropri appropri griffin jolliffe shortcoming shortcoming steeper larly diagonalized 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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output number number number number number error error error error error error error error error error error error results results results results results units information information problem problem problem problem problem hidden hidden hidden hidden based based based space space weights weights weights weights linear layer layer case case case case order order order order order order shown shown shown shown systems systems systems systems probability probability probability probability probability functions functions functions functions functions functions functions functions unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method approach approach approach point point point point point processing large large large rate rate rate rate rate rate rate rate analysis class class optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs shows algorithms paper examples examples small small small small task methods methods methods methods methods methods methods methods methods methods methods step step points points points points points points points points points points points points points points points process trained trained problems problems problems problems problems random random random random similar fixed fixed line general parameter parameter parameter parameter real approximation approximation approximation theory theory obtained obtained obtained term term term term note note note note note note note note dimensional result result result result variables solution log log log log log log log log log log log defined target target target target target constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard terms node science presented presented presented presented map map present present present phase activation activation low range range range press nonlinear outputs outputs continuous continuous sample sample sample sample sample sample sample sample sample sample sample abstract find find computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density density properties references stochastic stochastic stochastic stochastic stochastic stochastic ieee positive important mixture introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior effect effect generated generated generated generated variance complexity variable variable variable assume assume chosen higher higher higher previous theorem theorem theorem theorem bound bound bound bound type conditions represent represent represent represent distributed distributed expected techniques techniques techniques techniques techniques techniques techniques techniques techniques techniques proposed proposed scale simulations resulting resulting simulation simulation respect respect respect respect performed performed performed called mapping mapping mapping mapping mapping mapping optimization dimension study knowledge obtain obtain obtain obtain negative true true true true true true true true true compared compared application series provide define define define perform determined determined experimental goal distributions approaches approaches steps accuracy comparison comparison comparison comparison contrast train modeling modeling morgan institute institute department department version technique technique technique technique technique technique technique technique technique technique kernel kernel kernel kernel kernel kernel advances represents scheme addition ai ai ai computing directly view solutions estimates estimates estimates estimates limit limit determine requires choice choice choice approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate statistics statistics speed estimated basic pages give derived randomly randomly randomly randomly randomly randomly developed developed developed bounds area provided backpropagation technical feedforward group group group denote denote tested fast close close proof amount amount amount nearest nearest common common implemented implemented generate generate generate theoretical theoretical theoretical main square easily makes fit fit kaufmann objective probabilistic smaller underlying underlying needed unknown unknown unknown jordan technology technology character york consistent uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform empirical mode leads squared numbers window window window supervised idea idea attention choose choose description improve robust typical sense sense engineering engineering engineering dimensions dimensions sufficient approximately volume works tions tions smooth smooth smooth smooth achieve definition definition definition background generalized generalized grid bounded bounded bounded bounded bounded bounded bounded bounded bounded interval exists lead lead derivative derivative derivative derivative derivative derivative derivative derivative width width width width deterministic deterministic deterministic white occurs occurs generally generally demonstrate runs assumptions assumptions neighbor neighbor editors accurate faster faster practice practice practice asymptotic propose propose integration cycle cycle cycle cycle drawn drawn drawn demonstrated california california regularization regularization exist targets targets targets targets targets introduce introduce introduce derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives manner estimating mathematical modeled metric sensitivity multilayer multilayer multilayer multilayer multilayer electrical electrical gaussians expectation cycles john focus focus dependence estimator estimator estimator densities densities evaluate fraction translation converges smoothing smoothing smoothing smoothing smoothing smoothing smoothing slow iterative penalty penalty penalty penalty interpolation norm transactions precision includes kernels formulation weighting plotted plotted discuss mozer specifically holds holds reason straightforward straightforward importance uniformly uniformly uniformly comparing notice prob interested content notation realistic realistic nips minimizes correspondence ill ill attempt approximating approximating approximating acknowledgments parametric parametric parametric essential involving estimators hall giving tech applicable applicable tanh func func statistically smallest naturally possibly editor necessarily analyze illustrate ensure quantities multivariate multivariate inequality formula phenomena phenomena slope majority majority majority london stress tive mathematics universal universal describing lowest lowest addressed evaluating applies applies consistency consistency embedded embedded experimentally introducing posed posed characterize monotonic pasadena pasadena adjust adjust comments windows hints extreme cumulative cumulative cumulative cumulative cumulative cumulative feasible sort fix pick approximates flexibility proceed caltech caltech caltech caltech caltech wrong familiar monotonically hint hint hint guide preparation nonparametric moments repeat belongs tic initialize theoretically theoretically inf alternatively acknowledge abu abu slight mostafa mostafa annals poses monotonicity monotonicity monotonicity monotonicity monotonicity ideally solely suppressed demon continuity distri chapman parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen differentiation proach pos hornik option enforce enforce esti esti intensive differentiating manuscript spite bution picking picking drives fortunately ate discontinuous smoother err inherently possess petsche falling gence shortly huge modest sorted sorted regularizers preferable spent sat ascending ascending conver puted silverman machinery implementable univariate univariate univariate mag malik penalizing ies niques expects stochas suit stud amir stinchcombe interpolator interpolator interpolator itive ismail ismail ismail ismail ismail obeying sic sic sic sic sic sic sic sic sic sic sic sic mono nel regularizing sill atiya atiya atiya atiya strate yaser tered deriva nondecreasing tikhonov tikhonov suf fukunaga legitimate anticipated ker magdon magdon magdon magdon magdon magdon istic determin terministic integrable abilistic putationally yil ficiently quest encoun mator mator istics winston parisons 
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#*network network model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set networks networks networks algorithm number number number number number state results results results results results results results models models models models models models models models models models hidden based based based based based space space space space space space space space space space space space space space space space space space space space space space space space space space weights weights weights linear linear case case shown values values values parameters parameters parameters parameters parameters noise weight weight weight functions functions functions functions functions functions functions unit unit unit distribution distribution distribution recognition recognition recognition approach approach approach approach approach approach approach approach approach approach approach approach approach pattern point point single single processing large large analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix shows shows shows shows shows shows shows signal algorithms simple gaussian gaussian gaussian gaussian paper paper small work work methods step step step step step points points points classification process current current structure structure structure structure structure structure problems problems high high high similar similar representation representation equation equation equation section section section section vectors general speech parameter average average average average obtained obtained term term note note dimensional dimensional dimensional dimensional dimensional dimensional dimensional variables variables variables variables variables computation solution solution solution solution research log defined defined defined target target initial estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard terms terms terms terms left left presented map low low low sets maximum maximum range position components components components components components components components basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample sample sample sample sample abstract find density density density density likelihood likelihood likelihood references component component component component component due procedure procedure procedure procedure adaptive adaptive mixture mixture mixture mixture mixture mixture mixture context introduction complex hand hand estimation estimation estimation estimation estimation estimation estimation statistical statistical statistical effect variance variance variance variance tion variable variable variable variable variable variable variable variable variable variable variable variable variable assume lower lower measure measure prior representations chosen part multiple good represent represent represent distributed distributed techniques proposed correct forward finite resulting regression respect sum mapping mapping mapping mapping mapping means means factor factor factor factor factor factor applications applications em obtain artificial artificial samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples samples compared application define perform determined determined posterior posterior posterior posterior posterior posterior constraints constraints constraints constraints constraints distributions equal equal update dependent institute version technique kernel kernel kernel kernel kernel kernel kernel kernel kernel final exp exp scheme scheme scheme scheme scheme ai considered considered computing computing computing curves curves estimates limit conference determine significant approximate statistics statistics statistics estimated estimated basic basic condition condition condition weighted weighted criterion criterion criterion criterion lines lines provided provided finally depends sampling constraint constraint constraint constraint constraint achieved discussion covariance covariance covariance covariance covariance covariance transformation transformation transformation transformation transformation transformation transformation corresponds finding rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf nearest effective require require journal journal journal journal journal easily easily makes including fit fit fit simulated simulated smaller ratio character projection projection projection projection projection projection uniform leads leads principal principal principal principal principal principal principal principal principal iterations iterations iterations making international supervised supervised combined denotes denotes improved discussed discussed improve robust practical introduced introduced strategy subject relevant interest dimensions varying pca pca pca pca pca diagonal definition definition mixtures background background symmetric symmetric symmetric symmetric grid grid grid grid williams williams lead scaling scaling scaling wide derivative derivative alternative alternative feed occurs column assumptions reduce central central peak propose propose taking taking reduction reduction reduction reduction reduction drawn radial radial radial radial radial radial radial radial radial assuming targets introduce derivatives manner denoted areas pro construct edges written written written factors factors factors factors plot plot describes metric dimensionality transformations applying letters lee centered approximated discrimination measurements sec iterative iterative tracking initially distances calculate sufficiently norm expect existing handwritten kernels specifically priors priors regular regular uniformly modification latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent situation essentially road soc repeated repeated stopping stopping generative notation sampled vary realistic providing nips leading illustrates approximating approximating deal modelling presents american american transformed association association integral integral hall fewer investigated authors topographic topographic surfaces surfaces smallest measurement closest closest closest generalisation generalisation generalisation psychology equally versions explored submitted years great formula smoothness briefly stress stress purposes satisfied bishop bishop bishop bishop bishop bishop bishop bishop commonly projected projected arises radius radius greatly evaluating limits lack red differs differs chose chose redundancy multidimensional multidimensional multidimensional distortion distortion distortion distortion distortion distortion lagrange lagrange jth repre unity unity multipliers multipliers chemical obtaining fail exceeds governed ensures ensures regarded regarded evident sphere offers modelled modelled extensively alternatively stopped vari pdf pdf pdf pdf pdf pdf severe andrew posteriori radar gtm gtm gtm gtm gtm gtm gtm gtm gtm gtm incorporates planes planes preserving tibshirani tibshirani tibshirani tibshirani 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#*network learning neural neural input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number system error results results results results results results results results results results results results information information information information problem problem problem problem hidden performance based space space space space space space space space space space space space space space space space space space space space space space space space space space weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer case case case case case case case case case case vector vector vector vector vector vector vector vector order shown values values values values probability probability probability noise noise noise noise noise noise noise noise noise noise noise noise functions functions unit method approach approach approach approach approach point point point point point point point image image image image image image image single single processing large test test test test test test test test test test test test test test test test test patterns patterns patterns analysis analysis matrix matrix matrix optimal optimal optimal optimal form form form shows shows shows shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper examples examples examples examples examples examples examples small small small small small small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work task task methods methods methods methods methods step step points points points points points points points points points points points features features features features features features classification trained trained structure structure structure structure structure problems high high high high representation representation show show show equation section section section section fixed fixed vectors vectors images images images images images images images images images images general generalization generalization parameter parameter real real real real approximation approximation average average theory gradient gradient gradient obtained obtained note note note note note note note note experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result computation independent independent defined found found found found found table table table standard standard terms terms terms terms distance distance distance distance distance left left left direction direction map present present low frequency frequency sets sets maximum press components components components components components components components components components components components components components components components components components components components components components components components basis basis basis basis basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs abstract applied applied applied find computational references component component component component component component component due due ieee positive positive procedure decision context hand hand estimation generated variance variance variance variance variance variance variance complexity assume lower lower rules chosen higher center center center good conditions make fact fact fact proposed proposed correlation correct probabilities ing ing ing computed computed computed respect performed performed called called times times mapping mapping mapping mapping mapping means factor dimension natural applications applications applications obtain obtain obtain negative original original original original original original original true compared compared compared compared application desired provide provide provide provide define compute proc perform determined experimental experimental related related comparison larger larger larger connection connection support support support support descent descent source source version kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel exp exp exp exp exp exp exp scheme addition maps considered computing equivalent experiment experiment curve curve solutions solutions solutions curves curves curves curves curves curves estimates limit san top efficient upper upper choice approximate approximate approximate approximate approximate world world world world pages pages pages give con condition randomly clustering clustering lines lines product product product product provided provided selected iteration iteration iteration iteration iteration simply measured measured discussion discussion covariance technical describe describe denote transformation transformation fast close assumption assumption corresponds finding finding finding finding amount amount common common square square pixel pixel instance instance cluster cluster noisy noisy noisy noisy smaller smaller combination reduced account account coefficients fully interesting interesting significantly ratio projection projection projection york increasing special structures structures structures matching database mode leads principal principal principal principal principal principal principal principal principal principal principal principal principal squared squared squared squared squared representing details numbers numbers numbers numbers pre pre pre pre pre pre pre pre pre pre pre pre making bottom polynomial attention attention run added directions directions directions directions directions directions directions include include identical identical machines sense recently dimensions solve solve solve smooth yields yields correspond pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca achieve definition generalized exists exists exists expression studied deviation alternative white column half half half starting starting minimal row row row row row row row row operator numerical performs mateo taking taking taking drawn solid assuming minimizing start exist exist plane iii introduce question explicit digit digit digit digit digit construct construct construct written explicitly explicitly explicitly explicitly infinite infinite dimensionality text text text text unique gaussians gaussians gaussians springer implies implies extraction extraction extraction yield yield extracted reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction interpretation interpretation influence transform open evaluate fraction fraction centers centered centered understanding understanding margin completely digits digits allowed earlier smoothing additive additive spaces spaces spaces spaces spaces spaces neighborhood purpose closed transactions handwritten kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels activations eigenvalues eigenvalues vapnik illustrated maximize black simplicity reason compression compression selecting closely suitable maximal detect projections projections projections projections tend orthogonal orthogonal orthogonal ten ten fine verlag kind repeated interested lie contribution hold simplified dot dot dot dot dot dot dot eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue moves extract extract extract extract satisfies decreasing presents employed carried carried carried powerful wiley rise rise ideas project working comparable eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors cover cover understand closest editor editor editor necessarily perfect thought prototype versions algo mapped mapped attempts rows rows formula defining expensive briefly starts starts straight organized preprocessing choices located ran mation products products products potentially scientific projected circle optimize depicted depicted depicted depicted conjugate questions reflect haussler formulated span berlin berlin rely pittsburgh anti differs occurrence proven proven ordered suited germany chose conclude findings focused extreme restrict acm ratios ratios circular reconstructed fails satisfying satisfying satisfying satisfying satisfying replacing hope fail canonical intuitive substituting substituting substituting meaningful zhang iteratively equals equals equals regard reproduce arrive arrive belonging eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector explains std robert smola smola smola smola drop sch sch sch vec guyon employs boser big tor england reconstruct reconstruct reconstruct clas burges burges visualization hastie toy toy toy toy toy rithms approxi approxi annealed concentrate depicts projecting retain anal tively algebra retained eigen normalizing signs gauss resembles expansions expansions expansions expansions parameterization parameterization kopf kopf kopf const hilbert hilbert autoencoder autoencoder autoencoder december alex cast mill vanish nontrivial contrary autoassociative gmd gmd counterpart feasibility bumps bumps bottleneck gaus ings carrying carrying carrying focusing translates capturing capturing devoted denominator denominator cti indi ysis spots sebastian attracted oil oil dealt klaus klaus llx superiority reconstructions usps usps usps usps usps usps restart colt pushed mate deduce mercer mercer munich clarify devise dev miiller flips reproducing reproducing prototypical ans live kung extractor periments kij kij bigger recognizable resembling resembling cate plications bernhard joining superpositions extremum extremum extremum nel nel sidered icml mika mika mika mika instabilities eleven eleven stuetzle coordi ker ker biggest biggest monomials domly itsch rudower deliberately nates assert sians chaussee ull mallat iiz mtiller sifiers jasa 
#@Mika_S,Muller_K,Ratsch_G,Scholkopf_B,Scholz_M,Smola_A,
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#*network network learning learning learning learning learning model model model model model model model model model model model model model neural neural data data data data data data data data data data data data data function figure figure figure time time time time set set set set set set set algorithm algorithm algorithm algorithm number number number number number number number system error state state results results results results models models models models performance based based based based based based based based space space space weights weights order order shown systems values values values probability probability parameters parameters weight weight weight weight weight unit distribution method method approach approach point point point point point large large large large large large large large large large large local class class class class class class class class class class class class class class class class class shows shows shows shows algorithms algorithms algorithms simple gaussian gaussian gaussian paper paper paper small small small small small size size feature work work methods points points points points points points points points features classification process process current current random memory memory similar similar similar similar show equation general real real real real obtained note note note note experiments experiments experiments dimensional dimensional result result university threshold research log log log log defined defined constant table table estimate estimate standard terms distance distance node node node node node node node node node node node node node node node node node node node left left left left present present low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets range press components abstract find find find find computational computational computational density density density likelihood likelihood likelihood likelihood references due positive positive procedure procedure procedure procedure important mixture mixture mixture mixture mixture mixture mixture mixture action action complex complex hand estimation behavior behavior statistical statistical statistical statistical effect effect effect effect effect generated generated generated generated generated variance cost cost cost cost cost cost search search search spatial assume lower lower lower lower center bound bound bound cases cases required good binary tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree bayesian bayesian fact techniques probabilities probabilities probabilities minimum classes classes classes classes classes classes classes classes classes classes classes ing ing total total total regression regression regression multi sum sum sum called called elements elements regions means means means means factor dimension dimension dimension em em em em em em em em em em em em em em em em em em em em em em em em em em em vol compared compared provide experimental discrete accuracy larger larger larger larger fields support morgan morgan morgan proceedings proceedings report institute advances exp addition graph graph ai computing computing top determine efficient efficient efficient upper requires requires requires requires significant approximate statistics weighted weighted weighted weighted weighted randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed criterion criterion criterion bounds bounds bounds bounds provided provided evidence evidence iteration iteration iteration iteration iteration iteration iteration iteration nature nature simply simply simply simply measured discussion covariance covariance covariance increases increases denote denote fast fast fast fast fast fast fast close assumption finding short generate generate require journal journal end end instance easily easily easily kaufmann needed needed needed fully structures uniform database database database leads squared details call iterations iterations iterations max international international magnitude magnitude idea run run denotes improved recent resolution resolution advantage advantage pair typical typical apply apply introduced trees trees trees trees trees trees trees trees subset dimensions sufficient varying compare conventional conventional conventional conventional conventional axis achieve diagonal diagonal definition locations improvement entire deviation wide wide wide locally locally locally touretzky clusters clusters clusters pass conclusion reduce editors designed performs performs moody faster faster practice hard turn turn start areas suppose suppose pro monte construct construct pruning linearly linearly linearly dimensionality gaussians gaussians gaussians gaussians applying springer quality john squares viewed learner variation variation detailed evaluate operations lee centers centers suggested earlier calculation slow reduces intermediate distances construction construction advantages expect building building box box contour tests tests regular aspects extra suitable included identify build build build build build score essentially traditional verlag graphs moore moore moore moore moore moore moore return built notation vary write write ill ill ill maximization varied varied put accurately lippmann preliminary dataset dataset dataset dataset fewer applicable int root root removed circles closest necessarily created ensure observe art art art mixed extent contributions seconds seconds seconds seconds seconds seconds seconds cos trivial growth variances biology answer answer expensive worse handle inside strictly ran worst leaves leaves leaves ion ion ion ion depicted geometry meaning mellon considerably carnegie fuzzy items introducing frequently frequently ity mod spread popular popular monotonic parent parent cal datasets datasets datasets datasets datasets sums sums logp begins begins begins tile tile tile tile tile leaf leaf leaf leaf leaf leaf leaf leaf leaf arithmetic sharing aligned aligned identifying notes nat databases databases jth grows proceed proceed children children children air consideration minutes minutes held moment hope methodology splitting splitting splitting splitting spot symposium child child inferior zhang negligible pruned pruned searching tic advance foundations record record record ends sons statement omohundro omohundro hart fold fold fold fold fold default default default default default divide divide divide andrew andrew ics dense mind dramatically unchanged ure ure ure ure ure ure ence numerous visually equivalently equivalently benefits benefits job encouraging aij lit lit ical covariances covariances big rain remainder clas visited care community mhz num num bounding march met met rectangle rectangle rectangle proach speedup speedup win million pop algebra ation places els bill aaai answers tau picking rarely dim ble satisfactory justified multiresolution multiresolution multiresolution multiresolution multiresolution savings savings savings savings hat hat hat ers ers ers ers compete puts mirror mining mining ning distinguishing ples lying sym exploits est est est est rectangles ance gaus tical minimizer ensuring prune prune prune prune tim ized merit cti tit ues dist datapoints datapoints datapoints datapoints datapoints datapoints datapoints datapoints datapoints datapoints datapoints discrepancy ular cient whilst schneider visits tiny tiny iterates remember machinery froin draws clus ell missed cent cen nent ies indistinguishable indistinguishable accumulating accumulating ions han rising enormous ons comput del calling story oft tly tha depict millions subjected intro genera ijcai lai cedure wit varia axi slows pit speedups speedups mahalanobis mahalanobis xve xve eration oot ian oll rst conquer finance equiva fifteenth thi thi thi datapoint datapoint datapoint ellipses ellipses vet ach nmnber traverse coincident 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#@Moore_A,
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#*network network network network model model model model model model model model neural neural neural neural neural neural neural neural neural input input function function function function function function function function figure figure time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm number number number system system system system state results results results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models based based based based case case case case case case vector vector vector vector vector vector order order order order order order order order order order order order order order order order order order shown systems systems systems systems systems functions recognition approach approach approach approach approach approach point point point point point large local local local local local local local local local local local local class class class matrix matrix matrix matrix matrix matrix matrix form shows algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper size size size work work work work work fig fig fig points field field features process process current structure problems problems problems problems problems random random random high architecture show show show equation equation fixed vectors vectors images general general general general average average average states theory theory theory theory theory theory theory obtained obtained obtained obtained obtained obtained obtained experiments experiments experiments result result result result result result university university threshold computation computation computation computation solution solution solution solution solution research research defined defined defined defined found found found found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant standard standard standard standard standard computer computer computer terms terms distance science left left presented presented presented presented present present maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press press continuous continuous continuous continuous continuous continuous continuous continuous abstract find computational computational computational computational convergence convergence properties properties properties properties references due ieee positive context introduction hand hand estimation statistical statistical generated search tion energy energy energy difference difference complexity previous previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem cases required required represent represent expected expected expected expected expected expected equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations markov markov fact fact techniques proposed proposed proposed correct correct correct correct forward scale scale scale classes ing ing ing ing called called times means factor optimization optimization optimization optimization made natural global global global global global global global global global global global applications applications obtain negative original original original vol vol vol vol vol vol vol vol vol vol vol vol vol vol vol relative provide active experimental experimental experimental discrete discrete discrete discrete discrete discrete discrete discrete discrete equal mit larger larger connection nets selection report version version graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph framework framework framework cambridge cambridge equivalent equivalent solutions solutions solutions solutions solutions solutions trajectory trajectory trajectory san free vision vision con derived randomly randomly developed developed developed developed criterion provided finally processes evidence evidence arbitrary arbitrary arbitrary arbitrary denote denote denote denote tested corresponds complete complete stable stable proof proof proof proof short assumed theoretical theoretical theoretical eds eds future objective probabilistic pairs pairs smaller smaller hopfield hopfield dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical significantly increasing increasing special structures matching matching matching matching empirical principle details numbers max max polynomial polynomial polynomial polynomial idea attention produced run denotes denotes discussed exact pair pair typical reported reported practical practical introduced introduced introduced subject identical quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic hierarchical sense sense subset subset subset subset recently recently recently recently recently recently interest compare solve match match correspond correspond correspond converge converge converge trans chain symmetric symmetric symmetric exists studied invariant extended deviation deterministic starting starting trajectories competitive competitive central performs exponential exponential exponential exponential exponential faster constrained suggest suggest suggest strong mechanisms largest turn turn relationship connectivity connectivity connectivity connectivity connectivity connectivity connectivity connectivity minima program program program program program program program program program annealing annealing annealing denoted pro construct edges edges solving solving ways ways vertical mathematical mathematical belief unique develop frequencies minimization minimization springer versus stationary stationary evolution evolution evolution evolution centered converges converges converges recorded includes formulation formulation formulation formulation formulation instances assignment plotted discuss maximize maximize specifically specifically holds holds phys discussions simplicity straightforward straightforward straightforward importance maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal literature situation essentially characteristic characteristic characteristic characteristic characteristic notice verlag graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs kind contained heuristic heuristic success success stopping superior hold write relaxation relaxation relaxation providing correspondence correspondence attempt extract acknowledgments employed employed remain unlike powerful powerful powerful powerful poor poor poor association association association association association association association association game game existence reducing successive biol biol decisions proved proved func hierarchy fundamental fundamental notion math math math math math naturally naturally seconds mentioned asymptotically percentage percentage percentage inequality adjacent adjacent biology biology biology biology baum baum baum lies turns straight strictly strictly strictly precisely incorporate ran consequence res arises computers author author mechanics freeman axes readily frequently maxima maxima berlin gen proven proven tank tank prevent inherent sophisticated sophisticated attraction attraction eventually converged converged proofs cybern feasible proportion saddle labeling equivalence guarantee extensive optimizing branches concerned minutes promising mail logarithmic logarithmic guide combinatorial combinatorial heuristics heuristics spurious spurious spurious games games started ranging mjolsness mjolsness mjolsness loo iteratively induce induce decide regarded guarantees guarantees expanded topological vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices vertices originally francisco vertex vertex vertex vertex vertex cpu belonging lett lett characterization tures stopped cam johnson escape escape escape escape dramatically yale largely gold clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique clique kluwer ties ties ties ties ties formulate formulate perturbed perturbed theorems aij aij aij basins basins letting workstation auxiliary var mutually iff community genes interacting regularized iso guided interactive relates exceed drawback emphasized preprint simplex simplex simplex simplex induces induces struc behaves strict strict strict strict strict vice vice spite versa versa remarkable lagrangian bridge fortunately neumann stimulating converging establishes establishes returned optima rangarajan rangarajan rangarajan rangarajan rangarajan cardinality cardinality cardinality comprising maxi maxi cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques cliques evolutionary evolutionary evolutionary relational counterpart counterpart counterpart statements inform inform rem equilibria equilibria decades completeness developments mid amer elaborate sparc infeasible attracted virtue entities mum mum undirected undirected undirected favorably inability inability italy italy theo tics netherlands sought permuted bull parentheses concluded isomorphic isomorphic isomorphic isomorphic isomorphic isomorphic successes implication charac dsi zucker zucker looo simi visiting replicating borrowed funding discussing analogies akin subgraph subgraph collapse restarted intractability trast oper slowed barrow barrow orbits sgi resist adjacency adjacency adjacency garey customary tax imitation imitation seminal connectivities vided hastad suits dipartimento solv ious artif artif wijxj informatica eccv budapest tur invariably partment enjoys llo characterizations transposition similiar teristic indefinite 
#@Pelillo_M,
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#*learning learning learning learning learning learning learning learning neural input input input data data data data data data data data data data data data data function function function function function figure figure time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number number number error error error error error results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance based weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order shown shown shown shown values values values values parameters weight weight recognition method method method method method method pattern single single processing large large large large large large large large large large large test test test test class matrix matrix matrix matrix matrix matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs form form form form signal algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size size size size size size size size size size size size methods methods methods methods methods step step step step step step step step step step classification trained trained trained problems problems problems problems problems problems problems problems problems problems problems problems problems random memory memory memory memory memory similar similar similar similar equation equation fixed fixed fixed line line line line line vectors vectors vectors general generalization parameter real gradient gradient obtained experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional result university threshold threshold computation computation computation computation solution solution research research research research research log log found found found found table table table table standard standard standard standard standard standard standard standard computer terms science direction direction machine machine machine machine machine object sets sets sets sets sets sets sets sets sets maximum maximum press press press components continuous continuous abstract convergence convergence properties references due due due due due due due due ieee positive positive introduction complex complex estimation effect variance tion tion change difference difference classifier classifier chosen chosen previous previous previous previous bound bound bound bound required multiple multiple good binary binary binary conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions equations equations fact fact techniques techniques proposed scale scale minimum minimum minimum minimum minimum ing total computed computed multi performed performed called times times times times elements factor factor factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization dimension dimension knowledge negative artificial represented desired series series series compute compute proc constraints constraints constraints constraints constraints equal mit mit mit steps accuracy accuracy support support support support support support support support support support support support support support support support support report department version technique consists consists code code code code code code code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances advances joint difficult final ai ai experiment experiment determine full full requires choice choice choice world speed speed speed speed speed speed speed speed pages pages pages validation give condition bounds bounds bounds bounds product product constraint constraint constraint constraint constraint simply measured measured normal technical group tested tested fast fast fast fast limited finding amount short common require require require end easily easily fit fit objective objective typically smaller smaller smaller combination reduced reduced programming programming programming database database database database empirical empirical making stored stored stored stored magnitude polynomial combined choose light light light light light light light light light light light light light predict improved advantage advantage advantage property separate takes similarity practical apply subject machines machines machines machines machines machines machines machines machines machines machines quadratic quadratic quadratic quadratic quadratic subset subset recently interest dimensions approximately approximately tions solve solve solve solve solve yields match correspond diagonal diagonal diagonal sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse evaluation evaluation evaluation interval storage entire entire entire entire entire entire entire entire scaling scaling scaling scaling scaling scaling scaling suggests wide move loop loop loop loop generally pass pass minimal minimal minimal minimal minimal minimal greater segment segment conclusions editors editors editors measures numerical numerical numerical numerical numerical numerical numerical numerical exponential faster faster faster faster faster faster constrained constrained constrained suggest taking largest reduction variety min min relationship acknowledgements digit written solving solving solving solving solving sequential sequential sequential sequential sequential sequential describes describes implement implement category involves involves easy text adding adding minimization springer versus versus john choosing choosing expressed expressed expressed expressed expressed expressed depending solved updated decomposition decomposition decomposition decomposition decomposition decomposition sizes suggested digits updates updates processor slow slow sec sec sec reduces handwritten handwritten box box kernels kernels kernels vapnik vapnik maximize maximize absolute tests reason identified effectively svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm identify summary refer refer notice verlag quickly prob heuristic heuristic heuristic lie lie lie running running dot dot dot dot correspondence computes computes situations unlike varied optimized optimized hessian hessian hessian dual helpful rest applicable analytically analytically working attributes attributes attributes attributes attributes smallest smallest smallest subsets quantities algo algo ith ith finds finds years rows inequality slope analytic analytic analytic analytic analytic explanation analytical benchmark lies handle rapid worst worst commonly products products potentially projected projected optimize optimize optimize optimize optimize definite arises outer outer outer researchers conjugate conjugate reflect reflect substantially empirically pseudo lack share slower http http http passes passes passes passes achieves substantial windows yielding shifted classifying benefit www www www optimality lagrange lagrange lagrange lagrange lagrange lagrange lagrange lagrange rithm rithm girosi optimizing databases approximates discovery lecun multipliers multipliers multipliers multipliers multipliers multipliers multipliers multipliers multipliers multipliers multipliers platt platt platt platt platt platt multiplier multiplier kaufman kaufman murphy numerically keeping removing heuristics heuristics heuristics heuristics heuristics heuristics composition evaluations evaluations evaluations heavy ensures displayed overview belongs chooses chooses chooses chooses chooses chooses cpu cpu cpu ends storing relies exploiting speeds ignore avoiding default smola smola smola lem ics dense uci uci uci uci fitted dramatically dramatically dramatically unchanged leaving svms svms svms svms svms svms svms svms svms svms svms svms svms sch sch sch vec solves solves solves tables asked failed convenience utilize freund tor avoided reflected burges burges burges burges burges burges arising equality equality equality equality equality exponent exponent exponent exponent mhz dominated dominated dominated labs ocr altered overhead overhead overhead categorization library library library library breaks breaks breaks page page ignoring mix mix mix mix gorithm suggestions utilizing utilizing circumstances chris discretized kopf kopf kopf nested jointly jointly solvable 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#@Platt_J,
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#*network network learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural input input input data data data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure set set set set networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number system error error error error error error error error error error error error error error error error error error results results results results results results results results results results information information information problem problem problem performance performance performance performance performance performance performance weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order order shown shown shown values values values values parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight distribution distribution distribution distribution recognition recognition method method method approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image image single single single single single single control control large large large large large rate rate test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis class class matrix optimal optimal optimal optimal optimal optimal form form shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms examples small small small small size net work methods methods methods methods methods methods fig fig fig fig step step classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process problems problems problems random high high high high high high high similar similar show show show show section section section section fixed fixed fixed line line line line line line line line line line line rule rule vectors general generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter real real approximation average theory theory gradient gradient gradient obtained obtained term note note experiments experiments experiments experiments experiments experiments experiments result university variables variables variables variables variables variables variables variables variables variables solution research log log defined found constant constant table table table table table table connections prediction left left left left low low low machine machine machine machine machine learn learn basis outputs sample abstract applied applied find find find find references due due due due due positive positive procedure adaptive decision decision decision decision decision introduction introduction complex complex hand estimation statistical effect effect generated generated generated generated variance variance search search search search complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower measure measure prior prior learned chosen previous previous previous cases cases cases cases cases cases cases good good binary binary binary binary make make make fact fact fact fact techniques proposed proposed proposed proposed proposed correct correct probabilities observed observed observed observed errors errors errors scale minimum minimum minimum resulting classes classes classes ing computed computed computed computed computed respect multi sum eq eq eq eq eq eq eq eq elements means optimization optimization optimization made negative negative negative negative original original original artificial true true compared application cross cross define compute proc proc proc proc constraints distributions distributions distributions equal comparison comparison comparison larger larger contrast update update support support support support support support support support support support support support train train train descent nets nets nets selection report loss version kernel kernel difficult difficult difficult difficult exp exp exp exp exp exp scheme ai computing domain equivalent equivalent directly directly view limit top capacity capacity classifiers classifiers choice approximate world pages validation give give give give give give produce produce derived weighted weighted weighted weighted weighted weighted weighted weighted levels levels area area area area area types lines finally finally iteration nature simply simply achieved achieved achieved technical increases tested predictions rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf implemented generate generate role theoretical face ability ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis future makes noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy including including objective smaller functional programming programming programming programming programming character increasing increasing special uniform leads leads call iterations iterations iterations iterations iterations iterations iterations iterations iterations direct direct normalized early decay decay combined minimize minimize minimize minimize choose choose run description description improved improve property property pair robust ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble takes takes takes typical typical typical apply introduced strategy strategy subject machines machines machines machines machines quadratic quadratic quadratic trees sense recently approximately works tions tions smooth studies studies converge achieve achieve achieve sparse address positions sensitive grant lead lead lead concept concept concept concept scaling derivative predicted correctly boundary conclusion conclusion starting place valued central central differences differences bayes numerical clear clear practice asymptotic asymptotic asymptotic asymptotic propose propose hard hard hard hard hard hard hard hard hard hard hard hard hard hard presence reduction solid regularization regularization regularization regularization regularization minimizing minimizing decrease decrease averaged averaged averaged introduce introduce introduce introduce force base base base base acknowledgements digit derive construct construct produces written written winner estimating label stability dept dept changing confidence easy slightly text unique minimization minimization minimization minimization springer springer springer competition depending communication overlap learner influence influence evaluate controlled labels labels showed lee centers centers centers centers soft soft soft soft soft soft soft soft soft understanding sizes margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin partition partition partial dashed reduces false norm norm classified classified avoid formulation weighting weighting weighting vapnik vapnik maximize maximize maximize maximize holds discussions successfully reason reason middle middle middle importance differ modification divided effectively effectively effectively svm svm svm svm svm svm svm svm svm svm svm efficiently efficiently ten ten conf strongly strongly success stopping strategies write generalize providing minimizes minimizes hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses maximization maximization principles overlapping minimized powerful overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting exhibit exhibit optimized dotted dataset dataset dataset dataset behaviour behaviour tech tech project mse boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting analytically reliable maximizing maximizing understand analogous smallest smallest smallest coarse possibly necessarily necessarily changed changed versions versions observe generates submitted established asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically asymptotically ment separable separable waveform waveform improves improves analytic explanation explanation adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost majority benchmark worse worse worse worse berkeley berkeley satisfied bishop bengio sgn optimize optimize medical conjugate explained argument reflects apparent improvements limits bootstrap bootstrap experimentally introducing rep rep outliers outliers outliers outliers berlin gen maximizes maximizes cal achieves singer datasets datasets datasets datasets datasets plan germany kinds median eventually cumulative trade trade trade trade trade trade classifying lab college sv lagrange japan optimizing nat labelled partitions royal lecun establish plays multipliers fits wrong ments breiman breiman breiman breiman satisfying analogy analogy balance balance reasoning reasoning effectiveness optimally games bartlett schapire schapire predictors widths bad originally candidates ensembles ensembles april smoothed cancer cancer cancer bagging bagging bagging bagging bagging extends statement valuable alternatively ignore fold interestingly smola limitation limitation uci svms svms sch vec basically validity adopt centre conjecture additionally causing freund freund big big big classifies tor toy toy num ocr ocr regularized regularized quinlan quinlan emphasized sonar enforce voting son applicability margins margins margins margins margins margins margins margins margins margins port mini algorithmic august kopf breast breast confirm wins wins wins bold exper inequalities val usefulness proposal incorporation subtracted splice splice correctness classi meth tokyo retrieved ods amplified amplified spirit icl icl permanent gmd gmd essence fication seg shop mach mach neglected inst outlier slack slack slack slack slack slack slack slack slack unexpected unexpected explaining cortes boosted stat stat relax enforcing plexity dilemma mum icann icann klaus klaus aimed tie rated eralization unlimited colt acknowledged fur gorithms functioning overfit overfit overfit miiller miiller grove grove grove permitted trust trust shi ences bigger bigger tab arcing arcing arcing arcing arcing plications predominantly votes misclassifications loose funding bers schwenk estimations holloway regularizing regularizing regularizing regularizing cated surely ilwll clarendon regu itera itera onoda onoda onoda onoda onoda onoda positivity asymp iments ariaboost cer knew alleviate unnormalized delve coef itsch itsch itsch itsch rudower pothesis storm chaussee schuurmans schuurmans greg achievement thermore ficients thyroid thyroid larization rag rag lncs totically 
#@Muller_K,Onoda_T,Ratsch_G,
#t12
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#*neural neural neural neural neural input data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time set networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number system error results results results results problem performance performance performance performance based space space space linear case case case case order order order order shown noise noise functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions recognition recognition recognition method method method approach pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image processing processing processing large large large optimal optimal optimal form shows signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple simple simple simple paper paper small small small small size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature task methods step step points features features features features features features features features process level level level level similar representation representation representation representation representation representation equation equation equation equation equation equation equation section section section line line line line line line line vectors images images images images images images images images images images images images images speech real approximation theory obtained obtained obtained obtained note note dimensional dimensional dimensional dimensional result result result result result result result threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation computation computation research research log log defined constant constant constant constant constant constant constant constant constant constant table table standard standard standard computer terms distance distance distance distance left left left left left left left left left left present low low low maximum maximum maximum range press position position position continuous abstract find computational computational computational computational properties references due positive procedure procedure important important propagation propagation introduction effect effect parallel cost cost variable assume signals signals signals cases cases good binary binary binary binary binary binary binary conditions conditions conditions tree tree make fact fact region length length length length length length length forward forward finite finite resulting resulting resulting computed computed computed computed computed computed respect respect sum sum called times times regions regions regions regions means factor factor factor factor dimension applications filter filter filter obtain negative negative original original original original vol represented true application application series provide compute compute location location determined goal constraints constraints gain brain approaches mit steps steps accuracy accuracy accuracy accuracy accuracy accuracy larger larger contrast contrast contrast support support nets loss consists consists code kernel kernel kernel difficult scheme considered computing domain domain domain equivalent directly directly limit top top top top top top top top top top top top top top top top top stage effects effects conference efficient efficient full requires requires requires approximate speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed con actual finally depends measured arbitrary arbitrary tested fast fast fast fast fast limited corresponds corresponds complete finding effective implemented require main end pixel pixel instance instance instance instance degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree degree typically typically typically account coefficients coefficients interesting interesting ratio ratio ratio ratio ratio ratio matching matching operation operation details filters filters filters pre bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom magnitude polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial combined combined combined combined combined run run run run run run run run denotes denotes directions advantage property takes typical introduced pixels pixels pixels pixels pixels interest varying varying tions yields yields yields correspond achieve positions positions positions modified bounded horizontal horizontal horizontal horizontal horizontal horizontal horizontal invariant wide derivative derivative derivative derivative derivative derivative derivative derivative width width boundary boundary runs runs runs runs runs runs runs conclusion starting starting starting critical reduce operator depend faster faster suggest encoding encoding encoding encoding encoding encoding integration integration integration integration presence largest proportional proportional assuming introduce derivatives derivatives derivatives derivatives derivatives denoted written written written solving ways ways ways factors factors factors factors vertical implement involves easy integrated integrated integrated integrated adding applying quality extraction extraction extraction extraction extraction extraction extraction extraction extraction versus versus yield yield yield choosing extracted extracted depending depending squares squares squares codes transform evaluated evaluated evaluated operations operations fraction approximations approximated approximated sizes completely translation translation translation translation partition constants constants key reasonable reasonable convex combining combining boundaries boundaries boundaries penalty penalty valid filtering filtering topology precision precision template kernels combinations contour illustrated illustrated illustrated illustrated illustrated reason columns effectively effectively effectively effectively delta delta efficiently efficiently comparing invariance invariance invariance identity identity compact quickly quickly repeated cun cun cun interested list list write minimizes minimizes quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization quantization overlapping illustrates illustrates illustrates illustrates preferred approximating satisfies simpler carried varied integral integral recursive recursive recursive recursive recursive recursive recursive recursive recursive fourier fourier fourier fourier investigated applicable applicable applicable func cover cover cover cover fundamental necessarily extremely quantities quantities impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse impulse 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural data data data data data data data data data data function function function function function function function function function function function function function function function figure figure figure time set set set set set set set set set set set set set set networks networks training algorithm algorithm algorithm algorithm algorithm number number number number number results results results results results information information information problem problem problem problem problem models models models hidden hidden hidden hidden hidden performance based based based based space space space linear linear case case case vector vector vector vector vector order order order order order order shown systems systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight functions functions functions neurons unit distribution distribution recognition recognition method method method method method method method method method approach pattern pattern point single single processing processing large local local local local rate rate rate rate rate rate rate rate rate rate analysis matrix matrix matrix matrix matrix matrix matrix form algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper examples examples examples examples examples small small size fig step points points classification current current problems random high high similar show show show section fixed line line line line line line line line line line line line vectors vectors vectors general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation average theory gradient gradient obtained obtained term term note note experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional result result university variables variables variables variables variables variables variables computation research log log log log log log defined found found found found found sequence constant estimate standard standard terms terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance prediction left left low low machine sets sets maximum maximum maximum maximum range press components components components components sample abstract applied find find find find find convergence convergence convergence convergence convergence convergence density density density density density density density density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references references stochastic stochastic due due procedure procedure procedure procedure mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand hand hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior behavior behavior statistical generated generated generated generated generated generated variance search variable rules learned previous bound bound cases cases cases cases multiple conditions bayesian equations equations make fact fact proposed proposed observed observed observed finite minimum classes regression computed respect respect respect respect respect respect multi sum sum sum sum sum sum performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq elements elements elements elements means dimension natural natural applications em em em em em em em em em em em em em em em em em em em em em em em em em em obtain obtain negative negative negative negative negative vol relative relative relative relative relative relative relative relative compared define rates rates rates rates rates proc goal goal distributions distributions distributions distributions approaches steps steps comparison comparison larger contrast update update update update update update update update update update update update update update update update update update update update update update update update update update update update update descent source source loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss version technique technique consists individual advances advances joint joint joint joint joint joint joint difficult exp exp scheme addition ai framework framework framework framework framework framework framework framework experiment directly estimates estimates estimates upper upper requires requires requires significant statistics estimated pages pages give condition weighted clustering developed developed bounds bounds entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy finally finally constraint simply measured discussion covariance covariance covariance covariance covariance covariance covariance covariance increases increases describe describe describe describe denote denote denote denote denote denote denote close close inverse stable proof finding finding common common common common journal end instance instance instance typically smaller coefficients coefficients interesting call call iterations iterations iterations iterations making supervised supervised supervised supervised supervised minimize minimize run denotes element element apply introduced introduced introduced include side side sense dimensions sufficient varying observations converge mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures symmetric observation observation observation observation observation observation observation observation entire expression wide matrices matrices matrices matrices matrices matrices matrices alternative setting setting setting setting setting setting setting setting setting setting setting setting pass demonstrate runs half half faster faster faster faster faster faster hard california minimizing start min min min derivatives derivatives derivatives derivatives derivatives derivatives groups scene minima denoted denoted denoted denoted digit derive derive index solving estimating estimating slightly gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians expectation expectation versus versus choosing review stationary overlap densities updated updated similarly similarly similarly converges updates updates updates updates updates updates updates updates partial partial partial additive convex convex convex convex sec purpose add iterative iterative iterative iterative iterative iterative iterative closed initially initially distances sufficiently euclidean advantages batch batch batch batch batch determines uncertainty discuss coupled successfully straightforward aspects importance society differ modification identity characteristic composed composed conf procedures induced prob superior sin hold notation notation notation simplified providing minimizes maximization maximization acknowledgments situations remain parametric wiley wiley wiley updating scalar rest analytically analytically cover reading der taylor initialized ith inequality guaranteed tool located worst bishop mation potentially annual incomplete incomplete conducted experimentally lack lack price measuring measuring ture popular cal achieves singer singer singer singer singer singer singer expectations expectations expectations eventually multidimensional summed univ indices proportion formally guarantee lagrange lagrange modify oxford summing summing royal multiplier smith adds numerically tools simplify settings settings settings settings settings settings motivation date schapire sion induce decide den thomas thomas multiplied warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth warmuth santa hart summarize dempster dense yielded ure numerous constitute incorporates rubin annals sig deriving deriving deriving deriving alternating seek arg arg arg aij ideally conservative param param duda labs expand careful laird enforce isi esti algebra tune tune rewrite eters mix lems appearing handling january hid stay calculates cally meth meth att ods ods sian rel fol sis demands cruz ready inducing gaus gaus kivinen kivinen kivinen kivinen kivinen kivinen kivinen bauer minimizer minimizer minimizer shares replaces degrades newly newly cancel walker def ucsc permuted ative nation motivates motivates diverges manfred manfred exponentiated cse koller brevity brevity xlo xlo xlo xlo xlo gra eter helmbold helmbold inverses inverses rrt bij combi dient owi duncan deviates assures lows tedious titterington yoram offering preliminaries constituting xlz xlz slo slo slo sio sio sio sians ces ances encompasses isn oss covari scribe diminishing underscores 
#@Singer_Y,Warmuth_M,
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#*learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure set set set set set set set set set training training training training training training algorithm algorithm output number number number error error error error error error error error error error error results problem problem problem problem problem problem problem problem problem models models models models models models models models models models models performance performance performance performance performance based space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector order order order shown shown values parameters parameters noise noise noise noise weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions method approach approach approach approach approach approach approach pattern point point point single control large large test class class class matrix optimal optimal optimal optimal optimal shows shows shows algorithms algorithms algorithms simple simple gaussian gaussian gaussian paper paper examples small small small size size size feature feature work work work methods methods fig fig classification process process current structure structure structure structure similar show show show show show equation line line general general general general generalization generalization generalization parameter real approximation approximation theory obtained obtained term term term term term term term term note note note note note note note experiments experiments experiments experiments experiments experiments result university university variables variables variables variables solution research independent found constant constant constant constant constant table table estimate estimate estimate estimate standard standard standard standard standard standard standard terms terms distance prediction left left presented frequency machine machine sets maximum press basis basis basis basis basis basis basis basis basis basis abstract back find find find properties properties references stochastic due due positive positive positive adaptive context context introduction complex hand estimation estimation estimation statistical effect effect generated generated variance variance variance variance cost cost cost cost cost tion tion change difference measure prior prior prior chosen chosen chosen chosen chosen part part part part part part part part part part part theorem bound cases cases cases type type good good good conditions expected expected equations make fact fact fact fact techniques techniques proposed proposed length length length correct correct errors errors errors minimum resulting classes regression regression regression regression regression regression computed computed eq means optimization optimization optimization optimization optimization optimization optimization dimension dimension study knowledge knowledge knowledge knowledge knowledge original samples application cross compute compute perform experimental goal constraints constraints constraints approaches accuracy comparison connection support support support support support support support support train selection selection report department loss loss code code code kernel kernel kernel kernel kernel kernel kernel ai ai framework computing domain domain directly additional additional additional additional additional additional top capacity capacity capacity capacity determine determine efficient efficient classifiers choice choice choice significant statistics statistics world estimated basic pages validation give con condition bounds bounds bounds lines lines lines lines lines lines lines product actual provided finally finally processes processes nature achieved discussion technical technical denote close close corresponds predictions proof finding rbf rbf common supported main hypothesis hypothesis instance instance future future easily easily makes including fit fit fit fit fit fit objective objective smaller smaller smaller smaller smaller smaller combination reduced functional functional functional programming programming programming programming programming programming programming programming programming testing significantly significantly trials uniform uniform empirical details max direct normalized bottom polynomial idea idea minimize choose choose added denotes denotes advantage pair typical similarity practical practical apply subject subject machines machines machines machines machines machines machines machines machines machines machines machines quadratic quadratic sense subset subset subset sufficient conventional solve solve solve yields converge interval interval interval risk risk risk risk risk risk risk exists exists exists lead lead lead concept deviation matrices alternative width setting setting setting setting setting strength strength strength strength operator measures encoding drawn solid solid solid regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization minimizing minimizing user user exist exist question denoted denoted acknowledgements suppose construct written solving solving ann averaging remaining easy scales minimization springer choosing choosing independently depending variation variation evaluate operations restricted restricted decomposition margin completely converges diagram smoothing smoothing additive additive classical expansion expansion expansion expansion expansion expansion expansion spaces spaces convex sec add add interpolation visible sufficiently sufficiently sufficiently sufficiently sufficiently sufficiently construction expect existing box kernels kernels kernels kernels kernels kernels kernels kernels perceptrons sciences vapnik vapnik extension maximize discussions structural major major simplicity straightforward uniformly modification modification effectively situation tend essentially orthogonal characteristic contained contribution sin sin sin sin sin sin sin sin follow satisfy dot realistic minimizes minimizes correspondence hypotheses deal modelling modelling extend presents remain carried parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric parametric overfitting difficulty put put detail strengths dotted dotted dotted dotted dotted dual dual dual dual dual dual ml pursuit pursuit helpful rise rise project authors comparable proper complicated understand math coefficient naturally subsets observe observe observe explored simplest simplest contributions arbitrarily preference preference cos cos cos cos cos cos stanford easier operators choices choices choices inversion universal definite definite lowest arises people offset peter introducing splines splines dots polynomials polynomials berlin pittsburgh ture extensions chen datasets datasets comments display deviations median univ cor consistently picture picture shifted benefit sv sv sv sv sv sv sv sv sv sv sv sv sv sv optimality formally lagrange restrict princeton impossible multipliers fits adds tools stated stated viewpoint definitions definitions settings generalizes constructive nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric degradation motivation bartlett displayed arrive rich belonging exploiting grants explains fold fold insensitive insensitive insensitive robert smola smola smola smola smola smola smola treat unchanged outperforms outperforms sch sch sch sch guyon convenience boser residuals wahba penalized trends gained toy realizable approxi life expand regularized regularized regularized regularized regularized wise spanned spanned happen fea admissible williamson treating emphasis emphasis advantageous differently interior interior recogni kopf kopf sake sake nested hat jointly hilbert hopkins clarity alex concern incorrectly condi manually carries conditionally suffice statist semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric 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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure time time time time time time time set set networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number error error error error error error error error results information information information information problem models models models models models based space space space space space space space space space linear linear linear case case case case vector order shown shown shown systems values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach approach approach approach pattern point point point point point point point single processing analysis analysis analysis analysis analysis analysis class class form form form form form algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian visual paper examples examples examples small size feature feature feature methods methods methods methods methods methods step step step step features process process structure structure structure random high high high high high high architecture section section section section section section section rule rule vectors vectors vectors vectors images images images images general general parameter parameter parameter parameter parameter real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation obtained note dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result variables variables variables variables variables variables variables variables variables variables computation computation research research independent independent independent log log defined defined table table standard standard left left left left present low machine sets maximum maximum press components basis nonlinear continuous continuous continuous continuous continuous continuous sample sample abstract applied convergence density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component ieee decision introduction complex estimation estimation estimation statistical statistical generated generated generated tion difference variable variable variable variable variable variable variable variable variable lower higher bound multiple binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary represent bayesian bayesian bayesian expected make techniques techniques proposed proposed proposed proposed proposed probabilities observed observed scale scale human regression regression regression regression computed computed computed respect respect respect performed mapping means means factor factor natural em em em obtain obtain obtain negative artificial samples samples true true true true true true application application application series compute location location location eye related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions discrete discrete mit accuracy accuracy accuracy accuracy accuracy comparison larger larger update update proceedings loss implementation advances final final final final exp exp scheme ai ai ai ai ai ai considered considered considered considered framework framework framework cambridge cambridge computing equivalent equivalent directly additional estimates estimates estimates top stage bit bit bit bit bit bit bit bit conference efficient approximate statistics statistics statistics statistics world estimated estimated increase increase increase give give con derived derived weighted conditional conditional conditional conditional conditional criterion types types types types types types types lines lines evidence evidence iteration iteration nature sampling sampling sampling sampling sampling sampling sampling constraint covariance increases describe describe arbitrary arbitrary denote fast close close assumption corresponds finding effective implemented implemented implemented eds eds journal journal end end degree fit probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically underlying underlying needed jordan jordan jordan jordan interesting projection projection projection principle operation leads leads leads leads principal principal principal principal principal representing iterations bottom combined improve recent recent property separate typical typical introduced introduced include identical quadratic hierarchical hierarchical dimensions sufficient observations approximately mixtures locations observation observation observation observation observation observation williams williams exists suggests loop clusters clusters clusters generally demonstrate conclusions depend accurate accurate bayes bayes numerical clear exponential faster taking integration presence presence physics reduction reduction drawn demonstrated intelligence intelligence radial exist manner denoted appears digit digit digit digit digit digit digit pro monte monte derive carlo carlo longer longer generating estimating plot plot plot mathematical dimensionality dimensionality dimensionality dimensionality dimensionality angle applying extraction expectation squares overlap showed approximations evolution approximated approximated approximated approximated converges updates updates key key earlier purpose iterative iterative boundaries closed closed sufficiently transactions handwritten handwritten combinations priori extension plotted plotted illustrated mozer specifically specifically determining closely society effectively latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent literature efficiently efficiently computations mackay mackay capture quickly induced stopping dis running running generative generative generative hold gray gray involved michael powerful investigate difficulty integral integral integral dual mass biases dataset dataset dataset dataset dataset dataset ml pursuit examine giving investigated ideal variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational analytically dependencies dependencies variability topographic topographic contours naturally necessarily psychology illustrate illustrate illustrate prototype prototype prototype aspect algo logistic logistic logistic logistic expressions multivariate multivariate mixed mixed synthetic synthetic synthetic synthetic synthetic synthetic established guaranteed defining defining independence briefly tool london reasons comparisons tive tive purposes style located bishop bishop bishop bishop bishop bishop mation inversion reflects considerably considerably tional readily marked prototypes cal datasets datasets datasets datasets datasets datasets datasets expectations jaakkola jaakkola jaakkola phenomenon intractable sort writing rithm databases royal difficulties difficulties hope methodology methodology monotonically intuitively iteratively iteratively evident evident captured reveals offer papers vari vari outlined street gtm outline vec adopt simulating clustered clustered mutually equality approxi permits proba concentrate smyth noting increasingly outcomes inverting inverting induces applicability applicability permit exploratory tin exploited gauss advantageous styles lowe lowe firstly house tors mining drawing formulae incorporation ters petsche comprising cur implied implying brackets charles categorical categorical trend artificially rent maximisation maximisation developments microsoft microsoft tipping tipping tipping tipping tipping tipping tipping tipping tipping tipping retaining predic ables plotting recovers tailored posteriors maximising notably notably ting nuclear numbered british clus responsibilities responsibilities lose rendering visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation visualisation george maximise maximise generalised tlx indicative optimise unconditional secs secs tti tti optimising optimising ryan ryan optimised graphic varia dig strained necessitates alterna proposing topical ttt til til svens svens bilistic griffin convincing topo clude utilised utilised acceptably hierarchi ational historically provision quires elucidate guildhall illustrations guar xlt xlt summarise 
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#*learning model model model model model model model model model neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure time set set set set set training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number results results results results results problem problem problem problem models models models models models models models models models models models models models models models models models based based based based based space space space space space weights linear linear linear case case case case case case case vector vector vector vector vector vector shown shown shown shown shown shown shown systems values values values values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters noise unit unit distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach pattern pattern point point point point point single processing local local local local local local local local local local local local rate test test test test test test test test test test test analysis class class class matrix matrix matrix optimal form shows shows algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small size size feature net net work work task methods fig fig fig fig fig fig fig fig step step step step step step step step step points points points field process process current problems random high show show section line line line vectors images general parameter parameter parameter parameter parameter parameter parameter parameter parameter real real real average average obtained note note note note note note note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result result university solution solution log log log log log log log log log log log log log defined found found found initial initial initial initial initial table table table table table table table table estimate estimate estimate estimate standard terms distance science direction presented present low low low maximum maximum maximum maximum range position components components components components components components components components components components components components components components abstract applied applied back computational convergence density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component component component due ieee positive procedure procedure procedure procedure procedure procedure mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand hand estimation estimation estimation estimation estimation statistical statistical generated generated variable variable variable classifier lower lower lower lower chosen higher part part part center long long expected make make region region region region proposed proposed proposed proposed proposed proposed length probabilities probabilities probabilities observed finite classes classes tasks computed computed respect respect sum performed performed called times regions regions means factor factor factor factor factor factor factor optimization dimension global global knowledge em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em obtain original original original vol vol vol vol vol specific represented true true application define define compute perform perform perform perform perform posterior posterior posterior posterior posterior posterior posterior distributions discrete equal equal steps steps steps steps accuracy accuracy accuracy larger modeling report difficult final final final exp considered framework computing hinton hinton hinton hinton hinton hinton hinton solutions solutions estimates design efficient upper full full approximate estimated estimated estimated increase give give produce derived weighted clustering clustering criterion criterion criterion lines depends covariance covariance covariance normal denote denote denote denote tested transformation limited close corresponds complete nearest nearest common journal square noisy simulated probabilistic probabilistic underlying underlying combination reduced interesting empirical empirical principle principal details call iterations iterations iterations max max max max max direct idea improved improved improved improved improved improve improve improve apply introduced side inference recently works works solve pca trans diagonal diagonal mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures positions locations locations modified modified improvement suggests wide matrices matrices correctly locally move move move move deterministic deterministic column setting demonstrate conclusion starting trajectories trajectories neighbor neighbor competitive practice practice temperature largest largest variety min averaged introduce annealing annealing annealing question digit digit written simultaneously dimensionality consisting gaussians gaussians gaussians gaussians gaussians extraction expectation select decreases extracted communication viewed evaluated open evaluate operations operations operations operations operations operations operations operations operations operations decomposition digits digits updates partial partial partial reasonable calculation additive sec combining fitting intermediate symbol avoid handwritten candidate candidate candidate candidate holds holds successfully successfully successfully major selecting society latent latent efficiently efficiently post comparing ten ten ten procedures procedures prob neuroscience split split split split split split split split split split split split split split split split split split split split split split split split split split split split split split split split split split superior manifold manifold manifold manifold manifold criteria criteria criteria criteria criteria criteria criteria generative usual usual usual usual usual usual dayan quantization computes moves moves extract intrinsic unlike poor perturbation replaced divergence dotted successive successive tech tech applicable applicable applicable authors affect configurations facial created thought thought thought rank algo algo assumes separated synthetic synthetic synthetic mentioned improves london london widely strictly ran worst worst bishop arise arise laboratories involve toronto definite computers incomplete researchers parameterized experimentally experimentally marked slower continuously rep maxima maxima maxima maxima maxima maxima compares compares ture extracting maximizes datasets datasets sophisticated focused simultaneous simultaneous simultaneous simultaneous converged converged converged converged univ univ merging initialization consistently consistently ghahramani ghahramani ghahramani ghahramani ghahramani college redundant sort sort accomplished assign guarantee japan japan rithm rithm appropriately ordering royal spiral kullback numerically accepted accepted overcome held splitting settings effectiveness repeat utilized iteratively candidates candidates candidates candidates candidates candidates candidates candidates candidates candidates candidates candidates similarities initialize initialize repeatedly repeatedly passing extensively merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge splits splits designing summarize dempster std std std std std pdf executed escape lem speaking fitted outperforms visually rubin outperform accept 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#@Ghahramani_Z,Hinton_G,Nakano_R,Ueda_N,
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#*learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number results results results results results information information problem problem models models models models models models models hidden hidden based based space space space space space case case case case case case case case case case vector vector shown shown shown shown shown shown shown shown shown shown values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach point point point point point point point point point point point image image image image image single single processing processing control control control large large large large local local local test analysis class optimal form form simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper small small small size size size size size size size feature feature feature task task task methods methods methods methods methods step step step step step step step points points points points points features process process process process process process level level level level level level level level level level level level level level level level level level level level level level structure structure structure high similar representation representation representation show show show equation equation equation equation section section section line parameter real real real real real real real theory obtained obtained obtained experiments variables computation solution solution independent log log defined found initial initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard standard standard standard standard standard standard computer node node left left left left left left left left left presented present present present temporal machine machine object object object object object object object object object object object object object sets maximum components components components components components components sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract find find find computational computational density density density density density density density density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component ieee procedure procedure important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation estimation estimation estimation estimation estimation behavior statistical statistical statistical statistical statistical generated variance variance variance variance variance variance variance cost search search search search search search complexity complexity complexity complexity variable variable variable assume measure prior prior learned learned learned higher higher higher required good binary binary represent equations equations equations equations equations make fact proposed correlation correlation resulting resulting resulting classes tasks total computed computed computed computed performed performed called times regions applications applications applications applications applications applications knowledge knowledge knowledge em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em obtain obtain obtain original original vol relative samples samples samples samples samples samples samples samples true application provide provide provide compute compute compute compute objects objects objects proc experimental experimental goal goal power mit mit mit mit mit steps steps steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy larger larger larger connection update modeling report report technique consists consists consists kernel kernel kernel kernel kernel kernel kernel bias bias bias bias bias bias addition graph graph graph graph graph considered cambridge computing equivalent experiment experiment experiment experiment directly solutions curves estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates limit top top top top top determine efficient efficient full full full full requires choice significant significant statistics free free vision vision vision basic basic increase con derived derived derived derived derived derived weighted conditional clustering clustering clustering levels levels levels levels levels lines nature constraint constraint constraint simply simply simply achieved achieved achieved covariance covariance covariance technical increases increases inverse complete common generate role main journal easily degree makes fit typically smaller smaller smaller underlying underlying reduced block block block block interesting interesting significantly projection increasing database database database database database leads leads leads leads leads numbers iterations pre direct making making international bottom bottom bottom bottom bottom bottom bottom bottom bottom frame idea combined run description description description description description description description improve resolution resolution advantage takes takes practical practical practical practical subject side hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees previously correspond achieve trans mixtures mixtures mixtures mixtures improvement entire entire increased increased expression lead suggests suggests extended deviation deterministic deterministic deterministic setting place depend clear clear learns learns temperature taking physics physics physics largest drawn drawn drawn drawn drawn drawn drawn california proportional assuming assuming assuming start start start start start relationship relationship relationship manner scene minima minima annealing annealing annealing annealing explicit explicit suppose monte monte carlo carlo factors generating generating generating estimating estimating plot plot plot plot describes describes describes laboratory laboratory explicitly text gaussians gaussians gaussians gaussians gaussians applying springer quality quality blocks expectation decreases choosing independently dependence estimator interpretation interpretation interpretation interpretation variation densities densities sizes sizes similarly partition key smoothing smoothing smoothing smoothing smoothing smoothing performing combining intervals roughly closed closed intermediate assigned assigned assigned views views views degrees expect formulation retrieval retrieval retrieval assignment assignment recognize determines extension extension extension illustrated major reason straightforward middle efficiency capable uniformly society differ computationally computationally computationally computationally literature literature fine composed notice notice notice conf verlag repeated contained allowing allowing video video video interested content strategies quantity usual providing quantization highest highest leading maximization illustrates subsequent operating mixing camera camera presents presents presents law simpler parametric parametric parametric parametric parametric limitations mass dataset dataset dataset dataset matches fashion fashion int combine relationships relationships maximizing hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy hierarchy contours coarse coefficient coefficient naturally naturally illustrate ensure expressions switching contributions explain smoothness expensive expensive straight choices commonly commonly describing circle beginning lowest bandwidth bandwidth bandwidth bandwidth incomplete incomplete incomplete virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual improvements percent generic generic conducted leave reliability maxima http switch gains partitioning measuring characterize limiting parent achieves datasets logp trade trade trade trade globally pose pose pose pose sort www guarantee guarantee restriction databases jth royal reaching establish establish fits fits convenient significance exploit intuitive intuitive child composition lip consequences sphere sphere offers viewing viewing recog draw draw draw impact impact impact impact likelihoods captures santa characterization characterization dempster fold escape escape andrew consecutive temperatures ence logarithm rubin july nition poses superimposed superimposed superimposed assignments assignments big hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies hierarchies descriptions descriptions descriptions descriptions descriptions certainty avoids pub ftp ftp insights investigating harder conversely laird indexed attached placing meet lippman lippman lippman lippman lippman exhibited exploratory rose mix drives quadrant savings shot establishes mining proportions evenly resolutions resolutions fox attained successively successively thing positioning raised media media media media media denominator indexing indexing refine trapped repeating infeasible hij hij hij hij hij deeper coincides enforced enforced relying relying rated vast ames impressive tums canceling succession zij zij zij standpoint compose ogp numerator resort rin hierarchically rrt rrt rrt rrt coarser ficient hemisphere analogies optimizations summations leftmost derlying barbara gurewitz ita eling reporting sepa ida xlz hierar hierar columbia lti ali chical chical mains 
#@Lippman_A,Vasconcelos_N,
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#*network learning model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output number number number number number number number number error error error error error error error error error error error error error error results results results results information information problem problem problem problem problem problem problem models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance based based space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear linear linear case case case vector order order order shown shown shown systems systems values values values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise functions functions functions functions distribution distribution distribution distribution method method method method method approach approach approach processing large large large test test analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs form shows shows shows signal gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper small small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work methods methods methods methods methods points points features features features features features features features features features features features features classification classification process process process process process process process process process process process process process level trained trained trained structure structure problems problems problems problems problems high high high high similar similar show show equation equation equation equation equation equation equation section section section section section section section fixed vectors vectors vectors general general general general general general general general general general real approximation average average average average theory theory gradient gradient obtained obtained obtained obtained obtained note note note note experiments experiments experiments experiments dimensional dimensional dimensional dimensional result university university university variables variables variables computation computation research independent log log defined defined target estimate standard standard computer distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance science prediction prediction prediction prediction prediction prediction prediction prediction prediction direction direction presented sets sets sets sets sets sets maximum maximum maximum maximum maximum press press press press press press press press components basis basis basis basis outputs outputs abstract applied applied find find likelihood likelihood likelihood likelihood likelihood references stochastic stochastic due due ieee positive positive positive positive positive positive important important context introduction estimation estimation estimation effect generated generated generated generated variance variance variance variance variance variance parallel parallel tion variable lower lower measure prior prior chosen higher part good good good good distributed bayesian bayesian bayesian bayesian bayesian expected expected expected fact correlation correlation length observed observed observed errors errors errors errors errors scale minimum minimum tasks tasks tasks tasks total regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression computed respect respect respect respect respect sum elements elements elements elements mapping mapping means dimension dimension dimension study original relative relative relative relative relative relative relative relative specific samples samples true true true compared compared cross define perform perform perform determined related posterior posterior approaches mit larger larger larger larger larger larger larger larger train report technique advances represents exp exp exp exp exp exp graph graph maps cambridge computing equivalent upper full full full full full full full full full full full choice statistics free free free free world estimated estimated pages validation validation produce derived conditional criterion actual processes processes processes processes processes processes processes processes processes processes selected depends depends depends sampling sampling discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance describe tested transformation transformation transformation transformation close inverse inverse assumption surface surface surface predictions amount amount amount effective assumed assumed assumed main square smaller underlying combination combination combination combination reduced fully significantly significantly significantly ratio ratio projection special squared squared squared iterations magnitude magnitude idea idea run architectures directions directions directions directions directions directions directions directions directions reported practical apply introduced subset relevant relevant relevant relevant relevant relevant relevant dimensions dimensions compare compare compare observations axis axis axis axis axis axis trans diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal evaluation locations locations symmetric generalized interval williams williams williams williams williams williams williams williams williams lead suggests wide matrices matrices matrices matrices matrices matrices matrices matrices matrices touretzky setting demonstrate reduce operator depend depend depend editors differences sigmoid numerical numerical exponential suggest integration largest drawn demonstrated regularization assuming acknowledgements suppose generating estimating tuned vertical dept confidence confidence metric coordinates averaging infinite dimensionality dimensionality dimensionality dimensionality dimensionality interaction interaction adding predictive springer variation densities evaluated evaluated open decomposition decomposition decomposition forms approximated additive additive additive additive spaces reduces intervals avoid figures thesis formulation eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues subspace subspace automatic automatic mozer discussions closely uniformly poggio literature projections mackay mackay plots ten ten reached reached composed composed summary notice notice notice graphs allowing allowing success showing dis dis dis sin follow eigenvalue eigenvalue eigenvalue eigenvalue observable observable observable observable predictor predictor predictor predictor modelling bars bars carried carried overfitting investigate hall dataset dataset dataset dataset pursuit helpful project analytically eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors cover cover hill generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation predicting illustrate equally rank rank singular singular assumes assumes observe observe art multivariate multivariate multivariate explain phd neal neal neal neal neal neal years mentioned pairwise defining improves capabilities capabilities lies london turns turns purposes division arise commonly products scientific english toronto definite definite definite conjugate conjugate explained argument questions relevance relevance relevance amounts amounts amounts axes axes conducted spread popular datasets datasets datasets datasets datasets datasets datasets datasets datasets datasets logp deviations displays corrupted corrupted notes equivalence restrict girosi girosi girosi hyperplanes concerned discovery discover discover jones fails fails breiman breiman breiman breiman occurred occurred attractive determination determination reasoning affected responsible performances overlaps predictors predictors predictors predictors predictors predictors entry negligible lengths evident hasselmo entries entries advance treatment express infer creating verification properly belonging eigenvector discovered verify logarithm logarithm inferred tibshirani tibshirani reports reports affects discovering discovering discovering discovering discovering edinburgh edinburgh hastie hastie intuition chapman regulation investigating conversely spanned funded det eigen eigen normalised normalised normalised lecture observables remarks christopher agrees jointly suffices played tribution rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen sym triangular fair edition ance united fore datapoints ard preferable proximation italy quadrature superiority wright maximising maximising maximising maximising designated forrest british wii aver epsrc gression highlights correla gps gps gps ner mat manifest manifest manifest trigonometric trigonometric ofp recipes kingdom teukolsky aging compar optimised optimised optimised flannery mahalanobis vetterling highlighted andy eigenspace aerospace whittle whittle characterised characterised declines ive ison dai universities posit semidefinite semidefinite informatics cry marina utu 
#@Vivarelli_F,Williams_C,
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#*network network learning learning learning learning model model model model model model model model model model neural neural neural neural neural neural neural data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure time time set set set set set set set set networks networks training training training training training training training training training algorithm algorithm number number number number system error results results results results results results results results information problem problem problem problem models models models models based based based based based space space space linear case case case case case case case vector vector vector vector order shown systems systems systems values values values values values values values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions functions unit distribution distribution distribution method method method method method method method method method approach point single single single processing large large large large test analysis analysis analysis class class matrix matrix matrix matrix form form form form form form gaussian gaussian gaussian paper examples examples examples examples small work work methods methods methods methods fig fig fig step classification classification classification classification classification structure problems random random random random random random similar similar similar representation representation show section section section fixed fixed fixed vectors vectors general general general generalization generalization generalization parameter parameter parameter parameter approximation theory theory obtained obtained obtained term term result result university university university variables computation solution solution solution independent log log log log log log target target initial estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate computer terms distance distance distance distance prediction prediction prediction left present present present low machine sets sets press press position components components components basis basis basis basis nonlinear nonlinear continuous sample sample sample sample abstract applied applied find find likelihood likelihood likelihood likelihood likelihood likelihood likelihood references references component ieee positive procedure procedure adaptive introduction estimation estimation statistical generated generated generated generated variance variance variance variance variance variance variance variance variance variance variance cost tion change complexity complexity lower chosen chosen chosen part part part cases multiple multiple multiple good good good good binary conditions conditions tree bayesian bayesian equations fact fact fact simulations simulations simulations minimum ing simulation simulation regression regression computed computed computed respect sum called called times factor applications study study study study study knowledge obtain obtain obtain negative negative original artificial true true true true application application application desired desired cross cross cross cross cross cross cross cross cross series series series proc eye eye eye experimental related brain brain mit comparison comparison comparison comparison larger selection morgan proceedings report report institute institute department department loss kernel kernel advances joint represents represents represents bias bias bias bias bias bias bias bias experiment experiment experiment experiment experiment experiment estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates conference choice approximate approximate approximate approximate approximate statistics statistics statistics free estimated validation validation validation validation validation validation validation validation give con produce derived randomly lines provided selected iteration iteration depends measured technical technical limited close inverse inverse implemented implemented eds square square cluster future degree including fit fit fit fit fit fit fit fit fit fit typically pairs functional functional functional unknown unknown testing special uniform representing details minimize produced architectures architectures population exact exact exact exact typical practical include include subject quadratic quadratic quadratic quadratic interest highly previously observations observations approximately tuning tuning tuning smooth diagonal evaluation generalized generalized risk risk risk risk risk exists studied suggests derivative matrices clusters clusters reduce depend accurate numerical numerical numerical designed clear moody exponential exponential asymptotic propose propose taking physics sigmoidal intelligence regularization regularization regularization radial assuming variety min explicit appears produces index index solving solving factors sequential plot plot plot ann ann dept dept dept changing confidence infinite physical remaining easy consisting applying choosing choosing review depending influence lemma evaluated open open showed approximations approximations soft soft soft soft soft soft partial calculation calculation calculation smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing additive additive convex fitting intervals iterative iterative penalty penalty penalty box box weighting black black successfully reason selecting selecting society computationally included poggio poggio plots essentially conf repeated procedures prob sin sin running criteria duration comp quantity satisfies satisfies tesauro cowan minimized body body simpler remain replaced association association association hessian hessian hessian dotted mass mass giving history applicable int variational variational variational authors reliable structured func attributes circles circles trace trace trace trace spline spline spline spline spline spline spline spline spline spline spline spline taylor taylor ith multivariate baseline synthetic brown derivation drive lin mathematics circle circle circle calculations begin attribute attribute definite definite read bandwidth nsf splines splines ity span polynomials differs replace replace kinds age age unbiased unbiased implements patients wang wang wang wang simultaneous univ lot don representative ordinary newton newton newton www generator modify extensive extensive girosi girosi optimizing optimizing member concerned null jones jones outcome outcome outcome kullback kullback numerically convenient convenient fan replacing replacing efficacy mark star north modifications nonparametric filled filled filled substituting alspector entry heart indicator indicator matter refers draw extensively insensitive johnson lem fitted pressure liu liu ure street street street leaving leaving blood equivalently randomized randomized randomized randomized randomized randomized randomized randomized randomized randomized randomized randomized employs perturbed perturbed comparative wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba wahba tradeoff tradeoff tradeoff tradeoff tradeoff tradeoff tradeoff tradeoff tradeoff generalizations chicago chicago letting letting letting letting letting clas principled principled penalized penalized penalized penalized penalized penalized penalized penalized grouped wall continues uncertain disease sketch turning confusion siam minor preprint truth truth cubic cubic cubic simplex things rewrite mini manuscript demonstrating expansions corporate marks families families hilbert replicated moss bond trol rating weather weather statist statist statist inde spirit sian wisconsin wisconsin wisconsin handbook gaus wong wong minimizer minimizer minimizer minimizer minimizer minimizer minimizer minimizer minimizer stacked ized probabil replicate replicate replicates replicates stat searched pendent survival mir utans utans regional monthly madison madison madison favorable suggestion ronald clus ages penalties functionals aii aii reproducing reproducing dong lations klein klein klein klein klein klein klein klein klein dam dam dam govern govern attack progression arbib kauffman cited anova anova anova anova anova anova ein doubled ofp asa technically sification lihood lambda lambda lambda lambda summarizing compar mimics calcu yif commun downhill relearning raphson raphson raphson tering barbara observational liebler liebler tackled wisc wisc wisc arch sir cbms grace logit ison pack mizing campus cholesterol cholesterol cholesterol cholesterol proxy women inefficiencies inefficiency oix physician variates prelim dayton anew inary 
#@Gao_F,Klein_B,Klein_R,Lin_X,Wahba_G,Xiang_D,
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#*network neural data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure set set set set number number number error error error error error error error results results results results results information information information information information information information problem problem problem problem problem models performance based based space space space space space space space linear linear linear linear linear linear linear order order order order order order order order order order shown probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution method method method method method method method method method method method method method method approach test test test test test analysis analysis form form shows signal signal signal algorithms algorithms algorithms simple gaussian gaussian paper paper paper paper small small methods methods methods methods methods methods step step points field process process process process level level level level level level level level level level high response similar similar section section section section general theory obtained obtained obtained obtained experiments result result result university university university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold research research defined found found initial table table table table table table standard standard computer presented presented presented presented presented low frequency sets range components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis abstract applied applied applied applied applied applied applied applied applied applied find properties properties properties references component ieee procedure procedure procedure procedure procedure procedure procedure important introduction statistical effect effect variance search tion change difference difference difference spatial signals prior prior prior prior prior prior prior prior prior higher higher higher center required conditions represent expected techniques scale finite resulting resulting resulting resulting resulting regression regression regression regression regression regression regression regression regression regression regression regression respect performed means means means study study study knowledge knowledge filter filter filter filter filter filter filter filter obtain original original original original original original vol vol vol vol vol samples samples samples represented true compared compared compared compared application application desired desired cross cross cross cross cross cross cross cross cross series series series perform perform determined discrete discrete discrete discrete discrete discrete steps steps steps comparison comparison comparison source selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection report report version technique consists represents final scheme scheme scheme domain domain domain domain domain domain experiment directly design effects effects conference efficient requires free basic increase validation validation validation validation validation validation validation validation validation produce selected selected selected selected selected sampling measured technical technical inverse inverse assumption corresponds implemented implemented implemented shape shape shape generate supported supported supported adaptation journal square square square degree noisy noisy noisy noisy noisy noisy noisy noisy typically underlying underlying coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients ratio projection projection uniform operation representing filters filters filters filters filters filters filters filters filters filters filters filters filters filters pre normalized magnitude idea added added exact exact property typical apply relevant relevant engineering engineering previously calculated calculated smooth match achieve background background symmetric modified observation studied scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling suggests trial wide white demonstrate conclusion conclusion reduce reduce operator taking hard characteristics demonstrated demonstrated radial manner relation van written written written longer mathematical dept dept dept electrical applying applying applying formed blocks blocks blocks blocks blocks blocks blocks select select choosing family family review reconstruction reconstruction transform transform transform transform transform transform transform transform transform decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition soft soft soft soft translation allowed smoothing smoothing smoothing performing spaces generation generation generation filtering construction construction construction transactions includes thesis combinations combinations selecting closely uniformly society computations projections projections orthogonal orthogonal orthogonal orthogonal orthogonal orthogonal ten characteristic composed composed summary repeated contained symmetry symmetry symmetry lie involved sampled sampled sampled sampled sampled sampled wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet highest minimized collection requirements requirements relations relations optimized optimized dual dual dual dual mse ideal ideal root proper spline spline created impulse versions explored attempts stop piecewise piecewise piecewise smoothness smoothness smoothness smoothness analytic snr sections arc widely sgn commonly mathematics mathematics mathematics mathematics lowest depicted nsf substantially pure conducted capability leave leave leave cohen cohen cohen splines incorporated incorporated span span synthesis popular incorporating incorporating age median median median june representative corrupted college pick labelled reconstructed royal lost communications wrong wrong wrong mail mail obtaining methodology methodology moments moments moments composition published published published recovered recovered recovered recovered recovered recovered recovered moved bases bases bases bases bases bases bases eng relies broken papers adopted thresholding thresholding street corporation listed basically removal ties wahba wahba wahba mutually concentrated intuition community community individually fir fir fir projecting projecting scope library spanned refinement refinement refinement nasa nasa siam siam admissible admissible knowing retained nal subspaces september remarkable prefer families focuses aid bold mirror finer finer finer incorrectly shrinkage meeting beneficial wavelets wavelets wavelets wavelets wavelets wavelets wavelets wavelets wavelets wavelets wavelets wavelets wavelets wavelets interpolating complement south south bumps bumps bumps bumps bumps reviewed doubling vanishing vanishing custom replicates replicates replicates quadrature regional ames shrink shrink wheeler wheeler wheeler wheeler wheeler wheeler wheeler philadelphia philadelphia outlines sults banks orthogonality donoho donoho donoho donoho donoho donoho donoho donoho donoho gression fifty instantiations compactly compactly saving coarser coarser publications gov dyadic kevin contrasted observational onal johnstone johnstone johnstone carolina carolina cbms selections finest moffett incompatible lectures imi imi redefining 
#@Dhawan_A,Wheeler_K,
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#*network learning learning model model model model model model model model model model model model model neural neural neural neural input data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time set set set set set set set set networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm number number number number number number number state results results results units units units units units units information information problem models models models models models models models models models models models models models hidden hidden performance performance based based space linear layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case vector vector vector shown shown shown shown shown shown shown shown systems values values values values values values probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters unit method pattern pattern pattern image image image image image image image image image image image image image image image image single single single single single processing processing large large large patterns class class class class matrix matrix optimal optimal inputs form form shows shows shows shows shows shows shows algorithms algorithms algorithms paper paper paper examples net net work work work work methods step points field field field process level level level level level level level level level current current structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems random random random random random high high high similar architecture architecture architecture architecture architecture architecture show show show section section section section section section section fixed fixed fixed fixed fixed fixed line vectors vectors images images images images images images images images images images parameter real approximation approximation states theory theory note note experiments experiments experiments experiments dimensional variables variables variables variables variables computation computation research research research log log log log log log log log log log defined found found found found found found found constant constant standard connections node node node node node node node node node node node node node node left direction presented map map map map map map map map map present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine object object object object maximum position position position position components components sample sample sample abstract applied find properties likelihood references due due due ieee ieee positive important important adaptive propagation context introduction introduction hand hand hand stimulus stimulus stimulus stimulus dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated generated generated generated generated generated search change difference variable lower prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior higher higher part part part previous type binary binary binary represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed bayesian bayesian markov make fact fact fact techniques probabilities probabilities probabilities scale scale total computed respect multi sum called means means factor factor made made made made natural natural natural natural natural natural em obtain obtain obtain relative relative relative samples true compared compared application cross define objects objects location location determined posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior connected connected connected equal equal equal steps steps comparison larger contrast contrast morgan report institute institute institute consists individual layers layers layers scheme addition addition considered considered cambridge hinton hinton additional additional transition transition san top effects efficient full approximate approximate free increase derived conditional levels levels levels lines product nature depends sampling sampling sampling sampling simply discussion discussion describe arbitrary denote denote finding finding finding nearest nearest effective generate supported supported main end pixel pixel pixel easily degree fit kaufmann simulated simulated simulated simulated simulated probabilistic smaller needed reduced account segmentation segmentation structures structures structures structures structures structures structures call call numbers pre bottom depth depth idea idea attention choose choose run run denotes denotes denotes architectures directions separate strategy strategy include pixels pixels hierarchical hierarchical trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees inference inference inference inference inference inference inference compare axis axis trans diagonal diagonal diagonal diagonal diagonal background positions positions williams williams williams sensitive sensitive sensitive grant lead lead concept occur occur alternative white white white occurs boundary runs starting starting greater greater valued valued designed exponential practice mateo temperature temperature temperature temperature taking hard hard demonstrated turn introduce introduce connectivity configuration configuration configuration annealing annealing annealing annealing annealing annealing question acknowledgements pro derive construct ways generating generating generating generating plot plot plot plot mathematical distinct sensitivity averaging averaging involves belief belief belief belief belief belief stationary communication interpretation evaluated translation translation translation translation translation discrimination earlier calculation combining roughly visible assigned advantages transactions avoid expect sciences plotted discuss priors black black black black black black black black black black partially grammar structural texture columns capable included successful schemes comparing comparing invariance invariance invariance plots tend notice kind showing lie running built gibbs gibbs bar bar usual usual dayan dayan dayan providing highest highest employed explore explore remain poor essential exhibit exponentially limitations mass helpful rise fewer successive successive giving links investigated applicable applicable possibility possibility authors structured structured structured root root root root root root root encode hill circles circles plausible configurations illustrate created ensure adjusted sentences neal preference inside style constructing division leaves desirable controls circle lowest alignment explained conducted conducted readily lack peter http ture aim popular parent parent parent parent parent parent parent parent parent parent parent parent parent parent parent extensions marginal plan logp logp decreased decreased specifies specifies specifies converged leaf leaf leaf leaf displays gap ghahramani ghahramani newton newton redundant proportion www restriction zemel ordering null null arranged clamped accepted overcome intelligent resulted obtaining obtaining obtaining reasoning belong belong settings responsible child child child child slice ensures entry entry decide moved belongs branching arrangement arrangement entries artifacts infer indicator clean parse discovered avoiding balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced balanced parents speaking boxes posteriori unchanged slight shading helmholtz tables break instantiation instantiation personal superimposed multinomial multinomial affects edinburgh intuition picked retain retain retain multiscale multiscale pearl pearl pearl indexed suffer sweeps exhibited struc october inactive ate christopher mrf mrf losing suite broadly devised wavelets interpretations neighbourhood zoubin zoubin zoubin reality creation relaxed semantics translate ated stationarity experimented stems accepting tighter encourage conversations posteriors named symmetries puted forrest participate roots neighbour segmentations neighbours epsrc epsrc instantiations accompanying conducting forest forest forest forest forest geoff cre shapiro shapiro tying adams adams adams adams referring technically crossed crucially conversation proposals ensured deemed dictions contingent intuitions ive nicholas athe willsky willsky parses concen rts rts favour dai dai attract hospitality isaac isaac trate colour jective studentship informatics luettgen luettgen desirability emanating favoured quad quad anc 
#@Adams_N,Williams_C,
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#*learning model model data data function figure figure figure figure figure time time time time time time time time set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number number results results results results results results results results information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models based based space linear linear case case order order order order order order order order order order order order order shown shown shown shown shown values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters noise noise distribution distribution distribution distribution distribution distribution recognition approach approach pattern pattern point point point point point point image image image large large large large local test analysis analysis analysis analysis analysis analysis analysis analysis analysis optimal optimal form shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms visual visual visual visual visual visual visual visual visual paper paper paper paper paper paper paper paper examples examples small small small size size size size size size work work work work work work task task task methods step points points structure problems problems random random high high high response similar similar representation show show section section section section line images images images images parameter parameter parameter approximation average theory theory theory theory theory theory theory theory result threshold threshold threshold threshold threshold computation independent log log log log log log log log log target target target target target target target target target target target target target target target target target target target target target target initial constant constant constant standard standard computer computer computer computer computer computer terms terms terms distance distance connections science left direction present phase phase phase machine machine object object sets sets maximum press position abstract convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties properties properties references ieee ieee positive important important important important context introduction estimation statistical statistical statistical statistical statistical statistical statistical generated search search search search search search search search search search search search search search search search search search search search search tion energy energy complexity variable variable spatial assume assume assume lower rules prior prior prior chosen higher center previous theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound cases cases type required multiple multiple good long long represent tree tree tree tree tree tree tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected expected expected expected expected expected expected equations markov markov markov markov markov markov make make make make fact proposed proposed proposed length length probabilities probabilities ing tasks total total total sum sum sum times elements means means factor factor factor factor factor optimization optimization made made orientation global applications applications knowledge knowledge knowledge knowledge filter filter obtain vol artificial relative relative specific specific represented true true true true true true true true true true true true define define compute rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates perform active determined determined posterior posterior constraints connected distributions distributions power steps larger larger fields dependent words words words version joint responses difficult addition addition graph graph considered considered framework computing domain domain domain domain domain domain curve curve curves curves design transition san san stage stage stage detection detection detection detection detection determine determine determine determine determine determine determine determine determine determine upper requires requires requires requires requires choice statistics statistics speed speed vision vision vision vision vision vision vision vision basic condition condition condition derived criterion criterion criterion bounds bounds bounds bounds types entropy entropy path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path path provided provided provided provided provided processes processes nature depends depends depends constraint close close close close close close close assumption assumption corresponds proof proof proof amount assumed generate generate require require face probabilistic typically smaller smaller block block block block block block block block block block block block block block testing york edge edge edge edge edge edge edge edge mechanism special special special uniform uniform uniform details call call call idea attention choose choose choose light recent recent recent recent recent recent exact ensemble ensemble ensemble ensemble ensemble ensemble practical apply apply apply apply apply sense inference highly highly compare solve solve solve correspond converge converge converge converge achieve trans address address address background positions chain chain chain chain bounded bounded organization intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity concept invariant occur extended extended boundary demonstrate strength conclusion starting starting starting starting starting critical greater assumptions assumptions segment segment segment segment depend reward reward reward reward reward reward reward reward reward differences performs suggest hard presence characteristics characteristics characteristics intelligence intelligence start averaged averaged averaged derivatives acknowledgements suppose edges solving solving factors factors generating describes describes transitions transitions mathematical segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning pruning recall involves remaining easy events events minimization springer shift blocks blocks blocks blocks blocks select choosing independently focus expressed expressed review depending overlap transform transform evaluated approximations completely converges converges performing false false false false false false false false false false false false false false false boundaries tracking tracking tracking tracking calculate expect perceptual combinations formulation contour contour contour instances instances sciences determines determines prove uncertainty specifically candidate priors discussions determining determining middle society differ paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths included successful detect detect comparing road road road road refer refer verlag prob heuristic heuristic heuristic success interested follow criteria criteria strategies satisfy write highest intrinsic extend minimized minimized explore wiley difficulty difficulty difficulty difficulty difficulty rapidly put put put issues issues dataset dataset helpful scalar examine detectors proved workshop statistically cover cover understand fundamental fundamental fundamental contours contours contours contours contours contours contours necessarily integer integer integer analyze analyze obvious assumes assumes assumes observe observe detector detector explored explored explored explored explored shapes grouping arbitrarily submitted submitted submitted motivated defines smoothness defining failure briefly lies lies lies worse starts spatially stress sections satisfied precisely precisely desirable probable actor geometry geometry geometry geometry geometry geometry nsf geometric geometric geometric geometric geometric geometric geometric geometric geometric geometric questions improvements limits empirically leave leave detecting detecting detecting detecting detecting detecting rewards rewards rewards rewards rewards rewards requirement calculating characterize characterize branch branch branch reaches fall fall maximizes extensions extensions geman geman geman geman geman geman geman geman sophisticated conclude yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille specifies wesley lot trade representative representative representative representative notes addison optimizing optimizing recover recover branches branches branches branches branches branches labelled impossible impossible theories reaching establish fails kullback smith smith convenient imaging chance tools satisfying replacing contract hope removing reasoning effectiveness effectiveness intuitive alphabet alphabet alphabet heuristics heuristics heuristics heuristics heuristics substituting exploring embedding heavy combines james pruned von searching searching searching thomas thomas branching branching branching branching branching branching branching claim enable francisco francisco thin likelihoods summarize summarize stopped acknowledge limitation lem geometrical geometrical leibler break formulate tween par ease reject learnt learnt elementary bounding eliminating eliminating simplifying plate emphasize iri pearl pearl conversely emphasized anal geiger funded placing admissible admissible admissible admissible union port port port exploited ward simplifies mea helps demonstrating removes lecture laws laws january twenty quantify quantify quantify subjective hancock award rare rare konishi lying predictable minimax longest gence deter inst inst prune prune prune prune prune satellite addi terminology diverge clutter clutter clutter searched searched snow judge exponents zhu zhu zhu alization conver intel roads diverges throw membranes malik sual sual sual sual mined neighbours ticular ixi ixi discard subscripts comment gestalt gestalt survive survive survive survive survive survive spend till funding summarizing pol aerial substitutions quan aro iip sured subsections nary intuitions joined vax waste timization interscience generous ups straightfor llp patt discretizing daah detectability formulates logq numbering 
#@Coughlan_J,Yuille_A,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input function function function function function function function function function function function function function function function function function figure figure figure figure time set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output number number system system system system system system system system system system system error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state information information information information information information problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden based based space space space space space space space space space space space space space space space space space space space space space linear linear linear linear linear case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order systems systems systems systems systems systems systems systems systems systems values probability parameters noise noise noise noise noise noise noise functions method approach approach approach approach approach approach image processing processing processing processing processing processing control large analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms gaussian paper paper paper feature task methods methods methods fig step points field field features features features process process current problems high response show show show equation equation equation equation equation section line line line rule rule rule general general general general real approximation theory theory theory gradient gradient gradient gradient gradient experiments university university university computation computation solution independent independent independent independent independent independent independent log dynamics dynamics initial initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard computer terms terms science direction direction direction present present present activation activation activation temporal range range press press press nonlinear nonlinear nonlinear nonlinear outputs abstract back convergence convergence density references component due ieee ieee ieee ieee ieee ieee ieee positive procedure adaptive adaptive adaptive propagation mixture mixture mixture mixture introduction introduction hand estimation estimation statistical dynamic dynamic cost cost cost search search assume assume signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals signals prior chosen chosen chosen chosen part cases distributed expected expected equations proposed proposed observed finite simulations simulations simulations classes total total simulation human respect respect respect called called means means natural natural natural global global applications applications applications knowledge knowledge filter filter filter filter filter filter filter filter filter filter filter filter obtain obtain obtain original original vol vol vol vol vol specific define define compute proc proc determined gain gain gain gain discrete brain brain brain approaches approaches mit mit fields update update update update update update update train source source source source source source source source source source proceedings proceedings institute implementation implementation technique internal advances joint difficult delay considered cambridge cambridge cambridge computing equivalent equivalent directly directly full estimated estimated give condition derived randomly controller types processes measured covariance covariance covariance covariance assumption stable stable circuits circuits common effective generate generate main easily unknown coefficients coefficients coefficients technology technology transfer transfer transfer transfer transfer transfer transfer special special consistent consistent details iterations iterations sources sources sources sources sources sources sources sources sources sources description description description description improve advantage robust separate separate separate separate takes typical similarity sense sense sense sejnowski interest dimensions dimensions observations works solve solve differential differential differential achieve trans trans diagonal diagonal separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation symmetric generalized channels risk risk exists concept concept concept derivative derivative matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices predicted demonstrate hebbian operator measures measures numerical numerical designed designed propose propose taking assuming assuming ica exist exist exist introduce introduce introduce derivatives identification question reference explicit suppose suppose pro pro derive produces estimating laboratory stability stability implement implement easy easy easy develop develop develop mutual mutual mutual equilibrium minimization expressed review stationary estimator open open evaluate evaluate lee forms static partial filtering filtering calculate priori formulation bell bell blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind extension simplicity simplicity gamma sensor sensor sensor sensor efficiency uniformly society society efficiently plots refer refer procedures satisfy simplified simplified backward nips delayed observable maximization principles illustrates mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing jacobs satisfies presents remain updating updating rapidly kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman environments accurately divergence workshop workshop statistically measurement trace integer rank rank impulse algo separated amari amari amari amari amari mixed years residual residual developing theoretic derivation growing independence reasons sys filtered filtered filtered filtered commonly definite flexible leave leave employ employ employ anti proven marginal adjust enables logp boston june instantaneous instantaneous oxford japan rithm appropriately recover recover recover recover nat null null null nonzero enhancement kullback numerically adjusting adjusting moment exploit canonical canonical symposium substituting separating zhang zhang zhang zhang zhang entry realization yang enable permutation ahead ahead papers propagate ignore generalizing balanced pdf infomax posteriori dramatically rigorous email leibler validity validity dec formulate spatio param mutually cessing tems deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution fir statistic statistic covered det det eters nonnegative determinant realizations ally convolved convolved edition south cess cichocki cichocki cichocki cichocki cichocki cichocki cichocki cia decompose kong gij cardoso cardoso recovers nov comon suitably hong biomedical equalization equalization grown challenges cent noises multichannel demixing demixing demixing demixing demixing demixing demixing demixing demixing demixing demixing demixing namic arma equivariant equivariant shi riken riken innovation innovation innovation innovation innovation innovation innovation innovation innovation fundamentals parameterize choi lambert laheld elaborated unavailable tackle telecommunication varieties saitama wako ural 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#@Cichocki_A,Zhang_L,
#t12
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#*network network network network model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set networks networks networks networks networks networks algorithm algorithm algorithm output output system system system system system system system system system system state state results results results results problem models models models based based linear linear layer layer vector shown shown shown shown shown systems systems values noise noise noise functions functions unit unit unit distribution recognition pattern image image image image image image image image image image image image image image processing processing processing control control control control large large local local local local local test test patterns inputs inputs inputs inputs signal simple simple simple simple simple simple simple simple simple visual visual visual visual examples small size size size feature feature feature feature net net work cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step field field field field features level level current current current current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell random random random random random random memory response response response response response similar representation representation representation architecture architecture architecture architecture architecture equation fixed line images images images real real gradient gradient gradient gradient gradient obtained obtained obtained dimensional result university threshold computation solution research target computer node science direction direction direction direction direction direction presented presented present present present low nodes sets range range range range range range range range range range range range components components components outputs continuous sample abstract applied back density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog properties references due ieee ieee positive important introduction complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex circuit circuit circuit circuit circuit circuit parallel cost tion difference complexity variable spatial spatial spatial spatial spatial spatial spatial spatial spatial higher center previous type required multiple cortex cortex long long long long long long long long long long long conditions represent represent represent distributed distributed distributed expected chip chip chip chip chip chip chip scale finite ing ing elements elements feedback feedback orientation global global global global applications applications vol vol vol vol vol vol vol vol vol relative cross cross cross provide compute compute location perform perform perform active active experimental experimental experimental experimental experimental experimental goal related gain gain cortical power voltage voltage fields source selection department implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation version technique consists kernel kernel kernel kernel kernel represents bias layers layers additional additional solutions estimates design design design limit detection detection capacity significant significant vision vision vision vision levels levels provided finally processes biological achieved measured denote tested tested surface surface surface circuits circuits circuits circuits circuits short nearest implemented implemented implemented implemented generate supported vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel degree noisy including including including fit functional fully technology technology technology technology testing significantly edge edge edge edge edge edge edge edge edge segmentation segmentation segmentation structures mode mode mode operation operation operation operation principal direct direct inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition normalized normalized early light improved directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions directions reported reported lateral practical include include pixels pixels quadratic array array array array array engineering engineering interest works works tions tions tions smooth background locations modified grid grid grid grid grid grid grid grid grid gate grant intensity intensity intensity intensity alternative feed locally locally boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary demonstrate demonstrate strength strength conclusions interactions interactions designed integration presence reduction solid solid proportional selective selective plane plane plane plane plane plane plane plane plane van edges edges perception optical optical optical optical primary stability tuned implement implement physical electrical easy interaction integrated applying formed quality competition competition letters independently formation formation formation reconstruction reconstruction approximated constants processor processor diagram diagram calculation normalization purpose boundaries interpolation filtering koch figures kernels kernels kernels silicon currents currents contour contour contour contour contour contour contour contour contour contour contour recognize illustrated coupled absolute partially neighbors neighbors neighbors structural selecting selecting efficiently characteristic excitation excitation excitation excitation showing hold bar bar vary simplified simplified simplified cmos cmos cmos cmos cmos processors received received illustrates illustrates neighboring neighboring acknowledgments load extend extend bars selectivity selectivity selectivity selectivity selectivity powerful access access access access access access put optimized dual biases reducing links links combine contours contours contours gradients gradients voltages voltages voltages prototype prototype prototype portion noted extent extent electronic electronic electronic synthetic indicating ment ground orientations fairly adjacent spatially implementing implementing implementing implementing implementing implementing implementing directional directional directional directional directional directional directional transistors transistors transistors transistors grossberg grossberg grossberg localized robustness requiring pseudo tional axes axes fed detecting adjustable formulated resistive resistive resistive resistive resistive schematic summarized spread implements june room discontinuities discontinuities indices aligned fabricated fabricated fabricated interface acts controlling reconstructed reconstructed enhancement enhancement enhancement interconnected interconnected receptors inspired extending extending extending extending cellular cellular cellular cellular cellular cellular cellular cellular mail mos mos fan fan hyper hyper hyper hyper hyper illumination north capacitor spurious motivation motivation service combines james sim interconnections competing competing arrangement arrangement darpa diameter neuromorphic neuromorphic neuromorphic layout harris propagate fold adopted thresholding onr ccd radar street crossing ple shunting convolutional gaps gaps focal focal focal focal focal focal focal focal focal cooperative cooperative die convenience additionally ical quantized preserved subthreshold subthreshold interacting interacting oct argued acquired multiscale complementary rectified rectified rectified rectified intensities gilbert likewise williamson lighting functionality externally january august photoreceptors designs families loaded ers inhibited inhibited imple micro hopkins fabrication integrates excited thickness resolutions andreou ally interpolating parti optics symmetrical cooperation cooperation cooperation cooperation cooperation johns enhances curved curved bach aggregation mosis mosis bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs bcs filling filling subscript cauwenberghs cauwenberghs cauwenberghs cauwenberghs addressing addressing charles format aperture baltimore blocked dipole excessive excessive putation dispersion objectives clutter clutter clutter clutter jenkins converts demanding direc direc ece directionally directionally directionally excite nov superscript reactive schematically schematically rectification tiny viable lay boahen boahen symmetrically notational luo sponse news interconnects vittoz vittoz ori hexagonal hexagonal hexagonal hexagonal hexagonal hexagonal hexagonal hexagonal hexagonal veto orienta lat mingolla schaik gert gert scalable unidirectional opposing shrinks cluttered orien mirrors mirrors renormalization renormalization diffusive diffusive diffusive diffusive diffusive diffusive diffusive diffusive diffusive diffusive sar ambient cou spectively fills restore biolog succeeds jhu electronically electronically incurs tition optically pouliquen exert encompasses transac compe complemented inhi tationally polarized polarized bition muri simpli izing 
#@Cauwenberghs_G,Waskiewicz_J,
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data figure figure figure figure figure figure figure figure figure figure figure time time time time time set set set set networks networks algorithm algorithm algorithm output output output output output output number number system system system system system error error error error error error error error error error error error error state results results results results results information information problem hidden performance performance performance performance performance performance performance performance performance performance performance based weights weights linear layer layer layer layer layer layer layer shown shown shown shown systems systems systems systems systems systems systems values values values values parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight pattern point point single single single processing processing processing processing control large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate test analysis inputs inputs inputs inputs inputs shows shows signal signal signal signal signal signal signal signal signal signal signal simple simple simple simple simple paper paper examples small small size size size work cells cells cells cells process current current cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure problems problems random random high high high high high response architecture architecture architecture architecture architecture fixed line line line line line line line rule general general speech real real real real real term experiments experiments result computation computation research target target computer computer computer computer computer computer connections connections connections synaptic synaptic synaptic synaptic synaptic science phase phase activation activation activation nodes frequency temporal sets sets nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs abstract applied back back back find computational density density analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due ieee ieee ieee important adaptive adaptive adaptive adaptive adaptive adaptive adaptive propagation propagation introduction complex hand hand circuit circuit circuit circuit dynamic parallel parallel difference signals signals signals signals signals signals signals previous previous previous required required required multiple good good binary represent represent expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip forward forward scale finite simulations minimum minimum simulation simulation simulation simulation simulation multi multi multi multi multi called means factor potential potential potential applications applications applications applications applications applications applications applications applications applications applications filter filter vol vol vol vol vol vol vol represented represented compared provide provide proc proc proc active active active active active active active active active active active active active active active active active experimental experimental experimental experimental experimental experimental approaches voltage voltage voltage dependent source source source report report institute department implementation implementation synapses synapses technique consists consists consists advances layers delay delay delay delay delay delay addition experiment additional additional additional design design top effects effects bit bit bit bit bit conference requires significant world world world world speed speed speed speed basic basic basic channel channel channel channel channel channel developed developed developed developed developed developed developed area area lines path path actual actual actual provided processes backpropagation backpropagation backpropagation backpropagation backpropagation measured feedforward feedforward denote denote limited limited limited limited circuits circuits circuits circuits amount short synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse generate supported require main adaptation adaptation adaptation journal square vlsi vlsi makes development reduced technology technology block block block block transfer ratio ratio ratio ratio ratio ratio filters pre stored stored international bottom perceptron perceptron perceptron perceptron denotes resolution resolution resolution advantage pair pair reported reported reported practical practical practical introduced introduced side array engineering compare speaker speaker speaker speaker speaker speaker speaker speaker speaker differential differential achieve trans evaluation channels channels channels channels interval storage storage amplitude amplitude constructed horizontal studied digital digital digital digital digital digital digital derivative derivative feed flow conclusion reduce sigmoid sigmoid sigmoid sigmoid sigmoid designed designed designed integration integration external reduction reduction characteristics characteristics characteristics characteristics characteristics characteristics characteristics characteristics demonstrated demonstrated solid exist selective min connectivity acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acknowledgements reference van laboratory ann vertical changing modeled recall recall multilayer electrical easy spectral integrated integrated integrated minimization versus select select letters letters extracted communication controlled controlled showed lee lee lee lee lee lee lee constants updates updates updates processor processor diagram diagram diagram diagram measurements add add advantages advantages precision precision figures figures figures usa currents currents bell plotted columns middle post receives receives compact running simplified modular modular modular modular modular board board board board board board board board board board board board quantization cmos cmos chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips chips processors principles body unlike unlike poor poor essential requirements environments limitations ideal proper complicated voltages implementations implementations impulse der portion generates generates established devices residual residual advanced rows fairly slope slope floating majority diffusion correction worse nonlinearity nonlinearity implementing purposes desirable controls controls demonstrates summation greatly flexible offset offset offset axes axes conducted conducted lms lms lms lms lms capability capability capability capability capability capability capability capability capability capability car car car adjustable continuously switch limiting popular popular acoustics adjust electric electric inherent neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro neuro shaped distortion distortion distortion distortion distortion distortion distortion acquisition room analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue fabricated fabricated fabricated fabricated fabricated fabricated interface linearity null flexibility multipliers multipliers communications multiplier multiplier multiplier multiplier saturation ranges tools mos mos programmable programmable programmable resulted capacitor capacitor capacitor capacitor degradation degradation degradation tap alspector demonstration widrow propagated propagated interconnections multiplied young adopted severe severe incorporates creates medium personal quantized quantized peripheral resistor deep ijcnn maintained degraded douglas careful switched fir host harder electronics gilbert suffer amplifiers cubic dsp dsp worked accumulation advantageous distortions saturated allen capacitors fabrication fabrication hour engine resolutions operational offsets offsets poly characterizes receivers compensated compensated cho cho cho cho cho cho feasibility pin pin pin pin pin transaction watanabe microphone lsi proceeding propagates refresh refresh zone zone zone zone decoders cancel ito jung package package cummings multiplexing boards ministry canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling canceling cad converters converters converters tapped tapped tapped icnn dong etienne cancellation telecommunications contributed contributed faithful mips mips linearization backpropagated backpropagated fernando jayakumar lea unwanted specially interfaces negated negated collects pins pins choi choi choi quiet quiet quiet quiet loud loud loud loud loud loud loud korea korea spiegel distributes mcps installed interfaced cancelling soo dispersive ofleee holt anc winston 
#@Cho_J,Lee_S,
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#*network network learning learning learning learning learning learning learning learning neural neural neural input input input input input input input data data data data data data data data data function function function function function function function figure figure figure figure figure time time time time time set networks networks networks algorithm algorithm output output output output output output output output output number number number number number system system error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error error state state state state results results results information information problem problem models performance performance performance performance performance performance performance performance performance performance based based based based based space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer layer layer case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order shown shown shown shown systems systems values values probability parameters noise noise weight weight approach approach approach point point point point single single processing control control large rate rate rate rate analysis optimal optimal inputs inputs form form form form shows shows shows signal signal signal signal signal signal signal signal signal signal algorithms simple simple paper paper paper paper small small net work work work task methods fig cells cells step step points features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process current current current current current current current current current current current trained cell cell cell cell cell cell random high high memory representation architecture architecture architecture architecture section fixed line line vectors vectors general parameter real approximation average gradient gradient term term term term term term term term term term note activity dimensional dimensional university university threshold threshold threshold solution research table table table table table table table table table table table computer terms terms terms terms distance distance distance node node node prediction prediction prediction prediction prediction prediction prediction prediction left presented present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low low low low low low low frequency machine sets maximum maximum maximum range range range press components outputs outputs outputs continuous sample sample sample sample abstract applied computational density analog analog analog references component due due due due due due ieee ieee ieee ieee positive procedure procedure procedure adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive mixture context introduction complex circuit circuit circuit circuit circuit circuit effect dynamic generated parallel cost recurrent search search search search energy energy difference difference difference complexity complexity classifier lower measure measure measure measure signals signals representations representations chosen chosen part part previous previous previous previous type required good long long long conditions conditions expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip techniques techniques correlation length correct correct correct errors errors forward scale minimum minimum resulting classes ing simulation simulation simulation simulation simulation multi means factor dimension dimension dimension dimension dimension dimension natural filter negative original original relative relative relative samples samples represented compared compared compared application application application cross cross cross series provide provide provide determined determined determined determined constraints gain discrete equal power power power power power power power power power approaches mit voltage voltage voltage steps steps steps accuracy comparison comparison comparison larger larger support support descent morgan proceedings implementation implementation implementation version technique consists consists consists code represents final bias delay delay scheme scheme scheme scheme domain curves curves design design stage stage stage stage stage effects bit bit bit detection detection conference determine determine determine full requires significant significant significant significant approximate estimated basic pages pages pages channel weighted levels criterion criterion bounds bounds area types path provided provided provided provided provided provided provided processes nature sampling sampling sampling sampling sampling achieved achieved achieved achieved achieved measured normal feedforward describe describe transformation transformation limited limited limited close corresponds corresponds corresponds corresponds circuits circuits circuits circuits circuits amount short short short common effective implemented implemented require adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation journal square square end end vlsi vlsi vlsi ability including pairs pairs pairs pairs reduced account unknown coefficients coefficients coefficients coefficients mlp block block block block block ratio ratio ratio ratio increasing increasing increasing increasing trials matching matching matching matching matching matching matching matching matching matching matching matching matching matching principle squared squared squared squared squared max filters window window stored bits bits bits bits bits international supervised magnitude magnitude combined produced added perceptron denotes improved discussed pair separate separate takes takes reported lateral apply period side quadratic engineering engineering previously previously unsupervised approximately approximately calculated volume volume works tuning solve match match match match match match match match correspond differential differential differential differential differential differential trans interval increased amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude lead invariant invariant invariant invariant invariant invariant digital digital digital digital digital derivative derivative predicted alternative hybrid boundary setting pass half conclusion greater reduce reduce segment editors central measures numerical numerical numerical designed peak asymptotic weak weak weak hard cycle characteristics solid solid solid turn averaged base acknowledgements reference reference appears index index index winner laboratory metric implement implement multilayer linearly electrical electrical electrical electrical electrical remaining remaining scales scales integrated integrated shift shift shift shift shift shift shift shift shift implies blocks blocks blocks blocks blocks blocks blocks versus letters choosing focus depending depending stationary influence variation variation variation transform transform transform transform transform transform transform controlled controlled restricted updated showed similarly diagram diagram diagram diagram diagram calculation measurements expansion reduces iterative closed filtering sufficiently euclidean euclidean classified classified transactions precision precision precision precision avoid avoid avoid avoid recorded building building building building existing existing template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template box figures includes thesis currents inter blind blind blind blind automatic specifically variations variations variations variations absolute compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression compression middle differ encoded encoded encoded identify detect detect literature invariance fine reached summary summary success issue timing device device sampled sampled sampled sampled sampled usual backward backward backward providing providing nips giles quantization quantization cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos cmos leading chips illustrates subsequent operating load law body simpler stimulation transformed transformed transformed poor perturbation perturbation circuitry involving limitations biases behaviour matches matches matches successive giving school rest mappings muscle transistor transistor authors stream variability matched neu coarse coarse coarse coarse coarse coarse coarse coarse coefficient coefficient coefficient coefficient adapt integer onset opposite implementations adjusted aspect aspect noted taylor detector detector logic generates detected detected detected simplest phd attempts averages charge devices residual residual indicating ment ment adapted adapted capabilities capabilities correction considerable lin implementing filtered filtered choices transistors transistors inversion inversion inversion separately separately separately recording recording bandwidth alignment alignment alignment alignment alignment alignment conjugate evaluating offset amounts capability capability cohen item passed remove remove continuously continuously templates templates templates operate synthesis incoming incoming prevent suited suited achieves adjust richard enables enables chose implements patients patients patients wang wang wang wang june summed distortion ordinary indices aligned analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue analogue fabricated fabricated summing summing summing drift tem saturation khz khz adjusting mos mos loops loops biased biased ral shifts exceeds wilson evaluations evaluations evaluations evaluations introduces patient patient patient patient patient patient negligible negligible mental enhance heart heart heart heart heart heart heart heart heart heart heart accounts facilitate facilitate advance mlps eng record relies impact impact implicitly tures std std influences influences switches lag lag lag accumulated accumulated treat ure compressed incorporates poses feeding residuals residuals residuals jabri jabri jabri jabri jabri constitutes rhythm rhythm australia australia australia principe exponent exponent shifting conduction subthreshold mhz magnitudes compensate continues denoting intra intra plate transconductance distinguished funded electronics suffer book minor meet loading loading flower flower elsevier normalised normalised normalised normalised normalised differing struc corrections signs experi achievable council consuming january monitor australian designs loaded adaptively supply err morphology morphology morphology morphology optimisation converter converter calculates conversion conversion exclusively andreou manipulated detects classi attained bandpass reproduced consumption consumption safe safe mosis constraining sian dimen fidelity resultant subscript lags lags deter positioning gaus cauwenberghs fication comparator signed compromise jitter jitter jitter derives adequately excessive monitored col ripple configured tolerant align align align align align rhythms rhythms sydney sydney sydney sydney abnormal abnormal inability minimise minimise minimise minute ample capacitive capacitive aliasing puted nth cardiac feeds specifications dev dev mined beat beat beat beat beat beat beat beat beat beat transfor rail rail raymond ecg beats beats beats beats beats beats beats beats beats beats minimising diode tab raise reductions ventricular bucket bucket optimise ware avail morphological morphological optimised optimised minimisation marwan marwan wells sional squaring squaring squaring squaring brigade brigade targeted tachycardia tachycardia tachycardia compensating pur photomicrograph ultra bob bob quantised dummy sedal conserve duty mll pacing mirrored mismatches mismatches excludes excludes ential minimised minimised utilised 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#@Coggins_R,Jabri_M,Wang_R,
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#*network neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data function function function function function function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time set set set set set networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output number number number number number number number system system system system system system system system system system system system error error error error error results results results results results results information information problem performance performance performance performance performance performance performance performance performance performance performance based space case case vector vector order order shown shown shown shown shown systems systems systems systems systems systems values values values values values values values values values values values values values values values values values values values probability noise noise noise noise noise noise noise noise recognition recognition recognition recognition recognition method method method method method method method method method pattern pattern pattern point point point single processing processing processing processing processing processing processing processing processing large large large rate rate test test test test class class class class class class class class class class class class class class class class class class class class class matrix matrix optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form form form form shows shows shows signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple simple paper examples examples examples examples examples examples examples small size size task task task methods points classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process level current current structure random random high high high similar representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture equation equation equation equation section section section fixed general general speech speech real average average term term note note experiments result result result university university threshold threshold computation computation computation computation solution solution solution solution log found found found found constant constant constant constant constant constant constant constant constant constant table table table table table table table table standard computer terms map low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency maximum maximum maximum maximum maximum maximum maximum range range learn outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous abstract applied applied applied find density analog analog analog analog analog analog analog analog analog analog analog references component due due due due due ieee ieee positive positive positive positive decision introduction hand hand circuit circuit effect effect effect effect dynamic tion tion tion energy energy energy energy difference difference difference difference difference difference difference difference difference difference difference difference complexity assume classifier classifier signals signals signals signals representations representations learned chosen chosen chosen chosen part center center center center center center center previous previous cases cases type required required cortex cortex binary binary binary binary binary binary binary binary binary binary binary binary binary binary long represent expected make fact fact fact fact proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation length length errors scale scale scale simulations simulations simulations minimum classes classes classes classes classes classes ing ing ing ing tasks total total total simulation simulation simulation simulation simulation computed respect sum sum performed performed elements elements elements factor optimization optimization optimization made made applications knowledge filter filter filter filter filter negative negative negative original original relative specific samples samples samples samples true compared cross cross cross cross provide compute rates rates location perform determined determined determined determined determined determined experimental goal goal goal goal related constraints constraints connected gain gain gain gain gain gain gain brain equal power power approaches steps accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy train train train train dependent dependent implementation implementation implementation implementation implementation implementation implementation implementation exp addition graph considered computing computing computing computing domain domain domain equivalent experiment directly directly directly curve additional additional additional design bit bit bit bit conference conference determine determine efficient requires choice choice significant significant significant world validation validation channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel developed levels levels area evidence nature depends measured denote limited corresponds stable circuits circuits circuits short short short common common implemented implemented assumed assumed generate generate require end vlsi vlsi vlsi vlsi easily easily degree development sensory including auditory auditory simulated simulated hopfield reduced reduced coefficients coefficients technology interesting interesting interesting significantly ratio segmentation mechanism mechanism mechanism matching database database database database database mode mode representing representing pre direct window bits bits bits bits international international normalized normalized normalized normalized magnitude minimize added added added description light light architectures improve correlations correlations pair robust element element typical typical reported reported practical introduced array array engineering previously volume tions tions solve yields yields yields speaker match differential trans diagonal diagonal diagonal diagonal evaluation evaluation evaluation evaluation positions channels channels channels channels channels channels channels channels channels channels storage storage parts suggests digital digital digital digital derivative loop white white column column column column hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware runs half half half half conclusion conclusion starting starting minimal row row row row greater conclusions valued valued valued valued valued differences differences differences differences differences differences differences differences differences differences differences differences accurate performs encoding taking taking hard mechanisms presence physics reduction demonstrated minimizing decrease averaged averaged averaged averaged derivatives acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic force base question digit produces written longer ways primary laboratory distinct implement averaging averaging electrical transformations transformations remaining frequencies events events events shift yield yield choosing choosing correlated evaluated evaluated evaluate evaluate forms margin sign reasonable calculation smoothing normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization event roughly roughly add add iterative iterative closed remains remains filtering filtering norm classified classified transactions recorded recorded template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template template combinations combinations combinations priori instances illustrated maximize maximize specifically variations tests major simplicity reason extra efficiency presentation detect efficiently schemes issue running running content built sampled simplified surround surround surround surround surround surround nips nips quantization delayed leading automatically preferred neighboring neighboring decreasing simpler simpler transformed transformed transformed investigate strengths strengths optimized optimized limitations issues reducing investigated possibility scaled reliable reliable reliable proper complicated proved proved affect encode removed coefficient coefficient plausible implementations prototype obvious obvious freedom observe baseline baseline mixed arbitrarily electronic years pairwise pairwise pairwise pairwise pairwise band band formula agreement multiplication caused processed processed snr implementing implementing sections producing desirable cut cut sounds recording depicted alignment robustness robustness improvements improvements greatly greatly cochlear led transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient transient lack introducing recordings rep reliability templates templates templates templates templates templates templates templates templates templates templates templates templates templates calculating switch gains gains gains gains gains gains differs reaches tank decreased wang june june instantaneous realized contribute classifying spectra newton aligned aligned redundant ear assign tation optimizing optimizing optimizing optimizing unity addresses tem impossible fits adds consideration numerically chance adjusting overcome mail logarithmic affected capacitor exceeds exceeds symposium symposium spurious meaningful excellent mance ensures periods periods periods loo loo surprising perfor washington demonstration mel dif smoothed mem omitted omitted bins bins bins bins bins bins bins bins shortest belonging variants variants verify multiplying multiplying multiply multiply linked audio audio maintaining drop drop slight slight largely minus connec medium medium additionally acceptable spaced spaced affects possibilities representa quantized mammalian compatible careful plate guided rectified drawback covered denver transients transients transients transients transients compu pineda pineda pineda pineda pineda pineda pineda spite spite spite achievable algorithmic quadrant quadrant prefer virtually hopkins hopkins hopkins eral core accumulate dedicated contributes chan modalities ory lowpass lowpass johns johns bandpass bandpass bandpass bandpass neurobiological consumption safe amplified amenable accounting cutoff cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs cauwenberghs addressing nominal doubling baltimore ous tim ference kong plastic drawbacks preferable repeating neigh transferred ece hong tailored resentation saved rectification cir edwards edwards edwards edwards edwards edwards edwards intervening digitally digitally disk thirty thirty previ taps onsets tar simu lations implication critically correla omitting aligning correlator correlator correlator correlator correlator correlator correlator correlator correlator sev realizing logarithmically silence silence silence ware fernando fernando gert gert clicks doubled impulsive shamma differencing differencing differencing differencing timothy raphson nels jhu cont automate sixteen cuits filterbank unnikrishnan plementation plementation acceptably iscas iscas modifica everyday viously boring monterey laurel compromising 
#@Cauwenberghs_G,Edwards_R,Pineda_F,
#t12
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#*model model model model model model model model model neural neural neural neural neural data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set set set set set networks algorithm algorithm algorithm output output output output number number number system system system system system system system system system system system system system system system error error error error state results results results information information information problem problem problem models models models performance based based based based linear linear linear case case case case order systems systems systems systems systems systems systems systems systems systems systems parameters noise functions neurons method approach approach approach approach approach point point image image image image image image image image single single single single processing processing processing processing processing processing processing processing control control control control control control control control control control large large large large analysis inputs inputs inputs form form form form form shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual paper small small small small small small size size size work task task task cells cells field field field field field field process process process level level current current structure problems high high high high high high high response response similar similar representation architecture architecture equation equation equation equation equation equation section section fixed line line line line line line line line line line line line line line line line line line line line line line line real approximation average average experiments activity dimensional university university university university threshold threshold threshold threshold computation computation computation computation computation computation computation computation computation solution solution defined target target target target target target target target target target target target target target table table estimate standard standard standard computer computer computer terms terms science left direction direction presented presented presented presented presented presented map map low low low low low low low low nodes frequency frequency frequency temporal temporal machine object object object object object object object sets motion motion motion motion motion motion motion motion motion motion motion motion motion press press press position position position position position position position position position position position components components outputs outputs outputs abstract back find computational computational computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due due ieee positive decision decision introduction action complex complex complex hand hand circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior stimulus effect generated parallel parallel cost change change change difference difference variable spatial spatial spatial signals signals signals signals chosen chosen higher center previous required required required multiple binary conditions represent expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip errors errors tasks total computed computed multi performed performed performed performed factor factor made made natural orientation orientation global vol vol vol vol relative relative samples true compared application provide provide provide define compute compute proc location location location location location eye eye eye eye eye determined connected connected gain motor motor motor cortical power power power power power power power power power approaches approaches approaches voltage voltage voltage larger larger contrast contrast contrast contrast dependent modeling implementation implementation implementation implementation implementation implementation implementation implementation implementation implementation version advances difficult layers layers layers addition maps cambridge cambridge environment directly view view view view view view solutions curves design design top bit bit detection detection detection detection detection detection approximate world world speed speed speed speed speed speed speed speed vision vision vision vision vision vision vision channel coding weighted robot robot robot velocity velocity controller lines product provided provided provided provided finally simply biological biological biological increases tested fast fast fast fast fast fast fast fast limited limited close circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits implemented implemented implemented implemented theoretical require eds eds eds vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel development including auditory combination technology block edge edge edge edge edge edge edge edge edge edge edge head mechanism mode operation pre direct making making making window normalized early early magnitude attention improved population discussed robust movement strategy moving moving moving moving moving moving moving machines pixels pixels pixels pixels pixels pixels pixels sense array array array array recently engineering axis axis smooth smooth correspond address address positions positions locations grid grid grid grid grid organization organization improvement amplitude exists parts intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity digital digital digital digital digital digital digital digital digital digital digital digital digital derivative derivative hybrid hybrid width loop white column column column column column column column hardware hardware hardware pass runs runs conclusion row row row row row row greater segment operator modules retina retina retina retina retina retina retina retina retina retina designed suggest strong external characteristics characteristics characteristics proportional pulse movements min plane plane plane plane plane plane plane plane plane plane relationship targets targets targets targets targets targets derivatives program force appears appears relation van edges edges edges solving primary generating laboratory mathematical mathematical dept dept dept implement implement implement sensitivity coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates coordinates simultaneously simultaneously angle develop integrated events formed implies competition decreases extracted focus communication communication controlled lee modulation completely completely processor diagram key earlier slow performing performing normalization combining event boundaries boundaries tracking tracking tracking closed closed generation generation valid distances foundation koch koch koch degrees avoid silicon silicon coordinate coordinate formulation currents blind blind instances determines activated activated activated activated activated coupled black black sensor sensor compression aspects driven driven tend composed summary traditional traditional compact compact compact compact compact compact compact success superior superior superior superior superior superior superior superior superior superior superior superior superior superior running follow gray cues built list involved usual localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization cmos chips chips chips moves moves moves deal software oriented presents remain powerful circuitry mead mead mead environments humans reducing ideas detectors detectors detectors detectors int ideal ideal muscle combine scaled decisions trace trace voltages voltages voltages implementations der portion portion detector academic mixed mixed mixed mixed mixed mixed simplest attempts years great developing asynchronous sensors sensors sensors sensors sensors sensors track track track track track track track track navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation biology capabilities handle ganglion turns turns drive drive rapid straight implementing day worst cut cut scientific inversion angles attribute read computers auto auto auto researchers robustness requiring considerably fed quantitative autonomous autonomous autonomous autonomous autonomous autonomous autonomous autonomous car car car recordings treated resistive resistive resistive sharp schematic schematic schematic schematic maintain maintain requirement switch switch switch switch switch ordered realized realized realized pose gap picture acquisition benefit physiology labeling forming forming saccadic saccadic saccadic saccadic saccadic saccadic saccadic drift narrow approximates controlling controlling eliminate flexibility suppression cellular smith primate logarithmic mos determination resistance resistance vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle vehicle neurobiology star receiver guide obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle obstacle started combines overview overview infinity centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid centroid neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic offer saccade saccade saccade saccade saccade saccade cpu saccades colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus colliculus subsequently subsequently subsequently instructions avoiding avoiding thresholding switches switches switches switches switches switches switches switches outlined ccd escape skills maintaining crossing crossing crossing constitute kluwer creates ram focal focal focal focal focal focal focal focal focal focal obstacles obstacles obstacles obstacles forced responds trigger acceleration affects england associate laplacian realize realize realize illustration brightness mhz robots interact activate activate activate mediated altered argued fixation projecting intensities denver crossings crossings crossings barlow barlow resistors resistors suffer mimic mimic places avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance avoidance vanishes dsp steering steering steering steering steering priority radio radio triggered triggered triggered triggered triggered factored persistent lighting functionality corners corners spring loaded locate focuses capacitors micro micro hopkins hopkins fill hamilton morris illinois anatomy floor believed impedance laser normalize measurable grids optics artifact johns johns daily implied reality consumption senses cold deweerth deweerth deweerth deweerth essence enters motors motors baltimore baltimore promise zones decades zone zone zone zone replicates horiuchi horiuchi horiuchi iris orbit walking primates ece ece locating activating activating vdd rom ascending lens cummings cummings cummings cummings cummings pushed foveated foveated foveated engineers organisms boahen boahen earliest converting parasitic latch converters circumvent textured highlight disconnected etienne etienne etienne etienne etienne etienne cameras ralph wheel accelerate equipped equipped handles accelerated asynchronously asynchronously vehicles buffers follower follower mueller steer departure realizing realizes indoor compatibility ubiquitous slowing ismail persons atlanta lastly lastly masked collisions isolate isolate mimics tape backgrounds summations navigate symp newell microchip sparks sparks sparks accelerating spiegel oscilloscope oscilloscope dream offering harbor speeding slowed worm scalability outdoor compactness interfaced interfaced interfaced windowed programmability maker latches latches latches itc itc itc itc itc itc itc mimicking microcomputer rudimentary iscas staying centtold prospect broadcasts prototyping 
#@Etienne-Cummings_R,Ghani_M,Gruev_V,
#t12
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#*model model model model model model model model model model model model neural neural neural neural input input input input input input input input input function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time set set output output output output output output output output output output output number system system system system system system system system system system system system system state results results results results results results information based based space order order order shown shown shown shown shown shown systems noise functions unit unit single single single single processing processing processing neuron neuron neuron neuron neuron neuron neuron test test test test test test test analysis analysis shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple visual paper paper small work work fig process structure structure structure high high high high high response similar representation show equation section section fixed fixed fixed fixed line line line line line speech speech real theory dimensional result result result university university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation research log defined constant estimate computer terms distance distance distance distance connections synaptic direction direction direction direction direction direction direction direction direction direction direction phase phase low low low low low frequency frequency range range range range range position position position components outputs abstract applied computational analog analog analog analog analog references due adaptive adaptive adaptive adaptive adaptive adaptive adaptive adaptive introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior generated generated cost tion tion tion change energy energy difference difference difference difference difference difference difference spatial spatial measure signals signals signals signals signals signals signals signals signals signals signals signals signals representations chosen higher required binary long expected chip chip chip chip chip chip chip region proposed proposed length length ing ing simulation simulation simulation simulation human human human human computed called times regions mapping mapping potential made applications study filter original original original vol specific specific compared provide provide proc location location location location determined determined related related voltage voltage voltage voltage accuracy larger dependent dependent source source source source source source source source source source source source source source source source source source source source source source source source department implementation implementation version represents represents exp bias bias bias delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay addition computing computing environment design effects detection detection detection detection detection requires significant significant speed basic pages increase produce derived developed path path path path actual actual actual provided depends depends biological increases increases describe tested limited complete complete complete surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface surface circuits amount effective implemented implemented shape generate supported role role role theoretical theoretical require vlsi vlsi vlsi future easily auditory simulated needed account block block transfer interesting head head head head head head segmentation mechanism special special special database principal representing details filters filters filters direct direct direct direct direct direct direct inhibition inhibition produced sources improved discussed discussed directions directions resolution resolution resolution typical typical introduced moving moving moving period engineering dimensions sufficient varying axis axis speaker speaker speaker speaker speaker speaker studies achieve rl rl trans chain chain chain locations locations amplitude horizontal horizontal intensity intensity intensity studied feed width width width hardware pass pass pass pass half conclusion segment differences accurate designed designed sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound encoding propose taking taking mechanisms external external external external external demonstrated solid labeled labeled labeled pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse turn assuming plane plane plane plane relation pro longer longer perception generating generating generating generating generating generating generating generating generating generating generating generating generating label label label vertical vertical segments student simultaneously simultaneously physical electrical unique develop integrated frequencies frequencies events events events events events john decreases decreases extracted expressed overlap solved completely constants constants constants diagram diagram diagram delays delays event event event valid distances degrees expect recorded recorded recorded fire box includes silicon silicon silicon silicon thesis determines determines specifically successfully successfully middle aspects receives composed composed composed composed excitation excitation excitation refer soc soc soc success running duration cues cues cues cues built comp localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization simplified delayed cmos cmos cmos computes computes received moves moves acknowledgments transformed circuitry circuitry circuitry circuitry mead mead humans humans humans dotted dotted preliminary respond ideas office office complicated complicated encode encode surfaces surfaces surfaces surfaces measurement measurement measurement onset onset onset onset onset onset onset onset onset onset onset onset analyze opposite voltages impulse impulse impulse impulse impulse impulse detector mapped nervous speakers speakers detected phd neal charge band derivation biology caused caused caused caused caused worse london turns arise controls watkins sounds sounds sounds sounds sounds pitch recording depicted depicted depicted depicted depicted geometry nsf researchers varies varies composite composite led led led led led led led led led fed fed recordings detecting detecting detecting detecting detecting remove music characterize fall incoming serve plan replace display display display segmented shaped physiol owl cochlea cochlea cochlea cochlea wesley lab lab ear ear ear ear ear ear ear ear ear addison fabricated fabricated fabricated amplifier amplifier flexibility theories suppression inspired inspired smith ranges contract serves exceeds exceeds fires tap introduces negligible von von von moved arrangement dif viewing multiplied neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic lazzaro record environmental properly relies subsequently harris harris harris thresholding displacement acknowledge onr discriminate discharge ure drop latency encodes encodes bank possibilities principe principe principe principe reflected barn verified subthreshold relating emphasize echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo depicts ambiguous setup setup setup setup setup discusses responding knudsen amplification amplification ward echoes echoes echoes echoes gratefully fiat fiat fiat fiat fiat acoust acoust autocorrelation autocorrelation synthesized inhibit adaptively interaural interaural interaural played reflecting suppress fabrication award connects wavelength wavelength wavelength konishi detects detects detects offsets ray arriving iid reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection reflection mosis sis thresh thresh thresh blocked microphone microphone microphone microphone microphone microphone microphone microphone microphone microphone microphone microphone microphone microphone ears ears proceeding jose decode richer elevation elevation direc cancel sends sends jung jung localize localize localize localize localize rom albeit blasdel viable picks itd itd mag taps onsets suppresses suppresses suppresses azimuth icnn concluded binaural compose chiang chiang confused extraneous shoulder shoulder inspiration walls lacks reflections reflections reflections reflections reflections reflections reflections sponses transfers unwanted unwanted unwanted unwanted unwanted unwanted specially shadow envi spe amplify attenuated ser florida florida skip vides correlators correlators correlators correlators correlators amplifies amp resetting resetting ronment cially alx straightfor torso torso signifying gainesville gainesville decodes decodes fer mip ferences 
#@Harris_J,Principe_J,Pu_C,
#t12
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#*neural neural data data data data data figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output output output output output output output output output output output output number number number number error results information information information information information problem based space case case case vector vector vector vector vector vector vector order order order order shown shown shown shown shown shown shown shown shown shown shown shown shown shown systems systems noise noise point point point point point point point point point point point point point point point point point point point point point image image image image image processing processing control control control large large large local local local local local local local local local rate rate rate shows signal algorithms simple simple visual visual visual visual visual visual visual visual visual visual visual visual small small size work work points points points points points points field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field process current current current current current current current current random high high response similar similar similar show show equation equation equation equation section section fixed vectors general general parameter real real real real real real real real real real approximation average average note note note experiments result computation computation computation computation computation computation computation computation computation computation computation computation solution solution research research research research research independent independent independent defined constant computer computer computer computer computer computer computer computer science left left direction direction direction direction direction direction direction direction direction direction direction presented presented presented presented presented present present low low temporal temporal machine motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range position position position position position components components components components outputs outputs continuous abstract applied applied find analog analog analog analog analog analog analog references component component component component due due due due due positive positive positive important introduction complex complex stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus generated generated generated generated generated generated parallel parallel parallel parallel parallel parallel tion difference spatial spatial spatial spatial spatial spatial spatial spatial part center center center center required good long long long long represent expected equations equations equations equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make fact fact correct correct resulting resulting computed computed computed computed respect sum sum sum sum sum sum sum sum sum sum sum sum sum factor orientation applications negative negative artificial artificial relative relative represented provide provide compute compute compute compute compute compute compute location location location location location equal power power power power power power mit voltage voltage voltage larger contrast contrast contrast fields fields fields fields fields fields source proceedings proceedings report institute institute implementation implementation implementation implementation implementation individual individual individual advances represents final considered cambridge computing computing computing environment directly directly directly directly directly view view design determine requires requires speed vision vision vision vision basic pages pages increase increase increase produce robot area velocity velocity velocity types nature simply measured discussion normal normal normal normal normal increases assumption assumption assumption corresponds corresponds corresponds corresponds stable implemented shape generate supported journal square vlsi vlsi vlsi vlsi vlsi vlsi vlsi pixel pixel pixel pixel pixel pixel pixel pixel pixel combination combination combination reduced reduced coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients fully fully fully fully technology technology significantly projection edge edge edge edge edge edge increasing consistent mode operation representing details international magnitude sources denotes denotes architectures improved directions resolution robust robust robust robust robust robust separate introduced moving period period period period period pixels pixels pixels pixels pixels pixels pixels array array array array array array array array array array array array array recently recently engineering engineering dimensions highly previously approximately approximately calculated calculated calculated calculated calculated calculated calculated volume axis axis tions yields yields address locations locations locations symmetric generalized grid grid grid grid bounded sensitive entire increased exists parts intensity intensity intensity intensity expression invariant suggests extended rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation touretzky column hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware demonstrate flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow strength row row row editors measures measures measures clear practice encoding integration integration integration integration demonstrated california intelligence radial exist decrease scene program areas derive longer optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical primary generating estimating laboratory implement implement averaging angle unique unique integrated integrated integrated integrated integrated integrated integrated integrated springer extraction decreases national focus focus focus focus focus focus focus focus expressed expressed review depending variation variation variation variation evaluate centered centered similarly similarly similarly processor processor processor processor sign sign sign sign sign sign sign sign sign sign sign sign sign calculation calculation performing measurements measurements expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion expansion sec combining iterative remains remains foundation koch koch koch koch koch koch koch precision template coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate currents currents currents contour contour contour contour discuss mozer absolute neighbors discussions columns determining sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor suitable effectively detect detect detect compact conf verlag built quantity quantity quantity quantity involved cmos cmos cmos cmos cmos correspondence computes computes computes moves acknowledgments software software software receive situations remain stimulation stimulation varied varied varied varied humans integral integral integral integral integral integral periodic respond tech detectors int transistor scaled authors office variability variability func circles circles circles circles measurement opposite voltages singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular singular quantities quantities quantities quantities detector detector serial attempts defines massachusetts indicating rows sensors sensors sensors sensors sensors sensors sensors sensors sensors sensors navigation biology briefly spatially spatially ring precisely precisely division located located leaves leaves sgn geometry radius radius radius integrating reflects varies lack autonomous autonomous psychophysical adjustable requirement reaches reaches qualitatively pasadena suited sums decreased decreased summing summing velocities recover null purely purely purely unity unity unity unity impossible naval caltech caltech spiral spiral spiral spiral vehicle serves wire affected intuitively arrays continue connect dominant hasselmo viewing express neuromorphic creating contact contact subsequently balanced ccd rms rms crossing crossing crossing visually pointing creates uniquely expanding expanding expanding expanding expanding expanding expanding expanding expanding expanding trigger perceived letting mismatch community interact continues mathematically maintained elementary elementary elementary guidance guidance relating concentrate individually guided topic crossings rotating rotating rotating rotating rotating rotating rotating drops intensive ward article mix mix mix mix scanning stops covers heading heading heading scanned scanned stimulating photoreceptors inhibit inhibit suffers suffers virtually locate utilizes fabrication integrates compo sen periphery periphery periphery periphery periphery periphery periphery consumption consumption consumption consumption iti iti iti periodically relaxed zeros zeros charles aperture tained platform recovering decades christof ted relax relax prolonged direc nents clockwise saturates saturates saturates cir kramer rightward emulate begun ously volumes inhibits continu persistence persistence gra partic wheel unrealistic triggers vehicles higgins higgins higgins higgins higgins nical dropping counterclockwise sor replicating crossed crossed crossed persist radii radii radii radii radii radii contracting dominating dominating dominating dominating positivity deutsche chuck warren dxdy integrative quanti equate irregularities orthogonally cles compressive mus 
#@Higgins_C,Koch_C,
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#*network network network network network network network network network network network network network network network network network network model model neural input input input input input input input data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time set set networks networks networks networks networks networks networks networks algorithm output output output output number system state state results results information problem problem problem problem problem problem problem space space space linear linear linear linear layer layer layer layer layer case case vector vector vector vector vector order order shown shown shown shown shown systems values values values noise weight functions approach approach approach pattern point image image image image image single single single single single single single single single processing processing control large local local local local local local local local local local neuron shows shows signal signal signal signal signal algorithms simple visual paper small small small small size size size net net net work work task task methods methods methods methods cells cells cells cells points points field field process current current current current cell cell cell cell cell cell cell cell problems high high high response response response similar similar show show equation equation equation equation equation equation equation line line line rule vectors vectors images parameter approximation approximation theory theory gradient gradient gradient obtained obtained dimensional university university computation computation computation computation computation computation computation computation computation computation computation solution solution solution solution solution solution solution solution solution solution defined found constant constant constant constant standard standard computer computer computer terms node node node node left left direction presented low low low low low nodes nodes temporal temporal temporal temporal machine object object object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum range range range press press components components components components outputs continuous abstract applied applied find find computational computational computational computational computational convergence analog analog analog analog analog analog analog analog analog analog analog analog analog properties properties properties references component component ieee ieee positive positive important adaptive adaptive complex hand circuit circuit stimulus stimulus parallel parallel recurrent recurrent tion change energy energy energy energy energy energy energy difference difference spatial spatial spatial spatial spatial spatial spatial spatial measure signals higher higher higher type binary binary conditions represent represent equations equations equations equations equations chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip proposed proposed correct correct finite minimum minimum minimum tasks total computed computed respect mapping means feedback feedback feedback feedback orientation global global global global global global global global global global knowledge knowledge obtain negative negative negative negative negative negative artificial relative true compute compute compute compute compute objects objects objects location location goal related constraints constraints constraints connected connected discrete discrete discrete power power mit voltage voltage voltage larger contrast contrast contrast connection descent descent dependent report report report report institute institute implementation implementation implementation implementation implementation implementation technique consists advances represents layers scheme ai computing computing computing equivalent environment additional additional view solutions solutions efficient full requires requires significant speed vision vision vision vision vision vision vision vision estimated pages pages con condition condition velocity velocity lines actual actual finally nature nature depends sampling constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint biological biological achieved normal normal normal normal technical limited limited inverse assumption assumption assumption circuits nearest common effective implemented implemented implemented implemented require require journal vlsi vlsi easily degree noisy functional functional functional functional functional functional technology interesting interesting ratio projection edge edge principle principle leads leads leads representing early early minimize choose architectures improved resolution separate separate reported reported apply introduced moving moving moving moving include quadratic array array works tuning axis tions solve smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth definition chain modified grid intensity occur deviation derivative locally loop loop occurs hardware half flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow flow strength strength conclusion neighbor neighbor editors editors retina numerical clear performs practice weak weak strong strong drawn proportional intelligence regularization regularization regularization regularization regularization regularization regularization min derivatives derivatives manner minima reference reference explicit relation perception optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical solving solving stability changing infinite physical physical physical slightly unique consisting integrated minimization minimization implies potentials national independently focus stationary squares influence variation restricted showed calculation smoothing smoothing smoothing performing classical expansion convex convex boundaries valid filtering sufficiently foundation norm koch koch koch koch degrees coupling coupling coupling coupling coupling coupling coupling includes silicon priori currents currents currents coupled absolute phys discussions simplicity regular regular determining straightforward sensor society encoded computationally poggio poggio poggio detect notice prob prob conductance conductance conductance conductance conductance device correspondence computes computes computes computes ill ill ill ill ill chips neighboring neighboring acknowledgments load intrinsic presents law minimized carried poor create access circuitry circuitry circuitry mead mead mead varied steady steady int ideal complicated smallest gradients gradients gradients gradients gradients voltages implementations prototype der obvious assumes mapped mapped electronic electronic electronic crucial smoothness smoothness guaranteed navigation implementing closer controls qualitative robustness apparent fed autonomous introducing introducing posed posed posed posed posed posed detecting formulated formulated resistive resistive resistive resistive resistive resistive resistive resistive resistive resistive continuously continuously maintain requirement span ture modulated cal collective conductances conductances conductances conductances conductances yuille trade lab discontinuities discontinuities discontinuities indices sensing fabricated lagrange lagrange lagrange modify amplifier narrow velocities perfectly purely rigid multipliers multipliers fails multiplier multiplier fits convenient adjusting analogy fail belong optic capacitor intuitive motivation reliably photoreceptor photoreceptor photoreceptor photoreceptor consequences yang horn horn horn horn horn horn contact observer harris harris severe outlined lem lem liu shorter preserving forced expanding poses tween quasi ideally reports reports rain laplacian eric brightness brightness brightness brightness brightness capacitance disadvantage regularized march douglas douglas douglas douglas differentiation transconductance gilbert gilbert page prevents september supporting article simplifies behaves vice november rewritten versa satisfaction remarks algorithmic photoreceptors settling designs agents mahowald arrow capacitors suffices december fabrication practically unreliable subtracting equa impedance core core operational dedicated lying alan alan grids symmetrical mosis mosis legendre aperture gratings ini putation degrades expresses sat sat cient mal imposing kramer translational switzerland switzerland fur fruitful snapshots torre torre maxwell kung luo luo euler euler undergoing cyber duced vittoz follower unknowns rodney swiss disabled disabled intro wyatt straint closeness puting iip iin upwards delbrfick perceives preferably reporting plaid plaid tanner tanner schematics schematics neuroinformatics neuroinformatics thermore ttm suffi tential iim iim ami netics kirchhoff nash lutions misha sensibly 
#@Douglas_R,Stocker_A,
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#*network network network network network learning learning neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training output output output number number number number number number number number number number number system system system system system system system system system system system system state results results results information information information problem problem problem performance performance performance performance performance based based based based space weights weights weights weights weights weights layer layer case vector vector vector vector vector order order shown shown shown shown shown systems systems values values values values values parameters noise noise noise weight weight weight weight unit distribution distribution distribution distribution recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method method method method method approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point image image image image image image image image image image image image single processing processing processing processing processing processing processing processing processing control control control control control control large large large large large large rate rate rate rate rate rate test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis matrix matrix matrix matrix matrix matrix matrix optimal optimal inputs inputs form form form shows shows shows shows shows signal simple simple simple simple simple simple simple simple simple simple simple paper paper paper small size size size size size size size feature work work methods methods methods points points points points points points points points points features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process process level level current current current current structure problems problems problems problems problems problems problems problems high high high high high high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show equation equation equation fixed fixed fixed line line rule rule rule rule rule vectors vectors images general real real real real obtained obtained obtained note note experiments dimensional dimensional result result result university university threshold threshold threshold threshold computation computation research research research research sequence table table table table table table table table estimate standard computer computer distance distance science presented presented present machine machine sets sets range range learn learn learn learn components components basis abstract applied computational properties references due ieee important important decision introduction complex statistical dynamic generated generated parallel cost cost cost cost cost cost search complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower lower lower lower lower rules chosen part required required binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary binary long long distributed distributed chip techniques correlation correlation correlation correlation correlation correlation tasks tasks computed multi multi sum performed performed called times times times times times times times times times elements mapping dimension global applications applications applications applications applications applications applications study original vol relative relative relative samples samples represented compared compared compared compared compared application application application desired rates rates rates determined experimental experimental distributions equal equal equal accuracy accuracy accuracy comparison comparison larger larger support support train dependent department loss loss implementation implementation implementation implementation implementation implementation implementation implementation version version version version consists consists code code code individual represents connectionist difficult addition computing computing experiment design design design design stage stage effects effects bit bit bit bit capacity classifiers classifiers requires world world speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed speed vision estimated increase increase developed developed developed levels area path path provided processes selected nature associative associative associative achieved measured normal describe group tested fast fast fast fast fast fast fast close complete rbf rbf rbf rbf amount nearest nearest nearest common common common effective implemented implemented implemented implemented supported vlsi vlsi ability instance instance including including smaller needed needed needed combination combination reduced reduced reduced mlp mlp mlp mlp block block block block block transfer interesting interesting testing york york york york york york york york segmentation mechanism consistent matching matching matching matching matching uniform uniform uniform uniform database database operation operation operation operation operation details numbers numbers numbers numbers max pre pre pre stored stored bits bits bits bits bits bits magnitude choose added perceptron improve exact property property pair robust robust robust robust robust robust include period identical identical identical identical identical identical identical machines engineering highly conventional conventional conventional approximately calculated module axis axis solve match match match match match match match match achieve achieve trans sparse sparse sparse background evaluation storage storage storage sensitive sensitive sensitive increased increased grant parts studied wide wide wide wide width boundary boundary hardware hardware hardware hardware hardware hardware hardware hardware hardware hardware half minimal row row greater segment segment segment segment conclusions neighbor neighbor accurate numerical designed performs faster faster faster practice learns encoding encoding encoding encoding encoding encoding encoding integration integration presence presence presence presence presence presence presence presence presence presence presence presence presence external cycle cycle characteristics proportional radial identification configuration acknowledgements areas written index index primary label recall recall recall recall recall recall recall recall implement physical dimensionality slightly unique consisting applying john stages codes codes codes codes codes codes codes detailed evaluated operations operations static static sizes partition processor processor partial partial partial slow performing spaces intervals add iterative boundaries boundaries generation initially distances calculate symbol symbol symbol classified avoid includes silicon silicon retrieval sciences memories discuss coupled partially partially successfully identified identified identified letter letter letter efficiency efficiency closely uniformly maximal included build efficiently post post post orthogonal orthogonal orthogonal repeated allowing allowing allowing allowing showing criteria device device device device device device hold board board board thresholds thresholds processors deal software software software software presents requirements requirements requirements requirements put association reducing reducing matches giving project project project applicable decisions symbolic symbolic symbolic understand fundamental matched matched removed man perfect implementations taylor logic logic store store baseline improving motivated seconds devices devices devices devices devices great advanced advanced rows expensive sections choices commonly read arises sun greatly evaluating flexible amounts generic generic conducted fed effort orders completion passed slower slower execution execution execution http operate exhibits gains aim ordered gave gave hamming logical inherent implements www interface interface interface appropriately bin bin bin bin bin bin partitions encoder encoder encoder overcome held chemical resulted resulted reasoning reasoning reasoning reasoning arrays clock selects embedding sides buffer buffer buffer counting counting counting assembly enable occlusion bins bins bins bins bins bins bins bins storing card card card card card card card card card card card card projects speeds influences thresholding thresholding thresholding thresholding thresholding thresholding acknowledge divide dramatically basically kluwer bus bus bus bus ram ram benefits willshaw willshaw incrementally blue superimposed chapter simd acceleration workstation workstation workstation unseen mhz graphics uncertain convert thresholded met met altered maximally host host library meet meet meet commercial rarely accumulation achievable council ping heavily austin austin austin austin austin austin austin austin austin austin austin austin austin confirm shot ron connects engine engine engine returned returned diagnostic core accumulate dedicated dedicated html quick bottleneck concatenated concatenated platform satellite satellite satellite satellite recovering recovering mounted cope sorted benchmarks benchmarks benchmarks benchmarks benchmarks benchmarks benchmarks benchmarks mid holographic custom converts minimise aimed separator separator separator uniformity uniformity uniformity uniformity ascending vme vme vme vme vme vme vme vme vme vme british feeds counters workstations workstations widespread zhou zhou zhou zhou zhou zhou cheap jim industry chaining cards cards cards pipeline michie michie millions turner turner higgins concatenation accumulates additions investigates kennedy kennedy kennedy kennedy spiegelhalter spiegelhalter alteration viability libraries buses arch quantisation quantisation quantisation quantisation quantisation quantisation quantisation quantisation quantisation rnns rnns rnns speeding aerospace sgi quantised processin mother pack minimises favour dasarathy dasarathy mbytes mbytes ellis acted maximises neighbouts interleaving kll hts daughter 
#@Austin_J,Kennedy_J,Zhou_P,
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#*learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure time time time time set set set set training training training training training training training training training training training training training training algorithm output output output output output output output output number error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information information models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based space case vector order values values probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise functions distribution distribution recognition recognition pattern point image image single single single processing local rate rate test test test test test test test test patterns patterns analysis analysis analysis class class class matrix optimal optimal form form shows signal signal signal algorithms algorithms algorithms simple gaussian gaussian gaussian visual paper small work work methods step step field field classification classification classification classification classification process process process process current trained structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure structure random random random random random random random high high show show show equation rule vectors speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter average average states states states states states states states states states states states states states states states states theory gradient obtained obtained obtained term term note note note experiments activity activity activity activity dimensional variables variables variables computation computation solution research independent log log log log log log log log log log log log log log log log found found found sequence sequence dynamics initial initial initial initial estimate estimate estimate estimate estimate standard standard standard computer computer terms distance science prediction prediction prediction left left left map map map map map map map map map map map map present low low temporal temporal machine machine machine machine machine sets motion motion maximum maximum maximum maximum maximum range position position position basis continuous sample sample sample abstract applied computational convergence properties likelihood likelihood likelihood likelihood references component stochastic due ieee procedure important adaptive adaptive hand estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior statistical statistical effect generated search energy difference variable lower lower measure measure signals prior prior prior prior prior prior prior prior prior prior prior prior prior learned learned type binary long conditions conditions bayesian bayesian bayesian expected equations equations markov markov markov markov markov markov make techniques length length length length length probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed errors forward forward finite finite minimum resulting tasks tasks human human multi sum times global applications applications applications policy em em em obtain obtain obtain obtain original original artificial relative relative specific specific specific samples compared cross cross series series receptive receptive receptive provide provide proc proc related posterior posterior posterior posterior posterior posterior posterior constraints constraints connected distributions distributions distributions discrete discrete approaches comparison larger larger contrast contrast fields train source modeling modeling modeling modeling institute loss exp exp exp bias scheme sequences sequences sequences sequences sequences framework framework framework framework framework framework cambridge domain domain equivalent environment directly solutions estimates estimates estimates estimates transition transition transition transition transition transition transition transition transition transition transition transition transition transition transition top top top effects conference efficient efficient upper upper approximate approximate statistics statistics statistics statistics free world vision estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated basic pages pages increase produce coding coding derived derived randomly conditional conditional conditional conditional conditional clustering developed criterion lines lines entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy selected evidence evidence evidence evidence evidence evidence evidence simply covariance hmm hmm hmm hmm hmm hmm hmm inverse stable common assumed shape generate supported supported supported cluster easily easily easily including including typically typically smaller dynamical fully interesting testing special structures structures trials trials trials leads representing making window international international normalized bottom magnitude frame combined combined minimize minimize run description description description light predict improve recent exact exact advantage ensemble takes movement reported practical introduced identical identical machines machines pixels pixels pixels interest highly highly highly conventional conventional conventional conventional conventional approximately calculated volume yields converge diagonal diagonal sparse mixtures background background observation observation horizontal lead derivative matrices matrices matrices matrices loop deterministic white setting setting demonstrate conclusion row row reduce valued measures bayes numerical faster temperature taking taking strong intelligence labeled radial variety variety minimizing start start introduce manner program configuration annealing force reference appears digit digit longer estimating estimating estimating transitions transitions tuned tuned vertical modeled pruning pruning missing coordinates simultaneously involves remaining slightly consisting gaussians applying applying predictive minimization minimization minimization springer expectation expectation versus yield extracted review depending correlated estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator interpretation detailed open labels showed frames frames frames frames activities activities digits digits converges diagram key key key spaces spaces intervals event add add iterative iterative generation calculate calculate msec assigned degrees avoid expect handwritten color color subspace automatic uncertainty uncertainty maximize priors variations texture simplicity compression identified hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms identify literature literature schemes schemes tend ten ten capture verlag quickly graphs kind strongly allowing allowing heuristic heuristic video video video showing interpreted interpreted superior return lie content follow follow follow timing device notation sampled write generalize backward backward backward minimizes minimizes minimizes minimizes board leading maximization automatically consisted illustrates illustrates subsequent mixing camera bars body employed explore unlike essential essential relations relations estimators estimators estimators issues mass mass biases discriminant dataset ml ml ml ml successive office office office structured structured working maximizing contours removed induction naturally possibly editor analyze opposite extremely ensure freedom freedom mapped initialized initialized initialized multivariate improving utility grouping finds site site slowly track coded independence tractable baum berkeley operators arise laboratories scientific separately begin recording author qualitative alignment questions questions questions apparent improvements collected substantially understood orders detecting remove treated music rewards http calculating spread branch popular monotonic incoming proven extensions acoustics phone substantial logp electric segmented damage deviations tile simultaneous merging merging cumulative contribute initialization initialization consistently pose person room room room contextual notes writing writing writing guarantee lagrange extensive fix temporally velocities databases rotated approximates partitions discovery discovery discovery discovery discovery discovery proceed multipliers murphy murphy chance stronger stronger minutes minutes accepted accepted satisfying simplify automaton handwriting handwriting handwriting serves obtaining obtaining removing reasoning splitting splitting constructive days days hours eqn eqn eqn eqn meaningful weakly weakly weakly started separating ranging tone ambiguity predictors sides ascent dominant surprisingly record clean informative proximity messages variants captures omohundro omohundro summarize pen pen pen pen limitation counts empty learnable uci uci posteriori fitted yielded arcs arcs unified truncated entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic entropic listed equivalently removal expanding spatio welch retraining quasi medium seek mdl mdl mdl individuals multinomial multinomial multinomial england stands reconstruct musical intuition gained impose labs challenging efforts bump iso maximally acquired deleted weaker nonetheless register turning confusion confusion tones tones induces simplifies simplifies diagrams tonic tonic overcomplete rabiner rabiner drives lighting reversal excess reversed compositional prefer converging smoother virtually clarity outperformed calculates rissanen rissanen systematically strokes strokes strokes repository repository inspection bach bach bach bach bach implying accommodate fair inducing foreground foreground foreground segmenting occupancy inappropriate discriminating began entropies entropies entropies entering tutorial judge oil gross entered compress respects respects extrema web web superiority bernoulli notably writers writers claimed hillclimbing chorales chorales chorales chorales chorales chorales chorales chorales concise concise trimming trimming trimming trimming trimming trimming trimming trimming trimming perplexity perplexity melodic melodic exposition brings xlo xlo xlo descriptive descriptive cap cap extraneous premise accelerate accelerate interpretable interpretable interpretable handles agnostic anomalous depict shed opaque optimizer concentrating compressing wasted summarizing negated leapfrog elongation tiles merz merz logarithms logarithms initializations initializations backgrounds odds odds odds odds ambient transposed detrimental sparser atypical vovk vovk wll extinction extinction extinction lambert lambert stolcke stolcke ieice conventionally conventionally conventionally fractions sgi eqns eqns folds ellipses surviving surviving surviving surviving mitsubishi multinomials ooi ooi ellipse matthew broadway merl assert ologp bivariate inquiry sitting wlo kun oix wholly wholly reynolds reynolds eccentricity appropriateness europe adjoining discern logx accidental nici 
#@Brand_M,
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#*learning model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set algorithm algorithm algorithm number number number number number number number error error results results results results results results results information information information problem problem problem problem models models based space linear case case case case vector order shown shown values values values noise noise noise noise noise noise noise noise functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit distribution distribution distribution distribution recognition method method approach approach approach approach approach approach single single single processing processing processing large large large large analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal form form form form shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms simple gaussian examples examples small small small small size size size size work methods methods step step points points points level level level structure structure structure structure structure structure structure structure structure structure structure structure structure structure similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show general general speech speech speech speech speech speech speech speech speech average theory theory theory gradient gradient gradient obtained note note note result computation solution solution solution log log log log defined found sequence initial initial initial initial initial initial initial initial constant constant estimate estimate estimate estimate standard standard terms presented presented present present present phase frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal sets maximum maximum position position position position position position components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear continuous sample abstract applied find computational properties properties properties likelihood likelihood references due ieee ieee ieee ieee ieee procedure procedure important introduction generated change difference assume assume assume signals signals signals signals signals signals prior prior representations representations representations representations representations higher previous type required multiple good spike spike represent represent distributed make make fact techniques proposed length length length length length errors scale resulting tasks computed computed computed respect times elements mapping mapping optimization optimization applications obtain relative relative relative samples represented series series series series series series series series series define location goal posterior posterior constraints distributions discrete power power power source modeling selection report institute institute kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel represents difficult delay equivalent equivalent curves capacity determine determine efficient efficient efficient efficient efficient approximate estimated basic increase give coding coding coding coding coding coding coding types entropy sampling discussion technical describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary fast assumption complete finding finding finding amount short short short common assumed assumed require fit fit fit fit fit auditory probabilistic probabilistic typically typically typically underlying underlying underlying underlying underlying reduced account coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients block block interesting significantly significantly projection segmentation special matching operation representing representing direct making making magnitude description exact exact advantage property include period period subset sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski relevant dimensions highly highly highly varying varying varying varying works axis yields yields achieve achieve achieve trans sparse sparse sparse sparse sparse sparse sparse sparse sparse positions positions positions positions positions positions positions positions positions positions positions positions locations separation modified entire constructed constructed constructed invariant invariant invariant invariant invariant invariant invariant invariant occur occur occur suggests alternative column starting minimal minimal greater segment segment segment segment central faster constrained suggest encoding encoding encoding encoding cycle exist acoustic force appears index ways generating plot describes laboratory dept modeled averaging adding frequencies frequencies events events events formed shift shift shift shift shift shift shift shift blocks blocks blocks blocks blocks blocks select select letters yield expressed correlated viewed viewed transform transform fraction decomposition decomposition key reasonable additive additive additive additive fitting fitting fitting fitting fitting intervals event roughly boundaries remains transactions transactions transactions david expect kernels kernels kernels kernels priori formulation formulation bell blind instances extension plotted automatic variations variations discussions gamma determining selecting selecting efficiency encoded computationally delta efficiently efficiently efficiently efficiently efficiently efficiently computations plots essentially essentially orthogonal orthogonal orthogonal orthogonal orthogonal composed composed capture capture capture compact split issue contribution contribution contribution sin follow criteria duration duration notation localization michael dot wavelet wavelet wavelet wave wave correspondence acknowledgments presents varied involving pursuit periodic helpful helpful fewer fourier fourier scaled scaled scaled maximizing maximizing stream proved oscillation oscillation encode phases coefficient coefficient coefficient coefficient coefficient naturally onset onset nerve ith generates generates extent arbitrarily arbitrarily submitted finds optimum residual residual trivial crucial convolution convolution convolution convolution convolution convolution waveform waveform waveform waveform waveform adapted multiplication tractable stanford stanford choices leaves desirable probable probable probable probable potentially sounds sounds medical arises addressed alignment alignment conjugate conjugate freeman cochlear cochlear offset axes parameterized dots dots sharp sharp rep maxima howard chen chen logp shaped specifies univ contribute pose aligned redundant intractable optimizing optimizing tem nonzero khz promising difficulties occurred obtaining obtaining transforms transforms neurobiology star shifts salk salk salk effectiveness selects zhang zhang pruned lengths evident accounts offers bases express express jolla waveforms dividing limitation limitation infomax divide fitted unchanged yielded largely sine sine sine shorter convolutional ber ideally superimposed laplacian adapting adapting musical goals num blocking blocking disadvantage hughes terrence adelson ultimately multiscale increasingly normalizing challenge resembles overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete info preserves olshausen finer routines val evenly peaked inferring sliding convolved lewicki lewicki lewicki lewicki lewicki lewicki lewicki lewicki lewicki greatest shares simoncelli simoncelli simoncelli simoncelli ues routine cardoso cardoso repeats resentation extrema convolving terry fil poral donoho donoho binaural tony attack tha brute instruments signif portant plete genera replicating replicating minimally torrey pines denoising atomic xla xla xla saunders slx argmaxp argmaxp icant sitions bruno rive nyquist mallat mallat circumvented omission unresolved conventions sla grab lutions padded affords isting 
#@Lewicki_M,Sejnowski_T,
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#*network network network network network network network learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data function function function function function time set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output number number number number number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error state state state state state state state state state state state state state state state state state state results results information information information information problem problem problem problem problem problem problem problem problem models models models models models models hidden performance performance performance performance based based based based based space space space space weights weights weights weights weights weights weights weights weights linear case case case case case case case case case case case case vector vector vector vector vector order order systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight weight weight weight weight functions distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method approach approach approach approach approach approach pattern pattern processing processing control large large large large large large rate rate rate rate test test test analysis optimal form signal signal simple simple simple simple simple simple gaussian gaussian paper examples small small small small small size size size size size feature feature feature feature net net task task task task methods methods methods methods methods methods methods methods step features features features features features process trained trained high high similar similar similar architecture general general general general generalization generalization generalization generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter approximation average average average average states states states states states states states states states states states states states states gradient obtained term term term term term term term term term term term term term term term experiments experiments experiments university university computation solution solution solution independent independent independent independent independent independent log log log log sequence initial constant constant estimate estimate estimate estimate estimate estimate standard computer distance distance distance distance connections connections science presented presented map machine sets maximum maximum maximum maximum maximum maximum maximum maximum press learn components components components continuous continuous continuous continuous continuous continuous abstract applied applied applied back density density density likelihood likelihood likelihood likelihood likelihood references component component component due ieee ieee procedure procedure important important decision decision decision decision propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context context introduction complex complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical effect effect dynamic generated search search tion tion tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity classifier measure measure measure prior prior prior prior word word word word word word word word chosen higher required good good binary tree tree bayesian markov markov make make probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities forward finite finite finite ing tasks total total respect respect sum sum performed performed factor optimization optimization optimization natural knowledge knowledge em em em em em negative negative negative original vol vol relative represented true application application application application series rates rates rates proc proc proc proc proc proc proc determined determined experimental posterior constraints distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete brain power mit steps larger larger larger contrast contrast train train dependent dependent dependent dependent dependent dependent dependent dependent dependent modeling morgan report words department technique consists consists internal individual advances advances joint connectionist exp exp exp delay ai ai ai ai considered considered framework framework cambridge domain domain equivalent hinton hinton hinton design transition transition san effects determine estimated estimated estimated estimated basic con weighted weighted weighted weighted clustering clustering clustering provided selected selected constraint discussion technical group hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm transformation fast limited limited limited close inverse corresponds amount amount common common common assumed assumed assumed assumed generate role adaptation adaptation adaptation adaptation journal ability cluster cluster cluster cluster cluster cluster cluster makes makes makes objective objective probabilistic probabilistic smaller underlying combination coefficients transfer edge increasing special special uniform database language leads max direct making frame decay idea improved correlations pair subject identical identical identical identical trees trees inference observations works works tions smooth smooth smooth smooth yields yields yields yields yields speaker speaker speaker speaker speaker speaker speaker speaker speaker match achieve trans observation observation observation observation observation observation constructed expression expression extended deviation deviation deviation derivative derivative hybrid hybrid hybrid clusters clusters clusters clusters clusters setting setting setting reduce reduce differences exponential exponential exponential constrained mateo demonstrated demonstrated intelligence regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization averaged groups acoustic acoustic force denoted denoted denoted denoted denoted denoted denoted denoted written index generating ann label label label metric metric metric transformations slightly consisting mutual expectation yield extracted phoneme estimator influence solved solved detailed detailed labels labels lee soft soft soft soft soft soft sizes partition partition smoothing fitting iterative iterative penalty penalty penalty valid initially distances distances distances sufficiently sufficiently euclidean avoid avoid inter weighting grammar selecting extra hmms hmms hmms hmms hmms hmms hmms hmms suitable differ differ driven driven successful situation tend summary traditional traditional traditional traditional traditional traditional kind kind kind contained cun cun prob prob prob interpreted interpreted interpreted interpreted interpreted interpreted phonetic phonetic split split dis classify follow built built usual simplified simplified generalize backward denker maximization maximization maximization overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting overfitting investigate replaced replaced optimized divergence preliminary ml ml ml ml ml reliable maximizing stream stream stream stream workshop statistically waibel changed ensure prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype noted mapped initialized multivariate speakers speakers speakers generates improving improving simplest sentences sentences sentences isolated smoothness smoothness variances nowlan nowlan nowlan nowlan caused baum baum perspective sys style forces forces constructing constructing constructing incorporate commonly commonly mellon carnegie pure cmu capability share solla adjustable adjustable adjustable haussler incorporated ity ity prototypes prototypes howard pittsburgh fall fall fall popular resource asymmetric logp logp germany decoder shaped damage viterbi yielding yielding sharing sharing sharing sharing sharing sharing sharing sharing lagrange lagrange tation controlling controlling controlling controlling partitions flexibility plays multipliers multipliers kullback adds consideration numerically stronger chains overcome balance balance abilities abilities removing settings eqn eqn eqn eqn eqn eqn eqn eqn eqn eqn eqn eqn mance falls introduces sion codebook codebook perfor lang lang regard infinity uni jackel darpa darpa darpa initialize advance advance advance young young young young augmented exploiting alternatively pdf pdf pdf pdf pdf pdf assigns counts severe posteriori outperforms audio emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission emission street ent ent email leibler maximized forced smoothly icassp icassp icassp icassp tradeoff tradeoff tradeoff decomposed auxiliary auxiliary streams streams streams streams streams streams param avoids favor community wall management tems distribu proba proba oct simplifying guided tied tied drawback tively drops eters compu recognizers beam bility bility recogni pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs insufficient insufficient ters quantizer quantizer comprising totally totally totally tance adjusts feb feb transaction neglected prominent adequately penalizes sep probabil cope favors favors degrades phones rela nov mar traditionally mmi mmi mmi respec mercer solu clus tinuous penalties comprise perplexity miiller duce plaut plaut official penalization penalization kauffman tying tying tying tying tying tying tying tying tying tying native native fii reg knowl wsj wsj favoring augmenting regu quantize bahl bahl bahl bahl vides llt adaption xlw invari triphone triphone triphone triphone triphone triphone triphone timation argm argm gerhard gerhard jelinek reestimation rnj rnj triphones ances gopalakrishnan subvector subvector christoph pushes sensitiv regulariza tionship subvectors larization eurospeech rmeters 
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#*model model model model model model model model model model model model model model model model neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure time time time set set set set set set set set set networks networks networks training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number system system system state state state state state state state state state results results results results results results information information information information information models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance based based based based space space space space space space space space space space space space space space linear linear linear layer layer vector vector vector vector order systems values probability probability probability probability probability probability probability parameters noise functions unit unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method approach approach pattern point single single single single processing processing processing processing processing processing large large test test test test test test test test matrix matrix matrix form signal signal signal algorithms simple gaussian gaussian gaussian paper paper paper paper small feature work work work task task methods step step step step step step step step step features process process process current current trained random high high representation architecture architecture architecture fixed fixed fixed fixed line line line line rule rule vectors general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real real approximation approximation states states gradient gradient gradient gradient gradient obtained obtained obtained obtained term term term term term term term term term term term term note dimensional dimensional dimensional dimensional dimensional dimensional university university research research independent independent independent independent independent log log log log log log defined found sequence sequence sequence sequence sequence sequence sequence initial initial initial constant constant constant estimate estimate estimate estimate estimate estimate standard computer computer computer computer terms terms terms science science direction direction direction direction direction direction map map map map map low low low low low frequency frequency frequency frequency frequency temporal motion maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press press press press press press components continuous continuous continuous continuous continuous continuous continuous sample sample abstract abstract applied back convergence convergence convergence convergence density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component stochastic ieee ieee introduction complex estimation estimation estimation statistical statistical statistical generated generated generated generated generated variance variance search search search search search search energy energy energy energy energy assume lower lower lower lower lower measure prior prior prior word word word word word long represent represent markov markov markov markov make make make make make make proposed correlation correlation correlation correlation probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed forward scale finite finite finite resulting resulting tasks regression regression regression regression respect respect multi multi multi multi sum performed eq eq eq eq eq eq eq eq eq eq eq called mapping mapping mapping mapping mapping mapping mapping mapping means means means means optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization potential dimension made natural applications applications filter filter filter filter obtain relative specific samples compared application desired series series series define location perform perform determined related related related distributions gain discrete discrete discrete discrete power steps steps steps steps contrast contrast train modeling modeling modeling modeling morgan morgan morgan morgan morgan morgan proceedings report report report report institute department loss consists consists code code individual represents represents connectionist scheme addition maps maps considered considered framework framework framework framework framework framework framework cambridge computing solutions transition transition transition transition transition transition effects bit detection detection conference determine determine determine efficient full full full full requires approximate approximate estimated estimated estimated estimated estimated estimated con con coding conditional criterion criterion path path path path path path path path path path path path path path path path path path path path product product product product actual actual iteration iteration depends depends depends depends depends depends depends constraint constraint constraint achieved measured measured measured measured covariance covariance covariance covariance technical technical technical technical describe tested hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm transformation inverse assumption assumption corresponds corresponds corresponds corresponds corresponds corresponds corresponds complete common assumed assumed main journal end end including probabilistic probabilistic probabilistic probabilistic typically typically unknown significantly language principal call iterations window international supervised supervised supervised supervised supervised supervised early frame frame frame attention combined produced predict correlations correlations resolution separate ensemble ensemble movement include machines dimensions dimensions compare conventional conventional conventional conventional unsupervised unsupervised unsupervised approximately calculated module smooth smooth smooth smooth speaker speaker speaker match diagonal mixtures mixtures evaluation positions symmetric entire horizontal expression matrices alternative alternative alternative alternative alternative alternative generally pass pass pass pass starting starting trajectories conclusions bayes bayes numerical designed constrained constrained constrained constrained constrained suggest turn movements movements decrease averaged averaged configuration acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic pro construct construct construct produces estimating estimating describes laboratory laboratory laboratory transitions dept implement coordinates coordinates infinite involves text unique gaussians quality john national national national national dependence review review overlap codes codes codes codes transform densities evaluate evaluate evaluate evaluate fraction frames frames frames approximated partition measurements measurements measurements measurements measurements measurements measurements classical generation calculate msec msec assigned foundation david avoid avoid recorded recorded recorded perceptrons formulation formulation extension plotted prove maximize maximize maximize mozer candidate candidate closely hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms society society computationally computationally paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths paths vowel vowel capture capture capture capture compact stopping return contribution bar bar involved sampled sampled realistic backward quantization maximization predictor predictor predictor overlapping illustrates acknowledgments unlike powerful poor poor production production production production production production production production strengths strengths replaced integral integral recursive helpful fewer applicable scaled comparable notion analogous math measurement coefficient gradients gradients configurations man front algo assumes academic art speakers speakers speakers consist generates improving improving extent extent extent submitted attempts sentences sentences sentences seconds stop stop developing developing developing publishers smoothness smoothness smoothness waveform independence baum worse considerable filtered filtered incorporate bishop bishop bishop immediately sounds preceding conjugate conjugate empirically cohen employ employ remove requirement calculating vocabulary synthesis maximizes maximizes acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics phone replace germany hamming boston comments conditioning viterbi viterbi median median utterances sentence sharing lab room oxford summing temporally rithm partitions partitions partitions fits fits khz analogy automaton los los los los los los utterance utterance utterance utterance utterance utterance utterance bourlard bourlard bourlard bourlard bourlard bourlard preparation corpus carry exploring exploring repeat repeat lip lip started started james corre corre iteratively codebook male topological uni originally arrangement claim claim claim recog young young rich motions captures receiving pdf pdf pdf pdf pdf pdf pdf pdf pdf treat posteriori emission emission converted rubin kluwer maximized maximized nition magnetic welch female guess guess continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator boulder simplifying considers pos alternatives articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory xly tract september gorithm strict manuscript modal demonstrating sponding sponding pdfs pdfs pdfs pdfs pdfs pdfs pdfs pdfs ers focuses fre tip acoustical acoustical acoustical acoustical dissertation consonants consonants contributes inferring attained phonology degenerate vocal evolving america america lnp inde cutoff cutoff cutoff cutoff articulation articulation articulation articulation articulation magazine iterating cess dent indepen alamos alamos alamos alamos alamos alamos capturing microphone cepstral cepstral meaningless tongue tongue formulations versity mike claims viable topologically emulate lpc munich munich resampled resampled tinuous radially konig syntax nix nix nix nix nix nix nix nix nix emphasizes analogously jackson mon coil eval tain weaknesses tly tly useless tlx electro perceptually quence corpora matters native remap speak jaw jaw gov gov scofield scofield scofield ger recipes teukolsky articulators articulators articulators lly flannery strained gan vetterling uation deficiencies terior mor quently reside xiy xiy xiy xiy electromagnetic deteriorate windowed nasals reestimate reestimate reestimate reestimate reestimate tln pendence wlx fricatives ematical oratory 
#@Hogden_J,Nix_D,
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#*learning learning learning learning learning learning model model model model model model model model input input data data data data data data data data function function function function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time set set training training training training training algorithm algorithm output number number number number number number number system error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results problem problem problem models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based based space space case case case vector vector vector vector vector order shown shown shown systems systems values values probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight functions functions unit unit distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach point point single processing processing processing processing processing processing large local local rate rate rate rate rate test test test test analysis matrix matrix matrix matrix matrix matrix matrix form form form form shows shows shows shows signal signal signal signal signal signal signal visual paper paper paper paper paper feature feature feature feature feature feature feature feature feature work work work work task task task task task task task methods points points points features features process process process process process level level trained trained trained trained problems problems problems random similar show show section section section fixed fixed fixed vectors vectors vectors generalization speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter parameter parameter states states states states states states term note note note experiments experiments experiments experiments experiments experiments dimensional variables variables variables research independent independent log log log log log log defined defined found sequence sequence target constant constant table table table table estimate estimate standard terms terms terms terms distance left direction present present present temporal machine maximum maximum learn components components components components nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous continuous continuous continuous continuous abstract abstract applied find density density properties properties properties properties likelihood likelihood likelihood likelihood references stochastic stochastic ieee ieee ieee positive procedure procedure important important important important important important important mixture mixture mixture mixture mixture context context introduction hand hand estimation estimation estimation estimation dynamic tion energy energy energy difference variable variable variable variable lower lower signals word word word word word chosen chosen part previous previous previous bound equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov proposed length length length length length length length length length length length length length length length length length length length length length length length probabilities probabilities probabilities probabilities probabilities observed observed observed errors forward resulting tasks tasks computed computed computed computed sum performed eq eq eq eq eq eq eq eq eq eq eq eq called times elements elements negative negative provide define define define compute compute compute rates rates rates rates rates rates rates experimental experimental related related connected connected connected connected distributions discrete discrete discrete discrete discrete discrete equal update dependent dependent modeling modeling modeling selection proceedings proceedings report report words words implementation consists joint joint represents difficult graph graph graph graph ai maps framework framework framework framework computing curve curve curve curve curve curve curve curve view view view curves curves curves curves curves curves curves curves curves curves curves curves curves transition transition transition transition trajectory trajectory trajectory trajectory trajectory effects conference conference estimated estimated estimated basic con con produce conditional conditional conditional product product finally processes processes processes processes processes processes processes processes processes processes processes processes selected depends constraint measured covariance increases describe describe describe denote denote hmm hmm hmm hmm fast fast limited inverse inverse predictions predictions predictions predictions predictions amount amount amount short short short short assumed role theoretical require end end future makes makes probabilistic probabilistic probabilistic probabilistic probabilistic typically reduced dynamical dynamical coefficients programming segmentation segmentation segmentation segmentation segmentation segmentation special special special leads squared representing numbers max pre making international international international normalized frame frame frame decay decay idea attention denotes denotes discussed takes element element typical movement reported introduced side interest previously axis smooth smooth smooth speaker match differential differential diagonal diagonal diagonal definition mixtures mixtures mixtures background symmetric observation interval organization sensitive entire increased concept concept studied studied invariant invariant invariant invariant invariant occur derivative matrices matrices matrices locally generally generally setting setting setting demonstrate trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories segment segment valued valued depend depend tangent differences differences measures measures measures solid proportional start iii introduce derivatives acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic relation relation ways factors laboratory transitions label mathematical segments segments modeled modeled metric metric metric metric metric metric remaining remaining consisting gaussians applying shift extraction versus versus versus versus versus yield yield family family review stationary stationary phoneme phoneme viewed evaluated evaluated evaluate labels labels labels evolution evolution evolution frames sizes digits digits digits digits earlier slow dashed reduces intervals roughly iterative distances distances assigned euclidean euclidean transactions weighting illustrated automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic discuss activated variations grammar major extra hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms differ differ differ differ delta delta delta delta included build comparing invariance invariance invariance invariance invariance plots essentially identity traditional refer procedures decoding decoding decoding decoding prob phonetic phonetic return return duration duration built built built involved sampled sampled computes computes computes leading maximization attempt consisted consisted consisted overlapping intrinsic intrinsic intrinsic decreasing american investigate investigate exponentially exponentially integral issues issues issues preliminary hall hall rise rise scalar history surfaces naturally trace trace analyze opposite quantities quantities quantities precise separated initialized speakers baseline contributions defines defines isolated years rows band formula directed directed crucial defining benchmark baum processed arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc widely controls probable consequence english english english english definite definite geometry recognizing recognizing recognizing recognizing recognizing radius raw integrating integrating geometric geometric geometric varies collected spoken parameterized frequently switch synthesis synthesis summarized mod ture gen monotonic monotonic phonemes phonemes acoustics acoustics acoustics phone phone phone hamming conditioning viterbi viterbi utterances traces traces multidimensional multidimensional multidimensional cumulative initialization consistently pose proportion proportion assign databases signature partitions grows grows proceed khz significance alpha alpha alpha alpha replacing abilities occurring nearby tishby tishby tishby exploit receiver vowels vowels motivation meaningful prentice prentice ranging saul saul saul saul saul saul saul saul widths guarantees lengths lengths lengths lengths lengths lengths lengths lawrence competing tic initialize recog belonging park park vari displacement default speaking speaking speaking consecutive metrics metrics emission emission emission arcs arcs unified slight incorporates opposed transmitted markovian formulate nition welch exception aij aij aij aij aij aij generalizations associate realize param arising evolve evolve evolve evolve decays decays decays decays shannon signatures labs exceed names names names names names names emphasized enforce sized mimic syllables fea els recognizers recognizers recognizers recognizers recognizers recognizers recognizers unpublished challenge resembles handled emphasis rabiner rabiner rabiner rabiner beam argmax handling tom vii stochastically stochastically phrases phrases jointly jointly jointly telephone telephone jersey jersey jersey cliffs ave determinant determinant compo englewood consonants consonants consonants consonants contributes contributes normalize juang juang juang juang att rameters digitized prone evolves iterating signed ings bear mul united blocked rec ference cepstral cepstral segmental segmental phones nents lifetime traversed traversed traversed traversed traversed traversed traversed respects lived lived coverage infinitesimal ago lpc distinguishes mented contiguous aii segmentations segmentations multiplies multiplies nected ations resemblance formalize fundamentals parameterize decayed aug vocabularies viability puting acous ioo fifteenth relaxes imize asr asr asr asr outperforming florham trices windowed traverses trajec reestimation segmenta aries ances reviewing fanout ambitious ently erally discretizing comparably comparably mic sla newark maz fect tories attaching admitting 
#@Rahim_M,Saul_L,
#t12
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural data data data data function function function function figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set networks algorithm algorithm number number number number number error results results information information problem problem based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear linear case case case vector vector vector vector vector vector order order order order shown shown shown shown values values values values values values values probability probability probability probability probability probability probability probability probability parameters parameters functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition approach approach approach approach approach approach approach approach approach approach approach approach approach pattern point image image image image image image image image image image image image image image image image image image image image image image image image single single single single large large large large patterns analysis analysis matrix form form shows shows algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper paper small small feature feature feature feature feature feature feature feature feature feature feature feature work work cells step field field field field field field process cell random random high response response response response response response response response response similar similar similar similar show show show equation equation equation equation section vectors images images images images images images images images images images images images images images images images images general general real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average theory theory theory theory gradient gradient gradient obtained obtained obtained obtained note note result result university variables computation computation computation solution research independent independent independent independent independent defined defined defined defined found constant constant constant constant constant estimate estimate estimate estimate standard computer left left left present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase frequency sets sets maximum maximum range press press learn learn position components components components components abstract applied applied applied find properties properties properties likelihood references component component due due ieee procedure important important important introduction cost cost tion tion assume assume lower prior prior learned learned learned learned chosen higher higher center previous theorem theorem theorem type required multiple multiple good good binary bayesian bayesian make make make make make fact fact fact fact length probabilities probabilities errors scale scale scale scale scale scale scale scale scale scale scale finite finite resulting resulting total computed computed computed multi multi multi multi multi sum called mapping mapping mapping factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor potential potential potential potential potential potential dimension dimension made natural natural natural natural natural natural filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter obtain original vol vol true true true true receptive provide define define determined experimental goal related distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions cortical equal approaches larger connection connection modeling modeling report institute words loss version technique code kernel kernel kernel responses responses responses responses responses responses difficult addition addition addition addition addition framework framework cambridge computing domain equivalent equivalent equivalent equivalent curves san san stimuli determine determine requires requires approximate approximate approximate statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics world speed vision give derived developed levels entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy finally finally finally nature depends depends sampling simply measured covariance covariance covariance covariance tested fast fast close assumption nearest shape main main eds journal journal square pixel pixel pixel pixel pixel pixel pixel future unknown unknown interesting projection projection matching empirical empirical empirical empirical empirical empirical empirical empirical empirical principle representing details numbers filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters making making normalized magnitude frame light denotes denotes denotes denotes discussed discussed recent recent separate apply include identical identical identical pixels pixels pixels pixels pixels pixels quadratic inference interest dimensions highly works yields yields yields achieve trans sparse observation entire grant grant constructed intensity intensity intensity concept scaling suggests column setting half conclusion interactions interactions exponential faster characteristics assuming assuming exist iii introduce denoted denoted acknowledgements reference relation pro index perception perception optical solving factors factors estimating estimating distinct recall linearly physical easy easy scales scales scales scales scales interaction adding frequencies minimization potentials potentials potentials potentials potentials potentials potentials potentials letters yield yield review communication solved detailed transform fraction approximations approximations approximations approximations approximations approximations approximations approximations approximations centered forms approximated approximated approximated partition additive additive expansion normalization convex reduces reduces reduces coupling eigenvalues sciences prove prove discuss discuss discussions texture texture determining straightforward suitable society differ fine fine fine fine fine fine composed summary kind contained link showing dis dis gibbs gibbs gibbs write generalize generalize extract satisfies intrinsic intrinsic intrinsic intrinsic intrinsic extend law origin powerful perturbation relations detail dataset dataset dataset dataset dataset rise scalar int eigenvectors proved func coarse coarse coarse coarse integer integer illustrate rank aspect panel panel panel observe shapes simplest seconds seconds histogram histogram trivial defining unstable analytic analytic diffusion perspective easier precisely hyperplane arise arise begin explained reflects greatly greatly greatly applies empirically lattice share calculating perturbations measuring ture qualitatively song enables inherent inherent inherent inherent yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yuille yielding shifted newton feasible extensive linearity member null null null repre theories generality smith smith smith imaging ranges simplify fail preparation moments ambiguity ambiguity ambiguity ambiguity ambiguity james bialek bialek entry histograms histograms histograms histograms entries advance francisco francisco emergence april insight cpu informative informative considerations explains alternatively cam acknowledge counts mind unified solves reaction uniquely preserving convenience medium medium medium medium multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial examining examining illustration transparent quantized quantized quantized argue exponent shifting pami march relating maximally topic topic spanned emphasized preserve fea algebra induces differing corrections simplifies gauss bridge stimulating uniqueness ble resolve august inconsistent justification quantify influenced olshausen establishes tribution ning core ignores sity inde minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax minimax subscript zeros ruderman ruderman sentation inst inst convey stems ambiguities ambiguities ambiguities ambiguities ambiguities ambiguities applica clutter proximation pendent quantified quantified nov nov mumford mumford mumford mumford mumford mumford mumford mumford mumford mumford mumford mumford zhu zhu zhu zhu zhu zhu zhu zhu zhu zhu zhu zhu zhu zhu zhu tics statis offline motivates motivates clarify panels bearing notational trust univer possi ripley equiv equiv private variate variate funding richards richards degeneracy fined woods ship vastly raphson propor aro factoring uncover completing rounded alent alent multinomials neglects nlog cfi vided fmax stemming disregarded lear throws 
#@Coughlan_J,Yuille_A,
#t12
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#*network network network network network network network network learning learning learning learning model model model model model model model model model model model model neural input input input data data data function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks training training algorithm algorithm number number system error error error results results results results results results results results results results results results results results results results problem problem models models models models models models models models models based based based based based based based based based based based based based based based based based based based space space space space space space space space space space space space space linear linear linear linear linear linear linear linear linear case case case vector vector vector shown shown shown values values values parameters parameters parameters parameters parameters functions functions functions functions recognition method method method method method method method method method method method method method method approach approach approach approach approach approach approach point point point point point point point point image image image image image image image image image image image image image image image image image image image single single single single single single single single local local local local test test test analysis analysis analysis analysis analysis matrix matrix matrix optimal form form shows shows shows shows shows shows shows shows shows shows shows shows simple simple simple simple simple simple gaussian paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small net work work work task task task methods methods step points points points points field current current trained trained problems problems similar representation representation representation show show show show show line vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images images images images images parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real real real real approximation approximation approximation theory obtained obtained note result result result result solution research defined defined found found found found found sequence sequence sequence dynamics initial initial initial computer computer distance distance distance science presented map map present present temporal object object object object object object object sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets range press press press press press press press learn learn components components basis basis basis nonlinear abstract applied applied applied find find find find find find find find references due due due due ieee ieee ieee ieee ieee procedure important mixture introduction complex complex hand estimation generated search assume previous previous cases cases multiple multiple multiple good good conditions represent represent make make techniques techniques techniques region region region proposed correct errors errors resulting ing ing human regression computed performed regions regions regions regions regions mapping mapping mapping mapping mapping mapping mapping means artificial relative compared application application desired desired cross define define define compute objects objects proc proc proc proc proc proc proc proc location location perform perform perform eye constraints constraints constraints constraints approaches approaches approaches approaches approaches mit mit mit mit mit mit modeling modeling modeling modeling modeling implementation technique represents difficult final final ai ai considered cambridge cambridge domain directly additional view view view view view view view view view view view solutions solutions solutions trajectory trajectory trajectory trajectory trajectory san effects full full full free world vision basic validation give con coding derived weighted clustering clustering clustering clustering clustering clustering clustering clustering clustering criterion criterion types provided provided finally selected selected constraint constraint transformation limited limited limited close close close inverse assumption finding rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf nearest nearest effective effective shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape generate generate require require face face face face ability cluster including simulated typically pairs underlying underlying needed needed needed coefficients fully jordan consistent principle principle principle squared call max max direct normalized depth frame attention combined produced light recent advantage property robust similarity reported reported apply moving subset subset subset interest varying varying observations observations observations tions smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth smooth pca pca pca pca pca pca pca pca pca pca pca diagonal sparse sparse locations locations interval interval interval interval arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm arm constructed exists expression expression expression lead studied occur occur matrices locally locally locally clusters clusters occurs boundary boundary generally conclusion row reduce accurate clear largest radial radial radial variety exist plane scene configuration configuration configuration configuration configuration produces longer generating generating transitions changing modeled modeled modeled modeled metric metric coordinates physical remaining text boolean select select select independently review interpretation detailed transform open open restricted frames approximated approximated approximated approximated approximated approximated approximated similarly key key spaces convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex add add add tracking interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation valid valid valid valid sufficiently norm views views avoid existing figures figures figures figures perceptual contour contour contour contour subspace subspace subspace specifically candidate coupled coupled coupled neighbors successfully successfully texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture straightforward maximal poggio poggio poggio poggio successful successful literature literature identity identity traditional traditional road conf lie lie manifold manifold manifold manifold manifold manifold manifold built paradigm realistic realistic realistic realistic realistic realistic nips nips nips correspondence correspondence computes overlapping subsequent disparity extend camera remain powerful poor detail accurately mse mappings applicable variational proper complicated cover notion contours contours contours smallest closest possibly necessarily configurations configurations facial subsets subsets portion portion assumes taylor shapes shapes generates grouping synthetic synthetic synthetic mentioned piecewise growing growing growing growing growing adjacent handle inside perspective constructing bishop leaves describing geometry exemplars requiring consistency poorly splines span http switch synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis synthesis rely summarized mod fall prevent semi median multidimensional yielding cumulative pose pose pose pose pose pose lab lab discontinuities discontinuities discontinuities aligned www appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance appearance japan girosi tensor tensor reconstructed partitions discover jones jones exemplar rigid rigid rigid rigid rigid proceeds proceeds grow nearby fail illumination canonical canonical planar planar selects filled filled obstacle continue date lip recovered falls saul recovery gaze gaze tracker augmented gesture extends projects projects omohundro omohundro santa automated displacement displacement dense dense dense unified workspace workspace workspace forced smoothly warping param param remainder graphics graphics manifolds manifolds discontinuity distant expand enforce memo memo page dramatic prevents eters handled tour interior interior interior interior discontinuous inconsistent correspondences correspondences jointly agents interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpolated interpreting hull hull hull hull hull hull hull hull hull hull hull hull hull hull hull kinematic returned bregler bregler interpolating interpolating seed seed mill interpolate interpolate interpolate interpolate interpolate drastically safe alto sis physically physically physically physically ance ance faced enforces enforces violated dyer tit dof dof palo decompose extrapolation extrapolation extrapolation extrapolation extrapolation extrapolation bodies bodies rij tenenbaum tracked collision erroneous erroneous delete ample couple conceptually ther animation darrell darrell darrell darrell darrell endpoint endpoint tot ages outlines rendered rendered articulated articulated articulated articulated articulated articulated articulated articulated articulated imagery imagery imagery arms arms arms arms arms behaved deformable deformable rendering rendering rendering singularity endpoints eter render render render trevor trevor trevor renders safely groupings groupings groupings ditional warped elbow elbow elbow gions observa invalid shashua shashua mcmillan barbara cvpr cvpr offering eling marking adjacency siggraph siggraph siggraph tio dod erroneously precomputed beymer beymer appearances appearances synthe blends fare lyi backpropogation stu 
#@Darrell_T,
#t12
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#*network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model neural neural neural neural input input input input data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure time set set networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output system system system error results results results results results results information information information information information information information problem problem problem problem problem problem models models models models models based based based based based space space linear layer vector vector vector vector vector vector vector vector order shown shown shown systems systems systems values values values probability probability probability probability probability probability probability probability probability probability parameters parameters parameters neurons distribution distribution recognition recognition recognition recognition method method method method method method method approach approach approach approach pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single processing processing processing processing processing processing processing processing large local local local local local local local local local local test test patterns analysis analysis analysis analysis analysis analysis analysis matrix form shows shows shows shows algorithms simple simple gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual examples examples examples small size size work methods methods methods methods methods fig fig fig fig fig step field field field field classification level level level level level level level level level level cell structure structure problems problems problems problems problems problems problems random random random high high high high high high high high high high response similar representation representation representation representation representation representation representation show show line vectors vectors images images images images images images images images images images images images images images images images images images images images images images images images images images images real theory theory obtained obtained term note note computation computation computation computation research research research independent found sequence initial initial initial initial estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate computer computer computer computer computer computer terms connections node node node node node node node node node node node node node node node node node science direction presented map map present low low low low low low low low low low nodes nodes nodes nodes nodes frequency frequency frequency machine machine machine object motion motion motion motion motion motion motion motion motion maximum range press press press press press press learn position position components components components components continuous sample sample abstract applied applied applied find find computational computational density density properties properties properties likelihood likelihood likelihood references stochastic stochastic due due ieee ieee ieee ieee ieee ieee ieee ieee ieee decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation mixture mixture mixture introduction hand estimation estimation estimation estimation estimation statistical statistical statistical statistical statistical statistical statistical effect generated parallel spatial lower rules rules rules rules rules measure measure prior prior prior prior prior representations learned learned learned previous cases multiple good good good good good long tree tree tree tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov markov markov markov markov markov markov markov markov markov region correct correct probabilities probabilities probabilities probabilities probabilities observed errors scale scale scale resulting resulting human human computed computed multi multi multi multi eq eq eq eq elements factor factor natural natural orientation orientation applications applications study relative samples samples samples samples represented true desired desired desired desired desired desired series receptive receptive receptive compute compute objects proc proc proc proc related related related related posterior distributions discrete discrete discrete brain approaches mit mit mit mit mit mit steps comparison contrast contrast contrast contrast contrast fields fields fields modeling modeling modeling selection morgan proceedings report technique code code code code code joint joint joint ai framework cambridge cambridge cambridge cambridge directly estimates estimates estimates estimates top top effects efficient efficient full full full requires statistics world world world world vision vision vision vision vision vision vision vision vision vision vision vision vision vision estimated estimated estimated pages pages pages pages pages give con condition coding coding coding derived derived derived conditional conditional conditional conditional conditional conditional developed developed developed levels levels area velocity actual provided iteration iteration iteration iteration iteration iteration nature nature sampling constraint constraint associative measured discussion technical describe describe fast fast limited close assumption surface surface generate theoretical require pixel pixel pixel including including fit kaufmann probabilistic typically underlying underlying underlying underlying underlying reduced account jordan edge edge edge segmentation structures leads principal details iterations iterations iterations iterations max filters making normalized bottom early frame frame frame added improved improved directions recent resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution advantage robust takes practical practical apply apply moving moving include pixels inference inference inference inference sejnowski interest highly approximately approximately volume volume works tions yields trans trans trans sparse sparse address definition mixtures mixtures background background organization organization lead lead occur digital digital matrices matrices correctly locally locally hybrid loop deterministic occurs setting demonstrate runs flow flow flow flow critical place row row row assumptions assumptions assumptions neighbor neighbor neighbor editors editors constrained reduction intelligence intelligence intelligence regularization regularization regularization regularization turn min relationship relationship groups scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene acknowledgements edges perception optical optical optical optical factors estimating laboratory vertical vertical dimensionality belief belief belief frequencies gaussians applying springer quality blocks select reconstruction stages interpretation codes codes codes codes densities evaluated evaluated evaluated restricted showed frames frames frames understanding converges constants measurements expansion normalization normalization fitting boundaries boundaries tracking calculate visible koch perceptual perceptual color color color bell bell contour retinal retinal black black neighbors discussions texture texture texture compression compression closely computationally included poggio poggio efficiently computations computations mackay receives summary compact conf conf conf success link anderson neuroscience lie running follow hold gray cues gibbs gibbs sampled sampled sampled relaxation realistic surround quantization quantization principles overlapping neighboring neighboring neighboring neighboring intrinsic oriented simpler parametric put involving involving detail detail estimators graphical helpful successive giving relationships relationships relationships structured working workshop statistically understand surfaces contours matched attributes patch patch patch patch patch patch plausible editor editor editor quantities quantities expressions shapes ith message explain explain synthetic synthetic synthetic seconds neal scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes scenes ground ground ground orientations coded adjacent nowlan diffusion independence independence independence spatially sys bishop probable projected projected calculations localized patches patches patches patches patches patches patches patches patches patches patches patches computers annual researchers researchers freeman freeman freeman freeman freeman affine lack maintain operate synthesis synthesis extracting incorporating curvature curvature geman geman gave electric age redundancy shaped shaped univ pyramid pyramid pyramid pyramid pyramid don lab feasible oxford acm ratios arguments arguments arguments velocities velocities velocities velocities velocities velocities velocities girosi labelled jth jth suppression minutes determination intelligent loops loops loops loops interpret interpret reasoning ylx generalizes filled filled hours connect connect sion studying studying regard dominant schwartz schwartz histograms enable artifacts ensembles emergence modelled infer infer infer agree agree agree correcting likelihoods implicitly santa speeds explains propagate propagate propagate propagate cam cam avoiding accumulated consecutive verify visually sig equivalently super super break randomized randomized randomized cooperative reaction pentland propagating weiss weiss weiss weiss additionally seek causing chapter laplacian principled quantized quantized shaded attempted graphics graphics elementary ization reflectance adelson adelson multiscale relates pearl intensities geiger tively tively intl memo programmed matlab intensive ignoring computa completed served fiat fiat argmax argmax factorized restoration restoration fractal mrf synthesized european multiresolution blake viola viola transparency skin olshausen olshausen arrow interpreting connects peaked atick atick heeger quantizer interpretations interpretations bergen optics william factorization factorization factorization factorization communicate comm colors filling filling sis sis enter concatenated aperture aperture watson watson ized proceeding simoncelli simoncelli simoncelli adv adv ference movshon infeasible tenenbaum primates mumford zhu redlich tics statis berger beliefs pyramids respec anandan torre feel grove analogously sereno blobs blobs blobs blobs faithful proaches render embody saund heuristically didn occluding opaque lihood richards isard suspect photographs alterna sect derlying prey barbara cvpr burt factoring pacific factorize factorize analy mitsubishi siggraph caption landy willsky quantizers broadway merl merl merl irregularly irregularly revision synthesizing drawings schultz asilomar wlx wlo jepson lxl lxl compres synthe maxx maxx maxx wrote luettgen appended quad quad synthetically flames flames lncs 
#@Freeman_W,Pasztor_E,
#t12
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#*learning learning learning learning learning learning learning model neural input data function function function figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set set training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number system system system system results results results results information information problem problem models models models performance performance performance based based space space space space space weights weights case case vector order order order order order order order shown shown shown shown systems values values values values weight weight weight weight weight weight recognition recognition recognition method approach approach pattern point point point point point point image image image image image image single single single processing control control control control control control control large large large local test test test test test test test test test patterns analysis form form shows simple visual visual paper examples examples examples examples small size feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work fig fig fig fig step points points points points points field features features features features features features features features features features features features features features features features features features features features features features process process level level current trained similar similar similar representation show show show section fixed line line images images images images images images images images images images images images images images images images images images images images images images images images images images images general real real real real real real obtained obtained note note experiments experiments dimensional result result result computation research independent defined found found found found found sequence constant table table table computer computer computer computer computer node node node node node node science science left left left left left direction present nodes nodes nodes nodes nodes nodes nodes machine machine object object object sets sets sets learn position position outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied find find find find find find find properties properties references ieee positive positive positive positive positive positive positive positive positive positive positive positive positive positive important context introduction hand hand effect search search search search search search search search assume assume assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier lower lower lower lower learned learned chosen part part part required good good represent represent tree make fact techniques techniques region resulting resulting resulting resulting classes classes ing total total total human human human human human human human human human computed computed computed computed sum regions regions regions regions factor potential made orientation study obtain obtain negative negative negative negative negative vol true define compute compute compute objects objects objects rates rates proc determined determined experimental constraints equal mit larger support report report words implementation implementation version consists internal kernel advances represents responses difficult ai computing computing computing equivalent equivalent view top top top stage stage stage detection detection conference determine efficient efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper upper upper upper full requires vision vision vision vision pages pages give con con randomly randomly bounds bounds area area types types finally selected depends depends constraint achieved describe group tested tested corresponds complete complete complete complete complete complete complete finding finding finding finding finding finding finding finding finding effective effective effective shape generate require face face face journal instance future future easily easily easily makes makes including typically pairs smaller combination significantly projection projection projection projection head special consistent consistent consistent uniform uniform uniform database representing numbers international international bottom bottom bottom bottom early magnitude minimize minimize produced choose added added separate separate typical reported reported reported reported include include pixels quadratic subset subset highly varying volume volume volume works axis axis axis yields correspond correspond correspond correspond correspond achieve trans definition background background positions separation separation entire entire arm arm arm constructed constructed parts parts parts expression invariant scaling suggests wide rotation correctly move touretzky demonstrate half half half row segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment segment conclusions depend depend depend depend editors measures measures clear clear faster practice weak weak weak constrained strong hard labeled labeled labeled labeled labeled user user plane plane groups groups groups configuration configuration configuration configuration configuration configuration configuration force force suppose appears pro construct construct construct construct longer label label label tuned vertical segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments segments pruning pruning pruning remaining remaining easy easy text choosing extracted review depending interpretation variation open labels labels labels labels labels completely translation partial earlier reasonable dashed reduces intervals add add add false false false false false false false distances filtering filtering filtering visible query classified classified classified classified david degrees expect building building box box box box box box box retrieval determines extension mozer candidate tests tests texture texture texture determining determining selecting selecting identified efficiency included included poggio identify literature build build build projections projections ten receives conf quickly split lie classify classify classify running follow satisfy realistic correspondence ill ill automatically overlapping presents body body body body body body body body body body body body body body body selectivity overfitting collection collection collection requirements experience humans issues dataset fashion project incremental boosting boosting int ideal scaled workshop configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations configurations extremely versions greedy greedy freedom consist detected grouping synthetic synthetic synthetic animal preference scenes scenes adapted tool inside processed straight tive berkeley berkeley berkeley berkeley berkeley berkeley satisfied division division hyperplane projected projected projected projected projected projected projected projected projected projected projected projected projected projected projected projected projected angles definite geometry incomplete people people people people people people people people people people people people people people people people people people people people people people people people people people people people people applies double consistency amounts axes readily marked marked span popular tile tile tile tile merging merging pyramid pyramid pyramid pyramid pyramid cor realized pose person person person person person person person person person person person person aligned aligned redundant labeling labeling labeling labeling labeling labeling labeling labeling labeling labeling appearance appearance forming extensive ratios animals rotated impossible robotics children children children children fails ranges accepted check resulted obtaining splitting splitting selects reliably document falls schapire widths pruned pruned pruned lengths histograms searching searching searching assembly assembly hasselmo arrangement similarities permutation smoothed broken broken projects projects projects splits exploiting exploiting parents fly boxes usage shading shading listed kinematics piece poses incrementally incrementally par freund associate leg leg leg shaded shaded increment iff iff iff iff thick baluja management file bounding bounding bounding bounding bounding bounding bounding bounding rectangle rejected rejected books books books wise projecting projecting projecting flip pos anal million misclassified assemblies assemblies assemblies assemblies responding memo bring rewrite rewrite signs scanned interior primitives identifies european skin skin arrow arrow mirror pictures pictures pictures pictures pictures pictures japanese kinematic kinematic kinematic kinematic bregler bregler manually classi classi joints halves semantics carrying mach putative limb limb comprehensive boosted boosted boosted boosted boosted boosted sung repeating collections collections collections collections collections collections leung remarkably favorably plans trick posi excluding scribed accepts accepts sought lay froin froin missed corresponded articulated malik rowley kanade greenspan rejecting swim labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings labelings brute brute lozano finder finder straints joining lea flipping intell loose merges neg photographs grimson marking assembled fractions brady edit ive maxp converse localizing recomputed wearing wearing suits colour colour colour torso torso torso annotated posit fusing limbs bent fier fier tput ticularly 
#@Forsyth_D,Ioffe_S,
#t12
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#*network network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural input data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure system error error state state results results results results results units units units units information performance performance performance performance performance performance performance based based based linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear order order shown shown shown shown systems values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise neurons neurons unit unit unit pattern pattern pattern pattern pattern pattern pattern point single processing processing processing processing processing processing processing processing processing processing processing processing processing control control large neuron patterns optimal optimal optimal optimal form simple simple simple simple simple simple gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small small size task task task task task task task task task task task task task task task task task task task task task task cells field field field field features features level level level level trained random high response response response response response response similar fixed fixed fixed rule parameter parameter parameter parameter parameter parameter average states theory obtained obtained obtained experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity threshold threshold threshold threshold threshold threshold computation research independent independent independent independent found found constant table table table table table table estimate standard distance distance science science science prediction presented presented present present present phase low frequency motion maximum maximum range range range range press position basis outputs abstract back computational computational convergence properties likelihood references stochastic stochastic due positive procedure procedure procedure decision decision decision decision decision decision decision decision decision decision introduction complex complex estimation estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical effect effect effect effect effect effect effect dynamic variance search tion energy difference difference difference spatial spatial spatial spatial spatial assume assume lower lower lower measure chosen chosen higher higher higher higher higher higher part center center previous cases firing multiple cortex conditions conditions conditions conditions proposed correct observed observed observed observed observed observed observed scale scale tasks tasks tasks tasks tasks tasks tasks tasks tasks simulation human human human human human human human human computed computed computed respect respect multi performed means means factor feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study study study study specific specific specific specific specific specific receptive rates proc proc proc proc location location location location location location perform perform determined determined experimental gain gain gain gain gain gain gain gain cortical cortical cortical brain brain equal power power steps accuracy accuracy larger contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast support dependent modeling modeling modeling institute consists consists internal internal internal individual responses responses responses responses difficult exp exp exp exp exp exp bias addition framework computing directly curves curves curves estimates top top stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stage stimuli stimuli stimuli stimuli stimuli effects effects detection efficient efficient efficient efficient efficient full full full full full full full significant significant free world speed vision basic basic increase increase produce condition condition area area types processes nature inhibitory inhibitory inhibitory simply measured measured measured measured measured measured measured measured discussion increases tested close close close inverse assumption excitatory predictions predictions circuits finding amount amount assumed supported supported square ability hypothesis hypothesis hypothesis hypothesis easily degree noisy noisy noisy including fit fit fit fit fit fit fit fit fit fit simulated typically pairs underlying needed reduced account account account account fully fully fully fully fully fully fully fully fully fully technology mechanism mechanism mechanism trials filters filters filters filters filters filters filters filters filters filters filters filters filters inhibition inhibition inhibition bottom bottom early early early early early early early early early early early attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention minimize minimize added neuronal neuronal population population resolution reported introduced strategy strategy include period period period period period identical cognitive recently recently interest dimensions sufficient varying previously observations observations observations subjects subjects subjects tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning studies studies studies studies address background background background background background improvement sensitive entire entire entire increased increased amplitude exists trial deviation deviation derivative width width width width width width half conclusion starting greater assumptions central central central central central central interactions accurate constrained constrained mechanisms mechanisms characteristics drawn sigmoidal sigmoidal demonstrated california variety selective manner manner scene annealing acknowledgements areas areas areas areas pro pro produces winner primary laboratory tuned tuned tuned tuned tuned tuned vertical vertical vertical distinct modeled sensitivity sensitivity simultaneously linearly linearly linearly involves easy slightly angle events quality blocks cycles competition competition competition competition letters independently focus focus focus stages stages stages stages stages stages stages stages estimator detailed restricted lee lee lee lee lee lee lee modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation modulation centered similarly similarly allowed allowed discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination earlier classical classical classical fitting fitting fitting fitting fitting fitting fitting remains symbol koch koch koch koch koch koch koch koch koch koch degrees formulation inter inter weighting plotted automatic automatic uncertainty specifically variations characterized gating letter closely modification presentation presentation efficiently situation ten fine reached reached receives receives characteristic composed excitation strongly induced dis dis dis issue issue physiological physiological sci sci sci sci gray comp bar bar bar vary absence paradigm paradigm paradigm nips reach thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds thresholds cat automatically neurosci received oriented law poor poor poor poor poor investigate investigate investigate investigate varied varied varied varied varied put involving humans humans humans detail dual dual dual dataset dataset existence successive rest project behavioral behavioral investigated investigated possibility root affect hierarchy statistically statistically statistically understand examined measurement plausible predicts thought adjusted subsets formal noted fisher freedom detector detector pyramidal mixed extent extent optimum animal animal directed orientations phenomena improves inside perspective broad desirable desirable pool pool pool cut involve attribute res res meaning nsf explained requiring improvements conducted quantitative quantitative quantitative quantitative quantitative quantitative quantitative poorly poorly poorly poorly poorly poorly poorly poorly poorly psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical compares poisson aim cal pasadena substantial display unbiased findings focused attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional progress simultaneous multidimensional room redundant physiology appearance formally tation gabor narrow enhancement enhancement enhancement enhancement grey caltech inspired spontaneous systematic fits fits striate resulted interpret imply illumination modifications modifications enhanced degradation hours motivation falls zhang accounts captured reproduce viewing multiplied deg deg deg observer observer observer impact ignore interestingly vari onr dramatically dramatically grating yielded yielded appeared unified slight asked asked focal focal focal focal emerge bank lit ical superimposed param alter attempted peripheral peripheral peripheral increment increment exponent exponent exponent modifying cessing interact compensate interacting interacting oct oct retinotopic relate ullman overhead macaque statistic relates mask mask mask mask mask mask distinguished apparently outcomes tively pop happen simplex nal eters psychophysics psychophysics psychophysics increments wider transducer monitor justified tial crude quantify vis vis vis vis vis vis vis builds pouget observers observers observers virtually mst bold conceptual clarity broadly broadly char eliminates pronounced val physiologically sharply evenly heeger heeger heeger luminance luminance luminance discarded successively systematically screen screen screen quantitatively quantitatively bandpass reproduced absent pooling pooling pooling pooling pooling pooling pooling pooling pooling pooling attended attended attended attended attended attended attended attended attended attended attended attended attended attended attended attended attended attended electrophysiological ance saturating focusing focusing focusing modulatory modulatory spa massive putative christof unexpected ues spanning linearities modulate modulate modulate battery primates broader sixth quadrature exponents exponents exponents exponents pooled pooled pooled pooled awake pay dissimilar divisive manipulating implementable seemingly ana behaved psy psy concurrent concurrent prototypical tilted steep anatomically braun braun braun braun braun braun braun stein narrower multiples discriminations selec octave instructed psychol accompanied native maunsell maunsell modulates neur somers desimone mecha masking masking masking masking cedure discrim discrim nakayama sharpening sharpening sharpening strengthening downhill iiiiii orien klab dale calibrated electrophysiology treue compensating discriminates discriminates discriminates engaged neurobiol nism chophysical chophysical emotional engage recomputed attract cortices staircase psychophys multaneously sharpened acterized ination supra eccentricity atten consumes ero ero ech moran hum desireone controversial tle 
#@Braun_J,Itti_L,Koch_C,Lee_D,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input data figure figure figure figure figure figure figure figure time time set output output output output output output output output output number number system system state state models performance performance based based based space space weights layer shown shown shown shown shown shown values values values values values parameters parameters noise noise noise functions functions neurons neurons neurons neurons unit pattern pattern pattern point point point point point image image image image image image image image image image image image image image image image image image image single single large large local local local local local local local neuron neuron neuron neuron neuron neuron neuron test patterns patterns patterns inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form shows shows shows shows visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper examples examples examples examples examples examples examples examples examples examples small small small feature feature feature feature feature feature feature feature feature feature net task task task fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells cells cells cells points points field features features features features features features features features features process level current current cell cell cell cell cell cell cell problems response response response similar similar similar similar similar representation line line line line line line line images images images images general average average theory theory theory note experiments activity university university threshold computation computation independent defined target target target target target target target target target target target target target target target target target target target target target target target target target initial constant standard standard standard standard standard standard terms connections connections connections synaptic direction present present low temporal object motion motion motion press press basis basis basis outputs outputs outputs outputs outputs abstract applied back find find density properties properties references decision context introduction introduction complex hand hand behavior effect parallel parallel search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search tion change change measure measure higher higher higher higher higher center center cases firing type required long long long conditions equations make fact fact region region region region proposed ing tasks simulation performed called times times elements elements regions potential dimension natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation knowledge filter relative relative relative relative specific specific specific cross cross receptive receptive receptive receptive provide define define define rates proc location location location determined determined determined experimental related related discrete cortical cortical cortical cortical brain larger larger larger larger contrast connection connection connection fields fields fields modeling modeling loss implementation implementation consists represents responses responses difficult difficult difficult addition environment directly directly top top stimuli stimuli stimuli stimuli detection detection requires significant significant significant vision basic con con coding levels area types types lines lines lines evidence nature nature inhibitory inhibitory inhibitory inhibitory inhibitory depends sampling sampling sampling measured measured discussion increases group assumption complete complete excitatory excitatory excitatory excitatory excitatory surface circuits finding short short short assumed role role role theoretical eds eds instance instance instance instance instance easily easily noisy including simulated pairs pairs pairs smaller underlying needed reduced account account account interesting edge edge edge edge edge edge edge edge edge segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation mechanism special consistent leads details details pre pre pre pre pre pre pre pre pre pre making making making inhibition inhibition inhibition bottom bottom early early decay idea attention attention added membrane membrane membrane improved pair pair pair pair pair takes typical typical include include side dimensions dimensions dimensions dimensions dimensions dimensions dimensions highly highly compare observations observations smooth smooth smooth studies background background background background background background background background locations locations locations modified grid grid grid grid grid grid grid organization horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal horizontal invariant invariant invariant suggests suggests suggests suggests extended extended deviation deviation rotation white white boundary column demonstrate demonstrate strength strength assumptions assumptions segment segment segment segment segment segment depend interactions interactions interactions interactions interactions interactions interactions interactions differences sigmoid clear clear mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms presence solid solid solid solid proportional turn assuming assuming variety selective selective targets targets targets targets targets targets targets targets areas areas areas areas reference van van longer perception tuned vertical vertical vertical vertical segments modeled slightly unique unique unique unique unique unique springer formed versus versus versus versus potentials cycles dependence review depending viewed influence detailed open fraction centers centers understanding activities activities activities completely suggested suggested translation translation translation sign slow dashed dashed dashed dashed classical normalization purpose boundaries boundaries boundaries closed intermediate distances distances visible visible visible figures figures figures includes usa color color color color color color color color contour plotted plotted plotted activated activated candidate texture texture texture aspects aspects aspects closely differ included oscillatory detect detect detect invariance plots tend receives receives composed excitation excitation excitation summary verlag link link symmetry physiological physiological follow gray gray comp bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar involved sampled play dot dot highest thresholds disparity disparity preferred neighboring bars bars bars bars bars bars bars bars bars bars collection exhibit strengths periodic helpful rest detectors detectors detectors relationships oscillation scores understand contours contours contours saliency saliency saliency saliency saliency saliency saliency saliency circles concepts onset rev der assumes academic detected explain explain explain explain serial serial serial serial averages mentioned rows ground ground ground orientations orientations orientations orientations variances defining phenomena phenomena phenomena phenomena phenomena phenomena coded caused tool interneurons starts london processed straight straight easier easier filtered filtered arise commonly consequence ion involve acad opt circle circle demonstrates demonstrates incomplete qualitative qualitative varies empirically understood understood simulate simulate readily quantitative red red red red red red red red red psychophysical psychophysical psychophysical treated continuously dots psychological psychological schematic gains spread differs cal qualitatively qualitatively singer singer green green green green green enables enables extreme picture college contextual contextual contextual contextual contextual intractable oxford tation martin martin controlling neurophysiol theories theories theories interconnected interconnected interconnected generality stronger stronger primitive primitive primitive primitive primitive nearby nearby mark roles imply salient salient salient salient salient salient salient salient salient salient salient spot spot spot spot responsible responsible natl contexts respective widths surprising conjunction stereo stereo stereo sim originally bases enable enable foundations thin thin suggesting suggesting ends projects reverse reverse convergent influences influences influences influences influences default geometrical largely constitute shorter axe preferences ease ease ease ease ease constitutes resting brightness alter argue thick thick thick interact interneuron searches searches neurophysiological intra intra intra crosses douglas douglas mediated switched switched switched multiscale weaker breaks distinguished gilbert gilbert gilbert gilbert gilbert gilbert pop pop pop pop pop pop pop pop pop pop pop pop pop pop pop pop pop pop 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#@Li_Z,
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#*learning model input input data data data function function figure figure figure figure figure figure figure set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number system system error error error error error error results results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem models performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based space space space space space space space space space space space space space space weights linear linear linear vector vector vector vector vector vector vector vector order order systems values values probability probability probability probability probability probability probability probability unit distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition 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images images images images images images images images images images images general general theory term experiments experiments research research found constant estimate standard computer computer distance presented presented presented presented presented presented presented presented present low object sets sets sets sets press basis basis nonlinear nonlinear nonlinear sample abstract applied applied applied applied references component positive positive procedure procedure decision decision decision decision decision decision decision decision decision decision decision decision decision introduction hand statistical generated generated generated generated generated variance variance variance tion tion difference difference difference difference difference difference difference classifier classifier classifier classifier classifier classifier classifier classifier lower measure measure measure measure measure learned center multiple binary binary binary bayesian techniques correct correct classes classes classes classes classes classes classes classes classes computed performed called elements elements dimension applications applications applications knowledge negative negative original vol specific specific samples samples samples samples samples samples samples represented represented compared compared application desired provide provide provide compute proc equal equal equal equal equal equal approaches comparison comparison support support support support support support support support support support train report report report report institute technique individual individual kernel kernel kernel difficult difficult ai computing curve view view view estimates conference conference efficient statistics vision vision vision estimated estimated pages pages give produce condition weighted randomly developed developed area selected selected selected selected nature measured measured group tested tested surface surface surface surface surface surface surface 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pca pca background background background risk risk risk concept extended alternative correctly feed boundary demonstrate demonstrate conclusion place reduce operator neighbor editors differences differences differences differences differences differences designed demonstrated demonstrated labeled radial introduce identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification identification pro derive construct produces label changing confidence metric metric explicitly averaging remaining consisting consisting applying minimization springer versus versus versus national interpretation interpretation labels centers approximated performing classical classical classical spaces false false false false faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces avoid combinations eigenvalues instances recognize vapnik automatic automatic structural structural structural major major straightforward identified identified identified society modification divided svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm literature score score score score identity identity identity identity identity identity identity traditional traditional interested neuroscience return classify notation list write generalize generalize generalize generalize modular paradigm minimizes computes computes consisted consisted consisted consisted consisted consisted consisted consisted consisted consisted consisted operating satisfies experience varied humans referred referred referred eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors eigenvectors scores scores encode surfaces surfaces coefficient adapt facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial eyes eyes algo baseline generates submitted finds histogram slowly benchmark benchmark preprocessing preprocessing constructing geometry people people people people people pure remove remove formulated formulated characterize ordered achieves achieves returns returns extreme extreme person person person person person person person person person person person person person person person person person identifying formally formally rithm discovery adjusting accepted accepted accepted accepted los interpret disjoint receiver illumination canonical separating sion overview claim claim claim claim claim claim claim verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification verification probe probe probe probe probe probe probe probe probe probe probe probe gesture eigenvector captures adopted svms svms roc roc roc roc ple numerous hair hair validity encodes formulate formulate pentland expanding tween tradeoff tradeoff reports individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals individuals avoided burges burges verified modifying modifying community formance formance rejected rejected rejected rejected projecting projecting statistic frontal harder isi confusion meet rotating parametrized parametrized parametrized nal tel gorithm mea nist saturated identifies interpreting mining concerns manually huang normalize chan classi interpolating scenarios inspection spie spie fication fication saturating inform sur eigenfaces eigenfaces eigenfaces phillips phillips phillips phillips phillips phillips phillips terminology applica preprocessed preprocessed tutorial tutorial fundamentally locating acceptance acceptance acceptance puter accepts accepts accepts claims claims claims claims claimed claimed fac translating mercer ponent pared amples dictated rect turk ori departure standards fax gov deci parameterize identi masked masked alamitos ported sured facto probes probes reporting devising rejects rejects mathe matically haft haft moon wechsler peo mber mber mber evalua reformulating extrapolating ling ling ize bldg 
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm number number number number results results results results results results results results results results results results information problem problem models based based based based based based based based based based based based space space linear linear linear case case vector vector vector vector vector order order order order order order order shown shown shown shown shown shown shown systems systems systems systems values values values values values values values probability probability probability noise recognition recognition recognition recognition recognition method method method method method approach approach approach approach approach approach pattern pattern point point point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single processing processing processing processing large large large large large large large large local local local local rate rate patterns patterns matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix inputs form form form form form shows shows shows shows shows signal signal signal simple gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual paper paper examples examples small small small small size feature net work points points points field field features features process process process current cell problems high high response representation representation architecture show show equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation section fixed fixed fixed line line rule rule rule images images images images images images images images images images images images images images images images images images images images general general general parameter parameter real real real real real real approximation theory theory theory gradient gradient gradient gradient gradient obtained term note note note experiments university computation computation computation computation research research independent log log defined found initial initial initial initial constant constant table estimate estimate estimate estimate standard computer computer terms terms distance distance distance science left frequency temporal temporal machine object object object object object object object object object sets maximum learn learn learn learn learn learn learn learn learn position position position continuous continuous continuous continuous continuous continuous continuous abstract applied applied find computational computational convergence analog properties properties properties properties likelihood references stochastic stochastic due due due due positive positive important important introduction introduction hand circuit estimation estimation estimation estimation effect dynamic dynamic generated generated generated generated generated generated variance variance variance parallel recurrent recurrent recurrent tion tion difference spatial assume assume signals prior prior representations learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned learned chosen higher center previous previous previous previous previous theorem theorem cases cases cases cases cases type type required multiple multiple multiple multiple multiple cortex cortex cortex cortex good distributed bayesian bayesian bayesian bayesian expected make fact fact techniques techniques proposed proposed proposed proposed proposed correct scale minimum minimum minimum minimum ing ing ing respect respect elements mapping mapping factor optimization optimization optimization optimization dimension made natural natural natural natural global global knowledge obtain negative negative negative original relative true series series series series series receptive receptive provide define objects objects objects proc location experimental experimental experimental goal related posterior posterior posterior discrete discrete equal approaches approaches approaches approaches approaches accuracy accuracy accuracy accuracy comparison comparison larger larger larger fields descent descent descent descent descent morgan report institute department implementation implementation implementation implementation code code code individual advances difficult final addition sequences sequences sequences sequences ai ai ai ai ai ai considered computing equivalent directly directly directly view estimates limit san conference efficient full requires choice significant speed speed vision vision vision vision vision vision vision vision estimated estimated pages pages con derived derived randomly randomly actual actual backpropagation nature depends sampling simply biological biological associative achieved covariance technical describe describe arbitrary arbitrary arbitrary group group group group group group group group group group group group group group group group group denote tested tested transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation fast limited limited close close inverse assumption stable actions amount assumed assumed generate generate generate supported theoretical adaptation journal pixel pixel pixel pixel pixel pixel pixel pixel pixel ability degree development kaufmann auditory pairs pairs pairs pairs pairs pairs reduced account account technology testing york mechanism special special special matching principle principle representing details pre stored early produced denotes improve improve pair pair pair pair robust element identical pixels pixels pixels pixels pixels hierarchical engineering varying varying previously previously unsupervised unsupervised unsupervised unsupervised unsupervised approximately tions tions tions studies differential trans trans sparse address locations symmetric exists exists exists parts parts expression expression invariant invariant invariant invariant invariant invariant invariant scaling scaling scaling suggests suggests derivative derivative matrices locally locally deterministic white starting starting starting row row conclusions operator operator operator operator operator operator operator operator operator operator operator operator operator operator valued valued exponential exponential exponential exponential exponential exponential exponential exponential mateo suggest suggest propose presence turn assuming assuming variety plane manner groups groups groups groups groups groups groups groups groups groups groups groups groups minima minima minima minima question question reference reference reference reference reference reference reference reference suppose suppose suppose suppose appears van van van derive derive derive edges written written written perception perception perception perception perception perception perception generating generating generating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating plot plot mathematical metric implement involves involves transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations unique unique unique scales scales scales springer shift shift choosing family formation formation viewed variation variation transform open evaluate evaluate organizing centered forms completely similarly translation translation reasonable performing performing performing performing performing performing expansion reduces purpose tracking interpolation interpolation interpolation interpolation interpolation interpolation interpolation interpolation remains sufficiently foundation degrees expect expect handwritten perceptual perceptual perceptual eigenvalues eigenvalues priors priors black importance uniformly effectively driven comparing invariance invariance tend identity identity identity identity identity fine verlag induced induced allowing link link anderson interested neuroscience issue lie lie lie lie lie 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proach investigating pos intensities intensities translations translations translations translations translations translations translations translations translations translations translations translations zip dorsal sam minor rotating knowing macroscopic rewrite rewrite compu psychophysics gorithm shallow expansions expansions expansions mcculloch mcculloch simplification handling handling pitts pitts marks ping ping european hypothesized utilizes olshausen olshausen generafive finer tors dom dom essen essen concrete equa ventral ples sloan sloan constancy era senses remained ruderman ruderman ruderman ruderman ruderman ance faced ous translate translate neocognitron daniel ues noticed rotate rotate searched unaffected richer tal biophysics direc clockwise bright imaginary imaginary imaginary relying relying fukushima reminiscent sible infinitesimal infinitesimal infinitesimal infinitesimal infinitesimal infinitesimal infinitesimal infinitesimal infinitesimal infinitesimal gibson gibson ative articulated sual concurrent continu supplies transfor transfor undergoing undergoing contin chaining uous opera governs experimen counterclockwise imal imal mations scientists parenthesis tent labor loth loth invariants radians transforma transforma bulletin erated erating invari stating sinc sinc appropri tio alfred ofx houghton straightforwardly xli jepson elaboration conveying eccv cooperating cooperating formations ator ately infinitesimally infinitesimally ascertained 
#@Rao_R,Ruderman_D,
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#*model model model model model figure figure figure figure figure figure figure set algorithm algorithm algorithm number number number number number system results results results results results results results results results results results information problem models models based based based based linear values values values values noise distribution distribution distribution distribution distribution distribution method method method method method method method method method method pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image processing processing processing processing processing processing processing processing processing processing local local local local local local local local local local local local local local local local local test test test patterns patterns patterns form shows shows signal signal signal algorithms simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual paper examples small small size size size feature feature feature feature feature feature feature feature feature feature feature work work work work work work task points points points points points points field features features features features features features classification level level level level level level level current problems high high high high response response response response representation representation show section section section section images images images images images images images images images images images general general general general general general real approximation theory note note result result threshold threshold threshold threshold computation independent defined found found found found found target target constant estimate estimate standard standard standard standard computer computer computer computer computer computer computer distance distance presented presented present present low low low low low low low low low low low frequency frequency object motion motion maximum maximum press press press outputs abstract back find find computational computational properties likelihood references due ieee ieee ieee important complex complex stimulus statistical variance variance variance variance search search search search search search energy energy energy energy energy difference difference difference difference difference variable variable spatial assume assume lower measure measure measure measure measure measure measure chosen higher part previous previous cases type type good good represent represent region region region region region region region region region region region region region region region region region region scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale resulting total human times elements regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions means means means natural natural natural natural natural orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation filter filter filter filter original relative represented compared compared application application application compute compute compute compute objects objects objects objects objects objects proc proc proc perform perform experimental experimental related mit contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast support modeling internal internal responses difficult maps cambridge cambridge cambridge estimates estimates estimates estimates estimates estimates top top top detection approximate statistics statistics statistics statistics statistics statistics statistics vision vision vision vision vision vision basic basic criterion lines lines lines finally nature depends depends technical describe describe finding finding finding finding finding finding shape supported eds eds degree makes noisy including typically typically typically block block block interesting edge edge segmentation segmentation segmentation segmentation segmentation segmentation mechanism filters filters filters filters window window window bottom bottom bottom bottom bottom depth idea attention attention attention attention attention recent similarity similarity similarity similarity similarity subject trees subset recently recently interest interest interest interest interest interest highly compare yields correspond correspond correspond correspond correspond trans definition definition definition definition definition symmetric horizontal horizontal parts studied occur suggests deviation deviation derivative derivative correctly correctly correctly locally deterministic white setting greater greater greater greater operator operator depend performs suggest propose hard hard integration integration labeled labeled labeled labeled labeled labeled labeled derivatives scene scene scene configuration areas perception label label label label vertical vertical modeled confidence sensitivity explicitly simultaneously simultaneously involves scales scales scales frequencies gaussians springer springer blocks blocks independently dependence review review review depending modulation completely suggested fitting fitting roughly purpose purpose purpose purpose filtering visible david building building figures figures color uncertainty discuss discuss discuss candidate partially discussions texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture 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diameter creating eng suggesting specificity specificity specificity belonging belonging belonging draw park park captures captures explains characterization dividing dividing treat email job medium ideally flat flat examining eric intuition parzen parzen life searches surrounding surrounding nasa psychophysics simplifies vice versa neumann marks textures textures vis vis vis vis european european multiresolution oscillate observers skin house house east opponent opponent finer stripes pictures award seattle cord continuum subtracting bregler normalize heterogeneous bergen bergen curved curved alto relational pooling inducing comer reviewed distractors unusual unusual segmenting palo aggregate routine movshon distractor collections leung leung leung notions judge won won synthesize def def psych humphreys humphreys collect ames wolfe wolfe wolfe lacking med malik malik malik malik malik blurring textured textured textured textured textured textured highlight highlights greenspan shi 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#@Rosenholtz_R,
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#*model model model model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data data function function figure figure time set set system results results information information information information information problem models models models models models based based based based based linear linear linear linear linear order order order systems systems systems values values values values values probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight functions distribution distribution method method method approach approach approach approach approach pattern image image image image image image image image image image image image image image image image 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images parameter parameter parameter parameter parameter average average average gradient obtained obtained obtained note experiments experiments result result university variables variables solution solution research research independent log log defined found sequence sequence constant constant constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate computer computer computer science science direction direction presented map map map map map map map map map map map map map map map present low low low low temporal machine motion maximum maximum maximum maximum maximum maximum maximum maximum basis basis sample abstract applied computational density density density density analog likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component due ieee mixture introduction estimation estimation estimation statistical variance variance variance variance variance variance energy difference spatial spatial spatial spatial spatial spatial spatial spatial assume assume assume assume lower rules rules prior prior prior prior prior higher higher higher center multiple multiple multiple multiple conditions bayesian bayesian bayesian region region region observed scale resulting computed computed respect respect respect respect respect multi regions regions regions regions regions regions regions regions regions factor factor factor natural global applications applications knowledge obtain obtain obtain obtain obtain negative relative relative true true true true true true true true true true true compared application desired provide provide compute location location location related related related posterior posterior gain gain equal steps larger contrast contrast contrast contrast selection selection selection selection proceedings proceedings proceedings report report institute department department technique individual advances bias sequences ai maps considered framework framework framework framework framework computing equivalent solutions solutions estimates estimates estimates estimates estimates estimates limit effects effects effects effects full requires statistics statistics statistics statistics vision vision vision vision vision estimated estimated pages pages pages pages increase con con produce produce condition weighted actual provided finally finally finally finally finally processes selected constraint constraint simply simply discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance normal normal normal increases arbitrary group transformation transformation assumption corresponds complete common common common supported supported theoretical square square square pixel pixel pixel noisy noisy noisy noisy noisy sensory including simulated simulated probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic underlying combination technology ratio projection projection increasing uniform database database database database database database database database database database operation principal principal principal principal principal max max early produced choose discussed discussed exact exact ensemble moving subject identical identical hierarchical engineering engineering engineering observations approximately volume pca pca pca pca pca sensitive grant grant scaling alternative locally locally locally locally move demonstrate demonstrate clear performs exponential characteristics characteristics minimizing minimizing selective iii averaged derivatives scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene scene denoted reference relation pro edges edges produces optical optical factors factors factors estimating changing confidence recall missing explicitly explicitly explicitly coordinates averaging averaging averaging averaging averaging physical electrical scales minimization shift shift blocks select formation formation formation formation formation formation formation formation squares squares squares variation variation transform transform transform transform densities frames frames forms allowed allowed sign sign additive additive reduces visible visible visible visible visible visible visible visible visible visible visible visible expect expect box includes automatic specifically priors priors variations variations variations variations variations variations partially sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor selecting closely suitable suitable society society latent latent build schemes situation situation essentially capture soc conf procedures heuristic video video video showing superior lie lie lie lie lie contribution contribution contribution contribution contribution contribution contribution hold comp vary vary vary vary eigenvalue eigenvalue eigenvalue highest ill leading acknowledgments carried wiley production requirements exhibit varied put replaced replaced limitations ml ml ml ml ml ml ml ml ml ml ml ml ml ml ml ml ml rise scalar reducing reducing successive respond tech int combine combine scaled coefficient concepts editor perfect obvious obvious consist contributions motivated synthetic synthetic averages averages averages averages devices slowly slowly band band band band band band band band band band band band trivial sensors sensors sensors sensors sensors sensors sensors sensors sensors sensors sensors sensors sensors choices bishop arise arise probable ion involve circle nsf fourth affine consistency consistency offset autonomous autonomous reliability maintain marginal boston display display pyramid pyramid pyramid pyramid pyramid pyramid pose pose shifted benefit sensing leen leen leen leen writing conditioned recover dealing imaging imaging difficulties overcome simplify attractive efficacy enhanced enhanced regarded captured candidates express clean properly properly properly eigenvector eigenvector eigenvector captures implicitly fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion fusion posteriori radar radar ple rigorous piece piece aston email kluwer equivalently aircraft aircraft aircraft spatio spatio adopt smoothly corrected laplacian laplacian laplacian constrain principled arising diag impose impose graduate guidance guidance guidance rectangle surrounding proach complementary complementary complementary complementary complementary complementary intensities intensities intensities setup refinement nasa minor flight vanishes oregon lighting fiat reversal reversed reversed reversed inconsistent attributed multiresolution hat todd dropped accomplish burr polarity polarity polarity polarity polarity polarity subtracted clark spie spie spie spie spie spie weather compensated firm relaxed decompose ceedings tipping ece invert ogi ogi synthesize registration unlimited ecs ames ages posterjori fuse landing landing landing landing adopting rendered encounter cse zhou ncrg klein dictated dictated rue rue portland cre ergodicity visibility visibility proportionality appeal folded nical infrared infrared infrared ger insures roberts als fused fused fused fused fused fused fused reads ors reversals reversals reversals reversals attenuated attenuated attenuated refinements burt grounds terrain invoking compensates loadings tax taining ime ncc alg alg envision hnage fusing sla fio exercised yla misha hese penetrate 
#@Leen_T,Pavel_M,Sharma_R,
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#*network model model model model model model model model model neural neural neural neural input function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set output number number number number number number number number system system results results based based case order order probability probability probability probability parameters parameters parameters parameters functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution point point point point single single local local local local local local local local local local rate rate test analysis matrix matrix matrix matrix matrix form form gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper size size size work methods points field field field field field field field field field field field field field process random random random random show show show show equation equation line line line general general general general generalization parameter real real real real real real real real theory note note note experiments experiments result result university computation computation computation solution research log log initial constant constant constant standard standard standard computer computer computer terms terms science left left left left left left left left left left direction direction direction direction direction direction maximum maximum maximum maximum maximum maximum maximum maximum press position position position position position position position position position position position position position position position components components sample sample abstract find find properties properties properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due due due due due due positive positive positive positive positive positive positive positive positive mixture mixture introduction stimulus effect effect effect effect variance variance variance variance parallel parallel tion change energy spatial spatial spatial spatial spatial spatial spatial assume assume lower measure prior chosen higher higher previous conditions represent represent distributed fact proposed length probabilities probabilities probabilities probabilities probabilities observed observed scale scale scale scale scale scale scale scale scale scale scale scale scale ing human human computed computed times times times factor factor natural natural natural orientation orientation orientation orientation orientation orientation global global relative relative relative relative relative relative relative relative relative relative cross cross cross cross cross cross cross cross cross cross cross define define compute compute compute compute compute compute compute proc related related constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints distributions discrete equal equal equal larger larger fields fields fields fields fields fields fields fields source report report institute consists consists consists consists represents represents represents cambridge curve additional transition transition transition transition transition transition transition limit limit limit statistics speed speed speed speed speed speed speed speed speed speed speed vision vision basic con produce conditional velocity velocity velocity velocity velocity velocity lines lines lines lines lines lines product product finally processes selected constraint constraint constraint constraint constraint simply biological normal normal normal technical increases increases increases arbitrary arbitrary corresponds short shape shape shape shape shape shape shape shape shape shape shape journal square square square square square square square square square square square square square end end typically typically pairs pairs pairs pairs pairs smaller smaller smaller block block block interesting york increasing segmentation mechanism consistent consistent consistent mode details call call call numbers numbers max max max max max max magnitude magnitude magnitude magnitude magnitude magnitude decay improved directions directions directions directions directions directions directions recent recent pair reported introduced moving identical recently interest previously previously previously approximately approximately approximately approximately approximately subjects axis tions tions solve smooth rl rl diagonal diagonal positions positions locations symmetric modified interval interval interval interval williams williams williams williams williams williams williams williams williams williams williams increased increased arm expression expression studied invariant invariant invariant invariant invariant invariant suggests deviation matrices width width width width width pass pass half conclusion trajectories trajectories tangent numerical numerical weak weak weak strong strong largest largest largest largest largest drawn solid solid solid solid start plane plane averaged base suppose suppose solving plot plot plot dept modeled modeled remaining scales scales scales scales scales consisting gaussians minimization springer implies decreases formation formation dependence evaluated evaluated showed sizes sizes translation past earlier dashed dashed dashed dashed intervals closed closed closed closed closed closed closed closed closed closed closed remains intermediate distances assigned degrees perceptual priori priori priori usa contour contour contour contour contour contour contour contour contour contour contour contour contour contour weighting weighting weighting weighting plotted plotted plotted plotted simplicity reason uniformly uniformly paths invariance invariance invariance tend refer refer refer refer verlag showing interested dis dis symmetry symmetry sci satisfy satisfy satisfy satisfy eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue reach jacobs jacobs jacobs jacobs jacobs jacobs jacobs intrinsic remain varied varied scaled scaled comparable eigenvectors eigenvectors eigenvectors workshop affect notion contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours contours act act gradients opposite psychology noted freedom observe observe observe observe observe observe observe observe shapes shapes shapes shapes shapes shapes consist explain explain optimum optimum optimum optimum scenes ground orientations orientations orientations orientations defining defining analytic majority independence straight satisfied located located acad circle circle circle circle circle circle circle circle circle circle circle circle circle circle circle beginning begin begin begin begin geometry cybernetics incomplete greatly double pure completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion completion frequently maxima maxima maxima maxima maxima maxima poisson poisson poisson anti limiting limiting limiting limiting limiting reaches reaches lim univ discontinuities restriction princeton ratios angular circular circular satisfying logarithmic enhanced natl started respective widths widths widths infinity diameter diameter diameter diameter permutation horn passing passing motions motions eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector eigenvector speeds speeds summarize johnson assigns minus maximized maximized emergent emergent emergent emergent perceived perceived perceived perceived perceived spaced recurrence recurrence letting algebraic param acting acting magnitudes magnitudes approxi dominated dominated discontinuity life crosses crosses crosses crosses argued noting increasingly crossings intl particle particle particle margins drops travel psychophysics nec reversal reversal characterizing reversed corners impulses impulses impulses impulses impulses impulses impulses observers observers observers routines routines char tribution tribution comprising factorization randomness confined closure closure ings doubling doubling doubling doubling 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#@Thomber_K,Williams_L,
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#*learning learning learning learning learning learning learning learning model data data data data data data data data data data data data data data function function function function function function figure figure figure figure figure time set set set set set training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm number number number number number error results results results results results results results results results results information information information problem problem models models models performance performance performance based based based based based based space space space space space space space space space linear vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown shown shown shown shown systems systems values values values probability parameters functions functions functions functions distribution recognition recognition recognition method method method method approach approach pattern point point point point point point image image image image image large local local test test test test test test test test class class class class class class class class class class class class class class class class class class class class class class class class optimal form form form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple examples examples examples examples examples examples examples feature feature feature feature work work work work work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods fig fig fig fig fig fig fig fig fig points points points points points points points points points points points points points points points points points points points points points points points points points features features features features features features features features features classification classification classification classification classification classification classification classification classification classification process current current current structure problems random random random random random random random random random high similar similar similar similar similar similar similar show section rule vectors vectors vectors vectors vectors vectors images images images images images images images general real real real real real average states theory obtained obtained obtained obtained obtained experiments dimensional dimensional result result university computation research found estimate standard standard computer computer computer computer computer computer computer terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance science left left left present object object object object object object object object range basis basis abstract applied computational computational computational computational properties references ieee ieee ieee important important decision mixture complex complex complex complex behavior statistical generated difference difference complexity complexity measure measure measure measure prior representations chosen chosen chosen chosen higher part part bound cases good good good represent represent represent represent represent represent represent represent represent represent represent represent bayesian expected make make fact fact fact techniques techniques techniques techniques region proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correct correct correct correct errors errors simulations simulations classes classes classes classes classes ing ing total simulation simulation human human regression computed computed computed computed computed computed computed computed sum sum called elements regions means factor dimension dimension natural natural feedback applications applications applications applications applications applications study knowledge knowledge knowledge vol artificial relative specific specific specific represented compared define compute compute objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects objects proc proc determined determined determined experimental related constraints distributions distributions gain approaches approaches approaches comparison modeling selection selection selection selection selection institute consists consists individual graph framework directly directly curve curve curve additional curves design top top detection detection determine determine determine efficient efficient efficient significant significant statistics statistics vision vision vision vision vision give produce derived randomly clustering developed robot processes nature nature nature depends depends measured normal normal normal describe arbitrary denote denote denote limited limited close close close close predictions proof proof finding finding finding finding nearest nearest nearest nearest nearest nearest nearest nearest nearest common effective effective assumed assumed theoretical cluster cluster cluster cluster easily degree including typically typically account block interesting significantly consistent matching matching matching database database database leads squared representing details numbers numbers pre making bottom bottom bottom supervised supervised supervised supervised supervised exact exact advantage advantage robust robust robust robust robust element element element similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity practical practical apply apply subset subset subset cognitive cognitive cognitive cognitive cognitive cognitive cognitive cognitive relevant dimensions dimensions highly compare compare previously previously previously previously calculated trans trans trans trans definition definition background modified modified generalized williams studied deviation deviation wide alternative clusters clusters clusters white boundary boundary boundary boundary boundary boundary boundary column column column column column demonstrate half minimal minimal row neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor differences differences measures measures designed constrained taking presence demonstrated demonstrated labeled labeled labeled labeled labeled min min plane plane identification force question question question reference suppose suppose suppose suppose longer plot label mathematical changing changing modeled metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric metric implement category category category explicitly develop select select select john choosing independently focus focus review review review review correlated correlated correlated squares open understanding similarly past diagram diagram diagram diagram diagram diagram diagram key earlier spaces spaces spaces spaces spaces spaces spaces spaces spaces boundaries distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean euclidean classified classified david existing existing existing existing box box includes priori coordinate coordinate usa color retrieval retrieval instances extension discuss discuss specifically specifically specifically black black black black black absolute neighbors reason determining determining determining selecting suitable differ computationally successful identify score plots miller conf prob interested dis return classify classify classify classify hold categories comp quantity list vary vary minimizes attempt illustrates illustrates illustrates preferred jacobs jacobs jacobs jacobs jacobs software extend minimized bars employed explore parametric parametric parametric parametric parametric parametric parametric parametric parametric wiley investigate experience experience detail matches giving giving ideas ideas int int workshop scores notion contours contours contours contours math coefficient closest possibly man man analyze psychology psychology psychology illustrate thought prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype prototype friedman algo assumes separated store submitted motivated percentage inequality inequality inequality inequality inequality inequality pairwise agreement defining answer answer independence tractable worse handle reasons considerable closer closer widely division desirable desirable separately describing members members members members begin lowest exemplars exemplars exemplars exemplars geometric geometric percent percent substantially relevance lack car poorly psychophysical item employ employ treated frequently frequently psychological ity ity outliers requirement prototypes prototypes prototypes prototypes prototypes proven proven replace hamming median median median median median median median median median median median median median median median median credit credit calls wesley extreme extreme representative representative representative representative addison guarantee princeton acm pick databases logarithmic imply modifications intuitive loo loo encountered encountered guarantees bad histograms sim belongs spherical similarities similarities darpa israel occlusion mem reveals omitted omitted belonging draw sons designing omohundro hart appeared ter ent equivalently ber pieces classic rain rain arising unseen summarizes summarizes exam insights insights insights rithms crosses categorization worth union commercial things treating voronoi voronoi voronoi voronoi voronoi voronoi voronoi voronoi modal nec coming diagrams diagrams lems demonstrating simplification handling handling vis vis pictures concrete concrete concrete dichotomy 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#@Gdalyahu_Y,Jacobs_D,Weinshall_D,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training output output output output output output output output output output output output output output output output output output number number number system system system system error error error error error results results results results results results results units units units units information information problem problem problem problem problem models models hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based weights layer case case vector shown shown shown shown shown shown shown shown shown shown shown systems systems systems unit unit distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single single single single single processing large large local rate rate test analysis class class class class class matrix matrix inputs inputs form shows signal algorithms algorithms simple simple gaussian paper paper paper paper paper paper paper paper paper paper paper paper paper paper paper examples examples examples examples examples examples examples examples examples small small size net net net net work work work work task task task task task methods methods methods methods step step step step step field features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process process process process level trained trained trained trained trained trained trained trained trained trained trained trained trained problems random high high similar similar similar similar similar representation representation representation architecture show section section section section line line line images images images images images images images images images images images general real real real real average average note note note note note note note experiments result university computation computation research research research target target table table table standard standard standard computer computer computer science left presented presented presented presented presented presented presented presented presented presented presented presented activation activation low machine object object object object sets maximum maximum maximum maximum maximum position position outputs outputs outputs outputs outputs continuous sample abstract applied applied applied applied back back back computational references component due ieee positive positive positive procedure procedure procedure procedure procedure procedure propagation context introduction hand estimation statistical effect effect search search tion tion tion variable classifier classifier center center center previous cases cases cases cases cases cases multiple multiple good binary binary binary spike represent expected expected make make make make make make make make make techniques techniques techniques proposed proposed correlation correct errors errors errors errors forward resulting resulting resulting classes ing ing tasks respect performed performed made orientation orientation study study negative negative negative original original original original original vol application application desired desired receptive provide objects rates location perform connected connected connected distributions distributions distributions approaches approaches approaches approaches accuracy accuracy comparison comparison support train train train train train train train morgan proceedings proceedings report version technique consists consists individual individual advances represents difficult difficult addition graph graph ai equivalent experiment experiment directly stage detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection efficient classifiers upper full world world world vision vision vision vision con con robot finally achieved technical increases increases describe arbitrary group tested tested tested transformation limited close close complete complete finding rbf amount amount nearest effective implemented require require face face face face face face face future future easily easily easily degree degree makes makes including including probabilistic pairs account fully interesting testing testing testing testing testing testing testing character mechanism database empirical principal pre making making making making window international bottom early idea idea combined predict architectures improved discussed discussed takes similarity reported include machines pixels recently interest compare previously previously approximately approximately approximately approximately works axis axis tions tions tions yields yields match studies diagonal address background symmetric modified entire horizontal parts invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant occur suggests extended digital rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation rotation predicted alternative correctly touretzky pass pass row row row row row row row row row conclusions conclusions neighbor differences measures accurate designed peak peak faster faster suggest suggest encoding encoding encoding encoding strong reduction intelligence turn assuming variety plane plane plane plane plane plane averaged manner characters characters groups groups groups base base base acknowledgements suppose appears digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit digit written describes describes distinct slightly text text text angle angle angle angle angle angle angle angle angle angle angle angle angle applying yield focus detailed transform lee lee frames digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits digits discrimination discrimination key earlier slow measurements event classified faces faces faces transactions david degrees degrees avoid expect recorded recorded recorded existing template template handwritten handwritten handwritten handwritten handwritten handwritten handwritten handwritten instances recognize recognize recognize recognize vapnik vapnik extension automatic maximize activated candidate candidate candidate successfully successfully successfully reason closely closely modification computationally divided detect detect post comparing miller repeated procedures contained contained cun cun cun cun cun cun cun cun cun cun prob video video video video dis return return classify classify classify classify classify content simplified nips denker denker denker denker overlapping situations presents employed remain remain remain unlike unlike unlike transformed create access rapidly association preliminary preliminary preliminary matches matches successive school applicable office office working working workshop fundamental neu examined examined examined patch concepts reading configurations predicts extremely extremely extremely ensure prototype portion noted noted detector detector academic detected detected detected simplest simplest mentioned ment scenes scenes scenes ground crucial orientations orientations convolution convolution expensive briefly handle handle comparisons processed perspective straight sys shared commonly simard simard potentially recognized recognized recognized recognized recognized angles angles patches patches patches demonstrates author recognizing mellon mechanics geometric reflects carnegie cmu amounts conducted quantitative passed passed passed employ incorrect templates templates templates templates templates templates templates templates templates templates howard rely measuring pittsburgh pittsburgh incorporating segmented segmented returns returns returns implements eventually hints naive naive classifying discontinuities contextual aligned proportion mistake tation resources databases rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated rotated mobile tem eliminate eliminate rotations rotations rotations rotations rotations rotations rotations rotations rotations rotations lecun lecun lecun establish eliminated eliminated kaufman smith promising imposed biased hope nearby ral effectiveness alphabet days filled hours ranging respective encountered conjunction regard belongs jackel jackel jackel candidates candidates entries entries recog repeatedly repeatedly draw correcting subsequently severe lem sequentially informa dramatically yielded slight largely numerous unable unable misclassification kluwer guyon guyon guyon guyon exhaustive exhaustive convolutional nition boser ease spaced descriptions imagine reject clas avoids henderson increment increment increment exam intuition formance pami baluja baluja baluja baluja baluja baluja baluja baluja baluja ijcnn ocr activate guidance hubbard pomerleau pomerleau pomerleau hughes concentrate paired individually rejected surrounding frontal frontal ambiguous drawback nonetheless nonetheless confusion confusion rotating admissible applicability els increments increments increments challenge strict suggestions expense january finer jain jain bottou bottou returned returned vote vote vote vote classi tance frequent frequent prone sian upright upright upright upright upright upright upright upright upright upright upright upright upright upright upright upright upright upright upright upright upright 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#@Baluja_S,
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#*network network network network network network learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training training training algorithm algorithm algorithm number number number number number number number system error results results results results information information information information information problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based space linear case case order order shown shown shown shown shown shown shown shown systems systems systems systems systems values values values probability probability probability probability probability probability probability parameters parameters parameters parameters parameters weight weight distribution distribution distribution recognition recognition recognition recognition recognition recognition method method approach approach approach pattern pattern image image image image image image image image image image image image image image single processing processing large large large large large large large large local local local local local local local rate test test test test analysis class class class class class class class class class class optimal optimal optimal form form form form shows shows paper paper paper paper paper paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small size size feature net net work work work work work work work work work work work task task methods methods methods methods methods fig step step classification classification classification classification classification classification classification classification classification process process process process trained problems random similar similar similar representation show show show section section section section section section section section section section section section images images images images images images images images images images images images images images images images images images images images images images images images real real theory obtained obtained note note note note note note note experiments experiments experiments university variables research research independent independent independent log constant constant standard computer computer computer computer computer computer computer node science left left left left left left left left left left presented presented presented presented presented machine machine object sets motion maximum maximum maximum maximum range range sample sample abstract applied find computational likelihood likelihood references due ieee ieee ieee important mixture mixture mixture introduction complex hand estimation statistical statistical effect cost tion tion tion change change complexity variable variable classifier classifier learned learned learned center previous required required multiple multiple multiple good good binary binary binary binary binary represent represent tree tree tree tree tree tree bayesian bayesian bayesian bayesian bayesian expected techniques proposed correct correct probabilities probabilities resulting classes classes classes classes classes ing tasks tasks tasks total total performed times potential made feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation applications applications em em em em em em em em em em em obtain obtain obtain original original original vol relative relative specific samples represented true cross series provide provide provide compute rates location location perform perform perform active active active active related related related related related related posterior posterior connected distributions distributions distributions discrete equal equal approaches mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy contrast contrast train dependent modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling selection words consists represents represents difficult addition graph graph graph ai ai maps domain experiment directly directly directly additional design design detection detection detection detection determine classifiers classifiers classifiers classifiers classifiers classifiers requires requires significant estimated estimated estimated estimated increase increase validation con condition condition weighted randomly conditional provided provided finally finally selected increases increases describe arbitrary arbitrary transformation limited limited limited limited assumption complete finding finding finding amount amount amount amount amount amount amount effective assumed require face face face face face face face face face face face face face face face face face face face face face face face face square pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel future future easily makes including fit probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic pairs smaller underlying reduced account unknown jordan jordan jordan jordan interesting interesting testing edge edge empirical empirical details details iterations iterations pre pre pre experts experts supervised magnitude magnitude attention description description description description light improved improved improved improved improved improved improve improve pair pair pair reported practical apply include pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels pixels trees trees trees trees trees trees trees trees sejnowski sejnowski interest varying varying varying compare observations approximately approximately approximately works works axis axis solve solve yields match match achieve achieve trans improvement improvement improvement increased intensity expression expression invariant half half greater segment conclusions conclusions accurate accurate bayes bayes bayes performs performs drawn intelligence intelligence labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled labeled assuming assuming user user user user ica exist manner groups attractor areas pro construct edges describes label label modeled modeled modeled missing missing text text text mutual mutual gaussians applying applying expectation expectation expectation expectation cycles cycles select decreases dependence dependence dependence dependence dependence dependence learner detailed restricted labels labels labels labels labels labels centered discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination diagram smoothing normalization sec false calculate calculate assigned classified faces faces transactions transactions avoid thesis color retrieval inter inter inter candidate candidate absolute neighbors neighbors neighbors neighbors discussions discussions tests determining middle capable society divided wij build miller miller capture capture quickly graphs repeated procedures video interested dis dis dis contribution classify classify classify content gray cues notation providing nips nips nips minimizes quantization ill maximization maximization maximization automatically neurosci approximating neighboring neighboring neighboring acknowledgments presents presents bars bars employed unlike create difficulty difficulty rapidly varied detail detail limitations divergence preliminary mass mass dataset ml fewer reducing reducing reducing reducing examine school detectors detectors relationships dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies root working variability attributes examined closest facial facial facial created front friedman friedman versions obvious assumes detector detector explored explored explored explored explored explored mapped mapped simplest contributions attempts mentioned percentage histogram histogram directed orientations orientations orientations orientations improves improves improves adjacent independence briefly rapid easier incorporate worst immediately pool describing arises demonstrates incomplete incomplete mellon greatly greatly percent percent carnegie profile profile profile profile profile profile profile profile empirically cmu dark amounts amounts amounts amounts amounts amounts amounts conducted readily readily documents documents car poorly rep mod pittsburgh spread maximizes parent parent parent incorporating incorporating adjust semi semi comments shaped naive naive naive naive phenomenon pose person person person classifying lab ghahramani ghahramani ghahramani ghahramani benefit sensing interface formally restrict restrict ordering circular circular circular discover royal children kullback ments promising viewpoint hope exploit unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled cottrell cottrell degradation spurious spurious games mance bartlett bartlett ranging corre perfor regarded dependency dependency dependency dependency dependency dependency dependency dependency dependency dependency dependency dependency vertices sim belongs counting counting permutation vertex belonging splits dempster dempster parents andrew discriminate dramatically liu liu liu liu ure arcs unable thrun rubin leibler benefits pentland pentland restrictions avoided remote remainder attempted cohn cohn pami baluja baluja baluja baluja baluja baluja distribu approxi maintained mitchell hughes met wise wise wise scope frontal frontal gender employing monitoring laird discusses geiger maintains suffer memo knowing els aaai suggestions argmax consuming january monitor monitor monitor emotion termination termination fill fill incorporation exclusively classi positives maxi maxi rel fol filling scott cess tra tra dent acyclic sep violated indexing probabil mounted discriminating discriminating sented eigenfaces adv adv spanning spanning sung sung sung cations appli mization accuracies mum graphically graphically examines equalization availability centroids ities imposing comprises helped helped classifica ting ative lowing parentheses augment augment augment augment rowley rowley rowley cog pared cameras cameras plex susceptible susceptible kanade generatire generatire depen depen metcalfe metcalfe hurt hurt mccallum mccallum turk turk chow chow chow chow sponds sit orienta inexpensive overcoming probabilistically probabilistically davies cial discriminated ond holons representable interfaces wealth augmenting augmenting augmenting icml vital iip resented ret shumeet mately closes artifi henry drafts beled beled beled beled existed pis docu plicity arate fier fewest paying tremendously acknowl 
#@Baluja_S,
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#*network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural data data data data data data data data data data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set set networks algorithm algorithm algorithm algorithm algorithm number number number number results results models models models models models models models models models models models models based based case vector vector vector vector vector vector vector order shown shown systems values values values values values values values values values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions distribution distribution distribution distribution distribution distribution distribution distribution method method method approach approach point control large large large large local analysis analysis matrix matrix matrix matrix form shows gaussian gaussian gaussian gaussian visual examples examples examples small work work work work methods methods fig step points points points points points points points points points points points points points points field field field field field field field field field field field features features features process process level similar show section section section section line line line line line vectors vectors vectors vectors vectors parameter parameter parameter parameter real real real real note dimensional university university university university university variables variables computation computation research research independent independent log log log defined defined defined found dynamics initial initial initial computer computer distance science direction direction direction temporal maximum range range press position position position position components components sample sample sample sample sample sample sample abstract applied applied find find find convergence convergence properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component procedure procedure procedure procedure procedure introduction complex estimation statistical statistical statistical generated generated generated generated tion tion change energy energy energy spatial spatial assume measure prior prior prior prior prior required good good long conditions represent represent distributed bayesian bayesian bayesian markov markov markov markov markov markov markov markov markov make region proposed correlation correlation length length length length correct observed observed scale scale scale scale scale simulations minimum minimum resulting ing simulation computed computed respect performed regions regions regions means made orientation orientation knowledge obtain negative negative relative samples true true compared application cross provide provide define define compute location perform determined related posterior posterior posterior posterior posterior posterior posterior constraints distributions distributions fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields fields report report department joint difficult final final exp exp exp exp ai framework cambridge cambridge computing computing domain domain equivalent equivalent curve curve curve full requires choice statistics speed speed speed speed speed vision give produce produce derived derived conditional developed velocity lines product processes processes processes evidence iteration depends depends sampling sampling sampling constraint simply discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance technical technical technical describe group group tested close close stable surface surface surface surface surface predictions predictions common assumed assumed assumed supported journal journal square makes including fit simulated simulated simulated simulated simulated simulated simulated simulated probabilistic probabilistic typically smaller combination account interesting significantly york consistent empirical representing details numbers expert frame run description improved discussed advantage robust takes typical typical include period subject side side side side inference inference inference observations axis tions smooth smooth converge converge definition chain chain chain chain chain chain chain chain chain chain modified modified modified modified observation observation williams williams williams williams grant grant horizontal lead suggests derivative predicted correctly locally hybrid boundary boundary generally demonstrate starting conclusions valued valued valued valued valued constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained temperature integration assuming plane plane introduce acknowledgements monte monte monte monte carlo carlo carlo carlo produces index generating generating generating vertical sensitivity physical physical text angle angle angle angle angle angle angle angle scales adding adding adding adding john review reconstruction stationary stationary interpretation evaluated evaluated evaluated evaluated evaluate suggested reasonable combining initially figures figures specifically priors priors priors priors priors domains partially regular determining suitable computationally paths identify plots quickly quickly prob allowing allowing interested interested interpreted generative generative generative generative generative generative generative generative generative notation sampled usual realistic realistic realistic correspondence principles deal oriented modelling modelling modelling modelling situations origin remain american american wiley rapidly put detail strengths integral integral preliminary ml ml ml ml ml scalar rest investigated stream variability variability proved affect understand surfaces hill plausible possibly illustrate front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front front observe seconds neal neal neal years histogram histogram cos smoothness smoothness variances coded spatially straight division division describing describing describing toronto addressed questions improvements improvements varies evaluating flexible flexible flexible simulate simulate simulate simulate simulate marked splines remove remove http http http calculating wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind wind discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities discontinuities uncorrelated primarily www www www temporally conditioned conditioned chains hyper north north north falls ensures sides sides sides sides dependency dependency intended accounts infer ahead ahead ahead ahead ahead sons likelihoods adopted insensitive outlined outlined ics posteriori fitted ure aston aston aston aston aston aston covering spatio comparative corrected reports edinburgh edinburgh assess param exponent community discontinuity discontinuity discontinuity discontinuity discontinuity bounding frontal frontal frontal frontal frontal frontal frontal frontal frontal frontal library funded placing mcmc mcmc mcmc mcmc page ation union matlab eters lems resolve discontinuous christopher tial european spacing spacing spacing generafive fill conditionally conditionally conditionally poly html html curved cold corn metropolis metropolis metropolis assessed derives birmingham birmingham satellite ini ambiguities demanding crg clockwise putting forrest initialised strain strain univariate dynam poten ana stays asymptotics brings epsrc ncrg ncrg ncrg eter weaknesses weaknesses gps gps gps gps gps gps gps gps gps intend proj retrieving retrieving associa diagnostics diagnostics dan associ ford gle radford observa accessed kin kin scotland radians ian descrip completing sgi url tax initialise misfit bessel bessel bessel programme usefully atmospheric atmospheric atmospheric utoronto atlantic informatics differentiability oti burn kill kill ects kll kll zxt nomials 
#@Cornford_D,Nabney_I,Williams_C,
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#*network network network network network network network network network network network network network network network network network network network network network network network neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time set set set set networks networks algorithm algorithm output number number system system system system results results results results results information information information information information information information information problem problem problem performance based based based based based linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer order order shown shown shown shown shown systems values values values values values values values values values values values probability parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution recognition method method method method method method method method method method method approach pattern pattern pattern point point point single single processing processing large large local local local local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate test patterns analysis form form form form shows signal algorithms simple simple simple gaussian visual visual visual visual paper paper small small small net task task methods methods methods methods methods methods fig cells step step step points points points points points points points points points field field field field field field field field field classification level level level level current structure structure problems high high high high high high high high similar similar representation representation representation representation architecture architecture architecture show equation section section fixed fixed fixed line line line line line line line line line line line line line line parameter real average obtained obtained obtained obtained note note experiments experiments experiments experiments experiments experiments experiments experiments activity activity activity activity result result result university university threshold threshold computation computation solution research defined defined found estimate estimate estimate estimate standard computer distance distance connections synaptic science science direction present present present present activation activation low sets press position outputs continuous sample sample sample abstract find computational references due due due due due due due procedure procedure important decision decision introduction complex generated parallel parallel energy energy energy energy energy energy energy difference assume lower chosen chosen higher part part center center center previous previous type proposed proposed length correct correct finite total simulation regression regression respect sum performed times mapping means made made orientation orientation orientation orientation global global global study obtain specific represented represented compared compared compared compared compared compared compared receptive receptive receptive receptive receptive receptive receptive compute location location location location location location location location location location perform perform perform active active active experimental connected distributions discrete brain mit steps accuracy fields report words department implementation implementation advances represents represents final final final final layers layers addition considered domain domain equivalent experiment experiment solutions solutions estimates trajectory effects efficient full full full basic basic con area types types path processes processes selected nature simply measured measured discussion feedforward feedforward denote denote tested fast fast limited corresponds corresponds excitatory finding common common shape supported eds easily fit fit fit typically jordan projection projection york leads making making making idea produced produced produced produced denotes architectures directions resolution resolution resolution resolution exact exact exact advantage separate takes element typical typical moving identical identical relevant relevant relevant interest interest interest dimensions sufficient compare conventional calculated volume axis axis axis axis axis yields trans background locations risk sensitive expression lead lead occur correctly hardware hardware runs place place reduce trajectories segment segment segment segment segment segment segment segment central tangent retina performs suggest taking physics physics physics physics physics physics physics labeled labeled radial pulse selective plane plane plane plane plane plane plane scene identification identification identification identification identification identification identification identification identification identification denoted monte monte monte carlo carlo carlo index winner factors primary laboratory laboratory label distinct segments segments segments segments segments segments segments segments missing coordinates coordinates coordinates coordinates coordinates averaging averaging averaging averaging physical physical slightly slightly angle interaction interaction interaction interaction interaction interaction develop events events events events events events events events events events quality select select national dependence reconstruction reconstruction viewed viewed transform open evaluate evaluate fraction centered forms activities completely similarly sign sign key event event event event event event event event purpose tracking distances filtering assigned assigned foundation david thesis coordinate coordinate coordinate coordinate coordinate coordinate sciences recognize determines illustrated mozer phys phys phys partially tests selecting identified differ identify detect efficiently computations post receives refer lie sin sin timing involved extract acknowledgments software employed origin origin origin origin origin origin origin wiley production biases fashion fashion school detectors detectors possibility neu closest subsets noted detector detector detector detector detector detector detector academic detected established optimum devices histogram histogram histogram histogram histogram great cos cos crucial track track track track slope answer considerable processed straight purposes arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc ring ring filtered precisely constructing ran commonly projected projected projected describing res res radius radius meaning fourth fourth fourth fourth fourth fourth fourth double collected led readily marked dots compares passes gen incoming curvature curvature curvature germany simulator inherent sophisticated physiol college sort labeling forming oxford null null null null arrival inspired consideration promising determination determination hit hit hit hope obtaining ral responsible fires analyses ambiguity ambiguity widths displayed regarded moved conjunction belongs propagated originally israel israel israel treatment vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex horn horn horn horn horn horn ends belonging hart lett fold fold thresholding mechanical crossing arcs arcs arcs arcs arcs arcs arcs unable covering wiesel uniquely magnetic magnetic trigger generalizations hubel perpendicular mhz mhz duda denoting wise relates particle particle particle particle particle meet thousands tel tel tel tel failures status challenge tau covers appearing algorithmic satisfactory lated clarity proposal petsche outgoing tracks tracks tracks tracks tracks tracks tracks tracks curved curved curved hough hough server nominal scatter energies aviv aviv aviv aviv tens tens tens wires hits hits hits particles particles particles particles particles particles particles particles preferable extrapolation collision plotting plotting helix nuclear nuclear tinuous accelerator faculty simu expects superfluous superfluous quantum raymond rings rings rings rings handles uncertainties triggers collaboration fii indebted foster heaviside exemplified charged surrounds akin mech triggering triggering triggering triggering concentric concentric cylindrical erated sinc crn patent flux inl lective astronomy multilevel anism beverly sackler disregarded emanating emanating tre 
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#*network network network network network network network network network network network network network network network network network learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data function function function function function function function function figure figure time set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number system system system results results results performance performance based based based based based based case case case case vector vector vector vector vector shown systems systems systems systems values values values values values values values values values weight weight unit recognition recognition recognition recognition recognition recognition recognition method method method method method approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point point single single single single processing large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test test test test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class class class class class class class class class class class class class class class class class class class class optimal optimal optimal optimal optimal optimal inputs inputs inputs shows signal signal signal paper examples small size task task task task methods methods fig fig fig fig fig points field field field classification classification process process process process current trained trained trained random high high memory memory memory memory response response architecture architecture line line line line line line line rule vectors vectors vectors parameter parameter approximation average obtained obtained obtained obtained note dimensional university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation research research research research research research research research independent defined defined defined sequence sequence sequence sequence target target target target target target target target initial initial initial table table table table table table table computer computer distance distance distance distance node node node node node node node node node node node node node prediction prediction prediction left presented presented presented presented presented present present activation low low low nodes nodes object object object object object object sets sets sets maximum range range range range range range range range range range range range range range range range range press components components components components sample abstract applied find analog analog references component component component component due due ieee ieee ieee ieee positive positive important adaptive decision decision decision introduction hand hand cost cost cost search search tion tion classifier measure measure measure measure measure measure learned chosen higher part part center center center cases type type required good good good good fact techniques correct correct errors simulations simulations simulations simulations simulations simulations simulations classes classes classes classes classes classes classes classes classes classes classes total simulation computed made made natural applications artificial relative relative compared application application provide define rates perform perform perform active active active active active determined determined determined determined determined determined equal equal accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison contrast support selection selection selection selection selection proceedings department department internal code final final final addition ai maps computing equivalent equivalent curve curve curve curve curve curve curve curve curve curve curve curve curve curve additional view view curves curves curves curves curves curves curves curves curves curves curves curves stage detection conference determine classifiers upper requires choice choice choice validation validation validation validation validation validation con coding coding coding coding coding coding coding randomly clustering criterion criterion area types actual actual actual actual finally selected selected selected selected evidence evidence evidence evidence evidence evidence evidence depends tested tested fast fast fast close close close close corresponds complete stable predictions nearest nearest nearest nearest nearest nearest nearest nearest nearest nearest effective effective generate generate supported supported eds eds square ability degree makes makes simulated simulated simulated simulated simulated simulated simulated typically typically combination combination reduced reduced reduced fully block block testing testing testing testing testing testing testing testing testing testing testing testing testing testing testing testing testing testing testing testing york matching matching operation operation max making international supervised produced predict predict improved takes include identical identical identical subset subset subset subset subset subset cognitive engineering engineering compare previously observations observations observations calculated smooth smooth smooth yields match match match match match match definition definition positions positions observation grant suggests extended predicted predicted predicted predicted predicted predicted predicted predicted predicted correctly correctly correctly width occurs generally half half place greater greater greater neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor neighbor measures measures accurate designed performs performs performs performs learns learns taking taking taking taking taking largest largest largest largest pulse pulse pulse pulse pulse minimizing min targets targets targets targets targets targets targets targets targets targets targets targets targets identification identification identification question produces index index index winner winner winner winner sequential sequential sequential sequential sequential sequential sequential sequential sequential plot label recall metric metric metric metric category category category category category category category category category category electrical involves involves involves angle consisting frequencies frequencies frequencies applying events events predictive predictive predictive competition competition yield yield open evaluate organizing organizing fraction fraction fraction fraction fraction fraction centers discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination discrimination key calculation epochs sec sec sec event event false false false false false false false false false false tracking tracking remains assigned construction norm euclidean euclidean classified views views views views transactions transactions usa sciences sciences extension extension extension automatic maximize maximize activated activated partially neighbors neighbors compression aspects aspects identified importance society maximal identify tend essentially ten receives characteristic success success dis symmetry classify categories categories predictor operating satisfies satisfies law employed requirements requirements environments preliminary dataset dataset examine giving tech incremental scaled office office referred proper smallest closest predicts predicts predicts noted art art art art art art epoch epoch baseline extent electronic averages averages advanced analyzed navigation improves coded lies lies inside formalism pulses pulses pulses pulses pulses pulses pulses pulses pulses pulses grossberg grossberg grossberg grossberg grossberg grossberg demonstrates exemplars reflects fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy collected profile profile profile profile profile profile profile parameterized parameterized poorly poorly employ incorrect incorrect incorrect fall maximizes extensions datasets datasets boston boston june multidimensional representative identifying sort accomplished angular angular jth bin bin naval naval grows arrival extending city city determination determination determination familiar familiar familiar familiar familiar familiar familiar familiar familiar familiar familiar familiar familiar familiar intelligent hit hit hit hit hit hit hit hit los resulted occurring mark shifts shifts belong belong receiver knn knn effectiveness effectiveness corner selects mance mance document reset reset encountered encountered encountered equals equals equals induce perfor perfor regarded washington lengths lengths belongs belongs chooses viewing exposure winning winning mem bins bins bins canada canada belonging belonging belonging partitioned projects grants onr onr onr accumulated boxes metrics radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar resonance yielded roc roc roc roc roc roc roc roc roc rubin rubin rubin rubin rubin rubin rubin aircraft aircraft aircraft aircraft creates transmitted employs retraining exception profiles profiles profiles profiles profiles profiles ease spaced spaced spaced affects guess eric reject continues searches records categorization option alarm alarm alarm alarm alarm alarm alarm alarm familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity familiarity placing placing differing mea resembles accumulation accumulation accumulation accumulation accumulation accumulation accumulation stephen council identifies identifies identifies wins wins compete incorrectly exposed evenly evenly evenly agency alarms alarms attained raises ignores complement complement william approaching reflection gathered defense defense defense cyclic carpenter carpenter carpenter carpenter carpenter montreal montreal publishing retaining simula tal meaningless preprocessed activates predic permutations miss miss intersect intersect ross quarter retrained retrained nation rosen rosen missed tributed novelty niques icnn vigilance vigilance vigilance visualized expands poorer fifty unfamiliar unfamiliar unfamiliar unfamiliar unfamiliar unfamiliar unfamiliar unfamiliar comparatively emitter emitter emitter granger granger granger granger granger reflections reflections reflections establishment establishment accumulates scattering fined alamitos hemisphere nen nen nen nen nen nen nen nen nen nen nen nen nen nen nen ottawa ottawa weber asme libraries eration resets corp balances deemed discrimi judging ecole dasarathy dasarathy houston dimensionless proliferation continual incur boxed reynolds editing jagged jagged informations distort doubles recombined 
#@Granger_E,Grossberg_S,Rubin_M,Streilein_W,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data function function function figure figure figure time time time time time time time time time time time time time time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output output output output output number number number system system system system system system system system system system system system system system system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state results units units units units units units units problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden performance performance based based based based based based based based based based based based based based based based based based based based based based based based based based based based space weights weights weights weights linear layer layer layer case case vector vector vector vector vector vector vector vector vector vector order shown systems systems systems systems systems systems systems systems values values values values values neurons unit unit unit distribution distribution method approach approach approach approach approach approach point single single single single single processing processing processing control control control control control control control control control control control control control control control control control control control control control control control large large large large large large large large local local local rate inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form algorithms simple simple simple simple simple paper paper examples examples examples examples examples examples examples small small small size size size net net work work work task methods methods methods methods fig fig fig fig fig fig step step step step process process process trained trained trained trained trained trained trained trained trained trained trained trained structure structure structure problems random random high high similar representation line line vectors general general general general real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states states states gradient gradient gradient gradient gradient obtained note experiments experiments dimensional dimensional university university variables variables variables variables variables variables variables variables computation computation computation research independent independent found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial standard computer computer computer computer computer computer computer computer science presented map map map map map map map map sets sets sets motion motion range range range press learn learn learn nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous sample abstract applied applied applied back find computational computational computational references due due ieee ieee important important context introduction action action action complex complex complex complex complex behavior effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated variance cost cost tion tion tion change change signals prior chosen higher part part center previous type type good good conditions conditions conditions equations equations equations equations make make techniques techniques observed forward forward resulting resulting simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation simulation human respect multi called called times means optimization optimization natural global em obtain original artificial relative represented compared compared compute compute compute proc proc proc proc perform perform active determined determined distributions gain motor discrete discrete power steps steps steps accuracy accuracy comparison larger larger update train train train train train descent proceedings proceedings report department loss loss technique consists joint joint connectionist difficult final scheme scheme maps maps computing domain domain domain equivalent hinton hinton hinton hinton hinton additional additional view transition trajectory top effects efficient efficient efficient efficient upper upper upper full requires requires requires significant approximate approximate approximate approximate approximate approximate approximate approximate approximate world world speed basic con produce produce produce produce randomly developed developed robot controller controller controller types actual backpropagation backpropagation backpropagation sampling constraint technical feedforward feedforward feedforward feedforward group group denote fast fast fast fast fast fast fast fast actions implemented implemented generate generate generate main end ability future future easily degree degree simulated simulated typically typically typically typically smaller smaller needed dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical dynamical functional fully jordan significantly significantly significantly significantly mechanism special structures uniform principle principle principle leads details details pre direct making bottom supervised magnitude magnitude magnitude magnitude magnitude frame idea minimize minimize produced run predict improve advantage takes takes reported practical introduced strategy strategy subject subject subject hierarchical hierarchical interest sufficient sufficient highly highly conventional conventional conventional conventional approximately works works trans sparse sparse evaluation evaluation evaluation chain observation constructed parts invariant invariant occur extended rotation rotation alternative alternative deterministic generally generally pass demonstrate conclusion reduce operator operator operator operator operator sigmoid sigmoid sigmoid accurate accurate numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical faster faster faster faster practice practice practice learns propose mechanisms integration integration integration integration physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics physics external external external external external external external external sigmoidal sigmoidal sigmoidal demonstrated demonstrated proportional variety variety variety variety start introduce derivatives groups force force force force force force force denoted acknowledgements explicit explicit van van construct produces longer perception solving transitions transitions dept changing segments coordinates coordinates coordinates infinite infinite infinite physical physical physical physical physical physical physical physical physical physical physical physical physical dimensionality dimensionality involves involves transformations text consisting john yield yield independently depending influence influence transform evaluated operations operations operations operations controlled controlled controlled controlled approximations completely completely partial slow spaces normalization interpolation generation valid intermediate degrees degrees precision expect expect includes thesis combinations coordinate coordinate coordinate usa inter instances batch specifically coupled phys discussions successfully efficiency efficiency efficiency efficiency efficiency capable uniformly suitable successful successful literature post online road conf conf conf conf quickly allowing success link sci sci duration satisfy satisfy comp comp generalize realistic realistic realistic realistic realistic computes leading automatically automatically automatically principles illustrates approximating receive receive body body body body body body simpler production overfitting requirements difficulty environments mass fashion links mappings possibility muscle scaled symbolic cover fundamental momentum neu math predicts ensure front quantities assumes freedom freedom simplest simplest arbitrarily motivated phd massachusetts costs costs ground trivial crucial crucial variances glass drive easier producing producing producing forces forces forces forces forces forces forces forces forces forces forces forces forces operators operators mation universal beginning implicit implicit implicit begin toronto toronto toronto toronto toronto demonstrates conjugate requiring geometric apparent improvements evaluating evaluating tional simulate simulate cohen orders orders orders orders orders employ employ employ synthesis synthesis synthesis differs parent enables enables replace replace replace replace simulator simulator simulator simulator simulator simulator differentiable yielding yielding univ univ contribute initialization shifted lab ghahramani uncorrelated benefit college college tation acm acm velocities resources recover recover controlling unity discover rigid rigid rigid rigid rigid rigid inspired platt dealing numerically overcome replacing grow transforms transforms observing observing observing planar hours date passive passive evaluations evaluations conjunction realization widrow widrow widrow sim facilitate competing offers offers offers enable iterated express creating contraction offer offer arrive cpu contact canada motions motions pendulum considerations exploiting exploiting reverse santa valuable alternatively generalizing generalizing approximator automated vari stone divide dramatically numerous corporation achieving super super super july july july causing ideally generalizations amherst perceived ical ical hierarchies simulating simulating causal algebraic acting acting attempted invariances goals geoffrey graphics graphics graphics graphics graphics challenging proach speedup drawback superposition commercial permit nal dramatic dramatic compu mini mini simplifies gorithm locomotion moderate info preserves excess august august instability swimming impractical impractical assistance transforming spring water savings curse subnet king puts suffices suppress kinematic kinematic evenly proposes ally substitute normalize propulsion trol zoubin exploits exploits joints nontrivial sity physically physically physically fidelity terminates steve trend ically prescribed revow benchmarks replaces objectives constituent stems degrade repeating bodies tightly converts converts converts demanding sat broader synthesize tran tiny mike mike alexander comprises animation animation animation animation animation animation animation animation animation animation animation animation animation animation animation animation animation animation animation animation animation animation offiine emulate emulate emulate emulate emulate emulate emulate emulate emulate intel intel narendra initializing articulated articulated dynam deformable deformable utilization simu camp ulation timestep timestep timestep timestep univer attitude cybenko steerable premise wheel mission emulation emulation emulation emulation emulation emulation emulation emulation emulation emulation emulation emulation normalizes normalizes ner cheaper gravity indebted structurally namics quired decade coordinated lengthy truck truck truck truck actuators cies proximate cook terzopoulos terzopoulos terzopoulos terzopoulos terzopoulos terzopoulos terzopoulos torques hahn batches fleischer deviate ast ast rear numer parthasarathy dimensionalities friction friction conven hunt timesteps timesteps timesteps timesteps timesteps tackle incurs radically backer backer backer unpredictable istic siggraph siggraph siggraph siggraph resample barr monolithic nguyen nguyen nguyen sitions realism realism realism influential pending formidable reused plagued fects xerion xerion microcomputer uneven malization guidelines differentiability acted entail wheels drew outstanding outstanding unfor appreciably blvd ploy suspended dependen incurring tunately 
#@Grzeszczuk_R,Hinton_G,Terzopoulos_D,
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#*network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural data data data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number system system system system system system system system error error state state state state state state state state state results results results results results information information information problem problem problem problem problem problem models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based based based based based based based based based based based based based based based based linear case case order shown shown shown systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters method approach approach approach pattern pattern point point point point point processing processing large local test test test patterns patterns patterns patterns analysis analysis analysis analysis analysis matrix form shows signal algorithms simple paper paper small feature feature work work methods methods step step step step field features features features features classification classification classification process level level level current current current current trained structure high high high show show show show section section section section section section section fixed fixed fixed fixed fixed fixed line line line line line line line general speech parameter parameter parameter parameter real real real real real approximation average states states states states states states states states states gradient gradient obtained obtained obtained note note note note experiments experiments university university threshold variables variables variables variables variables variables variables variables variables variables log log found found sequence dynamics initial estimate computer terms terms science left presented present present present present present present low frequency temporal press press press learn basis continuous abstract likelihood likelihood references stochastic ieee procedure procedure important important adaptive decision introduction introduction complex estimation behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior tion tion tion tion change variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable variable assume rules rules rules rules prior representations learned higher previous previous bound cases cases binary binary binary binary tree tree tree distributed bayesian bayesian expected equations equations equations equations equations equations equations equations equations markov markov markov markov techniques techniques probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed forward resulting total performed means means factor potential applications study knowledge em em em em em em em em em em em em obtain obtain obtain vol vol vol vol vol true series series series series series series provide rates proc determined experimental posterior equal equal equal equal approaches approaches mit dependent proceedings proceedings report consists individual individual advances joint difficult final delay graph sequences directly curves curves estimates estimates estimates estimates estimates transition transition transition transition transition transition transition limit top detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection conference capacity efficient upper statistics statistics statistics free speed estimated estimated increase derived derived derived velocity velocity velocity types lines lines lines lines finally evidence iteration sampling normal normal normal normal normal technical denote denote tested tested assumption assumption corresponds complete complete finding amount implemented implemented journal journal square ability makes development probabilistic typically underlying underlying reduced account account account account account account account account account account account account account account dynamical dynamical jordan jordan jordan technology technology interesting testing mode mode call call call call call call call call call call call call call call call call call call call call window improve introduced introduced period period side hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees sense inference inference inference inference inference interest unsupervised unsupervised approximately calculated tuning tions achieve risk increased lead scaling correctly hybrid setting setting setting place minimal reduce conclusions conclusions measures numerical clear performs solid labeled user user user user identification derive derive sequential estimating estimating describes label tuned dept physical remaining easy scales consisting develop applying applying focus communication communication communication solved variation approximations discrimination discrimination discrimination past past smoothing smoothing smoothing smoothing smoothing smoothing smoothing smoothing performing performing performing false false false false false iterative filtering filtering filtering filtering filtering calculate calculate classified box figures determines determines plotted discuss absolute reason reason differ divided detect detect detect efficiently fine fine reached characteristic capture summary conf prob interested interested dis generative generative generative duration realistic nips highest automatically overlapping subsequent subsequent operating minimized powerful poor exponentially optimized dotted graphical graphical behavioral terminal int authors hierarchy circles traffic equally obvious algo taylor switching switching switching switching switching switching switching switching switching switching switching switching switching switching regime regime regime regime regime regime regime regime regime regime regime regime regime regime optimum great advanced guaranteed improves improves tool reasons day day bengio recognized describing describing describing lowest incomplete requiring fourth apparent considerably considerably pure transient capability capability introducing share detecting detecting detecting formulated formulated formulated switch switch rely ture cal extensions extensions acoustics phone phone phone phone phone marginal marginal substantial germany calls calls calls calls calls calls calls lab ghahramani ghahramani ghahramani tresp tresp tresp tresp newton benefit princeton rithm acts mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile discovery impossible lost communications chains occurred siemens siemens check occurring receiver affected affected affected modifications exceeds enhanced days days introduces saul saul saul periods appendix appendix displayed sides dependency regard lengths enhance accounts accounts accounts accounts accounts accounts accounts accounts competing smoothed smoothed card card card card card executed executed lem boxes metrics emission emission leaving roc users latency recursively ties markovian discriminative discriminative discriminative discriminative discriminative discriminative discriminative icassp quasi profiles junction junction ical big param evolve evolve evolve pij pij distant proba differentiation regimes register alarm alarm alarm places refined travel exploited struc mini inactive worked fortunately corporate satisfactory stochastically shawe smoother generafive hamilton hamilton hamilton hamilton carrier carrier carrier mining recursion appealing tribution resolutions alarms detects detects scenarios losses losses losses evolving daily america denmark edition profit iterating investment assessed capturing ized ized indi actively montreal costly initiated cations entering entering minute scribed volker volker helped sing jensen jensen kim kim munich earliest dash conveniently frank originating helsinki telecommunications telecommunications calling calling calling eter industry motivate attack ucl bilities hut hut silence business detec detec detec misses plete finland services wasted customers customers customers summarizing admit probabili unacceptable carriers illegal illegal illegal telecom andy companies typ mchp incom ineffective gaining worm telecommunication telecommunication telecommunication alleviate attacked haft trap trap marginalization acquiring intermittent mize marginalizing lots communica trai unsuitable ential caught plagued ett ett ett hierarchi cates universitd looses 
#@Hollmen_J,Tresp_V,
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#*model model model model model data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure set set set set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system error state state results units units information information information information information information problem problem problem problem problem problem problem models models models performance performance performance performance performance performance based based based based based based case case vector vector vector vector order order shown probability probability probability probability probability probability probability probability probability probability probability probability recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern point point image image image single single processing large large large large large large large large large local local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class optimal algorithms algorithms algorithms algorithms simple simple visual paper paper paper paper size feature feature feature feature work work work work task task methods step step step step step step points process process process process process process process process process process process level level level current current current structure structure structure structure problems representation representation representation representation representation representation representation representation architecture section section line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line rule vectors vectors vectors vectors images images images images images images images images images images images images images real real average average obtained obtained obtained obtained obtained note experiments experiments result university variables independent target target table table table table computer computer computer terms terms distance distance distance distance distance node node node node node node node node node node node node node science direction presented presented presented map map map map map map map map present low nodes nodes nodes nodes nodes nodes machine machine object object object sets sets maximum maximum maximum range range range range press position position position position position position position position position position position position abstract computational computational computational density density density properties references ieee ieee ieee ieee ieee positive procedure important decision decision context introduction hand hand statistical statistical effect effect parallel search assume measure prior representations higher represent represent represent bayesian bayesian make techniques length length length length probabilities scale scale scale scale resulting resulting ing ing computed computed computed computed respect eq eq eq eq eq eq eq eq eq eq eq regions mapping mapping mapping means orientation global global global study study obtain negative original relative relative relative relative relative relative relative relative relative relative relative relative relative relative represented represented cross cross cross cross provide compute perform experimental experimental experimental goal related discrete discrete discrete mit steps accuracy accuracy accuracy comparison comparison comparison update words words words department implementation technique technique consists consists individual individual advances joint represents final final exp scheme addition graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph graph framework framework framework computing computing computing computing view curves top effects detection full choice significant significant world world speed vision vision vision vision pages pages pages condition condition condition derived derived weighted conditional conditional conditional conditional conditional developed developed area lines lines provided provided finally finally selected iteration iteration iteration simply achieved denote transformation corresponds nearest nearest nearest shape shape shape shape shape shape shape shape shape shape shape shape main main main journal end end end ability ability development objective typically pairs pairs jordan interesting significantly ratio ratio york york york edge edge edge edge edge structures structures matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching uniform database database database database mode details details details iterations iterations max max max making international combined sources sources recent pair similarity similarity similarity similarity similarity similarity reported reported practical practical practical practical apply strategy identical side trees subset recently relevant interest compare compare compare compare axis match match match match match match match match match correspond evaluation storage storage constructed horizontal invariant invariant invariant invariant extended digital digital digital digital rotation conclusion assumptions segment segment segment segment segment conclusions bayes bayes bayes faster taking taking largest largest largest drawn intelligence turn turn turn turn turn assuming min averaged manner manner scene force base base base base base base base base base base base base base base base base base base suppose suppose appears relation construct construct edges edges ways describes segments segments segments segments segments segments segments segments segments recall recall recall recall recall recall recall recall metric physical involves involves remaining remaining remaining angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle angle develop applying applying extraction select select extracted extracted focus focus detailed detailed densities evaluated evaluate suggested translation sign sign key measurements iterative filtering filtering assigned assigned euclidean euclidean euclidean euclidean query query query query query query query query query query query views views views color color retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval assignment assignment mozer candidate candidate priors structural structural structural structural structural structural structural structural structural structural structural structural structural structural texture reason selecting selecting selecting middle closely closely closely closely importance modes literature literature literature literature comparing comparing comparing identity capture graphs graphs graphs graphs graphs graphs graphs graphs graphs graphs prob prob video content content strategies strategies device device satisfy relaxation relaxation relaxation absence realistic nips correspondence correspondence correspondence correspondence correspondence correspondence correspondence ill attempt oriented modelling extend explore powerful updating issues issues matches matches matches matches matches matches matches matches matches giving ideas project possibility working matched matched attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes smallest measurement measurement measurement measurement measurement psychology illustrate illustrate queries queries aspect shapes baseline baseline baseline baseline grouping established established established histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram histogram scenes scenes pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise pairwise developing formula formula formula formula directed directed directed directed directed distinguish improves independence independence considerable stress purposes purposes angles angles describing attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute author geometry meaning meaning raw raw raw geometric geometric geometric geometric geometric improvements affine consistency consistency consistency consistency conducted red red effort effort posed posed variant measuring aim aim aim hamming chose segmented progress june pose gap picture formally databases databases purely bin bin grey establish establish eliminated dealing ranges tools interpret interpret exploit methodology salient wilson wilson wilson continue exploring meaningful introduces vertices histograms histograms histograms histograms histograms histograms histograms captured scan scan scan counter arrangement bases bases entries tokens ballard bins bins vertex variants statement papers ignore intersection intersection tures severe andrew posteriori posteriori posteriori posteriori outperforms gold constitute outperform opposed diverse pentland adopt centre abstraction abstraction arg arg arg arg arg arg arg arg arg perceived hundred descriptions descriptions descriptions england assess manipulation pami pami pami pami cartesian cartesian library spanned covered indexed alternatives fea thousands refined normalised normalised normalised normalised normalised normalised gorithm mea resembles resembles resembles persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent appearing simplification simplification distortions primitives attributed correspondences correspondences correspondences correspondences correspondences correspondences firstly firstly firstly locate attempting fill mining mining mining hancock hancock hancock hancock hancock hancock hancock hancock lists rangarajan petsche edited conditionally lnp establishing cliques cliques relational relational relational relational relational relational relational relational relational rel rel rel rel rel rel rel rel rel rel centres approached contents contents assessed february prune energies convey convey devoted recovering indexing indexing spanning triple retrieve retrieve clockwise clockwise intersect minimise sought posterjori posterjori posterjori posterjori posterjori imagery associating refining neighbour maximise maximise sume southern brute intend shapiro retrieving retrieving signif joining focussed gestalt initialisation initialisation initialisation initialisation initialisation initialisation initialisation initialisation pairings optimised aerial aerial aerial strate ingredient libraries libraries corruption organising querying stressed barrow barrow neighbout neighbout nary realised characterised arccos factorised maxp dio infra infra gies swain flying ambitious graduated icantly erations barrel succinctly tribute invariably firsfly firsfly termine congruence realise recognising edwin binned surement 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural input data data function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set training training training training training training algorithm algorithm algorithm output output number number number number number number number number number number number number number number number number number number number system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state results results results results results results results results units information information problem problem performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space space space order order order order shown shown shown systems values values values values values unit method method method method method method point point point point point point point single single processing processing control large rate test analysis class class optimal optimal optimal optimal optimal optimal optimal form shows shows shows algorithms paper paper paper small size size size size size size feature work work work work work work work task methods methods methods methods step step features features features features features features process process level level level current current current trained trained structure problems random random random random random random random random random random random high high high memory memory representation architecture architecture fixed line line line line line line parameter parameter approximation average average average average average average average states states states states states states states states states theory obtained experiments experiments experiments experiments experiments result university university university computation solution defined table table table table table table table table computer computer computer science science left presented present temporal temporal machine machine machine machine press press press learn learn abstract applied find find find properties references references stochastic stochastic stochastic stochastic stochastic due due positive important important important decision introduction introduction action action action action action effect cost cost cost search search search tion tion change difference difference difference difference difference lower lower lower measure measure prior learned learned learned chosen higher part part part part previous bound bound required multiple multiple multiple good good good good long long long conditions expected expected expected expected chip make make fact techniques techniques proposed proposed length correct minimum resulting classes ing ing ing respect performed performed performed performed performed performed performed performed called times times times times times times times mapping means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor optimization optimization made made global applications applications applications applications study policy policy policy policy policy policy policy policy knowledge obtain original original relative relative specific represented true true true compared compared compared application cross cross series provide compute proc proc perform perform perform experimental experimental goal constraints discrete equal mit mit mit steps larger support dependent selection proceedings proceedings proceedings report department implementation version code code code code code code code code advances advances represents represents difficult final final delay graph graph graph maps considered considered framework cambridge computing domain domain domain domain domain domain experiment experiment environment environment directly design design transition transition trajectory conference determine efficient full requires requires choice choice choice choice approximate speed speed speed estimated basic basic basic basic basic basic basic basic basic basic basic validation validation give produce derived weighted weighted weighted weighted weighted weighted weighted weighted weighted randomly randomly randomly developed path path path path actual actual nature technical increases tested tested tested tested fast close complete complete actions actions actions actions finding finding common supported theoretical require require journal end future future makes makes objective objective simulated pairs pairs pairs smaller combination account account account functional functional technology block block block block block block block block block block block block block block block block significantly ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio character details call call numbers max max pre pre supervised supervised supervised produced produced produced choose run run description description predict architectures architectures architectures improved exact advantage takes reported introduced strategy previously teacher tions tions tions solve yields match differential achieve achieve achieve rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl address evaluation evaluation chain improvement improvement entire grant lead digital digital digital digital digital digital digital predicted deterministic deterministic occurs generally setting hardware runs runs runs runs starting critical critical critical critical minimal greater conclusions depend depend reward reward reward reward reward reward reward reward reward reward reward reward differences accurate sutton sutton sutton sutton faster faster faster taking hard cycle cycle demonstrated assuming program program program program program program program denoted denoted denoted denoted denoted reference reference suppose pro monte monte construct carlo carlo edges written written written longer sequential generating generating label metric physical remaining unique develop adding applying formed quality agent agent agent agent blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks blocks versus versus cycles cycles cycles cycles john yield choosing choosing choosing choosing national focus depending correlated correlated communication learner learner learner variation detailed detailed evaluated updated updated showed showed processor processor processor partial partial partial partial partial partial partial partial partial partial earlier barto barto barto barto performing performing add add valid valid valid string advantages david building building exploration includes maximize specifically candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate candidate domains absolute absolute absolute absolute major selecting closely importance maximal divided divided divided paths build build online ten conf quickly repeated repeated heuristic heuristic heuristic heuristic heuristic heuristic heuristic interested issue issue issue issue issue issue issue return return running running running running running running running running running running running running running follow timing hold built nips wave highest ill received received consisted consisted policies policies policies acknowledgments tesauro tesauro presents explore schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule schedule collection collection essential varied limitations limitations issues dual dual dual dual dual graphical fashion relationships proved affect smallest possibly integer opposite extremely aspect aspect versions greedy greedy greedy greedy greedy precise explored explored baseline massachusetts advanced preference developing directed floating expensive benchmark benchmark benchmark benchmark tool worse straight straight straight straight straight shared sites sites easier precisely choices choices choices ran calculations beginning beginning begin computers auto preceding nsf sun researchers geometric geometric geometric varies people evaluating evaluating leave leave remove slower slower slower frequently execution execution execution execution execution execution execution execution execution execution execution rely rely summarized instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction instruction maximizes proven gave gave simulator simulator simulator simulator simulator semi chose comments returns returns focused focused simultaneous cumulative cor equivalence guarantee martin acm ratios ratios optimizing resources ordering ordering ordering ordering ordering outcome chance tools odd odd odd odd odd held alpha alpha alpha alpha alpha height loops hit combinatorial hours heuristics heuristics heuristics heuristics motivation excellent programs programs programs entry entry paul induce overview overview overview dependency lang consequences scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling scheduling schedules schedules schedules schedules schedules candidates chooses chooses chooses specialized permutation permutation permutation discounted creating matter park broken broken tsitsiklis instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions instructions executed executed executed executed bertsekas bertsekas bertsekas bertsekas andrew andrew andrew sequentially mind metrics ence corporation corporation vec vec vec vec vec vec vec outperform discount super latency validity ties dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec dec causing tradeoff amherst amherst amherst amherst solely big big big big affects discovering assess backgammon intuition intuition execute execute execute execute execute labs searches iri speedup harder harder drawback setup commercial commercial commercial commercial holding rewrite helps opti preserves preserves consuming consuming designs suite suite suite suite hypothesized puts outperformed outperformed outperformed outperformed moss moss moss moss moss moss moss moss moss moss moss gram executing tuple tuple manually normalize longest edition semantics modern pointer acyclic inst mul assessed assessed ous manual manual tens experimented experimented rolling spec spec spec spec spec spec costly retaining rein observes precup precup precup save repeats compress orig orig orig orig orig orig orig orig wait evaluates scheduled scheduled scheduled scheduled scheduled scheduled ninth tially picks solu previ hypothesize earliest earliest insure equipment equipment equipment swim hoped corpora confer forcement tying microprocessor vised prog dag dag app app app app utgoff utgoff avail quadratically interacts lengthy rewarded sic compiler compiler compiler cache umass atom atom vious vious mas mas tiple proposing pipelined packard money publicly unavoidable microsystems exit compiled matically hewlett validating fortran pipelines pipelines pipelines mize depiction tically sachusetts sachusetts spending emit cle sched sched concisely rewarding customized idle propriate sequen saves doina doina backtracking calcula choos instrumentation outper italics 
#@McGovern_A,Moss_E,
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#*learning learning learning learning model model data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set training training training training training algorithm algorithm number number system system system system error results results results results results problem problem problem problem performance performance performance performance performance based based based based based based based based based space space space space space space space linear linear linear linear linear case case vector order shown shown shown shown shown shown probability probability probability probability probability probability recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method approach approach approach approach pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image processing processing processing large large large large large rate rate rate rate test test test test test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class form form form form form shows signal algorithms algorithms algorithms algorithms simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian visual visual visual visual paper examples small size size feature work task task task methods features features classification classification classification process current random high high high high similar similar similar equation equation equation equation equation equation equation rule rule rule rule vectors vectors vectors images images images images images images images images images images images images images images images images images images images general generalization speech real obtained obtained note note note note note note experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional computation computation computation research independent defined found found found estimate standard standard standard standard standard standard standard standard standard computer computer computer computer terms terms distance distance map map map map map low machine machine machine machine object object object object object sets maximum maximum maximum maximum maximum position components components basis nonlinear nonlinear nonlinear abstract computational computational computational computational density density density density density density density density likelihood likelihood likelihood likelihood likelihood references component due ieee ieee ieee ieee ieee ieee ieee important introduction estimation estimation estimation estimation statistical cost cost search difference difference difference assume measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure prior part previous type type type required binary conditions represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian make make fact techniques techniques techniques proposed correlation scale scale resulting resulting classes classes classes classes classes classes human computed computed computed computed computed performed eq eq factor applications knowledge knowledge artificial specific specific define compute compute rates proc proc proc location location determined experimental distributions gain equal approaches mit mit mit mit accuracy comparison comparison modeling modeling modeling modeling modeling modeling proceedings proceedings proceedings institute institute words implementation technique technique technique technique technique technique consists internal code individual individual individual individual individual ai ai ai ai ai ai framework cambridge cambridge cambridge cambridge computing computing equivalent directly curve view estimates estimates estimates estimates top top top top detection conference conference efficient efficient efficient significant significant world speed vision vision vision vision estimated pages pages pages derived developed types tested tested tested corresponds corresponds corresponds complete nearest nearest nearest face face face face face face face face face face face face face face face face face face journal probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic typically typically pairs pairs pairs pairs combination reduced coefficients technology technology testing testing projection york head matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching matching database database database database database database database database operation principal principal principal principal principal representing pre pre pre direct making stored international normalized normalized normalized normalized normalized normalized normalized combined sources improved improve advantage advantage pair separate typical typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity strategy subset subset subset cognitive recently relevant interest dimensions match match correspond correspond correspond pca pca pca pca evaluation evaluation modified generalized generalized generalized storage exists intensity intensity intensity intensity intensity intensity expression expression occur matrices alternative setting demonstrate critical critical conclusions neighbor neighbor neighbor differences differences differences differences differences differences differences differences differences measures bayes bayes suggest largest demonstrated demonstrated proportional intelligence intelligence intelligence intelligence intelligence labeled labeled plane plane manner denoted laboratory laboratory distinct modeled explicitly dimensionality involves transformations transformations slightly gaussians gaussians springer competition competition competition competition expressed viewed solved variation variation densities densities densities evaluated evaluated evaluated evaluate evaluate evaluate operations restricted decomposition margin translation performing performing roughly distances distances norm norm euclidean euclidean euclidean euclidean euclidean euclidean euclidean advantages faces faces faces views views views transactions transactions transactions transactions existing template template priori usa usa usa formulation formulation color retrieval retrieval retrieval eigenvalues blind subspace subspace subspace subspace subspace subspace subspace extension automatic automatic candidate priors priors variations variations variations variations variations variations variations variations variations variations variations major extra differ computationally divided effectively modes poggio poggio projections projections projections score score score score essentially essentially online online identity characteristic conf conf conf verlag repeated neuroscience superior superior superior simplified simplified simplified simplified leading leading consisted consisted operating deal simpler simpler collection exhibit detail dual dual dual discriminant discriminant discriminant ml ml ml int int eigenvectors eigenvectors eigenvectors eigenvectors matched facial facial facial facial facial facial facial facial facial subsets rank rank rank fisher fisher expressions baseline simplest advanced ment expensive purposes purposes projected projected members members alignment requiring fourth evaluating reflect double affine templates prototypes characterize qualitatively acoustics datasets electric june june june arithmetic cumulative irrelevant representative aligned primarily appearance appearance japan tation databases databases databases databases jones rotations replacing exploit methodology belong canonical meaningful entry encountered surprising captured competing competing competing ranking darpa iterated april april probe probe probe probe probe probe probe probe probe probe gesture relies likelihoods likelihoods likelihoods likelihoods likelihoods likelihoods avoiding default posteriori posteriori posteriori posteriori metrics yielded yielded yielded slight converted hair hair hair equivalently ber opposed july july formulate pentland pentland pentland pentland pentland pentland pentland pentland pentland pentland pentland additionally personal individuals individuals individuals individuals discovering ary mutually exclusive pami pami pami intra intra multiscale complementary frontal frontal frontal represen drawback inversely tij lda lda lda memo minor subspaces september october november lighting lighting advantageous characterizing august european suffers alex alex subtracting norms norms arpa arpa arpa physically gathered media sep sep subtle eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces sorted completeness costly phillips mir align deformations deformations mar mar week internally offline offiine ames deficit posterjori scored deformable divides geometrically geometrically expressing glasses tony rutgers whitened ences formulating occupy turk normalizes inexpensive eij als als differencing cutting whitening chellappa arl exponentials eigenspace eigenspace eigenspace probes eigenface eigenface eigenface eigenface eigenface eigenface eigenface eigenface mitsubishi afforded jolliffe broadway merl moon brunelli swets performer eccv rla halved lfi 
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural neural neural input input input input data data data data data data data data data function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time set set set set networks networks networks networks training training training training training training training training training training training algorithm algorithm algorithm algorithm output number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error state state state results results results results results results results results results results results results results results results units information information information problem problem hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based space linear layer layer case order order order order shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values parameters parameters parameters parameters parameters parameters parameters parameters parameters weight functions functions functions functions functions functions functions functions method approach approach single single single single control rate rate rate rate test test test test test test test analysis analysis analysis analysis analysis optimal optimal inputs shows shows shows shows signal algorithms algorithms algorithms simple paper paper paper paper examples small size work work methods methods current trained trained trained trained trained structure structure structure structure random high high show show equation fixed fixed fixed line line line line line line line general parameter real real average average average theory gradient gradient obtained obtained obtained term term term term term note university variables variables variables computation computation computation defined defined defined defined found sequence sequence sequence target initial initial constant constant standard standard standard standard standard computer prediction prediction left presented present present present learn learn position position position nonlinear nonlinear continuous sample abstract applied find find find find find references stochastic stochastic stochastic due due due due important important adaptive decision decision decision introduction effect dynamic dynamic generated cost cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion difference difference difference measure measure signals learned learned previous previous cases required multiple good long long long long long long conditions expected equations techniques proposed forward simulations resulting ing ing ing total total simulation simulation simulation computed respect performed called means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor optimization optimization optimization optimization optimization made natural applications knowledge original vol vol vol relative true compared compared series series series series series series provide define compute rates rates rates perform perform experimental experimental goal goal goal equal approaches update support support train train dependent dependent institute department loss loss version technique internal advances advances represents difficult final delay addition sequences cambridge environment environment directly curve curves curves curves curves estimates estimates effects effects conference full requires significant free world estimated derived area lines lines path provided finally depends depends measured measured measured discussion feedforward arbitrary assumption complete actions actions amount short short short short short short effective assumed role theoretical require eds eds eds eds journal journal end end end end end ability hypothesis future easily including including objective objective simulated typically account account fully programming programming significantly significantly ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio trials trials trials empirical empirical call pre making making window window window window normalized supervised supervised supervised supervised early early early early magnitude magnitude magnitude decay decay produced denotes denotes denotes recent advantage robust ensemble takes typical practical apply strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy moving moving moving moving include include include period period period period period period period period period period period period period quadratic recently recently relevant engineering interest interest interest varying varying compare previously previously calculated tions tions tions correspond differential differential differential differential differential differential differential differential rl rl positions positions interval interval interval williams williams risk risk risk risk risk risk risk grant horizontal horizontal trial deviation deviation deviation touretzky touretzky touretzky pass demonstrate demonstrate demonstrate demonstrate critical conclusions depend reward reward measures numerical designed moody moody moody moody moody moody moody moody moody moody moody moody moody moody moody moody moody moody exponential exponential propose propose propose taking presence presence presence external solid regularization turn averaged averaged denoted denoted acknowledgements appears index index index index index factors dept changing confidence sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity sensitivity dimensionality slightly mutual john yield yield yield yield yield yield expressed influence influence influence detailed detailed updated fraction constants allowed past barto dashed dashed additive additive delays expansion intervals remains advantages transactions transactions transactions transactions transactions avoid avoid exploration exploration box box box includes includes thesis batch maximize maximize maximize maximize mozer mozer mozer absolute holds major differ included included included committee presentation successful identify plots plots online online online ten receives cun success stopping stopping return return return return return return return return return return running strategies hold hold hold hold hold hold hold hold hold hold dot nips nips nips delayed maximization attempt attempt subsequent subsequent tesauro tesauro extend exhibit optimized dotted dataset relationships relationships authors decisions decisions decisions decisions maximizing maximizing proper tanh func func statistically possibly adapt psychology adjusted adjusted adjusted adjusted quantities versions der der panel panel initialized improving simplest utility utility phd averages established years years years years years years years years ment costs costs costs costs costs costs costs costs slope slope majority correction correction correction london tive widely incorporate controls watkins watkins watkins scientific members optimize optimize optimize reflect bootstrap frequently rewards rewards rewards calculating price price price price mod weigend extensions pasadena adjust adjust substantial enables neuro returns returns returns returns returns returns median progress traces proposition realized realized realized trade trade trade trade trade trade accomplished extensive extensive ratios ratios ratios optimizing optimizing approximates nonzero caltech allocation allocation allocation allocation allocation held multiplicative multiplicative contract definitions salient moments date published financial financial financial financial financial periods periods periods periods periods zhang zhang ascent bad forecasting evident accounts scheduling hasselmo hasselmo hasselmo dif darpa initialize enable ensembles ensembles ensembles discounted insight insight record properly impact impact impact dietterich dietterich insensitive influences market market market market market market market acknowledge trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading trading accumulated accumulated accumulated abu zipser zipser outperforms appeared mostafa outperform outperform outperform ent ties job stock stock stock stock stock stock stock stock stock expanding year year year year year year year year year exception tight trends trends formance maintained graduate denoting regularized emphasize noting voting voting voting voting voting voting voting voting voting suffer els nal dramatic port bill bill bill bill bill treating oregon continually technologies demonstrating gratefully reinforce portfolio payoff excess january january curse wins december december accomplish neuneier neuneier realizations month month month month month month month month striking vote bond bond ultimate economic economic economic economic economic economic economic economic losses predictable frequent asset asset asset asset asset asset asset asset asset elevator elevator neutral relaxed profit profit profit profit profit profit profit nonstationary gammon modern modern transaction transaction transaction transaction transaction shop assessed excessive shares rein security security security incurred incurred elegant markets oil dominate ogi monthly monthly monthly monthly monthly posi prices superiority investor cse cse buy buy buy buy buy buy buy buy buy buy foreign fund fund sensitivities sensitivities sensitivities revised portland forcement crites crites dft dft dft contracts contracts business predictability predictability notable aaa aaa wealth wealth wealth wealth wealth wealth wealth wealth wealth summarizing vances advocated objec equity methodologies pare leverage invested money gaining equ lagged reporting validating validating dollar matthew quanti influential diff diff war nonstationarity nonstationarity daah daah shock trades trades trades termine refenes ferences discourage expecta 
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#*learning learning learning learning model model model model model model model model neural input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time set set set set set networks networks networks networks training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm output output output output output output output number number number number number number number number number system system system system system system system system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results information information information information information information problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance based based space space space space weights linear case case case case case case case vector vector order order order order shown shown shown systems systems probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method approach approach approach approach approach approach approach pattern pattern image image image image image single single single single large large rate rate rate test test analysis analysis form form shows algorithms algorithms algorithms simple gaussian visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper examples examples examples examples examples examples small small feature feature feature feature work work work task task task task task task task task task methods points field features features features classification classification classification classification classification process process current current current trained trained trained structure structure structure problems problems high high memory memory similar representation representation representation representation architecture architecture architecture show equation section section section section line vectors vectors vectors vectors generalization generalization speech parameter parameter real real real real real real real real real real real real real real real real real real real real real approximation approximation states states states states states states states states states states obtained obtained note experiments experiments dimensional dimensional variables variables variables variables computation solution solution solution research independent independent independent found found found found sequence sequence sequence sequence target dynamics dynamics initial initial table table table table table computer computer computer terms terms terms distance prediction left left left left direction map map present low temporal temporal machine machine object motion motion maximum maximum maximum range learn learn position position position components components outputs abstract applied back find properties likelihood references stochastic due due ieee important important important mixture introduction action action action complex complex complex complex complex hand estimation estimation estimation estimation behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior behavior statistical statistical statistical statistical statistical statistical dynamic dynamic dynamic dynamic generated generated change difference difference complexity complexity variable variable variable variable variable spatial prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior learned learned bound cases cases type multiple multiple multiple multiple multiple good good bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov markov markov markov markov markov markov markov markov markov markov markov fact techniques proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed finite resulting ing ing simulation human human human human human human human human human human human human human human human human human computed performed performed performed means made natural feedback feedback applications knowledge knowledge knowledge em em filter obtain obtain relative specific specific samples samples represented compared cross series series provide provide compute objects objects objects objects location perform perform experimental experimental experimental goal goal goal posterior posterior posterior posterior posterior posterior posterior posterior discrete discrete discrete power mit mit mit mit accuracy accuracy accuracy accuracy accuracy accuracy larger train train source modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling modeling morgan proceedings proceedings proceedings proceedings version internal individual individual individual individual individual connectionist final addition addition addition graph sequences ai ai framework framework framework framework framework framework cambridge cambridge cambridge cambridge equivalent equivalent experiment experiment environment environment environment environment environment environment directly hinton curve additional additional transition trajectory san top top top top detection detection detection efficient efficient efficient efficient efficient upper full full requires statistics vision vision vision estimated basic basic pages increase con conditional clustering developed developed velocity velocity velocity velocity velocity types types types lines entropy product product finally finally finally finally processes processes processes processes processes processes processes selected selected evidence depends sampling sampling covariance describe describe describe denote tested hmm hmm hmm hmm hmm hmm hmm fast limited limited limited close corresponds actions actions actions actions amount amount common shape shape generate require main main ability ability future future future future easily degree including fit kaufmann probabilistic probabilistic probabilistic probabilistic probabilistic typically typically typically needed needed needed jordan jordan jordan jordan programming interesting testing segmentation segmentation mechanism special structures structures numbers international bottom bottom bottom bottom magnitude frame combined run description architectures directions exact exact advantage robust separate typical typical typical reported introduced moving moving moving moving moving include pixels hierarchical sense inference inference inference relevant interest sufficient varying varying compare previously conventional observations observations calculated volume volume module tuning tuning tions tions tions tions yields correspond correspond correspond achieve achieve achieve background background background background evaluation chain chain chain chain chain observation williams arm exists parts parts occur extended wide derivative matrices touretzky touretzky loop loop deterministic generally demonstrate starting critical minimal assumptions trajectories conclusions conclusions operator editors editors interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions interactions clear clear mateo strong integration largest largest drawn demonstrated demonstrated relationship introduce manner manner scene scene scene scene configuration denoted boltzmann perception laboratory transitions transitions mathematical mathematical modeled modeled modeled dimensionality remaining slightly consisting interaction interaction interaction interaction develop develop develop develop gaussians agent agent agent agent agent expectation versus expressed expressed depending depending viewed viewed interpretation influence influence detailed detailed open open frames static understanding allowed earlier combining combining combining roughly false false false tracking tracking tracking tracking closed generation assigned advantages views degrees coupling avoid building priori priori priori formulation strings color color inter inter inter inter inter inter inter inter subspace sciences recognize recognize automatic automatic automatic uncertainty mozer priors priors priors priors priors coupled coupled coupled coupled coupled coupled coupled coupled coupled domains domains partially partially major major determining straightforward efficiency hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms importance computationally paths driven detect detect build efficiently computations invariance essentially composed composed capture summary traditional traditional compact graphs kind strongly allowing video video video link interested interested classify classify classify generative generative cues write michael dot modular providing nips nips quantization highest ill reach maximization automatically consisted illustrates illustrates mixing acknowledgments software software intrinsic tesauro camera situations situations situations situations presents minimized body body simpler parametric overfitting kalman involving humans accurately accurately accurately graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical examine examine respond history school behavioral behavioral applicable ideal structured stream workshop encode coarse man analyze predicts extremely created created aspect freedom explored art art art art generates detected detected submitted synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic synthetic mentioned site site scenes scenes developing developing directed track track analytical independence handle handle processed rapid sys sys sites easier style immediately mation consequence separately separately separately involve describing depicted demonstrates incomplete recognizing recognizing recognizing recognizing recognizing recognizing recognizing recognizing alignment requiring virtual virtual people people behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors behaviors evaluating collected understood flexible flexible flexible flexible flexible amounts generic generic capability fed poorly detecting continuously http http summarized ordered extensions extensions extensions suited enables semi kinds conclude expectations attentional viterbi lim simultaneous yielding cor person person person person person person person person classifying classifying ghahramani leen intractable www www www appearance investigation temporally concerned discovery tem tem tem extending chains chains chains chains chains chains chains overcome interpret nearby scoring scoring observing observing hours continue continue exploring reliably weakly combines combines saul overview intended stereo stereo stereo den hasselmo centroid dif viewing recog express offer offer offer offer offer tracker tracker tracker gesture motions motions speeds influences pdf pdf boxes posteriori discriminate linked street summer roc constitute outperform recursively pentland pentland pentland pentland pentland pentland nition obtains covariances big ekf ekf warping warping causal causal causal reflected scenario scenario scenario summarizes interact interact compensate life bounding interacting interacting interacting interacting interacting interacting interacting smyth employing cartesian refinement alarm alarm esti memo mimic meet meet meet meet meet meet november walk walk emphasis rabiner gestures gestures gestures gestures gestures gestures heading heading august compositional compositional compositional compositional influenced trainable ferent agents agents agents agents agents agents agents agents agents agents agents adaptively lated hid accomplish alex char flows rare meeting detects scenarios rameters tracks tracks html html distorted deter semantics semantics dent feb robustly pin raised indepen media media media media acyclic merit greatest experimented ference accuracies accuracies accuracies accuracies accuracies accuracies notions mir tutorial walking graphically superscript accu hands saved devel superiority posteriors foveated ames blob blob blob blob blob blob blob blob blob blob blob blob chi chi chi chi chi chi chi chi chi chi heckerman inferences compose tony blobs blobs blobs heads chinese anomalous door indexes dag combi occlusions coordinated specially causality alert vienna interac interac interac interac parenthesis parenthesis pins pins iip barbara cvpr cvpr oliver oliver oliver oliver oliver oliver factorim rgb eigenspace adaptability noteworthy targeted eee surveillance surveillance surveillance surveillance surveillance surveillance surveillance surveillance surveillance shadows managed formu matthew slo sio sio thirds sitting calibrating calibrating calibrating practiced handed handed ited crossvalidation wholly bust porally mination arts 
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#*learning learning model neural neural neural neural neural data data data data data data data data data data data function function figure figure time time time time time time time set networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number system system system results results results results results information information information information information problem problem based based based based based based based linear linear linear linear linear linear vector vector vector vector order order order order order order systems probability parameters noise functions functions functions functions unit unit distribution method method approach approach approach approach point point point point point point point point point point point point point single single single processing processing processing processing processing large large local neuron rate patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix form form form signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian small feature methods methods fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step step features cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure random random random high high high high high high response architecture fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line vectors vectors vectors gradient gradient obtained activity variables variables computation computation solution solution independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent defined defined defined defined found found target dynamics dynamics dynamics dynamics dynamics initial constant constant constant constant estimate estimate left activation activation frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal press press components components components components components components components basis nonlinear sample abstract applied back find find find computational convergence density density properties references component component component component component component component component component component component component component component component component component component component component component component stochastic due ieee ieee ieee positive adaptive adaptive adaptive adaptive mixture introduction complex estimation estimation statistical effect dynamic variance parallel parallel tion tion variable spatial spatial measure signals signals signals signals signals signals signals signals signals signals higher higher part previous required good good spike spike spike spike spike conditions distributed distributed make fact fact techniques proposed proposed proposed proposed observed resulting ing respect sum performed eq times elements regions regions regions factor study study study study study study study study study study negative original specific specific specific specific represented series series define rates rates proc proc proc perform determined determined determined experimental experimental experimental experimental experimental experimental experimental goal goal connected power power power power power power approaches mit voltage voltage steps steps larger contrast contrast contrast contrast descent dependent dependent dependent dependent source source source source source source source department technique individual individual advances responses scheme cambridge computing computing equivalent solutions solutions stimuli stimuli determine efficient requires significant significant statistics free free estimated estimated estimated basic increase con coding weighted criterion types entropy entropy processes processes iteration nature simply achieved measured measured measured measured covariance covariance fast fast fast fast fast fast fast fast fast fast fast fast limited close assumption finding assumed supported theoretical theoretical main eds eds future combination combination combination functional functional unknown unknown unknown coefficients fully ratio ratio ratio york mechanism mechanism structures uniform making attention run run sources sources sources sources sources sources denotes recent recent advantage property robust separate reported introduced period period period sense sejnowski sejnowski recently recently relevant relevant highly highly observations calculated calculated correspond studies studies differential mixtures mixtures mixtures mixtures mixtures mixtures separation separation separation separation separation separation separation separation separation channels channels amplitude amplitude amplitude expression expression concept studied occur occur occur digital spikes locally touretzky deterministic occurs generally column demonstrate demonstrate demonstrate hebbian reduce conclusions central learns constrained demonstrated intelligence variety user ica ica ica ica ica ica ica ica ica ica ica ica ica exist min relationship manner question question denoted denoted denoted denoted acknowledgements pro pro factors estimating mathematical mathematical mathematical category dimensionality easy unique spectral spectral extraction expectation expectation expressed communication densities evaluate forms suggested spectrum spectrum spectrum spectrum spectrum sign slow slow iterative generation calculate norm norm norm euclidean recorded recorded usa bell bell eigenvalues eigenvalues blind blind blind blind blind blind blind blind batch plotted mozer successfully major major columns aspects efficiency efficiency closely importance uniformly encoded encoded identify oscillatory oscillatory oscillatory oscillatory computations composed excitation excitation conf decoding decoding induced contained oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations content content sampled wave computes hypotheses maximization received mixing mixing mixing extract trains minimized stimulation stimulation stimulation stimulation selectivity put oscillators dual periodic reducing fourier fourier respond school biol int possibility dependencies maximizing oscillation workshop statistically statistically understand coarse coarse measurement gradients analyze rev implementations amari amari mixed finds seconds rows ment slowly slowly slowly theoretic agreement analyzed adjacent adjacent reasons considerable rapid perspective sites sites widely organized desirable ion medical localized fourth fourth fourth considerably understood remove outliers release release exhibits spread spread aim modulated modulated modulated germany converged phenomenon gap spectra accomplished restriction arranged cellular cellular oja oja oja oja oja oja oja oja oja oja multiplicative hit hit hit hit hit hit hit hit hit hit symposium hours periods loo irregular sion studying equals regarded von washington uni hasselmo yang waves waves waves waves indicator suggesting contraction specificity sustained proteins agree concentration impact impact calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium calcium grants avoiding dividing divide ics ics ics ics ics ics ics ics ics ics multiplying yielded emission numerous sch super maximized cooperative axe spatio spatio kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis kurtosis convenience aij junction gene gene gene gene gene mutually activate regulation regulation deconvolution spreading oscillating oscillating oscillating intracellular intracellular intracellular intracellular intracellular intracellular intracellular intracellular intracellular intracellular transients jutten jutten jutten signs gorithm clinical fiat fiat stores differently resolve resolve marks quantify loaded realizations fre compo compo subtracting subtracting wavelength wavelength sen regulatory acid lewis cess correlates broadband broadband broadband broadband lar cichocki christof wagner initiated initiated repetitive spario spario spario spario spario spario yon yon yon cardoso cardoso prolonged nents nents herault herault comon comon comon comon quency excitable excitable klaus extrema extrema extrema stim alexander ago compartments puted europhys electrically ponent kurt functionals signaling signaling signaling signaling transcription transcription transcription transcription widespread cumulant karhunen karhunen ration ulation lations wtx neurotransmitter whitened whitened administration hyv hyv hyv hyv hyv hyv hyv hyv sharper grained grained cumulants ubiquitous transport reg decade coordinated entity initiate stimulate annu wavelengths wavelengths sory deutsche neuromimetic serf pacific conventionally exposures excita oscil imizing influx tumor pharmacological pharmacological pharmacological georg messenger vantage exten brussels equency cancelled sphered proliferation forschungsgemeinschaft ier lake zur zur zur zur separa gration pects tities formly 
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input data data data data data data data data data data data data data function function function function function function figure figure figure figure figure figure figure time time set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training output output output output output output output output output number number system system system system system system system system system system system system system system system system error error error error error error error error error error error results results results units units units units units units units units units units units information information information information information information information information information information information information information information problem problem hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance based based based linear linear linear linear linear linear case case case case case case order shown shown systems systems systems systems systems systems systems systems systems values values values values probability probability probability probability probability probability noise weight unit unit recognition recognition pattern image image image image image image image image image image image image image image image image image processing processing processing processing processing processing processing processing large large large local local rate rate test test test analysis analysis analysis analysis class class inputs inputs inputs inputs inputs form signal algorithms simple simple gaussian paper paper paper paper examples examples small small small small small small small small feature feature feature feature feature feature feature feature feature work step features features features features features features features classification process level level level level level level level level level current trained trained trained trained trained trained structure structure structure structure structure structure structure problems problems problems problems random high high high high similar representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture equation rule rule images images images images general general general real approximation term note experiments university university university university computation defined found found found found target target initial initial constant table table table table estimate estimate estimate standard standard standard computer computer computer computer presented presented presented map map present present present present present present phase low low low low low low low low low low low low low machine machine object object object object object sets sets maximum maximum press learn learn learn learn learn position position position position position position position position outputs outputs outputs abstract applied applied applied applied back back back find properties references component ieee ieee positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive important important propagation context context context context context context context context introduction action complex complex hand statistical statistical generated cost cost search search search tion energy energy energy energy energy energy energy difference classifier classifier lower learned higher higher higher part center center center previous previous cases cases cases multiple binary represent represent make make fact fact techniques region region proposed correct errors scale scale scale scale scale scale scale scale resulting classes ing tasks computed multi multi multi multi multi multi multi multi called elements regions regions regions factor made natural natural orientation orientation orientation applications applications applications applications applications study study filter filter negative negative negative negative original artificial relative true true true compared application application application application cross cross compute objects objects objects objects objects objects objects objects objects rates rates rates rates location location location equal mit comparison contrast train morgan morgan proceedings proceedings institute loss consists consists advances advances difficult addition framework framework framework cambridge directly directly directly directly directly curve design san san stage stage effects detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection conference full significant significant vision vision basic pages pages pages pages pages increase validation con produce developed levels levels criterion criterion criterion area area area types entropy actual provided finally processes sampling tested complete shape eds square pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel ability cluster cluster cluster cluster cluster makes rumelhart including kaufmann kaufmann typically needed reduced account technology block block testing testing testing significantly database operation operation representing filters filters filters filters filters filters pre pre direct direct experts supervised expert decay combined minimize produced added architectures architectures architectures architectures improve improve directions directions resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution typical reported apply apply apply apply introduced include identical pixels pixels pixels pixels hierarchical hierarchical hierarchical hierarchical interest interest previously conventional volume volume achieve diagonal diagonal evaluation positions positions positions locations improvement entire entire constructed horizontal parts invariant occur suggests extended extended extended extended extended digital deviation deviation touretzky touretzky touretzky clusters clusters half half flow conclusion critical greater reduce segment editors editors editors differences designed designed moody mateo mateo integration presence presence physics reduction reduction intelligence regularization regularization radial radial targets targets areas digit pro construct construct produces written generating generating laboratory vertical distinct missing sensitivity sensitivity sensitivity coordinates coordinates involves remaining easy scales scales scales scales integrated integrated integrated gaussians applying applying shift extraction extraction john john national extracted extracted stages squares detailed evaluate evaluate fraction centers centered understanding processor processor diagram diagram key earlier roughly false false false false false false false false false false false false false visible assigned foundation classified classified classified classified transactions david david david david handwritten box kernels kernels combinations combinations combinations uncertainty discussions characterized successfully included detect detect detect detect detect detect detect detect post post essentially ten fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine fine receives receives characteristic summary contained cun cun cun heuristic showing cue sampled sampled usual providing denker highest highest highest operating operating operating operating acknowledgments tesauro requirements experience detail detail detail detail detail detail detail replaced hanson lippmann mass mass mass mass mass mass mass mass mass mass mass mass mass mass reducing reducing tech workshop hierarchy statistically coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse coarse gradients editor adjusted subsets subsets subsets versions detector detector detected utility averages established integrate integrate integrate massachusetts developing separable distinguish publishers publishers convolution convolution growing improves improves multiplication drive drive filtered products products potentially beginning medical medical integrating improvements evaluating evaluating double freeman peter peaks peaks detecting detecting detecting detecting detecting detecting detecting passed frequently dots compares operate extracting suited suited suited richard conclude display neuro specifies diagnosis diagnosis diagnosis pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid contextual contextual sensing leen princeton acts count purely printed murray murray imaging imaging chance intelligent check contract occurring exploit implications repeat started mance combines combines james zhang patient paul perfor searching propagated propagated propagated similarities darpa enable recog april reader specificity passing splits exploiting exploiting calcium border border discovered propagate ignore fold cam robert onr informa roc roc roc roc roc corporation pointing nition encouraging encouraging propagating boser experiences chicago chicago chicago chicago chicago chicago chicago chicago chicago chicago chicago chicago workstation associate examining examining clustered reject henderson perpendicular diag pami uncertain uncertain thresholded rejected investigating pos funded inverting truth truth steering tissue november clinical clinical clinical clinical todd breast breast breast micro pearson keeler keeler eliminates burr integrates integrates distinguishing resolutions resolutions resolutions resolutions bergen positives positives positives positives positives positives digitized digitized arpa william spie protocol schmidt schmidt differentiate charles benign benign seg clues prune energies indi actively subtle polar discriminating regularizers mid ysis richer spots bright imaginary minute spence spence spence spence spence spence madison mentation tentative jackknife jackknife jackknife jackknife fbr fbr fbr fbr fbr fbr gupta missed rationale preset blur malignant malignant malignant malignant malignant malignant malignant cad cad cad cad cad cad cad cad cad cad cad cad cad cad cad cad cad cad cad cad cad niques subsample masses masses masses masses masses masses masses masses masses masses masses masses gerald undergoing jim steerable steerable numerals roi roi roi roi roi suit hierarchically steer micron micron micron reductions ditional edward clay clay clay sajda sajda sajda sajda pus spend ifp ifp notable tives smart vances detectable structed deriva kenneth negatives negatives negatives tangential tangential wee vidual leow crn unambiguously grams interprets ature campus sarnoff sarnoff ois ois ois aided aided aided aided drs pyra tbr arielson clinically 
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#*learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure figure figure figure time time time set set set set set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system system system state results results results results results information information information information information information problem problem problem problem problem problem models models models models models models models models models models performance performance based based based space space space space space weights weights weights case case case case vector order shown shown shown shown systems values values values values values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight distribution distribution recognition recognition approach approach approach approach approach pattern pattern pattern point point point image processing processing processing processing control control large large large large large large local local local local local patterns analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix optimal optimal form form form shows shows shows shows shows shows shows algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual paper paper paper paper paper paper examples small size size size feature feature work work work work task task task methods step points points points points points features features features classification classification classification classification process process process level level level level level level level level structure problems problems random response representation architecture show show section rule rule images images images general parameter parameter parameter real real real approximation obtained obtained dimensional university solution solution solution research independent log log log log log defined found found found found found found found found found initial initial initial constant table terms distance left left left direction direction map low object object object object object object object object object object object maximum maximum range range range range range range range range range range range range learn position components components components abstract applied applied find find find find find find computational convergence density likelihood likelihood likelihood references component component due due procedure important important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction introduction action hand hand hand hand estimation behavior behavior statistical statistical statistical effect effect generated variance tion tion classifier classifier classifier measure prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen higher higher higher higher higher higher higher part center previous multiple conditions conditions represent distributed bayesian bayesian bayesian expected expected expected expected markov make make make techniques correct errors forward finite minimum minimum minimum sum elements means means means means means factor optimization optimization optimization optimization orientation orientation orientation knowledge knowledge knowledge knowledge knowledge em em em em em em em em em em em em em em artificial specific specific specific specific represented application application application application application application application series series provide provide provide define objects objects objects objects objects objects objects objects objects objects objects objects objects location perform determined distributions distributions distributions distributions distributions approaches approaches approaches mit accuracy update update update update update update support dependent modeling modeling modeling modeling report report institute implementation implementation technique exp exp addition addition graph graph ai ai ai ai ai ai ai ai ai ai cambridge computing environment environment view view view view solutions solutions solutions top top top stage effects effects determine efficient free basic basic give give con randomly clustering clustering clustering clustering clustering clustering clustering robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels levels types types lines lines provided provided processes evidence nature constraint constraint covariance covariance covariance covariance covariance covariance covariance covariance normal technical technical describe close inverse assumption complete finding finding common common assumed require journal cluster cluster cluster cluster future makes makes fit fit fit probabilistic probabilistic probabilistic probabilistic needed reduced unknown fully interesting interesting ratio york segmentation structures matching matching numbers making international early attention combined run light improved directions recent exact advantage separate separate element element element typical typical reported moving include include identical side side side side sense sense relevant varying calculated axis converge converge sparse sparse sparse sparse sparse sparse sparse mixtures mixtures mixtures mixtures mixtures mixtures mixtures positions chain locations locations modified grant extended move move move move clusters clusters clusters clusters clusters clusters clusters clusters setting setting demonstrate starting starting segment segment measures accurate bayes exponential faster constrained characteristics characteristics characteristics characteristics drawn pulse plane plane plane plane plane plane plane plane plane plane plane targets scene scene scene scene scene scene scene scene scene scene scene force acknowledgements monte carlo written written perception perception perception perception perception perception ways ways sequential plot describes vertical vertical vertical vertical mathematical dept changing changing modeled modeled pruning slightly angle angle scales scales gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians expectation expectation john extracted expressed review review stages squares influence solved labels labels forms soft sizes sizes sizes similarly updates updates updates reasonable combining fitting fitting fitting fitting fitting fitting fitting calculate visible visible visible advantages box box box box box usa formulation formulation formulation eigenvalues weighting plotted plotted illustrated illustrated priors priors priors priors priors priors priors priors priors priors priors priors priors priors priors priors priors coupled successfully successfully sensor sensor sensor sensor sensor sensor sensor sensor society society encoded included included included included included identify post orthogonal capture summary conf graphs graphs graphs prob allowing allowing allowing showing interpreted interpreted sin sin sin sin sin strategies usual usual simplified providing eigenvalue eigenvalue leading maximization maximization automatically deal modelling employed origin origin command command powerful wiley wiley poor poor poor poor giving ideal relationships authors eigenvectors eigenvectors affect surfaces measurement measurement naturally adapt analyze aspect front front initialized ith detected extent motivated optimum preference scenes scenes cos cos cos cos cos trivial sensors sensors track guaranteed guaranteed guaranteed growing processed processed sections widely forces incorporate located immediately mation commonly controls probable recognized angles calculations lowest author varies applies reflect collected dark flexible flexible parameterized readily readily red red introducing incorporated incorporated schematic outliers calculating berlin mod ture incorporating green green green green gave germany expectations returns diagnosis lab primarily writing modify tation acm conditioned pick dynamically mobile mobile mobile mobile royal royal generality inspired fits smith smith smith smith smith smith allocation dealing dealing murray murray murray murray murray ments adjusting proceeds odd interpret interpret reasoning affected responsible guide guide modifications spurious infor iteratively scan scan scan scan scan specialized thin thin ends extends impact sons hart hart dempster dempster dense dense boxes boxes fitted truncated truncated logarithm rubin pointing misclassification planes planes planes opposed opposed blue blue ease ease multinomial reflected clustered clustered clustered clustered clustered clustered reject constrain constrain leg perpendicular perpendicular intuition community robots duda duda wall wall wall wall wall wall wall wall wall wall wall reflectance guided dirichlet cartesian cartesian cartesian cartesian laird hansen hansen hansen hansen sized accounted rod flight williamson williamson williamson williamson normalizing lems gratefully fiat beam parameterization parameterization parameterization parameterization parameterization parameterization prefer responsibility calculates returned returned concerns ters sen sparsely automation laser laser detects symmetrical rameters tended tended invisible invisible denmark acknowledges sparseness brought inappropriate tan tan hot collections richer occasionally direc scans scans ness undesirable volker sible biasing clus experimentation initializing optimiza positioned hyperparameter hyperparameter cap differentiated equipped uncertainties suit finder finder finder finder finder steer visibility visibility visibility visibility visibility noticeable mat rectly incor richardson richardson walls walls accumulates iee tti tti dates plete misclassifications hans straint oblique orien lows titterington titterington skewness surveys alt incom ellipses bined photograph interprets interprets matthew ellipsoid ellipsoids diagnosed ules recalculated iml recast chichester sors denser reformulating curie lfi 
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural data function function function function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm number system system system system system system system system system system system system system system system system system system system system system system system system system system state state state state state state results results results results results results information information information problem problem problem problem models performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based based based based based based based case vector vector vector systems systems systems systems systems systems systems systems systems systems systems systems values values parameters parameters functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit approach approach approach approach point single processing processing control control control control control control control control control large large local local local local local local local local local local neuron neuron neuron neuron neuron neuron analysis analysis optimal inputs shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper paper examples examples size size feature work work work work work work work work task task task fig step points field field field level problems high memory memory memory memory memory response section section section section fixed real real real real average average average average average average states states states states theory theory theory theory theory theory note note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments result result result result solution solution research research research research log defined sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics table table table table table table table estimate standard terms node node science map present nodes machine press press press press press learn outputs abstract back computational computational computational references ieee important adaptive adaptive decision decision context introduction hand behavior behavior behavior behavior behavior behavior effect dynamic recurrent recurrent tion change change change change assume assume rules part center center center previous previous previous previous bound bound good good long long conditions conditions distributed distributed distributed distributed markov make fact fact length correct correct observed errors errors forward simulations minimum resulting ing ing tasks total total total total total total total total total total human multi multi multi sum sum sum sum performed times means means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement optimization made global global global global global global global global global study knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge knowledge artificial artificial artificial artificial true true compared desired cross cross cross provide proc proc determined experimental goal goal goal related connected discrete power mit mit mit mit steps steps steps larger larger contrast contrast fields update update update source source source morgan proceedings internal internal individual individual individual individual advances advances delay delay delay delay delay delay delay delay delay delay delay addition considered framework framework framework cambridge domain domain domain domain directly view estimates estimates design design design design effects effects effects conference upper upper full full full full full full full full full full full world world world world world world world world world world world speed estimated estimated pages pages pages pages increase con weighted randomly path path path path path path path path path product provided finally selected constraint constraint constraint constraint constraint constraint constraint constraint discussion arbitrary tested limited limited limited limited assumption assumption actions actions nearest theoretical theoretical theoretical end future future including including kaufmann pairs dynamical technology increasing consistent consistent operation leads call call pre window window window window window international attention attention minimize minimize run run light light light light light predict architectures discussed improve improve directions directions pair separate separate separate separate reported strategy include identical side relevant compare previously previously previously conventional observations observations achieve rl rl rl rl rl rl rl rl rl rl rl address definition modified entire increased increased concept alternative locally locally white occurs setting hardware runs runs strength starting critical critical conclusions neighbor valued valued reward reward reward reward reward reward reward reward reward differences accurate accurate designed performs cycle characteristics intelligence intelligence intelligence intelligence intelligence intelligence intelligence intelligence intelligence intelligence intelligence exist decrease averaged pro construct plot mathematical mathematical mathematical changing changing simultaneously involves slightly integrated equilibrium equilibrium equilibrium predictive springer agent agent agent agent select review communication viewed learner evaluate updated sizes reasonable performing delays delays reduces combining event visible advantages topology david expect maximize holds holds successfully planning identified modification paths driven schemes essentially conf verlag quickly prob moore dis superior running running running criteria strategies absence automatically received received attempt consisted software routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing routing load load load load load load load decreasing presents presents presents presents employed difficulty difficulty rapidly humans game game preliminary hall fashion fashion links links rest rest investigated investigated int maximizing affect affect affect statistically analogous naturally naturally concepts editor editor traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic traffic ensure mapped initialized consist utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility utility regime arbitrarily arbitrarily submitted optimum optimum optimum ment crucial navigation improves improves improves independence caused baum worse starts straight purposes purposes purposes formalism formalism formalism arc arc arc shared closer precisely bishop desirable mathematics mathematics potentially optimize optimize optimize demonstrates addressed addressed alignment robustness varies evaluating reflect substantially dark fed autonomous share share controllers aim synchrony proven qualitatively collective collective collective collective collective collective collective collective collective collective chen sums sums summed aligned aligned aligned aligned aligned aligned aligned writing investigation restriction extensive perfectly dynamically concerned purely reaching establish clamped extending extending occurring intuitively service prentice heavy heavy heavy heavy introduces corre respective entry encountered encountered overview facilitate entries initialize discounted infer shortest shortest shortest shortest shortest shortest shortest route route route route route wolpert wolpert wolpert wolpert wolpert wolpert wolpert designing designing implicitly summarize automated automated bertsekas lem speaking boxes boxes constitute outperform outperform achieving achieving axe medium medium medium medium medium reports conservative assess queue summarizes concentrated modifying packets packets packets packets packets packets evolve cessing goals life life life interacting carefully regimes investigating nonetheless discusses nasa nasa nasa nasa nasa nasa packet packet packet packet packet packet applicability applicability aaai echoes littman factored factored factored factored factored factored factored factored factored demonstrating learners info reinforce laws remarkable externally send send agents coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin coin evolved evolved establishes loosely industrial outperformed concern concern concerns optima boyan sparsely schaal obey loads loads loads admission ultimate ultimate ultimate ultimate ultimate ultimate ultimate ultimate restricting outgoing artifact destination destination destination destination destination destination destination coins coins coins coins coins coins coins coins coins coins coins coins coins coins coins coins evolutionary feasibility bottleneck handbook ensuring ensuring ensuring spa spa spa spa spa spa spa spa spa spa spa spa spa spa spa spa spa spa spa adv rein settles settles utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities utilities markets optimizes gross repeats traversed tran tag superiority decides concurrently paid ames ames ames wheeler wheeler movie clamping rationale ant beat beat frank frank frank frank frank timestep timestep timestep timestep economics crafted routed concentrates concentrates havior sponds forcement turner turner turner turner turner internet internet internet internet internet internet originated foster traversing avail gallager gov gov gov pairings yeung economy pursuing print tagged choi timesteps timesteps fifteenth marbach traverse domestic downstream moffett moffett moffett centralized centralized centralized ringing simulators breadth nctions aft ceiling jeremy accrue arisen nash nash gree investiga surpasses 
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#*learning learning learning learning learning learning learning learning learning learning learning learning neural data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number state state state state state state state state state state state state state state results results results results results results results results information information problem problem problem problem problem problem problem problem problem performance performance performance based based based space space space space space space space space linear case case shown shown shown shown shown shown systems systems systems values approach point point point point point single large local local local local local local local local test optimal optimal optimal optimal optimal optimal optimal optimal form form form form form shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper paper paper small size size size size size feature cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step process current current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure problems problems problems problems problems problems problems problems problems problems high high similar similar similar show section section section section section fixed line gradient gradient gradient gradient term note dimensional dimensional dimensional result result result result result result result result result university university university university solution solution solution solution solution solution solution solution solution solution found found found found target dynamics table table table table table table standard computer computer distance science science science left left presented machine motion maximum maximum maximum press learn position position position continuous abstract applied applied applied applied applied applied back find find find find find references due positive important adaptive introduction introduction behavior behavior effect effect effect effect dynamic generated cost cost cost cost cost cost cost search search search search search search search search change difference difference difference variable variable variable variable lower lower lower higher higher higher higher higher higher higher part part center center center previous cases cases cases required required required required required required long represent represent tree tree make techniques region proposed length length length length length finite finite finite minimum resulting ing total total total total total total total total total total computed called called regions regions reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement potential potential potential dimension natural global global policy original original original original original original original specific represented true location goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal gain mit steps steps steps steps steps steps steps steps steps steps larger contrast support morgan proceedings proceedings report report version version version version version joint joint represents represents represents final final final final final bias addition addition addition ai directly directly additional additional additional solutions solutions solutions solutions solutions solutions solutions trajectory trajectory trajectory trajectory trajectory trajectory top conference efficient efficient efficient efficient efficient requires requires requires world increase increase increase give produce produce robot criterion velocity velocity velocity controller controller controller controller controller path path path path path path path path path actual finally finally evidence simply achieved discussion technical increases close close stable surface finding short nearest common square end end degree degree objective objective typically smaller needed needed needed needed needed needed needed programming increasing structures trials trials trials trials trials trials uniform database database principle representing representing numbers numbers iterations pre bottom idea run run run added improved improved improved improve improve improve improve improve resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution resolution robust robust robust robust typical apply introduced introduced introduced strategy strategy strategy strategy strategy strategy strategy period side side side side side side side side side side side side relevant varying compare yields achieve achieve achieve rl rl modified modified modified modified modified modified modified modified observation williams williams williams williams williams williams improvement improvement improvement entire increased arm arm arm arm exists horizontal parts studied studied trial trial trial trial locally move move move move boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary generally generally pass pass minimal conclusions neighbor differences designed clear sutton sutton hard largest largest largest largest largest largest largest largest largest largest largest largest largest turn start start start start start start start start start start exist selective plane introduce introduce manner configuration force areas areas explicit appears appears pro produces produces produces longer winner winner winner ways factors infinite dimensionality remaining remaining remaining belief consisting applying applying applying applying applying applying applying formed formed quality agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent focus updated forms sizes sizes partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition past barto barto performing performing spaces spaces add boundaries boundaries avoid exploration figures determines domains reason extra efficiency efficiency efficiency uniformly differ modification paths paths paths included literature build comparing tend fine fine fine fine reached reached refer quickly kind contained prob success moore moore moore moore moore moore moore moore split split superior lie running follow strategies strategies absence absence highest highest reach reach reach reach attempt moves policies disparity neighboring neighboring neighboring neighboring neighboring acknowledgments remain access essential investigate investigate involving involving detail optimized limitations game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game game existence fewer fewer fewer fewer successive ideas reliable reliable workshop momentum neu neu hill hill smallest coarse coarse gradients gradients gradients gradients gradients gradients gradients gradients gradients gradients integer extremely created assumes assumes freedom freedom shapes generates finds finds attempts mentioned mentioned mentioned theoretic costs costs costs costs crucial growing slope improves improves worse starts starts closer desirable cut potentially implicit localized depicted depicted robustness robustness requiring collected amounts leave atkeson atkeson atkeson atkeson marked marked marked incorporated continuously compares maintain partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning mod limiting aim fall achieves boston boston eventually multidimensional multidimensional lot trade globally consistently discontinuities newton college college assign assign pick dynamically partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions partitions turned proceed proceed proceed reaching reaching reaching reaching kaufman adds promising hyper hit balance resulted resulted hope operates modifications adequate exceeds planar continue reset falls introduces guarantees guarantees sides infinity infinity reproduce claim winning winning winning winning advance creating extensively partitioned partitioned partitioned splits variants subsequently balanced balanced mind yale yale outperforms outperforms outperforms achieving ties ties ties ties ties forced experiences experiences experiences experiences experiences rectangular modifying cessing goals wall wall discontinuity searches win win win win win win barrier barrier barrier barrier barrier barrier barrier barrier barrier barrier places continually gorithm coming triggered lems traveling corporate continued losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing losing maze maze maze maze maze maze maze maze maze maze maze maze maze maze maze maze maze maze maze curse focuses bold king termination appealing horizontally tip evenly settle ters discarded discarded attained lying parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti parti contrary minimax minimax spirit thing terminates acknowledges routes stabilize stabilize stabilize ically promise eighth excessive unexpected stabilization stabilization snake stems hole entering entering preventing newly newly newly aims contributing continuing putting repeats conceptually traversed aimed shortcut shortcut shortcut decides seeking seeking nation ronald deformed gorithms ramp cen rationale lose lose lose lose lose lose refining opening opening mission discarding encourages coarser reachable combi indefinitely pairings pairings pairings occupies vastly ccs ccs ccs finely finely perceives perceives northeastern northeastern ice ice thrust thrust barriers shortcuts aiming aiming aiming aiming aiming mazes mazes creased recomputed proceeded reso commanded commanded strat uneven shallower egy failing bustness lutions fewest penetrate 
#@Al-Ansari_M,Williams_R,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural data data function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure time time time time time time time time time time time time time time time time time time time time set networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results information problem problem hidden hidden based based based based based based based based based based based based space weights weights weights weights weights weights weights weights weights weights linear linear linear case case case case case case case case case vector vector vector vector shown shown systems systems values values values values values values probability probability probability probability probability probability probability probability probability probability probability parameters noise weight weight weight weight weight weight weight weight functions functions distribution distribution distribution distribution distribution approach single single single single single single single single single processing processing processing control large large large rate rate class optimal optimal optimal form form form form form shows shows signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple gaussian paper examples examples small step step step step process current current current current current current current problems problems problems problems random random high similar similar equation equation equation equation equation equation equation equation equation equation fixed fixed line line line rule rule rule general general general general general general general general approximation approximation average average average states states states states states states states theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term note note note note note result university university university university university variables variables variables variables variables variables variables variables solution research research research independent independent independent independent defined defined found found found sequence sequence sequence sequence sequence sequence sequence sequence initial initial constant constant table table table table table table table table table table table table table table table estimate estimate estimate standard computer computer computer terms science science science prediction left left left left presented frequency machine range range press learn learn learn learn learn learn learn learn learn learn learn nonlinear nonlinear nonlinear nonlinear sample abstract applied applied convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee positive positive decision decision introduction action action action action action action action action action action effect generated generated generated variance search search search search search search search search search search search search search search change change change assume learned learned learned learned learned part previous previous cases cases cases cases cases good good good long represent expected expected expected expected expected expected expected expected markov markov markov region proposed proposed proposed proposed proposed length correct probabilities probabilities probabilities observed observed observed finite finite finite simulations simulations minimum resulting resulting total total total total simulation simulation simulation respect respect respect respect respect sum sum performed times times means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor optimization made made made global policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy original artificial true true true true true true application series define compute rates rates rates perform perform determined distributions distributions equal equal approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches mit steps steps steps steps update update update descent descent descent descent descent descent descent descent morgan proceedings proceedings report report institute department department department advances connectionist difficult difficult difficult addition addition graph sequences framework cambridge equivalent directly directly directly directly directly directly directly additional estimates estimates transition transition trajectory trajectory san conference choice choice choice choice estimated give give give give give give give derived weighted weighted weighted randomly types processes iteration iteration sampling simply simply simply technical technical limited close complete stable actions actions actions finding finding short assumed generate theoretical eds eds eds end end end end end instance future future future noisy including needed needed needed combination combination combination technology interesting interesting york york special special special special special special trials trials squared squared squared squared squared max making international decay combined combined combined minimize minimize minimize run added light discussed discussed advantage advantage advantage advantage pair element practical practical include include include include period period period period period period period period period period period side side side side interest previously previously calculated solve smooth smooth smooth smooth yields converge converge converge converge converge converge converge converge converge converge rl rl rl address definition chain modified modified observation bounded bounded williams williams williams williams entire expression trial trial trial trial trial trial wide derivative deterministic occurs column runs conclusion starting starting place assumptions reduce reduce trajectories trajectories clear practice practice learns learns learns learns temperature intelligence variety minimizing start start start start start start selective force question question areas appears perception solving solving ways generating plot transitions transitions transitions transitions changing changing changing missing infinite infinite belief adding frequencies frequencies quality expectation choosing choosing choosing independently depending depending solved evaluated evaluated open showed converges converges updates past past partial reasonable performing performing spaces reduces combining add calculate norm recorded existing exploration exploration exploration includes thesis weighting weighting maximize mozer domains partially partially planning columns columns columns uniformly society modification genetic reached reached quickly quickly quickly quickly kind moore moore moore moore issue satisfy sampled sampled observable observable policies policies policies policies policies satisfies satisfies acknowledgments tesauro decreasing explore put replaced optimized divergence mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp hall reducing reducing incremental incremental incremental terminal terminal terminal terminal terminal analytically combine proper affect affect affect affect gradients gradients trace trace trace trace extremely automata automata automata changed changed greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy generates generates generates improving massachusetts massachusetts brown residual residual residual residual residual residual residual residual residual residual residual stop slowly slowly critic publishers derivation derivation guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed guaranteed starts starts sections sections choices worst worst actor separately mellon mellon summation requiring people carnegie carnegie empirically pure pure pure pure pure pure cmu cmu cmu cmu parameterized backprop backprop share rewards rewards http summarized summarized pittsburgh pittsburgh extensions prevent adjust boston unbiased unbiased unbiased unbiased returns eventually baird baird baird baird baird baird baird baird baird traces yielding yielding yielding bellman bellman bellman bellman bellman bellman bellman bellman bellman bellman tresp tresp ordinary www www www optimality equivalence guarantee guarantee modify summing girosi approximates nonzero nonzero fails air kaufman chance satisfying satisfying pomdp pomdp pomdp occurring fail modifications wilson exploring published prentice reset reset reset equals guarantees lengths searching hasselmo chooses chooses approximators francisco discounted discounted surprisingly ends horizon horizon approximator convergent mdps mdps andrew consecutive fitted pomdps pomdps outperforms unified unified leaving leaving july incrementally residuals acceptable tradeoff amherst certainty beta visited acting discontinuity lookup lookup lookup ambiguous sketch happen rochester rochester gordon gordon gordon wider littman rarely reinforce reinforce reinforce cliffs doesn oscillate russell stay calculates returned dissertation dissertation englewood ooo sarsa sarsa sarsa sarsa sarsa sarsa decaying coins kaelbling oscillates successor sponsored diverge entering unifying unifying unifying optimizes nondeterministic avenue avenue named rightmost narendra narendra diverges retains ending stuart gullapalli gullapalli instantiations mccallum reinforcements reinforcements makhoul primed primed primed primed primed primed twelfth shed instantiated instantiated cassandra successors chart ccs triplets northeastern marbach marbach resetting str unify lids tlt forbes forbes counterexamples boltzman counterexample 
#@Baird_L,Moore_A,
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#*learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural neural input input input input input input function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time set set set set set set set set set set set set set set set set networks networks networks networks algorithm algorithm algorithm algorithm output output output output output output system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error error error error error error error state state state state state state results results results results results results information problem problem problem performance performance performance performance based based linear linear linear linear linear linear linear linear case case order order order order order order order shown shown shown shown shown shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values parameters parameters parameters noise noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons approach approach point point point point point point point point point point point point point point point point point point point point point single processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control neuron rate rate analysis optimal inputs form form shows shows signal signal signal signal signal signal signal signal signal signal signal simple simple small small cells cells cells cells cells cells cells step step step step step step points points points field features features features features features process process process process process process level cell cell problems problems random random high high high response response response response response response response response response response response response response response response similar similar similar show fixed fixed general theory theory term term term result result result result result result result university university threshold threshold threshold threshold threshold threshold threshold threshold research research dynamics dynamics dynamics dynamics dynamics constant constant constant constant constant table table standard synaptic synaptic synaptic science science left presented activation activation activation activation activation activation activation low low frequency maximum maximum maximum press press components basis basis outputs abstract back references positive positive positive positive important important action action action action action action action action action complex behavior behavior behavior behavior behavior behavior behavior behavior behavior effect effect effect effect dynamic dynamic parallel parallel tion change change change change change change signals signals signals learned learned chosen chosen required multiple long long long long long expected make region region region region region region region observed resulting resulting resulting resulting total total simulation sum sum times times times regions factor made made made natural feedback feedback feedback feedback feedback feedback applications study filter vol vol vol vol vol vol artificial true compared compared application application series define rates perform active active active active experimental related gain gain gain gain gain gain gain gain gain brain brain brain steps steps larger dependent dependent dependent dependent source modeling loss loss individual responses difficult exp exp delay addition considered considered domain equivalent directly curve curve additional design design design trajectory effects effects significant significant significant significant significant significant significant significant speed speed basic increase con con con condition channel channel channel derived weighted developed developed developed levels levels area area controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller path path actual actual processes processes biological biological biological biological biological biological biological biological biological achieved achieved achieved achieved measured fast fast fast inverse inverse inverse corresponds stable stable surface surface actions actions amount implemented role role eds square ability easily simulated fully fully block block transfer interesting interesting significantly significantly york york increasing consistent matching matching matching matching matching matching operation operation operation leads details max pre early magnitude magnitude magnitude decay idea combined minimize minimize minimize run added neuronal neuronal neuronal membrane improved improved improve exact exact robust separate separate takes takes typical apply strategy strategy strategy period subject side side sense engineering engineering engineering interest varying previously volume smooth smooth correspond achieve achieve address definition channels interval organization sensitive entire expression lead lead lead lead lead studied trial deviation alternative locally loop loop loop white occurs generally pass flow strength conclusion critical place place greater central central central central central central central interactions designed designed designed peak peak peak faster learns learns temperature temperature temperature mechanisms mechanisms mechanisms mechanisms mechanisms mechanisms integration presence presence reduction characteristics characteristics demonstrated proportional proportional proportional proportional proportional proportional labeled labeled labeled labeled labeled pulse iii iii introduce manner manner appears pro longer solving ways ways stability stability changing modeled physical electrical electrical remaining develop develop develop develop integrated integrated integrated integrated integrated integrated integrated adding equilibrium applying formed versus decreases independently viewed detailed detailed open open controlled controlled controlled controlled controlled controlled controlled controlled showed understanding understanding completely similarly suggested sign sign sign diagram key reasonable reasonable smoothing slow slow slow remains remains remains initially advantages figures usa usa usa uncertainty uncertainty activated activated activated activated activated successfully successfully successfully gamma identified identified importance suitable modification modification literature post comparing traditional traditional quickly quickly repeated allowing conductance conductance oscillations physiological criteria criteria criteria device receptor receptor receptor receptor receptor receptor receptor receptor receptor receptor play correspondence binding binding binding binding binding binding principles operating operating operating operating operating operating operating operating deal rat load load decreasing law unlike production production requirements exhibit exponentially steady steady steady steady steady steady integral integral integral integral integral integral integral integral integral integral integral integral integral integral integral integral integral integral integral limitations existence rise rise rise rest project applicable plasticity scaled root variability variability pathway pathway pathway pathway pathway pathway pathway pathway affect affect affect fundamental removed removed act transmission possibly necessarily equally implementations ensure aspect aspect precise detector nervous nervous nervous switching switching switching motivated phd plant plant plant plant plant established animal animal brown brown brown brown residual residual site site great advanced crucial unstable unstable unstable unstable diffusion cascade perspective implementing closer closer sites strictly protein protein protein protein precisely located worst desirable nucleus immediately potentially separately begin bandwidth author robustness requiring improvements limits pathways pathways pathways pure offset offset offset offset offset poorly employ remove incorporated incorporated incorporated slower slower frequently schematic operate gains gains gains controllers controllers controllers popular achieves conductances substantial logical logical inherent inherent sophisticated attraction expectations begins extreme primarily oxford oxford appropriately neurophysiol unity receptors turned turned reaching inspired inspired inspired inspired chance chance adjusting satisfying alpha chemical chemical chemical chemical analyzing definitions integrator integrator integrator integrator integrator integrator integrator exceeds exceeds degradation hours hours hours hours hours hours introduces tone tone ensures james james studying displayed guarantees heart recovery smoothed rich concentration concentration concentration calcium calcium calcium calcium calcium calcium lag escape pressure pressure pressure pressure pressure pressure pressure reflex reflex reflex reflex maintaining blood blood blood blood blood blood blood blood removal removal reaction reaction reaction rejection revealed diverse trigger trigger lit stem affects affects resting gene gene beta tight cns cns peripheral gated formance insights genes mammalian activate regulation regulation regulation regulation regulation altered diversity afferents behave margins examination examination challenge challenge diagrams laws achievable achievable transduction transduction transduction transduction transduction transduction instability attributed crude settling utilizes evolved loosely hour hour conversion station disturbances disturbances disturbances disturbances regulatory regulatory offsets ray disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance disturbance functionally loads trol economic predictable predictable predictable attenuation attenuation attenuation attenuation compensated compensated poles cess nominal nominal kinetic kinetic raised transmit undergo undergo excessive excessive excessive monitored health deciding responded applica drawbacks spent survival converts demanding stand sensed activating undesirable undesirable undesirable devel damped undergoes scheduled consciousness concentrations clin clin cardiac cardiac cardiac overshoot overshoot overshoot overshoot aggressive released behaved plants plants plants signaling signaling signaling signaling multivariable stretch cancellation mammals neurotransmitter opening acti industry duced reactions reactions death sudden biochemical biochemical biochemical reflexive kinase kinase kinase kinase kinase pii pii pii pii pii pii pii pii pii pii pii pii relaxing decayed deprivation regulated viii viii subunits oped stably vital binds binds arch pres infrequent infrequent infrequent integrators integrators integrators abstracted invoking erating igi infrequently indications abruptly reside nts nts nts nts nts nts gregory gregory intermittent intermittent intermittent cancelling cancelling subunit cancelled richness merical premature vated nol 
#@Brown_L,Gonye_G,Schwaber_J,
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#*network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural data data data data data function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set networks networks networks networks networks networks networks networks training training training algorithm algorithm number number number number system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models performance performance based based based space space space space case vector order order shown shown shown systems systems systems systems values values values probability probability probability probability parameters parameters parameters functions functions functions unit unit distribution approach approach approach approach approach point point point point single control control control control control control control control control control control control control control control large large large large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test analysis class optimal optimal optimal optimal optimal optimal optimal form shows shows shows simple simple simple simple simple paper paper paper paper paper paper paper paper paper small small net net work task methods methods methods fig fig fig fig features process process process current current structure problems problems problems problems random random random random random high high similar similar representation show show show equation equation section fixed fixed fixed fixed fixed line line line general general general general general parameter real real approximation approximation states states states states states states states states states states states obtained obtained obtained experiments experiments experiments university solution solution solution solution research research research independent defined target dynamics dynamics initial constant table table table table estimate estimate estimate standard standard computer computer terms science present present machine maximum press press press learn learn components abstract applied applied back find properties references stochastic stochastic due due due ieee ieee positive important important adaptive adaptive adaptive decision decision decision decision decision decision decision decision decision introduction action action action action action action action action action action action action action action action action action action action complex statistical statistical statistical statistical effect dynamic dynamic dynamic dynamic generated cost complexity variable lower prior prior learned learned learned learned learned learned learned learned learned learned chosen chosen chosen higher previous cases cases cases cases type type type type type good good good long distributed distributed distributed expected markov markov correct correct probabilities forward finite finite resulting classes total total total total total total total total total simulation simulation multi multi multi multi sum sum called times times times times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor potential potential applications applications applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge em negative negative negative application application define rates rates rates perform perform determined experimental related constraints constraints constraints constraints distributions distributions discrete discrete approaches approaches mit mit mit steps comparison comparison comparison comparison update update update source source modeling morgan loss technique advances advances advances advances final scheme considered considered computing experiment experiment experiment environment solutions estimates estimates transition transition limit conference determine determine efficient upper requires requires requires choice significant significant significant statistics statistics statistics estimated estimated increase condition condition channel channel channel criterion controller types processes processes nature constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint measured measured increases increases close actions actions actions actions finding finding finding effective effective effective require require main end future future future degree makes objective objective objective pairs pairs pairs pairs pairs smaller underlying jordan technology testing significantly leads call call call call call call call call call call call call call call call call call call call call call call call call call call call call call call max max max max international normalized normalized normalized magnitude combined choose run description recent property property property pair pair robust separate takes practical apply apply period period subject sense subset subset recently engineering interest sufficient highly compare compare compare works solve yields converge rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl evaluation interval grant exists lead lead occur alternative alternative alternative correctly occurs occurs setting conclusion operator depend reward reward reward reward reward reward reward reward measures accurate accurate clear clear peak peak peak peak peak peak peak peak peak peak peak peak peak peak peak exponential exponential exponential cycle assuming exist program configuration configuration configuration configuration configuration question denoted denoted factors primary describes transitions changing confidence confidence metric implement simultaneously simultaneously simultaneously simultaneously infinite electrical integrated adding adding quality quality quality quality expectation cycles decreases yield yield yield focus focus focus communication communication learner learner learner controlled restricted updated updated updated fraction approximations approximated converges measurements measurements delays combining intervals event event event event event event event valid sufficiently existing existing existing includes priori priori priori formulation assignment subspace determines maximize maximize maximize mozer mozer aspects importance divided literature post receives heuristic heuristic heuristic video video link link link link link link link showing issue criteria criteria criteria criteria criteria criteria duration simplified nips nips nips nips reach maximization received attempt policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies policies mixing deal routing routing routing routing intrinsic cowan employed unlike carried access access essential singh singh singh singh singh singh exponentially accurately issues examine giving giving combine combine maximizing variability workshop transmission possibly traffic traffic traffic traffic traffic traffic traffic traffic traffic rev ensure greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy noted explored explored generates attempts asymptotically brown brown brown brown brown brown brown great trivial growth distinguish analyzed guaranteed rapid straight sys widely strictly choices immediately consequence potentially potentially potentially separately gradually gradually bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth nsf nsf addressed researchers improvements varies led readily orders incorporated incorporated formulated compares rewards rewards rewards rewards rewards requirement gains gains gains gains poisson poisson characterize maximizes maximizes resource resource incorporating enables semi semi eventually calls calls calls calls calls calls calls calls calls calls calls calls calls don bellman bellman proofs feasible optimality guarantee gabor restrict fix ratios ratios ratios optimizing optimizing optimizing optimizing optimizing nat dynamically mobile tem arrival arrival arrival arrival arrival arrival arrival eliminated extending communications communications cellular allocation allocation allocation allocation allocation allocation allocation allocation allocation accepted accepted accepted accepted satisfying satisfying mos stated stated attractive monotonically exceeds heuristics service service service service service service repeat started periods periods periods appendix appendix entry guarantees guarantees guarantees guarantees guarantees guarantees colorado colorado chooses approximators discounted discounted suggesting arrive matter horizon tsitsiklis valuable valuable assigns bertsekas treat metrics metrics metrics drop users listed solves accept accept accept accept accept accept accept accept accept accept discount discount tables maximized july july rejection rejection rejection rejection diverse ideally solely constitutes conservative reject reject reject reject reject principled visited visited visited penalized exponent boulder met met met rejected lookup lookup pos indexed emphasized emphasized alternatives funded funded figs packet packet exchange commercial holding holding holding holding holding holding ward completed littman rewritten argmax payoff payoff payoff hyperbolic converging ongoing ongoing savings telephone utilizes termination termination award boyan meeting meeting meeting meeting meeting meeting meeting ally heterogeneous admission admission admission admission admission admission admission admission admission admission admission admission arrives arriving predictable experienced voice voice profit profit inducing terminates enter broadband broadband carrying artificially ensuring ensuring violated allowable allowable deciding huge violate violate violate violate violate violate violate proximation infeasible entering ton tutorial accepting accepting examines repeats madison acceptance visits tong tong tong tong tong accepts accepts accepts decides decides collect collect satinder satinder desire engineers multiplexing multiplexing multiplexing multiplexing utilization ration plex queueing telecommunications telecommunications rejecting wireless violations violations safely mission arrivals kauffman departure plications plied internet contracts transport meets depart customers customers paragraph pol signifi signifi deterministically collects timothy timothy discounting payoffs haykin recommended recommended intense transmits telecom telecom telecom facto explo marbach expo overload overload overload imizing violating munication cantly icy sibility straightfor departs watkin career iis nate framed ncr overflow baveja earn multimedia multimedia ide 
#@Brown_T,Singh_S,Tong_H,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural input input input function function figure figure figure figure time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number system system system system system system system system system error state state state state state state state state state state state state state state state state state state information information problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance based based based based based based based order order order order order order systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values probability probability probability probability probability probability probability probability parameters parameters parameters method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern point single processing control large large local test test analysis optimal optimal optimal optimal optimal optimal optimal form form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms simple paper small feature work work methods methods methods methods methods fig fig fig cells cells cells cells cells step step step step step step step step step step step step step step step points features features process process level current current current current current cell cell cell cell problems problems problems problems problems problems problems problems problems problems problems problems memory show show section section rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter average states states states states states states states states states states states states states states states states note note note experiments university computation computation computation research research defined defined defined defined sequence initial initial estimate estimate standard standard standard prediction left left left left machine machine machine machine machine machine sets sets sets sets sets maximum press learn position basis abstract applied applied applied find find find computational computational references stochastic stochastic stochastic stochastic stochastic stochastic due procedure procedure procedure procedure procedure procedure procedure procedure procedure adaptive decision decision decision introduction action action action action action action action action action action action action action action action action action action parallel cost search search search search complexity complexity classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure measure learned part part part part part part part part part part previous previous previous type type type type multiple multiple binary long long long conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions represent expected markov markov markov make make make make fact observed errors ing total total total total total total total total simulation computed eq eq eq called called called mapping mapping mapping reinforcement reinforcement reinforcement optimization made made made policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy original artificial specific specific specific compared series define define define compute compute compute proc proc proc proc active active active goal goal goal distributions gain gain gain gain gain gain gain gain gain gain gain equal equal equal equal approaches approaches approaches accuracy accuracy update update update selection selection selection selection morgan consists consists individual individual individual advances difficult difficult difficult graph considered considered considered considered computing environment environment environment environment environment environment environment environment environment view view view design bit bit bit bit conference free free free free free free free world world world world increase produce condition condition condition condition condition condition condition condition condition condition condition condition condition randomly randomly randomly randomly developed developed developed actual processes selected iteration simply achieved tested assumption corresponds corresponds complete actions actions predictions finding finding finding generate eds journal end end future future future easily makes noisy fit kaufmann pairs combination combination unknown jordan programming special special matching matching matching leads call call numbers bits bits choose added description denotes population population population population population population improve improve directions recent advantage pair apply apply strategy inference cognitive recently highly observations works tions solve solve solve converge rl rl definition evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation modified observation observation observation improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement entire increased exists parts locally locally locally move hybrid hybrid hybrid hybrid hybrid hybrid deterministic occurs occurs setting strength strength strength strength strength strength strength strength critical reward reward reward reward reward reward reward reward accurate weak sound propose strong strong cycle cycle proportional intelligence turn start start start start introduce monte monte monte carlo carlo carlo perception sequential estimating infinite agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent expectation select competition independently review viewed viewed evaluate evaluate controlled showed completely completely converges slow sec purpose generation generation generation generation generation string string string string symbol advantages avoid expect perceptual perceptual perceptual instances assignment assignment assignment assignment assignment assignment assignment assignment assignment assignment sciences discuss holds holds holds partially partially partially sensor sensor sensor sensor sensor sensor sensor sensor selecting aspects symbols symbols identify literature literature build build genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic genetic receives receives receives receives receives composed summary refer refer notice notice conf conf conf prob prob prob prob moore return built delayed observable observable observable observable observable attempt moves moves policies policies policies policies policies policies receive receive situations singh put put put environments mdp mdp mdp mdp matches matches matches matches matches matches history int int int authors reliable hierarchy understand matched smallest necessarily formal algo academic message message message message message message message message message message message message message message message message generates generates generates directed analyzed guaranteed fairly adjacent adjacent adjacent perspective sys easier organized operators operators ran opt annual incomplete requiring people behaviors capability capability span pittsburgh aim reaches reaches reaches popular popular occurrence achieves plan sophisticated returns jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola lim progress credit credit credit credit credit credit credit credit credit credit wesley sharing initialization don don don don representative sensing addison japan discovery food food food discover tem difficulties proceeds city attractive check pomdp pomdp pomdp pomdp pomdp pomdp keeping carry alphabet wilson wilson wilson wilson wilson wilson wilson wilson wilson repeat repeat repeat repeat excellent combines loo holland holland holland holland holland overview intended intended chooses tic viewing record refers fitness fitness fitness fitness agree messages messages messages messages messages messages designing designing designing approximator stone stone default default default default mdps empty empty lem pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps covering covering covering leaming leaming leaming leaming leaming leaming markovian markovian markovian markovian markovian suboptimal distinction distinction distinction distinction conjecture conjecture reports possibilities avoided avoids care care care rithms goals wall crossover crossover gener execute records memoryless memoryless memoryless pop induces spite spite littman lems lems lems rarely ergodic payoff payoff payoff payoff payoff payoff payoff payoff payoff payoff payoff survey maze maze maze ally extracts manipulated goldberg goldberg goldberg goldberg tells tells restricting kaelbling kaelbling evolutionary evolutionary profit contents problematic tenth mutation generations generations ness suitably repeats alization aliasing aliasing aliasing aliasing availability availability availability pay evaluates evaluates evaluates collect claims burden psp psp psp psp psp samuel samuel samuel samuel samuel michigan michigan michigan michigan michigan michigan michigan michigan michigan michigan faculty ions roth ulation pitt pitt pitt pitt pitt pitt pitt stochas iai mccallum mccallum mccallum mccallum mccallum saving saving pain bucket overcoming ond woods woods woods cooperate discounting maxa gan brigade violates surveys css css css css css css css css exit veloped attacked escaping dejong dejong lots schultz hayes alc multilevel afford goto goto mes sage exceptionally alleviates tma zeroth zeroth disappointing disappointing equip 
#@Hayashi_A,Suematsu_N,
#t12
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model neural data function function function function function function function function function function function time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number number number number number number number number number number number number number state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results models performance performance performance based based based space space space case case case case order order order order order order order order shown shown values probability probability probability probability probability probability probability probability parameters parameters functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution method approach approach approach approach approach approach approach approach approach approach single single single control control control large large rate rate analysis analysis analysis analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper small small small small size methods methods methods methods methods step step process level current random random random high memory memory memory memory similar similar similar similar similar representation show show show show show equation equation equation section section section section section section fixed fixed fixed fixed fixed line line general general general parameter parameter approximation approximation approximation approximation approximation states states states obtained obtained obtained obtained note note result result result result result result result computation computation computation research independent independent log log log log log log log log log log log initial initial constant estimate estimate estimate standard standard standard standard standard standard standard distance phase phase phase phase phase phase phase phase frequency frequency machine press press learn learn learn learn basis basis sample sample sample sample abstract abstract convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties properties references stochastic stochastic stochastic due important decision introduction action action action action action action action action action action action action action action action action action hand dynamic generated generated generated generated generated parallel parallel parallel parallel parallel complexity complexity assume assume assume assume learned theorem theorem theorem theorem bound bound bound bound bound bound bound bound cases cases required required required required required required required required required required required required required required required multiple multiple good good good good good good good good long conditions distributed expected expected expected expected expected expected expected markov markov make fact probabilities probabilities probabilities observed observed observed observed observed observed observed observed observed finite finite finite finite resulting resulting resulting resulting resulting resulting ing tasks total total total total total total total total total total total computed computed computed respect sum called times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor factor factor factor factor factor factor factor factor factor made made made made natural policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy obtain obtain obtain obtain specific samples true true true true true true compared desired desired desired desired provide provide provide provide provide provide define define define define define define compute compute compute compute compute rates rates rates rates rates rates rates rates determined determined determined goal related distributions distributions equal equal approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches mit steps steps steps larger contrast update update modeling modeling proceedings words words loss version version version represents difficult difficult final final addition framework framework framework cambridge directly directly directly directly additional view estimates transition transition transition transition trajectory conference efficient full requires requires choice choice significant approximate statistics estimated estimated estimated estimated estimated give give robot bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds provided provided finally processes iteration iteration iteration iteration iteration iteration iteration depends depends depends depends sampling sampling sampling sampling sampling simply simply simply simply simply measured technical technical describe arbitrary arbitrary arbitrary denote denote fast close close close assumption assumption actions actions actions proof proof proof proof amount amount amount amount amount amount amount amount common require main main main end instance instance degree makes makes makes simulated simulated typically pairs pairs pairs pairs smaller smaller unknown jordan transfer programming programming trials trials trials trials uniform uniform uniform empirical empirical leads details call call call call call iterations iterations max max max direct direct direct direct direct direct direct direct direct making international polynomial polynomial polynomial combined choose choose choose discussed discussed advantage advantage pair pair pair pair pair pair pair pair pair pair pair separate separate separate reported apply apply sense interest sufficient compare correspond converge converge achieve achieve trans sparse address address separation separation generalized bounded entire occur setting setting setting runs runs starting greater depend depend reward reward reward reward reward reward reward reward differences accurate accurate accurate sutton asymptotic weak hard turn start min introduce introduce question denoted relation derive derive derive derive construct produces longer longer solving ways generating estimating transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions transitions distinct explicitly explicitly simultaneously simultaneously simultaneously infinite infinite infinite slightly slightly slightly slightly unique consisting quality quality quality quality expectation expectation versus yield depending stationary stationary stationary stationary stationary detailed suggested updates reasonable barto performing classical classical classical roughly iterative construction building exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration thesis prove discuss simplicity simplicity straightforward literature efficiently essentially essentially reached induced allowing return return return return return hold built quantity sampled michael generalize delayed reach received received received policies policies policies policies policies policies policies policies policies mixing mixing receive access singh singh singh singh singh requirements requirements requirements experience experience experience experience experience experience experience experience experience experience experience experience experience experience experience experience experience experience experience experience updating rapidly detail detail limitations issues issues issues mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp examine successive ideas ideas ideas applicable applicable ideal ideal phases phases phases phases phases phases notion man analyze analyze extremely equally ensure ensure aspect obvious greedy greedy formal formal algo assumes mixed mixed mixed mixed defines mentioned asymptotically ment derivation briefly briefly comparisons considerable rapid rapid rapid closer easier watkins begin summation argument argument argument fourth reflect transient simulate simulate quantitative red remove variant rewards rewards maximizes kinds conclude expectations returns jaakkola calls calls calls calls calls calls calls calls calls calls calls calls proofs proofs accomplished formally rithm arguments count grows proceed proceed proceed generality convenient proceeds viewpoint keeping obtaining operates observing fail implications implications implications implications intuitively intuitively phrase date repeat governed corre studying surprising heart uni captured entries multiplied multiplied advance discounted surprisingly surprisingly surprisingly clean late kearns kearns kearns kearns verification draw draw park park implicitly material executed executed executed assigns counts outlined multiplying multiply indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect indirect outline basically discount ber experiences recurrence recurrence simulating guess reflected alter argue argue favor distri intuition num execute execute labs careful emphasize sketch minor induces differing mini infinitely behaves answers mix walk walk bution demonstrating rarely reinforce argmax sponding handling handling builds drawing visit executing executing executing detects fixing fixing statements iterate subtle deleting ular notions avenue enhancing tran mal offered visits visits visits hypothetical versity unlimited ninth satinder ages complexities seemingly standing lemmas succession idealized idealized idealized ration brevity brevity namic oracle highlights dictated partic debate guiding meets meets technically pol walks payoffs closeness pute gathering gathering armed gather permitting mahadevan explo suffered intuitions interests florham clever informally nlog sitions subroutine forever icy enjoy enjoy enjoy contractions inforcement elim choos enjoys guar formalization basics odic 
#@Kearns_M,Singh_S,
#t12
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model data figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set algorithm number number number number number number number number number number number number number system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results information information information information problem problem models based based based based space space space space space space space space space space space linear case case case case case case case case case case case case case case case case order shown shown shown shown shown shown systems systems systems values values values values values values values values values method method method method method approach point point single single single single single single control control control control control large large large local local local local local local local local local local analysis optimal optimal optimal optimal optimal optimal optimal shows shows shows paper paper paper paper paper small small small small small small work work work task methods methods methods methods methods methods methods methods methods methods methods step step step step step step step step current current current current current current current current current problems high memory similar similar show show show section line line line line line line line line line line line rule general real real real real real real real real real real real real real states states states states states states states states states states states states states states states states states states states states states states states states states states theory result solution research research independent log log log log log log log log log log sequence sequence constant constant constant distance distance distance left direction direction direction map map map map machine machine press press abstract find find computational properties properties references important introduction action action action action action action action action action action action action action action action action behavior behavior behavior behavior behavior dynamic dynamic dynamic parallel search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search change change assume assume lower lower measure part part part part part previous previous bound bound bound bound bound bound good good good good long tree techniques techniques length length length length length length length length length correct observed forward forward finite finite resulting classes classes tasks tasks tasks tasks tasks tasks total total total simulation sum performed times elements reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor potential potential potential global study study study study study knowledge knowledge knowledge artificial artificial artificial artificial artificial artificial artificial artificial artificial compared compared location location location location goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal mit update update update update update proceedings proceedings proceedings proceedings proceedings proceedings proceedings proceedings proceedings institute consists consists consists code joint joint difficult graph graph graph graph graph graph graph graph maps maps computing domain environment environment environment environment environment environment environment environment directly additional additional conference conference conference conference conference conference conference determine efficient upper upper upper upper approximate approximate world speed increase give con robot robot robot robot robot robot robot robot robot robot robot robot bounds bounds path path path path path path provided provided finally finally finally selected describe arbitrary denote fast assumption assumption complete actions actions actions actions actions actions actions actions actions amount amount amount nearest generate theoretical theoretical require face face face end end end instance future future future makes including including including smaller smaller unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown unknown technology programming programming programming interesting interesting edge edge edge edge edge edge edge edge edge edge edge call direct international international international international depth depth depth depth early polynomial minimize minimize minimize minimize run denotes denotes denotes denotes improve directions directions directions property element element apply apply strategy identical relevant interest interest previously solve solve correspond correspond correspond studies locations modified modified grid bounded expression expression lead lead studied studied locally deterministic starting minimal minimal minimal minimal minimal minimal minimal minimal minimal minimal assumptions assumptions reduce conclusions editors editors central performs performs faster practice learns solid proportional intelligence intelligence intelligence intelligence intelligence intelligence intelligence intelligence variety start start start start min min min decrease decrease program appears construct edges edges edges describes explicitly linearly linearly applying quality agent agent agent agent agent implies cycles national national solved variation open updated showed centered centered understanding completely similarly updates updates reasonable barto barto barto barto spaces spaces reduces iterative initially initially initially initially initially distances distances distances distances sufficiently sufficiently sufficiently sufficiently foundation expect exploration exploration exploration exploration exploration exploration exploration exploration exploration exploration priori inter prove uncertainty uncertainty uncertainty uncertainty uncertainty domains holds holds successfully simplicity planning planning planning planning planning planning planning planning planning planning planning planning planning planning planning sensor maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal maximal paths paths successful identify identify efficiently situation online fine reached reached traditional notice graphs graphs graphs graphs graphs heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic heuristic success moore moore moore moore return return notation vary realistic realistic backward minimizes minimizes board reach moves moves moves subsequent neighboring acknowledgments situations explore singh singh singh singh investigate exhibit exhibit put environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments limitations incremental workshop workshop act closest closest closest closest closest closest closest necessarily integer integer opposite versions precise precise observe observe switching generates arbitrarily attempts stop asynchronous asynchronous trivial sensors navigation improves capabilities starts implementing operators worst worst worst worst worst worst worst worst worst worst desirable immediately researchers researchers fourth improvements pseudo leave atkeson atkeson atkeson compares execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution execution exhibits mod branch branch branch branch reaches reaches reaches reaches popular popular plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan plan returns returns globally college optimality formally guarantee branches branches branches branches branches branches branches branches branches mobile mobile printed grows grows robotics murphy contract guide planar planar planar planar selects exploring exploring exploring exploring repeat connect decide overview topological vertices vertices vertices vertices vertices vertices vertices lengths searching searching chooses advance surprisingly ahead shortest shortest shortest shortest repeatedly repeatedly kearns vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex vertex ends ends extends broken summarize integers switches executed executed executed executed assigns thrun thrun thrun solves solves super ram ties uniquely suboptimal arg stem stem stem stem stem stem stem stem stem tight tight visited visited visited visited rectangular robots maintained execute execute execute execute confirmed scope topic deleted constructs associates associates alternatives attached sweeping sta behave behave bradtke hofmann aaai aaai aaai suggestions suggestions advantageous resolve prefer agents prioritized blum russell russell russell stay visit station ning episodes believed believed fox longest longest schmidt positioning semantics successor successor successor successor successor statements discovers progresses neigh lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead lookahead observes tighter undirected undirected undirected checks terminate plans traversed traversed traversed visits excluding simmons simmons simmons decides iterates ixl executes executes executes executes lose prevented unrealistic charging gps interrupted interrupted interrupted rrt collaboration grained koenig koenig koenig koenig koenig koenig koenig koenig koenig koenig koenig koenig koenig koenig koenig koenig koenig restricts davies davies davies bor visiting visiting composing actuator lly situated restarted restarted dasgupta dasgupta dasgupta print print print georgia gatech succeeds mina barely gather sacrificing tains travels traverse traverse traverses traverses traverses traverses greedily batteries keams keams ofx ofx ttm etal attach reviewers nonempty interleaving informed interleave interleave igure telligence mislead interleaves 
#@Koenig_S,
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#*learning learning learning learning learning learning learning learning learning model function function function function figure figure figure figure figure figure figure figure figure time time time set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number system system system system system state state state state state state state state state state state state state state state state results results results results results results information information problem problem problem problem problem problem performance performance performance performance performance based space space space space space space space space order shown shown shown shown shown shown systems values values values values probability probability probability functions method method method control rate rate rate rate rate test class class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form algorithms algorithms paper paper size size work work work work work methods methods methods methods methods methods methods methods step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step step process level level current current current current problems problems problems problems problems problems problems problems problems problems problems problems random memory show show show fixed line parameter parameter real real average average average average states states states states states states states states states term result result university university university solution research research research research research defined found found found found found found initial constant standard computer computer computer science science science presented map machine machine machine sets press learn learn abstract applied applied applied find find find find find find find find find find find find find find find find computational references stochastic stochastic stochastic stochastic due due important adaptive decision decision decision decision decision decision decision decision decision introduction action action action action action action action action action action action action action action action action behavior effect effect effect effect effect effect effect dynamic complexity lower required good good good good expected expected markov markov markov markov markov markov markov markov techniques length observed scale finite finite finite tasks total total simulation performed called called called called reinforcement reinforcement factor feedback policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge artificial artificial specific provide objects goal goal goal goal goal goal goal equal mit steps steps steps steps steps steps steps steps fields selection morgan morgan morgan proceedings proceedings proceedings proceedings proceedings report report department department department joint delay addition addition cambridge equivalent equivalent equivalent equivalent experiment environment environment environment environment environment environment environment environment environment additional transition san san conference conference conference conference conference efficient efficient world world world world world world world world world world world pages pages give produce developed robot robot provided processes processes processes processes processes processes processes processes selected selected simply achieved discussion technical technical describe describe tested tested limited limited complete actions actions actions actions actions actions actions actions actions finding finding finding finding finding finding finding short short common theoretical theoretical require main face ability ability ability ability future future noisy fit fit kaufmann kaufmann pairs pairs programming significantly trials empirical empirical empirical empirical empirical making making international international international international choose architectures recent recent recent recent recent pair pair pair pair practical practical include identical engineering interest observations observations observations observations observations observations observations observations observations observations observations observations observations solve rl rl modified modified observation observation observation observation observation observation observation observation observation observation observation observation observation grid grid grid grid grid grid lead scaling suggests trial wide deterministic deterministic deterministic deterministic deterministic pass critical greater conclusions reward reward reward reward reward reward reward sutton sutton sutton sutton mateo suggest intelligence intelligence variety start manner denoted denoted denoted solving solving solving factors transitions transitions transitions transitions transitions modeled linearly infinite unique integrated adding adding adding agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent john depending operations updates updates past partial spaces add exploration exploration exploration exploration maximize specifically domains partially partially partially partially partially partially partially partially partially partially planning reason straightforward sensor sensor selecting aspects capable literature literature literature efficiently efficiently receives success success contribution vary delayed observable observable observable observable observable observable observable observable observable observable reach reach reach received attempt policies policies policies policies policies policies policies policies policies policies policies policies policies policies approximating approximating decreasing extend explore remain create singh singh singh singh singh singh environments involving limitations office office office decisions decisions attributes trace trace trace trace trace trace trace trace trace trace trace trace necessarily greedy greedy initialized initialized brown brown great costs sensors sensors sensors sensors reasons reasons widely precisely immediately ion incomplete preceding empirically empirically empirically conducted autonomous formulated formulated sharp variant variant variant rewards rewards rewards http operate traces traces traces traces traces traces traces traces traces traces traces traces traces traces traces traces traces converged yielding yielding yielding yielding www modify temporally animals mobile reaching reaching kaufman held pomdp pomdp pomdp pomdp pomdp pomdp pomdp observing surprising colorado colorado colorado francisco discounted horizon designing papers assigns treat pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated truncated unable annals discount smoothly acceptable descriptions visited acting robots boulder eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility eligibility memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless littman littman littman littman littman littman littman littman littman littman littman argmax survey algorithmic satisfactory attributed agents agents agents spacing finer russell russell russell russell russell affecting executing sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa sarsa html decaying kaelbling kaelbling kaelbling cutoff occluded episode iterate landmark repeating parr parr parr parr parr parr inability madison distinctions cent sondik sondik explores seventh providence providence imperfect designer designer twelfth eli eli cassandra cassandra cassandra cassandra cassandra reacting xls distributes unsatisfactory nction automate dozen fibre chrisman chrisman chrisman surroundings confronted episodic avenues baveja reinitialized 
#@Loch_J,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time time time time time time time time time time time set set set set set set set training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number system state state state state state state results results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance space weights linear linear linear linear case case case case case vector vector order shown values values probability parameters weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions unit method method method method method method method approach approach approach approach approach approach approach approach pattern point point point single single single large large local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local local analysis matrix matrix matrix optimal optimal optimal optimal optimal inputs shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple small size size size size size size size size size size size size size size size size size feature feature work work methods step step points points features features features features features features process process process process current current current current current structure structure structure structure structure problems problems problems problems random random random random random random random random random similar representation fixed fixed fixed fixed line line line line line line vectors vectors parameter real approximation average average average states obtained obtained term note note note result result result result result university university solution solution solution solution solution solution research research research research research independent independent independent independent independent defined defined found found found found found target initial initial constant table table table table table table table table table table estimate estimate standard standard computer computer distance distance distance distance science science prediction presented presented present present phase phase phase phase phase phase phase phase phase phase phase low low sets range range learn learn learn learn learn position components basis sample sample abstract applied applied applied references due decision decision decision context introduction action action effect effect dynamic generated generated generated cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search tion assume measure representations learned learned learned learned learned learned learned chosen bound bound required multiple multiple multiple multiple multiple good expected markov make make length length length length length length finite minimum resulting resulting ing ing regression regression multi sum performed called called times times times times times times times times reinforcement reinforcement reinforcement reinforcement optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization global study study study policy original original original artificial relative relative relative specific represented application application application desired provide define compute location determined experimental goal goal related gain equal power approaches approaches approaches approaches steps accuracy comparison morgan proceedings proceedings words department version technique technique consists joint difficult final final final bias bias scheme addition addition ai considered considered additional additional additional solutions solutions solutions solutions solutions solutions solutions transition transition trajectory san stage stage stage stage stage stage stage stage stage conference capacity determine requires significant approximate approximate world give give give give produce produce randomly randomly randomly randomly randomly developed types finally processes selected selected selected discussion increases describe describe arbitrary denote limited corresponds complete complete complete actions actions amount common effective generate generate generate theoretical journal journal square square end instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance future easily including including including fit kaufmann objective probabilistic coefficients coefficients programming significantly significantly ratio consistent consistent consistent consistent uniform principle leads details call pre direct international normalized normalized run run description improved improve improve improve improve advantage takes element reported practical apply moving subject relevant engineering highly varying approximately tions yields correspond studies rl rl rl rl rl rl rl rl rl evaluation evaluation evaluation locations symmetric symmetric modified modified bounded improvement improvement improvement improvement improvement improvement improvement improvement improvement improvement entire grant constructed studied extended matrices locally locally starting starting starting minimal row row trajectories trajectories trajectories trajectories trajectories reward reward reward sutton sutton sutton sutton faster asymptotic learns constrained characteristics intelligence start start plane decrease averaged averaged force base explicit pro van van van edges edges edges produces produces primary sequential sequential generating laboratory distinct distinct category coordinates easy applying applying predictive quality quality quality quality select select decreases yield yield viewed influence variation evaluate operations operations operations operations controlled showed sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes allowed allowed key barto barto barto barto slow normalization normalization sec sec sec sec sec combining neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood penalty generation distances construction euclidean euclidean thesis formulation instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances batch extension extension discussions aspects aspects aspects aspects identified importance importance modification divided divided divided included literature reached receives summary traditional compact notice repeated repeated procedures allowing moore moore moore moore moore moore moore showing interested issue return return running running running running running running running running running built notation list list sampled reach received moves subsequent neighboring neighboring routing routing extend employed employed involving mdp mdp mdp helpful investigated applicable applicable terminal terminal terminal terminal terminal terminal terminal terminal terminal terminal office maximizing complicated complicated func understand phases math coefficient coefficient closest possibly integer predicts predicts extremely illustrate created created baseline regime regime seconds seconds averages averages optimum optimum massachusetts asymptotically percentage site site site great rows developing improves improves expensive expensive starts starts comparisons comparisons inside satisfied sites sites producing strictly style scientific scientific acknowledgement involve describing opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt opt res lowest mellon raw improvements percent percent carnegie applies pure led conducted slower slower variant compares rewards rewards exhibits richard neuro returns returns focused eventually eventually calls calls yielding globally globally representative representative representative representative secondary secondary secondary feasible feasible feasible feasible feasible feasible extensive extensive restrict pick pick pick pick pick driving impossible outcome outcome systematic air difficulties adjusting held held operates effectiveness guide guide guide guide enhanced enhanced enhanced enhanced enhanced enhanced combinatorial combinatorial combinatorial combinatorial combinatorial combinatorial selects selects motivation excellent falls combines combines combines zhang zhang zhang zhang zhang zhang encountered enhance enhance enhance enhance enhance enhance enhance scheduling scheduling entries entries entries francisco proximity proximity proximity park park relies tsitsiklis tsitsiklis dietterich dietterich dietterich dietterich dietterich dietterich valuable approximator approximator approximator approximator approximator robert counts counts bertsekas bertsekas andrew multiply drop drop drop drop drop listed shorter shorter job alternating legal exception tradeoff tradeoff amherst reports reports examining assess mhz shannon continues guidance searches carefully afosr picked considers guided breaks sized inversely nasa ation normalizing worked helps tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour tour reversal reversal reversal fortunately opti traveling identifies european european neighborhoods neighborhoods tsp tsp tsp termination dropped returned episodes episodes boyan boyan boyan boyan boyan boyan boyan boyan boyan boyan boyan boyan boyan assessment normalize enhances destination salesman falling remained terminates tra shop episode episode predetermined hood hood lisp searched infeasible mization examines inserting avenue enhancing enhancing enhancing saved possesses visits unlimited belmont hillclimbing exceeded exceeded solu stabilized absorbing absorbing initializing mac necessity driver tours tours tours tours tours tours tours eval endpoints stein stein stein stein routed mission asserts ditional subsequence subsequence unmodified dropping guiding guiding pected athena quotient customers customer customer alternation alternation negated accomplishes chart ported vious uation stats sacrifice obtainable inclusive absorption ste reporting fourteenth decent justin precedence florham afb restarting conduct conduct truncate dial dial dial dial dial dial interchange undiscounted undiscounted bolling exhausted stances stances failing midway impoverished 
#@Barto_A,Moll_R,Perkins_T,Sutton_R,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model neural neural data data data function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time set set set algorithm algorithm algorithm algorithm number number system error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state results information problem problem problem problem problem problem problem models based based space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case order order order order order systems systems values values values values values values values values values values values values values functions functions functions functions functions functions functions functions functions functions functions functions functions functions method method method method method method approach point point point point point point point processing control control control control control control control control control control control control control control control local rate analysis class class class matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal algorithms algorithms algorithms simple examples small work work work work methods methods methods step points points points points points points points points points points points points process process process process process process current current problems problems high equation equation equation equation equation equation equation equation equation equation equation equation section section section section section section section section fixed line rule rule rule rule rule general general general general approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states states gradient obtained obtained dimensional result result result result result result result result result result result university variables computation solution solution research defined defined defined defined defined defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial constant estimate machine machine sets sets nonlinear continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract applied applied back find computational computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density properties references stochastic stochastic positive positive important important decision introduction complex dynamic dynamic tion difference difference variable variable assume assume assume assume previous previous previous previous previous theorem theorem theorem theorem theorem theorem theorem required required good conditions conditions conditions distributed equations markov markov make fact fact finite finite finite finite finite finite regression computed computed computed respect multi multi multi multi multi sum called called called called means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor optimization dimension applications applications obtain obtain artificial true provide define define define define equal comparison update support institute advances joint scheme scheme scheme scheme scheme scheme scheme scheme scheme ai framework additional solutions solutions limit trajectory trajectory conference conference conference efficient upper choice choice choice approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate basic con con con con condition derived weighted bounds area area processes processes iteration iteration iteration depends constraint simply normal describe describe fast stable proof proof proof nearest nearest theoretical require main journal hypothesis future future easily including needed combination combination dynamical functional coefficients coefficients fully programming programming increasing consistent consistent principle leads iterations international description resolution resolution resolution resolution resolution resolution resolution resolution resolution advantage property property property property element sense sense sense subset subset sufficient sufficient sufficient volume converge converge converge differential differential rl rl rl rl rl rl rl rl rl rl rl rl definition definition observation grid bounded improvement exists exists feed locally deterministic deterministic white occurs boundary boundary boundary boundary boundary boundary starting trajectories neighbor neighbor depend tangent accurate numerical exponential asymptotic weak weak weak weak weak strong strong strong intelligence exist introduce suppose describes describes coordinates coordinates coordinates coordinates unique unique unique springer springer focus review depending solved open controlled updated updated updated updated approximations completely converges constants partial performing spaces spaces convex sec combining boundaries boundaries interpolation interpolation interpolation interpolation interpolation priori coordinate usa inter plotted prove prove prove prove uncertainty black black holds holds holds holds uniformly uniformly maximal build build schemes composed compact compact compact compact compact compact verlag verlag moore moore moore moore moore running hold hold satisfy satisfy notation bar bar vary write hypotheses satisfies satisfies acknowledgments law updating issues issues mdp mdp behaviour giving terminal proper proper proper math perfect ensure formal defines integrate ment piecewise piecewise piecewise piecewise defining defining inside inside inside inside inside inside sections strictly strictly mathematics ion mellon geometric prop carnegie applies cmu cmu consistency tional atkeson dots requirement pittsburgh proven lim lim lim differentiable multidimensional cumulative bellman grey grey grey robotics establish mail satisfying stated belong belong introduces vertices approximators diameter april discounted discounted discounted discounted contraction contraction contraction contraction contraction contraction extends designing omohundro inf inf convergent convergent convergent convergent andrew leaving discount discount continuity continuity iff permits permits rough discretization confusion siam simplex simplex simplex simplex simplex simplex simplex simplex simplex simplex gordon permit challenge coming remark remark remark remark covers reinforce resp resp survey interior interior interior lation discontinuous discontinuous discontinuous discretized vis european hamilton hamilton hull schaal triangulation triangulation trol convention proves proves rectangles rectangles scott iterate recalled ira sponsored des deduce deduce deduce deduce deduce deduce deduce deduce deduce deduce deduce proving hjb hjb hjb hjb hjb tinuous tinuous stays iix regularly mere del del jacobi jacobi interna kushner kushner intend weakened realizes ams davies interpolator interpolator interpolator interpolator interpolator outward proximate ors puting gather ifs arrange exit supremum interpo erty discretize rll rll ffl rtl 
#@Moore_A,Munos_R,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural data data data data data data function function function function function function function function function figure figure figure figure figure figure time time time time time time time time time time set set set set set training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number state state state state state state state state state state state state state state state results results results results results information problem problem problem problem problem performance performance performance performance performance performance performance performance space space space space space space space space linear linear case case case case case case case case case case case case case case case case case case vector order order systems systems values values values values values values values values values probability probability probability probability probability probability functions functions functions functions functions distribution distribution method approach approach approach approach approach point single processing processing control control control control control control control control control control control control control large analysis analysis class optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows algorithms algorithms algorithms small small work task task task fig fig fig step step step step step points field field field process process current current current problems problems problems problems problems problems problems random high high memory similar representation show show equation equation equation equation equation equation equation equation equation equation section section section section section section fixed rule general parameter parameter parameter real real approximation average average average average states states states states states states states states states states states states theory note experiments result computation solution solution solution solution solution solution defined sequence table terms connections prediction left left left left left present phase low low temporal machine machine sets range press press learn learn position nonlinear continuous abstract convergence convergence convergence convergence properties properties properties properties references due due due due positive positive positive positive positive procedure procedure procedure important decision decision decision decision decision decision decision decision action action action action action hand hand hand hand hand behavior behavior behavior behavior dynamic generated generated generated variance variance cost cost cost cost change change difference difference difference difference complexity variable assume lower lower prior representations representations chosen higher higher higher higher higher higher theorem theorem theorem cases cases type conditions expected expected expected expected expected expected expected expected expected expected expected expected expected equations equations markov markov markov markov markov markov markov markov make fact techniques techniques proposed proposed probabilities probabilities probabilities finite finite minimum resulting resulting resulting tasks simulation respect respect respect respect respect respect respect sum sum sum eq elements mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor potential made made applications applications applications applications applications applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge negative negative negative negative original artificial artificial artificial artificial relative specific samples compared application application application desired series define define define compute compute rates proc related constraints distributions distributions distributions equal approaches approaches approaches mit mit steps steps comparison comparison contrast contrast contrast update dependent morgan loss consists consists advances exp bias scheme ai framework cambridge cambridge computing environment additional view solutions solutions estimates transition transition transition transition limit conference conference determine determine efficient requires requires significant significant significant approximate free world speed speed increase increase give weighted randomly criterion criterion criterion criterion criterion criterion criterion criterion criterion processes iteration iteration iteration increases increases arbitrary tested actions actions actions actions actions amount amount amount amount short assumed theoretical require main main instance future future future easily including kaufmann objective objective probabilistic smaller account account account fully technology technology programming interesting significantly significantly increasing increasing increasing increasing trials empirical leads leads leads max max max max max max international international idea combined choose choose sources description denotes denotes denotes advantage property property property pair pair robust takes element practical apply apply apply strategy strategy sense sense sense interest sufficient tions solve yields achieve achieve rl modified modified modified modified modified generalized bounded risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive sensitive exists lead extended trial alternative deterministic deterministic occurs demonstrate conclusion starting assumptions trajectories trajectories operator operator operator reward reward reward reward reward reward reward reward reward reward differences measures clear exponential practice practice propose propose start exist min min averaged introduce question denoted denoted areas explicit van van construct sequential sequential generating plot plot plot plot transitions transitions transitions tuned mathematical changing changing simultaneously infinite infinite dimensionality unique unique unique consisting events agent implies john family focus focus formation depending influence lemma lemma lemma detailed detailed transform transform transform evaluated similarly converges converges converges updates past sign epochs classical classical reduces event purpose valid avoid existing figures determines plotted prove maximize planning straightforward suitable suitable suitable suitable differ computationally divided situation essentially traditional refer conf graphs interested stopping stopping dis dis return return return return return return return return return return strategies strategies strategies hold satisfy notation quantity quantity usual usual leading principles policies policies policies policies policies policies policies policies policies policies decreasing remain parametric wiley essential limitations mdp mdp mdp mdp mdp mdp mdp fewer mappings int decisions analogous analogous neu act naturally traffic changed obvious obvious obvious greedy precise generates extent utility utility utility utility utility averages indicating inequality theoretic costs costs costs costs costs costs costs costs crucial publishers analyzed worse handle handle tive closer day constructing constructing worst worst worst worst worst worst worst worst worst worst worst worst worst worst commonly probable probable probable potentially scientific requiring fourth reflects considerably pure parameterized simulate introducing formulated formulated continuously compares rewards rewards rewards price price price price price price price price price price price price price price price price limiting maximizes popular popular popular incorporating germany germany inherent sophisticated comments neuro returns returns returns returns returns returns returns returns lim lim extreme trade trade naive person proofs proofs optimality optimality optimality optimality optimality optimality optimality optimality optimality optimality optimality modify restriction restrict appropriately recover acts acts acts controlling outcome outcome outcome outcome outcome robotics proceed allocation consideration stronger stronger stronger satisfying siemens siemens siemens siemens check reasoning implications modifications selects published financial falls sion sion encountered decide decide bad bad realization realization consequences consequences den chooses bases exposure discounted discounted discounted discounted discounted reader reader contraction contraction augmented roy roy horizon horizon sons tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis inf alternatively avoiding avoiding avoiding avoiding avoiding avoiding avoiding avoiding avoiding influences market market market market market market market market mdps mdps mdps trading accumulated bertsekas bertsekas bertsekas speaking speaking drop drop drop numerous minus accept discount markovian markovian formulate formulate formulate stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock stock additionally arg experiences experiences experiences avoided avoids intuition pij pij pij interact management mathematically lookup proach proach pos meta outcomes happen supports meet mini behaves littman littman tail tail portfolio portfolio fortunately argmax argmax preserves corporate corporate influenced losing focuses interpreting inequalities inequalities loosely loosely neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier neuneier integrates rare rare exclusively capital capital capital capital capital deals scenarios economic maxi losses losses losses losses stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks stocks asset neutral neutral restrictive profit ings trend trend transaction transaction transaction investment investment investment investment investment investment investment investment investment investment investment investment investment investment successor successor counted promise ensuring penalizes maxq maxq maxq maxq recovering stepsize stepsize stepsize manager markets simulates simulates examines couple enhancing mal bonds prices prices prices prices simmons simmons investor investor investor investor evaluates favorable seeking seeking seeking seeking seeking ative concise executes executes historical subclass buy brevity cap attitude attitude ralph ralph formulating quantifies tributions saving koenig koenig quantifying sudden itive deci deci athena assets assets living invest invest rock tiles vances deviate neg optimistic quan transi remedy contracting opportunities attains fulfills skip oliver analyzes distributes acta mchp mchp invested invested invested invested money money finance tral quantile quantile illus pessimistic pessimistic cash cash cash cash cash cash creasing pays tabulated cautious vie sulting tificial componentwise introductory lth import jen nega earn uncontrollable disastrous stor imperfections maz feeling asymmetrically 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#*network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time set networks networks networks algorithm output output output output output output output output output number number number number number number number number number system system system system system system system system error error error error error error error error error error error error error error error error error error error error error error error error error error results results problem problem problem problem models models models models based based space space space space weights linear linear layer layer layer layer case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order order order order order order shown systems systems values probability noise noise noise noise functions functions neurons neurons neurons neurons distribution method point point point point point control control control control control control control control control control control control control control control control control control large large analysis analysis class matrix matrix matrix matrix matrix shows shows shows signal signal signal signal signal signal signal signal signal signal simple visual visual paper paper paper paper paper small small small small small small task process process structure structure structure structure random random equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation equation section section section section rule rule rule rule general real obtained obtained obtained obtained obtained obtained term term term experiments result result result result result result result university solution solution research defined defined defined defined defined defined defined dynamics initial initial estimate standard terms terms science direction direction direction direction object object motion range range range learn learn learn position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position position components sample abstract back back back back find find density references component component ieee positive positive positive positive positive important important propagation propagation propagation propagation introduction action complex complex complex hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand hand generated generated tion change change change change change change change change change change change change change change change complexity assume lower signals prior higher higher higher center center cases good long long expected expected expected expected equations equations proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed proposed correlation correct correct observed observed observed forward forward forward forward forward forward forward forward forward forward forward forward simulations ing simulation simulation simulation human human human human human human human human human human human sum performed performed performed performed performed performed called times times feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback orientation study knowledge obtain artificial specific compared desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired desired provide determined experimental experimental goal motor motor motor discrete discrete update descent descent modeling modeling modeling report technique joint joint joint joint joint joint joint joint joint joint final layers layers delay maps considered considered considered considered directly view efficient upper requires requires requires requires requires requires approximate approximate approximate free speed speed vision increase give con con condition velocity velocity velocity controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller controller lines product product product iteration sampling biological biological covariance technical increases transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse inverse corresponds complete assumed assumed assumed eds square square square square square square square square end hypothesis unknown coefficients jordan jordan jordan trials trials trials trials trials trials trials uniform operation operation numbers iterations pre pre direct direct supervised minimize improved movement moving hierarchical teacher approximately solve trans background symmetric modified modified modified interval organization arm arm arm arm arm suggests trial deviation feed feed feed feed feed feed hybrid hybrid hybrid conclusion trajectories operator operator accurate numerical numerical numerical propose mechanisms characteristics characteristics variety plane relationship relationship configuration configuration configuration configuration configuration index index factors modeled modeled coordinates coordinates coordinates coordinates angle angle angle angle angle angle angle angle angle angle consisting minimization decreases decreases expressed expressed expressed expressed expressed expressed expressed expressed expressed expressed expressed expressed expressed expressed expressed review squares learner learner learner learner evaluate controlled updated approximated approximated approximated completely diagram calculation calculation calculation calculation slow penalty penalty tracking tracking tracking tracking tracking tracking norm norm norm norm norm norm norm norm norm norm degrees precision existing existing includes includes coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate weighting illustrated illustrated illustrated holds holds partially structural major major major capable capable suitable repeated neuroscience sin sin sin physiological satisfy involved consisted illustrates satisfies satisfies satisfies presents employed employed simpler optimized hessian existence scalar ideal root proper plausible noted precise nervous switching switching switching explain explain established established established established advanced cos cos cos inequality directed derivation straight sys sys satisfied circle circle definite definite definite incomplete researchers reflects flexible conducted conducted conducted capability biologically psychological calculating fall phone progress lab japan japan summing tem tem mail simplify city stated kawato kawato kawato kawato transforms observing child utilized mance perfor mel eng steepest steepest mechanical limitation rms rms rms rms kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics kinematics axe quasi ical acceleration acceleration jacobian stroke topic finger finger electronics suffer elsevier status excess conceptual dom calculates compensation proposes coincide disturbance disturbance disturbance disturbance tokyo tokyo coins fin sis feasibility deter ensuring suzuki limb dof dof amsterdam drawbacks stabilizing converts putational plausibility touch sition possesses thumb thumb thumb mined ishii fulfill tri accelerate cyber pilot realizing infant fax infants infants grasp imal fined surgery crease deriva solver solver solver solver solver solver solver solver solver troller biolog voluntary morasso verse leaning dlo dlo obt tlo memorizing influential operand suffering ned furukawa redun lel lel oio tsukuba netics matics axa axa axa ibaraki culated kine bunkyo dant questioned 
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural input input function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set algorithm algorithm output output output number number number number number number number number number number number system system system error error error error state state state state state state state state state state state state state state state state state state state results results results results results results information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem models hidden hidden performance based space space space space weights weights weights weights weights layer case case shown systems values values values values values values values values values values values values values values values values values values values values values values parameters parameters weight weight neurons neurons neurons neurons method method method method method method method method method method method method approach approach pattern pattern point point point point point control control large large large large large large large large local test optimal optimal optimal form form shows shows shows shows shows shows shows algorithms paper paper paper examples small small size work work task task task task task task task task task task task methods fig step step step step step step step step step points points points process process process problems problems problems problems problems problems problems problems random high memory show show fixed line line line line line line generalization generalization parameter parameter parameter parameter parameter parameter parameter real real average average average average average average average average states states states states states states states states states states note dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university university university university university research found found found sequence sequence sequence sequence initial table standard computer terms terms science left left direction presented presented present temporal machine machine machine machine machine range press press press press press press learn learn learn learn learn learn position position position position basis abstract abstract abstract applied applied back find references decision introduction introduction action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action action hand hand dynamic tion tion tion difference measure learned learned learned learned learned chosen higher part previous multiple good conditions expected expected equations equations markov markov markov fact forward scale simulations ing ing ing ing tasks tasks tasks tasks tasks tasks total total total total multi performed performed times times times mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor dimension dimension dimension dimension made made policy policy policy knowledge knowledge original artificial artificial artificial artificial artificial relative compared application define perform perform perform perform perform perform goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal equal mit mit mit mit mit steps steps steps larger update selection proceedings proceedings report report report report words department department department consists consists consists represents connectionist difficult layers addition considered considered cambridge cambridge computing curve bit conference conference conference efficient upper full full full full full full requires choice choice choice choice world world world world world world world world world world world world world speed basic coding randomly randomly developed robot criterion velocity velocity velocity path path finally processes selected selected depends discussion discussion technical technical technical technical tested tested stable actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions journal square square square instance makes makes development pairs needed reduced reduced reduced special trials trials trials trials trials trials empirical empirical representing making international international international early idea idea idea choose choose choose choose run description improved improve recent exact exact pair takes apply strategy hierarchical relevant engineering engineering dimensions dimensions dimensions dimensions dimensions dimensions conventional conventional approximately works works works tions solve solve solve correspond studies converge sparse positions grid grid grid grid grid grid grid grid grid grid grid parts lead lead scaling trial trial trial trial move move move loop loop loop white boundary boundary boundary runs runs runs runs runs runs conclusion conclusion starting starting starting starting place row reward reward reward reward reward reward reward clear clear sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton faster faster faster weak learns suggest reduction intelligence intelligence intelligence intelligence intelligence start start start start start start selective decrease relationship program areas areas areas perception solving solving vertical implement angle angle angle scales consisting adding agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent national stages influence open open controlled centered forms earlier reasonable reasonable barto barto barto barto barto barto barto barto barto slow slow performing epochs epochs epochs epochs reduces add closed construction david expect figures thesis thesis thesis combinations uncertainty discuss partially planning planning divided divided successful build receives receives receives receives receives road refer refer graphs prob prob prob heuristic moore moore moore content usual usual usual nips nips nips nips nips observable reach reach automatically moves approximating deal situations bars bars explore carried singh singh singh singh singh singh singh singh singh singh singh singh singh singh singh singh singh singh singh singh mdp mass helpful history history mappings mappings mappings terminal possibility combine func momentum hill hill hill hill act act coarse integer generalisation man opposite adjusted greedy ith ith switching epoch epoch epoch epoch consist consist mixed phd phd phd seconds averages averages averages massachusetts massachusetts great ment track track track track track track track track track track variances unstable slope slope handle reasons reasons considerable drive constructing operators operators operators located located mation controls gradually lowest author researchers varies varies people greatly prop tional car car car car car car car car car car car car car cohen marked calculating calculating measuring reaches maximizes plan richard semi comments traces traces traces traces lot lot notes temporally temporally angular angular angular angular pick pick pick pick driving acts concerned discovery reaching reaching reaching chance stronger stronger logarithmic replacing replacing stated primitive primitive balance balance balance roles definitions intuitively guide guide guide optimally carry continue continue infor cmac decide sides searching originally chooses chooses advance treatment insight reader matter belonging route mdps mdps mdps lem lem andrew boxes thrun leaming torque centre tendency tendency acceleration visited visited acting exam met books wise guided guided interactive eligibility eligibility anal hansen hansen attached maintains rochester bradtke bradtke things corrections mix suggestions suggestions lems tour reinforce reinforce reinforce decided tial agents agents agents essen usefulness engine boyan boyan boyan normalize fox sarsa sarsa sarsa sarsa sarsa decaying contrary coins denmark kaelbling fin niranjan niranjan niranjan deter bradford enter halves shaping inst backwards dean ming mountain mountain ysis elegant precup precup precup precup precup precup precup precup precup precup precup macro macro macro macro macro macro macro macro macro macro macro macro macro macro macro macro macro macro macro macro minute sition sition darker remember displaced cued suggestion scratch ously aware emphasizes wishes steep acknowledgment gullapalli gullapalli govern accelerate accelerate copenhagen copenhagen imperfect bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle bicycle safely mccallum mccallum cri bohr reachable gravity stance looo cycling specially rewarded rewarded race race race race race race race cutting umass blegdamsvej rand lution unbalanced recommended accelerating forget descrip conven infeng fifteenth fourteenth 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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure time time time time time time time time time set set networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number number system system system system system system system system system system system system system error state state state state state state state state state state state state state state state state results results units units units units units units units units units units units information information information information models models hidden based based based based based based based based based based based space linear linear vector vector vector order order order order shown systems systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability parameters parameters parameters functions unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method single single single single single single single processing processing processing processing control control control control control control control control control control control control control control control control local local local local local matrix matrix matrix optimal optimal optimal optimal shows shows signal signal signal algorithms algorithms gaussian gaussian gaussian gaussian paper paper paper small small small small work task task task task task task task task task task task methods methods methods step step step step features features process process process process current current current current current current current current current trained trained trained trained trained trained trained trained trained trained problems problems problems problems high similar architecture architecture architecture show show equation equation equation section section section fixed fixed fixed fixed line line line line line line line line line line line line line line line line line line line line parameter parameter approximation approximation approximation gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional threshold threshold computation solution research log log defined defined defined defined defined defined defined defined defined defined found sequence target target target initial initial constant constant estimate estimate science direction direction present present phase low machine machine maximum maximum press press press press press learn position position position position position position position position position position nonlinear nonlinear outputs continuous continuous continuous continuous abstract applied applied applied applied applied applied find likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic ieee adaptive decision introduction action action action action action action action action action action action action action complex hand hand estimation estimation statistical effect dynamic dynamic dynamic generated generated generated variable center center previous previous previous previous cases cases good good good good good good good expected equations equations markov make proposed proposed proposed proposed observed observed observed errors errors scale finite finite ing tasks human regression regression regression respect respect multi performed called called called times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor dimension global applications applications policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge em em em em em em em em em em em em em em em em em em em em em em obtain original original original represented represented series series determined experimental experimental posterior posterior posterior mit mit mit mit mit steps descent descent descent descent report institute version advances advances advances difficult exp exp bias scheme scheme scheme scheme ai equivalent experiment experiment experiment experiment experiment hinton trajectory trajectory stage stage upper increase increase condition condition weighted weighted weighted weighted weighted randomly randomly conditional conditional velocity velocity lines processes selected selected selected selected covariance technical increases increases denote denote fast fast limited limited complete finding assumed assumed assumed assumed journal end future easily objective needed account account dynamical dynamical jordan technology numbers numbers pre normalized normalized normalized bottom produced produced denotes denotes denotes pair apply apply introduced introduced introduced period period period period identical side calculated calculated calculated calculated achieve achieve rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl rl positions modified modified modified modified trial trial deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic white white white conclusion reward reward reward reward reward sutton sutton sutton sutton moody moody moody faster faster propose propose propose mechanisms demonstrated solid regularization introduce manner relation van produces index index linearly angle angle angle events events implies expectation review estimator estimator estimator estimator detailed controlled controlled controlled controlled controlled controlled updated updated showed showed centers approximated approximated approximated approximated partition constants constants earlier barto barto barto barto barto dashed spaces spaces spaces sec sec event event event purpose transactions figures batch prove successfully successfully suitable society differ successful efficiently identity prob prob anderson interpreted neuroscience return satisfy deal tesauro tesauro employed employed explore layered environments replaced game dotted proved coefficient man implementations adjusted singular seconds mentioned critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic crucial crucial adapted lin lin lin watkins laboratories probable actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor lowest cybernetics explained double double double double double double consistency transient conducted employ employ maximizes achieves logp ear japan japan angular angular approximates partitions royal darken darken darken proceeds intelligent height transforms ylx ylx performances interference iteratively regarded foundations discounted pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum pendulum subsequently subsequently subsequently balancing balancing balancing balancing dempster dempster dempster pen receiving avoiding rubin ent discount discount discount maximized torque torque torque torque pointed param backgammon manipulation werbos werbos inverted wise deleted laird atr atr atr article article article lems 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural function function function function figure figure figure figure time time time time time time time set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number state state state state state state state state state state state state state state state state state information information information information problem problem problem problem problem problem problem problem models models models models models hidden hidden performance based based based based based based based based based space space space space space space space case order order shown shown shown shown shown shown shown systems probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters distribution method approach approach approach approach approach approach approach approach approach point processing large large large large test test optimal optimal optimal optimal optimal optimal shows shows shows shows shows shows algorithms paper paper paper paper paper small size work methods methods methods methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig step process process process process process level level structure structure problems problems problems problems random random random random high memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar representation show show show show show show show equation equation section section section line rule parameter approximation average average average states states states states states states states states theory obtained obtained obtained obtained term term term term term term term term term term term term term term term note experiments university research research independent log log log log defined defined initial constant constant constant constant estimate estimate computer node node node direction map map map map map map map map map nodes nodes nodes machine machine machine machine machine learn basis basis continuous abstract find find find find find find find computational computational computational density density density density references stochastic stochastic stochastic stochastic procedure procedure procedure decision decision decision decision decision decision decision introduction action action action action action action action action action estimation estimation estimation estimation estimation statistical statistical dynamic dynamic change change complexity variable variable variable assume prior prior prior prior learned learned learned learned learned learned higher previous theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound required long long represent represent represent tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected markov markov markov markov markov markov fact fact techniques techniques length length length length probabilities observed observed scale finite finite finite ing ing performed eq eq eq eq eq eq eq eq called called times times mapping means means reinforcement reinforcement reinforcement reinforcement reinforcement made policy policy policy policy policy policy policy policy policy policy policy knowledge original original artificial represented represented represented true compared compared define define compute proc proc proc proc proc proc location location perform goal goal goal posterior posterior posterior posterior distributions gain approaches approaches approaches steps steps steps steps update implementation version internal advances represents difficult difficult addition equivalent equivalent experiment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment curve curve curve estimates estimates design transition transition limit limit limit stage conference conference conference conference conference efficient efficient efficient efficient upper upper requires statistics free free world world world world estimated increase con condition condition condition condition derived conditional conditional conditional entropy entropy path processes processes processes selected describe describe denote denote denote denote denote denote fast close assumption assumption complete complete actions actions actions actions actions predictions predictions predictions predictions proof proof finding finding short short short short short short short short short short short short short short effective require require require main main face end end hypothesis hypothesis hypothesis hypothesis hypothesis instance makes makes probabilistic probabilistic probabilistic jordan jordan programming programming programming ratio trials principle call call call call making international international international international depth attention run denotes denotes denotes denotes recent introduced identical identical trees trees sense subset recently relevant relevant relevant sufficient achieve rl rl rl rl rl rl rl rl rl chain grid grid grid grid horizontal loop loop setting demonstrate runs starting starting reward reward reward reward reward accurate accurate accurate accurate accurate designed learns learns taking taking hard hard largest solid solid proportional intelligence assuming relationship iii introduce suppose derive derive construct construct perception perception perception modeled pruning pruning implement averaging easy belief belief belief belief belief belief belief adding predictive agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent agent select national extracted expressed solved solved solved evaluated evaluated operations updated updated updated converges converges converges past reasonable performing normalization normalization normalization fitting valid expect perceptual perceptual sciences memories memories memories memories holds partially partially partially partially partially partially partially partially partially partially partially partially gamma selecting selecting computationally detect literature efficiently fine reached receives receives composed summary repeated contained prob superior return return return follow follow follow realistic minimizes observable observable observable observable observable observable observable observable observable observable observable observable ill ill ill reach received policies extract extract extract neighboring receive overfitting overfitting essential singh singh singh difficulty exponentially exponentially environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments environments mdp mdp hall existence history history history history history history history history history history history history history history history history history history history history history history history structured root root root proper proper proved adapt adapt automata automata automata perfect perfect ensure precise explain failure tractable satisfied satisfied satisfied leaves mathematics incomplete evaluating evaluating marked marked formulated dots rewards rewards rewards rewards rewards execution branch branch reaches maximizes maximizes popular occurrence singer semi decreased jaakkola jaakkola jaakkola lim lim lim leaf leaf leaf leaf leaf leaf leaf leaf leaf extreme japan summing homogeneous significance significance difficulties city check check hyper pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp obtaining tishby observing fail effectiveness child obstacle prentice ensures pruned dominant advance indicator warmuth warmuth route broken tsitsiklis tsitsiklis summarize dividing mdps bertsekas bertsekas lem pomdps pomdps pomdps suffix logarithm outline markovian markovian markovian expanding theorems theorems perpendicular concentrated surrounding associates exploratory rewritten moderate ergodic ergodic ergodic stores fortunately impractical suffers arrow arrow arrow arrow arrow ron ron executing executing proposes accumulate grids grids faced percept percept percept percept percept percept shares subtree subtree subtree subtree subtree subtree subtree histories miss miss oil favorably favorably aliasing visits distinctions distinctions grown occupied overfit percepts percepts percepts percepts percepts percepts percepts faculty accumulating lira compose mccallum mccallum mccallum cot overcoming walls misses hardness till till pol stochasticity loth loth lib ima limt creases iil iil chrisman chrisman abe abe verges icy goto ihl lla lla observ wla 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set algorithm number number system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results units information problem problem problem problem problem models models models models models performance performance performance performance based based based space space space space space space case case case case order shown shown shown shown values values probability probability probability probability probability probability probability probability functions functions functions functions functions unit distribution method approach point single control large local rate optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows shows shows simple paper paper paper paper examples work work work work work task task task task task task task methods methods methods methods methods methods step step step step step step step process process process level level level level level level level current current current current structure structure problems problems high high response similar show show show show show show equation equation section fixed line line line line general general general general general general general general generalization parameter average states states states states states states states theory theory theory obtained obtained obtained obtained term note note note note experiments dimensional result result result result result university university variables variables solution solution solution solution research independent independent defined defined defined defined defined defined defined found sequence sequence target estimate standard standard distance prediction left left left left left direction direction present present low low temporal machine machine machine machine machine sets maximum maximum range press press press press press learn position position components basis basis basis continuous continuous continuous continuous abstract abstract abstract abstract abstract abstract abstract abstract find references stochastic stochastic important decision decision decision decision decision decision decision decision decision mixture action action action action action action action action action action action action action action complex hand hand hand hand hand hand behavior behavior dynamic dynamic generated parallel cost cost tion tion change change complexity prior prior learned learned learned part part theorem theorem theorem theorem theorem cases multiple good conditions conditions represent expected expected expected expected expected expected equations equations equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov fact techniques region region length probabilities probabilities observed scale minimum minimum resulting total simulation computed respect multi multi performed called called called times elements elements mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made natural applications applications applications applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge original artificial true compared compared application application provide define define define define define define compute compute objects location location location eye determined goal goal goal goal goal related gain discrete approaches mit mit mit mit mit steps steps steps steps steps steps steps larger modeling modeling morgan morgan morgan morgan morgan proceedings proceedings proceedings proceedings proceedings words department technique consists internal individual difficult final final graph framework framework framework framework framework computing computing environment environment environment environment environment environment hinton hinton additional solutions transition transition limit limit trajectory trajectory conference conference conference conference conference conference determine determine full requires approximate approximate world basic condition condition condition condition condition developed robot robot levels controller controller controller controller controller controller path processes processes processes processes processes processes selected selected selected selected iteration iteration iteration achieved normal arbitrary denote denote denote denote limited limited close actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions proof proof finding amount common supported supported require main face end future future easily makes makes including including kaufmann kaufmann kaufmann kaufmann objective simulated typically pairs pairs pairs pairs reduced account programming programming interesting significantly significantly special special representing call call call max max pre direct international international international international international idea combined choose choose choose choose run run denotes denotes improved improved improved improved improved improved improve improve recent exact advantage takes takes takes reported apply apply introduced moving include period machines side side side side hierarchical hierarchical sense recently highly compare previously previously conventional conventional approximately tions solve converge achieve address address definition positions positions locations observation observation improvement improvement improvement grant grant grant constructed exists parts occur suggests extended extended extended extended generally setting demonstrate runs runs trajectories trajectories valued depend depend reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward numerical clear clear sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton performs taking demonstrated intelligence turn assuming assuming start start start exist movements movements movements plane plane plane plane plane plane averaged introduce introduce base base base base base denoted denoted denoted denoted suppose suppose produces written solving primary describes transitions transitions infinite remaining scales scales formed formed agent agent agent agent select choosing choosing national review stationary solved evaluate restricted restricted static static static static completely updates key barto barto reduces combining event event existing existing existing determines extension extension prove domains black holds holds planning planning planning planning planning planning planning planning planning planning determining determining straightforward selecting selecting closely importance effectively effectively receives refer kind kind dis return return contribution running sci satisfy comp write write dayan dayan nips nips nips nips reach received received policies policies policies policies policies policies policies policies policies acknowledgments extend presents powerful wiley singh singh singh singh singh singh singh singh singh singh singh singh preliminary preliminary mdp mdp mdp mdp mdp mdp mdp helpful history history history history history history history history history applicable terminal authors maximizing hierarchy analogous circles changed obvious observe switching switching switching switching switching switching switching consist improving improving arbitrarily defines massachusetts massachusetts site site site site ment inequality inequality asynchronous directed navigation worse inside sections sections closer sites sites sites sites sites precisely potentially potentially optimize lowest nsf nsf researchers people evaluating substantially empirically cohen treated dots rewards rewards requirement operate switch switch switch controllers controllers controllers controllers controllers controllers controllers controllers controllers controllers poisson characterize maximizes occurrence extensions achieves achieves plan plan plan richard richard substantial semi semi semi semi semi semi semi semi cumulative bellman bellman intractable feasible proportion guarantee temporally temporally temporally temporally temporally temporally temporally temporally temporally temporally temporally appropriately controlling circular mobile outcome arrival robotics robotics proceed reaching kaufman replacing primitive primitive primitive primitive roles synchronous combinatorial constructive selects started mance loo encountered paul negligible negligible schwartz schwartz consequences chooses chooses approximators approximators discounted discounted thin thin insight refers repeatedly ends park extends dietterich dietterich dietterich generalizing acknowledge mdps mdps andrew andrew andrew thrun shorter discount formulate amherst amherst flat flat hierarchies illustration options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options options modifying thick thick continues labs searches intra expand afosr option option option option option option option option option option option option option option option option option option option option option option option option option option option option option option million discretization flight bradtke bradtke aaai continually challenge strict handled picking picking picking tour gratefully fiat reinforce corners tom prefer termination termination termination termination termination termination termination ron russell russell russell executing executing executing meth meth meth tells att att joints tended proves weather weather weather weather weather weather weather ods ods ods kaelbling kaelbling kaelbling kaelbling fol ready planner planner planner planner terminates terminates terminates terminates terminates terminates ings cuts cuts tained tenth tenth maxq col landmark landmark landmark landmark landmark landmark landmark landmark landmark landmark landmark landmark behaving behaving das initiated initiated initiated ted cations appli histories histories histories histories altering battery battery continuing continuing continuing precup precup precup precup precup precup precup precup macro coincides parr parr parr parr huber plans subtasks courses courses courses tiny billion billion inertia ecs satinder satinder begun ting challenges duff duff proving sky sky lowing manfred encounter panels flips emphasizes closing landmarks landmarks landmarks crafted crafted crafted mission mission mission mission comers interrupted interrupted interrupted interrupted interrupted interrupted interrupted interrupted interrupted interrupted reactions feudal checking twelfth opaque interacts observa planned planned lly criticism terminating initiation initiation initiation navigate navigate eft leo elapsed elapsed harmon exhaustively accelerating crete sight perceives commit ass aea mahadevan mahadevan tick fifteenth fifteenth fourteenth navigating optional grace limk florham intelli factory initializes women initiating gent ett iis commitment commitment baveja doina consumes encountering encountering controllet 
#@Precup_D,Ravindran_B,Singh_S,Sutton_R,
#t12
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural function function figure figure figure figure figure figure figure figure figure figure figure figure time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results information information information problem problem problem problem problem hidden hidden performance performance based based based space space space space linear case vector order shown shown shown shown shown shown shown systems values values values values probability probability probability probability probability probability probability probability probability probability probability probability functions distribution distribution distribution method method method method method method approach approach approach single single single processing control control local rate rate rate test test class matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal algorithms algorithms algorithms simple simple paper paper paper paper paper paper paper paper examples small size size methods methods methods step step step step step step current current current current current problems problems problems problems problems problems problems problems problems memory memory memory memory memory similar equation equation section fixed general real average average average average states states states states states states states states states states theory gradient obtained obtained obtained obtained obtained obtained note note note result result university solution research research research independent defined defined sequence initial initial constant estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate direction direction present present present present machine machine machine press learn learn abstract back find find computational convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic important important adaptive decision decision decision decision decision decision decision decision introduction introduction introduction action action action action action action action action action action action action estimation estimation estimation estimation estimation behavior behavior effect variance variance parallel cost assume lower rules measure learned learned learned learned learned learned learned learned learned chosen chosen higher previous type type type type type multiple multiple good distributed expected expected expected expected expected expected expected expected equations markov markov markov markov markov markov markov markov markov markov fact fact techniques proposed proposed proposed correct probabilities probabilities probabilities scale resulting resulting resulting resulting simulation multi multi sum performed performed performed called reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor factor factor potential policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy em obtain obtain obtain obtain original original artificial artificial represented desired define rates determined determined experimental goal goal goal goal connected distributions discrete approaches mit contrast contrast proceedings proceedings proceedings proceedings proceedings proceedings department implementation implementation version version version consists consists advances joint difficult difficult difficult final bias bias addition sequences sequences sequences environment environment environment environment environment environment environment environment environment directly estimates estimates transition transition transition transition transition transition conference conference conference conference conference conference capacity upper requires choice choice statistics free world world world world increase produce conditional conditional types types product product provided processes processes processes processes processes processes processes iteration iteration depends depends achieved limited close complete complete actions actions actions actions actions actions actions actions actions effective effective theoretical theoretical require require require require future future makes makes including including including simulated simulated simulated underlying underlying needed jordan jordan jordan jordan jordan programming york increasing mechanism uniform uniform empirical numbers iterations iterations iterations iterations iterations iterations iterations iterations international international international international international decay decay decay choose choose light denotes improved improve improve improve recent exact exact exact exact advantage advantage property property pair pair separate separate takes movement practical strategy strategy strategy moving include include side sense sufficient observations observations observations observations observations observations observations works solve yields yields differential differential differential differential differential achieve rl evaluation evaluation evaluation evaluation evaluation evaluation evaluation modified observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation grid grid grid grid williams williams improvement improvement improvement grant constructed exists lead scaling occur extended alternative alternative alternative locally move deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic generally column column demonstrate runs runs conclusion starting place row row greater reduce operator depend reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward sutton performs practice asymptotic learns learns learns learns learns learns learns suggest reduction solid solid intelligence intelligence start manner minima annealing acknowledgements monte carlo written longer longer longer solving solving solving transitions transitions distinct implement simultaneously infinite slightly belief unique unique adding frequencies springer john national dependence stationary stationary stationary learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner learner variation evaluated operations restricted updated evolution evolution evolution evolution evolution evolution evolution similarly converges updates past past past past diagram diagram diagram partial barto dashed dashed roughly penalty penalty penalty sufficiently assigned avoid building exploration perceptual perceptual combinations extension discuss mozer specifically candidate domains partially partially partially partially partially partially partially partially partially discussions successfully columns columns selecting computationally presentation efficiently projections online online online online receives receives verlag procedures success success success superior play play absence delayed observable observable observable observable observable observable observable observable observable attempt policies policies policies policies policies policies policies policies policies policies policies policies policies policies approximating routing decreasing explore simpler singh singh singh singh singh singh singh singh singh singh singh investigate experience experience difficulty environments environments optimized optimized limitations game game game game mdp mdp helpful respond history history complicated act act possibly adapt extremely ensure ensure quantities message mixed arbitrarily averages brown rows rows theoretic expensive expensive expensive expensive glass glass glass glass glass glass caused correction correction starts shared producing immediately mathematics gradually preceding nsf improvements evaluating empirically remove rewards rewards rewards schematic schematic reaches maximizes maximizes maximizes maximizes popular occurrence proven qualitatively achieves sums replace begins jaakkola jaakkola jaakkola jaakkola jaakkola eventually traces yielding cumulative realized representative guarantee fix animals acts arrival plays difficulties simplify pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp efficacy resulted interpret exploit exploit removing selects selects heuristics obstacle evaluations ensures entry entry guarantees colorado colorado enhance schedules schedules schedules chooses multiplied indicator arrows arrows horizon park park considerations messages exploiting stone stone stone stone stone stone stone stone assigns assigns assigning mdps mdps mdps mdps speaking verify pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps multiply multiply drop constitute annals discount discount discount discount discount recursively job job job job job job job job job job markovian smoothly obtains seek verified queue queue queue queue increment wall labs searches boulder eligibility memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless memoryless enforce funded west placing knowing increments littman littman handled tail tail payoff payoff payoff payoff payoff survey algorithmic corners continued water water water water water water water east opponent opponent opponent opponent morris dropped russell russell russell russell russell inherently inherently visit attained comprising admission att arriving kaelbling senses server server server server server server server server server server server server comer halves tenth tim prescribed prescribed merit tails parr parr parr parr parr avenue aliasing visits visits distinctions waiting waiting waiting mike viable anticipate prohibitively satinder satinder seeking absorbing provably enormous incremented timestep timestep timestep timestep timestep timestep timestep timestep formulating observability twelfth walls cassandra eleventh finished renormalization renormalization viability jobs jobs jobs jobs jobs rounded notoriously timesteps perceives fifteenth rota interspersed florham chrisman enhancements finish summand iis baveja confounded confounded confounded prescribes prescribes prescribe occupying timely slipping 
#@Singh_S,Williams_J,
#t12
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#*learning learning model model neural neural data data data data data data data data data figure figure figure figure figure time time time set training training training training algorithm algorithm algorithm output output output number system system system error state state state results results results results results results results results results results information information information information problem performance performance performance performance based based based space linear linear linear vector vector order order order order order order order order order order order order order order order order order order order order order order order order order shown shown shown shown shown systems systems values probability noise noise noise noise distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method single single single processing processing control control control control control control control large rate test test test analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms gaussian gaussian gaussian visual visual visual paper paper small size work work work task task task task task task task methods methods classification process trained trained problems high response similar similar similar show show show show show show equation equation line line line line line line line line line rule rule vectors vectors images general real real average average average average average average average gradient obtained obtained term experiments experiments experiments experiments university university solution research research research research independent independent independent independent independent independent sequence table table table table table estimate estimate standard computer computer computer computer computer computer computer computer computer science science science left presented machine press press position position components continuous continuous sample sample sample sample abstract applied back back find find convergence analog references component component component component component component component stochastic stochastic due ieee positive important important decision introduction complex complex complex complex behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus dynamic dynamic dynamic variance change difference difference difference difference signals signals signals signals learned learned chosen part center previous previous type binary binary conditions conditions expected expected expected make make make make correlation correlation correlation correlation correlation correlation correlation correlation correct correct correct correct correct total total total human regression performed performed performed performed times means potential potential potential made natural feedback feedback study study study filter filter filter filter filter filter filter filter filter filter filter negative negative compared series proc eye eye eye eye eye eye eye experimental experimental experimental experimental related related related related gain gain motor brain brain brain brain brain brain brain brain equal equal accuracy accuracy support descent source source department technique technique internal internal internal individual individual individual advances advances represents responses responses responses bias bias addition ai framework experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment additional estimates top stimuli stimuli stimuli effects effects significant significant world world world speed estimated pages give condition condition condition channel derived weighted levels levels criterion criterion bounds bounds area nature depends measured measured covariance covariance normal normal tested stable actions amount assumed supported end ability ability ability future easily makes makes makes noisy auditory needed needed needed needed combination combination combination combination reduced reduced fully technology head head head head head head head trials trials trials representing details numbers making making stored decay decay attention minimize choose choose choose sources sources sources light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light light improve improve recent recent correlations correlations advantage advantage robust robust robust robust robust robust robust robust robust robust separate typical typical movement movement movement movement movement movement subject subject subject subject subject sejnowski sejnowski relevant relevant engineering highly compare approximately approximately approximately approximately subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects calculated calculated calculated yields trans background separation separation modified modified channels channels parts expression studied occur occur occur extended trial trial trial trial trial trial trial trial deviation alternative move occurs occurs occurs occurs setting starting greater greater reduce reduce numerical numerical sutton sutton sutton performs suggest external reduction reduction pulse turn variety minimizing user user user user start ica ica ica ica ica ica ica ica ica exist movements movements movements averaged averaged manner manner manner manner manner characters characters scene identification identification reference solving ways laboratory vertical distinct changing averaging averaging infinite physical physical electrical remaining events events extraction potentials potentials potentials potentials potentials potentials potentials john national national focus dependence dependence review correlated correlated correlated correlated correlated communication squares variation variation controlled ocular ocular showed lee static static allowed allowed allowed slow slow slow slow slow slow slow slow slow slow slow slow slow slow slow slow slow slow epochs epochs epochs epochs epochs sec event event event tracking valid visible eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg eeg classified classified avoid avoid recorded existing silicon usa color color color color color color color color bell blind recognize recognize uncertainty candidate successfully successfully reason extra maximal encoded literature tend road contained allowing showing return generative sci involved absence absence paradigm providing providing observable highest leading automatically received extend explore poor overfitting create create collection kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman environments environments environments environments environments environments existence existence existence existence respond rest relationships reliable decisions decisions comparable variability scores scores statistically statistically statistically statistically cognition cognition cognition analogous measurement measurement measurement measurement measurement closest traffic traffic traffic traffic extremely created changed der assumes assumes assumes assumes epoch epoch epoch epoch epoch baseline utility finds seconds seconds averages averages averages averages averages averages averages averages averages averages averages averages mentioned residual site ment cart cart stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop stop formula directed fairly waveform waveform caused inside drive drive drive straight closer sites recognized acad medical read recording bandwidth demonstrates recognizing recognizing recognizing recognizing recognizing recognizing recognizing recognizing preceding explained requiring virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual relevance flexible lack lack red red red red red red red red red red red red red red red red red red red red red red red red red red red red red red car car car car poorly poorly recordings recordings detecting formulated formulated continuously reliability differs occurrence occurrence proven resource green green green green green green green green green green plan enables simulator kinds kinds chose display display age neuro damage progress don picture acquisition room room ordinary physiology primarily interface interface interface interface interface driving driving driving driving driving driving driving driving driving nat nat count neurophysiol neurophysiol discover turned turned arranged eliminated occurred serves occurring affected corner reliably excellent separating mouse studying mental stereo artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts ballard ballard ballard ballard ballard ballard ballard tracker clean environmental environmental extensively discovered discovered stopped default severe dramatically linked yielded slight fellowship sig basically graded session session session rao rao rao rao rao trigger causing individuals experiences evoked evoked evoked evoked evoked evoked evoked evoked evoked evoked electrode electrode concentrated alternate alternate chapman chapman chapman gas graphics graphics file electrodes erp anal setup turning turning nasa rochester rochester rochester rochester amplifiers flight steering matlab ignoring experi wider correlate correlate triggered sessions sessions sessions sessions removes clinical clinical handled utilizing ate monitor scalp ave ave ave pictures concern rare rare rare engine returned substitution screen screen screen screen artifact artifact artifact artifact digitized frequent frequent frequent reality reality reality safe amplified colors colors colors colors colors quick quick quick feasibility feasibility feasibility ranged meant enter correlates nih counted occurrences actively mounted mounted lights lights lights lights lights lights lights lights lights lights lights lights lights lights lights lights lights lights lights lights 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wearing proces psychophys flashed ike ike ike watching existed stretches phs sors psychobiology elicits ects ects goddard drove noisier 
#@Ballard_D,Bayliss_J,
#t13
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#*model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input data data function function function function figure figure figure figure figure figure figure figure time time time time time time time time time time time time time set networks number number number system system system system system system system system system system system system system system system system system results results results results results information information information information information information information information information models based space space space weights weights linear linear layer layer layer case case case case case order order order shown shown systems values values values values values values noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons recognition approach approach approach approach approach approach point single single processing processing processing processing processing processing processing processing large local local local neuron neuron neuron neuron neuron rate test analysis matrix matrix shows gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small size size size size size size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work cells cells cells field field field field field field field field field field field field features features features features features features features features process level level level level level level level level level level level level level level level current current current current current current cell cell cell cell cell cell cell cell cell cell cell cell cell high high high high high high high high high high response response response representation representation architecture architecture show show show equation section fixed approximation approximation approximation theory theory theory theory obtained obtained note note experiments experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result university threshold variables computation independent independent independent independent independent defined defined defined target target target target target target target target target target target target target target target target target target target target target target target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant standard standard standard standard connections connections synaptic synaptic synaptic synaptic science presented map map map map map map map map map map map map map map map map map map map present present present present activation temporal temporal temporal object object object position position position position position basis abstract computational computational computational computational convergence convergence convergence convergence convergence properties references due due due context introduction action hand behavior behavior behavior stimulus stimulus dynamic dynamic dynamic dynamic dynamic generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search search variable spatial spatial assume assume assume measure chosen chosen chosen higher higher higher required required cortex represent distributed equations equations equations equations equations equations fact fact region proposed observed observed observed observed simulations simulations tasks tasks tasks tasks tasks human performed called called times times times times regions regions regions means dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made study specific specific specific receptive receptive receptive receptive define objects rates rates rates rates rates rates location location location location location location location location location location location location location experimental experimental experimental experimental experimental experimental connected equal equal larger fields fields support dependent modeling modeling modeling selection selection selection report institute words words words words words consists code responses layers layers layers layers layers layers scheme scheme maps maps maps maps maps maps maps considered framework framework framework equivalent experiment curve curves top top top top top stage stage stage stage stage stage stage stage stimuli stimuli capacity capacity full requires vision randomly randomly levels levels levels levels levels levels criterion criterion area processes evidence nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory constraint biological achieved measured measured denote denote limited limited corresponds corresponds corresponds corresponds corresponds corresponds complete excitatory excitatory excitatory excitatory excitatory excitatory amount short common common common effective assumed require journal journal hypothesis hypothesis hypothesis sensory including simulated typically underlying underlying underlying dynamical dynamical dynamical dynamical dynamical dynamical technology interesting interesting testing character increasing mechanism mechanism mechanism mechanism mechanism mechanism consistent mode mode principle principle principle numbers inhibition early frame frame frame frame frame frame frame frame frame frame frame frame decay idea attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention denotes membrane population population population population population population property pair takes similarity introduced period period subject hierarchical hierarchical cognitive recently relevant dimensions dimensions dimensions dimensions dimensions dimensions dimensions previously works works correspond differential differential differential differential rl sparse background locations locations bounded entire parts deviation feed deterministic occurs column demonstrate demonstrate runs row hebbian modules modules retina retina retina designed designed encoding mechanisms mechanisms integration integration integration integration presence presence presence presence solid assuming assuming exist selective selective selective selective selective groups groups question denoted areas explicit explicit explicit appears appears appears derive index perception solving plot plot distinct modeled explicitly simultaneously consisting consisting consisting consisting consisting integrated integrated implies competition competition competition competition yield independently focus focus focus focus focus expressed formation review review stages stages evolution evolution activities constants constants slow additive delays remains msec msec msec existing fire fire fire priori color color color color color color retinal retinal retinal activated coupled coupled absolute characterized gating tests extra capable differ differ maximal included modes modes modes spiking spiking spiking spiking build schemes miller reached characteristic traditional kind kind contained interpreted involved involved absence paradigm binding binding disparity extract satisfies routing intrinsic intrinsic intrinsic extend essential involving detail dotted existence reducing neu saliency saliency act plausible analyze psychology psychology assumes separated pyramidal consist detected explain serial serial serial serial serial serial serial serial serial integrate integrate integrate slope london processed processed perspective ring monkey pool pool pool pool pool potentially separately describing meaning integrating integrating integrating integrating integrating questions reflects populations populations populations populations populations populations items items items items items items items relevance experimentally experimentally red red red red psychophysical psychophysical psychophysical item item item item item item item item passed passed slower formulated psychological ity operate spread spread differs differs extracting incoming cal ordered ordered green green germany germany logical kinds display display neuro focused attentional attentional attentional attentional attentional simultaneous yielding indices refractory resources resources acts concerned enhancement theories interconnected interconnected suppression suppression spontaneous numerically siemens siemens imposed primitive serves transforms observing salient enhanced enhanced enhanced enhanced enhanced filled inferior repeat interference respective respective conjunction conjunction conjunction conjunction conjunction conjunction conjunction accounts monkeys assembly assembly assembly assembly assembly dif stimulated ends belonging arrows arrows adopted sequentially discharge latency latency focal focal focal focal reaction reaction reaction reaction reaction emergent formulate formulate adopt adopt seek reports flat simulating suppressed suppressed mutually mutually gated allocated allocated searches searches neurophysiological carefully challenging considers maximally guided termed termed assemblies assemblies assemblies assemblies assemblies assemblies assemblies assemblies pools pools priority priority priority slopes slopes spite handled handled utilizing utilizing lecture ergodic characterizing characterizing consuming corporate inhibit inhibited diffuse integrates rons functionally characterizes implying electrophysiological distractors distractors distractors distractors distractors distractors explaining explaining initiated distractor distractor distractor distractor distractor distractor distractor triple triple triple accepting attentive attentive humphreys humphreys niebur niebur unlimited postulated munich munich munich deco deco deco deco deco hypothesize necessity sual usher usher positioned acti spotlight spotlight spotlight spotlight concentrates iij otto treisman originated absolutely desimone topographically topographically topographically guiding duncan duncan duncan duncan duncan specially suppressing saliencies locus hahn illuminated dale ima analyzes inferotemporal mchp originates preattentive preattentive quarterly quently fourteenth psycho neuropsychology allocates conse josef ime steeper ferential clarified hierarchi ihi metaphor nput polarized memorial 
#@Deco_G,Zihl_J,
#t13
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural input input input input data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set set networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training training training training output output output output output output output number system error results results results results results results results results results results results results results results results results units units units units units units units units units units units units units units units units units information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space space space space space space space space space layer case case case case case case case case case systems systems systems values values values probability probability probability unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution recognition recognition method method approach pattern point point processing processing processing local inputs shows shows shows simple paper paper paper paper small net work work work work task task task task task task task task task task step points points points points features process process process process process process level trained trained structure structure structure structure structure structure structure structure high memory memory memory memory similar similar similar similar similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture architecture architecture show show show show equation section rule general general general general general generalization generalization obtained obtained obtained obtained obtained obtained obtained term term term experiments experiments experiments experiments dimensional result result result result university log defined defined defined found found found sequence sequence sequence sequence sequence sequence sequence initial terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance node node node node node node node science prediction left left left left left presented presented presented presented map nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal range range press learn learn position position basis basis outputs continuous continuous abstract references introduction hand behavior behavior behavior statistical effect effect effect effect effect effect generated generated cost cost cost recurrent tion change spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial measure representations representations representations representations representations representations representations representations representations learned learned learned chosen chosen chosen chosen higher higher part part part part center center previous cases type long conditions represent represent represent represent correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation probabilities observed observed observed scale simulations simulations simulations simulations simulations tasks human regression computed respect respect respect performed times mapping mapping mapping mapping feedback global global study study study study study study study original original original original original original original original original original original original original original original relative relative relative relative relative relative represented compared compared desired cross series provide provide provide provide provide compute objects objects location location experimental experimental experimental experimental experimental experimental experimental goal constraints distributions distributions mit comparison larger larger support train train morgan morgan report department version version consists internal internal internal internal internal internal internal internal internal internal internal internal internal internal internal advances advances advances represents represents addition addition graph graph graph sequences maps cambridge environment environment directly directly directly additional additional view view view transition transition san san top top top top top top effects effects effects effects effects effects effects effects effects choice choice significant basic basic increase give condition condition randomly developed types lines entropy actual actual provided iteration associative discussion close close close close close close close close surface surface short effective generate generate eds eds journal journal journal end end end cluster sensory kaufmann kaufmann pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs pairs coefficients coefficients coefficients coefficients jordan transfer significantly mechanism consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent consistent squared representing direct direct direct direct bottom bottom bottom bottom bottom bottom early early combined architectures architectures correlations correlations correlations similarity similarity similarity similarity reported reported reported reported include include quadratic array cognitive axis tions correspond correspond studies evaluation locations modified organization occur touretzky generally conclusion conclusion greater neighbor neighbor neighbor depend depend differences measures retina asymptotic asymptotic asymptotic asymptotic weak mateo strong strong strong integration presence presence presence presence largest external drawn plane plane plane plane longer factors sequential plot laboratory transitions transitions transitions transitions label explicitly coordinates coordinates coordinates coordinates coordinates coordinates simultaneously slightly interaction develop adding decreases formation formation formation dependence dependence dependence correlated influence influence controlled controlled labels labels labels labels labels labels labels evolution evolution evolution evolution evolution forms converges allowed allowed allowed additive epochs epochs epochs epochs epochs epochs epochs neighborhood neighborhood neighborhood neighborhood distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances distances euclidean euclidean euclidean building building exploration exploration figures figures includes coordinate weighting retinal batch batch plotted plotted illustrated illustrated illustrated mozer neighbors neighbors neighbors grammar identified identified identified encoded included included included mcclelland situation plots plots tend online online identity capture refer quickly showing interpreted contribution contribution list absence providing reach illustrates illustrates illustrates neighboring neighboring neighboring tesauro cowan minimized employed remain poor investigate rapidly association links investigated relationships relationships relationships tanh cognition cognition cognition examined examined circles circles circles circles psychology psychology psychology panel panel panel panel panel panel panel panel panel panel panel panel panel mapped hebb contributions contributions contributions contributions contributions contributions indicating band agreement analyzed defining benchmark spatially spatially spatially spatially spatially spatially spatially spatially spatially closer choices projected gradually apparent apparent reflect transient transient quantitative peaks introducing rep rep rely pittsburgh pittsburgh spread gen occurrence proven qualitatively contribute consistently consistently picture acquisition acquisition acquisition acquisition acquisition acquisition temporally temporally temporally temporally temporally narrow encoder connecting stronger city ral filled filled filled filled alspector analyses studying encountered paul conjunction mental scan similarities francisco emergence spatiotemporal spatiotemporal spatiotemporal layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout layout indicator proximity proximity observer observer projects sequentially fitted associations associations associations associations associations associations associations associations associations associations associations associations associations associations associations associations indirect shorter shorter munro munro munro munro munro munro opposed reaction emerge spatio spatio spatio smoothly solely tendency associate remainder distant distant distant acquired cosine emphasized examination examination examination wider scanning scanning scanning scanning scanned recogni inconsistent inconsistent inconsistent tial tial tial tial attributed coin eral manipulated petsche beneficial evolutionary sis sis physically experienced priming priming priming priming priming ben schreiber schreiber indirectly spa spa spa spa cleeremans servan servan allowable comprehensive spario neigh fundamentally caruana aimed corr corr corr corr visits visits visits scribed puted judgments permuted permuted permuted permuted permuted permuted permuted permuted permuted permuted permuted permuted permuted permuted permuted gun panels contiguous contiguous associating associating pitt pitt telecommunications proprioceptive resentations resentations associa button replicating tempo contiguity contiguity contiguity contiguity contiguity contiguity contiguity contiguity pertaining cup cup navigating precedence decouple clayton clayton promoting pertain uct prod coor hardy conclusive boring layouts 
#@Ghiselli-Crippa_T,Munro_P,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time set set set set set set training output number number number number number number number number number number number number number number number number information problem problem models models models models models models models models based based based linear case case order order order order shown shown shown shown shown shown shown systems systems values values values values values probability probability probability parameters unit unit distribution distribution distribution distribution processing rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis form form form shows shows shows shows shows shows shows shows shows shows simple simple paper paper small feature feature net fig fig step points process current problems response response response response response response similar show show show show equation equation equation equation equation equation equation equation equation equation equation equation line line line rule rule approximation average theory theory theory theory theory obtained note note experiments experiments experiments experiments experiments experiments result result threshold threshold variables research research independent independent log log log log log log log log log found target constant constant constant constant constant constant estimate estimate estimate standard standard standard science prediction prediction prediction prediction presented presented presented present present present present present present phase phase low sets range press learn learn basis basis basis basis basis basis outputs abstract computational references stochastic due due due due important important adaptive decision mixture context context context context context context context context context context context context context context context context context context context context context context introduction estimation estimation behavior behavior behavior behavior behavior stimulus stimulus stimulus statistical statistical statistical statistical statistical statistical statistical effect effect effect effect effect tion change change change change change change change change assume measure prior prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen chosen chosen higher part part center cases multiple multiple multiple long long bayesian expected expected expected expected make make make make correct probabilities observed observed observed observed observed observed observed scale ing ing ing total total sum performed called times times times means reinforcement reinforcement factor factor factor made natural study study filter filter filter filter obtain provide provide provide rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates rates active determined determined experimental experimental experimental experimental experimental experimental experimental experimental related related posterior constraints constraints constraints constraints constraints constraints distributions distributions gain accuracy proceedings version version joint joint joint responses responses graph environment curve curve curve curve curve curve additional additional curves curves estimates estimates estimates estimates top stimuli stimuli stimuli stimuli stimuli effects effects approximate world world world world speed speed speed speed speed speed speed speed speed speed estimated estimated increase increase increase con produce developed criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion criterion actual actual finally processes processes processes evidence evidence evidence nature depends depends depends constraint constraint constraint simply simply associative associative measured measured measured discussion normal increases fast close close inverse inverse assumption assumption actions predictions predictions predictions predictions predictions predictions predictions predictions predictions finding effective effective role theoretical theoretical main journal journal journal journal square end instance instance future degree makes makes fit fit fit fit fit underlying underlying underlying account account account account account account coefficients fully jordan block block block significantly ratio ratio ratio york york consistent trials trials trials trials trials trials trials trials trials trials trials filters pre pre direct making bottom experts experts experts expert expert expert early early early early early early early magnitude magnitude magnitude magnitude combined combined combined combined light light light light light light light light light light light light light light light light light light light light light light light light light light predict denotes directions advantage separate separate takes cognitive varying approximately approximately approximately tions differential address background interval interval williams occur occur occur suggests trial trial trial trial trial trial trial deviation predicted predicted occurs occurs occurs generally setting half strength starting critical critical critical greater greater assumptions competitive competitive editors editors reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward accurate sutton sutton faster asymptotic asymptotic asymptotic learns suggest suggest suggest suggest sound sound sound sound sound strong strong strong strong demonstrated proportional turn assuming assuming start relationship acknowledgements pro ways ways estimating plot changing modeled modeled modeled slightly slightly belief formed versus versus versus versus versus john independently independently focus dependence dependence dependence review depending stages variation variation variation variation controlled controlled understanding similarly suggested suggested key key key key key key partial partial earlier reasonable reasonable barto slow slow slow slow slow slow slow additive additive classical classical classical classical intervals foundation expect expect building figures figures formulation inter uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty discuss discuss black partially texture aspects closely closely importance delta delta presentation presentation post ten capture capture capture notice quickly quickly quickly procedures strongly strongly heuristic showing neuroscience dis follow timing hold satisfy satisfy satisfy satisfy satisfy satisfy write play dayan dayan dayan dayan dayan dayan dayan dayan paradigm predictor predictor predictor predictor predictor attempt attempt subsequent subsequent subsequent jacobs jacobs satisfies satisfies rat intrinsic body schedule parametric experience kalman kalman kalman kalman environments association association association association scalar successive respond giving ideas behavioral behavioral behavioral behavioral detectors detectors ideal ideal ideal ideal relationships relationships reliable reliable reliable tanh tanh workshop statistically statistically statistically statistically coefficient coefficient plausible adapt adapt predicts predicts predicts psychology psychology precise detector detector academic simplest arbitrarily seconds seconds established established established established animal animal animal animal animal animal animal animal slowly slowly crucial variances variances explanation worse london reasons turns rapid satisfied satisfied satisfied easier leaves laboratories separately circle nsf addressed integrating integrating fourth reflects reflect reflect substantially substantially tional quantitative quantitative quantitative quantitative quantitative quantitative quantitative peter incorporated formulated compares psychological rewards rewards rewards rewards rewards rewards rewards rewards rewards rewards rewards rewards rewards rewards rewards poisson poisson poisson occurrence proven substantial substantial substantial substantial inherent sophisticated sophisticated comments expectations expectations conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning deviations median median sharing consistently acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition acquisition formally fix ratios conditioned animals animals animals animals animals animals animals animals animals acts count food food food food food inspired inspired rational rational rational rational fails attractive imposed viewpoint occurring mark mark observing fail affected hint preparation intuitive presentations filled predictors predictors displayed schwartz accounts originally counter probe probe captures captures captures speeds speeds speeds yale ure drop unable unable gold shorter fellowship inferred opposed cooperative failed lit flat tor england causal assess remainder constrain factorial attempted attempted publication blocking graduate crosses carefully met met met relating anal paradigms paradigms sam responding responding inversely grateful drops differing ward manuscript circumstances circumstances circumstances rats satisfaction differently acquire acquire acquire acquire demand suffers compete king king dropped equa judged ignores fastest establishing drastically inset absent delivery delivery delivery delivery signed tical substrate silent col col freely wagner wagner wagner ysis rein preventing fractional fractional fractional fractional remarkably predic predic whilst whilst forthcoming forthcoming forthcoming forthcoming forthcoming ogy rom manipulations manipulations statis beliefs rigorously strongest paid pri suggestion unclear thirty gatsby gatsby gatsby gatsby inferences birds birds behav delivered altogether multiples concluding govern contingencies reinforced uncertainties reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements reinforcements psychol ucl ucl queen proportionality proportionality proportionality proportionality cot cot cot cot cot cot revealing revealing diction asymptote roweis collectively duncan funding labor irrespective coo coo propor remembered stressed extinction extinction extinction ret ret ret ret ret ret ret ret ret ret century mately ata rescorla rescorla rescorla improper grossly cussed flaw overestimates quires convincingly appleton crofts dictive basing repaired charitable prokasy 
#@Dayan_P,Kakade_S,
#t13
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#*network network network network network learning learning model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data function function function figure figure figure figure figure figure figure figure figure time time set set set networks training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output output output output output output output number number number number number number number error error error error error error state results results results information information information information information models hidden hidden hidden hidden hidden performance performance performance performance performance based based based based based based based based based weights linear layer layer layer layer layer layer case vector vector vector order shown shown shown systems systems systems values values values values values values probability parameters parameters noise noise noise weight neurons recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image single processing processing processing processing control control control control control large large neuron rate rate rate rate test test test test test test test test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class class class class class class class class class class class class class class shows shows shows shows shows shows signal algorithms algorithms algorithms simple simple visual visual visual visual paper examples examples examples examples small size net work task methods methods step step step step step features features features classification classification classification classification classification classification classification classification classification classification classification process process process process process process level trained trained trained trained trained problems memory memory memory response response response response response response response similar architecture architecture architecture show section rule rule general speech speech speech parameter real real real average gradient gradient obtained note experiments experiments experiments activity university computation research independent defined defined defined sequence sequence sequence target target table table standard standard computer distance distance distance synaptic synaptic science science science science presented presented presented presented present present activation low low low low object sets sets sets press press press press press nonlinear nonlinear outputs continuous abstract applied applied applied back back back find computational computational analog references important adaptive propagation propagation introduction action complex stimulus stimulus stimulus stimulus dynamic generated generated generated energy classifier classifier classifier classifier classifier classifier classifier lower rules measure measure measure measure measure representations chosen center type type multiple good good good binary binary binary binary binary expected make make make fact proposed proposed proposed proposed proposed proposed correct probabilities observed scale minimum minimum classes classes classes classes classes tasks tasks total simulation simulation human human human performed performed performed called called mapping mapping means natural applications applications study knowledge knowledge knowledge filter filter filter samples samples compared application application application compute compute compute rates rates rates rates rates rates location location active determined determined experimental connected gain gain gain gain gain gain gain brain brain brain approaches mit mit mit steps accuracy accuracy accuracy accuracy update descent descent selection selection selection selection selection selection institute department implementation implementation implementation consists connectionist considered considered framework framework domain domain experiment curve additional view view top top top top top top top stage stimuli bit conference determine classifiers classifiers significant significant world world basic produce condition channel channel channel randomly randomly criterion finally selected selected selected backpropagation simply associative associative feedforward increases increases tested tested corresponds nearest common implemented role journal square pixel pixel pixel pixel easily noisy noisy noisy noisy noisy noisy noisy noisy auditory pairs pairs needed unknown coefficients technology technology mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp increasing mechanism database database call numbers filters pre making international normalized bottom early early early early early attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention attention minimize choose run added perceptron perceptron denotes architectures improved improved improve improve improve exact robust robust robust robust robust robust robust element apply apply apply apply apply introduced pixels pixels pixels pixels pixels pixels pixels array recently relevant relevant relevant engineering dimensions dimensions dimensions previously approximately subjects subjects subjects correspond studies achieve achieve rl background channels improvement sensitive amplitude exists horizontal studied hybrid white conclusion critical critical critical place minimal hebbian operator neighbor clear asymptotic weak suggest sound propose propose propose strong strong strong mechanisms external demonstrated demonstrated demonstrated solid proportional selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective selective connectivity question denoted acknowledgements suppose appears digit digit digit digit perception optical optical factors confidence recall recall recall sensitivity multilayer multilayer category remaining remaining consisting integrated applying formed select select select focus review communication controlled updated lee lee lee lee lee lee lee lee lee lee lee lee lee modulation modulation modulation suggested digits digits digits digits converges roughly false false false false iterative filtering filtering visible sufficiently euclidean euclidean views views handwritten handwritten handwritten handwritten handwritten box usa color instances recognize recognize extension plotted mozer mozer mozer mozer mozer candidate candidate black black black simplicity straightforward capable encoded encoded modification effectively presentation situation essentially cun showing issue lie classify cues quantity quantity michael providing nips computes highest overlapping overlapping overlapping cowan minimized explore command requirements requirements kalman environments limitations dotted preliminary applicable comparable stream affect notion smallest coefficient adapt psychology psychology adjusted front panel panel panel panel switching switching switching switching switching switching switching switching switching switching switching switching switching switching switching switching epoch seconds integrate integrate years residual advanced directed directed directed coded coded adapted expensive briefly spatially spatially spatially drive snr incorporate inversion recognized recognized recognized recognized attribute read depicted depicted author recognizing requiring fourth people people collected conducted conducted conducted quantitative marked incorporated psychological psychological gains gains gains gains gains gains gains gains summarized perturbations extracting incoming incorporating adjust logical logical expectations attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional attentional univ merging extreme irrelevant irrelevant irrelevant classifying ordinary ordinary corrupted corrupted corrupted benefit contextual ear ear accomplished bipolar oxford fix temporally temporally acts theories plays clamped significance adjusting accepted proceeds removing imply repeat colorado colorado enhance propagated facilitate candidates candidates candidates candidates candidates candidates competing viewing initialize mlps young omitted late park eqs thresholding mind basically asked rao rao rao conjecture conjecture conjecture classifications obtains obtains trigger causing superimposed superimposed superimposed superimposed superimposed superimposed superimposed superimposed superimposed superimposed manipulation manipulation summarizes gated playing inverted boulder boulder thresholded thresholded thresholded switched guided supports behave dsp permit round round treating supporting stores hypothesized utilizes utilizes kth kth suppress suppress concrete normalize optics optics adjusts rectangles attended attended attended attended attended voice correlates acknowledges deformation modern neocognitron neocognitron began preventing attentive frozen superscript fukushima fukushima tag strongest strongest prohibitively kim kim kim pattem pattem pattem pattem panels ministry treisman treisman heuristically overcoming absolutely conscious ink kruschke flipping shadow masking pattems pattems pattems korea korea quarterly listening pergamon soo dimensionless numeral numeral numeral numeral admitted shin shin psychologists whichever lax controversy attenuates 
#@Lee_S,Mozer_M,
#t13
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#*network network network network network network network network network network network network network network network network model model model model neural input input input input input input data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time set set set set set set set system system system system system system system system system system system system system system system system system state state results results results results results results results results results results results information information information information information problem problem problem problem problem based based based based based based based based based based based based based based space space space case order order shown shown shown shown shown shown shown shown systems values probability probability parameters parameters parameters parameters parameters weight weight recognition recognition approach approach approach approach approach pattern image image image image image image image image image local local local local local local local local local optimal form form shows shows shows shows shows shows shows shows visual visual visual paper paper paper examples examples methods fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells points points features process level level current cell cell cell cell problems problems response similar similar representation representation representation representation representation representation representation representation representation architecture show show show equation equation equation section fixed fixed fixed line images images images general general parameter parameter real average obtained term term term experiments experiments experiments result result result result university threshold threshold threshold solution solution research defined defined defined defined dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial computer computer computer computer distance connections connections connections connections connections connections node node node node node node node node node node node node node node node node node node node node node science science left left nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal press outputs abstract computational properties references due due due ieee important introduction behavior behavior behavior behavior generated search search search search tion tion spatial lower rules rules rules rules rules chosen higher part center center center center center center center center center center bound cases cases multiple good conditions represent represent represent region region region region region region region region region region region region region region region region proposed proposed proposed length minimum minimum resulting resulting human human human human respect called elements regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions regions optimization potential potential potential obtain obtain obtain vol vol vol vol relative relative relative relative represented represented desired provide define experimental constraints approaches approaches approaches approaches approaches approaches approaches mit steps comparison contrast contrast contrast contrast contrast contrast connection connection connection words words department implementation version represents represents represents represents responses responses responses responses responses responses exp exp exp exp exp bias bias bias cambridge domain equivalent equivalent additional additional additional additional top top conference determine determine vision vision vision vision increase give give con con criterion lines lines finally selected inhibitory depends group tested close close assumption corresponds excitatory stable surface surface surface surface surface surface surface surface surface surface surface surface surface common common common implemented implemented implemented shape shape shape shape shape shape generate supported role eds eds eds square square ability sensory auditory underlying account projection york york york edge edge edge edge edge edge segmentation segmentation consistent consistent principle principle iterations making bottom bottom bottom bottom depth frame frame sources sources discussed directions pair pair pair pair pair pair pair pair pair pair typical lateral lateral lateral lateral lateral lateral introduced introduced introduced introduced pixels cognitive sufficient tuning tions solve solve differential background background background separation symmetric modified williams williams organization organization organization organization organization organization organization organization organization organization organization organization organization organization organization entire grant parts intensity studied correctly correctly locally white white white white white white occurs boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary boundary column demonstrate strength strength conclusion critical reduce segment segment segment segment segment segment segment segment segment central central interactions modules propose strong demonstrated solid start groups groups question relation pro construct edges edges edges edges edges perception perception perception perception perception plot mathematical segments segments segments segments segments segments segments segments segments segments explicitly simultaneously angle angle springer springer formed competition competition squares viewed solved solved operations updated updated evolution evolution decomposition understanding updates earlier dashed dashed normalization boundaries boundaries boundaries boundaries closed closed initially initially filtering coupling coupling existing existing figures figures includes perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual perceptual contour determines coupled coupled coupled coupled coupled variations black black black black black partially discussions determining determining society encoded wij essentially essentially capture verlag verlag strongly link symmetry criteria hold gray gray gray gray gray cues cues involved involved involved vary providing hypotheses hypotheses hypotheses automatically automatically principles principles neighboring neighboring neighboring neighboring neighboring acknowledgments intrinsic remain strengths hanson hanson existence rise rise detectors authors proper tanh hierarchy cognition surfaces surfaces surfaces surfaces surfaces contours contours contours contours contours contours contours contours contours attributes attributes attributes naturally plausible configurations opposite opposite academic generates generates generates detected grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping motivated massachusetts mentioned ground ground ground ground ground ground ground ground ground ground ground ground ground ground ground ground ground ground ground publishers phenomena adjacent diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion handle handle incorporate controls probable grossberg grossberg localized cybernetics radius nsf explained virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual reflects double double substantially generic simulate simulate detecting completion completion completion completion completion completion completion completion completion completion completion completion completion completion incorporated incorporated incorporated incorporated incorporated incorporated rep logical inherent boston wang wang wang wang discontinuities aligned tem tem plays overcome imposed belong belong belong belong belong salient corner corner combinatorial combinatorial combinatorial filled composition ambiguity ambiguity buffer buffer regard topological evident accounts sim belongs belongs belongs lawrence similarities occlusion occlusion young offer refers refers belonging extensively extensively erlbaum reverse implicitly valuable influences influences influences influences influences onr liu liu liu liu crossing unified incorporates rubin solves solves email kluwer emergent uniquely smoothly preferences junction junction junction junction junction junction junction junction junction junction junction hillsdale ary pub rectangular segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation segregation alternate grouped grouped grouped grouped rectangle paired paired paired wise iri constructs associates geiger geiger geiger gordon tune psychophysics signs signs status status status status status completed completed completed modal modal modal circumstances reversal lowe resolve corners rivalry prefer textures junctions junctions junctions junctions junctions junctions junctions junctions junctions ers jersey interpolated compete establishes eliminates award conversion incorporation triangle manually manually resolved resolved resolved resolved occluded occluded occluded percept percept percept percept percept shares illusory illusory illusory illusory illusory ceedings ambiguities bregman bregman bregman investigator hole disadvantages ohio ohio simulates bio mumford sition regional regional regional resentation zhu modulating modulating enhancing nections bistable claimed heat heat heat heat palm depths depths depths depths poral poral steepness laterally laterally ending percepts percepts meyer psy segmentations tilted resolving handles cis mingolla mingolla fragments strengthened gestalt gestalt gestalt gestalt gestalt occluding occluding occluding prefers misleading lai nakayama closeness pit columbus crete shapley holes qii oth chophysical competi pothesis simulta organizations ships neously initiates resolves combinatorially lishers diffi decompo bust configura diffused binarized binarized join tempt confusing 
#@Liu_X,Wang_D,
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#*network network network network network network network network network network network network network learning model model model model model neural neural neural neural neural neural neural neural neural neural input input input input function function function function function function function function function figure figure time time time time time time time time set set networks networks networks networks networks networks networks networks networks state state state state state state results results results units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units units information information information information information information information problem models models models models models models models models models models based based space space weights weights weights weights linear case case case case case vector vector vector vector order shown values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters noise noise weight weight functions unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution recognition point point processing processing processing processing control large neuron neuron rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix optimal inputs inputs inputs shows gaussian paper paper paper paper small small small step points process level level random random random random random random random response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar architecture architecture show show show show show show equation equation equation equation section section fixed fixed fixed fixed fixed vectors general speech speech parameter parameter approximation average average states states states states states states states states states term term term note note experiments experiments university university university variables variables computation computation solution independent log log log log defined defined defined defined found dynamics constant table table standard standard standard terms terms terms terms connections connections connections connections connections connections connections connections connections connections connections science prediction left left presented presented activation activation activation activation activation activation activation activation activation activation frequency sets motion motion range range press components components components components components continuous continuous abstract computational computational convergence density density density density references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic positive context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context introduction behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect recurrent recurrent recurrent change change change difference difference variable variable variable variable assume word word center theorem firing firing firing firing type type good good binary conditions conditions represent represent represent represent represent equations make make region probabilities probabilities observed times regions regions regions mapping mapping potential potential potential feedback feedback feedback feedback feedback feedback feedback feedback feedback applications applications study policy policy negative samples desired define rates rates rates active related related constraints gain gain gain gain gain discrete discrete discrete discrete brain mit connection support support report institute department department loss version consists internal internal individual joint joint represents represents represents connectionist connectionist responses responses responses responses responses responses responses difficult exp exp exp exp ai ai cambridge equivalent experiment experiment directly directly limit san stimuli stimuli stimuli choice choice approximate approximate approximate speed con con con condition channel channel channel channel channel channel channel channel channel channel channel processes depends achieved discussion technical increases arbitrary arbitrary fast predictions amount short short common assumed square needed combination functional testing ratio ratio ratio ratio ratio york consistent representing representing representing representing representing call direct direct direct making idea sources sources discussed element element lateral lateral lateral lateral subject subject side inference cognitive cognitive cognitive cognitive interest varying subjects volume module module tions converge converge differential differential symmetric symmetric symmetric symmetric symmetric symmetric channels channels channels channels channels channels channels channels channels increased occur deterministic strength strength depend modules practice presence external external external external external external california assuming exist areas perception perception perception perception perception perception perception perception perception perception describes mathematical distinct distinct changing easy interaction adding equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium versus decreases independently independently focus expressed review influence influence influence influence detailed densities densities densities densities showed approximations approximations approximated approximated converges converges converges additive faces precision precision perceptual activations activations determines discuss holds holds simplicity sensor sensor mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland mcclelland identify literature vowel showing neuroscience categories notation sampled write generalize law law law law law law law law law law law law law law law law law diego wiley investigate investigate exhibit integral integral mass existence existence existence existence existence examine examine examine examine rest scaled cognition trace necessarily onset analyze psychology psychology psychology versions versions logistic observe separated arbitrarily synthetic integrate massachusetts ground separable separable separable separable separable separable separable separable sensors sensors sensors diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion diffusion tive forces controls controls sounds sounds mellon mellon argument greatly carnegie carnegie applies applies fuzzy cmu psychophysical psychophysical cohen cohen cohen psychological http exhibits modulated gen phonemes logical lim lim lim lim lim lim instantaneous ratios ratios ratios drift driving acts controlling controlling impossible connecting generality definitions disjoint implications affected affected affected affected corner james pat belongs belongs belongs bases claim surprisingly hypercube formant consonant inf empty approx specification specification specification specification specification specification conjecture conjecture affects param cns capacitance intuition pdp argued interactive interactive interactive interactive covered alternatives alternatives accounted psychophysics examination simplifies inactive architectural syn remarkable fortunately factorized factorized corners corners converging jointly movellan movellan movellan movellan movellan movellan movellan movellan establishes char injected consonants chan chan chan factorization factorization factorization goodness goodness goodness essence essence brackets appro indexing tern dispersion dispersion unaffected unaffected ton excite oil inte nections phonological named named named named fac thinking picks separability separability separability separability separability ons eter brownian brownian structurally structurally structurally mated borrowed nel collapse straint contaminated contaminated grounded incre nels nels perceiving facto limt factorize factorize factorize factorize factorize erated mor relay sociated tition taneously meter factorizes factorizes factorizes evi simul ception ception javier incompatible incompatible incompatible conjectured imately dyi sharpness sharpness sharpness tential overt import submatrix trolled dimensionm adhere bitrary 
#@McClelland_J,Movellan_J,
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#*network network learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data function function function figure figure time time time time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training output output number number number number system state state state state state state state state state state state results results results units units units information information information information information information problem problem models models models models models models models models models hidden hidden hidden hidden hidden performance performance performance performance performance performance based space space space space layer layer layer layer layer case vector vector order systems systems systems systems values probability probability weight recognition method method method method method method method method method pattern point point point point point processing processing processing processing processing large large large large large large large large large large large rate rate test test test test test test test test test test test test test test test test test test test test test test test analysis analysis class class class class class shows simple simple small small small net net work work work work task task task points points points field features current current trained trained trained trained trained trained structure problems problems problems problems problems problems random high high memory memory similar similar representation representation representation show section vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors real real theory theory gradient obtained term note note experiments experiments experiments experiments university computation computation computation research research research research research research log found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics initial standard computer terms distance distance distance science science science science science science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented map map present present present activation nodes temporal machine machine machine sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets sets range range press press press position position abstract back back find properties likelihood likelihood references due ieee ieee important important adaptive propagation propagation context context context context introduction introduction introduction statistical statistical effect generated generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion difference difference difference difference difference difference difference difference variable lower lower lower measure measure measure measure representations representations representations representations representations representations word word word learned learned learned learned learned higher higher higher higher part center center cases cases type required good long long long represent expected markov markov make make make make fact length length length correct correct probabilities probabilities probabilities observed scale scale finite finite finite finite resulting resulting classes classes classes classes ing ing tasks tasks tasks human human computed computed respect performed performed performed times times times times times means means potential potential potential potential made natural natural natural study study study knowledge negative negative vol artificial artificial artificial artificial artificial represented represented compared application proc proc experimental experimental goal related related constraints connected discrete power approaches approaches mit comparison comparison larger larger larger larger train train train descent modeling modeling modeling modeling report institute institute institute words loss loss version version consists code advances advances advances connectionist connectionist connectionist connectionist responses responses difficult difficult difficult difficult layers sequences sequences sequences sequences sequences sequences sequences sequences ai ai maps maps san top top stage conference efficient efficient significant significant significant speed increase increase derived derived randomly clustering clustering clustering clustering types types types types provided processes processes processes nature nature simply measured measured discussion discussion normal technical arbitrary group transformation transformation transformation fast limited close close corresponds surface finding amount common common common generate supported supported supported require eds eds end ability hypothesis hypothesis hypothesis future development pairs pairs pairs pairs pairs smaller smaller underlying needed account dynamical dynamical interesting interesting testing significantly significantly character segmentation consistent consistent structures mode language language language language language language language language language language language language language language language language language numbers numbers numbers numbers numbers making making window window window window bottom early idea sources description predict recent recent resolution advantage advantage property pair pair pair include subject machines machines machines machines machines machines machines machines side cognitive cognitive cognitive cognitive cognitive cognitive engineering interest highly previously observations works works achieve trans trans trans positions increased increased constructed lead concept studied scaling scaling scaling suggests predicted predicted correctly correctly occurs demonstrate runs conclusion conclusion minimal minimal minimal minimal minimal minimal minimal minimal greater trajectories trajectories trajectories trajectories trajectories differences sigmoid accurate accurate designed clear clear mateo suggest largest intelligence intelligence intelligence start targets introduce identification appears appears pro pro construct longer longer longer longer longer sequential generating generating stability stability changing category dimensionality text text text consisting events predictive predictive predictive formed extraction expectation potentials choosing formation dependence codes variation detailed transform lee lee sizes similarly discrimination past key epochs combining iterative iterative initially symbol symbol symbol symbol symbol symbol symbol symbol symbol symbol euclidean euclidean degrees precision expect thesis activations assignment specifically absolute determining straightforward middle aspects identified society computationally divided symbols symbols symbols symbols symbols symbols symbols symbols literature build comparing tend tend ten ten ten traditional traditional traditional allowing showing interested dis superior issue lie lie follow device cues built built giles giles quantization quantization quantization quantization hypotheses predictor consisted consisted acknowledgments remain create experience varied integral issues examine project project dependencies dependencies scaled symbolic scores statistically cognition momentum matched matched neu neu smallest naturally naturally naturally closest closest concepts necessarily automata psychology created equally prototype versions versions versions versions versions portion portion formal logistic taylor mapped mapped academic academic academic switching baseline extent motivated phd sentences sentences averages years devices brown brown great ment crucial distinguish phenomena majority briefly benchmark lies london rapid rapid perspective shared style style style day constructing constructing bengio immediately arise arise cut simard potentially potentially grossberg members lowest lowest varies evaluating carnegie applies understood elman elman affine spoken experimentally lack lack peter leave documents cohen share treated http prototypes mod cal ordered suited singer datasets findings utterances utterances utterances progress sentence sentence sentence sentence sentence sentence sentence sentence sentence sentence wesley semantic sharing lot contribute consistently don picture representative acquisition college identifying sort www addison oxford count repre repre tem flexibility fails allocation bower minutes occurring occurring occurring tishby utterance ral ral imply krogh responsible corpus corpus corpus corpus symposium clock alphabet alphabet hertz hours motivation date reliably interference interference interference financial contexts contexts document codebook codebook codebook codebook codebook codebook codebook codebook codebook codebook encountered vertices vertices counting counting lawrence dif multiplied emergence infer creating creating creating offer offer jolla refers vertex theoretically grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical grammatical hypercube hypercube hypercube erlbaum partitioned likelihoods interestingly treat linguistic linguistic linguistic linguistic linguistic dramatically linked suffix suffix ence usage usage anns anns anns logarithm listed vec graded graded graded graded graded graded graded graded graded graded graded graded inferred validity validity creates removal obstacles employs tween distinction connec additionally ease ical possibilities associate assess remainder avoids avoids home trends intuition insights insights insights insights cessing paired switched topic harder distinguished distinguished suffer suffer book happen supports lippman retained exhibited els examination demonstrating removes rarely appearing appearing remarkable remarkable styles styles styles styles styles styles palmer acquire fractal fractal fractal fractal fractal fractal fractal fractal fractal fractal fractal allen allen impractical insufficient frasconi firstly king tors powers ron appealing rare distinguishing concerns gram gram gram sen assessment manipulated lying rtrl rtrl rtrl sliding sliding sliding reality syntactic spirit cho creation bradford bradford schreiber concatenated tra semantics tags tags tags tags tags sentation catastrophic catastrophic catastrophic servan unexpected tit ference cations meaningless meaningless meaningless meaningless meaningless meaningless meaningless meaningless meaningless meaningless notions sentations whilst tag tag tag manipulations manipulations devel internally enabled tie vast exceeded exceeded initialised continuation linguistics linguistics poral lacking encounter ministry widespread syntax ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical ungrammatical prototypical formedness formedness readers instantiations fund economics contingencies story violations havior pennsylvania corpora corpora corpora signif subsequence casey government government government lesser pertinent transport manage infants austria kruschke austrian austrian austrian austrian austrian tionist discourse discourse discourse discourse discourse discourse discourse discourse discourse planned federal vienna vienna vocabularies nll nll nll nll nll nll nll nll nll nll nll chines tackled atomic preclude uncover creases inevitably scalability tick ries suitability sixteen ascertain georg georg incidentally adaptivity adaptivity suggestive matical matical amnesia pending consult jectories fresh upenn renewal overt icantly opment suffixes creative fractals interleave guar imperial sfb bypassing schottengasse conforms trajecto 
#@Dorffner_G,Parfitt_S,Tifio_P,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural input data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure set set set set set set training algorithm algorithm algorithm output number number number number number number number number number number number number number number number number system results information models models models models based based based based based based based based based based based based based based based based based based based based based space space space space space space space space case case case order shown shown shown shown shown systems values probability probability probability probability probability probability probability probability probability probability parameters distribution distribution distribution method approach approach pattern pattern single single single single single single processing large large rate test test test test test test patterns patterns patterns patterns analysis class class class class class class class class class class class class class class class shows shows shows algorithms algorithms algorithms simple simple simple simple simple simple paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small size size size size size size size size size size size size size feature feature work work work task task task task task task task task task step features features features features features features classification level level level level structure structure structure random similar similar similar similar similar similar representation show show equation equation equation equation equation equation equation section section section section rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization real approximation average average average average average theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient note note experiments experiments university computation computation solution independent found dynamics computer terms terms distance distance distance distance distance science science presented frequency machine machine object sets maximum range press learn learn position continuous continuous sample abstract abstract applied computational convergence convergence convergence convergence convergence density properties properties properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood references positive positive positive positive positive positive positive positive positive context context introduction complex complex behavior parallel parallel parallel parallel tion tion complexity assume rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules prior representations word word word word chosen higher part cases cases cases cases cases multiple multiple multiple binary represent distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian correct probabilities probabilities probabilities probabilities observed observed observed observed observed observed observed observed finite resulting classes classes classes ing ing tasks tasks tasks human human human sum sum elements factor potential dimension dimension dimension dimension natural natural applications study study knowledge negative artificial specific specific specific specific specific specific specific specific specific specific specific provide compute compute objects objects objects objects objects objects determined experimental experimental posterior posterior posterior posterior discrete brain brain brain equal power mit mit comparison larger contrast contrast support support modeling modeling department consists consists consists bias framework framework framework framework framework framework framework framework framework computing domain equivalent equivalent experiment directly view view top stimuli full full full full free basic basic basic con con con weighted randomly randomly conditional clustering clustering clustering levels levels criterion bounds provided finally evidence depends depends simply simply measured discussion increases increases group group group denote fast assumption predictions predictions predictions predictions predictions predictions predictions predictions circuits short short nearest common implemented assumed shape shape generate role theoretical theoretical require main main square hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis future degree degree including including probabilistic typically smaller smaller smaller smaller smaller smaller smaller combination account account account account fully significantly significantly significantly significantly significantly significantly special special special special consistent consistent consistent consistent consistent consistent consistent consistent consistent trials trials trials trials trials trials trials trials trials trials trials trials trials matching uniform mode principle principle principle principle principle principle language language representing call call numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers stored magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude frame frame minimize light denotes denotes denotes recent recent property typical typical similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity introduced introduced include hierarchical hierarchical inference subset relevant relevant highly conventional conventional observations subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects works works axis axis axis tions match correspond correspond correspond correspond studies converge separation separation generalized interval interval interval constructed parts concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept concept suggests trial trial trial alternative hybrid occurs occurs conclusion minimal greater greater differences measures modules bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes numerical designed weak largest labeled labeled min min min min min min min min min iii iii iii iii iii iii iii program program appears appears appears digit construct written ways describes transitions transitions mathematical mathematical mathematical mathematical mathematical mathematical distinct distinct distinct distinct distinct distinct missing missing category averaging averaging averaging averaging averaging remaining remaining slightly slightly interaction applying applying shift independently focus depending learner evaluate fraction fraction understanding similarly key key reasonable slow additive additive spaces spaces intervals intervals intervals intervals intervals roughly roughly intermediate norm norm figures includes includes thesis priori instances determines determines extension uncertainty uncertainty uncertainty uncertainty priors priors domains domains domains domains domains characterized successfully successfully successfully successfully successfully simplicity simplicity reason determining selecting identified uniformly computationally symbols modes modes modes modes modes modes modes identify literature computations situation ten characteristic characteristic characteristic characteristic capture capture capture prob success return follow follow strategies bar involved sampled sampled modular nips nips hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses ill ill ill ill ill ill maximization received principles overlapping overlapping overlapping overlapping overlapping overlapping preferred satisfies neighboring neighboring neighboring situations presents presents law bars bars explore explore exponentially exponentially rapidly rapidly involving game game matches possibility cover understand cognition fundamental analogous hill smallest smallest smallest smallest gradients gradients gradients gradients gradients naturally concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts plausible predicts predicts predicts extremely psychology rev rev thought thought thought subsets subsets subsets subsets subsets obvious algo observe simplest explain explain explain animal asymptotically preference slowly distinguish phenomena fairly explanation adapted independence briefly rapid stanford stanford stanford purposes shared division broad broad incorporate probable consequence universal exemplars exemplars exemplars questions varies people people people people people people people people reflect pure pure pure pure amounts quantitative marked haussler employ treated sharp psychological psychological ity mod measuring spread spread fall fall popular cal extensions gave logical kinds kinds shaped converged multidimensional multidimensional sharing contribute consistently representative acquisition classifying proportion appearance assign assign formally appropriately pick pick animals animals count purely repre addresses exemplar plays fails fits smith smith consideration imaging odd odd hope scoring reasoning shifts belong salient intuitively intuitively intuitively intuitive selects meaningful ranging programs schapire displayed accounts accounts sim sim sim sim sim sim sim sim sim sim sim sim sim belongs candidates candidates candidates similarities membership mem augmented rich specificity ends inductive likelihoods likelihoods captures captures explains summarize instructions generalizing generalizing tures adopted default assigning counts consecutive consecutive leaving ple shepard shepard accept graded graded leaming leaming ber asked asked opposed emerge distinction distinction par exception acceptable acceptable arg generalizations generalizations generalizations possibilities certainty imagine conservative principled argue arising summarizes concentrated exam exam intuition magnitudes toy rithms num num gener gener mitchell allocated rectangle relating individually regimes regimes complementary pos categorization categorization categorization importantly anal nonetheless nonetheless discusses apparently apparently sized responding reveal meet fea applicability bring els gorithm correlate cube served preserves ble algorithmic impractical focuses lated evolved dominates powers powers powers powers loosely continuum peaked equa contrasts sparsely sparsely extracts judged contributes contributes interpretations implied falling amenable mcgraw rectangles rectangles meant generaliza replaces replaces favors modularity ysis hood cats assessing entering tal unifying unifying prime tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum tenenbaum heights alization alization ther acceptance mention psych psych rated rated thinking judgments judgments judgments judgments judgments judgments judgments draws bull mag ending ratings ratings cog densely densely densely fell gra endpoints multiples multiples multiples multiples multiples story emerging likeli preceded joshua embodies zation lihood kruschke bers photographs implausible documented argues leverage abstracted abstracted combina participants occured ilar logically logically logically instructive psycho tum sistent engaged mathe ify termined pioneered matical sharpens keams competitor competitor abilistic competitors psychologically psychologically sibility happened ofa nitude universe universe cix cix ihl participated cepts cepts workings ofy subordinate subordinate mathemati 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#@Tenenbaum_J,
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#*network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural input input input input input input input input input input input data data function function function function function function function function function function figure figure figure figure figure figure time time set set set set set set set set set set set set set networks networks networks networks networks networks training training training training training training training algorithm output output output output output output output output output output output output output output output output output output output system system error error state results results units units units units units units units units units hidden hidden hidden hidden performance based based based based based based space space space space space space weights weights weights weights linear linear layer case case case case order order order shown shown shown shown systems values values noise weight functions unit unit distribution approach pattern point point point single single rate test test inputs inputs inputs inputs form form form shows shows simple simple simple simple gaussian paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small work work task task task task task task task task task task task task task task step step step step step points points points points points points process process process process process current current trained trained trained trained trained trained trained trained trained trained trained structure structure structure structure structure structure structure structure structure random random random random random random random random random random random random random random random memory response similar similar architecture show show show section section section section section fixed line general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization approximation approximation average average average states states states states theory theory theory note note note result university university university university university university research found found sequence sequence sequence sequence sequence sequence sequence sequence target target initial initial computer connections science left presented presented present present frequency sets sets maximum range range range press press press press press learn learn learn learn learn learn learn learn learn position outputs outputs outputs continuous continuous sample abstract back back find find find computational properties references due due positive propagation propagation context introduction complex complex complex generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion change change change variable assume assume lower learned learned learned learned learned learned learned learned learned learned learned learned learned chosen previous cases type required required required conditions conditions conditions represent tree tree tree distributed correct finite simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations minimum minimum resulting classes ing tasks simulation simulation simulation human human human sum sum performed performed performed performed regions mapping factor made natural natural study em artificial artificial specific specific specific specific specific specific specific represented compared compared compared desired desired series series series series series series series series series series provide active constraints discrete brain approaches approaches mit mit steps steps contrast support support train train selection proceedings department represents connectionist difficult difficult final final final final final bias addition addition graph sequences sequences sequences considered framework cambridge cambridge cambridge cambridge cambridge domain domain environment environment environment environment environment environment additional additional solutions stage approximate world world pages pages con produce produce channel randomly randomly randomly processes selected backpropagation nature nature achieved discussion describe tested tested limited surface common common effective supported role require adaptation adaptation easily easily easily easily easily easily easily development development including simulated simulated smaller york york mechanism special empirical empirical empirical language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language language squared squared max magnitude attention produced produced produced produced produced predict population recent recent pair robust takes strategy include hierarchical array engineering engineering sufficient volume axis axis yields studies studies sparse sparse address address evaluation evaluation positions positions interval entire grant constructed parts concept concept concept concept studied studied alternative generally demonstrate runs starting critical minimal minimal minimal greater greater greater conclusions editors editors editors editors editors constrained constrained suggest propose taking strong strong hard mechanisms external drawn demonstrated demonstrated intelligence variety start selective relationship relationship relationship manner denoted denoted acknowledgements appears appears produces produces written index ways ways ways ways ways factors factors tuned dept dept interaction develop adding springer yield family communication communication learner learner learner learner learner learner learner learner learner learner learner learner learner restricted restricted restricted showed showed evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution evolution decomposition forms forms forms forms forms understanding understanding approximated past key epochs epochs combining purpose purpose purpose purpose interpolation interpolation generation remains initially initially initially string symbol symbol symbol symbol symbol symbol symbol expect exploration figures figures activations strings strings strings strings specifically specifically specifically grammar successfully simplicity selecting aspects aspects aspects importance uniformly encoded effectively effectively effectively symbols symbols symbols symbols symbols symbols symbols symbols symbols included presentation successful successful successful identity identity identity identity ten ten ten receives quickly repeated strongly decoding contained success showing lie running criteria sci sci device device comp comp list sampled generalize generalize generalize generalize generalize generalize generalize generalize paradigm paradigm paradigm paradigm providing highest subsequent subsequent approximating employed investigate difficulty difficulty humans humans humans detail association limitations recursive recursive recursive recursive recursive issues issues biases biases biases biases biases biases biases biases biases biases biases examine matches giving school structured root symbolic symbolic symbolic symbolic symbolic workshop affect encode cognition cognition hill hill hill hill concepts concepts concepts concepts concepts concepts concepts concepts concepts concepts adapt adapt adapt man analyze extremely psychology illustrate explored message extent simplest sentences sentences sentences sentences sentences sentences sentences sentences languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages languages crucial analyzed lies perspective arc closer easier ran leaves gradually demonstrates meaning argument requiring fourth questions elman elman elman elman poorly poorly completion vocabulary gen substantial inherent inherent decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder decoder boston unbiased utterances utterances contribute contribute pose don acquisition acquisition acquisition acquisition acquisition acquisition newton notes modify investigation arguments branches branches ordering encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder encoder impossible enhancement theories theories theories theories children children plays climbing climbing saturation smith iiii abilities biased biased biased biased biased exploit exploit exploit monotonically implications combinatorial combinatorial generalizes alphabet alphabet child child child child composition date exploring exploring exploring reliably reliably periods surprising regard dominant enhance facilitate facilitate facilitate facilitate facilitate facilitate claim emergence emergence young suggesting fitness reverse reverse generalizing generalizing cam johnson outlined learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable learnable linguistic mind unable users sine sine sine sine sine sine recursively emerge exception additionally hundred breaking australia australia australia remote remainder unseen evolve evolve evolve evolve evolve evolve evolve evolve evolve evolve continues ization life crosses learnability learnability learnability learnability learnability learnability learnability thresholded simplifying paired argued complementary weaker emphasized setup paradigms cubic cubic bring unpublished challenge manuscript species learners learners learners learners learners learners learners learners learners learners lecture appearing bridge compositional compositional compositional compositional compositional compositional compositional compositional prefer evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved evolved finer clarity tors proposal exposed exposed conflicting core core core core emerges alan alan comprising systematically evolving evolving evolving evolving evolving evolving company communicate communicate communicate communicate evolutionary evolutionary evolutionary iti iti iti evolves creation elec elec faced unusual february backwards generaliza talk wiles wiles wiles wiles wiles subtle imum facilitates altering decoders decoders decoders decoders decoders decoders decoders decoders decoders decoders decoders decoders decoders decoders continuing observes sends generations generations generations heights conveyed tailored parisi paid fac kim meanings impressive knight knight knight syntax syntax syntax brooks bradley bradley ponents taught highlight highlight encoders encoders encoders encoders organism amples queensland queensland queensland queensland assist resembling pathological bilities straints infant infants survive cai morphological tense minimally minimally minimally minimally minimally kennedy kennedy kennedy postdoctoral verbs lan lan les innate innate necessitates social social social resorting eleven assisted highlighted paradox compositionality richly pur semantically worlds worlds origins chomsky unlearnable guage guage janet janet sonable halted entirety guesses aided intentionally friendly norton brace bly yao melbourne maes 
#@Blair_A,Tonkes_B,Wiles_J,
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#*network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural input input input input input input input input input input input input data figure figure figure figure figure figure set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm output output output output output number number number number number number number error error error error error error error error error error error error state results results results results results units units units units units units units units units units units units information information information information information information problem problem problem problem problem problem problem problem hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance based based based weights weights weights weights weights weights weights weights layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case vector vector vector order shown values values values values values values values weight weight weight weight weight weight unit unit unit unit unit unit unit unit unit unit method approach point single single single single single single processing rate test test test test test test test test test test test test test test test test patterns analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class class class optimal form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper examples small feature net net net net net net net work work task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task task step step step step step step step step classification classification classification classification classification classification classification classification classification classification classification process process level level level level trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained trained structure problems random random random high memory similar similar representation representation representation representation architecture show show show show section fixed rule rule rule rule vectors vectors vectors general generalization generalization generalization generalization parameter approximation average average average average obtained note experiments experiments experiments experiments experiments experiments experiments dimensional dimensional university university computation computation computation solution solution solution solution solution solution solution research defined found found found target table table table table table table table table standard standard standard standard computer terms connections connections science science science left left presented present activation activation activation machine machine sets sets sets sets press learn learn learn learn learn learn learn learn abstract back find find references due positive important decision decision propagation propagation introduction complex complex behavior statistical effect effect effect generated generated parallel tion difference lower lower rules signals representations representations representations learned learned learned learned learned learned higher part part part part part type good distributed distributed length length probabilities errors errors errors errors classes tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks human human human human human human human human human human human human human computed computed multi multi sum sum performed performed called elements elements elements elements elements elements elements elements elements elements elements elements elements elements elements mapping mapping made made made made study study study study study study knowledge negative vol specific represented represented compared compared provide perform perform perform experimental experimental discrete discrete mit steps steps steps steps steps accuracy accuracy accuracy contrast contrast contrast connection connection connection connection fields train train train train modeling modeling proceedings report technique consists consists internal individual individual connectionist layers layers layers addition addition addition ai maps maps cambridge experiment experiment experiment experiment hinton hinton additional san san san san san top stage bit bit bit conference capacity determine determine requires requires validation validation validation give randomly conditional clustering clustering developed levels levels levels levels types types types product provided selected selected selected backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation backpropagation associative technical feedforward tested limited assumption common common assumed require eds journal journal end instance instance cluster cluster future degree makes rumelhart rumelhart including including kaufmann typically smaller needed fully technology significantly significantly consistent matching leads representing details pre bottom experts expert expert expert expert expert expert expert expert expert expert expert early magnitude decay decay decay combined run property property separate element element element element element element element element element element element reported reported reported apply strategy strategy period identical cognitive cognitive relevant relevant sufficient approximately subjects tions solve yields achieve trans definition observation interval williams parts lead deviation width clusters white white generally demonstrate runs runs starting conclusions differences differences numerical clear performs performs performs performs constrained constrained constrained mateo hard hard hard hard labeled labeled labeled exist averaged averaged question explicit explicit explicit explicit explicit van van van solving solving solving solving solving solving solving label multilayer coordinates involves remaining consisting develop springer springer implies cycles cycles focus squares squares organizing decomposition decomposition decomposition decomposition activities suggested sign sign sign sign calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation calculation performing performing combining add intermediate intermediate intermediate calculate calculate string string string kohonen avoid building combinations activations activations activations strings instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances variations black black simplicity reason determining middle middle aspects society included included mcclelland successful successful build build tend tend identity ten ten ten traditional refer verlag verlag contained contained contained contained contained contained success success showing interpreted stopping split lie follow list generalize generalize automatically attempt attempt employed simpler simpler overfitting overfitting overfitting overfitting xor updating humans humans optimized accurately hall investigated investigated parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity parity reliable structured proved encode statistically statistically statistically statistically statistically statistically statistically statistically statistically statistically cognition cognition cognition fundamental momentum analogous hill concepts analyze analyze psychology perfect subsets prototype prototype algo som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som som art established years developing developing benchmark worse processed organized day day day day day toronto annual researchers considerably considerably considerably empirically generic posed employ incorrect incorrect incorrect rep reliability reliability reliability reliability reliability reliability compares calculating berlin berlin rely aim aim prevent germany conclude findings yielding yielding displays displays investigation rithm appropriately labelled labelled count theories establish fails chance chance odd odd odd odd odd odd odd fail belong date date date date date date date date date date date date date date date date date date date date date date date date date date date date date date date analyses performances prentice programs displayed displayed overview mental intended den den den counting claim claim claim winning foundations surprisingly canada passing erlbaum inductive partitioned discovered discovered characterization material material material material material material material material material material explorations empty empty empty learnable learnable skills unable unable microstructure failed year year abstraction abstraction abstraction abstraction abstraction abstraction abstraction regularity decomposed decomposed breaking hillsdale demon clustered clustered clustered clustered eric illustration clas unseen attempted translated continues guidance guidance guidance guidance guidance guidance guidance guided increasingly topic quinlan attached distinguished apparently sam sam sam sam son indication ward october signs challenge develops accumulation algorithmic algorithmic january january satisfactory assistance assistance assistance assistance assistance cliffs solvable focuses focuses december inclusion lists incorrectly month month exclusively ters ters labelling contributes unlabelled unlabelled falling informatik neutral neutral neutral neutral neutral neutral neutral neutral neutral neutral protocol ranged gathered inaccurate february adequately adequately adequately eighth proceeding supposed simon simon amer decompose stems facilitates comprehensive marker elegant elegant elegant elegant ton collecting activa organisation fiir won men subtasks subtasks subtasks subtasks subtasks aimed week week week netherlands netherlands netherlands claims mate challenges claimed claimed necessity necessity necessity necessity functioning behavioural analogously concluded fell fell fell reproduction visualize interpretable gation decomposing decomposing pilot rrt resentations feedfor distribute distribute reg manage concludes dates dates dates dates dates dates subsection hardness sification exemplified intersections scientists graphic ume initializations initializations newell newell gan ins sight mor marking supervisor elf bench dennis inl ilk fakult reviewing decom mimicking backpropa psychiatry dehaene dehaene eindhoven leap ican universiteit calendar rial homogeneously 
#@Postma_E,Weijters_T,van-den-Bosch_A,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input data data data function function function function function function function figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm output output number system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state units units units units units units units units units units problem problem models models hidden hidden based based based based based based space space space space space space space space space space space space space space space space weights weights linear layer order shown shown systems systems systems values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise weight functions unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern point point point point single single single single single single single processing control control local local test matrix matrix matrix form form shows shows shows simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual small net net net net net net net net net net net net net net net net net net work task step step step step points points field field field field field field features features features features level level level level current structure structure structure structure structure memory memory memory memory response similar similar similar representation architecture architecture architecture show equation equation equation section fixed line images general general parameter parameter parameter approximation states states states theory theory theory gradient term activity activity activity activity activity activity activity dimensional dimensional dimensional dimensional result university university variables computation computation computation solution solution solution research research log dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial initial estimate estimate estimate standard standard standard standard standard computer computer distance connections science science left map map present present activation activation maximum maximum maximum press position position position position position position position basis basis continuous continuous abstract find computational computational computational computational convergence convergence density density properties properties likelihood likelihood likelihood references stochastic due due procedure procedure procedure procedure important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context behavior behavior behavior behavior statistical statistical effect effect effect effect effect effect effect generated generated generated generated generated variance search search tion tion tion tion change energy energy energy energy prior prior prior word word word word word word word word word word word part part center previous bound cases type multiple multiple multiple good long long long represent represent distributed distributed distributed equations equations equations fact probabilities probabilities simulations simulations ing ing total simulation simulation simulation simulation simulation human respect sum sum regions mapping dimension dimension dimension dimension applications knowledge knowledge knowledge em em negative relative represented desired desired provide proc location location location active active determined determined experimental experimental posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints distributions discrete discrete discrete comparison larger connection connection update update update update update update support support descent nets nets selection selection selection institute words words words words department department department implementation consists consists consists consists consists internal represents responses responses responses responses final final exp addition ai considered considered considered domain domain directly hinton view view view view solutions trajectory trajectory effects effects effects effects effects effects conference efficient upper upper approximate free free free basic con produce produce produce produce derived derived weighted weighted weighted randomly conditional levels lines actual processes processes selected evidence iteration nature inhibitory depends constraint associative covariance increases increases describe describe describe corresponds corresponds corresponds corresponds corresponds stable stable proof finding common common common implemented shape role role face face face face journal journal journal journal journal end end future makes rumelhart noisy fit objective probabilistic typically typically hopfield combination account account coefficients jordan jordan interesting interesting significantly increasing uniform uniform empirical pre stored normalized normalized normalized normalized magnitude frame frame idea minimize produced produced choose denotes recent property property introduced moving moving identical cognitive cognitive cognitive dimensions dimensions dimensions dimensions dimensions observations observations works tions yields correspond correspond studies studies studies studies studies studies converge sparse sparse positions locations observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation observation entire entire increased exists expression occur predicted alternative alternative touretzky generally generally setting setting strength strength strength conclusion starting reduce neighbor depend interactions sigmoid performs faster asymptotic encoding encoding propose physics physics external external external external external external external external drawn solid radial turn minimizing denoted denoted attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor pro derive produces perception perception solving generating estimating describes stability mathematical mathematical mathematical modeled missing missing missing physical involves remaining easy belief mutual gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians formed expectation expectation expectation select select select select select letters letters letters letters letters letters national focus overlap viewed interpretation interpretation interpretation interpretation interpretation influence influence evaluate showed soft partition updates updates key key key partial dashed spaces neighborhood intermediate visible assigned assigned faces faces faces views existing formulation formulation formulation formulation formulation formulation formulation color weighting instances sciences maximize mozer mozer mozer mozer mozer mozer priors priors domains black characterized determining straightforward selecting selecting letter letter letter letter letter letter letter letter letter effectively delta mcclelland attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors computations identity composed refer soc procedures procedures allowing allowing anderson neuroscience neuroscience lie content generative generative generative generative generative generative generative generative generative generative generative generative hold michael absence providing minimizes ill ill maximization maximization maximization illustrates mixing preferred modelling extend situations explore origin origin origin american create updating put history history behavioral incremental int structured complicated encode hierarchy cognition cognition cognition fundamental act coefficient coefficient closest adapt psychology psychology psychology adjusted queries aspect olfactory der formal mapped shapes academic consist motivated motivated neal percentage percentage trivial guaranteed explanation tractable lies starts tive formalism shared closer easier located desirable arise arise gradually english english english depicted annual qualitative qualitative meaning reflects evaluating items items freeman conducted conducted parameterized share completion completion incorrect psychological ity exhibits characterize spread gen fall collective achieves adjust richard logical decreased findings deviations jaakkola specifies specifies specifies semantic instantaneous sharing sharing don don don corrupted proofs proportion proportion generator restriction restriction restriction restriction fix arguments conditioned conditioned zemel zemel zemel zemel zemel homogeneous odor printed plays systematic fits difficulties difficulties adjusting attractive abilities interpret serves ral intuitive alphabet lyapunov spurious spurious spurious spurious spurious spurious spurious spurious spurious becker saul iteratively colorado colorado colorado accounts den spherical arrangement initialize hippocampus deg deg deg deg offer cpu cpu proximity proximity hypercube hypercube erlbaum variants designing characterization characterization ics ence ence specification specification achieving kluwer basin basin basin basin creates encodes alternating emergent emergent adopt tor tor basins basins basins basins basins basins demon avoids avoids distri intuition evolve cessing gained distribu boulder eliminating landscape landscape landscape landscape landscape scope interactive interactive academy integrals alternatives supports sta investigations intensive unpublished bution persistent served generarive compositional influenced influenced stochastically maze water morris tors responsibility responsibility wiring calculates calculates rare rare rare dissertation settle equa dog mcnaughton rameters rameters neurobiological implied lnp lnp distorted accommodate filling priming ings semantics unusual robustly fixing translate addressable ized probabil explaining percep hip hip localist localist localist localist localist localist localist localist localist localist localist localist localist localist predefined severely ace pull pull retrieve deeper formulations visits tie consciousness counterparts iter manipulating manipulating manipulating ative rightmost aware golden dynam responsive pal vation vation justifies kay strated assist doctoral asynchronously stant comers comers cot conscious 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#@Mozer_M,Zemel_R,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set output output output output output output output output output output output output output system system state state state results results units units information information information information information information information information information information information information information information problem models models models models models models based space space weights weights weights linear linear linear linear linear linear linear linear layer layer case vector shown shown shown values probability probability probability probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution pattern point point point single single single processing processing processing processing processing control local local local rate rate rate rate test optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form shows signal signal signal signal signal signal signal signal signal signal simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small feature feature feature feature work fig fig fig fig fig fig fig fig fig cells cells cells cells cells field field field field field features features features features process process process process level level level level level level level current current current current cell cell structure high high high response response response response response response response response response response response response response response response response response similar similar similar similar representation representation representation representation show show show section section section section line line images parameter parameter parameter real average average average theory term term note note note activity activity activity activity activity activity activity activity activity dimensional university threshold independent independent dynamics dynamics dynamics dynamics dynamics initial initial constant constant constant constant constant standard standard standard standard terms connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science prediction prediction left presented presented presented presented presented presented map present present present present present present present present present present present present phase phase phase phase phase phase low low maximum maximum range range components nonlinear nonlinear nonlinear nonlinear nonlinear abstract abstract abstract applied find density density references component due due due due due due positive important context introduction estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect dynamic dynamic dynamic dynamic dynamic variance variance parallel parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion change change change difference difference variable assume assume lower signals representations higher higher higher previous previous cases cases cases firing firing firing firing firing required multiple multiple multiple multiple multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex spike spike spike long long distributed expected proposed correlation observed forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward forward scale scale scale simulations simulations ing simulation eq mapping mapping mapping potential potential potential natural feedback orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation orientation study relative specific samples true true series receptive receptive receptive receptive receptive receptive proc proc proc active active experimental goal connected distributions gain gain cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical equal equal contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast contrast connection fields fields dependent dependent dependent dependent synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses consists consists internal code code kernel represents exp exp exp exp bias delay delay delay delay delay delay delay delay addition maps considered framework framework environment environment view view view view curves curves trajectory stimuli stimuli stimuli stimuli effects effects capacity efficient approximate free free free vision increase increase give con channel coding coding coding coding coding levels types nature inhibitory inhibitory inhibitory depends depends depends constraint simply achieved discussion technical feedforward feedforward feedforward increases increases increases increases increases transformation fast fast fast fast fast fast fast fast fast fast fast fast fast fast fast fast fast fast fast fast fast limited limited limited assumption excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory predictions predictions predictions predictions amount amount amount short short short short short common effective implemented assumed synapse supported role main adaptation hypothesis noisy noisy noisy sensory objective account functional functional functional functional functional transfer transfer transfer ratio ratio increasing increasing increasing mechanism mode mode mode operation details details details details max max max filters pre window window window window window window inhibition inhibition idea attention attention minimize added sources description membrane membrane membrane membrane recent robust robust typical strategy strategy strategy strategy strategy period period period period period highly highly highly highly highly highly highly highly highly highly highly highly compare compare observations calculated tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning correspond studies studies converge achieve sparse sparse address observation interval interval grant amplitude amplitude intensity intensity intensity lead concept invariant invariant invariant invariant invariant suggests deviation deviation deviation deviation wide spikes spikes correctly correctly feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed feed width column column column demonstrate half strength strength strength strength strength competitive competitive competitive competitive competitive competitive competitive retina faster weak weak weak weak weak constrained suggest suggest encoding encoding encoding encoding encoding propose strong strong strong strong strong mechanisms mechanisms integration demonstrated solid solid proportional decrease decrease averaged averaged connectivity connectivity connectivity question question pro edges edges edges longer longer winner winner winner winner primary primary primary primary primary tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned tuned dept modeled linearly scales scales scales interaction mutual mutual mutual mutual mutual gaussians competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition competition decreases decreases decreases decreases decreases decreases decreases decreases decreases decreases decreases decreases decreases decreases expressed review depending depending stationary detailed densities lee modulation modulation soft static static static static static static static static static static static approximated approximated activities similarly suggested key slow dashed dashed additive additive additive additive additive classical classical classical classical initially initially foundation expect fire fire inter determines determines plotted simplicity middle capable differ differ maximal maximal maximal maximal maximal presentation comparing miller excitation excitation excitation excitation excitation excitation summary summary refer strongly strongly strongly strongly strongly interpreted interpreted interpreted symmetry content timing sci sci sci sci duration gray comp bar bar bar bar bar bar bar bar bar vary realistic surround delayed delayed highest highest cat cat neurosci neurosci neurosci neurosci neurosci received operating preferred acknowledgments decreasing decreasing decreasing receive bars bars bars bars bars bars bars origin selectivity selectivity selectivity selectivity selectivity transformed investigate investigate investigate investigate exhibit exhibit exhibit circuitry exponentially detail detail strengths dotted dotted periodic postsynaptic rise rise reducing respond respond respond fashion fashion investigated investigated plasticity plasticity plasticity lgn lgn lgn presynaptic presynaptic naturally naturally onset onset onset onset onset onset onset onset man predicts predicts rev aspect assumes precise separated separated multivariate pyramidal generates regime regime regime established established preference scenes slowly costs orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations variances starts snr tive closer strictly broad arise mation consequence acad acad acad beginning beginning res read arises bandwidth bandwidth applies profile profile substantially experimentally sharp sharp sharp ity ity ity requirement release release release release release http operate berlin berlin berlin berlin berlin berlin poisson ture limiting modulated cal cal cal resource germany germany shaped physiol windows windows implements cumulative cumulative cor phenomenon phenomenon shifted ear cooper www amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier amplifier resources nat circular count encoder establish fails fails fails binocular numerically stronger stronger stronger stronger striate efficacy efficacy efficacy interpret obtaining analyzing operates operates operates shifts salient salient selects natl natl natl spurious infor sompolinsky sompolinsky weakly mance introduces periods sion perfor dif tic tic tic viewing viewing deg deg deg deg deg deg suggesting ahead saccades observer observer considerations projects statement valuable papers tures limitation informa slight depression depression depression depression depression depression depression depression depression depression depression depression depression depression depression depression ter ter ter ter shorter sig ent wiesel super super maximized transmitted emergent emerge revealed revealed nelson nelson responds obtains obtains resting hubel breaking letting evoked demon scenario scenario argue pub exponent modifying ftp ftp intuition cessing potassium regulation denoting intra simplifying fixation fixation macaque noting regimes investigating intensities intensities intensities intensities intensities weaker figs figs figs abbott fea obermayer obermayer obermayer obermayer obermayer nal normalizing behaves info advantageous scanned accordance justified sake ping vis hat ferent puts cornput finer broadly broadly broadly transmitter transmitter transmitter transmitter neocortical sharply sharply sharply sharply sharply sharply sharply sen contrasts contrasts contrasts intracortical intracortical emerges emerges architec carries functionally sliding sity leakage reproduced amplified amplified fol fol adapts ben transmit tical tained modulatory massive sur decades rent probabil fore rec sented saturate refine hypercolumn hypercolumn tivity lund enforcing activates recovers attentive bright exponents klaus parame sparsity sparsity sparsity nections tsodyks stim favorable perspectives lowing released poral testable signaling recur markram trust nonlin braun neurotransmitter proportionally faithful strated mexican sponds ori modulates sug somers synap synap synap christian ger masking lan inh sharpening dfg increas lows carandini weaken weaken weaken weaken sparser legend depletion distributing weakening creases faithfully shapley activ ulus stimu stimu stdev trec lus lus neurobiol adapta strengthen strengthen strengthen strengthen phe eff yishai baddeley levitt creasing sharpens sharpens pays lars exc exc signaled signaled signaled corti flashed flashed flashed wlo lev moti fonds gested inten geniculo pends areal citatory citatory culated polarized oby tracts 
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#*network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural neural neural input input input input input data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time set networks networks networks networks networks networks networks algorithm number number number state results results results results results results information information information information information information information models models models models performance performance space space space weights weights linear linear linear linear linear linear linear linear order order shown shown values values values values parameters parameters noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons pattern single single single processing large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal form form shows shows shows shows shows signal signal signal signal signal simple simple paper paper paper paper small size size size size size size size size size size size net net work cells field field field process process level level level level level level level level level level level level level level level problems memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar show show show show show show equation equation fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general generalization average obtained obtained obtained obtained obtained obtained term term term term term term experiments activity activity activity activity activity activity activity dimensional dimensional dimensional dimensional result result university computation computation computation solution defined defined estimate computer computer terms terms synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left presented low learn nonlinear nonlinear abstract applied applied find computational computational computational computational references component component positive positive positive procedure procedure procedure context context introduction hand statistical generated variance variable variable rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules measure previous previous firing firing firing firing firing firing cortex binary long long long long long represent distributed distributed proposed proposed observed observed observed scale scale simulations simulations resulting ing ing ing ing ing ing total total total total total simulation sum sum sum sum sum sum sum sum sum sum performed eq potential potential orientation global study study obtain obtain obtain negative original relative specific specific specific compared compared application provide define determined constraints constraints constraints gain cortical cortical cortical cortical cortical brain brain brain brain brain brain power dependent dependent dependent synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses joint difficult difficult maps equivalent curve additional effects capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity requires requires requires requires requires requires requires free pages con coding coding coding coding coding coding coding coding coding coding coding levels levels levels levels levels lines finally processes processes processes processes processes processes processes nature inhibitory depends depends depends constraint constraint constraint constraint constraint biological associative associative associative associative associative associative associative associative associative associative associative associative associative achieved measured discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance tested excitatory excitatory common effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective effective implemented assumed synapse synapse synapse synapse role role role require eds journal ability reduced projection mechanism mechanism mechanism mechanism mechanism mechanism operation operation operation leads principal principal pre pre inhibition stored stored stored stored stored stored stored stored stored stored magnitude added neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal denotes denotes improve recent property robust ensemble identical sejnowski recently recently previously conventional unsupervised observations calculated works studies achieve modified bounded bounded bounded bounded bounded organization organization organization organization improvement storage storage storage storage storage storage storage storage storage storage storage storage sensitive amplitude lead studied studied scaling scaling scaling scaling scaling occur occurs occurs column demonstrate strength place row hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian editors peak performs suggest propose mechanisms physics demonstrated turn turn variety decrease iii manner manner explicit explicit van estimating plot stability mathematical mathematical mathematical linearly linearly slightly slightly slightly scales scales adding applying applying applying applying springer implies competition letters focus review correlated squares overlap overlap overlap fraction forms suggested updates sign slow additive additive additive additive additive classical normalization normalization normalization normalization normalization normalization normalization normalization normalization normalization event event remains fire perceptual coordinate retrieval retrieval retrieval sciences memories memories memories memories memories memories prove coupled coupled phys successfully determining aspects identified identified importance maximal effectively driven driven driven driven driven driven driven driven driven wij wij wij wij wij wij wij wij wij wij wij spiking spiking spiking successful post post post post post mackay invariance plots plots plots miller miller essentially essentially essentially essentially summary procedures procedures strongly strongly strongly showing showing neuroscience lie cue simplified play dayan dayan paradigm paradigm paradigm paradigm neurosci operating carried carried carried transformed essential essential relations strengths association postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic school incremental biol biol plasticity plasticity plasticity possibility proper presynaptic presynaptic presynaptic fundamental neu math math math naturally plausible analyze predicting rev rev thought der hebb hebb hebb hebb hebb ith ith store pyramidal baseline extent averages growth growth growth analyzed phenomena improves improves biology analytical analytical capabilities correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction correction tool considerable turns tive involve ridge ridge robustness requiring requiring apparent greatly experimentally experimentally lack introducing marked continuously continuously biologically biologically compares maintain maintain maintain maintain maintain requirement requirement requirement requirement operate perturbations limiting maximizes incoming incoming incoming qualitatively prevent prevent prevent achieves enables enables enables logical kinds findings findings implements yielding yielding yielding cor uncorrelated identifying modify optimizing acts approximates jth proceed oja striate balance balance serves obtaining effectiveness intuitively modifications inferior inferior displayed negligible von realization evident originally tic tic israel hippocampus insight reveals ltp ltp ltp ltp ltp storing relies characterization interestingly discriminate schulten depression depression depression depression depression depression depression depression depression depression emergent revealed nelson willshaw willshaw pointed utilize malsburg var var beta beta preserved increment modifying mammalian degraded potentiation potentiation potentiation regulation regulation regulation depicts maintains maintains vanishes tissue tel tel coming tau tau tau utilizing stores preserves preserves ble accordance pitts ruppin ruppin ruppin ruppin ruppin ruppin focuses lated arrow developmental hemmen emerges regulatory contributes beneficial heterogeneous heterogeneous heterogeneous gerstner scenarios retrieved cooperation enhances drastically locality thresh dent modern indirectly bear tained catastrophic vanishing vanishing vanishing vanishing vanishing ous aviv aviv excessive excessive diverge sat chang bio modifies theo availability tsodyks enabled palm analyzer facilitation tinuous mild utilization underlie visualize standpoint cov cov cov tonal meilijson meilijson meilijson meilijson acuity depen economics bigger segregated cyber efficacies efficacies efficacies efficacies attain kempter rectly governs associa synap regulated eytan kybernetik rewriting raising conservation implausible numer annu zeroes succeeds cod incom incom ineffective ineffective ineffective ineffective ineffective tracing drastic tissues reside diminished erkki naptic naptic pending leslie additively mally wik isaac quantal uration circumvented complemented nate runaway runaway runaway gal delicate sociative abraham fective 
#@Chechik_G,Meilijson_I,Ruppin_E,
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#*neural function function function function function figure figure figure figure time time number number number number number number system units information space order order systems values values neurons neurons neurons neurons neurons unit unit unit point point point single large local local local neuron neuron neuron neuron neuron neuron rate patterns analysis optimal optimal optimal optimal visual visual visual visual visual visual size work methods methods cells field cell cell cell problems architecture equation equation equation equation equation equation equation equation fixed fixed rule parameter parameter parameter parameter real real real real real real real average average average average average average average average average average theory note note result university independent found constant constant constant constant constant terms distance connections connections prediction left present present present present maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press components components components abstract back find find computational properties properties references component component circuit circuit circuit circuit circuit effect change complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable assume rules center required cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex good make region region region length length length length length length length length length length length length length length length length length length length length length observed errors finite finite total times times regions means means factor factor optimization optimization optimization optimization optimization dimension made made made study vol relative relative relative relative relative represented application series define define proc eye determined experimental cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical brain brain brain brain brain brain brain brain brain brain brain equal power power larger larger larger support support support institute institute institute institute loss synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses exp maps maps maps framework curve curve effects determine requires requires requires statistics increase increase increase give con derived area velocity velocity velocity velocity actual actual actual actual actual actual actual actual finally nature nature discussion increases increases increases increases increases increases increases increases denote transformation corresponds corresponds circuits amount amount assumed assumed assumed assumed synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse supported supported theoretical theoretical require require require require require require main square square square square square makes makes objective needed needed account functional interesting ratio ratio increasing squared call call making bits idea combined minimize added added added added added added neuronal neuronal takes takes typical trees recently observations observations approximately calculated volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume volume achieve organization organization increased increased increased increased increased increased grant lead occurs half half conclusion minimal greater assumptions largest reduction proportional proportional proportional turn start start targets connectivity denoted areas suppose relation relation derive written longer longer longer longer perception ways factors primary primary plot segments infinite physical slightly slightly text consisting adding adding adding adding springer decreases decreases dependence fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction ocular ocular evolution understanding slow delays expansion neighborhood add calculate dendritic dendritic dendritic dendritic dendritic expect existing existing existing dominance dominance recognize determines characterized columns columns extra uniformly differ maximal paths identify situation reached reached soc soc graphs return physiological sci quantity vary vary vary reach reach neurosci neurosci neurosci acknowledgments decreasing decreasing situations presents explore remain remain perturbation perturbation perturbation perturbation perturbation perturbation reducing biol biol possibility root root affect understand notion removed extremely changed impulse portion separated nerve nerve nervous nervous extent explain ment growth biology majority caused sys ring ring monkey consequence consequence axon axon axon axon axon axons axons axons axons axons axons axons axons axons axons axons axons res res medical medical geometry meaning virtual tional maintain maintain requirement howard howard physiol physiol owl lab cybern physiology proportion oxford arguments arguments arguments tem impossible eliminate arranged cellular anatomical primate primate simplify balance neurobiology neurobiology wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire wire salk salk salk salk separating dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites topological lengths lengths dendrite dendrite dendrite consequences branching diameter diameter diameter diameter diameter diameter diameter young axonal axonal axonal jolla jolla agree propagate divide unchanged unchanged unchanged unchanged blood fellowship maximized ber perturbed perturbed perturbed perturbed perturbed perturbed imagine molecular alter trends trends favor conduction conduction conduction conduction conduction conduction conduction conduction num maintained permits hughes hughes retinotopic eliminating relating lond durbin travel eters rewritten cube cube cube cube cube cube cube cube cube lecture fiat arbors cable cable cable cable cable cable vii insufficient wiring wiring wiring wiring wiring subtracted substitute stevens stevens stevens stevens stevens placement placement intact sloan vivo attenuation subscript handbook charles nih ganglia ated greatest wires wires wires wires wires violate bodies bodies bodies nections perturbing anticipate vast volumes brains brains mitchison mitchison mitchison rail 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#@Chklovskii_D,Stevens_C,
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#*network input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time output output output output output output output output output output output output output output output output output output output output output number number number number number number number number system system system system results problem problem problem problem based space linear layer layer layer layer layer layer layer layer layer layer layer case case case case case order shown shown shown values parameters functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit point image large large large local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron test patterns analysis analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs form form form form shows signal signal signal visual visual paper paper paper small size size size size size size size size size size size size size feature fig cells cells cells cells cells cells cells cells cells cells points points cell cell cell cell cell cell cell cell cell high high fixed line line rule rule rule rule rule rule rule rule rule rule rule rule general real theory theory theory theory activity dimensional dimensional result result result result university defined constant constant terms distance distance connections connections connections connections connections connections connections connections science prediction prediction direction direction map low press abstract find find find find find convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density density density references due important propagation propagation introduction parallel parallel parallel parallel parallel parallel parallel tion tion difference complexity assume assume assume assume rules signals signals signals center bound cases cases type type type type type type type type type type type type type type type type type type type type type type required cortex cortex cortex cortex represent make techniques techniques length length length length length length length length correct minimum resulting classes classes classes total total total total total total total total total total human human respect sum eq eq eq means factor optimization optimization optimization study study obtain relative relative specific cross cross cross rates proc experimental goal goal related constraints connected connected connected cortical cortical brain brain brain brain equal equal equal equal equal equal steps comparison comparison connection institute version synapses synapses synapses synapses individual difficult layers layers layers layers layers layers layers layers considered design design limit effects determine upper requires requires requires significant significant approximate basic give give con con con con area area area area area area area lines lines provided finally processes nature nature biological discussion arbitrary close close close assumption assumption surface surface predictions predictions predictions nearest nearest nearest implemented shape synapse synapse synapse synapse theoretical theoretical require square square square square square makes objective pairs smaller needed interesting testing ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio ratio projection projection projection projection projection projection projection projection projection projection projection projection projection projection projection york special principle principle details call numbers minimize minimize run neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal takes typical apply include inference sejnowski dimensions dimensions dimensions compare volume volume volume volume volume volume volume volume solve studies sparse sparse locations locations modified grid organization organization horizontal parts suggests suggests wide wide wide wide wide wide wide wide wide wide wide wide wide wide wide width width width width setting place minimal row greater greater greater greater greater greater greater greater depend depend interactions retina retina retina retina retina numerical designed suggest propose presence assuming minimizing start relationship connectivity connectivity connectivity connectivity connectivity connectivity connectivity question acknowledgements areas areas relation derive derive factors factors factors factors primary plot plot implement implement minimization potentials focus squares squares densities densities densities densities fraction evolution forms understanding sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes sizes completely diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram diagram calculation sec reduces purpose add intermediate dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic existing existing inter inter inter inter retinal retinal retinal retinal extension holds discussions projections projections soc notice notice symmetry lie follow sci satisfy satisfy comp comp comp absence minimizes minimizes minimizes minimizes reach reach neurosci neurosci neurosci neurosci neurosci neurosci principles overlapping preferred preferred receive powerful circuitry divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence divergence helpful biol biol analytically possibility possibility root root root root complicated func understand topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic circles circles adapt predicts predicts predicts predicts opposite expressions nerve nerve shapes shapes nervous fibers fibers fibers pyramidal contributions regime submitted brown indicating ment agreement agreement agreement agreement adjacent adjacent adjacent analytical adapted ganglion ganglion ganglion ganglion strictly located desirable monkey monkey monkey monkey afferent pulses pulses axon separately separately angles axons axons axons axons axons axons axons axons axons axons axons axons axons axons argument argument argument requiring collected readily quantitative quantitative quantitative car frequently requirement rely summarized characterize branch fall incoming cal qualitatively qualitatively sophisticated fiber neuro unbiased eventually specifies specifies extreme extreme cybern redundant bipolar bipolar bipolar bipolar bipolar bipolar forming oxford extensive martin martin narrow narrow narrow narrow narrow arranged cellular anatomical anatomical anatomical anatomical primate primate fan fan striate striate keeping neurobiology wire wire wire wire wire belong salk salk optimally exceeds exceeds carry carry published overlaps cerebellar cerebellar cone cone connect connect connect connect dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites dendrites widths encountered equals topological dendrite dendrite branching branching arrangement arrangement arrangement arrangement arrangement arrangement arrangement arrangement arrangement arrangement arrangement dif diameter diameter diameter young express infer infer axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal axonal layout layout layout suggesting jolla considerations considerations considerations alternatively alternatively ure shorter shorter shorter sig graded covering formulate tween connec connec arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor arbor argue verified relate macaque macaque macaque macaque lond regimes spanned associates rod rod knowing wider wider tail arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors arbors agrees vis ferent bold arrow imple diffuse termination clarity morphology morphology purkinje purkinje purkinje purkinje connects connects wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring wiring affecting possess neurol neurol neurol triangle stevens stevens cones outgoing degenerate sloan andersen absent gence merged carrying sparseness granule granule watanabe surprise stacked mesh mesh mesh wires linking pact favors favors tivity tivity lund elaborate bodies bodies bodies bodies bodies bodies intersect ogy conver mented unequal violation mosaic brains mitchison correspondingly mary ons justifies dictated dictated nected interrupted exceeding arrangements arrangements arrangements arrangements arrangements arrangements arrangements arrangements arrangements misses diameters diameters nals graphic peters economy economy economy cording sparser sparser cid intersects intersects scarce arrange arrange sepa benefited orderly rods rods nar cajal cajal sectional sectional sectional topo conduct ttm inefficiency mension eur mulated denser layouts naively mam sinauer lii bors 
#@Chklovskii_D,
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#*model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input data function function function function function function function function function function figure figure figure figure time set networks number number system error error error error error error error error error error error results results results information information information information information information information information information information information information information information information information information information information information information information information information space space case case case case case case case case case case order order values values values values values probability probability probability parameters functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach point point single single single single single processing processing large large large large large local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate analysis matrix matrix optimal optimal optimal optimal optimal form form form shows shows shows shows shows shows signal gaussian gaussian visual small small small small small small small size size size size feature feature feature feature feature feature feature feature task task fig fig fig fig fig fig cells step step field field field field field field field features features features features features process high high high high response representation representation representation representation representation representation equation equation equation equation equation equation section fixed fixed fixed line line line general approximation approximation average average average average average average average average average obtained obtained obtained obtained term term note activity activity dimensional dimensional dimensional dimensional dimensional dimensional result result result independent independent defined defined found dynamics dynamics constant terms science left direction range press press position position position position abstract density density density properties properties references due due due due introduction hand hand hand hand estimation estimation behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus effect effect effect effect parallel tion tion assume assume assume lower lower chosen center center previous bound cases cases cases firing firing firing firing firing firing binary spike distributed distributed distributed expected expected expected fact fact region region correlation observed observed observed forward resulting ing ing total total human multi multi multi multi sum performed elements elements dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made study study study vol artificial artificial relative represented true compared receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive receptive define rates rates proc active active active determined distributions distributions distributions distributions distributions distributions motor approaches mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison larger fields fields fields fields fields fields fields fields fields fields fields fields code individual joint ai maps considered considered cambridge computing hinton curve curve curve view curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves curves limit limit stimuli stimuli stimuli stimuli stimuli effects effects requires increase increase increase increase condition coding provided provided finally nature depends depends depends depends measured discussion discussion increases increases increases arbitrary arbitrary assumption short common effective effective assumed assumed assumed assumed shape theoretical theoretical theoretical theoretical eds square square degree rumelhart rumelhart noisy sensory sensory auditory typically functional york edge increasing increasing increasing mechanism special special uniform uniform uniform uniform uniform uniform uniform empirical empirical leads attention attention combined neuronal denotes denotes denotes denotes population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population population discussed discussed discussed discussed discussed discussed improve improve resolution resolution resolution element introduced strategy strategy strategy strategy identical identical identical identical identical side subset sejnowski sejnowski sejnowski dimensions dimensions dimensions dimensions dimensions sufficient previously tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning yields yields yields yields yields yields yields diagonal diagonal diagonal diagonal diagonal definition symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric symmetric modified grid interval improvement improvement increased expression studied studied occur suggests spikes spikes width width width width width width width width width width width occurs place minimal minimal minimal minimal minimal depend depend depend retina clear suggest encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding encoding taking mechanisms drawn solid radial assuming selective min min min decrease decrease averaged averaged question question question derive written written written longer index describes tuned tuned tuned tuned tuned modeled metric remaining springer implies expectation decreases decreases yield family dependence dependence correlated estimator overlap overlap overlap variation variation detailed detailed evaluated restricted restricted fraction fraction centers calculation calculation reduces reduces reduces generation valid valid calculate visible illustrated discuss discuss discuss specifically specifically holds characterized characterized major regular straightforward uniformly differ maximal encoded encoded encoded encoded mcclelland mcclelland spiking spiking spiking spiking literature literature situation situation situation characteristic interpreted split symmetry symmetry symmetry strategies strategies strategies strategies comp comp comp list write dot decreasing decreasing situations carried rapidly put accurately accurately dotted existence existence existence fewer biol biol biol variability variability variability complicated encode necessarily aspect aspect quantities noted fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher precise shapes shapes shapes consist contributions years inequality theoretic theoretic answer worse inside turns broad broad broad immediately mation consequence opt geometry prop populations populations populations populations empirically empirically relevance lack lattice introducing share recordings dots schematic maintain poisson ture germany decreased decreased decreased physiol unbiased findings findings focused focused owl picture picture cybern cybern cybern secondary arguments arguments narrow narrow narrow narrow narrow neurophysiol turned turned arranged significance obtaining observing affected exceeds symposium infor recovered falls representational zhang zhang zhang widths widths widths widths widths widths widths widths widths widths widths widths widths widths widths widths widths widths widths widths encountered encountered bad lengths consequences uni arrangement diameter diameter specialized specialized eng interestingly baldi informa yielded unified basically validity gaps encodes encodes rao obtains tradeoff chapter realize barn alter visualization visualization distri distri distri diag jij jij rectangle projecting topic covered breaks reveal universit knudsen fea radio mini bution bution bution cube mcculloch advantageous advantageous advantageous advantageous pitts const const const institut insufficient european stochastically stochastically stochastically stochastically spacing broadly broadly dropped pronounced concerns konishi carries carries sym vanish proves enhances lnp inset crl brackets tical inst decades cats quantified mum tongue shrink deco conveys diverges radially radially radially radially radially radially radially radially radially radially radially exclude correspondingly roth physik physik adaptable zhao elongated erties stefan ations jii jii jii jii jii jii jii iden heiligenberg christian heaviside breakdown ode ode mln mln reads midbrain cram koenderink eft geometries impairment arl subpopulations subpopulations subpopulations subpopulations subpopulations subpopulations subpopulations subpopulations subpopulations subpopulation subpopulation subpopulation subpopulation subpopulation subpopulation subpopulation facto onal snippe abbreviated ceptive theoretische ffir outlook popula brussels tun tun dimensionless retrieves specializes narrowly narrowly narrowly fio narrowing 
#@Eurich_C,Schwegler_H,Wilke_S,
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#*network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model neural neural neural input data data data data data data data data data data data data data data data data data data data data data function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time networks training training algorithm algorithm algorithm algorithm number number number system results units units units units units units units units units units units units units units units units units units units units units units units units problem problem problem problem problem models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space space space space space space space space space space space space space space space space weights weights weights weights weights linear layer layer layer layer layer layer case vector vector vector order order shown shown systems values values values values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise weight weight weight weight functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method approach approach pattern pattern image image image single single single single single single single processing control large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate matrix matrix matrix matrix matrix form form shows shows shows simple simple gaussian gaussian gaussian gaussian gaussian small small size net net work work step step step step step step points field level level trained trained trained trained high memory similar representation representation representation representation representation architecture show show show line line line rule rule rule rule vectors images images images images images general parameter real real real real real real real real real states states states states states states states states states states states states states states states states states states gradient gradient gradient gradient term term term note activity activity activity activity activity dimensional dimensional dimensional dimensional dimensional university university threshold variables computation research independent independent independent log log log log log log log log sequence sequence sequence sequence sequence sequence sequence sequence sequence initial estimate estimate standard standard computer terms connections connections connections connections connections connections synaptic science prediction prediction direction map present present present phase phase phase activation activation low low low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine machine machine machine machine object object object object object object press press learn learn position basis basis basis basis basis sample sample abstract computational computational computational density density properties likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic ieee positive positive procedure important important action stimulus stimulus stimulus effect effect dynamic variance parallel tion energy energy energy energy energy energy energy energy energy energy energy difference difference spatial spatial spatial assume assume assume prior prior representations representations representations learned learned higher previous previous type required required required multiple multiple multiple binary binary binary binary binary binary spike spike spike spike spike spike spike spike spike conditions represent represent represent represent represent represent represent represent represent represent represent distributed distributed distributed distributed bayesian expected expected make region region proposed proposed probabilities probabilities probabilities observed forward scale scale simulations simulations simulations simulations simulations resulting ing simulation computed computed computed sum eq called times times times means potential potential dimension dimension made made natural orientation negative negative original artificial represented represented represented represented represented true true desired desired cross series series receptive receptive receptive receptive receptive receptive receptive define compute objects objects rates location location perform active active active posterior posterior posterior posterior connected connected distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions discrete brain brain mit steps steps steps steps steps steps fields fields fields fields fields fields fields dependent nets nets department loss consists individual individual individual individual kernel kernel kernel kernel kernel kernel kernel kernel kernel represents difficult difficult difficult scheme scheme addition graph cambridge computing domain hinton hinton hinton hinton hinton hinton hinton hinton hinton design design design top detection conference full full full requires requires significant approximate con con produce coding coding coding coding conditional conditional conditional conditional conditional levels area velocity lines lines path product product actual provided finally nature depends sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling constraint simply biological achieved achieved discussion covariance covariance covariance covariance covariance describe arbitrary arbitrary inverse inverse inverse inverse corresponds effective effective effective effective shape generate require eds pixel pixel ability future future future future future future degree degree makes makes makes rumelhart rumelhart rumelhart noisy sensory objective probabilistic hopfield hopfield coefficients coefficients coefficients coefficients coefficients fully interesting ratio york uniform operation operation operation representing numbers international bottom experts experts experts experts experts expert expert expert decay combined produced added sources predict population population population population directions correlations resolution exact property property apply moving moving period machines machines machines machines machines machines pixels pixels sense inference inference inference inference sejnowski dimensions sufficient highly varying varying observations volume works works tuning tions smooth smooth smooth smooth smooth symmetric modified intensity lead suggests deviation spikes spikes spikes matrices correctly width white boundary column demonstrate row segment segment valued valued valued valued valued valued valued depend editors central interactions sigmoid accurate peak taking hard solid intelligence assuming start force acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann van van produces longer index perception ways describes tuned changing implement simultaneously remaining easy belief belief belief belief scales adding adding adding adding equilibrium predictive formed independently reconstruction stationary correlated viewed viewed codes codes codes restricted restricted restricted restricted restricted restricted restricted organizing fraction approximations evolution centered centered frames activities activities activities activities activities activities similarly smoothing slow slow additive delays spaces spaces convex combining fitting add iterative visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible visible sufficiently kohonen advantages perceptual determines determines maximize black discussions major encoded mcclelland mcclelland mcclelland latent wij spiking spiking spiking spiking spiking spiking spiking post composed compact quickly quickly quickly allowing video anderson anderson neuroscience dis return lie lie contribution oscillations follow generative generative timing timing timing gibbs gibbs gibbs gibbs gibbs gibbs sampled vary dayan attempt mixing deal extend unlike create essential accurately accurately accurately dotted helpful postsynaptic postsynaptic fashion history history ideal ideal combine combine combine comparable complicated cover cognition act patch coarse coarse coefficient ensure obvious assumes logistic freedom freedom precise precise precise contributions explain synthetic neal brown brown brown brown formula convolution convolution convolution fairly independence glass lies london london perspective purposes sections closer easier broad immediately products 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press press learn basis basis basis basis abstract applied find find computational density likelihood references stochastic stochastic introduction hand hand hand behavior behavior behavior behavior behavior behavior effect generated recurrent tion tion change change difference difference variable assume assume assume chosen chosen chosen chosen part bound firing firing firing firing firing firing firing firing type type cortex cortex cortex cortex spike spike spike spike spike spike long long long conditions conditions conditions distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed distributed expected make fact probabilities observed observed forward forward scale finite finite simulations simulations simulations simulations resulting resulting resulting ing simulation simulation simulation sum sum sum eq eq eq eq eq called times potential potential natural feedback feedback global study study study original relative specific specific represented compared compared compared experimental experimental experimental experimental experimental connected connected connected distributions cortical cortical cortical cortical brain equal equal mit mit connection nets proceedings proceedings report synapses synapses synapses synapses synapses code kernel kernel kernel kernel advances advances represents represents represents exp delay delay delay delay addition addition addition curve curve curve curve curve curves effects conference conference upper full basic pages pages con randomly randomly randomly randomly bounds area types types types evidence evidence nature nature nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends simply associative associative associative discussion normal group group group group group 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boundary setting critical critical place hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian editors editors constrained integration physics external external external external external external external external cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle drawn demonstrated assuming exist manner manner manner groups groups groups groups groups groups groups groups groups groups groups groups connectivity identification question denoted attractor attractor attractor attractor appears van derive describes mathematical scales events springer formed formed formed formed formed formed formed implies blocks cycles competition stationary stationary stationary influence open showed forms activities completely suggested allowed allowed partial calculation delays delays delays delays delays combining calculate calculate assigned david coupling expect fire fire fire fire fire fire fire fire fire fire figures includes currents inter sciences sciences sciences memories plotted prove coupled coupled black characterized modes spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking spiking identify attractors attractors post post post post post situation characteristic composed interested neuroscience stopping split symmetry follow timing gray satisfy comp vary paradigm paradigm ill satisfies carried investigate investigate investigate accurately existence postsynaptic postsynaptic postsynaptic school school investigated investigated variability func presynaptic presynaptic math math transmission analyze obvious extent grouping motivated integrate integrate integrate histogram developing asynchronous asynchronous distinguish analytic analytic analytic analytic analytic explanation diffusion answer tive organized organized organized organized division calculations definite meaning meaning argument questions reflect understood understood led introducing solla solla 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connections connections connections synaptic science present low temporal temporal object motion press outputs outputs abstract abstract applied find computational references important introduction behavior effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect effect parallel parallel spatial spatial measure higher higher higher higher higher higher higher higher higher higher higher higher higher higher center center center center center firing type conditions equations make fact region region region region region region region region region region region region region region region region region region proposed length length observed observed observed observed scale scale scale scale finite finite finite finite ing tasks simulation performed called elements elements elements elements elements regions regions regions regions regions regions regions regions regions potential feedback feedback orientation orientation orientation orientation orientation orientation orientation orientation global global global global relative compared compared receptive receptive receptive receptive receptive receptive receptive receptive receptive rates proc location location location determined experimental experimental experimental related discrete cortical cortical cortical cortical cortical cortical cortical brain mit larger larger larger connection connection connection connection fields fields fields fields fields fields fields fields modeling modeling loss consists consists consists represents responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses considered experiment directly stimuli stimuli stimuli effects effects effects effects effects effects effects effects effects effects effects effects effects significant significant significant significant significant significant significant vision vision give give randomly levels levels area area types provided processes nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory sampling biological discussion increases group limited assumption excitatory excitatory excitatory excitatory excitatory excitatory surface circuits finding common effective effective effective effective effective effective effective shape shape shape shape supported supported eds journal noisy including pairs pairs smaller smaller smaller reduced reduced account account account account account significantly edge edge edge edge edge edge edge edge edge edge segmentation segmentation segmentation mechanism mechanism uniform details details call call call pre pre pre making inhibition inhibition inhibition early decay membrane membrane membrane recent pair pair pair element element element element lateral side dimensions highly previously observations observations observations axis axis axis axis axis axis axis axis axis axis axis axis axis axis 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noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit unit unit point point point point single single single single single single processing processing processing processing processing control large large neuron neuron neuron rate rate rate analysis analysis analysis analysis inputs inputs inputs inputs form form form shows shows shows shows shows paper small small small small small size work methods fig fig fig fig fig fig fig fig fig cells step step step step step points process current current current current current current current current current current current current current current current current current current random random random random random random high show equation equation fixed fixed fixed fixed fixed fixed parameter parameter approximation states states states states states states states states states states states theory theory obtained obtained note activity result university threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold computation computation computation computation computation computation independent found found dynamics dynamics dynamics dynamics constant constant constant constant estimate standard standard synaptic synaptic synaptic synaptic synaptic activation activation activation activation activation activation low frequency frequency range range range press press press press press press press components components components abstract density density density density density density density density density density properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due due due due due due due procedure adaptive introduction introduction action action action complex hand hand hand circuit circuit behavior behavior behavior effect effect effect effect effect effect effect effect effect effect effect variance parallel tion variable lower signals signals prior higher higher higher higher center firing type required spike spike spike spike spike spike represent represent tree tree equations markov markov markov markov region finite simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations simulations ing ing ing ing ing ing ing total total total computed sum sum sum sum performed performed performed eq eq eq eq factor factor factor factor potential potential potential potential study study study study study negative negative compared application series provide provide provide rates rates rates rates active active active active determined determined determined discrete cortical cortical cortical cortical equal power power mit mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage contrast dependent dependent dependent source modeling institute version version technique individual individual individual advances represents scheme scheme scheme scheme scheme cambridge cambridge computing directly curve curve curve curve curves estimates estimates transition transition transition limit top detection determine determine significant world increase increase increase increase increase increase increase increase give give give channel channel channel 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white white generally generally pass critical conclusions depend differences accurate numerical temperature temperature temperature temperature temperature temperature temperature suggest integration integration integration external california solid solid decrease decrease relationship connectivity program program denoted denoted denoted denoted denoted denoted monte monte monte monte monte monte monte monte monte derive carlo carlo carlo carlo carlo carlo carlo carlo carlo written estimating estimating transitions transitions transitions transitions transitions transitions transitions transitions modeled modeled modeled spectral integrated integrated frequencies blocks potentials potentials potentials decreases decreases expressed dependence dependence review squares influence solved transform densities densities densities densities densities densities densities densities densities densities open open open open open evaluate approximations similarly constants spectrum spectrum earlier slow classical closed closed closed closed generation valid msec koch koch koch koch koch koch koch koch koch koch dendritic dendritic dendritic dendritic precision precision precision thesis phys determining differ differ differ computationally divided driven driven spiking spiking spiking computations schemes schemes excitation refer interested neuroscience conductance conductance conductance conductance conductance conductance conductance conductance issue oscillations timing timing timing timing timing sci hold michael absence realistic neurosci acknowledgments decreasing carried carried perturbation investigate updating varied steady steady steady steady steady steady steady steady steady steady steady steady limitations accurately existence rise rise rise fourier rest rest rest biol analytically scaled referred variability variability variability fundamental circles circles circles patch patch patch patch patch patch patch patch patch patch patch patch closest transmission 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based based based weights weights weights case case case case shown shown shown shown shown systems systems systems systems systems systems values values values values values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise functions functions functions functions functions neurons neurons neurons neurons neurons neurons unit unit unit unit unit approach pattern pattern single processing processing processing control neuron neuron rate patterns patterns patterns analysis optimal form form shows shows signal signal signal simple simple paper examples small small net task task task task task task task task task task task task methods fig fig step step step trained trained trained trained trained trained trained cell cell cell random high high high high high memory response show show rule rule rule rule general approximation average average average theory term term term term term term term term term term term term term term note note experiments activity activity activity activity activity activity activity activity activity result result result university university computation found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target target target initial table table table table table table estimate synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science prediction left left left direction direction presented presented phase activation low low frequency frequency frequency temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine maximum range range range range range range press press press press learn learn basis abstract computational computational computational computational computational properties properties references adaptive context context introduction complex behavior behavior behavior stimulus statistical statistical dynamic change change change change difference difference difference spatial rules signals signals signals signals signals signals signals chosen chosen cases cases required cortex spike spike spike spike long long long long long long long conditions expected proposed observed observed observed simulations simulations simulations resulting resulting resulting tasks tasks simulation simulation simulation respect eq eq eq eq eq eq eq times times original relative specific specific compared compared series series series series proc proc active active active active active active active experimental discrete mit mit mit steps steps steps contrast contrast contrast contrast contrast support support dependent dependent dependent synapses synapses synapses kernel kernel kernel kernel kernel advances advances advances responses ai ai ai ai ai ai framework framework cambridge cambridge cambridge computing domain environment environment environment environment hinton top top top stimuli effects choice free free estimated increase increase increase give produce condition coding coding weighted area path provided processes evidence evidence evidence nature nature nature biological biological biological biological biological associative associative discussion covariance covariance covariance arbitrary tested tested tested close close close close synapse synapse role role role role role role role theoretical require eds eds eds ability hypothesis hypothesis future noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy auditory pairs smaller needed hopfield hopfield account functional block testing mechanism mechanism representing representing iterations iterations pre pre direct direct window inhibition inhibition bottom bottom bottom idea run added predict neuronal neuronal architectures recent exact robust typical reported lateral lateral machines side sejnowski sejnowski cognitive cognitive recently recently varying studies studies converge converge converge rl rl symmetric generalized organization sensitive sensitive studied trial spikes touretzky column half strength strength critical assumptions hebbian hebbian hebbian hebbian depend depend retina designed clear sutton external external external solid solid program base boltzmann van van van longer sequential sequential sequential laboratory laboratory laboratory laboratory mathematical physical slightly interaction predictive predictive predictive predictive formed shift select competition dependence dependence reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction depending correlated correlated interpretation interpretation approximated sizes activities activities activities activities activities dashed dashed delays sec purpose valid initially kernels usa usa formulation sciences recognize plotted plotted mozer specifically phys partially letter modification driven delta wij detect post post capture capture neuroscience physiological timing timing sci sci sci receptor sampled sampled providing providing illustrates trains stimulation stimulation wiley varied association integral integral integral preliminary preliminary postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic examine examine giving ideas school biol plasticity plasticity possibility dependencies variability pathway presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic fundamental analogous analogous math onset rev illustrate illustrate perfect perfect thought precise explored separated hebb hebb hebb hebb hebb hebb hebb pyramidal extent utility utility established developing adjacent lies sections broad broad products laboratories acad acad begin fourth populations offset solla solla pittsburgh pittsburgh pittsburgh pittsburgh anti anti collective song asymmetric asymmetric physiol owl calls instantaneous instantaneous contribute phenomenon phenomenon shifted shifted benefit modify temporally temporally temporally narrow acts approximates null reconstructed reconstructed reconstructed reconstructed discovery enhancement enhancement enhancement arrival wrong significance held alpha intelligent efficacy efficacy efficacy fail shifts shifts implications selects days hours natl natl fires motivation reliably repeat sompolinsky started slice slice zhang zhang paul enhance enhance hasselmo hippocampus hippocampus hippocampus cerebral stimulated ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp ltp clean clean clean clean clean kearns kearns storing reverse associations depression depression depression munro munro munro munro emergent nelson reports possibilities sinusoidal decorrelation reconstruct reconstruct reconstruct barn cohn cohn shifting community interact life potentiation potentiation potentiation regulation neurophysiological neurophysiological neurophysiological interacting scope flip interactive integrals integrals abbott abbott abbott supporting examination correlate factored externally inconsistent hundreds blum inclusion appealing neocortical hemmen hemmen hemmen ackley nmda slices measurable gerstner gerstner gerstner cooperation contrary vivo saturating jitter substrate emerged awij saturate saturate saturate wagner wagner facilitates facilitates facilitates facilitates repetitive lynch coincides kanter formulations coincidence berger tsodyks lasting nonlinearly vitro poo articulated articulated markram markram millisecond millisecond pitt pitt rabbit qualities story kempter kempter kempter unclamped shifter shifter shifter shifter shifter shifter shifter shifter shifter neurocomputing postulate 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#@Hernandez_G,Munro_P,
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fixed fixed fixed line line rule rule rule rule rule rule parameter parameter parameter parameter parameter parameter parameter average states states states states states states theory term term term term experiments activity activity activity activity activity dimensional dimensional dimensional university university threshold threshold independent independent log log found found found found found found constant estimate estimate standard terms terms terms terms connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic left present activation activation low low machine machine maximum press learn nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs continuous abstract abstract applied applied applied references stochastic stochastic stochastic stochastic positive positive positive positive introduction complex hand effect effect effect effect tion tion energy difference variable spatial spatial spatial classifier measure measure measure prior learned learned chosen chosen previous previous previous type multiple multiple binary binary long long long long tree tree tree fact region correlation observed simulations simulations resulting ing tasks total total total total total simulation computed sum eq eq eq means factor factor factor factor dimension dimension dimension made global global study study negative negative negative original original vol relative relative relative relative specific specific specific samples samples application application receptive receptive provide provide compute rates rates rates rates proc active active determined determined experimental experimental related connected cortical brain brain comparison comparison larger larger contrast connection fields fields support train dependent modeling modeling morgan department department synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses individual individual advances joint represents connectionist connectionist responses final bias bias bias bias graph maps considered equivalent curve curve curves curves curves curves curves curves limit limit san stimuli capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity efficient classifiers classifiers choice choice choice choice choice significant increase con produce produce derived weighted randomly randomly types types lines lines lines lines lines lines lines lines lines lines entropy entropy entropy actual actual provided provided finally evidence iteration depends achieved measured measured measured measured measured measured discussion increases increases increases increases increases increases assumption assumption excitatory stable stable predictions predictions short synapse synapse synapse synapse synapse synapse synapse theoretical main eds ability development development including kaufmann objective underlying underlying underlying hopfield hopfield account coefficients coefficients significantly edge edge increasing increasing increasing uniform empirical empirical empirical principle leads leads leads principal principal representing pre stored bits bits bits bits bits bottom early magnitude combined combined combined light predict neuronal population recent resolution resolution resolution advantage ensemble ensemble ensemble identical identical identical identical identical identical quadratic quadratic trees subset recently relevant engineering engineering dimensions dimensions dimensions varying compare compare conventional conventional conventional calculated axis axis tions solve studies differential achieve address modified channels improvement storage storage storage storage storage storage sensitive entire increased expression lead suggests predicted predicted predicted alternative alternative correctly occurs occurs occurs setting runs runs strength conclusion critical operator valued interactions differences differences differences differences differences sigmoid measures numerical numerical numerical numerical peak peak peak moody practice asymptotic constrained mateo temperature mechanisms integration integration integration integration integration integration integration integration presence largest drawn drawn sigmoidal sigmoidal california california solid solid assuming variety exist exist exist iii averaged configuration question boltzmann explicit derive derive written solving primary estimating estimating plot plot label distinct distinct distinct distinct distinct distinct modeled modeled linearly linearly dimensionality scales interaction interaction interaction formed select yield focus formation formation labels labels showed showed centers forms forms static similarly discrimination key earlier dashed dashed performing assigned assigned dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic dendritic avoid exploration usa memories plotted illustrated activated activated absolute tests major straightforward identified divided driven delta delta delta delta delta included modes build post post comparing tend orthogonal contained contained prob split issue symmetry physiological sci hold comp comp involved absence realistic leading thresholds predictor overlapping intrinsic trains difficulty relations involving strengths hanson lippmann dotted biases discriminant discriminant fewer possibility scaled reliable notion matched circles transmission predicts equally equally mapped expressions expressions expressions expressions expressions expressions expressions growth derivation analytical analytical analytical analytical analytical analytical analytical analytical analytical lies lies worse nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity comparisons comparisons lin lin tive sites sites sites sites sites sites sites sites sites sites sites located worst sgn sgn sgn arise separately acad calculations implicit gradually geometry geometry geometry geometry geometry fluctuations fluctuations requiring substantially substantially empirically empirically empirically empirically empirically empirically readily biologically ity ity http mod mod measuring limiting aim branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch branch fall maximizes maximizes cal suited substantial substantial redundancy summed irrelevant contribute contribute redundant ear primarily restriction arguments arguments linearity branches branches branches branches branches branches branches branches branches branches branches branches concerned count count count flexibility flexibility flexibility flexibility flexibility flexibility grows grows fails occurred logarithmic grow los los nearby implications exceeds exceeds natl elimination passive meaningful mance bartlett ranging representational representational representational representational perfor evident accounts dendrite mel mel mel mel mel mel mel mel mel mel mel mel mel den counting counting counting counting spherical soma branching dif hippocampus permutation insight ltp impact fold fold interestingly thresholding limitation counts learnable largely graded maximized break randomized randomized randomized restrictions abstraction utilize connec quasi spaced assignments assess param param param manipulation arising attempted gained biophysical biophysical biophysical num playing potentiation potentiation proba emphasize relates exceed increasingly tied indexed nonetheless nonetheless sized sized modifiable els tissue tissue eters eters differing mea lems capacities capacities replacement replacement replacement excess bility inconsistent quantify trainable trainable jointly virtually attempting opponent incorrectly visit formulae evenly equa nmda dedicated contacts contacts contacts compartment repository rel sis creation undergo massive responded responded validated stabilization routine moderately quantified notions permutations permutations biomedical biomedical lowered angeles angeles subsampled compartments terminated classifica boost boost boost boost boost boost boost boost boost boost boost boost throw sults utilization originating permitted nonlin eter southern southern suit cri discriminability logarithmically logarithmically overestimate tionist bers subunits subunits interac beneath danger geometries geometries sured profound steadily steadily targeted analy petersen petersen suitability preparations validating capac capac redundancies subunit implicated confronted confronted pacity terion atively usc usc attachment attributable interchangeable ind partment unfortunate ferences swapped hor izontal confines 
#@Mel_B,Poirazi_P,
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result threshold computation research defined found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence initial estimate connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science science prediction prediction prediction prediction prediction prediction prediction left left left left left left direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction direction activation activation temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal machine motion motion motion motion motion motion motion motion motion maximum range range range range range press press press press learn learn learn learn position abstract applied back back back back back back computational computational computational properties properties properties references due due due due due due due due due due positive positive positive important adaptive propagation context introduction action action action action complex complex hand hand stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical generated generated recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion tion tion tion tion difference difference difference difference difference difference difference difference lower rules learned learned learned learned part part center previous previous previous previous previous previous firing firing firing firing firing firing firing firing cortex cortex cortex good spike spike spike spike spike spike spike spike spike spike spike long long represent represent distributed expected expected expected region observed observed observed observed errors simulations simulations simulations resulting ing ing ing ing total respect respect respect factor potential potential made feedback feedback feedback feedback study study study negative represented desired receptive receptive provide rates rates proc proc proc proc active determined experimental experimental goal goal related connected connected connected connected connected motor cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical cortical mit mit mit mit voltage comparison comparison fields modeling modeling proceedings institute institute institute institute synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses synapses code represents responses responses delay delay delay delay sequences sequences sequences sequences sequences sequences sequences sequences maps cambridge cambridge cambridge cambridge transition top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli detection upper world increase developed area velocity velocity velocity lines lines lines actual nature nature nature nature nature nature inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends achieved measured feedforward describe excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory predictions circuits circuits circuits circuits circuits circuits circuits amount shape synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse synapse supported role role theoretical require eds eds ability hypothesis hypothesis sensory sensory sensory simulated pairs reduced unknown mechanism mechanism mechanism mechanism consistent consistent consistent trials trials trials trials trials trials trials principle details details max pre pre window window window window inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition bottom idea predict predict predict predict predict predict predict neuronal membrane recent recent recent recent property separate reported moving moving moving moving moving moving moving moving moving side side side side side side side side sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski recently recently highly varying varying previously previously observations observations calculated calculated tions tions studies background background positions positions positions positions chain chain chain chain chain chain chain locations separation modified modified modified channels interval increased amplitude amplitude occur occur trial trial trial wide loop white occurs occurs occurs occurs demonstrate strength strength strength critical critical place greater hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian conclusions editors sutton sutton peak peak peak weak suggest encoding presence demonstrated solid solid proportional labeled labeled labeled pulse pulse pulse turn assuming start start selective selective selective selective selective selective selective selective selective selective selective selective selective decrease decrease decrease connectivity connectivity appears perception generating plot metric sensitivity slightly slightly slightly consisting consisting consisting develop mutual applying predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive potentials potentials potentials potentials potentials potentials yield dependence similarly suggested suggested suggested allowed past earlier barto dashed delays delays expansion roughly roughly generation remains initially foundation koch dendritic dendritic dendritic recorded fire fire fire fire fire fire fire figures currents currents currents inter retinal retinal activated activated activated activated activated domains characterized maximal maximal maximal modification spiking spiking spiking spiking spiking spiking post plots plots plots plots plots receives excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation excitation refer notice allowing moore interpreted neuroscience neuroscience neuroscience neuroscience conductance symmetry physiological physiological physiological timing timing sci sci duration bar bar paradigm minimizes neurosci neurosci neurosci received subsequent preferred preferred preferred preferred preferred preferred preferred preferred preferred preferred rat oriented oriented bars explore remain stimulation stimulation stimulation selectivity selectivity selectivity selectivity exhibit exhibit experience circuitry put accurately dotted dotted dotted postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic neu neu examined circles transmission transmission transmission onset onset onset predicts predicts opposite adjusted panel panel precise separated separated initialized initialized simplest mentioned theoretic agreement explanation adapted interneurons starts starts starts ganglion tive closer closer located located monkey monkey monkey monkey monkey monkey monkey arise pulses consequence consequence consequence axon hippocampal hippocampal acad acad circle gradually medical medical recording qualitative preceding preceding preceding preceding summation percent dark dark dark experimentally marked marked marked marked marked recordings solla solla howard howard exhibits poisson anti ture fall occurrence occurrence incorporating conductances conductances song asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric decreased decreased windows windows phenomenon pose lab lab modify tation extensive temporally temporally temporally temporally temporally temporally temporally temporally temporally narrow null null null neurophysiol theories receptors arrival arrival arrival arrival chance chains chains chains chains chains chains occurred alpha striate striate efficacy efficacy occurring neurobiology neurobiology neurobiology salk salk salk salk optimally optimally presentations natl natl fires fires fires utilized governed zhang corre studying conjunction histograms dendrite dendrite dendrite dendrite dendrite dendrite sim soma soma soma soma soma soma reproduce tic tic exposure exposure emergence foundations spatiotemporal ballard ballard jolla jolla kearns kearns arrows arrows arrows arrows arrows route epsp epsp epsp epsp epsp epsp epsp epsp epsp receiving receiving receiving fired fired fitted zipser ure slight slight depression depression depression depression depression constitute ter latency latency alternating rao rao rao rao rao rao rao tween propagating propagating propagating propagating additionally causing preferences breaking evoked evoked avoided pairing pairing pairing pairing cohn cohn biophysical biophysical interneuron interneuron interneuron interneuron dominated potentiation potentiation potentiation potentiation potentiation potentiation neurophysiological hughes hughes retinotopic retinotopic douglas mediated paired depicts macaque win conversely flash responding tively barlow abbott abbott abbott induces exhibited milliseconds milliseconds milliseconds milliseconds milliseconds milliseconds milliseconds milliseconds prevents compu triggered utilizing info info stimulating sponding reversed ers hundreds inhibit inhibit blum cornput neocortical neocortical neocortical neocortical neocortical neocortical neocortical neocortical neocortical neocortical rons rons polarity physiologically exposed exposed emerges progressively triangle neocortex neocortex neocortex lying lying gerstner gerstner comprising periphery arrives arrives arrives compartment compartment sloan sloan tance approaching counterpart comprised enters kinetic kinetic kinetic fovea corn ensuring massive massive 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#@Rao_R,Sejnowski_T,
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values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution method pattern pattern pattern pattern pattern pattern pattern pattern pattern single large large large large large neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns inputs form shows shows signal signal signal signal signal signal simple simple simple simple simple visual visual visual visual visual visual paper small small size net work task task task cells cells cells cells features process process current current current current current current current current current current current current structure memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory response response response response response response response response response response response response response response similar show equation section section section fixed fixed line line line line line line line parameter parameter average average states states states states states states states states states states theory theory gradient obtained experiments experiments experiments experiments experiments experiments experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result result university threshold threshold computation independent independent independent defined defined found found found sequence sequence sequence sequence target target dynamics dynamics dynamics dynamics initial initial constant constant constant constant constant constant terms terms terms terms connections connections connections connections connections connections synaptic synaptic science direction presented presented presented presented presented presented presented presented presented present present present present present temporal temporal range range press sample sample sample sample sample sample sample sample sample sample sample sample abstract applied find properties properties references due procedure important important context context introduction complex complex complex complex complex complex hand hand behavior behavior behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical statistical effect effect effect effect effect parallel recurrent recurrent recurrent recurrent recurrent recurrent recurrent tion energy energy energy difference difference variable spatial lower measure signals signals representations chosen chosen chosen previous previous previous firing firing firing firing firing firing firing firing firing firing firing firing type type cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex binary spike spike long long conditions distributed equations equations equations make make fact fact fact fact fact fact techniques proposed correlation correlation probabilities observed observed minimum tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks total total respect respect respect sum sum sum sum sum performed performed performed called global study study study study study knowledge relative relative specific desired series provide provide provide provide rates rates rates rates rates rates rates rates rates rates active active active active active determined determined determined experimental experimental experimental experimental experimental experimental experimental experimental goal related related posterior connected connected connected connected connected connected gain brain brain brain equal equal equal equal equal equal mit larger larger support support modeling modeling report institute department synapses consists internal individual individual responses responses responses responses exp delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay ai ai framework framework cambridge equivalent experiment solutions solutions curves limit top top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects bit bit bit bit bit bit bit bit bit bit free free free free world basic increase increase con types evidence evidence evidence nature nature nature depends depends constraint biological associative discussion increases increases describe group assumption corresponds complete excitatory stable predictions finding short short common effective effective effective effective implemented implemented assumed main main makes sensory sensory sensory needed needed needed reduced account account account account dynamical dynamical mechanism mechanism mechanism structures trials trials trials trials matching matching operation representing max stored stored stored stored stored stored stored stored stored stored stored stored stored bottom bottom magnitude attention attention attention attention attention attention improved population population population population population population population population correlations element typical reported period period period period array array array array array array array array array array array array array array array recently relevant relevant relevant relevant observations observations observations approximately works module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module module solve solve match match match match match match match match match match correspond correspond studies differential differential differential differential definition background background background background background background symmetric symmetric symmetric entire grant intensity intensity intensity studied studied studied studied studied studied occur suggests trial trial trial trial trial trial trial trial strength hebbian reduce competitive competitive tangent interactions interactions interactions interactions interactions interactions modules modules modules modules modules modules modules modules clear clear asymptotic weak temperature propose taking mechanisms physics external external external external solid solid solid proportional proportional proportional exist selective selective selective selective selective selective selective selective selective selective selective selective selective selective connectivity minima identification denoted denoted attractor attractor attractor attractor attractor attractor acknowledgements areas index perception changing modeled modeled explicitly explicitly simultaneously consisting consisting interaction interaction interaction interaction interaction springer competition competition independently expressed expressed expressed review depending depending stationary correlated correlated correlated correlated correlated correlated overlap solved fraction fraction fraction evolution understanding partition past dashed dashed dashed dashed measurements normalization add remains remains remains remains intermediate initially symbol classified coupling expect figures figures perceptual combinations currents currents inter inter inter sciences plotted plotted candidate coupled characterized gating gating simplicity simplicity straightforward aspects identified identified extra driven presentation presentation presentation presentation attractors situation situation tend tend miller miller miller miller miller essentially characteristic road verlag repeated interested split issue contribution contribution contribution cue cue cue cue cue cue cue cue cue hold hold duration involved write modular modular modular modular modular neurosci neurosci neurosci received received receive situations situations situations minimized remain remain stimulation stimulation access essential experience varied put limitations issues biases matches matches matches fashion giving rest behavioral analytically reliable working working working working working proper presynaptic necessarily onset configurations psychology equally quantities store regime explain seconds isolated established spin ground agreement phenomena phenomena explanation explanation explanation analytical glass inside implementing sections closer precisely monkey monkey monkey afferent afferent scientific english res mechanics mechanics populations populations populations populations populations populations populations reflect capability experimentally experimentally quantitative quantitative effort recordings maintain http operate berlin mod measuring incoming incoming qualitatively qualitatively germany unbiased findings attentional realized consistently gap picture intractable www oxford oxford driving labelled null homogeneous neurophysiol connecting enhancement enhancement grows arranged suppression saturation ments held held imposed imposed efficacy transforms belong arrays presentations presentations overlaps reset ensures periods periods periods encountered evident uni reproduce parietal treatment express cerebral stimulated mem sustained sustained sustained belonging captures characterization influences acknowledge ics sequentially associations unified ple largely listed exhaustive revealed revealed diverse diverse tween par solely england suppressed stands scenario scenario scenario mutually argue exam magnitudes toy decays maintained maintained activate intra intra intra intra march emphasize guided guided guided guided guided guided frontal apparently funded afferents supports supports macroscopic macroscopic macroscopic behave refined experi inactive status coming persistent appearing bridge characterizing sees transduction transduction hyperbolic accordance inconsistent quantify send transforming reflecting appealing meeting artifact ory colleagues colleagues colleagues html totally frequent planck evolves absent remained south resultant electrophysiological stabilize foreground foreground foreground foreground foreground foreground foreground foreground foreground contents contents tomita modulatory substrate actively kuhn supposed fore primates primates primates checked cancel sends directionally tsodyks parisi reproduces reproduces postulated intervening intervening intervening intervening intervening rolls rolls rolls rolls rolls rolls rolls amit amit elicited dynam signaling singapore proportionally proportionally ore iai efficacies stant emulation noticeable noticeable noticeable associa nicely collaterals collaterals collaterals desimone desimone desimone desimone desimone desimone desimone parga parga parga parga parga parga duncan duncan reciprocally reciprocally reciprocally prefrontal prefrontal virasoro runge inferotemporal inferotemporal ineffective ineffective ineffective ineffective mezard cit cit cit cit coherently caption allel satisfactorily kutta realism exert 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#@Parga_N,Renart_A,Rolls_E,
#t13
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#*learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input function function function function function function figure figure figure figure figure figure figure figure time time time time time time time time set set set set set set set set set set set networks number number number number number number number number error state state state results results results results results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information models models models models models models models performance based based based shown shown shown shown shown shown shown shown systems values values values values values values values values values probability probability parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution single single single single single single single single large large local local neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows shows simple gaussian gaussian visual small small small small size size size size fig fig fig fig fig fig fig fig fig cells level current current current current current current current current current current current current current current current current current current current current current cell structure structure structure structure problems random high high high high high memory response response response response response similar similar similar similar similar similar show show show show show fixed fixed real real real real real real average average average average average average average average average average states states states theory note note activity activity activity result result university threshold threshold variables computation research log log defined sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant estimate estimate estimate standard standard standard standard standard standard standard standard standard standard standard computer terms synaptic synaptic science science science science left presented presented present present activation low low low frequency temporal temporal temporal range range press abstract density density density density density density density density density density density density density density properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic important introduction introduction hand behavior behavior behavior behavior behavior stimulus stimulus stimulus stimulus effect effect effect effect effect tion change change change change difference lower rules rules word word word word word word word center firing firing firing firing firing firing firing firing firing firing firing firing firing type cortex cortex cortex spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long conditions tree expected expected equations equations observed observed observed observed observed observed simulations resulting resulting ing ing total total total total total total total total total times elements factor potential natural specific compared application compute rates rates rates rates rates rates rates rates proc experimental connected gain cortical cortical cortical cortical cortical cortical cortical brain mit voltage voltage voltage voltage voltage voltage accuracy comparison larger contrast train train train train train train train train dependent dependent dependent dependent dependent dependent dependent dependent dependent dependent institute words words department loss code code code code code responses responses responses responses directly curve transition limit top top stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity capacity give channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel coding coding coding area area area types types types types types types entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy finally nature nature nature nature nature nature nature nature depends depends biological discussion surface amount amount amount amount amount amount amount amount amount amount supported adaptation adaptation smaller reduced account significantly ratio ratio ratio ratio ratio ratio ratio increasing increasing mechanism mode principle operation details details details direct window bits bits bits bits bottom frame frame frame description description neuronal neuronal neuronal neuronal neuronal neuronal denotes membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane membrane population population population directions robust robust robust robust reported reported introduced sense sejnowski sejnowski recently highly highly highly highly highly varying varying compare calculated calculated calculated yields studies converge rl channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels channels interval organization sensitive sensitive sensitive increased grant amplitude amplitude amplitude suggests deviation deviation deviation wide wide spikes spikes spikes spikes spikes deterministic deterministic white white white pass demonstrate half half half half critical depend depend depend measures measures measures accurate clear temperature temperature suggest suggest suggest encoding encoding encoding strong strong integration turn variety acknowledgements explicit van van van changing changing changing changing changing missing text consisting interaction adding potentials decreases dependence depending correlated correlated correlated correlated influence influence codes codes variation variation densities densities densities densities densities densities densities densities densities densities densities densities densities open open open open labels frames sizes sizes suggested diagram key calculation slow performing sec sec sec sec intervals generation remains calculate calculate calculate msec msec msec msec koch koch koch dendritic precision precision precision precision precision precision precision precision precision precision precision avoid currents currents inter inter maximize specifically specifically phys successfully determining letter closely encoded divided divided presentation plots fine fine fine fine receives excitation repeated repeated strongly showing conductance conductance conductance conductance conductance oscillations content timing timing timing timing timing timing timing timing timing timing sci hold duration comp comp comp comp bar neurosci neurosci neurosci intrinsic decreasing trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains trains origin wiley transformed rise reducing examine respond respond giving comparable gates variability variability affect encode encode encode encode encode encode encode encode cover notion patch patch patch patch patch measurement coefficient trace trace adapt rev nerve nerve nerve pyramidal seconds slowly slowly slowly considerable formalism formalism monkey mation ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion ion acad describing demonstrates fluctuations fluctuations fluctuations fluctuations fluctuations robustness robustness robustness robustness robustness robustness robustness robustness limits experimentally experimentally quantitative reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability reliability calculating mod reaches reaches incorporating conductances conductances conductances conductances conductances physiol physiol physiol traces traces traces traces traces yielding representative representative optimality modify investigation ratios appropriately nat neurophysiol neurophysiol bin tem spontaneous cellular alpha alpha replacing replacing keeping keeping tishby tishby tishby neurobiology implications presentations natl exploring infor utilized ranging irregular bialek bialek bialek respective thomas soma soma israel israel recovery cerebral stimulated mem suggesting bins refers repeatedly repeatedly repeatedly impact balancing std interestingly fly informa liu incorporates leibler encodes encodes encodes encodes encodes markovian expanding classic reflected capacitance gated conduction subthreshold biophysical biophysical mammalian potassium potassium potassium books macaque associates isi abbott macroscopic macroscopic macroscopic thousands normalizing microscopic hodgkin hodgkin hodgkin hodgkin hodgkin info info reversal discretized discretized inconsistent quantify huxley huxley huxley huxley huxley neocortical replicated injected unreliable subtracting carries maxi sliding vivo vivo vivo vivo vivo convolved leakage marder ionic kinetic kinetic kinetic kinetic jitter jitter jitter doubling steveninck steveninck steveninck convey ruyter ruyter ruyter tens newsome jerusalem behaving replicates replicates replicates replicates entropies entropies notions hebrew cient rieke fluctuation fluctuating fluctuating fluctuating fluctuating conveyed excitable excitable bair sodium sodium mainen mainen segev segev segev segev segev unclear epsps conveys vitro vitro excitability poral knight encounter 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#*network neural neural neural neural neural neural neural neural input data data data data data data data function function figure figure time time time time time time time time time time time time time time time time time time time time time time time time set algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output number number system system system system error error results results results results units units units information information information information information order order order order shown shown shown shown systems systems systems systems noise noise noise noise noise noise noise noise noise noise noise noise neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit approach pattern pattern pattern pattern point point image image single single single single single single single single single single single single single single processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing processing control control control control large neuron neuron rate rate rate rate rate test patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis inputs shows shows shows shows signal signal signal signal signal signal signal algorithms algorithms algorithms gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual examples size task task task task task task task task task task task task task methods methods methods methods fig fig fig fig fig field field field field field field process level structure high high response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response response similar similar representation show show fixed line rule rule rule images images images images general general average average average obtained experiments experiments experiments activity activity activity university university university threshold threshold threshold threshold computation computation computation research independent independent independent independent independent independent defined defined found found target target target constant standard standard standard standard standard standard computer computer synaptic science science science science left left left left left left left direction presented presented presented map map map map map low low low low frequency temporal temporal temporal temporal temporal temporal temporal temporal range range range press press press components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components components continuous sample abstract abstract applied applied applied find computational properties properties properties properties references component component component component component component component component due due ieee procedure important mixture introduction action estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical generated tion spatial spatial spatial spatial spatial lower measure measure signals signals signals signals signals prior prior higher higher center firing firing multiple multiple multiple multiple multiple multiple cortex cortex cortex cortex spike spike spike spike spike spike make correlation correct correct observed observed observed observed observed observed simulations ing ing tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks tasks human human human human human human computed performed times times times times times times regions potential study study study study study study knowledge filter specific true true true compared rates proc proc proc proc proc location determined experimental experimental experimental goal related related related constraints connected motor motor motor motor cortical brain brain brain brain brain mit mit larger larger larger contrast source source source source source source source source source source source source source source modeling proceedings institute individual individual advances advances responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses responses difficult difficult bias maps environment view design san top top top stage stage stage effects detection detection detection detection detection detection detection detection detection detection detection detection detection upper vision estimated estimated estimated estimated estimated estimated pages pages pages increase increase increase give give channel derived bounds types lines nature sampling simply measured measured measured measured discussion normal normal normal increases increases tested tested fast fast short common effective effective assumed supported require ability ability ability hypothesis hypothesis hypothesis sensory sensory sensory auditory pairs smaller smaller underlying underlying account functional functional functional fully significantly ratio ratio ratio ratio projection projection projection edge increasing increasing increasing head head special consistent consistent trials trials trials trials trials trials trials filters pre pre making window window window window window window window window window bottom bottom bottom early early early early early early early early early early early early early early early early early early early early early early early early early early early early early early minimize minimize sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal neuronal improved population population discussed resolution pair robust robust separate separate separate element reported reported subject subject subject subject subject subject subject subject subject subject subject side pixels sejnowski sejnowski sejnowski sejnowski sejnowski cognitive recently highly compare previously previously previously conventional conventional approximately subjects subjects subjects subjects subjects subjects calculated axis axis correspond correspond studies studies studies studies studies differential definition separation separation separation separation separation separation separation separation increased increased intensity suggests digital trial trial trial trial trial trial trial trial trial deviation deviation deviation deviation deviation width width pass strength strength row row greater greater greater assumptions reduce reduce differences differences differences peak strong integration integration solid ica ica exist exist selective relationship relationship identification identification areas van longer longer longer factors primary primary plot vertical dept dept dept simultaneously averaging averaging easy slightly slightly scales scales interaction applying events events versus versus potentials focus stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages stages correlated showed showed lee modulation completely similarly earlier earlier smoothing dashed event event event false false false foundation eeg eeg eeg koch koch precision precision precision recorded usa color currents bell bell bell blind blind blind blind blind blind blind blind blind blind retinal plotted activated specifically successfully successfully major major major sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor middle identified identified identified identified differ presentation successful identify literature projections invariance situation identity road conf strongly induced allowing showing neuroscience issue running physiological timing timing timing timing timing timing sci sci sci hold duration vary michael michael michael correspondence leading maximization neurosci principles acknowledgments situations trains trains trains trains bars bars carried layered essential difficulty varied rise rise rise int possibility possibility referred referred reliable reliable reliable reliable variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability variability understand neu neu smallest measurement measurement onset onset onset onset onset onset onset onset onset psychology equally adjusted panel assumes precise precise separated separated separated separated separated separated separated separated separated separated consist baseline baseline detected detected detected attempts averages established established animal histogram indicating rows band sensors sensors derivation analyzed coded spatially spatially tive immediately monkey sounds acad acad acad beginning gradually begin medical arises preceding nsf raw raw greatly populations populations populations populations populations populations pathways tional tional car recordings recordings detecting completion passed remove reliability reliability reliability reliability reliability requirement gave conclude simultaneous feasible sort temporally nat arranged establish lost spontaneous binocular wrong oja oja imaging imaging imaging ranges occurred occurred satisfying height height check mark analyzing removing affected natl natl obstacle reliably introduces tone mouse connect bialek respective displayed displayed displayed surprising histograms histograms monkeys monkeys dif parietal artifacts artifacts artifacts spatiotemporal suggesting shortest locked locked locked locked locked record late late late late late late late late late late late late late late late late late late late late late late belonging park pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter santa santa influences vari vari vari infomax boxes boxes boxes boxes mind crossing cholinergic neurophysiology shorter shorter sig latency latency latency latency latency latency latency latency latency latency latency latency latency latency latency latency latency latency latency latency focal reaction reaction reaction responds magnetic magnetic magnetic profiles corrected ical superimposed evoked brightness brightness attempted exam lobe lobe deconvolution met careful maximally fixation macaque frontal erp erp win eligibility accounted sta sta sta behave milliseconds slopes october october triggered triggered triggered coordination species expense characterizing tial ferent firstly abeles award neocortical neocortical returned anatomy compo bss bss bss bss bss bss separates positives ultimate merzenich vivo vivo reality falling goodness remained ranged fication jitter scatter trend steveninck tim tim ruyter sep spa detections detections began dow behaving behaving activates cardoso rela nents fluctuation fluctuation fluctuating weakness makeig makeig makeig jung jung jung bair mainen latencies latencies latencies latencies latencies exceeded corresponded ponent cent fil knight sual contiguous prevented ration fell sponse tonal acuity mexico mexico mexico neurophys neurophys albuquerque albuquerque albuquerque albuquerque visualizing tang tang tang tang tang tang accompanied berry maunsell iden neurocomputing downward sponses sponses vaadia button emitted identi ended alert isolate overlaid bergman differentially females meister barak extrastriate bitmap victor stdev sepa tection pressed ports electroencephalographic lobes ably ined tivation variabilities variabilities variabilities variabilities revision popula rts rts glance louis mckeown inen jnowski ential erage occipital occipital occipital occipital aft psychophysiology handed 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neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution method method method method method large large large large large large large large large large large neuron neuron analysis matrix matrix optimal optimal optimal form form form form shows shows shows shows shows simple gaussian gaussian gaussian gaussian gaussian paper small small work methods methods methods methods methods methods fig fig fig fig fig process process process process process process process process level level cell structure structure structure random random high high high response response similar fixed fixed general general parameter parameter parameter parameter theory theory gradient obtained obtained obtained note note note activity dimensional result result variables variables computation computation computation computation independent log log log defined initial estimate estimate standard terms science direction present present present present sets maximum maximum maximum range range range range range range range range range range range range range components abstract computational computational computational computational computational computational computational computational computational properties properties likelihood likelihood likelihood likelihood likelihood references references due due due due ieee decision context introduction complex estimation estimation stimulus stimulus stimulus statistical statistical statistical effect effect effect effect effect effect generated variance variance variance cost cost cost cost cost tion tion difference complexity complexity complexity variable assume assume lower lower lower signals chosen chosen part center center center theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound cases firing firing firing cortex distributed distributed equations make make correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation errors errors errors errors errors errors errors errors ing ing ing simulation simulation simulation simulation simulation respect respect respect eq eq eq eq eq eq eq eq eq called called elements means means natural study study study study study study knowledge obtain negative artificial compared compared compared compared compared compared rates rates rates active active motor brain brain brain brain brain equal approaches approaches accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison comparison descent institute loss code code code joint responses exp exp exp maps considered considered considered experiment limit limit limit limit limit limit stimuli stimuli stimuli stimuli stimuli stimuli stimuli efficient efficient efficient efficient efficient efficient efficient full full requires statistics basic give condition condition channel coding coding coding coding coding coding weighted conditional criterion product processes nature sampling biological biological biological covariance covariance denote denote limited limited limited limited limited limited limited limited limited limited common assumed assumed journal journal future sensory sensory account significantly character character structures structures structures trials uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform uniform representing call call numbers numbers numbers international neuronal neuronal neuronal neuronal neuronal denotes denotes denotes population population population population population population population population population population population population population population population population population population population population population population discussed improve correlations resolution advantage pair pair pair pair introduced include sense inference inference inference array recently interest calculated calculated tuning tuning tuning tuning tuning tuning tuning tuning tuning tuning achieve rl rl rl rl rl rl trans observation observation generalized generalized generalized generalized arm expression studied studied studied studied invariant derivative width width setting strength strength strength strength strength strength critical conclusions central central central performs asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak encoding encoding encoding encoding encoding encoding encoding encoding encoding taking physics radial radial radial movements averaged averaged relation tuned easy extraction decreases choosing reconstruction depending correlated correlated correlated estimator estimator estimator estimator estimator estimator estimator codes codes understanding activities activities activities activities activities converges discrimination discrimination calculation expansion sec reduces combining interpolation advantages determines determines prove maximize discussions discussions reason regular determining efficiency efficiency efficiency efficiency efficiency uniformly comparing comparing comparing invariance quickly decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding anderson anderson neuroscience symmetry symmetry symmetry hold hold involved write simplified dayan dayan dayan dayan dayan dayan generalize paradigm paradigm paradigm paradigm paradigm neurosci preferred preferred preferred preferred preferred preferred preferred preferred decreasing decreasing law law law relations estimators mass mass mass helpful applicable biol int int reliable comparable comparable variability proved encode statistically understand neu concepts integer analyze illustrate assumes fisher fisher multivariate amari amari amari amari amari amari contributions contributions motivated asymptotically asymptotically asymptotically asymptotically asymptotically distinguish analyzed improves improves coded turns turns turns turns cut cut cybernetics preceding fluctuations argument people greatly treated compares compares gen maximizes maximizes ordered chen comments unbiased unbiased cor contribute uncorrelated cybern notes japan zemel zemel generality primate satisfying settings sompolinsky ensures zhang corre negligible expanded enhance uni insight cpu relies agree eqs seung implicitly valuable interestingly interestingly baldi baldi johnson johnson johnson consecutive discharge unchanged maintaining maintaining rao rao rao rao rao rao rao rao rao rao rao convenience quasi quasi regularity aij aij guess formance formance denoting wise wise wise wise confirmed abbott abbott abbott abbott abbott abbott abbott det lecture expense lation agrees pouget pouget pouget suffers broadly assessment lnp lnp receivers receivers acknowledges modern facts neglected neglected sur sur decode degrades murata murata murata murata murata murata hood degrade simula accuracies accuracies accuracies accuracies cancel cient translational translational dissimilarity neglecting georgopoulos georgopoulos georgopoulos implication acknowledgment shi yoshizawa faithful faithful faithful faithful riken riken likeli saving saving notations arrangements attracting heiligenberg heiligenberg anonymous cram cram cram cram cram cram cram cram 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#*network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time set networks networks networks networks networks networks number number system system system system state results results results problem models models models performance based based based based based based based based based based based based based based based based based based based based based based based based based based based space weights weights weights weights weights case case case case order order order shown shown shown shown shown shown shown values values parameters parameters weight weight weight weight functions functions functions functions functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons method point point single single large large large large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns patterns patterns inputs inputs form form form shows signal simple simple simple paper small small small small small size feature net fig points field process process current current current memory memory memory memory memory memory memory memory memory memory memory show show equation fixed fixed fixed rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule rule general general general general real approximation approximation approximation approximation approximation approximation theory gradient term term term term term term term term term term term term experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity activity result variables defined defined defined defined sequence sequence dynamics dynamics dynamics dynamics constant constant constant constant constant synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic science science left direction direction direction present activation temporal temporal temporal temporal temporal sets maximum range range range range range range range range range learn learn abstract applied applied applied applied applied computational analog analog analog references due due due due positive positive positive positive positive important important introduction action action complex hand hand hand hand circuit circuit circuit circuit circuit behavior behavior stimulus effect effect generated generated cost cost cost recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent change change change change change change difference difference difference variable variable variable variable assume assume rules rules rules rules rules rules rules rules rules rules rules rules rules rules part firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing firing required good good good good spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike long long long long long long long conditions conditions conditions conditions conditions conditions conditions equations equations equations fact fact proposed correlation correlation correlation correlation correlation correlation correlation observed observed finite simulations simulations resulting ing ing ing ing total computed respect sum eq eq eq eq eq eq eq eq eq times times potential potential made made made made feedback feedback feedback obtain obtain negative negative negative relative compared cross cross cross cross series define rates rates rates rates rates rates rates rates rates rates rates rates proc proc determined determined goal related motor cortical cortical brain brain equal mit mit contrast update update update train train train train train synapses synapses synapses synapses synapses synapses considered cambridge transition limit limit limit top effects effects significant approximate increase produce produce derived levels velocity velocity velocity types processes nature nature inhibitory inhibitory inhibitory inhibitory depends depends depends simply achieved achieved measured measured measured discussion discussion increases increases increases arbitrary corresponds excitatory excitatory excitatory excitatory excitatory excitatory finding amount amount amount amount short short short short short assumed assumed shape synapse require main makes makes smaller ratio york increasing head head head mechanism special leads making magnitude magnitude produced description membrane membrane improve recent correlations correlations correlations correlations correlations correlations correlations exact exact takes apply side side relevant relevant varying conventional approximately works tuning tuning tuning tuning tuning tuning yields correspond differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential differential definition symmetric interval interval interval interval interval organization grant amplitude lead lead studied studied suggests spikes spikes spikes spikes spikes spikes derivative derivative predicted width generally strength strength strength strength strength strength strength strength strength greater hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian reduce depend depend depend depend differences differences peak weak integration drawn demonstrated turn assuming relationship relationship relationship iii iii derivatives derivatives denoted areas areas areas explicit relation van van derive derive ways plot tuned tuned tuned tuned tuned tuned tuned dept modeled implement averaging averaging averaging applying applying applying shift shift shift versus versus potentials potentials decreases dependence dependence dependence dependence depending open approximations lee lee forms approximated approximated approximated approximated activities allowed sign sign diagram slow slow measurements classical sec sec intervals intervals intervals roughly roughly roughly roughly roughly remains remains valid valid filtering fire fire fire fire fire figures figures figures activations usa bell determines illustrated discuss discuss holds phys middle identified effectively driven driven driven driven driven driven delta wij wij wij wij wij wij wij wij wij wij wij spiking spiking spiking spiking post fine receives characteristic excitation refer refer refer soc repeated repeated repeated induced induced issue return sin timing timing sci sci vary write realistic neurosci neurosci neurosci neurosci neurosci situations trains trains trains trains trains trains origin unlike wiley exponentially strengths strengths strengths integral integral integral postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic postsynaptic reducing reducing biol plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity plasticity presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic presynaptic neu induction trace adapt analyze opposite opposite rev illustrate changed precise hebb hebb ith ith store contributions arbitrarily explain integrate integrate integrate integrate integrate integrate burst burst burst burst burst burst burst burst burst burst residual residual slowly slowly defining defining fairly fairly inside satisfied precisely commonly pulses hippocampal acad preceding fluctuations fluctuations fluctuations robustness integrating people limits limits understood transient quantitative continuously continuously continuously maintain maintain maintain maintain robinson poisson poisson poisson poisson poisson anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti anti reaches synchrony tank tank conductances song substantial asymmetric wang traces instantaneous instantaneous shifted shifted cybern accomplished arguments arguments drift drift drift drift drift drift drift drift drift drift vestibular acts ordering ordering purely nonzero systematic numerically ranges occurred check occurring definitions monotonically imply integrator integrator integrator optimally presentations natl sompolinsky reset reset governed periods sion zhang induce consequences dif tic tic fish bursts bursts creating eqs seung seung seung seung seung seung seung seung jump summarize lag approx ure maintaining depression depression shorter latency latency descriptions causal pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing pairing illustration remainder argue decays lobe maintained potentiation potentiation potentiation compatible relate paired cij cij oculomotor oculomotor oculomotor abbott ation vanishes vanishes tune tune milliseconds interspike rewrite reciprocal tonic tonic tonic tonic tonic persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent persistent info reversed reversed ate autocorrelation autocorrelation tial quantify influenced lated dominates cornput cornput cornput cornput ron hemmen hemmen neglect subtracted core accumulate ooo gerstner gerstner vanish cur quantitatively reality suffice lags elec stabilize neglected shortly syst tens formulas stabilization stabilization stabilization stabilization adv wagner ted sebastian upward cancel traditionally nth ative abstr synapfic poo cog accord han simu markram cancellation georgopoulos persistence persistence persistence tain sketched quantifies kempter kempter downward roberts pairings shamma prefrontal opposing inhomogeneous llll ermentrout xie xie xie xie neg succeeding cid dirac illl differen conventionally conventionally imations lobes lobes lobes iiiiiiii iiiiiiii illill biophysically 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#*learning learning learning learning learning model model model model model model model model model model model model model model model model model model model neural neural input data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function figure figure set set set networks networks networks networks networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number error error error error results results information problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden space weights linear linear case case case vector vector vector vector vector shown shown shown shown values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise unit distribution distribution distribution recognition method method approach approach approach approach approach approach point point point single single single large large large large large large large rate rate test test test test analysis analysis analysis analysis class class class class matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal inputs form form form form form form form form form form form form form form algorithms simple simple simple gaussian gaussian paper paper paper examples size feature work task methods methods methods methods methods methods fig fig fig fig step step step step step step step points field classification level current structure structure structure structure structure structure structure structure structure structure structure structure structure problems problems problems problems random random high high high show equation fixed fixed fixed fixed fixed images general general general general speech speech speech parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation average average average average average theory theory obtained obtained obtained obtained obtained obtained obtained term term term term term note dimensional university variables variables variables variables computation computation solution solution solution research research independent independent independent independent independent log log log log log log log log log defined defined estimate estimate estimate estimate standard standard standard terms distance distance distance node node left left present present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine maximum range press press learn components components components components components components components nonlinear nonlinear sample sample sample sample abstract applied applied applied applied applied applied applied find computational computational convergence convergence density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component positive procedure procedure procedure procedure important important mixture mixture mixture mixture mixture mixture mixture mixture context introduction complex complex complex complex complex complex estimation statistical dynamic generated generated variance cost complexity assume assume lower lower rules rules signals prior prior prior prior prior prior prior prior bound cases cases required required required required long tree distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov make fact techniques length length correct observed observed finite minimum resulting resulting resulting resulting classes ing ing regression regression regression regression regression computed computed computed computed computed computed performed performed performed means means means factor factor optimization optimization optimization optimization optimization optimization made made applications em em em em em em em em em em obtain artificial artificial relative specific specific true true true true true compared compared application application define compute compute compute compute compute compute compute compute rates proc proc goal related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions distributions distributions distributions distributions distributions mit comparison larger update dependent dependent source source source source source source source source source modeling modeling selection selection selection selection technique joint joint joint joint final addition addition addition addition graph framework framework framework framework framework framework framework framework framework framework framework framework framework framework framework computing equivalent directly hinton hinton additional view estimates limit stage stage efficient full approximate approximate approximate statistics statistics free free free free free free free world produce weighted conditional conditional conditional levels criterion criterion provided finally evidence nature sampling simply simply achieved achieved discussion covariance covariance covariance normal normal normal normal normal normal normal normal normal normal increases arbitrary arbitrary denote denote denote inverse corresponds corresponds complete predictions predictions assumed assumed require require require eds eds journal journal square pixel instance instance instance makes including including fit objective objective objective objective objective probabilistic probabilistic typically typically functional functional functional unknown unknown fully jordan jordan jordan interesting testing special special structures structures structures structures structures structures structures uniform principle principal pre experts attention choose added sources sources sources sources sources sources description description predict denotes denotes exact exact separate separate typical practical practical practical include include identical identical identical trees inference inference inference array relevant dimensions achieve sparse mixtures chain separation separation separation separation separation bounded parts expression concept matrices touretzky generally generally generally demonstrate runs runs conclusion minimal minimal assumptions assumptions competitive differences sigmoid bayes bayes presence solid solid intelligence intelligence labeled turn assuming minimizing minimizing averaged manner acknowledgements reference digit digit digit digit monte van construct carlo edges produces produces solving solving stability mathematical student student averaging averaging averaging averaging averaging averaging linearly infinite text text belief integrated integrated predictive predictive predictive predictive predictive expectation expectation select extracted extracted family family family reconstruction reconstruction stages correlated interpretation open restricted updated approximations approximations forms forms forms approximated digits key dashed dashed reduces reduces reduces reduces iterative iterative iterative penalty closed visible visible msec assigned assigned assigned assigned classified david precision precision precision precision avoid existing handwritten includes includes weighting blind blind blind instances instances batch plotted priors priors priors priors priors priors priors domains holds discussions simplicity simplicity simplicity determining determining identified closely suitable society encoded computationally latent latent computations computations computations post post mackay mackay ten refer notice graphs interested dis follow criteria criteria gray quantity involved dayan nips maximization maximization automatically attempt mixing mixing mixing mixing mixing mixing mixing situations presents unlike parametric parametric overfitting overfitting overfitting overfitting put involving optimized hessian hessian hessian divergence graphical graphical graphical graphical graphical graphical graphical graphical graphical dataset dataset dataset dataset dataset dataset ml ml ml ml ml ml ml existence ideas mse mse mse investigated applicable variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational analytically analytically analytically dependencies office office maximizing affect analogous naturally naturally illustrate quantities quantities quantities quantities quantities quantities quantities quantities quantities quantities logistic academic neal averages integrate years histogram cos inequality inequality directed directed trivial analyzed guaranteed guaranteed guaranteed fairly analytical tractable tractable tractable london london turns turns snr snr snr precisely bishop controls probable calculations optimize optimize optimize optimize definite conjugate conjugate conjugate conjugate conjugate conjugate integrating integrating understood amounts peter treated music ity robinson price mod characterize ture limiting limiting limiting fall fall fall fall fall popular hyperparameters marginal marginal marginal marginal marginal marginal green logp logp logp boston conditioning jaakkola jaakkola ghahramani ordinary ordinary ordinary ordinary college intractable intractable intractable intractable intractable intractable feasible proportion modify restriction restrict conditioned conditioned optimizing optimizing resources approximates approximates reconstructed royal generality breiman satisfying replacing keeping exploit generalizes saul mental histograms belongs laplace multiplied treatment omitted omitted omitted bagging informative draw extensively variants parents severe divide uci incorporates misclassification misclassification misclassification kluwer ber ties emerge emerge emerge emerge kurtosis discriminative junction mdl mdl ical stem covariances multinomial param transparent avoids penalized penalized equality exam num denoting denoting regularized efforts considers smyth overhead overhead noting proach dirichlet dirichlet dirichlet termed mcmc xly commercial els nil nil nil intensive rewrite eters struc mix gorithm housing resembles remark opti factorized dim dim dim satisfactory impractical transforming jointly jointly house reflecting proportions proportions proportions proportions tribution compo sharply peaked peaked rasmussen ples emerges bss bss bss functionally meth ultimate zoubin implied ods factorization spirit gence iterating compromise acyclic focusing penalizes emerged facilitates unobserved mization icann posteriors posteriors posteriors posteriors posteriors posteriors posteriors posteriors posteriors posteriors posteriors posteriors conver colt attias attias attias attias attias nth vast jensen jensen draws heckerman nent responsibilities gatsby gatsby penalizing overfit widespread camp ogp ogp justifies renders waterhouse spheres ucl queen richardson dag looo prefers collectively regularizing ors batches carl incre divisions divergences ifs norwell drastic cosh engines ual factorizes factorizes expo precisions precisions precisions facilitating xio buffalo buffalo bic bic individ quanti hagai hagai cision dlog unresolved elegance incorpo wcin tightest baysian nential 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function figure figure figure figure figure set set set set set set set set set set set set set set training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number error results results results results results information information information information information problem problem problem problem problem problem problem models models based space space space space space space linear case case order shown values probability probability probability probability probability parameters parameters functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach point point point point point point point single processing processing control large large large large large large analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class optimal optimal optimal algorithms algorithms algorithms algorithms algorithms paper examples small small small size size size size size size size size size feature feature feature feature feature feature work work task methods fig points features classification process process process level level structure structure structure structure structure structure structure structure problems problems random random random high similar similar show equation equation equation equation fixed fixed parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average average average average theory theory theory theory theory obtained obtained term term note note note experiments experiments result result result result result variables variables variables variables solution solution log log log log log log defined defined defined constant estimate estimate estimate standard terms terms science presented phase frequency frequency machine machine machine object object object object object sets sets sets maximum range press learn learn components basis basis basis basis sample sample sample sample sample sample sample sample sample sample sample sample sample abstract computational computational computational computational convergence convergence convergence convergence convergence likelihood references stochastic due due due positive procedure important mixture mixture introduction hand hand hand statistical statistical statistical statistical statistical statistical statistical generated generated generated variance variance variance search search tion complexity complexity complexity complexity complexity complexity complexity complexity complexity assume lower rules measure measure measure measure measure higher part part bound bound bound bound bound bound bound type required required conditions distributed distributed bayesian expected expected expected expected expected expected expected expected expected expected expected expected expected expected equations fact techniques techniques proposed observed observed observed observed scale finite finite finite simulations minimum minimum minimum minimum classes classes ing ing ing total regression respect performed eq elements means optimization dimension natural global global study knowledge knowledge em em obtain obtain artificial relative specific samples samples samples samples samples samples represented true true true true compared application series define define objects objects objects objects objects distributions distributions equal equal mit steps steps accuracy accuracy accuracy comparison support dependent source source source modeling selection selection selection selection selection selection report loss loss loss loss loss loss loss loss loss loss version version version individual advances exp exp exp exp exp exp exp considered equivalent curve curve solutions curves estimates estimates estimates estimates limit effects determine determine determine determine determine classifiers upper upper upper upper upper upper requires requires requires significant statistics statistics statistics estimated validation validation validation condition derived derived derived derived derived derived randomly randomly conditional clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed developed criterion bounds bounds bounds bounds bounds bounds bounds lines entropy entropy entropy entropy entropy entropy entropy product finally processes depends depends sampling constraint measured technical arbitrary group denote denote fast limited limited limited inverse inverse inverse inverse inverse inverse inverse inverse inverse complete complete stable predictions effective effective effective effective effective assumed assumed assumed supported role theoretical theoretical hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance cluster cluster cluster cluster cluster development smaller underlying combination functional unknown unknown jordan interesting york york segmentation consistent consistent structures structures structures structures uniform uniform uniform uniform empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical empirical principle principle principle principle principle principle principle principle principle language details details numbers max max supervised decay added predict discussed correlations resolution pair robust typical typical typical sense sense sense inference inference inference inference inference inference inference subset recently relevant sufficient unsupervised unsupervised observations observations observations observations observations teacher calculated tions solve yields yields yields yields yields yields converge definition definition evaluation bounded bounded bounded bounded bounded risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk risk grant exists studied occur deviation deviation deviation deviation deviation deviation predicted predicted predicted predicted predicted alternative deterministic clusters clusters clusters clusters clusters clusters clusters clusters clusters occurs setting critical critical critical critical critical critical critical critical minimal minimal minimal minimal minimal minimal minimal conclusions editors measures designed designed performs asymptotic asymptotic weak temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature reduction drawn solid relationship relationship iii iii averaged introduce groups annealing annealing annealing annealing annealing annealing annealing question denoted monte monte monte van carlo carlo carlo index transitions label vertical confidence confidence confidence metric missing averaging averaging infinite infinite physical mutual frequencies frequencies minimization minimization springer quality quality quality expectation decreases yield choosing choosing choosing extracted extracted extracted focus review estimator estimator evaluated evaluated open controlled centered sizes key dashed measurements expansion fitting fitting neighborhood neighborhood neighborhood generation remains calculate sufficiently foundation precision precision precision precision precision precision precision retrieval determines vapnik vapnik uncertainty domains absolute characterized characterized characterized texture uniformly suitable suitable maximal maximal maximal maximal divided divided literature plots verlag stopping stopping return return generative generative gibbs gibbs quantity usual generalize minimizes hypotheses hypotheses hypotheses hypotheses hypotheses extract extract minimized employed wiley overfitting overfitting overfitting essential exponentially estimators integral fashion applicable reliable reliable statistically cover cover cover cover cover cover cover cover cover notion analogous induction induction necessarily predicting created der taylor precise observe grouping defines defines defines defines defines defines integrate histogram histogram histogram histogram stop inequality inequality inequality costs analyzed growing growing coded tive sys widely widely forces mation mation mation opt depicted radius fluctuations fluctuations fluctuations mechanics mechanics mechanics robustness limits applies empirically empirically consistency generic parameterized solla haussler haussler haussler formulated ity ity ity berlin summarized ture ture aim reaches occurrence occurrence occurrence asymmetric asymmetric asymmetric asymmetric asymmetric asymmetric enables germany conclude deviations deviations deviations cumulative consistently phenomenon saddle saddle guarantee guarantee investigation fix acm acm acm acm acm arguments member controlling plays simplify held held held biased occurring tishby tishby observing observing fail north exceeds moments sompolinsky document schapire holland histograms searching uni competing laplace israel membership april infer indicator indicator reader reader kearns kearns kearns theoretically partitioned seung seung statement alternatively vari ball ball learnable temperatures temperatures temperatures temperatures temperatures rigorous annals piece solves solves solves covering inferred inferred inferred inferred distinction opper ical assignments german suppressed auxiliary tight param avoids summarizes distri tems realizable realizable approxi approxi mathematically bounding denoting expand maximally wise depicts exceed increasingly buhmann buhmann buhmann buhmann buhmann covered weaker enforce sam tively universit permit prevents prevents hofmann eters struc struc mini differentiating resp resp achievable uniqueness generarive institut institut exper finer finer december ters ples marcus cardinality cardinality cardinality cardinality cardinality cardinality resolved informatik informatik era era era era spirit iterating compromise appro appro enforces bonn bonn bonn minimizer minimizer minimizer minimizer minimizer monotone ized supposed ysis imum imum amsterdam publishing rises mir mir mir excluded approxima proce fiir fiir inte mal rigorously heidelberg named lay supervision clus ponent continuation adopting overfit datum lowering originating logn generatire generatire iai cri ations pervised integrand rli rli rli bernstein bernstein vised revealing formalize genera mated dyadic balls balls ala sumption plug plug plug plug joachim butions advocated puzicha unsu erm erm erm iments loc finest istic determin din informally soo hnction regulates qual interscience terion ameters dures lth pirical pirical devi differentiability jli hem hem cobh repr protection logk methodological weighs unsuper parameterizes rth 
#@Buhmann_J,Held_M,
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#*learning learning learning learning model neural neural neural input input data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function set set set set set set set set set set set set set set set set set set set set set set set set set set set set set networks training training training training training training training training algorithm output number number number number number error error error results results information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem based based space space space space space space space weights linear linear linear case case case case case case case case case case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown systems systems values values values values values values values noise functions functions functions recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method pattern pattern pattern pattern pattern pattern pattern pattern pattern point point point point processing processing processing processing local test patterns analysis class class matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal form form form form form shows shows shows signal signal algorithms algorithms algorithms algorithms algorithms simple simple simple paper examples examples examples examples small feature work work methods points points points points points points features classification classification problems problems problems similar similar similar show show show show show show section section section section fixed line rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images general general general real approximation theory theory term term note note note note note note note note note note result result result result result result result university university university threshold threshold threshold threshold variables variables variables variables variables variables variables variables variables solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution independent defined defined defined found found found constant estimate estimate estimate terms terms terms terms distance direction machine maximum press press press basis abstract find find find find find find computational references component positive positive positive positive positive positive positive positive positive positive positive introduction estimation estimation estimation estimation estimation estimation estimation statistical generated parallel cost cost cost cost cost change assume chosen chosen higher theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound cases cases cases cases cases conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions equations equations equations fact fact fact techniques region region region errors finite resulting total regression regression regression regression regression regression regression regression regression regression regression regression respect sum sum eq eq mapping mapping means means optimization optimization dimension dimension dimension global global global global knowledge negative negative negative negative original samples samples desired define define define define define define define compute compute determined determined determined goal goal related constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints equal equal equal equal equal approaches mit accuracy contrast support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support train train train dependent nets report report report loss loss loss consists kernel kernel advances advances represents final ai ai ai ai cambridge cambridge computing computing equivalent solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions solutions limit determine classifiers choice choice choice statistics speed basic pages validation give give give give condition condition condition condition condition condition condition condition product product finally constraint constraint constraint constraint discussion discussion discussion normal normal normal technical technical technical describe arbitrary denote denote denote denote denote denote denote close corresponds complete proof proof proof proof finding finding finding amount assumed objective objective objective objective objective objective objective objective objective objective objective objective objective objective objective pairs needed functional unknown jordan block programming programming programming programming programming programming york edge details details details details max max minimize minimize minimize choose choose choose property takes takes element element practical introduced introduced include subject subject subject machines machines machines machines quadratic quadratic subset subset engineering interest sufficient sufficient sufficient previously tions solve correspond diagonal address definition symmetric generalized generalized generalized interval risk exists studied occur occur occur occur wide move occurs operator depend depend editors central central central bayes bayes clear taking minimizing min min min min minima force question reference suppose suppose suppose suppose suppose construct construct index solving solving mathematical changing modeled explicitly linearly linearly electrical easy slightly unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique unique minimization implies implies implies john john choosing family family family family family dependence interpretation solved densities labels soft margin margin margin margin margin margin margin margin completely similarly similarly constants allowed measurements expansion convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex fitting penalty penalty remains sufficiently construction construction david formulation formulation formulation formulation formulation bell vapnik vapnik vapnik vapnik mozer holds holds holds holds holds holds holds holds holds structural determining straightforward straightforward straightforward sensor suitable suitable differ maximal svm svm svm svm svm svm svm svm svm svm refer refer notice prob interested hold hold hold satisfy satisfy notation notation usual dot generalize minimizes minimizes satisfies satisfies acknowledgments extend remain wiley wiley hessian hessian hessian hessian hessian dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual scalar tech analytically workshop removed examined necessarily necessarily necessarily necessarily rank algo mapped improving defines advanced rows ment inequality inequality costs separable trivial trivial guaranteed guaranteed lies lies handle inside tive satisfied satisfied strictly strictly strictly strictly strictly strictly strictly strictly strictly strictly constructing choices immediately immediately hyperplane hyperplane hyperplane hyperplane hyperplane products laboratories inversion implicit definite annual argument requiring amounts share share employ pittsburgh fall semi simultaneous room proofs indices indices indices indices indices indices indices indices accomplished lagrange lagrange lagrange lagrange lagrange lagrange acm hyperplanes hyperplanes discovery nonzero generality multipliers multipliers multipliers multipliers multipliers multiplier fits convenient satisfying analogy replacing interpret reasoning imply imply imply imply exceeds substituting substituting motivation bartlett separating separating separating corollary corollary falls encountered lawrence omitted reader reader horn eqs sons sons statement implicitly alternatively summarize adopted insensitive johnson mechanical smola smola smola smola empty lem unchanged approx geometrical svms svms guyon uniquely expanding smoothly centre theorems theorems convenience boser exception letting australia continuity burges burges burges burges burges burges burges burges arising penalized equality equality rithms met emphasize retain enforce enforce enforce port williamson october mini mini mini mini differentiating strict strict strict strict strict technologies technologies circumstances lagrangian uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness uniqueness christopher jersey imple loosely loosely loosely loosely loosely loosely mining polarity polarity holmdel gram gram gram coincide coincide contributes petsche maxi sliding complement tube tube tube tube tube wisconsin edition south charles svs corn slack kuhn polar cortes primal primal primal primal primal primal primal primal primal primal primal primal primal primal primal tutorial tutorial attracted coincides ness imation ities posteriors colt workers mercer solu wolfe penalties necessity ies ies ies ies ies convexity convexity convexity convexity convexity convexity deformable wishes crisp crisp crisp crisp mangasarian rli sit primed schslkopf schslkopf schslkopf schslkopf eij transport lucent lucent lucent ifp rests ilwll objec nohl positivity positivity uation wll roger tucker neurocolt sociated nts alp adelaide adelaide extendable rigidly aft exerts jective definiteness definiteness definiteness equalities fletcher semidefinite submatrix oti constr 
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#*learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set networks networks training training training training training training training training training training training training training training training training training training algorithm number number number number number number number number number error error error error error error error error error error error error error error error error error error error error results results results results problem problem problem models performance based based based based based space space space space space space space space space space space space space linear linear linear linear linear linear linear linear case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order shown shown shown shown values values values values values values values values values values values probability probability parameters parameters parameters parameters functions recognition method approach approach approach pattern point point point point point large large large rate rate test test test test test test test test test test test test test test test test analysis analysis class matrix matrix matrix matrix matrix optimal optimal optimal form form shows shows shows shows gaussian paper paper examples examples examples examples examples examples examples small size feature feature feature feature feature feature feature feature feature feature feature work task methods points points points field classification process trained trained high high high high similar similar show section section section section section section section section section section section section fixed line rule rule rule rule rule rule rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors generalization parameter parameter parameter parameter parameter parameter parameter approximation approximation theory gradient obtained obtained note note note note experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional result result result threshold computation computation solution research research log log log log initial constant constant estimate estimate standard standard computer distance distance science prediction prediction prediction prediction prediction prediction direction presented map map present machine sets press components basis basis abstract find find references component component due positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important decision decision decision decision decision decision decision decision introduction statistical search change change change change complexity rules previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound cases cases required good good make make fact techniques techniques techniques length length correct correct errors errors errors errors errors errors errors minimum minimum minimum minimum minimum minimum regression performed called called called times elements mapping mapping optimization dimension dimension dimension dimension dimension dimension made made made made knowledge vol artificial relative relative compared compared application cross series provide define define compute compute compute compute perform perform constraints constraints equal equal mit larger support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support support descent dependent selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection proceedings loss version technique technique consists consists consists consists kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances ai ai ai ai ai ai ai computing computing experiment curve curve curves curves curves estimates conference conference classifiers upper choice choice choice choice choice choice statistics free estimated pages validation con produce derived derived derived randomly bounds bounds bounds bounds product product actual actual actual finally constraint achieved covariance covariance increases denote denote transformation transformation transformation assumption assumption assumption assumption assumption complete surface proof rbf rbf rbf rbf shape theoretical require ability easily noisy noisy probabilistic smaller account account account functional functional functional functional functional functional functional functional functional functional coefficients testing york edge trials database database database database database database database database database database leads leads principal call call max max international normalized normalized idea idea idea minimize choose choose description predict predict improve exact takes takes element element apply introduced introduced introduced identical machines machines machines machines machines machines side quadratic previously works pca achieve diagonal diagonal definition bounded improvement entire constructed lead concept concept concept derivative derivative correctly correctly width width width generally conclusion assumptions depend accurate constrained largest demonstrated proportional labeled radial minimizing min introduce introduce introduce suppose suppose digit digit pro edges describes describes implement category category category category linearly involves remaining minimization minimization springer quality implies expectation expectation expectation expectation choosing depending estimator evaluate centered centered margin margin margin margin margin margin margin dashed performing classical classical classical purpose purpose closed calculate norm norm norm classified classified handwritten box box box box box figures kernels combinations eigenvalues eigenvalues subspace subspace vapnik vapnik vapnik vapnik vapnik vapnik extension holds holds holds discussions characterized tests differ maximal maximal svm svm svm svm svm svm plots tend kind interested split split lie lie categories notation quantity dot dot minimizes acknowledgments bars origin origin remain powerful wiley poor replaced preliminary dataset dataset fashion analytically analytically authors maximizing eigenvectors eigenvectors func notion removed removed removed removed smallest smallest smallest smallest closest concepts predicts predicts changed subsets taylor precise mapped mapped shapes submitted defines mentioned mentioned stop inequality inequality inequality separable separable separable separable separable separable separable separable distinguish satisfied organized hyperplane hyperplane hyperplane products controls recognized definite geometry radius radius radius radius reflects reflect reflect red leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave haussler span span span span span span span span span span span span span span span span span span span span span span span span http berlin hyperparameters hyperparameters enables enables replace semi comments unbiased deviations deviations jaakkola specifies notes proportion sv formally lagrange hyperplanes hyperplanes discovery turned establish generality multiplier tools check removing removing belong intuitively performances lip separating separating corollary introduces surprising sphere sphere sphere sphere sphere dif diameter diameter cancer cancer cancer cancer horn passing card ball smola smola empty svms svms svms svms svms svms svms svms svms vec vec ent exhaustive bank pointed sigma sigma sigma opper tradeoff flat flat tight param clas clas burges equality labs considers paris unconstrained spanned misclassified france discusses esti refined williamson eters treating article remark lecture ferent shawe breast breast breast breast err fill tors tors mining incorrectly concerns gram ters ooo att computable putation noticed postal postal postal postal postal violate tutorial tighter coincides mar icann parame rescaling rescaling rescaling rescaling rescaling rescaling rescaling rescaling rescaling rescaling rescaling rescaling rescaling rescaling ninth mate justify penalizing penalizing functionals functionals functionals functionals stays winther rescaled rescaled rescaled hyperparameter iix ixi ixi kij haffner gin cial manage pred pred opened patrick chines scholkopf scholkopf fills vladimir noteworthy ttt artifi ction sifier parallels ellipsoid ellipsoid ellipsoid enclosing enclosing enclosing enclosing sifiers olivier erro understandable basics vlad 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural input input data data data data data data data function function function function function figure figure figure figure time time time time time time time time time time time time set set set set set set set networks networks networks networks networks networks networks training training training training training training training training training training training training training training training training training training training output output number number system error error error results results results results information information problem problem problem problem performance performance performance weights linear linear linear linear linear linear linear linear layer case case case case case case case case vector vector order order order shown shown shown systems systems systems values probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight functions functions functions functions distribution distribution distribution distribution distribution method approach point point point point point point single processing processing control large large large large large large large test analysis class form form form form shows shows shows shows simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples small work step step step field field field process random random similar show show equation equation equation equation equation fixed line line line line line line line line line rule rule rule rule rule rule vectors vectors vectors vectors general general general general general generalization generalization generalization generalization parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory obtained obtained note result result result result result solution solution solution solution solution solution research defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics terms terms terms terms terms terms terms terms terms left left map present sets sets sets sets sets sets sets sets sets sets sets range press press outputs abstract back density references due due due procedure introduction statistical dynamic tion complexity complexity variable lower lower rules rules rules rules rules rules rules rules rules rules rules learned cases cases binary equations equations equations equations equations equations equations equations equations equations equations equations equations equations equations make observed errors errors errors simulations simulations simulations simulations simulations simulations simulations resulting resulting classes respect multi made natural applications applications study specific compared constraints distributions distributions distributions power mit mit comparison comparison larger fields dependent dependent advances advances joint joint final exp addition considered cambridge cambridge computing solutions solutions solutions solutions curves curves limit limit limit top stage stage determine upper upper requires choice statistics free free free free free randomly randomly conditional conditional types lines lines lines lines lines processes discussion technical increases describe describe arbitrary arbitrary arbitrary limited close predictions predictions predictions predictions finding finding amount short common shape generate theoretical eds eds instance easily noisy noisy noisy noisy noisy noisy noisy including underlying underlying reduced dynamical dynamical dynamical dynamical functional functional functional fully fully significantly increasing special special consistent leads leads making making making bottom supervised supervised supervised supervised supervised supervised decay attention attention combined choose perceptron perceptron perceptron perceptron improve recent recent exact exact exact exact exact exact exact exact exact exact exact exact exact pair typical apply apply recently recently relevant interest conventional teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher solve solve studies studies background separation symmetric symmetric generalized generalized expression studied studied occur occur predicted deterministic generally row row assumptions assumptions hebbian hebbian hebbian hebbian hebbian hebbian hebbian hebbian reduce measures measures numerical numerical numerical numerical numerical numerical designed presence drawn drawn drawn solid turn turn assuming assuming iii iii introduce question question question denoted explicit appears appears derive construct written solving mathematical dept dept student student student student student explicitly averaging infinite physical involves remaining unique implies versus versus versus decreases independently communication squares solved solved solved solved evaluated evaluated evaluated restricted restricted restricted restricted restricted restricted restricted restricted approximations approximations evolution approximated approximated approximated updates key reasonable reasonable dashed expansion reduces reduces closed closed building perceptrons batch batch batch batch batch batch batch variations phys phys phys phys phys characterized tests tests tests successfully successfully simplicity closely presentation presentation build identity orthogonal composed capture capture refer compact follow write generalize generalize generalize providing observable ill deal situations simpler simpler remain carried layered layered layered overfitting overfitting overfitting involving involving preliminary scalar giving giving ideas analytically possibility reliable working circles reading generalisation analyze predicting rev expressions expressions generates generates simplest simplest simplest regime regime regime regime finds finds finds finds averages averages averages averages averages developing trivial agreement agreement agreement derivation phenomena analytical diffusion answer answer benchmark benchmark benchmark benchmark london london london london satisfied formalism formalism formalism formalism formalism formalism formalism precisely ran sgn sgn sgn sgn sgn arise mathematics mathematics involve describing describing calculations res mechanics limits limits applies relevance consistency introducing solla solla execution execution calculating proven green green lim lim proofs college college saddle saddle saddle saddle saddle saddle restrict arguments impossible eliminate theories theories theories turned extending systematic adds dealing numerically tools tools replica replica replica replica replica replica definitions monotonically monotonically krogh adequate hertz moments published excellent recovered ensures iteratively moved regard dominant realization histograms infinity ahead clean kearns kearns cpu extends agree reverse generalizing generalizing leaving leaving saad saad saad saad saad usage equivalently creates expanding scenario cohn cohn concentrated realizable mathematically annealed singularities insertion insertion integrals sollich sollich apparently preprint xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly xly macroscopic macroscopic macroscopic macroscopic macroscopic macroscopic macroscopic macroscopic macroscopic intensive answers cavity worked observables observables observables observables observables laws laws laws laws laws laws laws laws coolen coolen coolen coolen coolen coolen coolen coolen coolen coolen acquire satisfactory crude ongoing solvable solvable king king mirror powers dom obey obey markers conditionally conditionally conditionally absent absent closure closure deformation wong tained noiseless imum applica retaining retaining aims ansatz ansatz ansatz ansatz ansatz putting teachers teachers teachers teachers teachers teachers teachers teachers teachers reviews modifies hands hands complications theo aimed aimed aimed tong reproduces iterates emulate implementable draws mac biehl private mat kcl kcl kcl kcl integrations fax fax erf unrealizable decade strand strand mth mth mth ingredient inevitable aining aining oper cup erating fractions arccos arccos fdx fdx 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#*learning learning neural data data data data function function function function function function function function figure figure set set set set set set networks algorithm algorithm algorithm algorithm number number number number number error error error error results results results results information information problem problem problem problem problem problem problem problem problem problem problem problem problem space case case case case case case vector vector vector vector vector shown systems values values values values values recognition recognition recognition approach approach approach pattern pattern pattern point point point point point point processing processing test analysis class class optimal optimal optimal optimal optimal optimal shows shows signal algorithms algorithms algorithms simple simple paper examples examples size size feature methods methods points points points points points points points points points points points points classification similar show show show show show section section line line line line line vectors vectors general parameter parameter term term note note note note note note note note note result result university university variables variables variables solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution defined defined defined defined defined defined found found distance distance distance distance machine machine sets sets sets sets sets sets sets press position abstract find find references positive positive positive positive positive decision decision decision decision decision introduction estimation cost cost search variable variable assume lower lower lower chosen chosen bound bound bound cases conditions conditions conditions conditions conditions conditions fact fact fact fact fact region region proposed proposed errors errors errors errors errors resulting classes regression respect respect respect respect respect sum sum sum sum eq called mapping means factor optimization natural global obtain negative negative negative negative negative original original define determined constraints constraints constraints mit accuracy connection support support support support support support support train train train report version kernel advances ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai cambridge equivalent equivalent solutions solutions classifiers classifiers classifiers classifiers classifiers upper choice choice choice choice choice approximate speed estimated basic pages condition condition finally constraint constraint simply measured discussion normal normal normal normal normal normal technical increases corresponds corresponds proof proof finding finding finding finding amount amount shape main degree makes objective objective objective objective jordan leads leads leads call making idea minimize minimize minimize minimize minimize minimize produced produced improve takes apply introduced subject subject subject subject subject subject subject subject identical machines sense subset recently recently relevant engineering interest sufficient sufficient compare compare volume volume definition positions separation exists exists suggests suggests suggests extended boundary setting half place minimal segment segment segment depend editors bayes clear clear constrained taking taking largest minimizing minimizing user user start exist min min min introduce denoted explicit suppose suppose suppose appears written written describes label changing linearly electrical unique adding implies choosing choosing choosing choosing choosing national interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation interpretation controlled controlled labels labels fraction fraction soft soft soft soft soft soft soft soft soft soft soft soft soft soft margin margin margin margin margin margin similarly similarly similarly sign convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex convex boundaries penalty distances david formulation formulation formulation formulation formulation formulation formulation formulation formulation formulation formulation formulation formulation formulation bell determines vapnik prove prove maximize mozer straightforward sensor uniformly suitable differ maximal svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm comparing refer refer induced interpreted lie sin satisfy notation usual ill attempt satisfies acknowledgments minimized origin origin origin dual dual dual dual dual dual behaviour existence existence existence scalar giving tech possibility scaled removed coefficient closest closest closest adjusted subsets quantities versions freedom mapped improving extent asymptotically advanced separable separable separable separable trivial lies turns choices choices hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane hyperplane laboratories lowest meaning argument geometric geometric geometric geometric geometric geometric geometric offset amounts introducing remove variant requirement requirement http replace replace proposition proposition proposition proposition redundant feasible feasible feasible feasible feasible www summing summing summing hyperplanes grows establish adds check reasoning substituting bartlett separating separating separating separating separating separating separating widths vertices originally lawrence centroid shortest shortest eqs eqs considerations intersection dividing smola empty empty empty multiplying sch sch sch sch maximized adopt centre australia burges burges burges burges burges burges burges burges burges principled translated translated perpendicular perpendicular perpendicular perpendicular emphasize retain williamson rewrite technologies technologies differently uniqueness uniqueness uniqueness kopf kopf kopf kopf christopher australian justification jersey hull hull hull hull hull hull hull hull hull polarity polarity polarity holmdel coincide triangle separates offsets petsche nontrivial nontrivial nontrivial nontrivial nontrivial nontrivial gmd south slack allowable cortes primal primal primal primal primal primal primal intersect intersect rescaling wolfe positioned wishes crisp crisp crisp crisp crisp crisp dictated bennett penalize joining joining joining lucent lucent lucent arose arose absorbed axi axi midpoint ilwll substitutions nohl neurocolt halfway halfway halfway scalars iyi aixi aixi aixi aixi aixi aixi adelaide adelaide equalities rescale rpi nonempty oti oti sits 
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#*network learning learning learning learning learning learning learning model neural neural neural neural neural neural neural neural input input data data data data data data data data data data function function function function function function function function function function function figure figure figure figure figure time set set set set set set set networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm output number number number system error error error error error error error error error error error error results results results results results results results units information information information problem problem problem models models models hidden performance based based based based based case case case vector vector vector vector order order order order order systems values parameters noise noise noise functions unit unit distribution distribution distribution distribution distribution recognition method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern point point point point point point point point point point point single single single single single processing test test test test test test test test test test test test test analysis analysis class matrix matrix matrix matrix matrix matrix optimal inputs inputs form form form shows shows algorithms algorithms simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper examples examples examples examples small small work methods methods step field field field field field field field field field field field field field field field field field field field field field field field field field field classification classification classification classification classification classification classification classification classification process process process process process process process process process process process process process process process trained problems random random random high representation show show fixed fixed line line rule vectors general general real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average average theory theory theory theory gradient obtained obtained term dimensional dimensional dimensional result university university university university university variables variables variables variables variables computation computation computation computation solution research log defined defined found target table table standard terms distance prediction prediction prediction prediction left left left map map present present present present present low low machine sets range press press press press basis nonlinear nonlinear nonlinear abstract applied applied back back find likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references ieee procedure procedure introduction complex complex complex statistical statistical statistical statistical variance tion tion change energy energy energy energy energy energy energy energy energy energy energy energy energy energy variable variable assume measure measure prior prior prior prior prior chosen chosen previous bound bound bound bound bound binary long distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations equations equations equations equations equations techniques techniques proposed proposed correlation observed errors finite simulations simulations minimum total simulation simulation regression regression regression computed computed computed respect respect performed eq eq times elements elements elements means means optimization optimization dimension applications filter original relative relative specific specific true true true provide compute compute compute compute compute perform goal related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions equal approaches approaches approaches approaches approaches approaches approaches approaches approaches mit steps contrast contrast fields fields fields fields update update update update support support support descent descent dependent proceedings proceedings report department loss implementation kernel kernel kernel kernel kernel kernel joint exp ai ai ai ai ai ai ai framework framework framework cambridge cambridge cambridge computing computing computing equivalent equivalent directly view efficient efficient efficient efficient efficient efficient classifiers upper upper requires requires approximate approximate approximate approximate statistics statistics free free free free free free free free free free free free free free free free basic give give give give give derived derived developed bounds entropy entropy product product product actual finally processes processes processes processes evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence iteration iteration iteration iteration sampling simply measured covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance technical technical group denote denote fast stable predictions assumed assumed assumed assumed supported theoretical require require eds end ability easily makes probabilistic probabilistic probabilistic typically functional interesting projection matching uniform details details iterations iterations pre polynomial idea idea added added denotes denotes denotes denotes denotes discussed improve recent exact advantage ensemble ensemble ensemble ensemble ensemble ensemble element similarity reported practical introduced machines machines sejnowski recently engineering previously previously tuning tuning solve achieve achieve achieve trans diagonal definition definition symmetric modified observation williams williams improvement sensitive grant parts parts parts expression studied suggests extended derivative hybrid touretzky column setting starting starting starting starting starting critical interactions bayes bayes numerical integration integration integration integration integration physics physics intelligence radial variety minimizing plane targets introduce acknowledgements explicit explicit suppose monte monte carlo carlo written written written sequential sequential sequential sequential label vertical implement dimensionality slightly develop gaussians minimization expectation expectation expectation expectation versus yield choosing family family stationary interpretation solved solved transform updated updated labels approximations approximations approximations evolution approximated partition partition partition updates updates sign reasonable reasonable calculation calculation add iterative valid calculate priori sciences uncertainty maximize mozer phys major simplicity selecting presentation computations mackay plots online online online online online online identity heuristic showing showing interested classify gibbs involved subsequent approximating deal minimized minimized minimized simpler simpler simpler simpler parametric layered difficulty kalman replaced integral dotted dataset dataset dataset dataset fourier giving ideas ideas school applicable int variational variational variational variational working maximizing proper workshop closest predicting rev der submitted motivated neal averages integrate trivial derivation phenomena independence tractable stress sections formalism easier products inversion projected separately calculations toronto fluctuations mechanics mechanics requiring introducing solla haussler http http calculating extracting hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters datasets replace comments expectations jaakkola naive naive naive naive naive naive naive shifted saddle saddle saddle saddle www formally count nonzero theories dealing promising replacing replacing moment imply moments tap tap tap equals uni hasselmo steepest lett counts severe outlined treat leaving saad aston aston opper opper opper opper opper opper opper scenario avoids distri community altered wise integrals cation drawback sonar sonar sonar sonar preprint indication tune normalizing treating bution nonnegative tial marks justification jointly barber recursion rasmussen lnp lnp lnp deter brackets sweep sweep sweep iterate energies birmingham microsoft lund lund proximation aims aims ansatz inserting imaginary versity offiine manfred dash optimiza neglecting winther winther winther winther winther winther winther hyperparameter hyperparameter hyperparameter hyperparameter hyperparameter hyperparameter trust epsrc gression quantum classifi ripley kij rni diabetes integrand unknowns articles specialize linearization bernhard pima pima pima reuse overestimate ford crab crab cording clarendon gorman precludes ylz dirac merits ole datapoint dictions factorizes justin staff rnj rnj glance indian tempting tempting plugging sequen inversions sweden lla indians indians conclusive yla yardstick minimiza redefinition 
#@Csato_L,Fokoue_E,Opper_M,Schottky_B,Winther_O,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning data function function function function function function function function function function function function time time time time time time set set set set set set set set set training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm system error error error error error error error error results results results results results information information models models performance space linear case order values values probability probability parameters noise weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method approach approach approach approach point large large large rate analysis analysis class class class class class class class form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper paper examples examples examples examples examples examples examples examples small net work methods methods classification current current random random similar similar similar show show show show show show show show show show section section section fixed fixed line line general general general generalization generalization generalization generalization generalization parameter real theory theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term note note note note result result result university university university university computation log log found constant constant constant computer computer computer science science prediction direction direction presented machine machine machine machine sets sets press learn learn outputs sample sample sample sample sample sample abstract applied applied applied computational properties properties properties properties properties properties properties properties likelihood references positive positive adaptive decision decision introduction behavior statistical dynamic dynamic generated search change change assume theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound required good long conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions techniques techniques region region region region proposed proposed proposed length correct scale finite minimum resulting resulting resulting resulting resulting resulting classes ing ing ing ing ing total total total total total total regression respect respect sum called called times means factor potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential potential dimension dimension dimension obtain obtain original application cross define define proc proc proc experimental distributions distributions approaches mit accuracy comparison comparison descent descent descent descent descent descent descent descent descent descent descent descent descent descent descent report report department department department loss loss loss version technique exp exp exp exp framework domain domain directly additional view view estimates design conference upper choice significant statistics statistics pages pages pages pages validation give give give produce condition condition derived derived weighted weighted weighted bounds entropy actual iteration iteration iteration iteration iteration iteration nature sampling simply simply simply normal technical technical increases describe describe arbitrary arbitrary arbitrary predictions proof proof proof proof proof proof proof effective require main journal journal square ability hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance instance instance makes noisy noisy fit pairs pairs reduced unknown interesting significantly projection edge increasing consistent uniform empirical squared squared details call call call iterations iterations direct direct normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized polynomial idea produced choose run improved improved improve recent property property property property property property property property property property property property pair pair takes practical apply apply apply apply apply introduced trees inference subset recently recently recently sufficient sufficient sufficient sufficient sufficient varying previously previously calculated works definition definition definition generalized generalized bounded bounded exists lead lead lead lead lead lead lead lead concept concept concept concept concept studied derivative alternative correctly generally generally setting demonstrate greater conclusions valued valued editors accurate clear exponential exponential exponential exponential exponential exponential exponential weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak constrained strong strong strong strong strong strong strong strong hard hard drawn sigmoidal sigmoidal sigmoidal sigmoidal demonstrated california california california labeled labeled labeled assuming minimizing minimizing min decrease groups base base base base base base question appears appears derive construct edges produces written label changing confidence confidence slightly consisting springer implies implies implies boolean potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials potentials john decreases decreases decreases choosing independently interpretation learner learner learner learner learner learner learner learner learner influence fraction lee soft margin margin margin margin margin margin margin margin margin sign additive additive performing combining intervals roughly add distances sufficiently sufficiently sufficiently classified david david david thesis sciences prove prove holds holds determining selecting presentation identify literature literature literature conf conf conf verlag quickly quickly quickly interpreted return criteria criteria criteria criteria hold hold satisfy notation notation michael michael nips hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses satisfies satisfies satisfies satisfies decreasing decreasing decreasing decreasing decreasing remain create create exponentially rapidly replaced limitations examine examine successive ideas boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting tanh examined concepts concepts adapt analyze automata created friedman friedman friedman friedman formal algo algo algo logistic freedom freedom theoretic explanation adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost majority majority stanford berkeley berkeley satisfied easier strictly strictly strictly strictly strictly choices consequence sun researchers researchers argument geometric generic lack peter peter leave poorly haussler haussler ity aim gen monotonic proven singer expectations tolerance tolerance returns calls gap don classifying pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac pac proofs feasible www forming acm acm acm acm acm rithm rithm appropriately approximates jth repre breiman satisfying simplify imply imply imply imply effectiveness guide motivation bartlett bartlett bartlett bartlett corollary corollary corollary corollary schapire schapire schapire schapire schapire schapire corre iteratively paul thomas chooses ensembles insight omitted master master master master master master master master master warmuth warmuth repeatedly repeatedly kearns kearns bagging bagging rich draw steepest concentration variants dietterich santa santa robert robert robert robert robert learnable appeared minus annals ber preserving tibshirani theorems freund freund freund freund freund freund freund examining valiant valiant eric remainder hastie gained rithms bounding bounding bounding convert learnability carefully march met concentrate concentrate emphasize emphasize emphasize adversary adversary adversary misclassified voting voting meet ation margins margins margins margins margins margins margins september continually learners learners learners learners learners sponding sponding january august european builds ers lated cornput cornput cornput december december ron incorrectly formulae returned vote vote vote vote marcus interpretations cardinality poly poly poly poly poly poly littlestone baxter cruz cruz enter kivinen bauer doom sentation ensuring ized subtle putation probabil simon noticed drawbacks stat spent notions omit cient optimizes optimizes chang mason mason mason rated ucsc ucsc notably boost boost boost boost boost iter tially jonathan draws gorithms manfred manfred cse calling helmbold helmbold helmbold helmbold trevor oft arcing governs tunable hans script plug duffy duffy duffy commun mfiller leo onoda yoav yoav yoav annu annu annu overly leverage yoram divergences tremendous rob ariaboost wee equiva fro randomization expo aud imize nick malized itsch pothesis leslie alg sour eurocolt ott ott ott attract componentwise mines erally orem exponen kohavi fischer rre jerome taxget 
#@Duffy_N,Helmbold_D,
#t13
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural neural neural neural neural neural neural neural data data data data data data data function function function function function figure figure time set set set set set set set set set networks networks networks networks training training training training training training training training training training training training number number system system error error error error error error error error error error error error error error error error error error error error error error error error error results results results results units information information information information problem models hidden based based based based linear case vector vector vector vector vector order shown shown shown shown systems probability probability parameters parameters parameters parameters functions unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition pattern pattern point processing large large large test analysis analysis class class matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form shows signal algorithms simple gaussian gaussian examples examples examples examples small work work work process process problems problems problems random random random random random similar similar architecture show show show fixed line general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter average average average average average average average average theory theory theory obtained obtained obtained obtained obtained term note note note note note note dimensional result result result university university computation computation solution research independent independent independent independent independent independent log log log log log log log log defined defined defined defined defined found found found found found constant terms machine sets sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum press learn position components nonlinear nonlinear sample sample sample sample sample sample abstract applied find find find find find find find computational density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references references stochastic stochastic stochastic stochastic stochastic ieee ieee ieee ieee positive positive procedure procedure procedure important important adaptive decision context context introduction estimation estimation estimation estimation estimation estimation statistical statistical variance variance variance variance variance variance variance variance variance variance variance cost tion tion measure measure prior prior prior prior prior prior prior prior prior prior prior prior chosen higher higher center center cases cases bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected fact proposed correct errors errors finite finite finite finite finite finite minimum ing ing regression computed sum sum performed eq eq eq means dimension natural natural global obtain negative vol vol artificial relative specific specific true series define define compute compute compute compute location perform posterior posterior posterior posterior posterior power approaches larger train selection report institute words department loss loss loss exp exp exp exp exp exp exp exp bias bias bias bias bias bias bias bias bias bias bias bias bias bias scheme scheme scheme framework cambridge view design limit limit limit detection choice approximate statistics statistics statistics statistics statistics increase randomly criterion bounds types entropy entropy sampling simply discussion normal normal technical technical increases arbitrary inverse corresponds predictions predictions predictions predictions predictions predictions assumed assumed role role eds face face journal journal ability easily including including functional functional unknown unknown unknown unknown interesting york york special special uniform uniform uniform uniform empirical principle max normalized normalized normalized supervised produced produced produced produced improve improve recent recent exact robust ensemble ensemble typical reported introduced machines machines machines sense inference inference inference highly conventional teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher teacher approximately works smooth smooth smooth generalized risk lead lead derivative derivative derivative width width width width width white minimal reduce bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes bayes clear clear moody asymptotic asymptotic asymptotic temperature temperature temperature temperature temperature temperature temperature temperature temperature temperature strong strong integration physics drawn intelligence regularization user start decrease decrease averaged averaged averaged averaged identification question question denoted denoted reference pro solving ways label mathematical dept metric implement averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging averaging involves mutual predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive springer springer springer decreases family family family family family review review approximations approximations centered centered decomposition key normalization reduces combining interpolation valid valid initially initially construction transactions transactions expect vapnik vapnik priors priors priors holds holds holds discussions straightforward delta literature schemes schemes mackay situation situation verlag verlag kind procedures procedures procedures procedures procedures procedures procedures prob prob dis contribution contribution follow write michael generalize generalize acknowledgments modelling minimized minimized american estimators association hessian game hall matches investigated investigated boosting boosting variational variational analytically workshop workshop ensure aspect fisher improving contributions averages advanced theoretic analytic analytical tractable tool berkeley closer broad controls describing depicted fluctuations fluctuations fluctuations integrating integrating argument geometric geometric generic generic generic parameterized parameterized parameterized quantitative introducing haussler formulated continuously variant mod gen popular proven achieves logp logp logp logp conclude conditioning progress progress cumulative trade trade trade optimality recover stronger breiman motivation prentice recovered introduces introduces connect loo widths dependency forecasting forecasting consequences sim ensembles ensembles bagging bagging bagging rich likelihoods likelihoods likelihoods likelihoods statement generalizing robert empty temperatures temperatures ple annals solves smoothly smoothly opper opper tradeoff scenario scenario param param verified distri distribu gener gener ization playing denoting denoting expand topic emphasized hansen hansen hansen hansen hansen hansen voting funded parametrized els normalizing eters wider wider status bution lems lems lagrangian stimulating dim quantify ers jersey jersey cliffs mining suppress resampling tribution rasmussen englewood juang scenarios maxi denmark denmark planck fol deter mis tical neglected statements jan generaliza proceeding decades analyse analyse decompose ceedings murata hood initiated amax heskes heskes heskes mum inserting kanter ver alization dependences eralization stacking stacking cooling resampled manfred oooo biehl provably asymptotics asymptotics asymptotics xlo xlo xlo xlo kung ogp eter yoshizawa ror likeli invoked decomposing arcing larsen edward ljung kamm vague vague vague vague vague vague reads raising forecast regressions kai advocated danish carl ciently bibliography guessing kinzel chines lows rior poste imm wolfgang salamon attaining oid oid oid dlo dlo dlo dlo dlo dlo equating bay sequel cult dio zoo texts neuroinformatics lyngby kendall lars refered happened plying annotated pis dxp dxp variates councils por doo thor logq ido 
#@Hansen_L,
#t13
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#*model neural input input function function function figure set set set set number number number number number system system system system system system system system system error error error error error error error error error error error error results results results results results results results results results results results information information information information information information information problem models models performance performance performance performance performance performance performance performance performance performance performance based based based based based space weights case case case case case case case case case case case vector vector vector vector vector vector order order order order order shown shown shown shown shown shown shown shown shown systems systems systems values probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions unit unit distribution method method method method approach approach approach approach approach approach point point point point point point point point point point point point point single single large large rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate patterns patterns analysis matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows signal signal paper paper paper size size size work methods methods methods methods methods methods methods methods methods methods methods methods fig fig fig fig fig fig process process process process level level level level current current current structure random high high similar similar similar similar representation representation show show show show show show show equation line line vectors vectors vectors general general parameter parameter average theory theory theory theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained term term note dimensional dimensional university variables variables variables variables solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research log defined defined found dynamics initial initial initial initial initial initial initial initial initial computer computer terms terms terms terms connections connections presented presented presented map map phase phase phase phase low low low maximum range press continuous abstract back find convergence density properties properties properties properties properties properties references ieee ieee ieee important important propagation propagation mixture context introduction behavior statistical statistical statistical statistical 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efficient upper choice choice choice significant significant significant free free free free free free free free free free free free world increase con condition channel channel derived derived derived randomly randomly randomly levels levels levels levels bounds bounds types types types lines lines lines lines lines lines lines lines product product product provided finally selected selected selected nature arbitrary group denote limited close close close close inverse corresponds stable stable stable stable stable stable stable stable predictions nearest assumed role theoretical theoretical require main degree noisy noisy typically typically smaller smaller smaller dynamical dynamical dynamical dynamical dynamical coefficients technology interesting interesting ratio ratio increasing consistent consistent uniform uniform empirical mode representing representing numbers making making bits bits bits bits choose run description denotes architectures improved improved improved pair element typical typical typical similarity reported practical practical practical practical practical introduced include identical identical identical identical recently recently recently recently relevant highly highly highly varying varying calculated axis correspond correspond correspond converge converge converge trans trans trans sparse sparse sparse sparse address symmetric symmetric observation channels channels grant constructed constructed expression expression expression studied invariant extended wide matrices matrices matrices matrices matrices matrices generally column column column column column column setting setting conclusion critical critical critical row row row differences bayes numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical numerical peak practice encoding encoding taking taking taking physics physics solid averaged averaged connectivity connectivity connectivity connectivity program question denoted denoted appears monte carlo index index index index index index solving solving solving stability dept simultaneously averaging infinite physical physical dimensionality dimensionality slightly slightly belief belief unique unique equilibrium equilibrium equilibrium applying implies boolean boolean boolean boolean boolean choosing family family family independently expressed communication overlap codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes codes solved solved similarly converges partition sign calculation dashed dashed additive normalization iterative iterative calculate symbol construction norm degrees retrieval bell inter prove specifically phys phys phys phys phys characterized characterized characterized regular regular regular regular regular regular regular regular regular regular regular regular regular straightforward aspects aspects society maximal maximal maximal maximal encoded divided delta delta delta delta symbols literature literature mackay mackay comparing notice notice graphs decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding success showing anderson interpreted dis symmetry symmetry symmetry symmetry contribution content sci categories quantity sampled play providing leading received received received decreasing bars explore simpler carried carried carried carried carried requirements relations replaced replaced issues ml existence existence existence rise examine examine examine tech investigated investigated scaled tanh tanh tanh tanh phases examined examined examined transmission transmission transmission transmission transmission transmission adapt analyze analyze rev freedom expressions message message message message message message message message message message message message message message regime defines spin spin spin spin ground trivial analyzed unstable unstable unstable analytic analytical analytical analytical analytical capabilities glass correction purposes sites producing constructing choices choices commonly commonly products products probable consequence potentially acknowledgement separately recording addressed alignment mechanics mechanics conjugate explained questions prop relevance consistency capability peaks peaks peaks peaks employ formulated treated schematic http mod mod mod mod limiting enables redundancy attraction attraction attraction attraction attraction unbiased unbiased unbiased unbiased unbiased unbiased unbiased focused irrelevant picture corrupted corrupted indices indices indices indices indices indices saddle saddle saddle saddle saddle saddle saddle saddle japan investigation restriction restriction restriction restriction member perfectly tensor tensor bin bin royal proceed numerically numerically numerically numerically numerically attractive biased 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restrictions obtains obtains constitutes constitutes constitutes constitutes breaking breaking scenario deep thick thick thick num shannon shannon shannon shannon shannon shannon shannon shannon shannon shannon shannon thermodynamic flip flip flip flip flip increasingly integrals employing employing termed drawback covered intl preprint vanishes treating corrections supporting vice info observables versa palmer achievable saturated impractical invertible designs telephone dominates mirror char practically practically codeword codeword codeword emerges emerges obey obey hamiltonian hamiltonian hamiltonian tokyo vanish retrieved retrieved inset inset inset inset inset inset comm est subscript saturating saturating modern carrying wong media decoded energies energies energies syst ized birmingham proceeding validated saturate saturate saturate sherrington imposes enforcing enforcing enforcing disorder disorder incurred attracted checked retrieve ansatz phil coincides examines couple theo constructions constructions constructions comprises acknowledged europhys disagreement proving unclear disappear disappear mag mag comprise abs ire ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic ferromagnetic communicating epsrc sketched modulo ising ising ising erties resort mat retrieving validate validate validate rooted prog integrations gallager gallager gallager gallager gallager gallager gallager gallager gallager gallager gallager gallager unspecified para para para gov survive flipping sender rewriting sidered sumption sumption longitudinal ciently thouless transmitting corruption gauge monitors devising constituting acteristics equating nts obt optim yokohama decouple finitely constituted recipe irregularly xxx undesired dyn mes fer sage quest iie enjoys ish arid obeyed constr 
#@Kabashima_Y,Murayama_T,Saad_D,Vicente_R,
#t13
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#*network network learning learning model neural neural neural neural input data data data data function function function function function function function function time time time set set networks networks networks networks networks networks training algorithm algorithm algorithm number number number error error error error error error error state state results results results results information information information information problem models models models performance space space space weights linear linear case case case case case case case case case vector order order order order order shown shown shown shown probability probability parameters parameters functions functions functions functions functions distribution approach single large large large large rate analysis class optimal optimal form form shows shows simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian paper size size size feature net work work task methods step step step step step high high high similar similar representation representation show section section section section section fixed fixed general general general parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory theory note note note note note note dimensional result result result result result result university university university university variables computation computation log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log log defined defined sequence sequence sequence target target initial constant estimate estimate computer distance distance science science present machine maximum maximum maximum maximum maximum maximum learn components components components components components components components components components components basis basis sample sample sample abstract find find computational convergence convergence convergence density density density density density density density density density density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component component component component component component component ieee ieee ieee ieee procedure procedure procedure procedure procedure procedure procedure procedure mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation behavior variance search difference complexity variable assume assume measure representations chosen chosen chosen chosen chosen chosen part previous previous theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound cases cases good good long techniques length length length length scale finite finite finite finite minimum minimum minimum resulting resulting classes ing regression respect respect respect respect called dimension dimension dimension dimension natural natural natural global obtain obtain obtain obtain negative artificial represented application desired desired provide provide provide provide rates rates proc location location perform related related equal approaches steps accuracy connection connection department department department department sequences sequences estimates estimates limit limit determine efficient upper upper upper upper upper upper full full choice choice statistics statistics statistics statistics statistics estimated estimated give give give condition condition condition weighted developed criterion bounds bounds bounds bounds bounds bounds bounds bounds entropy depends depends achieved achieved measured discussion covariance arbitrary arbitrary transformation close proof proof proof proof proof proof common assumed require require main square end combination unknown ratio ratio ratio ratio projection projection empirical principle principle leads iterations max max attention minimize minimize minimize sources description description improve takes element apply apply apply introduced strategy side side side quadratic quadratic quadratic recently dimensions dimensions works yields achieve achieve achieve achieve achieve mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures locations bounded bounded bounded improvement risk risk risk risk risk risk risk risk risk risk exists exists invariant occur occurs generally generally setting runs conclusion competitive measures accurate taking drawn sigmoidal sigmoidal radial minimizing relationship relationship relationship introduce introduce derivatives manner manner suppose suppose suppose suppose index factors sequential estimating estimating estimating changing metric coordinates involves transformations easy gaussians gaussians gaussians expectation expectation choosing choosing family family family family family focus estimator lemma densities densities densities densities densities densities densities densities densities densities controlled restricted restricted lee lee lee forms sizes converges constants constants allowed key reasonable expansion convex convex convex convex fitting fitting roughly iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative iterative remains construction construction construction construction norm transactions transactions transactions building box box combinations coordinate bell bell prove prove maximize specifically suitable suitable suitable literature computations conf procedures procedures follow follow satisfy sampled minimizes leading maximization moves satisfies deal intrinsic decreasing parametric poor difficulty exponentially exponentially involving game divergence divergence divergence divergence pursuit successive fashion cover cover cover cover analogous neu induction induction smallest adapt necessarily necessarily man greedy greedy greedy greedy greedy greedy greedy taylor separated expressions established ment inequality inequality theoretic guaranteed analytic inside satisfied easier choices choices mation consequence separately involve universal optimize optimize considerably flexible parameterized achieves achieves adjust replace naive initialization optimality formally restrict restrict jones jones turned establish kullback kullback kullback kullback kullback kullback satisfying logarithmic fan held stated familiar balance ral disjoint selects bartlett bartlett surprising sides consequences thomas thomas chooses initialize barron barron barron barron barron barron barron barron barron barron barron treatment foundations inductive inductive tures robert andrew andrew andrew andrew andrew mind yale yale yale yale yale yale logarithm logarithm logarithm annals achieving achieving leibler leibler leibler leibler leibler leibler benefits randomized theorems monotonicity regularity seek mdl sinusoidal penalized penalized penalized equality approxi permits disadvantage expand noting importantly likewise bring tune williamson williamson reciprocal mix challenge manuscript helps cube cube cube cube cube meir meir chris achievable acquire builds hilbert hilbert establishes inequalities inequalities inequalities hull appealing compo dissertation heterogeneous norms characterizes counterpart monotone adequately prescribed mle mle mle mle mle mle hood proximation haven haven nents lipschitz picks jonathan jonathan jonathan ell completes multiplies news motivate likeli agnostic quantifies manageable theme superpositions plug dasgupta dasgupta ciently fll fll fll fll mina arbi precisions timation zeevi zeevi larry trary conv conv dlog verifying suffi plugging binations dxp sigrnoidal advisable 
#@Barron_A,Li_J,
#t13
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural input input input input input input data data data data function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training algorithm output output output output system error error error error error error error error error error error error error error error error error error state state state state state results results results results results results results results results information information performance performance performance performance performance performance performance performance performance performance based based weights weights weights weights linear linear linear linear layer case case case case case case case case case case order order shown shown systems probability probability noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions distribution distribution distribution distribution distribution method method method method method method method method method method method approach point point point point single single single processing processing control large large large large large large large large large local test test test test test test analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs form form shows shows shows shows shows shows signal algorithms simple simple simple gaussian gaussian gaussian gaussian paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small net work work work methods fig step step step step features process process process process process level level trained random random response response similar similar show equation equation equation equation line line line line line line line line line line line rule rule rule rule rule rule general general general general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization speech parameter approximation approximation average theory theory theory theory theory theory theory theory theory theory gradient gradient gradient gradient gradient gradient term term term term term term term term term note note result result university university variables variables variables research independent independent independent independent dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant terms terms terms node node science left left left left direction map present present present present present phase activation activation activation activation activation activation activation activation activation activation activation activation activation activation nodes temporal temporal temporal temporal temporal sets sets sets sets range press learn learn learn nonlinear outputs outputs outputs outputs abstract applied applied applied applied applied applied back computational references stochastic stochastic due ieee important important important propagation context introduction complex complex hand hand behavior statistical statistical statistical statistical statistical generated generated generated generated generated variance variance variance cost cost cost cost cost cost search difference difference variable variable assume assume rules rules measure measure previous cases cases cases binary binary represent equations equations region correlation correlation correlation observed errors simulations ing ing simulation respect multi called times times made made made applications applications applications study study study study study original original original original samples compared compared application series provide proc determined determined distributions approaches steps steps descent descent descent modeling modeling department version version technique advances joint exp considered considered considered framework framework framework framework cambridge cambridge computing computing environment limit limit effects effects effects effects effects effects effects full significant approximate approximate world speed derived derived developed area lines provided finally nature depends simply achieved covariance describe arbitrary arbitrary tested corresponds predictions common common assumed supported theoretical ability ability makes noisy including needed combination account account account account dynamical dynamical dynamical dynamical dynamical dynamical dynamical functional fully fully technology interesting interesting empirical mode direct making bits depth early early early early early early early early early early early early early decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay decay added added added added description description perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron improve recent recent recent correlations correlations correlations correlations correlations correlations exact exact exact exact exact takes takes reported practical introduced introduced identical side recently recently recently recently relevant interest teacher teacher teacher teacher teacher teacher teacher tuning tions solve solve yields yields yields studies studies studies studies studies diagonal background observation improvement improvement grant grant invariant extended extended alternative occurs strength strength strength strength strength conclusion starting assumptions hebbian hebbian hebbian central clear asymptotic weak temperature taking physics solid turn introduce introduce introduce derivatives minima question denoted denoted suppose suppose appears relation longer primary primary describes describes describes label distinct student student student student student multilayer averaging averaging averaging infinite infinite infinite adding versus independently focus dependence depending correlated influence solved solved solved transform open restricted restricted restricted restricted restricted restricted approximations evolution evolution evolution evolution evolution evolution translation converges partial additive additive reduces remains intermediate sufficiently sufficiently sufficiently assigned avoid activations activations activations activations activations perceptrons formulation batch batch batch batch batch batch batch batch batch batch specifically holds phys phys phys phys phys phys discussions extra importance symbols comparing conf prob interested interested interpreted stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping stopping issue sci quantity michael realistic nips minimizes minimizes subsequent subsequent acknowledgments situations minimized minimized remain remain unlike perturbation perturbation access collection steady steady steady steady strengths strengths optimized issues preliminary rise giving applicable applicable int ideal referred complicated affect statistically fundamental coarse naturally onset onset analyze rev rev rev illustrate ensure adjusted versions precise explored perceptton perceptton perceptton hebb attempts optimum spin trivial trivial agreement improves glass caused briefly lies formalism formalism widely widely desirable desirable opt opt opt opt opt opt opt opt opt opt opt beginning res res lowest lowest argument varies limits limits double consistency generic generic generic solla compares calculating monotonic acoustics marginal marginal green green green green green green green green green enables enables sophisticated progress progress progress yielding instantaneous corrupted corrupted secondary secondary saddle optimality summing arguments driving driving optimizing addresses connecting nonzero enhancement theories consideration convenient promising adjusting satisfying replica replica replica krogh krogh hertz hertz meaningful excellent introduces expanded sides percepttons percepttons laplace express express omitted theoretically adopted vari verify multiplying saad saad saad saad saad saad incorporates outperform reaction reaction convenience opper opper adjustment illustration pub formance insights ijcnn denoting regularized challenging careful increasingly weaker hansen tively preprint macroscopic macroscopic macroscopic applicability vanishes mea cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity cavity coolen coolen coolen fortunately expense ble monitor justification agrees water solvable solvable overtraining overtraining overtraining overtraining concerns equa bss bss coincide attained attained contrary inset counterpart wong wong wong wong wong wong wong propagates propagates costly trapped instant applica kong kong kong ables macro fluctuation hong hong hong superscript perturbative theo devel tong parisi europhys europhys counterparts suggestion fruitful retains rendering singapore amples bears duce unrealistic hoped notations resemblance grained adaline adaline adaline adaline larsen kcl gin simi intro variate mth deviates itera virasoro zard sacrifice hinges anticipated arbi namical bay customary arccos trary versatile larly magnified limn lished plagued ust cil adhering entific scopic approachable 
#@Li_S,Wong_K,
#t13
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#*network learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input function function function function function set set set set set set set networks networks networks networks networks networks networks networks output output output output output output output output output output number number number system results results results results results units information models models hidden hidden hidden hidden based based weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear layer layer layer layer layer layer layer layer layer layer layer order order order shown shown shown systems systems values values values functions functions functions functions functions neurons unit unit unit unit unit unit point point point point single single single single single single single single single single processing processing large neuron analysis class optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows simple visual size size size size size size process structure structure memory similar show show show show section section section section section section parameter theory theory term note result result result result threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold threshold variables variables variables variables variables variables variables computation computation computation computation computation computation defined found found computer connections synaptic science low temporal press press nonlinear nonlinear nonlinear nonlinear outputs outputs continuous continuous continuous continuous continuous abstract applied applied applied applied applied 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural data data data data function function function function function function function function function function function function function function function function function function function time time set set set set set set set set set set set set set set networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number number number number number error error error error error error error information problem based weights weights linear linear weight weight weight weight weight weight weight weight weight weight weight weight functions 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#@Mansour_Y,McAllester_D,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning model neural data data data data data data data data data data data function function function function function function function function function function function function figure figure set set set set set set set set set set set set set set set set training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm error error error error error error error error error error error error error error error error error state results problem problem problem problem performance performance performance performance based based based case case case case order order shown shown shown shown shown shown values values probability probability probability noise functions functions distribution distribution recognition recognition 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generalization generalization generalization generalization generalization generalization generalization generalization approximation average average obtained obtained obtained term note note note note note note university university variables computation computation computation independent independent independent independent independent defined defined found found constant table table table table estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate computer distance science left direction frequency machine machine machine machine sets sets sets sets sets sets sets outputs sample sample sample sample sample abstract references due due due due due positive procedure important important important important decision decision decision decision decision decision decision decision decision introduction hand estimation estimation estimation estimation estimation estimation behavior statistical statistical generated variance variance variance variance 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#@Bengio_Y,Nadeau_C,
#t13
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#*network network model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time networks networks networks number system system system system state state state state state state state state state state state state state state results results results units information information information information information models models models space space space case case case case case case order shown shown shown shown shown shown shown shown shown shown systems systems systems values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight neurons neurons neurons neurons neurons distribution pattern point single single single single single processing processing processing processing large neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis analysis analysis analysis analysis signal signal signal signal simple simple simple paper examples examples examples examples small small small size feature task fig step step step points random random random similar similar show show show show show show equation equation equation equation equation equation equation section section fixed fixed fixed fixed line line line approximation states states states states theory obtained obtained obtained term note note experiments experiments result university university university computation computation computation research research independent found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial computer science science science left map map map map map maximum maximum range abstract find computational references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due propagation propagation introduction introduction complex circuit behavior behavior behavior behavior statistical generated generated recurrent change change lower higher previous previous cases type binary binary binary binary binary binary binary spike spike spike spike spike spike spike spike long distributed equations markov markov markov make correlation observed simulations simulations simulations resulting simulation simulation respect respect performed performed times elements elements elements elements potential natural feedback feedback feedback feedback applications study study study study study obtain artificial compared application series provide compute compute perform connected gain gain brain power steps steps steps steps larger fields dependent source institute institute department version consists bias delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay considered computing equivalent view transition transition transition transition transition transition transition limit limit trajectory approximate approximate condition condition derived randomly randomly bounds lines depends depends depends biological discussion describe fast effective shape shape shape generate generate role theoretical main future makes 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#@Cowan_J,Ohira_T,Sato_Y,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model neural neural neural neural neural input input input input input input input input input input data data data function function function function function function function function function function function figure figure figure figure figure set set set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training number number number number number number error error error error error error error error error error error error error results results results problem problem problem problem problem performance space space space space space space space space space space space space space space weights weights weights weights linear linear linear linear case case case case case case case case case case case case case case case vector vector vector vector vector vector vector order order order order order order order order order order order order order order order order shown shown shown probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach pattern pattern pattern single large large large large large large local patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns class optimal shows shows simple simple simple gaussian gaussian paper paper 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constant computer terms terms direction map present present present present low learn learn learn components components components components components components components components components components components components abstract properties properties properties properties properties properties properties properties references introduction behavior behavior behavior behavior behavior behavior behavior statistical statistical statistical statistical statistical statistical statistical statistical effect generated generated variance variance variance variance cost cost cost cost cost tion energy energy energy energy assume assume lower representations higher higher higher bound cases cases cases cases binary binary conditions conditions distributed distributed distributed expected equations equations equations fact fact proposed correct errors finite simulations tasks tasks tasks tasks tasks eq called called called mapping mapping mapping mapping mapping factor factor optimization dimension dimension dimension dimension dimension dimension study study study obtain artificial specific represented cross cross related posterior posterior distributions equal steps comparison comparison comparison support support support support support support loss loss version version internal kernel kernel represents difficult difficult exp exp exp exp exp maps considered considered considered considered framework equivalent curve solutions curves curves curves curves curves limit limit limit limit limit effects determine determine choice free free free free finally selected nature depends discussion increases increases increases increases inverse corresponds corresponds corresponds corresponds surface surface predictions short effective theoretical theoretical main main end hypothesis degree including smaller reduced interesting interesting york increasing increasing consistent consistent consistent uniform uniform empirical squared details normalized supervised polynomial choose choose perceptron perceptron perceptron discussed directions directions recent advantage element typical typical typical typical typical typical typical typical typical machines machines machines machines machines quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic hierarchical recently recently recently relevant relevant interest dimensions dimensions highly highly highly teacher teacher teacher teacher teacher teacher teacher teacher calculated axis axis correspond correspond correspond trans separation improvement risk sensitive studied studied studied invariant scaling scaling scaling alternative correctly clusters clusters occurs occurs occurs faster faster asymptotic asymptotic temperature temperature drawn drawn proportional proportional assuming decrease decrease decrease averaged minima pro student student student student student student student student linearly linearly remaining easy easy text springer formed decreases choosing family expressed overlap influence fraction evolution understanding understanding understanding understanding understanding margin similarly partition sign calculation slow spaces spaces spaces spaces spaces normalization normalization convex intermediate norm norm avoid expect kernels kernels kernels kernels combinations priori priori priori perceptrons perceptrons formulation subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace vapnik discuss specifically phys phys straightforward compression aspects importance included svm svm svm svm svm presentation orthogonal orthogonal orthogonal composed notice verlag symmetry symmetry satisfy comp gibbs gibbs gibbs gibbs gibbs gibbs quantity leading leading reach presents overfitting overfitting overfitting essential behaviour mappings mappings scaled understand understand math predicting extremely extremely rev freedom perceptton regime regime spin separable separable separable analyzed analyzed rapid easier organized precisely scientific arises radius meaning meaning addressed mechanics mechanics mechanics mechanics mechanics mechanics mechanics questions behaviors behaviors behaviors understood relevance introducing solla exhibits ture aim gen lim progress irrelevant irrelevant indices indices recover grows generality generality difficulties tools tools alpha determination replica replica replica replica transforms tishby symposium overlaps overlaps sompolinsky expanded percepttons permutation contraction extensively merge captures papers papers lett lett posteriori compressed compressed compressed compressed compressed compressed compressed compressed compressed compressed compressed compressed compressed svms svms svms svms svms svms svms svms svms svms svms drop isotropic isotropic isotropic isotropic opper stem classifies avoided clustered clas toy toy toy toy toy toy toy impose crossover crossover crossover learnt learnt learnt learnt learnt learnt 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#@Gordon_M,Risau-Gusman_S,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input function function function function function function function function function function function function function function function function function function function figure figure figure set set set set set set set set set networks networks networks networks networks 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shown systems systems systems values values values values values values values values values values values values parameters parameters parameters parameters weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions neurons neurons method method method method method method method point single single processing processing control large large analysis class class class class class optimal inputs inputs inputs inputs shows shows simple paper small small small size size size size size size size size size size size size size size size size size size size size net net work work work methods step level level level level level level similar architecture architecture architecture architecture architecture architecture show show show show show section fixed fixed general general general general parameter parameter parameter parameter parameter parameter parameter real real real real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation theory theory theory obtained obtained obtained obtained obtained note note note note result result result result result result result result result result result result result threshold threshold variables variables variables computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation computation log log log defined defined defined defined defined sequence sequence constant estimate standard standard standard standard standard standard computer computer computer terms terms terms terms terms terms node node node node node node node node node direction present present present present activation activation activation activation activation activation nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes temporal sets range press press basis nonlinear outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract computational computational computational references references due due due ieee ieee ieee important introduction hand hand hand circuit complexity complexity complexity complexity complexity complexity complexity variable assume assume assume assume lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower lower signals chosen chosen part previous theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound required required good binary binary binary binary binary long represent make fact fact finite finite resulting resulting resulting resulting classes ing computed computed computed computed computed computed respect sum sum called called called elements mapping means means dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made applications applications obtain obtain obtain obtain obtain obtain obtain provide define define compute compute compute equal power power mit comparison larger morgan proceedings words technique consists advances advances final layers layers addition graph cambridge computing computing computing computing computing computing computing computing computing domain directly view estimates estimates san conference upper upper upper upper upper upper requires requires approximate approximate approximate approximate approximate approximate approximate approximate approximate basic pages pages pages give give coding derived developed levels levels levels levels bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds types types types types types types types lines lines provided finally discussion feedforward feedforward feedforward feedforward feedforward feedforward increases arbitrary arbitrary arbitrary arbitrary group close actions proof proof proof proof common implemented assumed supported role theoretical require require main main main journal journal journal instance degree degree degree degree degree degree degree degree noisy kaufmann needed account jordan interesting edge edge increasing numbers numbers numbers depth polynomial polynomial idea attention denotes architectures architectures recent exact property takes practical practical apply apply apply introduced quadratic subset sufficient sufficient calculated calculated calculated calculated calculated volume works tions smooth yields yields trans definition separation bounded gate gate interval interval constructed exists lead extended white demonstrate place assumptions conclusions valued valued valued valued depend depend editors editors sigmoid sigmoid sigmoid sigmoid sigmoid mateo taking largest sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal sigmoidal labeled labeled labeled radial assuming introduce question denoted denoted derive derive construct construct construct edges mathematical mathematical mathematical distinct recall implement multilayer multilayer multilayer slightly implies boolean boolean decreases yield yield choosing choosing independently lemma lemma open open operations restricted restricted showed showed approximated approximated approximated sizes partition constants partial remains valid valid valid calculate sufficiently sufficiently sufficiently assigned assigned assigned norm norm norm norm transactions expect expect existing sciences sciences vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik vapnik mozer coupled holds holds holds holds discussions simplicity reason straightforward straightforward suitable suitable suitable society society society computationally spiking literature build computations computations projections projections comparing receives refer refer showing sin follow criteria satisfy michael play generalize giles computes thresholds thresholds approximating approximating approximating approximating approximating approximating approximating satisfies acknowledgments deal cowan powerful american american essential replaced replaced hanson ml ml helpful existence working gates gates gates gates gates gates gates gates gates gates gates gates gates gates func fundamental neu math naturally naturally subsets precise observe multivariate multivariate consist consist arbitrarily defines established established established established mentioned mentioned directed defining growing analytic adapted capabilities capabilities answer multiplication multiplication multiplication multiplication multiplication multiplication multiplication briefly nonlinearity lin implementing tive division division division division division division division division immediately universal universal universal universal universal ridge ridge arises annual argument questions questions applies readily readily introducing introducing frequently requirement polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials polynomials calculating rely measuring germany conclude conclude neuro tolerance focused lim arithmetic proofs accomplished arguments labelled concerned count proceed establish establish maass maass maass maass programmable programmable programmable programmable programmable programmable programmable programmable grow grow los reasoning ral definitions definitions disjoint combinatorial combinatorial generalizes generalizes corollary loo induce uni approximators approximators barron refers partitioned variants statement statement statement papers assigning assigning dense boxes approx approx numerous indirect outline deriving chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis chervonenkis sontag sontag uniquely employs additionally equality approxi manifolds thresholded thresholded hornik hornik employing employing harder translations weaker superposition universit induces induces compu dichotomies survey survey sake concrete dichotomy dichotomy dichotomy dichotomy dichotomy petsche interpolating cardinality cardinality cardinality poly outgoing shattered shattered shattered establishing informatik acyclic tsoi tsoi simon cations appli tighter imation imation aimed constructions colt claimed proving justify univariate univariate koiran koiran koiran koiran koiran koiran koiran completes refining tational providence cybenko vcdim cited stinchcombe superpositions und mated hans alamitos spe dasgupta dasgupta dasgupta rests predecessors thereof polyno esprit schnitger schnitger schnitger shatter shatter shatter shatter referenced schmitt schmitt schmitt schmitt warren warren warren monographs karpinski karpinski karpinski karpinski fakult indispensable reals macintyre macintyre macintyre macintyre cific imi construc inductively flit ruhr ruhr chui nomials 
#@Schmitt_M,
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#*network network network model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input function function function time time time time time time time time time set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state results information models models models models models models models models models based space space space space space space space space space space space space space space space space space linear case case case case case case case vector shown systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions neurons distribution distribution distribution distribution recognition recognition method approach point point image control class class class class inputs inputs inputs signal simple simple gaussian gaussian gaussian paper paper paper examples examples examples examples small small small small work work step step current current current random random memory memory similar similar similar similar similar similar equation equation equation equation equation section rule general general general general general general real real states states states states states states states states theory term dimensional result result result variables variables computation computation computation computation computation computation computation independent independent independent defined defined defined defined defined defined defined defined defined defined defined dynamics dynamics initial initial initial initial constant constant constant terms map present machine machine sets sets sets press components components components continuous continuous continuous continuous continuous continuous continuous continuous continuous abstract abstract abstract abstract applied computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational computational density density density density analog analog analog analog analog analog analog analog analog references component component component stochastic stochastic stochastic stochastic stochastic stochastic stochastic positive positive positive important introduction introduction behavior effect parallel parallel recurrent recurrent tion variable assume assume assume measure measure measure measure measure measure measure measure signals word word part part theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem cases required conditions conditions conditions equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov length probabilities finite finite finite finite finite finite ing total human respect respect respect respect respect respect respect respect respect called called called called called called called called called called called times times times elements elements dimension study vol vol vol artificial represented application provide provide define define define define define define define active distributions distributions distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete power power power power power power steps update update update nets words words words version version version individual individual final final addition ai ai considered equivalent solutions transition transition transition transition transition transition limit limit san free give condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition condition types processes depends biological arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote denote denote limited assumption stable short common end ability makes noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy noisy including including including probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic underlying reduced dynamical dynamical mechanism special special principle language language language language language leads numbers numbers pre making bits choose recent recent property property property property property property robust robust practical practical introduced introduced moving include include machines subset subset subset recently sufficient sufficient sufficient previously previously previously smooth differential differential definition definition definition definition definition definition generalized bounded bounded interval exists exists exists exists exists exists exists studied occur extended wide matrices matrices hybrid hybrid hybrid hybrid hybrid hybrid deterministic setting flow trajectories operator operator operator operator operator operator valued depend depend central measures measures measures measures weak weak weak weak weak weak constrained hard presence characteristics min suppose suppose suppose suppose construct describes describes ann stability stability stability mathematical metric infinite infinite consisting applying implies implies implies implies implies extraction john letters family depending variation showed evolution evolution classical spaces spaces reduces sufficiently norm norm norm norm norm euclidean includes kernels kernels kernels kernels strings recognize recognize recognize recognize recognize prove prove uncertainty activated activated activated coupled holds regular regular regular identified letter letter uniformly uniformly differ symbols identify receives receives receives induced induced prob prob prob interpreted dis issue satisfy satisfy generalize leading satisfies satisfies wiley collection collection existence tech applicable applicable combine proved proved notion examined math math coefficient coefficient concepts necessarily necessarily integer integer integer integer automata automata automata automata automata automata automata automata automata automata ensure subsets subsets observe academic submitted motivated defines isolated established languages languages languages languages languages languages languages languages languages languages languages languages languages formula asynchronous asynchronous ground london sys sys day operators operators operators operators operators operators operators operators operators operators operators operators operators operators operators mathematics mathematics mathematics cut cut recognized recognized describing definite definite definite definite definite definite definite definite definite definite definite definite robustness share rep ity perturbations perturbations perturbations proven proven inherent chose boston gap gap gap restriction null null null null null homogeneous tem maass maass maass maass maass maass maass maass maass cellular dealing convenient chains accepted accepted accepted interconnection multiplicative check synchronous synchronous responsible generalizes alphabet alphabet alphabet alphabet lip lip lip lip weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly weakly corollary governed governed topological enable israel israel israel francisco foundations eng eng environmental sons inf inf inf inf inf characterization generalizing interestingly receiving treat verify numerous constitute tables sontag sontag sontag sontag sontag sontag sontag preserving preserving preserving preserving theorems quasi ease generalizations generalizations generalizations generalizations breaking associate acting acting acting favor management management tems mathematically execute rejected rejected parallelism covered distinguished discusses algebra induces examination strict completed architectural syn ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic ergodic uniqueness ble ate ate accordance unbounded agrees cornput industrial industrial connects measurable measurable measurable measurable measurable arrives recognizes appl statist evolves ben ben ben ben ben nonstationary deciding technion technion technion technion technion aggregate aggregate aggregate aggregate aggregate dist dist applica putational accepting accepting accepting turing deeper couple reminiscent alexander calculus serving theor roots siegelmann siegelmann siegelmann siegelmann siegelmann siegelmann calling rejecting rejecting rejecting rli rli rli ergodicity ergodicity ergodicity ergodicity ergodicity ergodicity ergodicity casey casey restricts checking probabilistically absolutely absolutely asa asa borel stochasticity fid fid fid tual haifa haifa haifa lattices iit iit iit iip crete neces oll resented holden chronous cit cit sary yer instants rnin rnin reals ternal countable birkhauser aforementioned kill rationals forgets strengthens collec nite atio odic abandon 
#@Ben-Hut_A,Roitershtein_A,Siegelmann_H,
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#*learning learning model model model model model neural neural data data data data data function function function function function function figure figure set set set set set set set set set set set set set set set set networks networks networks networks networks training training training number number number number number number number number number number system system error error error error error error error state results results results results information information information information problem problem models models models performance performance based based space space space space space space space linear linear linear linear linear linear linear linear linear case case case case case case case case case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector order order order systems values values values values values values probability weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit unit distribution method control control control large large large analysis analysis analysis analysis class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix shows algorithms algorithms paper examples examples examples examples examples small small small small small feature feature feature feature feature feature work methods methods methods methods methods points current current problems similar similar similar show show section section fixed vectors general general general generalization generalization generalization approximation theory obtained obtained obtained term note note note experiments dimensional dimensional result result result result university university university university university university university threshold computation research research independent independent independent log log log log log log log log log log defined defined defined sequence target initial initial constant constant standard standard terms terms terms terms terms terms terms terms left presented map map present machine sets maximum range range range press press basis basis basis basis basis basis basis basis basis basis basis basis basis nonlinear sample sample abstract back convergence convergence convergence properties references due positive important introduction hand hand hand statistical effect generated generated cost tion tion tion tion change change difference difference complexity complexity previous previous previous previous theorem theorem theorem theorem theorem bound bound bound cases type good good good bayesian expected expected expected make fact fact techniques techniques techniques techniques length observed observed observed observed scale classes respect sum called times elements elements mapping mapping mapping means dimension dimension dimension dimension dimension dimension dimension dimension made obtain obtain true true provide define compute compute compute compute proc perform determined distributions support support support support support support support support dependent selection selection selection selection selection report report words department kernel kernel joint joint joint difficult addition addition addition cambridge cambridge cambridge cambridge domain domain equivalent equivalent directly directly additional additional additional design design design design design design design capacity capacity capacity classifiers statistics basic basic basic increase weighted randomly developed criterion criterion criterion criterion criterion bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy product product finally finally finally finally finally finally finally sampling simply achieved achieved discussion technical arbitrary arbitrary arbitrary arbitrary denote denote limited limited limited inverse corresponds proof proof proof amount amount effective effective effective effective supported theoretical main main square hypothesis instance easily easily including combination combination functional functional coefficients coefficients coefficients programming significantly significantly significantly special special special special uniform uniform uniform empirical leads leads details numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers magnitude decay decay decay decay decay idea minimize denotes denotes improved improved advantage advantage property takes practical practical apply identical identical identical machines machines machines machines machines machines machines machines machines machines machines machines machines recently recently engineering engineering dimensions previously previously axis smooth diagonal diagonal diagonal definition definition evaluation bounded bounded bounded bounded improvement risk risk sensitive grant exists exists concept scaling suggests extended wide wide matrices matrices correctly locally occurs occurs setting setting assumptions reduce reduce operator operator operator operator operator operator operator operator operator operator constrained constrained drawn regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization regularization minimizing minimizing exist min min min min base acknowledgements explicit suppose written written ways dept dept confidence metric metric linearly linearly linearly slightly spectral predictive john john decreases choosing national national restricted restricted labels showed decomposition decomposition approximated margin margin suggested constants spectrum spectrum diagram additive expansion expansion spaces spaces spaces spaces convex sec norm norm david precision kernels kernels kernels eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues eigenvalues vapnik specifically domains holds differ differ differ differ modification poggio literature efficiently situation essentially identity identity identity fine traditional compact notice induced follow criteria hold notation quantity write dot dot dot providing automatically deal deal decreasing extend bars carried difficulty involving estimators dataset pursuit tech boosting root func analogous analogous act act possibly possibly singular singular singular singular singular singular quantities obvious taylor taylor taylor taylor taylor mapped mapped ith mentioned advanced formula london london inside stanford purposes operators operators operators operators operators operators operators worst sgn sgn immediately products products separately calculations definite auto auto radius radius evaluating led readily orders haussler employ dots characterize popular chen neuro proposition proposition proposition proposition proposition extreme cor globally spectra pac college college sv sv sv sv sv sv restrict acm girosi controlling count jones royal royal dealing consideration consideration convenient exploit exploit analyzing definitions intuitively modifications carry combinatorial substituting ranging encountered expanded expanded expanded regard counting entries treatment omitted horn relies characterization summarize cam johnson ball ball ball ball robert smola smola smola smola smola smola smola smola street appeared largely sch sch sch sch sch sch covering covering covering covering covering covering covering covering chervonenkis expanding classifies australia australia tight distribu learnability regularized proach enforce responding admissible knowing behave parametrized port williamson williamson williamson williamson williamson williamson vice expansions expansions expansions versa fat bridge council kopf kopf kopf kopf australian australian australian vii shawe shawe shawe shawe shawe shawe house inequalities alex alex dcs gram gram fij fij fij fij archi norms tells ignores sions sions sions factorization factorization dimen ben nominal dent doubling carrying sparseness cti cti cti cti sorted microsoft microsoft tightly gij gij eta decompositions whilst whilst sparsity sparsity sparsity sparsity colt colt shattering qij mercer mercer penalizing oij george donoho susceptible depen bernhard appeal nical canberra canberra doubled dyadic holloway holloway aug aug thereof carl carl ilwll tectures regu chines anu anu tedious atomic lib tropy deutsche obtainable obtainable wll saunders factorize moo moo stating neurocolt ida lkopf lkopf bianchi bob forp alon compactness rhbnc lives cesa ellipsoid eurocolt egham bsc richness richness endowed iiz forschungsgemeinschaft regulariza guildhall aut aut surrey proximately 
#@Scholkopf_B,Shawe-Taylor_J,Smola_A,Williamson_R,
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#*learning model model model model model model model model model neural neural input input input input input input input data data data data data data data data data data data data function function function function function function function function function function function function function function figure figure set set set set set set set set set set set set set networks networks training training training training training training training training training training training training training training training training training algorithm algorithm output output output number number error error error error error error error results results information problem problem problem models models models space space space space space linear linear linear vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order values values values values values values values values values values values values probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise noise noise noise weight functions functions functions unit unit distribution distribution distribution distribution distribution distribution distribution recognition approach pattern point point point point control large large test class class class class class class matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form form form shows shows shows shows simple simple simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples examples examples examples small small size size size feature feature feature feature work work methods methods methods methods methods methods methods methods fig fig fig fig step field field classification classification classification classification process process process process process process level trained trained problems problems problems high high similar fixed line line vectors vectors vectors general parameter parameter parameter approximation approximation approximation approximation approximation approximation average average gradient obtained obtained obtained term term term term note note note note note experiments activity dimensional dimensional result university variables computation solution solution solution solution solution solution solution solution solution solution research independent independent log log log log log log log log log defined target target target target target constant constant constant estimate estimate standard standard terms terms terms terms terms terms distance prediction prediction prediction prediction left left map map map map map map map map sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum press press components components outputs outputs outputs continuous sample sample sample sample abstract find density density properties properties properties properties properties properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references procedure important decision decision decision decision decision decision decision hand estimation effect effect effect effect generated generated variance variance search change change variable measure prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen higher type required good binary represent represent distributed bayesian bayesian bayesian bayesian make fact proposed length length length length probabilities probabilities probabilities scale scale scale finite resulting classes ing regression regression regression regression eq regions regions regions regions factor factor factor factor factor factor factor factor factor optimization optimization made applications knowledge knowledge obtain negative negative artificial relative samples samples samples samples samples samples true true true application cross cross cross provide provide define define define define determined determined experimental posterior posterior posterior posterior posterior constraints distributions equal equal approaches mit mit comparison larger larger contrast connection support support support support support support support support support support support support support support support support support support support dependent dependent dependent dependent selection proceedings report report department loss loss loss kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances joint difficult exp exp exp exp exp exp exp exp ai ai ai framework framework framework framework framework cambridge equivalent directly view view solutions limit top top determine classifiers classifiers full choice choice choice approximate approximate statistics free estimated basic pages increase validation validation validation give give derived derived derived derived conditional types product product actual actual processes processes evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence depends sampling sampling sampling constraint simply simply covariance covariance covariance covariance covariance covariance technical technical describe arbitrary arbitrary group transformation close corresponds complete predictions predictions rbf rbf amount effective effective effective assumed shape main square square end future future easily makes makes makes makes objective probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic smaller underlying underlying underlying reduced reduced unknown jordan transfer transfer interesting interesting uniform empirical squared squared call making international normalized normalized normalized normalized bottom bottom polynomial idea minimize added recent recent separate typical apply introduced include include subject subject identical machines machines machines machines machines machines machines machines machines machines machines machines machines quadratic quadratic sense sense sense inference inference subset subset recently recently relevant compare smooth diagonal diagonal modified williams williams improvement sensitive amplitude amplitude amplitude expression matrices alternative move width deterministic white white setting critical minimal row depend depend numerical clear exponential exponential suggest taking integration largest largest sigmoidal sigmoidal solid solid intelligence regularization acknowledgements suppose suppose changing simultaneously linearly linearly linearly remaining remaining shift choosing choosing focus estimator interpretation interpretation evaluated evaluated evaluated open understanding sizes margin margin margin margin margin allowed calculation dashed dashed additive expansion spaces spaces normalization normalization normalization roughly add boundaries boundaries boundaries penalty penalty penalty generation remains remains remains remains construction kernels kernels kernels kernels determines plotted uncertainty uncertainty uncertainty uncertainty priors priors black black discussions tests closely suitable society encoded svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm latent latent comparing plots plots tend essentially identity summary heuristic dis built vary write absence providing nips nips nips minimizes correspondence leading maximization maximization illustrates bars bars bars bars bars varied varied integral integral integral graphical dataset giving variational variational authors proper workshop smallest circles coefficient plausible editor illustrate ensure quantities noted logistic taylor academic multivariate simplest submitted submitted finds defines defines separable separable trivial crucial smoothness defining defining correction london london inside widely operators ran arise controls mathematics separately definite fluctuations integrating questions understood parameterized peter peter leave leave haussler http hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters qualitatively marginal marginal marginal marginal marginal gave comments neuro deviations jaakkola jaakkola specifies progress yielding naive naive naive naive contribute gap gap gap don shifted uncorrelated college intractable assign assign assign guarantee restriction narrow dynamically hyperplanes discovery nonzero nonzero grey royal replacing interpret keeping obtaining shifts ylx ylx intuitive intuitive intuitive spurious financial bartlett recovered ensures regard entries laplace laplace laplace treatment express properly eqs summarize avoiding smola smola smola smola fitted unchanged svms svms svms svms svms svms svms sch sch sch outline fellowship email kluwer equivalently maximized gaps gaps gaps gaps expanding adopt wahba opper opper opper ideally ical covariances letting reflected adapting burges burges verified intuition intuition community magnitudes toy proba individually individually singularities integrals rough importantly sollich sollich sollich sollich sollich breaks truth det det det holding prevents williamson differing differentiating hodgkin cavity spite chris fiat argmax sees bility corners kopf kopf kopf const identifies crude influenced shawe hilbert king interpreting mining cally contrasts couplings obey classi meth implied lnp ods tube era amenable wisconsin gmd remained hinge hinge hinge fication sparseness sparseness artificially slack slack violated developments comprehensive retaining campbell tutorial tutorial tutorial inserting ample conceptually icann llx restart colt posterjori diverges manfred analysed tommi correspondingly miiller winther winther reproducing hyperparameter xlo ror safety gps discarding unambiguous normalizes integrand integrand integrand integrand integrand rli schslkopf private kcl probabilistically shrinking flamework tunable dropping pleasure survive strand nel remedy intense typ greyscale greyscale tackle ker ole factorizes oid oid oid oid unnormalized dlo unambiguously unambiguously dorothy munication cussed dio dio dio uhlenbeck proxy ornstein overestimates incur guidelines submatrix determinants writes 
#@Sollich_P,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural function function function function function function function function function function function function function function function function function function set set set set set set set set set set set networks training training training algorithm algorithm algorithm number number number number number number number error error error error error error results results information problem models models models based based space space linear layer layer vector vector order order systems probability probability probability probability probability parameters parameters parameters parameters parameters functions functions functions functions functions distribution distribution distribution method method point point analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix form form shows shows shows shows paper paper small small points field structure structure structure random show show show show section section section section general general generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter real real real real average theory theory obtained term term note note dimensional dimensional computation research research independent independent log log log log log log log log log log log log log log log log log log log log defined defined constant constant constant constant computer computer distance science science science map map present machine machine machine sets sets sets basis basis continuous abstract applied applied find find find convergence density density density density references stochastic stochastic stochastic stochastic stochastic positive positive positive important introduction complex complex hand estimation estimation estimation statistical statistical statistical statistical tion complexity complexity complexity complexity complexity variable assume assume assume assume assume assume assume lower lower lower part part part part theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound cases conditions conditions bayesian fact forward finite finite finite finite finite minimum resulting resulting regression multi multi eq eq eq eq eq eq eq eq called times mapping mapping dimension natural natural obtain obtain obtain obtain obtain obtain negative negative negative samples samples samples represented true true true true true true true true true define define define define define proc distributions equal equal equal equal equal larger support support support institute words words words words words loss loss loss loss loss version consists represents exp exp exp exp exp exp exp exp exp exp computing equivalent equivalent directly curves determine upper upper upper statistics estimated estimated increase con conditional discussion normal normal arbitrary arbitrary arbitrary arbitrary fast inverse assumption proof supported supported main main main smaller technology empirical numbers numbers max polynomial polynomial polynomial polynomial polynomial resolution resolution resolution resolution resolution resolution resolution machines machines machines machines machines machines machines machines machines machines machines machines hierarchical hierarchical hierarchical hierarchical calculated axis axis axis tions trans definition mixtures mixtures symmetric bounded entire entire grant constructed exists exists exists invariant feed half half conclusion assumptions assumptions assumptions operator depend bayes bayes asymptotic asymptotic asymptotic asymptotic largest intelligence radial radial variety variety exist exist min min min min plane plane relation relation construct laboratory mathematical mathematical mathematical mathematical linearly infinite applying springer springer expectation independently lemma lemma lemma transform open open open evaluate converges converges constants constants constants expansion expansion expansion expansion expansion expansion expansion combining combining neighborhood neighborhood neighborhood neighborhood neighborhood calculate calculate calculate sufficiently foundation foundation precision priori perceptrons prove prove prove prove prove holds partially characterized regular regular regular regular regular regular regular invariance characteristic compact compact compact compact procedures contained manifold satisfies acknowledgments origin origin origin origin origin layered layered relations ml ml ml ml ml ml ml ml ml ml ml ml ml ml analytically analytically referred referred proved func func cover smallest smallest math math math math math coefficient integer analyze singular singular taylor taylor taylor fisher amari asymptotically asymptotically inequality inequality inequality inequality inequality inequality analytic analytic analytic analytic analytic analytic analytic analytic analytic analytic purposes satisfied satisfied division scientific english definite definite geometry geometry geometry explained pure continuously variant proven proven proven ordered logp logp differentiable pole proofs notes notes japan japan japan generality rational rational rational rational rational kullback ral ral ral ensures appendix appendix appendix expanded percepttons infinity infinity dif laplace inf inf integers empty divide entropic outline rigorous rigorous minus annals annals recursively theorems algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic algebraic jacobian jacobian ijcnn manifolds singularities singularities singularities singularities singularities singularities singularities singularities constructs covered emphasized union union det eigen nil nil nil normalizing remark lecture lecture remarks const const const const const continued continued neighborhoods aid establishes inequalities connects resolved tokyo proves appl comm comm poles poles poles zeros zeros cauchy watanabe watanabe watanabe watanabe watanabe ically derives aic murata rigorously sato sato jensen clarify ministry singularity singularity logn logn logn nonsingular identifiable identifiable identifiable identifiable identifiable identifiable identifiable identifiable identifiable stant bernstein absolutely owi lastly xlx xlx tth radii education iip attains asymp xlw xlw xlw xlw ieice yokohama elect multiplicity culture schwarz ferential ups ups automat totic xix algorithmically algorithmically algorithmically nalysis logx toda 
#@Watanabe_S,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural data function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure time time time set networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm system system information information information information information information information information information problem problem problem problem problem problem models models models models models models models space space space space space space space space space linear linear case case case case vector vector vector vector vector order order shown systems systems systems systems systems systems systems systems systems systems probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions unit approach approach approach approach approach approach approach approach approach approach point image processing processing processing processing processing local local local rate analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form form form form form form form form form signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms paper paper paper paper paper paper small task methods methods methods fig process structure random representation representation representation equation equation section section section line line rule vectors general general parameter parameter parameter parameter parameter parameter parameter parameter theory theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained dimensional dimensional dimensional dimensional dimensional result result result computation computation solution research research research independent independent independent independent independent independent log log defined defined defined defined defined estimate estimate estimate terms terms left direction present present phase phase phase phase phase temporal maximum press learn outputs abstract applied applied applied find find find find find convergence convergence density density properties likelihood references component stochastic due due ieee ieee ieee ieee ieee ieee ieee ieee important adaptive adaptive adaptive adaptive mixture introduction estimation estimation statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical statistical cost cost search variable variable variable assume signals signals signals signals signals signals signals signals signals signals signals higher theorem theorem theorem theorem conditions conditions conditions conditions distributed proposed proposed length length length observed finite minimum ing ing respect called called elements elements elements elements dimension made natural natural natural natural natural natural natural natural natural natural natural global applications applications knowledge filter filter filter filter filter filter filter filter filter filter filter filter filter obtain relative specific represented true true application series define proc goal goal related constraints constraints distributions distributions brain brain brain fields source source source source source source source source source source source source source source source source proceedings proceedings proceedings institute version represents difficult difficult difficult delay addition ai framework framework framework framework framework framework equivalent view view design conference efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient efficient full statistics statistics statistics statistics free free basic pages pages pages pages give give derived derived derived developed developed area entropy product product provided processes backpropagation constraint constraint discussion arbitrary group group group group group group group denote transformation limited inverse inverse stable circuits circuits effective role easily easily makes functional unknown unknown unknown coefficients block transfer projection increasing structures structures structures details filters filters filters filters filters filters filters filters filters filters filters filters international polynomial sources sources improve correlations correlations property robust element element typical apply side sejnowski recently recently recently interest interest interest interest interest interest interest dimensions volume volume works differential differential trans trans trans trans trans diagonal diagonal diagonal diagonal mixtures mixtures separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation lead studied invariant scaling suggests deviation deviation derivative matrices locally generally generally minimal operator editors tangent tangent tangent tangent tangent numerical taking presence turn ica averaged introduce introduce introduce introduce introduce identification identification denoted denoted denoted explicit explicit explicit pro derive derive derive derive derive estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating ann stability stability stability stability metric infinite infinite infinite physical easy mutual mutual springer family family family family family family independently correlated lemma lemma lemma lemma variation variation detailed detailed open operations operations operations operations operations showed decomposition decomposition decomposition decomposition forms constants slow spaces neighborhood neighborhood purpose calculate degrees degrees includes includes coordinate formulation bell inter blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind blind illustrated illustrated discuss sensor sensor sensor efficiency efficiently score score score score score score score score score score score score score score score score score score identity identity orthogonal orthogonal orthogonal orthogonal orthogonal summary refer refer lie lie lie lie lie lie lie manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold follow write play dot maximization automatically principles mixing mixing mixing mixing mixing explore remain updating updating rapidly estimators mass variational workshop workshop scores scores scores algo taylor freedom freedom amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari amari crucial derivation analyzed growing multiplication multiplication london spatially spatially satisfied style recognized circle geometry geometry geometry geometric parameterized orders remove formulated formulated berlin mod proven proven curvature curvature chen progress univ instantaneous instantaneous instantaneous ordinary ordinary newton proofs notes japan temporally temporally rithm enhancement theories communications overcome satisfying satisfying chemical analyzing belong carry published recovered zhang zhang zhang zhang zhang zhang yang yang april april permutation extends papers tures pdf treat speaking verify liu geometrical geometrical geometrical geometrical truncated dec formulate formulate quasi letting causal australia algebraic illustration illustration param mutually care cessing diag impose deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution deconvolution douglas fir fir fir fir fir fir fir fir fir projecting proach paris spanned drawback france france suffer suffer admissible page det els rewrite infinitely mix lecture remarkable factorized parameterization january august instability vii hopkins cornput cornput identically sided sided ally huang johns iid semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric semiparametric wisconsin gence poles vicinity format baltimore indepen cichocki cichocki cichocki cichocki cichocki cichocki cichocki cichocki cichocki cichocki shortly shortly dence sep syst cia riemannian riemannian proceeding proceeding putation adv derivations cardoso cardoso cardoso cardoso retrieve nov nov biomedical madison treats equalization tong bind conver multichannel multichannel multichannel multichannel multichannel multichannel multichannel multichannel multichannel multichannel ration demixing demixing pad equivariant equivariant eter shi wireless proaches nonsingular nonsingular nonsingular riken riken temporarily unknowns nxn nuisance nuisance nuisance nuisance nuisance nuisance nuisance nuisance nuisance nuisance nuisance nuisance nuisance nuisance fundamentals efficiencies recurrently telecom iin laheld sepa saitama wako anymore forp enlarge munication truncating timate timate integrable ologp ofthe lti lti aration iconip convolutive fori 
#@Amari_S,Cichocki_A,Zhang_L,
#t13
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#*network network learning learning learning learning learning learning learning model neural neural neural neural neural data data data data data data data function function function function function function function function function function function function function function function set networks networks networks training training training algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number number number number system error results results results results results results results results results results results results results results information problem problem hidden performance performance performance performance performance performance based based based space space space space weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector order systems values probability probability probability probability functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution method method method method method approach pattern point point point large large large analysis analysis analysis analysis analysis class class class matrix matrix matrix optimal optimal optimal form form form form form form shows algorithms algorithms algorithms simple paper paper paper paper paper paper small small size size size size size size net work methods methods methods classification classification classification classification classification structure problems problems problems problems problems problems problems problems random similar similar similar similar similar similar architecture show show section section section section section section section section fixed fixed vectors vectors general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real real approximation approximation theory theory theory theory theory theory theory theory obtained obtained obtained obtained obtained obtained obtained note note note note note note note dimensional dimensional dimensional dimensional result result result result university solution research independent independent independent independent independent independent log log log log log log log log log log defined defined found found constant constant constant estimate standard standard computer terms science present present present machine machine machine sets sets press nonlinear nonlinear nonlinear nonlinear sample sample sample sample sample sample abstract applied applied applied back find find computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density properties references stochastic due due ieee ieee ieee ieee ieee positive positive positive important important introduction complex estimation behavior behavior statistical statistical tion complexity complexity complexity assume assume assume assume assume assume assume assume assume measure measure chosen part center previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound cases cases good binary binary conditions conditions conditions conditions conditions expected expected make fact techniques length probabilities observed scale scale finite finite minimum ing total total regression regression respect respect called called factor dimension dimension dimension dimension dimension dimension dimension natural applications study study obtain obtain obtain negative original relative relative compared series provide define rates proc goal related related related related related update support support support support dependent dependent report report department loss loss loss loss loss loss version version technique technique technique technique technique exp exp scheme scheme ai view view view estimates estimates capacity efficient classifiers classifiers choice statistics estimated pages give give con condition condition condition derived weighted bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds bounds area entropy entropy entropy processes processes nature depends constraint simply simply simply measured technical increases increases describe denote denote denote denote denote denote denote limited assumption assumption assumption assumption proof proof theoretical theoretical theoretical theoretical theoretical main main main journal journal instance degree functional unknown fully projection york york york uniform uniform uniform uniform uniform uniform empirical empirical empirical empirical empirical empirical empirical call numbers numbers numbers numbers numbers numbers numbers polynomial idea idea idea combined minimize minimize choose choose choose description perceptron improved exact separate typical apply apply apply apply introduced include recently recently relevant relevant relevant dimensions sufficient observations observations observations observations observations volume works tions tions smooth smooth differential trans definition definition definition definition definition evaluation observation generalized bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded bounded risk risk risk risk risk risk risk risk risk sensitive sensitive lead lead concept concept concept studied studied derivative derivative derivative matrices generally assumptions valued depend depend measures numerical clear practice asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic asymptotic weak characteristics drawn drawn sigmoidal demonstrated regularization regularization regularization regularization regularization minimizing introduce denoted reference van derive construct solving estimating ann ann label mathematical metric metric metric metric metric metric explicitly unique events minimization minimization springer springer springer implies implies expectation expectation yield yield family family independently independently formation review influence lemma lemma lemma lemma variation variation detailed restricted lee lee lee decomposition approximated margin completely constants measurements spaces spaces purpose symbol norm norm norm norm norm norm norm norm norm norm norm advantages transactions transactions david formulation sciences vapnik vapnik vapnik vapnik discuss specifically structural regular importance svm successful computations situation essentially online online soc verlag verlag verlag interested contribution hold satisfy quantity quantity simplified minimizes minimizes minimizes ill ill deal decreasing extend extend law parametric collection involving replaced hessian pursuit investigated boosting boosting boosting boosting boosting comparable func cover math analyze illustrate perfect quantities quantities greedy algo assumes taylor precise improving explain explain asymptotically asymptotically slowly inequality formula formula crucial smoothness smoothness smoothness analyzed analyzed improves improves explanation explanation independence briefly purposes sections widely organized style choices hyperplane hyperplane hyperplane mathematics mathematics consequence potentially universal definite author sun sun researchers behaviors understood parameterized peter haussler haussler rely extensions achieves achieves replace semi extreme pac pac pac indices notes mistake acm appropriately jones wrong convenient logarithmic logarithmic fan imposed grow balance analyzing implications effectiveness effectiveness symposium combinatorial combinatorial combinatorial combinatorial combinatorial generalizes composition lip weakly bartlett bartlett bartlett bartlett bartlett bartlett bartlett separating separating separating schapire zhang zhang zhang zhang zhang dependency dependency dependency regard infinity entries entries barron foundations indicator extends relies relies inf inf inf inf inf generalizing robert limitation appeared slight deriving covering covering covering covering covering covering covering covering covering covering covering covering covering covering covering covering covering covering covering covering covering chervonenkis formulate restrictions theorems regularity hierarchies tight param clas translated ibm ibm ibm rithms discontinuity bounding learnability regularized regularized regularized regularized regularized emphasize voting refined refined williamson williamson gorithm circumstances emphasis lecture attributed families families families shawe hilbert hopkins fre svd anthony meth cardinality restricting johns sions ods statist statist dimen edition ben baltimore tained penalizes watson watson ized amer derivations vergence kolmogorov kolmogorov lid predic heights lipschitz lipschitz dependences tong tong jensen fbr samuel seemingly eter agnostic logarithmically superpositions ofp pollard pollard timal compositions compositions yorktown chines yoav erm erm erm erm erm russian differen wee wee sauer bianchi alon cesa alp alp quanti flavor transac plugging discretize loan ofa iill iill sifiers maxx tbr tbr quencies mysterious 
#@Zhang_T,
#t13
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#*network network learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data data data data data data function function function function figure figure figure figure time set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output number number number number number number number number number system error results results results results results results problem problem problem problem models models models models models models hidden based based space space space space space weights weights weights linear linear linear case vector order order order order shown shown systems systems values values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method approach approach point processing rate rate rate test test test analysis matrix matrix matrix inputs form form form shows signal signal algorithms algorithms gaussian gaussian gaussian paper paper examples size net work methods methods methods methods methods methods methods features features classification process process process structure structure random show show show section section section general parameter parameter parameter parameter approximation approximation approximation approximation states theory obtained obtained obtained obtained obtained term experiments result university university university university variables variables variables computation computation computation computation computation research research independent independent independent defined defined found sequence target initial initial constant table table estimate estimate standard computer distance distance science science presented map present present present position position basis basis basis basis basis basis basis basis basis basis nonlinear nonlinear outputs outputs continuous abstract applied applied applied back find convergence convergence convergence convergence convergence density likelihood references stochastic important decision propagation mixture context introduction complex estimation estimation statistical statistical generated generated variance variance variance complexity variable variable variable variable assume assume assume signals prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior previous previous theorem theorem theorem theorem theorem theorem theorem type required good distributed distributed distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected markov markov markov markov markov markov markov markov markov techniques techniques techniques region probabilities errors errors errors errors forward scale scale finite simulations classes total simulation simulation simulation regression regression regression regression regression respect respect respect respect respect respect mapping factor dimension dimension obtain obtain obtain obtain obtain obtain obtain samples samples desired series series provide define compute perform perform perform posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints distributions distributions distributions distributions fields train train selection selection selection report report report institute department department implementation version kernel joint joint joint joint joint exp exp scheme addition addition framework framework cambridge cambridge cambridge cambridge cambridge computing equivalent equivalent additional estimates estimates transition top full full full full full full full full statistics statistics statistics statistics estimated validation con conditional robot robot robot robot robot area finally processes backpropagation iteration technical technical technical feedforward group group denote transformation inverse inverse corresponds corresponds predictions proof rbf rbf rbf rbf rbf rbf rbf rbf rbf rbf short implemented assumed assumed assumed assumed square square square end end easily degree including objective dynamical unknown unknown coefficients coefficients york leads details details bottom early magnitude idea denotes denotes denotes denotes discussed improve directions robust robust robust robust robust robust robust robust robust robust robust typical typical reported reported reported reported reported practical apply apply apply introduced include include include hierarchical hierarchical inference inference recently relevant engineering engineering interest interest highly varying compare previously previously previously observations observations observations volume tions correspond evaluation chain chain chain chain chain chain chain chain arm arm arm arm arm arm amplitude exists expression expression lead extended feed hybrid white occurs column setting setting demonstrate critical place assumptions conclusions accurate bayes bayes weak propose propose propose propose integration physics characteristics drawn drawn sigmoidal demonstrated proportional radial radial radial radial radial user min min targets monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo written longer index index sequential sequential sequential sequential estimating estimating estimating pruning metric implement explicitly infinite physical involves involves easy easy slightly belief angle consisting gaussians springer stationary variation showed showed approximations similarly converges converges converges converges key smoothing performing spaces closed norm euclidean euclidean david avoid coordinate usa contour sciences prove uncertainty uncertainty uncertainty specifically priors priors priors priors priors priors gamma gamma regular selecting middle uniformly suitable literature build computations computations schemes mackay mackay mackay plots plots plots plots plots identity compact verlag interpreted dis dis issue lie sin sin follow notation notation notation notation notation delayed automatically approximating deal software extend wiley environments hall mappings dependencies working surfaces contours quantities versions multivariate arbitrarily neal neal integrate asymptotically advanced cos cos smoothness variances variances growing benchmark perspective implementing berkeley berkeley berkeley berkeley precisely ran describing addressed researchers robustness conjugate conjugate conjugate geometric geometric geometric geometric geometric reflect introducing formulated http http http http poisson spread spread weigend weigend aim green green green enables inherent chose chose chose focused notes www www ratios extending smith consideration ments ments stronger chains simplify determination hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper hyper star methodology affected nonparametric exploring started corollary loo loo loo sion respective regarded dependency demonstration histograms accounts advance express eng eng eng indicator theoretically informative jump jump jump jump jump jump jump jump jump statement cam cam cam cam vari acknowledge treat approx land truncated specification specification specification specification annals shorter shorter ber adopt adopt adopt adopt adopt centre convenience england england principled home distri num proba proba rbfs rbfs rbfs cation worth tively mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc cubic page union lecture ergodic ergodic appearing bility jointly confirm firstly reversible reversible reversible reversible reversible reversible reversible reversible dom cast tribution svr scenarios scenarios rameters contrary implied dimen presently centres centres niranjan fication dent indepen fixing ira objectives mid imum comprehensive ambiguities aims aims ables phy impor imation treats mention tics statis ele llx buntine buntine parsimonious parsimonious holmes holmes holmes tant regularisation regularisation cued respec adopting adopting freitas freitas freitas freitas freitas readers equi quantifies encouraged ditional unknowns uninformative uninformative nuisance nuisance flamework obser referring identi gee vague sumption butions mfiller mahalanobis lution biometrika infeng devising athe bilistic vations soda clude favour consult milllet llxi specifi bernardo librium ier ier integra avenues isation chichester wol stead noticing alphabetical 
#@Andrieu_C,Doucet_A,de-Freitas_J,
#t13
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#*network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure time time time time time time time time time time time time time time time time time time set set networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number error error state results results results results results results results results information information information information information problem problem problem problem models models models models models hidden hidden hidden hidden hidden hidden hidden performance performance performance based based based based based linear linear linear case case case case case case case case case case case case vector vector vector order order order order order shown shown shown parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise unit distribution distribution distribution distribution distribution recognition recognition method method method approach approach approach approach approach approach approach approach approach approach approach point point point point point point point point single single processing processing processing large large rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal form form form signal signal signal signal signal signal algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper size task task fig step step step step step step step step points points field field classification classification process level structure structure structure structure structure structure structure random high similar similar similar show equation section section section section section fixed fixed fixed fixed line line line line rule rule rule rule rule rule rule rule rule general general general generalization speech speech speech speech speech parameter real average states states states states states theory gradient gradient obtained obtained obtained experiments dimensional result university variables variables independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent defined defined defined defined found initial estimate estimate standard terms terms terms terms terms terms distance left left left presented map map present present present phase phase phase low temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal temporal maximum press press press press learn learn learn learn components components components outputs outputs abstract applied applied applied back find computational convergence density density density density properties likelihood likelihood likelihood references component component procedure procedure procedure procedure procedure procedure procedure important important mixture mixture mixture mixture mixture context context context context context introduction complex hand hand statistical statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated variance variance variable assume assume assume lower rules rules rules signals signals signals signals signals signals prior learned learned learned learned chosen previous bound bound bound bound bound cases required required good good conditions bayesian bayesian expected expected equations equations markov markov fact fact fact fact fact probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed observed observed observed errors forward forward forward resulting resulting resulting resulting resulting ing ing computed computed computed computed computed respect respect respect multi eq times elements means means means factor factor factor factor factor factor factor factor factor factor factor factor factor factor made natural natural applications applications knowledge knowledge em em em em em em em em em em em em em em obtain obtain obtain original relative true true true true compared compared cross series series series series provide compute proc proc perform perform perform determined determined determined related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints distributions distributions distributions distributions distributions distributions mit mit mit contrast contrast contrast update update update dependent dependent source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source source modeling modeling selection selection words version technique technique technique individual joint exp exp scheme scheme addition considered framework framework framework framework framework cambridge cambridge cambridge computing directly directly hinton hinton additional additional view estimates transition transition transition transition transition transition transition stage stage stage efficient full requires requires significant approximate approximate approximate statistics statistics statistics statistics statistics statistics statistics free free free free free free world estimated validation give produce derived derived derived conditional levels product actual depends depends sampling constraint achieved discussion covariance covariance covariance covariance covariance covariance describe arbitrary arbitrary arbitrary arbitrary arbitrary hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm transformation transformation fast limited assumed assumed square square square square square square square square square makes noisy noisy including fit fit auditory probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic smaller smaller smaller underlying unknown jordan jordan jordan block block leads principal principal squared numbers iterations pre making idea idea minimize choose added sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources denotes denotes denotes recent correlations correlations exact exact exact advantage property property ensemble apply introduced introduced introduced moving subject inference sejnowski sejnowski recently speaker correspond achieve diagonal diagonal diagonal diagonal sparse separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation generalized generalized sensitive expression scaling suggests alternative touretzky white demonstrate conclusion starting place depend sigmoid sigmoid accurate bayes practice learns largest reduction reduction reduction reduction characteristics characteristics demonstrated solid solid labeled turn assuming start ica ica ica ica ica ica ica ica ica ica ica ica ica manner manner denoted denoted reference relation derive derive derive solving factors factors factors factors factors factors factors factors factors factors factors describes describes modeled modeled missing averaging averaging averaging averaging linearly dimensionality remaining easy text belief belief develop integrated gaussians gaussians applying predictive quality quality quality implies blocks blocks blocks expectation family independently reconstruction reconstruction reconstruction reconstruction correlated correlated correlated communication estimator densities densities densities densities operations updated lee lee activities suggested dashed normalization reduces combining fitting fitting filtering filtering advantages building coordinate formulation bell bell blind blind blind blind blind blind blind blind blind recognize plotted maximize mozer coupled successfully reason middle capable hmms computationally computationally computationally effectively successful efficiently schemes capture capture notice notice notice notice notice notice superior superior issue lie comp comp comp comp notation notation usual backward backward backward ill leading maximization maximization maximization attempt mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing approximating situations presents presents employed unlike unlike unlike transformed optimized dotted preliminary graphical graphical graphical hall dataset ml incremental int variational variational variational variational variational variational variational variational variational variational variational variational combine structured maximizing maximizing complicated configurations configurations opposite ensure quantities quantities quantities quantities algo observe academic art ith multivariate amari improving mixed motivated defines neal neal scenes separable crucial crucial sensors sensors sensors derivation variances fairly analytical adapted tractable tractable tractable baum baum tool london london turns snr snr snr sys sys sys arise optimize res demonstrates addressed considerably flexible effort introducing passed requirement mod characterize differs gave semi jaakkola contribute ghahramani ordinary ordinary indices college leen intractable intractable intractable intractable intractable accomplished lagrange summing temporally temporally rithm appropriately conditioned conditioned recover perfectly approximates reconstructed unity unity tem multipliers oja stronger exploit affected generalizes repeat sompolinsky prentice separating saul iteratively mental forecasting facilitate yang omitted omitted eqs pearlmutter variants exploiting multiplying ure emission roc ple achieving kluwer equivalently equivalently deriving recursively isotropic isotropic isotropic isotropic isotropic isotropic isotropic isotropic isotropic welch welch restrictions aij personal covariances constitutes avoided scenario param adapting factorial mutually mutually mathematically termed termed anal suffer det parametrized parametrized eters simplifies mix unpublished spite remark rabiner info info info advantageous dim dim invertible invertible invertible invertible jointly cliffs reflecting compo proposes englewood coincide separates juang autoregressive sij vanish exploits proves suffice indirectly focusing mach cichocki adv adv adv ysis stems facilitates facilitates linearities unobserved unobserved unobserved wiener quantified gij gij fractional couple parra ogy imposing reconstructions reconstructions attias attias attias attias attias attias attias schreiner unmixing unmixing poral nent gatsby gatsby orthogonality orthogonality multivariable namic ixi ogp ogp justifies 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#@Attias_H,
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#*network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model neural neural neural input input function function function figure figure figure figure set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm output number number number number number error error error error error error error error error error error error error error error error error error state state state state state state results results results results results results results units information information information problem models models models models models models models models based based weights weights weights weights weights weights weights weights weights layer layer layer layer layer case case order shown shown systems systems systems values values values values probability probability probability probability parameters parameters parameters parameters parameters parameters weight unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method approach approach approach approach approach approach approach approach approach approach approach single processing processing large large local local local local local local patterns class matrix matrix matrix matrix matrix optimal gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples small net work work methods methods methods methods methods methods fig fig fig fig fig fig fig step field field field field field field field field field field field field field field field field field field field field field field field field field field field field field field level structure structure random random random similar representation equation section section section section section section section section section section rule approximation average average states states states states theory theory theory theory theory theory theory theory theory theory theory theory theory theory theory obtained term term term term note note note note note experiments experiments dimensional dimensional university university university variables variables variables variables variables solution solution solution solution solution research independent defined defined found found standard terms terms terms terms terms node node node node node node node node node node node node node node node node node node node node node present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets press abstract find find find likelihood likelihood likelihood references component procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important propagation propagation propagation introduction introduction complex hand effect effect effect generated generated variance variance variance variance change complexity variable variable variable assume lower chosen chosen chosen higher previous previous previous previous previous bound bound bound bound bound bound bound cases required binary distributed equations equations equations equations equations equations equations make fact correlation correlation correlation correlation correlation probabilities probabilities probabilities forward forward forward scale simulations simulations resulting ing computed computed respect times means means made made made made study em obtain obtain obtain negative original artificial artificial samples compared compared desired desired provide perform perform determined determined related related distributions distributions distributions mit contrast contrast contrast contrast connection fields fields fields fields fields fields fields support dependent department loss implementation advances advances joint joint joint joint joint connectionist final final bias bias layers layers layers layers layers scheme scheme considered considered considered considered considered solutions top top effects effects effects effects effects effects determine full significant approximate approximate approximate approximate approximate free free pages give coding weighted weighted weighted weighted conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional bounds bounds bounds product actual provided evidence evidence evidence evidence evidence evidence evidence simply covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance describe group denote fast fast assumption assumption assumption assumption assumption assumption assumption assumption finding finding common assumed require journal future including fit fit fit objective probabilistic typically typically account account jordan jordan jordan jordan jordan interesting increasing consistent structures structures trials uniform uniform uniform principle making making bottom bottom bottom expert denotes improve improve correlations correlations correlations correlations correlations correlations correlations exact exact advantage advantage advantage introduced include inference inference inference inference inference inference inference inference inference inference inference inference inference relevant interest dimensions compare unsupervised approximately approximately calculated works solve smooth correspond studies diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal diagonal address improvement improvement improvement scaling deviation alternative feed generally generally generally generally demonstrate half strength conclusion minimal assumptions assumptions assumptions editors sigmoid sigmoid sigmoid sigmoid sigmoid accurate bayes clear performs faster practice taking strong strong presence physics drawn drawn intelligence intelligence assuming assuming assuming assuming start averaged introduce manner groups relation relation longer factors estimating estimating estimating multilayer remaining easy slightly belief belief belief belief belief belief belief belief springer quality solved solved solved evaluate evaluate approximations approximations approximated reasonable calculation calculation roughly roughly closed remains remains calculate calculate calculate visible query david includes inter prove discuss partially discussions extra uniformly suitable society computationally effectively effectively wij wij wij score quickly repeated repeated repeated procedures procedures procedures procedures interested interested interested interested interested split issue lie notation notation quantity write nips nips highest processors approximating approximating approximating approximating acknowledgments simpler layered layered layered layered layered layered poor difficulty difficulty integral graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical biases biases biases biases biases helpful variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational root editor editor opposite extremely extremely equally equally equally aspect quantities quantities quantities assumes contributions defines defines neal averages averages optimum integrate directed directed directed trivial crucial explanation expensive tractable tractable tractable worse london london products mathematics potentially separately medical fluctuations requiring improvements peter peter leave poorly solla slower calculating calculating calculating calculating calculating parent parent parent parent parent suited marginal marginal marginal marginal marginal marginal marginal gave sums sums jaakkola progress progress summed summed summed cor college intractable intractable intractable formally restriction royal proceed generality clamped clamped clamped clamped fits numerically fan attractive attractive attractive financial saul saul saul saul negligible competing specialized kearns kearns vari vari parents parents parents parents parents parents parents parents parents parents parents dramatically sig sig aston aston kluwer conjecture convenience examining demon cohn distri considers sollich sollich sollich sollich sollich figs completed bution sigmoids stimulating jointly barber barber barber barber barber king drawing neglect beneficial arriving lnp sian gaus compromise sweep sweep sweep birmingham inappropriate modest ues repeating repeating repeating prime biophysics marginals marginals marginals marginals marginals marginals marginals marginals marginals marginals marginals marginals excluded whilst whilst broader quadrature quadrature quadrature tailored netherlands maximising fac ncrg rni rni rid kappen kcl unconditional technically cycling absorbed strate eft sil nijmegen bert lui factorised factorised factorised factorised factorised factorised factorised factorised parameterised parameterised rii eri nificantly ational 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#@Barber_D,Sollich_P,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function figure figure figure figure time set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm output output output output output output output output output output output output output number number number number number number number number number number number number number number number number number number number error results results results results results units units units units units units units units units units units units units units units units units problem models models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance based based based weights weights weights weights weights weights linear layer layer layer layer layer layer layer layer layer layer case case case case case case case case case vector vector vector order order order order order order order order order order order order order order order order order systems values values values values values values values values values values values values values values probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight weight weight functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition method approach approach approach pattern large neuron neuron test test test test test analysis analysis analysis analysis class inputs inputs form form form shows shows simple simple simple simple simple simple paper paper paper paper paper paper examples examples small small small small net net work work task methods methods methods fig features features features features features classification classification classification classification random random random random random high high high high high high high high high high high high similar representation representation representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture show show fixed fixed line images generalization generalization parameter approximation approximation approximation average average gradient gradient obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university threshold variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables log log log log log log log log log log log found table table table estimate standard terms connections connections connections node left left left left left left left left map map low nodes machine machine sets sets sets sets sets maximum maximum press press learn outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample abstract applied applied computational likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic positive mixture context context context introduction statistical statistical variance cost tion tion difference difference variable variable variable variable variable variable variable classifier lower lower rules prior prior prior prior prior prior prior learned chosen chosen chosen chosen chosen higher part part previous previous cases cases cases cases cases cases cases cases cases cases cases type type required binary binary binary binary represent represent bayesian bayesian bayesian bayesian bayesian bayesian proposed proposed proposed proposed proposed proposed proposed proposed proposed correlation probabilities probabilities probabilities probabilities observed observed observed observed forward tasks total total total human computed computed computed respect multi multi multi multi multi multi multi multi multi multi multi sum sum sum sum performed eq called elements factor optimization made made applications applications knowledge knowledge em obtain obtain obtain obtain negative original represented represented true true true compared compared application cross cross cross cross cross cross provide compute compute compute experimental related related connected connected connected connected connected connected connected distributions distributions distributions distributions distributions distributions distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete approaches approaches mit train modeling modeling modeling modeling modeling modeling modeling modeling morgan loss implementation joint joint joint joint joint joint joint joint joint joint joint represents represents responses exp layers addition graph graph framework equivalent directly full full full full requires requires requires choice significant significant significant significant significant significant significant approximate statistics statistics free free free estimated pages validation validation validation validation validation validation give give con con condition conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional types product product product actual finally depends simply discussion normal normal arbitrary group group group group group group group group group group group group group group group group group tested tested inverse corresponds predictions amount amount amount amount nearest common implemented assumed role square end pixel easily easily easily easily degree degree kaufmann probabilistic probabilistic typically pairs pairs pairs pairs pairs pairs combination account account account account account fully fully fully fully fully fully fully testing testing testing testing significantly york empirical principle representing call max direct expert expert decay decay polynomial polynomial polynomial polynomial polynomial polynomial polynomial idea combined choose choose choose choose exact exact pair pair separate takes takes element element reported machines quadratic sense inference highly previously previously works works yields correspond studies trans increased occur extended digital hybrid generally conclusion reduce reduce neighbor valued depend depend depend differences bayes bayes bayes bayes bayes bayes bayes bayes clear constrained suggest encoding propose propose taking taking taking taking taking hard drawn california proportional assuming assuming user groups groups groups groups scene connectivity connectivity force question tuned mathematical dept modeled pruning pruning pruning pruning pruning missing missing missing missing missing multilayer category averaging dimensionality dimensionality dimensionality easy integrated predictive predictive select yield dependence communication estimator restricted approximations approximated approximated similarly digits partition past reasonable smoothing smoothing expansion expansion expansion expansion expansion penalty penalty penalty topology topology precision figures combinations combinations combinations combinations combinations priori extension extension extension extension illustrated maximize maximize maximize priors neighbors tests tests tests tests simplicity regular selecting extra differ encoded detect build build build computations capture capture capture allowing heuristic showing interpreted split superior classify comp hypotheses illustrates approximating approximating deal extend simpler unlike unlike parametric parametric parametric wiley exponentially put involving association graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical biases biases biases combine dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies dependencies maximizing comparable tanh statistically statistically statistically neu plausible possibly possibly editor logistic logistic logistic logistic multivariate multivariate mixed cart pairwise pairwise pairwise variances comparisons stanford arc arc organized ran bengio bengio bengio bengio bengio bengio bengio bengio controls cut optimize optimize auto addressed improvements improvements improvements items tional tional orders orders orders item share incorporated mod limiting incoming marginal marginal conditioning conditioning conditioning conditioning conditioning conditioning deviations softmax softmax naive naive naive naive naive naive naive ordinary ordinary ordinary ordinary guarantee summing resources databases ordering ordering ordering ordering approximates null eliminate generality inspired adds dealing ments promising intelligent grow reasoning ral elimination contexts contexts ranging encountered pruned pruned pruned pruned pruned pruned pruned pruned pruned dependency dependency dependency dependency dependency captured counting chooses approximators multiplied smoothed smoothed canada canada hart fold vari parents parents parents parents parents parents parents assigning severe uci uci uci posteriori approx ure dna dna dna helmholtz sig basically basically equivalently ber ties encouraging tween theorems multinomial multinomial multinomial multinomial multinomial multinomial multinomial duda num decays distribu playing wise statistic statistic statistic statistic dirichlet dirichlet dirichlet dirichlet pearl tied inversely frey frey frey frey frey frey frey parametrized october experi architectural expansions expansions ble handling satisfactory curse curse curse arrow diffuse mining mining dom val condi archi systematically maxi maxi sions binomial binomial binomial binomial binomial binomial binomial binomial binomial binomial meant elec concatenated tained prune greatest montreal montreal hits ues unobserved hot kolmogorov ables mum approxima simulates putting web switzerland named ranked tecture impressive vectorial ire yoshua possi independencies independencies ences rue handles chow anomalous heuristically orderings orderings parenthesis probabili tuples polyno propor argues lauritzen iro mial stdev stdev stdev stdev nary multinomials multinomials multinomials imizing umontreal regressive montrdal universitd nificant marginalized lected 
#@Bengio_S,Bengio_Y,
#t13
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#*network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time set set set set set set set set set set set set set set networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number system system error error error error error error error error error error error error error error error error error error error error state state state state results results results results results results results units information information problem problem problem models models models models hidden hidden performance performance performance performance performance performance based based based based based based based based based space space weights weights weights linear linear layer layer case case case case case case case case vector vector vector vector vector vector order values values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution approach approach approach approach approach approach point point point point point image single single single single single single single single processing large test test test test test test test test test test test test matrix matrix matrix matrix matrix inputs shows shows shows shows shows shows shows shows algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper feature work methods step step step step step step step step step step step step step step step points process process process process level current trained trained random high similar representation show show show show show show equation equation section section section section section section section section section section fixed fixed line line line line rule rule general general generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter parameter real real real real real real real real states term note note note note experiments experiments experiments experiments experiments experiments experiments dimensional dimensional result result variables solution independent log log defined defined found found found sequence sequence sequence sequence sequence target target target target constant constant table table estimate estimate estimate estimate estimate estimate estimate standard standard standard terms terms prediction prediction left left left left left map map map map map map map present present low sets sets sets sets sets sets sets sets sets sets maximum maximum maximum maximum maximum maximum learn learn nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous continuous continuous continuous sample abstract applied computational density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood references due due due due positive important important mixture mixture mixture introduction hand estimation estimation estimation estimation estimation behavior statistical effect dynamic dynamic generated generated generated generated generated variance variance variance cost cost cost change change change assume assume assume assume assume assume assume rules rules rules measure measure measure measure measure prior learned learned learned chosen center center cases cases type type type good distributed distributed distributed bayesian bayesian expected expected expected expected expected equations fact fact length correct probabilities errors errors errors forward forward forward scale finite resulting resulting ing ing ing ing ing ing ing tasks tasks tasks regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression multi multi performed performed times means optimization applications em em em em em em em em em em filter filter filter filter filter filter obtain obtain obtain obtain obtain obtain negative negative negative samples true compared compared compared application series compute location perform perform experimental experimental goal posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions equal approaches steps steps steps steps steps steps comparison contrast update update update modeling modeling code code code exp maps experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment additional additional additional additional view solutions estimates estimates estimates transition transition detection detection detection determine determine efficient full choice significant approximate approximate approximate approximate statistics free free free world world world world world world world con derived derived weighted weighted weighted randomly entropy selected nature simply discussion covariance normal normal normal normal tested inverse assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption assumption complete stable stable stable stable common common assumed main adaptation adaptation adaptation square instance instance noisy including including kaufmann kaufmann probabilistic unknown unknown unknown fully technology technology mlp mlp mlp mlp mlp mlp block special special mode mode mode mode mode mode mode mode mode leads leads leads leads leads squared squared squared squared squared squared details details window window decay minimize added added added added added description perceptron perceptron denotes improved robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust robust practical apply apply apply introduced subject inference subset interest interest sufficient highly compare compare compare compare compare smooth smooth observation interval interval lead lead lead scaling occur extended extended extended extended width width width pass pass starting critical assumptions reduce reduce conclusions conclusions differences clear exponential faster taking presence drawn targets targets targets identification derive derive derive derive solving factors sequential sequential sequential estimating estimating mathematical student student student student student student student student student student student student missing missing infinite infinite infinite infinite infinite gaussians gaussians gaussians gaussians applying minimization john choosing family stationary stationary stationary estimator estimator estimator influence influence influence influence densities evaluated evaluated evaluate evaluate evaluate evolution decomposition completely converges updates allowed reasonable reasonable reasonable smoothing smoothing smoothing smoothing dashed dashed dashed dashed dashed dashed dashed dashed additive additive additive additive additive additive expansion add penalty penalty tracking generation valid filtering filtering visible degrees degrees degrees degrees degrees degrees degrees degrees degrees degrees degrees degrees degrees batch characterized reason reason middle middle importance uniformly uniformly suitable computationally divided included modes presentation score score plots plots plots plots tend online online online online online online online online online online online online online online online online online online online online online online online online online online online online online online repeated prob interested interested interpreted superior follow backward backward backward backward nips nips leading predictor mixing approximating load extend bars wiley overfitting investigate kalman kalman kalman kalman kalman kalman kalman kalman environments involving estimators estimators optimized optimized optimized optimized dotted dotted ml ideas mse mse fault workshop workshop examined measurement measurement measurement measurement measurement thought quantities obvious algo taylor taylor fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher freedom freedom freedom freedom freedom freedom freedom freedom freedom freedom freedom freedom freedom art art consist great vor distinguish derivation derivation derivation track navigation adapted purposes sections organized constructing immediately mation commonly commonly commonly commonly definite researchers explained fourth reflects apparent improvements percent flexible flexible pseudo pseudo capability capability experimentally outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers maintain maintain ture limiting hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters replace replace logp logp logp logp logp germany germany boston boston boston expectations extreme extreme extreme realized realized consistently consistently tresp tresp tresp tresp tresp tresp tresp tresp uncorrelated rithm recover recover dealing dealing significance siemens siemens siemens siemens stated scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring scoring obtaining affected infor repeat started heavy heavy heavy heavy sion predictors infinity thomas thomas iterated sons std avoiding avoiding treat sequentially outperforms annals sig ent deriving leaming ber adopt residuals exception exception exception lit covariances ekf ekf ekf ekf ekf var param adapting penalized paired pos employing indexed west west universit nal increments mix housing housing housing housing walk lems remark bility instability instability corporate corporate smoother smoother supply suffices ooo deals arrives sliding drastically company inde sian niranjan gaus cauchy cauchy cauchy outlier outlier outlier artificially backwards inappropriate inappropriate fore repetitions repetitions lange lange nice triple pendent infeasible huber fluctuating mal mal manipulations volker volker offline offline offiine offiine offiine offiine offiine offiine chi exhibiting munich munich throw tums freitas penalizing wanted sunspot cov eter handles oft tailed tailed tailed tailed regres percentages app tunable lengthy depart sumption divisions divisions underly leverage leverage mchp mchp terior llt llt ifs eat tains chances curvatures argm argm influencing recursions recursions timate owt gaussi gaussi fraser river stemming seminar disturbed writ writ jasa jasa cholesky troduced dicate 
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#*network learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function time time time set set set set set set networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number system system error error error error error error error error error error error error error state results results results results results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models hidden hidden hidden performance performance based based based based based based space space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear linear linear case case case case case case case case vector vector order order shown systems values values values probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition method method approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern point point point point point point point point point point point point point point point point single single single large large large local local local local test patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix inputs form form form shows shows shows shows signal signal gaussian gaussian gaussian gaussian gaussian gaussian paper examples small small small work work work methods methods methods fig points points points points points points classification process process current trained trained trained cell problems random random random random random random random high high high high similar representation show show fixed fixed fixed line line vectors vectors vectors vectors vectors general speech speech speech speech speech speech speech speech speech speech speech speech speech real real real real real approximation average average average average average average theory gradient obtained note note note experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation computation log log defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence table table table table table estimate estimate estimate standard standard standard computer computer distance distance science science prediction prediction present present present present present present present present present present low low low low low temporal temporal temporal temporal temporal temporal sets sets press learn learn position position components components components components components basis nonlinear nonlinear nonlinear nonlinear outputs continuous continuous continuous sample sample sample sample abstract applied applied applied find computational computational computational computational density density density density density density density density density density density density density density density density density density density density likelihood references component due due ieee important important mixture mixture mixture mixture mixture mixture mixture hand estimation estimation statistical statistical statistical dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated generated generated generated cost cost cost cost recurrent search search search search search search search search search search search search tion tion energy energy complexity complexity variable variable variable variable variable variable variable variable variable variable spatial lower lower measure measure measure measure measure prior prior prior prior learned higher higher higher higher higher part part part part previous previous bound cases type required multiple multiple multiple multiple multiple binary long represent distributed markov markov markov make make make fact fact techniques region proposed length length length length length correct correct observed observed observed observed observed observed observed finite finite minimum minimum resulting resulting ing regression regression regression computed computed respect elements regions regions regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping means factor factor factor factor factor factor factor factor factor factor dimension global global applications study em em em obtain obtain obtain original original samples samples represented represented application application application application cross define define compute compute proc perform determined posterior constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints distributions distributions distributions distributions distributions discrete discrete approaches accuracy larger dependent selection report report loss loss implementation version technique joint joint joint joint joint joint joint joint joint joint joint joint represents difficult difficult graph sequences sequences considered considered framework computing experiment curve curve solutions curves trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory bit efficient requires requires requires choice approximate approximate world speed estimated estimated pages pages pages pages give give produce produce derived derived derived conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional clustering robot robot area actual processes selected selected iteration nature nature constraint constraint constraint simply simply achieved achieved discussion covariance normal normal normal technical transformation fast fast close inverse inverse inverse inverse assumption assumption corresponds complete complete complete predictions finding finding finding amount implemented implemented assumed generate generate role square easily objective probabilistic probabilistic probabilistic probabilistic probabilistic typically underlying underlying underlying combination combination dynamical functional unknown coefficients jordan jordan mlp mlp mlp mlp mlp programming programming programming programming programming programming programming programming programming character york increasing increasing uniform uniform database database database mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode principle language language squared squared squared squared squared numbers supervised supervised combined combined combined choose added added description description predict perceptron improve improve advantage advantage advantage robust robust robust practical apply apply apply strategy strategy include include include quadratic inference subset interest dimensions varying varying varying varying unsupervised unsupervised volume tions smooth smooth speaker achieve trans diagonal definition definition mixtures mixtures mixtures locations grid interval williams improvement sensitive arm arm constructed lead invariant suggests deviation wide predicted locally locally starting starting place place minimal row row row row assumptions depend measures measures faster practice practice constrained constrained constrained drawn regularization assuming movements decrease introduce groups acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic suppose appears relation pro pro van van derive produces solving sequential sequential sequential sequential estimating dept dept missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing missing multilayer multilayer multilayer physical dimensionality dimensionality dimensionality easy easy interaction gaussians gaussians predictive predictive quality blocks blocks select select select select john choosing dependence review reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction solved detailed evolution frames frames approximated approximated completely key key earlier reasonable slow dashed performing measurements measurements construction euclidean perceptual perceptual perceptrons perceptrons retrieval automatic uncertainty candidate aspects extra extra efficiency suitable suitable differ latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes committee identify identify literature literature efficiently comparing online soc soc heuristic dis return lie lie sin manifold follow generative strategies strategies strategies hold duration notation sampled nips nips nips nips attempt attempt consisted consisted approximating acknowledgments deal deal intrinsic modelling modelling modelling modelling situations bars bars carried parametric wiley poor requirements exponentially put relations dotted preliminary mass existence ideas rest rest rest mappings mappings relationships topographic topographic fundamental removed closest plausible plausible plausible plausible possibly generalisation configurations illustrate illustrate illustrate aspect aspect versions der der greedy mapped shapes shapes multivariate multivariate multivariate baseline percentage indicating rows track waveform adjacent briefly briefly worse london london straight preprocessing incorporate worst bishop bishop mation potentially potentially potentially hippocampal universal angles lowest incomplete incomplete incomplete robustness geometric geometric geometric geometric geometric flexible amounts amounts tional tional lack compares span http synthesis ture differs branch branch wind extensions curvature green gave kinds sophisticated comments multidimensional multidimensional consistently consistently pose representative representative ghahramani ghahramani tresp corrupted indices www optimality guarantee oxford oxford tation temporally recover recover recover perfectly branches mobile reconstructed reconstructed reconstructed reconstructed reconstructed reconstructed flexibility flexibility enhancement plays lost lost wrong dealing resulted keeping nearby obtaining fail utterance utterance utterance utterance utterance responsible spurious infor repeat saul codebook negligible ascent searching assembly assembly centroid approximators mlps mlps mlps matter contact draw sons papers speeds approximator vari vari consecutive posteriori outperforms audio unable unable gtm gtm gtm gtm gtm gtm gtm gtm gtm rubin ent ahmad exhaustive exhaustive exhaustive exhaustive exhaustive opposed break torque markovian markovian uniquely uniquely isotropic isotropic isotropic isotropic adopt ideally solely superimposed superimposed acceleration warping imagine reconstruct reconstruct options continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity continuity toy toy toy thick learnt regulation bump retain proach cation anal discusses articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory prevents tract tract computa mix coordination remark picking picking picking styles trainable hat curse generafive generafive optimisation dcs dcs neuneier condi incorporation practically partly sparsely ray rohwer rohwer html vocal vocal company multimodal sian wisconsin bumps bottleneck cess gaus compromise charles steve feb indirectly ically ous jan jan adequately unimodal cope maximisation renals amer amer ysis ripple stat predic ables ables recovers sydney minimise tongue mar def treats centroids centroids centroids conversations reconstructions reconstructions maximising regularisation confirms plp plp analysed reconstructing reconstructing reconstructing inferences cooke datum classifi generalised estima discarding pointwise pointwise pointwise pointwise pointwise bernstein rameter apr apr lacks lacks roweis sheffield sheffield jerk hermansky attains crete parison compensates coarticulation attaining plication pergamon athe svens coincident griffin excessively minimises minimises sondhi sondhi clude minimised interpre instrumentation conti eurospeech asymmetrically rived 
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#*learning learning data data data data data data data data data data data data data function function function function function function function function function function function function function function figure figure figure figure figure time set set set set set set set set set set set set set set set set set set set set set set set set set set set set training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm number error error error error error error error error error error error error error state results results results information information problem problem problem problem problem problem problem problem performance performance performance performance based based based based based based space linear linear linear case vector vector vector vector vector vector vector order order shown values values values values values values values values values values values values values values values values values values values values values values values parameters parameters noise functions functions functions functions functions functions functions functions distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method approach approach pattern pattern pattern pattern pattern pattern pattern pattern point control large large test test test test test test test test test test test test test test class matrix matrix matrix matrix matrix matrix inputs form form form algorithms small size size size size size size size task methods step step step step step step step step step points points points points points points points points points points points features classification classification problems problems problems problems problems problems random similar equation section section section section fixed fixed fixed vectors vectors general general generalization generalization parameter parameter parameter parameter parameter parameter average average obtained obtained obtained term note note note experiments experiments experiments experiments experiments experiments experiments university university variables variables variables solution solution solution research research log log log log log log log log found found found target dynamics constant constant table table estimate estimate estimate computer terms terms distance presented machine sets sets basis basis basis nonlinear sample sample sample abstract applied find find find find find find references positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure decision introduction estimation estimation estimation estimation estimation estimation classifier rules measure measure chosen bound required required required expected expected fact techniques forward simulations minimum minimum minimum minimum minimum minimum minimum minimum simulation regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression performed performed performed called called times elements elements elements obtain obtain obtain compared compared compared series rates rates experimental experimental goal steps steps comparison comparison support support morgan report loss loss technique technique technique technique technique technique technique technique technique consists joint joint exp exp scheme considered domain equivalent equivalent equivalent directly directly solutions estimates conference choice statistics free free estimated pages validation condition randomly robot bounds area finally constraint constraint achieved measured technical describe denote predictions finding amount end ability ability noisy kaufmann objective pairs pairs pairs pairs pairs functional functional functional functional functional functional functional functional functional functional functional functional unknown unknown unknown unknown unknown coefficients interesting testing testing testing testing testing testing testing testing testing york increasing database empirical empirical empirical squared call direct international idea minimize minimize minimize minimize minimize choose choose choose predict predict improved improved separate element introduced machines machines inference inference inference inference inference inference inference inference inference inference inference inference inference subset interest interest interest interest interest interest interest varying varying varying varying compare observations observations observations observations observations observations tions solve rl positions improvement arm exists expression expression expression derivative setting demonstrate demonstrate demonstrate runs runs accurate accurate performs suggest taking taking drawn drawn regularization minimizing minimizing minimizing min min averaged introduce characters suppose suppose suppose digit derive solving solving estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating estimating plot plot describes remaining develop applying springer quality expectation expectation versus depending estimator estimator estimator influence influence solved restricted soft sizes performing measurements classical classical classical classical purpose closed closed remains valid intermediate calculate usa usa vapnik vapnik vapnik vapnik vapnik vapnik plotted discuss tests structural extra svm svm summary traditional verlag link interested satisfy realistic minimizes minimizes minimizes minimized dual discriminant dataset dataset dataset dataset dataset dataset fashion giving mse mse mse func removed algo observe observe art art massachusetts percentage adaboost adaboost adaboost adaboost london london tive organized constructing ran leaves laboratories angles ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge ridge collected conducted red leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave leave introducing calculating differs datasets datasets datasets datasets chose chose chose chose chose chose boston boston boston boston boston unbiased corrupted rithm approximates partitions royal royal biased removing splitting selects service introduces corre heart sim cancer inductive inductive inductive inductive inductive partitioned splits splits material treat uci outperforms outperforms bank sigma sigma obtains hundred param summarizes denoting regularized regularized proach setup setup margins rewrite rewrite radio eters mini mini article article spite breast house val continuum fij economic repository corn tical ues imum postal rij incurred mum coincides dependences statis prices effector miiller ons iix kij diabetes rect sponds holloway holloway discrim kin kin kin kin georgia onoda pare vladimir onal vovk russian russian stepping saunders imize delve rrr egham rive ination scribe technometrics census olivier thyroid mizes surrey tradition vlad 
#@Chapelle_O,Vapnik_V,Weston_J,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model neural neural neural neural neural input data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure set set set set networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm error state results units units units units units information problem models models hidden hidden hidden based weights weights case case case order order order order order order shown shown shown shown systems systems values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition method method approach approach pattern pattern point point point point point point point point image single single single processing large large large local local local local test matrix matrix matrix matrix optimal optimal form form form shows shows simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual visual visual examples examples examples net net work work work work work methods methods methods fig fig fig fig fig fig points points points points field field field field field field field field field field field field field field field field field field current current random random random random random similar show equation fixed rule rule rule rule vectors vectors vectors vectors images images images images images images images images images real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average theory theory theory gradient dimensional dimensional dimensional dimensional dimensional dimensional university university university variables variables variables research log log log defined found found dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant distance science science direction present machine machine machine machine machine machine machine machine machine machine machine machine machine machine machine maximum maximum maximum maximum maximum maximum range press learn learn learn learn learn learn continuous continuous continuous continuous continuous sample sample sample sample abstract computational density density density density properties likelihood likelihood likelihood likelihood references component stochastic stochastic ieee procedure introduction introduction complex estimation generated generated generated recurrent recurrent recurrent recurrent recurrent tion change energy energy energy energy difference learned learned learned learned learned chosen chosen chosen chosen chosen chosen higher higher firing required multiple cortex cortex binary binary binary binary binary binary binary binary represent represent equations equations equations markov markov markov fact techniques techniques techniques techniques techniques proposed proposed observed observed observed minimum human human human respect respect eq eq eq eq eq eq eq called means means factor dimension made natural orientation orientation negative negative original specific samples samples samples samples samples samples samples true application application application desired desired series define objects rates proc determined determined related constraints constraints connected distributions distributions cortical contrast update update support report report implementation advances represents difficult difficult exp exp exp addition cambridge hinton hinton estimates conference efficient requires significant approximate approximate statistics statistics statistics statistics statistics statistics statistics statistics free free free free free free free vision basic derived derived randomly randomly developed developed velocity types entropy entropy entropy entropy product nature nature sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling constraint simply discussion discussion covariance covariance covariance normal normal normal normal normal technical technical describe describe describe group finding implemented generate generate face face face face face face face cluster easily makes makes fit simulated hopfield hopfield coefficients coefficients coefficients direct idea choose denotes denotes recent correlations correlations correlations correlations separate practical introduced include machines quadratic sejnowski sejnowski cognitive recently previously previously observations tuning tuning match match converge converge rl chain chain chain symmetric generalized parts parts parts parts invariant invariant invariant invariant invariant suggests alternative deterministic deterministic boundary setting demonstrate competitive competitive numerical numerical clear exponential practice taking presence demonstrated demonstrated minimizing minimizing derivatives derivatives derivatives minima minima annealing acknowledgements boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann boltzmann monte monte monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo carlo carlo solving solving primary plot laboratory distinct dept dept implement dimensionality involves involves involves involves belief equilibrium implies john interpretation solved detailed densities open updated approximations approximations approximations lee lee lee lee lee lee translation converges updates reasonable normalization reduces iterative iterative boundaries boundaries valid calculate calculate sufficiently faces faces faces faces faces views david building perceptual activations usa bell bell bell contour extension discuss characterized major efficiency uniformly differ computationally modes efficiently efficiently efficiently efficiently mackay mackay mackay mackay mackay mackay situation road interpreted dis generative generative generative generative sci satisfy gibbs bar absence approximating approximating approximating modelling poor investigate investigate difficulty replaced limitations limitations accurately divergence graphical biases biases examine matches successive analytically authors maximizing analogous contours matched hill illustrate illustrate eyes academic multivariate generates generates utility utility attempts defines neal neal averages averages averages averages averages averages averages spin slowly cos adapted expensive briefly lies worse tive tive sections located commonly laboratories laboratories inversion acad toronto toronto apparent evaluating substantially axes generic poorly employ maxima calculating calculating mod incorporating ordered ordered extensions suited suited marginal marginal multidimensional naive initialization consistently representative representative representative representative representative representative intractable saddle accomplished princeton princeton princeton nat clamped clamped clamped kullback murray numerically height balance hope fail intuitively sompolinsky sompolinsky slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice slice displayed displayed ascent washington captured initialize iterated modelled seung seung seung generalizing cam acknowledge ball ple incorporates pointing leibler kluwer validity cooperative cooperative cooperative aij reflected shaded distribu gener labs elementary ization rectified rectified anal funded sam grateful tune experi technologies technologies factorized factorized factorized factorized factorized nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative nonnegative interior stochastically ave evolved evolved evolved aid interpreting reflecting mining mining mining tribution ackley compo ally progressively evolving multimodal multimodal multimodal multimodal multimodal multimodal multimodal sian evolves confined fidelity subscript subscript ben ben gaus mul united ears ears unimodal unimodal rec daniel mountain developments amsterdam tivity sebastian graphically puter anticipate fac ative ative mented nent reconstructing roots aii circumvent flips travelling nato fimction decomposing kappen ballistic indexes indebted galland reflections reflections lucent lucent proximate kingdom suppressing overlaid walks spe rodriguez derlying chines xixj xixj xixj xixj oliver translationally translationally translationally translationally nicholas slicing downs downs downs downs downs yishai yishai competi specular schultz caught contrasting factorizable haim nately cavendish stimulates 
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#*network network learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input data data data data data data function function function function function function function function function function function function function function function function function function function figure figure time time time time time set set set set set set networks networks networks networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output output output output number number number number system error error error error error error error results results results results information information problem problem problem models models models models models models models models hidden performance performance performance space space space space weights weights weights weights weights weights weights weights weights weights weights linear linear layer layer layer layer case case case vector vector vector vector vector vector vector vector vector vector vector order systems systems systems systems systems systems values values values parameters parameters noise noise noise weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions recognition method method method method method point large large large large large large neuron neuron neuron neuron neuron neuron rate matrix matrix matrix matrix optimal inputs inputs inputs form form form shows algorithms simple simple paper paper paper small small small small small net net net net work work work methods methods methods step step step points points process trained trained problems similar similar show show equation equation equation equation equation equation equation section section section section fixed rule vectors general general general generalization generalization approximation approximation approximation approximation theory gradient gradient gradient gradient gradient gradient gradient obtained term term term term note note note note note result result result result result result university computation solution solution research research research defined defined defined defined defined target target standard computer terms terms terms terms terms node science science prediction presented presented map nodes nodes nodes press learn basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs abstract applied applied applied applied applied applied applied back computational properties properties properties properties references component component due ieee important important adaptive propagation introduction behavior dynamic dynamic change change difference complexity variable variable variable variable assume rules representations higher higher center previous cases type type type required required required distributed equations equations equations equations equations equations equations equations equations equations equations equations proposed correlation correct correct forward forward forward forward forward resulting ing ing respect respect respect respect respect respect respect respect respect performed times mapping mapping mapping optimization optimization optimization dimension made natural feedback feedback feedback original artificial artificial specific specific specific application series series define define define define define define compute proc perform perform perform perform determined experimental goal related equal equal mit steps train descent dependent source modeling modeling modeling modeling morgan institute institute technique technique technique technique internal advances final final layers considered framework cambridge cambridge cambridge computing equivalent equivalent hinton additional solutions estimates transition limit top efficient approximate free free pages pages pages pages pages derived derived bounds types product finally finally selected evidence backpropagation backpropagation backpropagation backpropagation depends depends normal normal normal normal feedforward feedforward feedforward feedforward feedforward feedforward feedforward arbitrary arbitrary arbitrary denote fast complete complete complete amount common require main easily easily easily easily noisy including including including kaufmann objective combination unknown unknown unknown unknown unknown unknown unknown unknown mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp mlp interesting character character special special special special call iterations making magnitude magnitude magnitude decay decay decay decay decay minimize architectures exact exact exact property property typical practical apply apply introduced introduced introduced include identical identical sense cognitive approximately calculated calculated volume volume works works works yields yields yields yields correspond differential differential differential differential differential differential differential background background chain separation modified entire entire expression lead lead lead lead lead studied wide derivative derivative derivative derivative derivative white white white white white setting pass pass pass pass pass demonstrate strength starting place conclusions conclusions operator operator operator operator operator operator operator operator operator operator editors editors tangent tangent tangent tangent tangent sigmoid accurate accurate numerical clear moody faster practice strong largest largest sigmoidal demonstrated regularization radial radial turn variety variety minimizing minimizing minimizing user user introduce introduce derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives derivatives denoted acknowledgements appears derive index optical ways describes mathematical dept multilayer multilayer multilayer explicitly explicitly transformations applying applying applying applying john expressed dependence evaluated evaluated showed converges constants partial partial partial expansion fitting penalty penalty remains calculate calculate calculate calculate transactions avoid building existing perceptrons blind extension specifically domains discussions extra suitable society divided divided driven symbols symbols wij wij build identity ten refer conf quickly cun cun prob showing superior sin sin hold notation notation notation notation write backward backward backward backward nips eigenvalue eigenvalue denker thresholds consisted deal unlike unlike poor poor perturbation collection requirements requirements difficulty hanson hanson hessian hessian issues lippmann mass mass mass biases helpful scalar scalar scalar applicable analytically tanh concepts editor editor extremely illustrate portion taylor improving submitted chaotic chaotic chaotic great cos cos publishers derivation derivation derivation derivation derivation derivation analytic analytical independence multiplication baum implementing implementing implementing implementing sections formalism formalism formalism formalism strictly operators operators choices simard simard simard universal describing calculations optimize optimize optimize optimize optimize optimize auto annual exemplars mechanics conjugate prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop prop applies double double double double double affine generic generic parameterized calculating calculating calculating calculating calculating passes passes controllers richard lim differentiable differentiable differentiable arithmetic equivalence modify princeton optimizing optimizing optimizing generality saturation adds tools simplify imply effectiveness lyapunov motivation motivation evaluations excellent introduces ambiguity infinity thomas mlps mlps mlps mlps mlps refers refers erlbaum pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter pearlmutter insensitive lem approx suboptimal chaos chapter chapter chapter letting hillsdale auxiliary auxiliary auxiliary auxiliary auxiliary auxiliary principe principe eric jacobian jacobian jacobian jacobian jacobian jacobian jacobian jacobian jacobian jacobian jacobian jacobian invariances exponent allocated met differentiation differentiation complementary hornik library confusion parametrized holding ignoring differentiating differentiating differentiating differentiating november nec nec coming rarely stephen sees imple puts industrial determinant russell petsche characterizes william fair ready scott thresh steve lar corn problematic shortly penalizes talk supposed drucker percep gallant enforcing elegant obeys parra imation internally bifurcations deco deco mented earliest functionals ons encoders gression descriptive descriptive kuo kuo today mexico particu albuquerque sensitivities patrice quantifies subscripts victorri targeting joe stinchcombe tunable gary subsection spend referring funding suspect barak barak jacobjan tron mathe halbert halbert cga matical blackwell blackwell superscripts lucas olds jos oyi arguably 
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#*network network network network network network network network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural neural neural neural neural input input input input input input input input input input input input input data data data data data data data data function function function figure figure figure figure figure figure time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number system system system system system error error error error error error error error error error error error error error error error error error error error error error error error error error state results results results results results results units units information information information models models models models models models models hidden hidden performance performance performance performance linear linear linear linear linear layer layer layer layer layer layer layer layer vector vector shown shown shown shown shown systems values values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters noise noise noise unit unit distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition method method method method method method pattern pattern pattern point point point point point point point point point point point point point point point point point point image image single processing processing large large large local local local local local local local local local local rate rate rate rate rate rate rate rate rate test patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal inputs form form form form form form shows shows shows shows shows shows shows signal algorithms simple simple gaussian paper examples small size size size size size work task methods methods methods methods methods methods fig fig fig fig fig fig fig fig fig fig step points points classification level current current current current trained trained trained problems random high similar show show show show show fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule vectors vectors vectors images images general general general parameter approximation average average theory theory gradient obtained dimensional university computation computation computation independent independent independent independent log log log log log log log log log log log log log log found found dynamics dynamics dynamics dynamics estimate standard computer terms distance connections science science prediction prediction presented low machine machine machine machine sets sets sets maximum maximum maximum range press abstract applied applied convergence convergence convergence convergence convergence convergence density properties likelihood likelihood likelihood likelihood references component component component component due ieee procedure adaptive propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation complex dynamic dynamic generated variance variance variance variance variance variance variance variance tion tion difference difference lower lower measure representations learned learned previous cases cases cases cases cases cases cases type type multiple good make make fact length correct probabilities probabilities errors errors errors errors errors errors errors errors errors scale scale scale scale scale scale total computed computed computed sum performed performed performed called times times times elements elements means means means means means means means means means means means means means means means means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor made global global em em em em represented represented represented define compute compute compute rates rates rates perform perform perform determined determined determined posterior posterior distributions distributions equal mit larger larger contrast contrast update update descent dependent consists consists consists individual advances difficult considered cambridge computing computing computing computing computing computing directly hinton hinton hinton curve curve curve curve solutions curves curves curves curves curves curves curves curves curves estimates top top top top top top top top top top top effects significant significant approximate vision estimated estimated increase increase give give con produce condition condition coding coding coding randomly randomly levels levels levels levels levels levels lines selected iteration iteration iteration iteration iteration iteration biological measured measured covariance normal close close stable stable nearest nearest nearest nearest generate eds face face face face face pixel ability ability sensory sensory sensory simulated simulated simulated simulated probabilistic probabilistic smaller smaller smaller needed needed combination combination reduced jordan block edge edge principal iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations iterations max normalized bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom bottom combined combined produced produced produced predict perceptron perceptron perceptron perceptron improved recent recent exact exact exact exact exact exact separate separate takes takes takes takes include pixels trees inference inference inference inference inference inference inference inference inference inference inference inference inference inference dimensions dimensions compare unsupervised axis axis match converge converge trans diagonal diagonal diagonal diagonal diagonal diagonal diagonal modified modified observation storage increased increased exists exists exists exists horizontal expression expression expression expression studied suggests digital wide matrices matrices matrices matrices matrices occurs generally generally pass pass pass pass pass pass minimal reduce depend depend differences accurate numerical performs performs exponential exponential exponential largest largest largest reduction cycle solid variety start suppose appears derive derive derive produces factors factors factors factors factors factors factors factors estimating estimating plot stability vertical multilayer multilayer multilayer multilayer simultaneously dimensionality slightly belief belief belief scales equilibrium gaussians applying blocks versus versus versus versus versus versus versus cycles cycles cycles cycles cycles cycles cycles focus communication viewed codes codes variation operations updated modulation modulation modulation modulation modulation modulation forms approximated approximated sizes sizes sizes sizes sizes sizes converges updates updates updates updates updates updates updates allowed allowed dashed dashed performing epochs epochs sec iterative iterative iterative iterative closed initially filtering faces precision avoid expect batch neighbors neighbors neighbors neighbors successfully successfully successfully major sensor sensor sensor sensor sensor sensor delta computations computations computations mackay mackay mackay mackay mackay mackay comparing comparing online online online online online online online online online online online online online identity identity identity summary notice graphs graphs graphs graphs repeated decoding decoding decoding prob prob interested interested issue lie generative generative write simplified dot dayan dayan dayan dayan dayan dayan eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue schedule schedule requirements steady divergence divergence dotted graphical graphical graphical graphical rise rise matches successive fashion incremental applicable parity tanh workshop encode understand analyze created explored initialized initialized epoch simplest arbitrarily neal neal neal neal neal optimum optimum years costs sensors sensors sensors sensors variances variances variances variances variances variances variances variances variances variances variances variances analyzed unstable improves adjacent answer turns turns turns widely worst cut summation fourth people prop prop parameterized solla slower ity http http modulated reaches achieves achieves sums sums logp chose begins median median specifies converged converged softmax distortion globally pose person sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep sleep zemel approximates nonzero extending communications proceeds logarithmic logarithmic check preparation presentations filled substituting excellent excellent ranging ranging ranging studying colorado captured dif infer late kearns horn canada passing passing correcting correcting correcting messages cam convergent vari drop slight minus vec helmholtz weiss weiss amplitudes wake wake wake wake wake wake wake wake wake wake wake adapting modifying community diag diag diag diag diag picked smyth pearl pearl denver esti book loading behave frey frey frey frey 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#@Frey_B,
#t13
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#*network network learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure time set set set set networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number number results results results results results results information problem problem problem problem models models models models models models models models models models models models models hidden hidden hidden hidden based space weights weights weights linear vector vector vector vector vector vector shown shown parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise weight unit unit unit distribution distribution distribution distribution distribution distribution method method method method method method method approach approach approach approach approach approach approach point point point single large local local local local local local local local local local local local local test analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal inputs form form form form form shows shows simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples small size size net work methods methods methods methods methods points points points points points points field classification structure structure structure structure structure structure structure problems problems random random high high show show show show section section section section section fixed fixed line line general parameter parameter parameter parameter parameter real real approximation approximation approximation approximation approximation approximation approximation approximation approximation average theory obtained term note note experiments dimensional dimensional dimensional dimensional dimensional result result university university variables variables variables variables variables computation computation independent log log log log log found found found initial table estimate estimate estimate terms left left left left left direction present machine sets sets maximum maximum maximum maximum maximum maximum range press press press components components components components components components components components components components components components components components components components components components sample sample sample sample abstract applied applied applied find find computational convergence convergence density density density density density density density density density density properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component stochastic ieee positive procedure procedure procedure procedure procedure procedure important important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex effect generated generated generated variance variance cost search tion difference complexity complexity complexity variable variable lower lower prior prior prior prior learned part part bound bound required multiple good good long conditions represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected equations markov markov fact correct finite resulting respect means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor dimension dimension made natural global knowledge em obtain obtain artificial artificial specific samples samples true true true true true true true true application desired cross provide provide define compute proc proc proc proc proc perform related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior constraints distributions distributions distributions distributions distributions distributions distributions discrete approaches approaches approaches approaches mit mit mit larger support modeling report report report report difficult difficult difficult exp exp exp exp exp considered cambridge equivalent experiment experiment experiment hinton hinton additional estimates estimates estimates limit top top determine determine efficient efficient full full full significant approximate approximate free world estimated estimated increase increase validation coding derived derived weighted conditional conditional clustering developed lines lines finally finally finally finally evidence evidence evidence evidence evidence evidence evidence evidence evidence evidence iteration sampling sampling sampling sampling sampling discussion covariance covariance covariance covariance covariance covariance normal technical technical technical increases increases increases describe arbitrary denote denote denote tested fast inverse finding finding finding effective assumed role main main square ability instance cluster cluster cluster future easily easily makes fit fit objective objective objective probabilistic probabilistic needed reduced account unknown unknown unknown block structures structures principle leads principal principal stored bottom bottom experts choose run added sources denotes correlations exact exact exact exact exact exact exact exact exact robust separate ensemble ensemble element typical sense inference inference inference inference inference inference inference inference recently dimensions dimensions dimensions dimensions unsupervised observations works works works axis tions pca pca pca pca converge diagonal diagonal mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures chain symmetric bounded bounded matrices matrices matrices matrices correctly correctly deterministic deterministic clusters clusters generally generally column runs starting reduce bayes practice practice integration integration integration physics largest reduction reduction solid proportional intelligence start start decrease relationship introduce manner digit pro monte derive derive carlo longer factors plot laboratory dept simultaneously averaging averaging averaging averaging linearly infinite dimensionality dimensionality dimensionality dimensionality dimensionality dimensionality easy belief scales integrated adding adding adding gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians applying predictive predictive predictive predictive predictive predictive predictive predictive springer expectation expectation choosing review correlated detailed densities densities evaluate approximations approximations approximations approximations approximations frames forms similarly allowed allowed processor key slow dashed performing sec fitting advantages degrees precision precision precision avoid avoid includes priori automatic uncertainty priors priors priors priors priors priors priors columns gamma gamma straightforward middle middle closely importance importance importance importance importance importance importance encoded computationally computationally computationally latent successful efficiently efficiently mackay mackay mackay online identity capture refer conf conf verlag repeated procedures prob prob heuristic neuroscience split split contribution generative sci comp sampled vary usual highest automatically attempt moves mixing mixing intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic intrinsic modelling unlike unlike poor overfitting overfitting overfitting overfitting overfitting overfitting difficulty varied put relations detail divergence divergence divergence divergence divergence dataset ml ml ml ml ml fewer fashion incremental applicable int variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational analytically fundamental analogous circles editor created quantities quantities quantities assumes freedom finds finds attempts attempts synthetic synthetic synthetic neal neal integrate integrate integrate inequality inequality guaranteed guaranteed independence tractable tractable london london london choices ran bishop bishop bishop bishop toronto auto conjugate conjugate conjugate conjugate integrating integrating requiring greatly limits empirically relevance relevance pseudo tional tional embedded poorly poorly poorly employ maxima maxima maxima maxima maxima maxima maxima robinson http partitioning ture ture ture fall hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters parent parent suited marginal green conclude attraction unbiased unbiased unbiased progress multidimensional univ univ merging pose ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani ghahramani college college aligned redundant intractable intractable intractable notes www formally tation pick pick recover perfectly addresses grows plays spiral spiral spiral spiral minutes accepted accepted accepted accepted overcome alpha determination determination removing star fail splitting monotonically optimally heuristics falls appendix appendix appendix captured laplace laplace laplace infer infer infer thin indicator repeatedly roy splits splits exploiting papers inf inf inf alternatively avoiding avoiding avoiding vari vari escape boxes posteriori approx constitute incorporates deriving inferred inferred ties die die incrementally seek covariances multinomial tor england letting discovering discovering var assess reject remainder principled attempted attempted attempted mhz diag pami thick approxi disadvantage rectangle plate rejected rejected integrals integrals dirichlet dirichlet dirichlet represen monitoring monitoring portions happen loading loading loading loading loading mcmc mcmc mcmc mcmc mcmc normalised drops treating exploited article simplifies differentiating mix mix mix lems picking syn opti insufficient vis vis transforming stochastically hoc responsibility optimisation optimisation optimisation optimisation determinant dom stay proportions proposal proposal rasmussen inferring cardinality inefficient deals zoubin zoubin zoubin outgoing rameters nontrivial lnp lnp prone prone rectangles reviewed assessed repetitions maximisation costly adv adv adv mfa mfa mfa mfa mfa mfa unobserved tipping ard proximation proximation spent assessing occasionally unifying crg plexity ables approxima graphically inability tailored icann imation extrema mal undesirable posteriors posteriors analyzers attias attias maximising ninth jensen jensen fac pri nakano draws spontaneously initialised initialised responsibilities ana gatsby gatsby gatsby roots birth birth birth birth exposition maximise cov independencies govern concentrates waterhouse minimising gat selec encouraged ucl ucl queen death richardson neur neur shrinking shrinking shrinking roweis ond sampler technically cycling optimising mations roberts merges varia varia criticism thereof neut meters resorting dimensionalities dimensionalities dimensionalities dimensionalities dimensionalities dimensionalities dimensionalities deficiencies advan ellipses ellipses taneously precisions precisions simul delve matthew ances warrant tages caught ameters ameters prep interpretability iance awe ational matic wcin compromises rla yla infers infers yls bracketed cavendish transparently 
#@Beal_M,Ghahramani_Z,
#t13
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#*learning learning learning learning learning model neural input input input input data data data data data data data data data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure time time time time time set set set set set set set set set set set set set training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number error error error error error error error error error error error error error error error state results results results results problem problem problem problem problem problem models performance based based space space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear linear case case case case case vector vector vector vector vector vector order order order order values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability noise functions functions functions functions functions functions functions functions functions functions distribution method approach point point point point point point point point point point point single single single single single single single control rate rate rate rate rate rate rate rate rate rate test test test test test test test test test test test test analysis analysis class class class class matrix optimal optimal form paper paper examples examples examples size size feature feature work task methods methods step step points points points points points points points points points points points points points classification classification classification classification classification classification classification classification process level current current trained random random random high show section section section section section section fixed rule vectors general general general parameter parameter parameter real real real approximation approximation approximation theory theory obtained obtained obtained note note note note note note note note experiments result result result university university university university university threshold variables computation solution solution research independent found constant estimate estimate estimate estimate standard standard standard standard computer distance science prediction prediction prediction left left left direction direction direction direction direction presented present low low low low machine machine machine machine sets sets press position position position components outputs sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied back find computational likelihood references due due positive important important decision decision decision decision introduction hand estimation estimation estimation statistical statistical generated variance tion tion difference variable assume classifier lower measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure measure prior prior prior prior prior chosen higher cases required binary bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian region length forward finite resulting resulting classes performed called called times times mapping means made applications applications applications applications knowledge knowledge obtain obtain samples samples samples true compared application desired desired provide define define define define objects determined determined determined determined determined determined experimental goal goal posterior posterior posterior posterior posterior approaches mit accuracy comparison larger contrast update support support support support support proceedings report report department loss loss loss loss loss loss loss loss version version version version version version version version version version version version technique code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances joint represents exp exp scheme ai maps considered considered curve curve additional additional view curves estimates estimates limit trajectory trajectory trajectory effects determine efficient classifiers classifiers classifiers classifiers upper world estimated pages pages give con randomly criterion criterion bounds bounds product finally nature sampling constraint technical technical technical technical technical assumption corresponds predictions predictions predictions rbf common common generate journal hypothesis future including combination combination reduced functional unknown fully programming programming interesting significantly ratio ratio consistent consistent consistent uniform uniform empirical principle principle principle leads max max max direct idea idea combined perceptron perceptron improved directions exact property takes practical introduced introduced strategy machines sense inference inference inference inference inference subset interest approximately approximately calculated calculated volume volume volume volume volume volume volume volume volume axis solve correspond achieve diagonal bounded bounded risk risk risk risk risk risk sensitive sensitive exists lead lead lead extended deviation deviation deviation boundary boundary setting setting setting demonstrate demonstrate runs starting starting critical minimal minimal trajectories conclusions valued differences measures measures measures bayes bayes bayes bayes practice suggest suggest largest reduction characteristics drawn drawn drawn demonstrated california proportional acknowledgements suppose solving solving estimating estimating estimating plot label label label label label label label label label label mathematical confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence confidence infinite remaining adding springer springer springer expectation expectation expectation versus select choosing choosing expressed expressed dependence viewed restricted labels labels labels labels labels fraction margin margin margin completely suggested digits sign sign sign classical spaces spaces reduces combining purpose add intermediate calculate calculate advantages avoid handwritten kernels combinations perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons perceptrons instances determines vapnik vapnik vapnik vapnik vapnik uncertainty priors partially discussions simplicity importance society maximal svm svm svm svm svm svm svm svm identify capture capture verlag contained allowing stopping stopping issue symmetry classify paradigm highest highest mixing bars american varied put estimators association mass hall discriminant existence ideas project referred structured working working working working working working working working working working working working working working working working working working induction induction smallest coarse closest closest possibly generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation generalisation spline thought der der taylor great inequality costs crucial growth defining london considerable style incorporate located mathematics medical medical depicted summation reflects greatly experimentally experimentally effort reliability compares schematic berlin berlin berlin berlin berlin aim suited achieves achieves achieves marginal sums germany returns focused diagnosis pac pac pac benefit formally guarantee restrict resources hyperplanes hyperplanes approximates discovery royal proceeds determination hit obtaining reasoning carry financial corre guarantees dependency dependency intended heart consequences sphere advance treatment reveals indicator offer arrive record inductive considerations splits ball ball ball ball assigns accumulated uci uci linked svms svms svms svms ple rigorous pointing outperform opposed rejection rejection rejection rejection rejection rejection rejection rejection rejection rejection rejection rejection centre centre classifications wahba chapter conservative reject reject toy playing playing compatible proba met rejected depicts importantly zip funded sam induces flight flight flight obermayer obermayer obermayer obermayer vanishes refined normalised treating helps suggestions ergodic ergodic ergodic uniqueness algorithmic bility transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction transduction sake shawe hilbert lated inequalities industrial pronounced labelling labelling labelling labelling labelling labelling inferring scenarios tended repository cur reflection wisconsin irvine ensuring dence noticed postal predefined spent campbell tal aims aims aims argmin minimise minimise minimise hoeffding hoeffding klaus def def madison dependences maximising classifica classifica philadelphia implementable volumes volumes volumes volumes hypersphere hypersphere confident exclude 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#@Graepel_T,Herbrich_R,Obermayer_K,
#t13
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#*network network network network network network learning learning learning learning learning learning learning learning model model model model model neural neural neural neural neural neural neural neural neural data data data data data function figure figure figure figure figure set set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm number system system system error error error results results units units units units information information information information information information problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models hidden hidden performance based weights weights linear linear linear linear layer layer layer layer vector shown shown systems systems systems systems systems values probability probability probability probability probability probability probability probability parameters parameters parameters parameters neurons unit unit unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach approach approach approach approach pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single single single processing processing processing processing processing processing processing control large rate rate test test analysis class class class class class class class class class class class class form form shows shows shows simple gaussian visual paper examples small size size size work task methods step step field field features features features features process level level level level level level level level current current current trained structure structure structure problems random random random high representation show section section section section section section fixed rule rule images images images images images images images images images images images images images images images images images images images images images general general parameter parameter real real approximation obtained obtained note note result result result university university university variables variables variables variables variables variables variables variables variables variables computation computation research research research log log log log log log log dynamics estimate computer computer computer terms terms distance connections node node node science science science left present present present present present present present present activation activation low nodes nodes nodes machine object object object object object object object object object object object object object object object object object object object object object object object maximum press press position sample abstract applied applied back computational computational density density likelihood likelihood likelihood references component stochastic stochastic stochastic stochastic ieee ieee ieee ieee procedure important propagation propagation mixture mixture context context context introduction hand hand hand estimation estimation statistical statistical statistical statistical parallel tion energy energy variable assume lower rules rules rules prior prior representations representations representations chosen part part part bound bound cases multiple multiple multiple multiple good 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internal code individual individual individual advances advances advances joint joint joint joint joint connectionist layers graph graph ai ai ai equivalent hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton hinton view transition san san san top top top top stage effects efficient efficient efficient efficient choice choice significant approximate free free free vision produce produce derived derived weighted conditional conditional developed levels actual actual actual finally finally backpropagation nature sampling constraint constraint achieved discussion discussion technical feedforward describe describe describe describe describe describe describe group tested tested transformation transformation corresponds shape shape main journal end pixel pixel pixel pixel pixel pixel pixel ability ability future easily makes rumelhart rumelhart fit fit kaufmann kaufmann probabilistic probabilistic pairs needed combination jordan block block interesting significantly character head segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation segmentation structures database database principal representing call bottom bottom frame idea attention directions exact separate introduced introduced subject machines pixels pixels pixels hierarchical hierarchical trees trees trees trees trees trees trees trees trees trees trees inference inference inference inference inference inference subset recently observations observations approximately volume volume volume volume works tions tions smooth correspond correspond achieve mixtures mixtures observation williams williams parts parts parts parts parts parts intensity invariant predicted predicted alternative correctly locally touretzky white boundary generally demonstrate row reduce segment segment segment segment valued editors editors editors central central sigmoid modules bayes bayes clear constrained mateo mateo sound hard intelligence 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structural structural successfully texture columns middle society computationally effectively mcclelland latent latent latent latent latent latent latent latent wij successful identify literature efficiently invariance fine composed notice cun cun neuroscience lie classify generative generative gray gibbs usual simplified dayan dayan dayan dayan dayan paradigm paradigm giles denker denker highest highest overlapping overlapping overlapping overlapping satisfies acknowledgments deal intrinsic cowan carried put estimators hanson graphical graphical graphical graphical helpful links rest rest terminal variational variational encode encode statistically cognition possibly traffic man noted multivariate improving submitted neal neal neal neal neal years years great scenes directed directed publishers publishers improves london london comparisons shared easier preprocessing bishop bishop leaves leaves mathematics simard simard recognized involve toronto toronto arises arises author author incomplete recognizing freeman solla remove howard gen parent parent parent parent parent parent parent parent parent parent parent cal plan logp age sharing phenomenon pose pose pose picture classifying ghahramani ghahramani ghahramani college intractable intractable sleep sleep investigation tation acts zemel zemel zemel royal rigid children clamped inspired systematic promising viewpoint viewpoint viewpoint viewpoint removing removing removing fail grammars heuristics heuristics combines saul iteratively sim belongs jackel captured hasselmo competing competing advance francisco artifacts recog foundations canada belonging belonging belonging parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse parse captures dempster explorations parents parents default dividing approx rubin helmholtz aston inferred nition instantiation instantiation instantiation boser aij aij multinomial wake wake assess representa publication pij pij pij pij 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#@Ghahramani_Z,Hinton_G,Teh_Y,
#t13
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#*learning learning learning model model model model model model model model model data data data function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time set set set set set set set set set set set set set set set set set set set training training training training training training training training training training training training training algorithm number number results results information problem problem problem problem problem problem problem models models models models models models models models models models models models hidden hidden based based based based based weights linear linear linear linear case case case case case case case case case case vector vector vector vector vector vector vector vector shown values values values probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method approach approach approach approach approach approach approach point large large local test class class class class class class class class class class class class class matrix optimal form form form form form form form form form shows shows shows simple gaussian paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small feature work methods step field classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level level level structure structure structure structure problems high similar fixed line line rule rule rule rule rule general general general general general general general generalization parameter parameter real theory theory theory theory theory theory obtained obtained obtained term term term term term note note note experiments result result result result variables variables variables variables variables variables solution solution solution solution solution solution solution solution solution solution independent log log log log log log log log log log log log log log constant constant constant estimate estimate standard standard terms terms terms distance node presented present machine sets sets sets sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum components components basis basis abstract find find find find find find find find computational density likelihood likelihood likelihood likelihood likelihood likelihood likelihood references decision decision decision decision decision decision mixture context context context context introduction introduction estimation estimation estimation estimation estimation estimation estimation statistical effect effect effect generated search tion difference variable variable rules measure prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen theorem theorem theorem theorem theorem bound binary tree tree tree tree tree tree tree tree tree tree tree tree bayesian techniques techniques region probabilities probabilities probabilities minimum minimum minimum minimum minimum resulting resulting resulting ing regression respect multi sum eq called elements means means optimization optimization potential potential potential potential obtain obtain obtain obtain obtain negative negative relative relative relative relative relative relative relative relative relative specific specific application desired cross provide define define define compute perform experimental related constraints constraints constraints constraints constraints constraints constraints constraints constraints constraints distributions distributions distributions distributions distributions distributions distributions distributions discrete equal approaches mit mit mit mit mit comparison support support support support support support support support selection proceedings kernel final bias bias bias graph graph ai ai ai ai ai framework framework cambridge cambridge cambridge computing directly directly additional additional additional additional view view solutions curves estimates detection detection detection detection detection conference conference conference efficient classifiers choice choice choice approximate basic increase validation con con derived conditional conditional conditional conditional criterion criterion criterion entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy product product provided discussion covariance covariance covariance normal normal normal denote limited close corresponds complete complete finding finding finding effective eds easily including fit objective probabilistic smaller combination jordan technology technology ratio ratio ratio ratio projection projection projection projection projection projection edge edge consistent consistent structures structures structures structures structures structures structures principle principle principle principle principle leads leads leads representing details direct international normalized polynomial idea idea discussed discussed property pair robust typical practical practical include subject subject subject subject identical identical machines machines machines machines machines machines machines machines quadratic trees trees trees trees inference subset relevant compare observations tions tions tions yields sparse definition definition improvement exists expression expression matrices matrices generally generally assumptions assumptions reduce bayes designed exponential practice weak taking hard hard solid solid solid solid regularization regularization labeled labeled labeled labeled labeled labeled turn assuming assuming minimizing areas reference suppose edges longer ways factors estimating estimating label distinct explicitly involves involves easy text unique unique consisting consisting gaussians john john family expressed expressed expressed expressed depending viewed labels labels labels labels labels 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graphical hall discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant ml ml ml ml scalar fewer reducing boosting maximizing maximizing cover analogous analogous naturally naturally predicting der assumes separated separated defines averages preference preference pairwise pairwise separable separable tractable sections formalism formalism formalism formalism formalism incorporate choices involve calculations members begin optimize optimize arises demonstrates annual incomplete conjugate conjugate conjugate integrating evaluating applies leave adjustable haussler http ture differs maximizes extensions extensions extensions extensions marginal enables enables logp sophisticated expectations jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola specifies specifies specifies irrelevant lab lab lab ordinary intractable feasible www formally lagrange lagrange lagrange lagrange lagrange lagrange lagrange summing proceed eliminated 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#@Jaakkola_T,Jebara_T,Meila_M,
#t13
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#*network learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input data data data data data data figure figure figure figure time time time time time time time set set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number error error error error results results information information models models models models models models models models models models models models performance performance performance based based space space space weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case vector vector vector vector order order shown shown shown shown shown systems systems values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition method method method approach approach pattern pattern point point point point image image image image image image image image image image image image image image image image image image image image image image image single single processing processing local rate rate rate rate test test patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix shows shows shows shows shows shows shows shows shows shows signal algorithms simple 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computer distance science present low low low machine object object object object components components components components components components components components components components components components nonlinear nonlinear nonlinear nonlinear continuous continuous continuous abstract applied density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component component due due ieee ieee ieee procedure adaptive propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction behavior generated generated variance variance variance variance variance tion tion variable variable variable variable variable variable variable variable spatial assume assume lower lower lower representations learned learned learned learned learned learned learned part cases multiple represent represent represent fact probabilities probabilities observed observed observed observed observed observed forward classes ing computed computed computed computed respect respect performed elements elements elements mapping means means means means means means means means means means means means means means means factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor factor applications applications applications em em em em em em em em em em em em em em obtain original original represented represented represented represented represented represented compared compared series compute compute compute rates discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal equal equal equal update modeling modeling modeling modeling modeling morgan morgan proceedings report report institute advances advances joint joint joint joint graph maps computing computing computing computing experiment experiment hinton hinton hinton hinton curve curve curve curve curve curve curve design san san top efficient efficient classifiers significant approximate statistics statistics speed estimated estimated give give produce produce randomly conditional conditional conditional clustering clustering levels levels levels types types types types product selected selected selected nature covariance covariance technical feedforward increases describe describe transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation transformation corresponds circuits amount amount nearest effective shape face face face pixel pixel pixel pixel pixel pixel pixel pixel pixel pixel cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster easily degree noisy fit fit kaufmann kaufmann simulated simulated smaller needed needed account account account account account interesting significantly ratio structures uniform database principal principal iterations iterations iterations iterations iterations iterations iterations iterations iterations making window supervised supervised supervised combined combined produced produced choose added improve robust takes takes takes element practical introduced include pixels pixels pixels pixels pixels engineering sufficient sufficient sufficient highly highly unsupervised tions trans trans diagonal diagonal diagonal diagonal diagonal diagonal sparse sparse sparse sparse sparse mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures background background background background modified williams entire horizontal horizontal horizontal lead invariant invariant invariant extended extended wide derivative matrices matrices matrices matrices matrices rotation feed locally locally locally locally move loop clusters clusters clusters clusters clusters setting setting setting setting pass pass row row reduce reduce depend depend tangent accurate bayes faster mateo mateo mechanisms intelligence assuming averaged derivatives derivatives acknowledgements digit digit digit digit digit digit digit digit produces written index index index solving factors factors factors factors generating vertical vertical vertical vertical vertical modeled multilayer averaging averaging averaging averaging linearly electrical electrical transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations transformations slightly text angle angle scales develop gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians expectation variation variation detailed detailed updated approximations approximations modulation approximated approximated translation translation translation translation translation translation digits digits digits digits digits digits digits digits digits digits digits processor combining purpose add add add filtering filtering filtering foundation faces handwritten handwritten handwritten handwritten handwritten handwritten box includes includes perceptrons illustrated uncertainty neighbors successfully columns extra latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent identify build invariance invariance invariance invariance tend capture summary traditional repeated cun cun cun cun showing classify manifold manifold manifold manifold manifold manifold manifold generative built notation dayan giles denker denker highest moves illustrates mixing mixing extract approximating approximating neighboring cowan transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed transformed exponentially involving hanson accurately graphical graphical graphical fewer school project detectors variational topographic topographic topographic topographic topographic topographic topographic trace integer facial versions explored mixed finds finds indicating rows variances variances variances variances variances straight formalism arc bishop bishop bengio mation simard simard simard simard potentially angles angles toronto nsf people people prop cohen cohen incorporated sharp ity mod perturbations gave gave expectations expectations expectations consistently pose person person person ghahramani ghahramani identifying proportion proportion www www www writing writing extensive nonzero enhancement rotations extending imaging minutes held operates shifts shifts shifts shifts shifts shifts ylx ylx filled filled spurious exploring document iteratively appendix appendix permutation permutation thin rich captures grants alternatively material pdf executed linked emission gtm incorporates solves convolutional convolutional emerge poses poses poses poses discriminative ical suppressed certainty imagine invariances translated translated mhz stroke stroke stroke diag diag diag diag diag diag diag diag diag approxi manifolds denoting wise statistic frontal intensities intensities translations indexed accounted reveal loading algebra frey frey frey frey matlab november scanning scanning electron electron electron electron lighting lighting ble generarive generarive generarive pdfs jointly generafive generafive generafive generafive responsibility responsibility hull hull suppress illinois bottou compo thickness equa zoubin strokes degenerate accommodate tations ance ben tained inaccurate tan revow urbana clutter clutter ace ace preprocessed crg walking blurred blurred nents couple couple analyzers analyzers analyzers analyzers analyzers analyzers analyzers analyzers analyzers analyzers analyzers puted puted nation analyzer deformed deformed beckman beckman initializing confident gatsby nserc blurring cov cov periments possi transfor generatire generatire tlx uncertainties sharper sharper victorri ucl signif haffner combi ifp dur mations gee zlx gte script cluttered lxt lxt lxt lxt lxt lxt lxt aged combina greyscale greyscale invari igi aca waterloo disc ixt ixt ixt ixt marginalizing marginalizing needing imaged aat ologp ologp gent sem sem sem sem sem pentium expec ren prevalent icantly cedar brendan untilled microscope microscope xlt tea eled deforming 
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results results results results information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance performance based based based based space space case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order order order values values values values values values values recognition recognition recognition recognition recognition recognition method method method method pattern pattern pattern pattern pattern pattern point large large large rate rate matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form form form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms examples examples examples examples examples small small size size size size size size size size size size size feature feature methods methods methods methods methods methods methods methods methods points points points points features features classification current current structure problems problems problems problems problems problems problems random high similar similar similar similar similar similar similar show equation section section fixed fixed line rule rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors general general real real gradient obtained obtained experiments experiments university variables variables variables variables variables variables variables variables solution solution solution solution research research research independent log log sequence initial initial constant constant table table table table standard standard standard computer terms terms terms left left left direction direction direction direction direction direction direction presented presented presented presented sets sets sets sets sets sets sets sets sets sets range press press press sample abstract applied applied computational convergence convergence convergence density properties properties references due due due ieee important introduction hand estimation estimation behavior tion tion complexity complexity complexity complexity complexity complexity complexity variable variable variable rules rules measure measure chosen center theorem theorem theorem theorem theorem cases type required good conditions conditions conditions conditions conditions conditions conditions conditions conditions conditions fact proposed proposed proposed proposed proposed length length scale scale resulting ing total total total regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect performed performed performed called times times elements elements elements elements elements elements factor factor factor factor factor factor factor optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization made made natural applications applications knowledge obtain obtain original original samples samples samples provide define compute compute experimental experimental experimental experimental experimental experimental experimental experimental constraints constraints constraints constraints constraints equal equal mit mit mit mit steps accuracy comparison comparison fields fields support support support support support support support support support support support support support support support support support support support support support support train selection selection selection proceedings report department implementation individual kernel kernel kernel kernel advances advances advances difficult difficult ai equivalent experiment experiment view full requires choice free speed speed basic basic basic con condition condition condition derived derived developed lines provided finally selected selected selected iteration iteration iteration iteration constraint constraint discussion technical arbitrary fast limited limited rbf assumed theoretical require main main main main main eds eds eds future easily makes including objective objective objective objective objective objective pairs reduced reduced account fully programming programming programming programming testing significantly character increasing special consistent database empirical principle details numbers max making early magnitude idea idea idea choose run improved improved improved improved improved directions directions advantage advantage advantage element element typical reported reported practical practical introduced strategy strategy strategy strategy subject subject machines machines machines machines machines machines machines machines machines quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic sense subset recently interest sufficient previously approximately calculated tions solve yields background evaluation evaluation modified bounded bounded interval improvement improvement improvement exists parts scaling scaling scaling scaling scaling scaling scaling scaling scaling scaling occur extended matrices alternative boundary boundary pass pass demonstrate minimal minimal numerical suggest suggest suggest taking mechanisms largest largest largest largest min relationship program program program program program program program denoted denoted pro derive solving solving solving factors factors factors factors sequential sequential remaining easy slightly consisting adding springer select select select select yield expressed dependence solved operations labels labels decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition forms sizes sizes key calculation slow classical sec sec fitting intervals purpose purpose boundaries box formulation formulation sciences vapnik extension maximize maximize specifically determining determining selecting selecting capable maximal maximal maximal maximal maximal maximal maximal modification included svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm successful plots essentially traditional traditional refer verlag prob heuristic heuristic split superior superior issue running criteria criteria criteria criteria notation notation notation list providing principles principles illustrates satisfies software presents requirements investigate experience optimized integral dual fashion rest rest applicable applicable dependencies scaled working working working working working working working working working working working working working working working working working working working working working working working working working working working working working working working working working working notion smallest smallest smallest possibly analyze subsets subsets obvious algo precise detected motivated established percentage advanced inequality inequality inequality inequality inequality inequality ground derivation analyzed lies considerable hyperplane optimize conjugate reflects understood pure amounts tional tional posed slower formulated ity maintain requirement http summarized mod aim gap gap newton identifying feasible feasible feasible feasible feasible feasible feasible feasible www sv sv sv sv sv optimality optimality optimality optimality guarantee rithm girosi optimizing optimizing databases purely addresses eliminated platt platt kaufman convenient satisfying satisfying proceeds stated interpret hope reasoning north 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models hidden hidden hidden hidden hidden hidden hidden hidden based based weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear case case case vector order order order order order order order order order order order shown shown shown shown shown shown shown systems values values probability probability probability parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach approach point point point point point point point point point point point point point point point point point point point point point point point point point point single single single processing processing processing processing large large local local local analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form shows shows shows signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small small small small small small size size size size size size size size fig fig fig step step step features features features features features problems high similar architecture show show show show fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed rule rule rule rule rule rule vectors generalization generalization parameter parameter parameter parameter parameter gradient gradient 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likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component due ieee positive positive adaptive adaptive mixture mixture mixture context introduction hand behavior behavior behavior behavior behavior behavior generated generated generated variance change variable variable variable variable assume assume signals signals prior prior prior prior prior prior prior prior learned learned chosen higher higher higher higher higher higher higher part part center binary long long conditions conditions conditions represent distributed make fact length length correct observed observed observed observed observed observed observed finite finite finite minimum minimum minimum minimum ing eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq regions mapping factor factor natural global global applications em em em em em em em em em em em em negative negative artificial artificial specific true true application application compute related related related posterior constraints equal approaches approaches larger contrast update update update update update support dependent source source source source institute version version individual advances represents exp exp scheme framework framework equivalent equivalent equivalent equivalent equivalent hinton solutions solutions limit top determine efficient upper choice statistics statistics statistics statistics statistics statistics statistics estimated con condition condition derived derived derived criterion finally iteration iteration iteration nature depends constraint constraint discussion covariance covariance arbitrary arbitrary arbitrary fast assumption assumption assumption assumption assumed assumed assumed role role role theoretical square easily makes objective objective underlying reduced projection special consistent uniform principal bottom added added added added sources sources sources sources sources sources sources sources sources directions recent correlations exact apply include identical quadratic sejnowski sejnowski interest previously conventional observations observations approximately calculated tions solve match match match correspond pca pca converge converge converge converge converge converge rl trans diagonal sparse separation separation separation separation symmetric symmetric modified modified sensitive exists parts expression concept extended extended locally demonstrate critical critical critical greater clear clear constrained taking taking presence presence presence physics reduction demonstrated demonstrated assuming assuming assuming assuming minimizing ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica suppose derive derive longer stability stability simultaneously averaging easy mutual mutual applying implies implies implies expectation expectation expectation expectation expectation expectation expectation choosing national review viewed solved evaluated controlled updated lee lee lee lee lee lee decomposition converges converges converges converges converges updates sign additive expansion expansion expansion expansion expansion expansion expansion fitting closed valid intermediate intermediate initially visible visible visible visible sufficiently foundation foundation foundation transactions formulation bell bell bell bell blind blind blind blind blind plotted plotted discussions simplicity columns columns columns columns determining importance latent latent latent latent wij situation situation orthogonal orthogonal orthogonal allowing success showing symmetry generative generative generative generative generative generative generative generative generative generative satisfy maximization maximization maximization maximization maximization mixing mixing mixing mixing mixing minimized transformed investigate rapidly rapidly rapidly integral hall pursuit helpful analytically analytically analytically maximizing maximizing maximizing maximizing tanh tanh tanh affect statistically neu hill illustrate singular singular singular singular singular singular singular singular singular portion algo amari mixed simplest utility regime motivated serial attempts attempts slowly slowly crucial guaranteed guaranteed guaranteed guaranteed correction correction correction nonlinearity nonlinearity nonlinearity nonlinearity nonlinearity turns laboratories laboratories opt explained integrating fourth varies varies varies understood generic generic generic generic slower formulated rep differs qualitatively redundancy deviations deviations traces multidimensional naive naive naive globally consistently ghahramani aligned aligned intractable saddle lagrange tation optimizing acts discovery unity nonzero nonzero royal multipliers murray oja oja oja convenient interpret analyzing 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algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number results results results results results results information information problem problem problem problem performance performance performance performance performance performance performance based based space space space space space linear linear linear linear linear linear case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order shown noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions recognition method method pattern pattern pattern pattern point point image image control control control control large large test test patterns analysis analysis analysis matrix matrix matrix optimal form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple paper paper examples examples examples feature feature feature work methods features classification classification classification classification classification classification classification classification classification classification trained random high similar similar similar similar similar similar similar show show show section section section section line line vectors vectors vectors generalization generalization approximation average average theory theory theory theory theory obtained note note note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional result result university threshold threshold threshold computation computation computation solution research research defined found sequence sequence sequence sequence table table table table table table standard standard standard standard computer distance distance distance distance science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented presented present machine machine machine machine sets maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum maximum press press components outputs sample abstract applied applied find computational computational computational computational references component component component due due positive procedure introduction hand estimation cost change difference difference complexity complexity complexity assume measure measure chosen part previous previous previous previous previous theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound required long long long long expected make make make fact fact fact fact fact fact length length length length length correct correct correct scale minimum ing total total computed computed sum performed performed called called mapping means optimization made made made made made made made made made made made negative original original original represented represented compared define compute proc proc experimental experimental constraints constraints constraints constraints constraints constraints constraints constraints brain brain equal mit mit update update support support support support support support morgan proceedings proceedings report institute institute department implementation implementation consists kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances represents final bias bias bias bias considered considered framework design design limit bit conference conference determine efficient classifiers classifiers classifiers classifiers classifiers upper requires choice speed pages increase weighted bounds product product finally nature constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint constraint normal technical describe describe describe describe describe group denote tested fast fast fast corresponds complete predictions proof proof proof proof proof proof proof proof nearest implemented implemented square hypothesis hypothesis hypothesis instance instance easily easily easily makes including probabilistic pairs pairs pairs pairs unknown technology programming programming special trials trials trials trials trials trials trials trials database database database empirical squared details details call call call making making making making magnitude polynomial polynomial minimize minimize choose choose choose choose run run description perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron perceptron improved discussed improve takes takes element element element element element element element element apply apply moving subject subject subject machines machines machines machines quadratic quadratic quadratic sense sense compare previously works solve converge achieve definition organization storage risk parts expression occur occur trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial trial correctly correctly setting demonstrate minimal minimal row assumptions editors editors practice taking mechanisms minimizing plane manner manner groups groups denoted denoted denoted denoted suppose digit digit longer index solving sequential label label label linearly linearly linearly linearly linearly linearly slightly slightly slightly unique applying minimization springer springer implies implies implies implies john choosing choosing national national viewed viewed lemma lemma lemma operations updated updated labels labels margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin suggested digits converges updates updates updates sign sign sign sign calculation epochs epochs epochs convex convex convex convex convex purpose iterative penalty closed euclidean handwritten handwritten thesis perceptrons perceptrons instances instances batch batch batch batch recognize vapnik vapnik vapnik vapnik vapnik vapnik prove prove prove prove prove prove holds structural simplicity simplicity columns maximal computationally computationally delta svm svm svm presentation efficiently efficiently computations online online online online online online online online online online online online online online online online online online online online ten refer refer refer conf verlag quickly classify classify satisfy comp usual usual relaxation binding binding binding binding principles satisfies satisfies satisfies satisfies deal minimized simpler origin access collection updating detail detail dataset dataset dataset dataset incremental incremental ideal ideal ideal ideal dependencies scaled proved proved workshop attributes induction induction smallest smallest smallest smallest smallest smallest smallest smallest smallest coefficient analyze predicting changed thought thought obvious algo algo algo taylor perceptton perceptton perceptton perceptton perceptton store epoch phd finds finds formula separable separable separable separable separable publishers starts starts organized worst hyperplane hyperplane hyperplane hyperplane products products involve involve implicit conducted conducted conducted marked slower rep variant variant http passes ture differs differs maximizes maximizes suited enables chose eventually progress progress progress progress irrelevant phenomenon proofs proofs www mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake mistake 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#*network network network network network network network network network learning input data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number number number number number number number number number number number number number system system error error error error error results results results results results results information information information problem problem problem problem problem problem problem problem models performance performance based based based based space space linear case case case case order order order order order shown shown shown shown shown shown shown shown shown shown systems systems values values probability probability probability probability probability probability probability probability probability probability probability probability probability probability noise noise distribution recognition approach approach approach approach approach approach approach approach point point image image single single large large local local local local local local local local local local local rate test test test test test test test test test test test test test analysis analysis form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple visual paper paper paper paper paper paper paper paper paper examples examples examples small size size size size size size size size net net net net net net net net net net net net net net net work work task methods fig fig fig fig fig step step step step step step step step step step step step step step process process level current structure structure structure structure structure structure structure structure structure structure structure problems problems problems random high high high high similar similar representation show show section rule general real real theory note note note note note note experiments result result university university threshold threshold threshold variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables computation computation solution research research independent independent independent constant constant constant estimate standard computer computer computer computer node node node node node node node node science science prediction prediction prediction left left direction direction direction direction direction direction direction direction direction direction direction presented presented presented presented presented presented presented presented presented presented present present present present phase phase low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets sets sets sets sets maximum maximum maximum maximum abstract applied computational density properties properties likelihood likelihood likelihood likelihood references due due due due due due due due ieee procedure procedure decision decision introduction introduction estimation estimation statistical generated search search tion difference difference difference complexity variable variable variable variable variable variable variable variable variable assume assume lower prior representations chosen higher higher part part part bound cases cases cases type multiple multiple multiple multiple good long conditions conditions represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make fact fact fact techniques errors errors errors errors errors errors errors errors errors errors errors errors errors errors errors minimum minimum minimum resulting resulting classes ing simulation computed multi called called times times times mapping factor factor factor factor factor factor factor factor factor factor potential feedback applications knowledge original original samples samples samples samples samples samples samples samples samples samples represented compared series compute compute compute compute compute compute rates determined determined related posterior posterior posterior connected distributions discrete approaches approaches steps steps steps accuracy larger larger contrast connection connection fields fields fields dependent dependent dependent dependent dependent dependent dependent dependent nets nets nets morgan words department department loss version version version version version version version version version version version consists advances joint represents represents difficult graph graph graph graph graph graph graph ai framework computing directly directly directly additional limit top effects determine determine efficient efficient efficient efficient requires requires significant statistics world speed vision vision estimated basic increase increase increase increase con con produce condition weighted weighted randomly conditional conditional conditional conditional conditional conditional conditional lines lines entropy path path evidence evidence evidence evidence evidence evidence sampling discussion discussion discussion discussion fast fast close assumption assumption assumption corresponds complete proof proof proof common common generate main main main main square end ability hypothesis easily easily makes noisy including kaufmann probabilistic probabilistic typically typically pairs smaller smaller smaller smaller smaller smaller smaller smaller underlying underlying account interesting testing significantly edge edge edge edge edge edge edge edge edge edge edge edge edge edge edge increasing increasing increasing increasing consistent structures structures operation representing direct direct direct direct direct direct direct direct direct direct direct direct making making making making making making bottom expert polynomial polynomial idea idea attention minimize produced choose added added added added description improve directions directions directions recent resolution advantage property property pair robust separate takes typical apply apply introduced side quadratic trees trees trees subset subset interest interest dimensions dimensions highly compare yields yields definition observation bounded bounded bounded bounded bounded interval increased increased exists exists exists exists horizontal parts parts lead concept concept occur wide loop boundary boundary boundary pass demonstrate minimal greater greater assumptions assumptions assumptions neighbor neighbor neighbor depend central accurate bayes bayes exponential exponential exponential exponential faster faster faster practice hard hard presence cycle cycle cycle cycle drawn assuming assuming assuming user user user exist exist introduce introduce manner manner manner explicit monte derive carlo edges edges edges edges edges edges edges edges edges edges produces longer ways ways estimating stability vertical confidence confidence confidence category involves slightly unique mutual events springer versus versus versus versus versus versus cycles cycles cycles cycles cycles cycles cycles cycles cycles decreases dependence dependence dependence dependence dependence dependence dependence dependence dependence dependence dependence dependence dependence reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction detailed densities restricted completely reasonable reasonable neighborhood neighborhood neighborhood neighborhood neighborhood event add false construction advantages advantages transactions includes includes includes retrieval bell sciences determines determines prove domains neighbors neighbors neighbors neighbors tests tests tests tests tests tests tests tests tests tests tests tests tests tests tests tests tests tests tests tests tests tests texture straightforward selecting identified efficiency closely closely closely importance importance effectively driven successful successful identify comparing score score score score score score score fine compact compact heuristic link link interested interpreted split split running running hold hold notation involved involved involved involved involved leading automatically automatically automatically attempt approximating situations situations presents remain updating put detail divergence divergence divergence divergence divergence divergence dotted existence relationships relationships relationships dependencies referred referred reliable reliable reliable decisions decisions decisions decisions decisions comparable comparable understand fundamental notion removed induction induction induction induction induction induction induction hill hill hill hill hill hill hill hill hill hill hill hill hill hill smallest possibly necessarily opposite created subsets quantities quantities quantities versions versions obvious greedy formal formal observe logic attempts years mentioned mentioned percentage indicating great great slowly directed directed directed directed derivation growing majority expensive independence independence independence independence independence independence lies lies tool reasons straight satisfied arc easier widely preprocessing directional scientific involve beginning implicit members members members members depicted demonstrates mellon mellon addressed addressed robustness robustness robustness requiring greatly carnegie carnegie applies applies cmu cmu cmu employ employ employ employ remove remove remove frequently incorrect incorrect variant variant reliability reliability execution execution execution execution execution execution execution operate synthesis pittsburgh pittsburgh characterize differs differs popular parent parent parent parent focused conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning conditioning irrelevant representative benefit benefit benefit identifying identifying identifying identifying cooper equivalence restrict arguments appropriately conditioned recover databases ordering concerned concerned concerned reconstructed partitions partitions discovery discovery addresses addresses addresses discover connecting children children children children climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing climbing generality generality fails wrong accepted overcome logarithmic replacing intelligent grow grow scoring reasoning effectiveness guide child motivation separating loo surprising conjunction dependency heart histograms belongs facilitate facilitate facilitate branching branching branching branching branching branching branching branching branching recovery recovery recovery recovery impact exploiting reverse reverse speeds speeds propagate parents parents parents parents parents parents accumulated dense dramatically pressure liu liu leaving usage blood thrun thrun thrun 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semantics acyclic acyclic facts indicators emerged violated greatest deciding unnecessary insert stems stems ference preventing prime sebastian attracted disadvantages forthcoming separator mention parsimonious ascending intervening shrink shrink plain plain plain plain plain plain plain plain plain plain plain plain plain plain chi disappear disappear rendered mild mild confident feel widespread polyhedral emphasizes shortcomings today today today rejecting independencies independencies identifiable lend chow chow chow ditional worthwhile pathological probing heuristically percentages shrinking additions exemplified cheng cheng reversals necessitates orient orient orient opportunities tackled facilitated uai uai uai uai preferably directionality directionality directionality directionality directionality indications unnecessarily ascertain buildings combinatorics ivi bic bic bic unsuitable pendence orienting disjunction plagued lti maxx construc wrongly illuminating disregarding 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#@Margaritis_D,Thrun_S,
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#*network learning learning learning learning learning learning learning learning learning neural neural data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure time set set set set set set set set networks training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm system error error error error error error error error error error error error error state results results results results results results results information information information information information performance performance performance space space space space space space space weights weights linear linear linear linear case case case case order order order shown shown shown shown systems values probability probability probability noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions functions functions functions functions functions functions distribution approach pattern pattern point point processing large large large large large large test test test test test test test test test analysis analysis class class class class class form form form shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper examples examples examples examples examples examples examples examples small small small small size size size size size size size methods methods methods methods methods methods methods step step step step step step step step step step step points classification classification level problems high similar show show show section section section fixed fixed line line line line general general general general general generalization generalization generalization parameter real approximation average theory theory theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient note note experiments experiments experiments experiments experiments experiments university university university university university university university university university research research research defined defined found found sequence sequence sequence sequence table table table standard computer computer computer computer terms terms terms science science science prediction direction direction direction direction present present present machine machine machine machine machine machine sets sets sets sets sets sets sets sets press sample abstract abstract applied applied find find find find computational computational computational convergence convergence convergence convergence convergence properties references due ieee positive positive procedure important adaptive decision decision decision decision decision introduction statistical effect generated generated generated generated generated cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost search search search search complexity assume classifier classifier lower learned previous theorem theorem theorem theorem theorem cases cases good binary conditions conditions conditions fact techniques proposed correlation finite minimum minimum minimum regression called elements mapping mapping mapping optimization optimization made global negative negative negative artificial artificial specific specific true compared application desired provide provide provide experimental experimental experimental experimental distributions distributions discrete equal mit steps steps comparison comparison contrast descent descent descent descent descent descent descent descent descent selection proceedings proceedings proceedings proceedings proceedings report report report report report words department department department implementation version version version advances addition considered equivalent equivalent curve additional view view curves estimates limit conference conference conference conference conference conference classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper full full full choice statistics statistics pages pages pages pages pages increase increase produce produce weighted weighted levels levels bounds product product product product product product product product product evidence simply simply discussion normal technical technical technical technical arbitrary denote denote denote corresponds actions predictions proof proof finding finding finding assumed theoretical theoretical require journal end end hypothesis hypothesis hypothesis typically typically smaller combination combination combination functional functional functional functional functional functional functional functional functional functional functional functional functional functional unknown significantly special special empirical operation details details numbers international normalized normalized normalized normalized normalized normalized normalized attention combined combined combined minimize minimize minimize minimize choose choose choose predict predict improved improved improved recent recent advantage apply apply trees trees sense subset recently engineering engineering engineering engineering interest varying axis correspond studies trans bounded improvement improvement exists occur derivative predicted correctly correctly generally generally demonstrate minimal reduce valued editors sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid exponential exponential exponential exponential exponential exponential exponential practice weak weak weak weak weak weak weak weak weak weak weak weak suggest strong presence reduction california intelligence intelligence minimizing minimizing minimizing start base base base base base base base base base base base base base explicit suppose longer label label label label label label confidence recall electrical decreases decreases choosing choosing national national national national national viewed viewed learner learner learner learner learner learner variation detailed restricted restricted labels showed lee soft sizes sizes sizes sizes sizes margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin converges allowed calculation additive performing measurements convex convex convex convex combining add iterative closed norm existing existing includes combinations combinations combinations combinations combinations sciences sciences sciences sciences illustrated prove prove maximize maximize successful comparing orthogonal summary summary showing return return return minimizes hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses subsequent satisfies decreasing situations situations bars overfitting overfitting overfitting overfitting overfitting overfitting rapidly involving behaviour behaviour behaviour school school school tech boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting scaled referred referred referred maximizing maximizing maximizing maximizing maximizing tanh tanh act act act predicts quantities friedman friedman obvious greedy logistic motivated motivated motivated finds ment theoretic costs guaranteed explanation adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost majority london reasons comparisons considerable stanford stanford lin lin lin lin lin lin lin lin lin lin lin lin lin tive berkeley arc easier constructing choices sgn sgn sgn sgn sgn optimize res annual annual preceding geometric improvements peter peter peter peter adjustable http exhibits limiting aim aim qualitatively singer gave returns returns credit differentiable differentiable differentiable cumulative newton proportion www restrict databases hyperplanes labelled labelled controlling royal proceed breiman breiman adjusting simplify observing definitions monotonically effectiveness effectiveness games bartlett bartlett bartlett bartlett bartlett bartlett bartlett bartlett bartlett bartlett schapire schapire schapire schapire predictors iteratively guarantees chooses ensembles omitted omitted indicator cancer cancer cancer reader bagging bagging bagging theoretically theoretically dietterich inf characterization dividing smola ics speaking uci uci uci uci uci outperforms outperforms outperforms annals misclassification misclassification ent tibshirani ease perceived freund freund freund freund tendency classifies tor avoided australia australia australia australia hastie continues bounding march relate quinlan setup sonar voting voting voting voting voting voting suffer margins margins margins margins margins margins margins exhibited things round round round october oregon correlate learners accumulation accumulation august australian australian australian attributed european breast breast blake attempting loosely alex incorrectly pronounced concrete returned vote vote vote marcus marcus coincide splice splice splice classi characterizes baxter baxter baxter baxter baxter baxter baxter html repository repository repository wisconsin quick irvine terminates terminates fication elec doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom doom greatest greatest cortes drucker lipschitz theo mason mason mason mason mason mason posi accepts rated boost ative jonathan jonathan jonathan motivates steepness henceforth functionals functionals functionals overfit grove exposition ans supplies queensland helmbold schslkopf arcing matters rectly nical twelfth gin canberra canberra canberra negation depart eleventh holloway merz yif yif yif yif yif duffy terminating downhill labor labor neg raphson dale resistant anu anu anu onoda rounds rounds rounds rounds sacrifice limt ses ariaboost ariaboost ariaboost bernard fifteenth randomization gradi ionosphere itsch mlearn egham schuurmans ama fort mlrepository retical esis hypoth qld thirteenth thirteenth noi dth sembles 
#@Bartlett_P,Baxter_J,Frean_M,Mason_L,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model function function function function function function function function function function function function function function function function function function function function function function function function set set set set set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number results results results information information information information problem problem problem problem problem problem problem problem problem problem problem problem hidden performance performance performance performance performance based based space space space weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case vector values values values noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution pattern point single large large large test analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class class optimal form shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper paper paper paper small small small small small feature feature feature work work work work work work work work work step classification classification classification current current problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems similar similar similar similar similar similar representation show show show show show show section section section section section line line general general general general real real theory experiments experiments result university university threshold threshold threshold threshold computation research research defined target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target target constant constant constant constant constant constant estimate standard computer science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction present present machine machine machine machine machine machine machine machine machine maximum maximum range range range range learn learn learn learn learn learn abstract references positive procedure procedure procedure important context introduction hand behavior behavior effect effect effect tion tion tion tion tion change difference difference difference difference assume assume assume assume assume assume assume classifier lower measure word word learned part part part part part previous previous theorem theorem bound bound bound bound bound bound bound bound bound bound cases cases cases type type type type good good good good binary binary binary long conditions represent represent make fact techniques techniques region correct correct correct correct correct correct correct correct correct correct errors errors finite minimum minimum classes classes classes classes classes classes classes classes classes classes classes tasks tasks tasks total simulation regression regression regression regression regression computed multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi multi sum sum sum called times regions means factor made made natural natural feedback global study negative negative negative negative original original original original original relative relative represented represented represented represented represented true desired series provide define perform perform experimental goal goal related related related related related related related related related related distributions power steps larger larger update update support report report institute department loss loss version technique technique code individual individual individual represents difficult difficult scheme scheme maps framework framework domain equivalent additional additional effects determine significant world world pages pages pages pages increase give give give give give con con weighted bounds bounds bounds bounds bounds types types actual selected depends depends technical technical transformation transformation transformation transformation transformation transformation transformation limited corresponds corresponds corresponds complete stable predictions predictions predictions predictions predictions predictions proof proof proof proof proof proof amount effective supported theoretical theoretical theoretical theoretical end hypothesis instance instance instance instance instance future easily makes makes makes makes makes noisy including fit fit needed needed combination combination combination interesting interesting testing york increasing increasing special special special trials trials trials trials empirical leads details details call call call max max max max max pre pre pre normalized normalized experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts experts expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert expert minimize minimize added predict predict improve property pair robust separate similarity practical introduced include include identical identical sense relevant relevant relevant relevant relevant works works tions solve definition modified bounded bounded sensitive exists lead concept suggests trial trial trial trial predicted predicted predicted predicted correctly correctly hybrid hybrid hybrid setting conclusion assumptions accurate performs performs practice learns learns learns suggest suggest largest california solid start min min targets targets targets introduce scene solving solving describes label label label label label label label label label label label changing explicitly transformations transformations transformations transformations transformations transformations transformations remaining text text adding adding adding applying versus select family family family overlap transform transform transform labels labels fraction fraction updates updates updates updates allowed allowed additive performing convex combining combining combining add add add add add add add foundation foundation advantages advantages includes includes thesis variations successfully reason straightforward straightforward aspects extra extra extra modification driven committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee identify comparing comparing receives receives composed composed traditional traditional road refer refer notice notice notice quickly kind return contribution classify running notation involved generalize generalize providing highest attempt acknowledgments extend extend presents wiley poor create difficulty difficulty difficulty updating involving preliminary ml ml ml reducing ideas tech incremental combine proper proper affect func func cover understand notion attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes naturally predicting predicts predicts predicts predicts predicts perfect changed changed obvious obvious portion formal algo initialized improving arbitrarily phd attempts track analyzed fairly majority correction handle handle handle handle starts turns satisfied strictly desirable desirable mation attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute attribute researchers people empirically flexible amounts remove remove remove remove incorrect extensions plan comments progress progress irrelevant initialization picture classifying redundant mistake mistake mistake mistake mistake mistake mistake mistake mistake formally princeton rithm arguments concerned generality extending multiplier smith stronger adjusting logarithmic logarithmic multiplicative belong disjoint intuitively modifications modifications modifications date infor document combines representational paul scheduling scheduling multiplied multiplied multiplied multiplied advance surprisingly suggesting reader matter warmuth warmuth extends statement santa valuable hart balanced balanced balanced balanced divide ence converted vec ent creates ties ties break distinction lit lit lit lit lit lit lit lit lit lit lit lit lit personal classifies tor possibilities winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow adjustment modifying duda mitchell convert spreading categorization win voting confusion truth truth normalizing corrections experi wider wider gorithm nec tension chris chris chris stimulating nonnegative nonnegative nonnegative nonnegative transforming transforming transforming doesn attempting blum blum eral mistakes mistakes mistakes mistakes mistakes mistakes conversion vote vote vote vote vote vote vote vote vote normalize normalize normalize deals littlestone littlestone littlestone littlestone littlestone littlestone tended crl cruz kivinen kivinen indirectly predic inability tie ucsc colt favorable picks gorithms manfred initializing converting exponentiated feel divides niques han roth roth opens superfluous transfor rutgers rutgers rutgers equiv sev implementa superficial votes diction tolerate cumbersome 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#*network learning learning learning learning learning model neural neural neural neural neural neural data data data data data data data data data data data data data data function function function figure figure figure figure set set set set networks networks networks networks networks networks networks networks training training training training training training training training training training algorithm algorithm algorithm output number number error error error error error state state results results results results units information information information information problem problem problem problem problem problem problem problem problem problem performance based space space space space space space space space space linear linear linear linear linear linear linear case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order probability parameters parameters noise noise noise noise noise noise noise noise noise functions functions functions functions distribution recognition recognition recognition approach approach approach pattern pattern pattern point image single processing processing processing control control large large large local local local local test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis class class class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal shows shows shows shows signal algorithms algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian paper paper examples small small size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work task methods methods field features features features features features features classification classification classification classification classification classification classification classification trained structure structure structure problems high high show show show section section section fixed fixed line vectors vectors images images images generalization parameter parameter real real approximation approximation average average average theory obtained obtained obtained obtained note note experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional result result university university university threshold threshold threshold variables computation computation solution solution solution solution solution solution solution research research defined found found found constant constant constant table table table estimate estimate estimate standard standard terms terms terms terms distance left left left direction direction direction direction map machine machine sets sets sets press press press press components basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs sample sample sample sample sample abstract applied find find find find find find find properties references component component component due ieee positive positive positive positive positive important decision introduction introduction estimation estimation statistical statistical generated variance variance variance variance variance tion change change change difference complexity assume classifier prior prior prior prior prior prior chosen chosen center cases cases cases cases type multiple multiple multiple good fact proposed errors scale finite finite simulations classes classes ing computed computed computed sum performed called elements mapping means optimization optimization optimization optimization optimization dimension applications applications knowledge knowledge knowledge knowledge knowledge obtain obtain obtain original relative specific samples samples compared application desired desired cross define compute proc perform experimental related mit comparison comparison comparison comparison comparison comparison larger larger connection connection connection connection connection support support support support support support support support support support support support report technique technique consists kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances exp bias scheme ai framework cambridge computing domain equivalent equivalent experiment experiment directly solutions solutions estimates san capacity efficient classifiers classifiers full full full full full statistics statistics free world estimated estimated pages pages validation give con con condition clustering clustering levels lines product product finally nature constraint constraint simply simply simply achieved discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance normal technical technical increases describe tested transformation transformation transformation transformation transformation transformation fast limited close stable rbf rbf rbf rbf rbf rbf rbf rbf common common common assumed supported face journal journal end end end instance future degree degree degree makes including objective smaller coefficients coefficients coefficients interesting significantly ratio ratio projection york special database empirical empirical principal principal principal squared details details details details normalized supervised polynomial choose added sources description improved directions advantage takes reported reported subject machines machines machines machines machines quadratic quadratic quadratic sense subset interest sufficient axis tions solve solve solve solve yields pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca sparse sparse definition symmetric symmetric symmetric generalized improvement risk constructed exists exists horizontal invariant invariant invariant invariant invariant invariant invariant invariant deviation matrices matrices matrices matrices matrices rotation rotation locally width width setting runs conclusion minimal minimal competitive editors editors tangent tangent tangent tangent tangent tangent bayes bayes bayes numerical moody practice propose propose regularization regularization regularization regularization regularization regularization regularization regularization minimizing exist min relationship iii averaged introduce question explicit explicit digit construct construct written written solving winner ways ways ways estimating describes label tuned vertical explicitly infinite infinite infinite transformations slightly slightly slightly text text unique adding extraction extraction extraction extraction extraction extraction extraction extraction letters national extracted independently focus squares viewed interpretation solved solved evaluate restricted restricted restricted labels centers centers soft soft margin margin margin margin margin margin translation translation digits digits constants discrimination discrimination discrimination reasonable performing expansion expansion expansion expansion expansion expansion expansion expansion spaces spaces spaces spaces add add add sufficiently classified avoid handwritten kernels kernels kernels kernels usa formulation formulation formulation formulation eigenvalues subspace subspace subspace subspace subspace vapnik maximize maximize partially selecting closely maximal svm svm svm svm svm svm svm svm svm efficiently projections invariance invariance invariance invariance invariance invariance invariance invariance invariance identity capture verlag induced induced allowing interpreted dis superior superior lie criteria gray sampled write write dot dot dot dot dot generalize eigenvalue eigenvalue computes ill maximization thresholds subsequent acknowledgments deal deal oriented oriented oriented oriented oriented oriented oriented oriented oriented oriented minimized minimized minimized carried diego american wiley association limitations preliminary discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant dataset rest project boosting working maximizing maximizing comparable workshop cover analogous smallest act coefficient coefficient coefficient coefficient coefficient concepts possibly editor rank rank rank rank rank rank rank rank rank friedman versions noted algo fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher mapped mapped mapped mapped academic art art utility submitted averages theoretic derivation defining waveform coded coded adaboost adaboost adaboost adaboost expensive lies worse london stanford easier organized operators incorporate incorporate choices choices choices ran bishop hyperplane products products products products potentially scientific projected describing describing describing describing optimize optimize optimize medical outer argument virtual virtual improvements evaluating led led leave posed haussler incorporated dots incorrect variant span span span http berlin ture extracting maximizes maximizes occurrence proven incorporating ordered datasets adjust replace replace germany conclude findings median median yielding univ corrupted college intractable feasible feasible www oxford extensive extensive extensive restrict fix acm recover rotated hyperplanes null null impossible royal robotics numerically numerically darken overcome overcome analogy analogy analogy analogy operates wilson meaningful schapire ensures pat heart april cancer cancer grants fold interestingly avoiding robert smola smola smola smola smola smola smola informa multiplying maintaining street unified svms svms svms dna slight sch sch sch basically covering guyon maximized formulate expanding boser seek seek causing generalizations generalizations covariances freund german tor england australia remainder burges invariances invariances invariances translated toy toy rithms impose regularizer intra disadvantage crosses expand regularized regularized regularized regularized regularized douglas employing spanned spanned setup sonar fea margins eigen port expansions algorithmic kopf kopf sake australian attributed terns breast bold orthonormal alex alex dcs realizations realizations appealing anna anna splice restricting arrives factorization sian chunking sis gmd gmd gmd gmd edition gaus scatter scatter scatter scatter scatter sparseness inst slack denominator microsoft microsoft imposes demanding sebastian aims optimizes trick klaus klaus imposing imposing tics statis llx tong nonlinearly usps colt boost fur fur plain picks separability solu penalizing miiller miiller miiller orthogonality reproducing koller koller brevity kung kij kij numerator formulating chinese diabetes illustrative stant suit encouraged loses schslkopf schslkopf schslkopf schslkopf bernhard larsen canberra ijcai quotient favoring holloway nel thereof mfiller mfiller mfiller dfg polyno mika mika mika mika mika mika crucially shashua subclasses fang anu onoda scholkopf fukunaga yll parison iiw invari tackle ker mial biggest discriminates centering lkopf anymore str rhbnc lives scalars shortcoming underdetermined itsch storm eurocolt bsc ingly ances thermore thermore preprocess undesired dawid guildhall thyroid ada teresting cholesky lncs italics sthe 
#@Mika_S,Muller_K,Ratsch_G,Scholkopf_B,Smola_A,Weston_J,
#t13
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#*network network network network network network network network network network network network network network learning learning learning model model model model model input input input input data data function function function function function function function figure figure figure figure time set set set networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number error error error error error error error error error error error error error error error error state state results results results results results results results results results results results results results results results problem problem problem problem problem models models models models models models performance performance performance based based based based based space weights weights weights weights weights weights layer layer layer layer layer layer layer case case case case case case case order order order order order order order order order order order order order shown systems values values values values probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters distribution distribution distribution method method approach approach point point control large large large large large local local local rate rate rate rate rate rate rate test analysis analysis analysis analysis analysis class class form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper paper small small small small size work methods methods methods methods methods methods methods methods methods methods methods methods step points field level level level current current current problems problems random high similar similar architecture show show equation section section section fixed fixed fixed fixed fixed fixed fixed line line line line general parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average gradient obtained obtained obtained obtained obtained obtained term term term term term term term note note note experiments result result variables research research log log log log found constant constant constant constant estimate estimate standard standard computer computer computer terms terms distance science science prediction left presented presented present present present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes press abstract applied applied applied find find find computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic due due positive positive positive positive positive positive positive important decision propagation propagation propagation introduction introduction behavior effect effect generated search tion complexity complexity lower lower lower lower lower lower rules prior prior chosen chosen chosen previous theorem theorem theorem theorem bound bound bound bound cases cases cases cases cases cases cases cases cases cases cases cases type type multiple binary long long conditions represent tree tree distributed distributed bayesian bayesian bayesian bayesian bayesian expected make make fact techniques techniques techniques techniques proposed proposed proposed correct probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities observed observed observed observed forward scale scale simulations resulting resulting resulting simulation respect sum sum sum sum sum eq means made study study knowledge em obtain obtain obtain obtain negative negative negative negative artificial artificial artificial artificial artificial artificial specific true true desired define define rates rates rates rates rates rates rates rates rates perform goal related posterior constraints distributions distributions mit morgan proceedings proceedings proceedings department implementation version version version version version joint joint joint joint joint difficult difficult difficult difficult bias layers layers graph graph graph ai framework cambridge computing equivalent additional curves curves estimates estimates design design limit san top top conference conference conference upper upper upper upper full full significant significant approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate statistics free give give give con condition condition derived randomly conditional conditional conditional conditional conditional bounds bounds bounds lines lines product product product product product provided sampling sampling normal describe arbitrary close assumption assumption assumption predictions proof proof proof finding finding finding finding finding short theoretical theoretical theoretical theoretical theoretical main eds journal journal future easily noisy noisy noisy noisy noisy noisy kaufmann probabilistic probabilistic probabilistic probabilistic jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan jordan interesting consistent consistent empirical empirical empirical operation leads representing representing numbers numbers pre experts magnitude magnitude magnitude run run discussed discussed exact exact exact exact apply include inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference subset interest sufficient approximately approximately approximately approximately yields yields correspond converge sparse background symmetric symmetric modified generalized bounded bounded bounded horizontal expression expression expression studied extended deviation deviation deviation deviation correctly hybrid hybrid deterministic generally generally generally setting setting setting runs assumptions conclusions valued depend central central tangent interactions sigmoid accurate accurate numerical exponential faster asymptotic weak mateo taking solid solid intelligence intelligence intelligence intelligence intelligence averaged derivatives derivatives derivatives derivatives connectivity base reference suppose suppose suppose van van derive written factors factors factors factors plot recall missing multilayer multilayer multilayer infinite remaining belief scales predictive implies expectation expectation expectation expectation family family focus focus focus depending overlap overlap detailed showed approximations understanding approximated converges key slow dashed dashed dashed expansion expansion expansion expansion expansion expansion reduces roughly roughly calculate calculate figures extension uncertainty uncertainty uncertainty priors priors absolute absolute absolute absolute holds holds phys successfully simplicity closely uniformly uniformly uniformly maximal essentially refer graphs graphs graphs graphs showing interested running hold quantity quantity write michael michael simplified simplified simplified simplified minimizes leading leading acknowledgments law carried exponentially exponentially involving involving replaced optimized graphical graphical graphical graphical graphical graphical helpful fewer matches variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational variational comparable comparable proved proved func matched math configurations analyze analyze predicts queries quantities quantities quantities quantities portion algo algo panel panel panel taylor taylor taylor taylor taylor taylor taylor message finds established spin inequality inequality theoretic defining glass briefly tractable benchmark benchmark benchmark worse inside berkeley berkeley berkeley berkeley berkeley berkeley formalism formalism division division products involve medical medical evaluating substantially empirically empirically generic parameterized treated treated treated treated treated treated treated treated gen parent parent parent prevent marginal marginal marginal sums findings findings findings findings findings findings findings findings findings findings findings findings findings findings findings findings findings findings findings findings findings jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola diagnosis diagnosis yielding yielding ghahramani proofs proofs intractable feasible cooper cooper rithm rithm inspired murphy murphy murphy promising odd odd odd odd fan obtaining methodology methodology child moments substituting tap saul saul saul saul saul saul saul saul saul saul saul ensures encountered intended chooses infer kearns kearns kearns kearns kearns kearns kearns kearns kearns passing discovered summarize parents parents parents acknowledge treat treat andrew dense verify verify verify ence outline clique expanding theorems theorems utilize obtains weiss weiss junction junction big letting remainder verified intuition intuition proba carefully disease disease disease disease disease disease disease disease sketch anal slopes expansions expansions expansions expansions expansions bility justification converging barber barber evolved supplied appealing medicine unreliable concave establishing factorization cliques quick ranged ranged carrying sented ysis unobserved proximation infeasible infeasible optimizes suitably couple advice imposing posteriors viable gorithms gorithms heckerman heckerman heckerman heckerman fil sults tommi neglecting cumulant han idealized oij oij oij oij ising subscripts leak anomalous diseases diseases diseases diseases diseases diseases diseases diseases diseases diseases ditional dropping reformulation lihood bringing absorbed kevin symptoms legend fifteenth fourteenth bipartite bipartite veloped factorizes intuitions marginalization larry ang 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#@Jordan_M,Ng_A,
#t13
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#*learning learning learning learning learning model model neural input input input data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function figure figure figure figure figure figure figure figure figure time set set set set set set set set set set set set set set set set set training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm number number number number number number number system error error error results results results results results results results information information problem problem problem problem problem problem problem problem problem models models models models performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based space space space space space space space weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector order shown shown systems values values values values probability parameters parameters noise weight weight weight weight functions unit distribution distribution method method method approach approach approach approach approach approach point single single processing large large local local local local local local local local local local local local local local local local local local local local local local local local rate test test test test test analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form shows shows simple gaussian paper examples small small size size size size size size size work work work work work task step step points points points level structure structure problems problems high high response response response similar show show equation section section section section section section section fixed fixed fixed parameter parameter parameter parameter parameter parameter real approximation gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained term note note note note note note note note note note note experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional result university university variables variables variables variables variables computation solution independent independent log log found constant constant constant constant table table table table table estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard terms terms terms terms terms terms terms distance distance prediction prediction left left left left direction direction low machine machine machine sets sets sets sets range press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear continuous sample sample sample sample sample sample sample abstract density density references due due due due positive procedure procedure procedure procedure important adaptive context introduction estimation estimation statistical statistical statistical generated generated generated generated variance variance difference variable measure measure measure measure measure measure prior chosen chosen part cases fact fact probabilities minimum minimum resulting resulting resulting resulting ing ing simulation simulation regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect respect respect respect respect called regions regions means factor optimization dimension natural global global applications applications obtain negative artificial relative true true true true define define define experimental equal equal equal approaches mit steps steps accuracy comparison larger contrast descent descent descent descent descent modeling selection selection report report department department consists kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances exp bias bias bias bias bias addition equivalent equivalent equivalent equivalent equivalent equivalent experiment experiment experiment directly estimates estimates estimates estimates estimates estimates estimates estimates estimates estimates design design determine determine determine determine efficient choice significant statistics statistics free world estimated weighted weighted weighted randomly conditional criterion criterion lines entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy finally depends constraint constraint constraint constraint simply simply measured discussion discussion covariance covariance covariance normal normal denote inverse inverse inverse corresponds finding nearest nearest nearest nearest nearest nearest common shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape supported supported journal easily including fit typically typically typically needed reduced reduced unknown increasing increasing database database leads squared squared details details pre normalized normalized bottom polynomial idea idea idea attention minimize minimize minimize minimize produced choose choose choose description predict improve improve improve directions directions directions directions directions directions robust reported reported practical introduced strategy relevant dimensions dimensions dimensions highly varying compare previously observations observations observations observations observations observations observations observations observations observations observations approximately volume volume volume volume volume smooth correspond correspond correspond diagonal definition definition definition grid improvement improvement entire grant grant grant lead lead scaling predicted predicted alternative alternative locally locally locally reduce conclusions conclusions neighbor neighbor neighbor neighbor neighbor editors numerical designed performs exponential practice constrained suggest suggest suggest suggest propose drawn sigmoidal proportional intelligence minimizing minimizing exist introduce program base monte monte derive carlo carlo written index index solving estimating estimating plot describes confidence metric metric metric metric averaging dimensionality dimensionality remaining remaining remaining remaining consisting applying minimization minimization minimization minimization expectation expectation decreases choosing independently focus review review squares squares variation variation variation detailed evaluated evaluated evaluated evaluate evaluate evaluate fraction fraction fraction fraction fraction approximated suggested earlier reasonable smoothing smoothing smoothing measurements measurements measurements expansion spaces neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood intervals purpose purpose purpose remains assigned assigned degrees avoid eigenvalues eigenvalues weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting weighting extension extension plotted illustrated illustrated uncertainty discuss specifically specifically candidate partially neighbors neighbors determining middle importance suitable maximal effectively effectively driven driven literature post orthogonal orthogonal graphs moore interested interpreted lie satisfy satisfy satisfy notation notation involved vary vary vary absence correspondence predictor predictor predictor predictor predictor neighboring acknowledgments decreasing modelling presents minimized bars carried american overfitting investigate detail detail association optimized limitations recursive preliminary hall tech possibility referred eigenvectors eigenvectors eigenvectors eigenvectors tanh contours contours contours gradients man thought rank rank rank formal shapes shapes shapes shapes shapes shapes multivariate multivariate multivariate contributions explain mentioned rows ment cos distinguish derivation defining briefly tool considerable stanford stanford stanford stanford straight tive organized precisely choices choices consequence definite localized bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth radius nsf improvements considerably substantially led flexible atkeson solla employ frequently variant variant span http summarized summarized characterize differs ordered prevent conclude age age shaped deviations differentiable extreme extreme contribute proportion www formally restriction restrict fix optimizing optimizing optimizing databases controlling arranged numerically analogy fan familiar biased interpret viewpoint settings intuitive nonparametric meaningful meaningful performances recovered negligible regard regard forecasting forecasting accounts counting spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical spherical entries exposure artifacts reader kearns draw relies exploiting subsequently subsequently summarize assigns ics uci uci outperforms entropic entropic entropic entropic entropic entropic maximized benefits formulate formulate pointed residuals residuals big remainder argue cohn hastie hastie hastie hastie hastie hastie intuition toy toy toy decays distant disadvantage records places rewrite wider consuming hat hat hat curse curse blake neighborhoods neighborhoods neighborhoods suffers outperformed kth optima schaal normalize html repository repository repository drastically fair irvine irvine irvine shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping shaping nih fixing fixing fixing artificially artificially artificially cleveland sex stan stat aims attracted dard formulations hypothetical hypothetical favorable rightmost univariate univariate univariate shell conveniently fulfill gression discard narrower trevor trevor rings rings trivially doctoral roi discarding mexican mexican mexican ams diction shrinking meets parameterize misleading parenthesis merz dfg objec attains deutsche loca stretching preferably fractions contingent mother dms lives drafts stretched stretched shorthand chap ellipsoids mlearn warrant cle cle mlrepository orthogonally kit logk 
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#*network network learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural input input input input input input input data data data data data data data data data data data data data data function function function function function function function figure figure figure time time time time time time time time time time set set set set set set set set set set set set set set set set set set set set set training training training training training training training training training training training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number number number number system system system error error error error error error error error error error error state state state state results results results results results information information problem problem problem problem performance performance performance performance performance performance based based based based based space space space space space space space space space layer layer layer layer layer layer case case case case vector vector vector vector vector vector order order order order order shown shown shown systems systems probability probability probability probability probability probability parameters parameters parameters weight functions functions functions functions functions functions functions unit unit distribution distribution method method method method method method method approach approach point point image single single single processing control large large large large large large large large large 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current trained trained trained trained trained cell problems random random high memory similar similar similar representation architecture architecture architecture architecture show section section section section section section section fixed fixed vectors vectors vectors vectors generalization generalization generalization generalization generalization generalization generalization generalization parameter real real real theory theory obtained note note note experiments dimensional result result result result university university university threshold computation solution research research research independent independent log log log log log log log log log log log log log defined found found constant constant table table table standard standard standard standard standard standard standard computer computer terms node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node node science left present present present present nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine machine sets sets sets sets sets maximum press press press basis continuous sample sample sample sample abstract applied applied computational references due due positive positive procedure decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision decision introduction estimation statistical statistical variance assume classifier classifier classifier classifier classifier classifier classifier classifier classifier classifier previous previous theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound bound required required good good binary binary binary binary binary binary binary binary binary tree tree probabilities probabilities observed scale finite classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes ing tasks total total computed multi sum called called called times times elements elements regions factor factor optimization dimension dimension natural orientation applications applications applications study study em em em em em obtain negative relative relative specific represented application define define define rates determined experimental constraints connected discrete equal power mit mit mit accuracy accuracy accuracy accuracy comparison support support support support support support support support support support train train train train train train dependent report department department technique technique consists consists consists internal internal code individual individual kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances advances final final final final final graph graph graph graph graph graph graph graph graph graph maps maps cambridge cambridge equivalent equivalent top capacity efficient efficient classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers classifiers upper requires choice choice significant significant approximate statistics statistics speed pages pages pages validation validation validation give give con con derived derived bounds bounds path path path path provided finally selected evidence depends depends depends simply simply achieved achieved measured measured technical arbitrary denote tested fast limited limited corresponds corresponds surface proof proof proof proof proof proof proof proof proof finding amount short short implemented implemented theoretical require main main easily degree combination combination combination combination combination combination account jordan testing testing york york edge edge empirical empirical empirical details numbers numbers max max max max max max max max max max max max max max max max pre supervised polynomial combined minimize perceptron perceptron perceptron perceptron perceptron perceptron architectures advantage pair element typical machines machines machines side side pixels trees trees trees trees trees trees subset relevant engineering dimensions observations volume yields yields definition definition definition evaluation evaluation evaluation evaluation evaluation evaluation evaluation evaluation generalized bounded gate risk entire occur correctly correctly generally half starting minimal greater greater conclusions valued editors editors editors editors accurate bayes numerical faster faster faster faster faster practice practice propose hard largest largest drawn california labeled labeled labeled labeled labeled assuming assuming min averaged introduce introduce introduce suppose suppose digit digit derive construct construct edges sequential generating dept dept linearly linearly dimensionality dimensionality easy slightly unique unique unique scales applying minimization springer springer implies versus versus versus boolean cycles john john yield yield choosing lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma evaluated evaluated evaluated evaluated evaluated evaluate evaluate evaluate evaluate evaluate restricted labels labels labels fraction decomposition soft margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin similarly suggested suggested suggested translation allowed diagram slow spaces sec combining combining boundaries remains assigned assigned advantages classified expect building building handwritten kernels kernels sciences vapnik vapnik vapnik vapnik holds tests structural letter letter letter letter letter efficiency closely uniformly maximal paths paths svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm comparing tend summary refer refer refer verlag induced induced allowing allowing showing showing superior lie classify hold hold notation list list list list list list list list list list list list list list generalize highest operating preferred situations presents law simpler origin wiley create create involving replaced ml rest combine combine scaled scaled scaled root root maximizing comparable comparable comparable affect statistically analogous naturally man created created ensure quantities friedman friedman friedman friedman taylor taylor taylor taylor taylor taylor taylor observe mapped initialized ith ith baseline submitted great pairwise directed directed directed distinguish distinguish answer london reasons comparisons stanford stanford lin shared shared style style constructing constructing constructing leaves leaves hyperplane arise mathematics english radius radius radius improvements applies applies double double substantially substantially empirically solla rep http http http reaches substantial leaf leaf leaf leaf merging college identifying www www formally formally databases branches ordering hyperplanes hyperplanes hyperplanes hyperplanes homogeneous reconstructed partitions printed royal arranged eliminated platt platt platt platt platt fails consideration significance satisfying satisfying proceeds grow operates splitting intuitively guide evaluations evaluations evaluations evaluations excellent combines ensures appendix appendix infinity omitted omitted omitted matter cpu statement dietterich integers ball ball ball smola smola ics uci uci uci uci uci uci uci uci uci uci uci uci maintaining arcs arcs leaving svms svms svms svms svms svms svms svms svms svms svms svms svms svms svms svms svms svms svms svms svms usage sch sch pointing sig super reports possibilities clas continuity burges burges mutually mutually exclusive exclusive disadvantage carefully regularized indexed indexed misclassified misclassified placing page page places indication margins margins margins margins margins margins margins margins margins margins margins margins resembles fat fat fat fat ate font kopf kopf losing losing savings shawe shawe shawe shawe shawe shawe shawe blake doesn wins wins wins wins wins wins wins wins wins wins wins wins wins wins wins wins smo dcs eliminates distinguishing vote triangle separates separates poly html repository fastest shattered shattered safe amenable irvine terminates halves corn mis acyclic acyclic acyclic acyclic statements shares repetitions microsoft microsoft microsoft stat discrepancy herault resentation dependences cir usps usps usps usps shattering motivates experimentation tinuous overfit fogelman exclude periments discard dreyfus nato personnaz bennett multiclass multiclass multiclass multiclass multiclass multiclass multiclass multiclass multiclass multiclass multiclass proportionality votes reachable stepwise rooted rooted rooted rooted rooted neurocomputing dag dag dag dag dag dag dag ficient prefers holloway regularizing inhomogeneous merz ilwll ern terrain soulie russian asi unsolved tains crn evalu rhbnc pessimistic traverses revisited redundancies mlearn egham keams ferred moscow sulting nificantly mlrepository sifiers xex enlarging enlarging diagonals failing surrey redmond quote alphabetical nauka rected 
#@Cristianini_N,Platt_J,Shawe-Taylor_J,
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#*network learning model model model model model model model model model model model model model model model model model model model model model model model neural neural neural data data data data data data data data data data figure figure figure figure figure figure figure time time set networks networks networks training algorithm algorithm number number number number number number number number number number number number number number number number number number number number number system state results problem models models models models models models models models models models models performance performance based based based case case vector order order shown shown shown shown shown values values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach pattern point single single single single single single large large local analysis analysis class class class class class class class class class class class class class class class class form form form form form form form shows shows shows gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small work work work work work task methods methods methods methods methods methods points points process process process process current trained problems problems problems problems problems random random high similar show section section fixed fixed fixed line vectors general parameter parameter parameter parameter parameter parameter parameter parameter average obtained obtained obtained obtained note dimensional dimensional dimensional university university variables variables variables variables computation research independent independent independent log log log log log log log found initial initial estimate estimate standard standard standard terms terms left presented presented phase maximum range press press components components components components components components components components components components components components components components components components components components components components sample sample sample sample sample sample abstract applied back find computational density density density density properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component component component component component stochastic positive positive adaptive adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context introduction hand estimation estimation statistical generated generated variance variance difference complexity variable assume prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen center center previous cases good long represent represent represent distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations markov markov markov markov markov make correlation correlation correlation length length length finite finite finite finite finite finite finite finite finite finite finite finite resulting classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes ing regression regression computed sum sum sum performed performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq means means means means means dimension applications applications applications em obtain samples samples samples samples samples samples samples represented represented represented represented represented represented represented desired eye determined posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions distributions discrete approaches mit mit steps update report department department implementation version technique technique joint joint difficult difficult final final exp exp exp exp exp exp exp considered computing directly directly hinton limit limit limit limit limit limit limit top efficient efficient significant approximate approximate statistics statistics statistics statistics statistics free free give give derived derived derived derived derived derived conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional lines lines processes processes iteration iteration depends depends sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply achieved covariance covariance covariance covariance normal technical technical arbitrary inverse inverse inverse common common effective effective shape shape shape shape shape generate generate generate generate role role role journal easily easily easily needed account unknown unknown unknown coefficients fully york numbers numbers iterations iterations iterations making combined combined combined discussed takes takes practical practical introduced identical hierarchical hierarchical hierarchical hierarchical inference inference inference inference highly varying previously observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations observations approximately works tions tions tions rl trans mixtures mixtures mixtures mixtures mixtures chain chain chain chain chain chain symmetric observation observation observation observation observation williams williams entire entire parts lead suggests extended extended wide matrices matrices matrices setting conclusions depend competitive editors editors bayes taking integration drawn demonstrated demonstrated proportional turn turn variety start introduce minima monte monte monte monte monte derive carlo carlo carlo carlo carlo produces written generating generating plot plot mathematical mathematical missing averaging infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite infinite remaining remaining slightly gaussians gaussians predictive predictive predictive predictive springer john depending detailed densities evaluate sizes similarly reasonable reasonable roughly roughly initially initially advantages advantages precision building priori plotted plotted uncertainty mozer priors priors priors priors priors priors priors priors priors priors priors priors priors priors priors priors tests major simplicity gamma gamma gamma gamma gamma gamma gamma straightforward aspects efficiency society effectively effectively efficiently situation situation traditional notice notice notice verlag procedures dis follow follow gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs quantity write nips nips automatically mixing mixing mixing mixing mixing mixing acknowledgments modelling modelling modelling explore explore explore simpler wiley overfitting overfitting essential updating updating put detail detail integral integral integral integral mass mass mass mass mass dataset dataset helpful scalar scalar scalar analytically combine referred complicated encode removed generalisation generalisation generalisation generalisation illustrate quantities explored explored multivariate multivariate multivariate multivariate multivariate multivariate generates generates simplest neal neal neal neal neal neal integrate derivation variances growing fairly analytical tractable handle turns purposes sections sections broad commonly toronto toronto auto auto conjugate limits freeman led amounts http http limiting reaches hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters green green green chose comments shaped shaped unbiased multidimensional ghahramani notes www extensive conditioned conditioned conditioned repre unity grows royal plays plays spiral smith minutes adjusting keeping methodology nonparametric nonparametric substituting started connect histograms hasselmo surprisingly smoothed reveals reveals indicator indicator indicator indicator matter cpu belonging belonging relies concentration concentration concentration concentration likelihoods std lag lag empty spirals spirals spirals spirals spirals multiplying multiplying specification annals annals solves ent ber rejection rejection isotropic convenience spaced multinomial possibilities letting imagine avoided beta avoids attempted concentrated num crosses picked dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet dirichlet funded sam west west sweeps sweeps mcmc mcmc mcmc vanishes det det normalised tract compu infinitely handled lecture optimisation stay proportions proportions proportions proportions proportions compo evenly thickness rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen ples discarded ray rameters html concave concave denmark denmark counterpart subscript differentiate reviewed tained indicators indicators indicators indicators indicators indicators indicators indicators indicators indicators indicators indicators indicators indicators mul ated probabil sented applica derivations nents recovers ities tics statis excluding posteriors posteriors posteriors posteriors posteriors nakano ously standing specifications comprise abs stays dev exposition tational hyperparameter contributed tributions wild wild ations muller spreads indexes edward richardson richardson richardson associ lastly lihood radford radford observa zky touret vague vague vague vague tractability danish carl carl propor undertaken pertaining resented imm imm precisions precisions precisions precisions gilks gilks iog iog peculiar needing hitherto simultane consult neuroinformatics lyngby pentium ameters occupation occupation yil crossvalidation councils burn thor neatly 
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural data data data data data data data data data data data function function function function function function function function figure figure figure figure time set set set set set set set set set networks networks networks networks training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number error error error error error error error error error error error error error error error error error state results results results problem problem problem problem problem problem problem problem problem performance performance performance performance space space weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear case case case case vector vector vector order order shown shown systems values values probability parameters parameters noise noise weight distribution distribution recognition recognition approach approach approach pattern point point single single processing control control large large large test test test test patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns patterns analysis class class class class class class optimal optimal optimal optimal optimal shows shows shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper paper examples small small small size size size feature net work work work methods methods methods methods methods methods methods fig fig points points points points points points classification classification classification process problems problems problems problems problems problems random high high similar similar show show show equation section section fixed fixed line line line rule vectors general general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization parameter parameter parameter parameter parameter parameter parameter parameter real approximation approximation average average theory theory gradient obtained obtained obtained term term term note note note note experiments experiments experiments university university university university variables variables variables computation solution solution solution solution solution solution solution solution solution solution solution solution solution research log defined defined found found found found found found sequence constant constant constant constant constant constant table estimate standard computer computer terms terms science science science prediction left left left present present present low low machine machine machine sets sets sets sets sets sets sets maximum maximum press press press learn learn basis nonlinear sample abstract applied find find find find find computational convergence convergence properties properties properties properties references due important important important important adaptive decision decision decision introduction hand hand hand hand behavior statistical statistical generated generated generated cost cost complexity assume classifier lower lower prior learned chosen part previous previous theorem theorem theorem theorem theorem theorem theorem bound bound bound cases cases cases cases cases good good good good good good expected expected fact fact fact proposed errors errors errors errors errors errors errors errors finite finite finite minimum minimum minimum resulting resulting classes classes ing tasks tasks tasks regression respect respect sum elements optimization optimization optimization optimization dimension global applications study study knowledge obtain obtain obtain obtain samples compared application application cross cross define proc proc experimental experimental goal related related mit mit mit comparison comparison comparison larger larger support support support descent selection report report report report department department kernel advances advances advances difficult difficult difficult exp exp exp graph graph ai cambridge cambridge cambridge experiment directly directly directly view view estimates estimates limit effects efficient classifiers classifiers upper upper choice choice statistics statistics free world estimated pages pages pages pages validation validation derived weighted weighted bounds bounds bounds bounds area area provided finally finally iteration iteration nature depends depends depends achieved achieved achieved technical technical technical technical increases fast complete proof finding rbf rbf rbf rbf rbf rbf shape supported role role role theoretical theoretical main face face end end hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis future easily easily makes makes noisy noisy noisy noisy noisy including kaufmann objective objective objective smaller smaller needed needed combination combination coefficients jordan programming programming programming interesting interesting significantly significantly character york increasing leads leads leads details details iterations iterations iterations max max max max pre making normalized idea idea idea combined minimize choose run improved property robust separate ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble introduced subject subject subject machines side side side side side sense recently engineering highly approximately approximately approximately volume works works solve solve solve solve yields yields studies converge converge converge modified observation observation bounded bounded interval interval grant scaling derivative predicted locally move boundary setting setting conclusion starting minimal reduce depend depend editors editors clear clear performs performs performs performs performs faster faster practice practice practice asymptotic asymptotic asymptotic propose propose propose hard presence presence presence presence california regularization regularization regularization regularization regularization regularization regularization turn assuming minimizing user min min min min averaged introduce derivatives program program force base base base base base base base base base base question question explicit suppose suppose suppose relation digit construct written optical ways label dept changing confidence confidence missing averaging linearly linearly infinite electrical involves remaining remaining slightly slightly text minimization springer springer implies expressed depending interpretation interpretation learner learner solved solved detailed transform fraction fraction fraction fraction fraction fraction fraction fraction fraction fraction lee centers soft soft soft soft soft soft understanding margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin margin converges sign partial earlier reasonable reasonable dashed additive intervals roughly construction handwritten formulation determines vapnik vapnik discuss maximize maximize maximize maximize absolute successfully regular closely importance modification effectively svm svm essentially orthogonal ten ten reached capture refer conf verlag verlag kind prob prob heuristic success dis superior lie contribution contribution running comp notation quantity michael michael play minimizes denker hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses hypotheses maximization approximating satisfies acknowledgments extend overfitting investigate optimized optimized dataset reducing ideas boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting possibility combine maximizing comparable smallest act possibly necessarily analyze illustrate thought adjusted quantities friedman algo logistic fisher precise message generates utility regime finds optimum optimum optimum asymptotically asymptotically great inequality inequality inequality theoretic theoretic separable crucial crucial analyzed defining defining waveform explanation adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost adaboost majority briefly benchmark benchmark benchmark worse worse london inside stanford arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc arc easier widely strictly constructing bengio desirable hyperplane controls controls simard separately sun robustness virtual substantially empirically empirically bootstrap conducted parameterized marked solla outliers outliers outliers outliers outliers outliers http http exhibits berlin incorporating germany implements proposition proposition proposition trade benefit benefit notes primarily www www japan recover recover nat databases approximates approximates approximates controlling addresses flexibility royal lecun plays plays wrong significance breiman breiman breiman satisfying replacing imply effectiveness intuitive intuitive games performances mance bartlett bartlett bartlett bartlett separating schapire schapire schapire perfor pat sides heart jackel ensembles express eng cancer cancer matter repeatedly repeatedly kearns bagging bagging extends extends variants statement explains inf fold smola smola smola smola smola smola smola smola smola ics speaking speaking speaking uci uci uci street appeared svms svms svms svms svms svms slight sch sch annals deriving guyon inferred opposed tibshirani conjecture corrected ease tradeoff freund freund freund german australia burges translated hastie toy toy regularized regularized regularized efforts quinlan misclassified misclassified setup sonar voting supports likewise page applicability margins margins margins margins margins williamson gauss lems lems lecture lecture gratefully fiat kopf terns breast blake bold bold december loosely loosely alex realizations 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#@Mika_S,Muller_K,Onoda_T,Ratsch_G,Scholkopf_B,Smola_A,
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#*learning learning learning learning learning learning learning learning learning model model model model neural neural input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function figure figure set set set set set set set set set set set set networks training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number error error error error error error error results results results results results results information information information problem problem problem problem problem problem problem problem problem problem problem problem models performance performance performance performance performance based space space space space space space space space space space weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector shown shown shown shown values probability probability parameters parameters parameters parameters weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions recognition recognition method method method method approach approach approach pattern pattern pattern point point point processing large large rate rate rate test test test test test test test test test test patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal form form shows signal algorithms algorithms algorithms algorithms simple simple simple gaussian paper paper examples size size size size size feature feature feature feature feature feature feature feature feature feature feature work work task methods methods methods step step step step step step step classification classification classification classification classification classification classification classification classification classification classification classification process process level current trained problems problems problems problems problems random high high high high high response response response response similar similar show equation equation equation equation equation section section section section section section line vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images general general generalization generalization generalization real real real real real average theory obtained term term term note note note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university variables variables variables variables computation computation solution solution log defined defined defined found initial constant constant table table table table standard standard standard computer computer terms terms terms terms terms terms terms terms terms science science left left presented presented map present present present present low low low machine machine object maximum maximum press learn learn basis basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample abstract computational likelihood likelihood likelihood likelihood likelihood likelihood references component component due ieee positive procedure procedure procedure decision decision mixture mixture mixture introduction estimation estimation estimation statistical effect variable classifier classifier classifier representations chosen part type type multiple equations equations techniques techniques proposed probabilities observed scale scale simulations simulations resulting resulting classes classes classes classes classes classes classes regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression computed computed multi multi multi multi sum performed performed called called times times times regions mapping mapping mapping means optimization dimension made natural applications applications applications applications em em em em em em em filter obtain vol vol vol vol specific represented compared application application define rates rates determined related posterior approaches mit comparison comparison update support support support support department loss loss implementation implementation version version version technique technique technique technique technique consists consists code kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances represents responses final final final exp exp ai ai ai framework framework framework equivalent experiment experiment additional view estimates detection classifiers classifiers upper requires requires significant approximate statistics world world world give give coding derived weighted weighted weighted levels criterion criterion criterion criterion bounds product product product product product product constraint constraint constraint constraint achieved discussion covariance covariance covariance covariance normal group group group denote denote tested transformation assumption assumption complete rbf rbf rbf rbf common supported theoretical main main main eds eds eds pixel future makes makes including including objective simulated simulated needed needed coefficients coefficients coefficients coefficients coefficients mlp block significantly significantly ratio edge database database database leads leads leads principal squared representing call pre direct making supervised supervised supervised supervised polynomial idea idea idea idea idea minimize minimize minimize choose run run light light perceptron denotes denotes denotes improved improved improve recent property property property separate practical practical apply apply apply introduced include subject pixels quadratic quadratic trees recently observations observations observations observations observations observations observations observations observations works correspond diagonal mixtures symmetric observation observation observation observation observation observation generalized generalized generalized improvement risk exists concept concept studied matrices column setting demonstrate differences bayes bayes numerical numerical faster faster faster faster reduction reduction labeled labeled radial turn assuming assuming minimizing minimizing minimizing iii iii scene acknowledgements explicit construct construct written plot plot implement missing explicitly infinite dimensionality dimensionality dimensionality remaining unique unique springer springer implies john review review stationary influence solved detailed detailed transform showed showed centered centered centered decomposition decomposition partition measurements classical classical classical classical classical classical classical expansion expansion expansion spaces spaces spaces spaces spaces spaces spaces spaces spaces combining iterative boundaries boundaries penalty penalty distances calculate assigned classified views views views avoid expect building kernels kernels thesis formulation eigenvalues eigenvalues eigenvalues eigenvalues inter subspace subspace subspace vapnik partially partially partially partially discussions major columns regular identified svm svm svm svm svm svm literature efficiently efficiently score score score orthogonal verlag repeated prob dis criteria hold notation notation dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot dot eigenvalue eigenvalue eigenvalue eigenvalue eigenvalue highest leading leading leading maximization maximization maximization consisted deal decreasing oriented extend minimized minimized remain wiley wiley transformed optimized dual dual discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant discriminant dataset helpful tech tech mappings mappings mappings maximizing proper eigenvectors eigenvectors eigenvectors eigenvectors scores scores scores analogous closest illustrate prototype friedman versions fisher mapped multivariate consist phd attempts averages years residual indicating rows rows rows derivation derivation derivation waveform waveform waveform waveform nonlinearity london turns lin formalism widely constructing incorporate choices products products products products products products products products products products consequence projected projected projected projected projected implicit ridge ridge ridge ridge demonstrates incomplete populations pure pure flexible flexible flexible quantitative rep rep variant ture spread reaches maximizes maximizes popular popular ordered germany semi semi simultaneous ear accomplished writing formally formally lagrange acts repre nonzero nonzero royal multiplier convenient convenient breiman overcome satisfying held stated scoring scoring scoring scoring scoring scoring scoring unlabeled unlabeled belong belong canonical canonical symposium intuitive wilson published studying equals overview belongs uni centroid chooses viewing entries iterated membership membership membership membership membership indicator indicator augmented augmented augmented sons sons projects hart stone assigns assigning smola smola limitation unchanged outperforms linked maximized formulate tween tibshirani tibshirani tibshirani medium ical spaced constitutes clas burges visualization visualization 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#@Roth_V,Steinhage_V,
#t13
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#*neural neural function function figure figure figure figure time set set set networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm system error error state state state results results results results results results units information information information information information problem problem problem problem models models models models performance performance based space space space case case case case case case vector shown shown systems systems values probability distribution distribution distribution distribution distribution recognition method point point point point point point point point single processing processing control large analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix form signal algorithms algorithms algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper paper examples size methods points points points points problems problems problems problems problems problems random random random high show show show show show show equation section section section section section section fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed fixed line line vectors vectors vectors speech approximation approximation approximation approximation approximation approximation theory theory theory theory obtained note note note experiments dimensional dimensional dimensional dimensional dimensional result result result result result university variables variables computation independent defined defined defined defined defined defined defined sequence sequence sequence sequence dynamics initial terms presented presented present present present present low low low press components continuous continuous abstract abstract applied convergence convergence convergence convergence convergence convergence convergence convergence convergence density density density density density density density density density density density density density density density density properties references due due due ieee ieee ieee ieee ieee ieee positive positive positive positive important propagation propagation propagation propagation propagation propagation propagation propagation context context context context context context context context introduction hand behavior behavior generated generated generated generated generated parallel variable assume assume measure word word previous theorem theorem theorem theorem theorem theorem cases cases good conditions conditions represent represent distributed equations fact fact fact length correct observed errors errors errors errors errors errors errors errors errors errors errors errors resulting resulting classes computed multi performed eq eq eq eq eq eq elements elements elements elements means means means means means means means factor factor factor natural applications applications study obtain original vol vol vol relative relative relative true application desired desired desired desired provide provide provide provide define define compute experimental experimental experimental related related related posterior posterior posterior posterior posterior constraints distributions mit mit connection morgan code code code advances advances joint final graph graph sequences sequences sequences ai ai cambridge computing computing computing computing design limit limit limit limit san capacity full significant approximate con con channel coding coding coding coding coding randomly conditional conditional conditional conditional conditional developed developed finally selected selected iteration sampling measured measured discussion discussion covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance technical describe arbitrary denote denote denote denote denote denote close close close corresponds complete complete proof proof proof proof proof proof proof proof proof proof proof role journal journal instance instance noisy noisy kaufmann objective objective interesting interesting significantly mechanism special structures empirical details iterations idea attention choose light discussed discussed exact exact pair include include trees inference inference inference inference inference inference recently previously observations axis converge converge converge trans trans trans trans diagonal diagonal diagonal diagonal address definition definition symmetric bounded exists exists expression studied studied digital matrices matrices matrices matrices matrices matrices matrices matrices matrices matrices correctly loop generally generally setting setting setting setting runs runs reduce operator operator operator depend central central designed mateo taking hard presence labeled areas areas appears relation van factors primary plot vertical recall involves easy belief belief belief belief belief belief belief unique unique unique develop versus cycles communication viewed lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma lemma codes codes codes codes codes codes detailed densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities densities open operations evolution evolution understanding converges converges converges converges converges converges converges converges converges earlier iterative iterative closed topology expect instances instances illustrated prove priors priors suitable suitable differ schemes mackay plots plots plots identity identity refer conf graphs graphs graphs graphs decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding decoding success notation notation quantity sampled vary write write generalize highest ill illustrates approximating approximating employed explore carried involving involving involving limitations limitations accurately issues preliminary graphical graphical graphical graphical graphical mappings applicable int parity parity parity working understand plausible analyze expressions initialized initialized initialized initialized message message generates generates generates generates generates submitted submitted established established analyzed analyzed multiplication tractable tractable tractable turns stanford stanford organized division operators arise consequence consequence describing begin definite definite definite definite geometry explained limits freeman freeman understood tional axes conducted limiting aim maximizes monotonic enables expectations lim lim representative representative indices intractable intractable intractable intractable conditioned conditioned conditioned approximates establish plays communications communications convenient chance satisfying intelligent loops loops loops check check check hope reasoning definitions obstacle analyses analyses analyses studying studying facilitate entries infer surprisingly reader roy roy roy roy passing passing storing relies correcting variants captures statement papers assigning dramatically multiplying multiplying inferred transmitted dec monotonicity monotonicity monotonicity monotonicity weiss weiss weiss weiss generalizations covariances covariances alter continuity ftp community insights insights shannon relating pearl pearl outcomes algebra frey frey frey normalizing computa november jointly coin establishes establishes suffices possess possess possess coincide correctness conditionally ultimate ultimate nontrivial cliques restrictive concatenated dent feb feb indepen bear inaccurate inform proceeding formulas decades unnecessary ference omit marginals coincides coincides coincides mar rescaling ago burden switzerland iterates iterates iterates manipulating motivates aware sorts lemmas lemmas lemmas provably exposition compound bears independencies nonsingular nonsingular resort invoked pointwise mceliece resemblance plied publications richardson richardson richardson shed pertinent xii cheng intriguing chart possessing possessing derlying tedious wll trices probab revision proxy verges verges hori preparing benjamin stances zontal warranted upcoming 
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#*learning learning learning learning learning learning learning learning learning learning learning learning model input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function figure figure figure time set set set set set set set set set set set set set set set training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number number system error error state results results results units problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem performance based based space space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear linear linear case case case vector vector vector vector vector vector vector vector vector vector vector shown shown shown values values values values probability probability probability probability probability probability probability probability probability probability probability probability probability parameters weight weight weight functions functions functions functions functions functions functions functions functions functions unit unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition method method method method method method method method approach approach approach approach pattern pattern pattern point point point point point point point point image image single single large large local test test test test test patterns patterns patterns patterns patterns patterns patterns analysis analysis class class class class class class class class class class class class class class class form form shows shows shows algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper examples examples examples examples examples examples examples small small small small small small size size size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work work work work task task task methods fig points points points points points points points points points features classification level current trained problems problems problems problems high high similar similar show section section section fixed fixed fixed line line rule vectors vectors images images general general general generalization parameter parameter parameter real real real theory theory theory theory theory obtained obtained term note note note note note note experiments dimensional dimensional dimensional dimensional result result result result university university university threshold variables variables variables solution solution solution solution solution solution solution research research research log log log log log log log log log log log log defined defined defined found sequence constant constant table estimate estimate estimate estimate standard computer terms terms terms terms distance distance distance left direction map map map map present present present present present sets sets sets sets sets maximum range range press press components components components basis nonlinear nonlinear outputs outputs continuous sample sample abstract applied find find computational density density density density density density density density density density properties references component due positive positive positive decision decision decision decision decision decision decision context introduction hand estimation estimation estimation statistical statistical statistical statistical generated generated generated variance parallel tion change change change complexity variable assume assume lower lower lower rules measure measure measure measure measure measure measure prior chosen part part theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound bound bound bound bound bound bound bound cases cases type binary fact fact techniques techniques region region region region region region region region region region region region proposed proposed length length length errors errors scale scale scale finite finite finite minimum classes classes ing regression computed respect sum called regions regions regions mapping mapping factor dimension dimension dimension natural applications knowledge knowledge negative negative original original artificial artificial specific specific application desired provide provide provide define define compute perform determined determined goal related constraints constraints constraints distributions discrete equal approaches approaches mit larger larger support support support support support support support support support support support support support support selection proceedings proceedings report department version version technique kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances difficult difficult sequences ai ai cambridge cambridge computing domain domain domain domain domain equivalent experiment experiment experiment directly additional view view view view detection detection detection detection conference conference capacity classifiers upper upper upper upper upper upper full full full choice approximate world estimated estimated estimated pages pages pages give give produce randomly randomly clustering developed levels bounds bounds bounds types product product actual depends depends constraint simply discussion discussion discussion normal increases increases describe describe denote denote denote transformation limited close inverse corresponds corresponds corresponds corresponds proof rbf amount common common supported supported theoretical theoretical theoretical theoretical theoretical main face face face journal square instance objective objective smaller underlying underlying underlying underlying account functional unknown coefficients transfer programming interesting ratio ratio york increasing increasing segmentation database empirical principle principle leads principal principal principal numbers numbers numbers numbers numbers max direct making international normalized supervised idea idea attention description recent property property separate separate takes reported practical practical apply apply strategy subject subject machines side quadratic quadratic sense sense sense subset subset subset subset engineering interest dimensions unsupervised unsupervised unsupervised unsupervised observations teacher volume tions solve solve solve solve solve solve smooth pca definition separation generalized bounded bounded bounded risk grant exists exists studied move width width width width generally minimal greater valued valued editors editors editors clear clear propose hard hard hard hard drawn drawn drawn drawn proportional intelligence regularization regularization turn variety minimizing start exist movements min min iii introduce program force base suppose suppose suppose suppose appears digit written factors estimating estimating estimating estimating changing metric metric metric infinite involves easy unique unique develop applying applying springer implies expectation john john john letters letters decreases national national independently estimator interpretation influence influence solved solved densities controlled labels labels labels fraction fraction fraction fraction fraction fraction fraction soft soft margin margin margin margin margin similarly digits digits constants expansion expansion spaces convex sec purpose boundaries boundaries remains foundation norm norm norm norm norm david david expect handwritten box kernels kernels kernels priori coordinate usa sciences vapnik vapnik vapnik vapnik vapnik vapnik extension specifically black holds holds discussions characterized characterized simplicity simplicity identified extra maximal modification effectively svm svm svm identify identify identify literature tend ten capture compact compact quickly contained interested interested lie classify running manifold hold notation notation quantity dot dot dot generalize paradigm quantization computes computes leading automatically received attempt satisfies satisfies situations origin origin origin origin origin origin origin origin origin wiley transformed involving involving estimators integral dual dual dual preliminary dataset dataset dataset helpful applicable possibility possibility root cover cover cover editor opposite singular versions taylor taylor taylor taylor taylor taylor freedom mapped simplest attempts seconds years asymptotically stop inequality separable separable separable analyzed analytic caused briefly lies lies tool handle starts london considerable considerable inside turns arc easier precisely worst bishop sgn sgn sgn hyperplane hyperplane hyperplane hyperplane hyperplane products products acknowledgement meaning robustness argument fourth geometric questions evaluating evaluating understood offset pseudo pseudo generic generic introducing detecting employ incorporated incorporated variant ity ity outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers outliers mod measuring differs extracting fall fall chose conclude windows returns proposition proposition proposition proposition displays extreme trade trade picture picture picture proofs indices notes sv sv sv assign lagrange lagrange restrict fix fix hyperplanes labelled controlling discovery addresses impossible nonzero nonzero nonzero nonzero royal maass multipliers multipliers platt platt platt platt platt fails dealing stronger attractive hope tishby settings corner days motivation meaningful separating recovered falls respective equals equals moved conjunction dif augmented park exploiting statement alternatively robert smola smola smola smola smola smola smola smola smola smola severe outlined speaking speaking street sch sch sch sch sch sch constitute deriving covering covering covering covering covering covering restrictions convenience utilize ideally remainder burges burges penalized community mhz toy toy goals distribu mathematically parzen regularizer thresholded regularized regularized regularized regularized maximally scope exceed buhmann esti esti margins port williamson williamson williamson williamson williamson compu exploited struc supporting aaai ritter resembles lecture fat fat characterizing algorithmic kopf kopf kopf kopf kopf kopf australian australian european ferent shawe shawe shawe shawe shawe shawe firstly firstly solvable bold bold smo routines pictures loosely mining alex alex dcs concrete possess proposes extracts separates cardinality characterizes maxi complement complement implying unlabelled unlabelled falling falling falling spirit gmd thing ben ben faced svs svs svs svs svs enforces statements slack slack slack slack capturing cti cti mesh supposed supposed decades probabil terminology stems microsoft microsoft microsoft microsoft microsoft tipping ular primal whilst trick trick ver respects possesses devel devel nonlinearly usps usps usps shattering shattering ranked notably tially separability solu menlo rationale novelty novelty novelty novelty novelty earliest poten behaved tational live shortcomings shortcomings partic tlx pervised penalization inspiration bernhard originated absolutely canberra fax gions borel pollard mates holloway minimisation balls logarithms oped dfg mika unsu anu scholkopf scholkopf scholkopf tackled fayyad atypical facto deutsche proposing void fractions chances folds folds lkopf bob anymore arx tax rhbnc lives ols egham bsc formidable brussels pentium msr recommendations abundant forschungsgemeinschaft mtiller mani mani opment semidefinite disregarded conventions premature accomplishing guildhall seminar tural redmond redmond mator italics greek underneath 
#@Platt_J,Scholkopf_B,Shawe-Taylor_J,Smola_A,Williamson_R,
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#*network network learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data figure figure figure figure figure figure figure time time time time time time set set set set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm output output output output output output output output output output output output number number number number number number number number number number number number number number number number number number system system system system error error state state state state state state state state state state state state state results results results results information information problem problem problem problem models models models models models models models models models models models models models models models models models models models hidden hidden hidden hidden performance based space space space space weights weights weights case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown shown shown shown shown systems systems systems systems systems values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters neurons neurons neurons distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method approach approach approach approach approach approach approach approach pattern pattern pattern pattern point single single single processing processing large test test test test test test test test test test test test test test class class matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs form form form form form form form shows signal simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples small feature net step trained trained trained trained trained trained trained structure structure structure problems problems problems problems random representation architecture architecture architecture show show show section line line vectors vectors vectors vectors vectors vectors vectors general general general speech speech speech speech speech speech speech speech speech speech speech speech parameter approximation average states states states states states states states states states states theory gradient gradient term term note note note note note note experiments experiments experiments experiments experiments dimensional university variables variables research research independent independent log log log log defined found found found found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence target target target constant constant table table table table estimate estimate estimate standard science prediction prediction left present temporal range press position position position components components components components components components components components basis outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous sample sample abstract abstract back back find density density density density density density density density density density density density density density density density density density density density density density density density density density density density properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component component component ieee ieee ieee procedure procedure important adaptive propagation mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture context context context context context context context introduction complex hand estimation estimation statistical statistical variance variance variance variance variance variance recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent recurrent search search search tion change change difference complexity complexity assume assume lower measure measure measure prior prior chosen higher higher higher part part part part part previous previous previous previous cases cases cases type type type type type type type type type type type type type type type type required multiple conditions conditions expected equations markov proposed observed forward forward forward forward resulting classes classes classes classes ing ing total regression regression regression regression regression regression respect multi multi multi multi multi multi multi multi called means means means means means potential made made applications applications applications applications applications em original original samples samples represented compared compared compared perform goal distributions distributions distributions approaches approaches approaches approaches comparison larger contrast train train train train descent descent modeling modeling proceedings report institute implementation implementation version consists difficult addition sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences considered computing environment directly directly additional additional additional additional effects efficient upper choice significant basic pages increase give give coding derived types types types types types depends depends covariance covariance covariance covariance technical arbitrary group tested tested assumption assumption assumption assumption corresponds corresponds complete complete complete complete complete complete actions assumed assumed assumed assumed makes objective objective probabilistic pairs pairs smaller underlying reduced technology mlp interesting testing database database database representing numbers direct making making making making making international normalized supervised supervised frame frame description predict predict predict improved separate practical include side sense engineering interest varying conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional works speaker match trans diagonal diagonal mixtures mixtures mixtures evaluation modified observation parts expression lead occur extended extended extended predicted predicted alternative feed assumptions assumptions assumptions assumptions assumptions segment conclusions depend modules modules faster practice sound labeled labeled radial radial radial radial radial assuming targets acoustic denoted denoted denoted denoted areas explicit explicit explicit pro sequential sequential sequential sequential sequential estimating estimating describes distinct changing modeled modeled modeled metric averaging dimensionality dimensionality involves slightly consisting adding gaussians extraction focus review depending depending stationary phoneme phoneme phoneme phoneme phoneme phoneme influence detailed detailed densities densities evaluated evaluate approximations approximations approximations approximations frames decomposition approximated approximated completely completely suggested past past reasonable sec valid valid calculate symbol symbol symbol symbol symbol degrees building includes includes thesis strings extension extension extension extension extension extension extension extension extension extension variations black structural structural regular straightforward suitable suitable symbols symbols symbols build build build comparing traditional traditional traditional traditional traditional traditional traditional procedures prob phonetic phonetic phonetic phonetic phonetic dis generative generative generative generative generative generative generative generative hold built built notation quantity involved simplified absence backward backward backward minimizes highest reach automatically attempt neighboring neighboring neighboring simpler transformed put relations detail limitations issues mass mass fewer dependencies maximizing statistically possibly adjusted explored mapped mapped expressions expressions expressions expressions expressions expressions expressions expressions expressions expressions art speakers baseline grouping phd mentioned indicating indicating derivation variances variances variances defining waveform independence incorporate bishop bishop laboratories separately sounds lowest meaning alignment alignment requiring dark introducing posed incorporated formulated frequently http http calculating vocabulary synthesis rely phonemes phonemes phonemes phonemes extensions sophisticated utterances cor lot gap lab contextual aligned oxford japan japan restriction conditioned conditioned conditioned conditioned conditioned conditioned conditioned conditioned conditioned conditioned repre grey grey simplify resulted occurring removing responsible responsible corpus bad uni uni uni uni uni propagated candidates young express theoretically theoretically waveforms likelihoods summarize linguistic compressed usage vec aston maximized presenting distinction arg arg arg arg arg ideally covariances england england clustered care care simplifying rough library covered xly xly atr atr treating rnn modal modal modal modal modal modal modal modal modal modal modal modal modal modal lems 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#@Schuster_M,
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#*network learning learning learning learning learning model model model neural data figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time networks networks networks networks system state state state results results results results problem problem problem models models models models models models models hidden performance space space space weights weights weights weights weights weights weights case case case case case case order order order order shown shown systems probability probability probability probability probability probability probability probability probability probability probability probability weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach approach approach approach approach point point point point point point point point point point point point point point point point point point single single single single large large large large local test optimal form shows algorithms algorithms algorithms simple simple simple simple simple simple simple simple simple gaussian paper paper paper size size size size size size size size size work work task task methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step points points points points points points points points points points points points points points points points points points points points points points points points points points points current structure problems problems problems problems random random random random random random random random random random random random random high high high high high representation representation show show show show show section section fixed fixed fixed fixed fixed line general general gradient gradient obtained obtained note note note note note note experiments experiments experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university variables solution independent independent independent independent independent independent defined defined sequence sequence sequence target target target target target target target target target initial initial estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard standard standard standard standard computer terms science direction direction direction direction direction direction presented present low machine range press continuous continuous sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied applied applied find density properties likelihood references stochastic stochastic stochastic stochastic procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important important important propagation introduction introduction complex estimation estimation estimation estimation estimation statistical dynamic dynamic variance variance variance variance variance variance parallel search search search search search search search search search search search search search search search tion variable variable variable variable variable variable variable variable variable variable variable lower lower measure chosen higher previous previous cases cases multiple long long conditions tree tree tree bayesian bayesian bayesian expected expected expected markov markov markov markov make fact fact fact techniques length correct finite finite finite resulting resulting resulting resulting ing ing tasks tasks total total total simulation simulation multi multi multi multi sum sum eq elements regions regions regions regions regions regions regions regions regions means factor dimension made study policy em filter obtain obtain obtain obtain obtain obtain obtain obtain artificial relative relative samples samples samples samples samples true series compute compute compute perform determined determined goal goal posterior distributions distributions discrete discrete discrete discrete discrete discrete approaches approaches mit steps steps steps steps steps steps steps steps steps steps steps steps steps steps larger descent descent descent dependent dependent morgan department version technique technique technique technique technique difficult final final final final final final bias bias bias bias scheme scheme considered cambridge computing domain domain equivalent experiment experiment directly directly directly estimates estimates limit determine upper requires significant significant significant significant significant approximate increase con con weighted weighted conditional conditional bounds lines path path path path path finally selected nature nature sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling achieved discussion normal technical technical technical arbitrary corresponds complete common common effective implemented main main future easily easily makes including including including kaufmann objective objective probabilistic probabilistic probabilistic probabilistic typically smaller reduced account jordan block block block block block block block block block block block block block block significantly york york principle principle direct direct direct window window window window window window idea idea choose architectures directions advantage practical apply apply apply apply strategy strategy side trees trees trees inference inference inference inference inference inference inference inference inference inference interest highly varying compare observations observations observations observations works axis yields yields yields yields yields converge achieve chain chain chain chain observation generalized entire constructed lead extended extended digital deviation deviation deviation wide alternative hybrid hybrid hybrid deterministic occurs generally generally generally setting setting critical critical critical critical critical greater reduce depend depend depend competitive performs performs practice asymptotic asymptotic weak suggest taking taking taking strong hard hard integration largest reduction drawn drawn intelligence intelligence assuming decrease relationship annealing explicit explicit appears monte monte monte monte monte monte monte monte monte monte monte monte monte construct carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo produces ways generating estimating estimating estimating ann vertical distinct recall implement explicitly explicitly explicitly explicitly explicitly infinite infinite easy easy easy belief belief develop applying events springer springer blocks blocks blocks blocks blocks blocks blocks blocks expectation versus yield choosing choosing family independently independently independently independently independently independently independently reconstruction correlated communication estimator estimator estimator estimator estimator estimator estimator variation detailed evaluate restricted fraction partition partition partition reasonable spaces spaces spaces spaces sec event event tracking remains remains calculate calculate assigned advantages avoid expect exploration exploration figures weighting weighting weighting extension extension prove uncertainty domains domains regular regular regular regular determining straightforward middle efficiency importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance importance modification divided divided divided effectively paths paths paths paths paths paths paths paths included presentation successful efficiently efficiently mackay procedures procedures strongly prob prob heuristic heuristic heuristic heuristic interested dis issue issue issue issue issue gibbs gibbs gibbs sampled sampled minimizes reach attempt approximating explore simpler simpler remain create create create collection investigate investigate varied kalman estimators estimators estimators preliminary graphical graphical graphical graphical graphical graphical graphical hall fewer examine matches tech variational relationships root contours math possibly extremely greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy greedy observe simplest neal neal asymptotically derivation variances guaranteed turns turns tive purposes choices lowest depicted demonstrates demonstrates demonstrates argument improvements reflect double double empirically led conducted conducted simulate dots maintain maintain exhibits extensions expectations unbiased unbiased unbiased unbiased unbiased unbiased unbiased unbiased unbiased jaakkola yielding merging ghahramani feasible feasible assign restrict fix recover recover approximates establish establish climbing climbing climbing climbing climbing climbing fails convenient ments chance occurred tools overcome hope hope reasoning disjoint disjoint disjoint effectiveness intuitively intuitively selects saul ensures ascent ascent ascent demonstration captured counting branching infer thin thin thin surprisingly indicator draw draw draw draw draw draw merge merge merge merge merge ignore ignore avoiding verify verify verify maintaining drop indirect indirect indirect outperform achieving kluwer kluwer benefits formulate rejection rejection rejection preserving restrictions obtains obtains intuition grouped chapman dominated allocated searches inverted inverted proba proba esti mcmc mcmc mcmc elsevier frey computa experi challenge lems lems circumstances moderate moderate preserves unbounded impractical builds blake cornput clarity pictures pictures outperformed drawing dom cast russell tribution proposal proposal proposal proposal proposal proposal proposal ally correctness correctness systematically nontrivial sliding sliding sliding sliding sliding sliding statist fair fair fair comprised dent lar indepen metropolis metropolis metropolis metropolis successor successor successor successor ensuring ensuring capturing recovering cope repetitions repetitions repetitions subtree searched tal direc direc direc direc collision collision collision virtue terminate impor rigorously ascending tant biasing draws draws draws mild encounter devise contiguous provably subsample subsample koller trust allocate ticular condensation chaining forest nique decomposing entails depict depict reductions worthwhile heuristically richardson depended subsequences orderings orderings misses decomposes intro mates merges merges merges investigates successors successors successors successors isard elliptical spiegelhalter predecessors predecessors predecessors predecessors crucially dale dale increas objec exhaustively exhaustively preclude uai cont stdev 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#*learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model neural neural neural input data data data data data data function function function function function function function function function function time time set set set set set set networks networks networks training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number error error error error error results results results results results information problem problem problem models models models models models models models models models models models based space space space space weights linear linear linear linear layer case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise weight functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method method method method method method method method method method method method method method method method method approach approach approach approach large large large large large large large test test test test test analysis class class class class class class matrix shows algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper small small small small small small size size size work work work work work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods points points points field field field classification classification classification classification classification classification classification classification classification classification classification process process process process process process process process process process process trained trained problems problems random random random memory similar representation architecture show show show show section section section section section section section fixed fixed rule vectors vectors general parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average theory theory obtained term term note note experiments experiments experiments experiments dimensional university university university university university university university variables variables variables computation log log log log log log log log log defined found found found target constant table table estimate standard standard terms prediction prediction prediction prediction map map present present present machine machine sets maximum maximum maximum range range press press press press press components components continuous sample abstract applied computational density likelihood references stochastic due ieee positive positive positive important important important adaptive introduction introduction statistical effect variance variance variance search change classifier lower measure prior prior prior prior prior prior chosen bound bound bound bound bound bound bound bound bound bound cases cases cases type represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected markov markov techniques techniques techniques techniques techniques proposed length length length observed errors errors scale scale finite finite resulting classes regression regression regression computed computed computed computed respect respect multi sum called elements factor optimization dimension dimension dimension made natural knowledge obtain negative original true desired cross cross cross cross cross series compute perform determined experimental experimental posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions gain equal approaches mit mit mit mit comparison support support support support support support support support support support support support support support support support support support support support train selection selection selection selection selection selection selection selection proceedings report report institute department loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss implementation technique technique technique technique kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances advances advances advances difficult difficult final final exp exp exp exp bias bias bias considered considered framework framework framework cambridge cambridge hinton hinton additional design limit effects conference efficient efficient classifiers classifiers classifiers classifiers upper upper upper upper upper upper full full approximate approximate approximate approximate statistics free free basic pages pages validation validation validation validation validation validation validation produce criterion criterion entropy entropy finally processes processes processes processes processes processes processes processes evidence evidence evidence evidence evidence evidence evidence simply simply discussion discussion covariance covariance covariance covariance technical technical tested tested tested close close predictions predictions common common common end end end hypothesis easily easily noisy probabilistic typically combination combination functional fully fully jordan programming interesting interesting interesting interesting testing special special mode mode mode mode mode squared squared details call making normalized normalized normalized experts idea minimize minimize minimize minimize choose choose run description predict predict denotes denotes denotes denotes improve correlations ensemble ensemble ensemble typical apply apply introduced introduced machines machines machines machines machines machines machines machines machines machines machines machines machines quadratic quadratic quadratic interest dimensions compare compare approximately works works works solve solve correspond trans diagonal diagonal chain chain locations separation williams williams williams williams scaling scaling wide alternative loop loop loop setting greater reduce interactions performs exponential practice constrained constrained minimizing minimizing user user start min decrease relationship introduce reference suppose relation monte monte monte van van derive derive derive carlo carlo carlo written written ways ways changing averaging easy easy easy scales interaction gaussians applying predictive predictive predictive predictive expectation select john choosing choosing family focus review depending depending stages estimator estimator interpretation solved solved solved detailed evaluated evaluated evaluated evaluate restricted fraction approximations approximations approximated approximated approximated approximated margin completely discrimination sign reasonable smoothing smoothing expansion expansion expansion expansion spaces normalization add calculate foundation norm david david david existing figures kernels kernels kernels kernels kernels kernels kernels thesis thesis vapnik extension automatic automatic automatic automatic maximize maximize partially discussions successfully successfully simplicity columns straightforward straightforward modification svm svm svm svm svm latent latent efficiently efficiently efficiently comparing essentially composed refer quickly kind allowing dis issue issue running follow criteria gibbs nips nips nips nips minimizes acknowledgments deal situations situations bars bars employed powerful wiley transformed poor overfitting essential relations relations detail integral integral divergence divergence dual dual graphical discriminant discriminant discriminant dataset helpful fashion ideas rest project investigated applicable applicable variational variational variational variational variational variational variational variational variational variational variational variational variational variational analytically analytically analytically analytically analytically possibility comparable proper complicated scores attributes hill coarse gradients gradients gradients editor adapt adapt adapt spline spline spline equally logistic taylor baseline detected submitted phd neal mentioned piecewise smoothness track analyzed waveform waveform waveform adapted briefly tractable tractable lin closer easier widely day division choices bishop optimize optimize toronto definite annual nsf outer conjugate integrating applies relevance relevance consistency amounts generic parameterized peter peter leave leave effort haussler polynomials http http http aim maximizes hyperparameters hyperparameters hyperparameters hyperparameters datasets datasets plan logp logp logp germany chose chose chose sophisticated sophisticated expectations expectations jaakkola jaakkola progress differentiable differentiable differentiable lot lot newton accomplished www tation restrict driving nonzero generality kullback replacing replacing replacing determination determination keeping mark harmony methodology excellent connect sion james equals regarded regard regard laplace laplace laplace laplace laplace laplace laplace laplace laplace laplace laplace mlps indicator cancer reader master exploiting fold insensitive insensitive ics uci uci posteriori ence svms pointing misclassification misclassification leibler kluwer maximized ber randomized failed discriminative quasi wahba wahba opper opper covariances covariances covariances flat descriptions edinburgh edinburgh edinburgh var var tight continuity iff trends community diag pami geoffrey num relate picked retain guided pos termed monitoring sollich sollich refinement funded siam grateful placing placing applicability bring tin supporting challenge tau handled chris chris nonnegative consuming january generarive generarive generarive generarive justified christopher christopher christopher nested families families jointly hilbert hilbert breast suffers barber barber conceptual clarity broadly dropped dropped appealing visit tribution rasmussen normalize attained meth grids html repository fastest losses ods semiparametric sian sian wisconsin wisconsin binomial gaus gaus sweep sparseness facts minimizer minimizer minimizer problematic inappropriate costly datapoints ard infeasible prime topics tighter miss quadrature quadrature regional tics statis web thumb forrest clarify clarify manfred tommi tommi roots winther winther reproducing reproducing opens opens camp camp tony discard render chine attack attack tly diabetes tlx gps integrand rli sit pointwise karlsruhe confer pima pima pima regres nicely comment optimizer optimizer optimizer radford eigenfunction tual plug danger discriminants discriminants polyno carl observational scholarship vladimir sacrifice archive creases meila agreed ole cbms mial argmaxp argmaxp oid unnormalized unnormalized grace grace logit improper improper delve delve delve cult hyperprior hyperprior discrimina mlearn indian milllet dai dai rive sibility plugging utoronto expec kwok kwok informatics differentiability diffi imizes pressing marina 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#*network learning learning learning learning learning learning learning learning learning learning learning input input input input input input input input input data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure time time time time time set set set set set set set set set set networks training training training training training training training training training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number number number system error error error error error error error error error error error error error error error error error error error error error results results results results results results results information models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based space space space space space space space weights weights weights weights weights weights linear linear linear linear case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order order systems values values values values probability probability probability noise noise noise noise noise noise noise noise noise noise weight weight functions functions functions functions functions functions functions functions functions functions unit distribution distribution distribution distribution distribution distribution distribution method approach approach pattern point single single processing control large large large test test test test test test test test test test test test test test test test test test patterns patterns class class class matrix optimal optimal form form form form form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small small small small small small size size size size size size size size size size feature feature net work work methods methods methods methods methods methods fig fig fig fig fig fig fig fig step step step points features features features classification classification classification classification classification classification process current current problems problems problems problems random random random random random high memory similar similar similar similar similar show show show show show equation section section section section line line vectors general general generalization generalization generalization generalization generalization parameter parameter real real approximation approximation approximation approximation approximation approximation approximation average average average obtained term term term term note note note note note note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional dimensional university computation computation solution solution research research log log log log defined found found found sequence sequence table computer prediction prediction prediction prediction prediction prediction prediction left left left presented present low machine machine machine sets sets sets basis sample sample abstract find find find find computational properties references due due positive positive procedure procedure procedure procedure decision context introduction hand hand hand estimation behavior statistical statistical statistical effect effect generated generated variance variance search search search search search search search search tion difference difference complexity assume classifier classifier classifier classifier classifier classifier classifier classifier chosen part previous previous bound bound required good binary conditions equations make fact fact fact proposed proposed errors scale finite resulting resulting resulting resulting ing tasks regression respect performed called called elements factor dimension dimension dimension dimension made natural natural natural natural negative original compared compared compared application desired cross define compute compute rates rates experimental experimental goal discrete comparison comparison support support support support support support train train source proceedings report report loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss loss version version version version version technique kernel kernel kernel kernel kernel kernel advances final exp exp exp exp exp exp exp exp exp exp exp exp exp exp computing computing domain experiment experiment view view view estimates estimates estimates limit conference determine efficient classifiers classifiers classifiers classifiers classifiers full full full basic basic increase validation give give coding weighted conditional developed developed product product product finally finally nature simply simply simply normal technical increases describe describe describe describe describe describe describe group denote denote denote denote denote tested transformation fast close close assumption predictions predictions predictions predictions finding amount common effective theoretical require require journal journal hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis hypothesis instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance instance degree fit fit objective objective typically typically typically typically typically typically typically pairs smaller smaller block block block block block significantly increasing empirical empirical details details call call call call iterations iterations iterations iterations iterations iterations iterations iterations max pre pre making early magnitude magnitude polynomial idea idea attention combined minimize choose run description improved discussed discussed pair ensemble practical practical machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines machines side quadratic quadratic quadratic quadratic quadratic quadratic quadratic sense inference recently recently highly compare compare works works axis solve yields differential achieve diagonal generalized generalized generalized storage sensitive sensitive studied extended matrices matrices predicted alternative alternative column setting demonstrate demonstrate runs half strength place minimal reduce valued valued differences numerical numerical numerical numerical exponential exponential exponential exponential exponential practice asymptotic weak weak weak weak weak weak weak weak weak weak weak weak weak weak weak propose strong strong presence reduction regularization regularization labeled exist derivatives derivatives derivatives groups groups base base base base base base base base base base base base base base base derive construct construct solving plot plot label label label label label label label label label confidence confidence confidence confidence confidence confidence confidence confidence confidence implement implement implement sensitivity sensitivity easy slightly adding springer springer implies implies blocks blocks blocks expectation boolean john yield family independently focus viewed learner learner learner learner learner learner evaluated evaluate evaluate updated labels labels fraction soft similarly partition sign sign partial partial smoothing additive additive additive additive additive convex roughly purpose add iterative iterative penalty penalty calculate calculate assigned norm norm norm norm norm norm norm norm building building building includes includes kernels kernels kernels kernels kernels kernels kernels instances instances instances instances instances instances instances instances instances instances instances instances instances instances instances sciences vapnik vapnik vapnik vapnik vapnik extension extension candidate partially middle middle middle aspects modification included svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm build build build build schemes comparing plots plots summary verlag graphs graphs repeated induced stopping sin running built built built notation michael dot dot absence computes hypotheses hypotheses hypotheses predictor predictor overfitting overfitting overfitting access collection collection requirements exhibit association limitations dataset dataset fashion ideas ideas ideas tech boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting boosting analytically combine working comparable comparable proved proved statistically fundamental notion necessarily automata friedman friedman friedman friedman logistic logistic logistic art ith ith store switching generates simplest arbitrarily motivated finds attempts defines defines synthetic synthetic synthetic synthetic mentioned great theoretic separable separable growing improves adaboost adaboost adaboost adaboost majority answer expensive worse inside sys constructing constructing constructing constructing division ran ran arise circle depicted annual radius geometric geometric questions apparent apparent embedded experimentally lack share employ employ continuously frequently incorrect maintain polynomials calculating switch limiting popular serve singer singer singer singer singer singer datasets datasets datasets conclude conclude calls cumulative irrelevant pac pac indices redundant redundant assign formally summing extending adds adds numerically interpret bands belong eqn eqn eqn eqn eqn eqn eqn eqn eqn repeat bartlett schapire schapire schapire schapire schapire predictors guarantees belongs initialize eng omitted omitted augmented clean late kearns belonging passing storing agree correcting fold dividing robert robert robert assigns divide speaking consecutive uci uci uci uci uci uci uci uci uci uci uci uci uci uci uci uci maintaining svms svms svms svms svms svms svms svms usage shorter shorter ber randomized incrementally tibshirani tibshirani tibshirani tibshirani adopt convenience medium exception exception freund freund freund german forcing valiant manipulation penalized penalized penalized penalized penalized penalized penalized penalized iff concentrated hastie hastie hastie hastie num compensate realizable convert denoting learnability learnability learnability picked scope noting meta worth maintains maintains round round round round round round september signs stops learners learners uniqueness algorithmic consuming january august impractical attributed builds builds virtually formulae cally practically practically vote splice att att att att baxter repository repository weather suffice chunking chunking chunking chunking chunking chunking chunking iterating doom fixing fixing violated cortes cortes terminology degrades stems boosted predefined preventing 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#*learning neural neural neural input input data data data data data data data data data data data data function function function figure figure figure figure figure figure time set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number error error error results results results results results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem problem problem problem problem problem models performance performance based based based based based case case shown shown shown shown values values values values probability probability probability probability distribution distribution distribution method method method method method method method method approach approach approach approach approach point point point single single single single single single processing processing processing processing rate rate analysis class class class class matrix optimal optimal optimal optimal optimal optimal simple paper paper size work step step step points points features features features classification classification classification classification process current current current current problems random high high high similar similar similar similar representation representation section fixed line general theory theory theory theory obtained obtained obtained obtained university variables computation solution research log log log defined defined found sequence computer science prediction prediction prediction left left map map map map present present phase phase low low sets components components components components components components abstract find find find find find computational computational computational computational references component component component component component stochastic stochastic due due due due ieee ieee positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important context introduction hand hand generated cost tion complexity variable variable variable variable variable variable variable measure measure measure measure prior prior prior higher part center required good tree expected equations equations equations equations equations equations markov fact length finite finite resulting resulting resulting ing respect eq eq called called called times times times elements factor optimization optimization natural natural original original original original original specific true compared compared application application desired define define define perform determined determined related connected distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions equal comparison comparison update update proceedings institute institute words words words words loss loss loss version version code advances advances joint joint final exp exp sequences considered considered framework directly directly directly curve curve curve curve curve curve curve curve curve additional solutions solutions solutions curves curves curves curves limit limit limit limit limit limit limit top top top efficient full significant pages increase increase con condition coding conditional conditional clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering bounds entropy entropy entropy depends constraint constraint constraint discussion discussion discussion normal denote denote denote denote close close inverse complete predictions shape role main end end cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster easily objective probabilistic pairs pairs pairs combination functional functional fully jordan character york special consistent consistent consistent consistent empirical empirical principle principle principle language iterations max pre pre direct direct normalized normalized normalized normalized normalized bottom bottom bottom magnitude magnitude magnitude minimize choose exact advantage pair pair pair element similarity apply apply introduced introduced subject side side hierarchical subset subset subset recently recently recently relevant relevant relevant compare smooth yields yields correspond converge achieve symmetric bounded organization occur suggests predicted alternative locally loop deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters demonstrate demonstrate starting starting starting critical critical minimal measures bayes bayes constrained temperature temperature propose strong hard hard hard hard hard hard hard hard hard hard hard hard hard hard hard reduction reduction reduction reduction reduction demonstrated start plane plane plane plane plane plane plane plane plane decrease decrease decrease decrease decrease decrease relationship relationship introduce characters groups groups groups groups groups minima annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing annealing question denoted denoted relation relation digit construct generating plot transitions changing dimensionality easy easy text text unique consisting consisting mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual minimization minimization quality john focus formation interpretation interpretation solved evaluated evaluate evaluate evaluate evaluate evaluate operations operations fraction lee soft soft soft soft soft soft soft soft similarly partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition partition diagram earlier normalization remains valid initially calculate advantages transactions formulation strings strings strings strings strings strings strings determines plotted maximize specifically compression compression compression compression efficiency efficiency efficiency identify identify identify fine reached refer compact contained contained contained superior categories built vary simplified nips nips minimizes minimizes maximization extract decreasing decreasing presents explore unlike parametric wiley replaced association divergence divergence divergence divergence divergence dotted dataset dataset dataset dataset dataset dataset dataset dataset dataset dataset reducing ideas variational variational variational referred proper proved hierarchy hierarchy cover analogous smallest possibly necessarily subsets subsets subsets quantities greedy greedy greedy greedy greedy established percentage brown inequality theoretic theoretic theoretic costs trivial trivial cascade starts starts starts lin tive strictly mation mation members members english annual fuzzy collected empirically empirically relevance relevance relevance pseudo amounts car orders orders orders orders introducing rep maintain datasets substantial logp proposition semantic yielding merging merging merging merging distortion globally initialization lagrange lagrange tation member member recover recover nat partitions partitions partitions partitions plays multiplier multiplier analogy check keeping keeping mark tishby tishby tishby tishby tishby tishby tishby tishby removing disjoint ylx ylx ylx ylx corpus corpus heuristics inferior infor infor meaningful excellent recovered corollary sion sion bialek guarantees lang belongs thomas israel surprisingly suggesting merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge merge eqs eqs eqs sons splits splits splits splits reverse reverse reverse reverse reverse reverse reverse captures verify verify appeared appeared compressed compressed compressed planes suboptimal suboptimal tween obtains seek constitutes forcing clas magnitudes shannon shannon shannon shannon ization disadvantage confirmed categorization represen termed enforce maintains induces indication dichotomies rose unpublished manuscript nec ble stochastically dichotomy dichotomy evenly meeting gram striking emerges normalize cardinality cardinality ultimate concave concave concave inset constraining bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck bottleneck merged merged prescribed talk hip hip stems jerusalem predic pointers topics hebrew ohio couple resentation ver distributional distributional distributional distributional distributional undergoes jensen jensen jensen cooling ily anneal mercer linguistics linguistics concurrent ixi news news news possi lexicon agnostic mccallum notations ditional articles 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#*network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural input data data data data data function function function function function function function function function figure figure figure time set set set set set set set set set set set networks networks networks training training training training training training training training training training training training training training training training training training training training number number number number number number number number number system error error error error results results results results information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem based based space space space space space space space space space space space space space space space space case case case case case case vector vector vector vector order order order shown systems systems values values values values noise noise noise noise noise noise noise noise noise noise functions functions method method method method method method method method approach point point point point point point point processing processing processing large large analysis matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows shows signal paper paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples methods methods methods fig fig fig fig step points points points points points points points points points points points points points points points points points points points points points points points level problems high memory memory memory memory memory memory memory memory memory show section section section fixed fixed fixed fixed line rule vectors general general generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization generalization approximation approximation approximation approximation average states theory theory theory obtained obtained note note experiments dimensional dimensional dimensional dimensional result result result result result result result result variables computation solution research defined defined defined defined defined defined target target initial constant constant constant table standard computer computer computer computer terms terms science science range press press basis basis basis basis sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract find computational computational computational computational computational computational computational computational references component positive positive positive introduction variance variance variance search tion tion complexity complexity complexity complexity complexity complexity complexity complexity complexity assume theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem required required required required required required long proposed proposed proposed proposed proposed proposed proposed proposed errors simulations simulations simulations simulations minimum multi performed performed performed eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq eq called called called called called called called called times elements mapping means means dimension dimension dimension dimension dimension made global global applications em filter original vol application provide provide provide location active active active active active active active active active active active active active active determined determined determined determined determined experimental mit contrast contrast selection selection selection selection selection selection selection morgan proceedings proceedings proceedings report institute institute department version version kernel kernel kernel advances advances exp bias bias bias bias scheme scheme scheme graph cambridge domain domain equivalent experiment view view view design design san conference determine efficient estimated give give give give con condition condition condition condition condition condition condition condition condition criterion criterion criterion criterion criterion criterion criterion criterion criterion lines product product product product product finally finally sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling constraint constraint constraint measured measured covariance covariance covariance technical arbitrary arbitrary denote denote inverse inverse inverse inverse inverse inverse inverse complete complete finding assumed eds eds easily kaufmann objective underlying reduced reduced reduced reduced functional functional functional functional functional unknown technology projection projection projection projection projection projection projection projection projection projection projection york mechanism mechanism mechanism trials international supervised supervised supervised supervised supervised magnitude polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial polynomial minimize minimize denotes denotes property ensemble subset sufficient sufficient calculated calculated definition definition generalized generalized generalized generalized horizontal matrices touretzky column demonstrate conclusion reduce operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator operator depend designed mateo demonstrated solid regularization minimizing relationship reference relation relation derive vertical mathematical multilayer implies implies implies focus focus expressed expressed expressed expressed depending interpretation interpretation lemma lemma evaluated approximations forms completely partial calculation calculation calculation calculation calculation calculation dashed additive spaces reduces reduces reduces reduces intervals intervals purpose valid calculate euclidean classified transactions exploration kernels kernels perceptrons formulation subspace sciences extension discuss discuss holds holds holds holds holds holds holds simplicity reason reason society efficiently schemes schemes schemes schemes mackay mackay identity orthogonal moore moore moore moore sin hold categories providing providing minimizes minimizes ill illustrates satisfies satisfies satisfies satisfies satisfies cowan minimized american transformed replaced dotted incremental int scaled referred workshop induction coefficient coefficient integer integer integer extremely greedy academic averages mentioned publishers derivation unstable analytic analytic analytic analytic tive ran pseudo pseudo axes capability capability capability capability capability capability employ formulated formulated http calculating calculating summarized mod display proposition www optimality japan japan conditioned null suppression consideration satisfying satisfying satisfying intelligent obtaining obtaining obtaining imply effectiveness effectiveness passive candidates bases bases eqs designing adopted achieving achieving uniquely adopt theorems ical decomposed demon stands stands stands pub pub cohn cohn cohn ftp ftp ftp ftp gener degraded spanned sam compu removes rewritten neumann neumann hilbert hilbert hilbert hilbert lated orthonormal orthonormal adjoint tokyo tokyo optics spie era gathered gathered gathered actively decompose sition alization clarify sults ana suppresses reproducing reproducing reproducing reproducing reproducing tational ror strated tab penrose penrose penrose penrose trigonometric trigonometric trigonometric trigonometric trigonometric trigonometric trigonometric trigonometric trigonometric avail pling reformulated ric effec calcu nll trast ieice fedorov fedorov clarified ull china axa mathemat 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#*network learning model model model model model model model neural neural neural neural neural input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function set set set set set set set set set set set set set set set set set set set set set set set networks networks networks training training training training training training training algorithm algorithm algorithm algorithm output output output number number number number error error error error error error error error error error error results results results results results results results results results results results units information problem problem problem models models models models models hidden performance performance performance performance performance performance performance performance based linear case case case case case case case case case case vector vector vector vector systems probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions functions functions unit unit distribution distribution distribution distribution distribution method method approach approach approach approach approach approach approach approach approach approach processing large large test test test test class matrix matrix matrix matrix matrix matrix inputs inputs inputs inputs inputs inputs inputs form signal gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper examples examples size size size size size work methods methods methods methods methods methods methods methods methods points classification classification process process process process level level level level level level level level level level level level level problems problems problems random show parameter average average average average average average gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained obtained note note note note note note note note result result university university university computation solution solution independent independent log log log log log log log defined defined defined defined found found initial initial initial table table table table table table estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard computer computer terms science science science prediction presented presented map map map map map map map map map map map map map map phase low low low low low low sets sets sets sets sets sets sets sets sets sets maximum maximum maximum press outputs outputs outputs sample sample sample sample sample sample sample sample sample abstract applied applied find density likelihood likelihood likelihood references component positive important important adaptive context introduction circuit estimation behavior statistical statistical statistical statistical generated generated generated variance variance variance variance cost cost tion assume measure prior prior prior prior prior chosen chosen chosen theorem theorem theorem theorem required required good good good good conditions conditions bayesian bayesian bayesian bayesian make make techniques proposed proposed observed observed scale simulation simulation simulation simulation simulation regression regression regression regression regression regression regression computed computed computed respect respect respect times means optimization optimization optimization applications knowledge negative negative negative negative relative samples samples true true true compared compared cross cross cross define define define compute compute perform perform experimental approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches mit comparison comparison dependent dependent selection selection selection institute implementation version version advances represents exp scheme considered computing estimates limit choice statistics estimated estimated estimated basic basic validation validation give condition randomly conditional developed robot robot robot robot robot criterion criterion processes processes processes processes processes processes processes processes processes processes constraint discussion discussion covariance covariance covariance covariance covariance covariance covariance covariance increases increases increases increases increases denote denote tested close predictions predictions assumed assumed role journal journal journal square square square ability objective objective objective account unknown unknown ratio ratio york special uniform operation squared squared representing iterations pre making normalized normalized normalized idea run run run denotes denotes denotes denotes denotes improve improve takes element element element element element reported reported introduced strategy recently sufficient observations observations converge diagonal diagonal background evaluation modified observation gate williams williams williams williams williams arm arm arm arm arm suggests deviation deviation deviation derivative matrices hybrid touretzky column column column column column setting starting row competitive competitive measures measures clear practice propose propose propose propose assuming minimizing averaged introduce question denoted denoted denoted denoted monte monte derive carlo carlo written estimating ann dept dept modeled infinite infinite electrical adding predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive minimization springer quality quality expectation choosing choosing choosing choosing choosing choosing national independently interpretation detailed evaluated evaluate showed forms forms approximated sizes sizes sizes similarly similarly partition partition additive classical sufficiently expect existing existing thesis maximize maximize mozer identified society literature efficiently mackay mackay mackay mackay mackay comparing identity ten verlag strongly strongly issue issue simplified minimizes maximization preferred unlike carried carried carried parametric powerful powerful american american poor production investigate investigate association association integral integral ml ml ml ml ml ml ml ml ml ml ml ml tech scaled scaled referred referred maximizing notion man predicting created friedman friedman friedman friedman friedman friedman friedman expressions expressions expressions multivariate multivariate submitted neal neal neal neal neal neal integrate years improves improves handle tive tive separately optimize toronto toronto demonstrates auto conjugate relevance readily leave splines rep ity http http popular hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters sophisticated tolerance irrelevant irrelevant corrupted proofs www restrict restrict ratios optimizing partitions partitions royal plays numerically logarithmic determination removing removing removing methodology methodology motivation inferior meaningful performances performances performances performances performances mance respective entry entry perfor evident hasselmo infer infer insight omitted omitted belonging cam stone stone fly fly fly mechanical appeared logarithm logarithm logarithm tables tables tables uniquely gained distribu picked indexed esti knowing retained retained parametrized parametrized parametrized rewrite rewrite eters rewritten replacement copies argmax argmax termination replicated usefulness impedance assessment rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen rasmussen automation interpretations sian fol brackets gaus shortly ard ard ard ard stat predic predic phy singapore singapore ror tlx alternately gps gps gps rectly reuse reuse avail prefers pii pii pii eli eli mated gpe gpe 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#@Keerthi_S,Sundararajan_S,
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#*network network learning learning model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data function figure figure set set set set set set set set networks networks training training training training training algorithm algorithm number number number number number number number number number number number number number number number system system results results units information information models models hidden linear case order order order order systems values values probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition method method method method method method approach approach approach approach approach approach approach approach pattern pattern single processing processing test test patterns patterns analysis class class class class class class class class class class class class class class class matrix matrix matrix optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form shows algorithms gaussian gaussian gaussian gaussian paper paper paper feature feature feature feature feature feature feature feature net work methods methods methods step step step features features features features classification classification classification classification classification classification classification classification classification classification classification classification classification current problems problems random high similar architecture show fixed fixed line line images general general generalization parameter parameter real real approximation average average obtained term term term term term note experiments experiments experiments experiments experiments experiments experiments experiments dimensional university variables variables computation computation research research target constant table table table terms science low machine sets sets range press components components components basis basis nonlinear nonlinear sample sample sample abstract applied density density density density density likelihood likelihood likelihood likelihood likelihood references component component component stochastic due due ieee ieee mixture mixture introduction estimation statistical statistical generated variance variance search difference difference variable variable variable variable classifier classifier classifier classifier classifier classifier classifier measure measure measure prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen chosen part part type bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov markov markov markov markov markov markov markov make techniques techniques proposed proposed proposed probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities probabilities errors classes classes ing tasks total total regression regression performed performed performed called means means means factor dimension dimension dimension dimension dimension dimension dimension made made em em artificial samples samples samples samples samples samples samples samples samples samples samples true compared desired provide determined determined related posterior posterior posterior posterior posterior posterior posterior posterior constraints distributions distributions approaches approaches mit accuracy accuracy accuracy accuracy accuracy accuracy accuracy accuracy comparison selection selection selection selection selection selection selection selection morgan institute implementation consists kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances exp exp exp exp scheme scheme addition ai framework framework framework cambridge experiment experiment directly additional additional san determine determine determine determine classifiers full full full significant approximate approximate approximate approximate estimated pages increase give weighted randomly randomly conditional conditional conditional conditional conditional conditional conditional types provided finally evidence evidence evidence depends sampling sampling sampling sampling sampling sampling sampling measured discussion covariance covariance normal increases denote inverse inverse predictions rbf rbf rbf rbf rbf common eds eds journal hypothesis kaufmann typically smaller coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients jordan mlp mlp mlp mlp mlp mlp mlp mlp interesting interesting testing ratio ratio ratio ratio ratio ratio ratio ratio ratio york matching matching details details max max supervised magnitude idea combined choose choose denotes discussed improve improve improve advantage typical apply introduced moving hierarchical inference inference inference subset subset subset subset sejnowski recently interest compare compare conventional conventional rl trans trans diagonal diagonal diagonal mixtures evaluation evaluation chain chain chain chain chain chain chain chain chain symmetric observation entire parts expression lead occur move move move move move move hybrid hybrid hybrid hybrid hybrid hybrid hybrid hybrid width width deterministic deterministic editors peak practice propose propose drawn drawn proportional intelligence labeled labeled labeled labeled radial radial assuming min decrease targets introduce introduce areas monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo index index index index label label changing implement missing adding springer select select family densities densities densities densities densities restricted labels centered updates updates updates updates updates updates updates updates updates updates classical spaces roughly add add calculate kernels kernels kernels kernels kernels kernels kernels determines automatic priors priors priors priors priors priors priors priors priors discussions successfully gamma gamma closely importance importance maximal divided latent latent latent literature efficiently efficiently summary refer soc interested symmetry contribution criteria gibbs gibbs gibbs gibbs gibbs gibbs gibbs gibbs relaxation paradigm moves moves moves moves moves moves moves overlapping mixing satisfies tesauro cowan explore carried exponentially integral hall hall rest project proper coefficient equally subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets subsets der switching multivariate consist neal variances variances explanation london london sections probable probable probable acknowledgement separately medical incomplete conjugate summation people relevance relevance relevance relevance relevance relevance relevance relevance tional quantitative peter peter remove http http switch poisson measuring aim occurrence geman geman datasets datasets datasets green green semi semi boston comments conditioning conditioning conditioning irrelevant contribute benefit www www resources ordering null count grows royal smith allocation allocation allocation allocation allocation allocation accepted determination determination determination hyper los removing removing unlabeled unlabeled unlabeled unlabeled unlabeled unlabeled observing settings carry prentice corre von counting dif treatment francisco express express express infer infer infer reveals matter informative belonging draw reverse jump jump jump jump jump jump jump jump jump jump jump jump jump jump tures switches counts counts treat treat ics speaking uci uci posteriori posteriori posteriori ence truncated specification accept formulate convenience generalizations covariances multinomial affects rain beta assess visited diag chapman allocated denoting denoting denoting dirichlet dirichlet dirichlet anal funded exchange exchange exchange fea mcmc mcmc mcmc mcmc tunneling removes opti sponding restoration accordance ferent cliffs reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible reversible compete compete condi proposal proposal proposal proposal proposal proposal proposal proposes proposes englewood core explanations html repository repository alto multimodal semiparametric binomial irvine reviewed metropolis mach talk palo phillips unobserved ard ard ard ard ard ard ard ard ard ard stat expresses lid avg avg mal acceptance visits holmes intel freitas ministry counters notational hyperparameter xlo discard ripley ripley resort confer pima pima pima pima pima penalize death death richardson richardson neur transport und anonymous sampler sampler sampler sampler sampler sampler sampler sampler sampler sampler sampler subsection subsection austria public public austrian austrian federal vienna spiegelhalter midpoint biometrika cancels stats proposing proposing proposing lll subsections gilks ionosphere ionosphere ionosphere ionosphere ionosphere ionosphere altos hyperprior mlearn communities wine wine wine wine wine searchers telling mlrepository reviewers exchanges gratitude burn schottengasse 
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#*learning learning model model model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data function function function function function time time time time time time time time set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set set training training training training training training training training training training training training algorithm number number number number number number number number number system error results results results results information information information information problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models performance performance performance performance performance performance based space space space space space space space space space space case case case vector vector vector vector vector vector vector vector vector vector vector vector order order order order order order order order order order shown shown shown systems systems systems systems values values values values values probability probability parameters parameters parameters parameters parameters parameters parameters functions unit unit unit distribution distribution distribution distribution approach approach point point point point point processing large large large large large large rate test test test test test test test test test test test test analysis class class class class signal simple simple paper small small small small size size size size work work work work task task task step step step step points points points points points points points points trained trained trained structure structure structure structure structure structure structure structure structure problems problems memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory memory similar similar similar similar similar similar similar representation representation representation show show show fixed fixed rule vectors vectors vectors vectors images parameter parameter parameter parameter parameter parameter average average states theory experiments experiments experiments experiments dimensional dimensional threshold research research log log log log log log log log defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics table table table table table estimate estimate distance distance distance distance science science science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction direction direction presented presented map map map map present present phase low low machine machine machine sets sets sets sets sets sets sets maximum maximum range press learn position position components components basis basis continuous continuous sample sample abstract likelihood likelihood likelihood references stochastic stochastic stochastic due due ieee ieee adaptive context context context context context context context context introduction introduction complex complex complex hand behavior statistical statistical statistical effect generated generated generated search tion change change difference variable variable variable variable variable variable variable variable spatial spatial spatial spatial spatial lower lower representations representations representations representations representations representations representations part center cases cases binary binary long long long long represent represent markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov fact length length length length length length length length length length length length length length length length length length length length length length length correct correct correct correct probabilities probabilities probabilities finite finite finite finite finite finite finite finite finite finite resulting classes ing computed computed respect sum performed performed eq eq eq regions mapping means factor potential dimension natural natural applications applications applications study knowledge negative negative negative negative negative artificial artificial represented series series series series series series series series series series series define define define define perform perform perform determined distributions distributions equal power power power steps contrast train source source source modeling modeling modeling selection selection selection morgan institute institute institute words consists consists advances difficult difficult sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences ai considered considered considered computing experiment experiment experiment experiment conference upper upper full requires free free basic increase increase validation validation validation produce conditional conditional finally selected achieved achieved achieved achieved achieved measured normal normal normal increases increases increases tested tested transformation limited limited close close close close close assumption assumption corresponds finding finding amount amount short common common common common common common common common generate supported supported role journal end ability ability kaufmann probabilistic smaller needed needed account dynamical fully fully fully block block block 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symbolic complicated coefficient man automata illustrate created changed subsets der portion portion mapped mapped epoch motivated years mentioned percentage percentage great developing growing explanation briefly tool tool worse handle tive shared closer closer closer widely organized organized strictly day day day constructing constructing constructing constructing mathematics potentially universal universal english cybernetics requiring requiring percent percent percent peter share share share share formulated operate mod mod resource resource singer singer singer singer singer chose returns returns returns yielding extreme extreme sharing lot equivalence equivalence equivalence purely partitions repre jones jones fails allocation allocation chains overcome overcome familiar familiar tishby tishby tishby tishby tishby intuitive alphabet alphabet alphabet alphabet alphabet substituting composition financial financial contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts contexts codebook codebook codebook codebook codebook codebook topological topological topological forecasting lengths lengths searching captured reproduce bases bases enable treatment specialized specialized april mem reveals contraction vertex theoretically grammatical extends hypercube hypercube hypercube hypercube hypercube partitioned likelihoods likelihoods likelihoods influences empty speaking fitted unchanged suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix suffix appeared logarithm constitute annals outperform outperform ties markovian smoothly freund tendency letting associate guess continuity quantized unseen deep deep deep deep deep management mathematically dominated allocated careful paired books scope exceed academy increasingly increasingly increasingly increasingly option drawback indexed book book book mimic exhibited els els things exploited strict shallow shallow appearing appearing appearing consuming fractal fractal fractal fractal fractal fractal sake transforming curse virtually suffices industrial industrial inclusion cylinder ron ron ron ron ron rissanen lying ory totally daily daily daily daily daily sliding spirit spirit spirit fair enter feb prominent problematic huge spanning dow dow entropies spent quantified deeper forgetting mention rigorously prices tiny ago genesis genesis genesis genesis exceeded ministry historical beat blank volatility volatility volatility volatility volatility volatility volatility volatility volatility volatility volatility volatility volatility weeks fund economics formulating succeed havior comparatively subsequence subsequence theme embodies diction transport subsequences reformulated abrupt austria austrian austrian austrian austrian summarizing federal vienna lan interac creases eling aea quantizing quantizing quantizing quantizing extremal extremal quantile forecasts georg amnesia amnesia regulating troublesome troublesome troublesome senting transac guesses cvs cvs cvs lev suffixes suffixes sfb excel unfor schottengasse outper admitting engle tunately bought 
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#*learning learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural input input input input input data data data data data data data data data data data data data function function function function function function function function function function function function figure figure figure figure figure time set set set set set set set set set set set set networks networks networks networks networks training training training training training training training training training training training training training training algorithm output number number number number number error error error error error error error state state state results results results results results results results results models hidden performance performance based based based based based based space space space space space weights weights weights weights weights weights weights weights weights weights weights weights linear linear linear linear linear case case case case case case case case case case case case case case vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector vector order order shown shown shown shown values values values values values values values values probability probability parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise weight weight functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution method method method approach approach approach approach approach approach approach pattern point single large test test test test test analysis analysis analysis class class class class class class class class class class class matrix matrix inputs form form form form form form gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small size size feature feature feature feature feature feature task methods methods methods methods methods classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification process level current memory memory representation section section section section section fixed fixed rule vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors parameter parameter parameter parameter real real real approximation approximation approximation approximation approximation approximation approximation theory theory theory obtained obtained obtained term note note note note note result result variables computation computation computation computation research log defined defined defined defined target target table table estimate estimate estimate estimate estimate standard standard standard standard standard terms terms distance prediction prediction prediction prediction prediction left left left presented presented presented phase machine machine machine machine machine machine machine machine machine machine machine sets maximum maximum maximum maximum learn basis basis basis outputs outputs abstract applied applied find find find find convergence convergence properties properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due ieee ieee procedure procedure procedure procedure procedure decision decision decision decision decision decision mixture mixture introduction introduction estimation estimation estimation estimation statistical statistical generated generated variance variance variance tion tion tion complexity complexity complexity complexity assume classifier classifier classifier classifier measure measure prior prior prior type type required required multiple multiple multiple good binary represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations make make fact techniques region region probabilities probabilities observed errors errors errors errors errors scale resulting classes classes tasks regression regression regression regression regression regression regression regression regression regression regression regression regression regression regression respect respect performed made em obtain obtain negative vol samples true compared compared compared application desired cross cross define define compute location determined related posterior posterior posterior posterior posterior posterior posterior posterior constraints distributions accuracy accuracy accuracy comparison larger larger contrast update update support support support support support support support support support support support support support support train train dependent selection proceedings implementation technique technique code individual kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel exp exp exp ai ai ai ai considered framework framework framework cambridge equivalent equivalent equivalent additional design limit efficient efficient classifiers classifiers classifiers requires requires choice significant approximate free free world estimated estimated estimated estimated estimated pages pages increase validation validation give give give condition conditional developed lines processes selected evidence evidence achieved discussion discussion covariance arbitrary limited close predictions predictions predictions predictions finding rbf effective adaptation degree makes makes objective probabilistic probabilistic typically pairs smaller reduced functional functional york york york edge consistent consistent uniform mode mode principle leads principal principal direct making supervised supervised choose added added added predict improved advantage typical typical reported practical apply introduced identical identical identical side inference subset recently dimensions varying varying previously trans sparse sparse sparse sparse observation williams storage increased lead lead extended deviation alternative occurs boundary boundary boundary boundary generally generally generally generally demonstrate place minimal reduce sigmoid accurate bayes faster practice practice practice hard presence largest reduction drawn demonstrated solid intelligence assuming exist averaged averaged targets targets targets introduce introduce introduce introduce manner denoted acknowledgements digit digit digit written sequential confidence pruning multilayer simultaneously gaussians applying springer springer implies implies versus competition john squares overlap detailed updated labels margin margin margin margin key key dashed dashed combining fitting fitting iterative iterative penalty penalty closed closed interpolation initially transactions transactions avoid handwritten handwritten kernels kernels kernels kernels kernels kernels kernels formulation vapnik plotted automatic uncertainty uncertainty priors priors discussions major capable uniformly suitable effectively svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm successful mackay mackay mackay mackay mackay essentially capture repeated induced prob prob interpreted split superior superior lie lie sin follow criteria satisfy sampled sampled michael absence absence automatically illustrates illustrates approximating modelling modelling extend bars employed unlike wiley poor overfitting essential exhibit exhibit limitations hessian hessian hessian mass dataset dataset dataset dataset dataset dataset dataset dataset dataset helpful fewer fewer fewer fewer applicable ideal analytically combine authors comparable comparable comparable comparable encode naturally adapt generalisation generalisation generalisation generalisation generalisation spline illustrate illustrate illustrate quantities friedman friedman friedman friedman noted noted noted logistic logistic art art art attempts synthetic synthetic synthetic synthetic neal established integrate integrate preference ment developing formula costs costs crucial defining explanation benchmark benchmark london considerable satisfied formalism ran bishop commonly probable probable definite author qualitative integrating requiring considerably considerably relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance relevance slower treated requirement popular popular hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters hyperparameters achieves marginal marginal marginal marginal marginal datasets datasets datasets datasets datasets asymmetric asymmetric boston boston trade trade benefit benefit writing sv appearance grows platt wrong determination obtaining exploit methodology methodology responsible guide motivation overlaps excellent governed iteratively iteratively pruned dependency infinity treatment modelled membership membership membership membership indicator repeatedly splits implicitly subsequently fold avoiding insensitive smola severe outlined treat dramatically dramatically dramatically street svms svms misclassification misclassification adopt adopt ideally lit spaced clas burges principled principled unseen formance formance diag disadvantage inverted differentiation ultimately importantly apparently suffer dramatic computa infinitely challenge housing housing chris remarkable opti expense handling smoother house suffers suffers barber optimisation outperformed determinant formulae incorporation sharply peaked peaked svr svr svr lying functionally meth comprising occam concave ods tube implying implying edition counterpart sparseness tained artificially convey explaining benchmarks benchmarks microsoft microsoft tipping tipping tipping tipping ard ard disadvantages disadvantages disadvantages invert graphically minimise weakness icann sparsity sparsity sparsity berger strongest maximising maximising notably paid paid desire motivates mercer mercer mercer prototypical george wishes maximise hyperparameter hyperparameter hyperparameter concluding generalised generalised diabetes diabetes tlx attain saving entails schslkopf schslkopf bernhard pima pima pima lesser heuristically optimise nuisance iee atlanta notable optimising optimising negated mfiller mika 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#*learning model model data data data data function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set set algorithm algorithm number number number number number number number number number number number error error error error error error problem problem problem problem problem problem problem models models models based based based space space space space space space space linear case case case case case case case case vector vector vector vector vector shown values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method approach approach approach image processing large large rate rate rate matrix form form form form form form form shows shows shows shows shows shows shows shows shows shows shows shows shows gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian feature methods methods methods methods methods methods methods methods step points points classification structure problems problems problems problems problems problems problems problems random equation equation equation equation equation equation equation equation equation equation vectors vectors vectors vectors general general speech speech speech parameter parameter parameter parameter parameter parameter approximation approximation approximation theory note note experiments experiments experiments dimensional dimensional dimensional dimensional dimensional dimensional solution solution solution solution solution solution solution solution solution solution solution solution independent defined defined defined defined defined defined defined estimate estimate estimate estimate estimate estimate estimate estimate estimate standard terms terms terms terms terms terms terms terms terms sets maximum nonlinear continuous sample abstract density density density density density density density density density density density density density density density density density density density density density density density density properties likelihood references stochastic stochastic ieee positive positive positive procedure important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation statistical tion lower bound bound bound cases cases cases good conditions conditions conditions equations techniques proposed proposed proposed simulations minimum regression called elements elements elements optimization made applications em em obtain true true compared define define related constraints constraints distributions equal mit mit accuracy support support support support support support support modeling institute technique technique technique technique kernel kernel kernel kernel kernel kernel kernel exp exp ai ai ai ai ai ai ai ai ai cambridge equivalent equivalent solutions estimates estimates upper upper choice choice approximate statistics free free condition condition developed lines product product product actual selected sampling constraint constraint covariance covariance increases arbitrary fast fast inverse corresponds ability fit fit fit fit functional functional functional functional functional unknown unknown technology consistent trials trials trials trials trials trials empirical empirical mode call max max idea idea minimize robust practical apply introduced introduced subject subject dimensions dimensions dimensions dimensions dimensions dimensions dimensions observations observations observations observations observations solve solve smooth speaker speaker achieve trans diagonal diagonal mixtures mixtures mixtures constructed horizontal matrices width width deterministic generally setting operator operator operator accurate accurate numerical performs asymptotic drawn regularization regularization regularization regularization regularization minimizing minimizing exist exist min min min relationship introduce identification acoustic solving solving solving solving solving solving estimating estimating estimating estimating estimating plot ann involves text gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians springer select letters choosing estimator solved solved densities densities densities densities densities densities densities evaluate forms approximated converges converges converges expansion spaces sufficiently sufficiently norm norm norm box box kernels kernels kernels eigenvalues vapnik vapnik vapnik vapnik vapnik vapnik vapnik black holds regular closely svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm svm plots summary verlag kind prob dis eigenvalue ill ill ill ill ill ill satisfies satisfies satisfies parametric parametric parametric parametric wiley integral ml ml ml variational analytically func examined smallest math math math multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate multivariate defines synthetic synthetic massachusetts asymptotically residual advanced inequality publishers convolution smoothness definite definite res researchers red leave posed posed posed posed posed posed posed formulated berlin popular semi trade college notes proportion sv nonzero royal satisfying satisfying replacing nonparametric den belongs belonging insensitive empty metrics approx audio kluwer bank obtains laplacian parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen parzen labs ization outcomes outcomes outcomes outcomes outcomes outcomes memo admissible admissible admissible thousands article rose dim dim converging hilbert hilbert hundreds cornput incorrectly incorrectly tribution sian accounting restrictive gaus twelve twelve twelve twelve aip corn eigenfunctions phillips phillips zone predefined 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#@Mukherjee_S,Vapnik_V,
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#*network network network network network network network network network learning learning learning learning learning learning model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input data data data data data data data data data data data function function function function function function function function function figure figure figure time time time time time time time time time set networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state results results results information information information problem problem problem problem problem models models models models hidden hidden performance performance performance performance performance performance performance based based based based space space space space space weights weights weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear layer case case case case vector vector vector vector order order order order order order order order order order order order shown shown systems systems systems systems systems systems systems values values parameters parameters parameters parameters noise noise noise noise noise noise noise noise weight weight weight weight weight weight weight weight weight weight weight weight weight weight functions distribution method method method method approach approach approach approach approach approach approach approach approach point point single single processing processing processing control control test test matrix matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs form form form form form shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper paper work methods methods methods methods methods methods methods methods methods methods step step step step step step step step step step step step points points points points classification process process process process process process level level current current current current current current current trained trained problems problems random random random random similar representation representation representation show show equation equation equation section section section line vectors vectors general general general general approximation approximation states states states states gradient gradient term note note note note note note note note note experiments experiments experiments experiments dimensional university variables research found found dynamics dynamics initial table estimate estimate estimate estimate estimate estimate estimate estimate standard standard standard standard standard standard computer terms terms terms terms science prediction prediction prediction prediction prediction prediction left presented map present phase phase activation machine press basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear sample abstract applied applied computational computational convergence density references procedure adaptive adaptive propagation propagation propagation context context introduction estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation estimation dynamic dynamic dynamic dynamic dynamic dynamic dynamic generated variance variance variance variance tion tion tion complexity complexity complexity variable variable assume assume assume lower lower prior prior prior part part part center required expected equations equations equations equations equations proposed proposed observed observed observed errors errors forward forward forward forward forward resulting resulting ing total regression regression regression computed computed computed computed computed computed performed called mapping optimization dimension made study em em em em em em em em filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter true compared application series series series series series series series series provide provide provide provide compute proc perform determined goal posterior posterior gain gain gain discrete approaches approaches approaches mit accuracy accuracy comparison comparison contrast update update train train modeling modeling modeling modeling morgan proceedings report institute institute department department implementation consists advances advances advances joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint represents final final framework framework cambridge cambridge domain additional curves curves curves curves estimates estimates estimates estimates estimates transition transition transition san conference efficient requires choice significant approximate statistics statistics statistics estimated estimated estimated pages pages produce weighted conditional conditional developed robot actual actual provided iteration iteration iteration sampling simply simply achieved covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance covariance technical denote tested transformation transformation transformation transformation transformation transformation transformation transformation corresponds stable predictions rbf assumed assumed theoretical require square square square square future development noisy noisy noisy noisy noisy noisy noisy typically typically underlying dynamical functional unknown fully technology mlp mlp interesting testing consistent representing numbers filters filters direct international normalized magnitude combined run sources discussed discussed improve exact exact exact advantage separate separate separate reported introduced include sense recently recently engineering engineering observation observation observation observation observation generalized improvement increased grant arm scaling extended extended extended extended extended extended extended matrices matrices matrices predicted alternative alternative white column pass assumptions conclusions editors differences accurate accurate accurate accurate clear clear clear clear faster mateo propose taking taking demonstrated assuming assuming exist identification acknowledgements explicit monte monte monte van carlo longer sequential estimating estimating implement multilayer simultaneously simultaneously simultaneously simultaneously electrical formed expectation expectation expectation expectation expectation expectation expressed expressed expressed viewed interpretation solved restricted updated approximations approximations approximations approximated approximated approximated approximated past past earlier calculation smoothing smoothing additive additive additive performing expansion sec iterative closed closed filtering filtering filtering calculate norm norm includes thesis perceptrons extension extension illustrated determining straightforward effectively driven driven driven computations mackay plots plots tend identity superior superior running backward backward backward backward backward backward backward backward backward backward providing maximization maximization attempt presents transformed kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman kalman detail hessian hessian recursive recursive recursive dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual preliminary dataset rise rest mse mse mse analytically referred root root root maximizing comparable tanh measurement measurement measurement measurement possibly quantities quantities versions der obvious algo algo taylor explored improving phd chaotic chaotic chaotic chaotic chaotic ment variances glass glass glass glass benchmark tool nonlinearity snr snr widely producing products controls nsf outer improvements substantially orders solla compares calculating passes passes mod differs maximizes achieves substantial enables expectations simultaneous consistently ghahramani corrupted sensing writing rithm linearity approximates accepted replacing preparation symposium combines propagated treatment smoothed smoothed offer refers clean clean clean clean clean kearns propagate std std ics minus recursively recursively benefits nelson nelson nelson nelson nelson nelson nelson encouraging propagating pointed sigma sigma sigma sigma sigma sigma ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf ekf england eric illustration ary cohn mackey mackey mackey mackey community rithms graduate graduate ization relate proach iri esti sta sta page els october oregon oregon oregon gorithm november 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#*network network network network network network network network network learning learning model model model model model model model model neural neural neural neural data data data data function function figure figure figure figure figure figure figure set networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number error error error error error error error error error error error results results results results results results results results information information information information problem problem models models models models models models models models hidden hidden performance performance performance performance performance performance based linear case case case case vector vector vector order order order order order shown shown shown systems systems systems systems values probability probability probability probability probability probability probability probability probability probability functions recognition approach pattern point single single single single single single single single single single single single processing processing processing control large large large large local local local local local local local local local rate rate rate analysis analysis analysis analysis analysis analysis analysis class class matrix matrix matrix form form shows shows shows shows shows algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper small small size work work methods methods fig fig fig points points points points field classification structure structure structure problems random random random similar similar show show show show show show show show equation equation equation equation fixed fixed images general general speech approximation approximation approximation approximation approximation theory theory theory term term note note note note variables variables variables variables variables computation solution research found found estimate estimate estimate estimate estimate computer computer distance node node node node node node node node node node node node node node node node node node node node node node science science left presented presented map present low nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes machine maximum maximum range press press press press components components components components components components components components continuous abstract applied convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence density references due ieee ieee ieee positive important decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation introduction statistical generated variance variance variance variance variance variance variance parallel tion tion difference variable assume assume assume assume rules rules rules chosen chosen cases cases multiple multiple multiple multiple good good binary binary conditions conditions conditions conditions tree tree tree tree tree tree tree tree tree tree tree tree tree tree bayesian bayesian bayesian expected equations markov region proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correct correct correct correct correct correct correct correct correct correct probabilities probabilities probabilities probabilities observed observed observed finite simulations simulation sum sum sum sum sum elements means means means means means means means means means means means means means factor factor potential made global applications applications applications study em original original original specific true true true true true true true true true true true proc proc proc determined experimental related related related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior connected connected connected connected connected connected connected distributions distributions distributions distributions discrete discrete discrete equal equal approaches mit mit mit mit mit accuracy accuracy comparison larger morgan proceedings report report report department code joint joint joint joint joint joint represents exp scheme graph graph graph graph graph graph graph graph graph graph graph graph graph ai ai considered cambridge cambridge cambridge computing equivalent equivalent equivalent equivalent estimates estimates estimates limit limit san conference conference requires choice approximate approximate speed basic pages give give give give give give con condition channel coding coding coding derived randomly randomly randomly conditional conditional conditional conditional conditional conditional conditional conditional product product product product product product product product product selected selected selected evidence iteration iteration iteration iteration iteration nature simply discussion covariance covariance covariance covariance covariance covariance technical technical technical increases describe arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary arbitrary denote denote denote denote denote fast fast fast fast inverse inverse inverse inverse corresponds stable nearest main journal journal square instance instance instance development including kaufmann probabilistic probabilistic probabilistic probabilistic smaller smaller jordan jordan ratio special empirical empirical empirical iterations iterations iterations iterations iterations iterations iterations iterations max max max max max max max max max max international idea idea added correlations correlations correlations correlations correlations exact exact exact exact exact exact exact exact exact exact similarity reported identical identical quadratic inference inference inference inference inference inference recently recently recently recently engineering interest sufficient sufficient sufficient observations observations observations observations calculated calculated calculated calculated calculated calculated calculated tions correspond correspond converge converge converge diagonal diagonal sparse observation observation observation grid increased constructed expression lead extended wide matrices matrices predicted loop loop loop loop loop loop loop loop loop loop deterministic occurs generally row greater neighbor valued valued editors accurate clear faster faster faster faster practice cycle demonstrated variety exist decrease relationship relationship groups groups connectivity areas areas van van construct solving solving describes dept confidence confidence confidence electrical belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief gaussians gaussians gaussians applying potentials potentials potentials potentials potentials potentials potentials potentials decreases decreases decreases decreases decreases independently dependence correlated communication communication codes codes codes codes codes codes codes codes densities showed showed approximations understanding similarly similarly converges converges converges converges converges converges converges converges performing neighborhood neighborhood neighborhood iterative iterative iterative calculate calculate calculate calculate visible sufficiently construction topology topology topology topology precision thesis assignment assignment assignment assignment assignment assignment plotted uncertainty holds neighbors neighbors neighbors straightforward compression symbols wij wij build schemes essentially graphs graphs graphs graphs graphs graphs graphs decoding decoding decoding decoding decoding decoding decoding decoding decoding success running running running hold notation write write write relaxation relaxation relaxation received neighboring body diego powerful rapidly rapidly rapidly involving graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical graphical hall existence successive successive parity relationships root root root root root root root root root workshop understand plausible editor analyze analyze analyze quantities versions precise expressions ith message message message phd finds years advanced rows scenes pairwise pairwise pairwise formula formula formula variances variances variances variances variances variances variances variances analyzed analyzed analyzed guaranteed guaranteed guaranteed defining growing analytical answer answer worse berkeley berkeley berkeley berkeley berkeley strictly division ran ran arise mathematics potentially inversion medical researchers applies applies applies freeman freeman freeman freeman freeman freeman freeman freeman poorly solla slower incorrect incorrect incorrect incorrect incorrect maxima compares phone phone marginal marginal gave gave electric shaped median progress converged converged leaf leaf leaf leaf leaf leaf leaf leaf leaf leaf diagnosis lab lab intractable sort www writing approximates communications communications wrong wrong murphy stronger simplify intelligent loops loops loops loops loops loops loops loops loops loops loops loops loops check replica star reasoning definitions filled excellent dominant den scan enable omitted kearns horn roy roy passing passing correcting correcting correcting messages messages 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#*network network learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure time time time set set set set networks networks algorithm algorithm algorithm algorithm number number number number number number number system results results results results results results units units units units units units information information information problem problem problem problem models models models models models models models models models models hidden hidden hidden hidden hidden based based based space linear layer layer layer layer layer layer layer layer layer layer layer layer case case case case case case vector vector vector vector vector vector order shown shown systems systems systems systems values probability probability probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters unit unit unit unit distribution distribution distribution distribution distribution distribution recognition method method method method method method approach approach approach approach approach approach pattern point point image image single single single single single processing processing processing processing large large large analysis analysis analysis class class matrix matrix shows shows algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples examples examples small work work work work work work work work work work work work methods methods methods points points points points points field field field features classification process process process process process process level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level level current current structure structure structure structure structure structure structure structure structure structure structure problems problems random random random random random random high show show section section section section section section fixed fixed fixed fixed fixed vectors vectors vectors general parameter parameter average theory theory term term note note note note note experiments experiments experiments experiments experiments university university university variables variables variables variables variables variables variables computation computation solution solution solution solution solution independent independent independent log log log log defined found found found found found found found found found sequence sequence sequence sequence sequence initial initial initial standard terms connections connections connections node node node node node node node node node node node node node science left left direction presented map nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes nodes sets motion maximum press press press press position position position position basis continuous continuous sample sample sample sample sample abstract applied find computational likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic ieee important important adaptive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction estimation statistical statistical statistical statistical statistical dynamic dynamic dynamic generated generated generated generated generated generated generated variance variance variance variance variance variance variance search search search search search change difference variable variable variable variable variable lower lower prior prior prior prior prior prior prior prior prior prior representations chosen higher higher higher higher higher higher cases cases cases cases cases cases cases cases cases cases multiple good good binary long tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed bayesian bayesian bayesian expected markov markov markov markov fact fact proposed correlation probabilities probabilities simulation sum means means means means means means means means means factor optimization potential dimension dimension dimension dimension made obtain artificial artificial represented application proc determined experimental related related related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions discrete discrete discrete discrete equal mit mit larger contrast contrast contrast connection update morgan morgan proceedings institute implementation version version advances advances advances joint final layers scheme scheme scheme graph sequences framework framework cambridge cambridge cambridge cambridge computing directly view solutions estimates san top conference full requires approximate basic basic pages give con con produce produce derived randomly randomly clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed developed developed levels levels levels levels levels levels levels levels path depends sampling sampling sampling sampling constraint simply simply biological biological biological achieved discussion covariance covariance covariance covariance covariance increases describe describe describe describe describe describe describe arbitrary assumption finding finding short common assumed generate generate supported require require main journal end cluster cluster cluster easily makes fit kaufmann kaufmann simulated probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic probabilistic smaller account account coefficients york york structures uniform uniform uniform details numbers numbers numbers international international idea idea idea idea produced run run run denotes denotes improved discussed discussed discussed discussed directions advantage introduced hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees inference inference inference inference dimensions dimensions observations calculated calculated trans mixtures positions chain chain chain chain chain chain locations generalized williams williams williams williams williams williams grant scaling extended matrices alternative alternative move move move move move move move move touretzky occurs occurs occurs column column column runs starting assumptions depend competitive editors editors editors editors editors differences differences performs moody mateo propose propose propose taking demonstrated demonstrated proportional proportional intelligence turn min iii manner connectivity configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration configuration annealing annealing denoted denoted denoted denoted denoted monte monte monte monte carlo carlo carlo carlo longer longer index describes changing changing explicitly dimensionality easy easy belief integrated gaussians gaussians gaussians gaussians gaussians formed focus formation dependence review reconstruction interpretation interpretation organizing approximations approximated similarly allowed discrimination past earlier reasonable calculation calculation calculation calculation calculation calculation calculation add generation generation calculate calculate calculate visible visible advantages formulation plotted plotted plotted illustrated uncertainty discuss mozer mozer candidate priors partially discussions discussions texture simplicity straightforward middle suitable society build efficiently schemes comparing allowing link link interested neuroscience split split split split split split split split dis lie running generative generative generative generative generative generative generative generative generative sampled sampled usual dayan wavelet highest moves moves moves mixing acknowledgments decreasing modelling modelling modelling modelling explore origin origin carried carried carried involving hanson lippmann lippmann graphical helpful helpful rise successive history ideas ideas investigated analytically structured structured structured structured structured root root root proper variability hierarchy hierarchy hierarchy hierarchy notion hill coarse plausible configurations configurations configurations equally panel panel panel panel panel observe ith multivariate multivariate submitted integrate pairwise directed variances variances variances variances variances variances defining diffusion caused lin shared protein day division located located located leaves circle apparent collected offset offset amounts conducted lack peter peter marked marked marked solla solla remove dots maintain http poisson ture branch popular hyperparameters parent parent parent parent parent parent parent parent parent parent parent parent parent parent green green green gave leaf leaf leaf sharing representative ghahramani assign branches labelled connecting royal children children children children children extending accepted determination intelligent reasoning monotonically krogh child composition inferior inferior inferior connect sion decide searching searching searching branching branching viewing similarities similarities iterated infer infer indicator indicator kearns kearns arrows merge merge merge merge merge jump jump papers vari parents displacement displacement posteriori ence dna pointing recursively creates markovian formulate encouraging centre centre centre residuals obtains lit chapter individuals covariances covariances covariances covariances multinomial multinomial multinomial flat flat hierarchies discovering causal edinburgh edinburgh australia cohn cohn continues denoting disadvantage march rejected multiscale dirichlet dirichlet pearl pearl pearl pearl buhmann indexed attached particle sweeps sweeps sweeps mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc mcmc elsevier durbin durbin hofmann struc supporting behaves observables stores dim lation continued christopher generafive generafive reversible reversible proportions formulae returned proposal proposal concerns devised meeting proposes inferring iid evolutionary centres centres centres centres centres centres centres centres centres firm gence relaxed comprised sweep sweep trend acyclic metropolis metropolis metropolis metropolis particles wiener relax accepting lynch sydney phil lifetime icann ver edwards edwards edwards collect dissimilar subtract structuring forrest rightmost motivates diverges tinuous univariate distinguishes retains gatsby fogelman mitchison expressing epsrc ripley forest ucl realizing brownian granger adams adams adams twelfth indefinitely sampler sampler sampler decade ijcai calcu gallinari crucially remembered biometrika scotland effected proposing soulie chances ttt penultimate cie nection declines willsky cheeseman cussed levitt intelli petitive magnus rti dai inheritance inheritance thirdly jective chapters dawid informatics cry cry speeded luettgen firsfly icpr anc shorten minded accidentally sensibly 
#@Williams_C,
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#*network network network network network network network network network network network network network network network network learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure time time time time time set set set set set set set set set set set set networks networks networks networks networks networks networks networks training training training algorithm algorithm algorithm algorithm algorithm number number number 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patterns patterns patterns analysis analysis analysis analysis analysis optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows signal signal signal signal signal algorithms algorithms algorithms simple simple paper paper size size feature feature feature feature feature feature feature feature feature feature feature net work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step features features classification classification classification classification classification process process trained trained trained problems high high high high high high high high architecture architecture show section line vectors vectors real real 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variable variable variable variable variable variable variable variable variable spatial spatial assume classifier classifier classifier classifier classifier measure prior prior part good good good good good good binary tree proposed proposed correlation forward forward forward scale minimum classes classes total human computed times dimension natural applications applications knowledge knowledge obtain negative represented true application application application application application application series series define compute compute rates rates rates rates perform goal related distributions approaches approaches mit comparison contrast train dependent selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection report institute version technique technique consists advances joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint connectionist difficult final cambridge computing computing computing equivalent view view view view design efficient requires significant statistics world world pages pages increase give give give weighted randomly randomly conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional entropy product processes selected selected selected selected selected selected selected selected measured measured technical corresponds finding effective effective supported eds easily easily pairs smaller underlying needed unknown technology testing principal max max bits bits bits bits supervised supervised supervised choose choose choose sources property property pair robust separate include relevant relevant compare unsupervised unsupervised axis axis axis axis pca pca pca pca pca achieve trans separation separation risk risk grant suggests matrices alternative feed feed feed touretzky clusters boundary generally critical reduce conclusions editors clear performs moody moody moody moody moody moody faster faster faster largest reduction pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse ica ica ica ica ica ica ica ica ica ica denoted denoted denoted denoted reference relation relation construct coordinates coordinates coordinates coordinates coordinates coordinates dimensionality consisting mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual adding adding springer select select select select select select select select select john focus interpretation transform densities evaluated evaluate evaluate similarly converges converges slow euclidean advantages views david avoid existing existing existing existing thesis coordinate coordinate coordinate coordinate coordinate coordinate coordinate usa blind blind blind recognize illustrated discuss maximize maximize mozer holds holds structural successfully reason selecting selecting aspects extra suitable divided identify projections projections projections projections projections orthogonal orthogonal verlag dis classify bar michael michael play minimizes thresholds thresholds minimized bars bars parametric parametric parametric parametric transformed collection divergence divergence fewer fewer fewer project maximizing maximizing complicated statistically understand friedman epoch amari amari phd costs costs distinguish expensive expensive comparisons choices pulses acknowledgement percent evaluating relevance relevance relevance axes howard spread monotonic display redundancy redundancy redundancy damage displays irrelevant irrelevant acquisition redundant redundant tation conditioned eliminate eliminate eliminate eliminate fails kullback kullback wrong efficacy analyzing canonical ylx ylx symposium nonparametric meaningful meaningful evaluations evaluations evaluations evaluations evaluations embedding mance corre perfor dependency colorado hasselmo yang yang yang yang yang yang offers bases peterson viewing informative onr radar radar radar radar radar radar radar radar radar radar radar radar radar radar radar specification specification leibler leibler exhaustive july suboptimal arg arg arg arg visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization visualization equality equality increment gained graduate eliminating eliminating conversely attached distinguished ation jutten compu oregon curse suffers mining rare classi conditionally dimen fication mis mis mis mis mis cichocki sep discovers severely ece disadvantages herault ogi ogi walker burden cse tar visualize visualize visualize lations nato depen unrealistic visualizing visualizing visualizing visualizing visualizing yix yix yix yix yix yix yix selec sponds sug fax bundle bundle estimations mahalanobis neuromimetic beaverton asi slx oth keywords sionality ruled intimately explanatory gest intern complicate wechsler battiti aration llp noticing wilh vlx isting 
#@Moody_J,Yang_H,
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#*network network learning learning learning learning learning learning learning learning learning learning model model neural neural neural neural neural neural neural input input function function function function function figure figure time time time time time time time time set set set set set set set set networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number system system error error error error state state state state state state state state results results units units units information problem problem problem problem models models models models models hidden hidden hidden performance performance space space space space space space space space weights weights weights weights linear linear layer case case vector order shown systems values values probability probability probability probability noise noise weight functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method method approach approach approach point point single single single large rate rate rate test test test test class matrix matrix matrix matrix matrix optimal form form form form shows algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples small small task task methods methods methods methods step step step structure structure problems problems problems problems high high high high equation equation section section fixed vectors images general general parameter parameter parameter parameter approximation approximation average average average average average states states states gradient gradient obtained obtained note note university variables computation computation independent independent independent log log log log log log defined defined defined defined found target dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial constant constant estimate standard standard standard standard computer computer terms terms distance distance science science left present phase low press components components nonlinear sample sample abstract applied applied back computational density density density density likelihood likelihood likelihood references component stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due due ieee positive adaptive propagation context introduction introduction complex complex complex complex complex complex hand behavior dynamic generated variance variance tion energy energy energy energy energy energy difference variable lower measure measure prior prior prior prior prior prior prior prior prior prior prior prior chosen chosen chosen part previous cases required required required distributed distributed bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations equations equations markov markov markov markov markov fact region proposed proposed correct errors errors errors errors finite simulations resulting resulting ing total total total total regression regression regression regression respect multi multi called times times regions mapping made made natural natural natural natural obtain vol vol vol vol vol vol vol samples compared compared application perform related posterior posterior posterior posterior posterior posterior distributions distributions distributions distributions distributions approaches steps steps steps steps comparison comparison comparison comparison institute institute institute department department implementation represents exp exp exp exp exp scheme addition framework framework cambridge computing equivalent equivalent transition efficient efficient efficient statistics conditional robot robot robot levels criterion product product product product actual actual iteration iteration iteration iteration iteration iteration sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply simply achieved measured covariance denote fast inverse inverse predictions predictions common common generate main journal journal easily easily simulated smaller needed dynamical unknown technology technology technology character character empirical empirical empirical empirical empirical squared squared iterations normalized normalized early run run denotes denotes improve directions exact introduced introduced interest interest calculated works works axis tions studies differential differential differential trans definition chain chain chain chain chain modified generalized arm arm arm horizontal invariant invariant invariant extended deviation deviation deviation matrices predicted alternative hybrid hybrid hybrid hybrid runs runs conclusion starting assumptions numerical numerical performs practice practice temperature suggest propose taking strong physics physics physics physics california proportional proportional proportional turn reference monte monte monte monte monte monte monte monte monte carlo carlo carlo carlo carlo carlo carlo carlo carlo written transitions ann stability metric metric metric metric metric metric metric metric physical dimensionality angle springer quality letters letters expressed evaluated operations updated showed approximations approximations approximated suggested norm euclidean euclidean euclidean euclidean existing exploration exploration exploration exploration exploration exploration thesis priori candidate successfully aspects capable importance uniformly modification delta symbols efficiently mackay mackay mackay mackay mackay mackay invariance contained prob split dis dis dis dis superior superior sin sin sin manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold manifold gibbs gibbs gibbs relaxation paradigm leading reach reach load intrinsic intrinsic remain unlike carried poor perturbation rapidly put hessian mass hall hall dataset successive analytically referred reliable comparable tanh momentum momentum momentum momentum momentum momentum momentum momentum momentum naturally versions fisher art art amari amari amari amari neal neal neal neal neal neal neal neal mentioned indicating cos cos cos cos defining defining improves floating benchmark rapid rapid calculations geometry geometry geometry geometry geometry geometry geometry geometry meaning integrating geometric considerably considerably tional simulate simulate weigend weigend gen achieves geman geman geman geman geman geman marginal replace replace logp logp logp ordinary tensor tensor tensor tensor tensor tensor tensor approximates concerned systematic convenient replacing city city chemical chemical keeping mark definitions canonical canonical canonical canonical canonical canonical canonical prentice governed ensures entries entries israel israel israel israel informative fold pressure multiplying multiplying geometrical achieving rejection failed simulating molecular jacobian jacobian distri chapman distribu landscape guided integrals discretization discretization discretization discretization mcmc mcmc increments computa modal modal bution ergodic appearing restoration consuming consuming autocorrelation autocorrelation inclusion determinant drawing eliminates tribution tribution ters discarded fox hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian hamiltonian attained deals concave nontrivial implying andersen andersen andersen appl lags kinetic modern metropolis metropolis metropolis metropolis metropolis riemannian riemannian riemannian riemannian riemannian technion technion technion technion technion technion degrades stepsize stepsize drawbacks subtasks parame buntine eralization infinitesimal burden anisotropic anisotropic resampled disappear henceforth hwang hwang hwang subsample subsample masses hyperparameter persistence persistence qualities qualities equipped equipped occasional ergodicity richardson overcomes notable compar leapfrog leapfrog leapfrog leapfrog leapfrog leapfrog leapfrog jeffrey jeffrey spiegelhalter haifa haifa hamiltonjan necessitates chines accelerating flops flops flops yoram gilks gilks gilks ison duane duane duane uncorrected inefficiency semidefinite oix tence stricted stiff 
#@Baram_Y,Zlochin_M,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model neural neural neural neural data data data data data data data data data data data data data data data data data data function function function function function figure figure figure figure figure figure figure figure figure set set set set set algorithm output number number number number system system system system system system results results results results information information information information information information information information information information problem problem problem performance performance performance performance performance based space space space space space space linear linear linear linear linear linear vector vector vector vector shown systems systems systems values values values values values values probability noise functions functions functions functions functions functions distribution distribution distribution method approach approach single processing processing processing processing large large large large large large large large large large large large large large large large large large large large large large local analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple gaussian gaussian paper small small small size work work work task task methods features process current structure problems problems problems problems problems problems problems problems problems problems problems problems problems random high high memory memory response similar similar similar show section line line line line line line vectors vectors vectors general general real real gradient obtained term note experiments experiments experiments dimensional dimensional dimensional dimensional dimensional university variables variables variables computation computation computation computation computation research research independent independent independent independent independent found found standard standard standard standard standard standard terms terms terms science machine machine machine machine machine machine machine machine machine machine machine machine object object object object object sets sets sets sets sets press press components components components components components abstract applied find find computational computational computational computational computational computational density references references positive mixture mixture context introduction action behavior behavior behavior generated parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel parallel tion signals signals word word multiple multiple distributed distributed distributed distributed distributed distributed make make techniques techniques techniques techniques techniques techniques techniques techniques correct observed observed scale scale scale scale scale tasks tasks multi performed called called times elements elements elements dimension made made natural applications policy obtain negative original original original specific compared compared application compute objects objects perform perform perform goal related related related related distributions power power approaches approaches mit mit comparison comparison support support descent source source source source source proceedings proceedings proceedings proceedings proceedings report words words words words words words words words words words words words words implementation version version technique technique code code code code code individual advances advances advances represents difficult scheme addition ai framework framework computing computing computing computing domain directly directly directly directly curves curves transition conference conference conference conference conference full full choice world world basic pages give produce clustering clustering area types product product provided finally simply discussion discussion technical describe group group group group tested tested close complete complete finding finding common common common effective implemented implemented assumed shape journal journal journal square end instance easily easily easily makes makes makes makes development including including including smaller smaller smaller underlying underlying unknown programming interesting interesting interesting interesting projection mechanism special special structures principle language language leads leads principal call call numbers pre direct making making international magnitude combined run sources sources advantage advantage robust element typical typical typical similarity apply apply include subject identical machines subset subset subset subset sejnowski sejnowski sejnowski sejnowski sejnowski array relevant dimensions highly highly highly highly highly highly previously previously unsupervised axis axis achieve diagonal sparse sparse sparse sparse evaluation separation separation symmetric occur occur suggests suggests wide matrices matrices matrices matrices matrices matrices matrices clusters clusters white white occurs column column demonstrate demonstrate demonstrate demonstrate half half half half minimal minimal operator editors clear integration integration largest largest external reduction demonstrated variety user user user user user ica ica ica ica ica ica ica ica ica ica ica exist introduce question denoted explicit appears pro derive construct produces produces written factors estimating plot describes laboratory distinct distinct recall implement text text text text text text 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interfere public party maron maron singhal singhal envi reads portable portable portable portable portable portable cocktail choi rand packages packages packages packages packages packages packages packages packages packages manipulate puting libraries libraries libraries facto judgements judgements cray cray cray accessing biggest microsystems microphones compiled invoke afforded reside henry florham trices fortran interactively transferring releases cision jnowski supercomputers sigir deerwester deerwester restructuring mpi mpi mpi ently classically trix kwok communicates supercomputing residing residing innovative propriate org jections kurtotic teristics sors doc sheer endeavor ling anc entific transparently itly prototyping 
#@Husbands_P,Isbell_C,
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#*network network network network learning model neural neural neural neural neural input input input input input input input data function function figure figure figure figure figure time time time time time time time time time time time time time time time set networks networks networks output output output output output output output number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system error error error error error error state results information information information problem performance performance based based based based space space linear layer case case case vector vector order order order order order order shown systems systems systems systems systems systems systems systems systems systems noise functions distribution distribution distribution distribution approach approach approach image image image image image image image image single single single single single single processing processing processing processing processing processing processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large rate rate rate patterns inputs inputs inputs form shows signal signal simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual small small work work task fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells cells cells step points field field field field field field field field field field field field field field level current current current current current current cell cell cell cell cell cell cell cell cell cell cell random high high high high similar representation architecture architecture architecture section fixed fixed fixed fixed fixed vectors images general obtained activity variables variables computation found found sequence target target target target target target constant distance connections connections left direction direction direction direction map map map map map map map map map map present present low low frequency frequency frequency machine object motion motion maximum maximum range position position position position position components components components components outputs outputs outputs outputs continuous abstract applied applied applied back back computational analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references due due due due due ieee ieee introduction complex circuit circuit circuit behavior behavior behavior behavior generated generated parallel search tion complexity lower signals signals prior higher center center center center center center center center long conditions expected chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip chip make region region correct correct resulting resulting ing ing tasks tasks total total total human computed respect multi multi multi multi multi multi multi sum called called called called called called called called elements elements mapping mapping mapping mapping mapping mapping made made made made made made made natural feedback feedback feedback feedback orientation orientation orientation global global global applications relative relative specific application objects objects location location location location location location location active active active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye 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tested fast limited limited close close excitatory actions actions circuits circuits circuits circuits circuits circuits circuits circuits circuits circuits common implemented implemented implemented generate generate require journal vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi instance easily degree degree development development needed combination account functional fully interesting testing ratio ratio ratio ratio ratio ratio ratio ratio ratio mechanism mechanism special consistent structures mode principle principle principle principle operation operation operation representing details numbers magnitude magnitude magnitude magnitude magnitude produced produced sources sources description light light light light light light light light light light light light light light light light light light light light light light light light light light light architectures improve resolution resolution resolution resolution advantage pair takes 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sensors sensors publishers publishers publishers orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations orientations track coded biology biology biology biology correction processed easier division located mation pulses pulses pulses pulses recognized recognized computers qualitative addressed raw researchers applies fuzzy axes capability quantitative leave completion adjustable incorporated slower continuously frequently schematic operate mod measuring measuring limiting spread reaches reaches incoming incorporating prevent pasadena pasadena suited enables boston sophisticated comments age implements focused attentional eventually june june wesley sharing phenomenon lab aligned primarily addison interface restriction summing summing summing saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic ratios angular angular animals animals narrow narrow narrow narrow acts acts mobile addresses addresses addresses printed interconnected turned turned caltech caltech caltech suppression binocular numerically significance ranges ranges ranges overcome mail mail loops serves analyzing operates operates splitting shifts belong settings salient salient salient spot spot spot spot spot spot spot spot spot spot spot spot spot spot spot capacitor arrays degradation selects infor passive ranging loo sion sion studying conjunction topological intended facilitate assembly winning winning winning express neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic stimulated gaze gaze saccade saccade saccade saccade saccade saccade saccade saccade saccade saccade saccades saccades saccades saccades saccades saccades saccades belonging designing designing executed executed mechanical mechanical mechanical mechanical mechanical fitted fitted fitted fitted grating grating grating grating outperform kluwer kluwer kluwer focal break transmitted encodes encodes incrementally reports reports flat eric streams streams brightness transparent avoids favor shifting cessing interact march mediated relating individually insertion complementary intensities win drawback covered oculomotor setup sweeping inversely electronics exploited tel manuscript scanning triggered demonstrating demonstrating replacement functionality functionality externally assistance designs wins wins mahowald spacing imple micro micro micro micro micro micro micro micro micro micro micro micro morris suppress fabrication sensorimotor inherently rare returned dedicated optics colleagues convention quantitatively leakage communicate communicate permanent physically periodically quick quick attended deweerth deter deter meant addressing steve motors motors fovea gratings gratings ensuring convey wires enabling modest modest mounted mounted stabilization insert stan rotate rotate degrade instant custom custom spent spent spent horiuchi horiuchi horiuchi vergence spots spots spots spots spots spots spots spots spots tracked plexity sends bright inserting slip availability stim jumps jumps enabled enabled lens lens lens accessible accessible concurrently retinas retinas switzerland switzerland switzerland notably mate mate challenges pri pri syrup disk boahen boards prism prism prism prism prism prism prism prism prism prism prism prism prism prism prism prism prism prism mined behav shortcomings delivered proportionally sector sector contributed spotlight triggers occasional stereopsis vittoz vittoz peri noticeable inspiration embodies gravity gravity higgins sept sept requested bor disabled ford atlanta atlanta microelectronics reacting nystagmus reciprocally conflicts llll displacements ule lends patrick transmits buses buses triggering oliver reid gathering tains prisms prisms prisms prisms constituting anymore harrison lnt lnt deflection deflection deflection deflection deflection deflection deflection complements duty duty photograph sti seminal bishofberger visuo visuo visuo surroundings spending stereoscopic shut ulated friedrich friedrich brightest menting ents mines protocols emulating emulating emitting fonds iscas shelf shelf shelf diodes friendly dordrecht gratitude roland allo looms endless pioneering stimulates succes slipping odic 
#@Gyger_S,Landolt_O,
#t13
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#*network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network network model model model model neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set networks networks networks networks networks networks networks networks networks networks networks networks output output output output output output output output output output output output output output output output number number number number number number number number number number number number number system system system system system system state state state results results information models models based linear linear linear linear linear linear linear linear linear linear linear case shown shown shown shown shown shown systems systems values values values values values values weight neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit point single single processing processing processing processing neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron analysis inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs shows shows shows shows shows signal signal signal signal signal signal signal visual visual visual visual visual paper size net work work work cells cells cells cells cells cells cells points field field field field level level level level current current current current current current current current current current current current current current current current current current current current current current current current current current cell high high response response similar similar similar architecture architecture architecture architecture architecture show show show show show show equation equation equation equation equation section fixed fixed fixed fixed parameter parameter parameter parameter states states states states states theory term threshold threshold threshold computation computation computation computation computation research research independent defined defined dynamics dynamics constant terms connections synaptic synaptic node node node node node node node node node node science direction direction direction direction low low nodes frequency temporal object motion maximum maximum range range nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs abstract analog properties references ieee positive introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior behavior behavior behavior behavior generated generated recurrent recurrent recurrent recurrent recurrent difference difference complexity assume lower chosen chosen higher part multiple conditions conditions expected chip proposed simulation respect respect respect respect sum sum natural feedback feedback feedback feedback feedback feedback orientation global global global global global global global negative relative relative relative represented active active determined determined connected connected connected connected connected connected gain gain gain gain cortical cortical equal equal equal equal equal voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage dependent dependent source source source source source source selection morgan institute institute implementation consists consists consists consists code code code code code individual advances final bias bias bias bias equivalent equivalent curve additional additional curves curves curves curves curves transition transition san stimuli effects condition condition condition condition condition derived provided finally inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory inhibitory depends depends measured measured discussion increases increases increases increases increases increases describe describe describe group excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory excitatory circuits circuits common common common common implemented implemented assumed synapse synapse supported square vlsi smaller combination combination combination combination combination reduced technology technology ratio york increasing operation max max max max max max max max max inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition inhibition normalized normalized normalized normalized magnitude attention property property property property property property property property property property movement lateral lateral include recently engineering varying varying varying works tions solve correspond correspond correspond differential differential differential trans gate gate gate increased increased increased increased grant wide wide wide wide hardware hardware hardware strength strength critical critical greater reduce depend differences exponential mateo hard hard hard hard hard hard hard hard mechanisms largest largest external external turn assuming selective selective selective selective relationship reference reference reference reference reference winner winner winner winner winner winner stability changing implement consisting springer competition decreases decreases national expressed dependence depending soft soft soft soft soft soft soft soft soft soft soft soft discrimination measurements normalization normalization normalization initially initially initially foundation foundation koch silicon silicon silicon silicon thesis currents currents currents currents currents currents currents currents currents currents currents currents currents currents currents coupled phys differ driven poggio excitation excitation compact notice verlag quickly quickly split split follow cmos cmos computes principles acknowledgments receive modelling stimulation selectivity exhibit exhibit circuitry circuitry circuitry circuitry circuitry circuitry mead put steady strengths strengths strengths strengths strengths replaced respond biol transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor transistor office root neu neu act circles editor voltages voltages academic amari amari electronic wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta wta ment piecewise ground publishers analyzed nonlinearity starts sys sections transistors transistors immediately ion grossberg grossberg grossberg localized arises improvements generic variant variant variant variant variant variant schematic exhibits implements eventually traces cybern fabricated fabricated fabricated tation martin acts jth jth naval kaufman saturation saturation saturation saturation settings settings substituting introduces viewing winning neuromorphic lazzaro lazzaro lazzaro lazzaro lazzaro lazzaro 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#@Liu_S,
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systems systems systems values values parameters parameters parameters parameters parameters parameters weight weight functions functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit pattern pattern pattern pattern pattern pattern pattern single processing processing processing control control control control control control large large large large large neuron neuron neuron neuron neuron patterns patterns class class class inputs form form form form signal visual paper paper small small small small net work work level level current current current current structure high memory architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show parameter parameter parameter parameter parameter parameter parameter parameter real note experiments experiments experiments experiments experiments experiments activity activity activity activity dimensional result result university variables computation research research research research independent constant standard computer computer computer computer terms distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance distance connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections connections synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic synaptic node node node node science direction direction present present present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low frequency frequency frequency frequency motion motion range range press basis outputs abstract applied applied applied computational computational analog analog analog analog properties properties properties references ieee ieee important adaptive introduction action action action complex circuit behavior behavior behavior behavior behavior behavior behavior behavior effect effect effect generated generated generated generated generated generated tion tion difference difference difference difference difference complexity variable lower measure higher higher center center center cases type type good spike long long long long long long long long long long long long long long long distributed distributed chip chip chip length length observed observed observed forward forward scale scale resulting resulting classes classes classes ing ing total total total total total total total total respect performed called factor factor potential made made made feedback feedback study vol artificial relative relative relative relative relative specific specific application cross provide provide perform connected motor motor motor motor motor motor motor brain power larger larger contrast connection connection train dependent dependent dependent modeling modeling modeling modeling modeling modeling modeling modeling proceedings institute institute institute implementation implementation synapses synapses synapses consists consists consists internal internal individual individual individual represents represents represents bias delay delay scheme scheme scheme scheme addition solutions solutions design design design design limit stage effects conference conference significant basic pages increase validation con con con produce produce produce developed inhibitory inhibitory inhibitory inhibitory biological biological biological biological biological biological biological biological biological discussion describe arbitrary denote tested fast fast fast complete stable stable stable predictions predictions circuits circuits circuits circuits circuits circuits circuits short nearest nearest nearest implemented implemented implemented implemented implemented implemented generate generate role role role theoretical theoretical eds square end vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi vlsi future future easily development sensory sensory including including underlying underlying reduced reduced account functional technology technology technology block block interesting significantly edge increasing head special uniform operation principal stored stored stored stored stored normalized normalized depth depth neuronal neuronal neuronal architectures architectures membrane improve directions directions recent recent correlations advantage advantage robust element typical moving side array array array engineering highly approximately approximately axis address address address address address address address chain chain gate gate gate gate gate interval williams storage entire studied digital deviation move move setting half half greater segment segment segment segment segment segment segment segment segment segment segment segment segment segment conclusions neighbor neighbor neighbor depend editors central central central accurate designed clear weak weak weak weak weak weak weak strong strong strong mechanisms mechanisms cycle cycle demonstrated california california variety user exist movements decrease iii connectivity connectivity connectivity appears pro produces produces factors primary generating generating generating generating generating mathematical mathematical changing segments segments segments segments segments sensitivity sensitivity electrical scales scales scales consisting develop develop integrated integrated adding adding frequencies frequencies events events events events events events events events events events events potentials potentials cycles cycles review depending stages communication communication communication communication communication communication communication communication communication communication centered understanding understanding understanding completely constants constants diagram diagram slow delays delays delays delays delays delays delays reduces combining event event event event event event event event event event event event event event event event purpose add generation generation coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling coupling avoid silicon silicon silicon silicon silicon thesis thesis inter determines illustrated illustrated coupled coupled capable capable society society modification spiking spiking spiking spiking spiking spiking projections comparing invariance plots tend essentially dis issue issue oscillations oscillations oscillations physiological physiological hold involved vary relaxation relaxation play modular backward providing wave wave wave wave delayed hypotheses hypotheses chips principles principles principles disparity neighboring intrinsic receive body body explore investigate environments oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators strengths integral issues issues graphical oscillator oscillator rise reducing giving school muscle muscle working oscillation affect affect affect understand matched neu neu smallest plausible analyze thought thought aspect observe observe observe improving extent extent extent regime regime regime regime serial animal animal animal years devices devices burst brown brown brown brown brown great great great advanced advanced ment developing asynchronous asynchronous asynchronous asynchronous slope slope waveform waveform coded biology explanation floating floating floating floating drive drive drive rapid rapid perspective implementing tive sys sys closer closer producing producing transistors controls beginning lowest addressed addressed addressed addressed summation summation fourth greatly greatly behaviors behaviors behaviors behaviors behaviors considerably considerably tional autonomous effort effort cohen cohen detecting detecting passed slower continuously sharp biologically biologically span span operate exhibits synthesis mod measuring ture spread spread synchrony synchrony pasadena replace logical segmented segmented segmented attraction implements implements implements implements implements implements progress displays generator interface interface oxford tation restriction animals animals velocities addresses tem tem interconnected interconnected robotics eliminated inspired communications communications communications ments stronger stronger stronger stronger chains simplify interconnection programmable los los exploit synchronous date exploring exploring falls periods periods pat mental dependency dominant facilitate facilitate facilitate facilitate dif ensembles waves waves waves waves waves waves waves waves waves waves waves axonal axonal axonal neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic neuromorphic specificity waveforms passing designing implicitly receiving mechanical lag ics linked unable basin bus transmitted alternating preserving year profiles causing personal simulating sinusoidal spinal adapting queue queue queue robots goals impose generators generators interactive rhythmic paradigms reveal descending descending descending descending tune els slopes ward computa experi simplifies shallow tonic tonic tonic tonic tonic tonic tonic tonic coordination coordination coordination coordination coordination coordination coordination coordination leech leech locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion locomotion moderate drives drives drives drives drives tail tail externally bursting bursting bursting stephen stephen cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg cpg traveling traveling traveling traveling traveling traveling traveling traveling traveling traveling traveling traveling traveling tial swimming swimming swimming swimming swimming swimming swimming attributed send terns envelope hypothesized mahowald aid puts morris contralateral converter caudal caudal ron char identically connects rons val cord ters sen progressively architec mill arrives explanations cur cur tance marder falling protocol counterpart counterpart creation deweerth deweerth deweerth deweerth deweerth deweerth lags lags lags lags lags lags lags lags lags lags lags lags scott deter enter addressing addressing addressing addressing addressing twelve twelve dent stomatogastric files decoded substrate ganglia rent rent snake replicate replicate ues moderately facilitates facilitates facilitates custom custom custom configured configured imposes rises rises discrepancy segmental segmental segmental segmental broadcast rela ece ece ece bio rostral reviews parame puter nections uniformity illustrating synchronize ascending ascending mediate bifurcations translational manipulators vertebrates nation solu experimentation boahen lacking poten mined communicating interconnectivity analogously rising rising incremented behav ishii steep depen swim swim swim swim swim ror pipeline pipeline minch implementa stud axial axial axial axial axial axial axial axial hasler autonomously somers pling pling focussed establishment asymmetrical asymmetrical coordinated invertebrates atlanta atlanta implemen elicit reciprocally alamitos alamitos pfet prin ermentrout ermentrout kopell kopell kopell georgia georgia gatech gatech gatech testbed cou cou prey synchronizing ied sory pipelined pipelined coordi persists diminishes diorio lecar requisite commu richly cpgs exit duction decremented designate propa munications illus analogs tins initiating modelers ambitious ited queuing delaying delaying nication lam mic 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#@Brown_E,DeWeerth_S,Patel_G,
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neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron neuron patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis form shows paper paper net net net work methods methods step points points points current current current current current current current current current current current current current current current current current current current current current current cell problems high response similar architecture show show fixed line parameter parameter obtained experiments experiments experiments experiments result university threshold variables computation research research computer computer terms terms synaptic synaptic node node presented phase activation activation activation low frequency frequency frequency frequency frequency maximum maximum range range press nonlinear nonlinear nonlinear abstract applied applied applied applied applied applied applied computational analog analog analog analog properties references ieee important important introduction complex circuit circuit circuit circuit circuit circuit circuit behavior behavior behavior behavior generated tion tion complexity variable variable variable assume higher center good good good long conditions conditions conditions equations techniques techniques region observed observed observed observed observed observed scale scale simulations minimum minimum resulting ing ing computed performed regions potential potential potential potential filter vol represented cross provide location perform perform experimental experimental experimental experimental experimental experimental motor motor mit voltage voltage voltage voltage voltage voltage voltage comparison comparison comparison fields dependent modeling modeling modeling modeling modeling proceedings institute institute institute department loss loss implementation implementation implementation implementation implementation synapses individual represents difficult bias bias bias addition maps considered cambridge experiment directly curve curve curve curve curve design design design transition limit limit limit limit limit limit limit limit limit limit limit limit limit effects effects effects conference determine determine estimated estimated con con channel derived derived developed developed area types finally selected biological biological biological biological measured discussion increases describe describe describe close close close stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable circuits circuits nearest effective implemented assumed supported supported main eds eds eds vlsi vlsi vlsi vlsi vlsi vlsi future makes including including fit fit needed reduced account dynamical dynamical dynamical dynamical dynamical technology technology york york matching operation representing magnitude choose choose neuronal neuronal membrane membrane membrane membrane membrane recent pair pair pair identical engineering varying varying compare compare compare previously works tions yields differential differential differential bounded increased grant grant scaling predicted predicted hardware hardware hardware hardware pass demonstrate half half critical critical critical trajectories trajectories trajectories neighbor central tangent interactions temperature hard hard external external external cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle cycle solid solid variety program configuration denoted denoted denoted denoted appears pro van derive primary generating describes stability stability stability mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical mathematical confidence physical electrical develop equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium equilibrium springer blocks dependence dependence influence variation variation understanding understanding similarly similarly diagram diagram diagram slow dashed expansion generation generation msec foundation koch coupling expect building silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon silicon currents currents currents currents currents sciences prove coupled society effectively identify oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory composed composed road verlag neuroscience oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations oscillations physiological duration simplified relaxation delayed principles acknowledgments software load intrinsic modelling unlike parametric mead varied oscillators oscillators steady steady steady steady steady steady steady steady steady oscillator history school muscle transistor transistor transistor dependencies func understand understand fundamental analogous analogous circles circles circles circles reading analyze analyze voltages voltages bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation bifurcation der academic regime regime burst brown advanced slowly developing agreement agreement publishers unstable unstable unstable unstable unstable unstable unstable unstable unstable unstable slope biology biology biology reasons inside sys transistors transistors transistors transistors scientific demonstrates annual cybernetics nsf behaviors behaviors behaviors behaviors behaviors behaviors behaviors experimentally leave schematic operate exhibits berlin measuring cal cal boston fiber shaped attraction focused wesley room addison amplifier animals inspired ments ranges los north integrator integrator capacitor filled filled filled substituting analyses corre holland iterated neuromorphic insight insight mem theoretically calcium papers grants intersection fold incorporates kluwer big basins verified pub gated gated tems mathematically generators potassium neurophysiological efforts efforts interactive regimes increasingly rhythmic rhythmic transconductance oscillating funded tively exhibited exhibited exhibited exhibited experi mea elemental diagrams diagrams coordination coordination leech moderate sponding externally externally externally externally externally externally stephen thermal hyperbolic supply supply morris morris morris morris morris fabrication val val possess dissertation meeting operational separates chan raises hopf hopf 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#@Calabrese_R,Cymbalyuk_G,DeWeerth_S,Patel_G,
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order shown shown shown shown shown shown shown shown shown shown shown probability probability probability probability functions functions neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution point single single processing processing large large local local neuron neuron neuron neuron neuron neuron rate rate rate rate rate rate rate rate rate rate rate rate rate test test test test inputs form form shows shows shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple paper paper examples examples fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig fig cells cells cells cells cells step points points current current current current cell cell cell cell cell cell structure high high high high high response response response response response response response response response representation show show section section section fixed fixed line line line line line speech average average average average average average experiments activity result result university university threshold threshold solution independent independent independent independent independent independent log log constant constant computer computer distance distance presented presented present phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase phase low low low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal maximum maximum maximum maximum maximum range range range range range range range range press position components outputs outputs outputs outputs outputs outputs outputs outputs abstract analog analog analog analog analog properties references component component component due due ieee positive positive introduction complex circuit circuit circuit circuit circuit circuit circuit circuit effect effect generated generated generated change change change spatial assume assume lower lower lower lower lower lower measure signals signals signals signals higher higher higher higher higher higher higher higher part part center center previous previous firing firing multiple spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike spike expected chip chip chip chip fact fact fact proposed proposed proposed length correct correct scale scale scale scale scale scale scale finite resulting resulting total simulation human human respect respect sum sum means means factor factor factor factor factor factor made filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter obtain obtain obtain obtain vol vol artificial relative true true compared series rates rates connected connected connected connected gain gain gain gain gain gain gain gain brain brain equal equal equal voltage voltage voltage voltage voltage voltage comparison larger larger contrast support train implementation implementation implementation implementation version version consists code code individual individual individual represents final final final delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay scheme scheme cambridge equivalent experiment experiment experiment curve curve curve additional additional curves curves curves curves top top top detection detection detection detection detection detection upper full full speed increase increase increase increase coding coding coding coding developed lines actual provided finally finally depends depends simply biological biological measured measured measured increases increases arbitrary group limited close close inverse corresponds corresponds corresponds corresponds circuits circuits circuits circuits implemented implemented implemented shape shape require journal journal square square end vlsi vlsi vlsi vlsi vlsi vlsi vlsi instance easily easily makes auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory simulated pairs pairs needed needed reduced reduced functional increasing principle principle operation operation leads details filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters filters direct normalized normalized normalized bottom bottom bottom bottom depth added added membrane membrane membrane membrane membrane improved population advantage property pair robust takes period period period period period period period period period side engineering compare compare previously approximately approximately approximately yields correspond positions positions observation gate gate gate gate gate sensitive sensitive sensitive amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude intensity intensity intensity intensity intensity intensity intensity intensity scaling scaling digital digital wide spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes spikes correctly move move width width width width setting pass pass pass pass pass pass pass pass pass pass pass pass half half half half half half half half half half place reduce conclusions operator editors measures clear peak exponential exponential exponential faster faster sound sound sound sound encoding encoding integration presence presence cycle cycle cycle cycle cycle solid solid proportional proportional proportional turn selective selective decrease iii manner base base base acknowledgements van van index index plot laboratory vertical vertical vertical vertical changing changing modeled linearly easy slightly slightly spectral spectral spectral scales integrated frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies frequencies shift shift shift quality quality quality quality quality blocks blocks blocks blocks extraction extraction extraction extraction extraction extraction extraction extraction cycles cycles cycles cycles cycles cycles cycles cycles cycles john decreases decreases decreases yield yield yield stages stages stages correlated overlap overlap overlap variation variation controlled modulation modulation modulation modulation centered completely spectrum spectrum earlier reasonable dashed measurements measurements measurements delays delays delays delays reduces combining roughly roughly add generation generation remains filtering filtering filtering advantages building building building building fire silicon silicon silicon silicon silicon silicon silicon silicon silicon combinations plotted discuss absolute encoded effectively spiking spiking spiking spiking spiking spiking detect detect detect detect schemes reached traditional traditional traditional traditional refer quickly quickly sin sin content follow cue simplified realistic wave wave wave wave wave wave wave wave wave delayed delayed highest highest reach reach reach chips chips chips chips extract neighboring rat receive modelling presents trains trains trains trains trains trains trains selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity selectivity create create create create create create exponentially exponentially rapidly rapidly varied varied steady dotted rise reducing respond respond respond detectors detectors understand matched trace trace trace trace trace adapt onset onset created created created created perfect adjusted adjusted aspect aspect detector detector detector nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve nerve fibers fibers fibers fibers fibers fibers generates detected detected simplest electronic electronic integrate percentage slowly band band band band band band band fairly waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform waveform majority cascade cascade cascade cascade ganglion ganglion ganglion snr sections filtered probable cut cut cut cut cut cut cut cut cut cut cut cut axon sounds gradually gradually axons lowest bandwidth bandwidth bandwidth bandwidth demonstrates author nsf robustness explained explained cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear pure pure pure pure pure pure pure transient offset offset slower release modulated modulated modulated fall synchrony fiber traces cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea cochlea instantaneous instantaneous ear ear analogue analogue analogue sort narrow narrow narrow perfectly perfectly lost spiral spiral spiral adds adds khz khz khz khz simplify logarithmic handwriting bands shifts settings settings synchronous synchronous synchronous continue repeat introduces tone tone tone tone tone tone tone periods loo respective equals offers axonal stimulated lazzaro lazzaro arrive waveforms thresholding mechanical accumulated accumulated dramatically crossing sine sine hair hair hair hair hair hair hair kluwer responds responds responds responds medium amplitudes amplitudes amplitudes classic resting suppressed sinusoidal australia reflected eric eric playing disadvantage rectified rectified rectified rectified rectified intensities intensities intensities intensities intensities locking responding crossings barlow intracellular tones tones behave retained drops drops slopes slopes correlate resembles saturated transduction twenty carrier carrier carrier carrier carrier carrier periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity periodicity anatomy settle extracts coincide detects normalize artifact reality drastically senses senses ranged twelve remarkably settles sydney sydney coincidence coincidence leaky basilar basilar basilar steep steep neurotransmitter multiples octave discarding vibration vibration vibration vittoz correlator seneft schaik schaik schaik schaik schaik swiss shamma react react oscilloscope nsw correlators evans airborne traded andr 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#@van-Schaik_A,
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state state state results information information information problem models performance performance based based based based based based based based layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer layer case case order order shown shown shown shown shown shown systems systems systems systems systems systems values parameters noise noise noise noise noise noise noise noise noise noise noise noise weight weight weight weight unit recognition recognition method pattern point point image single single processing processing processing local rate patterns analysis analysis analysis analysis analysis analysis form form form form shows shows shows shows shows signal signal signal gaussian visual paper small small small small size feature feature task step step classification classification process process process process level level level level level cell cell cell structure structure structure random high high high high high response similar similar representation representation show equation section fixed rule speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter real real real theory obtained obtained term term term term term activity activity activity activity activity dimensional dimensional dimensional result result university university university threshold threshold threshold threshold threshold threshold threshold computation computation defined defined defined defined defined found constant computer computer computer computer connections connections connections connections science science science science science prediction present phase phase phase phase phase phase phase phase phase phase frequency frequency frequency frequency frequency frequency frequency frequency frequency object motion maximum maximum press press components components basis basis outputs abstract applied computational computational computational computational computational computational analog analog references component component ieee ieee positive mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction complex stimulus stimulus stimulus stimulus variance parallel search energy energy energy energy energy energy variable variable representations representations chosen chosen chosen higher higher higher part center previous firing firing type type good represent represent represent represent distributed distributed proposed correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation scale scale scale simulation human human computed computed computed called called elements elements regions regions potential potential potential potential potential potential global global global global global applications study filter filter filter represented represented represented represented represented compared cross cross cross cross provide active active active active active active active active active active active active determined related connected approaches mit mit steps steps steps connection connection dependent source source source selection report department department department implementation consists consists represents represents responses delay delay delay delay considered framework framework framework cambridge cambridge cambridge computing equivalent solutions limit limit limit limit limit stage stage stage stage stage stage bit choice significant significant speed estimated estimated basic condition channel channel channel channel channel channel channel derived weighted types path path processes evidence evidence inhibitory inhibitory inhibitory sampling achieved discussion fast fast corresponds excitatory excitatory excitatory stable stable short nearest effective implemented supported role end vlsi vlsi pixel pixel development noisy noisy sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory simulated simulated probabilistic typically underlying underlying needed account account block block ratio ratio segmentation segmentation segmentation segmentation mechanism mechanism mechanism consistent consistent consistent operation language filters window window inhibition inhibition normalized bottom frame frame frame frame frame frame frame combined choose sources description description denotes denotes population recent resolution advantage separate takes takes typical lateral lateral lateral lateral apply period period pixels pixels pixels inference cognitive cognitive cognitive recently recently engineering interest varying axis match correspond correspond correspond correspond studies mixtures mixtures background background background evaluation separation separation separation separation separation separation separation observation grid grid channels channels channels channels channels channels channels channels channels channels channels channels interval organization improvement entire amplitude width width white white white occurs occurs half place place segment segment segment segment segment segment segment segment segment segment segment segment segment segment neighbor sigmoid numerical peak peak performs suggest sound sound sound sound propose propose mechanisms mechanisms integration largest external external cycle cycle start start averaged introduce manner scene scene scene scene scene scene acoustic acoustic acoustic acoustic acoustic acoustic appears produces index index perception winner vertical vertical vertical vertical distinct segments segments segments segments segments segments segments segments segments segments segments segments category category electrical involves slightly unique scales mutual mutual mutual adding frequencies frequencies formed formed formed formed implies implies blocks blocks competition yield review stages overlap influence solved detailed evaluated evaluated evaluated evolution centered frames frames forms static similarly similarly slow neighborhood neighborhood neighborhood intervals intervals event remains initially foundation transactions transactions coupling coupling coupling coupling coupling coupling existing perceptual perceptual perceptual perceptual perceptual usa weighting automatic automatic specifically coupled black black black neighbors neighbors neighbors gating tests simplicity middle identified identified closely closely uniformly computationally divided effectively driven wij wij oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory oscillatory vowel vowel tend tend ten ten ten ten receives receives receives characteristic excitation excitation compact quickly showing interpreted classify running oscillations oscillations physiological categories categories gray gray bar bar sampled relaxation relaxation overlapping subsequent extract neighboring modelling modelling extend selectivity collection rapidly oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators oscillators steady issues oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator behaviour periodic links links links links possibility referred referred stream stream stream stream stream stream stream symbolic tanh oscillation understand fundamental phases phases measurement trace equally changed singular singular front impulse olfactory panel separated separated nerve nerve nerve nerve initialized mixed mixed mixed grouping grouping grouping grouping grouping defines seconds seconds seconds seconds percentage percentage brown brown brown brown brown brown brown brown brown growing waveform adjacent majority processed processed snr snr snr snr snr sections producing sounds sounds sounds sounds sounds sounds sounds sounds sounds pitch pitch pitch arises bandwidth apparent improvements populations double led amounts psychophysical share employ remove music maintain span exhibits exhibits branch replace coherent findings wang wang wang wang wang wang wang wang wang wang wang wang utterances utterances summed contribute initialization spectra physiology forming forming forming harmonic unity unity grey reaching plays inspired khz khz khz khz numerically held attractive primitive abilities bands operates belong belong synchronous corpus exceeds exceeds vowels recovered recovered tone tone male regarded overview evident modelled modelled bursts stimulated stimulated stimulated stimulated stimulated suggesting offer locked environmental environmental waveforms waveforms waveforms parse extends agree formant jump subsequently default lag lag lag lag lag fusion consecutive street ence drop hair hair hair email email bank encouraging centre convenience corrected ease perceived decomposed female female streams streams streams streams rectangular rectangular peripheral peripheral peripheral segregation segregation segregation segregation pij pij pij pij pij pij pij pij pij allocated allocated neurophysiological cosine synchronized synchronized categorization termed emphasized enforce mimic cubic cubic dramatic intensive behaves correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram correlogram autocorrelation autocorrelation autocorrelation autocorrelation autocorrelation hearing telephone telephone telephone telephone telephone telephone telephone dcs periodicity periodicity periodicity excited dissertation core extracts fox ooo resolved sij sij sij sij sij sij cooperation isolation neurobiological neurobiological neurobiological neurobiological implying icl longest longest longest longest raised prominent shortly shortly physica ears silent silent voiced voiced mid mid bregman quantified retrieve ohio ohio organisation intersect intersect conceptually pooled pooled pooled pooled enabled formants desire yij yij yij yij trimming snapshots laterally cooke cooke concurrent concurrent xij xij xij xij xij xij xij xij selector interfering interfering interfering interfering interfering segregated segregated occupy cis iij iij perceptually snapshot snapshot snapshot snapshot informal embodies fragments heard autonomously asa asa asa asa asa asa asa asa decomposes heaviside alternates sheffield sheffield investigators lij lij party alternation rock reciprocally harmonics jumping cocktail columbus synchronizing correlating listeners unsolved listening engines relaxes filterbank windowed segregate segregate seldom desynchronized desynchronized cortices intelligibility ellis arisen listener 
#@Brown_G,Wang_D,
#t13
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#*network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set set set set algorithm algorithm number number number number number number number system system error state state state state state state state state state state state state state state state state state state state state results results problem models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based based based based based based based space space linear linear linear linear linear linear linear linear linear linear case order order order order order order order order shown shown shown values values values values probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise distribution distribution distribution distribution distribution distribution method method pattern image single single single single single processing large large rate test patterns patterns patterns analysis analysis analysis analysis class matrix form form shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal simple simple gaussian gaussian gaussian gaussian visual visual visual visual paper size net net work work task task task task task task task task methods step step step step field level level current current structure structure structure random response response response response response response response response response response response response representation representation show show section section section rule parameter parameter real real average average states states states states states states states states states states experiments experiments experiments activity activity activity activity activity activity activity activity activity university variables variables variables variables variables variables variables computation computation research independent independent independent log defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence sequence estimate estimate standard standard standard standard standard left left left left left left left left direction presented presented map map present present activation activation activation activation activation activation activation activation activation activation activation activation activation activation temporal temporal temporal sets maximum components nonlinear sample sample abstract abstract applied applied applied back computational computational density density likelihood likelihood likelihood likelihood references component due positive procedure procedure procedure procedure adaptive adaptive adaptive mixture introduction complex hand hand estimation stimulus stimulus stimulus statistical generated generated variance variance tion variable variable variable spatial signals prior prior prior prior prior prior chosen part center center previous multiple cortex cortex binary binary binary binary long long conditions represent represent represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian markov markov markov markov markov markov markov markov markov make make make make techniques proposed proposed proposed proposed proposed correlation correlation correlation correlation correlation correlation length length length length length length length length length length length length correct probabilities probabilities probabilities observed forward scale simulations human human human computed computed sum performed called times mapping optimization optimization made global applications filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter filter original relative samples samples true cross series series series series series series series series proc perform experimental experimental experimental experimental experimental experimental experimental related posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions brain brain brain larger larger contrast contrast support dependent department technique technique individual individual responses difficult difficult exp delay delay considered solutions transition transition transition transition transition top top top top top effects effects effects detection requires choice significant statistics estimated basic basic validation con derived conditional conditional types finally finally iteration sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling simply measured measured measured discussion covariance covariance covariance technical hmm hmm limited limited finding finding short common effective assumed generate generate generate journal square end makes noisy including including typically typically underlying combination combination functional functional functional functional unknown coefficients coefficients coefficients coefficients coefficients coefficients block trials trials trials uniform uniform uniform leads principal representing representing iterations iterations normalized bottom bottom bottom bottom bottom attention run run neuronal neuronal neuronal neuronal neuronal neuronal denotes improve improve correlations property reported practical introduced identical inference inference inference inference inference sufficient highly approximately works studies chain chain chain chain chain symmetric observation observation interval interval interval interval interval entire increased suggests suggests trial trial trial trial trial deviation deviation deviation predicted predicted predicted predicted predicted predicted predicted move move boundary setting half half flow conclusion operator measures bayes propose strong integration integration proportional assuming variety movements selective introduce reference reference reference reference explicit explicit relation monte monte monte monte monte carlo carlo carlo carlo carlo longer factors plot plot mathematical implement averaging averaging dimensionality remaining remaining consisting consisting integrated gaussians shift independently stationary correlated squares influence restricted updated centered forms suggested updates updates updates updates updates reasonable reasonable reasonable measurements roughly roughly remains coupling coupling expect expect expect building box activations usa color instances determines plotted plotted uncertainty uncertainty uncertainty discuss activated priors priors priors characterized reason gamma society computationally effectively delta literature situation notice notice notice kind repeated procedures strongly strongly induced symmetry lie generative strategies strategies strategies strategies sci duration notation gibbs gibbs gibbs gibbs gibbs gibbs gibbs bar bar involved usual paradigm paradigm paradigm paradigm paradigm paradigm paradigm backward backward providing wave delayed observable leading consisted mixing neighboring acknowledgments modelling modelling modelling modelling modelling bars bars bars bars updating put integral integral dotted dotted dotted dotted preliminary graphical graphical periodic fourier rest rest investigated variational analytically analytically analytically analytically working neu coefficient necessarily onset onset thought thought front impulse der obvious expressions multivariate multivariate extent contributions explain synthetic synthetic synthetic seconds integrate integrate burst convolution analyzed analytic analytical analytical adapted expensive caused spatially inside turns sections broad acad optimize auto auto explained integrating reflects collected transient pseudo pseudo parameterized readily readily readily orders introducing treated treated psychological exhibits anti green green enables deviations deviations progress simultaneous lot investigation restrict recover recover grey grey royal proceed imaging imaging imaging accepted determination analyzing methodology methodology methodology shifts carry natl reliably governed connect loo displayed lengths lengths scan scan scan scan scan scan scan competing specialized thin bursts omitted informative concentration jump jump explains generalizing std lag lag lag lag consecutive verify resonance resonance resonance blood indirect minus inferred inferred rejection rejection rejection suboptimal spatio encouraging magnetic magnetic magnetic magnetic tween ease superimposed flat flat flat shifting thick rejected acquired conversely drawback hansen hansen hansen hansen hansen hansen paradigms breaks sweeping funded accounted mimic mimic mcmc mcmc mea vice spite handled handled handled versa characterizing generarive identifies bold bold bold reversible reversible eral medicine compo proposal partly partly rasmussen rasmussen rasmussen rasmussen detects inferring concave iid denmark denmark bumps correlates sweep trend trend trend trend metropolis metropolis metropolis metropolis metropolis metropolis vanishing blocked blocked blocked blocked noiseless trapped lange lange accepting nents activa scans scans scans scans scans acceptance pursued tics statis draws penalizing dev kronecker visualized sponse indicative wild wild sev raise indexes edward crossed crossed questionable negatively danish mri carl carl dale dale biometrika sured annular proposing imm nary crn crn crn nance gilks gilks improper improper improper vantage slo neuroinformatics mckeown mckeown lyngby lars founded reso tice jen ihi phs councils ceived invasive ley thor 
#@Hansen_L,Hojen-Sorensen_P,Rasmussen_C,
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#*network network network network network network network network network network network network network network network network network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input data data data data data data data data function figure figure figure figure figure figure figure figure time time time time time time time time time time set set networks networks training training training training training training training training training training algorithm output output output output output number number number number number number number number number system system system system system system system system system system system system system system system system system error error results results results information information information information models models models models models models hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based space space space space space space space weights weights layer layer layer layer layer layer layer layer layer layer case order order order order shown shown shown shown shown shown values probability probability noise noise noise functions neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons distribution distribution distribution distribution distribution distribution method approach point image image image single single single processing processing processing processing processing large large local local local neuron neuron rate test analysis analysis analysis analysis optimal optimal form form shows shows simple gaussian gaussian visual paper size feature feature net net work work work work task task methods fig fig cells step step field field field field field process process process process process process process level level level level level level level level level current current trained trained trained trained structure structure structure structure random random high high high high high high response response response response response response response similar architecture architecture architecture architecture architecture architecture section line line rule speech real experiments activity activity activity dimensional university computation research research research research research research found found found target target target target target constant table table estimate terms terms terms connections connections left left left direction direction direction presented presented presented presented presented presented low low low low low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal temporal temporal sets maximum range range range press components basis abstract back computational computational computational computational computational density properties properties references important propagation introduction complex stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical effect generated generated difference difference difference variable variable spatial spatial spatial spatial spatial assume lower measure measure chosen chosen chosen chosen higher higher part center center center center center center center center center center previous previous previous previous cases required conditions conditions conditions conditions conditions distributed distributed distributed fact region region proposed correlation correlation correlation length length length observed errors errors forward forward scale scale finite minimum ing ing total human human human human human human human human human human human human human human human human human human human human human human human human computed sum performed performed regions factor factor made made natural orientation global applications knowledge knowledge filter filter filter filter vol vol vol vol vol specific represented compared compared compared cross cross receptive location location location location location location location location location location location location location location location location location location related related related constraints constraints constraints constraints connected connected approaches steps comparison comparison connection fields train source source source source source source source source source modeling modeling modeling modeling modeling modeling institute department department department version technique individual individual kernel kernel kernel kernel kernel responses responses responses responses layers layers layers delay delay delay delay addition cambridge cambridge view solutions stage stage stimuli stimuli stimuli stimuli stimuli stimuli stimuli effects effects determine statistics free free free free free world basic increase increase validation con con produce condition condition condition condition condition channel channel coding derived randomly randomly clustering developed levels levels path actual provided provided finally processes processes evidence evidence nature biological biological achieved measured normal describe group group tested tested surface finding amount short effective generate supported role role role role require ability ability ability development auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory typically typically underlying fully fully fully transfer transfer york head head head head head head consistent trials matching uniform database principal squared representing details numbers filters filters pre pre window magnitude decay combined added architectures improved recent recent resolution resolution resolution resolution exact robust robust include subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject side relevant relevant relevant engineering sufficient sufficient highly varying varying varying varying calculated tions speaker correspond correspond studies locations locations locations locations observation channels channels channels channels channels channels channels channels channels channels channels channels channels channels interval organization organization entire entire increased increased arm exists suggests trial trial wide width width white generally generally generally pass pass pass pass pass pass pass pass pass pass demonstrate conclusions depend differences clear peak constrained sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound integration external characteristics characteristics demonstrated demonstrated demonstrated manner manner groups groups groups identification pro van primary describes ann explicitly simultaneously physical electrical slightly spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral consisting consisting develop integrated integrated frequencies frequencies frequencies frequencies formed quality expressed review stages correlated detailed detailed restricted restricted restricted restricted updated centered understanding similarly similarly allowed spectrum spectrum spectrum spectrum spectrum partial reasonable measurements measurements measurements generation remains filtering filtering filtering filtering filtering filtering filtering filtering filtering filtering filtering advantages existing template template illustrated variations black tests major determining sensor encoded presentation spiking tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn tdnn plots essentially ten characteristic summary traditional soc soc soc soc soc repeated repeated contained contained anderson split physiological physiological physiological cue cues cues cues cues cues cues cues cues built involved vary vary localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization play dot dot paradigm paradigm providing highest received consisted consisted moves overlapping overlapping acknowledgments modelling explore carried carried carried essential humans humans accurately hall behaviour fashion authors authors proper encode cover notion matched matched matched matched matched matched matched matched matched matched examined examined examined measurement coefficient plausible plausible man illustrate equally equally impulse obvious fisher explored nerve nerve nervous nervous fibers fibers submitted submitted attempts established animal mentioned band band band band band band band band band publishers analyzed defining explanation comparisons comparisons considerable processed processed straight arc easier easier organized producing producing filtered filtered filtered division division division division division division division division division division directional directional incorporate incorporate incorporate commonly sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds sounds involve describing bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth bandwidth demonstrates qualitative radius outer outer outer outer robustness virtual virtual virtual fourth evaluating profile cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear cochlear amounts poorly psychophysical psychophysical psychophysical passed passed passed passed passed biologically biologically compares summarized ture aim aim aim aim qualitatively prevent acoustics substantial substantial inherent comments specifies cochlea cochlea summed univ univ gap gap ear ear ear ear ear ear ear ear ear ear ear physiology physiology equivalence appropriately appropriately narrow narrow concerned establish khz khz ments accepted logarithmic logarithmic stated multiplicative imposed imposed viewpoint occurring bands reasoning reasoning presentations degradation meaningful performances ambiguity cone respective widths accounts sphere sphere lawrence spherical spherical spherical competing arrangement arrangement arrangement dif young matter observer erlbaum broken valuable avoiding vari numerous incorporates pointing hair ber ties ease perceived spaced flat demon australia australia peripheral distri chapman ization ization fir frontal nuclei nuclei associates confusion psychophysics struc vice bution demonstrating versa differently bridge acoust acoust acoust acoust acoust tdnns tdnns tdnns tial hearing hearing hearing hearing hearing jersey interaural interaural interaural played integrates fre fre cally condi acoustical acoustical acoustical acoustical acoustical evenly evenly progressively progressively chan carries archi placement periphery explanations explanations bandpass bandpass bandpass robotic robotic evolutionary lewis remained cess brainstem brainstem broadband broadband broadband broadband broadband broadband broadband broadband ild ild prominent derives blocked spa ears ears ears monitored tory simon sented correlational ference phones phones sydney sydney ness simulates simulates gross gross examines imaginary dominate reviews accu quency quency biomedical localize localize localize localize schneider nections ascending convolving tecture neti itd itd itd experimentation environ standing fil contiguous contiguous bandwidths divides mary originating binaural bypass standpoint nose leong chamber organ render strated interconnects encouraged encouraged illusion incor pertinent schaik vas vas vas vas vas vas schenkel schenkel markus pulled tual ditions ject ject semicircular vastly evidenced nels tering prey dominating argues argues vious scholarship nsw nsw undertaken listeners meter hemispheres hemispheres din fied electromagnetic spectrally spectrally craig realism realism andr fresh modi graceful corti porated jin jin jin jin isation crux nomenclature localizes congruence darkened mahwah chitectures audi predators 
#@Carlile_S,Jin_C,
#t13
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#*model model model model neural neural neural neural neural input data data data data data function function function function figure figure figure figure figure figure figure figure time time time time time time time set set networks networks output system system system system system error information information information problem problem models performance performance performance performance performance performance performance based space space space space space space space space space space space space space case vector order order order shown shown shown shown shown values values values values values values values values values values values values values values values values values values values values values values values values values values values noise noise noise noise noise functions functions distribution distribution method approach pattern pattern pattern pattern single processing control control control control control control control control large test test patterns analysis analysis analysis analysis analysis shows shows signal signal gaussian work work task methods methods methods methods fig fig fig fig fig fig fig fig fig fig fig points field field process process level level level level level level random high response response response response response response response response response response response response response response similar similar similar show show section vectors general real real approximation average obtained obtained term experiments experiments activity activity result result research research research log found target target target target target target target target target target target target target target target target estimate standard standard standard standard standard standard standard left left left left left left left left left left left left left direction direction presented presented presented presented presented phase low low low frequency frequency frequency frequency frequency frequency range position basis basis abstract back back back computational properties references positive introduction estimation stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical tion change energy energy difference difference difference difference difference difference difference difference difference difference difference difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial measure measure measure measure measure representations higher higher previous conditions conditions conditions conditions conditions conditions conditions conditions represent distributed make correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correlation correct correct correct scale minimum resulting resulting classes total total human human human human human human human human human human human human human respect performed performed regions regions regions regions optimization made made made natural orientation applications study study filter filter filter negative negative vol vol vol relative relative relative relative relative specific true true true true compared compared compared compared cross cross location location location location location location location location location location location location location location location location location location location location location location location location location location location location location location location location location determined related related contrast dependent source source source source source source source institute words department department department department department version technique individual individual individual individual responses responses responses responses responses responses responses responses responses responses responses responses responses delay delay graph environment curve stimuli stimuli stimuli stimuli stimuli stimuli stimuli stimuli determine significant free free estimated estimated basic give produce condition condition condition condition condition condition condition condition condition condition condition condition channel developed area product provided provided evidence depends measured measured normal normal surface predictions amount short shape shape shape generate generate supported role role role eds eds ability ability auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory transfer transfer transfer york head head head consistent consistent trials trials trials trials details filters filters filters filters normalized normalized combined sources light directions directions recent similarity similarity lateral subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject subject side side engineering engineering dimensions sufficient sufficient highly highly observations observations approximately approximately subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects subjects calculated calculated calculated calculated calculated calculated axis axis tions match differential positions positions locations locations locations locations locations locations locations locations locations locations locations locations locations locations symmetric modified channels amplitude suggests deviation deviation deviation deviation deviation deviation alternative width white white generally generally generally pass demonstrate demonstrate greater greater conclusions differences differences differences differences accurate accurate clear exponential suggest sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound taking integration demonstrated assuming variety relationship relationship averaged manner manner manner relation van derive plot plot mathematical mathematical modeled electrical electrical text text spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral extraction versus dependence review correlated correlated correlated correlated correlated correlated variation variation variation variation detailed detailed evaluate restricted restricted restricted showed spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum calculation calculation measurements false generation remains filtering filtering filtering advantages advantages recorded figures figures color inter plotted variations black absolute characterized characterized characterized sensor closely importance score score score score score score score score score score score score score score score score score score score plots plots excitation excitation excitation excitation summary soc soc graphs strongly strongly moore moore moore anderson anderson anderson dis lie contribution contribution content physiological follow timing cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue 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approximating acknowledgments bars bars unlike carried varied varied varied environments environments humans humans accurately hall fashion history variational authors removed neu examined examined examined examined plausible onset man adjusted adjusted front front front impulse obvious precise nerve nerve shapes extent extent band derivation analyzed analytical analytical briefly comparisons comparisons considerable considerable arc closer filtered filtered filtered filtered filtered commonly sounds sounds sounds sounds sounds calculations localized demonstrates demonstrates demonstrates demonstrates demonstrates outer outer outer robustness virtual virtual virtual virtual virtual virtual virtual virtual virtual virtual fourth varies considerably substantially cochlear cochlear cochlear cochlear cochlear transient offset conducted psychophysical recordings biologically ity calculating measuring aim gen extracting cal cal acoustics gave coherent shaped deviations cochlea univ univ univ univ cor representative spectra aligned ear ear ear ear ear ear ear ear ear ear ear ear ear physiology physiology physiology summing linearity narrow acts establish systematic systematic systematic khz ments accepted logarithmic viewpoint ral salient meaningful meaningful analyses ambiguity cone cone cone cone cone cone cone cone cone cone cone cone cone cone surprising dominant evident evident evident sphere facilitate facilitate lawrence lawrence centroid modelled reveals rich observer erlbaum erlbaum vari dividing lag geometrical logarithm pointing opposed revealed preserving perceived perceived spaced flat flat flat flat flat flat demon australia australia australia australia arising peripheral preserved trends insights duda chapman mathematically argued surrounding cosine termed cation cation associates associates preserve responding confusion confusion confusion confusion confusion confusion confusion confusion confusion confusion confusion matlab differing examination examination correlate correlate moderate acoust acoust resolve influenced hearing hearing hearing jersey jersey lated lated lated contralateral contralateral contralateral contralateral contralateral interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural interaural played condi condi tribution acoustical acoustical acoustical acoustical acoustical acoustical acoustical acoustical acoustical acoustical evenly subtracting anna manipulated manipulated trol periphery periphery systematically tended evolutionary absent hinge correlates broadband broadband broadband broadband broadband broadband broadband broadband broadband raised indepen ild ild ild ild percept blocked indi ears ears inappropriate monitored ipsilateral ipsilateral ipsilateral ipsilateral simon spec moderately asymmetry elevation elevation remarkably heights sydney sydney sydney sydney biomedical localize pooled manipulations stim ously itd itd itd itd itd itd itd utilization azimuth azimuth azimuth psy rescaled rescaled rescaled binaural binaural bypass nose nose amples chamber chamber strated ations prepared ner confusions signif illusion lesser eps eps eps eps eps shed depended schaik schaik schaik sponses sponses sponses asymmetrical vas vas vas vas vas locus hemisphere hemisphere hear calcu calcu viability scholarship nsw nsw nsw nsw judgements rounded tral erated bilateral ulus carded principally pulling icant rig hemispheres din din din electromagnetic spectrally spectrally spectrally spectrally spectrally spectrally craig chophysical reliance ellipse ellipse andr simultane jin recalculated recalculated recalculated psi centtold compressive ects darkened mahwah mahwah dently 
#@Carlile_S,Corderoy_A,Jin_C,van-Schaik_A,
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#*model model model model model model model model model model model input data data data data data data data data data data data data function function figure figure time time time time time time time time time time time time time set set algorithm output output number system system error error results results results results results results results results results information information problem problem problem problem based based based based based based based based based based space space linear case case case case case case order order order order order order order order order order order order order order order parameters parameters parameters parameters parameters parameters noise noise noise noise functions functions unit method method method approach approach approach approach approach point processing processing processing processing processing processing processing processing large analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs inputs inputs inputs form form form form form shows shows signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms paper paper paper paper size feature work work methods methods field process process process process structure structure similar similar architecture show show show equation equation equation equation equation equation equation equation section rule general general speech speech speech parameter parameter parameter real real real real approximation approximation approximation theory obtained obtained term term note note note note dimensional result solution solution research research research independent independent independent defined defined found constant estimate estimate estimate estimate estimate standard standard terms terms terms terms terms terms distance distance distance distance distance distance distance distance distance distance distance distance distance direction direction direction presented map present present phase low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency sets sets position components components basis basis basis outputs outputs outputs outputs outputs outputs outputs outputs outputs abstract applied applied applied back back computational density references component due due due ieee ieee ieee positive procedure important adaptive adaptive adaptive propagation propagation propagation propagation propagation mixture mixture mixture mixture introduction estimation estimation estimation estimation estimation estimation estimation estimation statistical effect generated variance difference complexity spatial spatial spatial spatial assume assume signals signals signals signals signals signals signals signals signals cases type required multiple multiple multiple conditions equations equations equations equations techniques techniques correlation correlation correlation computed respect respect respect respect multi multi multi multi multi multi multi multi multi elements elements knowledge filter filter filter filter filter filter filter filter filter filter obtain obtain obtain obtain original original relative specific represented compared cross cross cross cross cross provide experimental experimental equal power power power approaches steps accuracy source source source source source source source source source source source source source source source source source source source selection selection report implementation technique delay delay delay delay delay delay delay delay delay delay delay delay delay delay delay considered considered considered computing domain domain domain domain domain domain domain domain domain domain domain domain equivalent additional solutions estimates estimates transition requires choice statistics statistics statistics statistics statistics statistics statistics statistics free world world speed speed estimated estimated estimated estimated pages pages pages channel channel channel channel channel channel developed developed criterion criterion criterion criterion path path path path path path path path path path path path path path finally depends depends depends depends sampling constraint constraint discussion covariance technical describe describe arbitrary fast inverse inverse inverse proof implemented implemented implemented role theoretical theoretical theoretical theoretical main main including typically reduced account account account unknown unknown unknown coefficients testing increasing uniform leads representing numbers filters direct direct direct direct direct direct making making international international decay idea idea sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources directions directions correlations correlations correlations correlations advantage pair pair pair robust robust robust robust robust separate include period array array array dimensions dimensions highly works axis axis solve yields correspond correspond rl trans diagonal diagonal address mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures positions positions separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation symmetric generalized channels improvement amplitude amplitude concept invariant scaling suggests deviation matrices white generally generally row greater reduce conclusions differences differences differences measures designed practice constrained suggest taking taking characteristics ica identification relation van written estimating describes describes modeled implement explicitly physical physical angle unique spectral spectral spectral frequencies applying minimization quality quality implies implies blocks focus expressed expressed dependence solved detailed densities sign reasonable measurements delays delays delays delays delays delays delays delays delays expansion reduces reduces valid filtering filtering foundation foundation degrees degrees degrees avoid recorded recorded combinations priori blind blind blind blind blind domains domains phys discussions characterized successfully reason columns determining closely closely closely capable uniformly divided successful identify literature post plots essentially essentially road compact kind symmetry symmetry criteria device cues cues providing wave delayed delayed correspondence principles operating mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing acknowledgments presents presents presents bars carried requirements difficulty scalar fourier fourier ideal scaled reliable proved workshop workshop phases matched integer rev equally ensure versions versions separated separated separated generates arbitrarily synthetic synthetic synthetic synthetic synthetic synthetic averages great cos cos sensors convolution improves analytical independence caused sections strictly filtered filtered precisely precisely directional directional directional angles angles angles angles angles improvements applies empirically experimentally recordings prevent kinds conclude windows simultaneous instantaneous pose college college sort proportion primarily primarily guarantee extensive extensive princeton princeton ratios perfectly concerned concerned purely unity arrival arrival arrival arrival arrival arrival arrival arrival arrival communications systematic siemens siemens siemens siemens splitting receiver receiver receiver interference document separating separating decide decide moved artifacts artifacts waves permutation express layout arrive theoretically relies lett summarize outlined divide dramatically audio audio audio break break july formulate preserving expanding medium obtains spaced spaced spaced flat decorrelation decorrelation decorrelation care impose distant distant fir singularities cosine cosine employing employing france france inverting det det det det dramatic drops challenge helps simplification january january corporate corporate jersey east determinant determinant determinant determinant determinant affecting formulae distinguishing compensation core bss bss bss bss bss bss bss separates substitution symmetrical degenerate degenerate arriving attenuation receivers receivers receivers receivers receivers receivers receivers receivers receivers receivers receivers receivers receivers receivers receivers receivers binomial physically scott essence magazine magazine magazine brackets broadband broadband broadband broadband antenna tim decades modest wiener wiener wiener wiener wiener wiener rij schuster joseph argmin vries fractional fractional fractional fractional whilst invert spence parra rescaling pursued imposing alexander henceforth positioned orthogonality demixing demixing demixing demixing demixing demixing demixing bears multiples wireless gation arrivals unknowns resemblance decorrelated clay postprocessing absorbed kevin midpoint midpoint necessitates dictates bert absorption oth directionality compensating aids ine propa versatile dod rii lucas ris ris ris redefine dispersive wideband wideband synthetically zeroth ameliorate convolutive voices redefinition scr collaborators 
#@Jourjine_A,Rickard_S,Rosca_J,Ruanaidh_J,
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time set set set set training training training training training training training algorithm algorithm output output output output output output output output output output output output output output output output number number number number system system system system system system system system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results units units units information information information information information problem problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden based space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space linear linear linear linear linear linear linear case case case case case case case vector vector vector vector vector vector vector order shown shown shown shown shown shown shown shown shown shown systems systems systems systems systems values probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise unit unit unit unit unit distribution distribution distribution distribution distribution distribution distribution distribution recognition approach point point single single single single single single single single single processing processing control control control local local local rate test test test test analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal shows shows shows shows shows signal signal signal signal simple gaussian paper paper examples small small size size feature feature feature feature work work work task task methods methods methods fig cells cells cells cells cells cells step points points points points points points features features features features features features process process process current current trained trained trained trained trained cell cell cell cell cell cell cell cell cell structure structure structure structure structure structure structure problems random random high high high similar similar similar similar similar similar similar representation representation architecture show show show show show show section line line line rule rule rule vectors vectors vectors vectors vectors vectors speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter real real real real real average average states states states states states states theory obtained obtained term note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional university university university variables variables variables variables variables variables variables variables variables variables defined defined sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics estimate standard standard standard distance distance distance distance left left left left left left left map map map map map map map map map map present low low low frequency machine machine motion motion motion learn learn learn position position position position position position nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs outputs outputs continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous continuous sample sample sample sample sample sample sample abstract applied applied applied find find find convergence convergence convergence properties likelihood references references stochastic due ieee procedure important important complex complex complex complex hand hand hand statistical dynamic dynamic generated generated generated change change change energy energy energy difference variable variable variable variable variable variable spatial spatial spatial lower lower measure learned learned learned learned learned higher higher part previous cases type type multiple good good long long long conditions conditions represent represent represent markov markov markov markov markov markov markov markov markov markov markov markov make make make fact fact region region length correct probabilities probabilities probabilities probabilities probabilities observed observed observed observed observed observed forward forward forward scale scale scale minimum ing human regression regression computed multi performed performed performed called times regions regions regions regions mapping mapping mapping mapping mapping mapping mapping means means factor natural global global global global global applications em original samples samples samples samples samples samples samples true true true true application application cross cross cross series series series series series provide provide provide provide provide provide define define define compute location location location location experimental related constraints constraints constraints constraints constraints connected connected connected connected connected connected connected connected connected distributions distributions distributions distributions discrete discrete discrete discrete discrete discrete discrete discrete equal equal approaches update train dependent dependent modeling modeling words words words words version version code difficult final final final sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences sequences maps maps maps considered computing equivalent environment directly directly transition transition transition transition transition transition transition transition transition transition transition transition transition transition trajectory trajectory trajectory trajectory top effects efficient upper requires requires significant free estimated basic validation give con produce produce derived developed robot area lines lines entropy actual actual provided finally processes iteration iteration nature nature depends sampling constraint measured measured measured measured measured covariance covariance arbitrary group group group hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm hmm transformation transformation close inverse inverse inverse complete complete finding amount short short short nearest nearest nearest nearest nearest shape shape shape shape shape shape shape generate generate generate generate generate face face face square easily easily degree makes makes makes noisy noisy noisy noisy including fit probabilistic probabilistic probabilistic typically underlying underlying underlying underlying underlying underlying underlying underlying underlying account dynamical dynamical dynamical unknown block block character character edge head special structures database database database principle principle details numbers numbers iterations pre direct making window window bits supervised early early idea idea idea choose predict discussed discussed recent recent resolution pair separate separate movement movement movement movement reported reported reported apply apply identical side inference inference inference inference inference inference inference subset interest dimensions highly highly previously previously previously conventional unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised observations observations subjects volume volume volume works works solve smooth smooth smooth smooth yields yields speaker speaker speaker speaker speaker speaker speaker speaker correspond trans sparse sparse address address definition mixtures mixtures positions positions positions positions positions positions positions positions positions positions positions positions positions positions positions positions chain locations locations separation separation observation entire entire amplitude horizontal horizontal horizontal scaling occur deviation matrices matrices rotation move move move boundary boundary column column runs flow flow starting place place place trajectories trajectories trajectories trajectories trajectories conclusions valued valued valued measures constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained constrained temperature temperature sound sound hard presence presence proportional proportional user exist movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements movements plane relationship minima minima configuration configuration annealing annealing acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic force construct winner primary plot transitions transitions transitions transitions transitions vertical vertical vertical vertical metric explicitly coordinates coordinates averaging physical physical physical physical physical dimensionality dimensionality dimensionality involves easy text unique spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral frequencies frequencies versus yield choosing interpretation restricted updated updated updated fraction static completely suggested spectrum key key key key key key key key key earlier earlier reasonable smoothing smoothing smoothing smoothing smoothing measurements measurements sec sec roughly roughly roughly add tracking valid valid symbol symbol symbol symbol symbol symbol assigned norm norm kohonen faces topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology topology avoid building coordinate contour plotted plotted absolute characterized characterized structural successfully regular sensor sensor selecting capable hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms hmms society effectively paths paths paths paths paths paths symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols symbols included latent latent latent latent latent latent latent latent latent plots essentially capture capture capture excitation excitation traditional traditional notice repeated repeated repeated procedures procedures procedures decoding decoding decoding allowing video success link showing dis generative list list sampled sampled paradigm backward backward nips nips nips ill ill attempt attempt overlapping illustrates illustrates deal deal body unlike powerful powerful powerful transformed poor production production production production access essential essential essential exhibit difficulty kalman kalman kalman kalman relations limitations accurately game game game game game game game game game game mass dataset periodic rise giving history ideas mappings mappings mappings mappings mappings investigated investigated investigated structured structured structured structured structured structured root comparable complicated cover cover topographic analogous measurement measurement naturally reading configurations configurations configurations configurations opposite extremely extremely illustrate equally equally thought ensure versions panel freedom multivariate generates generates improving regime arbitrarily explain explain defines defines defines synthetic sentences mentioned mentioned histogram indicating slowly slowly slowly slowly directed directed directed crucial smoothness defining waveform waveform diffusion baum baum london spatially easier easier easier producing directional directional incorporate located located inversion inversion inversion sounds sounds sounds english read radius geometric collected understood axes axes experimentally posed posed dots dots dots dots dots dots incorrect passes prototypes rely mod spread spread ordered extensions suited acoustics acoustics acoustics acoustics acoustics acoustics acoustics acoustics decoder display viterbi viterbi viterbi june multidimensional extreme naive spectra college identifying sort assign velocities velocities recover recover recover recover discovery discover impossible khz difficulties city nearby nearby bands exploit utterance utterance utterance utterance lip lip recovered recovered guarantees topological sim uni captured initialize initialize winning recovery recovery recovery recovery recovery recovery young infer infer thin insight verification informative severe divide pressure audio audio audio audio audio audio audio converted gold ram ram gaps welch welch smoothly smoothly smoothly smoothly restrictions centre centre residuals generalizations generalizations ical covariances clustered reconstruct reconstruct continuity constrain constrain acting unseen unseen attempted attempted evolve articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator articulator thick thick thick thick thick playing playing mouth mouth mouth mouth mouth mouth mouth relate considers smyth smyth retain regimes names records win sheet sheet sheet sheet sheet setup attached figs discretization sam reveal inverting articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory articulatory cubic cubic cubic cubic places mini mini topologies topologies topologies persistent covers stores stores font discretized confirm generafive compete played lists flows flows flows inherently tip spectrogram acoustical coincide inferring ray ray ray neighbourhood neighbourhood america interpolate reflection multimodal evolves wisconsin wisconsin articulation articulation zeros handbook enforces raised energies ated recovering simon voiced winners bodies enforcing quantified neigh neigh neigh tracked tongue tongue tongue tongue tongue tongue tongue tongue tongue tongue trick madison accessible retrained puted thinking dissimilarity impressive articulated dynam snapshots gatsby centred panels contiguous inferences nix permitted neighbours neighbours neighbours neighbours neighbours neighbours neighbours neighbouring rutgers nected illustrative manageable ucl private private hexagonal inspiration reachable packing packing packing packing packing packing packing packing packing jaw roweis roweis roweis roweis associ abrupt ink obeying constrains readings readings articulators articulators regressions eft eft mahalanobis mahalanobis lends unsuccessful diffusive unvoiced fills ellipses ellipses waterloo ulations fictitious fictitious ellipse depiction sondhi precomputed paragraphs multimodality multimodality occupation occupation blackburn blackburn circled loglikelihood viously navigates impoverished eurospeech eurospeech ize actly mml 
#@Roweis_S,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural data data data data function function function figure figure figure figure time time time time time time time set networks networks networks networks networks networks networks networks networks networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system error error results results information information information information problem models performance performance performance performance weights weights weights linear linear linear linear linear linear layer case case case vector vector vector order order order order systems systems systems systems systems values values parameters parameters weight weight weight weight distribution method method method method approach approach approach approach approach point single single single processing processing large local local local local local local local local local local local local local local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate analysis analysis analysis analysis analysis analysis analysis class matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal inputs shows shows signal signal signal paper small small work work work methods methods methods methods step step step step points level level level level level current current current line line line rule general parameter parameter real approximation approximation approximation approximation average average average average theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient term term term note experiments result university threshold computation computation computation computation solution solution independent independent independent independent independent independent independent independent independent defined found found found sequence estimate estimate estimate estimate science prediction left direction present low range press press press press basis nonlinear nonlinear continuous abstract back back find find find computational convergence convergence convergence properties properties references component component component component component component component component component stochastic stochastic stochastic stochastic stochastic stochastic ieee ieee ieee ieee positive adaptive adaptive adaptive adaptive adaptive propagation propagation mixture mixture mixture mixture introduction estimation estimation estimation estimation effect effect effect effect effect effect dynamic generated variance recurrent recurrent tion change change change change change change change change complexity lower lower measure chosen previous cases required good good good good long long long conditions represent distributed distributed expected make fact forward resulting resulting ing respect multi multi times factor optimization natural natural global global global global obtain negative vol vol artificial artificial artificial samples samples application define define compute rates rates rates rates rates rates rates rates rates rates proc proc proc proc proc proc goal gain gain mit mit mit contrast update update update update update update descent descent descent descent descent descent descent descent descent descent descent descent descent descent source source nets nets modeling proceedings proceedings institute loss version technique technique technique technique individual individual advances advances represents exp bias scheme scheme addition ai cambridge cambridge cambridge cambridge computing computing computing experiment view trajectory trajectory san effects conference conference conference efficient efficient upper full full choice free estimated basic condition condition condition criterion product product product actual nature feedforward arbitrary tested fast fast fast fast close inverse assumption stable stable common effective implemented supported require main eds eds adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation adaptation future future including fit fit fit typically typically account account unknown unknown unknown unknown coefficients coefficients coefficients fully jordan projection york york special matching empirical mode max max direct international international combined minimize run sources sources sources sources sources sources sources sources sources sources sources denotes denotes improved improve exact exact advantage robust element element typical apply apply apply apply include sejnowski sejnowski sejnowski relevant sufficient highly varying varying varying unsupervised match pca achieve trans definition mixtures mixtures separation separation separation separation separation separation modified williams increased scaling scaling extended extended extended wide alternative correctly move move move touretzky column column column setting starting reduce trajectories conclusions operator operator operator operator measures sutton sutton sutton exponential exponential exponential exponential faster faster faster asymptotic california intelligence ica ica ica ica ica ica ica ica ica iii annealing force base base explicit index index describes changing changing averaging linearly scales equilibrium equilibrium springer quality versus versus national national independently dependence depending squares squares squares variation forms sizes sizes converges updates updates updates past past past sign sign additive normalization iterative iterative tracking tracking tracking tracking tracking remains remains valid calculate calculate foundation avoid avoid expect priori priori perceptrons bell bell bell blind blind blind blind blind subspace batch mozer mozer columns columns efficiency capable capable suitable divided delta delta literature efficiently online online online online online online online online online online online online ten compact conf conf verlag quickly heuristic link showing sin running running follow quantity bar ill maximization mixing mixing mixing mixing mixing mixing jacobs acknowledgments perturbation access rapidly environments environments replaced association accurately hessian hessian hessian hessian giving tech tech tech tech incremental incremental int int ideal authors comparable tanh tanh tanh tanh workshop func cover momentum gradients gradients gradients trace trace trace adapt rank versions assumes store amari amari residual advanced cos trivial track adapted expensive multiplication multiplication handle nonlinearity london considerable sys strictly products circle computers annual researchers prop empirically axes backprop employ rep rep http http switch switch berlin prevent conditioning conditioning conditioning wang baird june differentiable differentiable instantaneous globally newton newton tation tation acm conditioned velocities unity fails multiplier multiplier air oja proceeds serves serves occurring settings modifications symposium continue separating separating separating ambiguity periods predictors conjunction sim sim uni facilitate hasselmo yang tic francisco permutation warmuth warmuth arrows pearlmutter pearlmutter exploiting santa papers speeds speeds grants yale zipser saad vec vec vec emergent kurtosis kurtosis kurtosis tradeoff chapter constitutes affects affects edinburgh adapting constrain pub pub pub pub pub pub ftp ftp ftp ftp ftp diag diag tems deconvolution wise confirmed differentiation singularities player meta meta meta meta meta meta meta meta meta meta meta meta spanned preserve confusion suffer esti elsevier nil travel mini continually handled resp fft fft fft fft petsche discarded normalize characterizes arrives degenerate implied crl cruz kivinen kivinen carrying shop ically translate cichocki texas texas putation amsterdam murata schraudolph schraudolph schraudolph schraudolph schraudolph schraudolph schraudolph facilitates retaining cations elaborate inserting italy forgetting wright wright versity ucsc switzerland adap adap notably mate agation machinery exceeded ously perspectives ordinate unmixing unmixing temporary exponentiated exponentiated exponentiated singularity karhunen karhunen stochas braun skew beats almeida almeida almeida generalised renders linearization publications exponentiation swiss iee disabled patterson stochasticity stochasticity batches silva whitening whitening rests mfiller loth harmon scotland eckmiller diverging speeding typ radically ellipses rprop halfway simultane tempting modifi girolami owt erty houston houston signifies unobservable multaneously italian elliptic elliptic partials staying stray qth corso mentary avionics 
#@Giannakopoulos_X,Schraudolph_N,
#t13
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#*model model model model model model model model model model model model model input data data data function function function function function figure figure figure figure figure time time time time time time time time time set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output output number system system system system system system system system system system system system system system system system system system error error error state state state state state state state state state state state state state state state state state state state state state state results problem problem problem models models models models hidden based space space space space space space space space space space space space linear linear linear linear linear linear linear vector vector order order order order order order shown systems parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight method method method method method local local analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal form shows shows shows signal signal algorithms algorithms algorithms algorithms algorithms algorithms gaussian paper paper paper paper paper paper paper small size size work work work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods methods step process process current structure high similar similar similar similar similar similar equation equation section section section section section fixed fixed fixed vectors general speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech parameter parameter parameter parameter parameter real real approximation approximation average average average states states states states states states states theory theory theory theory theory obtained obtained note experiments experiments experiments experiments experiments experiments university university university university university university threshold variables variables research research log defined defined defined defined sequence sequence sequence sequence sequence sequence sequence sequence sequence initial initial initial estimate estimate estimate estimate estimate estimate estimate standard standard computer computer computer terms terms science science science prediction prediction prediction presented present phase phase phase low frequency frequency frequency frequency maximum maximum maximum maximum press outputs outputs outputs outputs sample abstract applied applied applied applied applied applied convergence convergence likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic stochastic due due due positive positive positive positive positive important introduction estimation estimation estimation estimation estimation estimation estimation parallel energy difference variable signals prior prior higher higher higher previous previous type conditions conditions expected equations equations equations equations equations techniques techniques techniques techniques techniques techniques techniques length length length forward finite minimum respect multi multi global applications applications em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em vol vol relative represented true compared compared compared determined determined related related mit comparison comparison comparison report department department implementation version technique technique consists difficult final bias bias scheme sequences considered cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge cambridge domain directly hinton estimates estimates estimates estimates stage stage stage stage stage determine requires requires estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated increase con produce produce derived criterion criterion criterion iteration iteration iteration iteration constraint constraint constraint discussion discussion covariance covariance covariance inverse amount common assumed assumed supported supported require journal future future future future future development including probabilistic probabilistic dynamical dynamical fully block block block block block block interesting projection projection projection projection database details iterations iterations max filters filters window frame frame frame frame resolution resolution typical similarity similarity apply introduced moving subject quadratic sense engineering engineering engineering engineering dimensions compare compare compare conventional conventional conventional observations observations observations observations observations observations tions diagonal definition definition definition definition modified observation observation gate lead lead invariant invariant extended extended extended matrices matrices matrices white column row row greater greater greater trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories conclusions numerical numerical numerical taking taking external turn user manner minima identification identification identification identification identification identification identification identification identification identification identification denoted denoted acknowledgements pro pro van van generating estimating describes transitions stability dept dept dept sensitivity involves involves expectation expectation expectation expectation john depending stationary stationary stationary stationary stages stages squares squares squares squares overlap detailed detailed transform updated frames frames frames frames frames frames decomposition similarly similarly similarly converges past past past partial slow spaces fitting iterative iterative iterative iterative iterative iterative foundation foundation norm advantages figures usa usa formulation eigenvalues weighting weighting weighting weighting subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace extension reason columns differ divided schemes schemes schemes schemes schemes schemes schemes vowel vowel plots plots plots identity identity orthogonal orthogonal composed refer refer moore split criteria criteria device duration sampled overlapping overlapping software software software software software software modelling modelling modelling modelling simpler wiley poor poor investigate kalman kalman kalman kalman kalman kalman kalman kalman steady hall hall ml ml ml behaviour giving tech tech tech project rank singular singular separated academic piecewise publishers waveform waveform waveform waveform waveform waveform waveform waveform explanation london reasons tive berkeley berkeley sys sys division potentially toronto res demonstrates robustness applies empirically spoken conducted employ employ rep rep rep compares compares robinson robinson robinson robinson robinson polynomials aim popular extensions replace logp logp logp logp logp logp hamming comments comments expectations univ univ arithmetic arithmetic shifted ghahramani ghahramani newton college college www writing temporally flexibility enhancement enhancement smith smith smith smith smith smith smith khz ments hope phrase prentice introduces introduces loo male guarantees guarantees guarantees sim modelled modelled modelled eng eng park formant formant formant formant formant formant formant formant formant formant sons likelihoods likelihoods likelihoods likelihoods likelihoods cam cam balanced largely kluwer bank restrictions icassp quasi arg arg england england england principled tems tems blocking gas pos termed breaks sam suffer siam esti grateful modality nal matlab matlab experi gauss reversed instability cliffs firstly firstly firstly firstly smoother smoother smoother smoother smoother adult dcs cast award supplied val svd spectrogram spectrogram spectrogram spectrogram ters subtracted assessment englewood autoregressive autoregressive zoubin tracks html randomness niranjan niranjan niranjan niranjan niranjan niranjan south cess sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid sid microphone merit silent ini maximisation maximisation maximisation maximisation maximisation ues proximation vergence prime crg disadvantages impor def def netherlands undergoes tant maximising cued motivates initialised initialised initialised initialised freitas freitas freitas freitas freitas fil analysed lacking gatsby noises noises kung arma arma arma arma arma arma arma tony preferentially encourages subscripts simplistic ucl rameter observability observability observability penrose ljung ljung initialisation initialisation initialisation initialisation initialisation initialisation initialisation initialisation initialisation initialisation initialisation cai sheffield sheffield mated cies lihood observa investigates minimisation rewriting ors ship cording instrumental instrumental instrumental esprit analysing itera methodologies infeng mclachlan duces suitability suitability situ gelb trices initialise initialise initialise initialise initialise soda olution minimises sto ces lob thirdly thirdly intelligibility intelligibility automatica investi ology pxp studentship moti frequen ban dordrecht favourably innovations frobenius ilarity smoothers scholar 
#@Niranjan_M,Robinson_T,Smith_G,de-Freitas_J,
#t13
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#*data data data data data data data data data data data data data data function figure figure figure time time time time time time time time time time time time time time time time set set set set set set set set set training number number number number number number number results results results results results results results results results information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information problem based based based based based based based space linear linear case case order order order order order order shown shown shown shown shown shown shown shown systems values values values probability probability probability distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition approach approach single processing large large analysis analysis analysis shows signal signal signal signal signal signal gaussian gaussian visual paper paper paper paper small small size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature fig fig fig fig fig fig cells cells cells points points features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification classification classification classification classification classification classification classification classification classification level level level current current current current current current current cell structure random random high high high similar show show line line speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech speech average theory term note experiments variables variables variables variables variables variables variables variables variables variables variables computation research log log log log defined defined defined target target target target target target target target target target constant constant estimate estimate estimate estimate estimate estimate estimate computer computer terms terms terms terms science prediction present low low frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency frequency temporal temporal temporal temporal maximum maximum maximum range press learn components components components components components components continuous sample sample abstract find find find find references due due important context introduction hand estimation estimation statistical statistical search search search search tion energy difference variable variable variable variable variable variable variable variable variable variable variable assume measure measure signals higher part bound type long represent distributed distributed equations correlation correlation correct probabilities probabilities observed classes ing ing total computed respect multi called applications study knowledge knowledge obtain relative cross gain gain gain gain gain gain discrete discrete equal approaches steps modeling institute words department individual individual joint joint joint joint joint joint joint joint joint represents represents bias bias bias bias bias bias bias bias environment estimates estimates estimates estimates estimates estimates upper free estimated estimated estimated estimated estimated estimated estimated pages pages pages pages give give give give channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel derived conditional conditional entropy entropy entropy processes achieved achieved achieved achieved measured measured close assumption short including auditory typically underlying needed reduced reduced unknown coefficients technology technology technology testing increasing database database database database language squared representing max window window bits bits bits magnitude frame frame frame frame frame frame frame frame frame frame produced produced sources sources correlations apply include inference subset recently relevant relevant relevant relevant relevant relevant relevant relevant engineering approximately volume speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker speaker bounded channels channels channels amplitude concept extended alternative locally generally generally critical critical greater greater conclusions depend depend depend exponential practice practice suggest suggest taking taking hard reduction reduction reduction reduction reduction labeled labeled labeled labeled labeled labeled labeled labeled assuming plane targets manner identification identification acoustic appears van van written plot label label label label label label label label label electrical dimensionality spectral develop mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual adding frequencies predictive shift shift shift shift expressed formation dependence phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme phoneme communication communication communication communication communication evaluate labels labels labels labels labels labels labels labels labels labels showed centered frames frames approximated similarly dashed dashed neighborhood perceptual perceptual usa weighting instances automatic uncertainty uncertainty uncertainty uncertainty uncertainty reason vowel vowel miller miller miller miller identity identity soc decoding interested phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic phonetic dis strategies duration categories categories categories realistic extend environments involving biases biases dependencies variability variability variability variability variability coefficient editor analyze psychology equally portion message message message message speakers speakers speakers speakers seconds histogram histogram histogram advanced ment band band band theoretic theoretic variances correction correction preprocessing broad ran mation mation mation english localized localized localized localized apparent improvements relevance howard characterize spread spread spread spread spread spread phonemes asymmetric asymmetric asymmetric hamming focused utterances globally shifted shifted classifying identifying feasible investigation databases databases extending khz accepted logarithmic occurring bands bands bands bands bands bands obtaining ral shifts ylx ylx ylx corpus carry carry carry date infor infor infor reliably schwartz yang yang yang yang yang yang april april april insight bins theoretically tures interestingly vari divide andrew linguistic linguistic linguistic linguistic informa deriving break transmitted icassp icassp classifications spaced adjustment quantized community graduate file file file file file file file file file file file march efforts relate cole complementary complementary complementary anal million reveal fea oregon acoust vii jointly telephone telephone telephone telephone telephone telephone curse morris morris dom hour hour illinois fre evenly fft maxi vicinity categorical categorical mis mis files energies formulas formulas formulas formulas ysis imum meaningless ece ables mum ogi ogi ogi ogi ogi quency walker fanty collect plp sults bearing bearing bearing bearing pierre french spans yix yix yix quantifies tributions reductions sept fax overestimate hermansky hermansky hermansky hermansky hermansky hermansky hermansky tempo targeted targeted beaverton stories stories stories rig rig asr asr enlarge yokohama variabilities variabilities pho underestimate jean netic informations informations phonetically vlx asymmetrically disposal 
#@Hermansky_H,Yang_H,
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#*model model neural input input input function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time set set set set output number number number system system system system system system system system system results results results results information information information information information information information information information information information information information information information information information information information information information problem performance performance performance performance based based space space linear linear case case vector vector vector vector order order shown shown systems systems values values values probability probability noise noise weight method method approach approach approach approach approach approach approach approach approach approach approach point point point image image single single single single processing processing processing local local local matrix inputs shows shows signal signal signal signal signal signal signal signal signal signal signal signal simple gaussian gaussian gaussian gaussian gaussian visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper small size feature work work work work task task methods step process process process process process current random random response architecture vectors vectors general speech speech real real real approximation average average average theory result university university threshold threshold threshold threshold computation independent independent independent log log log log log log log defined found found sequence sequence target constant estimate estimate estimate estimate estimate estimate estimate estimate estimate computer computer science science science left presented presented map map map present present frequency temporal temporal machine machine position position position position components components components basis outputs sample sample abstract applied applied applied references component component due positive important important important adaptive introduction hand effect effect effect effect effect effect effect effect effect effect parallel parallel tion energy energy energy energy energy energy spatial measure measure measure measure measure signals signals signals signals signals signals signals signals signals signals signals signals signals signals prior part required multiple cortex conditions represent represent fact correlation correlation correlation observed scale scale scale tasks tasks tasks computed computed respect times times regions regions regions regions regions regions means factor potential applications applications applications applications filter filter filter obtain negative specific samples series series provide provide define location location location location goal constraints brain approaches approaches larger larger dependent source source source source source source source modeling selection proceedings proceedings department department implementation implementation implementation joint joint represents represents difficult bias sequences ai ai maps maps maps computing computing directly estimates estimates estimates estimates estimates estimates san san top stimuli stimuli stimuli stimuli effects effects detection conference determine statistics statistics world vision vision vision vision estimated estimated estimated estimated pages produce weighted developed developed developed developed actual actual actual finally finally finally evidence evidence evidence evidence evidence evidence nature depends sampling sampling measured covariance covariance covariance covariance covariance tested amount common role face adaptation journal pixel pixel pixel pixel pixel pixel pixel pixel pixel degree degree development sensory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory auditory underlying combination functional coefficients coefficients interesting interesting special database language numbers direct window window inhibition international normalized normalized bottom early frame frame frame frame idea combined combined sources sources sources sources sources sources sources sources light light improve improve correlations pair pair robust separate separate element reported practical practical period side pixels pixels cognitive cognitive sufficient highly approximately volume module speaker speaker speaker speaker speaker speaker speaker speaker definition background background positions positions locations separation interval entire amplitude parts parts intensity intensity intensity intensity intensity intensity intensity intensity concept suggests suggests wide matrices correctly move hardware strength greater reduce reduce conclusions designed sound sound sound sound sound sound sound sound sound sound sound sound sound sound sound taking strong strong california california labeled variety selective relationship relationship relationship relationship targets derivatives scene acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic acoustic areas relation produces perception perception ways primary describes mathematical changing changing sensitivity coordinates averaging text interaction mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual events shift shift shift john national stationary correlated communication influence influence frames frames frames static similarly digits digits past past sign measurements reduces reduces false tracking closed filtering msec degrees avoid perceptual coordinate usa color contour contour sciences discuss discuss major sensor encoded successful literature literature capture capture notice strongly strongly strongly induced video video video video video video video video video video video video video video video video video video video showing interested neuroscience symmetry physiological physiological physiological physiological cues sampled sampled localization localization localization localization localization localization localization localization play realistic correspondence reach illustrates illustrates subsequent operating software camera camera camera camera situations situations explore origin diego diego wiley investigate experience experience rapidly put estimators issues helpful plasticity working affect topographic matched coefficient trace trace possibly reading eyes thought aspect multivariate speakers speakers baseline detected simplest motivated serial devices asynchronous crucial tool tool spatially spatially processed turns turns turns turns implementing shared producing producing precisely actor separately sounds sounds sounds sounds sounds sounds sounds describing describing pitch localized read recording addressed addressed robustness apparent people offset offset amounts spoken spoken psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical psychophysical peaks share employ employ treated measuring synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony synchrony semi sophisticated age windows owl trade contribute contribute phenomenon person secondary aligned gabor gabor jth enhancement lost inspired anatomical minutes promising adjusting interpret interpret utterance synchronous synchronous synchronous optic guide carry spurious spurious exploring lip lip lip lip interference periods sion enhance stereo monkeys searching captured competing centroid centroid centroid centroid dif exposure treatment suggesting jolla jolla fold thresholding audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio audio land ence compressed ple outline shorter inferred recursively benefits bank spatio encouraging encouraging perceived hundred causal streams streams barn barn peripheral exam community file file ization searches mouth mouth challenging mediated paired ultimately synchronized synchronized synchronized synchronized synchronized synchronized macaque academy nonetheless knudsen knudsen knudsen knudsen packet transients exploratory exploratory exploited psychophysics mea correlate correlate spite coming coming ucsd ucsd persistent rarely influenced influenced jointly locate locate locate locate locate aid movellan movellan movellan movellan movellan tectum pearson unreliable modalities modalities screen cur multimodal spirit feldman feldman tags jitter files platform microphone microphone illusory mid triple cepstral stryker stryker decompositions locating coincides bright localize localize localize localize saved accepts movie movie movie movie rendered snapshots sual formalized azimuth driver driver succession emphasizes live proaches lend disappears noticeable lea relaxing cies unwanted quotient wealth alternation overlaid midbrain ported squaring cancels andy rgb listening rectifying dummy cogsci cogsci javier buffered localizing localizing contingency contingency contingency contingency television enhancements influ andj surements fun tagging flashes flashes disrupted damental rre upside flames backed rently ficult feels formats 
#@Hershey_J,Movellan_J,
#t13
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#*learning learning learning model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure time time set set networks training training training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number system system system system system system system system system system system system system system system system error error error error error error results results results results information information information information information information information information information problem problem problem problem problem problem problem problem models models models performance performance performance performance performance performance based based based based based based based based space case vector order values values values values values probability probability probability probability probability probability probability probability parameters noise noise recognition recognition recognition recognition recognition method approach approach approach approach approach pattern pattern pattern pattern point point point point image image image image image image image image image image single single single single single single single single single single single single single control large test test analysis analysis analysis matrix form shows shows shows shows simple gaussian gaussian gaussian gaussian gaussian gaussian visual paper examples examples examples small small work work task methods step points points points points points process process problems high high similar similar similar show show show show equation equation section section line vectors parameter parameter average states term term term dimensional dimensional result result university university research research research research sequence sequence sequence sequence sequence constant constant estimate estimate estimate estimate computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer science science left left left presented map present low object motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion range position position basis basis abstract applied back find computational density density likelihood likelihood likelihood references due due due due ieee ieee ieee ieee important important propagation mixture mixture mixture mixture introduction action hand estimation estimation effect variance parallel tion change assume prior prior prior prior prior prior prior prior prior prior prior learned learned learned part part part cases required required multiple multiple multiple good good long long represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian techniques correct probabilities probabilities probabilities probabilities probabilities errors errors errors resulting human human human human human human human human human human human human human human human computed multi sum eq eq called times elements means factor potential feedback knowledge knowledge knowledge knowledge knowledge em em em filter obtain original original original artificial represented true provide compute compute proc perform perform perform determined posterior constraints constraints power approaches mit contrast contrast contrast support source modeling modeling proceedings report report institute department department version technique consists individual difficult sequences sequences sequences sequences sequences sequences sequences ai maps maps maps maps framework cambridge cambridge domain hinton view san stage stage stage effects conference conference conference conference conference conference determine determine full significant significant significant approximate world vision vision vision pages pages derived weighted weighted weighted conditional clustering clustering developed provided finally processes covariance technical technical tested hmm limited limited close amount short short short short short short require require main face journal end ability cluster cluster cluster easily easily makes including typically needed account technology testing testing projection projection matching database mode operation operation operation international international international depth depth depth depth magnitude frame frame frame frame frame frame frame frame frame frame frame frame frame frame attention attention combined combined minimize produced improved improved discussed recent recent reported apply apply include include subject subject subject hierarchical inference inference inference dimensions dimensions dimensions dimensions sufficient observations observations approximately subjects module module axis tions solve achieve rl diagonal address address mixtures background positions positions positions positions positions observation observation entire arm arm arm arm arm arm arm arm parts parts parts parts parts parts expression scaling extended rotation correctly move column demonstrate conclusion modules accurate bayes clear performs performs exponential largest demonstrated intelligence labeled turn plane plane plane plane manner groups base base pro longer longer ways factors describes vertical modeled modeled modeled missing coordinates coordinates simultaneously remaining slightly slightly interaction develop gaussians formed quality yield extracted independently reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction stationary stages overlap influence open evaluate controlled restricted fraction frames frames frames frames frames frames frames frames frames decomposition translation key earlier slow performing measurements normalization fitting tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking tracking interpolation faces views views degrees figures includes priori coordinate automatic automatic uncertainty uncertainty candidate black tests successfully successfully columns efficiency society society build build build projections receives capture capture capture capture capture conf repeated prob video video video video video video video video video video video video video video video video video video showing running running duration michael realistic providing received deal extend camera camera camera camera camera camera camera camera camera camera camera camera camera camera situations presents presents law body body body body body body body body body body body body body body body body body body body body body poor essential essential kalman humans humans humans accurately issues issues successive successive reliable reliable reliable working stream complicated workshop measurement measurement plausible plausible predicts perfect singular singular singular freedom initialized explain finds seconds massachusetts residual ground ground ground ground track track track track track track fairly reasons perspective sections broad bishop probable toronto patches demonstrates incomplete preceding virtual improvements people people people freeman freeman freeman freeman freeman parameterized rely rely characterize maximizes electric electric inherent inherent sophisticated returns focused begins simultaneous multidimensional initialization initialization initialization pose pose don lab lab lab ghahramani oxford optimizing reconstructed reconstructed reconstructed reconstructed impossible eliminate rigid rigid rigid rigid rigid lost eliminated adds convenient held removing illumination adequate adequate planar spurious published combines representational ambiguity sion conjunction intended lengths heart originally viewing iterated francisco occlusion occlusion occlusion occlusion occlusion occlusion infer tracker tracker tracker tracker tracker tracker tracker tracker tracker contact informative gesture motions motions motions motions motions motions motions relies davis captures santa santa cam severe divide informa poses adopt corrected corrected corrected seek superimposed superimposed reconstruct reconstruct monocular monocular mismatch leg favor alternate graphics careful proach ambiguous deleted tively intl truth truth indication treating technologies helps lighting lighting lighting lighting accumulation survey resolve resolve european confirm blake morris morris industrial appealing proportions fre conversion svd svd subtracting subtracting partly bregler bregler discarded markers bergen isolation joints joints tracks tracks quantitatively william reality lags gathered feb outlier artificially capturing manual limb limb limb degrade cations appli enforcing marker prolonged walking walking tracked tracked tracked tracked relying relying relying reconstructions reconstructions analyzers respec movie anandan articulated articulated articulated arms arms malik malik lose rendering divides singularity emphasizes cameras cameras anatomically quences condensation relied revised loses intervention intervention stance concludes occlusions persons observa cornell cornell crossed shadow bringing bringing isard momentary film orthographic eleven restore perona friction cloud easiest vides sight shadows assembled mitsubishi mitsubishi nicholas underdetermined underdetermined ithaca broadway merl obscure truncate bernardo reconstructs reconstructs clip clip clip fourteen professional distracting hardest wholly limbs limbs bent unnatural attaching confusing slipping 
#@Freeman_W,Howe_N,Levemon_M,
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#*learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural input input input input input input data data data data data data data data data data data data data data data data data data data data data data data function function function function function function function function figure figure time time set set set set networks algorithm algorithm number number system units units information information information models models models models models based based based space space space space space space linear linear linear linear linear linear linear linear linear linear case case case case vector vector vector order order order order order order order order order order shown shown systems systems values probability probability probability probability probability probability parameters functions functions functions neurons neurons distribution distribution distribution method approach approach approach point point image image image image image image image image image image image image image image image image image image image image image image single single single processing processing processing processing processing processing analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class matrix form shows shows shows signal signal signal signal simple simple simple simple simple simple simple simple simple simple simple simple simple simple visual visual paper paper paper paper feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature methods methods fig fig fig fig cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells field field field features features features features features features features cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure structure structure random random response response similar similar similar similar similar similar similar similar similar similar similar similar representation representation architecture show show show fixed vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images general general general generalization generalization generalization speech states obtained obtained obtained obtained obtained obtained obtained note experiments experiments experiments dimensional dimensional dimensional dimensional university variables computation computation research research independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent log log defined defined defined defined defined defined defined defined defined found found found constant distance distance distance distance distance distance distance distance distance presented map map map phase phase phase phase phase phase phase frequency frequency frequency frequency frequency frequency temporal sets press press press press components components components components components components components components components components components components components components components components components components components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis abstract applied applied density density density density properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties properties likelihood likelihood likelihood references component component component component component component component component component component component component component stochastic due ieee important adaptive adaptive adaptive context introduction complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex complex estimation statistical tion tion energy energy energy assume assume assume assume lower measure measure signals prior chosen chosen higher higher higher higher higher higher higher higher part center type cortex cortex good represent expected fact fact techniques correlation correlation observed observed scale classes computed multi sum eq eq eq eq called called mapping mapping means means dimension dimension dimension natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural orientation orientation orientation orientation filter filter obtain represented represented represented compared compared receptive receptive receptive define define define define proc proc location location active related related distributions distributions equal equal equal mit mit contrast contrast contrast contrast contrast contrast connection fields fields dependent dependent modeling modeling words words words version consists consists consists code individual advances advances advances responses responses addition addition addition addition sequences maps considered considered computing equivalent equivalent design vision estimated basic basic basic basic basic basic basic basic basic pages pages give con coding derived product provided selected nature nature biological measured discussion group denote denote transformation fast limited limited close close close inverse assumption corresponds corresponds corresponds finding assumed assumed assumed assumed role square square square square pixel easily makes sensory typically combination reduced coefficients technology significantly projection projection projection projection york edge principle principle principle principle principle leads leads leads principal principal details details details filters filters filters filters filters filters filters filters filters filters combined choose sources denotes correlations correlations correlations correlations correlations exact property pair introduced introduced identical hierarchical sejnowski dimensions sufficient observations approximately volume match pca sparse sparse sparse sparse sparse sparse sparse definition definition locations locations locations locations locations separation symmetric grid grid grid organization organization lead lead concept invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant width strength neighbor depend competitive clear clear exponential practice constrained taking strong strong demonstrated assuming ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica selective selective manner areas explicit explicit relation relation van van van van index index primary primary changing simultaneously consisting springer springer shift shift shift shift shift shift shift implies implies decreases independently expressed expressed formation dependence correlated correlated squares densities densities organizing organizing organizing organizing showed showed decomposition decomposition static static activities translation allowed classical classical classical normalization reduces combining neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood neighborhood purpose distances norm norm norm norm norm euclidean euclidean kohonen kohonen kohonen existing box bell blind subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace extension simplicity simplicity columns determining identified identified closely society differ modification modification divided latent projections projections projections projections projections projections projections projections invariance invariance invariance invariance invariance invariance invariance tend tend tend orthogonal orthogonal orthogonal orthogonal conf verlag verlag kind strongly interpreted dis symmetry generative generative generative dot dot generalize surround consisted consisted overlapping neighboring neighboring neighboring oriented oriented modelling extend extend relations detail limitations scalar reducing giving giving ideas detectors mappings int dependencies root maximizing statistically topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic topographic fundamental phases phases phases phases patch patch editor der der noted multivariate submitted explain explain explain explain defines defines defines scenes scenes scenes distinguish variances independence independence independence independence independence inside inside inside inside inside turns lin preprocessing products localized localized patches patches patches patches patches patches cybernetics explained greatly considerably tional embedded lattice recordings formulated http http berlin proven extensions extensions extensions extensions extensions extensions acoustics logp windows simultaneous multidimensional multidimensional multidimensional multidimensional multidimensional multidimensional ordinary ordinary ordinary ordinary uncorrelated indices www www tation gabor gabor gabor gabor restrict arguments animals unity nonzero theories royal suppression extending oja nearby nearby analyzing removing shifts belong combines introduces encountered encountered encountered dependency schwartz advance emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence emergence modelled express belonging tures tures interestingly consecutive geometrical logarithm vec equivalently emerge tween smoothly icassp classic classic mutually mutually invariances invariances invariances invariances invariances distribu life maximally macaque spanned spanned indexed superposition fea fea det jutten compu subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces subspaces topography topography topography topography topography topography topography topography topography topography topography invertible neighborhoods neighborhoods olshausen olshausen generafive orthonormal orthonormal tors condi seattle practically practically practically tuple tuple tuple tuple wavelets norms norms norms norms norms norms restricting maxi proves quantitatively bandpass bandpass enhances fin sis est gence gence sparseness dence energies energies enabling simoncelli developments decompose hood resemble expresses cardoso herault invert comon quadrature heidelberg positively positively ies helsinki plex whitened whitened depen tributions cis cis wild hyv hyv hyv hyv quence proj hexagonal orienta hut hut hut hut hut iden torus sponses finland hyvarinen hyvarinen tuples tuples tuples tuples tuples photographs couples neuromimetic spherically triplets analy nection skewed depicting mize girolami inen inen inen inen emer emer hateren hateren ects ale 
#@Hoyer_P,Hyvarrinen_A,
#t13
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#*network learning learning learning model model neural neural neural neural neural neural neural neural neural neural neural input figure figure figure figure time time time time time time time set set networks algorithm output number number number number system system system system system system system system system system system error state state state state information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information information models based based space weights weights order order order order shown systems values probability probability probability probability probability neurons neurons neurons neurons neurons neurons neurons neurons neurons neurons unit unit pattern image image image image image image image image image image image image image image image image image processing processing control control control control large large large large patterns patterns patterns patterns analysis analysis analysis optimal form form signal signal signal signal signal simple simple simple visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual visual paper paper paper small small feature net task task task task cells cells cells cells cells cells cells cells cells cells cells step field field field field field features features features process process level current trained cell cell cell cell cell cell cell random high high high high high high high memory memory memory memory memory response response response response response response response response response response response response response response response response response similar similar similar similar similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture equation images images images images images images images images average theory theory theory obtained term term term term term term term experiments result result university university university university university computation computation computation computation research independent log log found dynamics dynamics initial computer terms science science prediction prediction prediction prediction presented map low low frequency machine maximum maximum maximum maximum maximum maximum maximum range press press press position basis abstract back back back back computational computational computational references due ieee ieee important context context context context introduction complex complex complex stimulus stimulus stimulus stimulus statistical statistical effect effect effect effect effect dynamic recurrent search tion tion tion tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity spatial spatial spatial spatial spatial spatial spatial spatial spatial assume lower rules measure measure signals signals signals prior representations representations representations representations representations learned higher higher higher higher higher higher part part part center center center center center center center center firing multiple multiple multiple cortex cortex cortex cortex cortex cortex long long long represent distributed bayesian bayesian make make make fact region region proposed proposed observed observed scale minimum resulting tasks human human computed computed computed computed computed sum called called times means reinforcement natural natural natural natural natural natural natural feedback orientation global knowledge relative represented represented receptive receptive receptive receptive receptive receptive receptive provide provide provide provide provide provide provide provide location location location location location location location location active active eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye eye related gain gain motor motor motor motor brain brain brain brain brain brain brain brain brain brain brain brain power power mit mit larger fields fields fields fields fields support support dependent modeling institute institute department internal internal internal code code code code code advances advances joint joint responses responses responses responses responses responses responses responses responses responses responses responses responses responses bias delay delay maps considered framework framework framework framework framework framework framework framework framework framework framework additional design top stimuli effects efficient statistics statistics statistics statistics world world world world world world world world world world world vision vision vision vision basic basic channel channel channel channel coding coding coding coding coding coding coding coding derived weighted conditional conditional conditional conditional developed levels area area types entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy path path path provided processes processes processes nature nature nature sampling constraint constraint simply simply biological discussion limited limited limited limited assumption complete complete stable surface amount amount short short short short effective effective generate supported supported role role theoretical theoretical theoretical eds eds eds face adaptation adaptation degree smaller needed combination reduced functional fully fully jordan interesting significantly mechanism consistent details details direct making making window window window window window window inhibition inhibition inhibition inhibition inhibition inhibition stored international bottom early early early early frame idea idea idea idea attention attention neuronal neuronal neuronal neuronal neuronal denotes recent correlations resolution resolution resolution resolution resolution resolution resolution separate ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble ensemble movement movement movement movement movement movement movement movement lateral moving period subject sense inference inference inference inference inference inference inference cognitive engineering interest interest unsupervised subjects subjects tions tions differential sparse sparse sparse sparse address positions positions locations locations locations locations channels channels channels organization sensitive sensitive grant grant grant constructed constructed horizontal parts expression lead lead concept suggests spikes predicted locally move move move move move half starting place reduce reward retina retina retina retina clear suggest suggest propose propose propose propose taking integration external reduction reduction demonstrated intelligence assuming minimizing movements movements movements movements movements movements movements movements movements movements movements scene scene scene scene scene scene scene scene scene scene scene scene scene scene force force question areas explicit pro van construct perception perception perception primary generating tuned tuned modeled modeled modeled modeled involves belief angle mutual mutual mutual mutual mutual mutual events predictive predictive predictive predictive predictive predictive predictive predictive select formation formation formation review depending correlated interpretation interpretation interpretation influence codes codes detailed detailed evaluate controlled updated updated updated showed showed lee lee lee lee lee lee modulation modulation forms static understanding understanding understanding understanding understanding understanding sizes completely suggested suggested suggested suggested classical normalization combining event event event roughly false closed generation msec msec foundation transactions perceptual perceptual perceptual perceptual perceptual perceptual formulation color contour retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal retinal automatic automatic automatic uncertainty uncertainty uncertainty maximize maximize activated priors priors coupled variations neighbors neighbors texture reason aspects extra closely capable encoded paths paths paths successful literature efficiently computations tend capture capture compact compact compact compact kind neuroscience return return return return return content follow cues surround surround surround surround surround surround surround surround surround surround surround wavelet wavelet maximization maximization maximization maximization principles principles moves disparity camera minimized unlike american create access exhibit exhibit experience experience experience rapidly rapidly steady steady steady steady involving association existence successive fashion ideas ideas ideas rest behavioral combine dependencies authors authors working working maximizing variability statistically understand cognition cognition fundamental neu neu examined measurement coefficient transmission reading reading reading reading analyze predicts psychology facial facial illustrate created created eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes eyes front front obvious greedy assumes logic extent extent explain explain explain attempts established established integrate scenes scenes scenes theoretic theoretic theoretic theoretic orientations track analyzed phenomena navigation navigation explanation explanation inside drive rapid perspective forces constructing immediately monkey mation scientific scientific acknowledgement involve members patches linsker cybernetics nsf mellon mellon mellon mellon mellon integrating questions greatly behaviors behaviors behaviors behaviors behaviors behaviors prop carnegie carnegie carnegie carnegie understood cmu cmu generic fed fed leave solla solla remove biologically psychological ity span exhibits measuring pittsburgh pittsburgh pittsburgh pittsburgh ordered singer coherent coherent coherent kinds redundancy redundancy neuro specifies semantic semantic pyramid cor picture picture person contextual contextual contextual identifying sleep modify gabor gabor gabor saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic saccadic repre theories plays suppression suppression extending allocation ments stronger overcome chemical moment moment moment analyzing analyzing ral spot guide intuitive continue infor programs programs programs programs connect decide conjunction mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental mental buffer buffer schwartz schwartz consequences captured scan scan scan scan scan scan originally emergence discounted discounted ballard ballard arrive kearns kearns saccade saccade saccade saccades saccades saccades saccades draw captures captures convergent executed dividing assigns severe sequentially mind informa informa neurophysiology unified numerous maximized asked creates creates rao rao instantiation forcing decorrelation reconstruct adapting visited visited cohn peripheral modifying mouth fixation fixation fixation fixation surrounding surrounding macaque sketch monitoring barlow barlow pop pop stuck places exhibited nal overcomplete reinforce bridge quantify mcdonnell heavily emotion subjective subjective shot olshausen olshausen december essen rons proposal partly dedicated dedicated inferring neocortex wavelets wavelets carries frequent frequent lewicki periodically creation gathered shaping unusual unusual unusual fovea fovea fovea fovea fovea fovea transaction tical sentation rem convey mesh actively massive simoncelli simoncelli hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn hypercolumn plenum entropies resemble repetitive severely severely schema schema fundamentally mumford mumford reactive biomedical forgetting retinas sing remember machinery machinery ages foveal imagery lose mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic mosaic constantly constantly fatigue mere standpoint kanade acuity govern sketched erties duced foveation ori steer steer accompanied knierim illusion debate conscious fixations fixations fixations fixations sponses guiding modulus modulus collects discounting implausible dream vide loca suppressive gather gather paradox engaged hypercolumns hypercolumns hypercolumns hypercolumns hypercolumns hypercolumns greedily emotional snap peculiar philosophical stark stark aggregated unconscious unconscious unexplained semble exerts superficially embodiment norton norton modula lates foveate newark scrutiny feeling takeo assemble elucidating funda 
#@Lee_T,Yu_S,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model neural data data data data function function function function figure figure figure figure figure figure figure set set set set set set set set set training algorithm algorithm algorithm algorithm algorithm number number number number number system state state state state state state state state state state state state state state state state state state results results results information problem problem performance space space linear case case case case case case case vector order order order order shown shown shown shown shown values probability probability probability probability probability parameters parameters parameters parameters parameters parameters noise noise functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach approach point point image image image image image image image image image image image single large local rate test test test test analysis matrix matrix form form form form form form form form simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian visual small small small small work work work methods methods methods methods fig cells field current trained trained structure structure structure structure structure structure problems problems random high high high similar representation show show show section line images images images images images images images images images images images images images images images images images images general approximation average states states states states states states states theory gradient obtained term note note note dimensional variables variables variables variables variables variables variables variables computation computation solution solution research research independent independent independent independent log log log log log log log defined found terms terms map present frequency frequency sets sets sets sets sets sets position position components components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis sample sample abstract likelihood references component due ieee important mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture mixture introduction hand statistical variance variance variance variance variance variance cost tion change change change change complexity variable spatial spatial lower lower rules rules prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior prior representations learned learned learned learned learned chosen higher center center center previous bound cases cases cases cases cases cases cortex binary binary binary binary binary binary binary long distributed fact fact length errors resulting resulting ing total total total computed sum sum performed performed elements elements elements means factor made natural natural natural natural natural natural natural natural natural natural samples samples true compared proc active active active active active determined posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior posterior distributions distributions distributions discrete equal equal comparison update modeling modeling department code code code joint scheme addition ai ai ai ai ai ai framework curve determine determine efficient efficient choice significant significant approximate approximate statistics statistics vision vision coding coding coding coding coding coding coding levels levels levels entropy entropy depends sampling sampling sampling sampling sampling sampling sampling sampling simply covariance describe describe assumption complete supported adaptation pixel fit objective objective objective probabilistic needed coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients edge representing filters filters pre minimize denotes advantage takes takes strategy include inference sejnowski previously conventional axis yields diagonal diagonal sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse sparse address positions grant suggests matrices alternative correctly move white occurs generally setting reduce conclusions practice learns demonstrated variety exist averaged averaged averaged manner boltzmann appears appears appears van van longer index primary vertical changing modeled modeled modeled explicitly averaging dimensionality gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians yield extracted expressed dependence estimator codes codes codes codes codes codes codes evaluated updated fraction centered forms completely suggested dashed spaces roughly purpose purpose sufficiently transactions coupling priori bell determines illustrated priors priors priors priors priors characterized characterized major extra efficiency efficiency efficiency efficiency capable capable capable effectively included efficiently efficiently computations schemes comparing capture soc quickly quickly neuroscience neuroscience hold notation gibbs gibbs gibbs gibbs sampled sampled wavelet quantization attempt consisted acknowledgments oriented oriented employed matches variational variational dependencies dependencies scaled maximizing maximizing proved coefficient coefficient coefficient coefficient coefficient coefficient coefficient psychology created der expressions initialized initialized initialized established mentioned formula variances coded analytical adapted adapted tractable spatially snr snr snr snr probable involve gradually localized localized lowest patches patches outer integrating considerably reflect collected freeman offset lack calculating rely characterize differs differs extracting extracting marginal datasets logp logp tile distortion distortion initialization newton newton accomplished accomplished gabor summing tem royal dealing accepted accepted imposed imposed imposed imposed imposed transforms affected exceeds utilized regard ascent bases bases eqs davis davis davis davis captures assigning accumulated ber conjecture conjecture laplacian distri num challenging adelson flip lond multiscale win superposition superposition sweeps sweeps det inactive inactive inactive challenge modal overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete overcomplete bution opti const confirm olshausen olshausen olshausen olshausen olshausen olshausen dropped cast rare continuum practically sharply peaked heeger bandpass bandpass lewicki brackets cauchy cauchy nih sparseness adequately capturing emerged deciding tails simoncelli clutter entropies resemble mization argmin graphically offered sparsity collect attias attias ages seeks bimodal accord lowering aver ore critically whitened occupy duced perceptually notations cre factoffal noticeable jii orienta cumbersome intro flipping als overlaid overlaid overlaid overlaid advocated sil ternary ternary ternary ternary ternary ternary ternary ternary asi asi quantizing argmaxp argmaxp verse ivi perature bruno ila ila underestimates ali 
#@Millman_K,Olshausen_B,
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#*network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural data data data data data data figure figure figure figure figure figure figure figure figure figure figure figure figure figure set set set set set set set set set networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number results results results results information information information information information information information information information information problem models models models models models models models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based space space space layer layer layer case vector order shown shown shown shown values values values probability probability probability probability probability probability probability probability probability probability probability probability probability parameters noise noise distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition method approach approach approach pattern point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image large large local local local local local local local test test test test test test analysis analysis class class class class class class class class class class class class class class class form algorithms algorithms algorithms simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian examples examples examples examples examples feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work task methods methods methods step step field features features features features features features features features features features features features features features features features features classification classification classification classification classification process process process level level level level level level level level level level level level current trained trained trained trained structure structure structure structure structure structure structure problems problems random random random similar similar similar similar show equation line rule vectors vectors vectors vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general general general real states obtained obtained note experiments experiments result result result result variables variables variables variables variables variables variables variables variables variables variables variables computation independent independent log log log found target target target target target target target target estimate computer science direction direction present present present present low object object object object object object object sets maximum range range range range range press position position position components components sample sample abstract applied applied back properties likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic due ieee ieee ieee ieee procedure procedure propagation mixture mixture mixture introduction estimation statistical effect change change change variable variable assume classifier lower lower lower learned chosen chosen chosen higher higher multiple good good long long long long represent tree tree tree tree tree tree tree tree tree bayesian markov markov markov markov markov make make make fact fact techniques correct probabilities scale scale scale scale scale scale resulting resulting resulting resulting resulting classes classes classes classes classes classes ing tasks regression computed computed computed multi multi performed performed performed called mapping means factor factor factor factor factor factor factor factor factor applications study study knowledge em em em em filter filter negative original specific samples represented compared application application desired series compute compute objects objects objects objects objects objects objects objects objects proc location location goal related constraints connected distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions discrete discrete brain approaches approaches mit larger fields train train modeling modeling modeling modeling proceedings report individual individual joint layers graph ai cambridge computing domain experiment directly curves curves curves curves curves estimates detection detection conference efficient approximate statistics world vision pages con condition condition condition weighted conditional conditional conditional conditional conditional conditional conditional developed levels levels levels levels area area types entropy entropy sampling simply simply covariance normal normal technical denote denote short shape supported pixel pixel pixel ability makes development including fit fit probabilistic pairs needed needed jordan edge segmentation structures structures matching empirical empirical principle operation details call call max early correlations resolution resolution resolution resolution resolution resolution resolution resolution pair pair reported pixels pixels pixels hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical dimensions dimensions varying compare observations observations approximately volume volume tions trans trans trans diagonal positions positions positions organization entire move conclusion neighbor editors bayes clear learns strong strong presence presence presence presence presence drawn variety exist plane relationship iii targets introduce acknowledgements areas suppose monte carlo written index optical ways laboratory label label label easy belief belief belief scales scales scales gaussians expectation expectation expectation select john extracted extracted dependence stationary influence codes updated labels labels labels labels showed showed similarly discrimination discrimination discrimination discrimination calculation spaces false false valid valid visible david david expect template includes kernels combinations coordinate inter sciences prove candidate tests tests texture texture texture texture texture texture texture texture texture simplicity compression extra computationally build build build tend ten ten ten ten ten ten fine fine fine fine fine capture capture capture kind kind kind allowing notation gibbs involved sampled write usual michael michael relaxation wavelet wavelet nips attempt extract neighboring extend parametric create preliminary preliminary graphical behavioral dependencies dependencies dependencies dependencies dependencies dependencies referred structured structured root working comparable comparable variability affect examined act coarse coarse coarse coarse naturally concepts plausible editor editor aspect quantities fisher fisher expressions academic detected histogram histogram histogram histogram histogram expensive tractable tractable tive sys leaves leaves products angles describing read auto questions flexible flexible flexible flexible flexible flexible tional tional share share solla detecting detecting treated treated polynomials parent parent parent parent parent parent cal suited geman geman song gave sums expectations windows conditioning conditioning conditioning conditioning conditioning conditioning conditioning summed pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid indices appearance appearance appearance restriction summing fix fix princeton ratios ratios conditioned conditioned conditioned conditioned conditioned air vehicle vehicle vehicle vehicle transforms mark child child child child child child repeat paul paul dependency dependency histograms captured captured captured infer repeatedly kearns likelihoods splits characterization vari thresholding parents parents robert limitation treat multiplying multiplying roc roc roc roc roc roc roc roc ple corporation kluwer inferred aircraft aircraft aircraft aircraft benefits formulate encouraging restrictions ical spaced affects reject jacobian constrain constrain argue argue pub cohn care exam ftp ftp distri distri pami pami tems distribu parzen denoting proba argued multiscale multiscale preserve port worked november factored restoration bility twenty sake sake mrf textures textures influenced invertible invertible invertible multiresolution viola viola viola finer finer suppress condi condi resolutions resolutions ooo alan positives interpolate spie assp factorization minimax relaxed thresh approached unusual mul united inappropriate propagates discriminating discriminating simoncelli simoncelli hip hip hip hip hip hip hip hip hip hip hip hip hip hip hip hip hip hip hip hip hip hip imum jack jack expresses omit ables miss ying mumford mumford ample compress spence spence spence spence spence zhu zhu parra parra parra parra subsampling subsampling subsampling pyramids subsampled tie unclear ages justify fuse mild imagery blur accumulating subsample stuart densely persistence nato gat vehicles vehicles vehicles cis coarser coarser proportionality mat mat mat government lat absolutely jects doubt grasp clay clay sajda collectively public aerial aerial forty detectable tractability butions butions chellappa donald sar sar sar trast factoring factoring factoring factoring tiple statisti sara oll eat eat eat eat photograph willsky willsky aren lucas conditionals upenn sarnoff sarnoff attrac jeremy jeremy answering kindly attach mage mage luettgen luettgen 
#@Parra_L,Spence_C,
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#*model model model model model model model model model model model model model model model model model neural neural data data data data function function function figure figure figure figure figure figure figure figure figure figure figure figure figure set number number number number state state information problem models models models models models models models hidden hidden hidden hidden hidden hidden hidden case case case vector vector vector vector vector order order order shown shown shown systems systems systems values values values probability probability probability noise noise functions functions functions distribution distribution distribution image image image image image image image image image image image image image single processing processing control local test analysis analysis class class class class class class class class class matrix form form form form form form form form shows shows shows shows shows shows shows signal algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples cells field process structure structure structure structure problems random random random random random random random random response similar representation architecture show show show show show show show show section fixed vectors images images images images images images images images images images images images images images images images images images images images images images images images images general generalization parameter parameter parameter parameter approximation theory theory theory note note dimensional university variables variables variables variables variables computation research independent independent log log log log defined table table table table estimate estimate estimate standard distance distance node node node node science prediction prediction nodes frequency motion range range range range range range components components basis basis nonlinear nonlinear nonlinear abstract density density density density density density density density density properties properties likelihood references component component stochastic ieee ieee ieee ieee ieee ieee ieee ieee positive positive positive procedure procedure procedure important mixture mixture mixture mixture introduction estimation estimation behavior behavior behavior behavior behavior statistical statistical statistical statistical variance variance variance variance variance variance variance complexity variable variable variable variable variable variable variable variable variable spatial spatial spatial spatial spatial assume prior representations cases type good conditions conditions tree tree tree tree tree distributed distributed bayesian bayesian equations markov markov markov techniques proposed proposed correlation observed observed scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale finite finite total total multi multi sum performed made made natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural natural global applications em relative relative relative relative represented compared compared cross provide provide compute proc proc proc proc related related distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions discrete discrete discrete cortical cortical equal equal power mit mit contrast support dependent dependent modeling modeling modeling modeling modeling modeling joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint joint exp exp exp exp exp exp addition ai considered cambridge cambridge domain domain domain equivalent top top full statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics vision vision estimated pages pages pages pages pages produce produce weighted conditional conditional conditional conditional conditional conditional conditional conditional conditional conditional types lines lines lines lines lines entropy entropy entropy entropy entropy entropy entropy entropy processes processes covariance normal increases increases group close close close close corresponds corresponds stable stable common shape shape shape supported theoretical theoretical square instance makes simulated simulated simulated simulated simulated simulated simulated simulated probabilistic typically typically typically typically typically pairs pairs pairs pairs pairs pairs pairs underlying underlying reduced unknown coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients coefficients york york special special consistent consistent empirical empirical empirical empirical empirical empirical empirical empirical empirical max filters filters filters filters filters normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized normalized bottom bottom denotes denotes recent pair pair pair pair pair pair pair include trees engineering interest highly highly previously observations observations approximately volume volume volume volume tions correspond studies converge trans trans trans trans mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures positions separation separation observation generalized generalized generalized generalized grant intensity scaling scaling scaling scaling scaling scaling scaling scaling suggests suggests extended deviation derivative locally white generally column column row row row row row row row row row row conclusions editors reduction drawn drawn demonstrated demonstrated demonstrated solid solid radial min iii groups denoted denoted acknowledgements explicit explicit explicit explicit pro derive derive derive written index primary plot plot plot plot mathematical modeled modeled modeled modeled student explicitly electrical remaining scales scales scales gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians gaussians formed letters decreases family independently depending correlated correlated correlated correlated squares estimator estimator transform densities densities densities densities densities densities densities densities densities densities fraction fraction fraction showed decomposition forms similarly reasonable reasonable dashed dashed measurements classical normalization normalization normalization normalization normalization fitting fitting neighborhood intervals david building contour contour sciences automatic specifically priors absolute phys neighbors neighbors neighbors discussions characterized columns columns columns gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma gamma straightforward compression compression aspects schemes plots characteristic characteristic characteristic soc soc soc conf link dis dis follow satisfy quantity wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet wavelet overlapping overlapping mixing mixing oriented law explore parametric collection requirements exhibit exhibit exhibit exhibit exhibit exhibit exhibit exhibit kalman relations relations integral accurately divergence dual dual graphical helpful scalar scalar examine respond int dependencies dependencies root analogous contours contours contours matched matched coefficient coefficient coefficient coefficient coefficient coefficient necessarily rev ensure quantities separated separated shapes years mentioned histogram histogram histogram histogram histogram histogram rows agreement orientations orientations adjacent adjacent adjacent adjacent cascade spatially spatially sections sections shared division worst consequence opt opt members begin definite demonstrates demonstrates nsf raw raw raw researchers fourth fourth behaviors behaviors freeman freeman empirically empirically led flexible solla rely characterize parent marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal marginal logp logp semi display age conditioning specifies pyramid pyramid cor spectra uncorrelated notes japan martin member circular circular circular repre royal multipliers multipliers multipliers multipliers multipliers multipliers multipliers multipliers multipliers multipliers multiplier multiplier multiplier kullback fits fits stronger multiplicative multiplicative multiplicative multiplicative multiplicative familiar nearby nearby nearby star star exploring heavy heavy heavy heavy bialek bialek corre pat dependency dependency dependency dependency dependency dependency dependency schwartz histograms histograms histograms histograms histograms histograms histograms histograms histograms histograms histograms histograms histograms histograms histograms histograms accounts accounts captured bases bins bins bins kearns captures implicitly characterization vari fitted liu approx linked linked linked linked linked drop listed listed fellowship leibler removal dec july par examining laplacian laplacian decorrelation illustration illustration equality exponent distant distant inverted oct oct adelson wise retain multiscale multiscale multiscale multiscale multiscale intensities importantly anal flower behave bill september overcomplete info info info tail argmax sponding restoration tial multiresolution multiresolution multiresolution multiresolution jointly jointly hilbert orthonormal fill char char condi tribution proposal striking striking striking huang huang autoregressive alan diamond concave tance sis ruderman ruderman ance tical indirectly sentation mach inst mul spa linking tails tails simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli simoncelli adv mountain mountain frog frog frog collecting argmin fractional marginals marginals nov mumford mumford mumford quadrature mar mar mar schneider puter mike kim exhibiting syrup henceforth inadequate inadequate nserc ponents rescaled ticular gression flowers flowers steerable steerable tailed tailed tailed apr sug iden decorrelated decorrelated eps brownian stance obser cients lastly intell separations separations denoising woods chou displacements choi cvpr coeffi imizing imizing nyu willsky willsky marginally nlog vations coef coef coef imately asilomar pendence ancestor mallat career amine synthe gested ficients ficients ficients heavier concreteness cobh ancestors quad andrews mip kobe surge nev cascades 
#@Simoncelli_E,Wainwright_M,
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#*network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data data data data data data function function function figure figure time time set set set set set set set set set set set set set set set set set set set set set set networks networks networks networks training training training training training training training training training algorithm algorithm algorithm algorithm algorithm output output output number number number number number number number number number number number number number number number number number number number number number number number number number number system system system system results results results results results results results results results results results results results results results results results results results units units units units units information information information information information information information information information problem problem problem problem problem problem models models hidden hidden performance performance performance performance based based based based based based based based based based based based based based based based based based based based based based based based based based based based based space space space space space space space weights weights weights weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear layer layer case vector vector vector vector vector vector order order shown systems systems systems systems values values values values values values values values values values values probability parameters parameters parameters noise weight weight functions functions functions functions unit unit unit unit distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method method method method method method method method method method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image single single single processing processing processing processing large large large large large local local rate rate rate test test test test test test test test test test patterns patterns patterns patterns analysis analysis analysis analysis analysis class shows shows shows simple gaussian visual visual visual paper paper examples examples examples examples examples examples examples examples examples examples examples small small small size size size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work work work task methods methods methods methods methods methods methods methods methods methods methods methods methods points features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features features classification current current current current current current current problems problems random high high similar similar similar similar representation representation representation representation representation architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture architecture show show show show show show line line rule rule rule rule rule rule rule rule rule rule images images images images images images images images images images images images images images images images images images images images images images images images images general general general general general speech parameter parameter real theory theory theory theory theory gradient gradient note note note experiments experiments experiments experiments dimensional university university university threshold threshold threshold threshold threshold threshold research independent defined defined found sequence sequence target target target target target target target target target target target target target target target table table table estimate computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer computer terms terms terms terms terms terms node node node node node node node science science prediction prediction presented presented presented map map map present present present present phase low nodes nodes nodes nodes machine machine machine machine machine machine machine machine machine object object object object sets sets sets sets sets sets sets sets sets sets sets maximum maximum range range range learn learn learn position position position position position position sample sample sample sample sample sample abstract applied applied applied computational computational convergence density density likelihood references component ieee ieee ieee ieee ieee ieee ieee ieee ieee ieee ieee positive positive positive positive procedure decision mixture mixture context introduction complex hand hand estimation estimation estimation estimation effect generated variance variance variance variance tion spatial assume rules learned learned learned higher part part bound cases required binary binary conditions conditions conditions conditions conditions conditions conditions represent represent represent bayesian markov markov markov markov make make fact fact region proposed errors scale scale scale scale scale scale scale scale scale scale scale scale scale scale scale resulting classes ing tasks tasks total total total total total total total human human human human human human human human human computed computed multi multi multi multi multi multi multi multi multi multi multi multi performed called times means means factor factor factor potential potential potential potential made natural natural natural natural natural applications applications applications study policy negative negative negative negative original artificial relative relative relative relative relative specific samples samples application application application application series series provide objects rates rates rates rates rates perform active active active active active active active active active active active active active active active active active active active active active determined experimental experimental experimental experimental experimental experimental experimental experimental experimental experimental goal connected distributions distributions distributions discrete larger fields update update update update update update update update update update update update update support support support support support support support descent modeling proceedings proceedings proceedings proceedings proceedings proceedings proceedings proceedings proceedings proceedings report report report institute department department consists consists consists joint represents difficult difficult final scheme addition addition addition ai ai maps computing domain domain domain domain domain view solutions detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection detection conference conference conference conference conference conference conference conference conference conference conference determine determine efficient efficient efficient efficient efficient requires requires statistics vision vision vision vision vision vision vision vision vision estimated pages pages pages pages pages pages pages pages pages pages pages increase produce produce condition weighted randomly types types finally processes nature depends simply achieved discussion normal technical describe describe arbitrary tested actions finding common implemented shape generate theoretical theoretical main face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face face journal pixel pixel pixel degree makes noisy including probabilistic probabilistic probabilistic unknown interesting significantly significantly significantly significantly ratio ratio projection edge edge increasing increasing increasing segmentation mechanism mechanism mechanism special structures matching empirical empirical empirical language language language language language principal details numbers iterations pre pre window window window window window international international international normalized normalized normalized produced sources sources recent recent recent property property robust robust ensemble reported reported practical apply introduced include machines machines machines machines pixels pixels pixels pixels hierarchical hierarchical trees sense recently relevant relevant relevant interest interest highly varying compare volume volume works tions yields correspond trans sparse sparse sparse sparse sparse sparse mixtures background evaluation evaluation evaluation positions improvement sensitive sensitive exists exists exists intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity intensity expression expression studied invariant scaling wide wide wide rotation rotation width clusters occurs setting strength conclusion editors editors interactions bayes bayes bayes clear clear performs weak encoding propose taking presence presence external characteristics drawn drawn drawn demonstrated intelligence intelligence intelligence intelligence intelligence labeled labeled variety start exist targets pro pro edges produces index winner ways label label vertical linearly infinite infinite text scales scales scales scales springer springer versus boolean boolean boolean boolean yield national family dependence stages variation detailed evaluated evaluated evaluate restricted decomposition discrimination key sec sec sec purpose purpose false false false false false false false false tracking assigned faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces faces views transactions transactions transactions degrees building building template includes thesis thesis priori priori color weighting sciences sciences sciences automatic discuss discuss specifically specifically specifically variations variations variations domains domains absolute successfully texture identified efficiency uniformly society society society society society maximal encoded computationally computationally effectively driven driven driven svm poggio poggio presentation successful identify detect detect detect detect detect detect detect detect detect detect efficiently efficiently efficiently comparing situation capture capture capture quickly quickly prob success success success success link dis issue contribution criteria bar involved generalize paradigm highest received received extract poor poor investigate exhibit relations relations relations humans strengths issues preliminary discriminant fashion links detectors detectors int decisions variability workshop encode encode understand attributes attributes attributes plausible predicts predicts extremely facial facial perfect algo fisher detector detector detector detector detector detector detector mapped mapped expressions expressions ith consist detected detected detected detected detected detected detected detected detected contributions contributions regime motivated phd phd histogram indicating crucial crucial orientations variances growing fairly adapted expensive briefly benchmark benchmark benchmark benchmark benchmark benchmark correction reasons processed sys sys commonly separately separately involve attribute attribute attribute localized annual annual addressed virtual fourth improvements collected collected profile profile profile empirically cmu bootstrap flexible flexible posed detecting treated variant ity maintain execution http exhibits summarized ture extracting coherent kinds sophisticated windows june june yielding irrelevant naive naive naive contribute phenomenon pose pose representative pac aligned redundant sort www mistake mistake mistake appearance appearance acm acm rithm girosi databases databases rotated addresses tem connecting grows rigid kullback kullback kullback kullback allocation simplify multiplicative multiplicative primitive primitive primitive primitive primitive intelligent height hope mark imply illumination illumination illumination illumination symposium selects utilized excellent started heavy combines ensures ensures studying surprising moved dominant evident yang yang yang yang yang yang recog recog insight reveals warmuth warmuth repeatedly theoretically gesture gesture considerations cam automated learnable posteriori yale yale unchanged outperforms outperforms outperforms linked linked linked unified parsing numerous constitute diverse pentland pentland nition nition poses poses poses poses incrementally freund valiant winnow winnow winnow winnow winnow winnow winnow winnow winnow winnow rectangular rectangular rectangular summarizes favor baluja baluja tems degraded allocated allocated expand increasingly investigating frontal frontal frontal frontal intensities option indexed supports rotating rotating tune subspaces challenge vice shallow emphasis lighting lighting lighting lighting lighting versa scanned scanned scanned bridge characterizing resolve mrf mrf ers suffers locate utilizes blum suffices finer tors reflecting harvard harvard harvard illinois mistakes sparsely detects detects manually huang huang huang huang huang littlestone littlestone littlestone isolation isolation html vertically upright upright upright kivinen robustly robustly sparseness ira ming subnetwork propagates eigenfaces detections detections detections detections phillips phillips phillips ceedings stems urbana urbana landscapes degrade ambiguities subnetworks subnetworks sung sung sung predefined snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow snow rela predic locating nov sixth tailored tailored tailored equalization subsampled collect analyzers analyzers vast bruce bruce narendra rosen beckman linguistics exponentiated fogelman fogelman deformable rowley rowley rowley rowley utilization roth roth roth roth roth roth roth roth graham kanade kanade kanade cap discard nato nato helmbold discarding champaign simplistic corpora uninformative logarithmically autonomously dan detec conjunctive ended augmenting qian commun ingredients photographs eigenspace soulie soulie asi asi fifteenth oth spelling tally abound bench buildings osuna discriminator discriminator cartoon cartoon sitions discrimina moon wechsler wechsler abilistic enclosing discretize phrased cached tagging elaboration stood cropped acl retrospect surge promoted 
#@Ahuja_N,Roth_D,Yang_M,
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#*model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural data data data data data data data data data data data data data data data data data function figure figure figure figure figure figure figure figure figure figure set set set set training training output output number error error results results results results information information information information information information information information information information information information problem models models models models models models models models models performance based based based space space weights linear linear layer layer case order order shown shown values values values values values values probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise weight distribution distribution distribution distribution recognition approach approach image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single single single single processing processing processing control local local local local local local local local local local local local local local local local local local local local local local local local local local local rate test analysis analysis class class form form form form shows shows shows simple simple gaussian gaussian gaussian gaussian visual visual visual paper paper paper examples work task task task methods step step process level level level level level current trained trained trained trained trained high similar similar similar similar representation representation representation representation representation equation equation equation equation equation equation section line line line images images images images images images images images images general general general parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter theory gradient obtained note note note note experiments experiments experiments experiments experiments experiments university university variables variables variables variables variables variables independent independent log log found found constant table table estimate estimate estimate estimate estimate estimate standard standard standard standard standard standard standard computer distance prediction left left left left left motion motion motion motion motion press press position components components outputs outputs outputs continuous sample abstract applied computational computational references component component due due ieee procedure procedure procedure procedure procedure procedure procedure important important important decision context context context context estimation estimation estimation estimation estimation estimation behavior stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical effect effect generated generated generated generated generated variance variance variance variance variance variance variance tion variable variable variable lower prior prior prior prior representations representations representations representations representations representations representations representations representations representations part center type type multiple multiple good good conditions conditions conditions conditions represent represent bayesian bayesian bayesian bayesian bayesian bayesian equations region region proposed proposed errors ing ing ing ing ing computed sum elements regions regions means means natural natural orientation orientation global global global applications study study study study filter obtain obtain obtain relative relative relative relative specific specific specific specific specific specific specific specific specific samples represented represented true compared provide define determined experimental experimental experimental experimental experimental experimental experimental experimental goal distributions distributions distributions distributions distributions distributions distributions distributions distributions equal accuracy comparison train descent dependent dependent dependent dependent dependent modeling modeling department department individual individual responses responses difficult final exp exp exp exp exp exp exp bias ai maps framework cambridge cambridge computing experiment experiment directly directly estimates estimates estimates estimates estimates top top stage stage stimuli stimuli determine determine upper free free estimated estimated estimated con produce derived derived weighted weighted developed levels levels levels levels area types types finally evidence nature achieved achieved increases describe describe describe tested assumption assumption surface surface surface surface surface surface surface surface surface predictions predictions predictions predictions finding nearest assumed shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape shape generate supported role main eds eds ability degree degree degree degree makes noisy fit fit probabilistic probabilistic pairs smaller underlying underlying combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination combination account account account account account account account account block projection trials trials matching matching matching uniform uniform uniform database database database database leads leads representing filters filters pre direct making bottom depth depth depth depth depth depth combined combined combined combined predict population discussed directions recent recent pair robust robust separate separate separate separate introduced subject subject subject subject subject subject subject identical side side pixels pixels hierarchical hierarchical hierarchical hierarchical hierarchical inference inference inference inference inference inference inference subset relevant relevant relevant varying approximately subjects tions match match studies sensitive entire amplitude horizontal intensity intensity intensity intensity invariant trial trial deviation deviation locally column column pass conclusion place greater greater greater assumptions depend depend central modules accurate weak propose taking taking taking strong integration integration integration characteristics turn turn plane plane relationship relationship introduce manner scene scene question relation pro derive produces produces perception perception perception perception perception perception ways factors primary primary generating generating estimating describes describes describes describes involves scales interaction interaction interaction develop develop adding adding gaussians applying applying formed formed blocks versus select formation formation formation interpretation codes variation forms forms understanding understanding approximated smoothing dashed combining combining combining combining generation generation generation intermediate intermediate intermediate distances distances filtering assigned faces views box combinations formulation weighting uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty priors priors variations neighbors texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture texture middle aspects aspects aspects aspects identified identify essentially orthogonal fine composed repeated contained allowing dis contribution content criteria generative generative generative generative generative generative generative generative generative cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cue cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues cues sampled sampled vary vary play dayan paradigm realistic realistic providing overlapping subsequent disparity extract jacobs unlike powerful perturbation create essential experience varied varied environments integral accurately dual biases history ideal reliable reliable proved fundamental analogous surfaces surfaces patch patch patch patch patch patch patch patch measurement naturally naturally predicts psychology equally perfect perfect subsets aspect versions mapped utility utility histogram ment band developing orientations variances independence lies lies spatially easier projected separately separately involve res res res res res medical patches patches patches integrating considerably limits applies reflect tional generic conducted psychophysical psychophysical formulated reliability reliability reliability reliability reliability reliability compares outliers polynomials mod ture differs gen incorporating curvature curvature curvature adjust richard findings yuille univ univ assign forming gabor arguments zemel zemel zemel zemel zemel zemel databases enhancement enhancement enhancement extending binocular binocular fits simplify simplify held height obtaining implications motivation utilized combines entry displayed intended accounts stereo stereo yang yang viewing viewing entries entries occlusion young young infer infer infer rich horn agree std vari vari counts fusion ence shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading shading incorporates validity validity pentland adopt ideally ical certainty principled manipulation unseen pami cosine intensities indexed weaker reveal reveal inverting inverting inverting els psychophysics psychophysics psychophysics psychophysics psychophysics computa computa experi worked utilizing preserves preserves handling vis vis vis vis transforming transforming pouget observers observers observers adaptively exper exper err err eral concerns inferring inferring conditionally systematically screen cur curved accounting ance defense ous mesh mesh mesh violated sur stems aims utilities nov accu judgments nation malik ies exclude exclude underlie handles conducting tributions stereopsis entails entails rrt rrt weakened stud veto veto indexes lesser combi tex richards richards viii ship slant increas manipulate underly arizona arizona judgements iments completing johnston johnston combina shadows shadows lyl duces tii weightings weightings harmful landy landy landy ils ang psychophys managing managing managing managing underestimates sii trt trt trt trt teresting infers tucson neatly mite iment fib 
#@Yang_Z,Zemel_R,
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#*network network network network network learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set set set set set set set set set set set set set networks networks networks networks networks networks networks training training training training training training training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number number number system system system system system system system system system system system system system system system error error error error error error state state state state state state state state state state state state state state state state results results results results information information problem problem problem problem problem problem problem problem problem problem problem models models models models models models models models models based space space space space space space space space space space space space linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case vector vector vector order order systems parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters noise distribution recognition method method method method approach point point point point single single single processing control control control control large large local local local local local local local local local local local local local local test test test test test analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix inputs form form shows shows shows shows shows shows signal signal signal examples examples examples small small work work work work work methods fig fig step step step step step points points points points process current current trained trained structure problems problems high representation representation show show show section section fixed parameter real states gradient gradient gradient term term term term term term term term note experiments dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional result result result university computation computation research research research research research research research independent independent found found found sequence dynamics dynamics dynamics initial constant constant estimate estimate estimate distance distance distance distance node node node node node prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction left direction direction direction direction map map map present low low low low low nodes nodes object maximum range range learn learn learn learn learn learn basis nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs sample sample sample sample sample abstract find references component component component component component component component component ieee ieee ieee positive procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure procedure important important introduction introduction complex estimation behavior behavior behavior behavior dynamic dynamic dynamic generated generated variance variance variance variance variance variance variance difference difference difference complexity complexity lower lower lower learned learned chosen part center center previous previous cases good good good binary long long long tree tree tree tree tree tree tree equations make make make make make region region region proposed errors errors forward forward forward scale simulations simulations minimum regression regression regression regression regression computed computed computed computed computed sum sum performed called times times times regions regions regions regions regions regions means optimization potential potential potential potential potential potential dimension dimension dimension dimension dimension made orientation global global global global applications applications applications study em obtain original original original samples samples samples represented represented compared application desired series series series series series series series series series series series series series series define compute compute proc proc perform perform perform experimental experimental experimental experimental distributions discrete approaches approaches steps accuracy train train modeling modeling modeling modeling modeling modeling modeling report institute words implementation technique technique consists consists consists consists represents represents delay delay scheme sequences maps maps computing computing computing computing directly curve limit top top determine determine significant free increase increase increase produce weighted bounds lines path product product selected iteration iteration depends measured measured measured measured measured normal technical describe tested fast fast fast fast close assumption complete stable predictions predictions predictions predictions short short short short short short nearest nearest common common shape shape generate supported main cluster cluster cluster cluster cluster cluster cluster future makes makes development development noisy fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit objective typically smaller reduced jordan jordan jordan jordan technology technology technology technology increasing increasing mode principal principal principal principal principal principal principal principal principal principal squared squared iterations iterations stored experts experts experts early early minimize produced predict predict predict predict predict predict improved directions directions directions robust robust robust robust robust element apply apply identical identical side hierarchical hierarchical hierarchical hierarchical subset subset subset subset subset subset engineering engineering engineering engineering engineering sufficient compare previously solve match match match pca pca pca pca pca pca pca pca converge trans diagonal mixtures mixtures mixtures evaluation bounded organization entire increased amplitude exists trial wide wide alternative locally locally loop loop loop loop deterministic clusters clusters clusters clusters white white white column pass pass starting greater reduce reduce conclusions depend depend depend differences measures accurate accurate designed designed clear practice learns learns learns constrained propose taking hard largest largest largest largest largest largest reduction reduction characteristics characteristics sigmoidal regularization variety minimizing minimizing start plane plane iii iii introduce introduce identification attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor attractor acknowledgements van van van written plot stability stability dept confidence pruning simultaneously simultaneously linearly linearly physical involves involves slightly scales select competition competition competition competition focus review reconstruction squares squares squares squares overlap overlap solved solved solved solved organizing organizing lee decomposition decomposition decomposition decomposition converges converges partition measurements measurements measurements measurements delays delays sec sec sec sec sec sec sec sec sec sec fitting fitting fitting fitting add add iterative iterative boundaries boundaries boundaries boundaries closed closed closed closed remains assigned construction foundation euclidean kohonen existing figures subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace subspace selecting closely divided identify attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors attractors detect detect conf quickly quickly repeated stopping stopping split split split split split split split split split split split split split split split split issue criteria sampled paradigm backward backward giles giles giles giles giles giles eigenvalue automatically illustrates jacobs jacobs jacobs jacobs neighboring neighboring neighboring decreasing decreasing modelling minimized create create create create exponentially rapidly put limitations limitations divergence dataset rise matches project terminal terminal terminal terminal terminal terminal int int analytically possibility understand fundamental fundamental fundamental math ensure ensure subsets subsets singular singular singular singular bifurcation logistic logistic logistic shapes detected detected submitted chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic chaotic defines optimum formula formula directed smoothness guaranteed defining growing unstable unstable unstable biology caused benchmark correction correction correction correction starts starts reasons forces forces forces forces hyperplane mathematics mathematics cut scientific projected implicit optimize optimize optimize localized arises depicted bandwidth bandwidth meaning explained greatly fuzzy fuzzy fuzzy fuzzy flexible generic leave introducing share share detecting detecting adjustable adjustable passed compares http partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning partitioning spread spread prevent prevent enables shaped focused wang progress univ univ univ univ cor lot phenomenon lab discontinuities newton leen leen intractable notes www guarantee princeton hyperplanes hyperplanes reconstructed reconstructed reconstructed reconstructed proceed lost climbing inspired chance chemical chemical chemical chemical chemical chemical grow grow grow los keeping nearby splitting splitting splitting child repeat embedding embedding financial introduces surprising infinity den den initialize iterated membership creating creating creating creating creating ahead clean horizon pendulum eigenvector eigenvector splits splits implicitly santa santa santa santa explains default dividing limitation outlined outlined fitted verify outline covering recursively creates creates creates adopt pointed pointed residuals residuals residuals corrected chaos chaos guess imagine imagine principe principe principe principe principe reconstruct mismatch perpendicular perpendicular perpendicular perpendicular mhz toy toy disadvantage met fir fir projecting monitoring enforce son lapedes transients nec nec resembles lecture resolve instability instability prefer locate aid stay stay affecting visit laser laser laser laser laser laser detects fft fin fin fin fin confined counterpart creation enters robustly carrying corn alamos neglected stm stm stm shares cope sorted diverge noticed stabilizing stabilizing farber farber upward dilemma minute netherlands netherlands netherlands grown ago subtract deformed outlines outlines outlines outlines outlines outlines euclidian turbulence augment bandwidths bandwidths bandwidths bandwidths bandwidths bandwidths circumvent intersecting kuo kuo faithful takens takens takens takens takens takens takens takens takens rue triggers cre strange gravity fluid fluid attracting sudden secs concludes team team collapse collapse collapse danger memberships interplay kambhatla kambhatla stretching folding tude died finance carded escapes marc collapses pentium regressors eindhoven olivier subproblems exceptionally unfortunate extrapolating 
#@Bakker_R,Coppens_M,Giles_C,Schouten_J,Takens_F,van-den-Bleek_C,
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#*network network learning learning learning learning learning learning learning learning learning learning neural neural neural neural neural neural data data data data data data data data data data figure figure figure figure figure figure figure time time set set set set set set set set set networks training algorithm algorithm algorithm algorithm algorithm output number number number system system system system system system system system state results results results results information information information information information information problem models models hidden performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based space weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear case order order order order order order order order order order order order shown shown systems systems systems systems systems weight functions functions neurons unit recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition method method method method method approach pattern pattern pattern pattern point point image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image processing processing control local local local local local local local local local local local local local local local local local local local local local local local local rate analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal simple gaussian visual visual visual visual visual paper small feature feature feature feature feature feature feature feature feature work work task methods methods methods methods cells step points features classification classification classification classification classification classification classification classification classification classification classification classification classification classification classification level trained trained trained high high high high high high high high high response response similar similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation architecture fixed vectors vectors vectors images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images general generalization generalization speech parameter parameter theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained activity activity dimensional university threshold computation computation computation computation research research research research independent independent independent independent independent independent independent independent independent independent independent independent independent independent independent defined defined defined defined defined found found found found found sequence sequence sequence sequence table table computer computer computer terms terms distance distance distance distance science science science low low machine machine machine object object range press press press press components components components components components components components components components components components components components basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis basis outputs outputs abstract applied applied properties properties properties properties references component component component component component component component component component component component component component component component component component stochastic due ieee ieee ieee ieee important important important adaptive adaptive mixture introduction action action action action action action estimation behavior behavior statistical statistical statistical statistical effect effect dynamic variance variance cost change difference difference spatial spatial spatial spatial spatial spatial spatial spatial classifier classifier classifier classifier classifier classifier lower lower lower lower lower measure measure measure measure measure measure signals representations representations representations representations representations representations representations representations representations representations representations representations learned learned learned learned learned higher multiple multiple multiple cortex good represent markov make techniques techniques techniques techniques techniques techniques techniques techniques length correct correct correct observed scale classes ing ing ing ing human human human human human regression respect performed performed performed performed performed performed called factor factor factor natural natural natural global global global global filter filter filter negative relative specific specific compared compared compared compared application cross provide provide provide compute compute objects location eye cortical approaches approaches approaches mit mit accuracy accuracy comparison comparison comparison contrast support support source source source proceedings proceedings institute institute institute implementation technique technique advances advances joint final addition addition addition sequences sequences sequences sequences ai ai cambridge cambridge san san san san san san conference classifiers classifiers classifiers upper upper upper upper full full statistics statistics statistics statistics statistics statistics vision vision vision vision estimated basic basic basic basic pages pages pages validation coding coding coding coding coding coding coding coding coding coding derived derived derived derived randomly developed developed product provided provided provided finally processes selected selected evidence nature nature achieved achieved covariance tested tested tested hmm hmm hmm hmm hmm actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions finding amount nearest nearest nearest nearest nearest nearest common common effective effective assumed supported face face face face face face face face face face face face face face face face face face face face face face face face face face journal pixel objective objective underlying needed reduced reduced reduced account unknown coefficients coefficients coefficients jordan technology significantly significantly significantly ratio projection projection projection edge edge matching matching matching matching database database database principal principal principal principal principal principal principal principal principal principal representing filters filters filters pre pre pre window normalized experts experts supervised supervised supervised expert magnitude magnitude magnitude frame frame produced description improved improve improve improve recent exact advantage advantage advantage property property ensemble ensemble ensemble ensemble ensemble takes takes element similarity similarity similarity similarity similarity similarity similarity movement movement movement include include pixels pixels pixels pixels pixels pixels sense sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski sejnowski cognitive cognitive cognitive recently recently dimensions dimensions dimensions dimensions highly highly previously unsupervised unsupervised unsupervised unsupervised unsupervised approximately subjects subjects subjects subjects calculated volume volume volume tions tions tions pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca pca trans locations locations locations grant horizontal parts expression expression expression expression expression expression expression expression expression expression invariant scaling digital rotation alternative touretzky row reduce conclusions neighbor neighbor neighbor neighbor neighbor neighbor depend editors editors measures measures learns learns suggest suggest encoding reduction reduction demonstrated california intelligence intelligence intelligence ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica ica movements movements movements iii appears relation digit primary distinct distinct modeled coordinates coordinates coordinates dimensionality dimensionality dimensionality dimensionality dimensionality angle scales interaction interaction frequencies frequencies frequencies frequencies frequencies frequencies versus versus cycles cycles cycles select competition choosing family detailed detailed evaluated lee centers centers frames decomposition decomposition performing performing performing iterative tracking euclidean euclidean euclidean euclidean faces faces faces faces transactions transactions template template template template kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels kernels thesis combinations bell bell bell bell eigenvalues eigenvalues blind blind subspace automatic mozer variations successfully columns compression closely differ differ driven driven driven driven driven poggio successful literature identity identity identity identity summary summary compact link issue classify sin sci categories gray sampled wavelet wavelet wavelet correspondence highest leading maximization automatically principles consisted consisted subsequent subsequent mixing tesauro oriented employed employed employed employed unlike unlike unlike diego diego diego diego preliminary discriminant dataset dataset dataset fewer fewer examine tech project behavioral behavioral behavioral muscle muscle relationships relationships relationships dependencies dependencies dependencies dependencies dependencies dependencies dependencies eigenvectors eigenvectors topographic topographic examined measurement editor analyze facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial facial eyes eyes implementations aspect aspect der logistic fisher fisher fisher fisher fisher separated expressions expressions expressions expressions consist phd finds electronic rows rows scenes scenes pairwise agreement orientations orientations analyzed adapted independence independence independence caused tool spatially spatially spatially spatially widely widely located projected projected separately involve begin res medical lowest patches patches computers computers bandwidth recognizing recognizing addressed outer percent prop collected axes leave orders orders share share employ employ employ employ employ compares compares templates templates howard modulated proven proven gave gave inherent redundancy redundancy neuro findings findings findings findings distortion cor cor classifying classifying classifying classifying classifying classifying classifying leen investigation gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor gabor ratios ordering ordering repre repre repre repre spontaneous imaging imaging ranges tools city serves salk salk salk cottrell cottrell symposium symposium muscles performances performances performances performances performances mance bartlett bartlett bartlett bartlett bartlett bartlett bartlett recovered mouse paul perfor accounts bases bases francisco recog waves specialized contraction jolla jolla cpu cpu motions seung insensitive automated automated automated infomax yielded appeared ence ence drop sine sig super bank bank employs employs failed pentland amplitudes malsburg covariances classic brightness alter representa representa attempted cohn cohn diag ization hughes mouth mouth deconvolution march terrence maximally cosine cosine cosine cosine employing employing employing employing employing buhmann tied indexed anal anal register superposition superposition dictionary dictionary dictionary supports investigations investigations eigen mea vice november ucsd ucsd lighting advantageous versa restoration converging converging emotion emotion emotion emotion families families focuses movellan movellan movellan movellan movellan movellan movellan opponent opponent outperformed outperformed outperformed medicine engine subtracting atick atick luminance manually manually petsche wavelets wavelets wavelets wavelets wavelets wavelets attained meth colleagues convolved spie spie ods alto inde neutral neutral presently sis sis locality locality comprised comprised comprised nih tical sentation sentation sentation simoncelli eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces eigenfaces palo jose began ysis lange rotate predefined predefined predefined predefined pendent sentations yon joseph decompositions dependences friesen friesen excluding accessible concurrently animation terry ages ponent explores niques pared pared grove densely ration ons kanade discriminations erties rect turk quence discriminability discriminability discriminability warped vised quantifying decomposes decomposes redwood coder ended whitening discriminants discriminants discriminants testbed social cod cod surveys pacific downsampled downsampled graylevel graylevel lades lades analy sepa engines click duction discrimi utah javier happy asilomar brunelli stewart nificantly ships psychophysiology lth synthe surprised nizing consulting psychologists cropped outstanding surement 
#@Bartlett_M,Donato_G,Ekman_P,Hager_J,Movellan_J,Sejnowski_T,
#t13
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model neural neural data data data data data data function function function function function figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set networks networks networks networks networks algorithm algorithm number number number number system system system system system system system system error error error error error error error error error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results information information information information information information information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem models models models models models performance based based space space space space space layer case order order order order shown systems systems systems systems systems values values values probability probability probability probability parameters parameters parameters unit unit unit approach approach approach processing control control control control control large large rate rate rate rate rate rate rate rate rate rate rate test test optimal form signal algorithms simple simple simple simple simple paper paper paper paper paper paper paper paper paper paper size size feature feature feature feature work work work task methods step step features features process current current current problems problems problems problems problems random random random high representation representation representation representation show equation equation section section section fixed fixed fixed vectors vectors parameter real real real real approximation approximation approximation average average average states states states states states note experiments university solution solution solution defined sequence dynamics dynamics initial table table table table table table table table table table table table estimate computer computer computer distance left direction direction direction present low low low low low low low machine maximum maximum press press press press learn learn learn learn components components components components components abstract applied find references component component stochastic stochastic due ieee important decision decision decision decision decision introduction action action action action action action action dynamic dynamic dynamic generated generated variance cost change energy complexity variable variable variable lower lower lower lower measure learned chosen chosen chosen chosen higher previous previous bound bound bound bound bound multiple good good good good good good long long long distributed distributed distributed expected markov markov markov make probabilities errors errors errors errors errors errors errors forward scale scale scale finite resulting ing total simulation simulation simulation computed multi multi times times times times times times times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor factor factor made applications applications applications applications study policy policy policy policy policy policy policy policy policy knowledge negative specific specific compared compared application application application application application application application application application application application application application application application application application application application application application application application application application application application application application application application application desired rates rates location perform goal constraints gain power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power mit mit mit mit larger update update source source source source morgan proceedings proceedings words loss technique advances advances advances advances advances delay delay delay delay delay considered considered computing computing computing experiment environment directly directly transition transition effects bit capacity capacity determine efficient upper upper upper requires requires significant speed increase channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel channel coding developed levels levels criterion types path path product processes processes depends depends depends depends constraint simply simply measured group tested fast limited close corresponds complete actions actions actions actions finding amount short effective effective assumed generate generate supported theoretical main end end end instance future future future easily objective typically typically pairs reduced jordan jordan significantly significantly consistent call max max max max normalized normalized choose choose run run run run sources description improve directions recent takes typical apply strategy include side side side inference engineering solve yields rl rl address symmetric channels channels channels channels channels channels channels grant exists parts correctly deterministic setting setting setting pass runs conclusion starting starting critical assumptions reduce reduce reduce reduce trajectories reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward accurate faster faster practice practice constrained constrained hard mechanisms reduction characteristics demonstrated turn turn turn assuming minimizing minimizing exist introduce configuration base base base base base base base base base base base base acknowledgements longer factors generating describes changing changing modeled modeled implement implement simultaneously simultaneously infinite electrical mutual integrated quality implies implies expectation expectation focus focus stationary communication communication communication communication communication communication communication communication communication learner codes variation showed approximations sizes completely converges key remains symbol maximize maximize maximize mozer partially partially structural structural structural structural successfully aspects aspects driven included comparing orthogonal reached capture traditional conf conf quickly link stopping dis issue criteria criteria criteria criteria criteria criteria strategies device list list usual simplified realistic nips nips nips observable observable received received received received received received received received received received principles policies policies policies policies policies policies routing routing routing tesauro receive receive receive cowan unlike poor essential singh singh singh issues mdp hall terminal terminal terminal int int reliable reliable transmission traffic traffic traffic ensure portion explored mapped message message consist baseline generates generates detected simplest utility utility utility defines spin brown brown brown brown brown indicating ment caused reasons reasons turns turns turns sections closer desirable immediately commonly potentially nsf varies limits limits limits readily readily leave passed incorporated reliability ity ity rewards rewards rewards gen maximizes maximizes resource sophisticated age bellman bellman optimality formally acm acm optimizing dynamically mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile impossible reaching communications cellular adds allocation allocation allocation minutes mail mail mail mail mail simplify pomdp pomdp occurring wire receiver receiver receiver synchronous exceeds carry service service prentice interference interference introduces periods bad bad bad bad colorado colorado captured captured facilitate discounted discounted infer shortest shortest master kearns cpu cpu draw horizon horizon extends correcting impact tsitsiklis reverse captures receiving accumulated empty empty bertsekas treat treat maintaining usage usage usage usage usage usage usage listed discount discount discount discount inferred inferred inferred maximized transmitted transmitted seek drain drain simulating queue pub packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets packets management management management management management continues life life life life convert convert boulder simplifying considers lookup exceed emphasized emphasized turning turning turning gilbert packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet packet holding holding holding holding holding holding holding holding radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio radio littman removes rewritten rarely moderate info reinforce payoff slot slot send send send slots slots slots slots slots savings savings savings telephone cliffs termination supply clarity transmitter lists award identically identically concrete station station station station station station station station station station station boyan englewood chan measurable carries carries carries admission admission admission ignores consumption consumption aggregation aggregation aggregation communicate inde protocol protocol protocol protocol accounting ready comprised gathered transmit transmit transmit counted ensuring huge aggregate operated operated pendent occasionally battery battery battery battery battery battery battery battery battery battery battery battery battery battery battery battery battery ton ton ton ton sat observes examines impor wait wait wait wait tong web web web web decides decides waiting waiting waiting waiting waiting waiting tant intervening disk disk inhibits provably stays geometrically geometrically acknowledgment acknowledgment acknowledgment helmbold wireless wireless wireless wireless wireless wireless wireless wireless wireless wireless proaches arrivals arrivals kauffman reductions plications transport alternates interfere charged charged signifi delivers slave timothy discounting recommended recommended deficiency transmitting permanently telecom intent promote erating telecommunication telecommunication marbach taneously taneously plication simul simul conserve munications transferring munication malized cantly batteries batteries batteries qual browsing browsing browsing browsing unobservable managing protocols watkin career elliot recast ncr ncr multimedia provisions instructing ack 
#@Brown_T,
#t13
#!
#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model neural neural data function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time set set set networks algorithm algorithm algorithm number number system system system system system system system system system system system system system system error error error error error error error state state results results results results results results results information information information information information information information information information information information information information information information information information information information models models models models models models based based space linear linear linear linear linear layer layer layer case case case case case case case order order order shown shown systems systems systems systems systems systems systems values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise functions functions unit unit unit distribution distribution method method method method method method approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach approach single processing test test test analysis class form form shows shows shows shows shows shows algorithms simple simple gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian gaussian paper examples examples examples examples small feature methods methods process process process process process process process process process process process process process process process process process current current current trained trained trained trained structure structure problems random random random random random random random random random random random random random random random random random random high memory memory memory memory memory memory similar show equation equation fixed line line line general general speech parameter real approximation average average states states states states states states states states theory theory theory gradient note note experiments experiments experiments experiments experiments result variables computation log log defined found sequence sequence sequence sequence sequence sequence sequence sequence sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics dynamics constant constant estimate estimate estimate standard standard prediction prediction prediction prediction left left left left left left presented presented present present present present frequency maximum maximum maximum range press learn learn learn learn learn learn learn learn learn learn nonlinear nonlinear nonlinear nonlinear abstract find find density density density density density density density density density density density density density density density density density density likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic due ieee mixture mixture context introduction complex complex complex complex estimation estimation estimation behavior behavior dynamic dynamic dynamic dynamic dynamic dynamic variance variance variance variance cost tion assume assume assume assume assume lower signals signals signals learned learned learned learned learned learned learned learned previous previous cases cases cases type type type type type type long conditions distributed distributed expected equations make fact fact techniques proposed proposed observed finite resulting human multi multi sum elements means optimization optimization dimension feedback applications knowledge filter filter filter samples samples samples samples samples samples samples true true true compared application series define compute proc goal related related related related discrete discrete discrete equal equal approaches approaches approaches comparison comparison contrast train dependent dependent dependent source modeling institute technique kernel kernel kernel advances joint joint joint joint joint connectionist difficult ai framework framework cambridge equivalent equivalent estimates estimates estimates estimates top top top top determine efficient choice statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics statistics world world estimated estimated estimated pages pages derived conditional conditional conditional conditional conditional conditional conditional criterion criterion types types types lines lines lines lines lines lines entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes processes sampling constraint simply achieved describe describe denote hmm limited assumption assumption assumption assumption predictions predictions predictions predictions predictions finding common assumed assumed theoretical square end ability ability ability future future future future future future future future future future noisy noisy noisy noisy noisy noisy noisy noisy noisy probabilistic probabilistic probabilistic underlying underlying underlying combination dynamical dynamical dynamical dynamical dynamical dynamical dynamical unknown coefficients technology interesting interesting significantly york york edge trials trials empirical empirical mode mode leads squared squared max bottom bottom bottom depth depth depth depth depth depth minimize description description light predict predict predict perceptron perceptron recent exact exact sense interest sufficient sufficient sufficient sufficient sufficient varying previously observations observations observations solve yields differential rl definition deviation alternative demonstrate demonstrate runs assumptions assumptions conclusions editors tangent practice propose propose taking strong drawn demonstrated demonstrated solid solid solid solid minimizing minimizing minimizing iii iii iii iii identification explicit explicit pro monte monte carlo carlo longer ways estimating estimating plot plot plot ann changing modeled modeled simultaneously remaining mutual mutual mutual mutual gaussians events extraction john john yield extracted extracted dependence depending stationary stationary stationary stationary stationary stationary estimator densities densities densities densities densities densities densities approximated approximated discrimination past past past past past past past past past past past past past past past past past past key dashed dashed classical classical reduces purpose false box box figures perceptrons illustrated uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty discuss discuss mozer characterized characterized characterized tests importance differ differ driven driven driven driven driven driven efficiently efficiently efficiently essentially reached traditional compact compact conf interested classify duration sampled absence minimizes wave wave wave wave principles situations bars parametric parametric parametric parametric wiley exhibit estimators estimators estimators estimators integral divergence dotted dotted reducing ideas mse mse applicable dependencies maximizing maximizing cover matched math coefficient concepts possibly editor analyze analyze illustrate obvious fisher fisher fisher fisher fisher fisher observe academic switching switching utility massachusetts massachusetts mentioned mentioned residual slowly theoretic theoretic theoretic theoretic theoretic separable distinguish distinguish distinguish distinguish distinguish fairly explanation tractable drive rapid tive worst consequence opt implicit implicit depicted auto sun robustness robustness empirically understood flexible poorly compares price price synthesis synthesis synthesis mod mod characterize characterize characterize popular incorporating marginal logp chose focused lim differentiable room accomplished conditioned driving driving optimizing perfectly concerned purely unity flexibility outcome kullback adds exploit analyzing methodology nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric nonparametric reliably repeat financial periods paul surprising realization forecasting den den den captured hasselmo thomas waves waves waves waves thin insight matter informative informative informative informative informative informative informative informative informative informative informative informative sons captures implicitly implicitly valuable characterization summarize summarize fold avoiding market accumulated accumulated informa informa ple specification converted leibler stock residuals residuals residuals ideally ideally hundred associate principe illustration principled manipulation summarizes exam thick parzen parzen simplifying statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic statistic proach conversely termed importantly breaks preserve places exhibited differing differing differing increments increments wider challenge challenge strict modal modal modal modal modal spite walk walk walk walk walk walk served parameterization bility hyperbolic tom jointly jointly viola viola viola doesn ave realizations realizations identically distinguishing striking sity suffice asset robustly stationarity opinion discriminating violate entropies retaining wiener wiener wiener spots argmin argmin argmin virtue impor alexander seeking desire conveys sorts mild novelty sults categorize vation ogp accompanying accompanying accompanying innovation obser knowl insignificant summarizing summarizing summarizing walks grounded cesses stats eling ola ola collapsing abound compelling bot regressive pricing touretsky ener llp wildly 
#@Fisher_J,Ihler_A,Viola_P,
#t13
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#*network network network network network model model model model model model model model model model model model model model neural neural neural neural neural neural input input input function function function function function function function function function function function function figure figure time set set set set set set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number number number number system system state results results results results results information problem problem problem problem problem problem problem problem problem problem models models based based space space linear case case vector vector order shown shown systems values values values values values values values values values values values values values values values values probability probability probability probability probability probability parameters parameters parameters parameters noise functions functions functions functions functions functions distribution distribution distribution method method method approach approach approach approach approach approach point image single processing processing large large large large large local local local local local local local rate test test test test test test test test test test test test test test test test test test test analysis analysis analysis matrix optimal optimal optimal optimal form signal signal signal signal signal signal algorithms algorithms paper paper paper paper paper examples small small small small small methods methods step step points field field field field field field field field field field field field field field field field current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current current problems problems problems problems random random random random random random random random random random random random random random random random random random show fixed general generalization generalization parameter parameter parameter parameter real real real real average states theory gradient obtained note note dimensional dimensional result university variables variables variables variables variables variables solution solution solution solution solution solution solution solution solution solution solution solution solution solution solution research research defined defined defined defined target initial constant table table standard node node node node node node node node node node node node node node node node node node node node node presented phase phase phase low nodes nodes nodes frequency frequency frequency maximum maximum maximum maximum press press press components components components components components basis nonlinear nonlinear nonlinear nonlinear continuous continuous sample sample abstract applied convergence convergence convergence convergence convergence analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog analog references component component component component component component component component component component stochastic positive positive important important decision decision decision decision decision decision decision decision decision context context context context introduction introduction introduction introduction introduction complex complex complex complex complex circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit behavior behavior dynamic generated generated generated generated generated generated generated parallel search tion tion change energy variable variable variable variable variable variable variable variable variable variable variable lower measure measure measure chosen part part part previous previous bound bound type type long represent distributed expected equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make fact proposed proposed proposed probabilities probabilities probabilities probabilities observed observed observed scale finite finite finite ing ing total simulation human human human computed computed computed computed respect respect sum elements means factor factor potential potential potential potential potential potential potential potential potential potential feedback global global global global global global global global knowledge obtain obtain negative artificial relative specific specific specific specific specific specific specific represented application application desired desired desired desired desired desired desired provide provide define define define constraints constraints constraints constraints constraints connected discrete discrete brain equal equal approaches approaches mit mit mit voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage voltage fields fields fields fields fields fields fields descent dependent dependent dependent dependent source source source source source source source source modeling modeling consists code individual joint exp exp addition graph graph graph ai considered considered considered cambridge cambridge cambridge computing computing domain environment directly directly directly directly directly directly directly additional additional solutions curves curves curves estimates design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design design efficient upper choice choice choice choice approximate free free world estimated increase con condition channel conditional conditional conditional conditional conditional area types types actual actual actual provided provided provided provided provided finally selected constraint constraint simply simply simply simply measured describe denote fast close inverse corresponds complete proof proof circuits circuits circuits circuits circuits circuits circuits effective assumed assumed assumed eds easily easily easily degree degree makes rumelhart objective objective objective simulated simulated probabilistic probabilistic typically typically hopfield combination dynamical ratio ratio york york york mechanism special consistent uniform empirical empirical representing representing details details details numbers numbers iterations pre direct direct making making normalized magnitude magnitude magnitude magnitude magnitude magnitude magnitude magnitude idea minimize run sources sources sources improved discussed property pair pair takes strategy strategy include quadratic subset subset subset engineering highly highly highly highly approximately approximately calculated volume tions solve converge definition evaluation chain locations gate gate gate entire constructed concept concept suggests alternative deterministic minimal greater assumptions assumptions neighbor valued designed weak weak constrained temperature temperature strong external external external external characteristics characteristics characteristics proportional turn exist annealing denoted denoted denoted suppose monte carlo index solving solving solving factors mathematical mathematical modeled modeled modeled confidence confidence confidence confidence confidence explicitly explicitly physical electrical angle angle angle unique integrated equilibrium springer shift quality implies versus decreases choosing choosing expressed viewed controlled controlled controlled understanding similarly similarly constants processor sign sign diagram key key slow normalization combining fitting neighborhood neighborhood iterative iterative assigned assigned construction degrees degrees box combinations combinations formulation currents currents currents eigenvalues eigenvalues maximize specifically absolute major determining selecting computationally effectively mcclelland modes essentially ten reached characteristic characteristic characteristic road refer verlag prob heuristic link anderson satisfy satisfy notation quantity eigenvalue automatically operating operating preferred preferred preferred acknowledgments software decreasing situations law law law law law law law law law law law law law law law law minimized minimized schedule wiley wiley poor essential experience difficulty varied varied involving strengths strengths hanson hanson limitations accurately mass helpful helpful project terminal terminal terminal terminal transistor transistor transistor transistor transistor transistor referred referred referred variability necessarily configurations equally voltages voltages voltages voltages voltages prototype portion portion noted algo initialized ith ith improving mixed contributions contributions contributions electronic electronic devices indicating indicating indicating preference preference preference preference developing formula formula formula formula formula ground agreement guaranteed defining briefly briefly briefly briefly tool tive satisfied satisfied satisfied satisfied arc strictly strictly constructing constructing choices choices probable probable fourth fuzzy substantially incorporated incorporated treated maxima exhibits limiting differs differs ordered richard begins specifies specifies hints arithmetic intractable www www generator assign formally guarantee restriction rithm appropriately appropriately optimizing optimizing jth jth smolensky clamped clamped clamped convenient difficulties accepted logarithmic resistance harmony harmony methodology capacitor capacitor capacitor optimally adequate hours passive meaningful realization realization iterated foundations foundations indicator eigenvector designing integers vari vari numerous clique clique clique opposed opposed terminals obtains drain drain drain classic classic classic associate guess options resistor resistor resistor resistor resistor resistor resistor resistor mhz mhz mhz mhz insights compensate generators permits proba carefully efforts wise funded tively resistors resistors book nal matlab lems topologies laws laws satisfaction lation bility mrf mrf mrf subjective subjective capacitors supply kth flows functionally functionally functionally functionally ultimate convention computable ranged corn metropolis metropolis texas texas texas substrate dence correlational cons entering entering entering entering entering fundamentally ables cient imaginary reviews posi illustrating illustrating remember cooling tot engineers golden golden golden golden golden golden golden specifications optimiza embodied ralph proaches industry sketched sketched diode diode diode unclamped unclamped unclamped instruments flowing flowing incor probabilistically alterations kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff kirchoff expertise cording grounded grounded pute positivity confi requisite professor effi lent engineer engineer dia pentium porated rewarding diodes engi consulting skilling transis limita assisting 
#@Golden_R,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model neural neural data data data data data data data data data data data data data data data data data function function function function function figure figure figure time set set set training algorithm number state results results results results results results information information information information information information information information information information information information information information information information information information information information information information information information information information problem problem problem problem problem models models models models models models models models models models models models models performance performance performance performance performance based based based based based based based space space weights linear case case case case case vector vector vector vector order order order systems systems values probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions distribution distribution distribution distribution distribution distribution distribution method method method method method method method approach approach approach approach approach approach approach point single processing processing processing processing large test test test analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis class class class class class class class class class class class class class class class class class class class class class class matrix matrix matrix matrix matrix matrix matrix matrix matrix shows simple simple paper paper paper paper examples small net work work methods methods methods methods methods step step step features classification classification classification level current trained trained trained trained problems problems problems high high similar similar representation show section section fixed line line rule vectors general general general general general general parameter real approximation approximation approximation average average average average states states gradient obtained term term term term term note experiments experiments experiments experiments experiments experiments dimensional dimensional dimensional university variables research research independent log log log defined defined constant table table table table standard standard standard standard standard computer computer terms terms terms science science presented presented low low low machine machine object sets maximum maximum press press learn learn learn position basis sample abstract applied applied applied applied back computational computational likelihood likelihood likelihood references references due positive procedure important important important important mixture context context context introduction estimation estimation statistical statistical statistical variance tion tion energy variable variable variable variable variable assume assume assume classifier classifier measure prior word word word word word word word learned learned learned part part cases type type required multiple good represent bayesian bayesian markov markov fact proposed proposed proposed length probabilities probabilities observed errors simulations resulting classes respect respect called called called means factor factor factor dimension dimension made natural applications applications study knowledge knowledge em em obtain negative negative negative specific specific represented represented series provide provide provide define define define define define compute objects experimental goal related related related posterior posterior posterior constraints constraints distributions distributions gain motor mit mit larger support support source source source modeling modeling modeling modeling selection selection proceedings proceedings proceedings report words words words words words words words words words words words department department loss version technique technique individual individual kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel kernel advances advances joint scheme scheme sequences framework computing domain domain domain equivalent additional additional additional view view limit stage conference conference conference classifiers classifiers choice statistics statistics statistics statistics statistics free world world world estimated pages pages increase give derived derived derived derived derived weighted conditional conditional clustering clustering clustering clustering developed levels levels levels levels area product product product product product finally selected selected nature sampling constraint achieved achieved normal technical technical technical limited inverse assumption assumption assumption assumption assumption assumption assumption corresponds corresponds nearest nearest nearest common common common effective theoretical main journal journal square square square end makes development probabilistic probabilistic probabilistic typically typically smaller combination reduced account coefficients jordan interesting interesting york york york empirical empirical language language language language details details pre making making international international normalized supervised supervised supervised supervised attention combined combined run sources sources sources sources sources denotes denotes discussed resolution resolution exact advantage robust similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity similarity reported reported practical include identical machines machines sense inference subset relevant sufficient highly unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised yields yields yields match pca differential differential definition definition background evaluation observation organization parts invariant occur digital wide wide white occurs occurs generally setting demonstrate conclusion starting assumptions assumptions neighbor neighbor competitive central bayes exponential exponential exponential exponential exponential practice asymptotic propose propose reduction reduction demonstrated labeled relationship relationship manner manner base areas derive derive derive written index ways factors factors factors factors factors estimating modeled modeled recall metric explicitly involves text text text text text text text text text text text text text text text text text text text unique develop develop applying springer implies expectation yield national family family family focus focus depending overlap overlap viewed viewed interpretation interpretation interpretation labels lee lee decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition understanding approximated similarly partition constants key reasonable additive classical normalization normalization convex tracking filtering query query advantages precision precision exploration kernels thesis coordinate retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval inter inter determines specifically neighbors straightforward identified extra closely society driven delta svm svm svm svm svm svm svm svm svm svm latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent latent score essentially identity identity capture capture capture summary notice notice notice notice verlag showing interested interested return contribution contribution contribution follow follow generative generative generative generative generative generative categories categories categories list simplified board computes computes computes maximization principles principles principles principles illustrates mixing mixing intrinsic presents simpler american american american wiley transformed production collection collection collection collection collection association optimized divergence graphical graphical hall rise project investigated referred reliable root root root scores possibly predicting queries singular fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher fisher baseline amari mixed utility contributions contributions motivated phd plant defines brown brown brown great ment stop theoretic derivation derivation defining phenomena independence caused london london reasons perspective stanford closer products products probable cut english geometry geometry geometry geometry meaning conjugate explained requiring geometric geometric geometric questions questions improvements people people affine relevance tional generic conducted conducted parameterized experimentally experimentally quantitative documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents documents car haussler variant span price operate gains gains gains berlin vocabulary vocabulary summarized mod poisson popular popular occurrence occurrence proven extensions substantial substantial substantial damage jaakkola semantic semantic semantic semantic trade trade naive naive contribute contribute representative www japan extensive restrict conditioned conditioned acts databases purely food air kullback murray ments occurred satisfying satisfying held stated hyper mark tishby exploit unlabeled unlabeled unlabeled unlabeled unlabeled methodology knn knn knn knn knn knn knn knn knn affected intuitively intuitively canonical canonical corpus corpus corpus intuitive carry meaningful embedding document document document document document document document document document document document document document document document document introduces saul displayed displayed searching spherical spherical thomas dif similarities similarities similarities similarities similarities treatment emergence foundations foundations reader reader offer arrive theoretically environmental considerations seung exploiting implicitly automated market counts trading treat fitted verify informa approx geometrical geometrical geometrical geometrical svms svms svms svms gold rigorous email leibler tables tables tables aircraft stock uniquely bank distinction adopt discriminative year year conjecture multinomial multinomial multinomial multinomial multinomial multinomial multinomial multinomial german param param options rectangular community chapman proba relate simplifying scope topic topic dirichlet categorization categorization categorization categorization categorization categorization categorization emphasized memoryless memoryless memoryless memoryless memoryless memoryless geiger west exchange simplex union els port hofmann hofmann hofmann hofmann hofmann hofmann hofmann rose answers vice spite emphasis covers bridge parameterization parameterization parameterization parameterization january bility sake sake marks justification crude crude crude european families families families ferent house king hoc hoc hoc clarity december mining japanese appealing appealing proportions formulae exclusively assessment substitute classi cardinality rameters degenerate repository proves weather frequent curved curved curved company company company absent ready profit bottleneck motors cuts february united occurrences huge huge huge indexing indexing indexing validated opinion col addi aggregate aggregate stems initiated microsoft unobserved drug collections collections collections collections collections cars stabilizing spotting decompositions topics topics topics metal oil reactive imation availability pursued imposing distributional distributional subsampling subsampling subsampling rigorously prices prices web web subsampled billion billion billion named ranked boost challenges workers deficit deficit meanings meanings heckerman hypersphere banks correspondingly subsample orthogonality grain grain bag kronecker providence fell visualized implication news news today foreign identifiable administration compactly landauer simplifications told government revealing contracts congress combi ford referring dyadic proximate steel insignificant mln currency puzicha pereira pereira remedy biometrika topical dollars money ichi stories evans ida alike multinomials multinomials multinomials multinomials negativity optional submanifold strike aids tax bination dollar lots contingency contingency contingency spending conditionals additively shun deterioration wlx wlx msr sigir decom deerwester nations chief budget rice lection pirical docu docu barrel kass stricted exchanges concreteness earn earn director exclusion esting disregarding tiers 
#@Holmann_T,
#t13
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#*network network learning learning learning learning learning learning model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input input data data data data data data data data data data data data data data data function function figure figure figure figure figure figure time time time set set set set set set set set set set set set set networks networks networks networks training training training training training training training algorithm algorithm algorithm output number system error error error error error error error error error results information information information information information information information information information information information information information information information information information information information problem problem problem problem models models models models performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance performance based based based based based weights linear linear case case case case case case case vector order order systems values noise noise distribution method method method method method method method method method method method method method method method method method method method approach approach approach approach point image single single processing control large rate rate test test analysis analysis analysis inputs inputs inputs form shows shows shows algorithms simple simple paper paper paper small small small size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature net net task task methods methods methods methods methods methods methods methods methods methods methods features features features features features features features features features features features features features features features features features features features process process level level trained trained trained trained structure structure structure problems random random random random random random similar similar representation equation general generalization generalization generalization average average average average average average average average note activity result result result variables variables variables variables variables variables variables variables variables variables variables variables variables computation research research research research independent independent log defined defined defined found target initial table table standard computer distance distance science science science science prediction prediction direction presented machine sets sets sets sets sets sets sets sets sets sets sets press outputs abstract applied applied references ieee procedure important important decision context introduction complex estimation estimation estimation generated generated generated parallel recurrent change difference difference complexity variable variable variable variable assume measure measure measure representations learned chosen previous cases multiple good good good good tree tree make make make make make fact techniques techniques techniques proposed proposed proposed proposed proposed correlation correlation correlation correlation correlation errors errors errors errors errors errors errors tasks human regression computed computed performed called regions regions mapping made made applications study study original original compared compared compared application series series series series series series series series series series series provide provide define define define perform determined determined related related related equal equal equal approaches mit comparison comparison comparison connection connection connection train dependent dependent selection selection selection selection selection selection selection selection selection selection proceedings institute department technique technique technique technique individual individual individual individual individual individual individual advances represents difficult difficult difficult cambridge curve view estimates estimates limit stage conference classifiers significant significant statistics world pages validation validation validation give give con weighted randomly randomly randomly randomly randomly clustering clustering clustering clustering depends depends achieved feedforward increases arbitrary group group group group group group group group group group denote denote denote limited complete effective effective assumed generate generate cluster noisy noisy pairs pairs smaller smaller underlying combination reduced unknown interesting testing ratio ratio ratio increasing special database empirical empirical empirical empirical making normalized supervised expert magnitude idea attention combined combined description predict denotes improve improve recent recent correlations correlations correlations correlations advantage advantage advantage robust ensemble ensemble ensemble apply include period hierarchical hierarchical hierarchical subset subset subset subset interest sufficient highly highly compare previously studies studies achieve trans bounded improvement improvement constructed constructed touretzky clusters demonstrate runs runs reduce reduce conclusions editors measures measures measures measures measures accurate designed clear clear performs moody moody moody moody moody moody moody asymptotic propose propose reduction drawn demonstrated regularization relationship groups groups groups groups groups groups groups groups groups groups groups base relation pro pro construct construct construct index index index index index index index ways ways generating generating generating label distinct implement coordinates scales mutual mutual mutual mutual mutual mutual mutual mutual mutual mutual adding formed formed formed formed expectation cycles john yield yield yield national extracted independently independently independently independently dependence stages correlated correlated estimator key partial reasonable smoothing combining boundaries distances assigned existing box combinations uncertainty uncertainty discuss mozer candidate candidate reason selecting selecting selecting selecting selecting selecting importance effectively committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee committee genetic plots tend interested issue criteria criteria duration notation generalize leading received illustrates presents trains poor production production production production essential relations relations estimators estimators estimators reducing successive successive giving giving mse mse mse dependencies reliable decisions decisions decisions working workshop affect statistically momentum act closest editor necessarily analyze predicting subsets subsets subsets subsets obvious baseline baseline improving improving grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping grouping residual residual residual residual residual histogram ment inequality developing crucial slope independence independence starts reasons easier widely constructing constructing constructing constructing ran ran scientific members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members members optimize integrating reflects composite relevance relevance bootstrap price mod anti gen substantial redundancy redundancy cor cor lot trade uncorrelated redundant redundant notes forming forming forming investigation member member member member member member member member member member member member member member member member member member member member member member member member member member member member homogeneous jth promising proceeds stated balance hope removing published analyses excellent irregular predictors forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting forecasting evident infinity hasselmo bases mem mem mem mem late bagging rich impact shavlik vari market outperforms outperform outperform outperform ber break dec dec july stock diverse diverse year year intrator individuals decorrelation decorrelation shaded manipulation acting levin formance grouped graduate ization permits regularizer individually individually books names constructs sta els bill bill oregon aaai challenge housing expansions expansions picking picking picking achievable twenty marks supply december industrial industrial industrial industrial industrial dom identically resampling mistakes month month month month bond bond chan heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous heterogeneous economic economic economic economic economic economic economic economic totally inde cess nonstationary nonstationary nonstationary indicators jan jan correlational correlational bootstrapping bootstrapping bootstrapping bootstrapping degrade replicates preprocessed intrinsically observes ables conceptually monthly monthly netherlands burden jensen rosen tain economics hurt hurt hurt official official portland decorrelated badly business aaa bers bers bers committees committees committees committees committees committees committees committees committees committees committees committees calcu commit commit commit money erating ual selections duction xil bench rehfuss consumer vantage individ andj andj andj eighteen eighteen battiti educational bas unweighted meaningfully meaningfully artifical teresting logged pendently tee tee eco anc dividual andi 
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#*network network network network network network network learning model model model model model model model model model model model model model model model neural neural neural input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time time set set set set set set networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number system state results results results results units information information problem problem problem models models models models models models hidden hidden space vector vector order order order shown shown shown shown shown values values values parameters parameters parameters parameters parameters parameters parameters parameters parameters noise noise weight weight weight weight weight weight weight weight unit method method method method approach approach approach approach point point point point point point image image processing processing control control large large large large large large large test test patterns patterns analysis analysis analysis matrix matrix matrix matrix form shows shows algorithms algorithms algorithms algorithms algorithms gaussian gaussian gaussian gaussian gaussian paper small small small small small small size size feature feature feature feature work work methods cells points points points level level current current cell cell cell cell cell cell cell high high similar similar similar similar show show section line parameter parameter parameter parameter parameter real average average average obtained term term term term experiments experiments experiments experiments experiments dimensional dimensional university university variables research independent log log log log log log log found sequence dynamics dynamics initial constant table table standard standard standard standard computer terms connections connections science prediction left present present present phase activation temporal machine sets sets sets maximum range range press nonlinear nonlinear continuous continuous abstract computational convergence analog analog analog likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references component due due positive positive procedure procedure procedure important mixture mixture introduction circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit circuit estimation statistical generated generated generated generated recurrent recurrent search variable spatial spatial lower higher part part part previous type required multiple multiple good long conditions conditions conditions conditions conditions conditions conditions conditions represent distributed bayesian expected make region length scale scale scale scale scale scale scale scale scale scale classes classes classes classes classes simulation computed performed called times mapping means factor factor optimization made feedback feedback knowledge em em em em em em em em em em negative negative specific application cross cross cross cross cross cross cross series series provide rates proc proc determined experimental experimental experimental experimental steps steps connection connection connection connection connection connection connection connection connection connection modeling proceedings report report institute institute institute institute department implementation technique code code individual joint joint represents connectionist exp addition addition computing experiment curve curve solutions solutions curves trajectory conference determine efficient requires requires choice significant significant statistics world basic validation validation validation produce condition condition derived clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering developed levels types product product actual provided finally processes evidence nature nature simply simply biological biological biological biological biological biological measured measured measured measured measured discussion covariance normal technical technical complete predictions predictions predictions circuits effective generate generate supported theoretical require eds journal hypothesis cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster cluster future development development development including including fit fit fit fit fit fit fit fit fit fit fit objective simulated simulated simulated simulated simulated simulated smaller hopfield combination account unknown fully technology technology technology technology testing mechanism mechanism representing representing details numbers numbers numbers numbers numbers direct making international normalized normalized decay decay decay decay decay decay decay decay choose choose run run run run discussed resolution resolution resolution robust reported apply hierarchical inference inference inference inference inference inference inference inference inference inference inference array recently engineering highly varying conventional axis axis axis axis diagonal sparse evaluation modified bounded entire entire horizontal horizontal expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression expression lead extended deviation deviation deviation wide matrices matrices matrices alternative clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters runs runs runs runs runs runs runs runs runs strength minimal assumptions reduce trajectories valued reward central peak practice temperature strong mechanisms external reduction reduction cycle cycle cycle sigmoidal california california california california solid labeled turn decrease averaged averaged averaged averaged identification program annealing annealing annealing annealing annealing annealing annealing annealing monte derive derive carlo longer longer ways ways ways factors plot plot laboratory laboratory laboratory laboratory vertical vertical modeled modeled averaging linearly electrical dimensionality dimensionality dimensionality involves slightly unique unique integrated gaussians applying expectation choosing national expressed formation depending interpretation showed centers centers centers centers centers sizes constants processor fitting fitting fitting roughly roughly purpose iterative penalty generation foundation degrees expect existing existing existing existing figures figures figures includes usa usa extension illustrated prove discuss discuss maximize coupled partially determining aspects suitable society maximal maximal divided successful genetic score score score score score score plots fine interpreted return return sci sampled vary hypotheses maximization moves acknowledgments employed explore unlike schedule essential essential requirements circuitry circuitry circuitry circuitry put detail strengths strengths optimized limitations preliminary preliminary scalar reducing examine school relationships relationships relationships office comparable proved scores scores scores scores affect understand fundamental removed circles circles coarse measurement coefficient concepts nervous synthetic synthetic synthetic synthetic mentioned brown brown advanced derivation biology biology biology adapted stanford sites widely preprocessing protein protein protein protein forces division broad products scientific acad beginning lowest lowest incomplete sun improvements reflect substantially marked marked sharp sharp sharp sharp sharp variant variant summarized measuring monotonic proven pasadena pasadena pasadena pasadena gave substantial display simultaneous lab extensive ratios pick pick member discovery naval nonzero grows royal turned caltech cellular systematic fits fits fits fits smith ranges occurred alpha loops los contract scoring scoring settings salient modifications arrays symposium hertz hertz hours natl natl exploring mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness mjolsness zhang entry displayed enhance counting spherical spherical similarities multiplied infer infer infer theoretically proteins proteins proteins concentration concentration likelihoods likelihoods subsequently summarize dempster automated fly yale summer dna drop logarithm minus visually rubin shorter deriving inferred inferred cooperative dec july formulate diverse acceptable acceptable reports guess imagine gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene gene clustered clustered clustered clustered eric assess arising preserved translated genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes genes regulation regulation regulation regulation regulation regulation regulation regulation regulation regulation regulation regulation regulation altered altered differentiation smyth smyth synchronized player complementary nuclei laird nasa nasa nasa nasa likewise thousands molecules increments increments increments aaai technologies mann mann mann mann mann coming species lecture fortunately january satisfactory influenced jet jet jet thousand losing inhibited inhibited december dropped mining supplied stay affecting excited excited regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory regulatory inferring inferring inferring inferring inferring propulsion propulsion propulsion plateau plateau plateau plateau quantitatively reality denmark positional players iterating charles robustly alamos validated validated validated validated aggregate aggregate aggregate aggregate aggregate aggregate aggregate aggregate comprehensive comprehensive haven optimizes bio forthcoming enhancing sparsity encourage courses courses courses courses courses courses courses courses courses courses courses courses courses courses synchronize bind strongest kim kim kim manipulating stripe aggressive testable transcription transcription stuart stuart george genome klein wild hierarchically proportionality governs requested requested quadratically gov gov kinase regulated logarithms regulate memberships memberships analysing analysing barbara divisions garrett mol fruit prospects pacific worm jpl jpl automate ivi messenger rna forwards carr aggregated wold wold eve departs preprocess gausstans lam lam grn grn adequacy commonalities optionally optionally tobias 
#@Castafio_R,Mann_T,Mjolsness_E,Wold_B,
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#*network network network network network network network network learning model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural neural neural neural input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time time set set set set networks networks training training number number number number number number number number number number number error results results results results results results units units units information information information information information information information information information models models models models models hidden hidden hidden performance performance performance based based based based based based based based based based based layer layer case vector vector vector vector vector values values probability probability probability probability probability probability parameters parameters parameters parameters weight weight weight weight functions recognition approach pattern point point single single single control large large large local rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate rate test test test analysis class optimal optimal optimal shows shows signal simple examples net net net net net net net net net net net net net net net net work work task task field features features features classification classification classification process level current trained structure high high similar representation representation representation representation representation representation representation representation representation representation representation representation representation representation representation show show show show show show equation equation section fixed line real average average average average average average average average average average states states theory obtained obtained obtained experiments experiments dimensional result result result result university university threshold threshold threshold variables variables variables variables variables variables variables variables variables variables research research initial initial table table estimate estimate estimate estimate estimate standard standard computer science prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction prediction presented present present present low low machine sets sets range range range range press basis basis basis nonlinear nonlinear nonlinear continuous abstract likelihood likelihood references component due due due positive procedure important important important decision decision decision decision decision decision decision decision decision estimation estimation behavior behavior behavior statistical statistical effect effect effect dynamic dynamic cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost cost change complexity variable variable assume assume assume assume lower lower lower measure representations representations higher higher higher higher cases type type type required required multiple multiple distributed expected expected expected expected expected expected expected expected expected techniques techniques techniques region region region region region region length length correct correct minimum resulting classes classes ing ing ing ing total total total regression regression regression regression regression regression multi performed performed performed times elements elements regions means factor factor potential made study study study policy policy policy knowledge obtain obtain obtain obtain obtain obtain artificial relative compared compared application application application application cross series receptive provide rates rates rates location location active active goal related related discrete discrete power power accuracy accuracy contrast fields modeling selection report report department department department loss loss loss internal bias graph graph graph considered considered framework framework framework computing domain domain domain domain domain curve curve curve curve additional additional curves estimates limit detection determine determine upper upper requires choice significant significant significant significant significant statistics statistics world estimated estimated increase increase increase validation validation con produce produce weighted randomly developed types types types provided provided provided provided selected selected nature nature achieved achieved discussion describe corresponds predictions predictions predictions predictions short short require main main end ability ability future makes including needed significantly significantly ratio ratio york york increasing increasing uniform details details call call pre pre making making making making making making making making window window window experts experts experts experts experts expert decay decay decay decay combined sources sources predict predict predict population population improve directions directions recent ensemble element element element typical strategy strategy period period identical subset relevant highly varying approximately axis axis axis axis studies achieve achieve diagonal definition definition interval interval risk risk risk risk risk constructed extended extended deviation wide wide predicted predicted predicted predicted predicted predicted predicted predicted predicted predicted predicted correctly correctly correctly correctly white occurs occurs occurs column assumptions assumptions assumptions assumptions reduce valued depend differences measures numerical designed encoding encoding reduction reduction reduction reduction reduction intelligence assuming variety variety variety variety decrease averaged manner base base base base base base base base denoted areas explicit appears factors factors factors estimating plot plot plot plot plot tuned distinct linearly involves transformations easy develop adding adding applying quality quality quality versus competition competition competition competition yield yield yield extracted focus influence variation variation evaluated evaluate evaluate restricted restricted fraction fraction centers centered suggested sign key key earlier reasonable performing combining roughly roughly david existing includes contour inter inter determines maximize maximize activated mozer mozer mozer mozer major major determining straightforward selecting identified identified identified identified identified identified importance importance importance included committee identify identify situation plots plots plots plots ten ten reached refer graphs contained split dis dis issue return lie lie duration quantity list bar involved vary michael providing providing maximization maximization thresholds thresholds predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor predictor software decreasing explore explore remain remain wiley poor overfitting varied varied varied detail replaced dotted mass scalar history tech boosting scaled working attributes attributes coefficient predicting extremely perfect ensure portion portion assumes logistic mapped extent directed theoretic costs costs crucial growth growth fairly fairly nonlinearity reasons sys closer forces constructing bishop bishop beginning bandwidth annual annual researchers requiring fourth evaluating limits tional conducted capability capability fed parameterized lack leave leave leave leave leave leave car effort incorporated ity price operate howard switch switch cal green green plan richard sophisticated sophisticated sophisticated sophisticated sophisticated sophisticated sophisticated sophisticated sophisticated sophisticated sophisticated sophisticated sophisticated age focused deviations credit credit credit credit credit credit credit credit credit calls calls calls calls calls calls calls calls merging irrelevant realized naive naive naive naive naive naive naive naive acquisition acquisition room benefit proportion proportion primarily oxford ratios repre repre nonzero grey outcome turned lost lost lost lost lost lost lost lost extending communications communications cellular air ments minutes held stated imposed intelligent hit hit hit hit contract contract contract contract exploit methodology date date service service service service service service service service service service service service service service service service interference financial representational loo sion predictors predictors predictors predictors predictors predictors entry decide decide expanded colorado consequences den uni originally originally competing competing bases bases multiplied offer augmented horizon horizon horizon horizon horizon horizon splits splits valuable fold insensitive vari market market market market market market market market market market johnson johnson johnson johnson dividing andrew andrew outperforms linked yielded land roc usage usage usage converted unable shading shading listed ber benefits rejection rejection rejection adopt discriminative utilize utilize classifies examining realize reflected eric scenario scenario options translated translated tems maintained boulder thresholded carefully efforts confirmed landscape ultimately ultimately retain retain records mask associates associates million million million million million esti thousands retained bill bill bill bill bill bill bill bill bill radio october october october rose technologies vice factored utilizing replacement appearing satisfaction satisfaction satisfaction satisfaction survey acquire acquire january corporate corporate rivalry ongoing savings savings savings savings savings savings savings savings savings savings savings savings savings savings savings savings savings savings savings savings savings savings ers telephone suite termination termination hid december december december dropped carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier carrier mining mining lists suppress stay stay stay stay month month subtracting sen resolutions ally trol daily fin voice deter profit iterating comer ings pin media sentation sentation translates promise february united united recovering subtle probabil discriminating addi replicates elaborate months months altering incurred aims remarkably ables plotting markets markets plans avenue monthly monthly monthly monthly monthly monthly monthly monthly monthly monthly monthly monthly monthly monthly offered offered offered offered offered offered offered retention retention retention retention retention retention retention retention retention retention retention retention coverage coverage coverage anticipate terminated billion billion notably begun jensen jensen translating tributed constantly niques ponents rising categorize closing telecommunications telecommunications telecommunications telecommunications equipment highlights tain wireless wireless wireless wireless wireless wireless wireless wireless wireless wireless wireless wireless wireless wireless wireless ences industry industry industry industry industry industry industry industry industry industry industry industry crafted intervention intervention intervention intervention intervention intervention intervention intervention intervention intervention intervention intervention intervention intervention intervention lumped discriminability discriminability signif regres incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive incentive contracts business dates dates services services services services services services spend mated charges charges customers customers customer customer customer customer customer customer customer customer customer customer customer customer suspect ser carriers carriers carriers carriers judgement judgement offering offering offering offering offering anticipated collapsed dictions icant mensional harmful forecasts influencing influencing logit logit logit logit logit reduc domestic domestic includ discriminator dollar broadway seldom influ conjectured conjectured actu competitors competitors subvector swets swets newspaper pricing fee sitivity abnormally formly weekly 
#@Grimes_D,Johnson_E,Kaushansky_H,Mozer_M,Wolniewicz_R,
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#*model model model model model model model model model model model model model model neural neural data data data data data data data data data data data data data data data data data data data data data function function function figure figure figure figure figure time set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number error results results results information information information information information information information information problem problem problem problem problem problem problem problem hidden hidden hidden hidden linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case case case case case case case shown shown systems systems systems values values values probability parameters parameters noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise distribution distribution distribution recognition method approach approach approach approach approach approach approach approach approach pattern point image image image image image single processing local patterns patterns analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix form form shows algorithms algorithms algorithms algorithms gaussian paper paper paper paper examples small work work methods fig step step step points points points points points points features process process process process current structure problems random similar similar show show equation equation section section section section section line line vectors images images general general generalization parameter real real real approximation approximation states theory theory gradient gradient obtained term term term note note note note note note experiments dimensional dimensional result result variables variables variables variables variables variables solution solution research independent independent independent independent independent independent independent independent independent defined found found found found target target target constant estimate estimate estimate estimate standard terms terms terms terms prediction map map map map map map map map map map map map map map map map present present low maximum maximum maximum maximum maximum press learn nonlinear sample sample sample sample abstract applied applied find find find find find convergence likelihood likelihood likelihood references component component due important adaptive mixture mixture mixture mixture mixture mixture context introduction introduction estimation statistical statistical statistical variance cost change variable variable variable spatial spatial spatial assume assume assume assume assume signals signals prior prior prior prior prior prior prior prior prior prior chosen higher higher part multiple multiple represent represent represent represent represent distributed distributed bayesian techniques techniques region region region region correlation correct probabilities observed errors errors scale scale scale simulations resulting resulting ing simulation computed computed computed respect respect multi eq called called regions regions regions regions factor factor optimization optimization optimization made applications applications applications knowledge knowledge knowledge em filter obtain obtain obtain original artificial artificial artificial samples samples samples samples samples represented represented true true desired series define objects objects proc location perform perform posterior constraints constraints constraints constraints constraints constraints constraints constraints constraints distributions distributions distributions approaches approaches mit steps steps comparison contrast dependent dependent source nets modeling modeling modeling report institute technique technique technique technique technique technique consists consists consists advances represents represents represents represents bias bias framework framework framework framework framework framework framework cambridge experiment directly directly directly directly additional solutions solutions solutions conference conference determine choice choice significant significant free free free free free basic pages pages pages pages con channel weighted conditional clustering bounds area area types entropy actual actual processes selected constraint constraint constraint constraint constraint simply measured measured discussion discussion discussion discussion normal normal normal close inverse assumption surface surface surface surface surface finding finding finding amount implemented implemented assumed face journal end pixel pixel pixel pixel pixel pixel pixel pixel pixel cluster future noisy noisy noisy including fit objective probabilistic probabilistic probabilistic typically typically reduced account account coefficients coefficients coefficients jordan technology technology interesting interesting interesting database database database principle leads leads leads representing details details supervised supervised supervised supervised expert produced added sources improve correlations separate separate element element practical practical apply apply include subject subject subject subject identical pixels pixels pixels pixels pixels pixels pixels quadratic sense previously previously conventional unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised observations observations observations observations observations volume volume volume volume solve yields match match match correspond address mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures mixtures separation sensitive sensitive constructed digital white boundary column assumptions assumptions reduce editors measures practice constrained constrained constrained constrained constrained constrained constrained constrained constrained suggest hard presence characteristics characteristics characteristics solid solid assuming assuming variety user user user ica ica ica ica ica ica ica ica ica ica exist iii scene scene identification base base denoted reference explicit explicit derive derive solving solving factors plot plot plot laboratory ann changing explicitly coordinates simultaneously physical physical physical angle spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral spectral interaction interaction adding blocks family independently depending depending depending squares squares squares squares influence variation detailed open open open decomposition decomposition completely suggested spectrum reasonable additive normalization normalization normalization combining fitting fitting fitting fitting penalty valid advantages exploration box includes thesis combinations priori priori priori usa blind blind instances subspace automatic automatic uncertainty discuss mozer candidate priors priors priors priors priors priors priors priors variations characterized simplicity planning columns determining sensor sensor delta identify build identity fine capture summary summary contained contained prob showing interested dis satisfy write simplified wavelet highest maximization mixing mixing neighboring acknowledgments difficulty difficulty hall ml ml matches tech maximizing maximizing maximizing workshop affect encode statistically cover circles circles naturally editor analyze singular der detector mapped mixed mixed explain integrate integrate mentioned indicating scenes band band ground ground ground ground ground ground phenomena phenomena lies spatially inside preprocessing filtered choices choices located probable pool potentially potentially potentially inversion members begin auto explained integrating varies greatly considerably evaluating applies understood pure pure led conducted parameterized detecting remove incorporated incorporated frequently ity http berlin summarized aim aim aim aim aim aim aim gen substantial germany semi inherent yielding cor contribute spectra spectra spectra spectra spectra spectra spectra spectra spectra spectra spectra spectra spectra spectra benefit contextual sensing sensing sensing sensing sensing guarantee restrict princeton recover signature systematic smith satisfying alpha replacing bands bands bands bands obtaining exploit exploit analyzing analyzing removing removing observing north moments prentice recovered recovered introduces introduces ranging paul dependency sim viewing entries infer creating vertex vertex environmental environmental eqs pearlmutter ignore interestingly material material material material material material material material automated robert outlined treat posteriori posteriori ure land leaving ple corporation logarithm presenting obtains arbor additionally additionally arg hundred remote remote remote remote remote brightness remainder jacobian jacobian pub trends exam ftp diag alternate file distant reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance reflectance challenging plate considers guided intensities ambiguous library library library library spanned spanned monitoring importantly superposition responding accounted truth simplex simplex simplex simplex simplex simplex simplex simplex simplex simplex simplex exploited lems argmax simplification parameterization survey identifies australian assistance invertible thousand envelope utilizes mining mining determinant determinant eral proportions usefulness svd incorporation incorporation evenly wavelength wavelength wavelength wavelength wavelength wavelength settle subtracted resolutions petsche substitution html spie spie spie spie prone inde inde era gmd gmd materials materials materials materials materials materials materials materials scatter scatter scatter trend trend corn inaccurate inaccurate problematic tenth united recovering sur probabil discriminating particles das violate pendent pendent prime omit sensed spence spence spence spence parra parra parra parra parra klaus klaus andreas ply shrink unmixing unmixing unmixing unmixing unmixing unmixing unmixing unmixing unmixing unmixing unmixing unmixing unmixing unmixing unmixing tributed imagery imagery imagery michigan niques miiller miiller nix kronecker demixing brevity charac unrelated departure unknowns validate grained vised innovation innovation adams combi lighter reflections gov gov clay sajda sajda sajda sajda cients deterministically inhomogeneous inhomogeneous axi sumption strained mfiller ciently haykin tedious positivity positivity positivity positivity hsu lib wavelengths wavelengths terrain xla absorption absorption absorption absorption slx instructive kruse ida ternational constituting constituting landsat coe str origins vations gillespie maxp lucas sarnoff alx atmospheric atmospheric regressive nations teristics areal areal quire xix xix samoff unsuper periment 
#@Muller_K,Parra_L,Sajda_P,Spence_C,Ziehe_A,
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#*learning model model neural neural neural neural neural neural neural neural neural neural neural data data data data data data data data data data data data data data data data data data data data data function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time set set set set set set set networks algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number system system error error error error error error error error error results results results results results results results results results results results information information information information information problem models performance performance performance based based based based linear linear linear linear case case case case case vector order order order order order order order order shown shown shown shown systems systems systems noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise noise neurons method method method method method method method method method method method method approach approach approach approach point image image image image image image image image image image single single single single single single single single single single processing processing processing processing processing processing processing large local local patterns patterns patterns patterns patterns patterns patterns analysis analysis analysis analysis analysis analysis analysis analysis analysis analysis matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix optimal optimal optimal optimal shows shows shows shows shows shows signal signal signal signal signal signal signal signal signal signal signal signal signal signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms visual visual visual visual visual visual visual small small work work work work task methods methods methods step step points field process process level structure random high similar similar similar similar show show show show show show section section fixed line vectors images images images images images images images parameter parameter parameter real real average average gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained note note experiments experiments activity activity activity activity activity activity activity activity activity activity activity activity activity result result result university university university university computation computation solution research research independent independent independent independent independent independent initial estimate estimate standard standard standard standard standard standard standard standard standard standard standard computer computer science science left left left left presented presented presented presented presented map map map present present activation low low frequency frequency frequency temporal temporal temporal sets press press components components components components components components components components sample abstract applied applied applied find find convergence properties properties properties properties references component component component component component component component component component component component component component component component component component due procedure important important mixture mixture introduction hand stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus stimulus statistical dynamic dynamic generated variance cost cost cost tion tion tion change difference difference spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial spatial lower lower measure measure signals signals signals signals signals signals prior prior prior higher higher part part part part part previous previous multiple multiple multiple multiple cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex cortex represent equations techniques techniques techniques proposed proposed correlation correlation correlation correlation correct simulations resulting resulting resulting resulting ing ing total total total total human computed respect multi multi multi multi multi multi sum sum sum sum called called times times elements elements elements regions mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping mapping factor optimization natural orientation orientation orientation orientation orientation orientation orientation orientation orientation global global global global global knowledge knowledge obtain original original original artificial artificial artificial artificial artificial artificial artificial compared compared compared compared application application application application application application application cross cross cross cross cross cross cross cross cross series series provide rates perform perform goal related constraints cortical brain brain brain brain brain brain brain brain approaches mit voltage voltage comparison comparison comparison descent descent descent descent descent descent descent descent source source source source source source source source source source source selection proceedings proceedings proceedings institute department department technique technique technique technique technique technique technique technique technique technique consists advances advances advances addition maps maps maps maps maps maps maps maps maps cambridge experiment experiment experiment estimates estimates limit san top top top stimuli upper choice approximate statistics statistics statistics statistics estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated estimated pages pages pages pages pages pages con condition condition condition condition condition condition developed levels levels area finally finally selected selected nature depends biological technical technical describe denote fast limited close close assumption assumption corresponds stable common assumed supported adaptation adaptation square pixel pixel future future noisy noisy sensory underlying underlying unknown unknown jordan ratio ratio ratio ratio ratio trials trials squared squared numbers normalized normalized bottom frame frame frame combined produced produced choose added added sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources sources light light light light light improved improved improved improved correlations correlations correlations correlations resolution resolution resolution advantage robust robust robust robust robust robust robust robust separate apply apply period pixels sejnowski varying compare compare compare conventional conventional observations approximately approximately volume volume volume volume volume volume volume works works tions tions smooth yields yields differential diagonal diagonal mixtures mixtures mixtures mixtures mixtures mixtures separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation separation observation organization sensitive sensitive amplitude exists scaling occur extended extended extended extended trial trial matrices matrices alternative alternative touretzky width white white white white white generally generally generally generally column runs runs conclusion starting critical row row row greater assumptions conclusions editors editors editors editors editors editors editors differences moody suggest propose propose strong presence largest largest demonstrated demonstrated labeled assuming ica ica ica iii averaged introduce introduce denoted pro index index index optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical optical ways primary primary primary generating plot plot averaging averaging remaining unique consisting adding applying shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift shift quality quality implies blocks extraction extraction extraction versus versus cycles select select john yield extracted dependence reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction reconstruction depending evaluated evaluated restricted ocular ocular ocular ocular ocular ocular ocular ocular frames frames frames frames frames completely reasonable calculation slow performing classical spaces sec sec sec sec sec combining filtering filtering filtering filtering filtering sufficiently norm norm norm advantages recorded recorded recorded recorded recorded recorded dominance dominance dominance dominance dominance dominance dominance dominance bell blind blind blind blind blind blind blind blind blind blind blind mozer mozer absolute phys sensor sensor sensor sensor sensor sensor selecting selecting middle middle middle middle middle differ presentation successful successful build post plots plots plots plots identity orthogonal summary traditional soc video superior superior return oscillations bar modular delayed delayed computes highest maximization cat neurosci neurosci attempt mixing mixing mixing mixing mixing mixing mixing mixing mixing mixing extract acknowledgments intrinsic intrinsic intrinsic intrinsic camera minimized bars remain remain stimulation selectivity diego investigate relations hanson lippmann helpful tech tech structured workshop workshop workshop removed smallest measurement plausible onset onset analyze analyze rev singular versions versions obvious algo algo separated separated separated academic amari motivated seconds seconds seconds optimum percentage rows preference preference preference preference preference preference preference smoothness variances variances adapted benchmark worse london spatially spatially snr snr snr sections closer preprocessing monkey monkey monkey mation mation describing opt opt opt optimize recording recording recording recording recording recording recording auto auto raw robustness robustness conjugate summation summation summation explained argument argument argument fourth recordings recordings recordings recordings recordings recordings incorrect maxima calculating stack stack stack stack stack stack stack stack stack berlin berlin berlin berlin mod limiting limiting extracting extracting qualitatively germany germany tolerance yielding cor cor cor initialization shifted uncorrelated uncorrelated uncorrelated uncorrelated benefit college notes martin rithm rithm recover rotations platt spontaneous oja imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging imaging striate striate striate fail fail methodology shifts shifts shifts shifts shifts shifts shifts shifts shifts shifts shifts shifts illumination motivation infor separating respective monkeys hasselmo recovery artifacts artifacts artifacts artifacts artifacts artifacts artifacts artifacts permutation permutation permutation variants variants lett ccd consecutive grating blood blood blood blood blood blood blood blood blood blood sch sch visually medium additionally ideally superimposed superimposed constitutes causal decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation decorrelation concentrated biophysical biophysical diag diag diag compensate elementary reflectance deconvolution macaque macaque records covered reveal ation obermayer obermayer obermayer obermayer obermayer obermayer els tissue tissue tissue jutten jutten jutten answers mix mea resp argmax ping ping transforming converging ongoing shot cornput returned incorporation wavelength wavelength sen sen subtracted bss bss bss bss bss bss bss bss bss bss separates petsche autoregressive vanish artifact lowpass lowpass bandpass bandpass bandpass reflection fol fol drifting lar gratings gratings problematic problematic derives derives sep riemannian noiseless noiseless benchmarks benchmarks lund lund lund lund lund schuster newly newly ton cardoso cardoso cardoso observes permutations cancel plausibility plausibility optimizes substituted klaus courses courses blasdel blasdel perspectives lowing abstr fil subtraction pal pal stays blank demixing demixing demixing demixing demixing demixing demixing trust mammals periments ences jacobi jacobi jacobi jacobi jacobi jacobi nique nique otto mueller ucl ner ner coarser noticeable suc cot cot patchy sor sor simi scattering scattering scattering sheffield sheffield observa masked questionable questionable hyvarinen spe photon sphering sphering sphering sphering sphering sphering sphering sphering sphering sphering sphering sphering sphering illuminated unsuccessful stacks stacks stacks stacks stacks stacks tering sured onal absorption faggin autocorrelations trices trary judging olution levitt neous lowed smearing sphered lasted diagonalization simulta grinvald sem fie fie mtiller cific pops separa orthog salama oby cedures moval 
#@Lund_J,Mayhew_J,McLoughlin_N,Obermayer_K,Schiegl_I,Schoner_H,Stetter_M,
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#*learning learning learning learning learning learning learning learning learning learning model input input data data data data data data data data data data data data data data data data data function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure time time set set algorithm output number number number number number number number number number number number number number number number number number number number number number number number system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system system state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results results results information information information information information information information information information information information information information problem hidden performance performance based based based based space space space space space space case vector vector vector order order systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems systems values values values values values values values values values values values values probability probability probability probability probability probability functions functions functions functions recognition recognition recognition recognition recognition recognition approach approach approach approach approach point control large test analysis optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs algorithms algorithms algorithms algorithms simple simple simple simple paper paper paper examples examples small size feature work work work work task task task task task task task features features features features features features process process level current response response similar similar similar section section fixed line general general general general speech speech speech speech speech speech speech speech speech speech speech speech speech speech real real real approximation average average states states states states states states states states states states theory obtained obtained obtained obtained obtained obtained obtained obtained obtained obtained note note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments experiments result variables variables variables computation solution research research research independent independent log log log log defined found found sequence initial initial standard computer present low machine sets range press components continuous sample abstract applied applied applied back find find find find computational properties likelihood likelihood likelihood likelihood references stochastic stochastic due due due due important important important important important decision decision decision context introduction introduction action action action action action action action action action action complex complex effect effect generated variable variable variable variable variable variable variable variable variable variable lower lower lower measure measure measure measure chosen chosen chosen chosen chosen higher higher previous previous bound cases cases required required multiple multiple good good good good binary long represent represent represent represent represent expected markov markov markov markov markov markov make fact proposed proposed correlation correlation length length length length length length length length length errors errors errors resulting resulting resulting resulting ing ing human human computed respect called called called called times mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor potential potential natural applications study policy policy policy policy policy policy policy policy policy policy knowledge specific represented true compared compared application application application desired series series provide define compute compute compute proc determined experimental experimental goal goal goal goal goal goal goal distributions equal mit larger train train train train train dependent dependent source source modeling proceedings proceedings proceedings words implementation consists consists internal internal difficult addition addition addition ai ai ai ai ai framework framework framework framework framework framework framework domain experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment experiment environment directly directly directly curve curve curve curve curve view view view view curves design design design design design transition transition transition transition transition transition trajectory trajectory conference determine choice approximate approximate estimated give give give produce produce derived derived derived derived derived derived developed actual processes processes iteration nature simply simply discussion technical technical increases denote denote denote tested tested close close inverse corresponds corresponds corresponds corresponds corresponds actions actions actions actions actions actions actions actions actions actions actions actions amount short common implemented implemented role role role role role role role role role end end end end instance instance typically typically typically reduced interesting interesting significantly york york matching database database database database empirical empirical empirical empirical empirical empirical empirical empirical principle representing details details details details call international international choose description description improved population discussed discussed improve recent correlations correlations correlations correlations property property robust robust ensemble takes takes typical reported reported practical practical apply strategy strategy strategy strategy include include include include include subject recently recently relevant highly varying compare observations observations observations observations observations observations observations observations approximately approximately approximately axis solve solve speaker studies achieve rl rl rl rl sparse sparse separation entire entire increased lead lead lead suggests alternative alternative setting demonstrate demonstrate conclusion starting critical greater trajectories trajectories trajectories conclusions conclusions reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward reward measures measures modules sutton sutton practice weak weak drawn demonstrated labeled turn turn turn turn turn turn turn turn turn turn turn turn turn turn variety user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user start manner question question denoted acknowledgements pro construct written longer plot confidence explicitly linearly infinite involves text text text belief belief interaction develop events events agent boolean boolean boolean boolean select choosing choosing correlated estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator estimator viewed transform open open evaluate controlled labels labels showed understanding understanding completely reasonable barto combining roughly purpose purpose tracking assigned query query faces faces david existing includes priori retrieval retrieval extension extension automatic maximize holds holds grammar differ divided driven included presentation presentation successful build score score score plots plots receives repeated repeated strongly showing interested running running strategies strategies strategies strategies strategies strategies strategies strategies built built built built built built notation quantity michael providing automatically received received received received policies policies policies software software software software software software receive oriented presents presents presents presents presents explore unlike command schedule schedule schedule overfitting access access singh singh singh singh singh experience varied varied humans estimators estimators association limitations issues preliminary mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp examine matches fashion incremental authors authors working complicated workshop scores understand understand notion analogous attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes attributes closest necessarily analyze created created created created recognizer recognizer recognizer recognizer recognizer queries queries quantities obvious ith ith mixed mixed mixed mixed mixed extent extent contributions finds finds attempts electronic electronic defines integrate indicating site track track defining tool tool tool tool tool tool tool turns turns perspective sys sys formalism formalism formalism formalism choices choices immediately immediately immediately arise mation potentially recognized recognized recognized beginning attribute attribute read computers annual preceding robustness questions questions questions apparent apparent improvements greatly considerably evaluating limits collected collected empirically led flexible spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken spoken lack completion completion frequently rewards rewards synthesis ture gen fall ordered extensions qualitatively conclude shaped utterances utterances utterances utterances utterances utterances utterances utterances utterances utterances progress progress progress progress progress semantic summed realized trade contribute feasible sv sv sv sv sv sv sv interface formally formally investigation temporally temporally purely discover tem grows arrival arrival arrival ments ranges difficulties occurred mail mail mail replacing city city city city loops check hope hope hope obtaining obtaining analyzing utterance utterance utterance utterance utterance utterance utterance utterance utterance methodology methodology intuitively preparation symposium symposium intuitive composition date date exploring passive meaningful separating pruned expanded lengths evident counting chooses advance omitted augmented kearns kearns kearns kearns kearns rich theoretically ends draw messages messages statement instructions interestingly influences automated vari mdps mdps mdps counts counts counts severe severe empty verify approx largely users users users users users users users users shorter ent basically email email email discount discount opposed presenting markovian markovian markovian markovian pieces tween perceived perceived tor avoided options options visited visited summarizes favor levin levin insights tems graphics file labs labs labs labs labs labs thresholded carefully challenging relating emphasize confirmed confirmed confirmed confirmed confirmed confirmed confirmed scope interactive weaker exchange permit things treating treating experi completed correlate nec satisfaction satisfaction satisfaction satisfaction survey survey consuming justified prefer impractical quantify synthesized synthesized telephone confirm confirm confirm confirm pan hoc eral hour hour appealing meeting inferring att tracks ignores longest voice voice signed ings gathered gathered gathered gathered tained files indicators indicators counted promise promise parker platform unrestricted dence ini ceedings converts notions retrieve conceptually conceptually dealt walker walker walker walker walker walker walker mention devel imposing visits rigorously web unlimited satinder confirms challenges challenges exciting tums tums linguistics requests prefix explores trouble trouble closing closing mere cities cities confused depen render adaptable violations renders renders estima corpora corpora corpora corpora corpora corpora corpora corpora corpora departure departure departure departure departure departure realizes synthesizer silence requested speak prefers services contradiction initiative initiative initiative initiative initiative initiative initiative initiative initiative ended ended summarizing sender hear twofold oped testbed answered resets informational informational informational informational informational informational informational informational informational informational informational confirming confirming confirming balances surveys ins eee perceives permitting closes infrequently confirmation confirmation confirmation confirmation confirmation confirmation confirmation indications intemal violating msr browsing browsing imate caveats perceptions baveja ceived pitfalls asks asks warm reinitialized acl logged logged believes believes trip attenuate 
#@Kearns_M,Litman_D,Singh_S,Walker_M,
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#*network network network network learning learning learning learning model model neural neural neural neural neural input data data function figure figure time set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output number number number system system system error error error error error error error error error results results results units units information information information information information information information information information information information information information information information problem problem problem problem problem hidden performance based based based linear linear case case case case vector vector vector order shown shown systems systems systems systems systems systems values probability probability probability probability probability probability probability functions distribution distribution distribution distribution distribution distribution recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition recognition approach approach approach approach pattern pattern pattern pattern pattern pattern pattern pattern pattern image image image image image image image image image image image image image image image image processing processing large local rate analysis analysis class class class class class class class class class class class class class class class class class class class class class class class class class class matrix matrix matrix matrix inputs form form shows shows algorithms algorithms simple paper feature feature feature feature feature feature feature feature work work work task cells cells cells cells cells cells cells cells cells cells cells cells cells cells cells step step step step step step step field field field features features features features features classification classification classification classification classification classification classification classification process level level level level current cell problems problems random high high high similar show show section section section section section section section rule images images images images images images images images general general real average average theory obtained obtained dimensional dimensional dimensional threshold threshold computation computation computation defined table table table table table table table table estimate estimate standard standard standard computer computer terms terms terms distance science science present low machine machine object object object object object object object object object maximum maximum maximum press nonlinear outputs abstract applied back find computational density density likelihood references decision decision decision decision context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context context introduction complex hand estimation estimation estimation cost cost cost tion tion energy complexity complexity variable assume measure prior prior prior part part center type binary expected make techniques techniques techniques techniques techniques techniques proposed proposed correlation correlation length length length length length length length length length length correct probabilities forward resulting resulting classes classes classes classes classes classes classes classes classes ing total total total total total total human human human respect respect multi sum sum sum sum called called elements elements elements elements regions factor made applications knowledge knowledge vol vol vol relative relative relative relative specific samples samples true application application application application application application application application cross provide define compute compute objects objects objects objects objects objects posterior posterior posterior posterior posterior distributions distributions gain power power mit steps accuracy accuracy comparison larger dependent source institute institute institute institute department department department technique technique technique technique consists consists advances joint joint represents difficult final ai considered considered framework framework cambridge computing computing domain domain directly design limit stage efficient efficient significant significant free free free free world vision estimated estimated estimated estimated estimated estimated estimated give con con derived conditional developed criterion criterion criterion area area area types types types types types entropy entropy entropy depends depends simply normal normal normal normal normal normal normal normal increases group denote tested close assumption complete proof finding finding finding role role eds face square pixel pixel instance easily makes smaller reduced jordan technology technology technology technology transfer significantly ratio ratio edge edge edge edge edge edge edge increasing consistent database database empirical call call numbers making making international international experts experts early frame description element element element element element practical apply apply introduced pixels pixels sense relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant relevant engineering engineering compare conventional diagonal address definition background modified generalized improvement improvement sensitive arm arm arm arm arm intensity lead invariant deviation deviation feed white white white white white white white white assumptions conclusions conclusions editors sigmoid sigmoid accurate exponential exponential exponential propose propose propose presence presence presence presence presence presence presence presence presence presence presence presence reduction reduction demonstrated california california california manner manner manner identification identification identification base denoted acknowledgements areas areas explicit edges edges edges optical primary label label label label label physical electrical electrical easy text consisting mutual mutual springer formed extraction letters letters letters yield extracted extracted review interpretation variation variation labels labels labels sizes sizes similarly converges partial partial partial partial partial partial partial partial partial partial partial partial reasonable measurements measurements classical reduces neighborhood roughly false false avoid expect thesis formulation formulation eigenvalues automatic discuss maximize priors priors domains domains absolute discussions discussions characterized determining identified importance identify identify identify identify tend tend traditional verlag prob video dis dis return classify criteria criteria criteria criteria criteria gray gray gray list list list relaxation relaxation absence absence correspondence ill preferred situations body production investigate helpful rise rise authors referred maximizing stream cover examined coefficient coefficient detected histogram histogram indicating great ground trivial crucial crucial adjacent processed straight straight incorporate incorporate incorporate incorporate immediately mation laboratories probable potentially read computers author addressed relevance relevance tional fed readily red red red red red red posed solla detecting formulated incorporating incorporating incorporating incorporating pasadena pasadena song song song song song song green semi conditioning diagnosis diagnosis irrelevant contextual contextual contextual contextual contextual contextual contextual sensing intractable labeling appearance conditioned conditioned member ordering null impossible grey caltech caltech caltech plays plays systematic dealing imaging imaging difficulties simplify moment efficacy occurring illumination infor repeat meaningful iteratively belongs assembly arrangement chooses ranking ranking artifacts artifacts artifacts recog omitted kearns rich passing relies calcium calcium calcium calcium calcium calcium avoiding automated automated automated automated sequentially abu abu abu abu abu ence blood blood blood blood blood blood blood blood blood blood blood blood blood numerous mostafa mostafa mostafa mostafa mostafa corporation corporation incorporates visually vec tables opposed benefits nition utilize trigger blue hundred flat tor workstation associate remote remote remote diag management graduate individually descending descending confusion confusion confusion intensive intensive tract ignoring oregon microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic microscopic clinical clinical utilizing argmax argmax consuming doesn lists eliminates pronounced tribution tribution diagnostic diagnostic diagnostic diagnostic diagnostic diagnostic incorporation incorporation incorporation incorporation detects labelling labelling labelling positives systematically acid acid acid acid acid longest longest est locality lar carrying manual manual manual addi tit tit tit costly aggregate joseph ece entities abnormal abnormal abnormal abnormal abnormal abnormal abnormal abnormal bright examines ogi conveyed biomedical treats multiplications alexander malik bearing surrounded pierre regularly ixi ixi ixi ixi today discard crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals crystals particu bigger accompanying accompanying accompanying motivate identities identities plications amir iden amorphous amorphous amorphous amorphous amorphous amorphous amorphous amorphous amorphous joe fluid ismail augmenting sill sill sill sill sill sidered atiya collects yaser labor labor pres onal negatives beaverton argmaxp magdon arx arx arx josef busy hungry technol textual flavor generous outset cla swain automat binations llp llp llp llp entail invasive whichever nalysis recompute xiv xiv uri 
#@Abu-Mostafa_Y,Kasdan_H,Sill_J,Song_X,
#t13
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#*learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model data data data data data data data function function function function function function function function function function function function function figure figure figure figure set set set set set set set set set set set training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number number number number number number number number number number number number number number number number results results results results results results results results results results results results results information information information problem problem problem problem problem problem models models models models models models models models models based based based based based based based space space space space space space space space space space vector vector values probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise noise noise noise noise distribution distribution distribution distribution method approach approach approach approach approach approach approach approach single single large large test patterns patterns patterns patterns patterns analysis class class class optimal optimal optimal optimal form form form form form shows algorithms algorithms algorithms paper paper size size feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature feature work work work methods step features features features features features features features features features features features features classification classification classification classification structure structure structure random high high high high high similar representation show show show equation equation equation equation equation equation equation section section section section section section rule vectors vectors vectors vectors images images parameter parameter parameter parameter parameter parameter parameter parameter theory theory term term term term term note note note experiments experiments experiments experiments experiments experiments experiments experiments experiments dimensional result result solution solution solution solution research research research research independent independent log log found found initial table table terms terms terms terms terms terms terms terms terms terms terms distance left frequency frequency sets sets sets sets sets sets maximum maximum components basis abstract find computational computational likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references stochastic stochastic stochastic stochastic important introduction statistical statistical generated search search complexity complexity complexity complexity complexity assume lower lower measure measure prior prior prior prior word word higher center center required multiple multiple good bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian techniques techniques techniques proposed proposed correlation length finite minimum resulting classes classes total total total total total human computed sum sum sum performed performed performed elements means means means means means means means dimension made natural applications applications applications em em em obtain obtain obtain negative relative relative represented represented represented represented represented compared cross cross cross cross cross cross cross cross cross cross cross provide provide define define define compute compute compute active determined experimental experimental related distributions distributions distributions discrete equal approaches approaches approaches approaches approaches approaches approaches approaches approaches approaches comparison comparison comparison dependent modeling modeling modeling selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection selection report report report words words words words words words words implementation consists consists consists consists individual final scheme scheme scheme scheme scheme scheme scheme sequences equivalent directly san san conference conference efficient full choice choice choice world estimated validation validation validation validation validation validation produce weighted clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering clustering criterion criterion area entropy entropy provided finally selected simply discussion normal describe describe describe arbitrary limited assumption assumption assumption assumption theoretical main end cluster cluster cluster cluster cluster cluster cluster future easily objective objective objective objective objective objective objective typically underlying underlying combination reduced reduced functional significantly structures uniform language language principal representing details numbers numbers pre pre pre making normalized normalized normalized supervised produced produced choose denotes discussed directions recent exact reported reported reported practical apply apply include include subset subset subset subset subset subset subset subset engineering dimensions dimensions dimensions dimensions compare unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised unsupervised solve yields address mixtures mixtures evaluation evaluation evaluation evaluation generalized generalized increased studied clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters clusters runs runs runs starting assumptions assumptions reduce conclusions conclusions differences propose propose reduction drawn drawn labeled labeled assuming assuming assuming assuming start groups groups force explicit monte derive derive carlo written estimating describes dimensionality dimensionality remaining easy text text text text text text text unique consisting consisting mutual mutual choosing family family independently dependence evaluated evaluate labels labels forms forms forms understanding suggested suggested partition reasonable spaces normalization closed closed closed generation generation generation generation assigned classified classified classified views existing figures figures includes combinations combinations retrieval weighting assignment assignment determines priors priors priors priors discussions gamma determining determining selecting computationally computationally latent schemes schemes comparing comparing plots road road refer heuristic heuristic video interested interpreted split split split contribution classify content content content criteria notation notation highest routing powerful wiley wiley overfitting collection essential hanson integral referred eigenvectors cover notion removed coefficient subsets subsets subsets aspect formal noted initialized consist detected attempts attempts averages optimum histogram histogram indicating indicating stop ground ground track analyzed improves coded tractable reasons reasons comparisons style choices scientific implicit begin begin optimize english lowest incomplete conjugate explained apparent limits consistency consistency consistency lack documents documents documents documents documents documents documents documents documents documents documents partitioning partitioning poisson monotonic occurrence marginal marginal marginal marginal marginal marginal marginal gave chose semantic yielding initialization initialization initialization initialization identifying identifying intractable primarily primarily japan extensive arguments member concerned bin bin bin partitions partitions eliminated smith consideration overcome simplify simplify determination hyper hyper hyper unlabeled settings corpus substituting substituting meaningful document document document document document document document document document document document document document document document document introduces bad histograms histograms thomas centroid laplace tokens reveals omitted reader bins draw dempster counts counts empty verify appeared unified deriving maximized removal dec encouraging mdl reports assignments multinomial multinomial multinomial multinomial multinomial multinomial clustered clustered beta beta beta beta verified concentrated ibm ibm ibm ibm ibm token token token regularized efforts simplifying simplifying picked smyth dirichlet dirichlet setup discusses apparently reveal truth truth retained retained rewrite examination aaai helps suggestions vis phrases hoc clarity dom dom dom dom dom dom rissanen rissanen rissanen striking striking coincide substitute conditionally binomial trend occurrences occurrences lsi lsi lsi lsi lsi subtle experimented mle mle indexing validated validated validated validated validated jose jose noticed topics treats distributional distributional distributional distributional distributional distributional distributional suggestion hypothesize heckerman bearing bearing succession bag bag ences katz indicative discarding articles matters validate baker ijcai singhal pereira pereira tackled harry harry interplay topical topical topical topical meila ifs trec outperforming frontiers inheritance almaden almaden almaden almaden inquiry msr sigir sigir bernardo kdd deerwester disregarded dri acl 
#@Dom_B,Vaithyanathan_S,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning data data data data data function function function function figure figure figure figure figure figure figure figure figure figure time time time time time time time set set set set set set set set set algorithm algorithm algorithm algorithm number number number number number number number number number number system system system system system system system system system system system system system system system system error results results results results results results results information information information problem problem problem problem problem problem problem problem problem problem performance performance performance performance performance performance performance performance performance performance performance based based based based based based based based based based based based based based based space space space case case case case case case order order systems systems systems systems systems systems systems values probability probability probability recognition recognition pattern pattern image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image image single control large large large large local local local rate rate rate rate rate rate test test test test test analysis class class class class class class class class class class class class class class class class class class class class class class class class optimal optimal optimal shows shows simple simple simple visual visual visual paper examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples examples small small small size feature feature feature feature feature task step step step field features features features classification classification classification process process process level level current problems problems high high high response response similar similar similar similar representation representation representation representation show equation equation equation equation equation equation equation equation equation section section rule vectors vectors vectors vectors images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images images real real real real average average states theory obtained obtained experiments experiments experiments experiments experiments experiments independent independent log log log sequence sequence target target target target target target target target target target target target target initial constant constant estimate standard computer computer terms terms terms left left left left map map present present present low object sets sets maximum range basis abstract find find find computational computational convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties likelihood likelihood likelihood likelihood likelihood likelihood likelihood likelihood references due due due positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive positive procedure procedure procedure decision propagation propagation propagation mixture context introduction complex complex hand hand hand hand hand statistical search search search search complexity variable assume classifier prior prior prior prior representations representations representations representations representations higher higher part previous previous previous cases cases cases cases required multiple good good good good good binary bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian equations make make fact fact region region region region region region region region region region correct probabilities probabilities classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes classes total total computed computed performed performed performed performed called regions regions regions regions regions regions regions regions regions regions regions means factor factor factor natural natural feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback feedback applications knowledge em em obtain obtain negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative vol relative relative represented represented application application desired desired objects rates experimental experimental goal goal goal related posterior posterior posterior posterior discrete equal equal equal mit mit mit steps accuracy larger larger update support support selection selection selection selection selection selection loss loss version consists difficult difficult difficult difficult addition graph graph considered cambridge view view solutions curves design design design top top top top top top conference determine determine determine efficient full requires choice significant significant significant significant vision vision vision vision estimated pages increase con randomly randomly provided provided provided selected selected selected iteration iteration iteration iteration iteration iteration iteration iteration nature nature simply simply simply simply achieved measured normal increases increases increases arbitrary group fast fast close assumption assumption finding common common common effective effective assumed assumed theoretical main journal pixel probabilistic probabilistic probabilistic typically pairs smaller reduced account account account account block block block block testing significantly ratio ratio ratio segmentation segmentation segmentation mechanism mechanism database database database database database database database database database database database database database database database database database database database database database database database database operation leads leads leads leads call call iterations iterations iterations iterations iterations iterations pre pre making international international bottom decay decay decay minimize choose advantage robust takes similarity reported practical strategy strategy strategy strategy include side pixels inference inference inference subset subset subset recently relevant relevant relevant relevant interest interest interest interest previously solve converge converge achieve evaluation grid improvement entire entire lead lead concept concept concept suggests white white occurs occurs occurs occurs occurs generally setting runs runs runs runs runs runs starting place assumptions segment depend bayes bayes clear clear faster weak taking taking strong strong strong hard hard mechanisms mechanisms turn assuming user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user user start start decrease averaged groups minima minima minima minima suppose written written solving solving ways ways factors generating laboratory recall recall recall recall recall implement missing explicitly explicitly remaining remaining belief belief belief interaction interaction interaction interaction interaction interaction gaussians springer implies blocks blocks blocks select select select decreases choosing learner learner learner solved transform densities evaluated evaluated evaluate evaluate controlled restricted decomposition completely completely allowed reasonable false iterative valid valid visible query query query query query query query query query query query query query query query query query query query query query precision precision precision precision precision avoid avoid avoid exploration formulation formulation color retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval retrieval illustrated illustrated automatic priors characterized texture texture texture texture texture texture texture planning straightforward selecting selecting selecting selecting selecting aspects importance importance included included included included score score situation situation plots plots tend tend tend miller composed traditional notice notice notice conf verlag quickly quickly quickly contained allowing split return content content content content criteria criteria criteria criteria satisfy quantity absence absence paradigm paradigm providing providing hypotheses reach automatically consisted overlapping overlapping overlapping illustrates decreasing situations presents employed remain unlike unlike poor access difficulty rapidly varied recursive issues divergence divergence divergence divergence divergence hall int maximizing comparable fundamental patch patch patch naturally naturally concepts created queries queries queries queries queries queries queries queries queries queries obvious obvious precise explain explain synthetic integrate percentage percentage percentage indicating great ground ground ground crucial analyzed navigation improves majority starts closer widely worst desirable attribute patches patches addressed explained argument requiring improvements percent percent percent evaluating items relevance relevance relevance relevance amounts generic poorly poorly item incorporated formulated http rely rely rely maximizes prevent suited logp logp logp logp sophisticated returns median median tile tile tile tile tile tile tile tile june converged converged picture sort sort www labeling assign databases databases databases eliminate proceed significance simplify loops analyzing monotonically intuitive intuitive filled meaningful lip weakly searching searching facilitate relies impact designing captures omohundro explains limitation escape escape andrew metrics metrics visually visually visually users users users rubin basically session formulate pentland pieces blue stem forcing avoided examining scenario scenario avoids favor intuition community goals chapman denoting challenging emphasize wise argued depicts cosine harder isi happen truth truth truth stuck lippman lippman lippman lippman dramatic normalizing exploited vice versa achievable decided textures textures ers pictures recursion mistakes mistakes returned returned tribution distinguishing conflicting cardinality inefficient positives rating retrieved retrieved retrieved retrieved screen isolation drastically accounting stick media media media tical penalizes allowable mountain diverge cox entering snow snow snow attracted simulates beliefs beliefs beliefs llx llx llx llx encourage confirms confirms ames sky sky sky sky sky standing imagery imagery malik penalizing feel wanted live standpoint ogp ogp comput greenspan confused relied unrelated retrieving uninformative penalize cients austria favoring accessed vienna occupies tiles logarithms devroye lxt odds tedious inconsistencies returning coeffi prac grass argmaxp argmaxp argmaxp interests interests managed argm argm argm argm argm older lots abort troublesome ologp lugosi incoherent browsing retrieves mage soundness exposing lye 
#@Lippman_A,Vasconcelos_N,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural data data data data data data data data data data data data function function function function function function figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set set training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number number number number number number number system system system system system system system error state state state state state state state state state state state state state state state state state state state state state results results results results results information information information problem problem problem problem problem problem problem problem problem problem models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance based based based based based based based based based space space space space case case case case case vector order shown shown shown systems systems systems probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters functions functions approach approach approach approach pattern pattern processing processing control control control control control control control control control control control rate optimal optimal form signal signal algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper paper paper paper paper paper small small small small size size size size size size size size work work work work task methods step step process process process process process process process process current current current current problems random response response similar similar similar section section fixed fixed fixed line general general parameter parameter parameter real real real real real real real real states states states states states states states states states states states states states states states states states theory note note experiments experiments experiments result university threshold variables variables variables variables variables computation research independent independent defined found sequence dynamics dynamics dynamics dynamics dynamics dynamics dynamics initial initial estimate computer terms distance science science left left left left direction presented machine sets sets maximum press learn learn learn learn learn learn position abstract applied find properties properties properties properties properties references stochastic stochastic important important decision decision decision decision decision decision decision decision introduction introduction introduction action action action action action complex hand hand dynamic dynamic generated cost change change change change change change difference complexity variable assume assume assume prior prior learned learned learned learned part previous cases required required required represent expected expected markov markov markov markov markov markov markov markov markov markov markov fact proposed proposed proposed probabilities probabilities probabilities probabilities probabilities probabilities observed forward finite tasks tasks tasks tasks tasks tasks tasks total total computed called called times reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement made natural applications applications applications applications applications policy policy policy policy knowledge knowledge original represented compared compared compute compute compute compute compute rates perform experimental related related discrete power power approaches mit steps larger larger larger larger contrast modeling modeling modeling modeling report words words words department consists advances advances responses responses difficult difficult addition maps considered framework framework equivalent equivalent equivalent experiment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment directly directly directly directly directly additional additional additional transition transition transition transition transition transition transition transition transition transition transition transition transition efficient efficient requires approximate statistics free free world world world world world world world world speed estimated increase condition channel channel derived randomly developed finally processes processes processes depends depends constraint simply simply achieved measured increases increases increases increases denote tested limited assumption complete actions actions actions common assumed assumed generate instance instance instance future future easily degree typically typically needed technology significantly york increasing special special special consistent uniform empirical empirical mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode mode principle iterations iterations idea run light discussed discussed discussed improve directions directions directions directions property property property property property property property property property property property property property pair separate separate apply apply period side sense sejnowski sejnowski sejnowski sufficient previously observations observations observations correspond correspond studies rl rl rl rl rl rl rl address address address positions chain chain observation storage concept extended touretzky boundary generally generally generally pass runs minimal assumptions assumptions editors reward reward reward accurate clear sutton faster faster practice practice learns decrease suppose ways ways ways describes transitions transitions transitions transitions transitions transitions transitions transitions distinct distinct distinct modeled involves remaining interaction events events events agent agent focus stationary stationary viewed controlled evolution evolution forms sizes completely completely completely past key reasonable barto barto reduces exploration exploration perceptual perceptual combinations combinations coordinate usa formulation determines extension discuss mozer specifically holds holds partially partially partially partially discussions major simplicity reason modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes modes comparing online capture traditional road refer repeated showing issue issue issue running hold hold satisfy vary dayan dayan dayan paradigm realistic backward observable observable observable observable observable observable observable observable observable observable extend presents employed unlike wiley collection singh experience environments environments environments environments environments environments environments environments environments issues dual mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp mdp helpful fewer fewer applicable boosting dependencies office office symbolic proved workshop affect statistically analogous naturally possibly necessarily traffic traffic traffic traffic traffic traffic traffic formal assumes assumes switching improving attempts defines ment ment stop slowly sensors track improves briefly baum baum baum baum baum baum baum baum baum baum baum baum baum easier widely day precisely depicted sun addressed requiring items substantially substantially substantially empirically flexible conducted car poorly effort introducing share share remove variant variant ity rewards operate gen occurrence occurrence ordered extensions returns median specifies sharing trade initialization formally pick pick concerned addresses impossible arrival arrival inspired cellular kullback kullback allocation allocation pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp operates monotonically intuitively repeat started representational representational governed zhang zhang zhang zhang zhang regarded regarded hasselmo multiplied iterated infer arrive cpu environmental environmental environmental relies adopted executed mdps mdps mdps mdps limitation counts bertsekas speaking consecutive outperforms arcs drop drop drop largely unable basically basically leibler inferred validity break forced welch welch welch welch welch welch welch welch welch welch welch welch welch regularity regularity hundred workstation imagine auxiliary auxiliary illustration impose oct retain investigating memoryless nonetheless applicability compu aaai reinforce reversed handling decided water telephone eral hour hour hour usefulness conversion incorporation concerns floor floor meeting meeting tuple proposes maxi contrary reality elevator elevator elevator elevator elevator elevator elevator elevator elevator evolves evolves confined confined counterpart counterpart restrictive nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary nonstationary indirectly blocked huge lights noticed comprehensive kong kong cars cars cars cars cars cars exploitation oil examines hong hong repeats aliasing distinctions waiting waiting comprises samuel environ requests requests requests subclass subclass tational xij govern equipped departure indexes crites shed seeds reformulation reformulated ijcai yeung yeung yeung yeung yeung signifi envi choi choi choi choi choi acquires infrequent infrequent collapsed augmentation ultra ronment unnecessarily unnecessarily bay staff chrisman morning ust ust ust waits yan formalizing tea 
#@Choi_S,Yeung_D,Zhang_N,
#t13
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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning function function function function function function function function function function function function function function function function function function function function figure figure figure figure time time time time set set set set set set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number number number number state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results problem problem problem problem models models performance performance performance based based based space space case case case case vector shown shown values values values values values values values values values values values values probability probability probability probability probability probability probability probability probability noise functions functions functions distribution distribution distribution method method method method method method method method approach single single large local optimal optimal optimal optimal optimal optimal optimal optimal optimal form form form shows shows algorithms algorithms algorithms simple simple simple simple paper paper paper paper paper small work work work task task task task task task task task task task task task task task task task methods methods methods fig step points level level current current current current structure structure problems similar show show show show show show equation fixed general approximation approximation average states states states states states states states states states states states states states states states states states obtained term term term note experiments result result result result result university variables variables variables variables variables variables variables variables variables variables variables variables variables variables variables solution research defined defined defined defined defined defined sequence sequence target target target target target initial constant standard standard computer terms distance node science left left temporal temporal temporal temporal machine sets press press learn learn learn learn learn learn learn learn position position position position abstract abstract abstract abstract abstract abstract abstract abstract applied convergence convergence convergence convergence convergence convergence convergence properties references stochastic stochastic stochastic due procedure important important important decision decision decision introduction action action action action action action action action action action action action action action action action action action action action action action action action behavior dynamic dynamic cost cost tion tion assume assume chosen chosen chosen part previous previous theorem theorem theorem bound cases cases cases cases required required required multiple conditions conditions conditions conditions conditions conditions conditions conditions conditions represent represent expected markov markov markov markov fact correct scale finite finite finite resulting resulting resulting resulting resulting ing ing ing tasks tasks tasks human multi sum sum means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge obtain obtain vol vol samples represented represented represented represented represented represented true application application desired provide define define define rates rates location location location location location location location location location location location location perform perform experimental goal related distributions distributions equal approaches mit mit steps steps steps steps comparison update support source source source morgan morgan morgan proceedings department version addition graph graph ai framework framework framework domain domain domain domain environment environment directly hinton hinton additional view solutions transition transition transition transition transition san top requires world world basic give give give con condition condition condition condition condition condition condition condition condition condition weighted weighted randomly randomly randomly developed controller controller product processes iteration depends simply denote complete actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions actions proof proof proof proof proof proof proof proof effective implemented require main square square future noisy noisy kaufmann kaufmann kaufmann pairs combination jordan transfer programming programming special consistent representing call call numbers max max making combined combined choose discussed property pair pair separate separate apply apply introduced include machines hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical hierarchical subset relevant relevant relevant relevant axis axis tions tions studies converge converge rl rl rl rl rl locations locations locations locations observation generalized bounded entire exists horizontal suggests extended wide move move move deterministic deterministic deterministic column setting runs conclusion starting starting starting starting row reward reward reward reward reward reward reward reward reward sutton sutton faster weak learns presence drawn proportional intelligence turn introduce introduce boltzmann boltzmann pro sequential describes tuned vertical dept dept dept explicitly simultaneously infinite infinite involves involves easy belief unique unique unique scales applying implies focus expressed depending depending stationary stationary viewed solved solved variation approximations decomposition decomposition decomposition understanding completely completely similarly converges converges converges converges converges partition constants key performing performing performing iterative norm norm advantages exploration exploration exploration prove prove prove holds partially successfully planning planning planning straightforward selecting aspects aspects closely uniformly differ differ paths successful identify plots online identity kind showing return return sci sci sci hold comp comp comp comp write usual usual dayan dayan nips nips nips observable reach received policies policies policies policies policies policies illustrates subsequent situations employed employed explore access essential singh singh singh singh put put put put put put put put put preliminary mdp mdp mdp mdp mdp mass ideas tech tech tech terminal terminal decisions root root root root root root root proper affect hierarchy hierarchy analogous ensure obvious obvious greedy formal observe explored attempts defines brown ment defining navigation navigation navigation briefly starts reasons satisfied satisfied choices potentially scientific separately involve involve beginning arises researchers argument argument experimentally car introducing marked completion completion completion completion incorporated slower rep rep rep compares rewards rewards controllers parent ordered ordered ordered ordered semi semi semi kinds neuro expectations returns focused jaakkola jaakkola lim lim proposition converged leaf leaf univ univ univ cumulative irrelevant irrelevant irrelevant irrelevant irrelevant irrelevant irrelevant irrelevant irrelevant irrelevant bellman identifying identifying temporally temporally temporally arguments pick ordering ordering tem consideration satisfying satisfying simplify primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive primitive hit north north effectiveness child child child child child child child continue thomas francisco express discounted discounted discounted discounted discounted contraction contraction ends horizon horizon horizon inductive broken partitioned tsitsiklis exploiting dietterich dietterich dietterich dietterich dietterich inf characterization executed executed executed executed executed executed executed executed mdps mdps bertsekas bertsekas treat incorporates solves discount recursively recursively recursively recursively recursively recursively ties ties abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction abstraction exception preferences amherst flat flat flat hierarchies options options visited argue wall distribu execute execute execute execute permits convert boulder efforts eliminating sketch sketch constructs importantly option breaks refinement west west applicability permit permit refined holding exploited oregon oregon infinitely infinitely completed elemental walk littman factored picking rarely fiat fiat reinforce opti primitives east east termination termination termination termination termination termination termination recursion russell condi executing executing executing executing executing ham destination destination destination destination destination destination destination safe safe aggregation kaelbling kaelbling kaelbling south south terminates terminates terminates semantics carrying indirectly episode episode ous maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq maxq dean merit deciding col ceedings initiated notions omit precup precup macro macro macro macro terminate terminate parr subtasks subtasks subtasks subtasks subtasks subtasks subtasks subtasks wait terminated terminated terminated cooling belmont fruitful previ poral executes abs completes nix nix providence wishes predicate predicate motivate succeed safely safely struction invoked deliver deliver abstractions abstractions abstractions abstractions abstractions abstractions abstractions abstractions abstractions abstractions abstractions feudal feudal dag dag dag dag flamework athena ijcai notable composing icml icml discounting terminating programmer programmer programmer navigate navigate neut elapsed navigating navigating unfolding usable invoke invoke clever terministic subroutine subroutine mize finish sulting episodic undiscounted undiscounted undiscounted finishing corvallis lue bitrary delivering preferring 
#@Dietterich_T,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model model model model model model model model model neural neural neural input input data data data data data data data data function function function function function function function function function time time time time time time time time time time time time time set set set set set set set set set set set set set set set set set set networks algorithm algorithm algorithm algorithm algorithm output number number number number number number number number number number number number number number number number number system error state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results information information information information information problem problem problem problem models models models models performance performance based space space space space space linear linear linear linear linear case case case case case case case case case case case case case case case vector order order shown systems values probability probability probability probability parameters functions functions functions functions functions distribution distribution distribution distribution distribution distribution method method method method method method method method method approach approach approach point single single single processing control large large large large large large large large local local local local local local analysis class class class class class class class class class class class class class class class class class class class class class class class class class class optimal inputs form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper paper paper examples small small size size size size size size size size net step step step step step points points points process process process process current current current current current current structure problems random random random random random random random random random memory similar show show section section section section section section section fixed fixed fixed fixed fixed line vectors vectors general general general real approximation states states states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained note note note result result result university computation research research independent independent log log log log log log log defined defined sequence target estimate estimate estimate estimate estimate estimate estimate standard terms node node node node node node node node node node left presented map nodes nodes machine maximum maximum press learn sample sample sample sample sample sample sample sample sample sample sample sample abstract abstract back find find find find computational computational convergence convergence convergence convergence convergence convergence references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due important decision decision decision decision decision decision introduction action action action action action action action action complex complex complex estimation behavior statistical generated generated generated cost search search search search search search search search search tion complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity complexity variable variable variable assume assume assume assume assume assume measure measure measure measure prior representations representations representations representations word chosen previous previous theorem theorem theorem theorem theorem theorem theorem bound bound bound bound bound type good good good good good good binary binary binary long long long long tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree tree distributed expected expected expected expected markov markov markov markov make make fact techniques techniques length probabilities probabilities observed observed finite finite finite finite finite finite finite finite resulting resulting resulting classes classes classes classes classes ing ing total total simulation simulation sum called called called times mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement factor dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension dimension made made natural natural feedback applications study study policy policy policy policy obtain obtain original original artificial artificial artificial samples samples true true application desired provide define define define define define proc perform perform goal distributions distributions equal power approaches approaches mit steps steps support descent proceedings words version version version consists internal advances joint connectionist difficult maps considered considered computing computing domain domain domain domain equivalent equivalent equivalent directly view view estimates estimates estimates estimates estimates transition transition limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory conference efficient upper full full full full requires approximate approximate approximate approximate approximate approximate approximate world world basic pages give give derived developed developed bounds bounds bounds bounds bounds bounds bounds bounds controller controller path path path path path provided provided finally processes processes depends depends depends simply simply describe describe describe describe describe arbitrary arbitrary arbitrary denote denote transformation transformation limited close close assumption complete actions actions actions actions actions actions actions actions actions proof finding amount amount amount amount amount common generate generate generate generate generate theoretical require journal ability ability ability hypothesis hypothesis hypothesis instance easily including typically smaller underlying underlying needed needed needed needed needed needed fully fully fully jordan interesting significantly significantly special uniform uniform uniform uniform uniform uniform uniform empirical empirical call max max international supervised supervised supervised supervised supervised supervised supervised supervised depth depth polynomial attention attention combined combined choose choose choose choose choose choose added recent recent pair pair ensemble takes takes practical practical strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy strategy include trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees trees sense sense inference sufficient sufficient conventional observations observations observations observations works yields converge achieve rl rl address definition definition definition definition evaluation observation observation observation observation observation bounded bounded bounded williams williams parts parts lead extended extended trial feed move deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic deterministic setting setting setting setting setting setting demonstrate starting assumptions reduce trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories trajectories valued depend depend reward reward reward reward reward reward clear sutton performs exponential exponential exponential exponential exponential practice weak taking largest drawn drawn intelligence intelligence intelligence labeled labeled labeled labeled labeled turn turn assuming variety start start start start start iii question question monte monte monte carlo carlo carlo ways generating generating transitions label simultaneously simultaneously averaging linearly linearly infinite infinite infinite infinite infinite infinite infinite easy belief applying events springer agent boolean boolean boolean yield choosing choosing choosing family independently dependence dependence dependence dependence dependence dependence viewed detailed transform transform evaluate evaluate evaluate restricted restricted restricted restricted forms sizes suggested key key barto classical classical classical classical spaces initially construction david box includes vapnik prove prove discuss discuss maximize domains black absolute holds holds partially partially partially partially partially partially partially partially structural simplicity planning planning planning planning planning planning planning planning planning planning planning planning planning uniformly uniformly uniformly differ computationally paths paths build build build schemes essentially reached reached reached capture compact compact compact compact compact verlag quickly kind induced moore moore link showing dis dis return return return return return return lie generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative generative strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies strategies built write write michael generalize observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable observable highest maximization received received moves policies policies extend remain unlike parametric powerful transformed transformed transformed transformed transformed transformed poor create access access collection experience experience experience experience experience difficulty difficulty exponentially exponentially replaced limitations issues issues mdp mdp mdp helpful reducing giving history history history history history ideas links referred structured root root root root proper notion notion notion notion analogous analogous analogous math possibly possibly possibly man extremely extremely created created created thought versions greedy formal observe generates arbitrarily motivated defines defines defines defines asymptotically developing developing theoretic theoretic theoretic track track expensive briefly tractable lies starts turns straight berkeley berkeley easier day precisely immediately arise opt opt implicit begin begin begin optimize preceding researchers argument argument argument requiring behaviors evaluating applies pseudo pseudo parameterized simulate simulate readily haussler rewards rewards rewards rewards rewards rewards calculating operate maximizes serve simulator simulator unbiased unbiased unbiased unbiased returns returns returns focused baird baird leaf calls calls calls calls realized naive contribute pose pac proofs labeling labeling formally restrict appropriately recover repre arrival children children children children establish establish chance stronger familiar pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp definitions settings settings settings settings intuitively preparation generalizes generalizes generalizes child child child child child selects reliably reset corollary corollary sion equals induce regard ascent discounted discounted discounted discounted discounted insight kearns kearns kearns kearns draw horizon horizon horizon horizon horizon horizon extends designing designing adopted mdps limitation andrew pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps discount super tables exhaustive exhaustive recursively benefits incrementally smoothly additionally seek ease generalizations lit examining acting intuition continues gener labs permits thresholded carefully concentrate harder harder harder harder memoryless sized union treating tin exploited tel infinitely infinitely littman factored factored factored tau handled observables reinforce reinforce argmax achievable ate ping generafive establishes concrete floor tuple att shattered shattered william kaelbling era era elevator addressing tra tra tra trend sentation successor convey aviv dean histories histories histories histories histories histories histories histories infeasible infeasible plexity parr treats dependences reminiscent mansour mansour mansour mansour mansour mansour waiting waiting pushed designated disagree ative adopting tributed absorbing augment exposition koller koller readers sume calling labelings labelings labelings labelings tributions rrt sug vised reuse reuse reuse button deci cassandra replicating strate assures weaken leverage leverage leverage descrip uai preliminaries stating vmax vmax vmax vmax randomization expo dummy chernoff evalu boyen ang informally ols timate gest keams hori jectories jectories jectories generous enjoy gies undiscounted rnax intelligently soundness ivy ivy mains inductively sixteenth enjoys hanks 
#@Kearns_M,Mansour_Y,Ng_A,
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural function function function function function function function function function function function function function function function function function function function function time time time time time time time time time set set set set set algorithm algorithm algorithm algorithm algorithm number number number error error state state state state state state state state state state state state state state information information information information performance performance performance based based based based based based based based space space space space space space space linear case case case case vector vector vector vector vector vector vector vector vector shown systems systems systems values values probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters functions functions functions functions functions distribution method method method method approach point single processing control control control control control control control large local analysis analysis analysis analysis analysis analysis class class class matrix optimal optimal form form form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple paper paper small small size size feature feature work work methods methods methods methods methods methods methods methods methods methods methods methods methods methods points features features features features features features features process process process process process current current current current problems problems problems problems problems problems problems random high high high similar similar similar similar architecture architecture architecture architecture show show equation equation section fixed fixed fixed vectors vectors vectors vectors vectors parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average average average states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained note note note note note note note note experiments dimensional dimensional dimensional dimensional result result result result result solution solution solution research independent defined defined sequence initial table table estimate estimate standard terms terms terms direction direction direction direction presented presented presented map low temporal temporal temporal machine object press learn learn learn basis continuous sample abstract applied convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence convergence properties properties properties references component stochastic stochastic stochastic stochastic due ieee ieee ieee positive positive positive positive important decision decision decision decision decision decision decision decision context introduction introduction action action action action action action action action action hand statistical dynamic generated variance variance variance cost cost cost cost cost cost cost cost cost cost cost cost tion change difference difference difference difference assume assume assume assume representations representations chosen chosen theorem theorem theorem theorem type good long long long long long long expected expected expected markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make fact techniques correct probabilities scale scale scale finite finite minimum resulting ing ing total simulation simulation simulation simulation simulation simulation simulation simulation respect mapping mapping means reinforcement reinforcement reinforcement reinforcement reinforcement factor factor optimization optimization optimization optimization optimization policy policy policy policy policy policy policy policy policy policy policy policy obtain compared compared compared desired provide provide provide define define define compute compute compute compute compute compute perform determined related mit mit mit contrast contrast contrast update update update update update update dependent dependent morgan proceedings institute institute loss advances represents connectionist sequences ai cambridge cambridge computing directly directly directly additional view estimates san top conference requires choice choice approximate approximate approximate approximate approximate estimated estimated estimated pages pages types path product product product finally finally finally processes processes processes processes processes depends achieved describe arbitrary denote denote denote limited limited close close close assumption assumption complete proof proof proof common supported role theoretical theoretical journal instance easily objective pairs smaller jordan technology technology programming projection projection projection projection projection projection projection projection projection projection projection added denotes denotes denotes recent exact exact exact pair pair reported practical apply period sense sense sense sense observations observations observations volume converge differential rl chain chain chain chain observation observation observation bounded bounded bounded bounded williams williams improvement improvement grant grant exists exists exists exists suggests extended alternative generally setting runs place assumptions assumptions assumptions conclusions operator operator valued valued reward reward differences sutton sutton sutton sutton faster faster practice sound propose propose propose taking strong reduction reduction turn minimizing minimizing start min introduce derivatives derivatives denoted reference pro pro pro monte van van derive carlo ways ways laboratory changing recall implement linearly linearly infinite scales potentials john letters family family family family independently independently formation dependence stationary stationary stationary stationary stationary squares viewed viewed interpretation open controlled updated updated updated updated understanding completely converges updates updates updates updates updates updates past past key barto spaces spaces normalization combining combining sufficiently norm advantages transactions transactions transactions expect expect existing thesis subspace subspace subspace subspace batch automatic automatic automatic prove variations holds partially partially straightforward closely uniformly differ induced interested interpreted hold categories satisfy notation quantity generalize observable ill leading attempt policies policies policies policies policies acknowledgments perturbation singh singh updating estimators issues scalar ideas possibility reliable affect affect removed trace possibly necessarily analyze versions algo ith submitted phd established massachusetts massachusetts asymptotically asymptotically slowly formula formula formula formula formula critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic critic guaranteed unstable majority starts satisfied precisely constructing desirable arise products actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor actor scientific involve optimize definite arises nsf parameterized parameterized parameterized parameterized parameterized readily lack introducing slower slower ity span span span rely rely poisson aim aim aim fall chen conclude conclude neuro lim lim simultaneous differentiable globally pose bellman proofs optimality conditioned concerned concerned flexibility nonzero plays kaufman stronger chains chains satisfying replacing stated familiar hope settings intuitively modifications carry encountered negligible negligible overview overview guarantees guarantees realization francisco discounted properly roy roy tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis variants variants inf assigns bertsekas usage indirect randomized randomized randomized job theorems arg ideally letting avoided auxiliary stands stands rithms mathematically disadvantage afosr noting lookup lookup spanned spanned drawback weaker eligibility siam minor rewrite infinitely rewritten reinforce stores accumulation advantageous parameterization parameterization parameterization parameterization excess excess termination termination played episodes episodes exclusively possess carries meth suffice ods ready episode episode promise translate prescribed prescribed unnecessary ceedings stepsize stepsize stepsize richer incurred incurred lipschitz entered forgetting aimed winter mansour ecs vast belmont vin gra succeed aperiodic gramming ergodicity dient athena lai pol discussing irreducible rio critics marbach marbach guaranteeing ils scalars older vided andj andj icy ris episodic renewal automatica iis sensitiv reinitialized reinitialized prescribe delivering iiv 
#@Konda_V,Tsitsiklis_J,
#t13
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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model model data data function figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time time time time time time time time time time set set algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm output number number number number number number system error error error error error error state state state state state state results results results results results results information information problem problem problem problem problem problem problem models models models models models hidden hidden based based space space space space weights weights weights case case case case case case case vector order shown shown shown shown shown shown shown systems systems systems values values probability probability probability probability probability probability probability probability parameters parameters parameters parameters noise noise noise noise weight weight distribution distribution method method approach approach approach approach approach approach pattern pattern point single local local local rate patterns matrix matrix matrix matrix optimal optimal inputs form algorithms simple simple simple simple gaussian gaussian paper paper small size size size size size work work methods methods cells cells cells cells cells cells cells cells step step step step step step field classification current cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell cell structure structure random random random random random high similar similar representation representation representation show show show show equation section section section section section fixed fixed fixed fixed line general parameter parameter approximation approximation approximation note note experiments dimensional dimensional dimensional dimensional dimensional university variables variables variables variables variables solution solution solution solution solution solution solution solution independent independent independent defined defined defined found found found sequence sequence initial initial constant estimate estimate computer science left left map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map map machine machine sets maximum maximum press learn learn learn learn position position components sample sample abstract applied back back properties references component component stochastic mixture context introduction action action action complex hand hand estimation estimation effect dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance variance cost tion tion change difference variable variable variable assume assume assume prior prior prior prior prior prior learned learned chosen higher part previous previous multiple binary represent tree bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected markov markov markov fact correlation correlation length length length length correct correct correct observed observed minimum resulting computed computed called called called mapping dimension dimension made orientation orientation global study policy knowledge em em em em em em em em em em em em em em em em em filter filter artificial relative represented true compared define define compute compute compute compute compute location location location location location location location location location location location location perform perform active active active determined posterior posterior posterior posterior posterior posterior posterior distributions motor motor motor discrete discrete approaches approaches mit contrast update update update update nets version joint joint joint represents difficult addition maps maps maps computing computing environment environment environment environment directly estimates transition transition transition transition transition trajectory trajectory bit conference efficient full requires approximate approximate approximate statistics statistics free world world world estimated estimated basic increase increase con produce produce channel weighted conditional conditional conditional robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot entropy path product product product actual finally processes evidence evidence iteration nature depends depends sampling sampling discussion increases increases denote denote hmm hmm hmm fast corresponds complete actions actions common assumed supported end end hypothesis future makes noisy noisy noisy probabilistic probabilistic needed account unknown unknown fully jordan interesting uniform mode mode operation details filters making window window window window window window bits normalized decay decay idea combined light light light predict improve recent recent recent recent exact exact exact takes strategy moving identical inference inference inference inference inference inference inference dimensions sufficient sufficient compare compare compare unsupervised works axis studies locations observation observation observation observation observation observation observation observation grid grid grid grid grid grid grid grid grid gate grant lead studied alternative move move move move deterministic deterministic white pass row assumptions trajectories trajectories valued depend editors reward reward accurate accurate bayes bayes exponential exponential exponential weak largest cycle california intelligence start decrease introduce introduce groups minima question suppose suppose monte monte monte monte carlo carlo carlo carlo sequential sequential sequential estimating estimating label label label label label label averaging linearly easy belief belief unique adding applying applying correlated correlated open open labels labels labels static static updates allowed past key smoothing smoothing smoothing smoothing performing spaces boundaries closed closed remains filtering filtering filtering filtering filtering filtering filtering filtering filtering sufficiently topology illustrated discuss discuss discuss discuss maximize priors coupled coupled coupled coupled variations black successfully successfully simplicity sensor sensor sensor selecting closely importance maximal computationally computationally delta modes successful successful literature essentially online online online online online online online online online online online reached notice return running running running localization localization localization localization localization localization generalize nips minimizes hypotheses hypotheses hypotheses approximating neighboring neighboring acknowledgments bars explore simpler remain collection requirements difficulty exponentially updating kalman kalman environments environments environments environments environments environments detail accurately dotted graphical graphical graphical graphical mass ml ml incremental incremental variational analytically analogous hill circles ensure obvious greedy store submitted explain residual indicating rows pairwise sensors track navigation expensive independence briefly tractable tractable handle starts lin berkeley berkeley widely precisely division desirable separately integrating bootstrap autonomous autonomous poorly poorly passed treated commands exhibits popular qualitatively chen chen marginal replace chose returns returns conditioning specifies sharing ghahramani benefit ear intractable writing appearance formally restriction drift acts approximates mobile mobile mobile mobile mobile grows robotics lost lost lost climbing wrong wrong murphy murphy murphy murphy murphy odd familiar pomdp child date date entry topological discounted omitted matter papers ignore lag lag onr treat treat escape liu liu liu maintaining unable thrun thrun thrun thrun encodes formulate rao rao rao rao encouraging junction factorial factorial home exam robots robots robots robots robots alternate distribu continues uncertain projecting particle particle particle particle particle particle particle particle particle particle stuck page normalised ignoring aaai vice factored factored factored factored factored factored versa compete diffuse russell resampling visit proposal proposal proposal unreliable ally normalize fox fox fox conditionally conditionally seed inefficient exploits explanations ignores ignores sliding kaelbling longest backwards occupancy cope particles particles particles particles particles particles particles particles particles unobserved survival tightly sebastian observes observes virtue marginals marginals marginals dead dead slip reviews forgetting localize localize localize relying treats ess ess tics statis jumps simmons offline offline pri rightmost freitas confident concurrent flips stuart koller koller vation condensation heads equiv useless multiplexer multiplexer sharper ori entails unknowns matters koenig seeds autonomously walls obser visiting visiting actuators actuators ijcai proximate observa doors doors doors kevin envi dition tractability helping died uai spends sir alent lyl contradicts ronment dummy resample ining boyen boyen marginalizing forwards reckoning reckoning lift rii actu thinks thinks marginalized marginalized ifj ifj bust wheels territory jasa occasions xlt 
#@Murphy_K,
#t13
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#*network network learning learning learning learning learning learning learning learning learning model model model model model model model model model model input data function function function function function function function function function figure figure figure figure time time time time time time time time time time time time time set set set set set set set set set set set set set set networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system system state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results problem problem problem problem problem problem problem problem models performance based based based based based based based based space space space space space weights weights weights weights linear linear case case case case case case vector vector vector vector vector order order shown shown shown shown systems systems values values probability probability probability probability probability probability probability probability probability probability probability probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight functions functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method approach approach approach approach approach approach approach approach approach approach approach approach point point single single single large large large large large local rate rate analysis analysis class class class matrix matrix matrix matrix optimal form shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple simple simple simple simple gaussian gaussian paper examples small small net work work task task task task task methods methods methods methods methods step step step step points points features process process process process process process process process current current problems problems random random random high high memory memory memory representation representation representation representation representation representation show show show show show show equation section fixed rule rule general general general parameter parameter parameter parameter real approximation approximation approximation approximation approximation approximation approximation approximation average average average average average states states states states states states gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained term term note experiments experiments experiments dimensional dimensional dimensional dimensional result result result university university variables variables variables variables variables computation solution solution solution solution research independent independent defined defined defined defined defined defined found found dynamics dynamics dynamics dynamics dynamics initial initial constant constant estimate estimate estimate estimate standard standard standard computer computer computer terms terms node node science science science presented map present present low nodes nodes machine maximum learn nonlinear nonlinear continuous continuous sample sample sample sample sample abstract applied applied applied find find find find find computational density density density density density density density density density density density density density density density density density density density density density density density density properties properties references stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic stochastic due positive procedure decision decision decision decision decision propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation propagation mixture mixture mixture introduction action action action action action action action action action action complex complex complex complex estimation estimation estimation estimation estimation estimation estimation behavior behavior behavior statistical statistical dynamic generated generated cost cost cost search search search search search search search search search search search search search search search change change change variable assume assume assume assume assume assume assume assume assume prior chosen chosen chosen higher part previous cases cases cases required multiple good good good good good bayesian bayesian bayesian markov markov markov markov fact techniques techniques techniques techniques probabilities finite finite finite finite resulting total computed computed computed respect respect respect reinforcement reinforcement reinforcement factor optimization optimization made natural orientation applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge obtain negative artificial artificial relative relative relative relative relative relative relative relative samples samples samples samples samples samples samples samples samples represented represented provide provide provide provide define define define define define define define define compute compute compute compute compute compute compute proc proc proc proc proc perform perform perform experimental goal goal goal goal goal goal distributions distributions distributions distributions distributions distributions distributions distributions distributions discrete equal approaches steps accuracy larger support descent descent descent version consists internal individual joint joint represents represents connectionist difficult difficult exp exp exp scheme ai ai ai ai considered framework computing computing computing computing domain experiment directly directly view solutions estimates estimates estimates transition transition transition transition transition transition transition limit determine efficient approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate free speed estimated estimated pages pages weighted weighted conditional conditional conditional conditional criterion criterion product product actual actual processes processes processes processes selected selected selected sampling sampling sampling constraint simply achieved covariance covariance covariance denote denote denote tested fast fast fast limited close close close close close assumption assumption assumption assumption actions actions actions actions actions finding finding implemented generate generate generate supported require require ability cluster easily easily noisy fit smaller fully significantly projection projection trials trials empirical empirical empirical empirical empirical operation representing representing representing representing direct direct direct direct making bits decay decay idea idea attention combined combined choose description improved recent exact property robust robust separate takes takes takes takes reported lateral subject sense inference interest interest converge diagonal diagonal evaluation chain chain observation observation williams williams exists exists exists expression trial derivative derivative derivative derivative derivative derivative matrices alternative alternative alternative locally deterministic deterministic deterministic deterministic clusters generally setting setting setting greater assumptions trajectories trajectories conclusions operator operator operator operator operator operator operator operator operator operator operator depend depend depend reward reward reward reward reward reward reward bayes faster learns propose propose propose taking taking taking taking strong hard hard integration drawn sigmoidal intelligence variety start start derivatives derivatives derivatives program program acknowledgements explicit explicit explicit explicit monte monte carlo carlo ways estimating estimating estimating estimating tuned dept dept changing sensitivity explicitly infinite infinite infinite infinite infinite infinite infinite involves easy easy angle consisting integrated gaussians gaussians gaussians gaussians gaussians applying quality quality agent expectation select choosing choosing family family family expressed dependence stationary estimator densities densities densities densities densities densities densities densities densities densities evaluate operations controlled restricted restricted restricted completely allowed earlier earlier earlier reasonable reasonable slow slow performing spaces spaces fitting penalty tracking tracking closed distances distances sufficiently assigned foundation foundation avoid existing box includes combinations discuss specifically specifically domains domains domains black holds partially partially structural simplicity simplicity planning planning planning planning planning aspects importance differ modification delta successful build schemes schemes fine compact compact quickly quickly quickly induced allowing success moore dis dis return sin criteria generative generative generative notation write dot nips nips observable observable observable computes leading automatically attempt policies policies policies policies policies policies policies policies policies policies policies policies policies policies approximating extend perturbation access access access access access singh difficulty exponentially exponentially mead rapidly environments replaced optimized integral accurately mdp mdp mdp mdp mdp mdp mdp giving authors structured structured working comparable complicated complicated encode closest possibly possibly ensure ensure front quantities quantities portion portion portion formal switching multivariate multivariate multivariate multivariate generates mixed simplest arbitrarily defines averages years theoretic trivial trivial trivial track defining defining defining growing fairly fairly fairly independence tractable drive drive stanford stanford stanford stanford stanford straight tive berkeley berkeley berkeley berkeley sys easier precisely division angles optimize optimize optimize radius meaning summation argument evaluating applies reflect empirically led parameterized parameterized parameterized parameterized car car car car effort introducing introducing introducing continuously ity rewards rewards maintain controllers controllers limiting maximizes extensions enables simulator simulator simulator simulator returns returns implements median baird specifies progress proposition proposition proposition proposition differentiable differentiable differentiable differentiable differentiable differentiable softmax cor representative feasible accomplished optimality optimality optimality optimality modify restriction restrict fix driving driving driving optimizing concerned repre grows murphy simplify replacing intelligent balance pomdp contract contract exploit settings settings settings exceeds reliably reliably evaluations evaluations contexts slice slice slice slice slice slice slice corollary falls programs induce guarantees guarantees guarantees ascent ascent ascent ascent ascent ascent den searching searching originally entries darpa darpa discounted discounted contraction theoretically horizon horizon horizon horizon horizon horizon horizon horizon variants variants variants balancing automated vari parents parents parents parents mdps mdps mdps mdps onr andrew verify pomdps pomdps pomdps maintaining truncated slight users fellowship ent discount discount discount equivalently lane lane lane lane lane lane lane lane torque forced smoothly perturbed utilize par par medium assignments recurrence recurrence recurrence letting algebraic algebraic param jacobian jacobian jacobian care tems compensate life distant proba carefully picked weaker memoryless responding minor simplex simplex simplex induces induces rewrite eters infinitely infinitely differentiating differentiating factored observables observables observables resolve bility impractical converging families evolved russell executing executing tuple manually huang inefficient bat exploits sloan sity kaelbling differentiate enters twelve shaping shaping indirectly blocked dean subtle tails pact moderately infeasible meaningless notions omit avg ables marginals parr parr parr parr parr parr modifies tilt tilt tilt fur kim tially ronald landing absorbing absorbing absorbing absorbing absorbing roots driver exposition dbn dbn dbn dbn dbn dbn koller koller koller koller koller koller koller fragment ticular instantiations confused bicycle bicycle bicycle bicycle bicycle bicycle bicycle compactly compactly compactly tributions succeeded reinforcements reformulation reformulation reformulated powell genera ijcai gle gle representable kevin icml icml ported rand rand aro leverage limt trl uai uai sociated multinomials leaning boyen ang busy cussed pletely highway qual pays pays thermore encompasses senting summand kanazawa rion daca singleton crite staying staying riding riding forbes hanks muri 
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#*network network network network network network network network network learning model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural neural neural input input input input input input input input input data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data data function function function function function function time time time time time time time time time time set networks networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number number system system system system system error error state state state state state state state state state state state state state state state state results results results results information information problem problem problem problem problem problem problem problem models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models models performance performance performance performance performance performance performance based based based based based based based based based based based based based based linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear order order order order systems systems values values values parameters parameters unit method approach approach approach approach approach point point point point single single single single single processing processing processing processing control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control control large large rate rate rate test test test test test test test test optimal optimal inputs inputs inputs inputs inputs inputs inputs inputs inputs inputs form algorithms paper paper paper paper paper paper paper paper examples step points process process process process process process process process process process process process process process process process process process process process process process process process process process process process current trained trained structure structure high high high similar representation architecture show equation equation section section line real average average gradient computation research found dynamics dynamics initial initial initial estimate standard terms terms terms presented presented presented presented present present phase range range press nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear nonlinear outputs outputs outputs outputs outputs outputs abstract applied computational density density references component due important propagation introduction complex hand dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic variance parallel change change change change change difference difference difference variable lower lower lower prior representations bound cases cases type type required required multiple multiple multiple multiple multiple multiple long distributed equations techniques techniques region region region correlation length scale scale scale ing ing simulation computed computed times regions regions regions regions regions factor optimization optimization optimization optimization optimization optimization optimization optimization optimization made made feedback applications applications applications applications applications applications applications applications applications knowledge em specific application application application application desired desired desired series compute proc proc proc active constraints constraints constraints constraints constraints constraints gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain gain approaches mit contrast update implementation implementation implementation implementation technique technique technique technique technique internal represents difficult difficult final final final final final final final delay addition addition addition framework cambridge environment hinton additional transition transition trajectory trajectory trajectory trajectory trajectory efficient upper upper upper significant con derived derived derived developed developed developed developed developed developed developed developed bounds bounds bounds bounds bounds bounds controller controller controller controller controller controller controller controller controller controller types product provided finally finally finally processes processes processes processes processes processes processes processes processes processes processes selected backpropagation sampling sampling sampling sampling sampling sampling achieved feedforward feedforward limited limited limited limited complete actions actions actions amount amount common common implemented implemented implemented require eds eds eds ability ability future future future future easily rumelhart rumelhart development development including including including including objective objective objective objective objective objective typically typically pairs needed needed combination combination reduced technology programming programming testing empirical empirical empirical empirical empirical principle leads squared details details combined minimize produced produced produced run discussed discussed directions recent separate reported practical period period period period quadratic recently recently engineering highly varying previously solve solve achieve achieve interval interval williams entire entire entire constructed lead trial trial wide wide wide wide wide wide wide wide wide move loop loop loop loop loop conclusion place greater operator accurate practice variety variety variety variety minimizing minimizing user exist decrease identification identification identification base areas produces index solving solving factors primary primary primary transitions transitions implement develop integrated predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive predictive quality quality extraction select extracted depending viewed solved solved open open open open restricted updated approximated allowed past past past calculation calculation slow combining combining combining combining combining combining intervals closed sufficiently formulation determines coupled coupled tests tests tests successfully regular regular determining determining selecting identified computationally mcclelland build efficiently efficiently efficiently composed conf contained allowing success criteria strategies built quantity involved usual providing computes principles moves operating operating operating operating operating operating extract deal presents unlike poor production create exhibit difficulty steady steady steady steady steady steady steady steady steady steady steady steady steady steady steady steady limitations hall hall combine referred workshop affect cover hill created created algo observe multivariate plant plant plant plant plant plant plant plant plant plant years years great advanced developing developing developing developing expensive expensive expensive nonlinearity nonlinearity nonlinearity perspective implementing widely preprocessing incorporate products recognized recognized describing calculations researchers improvements collected empirically generic generic generic generic generic conducted readily poorly operate operate operate operate gains gains controllers spread spread spread spread prevent germany chose decreased june june benefit benefit indices guarantee martin martin martin martin rithm food food food food addresses flexibility suppression eliminated fits minutes accepted accepted accepted occurred tools tools tools tools simplify chemical chemical chemical chemical chemical biased mark operates symposium days hours hours prentice prentice excellent excellent introduces periods overview overview overview scheduling scheduling scheduling scheduling scheduling scheduling facilitate facilitate viewing late properly horizon horizon horizon horizon considerations variants papers fold johnson johnson johnson johnson johnson rejection suboptimal year year acceptable gene jacobian gained gas bounding ultimately scope retain conversely flower flower commercial commercial commercial milliseconds dramatic computa mini technologies technologies technologies technologies technologies technologies technologies expense survey survey stephen impractical european settling settling settling austin austin austin austin austin austin suite imple puts keeler keeler keeler keeler industrial industrial industrial industrial industrial industrial industrial industrial industrial industrial industrial usefulness incorporation disturbances ters assessment economic linearized setpoint setpoint setpoint setpoint setpoint setpoint mcgraw translates texas decades decades stan costly extrapolation cations appli topics dard acceptance acceptance saved parame parsimonious parsimonious parsimonious parsimonious parsimonious parsimonious switzerland fur mented historical historical historical historical historical historical historical historical historical historical refining refining refining refining refining namic namic delivered highlights dictated contributed jim industry relied safety karlsruhe straints fluid extrapolate ljung overcomes optimizer optimizer optimizer optimizer optimizer optimizer optimizer setpoints setpoints actuators grade grade solver documented garcia companies companies aerospace ttt ttt ttt ttt tionally hartman expo mize thirteen practitioners practitioners practitioners greg thermore houston preprocess preprocess proliferation ited cedar pirical nash doug 
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#*network network network network network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural neural neural neural neural neural neural neural neural neural input input input function function function function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure figure figure time time time time time time set set set set set set set set set networks networks networks training algorithm number number number number number number number number number number state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results results results results units information information problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem problem hidden hidden performance performance performance based space space space space space space space linear linear linear layer layer case shown shown systems values values values probability probability probability probability probability probability probability parameters parameters parameters weight functions functions functions functions functions functions functions functions functions functions distribution distribution distribution distribution method method method method approach approach approach approach approach approach approach approach approach approach approach point point control control large large large large large large large large class class class optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs inputs inputs form shows shows shows shows shows shows algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple paper paper paper paper paper examples small small size size size size net net work work work work work work task methods methods methods methods methods methods methods methods methods methods methods step features process current trained trained trained structure structure structure problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems problems random memory memory representation representation representation representation representation representation representation show fixed line rule rule vectors vectors general general real approximation approximation approximation approximation approximation approximation states states states states states states states states states states states states states states states states states states states states states states states states states states states states states states obtained obtained term note result university university university variables variables variables variables variables variables variables variables variables variables variables variables computation research research research research research research defined defined defined defined defined defined table table table computer computer computer distance distance science science science presented presented presented presented present present present present nodes nodes machine machine machine machine machine machine machine machine machine sets maximum press learn learn learn position position position components components components components components abstract applied back find computational references component component component component component stochastic stochastic stochastic due due due important decision decision decision decision decision decision decision decision decision propagation introduction action action action action action action action action complex estimation behavior effect dynamic dynamic search tion variable variable variable variable lower lower measure representations learned learned part part center cases type type type type required required required good good good good binary conditions represent bayesian equations markov markov markov markov markov markov markov make make fact fact techniques proposed probabilities errors finite finite finite finite finite finite simulations resulting ing simulation computed computed respect sum times times times times means means means reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor natural natural natural orientation orientation orientation orientation policy policy policy policy policy policy policy policy knowledge knowledge obtain original artificial artificial represented represented true compared compared application provide compute compute compute proc proc proc proc proc determined determined experimental distributions distributions equal approaches approaches approaches larger larger contrast update dependent modeling morgan report department version internal individual represents difficult graph ai ai maps framework framework computing computing domain environment environment environment environment environment environment directly directly additional transition transition transition effects effects full full full full full full full full full full full full full full full full full approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate world world world world world world basic pages pages give give con condition condition randomly robot robot robot robot levels area types product product product processes processes processes processes processes processes processes processes iteration simply technical feedforward describe limited close assumption complete actions actions actions actions actions actions finding finding amount effective effective effective supported main main main main face journal square cluster cluster cluster cluster easily kaufmann underlying underlying underlying underlying underlying reduced reduced reduced fully fully programming significantly trials database empirical empirical principle representing representing representing representing max max direct making making making making international produced run description architectures discussed recent recent correlations correlations correlations exact exact exact exact exact exact exact exact exact exact exact exact exact advantage advantage advantage advantage separate takes takes takes element reported introduced introduced strategy inference highly compare observations observations observations tions solve solve solve solve smooth address positions observation grid grid grid bounded increased parts studied scaling alternative alternative clusters clusters clusters clusters clusters clusters generally generally generally setting demonstrate demonstrate runs starting starting starting competitive reward reward reward reward reward accurate bayes designed designed designed exponential exponential exponential faster faster faster practice learns learns taking taking taking hard largest reduction sigmoidal intelligence intelligence start start min min min min min min min relationship averaged derivatives identification identification identification program base base base base base acknowledgements suppose pro pro index perception perception solving solving sequential sequential distinct dept dept implement linearly involves belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief integrated quality quality agent agent agent agent agent agent agent agent agent focus focus focus focus review depending viewed learner evaluated operations restricted restricted updated updated fraction showed decomposition decomposition decomposition decomposition soft completely partial additive convex roughly tracking remains distances visible visible assigned foundation foundation avoid expect exploration includes thesis thesis thesis dominance formulation inter inter assignment assignment assignment determines determines extension extension uncertainty uncertainty specifically specifically coupled domains domains partially partially partially partially partially partially partially structural planning planning closely suitable literature literature literature literature efficiently efficiently comparing situation tend refer refer compact graphs prob success dis dis running running running hold observable observable observable observable observable observable observable ill received policies policies policies policies illustrates approximating approximating deal presents simpler singh investigate difficulty exponentially updating rapidly environments involving detail replaced limitations mdp mdp mdp mdp fewer ideal decisions root maximizing comparable complicated affect act math naturally assumes phd phd defines seconds brown brown brown great piecewise piecewise developing theoretic sensors sensors sensors sensors orientations analyzed fairly navigation tractable tractable lies stanford stanford stanford formalism mation projected describing begin demonstrates author incomplete incomplete parameterized posed adjustable continuously ity maintain maintain http measuring reaches incoming suited marginal gave substantial chose decreased eventually specifies specifies traces univ univ realized bellman benefit sensing identifying www princeton approximates reconstructed reconstructed impossible extending minutes attractive intelligent grow pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp contract obtaining exploit exploit observing settings disjoint generalizes hours date guarantees bad darpa approximators discounted creating augmented cpu horizon horizon horizon park broken broken approximator approximator adopted assigns mdps mdps onr andrew informa pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps approx maintaining maintaining outperform discount aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft aircraft markovian markovian forced poses distinction medium decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed decomposed descriptions discovering acting acting penalized summarizes schmidhuber approxi approxi mathematically maintained maintained file challenging challenging challenging projecting eligibility anal memoryless maintains sized sized sized permit failures status status mix littman littman factored factored factored lems demonstrating rarely tension remarks discretized discretized impractical impractical maze savings savings dominates russell stay val val tribution gram tuple parti html sloan tance approaching kaelbling amenable fair meant meant comprised addressing format inaccurate files problematic ensuring dean deciding tan probabil proximation spent rein rein tightly infeasible observes marginals disadvantages parr parr parr parr parr parr avenue imation theo mate tially manipulating menlo ronald ronald sondik aii trouble stuart koller koller koller koller koller koller highlight concluding decomposing manageable visibility visibility forcement forcement snapshot snapshot overcoming assump decoupled powell decomposes ford ijcai cassandra cassandra cassandra cassandra proximate maintenance maintenance maintenance maintenance icml icml icml tractability cesses optimistic rodriguez rodriguez rodriguez rodriguez rodriguez aro manipulate expressive leverage inaccuracies intercept uai perceives sri sri publicly dozen worlds worlds ola boyen boyen boyen tioned wear andr marginalizing risks thinks decom catch retical exponen stray friendly observ observ realistically hanks tabular muri formalizing 
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#*learning learning learning model model model model model model model data function function function function function figure figure figure figure figure figure figure figure figure time time time time time set algorithm number number number number number number system system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results information information information information information information information information problem problem problem problem problem problem problem problem problem problem models models models performance performance performance based based based space space space space space space space space space space space space space case vector order order order order order order order shown shown systems systems systems values values probability probability probability probability probability probability probability probability probability probability probability probability unit distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method method method method approach approach pattern point single single single control large large large large large local analysis optimal optimal optimal optimal optimal optimal optimal form form shows shows shows shows shows algorithms gaussian gaussian gaussian gaussian gaussian gaussian paper paper paper paper examples examples small small size size work work work work methods step points field field features features features features features process level current current structure high high high similar representation show equation equation equation equation equation equation line line rule rule rule rule rule rule general general general real real real real approximation approximation average states states states states states term term term note note note note note dimensional dimensional dimensional result university university threshold solution solution solution solution research research log defined constant computer terms distance distance distance science prediction prediction left direction direction presented map map map map map map map phase phase low machine machine machine motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion motion maximum maximum maximum maximum range range range range range range range range range range range range press position position position position position position position position position position position position position position position position position position position position sample abstract find computational computational computational convergence likelihood likelihood likelihood references stochastic stochastic stochastic due due ieee decision decision decision introduction action action action action action action action effect effect effect effect dynamic dynamic dynamic dynamic dynamic generated generated cost cost cost cost cost cost cost tion tion variable variable assume lower lower lower lower learned higher center multiple multiple good long conditions represent represent represent represent represent bayesian expected expected expected expected equations equations equations equations equations equations equations equations markov markov markov markov markov markov markov markov make make make make make fact fact fact correct probabilities probabilities probabilities probabilities scale minimum minimum minimum computed computed computed computed multi multi times regions regions mapping reinforcement dimension dimension dimension made made made policy policy policy policy policy knowledge specific represented represented represented represented true compared compared compared provide provide provide compute compute compute compute compute compute location perform active experimental experimental goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal goal posterior constraints distributions distributions distributions gain gain discrete discrete approaches approaches mit accuracy comparison larger contrast contrast update update update implementation implementation represents represents represents represents difficult final final final scheme graph maps computing computing computing computing computing computing domain environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment environment additional view solutions estimates transition transition transition transition transition transition transition limit trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory trajectory determine upper requires approximate approximate statistics statistics statistics world world world world world speed give developed robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot robot levels area lines entropy entropy entropy entropy entropy entropy entropy entropy entropy entropy path path path path actual provided processes processes processes iteration iteration iteration iteration nature nature depends simply discussion discussion increases arbitrary close close close assumption assumption assumption assumption assumption assumption assumption assumption assumption complete complete complete actions actions actions actions finding common assumed generate generate generate role role journal end end ability ability ability ability ability hypothesis future easily easily easily development noisy sensory probabilistic probabilistic typically combination programming programming edge mechanism operation operation leads iterations early light light predict predict improve resolution robust robust robust robust robust robust typical moving moving moving sense sense subset dimensions dimensions sufficient conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional conventional observations correspond correspond trans sparse address address positions modified observation observation grid grid improvement entire parts parts suggests wide alternative width deterministic demonstrate conclusion assumptions assumptions reduce trajectories trajectories trajectories trajectories trajectories trajectories reward reward reward reward reward accurate suggest propose propose taking hard intelligence assuming minimizing question areas areas areas areas areas areas areas areas areas areas areas pro construct longer estimating transitions transitions transitions transitions explicitly explicitly linearly infinite belief belief belief belief angle adding adding expectation national national formation viewed open restricted centered margin completely spectrum spectrum spectrum earlier additive measurements measurements spaces spaces reduces reduces purpose tracking tracking tracking tracking tracking valid sufficiently sufficiently uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty uncertainty maximize coupled black black black absolute partially partially partially partially planning planning planning planning planning planning planning planning planning planning planning planning planning reason determining sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor sensor middle middle identified extra extra efficiency modification computationally identify essentially online capture traditional traditional traditional quickly kind contained success content vary localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization localization absence observable observable observable reach moves moves policies policies operating neighboring acknowledgments modelling modelling extend extend situations minimized command command american american create essential essential difficulty put environments environments limitations periodic fewer fewer reducing history history school scaled authors reliable proved examined measurement opposite perfect ensure versions algo panel panel panel assumes academic generates generates attempts ment directed sensors sensors sensors sensors sensors sensors sensors publishers track track track navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation navigation improves failure capabilities tractable tractable tractable lies comparisons implementing ring worst arise consequence potentially localized lowest mellon robustness fourth people people people considerably carnegie substantially cmu dark dark experimentally lack autonomous reliability reliability ity maintain howard rely pittsburgh maximizes prevent plan plan plan plan plan plan substantial semi converged pose pose pose pose pose pose pose pose pose pose pose pose bellman bellman redundant sensing sensing sensing sensing sensing sensing sensing intractable intractable intractable feasible optimality guarantee guarantee princeton mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile mobile grey grey grey grey grey robotics reaching plays lost lost lost lost lost inspired consideration ranges ranges tools pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp abilities fail methodology guide obstacle obstacle reliably iteratively sim uni creating shortest shortest shortest arrive arrive arrive arrive arrive matter augmented augmented augmented environmental environmental environmental roy roy roy roy roy motions considerations receiving acknowledge assigns dramatically pomdps pomdps pomdps pomdps pomdps land summer thrun thrun thrun thrun thrun thrun thrun shorter shorter shorter achieving kluwer ber job markovian obstacles obstacles obstacles obstacles obstacles obstacles tradeoff solely simulating certainty certainty certainty certainty certainty certainty acting penalized robots robots robots robots robots robots robots robots robots robots rithms num compensate distribu ization degraded degraded mitchell simplifying simplifying simplifying simplifying depicts statistic importantly nonetheless sonar funded normalizing intensive travel increments aaai continually modal modal stops tour rarely gratefully argmax tom suffers played pronounced continuum gram tuple operational laser laser laser laser laser laser laser fox fox fox fox grids sions prone kaelbling dimen senses positional positional positional positional positional positional positional positional positional positional positional positional planner planner planner planner planner planner planner planner planner planner planner planner schmidt iterating compromise adequately capturing putation probabil unaffected operated preventing sebastian sebastian continuing settles collision dead dead plans compress compress localize advice darker simmons claims lose augment concurrent ration weeks landmarks contingencies safety gps gation finder ner millions collaboration koenig rectly walls walls obser knowl cassandra alterations tractability deviate instrumental navigate intractability intractability meters inconsistencies inevitable confirming recherche hinges appreciated mahadevan explo navigating augmentation interests xlz nicholas nicholas vations arti reckoning reckoning involvement precomputed precomputed wolfram phrased undiscounted ships ships firmly fonds reli velopment mislead mislead navi 
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#*network network network network network network network network network network network network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model model model model model model model model model model model model neural input input input function function function function function function function function function function function function function function function function function function function function function function figure figure figure figure time time time time time time time time time time time time time time time time time time time time time time time time set networks networks networks networks networks networks training algorithm algorithm algorithm algorithm algorithm algorithm output output output output output number number number number system system system error error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results units units units units information information information information problem problem problem problem problem problem problem problem problem models models models models models models models models hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden performance performance performance performance performance performance performance performance performance performance performance based space space weights weights weights weights linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear linear case case case vector vector vector vector order shown shown shown systems systems values values values values probability probability parameters parameters parameters parameters parameters parameters parameters parameters parameters parameters weight weight functions functions functions unit unit unit unit distribution distribution distribution method method approach single single single single processing control large large rate rate rate test test matrix matrix matrix matrix optimal optimal optimal optimal optimal optimal optimal optimal optimal inputs inputs inputs inputs inputs signal algorithms algorithms algorithms algorithms algorithms simple simple simple simple paper size work work work task task task task task task task task task task methods methods methods methods methods step step step step step step step step step field field field field field field features process process process level current current trained trained trained structure structure problems problems problems problems random random random random random random random random random random random random random random random high representation representation representation representation representation representation representation representation representation representation representation architecture show fixed fixed line line rule rule rule parameter real approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation states states states states states states states states states theory gradient term note dimensional result university university university variables variables variables variables variables variables variables computation research research research independent independent log found target dynamics dynamics initial constant table table table standard standard standard computer computer computer distance distance science science science left left direction direction presented low nodes temporal temporal machine machine machine machine machine object press press learn position sample abstract find find find computational computational likelihood references stochastic stochastic stochastic stochastic decision decision decision decision decision decision decision decision decision context context context introduction introduction introduction action action action action action action action action complex complex complex hand dynamic dynamic dynamic dynamic dynamic dynamic dynamic tion change difference complexity variable variable variable variable variable variable assume lower signals representations representations representations representations representations learned learned learned learned learned learned learned learned chosen previous previous previous theorem required required good good good binary binary represent bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian bayesian expected expected expected equations markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov markov make techniques probabilities probabilities probabilities observed observed observed observed forward forward forward scale finite resulting resulting ing human human human human human human human human human computed respect multi multi performed performed performed performed performed called reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor dimension made natural study policy policy policy policy policy policy policy knowledge knowledge negative artificial artificial artificial relative relative specific represented represented represented represented compared compared series provide compute rates proc proc proc perform perform experimental related connected connected connected discrete discrete discrete discrete mit steps steps steps steps comparison larger fields update dependent report department department version advances represents connectionist difficult final exp exp exp exp exp bias graph graph graph ai cambridge computing computing computing environment environment environment hinton additional view transition transition transition san effects conference conference efficient efficient requires approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate approximate speed speed randomly conditional conditional conditional conditional conditional conditional provided finally processes processes processes processes evidence evidence evidence iteration measured discussion technical tested tested hmm hmm fast assumption corresponds corresponds complete actions actions actions actions finding assumed assumed assumed journal future sensory sensory sensory including kaufmann probabilistic probabilistic probabilistic typically pairs pairs underlying fully fully fully fully fully fully jordan jordan jordan interesting character york york york york trials trials numbers iterations iterations iterations making stored bits international early decay combined description denotes denotes denotes denotes denotes discussed discussed exact exact element element include side quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic quadratic inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference inference previously observations volume works tions solve solve yields converge converge converge achieve rl rl rl address chain chain modified modified modified sensitive scaling scaling suggests trial deviation matrices move white occurs column column runs half half place assumptions conclusions valued editors reward reward reward reward sigmoid sigmoid sigmoid sigmoid sigmoid sigmoid bayes bayes clear clear faster faster faster practice mateo temperature encoding encoding intelligence intelligence intelligence intelligence assuming selective denoted boltzmann appears monte monte construct carlo carlo edges edges perception solving tuned distinct distinct dept sensitivity explicitly infinite involves belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief applying quality quality agent agent agent select national squares learner learner learner detailed operations updated approximations approximations approximations approximations approximations approximations approximations completely similarly updates past reasonable reasonable additive performing performing convex convex combining remains foundation advantages avoid perceptual perceptual perceptual thesis uncertainty maximize partially partially partially partially partially discussions discussions encoded encoded delta essentially online online capture road compact notice success neuroscience running gray notation notation list usual dayan dayan backward observable observable observable observable observable observable correspondence attempt consisted policies policies policies approximating approximating acknowledgments decreasing bars explore simpler experience experience exponentially exponentially exponentially exponentially exponentially exponentially environments optimized optimized optimized issues issues graphical graphical helpful helpful fewer fewer fewer history investigated variational variational variational variational combine dependencies structured encode encode func analogous removed act act circles plausible traffic front portion portion portion explored initialized initialized improving utility seconds neal neal brown residual piecewise piecewise directed costs adjacent multiplication tractable tractable nonlinearity london london tive formalism ran worst mation mation watkins circle circle toronto toronto toronto toronto requiring tional tional parameterized parameterized parameterized red peter car car car car car solla passed incorporated slower slower slower rep rewards rewards maximizes extensions sophisticated sophisticated comments comments display findings jaakkola progress extreme initialization initialization initialization initialization bellman room ghahramani ghahramani ghahramani college leen intractable intractable intractable intractable cooper guarantee tation tation driving driving driving driving driving addresses grows held intelligent pomdp pomdp pomdp pomdp abilities observing reasoning reasoning settings guide filled slice slice slice saul saul sion ascent lawrence entries initialize discounted discounted infer ballard gaze gaze gaze gaze gaze gaze gaze gaze horn horn canada canada horizon horizon impact valuable mdps mdps empty pomdps pomdps pomdps approx approx emission ence discount tables lane lane lane failed pieces pieces encouraging encouraging encouraging blue perceived decomposed multinomial multinomial multinomial multinomial multinomial multinomial constitutes certainty factorial geoffrey approxi approxi approxi maintained ization proba simplifying relating echo wise pearl represen represen funded rochester rochester refined computa littman factored factored factored factored factored factored factored factored factored factored factored factored factored factored factored factored factored factored rabiner simplification january aid dom juang meth inefficient systematically zoubin bat transpose ods kaelbling zeros magazine indepen acyclic tenth dence dean tan moderately moderately yellow unobserved unobserved proximation localist localist localist localist localist localist localist localist cars cars newly crg parr parr resentation aliasing aliasing beliefs distinctions lasting backups clamping initializing sondik gatsby gatsby nserc hwang driver driver driver densely dbn dbn dbn dbn dbn dbn koller koller koller perceive persistence nose nose shoulder hurt hurt compactly compactly bilities 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#*network learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning neural neural input function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function function time time time time time set networks networks algorithm algorithm output error error state state state state state state state state state state state state state state state state state state state state state state state results results results results models performance performance performance performance performance based based based based based based based weights linear linear linear layer case case case case case vector vector vector shown systems systems values probability parameters parameters parameters parameters parameters weight functions functions functions distribution distribution distribution distribution distribution distribution method approach approach approach approach approach approach approach approach approach approach point control control large large local local rate analysis analysis optimal optimal optimal optimal optimal optimal optimal optimal form form form form form algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms algorithms simple simple simple paper paper paper paper examples small small small size size size feature feature work methods methods methods methods methods methods methods methods methods methods methods methods methods methods step step step step step step step points features features features process process process problems problems problems similar similar representation show rule general general general parameter parameter parameter parameter approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation approximation average average average average average average states states states theory theory gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient gradient obtained obtained obtained obtained term term term dimensional result result result result result result result result result result university university research independent independent defined defined found sequence sequence target dynamics estimate estimate estimate estimate standard standard computer terms terms science direction direction direction direction temporal temporal machine machine machine machine press press learn nonlinear abstract find convergence convergence convergence convergence convergence properties references stochastic stochastic due ieee ieee positive positive procedure decision decision decision decision decision introduction action action action action action action action action estimation estimation estimation statistical effect dynamic dynamic dynamic dynamic dynamic variance variance tion tion change difference assume assume measure measure learned learned theorem theorem theorem theorem theorem theorem theorem theorem theorem theorem good long long long conditions expected expected expected expected expected expected markov markov markov markov fact correct probabilities probabilities probabilities scale tasks simulation respect respect respect respect multi elements reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement optimization natural natural applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy relative specific represented represented represented application provide define compute proc proc proc related mit mit steps steps accuracy accuracy comparison update descent selection selection morgan morgan morgan morgan proceedings proceedings report report report report institute words version version connectionist connectionist connectionist difficult framework environment directly hinton transition requires requires choice approximate approximate approximate estimated estimated estimated estimated give condition condition condition derived developed bounds product actual processes selected backpropagation iteration iteration iteration iteration iteration iteration iteration sampling achieved technical technical technical technical arbitrary arbitrary arbitrary arbitrary denote stable actions actions proof proof proof proof finding require main eds instance easily kaufmann kaufmann kaufmann objective combination jordan jordan jordan jordan jordan jordan technology programming programming programming special special special leads squared max direct direct making normalized attention added architectures discussed advantage advantage advantage pair pair apply apply moving include side trees sense sense sense sufficient approximately tions solve converge converge converge rl rl rl rl rl rl rl rl trans trans generalized generalized bounded bounded williams williams williams williams williams williams williams williams improvement exists exists expression expression occur suggests wide alternative alternative locally locally locally locally locally locally touretzky deterministic starting place reduce reward reward reward reward reward reward reward reward reward reward reward reward sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton sutton practice learns proportional variety variety start start start start start denoted acknowledgements appears pro pro pro van van derive written ways estimating changing metric sensitivity explicitly slightly agent agent agent potentials yield family independently stationary stationary stationary communication estimator viewed viewed variation updated updated updated evolution approximated similarly converges allowed key key earlier barto barto barto barto combining combining event roughly sufficiently advantages david includes thesis formulation formulation formulation formulation formulation formulation formulation formulation formulation formulation weighting assignment automatic prove prove prove prove prove absolute partially characterized characterized selecting identified suitable orthogonal conf conf moore moore anderson anderson follow satisfy satisfy gibbs sampled write michael dayan dayan nips nips observable observable highest received policies policies policies preferred approximating approximating satisfies oriented extend extend explore explore simpler unlike perturbation essential essential singh singh singh singh singh singh singh singh singh singh requirements experience experience updating updating put estimators limitations issues mdp mdp mdp mdp school int int authors proved proved affect affect func cover notion notion analogous man ensure aspect greedy algo expressions finds optimum optimum massachusetts massachusetts residual residual ment slowly critic critic critic critic rapid immediately actor actor actor actor scientific separately definite cybernetics substantially elman cmu parameterized effort rewards rewards requirement proven chen chen richard comments neuro unbiased unbiased unbiased unbiased returns jaakkola jaakkola jaakkola jaakkola jaakkola jaakkola lim baird baird baird baird baird baird traces proposition converged credit differentiable differentiable differentiable differentiable lab lab proofs college intractable summing proceed establish kaufman convenient satisfying pomdp hope definitions generalizes selects obstacle bartlett bartlett appendix appendix encountered sides dominant realization tic approximators approximators approximators approximators discounted reader kearns theoretically roy roy park park tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis tsitsiklis implicitly generalizing approximator approximator convergent convergent convergent convergent mdps bertsekas bertsekas bertsekas bertsekas fitted pomdps summer unable discount deriving markovian theorems par amherst personal tor arising equality care insights rithms approxi labs compatible careful proach weaker eligibility sta page gordon gordon gordon gordon status worked reinforce reinforce reinforce reinforce reinforce reinforce reinforce parameterization parameterization parameterization parameterization parameterization characterizing lation discontinuous justification assistance mining affecting concerns meeting sarsa sarsa tells baxter baxter implying senses deter dent indepen noticed cations appli precup approxima approxima avenue formulations mansour mansour mansour mansour wright subtract satinder designated ranked tially proving proving gra gra expressing formulating imperfect gramming gramming neuronlike compatibility compatibility twelfth twelfth assure assure interacts decade dient dient athena icml icml 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#*learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning learning model neural input input function function function function function function function function function function function function function function function figure figure figure figure figure figure figure figure figure figure figure figure figure figure time time time time time time time time set set set set set networks networks training training algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm algorithm number number number number number system error state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state state results results results results results results results results results information problem problem problem problem problem models models performance performance performance based based based based based based based based based based space space space space space space space space space space space linear case case case order order shown shown shown shown shown shown shown values values probability probability probability probability probability probability probability probability noise noise functions functions functions distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution distribution method approach approach approach approach approach approach approach approach approach approach approach approach approach point point single control control control large large large rate rate rate optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal shows algorithms gaussian gaussian paper paper paper paper size size size work work task task task methods step current current problems problems random random random representation show equation equation equation section line general general general generalization generalization parameter real real real real real real real real real approximation approximation approximation approximation average average states states states states states states states states states states states states states states states states states states states states states states states states obtained obtained obtained obtained term term term experiments experiments experiments experiments experiments result result result result result university university university variables solution solution solution independent defined defined defined found found found found sequence target target target target target initial initial initial initial initial initial initial constant table computer computer distance distance distance distance distance distance science left left left presented map present temporal machine object object object object object object object object object object object object object object sets sets sets sets sets motion maximum maximum range range press press learn learn learn learn position continuous continuous continuous continuous continuous continuous continuous sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample sample abstract applied applied applied applied applied find find find density density likelihood likelihood likelihood references component stochastic stochastic stochastic positive decision decision propagation propagation propagation context context introduction introduction action action action action action action action action action action action action hand hand estimation statistical statistical dynamic dynamic dynamic variance tion tion change difference variable variable assume assume assume lower lower prior representations representations representations learned chosen part part part previous theorem cases good long long represent represent represent distributed expected expected markov markov markov markov markov markov markov make make fact fact fact proposed probabilities observed finite total total simulation simulation simulation simulation computed computed computed performed called called called times times mapping mapping mapping reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement reinforcement factor factor factor applications policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy policy knowledge knowledge filter filter filter obtain obtain negative relative specific specific specific samples samples samples samples samples samples samples samples samples samples represented represented represented represented represented represented represented true application desired define compute compute compute location location location location location location location experimental experimental goal posterior distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions distributions discrete discrete discrete discrete discrete discrete discrete discrete discrete discrete equal mit steps steps steps steps steps steps larger selection selection selection implementation implementation version version version kernel represents represents delay addition graph graph graph maps framework cambridge environment environment environment environment environment environment environment environment environment directly directly directly curve curve additional solutions solutions curves trajectory top detection detection determine efficient upper upper requires requires approximate approximate approximate approximate approximate approximate statistics world world world world world vision basic con derived derived weighted weighted weighted weighted robot robot robot robot robot robot robot robot robot robot robot robot robot entropy path path finally processes processes processes iteration iteration iteration nature sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling sampling discussion arbitrary arbitrary denote denote denote close close corresponds actions actions actions actions actions actions actions actions actions actions actions finding nearest nearest nearest nearest nearest nearest nearest common generate require journal future makes makes makes makes noisy objective probabilistic smaller account unknown unknown unknown programming projection projection projection projection projection projection projection head special database database database empirical empirical operation leads leads leads leads representing iterations iterations filters pre making bottom bottom idea idea added denotes denotes exact exact advantage property takes typical practical practical apply moving include side side sense inference sejnowski dimensions conventional observations observations observations observations observations approximately approximately approximately works axis yields converge address address chain observation observation observation observation observation observation expression lead studied scaling scaling digital correctly locally move move boundary boundary demonstrate runs runs assumptions trajectories neighbor neighbor neighbor neighbor neighbor valued valued valued valued valued valued valued valued valued reward reward reward reward reward reward reward reward reward central numerical numerical sutton performs practice learns suggest integration integration drawn drawn drawn drawn drawn drawn solid labeled labeled assuming min min averaged denoted denoted denoted denoted denoted monte monte monte monte monte monte monte monte monte monte monte monte monte monte monte derive carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo carlo factors factors describes describes mathematical recall metric coordinates coordinates coordinates coordinates coordinates averaging linearly easy belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief belief angle applying applying springer agent agent agent agent agent agent agent agent agent agent implies expectation stationary stationary learner learner solved densities densities open open updated approximations approximated converges converges converges allowed past past past past key barto spaces spaces spaces spaces spaces spaces spaces spaces convex add add false false tracking initially initially initially initially filtering sufficiently avoid existing exploration figures figures kernels perceptual thesis thesis extension plotted specifically specifically specifically domains domains domains black black partially partially partially partially partially partially partially partially neighbors neighbors neighbors characterized successfully successfully simplicity planning planning planning planning planning planning identified identified capable importance importance importance importance importance importance importance importance uniformly successful successful successful successful successful successful successful successful successful successful successful literature literature efficiently schemes plots essentially receives refer refer notice verlag success success moore moore interested interested issue return return return follow gray notation localization localization localization dot dayan generalize providing delayed observable observable observable observable observable observable observable observable computes leading reach reach moves policies policies illustrates illustrates illustrates subsequent operating camera camera camera bars employed employed american collection investigate experience difficulty environments environments detail association limitations divergence divergence divergence divergence preliminary rise history history history school applicable decisions func fundamental notion act act possibly configurations opposite illustrate greedy observe detected improving mixed arbitrarily submitted phd phd finds synthetic synthetic ment piecewise sensors defining fairly starts stanford stanford lin located watkins projected gradually depicted mellon integrating evaluating carnegie generic atkeson rewards rewards rewards rewards rewards rewards http vocabulary pittsburgh fall maximizes maximizes popular simulator focused conditioning specifies cumulative cumulative consistently consistently bellman college sort www formally princeton conditioned mobile mobile impossible grows grey robotics proceed establish fails fails minutes minutes minutes chains tools simplify height height height height hit moment pomdp pomdp pomdp pomdp pomdp pomdp pomdp pomdp observing modifications optimally symposium symposium corner corner hours mance encountered perfor sides counter viewing approximators discounted infer ahead refers rich rich draw draw horizon exploiting executed mdps speaking pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps pomdps leaving thrun thrun thrun thrun thrun solves discount recursively legal suboptimal incrementally tween additionally auxiliary acting acting penalized penalized publication robots execute searches denoting oct depicts projecting names translations maintains particle particle particle particle particle particle minor induces knowing thousands holding infinitely aaai aaai diagrams littman littman littman argmax survey unbounded insufficient agents agents solvable locate king russell injected episodes episodes episodes episodes episodes episodes possess floor sen proposes schaal extracts normalize fox conditionally html maxi kaelbling kaelbling kaelbling robotic spirit accommodate teaching planner subscript vicinity comer comer rotational hits hood repetitive histories histories histories derivations survival occasionally sebastian retrieve heights erroneous approxima optimizes reactive schematically beliefs beliefs beliefs accepts backups backups backups backups backups backups backups tums environ sondik penalties penalties mild devise devise bag koller pitt grasping condensation trivially succeed likeli told standards doubled grasp grasp grasp misses interacts technically technically cassandra cassandra rewarded mono isard icml unsuccessful preclude gathering armed sight uai preliminaries carded worlds worlds worlds tanner aren pentium kanazawa unobservable tricks annotated annotated narrowly intentionally tribute mizes paying inapplicable surpasses 
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